From bf6e3946e4c9637cb7c82da2e56aff019d64e485 Mon Sep 17 00:00:00 2001 From: Randall Holmes Date: Sun, 5 May 2024 09:09:33 -0600 Subject: [PATCH] NF draft --- Nfproof/maybedetangled2.pdf | Bin 501301 -> 501479 bytes Nfproof/maybedetangled2.tex | 8 +++++--- 2 files changed, 5 insertions(+), 3 deletions(-) diff --git a/Nfproof/maybedetangled2.pdf b/Nfproof/maybedetangled2.pdf index 74d8fac9d27354921eed4546909948010316390a..1715d95aa0182ae08679266def9b9391461c4e45 100644 GIT binary patch delta 26252 zcmV(zK<2--%pT{>9e>6gwA{7Gkc=p$) z9{@#aIJ>@x4WQ9zG#X!bL%$r}y?@B6J0apa&(piZ@lHq?mqm3~CS@$r{O-`+{U;K! z-0cN4qrWMq+udH4c{J*?8oyd@3_X9p?WBnGXwA^u-G2}N1o8D<9oI!#p!DQ!FREBp zHOn=V}zb37Y&;sM2<%Qyg0;?_|4eOQL~Q1E|Z?xY+X zPewZ*HIt~c%t{o5P3y*~aZ?zjBk(hruLCVb^faj_-+|Udj>F-=#Pi8CyR?cuGWg^$h1r)C$@}>;W4R)c&{pJ~vH|=Fo@uErX)q)P|z$4GPN0H9*py_#R zX8MORonLMYgX+5(&Y)tjHco$J=~eXUA!g$9H17z8Rai2ZYC~7@g({`st$J?u=-McQJI{%)+(eWSUbrwEpqz9CUWcna{#4Fis7$Z4SA1*hmtmPNm8 zsZP5u(&&?ZX5wL2WzjJ8Et$xIO>&vQwL_CkmU*7(+>jR0*M7j(Gq-=d*A;$eNT32_ zJhnLWnEr<4qAujndh`r7Ox^a45$-2&!0jVZ@O{#~9uW?(;q-X6Op>9Im{kV4*V^~G zfxn}E9*y(E#>?jG0K{c_>`W6}W-;xeV9id4Wlx*V5iU5bDOb0b+RF0xOctJ9Zyo{j z(BTi(n#WE94rW<~`>B6uKfu@M(J9k+FWjUPspv#x8cqcI+1xVVi{8x=>3@Lv�ZZpaA1$>k*o{7 zXLKY_KeAn{^Eg~5u_(pO1w)D7{Apo069E%L_vlXo;gcd4(?>PJ<;$v)V;**y^I5k> zxd6treAB2Ppb8cOR>DQ-x!{Vl^aYn5gBxcR`;hW{&Myl#^xAHLvV*X6h20t;&jAu& zoavvq%~vB0&~AT@FTS7l00g_g2ld*60emqc!hVZ1i9T>oi115sA;J%SmOTwq*KVn* zX1foDycBR*I|b-}(ij37d(Yl)QDcBOy7s`u{wjhm0}i0w8nmEe&Typ`Jj+N59IZx0 zd+itI>mjar1@g$ZBT2=$U*6z;<#E5_@QVx_eoI6QY#-q9n z@d*598Zli6-8`B0Lhwkctz+m0a(qehBxnvEoG0txj{t`8x`mk6KLN8~Cd$;{d-!}{ zf|8FQVGcmVa_}r+!$?1J4B^K5#?ijD=fl%rk)C&9<*g&>8F3-DPDn{s6naR$3 zFDn_H==wv%2jgK5t$XedS#5jIZF1VmZy7r{fkn!imT{d72U>*!B7dL1Pm?s;!sA@V zb)5!{|IMBODTfZhVps)~Y>t7>Hlw+?Ei>%BP*#7U2ujEwRN_P1hH$2?YnInFxf3iC zj+a4Cdh6hXlj#OKTu$h6jly&6m}AtP{&#C9P>HHgoiGm5Y-T1SxM0MH!8G%qFv?Ttbyn$Hw2t2>UwY z94DYM)QEyAqk&vTU>LgM`~V!5G=~AyJc#BT1!n%Le$Q3hFdD>|EKQ@&nhN%mN`u#j zQ^;6c5BcgXx5o@e5}1D85QD2%sKf^JhpX`f*YC{Mn996QUh#nzXY?vIi zvb1u-4+Hr18YDS~y(GMw0MS5Ec!fReQRCCJsKT*p=mWRfd|B~Hi5k~+!`V=sCbLDk zLZX%zMs=L9l8@QBl)?BjdMM6rGYx-Uq&3ZqGD`qSGk_2wUqi^+EmjZ$mqc=j{TDot z>MeIm^EglDn9KnZrolax=;%2VJ>G?=U{0c%KNOka`^y06z@#&0jd8dr5Fh9oL2uKk zn|!$7+(zcL&nKoGRWxM?RWLB0S;@fxSF}7t7zFL-6PGxzEpc<0Z|r;p%RhhrfI&C! zSslxC23$IL&h!We2Oo^*l#l#luCJj?K64*Ox!_vY`geYjcqS7;3BNF_4Q!i_E%N>ii$&`W>8G{6(YvL%J^=njJRrP5d zapb3X&-KWv%m)VLs~xOX1%-dJpEl1@#)V8**h|;qdONbM+fe~x&nSvjJeld5w8-SD zs?V3PkE%xKLU=(|A0u$cQjEYsKJa9Ikb&?h;xemm3Pdk8)S@sEZWKLqVi#sQs`C=j zjYj6Kqtno}e4l`iE?kOllZ>%Q^9%FLvMl0Ay(9PYgCh_hz1*e0Y+!$9kTb{WvB!IbCo{&f@Ugv1Y-JIfJwGJem1&5Jo=oRKz3_F?4=_VVcI=maZMd z7Gwyod`Mj5ljYKeMhE`hZvNKIppq%m>b0Bw_4nPZjI(S8VJfa+Ezr&2a}LsWy7+Wu zq(3=Q|310WeDy~EXYYSgSsjZ~-sCJ4ETKr|XFSzEQ6f;WpWt`qSiX5;dkM_^?4w4{ z3enNMN+?dMr3a%T)){<5#MLQZ%jdt%kTPel*;%z-bAIzE7m!$H zahB)XPu1k-_u+pLhBDlF0q~6Fov}RF_`lo)KVgPH9B7PQFJRiIhkGU-fo*b3EB-8f zXFX@jN#+2~PdYN1`j+kyRjq6Xxm}DP%dd^un{SL zl~_5K+%^)<^($s0vENfuJiunNGs(}|)drim9oZXTNK7|&co`ryGfw>1U4<&}XmR$9 z5)vpB3P4@>3ZKvKK7J9!T@exQo*?%n!%AJj%m3$?ne8-EV>TnB*UmC=sXK zf6xE^_$6M>$cive;=71g8{Kwhw--f!9vJmaTivymy4?f*kHK)=#et%>V^I|`NOKt* z)$S7DA<6@Z!a0g4>W@)>+hvD9)~YSlBpJ4Kw@*cQjK$qPj>973t=qw<_5y3}(=>H^ zNK+A<&*$HxEcz8bF^$N!qQ-x|Od}zkcBP+vBElldVUYs#bDZ>Zc%y#KSB?6Ah(+)X z52_4mhzM87Ba(iV{ymCQWmqNk3z0!7jT{E2HDqqN@fCk*aP9it9wigCtd%s%P^UL) z|9@1)3(3K43H3z!N=g6N=uPLO&jWIx)=yoFiUZB=_HlqsFtbymSF#B3=*Y`f%$yb3 z-cDM#lC?0!+ssi+=E&Y?j-M-kJ=o>q;`Ouo|JbsAW`DBEOYuxrx0hNC&ij$WxiSuv zwKRIbL%-~fX%ODnBMUPT)84?KX%Yvrs?gT1Nxui)*U)x@A`-MW$JNnnwHKyX{pYWAXkf^`BT>UmHt z`n#-&(BOJ_m>g!+#H?!NlYk{IXP6?LS6CSa`t)Bg{3J<0XZEYDvZMb};^@`=EC2ddx5Ay+f2j`fjy5XqQ zAa!kDnSZbUr%ES(V}C9cnIFlN;*FvCiQ?s=T4kKWKoptDA2B|qwP+#Xavu)+P{BBC zIf@%?El&|}l>1tD7bAN}PFJ+q3vuZIt^Iu{CUYoa>~_Y0DrgOV;cbG`+e$r88&k$~ zhT~pyrm(C+*Ga;R^J{yPU;hPm;QVd;RQasC#{P(k(>JO(#=IOyLEoG}k15739n)yJzy-U2E#U!jz%!P)3MyuAc?AY(OQa)+7Gwd-% z&`@5cTn_!4Tn-c?VPl5cfF00rk_a!V9^uVW27yG-|7)To|EsQ%ngs#ZX2xGmy@53@ zMv`P1BYAj;a~~rQ8&On*Nj@W9*;`H>heLQg9@nWOj!tQc%Yg&9FcXj<0CkX0$5ZmQ z%+oS`%4N`htZQn_>FesRnsnukOn5F;KTsR;;HHmxsAao{0e$odWdKs#43*-Pa>C*x z930>%X@ePFg#aX|jXwG8Go+l-cJ1toNpl!`&BKtJ2l?pWhZE~B9T+OXYqd}Nx&_22 zYY${LTv4wRDNdnIQ2)o4KGAiPg1{L5i&Io!D+)e$8lw-1gKiY&Gk_=$qw!T!92nws zx^S>V$w!ulMs;IXmT`NXAPsJ8=%8wm)%hEeC65AB*zyzSS7M&-<2my*{aRmZVgo3E6tOx_wjt;gEhSKp4B$^jDOh!bzZumsalKAwObqzA# zFGtdAwRC~SmF()RTL0;yG<@Bhg3T#{<0&nuB^&xrW)-tp6IYwHsvRn0 zv^S(@G8X}c1y?p%IG-#mNLia18_w{joNXvGuHsD)LPPNeogx~Q^L9vtwNr7<&a+GrB@Yft?`0axCJFo>6=>WNESa^1J;M8bo z9MCg?KnJH|awnj-v)djV6F~{U2N}ShGX+JqE?uBsQCGRLVk7LX;J3~X3&x807D6t6 z%pr$=x*rNxb+g|dH=rbk(aH%54v1s$h(~~nz%SF$@DtT0k63}@nMD);D%slW*Y~bW zEdVk-a#Uf@34;Gc4b;&52V^4k#pU85q>B+mPwSh9?kz6_X>1;MJ&41%nBZ0hm6e2O{;Z*b>K8!GNrD z#xVrDAhul*+&iQ>d$A>%B-_790HM;h9IfRvIxqe-0RraUu+ObSh$!RQg4*8Fpwq*_ z`RofbIq(RLKSn)p^9m;eG{QZ4go4IErSfVP`24-RuQ%^)J7{v=bqyu3hT6G*w*g9k zH`P=#!5^`Hz-ZZvfh4A`;NI^mX;p^?RdW`nCEx41yO98nNn>62vt2%V+K4a);ldx z2hX=M4C@&mb2u`PMf0EiADe&!EjLMbZbemDnvD+?