diff --git a/diagram_patches.pdf b/diagram_patches.pdf new file mode 100644 index 0000000000000000000000000000000000000000..1c3043912a50ee5f1dcf96cdbd9ff1a2f148cb1a GIT binary patch literal 40820 zcma&LQ;=rS(ysfJZQEV8ZFkwW?JnDPmu=g&ZQHg_ueHyA;zaCyvFFtokux*joFihy zjQ1gv7ZIanq+^99n_V1Qh2|h+Aha{Igy!LarvGhXYvycD$jZXNM)=(bj@~a{MLsWMTap_F#TN}9D@a6g~O#z z2}YmH{8%r1+%O<5hkr1$fkrZs%~Rr1>t9X^rWMT!$&?;=5F)5%f#t>%HjC_(N~BI(*N6Qi|?;F!bt($ zie5894qNq!5#`I*a@=El0_V(C=>B_ZRc_|@?U)C%KwaIwcV{Jm^z}Q>r#m>~^)LLC zUbYkXqDiQf?-!ip3w|r%qedwl5|@a#nGG;nShHC|6v?yMVYa}f_po)cvLISS=nW2i zK?BtaA!&1atH->mCxfoX;frq!uBV&^riGf9vd5UCdVX%#Q0fsp%fG(-AivQ*y>rDf zo4B28*%-SXYN<-?9dzzCkrcVGQYVCeuj7}%h*=xUvw;l|I#y}=dvrw#i>{`6#Caiz zb$T?y202sxq}`Q#jxK@^!rj;_wEfE#7|RNf33+q)NS*!75ul*ULKrxwss$czwFJF* zp@U1+&!-lMY)`YlRA53_sKojgG7)qdw?v^>E3@ciW%yqKhBHlWyEGko_;^ka z0G9P5c?)o>YL!6O_D~-2r4wtZ0D@?yM`Z^nwQ)HBMF-jMBfykv07=F+;KBu{$g09A z<7$ZsFet`$6v#t+;+|WbT zc`ob(qg?}IIvXmj3Ui=}OH2~k$F{p5IFoGxwA&suw8DE0Un}QA=p7@R=}`z9s7&=0 zPaPk7l9%aNDgL;qaM-?b5g_@!tu$ch2n(nab>q0|9lbXPRf5u5Gp< zy^N9fsk^K^tZRm{o*sh8f#)XW1`w$c^)*d!!ldG0F|@aM#Ac>8ahYpoqUIu8T?z2Q z3k>^-4HzqEsnx8!M!Ar}`eDNaW9=xYM3KyV;l%p#UB6i`cNG<$o0&Z|$M48hE`iB9#aVQGDtLZ8}9q)itDLncG$lqJwNAq6R6(*9zW|FYJ{ zj`}AeI$Svx8rSoXJBaSkgNc`Jd=3;=1%*vQZ1ukyQ2wg{82rByDj}m;7qdiXpl9Pu8o8&E^N5w=1whcv`w1~g z;r_-bn*15$F$tnG|6e5-;KbHe*1=^ssO&G}nb!rX%b2MDDaf13g!fR#jxAk~JRXF(WjrUAl@E=nOs@pT-Kw1AU1cL5TmU?R-)^k+idNSRIUK9}S|J!Yto)s=E^Ne)u`O9L2e zCaZ+W#|BasVhc+?VyI~A#Vb-@lhRpb(pJC(*MGj|sg#YbxP8H!G;BRXNC*`)&R>Xv zODmf|DqJ*<=TR`YF;|h#B%Io?R)_;s zXhktGT&}nIQ43t;34Vf4OiQ(a(xPjr4rEZW~VNWV`@jT~qYLnxR`nlOL zjwa`YN~g^dI&)=TP4U>Rbq*8Y2g2R5svDiEE4l4^Rs9REQrG*UX{FGpU!9Hw@aGxPiz{$;tmDW@98jt7EDcrxIuv(h)eM2U+%>J)&Oh^M>k}c}rysqR z7P6Wv@9%~TPblMYC*WaQkE$1x6MefYslGtbGF|H}@5g~vkJ^JWz2*T2GGni;^R^xp zKrN?(NPk&tgRRhRHPa!krm4<{46psso=nXcmQE2Wx?p0foDcHX94(}J%Wm>7KYuS$ zfYxZ;!=N6;JUsf`lJM$`Q={Z=U#fK}!W;>uK zsPsrn(rM=Ac^2Re?VV!X`JYp%x@0OS75veM3!RphR8|*FZ<}?=9ig-atjHYEVm_&H z0s;4I>WO*;U`4=n4Xf5_Se&0aUyos3@MO9S>u3ENFMMfrFm?c=HrUL{JGGw2(p$qY z`Q(&^E-U?dXyv^o4;+iOBsXXswo%R<0JlqAbs<+>shC z3l<0qR{5a^QYgcjLKKMH^D@~moe6_&1r(-Q309_>^;EfH5b zvD$&;R&!DD$E=ivz_n^=<9xaYwiLAs$3yOj-Us$#C?=@T zx)D&?EsZOqT*G0uNgN_JGy(pSx&jS#Jv}J3-w|@>mnkjSwvjTQfBpTYetV*5tF&4A zFKm3&RCOht<6~{Wh{XtQGce(rw>UxFUho59|1~B7!g)I?$-RS7tVUZ5JROYXgj}C& zYUxo)HTxoDQ#r%J*Sv5d$Aja~0)|AWbJpG;*~-Yx3(q01eTG2TeLtXF>NkSj3nxg_ zZ%n>gM39ZWEAT<=kUqn~SNA-j*MUPo0)`ZZdePop?qCNPp*WufHa&j@EJHw+p@Jhr z%6|H(Luj?ie(kcvZ59V|{E;qx?A1g;l5OKqLt>GzAoT_5$v$92#UbnfSjhv3tLV3a^CEdVgZOUj(OleJ?bI!_4hATD`}xj zE3w{9uPk$`FGh}{etXfN{ZHv+ zHMmt;Fpy?WxnvbXQR40(+#lA;;4>Do>|f3ZCxZ+wDHi)hbu!;3!)q%Lps*=Oe}JiV zy<;W>wg3$tEX!m3AWu&~W$>y@xu?E3Xse2Z%zW%z~^2vHWJF`}F5^^(- zVma~K+xeMT&&59Cao~NOoo~Q>ojMUAhui^EU{L94yQj=Z)(X?0AK>-e0kTK37ia5HVgo4~CxZb}4XvfnCZ{RzOB(@y!jdb-Tgr%ciY#Q4Lh1r?^g+u;@4K@I- zBQr|O@bs*6o$+U#cKK6aZ&}Peb7uQ1`I&Eb*VWu1@#}Y1S>|h*#@9F&FM=^X#~hq8 zq*}SmlG|-A;t7iW0`7;@qz^s?pRUI-#t(uC21J}(|9N5JPhUsfH3V$3QcSA3qM7}% z4WS!L2Eu$4%+#C(7K>#ejNG=7%S2-PAy1lbu-P{HVRqx%aUjn^zms#id$YvKUC&K= z`;nxRy%eL~{#jYmnrHfw$tWNN*33CwqnQIEr4!{m<)|!1g!Th1h0)H-Q>ft$mM2x& z>^?obSso+5v+XRUv}9O7DO4@2xHE%x6UBxPWRC18t5-~H>L>FqG>C73r&{$Kbc0Y*lbc?SDT zD3SeVbG~tr_G1ORdd9OWn`QI(Kh^Wbtd7_IlkAiI@m9oj-#;P^1L_X3k{Gh#1)lGq zLxS0vB54ZeLNu=BY#Z+3wz~4Zk;HDoYtcGow%bN3lDIP2Al6=u-Uv3VmEzxiw1O^j zpMmscEL!*hOARh9#Ns~1qE*T)XZo-ZtM#=PyW{Qmz~ilPN)0b$*v*CUS@kC#xs_Su zWmbwgs!%p37DLo%f(>2RVk<2KMSM$HjxDXh+Qhi0Q*WJEmHmHyU%7*c}(llTYcLENJ9+xa`0dx30IK_Jli7PoKugM ze)}-!qDk?1xvNhj=8O21*rwS3W}j4EFAl?2Q}uj51`g^AheJ3mfD(2%%X6B;8q|{{ zT>hcHd-GcDU=0!0pfKgTu-1NzouZM@=vOtJ#gtb#NRV&ObGWFd)hQD+s?8e?Y_kB4 z)8Q(`WeH(eLy~muOn&v+zudweAfiWYz%7mW#mCk_Xo9r$zV`;9yx4kJuK{CNLBxCZ-|Tn#w&?)lRCp?gXrkY)A_;hQWPCXxo-M-|V~*Su7+YogM$9mZ z_gF{Z(LiXdbat;gxCs&UO#*Of1nd7>ckXQ|FFq}|8i%aW&qt$-IoLD?Yop!6g+h|o zPPLP^IfAjnEC#)hpttxoVXv}1J=E9cTcWIhSE7Ld{hq$4Jt_E?QJ%V1irZ)!V-8Vt zra^=~K6ay4rVxH6IT|`>FA^B6+PGlYeBsuaDa`7qgxE=x$VlLwQK5EfVczPzA2MPON_e*~twGVd|UpuU;IsTru; zRYEQMp%nO&-<3IGR01iQ6|^VtZ9;6xmt|nTe2{qpX-P}u1g{>tcb@Z#3_45(eD$p_ zTV)jlW(7*G5p2I8`j8`o;D&Y4j2t+$$)w2g>d^LYdbHhRa-z};HTls}dy+-UG%2vP z*EAa+cZ2`(P=VWXvI{90Dv!r2ju{P_M42zjkndgTo^MsKzMo`Pg`#2Ku<^*LA9=IIL@pS)%q_b<9 z-oT;^$a&G#Yvb{<^UUqj((<9tW9?qGlbtH*{QG+Isk`6OgMhOJ9R23bPbjG{9d#0` zfLc=X^Llds?mL*StH&b5&78gyxl<-M^>zEJlQ?v45&M4pEDLw*?91`O-?4 zjB!RQyD{SU(TA2!b11B-v%V_Il(%q#;V~?@;qdL=L?HE~X0gosjJOG*Jp#JIZi#ee zofvNVXS@3(_UHTx;qk%y+Z*I-jjm3BYUbLwE*CkK-pF>%k~C=#9B`r`PT7i)kS=qNp zm+;lx@MACTo2SCf>3#R-likmT-)3#k3x%F0;)otCxe!CC3A_26sPUO+;(lHw_d!>= zJBikJ`up|$z3gY(MlD5m!zuQpdzIBo8QqVDf$#fBtnW|sQct&Xst-+$hgan_=6d~8 z1vKfqvUgQIXJGXRpi{2cCw#9g8I^T9#f9|Z9w(*YQp;W67Sm{hC!ddevAEd1Xa8t<@2Be&%UOXjF!cDIp7X0Zc*-K@qwljw62c5$wguVzWn_B6{k zE`Y7%m}KoWPCG_cY2vz1sSJlgdn$wTY2hsy4C%vRBu z*Fa^l>Bs)p{M%$tSC8Hl#7A>pM}&BxS&55}@BFfkb6g#6oRXYvyNHv^LYm#h)a!G< zeta-|8E(Fhev$4{>w9wS`;7dd5(OK9F?g@-c@8%PxxkRZk(>l|2@w46s_p0C5Zj{X zOm-09%n2MU-e)9h%PbKXdE8*|0a~vUIzwEky!fr?y3J8-+iH3?CUKM#a+}Kb&YJKe z^hf&e)l`)Y9@Lz2XWX5iI44ojHp4eF1&YAQY`vCF^Nu55!J~!HST!P6LdY|NKoe87 ztK_1JtK{zwv$vlHUzXz^AhFGS0F%tJN1wVMmvpCfCe zWqA`&+yR(lkZ=&x#>T~7LI5ObF9h&iVtpM}Kg0BF&sU-KuskYuh+pIngb)x|uzoF{ zC?q({qEIi;d2AMtJ`g}%9hZg}9vJ9Vkg%@DA2NwU0BIk*0nGdkXc5VtB0Wh4$p2BK z?-Gw;)%#l)n8TU_NS~1rDO>Lhz==TtZ3^NK(nyF2Q3~TKjuXb*3orl)H01eF2oRnJ z3KWb0@xQ*l_Cmy9Apka^pBe+P4>iCAyvwto9)UN3ed1!}!a4YVV@1a%!Rem@gn!^M z2`?G05m8b7TsQ`-bM0B!juUzGjw@;H}mp1?oa z)hM`o@GsvR^?