From ad06b49232bc7c9626e6f92bf7804127db51375b Mon Sep 17 00:00:00 2001 From: Enrico Bertolazzi Date: Sun, 18 Apr 2021 01:52:45 +0200 Subject: [PATCH] readme.rst --- EQ1.png | Bin 0 -> 21862 bytes EQ2.png | Bin 0 -> 34394 bytes EQ3.png | Bin 0 -> 14907 bytes EQ4.png | Bin 0 -> 13406 bytes README.html | 165 --------------------------------- README-saved.rst => README.rst | 32 ++++--- 6 files changed, 21 insertions(+), 176 deletions(-) create mode 100644 EQ1.png create mode 100644 EQ2.png create mode 100644 EQ3.png create mode 100644 EQ4.png delete mode 100644 README.html rename README-saved.rst => README.rst (93%) diff --git a/EQ1.png b/EQ1.png new file mode 100644 index 0000000000000000000000000000000000000000..4c1e2bdd4b4a4ce2a307b5271182fa0da4be040c GIT binary patch literal 21862 zcmcG!byOVBy7xO+&>(@}t|2%K3=V@0?hGE>1{h?p!QC|k3n4%VB!u8eaQ8rPcMI+s zEL@Vk&)Mfa_q~7p)}6I_y1J^KZ&h_y*QdIkiqTYuJjS8K0RRAxl@#T)0RWV|hp;f= zqlf?9^`l?_0MEifR#sC-5bydWuWZNLVHDB|~}XH340P;O4G|VM*rrn%dKuYOvd3~&mEvE?pC3(Ju(~5-VHsW}ISr@v77mo{ zRYT?DaOg~u783DgCTpf=*3A-|WFTZKKIuA8!3kT_L)@?+-Jbis;q1lL-{NAR>W_V* zi#W!Pa78@7TN`=VUMpww#zz4k#IH_4@B;lE3RO7ZQF2E*HjXqtq34<4Wt-Xe6y8=0 z?c~Skt%ijZSt^`WB?7&av|N;LQ*dcz2Qjti z34W&&3_VFIOUI)HCv4G`oSJ_|Rls9*?;k z=mTtg)V2{R;FgYlKPQv>)`$0i zph&+7d(6GCL#KFf4H?&eM&NRO?Gh`=ND$HgM2 z=5v`hh|G@5<^aTc$DZ&_1UdXN4Iy_3n&fK4XboS_&(H73_2jb!P(P2TL0;PBEVvxG z0df(W(3AC1#zK636RabLJnX|~Oy-Y12TKg}KK4P8B1D$~Ge={@&_7iT^CWG*2=N9c3Y>Ai`(&YuFTLK;c zv`osPBt!E-a$+m1N(0LD2&Kv^0}*J%ghhe@$L)u5OH%{73w*X!k2fJ=9TLC@Wju{LFONU9qQpe?BxD%fyE=qEA{PHf;O(6?fIi+vQxb@A- znsx5Nubt0Z?18VjxT4b)INo!8m>5$ZIT%}n4GVTVxB`Ds;sRm7*T6D+@u~Orv-VZM z4-TY`PzT!a#`iNHL3DMvaE7GDfn+O*`zkhb-qs&`|*Le#Bo@- zbzRUn{5Y_RSU+?Blm3A8%g-O7swJEyf>3AZ-Q>n3ap|TJ$lx9(TWK+in9?NPkfuBR6+{8gKcvUTR3$wV1Rl1ZuEN zs}ZVBOXklljppvQOtf$W6D1Q>u;g(JGbU3Rkp1HAeI8Bsg=q`BKP0VVw!@cp?+NE) zNs`;h{rRvStH*<$bKY4#BgzF)q8xG&xAV>hJ|Vu<%nbv={uomlKb}EuxWc?f zYIN!<>x8N=^&zDc=(iK9goSVWLHJZmTMWmOL*^N_zSP;5f~jMvyQxd>!{6%`d8pA! zAs5$ii@S^8ji&>(jofDwzl5;o>rAR|D_yGcsI>4+z;`|uZ+@WA=+E}@sNe87I18f) zkAD@vKtWeqIWKx3&B|6SRGr(iQMx9vhIu@7mO8s!|3*$y4cC*}<_g2L>qvtA8X{Y@`Wv;~^KmDqRui4u?G-)aM z4Yx;5o+Lhf!68)2Tt-sfSoz#_qD*=J`|9_D31WRvsl{h@vs2jq+1Jey@lQhK1!bw_ zyPp!v;D#ze`)E8arTbW z?x$}=HBX)W8YPf7GlyAAQ-{2ZT9s>S>c@j+rpFDlyG^^h-r0LEMuLTUseCWrAJ#R3 ztX)(J5NneG*Ei2E!tPG)TJDpNI}*^eFlX`k350&zpIYrRT<4##zIX7_397EBD`ELs zco@(tQDDJzw5+Wj`U z{iQj?qDiLMjqWF~-U)#z;VEvDq`E~U({^`h_BN;ie(WOAl;eHVRW9Fxzi8-_;aYS1 zcCzWy4eRA@AmW#^S%&`92qpsox1_3%&xh=(yS&F- zwt;@SBrG2I_V{~W1bn|?3loq^medXM_%(gazB9Ivf1A&Mt^b|oH%Y6xY;_gDr;Zq4 z^c-;3e{^FJdolpxj6QiIs=6#yd14~W`2qlJS3j;BltgI_oOU9USpow(+tbO>HN7uK zik=vzH)M}yD4+qDk1mVhzd0bp*StcF2 zS=>|ggz|7m zqEP*JSOMi30PSx)DgY4W06_nD9`%RwpI`FB@yF(0XSA1*089V?WA-7&ClB?%a--zs zq5W4FApDR90PDyqDg8Nv!3z9vm<1fFZEdOUp{JksYGl zS_`Qw@mm_HY52ISKrP*%?w%e{S7%>KWgI(CO)FOj&{_ke@1@SGq-Uiq4ADi(*%-=l z*tzTJ%ep`nwIFgLvS0^8LklG(Wi2Q|M&3&n%%Kd|0)h=ZaO89peBgT8FkNMREe&N$ z4-P>-5XcKI=$8pKZ4R#V2>SHn(KR#pw)a6y}Erf;iVMZSO zAWI)_#{YzejHS64LjP}MN91UbW<^o1OqIqaQ<+~lA*9!iRyF7kZ5${bKRD{DotgPX5| zte%sux*WeDpS?2B4q-3vZ2?h(A)velYKqz(%Jw>f7Fq}gLmeoD7pa6JqpE=fx+(F( zMU?pTczLZn>_8e2Wj9wHUk4>cq`rrXtd2X#K~T{eC<0e+9UXaTkN)>Krq_jdMBaFkcz z)7KNx7KF>ey%mwJyoMrLj!JGGDk>V@2pkSA5lca!tDT6Bq9U&{1m+F0^3f4-(&U$Q z^^|w^)q=RYS@R(*tW*Rc^2)AGuI|dpvNE3Xp4LDkc`G4h4ICqRxQvZ~m%O^1th<$h zpc+tD#!}zi(SjF>l;QV9@;LB2>ewo%>hfFg>Ug=yiU{*+Yv{^&K-BH|;7-oY+Bm*4 zt^y!FxQd9arL3}}laPzAlaa5bj2hI!(NG2A=%%Tz0CYs~*=af`y2E6woRB^i4z6kl z1e8z6Lcsv4jicm@gn+D#fQniOD@|V!6(M0EO_)!$%1s=nVHXaMZUnl2I45QMIy@gCd2rL7I9pwwgGqjll%AmsE6fC7sA5MG3ZwStu| z(gp`2%wY@CkcT-s0g(t7T`MCaT{RoA z*jHFhS;$V?(N)mR*$@Z8W66)u6p`a`RWgEjgP|@mF1%nFYZn<2emg~Pq?{oKSYBRD z#?=vQ4fj^iw9~K!%i72|3xgemWQ}aWLO7maEl)d;Em(s?#@b2-DhzfLlF=1b;1iaE z1Ho=cu(~Z6$^o_%21A6v0>WThpuC8otgf}3qNk9IqPv|f4u`WmSkM`4qiF}y^oH2l z=^NN-s3IV$Rx-{UU~3LJMPabJFhmomZtJbjW2f!q?S!!65K>1PLA?biWT1R5iu^8eJa8?ru8u6&(H@N8x3kf+ z)snZdcM-vH5EgO}6oIG;$?EgM)CJ`&g){|twGDWcEM47fM4LbDUH;3p$_)jzsBmLhj9*z=>25Or0 zvM%m6^n%<#ZeB*ohs7{@ad&H5QEfSef15vCNif=bc({u4@OXQBb9)PLySUr&@QH|s z@bL2U@bhy$;ot(N|D$VR>Eh`j!N~Zhp#T2; ztDZJK4*w|$j`(-89vaB=CxwTPo0sSRX6E5w`~P9~C*@yef7|u1;>7=miRvM2++|&y zoo(PAlK+&PtV}*&v42X>zasyXpnpaFDMkN^{8N(t75S$${VVcMiTYRMpHlU&$Ui0P zUy*-G*S{kFl(2tA{wZbuiu_a3{uTMBwEZjcPl@|ipz=1Btig#K;y zzf=CNmWKba6#PF7|3||AF#JO}Q3Guogo~5sAH+)X0fFK?|F78pZSfxiJ-CC1B>%rn z{#W$>wle%r`u`~Bf5!gXLY(Ih>Hi1$|23`n8~ZS?ki-$^`R_T3Bo0X;1vvm9;-@4B z*7ZTz55V>(`FV9O;Kw2z9Ng+&P0g{Q-0n`^IPLQV_BB*r-VyujtS`#($JyDJBrb6% zoz)k)nvNr*xhRejBTkLd;nZ(ZFskP9^xM-Mldgi6vIdy6*=3q|9HjCWp-(r z+aXW<&6tJVXc=qu#hm5tGy^FwDQXsL;Ui$D(i3E}p%twjaIS6zU#wQ}|cOEk8NmOjt*Ld%D$fTOR(D!8q ztni7+$V}O9+TUa5d>qrS56(vO8!u=8m}>^?sgty`5DO3YE=FT&-A2s$T)hdbNx1AZ zrZ7bB#FTyGgDa6d`*(0TM2fbqdQqw3x|K7-z7d20}Fr*rEHPDayOcX=%~(7|B# z>R^s)W)fo(o+s>{%CLanjY>H&KOf9^tjb$&AM2ijD~<9id^Z&R_A$Xd>0z5nGnK#> zSVQQ!z$d%VJlbOkNS-Mp{fZ+QZO|)U86x_Gufu!;8lF-CCZw);!6M^x-vYxCZH(K* z*V?rfr|LT>;NBZceDn|UlQH*KNyumD`JR480gTQWhoRojud!UOsqefAm2rjd@G)3k z6y-3|!z-HX)gmK4Jh?47&@i+P2CN5)3^{Rs_ka%$YBvNZ+8JBsXlg&-4>nl|V57TV zSikA_|9L59SNzk+(Pfx+-3n5n?iq%__Dl@xgOQ&nGoLQMYskTX*Fd>@L)wG!C>6yF zdV18EsmLk9KD9P?O(`l-ZN1xo+=K87;1qXWSc`KQgZ?V^$p>$+ADy;@Vb! zqPjuOX-b@SLqM&owz0~)K{=K6@m=$XZ~TXPZfpjrD6(~|FD&Rrin(1s$l1{F9*GjH zeHnTmGu$xwa%w)~g5UQ`;ebDbiK5E4v@S}LRnj?*N$i4`%S2l82V`bl&&U*$*@^|S zU$_2>e-b4^M7e(6G9-E0vytoIbB>mCa6Y?q_UooD4L1t~SAD`9+qV!u^1DYt^$%{VkVLD1Z`nd8(>H3zorbzCArqbNm#ymLrlcMfM;&_jp zzwg$apd+;W8!zVV=~OK!H$&6x%VWatOFJr;^w&mBn5#Nk-?+@HJ5=*522s z33;RM6pI;Rw-w@2NSZ38x<)kPgrG0%X zvm*Kn>t0N2b0{xHY`H3%Uqp@6|4f$Cy1RFx)O#3HS8?r|Gp;sQ%K(x692PJ`(xv)t zLiD2EAy1aj|3WxzkjG3RjCU}h#!Q2lues1g>WTa-l?5a2v7gwk>_15s~V`ys1OPnWI+7$46!KMR-6 zlD@t-#_4iEJuemhzU}R^y!kaeTAH1TD5CJ!wc0v|YpWBAZw@R91=Zh?OGhy@_lFrf zuFxm|7abq1&e_W->TtGZ5aSxV&8`&JqnWrXsal!{r~ZBpF9LqgrO)1S|Gt*s%xkm& zkqt|`y>lu1Ou`A&yKX`07$}IN^@7*44Zo{?x?f;y3p>v-_it~3!Zu6&>7{uM&DDPN zYLdU1Lae}0A2F-jf1+9SCbaJ^e-0=p`?Y#$PTcW$?1#iksP^@5oby08D%BT#0s@(D z!#$97&uAc#Kam?2@|VI>3s10;eXU+ym`|I3pVLu?9D%nU8GW%mv$_*sN6q$rtxllM z@6F@eUe`owHd_bkYWFw?Qht{lxZhX{B;M{xXvcIfN8C;3y#~2`*vD`@ai)--P^_;( zSb(#4Iajz{Hx;t)XSLBg3kJMF3yI0{)9%gB=-K2bWM%Z90Yy{C8_0fl=+`uwc!>~q zCx&(lju|!@-UN18Vu`LDWaBolu+~P148Or4@xJHe#iRXH7evcyU=M2`Y7UIg!Yu;Y zDCymVT*+FjXEJ>R3O(IFPFcy%8g2|_xm}D9V9GjZ4r^#Gjy?|XlgX<)qreHJcKog@ z)}5PlM&6_923e{g7bWn#?wjB*I8jr3EdKQEH&$es_9swN%a!g>p%6~IT(?(=|l~5Sq&xidxpxhc3rCZnOw2m zzYvZ^LT}d1c?7u>19AS);lZ3kT+`rD1WG)?GM{g8Qe)@LYx`(gGif12y0FO^$V}CT z)jAY7=ZzB2B?-$G@8-@GzGx#89m+bnF#-g3L@x#ZY zd4#!ugps((S5zO^!Mzy*F~p&5nD{|$kW%$*-g*F5Xt#m+>(y+5&O6oM`hl|axC>h1 zy^_hk4z6{XAiO&+!k|{yh2nr`=C$UdyH+Uq(I2>L2C(Xy7PNBV{?E||VD3R%_R2@t zbuV5dGZCtz`QXP&3P)URRsIK)gJg15t$mo*?$*yEEnd{D1ahV@nQMIzI1 z8If@0A~Iv0{|5a^dJ!`?v!ft+6j5$p=$Xc)|Eo) zuOd3h57ugNsk z2nMX`H6-zC2Or>Pi4sCX-eb-m24AX1(kC}Ma>JjJqcnrk+hwtvjSKcSPw(j7K+Qp*n3{{C5;L8%}}v$RaOo?*Q-c1_5DzhoViPeu(7H1@JKPup$l7> z+L`L-E8ha=wn-9|K9}3ePf~3#fr*9Vx=Fx&swvoc{Uh4BTHeO^TBsy4p}P^+)xgd} zVQ5KJzSLnozd!9S-%Ns~?<7U;@Cg=Wo_8lzHln9fbe3Iywf_oTjXk70Y!^UB)pm(H z6YB0)vwHo0X=5;Njz!G0;z)dB{%A)=ghHmzx!PXXmfT^(qjsLjej^d@nNa?;L8YqS z3l6$)PC!igbRfKmX5_{R=4s|IHH)O)yw2g?7oSFnD;)tnVa_axU!nA?SS<}S6&jiO zfU{X0Gr7V$XUO?#s=rg{Q{Y!{s~9TkTDH@aB~d7l1nrd1@lzlAqsKhgGGZoC$!B@3 zMDK-LsJYM$lA8|8@F=k!M;%YK#6SgRe;_o#Vb9yN5vatUXulhImb8htp{KJ7jkH-l zImjvL#509m@|3ZHgAXMvFQMyg?-P$>Hxq2r-G zR_B{t)IaMZina7;NOF`D($jWCUS1C^;Zc6rU3B-}Q?3TSOzOW*;ey!_{vIn)Fw-m# zyttyB%@PoG)ddpQlW>8RJG?b~^7KyUlsC6E;=at!p6#twZD-j+5DA1fN>*$WvoZqk zVaWnXH`=3#;u9`6tmOk!EK^8hRQM<~yjGxv;`J=>yLd-;QLN_x#^ohK@b^?XHF1IB zwd>Q5HHqS12V~Ltq{*J)WURlpHFmu#aXCQtq7tfgnawP>^?IS|oFYm0!KQgkBQzo( zb1=n%*%;~w`0iq>Dmw`lS4f>hb;==*OHT>9>lsHcd1oesmA~5Jwa3N!A!07t$LTW5 zl)Mw)V=Wl^Trg7|u%D=jq4Jjx8)@+!c z?Ncy!o9QR&ABgyDCFa@v4D$OPg)|R4a^1Bs{WcF%L56D*!<9b)Ho|?6AMLoZCMC&| z7AZ~0VqGYP{z%=2YpUgqSK>G>GfiZY>0P9e;S;iEH*`^E)CJxoq|@WqhTZ1FMEU|1 ziu6iO&!i{^Z58H{ZRhE--sutciJG}nJdd(b@nGLw5$PvUfceS#4Rsv8UCFPxWVZG1 zShbsWl3koS&D)ezXY+csHlX&(w&%r6W`7wiDSvYp3F@1`s4LI-ZpEX-iq^P6Nc&3U z_ardyCtn{)5(3&MgtY>+uMDTZ73NFdjgZ6>FWid6`X8C#|FRLl9xFTM`A|1siSgs{ z1o!@>vN+jAuqyF;C2g3Rq@B7?tAyvIwuPel{%|Td*TLAtPozUz&kQj z%b?8u?6Wl4fR8i5d6n-vAcS+v1-0I%__6sEHr2~d^aE`h^CxkcKsjGhFi=<+*OQKB8R8&QC9zaq! zVE`4eHSx`51QTdNwa_qH>rr{hpL8+B^j;Cht8*jy@>G~oyf>_`)EhBtheI$eP!mwv z<^r=f!Z>k1yLP3e3Mk5%39zLHxs&NgHU4tI1P8N|pDj>{HqfnUE&&ZE;n5wn)-wg; z&SZlN3tT%6;}@{KA;8(tT<;TsC#1F(kg#`8s&ThlTLmj)h zFRPC$C0+(c0*K$qZD>Rycg3QLrjJ?}+BfrYrH9MSQ}U!yuud53WS4hu+5{DbPWG;y zB{J8i9#iYQ5^9;w%`>z%5aKv|IrSCFuk#i~vLkFHXw9@`tgHm{hFsP@SGk}Ss|q;h zAE$&KzMJyRO=L8eiqExhh`Ja0h;HHy^|4>AWkO3QZE8ZIZNY`~FrnlX&ddy{aVjW- z$%nGc9+Tq>@HK1>A5G(MkMkLR#oN}^LUNWDv5*U45x-UJjaK*WB2&63Z2fxf90hZK zBzJWji$S^l-aSsI#JA1QYcIa11=2^kc3k8{PYWbl;Hjv@pxwRlgBpLFTyOa0pb99tNVrwyi?;X8&OkFNG=k4lCn#a@H?J+e!zY?GYEm;u7|SE2 zo4%=D)NzdcsmC?wjvqH1LUl3U%f5`Nd{*2LSGxOw*Ta1jtHHE^PUKASI;7{feQ@Un z%7-O}W-^5!2Zcxjv^HBAHxwD+3fEuF?!#K~w=Vhxq(>#LVU{y*&I>r5JczQmq9da0 zfyh{-@Z`*M(<d_DPuHaP zFX(QVKAe)`(6sG6bBjg zqdtE<@wHm|JQBNagGW!2zT-vcpO84_{4~*E;bBs~njI2^i}Y$p7Dq3GOK?