`)#0lp>4+kAW#OyLQ+7{kn`<| zL+^e*zxx}5g)={sK?W0p7$%1pCIPn?CIVfHe~np7Z{x@jzVELvatV!$wS0wBz`xkx1gOO)yoSM?0lO!~8KF}slXrr$;bfeDy}c{)EV+0` zH{~_GjNX};1EbUA@s?1pfLmP|NjH8&f5(?;@(~k9xfM?quh#Q0Lj|*bAAoic5?ad!~)2^XSV}FoSn0t(AkA^VB-7+ha$8i9bxhCt| zy<&!w)idzjCB4(BOY0R9g6Vs{%^P_=&yJoMM3cb)LkuvRHNJl2W112-G?m^!e+cu; z2O4H@56r$Ztp_+btY*o}_|y)-@Y8QeCeXEQKGU^q+idEZ2#||U?O{b9^K_FHRb12J z^fw%&Tfjl3T*-SO{bUU|VaUAW_mX}$n_XJHQ75zK=bd`!bWxOZt%@k&ZBax)6wpqY zn)H#7{1gFN%mtid_I5hEYxm0kf2`c>%5q7~!%4(cCEkRw8v+K9Y&EIDHn|XITS(S; zOoo%=N590SA_s!3Zg%~2blY{WfM59SZO7FQJ zwGR5l=PI>0_5jW;F^_)iKCn>|-&hHARdfD2;osqa5gsM;`aRe{(&9%vfAbrRZu{xv z?B38binM}VVY^vV{EN5!-d;L>?6yokXGN(t!{-WzgvT^TLJxpMB=p5}*WEdPFrNIS zdAqXpX1Hh4w=3aFb*rA5>k(e~T)<7wQRhrkJ5BeYtev>EHy5LXDzSZojY8zlt^*f9b>Ig@irT_uhd>u?5f5bbHg2D?kUcw;n zKN%e0ygiC{l&6*K#nn@Iw!L~wHhEanRS1xxlKD!Wq*tS21j1Fu)*UoVr7=uV5EF%R z%1{ngf|jT`umU=uveh?e8068=+86^{y_uraNbgvo_G;ha{%VRP-a8J!)wWLl&6$M( z{t>RMvs18PtU57)e-yQM-Wv&vbv0!Tvclmz(;M9aT@M(1y8rdV8mY|hyQ18|UD8)B zftGF>O5C<4L$3X;2T>BxcP6 zDEEw-`N4ipvx4G0B=){x68)@x6>PC&ujQY~l;OsBLad9wfB4KjIja@ zJF?_}S$0Uo7o`U{Nde!rLbw!KS!ECn1JAb=8HTrR3_wh_$E&_tcUHVO3i{ff7*Y07 zk4fFw0qklCGqNCVfCrU((&&*04+atNCw!Ew)ga=oGLk5?o5GdImZN~gL;$;F^rkas z<%#b2oK~r*e-f_@?OB&z$;+p-aCt$Dyx)z7bb7X`{D_ccK{+43XD3vaVuC$zk%$el zRmoHs59Vqv0u=jD3aGZ%Ls%Y+CwY;IuuS$b9ViRLdY+~7fh>guD(B*HyuDx5ddYJ~ z2~T+rD|h}2e3N*CYj&R}BWdHTM#zxm6nUYRPfM&OfBvUd9o*ck#Iv4Tk2s<`)IZT& zyxm4OiVBAzvUu~=ta|gO_H4=J@%wXx)0|F4>cEiI8S=?=x#6UZ(Gs^`zQC{fgRbqd zR#cV|tV{B?9NeL(E?FE8A17(?eU_+bJx=GS$yv|0r?1fe>7G?;!;!02g&^SBnioLw zqFUn~e*?-UA%ln4M4g8qoq#ua2&1fiDa>;;5n|^jld*_&F=|7c799d9D-ZbXo(cNt z&uk^R9!3Dg)zNdv;=v-lVuZYEr_O;9YSJ|G$l=i(FnZMJnWF#>mJ&p0H}C23rG#j( z@v2~s(IKo+D;JXsB+bH03Eqz|1FlYE=w$rKe^NH;HIGy}2o1H&s|o}VhU2}La*9VS z+sWXBmyYuSs++@E_g?c-9-iMgJl>6?I|Jv_eJ9cus;Qhm?pqC97H>EH;>{3anWSS# zb7qB@`AS}})3Pg!Q@s~!FL5@M0*{h?BL~LWy=V_5y(@81JEBHd1M}EdfQL5a%25}8u-iYyL;fMDL~+}JCfJ}5?WG3gn|ca28I$9pt`s#$GNfBQb^ zSQo$~2;i{0LU7FS3i7z7cjNH{xD67{*^b0paYsZrtRZQeAuHmwY=8lv_B68O+SFn< zC+(1&tYR2CUC^pj(3Q*72pNI}FaRZvg?vAi^oO;4WfuI(RC7=I&Rh+R*b+GrDN`=m z?pSlB8&k)aEfIuQiUiX1s%t ztJJ)0<)}O8o!Sb5wmKmaAhDT>wZr>Dni?mh?joBK-l2{nspG5`C<4vfjRv;WPH-K4 z8L>MIsA35D`^Y1NE$x3@tyx3ZV2|x!*3JLZ{pNjnNn5ZWVK3B$f5r!}M4}@Np?0Yh zM)1xAx13TjfX)j6b6V474uy4AXQr-Ey6m;maB8%GgG`I6_2gM{pB~E^0$BMEdR}!ci|*Gzh=<1GRE!q z?Nqu<%WfVI)l@N%VmW3ahuB`m+`>;v^#5N&o4Z6o5vT? zvNmh$qGsL5gp^rRZ&{N!nJ6mO4eW!@YMRbTT5Ki%O^PjtMStd^gdt1PvS@g>SDwn+ zg;?+f{;w!Qm>S|`uN};gq=K6Ocz-I7c8PpC{~WakLWVF-!UEU)qZyRf)~G4@>fTt+ zQX#UoilW`wd6*wip(wcDV=LL#e6l;;Q)}UQ1Lf}!)Q0L|v0+YR)mMx6>sZ2R z3>r~O8I1_Aj?n-NFvLNYuX&@4z3m~LAe+W)!=kMFB)#0_IAluU81hDZBwzd zl0}y1QC=lOar4}5{s3g%$^ojE@qGakhr7N4hr7N5x4XUsdp;003NK7$ZfA68G9WQ9 zH#snufnWv|1Ti={IG53n0w{m91yCH?(k+Y=+$HFc;O_1Y!QFk300Ru}?he7-g1fsr z1b4S!A$WrGIP%?d?)U#y@6}Yz%xYQPz4z)(L8he2AYx``0+h4^IWe#>GV=n&OwgIrP z0a!SBS-5zanE|ZK%sl@SXb0v6h#R|DnE~V(0kU==pd%uMn4P^l*vi7v>8;HF`~^^( z(g0X^c(~~QOb3YA0>M_M#vp*av6Cgx_N}6+u?;}g&eRI%aK43{Wt(1^zV|BO(Pr&C<&8FT1Lpxs$6g z7zlVX*jSkYL5^=3&LA@&81PmcpeiE=P_zev{tA}+D}WyG_t^kg7+L;9_jmRmL{^|b zlZ{PH?QHFhLGD%{3xK(m4G^FxDaYvK=0p!L2ATa4Xl&zX_m+Qe>|$(XV{Gyk@Mq`7 z07(&LfbrXae~;&A3bwL$a%6P0viV~~rax%jPFVtECT3@A3j{eiBL2~zxD^;^`gZK@ zOn=?1HOS5t(e0t7gLoq^t-|91R0 zLS$h9m|2-R0Zf1vRv^TG*x$@R^S|)h<%6x<0J_X?+G7DQ|MB_HKm9j(nc0DC-2Vyx z^M0A+qH;a<7)!$t(|C1^M zGPeWp{MGE+Dg95wE`Q%Y_20We1Nd()1-m!V0s++jXk3q(gW2@$i{<}W>3^pD{|WpL zmj9c^|93-@&NeoGx~c#4|9{-ZwpKRoe+Rs2*4gPz|MGTkTLAjsp_;(Ic2*u}X60=A zzr8X}#&3UnAOfl>f@KYVYkcmTnFh5y&ZnL2~PZ%@~stMzuP|AYU0CxJjWpef?Y zqMa#U(C50Kj=LHWLRW@^Zvt}^2b!rg44y0CPUiW%4Aw8ANGDNFK>G>DWQ{XlSBo(|FbM>JcJr_MHO%>9DLMui%yW6yi?_d58*(6^WqGn9Xx zqDRTHcuSroMO)yBlm*<*$sOA-EH+2f9tR34ci`hI14@c1Uh4PwOwiaekx^T1(h0W3 zWC?KWSr_ZFTW&H}T&*UK^oj{quZlKY^&BclJO{lGIrSb#@YFbUTC|}mmN-fEq@aF| zP-4iOdP>x=f&+`;r)a!QyIh#ugq_BMIWxPQP7?%sN;9;|(>k(RH^GnfXgu zkJ&Jn<2_m%?28-I47;K3?~{&Zw(kuflPDS+0|bt0+LCg_k?05`aqF{)oqzGP62cNh ze@x0u&uwLER6-gy)UP`@MWV^5K58FyMZ60eJlVr8Q!jfJsjkfB&crB0kcNMcjk#}z z3f-A>#+91h;T7M+4Be3pi+Q0A$-maD?7N=qx<1!0U|{BFEVED*MMGAw`GTdBtr#bF zK9?86L1@6!(2xDXTl}ew7S`*hBw|3&t7m^WU^UdQY*B)K>wWg4LkAR|VCQFMgA}*Z zm(<1^pm;P4Ks_sD;veDB?LMwM=zT446_p>PFXYnRvU4@p@3RW)iLy<>-Y zzxHgF8DE<*TMjIF`ug(Q!Y#16o=xN=KZM`}TW}2dKnEm`oI@bq2NDtTNCjB>Mfpsf zUC-0-v#HMDqXe6EmqW?+LoDLSkvPys-gZ+E2Ji8^QnBPZ`d=F;h`WCjG(}~jXEI6+ zG^m0)+;q-=7AD|&%w;?>W~oLd%HNREgskz8Hb?z*c~+XU^!v!qBJ)wv@W64Suzg@e z^0$R^P5<5*uF3Z2H99A_kh|B!guIJKlpI^7avC?PhrL)zR!&bNd-Fw0v~axNQ%~sd z(N-|e7MH~GE+k&3qu$VlKEGYe~PSJDD=u z&=);U#-2qH8cwh%Hg<117x`K@W3b;`W&{^|%Y&QF!FX(yL>GS;)g=q-R*lTtTkw5- z>Rj7f<#5Vk_<+Z!divPu*hc*U$Ahd)pDGkA^e9AYPP%pH6}RwfhB{y3MyhwHTNt(- z83SaU;p1@xJX?