From 335a04144a5b838be131f2fb783f476cbd5ccb35 Mon Sep 17 00:00:00 2001 From: "flyingscorpio@clevo" Date: Tue, 1 Feb 2022 10:18:58 +0100 Subject: [PATCH] Finish ex 2 td1 part 2 --- theorie-graphes/exercice.tex | 86 ++++++++++++++++++++++++++++++-- theorie-graphes/img/td1-ex2.png | Bin 0 -> 25957 bytes 2 files changed, 82 insertions(+), 4 deletions(-) create mode 100644 theorie-graphes/img/td1-ex2.png diff --git a/theorie-graphes/exercice.tex b/theorie-graphes/exercice.tex index 6a1cc9a..b5e6247 100644 --- a/theorie-graphes/exercice.tex +++ b/theorie-graphes/exercice.tex @@ -53,7 +53,6 @@ \node(c)[state] at (2,0) {}; \path (a) edge (b) - (b) edge (c) ; \end{tikzpicture} @@ -135,7 +134,6 @@ A, B, C, D, E, F \item Chercher l'ensemble des successeurs directs $\Gamma^{+1}(x)$ des sommets. - \begin{align*} \Gamma^{+1}(A) &= \{B, F\} \\ \Gamma^{+1}(B) &= \{A, C, D, J\} \\ @@ -148,7 +146,6 @@ \end{align*} \item Chercher l'ensemble des prédécesseurs directs $\Gamma^{-1}(x)$ des sommets. - \begin{align*} \Gamma^{-1}(A) &= \{B, E, F\} \\ \Gamma^{-1}(B) &= \{A, C, D\} \\ @@ -161,7 +158,6 @@ \end{align*} \item Chercher l'ensemble des successeurs indirects $\Gamma^{+2}(x)$ des sommets. - \begin{align*} \Gamma^{+2}(A) &= \{A, C, D, J\} \\ \Gamma^{+2}(B) &= \{B, C, E, F\} \\ @@ -175,4 +171,86 @@ \end{enumerate} + \subsection{Exercice 2} + + \includegraphics[width=\linewidth]{./img/td1-ex2.png} + + \begin{enumerate} + + \item Quels sont les successeurs de B, D, E et F~? + + B~: C, D \\ + D~: A, B, E \\ + E~: G \\ + F~: A, F + + \item Quels sont les prédécesseurs de A, C, D et G~? + + A~: C, D, F \\ + C~: B \\ + D~: B, C \\ + G~: E, G + + \item Quels points n'ont ni prédécesseur ni successeur~? + + Non. + + \item Quelle est l'extrémité initiale de l'arc $(D,E)$~? + + D + + \item Quelle est l'extrémité terminale de l'arc $(C,D)$~? + + D + + \item Quels points ont à la fois l'extrémité initiale et terminale~? + + Tous. + + \item Chercher l'ensemble des successeurs directs des sommets~: + \begin{align*} + \Gamma^{+1}(A) &= \{B\} \\ + \Gamma^{+1}(B) &= \{C,D\} \\ + \Gamma^{+1}(C) &= \{A,D\} \\ + \Gamma^{+1}(D) &= \{A,B,E\} \\ + \Gamma^{+1}(E) &= \{G\} \\ + \Gamma^{+1}(F) &= \{A,F\} \\ + \Gamma^{+1}(G) &= \{G\} + \end{align*} + + \item Chercher l'ensemble des prédécesseurs directs des sommets~: + \begin{align*} + \Gamma^{-1}(A) &= \{C,D,F\} \\ + \Gamma^{-1}(B) &= \{A,D\} \\ + \Gamma^{-1}(C) &= \{B\} \\ + \Gamma^{-1}(D) &= \{B,C\} \\ + \Gamma^{-1}(E) &= \{D\} \\ + \Gamma^{-1}(F) &= \{F\} \\ + \Gamma^{-1}(G) &= \{G\} + \end{align*} + + \item Chercher l'ensemble des successeurs indirects $\Gamma^{+2}(x)$ des sommets~: + \begin{align*} + \Gamma^{+2}(A) &= \{C,D\} \\ + \Gamma^{+2}(B) &= \{A,B,D,E\} \\ + \Gamma^{+2}(C) &= \{A,B,E\} \\ + \Gamma^{+2}(D) &= \{B,C,D,G\} \\ + \Gamma^{+2}(E) &= \{G\} \\ + \Gamma^{+2}(F) &= \{B,F\} \\ + \Gamma^{+2}(G) &= \{G\} + \end{align*} + + \item Chercher l'ensemble des successeurs indirects $\Gamma^{+3}(x)$ des sommets~: + \begin{align*} + \Gamma^{+2}(A) &= \{A,B,D,E\} \\ + \Gamma^{+2}(B) &= \{A,B,C,D,E,G\} \\ + \Gamma^{+2}(C) &= \{B,C,D,G\} \\ + \Gamma^{+2}(D) &= \{A,B,C,D,E,G\} \\ + \Gamma^{+2}(E) &= \{G\} \\ + \Gamma^{+2}(F) &= \{A,C,D,F\} \\ + \Gamma^{+2}(G) &= \{G\} + \end{align*} + + \end{enumerate} + \end{document} diff --git a/theorie-graphes/img/td1-ex2.png b/theorie-graphes/img/td1-ex2.png new file mode 100644 index 0000000000000000000000000000000000000000..3b43838c11194e9988c25c3fdd0f4b8ac5fbc773 GIT binary patch literal 25957 zcmeEtWmH^S&}AS52?-Y58fYXWI6;D2fB?aRySoR6#$AIu2~Kbi8rz9NtpFMl_`m?x*{Ih59lh2;P?IFVh--zH) z%>p0K?S(!oA|oTuuga`Edq(!`vxuOgv({k~>WJo7mnRv@R+~|bP>4V|xz_$BhqoHN z9cuYoG9>|Tp|50M_;*-iZO@cmC)GUvM6X-a{z)w8Q=7ACP|qhrKSdjdveyO0LZ8TS z5E=!exKVB)&Y%UWp^wKd!-mJ-u9mhd16@9SLPasTy3WC)${u{7|-VOWy@8ANI ze17>iwS51Lod8ArGbu1s{*5doo7&3bpK0KLD~X@~_jfjRCRF^(!rgz*APeC{{O@n^ zF9MIz$#s{X|9yf?sLdishKRtbH6;-PSvc_ zZ4cNT&qLRapc2mndz+Uw#b2PiuRM2Jaxw0Hxd_FoN8tdKY@oG!T?TOOZaiV@qMcH#}Eeyn_)h^39>y~1}v`?wL6 zINo~}2-Oia3M6q%tiWIu&zu4dshV9|pRg2a5=NUc9*somtTS6-*q^{?9eE`{l?s90 zwmaeA_!#@kPF?-92_%L*oaSYCy57?&P>#F;cE@O@{HRG5GO_4WFds>+QfsB@R$OT` zIA@rkIX8YU@p~=geNT(cst~2PBl%JU&U>YcuhPd!m=t29E(Q}REoOtsZ0$~Y*G7p7 z@U$?i7^^AiMb77^2D2XR{!%V&rgFOQe~t%_e(dadTsh2lzBM@SIB)4j>y3g}vAL}g zkYu)-)79e(RjGHN&Dgcg9l%|Bq0b`#r6K|Jue zI0l!#O>1W1uSp^!*-{vpkT#3M-`*!Z~<5&51N_?P`Vfl)xFxSw9elJtpK% zzH0vC!vlk2AmhePR%F*M)~0gn6Q&BXM0i|%dEaz!q7b5&zoH*tH6i$V11UeC_@!`O z@B%JnyEmyH?RQ*yB80Y7?>2*u1VhW<9S`TKKlmc?4CV(xGZ{ni7>!=rOwlU#WJU7L zS%U@{z0I&>A&TP+`qS@>W&`>02ix)VPz>L!c!%_R=a1PB^VS~JyD~yH`{Kw0)U-N% zh{+MEukBtAe{Mgk^^LC0J3&)hnZa^i3#RF+Id*L10<1mEf30Ku54x)cS{;Ej-|a@l zwko1d2)hu3=VrxMqkkGKf&Y72x1YW?Of@m2%J^BC7KOJX{2l*XQsVb?uhYEUB${H( z+16Ia^&(4MTBPBdmm%munITbP*6Exq0t5Y&{*y`scJvwX(-f92U;e=;KEUgCo+~v~ zVC{Jy=zwIB!<}?DhR>FE%e4}MCVty*vpjuYcFMlSdO4i*B6k5;S4k&5ap?dYrF zv(2x4ae*f>F}iA*Fpnx5=dw*ivG5M0ol)W&p+tYxG95Tpv9C;`S0&tvqqD{tn*P+Y zh%m&f22d=&`qrZHUtf=hIpGKOYthPloME_7i4&g{$^0H{(QEeFR4Q@*u1djo3gWll z$~^|-$$0yz42-G6QqB2@O0@y8i(f@kSoQk*ls zeTTNCS5bR_`_)-{6T?5biPieDV|04cDE@Ca2m=f+;1yyj!iC@LOCC_xH>_B=4+cn~ zcB)83??d|Ya}rouLwmr+1C1SYQjB=XV(^pXnNL|pP>F^DqFerXgBJ{VD$U3E;iZEm|2wlPigrB~oyw6NE3k05>hJqahp zC$XHtamjTR(l&5ZFiM2h8G7pWF%24p01Y=Mx6LZAmN@b|R9(>quxbsSTcjm>%3njM z0s>zZYk}%ZH~p0>o%WFmZHxQz;PpKI$6YNT5_Cs2<*8yf>ngI0G|0(FE)ssGbNol?x!F_a-Jl#mGy?7D4ZfWf{ z|6cpH55YP=GAUuysx02J8x5&O-`ah~x?!^=cmf?jAzp$weT&QZ?