`jhS3WTYADB=q0R!3u!b_+>`n7cPz8{x)n0|;7$|3^FkN_7j0bXld zKYn(GM-d@kus;5+RV=Tr_s58mLH8HUz2xVx5CfWwKuiQ z1NPmYaA9rz>1e;qeUsea-Uy)Y9eI>fyDLjU8-rM#Z|?FCfBhpuh?Wt>bPSqN z2;|SJ(7a>=e0eP$%;DiZb{n6MXdmclEb!2C;@R4qSWIhl$VWZK%5m$=+E^r(l#Cu> zL>5)Yzj_#N3n7N0PcwW;yKImfIp+r$$lwC<6k+6)&-ZmHh`l&b$z`;Q2N)ed0(>06 zfigh)X3t=&MDm6F^qQ!kfb(zXuVzqyK%m|-KUkzy(gzrYrBYd!jfQBuHXPjPHlG1cV>zhyLkF&@z8JTgu#gM?TKK{)#!c{#eH zHzM1h$LDAH$O+dUB(ZFFB{-J(+Uv)ZhrX#O`?YKBuCp)8!zL#T0uu8H6^ib(x1$L- zhio^_7PptF*iBk&JoV@tf8{Ki-*8r5+hptcy@D~>SAa(EqS5?5 z)RJArJ3K{)+HzD=Zd|THX1o4-npUqPx06rxq_T}9CJqY4M`=zuluh_7pR;Zk{RcuB z82He(b`iP&r}us4OC%T}wzCVA{^6OM>u}9Xo4R0^adA#py2**}3~Xk`wXc`mh0S7V z4qEq`ZbF_v<8GH#~k(T{MG zv^TuIpJaa0&BG0u>%9?bK7d5%LJbwhxAEM*IxGWWo=AMr2`S}bCy5#BvJUfd@|3VA z<$KunPPdhie^5hrN(_PBJ&R%f*YY?Y>-Ktgy1+)G2)#fP-k(?3vn08-oJ4wWcf!*t z<$%(iFnU{H*7URCl&!5O@HmrV`p$AVyk=!Xst`ErZBW;1dXo>a*35WyCaJy8aNS_c z(ZoBrw)06Qd#qLeu9Dt9tkhuU5Pw3=V{<8_GHOLSu1jW+#H3Lc*Ua7!Xrr3;N4LSV z(bej$wfr$J|7MSUf3320J5-W=y?a?D5RX6wbS-t0@DfzZjm4}yRmiK73)e8BD#yOt z(HFDP%4i(k@%N|d13-N6VKDpAv>c>M&`1KGyAMUr@{sIiHDxOa4B*ITBDp?sN^@$` z+13NJvZHry+#KaUuDa~F=kZ25LYCJ1iaivG?cKnL0we&c*kY zu_DjR7-UT$GOL(vZ*uVq=xNh^XB6vCs;6^^UXBFH==*A_aFu(T{?Muuo?uIGC%{eii zR~%V0lX|1GYo}5V1ucrblWEg5!^;4`P<)5i+e;&pB(LEKlRUCP)zHjm|B4+vF z(`o^3XLplf@_jO}GdIPP_}jDk?=D#f^A6ql)11h3xx9iG$k!c&WOhp#8S|XWXN)8l zy3K?jZIZRlN)DDuQxJ{2wA>)TX@W|RqLmPRMS#TGqlynLLQ&7po3@i*jNyx z1m#g4fpXQ>QA?*4w?UjV3Yssn#0*5u-`|1{Me7@RpT}$rqxbQ<-^q(~4_eBa6&WYi zMS)-|)GE=jOMIpf1o&dDJC$a$>(dy!d*wIb&M5as)U>G7?K;U$a+vd~;w~WX_RL%C z=yI=MJvCy8<|Fg15w3-->E^DO>NJ~2?5IHNP6@FHHyzH~@vgCYe`?9zB%cg^s}OXD z;<$Xs=>4de=q^WjVlA_{ah`W&qCP!VF(Nm8v9sa9qbdKmyj#0XML8tS_L^=QutJSJO_zk+@y4G~F} zB&oIbrXY}qRm=BPzFJ@AHmMO=&WHCcKoEe_<~gz8Hb7V@(l$kwo5yzBITuh-(Wk}O zSgUkNP!c+d4PDBHjD3NNLF1;xe`5u|D*I!a{gipT!9=?@jN^X}_vj`I)usWCnML@I z3O4FG4Y-yqeJ@fjxLRsI6uUkuwrVam0v}{r+wABm%l~RkQDr%`M|4iV<7>x}@g?`v z>dH_~PJ}9QL)Dt8BzI2w8H}6OT)?2>yDPNF<{^>R zl+j6RegE#;ScgWt0M`^xtlg5l$2u#-QTD!x8Ca>V@y6IqckQ&B&njvqYeyPtXTNSp z^=?t%bab%is6R_Ea1vt{?7xR9tJ1A+$F>rdc6=ECia~I0q%k&c!)eL}n&BZj;Trf~oX$rMSfhN{YNx5e_)!y$}gb z9=#n}ib(-5QkPKD7k+w#9ruwU2~M{5qa_Ao&k8xXxtRA<HcFwsh#NVFtJ28U+YMycjw_yO~UH_j)ofJ_W+EV%lx~Ez3AxN1VGL6VUt-YG;l;! z5#zGZnZH{ewL0NXrt#<$k#fCQCu4|0c_v6!^G``UIiKIzYXe> zb#F4=#{sG1WmQd_9rSBu_HVnLDhIN`(u?qC3^Dg&~}JNAqghQMs>p4N8P=7J~PAZHu7j4>{zE_W9(VF3qjgeU6ULu!gU3U zPD6YHokW>)a5ca0-N}qbmOEf_R=l<;*;EXs z$#YBI_Hc(9ndMN!l-k_3nOGUUy%wFrjlpVtOM+097VD^zhp8)uTX*g0wsk2G2`L6> z&TIOZGBpIP@nzlUQRfH0hS>PEVs4w?x!x>d#(lmupVPf0M9W9^iv~hzWlP4ROfkbt zpZ;uy)2#15hlh@%>1k6i4zXoTJD9&0l;VwyqnTh2v^BpR@>Irc5rTiMl`}W$80z@+ zK`>+Z;*c}sr+a=uIjr8k6Lx%u(vGTGr#{*yi>R`ZGfu* z+0pjqS_vht+}uyql5cK_XVTl2QC2oxm!XQ6q0me!LUM-=i@3%RKDW*x$Y`KT@VZpPK{G^26SOunC!+)t$@wOB?^+> zYjkX~Ylj-5rqdMiZbk@v+4L7FDQi8{MkEY?euPX`lM1;fi(xGbAtP3WEax0^2dh%!aQikskh@CseCF@% zQO)YKJ`N)*O=@S?VSQ|yEgGlO;wJIaG*zRLYpo@WwoKU71(nmH&g|){CesDlPM*Tg ztjJ0zAat;+wYm;?cQCV4u!+_ zB|1I$=OaiQ&?h;h{6HmuKcGlJcbbY3YmjtZz_;nkF@ zUcs{4-CZH`>yVWy4#Gv?|@ak|ZzaVxeE#%f?; zLl$hB)H9A4iQ7FqxG_d&Ec0YHw^h(Md&knQldzc78>7gowqh_fu3d4w5kD-LRDY9H zmnkXm$5)c@htIr{Lx|2!Z39PIblTHA$_LQL9F2~nM2UR7dm`0oOFX(1D>)YRlbDql zT4}W6zkJsQ`DnB7aPtN1Jm{E{+1!qR?{HV)U}q4pM8O4K_n?}n$4tu#QH8s;BAA-Q z&Qq<)Cz2gHr@Ba&;n|9zR=j9=dnUg6DeV}!5&1Bq*Ng;;m?zl{=NRm8@)l`v#}psQpb@K5NaH^LqBgXp4U9rS|ykST^@Q7 z!_GS?49hl?FY2}}FJ@}E^<3zToSwM=MZ%x6IVh+uXpLa3li0^E%O*+JzAK@zc;s6f zny&5qIZlZ5R&k!k1+v5LF1eN=GZGR96NwzhrlbWFV`uzHomRSW4hpr2i|@4Emka&H z;~zfdYEYmY(Ptr*IF_2?6WIzJXZei*0<@+%<-^k-oQkUbu->4ppbnV#86^3#fo}Tl zI6(=^C6Z~JQ!5f`j;H-?Hxd%@X1f)WeD3>XQj~^%LiM4`wPGB2)!oTDMAh_C(E;Xf zp*^zQGETm=;O9=+9{M_OXR_F9E>Wg`Pt92=Oc*v#wq8|3r}3smS6-}=#w9TmjI(ez zy(nYT`%`oSO0n({L{l!h6xE=TFg7WZjkpZ0@*KMdoM)y+Q+R19{uJ`i6zFxa5Sx21 zH@#}BhjL6R_?U_+{}TE2`jAd6Xay^an|QVWA~!S`npsIjSZH(_aQ`u5g z8ue(40df#xKGgQ)NNI*iWE%xDF408qCCTPT>cfHuQ9=SUU?VvSfX_P+#T4frM|MTv zh_K)o&T?7a-M}-K$de1wk>~Q65eQqeG|eRgU9`$4kV96%R|Q}1!Xy|`+2(N`EBU;m z@l2S=wL9euGxC#nA2Zx?ZtxJ3DziQ)c*LzMi+SyaaZn~2!!-4Hh=%e}im^hcK%&@d z86oRhTc1~x@b<#ye-b$aZvFdGQzo174FL@rS+Y`2Ej_}pRq}At&f+i;zXjy)_yLpT zeR7amT9%BwK|)YKD!FE03hZ&no`sKZQM(FL&cvyE0vBCy=M0^?tk-=6%~EK~xL6`G z|7-3vVh)wr$b{WL0?hspq3{qzq->mDs~!BIup%Gh<@{u5e3GJ!!ie!<@0T|!t+4d(G_r^3WYRS(N_`X(P&lArd)uyD!NT^o>|UTJu1cO7J?y78}9Vk%tNU-M{ z-IhUl^{=gI-8~F9WzK;uwas>OG#T!d+T)VV4WnLU=<;h;pKp(Y4If-&p^H*6fR%Bs z6iOTJhPprdQ|mG4=~evx{dg#d;%&PY*Hsz<9eo5}`fS^ay5CzdN_x6+i}<@UXSOif z6M5h zTmii8vaPppEylmO_4L7Oz31|dJrX@U+8CWfjr_4{O>D*taW4A13}-&R|B#yZ%O|sp zlW8slfCisAW5|!sK^X#p0>2-Ql7|4Q>t~r_mwIGs?a5@^~MjEb<_A_ zO{-(LB4>g~XOz`Zj7jz0#7~c6Gtb7TWk@_)?(~kDns@8-piDrv;)Y)F@$nspjnfAa z59Sx-9NCg4Dg-Sk#JoAJDsg{Wc(8J7rSbMTwN-K)y~~H5Ec`|d&z6wu+7!)x{~etJ zSI~PeYO@L0l!G3tM{}7Bt0ZrRw&eL?2ex{L$xl840qSC@k$aGSVrXw1abHc zRYdBph{9e_t;0U@oWQ9nQzH*D9r*i=hGlW)7(-Wc(J>baLI&{FeMaOTdoK$lkpz{~ zh-L@IyS)x5Mzey@N-~6;<#em_-~iV)S!|Z>UouYY<5I$Jf6Nez4rbWs&`zmODQ^>V zUf#G76tAD7)8FPUoOTRdF2qQw(Tk^6L+Oz9Jis$;k8B0h`)hnv7eflzT3th9sX860 zab*Mevj2kDVm#G{y69BNecB&Ygkkd-Txa^~VY+sh720>~aL%m?@6Iw*Jia4k6gOdj zY8F3u)^+2 zn93N>TKGK`8fTJD>mct(CF-sJ(j(g4o=kZ@Zw3)MYECQOrIdhISBoMpVbhzFl|K|V zRpPf*2#PpR=QkffW`g(iC0WI|EAT}@dzBhOv^Bem`#B9Z8ElfiKTpf0l$usWn4^We zlac>UWD?346sf`*9K_M5m;#s$#*y1Fw8^K#7`WH-e}0H>jwE(X+*_ zd=b8zk1`Uveu78*a!$_0d-Qhi&@XGu<@L1h3?uFSc5+6vVpu!