(zEKvL<*uS|an;lgzl0%dIEwwyUcK`vdy#hO(SUtR7;2GBaJQ|&{O_CdHV2PGtEqtkJ zI1zI|DrRF~05{>i+Qi_%BiuH#1$^B^5Uy>1`3irZ+w2wLDjxw(G{xrGQo^C$&*r!0 zZilbtODf|UmS##UXl74QS(V0b=jf`O^MhMFP;bOpqL(D{nxtJ1j0%Frs)#TqJ+Kc) z#Sc_aMV{6rqpXC*iX%E0B=_}N_-#u8C8*XpWnHuL?ilPGT%#>44~l4Z{-$X}Aw+AxRgg1Fa9%5_<5<7ePO3)2d$7O!JW}q zdl|e+iW+JXts9r5vF}{oEDb!6HsvDKpH{2nHZ2)1^Ob*V@G27;@rV zQzgGYon~7%vZhr-ZlbO#)z9uns@ z8-mdv~s!PPDv=4M&`=@%YpP9 z^{l2{l2LvR)f2yThc8`(8T4S1P$hrlGJvJ6@QqG3WoWM&Ymk#Nm;6V@V;nz{JLbtp zd$iwEHP9e}z?;uCjB5KyND#N7_(zoG7@^z;^En>1gIQ8`VLUw(^B)ZGD)0SN&FozC+NU7?Z~(XD-g2mJpsw#@4B2u8P-8;p2HqK*1NeIl}M8DsH*`WWi5n zWSuHVkY6%q$d05QAPr6ckVJS3kNLLm-SPs%5{^IACa} zZYGm$Y}V;=*V;npEFsgc_E=gMUSe$WE4{}-<~R$7m|}=c6qjq@Fa)ni9~@UYSOgST zGm(G~iv!S)EGDa!C=w&x02O8@-N`*}x$`2=rl*6cV{KD;`A^zr8`OV6w7l7OcF|@= zVfpzY@()TTK~W(Lpu+gj<7y|E1pSYVMd3p>7L=oNz><_ow4-Db4l}G7T15#2jyRNB zbv4U}_Zv1Y-8}7thBT1(^Y16f?Zqinv>IVyj&MW_dzRU@XfrKRNV`6rU9We4E^s4Vq zsA$Fw*;k0WygzB@Rns+^EeaZ#ZfZnw4q-A&=nOg0k33^zy{DIGP;S#U)kQuT7I_3t!}(%BL_t%I?=e zHeU2xzw}?W5Ziy_;W6V(0>>jpE@ndXg?FB_yD7{DqoK(eY6i@34`@)>4MkxVY*VjD}apVX7VqjA2co_qS8-~Q4On~xnN5Z2Cc0wm2l<1jgUnW9QtamKNPia_2LJeC$BMeg zztLWX02O~$OEiqqiv~p!>Lwp2(`|s*c~hxNZYHjFqO*v8k38G|d7ybaAkoT8k?~N1 z$JIm?s?Bjw6y76lXEA-Gfvho|)#3uGaPbM7vjly6ZPEnZ6r4)hdbJj>Nx*{YEAn9r zq?JE$$zx|%KFOH$Lj z>cowQ?yZn>vnUfIJ{I&PAvL_aJiUmto6J8Be-vsH*6)M9H)N9}cK2XU{ECDc7VC(u ziWNV?*FG?tF)s7)=^z=2`EJ7S5o~*eY9^&7j;99UB19G3n&B%-8S3^xaU)Yonx-kD zKgxdrOX4y|j(a?JJs}fv+ajDs+g^3?%}Q}=|CN707CNngq&ETSMgezknoH2jtMnH8E;p-*__$jJ51B>yV1P`PJrjUv} zARekeD~(svf7U$o|AMQsTII~u;DGX@{qD1^4Pr<{I$I9e`o()5a6-^2L9`XZF}jiS z05@432RT8#DNM<|x_a7^;uxQg_gV>B3&x$9U{J&e!MickiR60}Qj4}Ocvwgq^(TKj zm!jv096F5p56ToC0t4hF>JX65{LMJBoGMZ&zs4HYCqi9pH}~uDC~oij+jHt?vGpqi zl*GJ)p4JUn*N5k=pKr0TC{Kr=kdFC)wNhM539v;n$#+qm%*y7yOl|SM5F#E)-*25~ zWCO`mcfD9+5+$ekq8H;pIDTxrw^Dzf<3fMa_*f^UPprsOi9{B!sR)V@wQb28ct7Ze zn8}Gcw@|yLjto))7Nlfp(az_)RHK=_u#d#thU~hFtQ4aBJ_#!br$(J(r~Wpt9@yWw z4`kh}DeSXa1m|(hz=lu|UB}?^&!i-ul2DtK4VPS^DEKH8<*%0#`l21#OE- z29E^Eg6}AiS>Bw$b2;Hrl8qQ4F*;DyRT^aPEndrf2LEt+<9@quY+e}XSCT2hCM5AI zhEWAQM-&xu3--W21=e&*-AjM*s)VjpotV49H}r`;+D;_SnLpD;bFS~cKL$yDK(bYXCK|$eBv)2)hHNXg*7=kVi%C+LMZ!TwTN(xYxE3fCO zE41%HX~s1ZKBQ66?|rotTGh1;wio*N!>u5NnI6XVyO5nn{Z)TP^ZGlPU1tSRX*8-I zko6Zac!L_6WjIk}TAcI1bglMlCSPyIJNL<~^fT%;ZyuKLvrguoeaDs5umQN=&amO% zZ}1Ll9ES^}P~5}x3h~6QWFc~C{3*A3Y~{l#2x0beC%WO&^r=!kI{Ev?wjS)^ z+n9HVSi|q;VG52e<^=CFl6p4@hZ#;a*X_N+mR@UOQy!Mkz<#{{w&Yin9<}&Lmxo6_ z8przG$}p`|G|R&U=G=%#U+j2T-<0mi&wnPWEvNyOHgJFJzOm{+o{+hDqP7wQZXQVkv!*nr_E6T*1nsanL!{AUI~VYo+;{09`KQv6ErrEIpOq*FGhh z)$8fvY%uK{#tyq?u>BHwE)tQtCow}*Q^`z#XgJ|DASWt>z+p8vEg#X?NO8i;VK3Y) z6*g~k=No_9F#+^ke;fJE3DdRLth~xYGlNkS;dV80DIe!|`3JAToPG&dC%`Lr)L3DmmzVG7$X^I3G=a z6g{wTM=DaVD4Dfv-N0m`ce{5~=OVN5`}-(VGZJ*3GUg`cbrz&}?fl90qxGF*a=xWt zQ@VdqaD0w&bg5Dewa;e?rK*sYkx@Z3#6~Gin-L>}BNyMMlI4B7bsJKEEWoivLM;Smf& z6qS=g_aSlLkFW)MwI#4jV^=yNE#Y?cePe$#i_~h)Z)vxPU2U|EW3{@;+450H$2f+5 zd(|ko@?Np}x?Bfd!~kd>9yg#VoW9DOr-xWAbZDE9yJDN_BI9?uZMBa^Pevb>0saU> z*72FvtRfkL2b4sC26Y=p?^Qfz1k5qQkCSQcEIx~DBvQGBnuscy@mKE^8O+Ae&yjzj z_2;=P9M~=+$&$s_((+f;GO5-IV>XhJgZk6X1J0Zv9ehY29eca` zf^Z4WCTv#BwCKW5U2W2qjxVX5<*3 zqkosXRsjie+A5>Zs3{nY7=K-%IQ1kV8sT4#_=aU4{c4B>u^d9;t#eW7mb-tPoOy;V^xJUE zx2_4RSMvgC$ET(VLAJRygr|wdyCq!xBCtb)O*J8(vQmX0h{`H3I2GMtceH7-q`%IFPQr-(hF)BX79B(<_qzmT_AyzJ;$ z-x|#)WgUqiJPps#Tl(}n5PBa`O7MMv|JV00Ys1tZgJKqyuwOct2_&DRpS&Lu~%`UU9qru)BzDSN25Q zjJyy28U1bC1@99@Qq*^Q*WRiF=1*pt!Q%scnkIMGg0B}fgYOv~ku|-xl;y)e(0xgl z3qBxfB|0*Oj@ER*K^m|+=LSy4-lYTk-4p~(9x<=(BuQeE5 zeEL$}H%B#E`>{VaGxB`09N!^L%x}9_fUUr`u3@B@c^;25+d&UW$%9+K z@muYKSuH=agkK$s2TuCjzMAgm7zu2-Y%RDS4!Y^Kh-M#KwAWBXmc#hB)_U)WAoVOV zawcEdSU>o2XkIch%Vi`*hIqaj2O#rwU|@f4iRWk0ovZ6$gk;e7k491hw8jhK_Js*% zvJCOy6iH|=-j$Hc%kq)NNjFI`T~-|Mz8hbzfN|kSuHz5$iE_p7J~D~2Lek$}*5wpd zSP(I<2=+=!+1j4+IQ^};*)@!g=ZblsC?Pm)X7$d7BG05pPHogMDe9`uS9{RJH)4P0 z*T^8E*^JEo-8x2)6=AiC@Xt4= zS9n$SSYSuDb6{z>=d@TqidIDm6ZBpFf*R|SZ>inFOxuM|gPvd`8F~gJ1WjMm-X_UOMMY$bHJ-xJvukN^H0rvr}2BQTgqOX zUw>|!sN1~Y4BxC*rHsjfGrs%^)A;l6B!!pY!t-#$jt;)jmF^(=jqS z*O`~zD12|%Jsr8hDf+F)wQeuBYq!vOl9U)5RrJXf*YS0HYv(de^6F~8l=`sv3vmHW zRM7CU=w92y-##}QH`lLqD6|qUqi+!@&%B@NjVAamUADGbFx1>*cWt7`_0p(K)X=e{ zyvaEu)d!2eP32235I8J9^RY#*oQLyQmeC%F$i&c=Pw{qL_ zq$i#ucb=`4H_F~A6|!AcQ_pmC)6BlPol(Ic`&q>q(eq|D=@9dk^6`jF z)NhY&z6Wo+YHJjAzuIo;h<;yTJGwC~;d*NB{7Sy}$>qKp%}ba_dGxp$~CyK1pVYsSoriMRWaOshci zV?{X!ejoDeP@J^$NQG*sn2M$5{AM!mZ0Lng%UiYSbzd%5JK9Fb;Lp!E-CNpXEgR(^ z=5$f3c+H13m9d>e;R2}&t4D9EYaRD(FI#+O)se{O?_(ZEGD19Ey!3L=+seH*Gva-g?_9W?%o&i_N>;sk)ZfxAph0#fe96-cy||Wfd8H zgf#4`UDueHDe6^M)@AfAeP3PY>kN&TF|Pe)3d_Y#7Z_Pj^(vT^Am!oUTCBe0evZ~i zGhbca+FRd(Lp)nt6?v~_R^~a^w7NB@ESJ8JVzenJu%N8RH(0HGuH)w+N(9cDajy4iocd7 zmNxw&-)H|ulusT{+u?X%;>f$3o{n>PiRWt$itd>5SQao57^TdN~q#HtjxhS?>jcG^s7F8cE?x1Ln- z{JxBH3w4)?NeY<97Yhy#6GDm60_LrwKDwkoOL6^4^#~(^&y2nLIk`|Tsm0n ztDAZ@@3u=X-^|g2`B$cHCU_y@T6yGZ)su@O-9FXYpARdm?#;L>W#`h#r0=Tw_UE|^ zyMO;6C3|AHyjH{EioeD1M!icZo^S5Iu6r0bOM}8o3k*XSx0u{P!=J~E_GTxhZr}d5qqnt$tL>WE4@^hBmM*4)hJTsu{30s;>Uz5K>t2T^5m{1O zqK{Xm|0QRzH#eZt{Dw?IL_&hc-1e6q@s1BNt{6tX=Hss_Z1+$;A?9y%)uAoLqCLy> zW|8I}rQuD5d}<}L0@uz~UE;zU&Exg&54D*cTBG4_yk$oEkhW}_hMCAy713u^XV=x# zJ`PZwF3P`2MlErdxwK4io{5D{V{A&Ku1cn`^xRvB{v60zg;P=2&PPf^4M?JYBAStqP{pE1o#GwyRkg2-iwPd*Do{CUb3 z<=i{hhmp%WcG;r4%}u45S5sYg>tvWs`a<5Qrp;$RU67;9qB4)y1Wf)C@yxFJc|89b zq@!wJo4!