_K6 z<8`d`{GvewNb!r(jmpLe;snL`d!1Zc(ZKo2vH@6FsG8k!Wk6(q>7;7=JHvI4R;k_Y zVS|RBwq$} z_Rb3Zs(nQuh|(O4A>T}>6tH1 zp?IVZ%SoJCR}~3V&a0AcEh-0nP|#kaBTFuf>EvU=Eko47`roX~8nLc`GhcC7&*&>( zavuHp$vEA`$e7qvVHS?+-35J}X{-9YEQ0&fq3lg#9T{+TJ^~R{_y%GJ{@;4362hv; zbCicttmQ}tIKEOs6(8m5dy6v>fXlEl)eM#qQX#uUNqGN}D<(={8-?MEIyUQgaTzqk z6^>e-pdp-y5^F3@M+>*-+sfU8Sx;G%!s-?UfH%d4Ot-mFW}OWC^4#WLFgwD>~-2OH$^t$W}f zvI^jr4bOkO`ww+JMY!}wg~fFv1&paM8_N8unRh1(2le|U7MI@VSx1%Po!`qpz+8Wj zOy@z2^E~hBQ5YaI@A$+ z0UXY5Qe>{EJIVoC+xhnvsll*Z%$Nz+p^w`Si_4FT0k4T>R((sp9 zN6M(3(F>(XcmA10F!K37>U?T}gEa~ITIOT9lK>pJw%!(_FYx)QknJt2$TREkR?G^k zMXvMIC)|Lv#L$ypf zPC?R#&L?K`DLQx3@-iwYfc4c##5Mv>H3=YtTVovieHOYWQ1AJ?J>fL2`oob^x zMEGsT12RNdz#xROL?psNkrFu~ahzN|KfEW>N3h!l#V7Z%xRLv)ZoTPxX?`r%d454Z zl9%1>$^vS~Ze}2cv1MNWjqLX0rI_7@lFBn61%kt%*E0cJ{0Am`z1P4uK}O+(4qV-b z^Q{zX(YKAK;noAsk^M2h=V)41W$G~xjpazr-}*zz(!zW6(xf+9G3}tY+sYz78aAyj zs`j3PZUn06&F$Tsq@o2TfgLI|iaxc7ywm47)DkF_;o7AnrUckMX%Sue@@)Hk5ICal z;jF*XuEO}^5c(Mtb8K4SkjATYA~l>LqPZ5m&X874=QxBhSZZi&6@G{i#&2n?C-D+K zXCgST)cFxYbgaf(|zl60doX_2;ZzzBAR3v5f&Shj0D3Jq@nwbk&EE}7~ zVM-crqjHG`!FSYb-}ie`$RK=$pv3*xEzpp8I_RLg~bu=-&YXvj`eb^6aZ!@%$%u z2^PbzM#{=nOhVoD;-)KViU@}0mQ`5i%c-$!9wpxttF`d$KILZ&CQqzs`S2HxFE`!< zl|{N%w{THf2E!P|WuShh9Re~7$>c(x0o@Euy3MqOuX3Iy^>f2|7)p|&;6vuXZ!2*` zpJfO(%#&q&Ka^Bbi4(@gw(j}}P>u67@YJi?YrP=XMnzyXf1EL8Az=wkzed!x*4qRn zr8!sqig=^3p2D1(6@L^+)s;;ni`DG&j58=$smS}s&;KR6I5avBrk$@97q?y$L%38E z-eLKKOswRv0vYBoF{!FArc|SsQN>jXgLgd!6SRsU-prBv67pfb`P<=QzN3n$KoVYE1<1silmJ5`d2f$5JKMG{W4f@`8G0*uLj!Tycw;AL5NdDu4TYt1-up(@ zCRSug@0Y-zoAGxlt?YGAiTasB2y48xKloMrB|n&Wh98~0emyJr5lGy$Jk$M8*d--A7pe%~e+ zgkM%0c0ddSP9X#7ybWRDvcdE@xRlb9TFk6dzP&?vR6x{FTbi0m0*KC#h7_<>e|42i z9sm)}X4KAB5Rl<|hudChjU1O|3;3w3%D8oR{5aQl&i?yQI{3hKx;rj_;URN>V(17- zB>y!F@UN*NRRwY4{V4iVyT4iwGVtu2ScsIeW)Iz7mS-%$a*$xldDcsp0}I4ldhh?! zWio+XX(xyIEsU=Hr^Lwoi>@%^hJF9{@c&EZD(qyDE>vtg&=}cmI0p6rL^4=Q|xDtz$HNWB5Rj#u!dY*7W)?d3nEo&)iMi{^FNX@t!jQe_jOd)yzK^!l0oF$WB(Hb|U{wsarqx zfFm6mw}6ae#$`K=JDo)iNJh|rtYEUdle4ztX56+0O6I|TP}a^hMBH*WS*qmz3Vy;I zHcc26+-0{)vPY2gn-^`7dG2t2r1r#43%0_sdpUo-8_2*@Aq0$Wcw_V1yvHu+yce>P za?;J%ZBs&&QC?o>j3{L4oiM&H72NacA3T6V!IlD6!Zc$0_Q>PdZ5d!N>6Z?X!R;%N zwoFYPu!K$)8(=(gl->EnxNBAmbIk-Dd#lu^Zi&H(r1q1^-D-vXZT2^p2mtaM0Ae^Z2O~ei(f^X3~#jy62 zC}4Q~5nvsI<%WIfOfSwm-pG_;x>@w4SD5X8|BGFS7&cFri1_6f3=6>C?N1f=7p`Uy zGrF&$y3j5H2wLNQYbR}Zng?jAXE+WyDIG6i+cuHvbqZqR&_Nm0ZgOSIS^CaB_g>Jz zqIS{o0RC)7KeAZ6rJ47+9i<{NRyo5iKTf0Bd08t0}RQ0myZY^sc2aLy=nb-gij`L8^fyRwQOjAKwtv1(`4= z%s#Pb4ckr}^XZcC?**vz@;dZ6?G^ASA7DX{HonM-A5a8pmUW87UZw)Nxkf12pJ8uo z9bVKv{j#yU`j_NB3&Dk_p)05#0rfnR?{260C37VZs$T(i#B|YE^A-q1KgFlAh)JIS z*-{iTkinmUdwu{~g;z`V#?@Uy!m&I0y`76Ga9I{p94n9n9FE~w^???Q3%xI>-_|cQ zTy67jII7>z{gP7B0(DJ)BnD%HPDE@n`JHVU6!