From 7f310bd0de5f7a52c1532c05a3bf3561be07e93c Mon Sep 17 00:00:00 2001 From: "Claudio Maggioni (maggicl)" Date: Thu, 14 May 2020 15:52:49 +0200 Subject: [PATCH] hw4: done ex1 --- hw4/assignment4.m | 88 ++++++++++++++++++++++++++++++++++++++++++++++ hw4/hw4.pdf | Bin 0 -> 94872 bytes hw4/hw4.tex | 54 ++++++++++++++++++++++++++++ 3 files changed, 142 insertions(+) create mode 100644 hw4/assignment4.m create mode 100644 hw4/hw4.pdf create mode 100644 hw4/hw4.tex diff --git a/hw4/assignment4.m b/hw4/assignment4.m new file mode 100644 index 0000000..5f3ef2f --- /dev/null +++ b/hw4/assignment4.m @@ -0,0 +1,88 @@ +%% Assignment 2 +% Name: Claudio Maggioni +% +% Date: 19/3/2019 +% +% This is a template file for the first assignment to get started with running +% and publishing code in Matlab. Each problem has its own section (delineated +% by |%%|) and can be run in isolation by clicking into the particular section +% and pressing |Ctrl| + |Enter| (evaluate current section). +% +% To generate a pdf for submission in your current directory, use the following +% three lines of code at the command window: +% +% >> options.format = 'pdf'; options.outputDir = pwd; publish('assignment3.m', options) +% + +%% Problem 3 +format long +A = [4 3 2 1; 8 8 5 2; 16 12 10 5; 32 24 20 11]; +[L,U,P] = pivotedOuterProductLU(A); +display(L); +display(U); +display(P); + +%% Problem 6 +[X,Y] = meshgrid((0:2000)/2000); +A = exp(-sqrt((X-Y).^2)); +L = outerProductCholesky(A); +disp(norm(L*L'-A, 'fro')); + +%% Problem 3 (continued) + +function [L,U,P] = pivotedOuterProductLU(A) + dimensions = size(A); + n = dimensions(1); + + p = 1:n; + L = zeros(n); + U = zeros(n); + + for i = 1:n + values = A(:,i); + values(values == 0) = -Inf; + [~, p_k] = max(values); + k = find(p == p_k); + + if k == -Inf + disp("Matrix is singular"); + L = []; + U = []; + P = []; + return + end + + p(k) = p(i); + p(i) = p_k; + + L(:,i) = A(:,i) / A(p(i),i); + U(i,:) = A(p(i),:); + A = A - L(:,i) * U(i,:); + end + + I = eye(n); + P = zeros(n); + for i = 1:n + P(:,i) = I(:,p(i)); + end + P = transpose(P); + L = P * L; +end + +%% Problem 6 (continued) + +function [L] = outerProductCholesky(A) + if ~all(eig(A) >= 0) + disp("matrix is not positive definite"); + L = []; + return; + end + dimensions = size(A); + n = dimensions(1); + L = zeros(n); + + for i = 1:n + L(:, i) = A(:, i) / sqrt(A(i,i)); + A = A - L(:, i) * transpose(L(:, i)); + end +end diff --git a/hw4/hw4.pdf b/hw4/hw4.pdf new file mode 100644 index 0000000000000000000000000000000000000000..4bc59415ffe85dfcc132999784650ae3ddcaaf66 GIT binary patch literal 94872 zcma&MLy#^^v}jqUY}==7+qUbJZQHhO+qP}nw(*sX{`*DWQQyJK(azD1%-pdvR^}pA z5D}wgq+^99onIbVhh`>ZAha{Igy!Lark63XHFGv6WM*VxBm6%DnqJJp+S$aBkY3E% zz}ZB^#K_Lr1e%Wz+R53`#J~pHee*_VCTXh`tq-6#u-kkD4YoUE#?(u)B$p)#pK)D) zw-#2@Bf0i`+u3zBn(_7M0|XUWEP#Y8sA2VKSVMX)-Ywrva3|s8wX~6?XB8RRD?OhO($4f%`&NoVzKVW_ zs`s_4Iqp6(NlF=DgA;!;tqyRRRsUI$rZ2!v#{uf_u`QxCBTl0_kpnqPE+>GGw8J{E z5l;GEe3;`=C$kTT%+ooAbWqx@o~GCv?e@pvAyv$l`8y6PuB1+X_n-3-C@E&1OhE@A z8{-joH;yZ&P9LNAe3iICaCj`JQz$%O(aXFy%x`gz8qb|*=0LirHG7Y$dafWW&Bu^}< zAIt?PdIGPoU3dz{UtG^&nEmpi7}V~<9#1T)Ok$2w%IWQ7_qb0~tvwyMp_whNU#>Ac zl@ir0jm}-!JTGm;neDxe<4;otT8MVCe9GK#l|asLZ1x7BtB%gc(KZ&0zw z8ysz-#oHY8P7ud zN;FX)z@h*JuzmP`Iu) zh4NIaBz8sPGSAc&PF3x*YXb&@^Go!#U>nkJ;dAwqlC7-g5o1w&SW|*PL6d;;*IoqA z`LB;iHH}YuFkfiHh6dn8{~DUaM^~g6l9h5nQ;NzV!lfE5K4h6M8eT4XA%)c0-ZB_I z7q&q8Uy?M+Lv+c9J$^xy{vu<{%Q7ThDv|SGaA^QoWEL33P<|yD`)kMFpejq>K!&Uii|RZbuM zz$Tl#fsI_g(RG_bgocY^6LD>Jf{55IYjW#z|W&K}vXS^*CU|;&Xa&``qYr zM~J*if>Jn&MqW@;rtA%^#IGT`4E4yO*O~z;Fh!jRIfaBPl4kBNGm%wgVzfH1OUjv4 z(YJ@^@2*I4GzfYEpCMW@ev@3&b$|@xN?o~y>VJ#IuFmCq;?ur}$4w$FdGy*Yj82AI zZBDkDz$@6`^YTnf46L}I3JC*b+#@$w2TdjSA1kzi6zBW`G9sjFrmB}yb+lhuIgTlnE)mpoX+PtWl$gk1x&(92KB48PtB_>OhQ`BTpJbnp3d3b;)ig!% zsFrxH*hS3}P!!y$b7DihY_UhSTXLwdk_ay`4WZKTlz0nnyY=qw0byR|aU9+57T7)Z zUgapqDD}74i9ZFodOPu)2-SATwUohjs?5!Nl#ZyZQ_-}kDF^VCLa)tu_uh&Wv*t+D zMKR$iC2(zJY%g`LPs!x-JPZ0*8^o&tjcJ@(pnZ1##@n>2gGGu;VmRBI4~XGxG{?VW zSvy3yGAm=1Tp2b5o;;v7w5my&r8>T-7QHr8YZXLr{;TpB zl=e8x7{hRrM!Bezc!y?&%t@|(P*|z(LLV7PA$?#~sGMeXot*MPmC=GO$aK1&63V1+ z&1#wrelhTLW4K5xMF}jVD*+SS{vd{xei25sa%1a;R+7q91Fe1l?B{KEJFlNphUFYk zpGD1guif^>PrP~mz1w;7tE9jnKk8EBPM2ST08nTJUt~bi`;E&kzdcKj1yC#N%-TfF z^Q_A7l=H)Budc<24|AhYuZ83X=f>qoN$ES`W{u6A?iw1%n%p^C1xEmm+U5q6;BD8f zHsgwNaB^q}Jq07n-Sr)Pn9RX#=k`3S1*8O0Zl@~uIzeCAL3WkWkX8Y zw3MTyD=>7K5K~LA3ynuCvg#E((C8)w)}eVESr8mP(vfEXb9u;M;JdU^$t z1j2@{Ch+vdN&<>PUpBK7yO&~v90?5^24aT=9xscVy?2o#!+fsB8kp;bouZ`*S|{@G zs!3d@1cQ-$gh~KDt?HVlomeav`z>UWmM>?D(EioLOa-5wyxZc(1tIPE`r}WHEfsR4 zwn*!VCx=|kid0E}-zH*3yd|h<&3a178rAmT9i^919)?D#%zBLAZfafOD$c8AJ{sdU zn`uwajovI(W_!KkZ_(2``-QbsOfNbGR6&yw&a~&*{rjMEMq$`HpY1`=_VgBxWj;qR z`c&4M_xv+R%N zr+1`#GzHsVE$2da&yY1y$4aUMCj za#Et!kxQ{^nrE76uv`dAG>=4DVy|JTalXX%m9a^X3)kc1Kv*V3bumFCD`~-hkDP_- zgKo2i=1R0mUl&EFelR4JHBEF<|8N|dUPD4{`%5$mBUm#E^!K(_PFZ&kzc^n-{FI$g zDv1*Rg7IW~d?-sin;<+kzcSdI;*-hU8gOCVDkEd3yE^XTljXOC0ag%YM!sv>!!E{e zT-weocu+Ez3xIC+-_C0%=O8W*QBWjLvtGHZB(hKrrCCk;z zWr=j&-XrKC)s)!$D>fSaO~iyM@+caQ^3z-CgL%1ge|L9ra=G%Ox^D2jdeHO5uHyb( z{r%#fnZFAAz!=5{?2Xa0^NYUJ{_Gz-+98UBY;mx4g zi=&>13f2&X01|1tUT`D=gd~_;5_Z6gBJotR#X(X4Sx@oKa8%03Cptm`E@r@V_ix|o zYfW_u&u6yJY|rPePi{SvL=+?n6 zD=R`+cJwRy#jpGl-U0pc;1UL7Jmk6hss3693w+asZf+Ll=;Tw_fllI^hY1V@Xi8mn z+v?i#2v9)3L_vyn7S>%A;46S4TRO?U^|(+dNUB0W_Ncy<@u_LS4vx&Etf2*bl^}gp z%{((w7wSKlo0)M;&Y%I-eozrH+i#vbyn=qawaHO8QBFQF8in)qUHgptw{`l#DTayN z+9L<^vab+#_ZYp}aTLPi;^altVIloMgS|Gm{QYS20XM+EIl*7hdRBLjE`nV^H?=1H z--xbvR|GtIYUL2P=b;W^pYK1+_jbV$0YCESSBF_mQC4MOJosI9{7Z6jJg+OD7atFVI7|=vM~D#E zPyp#KU;bX-r@1ha-)#^8pox}@hfVP^=2|y*QAg|bb@3;bA0im#4WOHOZgn;ofa`~| zlPw=U_woVr;Me*INc_#4@^g9Di}~5(R&o?4@;l@FA^hU^C}#$~_$EKv?6|dEQ_c_Q z%>`TbQ;ym9i>}4RhWZ3#N8&trq8lr|jQ`>i52`>NfQ4BQZ(HO2)K3vO1nC8ZisbKa znyU@hslgzE9vpqvZ9hA2aOw2%Y1i?-bA$Ea=laoCgg1%~`O0GT#WNsA4hZzzztz?Z z)02Qcg=ohS!`?n`jR-K%L*KaS0C%IGK{N{+-TCg6Q-DIQzN3A_5U$~a4E_EI@z)>T zLmY$vE&BOWH*x+eAlP6P{2|VG+`0ZtpnwVK`U!#hCveAa$nT=TWlX=e?4#|dcH}3- zuTN;-p1z%S_ZoFmm1y~1$9(AmM?+J7{<3}UL(ngGp?1DW>TytI6Ck(OZSO4<% zuwXPqNPg`pP(@|+LhPnUbhGVMmJ3Mfq3Vj{hYyvnxvW-!tUAy`jSDh_&CP^Blc_&l zHmd z5XWU|(_|xJODqd9D|hPZ8vYvFsLIs==|Xq#|gwt5ZmM6zw!M&#Ui#KBS&JLqNM zUS{7&TqPJOyfO-X5yr)ABC*x5>tVUPp(F2cOaz}tABo;kaKiQe)M!}=JFirJJSnva zpUy5h-rN8Q#EDvpds5pGHq#$5y=z!!5qDT|U7q>V@+9{bYd-G0xr!8 zG;lueMuZlka9(vhuI-xH3Hdn`h+^Y;e^A*_cu)SOXMpBdZx%Q9FH*d12w&5aZ-J1G z9xH&En&Mi3Ng6a7`EirT140}@Q^kWaxNM62oK*R#g7u@9Sw%X`u$-e@nl;F4T#pQe zCXAs>dM%Tym4N&BMa8KM^XsX)eN$_otK2Z+cagKxy4SdPf;w-`fWx-8sH0UZZD(7N z+&&G`Oi0y~z(VwJQ@0qYR>w;zdJp-^rtD0oon^(c$=$7dNpm`9m$da$-K&HBC#IC! zG*Ve-a;Jd8mC3zZ&A^?ltU$+$XtS|DuCg`uPg#u(FaW09etpc}>iozjVA19GC?)JY zH~BAL71tp<*{3Z#6QV3F+&v!waoe*cMd|oszNezhPy)IPl?4?RDNhnv@rwgd4f0*U z*4bgLqZ2%Ve-kZ`ky0imDW8tus#z9HempVFB$6UyHf-l`hUN@gXQljF3t{yvqF0=e zWu_e9YdsYi5Br{tubf_eWSdhPg?gJH<>PDX5`DmdjWv(+xg>{6kn8kxdU>X}l(6Pi z?Wf%-FSONgX=*e4&pNWdLagsg2Wx0P#*M3;FeH8dd#f0|5UP?VT?LHjpTFPy&Rv|- z5ir6yp@5TJZ+`CGOxJ@vNxF|97!M+sJY1XLU<#m!nMXQ*zh{97cK%R#p{+mI#~ zm<@?ux~RdJUszeK8u(h?RqLz2+2&|_Gn5R{CRme!5phJ;6J<(x^e1zyZ++?r&<2w$ zNASas<-PxUFTWeqSDB9c-j>+1oHd6&LO#OiXBW>m2OE_ zinnz~&}6I&F`fhV82V3COEw2Ni(EUUWeF)~9_RbE8;ddY33U$q(wqnK9!oJz8XeKY zr>T;?jEN3cVSbiM-OpHtH#h9bKw%!)D$YL*(wZ$MUiJg0C9dPo8(S&+J&1qMo0zo) zKkaF1?jr0#Yz7~h8`kiZ;3I8RM{##{?+-G|DBC!P&7oH*4TO{vJ77iwM>t}HUNMhc zp`uTg?0OWt>pXF_7L}w8`Irq1vW3M~;=TJSdA<$NCsf!OC8%wM)Zh|Joi0!~nm>zAFqTuhUbh$eOW1dJGC&3A7}(l2 zV%dPNoih^2w6EllpCPc;48zuZKu`TE9bcz@QB$2rK6i{@hypcQcFU!RS=g{)`wpL% zvd(_zM$ywIu=egWr3arISI{=f2Vll}q>8}9cM1nDGh@jj7 zYsXwEy4t?WVg*9U#& z(R06AwKwQVa23LN`XFrPdQc{lt(sFMLPy2c$*kJ|oJ-}>$)NHFp8V3QL3vitP^OIq z%6}F5=*D!Ws~--+KweM7P)o8R#1WzINzl-S=KX7~{YYCePRFE7&$~_e>XeTrhygrh z1eN5nU{=?q=8bs_RDI_Jx-H*N!zOm!goIxiPssR*A6vpf6|7PP_$IR{&)w-F=TG=o zEHTn#=wR-=CeR6T)MJ-Df+RA5GM=XN^MniEj9q8kVk{QFW5iQOl@%+T^ad#GyPcl8 zk5Z2lB|$Y2F=caFTu`0-{*k6a%gI@-ZB8{Kiu(2-$%9hO2?*cI%Y^6APuiV);jU)C z`QG>Un_65GZ#5^t?T#vVX#whZx|Xz}fkZLs#AaL42KWIIv|Cyl|Mz$^qe5V#{Y~(d ziixpLIIo_}e*Wd=2Kfg7^|x9OV;A}qTgB~p7=QNqa+pQd)bJWU1%`%xIwY7VFT-PikbSpORO$W@zp;4)Fu6)Dd9>tFeK~oph(Om8y*07p? z<-XcXx_@=q=PhU_>GQ7qb51V!P#qBm2Aubd$BNg@FKX>{RyMRc5YGpx z`bYCj*|_Q!J3+#svd(i#2Dfb4DE*Yk`lcdUvG~-Y8JtrMMD?RN z(M$jUuN}_2YRI2I*(~dI-YZQ{=<3;d%33N^s>Y3vy(!L9ojVRcSb8&v(?Hs%h0E(l zlz*L8hmfypCZ9DGA>6|FswuS>jx(2QI0s&`wgamTnXSfUbH6;l7+0rYuOf>zUtm-I zv4DT*^*QUI(DWlDee>6^Yh%*G{&It~!sm?(jm z&v(*U=`U{*QDw-f)P~;vv4pcHrI~td87hd8QIouuP5nU)u;US@)0(84I;(#Jx(^Tz zQ_W1OD&mNt9&3Hx3ef;%Zr;;4O0iYI4%MCERn)zGE{E$SHL4-+ZKte-c3Zf?uf8DW zgHuPBrXTRkqLZ3oe|qh zZYJ{G4R_@Ee}l%(SP`cy`o zM_ok4S6+C!DAC~@hG$j*@5og?5-1@ zn(kZ2ji4*t9sKfIwFKg!JIYH)?kx=TH0{$2$Tm43mAz-ybn_(pU=QtFou4^`da9-x*5rXQbk&RJD?u5@o z*a!r~F1Yk$EL;r*bG9;0IE0`M<)nEQAsBEXE}Q+L9-jB?{#l)mQwhGaVd`r46eCL3 z-_2ssiiEl#*bdH~cbCl(ejRRk3?1uT)OFPKm#mjbz2o?83G2uqxz-1BN`~T_24{_I z-m1@Gd*a-^DF1rv-r38icEvagrE82!7$jK(n{&wS^Nuzmg&{B-krH#Yq#Mb+iT8mxn@)hx^8D zdRH~6gx^$mWc|P2wEYYMOmgna)^goh9!yOVKX{FZ-NosP0?}^ zv@%irrn*Uf>H(j-Z=^(}!#PATsvn?Ps#ThaU#~t5- zky0)XVm|Kn)=r9Y#6`-L*%&1*gE7S8KEYr|r(;;2m+AQ#F7|>)TYn#}glHWZ@7$n{ zu}67@<?4B@F3<9ejAJ+PWM|HrX26_%j#)66;j-$;v$B6zB2Jzv#|pIOiEh;vzHZ zxsh}$rTdNz*Oozv&TBdkc8mNPv^h0quP`FXK*V=$ycG$B-4kG?PI980;SVp2uTI#X zEqdrufs@l~i$k3eYTh;Y>ffpOOrwUfClNwrD)_a82&QMA&`~5p3qzF$x|%n_$5LD> z5kGyK*e(V1ZU5`OEA>N13d96POw@Va=TAk2JOjhj(woZixvF*$^>C(3tJ7w;O4#{E$O=`j>xJeF|f!YiyPnFL1kfirMGs zd;rHPQi6)<{hWP^M`Uo>Dee`noP9Ur{uT8-cNMO-_8nhSWl>Zo3nyd4cy-hvnW;{_ z6B#{kK(%CaeCq5arHO?_TBjC3^uKt;&%+_rnDKf94 zLGSCn-#qC~XtsHOsEPd@MJ}D!FGYc7WZnC0D58fYu5lb1Cl|hnrS5P)zeE=~sUD(* zG76K+Wpb14g#Z>9v*J!DZFj{`&(D34A0UN!68=4C_HfP>aP4K0j z&47LCXT>S*f{j4szTNnQTl#^DymOH?TdMx@k7rF1S_1by#g#rruJ+ERX7cEZq?_hmg zyM-t?NsW)ecB^csqZ2;-S8#vKx}@(h6(!depMpQ%6>RD4?xxi0LHl?+#A3kGf)OAa zm3M=l+>sc~dJLZ()IU3R;cAL75tZkpB~kdNt#42wW<3N)#RO(9 zCGOt<_Z!X6!&5`F%9QU$Fm(Vs>oV27iIwa~TvLVCCKL+tysvT4i4+$n%;AEkJSDPK z3*M8hGHl(9$Fg22*70AeKZT_KoVZm6(NoFi+*H81v!qajwWhPSx>&)rU7lDqpM(Kf|$_A ziJ*dHs0a1djh6#7ls7fSq~MNFx_$!Lftw`y`uKR(AD;h+=9WgU@-32xg71l%haj)B zmlyUnWj}=+8lVnag$2pvFAM_65o;Jbrfev^nV209?;5K@8l>n2OcZtcZdpz45PSjp z@gTQ7TO%lF-6`yO>g&l~`XrfY!9)mqbnI`#BTH=FD<6r9IslnPmQKp}=kOq{s9b`+ zyE_Z>%cs9*rk!9L9>vrKj?D^_vOtVwop4MPvO|lolDZfiPc+piA0dS&WJ5LGufF>& zaihs?pFDH%)cRx{j{{HyUJt7RL#*n{{)BU=>{{VOKSB%<0`bp06HMXdxcUuJA;@! zN>ofOQ2XsfKv2w6#v&>1_|Ek(nQ$%y9CGTtnI1tC^FprbCuHgz&)dizq-S@kvE0in z3Gh82%{_NDTjf>loGbJ1S<~Bs)M2ZuE8TUH zv+5rA9zyF7+^=dJaGtWE7Cn2JS9Vl>?