_=?;Ou%yH1{6fB%%N?xB04gZn23)i14InRZD`!Kpqduv@C^iv2a+$vwp( z%QEZKPe$C+lR6jq?u(E_(RB4=8oxb>HsZ~QF8}RSg^1)xgKV*)_`dg>K98RGrSHxo z^OGKGzjXR4_smvH%Ks*`NnggQ<93Qo;JE>zFG)TQgeq;|AhpDMXU1D0rTx<-KbKE= z9{Q$T_pRXenEsf{wlZIezFks}mv?xVW3kHf>fP5Cs%gR-AN0MIQ)xW&SGJvee(dWF zE8CQK8awA@MX3pi3Qm8a*2U^OIk$b@wB^a05ci_)4TqQJt4vb87%JF%`j0wouZ7bI zGC}F^Ud1l^&eRRRPPSC;2)o|krs1`f4a#f?yZrZ}xnfSncImP=X5AAaHVeiKZOzC_ zw2|{Fd4zYYmx}xCm!>F1*TxvZjz#w*+RAJ6jtXAqr9YOA?^WMavR8NY2A$eg=RS>R zAAR)=w>20R_HI8rmp!W|vcBXJSr<~O8mgUlORWnxue@q?ymoEWxtDi{_h)rCTlE@8AB)&LJ^sSQ2ewyy z)8YoUXGVQf;yqS-vD{^y;L@FM`~1Q-yj`?n`_q@leGOwW2QzGpn;e=ttW_w7n^*20 zuPTVpxZEgVp{9N9{Ge0MK#`?S;>Nx(J>tF-ab_b!vHQme_9LI%H7Z2oIfvUHgnQBnSK53ljANJkE0q-#I56Q8Fnqh*S41T23bQua~Il zRow5f?)Rz^1Mw%{3gwO_#cw*)n9r(jjClOf#WQ_EW;xNTNVJhfF& zUYOO>oEO1=JuCF>$7`0yPTjm)b3JFZNN@SkrZ&>`TJ68xdyQ}1}Pk-6| z@OtFDsDJ0X`ltg#Ma~zk=Oft%EN;l__(e@CH(9lk*K5-$`B~gL`AA&CZXcO?l|CWvHxoH}?XH(en(r_Fc4G|QMq>B3~b1u`>Aud8h&f9DM(-Y^Rm z?yDR%ZAi=2-twThd(!pP_LLSmn_D)w3Sx1k`3*ZD^(4r$za zaO;@&^-D9me6KE8=2TKPSbE|`V0g=x&w6}3cWd`aRXVZa?usL65_)GnM_WG143?dL zK{~1I5B69jHgZR__r@dJm>8M2883OlX_Nf7cAD<7E}`em^O$YmtuZUQDs_hHZj=ar zH!9|zbt+Ouzxib3shSUc9g7S3H%bbI7_hzJ?A1^IsJdJFcAus6)Zin@^Vqo6 zf7~<9_v>V%TJ|M!1qc~{5m6d%Q0QvKZTENw=%51zimS3c`f z%z0kZsHwP1%8SMZzlfj%rt=nW2(C-=S#?Y)Nz%F|B`GLFtNQP$tzMOAZSmf6fV7%zwMu{pFmATKJ5ryY znemLcX~i^R=v((UAMfY*1-veQm@3NnpD16zd+NS4F#BoGT#tvg>jd<{-+v(7Z^$_p z_-1B1#r*z@G$Rw`;wgCY%wqmzqU`K*hECp=s@NBsHB|hVGlnlNG$_Caqa>4h_r82JEUiEpgxP@$HiC#DjBo z^rl8BXlYLVaCE> zlWVH{(dEVG6t{WHs8EaA&Fi=5I<-3vmkO=9&YN8~w5NS@7Q5%wDcxB&b?uEy2v2|K zPq|_8mZJ;!l0*FbDDa=Hynu#Vy^Biw&M9V&1g>Qa%2aO<;5Tq4iwBNA_;k8`{X&yo zv%bZL-dOSWh6^3QJkku~5>|RGad^Jy!$;qA;U&l1kGZ8P{26jIXxe~wZo-#`=CP{E zyGxS`Oe=;9_1dO6mXfs@3ZntOuYI3cbzLgfKYXezM|MZkwNkl4#pC`)*+#JsFLjk0 z9GNpPW#DT67SB=2K7G_+XOP*0`F0sWVfYK_vZ)yhOaJCO-y+gF_SxQq;pP0w{00X4 zo3#>_De7AAu{&0aL+=avF`-kA;c;KNh6Wp9cOI z2c}Ql1Z+VQVSptQTL0KGu5kyHI&2mo6fZ#w2Vi>}}A;D0V;y}%kH0%sU zktnnWf>Aj8eH=LdxYrnlp-`p}G>vdV!r}xCZA{P@&TyP&Ndj6A!B}Dfg5U86Az>h| z2?k*)IPNrwA<%*ZL!k^b4#9C6fgA)jlI0-C(maGS8RQ4#3<4?%4ii|A!J!j_Twq9e zE`gAo&=DY4|8bD_AN)8)!wEvL7=gfE6Jskv`9a_;!5N3p6vr8gnV6Vk_!HcX5rRM| zctH|nIUAEG!`+x-IrUCrpgtj|Nsu!<*h3OSVL}2F$e?iPkR-*zB?dO3A*Vq|SPlv# zVAUU`%^S~tP&hc83na;sP{JV;N^{0hD22gX0eps&8lgy#h7(W#_){dP?g>U=6JwetI2A$Dppv1vG|tk{K|tAnkB>p) z7!(;VMc$9bh=6*hCqe_d6b8~_%ip!x(t1)&Hi#=u5m+yzNk zmVp#x7#Kl}pnqy?yzjCQEXcqcgVMp_xTA3U1bG5%IKpv|L>SnHgHq(!csPgC!GaXb z)c}147A3&Op7QYgo13Z&L|q`~>e;ioVzsQ?0oH9krK@`n?NqA6H%0Re$= z4hNdp1l2T#KS}|%;4a9(jRU|>a*zRi2!|RBC~XGrs9+Bq|0(WZTZCX(oX7E+25!R% zM}zhbLk+G_oU#LAo>g^3194d()bkucAr z3Rm1(hsVkAb@<(C9dSIcDRO9RsqJGnXdNAM`!0|4@eJDAX|{H5?``U;}}l zh!!YfSY7czhX&VA*h3b)6u=Dz6bYx^Srpv2p-sS@fwM8_yqqcl?tu?J!;``70`{5( z8i`{A`3A*(Ot>?U(-^px!uGa#o?n3gdTNGS+Gj6y&! zns_*j0ylN2B6z?^qY!~$;9Ub23>fHP@B_oxGX%^Fz{bgb9K39hkTW=fqF|5j{b#(k z0bzp6z(lWcj0UqI8$bch1sn%N2*D4!HU*0kU}Ko^%K4%HaFQZWi1mPtf?F@R2oo@4 z0vkoZ8`C%ezlz}C5&|b7&I45f-_JnUX&41i?0~>0qCg-ZlN~ zJKUT=cj3@75M228zA=XXIQ*c^!Wj%6pfHXy26tIF`@zF1=K=%XkN`bGD1c-91i#St z_!D3~xQ+qmah}`=h5(lVctP+e1t%P+I#?5ehfL5G;kgWt!}CCufCxYX!4;J=nMDDw zz~eBGNw5tB1tK`mwwZtE8wiYX_@NP)-SP=LJ^Vf>&W}Ej^0XMnEd) zt_GBWYwPMU+S<4tO=;7*nhRI_zeB7SYHA93c-pyp`no&r5CTqMEG@KTiLSAp(EkAQ C5c#qI delta 26089 zcmV(%K;pmW%^tPP9e?~%?A{7Gkc=p$C zKLCoS>dI5*vT40s^EUfccV$tWnP36ci4}hNrNspEznebhYUF!6jc%`UB?6OUUs zhQ({pmd91s`8AR246CqZP}PR4WD8YF_fv`JJkYkS z?zoLR;4modo_pAspo^r%9{t@|r~5{8KTi?7V*194BEnmMUv3yML_!r4`{5_L~XVaTU zKs|K%gSFr$a^)UG7S~yJ^Pqx{K$Kt~u>hz% z08|0W)Zff7d9bnY($Q0FAaR+;X<7y(K9G-*iHKUhjAlA(JP?0F3Jx*CBMV&Eqk1Im zLhl(3$BMpDhZk}FzKb-*xHh&N5wFd+EqDO@D7HJZF;GW>&m&*kYKloYpG)!H) zC90bBJ{Yo6z-8?ep#Mpu3ux>;Tfaq#0pjS{0~gz?2(}D3fO>0CgN`}FlUndBJt=Us z8U^jO-D56z-Z*(+slQ+kEfDCB z>N5Bvu%Btfa3OT_WI7AMBZ;>5p&Q8YCCQT@IaqL>terms82alLd|rP9X2DDpsloT~ z`M?APA7O>r0TIi=vxEa9{m4Fq8|xQG=hmJNZ-bZgybCRFT}jV~3%+$iO0uBP!wUd0 z*@;3?AXk5(33oBOyt0!9*JET}5J}FD^`v`#)yoax*jorHQxO+sz5+J_q%g2L4?Mu* zs9=9t$>>DSA3Q!N4`XQEbAO0x+k0-4(N_M**ueoTQr5JL>!di4DkKp3d-*<1(rgQl za~aol8YKSEw!xDqb{ZTH4A$9ZG#AI6AXLyS|JoPI%jmLKSw*G3ri# z+vO07LUgsIzP%TQh4(g`y_d<`(${gBibYrtJLR*`<_eHGhEk3Rj~YNBpa8a^j9@k( z?{Adj07a+DgPMWpDJ%n`QDbZHJM@8#`%z%l=8pH zfERz~!=>rsa3wggYChbTB+WfjzF?~2ysQ^I8S~^TpPR(FC<0USwB?qQI4c%=<;jLX zGOo&Ou~)INP!T7IT&yEv|6+C(1}r`TVrb7I3>s{(IPzG~saga?)Cnj!#4M)}ydSou^`L`q}%m{!#0pusz_D6af0@Q%8T?SCAvXzRozuv7Zd-nV_U(Ad?a30j>}` z0EZ>XVE`o$OLKStGk;ZoWGZeL4L9Rz>R zLJF(%7&4t3O!Wcs8LkQKWM34NmI014pl3-DJwlw;Fga>vY3GDwqG|PmX!;QYR}5>GSr_(z++c|vg9Lh zkS{!$Ya!qsMO{h9-V^t8tq+Kge%+h{aJt}>9L3?i zW4eGHa|CCpGMM>H3`RckRKz4&V(9z;!!(V#Em=G8EyxfGY)D-FljW>}MhE`h9{$$M zAc-i`>b05u^^eW0jI(S8VajV^FObb(B?W0aU3|DQ(*FyoFAc6FUzNxI>}@KmV^PYD z*Oftj$`v%#A1M&1*iL`&J98|{jo4lSGgn;H=vl!#8vdIB`6%MREkMU39)p(!bMspr zhpiiNr*W8$Ck#me3qNpG=?OgqCEMJ7Wkg(lO0V%-;tP)nmOC92ia#qmhc^FZfYh%y zuNAr|qI;wEFgtDkmk-wOe4y~;>oyMSaa=r+zP>6E8})e(7Px<;5<+WvEk)pPtIy;F z6kzW)Z$zgoSdIsb+3DY)Jj6gbhD;3r!