From 3e9929bb13d395a475ddfd4045cb00b3be5caa7f Mon Sep 17 00:00:00 2001 From: =?utf8?q?Jean-Fran=C3=A7ois=20Couchot?= Date: Tue, 13 Sep 2011 16:10:08 +0200 Subject: [PATCH 1/1] review 1 --- main.tex | 42 +++++++++++++++++++++++++++++++----------- scheme.odg | Bin 0 -> 10791 bytes scheme.pdf | Bin 0 -> 27531 bytes 3 files changed, 31 insertions(+), 11 deletions(-) create mode 100644 scheme.odg create mode 100644 scheme.pdf diff --git a/main.tex b/main.tex index 717ae3e..c134123 100644 --- a/main.tex +++ b/main.tex @@ -503,7 +503,7 @@ bits. Moreover, each binary output is connected with a feedback connection to an input one. \begin{itemize} -\item During initialization, the network if we seed it with $n$~bits denoted +\item During initialization, the network is seeded with $n$~bits denoted $\left(x^0_1,\dots,x^0_n\right)$ and an integer value $S^0$ that belongs to $\llbracket1;n\rrbracket$. \item At iteration~$t$, the last output vector @@ -529,12 +529,15 @@ $f\left(x_1,x_2,\dots,x_n\right)$ is equal to \left(F\left(1,\left(x_1,x_2,\dots,x_n\right)\right),\dots, F\left(n,\left(x_1,x_2,\dots,x_n\right)\right)\right) \enspace . \end{equation} -Then $F=F_f$ and this recurrent neural network produces exactly the -same output vectors, when feeding it with +Then $F=F_f$. If this recurrent neural network is seeded with $\left(x_1^0,\dots,x_n^0\right)$ and $S \in \llbracket 1;n -\rrbracket^{\mathds{N}}$, than chaotic iterations $F_f$ with initial +\rrbracket^{\mathds{N}}$, it produces exactly the +same output vectors than the +chaotic iterations of $F_f$ with initial condition $\left(S,(x_1^0,\dots, x_n^0)\right) \in \llbracket 1;n -\rrbracket^{\mathds{N}} \times \mathds{B}^n$. In the rest of this +\rrbracket^{\mathds{N}} \times \mathds{B}^n$. +Theoretically speakig, such iterations of $F_f$ are thus a formal model of +these kind of recurrent neural networks. In the rest of this paper, we will call such multilayer perceptrons CI-MLP($f$), which stands for ``Chaotic Iterations based MultiLayer Perceptron''. @@ -652,15 +655,32 @@ $\left( \mathcal{X},d\right)$ is compact and the topological entropy of $(\mathcal{X},G_{f_0})$ is infinite. \end{theorem} -We have explained how to construct truly chaotic neural networks, how -to check whether a given MLP is chaotic or not, and how to study its -topological behavior. The last thing to investigate, when comparing -neural networks and Devaney's chaos, is to determine whether -artificial neural networks are able to learn or predict some chaotic -behaviors, as it is defined in the Devaney's formulation (when they +\begin{figure} + \centering + \includegraphics[scale=0.625]{scheme} + \caption{Summary of addressed membership problems} + \label{Fig:scheme} +\end{figure} + +The Figure~\ref{Fig:scheme} is a summary of the addressed problems. +Section~\ref{S2} has explained how to construct a truly chaotic neural +networks $A$ for instance. +Section~\ref{S3} has shown how to check whether a given MLP +$A$ or $C$ is chaotic or not in the sens of Devaney. +%, and how to study its topological behavior. +The last thing to investigate, when comparing +neural networks and Devaney's chaos, is to determine whether +an artificial neural network $A$ is able to learn or predict some chaotic +behaviors of $B$, as it is defined in the Devaney's formulation (when they are not specifically constructed for this purpose). This statement is studied in the next section. + + + + + + \section{Suitability of Artificial Neural Networks for Predicting Chaotic Behaviors} diff --git a/scheme.odg b/scheme.odg new file mode 100644 index 0000000000000000000000000000000000000000..8debe12534f297b13f55ca4d8a5e8f31d05d36cf GIT binary patch literal 10791 zcmb7q1wd3y_ctINA_z!