>L%S0qe z7}t(py0TX1em8tdJgw->Zx)nK zV~H%{?}q3F0yuqa6S`xiJc+9);0~csn>4XFn~(W&)=AT`Uli;!lS>ljFYSb`c)vYK zz9}p`QjK&t;u7NH*u_YYlh|;W(&i&h=~T9_PTlXAssIeJJ`x**6So>$5av zlQ8IjxZShGV^maW$woP^Qm&C0mEBbNT+ATx(c9y`IB zJ0qxw*P5hYTw1*g+__O4l9$6&kv+mf4jr;OBMGnpLa}1FIa=RX$38OfU(d5P36+Ss zi<|uxxBBd0wSPHtlJG_+behhyq&38E6F!3hmDZWCeik;2SQu_ouH>@m#gFmSfDO;h;?=DMDBlaM($`%F{{0^ky$d8~>XITZz-0RNTR7Q2svMAC0rBd*-yTpzk|oSX)VV>};>6yea8`4!O-|f=-hF|H~l@ zC;Dwkp3Y4Souv$XHQ5pCE}Ac`7Rv@}^NHosdEEC#&xsE=2oGF4pdq9_JUOxVSl1nX zdev#c5_yA%KSS=y--#Y8*3!+{?&z4lFpN)H0bNQDLmJhOp+B2`SmHjnlKC<4h$<4v z2-3eL#Z%l7|MKvdOpLxg$YJ7 zyFiAXOvHfO74Z4}qXMa8gUcv4s<+ZZc$~eN+w;1ng`K>6-hIy2efsNZKOxNQp^slu z(m%!BuBZyY*or$0QMLbA8H{8in~$8PyIt%BM__Afuk>hb`x*N_`>^D^?VPe>fzkyq zS^1q3b$01yZ2}~?B{MO1&IneCI-UE1S9HO$a^DpD`E#$W|H@M%=(^CvToDyjJ)m=R z8oDpVtWj|d`@9;9E#KN68PK+~HE@nP+`X)^7lSR_Cg8L7z%GJdbo!Lx?Gt;Qi=tPWe#+t;`Kj<*d#sjA~yb&OvyrlRrikf z>F4&-ro17}oSK6lg=>0L@5&IG6^j@ndGa`oy zivHYud^-2}up=w_r%I`URstvC)=hS4_p*esLqtAtM~f#$SJ@AL^fSt4F8zR{v%{kS zUt7sv`osH%0tRIuYf_^G@{8Z=0jnCy8dcSnwGb{CC2PX4kltFT!=vV|T#+vgLMtX) zE+d0sG(HUWSQ5J!EF`f#o$J2`h`#RGpM)kHU46}iG?V_i_L6ClD8Hk*6Gq6xNX0h} zY*0jGNOMTXsqmx%B^a^H!C##mwKoS(MAhoO-5q!qIYdlf;dL*hO1|*wG8)3j&0D_V zMfH`sBnhPoG0wt$%}lK1(u~tals>#P5R8jk#n3JvfkD^P@>SJXgVR3Z7Blg|buxq1 ziwiGzGC!KB7hxE-;VM~$cONkuec3z+vm859DlwLpLxOk87V@}DQ>}uOrIi82vvxb~(v8U_ReF1zh}--oUJGR+j#YZ$N!0zR8=dkmmut{(pvB8-IphtX0Lba)p+T z^+J7OGiE%7UcT?V9~rQWVa%HcZGhFtPZ4JpoY~odLxrSt0_teS&CV1dB1@T)K zhMksC;u$mBw)K(Ucs@=&yV4&V5<#U7NvAib4P9p_>|!DJteD^PVqb%Q#3>b_ZV%x>Cw=h;CbdW?bNM+; zGFUUqUJjd|*c8}Ur6p3h*px)#SRg9tu1^HgEMiR?r0^xVJtI*3V=ly`qPft8@1TpA zDlhWFAkc~gcE!Pyh9_&Mhfnindnd1((F#?^x4%+r?i!tNzQBrmF5Z;aOV|4Rw>S5w z0Z&y?Jf3JSx}X2&7cR{JAV8(F>$tr&cYnr{q-`*AeUUXlsd0U3=!DEzPvspx$wT@{nILLhgQ3zf$dzL1+j7<#b}ibWNE=RL>dB?d?80C4JU=2H zxr7K7>+|f_J$M9LiR?vC1@j=0AF99NTwC2z=KAZ3l}l;%aBYFM+%5!W57}nKqd#l5 zeN!B^`xffYVu{hSl!f9+A{@~&5F$@u{0?LL;vPohw*bs)Q9PIecl_tJ&Zbn+KKq}EUMWipP*YOX&zw-jOC>eo3fs;!z7dU}RCNz0hm{RF`A z&LqZY>8KA&=X`sL-@gpMzO8m})k9+w7-=8ClhgDcXNUoRmv>ms<$H^1)cTWN^oX%x z>uZw}&ApCTv&;K7TA-$%yszt`C^N_sTlbR%_Juh$dGalGoMG}8*A&v-KperW=HH5b zWl->(I9AR``C;z2myS=fg@XbGiwMGRWY;{XDIYwzm9?~#A4cNbCp^Vkk9?GpoQOFM z2CMrpE-)nYMoZM0!t;0CC#PE~%P9Vw!U+6s(wCa+ ztx?+Y6S;2v8dk}cM+QbJx!7Y-Nph-`tkDdlv#}Cf#uQ;{3970173i6%JmK9@4n8>3 z9&8QqA2m{|k5@!rs-;%&n>FE$36I)JrnB%^vyznIlk?o<34HQh#rT{Qu~jRQ^@SQmB;9ji7fC)uKBZw3;=!1{ zv4J=IQyyvzMj;h8u~b9CXg|(B)xFr?G$^N8J98KN-I0ExSY&yHbdet>4Uds5L5)=K z*5H#|{b};PuAC{U?_DQJXa-saIP%ti0BWGWzSNI8tCw)qRofi?!**S4S!R!wgvWb< zIN84!FXF>W$waSu%wAfdabZH{6f7{KaKNs|a4)rLRKnOy(MN#njQVQxn==d5O!2so z$a3ASj4sjE(U~!HzU4J;ASJgG-MXVgDTgcfLMHfT`WFOGgU)}`$zOnC$+7a;?olwE zw*W!H=4J_xmf@z|(u;96&D*eQa*!%e01Zd87wg_R?;aN2gN)}fcwMl#1ij?VsBzL! zTUSnx9$~V_${RJ~#U3LtX&)^|jX#nh#kwHnl>}+@d|54w)sVz`{%ag0>&9hVtst_` z8eNjdpl+{(=tdz>)`M_Z_HxQ^3SSld!*-?w z%>_Q1=gmd-7O?0%H#RLJrTpG8>cm>&5zI%Zw(|!fT~CkwYXT+ZTO%abpIrzDLf%WR z*K3@CjK&XM-R|Cu7g0TEZ>-DeajI!ZUQRNYd-&^KPAU%snOnoNScWin^Lm{uamfM{ z@Y<~g)#i3h=RCOH1`V1d<^>I3b-xK^#-f5ex@(GopXORU4oOsR;px0Ixg9%mZAllH zn(!0gnLqC_3g99Q9#4FeMSD2s+a|wIQW)472pqF1G^B5np*gee85zFE>it!!#+27p z)+=w(wnhc{JLK45JvjO^Pce`4MoSBk7KgMShAg69=}!Y67PdeML_8xvR4F3>?3##+ zBfo2}H5l@;3st{f`IFJPLqBZI`@eTl1TzuhqYDS%W5zb(KgEKrCs4 z%QSQe_U$48{xA4Uy0MKVPzQ(HuXKza!&KY&t9~q_$Rq7C)2fGCr}QYDGk$o?vdG9y zz%qw*dOzAzJ9HwR@Gji(1EV4x*qLukb&>F)Qhyul{7_4{b7%IsxOz)A1{u!)Q8YF> zp6(#IGqZnkb*_0*r=y(9I;_-c`&}W&Zdhr>fm(QtKp17N%VlWNBewoBEyS3r_2IDA z`~pR7;<)#DcJL9~!*b)lcA)e;EIDm{J8l-agHs*G)VzEc)&Df_-&;-oRN()wOG5aA zZ}3~j=e}((k=;>%tSo6iuLPDupxGBzGbgfsXOYRu9MPy^qZg0=bJIysm7&|s0bM!Y z$UgV2X?H9jN6-RWCmS+O-i+H$mE(Gc`2;-l=!eH?fm(WDQmGqvEmq zpEs+7iC(0aVP4dQHYX`&JnrlWlKgGyERJF$m*lRm?%=Gr0`w8H2sUI&Fbw|0;u0Dm zy2c|JR98E95h=J}k9TwG6Y<}5vB$)UcFg-ojU8f5uAA20b492!uUj+7@_vkEw1I~U z$D8a&YTSlsoQg_s>`yEEK~7gp+IJwtO5bs)=YZhYYhPNj;MX$Glv_%Qnq)=ip6rI3 zsS=x2-p%_qB({`4Ya;kPJt;5k1$d^aF*=;r@hB>|# zOB`s5qjgVzBP!oVSQ`&AP1v4Od-)?VWLqC5$^qr8zIBCRYPGTI%A+kXx z4hVm*W?w8{V4eof;NbN_B#0t5MnED*LY#CEwMlT8IqQZBM7zc8rc5 zkKqoLUf(hKG>7=RPH*8&iLG4Og-Yb&O1CA)jCvl|?knv^*9wbb&&>QHZkUWu9S)un zF`X5WdMF2i?w={`w|K2W8Hyd>ZSau}o$zjT&(<-yT`(~b)q3b%i=$?46t>=d6yz%+ z@LzA=4$<;ib`TEDlaSwp0eBkx8jq)6m~a~@m)H+{zs!#7N}`e4XggYdCgv^&eM5P2 zvPFo_xSfc19K5f$yS_qtf8mPKOP6AwoBJM464XYr)5mPk=|g4yy}&&~go3sCaf9gy z{DmK~`E#GfPFGbFXH`+-+mfrYZyEUCCIYF0u}!_lR4D-=W}-VXgf@>^Zg+ERz1dXP zdc_;+u@{H@E38*5W7*ob}SB2iWABtsoF)=C^cJ0*!HL}Asv zqHe>|d)1{@evhodvdJrBlj{dDRsFN*aq>SVCr9za@@$M#MZJsKK0h*$G|g;{&lMT4 z${V>Virh{!s)%r-t_+{9AHsDY;H-XSpO21Z%eF`MHBal7^v^e>DHCBg@`LFbN#vm0 zb$~kI#I&1RxpSrG9%0;@9Ow6SE*067*y*^Rivz;a#}1^zneM(kYLf{L9lrV9GkeG- z`s;YDN4$RP#pZRX4PmeUpScV3OX< zlc}6ZZ!>zwmO`hB*c=+-ysGv{ZMa{DbBHFzK|7Sx@B1+s(;uriYTig{jzAgkSbz_F3s1qx&FerJ^AZwh`ZVvqfhvo?k?SH`DTW520YAncBwXs$n<@bIb_|ri=bv@JIuNY561xY~FOH*Qb_MJQ$ zJg5Ousvo3&ll=74HrcinO=7u^VMFL|Ac6Mw9SL@{ZHPy^Khs`~$(exg81m^%pK~3~ zFyD_GtwF>?FAAHpaY>TpFKkH*bRpNj?_OC$FbUjohqDf=&j(>`u2e$R^p0rQCD75X zy%Dq0adf(`EDHV~i$G)!Kk+N~Na@IMYQ_Xdt3Hjv_?lf9P_dlZmQLfgggZPl<&D%a z+J9UQI9ND49|{Q@y*wIJ7JgxQ|CK2Z?NgqWj4;DO2FfdO-OH>n{5)|}5Y5aB=99%- zB_=mE;sL{1l@&%YR;ZKNXVRLscdx_+!g6vDRDhIrSBF^W26?yq{46U5TeM9ne`0vC zN64A_3<2{hvK>408U?Yb+c5d!?OdCn?Og>w;F9*A3i?|jzayF z_46uP_dLb!UCyHrMwK+x0kA@FgIx;oR3SxmUau}m`ioDj*grK2!X19tD*R9)x5&p) z2%SYmlIdt?Qac7w~Qo=YFY+^7EGX!)gc?G`g~m3vK^M>pU2|0kqExoNk$F z@vk^lOk$eZMBaXL-$^{|oJu9Z)#s6v3~M3`%wZZvA&fq297CaZ(jpTRy(8VtTt2<2 zGa#oXeY@!nBwT@j-#+(o2!{8tJ=RW7nl2d8;+p$J6gq^=4Sd9hl24jI`rPJ{DycSE z*ZkY*%_7Q~nxS3KYdKT54{meNqtagJZH@Tp)pCZA%<#idSA5KL(CI7Px6GET9q+Ns zliC0NOuFdFT!S@34M6ZzUjDQ2I^qdsKycJFW}j6MW2ARL*XwRekZQpJ1!#=#c6nh3 zHLQef=@Y8GD5*iukDL-U@)Wq{mmLszO?F~nWq+VFknu6=ua6Nw0^$z5Ny}fLkqH|_ zqGB+sR=aM$A)c>-CbEAY>v=Z`VarS1@om%=`+wRv?|(M*{f{R`(3}z!M~x7ts1a38 zt1+TQ8(QVm-Zg8rMr|=-#IDhn)ZXDJt<|FTRwG7q1PxKEY7psWrU7#qp?K%2a?JaRdfOyQ~OD(T8I>>khP=*r)j1CJNM&+hhp7A_acENg-qzO zPPfKoRYiUjny<1_TKH$zfl@ok7RIXSnKU?nNx5pu=w27;cB2s`AuSJlj1ys?7) zUSk9gLxgRMhE&JVuA(=m@^4cq@JZpinZ8#9FAs2nh@EQ%Z{ItuAVFWJ2yf=q+u756 za@m_Bt7#(84L3}?IJy7yEIWRD5rZNq%b#P%lg9$(y=w}Iw!96^qSpkq18MIk@(p%F z%1;-ye6l)!+nY$w2`%oz7dY4_gu9!@KlASkUoGHDY_f=LJwDoYl(k zo8r4|c`Qk+rRfj&Kn+=x(vmI*m8r&03y7l`+TYl4Aa`QbDdgT@e6;2~1NE+0J~GpajI&zf zAU~zYe+`QHl<9AGLHmAN(XJh}eWzX4_`!wFip8yHU`nL>hEw#`WwWsMtf!F6)`j*2uD?1F^$Twk!TNnj417?|}%+v;-rkAfR834tc32&1->V3 zc_V?Yw~x0d)|H6@=Y}$^dDm2kk*H)S_l5LZ1dtjGc%Rw?Y8qzF*S9e&{y2%TP1F-E zGzx=2(_7!_t7hm%*>iEPpjmH!LlQ86C>g6$)AEy%eIys=J`RAG3A~Or_brYb%zF7M zLZLKES*$G2jcQg5wroXkqFeYZ48-xw8WzuzGHKk(X^bL+A1{0`e&!O;oO1c7NcdPG z+3oW&$6G1jil0j+zfyW*IlOU&&9YLWa~?$_ULzwotJOS5#ca!>pQ-0hta+CwF9n~a z9gHx@Tp*qiMrwxp>mMflbl=H#G%|X)RIT1qVFt|a*h=`VEvtM?wvEA+s#3<^VX`>1 zf7G}#!KA4j+^rFtilsDQoxwY?sCU;xifrOg$$4Y5cwc*g12=`>P{x@>h7|IV^PYhi z`ik4DHlt%>mR=o%@n!s!t}d$mk>DM~cNcQPL-;%&yW?EXX{CO`PRJl+R2<+CC-D!w zKRO^hS~Jf# zooKt|GrCVA2r7aI`$@(%g*7;;{(Jf}x=vcka*qkoG22IRgdQDaR7@`ZBZ}rnm2Uwn z);5~Qn-RFX!w=sY_kMmVvfe&k>nnD?$Ct6nzr^bMuLX~y$ssD$(nU5z{2o+|iyOd{ zM~9pr8%U1RHM~EyHb7k-XlV{`-YvsGQ5JCi&92>JR~?7+oJ%)w;l2)twN9UT@r@() z?tb+YJ)vY=UQD(CAN)7t%AgsQbMnTk2|D?NTb7h3e5IEgu-48dVIJPl6)(lar2aa? zN}&+1Vw2iK!W&X7cCSy)tksHIVD*-4oQdooR=N! zp-;A*8yvI^_q+UX2&iYe(41Lc=W*ID@p;e&3FvpMC{&BLr(Ds0@6pD#Z%;yp{6MH1 z*mivNArB&wQ&@Rf3hNBWu;k)Cg~YsS-LYZZt-dEUqLcFB&- z!~-Qnyw}PAjuCjisq4+Z1vHkRyaw$|-%FX;sHK1ghcrggnpGD1 znpGwrV57gaah7rjM-bUO&6Uyp=xE9L@v`s#%Fj14km#bSG z>XYtwHZhngx$hWP_Wcd$Hjes6yhPcF=5;IXGL%BUzc>KOFAjtcPP56IT}rOEG$`>c z3uK{$PQg|W27lsi+ZG%*tA9Jn?Y}0$mZV*Ezpg72OVwwI1iUEG&)i^zbKBtupzd ziDAFn-}I1L?jF6+!{9@S3KHxZnP^JJIJT7ol+7?43JH!gm zhp_HszM3~%eR8j8A=q8mTok{B#VgcV%Bhi?l4kYh|DWH{$ICoLCF|Gcf@d2GB+fSY zSuSu3XHSqSc~&9Mv%UYin1F_nFZp>F2(2UK=*b+>@9YOgY}{ZFf&fjGtm{gfU*7E* zdRP6fW4p+%zzH+;$ihx{#t6P%+v1wDYq_Jl;2Kh}J}8edLeeB;QowkHfM{y??aL>X zj(=+-iLU16_f=v~o`reBb6sI%9=`*f;DM(e;-8NHnOkyoX`!k8=Pot5fm@Kf*jY(H z$WH1?#U$|Y4fdDN^k6`X$?}QQ6vJxN>(}AldwfHnhA2Kd&dG$xuM!;p`jcDzB!xMd zo%IicwT^Z0XWy?zYUOue7P={D4>`s*07u#+d$(F#aoAePLjoo+*5i!J#b^NrgFdcg zb4p2CSo+yh!pE7+wyppvqbyl5;WS7+1kijX%&=y5z~io1QbtpIZUd0pcl&%TWGD`O zlE;UFKEQYm&hI#LxphpK%{^h^y=eVVC?oy$!gBSdJNq6(T*^uI<5oy@(50jrV)Ri* z^M8+72V#&3Ox>N+F-7hEVLPJ{)Cj^(^5FCmWcP%YmytuYd+*_a&he8XKV#Qq_ zu3q=v`+n~IyziGQ$FZ^|GjslD%~~__JJ&gh(biPL#iqnYLPEk-QC84JLP7yOrez7x zAHQqktf`QYo|FOTx}hkZIF7r+391ply_P=HF z9waC3_H#Waq%K~k-6Y_I+L9SEj>tD74U>_nuJ?sgr0IPnFQE-Z;owCo?M@p@Q-Qd< ze?b~me(?1RdO{z2U)k6@Co}X=wRMQbPm821zM=jxJ`4W}6$yc*#mJ2sN{(`7Ab`Vy zO)58=(Tl_|q3_m`YRDm~H?s87g=l>t*#wEc%CmjS8A))lFi)p{EGk%#7U)BGqG*LA z=*@s}7-1^Cp)d?PIl&?6AZU?1uhI7ecZfq<>zcwk=*JA7T=^M=LGog?5i*D#LZ7B>UcSS%6P z^9U=_&6DG9{Yz?Zn}W@21PD)rUy}mg9JL6UDgp^Txi1q7TNaPN`&8(n$6_>vw;N42 z85gzN=q*J~3cn;{)Euhz)B8|nq=qkkJ$=O}+NfuAO3kBH0>hNF+?07KIJENP7&`R$ z_nG(;L`gN7PicV(TXa+@Tafc@!Rll@FO?