#&@R@7<1iH%vH7Zon_<6&GrG)IH zTADBlVx7VI9qvv6TR#6~g_Jpa$l~>p5FiGJ9|?r^smPTY5;8wz3}N zb~b`6&t7>Dcn;QapRbk~r|C`Qn4UgO^v58Kt}S>&BDCktSR&2h8uEqPSfc#FSOVTY zSz%pr!pMODHc3NuHG3YU=bRE5mf<<~@ZXztKq2VC44gpg5*`2V<5zwiKNO+(I_m!D z{GS8-_W{*}FckSW*U?sQ^3%gS!VgVkXm}MYpT}9^|Bt0Q|;ei7xSjLUtt-<%&eX`aW2{c&?h4sn_l zn{&1KEfOEI{l_fH#A*BQ^Uoi@r1KF)86UEAlaT89rtNkoQhyQsxy_D|GFEpj32u^m zBo&qZJxOzAREwIfekJi^XBz38s#v+@%2zD%=+^by9a<*orB>1?Lyg|39jt(EIqOB&!c>bTU>Xos7A-5&EOzVk;Bmm;OLfkX2w zjbv4!uYHw@M_!j}JEuqlHJFg5 zW>`1|+EmUIevo9KGrP5={&K}5r(pvP8@YsjlAyqIBTYt{tMqA561Z?G@*4@>}9>D2_K6@oC z?aC@i0#Z)9=7@Y>$N>rdbYhHn#w z$`{==_V0jS{+%bBA}ps#)Hf$M#vD@@Aj@wLq>>7ws-dmqhzh7Ljl?s&QPVFpDR~zl zxPNp5sne05Epr`0R)2W=2J&~AKhOqqoHFAO1)oj_-k^A>D)wG~GZLNrftu{D@g|JN zz@1#0pYj8ScM7}5GJ{n&eb_!UAygnnI9kR~0e#+v(aJ|(Sw^2Y>|m569SaFbFm~{V z1|s=Dm^EB9|^q@Gwx!h<}1WP!x>YC}5a{HR?$Vb9bR-of$4}FpA`w z_26`S54)X32-axkN?n6hOIvp6S5cG>w=*0tWz-NV6Ou#w4#`1cBrMEO9hd{gO_ty_ z)g!r?+ko}>%jiv0lFO=Vq-H~)wYt*z&^uD&QzXmgDRPMS=^>=Z<4O{hadsGUsDF{Y zW#HKFnkh*~WzySl~SfEQ0D7k}m-t<%rp} zcP~Pw8+y&%0L)H4dG6uOh8qXEE`JcTI$*wTfiB8Au$YzY=p~HekZOQMT`+>2h8n>L z!-BWN(F;RtV5OQ#@0aZng5(o5Zj!-AUM{){44F5SN0ih`@zBY)IcEAlR)7ZsH!F#V zVOgG%5^G8Hxzm_?D0I3}2xdS}9tY!YAsq~9`lIlaL&+z$hd%XvH@0zqmw%uPZfj`Z z$)c(cHxx_m1)8vSzUrl~^~F<{BAHIGjVFxgZvba<7qNwzRxx_`FnUB0 zfS}U$GFZzfI!*pO(gD_9+2nmZh@{|m1=WM2;Yjy;AF{8kyUX{J!1vSEe-q zEiHcnw8O*Vtvr2Un+e65mkDPxV5jPtDihnu@u}02)CIkTU-+2uD-P!cs%S1b`mqWe z&~lZI&d;bSOQZ1%#crLXUTM{-0RB_JJE6$qLwV$@6$`uG{dj)&KM0cN$df?^6N4xw zhbSfiwZ_(GhuVu+UHz)Aca{F~`01yIyuL}2O;Z%<&ExY;l4YB!tZ%Bg+9YXl^SHbD zPgHD@+xvuu(LZjpBpUqax6Yo%+y6fP^3y}o+%%h}OiO>>AK%<3^(Lzu?EKuDS39;( z-TQ5wMR&LNMV3aVgY5=C&}Z9rxA%FIMb`Vtc);7?XaG$oo$dLX(oEl*?P!M{_%}Nq z0JZq|cR!jV;Ne+uM(7mEDN5jNTcU9i!vu>6TFMfLmP| zNH=an$LD`>^cfR-xnGWYRP7XWAb@$0A6jsBW{eg-(L`0g4lmf zwl{y|O-)RjrhX@<+|qR&knP?Ok{F!FdDQkhV3~0wi|D!Cj=+outH;Qf=K4XWPOVc& zXr`%SU;x3V$uW;=;*r5B;(^($vGy|`Q|Ed^p*MdJ!o1$n0fu?p1GDW+>i~`eRx`Jd#QCeJUac|3@iipUv1b)&~XZl`ZhgEBg?5<#-YVbUK4e)L;dDsmvm>gJ)J zk8Zo}9q=2!z3qA9CT-YH_FTv>c2b?MGYP3^^4C!^>yq399v=@ z{n)K%yClA`67r1I69(bmZif*bCG+~-SxxrEmcTi(0uDeW zt8dUq$fL2fAq=*9GexP1-myaM*}ld7RTN8{8#o3RWflFKlM4g<6I@wm=U{)sSao6o zDQY`7XCy3E#hf_EiUHq+-sl$Sy2s$l!`HhtQW1Rf2JVu+av^`krL%|@2kTlnOrUXI zPRfRGKm(CUUI)7)%!>{840;dZ2#%OH9_{`h+zvFThpQvA<^hy@M$LR@zr{&LaUK%8 zZkR+rt6u?I%-L(XS2AU|F`j=A>*6myOHa=0MZb7r;mJjTGuDnI+F_O*67fap0Zy{O zt5yh?LeHYti)a{ly)B3mXNSoH5o}LZ{jkGP@yy$_pk#?i=!qA3&#J7xjw4M{A=2_< zD7nT`px6gcK(M`8oQM19iF_dZ;F==-Z*dXJ+ZZb@8QB64p8{8Tp|?a+>u`FqIK2v|Cwh8Hr_-^? zW=+{4xU!_|+q?l1`OtrN3{%P`CPRkjh{{7DodJz^yp%MBxxrYgUy3N~xR~CH!+m>H zsP$n=@{$E5zdi7MKmX}U4THy$`<|Rc02*9GaYjhAJ2N^#A|W$R?1jzDW2E~Gi=j~- zBI+S~`oLE^+HjRO`{UUban&_Cvyuw9>Bx(v2%6n9;SZKF9;bht)kr~TRmoB#1YtO) zIHc?}YNv5H4vva4f5f_F!d?n1mIt zyy&TJ@amdE1x|SKSW{~Wy6A2c%k&ISc4pC=D5AYSLx*s{L*Q`W`Gq;mNn~JZq3bS~TU@w} z6*9$N6}7rI0)8`&V#$DkN0{w&Zt9gz=M{qxA^^T?G%`Ni1B)ptRvT1R&pOrxFbM)U z(5}Tl%^rWUh9X}-O#1`i)=OHWF-zIVm}v)t5v}w+~skCa8BQatDzBFBBvgC%;ms6 zYwjIVA&t@q8nFhAI6mtd(8BmQQQen|En6<)?Bs`MEMaiX2Ywh=$x^wg^+&@k_R_)8zigCXgA=i zy~bj#4y?;iKM{0VHofX{ZdSHBec7XC6y=Yq)yej)tZ{u z*@qHJskzc5=m)hG1Z{OfBtT*_RaLv|LYhl*Qg@L}UWMueBB{cxmLvi#8(9Xn)y{Ag zd>OIZkEmM+`F-LM!j^Vc&ep6UY_$7!H0$R7O$ikSR&DphERVy z0;m*%cP6;yl!^i5zXU94jW2U3tg|{Z_aoxVE*=f%5*{36T0$GwtP%YIidz~R+=D9tYz6<{H|9Y?=|1h}xpJ3VFk@WnWLDR|* zx3AmjXKA8b^oe+=riy`-#~~Bhg~lc3F8riK?z}lifncY39$N0X^rvjt?UaAsXRJB* zVRLEj-(R=Pqt?^pW;Fkkb_)BX`#j~Yj8xL>PB}#;Z43WaFpkB-xOS(TN9)Z||Cs_C zcpCpN)KdNM`1>UF5Mw^H#=`o=ze;O~qL}p^Iuo$KrX->5$-)K1|1)P-$nf8dC=vfx zvtSpGmk-~DjD_&HhQk!8#G@_dge8oTzP&N10vdIfgbV!@(UY>=)D`hND>iwo|Kt`a z&wcvqi_bXUJVzH-`KDH*B z=(;;~f$ga!Y2gOY-23-JsV-cQIm`^hz{6PFKfyo-KD2d9#)W_oylZ>XRUL;~l5r-l zbg^z%+je86fQEjvx~J&$TLlfynS0Lg!OEm<8nY?04x?4#6nx$*lTn*w3h2-WZ9X$O z+5NJA;Z=vE-TsURhLyo@=&r(wJ1c>z5LrE?(X;pQg;b;j;DbEduknJrct{9pY)C^x ztvOy3shE<7IkjvijV3OC+LnK&WO4osQD0%TE(^+^XtIXaOZ3dM_Sf#NL`cXugmky50{4jEghHAoQ( zfphS1a*G1wG=Mz30B&wRPHt{qOh!gMFx(mRw;7Ys00eUfLm{I7BFMo&R`4gAf4mj^ ziKhXD08~Ak0X%#F9zjtaAyIB_053PU$o~+bFj0WKl_%I1puq`Hg+f5?n2d5zS05PI z-U0qp=70VISZr7UJR%}OFaHb&$hd%DU>hq4K*I{|0CIV%Xk+CJ(1qH7L2#e{O2H!T z0EfGZa&dWid2w2~xN|~b_L8hGe*s=#xB~zPatFaYLAHQD1_o$axq$wfj1!X)pyvQ~ z|I4lmwS#+E!9ai~gEQC$1aW_g@POEYV1TFM09_SzfR-x=@)ueCFTzW}-)95h;pF*G zy1%3UNCbxb8Ej=^19fq=g7|SwfSa3J zNQ55%asz<8Z5+7%NU!JPe+v53$@7Q#X@UShSEwt%?r8{60N4)n^n>Z=ZsiFAz+oPs z0Kb1b{u^QP@BnPVHgJG7$Q}&A{3rX98D#ete!6@Z*c)KV{iHn}0QVoC|NJw1l9w$M z;_UMe{m=X5QdUzkP%~uzYvTX-WM!e=06z{segFrr01rS!SQsEAf4~h0`0p&*R^Y$8 z;Ql961!4yUi2T*;(<%K=!=8WNKg-{{!3y~AT$<1)(SiUh|7iRbw*a@z(-+VGv(o$M!@;z;qjnmW1;r^t^KV6`w#rf}&3J@Ep?H?P)DfpBe^maYCT*rx3u?cmV)AC=BzD8x`VxlFc8czmO1se@o*(NchPI{0H#?xOD$P zPfWxAAdx3z^&iB~58!%QeV2bMe@w<@`!C1?-~#;z3Ov=ZgL=UJ<$ucH@GmF;-~#^( zK2>x27Ze6?IsXfa0JvQKfjm!@A^(C;m7)K1DhS|meG(z`U%l}>6?6Zmw@fR`UmnpMfm(v;i)-a5bQ7df8Cso2MqS~cKx|qPuKcC_|JzD1o8&i zU@px=ZN$PH8^XG->t!gtIQG6s%rNd5X0melEy21yZgJ4lSnF~_HekPG(ndext?nqW zTuLv~-ur!RZ$gjkNY&~5?SE&H44m5Q#9W*t8JZ~le=5^BNR2_op(nlXfA8jR5bT89 zj@YBhSm@>;)Q} zgZdd8!KpXy?B%Z+f`W-hTGeEB%z%@4zA`_PP2Pl?Ip4KvJzn=-at3k}GHT>Yg0U$k zKiR`{e^t^2zlyRA*jUCKN%#1c%Nri&Ll)mXP2e@`=-ix%aYB@ZoQw;ZNF_FIqeD5x zrJODWjX&>nRdvH#Q7Bn*9M3wB>58uU;uD=?#S^Km`)Z8Y5e`BdY-QFFvZJ*oV6@0X&M>o3aJ)$yu zrs_K#<$1Kj=1g?@(QsKDTXq7V!