(j+tp0*_2tK`>9vO zQ^__6| z|A4rjf=B%yASKiP2~x5$a{dpCWFq8X=4AYz-Txm_amltrSm)GYi4GlOVDC#GB)RZA;h^Nq| z{{D|aE&yVK5T8L5XD~3U7zZ}@7!1r06hLU;5EsTlK;V}XD|e|EVr%cY}!Dkx)Z}#8TMJkq*n1%Y?14}HdHd|`YI%3v`T(>z zYPUJ#f9f;<;IfD_{H@&?ApIlY@ZdZE`7k`pf{IaaC`c&DGVm`kIY_A950D7vLWNv@V6+38@Fl-V1K}voQ;P ze)ha;cVGkJzrMf7cXVDN+E z1WE!B^78T`HUtLLLI5tUPC!5LwtHvrK2wn&aePV%DSEf2@OE$IK{+7z0Y0yN@VAY3 z;2?ye}ffF$z*qdOC;rnHMe#mB=tr^Pr|9RW)JB^~zNZHcU*aP8k2*l6C6v|gtEPa#F#ziXd-414wUYVn>wqcXBYTAghEY=}1DHX+O`moB1Cq}*x2XZyMT z=~zL-AI6C(pFF9!Wo}~^-U5}zkz4g0qnq6Uzhqr8=ros{x9NiKtdp9}ShXC=#v#8T zpx#XUm=%u{9WWy7!25H7WR7|supafP5KXo+AdMjk;1c4Nsk(J3W=}zTQ=WF@AFL0Oi6^(=;hH8N_$oCqYhXUsMzY$ zAyw})bqD9x(^Zj4DP3_k|C<;)TOTfNM@E4p2abYL^E~IlCWR({rte5rXP;u9Dl z;8b(~+tac$^n_a=qsiGRl3*m7b>{-7kfn()Al$(xBKhL3QXT-H=U zI&vSYu`G5Rk%S^^SYHJh_!{hnJ)b?+nwS(M`zNj^AGiwR{w^(o?_3bSm=kpz?h^?^ zS;4n*sg6yC1LldS9#v8Gw!|6f?I0I(0x$i6kY{thN4@t*U zUf{g}QkS9GbH|0*(b0WM;m&3hT`aYi?l{7bH!C94jOS7wM#92bSynL(Mzo?=_gxXh zM9NvOz;;Go6C?i4s=&FWQDMXDaA?PGmH6N)bKM5HuZ+XUUiV1Op?v)Db3~1LwH|EY zSF4RC`qg-RGh~{PI%8Y?)`EnRW%kxlvwJ<^^Rz77HT_qfx;|V$6@xGN z>IP^WVuYk{@UL2?N!y^poNB4M5s@uU5!Ncq_t7QV*+t{uFM(<=5TSF2X$5K1w0v_*V6qB=$o2W^9NJ++vCb?ze($vsQbg_L#uy?wV zd=i<@Dl$u8a41S-WAitIl}iFzC>FnnXd+R`3q*Wc z6KqwRCKNsFIn4diJz46NC(9KLp5oK5l{ejE)yp!-B|srCa}$aiO4daHM@a9=C8OW&3J5)Pgwq{(gQAn?@vMm8KM*#LI+R zv9~F1YR4rj>g_@bCa7mFSA=MUK_vn6+KSw7F(o5t??OMz?tkGd3|1%}=UmT)CL($@ zs63lS0Jb%`#mvox{-6?DfcTJ-Vk2lHXb0W^Tj8{n@_Al>pu%4Gwc$Fa>{ZctM4oP$ zn$G#l>n8M|3nWO5GQn(;-UC2!iyNEgECwW1=CpW76DWz|vQ6d^aU+bYvw1k4vj}3X zOZ9i0+N{NBVeXx_{y?;>LG=07>OlspNEN!`oPk-mrbnmCZeNmEkNKi-H3K{rR#XpG z-axS&VW$4Rf#cVP>RS(o8cy-=gJ(z2;>Z2~@!&-k6X;te#@xV|iVBNN%gl3hQT%VErMfM;j zF=d(8Dzu*ibaA$b^jGVGI6liz9~hx(wRPw}39!rHQtzjgDI4`Kai<5lYWK)YZF%m+ z-EU$~JUiitu<;gGvYFE({0%OA4CHGQ?2V0~v>AZcQ*v_EZku^@U4vbE`tpwaQIAq& z;6g`gysXcx(~@aNj$$(-C9tEBLuoV`yu-GU^tDG48q0D+ZNI;khz+X@uPp6Sp>zc_ zRqBvOy0z$l*booC09XC(AGdxio0As0_g~0qZ&PUn=X&Ys9B`zs>&t0H*}6e5?ceQ_ zl~j|F)HUYU4INQ;5(Ft_nCWXjVXmn%#v2U=D^*r?vF;@Qq=XZfs4907lX#bz5OmHo z$pEPnQMpUk25G(~ibn>TFd0zKLu&^%?hq40c5=5Np)a|$52tE!Z)#W}+_cHhKVo(^ z_~4C4is4i|R*lCn}em%;#dZ(gxO;ffME$i0*w8LzGc+Zc;jH3=!+s;8&aS{z<1dCTg;0H;Htn$P}W9`DB119y*Y{xzHTpuy%z5PUKXJDj)c7+}?GiRy)qNLr2 zjGfr!P!N4HG1%6Oz?(}SCpMfc$ByG(CT-&sKd)gZttGgJVXgc_cJ+=T=~7w6n-wo~ z#lguLA-5eb*+-o?>$RNq4wG25#?}0$Kza~-SH-YA?bR*s(u+rC!G#zAmX`C_Uq4lR zuG))^clwm7MERaT;um!_;%S(2vC-Kb1sHQzNiyMeO~pB2MWLC^IcRy3Jgx^Jl!8HM z>QzRSWr-MQn&9w`vVe7-VVfXp71^AE@%Ew&|Gk`CN1Ga)tsFyh^(!8E?ogeUwS;0N z$CvjTyS4KOueW#O5Sk(*b{fA1A07v|gdEenr6!BA5$BQI}ExL`d(E6IT z9u&Q{?j;&CW#yPio)D1pQY1w~stFf8k|?&@oChObm2PwQB}cDeIVObjzd zfeW@u6iwZ8)9ClL_sbKIqaj$|6qT7)lCiJDc1ASczWqLv^31d$f^lP!A0WmqfATh)w5p&lPgWfq=9L-4Obbb?PTan6`cq+L=%d3jOJ`c_$>*|l<49)NcYbZm3XA;*HMHqWiJC$4u zJXOrH8N*w_3Q-->Zs6Y)EhlNCf7u#6YVv@BCHT;i@uJoYx(g4)Uv z)})=^tHl^L?KrR=KDE5T5OOueKnAL{?4_32?#3K{FDdI+o4DI@Mi%O*&zsCa7L(7_ zFk)$Sn5@;>4R&(k@zkx9(bV8c}(E`hILEs z;D7WIp5OBI_(!xwkA7PvQ}O;BzFn-+1`evS5%$@ELnI0c`tx!5ZNew6aI7{O{QN(R z-7}bIVS9z)v2EM7ZR3n>TW4(Bwr$(CZQE8(isVZ17b$lCmAkm#XNB2j#^QuDnqK1V zpOrtZK=*w9Hrjp*ba(_zx!;wSiOkODj8=2fhkVV2iL4oM$%K@c%NW0)G^YFv?SHZ z7=J&}=6r{Z2})MB1$B(idU@ssiRLC8PxraDZ(@G>tP%Tc!A*3NNLyi5SWbk*d_q_wrW1f)wD1v2ry0(mazcACCx2WUACe#*k2YzOV*IEM783YCt5`^>jHtS04E- zDT%qmdpq6mG1G;woGmA|7XADDeYPII^^>`+5=eEai{5LXY+OF=k440-R_`oyCA3G z*EumPIC+BmE>8KZDVwm7TZKPOfeA~W!^DBnQ;@Q$9>*+$rxvIT=i^E0e>B)Me7i)d zSaqJ?1j9SNB9n~_?CpeCk-SxekXxJ|=$;B|JcUS9+rEc%?`1(UG@~1@T#SiqF_`4^x>Aw7a+)w7F#+X$c*W^*1ye)Uo+Sj#fkD;)Fl-rW-seq-UsB7*F-J zuBE4DkX+$}`T_e+5#yQPw-Tu^i(?gOi)31)N}Nd-G@XA%73 z<^@jyN*2q}gvh%Ln71WhOPP>!s!wO1_FaA0gaBl5k&hSX50RV=&Ffjv%!`qa$Rv#C z5gUXE!zU||uawu&(;*i)GI7Nd`tRa88TX#b%` z&+A62qEwMd;D$b5Cf{4dfkV!e`oUa@299QW$FBG*(eOc4MVas#yMY8h-?zg+qIfVz zQ+&#Df-S~s0_0uFhUy68<70z;z+ciP(Qu6c91Z0%)Q(nJsGdHc_ZImc!=UqiAH}*sm`8Wm;C^f3s)H1<)GADu4 zy=)@fG;|ZWF`u{>2J!+3NxW*&kULa37>~8fNUJ#;GbjU;gx$gU|ag_!`0ZbbgR@>G(Bj|L^*N^a|>;=qX?j#IXTbKBt$ zb_$AB?y=Fgx=<6$N+uRa5d~H5P4#$FdqNqhZrr^LWKiy+5SyurajI@8S5)wJ2g~{W zjmcNXvne#D{V}N__WbUdsx@v-=*RY)QW#16F+bZoYvEmf!R)hEw~26aLuy>IBiM-O zH&59c7CvB9`bfK0B(5(1h%U013UGyAcT>Be6QCln{cl5VPV;g&ewg|4QY z#w=@9RsKW-DslQJ%rz^~P32%uobhA`jxk<6R>B~+ZuoQEohwd@T#k)g5+;9SuR@hC z7cxBjPJQ{%e6^qs7>NX71iqa^O3!K8f%+XoB~^~4gC;&QQ?~D!OFSjtP$3!Kc&4nn zRe|oM6UxVu*h7Usfq&E1xgzXXnnwlH{qZxXJSV&}nf>ENI+>Q`IzRFR$UEdtKzxT? z3b0+1Z)JzYWB+=LLVYp`;>%y;_do8*T>u(e)k15aR0uS^em)g3OVhhv zE_~9W2bIJ7ulpdcuCR@|iwp<0DVnMjDuS#e;tt9;KzDeTb>LlZ&METGJnn{MnXd&U zB7<`JR_tIVbkl`xKwUt;4Da$W*}4VAw}5)?W4@-qkA$Q9sevXl(mwM?`#gqIXm(hL zKl$xsiyH;F)a_wCOKfXm>FcNsEZAfx__lpHj5W%X41YRV^%lQRQ_qMjq-$-<>q$3R z;}W%@ZE~p&G;U+m8=mfB8aBVnXL0$s;?%E4d0wlOCUM7;tqXrWP1v=UUwv~-pqgP% z?;$i8xZcMd?fS1nV<)V|4#Y9TnIz6H1l$7`B zniV!BDUXFS_&_T}EhU0H5ZkhTg8Arr*rJANcZQYoeW#x(C}eQ@clhxC^_&*v(ffKD z|LH^t5Zt-d!{i$E#Nb>;dltRpLYFzKV6ga$kIPAau+ShkGkIOXdqTDA^IqSMnrQAX zaiJEWx`WnO=UUB|><_t5T_PGG6}{xyKkpjK&4ejoWNr3&%A49Rb@U=OfyKO~&25}h zbent&wMyeJTa4$zYc6ayCdcUgc1uq$d%p7-N}WPvj1Qd^7{0*l_?Pw6xHy}WBs#l_ zopn=JYIpVoew+UjN|&4AkMbu{+Qz~I3cvY5HV}_xT-UC?f~`IJsQ&@lv5lZ%gIwHD zA;m~J+jApj$vjBlmKaa*BlRP0#irBbIf=3+l`>8^OVv!@tp|YU6G1DTjAyl>eLm zRn`LHd&~+iT*%L2jY$vI_$yAeoYe^PS^jkZ+_Y3gwA_7UmlHmW0td}AzU+B%uvsf=;uYo4a423x7w zV3rxU88WUd48Qv#?M*bi1~GvQRB)U=n(nfTna{EB35hGMk_gY~hYhnTyabJvo=>6x zor==LfkL2vzWGDC*piuW6+%y;iG9wiQoIh_9zKdGejc$03#O>?VlO zUS?!Or&Xkj=(8Dk!0aQKHhH$~-7`#(>z5UiMGx39sDWHY_42G!b!-4-(nhv~pAlw}sgf=I*BfV&Dthk7L%C=!x!a;ON+YAXb6 zV7)N0f~F5)1khgCe_?q0@q3~tl+lY0a3EFw1(bBy=oWSt!tu(JsFh5iFG(+TI*5K5 z_&C3g!hCJDMa7FEyCQD-j2GR)N>$Gvp}_*UCMPd%ip8|M@o(1&vRDr|VGM+qVYZ{6 z&M+v^mWqM;qyw4&X{oN@3;mNu3%6Nz!GkmFOAB;rwwq3MR?J6@>ceIfs+EQejUe6P zhTIKbyu)f}46Z_{nQ^;r)2HCzf{moG>KvcloP}rh&X4Ks+IA{RQGGqo3@smP1~?