ssw_missing_links.py

#!/usr/bin/python

'''
Missing links in various Secret Society Wars maps.
Just takes these huge lists out of ssw_sector_map.py.
'''

# Copyright 2010, 2015-2016 Squiffle

cycle_13_war_links = {2: [35], 4: [5, 37], 5: [4], 6: [39], 7: [40], 8: [41], 9: [42],
                      11: [12, 44], 12: [11], 13: [46], 14: [15], 15: [14], 17: [18],
                      18: [17, 51], 20: [21], 21: [20, 54], 22: [55], 23: [56],
                      24: [57], 25: [58], 27: [28], 28: [27], 29: [62], 30: [63],
                      31: [64], 32: [65], 34: [67], 35: [2, 36], 36: [35, 69],
                      37: [4, 38], 38: [37, 71], 39: [6, 72], 40: [7, 41],
                      41: [40, 8, 74], 42: [9, 43], 43: [42, 76], 44: [11, 45],
                      45: [44, 78], 46: [13, 47], 47: [46, 80], 48: [49, 81],
                      49: [48, 50], 50: [49, 83], 51: [18, 52], 52: [51, 53],
                      53: [52, 86], 54: [21, 55], 55: [54, 22], 56: [23, 89],
                      57: [24, 90], 58: [25, 91], 59: [60, 92], 60: [59, 93],
                      61: [62, 94], 62: [61, 29], 63: [30, 96], 64: [31, 97],
                      65: [32, 66], 66: [65], 67: [34], 68: [101], 69: [36, 70, 102],
                      70: [69], 71: [38, 72], 72: [71, 39], 73: [106], 74: [41, 107],
                      75: [108], 76: [43, 77, 109], 77: [76, 110], 78: [45, 111],
                      79: [112], 80: [47, 113], 81: [48, 82, 114], 82: [81, 83],
                      83: [82, 50], 84: [85, 117], 85: [84, 118], 86: [53, 87],
                      87: [86, 120], 88: [89, 121], 89: [88, 56], 90: [57, 123],
                      91: [58], 92: [59, 125], 93: [60, 126], 94: [61, 95],
                      95: [94, 128], 96: [63, 97], 97: [96, 64, 98], 98: [97, 131],
                      99: [132], 100: [101], 101: [100, 68, 102], 102: [101, 69],
                      103: [104, 136], 104: [103, 105, 137], 105: [104, 106],
                      106: [105, 73], 107: [74, 140], 108: [75, 141], 109: [76, 142],
                      110: [77, 143], 111: [78, 112], 112: [111, 79], 113: [80, 146],
                      114: [81, 147], 115: [116, 148], 116: [115, 117], 117: [116, 84],
                      118: [85, 119], 119: [118, 152], 120: [87, 153], 121: [88, 122],
                      122: [121, 123, 155], 123: [122, 90], 124: [125, 157],
                      125: [124, 92, 158], 126: [93, 127], 127: [126, 160],
                      128: [95, 129], 129: [128, 130], 130: [129, 163], 131: [98],
                      132: [99], 133: [134], 134: [133, 135], 135: [134, 168],
                      136: [103, 137], 137: [136, 104], 138: [139, 171],
                      139: [138, 172], 140: [107, 141], 141: [140, 108], 142: [109],
                      143: [110, 144], 144: [143, 177], 145: [146, 178],
                      146: [145, 113, 147], 147: [146, 114], 148: [115, 149],
                      149: [148, 182], 150: [151, 183], 151: [150, 184],
                      152: [119, 185], 153: [120, 186], 154: [155, 187],
                      155: [154, 122], 156: [157, 189], 157: [156, 124, 190],
                      158: [125], 159: [160], 160: [159, 127], 161: [162, 194],
                      162: [161, 195], 163: [130, 164], 164: [163, 165], 165: [164],
                      166: [167], 167: [166, 200], 168: [135, 169], 169: [168, 170],
                      170: [169, 171], 171: [170, 138], 172: [139, 173],
                      173: [172, 174], 174: [173, 175, 207], 175: [174, 176],
                      176: [175, 209], 177: [144, 178], 178: [177, 145], 179: [212],
                      180: [181, 213], 181: [180, 214], 182: [149, 215],
                      183: [150, 184], 184: [183, 151], 185: [152, 218],
                      186: [153, 219], 187: [154], 188: [189, 221],
                      189: [188, 156, 222], 190: [157], 191: [192, 224],
                      192: [191, 193, 225], 193: [192], 194: [161, 227],
                      195: [162, 196, 228], 196: [195, 197], 197: [196, 198],
                      198: [197], 199: [232], 200: [167, 233], 201: [202],
                      202: [201, 235], 203: [204, 236], 204: [203, 205],
                      205: [204, 238], 206: [207, 239], 207: [206, 174],
                      208: [209], 209: [208, 176, 242], 210: [211, 243],
                      211: [210, 212], 212: [211, 179], 213: [180], 214: [181, 215],
                      215: [214, 182, 216], 216: [215, 249], 217: [218, 250],
                      218: [217, 185], 219: [186, 220], 220: [219, 221],
                      221: [220, 188, 254], 222: [189], 223: [224], 224: [223, 191],
                      225: [192, 258], 226: [227, 259], 227: [226, 194],
                      228: [195, 261], 229: [230, 262], 230: [229, 231],
                      231: [230, 264], 232: [199], 233: [200, 234, 266],
                      234: [233, 235], 235: [234, 202, 268], 236: [203, 237],
                      237: [236, 238], 238: [237, 205], 239: [206, 272], 240: [241],
                      241: [240, 242, 274], 242: [241, 209], 243: [210, 244],
                      244: [243, 245], 245: [244, 246], 246: [245, 247],
                      247: [246, 280], 248: [249], 249: [248, 216], 250: [217],
                      251: [252, 284], 252: [251, 253, 285], 253: [252, 286],
                      254: [221, 255], 255: [254, 256], 256: [255, 257, 289],
                      257: [256, 290], 258: [225, 259], 259: [258, 226, 260],
                      260: [259, 293], 261: [228, 294], 262: [229, 263],
                      263: [262, 296], 264: [231], 265: [266], 266: [265, 233],
                      267: [300], 268: [235, 301], 269: [270], 270: [269, 271],
                      271: [270, 304], 272: [239, 273, 305], 273: [272, 274],
                      274: [273, 241], 275: [276, 308], 276: [275, 309],
                      277: [278, 310], 278: [277, 279, 311], 279: [278, 312],
                      280: [247, 281], 281: [280, 282, 314], 282: [281, 283],
                      283: [282, 284], 284: [283, 251], 285: [252],
                      286: [253, 287, 319], 287: [286, 288], 288: [287, 289],
                      289: [288, 256], 290: [257, 323], 291: [324], 292: [293, 325],
                      293: [292, 260], 294: [261, 295], 295: [294, 328],
                      296: [263, 329], 299: [300, 332], 300: [299, 267],
                      301: [268, 302], 302: [301, 303], 303: [302, 304],
                      304: [303, 271], 305: [272, 338], 306: [307, 339],
                      307: [306, 340], 308: [275, 341], 309: [276, 342],
                      310: [277, 343], 311: [278, 344], 312: [279, 313],
                      313: [312], 314: [281, 347], 315: [316, 348], 316: [315],
                      317: [318, 350], 318: [317, 351], 319: [286, 320],
                      320: [319, 321], 321: [320, 354], 322: [323, 355],
                      323: [322, 290], 324: [291, 357], 325: [292, 358],
                      326: [327, 359], 327: [326, 360], 328: [295, 361],
                      329: [296, 330], 330: [329], 331: [332], 332: [331, 299],
                      333: [334, 366], 334: [333, 335], 335: [334, 336, 368],
                      336: [335, 337], 337: [336], 338: [305, 371], 339: [306, 372],
                      340: [307, 373], 341: [308], 342: [309, 343], 343: [342, 310],
                      344: [311, 377], 345: [346, 378], 346: [345, 347, 379],
                      347: [346, 314], 348: [315, 349], 349: [348, 350, 382],
                      350: [349, 317], 351: [318, 352], 352: [351, 353],
                      353: [352, 386], 354: [321, 387], 355: [322, 388],
                      356: [357, 389], 357: [356, 324], 358: [325, 359],
                      359: [358, 326], 360: [327], 361: [328, 362, 394],
                      362: [361, 363], 363: [362], 364: [365, 397], 365: [364, 366],
                      366: [365, 333, 367], 367: [366], 368: [335, 401],
                      369: [370, 402], 370: [369, 403], 371: [338, 404],
                      372: [339, 373], 373: [372, 340], 374: [375, 407],
                      375: [374, 376, 408], 376: [375, 409], 377: [344, 410],
                      378: [345, 411], 379: [346, 380], 380: [379, 381],
                      381: [380, 414], 382: [349, 415], 383: [384, 416],
                      384: [383, 417], 385: [386], 386: [385, 353, 419],
                      387: [354, 420], 388: [355, 421], 389: [356, 422], 390: [391],
                      391: [390, 392], 392: [391, 393], 393: [392, 426],
                      394: [361, 395], 395: [394, 428], 396: [429], 397: [364],
                      398: [399, 431], 399: [398, 432], 400: [401, 433],
                      401: [400, 368], 402: [369, 435], 403: [370, 404],
                      404: [403, 371, 437], 405: [406], 406: [405, 439],
                      407: [374, 440], 408: [375, 441], 409: [376, 442],
                      410: [377, 411], 411: [410, 378], 412: [413, 445],
                      413: [412, 446], 414: [381, 415], 415: [414, 382], 416: [383],
                      417: [384, 418, 450], 418: [417, 419], 419: [418, 386],
                      420: [387, 453], 421: [388, 422], 422: [421, 389],
                      423: [424, 456], 424: [423, 425], 425: [424, 458],
                      426: [393, 427, 459], 427: [426], 428: [395, 429],
                      429: [428, 396], 430: [431], 431: [430, 398], 432: [399, 465],
                      433: [400, 466], 434: [435, 467], 435: [434, 402, 436],
                      436: [435, 469], 437: [404, 438], 438: [437, 471], 439: [406],
                      440: [407, 473], 441: [408, 442, 474], 442: [441, 409],
                      443: [444], 444: [443, 445], 445: [444, 412, 478], 446: [413],
                      447: [448, 480], 448: [447, 449, 481], 449: [448, 450],
                      450: [449, 417], 451: [452, 484], 452: [451, 453],
                      453: [452, 420, 486], 454: [487], 455: [456, 488],
                      456: [455, 423, 457], 457: [456, 458], 458: [457, 425],
                      459: [426, 492], 460: [461, 493], 461: [460, 462], 462: [461],
                      463: [464], 464: [463, 497], 465: [432, 498], 466: [433, 467],
                      467: [466, 434], 468: [501], 469: [436, 470], 470: [469, 471],
                      471: [470, 438, 472], 472: [471, 473], 473: [472, 440],
                      474: [441, 475], 475: [474, 476], 476: [475, 477],
                      477: [476, 478], 478: [477, 445], 479: [480, 512],
                      480: [479, 447], 481: [448, 514], 482: [483], 483: [482, 516],
                      484: [451, 485], 485: [484, 518], 486: [453, 487],
                      487: [486, 454], 488: [455, 521], 489: [522], 490: [491, 523],
                      491: [490, 492], 492: [491, 459], 493: [460, 494],
                      494: [493, 527], 495: [528], 496: [497], 497: [496, 464],
                      498: [465, 499], 499: [498, 500], 500: [499, 533],
                      501: [468, 502], 502: [501, 503], 503: [502, 504],
                      504: [503, 537], 505: [506, 538], 506: [505, 507],
                      507: [506, 540], 508: [509, 541], 509: [508, 510, 542],
                      510: [509, 511], 511: [510, 512], 512: [511, 479, 545],
                      513: [546], 514: [481, 515], 515: [514, 548],
                      516: [483, 517, 549], 517: [516, 550], 518: [485, 551],
                      519: [520, 552], 520: [519, 553], 521: [488, 522],
                      522: [521, 489, 523], 523: [522, 490], 524: [557],
                      525: [526, 558], 526: [525, 559], 527: [494, 560], 528: [495],
                      529: [530], 530: [529, 531], 531: [530, 532], 532: [531, 565],
                      533: [500, 534], 534: [533, 535, 567], 535: [534, 536],
                      536: [535, 537], 537: [536, 504], 538: [505, 539],
                      539: [538, 540], 540: [539, 507], 541: [508, 574],
                      542: [509, 575], 543: [576], 544: [545, 577], 545: [544, 512],
                      546: [513, 547], 547: [546], 548: [515, 581], 549: [516, 550],
                      550: [549, 517], 551: [518, 584], 552: [519], 553: [520, 554],
                      554: [553, 555], 555: [554], 556: [557, 589],
                      557: [556, 524, 590], 558: [525, 591], 559: [526],
                      560: [527, 561], 561: [560], 562: [563], 563: [562, 564],
                      564: [563, 597], 565: [532, 566], 566: [565, 599],
                      567: [534, 568], 568: [567, 569], 569: [568, 570],
                      570: [569, 571], 571: [570, 572], 572: [571], 573: [574, 606],
                      574: [573, 541, 575], 575: [574, 542], 576: [543, 609],
                      577: [544, 610], 578: [579, 611], 579: [578, 580],
                      580: [579, 581], 581: [580, 548, 582], 582: [581, 615],
                      583: [616], 584: [551, 585, 617], 585: [584, 586],
                      586: [585, 587], 587: [586, 588], 588: [587, 621],
                      589: [556, 622], 590: [557, 623], 591: [558, 624],
                      592: [593, 625], 593: [592, 594, 626], 594: [593], 595: [596],
                      596: [595, 597], 597: [596, 564, 598], 598: [597, 631],
                      599: [566, 600], 600: [599, 633], 601: [602], 602: [601, 635],
                      603: [604, 636], 604: [603, 605], 605: [604, 606],
                      606: [605, 573], 607: [608], 608: [607, 641], 609: [576, 642],
                      610: [577, 611], 611: [610, 578], 612: [613, 645],
                      613: [612, 646], 614: [615], 615: [614, 582],
                      616: [583, 617, 649], 617: [616, 584], 618: [619],
                      619: [618, 620, 652], 620: [619, 621], 621: [620, 588],
                      622: [589, 623], 623: [622, 590], 624: [591, 625],
                      625: [624, 592], 626: [593, 627], 627: [626], 628: [629],
                      629: [628, 662], 630: [663], 631: [598, 632], 632: [631, 665],
                      633: [600, 666], 634: [635, 667], 635: [634, 602, 636],
                      636: [635, 603], 637: [638, 670], 638: [637], 639: [640, 672],
                      640: [639, 673], 641: [608, 642, 674], 642: [641, 609, 675],
                      643: [644, 676], 644: [643, 677], 645: [612, 646],
                      646: [645, 613], 647: [648, 680], 648: [647, 681],
                      649: [616, 650], 650: [649, 651], 651: [650, 652],
                      652: [651, 619], 653: [654, 686], 654: [653, 655],
                      655: [654, 688], 656: [657, 689], 657: [656, 690],
                      658: [659, 691], 659: [658, 692], 662: [629],
                      663: [630, 664, 696], 664: [663, 665], 665: [664, 632, 698],
                      666: [633, 699], 667: [634, 700], 668: [669], 669: [668, 670],
                      670: [669, 637, 671], 671: [670, 672], 672: [671, 639],
                      673: [640, 674], 674: [673, 641], 675: [642, 708],
                      676: [643, 677], 677: [676, 644], 678: [679, 711],
                      679: [678, 712], 680: [647, 713], 681: [648, 682],
                      682: [681, 683], 683: [682, 684], 684: [683, 685, 717],
                      685: [684, 718], 686: [653, 687], 687: [686, 720],
                      688: [655, 721], 689: [656, 722], 690: [657], 691: [658, 724],
                      692: [659, 693], 693: [692], 694: [695], 695: [694, 696],
                      696: [695, 663], 697: [698, 730], 698: [697, 665],
                      699: [666, 700], 700: [699, 667], 701: [702], 702: [701, 703],
                      703: [702, 704], 704: [703, 705], 705: [704, 706],
                      706: [705, 739], 707: [740], 708: [675, 709, 741],
                      709: [708, 710], 710: [709, 711], 711: [710, 678, 744],
                      712: [679], 713: [680, 714], 714: [713, 747], 715: [716],
                      716: [715, 749], 717: [684, 750], 718: [685, 719],
                      719: [718, 752], 720: [687, 753], 721: [688, 754],
                      722: [689, 723], 723: [722, 756], 724: [691, 725, 757],
                      725: [724, 726], 726: [725, 759], 727: [728], 728: [727, 761],
                      729: [762], 730: [697, 763], 731: [732, 764], 732: [731, 765],
                      733: [734, 766], 734: [733, 735, 767], 735: [734, 736],
                      736: [735], 737: [738, 770], 738: [737, 739],
                      739: [738, 706, 740], 740: [739, 707], 741: [708, 774],
                      742: [743], 743: [742, 776], 744: [711, 745], 745: [744, 746],
                      746: [745, 779], 747: [714, 780], 748: [749, 781],
                      749: [748, 716], 750: [717, 783], 751: [752, 784],
                      752: [751, 719], 753: [720, 786], 754: [721, 787],
                      755: [756, 788], 756: [755, 723], 757: [724, 758], 758: [757],
                      759: [726], 760: [761], 761: [760, 728, 762], 762: [761, 729],
                      763: [730, 796], 764: [731, 797], 765: [732, 798],
                      766: [733, 799], 767: [734, 800], 768: [769, 801],
                      769: [768, 802], 770: [737, 771], 771: [770, 804], 772: [773],
                      773: [772, 774], 774: [773, 741], 775: [808],
                      776: [743, 777, 809], 777: [776, 778], 778: [777, 811],
                      779: [746, 780], 780: [779, 747], 781: [748, 782, 814],
                      782: [781, 815], 783: [750, 784], 784: [783, 751],
                      785: [786, 818], 786: [785, 753], 787: [754, 788],
                      788: [787, 755], 789: [790], 790: [789, 791],
                      791: [790, 792, 824], 792: [791], 793: [826], 794: [795],
                      795: [794, 796], 796: [795, 763], 797: [764, 830],
                      798: [765, 831], 799: [766, 832], 800: [767, 833], 801: [768],
                      802: [769, 835], 803: [836], 804: [771, 805, 837],
                      805: [804, 806], 806: [805, 807], 807: [806, 840],
                      808: [775, 809, 841], 809: [808, 776], 810: [811, 843],
                      811: [810, 778, 812], 812: [811, 813], 813: [812, 846],
                      814: [781, 847], 815: [782, 816], 816: [815, 817],
                      817: [816, 818], 818: [817, 785], 819: [820, 852],
                      820: [819, 821], 821: [820, 822], 822: [821, 823],
                      823: [822, 856], 824: [791, 857], 825: [858], 826: [793],
                      827: [828, 860], 828: [827, 829], 829: [828, 830, 862],
                      830: [829, 797], 831: [798, 864], 832: [799, 865],
                      833: [800, 834], 834: [833, 835, 867], 835: [834, 802],
                      836: [803, 869], 837: [804, 838], 838: [837, 839],
                      839: [838, 840], 840: [839, 807], 841: [808, 842],
                      842: [841, 875], 843: [810, 844], 844: [843], 845: [878],
                      846: [813, 879], 847: [814, 848], 848: [847, 849],
                      849: [848, 850], 850: [849, 851], 851: [850, 852],
                      852: [851, 819, 853], 853: [852, 854], 854: [853, 855, 887],
                      855: [854, 888], 856: [823, 857], 857: [856, 824], 858: [825],
                      859: [860], 860: [859, 827, 861], 861: [860, 894],
                      862: [829, 863], 863: [862, 864], 864: [863, 831, 865],
                      865: [864, 832], 866: [867], 867: [866, 834], 868: [869, 901],
                      869: [868, 836, 870], 870: [869, 903], 871: [872, 904],
                      872: [871, 905], 873: [874, 906], 874: [873], 875: [842, 876],
                      876: [875, 877], 877: [876, 878, 910], 878: [877, 845],
                      879: [846, 880], 880: [879, 913], 881: [882], 882: [881, 883],
                      883: [882, 916], 884: [885, 917], 885: [884, 886],
                      886: [885, 919], 887: [854, 920], 888: [855, 889],
                      889: [888, 922], 890: [891, 923], 891: [890], 892: [925],
                      893: [926], 894: [861, 895], 895: [894, 928], 896: [929],
                      897: [898, 930], 898: [897, 899], 899: [898, 900, 932],
                      900: [899, 901], 901: [900, 868], 902: [935], 903: [870, 904],
                      904: [903, 871], 905: [872, 938], 906: [873, 907, 939],
                      907: [906, 908], 908: [907, 909, 941], 909: [908, 910],
                      910: [909, 877], 911: [912, 944], 912: [911, 945],
                      913: [880, 914], 914: [913, 915], 915: [914], 916: [883, 949],
                      917: [884, 918], 918: [917], 919: [886, 952], 920: [887, 921],
                      921: [920, 954], 922: [889, 955], 923: [890, 956],
                      925: [892, 958], 926: [893, 927], 927: [926, 960],
                      928: [895, 929], 929: [928, 896], 930: [897, 963], 931: [932],
                      932: [931, 899], 933: [934, 966], 934: [933, 935],
                      935: [934, 902, 968], 936: [969], 937: [938, 970],
                      938: [937, 905], 939: [906, 940], 940: [939, 973],
                      941: [908, 942], 942: [941, 975], 943: [944, 976],
                      944: [943, 911], 945: [912, 946], 946: [945, 947],
                      947: [946, 948, 980], 948: [947, 949], 949: [948, 916, 982],
                      950: [983], 951: [952], 952: [951, 919, 985], 953: [954, 986],
                      954: [953, 921], 955: [922, 988], 956: [923, 989], 957: [990],
                      958: [925], 959: [960], 960: [959, 927, 961], 961: [960, 962],
                      962: [961, 963], 963: [962, 930, 996], 964: [965, 997],
                      965: [964, 966], 966: [965, 933], 967: [968, 1000],
                      968: [967, 935], 969: [936, 970], 970: [969, 937],
                      971: [972, 1004], 972: [971], 973: [940, 974], 974: [973],
                      975: [942, 976, 1008], 976: [975, 943], 977: [978, 1010],
                      978: [977, 1011], 979: [980, 1012], 980: [979, 947],
                      981: [982, 1014], 982: [981, 949], 983: [950, 984],
                      984: [983, 985, 1017], 985: [984, 952], 986: [953, 987],
                      987: [986, 988], 988: [987, 955], 989: [956, 1022], 990: [957],
                      991: [992], 992: [991, 1025], 993: [994], 994: [993, 995],
                      995: [994, 1028], 996: [963, 997], 997: [996, 964],
                      998: [999, 1031], 999: [998, 1032], 1000: [967, 1033],
                      1001: [1002, 1034], 1002: [1001], 1003: [1004, 1036],
                      1004: [1003, 971], 1005: [1006], 1006: [1005, 1007, 1039],
                      1007: [1006, 1040], 1008: [975, 1041], 1009: [1010, 1042],
                      1010: [1009, 977], 1011: [978], 1012: [979, 1045],
                      1013: [1014, 1046], 1014: [1013, 981], 1015: [1016, 1048],
                      1016: [1015, 1049], 1017: [984, 1018], 1018: [1017, 1019],
                      1019: [1018, 1052], 1020: [1021, 1053], 1021: [1020, 1054],
                      1022: [989, 1023, 1055], 1023: [1022], 1024: [1025],
                      1025: [1024, 992, 1058], 1026: [1027, 1059], 1027: [1026, 1028],
                      1028: [1027, 995], 1029: [1030, 1062], 1030: [1029, 1063],
                      1031: [998, 1064], 1032: [999, 1065], 1033: [1000, 1066],
                      1034: [1001, 1035], 1035: [1034, 1036], 1036: [1035, 1003, 1037],
                      1037: [1036, 1038], 1038: [1037, 1039, 1071], 1039: [1038, 1006],
                      1040: [1007, 1073], 1041: [1008], 1042: [1009, 1075],
                      1043: [1044, 1076], 1044: [1043, 1045, 1077], 1045: [1044, 1012],
                      1046: [1013, 1079], 1047: [1048, 1080], 1048: [1047, 1015],
                      1049: [1016, 1050], 1050: [1049, 1051], 1051: [1050, 1052],
                      1052: [1051, 1019, 1085], 1053: [1020], 1054: [1021, 1087],
                      1055: [1022, 1088], 1058: [1025], 1059: [1026], 1060: [1061],
                      1061: [1060], 1062: [1029], 1063: [1030], 1064: [1031],
                      1065: [1032], 1066: [1033], 1067: [1068], 1068: [1067],
                      1069: [1070], 1070: [1069], 1071: [1038], 1073: [1040, 1074],
                      1074: [1073], 1075: [1042], 1076: [1043], 1077: [1044],
                      1079: [1046], 1080: [1047], 1081: [1082], 1082: [1081, 1083],
                      1083: [1082], 1085: [1052], 1086: [1087], 1087: [1086, 1054],
                      1088: [1055]}
# I didn't capture these
cycle_13_late_links = {}
cycle_14_links = {2: [34, 36], 3: [35, 37], 5: [37, 39], 6: [38, 40],
                  7: [39, 40, 41], 8: [40, 42], 9: [41, 43],
                  10: [42, 43, 44], 11: [12, 43, 44, 45], 12: [11, 44, 46],
                  13: [45, 46, 47], 14: [46, 48], 16: [48, 50], 17: [51],
                  18: [50, 51, 52], 19: [51, 52, 53], 20: [52, 54],
                  21: [53, 55], 22: [54, 56], 23: [24, 55, 57],
                  24: [23, 56, 58], 25: [57, 59], 26: [58, 60],
                  27: [59, 61], 28: [60, 61, 62], 29: [61, 63],
                  31: [63, 65], 32: [64, 66], 34: [2, 68], 35: [3, 67],
                  36: [2, 68, 70], 37: [3, 5, 71], 38: [6, 70, 72],
                  39: [5, 7, 40, 71, 73], 40: [6, 7, 8, 39, 41, 72, 74],
                  41: [7, 9, 40, 73, 74, 75], 42: [8, 10, 74, 76],
                  43: [9, 10, 11, 75, 77], 44: [10, 11, 12, 76, 77, 78],
                  45: [11, 13, 46, 77, 78, 79], 46: [12, 13, 14, 45, 78, 80],
                  47: [13, 79, 81], 48: [14, 16, 80, 82],
                  50: [16, 18, 82, 84], 51: [17, 18, 19, 83, 85],
                  52: [18, 19, 20, 84, 85, 86], 53: [19, 21, 54, 85, 86, 87],
                  54: [20, 22, 53, 86, 87, 88], 55: [21, 23, 87, 89],
                  56: [22, 24, 88, 90], 57: [23, 25, 89, 91],
                  58: [24, 26, 90], 59: [25, 27, 91, 93], 60: [26, 28, 94],
                  61: [27, 28, 29, 93, 95], 62: [28, 94, 96],
                  63: [29, 31, 95, 97], 64: [32, 96, 98], 65: [31, 97, 99],
                  66: [32, 98], 67: [35, 101], 68: [34, 36, 100],
                  70: [36, 38, 104], 71: [37, 39, 103, 104, 105],
                  72: [38, 40, 73, 104, 105, 106],
                  73: [39, 41, 72, 105, 107],
                  74: [40, 41, 42, 75, 106, 107, 108],
                  75: [41, 43, 74, 107, 109], 76: [42, 44, 77, 108, 110],
                  77: [43, 44, 45, 76, 109, 111],
                  78: [44, 45, 46, 110, 111, 112], 79: [45, 47, 111, 113],
                  80: [46, 48, 112, 114], 81: [47, 113, 115],
                  82: [48, 50, 114, 116], 83: [51, 115, 117],
                  84: [50, 52, 85, 116, 118], 85: [51, 52, 53, 84, 117, 119],
                  86: [52, 53, 54, 118, 119, 120],
                  87: [53, 54, 55, 119, 120, 121],
                  88: [54, 56, 120, 121, 122], 89: [55, 57, 121],
                  90: [56, 58, 122, 124], 91: [57, 59, 125],
                  93: [59, 61, 125, 127], 94: [60, 62, 95, 126, 128],
                  95: [61, 63, 94, 127, 128, 129], 96: [62, 64, 128, 130],
                  97: [63, 65, 129, 130, 131], 98: [64, 66, 130, 132],
                  99: [65, 131], 100: [68, 133, 134], 101: [67, 133, 135],
                  103: [71, 135, 137], 104: [70, 71, 72, 136, 137, 138],
                  105: [71, 72, 73, 137, 138, 139], 106: [72, 74, 138, 140],
                  107: [73, 74, 75, 139, 141], 108: [74, 76, 140],
                  109: [75, 77, 141, 143], 110: [76, 78, 144],
                  111: [77, 78, 79, 143, 144, 145],
                  112: [78, 80, 113, 144, 146],
                  113: [79, 81, 112, 114, 145, 147],
                  114: [80, 82, 113, 146, 148], 115: [81, 83, 147, 149],
                  116: [82, 84, 148, 149, 150], 117: [83, 85, 149, 150, 151],
                  118: [84, 86, 150, 152], 119: [85, 86, 87, 151, 153],
                  120: [86, 87, 88, 121, 152, 153, 154],
                  121: [87, 88, 89, 120, 153, 155], 122: [88, 90, 154, 156],
                  124: [90, 156, 158], 125: [91, 93, 157, 159],
                  126: [94, 158, 160], 127: [93, 95, 159, 161],
                  128: [94, 95, 96, 129, 160, 162],
                  129: [95, 97, 128, 161, 162, 163],
                  130: [96, 97, 98, 162, 163, 164], 131: [97, 99, 163, 165],
                  132: [98, 164], 133: [100, 101, 167], 134: [100, 166, 168],
                  135: [101, 103, 167, 169], 136: [104, 168, 170],
                  137: [103, 104, 105, 169, 171],
                  138: [104, 105, 106, 170, 171, 172],
                  139: [105, 107, 140, 171, 173],
                  140: [106, 108, 139, 172, 174], 141: [107, 109, 173, 175],
                  143: [109, 111, 175, 177],
                  144: [110, 111, 112, 176, 177, 178],
                  145: [111, 113, 146, 177, 179],
                  146: [112, 114, 145, 147, 178, 180],
                  147: [113, 115, 146, 148, 179, 181],
                  148: [114, 116, 147, 180, 182],
                  149: [115, 116, 117, 181, 182, 183],
                  150: [116, 117, 118, 182, 184],
                  151: [117, 119, 152, 183, 184, 185],
                  152: [118, 120, 151, 184, 185, 186],
                  153: [119, 120, 121, 185, 186, 187],
                  154: [120, 122, 186, 188], 155: [121, 187, 189],
                  156: [122, 124, 188, 190], 157: [125, 189, 191],
                  158: [124, 126, 190, 192], 159: [125, 127, 191, 192, 193],
                  160: [126, 128, 161, 192, 194],
                  161: [127, 129, 160, 193, 194, 195],
                  162: [128, 129, 130, 194, 195, 196],
                  163: [129, 130, 131, 195, 197], 164: [130, 132, 196, 198],
                  165: [131, 197], 166: [134, 167, 200],
                  167: [133, 135, 166, 199, 201], 168: [134, 136, 200],
                  169: [135, 137, 201, 203], 170: [136, 138, 204],
                  171: [137, 138, 139, 172, 203, 205],
                  172: [138, 140, 171, 173, 204, 206],
                  173: [139, 141, 172, 205, 206, 207], 174: [140, 206, 208],
                  175: [141, 143, 207, 209], 176: [144, 208, 210],
                  177: [143, 144, 145, 209, 211], 178: [144, 146, 210, 212],
                  179: [145, 147, 180, 211, 212, 213],
                  180: [146, 148, 179, 181, 212, 213, 214],
                  181: [147, 149, 180, 213, 214, 215],
                  182: [148, 149, 150, 214, 215, 216],
                  183: [149, 151, 215, 217],
                  184: [150, 151, 152, 216, 217, 218],
                  185: [151, 152, 153, 186, 217, 219],
                  186: [152, 153, 154, 185, 218, 220],
                  187: [153, 155, 219, 221], 188: [154, 156, 220, 221, 222],
                  189: [155, 157, 221, 222, 223],
                  190: [156, 158, 191, 222, 224],
                  191: [157, 159, 190, 223, 225],
                  192: [158, 159, 160, 193, 224, 226],
                  193: [159, 161, 192, 194, 225, 226, 227],
                  194: [160, 161, 162, 193, 226, 228],
                  195: [161, 162, 163, 227, 228, 229],
                  196: [162, 164, 197, 228, 230],
                  197: [163, 165, 196, 229, 231], 198: [164, 230],
                  199: [167, 233], 200: [166, 168, 232, 233, 234],
                  201: [167, 169, 233, 235], 203: [169, 171, 235, 237],
                  204: [170, 172, 236, 237, 238],
                  205: [171, 173, 237, 238, 239],
                  206: [172, 173, 174, 207, 238, 240],
                  207: [173, 175, 206, 208, 239, 241],
                  208: [174, 176, 207, 209, 240, 242],
                  209: [175, 177, 208, 210, 241, 243],
                  210: [176, 178, 209, 242, 243, 244],
                  211: [177, 179, 212, 243, 245],
                  212: [178, 179, 180, 211, 244, 246],
                  213: [179, 180, 181, 245, 246, 247],
                  214: [180, 181, 182, 246, 247, 248],
                  215: [181, 182, 183, 247, 248, 249],
                  216: [182, 184, 248, 249, 250],
                  217: [183, 184, 185, 249, 250, 251],
                  218: [184, 186, 219, 250, 251, 252],
                  219: [185, 187, 218, 251, 252, 253],
                  220: [186, 188, 252, 253, 254],
                  221: [187, 188, 189, 253, 254, 255],
                  222: [188, 189, 190, 223, 254, 256],
                  223: [189, 191, 222, 255, 257], 224: [190, 192, 256, 258],
                  225: [191, 193, 226, 257, 259],
                  226: [192, 193, 194, 225, 258, 260],
                  227: [193, 195, 259, 261], 228: [194, 195, 196, 260, 262],
                  229: [195, 197, 261, 263], 230: [196, 198, 262, 263, 264],
                  231: [197, 263], 232: [200, 265, 266],
                  233: [199, 200, 201, 265, 266, 267], 234: [200, 266, 268],
                  235: [201, 203, 267, 269], 236: [204, 268, 270],
                  237: [203, 204, 205, 269, 271],
                  238: [204, 205, 206, 239, 270, 272],
                  239: [205, 207, 238, 271, 272, 273],
                  240: [206, 208, 272, 273, 274], 241: [207, 209, 273, 275],
                  242: [208, 210, 243, 274, 275, 276],
                  243: [209, 210, 211, 242, 275, 277],
                  244: [210, 212, 245, 276, 278],
                  245: [211, 213, 244, 246, 277, 279],
                  246: [212, 213, 214, 245, 278, 280],
                  247: [213, 214, 215, 248, 279, 281],
                  248: [214, 215, 216, 247, 280, 282],
                  249: [215, 216, 217, 281, 283],
                  250: [216, 217, 218, 282, 283, 284],
                  251: [217, 218, 219, 283, 284, 285],
                  252: [218, 219, 220, 284, 286],
                  253: [219, 220, 221, 285, 286, 287],
                  254: [220, 221, 222, 286, 287, 288],
                  255: [221, 223, 287, 289], 256: [222, 224, 288, 289, 290],
                  257: [223, 225, 258, 289, 291],
                  258: [224, 226, 257, 259, 290, 292],
                  259: [225, 227, 258, 260, 291, 293],
                  260: [226, 228, 259, 292, 294],
                  261: [227, 229, 293, 294, 295],
                  262: [228, 230, 263, 294, 295, 296],
                  263: [229, 230, 231, 262, 295, 297],
                  264: [230, 296], 265: [232, 233, 298, 299],
                  266: [232, 233, 234, 298, 299, 300],
                  267: [233, 235, 299, 300, 301],
                  268: [234, 236, 269, 300, 302],
                  269: [235, 237, 268, 270, 301, 302, 303],
                  270: [236, 238, 269, 271, 302, 304],
                  271: [237, 239, 270, 303, 304, 305],
                  272: [238, 239, 240, 273, 304, 306],
                  273: [239, 240, 241, 272, 305, 306, 307],
                  274: [240, 242, 275, 306, 307, 308],
                  275: [241, 242, 243, 274, 307, 309],
                  276: [242, 244, 308, 309, 310],
                  277: [243, 245, 309, 311], 278: [244, 246, 279, 310, 312],
                  279: [245, 247, 278, 280, 311, 313],
                  280: [246, 248, 279, 312, 313, 314],
                  281: [247, 249, 282, 313, 315],
                  282: [248, 250, 281, 283, 314, 315, 316],
                  283: [249, 250, 251, 282, 315, 317],
                  284: [250, 251, 252, 316, 318], 285: [251, 253, 317, 319],
                  286: [252, 253, 254, 318, 320],
                  287: [253, 254, 255, 288, 319, 321],
                  288: [254, 256, 287, 320, 321, 322],
                  289: [255, 256, 257, 290, 321, 323],
                  290: [256, 258, 289, 291, 322, 324],
                  291: [257, 259, 290, 323, 324, 325],
                  292: [258, 260, 293, 324, 325, 326],
                  293: [259, 261, 292, 325, 326, 327],
                  294: [260, 261, 262, 295, 326, 328],
                  295: [261, 262, 263, 294, 327, 329],
                  296: [262, 264, 297, 328, 329, 330], 297: [263, 296, 329],
                  298: [265, 266, 332], 299: [265, 266, 267, 331, 333],
                  300: [266, 267, 268, 332, 334], 301: [267, 269, 333, 335],
                  302: [268, 269, 270, 334, 336],
                  303: [269, 271, 304, 335, 336, 337],
                  304: [270, 271, 272, 303, 336, 338],
                  305: [271, 273, 337, 339],
                  306: [272, 273, 274, 338, 339, 340],
                  307: [273, 274, 275, 308, 339, 341],
                  308: [274, 276, 307, 340, 341, 342],
                  309: [275, 276, 277, 341, 342, 343],
                  310: [276, 278, 311, 342, 344],
                  311: [277, 279, 310, 312, 343, 345],
                  312: [278, 280, 311, 344, 345, 346],
                  313: [279, 280, 281, 345, 346, 347],
                  314: [280, 282, 346, 348], 315: [281, 282, 283, 347, 349],
                  316: [282, 284, 348, 350], 317: [283, 285, 318, 349, 351],
                  318: [284, 286, 317, 319, 350, 351, 352],
                  319: [285, 287, 318, 320, 351, 353],
                  320: [286, 288, 319, 352, 353, 354],