_z%wmt*{6l77|uFHmP7J2B%JpG_j~?+NCk zmv9ixWvfK+F*1|w9;Uw5>A=+E<3JBlA^Xljdfxa>&fU)B1nb$~q$En0(30=f5j5Y0 zE}n5`)=Xb1=KfGOg0)N*ivz>oiVM)uMx0)2#~GVhOp0Ezarxv>v%3>f+AV-^ulN8< z)7jlMWjsyASPE76mO0HV4jk5KUczp*lX(-QGupQ%Jzw|_2apd#SkVvQ zeYdg)5f{GE7_~3wf^F*G$6EJo%ng`cLP(GzoHF8jyQdvu4@rHC=wQk2#_GuQ-BvX* z>o=o0jIF!k%`c%0bl&SW%jjpHESjeewgjb z%u=I^x)V(4n(li)+~7i4vuH569%X>@aKLZ(_+O@0nSS~!td6)OgUIvOX77x{+e3QD z0i!S29Kj|~P~NSuo>sX?-tCq6aNc*aC#v;ppl*+$3qKP|m5!>AzZt0)2=zSq-eJKf zIV!@AxBKKc<(+WHUQDo6?B;;$xvbT~43Y9NW)onThjE?z?%869N$V2r(D&(x?lj6> zeBte1IZP`Ft!%dUpqIRCDK-r(K>DIcQZ`-r6;PZ(-*3dL#kNpMjXX;cOmTnKIdgC0 z8BA`{N%QN)`0>{HekkAV1YLT>w(t@g1VtETyV9`hkNLt?GBrrsnFdZ>3z40n+^~#q zck0)#Ii}FQH=l<;gkg@z)Hb4cyhmraK8(x_U`t!)DRCX^R+T1K5>6Gu9m$GjVQ?T2 z_!_TaF;j}Q^W&`iIz)ri&W6Wb6xn=j^jCl-HA$pkbG$+b=K5vS6n1eUr>s5!=jEZz zv}~=Q^YMNY9-KW~5=0MOhnX|0B6VXNLVV_q@s9|Ng`V>z>LozSgCl>%`hg zKJIe`ctcNb9UE@Gc46&v>`J0lNsu=#wNkk1MLpr#4wh96yApea?#1nA!BHG{AhKKO zG@r%JlXC0zW4)_!4l43E7cRhvMuWO9F!{mNB}M<3zRJ-FJXI!(uUj1e z8E7!h#jpeiQfP^EQ7qK-i%TMP3eT6>ESkfh7V%$bZmnC;ld?k&H=5gn$Suty2c;~s zf;vD&bd}Gyk3Ts$X~hu!%R4`4t4&2KXm%g-Gn(sJ{p8iP7_rItH9RIs&!2CZ(0TUq`E8G978nCmnGyPwy2CiWLl6N-Q2x$rNs2Kd6XXZ(F zc48P{L0}m{hURzhh)N{NoGU3}{QZlI6Ok7KAs4-i>HwT)y#GfuFst#%_0e0?@zQ(M z9hxk*>Zdjfs}G?f-lxz-Bv1g(&o42C1_t&Q5ac6N@Q+VfK@4>a_^}~3W(_6c)rV{! z_G3VeS73m)Q3frV7oi2k&A+_>27&?>AVMZogd#*F1Okoxl@%c*1&Y+CPsbC8LdcKx z7v_c3Ktr_cl}HaFhR!(y$OHZN9}R?zfpPMF10U}cLS%r*fSV5{_Mg}+Ijw( zd!$BSSUdxKzdzuRUdim3P+<9RbPSNFw*jvA!CQg}K+dlI0hwe1V{p*FQPuAl0T6d) zPC$fw^L>Ng_djTm;J-Jpp#q4tw)*Y#u(v?A=0F02I|_K-c=YM|Jdc0Tzm!4SbC zVZtNBf%0#G$`OVWe${}5_1Mqt5TB-^Z~xBk!5x6ti?{uO3*Hc3pcnE(sK-F{7xEMW z`Tj+DJBvgF1zsN@r0}O*{sT__<>uUsW%;{??eim%j?fPro=N}-^!5C8H3eP6zzw=R z^1Ao5Cq8XwXkJ`kH~n39;urAn07>A_U+0hLuO^@k3JC-S1@lKl6bvZf7q%EC^qcaS zKYL~W1=9ab@41lu5|G*R6YhUB7i>S`sQa}Pdz>IiU2~ZBai9{+l+W_;Q!0M0{XFbZ7F!8pIiGI zQ(4e|?hqfu-Tq}oY=A$>Kv14T2Mgx#CC%u!5#u|P2?GniBI@4nyF&-0i-`E9hw0f* zID3vW3_?4#hlt9{|0`1g8b)~S3zz9%4+#`466gc9Fcz%~1@a|$9?=~1@rBOhpN9}D zP@n^J{sR2x1(M{Tju|ZC&)d%YE6_HWWn5zjC&yRduh8%>Vc*;xLHs&BWJLXAaQ?ME zzAc^po}ci!JAQ6$Z6E#gFSsBuP_w7E!Z{s}ejob<#zUMhVXlO;)Uw@7frVe4-yV@d zIRdH>2YZaagct{_NOSJ$#LnZX4uQv8g3As`RMMIs{Klz=TwvO)#wU+8lm}57-@GhW zU*)g^&1b~@q+eMH6#d5xN>3ZcpS0Du=drat_1CtfB4jF|7Q;r6)!cDP}7T4W&Cm3@Ww2B&iy#l~cKS zx}8GT)0^%AB#%33jGSQNQOpi=g}?~~{FV$l^(~7Yh9pP!o%SCVw7c^nZ$5KbNuP_% zk3sf~o-ea-j_GJ$w{e4cBIU&HjhN`@;V=X0$@P1-PP%581P0ItpY?zmF+X8mFLfMH zDIAI)gV;VnxkMAM^}hFOJ#MY-sh8 z*#h}5syxSt)O1fz4}LH4Yy~z9m&<-OJUtWV4*7{1bsHkJ#jb9ajq!T%zE%E`tRrHL zVat%|ze%*Zqr+X2lf={t1JZRG@EckPjr?jDk?TlVypOL^%BvrW?%3WRCumNt3M*>a z%QgTrT@}3#@}jy5ff?>Kfa@{?L%8;eYz_dK!-!l_&gL09s2tS^#R%QvlO|LK(Uz_% zj^m|QQc2c5tVSY3`yzcd2{~E0DztXi2=qdrkDcV~@wxvuT|jWu>bW?eG;!)a$_-V{O?AjN2=Hhv*& zZ8c~YG3EPlbc1sp6fNhtNRm3)zQiB8{N-CI)?5DQ6R+_G6d}CqY!@5Xw>xH`F2j(8 z3V3_`iF9tyd)kR<nDE%VoGTTeF*->OF`QM24;0cFzQ6D=-n5e`IHyoUp&UHRO{ksWd zAI(R~;&Y3o2t?|Ac^3Bfg9>IG-Cd(rgj9E0=rKAeL7{bON3@gU!{#oZDQwjninXBR z1Mu1}pj2o%P0_xeW1q#$xZ+fMVq_V~>Pz5+!7t7A7T)My*w1gaz+uTP*phaWXi8Jwl{&Mn|t*bnd{ju^e#ErjoTSa@%#O-CH^ze%r70f zhI|k$Xlo}ZD{hM{z`mOH{f<1Hwu02PX$R<202p4!e`JHS7q? zf@U_z6)wEU%{FNhD48$Hj#Wyc`FExSo4~z=mqNBDYWiOr29&7zr>b>*?U;Gdz~6wIBv=?j;h|Y zT-KI7SaRrZ;p?vJ-6lup13t=CL9@Ok;hR~|m4vG0>8j6mEBrBFxsPo(4B+ zzSsV{>TXKcw(P-{<(Vv3i|K(1KM3xP#91muP*m%iOcRyw#>^}_VI@iT)@*K7owOiJ z#t9q@w&el+ZWz#ss55r|Kq2=cSrP`A-riGf#29+Kz3=CRoO}S)56AmRU4DZlbY=Hp zrTM@fxz>pD+mX9>L=IAd{>W7C3NJV*f zZL-)igc)%myOR;D2DbvlE)9SJ_*DvK>2n~%1Y^Ss-)L^DY{K%KfTw69b z`tY4aoP_ypBwF1em)_`W^%){+mP@D*AZU99mz8>Cqq=tz`epDqe2jQc4ppTP&VKKL zHyzSps9TK@Z6Sc1$mQ|5nGO=*ui;QNWI%->(jgO*K74wH&Rq$mlaR|kWdSqPY4wra zW$J9*Rr_H~)X3Y~BR!Z~x|l3eW#yYzOc)*1O#>N%bDVT%`v_5--8CqN_TWAfmH5v2 zx=vdP7q(KY^+Z?PoLD`ZMNB(PV*oYR?V15KsN3Yb>bVd@n?}WiS8_vu`=0wO+o?iS zb0``Va~#^dDQ9&grnuKRBwcz21`S?6vyn>^{H@*xBAX3UQwA!;u*V*>d#+z#f7*|n z9VWa(8qqZMW6ZhQtK>@hS+RDVR@rX#SfyFEwfO+2dO(^C;oVzjFh&;0ivc?L!w3Z+ zU@%gU*xkxx>}sx*X`C<%41oWp$GMy#zT9^Mj%BDMiiUIVwiG?}>brXm(jfq?Zd96; zjFb1?IAVcSJ%7t&yqMO0Qjbq?L|Y)7DzRf3N@Af!ZX$Du6D`+*+#?$hZvgD$kqHS| zU_WOJ=ury=ixP1$SDt31ysnLGA6bKSL~c8~l2-+WVPIejF>>&qzor~};-jy{Nx)iM z$OL|pwa3Up(5On=c%Yx_3^-}iIy6@d5glfnI=H9?jo4`!4T4zOV1kRAP*fZ#>V{2b zh3qyFOZ=JbW%L|X54HGV-Cfb*(tRFm^PK23_6gD(4vPS(-mQ<`(Vva(c~mqR^L@0>ryDiPu8C(fnPdMGUJKZEG(~d zVaGdQ%AIBvm)zMGIt=Y)k6>Mw_fY)1<1s`&$gv%`4etPSV1qtdyhh6(Z$wAN{dc*> zPR8GvLoM;I3r0r_Q)R>^OWjx6=PR2n=kC;%@>I5&LjbGK){~955Odh?KDcB9$x3kH zRBTX&VW8K;s~DvN*h6tGHnUQ}cV1pd2<#YHRgGvYN}qaefs}-L+hEDBh}PPOll1#} znMjW1fc0f_6jp;{Xrk-+vhXE4ZOrBj=$ljpnxt}D%ua6Ub#y!a_r4CXI@Y9ooLqOC zSP|+DONIh%E|aKE9fY>5AtA!?0ll$Y6?+DOQ-cjD)huz_S{cd|7HSc*Tzmo3a$_<} z0OIn>AD+>+A!fD zM?H+qggXe2{_d8$^sz>=(b(g<@T+nMZ`n|e^X4B}%h+P?45j~gZl-3n5q3!C_ zJ3Bc&*WSFyg@GfE0Bh3+BOkR_>4%$3GlZIHk%^96a#`Y`=h{CqWS)-%#PL02Xyowe zQ?8nausH+=ZXLUqY(SZt0CEFfz1Sul{4S0h0a?a`KYeHv!|MrXnHA5 z_I;a4nI_@!LCa68TA3|#4_kJ#({41}^~V*MRKy{8LyqzEMYr>mXeZ(d8@z?*&$Z{V zLzzMUy~}{1N*&_CATBUXJ=vmYZm6#*_c1`sA4Xg->1*1?eBI4@&SH7;YiFzQK%WoN0E96;0c< zrHT@;OU_kOd8(CeMVxmy=&wtL0v&|H6v!n-(S|iZZ~atmDRPE1Wv9~O;;=Jeq&&WiH)y$BrxoQCn)f;awh*q>;md+WA=LQ0TZT?N|lb3F7>bp zy5Qgpv0G!GlUiep5cBe^cElCAAK)!M+X7#V9yI7HkfW}U?E8iBtdX>{X-x6sdSN!A$eY{BR`2rTA~7)R?-afAxT9% zK#f+sZW2KGwK}}fJ!KT>aUBj``pISGd3_)BoJmaHs3Agc`ko%`J=zPg6L87R%i_tQ zRCwO2Sf|*TJehh$+3OO(d!5T$NI}{FYF-;duC>r?bA)2e+YJ@#U#)Xg@B7eDnH`Zb zTw8JL=@xbFUuuKb{mLZ0$4(XZ*7QyuQ8A34HYRyP9w#)n&+J=FA|w1YE?pF?R9&&? z^LJKPJV&iU(_PaQ5Gtv~rW90H7U3!&G$#91iqTNV)9=zOaOz{-F_}|&`eQ`#a4|Xc zFRfVXVbksKA;H6t^9aVpR4*vL_wYXUzK3ZGajat-w)7EF4DxRY*2`M3L=Na;>)ctq z;lt6pz$^F7|HIfh1nJU*4YqCDecQHg+qP}nwtd^SZQHhO+ud(#zRkqM#Qcj{R_!u! zQ<>*Hrv^DaGq6(`=2$p)-{qJTDfCnL0L*R9(ZWsFC$|6U_p_7KoA(gM+9N-ewGXxH z7Of81neQUyl+y`m(sTBWYAM*mntkRkv}*tD8+xU9nTlXn+y`7G6@^M!aL|-09G1#0 z$Gc(N8tqYF6Hgm20s!46D72uZnbr7a9V($zpivEODJwh}(d}ufY-|gYp<1zQa~q2*MCv$l=)QD5Mr+&~ zkDo~6(7!bPy2(V?%MT8v_1@K0NWOAbv>F9Zcdq(uDfuX}n(QtTkAL!0jl@ zcH48uU@SH7ik5_q!lCz6_i|JWL+nOtpIAV#>V-9Xl~HIXm;)=Cv5IW^XjVWGtGXH+ z$nRrJtmuGgTFpiXx7-T-D?>565X=ak65h7n=Y7v|OQ5`o_wDEdZ<@9AJ42Zl3T>;F z%Ku%XR^8B~c*`9(Or82!MmjL~Cz)J_6hRta_}AL|J+DL2m3M^eK9VvMM-6;{Yj~J%J~xJ4D0+kUuxIQlqppSR z55XoYD|XF?NlA*Ue2m4^aDGrGQh}5Sw8)tm>Hhur#46WdU53ihHBJpSlW}-a;!kRs zI>L}K9Uz%JMQT0R4I3D3{V#4*)~h3?v-zWb=fG2zS>jxqtp3;vKLO2Ybsw31Lirjq zzLtgVWKURrOyIoXX&Ocv+0}$No4bHi@qA~Cfgi`?`i7d&m+W>N%HSR z*DWouS2`Pm#DPMAb(^>*)ovBPLvaTp-WR9gZ_0Q8)5rKLH1LaAl0`mrrPFsOt>W^_ z*o00%g3*BVUqE0wbIG|*>|kX#G)zRFr1iVLZR%LcZLK8Yy; z%<4n}K32jjO3DLQRhwps&dYwBdGeojc!N=|z>(}c@`jsi0lG=wRpe#fJlvyzn%25# z{y!!iPwt^FyR!!d^YiT7AL{Sa4|nzBagcP!2}I*X^sMC#`A%;FQy=2Zbn-=6hfhWd zTKjqQ!fi}4L>%3p%(_T_&7Bg_brZ^J28`HaIEsW6c;QyJ-|FUIR&C72c3Dfc9*l*4$EoFX>W@&HP2n7M!yGpA zE3SwT@meK^y{>}y;V!jhYn@vgdX_q5vuf{y6j)K1#JG{ns(iRXQ$Kl{`mrn2_$eGi zG4_9-?6U!UscWstB^MZ>EEb;{Jlq}Mw%6ca;*1%$(-cU&(a^i;>XNP5>qg-cfjN6g zYh0P$;gl)9+J-w*c=iOn*{voR;ce|H3D9fClPJzPpKS;swWK^$$FcsCL3dZx=H%wg zd#qW0Bodwwir}{ijgpkos1ALObJ6j-%ZO6B3VOwF=bvVzy187glulzCKEf*xiMcMgq~x?)YXWWXQ-!o_wS4k6kdR zhIC0sWiac+5yk7HFGErA*i4P+!ckZ&-shGuM`d=I#1f{;UW98;Ap34I0oiQdK+T|f zU|2Z1jWHFA0LK#ucEnug+1o2~JaoUx)+b;e_yCf_#t6II{+xp%so(BYRdJ!#%WRy4 z^GSKQn60b`|HS(y8xmjQX~0^YP;X@JGyZ=3q$&GBaCO!uyysZM;V}uul*GwB)5$2w zJhCmH#rLB_lDROQTH2)?cu_ZTGTp`3l0^fQIKnzDvSkpx31yh|;z9Z-cnY-piJy9w z*OBriv6*dZ;hP8pJ-jVGbaLzAbw&Y-aHgRzgP8bI=*Q?haoNg#3czeBZdSoEM(*7- zE88Lh*Bo#vYexgifFAP4n?XSmUuly?N3%uu8(xfpH_hcObp$?4KbQ$E3nP#1Y~q@= zrCYtlqD7eA=?Mw$guYmPa6LgARvW+q)vcsY-?XbozZEyhLuyRhALWpPgio!Db5y)K z$$2=MRLq-*g9};!BCea>_T^{M)76_C*|=2pEvN*zNTh)Y)YZtiw z*<(vvWLWB7_k_i~4I#r$tEN$1_}t~AqgN_1zbU$doe7Li-^_m~E0!Pqy5a$s`$Ova z#&#*v^jEyehF!y4*2YVX6T9@oBw4{N;9C{#cd9q*^;f1J!8j9FYr@3()8a!8F3(`M zNN_JXo5{oU8*tfSaLue}=W;Li=HRd<%LGei!b%AM@CDH6Oo#cOm~!2t73>Bcmh$Q9 zhYPfQVRy@a5kCS8)75sSx=r7IgC_;g+z>_IV^`|0-r{lMC3}2D)4$~oTdY)hYq;0G zjga(LTu#{8WT<)>HFSM5*n1GCpevzdekq@5aaF8aC;C1D=^mcnGXxoD3C)X{>!>$S>IHOs4}%24a)`|(O@y}I36VioH~lK;{Q9a*Ik_NcNG8i1rd^qcCe z!?XE6J{19TPTg?+S2?mx(>jsUT7WY4>B^*EdK?NC1g4*9*7u_$^a#9 z`p`}!Qa!K07BWb90ncv{SXDbb%n9k_(9!MfEWDe56L+VEbiE_U_5mes00tbivtzIz za32-uaz8?SUxnjQ1CWc&{&*kAW}Mo8_fxQN4rle@!Uj;sx=}PBFwVf+ISBJ=D!}F3 z14#aXsy`tA(aT;upa|UOJ12khUwSa{FG&dDKXC|h1|bx9hVb=4TSGvXkJQ_gh-ef* zF#$giK{p9;?jHsmjN1e@o{;ZLf3f~B)IbC6F@0qbq8x&_3lViBIDGEmdHSVwbeVC1 zJ$DoZgTe(09e&@+W88uSZ|`(b%>8$zA5>q`re(e|Gt1J`}1UTOT3dR7sDU9U)r^4?nO!M1xZ)Okt7MKxYcLEU% z=;!DAbLLsjP(eJT=ZycJpX5|ANnJ@nVgEhru`igJIgS8`fu0X3AX*&=3JBN}99YPm zf$vvS92D-i3vr*nBMORUtShDu(9>1!|8o7>2Bq=4i^SgVkD=_`okS1U4~Sos4FC}s z-vNF8t$E|8`sK*@t$qAe0rmsr+t)mB0f_k(g$CY=X_2Zip2BZ|h?%oN)LW6jy_;vkg zxEBK7YkV8;UPO;w?3D)G=eTl6il6gC>HP^9JMz!?0~CKo_{85C(%#v=z3@&_#|`t_ z`0K-Hz=((iX74qKOpIZojlTR`C6u|DW9=&N_2c)*0IF9T$isrC622Yr@uqPT^Nf9B z^l?%5$CG7i&Wd@qj~SCZzDKR{g5T@$_qZ@^ufDX+huiTJ)t7emDkjV^s2+h%n_n?Z zu6e!$R5qABs2p7##cHQuM(F&zxzd+<_Isj;*psMapS&e?HLB1Bof!wYC&!ddrN^{w zwz403WXXLBVIh!zH$8-+qJ)_`x-I)?q%#eb&h^D*4%xrt8|9$x7^B{+A1{bF74@n# z;be?{Eo+LX-AnzvHAm{uv_b%oEu+nrB^V7-_vtC;^UW7JfsWc5XzSH3i?_=TZs;s` z>D3!sq`%0OC!n40u-L^ks&KWYr|{tEN!OPOn3&H+er&qG`eB*?(`6rZ3QDD1pXxZq?uU6n__ zS;nRDkeyli%v9d*Ni!y2SS#N*@ssvB|MN+Gv#=d{IHUr zPazZ(pC^I0v#c}TSb7K;hFQW9;^^dRdZ|M(`Nx%qW&U5d3wenc{n0C0@CEKHJ{-=f zXBBI@x@T%z4nsf>SeC%2VfaM{f-7*ojS|KLfAe_7!Qi+1})%$LuDj7{rt-cXdQO>ytD}(#TdJC$vK3L1!sT z*?s`A%IPeB_CiOL$~A_XGs{S@sd?Y#on}IHFCa@3=HS1%IdrAhiW1ekzc}~mIu)Lr zZ3{`hm+Kin932i;5%g=;sYH8@hW31f5KHPx&_;8Q<<*LEEtiW)$_(X5O5!rg1fFCr z5;;=l@rfWSK;}F)+3{?OS%YNo+Ja0TXr$mCtrZh$LMv8y0qZbdN8}*AuZi#FW}=2S zM6(eaEwm&iu#U_f*|VLOqQ>Egf3;jDQ?=hm14jWdw5~!1;l$9kev9+Kowr}j_j8b> z&v+{}3^OE}UI9Gpyj85WY0j-$J@Hs15hw<``8ag0g1TzF*N!#E6__O5;@TaJ%_nUv ztsOSV=|}POUHt194oao~*t+UgTQ|KRXU!5Hrz*TeCZJHzBD$|3TyRct(DUn5#q@b# z>tv9TE{3$RDty@0RcvC;v+kpz?gKDEK;9u8z6vBKQ^=C$WJfTMGQkHOoU~duURe^g z0l6J2hX+9y8>R0^w)9>e7W`ZV5)w)-?TK`EGo^QJ2hbt>SQegkvHtlz$ zRBKP$QaWc729pJuf=vy>Cmc<@nb?B)0$Ev?ZC@f>3Gps;Br##??&x(8O2V$*$PbOc z`h^IdJuf6Og3%k=28Uh62k%HGZmL(gYas?$)PbIu*N?I9v9zn@YG1g2tS&rNE3YC_ zW~A^herm1L_+1|gp4hTaE*@$%l>#}18Jwz--ikX7U%oh1Eymv}cWdN!%b7N_C~3PX z$Ci#Xd#asMRQRB0^n$eo+ZnUpV7aO1Vs(UTL&zlyRDmcvlRX&ZQFwZ2*0T&GY;D&KrWXXnGe1gB7W z{?wqP0*XMY^`q0@kd>^U!O6_YTSPZ+*mdcU?yoPS6KfdwL#jb*5xHlC-Bzu3Bm@}L zDqZ6aZ5FGMHQU&@xj^BYX`ck$tQ=+&47iE^?JuN{wBv1#K2(c%d0xewc@_=d3*%$L z3Goe%VPs5`hlS6}*!yU4g7A zM5zb$F6*!IvVuP(^tL@RpQ0I2+WgRpJy3mq1-V|&&V7&;c_jhzOZk>hIdDGY!s2oX zBQ?