}-; ze^TVuxCe>S;j@edb2%t|=8#W^eOb!Bm}HJ#rOn&fLG zssETMN)Vtl7isDzdJrvF>tI9m|E`D`687lV9}QTJ462-0c)3BI|J$t#iBz)Nk=s1O z`)hiG&fo*HQUB4mz@zZ!E-*Rvs2I7Af61u!CAZO2jV<=FhmkUTN8F2^b!j)Y15mSVG`-MIEon)@}yQmpV(sc)!9 z8nqJ}AL5kr+V>FjZ8>JJMC+Gi|N4$SX9Gf}s8iWbcrr;`%GTv-sB@A11tM;@& zWHRL-T?DEsF<_qo!Z-cRpc5%N=eO}1OVv}n_Jmr8E1X2(dILhKWVbC|6RCl$QtilP za?dsj(+#YNgv_^{a`N9@s)|+HJjc}ReZzL~d?{Xus`qW_=8}I-f68n>O_YA=qs@5j zM)4ueXod4^;8v>Ov_rNaswoEV(nj-SK@ttE$)>0N&+KjIE^U8CR)gU-9GBCMg{nMi z0s;x9E-TD~YLcI-3H|PwVHVUSV+|=;s6GjSOBDWoz>wm2!GWgyPZ_cqi9(JlR}|>M zq>(`*nYv_m zX`bUo0TB&Sv19m3^L+U7)S?+7<}HcMMKc9SY)tL^XReE|ZSVNIEddZRO<|(B18$C! z^qH>3Si&ByoU^$(+E~DH3x}JCbjQ>N=y4rG`hDlaTlB(KfBzUSjTl&}4Ux!(HZjX? zzPOWcCwiS&TBXpiGFNIzD}M%XS(&U;;6u$!5Ze5nelzjHOGPUGakkaaxG-eG>KH59 zJ=bU)vQSN3>`7BPrW#bjB&xkZhCu(hD;Gv2Nxkj~r~0jDM=+1@dSht~NKC887eh-% zDGFR2Vd|e=e@cAz)IkqoU0AkdXl<*`pP(4y6z#nC*s1zk7ndHrg4>yL^RbK+gT{K7 z%)p;ITOSIN|=E!PGi(h8R0KTA(HOYOsB&%WJ!@0|S8 zLXh}^Ii39LB;Tr~6Pq4(3rp=gv;2NsK>^?*hiM;+Ld}VcDjlD@C@P3erucZZWDFbC zS0#sN;5_(h6Ol(!7NbhhNfM5&lX=OzBj zjrIr5xB5;+PK_BHKeBgQV%aj>kX!4NS}D%~e?nu;FYKxrLpybZgMv(j3@16ilf)*+5H2Ih4w73w+-X<|#p=M0&?&Uzn5D+ynvf zN(sFq{Y~i12XQ}mDOfGoy`TO*+6s1g%#G*gr{uD()qFf*rpWq*thVxzZ?7Bw?EL6` ze{hwS!-T5La8`C>m!x?)frw|pOp*^9B|5W;3%qTnR@7FL{zpbg$s6?<%6%)KcVRzW z_?<0XHxLW)O-^7`b~D>qAzE5Nsc!9{ye*;AVn0QSHADTa!P#&`r8zvEKfpl% zl)SF283h|qu2Cs_snv=u$h=ubzBPgGe_Y&18THt zA?0;kG_Zs65WGYC@j7kB)L3sowe4|FdarlktjxX5*TKwB9TP>xcgD7BEMaV-fBDzY zcw5V;;$j(%TW#yGxCjnNX>#OI9ULXajJ~-nddS(HX>!M;O`psG|sXo{Kt)|EE)c*S|cyk^J^-3?D1rMNWX22HK;8%8Mi=DFbGId(|+>Cv( zCAm9BZUxu3{St!jhjPRXJkhW1Q9FyHddV~wynIASTmOn;s3vK3ce0pAUADezf`DFi zw*j&FwD;nn|E!JLm6Vj5e|Q`~gz&{ET$KPnSxv}9UH*ktN!m}leHESxDydmVct7)~ zuqYQxoJzh@QNc1g8p5Y$!I)tb^2p5R;-TzC4ewyT0N1(R`HPOhpCzK20_!?OdiH$# zRX)(6yd7$R;e(VkdyF()Wunvh(e&NTti|k;5ozK%)I|^CuDFP+f0t{=TnVif)1Tpr z?o9G{-weMwAKA4`Ml zKtHBFCh>0!XL28i`+{97Xhb()PYmqfy56YtZCT-1Uk2KLWXY<;hB9+eH5eZh{ZLW-4quanTY1_|Nk_{<%Z~|ps zY(R{P$If_~5j*+AA<4mN)O}iV93+}D@3tgFNbLnAz8RW(e~*u`pn3;44LmOAD+JQi z_btPPN$~MUkjyus3;0L64Ak z#03Zz$9Ve@#%D#sJ^Xc$j>c{~W%v-aGe$R;$&lF3fN~z87H!4i@p&cA=0JHfS4Nhh z4QBB3J)YD>e}Mv@WZ_0iF6@qZG=q+vy7He(wer&GA}zji!*lbiBP(UZzx2tXUHcDl%khyIG$xcJvl!cUWsm;%Ch>gcF>|9t`x zCiL9yL7a6vm=Nw(OOQ_2Ye*{xKwThOhhXm;muU=Ae>WAGX=+H27SID!PI@P~r!+8u zRpyIuTj!|#x$dQ-;X&{l65w*JhftH-^OMeNM;B+zh?s1?0=m^xauHZc*jI{pFvby{ zrN@9UU4sAvMWYQ$#f`px)}7WTvDX1B6}WBq*S3;jF(VYuKH-d|-#n+a@A!a@is-C= z2lXtwe~&3($8UV0!{{q9z)+!&faoFKN~|gfRLc1EscCgA($i&qw~>_b@}|GDpmCbW ztXe`_E+Fh~)q;0*c-HCul8BJ$>ktywkr?Q`lF&j5YMDyMj$I#DNAfR>nBTPI z8$WXLL3Fy?{=5mPij!jT^GOimAU@GcCC8-5e=FA4PHEX=OB&2FvE?g3Nja*H4Gr^v zTeApTby<%#7O%{aK_^I@ht>40e-baoU3pl-=6Mg8;llO9c ze^Djocvdfia$AG(#Znjes>K)u=RN1Nm*ytvz1;g`r#&CSs@Llt%JfGp!Z;I}LX7}V z+zl=jQW`9KvBOku4Lb_I#gyNQeAF1J@u9k2$`IE8`S;x4&~Lx~^ts%%vMUV@s>qe$ zlT!GVzzM`Fki|jVK-~+@K((3B_t!eFe_(Idr)Fq^O-U?8Mkm!$LXz&A4g@U6(n?-# zZgI_?n#05dq$or_EuP{^>f~xJD4BrKL#sEga+B>dB3vc>B4#XbN3ytQmB%GnJ~w$7 zcF&ag`se74HSHLvXzbM4v2B!u34SC-AG0~AT{aib$OQ_FdvbWyvh8W$E+$6Ze_W*V zgcuaR#Rf-8?G}fq%G!k&lIMM;2EIi?2m9?R(>L)uV6lWF7E;;|zV5;l{=hMxuy7pS zJx(Nj%@S~uLv|OvPokHLriZ1GksGF6^FGA#hwE%qk)>~(-ve__Zj?86^bcb8>=ew; zq~hPj;R`7un%PTzV;jyY%G8Bxf9`qx5fQSq=N>AmBev$MuM}TY@^N#uD}5IYoGDF>~Ab90U|un-@3VbciopVqXy8f zJW!+ef07>5yAPKrJ@<)vRZ1#%u8L5|8qBoO>!K0ONQtsjIM#!n{R%~#tD79h(L05z94+7nKqzBI?7_AwPEKG_1%Rb5z|2hD=PiXmxZAE?6~>g z>_wyuqe;B`V2iAGvU$FqC_gNz%;b)S&1~2YgMz2xI>MSz*+M_ve>B(bX;5;vcST$k zExZ~Zc|d~>(XL!1T)1=?V7_}7N!*JIHhC(bVeLrfBxR#2k5ZP$T3qV0!1clpjVOBAwm8I60 zzuQi)A!EjEYPl{N3_{sdx|V)1>6&_)Yi7X`7rjNxIovRw#$u1&P0jwMjo_8#raBD z?KIZB8c3j;=X=p?poN9&4KQ%U$XmEw<}gD6qDzqW3P@ape^%&|p)j+B8=UhIIqPF6 zrQ^h%o(K=w5AD=)SY6A~PcuFLfhiB}EZKT;u=Nhv{TMa&ci_b zGtg}O%ftAAxocXPl6l3vMW-e%>sOaMhYg-8YghZDNUd1NMLGoQ1Q&UT^6zJlFMc~+ zyQddBNVa5Ke}*R)SjE57u4j4e$f#W#(Ka$FiHq5+Waylx9y}$5l$95`+kATS_7}=p z@;j!!7zd9_1g35p8N>(%ytt6~S;pH05t~=q*e{e=UaVseZdcyiUp7Z$^7TqbXhf9FwJF1S+mj@dTG?K;wH7@w{h zMRZT%=y%nPL#yhOYiuZV6U7Wc77_6V*`S#LXZ(ES-XlkLNcm`W=+1NQvv2CrTi#i| zSOf%P3^^s|I`PWnNbWIFg_<|49g+imrzGs~qmR;Auk9UW)>4_hBduk%ZN=+$%FL$| zUe3_rfA$x7&h5D@VyV(4zh@J#eb1%afHd+ENkU^xB*2K;bOp$_bt}Wmt{H0k^~JU) zf}$XX!exr-4^G^oFEb{Znj!L()H@#!XdTFi<4XK#2~O1xBn75pIR#kMwr+`MB-zm; zLfQE{edeSqh}Ti`5+-HmzMC4;wspO^#Hgm`f3Up6k4uYwlYBOwOjlOU;s5RuXrKWT z#IR++cZ|QP@~Q<<6m-fB35@5yG?Q0KkR#POX4| zd7DA>kQqIIo$q=%&lGOv$bS{`hg!`C=Y2;Md^d0CGJC9{1Z)yf~;gzI@nODFL8 zf6j`(oS!cQ&gJ|p4&@Bi%|>G%A(dvr?T$%)H85q?n`dpfQAAg)xnAbFL~Panojb)Y zvCBDe4bnM-sURPZ-QU&yTHrC{Te{5^tIhiTPpLZ(+49I7lY{J zy54?YIrWoLvBz@voOjHVJ^iaq7frIyXd`GK#gZ0EGns5uT3D$-2s*EF<<;~`8{a~X zSbTfa?pQ;~giHqaj`zTl-3h=UwV_nLB?7Lrtwmb-gZ2HPVlr!$CfXb=f4^)^HKxEC z#5wXZ&a_l~!s$8JX+DDT%gX7(X+Mo^NvL^jcY+W0 zsis)pW3HFe6pQ(%2F~Ug;!(kz&C9Z%pbSI8M$HS8UsYZWIc3P*;jy34!l$>HQq$kli`rh4Lg(B}_DoK)u1ivLmSs7-b4@-0pd!)&MF(7;C72Xly zm>#|7<0;!