=l8Bk0_-kE$$N{yL=tkge?u<&hgF zFldIH2{>xFpLX^{NVpIp!|4(R)sTm6NfYl-3W*Z>ELr^%$!Oq*S{#0k#ePU%3naEf zZc?o@daXbYOVB&raDR}00MvFxyBw*`L&I}32|#B{CM?k%oO&8%@|`33HyFMKbjy72 zXhd_0AGw_Ti4!Y!)SPA;l7B4QUt#{zxA6{R7cyiz)1vYYfdy6D=i#5vFCZVrN2Cle zhCXZ1yz|QvU3>0Uwn$*PHCVqxL!q2(O72Dl7^_YrklhlRJQ?=KW486?68a@~P33$$ zpu~Flgv9**A}8XocJQy0jre;Vw;aOf#pgL&RJJ3@Sk++vGDNZq&qZ~%Qu*x*4&2!5 z9-bnpJ4}FCR~TS)y|Q`vL8hp=nu))I{3&S*=~~e4uo$A^-YXNL$@5v8oAAM{^Cw%c zb6vr&PjydZwkF~=aNIMA^|+ zyW;SI`VSwpwuBIKX$TL9bns$kD~-=<;eJ$W7VXl)wtHOwI0I^xq-|zvt1Ozq&<7J{ zbY4xs>&B(NFr|1z{Ru+md}5(EQM#uCOm7YyIaaKZ-aq}r5;I2HH*%>%v0@T@THtBL zPt|W(0c)!Uy=*KFrwu-VWFHKmd!G1$o^HC20i04$lF$_SA)Ue=o|M~hsg{O72;lK3 zzQR;JxGQ67&RvGX^Y(0Wcab!bA9}Nypbhm0Py!H-K1*RVP2QO1c8C{C!&8G?Ss`XDG5vuQ4o1IeMQ0wyzf=wfR^Q0iwTS=s5Lyuy zAVo`ERIezOUZ)fh5ph^O%uP36ML0F;pAT{vk2~e+AdBQU@>PCRNj73yj`eJkNiIQON*H!~T(o?q`gucCZ3ETE%tDX2ZqZ`QkbUQrE6%5|U&x%;f0K)NP0w4%3IxTwu1r9nK z!GXru#bx;hoz=h223w}S4#1@i8AUzz3i4ER`>phexeu!pP%ECS*PI8I#3FQ~l!gfeex1L> z8#qv)din^IdGWMB=a_(nnI8xcu9EpH%ca5Fx(%dpU$2ESNjxZ=W`+ba3 z1yFj_atiE{cxYb!Oa$2NL=5l{u5-nv#Q>yYglgIKQeF53lRu3=nYhPILH3v1$Iw16GpnHxRDWzXTRpLU*gQvQSHUI-FY zz)chzvuIPBn3amvIxRjea`ft$zcJDRq^EZ5S8u}~@CThMrn-Qw9}UFXe*0f90B6ip zh45c};V9fFeGSkDsWHBtu5~WjE8WsH>1-K7A8v!tV*}T+`noDCVYYM!yOp+Hb?@+b zipdw!)v7wjeo+jWDoF2lD!Il6#6Wl-zVnD zNb&I6zH+~9fa?iBMAlO*$nUAWcIMHEkZB1aV46akj7Ek~Y70F;K^c76o1 zTg(W!1t~H2I4IVXEtONOJoKw1HB_WcKFO($&oKS7=K}hGwU`u{((KQ~DQmghtOi;G zH4X!3;13iD!xRj5{4ZN>D$VX6zgB+b>9)_fU+4xw-1m!X`7S3E@aWZIi(bdHGHU|C z0XTn7mEU(BiV($R(N8r|0#T3G%aG%y>*l?}UvCpyg1j&gI@~Bk5;17?MFR@rCx0mi zZUvR0W23WS;oJjIhfDCm7s@oZz-h@ z`jUTh1&Q5uLmtG01o8=S+LkdWvckU*#Dy0r!=nI3izQGK0xP`dicCbkO1cp+>(Fo3 z@9qiETT$FWG!TiW&laWTB=xwE!|k)Go>Wpr6cP3GU<~#A=0k&}=)XQTC2sE)@>aaGi-|}(Qu-WT(G=AO? zOoJik{o=9bb$o4Oj$yIIft{$HSoLUmNFyp`23(q-Hb7x_Uq(kOEi!Lc!0+T3 z-7ZJxEQb8eLoVHA$t0CkxP4j39M-q_pIktL$&~NC!4}?Jy}icYX9?N#lpBoCix4PB z(g3hIa_31206ssY7XK3%fEoD#zC1cG8imf86R3&X_-X{w#%45}o~Bu6G)Tx-EAj(P zmaaKmlCdckmBVUb#_nS}y1awuD}hN#$`NUx=FI&@;U6(n%Qd{c$ZtDz^j z;&vpEuVZ`lxgd3l&&R77eg6B|;j1yGbHI20=TUHeyEP0&zq4QQM$+=QoK)>rsc+kE zIBs^kDG3OC&M3YG@6ye^bXr~N@w!uZ^+2569S0`$z}j)Xk^wQ?2j``^F#IWVQi2cf zR}=}73Yu~cRooy#xV&zlonf2r`lE!XKk>H-Ibo&MO#pg;wi=+iDr4<*IQk5}oT)l2 zr-t4}kM>Iqb$n$}+a}{~`+nq%#0GGP8s&PQYUVb7hBAb(`#FiAjCrk^;lZ*Vz-8O; zk!z87Y29PW9l1(f2F*Pm)#*AvdfUw_#dQa8a(o z2xmZo$VplVc&ivr5tAZO#Ya2|TK9}d_kKOQ?5rCyB1Rk9ju%35<-Ts*u`-amamu|H zrZoB?u+yKzw0Vl0OBz7@w{B=A1I*I&B@s9~n$Dy1Q6I!>L|UMa=a0+0boj;32hgFv zF>Sp-{h!lV*l8?Zy(X>PCHB z9|HBxv@ql~F%>vCM|0 z<|QMI2;{Ri6BXX-&9KRj07zZD&E^DZPt&9TXK9?7%Bjg&17-)RwXoSQJ^{H1UWpHD z7SCJE)6*fR=JPR0#>+*97w4Am87Pr^hdQgunPFWM0`dUM$*wz(^Pl&{?