#BMs7>N+S(Yy9+F^?7F)&A|joFfRuoM(k-o&ASERw-KnI~ zh~J_Qk3P?<@Av)(cK6=7=ltf(oVjy<=gigBxP(cDhK7rV_QHi%F8vZ;D-RkP+W7}n zg$4mbKuAv*$OZ;;1_Nx6V5kefn+uQ+YJ&hH_@FS53lIu$g@9a;eD-h~m;)Gq(ESdG zi;Mdm5QXt~AwV4gpf1RBX%C3=hS`M6l&HA${iIDRp^Q|6;8sB?I| zoocQ^D0#qtF><)DMCLKVkkoSXedn@%E%Z(-L}J)v^|JHM!k47y@EJ)v4`I|fM((}O z5>FjpE#=+F@$)j86&ee-O<_OEadI_HXnQAcBPFt-%(aUG8~;uJqbx|1UV(9;33ugu z2O}5BD^V|5|RB8?i=C7pfFJ~VIv9a06?5$>d1q|k@q}sL1Uy=d(1*wi?E>5Vh`pvRn zC+HDXcS+N`em$AmPakg{Kp>5NpJR5k3KL${ZXu0!^F&IB!L{pA(fNwvRp=Xp$)Q!+9m|oDAD(Jov#T*q zEFVr6j=8mwsi8hzxNTG&G1s6@Qw?C;wvrCsW>OArt70@3(2^Kl0~nYd@(eF zbDpE`m|jo&xScUAk`tQm4a*{*HM|-4S^e<@dSh*V71mLn!F>YU;^7*3N8UsL=Qp~L zd?F*BZU5Z2HEaHKiF}lN2{(sA2;Q|)smVIT$C#uF+LetT7HPf2xWZAWiEFHkCJ)3P zP8y`eSHj0EoF#VB=!)$#fW4R#F-7yeU+j_e&iy3JX^ww=s2sBiI*AwZ5-W=aax=D# zl=A69Tz5dE<=dS1)eW}C9OaSfeC9{l!1PB^U&#mO*s{{q-*BW7IpQHF;#!WDBf0Jm zk!%KL7(VT0FiaXWO<3f;_hJ*ZkuvUeFh zIq_eF{X^T{kDDU~S7cU+`kq#o#{krZj!4_*F+;-iAKVXq&~;*#yq!FuP+G0N!IKTk z(D+E|Vey=cE8bDJ!v??7t1w99u6(1>x1*Di8zpIv`QG2AdiU%#m`Izrzn9)^j75tE z(>T?klu5xid8p7S8_1JcwJd!^m?XY=AhdV8Q<}-}W4L~iv&RD#*e&Z6j!c*g=Y*p& z88VEa+3s=cyrMo)gL=THa3)NSRO8S`2!#ND)Q`7d!1XE5cwEnGN*%uOhlfwztinC(`ZPJc~6L_!RojswD&>Do$E36K$sHaJhkp4C7oR@t&=)ySiSd51nW*^ za%<1+F!y;UoI@33kZV%G*bb5*&|jL#X%kcxg;7u9g4JkwKuF7ET=x~cum=i zrn0YQx}N!LyA=r?1GktXj!i<{c?2|8UfWNvZs4QEW`p&&mxU&l4LeF`Wp5y8eH0VZ z@=l*kb_+?*?zVgxw_hVda^UW-xgrOtOFw?8bw$b{8}FX9O}>}r(7QP%Xj`ObTeM)X zpQ-&gbvs!E)0%lofwxkMX=hJY$au|!u?#u5h74dGl2I!@kd%Da#eM2qpW9034wouw z4wG^%*d=(L$b{L<*%6F3@@yri1D~9K`$=)=aUhV8DW54txM`NsVn1VCjd9&j%7W6u zsc~FO=F9O?15Q{grl+CU#}3cz3HHsD`iXCqG~ggG@2u6tI|)6%}Y zZc?HhE$!4O0_m31OKyB5+S|E_W1)M-VmynfGxsU~ov|ltL+IkS_Tr_Fe7o3M1S44z z4rXaC!QNWk8=^%D1n_!_#fJc_u~}!xi)4ERsojL}&vkvCW?EBX#M&k&GVQ^l;^M&O z(D5p5(Wg1O2k%zDA_j20W8+|sVk|}q;?kU;5-1@WG-T5_35ANf14pr#O z(Z)@TF-xMz=C%RKqx=41-!ODFaB$r=oD+#~(9j$>(a`?<6van9MG;6(XAt82Av$Gl z1)aEY<^D{LfB_O(e)a(j;MX32PzqRc1-+P%;?<*|xkaYV9d*LCU$a%MQ_jNG8OJLD zUl#!zS?7AV&rd}k1iKsYPfvl6$naXm>sI2;AKX>NqfIn-hg*(54nj9;KX2{^6C|** zwtP-h0R5*0iM=$u_9Yc#H z)Tt}g_>di8VE0lE#Oc^mH-C4s6MtP(TAks_t4-eKkH*>s)U<8^V^J)tLtg12c8)E2 zA)%k%e;icP8L)_7XG$_0ewz>T^S|N9C(#v%@5kL~u!XVMYQnP4&HF{8$DC0vhFQ2<3iCJmc`5#bNe$z2+Qkb3R>sc zSoxwGtXSdUw>p&{81%3U+69phFso>{8O3?BY7j-#WAC<*u=0?d236Dr-4FE0f@4t651GQNuoOIs|K=t3e2OB79brzcvtsM~ej!2oKo7F$3D`F?Y4c(>O`B2Ld zRA4`m<0|yP0U)+66A}9%o2UXaioPJ+p8-^~)U{%DbS!5Ne9qBNzR49i>yfE^utw6F zU)P(21`(8JWVm8H#5Wh9J8sfnD3aW3rx(X6$%s!@VAL9@oZ*JsB3v1)Vj{$4_XgPXsI&Ig1wd#)s*1FZHT$kgDts822=jAy4cYtH{22PqT)?^?B+u2 zw2$?*(o)i1kL=v-NMz9@VgTmH3=H?)vE@84p&O!c)lH6#nSAbmCltxRGw&YSzX-%_ z)>=_v7Lj36T;V5uR`HmLEGh?eAjYBOu*5wKXN2NG;Ejh=YLwOanyw)T~ zrEEWAoLSXjShBQNsfmNbTq^d3iw9H+Cd=o0W>%OIu%8cB9(U3r*600LrWzLMGka39 zm#-SN+8k`N(S}5GNnqr8K3=+3dOg-i`9*4c!BCMesMB;>@Wg{yOGsuTjzzrW1+87t z^izAsEb8dGk3wdq`A^Wu#6Cacdp$~Cw|BxF-A?MIbcC9KKJGO3o#8+3qBQVkMC@6)AqTeq;AJUl4ak6}ml<$0pUM z(j|M^PSKc0AwAjEh=$w5CL~Z_HP?gjZzXi-kq;{XIr2Sz$4x$~8*@jG@Twm!Jj2NV z>$d`0OqVjunM2&x)Tq8nH^DnTIr8m?yhu?{vQBx3@|zH*^lFjRb7#YJFhY91WP$1Ll9~U%-u)i`u>$mG#kU z9(vy${8S-UdBA!9Rj;-Bqm(;t^{sdN2RUv8M17ViHgskU3u=Z%L=i+#XK~y#)WOlOcP~lVV9VOs>6g(r^Q`LEl6p(8toTUHD%>F`hV!U8 z#JFCaeu6cqUW-}e!BcqAvVb#rz({BqS-D%%Ra4hQC1U1J_(9oOhB#qsZEC8Jag5q%@l718s*sOQFv?S^;FuZ zw*@(qlA`02NoTpXOIbs))O67F4gSv&!;aN1$3`8l|K>1?3@8g+ zkb#RBU3dw|IfjXbcK-Puql1t(=Ttyi4)w+827)6{QMwGXAfEs;Bgh2+1%h4dWta^O zRC&dj}p)07&v8aOXuu_%@6vRTqThk4rMlu5cI0?;*aViwy*XkVFC`e~tAe zf0dT}-q4R44`;B8lMJ&15($&!=XZB^=W`e4gTn3k1tlaT_`hFe{;Me<;BPsYE8O|J z6cE4$~Yf0sFqE;13j(+lBZ&5Y9+`D9}y_4z%M#oiNK@%-M72%1VECG1vu+ z1lynn4GywFLgBKvKsGMCs;Ktf+IB}4^8|FY>P;Ex9WURe<5 zw;cir1~7j20@U^#1~tuHU682tNr;(WR{F15B>BU$7iWJXe6Rj8;aBzFjocgWaVt$5l7$dGSc->D#Pd?dJ0BLdu1D}=gi6#8fHC)kx zYeedyetzoYx?wM`klwza_Et3elS?