{H zLM)k0KT|uY^tL5VY{fCS;SG5l&sb=*xKr5;W0zAmjgy&Gm2o0*_15IR9bFWcGZRbr zy#4+-AtW(}F6>jP{W@6zZQqvXP0sF=kmWXpjiL>4G1ae0dbz`ubx^mWE5hUkm14xSwTckW{g15bxK{m`mp7X3w44q zwW$yfbfHQg2D%VjA?KeMSAG#U6hKFK6@ao!^>D$Qn1kDQ7q^mkI|4gSQOZxhd$Q~v zE8F=_LQ6KXoNMxzgtX>RAC(vNCdO3@G(zOJJgObr|^3lRSel)-W65EfvDM zHgbU9oIZ|eFlrm5E73n{V15kaAi6;1mxv!bcp4W(WOF;Od7Lls{?zAKd`TTA?nV+5 zhm@ijqbIw@V)(DFJ{?qCvQ~_0-S((4MY+7+mYdV_3U??lP_+U@%p5ez(whO`2fuYa z=4Leq*q45OgZzn~Q-{pKE=5Pf=(W`|bz+fNIfu8H&avDJa67Xt`;h+?a%{iQM#EVs z47egOlvE63{@62=CXL5w@hQr5twDo{KId^F9ePPCqlf2Grs`nKritBX{X&%yn3;N- zUjhi<$Rl*`XorITPNQ^39$qqRJgN+qS`N!EfT-u|L_6&qa*oSY@M6WtFc`_x%jS|v zC4Rj$3M3rlV8V)EMCN>5at=KI+_Uspqy|i(!VD`tVGk@@uPfmYgK1X6Oj5i~jjteS zbYc-33GgCC^g(etjj!5souw+I@agP<4=J% zYjoYvN7l?S%iRQZg4mJ-eZO#XXI%QQ4c+LWC!bAX6lbP6l{QX2kK{r$TMuP1(H6mHA zLa?o2ME@iXm*(|;Ggg{hc2TBrX$wY(NJ ziWien9Bzimm zPcUQ!K0a^k5`+GW_o%LHh0w8~J_2?sqF&U`3pL`U;C;&TM#w_BL7;f)B{U${?>ln; z>C|X^YxFx zjEb{Wi$ad*%y`TzG`%VL(G;Sg_Su0~#5Bc?$3QyfPh8d#BzpLzT zoi6sA(AA44_Yb7->3H>X0^{k|LY%EMNHMZdu^0YoYX^<|C%Y$kw0PJ6fn@L=l^$gj z@b5~cQ)q@iQ^@y_|&z~fzOJp|;#KwGs%Vx{; zz<<{gmu_r_EJqeHH()0YCkD3zGOCF}bU7b%z=GHf8~M<~WV>Ggn3;AE9){8EJ$F1~ z|K{JTTYPi9*F8e8A}epNLN+DzI){^}eW7U^AJh~7Icq#3{;(;Rs^3pYu_7QV|GtD3 zGr$o<9!Hyyvz@5C%$Hyl4#j8Gqsc*zDn4FojLR_1SgvqN83v!vaILw~J6&W2owNkm zZrQTdPeHabgB6Dl?Nq#|xY6C6yYTE>e5K|xw4P4Vr^V#qG*l8lrV&ZZXQUjERM)Sa{K_LL50TlZ$?2!0=2f+^ zj)aM7?S_pW-U2(1;Puu^qcFfq(6^(q^x_e0T+TLr?{qya>zW8ch0cx(EOlXw)vAHw z3hU3BEkJ;N;^4{v7SFpPR@Dr_uG^`UBvtR?o*>|kAT~*M{Q8B&m_F-9ZWkgpbP_mI z=q%4R3XhDc#+i}E&r2BVtFc|+ihtpqqtMyn!)i+6Ok(XwPrEb?$Rra*{X)GbXd+s9 zt>chE`brHW;%%pGl_J8u1!T)s40`Pt`a zOIGE4!j4~Tco|}EQ<^*5Vq;|Bn~FO|~!&0i1 zW+v?Fmfekl@8uBOZz+`kWvO`Fd?PXaB`Kk{`?EyloW>ZQcQj&kD|aC6m~c0&VBBca z2;!Mq@fgY0J_D#rmsb*n(kkCXofK2#?qm{@?utr0ot_^3T6y!gJVU|~bm7Efg%oW{ z!zzKWDMnHH?K-_JU{&G?(yV|uQ}M=UzrOQOMvOmm;NQWtUxARVo6zxLk|w!Bc{t-J z@p0+!3?W{^;*r|38RlrE%g#mD!1!zk;q|Qy89xzwQ6&x?w~B5O&8A9U%EL)$FeoNS zQu4hoQ2yz56H|_tE*7r3+jLtIQh+X<^-uiMJyOCsttxWn`4nFi2Nxoh=LNBI5=uz8 z%$V!VbrH`v6h-=QKEBucz&En#_`o{5c8x#!q8~>?CUYUGR$r4U-|7YlIX47)vWbEN z)`#lWQKe#Zy;A2NJk#h|&?OOc<-(*h{h+^Cx~-*Avt6~{^;vKsGs?|KvlaFP8e3{q z-&^LL@_B`MZPSH>b|z%Sy_Kq1x4!_6f7!181Ds;{k8q0Ve(Ti<~IC#()40R~MU zIM^fb+WPapIr*C2AAnC}j0xBnk+5H3`p^Kud3GjuijNT);BbJ74sJj~Ac3$t4iOO? z7_f)He#2iTk%A%r2L<>xScO3NvIvpBEr2UW33NM@tr=3 zJaQZx_@&_Xeg!-R?7dq@{|p7QwcLR>fGYuS&$dlHL*63V4djRbKsyjQdn=5A>ydt3 z17Kl5yBn~J@-pCNZT+y`sO4X#J;0xBEP^2Thg*AJ&tEtY@h^uEO)cVVojeFTjsZAx zXx9M1W|ZakIbCx+0u+PCO@xc1kgoes4}pC-g-Yx|{%~Rc2qrFpGg)t6wNumRfX=+_ zx2-+7UTTnUIHyHp(4c6Xg>}pjflff5Q*wCm{wlkU8`uwKRdJ97WdHX|YiRMcwI90v zk!?_8Kflh7LFJ?0mNrDdAL7Qqe19Q*26Yh_n4oqb1KpLEyxsoiZXJE!q`2LK%&%_- zItlc=YgtGJ{x;gH6L3F=K#x8@^Ca#m_(%C+Ut$0dpeBE9Q4c`It}h~i ze{}~21fcy>@Q5v(uOIFRHk2P%w7uWA3IgkRf%@Kr?(>CSq?b3(4;){5F!H-zBMTxs z3}|4-uh6{`eZsouY4oGt^b=q0pWn4_?up;vz2D5(g3iQ6eA-dF=U;JXmk@6E-|F7| zO74%4Ppq*_Sb?wFa>A=xmu0{8zU}N^waS2yohv_>ftmAN*`Q9!fo^@a4g03%Z$0IA zY1=!`{;WNSG`0oUpHF|FqhP=O-@?vyDyz}V(2z}7{NFNtcIkg~ii)5ro~^evQcnT{ zLNq^b$1f9cmw=D}%&{?qjiHtw1}xwWLE`Z5s?7mL+c4#(Dn^9 z;2Zb>Sg_^S4@lr2naU$TF#d(700HU$1r+rsDD@R!Bp7?=M*so~K=}1z&sX^M8xTPF z;E($qS-XV)s@5>Zlv|qnOhQ*)merHt3UQ$ zD=u+dEThIzEHCbBI`!hIt5va4A#=XT0B^w;&jSE)XL^CuBdSsoe=fV}g)Rai!)Am@ z$q|3O48_A5b`HUZZUy-3PsjE`?KN6KhYv{XAGdesiOgr|oCULEIu4;rZ1latsvNVU z&NRppq=^i88d`Kakt4YZ-5m|I7zhQEZh3k_hbM+`cYIXV>wX%}=_+T5)IUD_C?W$@ z!UYl)ipRSq(2hN$eaXPF2V=(V@btEmKxLp1ijqjK$2tfbBoAd7sj8t2bK3{&_)O4D zv!HL*b8~aP`-TKx8q>Hp=6XC4hk3{C>nxWY(ZX%FZ+_$s+d@=($ETG$_LrVC;SlAA z0sRhxcmJ}?LrM1(rWL9mf@E7j0~n(*NzY@(li3)Ft<93Sd4n9hQb+|THGt(umR)8m zJ#UqgRv|in$4-K_gC-q5dLH0aZR{02(>5iYg5fZ~uH5Yc2}%v+1}Kxob$0J70c;M) zJFP@r$q%)3_F^DiQs6ufKPywJ&zEhWiovoZ0=93LLq0{|8ZufGZJ4WF`Zu~i<`dmu zLG|*`tUY(fb`zdDCN~vA<)DTx5O7K-7ShkwJvyP0>`c+zo9WS5XlSF%bNG5DB0^-C zyfkJQH63Np@-bB;Yg3KQ+SZ=1y}{DFI2ucSA2J%(e&I5qKKGh051?&OSEO`dCx-H; z$#r7_i>`HbHWwc8M@^Z^WYCm@uYq57=;Wo>CS}xUV0=c9$?XiH#WiK!Sf-Q$4W>&{ zr$UW6x!0~ab!7I2cBVJQS2k{qy%}_#+FR6-pvhU;;>K>Bq-yaDxd`;MifzD-zq_Lq zrpF(SHOcNpp}M_Q4~}XQC-6N%&xZ;tu|?UN=~NCjaBaz4R(L#a2B5I zB8AJBlXE|k^CocE!;6EsyFCWzU-R?Du$>@E_&XD;wkQ=F9#iWW)Ywp7qtqHnVM0>5 zJ2gZ?bfNtH>u)XIXu;@u=+q7pho3sJ7!Wnu){kK;+tWCC;YT-~e|Hy(wC>-$O;vFk zg$tn7IBVcYV@ns77h(NF06{3WCnL0PxRLJ#Eq-S{CDIs+@Av%g*DrUHxlZr`>hta< zb6RI5sp4u*%aHUb77kFQ)!5dlXW@m66bbS*lePBmUo(ZR>9ng8{>Ujws>-_uS2WvE z&#xivX~NPYAy}pF_FD zwV)ibCX1pH1_mjdK++>e7vx$&vukin3tBKYxDCrkJj{gvT4^6iN|8m<0D#jQ^uyyK~3%e3rgs>YRTb&j5p2~ zexA7PgG{e?W;kCAH9#RJ4eG=2db1ANf9A1Hjh@$t`;bGjJ2D+Sr2nYjB$cW!W)G!u zY?hPhOrf%l?>pRqh%8UIZlCR{~%wxr4Hd|EN*DZELOuxl{fzq12n8^AHIp zidHpfvOw?5r5K=L7-_k*J{*62xF1?@2ahLLfHt?g>_>#A4{#S$ zIfY3s8Rljd7zx_!neb;5>3dAsS$=H$A7v}&U~Wy&_Iuk07qvx`b?m#N_-?FbNMteV zP{wR(+KIb;xmQSeglQEK9Z!^_GT|AtzTOx0&+R$oSf`tz@281=p9W(i!e-UWJom`q zW1QHMKA{$1?^e39dJ&FZbz8;$G&@z9-;h&dhmCFAJ%{AGH{gR(Tu@)S$4?AfzS&L0 zcO1~gXDK zJ_#vvAh5uEdla2u+_+E1RGkR)fhiBV28|v-ehPlt)92cQPGw5QW`d2m_b*WY*fEW) z!glVs+g;`jYD{ry6C-?sZbQMzHgQ{+eAVGoS$CIiC2FtB0xV6&a0FGnaJkDpIi*T* z-V(##>y#Agimh!xqvO0Wr$pkc+9jzQsb~?AJrrN`apmnvd=Q@UO=@uu~-%6^Efj!l_X+Fc(m&`wo zKK7_CJjVB;Wk`qgKDt32=L6oj7$!=Dzie8Ocyz_tbxTi@?xQfdXeMc)rG1+p8qWy~ zZW%v*e-RH~Elm__nO+xj0%?YcKG0B@Wl{coM^e7&rYA1n@If|&#P7k@_N9y-(8-pK zooww6QI?V-wgN*WcZK=N{}AoMo1Uh0bn}XmmoX`&bG*b#WMoo7%`uHS>H3KHWq{KE z;J<8{K837?n`jY@T7i-Gjs|Tt?!Ra7QF>;bJys9m{LOes$v>#}Z4vZKw<~ACaOW<~ zFWg`kF1pHF;k^<3)7@^FuItLaTpc8>enp=n>1I%4I zG22d_F7oGtCJf8P2k{N$@~>DN%>2M{d;>ibiC1GIqIKJss%wsO5j!