^Glbe=;qy|NMhgK+(Z;zl6l4X9Hq$nrSj&i@761nQ##kDz5TZm((`mzban7)1BPngT{TiEXtNwXZ6;>;`-nubcpQCQ5->8%OQ;Bcz8(MJ2d4H+KFX8ezG%@4Mm#~0N zJ{Eyo32jSdFadZ#-g4HAI^5~bY0yZvT$32qf+BJ1HH_gwVq>$Pdi={HFkD7f(@d9n zU#OuLBO}yRenzCqZ;_)3&FJ1~XVBA7t$E*!Htoj*m0>AYI%rKRiez*R^A_tdwz(hp z4x%=nmK!#4bf5EO?Dily6&py;B;LK!oVCw!g=;-Qw;=bMzhiKV=p6-s{7;h!@K+%$HH_}cnE>g{IY*q+T=%))n_p3gosvNxsN zC~GQB(VXxEy2DPBOl15cHrRwH8Lp6B?MbCI**EtY1=x&n%)qH%ap;#hT13L{t2Odo zLcdvKe}lU|lKNwy?XdK(CNBbv?yMqfV?G=tBF;63IBex`WisFPLK?uSHa#O&+t9J%zGXgX2V{~X}lVR)m7 zA?2mNO^C92*8eq9#jYWh>L-P;<{RN=HaLmfj`EMOz!Suvb@fFRp668a<1F{8#m2(B z$W8vOZz&AibpPr4Z1Wj$kSjuuYMra1M8kWJ!6UL_Y*rk!u&m6!P}t>eWJT@er}bv) z(Yi>8#>(DYcV@1D27)I+ez?iA6@Y87Th{c1%>wb@{Q`7e|?YgmGtn=X;H$}R7L^$|Olmsq%DM2Ns`b?r(wR^j*i z@}Ym;H}nJS2xQ+rQvx$`vz5o0&^4g8_$;+Ki&-Wkp^}%Gzr>Q=XwnzD22_w;-<^}5 z{)rRI8=~wz$7tj;R|`%XnM@>&ha9Vz2(z|&G~HPA1$5NqMSBQXeQ{E!ZkQVX7CLn> zaCLaxTIjo%T{&R&J|85ml(0D6S;x}zBd5YcVQcjTLbFs!v1HGAv)CBIle&N~#(H11^W9MvEU#CO9s zmXpIr!lAek4YoZEwC*d>@HM2hU&fD@`FZ>2*!+E{nURS>Vbr%3;O%KFLIlkj!J}h* zzmnyN^O>y*W!b7oS8W0%W_v7B6@boJ3H?OOiuBlx`JDd3`PUOAEgFB~Ld%?0B|+u} zw);(IX}biLm4BK5&i53RSn@m=SJO@j{N|h(a>mdnn+&LpT;$#xpM%4-Yh+pK>&R{D zZK;8u6{l3ERHC>}zf>RU9GBli2e2$KKChBGGLF`~Z+vb-`D(xtwXb6`ZW)h@=lR!i zE5&PD`SryzrFy}fOdi>FP!}h@`VP1$1nl(f^_X{tvAvbB>iP>MEd=PiN`{L=re9vb z}yMjtH7rxdNA@iZI{OqqNAb!CB&ynb%b}J>q#Y zB;{c)hm!PkP=BS$Z>BRXY_k6}#S)%0zpP~xcM}Si5peA*7=i^dJjng{)aNTi_W19I zuY=lDJFC%i&bd1qmBZ$a8>zn`)~XKRL)vj2iQ50Bx7!zQ3KGDxvw_6^RbT#=<&-_< z__`oD++!=OBINP2IT~}4drd-)+3SS z2nBI)hl)X24PH!NuLU{%6TFRwQjS?JHmr~G^T45T8WZh|eR{ggPI!OqtsL z-?0pp6qr`)vA%g*E;N3JsgI8M1J8zVFVvKdC#OSR_BT}ezj4Q!7=ujUf}Gl`x3tO* z2sk9`6N>)DtS*s~WODpq;q?2QQV$Vj-A~Is2K+4#k)ro82AiT39r79>5#)(lKAR$f zx5u*O1EqH12R%il_W4s-Q5FjfPtD&}DW*iGTj)s?kvQvGu-5R%*)Ctjt(2+=WK*J- zr?v$JWLJ)!)@C>8G~R2Z8=t}>goy3RP@~%ON@ZVzIQqgq^MnN*d65Lh)h%jNcqyk% zF&xedkq_2(7YMv)gSG&{!4g9!x2APIl~A2LpTG1pufETe=mbg^THUwIac(oNqi9&e z!v-rpF`{T4A+OGj7H!bRZhab9a~=*z6e>|Jr2VusRjca@u1V*!LtsYD+879lG1ZSH;uQ@R1xrqb_44O>V6{L$Dt|%gV5>=TV<87K zbXV{qkB(TRLtA#Vo3bI;Drpd>F163U%O}Hq*STm78=d|7?+#RDy6lWg+EhTo^>l zDLi9cKhSF^j?S%q&{P3|?i7tBbR2!@%D=`_QGQ>(MdR|1{5X-e*BPOBkv$96TSbpS zYOK@L(I6yda59`Gxn@M$+}OUw!yR9xRQtWz+W*z674Bu|W~CgqTqGBjlMowQNDm zlBsqt?kF)FXyRWPgT+rArnh^JYa^LwUdWd7HLl$Rn#Wxa>@Z+hL&VK}jlHtU;C*ZS z?FtrkSE(sp!WI6~|7i5$M!3r6l)RB4r2nclDDMkKJH^`4x{#m(Kp#&VH z(-##T$*~Kla0nDRr`wc$XKO4p3neaVMtsCD^*VU#?-R+AV!)0KFmZuA{L| z%*0p)?~ta=eMk~2)!$-UL2=;Z+34`{rYowzPr@>2xM_?T5dGry$xWaCmov6wa~nG7 zko;ttOL^6_U7Z>I>RB?UgWw}Gr#_fplSb8>(5sn6$$1IRB(olpp)LIx-O5HFA8(Oa z>rb2I`;XoQ2}e%nbfCG2aLUk8$3W-%Zm#93nNo+4Gkg?Q93*FHqV2(tV&aL(y|V@v z(R?J*Vt2;YmBQJ%@0s2VLpCqmDn4Hpj(8Yq`Z+xA8=2nu4CK4BpCQ(mmcO6|Kbl)& zOk*{?zjVj@yTLb5P-o_$D@|2j<@S+@(0%w7bfUD0`1@cFL2OCVaQn{*{0qfSq*R6V z?=^j!Y$q(p3i@ql$>Iuao<){C{eGx#9{E>>i@wk}$r`D9@^Xs|{I|gzeu60`cfK>G}6g zFt7ERSF(xnxi{snZ{prRo0>e^09qk2NSTbUhMO)SKmFuJlNE0Iq~@Cx+qV*!Chvf$ z^Uyzp{wFV4=ys5Q3#_>08<-UH#LxT?j$u6Jg36IH;@)3Y8FA3 z_~^@^vy9Gii{Dn1ZcX0VEilI|12FVBw9h|4e3A5X=9U-%-P2zsr%*&6 z#E~ai5Qr_I?h@V1Mo^h&hD%g)4~BBgh)PvU_CZG1WMJ7qadA#H7##7BJX5pTirA3?zyb4t6%I?ee3h zNz^Zl5f8X~=DmfY6!eYZUpOS*CPlt=gScOBNRN1EZqZE-n9OO)Os2eB7g{NMH@=Xt zhuXxI?3yNRSi{FM2&yj_J=o-*(l3imFRVlbI;mTRbt|gc9+|i+i89Lje1_banOD=; zb8IZn(Yqe2=|ZYf>n1AYq@dkPk3rIq&t~q#aN4XmO%Q& z$aiSe=r)!fn`Ulq5?CJNxkzzv1aQ4?l^SiRA)IVT=}2q3@rldNdQ>Cpn{$6fp+`0i zox8a`Ke3j+WzFa6r|YLCrsLKsooVX*9<=?G;MDFvQ&V<{vlMF@89clyLpPuBfi*NF zU{Uc8w3IEY2NLU=(a38dRa)$fXYOnUFASJ z8Y>l;D*cR}MmqT{Hgv|8La*d5CO;cX*W-8lUI~1v>wc%|KcZ~|gGVxQnYJtg4yPBJ zuvPr1-*9=PokeDz=NO!Tm;Vx$`*KEqp_1ODb6K?FU1$p6EvC>CKH)vOJX8_z6)+H5 zKOlgZHbMOtEw5epIb>vcmV%6#oi0l!0`jr;m6HXFL=thV+4_s>i*8vj1>ayTsZ#hVrr`OMB!{L0H$flY^;FSNn;}dm?SGV> zilfVg6^ygxpuOKVX)OoEWm!)Z(j|W)fn+?Bwd4P{p}-0{{`Wf{weAYG}_J#u$#JPXrx^7{Ea2KT(&J($$6etbe_b>ip9 z^9$Kb&s;90tVe8SC*NmRo}PMuXMuNAJST0l2CwCjl8taQJGm5Y6qVQefwLPdkLrUj z;I8RWlLk)~P1{;Tp4xUM58!uxkpC`G2<6xPhpU*AJ92yG4`=crIIUOy`DD#-O0&AD zy%7wP*{QK8S-0p;xs|qfdZ(`mX{`7}4S=6cmF-S49gBeFeBZ1RF0e#-+D9fV>s9L5 z>G!a`D+oG2(8-<+V6Ac05cF!9RH1o79+451X!aj8??u}oPcfc=bH-%fMMTDRzE~gq zoc!DMg>VD24JS&ym$ofI;8ey_(&|I&{S?-Wey;mHP6UsNWSROElEk!vJBLI_J$xNTZ&|xPG^M0}gIf4%x>&3jKXWZb$DxAo4WZH~Tx$Wn9>(bDT zG@)@e*_}Nz*7i?5uRV8p_i+ks8i89WkZ}p;DaknaG@aydl-bVhb$A+IwU<~Jb%K~qyfb#>;=$In3s*JwDKWn`)uXHP$JHNZ{S zm|1QB@!gZQem zP-=RwX_fD7jNb^j6fY4It{;>1KyYy#n5R!~_=5fD%@U^7-}VSBPqwbD?vH5C8sIaQ zi$EWqiJ6yf#2ap`TBdqLos?^z_llPG<&k-YM{5XfbF$HW0mbPaE`m~7qIwjtcWAYjrN7RVX1heofd8^qA=P@}WDGnbC z@0&g>UjA3wt7E53$hOb_6s~zbbeTu?SJn6V?c8boO2ebg@Ai#Q{*!2p(v%hqhbt3Aby`Yu-O{)&;3} zOg`H+Z`OetrpW^jLe10d)GFjRc{4l8D7R&Plt=g)hcSs#m(AtdOk3i3&T(pKtBeS2 zM1Z43jgBq(c$?_-gE+0>s`)=yIL!Z}g~Q7AzrCCPf()GhvxURK$mn@_p^C(#h}a|Vk$T?w-g*E2 zw)EQ1X!UV<-ZPsr=PRBwij0;rz&`Y;f;WwLPUa?E-xpC1pYxHy1qpqc5K*$q!2?55cX5FX_z2YJQ))<{fq^^*2@wB+ z5bKBrHX^yFvnj;lmd6ALCjgOShcuFf z7hr>$M7RvuU4S`+S{Bq8$fvCHPc}er6E4UW_4MH3;b|w5ldub^ssY2Lmfurl zmqaf=fD8QvuKEFX0Qvok`zIau>pus_^p_ee_*X7WLz5^wo5+CyYa7D?)Hwu%?O3%# zF_%*A518FIER>@N@%#spJJd9?Q6$9IEgnd6+9HV1Jm?P_!Qv$PX^fB)iD6uy*zt!d zgzu!2gEe+Y5-M7p5QyIk1*~(ZRzdtu^x53Z-+p8QhrB*GT&(TQ(>0`3yICGDhxBM% z70Fiys7>(qE%X0^LOz2&0_CtsmzJhuPgUKuX)Mp~NMBR2x&3Qn*avXUf{4H` zp&J4V{y>DJ!}u^F9i4){zCSGY@~}VO z9gq+~e&0Vm%%V$EIKb}D0NkHXKTouk7n2ist{<7NyYyz(LDci1ktxLELv$eE0Ru)T z$`HNxpQadcuvc~5{66QDeRilnIKN%G&s^VCrf+>%{eZN;>jA&CrEvmF7%(Q^StsOw zfd8QbK!5n1zuhN);}82PzwBv$@4}9E{`i`L&N9yF>GPf<85&p(7*#u6=8TSkpB>UKAwL`y;!}v0^`L^9n?L8%Slyen zbsQt73Tj};x0lYm=AU{0k$I3NCjtIH60A(WA%7&AHx>Ho9@5}NuP*X@#|LVVR{KK6 zX#PO`XUPb41D#iiYl8?7GHMm9D$MOILp(YRAyc}*An`Ua%tIW&yt~eT5DO4Ad*%G; z+wS8v_y_b4@|Cdk&%d!Bd(;_Zg7-aghRx?M+n*vj8V+@Jm%YA?klPRa*Sj%bn3oVO zV6!qLH6xX8eQyp~S!7rn1Co%mx8TSCoI`JHSdx$b+eqS8EKpXdbZf5fshTGyMw1(K+u z%Ynbco2}yEk@wirH=h}p1k;F8$Dzr>+RIyit)!S$B`ZXq`)VwTGHE|u*1+Q?G#k~k z4};W;WOK_Z%a*Dl+H`?Xcq=1Q`JUfqP~DeY#K5V$AZz^1;e?T=B3~4z9*@+n=FWCL z6Lhb8ljIJKD;)I0RK)4h0yZUWj%E*`&F8ymEBdsWhX$PlpJpi|w12To)Mqbbo)vkIgIeE0yXCobk7Q-*)oV+!x(84$tgU+-h))tQ^hz3v^B751K+ zTXcF;NMldX_*dMEZ;;crBYAonhsm;u6~b(mq^g;YFEx$L!Xc(NA)=FRwQ`S6**)sc zi>hxd$NC>xa9*+djQ`BoQDgJrJqHaJyQ+Xt}35y7eOW+jS=RZ z+w7~OzmwZoNT+52@5-}}HI1?mMudDI4)HvV(R&92j|j%JCYw9B?aY?SK1ic%psC$E zHoK@AId1W{(o`b5X;CumgJ148I|b5lj4v%aVdy@dD!-!ARC7GX??G*RzlQlGN$V8d z?NX2-NER~~+z6)k6g8fHz@lnJkZ|V%q+H}4-7N*5#sG3SDZ8#^l-aVrrj(f>7n4DK zc2W(&%vQ{@xay+tnjF~qI)dTxn=)mJC`;dyCnE~oq7KHca2SQXjg5cL*mL!tea@?; zth6Lk84hL=P(-KKU%VHv%Rt(2qc~+B zIM!L}IVzTVenl;kTmE>^$HjLSt5?2^O!xNlzBo_e;=|RNu@JVm`r$rJfkht?oW#-I zc$R~rv~`p;WSPO2gBy@kAw3PQcIA}IjsU%I9*Zk0S`i~{*{o}XQ`Q5@^qEbvE4V=_ zKKy41ZZgkm>CW|W|5ctgcCxYt%R@Zc)G~d*!u|nSSB2q4QdO7y?EN{DO3a=ZSh(T3 zv=wv{m@sCRB2CzgJqX8M)LhbTR)X9!Zao&=j!+n<#Mw|bn7E?GkMYaS|PxD-pVW%pF|S? zVeFM%YlMgi9sTaD?d&ORuUOX7G|*J#7S>)?M=65)4HPdcbu70gH#$Yfzki5ycsrd+ z=dD1yJm!UeqQ?^3Tl~~O^#p73lE3_M!ph<(<5c+Q8gY`?7Zi=&+Eku z^txkJW`DuhmzwmOwnHFbA0ZYTRHFGjyFB{vv zIXryHrQi?BamT9g?Ry$tf)dipYUV*gQ;uS4Q?ov*P5WJmT2yachpb~MbRnoW#u=k7)o9(sh<`(Jlr(aWDJIfn_+r`Ma zz_rSEz!nx|XeW)p7JPLyVy|)A;bY< zz@x7@ijMp`&iQAQJxA0zg>Sno@2no$k)gl);ZMNLN52lUs1z%)vTIM$#5m%VhV6bQ zDy3H&V-?@e&3?}5ZXG^W|9rxoc}>RxVk5iuIqSuy7@l$eAHom0W%lR;H$gR_Cw25{ zJ1(|s%Y%j!*X4<20kA8?7#q4?afDGauy;%3XzZMrY(jWG%D0FDR3~qGb_( zYC`W}nAGAj&@$3hmbthV&)n>P8}dirR7*BE%7;n?x@f~;V}K;ULYs*25T5K!*E@a- zz63oqFR1Qe6O2r2Z6qF7X)s&47Jc401-7e!AY9lhT27F@?b&K3rltfWRtqyB`@ z35;dl!PZy##DI!JABD#r7zL@%vtC*5J%X?GTa}^~#eF2d395_j8#WHbiUr9M$3$RC zM;<0a{j=?UFpwRB(N&L^b`<2qKh0!ev*`101{n9cVOJL{G+w72aDE^NzWvqSD#)Or z2N3AOH*F&{D1>}iIAKBVY=IJS-P2%behS(uaBjzOZ;Lwk(uP~J7R|8AZvXU-Qw2Xy zJfCSK0zep;Luh2D2Eq28Mq_za2VYT7cYKU3W$S^T-fk%DubH_jlY??1B!41m1k-7} zvBB{7!PMBI;e( zk2AXZhy54{<7D^>iCu4T>*WlW?^pSzrdzT1dMkWI?=wR!KWD4r(&n!oe+D;dkrO5V3GP@c6xmxtE3 zln06wN0@svbwedMz8&3XhT86~|9zY&DXf-gE~XJ;$%x4OD3vWr-OR(7jrF{(k!old1ls z%v9VN+zNmmEBIf#7!o->ZYtf2?al*Q4pOe~V*uTeKWn#a(-Y)%T_At~2;wo_+bP)~ESwGIL)y=)y4PJt+B2e`dh~ ze8aOKK&l(Tnkz6Nn?R6l@+6ZQ__6W3YYxyIfa4j#F6NAKcAje&%=~ErtoZmx2<>!WLZlwAexYtuf%^7+siVn6SfvH^p!qSI z{2op@)+A58C`!JyA}Yqrx}c_*{1qIGm})R7_1dNQ$MAZjqdcYISLi0mu*A?W{D%AA zar-gDw67D~CpTYnKz6inK9W_7Sc|y%DPtA}-_VNxS%wkbP2K=gKIn3yUE)=Q#lB|J zLBF9N9wvwi@r6ugyjB1S0REdX$uC~1*@ljTP~rF=RIv5)V#9Pc6M912t%`3M6`W+qiqOeVIzSME*aqt!Vz zlR#nbdvGB}*GKVQljmfNd|XC7A;?o5#rND3tBZS}56m!ci(kSJ%MsPEIX)o?n-Msg zyUG@ZT+>qLZ?Sf!7C*(Yd)f6RKoZmd_ZdNxz%5)dZ-LdaQyZV!+Rw$^L;C!Bw_&jC z5_?CxXj$6rcQUb&B0bSuyEEizv6U~mCzlqk;EJn;@eq zO$-kTNlg&mweYAn9wMw>`dUdxN1fn%^p{B+B1vi=056%>lwz@*#U$+7wf!l!RLVi{ zhmgld->}Kn?t;5j+d<|RU%okq{5uLvzn4SDr>c1Dj~L^UT%#q0;|+ay_P^LVrzSyw zEeW@+Y1_7K+qP}nwr$(Cr)}G|-FIRmHg+Fwz11(MIwv!~TzE-010jjhO`5WH%0UrD~gTX$-vCs@)OI_mywx!m1#)QEZ{g*>5N^p`e?jex$%tq(NnC-C zLOsS{De{Uc=iL$WO5VL(h0a0OHBeu1kk3;?HbO1t#cir#5-M3>C` zsn`M-dpbv3t_MD6x<=_z)tR^YzShsdzu9t> zaIKr5*8uUyNl$128~MfT%XkrF10IAF0Z~1%R8i7K_QVL5j`Hrc>$SWJdLkLxG7w>x zaN5>K+Sw8tvPeX@MI?gj_7IE`OPo~&){y?Wn3md@LmwZv{XDd0I_@us{C;+D|H*Cg zI; zasrFzsGF{M8Dd$bm|EW9SJ~tYP*qb=of_g%QLmJ-G1xC|`JY5KrV9;T)tuUB?#X;A z-mR|zPRS(h1kwgZvnXaBEY#8lgh~7k9tDZYxcj$j!R#C%o3ko3htBqi)3Q)Y;;Zq& zAk(HDF4eg-2I7`H!Q-`w=A_%^#S*BUi+gkSF<2cAci|L$X~&*;1b8D-FqM@3v1y%`-DLty}Gs0Q~=2+#-?S-GA>L|z{F6&)O82`^M9lS+n= z#{t6eUPr4|IO*X(e{yZ_=+j3!#d&;OUU;mW8xGTO?KM)K{&HwIGA$l|q1tr|#mcJu zVA@-%<3_AV@gSn{Guy0>1BX1JEgUt|u(_S;ok=wu-JEA5|Jq}a$@UuE_WJH%Orc6? ziVgOuIoaEN?U*Y=g91LS6SGv8E#;~W8SrS2l&tH)m@G6x>jhL1OJw`;aBH!$L zO-mpcRR5^n?3crwI6Pwn{1J#|g?ox|TOB@k>rHhs299y+KQnJbAKXqt zyY+&ViTo_>PHhgw0%`3{$b} zN%@;9vXBK*yO&IhxsftWQMtSWk^#O+_30?+G=f1t{gR2UKp zd5i!ay&YN>;&&ymm3qCK+ZMwHarJiBd-R2cVx*pVv+WU4!ijnz6v57BXa+%e&O6cq z>SrCQG!D>g4GY@926+V_MZmu$Re5>LubN$8w+v*^Jbil}>M0TmS-u~z_^*RW+vGtY zuhxCR4yHX-W(DO&9H!iL(_KRY<7KHcp=3h&-p$5QT62A1K#FK)R z3xKadGf1CpkyI2+h1i^K##kaU9LUfvULa$*&LZpF()9CjNG#`VHQa#D*J>%X07=QC zmI}T8ug?(cuW-R(V_1-}5pl)M+l@@CgO6!IdfrJmX+>^9&g>+wkJ9a2aC_5?K zM#VB(r^^<_{G>vcqoTsLhKM-pm~fv|muw)Bv&S#qB5&Ul*yyClxyxB(6RR=JTzvKT z6LW_yUg>g77((+ij)@w;4#KMJ+a#&(DG2#T@wxc0DlUlN#fGlKSMZU$B(=Pi7gv1p zq{GG|9n|VazWZS@ihDXd9}V}z9e^je-v!t=EPp>A4{ehVhF6IIDs?FjI<(5`8?sGE zmVLpQ#D2(PW%u`IKSK1Vp0GuMEqkBwUT@-rOCDb$EdMl1gHy{CW4*0a@)8b2-)yTZ zkKj#HzPcp6XFJmFN!2;FZyHHZ6SMAAAgUXmv~;z7dQw}S!s_3U{~gqn&JoGwKMyZU zy6pJHNnLY$I3f6pA^0T*j6xG^^V&;%u1tEtwNGM?QrXb`puVfzU(r~rtA!5pYkBZ7 zHggVDG`LMd8XaG`gP}%*oVIKls)7aY$2i38-YQ`3vewNB?0;XQ*o7eALUa1 z#a~7sp#;kz`9jZ#z1LEUY(zN7U2M<$RGBkV_derR{APA`8FZd|ub6B=byuCu#g(IoT*|dPdb~m+D96|BIQC3K&(I}t^ z9Sk6vDOrlyp*(YoqCn-o;G6f4Z*WKr6`Ub6481xC?