>Akli8e;ty@V01jUJVR}U{c&{RlX7T5hA6!OmUfp>F~a&)z>@dHi|u(L zXyqMsEA}qzd;FKro}_AwX>t3mUVXKD+-kOl;hzUS8d_gpNPdGCWSsmC0G138Af%tt zIa*WZ=C`0&)g2&Ae$TVDFi7fnMPla;n4deSKZ|K&v_kDXe<93r*Nh|Lvj|s>cy%Nl z+T4A)FuOkU(hQeY_nhItU$$=f3)?irI1r}5=S($Hd@NaRGm@u;7iwHb#Nul<9mf~0 z^ySARQvkdR9KUiKgeMpAeK)hphS6lP4}CtUz|E~GlWxU>95af)q%Dfj`ytfItn$B(`%g+pnz) zU&|Ade4w|hgzs4(B{K$&$SFKvee9eL6}#H%b5F&Dee1#l0Utg~RixWEu`Hmz{CTmM zEAAT_77Es`H7ewhxz4opjwKmWwiHZePw(a54Z&*8e^s6Gy;8l#Mog4SC0n^>4T{ze zC-fI)%u%VptQf%(8DAOvY8g%Gud3-diyTJQ-E0Hl12Pw}ZY_Zj=~KO^Z#tS|)CHi*Z!?T-)nk&qF^N@3Ik=`b zt4N(we{VJ?=YB2^AOy;j6x7F&t55V<5U&&)M4IYG4R728Dvh_P!^timX41Mp;b;oS z>Q1XoEa}N9MpQEp*wE7@D7IGfM3T9%jqO}(NKlLRuZ3RBaIOaZk}8BqzFwBJLsQf+ zXQ!yh5Iy7bPlg$a(@b4%YeI*5=AWs_Z@8Fnf2~tA~Gmh9LUsAimTu!5mtH6wa z<8(H!e6SNpZDoh)ozOr=k1l%4`$}V!FP2Mv(IhXclDl3Op~RoIwTW#WXO%*G@Yp_E zmge4umz!JvE1?DZBb&48 zoyX#Oijyh?F&dzs)U^n^n#!(G`^3X-c;W%CKWUSgZ%fSc-$eOxcvvFUp<3o88Fyco zHH&kt`UyK|YMmok^>-01T?m~|RoW!%f0?+#u9}Za`wg*v8&C5qg6Mq zx7OEMcip@8I_K=O_kQ-XpYyK!i`{my}>3c+Hrh?1_UHj)@F(Qj8@ImGhwWa!x8$W*- zRhnd)*>9XVX7`|f#At^gflpMPLe~4pRg+vpkbpwF%iO>SgSXidMLV0eMH_zHJL%(1 zHwmITQk*o1THRr;mZx1A7J%P;t7~B+k+V6zT6N>teRmH^W0s>X&n{W(5mCB&hB5hS zleSq)nUbH>X2Y@3;tLaKqoB_u){VZ;9I3ySZB-{1o}Cjjt>K!4lia1_ z;_oX9W|ultaVuY$cHg+)AsQjMy~1x^)jgTCjinyaS|tY))AnRdvW^{Lr0IOn^kB`q zH!sa}%*-{a67-T*SH5z-d{-^>?n*T^#3f=RCjF#SuCllG@7E_6-_`2)D>MJ?_CAT6 z2eIC6V!>5c$K02GU|TYtHB{Qk`6$TW@Ye88Z>OB&%Qy7}b2?XhQ-wz*zEzz}-|Y=k zInYsVop$NzJk6VfBTbi0Dl!S&+O>U$i@-?aIpz_&+0IH_;#_2L>k_vfpLLnOc5RXm8lwB(dgeJL zXv==_sWmMP&EKUG(Y(+n_jB&J$1iQT#!Q2dDzO;V(KZ#Y*oyd)j`O>X|1Ao+oOfIL z{8^L3hAm?ppXG)`EzvBD8fPn|bUv#qL-xU{!jvZFn7rQI)VIt>F6rNOr`A+1J49Ef zhXt01W@UIhStsRL`7mo?;f3Q?yAn+b)c=d?3$xBN?a7Oqss7o7qkh8+werC|^=Q_8?TzRcHYV@`Hbr(x(j-;<2r8*+1 z+A}Fr(+i&@dPw7NQ+2D-RBlGliBE@L96sIgLN#7qMjc70yB=OYS;8`VWi4~rbpER= zL31DNQK@sDyh*-BR_^Tkg6?xcb?bI~l3%NDpHdO!+G(;INmp(u!g^mSxnX!B7Zr&-Y;mbFBv$82)I^}8YxkINfoNGPtCIDahU zFxyfx{@J-k^0MT*{nc(ejaxR)YUg6cge*jRtluf-_@9|Fl|A2Z$Z6L8WX-2mwBa?G z(7J^}V&}_Bv1F^yCC9uxoi;je%x;dcZA?>L=sNd?mif5$$6xmSv!egp{3iOS=Iw`A-v*;3jfZty}(FHR%9opLTbVKMFyB4QR>ydN1 zYD>F2-*~OuAurgLaHr3AP}%F6hD@jGXzweWx$7cdY01(Ne`Fh~GE+l^>6dka9))Mp z=su|<6PO5VkCpb0wbqLhcTJny>|}4hB`dJM^s3|w_YwZr_vMdvNICV!&LmtlWo2q# zWI*7&$rs7viaR#CuW?^*J7f38@=0S){^={QSsVM&k9&9O-xGT1%v-fJvy;PW^bik` z>~qUGDko(yq`k-Gl7@Klo2ZYo584@&<~Y)Tjw9*T z`{MI+JJnWv(dbwqS7Q4(%lwSUeD%(@c=7Ptl`0(Rn31s1+qr!9ql+h;6YAz&I;vlK zsyoQyc(RB4t_zL^((SFIiT&dDYTv9i@2(m>PA|WxD)P=u+QL=;LR;y|+|uV3RZpiS zdUEfa4h>WcXlCW_)3b=_N}PD_W^aC!hsykGf$Y22s)c`An^!%?(hYU54$ixiz@F4I z@r=D?pv@UX35r|R&McELF{!+Fr6ojV%Wffw#?KC~<^%^9#CEuox-ZtMBoacoqq1x@Mbl$gqu+Y$P zx!$A}f4@Y^(N#mayCSE^_zse~dqzh&bZV)iu z)+fVqz2;0D@2UCDNFYT=9o%tGPB2r}#Ct)}zu_(!S8cCpn?IT@5in1nh>kV%d^~As z_lZbLHvuav#g#mq8rXjz%H#c}vC+H3LrTTXjGDF^TLo-ARUz%xoAYUdjZNLT>Csuw zUi9Xy^fY}D(o!m68X&j)a->$dir1B@vhq_oADMg+LDGnJ-vaF*f%2`tNQ@&t1t`i+r9JVdEuF%;Y;2#!yVL)o5i$vn%H-aT8+dls#+bGBu>^>5< zd2J1~IWJiH$=~V&oLQ^t`g5ZW=HU+8VzhKlCq*6GU@eupEY%~WAg@=?UMNn>CI3}g z|C46yg4>C++9hV>JN7^X+EUR%*=%3;l-?)at0*V%% zR3L5y|LJ6r+WR~*e_fTjO?T|G<{i?paiJ5bJ#UL&AKyJ7&m7?NkKyjVxh*ws|I5^o zZCIXOLzixSU?S0by#9vHf~gK&2e)(=)lOehR6p=n#EiG9t%ena_QhVuF7=L^E2otw z<685jFE`Lts2#f+pM8I9qI3NwIbDzTtM%l$)aYK)&!~B8@)Gw4FJ&uw+9Izn`E;KQRzD_{rNwO%T}s% z-X7WFJMRxep`Dxo9P=8Fczfk?`qr9kQg>PlQb$n9$yJd4M_N||-xPSG&ZI=2AZFLmo0&mn$ zAxh%bXFDt}m`i0(4NbaBJU)I|CSq2|%+Bg6nX-$bY--4zOEw-YM&d>a73m47)a~;P z-T%af-K%;ner^_dRp0PZ%FGi55M+Xz}#J`5Oit-k)j`b{oHR zAW-Uc(+IhMEsjRZl^q{T%nN(!=iwgvqTjiG>;)|Mn3jdN(BT13xi@R*UYV{x`s0>$ z?LKE2RMzNaHf!VARITW}xA$#xF&eY3ce~ZrX&rB*EW-rn{U4ZQjZ9u$o`&z@(v-XH zxzIgFJZ`mJb)9)xS8MAG(e@qN?@789NA5Wjm@|1ohxI4pz7gH8&%2)+t2KY0ZIDNL zG@>ql`GAY@$jW7Mqf#H#7`lfmf*+cApZd3_s9v$*EczpOk4V`)8I_+p;sIW=aXy&yG*K zEq>Lu_eqHBr#)8N-)q0Q^r~>ZXJuMK-z)UwVn3Ol`SyWo7oYUpZ>`!H5E8gs zu5C-)*%_Rx9o`)gyI}V7&ee+&j|itm+dkV6S-r48<$zUkq4m~J{x8+NXG_#73L3X= znrOXV$=J4Hsgd=UFptEGF{*|h^@Y)TpU{eB<#s+ zT`Kgk-);E~Vvi5`<7J!g9!N-$|9o!Mq=Cro75f%7u~`-W#i;)w8etQq80l7fv}vFK&FD-sHDY9Dj>Fxs>(QI`j+8oJ zRXnOx$=I$?D@}HO`-c}!>$_e=Ulh-@zFu#z-!4iw=#IjTa`JTa>!Y{+yk0bG9$u^8 zGLU>W@2O^c<<;m@OEn6=h>Y~^pEvaL*|-dKVGUtpGb1~*xLS4LV{tn*gr^H_^l@?7 zo1h^K{uz^0yppoS?9{OVJ`rWm)K81fg+;h?D(GM2RC93UuWAPCD)P#C~QlPJ87rZ9LN zijf!ttwS*a#et3cEmz<`mV_1(3=NVsd^5pdG;BjqPzxw82uiRh90-b01o7*1mmrv0GfxdLvWm8;mqKmOz=94r8v0h5S$`e$O*84KIS=L zFgOb=PBC!Z0ZZ^oM}P+Vc0uk}`f-Ya0Yb1C#!DdqcEiyTIE%s25eQAffe;ik9GFA- zC-{yLg5b3sLIPOBj!6_WBa|5eWFO8Ji4hFnhSMB;LlQ$VxD`o~hCzssBtO*vZX|RW z09KlXOF}XT{=K!ipXdiZP`+c(-B5HCO7qrHD22dWK{6-|YJ?(jXfMb=MPj_o6v|NW zWk6O*-ep*nfItY&BY4C`<1~-HX@GQ;gQH^!UX5uQ=XC^4W4w+4%Sb2-ApPuczyZ85 z;OAvO%EW!2lL&*bBpfkKgQ7qeWJr_;E`~&gk;)J?F(?M(hyWFVvjFBFPV-ufVM$)y z8NggWZvFGpBu>EK0)T^w3jw^qD<|MpK+9kG?-vKK0EBQyurv+RGB^-ehi3*wFa(8K z3fp1tc8FRf_FjChzvwrC`w~Plk#i+e{cXekb?RXLBZt3p&A1l zKp_+f2m^y{fb=LhgWxBq#IFo;UsWPFkbxb8CI<0APT=tgfDY&qgBcDeE(8`OAb|)4 z2ZD1rkJG_{B+S)dGXu|jVB=9Ruwn2#0BVMYc>&m{uN^j&|DWl{0c;=;f@C2Kj1K}w zX&6WZ4n_i$EgbYLToRyYu;2E6tv?ubBm!?HfMS5C6_f-d7IH!YB*8T%!94g?<8LJ< zfYRfwBRQ7f8yT3nP%vg0o?}1)yuCmMz>Y}@<$;yLL4OVf0^{C|y977z`bEzn^+$6!S8SQLm76od5N zkiv%_4Zue645bBKVxqd2IYg+fn33agwr^$6@d+mB4{sof1@z@fZ#|t{RDXB!vq2(E5`edhA21zwkc2QvesA3UYNU!*ZSVq)mC(l6UL{YQZG z59j5fPjKK19yH5=jpQ8&unG?+@S>+-)&rzW@B*PY7A%EsNQ3tQRAYh$(;R9=Fd)Ep z7I-iCHUv#dAmPB^fY$-;A0jxV-?