>${*8*#VrIfa$t+~|SW!KYD zETYanL|)y^Jr<#`1-aPr?}`b-&H7BZbw(10o0~Dqnz^@ zV_LG2iPj}+NPb|elmqa1cFnQsWZ7{(-4u%E%|DAo!G1G&vahZ;q0yv{>J=}&-%{iw z=quHkt9nPU{jPoVZ~H+KDz#rG?xvnx&g^+4VK3J~zXIW&MnxB%;PUT;nqg}`u^H|8 zVIQn);?JpQ;>WUz%B##7Hk=Ai+qOK=0dWg<#MH0lVVOChLRVZ@H2%$cRX$ra4)TOm zoO(WnflIZm6e{}Av@oDC3Kf}SHlUi`5?k6K}}b8B@~bT|%OCfB~P%MaJIMIk2H69*U2 zr0o)1mo=iv7~6m0w4ko23?b5&93R*vZM}?Gy}&q;FA!c5NZ2jqQt5?zPr6@XYm=MJ zk6d~;_|^DF!^7Y*^VR9-Qh+EPy!cac%A(uUlYT8^}Om^g+|P2H@!L zw#QwGZ`2Y=Q1WuCF)ROV=6Ll!K-}cERUs!s5hUXId_^B@XjHh>9==x|zjRE_qaAK5 zXQ;+II04(Mzrw>#o=_6!lGk;q3m_Mz0M2nNP{FTFfDo zd9y&L<%c&Wl>hawxXH=-1Rju%^MbJgt#W6WZ~fi6&AE7gw3{sK8e45T=hF-v`Ji+( zy}YZpom(%xJr!W(db|i=z~wQI-QsnFBg48yd|Ajel=?bN2{z!41z1Q9adi6b#UXx+ zPDUS3JV;(^Q7+|*{nzAZt{`1*1D3>SM>T_c3tL+@b#<)m#ga>mm-EeJXK9zsy0V=v z6VCDEtHGAmLFmo@1xwKQ2IC-a58Z&_lapT$kMb$v@RGMExEmduG$p%-*BN$ab8WfB z3Wg>0QsKi(hebJdZx3KICj>D-hqb)}l4YY#P4c6sYmSAjis`HBh8&)V(E2P*hVL}1 zkG442d4_pJc{x3D*|~Pu|zA{AqJu@{<|012X3 zwMX@L>pNLffy&Qt#SUMWfYEt4$m$Z`7t#U7?X~MzoZzwEjneVuh^q)K7|HGoBq1bm zW>23t?>Q!X?I(JLD#DMz>6x^m@N@UcZcx@Ho?m9$cb{U%xn5bW=^V-&K)Hdnz^zHk zZS>xnr94wKR~o|M-(4sPL+4HI=>By!>s@z*s-s}InfE~Yroc#Sm=?I4eQ<>4d$F4E z@Uik!U7xq5ydI4LDf5-g0kH_~H}u>yoiRc5?9hOWXvk&E?(7^DJN)V!(q%^YMf5R& zwMvdksH;+jby8ywd%!aF$^8%nycs5R4HCV7QJ^|cl0p8P=_t5a^TXVbEASvUEH#-c z2s?gE*JpuFwcyEU*ldnxUjHnU&;D~1nRMTVIxi z`UC44NMyz0Vhm1SR;i~t79FPOM{aW0o$!40fdTwr1pYy%b5{X?~(W7^gZIY-5 ziO(^4Afgihl@k*0;ZupdcR*oc;q{TX#H-eo3jNA@k^D(_3t&(rqN&IVEhUGxZ^}Mn z|K-JR)Mxu-3~`^|Cem;AQNJA8|A%7Uzjao5jR~0jI5g8W%PKd2)rgruw14PrdRrmf zW1s2hvw$fhx72P#ax&d|6pRMxFuHZ4Pi$iNDgbp0i+Q5Wd=^)8&)!*Ui32cnw_K@D z@bpQ%tk-&{xINV+003xECrGjpi%SB`6{VXhG-RY)K~NPJN>%1ILFr&)6&Wjv1L1_) z=+zZ%l(f7I{9HzR=xEK!mTwUUhbE)F^G^YpBuI@Ix_VWdy@n+!QW&&1NyOaRj92qP z>YitVX~DYr+&A^#OTJ5>@R?LHruK*=nPfD9?q9BieRRY*_D9ttrcA6LsQK$l(v*3G z9%i~1Q^;R(unJr~8<$M6XfR{xeVzdEN#K~ojyhB)N=LNlQ`8qic8sh1=D~NloRQXi z8tL_{B4jWKiEH`;bE{i&ir@@=drqZA)y(b8$VT=);mHq;@D zr$M6<(s_(IPybJ+h)&jfL?K!u!74f4x@fA7tjLa~27h)iA)LN%yw+Vl!&A8oj>_k#;>YHTy_g zz{mEA#f&v|7BoyrXxg0gn|1qYWN7t@0flz`E96-sd2{QL5B5lKAv*H@_KSA(ve8Ux z#vYmrxsWAVK5U+?i3gcyh#g2g)9@DiQN$BnFyjptNIk>k1#5d0t#Fz{0WuX(>qWJT z158O=JK|aM;GJN}rAy!p^ak!A=gc%sbjFr{;cY&oGTG`6eForz$2F{_|0>jD;)ZKZ z{#1FIM-tA=3K^eoed-syLyDGZVTO)T-7VTggiak!e#BMzdP*8GW+8q*FN=MG(XUhZ z3+==g4t~t7R51_4AA=666SY;YUG~UbHhxFE#bWLt5 zdy9D+Aiv%uPs?OhC5oflZsiqVrrse=-oy>lE<3!y`4)r zSm~=WTvO!Gf-5`?tra$WCpyCF@C(s=9tjI} zdHndhEJyy)NY~2Y-54C&RiGBTfbsJeMz5!bL!t1%&m%f0E6ckIJl$PX;4c=e)GJImbW zkf+75Lr3ig5^K$&m~GqvpRI;}Z2X$>Y2O>^Zr1oDt?D|vKN>)-dc@P3-Toz|z0(qE zPNt7#1K)@WG*E2A+K7HF;q;b9W24?t5lCqfIiVmjX@!#bWLpL%NZ4V{y8{P&q3ehR zU8}|sxtfxTsv(KKqItj=sO}I8dlCuru&qDamKGX+yUZnK3dMm#OAR!$v&!{(s2Y}A z1rpe4%T23qn3w_v668KumL)Y>WDfLN8Zd2WA2wRwSpkP95+V$D0j~V^#PZM6k@oG} z&T}9WCQ_ZNx&CA8KI!w*avpzGuLfS7T~_yaD+Bqd(^1CKgmG4_4ZQ@zuC3VuntfYg zC&;`EWj8ZUM>5$Oyr*5a5ZP8X5=gPN=&x%ZWz|ToDlc9b@2?>hZ$8ZG3R6Q0DL>nj zC%{~|zc2h5Z*KE;qGSnasp9hLDTw=Oq90A+7y(5Wf8uZPwqG}2?rg-V7#i=L4l-`F z$%#_eV)WE|)LYJaC`D_+j443d^d<2Q2kstXVumRfV8nvERWg4BOy+}s?$7`b%m6wz8R!jOr@sRW-YLMW5kXrZ#*WW@7x7}wcD>8+@R#DAo+pBajW*JKwpyVh zk-XIM-rY+U5hJ~35$C=K^(gJ{2Sav&;?>+%)i@;y?+`&6;Dno(+w`&bw8ruHpR&RP zal7Ow=yN;?g)oq%R=gi@bR@q9D(}(6sS0D+&ev^1w0>^cIoKm#!js{t{0gj>!JFy7 z-SG@nDGJUJc=M(2tJW!ZBrZsml(TI4?zYF?G}KnWOPlAp69HwPLRSCYts?bj)|lX? zK!1M#<>=ka`kI;MN9b;21_&jR1}N z*J&1)2VNNxF3b)AchtmEJ-%DyD6uJ_j87qKT$@|sJ6x>QGZ~LtjZwv-aF>>>yyMuwb`cZX1Hl1`nn-Fe(cS8m)=f{}3Wig5{X|Um3N8=tFAsHGdBa%*r=VEo z&;hTu-pmGAocZrzF6;!n<@DW&mgzk>Yt8zwTy8U4&HXz9nG0M38>uj-RLziF$F6H` zN)G})$I6oOsVKZ@V=j^?Z{4+aw6{S+%>XnV$t@Q2RIeuoZLiVCA@*WWPUODlp-Swv!k+9#5TjZ-|) zA#EURCQBU?+n+}AC+W|$TWccWY;45g_;hVEtpLBh{M+1tP0HDlF=<_FRO7x!UrZd` ze%VIj`Pus^T$gj&*<}rcaPEusSY*kR zP$rN4fa(2gSNgu#q6fLGN`~fhxl_^j7w-LBK2&try7ABtWA zLq)Z^-sQh*s4im%>Y7F!ZOoa5(iRI@cdXgF_p{D&KC70g)9aJ2q{g4KeJA&j@mrbB zbw*fW4h%kt3T?;3$cX4FE5r1_dau0!c*Co91@_$#m$lcjmWM$$nB$A0(2<+U(Yq_S zg0xZq4=AX(se0pbVrTb_p?Z5FW$pDgc2#H^=5CS;kK`TrG5Zczr3%c?&qBq}#uXIp zJCy~%k!R$R1shhoZSr{;JUdf_H~lxYWP4KRbzgRCb8J7R(~qZ4Recwmldwd01+DFmJs5r?6&YVxZ+K$tL8HzJF#5T3r1_Fx2I*(OmM)_vlOrvV zraqf`76`X!=8^Tj_-VJh<+UM(vo`=q*t|YAs@+$81vh~-L%BDf)cpdkx$(j>?)qX~ zD#?znp}-zZNBRe?D!gCvmll1xMl*9jA|C0H@Y9CiWN~Bbd<#z1Lvr%g*2h$1P%l=> z;1>Bx(E+PWf<%f*=)<;xX~LUDXYOXLR7WRe2l;aTfNZq{FD7r_o4fS<20mY_;u z!Iny(K(UH&yrDF%@4g)lT7YJ5dSs)}2mT!kTwSuBx-w>=$2GN>YQbtYo^3&m)ITSq zGe1(VPnsL0J|W(}<@6`-8brdDY6z{T(oB}3K$ha$$NeAcZ zwqn{(xyV)UIrCn+J@zD2wq)&-PM-t#dg1A!*%sYsr5gcSfexUcNJnpPOiMyuDRN|# zTlmll9y8XQhDjFjWX;h8<#I1iKAd9d-nG=cH^s#YGE)_6ODf?hLyS_gn4ayqLWB7c z=e=ZzPE!qsY3r$W)6(0zf$`(I^^pa7e%g5Qrd*e&;+43U^iWsF9#vkf;=P58wzuSS zm%E#2g`+GOQVnIe;GdsH#_5gI_$a;HX2-5}c|FsoA7;G!#vb=gP6N-)6VaTAK)M%H zgND!aapp5?-^9a85vm^#*JBFKL*AE+BL8(#mD6;REA94g%SIqTKqAQxe4<+5h6s3yK{=;T@kp#85IvVbMiA^#|9SO!?P*={q_!gM zWo|T^nM&`LZy1;;G8?151!x7Y>@$$i732ei^ebq|Z_fh|5C9k>Cm;x#ov;KE6zcz7 zyVsEI!-IgpA-nHIh``h5CYdNP4iy1x-e>R&Ax9yA0D*{*fQXQSfB*;r0U7!Q9N;AZ zkov2O0Pe?zF8~Y&Onj$-x_{Gyhd^#dVwvlU2Z%!;=a<*kMlpM9@7IOB1`N~?2-tKT zH>1zK6hpvG(T4yR;1}QX8y_G%ff??cx_A2e@^aGXBz)J;n`O-54zPnz^lv;S3c%CN z9~Yok6YOlQ-T${`By<*v!7+s3hXZCmM#7F8o&mtbPe?!?0|@m1(h0y5K%o;DX1N)l zp?Dd7HG!vj9}wGktFK|nmI#eVfJ$%?9o!T*1gbMh&wsH3%E`xC(96*S9 z?|l+qb@c%hg_3j3{rYnMI0e&FK-l~F#Q}KMA%lec-d<5KuiejLvHHS?!S@LPi1G{i z_0_KS=2R)bIQb3c_56nX;xYDy$9L2e5WeoF{2nVS_}B7#I@^y=s*h5R__nP5QN+(}yt4G;lv!^3myc`a2b zQXBa75=bS(>F4emgWWy$?