                  321: [287, 288, 289, 353, 355], 322: [288, 290, 354, 356],
                  323: [289, 291, 324, 355, 357],
                  324: [290, 291, 292, 323, 356, 358],
                  325: [291, 292, 293, 357, 358, 359],
                  326: [292, 293, 294, 327, 358, 359, 360],
                  327: [293, 295, 326, 359, 360, 361],
                  328: [294, 296, 329, 360, 361, 362],
                  329: [295, 296, 297, 328, 330, 361, 363],
                  330: [296, 329, 362], 331: [299],
                  332: [298, 300, 364, 366], 333: [299, 301, 367],
                  334: [300, 302, 366, 367, 368],
                  335: [301, 303, 336, 367, 369],
                  336: [302, 303, 304, 335, 337, 368, 370],
                  337: [303, 305, 336, 369, 371], 338: [304, 306, 370, 372],
                  339: [305, 306, 307, 340, 371, 373],
                  340: [306, 308, 339, 372, 373, 374],
                  341: [307, 308, 309, 342, 373, 375],
                  342: [308, 309, 310, 341, 374, 376],
                  343: [309, 311, 375, 377], 344: [310, 312, 376, 378],
                  345: [311, 312, 313, 377, 378, 379],
                  346: [312, 313, 314, 378, 379, 380],
                  347: [313, 315, 348, 379, 381],
                  348: [314, 316, 347, 380, 382], 349: [315, 317, 381, 383],
                  350: [316, 318, 351, 382, 383, 384],
                  351: [317, 318, 319, 350, 383, 385],
                  352: [318, 320, 353, 384, 385, 386],
                  353: [319, 320, 321, 352, 385, 386, 387],
                  354: [320, 322, 355, 386, 387, 388],
                  355: [321, 323, 354, 387, 389],
                  356: [322, 324, 388, 389, 390], 357: [323, 325, 389, 391],
                  358: [324, 325, 326, 390, 392],
                  359: [325, 326, 327, 391, 393],
                  360: [326, 327, 328, 392, 393, 394],
                  361: [327, 328, 329, 393, 394, 395],
                  362: [328, 330, 394, 395, 396], 363: [329, 395, 396],
                  364: [332, 398], 366: [332, 334, 398, 400],
                  367: [333, 334, 335, 399, 400, 401],
                  368: [334, 336, 400, 402], 369: [335, 337, 401, 402, 403],
                  370: [336, 338, 371, 402, 403, 404],
                  371: [337, 339, 370, 372, 403, 405],
                  372: [338, 340, 371, 373, 404, 406],
                  373: [339, 340, 341, 372, 405, 407],
                  374: [340, 342, 375, 406, 407, 408],
                  375: [341, 343, 374, 376, 407, 409],
                  376: [342, 344, 375, 408, 409, 410],
                  377: [343, 345, 378, 409, 411],
                  378: [344, 345, 346, 377, 379, 410, 412],
                  379: [345, 346, 347, 378, 411, 413],
                  380: [346, 348, 381, 412, 413, 414],
                  381: [347, 349, 380, 382, 413, 414, 415],
                  382: [348, 350, 381, 383, 414, 416],
                  383: [349, 350, 351, 382, 415, 416, 417],
                  384: [350, 352, 416, 417, 418],
                  385: [351, 352, 353, 417, 419],
                  386: [352, 353, 354, 418, 420],
                  387: [353, 354, 355, 419, 420, 421],
                  388: [354, 356, 389, 420, 422],
                  389: [355, 356, 357, 388, 421, 423],
                  390: [356, 358, 391, 422, 424],
                  391: [357, 359, 390, 423, 425], 392: [358, 360, 424, 426],
                  393: [359, 360, 361, 425, 426, 427],
                  394: [360, 361, 362, 426, 428],
                  395: [361, 362, 363, 427, 428, 429], 396: [362, 363, 428],
                  397: [431], 398: [364, 366, 430, 432],
                  399: [367, 431, 433], 400: [366, 367, 368, 401, 432, 434],
                  401: [367, 369, 400, 402, 433, 435],
                  402: [368, 369, 370, 401, 403, 434, 436],
                  403: [369, 370, 371, 402, 435, 437],
                  404: [370, 372, 405, 436, 438],
                  405: [371, 373, 404, 406, 437, 439],
                  406: [372, 374, 405, 407, 438, 440],
                  407: [373, 374, 375, 406, 439, 440, 441],
                  408: [374, 376, 440, 441, 442],
                  409: [375, 376, 377, 410, 441, 443],
                  410: [376, 378, 409, 442, 443, 444],
                  411: [377, 379, 412, 443, 444, 445],
                  412: [378, 380, 411, 444, 445, 446],
                  413: [379, 380, 381, 414, 445, 447],
                  414: [380, 381, 382, 413, 415, 446, 448],
                  415: [381, 383, 414, 416, 447, 449],
                  416: [382, 383, 384, 415, 448, 450],
                  417: [383, 384, 385, 418, 449, 451],
                  418: [384, 386, 417, 450, 452], 419: [385, 387, 451, 453],
                  420: [386, 387, 388, 421, 452, 454],
                  421: [387, 389, 420, 422, 453, 455],
                  422: [388, 390, 421, 454, 456], 423: [389, 391, 455],
                  424: [390, 392, 456, 458], 425: [391, 393, 459],
                  426: [392, 393, 394, 458, 460], 427: [393, 395, 459, 461],
                  428: [394, 395, 396, 429, 460, 462], 429: [395, 428, 461],
                  430: [398, 431, 464], 431: [397, 399, 430, 463, 465],
                  432: [398, 400, 464, 465, 466],
                  433: [399, 401, 434, 465, 466, 467],
                  434: [400, 402, 433, 466, 467, 468],
                  435: [401, 403, 436, 467, 468, 469],
                  436: [402, 404, 435, 468, 470], 437: [403, 405, 469],
                  438: [404, 406, 470, 472], 439: [405, 407, 473],
                  440: [406, 407, 408, 472, 473, 474],
                  441: [407, 408, 409, 442, 473, 475],
                  442: [408, 410, 441, 474, 475, 476],
                  443: [409, 410, 411, 444, 475, 477],
                  444: [410, 411, 412, 443, 476, 478],
                  445: [411, 412, 413, 477, 478, 479],
                  446: [412, 414, 447, 478, 479, 480],
                  447: [413, 415, 446, 448, 479, 481],
                  448: [414, 416, 447, 449, 480, 482],
                  449: [415, 417, 448, 450, 481, 483],
                  450: [416, 418, 449, 482, 484], 451: [417, 419, 483, 485],
                  452: [418, 420, 453, 484, 486],
                  453: [419, 421, 452, 454, 485, 487],
                  454: [420, 422, 453, 486, 488], 455: [421, 423, 487, 489],
                  456: [422, 424, 488, 490], 458: [424, 426, 490, 492],
                  459: [425, 427, 491], 460: [426, 428, 492, 494],
                  461: [427, 429, 495], 462: [428, 494],
                  463: [431, 464, 497], 464: [430, 432, 463, 465, 496, 498],
                  465: [431, 432, 433, 464, 497, 499],
                  466: [432, 433, 434, 498, 499, 500],
                  467: [433, 434, 435, 499, 501],
                  468: [434, 435, 436, 500, 502], 469: [435, 437, 501, 503],
                  470: [436, 438, 502, 504], 472: [438, 440, 504, 506],
                  473: [439, 440, 441, 474, 505, 507],
                  474: [440, 442, 473, 506, 507, 508],
                  475: [441, 442, 443, 507, 508, 509],
                  476: [442, 444, 477, 508, 510],
                  477: [443, 445, 476, 509, 510, 511],
                  478: [444, 445, 446, 510, 511, 512],
                  479: [445, 446, 447, 480, 511, 513],
                  480: [446, 448, 479, 481, 512, 514],
                  481: [447, 449, 480, 513, 515], 482: [448, 450, 514],
                  483: [449, 451, 515, 517], 484: [450, 452, 518],
                  485: [451, 453, 517, 519], 486: [452, 454, 487, 518, 520],
                  487: [453, 455, 486, 488, 519, 520, 521],
                  488: [454, 456, 487, 520, 522], 489: [455, 521, 523],
                  490: [456, 458, 522, 524], 491: [459, 523, 525],
                  492: [458, 460, 524, 526], 494: [460, 462, 526, 528],
                  495: [461, 527, 528], 496: [464, 530],
                  497: [463, 465, 529, 531], 498: [464, 466, 530, 531, 532],
                  499: [465, 466, 467, 531, 533], 500: [466, 468, 532, 534],
                  501: [467, 469, 533, 535], 502: [468, 470, 534, 536],
                  503: [469, 535, 537], 504: [470, 472, 536, 538],
                  505: [473, 537, 539], 506: [472, 474, 538, 540],
                  507: [473, 474, 475, 539, 540, 541],
                  508: [474, 475, 476, 509, 540, 542],
                  509: [475, 477, 508, 510, 541, 543],
                  510: [476, 477, 478, 509, 542, 544],
                  511: [477, 478, 479, 543, 544, 545],
                  512: [478, 480, 513, 544, 545, 546],
                  513: [479, 481, 512, 514, 545, 547],
                  514: [480, 482, 513, 546, 547, 548],
                  515: [481, 483, 547, 549], 517: [483, 485, 549, 551],
                  518: [484, 486, 550, 552], 519: [485, 487, 551, 553],
                  520: [486, 487, 488, 521, 552, 554],
                  521: [487, 489, 520, 522, 553, 555],
                  522: [488, 490, 521, 523, 554, 556],
                  523: [489, 491, 522, 555, 556, 557],
                  524: [490, 492, 556, 557, 558], 525: [491, 557, 559],
                  526: [492, 494, 558, 560], 527: [495, 559, 561],
                  528: [494, 495, 560], 529: [497, 563],
                  530: [496, 498, 531, 562, 563, 564],
                  531: [497, 498, 499, 530, 563, 565],
                  532: [498, 500, 533, 564, 565, 566],
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                  534: [500, 502, 533, 566, 568],
                  535: [501, 503, 536, 567, 569],
                  536: [502, 504, 535, 568, 570],
                  537: [503, 505, 538, 569, 570, 571],
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                  549: [515, 517, 581, 583], 550: [518, 582, 584],
                  551: [517, 519, 552, 583, 585],
                  552: [518, 520, 551, 584, 586],
                  553: [519, 521, 554, 585, 586, 587],
                  554: [520, 522, 553, 586, 588], 555: [521, 523, 587, 589],
                  556: [522, 523, 524, 588, 589, 590],
                  557: [523, 524, 525, 558, 589, 590, 591],
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                  568: [534, 536, 567, 569, 600, 602],
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                  570: [536, 537, 538, 602, 604],
                  571: [537, 538, 539, 603, 604, 605],
                  572: [538, 539, 540, 573, 604, 606],
                  573: [539, 541, 572, 605, 607],
                  574: [540, 541, 542, 575, 606, 608],
                  575: [541, 542, 543, 574, 607, 609],
                  576: [542, 543, 544, 608, 609, 610],
                  577: [543, 544, 545, 609, 611], 578: [544, 546, 610],
                  579: [545, 547, 611, 613], 580: [546, 548, 614],
                  581: [547, 549, 582, 613, 615],
                  582: [548, 550, 581, 583, 614, 615, 616],
                  583: [549, 551, 582, 584, 615, 617],
                  584: [550, 552, 583, 616, 617, 618],
                  585: [551, 553, 617, 619], 586: [552, 553, 554, 618, 620],
                  587: [553, 555, 588, 619, 620, 621],
                  588: [554, 556, 587, 589, 620, 622],
                  589: [555, 556, 557, 588, 621, 623],
                  590: [556, 557, 558, 622, 623, 624],
                  591: [557, 559, 592, 623, 624, 625],
                  592: [558, 560, 591, 624, 626],
                  593: [559, 561, 594, 625, 626, 627], 594: [560, 593, 626],
                  595: [563, 629], 596: [562, 564, 628, 629, 630],
                  597: [563, 564, 565, 598, 629, 631],
                  598: [564, 566, 597, 630, 631, 632],
                  599: [565, 566, 567, 631, 632, 633],
                  600: [566, 568, 632, 634], 601: [567, 569, 633, 634, 635],
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                  603: [569, 571, 602, 604, 635, 637],
                  604: [570, 571, 572, 603, 605, 636, 638],
                  605: [571, 573, 604, 637, 639], 606: [572, 574, 638, 640],
                  607: [573, 575, 608, 639, 641],
                  608: [574, 576, 607, 609, 640, 642],
                  609: [575, 576, 577, 608, 641, 643],
                  610: [576, 578, 642, 643, 644], 611: [577, 579, 643, 645],
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                  615: [581, 582, 583, 616, 647, 649],
                  616: [582, 584, 615, 648, 649, 650],
                  617: [583, 584, 585, 618, 649, 651],
                  618: [584, 586, 617, 650, 651, 652],
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                  620: [586, 587, 588, 619, 621, 652, 654],
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                  622: [588, 590, 623, 654, 655, 656],
                  623: [589, 590, 591, 622, 655, 657],
                  624: [590, 591, 592, 625, 656, 657, 658],
                  625: [591, 593, 624, 626, 657, 659],
                  626: [592, 593, 594, 625, 658, 660],
                  627: [593, 659, 660], 628: [596, 662],
                  629: [595, 596, 597, 630, 661, 663],
                  630: [596, 598, 629, 662, 664],
                  631: [597, 598, 599, 663, 664, 665],
                  632: [598, 599, 600, 633, 664, 666],
                  633: [599, 601, 632, 665, 666, 667],
                  634: [600, 601, 602, 666, 667, 668],
                  635: [601, 602, 603, 667, 668, 669],
                  636: [602, 604, 668, 669, 670], 637: [603, 605, 669, 671],
                  638: [604, 606, 639, 670, 671, 672],
                  639: [605, 607, 638, 640, 671, 673],
                  640: [606, 608, 639, 641, 672, 674],
                  641: [607, 609, 640, 642, 673, 675],
                  642: [608, 610, 641, 674, 676],
                  643: [609, 610, 611, 675, 676, 677],
                  644: [610, 676, 678], 645: [611, 613, 677, 679],
                  646: [614, 678, 680], 647: [613, 615, 648, 679, 681],
                  648: [614, 616, 647, 680, 682],
                  649: [615, 616, 617, 681, 682, 683],
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                  654: [620, 621, 622, 686, 688],
                  655: [621, 622, 623, 656, 687, 689],
                  656: [622, 624, 655, 688, 690],
                  657: [623, 624, 625, 689, 691],
                  658: [624, 626, 690, 691, 692], 659: [625, 627, 691, 693],
                  660: [626, 627, 692], 661: [629, 695],
                  662: [628, 630, 663, 694, 695, 696],
                  663: [629, 631, 662, 695, 696, 697],
                  664: [630, 631, 632, 665, 696, 698],
                  665: [631, 633, 664, 697, 698, 699],
                  666: [632, 633, 634, 698, 699, 700],
                  667: [633, 634, 635, 699, 700, 701],
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                  670: [636, 638, 669, 702, 703, 704],
                  671: [637, 638, 639, 672, 703, 705],
                  672: [638, 640, 671, 704, 706], 673: [639, 641, 705],
                  674: [640, 642, 706, 708], 675: [641, 643, 709],
                  676: [642, 643, 644, 708, 710],
                  677: [643, 645, 709, 710, 711],
                  678: [644, 646, 710, 711, 712], 679: [645, 647, 711, 713],
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                  682: [648, 649, 650, 714, 716],
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                  684: [650, 652, 683, 685, 716, 718],
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                  688: [654, 656, 720, 721, 722],
                  689: [655, 657, 721, 722, 723], 690: [656, 658, 722, 724],
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                  695: [661, 662, 663, 694, 727, 729],
                  696: [662, 663, 664, 728, 729, 730],
                  697: [663, 665, 698, 729, 730, 731],
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                  705: [671, 673, 704, 737, 739], 706: [672, 674, 738, 740],
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                  716: [682, 683, 684, 748, 750], 717: [683, 685, 749, 751],
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                  744: [710, 711, 712, 743, 776, 778],
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                  818: [784, 786, 850, 851, 852],
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                  822: [788, 790, 821, 854, 856],
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                  828: [794, 796, 860, 862], 830: [796, 798, 862, 864],
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                  836: [802, 804, 835, 868, 869, 870],
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                  838: [804, 805, 806, 837, 870, 872],
                  839: [805, 807, 840, 871, 872, 873],
                  840: [806, 807, 808, 839, 872, 874],
                  841: [807, 808, 809, 873, 874, 875],
                  842: [808, 810, 843, 874, 875, 876],
                  843: [809, 811, 842, 875, 877],
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                  845: [811, 812, 813, 844, 877, 879],
                  846: [812, 814, 847, 878, 879, 880],
                  847: [813, 815, 846, 848, 879, 881],
                  848: [814, 815, 816, 847, 880, 881, 882],
                  849: [815, 817, 881, 883], 850: [816, 818, 882, 884],
                  851: [817, 818, 819, 883, 884, 885],
                  852: [818, 819, 820, 853, 884, 886],
                  853: [819, 820, 821, 852, 885, 887],
                  854: [820, 822, 886], 855: [821, 823, 887, 889],
                  856: [822, 824, 890], 857: [823, 825, 858, 889, 890, 891],
                  858: [824, 857, 890], 859: [826, 827, 893],
                  860: [826, 828, 892, 894], 861: [827, 893, 895],
                  862: [828, 830, 894, 896], 863: [831, 895, 897],
                  864: [830, 832, 896, 897, 898], 865: [831, 833, 897],
                  866: [832, 834, 898, 900], 867: [833, 835, 901],
                  868: [834, 836, 900, 902],
                  869: [835, 836, 837, 901, 902, 903],
                  870: [836, 837, 838, 902, 903, 904],
                  871: [837, 839, 872, 903, 904, 905],
                  872: [838, 839, 840, 871, 904, 906],
                  873: [839, 841, 874, 905, 906, 907],
                  874: [840, 841, 842, 873, 875, 906, 908],
                  875: [841, 842, 843, 874, 907, 909],
                  876: [842, 844, 908, 910], 877: [843, 845, 909, 911],
                  878: [844, 846, 879, 910, 912],
                  879: [845, 846, 847, 878, 911, 913],
                  880: [846, 848, 912, 914],
                  881: [847, 848, 849, 913, 914, 915],
                  882: [848, 850, 914, 915, 916], 883: [849, 851, 915, 917],
                  884: [850, 851, 852, 916, 918],
                  885: [851, 853, 886, 917, 918, 919],
                  886: [852, 854, 885, 918, 920], 887: [853, 855, 919, 921],
                  889: [855, 857, 921, 923],
                  890: [856, 857, 858, 891, 922, 924], 891: [857, 890, 923],
                  892: [860, 926], 893: [859, 861, 925, 926, 927],
                  894: [860, 862, 926, 928], 895: [861, 863, 927, 929],
                  896: [862, 864, 928, 930],
                  897: [863, 864, 865, 929, 930, 931],
                  898: [864, 866, 930, 932], 900: [866, 868, 932, 934],
                  901: [867, 869, 933, 935], 902: [868, 869, 870, 934, 936],
                  903: [869, 870, 871, 935, 936, 937],
                  904: [870, 871, 872, 936, 937, 938],
                  905: [871, 873, 937, 939], 906: [872, 873, 874, 938, 940],
                  907: [873, 875, 939, 941], 908: [874, 876, 909, 940, 942],
                  909: [875, 877, 908, 941, 943], 910: [876, 878, 942, 944],
                  911: [877, 879, 943, 945], 912: [878, 880, 944, 946],
                  913: [879, 881, 914, 945, 947],
                  914: [880, 881, 882, 913, 946, 948],
                  915: [881, 882, 883, 916, 947, 948, 949],
                  916: [882, 884, 915, 917, 948, 950],
                  917: [883, 885, 916, 949, 951],
                  918: [884, 885, 886, 919, 950, 952],
                  919: [885, 887, 918, 951, 953], 920: [886, 952, 954],
                  921: [887, 889, 953, 955], 922: [890, 954, 956],
                  923: [889, 891, 955, 957], 924: [890, 956],
                  925: [893, 926, 959], 926: [892, 893, 894, 925, 958, 960],
                  927: [893, 895, 928, 959, 960, 961],
                  928: [894, 896, 927, 960, 962], 929: [895, 897, 961, 963],
                  930: [896, 897, 898, 962, 963, 964], 931: [897, 963, 965],
                  932: [898, 900, 964, 966], 933: [901, 965, 967],
                  934: [900, 902, 935, 966, 968],
                  935: [901, 903, 934, 936, 967, 968, 969],
                  936: [902, 903, 904, 935, 968, 970],
                  937: [903, 904, 905, 969, 970, 971],
                  938: [904, 906, 970, 971, 972], 939: [905, 907, 971, 973],
                  940: [906, 908, 972, 973, 974], 941: [907, 909, 973, 975],
                  942: [908, 910, 943, 974, 975, 976],
                  943: [909, 911, 942, 975, 977],
                  944: [910, 912, 945, 976, 977, 978],
                  945: [911, 913, 944, 946, 977, 979],
                  946: [912, 914, 945, 947, 978, 980],
                  947: [913, 915, 946, 979, 980, 981],
                  948: [914, 915, 916, 980, 982], 949: [915, 917, 981],
                  950: [916, 918, 982, 984], 951: [917, 919, 985],
                  952: [918, 920, 953, 984, 985, 986],
                  953: [919, 921, 952, 954, 985, 987],
                  954: [920, 922, 953, 986, 988],
                  955: [921, 923, 956, 987, 989],
                  956: [922, 924, 955, 988, 990], 957: [923, 989, 990],
                  958: [926, 959, 992], 959: [925, 927, 958, 991, 992, 993],
                  960: [926, 927, 928, 992, 994], 961: [927, 929, 993, 995],
                  962: [928, 930, 963, 994, 995, 996],
                  963: [929, 930, 931, 962, 964, 995, 997],
                  964: [930, 932, 963, 996, 998],
                  965: [931, 933, 997, 998, 999],
                  966: [932, 934, 967, 998, 1000],
                  967: [933, 935, 966, 999, 1000, 1001],
                  968: [934, 935, 936, 969, 1000, 1002],
                  969: [935, 937, 968, 1001, 1003],
                  970: [936, 937, 938, 971, 1002, 1004],
                  971: [937, 938, 939, 970, 1003, 1004, 1005],
                  972: [938, 940, 1004, 1006],
                  973: [939, 940, 941, 1005, 1006, 1007],
                  974: [940, 942, 975, 1006, 1007, 1008],
                  975: [941, 942, 943, 974, 1007, 1009],
                  976: [942, 944, 977, 1008, 1009, 1010],
                  977: [943, 944, 945, 976, 1009, 1011],
                  978: [944, 946, 979, 1010, 1011, 1012],
                  979: [945, 947, 978, 1011, 1013],
                  980: [946, 947, 948, 1012, 1013, 1014],
                  981: [947, 949, 1013, 1014, 1015],
                  982: [948, 950, 1014, 1016], 984: [950, 952, 1016, 1018],
                  985: [951, 952, 953, 986, 1017, 1019],
                  986: [952, 954, 985, 1018, 1019, 1020],
                  987: [953, 955, 1019, 1020, 1021],
                  988: [954, 956, 1020, 1022],
                  989: [955, 957, 1021, 1022, 1023], 990: [956, 957, 1022],
                  991: [959, 1024, 1025],
                  992: [958, 959, 960, 993, 1024, 1026],
                  993: [959, 961, 992, 1025, 1027],
                  994: [960, 962, 995, 1026, 1027, 1028],
                  995: [961, 962, 963, 994, 1027, 1028, 1029],
                  996: [962, 964, 997, 1028, 1030],
                  997: [963, 965, 996, 998, 1029, 1031],
                  998: [964, 965, 966, 997, 999, 1030, 1032],
                  999: [965, 967, 998, 1000, 1031, 1033],
                  1000: [966, 967, 968, 999, 1032, 1034],
                  1001: [967, 969, 1002, 1033, 1035],
                  1002: [968, 970, 1001, 1003, 1034, 1036],
                  1003: [969, 971, 1002, 1035, 1037],
                  1004: [970, 971, 972, 1005, 1036, 1038],
                  1005: [971, 973, 1004, 1006, 1037, 1039],
                  1006: [972, 973, 974, 1005, 1038, 1040],
                  1007: [973, 974, 975, 1008, 1039, 1041],
                  1008: [974, 976, 1007, 1009, 1040, 1042],
                  1009: [975, 976, 977, 1008, 1010, 1041, 1043],
                  1010: [976, 978, 1009, 1042, 1043, 1044],
                  1011: [977, 978, 979, 1012, 1043, 1045],
                  1012: [978, 980, 1011, 1013, 1044, 1046],
                  1013: [979, 980, 981, 1012, 1045, 1047],
                  1014: [980, 981, 982, 1046, 1047, 1048],
                  1015: [981, 1047, 1049], 1016: [982, 984, 1048, 1050],
                  1017: [985, 1049, 1051],
                  1018: [984, 986, 1050, 1051, 1052],
                  1019: [985, 986, 987, 1051, 1052, 1053],
                  1020: [986, 987, 988, 1021, 1052, 1054],
                  1021: [987, 989, 1020, 1053, 1054, 1055],
                  1022: [988, 989, 990, 1054, 1055, 1056],
                  1023: [989, 1055], 1024: [991, 992, 1058],
                  1025: [991, 993, 1057, 1058, 1059],
                  1026: [992, 994, 1058, 1060],
                  1027: [993, 994, 995, 1059, 1060, 1061],
                  1028: [994, 995, 996, 1060, 1062],
                  1029: [995, 997, 1061, 1063],
                  1030: [996, 998, 1062, 1063, 1064],
                  1031: [997, 999, 1032, 1063, 1064, 1065],
                  1032: [998, 1000, 1031, 1064, 1065, 1066],
                  1033: [999, 1001, 1065, 1067],
                  1034: [1000, 1002, 1066, 1068],
                  1035: [1001, 1003, 1067, 1069], 1036: [1002, 1004, 1068],
                  1037: [1003, 1005, 1069, 1071], 1038: [1004, 1006, 1072],
                  1039: [1005, 1007, 1040, 1071, 1072, 1073],
                  1040: [1006, 1008, 1039, 1041, 1072, 1074],
                  1041: [1007, 1009, 1040, 1073, 1074, 1075],
                  1042: [1008, 1010, 1043, 1074, 1076],
                  1043: [1009, 1010, 1011, 1042, 1044, 1075, 1077],
                  1044: [1010, 1012, 1043, 1045, 1076, 1078],
                  1045: [1011, 1013, 1044, 1046, 1077, 1078, 1079],
                  1046: [1012, 1014, 1045, 1078, 1079, 1080],
                  1047: [1013, 1014, 1015, 1079, 1080, 1081],
                  1048: [1014, 1016, 1049, 1080, 1082],
                  1049: [1015, 1017, 1048, 1081, 1083],
                  1050: [1016, 1018, 1051, 1082, 1083, 1084],
                  1051: [1017, 1018, 1019, 1050, 1083, 1085],
                  1052: [1018, 1019, 1020, 1053, 1084, 1085, 1086],
                  1053: [1019, 1021, 1052, 1085, 1086, 1087],
                  1054: [1020, 1021, 1022, 1086, 1087, 1088],
                  1055: [1021, 1022, 1023, 1087, 1088, 1089],
                  1056: [1022, 1088], 1057: [1025], 1058: [1024, 1025, 1026],
                  1059: [1025, 1027, 1060], 1060: [1026, 1027, 1028, 1059],
                  1061: [1027, 1029], 1062: [1028, 1030],
                  1063: [1029, 1030, 1031], 1064: [1030, 1031, 1032],
                  1065: [1031, 1032, 1033], 1066: [1032, 1034, 1067],
                  1067: [1033, 1035, 1066], 1068: [1034, 1036],
                  1069: [1035, 1037], 1071: [1037, 1039],
                  1072: [1038, 1039, 1040], 1073: [1039, 1041],
                  1074: [1040, 1041, 1042], 1075: [1041, 1043],
                  1076: [1042, 1044], 1077: [1043, 1045],
                  1078: [1044, 1045, 1046], 1079: [1045, 1046, 1047],
                  1080: [1046, 1047, 1048], 1081: [1047, 1049],
                  1082: [1048, 1050, 1083], 1083: [1049, 1050, 1051, 1082],
                  1084: [1050, 1052], 1085: [1051, 1052, 1053],
                  1086: [1052, 1053, 1054], 1087: [1053, 1054, 1055],
                  1088: [1054, 1055, 1056], 1089: [1055]}
# I didn't capture these
cycle_15_links = {}
cycle_16_war_links =  {2: [34, 36], 3: [35, 37], 5: [37, 39], 6: [38, 40],
                       7: [39, 41], 8: [40, 42], 9: [10, 41, 43], 10: [9, 42, 44],
                       11: [12, 43, 45], 12: [11, 44, 46], 13: [45, 47],
                       14: [46, 48], 16: [48, 50], 17: [51], 18: [19, 50, 52],
                       19: [18, 51, 52, 53], 20: [52, 54], 21: [53, 55],
                       22: [54, 56], 23: [55, 57], 24: [56, 57, 58],
                       25: [26, 57, 59], 26: [25, 58, 60], 27: [59, 61],
                       28: [60, 62], 29: [61, 63], 31: [63, 65], 32: [64, 66],
                       34: [2, 68], 35: [3, 67], 36: [2, 68, 70], 37: [3, 5, 71],
                       38: [6, 70, 72], 39: [5, 7, 40, 71, 73],
                       40: [6, 8, 39, 41, 72, 74], 41: [7, 9, 40, 42, 73, 74, 75],
                       42: [8, 10, 41, 43, 74, 76], 43: [9, 11, 42, 44, 75, 77],
                       44: [10, 12, 43, 76, 78], 45: [11, 13, 46, 77, 78, 79],
                       46: [12, 14, 45, 78, 79, 80], 47: [13, 79, 81],
                       48: [14, 16, 80, 82], 50: [16, 18, 82, 84],
                       51: [17, 19, 83, 85], 52: [18, 19, 20, 53, 84, 86],
                       53: [19, 21, 52, 54, 85, 86, 87],
                       54: [20, 22, 53, 86, 87, 88], 55: [21, 23, 87, 88, 89],
                       56: [22, 24, 88, 90], 57: [23, 24, 25, 89, 91],
                       58: [24, 26, 90], 59: [25, 27, 91, 93], 60: [26, 28, 94],
                       61: [27, 29, 93, 95], 62: [28, 94, 96], 63: [29, 31, 95, 97],
                       64: [32, 96, 98], 65: [31, 97, 99], 66: [32, 98],
                       67: [35, 101], 68: [34, 36, 100], 70: [36, 38, 104],
                       71: [37, 39, 103, 105], 72: [38, 40, 73, 104, 106],
                       73: [39, 41, 72, 105, 106, 107],
                       74: [40, 41, 42, 106, 107, 108], 75: [41, 43, 107, 109],
                       76: [42, 44, 77, 108, 110], 77: [43, 45, 76, 78, 109, 111],
                       78: [44, 45, 46, 77, 110, 112], 79: [45, 46, 47, 111, 113],
                       80: [46, 48, 112, 114], 81: [47, 113, 115],
                       82: [48, 50, 114, 116], 83: [51, 115, 117],
                       84: [50, 52, 85, 116, 118], 85: [51, 53, 84, 117, 118, 119],
                       86: [52, 53, 54, 87, 118, 120],
                       87: [53, 54, 55, 86, 119, 121], 88: [54, 55, 56, 120, 122],
                       89: [55, 57, 121], 90: [56, 58, 122, 124], 91: [57, 59, 125],
                       93: [59, 61, 125, 127], 94: [60, 62, 126, 128],
                       95: [61, 63, 127, 129], 96: [62, 64, 128, 130],
                       97: [63, 65, 98, 129, 130, 131],
                       98: [64, 66, 97, 130, 131, 132], 99: [65, 131],
                       100: [68, 134], 101: [67, 133, 135], 103: [71, 135, 137],
                       104: [70, 72, 136, 138], 105: [71, 73, 137, 139],
                       106: [72, 73, 74, 138, 139, 140],
                       107: [73, 74, 75, 139, 141], 108: [74, 76, 140],
                       109: [75, 77, 141, 143], 110: [76, 78, 144],
                       111: [77, 79, 112, 143, 144, 145],
                       112: [78, 80, 111, 144, 145, 146], 113: [79, 81, 145, 147],
                       114: [80, 82, 115, 146, 148], 115: [81, 83, 114, 147, 149],
                       116: [82, 84, 148, 149, 150], 117: [83, 85, 149, 150, 151],
                       118: [84, 85, 86, 119, 150, 152],
                       119: [85, 87, 118, 120, 151, 153],
                       120: [86, 88, 119, 121, 152, 154],
                       121: [87, 89, 120, 153, 154, 155], 122: [88, 90, 154, 156],
                       124: [90, 156, 158], 125: [91, 93, 157, 159],
                       126: [94, 158, 160], 127: [93, 95, 128, 159, 161],
                       128: [94, 96, 127, 129, 160, 162],
                       129: [95, 97, 128, 161, 162, 163],
                       130: [96, 97, 98, 162, 164], 131: [97, 98, 99, 163, 165],
                       132: [98, 164], 133: [101, 167], 134: [100, 166, 168],
                       135: [101, 103, 167, 169], 136: [104, 168, 170],
                       137: [103, 105, 169, 171], 138: [104, 106, 139, 170, 172],
                       139: [105, 106, 107, 138, 171, 173],
                       140: [106, 108, 172, 173, 174], 141: [107, 109, 173, 175],
                       143: [109, 111, 175, 177], 144: [110, 111, 112, 176, 178],
                       145: [111, 112, 113, 177, 179],
                       146: [112, 114, 147, 178, 180],
                       147: [113, 115, 146, 148, 179, 181],
                       148: [114, 116, 147, 149, 180, 182],
                       149: [115, 116, 117, 148, 181, 182, 183],
                       150: [116, 117, 118, 182, 183, 184],
                       151: [117, 119, 152, 183, 184, 185],
                       152: [118, 120, 151, 153, 184, 186],
                       153: [119, 121, 152, 154, 185, 187],
                       154: [120, 121, 122, 153, 186, 187, 188],
                       155: [121, 187, 189], 156: [122, 124, 188, 190],
                       157: [125, 189, 191], 158: [124, 126, 159, 190, 191, 192],
                       159: [125, 127, 158, 191, 193],
                       160: [126, 128, 161, 192, 193, 194],
                       161: [127, 129, 160, 193, 194, 195],
                       162: [128, 129, 130, 194, 196],
                       163: [129, 131, 164, 195, 196, 197],
                       164: [130, 132, 163, 165, 196, 198], 165: [131, 164, 197],
                       166: [134, 167, 200], 167: [133, 135, 166, 199, 201],
                       168: [134, 136, 200], 169: [135, 137, 201, 203],
                       170: [136, 138, 204], 171: [137, 139, 203, 205],
                       172: [138, 140, 173, 204, 206],
                       173: [139, 140, 141, 172, 205, 207], 174: [140, 206, 208],
                       175: [141, 143, 207, 209], 176: [144, 208, 210],
                       177: [143, 145, 209, 210, 211], 178: [144, 146, 210, 212],
                       179: [145, 147, 211, 212, 213],
                       180: [146, 148, 181, 212, 213, 214],
                       181: [147, 149, 180, 213, 214, 215],
                       182: [148, 149, 150, 183, 214, 216],
                       183: [149, 150, 151, 182, 215, 217],
                       184: [150, 151, 152, 216, 217, 218],
                       185: [151, 153, 186, 217, 218, 219],
                       186: [152, 154, 185, 218, 220],
                       187: [153, 154, 155, 188, 219, 221],
                       188: [154, 156, 187, 220, 222],
                       189: [155, 157, 221, 222, 223],
                       190: [156, 158, 222, 223, 224],
                       191: [157, 158, 159, 192, 223, 225],
                       192: [158, 160, 191, 224, 225, 226],
                       193: [159, 160, 161, 225, 227],
                       194: [160, 161, 162, 226, 228], 195: [161, 163, 227, 229],
                       196: [162, 163, 164, 228, 229, 230],
                       197: [163, 165, 198, 229, 231], 198: [164, 197, 230],
                       199: [167, 200, 233], 200: [166, 168, 199, 232, 234],
                       201: [167, 169, 233, 235], 203: [169, 171, 235, 237],
                       204: [170, 172, 205, 236, 237, 238],
                       205: [171, 173, 204, 206, 237, 238, 239],
                       206: [172, 174, 205, 238, 239, 240],
                       207: [173, 175, 239, 240, 241],
                       208: [174, 176, 209, 240, 242],
                       209: [175, 177, 208, 241, 242, 243],
                       210: [176, 177, 178, 242, 243, 244],
                       211: [177, 179, 243, 245],
                       212: [178, 179, 180, 244, 245, 246],
                       213: [179, 180, 181, 214, 245, 247],
                       214: [180, 181, 182, 213, 246, 248],
                       215: [181, 183, 216, 247, 249],
                       216: [182, 184, 215, 217, 248, 250],
                       217: [183, 184, 185, 216, 249, 250, 251],
                       218: [184, 185, 186, 250, 251, 252],
                       219: [185, 187, 220, 251, 252, 253],
                       220: [186, 188, 219, 221, 252, 254],
                       221: [187, 189, 220, 253, 254, 255],
                       222: [188, 189, 190, 223, 254, 256],
                       223: [189, 190, 191, 222, 224, 255, 257],
                       224: [190, 192, 223, 256, 257, 258],
                       225: [191, 192, 193, 257, 258, 259],
                       226: [192, 194, 258, 260],
                       227: [193, 195, 228, 259, 260, 261],
                       228: [194, 196, 227, 229, 260, 262],
                       229: [195, 196, 197, 228, 261, 263],
                       230: [196, 198, 262, 264], 231: [197, 263], 232: [200, 266],
                       233: [199, 201, 265, 266, 267], 234: [200, 266, 268],
                       235: [201, 203, 267, 269], 236: [204, 268, 270],
                       237: [203, 204, 205, 269, 270, 271],