$O-q=P5Sg+yPJ6u1K-{6|J>M zJJ1LrR{>Z0U38wRtewbi;1ST=6j?UVv@G(wI*gJBPn-G)<89}K7mXUaf$f4>dt!Z| zj16t^*~#Gh`?i<5GYg65b(jZ|8hMG(Gs!J7z@SK)&5+jt;tsVZE@4qf*{rL5tt9B9 z9&e1CJndKWJoLx619tOMw5c%JT|fJDaF9~X>e@jDW*pUSUG{_-hvE6zGkBRoCCfA~)fYZ(nx!nAmSAkgJnCCx&C)wo%vQ@D zSRnhM!`=-w5`o38+=1O}gMCe`4sf{36xWKG%Tc7a7K9z0q-rm0y2n_DUQZGARecvS zj^y0UZ0EtaXPO;v!?N}2%7E_9plDzN^Mx1$ziukE=JW}HP99<&yg&|_iDSp4V44N) z`zmDQ84|S$8BNt+-=9Cb@<9TE*MLt-O#Zbt#h=P0Yr=Bclflho3Qv1&=DGgsb=We` z8|bg8#^GO_`^Nrm$Xpv&)VQKmZC6{8dFd#wwat^dde+of@>{(f0=av)Ba@3gv*ZxU z?8D$0h?LR`h=7#lHc2oHlfdjrYW6N!5-`hZ{5BkzOQv7Q2Sylz>DsKX0NS_MvJ4)n zbW4^sq5rhBNA!1wUJN`8^eC@6&0?zS%`M15IHn-piqY(ZfyhG{|=;W5K}v7+TOo?sGHj=zr9-+ zI>Htn$LW@rW8ZI`XI*Jz#&VU{_07&UmZTzzi>QJVxKe&H@K{PhN<;`eer@^a1em^o zftjI!K~P!oQoU;n@Q+bw*%Ae!x_U;!l4nF_~8y5f-mw!rB zTuN442x$N4;NT~o7`Pd)e{e)s3kQD!B>pJ?P-nkVBp16UhnALRM=#D}ULF7@lO_Na z9Ua?{-adeWSAJ7V1|&qj`GF;9vme*|)G%EBjlLJSmbF z8Y#G$6oDp~e^^Tu3P0=_kh3dzCa^CWj67ol_>T?-5;qC|(8R{ET~}vNNL5$_6T+Qo zeG@Bip!UwcVEGBZS^wrffQtsGe5aaK)x#8)-9je`dt)Y#X;m66H+6gHDg@TIz zxK_Y#@~Pp8_4V1s;E|!tYnSlJE~A}JDo92Y*V-nqKrQWE-(ym}D_CYv%XZZJZB`2? zhr56GFCgj)zEjk$NO~6sqg7ya&X#{8;%|F*#@=s>29OS5HZ?W%RyQ_4J`%v0h3Uwb zmhRBxpEtDekIgUDfV#G#Afo<*8i@S57SOwE=$*}xVH^m17gyj9&tHizxbD<@48Qu6@~bD zW#xk3u7h7kLqoV+06S4vH~=CnGAjSHF!28AaiF_zJroqAOTR|_cQ$2I<9&d=Z?5$= z+HW$0SHGLQlf3PG(674G#G%bOAVB8dnRZ@ivZ(bPP#EI*O3HX49$JvE!XU9Kt!<~G-+-@fYVs_{+S z@IdP8pG{FKGzu%Z{Eo<$s*L5`p@%k|$JfMljUazYINFsyJrn>UD(K1I{TU+K6&(VypD0hIV(qEBmyRoT( zo0{-nb#``Nt*h(bm^U4qrgyw}lzx~mwSY_5@8ykO^>*J!Sz9}#dpu~a&#aNfshQy) zJrq`erjX}8%B#MDPrSxH4{)|qzE~fphA-gWV~c0-BM^G6U%=gq#!uh}p!8q%tmhj1 zIlMa>gD^j=yOYnCvtNO}l7lz8Z`8}Tm%G3#f7IWVsezBU<##{Lf&0{^qMWQrJVQH+ zUj^h#t&QKtY`fyg&BJ@T@0BgT<(<^{_2mhSH?g#xM2BblH=@1k+U*~II~)7oqEovY zzw)M@bC2(=%dA`Q{Ks9xU#3b^+Znr*j-TiB?&*8KJH1~Fe}1`qjIWEtAPm2786oji zogDH2@WXwy0gnlxYiCW-Ta{DWHgMxL1l7U5X$+#K&_ARB_s0k327$DA$qcoisy z8}86z9;`5`6*8eTIF&fdj-x-hlqcv$%tg<@QfTDR(oU!jlJS|pvQ}muemkq`@J{8EO@ z8gN8CVoJ0pFYcjx6v@-m0)b>MI20a;5KkZqYcU+cwrt(kAaidFM-=NB@7Gt;ln_Ot zV6b7k2`!ELeGCf_RUs)mf0a6~Q7HMaHj z`SVN>X8nyD?_LU%uZ~O2Ci0CJs4z0qzk3}B2I*c9Pz9X#UF4%hGY4H;Hgibe&3siA z9D@y{*(XQfnitV|RYdgOLc7a1opyulW>!wLr?ZTh5t%kk#I;leck#H${ic>3{-Mu% z9!oC5O(}L45ya}GrQgB)Ui{WD*`f5;_E$;OUO$^NX=-;em%dn8sIj&G1#dl%o#yPJ zl0MtEQZyWRCsNGqktC@hdmi$|M!`yJYbY8?M3DrUxqd>Tw2o$3YB~l@Fg$MdEkm?k zCV2pL=&4sVUB`|+)lP-GE5isVdM<4Fr5qBP2tj7=wZQ4d&VfHE7Z!<~ZGZr!=+9WAg<%$TGR4 zstAUNH=HxYfvl=K0G!BVMdd|hDap1m+%U~~C{Y*|QH_)zC%QgSuSO60D(pnI-_1a= zOO7G3N~Os<6@7y2QaT-vCA2-s9#50IH0jGCWRpN@c-Q8%%re8!5$k5%^f*;-@?I^2 zV1VkGWKoB(W>g&M#fNf7<9S?C8=V+#mD-mjt8$%|TL71?N$YM`<{-0a;^?0#$4G12 zHg`OVjC6k6VYPc=tLaklzMyy+(?+P3?^eBbia<~dt@wg5fUkD2H!%vwSpuGckTTO+ ze9HeN@>y@>^!?CMpX zVBjreU#?9i!^D%D;}$KvRo%`vMP!nnJFgfk%a*D$1@A15dhRe1Rl*Ud__{$UY@Rg_ z#JmS7rpMy@8u7b(?;YBV2VE8e&4ki*Za$6-g?D#OHEm4W}>DBsj+(GoK+q>-kqpefK<(u zofezk&{^$>FKU`{at(vry)ofwCcpTn!z2!iHcTLQ$5cOeQ>JYZUTOVXz*`00SkLMD zV2;r134Gr|3X$!gl@W9EkOC{pusRendIKp@iY*WEQq9(2few_^D9!$e}_O!k;;H4`|wsvPPdNvn*AoH(fS>VZqN(EU(8IEZN)AMAKefGnI3l^4Y+&k9mEiVr)$Y}F{TeLe;3ha?4MzP*M z1q*Tu%@m`9G_Exj+?FCFlw7FN(VdwQSZ>rOw++T4a4aB8clN41XeAh>yfQFmDU-ta zBExkf;<;$q0FY9gqoX&O>;)*I7ppsdC8gii!wr&4hg844`Ki6@-V$ST)>2fFRv) zT#kS#=uPTY`>Azr!QZdiL{Nnm+zJ6TWlk!oHOFdKk6 zPr{~hu)3vkr~V+lVkDjj`(n)1H4{6FMb;I0oA-egcnIY*miw$$pQrSNlN#r1!f11m z;8!gE#jA+jWlyItRzaw$$`&O{<1z=ZOTCl8BF#hGftH-x`K|u_zwJgek9Cp(Zx2z)Y9|EV?+-pS;Tmn9Uxl z5OB->k&01eS!25JXULf383$_j2d3)u+x(%f0r(IEy{0!Ano>d{yqkX?l}TCqsDw*e z`2M+h9>(?tO!RPG1*&}GpH^qHRwu02;DgDh*a0KrCs4h=K!DRo44xquc244vj}r_M zXf8OVX0(WniY;y{6~pT*=c+HXgSK{6?H>eDM}{qOAr^oS_oy75cFhue+grI(M4vYI zR@oKo8OP3M&a~8tlx%!mH04Y^erZq%H^0wF4faXk>qg;J9ns8@H2r{G=zb2FR0ZQ= z<}-o3GR2Wo{JrWK$jVFA*hjw3Dqd#)5ZHpzopeYG1J_nuOOe%P|$~wiJxVKA<2+ z`E!^O?|X@{kUuIAv4)#K=mxnnUyAqF;NR9WNli$*5*`p~jtsv#D?*W<^fKb_gD$m0B(w_+lIw2jN z69a*gm$&>&*yRMn7K9cdNbve`Ep3!}R~gsL@xV!qs%njvA+T zeXj@*!5u$;>znBwVwVb}PYAuVSS@yoi!zy7J%4bS}8;sIF<3?kHgy$-CX_l49(NQT* zgQ?P4OG+%e)=*=9_Nk9xS&M(NB6^s>%PI}3o}5}F#G!Sj5NB{d!2RbH+u@9+K{XOC z9!&vJBJL+N!`DiI%emeIZ>m*Aja$FxNV}g08b?w>J$xU7gKI=#5a&7Q)af!V-v6V% zK~Pq!Poy{P1{)GytWnZ8D~eO0Jj}A4ZuG+PgXXp%{xai)JK5DfcjOYu8oq~~^1F4* zcuda1J-#fZ9SiV=d~>RieHbG3i%fz#67_9|Dk4ttO4we4Vc-In5noI%!ZQ`G9)7pB zyB1!WIx+}&qETc$gv8D;V@dvTIDVk503LWTf4Y>#C)qD$zRe0zfth0#sy0+)coo6_ zATKMHBZf>V65Z7`18oL2=baV>MA_tF9$~lNM?pvp+D0nX6WV30Ztn^)TDf?5Vtf zOIcVW0=lnH+5~oi@+;UJhtyjhotVt@o&k^U6f0qa3_{)N78v7!6pjicGj8u4Bz4GF z=Z>2vTB>1EkIz-kAo3rI(|2~zCz5?|Wh``_UtW3=PNAX}o{`r{8-kAh2jTi#Fee4) zCIa0dR3tA0;uk|~ugw3_k+4qj#Pav3HK!Uz;ipt;CVwvj8llA2(GC&nbhIyBLPm!v%V~n9DQ{cBM$>#~b2g1(x&R4C=If#-v#sbDT=M4_)kEl1rV}27lQ#ug4IC1aQgs$C%E#lsDPj z?sw{l&Q|Qc@{2G;@d=Tm!8P>~tND_erSFsQQ;qg#Z_Se3ErmxD=6s{~o%)u~kZ)u>N8kD&!&j=ulG*IS4I!!`2j&4;8bc1g)r5nfS^J&* zlHEH0%~yans2&OKD%i>{wocoWDyKJmlTyW%aUFVaSCE__fBYQDb0i}D@GLOD!CG}ST zj7RzD1E!yn!04!MG9(o%oNOj9QUXF}=c=)!M#FGyM#P_u20Gt}$D|Md-$;G$vTas; zRwm`Axb_5Lh9suu4sasO=M$A@B5jbGDt?}SB!arGPOj(Kg{gpy11LXGKTP1-g}(<^ zC&f0o(v}3N3R0yH;~+gq8ICDkn0;B3DOn0^j1C3K@1_?vTq&Reng$UtI1Iq2PhazF z^I4H5Dn5v6wrU5;J0nB}gec^Tf(%i~@eDntpHvXWi!H`l5yD<6Z}RH0gxvas;$EMP zN~a0}ecm8M&~ws6y@c1-k$Fv4z&8I)r>8&cl7hg0|kq z)2%@fAlMAE;%z2LGyic&MbNF+>OBI>UJO*{fM^bwQ(k5kM4g!;HkhWArAM^$UHgXZ zX;TeykxlCReeUOcK?P!&3vy-iOLH}P01d4H1mztPSJlGA?Q~*%UImh4bSc)pu-0?A z(vi`!k6a3OFpwk%(mZrXO7J0p3cmx45UI4Q&j|4lpPb%}2xdCSNo6tLx52AD2t3#3 z^gUx`>qHV5t7*=%*DxAJ@;q-PHaZjQ_AA5DWAf$-l?W4&XiE{rr6e(YChC@(k#jos zrYPpD4Q;7-EdAd+aF!YP%*ivNGi-ecI$lTyunu*j-@{IGx0pu))ZuFY$n)WwF8N!s za{wIYdcFZqQXO%ICoRcq|N4hDV&yEH;WW~umuVQwj#jD83-Z~eO!*_p;cU9!Gh=>= z?5FAVrGBF|)j|bj04*~aoc*;IE|>2lLV5}_h5c}pZfS!ShfZmg#8zvN2J>qq)*N#Zsjgha*hC&|{okvTDEL*h4lbVnjvi?XV1 zerT)g>_xabJzEyOuvN=1T8}nneeVuaKE}u3LPYCd0F|x#8g^i3_l|!%D;0$Jp7E1l zngse+7&_0b921Sg9&*;3^QC|b>8NxXV@bnxi00s(X)P^IVdB98S=!3n;To2pE+RT? zRdO`>>>z86DrV_6epml^n%$g@c4tRV^X%jMa8`o1^LNLBxG*VBW|0>h%7%2m%Fi^8 zOR=Ov0xGkkqg<+OsVle;X#o>y7TVpueL&W;-M{*5F>RNPxyAr$SYdDX*J3U#PmR}( z5X5EK|99@8NRaLQ`^tWEsr=cJP=(ffEZV>Snu8^D%8FdcG&m%E>Lx@yJjTt?Dlprn zLYCo(i)H(-m!4zJ2W)g^GajH3WnX^>49H;{_B?505@_I(u*=9(I56{$v9yoiv1C(;R}7sFGYPV`>djxSYbMK_ zoA(pARpi`!SPPKc`y~siy22xhsJ3@0hk5R$XA^f ztIpGA>Gur3U4eMUT~LF*SIUJy>B)&xiB99JFM`mLRfcMYTR3k%H-Pf!us-1NCkDkH zwZIgyZLVueGsMeE27ks_Y;S-ec>;aLU-i9|WlIyVaM&UI-7+zbpD-XG|CMNg=0$=H zihH3tdS)k*XgW-7G<*?8^BL&WOoxXvG`jH>wP8ej(2M8K53zgGx}aEjg~~IJqq2`7 z{0Q$M(^mJV3iRhK?5}|Zj9xV52`x%@g!Gb{z0!ZGoP97_t^6BVVUgaNGTs?TMjZye z-;&;2BPlKGO2%{@h#fwe^_~h!J>>eEs#!UxTYOThJ9CWotU?xdKzgXH(wKXF;wmK^ z0a`W%>%Z7sR)OOrz5C< zzd`+T9Sv$g*bFqh929UBbZgFs;!ZKCsP%r@^_|=s*G=*lUIJCR5Xyb=mVZ@aS7EUc zK6Cxep|_8FWn!^X(o2#YM>~K|zM3J;c4l#n!W0=66t$6Z2g?=jm>-$6Dpf#1Cb>Ywf6cE?i=o= zb)|CtXuT7NM|1<7?sy9QfTC%HD7>)2&kvu0iXkk^INLv2&i6TwvQ}xG z(k>!-lH~?KGNip>(-80ge17HCC7;*kIk*So(t1lg)-p&2L3LxyUZ zLtf=mYz-U5F?kplBWYraMjB8#0VCcv+9p-u1gW=2PW!n4`xlUuM8JC-k$k`*j4pV} zg@YB}ye;Rz!j(!PbD&r3X+tC;re+boHH58p*sZz*pVGJAM-!|Km!HFdQpf>dUQ!|! z$^$Qmwy<@|az_Nnd16Y%>TU{KNMKGR&IXXEZjELr|LbO$GAFB+3~f}TfeD!EJ;j;7 z6wzQ{v&R*z+71a#@a@QwP$ti+gPZEH>7>hZADY#`Ko4%J0DMM9dH|xC8`Zz%l@ih8 z^g$7P(3K|+^rFPQkhE$E7`zwur3K<&aip)6K!VLd^P*f@P=jlwte9omt5(I>E)}2;g1@Z;31cX`FLob77>(W{XarMK(Hk?9E$Pau^ zV1)q}ygc#d@D#`1(6aeHYoHBt3pe_%y*Le-sTqrtE6uoi$@$A;!{$!x#J&H;&2{fZf8MO^^< zfUzS>@q}B^nI-@(B@g3qJhBE)HiAgzmd#`(q|V}|^wbj#@Dv9MZ8R1bvET;U^@J(@ z=_{Xv+Z{{9(9I}}WuQo*-woSQJRO6lY04Ts;$zVVWEak}`r7E3B)n*IQ&Gesg?{g# zU)QE>3mx`gVa!OpfkB@+uXKt;mPT&eM-x+Gfk0sOA}5SOd6_{f&*z1f9@lGXU|=>z z_l=PcIS-`qi2WEi@5c=-K$&%yX->c!mkwN=Vs>&Nj^QPg z<+fd~!P)w}Yq2h52=>0^B-wop-(dDe&ap`{gU45QFz)VqFR2LC-EmnK--p)Vo|Xb~ z)~wHbCbrjl(9fo!4*q7w6`hXF>O-ZSGA-e2|Oein58- zRyyUDu^sOniYXqQI?;5$s?WDc=s-e}8IE{DuD33QeRtJPKHJxEBOu+8Zb=%Q?glTn^-qwAOi06OiIHE0sjOYuL?% z-BI3jzJ#lwc`W9$*5mr?nF+TDw-Tb7Xfx3gqT~K^GFTF{foEUWg@T{}quk00YW{^; zdT0M^uxd}Id6!pm=i=diu@pD>aUIoQp&w7w3V12$GGpCoS33Te*T{{r@>EyZA6>L% zJ7V2CWa&J!w)-C=PkG{{7`;8UrIi|I`=6?7*EV3zK1fF8rA(OS(GBUPH8A2>3qN3* zicvFZhV?IMbKC^pC2Q89Lq#^P4QnT_g}qP|s3V%n6pTs)&P3wusx4w+0*(8FBe>vE z_P@`=2AQKZ7d~ZsYoh4XGQiJ?VK*Eo9D{k-w$Uidv={7)EZ>kgQu7EJ<;jea%Xu>3 zqe#u-Vjw+vEK2m+H!5p5vkxA6!*`FchBLd@Rdf4Pi&1|^;v-NIO`)Y3QD21}y6bzj z4B_+(_H>UGQ@=<02RFgFYKBjv_D@h&Eq&z0HY_%L16++=t7jZWreCt+jGs8x7 z?FL#A`~!xi%Eg=9qz}hcyH`JvT-z6fU7B}v3CGS%lNaAZ*g;X7&zXP);3BUp=%yuj>0wP4o9fU#+ z2H&X5Z+5uzj?dkb3(`Rz4G`B*ldxwEBiHSoRk%hA^n2hx!BcsTWj|241|9NrLEHu) z`Rzv@*<3w+Q|>TSQ}!Z^ybe4TIoqsO>p|QlN?=zbP~Z(noa$165;fMyZ7Y3ym@I`O zYna(@^PHtU?RI5GHj~#!ad9`3u(JQHZ~yUADG1u!-ulRKF%KA)mE>@BR>h44K`3}Z zO2d{}aZGMwkh2V|&F6+}4Cxz3YE9v5MjBcq7z~!zF8Qs-38M{cE|)?4rD~3$+{g7q zR$XjzAc(f@y1`qeA(Nn;UgB#jot0+vdL_>Gx;FM39y`u&!fbD zA3hYMwbi19!&4+W_wyI`Yndb~xF8CVqp?{A=T^!xwF^Uj!UAMKzzjx$7ulf*_{w?5 zL?}Q?k(ceFa+!{ZvF-EPEbJarFx9Ir%fspCMui#v?W@TpHao*sRrGhX2hsaxb1xGeua=h%V0^w zW>lvxD-gJ4q|w{K$(*Us^(0@pm1XLb^t<{+mZ8rKd|dOP%$`*~Ad7E5xja~mJ5i1* z6gw@hs-8Fn%H%Me+bSoG$}M9_7*gPq4(j?>Q@2B_HizBC8a)Y>zZ}QXN>89A9$~2H z)AEBzM;~0q)HJu7WNtF7o_3P|hN;@ccqvIuik+ue$05G7TY)~$<{3zjsvi;FRB|6f zLp0iEN%5<+-1ysTRbR=S7Cr1iXB;;XWr38cu4&;Odi2KmsD^l5RJy{;*Qnx$>5)#^ zG-S4O1h0QuY(o*)dO(Yr9dzG7AHyh{_QF2%WD?uE*6SJox^j6>$e1MkVI;2@3+Pbu zM{MD!Wq>KPq-cQGAMmRu#>svLsteHO6DY_sbg$n&t5O9kv{^rh&=G6Ec{`T7o~Z z@TAZ(l;Arn?4ZHb>^rw89i_Dr-%%Ey0iQ}+14eM!;tR*TPcV*`UN9ps{EG91V?;54 z&GIdrFsqg~pxCv&&*ZM8iJ!nJiE;0{jjoU(H(v8ATb&f++{1&F8u*|`s)pNylH>Sd zUuDY!?g-CRsExX^?>uEH$gd`SxL?~e(v+g#@};)B-Vc;E^mg^`87{a(!3!VZoc z_743yA!eE;xx`(2LN8}-zB;g5S4RAgF<+Rmv(5{}qa~q{e{kNCZB8Q_?{&y35cts5 zsAe5u+Q|w^dN#9_lr{J}1n{!HsVuBn%#F6*yv+2@a%^&f^2KFImPx;#+IuT31VJz@ z%bE9)d%myPeyIg@5e;|lA6V^?G1y3v@{$^74IZI+8$oYGLGF}PwtSsicQ}oqhPQm?(PbI_PT)P#dV$0- z0k$z*(QT-pCTq}T_LYAjQf zRA=tf$W?#8ULQp0QCb(wE(O($xg*F^VNgm|8*^b&(2Ed{z-MtD8zWlcaR9C5477Rz zH*UDxJJhXFynazw^&0&6BR0-g31ETUb5E6c7eWs%Tigwi{zTwme%Sy3gY_6MZ2SGS8k&)SFrEtgMN3l=~lw& z%*CE5DDlOqy{pWD33cG>J0?~`jiNqV)O|LHLg|$n-{fs0Z5TG1yUrKoGvoZT2@=k} zjYGqKLf}z;fC^yMnZDL1Y@3)-H2N0IBN&fP`b0XHfZK|#hIDgt1^dx_ zXb#jR0qSukC74Ly{aN_e4E7d5GV2@p{f&~_NWz-)n%`epRoRA7G=YKHoiS~4-Wo~SCi#$#~(PS6L3C#gr zKspdTgscY{PQ;}{k8sCsvpJ@vKUqZ?P_xiL?BypbNG>M1TD?G`Z4IY6UTV3kO)a6s zJJ`vxX&a6WM@ueH#l+dkyCYW$uixwQd`R_*E)j2k#Gx?y@N@pQN?T}V*dt*c_;#Kr%Xcy?shcf0zag&*;$;wdP zlXrC=5R5vn_b*-RyTZJ2wC-Oq?Sb-;K1!+Qo&q_IIMp^2AVwKEO>P}c0~r3?l#@Vz z)W(L+pPl&(!=iP%q7_MU$;wVOw-TS*ebszE1kdPS3T@l=gW5m~*?I*R$R8;5JHcRQ z;uuZADGlhy-2^}qeOEmhtwQ0)L0l}|j(m4R6zl~W(mXWOb>pjAhfZFC-<~`01ljv8 zBrprO@@PPigCsDcM_O30nfWBD)UqkLwws`dLxNS!MSsGQ@cD;-jV^E0yiRwo2Az