@9by;#oE#=tI2m|FxpvF&yM_DxChBa}}Z z^U--5BI>nrHyV5E2>!wBM;@Hf-AuF`f3$?+gC*lmJRZ1|B-xHti)d~QHEXIA9=E>FPoir3oE$@@n{p5ugscBgL-SY_He^{Y3LjdfI_Qe!y=)7b3blGW{> zWG@o(9)|HOeIOD#2BK{Cg$<#}rGDnrusHY}LP8=}UYgQcjS3`8Z$jJ+qHHoWnmc3n zhqIW3A0Hse?-8BvoLlvk@E1JsFQK-TjCY;bEE{Q;HP$$IWWs6B@YPMIlSM-D0w?Ns zDE{a`>#@lk^%HKsPsCrF%c^s$o^&taCt`CM%U9>Qkm*Uqj~Q{`d*^gJvR6;;^~Dyi zrHq;x#@MmzP!&?J^ufsd8=#*&bvFO>GIjEf|N^ z9ovQXi=V=S`T!)qs5EavA)GeFYTPNZn^;K%8>AwUH`%DDIok$GWplXyYV50n;`q94 z1A!1AxCPB%!5Q4$-7UBct~0m=4HBFH!JPz$!8HU3?l8f9a8J;|F2DPI@6}gzU)6n8 zUDc=itnRaW|FKq`-e>RAAGvchANvD66=qz>yj*YYyNIv6=vHzNc?7acfJqvH8?9}AkQt*(R( zH6*Z^oCvBdaj}*n)paRj4Qo)C!pcT>4C_%ZL0lBp(KRhN~FF1K~n+ki`O$a#f z!RKxBR^Nm1ap%kaPu-Z`St+9&=`(L@7lj7%4?gQg7{T8U`77AB*hHL6dWfVTR$BDA zYl56so@^u#Gp_`#m@{Cae%XS1Oatfn$V0q_N@9??8`6rb(b?F=I+KxAbGsH2RkjvEU^RnlPxK2KQUX{s#qlHa|zUM9o zOEtq`z{|=h7BXlDN&S#A#cbs4y|JJKNjFE{yXZG{($sgKdi(tju;L#xx3;ZbXTA>Y z<@~!CANuk!u%;QEfEcw(ocOI_gMlX|{0chTL!&)dtamZL#cLYRisnl{_UBD450@}` zy2D5=@6k|oNeg5w;7)}E^;|wr$ZUA83x0Ha-}qrKFSW5ckq;_N z;&W+Z&WS?}AFTE{Xos5GavN}K)7qk1;wqO#PDP2?;1oTA<+%}vf{N;k&ak{xFr+^i z4#m;PP4IKu{>F0M)l&FlVv`2{S759~U0-u)>R|_UE2RR zRn$8#e4s+U2qW;fM&hBL$&jJj*W+KT7$_xNGPiAz6q&*`k1O!*Em!>@`;@Y|(`cQ22}M z%6_oesK#aqoE{o4)qgNEUIVoyUevT(F!cfMNz;&EBFGNl)>-{?6=RMszK|_aM zr%OEI**Sc>?lwWazS#q!Ki+U%s~)~{1ddO%hN-(0iIRC+jj+rG(@NNc21<_vr3q__ z`ucR`y;! zhIS#TGA~RX5jJaV9h7V?**<7w>%_0}o)?8YCK^6L$U&YyA*YZ(!C%7ZfpXBAWp(_| ze@GEpsaX=|r)F%HbdESjV}JGYX0(r~NoY8#VciQ!pZ#LugiVDajYi99LQv@M!XpK4 zef3mBQU6@yul1FH(VSrJPEDDkR5ktOX}XfK(!7-Rs!aEKB7dB*i$8wnx~tb0c~1YH zdG*E3W9?M6BH>=?__>C6f$x;7Va2tkkA!3FH07s|$d10XIg~Fr%UM?TRHUYj*~2*1 zvbq~`{2fL`rglkdD$apR(cxaOgo+hHgM8A68$f>}=05F(Web^E@Xu{@`gnR1yVYuC z&1+J27>b~*`v^W@bmG1Lk5AColfe5o_LWDxNf90?NxyD#T%xfq&^$;+1eV)w$Ux$l z`_5eMwo5=55G(G`sKT<6t-i)ZfArcX1C>^q^ zPCw&oAZ1OTzwQtcm%{Fk87SXiuta~zTt%q8%WK^QqZ_6WMEn{1B`5xzxLm<7$rbGj zzB;)=Ovfc6JMgR7{Zgu%7%;ZXnm2XPE_x!9B9W=zf86O1&$W1qhL#k|el%iBoE9v} zFRIt;dmm9f`F;IG6?|DzgZsy1BNWW@d)rC_M9t2o(tT4o{*`Eo@ajdlpXXDN&s%-A-5YtZl|`%6x|znKXw%KIYCW+dp}*^+&prZz?Q^le(7H-Z@@26L*h@K#1>>cjQg(TRxkoHFL!CkMC|Lg_}waxVC9lTjzVJ0mApppoRwNDq7@-eTA^)#wG&~F&iOQju37vPyQs+Gt9G{ z?5w+?0y)AC&FbnPQBnBs9XtIXq1Og&)#|M?Ro&*`tMF|FNW1rMN;sro7@Va}ZrUOI zlf+>1xjqKZrRPE?4uJ`?)rYeDHpEe}#{M15l``XG#R5*YU%B49v-YR|(MvKt=*7YZd=Yrhc@=fdwzfw#s-orj$ZbgWEk zBgT~KQtdj~E1S^qpswVQnmvV_{>?7C?~^Ra#QMIT6^!Hli|KumW1k|-T*hWdEL3?4 zCTi>I@og4{TPnBq(NgAXB*Aulhu1X=rZ}hyRq@v(AY%_sl_`qZq?HqPJ-2V6QRQJ- zB^bFk(Dq~6VrZL;TLFUx4xf*X?1>F$;LdUSH4xbYvfW2x}FhM{RZ5N z)uQq)Q;D`%yw6T$P(Ar{oOJkOpq0&ICidF)Z_1a<cj1NF;HY>t4c?ROE)kpE z!Zu$gVkZwYuh1`rIdKrtje%4)5^&MZD0zmPh+~zgf{_uh<07!TPSbIu4Q?i>tTjAa zFp)R{?EYkMX)g*{*7^>wer7L(uJ2_9D%fF2Q9tD*<54+{B~5>tkS9-S7XtF8ga-rE z@L9}JRfVQbSXWrdSkk@n$xMK%zt!Axiwk>48dWN(ajw-4gd{Q2vjT{;$dXU&G*CjR zGQ9GKgX*g7GFErSqd$!K#y@b+ed5e&NURS^E4pO<*0NvSKcS=_+< z1)GqdY_O@4k9y@wE2{oP$1EeiB(qXtx~lE6x(nMz?N{eM(Cs2MJK$_~jF*=K>wBqW zd56djfl!$Rr^nr?u^So|4C9j3ss%P(hXh7pz64wOO}uN^^v&#}pQYWebpOW$w){P?p_>q^W-)&9IMT<-S+%78a>QL2<{gsyCx zXoIbr1U1H8zNEWjcQ9I`1QA=}@gqOND+(5fZoI9)H=dkQKNVydG z-4z7-DTs9ypVgSa+7$B2XTGmMKv^;k^t1R-NUAzM!t0xxI+o`8UqJFoKS537%1J$7 z45a;Je4Ig)e-zMD4?ZTSIK?lWO(rZhjg7{m%P_DxOg7lSh#m6bEU|&32lzQ2Btvgi zD;~D?bplVwHTV#wy6_8U8Te1?~2B{di`5&_(o|?4(uF0&tmBzTKE1) z=4xixf0jgIAq#k?JYB7RYLIKf3dfnUkH|lbAlfUbjiyQJ+uO}84@%Bd!%0{BmdmNo zbp^LxwNLCon14-M-GT{%Jswog6~mmGcw6ME2*03WJ-(KSikosc}yRafd-)ThPD z^_NSJ^o}O8xIqxm<6#0;Z+-A{h<>UO_d_nAJR5z*4BVQT# ztJ|W=$Tyi&YMNiSAC_cAw~hMXVE0xz-Ll{hUhNQ@-$-LGi~`5H)gw;%)I?HgAljBu z$m$EBu86+ATbCWBrRF314nm1#$>Eh{D2j9s{gji&Id{FDXolj~8PeRg;k0lk94=34 zyroG4Zwej>I8E`MjplusmcGvWKG?-@V@quZL115Hn&=UXIuKo#ofDMs#eKiRHwVPY z))F?tWtsb00iRwv@iI7VM<5Vm$R%w@f@!>p)$n6+eRN#bHZH@?nyV-N?r%i4cnspC zn^V#BEcR!ILPcTDK06@*mp^9T?_BSG#NO3E2YzBoz)1%1c%Ko{!dx)R>HWId?x6OWDZ+yOQ z7lpoV-_Od;LDNAw*4&fpEm0$=#j@5lT;(YZ#^sshAG4pyAM^Hp)pKHn(T!RB4SAPs z+0@fdj*{=5dOn%6Qrju}ao1%P;bKxHAbPaVacAg|n^JJhsDZUaeKFg6ckz%poZrg* zC5E)0Urtgq!R9nL{8;N9K5@p4)WejH+}7r4i_<46!@q?E;ivA>nvuuo%VCc)5dn`| zn^zCy4A~?c1I6k-`{X%AeeKkGp3F^KPyQ+hBH#YnyFs_>ylr5a%sXvWM}A=qRMXhL z!w%!E6Pc{QaCI}`A8>3-tNySTPlD972D2?nORc~Q`ISI;g)td~mtj1*H@lm-zUloiC&kLg4 zt}q80VuLLID%uJ6B(o&=J@I0t&lS9Yw9Y^vbNE%ZZyqoqHj}9ByBlsV=u<|y&LSnY z>is(@fmODSTBne4n{&jE->P<1Gdb<}G@Oiw_H!c4{CBF>c`_PS-K~6P za?^W7%#gB5r!E{mt$?dLn*qVsF@SIoag3);=4}&-T&&vYNuIKX zD^USK22|ImS9X(d?W8`QxbwnEozJ6*<`?(vgf^Qlfiq1c7H#}%rO8y_eZ+&^*2~81 zwqPxmv4v`VaaLB9M24eNrPJu-lFYRU2az8E-VGzPz>2X1dX;TNA0BRB>a5v<*<{ zGu{I?=T0sM#}_Km46E_HBTD3)Dl-9=t6oN^96Ew4z8jkEo7-oa1857)LmQ(-4Sz%; z3kOOoZI>`Vj$VI_4`7=~^S7PSA&%b%kQ#rGo*PYzysFlEZ1t=e=NTIwGJ0K_ z^F4HkSrYW8?Ct zB*hY*Wwtm~f&7W!f;xxG)w9yU)YEa{LX|C{^JC^&h^i~dG?bT|@q$sQA1bebaGL42 zy6ML7)3Zn-Wyp#WqggPPwz=9hvs7UvQrxO5%-&) z^c+TVd$(+F*gFbrm@~J`RCIHie2l$cEaI>NosC>H4VL0^_Gfwl`fmKSXP6)e+30k;1ix*Xqt=sxyja+v@~l@PG|4TVrqbdTf~vyuX2@k{1ja;DSYu@IFwxrNTHCuUX+BU)4bzSABs&p5bZ&eQ^Gqy+ z?HgC=R?#dCa8$GpYoLkk-rK!DF5#~GLvf8mLyX&&XGp6xqPLJi^4H}sox$GIOT3(? zvi}*O^vOooP10`WstA8E7%&s$b|8) zH`%+o$XIxQ0E{w1TpXPI9DJPIoP0b2y!49_@KSL^=`q64;Ya|2lefN~a2 z5D*4XLr2ztUCz_V$e$&s0MEz2>|q7yfxwXGp#j|NoIISof?RyOY+USo z|HsZ}{PVY|*n5Eh&qnb9twCN)07o|q4?76R0^s%UXZhH<*t!1c!VnYt$Dgj24j8=u z;Y6Khw*Y|ZmJZq;&KN*70M~P22swK&!~?*|_kXwA0dR8g^ZfsYcdPW4T(|O~>(tj0pg35b?W?pZ_wi7?est zKBGc=u56i7*;a6UY7svVJ9Sh)qA|INiuw%g^HrBZ#V`qrPDgH#PqkX9uA#4!jE0O8vKAo*XI(+ODw34s5)lEx@M1ZL(fRGm zL=(c>fCH9HB#;QT*LEI@17sfs&j@((``0Ggmha!}d@u`$g=4dp=6RqS?2y z2+mU1=AFzUxhj!8=2!