                       238: [204, 205, 206, 270, 271, 272],
                       239: [205, 206, 207, 271, 272, 273],
                       240: [206, 207, 208, 241, 272, 274],
                       241: [207, 209, 240, 273, 274, 275],
                       242: [208, 209, 210, 274, 275, 276],
                       243: [209, 210, 211, 244, 275, 277],
                       244: [210, 212, 243, 245, 276, 278],
                       245: [211, 212, 213, 244, 277, 278, 279],
                       246: [212, 214, 278, 279, 280],
                       247: [213, 215, 248, 279, 280, 281],
                       248: [214, 216, 247, 249, 280, 282],
                       249: [215, 217, 248, 281, 282, 283],
                       250: [216, 217, 218, 282, 283, 284],
                       251: [217, 218, 219, 283, 284, 285],
                       252: [218, 219, 220, 284, 285, 286],
                       253: [219, 221, 254, 285, 286, 287],
                       254: [220, 221, 222, 253, 255, 286, 288],
                       255: [221, 223, 254, 256, 287, 289],
                       256: [222, 224, 255, 288, 289, 290],
                       257: [223, 224, 225, 289, 291],
                       258: [224, 225, 226, 290, 291, 292],
                       259: [225, 227, 291, 292, 293],
                       260: [226, 227, 228, 292, 293, 294],
                       261: [227, 229, 293, 294, 295], 262: [228, 230, 294, 296],
                       263: [229, 231, 295, 297], 264: [230, 296, 297],
                       265: [233, 298, 299], 266: [232, 233, 234, 267, 298, 300],
                       267: [233, 235, 266, 299, 301],
                       268: [234, 236, 300, 301, 302], 269: [235, 237, 301, 303],
                       270: [236, 237, 238, 302, 304],
                       271: [237, 238, 239, 272, 303, 304, 305],
                       272: [238, 239, 240, 271, 304, 306],
                       273: [239, 241, 305, 307],
                       274: [240, 241, 242, 306, 307, 308],
                       275: [241, 242, 243, 276, 307, 309],
                       276: [242, 244, 275, 277, 308, 310],
                       277: [243, 245, 276, 309, 310, 311],
                       278: [244, 245, 246, 279, 310, 312],
                       279: [245, 246, 247, 278, 311, 313],
                       280: [246, 247, 248, 312, 313, 314],
                       281: [247, 249, 282, 313, 314, 315],
                       282: [248, 249, 250, 281, 314, 315, 316],
                       283: [249, 250, 251, 315, 317],
                       284: [250, 251, 252, 316, 318],
                       285: [251, 252, 253, 286, 317, 319],
                       286: [252, 253, 254, 285, 318, 320],
                       287: [253, 255, 288, 319, 320, 321],
                       288: [254, 256, 287, 320, 321, 322],
                       289: [255, 256, 257, 290, 321, 323],
                       290: [256, 258, 289, 291, 322, 323, 324],
                       291: [257, 258, 259, 290, 323, 325],
                       292: [258, 259, 260, 293, 324, 326],
                       293: [259, 260, 261, 292, 325, 327],
                       294: [260, 261, 262, 295, 326, 328],
                       295: [261, 263, 294, 296, 327, 329],
                       296: [262, 264, 295, 328, 329, 330], 297: [263, 264, 329],
                       298: [265, 266, 332], 299: [265, 267, 300, 331, 333],
                       300: [266, 268, 299, 332, 334],
                       301: [267, 268, 269, 333, 334, 335],
                       302: [268, 270, 334, 336], 303: [269, 271, 335, 337],
                       304: [270, 271, 272, 336, 338],
                       305: [271, 273, 306, 337, 338, 339],
                       306: [272, 274, 305, 338, 340],
                       307: [273, 274, 275, 308, 339, 340, 341],
                       308: [274, 276, 307, 340, 341, 342],
                       309: [275, 277, 310, 341, 342, 343],
                       310: [276, 277, 278, 309, 342, 344],
                       311: [277, 279, 312, 343, 345],
                       312: [278, 280, 311, 344, 345, 346],
                       313: [279, 280, 281, 345, 346, 347],
                       314: [280, 281, 282, 315, 346, 348],
                       315: [281, 282, 283, 314, 347, 349],
                       316: [282, 284, 348, 350],
                       317: [283, 285, 318, 349, 350, 351],
                       318: [284, 286, 317, 350, 351, 352],
                       319: [285, 287, 320, 351, 353],
                       320: [286, 287, 288, 319, 352, 354],
                       321: [287, 288, 289, 353, 355], 322: [288, 290, 354, 356],
                       323: [289, 290, 291, 355, 356, 357],
                       324: [290, 292, 325, 356, 357, 358],
                       325: [291, 293, 324, 357, 358, 359],
                       326: [292, 294, 327, 358, 359, 360],
                       327: [293, 295, 326, 328, 359, 361],
                       328: [294, 296, 327, 329, 360, 361, 362],
                       329: [295, 296, 297, 328, 361, 363], 330: [296, 362],
                       331: [299], 332: [298, 300, 364, 366], 333: [299, 301, 367],
                       334: [300, 301, 302, 366, 368],
                       335: [301, 303, 336, 367, 368, 369],
                       336: [302, 304, 335, 337, 368, 369, 370],
                       337: [303, 305, 336, 369, 370, 371],
                       338: [304, 305, 306, 370, 371, 372],
                       339: [305, 307, 371, 373],
                       340: [306, 307, 308, 372, 373, 374],
                       341: [307, 308, 309, 342, 373, 375],
                       342: [308, 309, 310, 341, 374, 376],
                       343: [309, 311, 375, 377], 344: [310, 312, 376, 378],
                       345: [311, 312, 313, 346, 377, 379],
                       346: [312, 313, 314, 345, 378, 380],
                       347: [313, 315, 348, 379, 380, 381],
                       348: [314, 316, 347, 380, 382],
                       349: [315, 317, 350, 381, 383],
                       350: [316, 317, 318, 349, 382, 384],
                       351: [317, 318, 319, 352, 383, 384, 385],
                       352: [318, 320, 351, 353, 384, 386],
                       353: [319, 321, 352, 354, 385, 387],
                       354: [320, 322, 353, 386, 388], 355: [321, 323, 387, 389],
                       356: [322, 323, 324, 388, 390],
                       357: [323, 324, 325, 389, 390, 391],
                       358: [324, 325, 326, 390, 391, 392],
                       359: [325, 326, 327, 360, 391, 393],
                       360: [326, 328, 359, 392, 393, 394],
                       361: [327, 328, 329, 362, 393, 395],
                       362: [328, 330, 361, 363, 394, 396], 363: [329, 362, 395],
                       364: [332, 398], 366: [332, 334, 398, 400],
                       367: [333, 335, 399, 400, 401],
                       368: [334, 335, 336, 400, 402],
                       369: [335, 336, 337, 401, 403],
                       370: [336, 337, 338, 371, 402, 404],
                       371: [337, 338, 339, 370, 403, 405],
                       372: [338, 340, 373, 404, 406],
                       373: [339, 340, 341, 372, 374, 405, 407],
                       374: [340, 342, 373, 375, 406, 408],
                       375: [341, 343, 374, 376, 407, 409],
                       376: [342, 344, 375, 377, 408, 410],
                       377: [343, 345, 376, 378, 409, 410, 411],
                       378: [344, 346, 377, 379, 410, 412],
                       379: [345, 347, 378, 411, 412, 413],
                       380: [346, 347, 348, 381, 412, 414],
                       381: [347, 349, 380, 382, 413, 415],
                       382: [348, 350, 381, 383, 414, 416],
                       383: [349, 351, 382, 415, 416, 417],
                       384: [350, 351, 352, 385, 416, 418],
                       385: [351, 353, 384, 386, 417, 419],
                       386: [352, 354, 385, 387, 418, 420],
                       387: [353, 355, 386, 419, 420, 421],
                       388: [354, 356, 420, 422], 389: [355, 357, 421, 423],
                       390: [356, 357, 358, 422, 424],
                       391: [357, 358, 359, 392, 423, 425],
                       392: [358, 360, 391, 393, 424, 426],
                       393: [359, 360, 361, 392, 394, 425, 427],
                       394: [360, 362, 393, 395, 426, 428],
                       395: [361, 363, 394, 396, 427, 429], 396: [362, 395, 428],
                       397: [431], 398: [364, 366, 430, 432], 399: [367, 431, 433],
                       400: [366, 367, 368, 401, 432, 434],
                       401: [367, 369, 400, 402, 433, 435],
                       402: [368, 370, 401, 403, 434, 436],
                       403: [369, 371, 402, 435, 437],
                       404: [370, 372, 405, 436, 438],
                       405: [371, 373, 404, 437, 439],
                       406: [372, 374, 407, 438, 440],
                       407: [373, 375, 406, 439, 440, 441],
                       408: [374, 376, 409, 440, 441, 442],
                       409: [375, 377, 408, 441, 442, 443],
                       410: [376, 377, 378, 411, 442, 444],
                       411: [377, 379, 410, 443, 445],
                       412: [378, 379, 380, 413, 444, 445, 446],
                       413: [379, 381, 412, 445, 446, 447],
                       414: [380, 382, 446, 448],
                       415: [381, 383, 416, 447, 448, 449],
                       416: [382, 383, 384, 415, 448, 450],
                       417: [383, 385, 418, 449, 451],
                       418: [384, 386, 417, 419, 450, 452],
                       419: [385, 387, 418, 420, 451, 453],
                       420: [386, 387, 388, 419, 452, 454],
                       421: [387, 389, 422, 453, 455],
                       422: [388, 390, 421, 454, 456], 423: [389, 391, 455],
                       424: [390, 392, 456, 458], 425: [391, 393, 459],
                       426: [392, 394, 427, 458, 460],
                       427: [393, 395, 426, 459, 461],
                       428: [394, 396, 429, 460, 462], 429: [395, 428, 461],
                       430: [398, 463, 464], 431: [397, 399, 432, 463, 464, 465],
                       432: [398, 400, 431, 433, 464, 466],
                       433: [399, 401, 432, 434, 465, 467],
                       434: [400, 402, 433, 435, 466, 467, 468],
                       435: [401, 403, 434, 436, 467, 469],
                       436: [402, 404, 435, 468, 469, 470], 437: [403, 405, 469],
                       438: [404, 406, 470, 472], 439: [405, 407, 473],
                       440: [406, 407, 408, 472, 474],
                       441: [407, 408, 409, 473, 475],
                       442: [408, 409, 410, 474, 475, 476],
                       443: [409, 411, 444, 475, 476, 477],
                       444: [410, 412, 443, 476, 478],
                       445: [411, 412, 413, 477, 478, 479],
                       446: [412, 413, 414, 447, 478, 480],
                       447: [413, 415, 446, 479, 481],
                       448: [414, 415, 416, 480, 481, 482],
                       449: [415, 417, 450, 481, 483],
                       450: [416, 418, 449, 451, 482, 484],
                       451: [417, 419, 450, 452, 483, 485],
                       452: [418, 420, 451, 484, 485, 486],
                       453: [419, 421, 485, 487], 454: [420, 422, 455, 486, 488],
                       455: [421, 423, 454, 487, 489], 456: [422, 424, 488, 490],
                       458: [424, 426, 490, 492], 459: [425, 427, 491],
                       460: [426, 428, 492, 494], 461: [427, 429, 495],
                       462: [428, 494], 463: [430, 431, 497],
                       464: [430, 431, 432, 496, 497, 498],
                       465: [431, 433, 466, 497, 499],
                       466: [432, 434, 465, 498, 499, 500],
                       467: [433, 434, 435, 468, 499, 501],
                       468: [434, 436, 467, 500, 502],
                       469: [435, 436, 437, 501, 503], 470: [436, 438, 502, 504],
                       472: [438, 440, 504, 506], 473: [439, 441, 474, 505, 507],
                       474: [440, 442, 473, 475, 506, 507, 508],
                       475: [441, 442, 443, 474, 507, 509],
                       476: [442, 443, 444, 477, 508, 510],
                       477: [443, 445, 476, 509, 510, 511],
                       478: [444, 445, 446, 510, 512], 479: [445, 447, 511, 513],
                       480: [446, 448, 512, 513, 514],
                       481: [447, 448, 449, 513, 515], 482: [448, 450, 514],
                       483: [449, 451, 515, 517], 484: [450, 452, 518],
                       485: [451, 452, 453, 517, 519], 486: [452, 454, 518, 520],
                       487: [453, 455, 488, 519, 521],
                       488: [454, 456, 487, 520, 522], 489: [455, 521, 523],
                       490: [456, 458, 522, 524], 491: [459, 523, 525],
                       492: [458, 460, 524, 526], 494: [460, 462, 526, 528],
                       495: [461, 527, 528], 496: [464, 530],
                       497: [463, 464, 465, 498, 529, 531],
                       498: [464, 466, 497, 530, 532],
                       499: [465, 466, 467, 500, 531, 532, 533],
                       500: [466, 468, 499, 532, 533, 534],
                       501: [467, 469, 533, 535], 502: [468, 470, 534, 536],
                       503: [469, 535, 537], 504: [470, 472, 536, 538],
                       505: [473, 537, 539], 506: [472, 474, 538, 539, 540],
                       507: [473, 474, 475, 539, 540, 541],
                       508: [474, 476, 509, 540, 541, 542],
                       509: [475, 477, 508, 541, 543],
                       510: [476, 477, 478, 511, 542, 544],
                       511: [477, 479, 510, 512, 543, 545],
                       512: [478, 480, 511, 544, 545, 546],
                       513: [479, 480, 481, 545, 546, 547],
                       514: [480, 482, 546, 548], 515: [481, 483, 547, 549],
                       517: [483, 485, 549, 551], 518: [484, 486, 550, 552],
                       519: [485, 487, 520, 551, 552, 553],
                       520: [486, 488, 519, 521, 552, 554],
                       521: [487, 489, 520, 553, 554, 555],
                       522: [488, 490, 523, 554, 556],
                       523: [489, 491, 522, 555, 556, 557],
                       524: [490, 492, 556, 557, 558], 525: [491, 557, 559],
                       526: [492, 494, 558, 560], 527: [495, 559, 561],
                       528: [494, 495, 560], 529: [497, 530, 563],
                       530: [496, 498, 529, 562, 563, 564],
                       531: [497, 499, 563, 565],
                       532: [498, 499, 500, 564, 565, 566],
                       533: [499, 500, 501, 565, 566, 567],
                       534: [500, 502, 566, 567, 568], 535: [501, 503, 567, 569],
                       536: [502, 504, 537, 568, 569, 570],
                       537: [503, 505, 536, 538, 569, 571],
                       538: [504, 506, 537, 570, 571, 572],
                       539: [505, 506, 507, 540, 571, 573],
                       540: [506, 507, 508, 539, 541, 572, 574],
                       541: [507, 508, 509, 540, 573, 575],
                       542: [508, 510, 574, 576], 543: [509, 511, 575, 577],
                       544: [510, 512, 545, 576, 578],
                       545: [511, 512, 513, 544, 577, 579],
                       546: [512, 513, 514, 578, 580], 547: [513, 515, 579, 581],
                       548: [514, 580, 582], 549: [515, 517, 581, 583],
                       550: [518, 582, 584], 551: [517, 519, 552, 583, 585],
                       552: [518, 519, 520, 551, 584, 586],
                       553: [519, 521, 585, 587],
                       554: [520, 521, 522, 555, 586, 588],
                       555: [521, 523, 554, 587, 588, 589],
                       556: [522, 523, 524, 557, 588, 590],
                       557: [523, 524, 525, 556, 589, 591],
                       558: [524, 526, 590, 592],
                       559: [525, 527, 560, 591, 592, 593],
                       560: [526, 528, 559, 561, 592, 594],
                       561: [527, 560, 593, 594], 562: [530, 595, 596],
                       563: [529, 530, 531, 595, 596, 597],
                       564: [530, 532, 596, 597, 598],
                       565: [531, 532, 533, 597, 598, 599],
                       566: [532, 533, 534, 598, 600],
                       567: [533, 534, 535, 568, 599, 601],
                       568: [534, 536, 567, 569, 600, 602],
                       569: [535, 536, 537, 568, 601, 603],
                       570: [536, 538, 571, 602, 603, 604],
                       571: [537, 538, 539, 570, 572, 603, 605],
                       572: [538, 540, 571, 573, 604, 606],
                       573: [539, 541, 572, 574, 605, 607],
                       574: [540, 542, 573, 606, 607, 608],
                       575: [541, 543, 607, 609], 576: [542, 544, 608, 610],
                       577: [543, 545, 609, 611], 578: [544, 546, 610],
                       579: [545, 547, 611, 613], 580: [546, 548, 614],
                       581: [547, 549, 613, 615],
                       582: [548, 550, 583, 614, 615, 616],
                       583: [549, 551, 582, 584, 615, 617],
                       584: [550, 552, 583, 585, 616, 618],
                       585: [551, 553, 584, 617, 618, 619],
                       586: [552, 554, 618, 619, 620],
                       587: [553, 555, 588, 619, 621],
                       588: [554, 555, 556, 587, 589, 620, 622],
                       589: [555, 557, 588, 621, 622, 623],
                       590: [556, 558, 591, 622, 624],
                       591: [557, 559, 590, 623, 624, 625],
                       592: [558, 559, 560, 593, 624, 626],
                       593: [559, 561, 592, 625, 627], 594: [560, 561, 626],
                       595: [562, 563, 629], 596: [562, 563, 564, 628, 630],
                       597: [563, 564, 565, 598, 629, 631],
                       598: [564, 565, 566, 597, 630, 632],
                       599: [565, 567, 631, 633], 600: [566, 568, 632, 634],
                       601: [567, 569, 633, 635], 602: [568, 570, 634, 635, 636],
                       603: [569, 570, 571, 604, 635, 637],
                       604: [570, 572, 603, 605, 636, 638],
                       605: [571, 573, 604, 606, 637, 639],
                       606: [572, 574, 605, 638, 640],
                       607: [573, 574, 575, 639, 640, 641],
                       608: [574, 576, 640, 642], 609: [575, 577, 641, 642, 643],
                       610: [576, 578, 642, 644], 611: [577, 579, 643, 645],
                       613: [579, 581, 645, 647],
                       614: [580, 582, 615, 646, 647, 648],
                       615: [581, 582, 583, 614, 647, 648, 649],
                       616: [582, 584, 648, 649, 650],
                       617: [583, 585, 649, 650, 651],
                       618: [584, 585, 586, 650, 651, 652],
                       619: [585, 586, 587, 620, 651, 653],
                       620: [586, 588, 619, 652, 654], 621: [587, 589, 653, 655],
                       622: [588, 589, 590, 654, 656], 623: [589, 591, 655, 657],
                       624: [590, 591, 592, 656, 658],
                       625: [591, 593, 626, 657, 658, 659],
                       626: [592, 594, 625, 627, 658, 660], 627: [593, 626, 659],
                       628: [596, 662], 629: [595, 597, 661, 663],
                       630: [596, 598, 662, 664], 631: [597, 599, 632, 663, 665],
                       632: [598, 600, 631, 664, 666], 633: [599, 601, 665, 667],
                       634: [600, 602, 666, 668],
                       635: [601, 602, 603, 667, 668, 669],
                       636: [602, 604, 637, 668, 669, 670],
                       637: [603, 605, 636, 669, 671], 638: [604, 606, 670, 672],
                       639: [605, 607, 640, 671, 672, 673],
                       640: [606, 607, 608, 639, 672, 674],
                       641: [607, 609, 642, 673, 675],
                       642: [608, 609, 610, 641, 674, 676],
                       643: [609, 611, 675, 677], 644: [610, 676, 678],
                       645: [611, 613, 677, 679], 646: [614, 678, 680],
                       647: [613, 614, 615, 648, 679, 681],
                       648: [614, 615, 616, 647, 680, 682],
                       649: [615, 616, 617, 681, 682, 683],
                       650: [616, 617, 618, 682, 683, 684],
                       651: [617, 618, 619, 683, 684, 685],
                       652: [618, 620, 684, 686], 653: [619, 621, 685, 687],
                       654: [620, 622, 686, 688], 655: [621, 623, 687, 689],
                       656: [622, 624, 657, 688, 689, 690],
                       657: [623, 625, 656, 689, 690, 691],
                       658: [624, 625, 626, 659, 690, 692],
                       659: [625, 627, 658, 660, 691, 693], 660: [626, 659, 692],
                       661: [629, 695], 662: [628, 630, 694, 696],
                       663: [629, 631, 695, 697], 664: [630, 632, 696, 698],
                       665: [631, 633, 697, 699], 666: [632, 634, 698, 699, 700],
                       667: [633, 635, 699, 701],
                       668: [634, 635, 636, 669, 700, 702],
                       669: [635, 636, 637, 668, 701, 703],
                       670: [636, 638, 702, 703, 704], 671: [637, 639, 703, 705],
                       672: [638, 639, 640, 704, 706], 673: [639, 641, 705],
                       674: [640, 642, 706, 708], 675: [641, 643, 709],
                       676: [642, 644, 677, 708, 710],
                       677: [643, 645, 676, 709, 711], 678: [644, 646, 710, 712],
                       679: [645, 647, 680, 711, 713],
                       680: [646, 648, 679, 712, 714],
                       681: [647, 649, 682, 713, 714, 715],
                       682: [648, 649, 650, 681, 714, 715, 716],
                       683: [649, 650, 651, 715, 717],
                       684: [650, 651, 652, 685, 716, 718],
                       685: [651, 653, 684, 717, 718, 719],
                       686: [652, 654, 718, 720], 687: [653, 655, 719, 721],
                       688: [654, 656, 720, 721, 722],
                       689: [655, 656, 657, 721, 722, 723],
                       690: [656, 657, 658, 691, 722, 724],
                       691: [657, 659, 690, 723, 725], 692: [658, 660, 724, 726],
                       693: [659, 725], 694: [662, 695, 728],
                       695: [661, 663, 694, 696, 727, 728, 729],
                       696: [662, 664, 695, 728, 730], 697: [663, 665, 729, 731],
                       698: [664, 666, 730, 732],
                       699: [665, 666, 667, 700, 731, 733],
                       700: [666, 668, 699, 701, 732, 734],
                       701: [667, 669, 700, 733, 734, 735],
                       702: [668, 670, 703, 734, 736],
                       703: [669, 670, 671, 702, 735, 737],
                       704: [670, 672, 705, 736, 737, 738],
                       705: [671, 673, 704, 737, 739], 706: [672, 674, 738, 740],
                       708: [674, 676, 740, 742], 709: [675, 677, 741, 742, 743],
                       710: [676, 678, 742, 744], 711: [677, 679, 743, 744, 745],
                       712: [678, 680, 744, 745, 746], 713: [679, 681, 745, 747],
                       714: [680, 681, 682, 746, 747, 748],
                       715: [681, 682, 683, 747, 749],
                       716: [682, 684, 717, 748, 749, 750],
                       717: [683, 685, 716, 749, 750, 751],
                       718: [684, 685, 686, 719, 750, 752],
                       719: [685, 687, 718, 720, 751, 753],
                       720: [686, 688, 719, 752, 753, 754],
                       721: [687, 688, 689, 722, 753, 755],
                       722: [688, 689, 690, 721, 754, 756],
                       723: [689, 691, 724, 755, 756, 757],
                       724: [690, 692, 723, 756, 757, 758],
                       725: [691, 693, 726, 757, 758, 759], 726: [692, 725, 758],
                       727: [695, 728, 761], 728: [694, 695, 696, 727, 760, 762],
                       729: [695, 697, 730, 761, 762, 763],
                       730: [696, 698, 729, 762, 764],
                       731: [697, 699, 732, 763, 765],
                       732: [698, 700, 731, 733, 764, 766],
                       733: [699, 701, 732, 765, 766, 767],
                       734: [700, 701, 702, 735, 766, 768],
                       735: [701, 703, 734, 736, 767, 768, 769],
                       736: [702, 704, 735, 768, 770],
                       737: [703, 704, 705, 738, 769, 770, 771],
                       738: [704, 706, 737, 770, 772], 739: [705, 771, 773],
                       740: [706, 708, 772, 774], 741: [709, 773, 775],
                       742: [708, 709, 710, 774, 776],
                       743: [709, 711, 775, 776, 777],
                       744: [710, 711, 712, 776, 777, 778],
                       745: [711, 712, 713, 746, 777, 778, 779],
                       746: [712, 714, 745, 778, 780],
                       747: [713, 714, 715, 779, 780, 781],
                       748: [714, 716, 749, 780, 781, 782],
                       749: [715, 716, 717, 748, 781, 783],
                       750: [716, 717, 718, 751, 782, 783, 784],
                       751: [717, 719, 750, 752, 783, 785],
                       752: [718, 720, 751, 753, 784, 785, 786],
                       753: [719, 720, 721, 752, 785, 787],
                       754: [720, 722, 755, 786, 788],
                       755: [721, 723, 754, 756, 787, 789],
                       756: [722, 723, 724, 755, 788, 790],
                       757: [723, 724, 725, 758, 789, 791],
                       758: [724, 725, 726, 757, 790, 792], 759: [725, 791, 792],
                       760: [728, 761, 794], 761: [727, 729, 760, 762, 793, 795],
                       762: [728, 729, 730, 761, 794, 796],
                       763: [729, 731, 795, 797], 764: [730, 732, 796, 798],
                       765: [731, 733, 797, 798, 799],
                       766: [732, 733, 734, 767, 798, 800],
                       767: [733, 735, 766, 799, 801],
                       768: [734, 735, 736, 800, 801, 802],
                       769: [735, 737, 770, 801, 802, 803],
                       770: [736, 737, 738, 769, 802, 804],
                       771: [737, 739, 772, 803, 805],
                       772: [738, 740, 771, 773, 804, 806],
                       773: [739, 741, 772, 774, 805, 807],
                       774: [740, 742, 773, 775, 806, 808],
                       775: [741, 743, 774, 776, 807, 809],
                       776: [742, 743, 744, 775, 808, 810],
                       777: [743, 744, 745, 809, 810, 811],
                       778: [744, 745, 746, 810, 812], 779: [745, 747, 811, 813],
                       780: [746, 747, 748, 812, 814],
                       781: [747, 748, 749, 782, 813, 815],
                       782: [748, 750, 781, 814, 816],
                       783: [749, 750, 751, 784, 815, 817],
                       784: [750, 752, 783, 816, 817, 818],
                       785: [751, 752, 753, 817, 818, 819],
                       786: [752, 754, 818, 819, 820], 787: [753, 755, 819, 821],
                       788: [754, 756, 820, 822], 789: [755, 757, 821, 823],
                       790: [756, 758, 791, 822, 824],
                       791: [757, 759, 790, 823, 824, 825], 792: [758, 759, 824],
                       793: [761, 794, 827], 794: [760, 762, 793, 826, 828],
                       795: [761, 763, 827], 796: [762, 764, 828, 830],
                       797: [763, 765, 831], 798: [764, 765, 766, 830, 831, 832],
                       799: [765, 767, 800, 831, 832, 833],
                       800: [766, 768, 799, 832, 833, 834],
                       801: [767, 768, 769, 802, 833, 834, 835],
                       802: [768, 769, 770, 801, 834, 836],
                       803: [769, 771, 835, 836, 837], 804: [770, 772, 836, 838],
                       805: [771, 773, 806, 837, 839],
                       806: [772, 774, 805, 838, 839, 840],
                       807: [773, 775, 839, 841], 808: [774, 776, 840, 842],
                       809: [775, 777, 810, 841, 843],
                       810: [776, 777, 778, 809, 811, 842, 844],
                       811: [777, 779, 810, 843, 844, 845],
                       812: [778, 780, 813, 844, 845, 846],
                       813: [779, 781, 812, 814, 845, 847],
                       814: [780, 782, 813, 815, 846, 848],
                       815: [781, 783, 814, 816, 847, 849],
                       816: [782, 784, 815, 848, 850],
                       817: [783, 784, 785, 849, 850, 851],
                       818: [784, 785, 786, 819, 850, 852],
                       819: [785, 786, 787, 818, 851, 853],
                       820: [786, 788, 821, 852, 854],
                       821: [787, 789, 820, 853, 855], 822: [788, 790, 854, 856],
                       823: [789, 791, 824, 855, 857],
                       824: [790, 791, 792, 823, 856, 858], 825: [791, 857, 858],
                       826: [794, 827, 860], 827: [793, 795, 826, 859, 861],
                       828: [794, 796, 860, 862], 830: [796, 798, 862, 864],
                       831: [797, 798, 799, 832, 863, 865],
                       832: [798, 799, 800, 831, 864, 866],
                       833: [799, 800, 801, 865, 867],
                       834: [800, 801, 802, 835, 866, 868],
                       835: [801, 803, 834, 867, 868, 869],
                       836: [802, 803, 804, 837, 868, 870],
                       837: [803, 805, 836, 869, 871],
                       838: [804, 806, 839, 870, 872],
                       839: [805, 806, 807, 838, 871, 873],
                       840: [806, 808, 872, 874], 841: [807, 809, 873, 875],
                       842: [808, 810, 874, 876], 843: [809, 811, 875, 876, 877],
                       844: [810, 811, 812, 876, 878],
                       845: [811, 812, 813, 846, 877, 879],
                       846: [812, 814, 845, 878, 880], 847: [813, 815, 879, 881],
                       848: [814, 816, 849, 880, 882],
                       849: [815, 817, 848, 881, 882, 883],
                       850: [816, 817, 818, 851, 882, 884],
                       851: [817, 819, 850, 852, 883, 884, 885],
                       852: [818, 820, 851, 853, 884, 886],
                       853: [819, 821, 852, 885, 886, 887], 854: [820, 822, 886],
                       855: [821, 823, 887, 889], 856: [822, 824, 890],
                       857: [823, 825, 889, 890, 891], 858: [824, 825, 890],
                       859: [827, 893], 860: [826, 828, 892, 893, 894],
                       861: [827, 893, 895], 862: [828, 830, 894, 896],
                       863: [831, 895, 897], 864: [830, 832, 896, 897, 898],
                       865: [831, 833, 897], 866: [832, 834, 898, 900],
                       867: [833, 835, 901], 868: [834, 835, 836, 869, 900, 902],
                       869: [835, 837, 868, 870, 901, 903],
                       870: [836, 838, 869, 902, 904], 871: [837, 839, 903, 905],
                       872: [838, 840, 904, 905, 906],
                       873: [839, 841, 874, 905, 906, 907],
                       874: [840, 842, 873, 875, 906, 908],
                       875: [841, 843, 874, 907, 908, 909],
                       876: [842, 843, 844, 877, 908, 910],
                       877: [843, 845, 876, 878, 909, 910, 911],
                       878: [844, 846, 877, 910, 912], 879: [845, 847, 911, 913],
                       880: [846, 848, 912, 913, 914],
                       881: [847, 849, 882, 913, 914, 915],
                       882: [848, 849, 850, 881, 883, 914, 916],
                       883: [849, 851, 882, 915, 916, 917],
                       884: [850, 851, 852, 916, 917, 918],
                       885: [851, 853, 886, 917, 918, 919],
                       886: [852, 853, 854, 885, 918, 920],
                       887: [853, 855, 919, 921], 889: [855, 857, 921, 923],
                       890: [856, 857, 858, 922, 924], 891: [857, 923, 924],
                       892: [860, 893, 926],
                       893: [859, 860, 861, 892, 925, 926, 927],
                       894: [860, 862, 926, 928], 895: [861, 863, 927, 929],
                       896: [862, 864, 897, 928, 930],
                       897: [863, 864, 865, 896, 929, 931],
                       898: [864, 866, 930, 932], 900: [866, 868, 932, 934],
                       901: [867, 869, 902, 933, 935],
                       902: [868, 870, 901, 903, 934, 936],
                       903: [869, 871, 902, 904, 935, 937],
                       904: [870, 872, 903, 905, 936, 938],
                       905: [871, 872, 873, 904, 906, 937, 939],
                       906: [872, 873, 874, 905, 938, 940],
                       907: [873, 875, 939, 940, 941],
                       908: [874, 875, 876, 909, 940, 942],
                       909: [875, 877, 908, 910, 941, 943],
                       910: [876, 877, 878, 909, 942, 944],
                       911: [877, 879, 943, 945], 912: [878, 880, 944, 946],
                       913: [879, 880, 881, 945, 946, 947],
                       914: [880, 881, 882, 915, 946, 948],
                       915: [881, 883, 914, 916, 947, 949],
                       916: [882, 883, 884, 915, 948, 950],
                       917: [883, 884, 885, 949, 951],
                       918: [884, 885, 886, 950, 952], 919: [885, 887, 951, 953],
                       920: [886, 952, 954], 921: [887, 889, 953, 955],
                       922: [890, 954, 956], 923: [889, 891, 955, 957],
                       924: [890, 891, 956], 925: [893, 926, 959],
                       926: [892, 893, 894, 925, 958, 960],
                       927: [893, 895, 928, 959, 960, 961],
                       928: [894, 896, 927, 929, 960, 962],
                       929: [895, 897, 928, 930, 961, 963],
                       930: [896, 898, 929, 962, 964], 931: [897, 963, 965],
                       932: [898, 900, 964, 966], 933: [901, 965, 967],
                       934: [900, 902, 966, 967, 968],
                       935: [901, 903, 936, 967, 968, 969],
                       936: [902, 904, 935, 968, 969, 970],
                       937: [903, 905, 969, 970, 971], 938: [904, 906, 970, 972],
                       939: [905, 907, 971, 973], 940: [906, 907, 908, 972, 974],
                       941: [907, 909, 942, 973, 974, 975],
                       942: [908, 910, 941, 974, 976], 943: [909, 911, 975, 977],
                       944: [910, 912, 976, 977, 978], 945: [911, 913, 977, 979],
                       946: [912, 913, 914, 947, 978, 980],
                       947: [913, 915, 946, 948, 979, 981],
                       948: [914, 916, 947, 980, 982], 949: [915, 917, 981],
                       950: [916, 918, 982, 984], 951: [917, 919, 985],
                       952: [918, 920, 953, 984, 985, 986],
                       953: [919, 921, 952, 985, 987],
                       954: [920, 922, 955, 986, 988],
                       955: [921, 923, 954, 956, 987, 989],
                       956: [922, 924, 955, 988, 990], 957: [923, 989],
                       958: [926, 959, 992], 959: [925, 927, 958, 991, 992, 993],
                       960: [926, 927, 928, 992, 993, 994],
                       961: [927, 929, 962, 993, 994, 995],
                       962: [928, 930, 961, 963, 994, 996],
                       963: [929, 931, 962, 964, 995, 997],
                       964: [930, 932, 963, 996, 998],
                       965: [931, 933, 966, 997, 999],
                       966: [932, 934, 965, 967, 998, 1000],
                       967: [933, 934, 935, 966, 999, 1001],
                       968: [934, 935, 936, 1000, 1001, 1002],
                       969: [935, 936, 937, 1001, 1002, 1003],
                       970: [936, 937, 938, 1002, 1004],
                       971: [937, 939, 1003, 1005],
                       972: [938, 940, 973, 1004, 1006],
                       973: [939, 941, 972, 1005, 1006, 1007],
                       974: [940, 941, 942, 975, 1006, 1007, 1008],
                       975: [941, 943, 974, 976, 1007, 1009],
                       976: [942, 944, 975, 977, 1008, 1010],
                       977: [943, 944, 945, 976, 1009, 1011],
                       978: [944, 946, 979, 1010, 1012],
                       979: [945, 947, 978, 1011, 1013],
                       980: [946, 948, 981, 1012, 1013, 1014],
                       981: [947, 949, 980, 1013, 1015],