_fUPfw zw3J5N!J>JlTS})%XKj^2&oa{61=~*F2WlsT$@Nsr4d4#)B!9|`ZHSC~N*aiRNlwk@ zx(tcRjmzakiuH{>=9>v|xHJnRcL7XG+GS(Gxcz9(%w5RG=Uz| zI?VJi>^h=qG^%dfI@~>!fF9(@r-`9y-=DT2@r3Vw$6J<>`cAQhQQJfRf}S}dYLbwt zpSm9Snm{BX29>^0S&%5Hgpop7m=UxwY`Q^Jf>NO%OmC9nzk#vA>p>)z^~8Kv`%b`0+<+y3WfQ^Ci`UE0>wpkBBQPh9Q3xuc z`9iglP|;7lM!m+r23nI|!?I$l&lQzrOo><4WDe2gic#ZW&PbU}J5Nqbt4a1(b{%oF z_H3XMi+>FwO;a1z-}trx+u+<_+W^Lr4n(b~#k@Uy-uRr8ed+nTbhUKaQF{GcN2Rke zR$b5Xxbm54(2m27*^Y&yqhqF{v}4+|f+NmM<;;228@+&nb4@d)Z#r+@<<;;QTGV{h zyNkGXIqR|)e8tTjoeAPB;Vzr`s`+LA>x$!~(4d2x;3XxFprha`!5VwXxf1(D`v$=> z2T~^k2iob5l7%wGFAXzRPVUW{PBZp2v+pZ}3N+??W)f${=gdnxO>R2Q^=MKP-)WZP zS(Jh8a>t*)fs2D$iyF5juSHIOpME{1H7lxl!=ogk)GFs&3x5gk%1g|9Y2L8H)k)b| z>~D6R{qdc&l8jbJM6=`NCEnAAHYVas*L&#Jc`QK@|a?kjuGlK7gjP2boI~b zeHtvKyBb-xV;BY=Q4-*m>J!dZu`WpM<+#uNMtv#5>Vm1a_QVHXT(B=F>ck418so zu=y}XV@NZnJV!KVFqZ{SgiE$kwmR(#UhrO^?Q`z~BwtIS(&kFS{idYY{CUouPj0t< z{$@FIJl#2KIUhf)Ir}&=Z8ON1#W!(95cnd9^pg6>@7L~6ldXX63oRMDF4L}W!CGwd z8U*U|(uGT_Q~A4HGhLjagvo?;ECrmCjLB3GvP<4!j%d0jrY)?ou#CRNK7ZOhA}(BM zlG~`?V|hc;gfAi^UZ%hFir9%@jf7)%(%DjE(##Uf((O}7v)wA7GB9#j>Gx|SK7Tn> z@#|E{UuitfIY~E3HF}ZYjCYaGnDU!A;Tv)>_p|;Fe8PNd*_#l8u^2O&0Khm89JH*J z7M-@nI-~ASeLyKAa_@{H1@-UUkC=<;iQyzVU|wJwNn1=6O8c6&o3>gKQ35XY(x8>` zTiL*=7_2Co&J@%&_E=183VU9tH>*AY%?^IX(Dx=UE%k}Ykzv;Dq8cq=r zpC12>g08K8S$toXm90^@F@I?D-MZ8|#?jni0NVWv)t)r2hw9PlvW5GFs>XoGuwD*m zel+(Yy?+XEN~72>4Y>3E_;O)KdPmUJ#%=s768rL4TDV;s^s?}SXU&b?d38f0{Esj5F6kxeI`aQev7XS+nO9o5rN0qD6=IJIc zsKZ6;k5%Dxhjf)OIM2CBhac8Qg{Bf%#m&^2noP#YSV)aqMS10AU3}}_uLIMrs(ZM- z-|TVXGjmSicg!^;wH@^wZZkEizem?b_h*O=MczTHpIe+b{yuH~RV7&|Tw7d|R=Zo7 zSOYh5?F{~TjZYOpRWpY=w^t=pVP6x%-;sb*^j+@_roN2$9cE1 zg|PLROF)N|-_627&g$F&?}|?S`nu-Pc#YZ7hsE8_-Cf_@J@YT2!oyVl7bOSn9U|7Q zYQ>)Gvq9H49OvP8$9G*1$wz$&PjoOA@%ZtD@9j@uzZtFzk6B9`eDp#Z>)NYWn%|zd zZTx64=$e(6Nw{(NMHt5rqr=NsRffm+2bycHuvmRsv> z-fU;(4eP~ju;-LM0~B}pd^|?X2os37J$T>m z_K5s+O<39Y9}4t64;sB;3m1?{mIjA-UCv)W-}(Bj@V1Zv%W#zDo}}ASzOexb(N2tH z%z<<|c6bAgJ^m!Z6@C0#T>ZOD{jsSimpPJPujWzvxHNKi@Vqmb+$s>Mzc-T{RonOC zODU02=7-#=EYK4q=D5PbEHor-%Nqh|K|yj6!P9zD^Z?vYm{x|JMkK+H1* zs1|X@)YpoM78kOFVHlV1AIMsaq7^AlC*L3;p?ldtRBSagkT@RSKQNI{ktvbT9#hDV zhcq(Pf2Tpn>_|`kviA{Z}2$$MavG3Hyo`9OKGA?gldUSdKb-p2 z?KHq}1GtWsx|oBjgP^dZuA4PT#R2NBz^S3+qUK`j>kn{Lfy1%A;QGFv07n}EO@9F! zn3#xwD**1JZLR3!q2{D0Z0)ZAQCBfg*Yo0+^W%lXY@q7ya5Z~H0UZR$Mb*_vUK870 z!^IA4B%onrtnBKn1LU*;J9~QBI*J1Q9W-6Vgyng~V9stjAWZ`u7mx>^tCg3xs31(4 z6D(j267|$F(7_hwRMt}Q<%9_<^SKIY`l|?O>S<`G7&#kSLsZ=r`BeRERoxA(;2=X6 zPb)Eivz3ql2ny#1+v>QfAYAb!OB*8FhdtRkO$O21RJU=U=0R1+v#e`Bh=-c1r0#D z&IUT3PJHrqHmbU6x-hW3n~|QPu9Gc@SI5=PL*L0)PY$LIRnXS~**QB~VJqq@!5sO$ z-1S^tY&0B=wS-;V)D#62f!e&TP#t}cA>5GPP|QvQ;;tbIfcdyN`Dxi|YuUPk?OYv{ zJzxS_*aohgBJN@W2Eq`Kh=97EKc5ZU)5^t5z{bs<*BasA>tpR>AP7Nvae z^LjzN#GL$HT=)zX<$xkC*alEPZIGynw>R8dUfV~^*U{e40}3JFU`Jh5 z2Lo*nLtQJNjlZgZl9Ps;iif;6K;6Ya)kf3}+lWup#zR5KRT%6g=H?@+W$a)eB5$qX zpk}1XXXpeM;8kR!*a&B5e>F7&M?P;Q zQAG`FFj&FBoev80*D@6L2LM4X4z?-?14Atz9UljnwT-uyqpE_A7(~ax*U=XYbb}jU z14O)Bl(abcG~M(aG;FPTb)D7pJV2@-e|Z}K19G%-`-!;4`HP)<&`L?q+f9@o zlM`D5=%@t*a|#00)$LT^c52!{Ya5_E zr-Fefkk1o{umK8lDrkzzSqaJs_^Nx@scPFP+1hymUyXtt_*cphp+96zw?2P~l4gjFB4ba)f-pR*T$=Oedj}s(< zEeg~W1PTah_y|I5efa=(R#uL3o_gK}YMg3n-nyKEa1m!)ZwSO&lT(mi%-2T1*Op%s ztY)WS0M!sSP!WY<>&t7p>$+O&f&glEM*Ma_PGg|0KU7snS5pxztOVy(S9e#0JHdQh z-E4I<;I3dFBLN#-e_I`UP6rpLwKFfafUT~vt&@?Ep}K>Cx~sehLL2O?Ehwih1O!SU z`Nonf$h07apj!tCbB8!o}?`VjxK( z#2=F`HeOJAgo`uWQyd}1_@{>WWBRXb03-dMDqc=fj1UcNdU;n58+sugK^|U4>Bn#x zy`+b=t+=iN=wIfKzoZ!Ly}aDS0RUfLUmjlp9#;=L0H2tc7=V`_z|YV9ScBWs5AFp; zaKk;B{ucQ!9R(Xtn1_R#mxC*u{x4mqm8-Xx6eHtb4gL4$@9VTdIQ&mbaL<2r>#>7? zze)gnJiLJamzkG??f-|_UnPH={pr`=%}M?xCa&*k<00?r;$j2$lK!V`Wo1GDCH^U2 z|A_ok#{Locr=0yG@=sa&N93RK_K(OvW$qu5f6CoIBL9@Ve~bJ>{{9j9rwslh@=rPZ zN93Qf_>agxTgdZ~ACEAZ(l=3J#C>@q7fMw2&zOzpVbV3Wre>*bL*pXrL-yb&tkyI3bUN z`UvA=Z-atL?@_1Zfi|GN#@C#a@n4S6kidy`>_DM^wh7rJDQ z@`Ei3`UUY3A?nF-Z2-gYA_VEbuFs8-p&P3>ZVP%+>hXBh8gZe!FRK@3Pn!hQClrgw z%-?<$Jr*L^5Y*$}-kcD+;L6*aKR&X0SZr&tm2#qS-UlkxGrhj8ZGE2m)Vkbf%KR34 zcuHkv0}d+$marW>Y2TC{z!z)z?Rovnv;H+KOmIoOLyK-vL42z78r{2;@_1(_cQs}) z?LItm^M2q$Le&CL-9@;P;$$()IU8^BYf@!zI>0rTC|OmBb?RG|ljhL)T_)XYVkFJ|?G?W=iHn%&iuz~Oc`JRC{nq4>MW2m;a%)T1pd`Ii zQKB1@Pa^|(a+>FHp{U09{i^d7+-Xnm^^;#LYzGMV+#;O~Ui!I12Ea z-XE3dy@}~qqj{70Y^PH4^jX$~?AhLF{=?HNhOLLrE(OiiuP@5pGOgmVvBmBbt||S; zoP9@!tV!N{Z}-V$_;FJAQ-#s0dyixyi!lk{-y_n2l-@`UYw`j}n7k;n73B2>(-ApSOd|!YgUit6) zBGt;F%~q%6BrCsQ{&I=sg@ws@bTZ+_nmXi+?2bB8*B^javu*@1`P%4G^E=so*TtSs z7|RB$gH{SWBh&Tk3%IO?n;!4$(1K~eQOC>Xuq|@@cUWPi!E{YKGCcSzOVx0*pBMB3 z0_GD1?JFPLmM{YITk)Dp+h@N^eGaq!VAk>#5cLVB>DDr ztzs<_i7kFDQt;1YQih>G8wDgM9?AWgPn4fSNjZ<-gT0&nnO_o zoMK`P?MhYAa}|Pt=N#$j3OCs<6^7VuAGmY&N8TnRKdiYk>H{~lj!qNK4v7nfyM+lh%n_H=-gxz8zm`~EqiDs{MS z6E?S4ZC5S--YdcIsDs*tF#6`EK>y)+6l%$Q75;1TXy(A?1^rZ^xmOvv#oXd&?Ls#J zh87t(bhs!#Tt`FFuc5c4G8>`gb7}YY-3RNDo`r3X_wKs?>gt+oVgja6@bipK_=z%wmx zXLFY_&uoI-xy2*8mKe~y>C47V$kz~Ym7J{?JjZfV1L#YNY$J`EoGd|V4>Q!R0|$BV|~EaB9E%I(g#KH=he4xddDA190Mr+b=)iff30S-XRWb^ zFPdcO_YcBBcSDkt=KLaAnaLT1OnRP2r1ClE7C7m+INWtmKju#XWJSPHbQF+~D4^|2 zDabV(P=4spuMo6+6KM>+qBozItAzwpGNEvPq-&`=dOkQbkTyi|IGG11+{~$!3Z4_V zW!QagOl${)6`SJg*W98{1}S!w);f+BemOj7K>88^6QK<7 znT((AlH*c?CxMbmM3urvnaGvx(?&CETI1Wg^@5j1vkugY3`4KVcF0DbK}5+P`1MUS zI3rAe&Y}gn`T^14T9E|3)@6ZrN8_bV}hq-dgNL1N>#m^KR$PTL$ueOG4_;T3qX#Lmf*y^Txzf>g0|ULMBg^Mud5JP{;hJ|@mT|rVz1+1_(eoRvtD*R^#M|^FETQ~ocRPvu zN^wg2EwOcE&+;wzqb}+<_KZ}Arlt`$xQMQAdsoF-i0!?vNke6%9qACl$?G6Dnimlh z(R549CUz8kD9nTz*N)#pK2`AMbzQASZbfFt0k{;zlFR*^Qi{Y&)2Yr}Uv&5~?5<)R zz%Hr=zXZoWO?M3Yid>F<;DJ2{H4XONPEFq4WwieW=;aoHbg+he?7`lgE0(7R-axBp z@{0mgCG`dVnnAWGd1PaR(dfuVk)`q&d(^$?N+afTVbxjHS^4ug8R?Eh2DQce5an11 zgyRP)tCh;Fkl}ajV4I9aH7;Hdcj}LQ>fxj4jl1y}v`bi`OFs8tlNr5Uf?iCL4bSux zxf2QFZjz@|zv%@F-up!2YObXzU(BKKhYuI@H|7vmOBL3LP^{d^ZnYIo zf$cu97tr3h57f;hLN2Ks^;o*aEn`?aZlCT`j@*1Ojcjv!)7{GlbEDjPy61IKC%g8v zf%o$T^)$^y5WS$JC)uRAK`pl?R4{>fHP1}T4NXvzk7pR?P{MO^EbKyGc-RxT>_o}* z-uhzoGgu=BX;}vy3!eaTa&olN(-vqh&75Fs^7ZS~s|w?ec>+xPJL&S&V*gX^iBU%9 zHd+4DnHK~z^q+6E3_Hj&LS7|a^vOyy>BSGA53Vj;lISZ>U+~z&91B$UKH9|k%b=|; zm5|vzUvKc28V;MiV^rq*VljJp1+pN_JAQ%543TkuxBe9^AGs^14)ZX>x>uUgoG-E4 zkDxpu z*`c81XXYa21Mj9}gQ-atwI^#rb7-ZNTRAtb&6hlg)w3j-%Dj{CemU9Qiyu!1LoPJZ z$jy}fFoI*4KE*;iGMmB4ft(UP>WmS%k&)Vp=P3wZJaC3ZbK=KoBA=l2=$QMJ z=V#zx3H}#*wp8BTwfp77>x$eg+<{8%G{=U!!GsOn!;JR#flQovLwICi3cD}gc?V)& z_#Gm!{-Q9^j{D)L8!AsclEPZPclz|~D?r%0jD!Pj1LrkMIsUIY1{6`4pCV6OfBQb8 z((13yVt(i?ZE2-p7KxaUF&r;k6#Q2IO~-cMBCxCY^i0mXw@jh@M&B8)qJ@n_rBIMd z!F~eXwS`>PYpERD(dCTgydQeW>0K%8JH_i>bK6UsTo7qCN$L9bs-c9S1BVYbd%f#? zd}d}d8gzCc8cnMAWPR>;h19kl=E3K?#MB4F@kmuw?X3NO-Up*Z3mNZ7f01JbprC zYK{4s6e4_jG4rjpLQq}1QpuUh^d;63zRAL6dig~D9H%6zD3pX&Qed2f`BMnzPG336M~`Q<92xTsJc{gGtfYcFgWqeHs03lkJwzagpw9tDpE zi&idzF;nX~JY+C&$nMho=o@%hU7K>3NM*jWOBfL{8;!MB^R2ig-4=QGXDRYp;V!&y z&Rqx=^h5Gi;yMk?{pcBlv;KoAIHMS48hyfOzK&1}19iom%^9hO{oKr#^TLd(!MrXJ zA-U=u)o!xdMJC7?Z!Pbws;h(iVBE)?sw&dP0cr25m@phEhzXv-3YIbGZWgvO$d2dS zBLtMZnAT!AX3m&}-f;u$LLx+VO<_$dF@81s{Mq`V>2CSQphJl<@oLY|EHQ$ukj7G9 z^$c(%$e0Vep4P>wDVQ$(JQO~7$vap&tHyX+tPPwgf5?7G^3YSi{ehpLI+;XzFJhS& zvwDPh<~mZ`e(gf@#J!k!vEqYG>NSnm#R4j6>`jE`E6b&$4sP?{QN*t zz2X>>?wpKU$IeQH!jI?8&~yD4lH{Z?f@KN`L$f9D|GX%CX9RXXT^|}rW93czIzQIW zNJvcQ-bq8Ga3LDITsKH%#ET!^nyc{yLm`ucx20Vmo-B*UjB8aV_{n;68>jL5w@8W@ zntU1_yat`EJB*FXEL2Ihlb-`gqQVc{79VSGqjCe%2Gtn8HqXhep>goLV5Wk%>Q~c2 zCPiauXAMHT=PFGYs1^HPDj=DD4olip#Tp}_w|cUV+kW&*>hsnZz{u1GVY0cTsrHFX zrp%bsSr=KZ66KmI&?=JT%=Md|TzvrtY+R6E6n5Dp@yg`NYO~&ZSACdbAU%MY-iVbx zwn!WcSy!UKx*fddc=0N$_oa%nqNZ+3^bbw4h1Bqr8dsA~~G-32I#9B$Rd`j+Z z=D?9L*JY9g;}=Z}%+@z7h99a8t0~_4T;`#UCyn#w9tNs*nF9ts9CnqjU_`dP7D0@y!! z0#}#;pm-d8C|FdeRCw6BFJt@ujd1-lF7fwxl&O?$;Zv$df2LubW97xf9=Tz?+Uee2 zU8g?iCh%^D;`o$^-s$xTwX={_xJ@eV0VAkINU@=^nA_wGo05@fj)$P1>7?`v*7qMl z^`X~{VV6J#a7U+C$qJ5hwDXIVOc#t5eig5;#_zq47~`3eMTzHqRg!35;1l;z$XGNc zFtLtql{M*FD$0(o6m#+fgtbhS!(t8qF( zPT;IB4j$-;DlX&TfN4pv@prV!lo^wE{ky)%X8F4r=nt#w#hSd6CoY8F5lS!ZTtVMW z2QsTYlH=z>sK$GZV{7+2cm7u^cmH`XbdnC8vC= z$iun=kyX7Dve4u7Rnsv1sLnT5twlu*3ou*|Nquo|Ybl7rv;Zl$)@Ar_7p_g%} zkR>yA;M5!#NwCh>O=A3Lh6|7q@~YvFG^kEn+`0?X^uAa-WubuZ=D$^CwGBIl_Cpp5 z@$_SP!)gdtpD#V{em+9iMpDT*J>D5E^2?GNAF1c zH?{-~DDb@>KRABUlXm!tJEq6VdOroT|KOsmGGn#*%g8NBr|WcTAD*1;%_Gc>tLCeYm7lytEL6;o)jH|?jE~wWs(e^iyA=3B1hQ6eI;5I}4MVw4C zo{RDx8TEMemmGh4>}ls>@q?VVmsr8#9r3AT?=LFBd;$^h`d-;& znxvtY!O#IoQ}LoXDprr(yFT<%v@sA%Ebr*!e<9fVNu<)1f@b_AoR&VZw@n`!Sol5xHab?+6w9+Nz6tjHu z&+NlJ(wS4sIGIHo-9B4Ens&+aKP;kDtoT3j>ZO`i4A`C!e*f{|B3R{xy-CLV1~(d1 zH%ojThWE&h=Ax|DSBQke&n?fSSVuBnAtT(%($rhe@l9dmV%E%~X zN}9N2Ex(DQ62a*1W=`^2Sl9$6&vTl=F1ijlhCC^BI%wyB%hhH>TLeVvT$Er04q2Oz zY^uXX4z`iauRd{=G4ytYE9q0KWBCk9*EKWUR%3p~Rp2>E)pHZ)f&@oS4 z%S|?W3=Ug$y+LAFN5jyMG7f!A{QkA2uU` zXl=SMGi8`v|GfXljIhZS4YNWm&a#YjyH;A%e`nPYDKA@_<;5tIuO89~VqiVt62%56 zTnF}z3E6Yacf8)8Z)jFvoO~HBY88B$YRHXp1ZPaT)5{TU_!fFZVs7P|HITqwSyf;1 z!lGg5dHza1r`qLNqbxsx6(|`3?tLyvF~R1;I;ZS)qxCtf@F9IV>7hY&X^LeH#6bkV z>3?AdqyKg$9B)GZYH*>B52eU;0A1|ECuG%@&olUdS4S$yuO3?LQQIPP;(`M^jvvR7 zECiDoXrI$iiyysfBLSvbkc-0Leq5G@qBhOd)1|&~JF=G5m$-yf$~}&p?vHyY;Feo? zEl|g&iJ@LgNBJV{qU zQDsiplSQLvi?iJwo`&v?|9B65M^m3Re5hH-8#@?%kQJeYNe9C@CDwFcTbWxZsw_n% z@k%kX6kaS>H3o?|`q3a`txsrk<1ojjw{6nW=Ly%E;H$Yq%=6jIiAY!SD#GscN9boS z3VG;^h}fQE5n0bzw@sB=;};+M6aD6#IkCro4Ap(w%sNoGyIG-F51a3VO*%T9tq9Gv z5jH^?;P%siXiy``vs=Nz@RFu`-q_o8Z?MD`?