&t>kz+jDo z(QJmP@05JPVyX{+0rHC`{Lzz~=KKsG0RL5Y6#(DH4>xST_1^Z~`{tQl>-}DDjI~x2 z_OlBxA7)q}EP25^_dd&XHP#Z<@f~FEr|bbrTJc}{!m_FU)?Rd80b3+bL~?2iU>f0h zbh2CCoseUy>s~>sqK^ZG!QXAHfSm}%eE9+f2npm~X3s!!n=LaSiD9PfpUvUTCZQvR z%yaVRd4D{;db9g&n$wc1MFNarjKiYb8|k+-GZm5wKqR|C-+a$ER(_O6O(o7>H876= z4?uv45Qo`hASy%MN*L>qfKTkG8NwhEHQLM4Xk0l+EHl1ZzlcjzM^$Kgq|%4U8xAZ3 zfZtV7UA-7Zm4971^Acqu@efskMuo$!JeO=;Z5DUz2*vf18{_N{&-uVnl9;=r0%muN z44NYIv#?!9HtNG)T zcJw@vjWS8imtb{i!BZ{#CbG?uYDJW=7jRaWQq@&Xmq6W4z}@dx_2YpKtsG&eohks`HbH)2P%;$Ch+v7SM zi&Man;X+mT^lOG1MKR@>Ju#+DG8-#y2QK$23)S;NVZ=|*BB|syco};qY*^B z6r+v80p;j?Q8Cf-ku83&hgDJg4rL-tKty??Q;gsTsfQrSXr^v+7aQu8i=HNVWfN~YJl|)Em4`@xg z?H4o>0hqOM)ENFiF-OJvJ0nhI~@TU9|GBs|$ZE4+F2&X^TuPf4#LiBOeDpycm$eq|_BU;0K)gP~Z zxSI^)y?Z!j0S+kv6o4UUP(Cq3zg z^%W8W12SAcj?**ptw_;LcsYmz$JB)J(>ecBjF-ZKYDi>(?j%njR`wQR)h*WBFoDLE z@HOZ7X(5*lH)*<_;@Ty``6{p=235mBg`}>DD?`t1Lb~h^dpt(1g>;{3OV#kK29PF~wggTodr` z;PzZg23knerH932FjBtL9=~t_Ov_o-O2O5LA3#T2axa9B*9-Pei{F&FQt3lJFSuNG zPyC4{$+(-y>u~~7?^8S!pR<+c>FAx^6F13;S%z{YSlPj%H8NNxoN!wjvgGApRX;CE zGz2+_6mQ$ifG@{gROIy|nINoJhRCYU8}g1X*JyfySR!g`ZYuq=js|iS!cXddt{(y# zDpJFVI7ImR6V!q$+xE#S{{{d<@fsPpgSYenU%&qF_Fnj#>JG;PMK zui>$IfH5ei&a!v&PV-DT)nTg1-(U&>2wbAx2c}y)Ak*Jq&2K&0Uwd{ho1|*EGbJC@ZuO; z_}*mhOt{&zTQyEtJxUQDo^=AgQbASczS2}@x+DqQ$Kk}`!d>KOkYhO&9Uji=0Fm+k+|H+km|8IA&*0!z3&=jMVphwtU{IA^I8wT?L(0U&t4^ zB!3~JMD`%I`1DHO8EA;r7!n`SqK|&s9(p6z71c`IKs}tn-!iMSKh`kdGwb7H;&L@y zrtFCK(swAC&7879d)nV@&9O_Fu{qdV^>#BM&z;eV z_W`sJLGb!v)8tmKHZfHf^WDbXeyQ<OU`3|yIyq+L+Qo_U@d$b+rEm`@e;5_VCYa=(*bE5UNyXk#+;(Ng&|!%R1G#%94x z@nli1ABx%QMY3grHO^7eJ;)h;Fq@NfSUU4 zP%S;THRJKX_|zvAU@r9KWD5uQ^REu@qjtjZ2Oh$?l_MGIi}0}VYlo!zIuybaSt5MV zxbm0b$4?5Z>7Q-WFyanOh~nGopc={WC7yh|m$o&3i8__=)li*OG}|SK2-N4TS2q0yAX~yB_DdWJqN+wNW!_} zH+g+o{U@>z2k)3PJ?#qm+J&>*VF=&)OTj;_;`^IzLT5I$n`l_k(;vK!@$7^AV|n=e zZNPnwVm*HP6-Nr(9KsPd;eIcE%TWJn`ix`fC}l0e6aefq@lpiUF1i{KaD>b^vU~XW zP0$q%5!`{+bI%RJjB8BmmdC41v0rwv7pT>WS-G?tkE3a<;J`rM77gvQ?+Ik^qTEq+ zkG5rcQ7NUvWk&)1LwXg+Xu^NK+~_hMowj|iu(jSmBS@b+(_o}x^Hl7FEu8qP6-HPSaoHfE6=t=-S`Enh>I#k6>*^Q1T{mp`TdU{+EYv4ALO!O!pkE?~t zn#Eou!=Lt~?)G#s&m2Vb@Kb`RP8-{I;}HvRq72+>YW>A5TZVNmb|=HM4Xo(|XQD;P zBHwc=EXJxwjYU~v`@Gix;T|5_722dfSk+%}G zk?!W|>AG>2#@wqF3OC92D-?y9jsw?eqITzDNo+?shWZ7XxAdY#2gvB$0S!&sJ$sSH zL6@XYnCRcEM%vy|03 z)J86ZKrv%qCM5a|=UV0rS{GSw?5N3gY<_6 z7y*$rQ@%F%H@Y2a^UPs04J1UF{0k7e(8^Qa|H4@T@+Q#{7aSIS!)yj;BLRpV*hjj-tzEK);zVi~q*QvT~5Ud{MH6 zgV9JU@%#RD;ZbcIX1XD~Pw6}KGRzus!%1?`E!VVzXkFS@zXIKk*!hKO4zQubQqb#4 zeJ5~yA-|rtS)JevnqStdl=u>UimfU~TbD)E^TyScR#q#1+;bJ+K6?CN^wen0*0A?- z7;T^B$KU*(eKst%RCM~xSAY?t9`dCSQlopu?8Tb?(G^|4s5z;=wk%pSyI+B@T=B7$ z;o$zb1+s(gPEKX%r&a>(i8Z~3Qyj14aZY9~_<;Y^wG%n>;%&3(LpaCBAf{j92PQ5SaayIGmDq?