                       982: [948, 950, 1014, 1016], 984: [950, 952, 1016, 1018],
                       985: [951, 952, 953, 1017, 1019],
                       986: [952, 954, 1018, 1020],
                       987: [953, 955, 988, 1019, 1021],
                       988: [954, 956, 987, 989, 1020, 1021, 1022],
                       989: [955, 957, 988, 990, 1021, 1023], 990: [956, 989, 1022],
                       991: [959, 1024, 1025],
                       992: [958, 959, 960, 993, 1024, 1026],
                       993: [959, 960, 961, 992, 1025, 1027],
                       994: [960, 961, 962, 1026, 1027, 1028],
                       995: [961, 963, 996, 1027, 1028, 1029],
                       996: [962, 964, 995, 1028, 1030],
                       997: [963, 965, 1029, 1031], 998: [964, 966, 1030, 1032],
                       999: [965, 967, 1031, 1032, 1033],
                       1000: [966, 968, 1001, 1032, 1033, 1034],
                       1001: [967, 968, 969, 1000, 1033, 1034, 1035],
                       1002: [968, 969, 970, 1034, 1036],
                       1003: [969, 971, 1004, 1035, 1037],
                       1004: [970, 972, 1003, 1036, 1038],
                       1005: [971, 973, 1037, 1039],
                       1006: [972, 973, 974, 1038, 1040],
                       1007: [973, 974, 975, 1039, 1041],
                       1008: [974, 976, 1040, 1042],
                       1009: [975, 977, 1010, 1041, 1042, 1043],
                       1010: [976, 978, 1009, 1011, 1042, 1044],
                       1011: [977, 979, 1010, 1043, 1044, 1045],
                       1012: [978, 980, 1044, 1046],
                       1013: [979, 980, 981, 1045, 1046, 1047],
                       1014: [980, 982, 1046, 1047, 1048], 1015: [981, 1047, 1049],
                       1016: [982, 984, 1048, 1050], 1017: [985, 1049, 1051],
                       1018: [984, 986, 1019, 1050, 1051, 1052],
                       1019: [985, 987, 1018, 1020, 1051, 1053],
                       1020: [986, 988, 1019, 1021, 1052, 1054],
                       1021: [987, 988, 989, 1020, 1053, 1055],
                       1022: [988, 990, 1023, 1054, 1055, 1056],
                       1023: [989, 1022, 1055], 1024: [991, 992, 1058],
                       1025: [991, 993, 1026, 1057, 1058, 1059],
                       1026: [992, 994, 1025, 1027, 1058, 1060],
                       1027: [993, 994, 995, 1026, 1059, 1061],
                       1028: [994, 995, 996, 1060, 1061, 1062],
                       1029: [995, 997, 1030, 1061, 1063],
                       1030: [996, 998, 1029, 1062, 1064],
                       1031: [997, 999, 1063, 1064, 1065],
                       1032: [998, 999, 1000, 1064, 1065, 1066],
                       1033: [999, 1000, 1001, 1065, 1067],
                       1034: [1000, 1001, 1002, 1035, 1066, 1068],
                       1035: [1001, 1003, 1034, 1067, 1068, 1069],
                       1036: [1002, 1004, 1068], 1037: [1003, 1005, 1069, 1071],
                       1038: [1004, 1006, 1072],
                       1039: [1005, 1007, 1040, 1071, 1072, 1073],
                       1040: [1006, 1008, 1039, 1072, 1073, 1074],
                       1041: [1007, 1009, 1042, 1073, 1075],
                       1042: [1008, 1009, 1010, 1041, 1074, 1076],
                       1043: [1009, 1011, 1075, 1077],
                       1044: [1010, 1011, 1012, 1045, 1076, 1078],
                       1045: [1011, 1013, 1044, 1077, 1078, 1079],
                       1046: [1012, 1013, 1014, 1078, 1080],
                       1047: [1013, 1014, 1015, 1048, 1079, 1081],
                       1048: [1014, 1016, 1047, 1080, 1082],
                       1049: [1015, 1017, 1081, 1082, 1083],
                       1050: [1016, 1018, 1051, 1082, 1083, 1084],
                       1051: [1017, 1018, 1019, 1050, 1083, 1085],
                       1052: [1018, 1020, 1053, 1084, 1085, 1086],
                       1053: [1019, 1021, 1052, 1054, 1085, 1087],
                       1054: [1020, 1022, 1053, 1055, 1086, 1088],
                       1055: [1021, 1022, 1023, 1054, 1056, 1087, 1089],
                       1056: [1022, 1055, 1088], 1057: [1025],
                       1058: [1024, 1025, 1026], 1059: [1025, 1027, 1060],
                       1060: [1026, 1028, 1059], 1061: [1027, 1028, 1029, 1062],
                       1062: [1028, 1030, 1061], 1063: [1029, 1031],
                       1064: [1030, 1031, 1032], 1065: [1031, 1032, 1033],
                       1066: [1032, 1034], 1067: [1033, 1035],
                       1068: [1034, 1035, 1036], 1069: [1035, 1037],
                       1071: [1037, 1039], 1072: [1038, 1039, 1040],
                       1073: [1039, 1040, 1041], 1074: [1040, 1042],
                       1075: [1041, 1043], 1076: [1042, 1044], 1077: [1043, 1045],
                       1078: [1044, 1045, 1046], 1079: [1045, 1047],
                       1080: [1046, 1048], 1081: [1047, 1049],
                       1082: [1048, 1049, 1050], 1083: [1049, 1050, 1051],
                       1084: [1050, 1052], 1085: [1051, 1052, 1053],
                       1086: [1052, 1054], 1087: [1053, 1055, 1088],
                       1088: [1054, 1056, 1087], 1089: [1055]}
cycle_16_late_links = {2: [34, 36], 3: [35, 37], 4: [5, 36, 38], 5: [4, 37, 39],
                       6: [38, 39, 40], 7: [39, 40, 41], 8: [40, 41, 42], 9: [41, 43],
                       10: [11, 42, 44], 11: [10, 43, 45], 12: [44, 46], 13: [45, 46, 47],
                       14: [46, 48], 16: [48, 50], 17: [18, 49, 51], 18: [17, 50, 52],
                       19: [20, 51, 53], 20: [19, 52, 54], 21: [22, 53, 55],
                       22: [21, 54, 55, 56], 23: [55, 56, 57], 24: [56, 58],
                       25: [26, 57, 59], 26: [25, 58, 59, 60], 27: [59, 60, 61],
                       28: [60, 62], 29: [61, 63], 31: [63, 65], 32: [64, 66],
                       34: [2, 68], 35: [3, 67], 36: [2, 4, 68, 70], 37: [3, 5, 71],
                       38: [4, 6, 70, 71, 72], 39: [5, 6, 7, 71, 72, 73],
                       40: [6, 7, 8, 41, 72, 74], 41: [7, 8, 9, 40, 42, 73, 75],
                       42: [8, 10, 41, 43, 74, 76], 43: [9, 11, 42, 44, 75, 76, 77],
                       44: [10, 12, 43, 45, 76, 78], 45: [11, 13, 44, 46, 77, 79],
                       46: [12, 13, 14, 45, 78, 80], 47: [13, 79, 81],
                       48: [14, 16, 80, 82], 49: [17, 81, 83], 50: [16, 18, 51, 82, 84],
                       51: [17, 19, 50, 52, 83, 85], 52: [18, 20, 51, 53, 84, 86],
                       53: [19, 21, 52, 54, 85, 87], 54: [20, 22, 53, 55, 86, 88],
                       55: [21, 22, 23, 54, 87, 89], 56: [22, 23, 24, 88, 90],
                       57: [23, 25, 58, 89, 91], 58: [24, 26, 57, 90, 92],
                       59: [25, 26, 27, 91, 92, 93], 60: [26, 27, 28, 61, 92, 94],
                       61: [27, 29, 60, 93, 95], 62: [28, 94, 96], 63: [29, 31, 95, 97],
                       64: [32, 96, 98], 65: [31, 97, 99], 66: [32, 98], 67: [35, 101],
                       68: [34, 36, 100, 102], 70: [36, 38, 102, 104],
                       71: [37, 38, 39, 103, 104, 105], 72: [38, 39, 40, 104, 105, 106],
                       73: [39, 41, 105, 106, 107], 74: [40, 42, 75, 106, 107, 108],
                       75: [41, 43, 74, 107, 109], 76: [42, 43, 44, 108, 110],
                       77: [43, 45, 78, 109, 111], 78: [44, 46, 77, 79, 110, 112],
                       79: [45, 47, 78, 80, 111, 113], 80: [46, 48, 79, 112, 113, 114],
                       81: [47, 49, 82, 113, 115], 82: [48, 50, 81, 83, 114, 116],
                       83: [49, 51, 82, 115, 116, 117], 84: [50, 52, 85, 116, 117, 118],
                       85: [51, 53, 84, 117, 118, 119], 86: [52, 54, 87, 118, 119, 120],
                       87: [53, 55, 86, 88, 119, 121], 88: [54, 56, 87, 120, 122],
                       89: [55, 57, 121], 90: [56, 58, 122, 124], 91: [57, 59, 125],
                       92: [58, 59, 60, 93, 124, 126], 93: [59, 61, 92, 125, 126, 127],
                       94: [60, 62, 95, 126, 127, 128], 95: [61, 63, 94, 127, 129],
                       96: [62, 64, 97, 128, 129, 130], 97: [63, 65, 96, 129, 131],
                       98: [64, 66, 130, 131, 132], 99: [65, 131], 100: [68, 134],
                       101: [67, 133, 135], 102: [68, 70, 134, 136],
                       103: [71, 135, 137], 104: [70, 71, 72, 136, 137, 138],
                       105: [71, 72, 73, 137, 138, 139],
                       106: [72, 73, 74, 138, 139, 140], 107: [73, 74, 75, 139, 141],
                       108: [74, 76, 140], 109: [75, 77, 141, 143], 110: [76, 78, 144],
                       111: [77, 79, 112, 143, 144, 145],
                       112: [78, 80, 111, 144, 145, 146],
                       113: [79, 80, 81, 114, 145, 147],
                       114: [80, 82, 113, 115, 146, 148],
                       115: [81, 83, 114, 147, 148, 149],
                       116: [82, 83, 84, 117, 148, 150],
                       117: [83, 84, 85, 116, 149, 150, 151],
                       118: [84, 85, 86, 150, 151, 152],
                       119: [85, 86, 87, 120, 151, 153],
                       120: [86, 88, 119, 121, 152, 154],
                       121: [87, 89, 120, 153, 154, 155],
                       122: [88, 90, 154, 156],
                       124: [90, 92, 156, 158],
                       125: [91, 93, 157, 158, 159],
                       126: [92, 93, 94, 127, 158, 160],
                       127: [93, 94, 95, 126, 128, 159, 161],
                       128: [94, 96, 127, 160, 161, 162],
                       129: [95, 96, 97, 161, 162, 163],
                       130: [96, 98, 131, 162, 163, 164],
                       131: [97, 98, 99, 130, 132, 163, 165],
                       132: [98, 131, 164],
                       133: [101, 134, 167],
                       134: [100, 102, 133, 135, 166, 168],
                       135: [101, 103, 134, 136, 167, 169],
                       136: [102, 104, 135, 137, 168, 170],
                       137: [103, 104, 105, 136, 138, 169, 171],
                       138: [104, 105, 106, 137, 170, 172],
                       139: [105, 106, 107, 171, 172, 173],
                       140: [106, 108, 172, 173, 174],
                       141: [107, 109, 173, 175],
                       143: [109, 111, 175, 177],
                       144: [110, 111, 112, 145, 176, 178],
                       145: [111, 112, 113, 144, 177, 179],
                       146: [112, 114, 147, 178, 180],
                       147: [113, 115, 146, 179, 180, 181],
                       148: [114, 115, 116, 180, 181, 182],
                       149: [115, 117, 150, 181, 182, 183],
                       150: [116, 117, 118, 149, 182, 184],
                       151: [117, 118, 119, 183, 184, 185],
                       152: [118, 120, 153, 184, 185, 186],
                       153: [119, 121, 152, 154, 185, 187],
                       154: [120, 121, 122, 153, 186, 188],
                       155: [121, 187, 189],
                       156: [122, 124, 188, 190],
                       157: [125, 189, 191],
                       158: [124, 125, 126, 159, 190, 192],
                       159: [125, 127, 158, 191, 192, 193],
                       160: [126, 128, 161, 192, 194],
                       161: [127, 128, 129, 160, 193, 195],
                       162: [128, 129, 130, 194, 196],
                       163: [129, 130, 131, 195, 197],
                       164: [130, 132, 165, 196, 197, 198],
                       165: [131, 164, 197],
                       166: [134, 200],
                       167: [133, 135, 199, 200, 201],
                       168: [134, 136, 200],
                       169: [135, 137, 201, 203],
                       170: [136, 138, 204],
                       171: [137, 139, 172, 203, 204, 205],
                       172: [138, 139, 140, 171, 204, 206],
                       173: [139, 140, 141, 205, 206, 207],
                       174: [140, 206, 208],
                       175: [141, 143, 207, 209],
                       176: [144, 208, 210],
                       177: [143, 145, 178, 209, 211],
                       178: [144, 146, 177, 179, 210, 212],
                       179: [145, 147, 178, 211, 212, 213],
                       180: [146, 147, 148, 212, 214],
                       181: [147, 148, 149, 213, 214, 215],
                       182: [148, 149, 150, 183, 214, 215, 216],
                       183: [149, 151, 182, 215, 217],
                       184: [150, 151, 152, 216, 217, 218],
                       185: [151, 152, 153, 186, 217, 219],
                       186: [152, 154, 185, 187, 218, 220],
                       187: [153, 155, 186, 219, 220, 221],
                       188: [154, 156, 220, 221, 222],
                       189: [155, 157, 190, 221, 223],
                       190: [156, 158, 189, 191, 222, 224],
                       191: [157, 159, 190, 223, 225],
                       192: [158, 159, 160, 224, 225, 226],
                       193: [159, 161, 225],
                       194: [160, 162, 226, 228],
                       195: [161, 163, 229],
                       196: [162, 164, 197, 228, 230],
                       197: [163, 164, 165, 196, 229, 231],
                       198: [164, 230, 231],
                       199: [167, 200, 233],
                       200: [166, 167, 168, 199, 232, 234],
                       201: [167, 169, 233, 235],
                       203: [169, 171, 235, 237],
                       204: [170, 171, 172, 236, 237, 238],
                       205: [171, 173, 206, 237, 238, 239],
                       206: [172, 173, 174, 205, 238, 239, 240],
                       207: [173, 175, 239, 241],
                       208: [174, 176, 240, 241, 242],
                       209: [175, 177, 210, 241, 242, 243],
                       210: [176, 178, 209, 211, 242, 244],
                       211: [177, 179, 210, 243, 244, 245],
                       212: [178, 179, 180, 213, 244, 246],
                       213: [179, 181, 212, 214, 245, 246, 247],
                       214: [180, 181, 182, 213, 246, 248],
                       215: [181, 182, 183, 247, 248, 249],
                       216: [182, 184, 217, 248, 249, 250],
                       217: [183, 184, 185, 216, 218, 249, 251],
                       218: [184, 186, 217, 219, 250, 252],
                       219: [185, 187, 218, 251, 252, 253],
                       220: [186, 187, 188, 221, 252, 254],
                       221: [187, 188, 189, 220, 253, 255],
                       222: [188, 190, 223, 254, 255, 256],
                       223: [189, 191, 222, 224, 255, 257],
                       224: [190, 192, 223, 256, 257, 258],
                       225: [191, 192, 193, 257, 258, 259],
                       226: [192, 194, 258, 260],
                       228: [194, 196, 260, 262],
                       229: [195, 197, 230, 261, 263],
                       230: [196, 198, 229, 262, 263, 264],
                       231: [197, 198, 263],
                       232: [200, 265, 266],
                       233: [199, 201, 265, 266, 267],
                       234: [200, 266, 268],
                       235: [201, 203, 267, 269],
                       236: [204, 268, 270],
                       237: [203, 204, 205, 269, 271],
                       238: [204, 205, 206, 270, 271, 272],
                       239: [205, 206, 207, 271, 273],
                       240: [206, 208, 241, 272, 273, 274],
                       241: [207, 208, 209, 240, 273, 274, 275],
                       242: [208, 209, 210, 243, 274, 276],
                       243: [209, 211, 242, 244, 275, 277],
                       244: [210, 211, 212, 243, 276, 278],
                       245: [211, 213, 246, 277, 278, 279],
                       246: [212, 213, 214, 245, 278, 280],
                       247: [213, 215, 248, 279, 280, 281],
                       248: [214, 215, 216, 247, 280, 281, 282],
                       249: [215, 216, 217, 281, 283],
                       250: [216, 218, 251, 282, 284],
                       251: [217, 219, 250, 283, 284, 285],
                       252: [218, 219, 220, 253, 284, 286],
                       253: [219, 221, 252, 285, 286, 287],
                       254: [220, 222, 255, 286, 287, 288],
                       255: [221, 222, 223, 254, 287, 288, 289],
                       256: [222, 224, 288, 290],
                       257: [223, 224, 225, 289, 290, 291],
                       258: [224, 225, 226, 290, 292],
                       259: [225, 291, 293],
                       260: [226, 228, 292, 294],
                       261: [229, 293, 295],
                       262: [228, 230, 294, 295, 296],
                       263: [229, 230, 231, 264, 295, 297],
                       264: [230, 263, 296],
                       265: [232, 233, 299],
                       266: [232, 233, 234, 298, 299, 300],
                       267: [233, 235, 268, 299, 300, 301],
                       268: [234, 236, 267, 300, 302],
                       269: [235, 237, 270, 301, 303],
                       270: [236, 238, 269, 271, 302, 304],
                       271: [237, 238, 239, 270, 272, 303, 305],
                       272: [238, 240, 271, 304, 305, 306],
                       273: [239, 240, 241, 305, 306, 307],
                       274: [240, 241, 242, 275, 306, 308],
                       275: [241, 243, 274, 276, 307, 309],
                       276: [242, 244, 275, 308, 309, 310],
                       277: [243, 245, 278, 309, 311],
                       278: [244, 245, 246, 277, 310, 312],
                       279: [245, 247, 280, 311, 312, 313],
                       280: [246, 247, 248, 279, 312, 314],
                       281: [247, 248, 249, 313, 314, 315],
                       282: [248, 250, 283, 314, 315, 316],
                       283: [249, 251, 282, 284, 315, 317],
                       284: [250, 251, 252, 283, 285, 316, 318],
                       285: [251, 253, 284, 317, 318, 319],
                       286: [252, 253, 254, 318, 319, 320],
                       287: [253, 254, 255, 319, 321],
                       288: [254, 255, 256, 289, 320, 322],
                       289: [255, 257, 288, 290, 321, 322, 323],
                       290: [256, 257, 258, 289, 322, 324],
                       291: [257, 259, 292, 323, 324, 325],
                       292: [258, 260, 291, 293, 324, 326],
                       293: [259, 261, 292, 294, 325, 327],
                       294: [260, 262, 293, 326, 327, 328],
                       295: [261, 262, 263, 327, 328, 329],
                       296: [262, 264, 297, 328, 329, 330],
                       297: [263, 296, 329],
                       298: [266, 299, 332],
                       299: [265, 266, 267, 298, 331, 333],
                       300: [266, 267, 268, 332, 334],
                       301: [267, 269, 302, 333, 334, 335],
                       302: [268, 270, 301, 303, 334, 336],
                       303: [269, 271, 302, 335, 336, 337],
                       304: [270, 272, 305, 336, 338],
                       305: [271, 272, 273, 304, 337, 339],
                       306: [272, 273, 274, 307, 338, 340],
                       307: [273, 275, 306, 308, 339, 341],
                       308: [274, 276, 307, 340, 342],
                       309: [275, 276, 277, 341, 342, 343],
                       310: [276, 278, 311, 342, 343, 344],
                       311: [277, 279, 310, 312, 343, 345],
                       312: [278, 279, 280, 311, 344, 346],
                       313: [279, 281, 314, 345, 346, 347],
                       314: [280, 281, 282, 313, 346, 348],
                       315: [281, 282, 283, 316, 347, 349],
                       316: [282, 284, 315, 348, 349, 350],
                       317: [283, 285, 318, 349, 351],
                       318: [284, 285, 286, 317, 350, 351, 352],
                       319: [285, 286, 287, 320, 351, 353],
                       320: [286, 288, 319, 321, 352, 354],
                       321: [287, 289, 320, 353, 354, 355],
                       322: [288, 289, 290, 354, 355, 356],
                       323: [289, 291, 324, 355, 356, 357],
                       324: [290, 291, 292, 323, 325, 356, 358],
                       325: [291, 293, 324, 357, 358, 359],
                       326: [292, 294, 327, 358, 360],
                       327: [293, 294, 295, 326, 359, 361],
                       328: [294, 295, 296, 360, 361, 362],
                       329: [295, 296, 297, 361, 362, 363],
                       330: [296, 362, 363],
                       331: [299],
                       332: [298, 300, 364, 366],
                       333: [299, 301, 367],
                       334: [300, 301, 302, 366, 367, 368],
                       335: [301, 303, 367, 368, 369],
                       336: [302, 303, 304, 337, 368, 369, 370],
                       337: [303, 305, 336, 369, 370, 371],
                       338: [304, 306, 339, 370, 371, 372],
                       339: [305, 307, 338, 340, 371, 373],
                       340: [306, 308, 339, 341, 372, 374],
                       341: [307, 309, 340, 342, 373, 374, 375],
                       342: [308, 309, 310, 341, 374, 376],
                       343: [309, 310, 311, 375, 376, 377],
                       344: [310, 312, 345, 376, 377, 378],
                       345: [311, 313, 344, 346, 377, 379],
                       346: [312, 313, 314, 345, 378, 380],
                       347: [313, 315, 348, 379, 380, 381],
                       348: [314, 316, 347, 349, 380, 382],
                       349: [315, 316, 317, 348, 381, 383],
                       350: [316, 318, 351, 382, 383, 384],
                       351: [317, 318, 319, 350, 383, 385],
                       352: [318, 320, 353, 384, 385, 386],
                       353: [319, 321, 352, 385, 386, 387],
                       354: [320, 321, 322, 386, 387, 388],
                       355: [321, 322, 323, 387, 388, 389],
                       356: [322, 323, 324, 357, 388, 390],
                       357: [323, 325, 356, 389, 391],
                       358: [324, 325, 326, 390, 391, 392],
                       359: [325, 327, 360, 391, 392, 393],
                       360: [326, 328, 359, 392, 393, 394],
                       361: [327, 328, 329, 362, 393, 395],
                       362: [328, 329, 330, 361, 394, 396],
                       363: [329, 330, 395, 396],
                       364: [332, 398],
                       366: [332, 334, 398, 400],
                       367: [333, 334, 335, 399, 401],
                       368: [334, 335, 336, 400, 401, 402],
                       369: [335, 336, 337, 401, 402, 403],
                       370: [336, 337, 338, 402, 403, 404],
                       371: [337, 338, 339, 403, 404, 405],
                       372: [338, 340, 373, 404, 405, 406],
                       373: [339, 341, 372, 405, 406, 407],
                       374: [340, 341, 342, 406, 407, 408],
                       375: [341, 343, 376, 407, 408, 409],
                       376: [342, 343, 344, 375, 377, 408, 410],
                       377: [343, 344, 345, 376, 409, 411],
                       378: [344, 346, 379, 410, 412],
                       379: [345, 347, 378, 380, 411, 413],
                       380: [346, 347, 348, 379, 412, 414],
                       381: [347, 349, 382, 413, 414, 415],
                       382: [348, 350, 381, 414, 415, 416],
                       383: [349, 350, 351, 384, 415, 417],
                       384: [350, 352, 383, 385, 416, 418],
                       385: [351, 352, 353, 384, 417, 419],
                       386: [352, 353, 354, 418, 419, 420],
                       387: [353, 354, 355, 419, 420, 421],
                       388: [354, 355, 356, 389, 420, 422],
                       389: [355, 357, 388, 390, 421, 423],
                       390: [356, 358, 389, 422, 424],
                       391: [357, 358, 359, 423, 425],
                       392: [358, 359, 360, 393, 424, 426],
                       393: [359, 360, 361, 392, 425, 427],
                       394: [360, 362, 395, 426, 427, 428],
                       395: [361, 363, 394, 427, 428, 429],
                       396: [362, 363, 428],
                       397: [431],
                       398: [364, 366, 430, 432],
                       399: [367, 431, 433],
                       400: [366, 368, 432, 433, 434],
                       401: [367, 368, 369, 433, 434, 435],
                       402: [368, 369, 370, 434, 435, 436],
                       403: [369, 370, 371, 404, 435, 437],
                       404: [370, 371, 372, 403, 436, 438],
                       405: [371, 372, 373, 437, 439],
                       406: [372, 373, 374, 438, 440],
                       407: [373, 374, 375, 408, 439, 440, 441],
                       408: [374, 375, 376, 407, 440, 442],
                       409: [375, 377, 441, 442, 443],
                       410: [376, 378, 411, 442, 443, 444],
                       411: [377, 379, 410, 443, 444, 445],
                       412: [378, 380, 413, 444, 445, 446],
                       413: [379, 381, 412, 414, 445, 447],
                       414: [380, 381, 382, 413, 446, 448],
                       415: [381, 382, 383, 416, 447, 449],
                       416: [382, 384, 415, 417, 448, 450],
                       417: [383, 385, 416, 418, 449, 451],
                       418: [384, 386, 417, 450, 451, 452],
                       419: [385, 386, 387, 451, 452, 453],
                       420: [386, 387, 388, 421, 452, 454],
                       421: [387, 389, 420, 453, 454, 455],
                       422: [388, 390, 454, 455, 456],
                       423: [389, 391, 455],
                       424: [390, 392, 456, 458],
                       425: [391, 393, 459],
                       426: [392, 394, 427, 458, 460],
                       427: [393, 394, 395, 426, 459, 461],
                       428: [394, 395, 396, 460, 462],
                       429: [395, 461],
                       430: [398, 431, 464],
                       431: [397, 399, 430, 432, 463, 465],
                       432: [398, 400, 431, 464, 465, 466],
                       433: [399, 400, 401, 465, 467],
                       434: [400, 401, 402, 466, 468],
                       435: [401, 402, 403, 436, 467, 469],
                       436: [402, 404, 435, 468, 470],
                       437: [403, 405, 469],
                       438: [404, 406, 470, 472],
                       439: [405, 407, 473],
                       440: [406, 407, 408, 472, 473, 474],
                       441: [407, 409, 473, 474, 475],
                       442: [408, 409, 410, 474, 475, 476],
                       443: [409, 410, 411, 475, 476, 477],
                       444: [410, 411, 412, 476, 477, 478],
                       445: [411, 412, 413, 446, 477, 479],
                       446: [412, 414, 445, 478, 479, 480],
                       447: [413, 415, 448, 479, 480, 481],
                       448: [414, 416, 447, 449, 480, 482],
                       449: [415, 417, 448, 450, 481, 483],
                       450: [416, 418, 449, 482, 484],
                       451: [417, 418, 419, 483, 484, 485],
                       452: [418, 419, 420, 453, 484, 486],
                       453: [419, 421, 452, 485, 486, 487],
                       454: [420, 421, 422, 455, 486, 488],
                       455: [421, 422, 423, 454, 487, 489],
                       456: [422, 424, 488, 490],
                       458: [424, 426, 490, 492],
                       459: [425, 427, 491],
                       460: [426, 428, 492, 494],
                       461: [427, 429, 495],
                       462: [428, 494, 495],
                       463: [431, 464, 497],
                       464: [430, 432, 463, 465, 496, 498],
                       465: [431, 432, 433, 464, 466, 497, 499],
                       466: [432, 434, 465, 467, 498, 500],
                       467: [433, 435, 466, 468, 499, 501],
                       468: [434, 436, 467, 469, 500, 502],
                       469: [435, 437, 468, 501, 503],
                       470: [436, 438, 502, 504],
                       472: [438, 440, 504, 506],
                       473: [439, 440, 441, 505, 506, 507],
                       474: [440, 441, 442, 506, 507, 508],
                       475: [441, 442, 443, 507, 508, 509],
                       476: [442, 443, 444, 477, 508, 510],
                       477: [443, 444, 445, 476, 509, 511],
                       478: [444, 446, 479, 510, 511, 512],
                       479: [445, 446, 447, 478, 511, 512, 513],
                       480: [446, 447, 448, 481, 512, 514],
                       481: [447, 449, 480, 482, 513, 515],
                       482: [448, 450, 481, 514, 515, 516],
                       483: [449, 451, 484, 515, 516, 517],
                       484: [450, 451, 452, 483, 485, 516, 518],
                       485: [451, 453, 484, 486, 517, 519],
                       486: [452, 453, 454, 485, 487, 518, 520],
                       487: [453, 455, 486, 488, 519, 521],
                       488: [454, 456, 487, 520, 522],
                       489: [455, 521, 523],
                       490: [456, 458, 522, 524],
                       491: [459, 523, 525],
                       492: [458, 460, 524, 526],
                       494: [460, 462, 526, 528],
                       495: [461, 462, 527],
                       496: [464, 497, 530],
                       497: [463, 465, 496, 529, 530, 531],
                       498: [464, 466, 499, 530, 531, 532],
                       499: [465, 467, 498, 500, 531, 532, 533],
                       500: [466, 468, 499, 501, 532, 534],
                       501: [467, 469, 500, 533, 534, 535],
                       502: [468, 470, 534, 536],
                       503: [469, 535, 537],
                       504: [470, 472, 536, 538],
                       505: [473, 537, 539],
                       506: [472, 473, 474, 538, 540],
                       507: [473, 474, 475, 539, 540, 541],
                       508: [474, 475, 476, 509, 540, 542],
                       509: [475, 477, 508, 510, 541, 543],
                       510: [476, 478, 509, 542, 543, 544],
                       511: [477, 478, 479, 543, 544, 545],
                       512: [478, 479, 480, 513, 544, 546],
                       513: [479, 481, 512, 514, 545, 547],
                       514: [480, 482, 513, 546, 547, 548],
                       515: [481, 482, 483, 547, 548, 549],
                       516: [482, 483, 484, 517, 548, 550],
                       517: [483, 485, 516, 518, 549, 551],
                       518: [484, 486, 517, 519, 550, 552],
                       519: [485, 487, 518, 520, 551, 553],
                       520: [486, 488, 519, 521, 552, 554],
                       521: [487, 489, 520, 522, 553, 554, 555],
                       522: [488, 490, 521, 554, 555, 556],
                       523: [489, 491, 524, 555, 556, 557],
                       524: [490, 492, 523, 556, 558],
                       525: [491, 557, 559],
                       526: [492, 494, 558, 560],
                       527: [495, 559, 561],
                       528: [494, 560],
                       529: [497, 563],
                       530: [496, 497, 498, 562, 563, 564],
                       531: [497, 498, 499, 563, 564, 565],
                       532: [498, 499, 500, 564, 565, 566],
                       533: [499, 501, 534, 565, 566, 567],
                       534: [500, 501, 502, 533, 566, 568],
                       535: [501, 503, 567, 568, 569],
                       536: [502, 504, 537, 568, 569, 570],
                       537: [503, 505, 536, 569, 570, 571],
                       538: [504, 506, 539, 570, 571, 572],
                       539: [505, 507, 538, 571, 572, 573],
                       540: [506, 507, 508, 541, 572, 574],
                       541: [507, 509, 540, 542, 573, 574, 575],
                       542: [508, 510, 541, 574, 575, 576],
                       543: [509, 510, 511, 575, 576, 577],
                       544: [510, 511, 512, 545, 576, 578],
                       545: [511, 513, 544, 546, 577, 579],
                       546: [512, 514, 545, 578, 580],
                       547: [513, 514, 515, 548, 579, 581],
                       548: [514, 515, 516, 547, 549, 580, 582],
                       549: [515, 517, 548, 550, 581, 583],
                       550: [516, 518, 549, 551, 582, 584],
                       551: [517, 519, 550, 583, 584, 585],
                       552: [518, 520, 553, 584, 586],
                       553: [519, 521, 552, 585, 586, 587],
                       554: [520, 521, 522, 586, 587, 588],
                       555: [521, 522, 523, 587, 588, 589],
                       556: [522, 523, 524, 588, 589, 590],
                       557: [523, 525, 558, 589, 590, 591],
                       558: [524, 526, 557, 559, 590, 592],
                       559: [525, 527, 558, 591, 593],
                       560: [526, 528, 592, 593, 594],
                       561: [527, 593, 594],
                       562: [530, 596],
                       563: [529, 530, 531, 595, 596, 597],
                       564: [530, 531, 532, 596, 598],
                       565: [531, 532, 533, 566, 597, 599],
                       566: [532, 533, 534, 565, 598, 600],
                       567: [533, 535, 568, 599, 600, 601],
                       568: [534, 535, 536, 567, 600, 602],
                       569: [535, 536, 537, 601, 602, 603],
                       570: [536, 537, 538, 602, 603, 604],
                       571: [537, 538, 539, 603, 604, 605],
                       572: [538, 539, 540, 573, 604, 606],
                       573: [539, 541, 572, 605, 607],
                       574: [540, 541, 542, 575, 606, 608],
                       575: [541, 542, 543, 574, 607, 609],
                       576: [542, 543, 544, 608, 609, 610],
                       577: [543, 545, 609, 610, 611],
                       578: [544, 546, 610],
                       579: [545, 547, 611, 613],
                       580: [546, 548, 614],
                       581: [547, 549, 582, 613, 614, 615],
                       582: [548, 550, 581, 583, 614, 616],
                       583: [549, 551, 582, 615, 617],
                       584: [550, 551, 552, 616, 617, 618],
                       585: [551, 553, 586, 617, 618, 619],
                       586: [552, 553, 554, 585, 618, 620],
                       587: [553, 554, 555, 588, 619, 621],
                       588: [554, 555, 556, 587, 620, 622],
                       589: [555, 556, 557, 621, 622, 623],
                       590: [556, 557, 558, 591, 622, 624],
                       591: [557, 559, 590, 592, 623, 625],
                       592: [558, 560, 591, 593, 624, 626],
                       593: [559, 560, 561, 592, 625, 627],
                       594: [560, 561, 626],
                       595: [563, 628, 629],
                       596: [562, 563, 564, 628, 630],
                       597: [563, 565, 629],
                       598: [564, 566, 630, 632],
                       599: [565, 567, 633],
                       600: [566, 567, 568, 632, 633, 634],
                       601: [567, 569, 633, 634, 635],
                       602: [568, 569, 570, 603, 634, 636],
                       603: [569, 570, 571, 602, 635, 637],
                       604: [570, 571, 572, 636, 637, 638],
                       605: [571, 573, 606, 637, 638, 639],
                       606: [572, 574, 605, 607, 638, 639, 640],
                       607: [573, 575, 606, 608, 639, 641],
                       608: [574, 576, 607, 609, 640, 642],
                       609: [575, 576, 577, 608, 641, 643],
                       610: [576, 577, 578, 642, 644],
                       611: [577, 579, 643, 645],
                       613: [579, 581, 645, 647],
                       614: [580, 581, 582, 646, 647, 648],
                       615: [581, 583, 616, 647, 648, 649],
                       616: [582, 584, 615, 617, 648, 650],
                       617: [583, 584, 585, 616, 649, 651],
                       618: [584, 585, 586, 650, 651, 652],
                       619: [585, 587, 620, 651, 652, 653],
                       620: [586, 588, 619, 652, 653, 654],
                       621: [587, 589, 622, 653, 654, 655],
                       622: [588, 589, 590, 621, 623, 654, 656],
                       623: [589, 591, 622, 624, 655, 657],
                       624: [590, 592, 623, 625, 656, 658],
                       625: [591, 593, 624, 657, 658, 659],