`-7x){r>?HJpGjD#2%dFr0a_ z<8Ww9IlopH9^bY3gFd1K{yYp-lSMyVbm!CHjCC*j8#xex5+^X*uA>R*9o#skNc(r4 zrBgTL=hNuftPzrhtV>rC_9K!tQjgLC<9wVzTJO}_y2#50A*mM$1aCtvyC~243?!t{ z`VuT$buitqib>Df5H^on6Jg~9$sMcntjai=naCtu!*0VdG?g!@sqnLuGT5|89-pbN zn{#iwCpNKPJ(b=WVRkU2t%VP~UT{;Nrdp91S~Lzkj}nex)sC|2HAj1fY%77X8&elv z@?!QK#u{vh=Ajh^<#}zZq=PoF8R49Mn@kM)Stvd|^x~7OWMJd?&;EWHSgW3HPHIfF zvBxhNwk6c1=W09%@d|w|67l6B*DSb- z64qF`*UB31{op>wtRW9wMZ%Pg=e#pCeXJiKDArQA;QK_mB2bnC&MU+819{nC zj5@)6#Lo-}`|e0w;+q%#n0Rd03xY~m9X|&sA0O(k!`U27e#57_T4Y?8LiK6%41*Un z3quL?pRxUns)7qi(&O)C11{=U*v%ZnFIEE#@tilkm?t) zRjwfRcd`hi;5AhImSvokBf)O$DDfTsDU67}S(D4YzHTPP%7odv^pj6GR!h_iG~uvw znx`7c`%wg4G26xpc)7Kj`ARm*9-$bCmUNg)O)eJc zp*-T7s=6^;{T?lhNG#q0YYb9YzUtVskQL3UHB;_N=h!oLED)$yoIB4x~2_wB2 zdX>s+Oq<0{9~%hv=1P_ogawjHB){+5x5%|$#druT@yyle3{2%tFFuSdwf*k<7}<3g zivDta0W!s1Yo4+^;(T{6ID1jkK9q2sso+!M&?Wn&U|S{dB1pMBl>K_S#sK};+`9Wa zR=Zje-I8pbrSy?1vYD31qC1p)wT28M2?Rqt7 zqJoQC)w4}yhKpJn@XzzqP4;%gWF}FO6I)q%8zNO$uDUs7@idP~1ri4*XU}PpZ*+@r zl;7_S$qoIk4E23`^3tWP`e2kf^c5@E3dlnJ+|Y&G8$;1*iydT=T|{In3`5qw?y<_z zzGSD^D$!nYf+u%uY`NxP8l&#b0z3;SU%YWwwj$5Q&0ZFNRqgSim#g5?C2;D?|1oj zx>+^%72;(Y=46rA-(i^V&Du)AXr^r5Unva;P)j7z;TYX0=erI+Wr{<}c-&O2-u_At z++bMsL?ho}erCQCF7o-J*YrFy`Q}9NFczItNily^)OwX(jYHge^5b9TSv41VV%*MM`ez8v1aRqi|LO!P^1qx@8Kx`tgrh6!>wzcr}N zF?~%(lUxRBc{*Pq>ixK)OFnl^4D=$Yg=2Wm>?N&rikQnrDkW_Bx=|DRxZ2^Ib)%?C zuAP1u(}F1$Na?9iIbaPBVyX6O~@ZI;@vGWO9%12A7@sWjTDjiT-QOWNIA~w5M=ekCas9v56atM=Q}I0 z!JM)87X)!zYCklGXx~$>GzH%Hewbaq{(eqF@&Z-(J*`Ljc&<$flJN zirEC|Rpv7;-IHadZ{coGja^b9r;4ocA;*a$T^Kbmbr@z*Cc;uB4rq*ND|l@d*yYSN zDG_WX+jr9qiYW97>h=z15JnYUssB+{5_N)@`d!5)C}CM>lABktjCby|Zz%Z~i!+MZ zmZE;s^@@%FKbFV(@{YtCx<>|FaKMm4v#EVib_;(gtq~^gowSSTQ~D#Q@|ETKlT`8T zmPxETE7Q?&x>qP;4F1Q^Hxr9YUg29>$w>au5$LIgAXbNFe~sjMNRr5;!Lnu8ya{4g(iJ_|Cc77O#o@Z&5xZ0*osx_jP>f4q~obq42Z zD?jIp=n1-=&PRMlyv|8FO(Q_$Z${;U9v?zgCihl712ZwOmKz>0scJj`wR2v!)T3;# z`S%BYp?rFbR~PvV<@s<(NVDh&bQSFy7Jp#Ym_+3$&mfFrs5BX$olSdeuYW^P4H?Bh)VNKDr^RS4K0OgX<$F z0F_8ly{NK3uHG20Zu_jRxTGXcbZ2Zcg#a5IUEEBc$Bz-IRl-3rbp3&BbH`~=>uG7x zJM&s#kW=1k3hiZg<-GS<3p3|v3em@M)pvExNm@F+qiHOpD9BH&tn_O?3XdwxHb>!t zYq`4J65kX(aD^({u$-y)J`KgtAYdPiFxs1W`C1)(Q}wywW^$QY<9IX2J}OjoPv80( zMCqwUU&NWB)8HF1H~Cizv;$>Au@Y!0Ya2_oX$e%e)}#A+7^Tk{FJ9@h>j-$j%0&ID z72oAGBumN3B>QH`caGyX0Ylf{;U+dicqyfgt8IOv5{8%rrcbmn)VA~}1=pXS1|tq~ z-qeC*Fc_8gpoJeH z#c_I8Lx^*acmK7*M}~&h`udR{A!YbhJ>wk6k-|iyZ<^?c@4jl0T^h>!TuAd1*B49+ zmLYxID9~-0)wGy0Rt?#exjzce^X(Pg{!AG;jY&Wo`kJs^1}oPM`<1IxSK+)r3a&z4 z#;*0+R+vL-#9*Bc%ry5Xh%)#=kRW;ndmQY+$w8@Zg57 z|5}>5cM$k91;&nF$vz3%eQ_a+?~3q7hWA_4;eGHUqLGzcKg}WfVH9NHhN7lYe*3tw zwA?))@@gS7EFq_{S}m_s&!So{_T*t^uhXg2y{}6Onm@D%D4p;3&}Np*J3Y|A;utM%Xm^ zZzpP2a0S|pU;`l^=gFG(E?BR&8)uu3-!8ggoc*ir1y+36ON-2<;L3f=ax6xP|Jr1g zPyijTq=nPSrlhi(Qq){z537Daz;cyfYc1_f{rX{O{m~We+2yc;yE&A0x;74L!f#qT zWc*|R@aH9uy|m;q#1pZ)w4wv+Lb~-QJZ*2li5HCRy;xzU9cow!P=o;RFz5--p+R;X2qRbiJOPi zVf494-*FFAlQF}%Q+%@noKhC00`nJx9|FVQSo9uKr9H23w49Gnr5ubKI6#dXuf1VF zx_%SyO42)s!`zq$pttQew(rO91rdU|7}%7As@}{ezd-$*e^Rh>QU~MgIEuvN>%za& z)?BEE9Y?KKMb^y}F|Brr@fgkq?nY}UBJeG_I&;xdS^STeGr0-TmxR&T>TY+dbRKkA zHs6YPrzg}PB@Rwtf0jEUPW&b$bU%RpdgyYc;y}YQfeIP-{b3~JCXzRMFy;VY!U!(_ zL|90s0pLAtZ1>IGGj9mDE;P^>B7(6=+oi6Do)aj1cwAN(Q3i+hoaedx`|GdNZX%tG zLLTGbCi(gZrT9x>Z#6Ux6r+z~SBJ*iC9jn7GMxp5lG(8{a^$E-Rtd{1!wlY1ZcAYZ zJ6k;~bHirp!b2F=9bX$;22!KC=@1UO1h%?iEit90II+(|^L|CdGOV1Sd2WloCiC*! zepW4i;7-yG)ODh=`u(zeZh%i(5$l8M)K8nl* zsvLO@Wwv4$bCr&yL1A6puj<>Px$IxsH*3qBnjoKK(XcQ2zW!vSjrC33S~ks)c@#yC z2$ZeNn&Lh~goz?o=ARUao23x)Iu?o{EbG5C?E&Z`Sj#nxo+I)Lw!n5}%?^E2O)#k2 z(pFuGePo-epFnet%*=>gU0l-wy>>`ec$zb+F_nL8so+rwTVFhs*@9*bGx4K-s`w<_ z--Tl~&@JP%hbnx>bY~K`fe$j)x_Y8(KK{j#7WLEb989m(2pY&Mj12U*I|X1Exsb7O z-44}L&rf%CAEp=RS!JeC9^H3RcJxghoXWYzVZ2_nU~k${on;F(oW)eB@ov;#U5rU{ zk&(yWdgTG&juQ5*rasvPyskou)VmAGM*Yw-IHLPwju{ z`K^{hC-N}T?7F>M#wLtWX=FTe6S;4(>Fr8(*jD3IJ(6-!$*~8NAc6GZgPp}i@c@&r zNg)T3izPf$N=&bQ8R-a5|Lyb|1`W&7SkdSGB9)gv1^qZiB$25!mi8wy^yO%8aRZgi zG$aBpP~1z(8to>o)tnU)wBiq*>|7}+VeR-aI@JiRzx~Cl_Kv|!wShOjhG>at|Qh&T)ZEcadElb?`zSBU_FM6!VgNWN=?;;VqZ^Qov`n+n-n_NRmE$65{H zAm>V|AiliG29{0r>Ic=l{NnjnD9BH(nmz3ZuwD+kS%#EEWZTXpG|+MUY`s2Gaj-Ax z`gXLO5HQ-!xmCUyF7%z{d-EX_M=)NNzIVC^nMv%2l*TD9C2AIYLC#sbJ77D3xbBO- z#=ePXoeo3l%0_(4b&dRGUczO4LQ7caF-=7%J?`s>h?VG=rVez@iW4@W*1k}^2K#!C zIdAk&0sbrCVQyJ6Qo|hkx4soLsN=CP8C-|iI;8>$XHL?+1^c4YsxZI8-paCJhhZe4eBePOrpG&qAQ7$nK6M4yPM zTxpj)Y!67#Jwp?40vMC{0iPNQ9xWxp@hy91H-n5Lsc5 zh0+#iHf4XtagUDV#u>R#m~P9XONjeb$x+DYcd`^Bdy?sN`WVcF^%(828Br<9Om#fG zwxz1Y*NohVNb%Cn*?rpi>Fb#EQ!=G@s}c_$x&F(C0KlGS!gZuB?O^T@^^(sV;oygi zvHFL>%RpGI?CvPA1?aQcwEXz!D3;1~{`&8MUXvC&m8f6h=TY?W^FX8Io<+K)-ud{^ z&oRQQh%!AiKISr7?FGACVj9e1_VCKo2~_`O&NzGK&6ud#-yS~ejm4jY?fF4h5zoMb zcjQi%baAgR$6Zt&zQ~=KRy`R;*8U|C5`)jC%pLvW+&Ulx@L5*|Vw}-;(oT;uiW+fl zl{BCY!7TR6hOE9}qN?wh_UP%qWmPI@Ct$b3ndT!#iPajo)W?A(O4`RE4Vjoo?s}wk zo&WcfpzV@_r7JRd?!7LwQse9@Kpf2w-N=*pt5 zTQ|0CyJFimE4H1AcWk>-Rk59lZQHhOTW8n%o^$W_{oAeWe{-%i*BImJz0Y-}$zL5{ zS(UmdT!XtomOxp7e)VnQmVC3{&JyqoRb}}3&d!1&-RzfAvZwYp{tRuLI>dBRtIoRd zzI1w}Ou(Ju@OG*icSqr80ir}lK!;G{;W6 zdfYLk>6eeRC?eq#1$&Axhnhfee9LR3JQSqy+KWAWQth!82d`xTKSDQ3BdDF6qQK~M3RzMaicL~i?1|!To8Htld zv`~bykoShQNR+A}<(B4`G^#`-w@=yzq0%D~%s#=@+@@UY%FFCdZ*^rq6LJFCLbMWASP{ zhoGj5zSuor_F2Xvgl90nLS)XubxZmBJj%2R%fX) z5vjh+d*#y3#AO*)?eI9|CpFZ!aKj@Qc4#n9e@or)rxWtF_zP>5vu;VGjyc%;3!qMo z-KncWavOSvr28fgs$qDpm zXmr9Kn`V=UT#BLa`S?(CT#fVQH?_*uVQXDc!CpG zKV(TU*mvS@zRsVKN2cR1QjU6lT1ZIbakRC(8b{-2qh0hgB)l4Ze5P>Bg-kHEWB1~u z>s*-W-K<`mwhTfi7{f6QH%32R4Jc;(P5Mqv=E!L(Rk`o)+&4z)N*_5boy{(jR(*=a z5QNn9r@b05jT$nu$m0@pK!VTGZjQDctnoe&t&Yk7oTLdS4>}+;OcQYm$5xMQ8m+Q$ zRn@L(kW*M$RiT$@d4dqH7*D)&1JN&hzT2+}d?FvJ+oq z0^6QkQ^A^tZs&jPM?&g#a6c5ZH^k#XuREgzRI{($KE}I3$?jTHh2Y z{{3a%Z(XHlkdEK({+^VlLSPnFwk9au z{%T-m5V6zXYSP$({kmr{&c}f?@v&*Wo>5&Ft=V;5rQDuf<^S@|UxN~%DP&i(H|Hf? zi{!8cDtQQLBSemzPsaI|B#^%P!M+vIgdB>M=Ui){w~sJFRN(Mw;ex?)v>ALY4oWZA z8gSS-u061x!yo8hl>kZ2%BF&JsKQpn`WVojZ%0Fnww{1rI#?AE%R(M^YzR*YyB}MA z{`o?4bn3koW?!?;7doo!FY5PacYQ8vne*5FK|BDkG^HEi3I;IpE@7H1?S&mtzNXED zDtWOVc}?f&Fr`B@8W%SPwHM~k?g_erY;;zIDFttIO2JO08~rK+@iSI<9$*Nk5cMB*_a*R#+3%gXDU$ni0q6WxnGV zE5YO)HZC@E(@)`r|2|8~>j(9hukGuNHUjZ(|B4|92n-Y*EN^wJwuIqVqp_Lc2$hj# zu{vobDv4&l5WMj)GTSH}p_DC|h%7j>1chI`TP^cKK!iA4-Y0V z7HjuY;s^3)^t$KoiBVQ$I=}9kgQ1lh#y@|S>S6lNe5cF4h7FKvP!dJGes*;MpDT`w zIpi$w_SaB<#N7{{kFlep$WY<-S7SN+Y`rZJHVd=wRCX9`rH_3QDNXSEmkvE;ZNMV_ zuE5QHBB`y0=r5)IQ)L8XX@ozP(XVpyzJo@q?AkIkrV4n$Z+YyEoBr`K)jQaC!D3ol zS%N>n$~W+4g#@tqL6Vm=u}1Lt1-#P2`)EED|Fn)eT}*jR^1dHHF2mfR2qb{_!upIH z#ccO_yoMG~VmGI<7cnh)DV;QCKJdS^mH+RFd7wx3|Cc7hy07f#X zDpRZ5?n{;_IZ2-(%*ZQ^rLE$>HA-m{CXc2+KM5fv-3t?69JOv#U3NxSG+zLr{Cu7p zNkHk>+!aHGHi5;_3J>4GHVJ+TNB{=}d|yZCvp==5AkWQ)>_;UUQsCrRp_LT&>0QU5 zM&0;SyEBiODR0syiB4kFCvylX`LfT}QpN{Asce!#mL#wwhbGGK1|s6FajLKBIY(TT z`(d%9H(^lmM6}cO6;TScoc(WuroydTH8q>xBF%L3p57eue#y+6zreZ57YtV_Rqdmn zI8wd_H?@NmiWY)I;_jU}T(^@=ObK zS!Bt~QxkJqgzHbL^g7{T45k}&VQ$y%2L3bJvy$_4<1>cPvL(mR0BHF=ggWsUEVUM{ zPG)p44Dp6-&p4xvZJq_bb(7e4yOoyG_)&qsfxR;YJ@ z+cOU{rl7R&LuiQ2h(A2I%j{v)xS~EymF#*<@C8`|oc9bUzY)$aC%jsgi~MRH6A?}3 z?>xWk=C?YJt*GA6zT$G%H9M*^&69^+>XOe+t5V&j5u(pL7snP|5n*sR_DG=5VPR2z z-60EThi7NUyUW{4W6;h}EQACTA>*vt%uXTLg`=^|8d8xR^Qq)gogwh|UlK0dX(8LB ze!ndqVI=JU!sAYb3bC8%z!RBU zh{HDpI+rqLd9vNAE>PsBM6oJJg=MV3_&a#s$R*_$yTUCP>3AwJ2>o3znR}hE8N8ea zQz;<@NikKY6VyTWhC0FwlZmJk=nl6Nv*?owoWx_m8;gN*tm~EKxJ4NyNt??yzqOdv zUXqwdhK7hneB>w#C&!`_QcH^B?=d>ZV>B!?E0b5p)sVqKqNYFAKW*=hc6G+ukr8FV z^&@*u_%|)mx}s(las)Qf=j>O|K)pdXHji16g?^n^jF{xYaT<9vme5XZ3p`|!;k5ZJ ztL(a#Exm}y!#K5@1~HMaxW^dO#;q!cSO}>xye|&TmJv4C z$@qZUdiMh<^jr}#Xe!!$Z3j(A&QnI{4;k|`A!SnT1?hMaE7yatUan!zRAe4wFQ_uT zq*6j0&lii#F<6m=m<`2gZSFswasTMPgn&BcFT83BU79SN-? zn)9L?*)pjZ9>t@NEV!RT{`BHjN9&=i97HRgHOfs)G;_Wg&}fGp5vOV3Y8_NEkqX!&y)gKJnEShy615H-Z%wa|ms+M6**@-B0;4{71X-alRoS82xtb!! z*Tz&mnLcLD!X$CyPHm@c{N0vaZ~4|9q_f94X!+GRDn0rEI?YHSF48p>^Ac~FBk^(3 z>Bz_17W3zKXRfsn1)F3yS{Uf~yJT@3hqs{&$tQMhYkHAFkuZLE+`vhkZeML&6cl>` zx@AwbT|1w|?131NAwCNje2Zx#F^DZ5qW@*@tyhMSWmLYJYd(70q_r-aF2q7%wjB9s z*CGt3;4sqYiwNau{*j-5A3RVSwIns7Mfra@e9;+@!`EO%h`qBypD6>EK*ZFj(c9%r zz7ONbL_bS3>}t$uVNQB5QU-*wp>$40HN)FV)r|+8Ca=eP9U{Vi*o6B?HiZ8otR5d#(BNZINJ9+`%A1 z9TK@Za?iP}sjVkX!Ffsjh2Jj(HO9PH6$npDIR0jqHLu&bpQCy% zkd%dM1nMAJM689KGMT5V5_!jkR3zT(=-r-Fgd~p&CvO&fHbaz_f_ggXHU*yAO@?t2 z$DKdHNJ4mKd70%aJP#Ol%8%^?L*1Uy2HWMBf!xt~?Dcp2Q}-o>{;RicfgsQsVdD~& z6Q|A+iTg~t&(+tTp`dPb9(pK_a9DqqY? z2W1ll`3Xk69D`x5w{%A^I)-YFZPJ`@n~ad<_l@ehjSCIrww-SK4P5_E&|VF||6X$! z8YcJcr1P9o9z~qEB6qFUzPY52m>i0%R)3$jXZ_%#AFA0nrnFj^EJplz)h)zqX7S;y zuy^tanR8aA$&uLTj~F!n?&^IjG>9bYV)dU%<%#FW+OoCtKX~WovOM4DoN^+4>Mur8 zXC(?5&-b}?QyA;|EXELq9)-zUE5WUvs>|&npilR{7;<{7x_~UFa52gADtMYBgyC16 zWuXt#_0)QmXHov&TD0%0h7AUvHiD{RyT?i|HfS_qi91hf`$)IF@SlxY^GC~(odwyL z`~!B4wrF8F0TouTX&-D>|gv1#DT5Jxm%7>I=Bzz92IdOSOf2Uo(FR399snOuT zJVhL)ftU#a8;s6kpa*#bORSm#)|XIH*7#eV6f&T5rXu_$Y4;?KL02xVbygMbDH#NW zj^JMwz%7_*1|q%#*bApG{<#&>*Uj@kWgE(k-?5NR%oX0^Tb+e09;INq!f92o_d}vWF9Gj%c9U!dMIdw8 zu$jR^b)_UdcRaOet^fV&o!rWfn3}MB&qX_`yT?uO71p{o`Y|aQ1t_MrUjOjoRyl4U z1?1nUe*k5JS^KWcZN64i?