#@dk$-tp(DcR<(iN7>E{mEtdRAU9FN&;cUL~) z?u(v31@0)(_@zl(pWYoJ-Oj(M?3EmncF}1#2;aUPPz({7}ff^NAu2Ctum7MMhWR3XcH;BnxBIT%# z#KvGdxShY46MwU8Mnsn$g2c%6!JaG4um*x)_JeHKKp{v@j0BLHWuh}$Y{@h#hHoz(X0I*|EV>nTD95}} z!VjEJT9G~<*uj!0@tCU?jqfrKeag*ekf&=%Ox&BcWWfr`>`W>O&@Syk$q*R0M^8aJaW&u-&g z_aFt;fCEKp#p#lv3e15WEU~G%+ zzp|e*3-qgkuXuq1RAm#3+wa0$myxN5XCavr$&NpoX2suo;zbWps$J>LUs()_qu_~y zyUk{7Q^RMTJ+4AQgLT6*sQ=0dX~?lGPi>6-H~y_fE}jH3t2$8V@e_0%^yDmAJ}?;5 z)<_2T-IO?Tq79)tD0&42)!(A0h(Q55?R88*IV4-ZlIU8oa}nz14p}jLkuI& zfl47}%w>+-rzFhY_{eMvucxfoOGdg?eam-ZK9e&*kH~sNEv)8?l1$q`H4&HD^86Y;)W#{|@}vp7Eg`n_o%YNJ z)P$p^Ypq=8iUx%#q1>k#*;Swi=rCuned9;VLf~(5<=G$yrb_+Dw84WJeW-Wk;|7f~ zBe&J{V#c?~8ISArc+JO{FDafC2X%%Ir59jUz5Xs9!&1l({aeq3(P8-uBve9zBU4cx z=3uF=T1Y$WEs0Zo%Sh5$mU2ldapE{<7lY4! z3qD@t@zWRnWY}a1TYvP?JPUhJH0st06E|n&j-R!==p1ibC#XIROs1yn?MSe{ro8h_ zZV#GaUS3AriQIMZR+un$$1-yC&^k7(mWGVBH zcSey@yQ0HnhagHFF=w4&Z9-QEJOYI`B5zAqOTMp z+9GNdE?wLj*EWu=92X|}f1h~8f2>FVmF=`WN8`D^m0 zvt-v#@8Gy0Q~JbV`>>k<-Gw}KLo&-GH$iFP5eaH?-u~yW+E07a?+ymr%grVWi%y~g z1v|Lxr%Jk$AK=}1Rpnl7F=-!$CD!UM1zl7ra%4;#ZQ@jCK>A_krp_dj&|JymK$7IJn<;qaB_9q4W(> zm*H=2AwTQ4Vs}gf*6!;>9qDhj1_Wg>yMflM>8#?w;rPWsbK{Oiph-^UCrRl?s3o3d z7er>bB-K@b1B#SdUo^iEL*MQn|FRYYWXBN&Uo138wsTAEz0sY!3yfQA0xewIoj&r6(VN2Y6UKF$PkWs81 zs4)GP`8AFYa!Uu~<$!*eph?@p?UcgVS7PFIcKdN=y^$vL#oG)O%^)0T*6-_hv9c5G zhfeJa&)%qy`W;FDXq1ToNlbs$I%olu(sUFToJz!t@2psxR?$M+xgU9g*7=3}l`(ZGV~B=(StT$Hf8u>3-?D0%TsG8Br|s>tx`lDdpjW?9A8r!M2;XNyyvyE4$%P z0)y)W?+mlzf4u;1rc|39ns-2%DD;z*p>=5LVu-o1NRP4O08#V>=G^IKsMTE6jw5c5 zNZ6jOGGm5AxRkAMUan{=mcZ$q@4MNX_es#3$x_eDmZ$rca%05{+??S+SR)YN)fqEy z9uENlJ{CJ*_)nxWk8&p-H9RFO68I6NX0sy|XR2u(p0dYJluA1CnA?j)pZD`-LWeowU^~dIUOY6u4kj;s0 zil#{R-aeYuB1ty3TL7jct!uV_{7?Ry?|Gx3+v^qse(=os^KAE7;Ee?YBP}chfW>X~ zK$=eNSMpncM!y*upDu%An{9jC7=HN%^;+Wy&_n(r-&n6qcl1QN%YA35Vy zNz3BA&2A?6I?QYu9^f&t#0xzUJ0nNBxu8<#*W4)q&wlTOm^1KXE||upAI{C(J_=ox z8rm^vOV`wgJr<(UwygQD46Nw>IhM165R-eIF(h5-PI(Q^5mi39YG;K$^3OmUOC`aBwPM_X&Gbt{h5cp=OMZma^7E*7*lSsECV=_vvk4i2P!_88E8zM0y4*t zzI#n8wFwuT0k&=#H?C*d4|1!a0jJH%! z--=WBlZ0ggliHtoJB5ZkB5#Kxf$ZbESH+Tg&7_igIZt4V1{SEIg?`rp|BvT9rI8pw zpM!^^(~Vkgm)y8)q!+Lnxue9Tpmws-S1uI}EM**`&TKs(&`pZRO0fWMO<)=M)&!>> zd-x%EJ>#Ksa} zZl)Xo-0VJjmUsR23Cr5+_Ncd%6B>8On3?k3-5XFB=*nh7u)j_{pibzGuu3HJzF>7a z($IsyAspE>>`y1H!_#ya1=_RPHKZg*+?F=9pYEnznz0aN^xREuCAo~j(df5e>CQ%h z1YN(kKVFx=fCsJFL!VEJ>Rrpm^%m9vz-%gLd~!luiJ!*3o&;~3=p!79({@vYCl)cc+kp5dVYJax3T@a`Ti(W-Ng+lP)c_U zvlKl=y`y1DFCp|MtVD>ZIxhyPfZ3p_NrTipZ6wXW$l}`WbJN*KtESUp9DAk7Pl^UZ zY*Z$tZCeGsi!SQ`z5Y@m(}mcm$hy+xIYBc0?uziBiMqWvPbWD~&?6^(IjO|>FZ9|@ zH2w(c_T!Waimb<*biSXJX;H?Q#+uT`Gp>!HsmT7J%ylw6a4eN5%?RAlD+OdAW$QS>Ds0H94C zugB688$ZIOmeC?^w#OEk#lj^#tA8iz9G=Vz2tn*VLuigJY^6ec0X`Nr?gJ|vV?h^I z5@0~OA$YF&0NMxwg)U4N-hMl*{p!q?D6@&L143T7)R+ugrqVCr*PHopu!Pq_4ZKe` zdz|pI`SzCYOmj<8bD3d7o%D1ltA$3Sx*h$VeAtVdc-I`}o^~rg?I9_^g*AUh z0qT|zWMN_fPc25Ax(^)8cnoj|K=9J$*<#A;PoVA`qZn}p@zG*spF3}dZ#arPrnx$ zu1EA0e_P1aJX1mjPt8T>b}SvvJbMz`JYnP{y0B@J)BcvN&lYVI_0|$$}QMc z7Y@XiHS<^)nxWQu1Q=(AXD_zRNx3TSw6A3AF{|52sx3I#-tiywM0)QLVHVB+awY6Y zV;=X=8A6vs7w+p&lR2}M0dtWz}{q51v2pQy(=o3)~ z$8-1n+TXQ)PvGa8o)qU)K{3^K9gQ40k{W?~_~F(ZIWz6<_jLI{spYrkie3~3lWA8T z?|=8WN{9<1VSgVzt<<}EPDR!49ZGCTj@vxBns#^IGC?TkjK#5a%~#7gj>mI|gQrws);%2HIYRUG`{Ls)79>$*jyr zW_Y@%&@%R9pV6r--~N$mw<(G2@tl$`VwnoRD-y>2X5t#H(r)cc5xn|Q*5GGmTJqKD zeW^ulyluPR-LR~M@Q%)(^70cUk(O79>G2odNMjN=**R|qh;(Ky5!Tt;s5Py2@pLnu zD@b#5>r*r*t9D@c7833Hg!TChzh@!EU=8t=hv)2W&$>mk>4V`8{uadT{4X@a#8}+)E+J2G(En(}(wPPt_a_0a8T1L&j$ybD%k> z7*fy4B7^A&afmWdFLrwS?I~R;>OzRF0cKZJeb@V4pIQ(*9n*7(5VTWu6nRAGG|@+* zey_=Yb7xW| zw_7V{7Sze}lZ9G|%=%W9$5^5~t;xt+6f4{G1YV+dwQ~9`Pu!C7(4?&`u&CqlFbbON zWl&75wqaDI@DXGe_Lp_icrvufXNO~td(V4VdU|~qL~&j?C;-(KFq-c|s#SI>g0}uo z+0p%k#l-}Mb^PAFw@F*O_U|HUqTg<*R4$CxeZ(33u(RPoIooq-koHq*@7))h()e9; zAy_cOv*TrKN9xUh`wz58_L=Qv>9ll0ere*VJ5S#W%1+C=7p4~wbb_yVV4Z;UT`-?J zBaNsL&(>vesEs{Mk;;`4<%k&`FKW`bJdjMd+Rqtb)4(<(%M{u$TA|4;zUAF?ltgz> zN^ns@AW12-s_MlG)KO+0@u!{; z8`gU=z9n|4_snZ`hpJtPzz6F4DWUq8>X>P$ulh?@D;E1HIKF+pmP1?BBN%Wh@!VK4 zbd-QRuaLpaDx-x^l`Vg69K=kdSfcx`H2BR}tYtw0Gu)=6lK)zJ~0X;~_gs zqglmlwvWIj;~q;`(A87H^9%a`J>kQmjem*ypWN-X(TGfLWDu|jMQHRBEG$BKi-`Wk zoP{~`ykwu*>qV2gLI3_q?qEowK6}%|YOiz~|G_ednm~M*Dpjn>o{<+F_J(wFWwOa7 zVDOUjtcX(pN}wssA;$jK*em4RyIq!>L!KgRd2%=*O`436gU;&9R%(bSLz0;Yh8*Yh zJM=bJNbZ>{b)J<|)xhO)8*Ja`&^LVqS~MklRD?zHa9mKrWv6qn7RsuuZW#&!$aGap zclADpA^B%|tJM7jtNS&6%DxfnWMz3<=KU?rA`j#DTDQD91)hO?wnfa4z+QhchcEsY zb;}7X{}leKms=tTfu0AFwr2JmRFai_@h_e+(8fmy1DK zf^zr#FjVE={&~GzO~HN2dV9wz-GX374eexg8T)C+((}D9Y59dq6^sSBRj6^4}|pCYkqwz`~2&kZL`pH{yj;Nt&k!`;#zNM zm1J}{ZOPO_08fJY0w-uas2(NEbN^7oB!=A@DdnWdI0NE0J#@zSr1s6XJvZ^c8ge;> zm2R%^&ChnF);7rZ^Cw(w*tSQpc+_07!UpY(e$AE-{B6+Y?^R8TR-lyq`2x<+;y!^@ zRkbtXuU!9h3<7ksfSTNWFU#WB+I3%(oq05yOKqA>si20hQN%gZ3k;(=3*(0w6s|xi zpkQ#~VjccjYkx1-#Xlo%9KW%|1;SS>@BT!}Q_FU~`g*{;T z&5mbS1fxTzPPc&wLHgRv^Ww5jT+l!no@hO zUVRW~ptE60B_6zU;f{P@X!U#8`BMdWI0bM1YNODh#{&1IzW0$xKlE85`s?1WTdyLI zi#Hvc(eyWyI{$|_)X`zvD7Hvn%;XBXC7HltS`KxK zt@4}QrG|rm3b`ENC1=GQW*P_B9^GmfpWt`OoqdFdK+J{zN~@FHw0U9(a+$54mA||^ z{za?VI=kS{rrl`D-j{|mMFnNa#jb(1&+#0uUoJ|{BkEXI&bN@qk0V;3zqGMBdrX0j z@wJG9?puCP2`!3KVTs?C!M zF2jA?4g1>P!=ct;UP22TJIWalq7eQDwn)XHr%OEsx% z*tj|XMg;Z@PZQ@fJl(MJx=}8r`vBkHXsBr;pMHZLw=r2@oeo#uicJt4epiFZ-68~k ztTR{WTKxpXuaii~O3OW8SbNWMaqr`igMp~olu88kxlRPLP(o6Q9%H{!y2(VB_XVNQz9W7P zidNyX8dy(GWMYROJ+tu~gOX!M4mGF_!0YLqV;W=RVf&Ho*7=U4Qx*SFLP`P@ zgEUMjx3}%hvB8$*gbUp=da4V)1_n^z!