M3SZ^;YByFD<)GV8=^rO-)OY-f!!)emNBx@r0dc97RQ7Yc zLeOP^J-T~1lI^4lD1CiBFqjs<^#F~ALFnpfRw;fGnccmXW4QUvVlxEh_5CrW3`frD zO3lW5c}d}W^E_BxmwLS-TqSYv#c z8(M)BP{IR_cuT^>m|LFA7Vt+83INuF99!P_mE#zDp2s3k?kp#Rhbr-`npa~5HrpQx zS=B2nk+G$5nA)5Ra{MZSnZ7(BObB5D}9|eGGKyo2xCYfCQe0N4v6U4^#~1U~8YIwnY8Cc}_{h6d^sK$kp(4Lz$9 zSkJR3=;LT4q1n>{&+Vcg@#6u!Ps((<_~&`n?PVRw@iqpzsA`@YQTj9$+Ejaxs_HF_>I{xKbW&BQRg?ZXw&&j1| zYMu67jUO!q>XPuXng~qC>8`Rlopj50$j5VIOHhzmH^N&Wq=ljK$tI0?Y$@_1vNOeM zyxbJIJQv3XzrR!Us~4P}#vX2hqns<$tY1eT>w5>8#DYP33NJog6b$bYRbJX0)_B25 zLAJ`|NWzVk#6sY3;v9l{`QBu!cV@SA=_~#^G$oP>GZIp5iM&&Aq;+wV#GZzHnOxEbM=n;_wO4 zLW07nF}GpHs9YgZ>vmrRVvxCurgVp#_?AQPeIjjtzlazoOX_&;$cAHI0eZ6Z)Hq>S z40I+c)rcCB$V%6E8Y(l=;Bb!DV=cvPJROeJk#8;1j^kZ9`D=JDA}rRac-_((mJpMd zu&2XO76J@~USa@~Nc!u&oEDPMvFE_a}gh(rWvQxSMepof@a7mAdOTJ~i3c`vgK| z5Y9F449U!(1@Q+gY+@s9`!B&?xT~c1YOR-L{P7;j$NMJ@_7cYLVC&n6jq#&wsj0X= z8Jm9*Qu1h~xUyzGRV&%%lGquuaHHVK~GYdrz%M$d#$a2^sNaGDyB%IP%~2k@%pd3 z9Ip8i-7`wb3dS2BN~;*!3N(F0D^ojgy2)AdH&?=Vb{1`8L~pZ_6*c!t~w~T{D4$z+{kEQ?VBo@fzxK-PD@Q#k6K*wP`-8>F^|ngEVpha4 z2Y6DrS^ruM=?N|hK%2-XQbkb#w`NqCKS?~1cuUj=5sOkZ)@fFMYp%j*W9T7Bp3kZ@ zMlt*ez08rpglkp_n=0aKs_?wZ6IN*`qeqNtm3ycAG$%gk!l5`}LY?38bKfHdxG}GP zj<#6@XlFKuX!29WwC(E`AeSiw`af`9Z2yV#Vq^QCMq(xcPF5Dy|A=`purV?HUoo#% zPz9ZJEZP`h2Y1UY+@Q`*ZvqYASeL__8bP4`ZQ6d^AaL@wPErJ#woq}ilbNaRU;Sr2 zSJhX|{F~<254YUX5|ve>)Vh!iU{gW^bu~FQIKhCFC^B;VfZ*Wl*x+F3%rrIZBP;l? z$rzbRXcsp?!M>nhs01gltoEL@;%OcI0~G>;fIr#10m;~X?^+4T@(IDfeZ&2PcliPl zjRXQ4Q@AFO3WmTGLVW`0CR&scMd{3A8zavp)BbpXFlaFVa)5w*Y5WU-NN@t?|H>0E z3XD#yfL%P!Eey@z=Yli>0&4VrRf7cAMwXWq6LPl)2ZN`l`a@w4Y-lIOfbIa=Hvm`y z=>*K(3rP3a4Ff7Nf$!waY{r@ZY_St2^WA78QY*tV|AAgcb>Nx+{dDx0b_UV~%zGuA z0@8w*1t$<7znE2D<^a%pwcUUY4URv$H?>#0p#ppSNz*hm1aNU?2J{GPSO%aC;6O_z zsp~qtx|#rH29vviW-oLJ=|0Tv%n99@@6vtv)a<}xQWgMHdJsRNv%>?JNB=ml6QG7) z*~D-6%yiu}Ky4{O9Gn0Hb@Zd%%VaQ4U|PMF?db2>PDIn=(%{{DXQK4<_gz<@k7wyWMrYi~}VUk9fjwqAz2N5>Ej zpej8HfNue{zI1#Od~{}ag1+T-*t63|`%!;llYi_I>DU0O0bCPUVB&B2j}e&Gccebt zF6I#=!-2;<9(lmw>*?)36OpH;P~VH*Z^*A>&lQzZ2NTl9lt0tYCOIYKJ;+;~lQXbJ zy9Xx#5Kk8XA0A-9uD`k>JMeciRGhyOYM&ZHKwo~e?|R8E&DwYEqxqXP8wTL7t~BZc zkrqL~K7MTP{@!t&$NRyTzuE^r<*z@`ukP`0>HV*6LREJ6H@;mM|JN^mYbNm6&Sh-? z`gBKo&zU~x0~6>!LFzK_4`(BlfOJCk;I9{|&a~c%0FaIC?<-r7j)`ENfV68uW$1Li z(feY}qxaaApg{rG5a`pV8epB1lfzg1t!V?zm7X13I=bl3K2Q(LjDKqiptb;wzdQ!| zt#v?VV`C;d(`a-;n};VLUk-hd1?1D0@F0L28^h2uDd?ThEW81zqu7t{pW1hTE2Ump ze*!)_fX*-e2<*O^JN5&AK`npc!1RBLrv!k2?F0L#Z1B$GUIOv}+&B0mFUqHZ!KvXB zd+b|jed>tp$6hB7z^elP{&Y9D-=Hr5x6gmm7r0-6ne>;v|C%QJ8}#CSgLnX5{GX3~ zU=7^A(S6P@U+CW!#tz}%^urDIPp-b4V80p3=%;>yf7>4ai?0HGSl}5FqF8F7YdUNZ z3mOV`wHGo8bCai!OjC4HWJzN zj(q{&9c_)wQue+ci`KsfCy$OJxd0#2OKh-;zWwCme7^u&?{5+ES1X=&b~+SSr|)Zj zKKrL_#V^yqgwEexT>E{}f;_G_%3_rxf00!%8_#iLgg+=-UfW39TOL$@u$A`%v2Qm4LVtn9*1TCX{glNCL@Yx7VYJ3I5DYE!@PdLlcv-u=1=`RGP^M& zNuZ6Fy$6ovcaSRojNBO_e^h;D+h(?Qk9!lY*MZyJK1iKcV81Gpx5>7Mi_L==YXXIb zk25cp6yjX`emV=&<_g)!d{!lCU6kxPUzxS_v6MbklHwS+J8d}27C>!l`grx=5F+u51xq2ZA%)`cDA4vAU1!X-25iR zUP#fd*ffVblb-!5_Y&C~EKn(a>UuFT6uu>>bFgY(C0iCbbPCNLoC1z+SXWf0LZZQs zO&WLzTdxgizWpF*5~xq!ugOE8d<4jxb;D*30_oy_o{zq+Qv z2b1TKeP39`Sg#fl=OquC4`08DiGF}U`YMGDoUPMg6#YqCb{N=~kjhie5mA#x0X-JV z-f3%jH_192JbQ2|3OM0`yLj0Q&C3|#?~Z_&gd_g~ z^H^D5t1u0+g<-Fqqt8?YEV>m3(i|H!nnbZ0ljD1y*nlkDu}Hd~p`TRu^*+pYfC=mr z?&2)I_(WDS`L0?G@Q|9nmF)JRHhIKHdLdLXf~BN87jd0>IWskGTtOK4Dt z@3*7o)rsi%ta<$4HLfns<;C0WL>FfHm0@XcUS+Pey;w;7_a76CU{4+9pQP(Ak_{1G ztIVvDv<-{Ce5jUBeKw+RFT!4mHiu^9WK0ap^|e0th?yZ;NULJ@RGrWm?PDh{R484J zAs+nLbpmL|yVj-q3gza4R^0Bo!SOcP>)>L8&Zf4PnUx2!FKg-S3HQMibvR_G`iF?# z-V`>dnVm*oD4{vW$MvWfMR=~WBs2UtjDc;%$8%qnsMwJxhT_M~a`>54_;L6Hpj}fQ zh_&Mdd2O$5A27HdH&M2#e-t!Qn1y}_O=&NxCbDYKDn(*nl0tOu`tEm zTcIOFAuGSN9si*Q=DfGFf7tTM2o@)dpBk}Z$y}2tJHEvI1!764wXHkeX`aoaNs(d; zhQJ+yxkcv^^(SH?I67AO`?=zPicjoF-SE;iPP_8wUuoWv(Ml7_y#eoM(akoFV?8A- zTxXekGUu++4088%AP^#uGzzQ*{6p-iq1E5kXj@OSn92x6o!X8BJ=MQXv}0f!bz@a=%JJ+G;aPVtUKq)u1*cmyKY`= z*M?{O(xyi(WjP{e)VB(*(P@9Hj|UqjgGR!#5L9_QcClnYxlu{om9{hmAXfOp*RxtJ z<(lQQPD<32WZy86$rKDoL&dz&T&?Hn9X*fp4)SQ{hM$7d+h26JZT5lvtx~L}@$uPn z7UgoNR-~q1s=rn4lyBnV7nm+8dRi4H*4|!vV!{R6^RGzW>$u2J$s-7#w&PUei0!@e~=mp1nUYi#5@?f3JR$R_fI)^?$aRdd1dx4BK)Z5glMBE>!_7Y+9QrEatC zk{>mrWw7KixHP-+pnn+A;;k&BYJcB~z85DZ>#rmuTasWbqPv`J(%-EeQV{(Hq4_Kl z+mx?T@uog3mWAMJOVM)4n;^IgRnrrrCO;a*V%N=fk2I}YldWT^MCm?4`e>%3(dI!CP=jY$DhL95 zDTj(|r63y1T%XchB$bzrRAdo1K|f4kAL=)_P|>&p1Dn$_tCiA6xAWo8rqx5uG1H)t z4405VA+8*fW$E5Xgf7+n2%5HROc)b#(BfM;_RM(r@v2swFJY8AZO@bX>lmA#RMyK4 z5OvLY25*Oj^DEs=4`% zUTVL=dkm;^h;Fkv_TnrH6T>b$GNbNf|M=2~J($b1!nwfg_B7xl+jtJl@D0WKB`p9yc%hye^vA1)h z@u8LKN0p@+(Yw-fBE(k8!i-up$&08GD~6yziN6{DVe#6-vd^z|GXBY%cc1+StEnE4 z`;z9I@-EIF1c{3Zlav7aOR2}=3IN~ss(g$BpfghS)m=lu2G~QsHpSV;cAgHZXH=#^ zxRM=MrU^V|sDWgDpD{%JsF9~CNZCSJY`nWVY;x|h!9MEUJ~_HriI#v*jqMNz$Y_#z zf(`!ksH#YHgrt3bk~vI#x{~FZ1>H?IR|15Nm>*a?Jw-frRCf!h3=KKi@X?iqj-s6; ze~m1c+t?4ZvcK&~-r5YR-IT5ptoiiMU}2LT4Mqi8jd86jJLkZT*rLCxSC(aKTUP^D zXfg06UeP|E=t%~b6~Z9fmBUSSwRYk7^AxzdQO8djZI|E;U0AQJu|UBNb8jzO zj{G+McS!4PI2SRq`Q9$QKPam&;%?-DWSwEt9ryxB zVAAngWQ?%UcT(qR0?Z%L*LW(lO%gzH(#us1lpvJ#BP+71{!0X4m<<_X(wc_*f~iB* z_Ub*j6h0ev#A+vArt@iN+$FQXg7YP#)bspvOWJEm;%4@I)#H-K&xf1nWRI3j4QtM2 zXJR}=;^py4$OeW?G%S22+lL)F3N`h@MRxAt78Lq1{n~UAtw2sg6+2~vwPc<(eR~%K zp?&O5!dN@y0)?eQrud8iGrq2*Wmx-qxRe6=bqe}3qSV%Q4e2Rj1e;_H)vS48JF`U` zFQy~jb~fH>R>Pbg1~O}S>DP0hbyJ2LENntapQ7Da*fFs7f^`!bG}#%l$7L9YZiGlw z-L+Qe!C-rMtXFjd3cw&K%HjC0q&vrK(eZlJ9s2bEcqN^ee=T=rJX?AeAI$K#O71Zv zQX?xPMp)N`TGNBEcsgh$SE;)5FV+3M|BGOo>=swtRz_K3{Kh9Sw4Z;#%J1Ao<%|FeKCKA zG{Fj51BtkW*@L}NbJ&d4nf>BSY`rWml{}dY8>NLRt4jB?0z`@}1DtYOfb47nh^Of` zT!@>+6iz*hGOL7iB`$kqzkLb7AWtN&uQ=Ki8oFi^+OBoO#?vS5h*1_{5!#QO4p@&| z!s)p}bh5i_7%YkNMl2=3Tph6X14+Z@b;fMMexf26TH<=4c`guwu@_gSSiZh|PZO}# z4Ra&Dtd_|TcfJ_E8*^6>wNGkVftHv%$HLu^nayuYiIktQ?p?yFFbgzgSgYW3Pz3)#)uH1%*`4JRG?{RUFReuxUtp$MWB!(WeUY*z@iB#%y=& zznt6-pqFCYu>B_Dre>Qj7+)S(AfrJ?kbSkW6Y?P-)Cr{)D9!5)j@DvLW^fZmuwypb zNG4|QMmN7wev~;NSope5DQ!3QiuVmwPu>cZTZ~GMYl5-_8UKApuiRSKjzyAimYg4Q z9y%JPFFPk-aSs&^@m>H8vQ-qq(Y&F)@&5G~F?=uXfIOjfKa){OP&xSv=~CN`!5Ae- zYxPuqq8_LP7E~YlQ&2?Yxhc8b2Ke9;){*}T`qF@iGS%JT78HM2<%3B(&g&@zwytlm zMp`QydO^gTZ7+-4GO;BpF@>|}UfY{8QLq$j6{-?A1ZnG;#PTu92>BC!w=_m|!l6}& zM9$9G5b|ZyYF+P=gJ!h9lnIhDUztP%(VX53)|wsznTJLMBEEP0*8d8-AUD1#4iQfk z%7NO5#g8)0NY2EUWnn(U^5-!5zhrOVk>bm%pN3j$PLl~9Ce1lwCWvO0oRwVY+ zL_QuT0o411A7RWLv9VA66-kU4jg=AS1k3UalrqIP&B4N;mfd?VD^<>k#TP7!G1sm0 zw3;ESqBHOD;WDRMT5m6W70UtY$?#}qyA#~t?So6DW_5d8enUeqs#aYGdP@fzD9Bu~ zsif|V=uv4B)Ob)DR0ugf%V)veh=dEF3FqnJRT((ev)m{z$8;`PP$!cs4g|B6G3p3aUCHEG;uA{@a<4Q_*TKw}a~*yt383 zGq*^Gvc@wO-%kn)sIK@o1I~<^-xDPBS#?T6L_88_`VXTy`0R1;J8J>|gLnDhYs_xG z@f^p^K+#$gYzJ!3Up_$H%c%!bl284kb6SpvRzrqcAvRY{z&r3!J^n(oct~!xWByD$F-GYauU;zTP7SIxtl2f3# zF9{dxe{ar0RO#b0J4C^N_ec6I0(oXYJneX#vR)W4QyZcWU#YfwtZ&`;CvDN+Xf3G>77IeVs_-w{*;zQHo*f^mTUdQ{64hE(>m!*8^L7@=SiPIBOnZ2&~~KCh~b zFXB!}(Tf$?_%T$gmaK&tMf;~+$OUV5v%&b2W*Pl?x^QaLrxvHg)y6=K&}jBSR?=&z z?hsh1T%fN&FWTRWTUX>Na+k+N(jfrHn;pVyUUuQgC2cOm-ce8V1!hhA!#K%M5Spmz z5A{zK;I#6696WjM>;jGN!8T|VK|4{1{qnNqc0$0`QSCi=iQs%HSegv^E14(4hWbi- z+l;!LrC!v6cz{R+$sr)rP^UwROu5r3yma2MP^ zcCGih0h*)x`yrW5z1--9XG{~CH|_6lF4}_0Yun;q0?nlPV-FkE#7%B) zrrjBKU=+0={xx-<^2Ls~#oEegjNWf(7Zk^U^RJ?VGjE@bKtdC!1zx_pL292L(4rx9DH z`wd0s?iFsf=+MTF)wwSv&5CGJ-4I9XJYLT}FHtUo@>xUP)`iiL9Nl#$N4B(KNa#r!^CvhVXgp4T&2nT8OQ2O!$Fz&z3APsp6}9&}N*hK6aA zi-{r*UyezA%L@l@?~xovBHL-4{FRiNz`^|6`>Z`P=dWL1i0J~6UbwRL{Sn$fF&w$yZ=eVVPamnRB-8?1(PS`~lLk5M z4~u_2J%UFRt$8oPK|SO55%+K3vIck7v+FHB6=lq6j<0Z$;8`H4Sp&scuZuQ*W{hAd zPDW}%hVd>-{`EutT85>|3Z*!yFa9~In_lcg95Tb zxcGzQw^7kZ&ldUK^ah%ura47B%Av%m2`jkRPyI%WxS#(52e1 zzkYUJ+#)@lMQxpI*-3bV>TN7ea=`l@7=(X~tADI3JsCQQbm41%<{r4FKzl}p%O;=J z9_3&{;+Lw;E<=Q!;_mDqBz=16-NK)Adqux3!i0L`E^k|5-9HBpI;pYrrh=cMM7z04 zLtC~Q^y_+nn}I^;r)Vj>w-GdDwyC|NwpiU^JY?TW0gs0QeB<6DipJa&rH30uhnfn5PoMx^O8-~9G!yiP8L4OS3UVLHN?qW zx$~aZBY~Mt(*AmU%;>BD+4=g2As|`BDBZDOqRy%I@hD^ zc`1Kuehd8eWz~LYj~Jxulgjz<)uw_eXc1~rZZF<@qevElxe z0RfdKQM|xZ25KZlCQ4TYDBb?EC}bYa6V&EwxRND}HO@mfzvEdk7cmigUNtM(+`M$| zc3pjDL|)BW;#)x+)l&tuD?}@f3Nw^7sB$-xAynB=9nB72C~QyOgU{Ma>1m(NyDii> z;@WKD+OuZp3!+lr?pYj#zB2H4um_E$Z?!Y}gd`Wo=ErTmQ=_Gj;IG!-tcVZaA+{Fz zLl@;7!t;y}2ozteUirQ%eBvI34(S0J$%nW#$7vY#F9Ol^ELfe1$kqnNQ0kIHM@?JF zbFR#cP-{m&izSEC{wh_WjZckH{pSlSKG>ys~*PxN5- zE!9m4I@9@QCyH;cC)DOVNNQYBs{`B&8IXP(C^EtL%|HP70yt4yVjSI*o;l-TO;6F^ zv7kM4kVmfA(wiu>_Q&9M{1>3_xE0(nV z?T0hv8*`}XW?0wY8A1EX562!}c;?GHOddZfTPzTduF>Sn#iYijlnFbhg0sv4{nHxz zF(oc^&w!D1-XK*ImQsL`9`w^G+GdDH^}U2-15*MHGQ0h<`E^IP*rMyo-SCnkc8_DP zGU~5m@tqzwMcjnWR7Da~lS?di)z;=sh2TGC5beRG#1h*`wf5IKA=zA#9V#tA%Z7YosfPx`DY zgF@#gn~1@J&RGZVY4!Q|5aSRHXE6ZE+mBKU&ZTK810Q}5Vr?~rUo%117OO*=V+IQ` z^wC9-{3{gea9{rKwO0jLXhZF)a1SSz$%PWQosp(*cNtH~F;m$cWN@A=yCO9^MNC-H z9X4~9Y8y%-ZVtsNx#9UvvrQ1jkVB@&&N2Y7uCeW@veLtN(PlXzNYx3M;D+!#3#(xofpf?fSi7AAS;<*|FQ`f?7cSRX!?qaGH!C>5GiT1-}qsfzUP2alUc!<>W zYOo%`S8Ho|C=YVguMF_QnRa~Ay@dE=kWNv%-mj2FD&)=+UItNgoI-Nfuw4w~H6{>r zjw%a4u2a%%^xYbal{*HBIX!0$^z_6O=CzJ!IITSg{S(B8%jioiIrtGsv|2i zf+xkCf5MavVWRZQY*l=khbK&TN+x=UN~0>Oop2!@{z+bC1djX8)^RZA>MH)(5WK9! zDR-P93xSzbc7(9pJ`%@AU>4=aRNcfmJ~3}usv#pCU4xtQA^FhY0jg}1Ex4p@Xu%S1 zBNrMz`uws05wCgfo7WmJ+7mX%v_c2G4}41VwJyY`?RRjB^)lRL=dqJ0(fPv_h14Rb z&Y9Xsd?_p;=A=pH7W#(cO*MMmBkf%_*s%QlAfI->aFD%$ot_dV)vUZ8%03bdsvcI0 zWB#YrgW7ORDsFld>q_PMY(FA??@+{g>ZxF_^G<%v2wGen+E&z*7i| z8%?{M{Hn^Qsf&J@onz;4EjFFKOk#9aR`4! zo`E%2(N`r#K)Fh{Pm-h<14h;&ZE7(W4*H$C7OpyX;DBdCAl#Yv2qWnkl~`_FWj<$_ zr^|W}HL{9QnH(=w(dW)pM`sUX_CiuVBoS(qoV7v+**hXTl1q8^kqSuHOYUNhH1p3< zPy!o9FFK9Wp(V!-+A#JC8(h6Z&e?||cfHv!K6U9?!;=c*o^pLQyN4Xbg3~RoM80yk zPvahAyaOva?g(y#)z$R!aX4?{e{Gyx(c-&H0NGIZ$DkWmg~Xpi;%}km;irgC=~3-b$}hEl1f8J5s0I8Q1Q9TPw4KjK)3B$Z(a=Q5Tj2V<8` zzEPnc(_*oZDRk|2qs}e1OMkh8W~I-8V#v=NfdFp41wn#Jtr zoi2&?e!cf%YbAb|oxOi6I}(}49zzfs$C}lw0-yv#Nh-&859=s|HYPF*F>ca}20S8O zXfk~}%`SE-DnTAR?stM%z(56r{qg1?t&$&I*+=6LZ8YL}LpV$JwV;%fdu`Za=V1ch zUQ>^WZ>)~yK>nxBSEnLB7y|OiHBM9(jmkWE?qE@Ts1Q+|JvoZ2@JUC=%KQ$o3ifKt zu9)-$G&i$dQ{WgU&bE%hwoqLPMZ;zPAKZy>8(vM12!@wqV1ggd0p5#BOs?c$yl zhwq41?B6zDvfO=lf3ZRT!Y)B0fSDc{HHuCAyj?#K3}I67qA&F%w+h;ybAB6zPgFFz?);v6tqI!MVcQKYYW4&%=>739eS-S+34Kz=3l6 zZtNUqM4o0IS+7kzDrc_lDw+`si!}_#tkDi*hzz=9lhK!P+pUoJRQkKE! z=4ovikqV@+$31B;RFdU~-K)8*2lNn%WeL2UD2;lneY8Qt0Kb!JBuq0RMP@IP>S&0fXCOxpDD_TmZNC_qLfVT zk8UZbuW>Bv5j2k5ctt5D_h}7lKx{lV;1UlQ237f+qK8t4+rsjm`?#YrO$5$g_cp@##nSniJ|J%DmAZzJ*B(;yezXR1}t~$hW#kS1U1gf z-8-dodN-5B$_b+smA?g$1C&JTLis9)cOzO*=Jl*MROdZJ>lsVUwh^_tL* z?cb!M1v(CRNjoyiw>5QF90$oV4PVO~dOd&Sw>;9qh;p~(H3kY6nL-e1U?1a1J2HJ) zrN!rXR>9oJ%GN>nkI5J(TeR?-b$#++z7n~y*pn+xJiV{d=ak=-3}&q-6)59fp(I1W zc@WE5!q;C{Y_mE%g!MtcSMq!