=R_8CQr_fYQ|36D1tMv5EWfzxyzY+W&aiUXVUpGQ#gm9 zV(eQX^A3zsWw6ze2-Y7>=-dh}=XL>eD0ZouM*^bZD#82C#o`$DF&Q+@n0**ZSP``b z-69aVL(kAx-~ir{W@nvZ_0-5#dIf%IpzdBN8}1MRxi((Hq4}P8Fb&}`E#KYLcA{$Woe%ARuJY{e5#PFGMnRCOk(hO?o)@i<5QFr>`^9pLX9 z?zQnn0!#aF%q$q5HVj|#Fcf_+A7Kel{x!rLebMtPZ|99o~ zo*>W)C1Gnts)uMmzi^ED>QA%EHGc zBL&A+PO+EN4J02zn)>WbtXL& z-x?)aXx`}NnJq|CW>9ajo| zYqd(y4>{GAGkaq@@EOPA(;Pl6g(5DjojWbLO~S1i5zZM;Mi6OslrnAPqcJ+2wx_Z# z)%U7J5mbs)*E{$GJ+QoBARoh6bo$Fr zO1ZwROc(Xow60o4vdB3RsJhBMy809Xo`h6XZ#W|LnW*AM2*e{|<-E$p_aa7E#O}$2 zd|37T=(8_a?O|`q6+v{kKYK+MJwbTOaFcM^^%L-;fWlzLD;J-)VR}wNiqQ#)A*o5* zb7B30Q&LWv>X+fRc9_P{?P|vpGMqawk%c+1-6^r&Y)i-y!Sk_M__Z}75XNVexLO%> ztv$<7oiph${oH8!ymBz&OVlnEp>=HSyI`(AsDFxf0C}yd`w~~BeCt2TVVG#JAa*yh$Mb9Ux?1WXHnXpx6ekA0 zMY#2MVbO%h&D%#lb|AUD2SiQQEgFN*?Z+_Qc6{gF<|jxE?N)D8WgA{c?Qv@Su# z(}~umv@rVjZ}HK3g(PWVSL@L;MEz5@5=lAXmZ_N)yR6u zWL^^gsS$<^lbOi*2cFK7oD-8YDKW{AHpg`krrY)bN1DuWt+|sCuq=f3ReRvX^9(nC z9V~jyU26pMvwoqYYZ|2J3U%mrdTrk%ivg-_D(YVecM#+*J>&x#hr zv7L5U4R(<{=&jL|Q&WjTG|Xii&=9|BfUuM7Kd`fYFcQCf-3>+WThIJIId?yL$Z&s2 zc?Cr>pOta0kAYT6S(bfKRp`jaYkuF}ob!FeOB(MlPKkm{O6GUBq725UFZ*lI6P_0; z;Q3A1U)*ViJ~v>SHylYF2?7czwj9TK4Mb%BGE4HtK{>)4)%L074*IKOsqSMT4PiXL zPz3ptSx6$nY!>G8Y_t9<$Nei~Q3!2mtN zIXgBgD*T5XYk* z%{a??J6cbNn$cm|rGM$ul)J}d1}s1xemOEEY3$B=jeeB3w_D>Ai(D!nlNt}^YnAjy zbJ&e!bj#O0w&EU&Xi*!3(pIrqOkoOzLycCfJsF9>>ee%14J+Dg`V-ToS3}l)2}4lc zmJonqg5F*44iV^X(I-QqZvxQEx*bkgok$?ma!MhN6w6cnA13fI=f06#TK+R(8x`Pf zMRpaCkM%h@obH3UKx@o01&f{<4`+n!`WKE!C zV8Vu)vAXH915T}bVq<{QJvpI2_U6z*Me ze@-?<6T@T=YBrrbQ4e_1=5iia*uE#Dkg{(l$YE-X+WGvY#jvT zrRX>Ss((%o0kEi3cuAKMFg^3&a%7)#hfF(%@YpJQ>L5ASCCeEKDGRZi;5Z=pOSleI zn0$Fr<_J3XG3abJ(!Q>&S6){AzDN;zC!a4VeD_%oEvNa^wTa#}^seb2jfgo`lsQy; z)0S-Yi?HhmS)awQ{C&=KJw*0k%B8w2aC>VjJCR&0k4#0BxZSZevrv5;D<{bU;%{%g z(ywxlW<71oW=7*O8>@bq#+$fqiV_=Rvp>*r0Z=e0;hfi5e#(TJ;DbwALmPvfC!G%T zk*2X7q_MCC!m$N|X*`C@4K1uy+~O_G`GTYu5vzuzR6qqHB0H*$P5H~6Rgwp8I%$a5 z94VwoDq-$>gBGsu<>|+2VBC1ENh=C+<*IR%5}XJguE#%`bkZ4PxIN!h9x{k2u)y#h zsNME15hw^#xTq`Vr4z67P3 zQ)>sld4up%{dSU5a?i9Nd22P~Q zd!tU@CZ3GBfzqZbKsZ`PNAeBZq> zv`2Ni81ouPVw_gnaw$fz(mbp@@YEM zfHX}L=z)%`^TYc^J%l!85p4~M|Ki*6f-&unuiwZTgb{F8&L&1|Xcdif-zA;qQDW*_ zM!@Z>f1ZmmRU4+vNn&tbN8*6TlK|eL;3kxhp=>ByZ0Y`{XsS)Lx3IbhImTJMgr}>} z(Xie8q)dPbdJ{Mgc?aRYjtydwL6P7-kD`r7-s+?)O3xNY`30$XCYKzV>j|Qh--N{& zgvu%a8{q+xEqi6(m0-tbe*?x%R4*>fLFX{&!rX2EvUjIk?d5=#rN+80(Hnp#d$(>k zS3CYY<4?)*Ihc-FfC2+$bIylu+hl3Rt)V^2wx?|{`BW(RbP|fw#8m5m*B?cxrfz>Z z>n*<&A&sQAR-Ia&nmLWjt>3(Bi2At^$W5J4V$!+{cAten9;>=wTn86uU(N6_F0>WG z6V8cr^1UMPMjeOnLmP>rs{Ewh{;ysa=3_{yC7T9B$b{*l{7+a2BjPfLC9M9SKdP!J zqpFY^+2vt$(&U(8ZowMyFC{f~HoLyh^#Y;(NRV|3uFV?_`mD#E&eS-6&Fz-x$OT#n%H2(l3|l(f74F9vO; zEgx>9AROyYem@k56#Qq#ctH_EmR&{5T#@6Q%wzC_O(jbHHkzKL%2F(H< zaDrbA6nbodjpUKbn`rFDCHN~bIi>EiyfoV1Km2&b|5$Rn69{3^r5-+g!+nEo8mmT_ zrn!R4z+bAcc8$&Mj|0x%+z|js1c4AzIg`V86eB4mKR_*>QBq{)hKH z$`LV*?ikT+FBIT$0(5#;i$Kx7;!|~(Be{>v+9#~6t`2)5K~6``B>i9_Mp%h2(|TvR zm`Cht03MZiNTiV(T^5`V)*i$e@b+FFHSMHI(FZU4Y<2xl)hhl&ivq5=SsBk3nNLko zaDS(Y_!?cP=@mZoJU`93Ni-cK{5NMY@T|T@;hBtW(W$hO;pw zOhvCq^ziKiV_HU|z}pek3L6DvEmKRg1xORG48r!ey@O zQ1)h>xtUUiT|*PbVktL+ zA@eD(p0t;6YjzZ+;kt_c|K{p2oy(SvdY{M!dlaEYr?%NMorE9Gp|sx&8ZOAl{^*tN ziT-ki&;bT-#WCB&A_q2|?1~9zmhdr~(|CVq0D|6}J6jM1=Lgbd^CW=Dd4`Q~tz6LP zoX5jknZYNpRM&MD#(23xJ?$_l%oP4@ zpkVt)!*Bca=M)X(dq>2j4?N+8Vh<;5)guofrXC8hUILrYgepuQ*Pk@M6&{wspyF)D zGSPNg0P$>_3)T+@KiYLa$PW?QVNjnL$fJk=Fz}|$@X#s+5L7p(J-uHrmDGkTMEGt` zT(0R1a<}dOpWnQb?LU6=5$ffu|M<->e;#yG1o=dTcvg$|RP}`&5ZJydQHvx&?m*$& zAiKSFjf3@EN0_d$x{+Se^#pO9-O8^^0G_WTJ3>LR2tqOEL+=U`?1*=qMIE5FG+nf; zbzLZ2uu*shfbAaT)b}-(FOXiK-Ml_khUlcWuJA~;b@0-EO9RQoO8mwPsJ5?jC(PG` z={zrV$#n{}l>&;-huJWJoFV+wB~;u;{sZ;{|FUwa)){rN(t|J{@yJ+n#R+VL_Z@p$ zseeP!#nE$O?RuR+4;BHNEGl{VS58#>0p@W03%+^Bw1PvOL<`}S;Zl>QqokRc=q{{V zkIyyC+0+)#ffoWUiZU^m4Fi$+np6U`n2`&U#cDA0zx2ul^6oJDe}p8^licZ>z8qhX z0ECw$iBcJ4-VMh*<5!DSdG0FGalBIV(MsxalPuZPl{2Nrgu=^9(nMs1uB^C)TKC;v zWKut>>y3F+k5s%!4j!L35%MYd6$D;Fu(edAv*E|Z^0;^+7|LVMu)t_hM$mQ;#jlP3 z7h7Q)O+6J$o&W<=jhn-4Y9p+Xav{3+?gJq0_zL*)UHD*WM3xqE`Tg~gaAd6&_8(6; zl<;7`(`adyloyCj;Jv0r$%vwb0VP3YiU z0#A!8B0F#|8R%R_Nf6x5#y3qdmLCDyx#=Nm)VrEW26oJT1DsS_db`Bg*)G5s&spKY_K-2)l%Kv0Sh^P|{4q0MK?~e68Xo^aG84oQj1fo|kuYnOhTM|+>G*mW> z^KD{sbvL4jH{mx+Xi(M5hi|%;Bk~1I=Vo(gPINL*P1{Ra$mR_a1u8S0mq0RN%s)@K z=6GGX7~7BwKZw9G*T{6{ag5S_EkFSU@SNPh%Xh#cLjvv%EDcNoPmzB|ELUG6I}r-k z=gxmQcfTl?6sX&O3;eO?mCga0IO&p05E8Il0S#<*p@By4cPz!a{9`b+(EN_Kl%R}c z5q!ID&#Tc~_F)hJ6&u%KT}A5IMg7l#HzU}K95Otgfdv(BfDOFQI<>Znj4Hq&d8sfi zh1atz3njrJ>}$#m3XK!jKNFVSM%qJ4@tHP1CbF1BCc+i?b#B@qaYVSFiDu=RNP?Bu zn64gS{JjkTP%Y2L#Me@1X!}>LPqzvgvMVvm;Rh5ewY698uD=Sh?4;aVA0+V)!>?60 zBCC67l91?vmW(!APv!|5xJ9E zt8J6rSc&cuNWh~Q$KTcp$R$eC{1gze`&RVQ8>L#ptTLMwtKF44;KicHG^Ny0^Y1B3 z(U+R>!A<-T!X6DqWC6&2GnS_xoGCD#q-j2QPXjut6jAeUkF+lQb-VHiCCc%L*S@RfJEh2lbE z=9=ViF^49brl}0rgr1dw)thPzF7T)ad&Dm|on3~k$cGgn@4jHROu>;q;BX@08 zhw5Km`Co4MoCqJHQmvm@G1#71j-60*kj2vLjS6YR_Pie7fA;=&=n*X(fG)|f%W@;z z=nApz@SMG9m#^Y1=W{D-p^nk$QE7(G5yI!fI4zh;qe@2510mV28#m?Wy&KF(^kcMX z0zBCYw2QZ3?!z5!SFGSIVlD$=<{AwLpboYslb1#KLsLl*k*ZU+Q|GIeu=;e&K4*gY zM)VLRfvV4s+K!C>kY+`Hi>S*PGtuS-rULWwy=&1L9~=)SEei3Qjrfy0E5cog-gBA(Ie9TZbx zK>*T1=@^}N%u2)hK9tXqTSrPz2YpXrz4*)KTlv48tga}^uhWd_A%|26$y2-bfec5V zIxrrZ6ti2Lrh!1wjJ?b{+V`#>-l&1rAAJ?N>{I8aY1%GSLC2D>_ezlxX*j2y%gvt zdsS_otAW1kYWwN<<*?+XN4(w{e15p55_a=JDs|G%a}Vk(DaP1^SC87y_sF|oV&<5g zxb(&CeCyt*jEsVJ8Wx-OO(+60@Nrp{Ev6pAY_I=m^Pl;g$kbo;PR_*e^M>=`onp-h zK7*;Hu}8~wQEX0_z9B#P>s>6C__P~BRQ5QdOfncAZI%|_?^MI@ze($8NWffI%60M` zOq&T9nlinW+K@75dV!@APy;K$A zRt+Fq43rMcPKT=9a*&T0u+tT8w`k2drx2q=F2gWou;Jh}E^dDO`dxC=gXC2Mdu*yk zDg*INk@-=808NG&j0mM8N#PjI@TWV@MrI04W1PIlCq0S5x32CRhXdpkuB$vr5PTdq zLi1n0v?_aNUdmrUjhJ5)`mTy0aAGT?OX83-uLW+g_%Ra%=R+~L)t{Q)aK@&-!HK>}s z`B=XVR-54J4~&9tG?d0M3LM3u@Oa`8qu6Uo6|bHS+a7qJv>iNV=>Z9>DAlaUuWHx< zh&tmXEz24u2^o}3KA0$7rs9s8KX5I67MQ6=1OIF-Xr|Gp8}bqBlFVcRh6aeKsad0( zJt-*;@QaXa`HM~oCBKK02yIlqzEeVbw|~)GUmF6;K$0J*FwfOg4jO<7U_n9*I?|}< zHAMuBzP2Y6v_N=dB2{q>Rj>yjMi3YWDXhv6a@xo<%aC{~1SbMB_~b1~g1*)W7Rn*f z8{GZTN}{(S75YarZFmGy_a~K3DFO5N6D}lvB8KoDal_s0gbzcCu8xu!gdQe_cs73D zgy6n^0}Qoj68HBi8XHFMV@d`5$uR1Ppf#Gv+Bm&Hk`M9G>)p;-ERRIy-c&$fp33@H zEz;*ISx?6lU;9e`1I!JwN6eRz0`&9PlKBG~V|vsn6HVF6X2oz^3PBgYe)U#lR}S_P zIW#zqsmz4}a=5L#OJZ)^Lo>tje6~pz`v9}aBZrMnkJG{& z@+y$nU4@vv`$0?AAe|7s%J6nIMy1(*u**^c-ZHl*Cek_J3Q3K?p`0b3v&uq5g?;=) zBm-8wX5q&}*gN~aEsgZgfX~eX#x108k-GfxV8lx@{FMuO4^5@E(NaAa)3PjypccAz z9l`7{2iLQc!GHzQlT>8DMyl6vaC#pI23^oNz(o84Ck(l{fL zB%l1$8>?mJpyno`gUnYG{Rs7U&j0AhtlWWR$^3bIfF>~b5(G2_jB?ct$H3Ca&S`>o znY;JVmM*X9ORN|B0iB+*Tvpyn{7krDh#v7IbqRCFg^%JV zk-MFMaur-of4GcP86%yB;)>qus~YAj;6*i&am;$(+&)s7?9YBoOz z5cqKJ$W^-16@zw}r;HY|JHeluP35*xk{Hu7gvv z_F-5Z@r_h!&ld8$^ygJu1qs2-mQ#no1^E=ymBw5scS5WTK7ur567#5}m{w;t=4jF` z^XkNZ6@k)D5D2gaLIwhH-4dZ7FbVuazaL2eCh$=;7MeWk_i@iNzeoZ`WtvL4ttzjk z>F^$BR9mB|rhk8{>hH(%4lL9S8eBRKt96<9O}-zha@i4slh!ot1GpiNn=o9}zpHbo z*(?kWRFSW4+)52L2ZiAXF=)>FnzAJ=|AE31K>_3bb;Fa+DyzB5OZ8+{)L37v*WU+#i2p9qEwp;Y#bK1v880#$ky&^+oQi^JaeVy zb8Qs3t6od(cv@%M>d0&XUJ%lW4sk><8(5_cFE)ur*ENP{4I}c#6ZABKMC+{KUuHWn z;S&don688R3^lteva*Nt#+D?NlGuWB8lmTTLwn2KO-_C5RrhG{)D@)XhJW%Nz+$P)A%vD;P^!(#QC)_@SEoSZQZ9q z3}8SYJ-e5Bc<~P!AvRlTRoq0YAhsC<4ydG29I8?941os-*A$FaWWbR_^YPQeVY8EE zQ|T4ETC_Bq&uq1iyYJl5-g1k}`ANSk+V?bG!>Ih>od=s+A_Nt3`@FzEhG=u&@-z$> z>{iD0@I9-eT{TELP_mMR1DWv;&`m=;x@aO**4%q(FO*5`l^j}a zY!pR=8MbIpi#lFmg^mu(cZMaBbHn%1y6oF4l=VC(D>&XTn!(dD3Yxt`M7xXK(TlhI z>4{;>4`6L3Rl=EKi@DFl=&}F&u0zY8@|m1iZ zEzJapIMY@Q!UfO9l73W?3Nz{0OVporx52jk))-6+h(iIe_-&pGpEHh-f);58Y9|B< zYZ>oy`%7If**6f#`PDMocRk?3jus4?_z>I?A*L2pHx|RcX=_S8(My5 z3UNk)o@A71bl4%dV*@c=EkiupzVm&-G0;{&Svz@_&zVE+P?bmCl3DTPue1KFy({Lz%?*V-djJ`z455Nu2*=JfNp)UWk9;FRdRH3Y!HB=^1|6<#a;ae&fQG z$C1u{d%-^0l6yxUZ0qMsSg?dR4+xNMO?W@F^^|X>p&em9CwJhIt=GYcx;}D#-Y#*v z%)o*Q(XFS~y!rVNRz?i^$3SDq8%DvQKsuHLS`ucehmq2ttE;xtA=3ipIo}Bhw=awh zzMw7{NyLBXGTuoDM&lADjcRNXL+EP~Vk`%pG&;wXig!MfjYvHP8Wm0uJXjZO&lv2= z)N<;90{=Uy^Uoo*v^(37&SJ~9E(ic;bEVT3`ErRYf78Mq{MGMCDt02t^2^i%*8e=? zpkQ{)wIJ$PBQVThhbY7QNX*oGk`3F|`+pSuS7X`7m@x#_K~&YJe-mA*c9wrt*B&}a z%Nwc@$SjmpR6Z3^HQrb@+N@|t3IFyYFSK)ty=fGou7-;d7K9kAnO2M$hMACHo~Pt7 zths-X*llswre8N64zw(i2rmXB;-j?hhg)ztR5=e~!WBy3DYQwh>%6veqnD#W0?~=GQP%fy&$V@Bj}{Q< zMaX1lC(OxCaiw)o*fsFAhaQ{t#^U$t*JamQH~wje{rb*aL81vf@&aGtx`ohWigzUD TexCok5K~4%QM^*rDCqwHYWh#X literal 0 HcmV?d00001 diff --git a/EQ3.png b/EQ3.png new file mode 100644 index 0000000000000000000000000000000000000000..c160439d6d234aa39ff63bb3dd20c3e557ed07c3 GIT binary patch literal 14907 zcmbuFcUTiozxG4#9qGL)HIUGI3oW4&x^xIFv_R-xdKE!H5D=6mO`1ptrHB;iqJq+; z7irR7^!J?eJmr0I{u$ii)15iVB;akEfH1yCVRgk&yKm&otA7Heydgl>KF$V@!wYC+u{J zUP3lDL-MS2Y)VKxfzmtJJw8)BzGvT*t2h$j{A_+4HLm(!X7s7`E2f^^q2;?FAwcXX zJiU<}yV`x?J0^FUpLvl&6yZc`!ZD=M1Q?{H)mrY0rq48-q$_2Kz~lo0UUX*;XKI>y zdw&GH*SJ9khGMZLURO5s&MFMtRBi0zh_V1Qq*tJw$&bm-u>k=Dx*USo5pp$VU);n3$e56b0F=@tOCD&N)#cK~?4_^JNe;n*-Ri;_RZk(wO< z?8lC`A7d%MqB>}QbVNkmPX0=+@v-6pPHyh`gR$+d^D(C5u~nzESE9AH>~Zl94`p|^ zZyLZi7KcYGoNjZyFN7XJ-tr&DiM3~0kUzKa8w_3gkYlP=&E9qAAj=OA@SJd!LQ^Yv zDu&m-?