>O#*-{PL&v-7REx+jT7fIW{j?I~)Cf!3L-RPN$=KfNWIZx6 zdY=CNv#!3DD>$EwJJ-4bdPRAO%ch;=qL7ap-oQ`UKI-6^kXTH615*ZORRhAged-s} z1m$Xy5<*K7^baWZMhdiW%pt>78SWC3s1QD#IwU=QsksnCTXh*^0B|n~N z0D1ctGOsceF30|yF|h7#JSTJ#U)F>3J{C-EW=(nF;8^pt<6RF6-zbg`6a+#&Q%S~# z9s~n}K{wk2Lq0dXdq+oK1~^z}WEG+3Z+}0`_v#lj=m^l@muSBpeYGvpP~>$+QF53d zX0&YOK;V((>Lf}P`%SlPbSDgExnB@sX?Pns!RXi5)l^~Kg9jI5lai*W!{ifnS!W<6 zj`nHadWs&q9r)?Nft)omH#q1c{p#J%CyDo~8dE2_%#Fz_Aobjp4aWh!h2eUNAJgKu zL@f2TdMhNW^#}grk7u%7(#9PTH<1-)uX+z9mMM1PPJ?>0XwRO0E_I9xg8-w%N4X%U zA*%TpqDspN;Ul=wd|;Q5=sVS)E`AS-U7JA%f|NHKT0C-|_YzlYlv<=e#%me>oGO3R z=PfE+-Fu^NtcmbV-L9alMsVn_iv(31*lQp^&*!?jbRMVEgiFx9{R8dQpoNuEde$2k zOe-qgXUbkiE9ot`Yw?|PGX9f8Vhs&Olfxd9C&!cR13ow(j%kJKBVrv3!uVVxSH-QK zQ&iqj;8bHTM`Pc0yF~J9kWxt|Y+w=8127Wdm6em0<(7KhFq&IX zic?aMM~+)SijPl5nopLCkDrrU4Di20o<~sux!68Sir~LF5dipyGo3u1IUFeG^ehxI zAS+jE&_9d|@px7uXAGZ3%8_=wP>mNdQzp2wx9A8S>N-?pL-$X5wQrCW?TAjf1t9z% z6#WZXd+`_s59MbC3{;oVwHjIqd$GLX0$ZUy8&7Pa9hNLVzRfTG#a{xfhkW}{)NzSG i8tZ>e_&+@e@vs1U_&lo}1`h`hKOY7?y{x(%#(x2(VVa2m literal 0 HcmV?d00001 diff --git a/diagram_patches.tex b/diagram_patches.tex new file mode 100644 index 0000000000000000000000000000000000000000..42dd2365c9124f5d9d8ad69fb431bc4ce5c8e63a --- /dev/null +++ b/diagram_patches.tex @@ -0,0 +1,72 @@ +\documentclass{standalone} +\usepackage[T1]{fontenc} +\usepackage{amsmath} +\usepackage{amsfonts} +\usepackage{parskip} +\usepackage{marvosym} %Lightning symbol +\usepackage[usenames,dvipsnames]{color} +\usepackage[hidelinks]{hyperref} +\renewcommand*{\familydefault}{\sfdefault} + +\usepackage{bbm} %For \mathbbm{1} +%\usepackage{bbold} +\usepackage{tikz} + +\begin{document} + +\begin{tikzpicture} + % Cirlce + \draw[gray] (0,0) -- (10,0); + \draw[dotted] (0,2) -- (10,2); + \draw[gray] (0,2) arc (90:270:1); + \draw[gray] (10,0) arc (-90:90:1); + \foreach \x in {0,...,20} { + \draw ({0.5*\x},0) circle (0.04); + } + \foreach \a in {-3,...,3} { + \draw (10,1)+({\a*20}:1) circle (0.04); + \draw (0,1)+({180+\a*20}:1) circle (0.04); + } + % Numbers + \foreach \x in {0,...,20} { + \draw ({0.5*\x},0.3) node {$\x$}; + } + % Patch P + \draw[red] (0.5*6,-0.5) -- (0.5*14,-0.5); + \foreach \x in {6,...,14} { + \draw[fill,red] ({0.5*\x},-0.5) circle (0.05); + } + % S cap P + \foreach \x in {7,8,10,11,13} { + \draw[fill,blue] ({0.5*\x},-1.0)+(-0.05,-0.05) rectangle +(0.05,0.05); + } + % S \ P + \foreach \x in {1,2,4,16,17,19} { + \draw ({0.5*\x},-1.0) circle (0.07); + } + \draw (3,1) node {$P_\mathrm{min}$}; + \draw (7,1) node {$P_\mathrm{max}$}; + \draw (0.5*1,1) node {$S_\mathrm{min}$}; + \draw (0.5*19,1) node {$S_\mathrm{max}$}; + \draw[->] (3,0.8) -- +(0,-0.3); + \draw[->] (7,0.8) -- +(0,-0.3); + \draw[->] (0.5*1,0.8) -- +(0,-0.3); + \draw[->] (0.5*19,0.8) -- +(0,-0.3); + + \draw (0.5*2.5,-1.5) node {$\leftarrow S_\mathrm{left} \rightarrow$}; + \draw (0.5*17.5,-1.5) node {$\leftarrow S_\mathrm{right} \rightarrow$}; + + % Rectangle around legend + \draw (10.7,-0.2) rectangle (12.3,-1.8); + + \draw[fill,red] (11,-0.5) circle (0.05); + \draw (11.1,-0.5) node[anchor=west] {$P$}; + + \draw[fill,blue] (11,-1.0)+(-0.05,-0.05) rectangle +(0.05,0.05); + \draw (11.1,-1.0) node[anchor=west] {$S\cap P$}; + + \draw (11,-1.5) circle (0.07); + \draw (11.1,-1.5) node[anchor=west] {$S\cap\overline{P}$}; +\end{tikzpicture} + +\end{document} diff --git a/main.tex b/main.tex index 99efbebcbbbfe427b05ceb54fb0492d99dc576c4..01228e329899eaf5b0110e8e974a1a9abfc9358f 100644 --- a/main.tex +++ b/main.tex @@ -603,20 +603,67 @@ Note by Tom: So $A^{(\mathcal{P})}$ is the event that the set of all patches is \rho_{S(f)} R^{(P)}_{S(f)\cap P}\mathbb{P}_{S(f)}(A^{(P)}) \tag{by definition}\\ &= \frac{1}{n}\sum_{S\subseteq [n]}\sum_{P\text{ patch}}\sum_{f\in\{0,1'\}^{|S|}} \rho_{S(f)} R^{(P)}_{S(f)\cap P}\mathbb{P}_{S(f)\cap P}(A^{(P)})\mathbb{P}_{S(f)\cap \overline{P}}(\overline{Z^{(P_{\min}-1)}}\cap\overline{Z^{(P_{\max}+1)}}) \tag{remember Definition~\ref{def:visitingResamplings} and use Claim~\ref{claim:eventindependence}}\\ - &= \frac{1}{n}\sum_{S\subseteq [n]}\sum_{P\text{ patch}}\sum_{f_P\in\{0,1'\}^{|S\cap P|}} - \rho_{S(f_P)} R^{(P)}_{S(f_P)}\mathbb{P}_{S(f_P)}(A^{(P)}) - \sum_{f_{\overline{P}}\in\{0,1'\}^{|S\cap \overline{P}|}}\rho_{S(f_{\overline{P}})}\mathbb{P}_{S(f_{\overline{P}})}(\overline{Z^{(P_{\min}-1)}}\cap\overline{Z^{(P_{\max}+1)}}) \\ + &= \frac{1}{n}\sum_{S\subseteq [n]} \sum_{P\text{ patch}} \sum_{f_P\in\{0,1'\}^{|S\cap P|}} + \rho_{S(f_P)} R^{(P)}_{S(f_P)} \mathbb{P}_{S(f_P)}(A^{(P)}) + \sum_{f_{\overline{P}}\in\{0,1'\}^{|S\cap \overline{P}|}} \rho_{S(f_{\overline{P}})} \mathbb{P}_{S(f_{\overline{P}})}(\overline{Z^{(P_{\min}-1)}}\cap\overline{Z^{(P_{\max}+1)}}) \\ &= \frac{1}{n}\sum_{S\subseteq [n]}\sum_{P\text{ patch}}\sum_{f_P\in\{0,1'\}^{|S\cap P|}} \rho_{S(f_P)} - \sum_{f_{\overline{P}}\in\{0,1'\}^{|S\cap \overline{P}|}}\rho_{S(f_{\overline{P}})}\mathcal{O}(p^{|S_{><}|}) \\ + \sum_{f_{\overline{P}}\in\{0,1'\}^{|S\cap \overline{P}|}}\rho_{S(f_{\overline{P}})}\mathcal{O}(p^{|S_{><}|}) \tag{see below} \\ &= \frac{1}{n}\sum_{S\subseteq [n]}\mathcal{O}(p^{|S|+|S_{><}|}). \end{align*} - - The penultimate inequality can be seen by case separation. - If $S_{><}\subseteq P$ then already $\mathbb{P}_{S(f_P)}(A^{(P)})=\mathcal{O}(p^{|S_{><}|})$. - Otherwise if all elements of $S_{><}\setminus P$ are larger than $P_{\max}$ then we view the last summation as $\sum_{f'_{\overline{P}}\in\{0,1'\}^{|S\cap \overline{P}\setminus\{S_{\max}\}|}}\sum_{f''_{\overline{P}}\in\{0,1'\}^{1}}$ and use Lemma~\ref{lemma:probIndep} to conclude the cancellations pairwise regarding the filling of $S_{\max}$, i.e., the value of $f''_{\overline{P}}$. We proceed similarly when - all elements of $S_{><}\setminus P$ are smaller than $P_{\min}$. In the last case we again proceed similarly, but now the cancellations will come from the interplay of $4$ fillings, corresponding to the possible filling of $S_{\min}$ and $S_{\max}$ simultaneously. - +\begin{figure} + \begin{center} + \includegraphics{diagram_patches.pdf} + \end{center} + \caption{\label{fig:patches} Illustration of last steps of the proof.