(RU;b zEq{FJ%gfwXxsM+8gPnLfWEe>U1EO%BisQetb$ODFkN0%4GHCLQqs|&oC#6oE*Z=z7 zQ+AdY7H0X~Rab&)8p3Amaf}CDtZR_Pn)U6c_>DQ$~+MtAs>Sc>?PcwvCI#b zgYtwbaHg8~-qGo2v0_mxaAzzfS_r(iW^pSHIxt$tb2>$?Hjoxeks1C-iE4FsIwr@C zZ6->C;j|m$)0f*OB4;Bh-wv{=JKsI)0NzI=7XqoX)}}KbvRz97kg7V-XE^Hcs@FZB z3)jr&<{<)%eFU!%jd0X9CPuZ{1wRDoLe26A(&e7QE2XE$mNuMwZc|0b3#Er)?L^N9RpsN z?|ln*I!D z8Sc$~j(xQEG_}BG*I#uoJGXLl^x?>i*ta{bjf$#+uDw~p9v0E3bT0M=_w5yv{mCA( zxodCv<=lh|Ot0&z@bV$+Ad_xj`!xda8s@8Sqi@)>T8j&-Y8Duo<*T0gt2(CC_MUl( z?e*qq2ken_`aKnnAyVdFuV{>V_->v!NGfDV&cCk1xPM{4u2J`TP(_)?O!}768HsJi z*4|E{{Is-8r(!BxH2m^W?>Cmfalx|4NDlqVS_p}gz-CW}tFZ#h+yM0+;*BHJssSC5 z{E34NqNnY~+;2m5+cKg1ldDw2`LXpM=DeSk4xjrDmyhA@aqhM9)AblHiUakz&xo9CSF2xVwi6rn z3L5ybvU!Sm>>S*=oH4x7wi&ihV#OO@pGO4xQp>=c!c{50wfSYItka)J{;Ak$)d^ml z$EJht-Us7!6*DtsW#vWhhbe0fJsBW&#g3q+l7V$k>C8qykKc3U|&G69;^-pRCv zJnuwqhFVp)U$*pBro?FoYiN-5Qr|o^&9*p$XCA#(Bm&PXC>)UN3#xp^oW;B$XNK+B zcXDRBK(I4GkU+>T+nFJ7yzTeF8K+1k@`KE?iPs~IEuo^X)4oPt0Rq1DLn+$9wCYi zPi?QZKM-&?IHFTkD?7?)PxCh*nC2stPm<&+sG60Xhesq4i&%ZN?zyiixJc$2=>=>H zT)6AjpHIxkB;c$-uiO;2fSj;MSlU-tn(3LKO7R%5lYA|=kwa+`Y`1a7*S%LV(by;b zG(yl3d!+)=ToepYlY&S|PbGm)M#B;-dY1+jLhrIs&{fe%Vx@4?sJrTs-k}hAogog+ zdDWQ^;;sG2m{j-n$)jOWQPIjuV^NV^EdYxRwJA-?(3n!C+fB|-@Egj;d4fMm9aI(=ef#CS=^n0uGq?NDx4Wn0IJu8vhPdQ%sVCs(} zD@aJJ7$swnA#zW`?riwVYtbC~z)?b9&8&ggy2|Ag9rKj#jP06kou-E7XZ79pPT6of zHXbt3jXw?|ugLve-!6tPkf~&2gBNifpc4b4JY2-2mTA8I&A^Fb-`}h8a3ZCtqEj>8 znE`Z?nw-zgGK7Jdv2;*fMV~qsmXViO|0=?_D*1hsk=3RL2Q~mah6O9As~dkik}xay z&6XFs?s$3I8Y;jvR8c0GbR<`h#d$tZkbXo-Voc2j!K(rtmrnXn;X5B&< zD==O@r>IOM89{^laJ?%@nxi`0wwFa)v_!hY>4fMl(mnFWMfM%C5ds`1G8q zs;l{yDWKk+qPEt!uQgdA9)H2EAIHMSbmY<%bMX(F18)gYIb3h1Ta{P=>Ri5iNiz2Y zOD;=zKKD^xw(eGIs9@h!r>9{rb66rK&U-snn=Zv6<+W3ThOrrQ>D}d(Y-`&sFBhH6 zYum;6C#M5;i`TbnwYxu_4C*iCOA0=qgFqm2JYPNSUQQCon}!v--H*wmp-n4&ZxwPW zrM)#v@B!Y`T9`6(nM@FQ4M|M0!^mOe6En)pE^C1}&3?(dsk}|nfYmZe8vNPV5pi;j z?N@zTy&xhYMelMPd#Gr)ni#Bx6gJ^?F!DAi!(u}wbkVB3{HVl56|;BHknWrDxc@g* zc&9~TtxSgN*_cQ_7QU&ur2P7I>GV^Y^FXd9S%f+O6{lTCC2s%BWH?YvMhWU-2e$u< z`yqt*Z2$mNIP{&W@dI4p@W1v=FQH&?&I3O*jPoy4`2l+oAO5KO@lA{R`8O06BN7UA{_k20zp)V& zHray^{EA>C#0G}=FNXfEgXc8Y^_SuN-QG7Ls!;?g$Bv@+-}ClMX6A_b8)Uv)B^@5e z{jygW$Fd*beL}+{s$hL4Up3W$cVa!%5vvxfba)USaMQFjlqE~sJ~`OJdF>>sS3*(@ z{`E+dnS;Lx%kJgUu#VF-o^Co;Vi4~Zc)Y~IGkrqNqT-15q@OS`U0EKa;uq%_Dy}z? z=TK}_{VHIPT?r$cU4gdyn1d?`)sKW+j0(D!c9EXGT^=Sy zV$_lOp7o~Gh%5N`H(6kUEgLcuFJ-e3v=l0)CDYS=l-^g(pe79OaD9ym?&TMMn=Ygv zVOOdBG9K2KY0@dpGP8!SM@t?!;B=t56~Z2+XUBWZN{@XcGI@zFf^h#a?x zV)ng7)_a8@XV0+mBY&HtWf{wnhOGmiHbtI{H|ScXpCFc9hJ}{4+^^l1K9%ouySg&0 zD$Ob-c59-xo{o+@!G|+<8LychUNg487WsbL-S3Uci_?|Lw?`no(^~=a_%G03DVBC) zbvq-HWV#j(^FvxoX)&d2@jK)BJs=xYu2Nd3U3Uep|RbkmzDJ_EAj@ z?+Ete*edEtgOb^ZEqAk7k8uNG(HLN>t{ngq_P`?&k*IosUOOQ|XI-TjpQ(-;F+-a1c(h;JX_HKT`+ zYzvy(r5rv6A&nge_MfVQ@LJvJ29=Q-TVwKa0=4#YfLX^Go11nJXH&=-v01E!#`9|~ zH?LP_X)Mw!S;!ZE*-M7l>=1i2d|K*1$rtH0_BLJg$5Xx>KN#JIN%eTj6t1)&43|OSjZ{KXx zDouYx#>Kpr_q#4zWhSRy(>ckIWaT=aSeS;nO~X2{!xPSzu%2;y17BysrWd%>o=(cv z)W@Y@n0@oqpfriDfEy^TU&*>vrru|?2ZZHwMw=NW&rcl#8|c=ENC}*Jn_{mnb28}< zXan73^yKO}3tLaAEYo+WE@NasmwDs{X!65ubUJYA-|49>+PK=2{&1YZ+=wFt@KUTr zLythD;0~_f@B*(>fH^hoq}7ey*Xdche&mUj;lXanjY{vU8;uDjfJa#38@Qm)dW!dw zY8>maTi)5%MaW!*2{TQzuQGodQ;DwYxeFV)ldQa?D2C8}INiRh8?To(+pDbCGY4d~ z5f?drSU^&3lW2?KvM17}y*Nr@fTjNtW~#wy1Y%sNW1Rb!G|cOSO2lLlHpAU0SYVn``S z6<03!Dlzaj1=rlj;90kNX0&OT(1Ou5en$NWybfTs{^{!KJ%7vDkH@#as*ST~*3=YS zWgvkK640zZEPBPZeVaD-G+W48B#@IG2R__RZ8QioIyggQCLc74ZZx8wKhpf;4-c+j zp`krxxp<`gZY3p0t)yBi1`514wN?2csEn5#2=V=WqRMzJmllC5fd{F~yRvt?^TTlC z&GI-ha41u6mM+S9zQuK!!6a8Vr@(5HnxMYF6}drGVo5wg<{gp!+Nl+>$BK{asvh5q zJe>52IBtRctKv_k7OBUN1Gr;;K2E9+$Yo~(8Mxyb#$GA2*H`lMrR|4%U7u;)vSGlSeJO{anPptoBlr`_sUO zP6RTsK7-Co!2E~M$m`CwvtK&0PNz<|YRkk6vUx;@57Q$(X@rG{?=L+UEm=%2fq%t1 z_k{`U@w1!gXlNi*3R+hK9fJ(*&o7Cg9P&%KcxCKD>%xb>?rxvI3HGz-p$>m}FYMon zzh=VEH@|E8i7A0 zoBoY*u64oA&Z*tc0-^g)UiAl}cL93Qp`RdVXy?T4XKDQn=s#)RKRx(U6AkU3ojm&u z(ofp=XOweZ^s|W2|7RzErGbCO`KL9`zrp!Q3;$P?%-^8=q=|n%Q)5xxd%<_qw0wdA*+V53?L|ET7}}tnbg~AZvNdNKr*eja{~5 zG4&Cl+(l1zG+OzDtB;$%yOaj>jg_*I#}$89UnymyD;NA-kGZNh3Bta_F)!OQ&m;zJACR;|6xrH)za{u z7(t#2L3X9ha}noQ*yr{5fD|^K{jNTjejf~a_iF*arv2?zll}K^)c#!Bnc%Cg%9a=0 zT$RmTFL_)zio;7e9DIac!>5FqY z?dtEK3=uA+Z0Ze-VgPk8#QPhc_J@d*I`XeRwiXvXU0wX8RDKO?#ST%cY=HCeheq|2 z`n5~Hef9g&eogbQU6WG&wKl2W7Uw6WZ02#vPs)M)*V3)n9i^ZV0-#l?{2J}|t}1_Y z{k^Bb1^)|IaBlw|;&%$nUHvayf?A|hes%ck+?szM;7>x>l`SmIrBpDO-)H(o*S{92 zY^BNmtDDtdmhp?qf46F}YyG|T*T>%*PX}D||F!$SZQQRdxq|aOef5HitMW0|Ko1vJ zE90Z=%4a<;L7bzma)@2o#MQ&i9XbdVRd(g09{zrouD%91@2fbUU&o`x{ySqSA2T@f zFRuDG+o`H)9?`;JerJlEp`B%bTOZ;KSKtx=J+PfozyM(Sy z(A-SS@Lju@nW5HDs2yPD-Nm;@MW2QL)CI)eYXYhfHy^S}AAQxd+v*cl=I}+|NH%ss zAz=|w*?n^I`wyt8YiMd6(Ka|{Xk=_+di?YmYn!vScJ?lpTra!1dwBZ!2LuM;gRe*3 zh>nSki%&?ub^A_6=G}W)kMbVpKPf1D`mD69yrQz|^_%MEme#iRj<@gL_xAOF9vB=N z9wAevzs!7{ots~veP3PsvAzLr{`^H341oWOEa>k)(gke-j0rjk=pZ1vU`#>32k!=AP@Zi_k!FHj?!YACt(;-d@Q9PX(>Q~#O>bYQ^hl{ zB2&eAIY*2CV$CB`j5>qi^_>@UIYS-{3hd2Xi!@bk~zU_@_zMM%#z*YS@ zeJROkyKj7%i{7&P4h`X1y1q4&thO#!;{4siY(Zd;%nwpl^Vw(qG27y~;% z6?g0fGKY7I1FJZ0P67unlLAc`LFBu&ftvIS|g!lot!88b&Od z%N*u^W=7IabEUQ_BFw8ImnW^t5&~l8^p;<|eJ&Geed)aQr7LB-#`REojJ^h8g5wi= zItNv#Ntw^sZF(gkN2;>2?+4!dVa=9OdV*YSjmeC$5eL8VXN&h=l6d5qI@)b_0QV9e zf??uO>R_v)CfTBi3v1?(SR&EMO$rSzaxQaO{M2z3jM#ld$&%0De3}t}7Moh>z{OQt zwC?~3B&G_Blxn%Q2kb3PLX!J?(ar@9b}~N$TCEP6dtis-k%auojH9co`h`V(7KrpF3emdF3P2tV`hz@`s z-`!S!5Ukp=@IsYUMipmUM2iYVzIZ}wy=LFEzy3|Xi@Ue?iIgPTop?I!&y;tBd@LAG%`d7|D~d@*Mrf`F>c~`!t;A%ZZxjiv@sX? z*!AXx1Ur%rubFs2qew0?X9sYz7$K5_mayb5uU0JAZ2w+u!=8$|KJ~jUk;_A+%f^?C zug$#Xs)!Q5ec`h?5a6^Q{7lBO(j7oYs>|u}{>ip5-B`=)6FC#YBO|h9H@cMX&$R46 z@L1{dm7Le#^u$w=x2yV5-hkFM87o@Vh7_~+48lnEJ&6>#@QIw_(P_4~y~cW6Ao;`LRc>8( z_+a5L6N7=YQ)CqA(8^HTPOp~(aZMBApVcRM9ZjDItJR5qbm+X-?5Xi_bZ?TN_p|36 z@bJeuyMU`%#!Dnh4Hh|XuW@Hfm`;2%uvEOa>R1EyX=zoupGIazQgPcEFjl{zzDpXlxut1@Ei*GS#Yw0LMMI2a7!RicHt@rrBlseBYFsNtG!C zwi>3~n!Ajxx9<)FKS#sa4^`b$#H+gcn$Q}%!=GlObPu=Zzm)kQ9$KJfm7gLike%!%Afi19O z51;DuV3G6k@I~a1MT?U(HFohHHMJ$|V2`?@P^(7ZV3A+`!g{*>xzUXJH?By5aMc+* z+e^Nzx^r+ckv*)-nZMR+2VhYz)sZSYmL?ENXFJKvVl7o3KN>=`bq2 zZ128h)hIaun8Uh2&kygj_91}yDfWT=8|FUIg0ws$kU9MLKX?PHq$CJ~pgFRGurHtR#+1pn56%RWft6bLRB&)&lcYfX_a8cUySJGGY*XgmNn9wsG=kUU zi%I}~Ofu6osK}NOHvdT&h&AmgzU;mFK>PFFkb>n^6PC?$Ic9Gz%cYwGf&G9b;tn`D zRnp=dC-liHYb9nns_muHC{AFm_uZ3)ft*N%IrbApjqhT*MBM%PIXfRi>WGK;r+udeM8ezv$sHgUA7wyuN_>L9)uLVZ zxISD_6_GGyMtK55|5w+PQ&|9?Z9sL7As9}h_?;7#x#nyRFW5&< zOTSfIdYJt9&U)^_(Nnf$eK~O^cX$V4Ntrqm?n+&0J6e!t+)NZ&-2rZo0M4KXF4lQX ziC_&G5sPUg!=?w32cjr~Q8e~}pR4+PbaSuWj}yfcDbAdp)$mu+Qtg@R)bhlIx5Dry zsUF0Y<(ql$q@$DdFJIPTM_8EyVT$uPJUv)1i(QQ29YDB3F~lO)o|Zhhel|Sg>#~+> zN~-Xi9L7T?hBVbF|^IUHcL+QQGZ>JU3GR;~SodYpcIIyl!= zfU%gUhf3Q4%2J{z%Hb#&gPk!#LLPj9Q|t5y;1Z)~M0jUtXQT&++)?^WoP92=Pclrp zFQ1l%tPPU|GYx2|OBGu%u%t!%wsvf6MW|ToM&;Sc+5Ko$51;of3#?P$wMBu=q7E!v zy(9@+;k@+f1sz)-syS^OK1+R4M^-#8$8Ol`u^AHBEw+!fs9Wp~+ok~%Y=F^ElJsvF z5o54@rjSGoy|+n}Y;z0qK7zqRErorzo*D+TX6>`tjJy?dZnYvNm>ED0UH@Mq4){#N zh{Dv_*3^_J3+jtIw9?sTXSS84u7dblU6;rDy6vw7w?DiZe}&{;+Z5(}p&i5g6!>Xu z_-U=1dv3%ccFjR+NzGezL_x>QHb#)uMK3OKakn1oIMDYGJhZwJkL6YCj`_)KpWl`I zv7p#_Y#%9aPBe^bpo}necZtj#&c^=XW2?-yytgx_gu}Tl$lWbmMjf`<6kO}KPH#8L z3|)~ehqHnd>unpgE^)+`=@qB)JryR?VFQeSvG{q((SHXQy8yx<1;^&)j8HE=O~EyH zDTQ>iJD(T~J4oe9_~OX_AuA(Wcq=n6BYk)CSU8^F+YQ)g;09w2Xg<-8@uU{}{Q7+I zw$-@O;>waUA&6It^Lar}l%AN{|0TL0Y-}0s0IjPn3XJ*PTU>Z-Av_y;L$+k4 zKXtk8L2|3z{JpbpfbdYZUkinOpIo|Eg5Lp*wsQzU1#~6qi>ea*O6xVHC>QVCVe=rx z*Ka=few?tsCHffSvC1u=@!{r8J#poT9bk$?EM-JYb+fzY$bjaLzG3#h>MLGa`Qb4V zx-qCA8tMr-#{Euo}O(g=5Mm^C&K8~S911KKR(5|TvH+y zINoN{y+_)`+byM_u~bRh0q~dLRomh8UC-y7Uu{I8IcU;NgFjsti;MJ$xnM%GnTMzd zP6=ao{*Hk+e)6I4fr*%Kj1lO!rA=@I6}SB9{M7u))EAJ?+Z`iAW62}e5$w9I;U0}T z&u{E`zO1CTU&OBeK&;fOv_oG{0LYRs1m3L8-eM_p%MHx4rhY7TB|q@Na&a9#TT_~$ z;CQUG^4`;@(m&3I%fr8tSQw+kGUHVAsXWkF4~*%2=EWaMGRw5;ExDptVS2dAwXXG( zj89t};M2*+G^+-qNGfhWTqE5eR?em_g~<_2YkI?k9SG>MoIc~6;IEP9N6m)%#X^pa zU3z_K0&`5UT=Tp;e4!z#p**&!J5{lGlzy1zyCC``<&5)uP~feh@sY@@A`kEJCZwyp zW;)z-gc7dRjS3r{EGubA<@1u{8LahF?~W^vN~<8lELcO{0VL-&QC#E%Q@6qV%(pQ^a+CaQOyyU!-oNI0JAG46QlG3m z8oTa7D~VSlakx+N((4RtvfuW(eO9aa#^HVZ#L_5ND^2E#84obV!3TVFhrffoKGMj> zaZq>bD1jNoPaL{+f?As?H0Y!eujZ9qAP5C8r!N(L;}GJKK5~KOtC&#WrzT(n#qGrq z`rP1Ae95ChM7?I*X}U>cu!uV05c2qCMMdzmLSfM%UbgJLstp8|BNFaR%5jsGnu|1Q zS(^}pljfWjJpVq!@J6qSq zbep}3UiR@>K4&b>yEh{!5WUNqIUNs~>S%&uuQENj#FRGOwtiaw8qsH9g6~raPo8_0 zPTGW5d)U(WM1RJ)@OQ#7lI$ku;ByE5riC%rY>gWsgMBR+RSg z!-^~Sr&5^4@3fnL8iB0^{0%wzJCK3WZJ=8>l#iKitWCx`2`CY(1Gwx7P-v^*tSuFv2iPS+)STLAaTK$>d8?_qqt%?fqt#jEjJAiz1A5Ca;Vl_! zDG#5s7(uj-%adsN=^mdM8~~Q=W zd8yx48Lcd!`gdKYg*SKve71vQpR#e9-5Lg#^u$q(-Ek;By2E39)#>dd1_0{lgQttU zHmaoCCVAAi+PwqUUfaD$uD$S;-A)gv*J^Bf3!vET#NLG=KvIk3f$BaY8TlFO$+}25 zJU*Q_sLVGeq7A57FZG+*P-bbM>j0 zdNaC1XUbOeBs0m~o2G89*ezMXhM!ks!sUrg>fTqDA&tC^YZIaxF?0uOt&6%TA@_j8 zodh|l=g))5>^ucez7ylVz~?Q(wcQ%K5Jzd15!BtqXZ2pv)amwh#Yr1{Z5~Cgm`{A0 zk8i-gY)ZGD=Q-n-4qN$?i(z__*QQeePbbytS8rZ{52leEvgKEj5iw87l9kwwjLVU5 z`^U67c~nNiwTR%U38@_*FA*%-0V1wj>;O`haMYAroSnqk^%U?$l0IzUo5}mFr1>vl z{=f=o`7>$84c6OHoH(F*A|5BXLsXobPj(u#_bNLB+Lc50vG4 z<_OV}-)2*gQ8)*KfdY2^r5ADO`q!Unaroh6_@}OxNOuez)|0IJCmryctiV<$7a?oN zKQ2u{wuxZeXp;%JA7XCUwt~^!ea{nifS2n7Dkl)n7q8#aLmmAS-TbSJB6w*ia(5Jj z0x39wq0{4%x)#mVtxncmMd<~RB96koFP=Yp-;#C)@&$<|+i|t>)uia`4w6uqEPkUI zBm5?1#e|xf_#of+;_H+Ag+1UE6X{Yp+>Nzl3J3TmK{1%nL(m$0*BUw z!Rli^;S)XWIztphc#BOWz z#}R^Oq&t&hf&zEJy3d9CYD~VYx`CVNQCo>431jww8;$k?wC)R2lY(BR7*aL%N7(hp zCVe;N9%c)_m5S5{el(lQ>TS77<^+0Bf7)X@H_>&kHi6ru8LhWUYKZ=cNw zd!LWL4}_hHWYGr(se_HqoOmxve}m|0XBx}HY13Lo9C`n!)teZTg36dy6s zbi>y#=~fz&0Gd;?o3PAu-X{bsl_hIEYj-yK`Rd!tImZhboc#F z*o`TFdpjr7CFJRXrpoC2`c3re*zr*-`5wW`E<*sD+(UE~)nLoze-|IfVuj-e8S=;^NoFt>`R*ZD zYdkd`B7WfGiS+p(uC;qF6hrMwD2umYEB_&Qe~g1jC*Wy5`BS7DlDdQCg7DU_twZjO z_i_Ep_q?xUGIsf)rD?g`osA5>KEkf423AnaNVpfR`^0|UCN~LnfHgz5yPn4qar&R- zP29MZ6c;88T1+|f(+z14Mn~~(`W0S9PcIrsr?IjZ){Wo0bLLul%gupsEo=l)YzH6* zyI)U@lL8&5QxWqo?>c>=dpya%`FYPBvxAjemqO>mRj(5|BmMLwXa6-Lf@^v*9>W2; z6wFm;CRe;(`{wOpUGeFlru5svpg~R>;ZtY$>|S>00#>E~zn+Np4$u~gY-tcc!>Nx} zj0V0Aq8+@013U`tM~a5+i_2Zd&Y8UyxD01!x=%U|to{6(dH*xX18*d{yLtPyI0=KN z;k=ry$(~5$xo9-x8g2SIdLCKha`6h_@#$8*9MYb5u=WY=2k!ZD<2S(vcu@{p#0>T(Ud^AYTTQpa^zUxh0jY{dA#z#-7TW zJbdi2ff?HFu`KHcMP8bM1Bsh^^bTpG$MPel(g>effL0P=6*e+ip4y1xraL9B zroTiDdmWvgH4euBms^Xt$-pg}e8|-4~oIHCt=ChYT8t zsDpc6_Mvgb3s>jtUsPYQ|2k;kT+!*R^vJtCi1XNEIlb=@kpMHi4s;BmeVlH~fzyyJ z#F2s)l6bwC(|8>EbiufTM~0tA;39TVI`PV0tJS$e9(R2_^0Tmv(?ehB!4RqVQYTp1R612XAGQiu7g5RPm3R zLne8mMmWYh7&-EN&_#_fiO{lnfZmLZI#oU-28?TlebcQ;R&FeM4Bpt_g z>{RI2n2!C)$i0-0vC3QgMJb4932t379>uk`bL z<4j=et8mYU-j908tok*IdME>YNORc!CQK)a>Vd{)!y}e zhn~*_iZDeUht~l2En%T#tUv=@z}T2p3VK=NSmc^*`W&1EeY0h282#xMW!cH~wwV{W z$^w@PwAuiCNn?X3n7yt@osF+&qU(d2G!DmJwc?BGE6q83sVAfNm3TiN>fV#CHJrv+ zm^yq&9{e^42m-C(Z~>zab7VV*AxSp@6Q{V0AXw+8a$5*eq+==-Iec&=<`x+wkayQ~ zpj1EBpFbEz<*TXC)X>@qqu8bo`CvlC|#NOrLK1DHl)JosTJA*U3&p zZ#fj^ZRSZmV|E$z34S*ME20)O6M4hr==R|DmLy_d8k*jTr-BBI`IaP`Rv?? zJYVhVXwuz#Gs%GuXJ@6;;D-<|!mmDD?d&UEfx*w%k~2a+(VGDA+ZpaUh*@F8GQ%-ODaaxChE zNqKS9X!ol(#EpDUVB;TcFPaGl7C^>MLU(W`s(k{Hbp+|6aWhoR2s?3U;Oo!0)ZAPo z@t+MCk_3fkSFx`!a+NG!!3fGlix=u_dfih19g2tlH0}SHO875oJ6OsNDCoRAb1L0J zPaY1%|E~ESM7JFvMszIU*n~`9cl=|n!4LiUq55Sj)pN5G;krNnNkyCFW zbB;e7j0!gqn5VHNxxB(vVE2fdc#y6~6qRn@J0+B-aGB@e?g%qG&f=n#2LcEH^az@nm6GwKDm%MCs?dt>%_x9N=H`YR3Q#3n38+Tbx+a{HZ-Ew(G z@S+~GCwc3tkJ|Y-%rhNHV{qt+V5xm5P9LpL-so#DRJMvA;`yEHk{g!F120SIc1A!+ zXk|y6S%zLi8D!!d&9FfX*$mOJ6*^aK6e>j?fc)vFw7^*gy5TZvcT)~&gdx?lr(^J4 zUG`cR6wuyh^pp`hsv0Huq^^fHw9iXo>K*Ts1{){trQ9%{!13axo%&pyx4hIJwHv>_2&EYP47ML(nD7}>cJ9ui z1m566HlVY=>+#hR7pO{gax(=G3^}ss&3NbH z24zFh7fm46My%x`wP>;J4L2A}4US@M7~Nh)!m(-p>jH;Ei%#7o_UXu1o!mAaH|V!S zNbdj~+3k{2)8xrUqKM~J&7XCr+nA7?BgDq^`TCKD=!d^{^D?6^XV2G-HWZSu+jH{z zsA(S#ZRnf#N$E*?@1f9<;n)i3;2#BWIgrHYzTmwQmaQK91sXnV&tidD%zz%I^f0m9 zohbx29JNkNz?Y~aqwOW%5Jko^>kq_NjNZVlu$6GWK-NQ{N*k0C5sEF2&WLz4 zSTwX$FN*O?)CT_CS~Pq;dozsx-VQK3*~$=n^E3GRI!TVvsR!lw{^ioMNWLMba^Z8v zM(~*}BbSTajnEHH_Uhd3crpl~o@wS=$^<69ch~ahhx^b+0%!fsf$CqWYxxazUu|m@ zYbKB6vO?jN@wXAqQF|hukZ>9Z0BIV zAZVJ5_lWq0wQ2SLRm=T1EC!nm(*et` zcs(zwl8d}U^gxQ!?P)8EG#W*jgD!KcWdeDtDQj>vjct`N^bW> zfgdFZ0){Hr(xtoB00T7*sp~njeoc9{ZSJL28>EZLAAC(+(oJQufW_a!D|X<0|BrG0 zW2s#O0oh`#uO4hvv9Wf1j>|=2`Y}3mWUm?5*=gm7=kI?AIqfY?L~Zm(h97xK^eh>U z5mI@#WkgWnOL>(lINugKwXX|+@H;N&twRBjT8IU&Rc%dDZw)Q|boiT>seHmEsyf*xaB?)`Q5M&-xl)Z2Wa@ zq%E0l`*BO*#$A_%$32LIus)Jzv+2|hKuYBWFOPov>XpH}11$Fc4@Vl-f*&Mjwlu`8 zQyuUdO``ki(4TlVscFUQ++uOi?8Czh{X2`{}L@itO0A?aDq7%(OP6y)D6d%S$uBG3l0ig|4yN_TWro=gI_d3ZO89+fZ&*K>rf1s zhH9PMl9${El>{dJPb&Uvy%rplT7L)v@|MO^;tR*dJ#*ChdFn}IW#nkZ`qQx7sZxgm z1!1&WuRuI89zs7<9?^q9(pERWmlw6B>AU|YwB|w0pG(cx&pDTt3%;4N8kW6qzqnBi zHV;8PX4F-3$>=^RF~)l-z+q8r$#Z66 zr6(@aP+rv>^7K*#^>V>eaN&n=LFN?KzHg3kT2n>i4tWm8^rtt{pCAQ*ZqODhp}qrb z?#9469_vj8&Qg%^#m{Y#E38-eK$7M2w;>V*xv(98wP8uRc(sUbPmPWB&Sp5)Dv~{X z+)^16FP0xb;14X5mJ4SHoGd6@r9hCNK)|E0?}pDt=8D!(!<7Rc5Oh|O-!Jv!3Y9?h z?Er7xAXuQ@Vgj?Dwy(Gtw*!PM1*y8xa=9E2uV2}Iux5u|QkcTFjG85V=|;p{5j4W& z(~DcTZs|!z6o5iaq9&*E@j3=&96k2))V9>E8AHJTlL05Ibfip*3SIu8@fUff<3Nh- zg$JB|t?5R@7(-61w4V6Khf@~Jo=q`DQ{&uJ%~Jsd`bxx=d^OnY2x)O}OUFw!c%-C} z7+ZB#A)L_#gVuK|d69R5-9U(~d)~Za^D0AU`w~khSMthSJ52xYU#Y@o|cC;*5_f%kQJ&h*CDaduY-AyZf;n4+w|Ex=Mg;|&b>lW zr9wOG0W4W~`?3E?|I|cDBu%1p2k5LyKr1R1L&b8VpYwa$8$eECK4i^a)*qQeeb*o` zncMH$8pI-N&Aq}*7_^w}E4J6~Sk1m1yB=i0lBRo z@$8wJ@|EAy@sj6WuuT^OA<@y>F;Crag&vtNoor7&q`axP>6&8w!^TQqk`k`?SEnF2 zHl?16t_{Wqc@=@NEflQ4@QYC_zsF(I0?$h6Ua=vOeTE;|%tyt9U8NHM8jcNAn6_Bl z_Ab`X?LxH?;gbth)wSzYEE0!XZAz{w9G{UrSeaR%xZ$u^a6~72j~?PR2&Z&JFl4!o zPPSands6o#tvWNd!bGyes`vhyL$>MBcf#nUi#6h$d54;Ek;Z>o-T&6_=j?K`|3p9X zctLw3PTkC0^VrMZa?6_;!rqTgWduvavFG}lLghO-nQd79dQAd}n`<&6Oz_=Ct@qPm zSdo`X&QI6-or(Cj^M3v}a-PEX+quI((_xUPV>uUB&Qo(zXPiB`_w`pKzH@@oNH%wo zKdOR!1v7%ylse$ijR1humx0~t4M&Te*?vfn(8voWuf+WHDWQqA3HA!Rl~T{`_k(VM zOyz%kC@p)RQz!3(%oJHT$&$r?0=4}xOsYicIB;rhlD)C|YvEfX?r+~- z4~(c9pAk%-%8}7}2YgQ*j-8TgF1DEJXb#1-F+`v;%aS&Gr%dh#ii1f?vjZ9L7rHe{ zw=={F(iJRA^`;KWhyN-~TpD_mFd;t$2@Y%j0b|kVGp8B>?#RD;j=vi@Dl%!3rb6pj z94D8583W&&8(r8QQdBEG>OHvu*$pUH1^;&lm*Rfmb%H}kT)M4{RjPP`h@%BF&vhtC z*JZGd11$$LMXRFKyc(FjR#k5Pzyg!z57DK>F!$o&3$HPK9a35%;+DJk^BAAP5Swcj z0&`fta;WZkrlsxBi|A)dKZFKeRg@Q}BzW&({*mS;#k729>nNz9d%U})f!BY@fjpS- z;u25Og=t%>0giVT$0{3)LUdwu(~l(GZ9nCg0Bod`|HTwYde9JLxk!eL1ZKmbG^ejk z^zzAjlw{G%rJvQF=$;TVT|IDXBhUL&gR!x=CE^|`4ub`i3`^Q;@lj;THKEq=z1^K& zyO*|Kxk(+{jt0b4o4f*%1p)% z$iMs6$Q+K8>0yXMNeQ3g0&sP@?!GC`L)FpUnQQv4h0CMr`yJN^#_xg&T2l90U=*nj zPlAA-m~iyrHk4Sg^k4~{jat*v2d+|Nvx9>&w6A>I6%#jm6RN$`PZ^tvnvqYRinZ-is}wKu ziKfR=H#hXZ=}9R5CH6*ydrs1Hw+jd&mr3dkH_#$aoySTxz%fgZu^W4iP6Wi}ZXJ$0d*qM_K9{STgWyv}a(YFTYn?=%!}C+rM}q^i z0-vgOxfCA~!46j~FbAP8Z5}heicn-vafgo;{=pB-t~OTBVOEFqzwkndePJiqHhDG@3Um4KF{q@; z-B-{gAyfViC>ZB_Z(~A7xk}C8W$k}jcaRQ!)QUO$%FG0|WIs^x81HA=U$IR*Q_<&d zjuCoO(@=l!Ld=Mah+EJ_ra~ayv<)E4ir4FI=hD=RKbB14B1*U4kyUNKO&m?A_fh$;Y`n||)jNF{%h9o`i~Vs8@209g-OjJIE5N>Uoi1S?@f;``ez7(@F|t(uL~Q9GY+i)^2X>5XElH{u zp=mD3Qg(omy!8aC_lHN*Q%M=xXCss@$lh6AdlS9h9Q1)nYS6a0H78B?`&IjqM?8vGVa z#*Vn1q>^Ikd#005w*+Rnc1QVdt$u0Q=YsLDMoT|iO%MEXD+^f1MG*z-b?^r3@wMCc zFxYR}sDzc3+9MF&pb<^kX75;3KB%xip7JIl%j4&x0Pksc#Kdjb6bgzwDG$L| z+A2k8q5`Ttr>hin?Et!p{;xGmcL2hIkam{KcB-%Ze}Y!CXge~B6aP)Wf!dJdFQ(|y zvhhqXL=3#~s-D{bxUQPU{<3915Xs6Cj^;KaNiw?c-LkCyOut6ez%~SHY>fvsU)uq$ zTfst)c7-%(o{GrW((9B$d>X;LdJM)M@2eO`oUZ8icRVWaro5r_4y0Y>V0WeiWK`4i znZD38PnK2T) zP`m{hzTY_H5jF1G>&cV{{H8Ry*Z_r4WBt#H(=}!F6<29vM;AmSOcq$BdRQv{OBq3Q zTQ*~q>8G>S16RYu2wL^uy)S%|ETPDvYVXvb1CKZH7jBuoH$h&3j(Pq2_dbjA>V}5u zgpu|UjV!OkST=E$LfLzFsRDqhTsTxs`I)@EZ)H95bNOVPlTt;7a#SUM{$Mm(**6+n zC1W%$Sxgjx?@yB)7>^O~e$aF?&lbQu__yB#L6s2PC@@V>1xrZ>o!Dudichtmf)VQl z_2f?w1c;_+@{DU%Nk`@>l2dQjd<1fOl4zK&ycQjSBb2Wzu-Eob`jys<{Wy=qVBb$6>p zf$s3NkG}~4Eoj{Z)ST%uX4i2AbwHZ-M={+R1 z>^^H^rJ^_WzYr0`I~c0tYt88!ber1l^=6Wwte*&(3|o zFLbod>g%z}(&)OJukMyxD!E+5SSR*UFlY(_z?9l4W{>+6Z}>S|Fe-nN4z=q#uhTSkpeIHU-GmN<0~Dd4cc5jn_s$h|ak?QG`zGJlHuQc1?_{>PRj! z7jmpwAovC5{=0F6^S4e&Ko_LQ4Lo=Y=L#Wh!3tN*gODrZ`y$;(jtJ3gpkfH52DqD| z=x~-Qqm4*-k;KrU26Td6PIo}B#2Q!2Dw#l`L+W+CDerviR`n#`LC~FFm^>AC1C4X> zeuD37uEsPx89gWaMI-BTlIBeVZ6-cz)7{|#oI~eTRj&r;a;JwMxrg38HB2~*NSUE# zBrvpMMi)EXsFwg(UGm*ba|xatdzWtU-{*5T?4YkVrD3rn4m!tt3O1) zIKYr6oa%f25WFZ|3{wJ3 z#zCk=`ccGz3>(!V`(qQy>R{D*B$vbk==#-PT%SLJEFDR3M9udQ^0?_{@8GzDNvu616=Vyf2<2k^9=V|KeB{@RRRPMZAhlWN_5cW?Pm* z3_lf^;dVDl_xmf%&bvKx(C+rw5BYc&;vpThJppKlYf@t|YNb%Z56g;QXhu|34XT04 zVV%m86+wDVLTmU*-$RSD}1`{jqz%l6Z2>q zg|>uMipLjuO^@Tx@)SIxQ5n30Ov+&qHy{(m7p@tgHulz=s7Ie-yk+zss0+759RI^l z|AUAAocb>`Q;{OHEn_;X2lg`xiO)aFs9x!XvIZT@w_zjn%l$9>aZ%9C<{ydsTx(xZ z2MYZ7l`ZGJ6!uGQGKH&SL_I1;G+Ri3`}*-BH*-;HU%0xqxY*8HlIufG}Nv%N)G?IDG=LB=xWOJL&r_y{4ca`;^JKkM45`UCToBi+qAK)k5# zLXq91yJ&Rzvu$?W+Jwff^I1S5Su)@6IekCq^4zIReP$!J{M$XdpP3=88Y>%+oW3GNyR7Gl!nE` zVQdXczQ;8;9y*R>fl7TL4|6CBCOF7!yB!}9pc znLxlM`^0OHwRd+VUOWf*9ZUquPZy5vjoPqt6oB`;|G^+g1Q-n!B=lEoVtD8>St4P3 zyZB6>eZvW74K@w-uhkgQkI>_mmqYRiW+Rt67e2eG1=kFLl>YTW0x?f`SqW%ZK>j38WSSa zuKb>H(eaPhX07h z4qDeochk$ODpckzO_xi!?}?RcDgAHdI?#Il#s{;I^rLy9v>*z)zlau*SQ&y$+|h#p z;y&7;3%s%w?^9O{wGHJr^z{(UlMoQy+)CXSLAm$5zNP3ys`u0R8#CogM-lEyOLsR^ z&KVyJUa69f(vu`oSE1U=c&HA-(Qm6x+A)VHg1?fpyO*NBUEot+ynB)4j$03qf$P}z zAbS3DNi$g9dV%?gBd>eurum*5PNLw=JZYs{l=1y%y01Lfci)#>Z(6J1R+5mhQWdeisxKZX&vYF!5;-)BM1tZ}vfxTlcxHKoR8 z*^h184P;J7rNI_+;8a9(y_h>2d6L~$O)%!{n>TM>-&s});K=-HmUwS0Gs{g{Q98XN zr4fJ)LmY&<5B+0>Pm;T7$i+-r>KSIdPLnf_;>j|MYUS0FF56o_4+JAfHmAlc5p(zX zTl_dRHTq;KzZc?XlA{!!iaCvRF~590NIGH*Bp4l$GvZOQ;$wQ~DwGWp#@T4vmkZ_$?; zE~Vjyk@O|5w`-!;K59Od`Xe9vi^GDA+ev~8^?X$BN9aTE2>~z6B%{egLzgu2{RxGR zv3N?Sh1_FH6Q~l)c`B97!wE*kMH6@*7I8`I^)0Q9y6ovJzh+b@k{YPvYhh)o2J8PD z-~OG8|MCf?^X+tM6pzMIw!z>-Y)Jc;@ zcs2NR%3%i(baIjsF`$4Q=tP>J%~sDv7O9* z2D@9Wn$V^)eEW@43^`vsJ|Bs+H1-6j9u02D*b&0&1YNg!uwK&n_*ckry1{Q1iurv1 zyJPux$#-M7(z|?Y@2|egg^F66E5T8>t-8bOH|yWr@F()%9ZtNty=_12eVf7hTcO8U znw!-oT7SzF%uw*#cu4&i``BaR{F<_QT}$DHk6R#CdjB5HZSDl2)f)HCTSqDeLbu<3u;&8jQL;szjqZP&REsTSfljvQ9cRm|F zI^nV5b^9Jt_oY5FlQ7SjaD8UD9*W<13z*9g^#d*Rw)5)MJy2ZY!cd-_x0H4u(fy(B z`J}t?|EISrkB4&Y`?nm4$|#`{Gbc2%jTy$)n6ZVDkg~?4F_;)5MkZubq+}^dr_Hp9 z>PSThAw=2`ME>FIQybDsA-?|Xmzal7W)f6IOSuIu-^zRrg`uRS+0 zKeU21PRyut_lSU zopIKY(k1>StNI+Lc9z??JzSYp)-ZvRXen@ce|GApD=N0)7u0ac@KpW!H?)&BkO@1d z>{N+ZUA7NL=AukSPg`XFU83Yb-Le7JT&7fCVSX&m>}u=4N|_9ra{AkZ7SXtOvRiH@W@I8j#F|(qI0S`@ z6`Nh*A-E~mfg2Q&(9B!WW8JGBq70pEprsq3dhDb35c*Y$4v}3%AUbmie%0We!CMjb zT$jCm84-4O_ER(R?|WOrrJAp)t7qpOaH9BVy;eajTqh~N((0V>1ul(aYsx)3Kix+@ zt0|$!W<{zztvsy2d30j0bD)x)6@&FtHI97gxP^U^J~Ywt;|122VSQZyd>%4Pi+h~o zV8#tqIGb_SI*V4lvc`A9c0s?K$Bg6g-36DDW%L~oHMp3a@vCwcMHy?A$VceE)VTYE zbp-6G(5NAVI43qX*WN|O55CwXXTGkZT$Iw%Ome{vh0yg%tCeh4Jx!1^+8|m)J<4a72Z3K`4zem|-o(DPH4-UzoYlmuh2qA)ue zM01&3oDV{Prkd)KB1LZ z(QW=%p~qtLQHi`|`yQ0Jy_W;Kg&vBY?;Z>F@r}4{U92O-SMACLVy! z&GsnudiFyz$r_^~UiyWT9>_A~An7PkQQ3#1%Xpgf7p1=Ls_nIw4tL;3!j@s=Wjgox z_0{+^z#AWXbi9Z-7A4$QWL;!q+SD>#J|K5i?r@WHfW~X9Y~k}{?!E5PIR6%(p{exN*S?8+ zY&hD)LnfEY*5$DzRi{&?b;ufXQ2#x|MQDN$%M{}g*wZ$)&a$UkMicJ_0uMILm+s!B zjd{JhWVUUMlU5o!plp?b+;zbD7|iaA?I-SsS{+TtqQX5d1Nj+bN!+f0bJ{@SuDq^UDVV z($&qvy61oHo$~Z(PU7Vp&e>orpTEBZ!yr_jiK&ea=qzSWRjM(p+qr6$9F4q-OX)u5 zPn4e;70-mGDmLr^`^u?>T=6v7qJpMK5ynks>~#F|2Ahi&0jOd^_|FDw+|j2US68Qo zTjuY<<>+mMcJg)tw{{MVbE7NrqNmq6xGY1N{4)0{yggN=&ciM2JX>eOb8kez1=tRD zQX)>SXLhwwcv-vZi;!9A=k?*2+bu(u2MoA~RY(j3nhdB2U;9F%KNX_4;8Gse{0PDe zH*hCR+{AfdOULHPXC7ngoST!@Z+R0ys#B>!MyUutf>ps*F?zukp-72rN4s;W@WXa} z7rMNL<bR;{8SY|>akjObg}MIm*JBoL#OWCUgBaJ_93M(0E(7)wMFPDaFAbsTi-Kl z`lNCW%9Tkc-8f5e?6qajKjxmRp}O9{@+`x#F<@Dgd5&t;72#FrTkXd9_`jU0AE;gZ zB%ngsmX-H0!2hxxp5M45FQqoOK%M=%e_SHPZM%h|+g?k`>JZOCV}&g`sKky%gg4uo zE^*Iy_D%biti5L~AM_hAMlalW)3zgU>08C%`1=(rq5fhu&S2Nn5$sW#*g&XWi4yP`C>`JGPXqbqj3V5EWzFcfV$DNrf<1S9Aj z6~48sZ{^r;JtrHPyPHppA2V4UWpKQcm{_v(0h?GQXDdaiY1qh3NLNac9y*fg{9#cP zGt3!DdY$qNTE~~Et}K<{u_WLb~vG_`a=z34Sk8HoEl1!$RH*6MaIw@t5m@u|ai z4{vVPDV=XdIDE5*Hj*nN20UKk;-Cy*Z4tX^hf8c@=OE~A$J&y2*Lt3rwpL6g0CV)^ zue8XM`wMV&qPAV| z{j7z>vNw=NbVe5eZ5eNR60gEp{IsPi(_}zoxSnk1u@4 z0v^%8HRzgV#_xL-qOpvFll$44tQ#H-rw5z?JdX1$XRiYz{DD>$FEyFDXQcB^tIOmZ zlyv&?V3n`%A}*oFsj{c28y@FS<{_Dq9TOqO7~7?{cD6NZ`*oeY%OAU1%B_8_xynxT z76VllDZvf7lo4CJr0a=>oRt&Bb)o*`>GS|sm+ib48>>@~KhahYoDBY#%ZhJwM{k5f z7fhVdYjKY~nt;Qm4;C)2o^D&`l$$spt9VhRGd{6;#WJBDQs=3|#Xrw<93;wMYbDB9 z!4)OS9o_EmKE<^4g)x@K$K1`M;P=YPgsUrQ@oAEHVkO}q#!px5r3aT9aVCz+=jF*N z*pxHx!CGwZ4GFzqka{}GL4@?~zLlW~Ls_`39pjpQHEWWt!?F@ustF$2IpBJN(CIy_ z>n%1J1F5=GsZxvYxVf9(sYXnYcbLFkA&zxvb5f`Jls1t9j%#zXMD0(EB+r!N1NQG$ zWbVCs+jl!FDA-sUte;J-GdNuYz$(%@((n*weoxaR-|$yGFTPS8@FNqSgL>LoRS7d@ ztseUu_)AMgUE8JjQ?K6T)ON)|_=htN&CI7Y>>JM2%pn_x4Q+E!$|?O>Ux?p4do8Pw zr_XiDgxUAFZ>}c9PHyUW4qVEt!L`EGn1OBmEpHBb^EQvU5jbxVBf=W>!L?xw_5FiDWo8`AQhziD zg$^gTlQ;s8^@~c4`W#x-Xxy1GR&go&*qS3noEH~!71^t!)SLNFSwhqi&yrFu>55-qeH z-o2*vqSt5Rnh!o_4Y}6_stC8{!X&uN@-sGR`@8nRZ0je~);H5KD0}K#P3BE2`OeFn zoEN40gD=5<-X{J-0g2E`z9gHKK(Emuu3!*1yv*H;pFNaAmVTr0K5@M&QxzJ6bA3>v z{cydCQYr3}vLM(!Sj^q#l4{wj&kP4^?-0v{MvWH&qSX$=yGB3E<85KH;)WX1^N$we zCiQ}t_xF-9m4t-^Ht=hdAyf@ZB`u4rl^U=r4P!#wv}*h9%y8-)^a?J|7Q&w%ftVFm zj5XD7Im8$~g5hm4b=HOLeZ3Aj^U}^tqhJmy%@xYN99iE1VP{yk`UxwGm*}RqKe*fK zJmN6h=Tec~eJRQ)?D^yqyZxHKYIfbb%PhhcA6=bam#8xDx9^S%?HjR1dK>cn?mOA# z<>Y$gxIey)n9czq0FSV?Ee?|r^&>VhqgB}=d6|TF@{}yM?QQTYOSG++A{Q2QaD8jV zcfnE7#Znx($~*AF7TUoOHD3^vw&&fL3c_I^gm<9c_*wq)0GMC~|)q$`9-_{zah*}R}R=zhk})~Ls? z!{`@a-gRKDGAiDG%eQ@bUG6a4GIrKI@syu@E_x0sS_xfdFB8i7V)g#vwCAgR_3bv| zUni0V@d|ag_0&m%q;FVc22gT1>_XoWDgFoWo!z^*cc^s6pndaHY$x-8Ms~-jM}ML6 z-4nfo>Z;k(bs{vbH!%jNoktj=97Tz~5}6cXw&Mo)cpiH1q)@pNC@G&oXTqBmoP*t2 z$K(m!H`2!8+@;F3J!gOp*}yF)aK~q_@>N^+*O4k-f<1`R7Pnr3Kdm&Z@=Z6PsKSn9SC-x-R?-#nrfp-u z`lhGF8pr}@g>lCN#iS&~27X?Q*Haosl*7AYij!(!>hN4la>jE+RmOP__$-bXw;JVT2SsJhi_*#b7&~y5@Wzzm zGkXFCwrvNjuhso8!%@E5ru}P@N6fIbm|lLRaGa#YZ}kzhknjLjd+e6Hyv8RER!TM+YMy_z z+Vy5qCO2ODL%yp73mcQ8*^{e|snwn*3#I&A^G4{!r~6M&Gi%O7*n{h864XEpnr@@e zGe)p$1HmV$Wwd*hVcX+ZJRJ8%=Odoys%Mpf1FqZ6Jyeq%^I+@Jc##l%t%q;exitCN z1iS_#x%nbs8dhRnq;~NJ1K%A5zbw=@;di%OQMRPMi^AtKKWtn@oU|&PS`GY$6sGt% z;G8{}!c;Vd$FXi@0L#YzyxHV#_TAbC9dMrBi{kk&Pj$D{R)$dqIe%EMd}9OrL%#_>U{Y8I;Ou(l{9=1{5`QU^YdHtyDdncjxD64hV-aT$_g0^L zXIT__Dt|QI2iLPqs4TLv<4)xHnN3`WvX-CHbPCv2*hL+A`Qswj?q(w>G97*}yZQlH_As9LLl){d8CKsjZ5% zon9Abw!v7zhjVmtEBAO$QX(+I6iQ_Hbu{*P<#FyFf&`Az<%>P2G|%UBVt>XqxuZxq zjPAY>s|ylIUDXe4Tl^~Um=_`0hY5Fi?KHx_9FX(&KTZDm~J=#NBCz zK#$Y^U-kG8mL;Nd%>pcle@DOgi1P3map5D_#TWbsanu(824|a1U$7F;+SuQr5^w|t zfMf6@(-Aw#K9m3>v}^*+$i5V-upqKS*ygRIFh7!k7m|P%#}PaQ z;0hWH&p-|Dk60hU2y!sVXtmjvO%|&K85o8PY9JNBP#_po|A1gah7s~(5kv4UNJb$M zAG6T?jF8SYb_hC+=I=+LBQTl z@ShRVmrf5fM4>`MLp4LSHEBUUD71lr0ZI#l!eBH&4vpZw0d!A>MnJG4Xzyc3D9&Gt z1q5q;?2{&mMnzGaQD{vq)R%_L!Ek~ofpiKj03m4Db0;l?4#uFn(?H8W8>@lV#gH`6 zXfjDd3p^S+STY8UM(b#U3}0Fb{HBNh))e>ww51KE0K6Fjgb}Y05;@2SX=%3!Vd+Z? zrhjT0p|7cjMxs8C{2%BLpvaHM4#@a<@Hmji(1zwk@!o3=&`t0dEi_s~%K#8$D;jHv z1%J9~S{OquEgb5*oPgw@s2Md!R+hgLAh-%Q>=IGvt> zHa7oxLa9^%p9}ICn$t)jRDfc#!TfJ>(LYFdFVfd;28IOre-soi5{m3k7W60>&>ju? z=|wX1rUg+w1#BJ|=uaVe3b-Eycod1pfgkA7QQwDFU%F^!E(#F+wsl z0FsDjh(8^P4<`A7x-|oXKh3{C1^?;gV?osKmHmJ^ACrKb145y`Y7x9R;vahcxr%;Q zoj@TQAwva<@eisQ^E(#K7eQC~k({pu;5Y)=0W&U;9u;##f#_)&ptaFh@Cc+1silPk z*?@HZMUKz>ukt^YBGAZI0j*WOQgQ89SRh6a*;`x-0q}VQdhgSN(8Xf4u?TO(mo#mC z0AVC}5CNalFuDd9fGG5DXsU<-YhriK1NJ}j8p@AB#B{ILz}57KlD z{@4Z<{e4*sDEiGf=s})93k3nJD+J1c5=I7dfIw}b(Evabpz#&}4i(@{LkQ>%Afz^! zBiwKX7N)vpXmc$SEZWRMM+c*;ZGzFkn4z_>CI&j%rWW|W&fzY=ehQ|02GKuGJVp<# NttYOmyx!JA{9nlVP$U2V literal 0 HcmV?d00001 -- 2.39.5