(m+4cQ=3heyu0Z66wqgBPvN}X4r~{+bq;D?aQLB4CMpG|5H^OtPQD^j3x>ES|3m1L<3EKynOWKYJLbtmz{bGvKM~OX?e=HmWcmMUe}eym+g}}= zWz)B}6;*VZqGBk5*XXv}%HAq9f!|!*Gw-4X1Gmr^88?utC7>8gpf*rC_vy)s2~BO z6Tuu#*h9!qViGWIp@cpL5Z&wU(}e^DMrg8SfFcJoFbGb;0?tZM`fX=o;8_h2lkO!d;fTE_RW&iFCfGRx& z5*XkhAecc4_7ZeDBG3y+1|b0h1=M3aLKl=BMM`TH#tcNS}fo zfN~i<$~n9%*q0T$0mMttkDW{g4g`aH@cR#9HldCJpaBU=0J6sbfkGSoOh5b$j3|&p zJD?fY2LQ1>#aDd&4?eJ9pMDWw1XT17_m=)nFHrwpZ*D&V#K0sr%xK?U4FGxuIf_AX z34M%E5eT3`+atYj-Cug3Q}`F~L7sj&j^N$UU_h-3G605}-rkPKPy)jp3VlQUjMG{; zQNPfBSWV=cs<^v{paI36quz_f0K!6qttCdH-qj00age^?pB!BS2lI4&T8>Z8XpKHY zK0gKA*j^e3qK9778U+*qBoH9U$uXb;J^%`=1F{F|HqH_34{gd1>6l7>k}>RkScm>* z0NB8G0Y~}=0{uFElmMX*LE)gE&Vzh*Cq=~oW|$x#4nbW*hlk#x!y$!qe)p}DLxA z8V&#~w+N5&6=VAAdMg0FuPcGw1p!QcQKGXKdZAu^tv|c`5rg6HW;MbfaEuB8c6tHr zz>`1(9r*wJ+GqT_z3oLer>3iYmeJgNWVG}sO z1pNLjM}30Vg)Nw2;II8%x+v)5fGZo&<^AOq$*4txfpujIDi5oJGgt(1|3d3$){x9M+kYOcZ-yi0_>9@!4QtqX1pPT zgg_depTms$i8Tm_V896+Xa{h(4h7Ibka*DlOi2NVcsno%Lr(f7W*CBx9Gbs)J#f_g zb^V<-q(FfUO_-GRr%>ErsIC_RS% zFOE!KJMF)6#H;e&=Z4p`z9NFP`qOvxKD);p&a!x)dU|v_is2xZBF68l%*l?z-EGvMMP4HAsK!Z{Vv}fsuJ{9| zaizjAJSG@~)ZrTX`+=ABvArKZekod%Zqs22bVR57~>Xf-{k4$aS?arreQO=Jmk%S%Hi@2{*VsU9x;% zidYCMOG5nS-dj3 zkf`cCzhf1(YCWJ)P`cv_= zVRcvDF-D4}y~Hx~^|&pNb-H{HUYor9iZ+DPIjH>fJrs^!mY&aS5rd$=|2I$RwlcxQ zmocyN;L}credCDS(P@Q(>cABO~)GCn-#gg{jsvzNZ4W)zFExCkNIrIMg5vJ z(ZC0(oz_m+MQjrBTYz@vFNO>JCO8eboV{V){)T=ze>nS@9>2?lr$I47Lwz2rW;IFeUJqePoZ=GQU zQ$HK_Rr_toUp&GEMl1}?TJ@<50ToSY0OX@gG+fs8+0>p-fiB&~YmWvecWRpZG#Yfn z)@k+)O7oa*@+ekNPgv<9jiHS6S2fDWG&y=44i>;3vX23~aCFh{OhJug*1H~5dmi)R zz6A@q1{?2*u}{`8X#aKp@qd9U#eJBS#u zY-y)C)TT=F8&APAU$!EqN|RZa^9RecKC1)kr<|s7U)#y)m}4uC^X9pJB2n)H*KCzh zlB}d$@cOSxkirENYn;%fHR@M>5<#_He9$eRW;EoKUG7$h2D$*~URQxj7ffU8iE8}p zHD+!;=}LkNRt6J%V$VK@wa0t8zK*S(3uWbZ4HelP?~yNXpqCoUXY3}n+cPjDI*M7u z9>7%i6&V_$w+C$#B?Hfm*F}8ByiHzcb@jO zuv!ah(U-1EcGYX+BY*J7Y66%#xpd8yFazzFt4fVLUvopGJthlGu^gP_Jpb5rNPJdT zi>NG6$13);Uq^nDSQ26@LXFS9wFK;>mtzUw7msorXg}fV*(Ej2^q4`+^M0s=cHVBp z{yA!Pfsl^YmRWZ0y~u?^Y{Thr$GI_?1&>SMv!}$vH_in=vbW1^_mz7<)j09*Ga*dT zA8iq_ef`KuFA-N9T*;I_wn3B#f#RP!IP_u4&NE=huCDMPvK)I3QCuR~EDGDGwt9Yk zHc0EJL-%3(PT2PR$cz&iPFR{!EWhal5e6*bQRsE28*06z=w6>60N*ag>A50bG?VYz zW&glF&^@0W88Zp{0XRV&8IEC`5X+isDlWzFd zi)lOiq^kvds!&>4F3%w=3R1@U_^?~yzG}%QHs3XlRKk%5`-;@*0S)(I;guy#-jgsP zfIKcDyf4~)>Fp>UH&smCv`l}SlJa9NPw*6iS8-Oo;9Pale77>PimeZS$TpmEo-*wc zk>Rcex{nVX?(TQN7j?Cz>)VN~QbRpm&jUM1o4WW({`(lefa3)#EJNmRbX}N>2a#`jjaN>1V#;& z-*i#W;jRf2v)WYm>EJ{jjf5;=+|~Ahpjgk)?A`ODwN)*SA4`6xn+O}hR^@12dKx`P z&!N)enRcS+_2;UzBihU_Cvd*s>Fs$q7C zetuuF;fOpM+vGJc20tFeG+N@`QY^OS%vRR!lKEr``Mq&&8%^eqa+X9Sr-Tt=iq!Uz2?RT8ZqIw;I^3t^2fG5>yV*`=|Ue`-^zHE zYOi48A=J1kP-y0Cd6t|RU@PPSvB6;@f%G))N9I1T>SD(|UXN+ANOse7^a^9}x7UNLLnIHANh%XI5uMVY8P6e#E+CyuX)R z>n~|s@@ZDa*Hdn894<;$l4{@O15rNX5(~an-H(!DvDfsZ!Ss;9iDLLjcZ2tY39hUN z->)XTlY5v~W>rJ;L=w1HH{a*?rMCewR<|3EL07dZ`Qhw&x@g+S5)l6u`GURLr~AXD z?dBN|FviH;P<*n15MnKwtgBq|%AuJof7elF_bhdI#r>fNrn?5~x)r$9C-|S6)CIpA zM2d-asU-e}&rR+5ud0EQe$91^4GCHU5!F_j_8&BrV)e$IvYtDt8l9Q-ASVJ+MHSYi zX3~A&&A;{&*pV77DIn>yCG;<@xqN~G|DJ?lFFHoEQP^qvOh=!CX+d} z*G|;NL|FN&^%=h=`bW;;a>fdMc_1{S5L5S$53Ub2xVH07*bEY98U=4l^-^a0MNwbW z=Gg~zz9)WaLD|vl^P;=e9vJDbI;!`JY3&f-oxURhAWiTnm?{+%03#S&;QVcHJG@Ho(udmUDjy)EV4A0T)xBim)tFWeL`@@bC(n=e8F8+Y7qrq#(RZlmHHcVCaQiCC|} zqf^%Hcu)$M*#djT)P`X+pRZDq7`=+lAo%{tzh`ahR z1M;7Xo%dFzl?XVuWzzPumT}{@09{cB2I5A{-(^Xw!RV85C-eAh^h(M0$H-!2M+N9f z9NFaT99ZF)&6~RmoIh@pjKTX_H-d-l{p^%(KvL+E2tFXQ0p7=x^Uqwgc+Jx>W2Fq)gceg1m{}Gg= zI)KjHga^E|I`&%v0X3z*pH?3W9;z{?kNI!o0Ym6^$nK$Av&;hf<}R(r^0zl6aEkqG zLVFRN@I6bE6y|){_2PKh%c6JI$a%}Rg;iIDWa81tnNfY3M9+p};Bjf1&IM7$eJd>R zSq5R`Qd$vIg$iZvX3aCiv}Imf((9er-{tJuYaZ*cr^RgokZf}~B9&AxLOkp=PxNRk z6F&_qO1Z#xS20ZxO2_A!Ny9beu*GnT=v)4rbQ;jruOmKq}cO4^zbCH z7?V`7iFzWIxKCQWB?c?CT#IHSgogrn^!?VC6!cTFldhQ2lnhQV&QB(9`Af=kr72R^ z_4my9K{dOajBN!NLNBrhGmpka|ddHqQ~9Ucx(2EuivTHI}e9*$=_f(@pa zr#-HBMb(#<093u;OxnizuyhXJton54fer%MRDm$fHw@!h&-b2pHOHz^#*@3Oav*fj z@4NI+hlY5g^gZe=WPUBoD54$ewDR7;pS9{=3l1U5NrLSu&Gk3RC)--VgMGuFE>GcB zr(`XH?^evk`+YW>NJw2{1J&V}Z&$6|A*sjd?qEq{)Wb6!ss;?(!XD9p@+v{~Hz|YZ ziPt++KF5otF5KWa{9@BqYbeQic6~jqhlJ8}$Va)4mHY{Mcrbd-1dL2{S=6MR^_&D( zlV!5F9d5|7zRwFa1d$$z|?K>`rEApBQKil8>SiY9~br(!W z1NR)gFaSiY@STNVo`5F7o4vk*T$D>zK4L}>HOqfB;F>-U<=w2c(|c7Wvp@HY{`%un z#Ot#x_abG;Vv=&jtKsrISpyfui93a#aJ%2XPJQkg%o=zygt#h|dv2U?Kr+7OM*-fmSPmapc!K$w0 z4!)H`YY`0wR7ua7)x7mP{05!t)!ot$I6dy1e?pdE!#dXhR>haEF*5zqt`%YS@mBXQW2v z&?(r5z`o)ogShuH=l#nUc&^hT-Kw`vQC3eFDn3Wma&BzdjevD~W+O#H2u4hAQ)2n^ zLZETp@A@Ma65bdldKzr#8JxiL%pDjWWtW3XGKRs!LaeT#kGi1JO;Tru2 z#|_Fm)8PLxc22RGz-`(ur=7Y}+qP}nwr$(CZQHiZscrMAy^}9_H=BHWu!r~go&0g( zhlFD{K?lqKm-_h3CxK2{8e^&-<~_`8Qu6%n+&XhD7-LEnfkp!9dzp z{27~0*F+(o%lmKjXu*wp622RICDBGId{}JUrCYDcxH;ZWNt{`3erY}<@tL=FI+o)K zFqP26zI^|IgWj{zRa?7Tu&_B73N4m=o^*%T5qr}UTSa5BCtq#LDl3h$81qk`j=S`E z6?D5!v&EjdNL=2Qz0M1seOrYKy0=?2kE5fvQnYK5wP!H465H1T0=*|Q6|8=RCbxAe zxW|e+Or%AQdS93jYk0l{_@gk&)R@Y+2(e99kYEv$+56LN7g^bvn4K*7#4KT*#U>O} z{S%KV=JU5MKS~#s2kH?T5s6Wy#!iJ$5v@=&I(Dd9oOhy;8M~5nxnDFoy$EG&7uj69 zH1_7QvI=Y15xGlifAFdLhV`6_^o(WAkN~rP(y97X}3H&?(Xno(nh8p%EfMls?pltteo1ZDfh-sdFv4BxQ&B8J!a1gaW7Kvi`vu_IOxq3Zz=U@_PF=#GWKQUKAfo~F^1 z0(6S>vuC|M8yH@NGT#o-Y$gi%l(yex7Ko3eObHW5MPbaDNR&SG)UqIyqv@Cs${w;M zDsw35+nPagv&`SNEVe}Bfr-<35B)e;!M7tS@Q;A_ZvD)cAl9a{(O(;5&5TXM<9?X> zf@D?IZ@B|)1M^GRPn`7>Yd;)cb=&>^yQmzc@7a+)a?o)zcDeUV!4%lnECcWW0-9=K z|Jfq+XT_*5g@C9pU2`3*6n>5F^3qIYmv+T?l)FC-aSdb<#NbUfx{#u3%LnNX?nm2Q#v*NeEo8J3r_#}}@0J_w~FvZHk zOxCTHRpi8SqG9pI?)RFgdf&#&Z!e!VQO2QBtocCXY&EGqhnFPmf_*F_(}1 zH;d&3FRA14<_Z9U%^LHJxvy`UZN&`OdkX&Ie_wzen>pdTydavr&Lr zqH>{zSn}M+W-(r`tPlh>UuR78pxbKtt`)1t;iRr9>m}mmm`;k7R94f}-i&__T*X%O zfZe>oW#%$BJLoLOM513)!|PRqr#ns-oESPod^bZFYE{ym^ymG%e?bt9;~y z898gIcT_bWjmurPrT&1kduS8?|B~E4RgE6s&d?HyoBKZ^90NWBD?RIfCPsWVRyL0R zO#f4oV`pPx`F}Mm{})Nl4O|}CbCXV-2!H!*5l1S_*)39BlDfYBYVc-}W)YTf8%kU} z(pg;G4Kh5q*`IuSxAK(dl1B5I>ib`P0!LGIv}b5Hz?B{=9ttM%2psTR90a)q zb{H50M9>=qB=EJmT2!AH>=9zbjOEt=qCUDZ!0#SqAK!`?N~uw_aJbn(-anKJ36rtAUGm10EP?U6J>1Wm!Z#3Iv#2!2+WXS`XkCzw}Alb2|$Y>X5v>@$m4xRqG&l z)3*n~kiqvOMLUC``y=4DLyW`SQR(={wm_e`8G64~0}+YQAHZ8fHi>y^4haAu0|9Ra z=0he2axKAuLF9Xb!YsD{b=Kma;ThEMfpGixNrD0afPYwD(w^yr^v~=}thBV!qpDbz zuwYz()`AG|{c9sp@fM*cK*T#cx zY4$?}&gG`|Ehb-|#U-wDPWKx*_y_(3NDxFA3=C|T*dHh!3+Tw?a{OniJ)w>2jO~Ff zI&yb+73Bn~UaSNN0I?Y)&-dC3X$6k}^xF;M?c>{Sw2#6YA3-0YRRqMEA5NeAn{P#d ze*7Cg=7Jmh3Y;E^9~Kt@|L*ePWeS8v%axvd_yg~Lcjnlyu+pM3fAEWIzfS`Sik{A& zt}dS3Urk;Z2nZPg2`Ib(_xq={&OWCGW6qWDo3f zGZhYor2!vkj1Sb77N1Z*>K)|UFYe7Qof)p+H@8Ng#)Gw|% z%u{#^;(Kq=N1#V8h7j`i!$Ah3ljq;-b1$!HbP>gY1+&EUYvM02d25q0DW{pfS#|v# z84gmtZ*OJitsJG04B3wst|`P7zk2)o*WH7Ffp{_$P)aUeKkl!wpJlnF@Q2O*8k-z} z@+Pym&ymj{=&zWc^Ibo5a=OoaKY~JXBz!hE<-_k(M6kQfp{;#C(7``IzDxHXVW>cN zU4^o6k9xcz0e%HP&*afiBPa*4uVdYi{&>Iu{+!}IL<8hN&D1`NWRhYc?8i7U<*(O- z+okhtwuY4^FwA zC&Y7!m8UU_?CxHtJJlCx!ffQ($!asHJEXVdZ}{Q7K1wI-sTscZ=dTs@Fr=O2>Rs=1 zH=hGFL^s$rRVw&D4t$UX8GoNTYdcg1`b4veN z${aj^gRLE2t1r>B2ip8J8yjLJ9p~jAjN+@r#;92;NIH<2NDZLP@Vr;l0g68qE9OCa z3o;nn-AttHo z{SNdb{dS!+m|KFKHePISMH>9a10(oYCG)z zHEX57ZOYZ*46%eLj;W>U`0 zQe3c~cTNT>Z6W=Y)6IX>bNk)+r*QCh!egJG7DcmZU|zV$c>c9RsKQ`nrPDm?rqBqJ z!qOz(oijBcnZgN82sDaaKuuoUn-@45HhjNDUd_j}YsHeTl@&#q`BBNa|qr1|e=HDlj|1u_9G@3-O0zB)cxiB?s~=QFVUILhczz+G2Z@h{jSYjHze& z0w+#5!ZKw*Iu9C3^}wvejCfAKcNMX-;xmc$gCK=@-zJaN%{BUdGLYrBS`sxDR_D-g z*HAG98X4}<;63R2ln zX20uk>7K%G8i;`gOvrfxS96tPcVn)gvyU_owLxX0=9h0iBk#*7yvzjo`6z!D=e*=e z7`Z6@_)Ou1%+>{nhO1m};7DR0G$B1W^WxEU#uT0wz-2W7hN{XyqQ)nS0g3LN%Of+c<_|0gW(P9gk;OOMG`E^4aFICN>ytH_83*b?R7sS zLq1rrr`;)x7B6}xHMv0shaXo&gxjlmYuxn36(@0(udxJCmOK4CpDi8way--PztU6U zM2>N*Tf_}jwJIqk?aOck zsPpPo%4mWY$ohNdCGd@P5p&^PS=vZgYYx>Sxmw=l%jIaTsY)9MGs)^E4;Y;b4xIU5 zvD5V=DO$R*i>EM%P^FLN_uw$NAG5G-hgD`IX?HSrrrt$+uc#UHn2-d0Apx}cBptN- zw@G^^`z?q7>ty$Ads5diJ}*}@V1D7oml-q9lKO<+{im6`BdiUvomJ6VG@SAEsnGUu zJXJM{z(JC%l|rQO#Ns;{Nzp5cZE2tf1b5cZW2u_A#?Jz(Y?1+`Baw)=9sxCRVclUQ z^7*fns+{%jJ>20Aq$otg`mU3ECUQ;o(MhW0W|OH4UTB)uhV>VzD`S?wm)S})lTz&+ zrw+bSiuqiZy(%)HPzA@^q%h}$EX~6-faHp+UiuOGj}>Oso%N8H>y}@PG*t@k=x(An z1jn(z_+0s{Vbp?Gbrk4sKag#!NvLANN*&^J{6DGOh$|dY#1@QGf&@2XamarcOTclR zwxL_gf~5Ty7e%XrqgoN=b7(S{DnSpu$Pn1MrqA=cBOu)O-R1kp9%w)jBtaVsHd zw73t2D9_iEnp?A*_lQX7@$*?~x9)~rCwQTtHAMSTkt7Iz-6QL%B+eY+5P;S97x7Pr z+V){LG5DkG?$Nax$xaJ~-a7X2>On%}E<>kweU(EYs_7Q1t%al(=rZHfGL?l2k1x^K6O(2$DsjBO3G;?XwgR4-Y> zOF@lEP~6eA^K1=rp^LF22F8 zDHWww7c&vSAjwJ;U-H_-OtskuLIJIp{-i$K{DBMWGm(;vd&bR{)>ORjoTnu zkXrHkXnUI--jER$GOk;Fap&4$Qz&+&JMoVNfNhwQszlAgKeUk18Nxmi+NRSU&;JgP z=s!YZV7Xr};aP6DkTx&}KkmwT4`u<<;F(p8&_;M8d7O%N)u@+tSDV9cn{1}Vo`W_v zq7J4)gKezbUUQl>;q*Rv^IWZq*UGM)ZojaAa^twxzn$B@&|ah!om|1d?wx%pTI737 znVP08PoPo5R7NLf5Vq5Z#>(?Wd@Oe7=3@rO7uf)>S{4u*^63*)cCa!rdg@bsRqp{` zDi-JvecUxN3lmHD-gqDOR+5dSKmlis`9}Q#A2}frSo+H&m5-JkLsPyU7RXIyYc#a| z-L)O{U52s!;9#I6{w^={nUii@(Pvxw{GM{1;fR-Z(;!!X00y>qRXTH9QVjg8jR(V> zX>c68i0uBQoS4y8<}(CG;2kVpmWrVRjkxqNu5-8fzAv@S<^YpO$ct##f_56egy~!> z?2G@^mF@>h>8RbiMyRUMNj7sqJ^0pEtCbI1$LTmR0MN48#4_XzL+cs@eU4p-Khf%2 z4Aq(9S6|CO_rxnRkA3eFDp~j#x6J;Fg7)v$$=azN=R;w*iUC8ulJ{}D1_`c5s!soz z!N$_t><*8zRi~%9>aEY&BtF!D3Vh-#^&5Vjq6ssAhlcM`2^Vd$QPX~w_C9nUKnW6_ zT1f-SfvvkGPTozglQUZ~ywf6RX`H6e?jwCWyudy=;kSRaQ?{owG_9lg^sBtJ%H(Ut zl%ERj&X9+Z=TL0?-t%^Qj1|6;n*GU0!Zhcqfc-wGHg;h6ay-(x0`Vbuj)CkTk&C+* zk%eV(6&>>>SqN+fw@<|qpmKruu{Djq;2}6xi}*-#>TLa$h~dr*Nr$SdAFpx*_Ej>mnz3JD<9Qdrg8y9a=T3k_Q1n@}$ZmEf9+WaS7 zit6G9)K5X~7p#}TH68Ja^&vusQZpvBln{9Tj(P808~yMZ`^%K{3W6g1SI-H@w|2o< zbN{cGpxTB{o7Us;u8{yklC%U0uft0(BkW)Gs{2ASBw^t9|5;64%atw$0 z$MW%F0u+0A=y{_%^f*n2Gp2Fsb)&-v%qw{FN(EH)sT)JoI-NH11hW^~V{K=E_xz;x^o`iu3U+ zWsO{}Luw|cZgPYRw(t)lMUoncp`}4HpyKaRP5ylm)NY-T-GiY?3>kzAl!x|{Y;9}xtD z8Yw+%)r3`eFNHPp8))6@U5kj$X6@ZJZ|}%A@g4Q6nlxXa@IVhe4Wsc~J+N*5`t*K^ zhbghbPKxp^oD?r5j0;5t@0pKBaD^ZVx_?Z8_0AwQjXcRSK)8_RMHC%NCOXf zrC<45HraSluRJD;Xawu)uRGEHuGrNWjE!o};lY(xH||6HeuvZyH^owgQA7H13flKA zcOs`Lb9TP;&n-%)a93|$z{Mlde(z!NzSEVPvkmn=8jmp!qZIkfsw;Uh*=wUmDw;u? z)ao3X;ZQ--R13$R#NVHb%FdnQZ{pSYst!3?icAicWQ-l2$KDM5BXCM%1<2u5oQur^ zo`DI$tlU`IfP?Lu!LziM+z^EP7fYJuG?yzzKzM=voT>=q%8saohs$g{mVAlQE-!p| z$JSr$972O!fREUXkkrXZ5ZA*cHV@+CQz`?-<0MSFQOjyI>@qgkGbV3>kRHwL?o73j zTt&@5kJDZ5JdivYJ2sx_S9b`&NPOTMNwF}4{%`1Kk(JVW{Dec8d>3uE*q@|Ny)Qr< zX^fawOtm-#+Pb+$HRBY8P)Wdf8m}=?Wm6@UE?yht>#Z>3@)DX#Wj5|my`&``z@B7O zRndpDgKdoa;|Ri9)o~(|W13^6z4$zze*C`okd*%y$y?3$&b- ziLtdTv_Hlm`q9r7eZkeuq>C((=d?=s-?F>++GnA}Hq9eZweAUAn2j~$zQ_Eii^dp(&qVRy$}^B;6JfljajX1+Rz`J`i8LCmwt2-l@S^X1y}u49u_w5lvQCeV5($sADB zSWO{fFtH9sD3%}$wWY12%>{^v){l$L8my`LyjA92q7F>*1T`a^x+FP-42#!3xd)pg z%CqceIXfMv#DRBbxOgX0^Om5w{OHIh-4;9px4x$Y7WZiDLyqg2r6v{FFnU zV&X)VN>|F(Oig~#25LFo_y+&M7Aa^eXluD)Vz9^AP1b*ncRI5_igwmXH7w@ap4-D8 zu%*qh_oOI7Pk}m8yqY7|P$Zj??I&py&>bAgxmhdab+zIW`8APQ5roI>+@zI3?S0VU zCz!3E_L2dzhBZi|)`<#O>N5wKyx!UlZ{w=SkYFG62{9M6chWATQY(H0?igxLdI70a zUtKpaxfk;8?fE4Utc_GHiNefH)M69ox*~r1=*cy79+_RQS1t~>OiQ}<*YM!q%izTa z6X1Sl*=ms!FT0d!!<-rExQXj=I8ZEDLH4~J#~pz+M8;3nZWExTNkFfdm3XxD_Z#w5 zS@g*9n3P*I*`R`2-j`QMhbWV0Cru4kap-{jX*;Atuy4P29F&U-SksN*W)XrZvUQ+j ztTajZa6!qp-!;S*x+2EwiOM5b6!E1hbM$Mo5G_c{70#z4_K)KwhJ!QBhe+%1l1NVB zG|#fmWe6mrMICpqo+G$hX{@aR8@Iw|gd;n6bK%cXtI&%S22 zP89kuMrqaSYF3+t8dJJ}gH%#wP**z-z7Du z{JTUK)JF0|U<+v>#{}-tj8E>Jqo1z-y^7exXx!fk+K`z$;{oB}PqtZV7o9#S z#zs-udD#N8vmgM&=J?xT!`@G(x!c%BE6E1rTU$K)7gRtDpEG>QBk*PM|sodi{&v*5K4 z#G9JZI`VqsA_q-PjrS5yTY}xpSVoYMCc$kHm zheI6W_OUrq8e5;AYo@hlZCwVoSDaWX8-q5HEOS-1FJW|vFxg8q#yC_qWqhzcADLJq z3iKu!x>&%A($^=VDYOvs0>es$!|Uz(?Mb=-(3ImF5(|q59f4p0wDdZG4SxyvDPAS9qIReNM6+~-G{g6 zVGAp$)p+|QL;j_X^DLmuuBY~Ks~Q&fv&I2u?WNL@^${_mw>+be6u^^)Wo6!WxZQH= z`|N4uZ{40IVPoo_g8Y=c-z0q)o^Fo?Filw2%e1qET56@BS{q?$O;@eeJF)xKEIL6ihgFi@jT^$H9zel4H>u_a9*g)Mhm&!)M3=vB()2{|dVo=$w83wxdR5GW zdgFfbD|nDId`hP5F_M5eJ2i(Ve`mtTey*5MUqUh=-22jYrQam1ZtHszjp??{ZSNoC zkT#OK=`FID1s0y_W3AS_Ehya@cn_FteP#h+vUcoq;uI^3OYh8NFpr8aZwI};8LhR= zK9g;gWcEO34BRVF>hO%q=h=S0@cx<=2slOM<>rW|{apZW?czpr2st@!WY%7U|B~7V!LqXj(b9LEXKE3sV*k#(7%G5<#w)QjetlHeAtOtXr(5ER5^z%5VX| z@i|F{gSldjk(53>>(P_&yiN#Ny3X&R%eduM<(EmKz=ka1I9uw1O{c^s->jSs5w8)= zqg|ohfdTo*UBUIJnlcd{Vc5XyUWMYKR7Iu9Ch1C+NFGDX^WUONWTwX z`NwGPyh`egp~iGGTY%`fGYLy1y+qr0PZno8cRG- zsyC~z7^cVL#?(n*isi7p4mQdSa%S(tk7D{IEg2RT9_P5R;EiFeY8c0s-vYCq)H6jF zx|{dWE9H56y$f&vAu1Kmo__r2-S$2+`al(<%90y!pTj#x%Njc?AFRTn2 z_%wEht!HB#m|B6+UwH1HE2@SRXd+aX*Yg2ktd+`@RRUjC5P(7J@CBUUb&|x3dbFe< zvQw3}^!ax;?t0t!tqOcqPX@Mj$uTaNJlSH=6*DFE`gu|Sdm6Xul6CgrJ{QBVgg_gm z)kIU9$OV;UVkFJGQ%2gYoU3S2b}_f3PkR<3d>-aK(I*B5(N+de1x2^71Oovxa@-qN zXg*iAXuRfy`hz%sT2xf;}se-+E?D<>EqCm$aR9&`1 zPP0pQ5|+F=f=TjHiC{wA>sb2CtQ-x^!*ntFAsK$J)iepjLk1P181$k&khkdempwJW zc%q4DQ!zd!)nhp$AV#udF1uADwu6t?x zQqyJ9s>PFF$?NA$p$b)FL1;e)aGZSRZbpt{5fHQ?1h$VnUHE?^PZDOX0ArZrLr3vw?eac<;0$1iSo_f$Y=zb8-xm}D~cqHsbYe2O2VV) zV|w3HQGCy|Q8}jRaAKN03&FNv&sq7-CVk)C`*mOGVyhq4U|sk5;))|hKYy@e^04jI zlbT{a=OR?dGE)ZKsz~EL$S8$li#VJux>$u0S?h(nP~q#zvt|>$}os-ExpNY6L%k)m#aa3MBl#hM)2djHSfvVmW4^R0=X(A zVUodsr)EX{EZC`pso-l(ly4CS-=>?M-#*xt9ZkhkOGZnCHRZ9Q()+CTQw%j@(BB@Y7 zZIDW{w}o)6cnaOs6Tn0*+zZ{Dz4y;gylL3l740418+ZJP6;6>R)Ng=Uegnr zAkZL$mM87kzWd=MS4TXt6lc}qMtn5X5Oq0-9BBp3hMO+f{#NQX1hV0ri2-X-fel!m zY@Z;yN2*NICcDDQpyQMqWvA?xf!cs4HJZIgr>J_p$D#Bgv6>wMJl)x7yR|o8+9yjq z2leXK*`L^W@Q^&HbYfdjI7by&B>w(Mei~wDzCnlkSzj;~9?9#{&&!@D1a0yC+G<@H z*LVte=m!(Nce%bUyL-@$VT;*(9(;LP|D-h=2{#tIiC#yc=$tv>!2|iA;AVOo?x)U5 zn-jDvJn|~`Q99eWr=ecj&j45^N5&cHpgF?}g1md}pJOSZaY<1=5#lf|y|J zEK;YoWByGf5GkRkRF^o+boi{UkG>Fj&yx0_Ii^&fY9NWQ+jJC_j0SN+_Si)dM4E(5 ziuJ8I1<4^?=TTbUewMDZ<&zt|yj=?FlL3J2TPjxM`Q4max+<=Q4Lu<7{nGB3VTpO=q=`^z=OM8DVZ5l9$eGiJe~gqsBZy)-3v@#bZh9$Moc_C@Pzj zuxS*IcD;9lF#stWdVOzsX{IfNBasmqrDWpj8A?yKR+5el!5WV|*5zi@l}#G~0p=;D^nH1fD2w zGojviPq;}5Dz;`bJXmAQ61vS}_}DLK0vawYQnD1RQ5D_U8%g=&dGRT15~>IGx+48o5_U$ftE2iv98M_rfJ}W+x3#=@tAnL&nOE2u z9MOajj_7^pYUCMYH@VDNMv1;wu4}vY)kp3L`rFAzFIbsK^q&y-+FrR?L_r9*of(jn z0ynDB5&P*C@+*xE)vhY;GLp~*DDHY_Fq2tC++kJ-6E+WrgUl|aP4-bd_1dg?+@dsP zCIKd4=_E-ayI(NQ=tLE6FC3b8=J3SKjxG^1CvzDhGdAyV?$&X2L)nXWXG8~JXxlo( zGOeC$tUP7#9O|Pe&B@G72L88dnUd49L``+Sl^gEwb#KfTzV9{b^^)$TJ`kT6R(&YiQhZ=O^Nw1MC0UmEsP; zytTd38*aW}wFI+pi66e>bt{a+6l5?>UWC*WdZq&zA&byMX8DM!6aGgBG7#)u25{2z z();qGclohW&GNuC=ljg-mG^bU)D)T`vFfh|7uXy^NrXtQ3(T9(&Mz?4FAW3<1QPP< z&oAJusw#vI1^0zDX2ufQ*)bFkdH=o=Aj-P(m&I|!P`X3UBz*`^E%O3{@ z4*ZPV3Q*9kzzu`|0*HbP>>^tD#+O5Y`R6r3@-2e{A)h)2=0Ah_SvrMt4eH3>dfPI% z(_;brKn3xdl7I;VpI^a<k9hX5m1qCjg-VFVeb;v>%qYd8Prr^K;H+-o48XgMS zg#>nb@~@=$-p?oa^fP+?mla1RCnY4L2J-I&$=}h3_}0The{bja!}1$C!vy)%j;96U za>kekO2QPssrReLlUfCXr|wAP|GxJlMV8qCQYjWl^N3JN{6->4|!H6tnfmsma6iQ;~vz zK|(@?0||?S00aLk#)J<1nmFY1UPf>g_g~XHFPuBSP3HMA_dlHTw+H#gkiv>krA6+) zw=2*B3JK7E%2}f}l@)v|9fgDhi0- z))pVn+qrIm%D_Jl$di&l{&v^!pGSotp1c_vNXH1MAMQN#r>X&j9}%dJX8aoM9SZ>r z4rV)2FV(O3*R#Eo5SE`6WX{X( z-$iStdaoSj2gViBos*mV zl((=Ym$NCN($lYh9eg^_pIY71kh-%=Gs6buFLcuQ4rcIPeF3w$laK<78*ve(Vs%Nl zq!$bbo9RXwO=MZq+96S{zioPUyj`~Ud!N*;;rC$3If)D;i-bldj$N+|cv*}LHAG-D zHR8F6oS5eB=#`l;yGFgCyj*E_QKcTX&9*-^PWHy)Zk^se|AxduGj~=AQxc6^kb5s@ zIEE#@TaY6;En#gltR02SAxkPDrCUJd5Ur)!ZHCk8$)Y^AkUm3uENxm*f$c7PFmCNB zL?P!UOkQj9mbUGTvwqIXxz|xpYy^~X=7{9BKm|ImraP#UfX!Ww78-)-uewt2n9C4E zNzKkMGoWD_I^+gJY1qW>cGX8rNg^XOOQ!_#UHm*M>I$RHo-rDmHQJM8K;f5}kgTe7 z)yy2VUobrShuv;Y>8f{}e;E&-yZ-%X9jF~ABA!C~H94^d_V>BECwF^Tlx4pOzIaqy zlCT^zM#H#_#mw9GQ#s#Pmp0YbDlBr?NTZ>{;l$mD;J{mGQA22kCK|?uo9W)ZBcI|A zp<@|c2}~UtrEsX8cnGsZ2`>}~uLd?>XG!@#p08q)uUg&Z2Tm23RvVG8fHqZ3ckCD( z>&V8{MS0lo`p}->DjScci9Mo)jAQP%JkfxaBN91kz|{e5p3f#{4c|0VN>z*}Oq}d_ zHjH+gFUR!!cl#}d&*>sdihfL09PCTQHE5(?9TRfjZT#mo4x*v{Ty0D8RR<|^ z0g=JGxCw}XqnAQpW(eNsaIUbgSoRn(;FWza8)MPkpWB4M~bI5r~YL zd!_WUG;4}WjJuCXHf7X+%;NNSIFLGw6epWLRFzn8d$GaaD74hTA|X*a*zE?7xvqc5 zE6#PAaBj*#c)FD`n%_9Qgjaf*cVU@e(TUmg8;7Z0=$*#rq znwq^4Qj21$VN<&5jp~6YY{S328UgA}i+tge(T~oA&}~O=URCEI(YTWV=8%$RZ1Nc+L`lqM7vkQ?!r+lSg^8cuXX zld-JDi?M2gR-4J7Fju%~NinJuM9 znYzb~=aL{PmsY`+L(gaIh!}Cuxx=cbKe)s9v%t>T#$ys-4cm}uVqqNh3We8h7u~k+?##p zP#WHid~O&(X2|f@9;c0wsn@hRhQs@yJ9#S+&nuXXzMsyr(2k$gjxy$h!Ur|_Y{i8F zo%tdVU0u5_>z(;pO|)DGGtl9z|KhvH`ji~ae}TKJ@+*?k_|PfjesI*>&z!8Bc?#gH zWttfV^su*vngTC3Ymbj8(Y+7>xN4*wUD?H`MUkQhQr}+T(O-1p81qWwciXulb=-ND zEv$cb*l;!54L!v!N=FKSKWD1+Tqedt`>i<=u+9s&&r0-jW)bj zb_rhZ>w}8Gu`7Yb)g~;n$BnG}^cvY(#-DVyu(tX4js0$3;tM^|5VwhtR78#qI+f@Z`90j$E(bEllW*T6LCnr6>f~g-ci!pI_ryJP?#l#RM;>waq|udx zLL~&>$DQf7YohAz4z=Gg2Iw-bCGF>P3MDg@p{`ni?U>TX6lznXIFP^s?><^~xAv50 zfH%iQa9ab#*0}|D?&I6@3%BdtP>wHmM*-oH#RY<9m6ZHaj8!qlyc|2MFgRbwLP)F5!yeN#^AQf z*B>gG9i$yG$tP~tTz(Vb|%xc@v%#sMlVNPvv#1eNFP1j)!MP=_qJhI(AoE zeHp!yhnn2hb@bv%?uqW~FRdh(sp+>lD|4X=P*VY)Jmq9G5j_})ZjlKv+7Rc44L-I; ze=X%65@J4%WcMP zu9J+-Y^c>2bbo++q6s&66b>|KOAf*>5+vy95#*J;X;3ChG<|m0M4wvCG2@Or{aFuW zaQT-(1g(2Exf>AQ7bgL{DtOn0rsaN(v8Q3v0#i8_BJ^gYm!B5tc(H(GjxNZ_?(S;q zup=q<3ls&XRwI9SPm8ert|?imd%`q$3~0upwVU(IV}Lu@YbP^+`nbyo9o;R>!}geY zb4lv$r~d&eI)fq1Pf*)a*5$=Md}XNb219!$5om3HNv!nd3F_P-+qmjzCGS)~MfO8^_ZPcQUfK5IkADGz_TZf7s zKE&3GmukGNUD?}!WnDfS)MmETf64LlW~3gg?~e$3b!2sIbKR(?32EkHGEi`G4iWdc zy>lOvL{xRO(RC)ip?&kNkf@J3ry6NgID-GNj&6on+YN~sdcGo!Hgwf-2?Cw1BmF9| zHEf#iGwTd?`E==OXxnZY?nPzdgvQ~#v(5j2P>&B=lGn8HCum|!`WBqTKELFgcoEhUcst#}mE*e* zH=;VJrdC4=y0?LMBP9z4nNs&}(bjpg88ffXpd)dq^1NWm9(l;mlHxD<-mk5>OW72b zhWdGr0sz`a#q37d+%Z!dTjR^IQ>r{|lrve3QK^5KMI(Yh@r81Cok3x@bB<+6cQkCK?>J-|sph9VM99_m+ai^Y zpuIw;RVzzohJ)wjP|8B7^kueUzAmV-$exlg3F}0{2z>cE>NJj*T|tg)C*iSUeBl`% ztYq&BHMRK#fbxW6SlE0C$XeE6!RJ^s)Js`O&|5Lg~oeRpY9)1sDewoCy78NcwLJTu(Hq?3*$g&Oj(nAOT|>@ zjzC=EgXmkejVdsXaC$0fV>L=J!~GL(^N?BZeYT1(GU}d38TOQ8NF~Ki>7x*qNHG6}nz+;{%u$O^)7&sCPN?Eu@aD4GI zJ|kUkOSV$I*h6B1{LALRud4i@+#;yd7g8H(5qzV`} zm)0mA6h~gc z5ksFt>;i)pMo=uRM1#!WHkjx+HhM@phK&H#_ThaK?RS>NWQ|OR!@tss&Q&_q8D$J> z@WjhiO_h(Y%x=MtryV7|bQF>#^T3a+!kSNA!HmWseimsyr)hG-nBF& z^hI-eu05ZKqGbGeaakQ8X9e>`BoNLsTl152fX~3r3uq}Hx#Nx7Zq}S!+8&tYjTVOK z#H=he#7$XwYn3n80A20BW5B>GPQQZf6Qj9Gt^T+T9^I1di~NHnj6Iy!R!WTj(`9=j zLGHF~oXa-)d`yiy?m3wyEC-oSPPZ?K_dDAd1Z)K~$u00IDj{p1^tD1ZapbBYHx+uE z9c@|O?4LuUb_$oOlC)6EPMthJA2SEiy$aqsC#(y}kr_@h!XoQ}L%)VXk|NkeBShh4 zPjWOP@T7iKSm@+l3yG=iBIhnmI#-6Z0>~(sqR{VEKug-{8RR)|A{h6nOl#Y=U zy$1BQ-BRHNdlD{EtC~!thji5lIq}{=a!-C0JcojWNW?)!uZBumbx?^zV^LA=>N13n zE@5_r8TaH;TtBS8bFU>u8>ORF;d_@HnD&_lZwnD}PyfNoz@0kL!_nKt2>Kv?Dw13u z-74C8)EWGww5FMxqr#3|DnFQiLIK)eZ2%cw4YHn6n9}8$Hc0Z?=X8o_R+ts`ZlKFk z!QDU4a+8lU!*3zM!LvU2Hilonus|v&&Li@qLbT6&CEpUHy5n#U74n9|)FX02#ch!N zW`7_k5>56YR<*c&uBu(6F?3vC!ybx6?q}vYi_U0~8`>3>Bid6M_;@mc9|_MsGB5N; zYR$jQ6*Kf+Wg4l`YHiL1=-=>{$l78A0`C`+v$n5QSTxl>vJZYE%gK01X_rE$FsAw2 z=od3V-4Hn$4%nJDqT-kn z5XMAaGzbY2#VrD-A)K4_{*uaHl~y1~GT4$VWD;G&T5m~ z@oDs)epvg55!j}ilO;K-c|35DObY3BbDY>ksf2yvZ{9Jr&{nu4+US{R`Ue8}ZhrIk z;|n^zj+7AxszWcq^^@B-tI;%cdb3$2 z>x^rOPN9GZ7-TEjlC{hOml-a;UIdZE0wz90x)n%dpW$5#hF zFg0AHLF*i>=FB$O-B~kMl;Y1IjX5Q_a40mbnn%{V+4YSKy0S*`eZIKBMO)1}S z#!Qn9w~)5kwtohj_9PYGd1yqq?Sb4v@I};MIVI-W^isNR{seJz+lSn#Lh?S~Yay1% z3urAYu_tA{eN8RmYAi{>gHv+wAb3;%N2tTlv2EM7lat^5 z?z#0<-LLALs{O}aYxk<|>Z-kWS3lkT+*{2>*i|p2KNCw9=*_4~oW1*cAwBvg=`voF zr?$Vl?`W+yd}VcP*>A0Jcvl~e#?%X1C`881R)j4cCff4X&9RzLDd_{nHLaH!s8(08 zgv)WRF1pQ=x}QyvXhp6-581n-d_Vhd-d2GJUV-<7PdMMF$hP4wa-J<8cLoQ~>YLHo z#``yc{5H$t#~t~6d=>2eiThj+IiRTK<~|O*7EF>UK?^yxH}O_aTIR}ogTXdBRk_O4 z=Q~%wM4}-mrHbpz;`g%9+q+M;e0Sw*`Y0`;4)WB{TRzz1 zpW>tkAAg4+tvT;N%TaR}wP|T)Wa5#=Zf+*8ppi>6x20;jxn6&mr%K3SGnX|M;3tmc zk~*>BC$@YyhjBctoIUs~XIhVx3NFxXRYOomf%JqD#If$TpG7cV>O550x&Z$s(B|Sz zqt0lmg7Cc^%{#JO$6}h==sxaUdZN+hSnzb|z3FTRH<4YJVT)Phrry1zSnL!pkYyge z^&~3opgEQqC4y1_=WWKb923m9!j)Sr0F}I3VD}T<*glTid+ZPa_WV7s!~U`bea>bzLB2i#=JAR)Cng4&2Yi@NQ0yKG^Hl1K;0r2R!G&=*ynuoAjz2DN4{`exuKAo($HT zW#s5GExYWX6V58GaN5sflQ$Y&)CL?Px0Z5{Ax^^7D#6B}B-nRJ?F`VT3P(!c*cbYk~P{=v}-&wt8*Z ziR&I`>;4aE&v+4wzUgd|1Zkp6d7$&J(m3eG*A~rP9VGG-K_4AXm2`9fsqFS)@9_1z z9AXiap>%Y6Tv=|PIzejPSIo_|)aH-8y3*T`HkJ*Gi+Z%gtK*%0t*pJ(pFBm&!((#j z`V2Vima@}KtHlw{C_!F#hv_ZG9MuF$IxqC-6hCq04?~m1?=heebp&)-ULY&VR}^;7 zb}=G;3po5b>=gY0&0y_&m>{ZU$+GH(%_8Sy#IIk-*aD4;{>L~clc0t6d%%xuyiNGd z2lCY-wxd>dj<_=}Kj2ID=zWG`to;~QWu}0v)?TDR5M{D8p#8UKL|k|gQJAJtYoj#z z9Q`~GFlI26ac1jx#5Crih$b#S8rfR1JI4&6^5{I=TOfHIznX0~E^o zAE8i|e}_Vuxq$zvL7#(}1Ngs&Le(KulC;}O`caC&$>#FCju53Rju8n=A+Zf1O+zmr zg}&p8!a!Jnixw5N#UsOj!oB=K+@p5Fsps{Bb40;Suzeg9|hVZkbbon1qTnauyzyd-T?VS~4w>%RHP zEuaM42|m3w)P|7eHFjnAf0bt75pPx7GP&$`QE5P5ahO8&f`~zo_4kRA1u&@t#?TBW zKWW?ZQ{m2<6tA#;p8uU3gg6GP?`H?S4O;D~6#yY(T_S+&%Ujd;<^Np2n#2%PK!y$x zVG_hkBftlJ;^D>&UH;HCLL!2A1lNMrZ=i%mf4YBuOvF&rRUqpbKK+70Z}-(b@=UAq zhi^-F{Z`R2;&TLv_zge-xkY7E3JMCs=u`|0Fn6zJ*g8yaH9+u>2UUqBl7IxiihkSK zE*jTQX^<>G1SqVl+&V&%x{44`u20OCV*fG_@K^Gu&y*Lt)KA&%u7Wo`lF!LN!e%b6 zcXp?b#!n=cC7g@Bdn`~|Ee?2Bkox!~X2CbgdGH4_^9BQj=FD3^t$AksGXNFftk&=V z4ILCF{H=TY2+Cd_TLmj7VCge{jA-p>v5c$xiy(mv_v6&I+Y<)*EewH25Bck-9WZcm z(*zSrkn4A#DkK;;rRPLJMgs|6sG!g2527X~ymb43(uYWfe(?Q7rR)0ri*B# z;S#0Z%aWDOr~-kDsy94+$9if7&pm~=aZhT1*Qxu|>~C^fa|W?<2uO)yBPoY4#?nLM zntnuAtjMA!JXHB;t%4=FsWy>^rNF;|yXnJy9%=5CSC-4)Kg7^H=YKeUJA(K2k(@~C z@%N~RTdxnmvKi=m!I-r&l_Hdm_$}$gqQZgO`Zp?ckdT_aZz|iJUbF8j$ur?<=Hgle zdwF2lm>iWHsyw}Zv!Fk6A$?X*C^s}yCbnBk8%aphAr)g*;C-_v^Je z26Wa$$E!8F_A~DR6fJ-^NNjel43cPW(zJB<{MUrbAmDp<==c!647gOE@+S8}a2X$kd&II>-xq&0*_D zryfAj0y0!j{DeY|O>1CJBMiX0HB?!(h`kyZAW>ZbEXy(U};XteFu2_4*e+g1O}$Z0^@3v5plABVu}2&FfY zDaPoHxue73NhGxBu*DJyl zPK6C;G~B1qCzng7IJjMIt9EZAylfvW1dyCynGgm zXkj}X34sgL@bRr!Q76T;5`H97NECs8cu*5YKW_Q`0O>L0WGPIb@x+fVU}K!Xb~sN)xwO8Kmut>peHt-+ zM!veJ6(6;lxQcIl>wjIhy<86!R9uf@-PhZc3~^S}amE+Pdikjv@HXKTGB}XJF+i3J zZF$O~l!&v@zv&e@E2F)D3?l~RHt@un(Y+qbq=-h=xU~iPwCB~<8CboN+DwxM)8HzN z8){r3-u=92xXgjjiM%+|9kT4GJ5i!!FtM*5F#DPZ89Ses3q4F{3w18Y8W1uzzS^`} z^^58Bi1!VjuL&*p5Z701GW^|%O1dPM1*5tZy(ZKW3nc;D0^oh39rEsY)PHI!%3Aj&D zUYvd_&+`6S(|*E|rV>z~(3m9}NtD3?#g3*90mWuVe>Hzq1gUyl`5vHlcwk->zg@)!E^)P2iL5x`$SC04? zf-$5*8bwaMfXlCkaXrO;;wkBixhljTpWceo)ja^zWorV7g=RI51k4VA*ZwHG75~8f zQv`kyJBgvq75LHP)O4D(Msy1s)-p?Raugc~=di*ek zKvmfwV;Qbhep^g`TkK7SCh^y!kIrq|2;-*A&F`)Tvy&`D4>SxGHkqztPZNY+WZ+D5 z<~i{+bR8sjSR5C4M3<6^G7r2Yh=k|FQ)-x~cm}-M6Qz$8f+bz4BZzp$kzehIYPw+G zmAU?$U6|B6Zq1cuQh}P&cTAnRg%Z5Jk41r@t30L@Se)W_W`WaxYUo1C&kMk}s_Qo1 zZg_<8U7WAVRYr#|LMO&;t?Ik`REt7N=;3k|Pu z&9f+{bX3Za9x_+?5zb+l6M}xk`J85ozA8mAwAzbDo^pmh7e_AnV~={pE(o_le(qYU zb>Y-Gxv+{5mpg?8Z%d3%xvG&=_k~O^AWw|qneqe^-bC5R_B>#oi%Vs@L@#RgWIl=@ zN$uDGjvGL#DJZ6TvOQlK08X*7dc%iR#b*Q3<75;@DGUD@5 zMwM2qnEkFo+65br7p;!c%EgkOV{tF%*HW2Y%F`)JJFa%(Sq*sM4w6fxS_3a*TMhDa z7*!j{qB~~Y6+#82lcvv#*;R;rYYZwfsSG>ai^BSY&KQc6ilk#e7-8^}cI)mOTWpGT zf1TVEmEoOTtvhyEnnbTqHz}lpMmpJ&&7}=nhoM^I`Dvr=0F-4{hL2^OHU`DWp!1T! zKB&-?f8%ajdLvg=Ex#L{I{sUhG`M5nMXTF#NY)Kb?pf;;bouPsbo-FvUfQ(+!f{co z`;VyaO7gnPT^JnJ4vnhyrTbSAPBx=(u|uJ_YAFS)+&gQ-E$@x|s<;bRYp|s84L!zv zxOIffVB$2>PdOoZ(7l&D;p{6sa0pUI%?OKvQQ7OXM8zL;McHU)-s%u)Qhr{erZ?i` z8IR{EqP)~=R^L-|EKjKT39MVEic$-118;4eH_0_)4h`y!qG*$Z1l#1T z=eKV8>r_ll!si}i)^XQEOOCH}jPs?J4)zk;BmEu1-45!JOfq3mB0}aW_20otjHB0l z0_1qH!u1*US`6FjC_0&yDe4R?P9v2iz0#K37WYov(aomgN_?Q8o9)+#=HUftd1- z-=rhqt)Dkez#SFVO&3epM&|@BLo%{bRSB4wjX$wd1ok!yj3fJQFP-nrs9DdqtQ?hn zbRV73Sw0Q%J`(+#ASPmhSgTUrhQFnVXu}eognTn{+!-XCu=T~VK*9?qhbx<>BQyfG zVfl(uvI}%JR6qj4d6F22JiU`uwNR_UB8<4D$r;n-k!OpS()jW77EGx}K6!4$4XajR?s$IF5*;tblq*l$MRZPG0s5;HoQ1asZ!8)oZ`qpLpFs2(4hFG~FZ80t80n%>uAGlc;B%`~Egf%DZO=6W#>`0Q4&gdzf5p3tG!&2m z#bu-FNsCE=Zc_JEPSLfD?NR(sy42+*CsMLXHS(5Zx2^rPBSNML4Sa-`2QA!mjG@^H zFhZla&UI#VX8U!s&f^&^&Ji8->dQQj!%521eGpdI=shbFpr=_#(C{>%m7eL;L#^VS z%;Xc8i>yD}Ka)p2TbI-i!<{rmk2c79<`if4OGmUd37)|GqEo42`z%w^N+Mi}(!8c) zz&ss7d<{86x|*x1+W=J=LYsdmWfm2Er8P%B6Df#yN%J%s)u^nwEqP;PVp%1o+rm_7 zZ=x%6E2a}w+Q>y8xwfp%msh&mBezS&TytO3f9=5a&GA?Kjm7cD>MWoYc{5;mKUGXw zeVo1aK#rPSG2YOgp?RIzzqnD302@r72c>pMCzikCj2E9S>u6pNz|EEy&k(# zzFMj@tsHecHoTIiyM+!|sBS9}R4%K;$-vy$!Pp=?V4t08hU=R~7FH)WTJ@Mmg`fo| zXs4#_c`}Vj)E#i=`Y4%@I7-{YhqN66!xr1xK`WO**hjSgDLe(j*K^yp#C=f3b7xQ_ z%=!^g0=1l}w>Z7iyFF8#RlewsuFc0xGL=LCF9bUE@$jVE!AGhWifXAtjLhslfJE%q%3y>%xTXmg*|!+Qq069 zVrW%V7o*yCIWStn6Nu^5k;DCQK5sgP)$DhH5hb=rTTp6s)wJ-+3HOp}(XknRB!{aA z4Xw?=>;~BgO-epTfT@&Zh1<=Qly4!As7c_j>xmJVZa+jLfw;@PaZ(dozV>hu;!=EJ z8?d8%B83yG@fSO1sceCe=SfI3So)<@+z@g>i>EW1Y-$XIkAu_z$bdXRW*(7Ca^?+) zSe=7>1YjBW;5MtTul%pCo)iqqE|N`~R=<4V&92VyMMz6_);u9E>P#2!r5AinZagGI z7R*r73V{=>eG`(zOqZ_RgpbP$+1<_*stt)Df#Do2n+HqGrCO^n$extDw%EwPqBVr4 zA5b>1FDw|cRw&zLsOqpAbM40Bl$iVnobUX_0zXa@42TCo)%fzH6;Y4`uln$wKGUDt z=wJ3qxtQz(M#+W6S5IuI-*m|kgz0|ES05iBwh$2uF*n@jSfPbPUAMuJ4rqgnRG-%A ztV7cD`ZSlt_Gxb-#F;#iZ5QC+61@IsrWVZ@+?jSrIPuPATa!CH|J4#|XUNd4DpHRv zk&^qmXYExm5xFv@9W*;!>X1Ngh#aG`>tfMaIdfgThsMtt{nO>N0-+^FOI_>=)yI3o zE2^3}C|UTne+a?TBiIOq^>RLF{q_71o`h3&IB{9YRUjgEcfWwD(U_Kj#g~(DZ)5cI zQhJRB;S^>IjTW;sXhJooZqYLE&k8-a^OERd&pA|YCgsaLhX-qsU=fR&gv0cjLUKXK z(ALF?r~&K;9eJAw(M$7dOxkWj@N(agO@Uon%DWjtu4ey+A3tz2M$I~jH7Hj80%l_h zw>`o%7yDJiYr39}V4H0N&!}JWar#V`bI|2F$d-R3_JVLN6l&y zUHVnIm`GG-ikg8yjn&89_~uxuI-KovVC|e^EIBj1I1(Z9MaBqOX@!+r^6I3%!b)!< z-b)wyoUPK~v*N+ba_v3AKgqO`fuy)BCgMlu9HZOd<`ELNhIi{Z_TG`aPES(bq)an^ zj{8qq?BgCmR5YhLqI>Vs!88Q7)Bo;rq7|o8EW*a^Lliw_5&meUf>(|;Z>=9rbEK1S_;K?rPY;~ojzh-C z4AJoi7&!4W0y&uSBI#ZAgudejrcBBtVJW>7CoWBg9Q>QX`6uk$hC;H_({33EM1{X- zZ8ff8Lg`B=xBYKV}4VaCO!tW?6Y(x6k3`czB7jq=%4y)O2pob9L= zw9txR;pI;@1Z-Yv8K`I)t7@cg^(QsFE2Uqx2K@eZHl}wZ0yb79_bYxydZa?@^dohyj*tR@{!w z{g<*^^h#}?ztBh-)&%B%_f!qYJ0{(AO`a|O9Z(=f{7Wy8qyiGPH5HA&dngO>>M@*? zK9oY&JgwuyL*AOnBjqqNY1ov(CNjEl_JFTrUJ?`Y(+a_zCUS>$$#6RidxKm_izeH{ z&8|%1L9hU#N%&CFxFX$bD2=De9MuYR*cbP&EOEl8w@!6eZ6W;6z*+yQhJ!IDqKnGJ z#UTt0w-oT|(reKKJ=8Gu1pF)1mjkR(2b7w6_!aCX-?ESD>iLV37m*6KX}Ba>lEH6j z%|$0qd#UNcyE=d7^BPFKq~452Nh8P<++4lhGopoib!9|w&uy#BOMH8ug&kBBubwVBL`S#$T%-oX^I@edu7&s~^Z&Faoeg1fjYc} z`O?J7qdV+r_EX3p4sL{XYX5kS@C4X=$bQ!gDY&cVQK{uzlz;EA<*X~UbE{s58F;oi z_0*9_?VQFcjAbKQ7t-ph8I3I)bP^rM$X##j=UF1RIg3aW_N^f{F`3Q^(N*triiq&h zQB6b+&bQ3yz=`Z^Pe1qMg&__})Gf@E9#wTtDM85=4PQ*iBwT!+kthbNnx)PV$UhR- ztS1eZ-)Grh;jcr3dk9&a;MDE5MKdWhcVu+ zWx{FU9`k7l{iygpynp=6#X~$WR1lrILd$K=S^qPjx8T}(xuvkiwgjwe#%)7IoxEqT z1f=|s8vlm5&T8RI;dsK~;)G$i`d3>1ZIdrnW}S*n!xsKzE$pUFv{G1WsgYG%^Z2q! zWpI%d<~}7knXOm<&yR(|XPHW4hg+p0B!~w_g0W$@r%UHe z3+EhEUQ_l@TJyrhilxsDLmSDIl~Sww*wjmu|$Q&iLR9cOTrc<$1j5vu}YdZ*hfOQ)XaCTcCrI(40!v*KIFbdsTx{Mwy= ztJx9Vmb7Y4a)i5w&Ow!$P)hombUsG>X7-DNJYcDa%_wzH{?XXHhn6N7Z$=gi_!cAG zJ;QI$tUtj|$NwGuCg(tOxa}U-9UAU5$Y$ zTK4dv$lU(bygdieNm9jw@5&DR5*Nkoir_p;SABc#8uN|f-o-$Z;&1RsbzC{slBgsn z?7uoiE9MyYYDn|3N{YoiH$N@fv#u0Lf-bM3Xz+zje z(B<4)*RIIn!?M!&?!HOiKB;7RwXuEv$Uh6r7KO>h($ObIxn}R2K(G_%NPerVVSUTk zQbWt%3DVuiB^hd@(dpUUr)_lGO|KjkzVBGiilQYq$PPuA*3rX`Epma)&VVwWVT;N9 zr6M`|Ft6GMCt4N)NnR=z=9RIEB%lsvzl9w{psSp;01x#LyU-h~RuC$=ZnsVl*NT~P zVvESxuAE|;s2^-^^GSv8@Y0b$r)K0T`TS;%fU)&?q$%(sy(FnVk~FSd-_%lZ(pY&n zF0-l>TVZi{+Fatskj8UZc{ib~OR?7HB{<_yhH?Bwk_Q0G8)3QjnXa`(+-Z>+FK1_m zY>ld`z!*#E9ekm5|9Tf&M?SHpS}&*m1N6x8Z_uNHqn)vfk%=RK%HG&i#YBUinSqsw z0mwuR%P8V#V&H7|_2g^&zn2zvwxR~kCIBi?ZXgqoiHVJwm6?qV2xOsU0#Y(DQGUtE z+8O^(A}Wps_Vy;m07h{GYbO&}Mg*R@9?XNhrJ1aQQpu}+1Un`Q4a7A2rF*k=;RClvi-kiQ~;2jne%@OyH;tg z+TwAc`YftnIba2aKjI<7Bl9R$BLXLUzyzpV2Nz=KJjl6r&lWGsNyuHKapDZ&C;W_&6YB#U}uEP4ok#V{pV`gs1_6S(Q6`d%NuzD zPG&F!dKo-FIef$lMQm;=N38xk3}ZnrWL7vKO~Y5$0ck=wb6XBOiK%{2LJ_{cd%Sb) zQi`Pb^Tzut-}Aw$D(PP3w#RH@*z9mYI^97}57Qu@$J$uw;-6VlL|TVIMJIM#LK(Y0 z$`Hh}RyzS)PX)*vh(?@)Adp6dvhY+$U6N&rmSz07dq|aKlX`a zemI_!Olb@=;Lvu9*P4!)`)reM>n)(`+-#d`y0Add)ni$q>EfCDTRt*`{8BfPq$Hp| zEOFr@prR?xq+;}9O0Atqw_+&g)BGFBSRQREM)8qgg;$AEi=1a>7yrUDCI1&1>x;+; zc44#<>kyR|2~=RB1?iQ=N<|c_>@{Q^IJ-HoU60^_O42g_8a>&N`5Nqj+%gc?5I1up zMfz2nT`B%d#=Z)?8Gw9-iZWzl_r+<|bV zye|&lIjr#nqHTF;h^uzv`5_6!a-%iT&!E&yn&ro>h=mynt0zoLTA)P6I8ZCHoJ87Q zE#3Vh<)>umxnC70-~8I(|xcdyk-XQtCYC@p5 zsC#VAEM%x{sbij>mW!a>roeVJX`>!Vxz|J5E~@F0Iu~Mnm!N5Th#(C z-@mEphR;P+)VZ3jtfxnnDu3}1g#20=&_InB^7#Ilw5*6k@+V9Vj~r<84N?BXhJD^tGgdx6#p+|z8E4=BB^ro_lvn0nKS=b!u~q#ES9Z2(&9jC z{F-r7;d1}l*gao%YW7VnQ_k4(8H;{fnADlR*9rURLMqs-Qa&E`b~sTWe_W+zo^zy4 zQDn!H2H(6Sf8DM`KZCp#F;z3X!C1hQmR$>OR2DYXVQ`j(iyRZ8%C^3PUY5JOg^M(| zYjCro7c!fpQZyF}n-c>P`cIT3IqI01?_j97vZbe23j1jI3Fl#@RA-pXMCs!eAj$rm zcY@?b7L?NEm<{-diAa2$gc6Yrh$ZY+p7IV2Rx`@l+Tr2ffsEga@je|b!l7EU2;DDq zb`CdWN;N!xN4xZSTDM&CqDAgLIHG3-eaqI$M{G1{SEFfV zP_pB+kQ^xOEn9MkQ>nPWaf93wslV_z;wqg-i7|Hao= z?r>{z?cwaJTW!kv#cf$)wpbeVXZp>O_l@FkF*UWf-<(_1)!W7vb9~R5pTvbAsK^KY z#_{UxdUud%XnIzsG+II-i=9t)`m|PCes#lj<*{BHm;5PP+=IAlh}L6%OnjEbgS4w5 zU$X(Jo|18sAKzQw{5YkM!dRIh>@oSe7`bw?OU-+XNLQjhOt zaz^2n4Cxrv^L-i+!_}CEDzEQHEd(XeN6^27Z(#{7fx3>vWkKE~QF0*}0HHrl?Pfb47L>)_zzCoeW~0)YWy zuL@YyNh%=1fHGn7&-St2cwlyOV-#M~Zop)sj&Eu2WM<8HQS;l#HV47_xmZ|G_h9d% zXjqNFg^Z8p+U{6sIYX?k4VA|E;ZvN_0fRDvnd92nVLwG`A&frOMyW}rrqcpw8j?K3vY254(gXWstHZ6ISg z+9(nHA%fr7O2sm_YyPF*Tb(si#yD0zC2!Z`UX(${l&JTmgjrM+myht8_Oq#MLq4w^ zO({WjQfd24)$Kl~!*9d7fo-m`c>UH+==@dfsJS%Ymu*F`jqzDQHo z`~kt5z_tw@wUfwW%AelbYVK9nsPy-OL zZLdKm>|3LDq98465i(a|=Hfo#GvWM2t23cub7x}Y>HTQ=HV3aYi|^N6iyA{J{R93X6G@&M@Q!=a*))+ zo;GxJfE%qq$9LEJq4mLeEZQ4)5D&zsZ`45K&;Q@$PR<67&hCz1PUd1|{o+U>Cl`|! Ghy5=qqFqY> literal 0 HcmV?d00001 diff --git a/hw4/hw4.tex b/hw4/hw4.tex new file mode 100644 index 0000000..fdca43e --- /dev/null +++ b/hw4/hw4.tex @@ -0,0 +1,54 @@ +% vim: set ts=2 sw=2 et tw=80: + +\documentclass[12pt,a4paper]{article} + +\usepackage[utf8]{inputenc} \usepackage[margin=2cm]{geometry} +\usepackage{amstext} \usepackage{amsmath} \usepackage{array} +\newcommand{\lra}{\Leftrightarrow} + +\title{Howework 4 -- Introduction to Computational Science} + +\author{Claudio Maggioni} + +\begin{document} \maketitle +\section*{Question 1} +$$L_0(x) = \prod_{j = 0, j \neq 0}^n \frac{x - x_j}{x_i - x_j} = +\frac{x - (-0.5)}{(-1) - (-0.5)} \cdot \frac{x - 0.5}{(-1) - 0.5} \cdot +\frac{x - 1}{(-1) - 1} = -\frac{2}{3}x^3 + \frac{2}{3}x^2 ++\frac{1}{6} x - \frac{1}{6}$$ + +$$L_1(x) = \prod_{j = 0, j \neq 1}^n \frac{x - x_j}{x_i - x_j} = +\frac{x - (-1)}{(-0.5) - (-1)} \cdot \frac{x - 0.5}{(-0.5) - 0.5} \cdot +\frac{x - 1}{(-0.5) - 1} = \frac{4}{3}x^3 - \frac{2}{3}x^2 - \frac{4}{3}x + \frac{2}{3}$$ + +$$L_2(x) = \prod_{j = 0, j \neq 2}^n \frac{x - x_j}{x_i - x_j} = +\frac{x - (-1)}{0.5 - (-1)} \cdot \frac{x - (-0.5)}{0.5 - (-0.5)} \cdot +\frac{x - 1}{0.5 - 1} = -\frac{4}{3}x^3 - \frac{2}{3}x^2 + \frac{4}{3}x + \frac{2}{3}$$ + +$$L_3(x) = \prod_{j = 0, j \neq 3}^n \frac{x - x_j}{x_i - x_j} = +\frac{x - (-1)}{1 - (-1)} \cdot \frac{x - (-0.5)}{1 - (-0.5)} \cdot +\frac{x - 0.5}{1 - 0.5} = \frac{2}{3}x^3 + \frac{2}{3}x^2 -\frac{1}{6}x - \frac{1}{6}$$ + +$$p(x) = \sum_{i=0}^n y_i L_i(x) = +2 \cdot \left(-\frac{2}{3}x^3 + \frac{2}{3}x^2 ++\frac{1}{6} x - \frac{1}{6}\right) + +1 \cdot \left(\frac{4}{3}x^3 - \frac{2}{3}x^2 - \frac{4}{3}x + \frac{2}{3}\right) + +$$$$ +0.5 \cdot \left(-\frac{4}{3}x^3 - \frac{2}{3}x^2 + \frac{4}{3}x + \frac{2}{3}\right) + +0.4 \cdot \left(\frac{2}{3}x^3 + \frac{2}{3}x^2 -\frac{1}{6}x - \frac{1}{6}\right) = -\frac{2}{5}x^3 + \frac{3}{5}x^2 - \frac{2}{5}x + \frac{3}{5}$$ + +$$\frac{\max_{x \in [-1,1]} |f^{(n+1)}|}{5!} = +\frac{\max_{x \in [-1,1]}|\frac{7680}{|2x+3|^6}|}{120} = +\max_{x \in [-1,1]}\frac{64}{|2x+3|^6} = 64$$ + +$$\max_{x \in [-1,1]} \left|(x - 1)\left(x - \frac{1}{2}\right) +\left(x + \frac{1}{2}\right)(x+1)\right| = +\max_{x \in [-1,1]} \left| x^4 - \frac{5}{4}x^2 + \frac{1}{4}\right| = \frac{1}{4}$$ + +$$\max_{x \in [-1,1]} |f(x) - p(x)| \leq \frac{\max_{x \in [-1,1]} |f^{(n+1)}|}{5!} \max_{x \in [-1,1]} \left|(x - 1)\left(x - \frac{1}{2}\right) +\left(x + \frac{1}{2}\right)(x+1)\right| =$$$$= 64 \cdot \frac{1}{4} = 8 \leq 8$$ + +The statement above is true so p satisfies the error estimate: + +$$\max_{x \in [-1,1]} |f(x) - p(x)| \leq 8$$ +\end{document}