} +\end{figure} + The penultimate inequality can be seen by case separation as follows: If $S\subseteq P$ then there is no splitting into $S\cap P$ and $S\setminus P$, and we already have $\mathbb{P}_{S(f_P)}(A^{(P)})=\mathcal{O}(p^{|S_{><}|})$ simply because the patch $P$ must be filled with zeroes that were not yet in $S$, so this is at least $|S_{><}|$ resampled zeroes. For the more general case, assume that $S$ is larger than $P$ on both sides of $P$. This is illustrated in Figure \ref{fig:patches}. We will focus on the following sum that was in the above equations: + \begin{align*} + \sum_{f_{\overline{P}}\in\{0,1'\}^{|S \cap \overline{P}|}} \rho_{S(f_{\overline{P}})} \mathbb{P}_{S(f_{\overline{P}})}(\overline{Z^{(P_{\min}-1)}}\cap\overline{Z^{(P_{\max}+1)}}) + \end{align*} + By Lemma \ref{lemma:eventindependence} we can split this sum into two parts: the part to the left of $P$ and the part to the right of $P$. Define $S_\mathrm{left}=S\cap[S_\mathrm{min},P_{\mathrm{min}}-1]$ and $S_\mathrm{right}=S\cap[P_{\mathrm{max}}+1,S_\mathrm{max}]$, so that $S\cap\overline{P} = S_\mathrm{left} \cup S_\mathrm{right}$. These are also illustrated in Figure \ref{fig:patches}. Then we have + \begin{align*} + \mathbb{P}_{S(f_{\overline{P}})}(\overline{Z^{(P_{\min}-1)}}\cap\overline{Z^{(P_{\max}+1)}}) + &= \mathbb{P}_{S(f_{\mathrm{left}})}(\overline{Z^{(P_{\min}-1)}}) \;\cdot\; \mathbb{P}_{S(f_{\mathrm{right}})}(\overline{Z^{(P_{\max}+1)}}) + \end{align*} + and hence we can split the sum. Without loss of generality we now only consider the `right' part of the sum: + \begin{align*} + \sum_{f\in\{0,1'\}^{|S_\mathrm{right}|}} \rho_{S_\mathrm{right}(f)} \mathbb{P}_{S_\mathrm{right}(f)}(\overline{Z^{(P_{\max}+1)}}) + \end{align*} + Now further split this sum over the value of $f$ at position $S_\mathrm{max}$: + \begin{align*} + \sum_{f\in\{0,1'\}^{|S_\mathrm{right}\setminus\{S_\mathrm{max}\}|}} \sum_{f'\in\{0,1'\}} + \rho_{S_\mathrm{right}(f\,f')} \mathbb{P}_{S_\mathrm{right}(f\,f')}(\overline{Z^{(P_{\max}+1)}}) + \end{align*} + and we use the definition of $\rho$ for the sum over $f'$: + \begin{align*} + \sum_{f\in\{0,1'\}^{|S_\mathrm{right}\setminus\{S_\mathrm{max}\}|}} + \rho_{S_\mathrm{right}(f)} \left(p \mathbb{P}_{S_\mathrm{right}(f\, 0)}(\overline{Z^{(P_{\max}+1)}}) + (-p) \mathbb{P}_{S_\mathrm{right}(f\, 1)}(\overline{Z^{(P_{\max}+1)}}) \right) + \end{align*} + Now we recognize the setup of Lemma~\ref{lemma:probIndep} with $I=S_\mathrm{right}(f\,0)$ and $I'=S_\mathrm{right}(f\,1)$. The lemma yields + \begin{align*} + \mathbb{P}_{S_\mathrm{right}(f\, 0)}(\overline{Z^{(P_{\max}+1)}}) &= \mathbb{P}_{S_\mathrm{right}(f\, 1)}(\overline{Z^{(P_{\max}+1)}}) + \mathcal{O}(p^{S_\mathrm{max}-(P_{\mathrm{max}}+1)+1-|S_\mathrm{right}|}) \\ + &= \mathbb{P}_{S_\mathrm{right}(f\, 1)}(\overline{Z^{(P_{\max}+1)}}) + \mathcal{O}(p^{S_\mathrm{max}-P_{\mathrm{max}}-|S_\mathrm{right}|}) . + \end{align*} + Entering this back into the sum gives + \begin{align*} + \sum_{f\in\{0,1'\}^{|S_\mathrm{right}\setminus\{S_\mathrm{max}\}|}} + \rho_{S_\mathrm{right}(f)} \mathcal{O}(p^{S_\mathrm{max}-P_{\mathrm{max}}-|S_\mathrm{right}|+1}) + = \sum_{f\in\{0,1'\}^{|S_\mathrm{right}|}} + \rho_{S_\mathrm{right}(f)} \mathcal{O}(p^{S_\mathrm{max}-P_{\mathrm{max}}-|S_\mathrm{right}|}) + \end{align*} + One can do the same for the `left' part, which gives a term $\mathcal{O}(p^{P_\mathrm{min}-S_{\mathrm{min}}-|S_\mathrm{left}|})$. The part of $S$ that was within $P$ gives $\mathbb{P}_{S(f_P)}(A^{(P)})=\mathcal{O}(p^{P_\mathrm{max}-P_\mathrm{min}+1-|S\cap P|})$. Combining these three factors yields + \begin{align*} + (\textrm{left part})(P\textrm{ part})(\textrm{right part}) &= +\mathcal{O}(p^{P_\mathrm{min}-S_{\mathrm{min}}-|S_\mathrm{left}|}) \cdot \mathcal{O}(p^{P_\mathrm{max}-P_\mathrm{min}+1-|S\cap P|}) \cdot \mathcal{O}(p^{S_\mathrm{max}-P_{\mathrm{max}}-|S_\mathrm{right}|}) \\ + &= \mathcal{O}(p^{S_\mathrm{max}-S_\mathrm{min}+1-|S_\mathrm{left}\cup S_\mathrm{right}\cup (S\cap P)|})\\ + &= \mathcal{O}(p^{S_\mathrm{max}-S_\mathrm{min}+1-|S|}) + = \mathcal{O}(p^{|S_{><}|}) + \end{align*} + as required. This finishes the proof. + + ~ + I think the same arguments would translate to the torus and other translationally invariant spaces, so we could go higher dimensional as Mario suggested. Then I think one would need to replace $|S_{><}|$ by the minimal number $k$ such that there is a $C$ set for which $S\cup C$ is connected. I am not entirely sure how to generalise Lemma~\ref{lemma:probIndep} though, which has key importance in the present proof. Questions: