From fa598939a89e7fc72fd98baeeebbf13ed9cf7fa0 Mon Sep 17 00:00:00 2001 From: Bertrand Benjamin Date: Tue, 23 Mar 2021 12:33:16 +0100 Subject: [PATCH] =?UTF-8?q?Feat:=203E=20sur=20l'inf=C3=A9rence=20Bay=C3=A9?= =?UTF-8?q?sienne?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- .../3E_ADN_Sophisme.pdf | Bin 0 -> 41323 bytes .../3E_ADN_Sophisme.tex | 21 +++++++ .../02_Inference_Baysienne/exercises.tex | 56 ++++++++++++++++++ .../02_Inference_Baysienne/index.rst | 8 ++- 4 files changed, 83 insertions(+), 2 deletions(-) create mode 100644 Complementaire/02_Inference_Baysienne/3E_ADN_Sophisme.pdf create mode 100644 Complementaire/02_Inference_Baysienne/3E_ADN_Sophisme.tex diff --git a/Complementaire/02_Inference_Baysienne/3E_ADN_Sophisme.pdf b/Complementaire/02_Inference_Baysienne/3E_ADN_Sophisme.pdf new file mode 100644 index 0000000000000000000000000000000000000000..f65fe927a6e35edb49e555297ab557f84341915a GIT binary patch literal 41323 zcmce-W2|V+vMxMr+qP}nwr$%s*0gP`X|8G8wryMAde1pKImvgEd;jd+N%!dPs?ixw zs#2ZtREktVM2wb^junb@c5!GGiiLoIz~0CTiiZb^Ud7YFlz?7C-pI<-*aeDS+11G9 zzjnmzoou1#g@o)q2(%gg>N7I@SJ#E2|3~s)Z!tpA%Nn{kS^m{v{HyU-{?GVVL&?BP+rGw7;iV+PIiH5zvd-7`m8>m>S!gm_qUKK{>lP znHt(cd8{wMPb*MN?*ajUe*xY?ncA8BkL2&{pHFB1d+>h-0>{4#0_T4W0^>i%`L~#X z@gI}_XY9bp^lt<4pK~V0f15Wk{bS?*j3t=6Z2vhB|9I}d z1qAc|z9ar8e6zAJvi*1b{=bLsD;@2)O|}NVm)cWbjykOLxd;?j=sJxk&9PAmV8WD#cEe=%LEmC|uiXwz=b>Bnwa2 zP^v-?^1IUT)(iV?-@8M9eZDr&TrzCJej>@kS-c^`#OSGs zuj7y1HF<4JaMvDGO@%Y7EU>3%Ei)p74ga1`AT7BDl_Ld5tY{8b^^M1OYKxDx3G&)J z0sCG4dc;|sWaD8=Lqp^fQHnyC>#Qkv`EF1B0l7jV z8Dduamx=0#!hAeAV7QlsnVxr4V866nI&#ePVVa^yDX3j}5|{}+`~1!5SlZ7)CtAQ3 zOs3C|;SX!5Fa>D~jP}lyUO-h8$lDi5q?6uQAdO}@)}ug&9xbHvkCkJ|3)g^mlyIhB z2O!u@D43!JGRg%qw!g^wdC=a(LM$^)Tl4^dk80oAm}1Edvx}MBMK&f_Xo@M4i8J}4 zgd#jDH^?2)sc>Ku+nR^TmEua#$|schBLGw#K}7<+POXV%P2~>bs3x@YqWiNp;(UC# z`L?wPU7!uMpxx#|G!y!E{XR#x-A!)X@ziN)4bR&gjco1>eU$ zZ+6tfr-Y7lS25eRFEB7@qNiMyNZeWj#~rCh*+eypnOM02SqRU7so(pJE-w-;HQq0tU(X^;g8e<&#;*&wuCGGXC??)#xA0XUYd7OT9rYSL~Hf9K5#6yd?0ny zxH;*XgYBR?Nw5}Qh^B*1sguZDNuTR3RGZj=v6>SSX)VZjIG=Jc#@Nzf5E9PhDhLy}~@=CWWKBbux)=S;==JG;sHFlExHy(pnHkky;| z%6-DYRiOXkuEOrNWvi0NqdnBJSdpYxo61f7xsHIv|Dc`wTjXh(w`#nlbiYKGFx3#+ zERsdV@z-SGSkv+wTeA+|?zmECz}~P!fL#J8)$R!>d_?<7=~32+=Arcn59pGmmoe?3 zdO}3~qD**cL2?E)@RO1A6{HFpJ%(BX6?~D5U4uj@6iPSl9P_!)lgn?70U&(hUNalLhrrp)&Qnk zT9k^MQG}gj2LRn?fA|k_bX%0UQ^ghbRf0YpHi(~)KpNUt2$BdA)EDt9mD{*rTj@?W zSf&P4;sIc5_i3&bH9ad~E>Tt=H+=Q?sTT>3OR?Q!o9T@#j^rgoxIzoDdp7L+Kl@lra%_`x3xYQdYLN~ee! zxqT)Y%-R{Ar5TMTd!jesE41TP!*#0CZcr=E3A;F7mz$-7tqT^YJX6CX< z06rVfII%K2$QWwH412T*Az}TZfh&*Ny=wwR`&A}7pxaT~=7F?V#&|04yI=Z6c=a?> zN40vW?I0BBiDx zwUuY@Eh3I@ltRLryYn@5c&%SlW>25E?b+L_9RyyN3SFnRF`!ze-en1E# zMdn@>Y5Y^&arOpp$#W`&Fa5ynU?DXLK)MFNnUroDe_FTLFp&yz2Jy=E9BcYYsvC4# zchC?=T=RM_JQS*cixg8U*a~zNbKds~f*E8^(Hx<$NRA-?_YScmz2At$i@2PhLDdIw zu)lMYwjV~5HsJ3RspYwA3YvRRmkg3#r7)*z-m3jw&P#Qo(=o*cvP6o2* ztrn39Fi5amK1L{1_iZlt5Uz=utF>Z_QGs6bwSA z6ufxO!ldH?&ogC983txqiQ6bDTzz717@XN>16hKGVUi4Ufd`CGp}>4*yadW5%oYtZ zz*TDl5nYV~8_z_;x}}Q>Fkd4qzzz!<%HOknRt>@w+a6x5S_!I(Z(P z3LH=J%y5ovRANo_C3@Gu@W35~Z|y??g;-8_OQ}3|p!lQR-VutiN`3q3=q}eVF9AxP z2|z`#Z?Lu%?RS11gdj19qoc$8*>J-g4#A;Eb#yc&bWgUmUH?FTSiL*(tt!C-d2lrm zX+%XJY?>gSSjJ>c9e@Nz1lDkopaU9295lkLTSEYnxj_0-#ON{iYT%b|FUruLKk6qS z14Ud1pvco|F^HQeYCFvmLMcg!XwghN`s9izKFrIo>eub3yA@9y@In>LC=x=!j*}X4 zkrQvL7d0!?qtvUD2Gow0(E|LN4C#g7YSSKF^x^Yp8w(^ZFj-eDH*^$|Y-9$j9CYL& zqZF?b*|@#GX(ksy7Y?Zw_{1S>@lu}5#*p1Skkq#am2qYtjS(}Lprva;7SD%@VZ^Oj zRuK%FX(okpz$YDO5&Xw~RgyD1GY&^+2x!}MjtBWS!C{0CsjHh|o6_9h+vsHujDX;B z$a+*ygnBacQc8&{%2Ie7rJ6pt?RUYv$^kt)nASolv7`|+kMp&hZ~&~(gN#k-rn7Aw!S_DY0~3RQ$8;@y*o;2kGGav+fyTm52c^mYVA zHU;C8J;Z!xN#F$-W8Gi)!`x$B^++u4PdxcZT=ZkHS|KAd^ANpiSuar;Y0Qk6tn#3{ z#$xaA@m)pv@sqA?xHpmdK*tMEdMP6{00|vQq}ts~88pC?I~f)!aq2quhRzh#K~6;yp{KUQ;X$J%d)pgh%C;1)d7jgk*c%P19y;$^W&fw{#{Fow)F4%A zx4|w9JeW86AR_}sGeQMkFL79kZOeh^c6?u%@qv?4{%dBJDNCv@o`;1dk+Ypimj`^{x4wTQ#i&v7y|#! zJ7I|}FJZ9biJ&C-a)0QMYuIL$w2$i%+Evw%En<%K>$RMmz9ABp1Q=*hq2QuWxV=dT zAv^ez@WS4y>^F%8+ogn2HHsg??m7bo9r8RF{Z{W{?bP%ODZiu@-3-aBOzw-DP@c6l za|70)wNK`b*8<5EPm!i81WFX!d0 zO}s2y#NEUF3n!BvCP)@t-D`r)l}$F@fqu$1bl_GVCBj>0`pJ6jW>K_K=wCccBcGZ; zbn<|5eU}}U2_yuSb}^HKW!V5We3IzQiKvDsjWL*!B{W(?P&$F@I`~lPDbfyHXsp#I zCvW;0%Hg5u{$b+eD4>zaUW0ir^Ei8ci4x4#UP@o%hv~XILF&8>!y8GrGSxW81>8g4 zxv<(}+<9p#0rw^;PAC~jjT)PFvSjox)1b^cBrsX}YwISNfqW-}5?WZ>H3|=OP0U~G zp4#catbeLBF10zqOcE)e?jFbKN&HK0&=NcintAXz?`VqQvlmcFXX8D3>XC12Xdmw^ zE=lA}(oy!)lG@W<9X{e+(~8LS$kmwIOAUL{{zSeK1R~$raq5DVvI+Ek4A6)Gnk8%G zDt8O$4bkY#wf57@GsxbP=yUifQB`CgfV2K4QnPaU#4){o<-Fg#b3SZ42#yOSUb9?11&f|b8KGMl1&QLo7*L&J|7i4!LYP!^uYmd z414%QHV$ZYMio-j+`3`#!uPe7>c!>cX1Siy8<9mobvr+IJ04SsUsLJkl@E+Ku2{T# z*|ZHD4_5o}%B7wZ@a2q;O;Dn3Mxc;MY5e>?@*~@~LEa{pj)%jcfCnJ#-@Gu9b{@3W zxAG1fSw$dB%vGdjibA@2pE1+XZTfnJU}$@o(h+~!~CR;`#zZM&{XG{ zRrX`k$A2E~NwRitLP%5yP=*qNFpkAJO9#qRy}Hop!~f1m1S%mjs^P^0D~f?@Y~GgO2J3AH~(w@6{$>YSF&KK ziN;V!MKkJvp4$7lFJ}s%b^;eglR)yEDq|!DTBx07ha-OaIszZSRt;X5tK0^P^H&W; zZ4acYw*#C~@otUe-cc?J6yB^JSD?v!g}$H3SA}inwb}fm(8_B@q8^hbf1P= zhO+K5m#HI2-y}VR5|*+M2D~^l;W~aE2RiJovOF-0&HCC7FR9E5d7YN#SDeoL`zq1B z)aG*aXqxht23~8vAed-;HoDHA2AgZ^Uo3DfL)0}v)68=PRI+iV8|^#xb^HwqAGn5a zG`Bbfi3$*jV6}PTx4zPNnVhyJtS#(zX_rOdFVgTOqBg{Qr&sftex>%AM>C8~bm9r} z(hq|5IoL;z9?DzD$rh}uOMh?D=9t(6qMQ<|${K4KgcmDU)+}ow=9{)5xCgdi!`D=J zQEqiVsq~lzRs2noh4kJV?)Dw!*EQ`E{o3$6dat8g*xQ0GC)83Z?;gFjCib@jy|$PF zCsKdTB1hi*9}aPP?hC!0aRU7A7g0@ptJSRm3vNG)?JDy?uuW`7Hdy`dgRL9x%a- zB(#{D$KX5$jhiBg#yW}Z=4iU$%AhW6j3~DOEhgRUtfGsdgE5!fJ_Cg=kYlDqLoE6M zr8*xi{sA85xq%kzw-s>;(_yhNCaBQ9rN+~#hRtJmns=Ien)jHIG|03sP!=y$FZ8rE z3&}qp=5v=i{=>)+p@KjOLd+5H*-z=B)?oy9MG^fhsPLq&9bz`VdTp0K*Mi;UVS{@$?Dii_n2bJ4Zxyhsf1EU zQ9RkS$}{^jh~$B9?_u!UQx4{m{HFV5CasvvOTy*t?0&g!`O~#kR`)=@i*;GZyIsLS7ojE@>HeWhHomcC+pX^1 z(Zass31}rabrN*(yopYq9VkprEH0wjRY)**m(6D^Vm_$P7xWv~~J0w9?9 z+f0@k2ki_nUGP>s2q<2E=Z4?8(;5To==6r?&3uWWRph!?=# zuN(qo7aau+C_e~EK>&yf?Dbpwx(4+gpF5sEYe@luh2XB$I-UC1e|qct41R{c>jd<> zx+HX%&~_JKCWG&rU36_}?vDP2$K3XZUsFv^LVSkV^GB8;=%<}A;N+)A7uNhJqA5Xm zjq95abzT(n3^064bl>I@AS9&-`t!yW7zO5+t4QIl`yAbgE*-?y?7q-k&%p<+uweguU<=#Z9YqTnq$4FwU9hcFPTe8{x;2fg&OR&5QM!J<@>wH9it}Zt-w{*YSphb)oXOg0N~pRDgzpwQh=Lvw^1KtHg%c{g(e zf4M`r-aKPT3Xy2z;Qr5zImCyHDsJRwT9>4Vv$_pQo_fhkJf8f;(ZzaPMB* zQL*qjw$`A_iJ)_My$Qy)hnW{BDCH*G(5rZ?DN4pawC5mH5?`xm<52hs)>v8)Ka8SX zM6dTv<9+FH`v#0>NjP+p>{^QQF?G2|4`*fFzJK-$_o)8le?M1OlpsKvNw?}%Z(Mg1 zbB{{ToOE*jP}*vWo_o2D`PFZ6LAoDR0&p7Ii*SsoIyw?M_2+}NHH9I)DYf+#h_TA0 z(XMUZIMR$y@F(uLLq<(D#iHIK5|kxnbo&v-xTIF6~LdNKBFi?F@%|)g6!)M4hFSH2}q% z-=%-Reze8mwJ|&M+M9Xr)eoY}JLoCyUBK6M1}Z^b3~_0Lc0^*K!Rl4a(gr6zCMqy^ z%4{+7Ay@N4$XpT6We&}nCHvo;OdDbK$7P)xHBN8ICF@?6G_F_|^UJ9W7sFrPXCX?12B{r)yQX!ll4^Mttb%#x^AzFCod zmPfS$r*U*i;i=(0A9@@F%1V>%brwn@E$D-PCQk;H*>E=_R9;sH24dC2Xhm?E?ect3 zGH(ZFBy`l1<2vp~ACMQ_n_^qC&y9*qj~~PH>bNSg(7*x@wCC4=z845xW2Ld{-{E<3 zJZxYlzI2QRp8>I$KiA1cGft$io*Vy#v61PUZ1E4OOYXTQ4ik+9&g0ZZ18 zdxl{h+-tdZg~$C>h+DQ{-!55!V?^5XEHiQ)I3q6rdE@VDs&p!Wu?|7Lf%~Z6#cz>U za%9oTS)aEm+$XwtG(bqqsJiYTxTno8G_tWDc^+t(uxMKL6dN+|S|=KBDze$U)Oj#G zUr*F{mwb{I!rRP@t%>87$R+%wavaBVBcTHi>2=^dX*3~oZntIikkl7^Y$zMVvs$P3 zHW*Ppvx-|6V0Jhx%E)-(^XMsesQ{*<$ELzwv2P<_0gee1z#O?l)?^6bJzCdvL|4W{ z>gB})9ODC)M_nuGXcehsg{0I>yJqzCc6~ez=M3_tVcQ}by1semdxsC!tv_M)!Zjh0TGQK&gmb6r&=ta0Bh3A_g& zb*^rpy5?h9>UV^8w~jv7-*qYloJu;{y)etWJloznPqP z;;U@nvE*G+_p2*IZV)LjDrFpU49`wGWSgoktDAmvCr%T232V`rl1@5C>os89HvL!A ziKKd7#-988-mK31fI5h=3RQ|;VgfE;ilo{_$f|nbuZv1X5>z0i-!;1yB_La4eVQc2 zd%$s7LzBqB{)opfSW?Zq&CbE~DmaYcaBSMp^fhA9V%?hE zft{cuDmpAtAvA+)Zl=&j6onO8Am4d5t1KH8ZCCF|_O~ie2x4V0AC-}D;t|6RZt&*U z_z$5c6(R6V0=Z9?T0|)*E5S^I!~))`B4%nc=J-0O07tUV<~SZ0l=sIF<=$9_GCOI0 zg&ne&{PS3|XsnAaygQrAvE9zH#2qwszF<$Us?}`lUHPBPQu++)Zt`Tn8F8uoli!^y zTBZpy?6L;!akfrXw*-4LR$HFrnEP^3$_w*aW>D$-zwtrg>zL^W#8ak7XK3Lh`6*W_ ztEp|f63crzY&x;;jUL&8c16l=OmFMPrj02<(K#4(MM;S|{h*7t?Xj!$UOt0W%D@*C zq=U*5=B_wZekJuMc4nQ;3M|HxuVfDgdkqk~2Yuu>mn@_{idAwzQYj8|C`rLn){61B z_4nav$g&QdEL3h-fj!h<*Wc)y9R$8&j&ON)XMy_gQUSkL`+tiBxwkNKMZwR#n} zC-n28{g4-=DNl!X{c9U%)9%7zR*&0u))5u0tjZ@lZ4md+zK}v?Q{Gv5?qSpMY_)B> zIoSR2gt@Z6d$3pV27XWj&d9ya%@90~ab)Eq$C!_G%i!tH=mJ1WhP&d4dBXMA@fY=8 zsF>(uQZ;aMzg>qr-=A%@mzRiJEb4(rI^c=tkrci<9nvfey&Q3J9pNZJ0s&pVxzA#=@!#pp@yngvh7EKlLZh5RVR@q_GMkmhYGYJ=V zkEEO>Gl^+e$ALUQZV#N7kMc5h4{+D)HB5Fh){;51|D;O2Nciuah_UhV`Fe(`46WW= zIBXbZkVj%-wQBMoej|>(pRuLznxN2Ot=9ja6ufy^Ga)%_+AC zbrRVJ((M{1*!(mw{L!<1&lIBe@}noNmTZzeeTe)V_M%qmY~$%MjN6P~8F64K0ca_0 z6`3zCp2F7T0)$Y>H-0lE{c1oyJGCJFe4Ge1fx_?%av9hVkopvovQu;XBN6V9zM>*G zebVgU)^VsI%1yoZHv=d|M08Z)t3cFc7|>}c);K5Rz*-v@6`a(I=iLz*TG#Y7RhvGrybFVl+7GWk1y~ zhDiV1I5E4Tu(r=AmMHVqQk7`AzBPD>iSD!P@X!<+U97Yl55$MQ2JKw7>a(leSY=R_ zF>UozvU@lo(`u>9Z8y)Q6a7M8I-GhtzGRb@=*H+nb=+jEKc7)0Q)*gUs~DGinpbX1 zBU30P55sUw)sC~QQ4n5l)TK?ycAG@QnopzIcvr9X+HpCis0`NwX@O-p!vvZc#@0%l zo30~)*4j1q67cD;_b%27=>gAcS2e)nDG)=ri zTS31aIKD+yP^yIbs$fJHSXW&c8LCE0ra;~SQD2?gGoeK1poZY(CJC5^1kE-AN7li%aOqmg@X*)I+7$wQUHq67ZFvinF*b) zfx9@k9=a~^B16KpD~SwRCZB_JR&r-?|M`cHv4^ijdC1~fDrkp{Ml>GCiiDJ*>^`== z@fbASbB>Ne8o4wer-D<`&o=cmUaCfu6**tyYnrgowIIX?9IhCa=izN`a%tKM9*?fM zAUp*Al%0S)f+E<=t7_9#z=>MX8#pYh(h?=N7(Q+g-T&A>&`>E#BTW z#0f&XjG&ubbUfNXyS>J`m1YMl=hv#&Y+E%_VJazSuJfiO%KVMg>pH4w$+R}28bg}M`4lNSg$K=LuPScd*fniOd1q&w%*v?RIq_(8i>#LJHV)aF zY!ucP=a-^~f%^iza1mAbs(L|vmGGh+6wqk@R8Yq=;OQ+7=6ZS=nSHg;uokIrHgSSu zb|I)8AKaoMVj5beWlc&>bc{!5rZGUTB5LCC>Br=beI4nR4l5E?sh9Gmv>IlT#e^RJ zkgU|4qwx{~vk0*(x12^xa$nBe+(&|( znkrt@8%gBooKPlSO&~v#?IH1NUz|K*eur(>>XtQ9GF;wDrwvjjS$30GRlBwR#vx;@ z`s1-x`s7H1fBcU2_lAoZ@r?(xQ*N_@8<>M>J9VOAzvP*Rd7uJ6I4w@*fN3`^-*nVH%u_oP3u{g=) zLZ;J<$K8dbwO>&7$w7vz!x%ex8P|!jKK{M=B=qu*y{SQQ&{&K#_F3{W*K0eex2&t) z?*g`E8MP+^yi(Wx=fH?wKQC<%WJjL{sVfF~5*OFk_~hg(kM0-MyAYw+ z;ad(ll`STlVbxt4l?)$#RKq!P8IV=MQMaym+OeG|FKrCfIf~YWlJfC5;7hEy{8`@XIc>Bwl&RM0xN4cQ4;JGAeu|A@Yk3cHw^ts=9&^`h@V8@e z9rt-syWz=k)_6h7+~QlK}UI|w+rQv`jPUj^!%)2{LypCxZCyV zAV&W$SVSS-CS5twCb$>St-Q_Bi_S#pmS)Lu z(vCz+!cJqXMEKfH4c`{FZ%qYmj2k%4yp7jNQd+e(TO2n=ij^Hz- z7_`E27zTMFu3pEst)|4mTsAb+Xyw+{6`LuZ?mJPljn}UfYM(0pqtlIxB{BIw#_v{D z$~h?ySNvJEZ2k!wwL3;H=xUam1SW9&o#3jF(;gn9Q^}^Yu(TeNEG=%Q&W{J2bLxrg z%s%5W?63|E-+8Pj}3NnE27bKz50 z4AXg0bep>!kCJr6iH}5w+FkCgbf{u-8p|xV-`*~3L@J!}C*IVN2|Q+$ho7%5;nLO3 zT%w#(i{gbKgMVDWdCaOWhw@MFtz=}D)k2^NaVv7I-HVhSKFzJ_IZYoHaC=(F`I7XT zYdMR=3Ljj?VE>XPnFiyRPBO-VNeAm%r`M@qh*UKc>o<^_m-M-=^* z&+8a$p`&9NbbOY?K)@$}q{nRZ2S30b6L|lJIt{k}UFGmEKAWAB?O&`l(?5kJ%&h-f z{%<~;k%5ho<^Pe-c6BvX!4=4)xdsW}MTft>wi65jrGtCfzs4d!*xcGe{@ed)dS>o! z+tZy7azAI^mEGs(=X_-qqsgk6qJk}A29(;^;W5X}>x#d830=r{_>r)eJb1<<&q}FCoopxgHQ%`*dsd(s~VgDomDmf zH~uTiY%D)z_^Ce|G}gvO(7Rvu8wBPZKlRu5GXdS7%syJZJ=T=#Tp8HGfcoF+@jsFY zPAv`Z^dI`)Q!hWl%uQ^qPCxpCKO{cjKL^tQ`rrIt4RT>>$HRqerD{K1X>CQxZP*ya zHrFOLU<`~+P9Q(-x?5l%ZgotpfYcjYnLh`(fEb!ec}cE(T&u1rmUm|Owhs;}TSmzTS@FRY*Hh5p_@=C(%PD+CyqU~FPqnXRnH z@O9;I7QR&|q%NkL*yaZUS3PiDqOaZ5kvC4aS7m>C7ht{hRtqgoF8x*)$c`bk@5F;k z$mpU=w!_q=Fz~OHY^kdv=iq`@NJ@7fA`jHfTYTSs!Q}&Xz>cE46e^m|KB<|6p~dxm zTiMfnNoWPM*MAmFUIOKoekVhMTJaFUd^5wtb3>^JWLbD=w`ruDPTF+PlpHjVzG~vs zFU~1T?Lc6kxcxX$0vErjLG9f!R_1)#zSk?<8?vJZcJ`4Ngjuy}-#$f~?4U{#`H=}?|ncT#NJDzry*c`i^rD#gu`1pxag>yv=M*n|%S zIt;F|U2kQP-O;i<+S9upy#4HGy9qLnoUGIAg}dJj~Oyc6%31V?*<@s}{YR*s?l-W*!z%S5lyD>r?s!*+=hpT6*Ums@5BbYUk+%dUoFTOW zCJReMXs5b+02j_oY6{*>bmne*#-s|KHR_d(WiQziD_d;${0ciAb1D0T|8f{atIr`x z>|mib2f0id`?D!uV#&*+WiZ0r>7^Mn3WJZN|7SODoBoS{xG*M5$Yj0*Rw{jMA15ChLj`aLNqs6;&DhhJExVG6;^; z6m>`hsT}NgA_S*-&4Db;A2gZUm4#njHtDp^I(g49!La)QvcGuN4cu||`+GP8HkSvx z^LV+)w(7qam3%fQoMu>^gL(bix#7K=$mssr94^zk=4?U!*zeV@KMY0QZoxv zab)5ATu6!0lw@I)@GS+0*X>n9lBKqJFYHOT|H0^%xw$lBpW<>EbFNzb`Xk>SL+%w# z2ZqYs&zlF6_ZdK#FoozBN6`R`2`0OdwUxbR^E(+ndzy~0K@K6Z8%xHImf8M$;erB! zHZ4k~SmUyg<9T9<<;J|Ln#aBFS|HHiHs5*s%u#QHTK^6#Gv91i;`FV_HHxNK2hs+k zAz#C>qA@}vK;QGDk%;o7#XpoPaEPoV{f`b5CnM6rU~u0xSfrN~X0hDuSdkJgBSOZE zB??PMgy4a{uw0yD*XqUWWW?(%{DlLFzan?F)7QnQ*ynr}94|R!oh-E1USAXdSuMM! zQFUBQPFVg;Aj$-vxaxkXs_GsU(eEc(i{_BUMt?H~JGd3u{>coYwLTswn1FOipFm^E zxU{2+PX>`k7#rlqpqPZsy7`vd!R(7#sf^NaC6NZoEFhqvdNIG*S+K5PRA+!HzSnn1 ztuVYiB^Cp>&01Tad0kKS=N0pIhW7V)I+!1z1|=>We~O$J`P>k1E3AS=p~SwbOX?9& z)bZdpv6@j@?@B4`x`Jf!Wwt+={XH`Y&3*j&@XVoBxt|HKCpO}T%&{p)y|?#<$zQIY z6*Am=DJ4WN)Q6JPJ)Cyjb6Aod?|$N&s;z!>Y^H5zLSR^!b|vzWVrLKoh?PvMqJW8KY*>{UxUFtUYQw7tvRe-nKYIx34up?!9L&yU^$A|J*Bl z)W=D)2#MN6RakGrc{Wdz~Q zec`4F6(|rq**S(;A+)P7n?q}AMGZQfT_%*6Wb09tC)j;eaD!lsWS8ry*;m=zeeKH( zsv@Lw(GA1T5_u8b6YP8P%|?e5O++$Oopl{TrWaSo*?HCo}&BSOAk6N8oVU$Nvgy@!Mhjrl6hop^4oPlR&{sr zBV}FPmJ+Oyz3P-+eSIVSLxqYJfCdZyW8JkC!Y z+nLZ}&Qh6#y=EWzyYIrdo^4oE`ZOY2MmMo|{Kj~oz^86tr;mNfnoXz-NdEPXeRi2t z8}? zPQbeOj9V-F-p?mwP2V{Yhg6!ekc55n#n9v?2+L+#v*%H#SW-Quz4ueXZ3~K$!|c+g zPFxlu)&C461fU|?eVxUDtk*A+w`PB*V)R2H4@yMkS9MrZxaR(z{5CpQT^ig9+1)t} zkC-lTzCGfKHL0I$kg5la$%&G?#nB^}*__Hx-O^_O?kIlBK;x!oG;^vhayt1^Ihvif z7~wn$7H@VeWiI?-=h4XYP0exbFXaoKZzDSKUX<9>6})>c6Npt&n`bjAG@kKeyz3yI z^iBBN*}a?O3l$cQGdMW&DXam`!r?Y_&O_T-ei~>mz2A(iLf1Trhv}cj_70I@$@}Fo zsWzz_6i}h_B$sneP?2m1OPt&Rn-@9w-LJW32UhS#D+ncB#9iY37cR*A&T(Gk&TeUu zjS|##UPi=%n+}OfW{%S*tb#FvhUm7e0F8lgN}p%NL>>!Sc3?aV;b%tPc7k#5!O$|e zG8fAQx_-RtA}{Xbc5rwmRD&EbB;{phpXXNbtA~_ZNXpAqrL>Z(NvAt5PCIwGQN++S zuz@q+4!^>xZ~GL|7^~inXNf&A)SYBWAv(TiW9MQ9kI+h?C?h)ihF^1AnazH7c)-Yv-t(;Dt2~sJaN)BsyfYK%moU1dp`qZO$6~>Knql9 zn-@FincEg-!}Pz(FdYd65_n*2OJ!TQ*MH_gXN8aKBl%9EZvJ(+d_Gb+tsN3Z5Z+dU zL%jL?sCcURdsQ?m^D`!)1z?}rck$8z%|@4NvRuoLPpFun{}yJ&6$Bz11rKr9Z+)PA zhH8BT1|#BY_zSj5tnk^{H<^rcT}!y*ql#l7saovGxX_*)SV!FY#P93;u#Dhjo9(_v z-k2tDBTLecUc3?$2fN!@zUp1tJSt5PUUPt}o*2sv{wRY~GE>{VnxRTJ_`t)(ghGo~ zmgBh@v|LJUpR_E^YZ13IZ@lE7n~>H1Ey|s^3{`I;+rG~2N#q3}O{p@l>Yi}S6o%8XLm-OaQC7byhD)qM0ujr+ z$L-&F3vf|5be@-Tz_d~OLfkmeiRJ^hmE?#ni@SBSDm*y-V*M%cV?;8XVWV4e_d%kn zm!Z;26e%uT0Xr9T93quOwq?R)7+yrt3py}1OS`P}=$EEWSd5idO3)@cXHxR9u+y0_ zP0q*TWnyWB3-sma)i16GoxM8N_C(nXOqX~-c-wcgo`RL7OSB2g_3xwBybr>wIbbz# zoGqDG*E(r3Q#f7(Cdm_x_O!C3k$`_X^ZEn+r$@8=XxvXe?A^ zA>oPQcK?tFt6r(>KeqBj8ORuY8lEBprK8US20hS1Cgpr>7Z%i_Xhqtls3dmd!kOR1 zRGa0)8w;Lt?U)~&^wS`|hDYSlLzwrHHUhdoHS#*;#$+N`+w>>AN~@Xtu6w}-raTW% zFyaI<3-t9Bk*hHsOG6J>-JdPc8{Pkwj;O-##1*mnH4!7JK{eNU+AaK)1y{@(B@Db@ zb}j0zAu^vk6SM?$x0ZUQwF7#}@9P!3$d|>r*LyKu>~$(pGKbfig!&PLIh*mV2PVCN zz4I`Ih9nCZw*4?~GzA#5?C?8Y^S3_cRJUgR&??cijlIxh_5N7|v%qy960~hQpZ2mt zxDgH;Usn~w?M^1%Zb)Zl!#}_BgTUEP zo?*y!Hu90D%HW^dxZ@v>8Uul#iq3r5(Vl{7ivc5{fARodKYH@gm0i_yJSQC2wA#pw zw8H@Ekyy_uwe{|*?z6(lQxL}N!9C9?2!F|DDyW!GyOP-4=6$2;(aWKK+`icRVRsx+ zQug`T43*Wr0q!YG((osqa8i(LFpsN1y-h8r|JRPn*o8T5j2@u^#A--)za(NB(HmgEWs2n)Ib!w-7URv4=-SBl{afP!ikoCec+dwCeyx4=Ig3ju+l(26 z`9r%pw)z!?3&39S2-`rrdB3?v(h~*FT$Ih;1lu+#Z?P>Haj9AHlzqAWm?3YWT-)XU z|1tJXL7G5IyJl6FZQC}!vTfV8ZM(W`b=kIU+g6utot~N4|Lll45pyor^}5M?^35kF zA(lj^{-jYL*DXSMJA~l!B!pS@yJL<=sQagVFe%DbRlaNlgrt|Vgs0>XKL2qQda_m6 zz&OSN;en>OjAZPc(Q!8+PS$>^(E%u+5h2v)a^0@Xd$O^xF|C&WE*vFN$^bfyDXguH5N4y=JKWUVkIzIYU zREhb7KNHAP1je2;s9?-kt`O5~MR=0rGvzTk{qIlV!87@?ZEZH)pW=G1;^ZDo$CUmg z;&?U*q*__1TKaQA@y;|*BDoX=%&_wE8YTa3wU;!Dl+pny(L+z`J#* z>5x_1Q5okK(8IhF)*#U*M$w1YBU@!s&x+>&5jD&*hle@sLC39R^9;j*b9Oov9p4Ej z&rl97YN7tOBWGs;QG)n{V6p76thX?0AF``zVArVQXRp4QM}#|;`qXy)_6E$!!ydhL zcKTwfCVf#%egICs`yO8auO(Wwb}uFlda!DUw9AKh+m89U+RMVtK3Kdm44kc%%qBS1 z?)s@9Q92Q{CQ>f!E8PlLB5n8?#iPFhQN8J>0#-4=@_l}`n}aKfUN7cm=KOXsVs zsQ$u+TClsPWX)0_GN@Q|KoR#L!J1@7M~ zxM&U7+$4ZblWVbpUqBivWqOHrTWU4(2~8S#ao0~}SmM!<0NJehRi+4B^l@O!9V6=d zXGo6%Rce8{da3Q;R-!ycnf`pAy8{dHTMz?a`FJOjEcR^ae}z-l0`$v8;%c3OCa-_8 zKhbUALSfkUhjUAaLlMo}xPDzv)PFwC6FeUmkF}M_o_k3=9VyCUUdq5XAo{kM7gHZo zEu4y`|YW4v{ zHyXyA8@tX3B)lB>5Q~+ofA@htIC@eFqub}yQMadE*+xDpT3$;HN60eK zi6&_bIkGC#hRaj{I)<*<+UurFAcqWtpj3oJN6B~fUq~k7x5p;@P~XG_K7@IS>v|I1 zJ&xD+o|GJhC}sMf%nW84hW0ID`3}IM?2V|1OjqqZg!z%F`aXVtn* zai46Ow6aqarKPpBhOho!{2SF%y;v-qx07tg)!a;jR1@QL%5*j7W-ddDzN>29}#iVSnU&4-JAozye|YjhaZK*vKO32g249r>Fnd<*qt zQfr<+vTPX}EoUu`gP&X9H-4L==yr_imL3&ye))}zOYN2%0VJT2t_dWwf>?^jGbG$> zP)Xya$ZDXQwr7b0uOB^!fdlT-gC6>L&p_wTPDQx0_e$A8~{a! zxI5v*@OfD&eGMZEboV??07&Z6*WOnCE6DH&Q@d6dR`#h@pHbhHqaH8? z%&q`0N#SJe3_Pr6H9g3NDcjPMJ^@un0i&%@9%Uveg?He&IVDx*?t>?m5pOg}i#E-N zDmaV9hwP=9NbIq`+Vt8MB_Xc=41hVE-tHLsav8F@dj!fd!=<6s;@HRv{EX8qOnU#z zPt66W{j;elNcFIIcBH7>KFM-ph0ItnMp!K1G`S}+GNV&_GHBB=dpCNS2gS9=uP10w zZDBnj4>kNN{m-q4zhK#9CNkLvD*H=0uvVugXM~H>iY~|l5_iqGzAF4Am8IoeAqkx| z3b?PMYF%2CiWs-IOwHSnmD?f>+9X3O-ne~!YOUx%_94kW=qjdXn`2F|in#7X-V@3F zA`ThXj^E0H+)ikTD^J(}71;odw1FCs%Z`$f;%Y zy_7tYoTa)f{3X-Um+w)89js(V#%|eSp&Nw=AH7|({VMOdxE4%tZ{T%k8VoBh|NO~z z1gntw(g)PEO7ny8t}}pDb}*62Yn-wNEAlZb5_`K5akb7cI+Q+F(j+}az>*huMR(B@ z>9o|R=`NdjTwBT*hT+2PA=~~U#;PDH9uK1JTV4p9bxF6aUErP{X~Nl)3e`Jhn-yz8 zSxunBWVUAOo`awhi8)lt)l1zNL&n42_4u*9A=Nfgf3)d_8iQ9^5Qt^J$(4KtXF!7c z@a!(luX>Z*vyh~zKyI?2Howp;wSn*(wkbSBty0!Nk-KWNK^~N~r;lKv88Z>I4p06X z$R-NlS-Fv9748302swF_s0rZOXrl(swAWaQjVaxr&axTGf1p45{5mp5Pf z{8=|YL7PIe9sQQnZOLUw6T(l;&TT4oyNqyx_9=!X?W(j(9W_m%dz&)%A|#u8W2v#n zml5Zpe>}VH%>bKrV|8xq&rRk(YL-CQNvN(KhLarn4HjCy_e-~}f;l^hzclSfxW%WjAK6ICG%eh` zTcGqx{=g1?z4>*#4h6Zska`n3hzsV=P4T@Y-{$YeXTRQAR)F?3BfSji;&vyr@4&}L zS0OwF?owz{5z2~7XYotS3OmlF5=#9$aQ~XEsahap)_cUWQ4}PQSjE1dofer~G=_}mWj^)>lJVS^a zJ#}uE7(0Tmb2ExJuFkXP37XA^dHGMeM5 ztN_(^G^O^PGdXfrCJtbbmYgKi)nZwFO=s7J=sL~8H4EtqY6sS<+eo;;%JG1%voCk+ zOdGm9)49TvEHxCy4ZmDvK_h!Lus}YSsOWJbOH&(1Q}O3x+{qC;}%|$EQxjPUdmXvP+wmcnQ0&~OkutBJ>!=XJQZVvRM1beCMaK^2x9H2vj(>zm7l?i z4PB7mtjyBobSg=&oj8CDVA^G9va^XpKMCN+Q3?5!a3p!?$&a_ToOhOF~yz{ zMGyYx;NK)^5s&2vaE4=t5pt~M_U~Ub*cma{zMKGA!TaWE)>J)btK(Az)onG4cyxmW z*@9{n{lSm~GOmb6rJ7o?3Rd;C$`F!UEc^}+J{2ZYBb$T-IaL1`%TSLWv$5J-Hf1(^pS%tyZl6AK?&tW+|kUxJ%7iOGecn3j`oPXdg2LYgQLG{L)YNoY}0I&Nu*h$S#r9D zdv`tu0;N_YMjQd}uBgO%$K8fnKl~24r0{wnsFE6V?@a3d2*@v|lY1L@--CtpfyAuB z(1IoyOBf=6o0O+TCr@}RB>UyyQM8*?h2>w_0tY#GIlGKwdWvkZIM<;={3YD%%~{D9sU-{u~y|3O&p zqD;k9m?B|Ha8r;r&WGRE+&6<e%FbJkXK4jjaujVwjdR!De;WHFeqm>t`4IE4VG%cjoeN%e70CANbAtg^<~jH_s=O ztlx-p=12O5i&b7pZ{kle=B+DYBxeyZr?c_16yq4jnWpWPn3Wim(taxqntsb%_iiGtxprAU*mpYD~}_)Mszy5zVai! zIH5A#xzwrOI87y*Qs6{r;q*5mKW;23`8;UVBY;Tx7*}~9?&*lYW$Qp2Uu{;KFP=~9 z@8=rk1$%eZhAa}5qEhP~WsrR%pXc0ady9Tl?GJ8)|3{5c3d!84BvqrR0$#&z&W-M& z|2?HED2+S4bg&eZ^nJP!r_#=7^$l6XuKAczef!=85{v`sTh*yQK*l4ywkaCpae0SR z#2l@tA@=z*X=OEm+yO`)kjoj~ZRGtWe9w$a<)2xnZK#2Oc7Xh>(L~SLcp8#9NM1*? zTU^J1KB>t6vp?;RBG5er;tY3`>|Cpu|6(C{@vLoRWYbFsEeV6vG})m9(YS=__+{i6 zH<`*zG@6BLJ&wk(5GS<9Eg`_J z0DhfUlDXNe45w{9EIusHyWCOK>601QUaHw4Bc#pw)#Y!9E2gHDkmV_NBVS>!PHXr4 z%G-v0!&D}Mk6~Q}ddLFzf)UhGcIAOtTgqbp2j4Y!+=!z^NbkMpSj*pRn4EhfJ}P3) zWR9KfIhd+_GGc$V%%e%Uw$cN6I4TOuZ-(S)F4TfYHB6tqe=ZzkC@j2wG`Z`$GPWuO6>9uZTLv@NvTn0Q@3TV2ug# zP4Az#B&pVa1Fy`gdQO>$j^Si+^D@~-RG+vh7v#CcJ5e%avC90VcWWwn-OTV-IT ze#KISpD=}ZHj=-Rk^pT3+iK#-CGA7yjov{mp z-0=2#h?@kQ)}s)E{;~v+3$k$6ES=`76cJ+@=(HkBgRD*D5N(QwYV~YEIiowh^X(2J z^r$N-5^0N_pky5tPJG6NKG9nVzo}ZA)ZXyDS|EeWC_Bk=t`r7|TXYn<30}##aL+INW&9@t5Wi!ldanv-G@+^-TgN%1(zKZIOb{-&h2!R3-e1zaLamX z7118C@v|tVa=rl6T!>ad%0>wAHGUcJN}DSwB)O+t7F~2Ys=Ga1fOY;msVWXht?PLN zf^fbnYt`o`r+HBV?S^GZ_aQe!og7fdfCufw5amq#8dgiYf;J%7MO`B70p4`S$Nl3D zwN%XUNP>zVn-AWK;CIeT;qL|I-Pl~XD-?USw$+Bf9VP3C8d@Kv>DbSpZ^USYaq9=C z+yLIVR{K)btMU^|tIiw1x~VS@$z9KB1OFaa0Z&FRW#L$*Z}MlndXQe;Ro|+0L3_Ox z)<6oas3@K(6L~k4dXo@6Rj-$Gy>#ZRMQ4iuY>)Dz?)XesuHFvexO?}fZn;Qm!es1( zd=82bDIVrPP9I!Fjn04_Q6_3oGCF`}9q$Fc2WEori~}TDeI8|WZYdQ>EI;pTLZrU}^y$vH zm*ClLL;i3rC2x*EbnqQiUncI?%4^q;7pUDZ$@6l&h|0_So-5bWiaiSJ!5}s7eDcfV zDKjBGhChpmn&yRsj+)TO#vb{Jb^w{Px`}8XxNL2RZlm-ZflFE>#fB=blS;^(9%_{q ztQw4@HD-=&WD=7U`U}D{V^#L_BnVrs1ot}KJU5+Q0>SfQ?rxfOlx2x_Bzc<1dKyl$ zCXFSWiB9Zle1J0f6m)Oa}j*_58WTeU*7B!ek0ldaUQh%0%DDj1hKZYAm%tq=BaMvSBjS z7f+hh8gji++GH|Q{pO)-_JeQM-N*my_XpSPMOW=ZSMA|z;4ADtv6KXWJGmo^Mi3M_ zYz%1snV3r>p_38GJ-{v9ZwiX;lW=pgKABp(kKin))! zIq-CVmGBSv1X?I}n#ixKuE5?=Rrf*8KQqmQt$&P+4g>_ne*x2wP+R%Kum6Pgd3e{+ zL=jTE_@!jhC=E{!gB?rtEea3`kYWo0ZRF$5)v*3s0gdUZrzAv;5Ly3mTxlfRo6{43 z8EYq_MEv#n6)Heh9N>=@pmsV)vaQ3k^K-S(>M95;J8J)T};LjrgUp)TWkB8^2 zxlxdRPZ;9ujn=yzDC;jU)XzMVA4$cRK7(&tkz0HCZ-nWUe<9^>f&+di^0M7HNYqdN z_h!fzOje=sW#HgnQ4+z!_JTz}Kyx0hO&HLY5#)rpfzK_NJm+!myy~RT;ewq7u-mtP zcQ3$D0|yL#`eJbBAfH1t}r^6$YHFq5mIk> z6x)58%Re zNS3y*fAUSCo%OY7I=4N%^63+bQYRzJvEjY+&F^4Le?- zUlLmy6e>v>M>=IJl4_r#{9EvqA-aC;4ro^VtA%bd(PM{ZeLyJ+NWC$qhU zpcRm&&3pmxQOx~Pj6LL#x*fL@HVF8G_g!c>HOz(|jVm-ap?FapyxN3%@X?+(PEhQd z{xzQ_k`T@26Ya&#@iuMrOAS{&YY9F^%8a7)(7hH#IPiMi+pO0McUEoNU$-de#&)Cb zboE6injuWds}a||kQR9lZv9Q6FfdBe#PTb8dg@#H6YLk=-JWvWPZW$SIaZ7UKU;!! zINrl7nY4a?@{G~24hWX%Stqf?*!s+)lSSI%NvK?s>=z9iEPs>qaH#1`Z2Fk(P^3~( z2H?Y0$sfa`M6-;N(@Uz8u*|n(ZJ)#OE4@`?MB5XAH3bbUO*| zj5S}&KXiPHK*36^yRnm~VhO#p8aS#7Ik?w9Z9P)fua;Tj3G@m8gPR&Pwm&(c%VZRgrN!A?>3OK|^dvmf#-QjkylyB9h zYqGCusC8`b$n#9FJUlmwsPgufb6oTCWpd#;**hM&St{!+GAp`mNDu?#Rv&!tit*#A zuS(ly}}$1Aa$p0Sf5@t&3kqvtVetI?Lv zO|$o3s1BJAEG{hjFaj(*T43kT9*KwRqACC>Q(96k%m}d9T&iDM;HFc(d^Md>OGS9} z-J)<$K5G8~Dil&B3!_gf>FEr!!A`QNzlUqAJNN@vLrb1ab)49X_yRmehf90X)}I_V z6<@yn5O4c1o=06LAnD@%7ell_!)f`hhPYAfV}k*e9(QRJP)QeInX0TDf~>h2IOa;N z0n)fdrrE+5Je9=?{^HU2l)jNhf811=%9mc*Lscv9ho?v|BHF(@lkeoQ1ZTi(%V)#t zT`GdkAQqG1k$Z>+576}AosoE!KG(1LYU%5^3O#bEY$yTPU&RY7ZYFOwg=vya5>5=Z zzb5G^&2bqp@(&2-VlCUf%R=-%QLLqb=r%mRM6iJ_1 z4oOIFKW#h!CAE|EQuHu$6o}k~hXq8+08V$+1o8-{=R)$Fm_{dg3OM)Q2^zs)*K@Vs z>8ZMcR=OxW7cNfb={BBi0@J{q9Tim@>OVmNymo&rMo{D7JM=Mp3e92ynvXR+LuRFo&sPk4}z1GIjw6EFGk*-V@h20m9dBjKc$HoY}{Y1-0 zQS2?+`6~4DNGRSnI9Po*Wt*%TmEvaLKz-Db=Ah*Ykw>a)q*mPLpn9x*$#b>@y9SRg zP}i>=C`Os)_h(}1b&oUd@7!?Tis%L}u!}j42iuj$1!rn7ieDh*-^w-I|NOSGV+K$q zD0+`B-mzW*{Hfp~G5^ z{-i-@+lRoKNS;(gO!aopJJ>fOeO8JoY_>wDwR z5BHkzNi&%8htQ2EX<`-(m9t-QciC!kzG|p(_ZxFfc>obw-{|eY+SmERJ7Rrho3Ojx zwmCO~%t2jMu55ku#F@NtW+B`9)u(e)4huiSM6Ig3PhU(Wez*6}w9WKR{!%JdO+17S zC}-|C!KVS&!s?baYY_%+P9J4}hx}pXq|Wocd=&+PVsPmt%nTJ7d$Pg&_qF%-xbfix zEE1IG)bc6f=L|_JJnx_RLAe?%oQ;1H!Y%6`YF-pIiC=o2q@(Ks?S)Icrh2EJhqTc_ z*hjO!P(a&qHPw-bLxYc>Apt#zvsPOtu7sgdpd0q|ra}FJsQKbDt z1netb?)^mLwVdhv(Mzo^*1(#!z7t?toA(sOAya<&24==-T1sjnkfqqe_RBvTYh)Ic zTsHM=K!X&3fEdFe+hjix7v5k_T`s6Mwj@PzFQ~q#Icb66Z^4e1`N!Mrzom|I_LjRi z0(38WE)wi`(bRm7IL$4((VT-KtlI_Uz4~30zYW}Q26L976IoGFV;b%|ZaU)X+9C}i`s!8>HT_FYkoFkJ!_rDSq2&JPs{DJp-%Mq4?uxdX^%9rk(2&&DF+h9(Y?RSxASJl+mI{ z3OI+;+adR|VaZ_rS%tZ#c`V9fugibqVes2QG_ZkK zB%<}<4-na>(B=_Yj9QG^l|J=0uJ6fi%sc+52tto=HYRJVb`uy9ps*$SkFkeJza(ua za3!acyt6W>&V_OrX0Y!p29n(HA*?z>iTlv{^H6W#t?%~m~7jk&J1P|S9 zprI-~d-$SnS~n#P3Dyoi4T|uhwxm175=U}boE({&5Y#`Ix%*se*ls3@M>q#9Q!~4n zw!fElr)lw^^B7}+JzE>dgennOz#S!B>vgv3Biu#x$#;{!`*nf;co`2LM{{7yWr^`j z9&tK?jsb{mVJ)*ja{Y*UufI^p605BcM{VsbO0eBOW%14CJTq-d7YC-DgSV3O8bAh^ zY}ta7#$;Y%&+tEIu3S$$A^(2Qb``I-HyRF#iwA>1ouN1-wOnfHC@SgXJ?&U6aK+n9 zM=EHiofn4p)ej00m?n1+PbRX%YFHV4U^>{tHY?l?+Df4w(!Kxl%!JX^)MMWIDmaSO zp`PZ4Om42)Fh}`SMJ)~$9;Qkf0Svi8D@`Ayp1;2@Wpa)t=Q&%sOF8oAOl`Pk`_lqk z_oIu#&Z>E11tev^t)iGc)!JqopVxhzl@mt;-*h_z`o9{;_s6KC*$h`OA_vANN%Vs2 z86DSF7cu?WBmgF>yY3L>%L2f`*b~mz*o^nr!dx22+OG?T+H5U^FE|IapZB)QHW(2# z3Q6>=;4k$!CfjtcBVAU`Uv74F2lt`zxvCJuD2<}28z0o_*Ml6_bRS%JSI`pXn%YtL zda1}~lw^eyoY-Sk>cAA0f%PUyWC*p`a?bPp<&jp>QY)S}0>Xpt23$T^z3--WW$aG@ z1}DEf!Bzy-LLR?4kvglo+<{!gz)Ap{cIhwcm#~sGf`nhs-gCT3(j`}w0NQ0kRYzh= z+o4~a{){DpmmXjHO>RM-nql3BL9tplWNZ{j=i{^CRh_Z-;#E$tNTV^=x(}O8M%QAG z=ZhXGoQs6gfRJRWz_J;VLX>X@<(Trxm&p2EhD=mb`?MT7ubma6OeN{0m5}z$vsFNL z$a!n`>5DpDVUS)JYMdS}wcRraD2KTV&6XVBxRYtk4A>GEfI`0|^kab$j{cd$k-uzy zZfa8+ULlJx{x9@aiey{8L+`20WJadt=;^>X#mV}y2D1AAA!XT-8&sOlElAq{%XC88 zgNOGWL)Ysm{`?B1H2r!~8DpmEn2eHkF52YWqK=<)bn%!ihO>nkcD<_&q^s3um@_ott^dCAqp;CHU*Wc z?kA}vGr2C+V@T^$2vg=p18+Nts_KnnPP2C{_9#c*y<69AK^z3S^a5u4%O`Q!p)A_= zJeU$K?%i+hlW*h;-g(G1rRVZ_NGD2y>=_kzujc5r4jX=D3iY?Yj*$i#t6^g=Pvs6^ z66Xxc#FNtSn=K2MQo*?`cT{*U$q~t81Ke7wz?FZsWf@)>;aBM?st?pC@$k(kxan13 zw+S+zBoR$v@bLKub-4@~je#IB*~ih|sO>Li$3bGk_3$Kx4!av@My_*zrXIAXS|QR# z-Cv66&h>Ue(+HOB@dPjvY0M6ofo+dO-!71a!0EUuR=00-n5e6i?}&(kWSe(*6Hxsg zZR~jHpLK!Py7`?zG3s3<$#bO=Rry}e)(b(eupHDEPR?=RA%DLuWs|dPeAu|%@Twe) z>8wIz{+#71`BwzBoG7i_xAG z2t7f(5ek>QhT;`N$0e(SlU4^4oud^|x`|aaCN)!Dg5d03*MQO70L+Og0)z`*YZ<rgPy%Xs(U7sA` zzkYmReYdH7e_h5(0Sr?w0!H~H+(FoHH&7Y_mr`4mG;MFAahkPt5z96@wAgxDS^xh1 z7_g;22lgM(e~oJ2buMrD1(hS9qwt?|D#Xjil0nWywWr z)7k`|TjHlYi43Jd(~k!M!E4EBRWfDd-BmkUu|qfqA~RsSIZ(D9|J1WZ6J
&WI6 zFb6Mqs9A9$oa1r8=p*57w+pj$ue455)V^1uP%A$X?vPG_Vg>O%F5fVzG&vrJ!&-0l z>5QeHDeDX`4wW8g4H*cwBa1Mj!?!plh^EB&?L1Ge84Tua$;G>DeB>L3!`uvAsfbmv z(L@xFSvp#ZfQ`*TAc|=xp3clbCf9WiQw=aiYW(LBOr34*>Ic;@bEsXRrI3yFDwg+d zC*)=lC!=u@+Jv2?V%&TiHWYd@MvW)YBT(f4Su4^vk^R?vqx&M1adL`kbg}gSl;@E! z?hYk;$n3Bu-*@&&%i$}{F)qQh48Zi^n*4H;PULW@ci{DAN{v#We|K#d*_|-1xb%}O zt9>Tvz<;)^Ss5e(Qjm-e=$t+yO}PmvPdcI$_4|h)yfu%MdN3fu7+*QqA+JMy#M?b7 zwjY2WS04wK;ld}V*;-2OkA&cSO%@r}c^Cy30sv$Bo!ewonXv1-&@bg> z;o6q)2&3y#WoD#V$!l|_q8+(mF3`9*56O|FCZz$@o*GI$yttH*ht`}8)iJ3`WZ-bi znNbnabAMT?FPA-=c9tgt#Z~7IVL|-yP?(8qC#nyTk7#|KBNZjj(cQt0*Fi^TIw*Sw z-(JV$egPWW%8I1df#_`@57HY65FQQFUq30ON^hPTucLEB;FLsTW2B%2eF`ny;7WV^ zP~K9QkwjB?;G+U^h-fSZuNy$Hr)1rbK)P06;cMaYw0jr7A#GOT;_Hf}^HqBi9^W`A zE_6cP&Md_J&iCYwDR!08C!}sO=RN>ByXy31$9fHR*-Y-x9fh7W9vstD3gSP7RV_(t z3qbqj?~_jZ<^54l=ExADvh+G>x;^%$)M#?SP%yTNEf4|s8W$CP7?^sX*9z@zHfR@(#SL!)C~nK zwUV>){VmFQi^>?TVnMY27LbOQU;6$m2q_XbQKe6|%6owmK^?U~vZ#T&b)putk2Dr`d@iPoXAbe#l?;{Nd)}L}Dq;!~^8R2BQ8!=??hNUL-U;e>5ei^P+u>XSi$;|pft?@`5O0CZ1&KA{ zBSZxH_E&ttoIFVlW>5NkfB_+J`E$=(h)4)#^9+hvrj4k3sU z6#3>r{z&PK0{izGbGWr&xdM#9m@NW`Ld@)DQc_dxiAZ^tAp*aQLB<>5AqR7DaAApl z@j=Idz;XxxeG;L^{E0a&;}Io7>;nNG`lNBohw*UWSo@u{mgJHC(ew2th0E9mDgFr9 zO2LN(HWoLZ5X0EW%rk$7GdCZFgFw z_U>O({0qbL4+5jo&l}lzV+V)^r-=(Mv8 zyD`V>3ZF^v+rWst;^5i%^X+9zDRj1EK~;b12-_^Z;3}9!ar6Vnb-gyj62M!Y#fv=L zEjN}0g2&U0WYDZlp;} zmfh=-HeQ~V5RYyIO$uTIktBCK6;h0uu9`W^0?jfIs)OoqjHJ0qhquDKEHv{u@Pn~> zZ9_~{nfKqImHPrFcZX_K+v`cWcyPb+2JP+Mc0Ma=3?T#he&YNFSJEuC=LzJ>^A~_pGKS4{! z;=<75O5}&kRmL4@BeynI%4lhi*}zmIH8BIWbu~G~=7f{0pjZ6^nC5=CH1r1Ds8g=`S>JT2i?TC}C^C-L*H z-QxEC`uoB2{qoU?Kks{VySPg-s|FhNWCQkvYo#EMRO{9knyO{i zDCs%7L;(LruTa-Q_IJ{jf3MI>P^yT|I>~=$YSz8#E(cAGgf8r!X(T94HJ>($zip!a zVaO6??xvkD7N0TuJGIUs3;KgZ57g0!MNJ47-Bp(`MC^! zT7bF&ph4=zpQl1n!6s%m-tV7v?;NGgdkCFQNM{SN+x}V8(h<;+3YU9cSeQ?p2u?Uv zVsh2USrO;t_D50uL-Gz2Tyi~Owh-Qt*vWHVB{8hsGN&hcGXY2}mtlw+ZHY+~yHGO9 z_-Bbw0rqz+;fQOF*$29la%uwdS9-f)_Ex4mN&HvH~ko-?$WECda!<1Q7ht@ zYmncq!X4A};wrZjAO0uQ)tbMQh_3i+5u^h)UEfQgm=~qW)42)r$> zPhnRzRliszc^2U%VxM05h~oUPfri7UTI$t=Pzra0z#H1&q{&TwQ~SgOBnwZVRs7!m zk-FQio9AnO&^S_yX{!EQvMip9$-@#cORd`Dpm#iI@>i&sm%0GXLGO*abQ2FFgQVvD z#>$U(rLv#SP+%u+f+gy+a!yiJ-M2})b%Rz7S1R`3gx_yrP{Y+7lH^h9Lb-5txsY;_ zJ39#;_8niFbk2!N*_lNku0vK9dwfNGjg+a<4~wqGb?CDCjOU%BtGXpcf7)uTGn6T( zu$C=XIa%fCS+Wn_tjrqEhN`}qS|kjK|3M8FuE3>UTB8R{QOcIbZXRLfnDz~?c5lxG(1AFn70?5zs+k*`m>goM!hlx zOkZttqvBsOPnQul5f<3n@%#6g_G$@yqg7cF{W0FE>ve8@hHplr_SsI$&o6~Lma+d$ zE%bk#mHyAI+yB%;Oss5x|98;L#>oCZj-mf9hS)e+{~xE&|H+`))stuG;qjWwLb)FItI(SA%&Kx(}XVM(mFLcCx%xuQNe`5I`PKk=2Y+ci`Osi z%{=#%XO?revCGV(Jw`@UB|G6aqb%t!5@K@bRIn*VVlO>naz=G~1PD|haFiGWMlgn2 zEZjrjkGQO$)n8#kg9(u9EFx^EQ^3M?<=h5-5C7DaQ5evO7$AMj4Tw;hjG%}R!KUBj z#EK08nK;nDM+m#O3{bnQBpCEjx0c~ZU_KcD0unO)Fc$rYjHpD#EPH=pK2s|rMcN1a zP7~2lFw%fPw-_-QG!e%__nh9YkVQKqhz&5~3G3L z96-VTx>K|0Ghh;ea}4Ty54^);qHaOd0i$RU|NZ`YJI$gKY-T~;-~U(GINXK+6XKEZ zE?=Mz{L>2Y@B@Eh^$=g(nL$XwuR%dTXJYPpQDyBB;`oPQKBb?2gq?3gykB#PzS9h#KDwC% z_I^-mgB@=JxXTH3c)u-Sf3Jjm^kv8HVNw8qf{Ag*^URz>SYVHV#rtC7EnaU(eu)eb z#{axdZSBcjLt8oH4yzxV`BFagaa}1y%hD-f|r%VoJ086iP zaHK@N#Q@n0nc@SQ3MT|3jS?_|Bnn6akRuXqAr0R|N=pF~Ht&}3C$M4yVSNRgK=Oqv zlfnhy$|t}AIlV&&Lh(@)LFAYB(is^DQJ=CXzykHly(NM^o*MkLNPIu<-nrd!pb*0c z=*S8CkrV;WV+ei)=*$X00UbRfBnKeJGwg5Yq=?k@&k6+nZ9Im=^UM_*&>)#$Ar*XBCxR23cuxivrj}Teihwl=3DiWw@iT8@(%`8+$VB{{f?;3!1 zZu&w?L?@bNm)Ujf9dP*58N|!&k3zq9w7#l$uhv%E3nI?c#Na%UZ@1wcBMFvRySMbj znEEUxo>nq!`=7N4j_7w%ONqwBMG_mQriLjXg|k(fu%=b0mBqxg{Js6tnsR3ig`2qx zzsU7Il<%CAB)U4&&tF`GhX3tjflCg>rvV7gGzzeu!xFIyBFbS zo}6r+l<4v~k-pRAU}3dAO#C=9EpXluMFyv%gEL;Cc7QAlk$tPqCQ(F~^Jkx)Wn;oD$kX~tpo81K^@UbyFuuX z<_#%|hmqw!qL%eKZe-l1tWLksO1TBuh|UbR z9Q?FFTrotOyeyG{ac#49r74_uEV$ct@HA#FWm4A1aI6$%x#9z4HSZyNZN_-Quo2AoMuYq8VuFAVW! z>gliUhj7sFn=a(1#(|~D3VxJULi>dLN5tjqMiVI4y^|Ewi@W?B*;9TZ>|U>Y*Jnh_Im#Oc0FqxJb3chsFB?2BD#4pxc!aV^)az&<#YeALTxu! zk-&M6tK*f>-vr}ZGl0C;RYc4+4PtRfH^jAZp2{U_^q9M}EAM-MHaWX}M<9(vGpY@G zXmVdjcHL9OCP7?xuDTX3Pt{uO%Safx*c>%9b^!rrz>{pvxf2E%PS!XL(SGgv=H>Vj zaq)Xi^h^b|!v)(G=k@I6Ib~QA46WVoZ!gTW9TW*9-a zB)HDrYnx)CJ0}C%^*oLyACL=E0&NyIq}=S!GI?&NQAdNr^}~Q3jx7Pj#rA7X_L|_E znJfZif0w2kB~#i2Y>#8VX^jipdZ10)=Beo65z_p+lt{+DZT>R)qr`1_ynEi49B~9s z?&(fy&0w70ODILZwhuQo4m*^tA03(ySc+>P>ISnmxYZjDwq(A+cL#Uws3?*#zS!y11H4OQFVW5STJbsz6aRGKj7V>awwZ zC;c@$?^@(gIxQc|W;J1;aUM3hX5KtRG&BEkaBdmofTOkL=f|0HO?J=k&1^5ZAGaYb zYT%w8eWN;?8!mfDn<%v+w$h^wnI*sX-^!!u4r0JwKo92@E5z`02jJOV2z^Z-csoz&2IQ!`r{YJJBOh) zlkk|tyIhL^;5I!-xp=X)f}Z8cX=k`T7|bi&nTCJqp;^m&eNd9C`(VQf<=^TsUrW`t zXP6E5hyK0fGT~i6Q6`El>Pz%7X?#J)Acx!CW$`G_$5yL8sNG!;^}+{VWxpb4+e0U5 zf{eOjJ4DeIl?S@>{pgI`q>qV1dGlr)wMx9szp|huq_Q#Gb5%_;e6sXGWuI!xhF`r( zrLTW1g>^Bi1{PMbrjd99O=C20JlyR{J?=&>09L|TM*OnQm{N`p+kDqY8a^2XVxR~L<_mxu^Vd*PF z46v$tYW)1-d1D{q=FoPx#jt{iP`LI@kul^}i*6P428-)LQ7oj^;Hf2_LDl+$PeORJPbj2mc&?0tz8a|#|$H6;u zzN~BK-CQ%ajH%97-Q715ow{q7lqwv5Va(-HKs;`+Cp|n)#pjLmhaup84OPV@uZ2}7 zV@BoL!>)FPYaT+AOjRJGKy*5KB~cuvmR%}!V`lj!j1sNq$~H%->1Zq5LKWC_EN#2J zDR^{CYr81240MUVXhYzGdCGmhxvK3x!13$7ARS_Fn$!DyTSeI;pmjf;nLj3KF!?i&mTj=dbB*Ug>#k^Rr;0Z% zP_j+t9{Ae+^MvBGTI^ULU~C0;;oA`#URT;3SwF#0DYdHR>@D*(ynvsfxyDxnf0e3Y zk?p1JQJ$WPJ}`~vrZKwW;L2oy*y0QoikUxmbzwl^DWU(B%l+cSa!cl{7In_~^tFNo zV|t))y&AigkhI4dUN#FHK9hlzYrAQQ*6yLW5Ttpn_=Ob@d^)F$%)f}S_^Px;Jlt9{ zi(pF`^Twy;Tu*SmIJN(WpbvK=xLZyYOFKb>TYxZ-FgOGm zn1R9FWgrlo0D)m}%P_cWAh_EA3GN;OgdoA)gIj__AV_doe*5lzwN>v|wOiFyeedn( z%IW^2@6+e$b3_;uDu4g3Z>QCgJkce6$I}(AFPU3{Va6`VbBMluYhir+`O@6(jd(>j z7H;c#khJEN5&<+;WRAz;hT5&9p`pd%94~>~)Hj)Sa(lHyYvR<=%=BeOFX%U#Qw=ID zTXSM~)FJ%w_VQzMwK`gn{q_Jvo*?gWy%!-LQ6?$^` z5rR5OpoTM6?sGnqu(%F&GerwlUsZFd&|Pm5q`T{M^t`X4A}zLWMte?Z>If)@eWR$2 zJknC!Z4v)NV@o;b)49vp+EC33t)48+m&q?$4HupfEDy32N8t?IP9#_|SbN%jbp(u@ zwja7Qt-s|M(JNG{`%FpCdN$DMmNeluqc>56aj&ceUTthBD}8Cgdkg8DKh-r+H8bGN$-N5WcOhdLS2Aph>j z3AP0Z&nTkA_~``9EkMFiR$lCjr$xoi@iu^HlU7gRL0YzfxfT63MF&0I@-1nO_>Pm7lz%xb;uQ;x|ea_hlRi}2oDRUdX@Uy*;3OWshQXC zvv19C>{bq`gFLM=J>@-mS?Ue=R~dUkC!~1TPK{;b-%fgCpN#!W6KiP|K{Z#sqyz}h zPpI9K4_E3sT8XY#ax>PcM1#I7+mYykxzd)zlvRbP;C zW0o6Jv>!3{PKoHGs627|=g)D>5~*p?7dFWa^ksEPuhSQ(XS;)veY0&MeN$&BE1l}B zQoJjsSX$^k7%x4GWmo+7PG;bS<*@N@IUKvGjhCon zpYx5+sn{0M3?|W&({`7|34D{c*J{g+SKkiEc&6}kWABaGe zd{w72`Nww$%5_NyRUAuZDX-&SEDqLZ=1a=F-(~a3iM}w)z7H`oXLe;@5@u&>*GrEa zo$fa-v}e7p^;mzTxO%`7yb#P=M@?^0mYYg9Wg%I&x>epcSVbtt)y=Xq)QL%{^pNfE zSqqJy0QzbDfC;+gelFjrvUtAtH*dy3Y7YGG@FmM`>5PjeukG`I(2bc|6`$*ntA;hb zn|!W{Tv*Xk1lG=C<6e^$#fJoGG{(9PZhtDP+~;75B)W>KRP~+YzJ0#7@r}Me-fKbpzKyNp1epFb0UkzIh;Nn|}rdeaxf($>Z+^`chLftwY;IL{M z0$t{&9hJKDDP2x96sKfjh?>i^mAnJ>3gkRvXK(zN;l#s{;oF~!zL#FD#%;Rbl;GLK z-0Hvnt2QZ7wZD~ervEMW?7-E8oFe9GfQ2BvSIWWrSFe5S?fbf!HQ)3X(AJ-Xw)=F< zp#6rg+~b0_bc7rueE#oy!sm9TQz-jYbx5%0ZDIfw(&9M2sTnu@B~K}|vrL~DG{ml& z`|C7u`J;*5e=MjG^2jJ~#mik$jQamJFhmXIYTQ>Y`E)RT)r93u9Yy}B-o?gTj&Nct zWOI0*vsm2p=H@iDzP%2QP&cz*Nt4^1 ztlXcv9kImMW#>_zSc~uFKIz~10$1FB0Wjpy#WNj*%eB@dAuFV~xah6YB?;^MKFTon zEdT!O{0v`cm7v7&3yjWZP6?5jYLF@L*j_E#;jFSpw*dP`^6Th|ozl>w<3k2$9t?C)ZyJ2s)jGkVH-2>{cs6SFe+4tX2Rib&%EWd;#v0`l%FG!P^aKu8>yPmRl{jJCy ze%Tf-eR-RE<->ZDL^eZkX$4KgS*Xh%{m_riWJ4`>Bu!d!c(?(02#Muhkj9fPkfBCr z0_#e`?{F1yc-i^V{Z4D z*r%bG4X(9+67m5arRR9f>O1S5+fx3qJxEx@-$?S4Mqr1w^Y_E71qYwd)^F8jQg(kx z2Az+4#?j!KaaA->P}Pj%nyrgr?w0(J!Xz;a$}Xx)tpFRDJz(u)U-1*Us<8i!z;k5t zF`!E53$%kgB$vGAQW*)Jik@3+Ic1R~bN2966X*@iLw8a^8fFvH0G9c7xnCG)I*s!$ zMLt%6uG5D;ExWJf;NS%YZt-R0YXC#Rvl*NECH0DjjC20lO<9~#_rADmp1=UpZw(r2f`1h{iG~XV`sM!k z&Q85MwjN`z&@2vVL&nnAc3E|NJm2%?uC$l)6d9zo>zetzbvi%qEZeW!?02B&D07DS zxu1ALVd)@|0SQo-_!x1xVQ1yA-x0Vg&G`PCOGgvG{j0Ut?~c{`l9*`j<~Ek@);ic0 z3b}3#MwZ|(o3&lBFYBr0C%z)vE*~y!66qxc5OvxWEFCeK;zC{iR9tx(sS}&a-sQ*P zkwqIN37*_cso%vx!4?dxUbKv!Po9m}J9v-oV(?!(Ox?OtPcJYJi;8WnL#y=)mW6t# zCo^6kwtCHO#gz@CtVjLHO`EBYLLFf_oY@!>n_5!M3s+4gD$fJ5NxryfmaQU6vqV<> zk|i|u3WkDmHoaSe#dH;#lrfxH2 z*+UngyA8@3Xzl5YKq3*A93WMMr@Ir>35Tsyc?}ESwz0#J~=TUIAw>LL)bo|EvZEG7B z;KT7RL%4vt2&Buy)IbOiA3vXfFc>Pp4d#LVw}B7%ho!68xFLWKi{b@IBjMH$RYzA3 z4xpX08OquPVFq;juOXm35FRiGzJ$a-ck>@l2lRh3X$yF8a|z^Oyyhl{IH6PDV&7CM4uehY@bZrHZ076m zRJBXff=|m~>4{v)acPrW0%>%pf@e=GNNovsD`YT{Z_}`dPVEB2A{kf`e9i4OFmcAV z1F1p+_JNiRz&AJvW9@mWW4xr1d3sQ?kGRoT6LLmU)z(V3efj4X?_zVJ>ZDDgW`Fe( z{+6d~UiQoOtR5v9P&UXKs%^EpDY;KNzdbtf329IXe zWL(^D6gY zjgb`x#r|`ymocu7tDpzw&u60MdW4#_mm$!_pxsK#hCtiBJ|GiCuTn!QYi%-ufBL3_ zxAk2oX*_>TJxSQn+h==WWMOOYzYnbqW{YgYjo8zs!WYF#O0w5%UuYM^35kDnUz{8} z;0?@`FxJL&XfKa7zKsjy^Gk~MA?eY6uWqx)>>uL%XZpw7A&>^0vS@l zY#Ha>RqDeNP6@RwC`re%RRfkeKh!d0CqH=zRGK%y{HYoBAtmh5VlcWiunNQLU621d z=t4R!Oo++rYL!=+F_HuIl+BEun>?i<8?~N~HP(OA@>u5XCCKlWcPu^bsSl_)KIe~n zFQ`}yAUM2#h~9c#ZK60?PNR66TbgHvExax-Nq>QXR{Uita%q-8nRobpn)u0`3qOGw z6Pxt{7nsALxQRVEY>r<`W-)pjpgr1Bm2ue=`vGY(vw^~w8MN(^4BV~VY_o#-4_PJd zpD<(Gl-Edc7cV`>eI&IG>7icRrAViqW%TieH%F`D*_V9=`gfb}#mILVkdk zD4V4j0WeTC3g52xe{3mQc|0iTkLZdDi>D>qnXNXLNJlSWWz>I^kyj|IBHm?WN_3Di z#vkt#b;Q(RB>&JLKgquIfitl%UTFxb6g?S_G>R`>!>_mcM#Rn^S6pFHkSzbZ0i!!N zN56*Bx;*zckn(#Xtbr^U9DWzEh@<_|XUx90tv${{w2oXxalWF=m77TOcU)e%jgL+> zG;GrF^d`R_FgicG{Oi5G#Jv0@U_Q@j2C!$H+3N5$&24u9N~jFtr7uJskj>9iBIFNI9e{8|;RTE!WwDf0j8de(Muhlt z;S{i=PP^VDPtq)9B<7FFB!mi^U`cgd3WuS+2Nk8j5TUCuKlW}YEv+d;izv`D;nkY} z9j;GJapkyxw-)*;n8VsePknA6%Do1}*f=&nlSZ1x6qcn>V@IS3=6GKD2H!;$V&HGf zRP}>HLe*>epHGv)EPA{2J^(aFx=wkBPhS41Mbkec2iu8EYbD5J6&mvl&^fTj zq-@mUd;YM|alf;%TaaOMd$$;)`&P6duhSV>EL}<5&WxiLMk&K7GM31N{`*NUF@OjQ z4%8M2!KwqO)ysvwD30+eQ7m}c_UJjNYt_&tjw8J54bC5a04FY0MhMGlh&If&wKCs= zYV8TwgfsulkzrE5)VGe*_!H5zyXq_P=dn1S!|fuO1QK_ZlLtE5xuY0r7@Xu85(T@c z-(o*+!XIPnLqGRmb=Bf}ord_N9fiM}!kRV$yI1lfXA1I^<{aqhKu2soMZRm7-Bd0l zQ`4&lFc?TSt_BnMedX~m2$~m_FS0B+izXl9NYh&6ULWar=LqUZcO8^>CI)L4i(!BH z(N6X!!dAL~1)l3o$|sETPAOBGSy(CVK>5}7qw>fdM(M`Ou^;#`@}?+eN?WEnMuJav zFLcf6HpkxW(P>wqJ8|e(lPh$!kWZ!o!pMAQ2Q2a=p2gn**g%W;!hX#x{LN^4+78)? zCDOv;SUR2f#EEZY%}nMaBBt+>ip2lAwhdUp3_g1CX>B@1` zxhFl1Z3ph+3E$|Ylh5~}mQ@xI!KhWsPXQ;76Yu`5n;`#Xn|{e5KDK(buM~Es4T6K~ zx0$Br{#Vs;{WbK%YzD50ub$#z(|itL)M5~osj)R?w}r9q5XmT?Qh`4m9_Czd-T@{q zX^t;(B@1J%``Gukbo?crtKVRcD(IZ`pSX~}q0h)ts}04vzQ`R3qVxTcBUmib=_AS& z*M2MSp8&gzBXPMI6X)8Zq(2&`+rFu{XZ4#c&o1S)9_r1pf}2Vy-nUL^#mg$c(y=O> z0PzdviRTA!)Eja^OyjGIM+P6?_eqZUK0hOn7*Wl?dmN53xz<%|3|0El6l8CYJDd&Rb%C_g0}ylpP4hmA8+q&aI-ekZ`_3V zEyubrJygu<(~+j0DyK$<^hgE$@Qiq0#MdWVmxG=3ru3kYll`9rCLxs0dS(LDfN@S8 zFP7v+&O{HE_zTuUK0zh;6M`3;c7!Egc~5_CZ`_rguY7Z8eMU}ht=~u*HA6{Pg{$oF z6~95SCwN`q_Jwra)?TxN@7XW0%(%gZ%K7n=X10dPFMlcvoGL`M#rt=U!i?fEeOrHu z>6cZ8L-y^rx}QXCb~4<=y6Mf8$T3T^HimQSx29Ca+!XCC%*bOG{$=#yPBR=^Ay<*Z zZVjJE*#w4=HepBx*6FHA6H2@3ryG4TQ*KMbN_p4%J`@hwXRK)=_gp!4*Z*{ho6;Pr zu0-1jym2Iab6z#56rw>I`L-{FVlOZm@2xROW#8N>V{M+z*T*@^EV}W2G(A;V9_w<= zv|${0Z4$cK4h8BAtA>A!k=1o&cc`ZGL7AfMqucT`vtQd`>+oT`bl7}wXlF|)E!f{8 zO8oAnkr*)H?Bc!8Sd?9}B|s`QWI}wx&i4kI;i!Kz6M;Np)vT3Ggx?kWumK(IJs4;kVpq!{POl*8wxHP5+B0XcOk)>|b8%4h7K~`l? z6B}=vi0?gbp8e(p73K1oG*`HLnX@_EW1(8ii52P>IbPZAww#lcM^5Jc zfL}!~Tfb|!LOM-gA6!cx*PAH^!ZVb5!;sc&a}auZgPoGlau%Z26fM!7?gqLVCp5(8 zjl8s@kIB8Gx=M(a02D#-jMNrGo0%)8o9wpSxkXZ!3uE`H+m#-tzJbGWX|zI-Q+Cn6 zkM}<(E7w+Qd7U@YdE8Z=NseaXrHIaMj6zK7dmT?r$*9uqG2`al>;FG2iT~fW`1)E1 zOMH;BqXohPXv7N?5-`RGy|(c}Je2T3dO#yS;6wVfhc+!IClpW!{Lo+PAGoCx@INWn zKNUHkk(eMq7$Pe#CoCW%C#N9GFT)Fl$_qhd6@-N4`DNr~1SNp~JLF-Oe+jJ~$cwdW|tDJ88yR>S^eKeS!}^cv&_+hx|1 zG~dz!HJy=qt7)|e#^9-$<8zJ-Hdf^YV!+UEaf*awBV2}ZLxqR(qOrMhgIQ4Ho#3mq z9_*OvKo}jIU}5&%IpnT-5BYTIWXTt`61y^v8S9t(zOjoE=h;typr2pD%JN?l#lJ7A d|NVivpv;gcj|T>d&(A9a6~bp>k=Ibb{|{3WgC76@ literal 0 HcmV?d00001 diff --git a/Complementaire/02_Inference_Baysienne/3E_ADN_Sophisme.tex b/Complementaire/02_Inference_Baysienne/3E_ADN_Sophisme.tex new file mode 100644 index 0000000..bd60739 --- /dev/null +++ b/Complementaire/02_Inference_Baysienne/3E_ADN_Sophisme.tex @@ -0,0 +1,21 @@ +\documentclass[a4paper,10pt]{article} +\usepackage{myXsim} + +\author{Benjamin Bertrand} +\title{Probabilités conditionnelles - Exercice} +\date{Mars 2021} + +\pagestyle{empty} + +\DeclareExerciseCollection{banque} +\xsimsetup{ + step=2, +} + +\begin{document} + +\input{exercises.tex} +\printcollection{banque} +\vfill + +\end{document} diff --git a/Complementaire/02_Inference_Baysienne/exercises.tex b/Complementaire/02_Inference_Baysienne/exercises.tex index 4733551..ba65239 100644 --- a/Complementaire/02_Inference_Baysienne/exercises.tex +++ b/Complementaire/02_Inference_Baysienne/exercises.tex @@ -95,4 +95,60 @@ \item La probabilité ait été payé avec le paiement sans contact est de 72\%. \end{enumerate} \end{exercise} + +\begin{exercise}[subtitle={Tests ADN}, step={2}, origin={Création}, topics={Probabilités conditionnelles}, tags={probabilité, simulation}] + \begin{doc}{Tests ADN} + Le test ADN le plus répandu consiste en l’analyse de micro-sites. Ces régions de l’ADN sont situées dans des parties non codantes, qui varient beaucoup d’un individu à l’autre (on parle de polymorphisme). La forme de chaque micro-site est commune à environ \%5 de la population. Mais la carte complète formée par l’analyse de 11 à 16 micro-sites testés est presque unique, une sorte de « code barre génétique » à ceci près qu’il n’est pas garanti que deux personnes aient forcément des codes barres génétiques différents. + + Et c’est là qu’il faut être prudent : tester n’est pas identifier ! Partant de deux échantillons, un test positif donne une probabilité qu’ils proviennent de la même personne. Un test négatif permet d’avoir la certitude que ce n’est pas le cas. + + On aboutit ainsi à une sorte de paradoxe assez impressionnant : plus on augmente la taille du fichier, plus on est sûr qu’il contiendra des doublons ! Ce qui veut dire que, même si on arrive à un test très fiable (disons une chance sur quelques millions d’avoir le même profil qu’une autre personne), en fichant tout le monde (en fait quelques dizaines milliers suffisent) on est