-xespil@>gW7>=&~~Xk2azQY(x&c@Bt{cSYa0z}8jVg))Zo+nXvoTRTDrJ^)>l#v>*yGptuN0ut<6F41N* zM4v=B#SH@6Il|lqp^=iZraxG<#~#MMtJ>y1f0YqZFIpT=RkF0HY-<f|d+Z z8H8bq@VmTCQxum9;-c+j<1)&XnPDgAtvGzQt4$caZ0vi%9q7#$oG&m)WU?X1&N!S% zY2Vz82(^oL5n*r9O(Y8AzyH`uxrh$lGl2Ai5T4Rb~ndR5_OU> zec{B!Ff&%im$@azj%leO9r71R(nq$e$4%VL*fQ}2?{w_e>p4w9HZ}wGG}|2hMm;6L z8z1*s7|aC2B%fMtsQ*kmeqAYcC+krw`1Q{>A$lp1$~`ZY-;wkSrGLmyeD&Y~F--^& zJ{^;Y=NHr1CrMBE0g33uLy_rlmouwKI+ySn!FHVPn3dw<;=V#Z5hnl>--DLGQ|E%O zp8MW_Lf>`x;mQQZb5ava{C$@qg1x((Hn=Y%+l~%64p_^#9{1qsw3IP4DP`gCr*vX{6_p5AQZjzjr5Cx+&B6SyxJbNC^oK` z*l`NZw@md)`Q#EY3D|7K8eqz_QVx0zaSq7Jpydix(39{@`x`kA)hhxJfny9`FKI7(uSz_y}a%3cH=x~J_2qb9pab;!9WS*p_X4a$! zX?PB~I{3a~luFKr&}3>48n1j^v0vd|;ayQmq8CQakFTcf+`OCC+@=xCGjA%yieR(;)2Y*=v-e+gSX{K97&1Rh zt=1_gwJtMqelmKm04WV=dDiel_Ls!Zou89GS*)Jb6bPwHsJAGiYmsrtuBWL_ z5N}KE`pB*Eefg)2ry|I0gzQkjivynJ$^KA#)WBKF_mq3AzBV6fdCC(?G~0)mGCg=` zVYtu{XdjIG#THCA_ayhn6P(=DoN5snrx`aL2{IsUZmoy{@>)hEt;cRfq>_FoIgE%Z z37@F-9XyFNNl9B~m}{7FI5hk8WjP#LB~T>>_kdr`tj$nWubWGl-ngpN+s@;A%zVmk z3bc1~eqz@)*Zk?EqM(?0pk}V7XSYUfM1DLhHniYM4DT7%B>SvwNuQ(o)W=Ev4b$a- zAp*a{+wtvz+GNtE+XBI5n~~cvXFum`-wfaAqiFA6%g+X~lHFKNL)wqe8V{=a3z=_* z-c53kIkpWmn=sF6%u>$6XCEU|k+LleEpEHuQ{XAiuHde)Y`!cu%M)2-;Dj7+kkEszZ98^PVDx(d!+mR(=N zbb04s5QhdXTU+ec-BVF4T9mwtiJiaAeL=P z0TOxY%h;Xarvvg7Q4eC`9>t+zHe+}mAn`j`o#?ZfXUJz*cj@JMFIBPGIr!|1-@;Pw z#SK)f|5OiBA5C&kGf2~lpC>;C&Wo5ce3hmspp)`Ge%mG@F0z!fW=cMsV8t9PJSv2Q ze9_H}&s^e}h6XY1F(^n}yJO1P2KDa7%qH|C@Kf$_ec~O;oPQ{mIhnbYxmX%gYV-mH zV^IiPSRtzDuXr|<4K^_MnNMwuyjN^Eqw_=a6e_IUB{GfNd|9zxMz1^k#2@u$4Ym6- znm#7^QSw)M*4Oo4q<0m0cpJnU3J2Dzm*tl64rcd*ajv7ZdNKuWUcP@>_UZalRYUND z$X-6%!g#@XwxA5Ej0UN77}9-r^h?JF)Ojx=BCiOTp5|nVdn z;%<6=8QwLcqL6aovQCl2DW-m$S|bUOg9o{91RNYhQaz*!V$fJ3-KU6flY#10jFO>0FIKBK{n5!URz5iw$_3>z_*jhGRYU=y+N7T@T z!LVcDaCHHdbea`GyU(HP;52Afa#qMPt#u)g^GAR6lOGao$OBKgjso<>yIQp_(gm}C z$6hU$PiHzRFL+M3!hFv>tRI`qe#B!Z6OxAp1e86Qz1q&${uuXkVxV!rSocHWl!9My zP^rYr)5AT(u)RQ@K=C<~leiPsrm>yEn=|L}LfQ-7)6@3!PP(AhZQ+tG|IWjJX>oE1 zuN%MXtsaS0&yTK@Uz0Jw5#h1nG1Sap9uc^CjR2p6Z z0$Qm6=6ryk!}}MuiH9E~1mX|#rJ>&x>JKd?1?~gDy*dZ2qw*NtVRP=Z%8N>Xx4qeP z*m~&Gk1r_AvfG|aJceKaxRQ#CAL9V@Y%a*{`V*ScKfaQXOHzT7Jvr;;8fn`1QcQZ zS2RXq5!QdD0Svcg03|~eP0inXB_)V0$ko;kZs1^~8~}$v#Xu77TFxd?t_YtXexSRW zx~Ql#)KJ;L&ddw$WA5x@plRaZqpRfX@9XC)p-TvI2dbNUIGT7E`9mD+^aAwU4V`qL zU^59bKM!RCU6ieZDp(^xR|II{4TBlmDtl`p)dREv|aY>v?N>Y3XT+=>)1kG(^qB0?nlmQW^+94^I!@AUj_VeX#%&b$t(U z7eaGMEk8XwaV2vTsELxltDBdBtG|k;m#eO(uaUEZHo`8@(_0^G>!*hHasrE>L?v9k zfKoxC8mcXv}QLLF^kV-X!YxDJ1iqc6zbNzBm2Mb+I)-9bt@ z(8Nv6$J$veF2|-d$rV@@I5q@DbKiWahOVY^z9PAIVb=R~-fPGyEb-W#*cJ2<6O8n~1x)6vn!qm~%j~^^7?5hOxlyq}L zcx$_BYw)Y<>bux$YZ$nKR5T5}fu6n++GurzN1z0uCJF%ts=@;$QAVD2_5p^f2qljI zLs1nYxEEAP>b5tal8%OsE`jd$X13ZU`e+e;Q!O`jgf7g}*~L4^)t}H6;_P9LF!nQa zagz)H>Px_bbZxakDs~VwIKaqQOHksA=z^7G$StM5y5{Y=kz_H4P9&N{Q(sZT0mWbd~Lm4cz@yJk+(kfJVlm8s-7c zChqq3Xw5(~F;6#7FE@TQXKnES5lIb|079TqfS!XCOv;#FS6s{2P24QV(-3OvZswwo zMyqT1slkjqd;|6Dz=mq(qFN?qK46eG%tuN@#a1axUywv=hjYO5;C^r;gkU84c z%N_&~a{)r_)Zl??=Kji#s@kT3_V$t*aFh}p=%8lg=&AZs(%uPh}A5s_3z zf;BYI%Kpv#Mj)t*;aG)o@jwhk2 zl8J$fuAPCVH`G(bNgwFwEaqUK!td-Zr3$rG5|wgw5QAulYx#()>i|Kf8ulzR!HC-%HG!9gnJ)l9!~J{1&@|xMzokaDi;*eH z6b6;H_w*35b?~%v6bkV0x{U?^WCNsclOB#JTebiXccia$fE>r42!#or;j6>m=IV9$RU3_xy2^yuT^0yTIWAe8o{ih{=Nz*?j ze@oOqCVxxSKPG=m);}hHOV>Xp|4CTcKV(3z;ZN@EbAmjftnhz7bI23gjNJGD04#Ny zs!B!y7&}%(0o2nSH)Fd_ngKlRJngh7cD9vz8ZU-uKn)bwgXSy@S7p0%#m17 zh=c!VzVBN8V!qVPQ8-IvuWYHP_R~O=vU4T3oF9W!zU!dMAsf|nCe-+Ib5icfqV!3j zEQ`}|JDqw2XE#MW1LlP0u&8f;HJoxtky^bmWwShJR!P2AZ6`~0wI_d64afglFBPC( zL_(fEYJOj=jF;E`N@r!{LusFB*OpHH3)`uJhl%L;=p8Z{LaUk=;%c)~$qz?F$MS1t zwae&>L&GQ#FP~ECY`@U9VQ(*_)i)`9?dvnB3fYu(urb_PJ(t8}!bnwYQvt|g2i~~R zyyePSTo}c(FYXILL;3nIozL6#=H1MYEN+^f=$$nZR|?Gh(I$NP`#HZ`&y6ht;J$rJHg&@n)z?=Bk+QudQ=19ZAu^ zt8${i1o2PhbW)pPK3xGaV9MaJeE883=%0S^!w#X^1Vm#jQ86C}IkCU6h(wW>laJOU zsmcw(-snfaWjWzxZcFt|aZm2@(pk5=#5r8^#g@dhWIetK~K`@lE_3FHqhN`yn zd=fE$$JZY`_`@=}OK~COHipd|yHaU3Xwb_IAvyZWFB~CFD;;OfuJF4fZ%4&%lizLg z`g5p&O-@iut(xmm_@0YK~z4v=@#H`h2IFo6gxzML<>?v06OyqKDsJ8h( zsHQj8^DwTKoa!9ZHxJXc_a=h2l+FJlNawba9y_Mhp zaZjE(U08V}DM*Z|u)HhEtr8=oUG2oLMOuYDi}Qos{MShb+EBI0Me8JBL(l~0Ya)tlmN}9!XUYpUT}h zN1vVtippQ%^UObHdUyOmO_YaB^VLhR^Y-1J558v!!t=jUFOJ`d)f4=+IP~LDs@Z+< zG^H-#$VlLV+o(e?ajA5n#X=H3{>)R#wE%Y!ZqD#KK6EX+P7TrovriQ9NTxI$ z@6J;oN8AYq%5ozPwgr_V(pqSGW=&1szHeYjj38G>kUWTwZ^Ru&7-uSe)vIs&2)?I! zg?fH(a@*a7^9h1t*8lD^2nE;nral3E`-KW)W*^m8beSY2y3V5h`6p$hrHay(I;? zYswOVuOz=*KPqv^glT)8MW*1HT>GibyZ}m?G zm}C}$yNc-)tV(Wst|3?Wn*8Eg2j0s?!MON6Tvy;c#)9`=Q~T71_W>vV(TYSr@@LZG z5TaS~$JhlnN4s)xL908Z1xi7eFe;lj(x2mrJ0-NW@1}seXhG~VahUd+HNQ!%P99Wd;mS}16R6MO-9B{^M2q1W`cjhi( zXlP)g7n9BtK00guAk=6d+5SBP7FsPl^ALDs@5;qC9esCtBp*{3~PW zK5-7!PClR|c&Ks#uk~T5Ox^{hGKiWGOH}j$<)`$`#{wrU>ynAx`}-yK9OOHDnV*sy z0`aziA6ZQz>-{rNMTg?!&sAD{=zHN~-rJXGfQrD*t9Az#cAh?)QmS`1tIPs>#17?- zJP&ax^`28Lw(<9<_SM@Q$vzb%by%FFaL%-L!tCT7YjZ2ojCp~wO-(yEz3#4b#|I13 zR*3pp{CX(OF421bsR$pwYW}E5K^IVgw+M6v6kUR^C3>5PQo73fby2xISxsB(OrkOL zOg3pfCsu1K^VIKGf5*6YHMTZ{AGgT5mHs|>H^#P3ak}tR2xfNZBE0jdJq)2MuVTbU_r(U+W8wXfcNWLr5|)t)AtzYL*Zy?)Mo zQZy!)mOAjf>|)UbUmi>k5lCJpqmA6gDk@xvzTbl)Tx`fpjQOZKfcvOf%nz35*azmYrv4vKCjKx`?#LF4a|rhJAQvdd{bfmtzL;_dHY!p1p*Uu?&7>W)w`uF1AyRfR*H3Cq9Nf zR3!46UtX6bIbw8+sPW=beL$IQetCopma-56ed6+Ax1fl$PDvz}?oMP;55%R2aY2Nq z%T7sHjKo6BH9nX#?H7Ah=iG}sbHo^suWp`|G!pYiO~kNE5n_&x`BE-DD<(2=QQ52_ z)SD4;Ct<~Y$E0F0Rih%cI2 z0oRH>&|WvLt*b&XF{n&#FnT$HDuMOEOzMqqT~TJ&L!mhkYM8d{*4d#%(*=nF`1XZA z62)_xiL?)dd<4g}MIBa*IXV?L=@CwmY21AxWt3qpH98%_q zNJl{E+}(RgJ>#fsO%)~8?!@v*;-_pRjC!NDVJwO{BVp#H;rmliB;V#>+rSTdu9K%O zA|26ASkKz0Z=!~%R2>%^l*cd&d%CFOe*i;Ubn{>49}!Ij8r$EE!UR6@R!nnrJG}r+ zMry)$-c*MZ!l41Xtkr>bE6ntg9 zn1mLl#oAG)=oBfs<&Qj{G_46iWnZcENIkoSlXCz6BrZHQEaK*y_*j6=)hF>C*zp_b5_Q)vW1HQa)0yn2+=1B$*ho+N1o3{F3qu6quhZjnPAC4#;-udi$UE1qdVIY; zPOK(KvoXy(hQL9Cl;^*eTB&cU)3en)@zMpRL}cHOBb~kq)9iS5X*wAw|dc}6S z<-z3*6vzwmW3UZEm^&ZSzcimi){2Jj`STm;(IFOFT+ee{-(xkuR@nU5C26hgxyssk z7o&vN{5j<}uv2)h5mDKBa?6pJacIuiV@SG;z26KC+sm6wFRMd;ln2G zm}!si={%Y24J)jk8Es}j^QBfFhgKe66w)sb(_t3!O*b32eI@H!S*LNEEfaZ4(nW-d zsz%yq7~~jyYStNEoM0^xDIEODe#cdEb3bHx2ohEF;>g#XeOy@@&#*%+HFSE~CY)j} z*chp}-h-R@eYSxuGGtVil=00k=DZhz1V4u|PxBXdzC9LEUVIj->$Sq+!#nY_YkEWN z<+wJD@m8Y#OBXn#Z2Mgo_>+t0r;Cto{5_9@HO8=7PqEK{U->_l(GWWu-G5)Pu5D+ zuR(?^JHB=jgr+w)J}>fK7FDuvBf0Lp`Ef;RE$)QtS9ah zUrvP$dG%wLoh1nn6X(~0GH_Op$8dzaF8L9=O?(tMPXMfs1qtmB&X^?M-Cp)`LWX?3 z$^jp?rP9AefjceAjrX?hK}DspB!Yr!mW*!vmN8+&b6N^?>NVjuG|!e4-$~?qkFz`s z&&F|<4AE$T5nNOxbG13iJ)2Il($P4JyffUgi7-kJfmGcV<~0 z&q8<;+6W9GpNg13gbPD@VBW9EW^#omwiV>eHkx+|%P z`~_x48zjVeV8Nc7WSk8j%w)-)+hAYLNUKVPOdX7{^QK^7*~akPB$nLSV1|2`e!GA0 zsLCqF>23|YQf$JAH%-*2hS8xnhS-nj8O+K?(Nn--vO(7v6(d64MvsLt(qrgr+d5zH z&>#+PH9zNZTU&GeJKi45!5|g;sKr{&0LK~@9>J#e?`m!Y@5!c}lA(yQFcPAw2cayL zbi8F{zra=E5tr|q&JOR+Q=P&w>^@CpUT4V$EUFwfc@V`ig30&~BN+1?D)T>hCCP4i ze2b~~HVDEE;dzSMHhP_K0XqjAJ3Z}d08V8?AFv!Jz(V)T9~47 zuj?{|cgid8`crqeiQ!k@;l`hY?KiI%S8Z%h5`fH9udo)?uQZi&R@G7`4t>q#ucJA~ z6Y&w9@f@6Ix`O?^7)FvZjLUaGi#%&@?;7sh<=?;#ITxp%@G~V3n5li&i;0;X#`7Rm zw(a#0ELr5&%-R{4esIlkYD2Ab{X707QMCz0jmcJc=?}-4S)v`McG!!1jlxz(1rfqy zm;Q!cac_bA`Z67Vc6Uh3pT81R%J$H?>E?|x5XwKd9 zILXwNA%9y9BLD??>-&aVG*F6EHR(_R`Su8vpsGWT*`I#gA5)8F`8oFDeiG*WZ>hPT zNJh(bmz$ywq=Mk4s!1!BxpLle9o1{d9<#4;c9gv**>=(0S=ntPWS4772BEU1T|!oG zrWTeE{K+3?a8oqUN(7%@%NFi<>IC8H2E;8{o<4xxD*%Jr%`vqT61rP9I=5qGHl={} zREFl&1s-C%Q(=ED&)TQPiv%?NB0{e#D0!9wQzz0E2T1paN0z%aUfB@sK6z<``!Ra= zfvkIeg5;uL3%Bu;ceitCUgUaEFCxN6uW)cGabZGHdt)8ZaW;>#GcUI3v6T*Tp%o0y z)?s}_Ny_q|{vQ@q%T$!z*^cqxD^IbY3_{l00ue>w(5SJ&TH2`=rltdNx+vqvV`z@Z zrCR03u|*FAKJb4=4~dCsPfnqGei@%lCgpIm1>|H@?+n06Gxr)P?vX?9=IJ)~R1!sv z-(}s2E8fRaCQ|sJ-SxhAQ8;{DyV>zIdYDH*V&9JCeJ_1itX1ub=a&j2e$Ro>R*BDN zgi>iT?~rHY!k<4H4X@u|36*kvK@kNLzT0c55MEHQD6KIbWjwCteWRtoaa^P^3nFBC zo$k_$NzP+BR-1%6p0y11kli&3;XDbgyi@5sjqZ)!8_NV)!$^a6M|cbne0&)yrp`E= z7}h0iIeR#$yvbb>^VG%L*;ovW6d_^GZp^GI4vmen$z1M z^UIqN!p9nLhO(9t4()_jR-ClR|l>;7WdlNc@I3Zk?v;^yp1l%yr0O zzo9%VdYy;=`8Vy-J|(f}O#nG$T<|cDY^KKnyHkx@XM{!!hq7RE%)_-azCd@GU^l?< z?dI~GCRS{_j8X4jGz(`HQGoGr#uxY`>P#D*owrv>9?Q}f{k8ApU)_&BGdp$^AsEQN zrbt_UD)=<$d~2T8K1L`RIuK$8<;ZrP?EhG z?TKCZQ;mH$$}y;{n>SK0)ZS%q05*VY5xgd=)S)*aGrrRBwI*oUlYRKy5ukFEC$&=@ z@^&Py`in&H6_Sc(N$XJ=E>q+r-%*M%9uR`DnwRq}DLh|Xnt2o+Z*B~aT_EQ8dT=FQ zNK8gIq(vNXMV^Vm-4j_h%B8WYNZxsr)7|XxW;61^5~Z(en(7>`J+>|H0AU@^Qw4#^ zXF$s)YF*+4#nOH&6(itro7>i&p-|~auP$?3Pik~`ty$GMN7gr)q7r9{W3DmTU2!*{ zESO-@>tyvhOeoju#ZI%vlWP}7g8G6w5Px4aPM3xl~(5k{$~CzQ>)7 zBwN$TIIRa_wabsrMrl3UH(OrCQ;A3R`Bq6 zkH17wE>3}`5g59fPR*S<(!Eh#b~M%%UrQzrzX$D$6+Tc97qwrT@H_)v@*X_gA&m6; zVW}*D3U zp8xAKGIJq=Bd>8hOM8j=;h^H@%hj~d)g&G$a`SVW&sSN22o}Bzpx}`4rr{W@S`H;Y zE(4s$!i)MiWBBFgMaYHOp!T6DKIftGypZieg*DxTojU$iIlr&stD84cf}G65s$>MZ zD>m!02%(7_OLE5hmYz5zfa#GBL(f<$^Ek*Y!~U#mMbfDNMi=JRR}l0h-LfWRt=e~_ zi=u6?Ur|w#TWw=5opN1Yc_8LlZfAPf=)bG0D@RPWrv4NUw7y*;i>zV?4Cl;_{OEcg zH3lIe2t2ppwfPx7mB5d<&Dwx@ WGy%3}d-(euI!!el)f#1+sQ&}}IRUQ# literal 0 HcmV?d00001 diff --git a/EQ4.png b/EQ4.png new file mode 100644 index 0000000000000000000000000000000000000000..329efa7751901232911b3b9cbc91dec773209775 GIT binary patch literal 13406 zcmbulcUV);+Ws4QlOmvWse)1igeruR(0dC3K}vuWAOr{{bfgMM5$R1pkq**Sq@z@6 z(k)0)1nIpfaQM3S+3!B@`JI1`>$)a0d7ioN$>f@~K5N#s9vB;H(NeQh0{{S89c`%T zWu1Om*cr$#KgpH|!~nn*2Q&m?tOJ4Y7<+lRpxvAS0PP2985HnTOO~)LIVs-CTIa}C z=qzdS)h=ot9y5ltWKu@WSSq!52DgRb6v9RG>J@x(FcBUfzG{rg=P46rld_4TYb?SS zv{a}KmHZ2(k+aPl?-Avr+|*wWX~JAsEcyB&jetHD7Tu-p2)0zSan`3d!ia@|fRc{X z!Bic%r{@@8K>Nav5KO`ocV1rKHLcQnQL(a3CUpa#t@us9Eg^&cgcRUUWyB{&8pcX| z0F$P?Dy<8^J7R%rdSodqZ`S`Q#+`9#Hu)}qr^5U72R8udV`09@+rj7%&?&+>oI5e4h!|sN!wEwv*;V0eD9J z{i=>`;6$VlqWhF6xKBI?tIh1h)aS6+l8H(KOY1TBgkSNaQPeZ<(=i{iI{Pp^CzJ3!g2GJ?eS|b&8zXdf7ZV$k9&l?l4pd0@vELA5&rhMb z0U4$+;h{fIrypTVs!qRhL+#-Tcg3E4C873q&v_X_&7eV-pL=I;l=Fo^G$SPT>RVtD z2{wUZKExl?Lf*L?E$vy5f>Qa!bc0Eeik@nk$~N-TxW>&7HI7-7%}*|X7Cl*ZE(xF1 z3-bMeoAj-akyl{sm0VByS9CP=ks^WWVt22-pK4`qzM0zJS@13FJj~D!KX?y$L7uVPM ze9b$H16RhjZ?Id5g~;dItZ3~g9lR=+xt8|$HR#oTbCB`FaP`hg^>?&A;>qvR3gn3%d(^BwYZU!ci{? zN65S{9^0OP0`DKN-ESZGp3zy_P;R52P;K4fwrbS@K&q}L5KH!e=bC`lLNFp`Y}%4bsP!_xtiBg_4+Kneffs?Ch|?_n_ArUchQS_51wt`uD>mE>(lM3 z$9j)%4DeXwV6+aN3z~YD#+Ob`X#Pb1wEby^!C=xcU`*-+6hkvvK6zM?XBPP6(9l-v zi%DKpezmxzU3Ht;S>&nvK|2bREhZM5t|{_V?D^!l;n?Q*9A;Fe2aN+Av(tbuplnbz zN@@Bj>LaQS^c;QN6^6bs(eiZmxyD%Cq@$~6 zrgRJTcrMm~8S~h+VW4z&C0`P|j#BFPFWC`X8t(~4;CqiBE{@0nGScU-1i4dv*8ELk;@D%kTokfct>Z<6I~ z8wnvaO!1U7uiwGq>EhM&?hFbHG7bi(A61sZ^eaRwWMJ;Fv#I4Nrm7#-a_|cb~TtG9Zlx^uHyc?dij5*?g(CPPs~GR`~gP~7dTH8D1B zvI1Z7@2B$FyVGgmf(8hD5&M&xM8QF zr-19C|K0e_5$899T$WtZ+S82Fu;~nJB39`o`%BkN&=K&6Y*TDgLMc~?^hS;nmheGY zC_wzsZSVKW_l=tenEjszO^3tV)dy|;6V5%78ImI>3_ii~+2gOB_fDHw&NY~^-gOXr$mnBv}K0}K6zlJfEi zJ6gOoNW2}>TlQmLD?n>F-Yv;ANjLT*!vXN4q&52&#jAO&3Z4gV-$=?zE@m#n83rHN zas^5Zi(@rE8>PmkE(%WS2XJn&tH_?Q} zXU}IV>I0*~yM!GIV#Pl41f(#f)GPcjz`AV?e=cl!+!B29?RUcOZbvT9>Q}8DmG&^T z=WlgP1y{2d?jSB#9r`go=1Ph|S|jt%uB4-QufUU+yA&Ek8ZsIlNWl>$dA-1N|EYJg ziS-%7A*P(L-)EdbbRLGEY~o+XFM~6CvtRmvrBu8_J`q=tJ);S@9xd^?F}C@Z-9N*X5`@DAvsmkVEIAEO`Z3}VF(@3s)A+Mo?j5oNzV9O$W}?G1)juwAz4s1>`S;|#8RNl7R!))v~ z{-{tYm#rzTPOVuhPprmTd9;RnKc(l0_4^V4muyy@!8Ywm$9%7kCDTUlSHw}5jdFP4@JcZRENciwzlYh7FO%UQoS z7AD)r5peW$>vfBqlZRfh_tI4G=`Z2Kh_l_Z_KW15?uR5M6d&oN=w;7Qdx#C*)52ZB zr)XcZ(E8ff6*n87?cu&HG{M@ZASw@kp?_SB=au! zP=$$w$uWHYFVjKig2AdhCdDLMsur(ZOy8vRwEVQVP15T*0{?1HRnDs18|;pUa%-O7 zuXi;X?R0Zi{u#KJzw@VB%YO+Tt%Z0WyW3@0PLEOW(u;%j{r#WkOrNc%tdGUyf9P%K zwJ>^LFrnfT81PiC@@RLq9xF6XI6qTP||)o_aA<_nf4t5^-T{n0!CfSlSHuH#~001&?1 ze^3HQiP!;Tmo1{p0w&`4Pg|4d7J%eW{Bna5g9ecPyN}^z{m+qnS^m-dt0s9A4WPK( z&ZJyM{GSm2r+4}jlK-^XFLMAjGl-7PKed{grj|6u!4YQaWUlTH(}c=M%em=_SbBLu z;nE5odRB(s`c4o_eQ$4wk1Pb{Xsrct(}Uyny`XA9EKG`8!3RVzfcgZuJ7OJuQ2J;W zON^wcvyr2ME8HCEfweT$!pLJlZVq@;90sGQfpqZH@i(yaaIlbosf$Qi8&Lb|8_9V( z!GY#z>i}P@v5&F2go_c}1+8TvCFyDCqkuFq_trCXv#>;I`eV(s+;OH}vThpQQf}t% zFb_G1KD8FkU55a|7;AuF4w6=C&c3Edb1XvJ1Y+QBYN`hT$s&9R@?PpVEnPE|o4lEO z0L)iP+Dpn8=Lo|~fV800a#qf=B0h3BZD|xz#>fmOYmGIRN1B=%B8<==0!YDA3hU(t z^Kr8BlJqh_p*-OPH5msPoCF%E;SSgFaHqCZaCGzZ@pO>#!r`T)UA(Q;^q~O;ntD?f`t)K%L?Zu?Iev-&^DFz2N|I(6>N+|5wO)q>hoOV>~n5A+d{_Q3c#sas)Da8qw*2YCevbp;CA~Nm(6T6M1)cw1r%N7Q!Fs12qIXxoJpwI^aC0t@T{d?p_u;UefC7 z<~R*&eY~fPrI(Suv!yH?r!R?cm4TR{yxm-|7C0F>XCPM7#}a7m3^zkKf&%oN3}mQf zCFG?nrCqU7K!T+%Rw@83>*)-##(J8eHBAgW@w$?_>K^*8My@C=90BfSg3y#Q*Mw=i z`?z9sujR**L9Z3TO zO2JGUVuo-xa=_^7S@~jgAR^w>K8_-8KrNK1wV|(-f`^-_i3|dU3@~uQnn}u9>c~kU zP$)T9sDX?J#7j!V0Ojt8adX!bG1N2HBZy#})itP*F2-)AM)FPymUvxjDK8^mq`HNS zl?GH>!CJvs0&68AA?a->fdKl-LoiSm2oA0*=Zm*M_((guI?3rmLDXup0cMWwZtf1c zNJ&kcr?evhTsl~ zm$#ayuNuMEPs`VjTHVV}(^1|)QbZjog0zr88Au=zz8-3lQaTV{kh(8O%|Q<8C84G* zp##?g!mM09T%>i-5;zkzHMpsc8xBH^kyQ_n)o=r8s?7P)_4(hsE#U#DRR^%ZFGzN?uMbil$J_ zf6FhwDf6N5c$}hygrA?ExSzDRhZj;pQb9pM0w^URB_(#*L(H3i#XILoS?)%83{>opv3=4 zhDW>nf5`sH{7d#{UjG_S=^ryi3vXvHh=;qoGZqj2TjB}w`>WmgTk8EW`CIb+G5K5i z{W1Al0{$`iTMGU$`CAhHG5K2>{xSJmBK|S?TPprB`CBsnG5K3M{xSJmLjE!NTT1>h z`CC%{G5K3s{xSJmV*WAtTWbC>`CD@SG5K41{xSJmg8ni2|3guwKk)c}T<`w}J^x~X zG1}kR4Gu+L!od3yQ(#FM;J;P>JM({3TK$hwO7_2n|CRVJ;XhDPgqu2hd${@hLq)J8 z2&5$O|BC)^#s3H_uxLD3>fe(875?8UtN+RW*Es(j{kK9%;vYEw7p(tvC-5hFc`E>> zR+9M7Z3UP*;_J_M000}M4phzDpJ>B|3eRlOd|r_u5GhtUqzKZ3%sd*UVzp#{XR`b- zX&!Le;}?w^ULoAlCB|-#3h)!hu^UrxB7<~X^68a~oW?vkZBPj#IOgm~E_UsDvr31d z4|=UzFi(#dI(G}8E^%2d{!4lD(Nycj#n;ewjfo)E`(Z&{C(ZoN^jHW5-r@XcR9vCv zP+B(c=#}sab=A4`pzaiWjGnmP@}200*mlgbiq8!;-|y{JSu-TRl>c!jTJYH@SzWU8 z5Op(@I%-+`L%G}SDvQQ@8ibfV11-~O@o&!oCSRc-I#Xk?=JQo%t0RKD_(+fk8VIj3 z%n?Zq>OX1Xf0o3BtK|Fc%aV8VfoSl?MB?Ht{~4{k+t8A$lK$L=+UqJvYfU0B}7>Go#@QV#eah82m#VD6->`A#pyv!xFu2A` zM2=rmgN&K2M>{@JTlu!5^K$f-^9hNcA9z9M%aSp3>rvmYyimLVy&ln>a)Iy9g5o;u z*4=%d4CCXzz2`(?3cVvnxAl%h`Ax zG^NlxCLwzrKmF*VD1l;vSRS0IQ#ErRZbpg9FUDk{ShD)?8Sw#6$Q9P{H&`Wy`s-Z#^KxcnZWkBC5F3`Wc3O z$_(r*fv{PU+G)rpW|A7a$6J=eb*1W>Rl7};9Wc|m0^0ry#hphL)%PHvBu(QnfSlnp zfa}0HVQpG`SCSSHRI-R*+%{yHqrk%I5>4UlgYg~9!yjHlw4k9XK7~yFp`Smrn~)i! zi9ZV@@a(^#3P{lPy;I=#G;?Sd`@=P{aO=ALYx5LBw_s=K{Y=ZDae^t|GZF5Y(;3CE ztM1L-%&fnzY+VoZP>jpEyT$eHiPrg4f@hZYDK09AAwlAqlNjs8TH@P8uF#*Wa#`nM z6VcWeCtPWB`j8F$75<~6EzH_d*5VhSr_}WU?>R9eL-HI&jYsv|r8Ib$d2AH*)S(xh z{v(aVhUfJ~Lr2l?o|7eSCuvhyL{KE)$Jlby?sg-|_9bX*m&E5u!w2v;_A;=l646hu zRn*>lAwF({2OLF2*er&~tiX0oprJCQ&nIM<-SSkop0S7Wt(80^|GqtAGDeS} zJ+~q>&E=!#-1od(zg$?w?Xsg_{q)F35t4Dw$bh_IqZGZf)&cpu>D8l?IH%dyZzUHS zIf2=j@~jjZa(W%Q?{0uosyUwuv7Xcov0v>60jXo=-{`o?MBbVGZrU>8&W;$W&XzB6 zl=Go*rFqy!9~-j@C%I;E=ZR;_CTn)Sp;p*w<}i*8Oj0NOjcx`8+YUN*}`y82DyU=W~Q%Eu!iLGOM>$i zja}nr>uG7|T>QxMwo7YFA_8~3s`DyDUnP4)uKB_0?6wtAc(UtLfIZC>E5&u`fl}z3 zbfB;G*EI2JLbxY>5ZRm%Zt1b@Eypt~B}5T$RUmFeOJkpm_Fkj)mU8x%Q-dB*cn)ww zqWqpI>aod=OIP}l6nRQo?-mJWNJ=G2@scBf?gxyt z^}1$1e^!fCaiyxJEfwSBcl z+&sAZnaVuJjVmTR%I5<6&)BJNzIk$jI7?#HOzQmAQVa?FY}u!zLJ=)c-$L!~9v)M7 z5WPAw#lr46y8zkMfzq16n2Wfz3n*+p9}NXtN6Uzw+>-XGO}5aS>=vJ&roAHC;G6eK z*1DAZi2x8B0%R&LpFw7-ZTr&tfD;qnv#}N3>EocTKG(NdyXKS}yh1l^QJ&S`(zq{t zMEj-gS$A*a+HVCO2A8iy1t@%OtHdN3)8S1mYrRrRxoHQz-S@j#@ZCamb&Ys~&yM~9 zR@h2{BG*G9H&4-vR);p{`IjYi*5GRXGWYvorkqSb$wfvy?ND2W?dMlxJF^tktZVOY zemb1`7-XjULGgBuTVrV1{qLW2?v>4Hk+N`j>H>PV#4n&5wTqttI||y6niwK z>Xc9vO+vfR*gBw5D_UZu<_QxiGZ8QKqKh^qVYlDU&)H915_~H86#TfbFD!`CWQHr@ z1*En|J)+JZ{`guQyFd;A@y_w(U?6X2DtE5v3tV$q4Ob`s76AS1YsM^vT}WSQz{%#z3p}X($Zwo@1|+enrv0pTgiLr%rvn3^!|0 z^?M4J?8gtj3R4^8U-{~t=(mPmE^2S;rU=q`x7KL^Y8S25J@-s)7zX=sAmPGK#D7(T zuCap|Kf4XG8hX4D91Hm5qjkHuEmVH*098Wk!9YWP9XNdKU(X#l)wSsUvE!*~o1s*^ z6q(M+=PDN3grJ%Unpl~PS81jV^q+s0A8^_{3su=ToiDULqP?c!$VD?v5%|#p#1}%% zP26>Z<4f#)<%KWS{k7g^oJyFO6|Xzg;=gI2L_w}*(kZ^g$DwN_;T^?Zzi>WkSjrz( z{VWR;25cGOQDI~+c(isL%XGeM5To2j=kV`)YdC1YlRTpx!?wvyM2gm?fF08H2qOC4 z*|$D1RH-MgIDWpDG4Hr$1)x;tvZo&O5aOqtOi{FJj@^Iijd$@RA|;xKt*2`y>zzC) z)edgIO2qB_Fd~HO>@#~3bB3OIDWI?xcX7MK zh$qNn|9z3|)N6&Jg8a(hsHAhcuan7xZ6Z6{$Xn|aM70#6PfpI< zvPERzO(`u59#J&8S3*J2JbU8(wx@$~fb^W57K~uH_dwZ)xE_=mnq-u~Qjw&7@Z4++ ztgH5|k&wl6j3C+q~ZMWW)4}Ca%A+TM%|04b; z7h6c1cLj}yng4=}Y|!q!Uh8OaIjvIyfPmAS}QBoPUDp|WC4e>d>*PYl^iKP6sp zi9}|N@R9Ixi%k3daPS$ z)okMkPScNcev&nE=RkoL&?MuNnCMiFYrgFR?U^=fIro3H>x-f7Y?!&yb) zl((IUpW77z56K!`_BuRcKwf>k&Y{0${tHgBTr;pG)f=HwBM=^PEl%Vf4Yw!pI~9;5 zd+yq24I!GoSKF=IE?qii{vQ7>uvU7$`u}o(GRaWKA@QuaNAXUA)+F7Su z=vAmb2ZDd^%`oTo(yt_g3N|BBRlS@K7Kbn7pvu2>xS?_tmQIlqMghhTN%5kI^ z8)MKwTo-uDSG9=82K?~4{`l{nAqk%mAwcL_c18V3$Bfp*K<}VKx-JT>}jMl{9(8wy-T3#=;IvP6XKp#seHM2 zUHt>BEV%=t$LTD5Hosf^T&uVMeqqV)qfXxH@4adOwR+0V{@7u_hwJILx9n~c8BIFh zt!c43(uH0NR82K4i6)EAUO2bTXTWFV%!wX7$F^Rs(b$#>?XMQ}O&NMBTX9;nPwqR?-|M+`SNKpETX3BV7efTU zn9&DnyVHMFD47ke75)jl>tJ+G6-<|A@u{f8%}3Wuql$Y+bzM3BT_D`?hh%O9+meP1 zM;i_9u=RqkDflz7kp~9~XF(DZ`{OEEp>91c*uIu#514W>#COl&m_3nLrI5MF>YD$@ zSK%riqR9N`{22?b+z`LCK@05_&cl#!9#k>OSwb9orD-UPPj;|?_ND0&yr(zH1A1Gb zR%BSwPj>&-%vrbXs6X${V9=Acsfp$98T@x;U_o6mZ$?w7S$eTeR=-qV|70>8h{Y;E z4Mi8Ne^O{V_veJKfL9u;xXdH*xs@ypZ$GI$cw#xamteDFLDSUhh1f3@II;-Gcvham zeZsYMe0Qu}Cj1UJu1%Xz*K#&MQIX}^KZkP9`}RI=ElnEiI{s)^ydjx&tjOcd2 zoYpN;#70;7JwA5x9bTJ(g!x(nG2>pXLR}#J!X3x44tb|8ue*<@YoJIMrtren1?|;> zTScM23CbhK*`0S2AET|3Nv**aD!65a+;KOibxk95!{%Gq^(MlbQ*Sw1mksh+3!T8g z-1GbMTqKpp!Vw&T-kez%FdmP$)9krv)C^xAEz%cgOfZya>vjDwV6c0KR4(F-%lZ7F zyEQ;^C6(-F<>^7R(X1tVt<^zM*A+nxx9 zz9-qV$=s#LdfSF<7z=-pM=wewcdVO_>LotwWU*tMzDhRq^jDH-Z5d`)C1+4}*BJMb zevrK6F!SySEGgDyVNmnFk-Kytz2KbW`B!J^_?TdgcS;Cr|BfErpz&9AOvhy*!Ynx} zVIF4w-XwQdO2O+OZipL6f@cSg|bw? z>xQ$wlSI`ku5Cvw(4bt}1D6{PUGl5-egJhK?2N`=3eR&QyH!)!Mu z+_Lj5mCo->jki$w2>yBnP*V@`}h>Odc(n$qQu7j$<{vNz{v zJgKN+5B2xbH{vjm3Srq_!_43~HP2o{z*YN+3tP(mu>J7&{RT|B50Ml00yTFYeRV2W zBPv#?v(p>QEC{UPXAb;qs2Y~N*~Wc^x`5>8SDImmr)BGN^aZ@T6K!{sj+Bx7y*Ws>vTxQE+q`7{vCnZ^z^t{fevQZo$c;&9cOIDlP@Df*GBlMG5d%g{i(at z$rHC-KU?FS97`@AJiH%XHi?UM8OqS)1ybIJ=)Oc`b;?NzH5-lDhgxEEw^-QSruHki zI@Rf3Z^kTd3aw%7#tV{VNw668;)o8mw;%lN$A*UEbL~{?QbOPGLGHI(j z2m`xsw^tobL|hQXpII0!I~%qiSE7Aq=4(p|`Vw>fC)PeaamdQgzh49HtgvW;3~8Zd zg0o>4QHp?sk4AeW*NAt~nQmoA&E`S3eDCOgp>E!Pm+i7WK~LP(8~;!e|8obuJ=yf6 z!)*y~+dh5vyD{a4LE#VYj_4h-4-sxOpx=!iE$j-(D<)li+0(1mP}-Rii)Xhu1-}m; z%<235ZqzgIMC^VM#LiY&KF@Q-me#Y| z2FR|F7i=1VmBp+x)1ng2P7-;~iZruAcf&!WGz}+DpASCUc2{&|7F)CT#gh1h?)i56 z)pWB_3SE34b|PLinking Number -