                       626: [592, 594, 627, 658, 659, 660],
                       627: [593, 626, 659],
                       628: [595, 596, 662],
                       629: [595, 597, 661, 662, 663],
                       630: [596, 598, 662, 664],
                       632: [598, 600, 664, 666],
                       633: [599, 600, 601, 665, 667],
                       634: [600, 601, 602, 666, 667, 668],
                       635: [601, 603, 636, 667, 668, 669],
                       636: [602, 604, 635, 637, 668, 670],
                       637: [603, 604, 605, 636, 669, 670, 671],
                       638: [604, 605, 606, 670, 671, 672],
                       639: [605, 606, 607, 671, 673],
                       640: [606, 608, 641, 672, 674],
                       641: [607, 609, 640, 673, 675],
                       642: [608, 610, 643, 674, 676],
                       643: [609, 611, 642, 675, 677],
                       644: [610, 676, 678],
                       645: [611, 613, 677, 679],
                       646: [614, 678, 680],
                       647: [613, 614, 615, 648, 679, 681],
                       648: [614, 615, 616, 647, 680, 681, 682],
                       649: [615, 617, 681, 682, 683],
                       650: [616, 618, 651, 682, 684],
                       651: [617, 618, 619, 650, 683, 684, 685],
                       652: [618, 619, 620, 684, 685, 686],
                       653: [619, 620, 621, 685, 687],
                       654: [620, 621, 622, 686, 688],
                       655: [621, 623, 656, 687, 689],
                       656: [622, 624, 655, 688, 690],
                       657: [623, 625, 658, 689, 690, 691],
                       658: [624, 625, 626, 657, 659, 690, 692],
                       659: [625, 626, 627, 658, 691, 693],
                       660: [626, 692, 693],
                       661: [629, 694, 695],
                       662: [628, 629, 630, 694, 696],
                       663: [629, 695, 697],
                       664: [630, 632, 696, 698],
                       665: [633, 697, 699],
                       666: [632, 634, 667, 698, 700],
                       667: [633, 634, 635, 666, 699, 700, 701],
                       668: [634, 635, 636, 700, 701, 702],
                       669: [635, 637, 701, 702, 703],
                       670: [636, 637, 638, 702, 704],
                       671: [637, 638, 639, 703, 704, 705],
                       672: [638, 640, 704, 705, 706],
                       673: [639, 641, 705],
                       674: [640, 642, 706, 708],
                       675: [641, 643, 709],
                       676: [642, 644, 677, 708, 709, 710],
                       677: [643, 645, 676, 709, 711],
                       678: [644, 646, 710, 711, 712],
                       679: [645, 647, 680, 711, 712, 713],
                       680: [646, 648, 679, 712, 713, 714],
                       681: [647, 648, 649, 682, 713, 715],
                       682: [648, 649, 650, 681, 714, 715, 716],
                       683: [649, 651, 684, 715, 716, 717],
                       684: [650, 651, 652, 683, 716, 718],
                       685: [651, 652, 653, 686, 717, 719],
                       686: [652, 654, 685, 718, 720],
                       687: [653, 655, 719],
                       688: [654, 656, 720, 722],
                       689: [655, 657, 723],
                       690: [656, 657, 658, 691, 722, 724],
                       691: [657, 659, 690, 692, 723, 725],
                       692: [658, 660, 691, 724, 725, 726],
                       693: [659, 660, 725],
                       694: [661, 662, 695, 728],
                       695: [661, 663, 694, 696, 727, 729],
                       696: [662, 664, 695, 697, 728, 730],
                       697: [663, 665, 696, 729, 730, 731],
                       698: [664, 666, 699, 730, 731, 732],
                       699: [665, 667, 698, 700, 731, 732, 733],
                       700: [666, 667, 668, 699, 732, 734],
                       701: [667, 668, 669, 733, 734, 735],
                       702: [668, 669, 670, 703, 734, 736],
                       703: [669, 671, 702, 704, 735, 737],
                       704: [670, 671, 672, 703, 736, 738],
                       705: [671, 672, 673, 737, 739],
                       706: [672, 674, 738, 740],
                       708: [674, 676, 740, 742],
                       709: [675, 676, 677, 710, 741, 743],
                       710: [676, 678, 709, 742, 743, 744],
                       711: [677, 678, 679, 712, 743, 745],
                       712: [678, 679, 680, 711, 744, 746],
                       713: [679, 680, 681, 714, 745, 747],
                       714: [680, 682, 713, 715, 746, 748],
                       715: [681, 682, 683, 714, 747, 749],
                       716: [682, 683, 684, 748, 749, 750],
                       717: [683, 685, 718, 749, 750, 751],
                       718: [684, 686, 717, 719, 750, 752],
                       719: [685, 687, 718, 751, 753],
                       720: [686, 688, 752, 754],
                       722: [688, 690, 754, 756],
                       723: [689, 691, 755, 756, 757],
                       724: [690, 692, 725, 756, 758],
                       725: [691, 692, 693, 724, 726, 757, 759],
                       726: [692, 725, 758],
                       727: [695, 728, 761],
                       728: [694, 696, 727, 729, 760, 762],
                       729: [695, 697, 728, 761, 762, 763],
                       730: [696, 697, 698, 762, 763, 764],
                       731: [697, 698, 699, 763, 764, 765],
                       732: [698, 699, 700, 733, 764, 766],
                       733: [699, 701, 732, 765, 767],
                       734: [700, 701, 702, 735, 766, 767, 768],
                       735: [701, 703, 734, 736, 767, 769],
                       736: [702, 704, 735, 737, 768, 769, 770],
                       737: [703, 705, 736, 738, 769, 771],
                       738: [704, 706, 737, 770, 772],
                       739: [705, 771, 773],
                       740: [706, 708, 772, 774],
                       741: [709, 773, 775],
                       742: [708, 710, 743, 774, 776],
                       743: [709, 710, 711, 742, 775, 776, 777],
                       744: [710, 712, 776, 777, 778],
                       745: [711, 713, 746, 777, 779],
                       746: [712, 714, 745, 747, 778, 779, 780],
                       747: [713, 715, 746, 779, 780, 781],
                       748: [714, 716, 749, 780, 781, 782],
                       749: [715, 716, 717, 748, 781, 783],
                       750: [716, 717, 718, 782, 783, 784],
                       751: [717, 719, 752, 783, 784, 785],
                       752: [718, 720, 751, 784, 785, 786],
                       753: [719, 785, 787],
                       754: [720, 722, 786, 788],
                       755: [723, 787, 789],
                       756: [722, 723, 724, 757, 788, 790],
                       757: [723, 725, 756, 789, 790, 791],
                       758: [724, 726, 759, 790, 791, 792],
                       759: [725, 758, 791],
                       760: [728, 794],
                       761: [727, 729, 762, 793, 794, 795],
                       762: [728, 729, 730, 761, 794, 795, 796],
                       763: [729, 730, 731, 795, 796, 797],
                       764: [730, 731, 732, 765, 796, 798],
                       765: [731, 733, 764, 797, 798, 799],
                       766: [732, 734, 767, 798, 799, 800],
                       767: [733, 734, 735, 766, 799, 801],
                       768: [734, 736, 769, 800, 802],
                       769: [735, 736, 737, 768, 801, 803],
                       770: [736, 738, 771, 802, 803, 804],
                       771: [737, 739, 770, 772, 803, 805],
                       772: [738, 740, 771, 804, 805, 806],
                       773: [739, 741, 774, 805, 807],
                       774: [740, 742, 773, 775, 806, 808],
                       775: [741, 743, 774, 807, 808, 809],
                       776: [742, 743, 744, 777, 808, 810],
                       777: [743, 744, 745, 776, 809, 811],
                       778: [744, 746, 779, 810, 811, 812],
                       779: [745, 746, 747, 778, 811, 813],
                       780: [746, 747, 748, 812, 813, 814],
                       781: [747, 748, 749, 813, 815],
                       782: [748, 750, 783, 814, 815, 816],
                       783: [749, 750, 751, 782, 815, 817],
                       784: [750, 751, 752, 816, 817, 818],
                       785: [751, 752, 753, 817, 818, 819],
                       786: [752, 754, 818, 819, 820],
                       787: [753, 755, 819, 820, 821],
                       788: [754, 756, 789, 820, 822],
                       789: [755, 757, 788, 821, 823],
                       790: [756, 757, 758, 822, 823, 824],
                       791: [757, 758, 759, 823, 824, 825],
                       792: [758, 824, 825],
                       793: [761, 794, 827],
                       794: [760, 761, 762, 793, 826, 828],
                       795: [761, 762, 763, 827, 828, 829],
                       796: [762, 763, 764, 828, 829, 830],
                       797: [763, 765, 829, 830, 831],
                       798: [764, 765, 766, 830, 831, 832],
                       799: [765, 766, 767, 800, 831, 833],
                       800: [766, 768, 799, 801, 832, 834],
                       801: [767, 769, 800, 802, 833, 834, 835],
                       802: [768, 770, 801, 834, 835, 836],
                       803: [769, 770, 771, 804, 835, 837],
                       804: [770, 772, 803, 836, 838],
                       805: [771, 772, 773, 806, 837, 839],
                       806: [772, 774, 805, 807, 838, 840],
                       807: [773, 775, 806, 808, 839, 841],
                       808: [774, 775, 776, 807, 840, 842],
                       809: [775, 777, 810, 841, 842, 843],
                       810: [776, 778, 809, 811, 842, 843, 844],
                       811: [777, 778, 779, 810, 843, 845],
                       812: [778, 780, 813, 844, 845, 846],
                       813: [779, 780, 781, 812, 814, 845, 847],
                       814: [780, 782, 813, 815, 846, 848],
                       815: [781, 782, 783, 814, 847, 849],
                       816: [782, 784, 817, 848, 849, 850],
                       817: [783, 784, 785, 816, 849, 851],
                       818: [784, 785, 786, 850, 851, 852],
                       819: [785, 786, 787, 851, 852, 853],
                       820: [786, 787, 788, 821, 852, 853, 854],
                       821: [787, 789, 820, 822, 853, 855],
                       822: [788, 790, 821, 854, 856],
                       823: [789, 790, 791, 855, 857],
                       824: [790, 791, 792, 856, 857, 858],
                       825: [791, 792, 857],
                       826: [794, 859, 860],
                       827: [793, 795, 828, 859, 860, 861],
                       828: [794, 795, 796, 827, 860, 862],
                       829: [795, 796, 797, 861, 863],
                       830: [796, 797, 798, 831, 862, 864],
                       831: [797, 798, 799, 830, 863, 865],
                       832: [798, 800, 833, 864, 866],
                       833: [799, 801, 832, 865, 867],
                       834: [800, 801, 802, 866, 868],
                       835: [801, 802, 803, 836, 867, 869],
                       836: [802, 804, 835, 837, 868, 870],
                       837: [803, 805, 836, 838, 869, 871],
                       838: [804, 806, 837, 839, 870, 872],
                       839: [805, 807, 838, 871, 872, 873],
                       840: [806, 808, 841, 872, 873, 874],
                       841: [807, 809, 840, 873, 874, 875],
                       842: [808, 809, 810, 843, 874, 876],
                       843: [809, 810, 811, 842, 875, 877],
                       844: [810, 812, 845, 876, 877, 878],
                       845: [811, 812, 813, 844, 877, 879],
                       846: [812, 814, 847, 878, 879, 880],
                       847: [813, 815, 846, 848, 879, 881],
                       848: [814, 816, 847, 849, 880, 882],
                       849: [815, 816, 817, 848, 881, 883],
                       850: [816, 818, 882, 883, 884],
                       851: [817, 818, 819, 883, 884, 885],
                       852: [818, 819, 820, 884, 885, 886],
                       853: [819, 820, 821, 885, 887],
                       854: [820, 822, 886],
                       855: [821, 823, 887, 889],
                       856: [822, 824, 890],
                       857: [823, 824, 825, 889, 890, 891],
                       858: [824, 890, 891],
                       859: [826, 827, 893],
                       860: [826, 827, 828, 861, 892, 894],
                       861: [827, 829, 860, 862, 893, 894, 895],
                       862: [828, 830, 861, 863, 894, 896],
                       863: [829, 831, 862, 864, 895, 897],
                       864: [830, 832, 863, 896, 897, 898],
                       865: [831, 833, 897],
                       866: [832, 834, 898, 900],
                       867: [833, 835, 901],
                       868: [834, 836, 900, 901, 902],
                       869: [835, 837, 870, 901, 902, 903],
                       870: [836, 838, 869, 871, 902, 904],
                       871: [837, 839, 870, 903, 904, 905],
                       872: [838, 839, 840, 873, 904, 905, 906],
                       873: [839, 840, 841, 872, 905, 907],
                       874: [840, 841, 842, 906, 907, 908],
                       875: [841, 843, 876, 907, 908, 909],
                       876: [842, 844, 875, 908, 909, 910],
                       877: [843, 844, 845, 878, 909, 911],
                       878: [844, 846, 877, 910, 911, 912],
                       879: [845, 846, 847, 911, 912, 913],
                       880: [846, 848, 881, 912, 913, 914],
                       881: [847, 849, 880, 882, 913, 915],
                       882: [848, 850, 881, 883, 914, 916],
                       883: [849, 850, 851, 882, 915, 917],
                       884: [850, 851, 852, 885, 916, 918],
                       885: [851, 852, 853, 884, 917, 919],
                       886: [852, 854, 918, 919, 920],
                       887: [853, 855, 919, 921],
                       889: [855, 857, 921, 923],
                       890: [856, 857, 858, 922, 924],
                       891: [857, 858, 923],
                       892: [860, 893, 926],
                       893: [859, 861, 892, 925, 926, 927],
                       894: [860, 861, 862, 926, 927, 928],
                       895: [861, 863, 896, 927, 929],
                       896: [862, 864, 895, 928, 929, 930],
                       897: [863, 864, 865, 929, 930, 931],
                       898: [864, 866, 930, 932],
                       900: [866, 868, 932, 934],
                       901: [867, 868, 869, 933, 934, 935],
                       902: [868, 869, 870, 903, 934, 935, 936],
                       903: [869, 871, 902, 904, 935, 937],
                       904: [870, 871, 872, 903, 936, 938],
                       905: [871, 872, 873, 937, 938, 939],
                       906: [872, 874, 907, 938, 939, 940],
                       907: [873, 874, 875, 906, 939, 941],
                       908: [874, 875, 876, 940, 941, 942],
                       909: [875, 876, 877, 941, 942, 943],
                       910: [876, 878, 911, 942, 943, 944],
                       911: [877, 878, 879, 910, 943, 945],
                       912: [878, 879, 880, 944, 945, 946],
                       913: [879, 880, 881, 945, 946, 947],
                       914: [880, 882, 915, 946, 947, 948],
                       915: [881, 883, 914, 916, 947, 949],
                       916: [882, 884, 915, 917, 948, 950],
                       917: [883, 885, 916, 949, 950, 951],
                       918: [884, 886, 919, 950, 951, 952],
                       919: [885, 886, 887, 918, 951, 953],
                       920: [886, 952, 954],
                       921: [887, 889, 953, 955],
                       922: [890, 954, 956],
                       923: [889, 891, 955, 957],
                       924: [890, 956],
                       925: [893, 926, 959],
                       926: [892, 893, 894, 925, 958, 960],
                       927: [893, 894, 895, 928, 959, 961],
                       928: [894, 896, 927, 929, 960, 961, 962],
                       929: [895, 896, 897, 928, 961, 963],
                       930: [896, 897, 898, 962, 963, 964],
                       931: [897, 963, 965],
                       932: [898, 900, 964, 966],
                       933: [901, 965, 967],
                       934: [900, 901, 902, 966, 967, 968],
                       935: [901, 902, 903, 936, 967, 969],
                       936: [902, 904, 935, 968, 969, 970],
                       937: [903, 905, 938, 969, 970, 971],
                       938: [904, 905, 906, 937, 970, 972],
                       939: [905, 906, 907, 940, 971, 973],
                       940: [906, 908, 939, 972, 973, 974],
                       941: [907, 908, 909, 973, 975],
                       942: [908, 909, 910, 974, 975, 976],
                       943: [909, 910, 911, 975, 976, 977],
                       944: [910, 912, 945, 976, 977, 978],
                       945: [911, 912, 913, 944, 977, 978, 979],
                       946: [912, 913, 914, 978, 979, 980],
                       947: [913, 914, 915, 979, 980, 981],
                       948: [914, 916, 949, 980, 981, 982],
                       949: [915, 917, 948, 981, 982, 983],
                       950: [916, 917, 918, 951, 982, 984],
                       951: [917, 918, 919, 950, 983, 985],
                       952: [918, 920, 953, 984, 985, 986],
                       953: [919, 921, 952, 985, 986, 987],
                       954: [920, 922, 955, 986, 987, 988],
                       955: [921, 923, 954, 987, 989],
                       956: [922, 924, 988, 989, 990],
                       957: [923, 989, 990],
                       958: [926, 959, 992],
                       959: [925, 927, 958, 960, 991, 993],
                       960: [926, 928, 959, 992, 993, 994],
                       961: [927, 928, 929, 962, 993, 995],
                       962: [928, 930, 961, 963, 994, 996],
                       963: [929, 930, 931, 962, 995, 996, 997],
                       964: [930, 932, 996, 997, 998],
                       965: [931, 933, 997, 999],
                       966: [932, 934, 998, 999, 1000],
                       967: [933, 934, 935, 999, 1000, 1001],
                       968: [934, 936, 969, 1000, 1002],
                       969: [935, 936, 937, 968, 970, 1001, 1003],
                       970: [936, 937, 938, 969, 1002, 1004],
                       971: [937, 939, 972, 1003, 1005],
                       972: [938, 940, 971, 1004, 1005, 1006],
                       973: [939, 940, 941, 974, 1005, 1007],
                       974: [940, 942, 973, 1006, 1007, 1008],
                       975: [941, 942, 943, 976, 1007, 1009],
                       976: [942, 943, 944, 975, 1008, 1009, 1010],
                       977: [943, 944, 945, 1009, 1011],
                       978: [944, 945, 946, 979, 1010, 1012],
                       979: [945, 946, 947, 978, 1011, 1013],
                       980: [946, 947, 948, 1012, 1013, 1014],
                       981: [947, 948, 949, 1013, 1014, 1015],
                       982: [948, 949, 950, 983, 1014, 1016],
                       983: [949, 951, 982, 984, 1015, 1017],
                       984: [950, 952, 983, 1016, 1017, 1018],
                       985: [951, 952, 953, 986, 1017, 1019],
                       986: [952, 953, 954, 985, 1018, 1019, 1020],
                       987: [953, 954, 955, 988, 1019, 1021],
                       988: [954, 956, 987, 1020, 1021, 1022],
                       989: [955, 956, 957, 1021, 1022, 1023],
                       990: [956, 957, 1022],
                       991: [959, 992, 1025],
                       992: [958, 960, 991, 1024, 1025, 1026],
                       993: [959, 960, 961, 994, 1025, 1027],
                       994: [960, 962, 993, 1026, 1027, 1028],
                       995: [961, 963, 996, 1027, 1028, 1029],
                       996: [962, 963, 964, 995, 1028, 1030],
                       997: [963, 964, 965, 998, 1029, 1031],
                       998: [964, 966, 997, 1030, 1031, 1032],
                       999: [965, 966, 967, 1000, 1031, 1033],
                       1000: [966, 967, 968, 999, 1001, 1032, 1034],
                       1001: [967, 969, 1000, 1002, 1033, 1035],
                       1002: [968, 970, 1001, 1034, 1035, 1036],
                       1003: [969, 971, 1004, 1035, 1037],
                       1004: [970, 972, 1003, 1005, 1036, 1038],
                       1005: [971, 972, 973, 1004, 1037, 1039],
                       1006: [972, 974, 1007, 1038, 1039, 1040],
                       1007: [973, 974, 975, 1006, 1039, 1040, 1041],
                       1008: [974, 976, 1040, 1041, 1042],
                       1009: [975, 976, 977, 1010, 1041, 1043],
                       1010: [976, 978, 1009, 1011, 1042, 1044],
                       1011: [977, 979, 1010, 1043, 1044, 1045],
                       1012: [978, 980, 1013, 1044, 1045, 1046],
                       1013: [979, 980, 981, 1012, 1045, 1047],
                       1014: [980, 981, 982, 1046, 1047, 1048],
                       1015: [981, 983, 1047, 1048, 1049],
                       1016: [982, 984, 1017, 1048, 1050],
                       1017: [983, 984, 985, 1016, 1018, 1049, 1051],
                       1018: [984, 986, 1017, 1019, 1050, 1052],
                       1019: [985, 986, 987, 1018, 1051, 1053],
                       1020: [986, 988, 1052, 1053, 1054],
                       1021: [987, 988, 989, 1053, 1054, 1055],
                       1022: [988, 989, 990, 1023, 1054, 1055, 1056],
                       1023: [989, 1022, 1055],
                       1024: [992, 1058],
                       1025: [991, 992, 993, 1026, 1057, 1058, 1059],
                       1026: [992, 994, 1025, 1058, 1059, 1060],
                       1027: [993, 994, 995, 1059, 1060, 1061],
                       1028: [994, 995, 996, 1060, 1061, 1062],
                       1029: [995, 997, 1030, 1061, 1062, 1063],
                       1030: [996, 998, 1029, 1031, 1062, 1064],
                       1031: [997, 998, 999, 1030, 1063, 1065],
                       1032: [998, 1000, 1033, 1064, 1065, 1066],
                       1033: [999, 1001, 1032, 1034, 1065, 1067],
                       1034: [1000, 1002, 1033, 1066, 1067, 1068],
                       1035: [1001, 1002, 1003, 1067, 1069],
                       1036: [1002, 1004, 1068],
                       1037: [1003, 1005, 1069, 1071],
                       1038: [1004, 1006, 1072],
                       1039: [1005, 1006, 1007, 1071, 1073],
                       1040: [1006, 1007, 1008, 1072, 1073, 1074],
                       1041: [1007, 1008, 1009, 1042, 1073, 1075],
                       1042: [1008, 1010, 1041, 1074, 1076],
                       1043: [1009, 1011, 1044, 1075, 1076, 1077],
                       1044: [1010, 1011, 1012, 1043, 1076, 1077, 1078],
                       1045: [1011, 1012, 1013, 1077, 1078, 1079],
                       1046: [1012, 1014, 1047, 1078, 1079, 1080],
                       1047: [1013, 1014, 1015, 1046, 1079, 1081],
                       1048: [1014, 1015, 1016, 1049, 1080, 1082],
                       1049: [1015, 1017, 1048, 1081, 1082, 1083],
                       1050: [1016, 1018, 1051, 1082, 1083, 1084],
                       1051: [1017, 1019, 1050, 1052, 1083, 1085],
                       1052: [1018, 1020, 1051, 1053, 1084, 1086],
                       1053: [1019, 1020, 1021, 1052, 1085, 1087],
                       1054: [1020, 1021, 1022, 1055, 1086, 1088],
                       1055: [1021, 1022, 1023, 1054, 1087, 1089],
                       1056: [1022, 1088, 1089],
                       1057: [1025],
                       1058: [1024, 1025, 1026],
                       1059: [1025, 1026, 1027],
                       1060: [1026, 1027, 1028],
                       1061: [1027, 1028, 1029],
                       1062: [1028, 1029, 1030],
                       1063: [1029, 1031],
                       1064: [1030, 1032, 1065],
                       1065: [1031, 1032, 1033, 1064],
                       1066: [1032, 1034],
                       1067: [1033, 1034, 1035],
                       1068: [1034, 1036],
                       1069: [1035, 1037],
                       1071: [1037, 1039],
                       1072: [1038, 1040, 1073],
                       1073: [1039, 1040, 1041, 1072],
                       1074: [1040, 1042],
                       1075: [1041, 1043],
                       1076: [1042, 1043, 1044],
                       1077: [1043, 1044, 1045],
                       1078: [1044, 1045, 1046],
                       1079: [1045, 1046, 1047],
                       1080: [1046, 1048, 1081],
                       1081: [1047, 1049, 1080],
                       1082: [1048, 1049, 1050],
                       1083: [1049, 1050, 1051],
                       1084: [1050, 1052, 1085],
                       1085: [1051, 1053, 1084],
                       1086: [1052, 1054, 1087],
                       1087: [1053, 1055, 1086],
                       1088: [1054, 1056],
                       1089: [1055, 1056]}
cycle_17_links = {2: [34, 36],
3: [35, 37],
4: [36, 38],
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6: [5, 38, 40],
7: [39, 40, 41],
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25: [57, 58, 59],
26: [27, 58, 60],
27: [26, 59, 61],
28: [60, 62],
29: [61, 63],
31: [63, 65],
32: [64, 66],
34: [2, 68],
35: [3, 67],
36: [2, 4, 68, 70],
37: [3, 5, 71],
38: [4, 5, 6, 70, 72],
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46: [12, 14, 45, 78, 79, 80],
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51: [17, 19, 52, 83, 85],
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63: [29, 31, 95, 97],
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66: [32, 98],
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91: [57, 59, 125],
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100: [68, 133, 134],
101: [67, 133, 135],
102: [68, 70, 134, 136],
103: [71, 135, 137],
104: [70, 71, 72, 105, 136, 138],
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106: [72, 74, 107, 138, 139, 140],
107: [73, 75, 106, 139, 141],
108: [74, 76, 140],
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110: [76, 78, 144],
111: [77, 79, 112, 143, 145],
112: [78, 79, 80, 111, 144, 146],
113: [79, 80, 81, 145, 146, 147],
114: [80, 81, 82, 115, 146, 148],
115: [81, 83, 114, 116, 147, 148, 149],
116: [82, 83, 84, 115, 148, 150],
117: [83, 84, 85, 149, 150, 151],
118: [84, 86, 119, 150, 151, 152],
119: [85, 86, 87, 118, 151, 153],
120: [86, 87, 88, 121, 152, 153, 154],
121: [87, 89, 120, 153, 154, 155],
122: [88, 90, 154, 156],
124: [90, 92, 156, 158],
125: [91, 92, 93, 157, 158, 159],
126: [92, 94, 127, 158, 159, 160],
127: [93, 95, 126, 159, 160, 161],
128: [94, 95, 96, 129, 160, 162],
129: [95, 97, 128, 130, 161, 163],
130: [96, 98, 129, 162, 163, 164],
131: [97, 99, 132, 163, 165],
132: [98, 131, 164],
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134: [100, 102, 166, 167, 168],
135: [101, 103, 136, 167, 169],
136: [102, 104, 135, 137, 168, 170],
137: [103, 105, 136, 169, 171],
138: [104, 106, 139, 170, 171, 172],
139: [105, 106, 107, 138, 171, 173],
140: [106, 108, 172, 173, 174],
141: [107, 109, 173, 175],
143: [109, 111, 175, 177],
144: [110, 112, 176, 177, 178],
145: [111, 113, 146, 177, 178, 179],
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150: [116, 117, 118, 149, 182, 184],
151: [117, 118, 119, 152, 183, 185],
152: [118, 120, 151, 184, 186],
153: [119, 120, 121, 185, 186, 187],
154: [120, 121, 122, 186, 187, 188],
155: [121, 187, 189],
156: [122, 124, 188, 190],
157: [125, 189, 191],
158: [124, 125, 126, 190, 192],
159: [125, 126, 127, 160, 191, 192, 193],
160: [126, 127, 128, 159, 192, 194],
161: [127, 129, 162, 193, 195],
162: [128, 130, 161, 194, 196],
163: [129, 130, 131, 164, 195, 197],
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165: [131, 164, 197],
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170: [136, 138, 204],
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174: [140, 206, 208],
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186: [152, 153, 154, 218, 219, 220],
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188: [154, 156, 187, 189, 220, 222],
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190: [156, 158, 222, 223, 224],
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210: [176, 178, 209, 242, 243, 244],
211: [177, 178, 179, 243, 244, 245],
212: [178, 180, 213, 244, 245, 246],
213: [179, 180, 181, 212, 245, 246, 247],
214: [180, 181, 182, 246, 248],
215: [181, 182, 183, 216, 247, 249],
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220: [186, 187, 188, 221, 252, 254],
221: [187, 189, 220, 253, 254, 255],
222: [188, 189, 190, 254, 255, 256],
223: [189, 190, 191, 255, 256, 257],
224: [190, 191, 192, 225, 256, 258],
225: [191, 193, 224, 257, 258, 259],
226: [192, 194, 258, 260],
228: [194, 196, 260, 262],
229: [195, 197, 261, 262, 263],
230: [196, 197, 198, 262, 263, 264],
231: [197, 263],
232: [200, 233, 266],
233: [199, 201, 232, 265, 267],
234: [200, 266, 268],
235: [201, 203, 267, 269],
236: [204, 268, 270],
237: [203, 205, 269, 270, 271],
238: [204, 205, 206, 270, 271, 272],
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240: [206, 207, 208, 239, 241, 272, 274],
241: [207, 209, 240, 273, 274, 275],
242: [208, 209, 210, 274, 276],
243: [209, 210, 211, 275, 276, 277],
244: [210, 211, 212, 276, 277, 278],
245: [211, 212, 213, 277, 279],
246: [212, 213, 214, 278, 279, 280],
247: [213, 215, 248, 279, 280, 281],
248: [214, 216, 247, 249, 280, 281, 282],
249: [215, 217, 248, 250, 281, 283],
250: [216, 217, 218, 249, 282, 283, 284],
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257: [223, 225, 256, 258, 289, 291],
258: [224, 225, 226, 257, 290, 292],
259: [225, 291, 293],
260: [226, 228, 292, 294],
261: [229, 293, 295],
262: [228, 229, 230, 294, 295, 296],
263: [229, 230, 231, 295, 296, 297],
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282: [248, 250, 281, 314, 315, 316],
283: [249, 250, 251, 315, 316, 317],
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520: [486, 488, 519, 552, 553, 554],
521: [487, 488, 489, 522, 553, 555],
522: [488, 490, 521, 554, 556],
523: [489, 491, 524, 555, 556, 557],
524: [490, 492, 523, 556, 558],
525: [491, 557, 559],
526: [492, 494, 558, 560],
527: [495, 559, 561],
528: [494, 560],
529: [496, 497, 563],
530: [496, 497, 498, 531, 562, 564],
531: [497, 498, 499, 530, 563, 564, 565],
532: [498, 500, 564, 565, 566],
533: [499, 501, 534, 565, 566, 567],
534: [500, 502, 533, 566, 567, 568],
535: [501, 503, 567, 568, 569],
536: [502, 504, 537, 568, 570],
537: [503, 505, 536, 538, 569, 571],
538: [504, 506, 537, 539, 570, 572],
539: [505, 506, 507, 538, 540, 571, 573],
540: [506, 507, 508, 539, 572, 574],
541: [507, 508, 509, 573, 574, 575],
542: [508, 509, 510, 574, 575, 576],
543: [509, 510, 511, 575, 576, 577],
544: [510, 512, 545, 576, 577, 578],
545: [511, 513, 544, 577, 579],
546: [512, 514, 547, 578, 580],
547: [513, 515, 546, 548, 579, 581],
548: [514, 516, 547, 580, 582],
549: [515, 517, 550, 581, 582, 583],
550: [516, 518, 549, 582, 583, 584],
551: [517, 518, 519, 552, 583, 585],
552: [518, 520, 551, 584, 585, 586],
553: [519, 520, 521, 554, 585, 587],
554: [520, 522, 553, 555, 586, 588],
555: [521, 523, 554, 556, 587, 589],
556: [522, 523, 524, 555, 588, 589, 590],
557: [523, 525, 558, 589, 591],
558: [524, 526, 557, 559, 590, 591, 592],
559: [525, 527, 558, 560, 591, 593],
560: [526, 528, 559, 561, 592, 594],
561: [527, 560, 593],
562: [530, 563, 596],
563: [529, 531, 562, 595, 596, 597],
564: [530, 531, 532, 596, 598],
565: [531, 532, 533, 566, 597, 599],
566: [532, 533, 534, 565, 598, 600],
567: [533, 534, 535, 599, 600, 601],
568: [534, 535, 536, 569, 600, 602],
569: [535, 537, 568, 570, 601, 603],
570: [536, 538, 569, 602, 604],
571: [537, 539, 603, 604, 605],
572: [538, 540, 573, 604, 605, 606],
573: [539, 541, 572, 574, 605, 607],
574: [540, 541, 542, 573, 606, 608],
575: [541, 542, 543, 607, 608, 609],
576: [542, 543, 544, 608, 609, 610],
577: [543, 544, 545, 609, 610, 611],
578: [544, 546, 610],
579: [545, 547, 611, 613],
580: [546, 548, 614],
581: [547, 549, 582, 613, 615],
582: [548, 549, 550, 581, 614, 616],
583: [549, 550, 551, 584, 615, 617],
584: [550, 552, 583, 616, 617, 618],
585: [551, 552, 553, 586, 617, 619],
586: [552, 554, 585, 618, 619, 620],
587: [553, 555, 588, 619, 620, 621],
588: [554, 556, 587, 620, 621, 622],
589: [555, 556, 557, 590, 621, 623],
590: [556, 558, 589, 591, 622, 624],
591: [557, 558, 559, 590, 623, 625],
592: [558, 560, 593, 624, 625, 626],
593: [559, 561, 592, 594, 625, 627],
594: [560, 593, 626],
595: [563, 629],
596: [562, 563, 564, 628, 629, 630],
597: [563, 565, 629],
598: [564, 566, 630, 632],
599: [565, 567, 633],
600: [566, 567, 568, 632, 633, 634],
601: [567, 569, 633, 634, 635],
602: [568, 570, 603, 634, 635, 636],
603: [569, 571, 602, 635, 636, 637],
604: [570, 571, 572, 605, 636, 637, 638],
605: [571, 572, 573, 604, 637, 639],
606: [572, 574, 607, 638, 639, 640],
607: [573, 575, 606, 639, 640, 641],
608: [574, 575, 576, 640, 641, 642],
609: [575, 576, 577, 641, 642, 643],
610: [576, 577, 578, 642, 644],
611: [577, 579, 643, 645],
613: [579, 581, 645, 647],
614: [580, 582, 615, 646, 647, 648],
615: [581, 583, 614, 616, 647, 649],
616: [582, 584, 615, 648, 649, 650],
617: [583, 584, 585, 649, 650, 651],
618: [584, 586, 619, 650, 651, 652],
619: [585, 586, 587, 618, 651, 653],
620: [586, 587, 588, 652, 653, 654],
621: [587, 588, 589, 622, 653, 655],
622: [588, 590, 621, 654, 655, 656],
623: [589, 591, 624, 655, 657],
624: [590, 592, 623, 656, 657, 658],
625: [591, 592, 593, 626, 657, 659],
626: [592, 594, 625, 658, 659, 660],
627: [593, 659],
628: [596, 629, 662],
629: [595, 596, 597, 628, 661, 663],
630: [596, 598, 662, 664],
632: [598, 600, 664, 666],
633: [599, 600, 601, 665, 666, 667],
634: [600, 601, 602, 666, 667, 668],
635: [601, 602, 603, 667, 668, 669],
636: [602, 603, 604, 668, 669, 670],
637: [603, 604, 605, 638, 669, 671],
638: [604, 606, 637, 639, 670, 672],
639: [605, 606, 607, 638, 671, 672, 673],
640: [606, 607, 608, 672, 674],
641: [607, 608, 609, 673, 675],
642: [608, 609, 610, 643, 674, 676],
643: [609, 611, 642, 675, 677],
644: [610, 676, 678],
645: [611, 613, 677, 679],
646: [614, 678, 680],
647: [613, 614, 615, 679, 680, 681],
648: [614, 616, 649, 680, 681, 682],
649: [615, 616, 617, 648, 681, 683],
650: [616, 617, 618, 682, 683, 684],
651: [617, 618, 619, 683, 684, 685],
652: [618, 620, 653, 684, 685, 686],
653: [619, 620, 621, 652, 654, 685, 687],
654: [620, 622, 653, 655, 686, 688],
655: [621, 622, 623, 654, 687, 689],
656: [622, 624, 688, 690],
657: [623, 624, 625, 658, 689, 690, 691],
658: [624, 626, 657, 690, 691, 692],
659: [625, 626, 627, 660, 691, 693],
660: [626, 659, 692],
661: [629, 662, 695],
662: [628, 630, 661, 694, 696],
663: [629, 695, 697],
664: [630, 632, 696, 698],
665: [633, 697, 699],
666: [632, 633, 634, 698, 700],
667: [633, 634, 635, 699, 700, 701],
668: [634, 635, 636, 669, 700, 702],
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670: [636, 638, 671, 702, 703, 704],
671: [637, 639, 670, 703, 704, 705],
672: [638, 639, 640, 704, 706],
673: [639, 641, 705],
674: [640, 642, 706, 708],
675: [641, 643, 709],
676: [642, 644, 708, 709, 710],
677: [643, 645, 678, 709, 710, 711],
678: [644, 646, 677, 710, 712],
679: [645, 647, 680, 711, 712, 713],
680: [646, 647, 648, 679, 712, 714],
681: [647, 648, 649, 713, 714, 715],
682: [648, 650, 683, 714, 715, 716],
683: [649, 650, 651, 682, 715, 717],
684: [650, 651, 652, 685, 716, 717, 718],
685: [651, 652, 653, 684, 717, 719],
686: [652, 654, 718, 720],
687: [653, 655, 719],
688: [654, 656, 720, 722],
689: [655, 657, 723],
690: [656, 657, 658, 722, 723, 724],
691: [657, 658, 659, 692, 723, 725],
692: [658, 660, 691, 693, 724, 726],
693: [659, 692, 725, 726],
694: [662, 695, 728],
695: [661, 663, 694, 696, 727, 729],
696: [662, 664, 695, 697, 728, 730],
697: [663, 665, 696, 698, 729, 731],
698: [664, 666, 697, 730, 732],
699: [665, 667, 700, 731, 732, 733],
700: [666, 667, 668, 699, 732, 733, 734],
701: [667, 669, 702, 733, 735],
702: [668, 670, 701, 703, 734, 736],
703: [669, 670, 671, 702, 735, 737],
704: [670, 671, 672, 705, 736, 738],
705: [671, 673, 704, 737, 739],
706: [672, 674, 738, 740],
708: [674, 676, 740, 742],