sûr d’avoir des doublons. + + En matière de justice, le test ADN est avant tout une confirmation (ou une infirmation) d’une enquête déjà menée, et non un moyen de trouver des coupables. Ficher tout le monde, outre les problèmes éthiques que cela pose, serait avant tout une porte ouverte à l’arbitraire et à l’injustice. + + \textit{Source: } \url{http://images.math.cnrs.fr/Coincidences.html?lang=fr} + + \end{doc} + \vspace{-0.7cm} + \begin{doc}{Fichier FNAEG} + En France, le Fichier national automatisé des empreintes génétiques (FNAEG), mis en œuvre par le ministère de l'Intérieur français sous le contrôle du ministère de la Justice, gère les empreintes génétiques utiles à la résolution d'enquêtes visant les criminels, les délinquants mais pas les contrevenants. Il est déclaré à la Commission nationale de l'informatique et des libertés. + + Nombre de profils en 2018: \np{3 480 000}. + + \textit{Source: Wikipedia - Fichier national automatisé des empreintes génétiques} + \end{doc} + \vspace{-0.5cm} + On cherche à comprendre le sens du dernier paragraphe du document 1. Pour cela, on réalise un prélèvement ADN sur le lieu d'un crime et on suppose que le criminel est déjà enregistré dans le fichier FNAEG. + \begin{enumerate} + \item Quelle est la probabilité \textbf{a priori} qu'un profil pris au hasard soit bien celui du criminel? + \item D'après le document 1, déterminer la sensibilité et la spécificité du test ADN présenté. + \item On sélectionne un profil au hasard dans le fichier. Le test est positif, quel est la probabilité qu'il soit le criminel? + \item Commenter le dernier paragraphe du document 1 au vu des calculs que vous avez réalisés. + \end{enumerate} +\end{exercise} + +\begin{exercise}[subtitle={Sophisme du procureur}, step={2}, origin={Création}, topics={Probabilités conditionnelles}, tags={probabilité, simulation}] + \setcounter{doc}{0} + \begin{doc}{Sally Clark} + Sally Clark (née en août 1964 et morte le 15 mars 2007) est une avocate anglaise qui fut victime d'une erreur judiciaire. Elle fut accusée d'avoir tué ses deux nourrissons sur la base entre autres d'une mauvaise utilisation de la statistique. + + Le procès se base sur un diagnostic de syndrome de Münchhausen par procuration par le pédiatre Roy Meadow, fondé sur une démarche statistique incorrecte. Il prétend en effet que les chances que deux enfants d'une famille riche subissent une mort subite du nourrisson sont d'une pour 73 millions (résultat auquel il arrive en se basant sur un chiffre tirée d'une étude qui affirme la probabilité qu'une famille aisée non-fumeuse dont la mère est âgée de plus de 26 ans fasse face à la mort de leur bébé soit de 1 sur \np{8500}.). + + \textit{Source: Wikipedia - Sally Clark} + \end{doc} + \vspace{-0.7cm} + \begin{doc}{Sophisme du Procureur} + Sally Clark fut condamnée pour meurtre en 1999, suite à quoi la Royal Statistical Society publia un communiqué mettant en évidence les erreurs statistiques du raisonnement. En 2004, Ray Hill, un professeur de mathématiques de l'Université de Salford publia un article estimant les probabilités de chacune des hypothèses4, concluant que l'hypothèse du double accident était entre 4,5 et 9 fois plus probable que celle du double meurtre. + +On découvrit que les rapports d'autopsie des deux enfants avaient ignoré des éléments à décharge, et une cour d'appel invalida le jugement et innocenta Sally Clark le 29 janvier 20035. Malheureusement, les trois années que Sally Clark passa injustement en prison causèrent chez elle de nombreux troubles psychiatriques, en particulier l'alcoolisme, ce qui causa sa mort en 2007. + \textit{Source: Wikipedia - Sophisme du Procureur} + \end{doc} + \vspace{-0.7cm} + \begin{enumerate} + \item Expliquer comment le pédiatre arrive au chiffre de 1 sur 73 milions. Pourquoi ce chiffre est critiquable? + \item Le nombre annoncé par la Royal Statistical Society est qu'il y a a priori une chance sur 500 milions qu'un double infanticide arrive en Angleterre. Estimer d'après les nombres donnés dans l'exercice, la probabilité que, sachant que Sally Clark ait vu ses 2 enfants mourir, elle soit coupable de double infanticide. + \end{enumerate} + + Explication vidéo \url{https://peertube.noussommes.org/videos/watch/playlist/cf21ffd6-9b0d-4339-9c22-db71afbf8d4d?playlistPosition=29} +\end{exercise} \collectexercisesstop{banque} diff --git a/Complementaire/02_Inference_Baysienne/index.rst b/Complementaire/02_Inference_Baysienne/index.rst index e0fe610..89d9caa 100644 --- a/Complementaire/02_Inference_Baysienne/index.rst +++ b/Complementaire/02_Inference_Baysienne/index.rst @@ -2,7 +2,7 @@ Inférence Bayésienne #################### :date: 2021-03-15 -:modified: 2021-03-16 +:modified: 2021-03-23 :authors: Benjamin Bertrand :tags: Probabilité, Bayes :category: Complementaire @@ -45,7 +45,11 @@ Bilan: Reprise d'un exemple traité et vocabulaire associé aux tests. On repren Étape 3: Application aux tests ADN ================================== -Travail similaire sur les tests ADN +Utilisation des probabilités conditionnelles pour comprendre les tests ADN et le sophisme du procureur. + +.. image:: ./3E_ADN_Sophisme.pdf + :height: 200px + :alt: Description Bilan: Formule de Bayes