$%0Ga!WFg)~COIYo<105LFv2dq>Nlnpl^(RFps__s6H0W=T{BZ>6 znK;8V5xuo~ixwG@ixwL!UIf5rV6b>duIYjQBJ~y_B(2YAD=hebm#k9I))w>ibMo;E V@Nsb!BUlneSutg00}Dg3{{afU$}a!_ diff --git a/Nfproof/maybedetangled2.tex b/Nfproof/maybedetangled2.tex index 4942640..c86007f 100644 --- a/Nfproof/maybedetangled2.tex +++ b/Nfproof/maybedetangled2.tex @@ -47,6 +47,8 @@ \subsection{Dated remarks on versions} {\bf initial note for the previous series:} This document is probably my best overall version so far. The immediate occasion for its preparation was to serve students attempting to verify the proof in Lean. A formal verification should avoid metamathematics, so it is the fact that the structure defined in section 3 is a model of TTT which should be verified, and further, a finite axiomatization (mod type indexing) of TST and thus TTT should be verified in the model in lieu of the usual statement of the axiom of comprehension of TTT. {\bf This program has been completed, on the Lean side.} \begin{description} +\item[5/5/2024:] Updates to the postscript. + \item[5/3/2024:] Added a postscript commenting on philosophical relevance. \item[4/30/2024:] Sky points out that formalizing the new cardinal parameter conditions requires $\lambda \leq {\tt cf}(\mu)$. @@ -1384,14 +1386,14 @@ \section{Conclusions, extended results, and questions} \subsection{Postscript} -Inevitably, philosophical issues come up in connection with a system of set theory proposed by a philosopher. I get a lot of congratulations for vindicating Quine's foundational agenda, and in fact this is not part of my purpose here. It is not even clear to me that Quine {\em had\/} a foundational agenda in which his technical proposal of this set theory had a special place. +Inevitably, philosophical issues come up in connection with a system of set theory proposed by a philosopher. I get a lot of congratulations for vindicating Quine's foundational agenda, but in fact this is not part of my purpose here. It is not even clear to me that Quine {\em had\/} a foundational agenda in which his technical proposal of this set theory had a special place. The results of this paper show that if one really wanted to, one could use NF as a foundation for mathematics. It is odd that it disproves Choice, but the principle ``power sets of well-orderable sets are well-orderable", which holds in models constructed in this way, supports most applications of Choice. Our opinion is that Quine's proposal of NF was based on a mistake. He discusses whether to assume strong extensionality in the original paper, and his explanation of reasons for choosing strong extensionality contains an actual mathematical error. We believe that the correct system to propose was NFU, and if he had proposed NFU, the history of this kind of set theory might have been different. -NFU is serviceable as a foundation for mathematics, and consistent with Choice and various strong axioms of infinity. -The type discipline of stratification is unfamiliar, and it has been remarked that working with indexed families of sets is extremely awkward in NFU (and would be similarly awkward in NF). The view of the world which NFU supports is basically the same as that of ZFC: the natural models of NFU are obtained by considering an initial segment of the cumulative hierarchy with an external automorphism which moves a level, and NFU can interpret discussion of exactly such a structure internally. +NFU is serviceable as a foundation for mathematics, and consistent with Choice and various strong axioms of infinity. It is odd that NFU + Choice proves that there are urelements (the same odd fact that NF disproves Choice), but no more than odd. +The type discipline of stratification is something that one must work to get used to, and it has been remarked that working with indexed families of sets is extremely awkward in NFU (and would be similarly awkward in NF). The view of the world which NFU supports is basically the same as that of ZFC: the natural models of NFU are obtained by considering an initial segment of the cumulative hierarchy with an external automorphism which moves a level, and NFU can interpret discussion of exactly such a structure internally. Unlike NF, NFU on introspection can tell one quite a lot about what its models should look like (as ZFC can with its own awareness of initial segments of the cumulative hierarchy; in NFU, analysis of the isomorphism classes of well-founded extensional relations gives both an interpretation of an initial segment of the Zermelo style universe and an interpretation of NFU itself if one has strong enough assumptions). NF tells one very little about what its intended world is like (it can, being an extension of NFU, internally construct a lot of information about an interpretation of NFU with lots of urelements, but there is not an obvious way to find out how an extensional world is constructed from internal evidence in NF itself).