709: [675, 676, 677, 741, 743],
710: [676, 677, 678, 742, 743, 744],
711: [677, 679, 712, 743, 744, 745],
712: [678, 679, 680, 711, 744, 746],
713: [679, 681, 714, 745, 746, 747],
714: [680, 681, 682, 713, 746, 747, 748],
715: [681, 682, 683, 747, 749],
716: [682, 684, 717, 748, 750],
717: [683, 684, 685, 716, 749, 751],
718: [684, 686, 719, 750, 751, 752],
719: [685, 687, 718, 751, 753],
720: [686, 688, 752, 754],
722: [688, 690, 754, 756],
723: [689, 690, 691, 755, 757],
724: [690, 692, 725, 756, 757, 758],
725: [691, 693, 724, 757, 758, 759],
726: [692, 693, 758],
727: [695, 760, 761],
728: [694, 696, 729, 760, 762],
729: [695, 697, 728, 761, 762, 763],
730: [696, 698, 731, 762, 763, 764],
731: [697, 699, 730, 732, 763, 765],
732: [698, 699, 700, 731, 764, 766],
733: [699, 700, 701, 734, 765, 767],
734: [700, 702, 733, 735, 766, 768],
735: [701, 703, 734, 767, 768, 769],
736: [702, 704, 737, 768, 769, 770],
737: [703, 705, 736, 769, 770, 771],
738: [704, 706, 770, 771, 772],
739: [705, 771, 773],
740: [706, 708, 772, 774],
741: [709, 773, 775],
742: [708, 710, 743, 774, 775, 776],
743: [709, 710, 711, 742, 775, 777],
744: [710, 711, 712, 776, 777, 778],
745: [711, 713, 746, 777, 778, 779],
746: [712, 713, 714, 745, 778, 780],
747: [713, 714, 715, 748, 779, 781],
748: [714, 716, 747, 749, 780, 781, 782],
749: [715, 717, 748, 750, 781, 783],
750: [716, 718, 749, 782, 783, 784],
751: [717, 718, 719, 752, 783, 785],
752: [718, 720, 751, 784, 785, 786],
753: [719, 785, 787],
754: [720, 722, 786, 788],
755: [723, 787, 789],
756: [722, 724, 757, 788, 790],
757: [723, 724, 725, 756, 789, 791],
758: [724, 725, 726, 759, 790, 792],
759: [725, 758, 791],
760: [727, 728, 761, 794],
761: [727, 729, 760, 793, 794, 795],
762: [728, 729, 730, 763, 794, 796],
763: [729, 730, 731, 762, 795, 797],
764: [730, 732, 765, 796, 798],
765: [731, 733, 764, 766, 797, 799],
766: [732, 734, 765, 767, 798, 800],
767: [733, 735, 766, 799, 800, 801],
768: [734, 735, 736, 800, 801, 802],
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771: [737, 738, 739, 772, 803, 805],
772: [738, 740, 771, 773, 804, 806],
773: [739, 741, 772, 774, 805, 807],
774: [740, 742, 773, 775, 806, 808],
775: [741, 742, 743, 774, 776, 807, 809],
776: [742, 744, 775, 777, 808, 810],
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778: [744, 745, 746, 779, 810, 812],
779: [745, 747, 778, 780, 811, 813],
780: [746, 748, 779, 812, 813, 814],
781: [747, 748, 749, 782, 813, 815],
782: [748, 750, 781, 814, 816],
783: [749, 750, 751, 815, 816, 817],
784: [750, 752, 785, 816, 817, 818],
785: [751, 752, 753, 784, 817, 819],
786: [752, 754, 818, 819, 820],
787: [753, 755, 788, 819, 821],
788: [754, 756, 787, 789, 820, 822],
789: [755, 757, 788, 821, 822, 823],
790: [756, 758, 791, 822, 823, 824],
791: [757, 759, 790, 792, 823, 825],
792: [758, 791, 824],
793: [761, 827],
794: [760, 761, 762, 795, 826, 827, 828],
795: [761, 763, 794, 796, 827, 829],
796: [762, 764, 795, 797, 828, 829, 830],
797: [763, 765, 796, 829, 830, 831],
798: [764, 766, 799, 830, 831, 832],
799: [765, 767, 798, 800, 831, 833],
800: [766, 767, 768, 799, 832, 834],
801: [767, 768, 769, 833, 834, 835],
802: [768, 769, 770, 803, 834, 836],
803: [769, 771, 802, 804, 835, 837],
804: [770, 772, 803, 836, 837, 838],
805: [771, 773, 806, 837, 838, 839],
806: [772, 774, 805, 807, 838, 840],
807: [773, 775, 806, 839, 840, 841],
808: [774, 776, 809, 840, 842],
809: [775, 777, 808, 841, 842, 843],
810: [776, 778, 811, 842, 843, 844],
811: [777, 779, 810, 843, 844, 845],
812: [778, 780, 813, 844, 845, 846],
813: [779, 780, 781, 812, 814, 845, 847],
814: [780, 782, 813, 815, 846, 848],
815: [781, 783, 814, 816, 847, 849],
816: [782, 783, 784, 815, 848, 850],
817: [783, 784, 785, 849, 851],
818: [784, 786, 819, 850, 851, 852],
819: [785, 786, 787, 818, 851, 852, 853],
820: [786, 788, 852, 853, 854],
821: [787, 789, 822, 853, 855],
822: [788, 789, 790, 821, 854, 856],
823: [789, 790, 791, 824, 855, 857],
824: [790, 792, 823, 825, 856, 858],
825: [791, 824, 857],
826: [794, 860],
827: [793, 794, 795, 828, 859, 861],
828: [794, 796, 827, 860, 861, 862],
829: [795, 796, 797, 861, 862, 863],
830: [796, 797, 798, 862, 863, 864],
831: [797, 798, 799, 832, 863, 865],
832: [798, 800, 831, 833, 864, 866],
833: [799, 801, 832, 834, 865, 867],
834: [800, 801, 802, 833, 835, 866, 868],
835: [801, 803, 834, 836, 867, 869],
836: [802, 804, 835, 837, 868, 870],
837: [803, 804, 805, 836, 869, 871],
838: [804, 805, 806, 839, 870, 871, 872],
839: [805, 807, 838, 840, 871, 873],
840: [806, 807, 808, 839, 841, 872, 874],
841: [807, 809, 840, 873, 874, 875],
842: [808, 809, 810, 874, 875, 876],
843: [809, 810, 811, 844, 875, 877],
844: [810, 811, 812, 843, 876, 877, 878],
845: [811, 812, 813, 877, 878, 879],
846: [812, 814, 847, 878, 880],
847: [813, 815, 846, 848, 879, 881],
848: [814, 816, 847, 880, 881, 882],
849: [815, 817, 850, 881, 882, 883],
850: [816, 818, 849, 851, 882, 884],
851: [817, 818, 819, 850, 883, 885],
852: [818, 819, 820, 884, 885, 886],
853: [819, 820, 821, 885, 887],
854: [820, 822, 886],
855: [821, 823, 887, 889],
856: [822, 824, 890],
857: [823, 825, 889, 890, 891],
858: [824, 890],
859: [827, 860, 892, 893],
860: [826, 828, 859, 861, 892, 894],
861: [827, 828, 829, 860, 893, 895],
862: [828, 829, 830, 894, 895, 896],
863: [829, 830, 831, 895, 896, 897],
864: [830, 832, 896, 897, 898],
865: [831, 833, 897],
866: [832, 834, 898, 900],
867: [833, 835, 901],
868: [834, 836, 900, 901, 902],
869: [835, 837, 901, 903],
870: [836, 838, 871, 902, 903, 904],
871: [837, 838, 839, 870, 903, 905],
872: [838, 840, 873, 904, 905, 906],
873: [839, 841, 872, 905, 907],
874: [840, 841, 842, 906, 907, 908],
875: [841, 842, 843, 876, 907, 909],
876: [842, 844, 875, 908, 909, 910],
877: [843, 844, 845, 909, 910, 911],
878: [844, 845, 846, 879, 910, 912],
879: [845, 847, 878, 880, 911, 913],
880: [846, 848, 879, 912, 913, 914],
881: [847, 848, 849, 882, 913, 915],
882: [848, 849, 850, 881, 883, 914, 916],
883: [849, 851, 882, 884, 915, 917],
884: [850, 852, 883, 916, 917, 918],
885: [851, 852, 853, 886, 917, 919],
886: [852, 854, 885, 918, 920],
887: [853, 855, 919, 921],
889: [855, 857, 921, 923],
890: [856, 857, 858, 891, 922, 924],
891: [857, 890, 923],
892: [859, 860, 926],
893: [859, 861, 894, 925, 926, 927],
894: [860, 862, 893, 895, 926, 928],
895: [861, 862, 863, 894, 927, 928, 929],
896: [862, 863, 864, 928, 930],
897: [863, 864, 865, 929, 931],
898: [864, 866, 930, 932],
900: [866, 868, 932, 934],
901: [867, 868, 869, 902, 933, 935],
902: [868, 870, 901, 903, 934, 935, 936],
903: [869, 870, 871, 902, 935, 937],
904: [870, 872, 905, 936, 937, 938],
905: [871, 872, 873, 904, 937, 939],
906: [872, 874, 938, 939, 940],
907: [873, 874, 875, 908, 939, 941],
908: [874, 876, 907, 909, 940, 941, 942],
909: [875, 876, 877, 908, 941, 943],
910: [876, 877, 878, 911, 942, 944],
911: [877, 879, 910, 912, 943, 945],
912: [878, 880, 911, 944, 946],
913: [879, 880, 881, 914, 945, 946, 947],
914: [880, 882, 913, 915, 946, 948],
915: [881, 883, 914, 947, 949],
916: [882, 884, 948, 949, 950],
917: [883, 884, 885, 918, 949, 950, 951],
918: [884, 886, 917, 919, 950, 952],
919: [885, 887, 918, 951, 952, 953],
920: [886, 952, 954],
921: [887, 889, 953, 955],
922: [890, 954, 956],
923: [889, 891, 955, 957],
924: [890, 956, 957],
925: [893, 959],
926: [892, 893, 894, 927, 958, 960],
927: [893, 895, 926, 959, 960, 961],
928: [894, 895, 896, 929, 960, 962],
929: [895, 897, 928, 930, 961, 963],
930: [896, 898, 929, 962, 963, 964],
931: [897, 963, 965],
932: [898, 900, 964, 966],
933: [901, 965, 967],
934: [900, 902, 966, 967, 968],
935: [901, 902, 903, 967, 968, 969],
936: [902, 904, 937, 968, 969, 970],
937: [903, 904, 905, 936, 969, 971],
938: [904, 906, 939, 970, 971, 972],
939: [905, 906, 907, 938, 971, 973],
940: [906, 908, 941, 972, 973, 974],
941: [907, 908, 909, 940, 973, 975],
942: [908, 910, 943, 974, 975, 976],
943: [909, 911, 942, 975, 976, 977],
944: [910, 912, 945, 976, 977, 978],
945: [911, 913, 944, 977, 978, 979],
946: [912, 913, 914, 947, 978, 980],
947: [913, 915, 946, 948, 979, 981],
948: [914, 916, 947, 949, 980, 981, 982],
949: [915, 916, 917, 948, 981, 983],
950: [916, 917, 918, 982, 983, 984],
951: [917, 919, 952, 983, 984, 985],
952: [918, 919, 920, 951, 984, 986],
953: [919, 921, 985, 986, 987],
954: [920, 922, 986, 987, 988],
955: [921, 923, 956, 987, 988, 989],
956: [922, 924, 955, 988, 990],
957: [923, 924, 989],
958: [926, 959, 991, 992],
959: [925, 927, 958, 991, 993],
960: [926, 927, 928, 961, 992, 994],
961: [927, 929, 960, 962, 993, 995],
962: [928, 930, 961, 963, 994, 996],
963: [929, 930, 931, 962, 995, 997],
964: [930, 932, 965, 996, 997, 998],
965: [931, 933, 964, 997, 999],
966: [932, 934, 998, 1000],
967: [933, 934, 935, 999, 1000, 1001],
968: [934, 935, 936, 1000, 1001, 1002],
969: [935, 936, 937, 970, 1001, 1003],
970: [936, 938, 969, 971, 1002, 1004],
971: [937, 938, 939, 970, 1003, 1005],
972: [938, 940, 973, 1004, 1005, 1006],
973: [939, 940, 941, 972, 1005, 1007],
974: [940, 942, 975, 1006, 1007, 1008],
975: [941, 942, 943, 974, 1007, 1009],
976: [942, 943, 944, 1008, 1009, 1010],
977: [943, 944, 945, 1009, 1011],
978: [944, 945, 946, 1010, 1011, 1012],
979: [945, 947, 980, 1011, 1012, 1013],
980: [946, 948, 979, 1012, 1013, 1014],
981: [947, 948, 949, 982, 1013, 1015],
982: [948, 950, 981, 1014, 1015, 1016],
983: [949, 950, 951, 984, 1015, 1017],
984: [950, 951, 952, 983, 985, 1016, 1018],
985: [951, 953, 984, 986, 1017, 1019],
986: [952, 953, 954, 985, 1018, 1020],
987: [953, 954, 955, 1019, 1020, 1021],
988: [954, 955, 956, 1020, 1021, 1022],
989: [955, 957, 990, 1021, 1022, 1023],
990: [956, 989, 1022],
991: [958, 959, 1025],
992: [958, 960, 993, 1024, 1025, 1026],
993: [959, 961, 992, 994, 1025, 1026, 1027],
994: [960, 962, 993, 995, 1026, 1028],
995: [961, 963, 994, 996, 1027, 1029],
996: [962, 964, 995, 997, 1028, 1030],
997: [963, 964, 965, 996, 1029, 1031],
998: [964, 966, 999, 1030, 1031, 1032],
999: [965, 967, 998, 1000, 1031, 1033],
1000: [966, 967, 968, 999, 1032, 1034],
1001: [967, 968, 969, 1002, 1033, 1035],
1002: [968, 970, 1001, 1003, 1034, 1036],
1003: [969, 971, 1002, 1004, 1035, 1037],
1004: [970, 972, 1003, 1036, 1038],
1005: [971, 972, 973, 1037, 1039],
1006: [972, 974, 1007, 1038, 1039, 1040],
1007: [973, 974, 975, 1006, 1039, 1041],
1008: [974, 976, 1009, 1040, 1042],
1009: [975, 976, 977, 1008, 1041, 1042, 1043],
1010: [976, 978, 1011, 1042, 1043, 1044],
1011: [977, 978, 979, 1010, 1043, 1045],
1012: [978, 979, 980, 1013, 1044, 1046],
1013: [979, 980, 981, 1012, 1045, 1047],
1014: [980, 982, 1015, 1046, 1048],
1015: [981, 982, 983, 1014, 1047, 1049],
1016: [982, 984, 1017, 1048, 1049, 1050],
1017: [983, 985, 1016, 1018, 1049, 1051],
1018: [984, 986, 1017, 1019, 1050, 1052],
1019: [985, 987, 1018, 1020, 1051, 1052, 1053],
1020: [986, 987, 988, 1019, 1052, 1054],
1021: [987, 988, 989, 1053, 1054, 1055],
1022: [988, 989, 990, 1023, 1054, 1055, 1056],
1023: [989, 1022, 1055],
1024: [992, 1025, 1058],
1025: [991, 992, 993, 1024, 1057, 1059],
1026: [992, 993, 994, 1027, 1058, 1060],
1027: [993, 995, 1026, 1059, 1060, 1061],
1028: [994, 996, 1029, 1060, 1061, 1062],
1029: [995, 997, 1028, 1030, 1061, 1063],
1030: [996, 998, 1029, 1031, 1062, 1064],
1031: [997, 998, 999, 1030, 1063, 1065],
1032: [998, 1000, 1033, 1064, 1065, 1066],
1033: [999, 1001, 1032, 1034, 1065, 1066, 1067],
1034: [1000, 1002, 1033, 1066, 1067, 1068],
1035: [1001, 1003, 1067, 1068, 1069],
1036: [1002, 1004, 1068],
1037: [1003, 1005, 1069, 1071],
1038: [1004, 1006, 1072],
1039: [1005, 1006, 1007, 1040, 1071, 1073],
1040: [1006, 1008, 1039, 1041, 1072, 1073, 1074],
1041: [1007, 1009, 1040, 1042, 1073, 1075],
1042: [1008, 1009, 1010, 1041, 1074, 1076],
1043: [1009, 1010, 1011, 1075, 1076, 1077],
1044: [1010, 1012, 1045, 1076, 1077, 1078],
1045: [1011, 1013, 1044, 1077, 1078, 1079],
1046: [1012, 1014, 1047, 1078, 1079, 1080],
1047: [1013, 1015, 1046, 1048, 1079, 1080, 1081],
1048: [1014, 1016, 1047, 1080, 1081, 1082],
1049: [1015, 1016, 1017, 1050, 1081, 1083],
1050: [1016, 1018, 1049, 1051, 1082, 1084],
1051: [1017, 1019, 1050, 1052, 1083, 1085],
1052: [1018, 1019, 1020, 1051, 1084, 1086],
1053: [1019, 1021, 1085, 1086, 1087],
1054: [1020, 1021, 1022, 1055, 1086, 1088],
1055: [1021, 1022, 1023, 1054, 1087, 1089],
1056: [1022, 1088, 1089],
1057: [1025],
1058: [1024, 1026, 1059],
1059: [1025, 1027, 1058],
1060: [1026, 1027, 1028],
1061: [1027, 1028, 1029],
1062: [1028, 1030],
1063: [1029, 1031, 1064],
1064: [1030, 1032, 1063],
1065: [1031, 1032, 1033],
1066: [1032, 1033, 1034],
1067: [1033, 1034, 1035],
1068: [1034, 1035, 1036],
1069: [1035, 1037],
1071: [1037, 1039],
1072: [1038, 1040],
1073: [1039, 1040, 1041],
1074: [1040, 1042],
1075: [1041, 1043],
1076: [1042, 1043, 1044],
1077: [1043, 1044, 1045],
1078: [1044, 1045, 1046],
1079: [1045, 1046, 1047],
1080: [1046, 1047, 1048],
1081: [1047, 1048, 1049],
1082: [1048, 1050],
1083: [1049, 1051, 1084],
1084: [1050, 1052, 1083],
1085: [1051, 1053],
1086: [1052, 1053, 1054, 1087],
1087: [1053, 1055, 1086],
1088: [1054, 1056],
1089: [1055, 1056]}

cycle_18_links = {2: [34, 36],
3: [35, 37],
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31: [63, 65],
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102: [68, 70, 134, 136],
103: [71, 135, 137],
104: [70, 71, 72, 105, 136, 137, 138],
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106: [72, 74, 105, 138, 139, 140],
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108: [74, 76, 140],
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110: [76, 78, 144],
111: [77, 78, 79, 143, 144, 145],
112: [78, 80, 113, 144, 145, 146],
113: [79, 80, 81, 112, 145, 147],
114: [80, 82, 115, 146, 147, 148],
115: [81, 82, 83, 114, 116, 147, 149],
116: [82, 84, 115, 148, 149, 150],
117: [83, 85, 149, 150, 151],
118: [84, 85, 86, 150, 151, 152],
119: [85, 86, 87, 151, 153],
120: [86, 88, 121, 152, 153, 154],
121: [87, 89, 120, 153, 154, 155],
122: [88, 90, 154, 156],
124: [90, 92, 156, 158],
125: [91, 93, 157, 158, 159],
126: [92, 93, 94, 127, 158, 160],
127: [93, 95, 126, 159, 160, 161],
128: [94, 95, 96, 160, 161, 162],
129: [95, 97, 130, 161, 162, 163],
130: [96, 97, 98, 129, 162, 164],
131: [97, 99, 132, 163, 164, 165],
132: [98, 99, 131, 164],
133: [101, 134, 167],
134: [100, 102, 133, 166, 167, 168],
135: [101, 103, 136, 167, 169],
136: [102, 104, 135, 168, 170],
137: [103, 104, 105, 169, 171],
138: [104, 106, 139, 170, 171, 172],
139: [105, 106, 107, 138, 171, 173],
140: [106, 108, 172, 173, 174],
141: [107, 109, 173, 175],
143: [109, 111, 175, 177],
144: [110, 111, 112, 176, 178],
145: [111, 112, 113, 177, 178, 179],
146: [112, 114, 147, 178, 179, 180],
147: [113, 114, 115, 146, 179, 181],
148: [114, 116, 180, 182],
149: [115, 116, 117, 181, 182, 183],
150: [116, 117, 118, 151, 182, 184],
151: [117, 118, 119, 150, 152, 183, 185],
152: [118, 120, 151, 153, 184, 186],
153: [119, 120, 121, 152, 185, 187],
154: [120, 121, 122, 186, 187, 188],
155: [121, 187, 189],
156: [122, 124, 188, 190],
157: [125, 189, 191],
158: [124, 125, 126, 159, 190, 191, 192],
159: [125, 127, 158, 191, 193],
160: [126, 127, 128, 161, 192, 194],
161: [127, 128, 129, 160, 193, 195],
162: [128, 129, 130, 163, 194, 196],
163: [129, 131, 162, 195, 196, 197],
164: [130, 131, 132, 165, 196, 198],
165: [131, 164, 197],
166: [134, 167, 200],
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170: [136, 138, 204],
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172: [138, 140, 204, 205, 206],
173: [139, 140, 141, 205, 207],
174: [140, 206, 208],
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178: [144, 145, 146, 177, 210, 212],
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187: [153, 154, 155, 188, 219, 221],
188: [154, 156, 187, 220, 222],
189: [155, 157, 221, 223],
190: [156, 158, 222, 223, 224],
191: [157, 158, 159, 192, 223, 225],
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193: [159, 161, 225],
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197: [163, 165, 196, 198, 229, 231],
198: [164, 197, 230],
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200: [166, 168, 232, 233, 234],
201: [167, 169, 233, 235],
203: [169, 171, 235, 237],
204: [170, 171, 172, 205, 236, 238],
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210: [176, 178, 209, 211, 242, 244],
211: [177, 179, 210, 212, 243, 244, 245],
212: [178, 180, 211, 244, 245, 246],
213: [179, 181, 245, 246, 247],
214: [180, 181, 182, 215, 246, 248],
215: [181, 183, 214, 216, 247, 249],
216: [182, 184, 215, 217, 248, 249, 250],
217: [183, 184, 185, 216, 249, 251],
218: [184, 186, 219, 250, 251, 252],
219: [185, 186, 187, 218, 220, 251, 253],
220: [186, 188, 219, 221, 252, 254],
221: [187, 189, 220, 222, 253, 254, 255],
222: [188, 190, 221, 223, 254, 256],
223: [189, 190, 191, 222, 224, 255, 257],
224: [190, 192, 223, 225, 256, 258],
225: [191, 193, 224, 257, 258, 259],
226: [192, 194, 258, 260],
228: [194, 196, 260, 262],
229: [195, 197, 230, 261, 263],
230: [196, 198, 229, 262, 263, 264],
231: [197, 263],
232: [199, 200, 266],
233: [199, 200, 201, 265, 266, 267],
234: [200, 266, 268],
235: [201, 203, 267, 269],
236: [204, 268, 270],
237: [203, 205, 238, 269, 270, 271],
238: [204, 206, 237, 239, 270, 272],
239: [205, 207, 238, 240, 271, 273],
240: [206, 208, 239, 241, 272, 274],
241: [207, 208, 209, 240, 273, 275],
242: [208, 209, 210, 243, 274, 276],
243: [209, 211, 242, 275, 277],
244: [210, 211, 212, 276, 277, 278],
245: [211, 212, 213, 277, 278, 279],
246: [212, 213, 214, 247, 278, 280],
247: [213, 215, 246, 248, 279, 280, 281],
248: [214, 216, 247, 280, 282],
249: [215, 216, 217, 250, 281, 283],
250: [216, 218, 249, 251, 282, 284],
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258: [224, 225, 226, 290, 291, 292],
259: [225, 291, 293],
260: [226, 228, 292, 294],
261: [229, 293, 295],
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263: [229, 230, 231, 264, 295, 296, 297],
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268: [234, 236, 267, 300, 301, 302],
269: [235, 237, 301, 302, 303],
270: [236, 237, 238, 302, 303, 304],
271: [237, 239, 272, 303, 305],
272: [238, 240, 271, 273, 304, 305, 306],
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278: [244, 245, 246, 279, 310, 312],
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283: [249, 251, 315, 316, 317],
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301: [267, 268, 269, 333, 334, 335],
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306: [272, 273, 274, 338, 339, 340],
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311: [277, 279, 310, 343, 345],
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314: [280, 281, 282, 346, 347, 348],
315: [281, 282, 283, 347, 348, 349],
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320: [286, 288, 321, 352, 353, 354],
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322: [288, 290, 323, 354, 355, 356],
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324: [290, 291, 292, 325, 356, 358],
325: [291, 292, 293, 324, 357, 359],
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327: [293, 295, 326, 359, 360, 361],
328: [294, 296, 329, 360, 361, 362],
329: [295, 297, 328, 361, 362, 363],
330: [296, 362, 363],
331: [299],
332: [298, 300, 364, 366],
333: [299, 301, 367],
334: [300, 301, 302, 335, 366, 368],
335: [301, 303, 334, 367, 368, 369],
336: [302, 304, 337, 368, 369, 370],
337: [303, 304, 305, 336, 338, 369, 371],
338: [304, 306, 337, 370, 371, 372],
339: [305, 306, 307, 340, 371, 373],
340: [306, 307, 308, 339, 372, 374],
341: [307, 308, 309, 373, 374, 375],
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346: [312, 313, 314, 378, 380],
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349: [315, 317, 348, 350, 381, 383],
350: [316, 318, 349, 351, 382, 384],
351: [317, 319, 350, 352, 383, 385],
352: [318, 320, 351, 353, 384, 386],
353: [319, 320, 321, 352, 385, 387],
354: [320, 322, 355, 386, 387, 388],
355: [321, 322, 323, 354, 356, 387, 389],
356: [322, 324, 355, 357, 388, 390],
357: [323, 325, 356, 358, 389, 391],
358: [324, 326, 357, 359, 390, 392],
359: [325, 326, 327, 358, 391, 393],
360: [326, 327, 328, 361, 392, 393, 394],
361: [327, 328, 329, 360, 393, 395],
362: [328, 329, 330, 394, 395, 396],
363: [329, 330, 395],
364: [332, 398],
366: [332, 334, 398, 400],
367: [333, 335, 368, 399, 401],
368: [334, 335, 336, 367, 400, 401, 402],
369: [335, 336, 337, 401, 403],
370: [336, 338, 371, 402, 403, 404],
371: [337, 338, 339, 370, 403, 405],
372: [338, 340, 373, 404, 405, 406],
373: [339, 341, 372, 374, 405, 407],
374: [340, 341, 342, 373, 406, 408],
375: [341, 343, 376, 407, 408, 409],
376: [342, 344, 375, 408, 409, 410],
377: [343, 344, 345, 409, 410, 411],
378: [344, 345, 346, 379, 410, 412],
379: [345, 347, 378, 411, 412, 413],
380: [346, 347, 348, 381, 412, 413, 414],
381: [347, 349, 380, 382, 413, 415],
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383: [349, 351, 382, 415, 417],
384: [350, 352, 416, 417, 418],
385: [351, 353, 386, 417, 418, 419],
386: [352, 354, 385, 418, 419, 420],
387: [353, 354, 355, 419, 420, 421],
388: [354, 356, 389, 420, 421, 422],
389: [355, 357, 388, 390, 421, 423],
390: [356, 358, 389, 422, 424],
391: [357, 359, 392, 423, 425],
392: [358, 360, 391, 424, 426],
393: [359, 360, 361, 425, 426, 427],
394: [360, 362, 395, 426, 427, 428],
395: [361, 362, 363, 394, 427, 429],
396: [362, 428],
397: [431],
398: [364, 366, 430, 432],
399: [367, 431, 433],
400: [366, 368, 432, 433, 434],
401: [367, 368, 369, 433, 434, 435],
402: [368, 370, 403, 434, 436],
403: [369, 370, 371, 402, 435, 437],
404: [370, 372, 405, 436, 438],
405: [371, 372, 373, 404, 437, 439],
406: [372, 374, 407, 438, 440],
407: [373, 375, 406, 439, 441],
408: [374, 375, 376, 409, 440, 441, 442],
409: [375, 376, 377, 408, 441, 443],
410: [376, 377, 378, 411, 442, 444],
411: [377, 379, 410, 412, 443, 445],
412: [378, 379, 380, 411, 444, 446],
413: [379, 380, 381, 445, 447],
414: [380, 382, 415, 446, 447, 448],
415: [381, 383, 414, 416, 447, 449],
416: [382, 384, 415, 417, 448, 450],
417: [383, 384, 385, 416, 449, 451],
418: [384, 385, 386, 450, 451, 452],
419: [385, 386, 387, 420, 451, 453],
420: [386, 387, 388, 419, 452, 454],
421: [387, 388, 389, 453, 454, 455],
422: [388, 390, 454, 455, 456],
423: [389, 391, 455],
424: [390, 392, 456, 458],
425: [391, 393, 459],
426: [392, 393, 394, 458, 460],
427: [393, 394, 395, 428, 459, 461],
428: [394, 396, 427, 429, 460, 462],
429: [395, 428, 461, 462],
430: [398, 431, 464],
431: [397, 399, 430, 463, 464, 465],
432: [398, 400, 433, 464, 466],
433: [399, 400, 401, 432, 465, 467],
434: [400, 401, 402, 466, 467, 468],
435: [401, 403, 436, 467, 468, 469],
436: [402, 404, 435, 468, 470],
437: [403, 405, 469],
438: [404, 406, 470, 472],
439: [405, 407, 473],
440: [406, 408, 441, 472, 473, 474],
441: [407, 408, 409, 440, 473, 475],
442: [408, 410, 443, 474, 475, 476],
443: [409, 411, 442, 444, 475, 477],
444: [410, 412, 443, 445, 476, 478],
445: [411, 413, 444, 446, 477, 479],
446: [412, 414, 445, 447, 478, 479, 480],
447: [413, 414, 415, 446, 479, 481],
448: [414, 416, 449, 480, 481, 482],
449: [415, 417, 448, 450, 481, 482, 483],
450: [416, 418, 449, 451, 482, 484],
451: [417, 418, 419, 450, 483, 485],
452: [418, 420, 453, 484, 485, 486],
453: [419, 421, 452, 485, 486, 487],
454: [420, 421, 422, 486, 487, 488],
455: [421, 422, 423, 487, 489],
456: [422, 424, 488, 490],
458: [424, 426, 490, 492],
459: [425, 427, 491],
460: [426, 428, 492, 494],
461: [427, 429, 495],
462: [428, 429, 494],
463: [431, 496, 497],
464: [430, 431, 432, 465, 496, 498],
465: [431, 433, 464, 466, 497, 499],
466: [432, 434, 465, 498, 499, 500],
467: [433, 434, 435, 468, 499, 501],
468: [434, 435, 436, 467, 469, 500, 502],
469: [435, 437, 468, 501, 503],
470: [436, 438, 502, 504],
472: [438, 440, 504, 506],
473: [439, 440, 441, 505, 506, 507],
474: [440, 442, 475, 506, 507, 508],
475: [441, 442, 443, 474, 476, 507, 509],
476: [442, 444, 475, 508, 509, 510],
477: [443, 445, 478, 509, 510, 511],
478: [444, 446, 477, 510, 511, 512],
479: [445, 446, 447, 480, 511, 513],
480: [446, 448, 479, 512, 513, 514],
481: [447, 448, 449, 513, 514, 515],
482: [448, 449, 450, 514, 515, 516],
483: [449, 451, 484, 515, 516, 517],
484: [450, 452, 483, 516, 517, 518],
485: [451, 452, 453, 517, 518, 519],
486: [452, 453, 454, 518, 519, 520],
487: [453, 454, 455, 488, 519, 521],
488: [454, 456, 487, 520, 521, 522],
489: [455, 521, 523],
490: [456, 458, 522, 524],
491: [459, 523, 525],
492: [458, 460, 524, 526],
494: [460, 462, 526, 528],
495: [461, 527],
496: [463, 464, 530],
497: [463, 465, 498, 529, 530, 531],
498: [464, 466, 497, 530, 531, 532],
499: [465, 466, 467, 500, 531, 533],
500: [466, 468, 499, 532, 533, 534],
501: [467, 469, 533, 534, 535],
502: [468, 470, 534, 536],
503: [469, 535, 537],
504: [470, 472, 536, 538],
505: [473, 537, 539],
506: [472, 473, 474, 538, 539, 540],
507: [473, 474, 475, 539, 541],
508: [474, 476, 509, 540, 542],
509: [475, 476, 477, 508, 541, 543],
510: [476, 477, 478, 542, 543, 544],
511: [477, 478, 479, 543, 544, 545],
512: [478, 480, 544, 545, 546],
513: [479, 480, 481, 514, 545, 547],
514: [480, 481, 482, 513, 546, 548],
515: [481, 482, 483, 547, 548, 549],
516: [482, 483, 484, 517, 548, 550],
517: [483, 484, 485, 516, 549, 551],
518: [484, 485, 486, 519, 550, 552],
519: [485, 486, 487, 518, 520, 551, 553],
520: [486, 488, 519, 552, 554],
521: [487, 488, 489, 522, 553, 555],
522: [488, 490, 521, 523, 554, 556],
523: [489, 491, 522, 524, 555, 556, 557],
524: [490, 492, 523, 556, 558],
525: [491, 557, 559],
526: [492, 494, 558, 560],
527: [495, 559, 561],
528: [494, 560, 561],
529: [497, 562, 563],
530: [496, 497, 498, 562, 563, 564],
531: [497, 498, 499, 532, 563, 565],
532: [498, 500, 531, 533, 564, 566],
533: [499, 500, 501, 532, 565, 567],
534: [500, 501, 502, 566, 567, 568],
535: [501, 503, 536, 567, 568, 569],
536: [502, 504, 535, 537, 568, 570],
537: [503, 505, 536, 538, 569, 571],
538: [504, 506, 537, 570, 571, 572],
539: [505, 506, 507, 571, 572, 573],
540: [506, 508, 541, 572, 573, 574],
541: [507, 509, 540, 542, 573, 575],
542: [508, 510, 541, 574, 575, 576],
543: [509, 510, 511, 575, 576, 577],
544: [510, 511, 512, 576, 578],
545: [511, 512, 513, 546, 577, 579],
546: [512, 514, 545, 578, 580],
547: [513, 515, 548, 579, 581],
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549: [515, 517, 581, 582, 583],
550: [516, 518, 551, 582, 583, 584],
551: [517, 519, 550, 583, 584, 585],
552: [518, 520, 553, 584, 586],
553: [519, 521, 552, 554, 585, 587],
554: [520, 522, 553, 555, 586, 587, 588],
555: [521, 523, 554, 587, 588, 589],
556: [522, 523, 524, 588, 589, 590],
557: [523, 525, 558, 589, 590, 591],
558: [524, 526, 557, 590, 592],
559: [525, 527, 560, 591, 592, 593],
560: [526, 528, 559, 592, 593, 594],
561: [527, 528, 593],
562: [529, 530, 596],
563: [529, 530, 531, 595, 596, 597],
564: [530, 532, 565, 596, 598],
565: [531, 533, 564, 566, 597, 599],
566: [532, 534, 565, 598, 600],
567: [533, 534, 535, 568, 599, 601],
568: [534, 535, 536, 567, 569, 600, 602],
569: [535, 537, 568, 601, 602, 603],
570: [536, 538, 571, 602, 603, 604],
571: [537, 538, 539, 570, 603, 605],
572: [538, 539, 540, 604, 605, 606],
573: [539, 540, 541, 605, 606, 607],
574: [540, 542, 575, 606, 607, 608],
575: [541, 542, 543, 574, 607, 609],
576: [542, 543, 544, 577, 608, 610],
577: [543, 545, 576, 609, 611],
578: [544, 546, 610],
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580: [546, 548, 614],
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586: [552, 554, 585, 618, 619, 620],
587: [553, 554, 555, 619, 620, 621],
588: [554, 555, 556, 620, 622],
589: [555, 556, 557, 621, 622, 623],
590: [556, 557, 558, 591, 622, 623, 624],
591: [557, 559, 590, 623, 624, 625],
592: [558, 559, 560, 593, 624, 626],
593: [559, 560, 561, 592, 625, 627],
594: [560, 626],
595: [563, 596, 629],
596: [562, 563, 564, 595, 628, 629, 630],
597: [563, 565, 629],
598: [564, 566, 630, 632],
599: [565, 567, 633],
600: [566, 568, 601, 632, 633, 634],
601: [567, 569, 600, 633, 635],
602: [568, 569, 570, 634, 636],
603: [569, 570, 571, 604, 635, 636, 637],
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605: [571, 572, 573, 604, 637, 638, 639],
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607: [573, 574, 575, 639, 640, 641],
608: [574, 576, 609, 640, 641, 642],
609: [575, 577, 608, 610, 641, 643],
610: [576, 578, 609, 642, 643, 644],
611: [577, 579, 643, 645],
613: [579, 581, 645, 647],
614: [580, 582, 615, 646, 648],
615: [581, 583, 614, 647, 648, 649],
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617: [583, 585, 616, 649, 650, 651],
618: [584, 586, 619, 650, 651, 652],
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621: [587, 589, 622, 653, 654, 655],
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623: [589, 590, 591, 655, 656, 657],
624: [590, 591, 592, 625, 656, 658],
625: [591, 593, 624, 657, 658, 659],
626: [592, 594, 627, 658, 659, 660],
627: [593, 626, 659],
628: [596, 661, 662],
629: [595, 596, 597, 661, 662, 663],
630: [596, 598, 662, 664],
632: [598, 600, 664, 666],
633: [599, 600, 601, 665, 666, 667],
634: [600, 602, 635, 666, 668],
635: [601, 603, 634, 667, 668, 669],
636: [602, 603, 604, 668, 669, 670],
637: [603, 605, 669, 670, 671],
638: [604, 605, 606, 670, 671, 672],
639: [605, 607, 640, 671, 672, 673],
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641: [607, 608, 609, 673, 675],
642: [608, 610, 643, 674, 676],
643: [609, 610, 611, 642, 675, 677],
644: [610, 676, 678],
645: [611, 613, 677, 679],
646: [614, 678, 680],
647: [613, 615, 679, 680, 681],
648: [614, 615, 616, 649, 680, 682],
649: [615, 617, 648, 681, 682, 683],
650: [616, 617, 618, 682, 683, 684],
651: [617, 618, 619, 683, 684, 685],
652: [618, 620, 653, 684, 685, 686],
653: [619, 621, 652, 654, 685, 687],
654: [620, 621, 622, 653, 686, 688],
655: [621, 623, 687, 689],
656: [622, 623, 624, 657, 688, 690],
657: [623, 625, 656, 658, 689, 691],
658: [624, 625, 626, 657, 690, 692],
659: [625, 626, 627, 691, 692, 693],
660: [626, 692, 693],
661: [628, 629, 695],
662: [628, 629, 630, 694, 696],
663: [629, 695, 697],
664: [630, 632, 696, 698],
665: [633, 697, 699],
666: [632, 633, 634, 667, 698, 700],
667: [633, 635, 666, 699, 700, 701],
668: [634, 635, 636, 669, 700, 701, 702],
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671: [637, 638, 639, 672, 703, 705],
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673: [639, 641, 705],
674: [640, 642, 706, 708],
675: [641, 643, 709],
676: [642, 644, 677, 708, 709, 710],
677: [643, 645, 676, 678, 709, 711],
678: [644, 646, 677, 710, 712],
679: [645, 647, 711, 712, 713],
680: [646, 647, 648, 712, 713, 714],
681: [647, 649, 682, 713, 714, 715],
682: [648, 649, 650, 681, 714, 716],
683: [649, 650, 651, 715, 716, 717],
684: [650, 651, 652, 716, 717, 718],
685: [651, 652, 653, 686, 717, 719],
686: [652, 654, 685, 718, 720],
687: [653, 655, 719],
688: [654, 656, 720, 722],
689: [655, 657, 723],
690: [656, 658, 691, 722, 723, 724],
691: [657, 659, 690, 692, 723, 725],
692: [658, 659, 660, 691, 724, 726],
693: [659, 660, 725, 726],
694: [662, 695, 728],
695: [661, 663, 694, 696, 727, 729],
696: [662, 664, 695, 728, 730],
697: [663, 665, 698, 729, 731],
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700: [666, 667, 668, 732, 733, 734],
701: [667, 668, 669, 702, 733, 735],
702: [668, 670, 701, 734, 735, 736],
703: [669, 670, 671, 704, 735, 737],
704: [670, 672, 703, 736, 737, 738],
705: [671, 673, 737, 738, 739],
706: [672, 674, 738, 740],
708: [674, 676, 740, 742],
709: [675, 676, 677, 741, 742, 743],
710: [676, 678, 742, 743, 744],
711: [677, 679, 712, 743, 744, 745],
712: [678, 679, 680, 711, 744, 746],
713: [679, 680, 681, 745, 746, 747],
714: [680, 681, 682, 746, 747, 748],
715: [681, 683, 716, 747, 748, 749],
716: [682, 683, 684, 715, 717, 748, 750],
717: [683, 684, 685, 716, 749, 751],
718: [684, 686, 719, 750, 751, 752],
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720: [686, 688, 752, 754],
722: [688, 690, 754, 756],
723: [689, 690, 691, 755, 756, 757],
724: [690, 692, 725, 756, 757, 758],
725: [691, 693, 724, 757, 758, 759],
726: [692, 693, 758],
727: [695, 728, 761],
728: [694, 696, 727, 729, 760, 761, 762],
729: [695, 697, 728, 730, 761, 763],
730: [696, 698, 729, 731, 762, 764],
731: [697, 699, 730, 732, 763, 765],
732: [698, 699, 700, 731, 764, 765, 766],
733: [699, 700, 701, 734, 765, 767],
734: [700, 702, 733, 766, 768],
735: [701, 702, 703, 736, 767, 768, 769],
736: [702, 704, 735, 737, 768, 770],
737: [703, 704, 705, 736, 738, 769, 771],
738: [704, 705, 706, 737, 770, 772],
739: [705, 771, 773],
740: [706, 708, 772, 774],
741: [709, 773, 775],
742: [708, 709, 710, 743, 774, 776],
743: [709, 710, 711, 742, 775, 777],
744: [710, 711, 712, 776, 777, 778],
745: [711, 713, 746, 777, 778, 779],
746: [712, 713, 714, 745, 778, 779, 780],
747: [713, 714, 715, 779, 781],
748: [714, 715, 716, 780, 781, 782],
749: [715, 717, 750, 781, 783],
750: [716, 718, 749, 782, 783, 784],
751: [717, 718, 719, 752, 783, 785],
752: [718, 720, 751, 784, 786],
753: [719, 785, 787],
754: [720, 722, 786, 788],
755: [723, 787, 789],
756: [722, 723, 724, 788, 789, 790],
757: [723, 724, 725, 789, 791],
758: [724, 725, 726, 759, 790, 792],
759: [725, 758, 791],
760: [728, 794],
761: [727, 728, 729, 793, 794, 795],
762: [728, 730, 763, 794, 795, 796],
763: [729, 731, 762, 795, 796, 797],
764: [730, 732, 796, 797, 798],
765: [731, 732, 733, 797, 798, 799],
766: [732, 734, 767, 798, 800],
767: [733, 735, 766, 799, 800, 801],
768: [734, 735, 736, 769, 800, 802],
769: [735, 737, 768, 801, 802, 803],
770: [736, 738, 771, 802, 804],
771: [737, 739, 770, 772, 803, 805],
772: [738, 740, 771, 804, 805, 806],
773: [739, 741, 805, 806, 807],
774: [740, 742, 775, 806, 808],
775: [741, 743, 774, 807, 808, 809],
776: [742, 744, 808, 809, 810],
777: [743, 744, 745, 778, 809, 811],
778: [744, 745, 746, 777, 810, 812],
779: [745, 746, 747, 780, 811, 813],
780: [746, 748, 779, 812, 813, 814],
781: [747, 748, 749, 782, 813, 815],
782: [748, 750, 781, 814, 816],
783: [749, 750, 751, 784, 815, 816, 817],
784: [750, 752, 783, 785, 816, 818],
785: [751, 753, 784, 817, 818, 819],
786: [752, 754, 787, 818, 819, 820],
787: [753, 755, 786, 819, 820, 821],
788: [754, 756, 820, 821, 822],
789: [755, 756, 757, 790, 821, 823],
790: [756, 758, 789, 791, 822, 824],
791: [757, 759, 790, 823, 824, 825],
792: [758, 824],
793: [761, 794, 827],
794: [760, 761, 762, 793, 826, 828],
795: [761, 762, 763, 796, 827, 828, 829],
796: [762, 763, 764, 795, 828, 830],
797: [763, 764, 765, 829, 830, 831],
798: [764, 765, 766, 799, 830, 832],
799: [765, 767, 798, 831, 833],
800: [766, 767, 768, 801, 832, 833, 834],
801: [767, 769, 800, 833, 834, 835],
802: [768, 769, 770, 834, 835, 836],
803: [769, 771, 804, 835, 837],
804: [770, 772, 803, 836, 837, 838],
805: [771, 772, 773, 837, 838, 839],
806: [772, 773, 774, 807, 838, 840],
807: [773, 775, 806, 839, 840, 841],
808: [774, 775, 776, 809, 840, 842],
809: [775, 776, 777, 808, 841, 842, 843],
810: [776, 778, 842, 843, 844],
811: [777, 779, 812, 843, 844, 845],
812: [778, 780, 811, 813, 844, 846],
813: [779, 780, 781, 812, 845, 846, 847],
814: [780, 782, 815, 846, 847, 848],
815: [781, 783, 814, 816, 847, 849],
816: [782, 783, 784, 815, 848, 850],
817: [783, 785, 818, 849, 850, 851],
818: [784, 785, 786, 817, 850, 852],
819: [785, 786, 787, 820, 851, 853],
820: [786, 787, 788, 819, 852, 854],
821: [787, 788, 789, 822, 853, 855],
822: [788, 790, 821, 854, 856],
823: [789, 791, 824, 855, 857],
824: [790, 791, 792, 823, 856, 858],
825: [791, 857, 858],
826: [794, 859, 860],
827: [793, 795, 828, 859, 860, 861],
828: [794, 795, 796, 827, 860, 862],
829: [795, 797, 830, 861, 862, 863],
830: [796, 797, 798, 829, 831, 862, 864],
831: [797, 799, 830, 832, 863, 865],
832: [798, 800, 831, 833, 864, 866],
833: [799, 800, 801, 832, 865, 867],
834: [800, 801, 802, 866, 868],
835: [801, 802, 803, 836, 867, 868, 869],
836: [802, 804, 835, 868, 869, 870],
837: [803, 804, 805, 869, 870, 871],
838: [804, 805, 806, 839, 870, 872],
839: [805, 807, 838, 840, 871, 873],
840: [806, 807, 808, 839, 872, 873, 874],
841: [807, 809, 873, 874, 875],
842: [808, 809, 810, 874, 875, 876],
843: [809, 810, 811, 875, 876, 877],
844: [810, 811, 812, 845, 876, 878],
845: [811, 813, 844, 846, 877, 879],
846: [812, 813, 814, 845, 878, 880],
847: [813, 814, 815, 848, 879, 881],
848: [814, 816, 847, 849, 880, 882],
849: [815, 817, 848, 881, 882, 883],
850: [816, 817, 818, 882, 883, 884],
851: [817, 819, 852, 883, 884, 885],
852: [818, 820, 851, 884, 885, 886],
853: [819, 821, 885, 886, 887],
854: [820, 822, 886],
855: [821, 823, 887, 889],
856: [822, 824, 890],
857: [823, 825, 889, 890, 891],
858: [824, 825, 890],
859: [826, 827, 893],
860: [826, 827, 828, 892, 893, 894],
861: [827, 829, 862, 893, 894, 895],
862: [828, 829, 830, 861, 894, 896],
863: [829, 831, 864, 895, 897],
864: [830, 832, 863, 896, 897, 898],
865: [831, 833, 897],
866: [832, 834, 898, 900],
867: [833, 835, 901],
868: [834, 835, 836, 900, 902],
869: [835, 836, 837, 901, 902, 903],
870: [836, 837, 838, 902, 903, 904],
871: [837, 839, 872, 903, 904, 905],
872: [838, 840, 871, 873, 904, 906],
873: [839, 840, 841, 872, 905, 907],
874: [840, 841, 842, 906, 907, 908],
875: [841, 842, 843, 907, 908, 909],
876: [842, 843, 844, 877, 908, 910],
877: [843, 845, 876, 878, 909, 911],
878: [844, 846, 877, 910, 911, 912],
879: [845, 847, 880, 911, 912, 913],
880: [846, 848, 879, 912, 913, 914],
881: [847, 849, 913, 914, 915],