A C++ class with MATLAB interface for the computation of the linking number. Given two parametric closed curves \mathbf{p}(t) and \mathbf{q}(t) where

-

\begin{array}{rcl}
-  [0,N] & \to & \mathbb{R}^3 \cr
-      t & \to & \mathbf{p}(t)
-\end{array}
-\qquad
-\begin{array}{rcl}
-  [0,M] & \to & \mathbb{R}^3 \cr
-      t & \to & \mathbf{q}(t)
-\end{array}

-

and \mathbf{p}(0)=\mathbf{p}(N), \mathbf{q}(0)=\mathbf{q}(M). The linking number L(\mathbf{p},\mathbf{q}) of the two curve \mathbf{p}(t) and \mathbf{q}(t) is defined as the double integral

-

L(\mathbf{p},\mathbf{q})= \frac{1}{4\pi}
-\int_{0}^N
-\int_{0}^M
-\frac{(\mathbf{q}(s)-\mathbf{p}(t))\dot(\mathbf{q}'(s)\times\mathbf{p}'(t))}
-     {||\mathbf{q}(s)-\mathbf{p}(t)||^3}
-\mathrm{d}s\mathrm{d}t\,.

-

which can be proved its an integer (if the curve do not intersect).

-

The library can compute the linking number of two piecewise linear curves where the curves are defined by the support points

-

\{\mathbf{p}_0,\mathbf{p}_1,\ldots,\mathbf{p}_N\}
-\qquad
-\{\mathbf{q}_0,\mathbf{q}_1,\ldots,\mathbf{q}_M\}

-

C++ interface

-

Load the library

-
-

Instantiate the liking number manager:

-
unsigned max_curve_stored = 2;
-LK_class lk(max_curve_stored);
-

the class lk can store more than two curves. Now insert the curves by points, incrementally

-
unsigned ncurve=0;
-lk.reset( ncurve ); // initialize curve
-
-lk.add_point( ncurve, x0, y0, z0 );
-lk.add_point( ncurve, x1, y1, z1 );
-
-// ...
-
-lk.add_point( ncurve, xn, yn, zn );
-lk.close_curve( ncurve );
-

and compute linking number

-
unsigned ncurve0=0;
-unsigned ncurve1=1;
-
-int lknumber = lk.eval(ncurve0,ncurve1);
-

A curve can be inserted by passing all the points stored in a vector

-
std::vector<Tvec> a;
-
-// ... fill the vector
-
-lk.add_curve( ncurve, pnts );
-

where Tvec is any structure or class such that the field x, y and z are available. Another possibility is to use a n x 3 matrix as follows

-
double curve[npts][3];
-
-// fill the points
-
-lk.add_curve( ncurve, curve, npts );
-

linking number can be computed in one shot passing two vecotor or two matrices n x 3 as follows

-
// mode 1
-
-std::vector<Tvec> a;
-std::vector<Tvec> b;
-
-// ... fill the vectors
-
-int lknumber = lk.eval( a, b );
-
-// mode 2
-
-double curve1[10000][3];
-double curve2[10000][3];
-
-unsigned nseg1 = xx; // number of segment of the first curve
-unsigned nseg2 = xx; // number of segment of the second curve
-
-// fill the points
-
-int lknumber = lk.eval( curve1, nseg, curve2, nseg );
-

Having loaded m curves it is possible to compute directly a matrix of linking number where M_{ij} is the linking number of the i-th curve vs j-th curve. For example

-
unsigned i_curve[] = {2,0};
-unsigned j_curve[] = {0,2,1};
-
-unsigned ni = 2;
-unsigned nj = 3;
-
-int mat[6];
-
-lk.evals( i_curve, ni, j_curve, nj, mat );
-

and matrix mat contains (using Fortran addressing mat(i,j) = mat[i+2*j]). the following linking numbers:

- ----- - - - - - - - - - - - - -
L(c2,c0)L(c2,c2)L(c2,c1)
L(c0,c0)L(c0,c2)L(c0,c1)
-

MATLAB interface

-

Matlab usage is very easy, there is a unique command lk with a variable number of arguments lk(p1,p2,...,pn) where pk is a n x 3 matrix storing the points of the piecewise linear curve.

-
[L,err] = lk(p1,p2,...,pn);
- ---- - - - - - - - - - - - - - - - - - - -
LLinking number matrix
L(i,j)Linking number of curve i vs curve j, L(i,i) = 0
errlinking number error matrix
err(i,j)L(i,j) error, if < 0.5 the L(i,j) is certified
-

Installation

-

Download the toolbox from here and install as usual. After installation compile the mex interface by running CompileLK on the MATAB command window.

-

Reference

-

The algorithm used in the library is detailed in

-
    -
  • Enrico Bertolazzi, Riccardo Ghiloni, Ruben Specogna, Efficient computation of Linking number with certification, 2019 link at arxiv
  • -
-

This implementation of linking number was used in a various paper here listed

-
    -
  • Ana Alonso Rodríguez, Enrico Bertolazzi, Alberto Valli, The curl-div system: theory and finite element approximation, chapter of the book: Maxwell’s Equations: Analysis and Numerics, de Gruyter., 20-19
  • -
  • Ana Alonso Rodríguez, Enrico Bertolazzi, Riccardo Ghiloni, Ruben Specogna, Efficient construction of 2-chains representing a basis of H_2(\Omega^-,\partial\Omega;\mathbb{Z}), Advances in Computational Mathematics, vol.44, n.5, 2018
  • -
  • Ana Alonso Rodríguez, Enrico Bertolazzi, Riccardo Ghiloni, Ruben Specogna, Efficient construction of 2-chains with a prescribed boundary, SIAM Journal on Numerical Analysis, vol.55, n.3, 2017
  • -
  • Ana Alonso Rodriguez, Enrico Bertolazzi, Riccardo Ghiloni, Alberto Valli, Finite element simulation of eddy current problems using magnetic scalar potentials, Journal of Computational Physics, vol. 294, 2015
  • -
  • Ana Alonso Rodríguez, Enrico Bertolazzi, Riccardo Ghiloni, Alberto Valli, Construction of a finite element basis of the first de Rham cohomology group and numerical solution of 3D magnetostatic problems, SIAM Journal on Numerical Analysis, vol.51, N.4, 2013
  • -
diff --git a/README-saved.rst b/README.rst similarity index 93% rename from README-saved.rst rename to README.rst index a68efcd..7fb501b 100644 --- a/README-saved.rst +++ b/README.rst @@ -3,11 +3,13 @@ Linking Number A C++ class with MATLAB interface for the computation of the linking number. -Given two parametric closed curves :math:`\mathbf{p}(t)` -and :math:`\mathbf{q}(t)` where +Given two parametric closed curves **p**(t) +and **q**(t) where -.. math:: +.. image:: EQ1.png + :align: center +.. \begin{array}{rcl} [0,N] & \to & \mathbb{R}^3 \cr t & \to & \mathbf{p}(t) @@ -17,31 +19,37 @@ and :math:`\mathbf{q}(t)` where [0,M] & \to & \mathbb{R}^3 \cr t & \to & \mathbf{q}(t) \end{array} +.. -and :math:`\mathbf{p}(0)=\mathbf{p}(N)`, :math:`\mathbf{q}(0)=\mathbf{q}(M)`. -The linking number :math:`L(\mathbf{p},\mathbf{q})` of the two curve :math:`\mathbf{p}(t)` -and :math:`\mathbf{q}(t)` is defined as the double integral +and **p**(0)=**p**(N), **q**(0)=**q**(M). +The linking number L(**p**,**q**) +of the two curve **q**(t) and **q**(t) +is defined as the double integral -.. math:: +.. image:: EQ2.png + :align: center +.. L(\mathbf{p},\mathbf{q})= \frac{1}{4\pi} \int_{0}^N \int_{0}^M \frac{(\mathbf{q}(s)-\mathbf{p}(t))\dot(\mathbf{q}'(s)\times\mathbf{p}'(t))} {||\mathbf{q}(s)-\mathbf{p}(t)||^3} \mathrm{d}s\mathrm{d}t\,. +.. which can be proved its an integer (if the curve do not intersect). The library can compute the linking number of two piecewise linear curves where the curves are defined by the support points -.. math:: +.. image:: EQ3.png +.. \{\mathbf{p}_0,\mathbf{p}_1,\ldots,\mathbf{p}_N\} \qquad \{\mathbf{q}_0,\mathbf{q}_1,\ldots,\mathbf{q}_M\} - +.. C++ interface ------------- @@ -137,7 +145,7 @@ two vecotor or two matrices ``n x 3`` as follows Having loaded ``m`` curves it is possible to compute directly a matrix of linking number -where :math:`M_{ij}` is the linking number +where Mij is the linking number of the i-th curve vs j-th curve. For example @@ -214,7 +222,7 @@ paper here listed - **Ana Alonso Rodríguez, Enrico Bertolazzi, Riccardo Ghiloni, Ruben Specogna**, *Efficient construction of 2-chains representing a basis of* - :math:`H_2(\Omega^-,\partial\Omega;\mathbb{Z})`, + |EQ4|, Advances in Computational Mathematics, vol.44, n.5, 2018 - **Ana Alonso Rodríguez, Enrico Bertolazzi, Riccardo Ghiloni, Ruben Specogna**, @@ -229,3 +237,5 @@ paper here listed *Construction of a finite element basis of the first de Rham cohomology group and numerical solution of 3D magnetostatic problems*, SIAM Journal on Numerical Analysis, vol.51, N.4, 2013 + + .. |EQ4| image:: EQ4.png
#include "linking_number.hh"