882: [848, 849, 850, 914, 915, 916],
883: [849, 850, 851, 884, 915, 917],
884: [850, 851, 852, 883, 916, 917, 918],
885: [851, 852, 853, 917, 919],
886: [852, 853, 854, 918, 920],
887: [853, 855, 919, 921],
889: [855, 857, 921, 923],
890: [856, 857, 858, 922, 924],
891: [857, 923, 924],
892: [860, 925, 926],
893: [859, 860, 861, 894, 925, 927],
894: [860, 861, 862, 893, 926, 928],
895: [861, 863, 896, 927, 928, 929],
896: [862, 864, 895, 928, 929, 930],
897: [863, 864, 865, 929, 931],
898: [864, 866, 930, 932],
900: [866, 868, 932, 934],
901: [867, 869, 933, 934, 935],
902: [868, 869, 870, 903, 934, 936],
903: [869, 870, 871, 902, 935, 936, 937],
904: [870, 871, 872, 905, 936, 938],
905: [871, 873, 904, 937, 938, 939],
906: [872, 874, 938, 939, 940],
907: [873, 874, 875, 939, 940, 941],
908: [874, 875, 876, 909, 940, 941, 942],
909: [875, 877, 908, 910, 941, 943],
910: [876, 878, 909, 942, 943, 944],
911: [877, 878, 879, 943, 944, 945],
912: [878, 879, 880, 913, 944, 946],
913: [879, 880, 881, 912, 945, 946, 947],
914: [880, 881, 882, 946, 947, 948],
915: [881, 882, 883, 947, 948, 949],
916: [882, 884, 917, 948, 950],
917: [883, 884, 885, 916, 949, 951],
918: [884, 886, 919, 950, 952],
919: [885, 887, 918, 951, 952, 953],
920: [886, 952, 954],
921: [887, 889, 953, 955],
922: [890, 954, 956],
923: [889, 891, 955, 957],
924: [890, 891, 956],
925: [892, 893, 926, 959],
926: [892, 894, 925, 927, 958, 960],
927: [893, 895, 926, 959, 960, 961],
928: [894, 895, 896, 929, 960, 962],
929: [895, 896, 897, 928, 930, 961, 963],
930: [896, 898, 929, 962, 963, 964],
931: [897, 963, 965],
932: [898, 900, 964, 966],
933: [901, 965, 967],
934: [900, 901, 902, 966, 967, 968],
935: [901, 903, 967, 968, 969],
936: [902, 903, 904, 968, 970],
937: [903, 905, 969, 970, 971],
938: [904, 905, 906, 970, 971, 972],
939: [905, 906, 907, 940, 971, 973],
940: [906, 907, 908, 939, 972, 974],
941: [907, 908, 909, 973, 974, 975],
942: [908, 910, 943, 974, 975, 976],
943: [909, 910, 911, 942, 975, 976, 977],
944: [910, 911, 912, 945, 976, 978],
945: [911, 913, 944, 977, 978, 979],
946: [912, 913, 914, 978, 979, 980],
947: [913, 914, 915, 979, 980, 981],
948: [914, 915, 916, 949, 980, 982],
949: [915, 917, 948, 950, 981, 983],
950: [916, 918, 949, 951, 982, 984],
951: [917, 919, 950, 952, 983, 984, 985],
952: [918, 919, 920, 951, 984, 986],
953: [919, 921, 954, 985, 987],
954: [920, 922, 953, 955, 986, 988],
955: [921, 923, 954, 987, 989],
956: [922, 924, 957, 988, 989, 990],
957: [923, 956, 989],
958: [926, 959, 992],
959: [925, 927, 958, 991, 992, 993],
960: [926, 927, 928, 992, 993, 994],
961: [927, 929, 962, 993, 994, 995],
962: [928, 930, 961, 963, 994, 996],
963: [929, 930, 931, 962, 995, 997],
964: [930, 932, 996, 997, 998],
965: [931, 933, 966, 997, 999],
966: [932, 934, 965, 998, 999, 1000],
967: [933, 934, 935, 999, 1000, 1001],
968: [934, 935, 936, 969, 1000, 1002],
969: [935, 937, 968, 970, 1001, 1002, 1003],
970: [936, 937, 938, 969, 1002, 1004],
971: [937, 938, 939, 972, 1003, 1005],
972: [938, 940, 971, 973, 1004, 1006],
973: [939, 941, 972, 1005, 1006, 1007],
974: [940, 941, 942, 975, 1006, 1008],
975: [941, 942, 943, 974, 1007, 1009],
976: [942, 943, 944, 1008, 1009, 1010],
977: [943, 945, 1009, 1010, 1011],
978: [944, 945, 946, 979, 1010, 1012],
979: [945, 946, 947, 978, 980, 1011, 1013],
980: [946, 947, 948, 979, 1012, 1014],
981: [947, 949, 982, 1013, 1014, 1015],
982: [948, 950, 981, 983, 1014, 1016],
983: [949, 951, 982, 1015, 1016, 1017],
984: [950, 951, 952, 985, 1016, 1018],
985: [951, 953, 984, 986, 1017, 1019],
986: [952, 954, 985, 1018, 1019, 1020],
987: [953, 955, 988, 1019, 1020, 1021],
988: [954, 956, 987, 1020, 1021, 1022],
989: [955, 956, 957, 1021, 1022, 1023],
990: [956, 1022],
991: [959, 1024, 1025],
992: [958, 959, 960, 1024, 1025, 1026],
993: [959, 960, 961, 1025, 1026, 1027],
994: [960, 961, 962, 995, 1026, 1028],
995: [961, 963, 994, 1027, 1029],
996: [962, 964, 997, 1028, 1029, 1030],
997: [963, 964, 965, 996, 998, 1029, 1031],
998: [964, 966, 997, 1030, 1031, 1032],
999: [965, 966, 967, 1031, 1032, 1033],
1000: [966, 967, 968, 1001, 1032, 1034],
1001: [967, 969, 1000, 1033, 1034, 1035],
1002: [968, 969, 970, 1034, 1035, 1036],
1003: [969, 971, 1004, 1035, 1037],
1004: [970, 972, 1003, 1005, 1036, 1038],
1005: [971, 973, 1004, 1006, 1037, 1039],
1006: [972, 973, 974, 1005, 1007, 1038, 1040],
1007: [973, 975, 1006, 1008, 1039, 1041],
1008: [974, 976, 1007, 1009, 1040, 1042],
1009: [975, 976, 977, 1008, 1041, 1043],
1010: [976, 977, 978, 1011, 1042, 1044],
1011: [977, 979, 1010, 1043, 1044, 1045],
1012: [978, 980, 1013, 1044, 1046],
1013: [979, 981, 1012, 1014, 1045, 1047],
1014: [980, 981, 982, 1013, 1046, 1047, 1048],
1015: [981, 983, 1047, 1049],
1016: [982, 983, 984, 1048, 1049, 1050],
1017: [983, 985, 1018, 1049, 1050, 1051],
1018: [984, 986, 1017, 1050, 1051, 1052],
1019: [985, 986, 987, 1020, 1051, 1053],
1020: [986, 987, 988, 1019, 1052, 1054],
1021: [987, 988, 989, 1022, 1053, 1055],
1022: [988, 989, 990, 1021, 1054, 1055, 1056],
1023: [989, 1055],
1024: [991, 992, 1058],
1025: [991, 992, 993, 1057, 1058, 1059],
1026: [992, 993, 994, 1058, 1059, 1060],
1027: [993, 995, 1028, 1059, 1060, 1061],
1028: [994, 996, 1027, 1060, 1061, 1062],
1029: [995, 996, 997, 1030, 1061, 1063],
1030: [996, 998, 1029, 1062, 1063, 1064],
1031: [997, 998, 999, 1063, 1064, 1065],
1032: [998, 999, 1000, 1033, 1064, 1066],
1033: [999, 1001, 1032, 1034, 1065, 1067],
1034: [1000, 1001, 1002, 1033, 1066, 1068],
1035: [1001, 1002, 1003, 1067, 1068, 1069],
1036: [1002, 1004, 1068],
1037: [1003, 1005, 1069, 1071],
1038: [1004, 1006, 1072],
1039: [1005, 1007, 1040, 1071, 1072, 1073],
1040: [1006, 1008, 1039, 1041, 1072, 1074],
1041: [1007, 1009, 1040, 1042, 1073, 1075],
1042: [1008, 1010, 1041, 1043, 1074, 1076],
1043: [1009, 1011, 1042, 1075, 1076, 1077],
1044: [1010, 1011, 1012, 1045, 1076, 1078],
1045: [1011, 1013, 1044, 1046, 1077, 1078, 1079],
1046: [1012, 1014, 1045, 1078, 1079, 1080],
1047: [1013, 1014, 1015, 1048, 1079, 1081],
1048: [1014, 1016, 1047, 1049, 1080, 1081, 1082],
1049: [1015, 1016, 1017, 1048, 1081, 1083],
1050: [1016, 1017, 1018, 1082, 1083, 1084],
1051: [1017, 1018, 1019, 1052, 1083, 1085],
1052: [1018, 1020, 1051, 1084, 1085, 1086],
1053: [1019, 1021, 1054, 1085, 1086, 1087],
1054: [1020, 1022, 1053, 1086, 1087, 1088],
1055: [1021, 1022, 1023, 1056, 1087, 1089],
1056: [1022, 1055, 1088],
1057: [1025],
1058: [1024, 1025, 1026],
1059: [1025, 1026, 1027],
1060: [1026, 1027, 1028],
1061: [1027, 1028, 1029],
1062: [1028, 1030],
1063: [1029, 1030, 1031],
1064: [1030, 1031, 1032],
1065: [1031, 1033, 1066],
1066: [1032, 1034, 1065],
1067: [1033, 1035],
1068: [1034, 1035, 1036],
1069: [1035, 1037],
1071: [1037, 1039],
1072: [1038, 1039, 1040],
1073: [1039, 1041, 1074],
1074: [1040, 1042, 1073],
1075: [1041, 1043],
1076: [1042, 1043, 1044, 1077],
1077: [1043, 1045, 1076],
1078: [1044, 1045, 1046],
1079: [1045, 1046, 1047],
1080: [1046, 1048],
1081: [1047, 1048, 1049],
1082: [1048, 1050, 1083],
1083: [1049, 1050, 1051, 1082],
1084: [1050, 1052],
1085: [1051, 1052, 1053],
1086: [1052, 1053, 1054],
1087: [1053, 1054, 1055],
1088: [1054, 1056, 1089],
1089: [1055, 1088]}

# There was no anarchy period before war 19
cycle_19_links = cycle_18_links

cycle_19_post_war_links_1 = {2: [34, 36],
3: [35, 37],
4: [36],
5: [37, 39],
6: [7, 38, 40],
7: [6, 39, 41],
8: [40, 42],
9: [10, 41, 43],
10: [9, 42, 44],
11: [12, 43, 44, 45],
12: [11, 44, 46],
13: [45, 46, 47],
14: [46, 48],
15: [47, 49],
16: [48, 50],
17: [49, 50, 51],
18: [50, 51, 52],
19: [20, 51, 53],
20: [19, 52, 54],
21: [53, 54, 55],
22: [54, 55, 56],
23: [55, 57],
24: [25, 56, 58],
25: [24, 57, 58, 59],
26: [58, 60],
27: [59, 60, 61],
28: [60, 62],
29: [61, 62, 63],
30: [62, 63, 64],
31: [63],
32: [64, 66],
34: [2, 68],
35: [3, 67, 69],
36: [2, 4, 68, 69, 70],
37: [3, 5, 69, 71],
38: [6, 70, 72],
39: [5, 7, 71, 72, 73],
40: [6, 8, 41, 72, 73, 74],
41: [7, 9, 40, 42, 73, 75],
42: [8, 10, 41, 43, 74, 76],
43: [9, 11, 42, 44, 75, 77],
44: [10, 11, 12, 43, 76, 78],
45: [11, 13, 46, 77, 78, 79],
46: [12, 13, 14, 45, 78, 79, 80],
47: [13, 15, 79],
48: [14, 16, 80, 82],
49: [15, 17, 81, 83],
50: [16, 17, 18, 82, 83, 84],
51: [17, 18, 19, 52, 83, 85],
52: [18, 20, 51, 53, 84, 85, 86],
53: [19, 21, 52, 85, 86, 87],
54: [20, 21, 22, 86, 87, 88],
55: [21, 22, 23, 56, 87, 89],
56: [22, 24, 55, 57, 88, 90],
57: [23, 25, 56, 89, 91],
58: [24, 25, 26, 59, 90, 92],
59: [25, 27, 58, 91, 92, 93],
60: [26, 27, 28, 61, 92, 94],
61: [27, 29, 60, 62, 93, 95],
62: [28, 29, 30, 61, 94, 96],
63: [29, 30, 31, 95, 96, 97],
64: [30, 32, 96, 98],
66: [32, 98],
67: [35, 101],
68: [34, 36, 100, 101, 102],
69: [35, 36, 37, 101, 102, 103],
70: [36, 38, 71, 102, 104],
71: [37, 39, 70, 103, 105],
72: [38, 39, 40, 73, 104, 105, 106],
73: [39, 40, 41, 72, 105, 107],
74: [40, 42, 75, 106, 107, 108],
75: [41, 43, 74, 107, 109],
76: [42, 44, 77, 108, 110],
77: [43, 45, 76, 109, 110, 111],
78: [44, 45, 46, 110, 111, 112],
79: [45, 46, 47, 111, 112, 113],
80: [46, 48, 112, 114],
81: [49],
82: [48, 50, 114, 116],
83: [49, 50, 51, 84, 115, 117],
84: [50, 52, 83, 116, 117, 118],
85: [51, 52, 53, 117, 119],
86: [52, 53, 54, 87, 118, 119, 120],
87: [53, 54, 55, 86, 119, 121],
88: [54, 56, 120, 121, 122],
89: [55, 57, 121],
90: [56, 58, 122, 124],
91: [57, 59, 125],
92: [58, 59, 60, 93, 124, 126],
93: [59, 61, 92, 94, 125, 126, 127],
94: [60, 62, 93, 95, 126, 128],
95: [61, 63, 94, 127, 128, 129],
96: [62, 63, 64, 128, 130],
97: [63, 129, 131],
98: [64, 66, 130, 132],
99: [131],
100: [68, 101, 134],
101: [67, 68, 69, 100, 102, 133, 135],
102: [68, 69, 70, 101, 134, 136],
103: [69, 71, 104, 135, 136, 137],
104: [70, 72, 103, 105, 136, 138],
105: [71, 72, 73, 104, 137, 139],
106: [72, 74, 107, 138, 139, 140],
107: [73, 74, 75, 106, 139, 140, 141],
108: [74, 76, 140],
109: [75, 77, 141, 143],
110: [76, 77, 78, 142, 144],
111: [77, 78, 79, 112, 143, 145],
112: [78, 79, 80, 111, 144, 146],
113: [79, 145, 147],
114: [80, 82, 146, 148],
115: [83, 147, 149],
116: [82, 84, 148, 149, 150],
117: [83, 84, 85, 118, 149, 151],
118: [84, 86, 117, 150, 151, 152],
119: [85, 86, 87, 151, 152, 153],
120: [86, 88, 121, 152, 153, 154],
121: [87, 88, 89, 120, 153, 155],
122: [88, 90, 154, 156],
124: [90, 92, 156, 158],
125: [91, 93, 126, 157, 158, 159],
126: [92, 93, 94, 125, 158, 160],
127: [93, 95, 128, 159, 161],
128: [94, 95, 96, 127, 129, 160, 162],
129: [95, 97, 128, 161, 162, 163],
130: [96, 98, 162, 163, 164],
131: [97, 99, 132, 163, 164, 165],
132: [98, 131, 164],
133: [101, 134, 167],
134: [100, 102, 133, 166, 168],
135: [101, 103, 136, 167, 168, 169],
136: [102, 103, 104, 135, 168, 170],
137: [103, 105, 138, 169, 171],
138: [104, 106, 137, 139, 170, 172],
139: [105, 106, 107, 138, 171, 173],
140: [106, 107, 108, 172, 174],
141: [107, 109, 173, 175],
142: [110],
143: [109, 111, 175, 177],
144: [110, 112, 145, 176, 177, 178],
145: [111, 113, 144, 146, 177, 179],
146: [112, 114, 145, 178, 179, 180],
147: [113, 115, 179, 180, 181],
148: [114, 116, 180, 181, 182],
149: [115, 116, 117, 150, 181, 183],
150: [116, 118, 149, 182, 183, 184],
151: [117, 118, 119, 152, 183, 185],
152: [118, 119, 120, 151, 153, 184, 186],
153: [119, 120, 121, 152, 185, 187],
154: [120, 122, 186, 188],
155: [121, 187, 189],
156: [122, 124, 188, 189, 190],
157: [125, 189, 191],
158: [124, 125, 126, 190, 191, 192],
159: [125, 127, 160, 191, 192, 193],
160: [126, 128, 159, 161, 192, 194],
161: [127, 129, 160, 162, 193, 195],
162: [128, 129, 130, 161, 194, 196],
163: [129, 130, 131, 195, 196, 197],
164: [130, 131, 132, 165, 196, 198],
165: [131, 164, 197],
166: [134, 167, 200],
167: [133, 135, 166, 168, 199, 200, 201],
168: [134, 135, 136, 167, 200, 202],
169: [135, 137, 201, 203],
170: [136, 138, 204],
171: [137, 139, 172, 203, 205],
172: [138, 140, 171, 173, 204, 205, 206],
173: [139, 141, 172, 205, 207],
174: [140, 206, 208],
175: [141, 143, 207, 209],
176: [144, 208, 210],
177: [143, 144, 145, 178, 209, 211],
178: [144, 146, 177, 179, 210, 212],
179: [145, 146, 147, 178, 211, 213],
180: [146, 147, 148, 212, 214],
181: [147, 148, 149, 182, 213, 214, 215],
182: [148, 150, 181, 214, 215, 216],
183: [149, 150, 151, 215, 216, 217],
184: [150, 152, 185, 216, 217, 218],
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332: [298, 300, 364],
333: [299, 301, 365, 367],
334: [300, 301, 302, 366, 368],
335: [301, 303, 336, 367, 368, 369],
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352: [318, 320, 384, 386],
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363: [329, 362, 395],
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437: [403, 405, 469],
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520: [486, 488, 554],
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550: [516, 518, 582, 583, 584],
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553: [519, 521, 585, 587],
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563: [529, 531, 595, 596, 597],
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632: [598, 600, 664, 666],
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634: [600, 602, 633, 666, 667, 668],
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637: [603, 605, 671],
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662: [628, 629, 630, 694, 696],
663: [629, 695, 697],
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670: [636, 638, 702, 704],
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686: [652, 653, 654, 718, 720],
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688: [654, 656, 720, 722],
689: [655, 657, 723],
690: [656, 657, 658, 722, 723, 724],
691: [657, 658, 659, 723, 724, 725],
692: [658, 659, 660, 724, 725, 726],
693: [659, 725],
694: [662, 695, 728],
695: [661, 663, 694, 727, 728, 729],
696: [662, 664, 697, 728, 729, 730],
697: [663, 665, 696, 729, 730, 731],
698: [664, 666, 730, 731, 732],
699: [665, 666, 667, 700, 731, 733],
700: [666, 667, 668, 699, 732, 734],
701: [667, 733, 735],
702: [668, 670, 734, 736],
703: [671, 735, 737],
704: [670, 671, 672, 705, 736, 738],
705: [671, 673, 704, 737, 738, 739],
706: [672, 674, 707, 738, 739, 740],
707: [673, 674, 675, 706, 739, 740, 741],
708: [674, 675, 676, 709, 740, 742],
709: [675, 677, 708, 741, 743],
710: [676, 678, 711, 742, 743, 744],
711: [677, 678, 679, 710, 743, 745],
712: [678, 680, 713, 744, 745, 746],
713: [679, 680, 681, 712, 745, 747],
714: [680, 682, 746, 747, 748],
715: [681, 682, 683, 716, 747, 748, 749],
716: [682, 683, 684, 715, 748, 750],
717: [683, 685, 749, 750, 751],
718: [684, 685, 686, 719, 750, 751, 752],
719: [685, 687, 718, 751, 753],
720: [686, 688, 752, 754],
721: [687, 755],
722: [688, 690, 754, 756],
723: [689, 690, 691, 755, 757],
724: [690, 691, 692, 756, 757, 758],
725: [691, 692, 693, 757, 758, 759],
726: [692, 758, 759],
727: [695, 761],
728: [694, 695, 696, 760, 761, 762],
729: [695, 696, 697, 761, 762, 763],
730: [696, 697, 698, 731, 762, 764],
731: [697, 698, 699, 730, 732, 763, 765],
732: [698, 700, 731, 764, 765, 766],
733: [699, 701, 734, 765, 766, 767],
734: [700, 702, 733, 735, 766, 768],
735: [701, 703, 734, 767, 768, 769],
736: [702, 704, 768, 770],
737: [703, 705, 769, 770, 771],
738: [704, 705, 706, 770, 771, 772],
739: [705, 706, 707, 771, 773],
740: [706, 707, 708, 772, 774],
741: [707, 709, 773, 775],
742: [708, 710, 776],
743: [709, 710, 711, 775, 777],
744: [710, 712, 745, 776, 777, 778],
745: [711, 712, 713, 744, 777, 779],
746: [712, 714, 747, 778, 780],
747: [713, 714, 715, 746, 779, 781],
748: [714, 715, 716, 780, 782],
749: [715, 717, 750, 781, 782, 783],
750: [716, 717, 718, 749, 782, 784],
751: [717, 718, 719, 783, 784, 785],
752: [718, 720, 784, 785, 786],
753: [719, 785, 787],
754: [720, 722, 786, 788],
755: [721, 723, 787, 788, 789],
756: [722, 724, 757, 788, 789, 790],
757: [723, 724, 725, 756, 789, 791],
758: [724, 725, 726, 790, 792],
759: [725, 726, 791],
760: [728, 793, 794],
761: [727, 728, 729, 793, 794, 795],
762: [728, 729, 730, 763, 794, 795, 796],
763: [729, 731, 762, 764, 795, 797],
764: [730, 732, 763, 796, 798],
765: [731, 732, 733, 797, 799],
766: [732, 733, 734, 767, 798, 799, 800],
767: [733, 735, 766, 799, 800, 801],
768: [734, 735, 736, 769, 800, 802],
769: [735, 737, 768, 770, 801, 803],
770: [736, 737, 738, 769, 802, 804],
771: [737, 738, 739, 772, 803, 805],
772: [738, 740, 771, 804, 806],
773: [739, 741, 805, 807],
774: [740, 808],
775: [741, 743, 807, 809],
776: [742, 744, 808, 809, 810],
777: [743, 744, 745, 778, 809, 811],
778: [744, 746, 777, 779, 810, 812],
779: [745, 747, 778, 780, 811, 812, 813],
780: [746, 748, 779, 781, 812, 814],
781: [747, 749, 780, 782, 813, 814, 815],
782: [748, 749, 750, 781, 814, 816],
783: [749, 751, 784, 815, 816, 817],
784: [750, 751, 752, 783, 816, 817, 818],
785: [751, 752, 753, 817, 818, 819],
786: [752, 754, 818, 820],
787: [753, 755, 819, 820, 821],
788: [754, 755, 756, 789, 820, 822],
789: [755, 756, 757, 788, 821, 822, 823],
790: [756, 758, 791, 822, 823, 824],
791: [757, 759, 790, 792, 823, 825],
792: [758, 791, 824],
793: [760, 761, 827],
794: [760, 761, 762, 826, 828],
795: [761, 762, 763, 827, 828, 829],
796: [762, 764, 830],
797: [763, 765, 798, 829, 831],
798: [764, 766, 797, 830, 831, 832],
799: [765, 766, 767, 831, 832, 833],
800: [766, 767, 768, 832, 834],
801: [767, 769, 802, 833, 834, 835],
802: [768, 770, 801, 803, 834, 836],
803: [769, 771, 802, 804, 835, 837],
804: [770, 772, 803, 836, 837, 838],
805: [771, 773, 837, 838, 839],
806: [772, 838, 840],
807: [773, 775, 839, 841],
808: [774, 776, 809, 840, 842],
809: [775, 776, 777, 808, 841, 843],
810: [776, 778, 842, 843, 844],
811: [777, 779, 812, 843, 844, 845],
812: [778, 779, 780, 811, 844, 846],
813: [779, 781, 814, 845, 847],
814: [780, 781, 782, 813, 846, 848],
815: [781, 783, 816, 847, 848, 849],
816: [782, 783, 784, 815, 848, 850],
817: [783, 784, 785, 849, 851],
818: [784, 785, 786, 850, 851, 852],
819: [785, 787, 820, 851, 852, 853],
820: [786, 787, 788, 819, 852, 854],
821: [787, 789, 822, 853, 854, 855],
822: [788, 789, 790, 821, 854, 856],
823: [789, 790, 791, 855, 856, 857],
824: [790, 792, 825, 856, 857, 858],
825: [791, 824, 857],
826: [794, 860],
827: [793, 795, 859, 861],
828: [794, 795, 829, 862],
829: [795, 797, 828, 861, 862, 863],
830: [796, 798, 862, 863, 864],
831: [797, 798, 799, 832, 863, 865],
832: [798, 799, 800, 831, 864, 866],
833: [799, 801, 865],
834: [800, 801, 802, 866, 867, 868],
835: [801, 803, 869],
836: [802, 804, 837, 868, 869, 870],
837: [803, 804, 805, 836, 869, 871],
838: [804, 805, 806, 839, 870, 872],
839: [805, 807, 838, 871, 873],
840: [806, 808, 872, 873, 874],
841: [807, 809, 842, 873, 874, 875],
842: [808, 810, 841, 843, 874, 876],
843: [809, 810, 811, 842, 875, 877],
844: [810, 811, 812, 876, 877, 878],
845: [811, 813, 877, 878, 879],
846: [812, 814, 878],
847: [813, 815, 879, 881],
848: [814, 815, 816, 880, 882],
849: [815, 817, 850, 881, 882, 883],
850: [816, 818, 849, 851, 882, 884],
851: [817, 818, 819, 850, 883, 885],
852: [818, 819, 820, 853, 884, 885, 886],
853: [819, 821, 852, 885, 886, 887],
854: [820, 821, 822, 886, 887, 888],
855: [821, 823, 856, 887, 888, 889],
856: [822, 823, 824, 855, 888, 889, 890],
857: [823, 824, 825, 858, 889, 891],
858: [824, 857, 890],
859: [827, 893],
860: [826, 892, 894],
861: [827, 829, 893, 895],
862: [828, 829, 830, 894, 895, 896],
863: [829, 830, 831, 864, 895, 897],
864: [830, 832, 863, 865, 896, 898],
865: [831, 833, 864, 897, 898, 899],
866: [832, 834, 867, 898, 900],
867: [834, 866, 899],
868: [834, 836, 900, 902],
869: [835, 836, 837, 870, 901, 903],
870: [836, 838, 869, 871, 902, 904],
871: [837, 839, 870, 903, 904, 905],
872: [838, 840, 873, 904, 905, 906],
873: [839, 840, 841, 872, 905, 907],
874: [840, 841, 842, 906, 907, 908],
875: [841, 843, 876, 907, 908, 909],
876: [842, 844, 875, 877, 908, 910],
877: [843, 844, 845, 876, 909, 911],
878: [844, 845, 846, 910, 911, 912],
879: [845, 847, 911, 913],
880: [848],
881: [847, 849, 913, 915],
882: [848, 849, 850, 914, 915, 916],
883: [849, 851, 884, 915, 916, 917],
884: [850, 852, 883, 916, 917, 918],
885: [851, 852, 853, 917, 918, 919],
886: [852, 853, 854, 918, 919, 920],
887: [853, 854, 855, 919, 921],
888: [854, 855, 856, 920, 921, 922],
889: [855, 856, 857, 890, 921, 923],
890: [856, 858, 889, 891, 922, 924],
891: [857, 890, 923],
892: [860, 925, 926],
893: [859, 861, 894, 925, 927],
894: [860, 862, 893, 926, 928],
895: [861, 862, 863, 896, 927, 928, 929],
896: [862, 864, 895, 897, 928, 930],
897: [863, 865, 896, 929, 930, 931],
898: [864, 865, 866, 899, 930, 932],
899: [865, 867, 898, 931, 932, 933],
900: [866, 868, 932, 934],
901: [869, 933, 935],
902: [868, 870, 903, 934, 935, 936],
903: [869, 871, 902, 935, 936, 937],
904: [870, 871, 872, 905, 936, 938],
905: [871, 872, 873, 904, 906, 937, 939],
906: [872, 874, 905, 907, 938, 940],
907: [873, 874, 875, 906, 908, 939, 941],
908: [874, 875, 876, 907, 940, 942],
909: [875, 877, 910, 941, 942, 943],
910: [876, 878, 909, 911, 942, 944],
911: [877, 878, 879, 910, 943, 945],
912: [878, 944, 946],
913: [879, 881, 945, 947],
914: [882, 946, 948],
915: [881, 882, 883, 947, 949],
916: [882, 883, 884, 948, 950],
917: [883, 884, 885, 918, 949, 951],
918: [884, 885, 886, 917, 950, 952],
919: [885, 886, 887, 951, 952, 953],
920: [886, 888, 921, 952, 954],
921: [887, 888, 889, 920, 922, 953, 955],
922: [888, 890, 921, 954, 956],
923: [889, 891, 924, 955, 957],
924: [890, 923, 956],
925: [892, 893, 926, 959],
926: [892, 894, 925, 927, 958, 960],
927: [893, 895, 926, 959, 961],
928: [894, 895, 896, 929, 960, 962],
929: [895, 897, 928, 961, 962, 963],
930: [896, 897, 898, 931, 962, 964],
931: [897, 899, 930, 932, 963, 965],
932: [898, 899, 900, 931, 964, 966],
933: [899, 901, 965, 966, 967],
934: [900, 902, 935, 966, 968],
935: [901, 902, 903, 934, 967, 969],
936: [902, 903, 904, 937, 968, 970],
937: [903, 905, 936, 969, 970, 971],
938: [904, 906, 939, 970, 972],
939: [905, 907, 938, 940, 971, 973],
940: [906, 908, 939, 941, 972, 974],
941: [907, 909, 940, 973, 974, 975],
942: [908, 909, 910, 943, 974, 976],
943: [909, 911, 942, 944, 975, 976, 977],
944: [910, 912, 943, 976, 978],
945: [911, 913, 977, 978, 979],
946: [912, 914, 978, 980],
947: [913, 915, 948, 979, 980, 981],
948: [914, 916, 947, 949, 980, 981, 982],
949: [915, 917, 948, 950, 981, 983],
950: [916, 918, 949, 982, 983, 984],
951: [917, 919, 952, 983, 984, 985],
952: [918, 919, 920, 951, 984, 985, 986],
953: [919, 921, 985],
954: [920, 922, 986, 988],
955: [921, 923, 989],
956: [922, 924, 957, 988, 989, 990],
957: [923, 956, 989],
958: [926, 992],
959: [925, 927, 960, 991, 992, 993],
960: [926, 928, 959, 992, 993, 994],
961: [927, 929, 993],
962: [928, 929, 930, 994, 996],
963: [929, 931, 997],
964: [930, 932, 996, 997, 998],
965: [931, 933, 966, 997, 998, 999],
966: [932, 933, 934, 965, 998, 999, 1000],
967: [933, 935, 968, 999, 1001],
968: [934, 936, 967, 969, 1000, 1002],
969: [935, 937, 968, 970, 1001, 1003],
970: [936, 937, 938, 969, 1002, 1004],
971: [937, 939, 1003, 1005],
972: [938, 940, 1006],
973: [939, 941, 974, 1005, 1007],
974: [940, 941, 942, 973, 975, 1006, 1008],
975: [941, 943, 974, 1007, 1008, 1009],
976: [942, 943, 944, 1008, 1009, 1010],
977: [943, 945, 1009],
978: [944, 945, 946, 1010, 1011, 1012],
979: [945, 947, 1013],
980: [946, 947, 948, 981, 1012, 1014],
981: [947, 948, 949, 980, 1013, 1015],
982: [948, 950, 983, 1014, 1016],
983: [949, 950, 951, 982, 1015, 1017],
984: [950, 951, 952, 1016, 1017, 1018],
985: [951, 952, 953, 1017, 1019],
986: [952, 954, 1018, 1020],
987: [1019, 1021],
988: [954, 956, 1020, 1022],
989: [955, 956, 957, 1021, 1023],
990: [956, 1022, 1023],
991: [959, 992, 1025],
992: [958, 959, 960, 991, 1024, 1026],
993: [959, 960, 961, 1025, 1027],
994: [960, 962, 1026, 1028],
996: [962, 964, 1028, 1030],
997: [963, 964, 965, 1029, 1030, 1031],
998: [964, 965, 966, 1030, 1031, 1032],
999: [965, 966, 967, 1000, 1031, 1033],
1000: [966, 968, 999, 1001, 1032, 1033, 1034],
1001: [967, 969, 1000, 1002, 1033, 1035],
1002: [968, 970, 1001, 1034, 1036],
1003: [969, 971, 1035, 1037],
1004: [970, 1038],
1005: [971, 973, 1037, 1039],
1006: [972, 974, 1007, 1038, 1040],
1007: [973, 975, 1006, 1039, 1041],
1008: [974, 975, 976, 1040, 1041, 1042],
1009: [975, 976, 977, 1041, 1043],
1010: [976, 978, 1042, 1044],
1011: [978],
1012: [978, 980, 1044, 1046],
1013: [979, 981, 1045, 1046, 1047],
1014: [980, 982, 1015, 1046, 1047, 1048],
1015: [981, 983, 1014, 1016, 1047, 1048, 1049],
1016: [982, 984, 1015, 1048, 1049, 1050],
1017: [983, 984, 985, 1018, 1049, 1051],
1018: [984, 986, 1017, 1050, 1051, 1052],
1019: [985, 987, 1051, 1052, 1053],
1020: [986, 988, 1052, 1054],
1021: [987, 989, 1022, 1053, 1054, 1055],
1022: [988, 990, 1021, 1054, 1055, 1056],
1023: [989, 990, 1055],
1024: [992, 1057, 1058],
1025: [991, 993, 1026, 1057, 1058, 1059],
1026: [992, 994, 1025, 1058, 1059, 1060],
1027: [993, 1059, 1061],
1028: [994, 996, 1060, 1062],
1029: [997, 1061, 1063],
1030: [996, 997, 998, 1062, 1063, 1064],
1031: [997, 998, 999, 1032, 1063, 1065],
1032: [998, 1000, 1031, 1033, 1064, 1066],
1033: [999, 1000, 1001, 1032, 1065, 1067],
1034: [1000, 1002, 1035, 1066, 1067, 1068],
1035: [1001, 1003, 1034, 1067, 1068, 1069],
1036: [1002, 1068, 1070],
1037: [1003, 1005, 1038, 1069, 1071],
1038: [1004, 1006, 1037, 1070, 1072],
1039: [1005, 1007, 1040, 1071, 1072, 1073],
1040: [1006, 1008, 1039, 1041, 1072, 1074],
1041: [1007, 1008, 1009, 1040, 1042, 1073, 1075],
1042: [1008, 1010, 1041, 1074, 1076],
1043: [1009, 1075, 1077],
1044: [1010, 1012, 1076, 1078],
1045: [1013, 1077, 1079],
1046: [1012, 1013, 1014, 1078, 1079, 1080],
1047: [1013, 1014, 1015, 1079, 1080, 1081],
1048: [1014, 1015, 1016, 1080, 1081, 1082],
1049: [1015, 1016, 1017, 1050, 1081, 1083],
1050: [1016, 1018, 1049, 1051, 1082, 1084],
1051: [1017, 1018, 1019, 1050, 1083, 1085],
1052: [1018, 1019, 1020, 1053, 1084, 1086],
1053: [1019, 1021, 1052, 1054, 1085, 1087],
1054: [1020, 1021, 1022, 1053, 1086, 1088],
1055: [1021, 1022, 1023, 1056, 1087, 1089],
1056: [1022, 1055, 1088],
1057: [1024, 1025],
1058: [1024, 1025, 1026],
1059: [1025, 1026, 1027],
1060: [1026, 1028],
1061: [1027, 1029],
1062: [1028, 1030],
1063: [1029, 1030, 1031],
1064: [1030, 1032, 1065],
1065: [1031, 1033, 1064],
1066: [1032, 1034],
1067: [1033, 1034, 1035],
1068: [1034, 1035, 1036],
1069: [1035, 1037, 1070],
1070: [1036, 1038, 1069],
1071: [1037, 1039],
1072: [1038, 1039, 1040],
1073: [1039, 1041, 1074],
1074: [1040, 1042, 1073],
1075: [1041, 1043],
1076: [1042, 1044],
1077: [1043, 1045],
1078: [1044, 1046],
1079: [1045, 1046, 1047],
1080: [1046, 1047, 1048],
1081: [1047, 1048, 1049, 1082],
1082: [1048, 1050, 1081],
1083: [1049, 1051],
1084: [1050, 1052, 1085],
1085: [1051, 1053, 1084, 1086],
1086: [1052, 1054, 1085],
1087: [1053, 1055, 1088],
1088: [1054, 1056, 1087],
1089: [1055]}

cycle_19_post_war_links_2 = {2: [34, 36],
3: [4, 35, 37],
4: [3],
5: [6, 37, 39],
6: [5, 7, 38, 40],
7: [6, 39, 41],
8: [40, 41, 42],
9: [41, 42, 43],
10: [42, 43, 44],
11: [43, 44, 45],
12: [44, 46],
13: [14, 45, 47],
14: [13, 46, 48],
15: [47, 48, 49],
16: [48, 50],
17: [49, 50, 51],
18: [50, 51, 52],
19: [51, 52, 53],
20: [21, 52, 54],
21: [20, 53, 55],
22: [54, 55, 56],
23: [55, 56, 57],
24: [56, 57, 58],
25: [57, 58, 59],
26: [58, 59, 60],
27: [59, 61],
28: [60, 61, 62],
29: [61, 62, 63],
30: [62, 63, 64],
31: [63],
32: [64, 66],
34: [2, 68],
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563: [529, 531, 595, 596, 597],
564: [530, 531, 532, 596, 598],
565: [531, 532, 533, 597, 599],
566: [532, 533, 534, 598, 599, 600],
567: [533, 534, 535, 568, 599, 601],
568: [534, 536, 567, 569, 600, 602],
569: [535, 536, 537, 568, 601, 603],
570: [536, 538, 571, 602, 603, 604],
571: [537, 538, 539, 570, 572, 603, 605],
572: [538, 540, 571, 573, 604, 606],
573: [539, 540, 541, 572, 605, 607],
574: [540, 542, 575, 606, 607, 608],
575: [541, 543, 574, 576, 607, 609],
576: [542, 544, 575, 577, 608, 610],
577: [543, 545, 576, 578, 609, 611],
578: [544, 546, 577, 610, 612],
579: [545, 547, 611, 613],
580: [546, 548, 612, 614],
581: [547, 549, 582, 613, 614, 615],
582: [548, 550, 581, 614, 615, 616],
583: [549, 550, 551, 615, 616, 617],
584: [550, 616, 618],
585: [551, 553, 617, 619],
586: [554, 618, 620],
587: [553, 555, 588, 619, 620, 621],
588: [554, 555, 556, 587, 620, 621, 622],
589: [555, 556, 557, 621, 622, 623],
590: [556, 557, 558, 622, 624],
591: [557, 559, 592, 623, 624, 625],
592: [558, 559, 560, 591, 624, 626],
593: [559, 560, 561, 625, 626, 627],
594: [560, 626, 627],
595: [562, 563, 628, 629],
596: [562, 563, 564, 628, 629, 630],
597: [563, 565, 629],
598: [564, 566, 630, 632],
599: [565, 566, 567, 600, 631, 633],
600: [566, 568, 599, 601, 632, 634],
601: [567, 569, 600, 633, 634, 635],
602: [568, 570, 634, 635, 636],
603: [569, 570, 571, 604, 635, 637],
604: [570, 572, 603, 605, 636, 638],
605: [571, 573, 604, 606, 637, 639],
606: [572, 574, 605, 607, 638, 640],
607: [573, 574, 575, 606, 639, 640, 641],
608: [574, 576, 640, 642],
609: [575, 577, 610, 641, 642, 643],
610: [576, 578, 609, 642, 644],
611: [577, 579, 643, 645],
612: [578, 580],
613: [579, 581, 645, 647],
614: [580, 581, 582, 646, 647, 648],
615: [581, 582, 583, 647, 648, 649],
616: [582, 583, 584, 648, 649, 650],
617: [583, 585, 618, 649, 650, 651],
618: [584, 586, 617, 619, 650, 651, 652],
619: [585, 587, 618, 651, 652, 653],
620: [586, 587, 588, 621, 652, 654],
621: [587, 588, 589, 620, 653, 655],
622: [588, 589, 590, 623, 654, 656],
623: [589, 591, 622, 624, 655, 656, 657],
624: [590, 591, 592, 623, 656, 658],
625: [591, 593, 626, 657, 658, 659],
626: [592, 593, 594, 625, 658, 660],
627: [593, 594, 659],
628: [595, 596, 662],
629: [595, 596, 597, 661, 663],
630: [596, 598, 662, 664],
631: [599, 665],
632: [598, 600, 664, 666],
633: [599, 601, 665, 666, 667],
634: [600, 601, 602, 635, 666, 668],
635: [601, 602, 603, 634, 667, 669],
636: [602, 604, 668, 670],
637: [603, 605, 671],
638: [604, 606, 639, 670, 672],
639: [605, 607, 638, 671, 672, 673],
640: [606, 607, 608, 641, 672, 674],
641: [607, 609, 640, 642, 673, 674, 675],
642: [608, 609, 610, 641, 674, 676],
643: [609, 611, 675, 676, 677],
644: [610, 676, 678],
645: [611, 613, 677, 679],
646: [614, 678, 680],
647: [613, 614, 615, 648, 679, 681],
648: [614, 615, 616, 647, 680, 682],
649: [615, 616, 617, 681, 682, 683],
650: [616, 617, 618, 682, 683, 684],
651: [617, 618, 619, 683, 685],
652: [618, 619, 620, 684, 686],
653: [619, 621, 654, 685, 686, 687],
654: [620, 622, 653, 655, 686, 688],
655: [621, 623, 654, 687, 689],
656: [622, 623, 624, 688, 690],
657: [623, 625, 658, 689, 690, 691],
658: [624, 625, 626, 657, 690, 692],
659: [625, 627, 660, 691, 693],
660: [626, 659, 692, 693],
661: [629, 662, 695],
662: [628, 630, 661, 694, 695, 696],
663: [629, 695, 697],
664: [630, 632, 696, 698],
665: [631, 633, 697, 698, 699],
666: [632, 633, 634, 667, 698, 700],
667: [633, 635, 666, 699, 700, 701],
668: [634, 636, 700, 702],
669: [635],
670: [636, 638, 702, 704],
671: [637, 639, 672, 703, 704, 705],
672: [638, 639, 640, 671, 704, 706],
673: [639, 641, 674, 705, 706, 707],
674: [640, 641, 642, 673, 706, 708],
675: [641, 643, 676, 707, 708, 709],
676: [642, 643, 644, 675, 708, 710],
677: [643, 645, 709, 710, 711],
678: [644, 646, 679, 710, 711, 712],
679: [645, 647, 678, 680, 711, 713],
680: [646, 648, 679, 712, 713, 714],
681: [647, 649, 713, 714, 715],
682: [648, 649, 650, 683, 714, 715, 716],
683: [649, 650, 651, 682, 715, 717],
684: [650, 652, 685, 716, 717, 718],
685: [651, 653, 684, 686, 717, 719],
686: [652, 653, 654, 685, 718, 720],
687: [653, 655, 719],
688: [654, 656, 720, 722],
689: [655, 657, 723],
690: [656, 657, 658, 722, 724],
691: [657, 659, 692, 723, 724, 725],
692: [658, 660, 691, 724, 725, 726],
693: [659, 660, 725],
694: [662, 728],
695: [661, 662, 663, 727, 728, 729],
696: [662, 664, 697, 728, 730],
697: [663, 665, 696, 698, 729, 731],
698: [664, 665, 666, 697, 699, 730, 732],
699: [665, 667, 698, 731, 733],
700: [666, 667, 668, 732, 733, 734],
701: [667, 733, 735],
702: [668, 670, 734, 736],
703: [671, 735, 737],
704: [670, 671, 672, 705, 736, 738],
705: [671, 673, 704, 737, 739],
706: [672, 673, 674, 738, 739, 740],
707: [673, 675, 708, 739, 740, 741],
708: [674, 675, 676, 707, 740, 742],
709: [675, 677, 710, 741, 743],
710: [676, 677, 678, 709, 742, 744],
711: [677, 678, 679, 712, 743, 745],
712: [678, 680, 711, 744, 745, 746],
713: [679, 680, 681, 714, 745, 747],
714: [680, 681, 682, 713, 715, 746, 748],
715: [681, 682, 683, 714, 747, 749],
716: [682, 684, 717, 748, 749, 750],
717: [683, 684, 685, 716, 749, 750, 751],
718: [684, 686, 750, 751, 752],
719: [685, 687, 751, 752, 753],
720: [686, 688, 752, 754],
721: [755],
722: [688, 690, 754, 756],
723: [689, 691, 724, 755, 756, 757],
724: [690, 691, 692, 723, 756, 758],
725: [691, 692, 693, 757, 758, 759],
726: [692, 758],
727: [695, 728, 761],
728: [694, 695, 696, 727, 729, 760, 762],
729: [695, 697, 728, 761, 762, 763],
730: [696, 698, 731, 762, 763, 764],
731: [697, 699, 730, 732, 763, 765],
732: [698, 700, 731, 764, 765, 766],
733: [699, 700, 701, 765, 766, 767],
734: [700, 702, 766, 767, 768],
735: [701, 703, 767, 768, 769],
736: [702, 704, 737, 768, 769, 770],
737: [703, 705, 736, 769, 770, 771],
738: [704, 706, 739, 770, 771, 772],
739: [705, 706, 707, 738, 771, 772, 773],
740: [706, 707, 708, 772, 774],
741: [707, 709, 773, 775],
742: [708, 710, 776],
743: [709, 711, 744, 775, 777],
744: [710, 712, 743, 776, 777, 778],
745: [711, 712, 713, 746, 777, 778, 779],
746: [712, 714, 745, 747, 778, 780],
747: [713, 715, 746, 748, 779, 781],
748: [714, 716, 747, 780, 781, 782],
749: [715, 716, 717, 781, 782, 783],
750: [716, 717, 718, 782, 783, 784],
751: [717, 718, 719, 783, 784, 785],
752: [718, 719, 720, 784, 786],
753: [719, 785, 787],
754: [720, 722, 786, 788],
755: [721, 723, 787, 789],
756: [722, 723, 724, 788, 789, 790],
757: [723, 725, 758, 789, 790, 791],
758: [724, 725, 726, 757, 759, 790, 792],
759: [725, 758, 791],
760: [728, 793, 794],
761: [727, 729, 762, 793, 795],
762: [728, 729, 730, 761, 794, 796],
763: [729, 730, 731, 795, 797],
764: [730, 732, 765, 796, 798],
765: [731, 732, 733, 764, 797, 799],
766: [732, 733, 734, 798, 799, 800],
767: [733, 734, 735, 799, 800, 801],
768: [734, 735, 736, 769, 800, 802],
769: [735, 736, 737, 768, 801, 803],
770: [736, 737, 738, 802, 803, 804],
771: [737, 738, 739, 803, 804, 805],
772: [738, 739, 740, 804, 806],
773: [739, 741, 805, 807],
774: [740, 808],
775: [741, 743, 807, 809],
776: [742, 744, 808, 810],
777: [743, 744, 745, 809, 810, 811],
778: [744, 745, 746, 810, 811, 812],
779: [745, 747, 780, 811, 812, 813],
780: [746, 748, 779, 812, 813, 814],
781: [747, 748, 749, 813, 814, 815],
782: [748, 749, 750, 814, 815, 816],
783: [749, 750, 751, 815, 816, 817],
784: [750, 751, 752, 785, 816, 818],
785: [751, 753, 784, 817, 818, 819],
786: [752, 754, 818, 819, 820],
787: [753, 755, 788, 819, 820, 821],
788: [754, 756, 787, 820, 821, 822],
789: [755, 756, 757, 790, 821, 823],
790: [756, 757, 758, 789, 822, 823, 824],
791: [757, 759, 823, 824, 825],
792: [758, 824],
793: [760, 761, 827],
794: [760, 762, 826],
795: [761, 763, 827, 829],
796: [762, 764, 830],
797: [763, 765, 798, 829, 831],
798: [764, 766, 797, 799, 830, 831, 832],
799: [765, 766, 767, 798, 831, 833],
800: [766, 767, 768, 801, 832, 834],
801: [767, 769, 800, 802, 833, 835],
802: [768, 770, 801, 803, 834, 836],
803: [769, 770, 771, 802, 835, 837],
804: [770, 771, 772, 805, 836, 838],
805: [771, 773, 804, 837, 838, 839],
806: [772, 838, 840],
807: [773, 775, 839, 841],
808: [774, 776, 809, 840, 842],
809: [775, 777, 808, 841, 842, 843],
810: [776, 777, 778, 842, 843, 844],
811: [777, 778, 779, 812, 843, 845],
812: [778, 779, 780, 811, 844, 846],
813: [779, 780, 781, 845, 846, 847],
814: [780, 781, 782, 846, 847, 848],
815: [781, 782, 783, 847, 849],
816: [782, 783, 784, 848, 849, 850],
817: [783, 785, 818, 849, 851],
818: [784, 785, 786, 817, 850, 851, 852],
819: [785, 786, 787, 851, 853],
820: [786, 787, 788, 852, 853, 854],
821: [787, 788, 789, 822, 853, 855],
822: [788, 790, 821, 854, 856],
823: [789, 790, 791, 855, 856, 857],
824: [790, 791, 792, 825, 856, 858],
825: [791, 824, 857],
826: [794, 860],
827: [793, 795, 859, 861],
829: [795, 797, 861, 863],
830: [796, 798, 862, 863, 864],
831: [797, 798, 799, 863, 864, 865],
832: [798, 800, 864, 865, 866],
833: [799, 801, 865],
834: [800, 802, 866, 868],
835: [801, 803, 869],
836: [802, 804, 837, 868, 869, 870],
837: [803, 805, 836, 838, 869, 871],
838: [804, 805, 806, 837, 870, 871, 872],
839: [805, 807, 871, 873],
840: [806, 808, 841, 872, 873, 874],
841: [807, 809, 840, 873, 874, 875],
842: [808, 809, 810, 874, 875, 876],
843: [809, 810, 811, 844, 875, 877],
844: [810, 812, 843, 876, 877, 878],
845: [811, 813, 846, 877, 878, 879],
846: [812, 813, 814, 845, 847, 878, 880],
847: [813, 814, 815, 846, 879, 881],
848: [814, 816, 882],
849: [815, 816, 817, 850, 881, 883],
850: [816, 818, 849, 882, 883, 884],
851: [817, 818, 819, 852, 883, 885],
852: [818, 820, 851, 853, 884, 886],
853: [819, 820, 821, 852, 885, 887],
854: [820, 822, 855, 886, 887, 888],
855: [821, 823, 854, 887, 888, 889],
856: [822, 823, 824, 857, 888, 889, 890],
857: [823, 825, 856, 858, 889, 891],
858: [824, 857, 890],
859: [827, 893],
860: [826, 892, 894],
861: [827, 829, 893, 895],
862: [830, 894, 896],
863: [829, 830, 831, 895, 897],
864: [830, 831, 832, 896, 897, 898],
865: [831, 832, 833, 897, 898, 899],
866: [832, 834, 898, 900],
868: [834, 836, 900, 902],
869: [835, 836, 837, 870, 901, 903],
870: [836, 838, 869, 902, 903, 904],
871: [837, 838, 839, 903, 904, 905],
872: [838, 840, 873, 904, 905, 906],
873: [839, 840, 841, 872, 905, 907],
874: [840, 841, 842, 875, 906, 908],
875: [841, 842, 843, 874, 907, 909],
876: [842, 844, 877, 908, 909, 910],
877: [843, 844, 845, 876, 909, 910, 911],
878: [844, 845, 846, 910, 911, 912],
879: [845, 847, 911, 913],
880: [846],
881: [847, 849, 913, 915],
882: [848, 850, 914, 916],
883: [849, 850, 851, 884, 915, 916, 917],
884: [850, 852, 883, 916, 917, 918],
885: [851, 853, 886, 917, 918, 919],
886: [852, 854, 885, 887, 918, 920],
887: [853, 854, 855, 886, 919, 921],
888: [854, 855, 856, 920, 921, 922],
889: [855, 856, 857, 921, 922, 923],
890: [856, 858, 891, 922, 923, 924],
891: [857, 890, 923],
892: [860, 893, 926],
893: [859, 861, 892, 894, 925, 927],
894: [860, 862, 893, 895, 926, 928],
895: [861, 863, 894, 927, 928, 929],
896: [862, 864, 928, 930],
897: [863, 864, 865, 929, 930, 931],
898: [864, 865, 866, 930, 932],
899: [865, 931, 933],
900: [866, 868, 932, 934],
901: [869, 933, 935],
902: [868, 870, 934, 935, 936],
903: [869, 870, 871, 935, 936, 937],
904: [870, 871, 872, 936, 937, 938],
905: [871, 872, 873, 937, 938, 939],
906: [872, 874, 907, 938, 939, 940],
907: [873, 875, 906, 939, 940, 941],
908: [874, 876, 909, 940, 941, 942],
909: [875, 876, 877, 908, 941, 943],
910: [876, 877, 878, 911, 942, 944],
911: [877, 878, 879, 910, 943, 945],
912: [878, 944, 946],
913: [879, 881, 945, 947],
914: [882, 946, 948],
915: [881, 883, 947, 948, 949],
916: [882, 883, 884, 948, 949, 950],
917: [883, 884, 885, 949, 950, 951],
918: [884, 885, 886, 919, 950, 952],
919: [885, 887, 918, 951, 952, 953],
920: [886, 888, 921, 952, 954],
921: [887, 888, 889, 920, 953, 955],
922: [888, 889, 890, 954, 956],
923: [889, 890, 891, 955, 957],
924: [890, 956],
925: [893, 926, 959],
926: [892, 894, 925, 927, 958, 960],
927: [893, 895, 926, 959, 960, 961],
928: [894, 895, 896, 929, 960, 962],
929: [895, 897, 928, 930, 961, 963],
930: [896, 897, 898, 929, 931, 962, 964],
931: [897, 899, 930, 963, 964, 965],
932: [898, 900, 933, 964, 966],
933: [899, 901, 932, 965, 966, 967],
934: [900, 902, 935, 966, 968],
935: [901, 902, 903, 934, 936, 967, 969],
936: [902, 903, 904, 935, 968, 970],
937: [903, 904, 905, 969, 971],
938: [904, 905, 906, 970, 972],
939: [905, 906, 907, 971, 973],
940: [906, 907, 908, 941, 972, 973, 974],
941: [907, 908, 909, 940, 973, 975],
942: [908, 910, 943, 974, 976],
943: [909, 911, 942, 944, 975, 977],
944: [910, 912, 943, 945, 976, 978],
945: [911, 913, 944, 946, 977, 979],
946: [912, 914, 945, 978, 980],
947: [913, 915, 948, 979, 981],
948: [914, 915, 916, 947, 980, 981, 982],
949: [915, 916, 917, 981, 983],
950: [916, 917, 918, 951, 982, 984],
951: [917, 919, 950, 983, 984, 985],
952: [918, 919, 920, 984, 985, 986],
953: [919, 921, 985],
954: [920, 922, 986, 988],
955: [921, 923, 989],
956: [922, 924, 957, 988, 990],
957: [923, 956, 989],
958: [926, 959, 992],
959: [925, 927, 958, 991, 992, 993],
960: [926, 927, 928, 992, 993, 994],
961: [927, 929, 993],
962: [928, 930, 994, 996],
963: [929, 931, 964, 995, 997],
964: [930, 931, 932, 963, 965, 996, 998],
965: [931, 933, 964, 997, 998, 999],
966: [932, 933, 934, 967, 998, 1000],
967: [933, 935, 966, 999, 1000, 1001],
968: [934, 936, 969, 1000, 1001, 1002],
969: [935, 937, 968, 970, 1001, 1003],
970: [936, 938, 969, 1002, 1004],
971: [937, 939, 1003, 1005],
972: [938, 940, 1006],
973: [939, 940, 941, 1005, 1006, 1007],
974: [940, 942, 975, 1006, 1007, 1008],
975: [941, 943, 974, 976, 1007, 1009],
976: [942, 944, 975, 977, 1008, 1010],
977: [943, 945, 976, 1009, 1011],
978: [944, 946, 1010, 1012],
979: [945, 947, 1013],
980: [946, 948, 1012, 1013, 1014],
981: [947, 948, 949, 982, 1013, 1015],
982: [948, 950, 981, 983, 1014, 1016],
983: [949, 951, 982, 1015, 1016, 1017],
984: [950, 951, 952, 1016, 1017, 1018],
985: [951, 952, 953, 986, 1017, 1019],
986: [952, 954, 985, 987, 1018, 1020],
987: [986, 1021],
988: [954, 956, 1020, 1022],
989: [955, 957, 990, 1021, 1022, 1023],
990: [956, 989, 1022],
991: [959, 1024, 1025],
992: [958, 959, 960, 1024, 1025, 1026],
993: [959, 960, 961, 1025, 1026, 1027],
994: [960, 962, 995, 1026, 1028],
995: [963, 994, 1029],
996: [962, 964, 1028, 1030],
997: [963, 965, 1029, 1030, 1031],
998: [964, 965, 966, 999, 1030, 1032],
999: [965, 967, 998, 1031, 1032, 1033],
1000: [966, 967, 968, 1032, 1033, 1034],
1001: [967, 968, 969, 1033, 1034, 1035],
1002: [968, 970, 1034, 1035, 1036],
1003: [969, 971, 1035, 1037],
1004: [970, 1037, 1038],
1005: [971, 973, 1037, 1039],
1006: [972, 973, 974, 1038, 1040],
1007: [973, 974, 975, 1008, 1039, 1040, 1041],
1008: [974, 976, 1007, 1009, 1040, 1042],
1009: [975, 977, 1008, 1041, 1042, 1043],
1010: [976, 978, 1042, 1044],
1011: [977, 1044],
1012: [978, 980, 1044, 1046],
1013: [979, 980, 981, 1045, 1047],
1014: [980, 982, 1015, 1046, 1047, 1048],
1015: [981, 983, 1014, 1047, 1049],
1016: [982, 983, 984, 1048, 1049, 1050],
1017: [983, 984, 985, 1018, 1049, 1051],
1018: [984, 986, 1017, 1050, 1051, 1052],
1019: [985, 1051, 1053],
1020: [986, 988, 1052, 1054],
1021: [987, 989, 1053, 1054, 1055],
1022: [988, 989, 990, 1054, 1055, 1056],
1023: [989, 1055, 1056],
1024: [991, 992, 1025, 1058],
1025: [991, 992, 993, 1024, 1057, 1059],
1026: [992, 993, 994, 1058, 1060],
1027: [993, 1059, 1061],
1028: [994, 996, 1060, 1062],
1029: [995, 997, 1061, 1062, 1063],
1030: [996, 997, 998, 1031, 1062, 1064],
1031: [997, 999, 1030, 1063, 1064, 1065],
1032: [998, 999, 1000, 1064, 1065, 1066],
1033: [999, 1000, 1001, 1065, 1066, 1067],
1034: [1000, 1001, 1002, 1066, 1067, 1068],
1035: [1001, 1002, 1003, 1067, 1069],
1036: [1002, 1068, 1070],
1037: [1003, 1004, 1005, 1069, 1070, 1071],
1038: [1004, 1006, 1039, 1070, 1072],
1039: [1005, 1007, 1038, 1040, 1071, 1073],
1040: [1006, 1007, 1008, 1039, 1072, 1074],
1041: [1007, 1009, 1042, 1073, 1074, 1075],
1042: [1008, 1009, 1010, 1041, 1074, 1076],
1043: [1009, 1075, 1077],
1044: [1010, 1011, 1012, 1076, 1077, 1078],
1045: [1013, 1077, 1079],
1046: [1012, 1014, 1078, 1079, 1080],
1047: [1013, 1014, 1015, 1048, 1079, 1081],
1048: [1014, 1016, 1047, 1080, 1081, 1082],
1049: [1015, 1016, 1017, 1050, 1081, 1082, 1083],
1050: [1016, 1018, 1049, 1051, 1082, 1084],
1051: [1017, 1018, 1019, 1050, 1052, 1083, 1085],
1052: [1018, 1020, 1051, 1053, 1084, 1086],
1053: [1019, 1021, 1052, 1085, 1086, 1087],
1054: [1020, 1021, 1022, 1086, 1087, 1088],
1055: [1021, 1022, 1023, 1087, 1088, 1089],
1056: [1022, 1023, 1088],
1057: [1025],
1058: [1024, 1026, 1059],
1059: [1025, 1027, 1058],
1060: [1026, 1028],
1061: [1027, 1029],
1062: [1028, 1029, 1030, 1063],
1063: [1029, 1031, 1062],
1064: [1030, 1031, 1032],
1065: [1031, 1032, 1033],
1066: [1032, 1033, 1034],
1067: [1033, 1034, 1035],
1068: [1034, 1036],
1069: [1035, 1037],
1070: [1036, 1037, 1038],
1071: [1037, 1039, 1072],
1072: [1038, 1040, 1071, 1073],
1073: [1039, 1041, 1072],
1074: [1040, 1041, 1042],
1075: [1041, 1043],
1076: [1042, 1044],
1077: [1043, 1044, 1045, 1078],
1078: [1044, 1046, 1077],
1079: [1045, 1046, 1047],
1080: [1046, 1048],
1081: [1047, 1048, 1049],
1082: [1048, 1049, 1050],
1083: [1049, 1051, 1084],
1084: [1050, 1052, 1083],
1085: [1051, 1053],
1086: [1052, 1053, 1054],
1087: [1053, 1054, 1055],
1088: [1054, 1055, 1056],
1089: [1055]}

cycle_20_links = {2: [34, 36],
3: [35, 37],
5: [37, 39],
6: [7, 38, 40],
7: [6, 39, 41],
8: [40, 41, 42],
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29: [61, 63],
30: [62, 63, 64],
31: [63],
32: [64, 66],
34: [2, 68],
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63: [29, 30, 31, 62, 95, 97],
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88: [54, 55, 56, 120, 122],
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99: [131],
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102: [68, 70, 103, 134, 135, 136],
103: [69, 71, 102, 135, 137],
104: [70, 71, 72, 136, 137, 138],
105: [71, 73, 106, 137, 138, 139],
106: [72, 73, 74, 105, 138, 140],
107: [73, 75, 139, 140, 141],
108: [74, 76, 140],
109: [75, 77, 141, 143],
110: [76, 78, 144],
111: [77, 79, 143, 144, 145],
112: [78, 79, 80, 144, 145, 146],
113: [79, 145, 147],
114: [80, 82, 146, 148],
115: [83, 147, 149],
116: [82, 83, 84, 148, 150],
117: [83, 85, 118, 149, 150, 151],
118: [84, 86, 117, 119, 150, 152],
119: [85, 86, 87, 118, 151, 153],
120: [86, 87, 88, 121, 152, 154],
121: [87, 89, 120, 153, 155],
122: [88, 90, 154, 156],
124: [90, 92, 156, 158],
125: [91, 92, 93, 157, 158, 159],
126: [92, 93, 94, 158, 160],
127: [93, 95, 128, 159, 160, 161],
128: [94, 96, 127, 129, 160, 162],
129: [95, 97, 128, 130, 161, 163],
130: [96, 98, 129, 162, 163, 164],
131: [97, 99, 163, 164, 165],
132: [98, 164, 165],
133: [101, 167],
134: [100, 101, 102, 166, 167, 168],
135: [101, 102, 103, 136, 167, 169],
136: [102, 104, 135, 137, 168, 170],
137: [103, 104, 105, 136, 169, 171],
138: [104, 105, 106, 139, 170, 172],
139: [105, 107, 138, 171, 172, 173],
140: [106, 107, 108, 172, 174],
141: [107, 109, 173, 175],
143: [109, 111, 175, 177],
144: [110, 111, 112, 176, 177, 178],
145: [111, 112, 113, 146, 177, 179],
146: [112, 114, 145, 147, 178, 180],
147: [113, 115, 146, 179, 181],
148: [114, 116, 149, 180, 182],
149: [115, 117, 148, 181, 182, 183],
150: [116, 117, 118, 151, 182, 184],
151: [117, 119, 150, 183, 184, 185],
152: [118, 120, 153, 184, 185, 186],
153: [119, 121, 152, 185, 186, 187],
154: [120, 122, 186, 187, 188],
155: [121, 187, 189],
156: [122, 124, 188, 190],
157: [125, 189, 191],
158: [124, 125, 126, 190, 191, 192],
159: [125, 127, 160, 191, 192, 193],
160: [126, 127, 128, 159, 192, 194],
161: [127, 129, 162, 193, 195],
162: [128, 130, 161, 194, 196],
163: [129, 130, 131, 164, 195, 197],
164: [130, 131, 132, 163, 196, 198],
165: [131, 132, 197],
166: [134, 199, 200],
167: [133, 134, 135, 199, 201],
168: [134, 136, 200],
169: [135, 137, 201, 203],
170: [136, 138, 204],
171: [137, 139, 203, 204, 205],
172: [138, 139, 140, 204, 205, 206],
173: [139, 141, 205, 206, 207],
174: [140, 206, 208],
175: [141, 143, 207, 209],
176: [144, 208, 210],
177: [143, 144, 145, 178, 209, 211],
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179: [145, 147, 180, 211, 212, 213],
180: [146, 148, 179, 181, 212, 214],
181: [147, 149, 180, 213, 214, 215],
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183: [149, 151, 184, 215, 216, 217],
184: [150, 151, 152, 183, 216, 217, 218],
185: [151, 152, 153, 217, 218, 219],
186: [152, 153, 154, 187, 218, 220],
187: [153, 154, 155, 186, 219, 221],
188: [154, 156, 189, 220, 221, 222],
189: [155, 157, 188, 221, 222, 223],
190: [156, 158, 222, 223, 224],
191: [157, 158, 159, 192, 223, 225],
192: [158, 159, 160, 191, 224, 225, 226],
193: [159, 161, 225],
194: [160, 162, 226, 228],
195: [161, 163, 229],
196: [162, 164, 197, 228, 230],
197: [163, 165, 196, 198, 229, 231],
198: [164, 197, 230],
199: [166, 167, 232, 233],
200: [166, 168, 232, 233, 234],
201: [167, 169, 233, 235],
203: [169, 171, 235, 237],
204: [170, 171, 172, 205, 236, 238],
205: [171, 172, 173, 204, 206, 237, 239],
206: [172, 173, 174, 205, 238, 240],
207: [173, 175, 208, 239, 240, 241],
208: [174, 176, 207, 209, 240, 242],
209: [175, 177, 208, 241, 243],
210: [176, 178, 211, 242, 243, 244],
211: [177, 178, 179, 210, 243, 244, 245],
212: [178, 179, 180, 244, 246],
213: [179, 181, 245, 246, 247],
214: [180, 181, 182, 246, 247, 248],
215: [181, 182, 183, 247, 248, 249],
216: [182, 183, 184, 248, 249, 250],
217: [183, 184, 185, 218, 249, 251],
218: [184, 185, 186, 217, 250, 252],
219: [185, 187, 220, 251, 252, 253],
220: [186, 188, 219, 252, 253, 254],
221: [187, 188, 189, 253, 254, 255],
222: [188, 189, 190, 223, 254, 256],
223: [189, 190, 191, 222, 255, 257],
224: [190, 192, 225, 256, 257, 258],
225: [191, 192, 193, 224, 257, 259],
226: [192, 194, 258, 260],
228: [194, 196, 260, 262],
229: [195, 197, 261, 262, 263],
230: [196, 198, 231, 262, 263, 264],
231: [197, 230, 263],
232: [199, 200, 266],
233: [199, 200, 201, 265, 267],
234: [200, 266, 268],
235: [201, 203, 267, 269],
236: [204, 268, 270],
237: [203, 205, 269, 270, 271],
238: [204, 206, 239, 270, 272],
239: [205, 207, 238, 240, 271, 273],
240: [206, 207, 208, 239, 272, 273, 274],
241: [207, 209, 242, 273, 274, 275],
242: [208, 210, 241, 274, 275, 276],
243: [209, 210, 211, 275, 276, 277],
244: [210, 211, 212, 245, 276, 278],
245: [211, 213, 244, 277, 278, 279],
246: [212, 213, 214, 278, 280],
247: [213, 214, 215, 248, 279, 281],
248: [214, 215, 216, 247, 280, 282],
249: [215, 216, 217, 281, 282, 283],
250: [216, 218, 251, 282, 283, 284],
251: [217, 219, 250, 283, 284, 285],
252: [218, 219, 220, 284, 285, 286],
253: [219, 220, 221, 285, 286, 287],
254: [220, 221, 222, 255, 286, 288],
255: [221, 223, 254, 287, 288, 289],
256: [222, 224, 257, 288, 289, 290],
257: [223, 224, 225, 256, 258, 289, 291],
258: [224, 226, 257, 290, 292],
259: [225, 291, 293],
260: [226, 228, 292, 294],
261: [229, 293, 295],
262: [228, 229, 230, 294, 296],
263: [229, 230, 231, 264, 295, 297],
264: [230, 263, 296],
265: [233, 266, 299],
266: [232, 234, 265, 298, 299, 300],
267: [233, 235, 268, 299, 300, 301],
268: [234, 236, 267, 300, 301, 302],
269: [235, 237, 270, 301, 303],
270: [236, 237, 238, 269, 302, 304],
271: [237, 239, 272, 303, 304, 305],
272: [238, 240, 271, 273, 304, 306],
273: [239, 240, 241, 272, 305, 307],
274: [240, 241, 242, 306, 308],
275: [241, 242, 243, 276, 307, 308, 309],
276: [242, 243, 244, 275, 308, 310],
277: [243, 245, 278, 309, 310, 311],
278: [244, 245, 246, 277, 310, 312],
279: [245, 247, 311],
280: [246, 248, 312, 314],
281: [247, 249, 315],
282: [248, 249, 250, 314, 316],
283: [249, 250, 251, 315, 317],
284: [250, 251, 252, 285, 316, 318],
285: [251, 252, 253, 284, 317, 319],
286: [252, 253, 254, 318, 320],
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288: [254, 255, 256, 320, 322],
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295: [261, 263, 296, 327, 328, 329],
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297: [263, 296, 329],
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299: [265, 266, 267, 298, 331, 333],
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301: [267, 268, 269, 302, 333, 335],
302: [268, 270, 301, 303, 334, 336],
303: [269, 271, 302, 304, 335, 337],
304: [270, 271, 272, 303, 305, 336, 338],
305: [271, 273, 304, 337, 338, 339],
306: [272, 274, 307, 338, 339, 340],
307: [273, 275, 306, 339, 340, 341],
308: [274, 275, 276, 309, 340, 342],
309: [275, 277, 308, 341, 342, 343],
310: [276, 277, 278, 342, 343, 344],
311: [277, 279, 343, 344, 345],
312: [278, 280, 344, 346],
314: [280, 282, 346, 348],
315: [281, 283, 316, 347, 348, 349],
316: [282, 284, 315, 317, 348, 350],
317: [283, 285, 316, 318, 349, 351],
318: [284, 286, 317, 350, 352],
319: [285, 287, 351],
320: [286, 288, 352, 354],
321: [287, 289, 355],
322: [288, 290, 354, 355, 356],
323: [289, 290, 291, 324, 355, 357],
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327: [293, 294, 295, 328, 359, 361],
328: [294, 295, 296, 327, 360, 362],
329: [295, 296, 297, 361, 362, 363],
330: [296, 362, 363],
331: [299, 365],
332: [298, 300, 364],
333: [299, 301, 365, 367],
334: [300, 302, 368],
335: [301, 303, 336, 367, 368, 369],
336: [302, 304, 335, 368, 369, 370],
337: [303, 305, 338, 369, 370, 371],
338: [304, 305, 306, 337, 370, 372],
339: [305, 306, 307, 371, 372, 373],
340: [306, 307, 308, 341, 372, 374],
341: [307, 309, 340, 342, 373, 375],
342: [308, 309, 310, 341, 374, 376],
343: [309, 310, 311, 375, 377],
344: [310, 311, 312, 376, 377, 378],
345: [311, 377, 379],
346: [312, 314, 378, 380],
347: [315, 379, 381],
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350: [316, 318, 349, 351, 382, 384],
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368: [334, 335, 336, 400, 401, 402],
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370: [336, 337, 338, 402, 403, 404],
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384: [350, 351, 352, 416, 417, 418],
385: [351, 417, 419],
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387: [355, 419, 421],
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423: [389, 390, 391, 424, 455, 457],
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425: [391, 392, 393, 424, 457, 458, 459],
426: [392, 394, 427, 458, 460],
427: [393, 394, 395, 426, 459, 461],
428: [394, 395, 396, 460, 462],
429: [395, 461, 462],
430: [398, 431, 464],
431: [397, 399, 430, 463, 465],
432: [398, 400, 464, 466],
433: [399, 401, 434, 465, 466, 467],
434: [400, 402, 433, 466, 467, 468],
435: [401, 403, 436, 467, 468, 469],
436: [402, 404, 435, 468, 470],
437: [403, 405, 469],
438: [404, 406, 470, 472],
439: [405, 407, 473],
440: [406, 408, 441, 472, 474],
441: [407, 409, 440, 442, 473, 475],
442: [408, 410, 441, 443, 474, 476],
443: [409, 411, 442, 475, 476, 477],
444: [410, 411, 412, 445, 476, 478],
445: [411, 413, 444, 477, 478, 479],
446: [412, 414, 447, 478, 479, 480],
447: [413, 415, 446, 448, 479, 480, 481],
448: [414, 415, 416, 447, 480, 482],
449: [415, 417, 450, 481, 482, 483],
450: [416, 417, 418, 449, 482, 484],
451: [417, 419, 452, 483, 484, 485],
452: [418, 419, 420, 451, 484, 486],
453: [419, 420, 421, 485, 486, 487],
454: [420, 421, 422, 455, 486, 488],
455: [421, 422, 423, 454, 456, 487, 489],
456: [422, 424, 455, 457, 488, 490],
457: [423, 425, 456, 489, 490, 491],
458: [424, 425, 426, 490, 492],
459: [425, 427, 491],
460: [426, 428, 492, 494],
461: [427, 429, 495],
462: [428, 429, 494],
463: [431, 464, 497],
464: [430, 432, 463, 465, 496, 497, 498],
465: [431, 433, 464, 497, 498, 499],
466: [432, 433, 434, 498, 499, 500],
467: [433, 434, 435, 499, 501],
468: [434, 435, 436, 469, 500, 501, 502],
469: [435, 437, 468, 501, 503],
470: [436, 438, 502, 504],
472: [438, 440, 504, 506],
473: [439, 441, 474, 505, 507],
474: [440, 442, 473, 475, 506, 508],
475: [441, 443, 474, 507, 509],
476: [442, 443, 444, 477, 508, 509, 510],
477: [443, 445, 476, 509, 510, 511],
478: [444, 445, 446, 510, 511, 512],
479: [445, 446, 447, 511, 512, 513],
480: [446, 447, 448, 481, 512, 514],
481: [447, 449, 480, 513, 515],
482: [448, 449, 450, 514, 515, 516],
483: [449, 451, 484, 515, 516, 517],
484: [450, 451, 452, 483, 516, 518],
485: [451, 453, 517, 519],
486: [452, 453, 454, 487, 518, 520],
487: [453, 455, 486, 488, 519, 521],
488: [454, 456, 487, 489, 520, 522],
489: [455, 457, 488, 521, 523],
490: [456, 457, 458, 522, 523, 524],
491: [457, 459, 523, 524, 525],
492: [458, 460, 524, 526],
494: [460, 462, 526, 528],
495: [461, 527],
496: [464, 530],
497: [463, 464, 465, 529, 530, 531],
498: [464, 465, 466, 499, 530, 532],
499: [465, 466, 467, 498, 531, 533],
500: [466, 468, 501, 532, 533, 534],
501: [467, 468, 469, 500, 533, 535],
502: [468, 470, 534, 536],
503: [469, 535, 537],
504: [470, 472, 536, 538],
505: [473, 537, 539],
506: [472, 474, 507, 538, 540],
507: [473, 475, 506, 508, 539, 541],
508: [474, 476, 507, 540, 541, 542],
509: [475, 476, 477, 510, 541, 543],
510: [476, 477, 478, 509, 542, 544],
511: [477, 478, 479, 543, 544, 545],
512: [478, 479, 480, 513, 544, 546],
513: [479, 481, 512, 514, 545, 547],
514: [480, 482, 513, 515, 546, 547, 548],
515: [481, 482, 483, 514, 547, 549],
516: [482, 483, 484, 548, 549, 550],
517: [483, 485, 549, 550, 551],
518: [484, 486, 550],
519: [485, 487, 551, 553],
520: [486, 488, 554],
521: [487, 489, 553, 554, 555],
522: [488, 490, 523, 554, 556],
523: [489, 490, 491, 522, 555, 557],
524: [490, 491, 492, 556, 557, 558],
525: [491, 557, 559],
526: [492, 494, 558, 560],
527: [495, 559, 561],
528: [494, 560, 561],
529: [497, 530, 563],
530: [496, 497, 498, 529, 562, 564],
531: [497, 499, 532, 563, 564, 565],
532: [498, 500, 531, 564, 566],
533: [499, 500, 501, 534, 565, 567],
534: [500, 502, 533, 535, 566, 568],
535: [501, 503, 534, 567, 569],
536: [502, 504, 568, 569, 570],
537: [503, 505, 538, 569, 571],
538: [504, 506, 537, 570, 571, 572],
539: [505, 507, 540, 571, 572, 573],
540: [506, 508, 539, 541, 572, 574],
541: [507, 508, 509, 540, 573, 575],
542: [508, 510, 543, 574, 576],
543: [509, 511, 542, 544, 575, 577],
544: [510, 511, 512, 543, 545, 576, 578],
545: [511, 513, 544, 546, 577, 579],
546: [512, 514, 545, 578, 580],
547: [513, 514, 515, 548, 579, 581],
548: [514, 516, 547, 580, 581, 582],
549: [515, 516, 517, 550, 581, 583],
550: [516, 517, 518, 549, 582, 583, 584],
551: [517, 519, 583, 585],
553: [519, 521, 585, 587],
554: [520, 521, 522, 555, 586, 588],
555: [521, 523, 554, 556, 587, 588, 589],
556: [522, 524, 555, 557, 588, 590],
557: [523, 524, 525, 556, 558, 589, 591],
558: [524, 526, 557, 559, 590, 592],
559: [525, 527, 558, 560, 591, 593],
560: [526, 528, 559, 561, 592, 594],
561: [527, 528, 560, 593],
562: [530, 563, 596],
563: [529, 531, 562, 564, 595, 597],
564: [530, 531, 532, 563, 565, 596, 598],
565: [531, 533, 564, 566, 597, 599],
566: [532, 534, 565, 598, 600],
567: [533, 535, 568, 599, 600, 601],
568: [534, 536, 567, 569, 600, 602],
569: [535, 536, 537, 568, 570, 601, 603],
570: [536, 538, 569, 571, 602, 604],
571: [537, 538, 539, 570, 603, 605],
572: [538, 539, 540, 604, 605, 606],
573: [539, 541, 574, 605, 606, 607],
574: [540, 542, 573, 575, 606, 608],
575: [541, 543, 574, 576, 607, 609],
576: [542, 544, 575, 577, 608, 610],
577: [543, 545, 576, 609, 610, 611],
578: [544, 546, 610],
579: [545, 547, 611, 613],
580: [546, 548, 614],
581: [547, 548, 549, 582, 613, 615],
582: [548, 550, 581, 583, 614, 616],
583: [549, 550, 551, 582, 615, 617],
584: [550, 616, 618],
585: [551, 553, 617, 619],
586: [554, 618, 620],
587: [553, 555, 619, 620, 621],
588: [554, 555, 556, 589, 620, 622],
589: [555, 557, 588, 590, 621, 623],
590: [556, 558, 589, 591, 622, 624],
591: [557, 559, 590, 592, 623, 625],
592: [558, 560, 591, 593, 624, 626],
593: [559, 561, 592, 594, 625, 627],
594: [560, 593, 626],
595: [563, 596, 628, 629],
596: [562, 564, 595, 628, 630],
597: [563, 565, 629],
598: [564, 566, 630, 632],
599: [565, 567, 633],
600: [566, 567, 568, 632, 634],
601: [567, 569, 602, 633, 634, 635],
602: [568, 570, 601, 603, 634, 636],
603: [569, 571, 602, 604, 635, 637],
604: [570, 572, 603, 636, 638],
605: [571, 572, 573, 606, 637, 639],
606: [572, 573, 574, 605, 638, 640],
607: [573, 575, 608, 639, 640, 641],
608: [574, 576, 607, 609, 640, 642],
609: [575, 577, 608, 641, 642, 643],
610: [576, 577, 578, 642, 643, 644],
611: [577, 579, 643, 645],
613: [579, 581, 645, 647],
614: [580, 582, 615, 646, 648],
615: [581, 583, 614, 616, 647, 649],
616: [582, 584, 615, 617, 648, 650],
617: [583, 585, 616, 649, 651],
618: [584, 586, 619, 650, 652],
619: [585, 587, 618, 651, 652, 653],
620: [586, 587, 588, 621, 652, 653, 654],
621: [587, 589, 620, 653, 654, 655],
622: [588, 590, 654, 655, 656],
623: [589, 591, 624, 655, 656, 657],
624: [590, 592, 623, 625, 656, 658],
625: [591, 593, 624, 626, 657, 659],
626: [592, 594, 625, 658, 659, 660],
627: [593, 659],
628: [595, 596, 662],
629: [595, 597, 661, 662, 663],
630: [596, 598, 662, 664],
632: [598, 600, 664, 666],
633: [599, 601, 634, 665, 666, 667],
634: [600, 601, 602, 633, 666, 668],
635: [601, 603, 667],
636: [602, 604, 668, 670],
637: [603, 605, 671],
638: [604, 606, 639, 670, 671, 672],
639: [605, 607, 638, 640, 671, 673],
640: [606, 607, 608, 639, 672, 674],
641: [607, 609, 642, 673, 674, 675],
642: [608, 609, 610, 641, 643, 674, 676],
643: [609, 610, 611, 642, 675, 677],
644: [610, 676, 678],
645: [611, 613, 677, 679],
646: [614, 678, 680],
647: [613, 615, 648, 679, 681],
648: [614, 616, 647, 680, 681, 682],
649: [615, 617, 650, 681, 683],
650: [616, 618, 649, 651, 682, 684],
651: [617, 619, 650, 683, 684, 685],
652: [618, 619, 620, 684, 686],
653: [619, 620, 621, 685, 686, 687],
654: [620, 621, 622, 686, 688],
655: [621, 622, 623, 687, 689],
656: [622, 623, 624, 688, 690],
657: [623, 625, 658, 689, 690, 691],
658: [624, 626, 657, 690, 692],
659: [625, 626, 627, 660, 691, 692, 693],
660: [626, 659, 692],
661: [629, 695],
662: [628, 629, 630, 694, 695, 696],
663: [629, 695, 697],
664: [630, 632, 696, 698],
665: [633, 697, 699],
666: [632, 633, 634, 698, 700],
667: [633, 635, 699, 700, 701],
668: [634, 636, 700, 702],
670: [636, 638, 702, 704],
671: [637, 638, 639, 672, 703, 705],
672: [638, 640, 671, 673, 704, 706],
673: [639, 641, 672, 705, 706, 707],
674: [640, 641, 642, 675, 706, 708],
675: [641, 643, 674, 676, 707, 709],
676: [642, 644, 675, 677, 708, 710],
677: [643, 645, 676, 709, 710, 711],
678: [644, 646, 679, 710, 711, 712],
679: [645, 647, 678, 711, 712, 713],
680: [646, 648, 681, 712, 714],
681: [647, 648, 649, 680, 682, 713, 715],
682: [648, 650, 681, 683, 714, 716],
683: [649, 651, 682, 715, 716, 717],
684: [650, 651, 652, 685, 716, 718],
685: [651, 653, 684, 686, 717, 719],
686: [652, 653, 654, 685, 718, 720],
687: [653, 655, 719],
688: [654, 656, 720, 722],
689: [655, 657, 723],
690: [656, 657, 658, 722, 724],
691: [657, 659, 692, 723, 724, 725],
692: [658, 659, 660, 691, 724, 726],
693: [659, 725, 726],
694: [662, 728],
695: [661, 662, 663, 696, 727, 728, 729],
696: [662, 664, 695, 728, 730],
697: [663, 665, 698, 729, 730, 731],
698: [664, 666, 697, 699, 730, 732],
699: [665, 667, 698, 700, 731, 733],
700: [666, 667, 668, 699, 732, 734],
701: [667, 733, 735],
702: [668, 670, 734, 736],
703: [671, 735, 737],
704: [670, 672, 705, 736, 738],
705: [671, 673, 704, 706, 737, 739],
706: [672, 673, 674, 705, 707, 738, 740],
707: [673, 675, 706, 708, 739, 741],
708: [674, 676, 707, 709, 740, 742],
709: [675, 677, 708, 741, 743],
710: [676, 677, 678, 742, 743, 744],
711: [677, 678, 679, 743, 744, 745],
712: [678, 679, 680, 713, 744, 746],
713: [679, 681, 712, 714, 745, 747],
714: [680, 682, 713, 715, 746, 748],
715: [681, 683, 714, 716, 747, 749],
716: [682, 683, 684, 715, 717, 748, 750],
717: [683, 685, 716, 718, 749, 751],
718: [684, 686, 717, 750, 752],
719: [685, 687, 751, 753],
720: [686, 688, 752, 754],
722: [688, 690, 754, 756],
723: [689, 691, 755, 756, 757],
724: [690, 691, 692, 725, 756, 757, 758],
725: [691, 693, 724, 757, 758, 759],
726: [692, 693, 758],
727: [695, 728, 760, 761],
728: [694, 695, 696, 727, 760, 762],
729: [695, 697, 730, 761, 763],
730: [696, 697, 698, 729, 762, 764],
731: [697, 699, 732, 763, 764, 765],
732: [698, 700, 731, 764, 765, 766],
733: [699, 701, 734, 765, 766, 767],
734: [700, 702, 733, 766, 768],
735: [701, 703, 767, 768, 769],
736: [702, 704, 737, 768, 770],
737: [703, 705, 736, 769, 770, 771],
738: [704, 706, 739, 770, 771, 772],
739: [705, 707, 738, 771, 773],
740: [706, 708, 772],
741: [707, 709, 773, 775],
742: [708, 710, 776],
743: [709, 710, 711, 744, 775, 777],
744: [710, 711, 712, 743, 776, 778],
745: [711, 713, 746, 777, 778, 779],
746: [712, 714, 745, 778, 779, 780],
747: [713, 715, 748, 779, 781],
748: [714, 716, 747, 780, 782],
749: [715, 717, 750, 781, 782, 783],
750: [716, 718, 749, 751, 782, 784],
751: [717, 719, 750, 752, 783, 785],
752: [718, 720, 751, 784, 786],
753: [719, 785, 787],
754: [720, 722, 786, 788],
755: [723, 787, 789],
756: [722, 723, 724, 788, 789, 790],
757: [723, 724, 725, 789, 790, 791],
758: [724, 725, 726, 790, 791, 792],
759: [725, 791, 792],
760: [727, 728, 794],
761: [727, 729, 762, 793, 795],
762: [728, 730, 761, 763, 794, 796],
763: [729, 731, 762, 795, 797],
764: [730, 731, 732, 796, 797, 798],
765: [731, 732, 733, 797, 798, 799],
766: [732, 733, 734, 767, 798, 800],
767: [733, 735, 766, 768, 799, 801],
768: [734, 735, 736, 767, 800, 802],
769: [735, 737, 770, 801, 802, 803],
770: [736, 737, 738, 769, 802, 804],
771: [737, 738, 739, 803, 804, 805],
772: [738, 740, 804, 806],
773: [739, 741, 805, 807],
775: [741, 743, 807, 809],
776: [742, 744, 777, 808, 810],
777: [743, 745, 776, 809, 810, 811],
778: [744, 745, 746, 779, 810, 812],
779: [745, 746, 747, 778, 811, 813],
780: [746, 748, 781, 812, 813, 814],
781: [747, 749, 780, 782, 813, 815],
782: [748, 749, 750, 781, 814, 816],
783: [749, 751, 784, 815, 816, 817],
784: [750, 752, 783, 785, 816, 818],
785: [751, 753, 784, 786, 817, 819],
786: [752, 754, 785, 787, 818, 820],
787: [753, 755, 786, 819, 820, 821],
788: [754, 756, 820, 821, 822],
789: [755, 756, 757, 821, 822, 823],
790: [756, 757, 758, 822, 823, 824],
791: [757, 758, 759, 823, 824, 825],
792: [758, 759, 824],
793: [761, 827],
794: [760, 762, 826],
795: [761, 763, 827, 829],
796: [762, 764, 830],
797: [763, 764, 765, 798, 829, 830, 831],
798: [764, 765, 766, 797, 830, 832],
799: [765, 767, 800, 831, 832, 833],
800: [766, 768, 799, 801, 832, 834],
801: [767, 769, 800, 833, 835],
802: [768, 769, 770, 803, 834, 836],
803: [769, 771, 802, 804, 835, 837],
804: [770, 771, 772, 803, 805, 836, 838],
805: [771, 773, 804, 837, 839],
806: [772, 838, 840],
807: [773, 775, 839, 841],
808: [776, 840, 842],
809: [775, 777, 841, 843],
810: [776, 777, 778, 811, 842, 843, 844],
811: [777, 779, 810, 812, 843, 845],
812: [778, 780, 811, 813, 844, 845, 846],
813: [779, 780, 781, 812, 845, 847],
814: [780, 782, 815, 846, 848],
815: [781, 783, 814, 816, 847, 849],
816: [782, 783, 784, 815, 848, 849, 850],
817: [783, 785, 818, 849, 850, 851],
818: [784, 786, 817, 819, 850, 852],
819: [785, 787, 818, 820, 851, 853],
820: [786, 787, 788, 819, 852, 854],
821: [787, 788, 789, 822, 853, 855],
822: [788, 789, 790, 821, 854, 856],
823: [789, 790, 791, 855, 856, 857],
824: [790, 791, 792, 825, 856, 858],
825: [791, 824, 857],
826: [794, 860],
827: [793, 795, 859, 861],
829: [795, 797, 861, 863],
830: [796, 797, 798, 862, 863, 864],
831: [797, 799, 832, 863, 864, 865],
832: [798, 799, 800, 831, 864, 865, 866],
833: [799, 801, 865],
834: [800, 802, 866, 868],
835: [801, 803, 869],
836: [802, 804, 837, 868, 870],
837: [803, 805, 836, 838, 869, 871],
838: [804, 806, 837, 870, 871, 872],
839: [805, 807, 840, 871, 872, 873],
840: [806, 808, 839, 872, 874],
841: [807, 809, 842, 873, 875],
842: [808, 810, 841, 843, 874, 876],
843: [809, 810, 811, 842, 875, 877],
844: [810, 812, 845, 876, 878],
845: [811, 812, 813, 844, 877, 879],
846: [812, 814, 878],
847: [813, 815, 879, 881],
848: [814, 816, 882],
849: [815, 816, 817, 881, 883],
850: [816, 817, 818, 882, 883, 884],
851: [817, 819, 852, 883, 884, 885],
852: [818, 820, 851, 853, 884, 885, 886],
853: [819, 821, 852, 854, 885, 887],
854: [820, 822, 853, 886, 887, 888],
855: [821, 823, 856, 887, 888, 889],
856: [822, 823, 824, 855, 888, 890],
857: [823, 825, 858, 889, 890, 891],
858: [824, 857, 890],
859: [827, 893],
860: [826, 892, 894],
861: [827, 829, 893, 895],
862: [830, 894, 896],
863: [829, 830, 831, 895, 896, 897],
864: [830, 831, 832, 896, 897, 898],
865: [831, 832, 833, 897, 899],
866: [832, 834, 898, 900],
868: [834, 836, 900, 902],
869: [835, 837, 901, 903],
870: [836, 838, 871, 902, 903, 904],
871: [837, 838, 839, 870, 903, 905],
872: [838, 839, 840, 904, 905, 906],
873: [839, 841, 874, 905, 906, 907],
874: [840, 842, 873, 875, 906, 907, 908],
875: [841, 843, 874, 876, 907, 909],
876: [842, 844, 875, 877, 908, 910],
877: [843, 845, 876, 878, 909, 910, 911],
878: [844, 846, 877, 910, 912],
879: [845, 847, 911, 913],
881: [847, 849, 913, 915],
882: [848, 850, 883, 914, 916],
883: [849, 850, 851, 882, 915, 917],
884: [850, 851, 852, 916, 917, 918],
885: [851, 852, 853, 886, 917, 919],
886: [852, 854, 885, 918, 920],
887: [853, 854, 855, 888, 919, 921],
888: [854, 855, 856, 887, 889, 920, 922],
889: [855, 857, 888, 890, 921, 923],
890: [856, 857, 858, 889, 922, 924],
891: [857, 923],
892: [860, 893, 926],
893: [859, 861, 892, 925, 927],
894: [860, 862, 895, 926, 927, 928],
895: [861, 863, 894, 927, 929],
896: [862, 863, 864, 928, 930],
897: [863, 864, 865, 898, 929, 930, 931],
898: [864, 866, 897, 930, 931, 932],
899: [865, 931, 933],
900: [866, 868, 932, 934],
901: [869, 933, 935],
902: [868, 870, 903, 934, 936],
903: [869, 870, 871, 902, 935, 937],
904: [870, 872, 905, 936, 938],
905: [871, 872, 873, 904, 937, 939],
906: [872, 873, 874, 938, 939, 940],
907: [873, 874, 875, 939, 940, 941],
908: [874, 876, 909, 940, 941, 942],
909: [875, 877, 908, 941, 942, 943],
910: [876, 877, 878, 942, 943, 944],
911: [877, 879, 943, 944, 945],
912: [878, 944, 946],
913: [879, 881, 945, 947],
914: [882, 946, 948],
915: [881, 883, 947, 948, 949],
916: [882, 884, 917, 948, 949, 950],
917: [883, 884, 885, 916, 918, 949, 951],
918: [884, 886, 917, 919, 950, 952],
919: [885, 887, 918, 920, 951, 952, 953],
920: [886, 888, 919, 921, 952, 954],
921: [887, 889, 920, 922, 953, 955],
922: [888, 890, 921, 954, 956],
923: [889, 891, 955, 957],
924: [890, 956],
925: [893, 926, 959],
926: [892, 894, 925, 927, 958, 960],
927: [893, 894, 895, 926, 959, 961],
928: [894, 896, 929, 960, 962],
929: [895, 897, 928, 930, 961, 963],
930: [896, 897, 898, 929, 962, 964],
931: [897, 898, 899, 963, 964, 965],
932: [898, 900, 933, 964, 966],
933: [899, 901, 932, 965, 966, 967],
934: [900, 902, 935, 966, 967, 968],
935: [901, 903, 934, 936, 967, 969],
936: [902, 904, 935, 937, 968, 970],
937: [903, 905, 936, 938, 969, 971],
938: [904, 906, 937, 939, 970, 972],
939: [905, 906, 907, 938, 971, 973],
940: [906, 907, 908, 972, 974],
941: [907, 908, 909, 973, 975],
942: [908, 909, 910, 943, 974, 975, 976],
943: [909, 910, 911, 942, 975, 977],
944: [910, 911, 912, 976, 978],
945: [911, 913, 946, 977, 979],
946: [912, 914, 945, 947, 978, 980],
947: [913, 915, 946, 948, 979, 981],
948: [914, 915, 916, 947, 980, 982],
949: [915, 916, 917, 981, 982, 983],
950: [916, 918, 951, 982, 984],
951: [917, 919, 950, 952, 983, 985],
952: [918, 919, 920, 951, 984, 986],
953: [919, 921, 985],
954: [920, 922, 986, 988],
955: [921, 923, 989],
956: [922, 924, 988, 990],
957: [923, 989, 990],
958: [926, 959, 992],
959: [925, 927, 958, 960, 991, 993],
960: [926, 928, 959, 992, 994],
961: [927, 929, 993],
962: [928, 930, 994, 996],
963: [929, 931, 997],
964: [930, 931, 932, 965, 996, 998],
965: [931, 933, 964, 997, 999],
966: [932, 933, 934, 967, 998, 999, 1000],
967: [933, 934, 935, 966, 999, 1001],
968: [934, 936, 969, 1000, 1001, 1002],
969: [935, 937, 968, 1001, 1002, 1003],
970: [936, 938, 1002],
971: [937, 939, 1003, 1005],
972: [938, 940, 1006],
973: [939, 941, 974, 1005, 1006, 1007],
974: [940, 942, 973, 975, 1006, 1008],
975: [941, 942, 943, 974, 1007, 1009],
976: [942, 944, 1008, 1009, 1010],
977: [943, 945, 1009],
978: [944, 946, 1010, 1012],
979: [945, 947, 1013],
980: [946, 948, 981, 1012, 1014],
981: [947, 949, 980, 1013, 1014, 1015],
982: [948, 949, 950, 983, 1014, 1016],
983: [949, 951, 982, 984, 1015, 1017],
984: [950, 952, 983, 985, 1016, 1018],
985: [951, 953, 984, 1017, 1018, 1019],
986: [952, 954, 1018, 1020],
988: [954, 956, 1020, 1022],
989: [955, 957, 1021, 1022, 1023],
990: [956, 957, 1022],
991: [959, 992, 1025],
992: [958, 960, 991, 993, 1024, 1026],
993: [959, 961, 992, 1025, 1026, 1027],
994: [960, 962, 1026, 1028],
996: [962, 964, 1028, 1030],
997: [963, 965, 998, 1029, 1031],
998: [964, 966, 997, 1030, 1031, 1032],
999: [965, 966, 967, 1031, 1032, 1033],
1000: [966, 968, 1001, 1032, 1033, 1034],
1001: [967, 968, 969, 1000, 1033, 1035],
1002: [968, 969, 970, 1034, 1035, 1036],
1003: [969, 971, 1035, 1037],
1005: [971, 973, 1037, 1039],
1006: [972, 973, 974, 1038, 1040],
1007: [973, 975, 1008, 1039, 1040, 1041],
1008: [974, 976, 1007, 1040, 1041, 1042],
1009: [975, 976, 977, 1041, 1042, 1043],
1010: [976, 978, 1042, 1044],
1012: [978, 980, 1044, 1046],
1013: [979, 981, 1045, 1046, 1047],
1014: [980, 981, 982, 1046, 1047, 1048],
1015: [981, 983, 1016, 1047, 1049],
1016: [982, 984, 1015, 1017, 1048, 1049, 1050],
1017: [983, 985, 1016, 1049, 1050, 1051],
1018: [984, 985, 986, 1050, 1051, 1052],
1019: [985, 1051, 1053],
1020: [986, 988, 1052, 1054],
1021: [989, 1053, 1055],
1022: [988, 989, 990, 1054, 1056],
1023: [989, 1055, 1056],
1024: [992, 1025, 1058],
1025: [991, 993, 1024, 1057, 1058, 1059],
1026: [992, 993, 994, 1058, 1060],
1027: [993, 1059, 1061],
1028: [994, 996, 1060, 1062],
1029: [997, 1061, 1063],
1030: [996, 998, 1062, 1064],
1031: [997, 998, 999, 1063, 1064, 1065],
1032: [998, 999, 1000, 1033, 1064, 1066],
1033: [999, 1000, 1001, 1032, 1065, 1067],
1034: [1000, 1002, 1035, 1066, 1067, 1068],
1035: [1001, 1002, 1003, 1034, 1067, 1068, 1069],
1036: [1002, 1068, 1070],
1037: [1003, 1005, 1069, 1071],
1038: [1006, 1070, 1072],
1039: [1005, 1007, 1040, 1071, 1072, 1073],
1040: [1006, 1007, 1008, 1039, 1072, 1074],
1041: [1007, 1008, 1009, 1073, 1074, 1075],
1042: [1008, 1009, 1010, 1074, 1076],
1043: [1009, 1075, 1077],
1044: [1010, 1012, 1076, 1078],
1045: [1013, 1077, 1079],
1046: [1012, 1013, 1014, 1078, 1079, 1080],
1047: [1013, 1014, 1015, 1048, 1079, 1081],
1048: [1014, 1016, 1047, 1049, 1080, 1081, 1082],
1049: [1015, 1016, 1017, 1048, 1081, 1083],
1050: [1016, 1017, 1018, 1082, 1083, 1084],
1051: [1017, 1018, 1019, 1052, 1083, 1085],
1052: [1018, 1020, 1051, 1053, 1084, 1086],
1053: [1019, 1021, 1052, 1085, 1087],
1054: [1020, 1022, 1055, 1086, 1087, 1088],
1055: [1021, 1023, 1054, 1056, 1087, 1089],
1056: [1022, 1023, 1055, 1088],
1057: [1025],
1058: [1024, 1025, 1026],
1059: [1025, 1027, 1060],
1060: [1026, 1028, 1059],
1061: [1027, 1029],
1062: [1028, 1030],
1063: [1029, 1031, 1064],
1064: [1030, 1031, 1032, 1063],
1065: [1031, 1033, 1066],
1066: [1032, 1034, 1065],
1067: [1033, 1034, 1035],
1068: [1034, 1035, 1036],
1069: [1035, 1037],
1070: [1036, 1038],
1071: [1037, 1039],
1072: [1038, 1039, 1040],
1073: [1039, 1041, 1074],
1074: [1040, 1041, 1042, 1073],
1075: [1041, 1043],
1076: [1042, 1044],
1077: [1043, 1045],
1078: [1044, 1046],
1079: [1045, 1046, 1047, 1080],
1080: [1046, 1048, 1079],
1081: [1047, 1048, 1049],
1082: [1048, 1050],
1083: [1049, 1050, 1051, 1084],
1084: [1050, 1052, 1083],
1085: [1051, 1053],
1086: [1052, 1054, 1087],
1087: [1053, 1054, 1055, 1086],
1088: [1054, 1056],
1089: [1055]}

cycle_21_links = cycle_20_links