_KWPj5($9g3Y+Uk1Wai4PDCO(v{Nt$VLG0@rHggCB9$p2?V1A+> z$#6{&Xy`HMa`m^gz z$lf-%DII{)Z6W*XOH~>_M4!JDGsE(AGjiG1J!qwwh@4>; zMBPG94Rrjaj;4&Tdo~><%nWgxHVBedLe_zMNZ(cM<`f0@X3BJ<&Joj+f_$LLXk*LK`n_vt}RD&khP`EIqJ(DVgbL9|{HkS+})g~`m=&qqiy^g1J z+*SR>%B{)8B~8d2QC;H+#}4xSp3XjGqKQ}?W+W6r?O>7O@T`d${(&L8Cfg0VIJKbL z)5ov-skX7WuN`gxXl|gvoWhTiK9ErXN!eR4<$U7A#$Wh~Q^8b^H8ug8d-)!Wd6+LW zZNZ$;+z69sy*te~BcLpf4}+1QlP)`>joclXUk-)jWhl~BfO&3F@M5fjMCYfgbefNK zO&^XGOc)IIRi<_g6fPSHnWJ8%>19ZrSewe!kvZ0R5qTn>aKlS*BaaSS22&aZ?-`H~ z(MTR)o(P5Pl8L>Ak$_ANW^^!D;+h`Cta9aaeq0BaeAXdMWS!R?w zfj8AQ2(PSc+TfT*V^U)Ey1q%=BDS;dm1k!`&1_!Hw+gNmaDo82nte&VyYp$pb&@Df z+&Br571Lgjt56Rzn1&429ZiSA$4S<@RW5VC4T5-Z*Y6yzRbaNpf8rM=R>OgM@ngke zLhw&}wok?B5V(bWkV$oY)NYEbz)aaN8T}#;?Ofo`M5R#Z+CBVpzh6P!E`dgFXNkhs zW~>i3tSwzfJ=BblQ96rQXEEO#yEiMuS}{_iljB9IA<^?YI?khqX`A!Ie_+_*38@sS{)ggwU6s(*sw^7_Z) zUV;O}*znNRa|+!c;Y_u>*-}L;JsoYl#QvR8hEKtm-3TigP8bPW6jOE{FU18QJmgvfl5bO@ z=xKT^E9{6kpz!quVEw5wP>51CM4~B)jaXizmF`bI$g3Y>iHj}#1yHEQcEmhvmE;<0 z7#lxm;1u)amK7M?R*4cL(!#{ht<=!1MYFdj0_{9TS&szv z0(eApfm0eF5d2Y!+7*LB0-x=(?lvU1H`}wnKFI2$Wpf5DW+Im`dy@o)x*3JJ#F49$ zah2bx_^yx%R;Sq+aGs5MmFDNu1L9yl3qB*=;1sSfJQ&F_UEeV)_yfk1=8vD;eD`Qb z6@;AoJInJ6y@tb@vQy|hMeuNF*KqYy)3&p#pkeZX&o0Jsgnr@8c0N}me*v@H$4evH zAKi)C=NJ1t-f1`&QZuxPiiC4Np%Z2h{J*zYxtS}M=6b2>>IvSpyp>fQA?oUP4eoZD zTb<|KwRr*6=0{=}xtf$QS$Oc5OI(v^MF?nxL19~DQ>eL2oi4*Abra5y-EB{qu#Wq$V!b&Ze$vQEA|1mB);+ox4RuU?&?|@D~?n#(oGTAs#B!%?+ z)XT4CNqdAJ=a2VSttim8VIMy>pT2C4VGWF+v${)!L|=(Y+6YAU#M0DK_u>ovh<^Vf z`3Y?0bLJbb{BBX3ORJom8E2L>{J~)aFS}PXb$Sp|jcpX-20nJR6vB?fIxo3-4A}i{ zoh+#!u6)a=m8%FNweOeSzzRRT>z)eH&*OHt){0)@shrL;2`4&rl~lFjM%v?H$@-~l z)j?UTDCm+Ba#G!$upzFElG%liFJvv_D?;;w(<#|tr!fjN1TDXQ?peBcfG6o6m>KbR1gXJfjlRT&<==KR0|1m^V4wtV^EYy< zu*xisx^vQHu!{nCz3wbDq47vmK-E58ZuR{|ixzErhUt2; zr^fFYKsDd{7V$<~$l3`VXuFs-$}CbMGPuCG>lx=0fNM`2!v+s7C}B_G0kPPQiwR%phfGxkcQyE6 zNDzI(8&Ac2#JAk7Ryv&M7**JMPWC!}#^&CVbjfB@u_3oM^c7KmE*1|V?^r3@?b6#MIx zD8Z8`VB-f=;t)THgpl=oBYl}!D5XoXguReNEnLk#0QH#y{vB=3TBf&p>FMjVaYDri zAZWlB=FLIxSTk0c!`al0Avhp;$SEnUu%1UXMKBDBTqJ$KEa8N{jhPy9%DAR4zcB!# zRPWvzu@6MDlyevINel#!{;?LJzZ+#kd*le=7V;ed*JE4!X@7!fg>m^UTU22*Qr+Uk zHE!?`UHOryL`zzC5b(eLftN3L?+p3<>7=LCT#}VAAz4|UJjm@ba$IjbTwRP2Yas26 zXSjC!>MNkvlVlpv@>V7|cfjXFn}uEGG8W(Cq;zr_;jj{r=a5|q%M5>pXY6V^)>aFp z`O=wpB?!ELwC6QrIUU&!0}@!e`I%p|{g;^fpaD$36wih(s=Nu*80ByGx967h*vaq3 z$m!J#JTE+jbmhoczbl#hj_yTA8(&l!bQCOhprKr}UinC_J3-il2yv}oN%29*vm zzoNj!Cb!I_N1YAy5xP>h0_GKEnBqtm;uF6Bb~RXIp`%$P110fj8r`iJ|UYTKZp(G(Fqcgc`X%yd;fmRlcNDjrRwjQ#Lr z#Geu+4cU*|RO=*cMJSUD&M+r9Ih}2dzp;Gh$Mqi`&Am&So@ixrp%$aee5)PohgC2n zuPi$40}N{~v6Kn2?DoKM#nnS8YN0fLh4mI1@AoGFDzf$_K@kjk&P!Th$LIs+4dH;=`$Vi z0awoa#1;!9Wq)J+FG3~&gu!-w{FYlVz{xnjIMkf90Vl)>aWPDfWxb;AIb4jaoyCjG z@Lh_Qk_W%n`)F>LcE9wm6WTWa`EoBN2%2-=VDbB%uTuEXpPA3m{7h>Q30JN=?${zp zk8*+GM#-g@)JlR019P=+Dv*$Ahtq)c$YO$anr%d!P26dH)Y)cWfrh0Ya!Zk?pSy0w zNlAJZ2UU?GB1KJpDm$G8kyu=HHFs5mNrD8lQrhC}`Czk9V;lpw2dN;BF@ZPdBdjc; z5SD8y2Y=3O8aAYteJFATZfmYPp^s%YSr#@gW1LUX#DXv;dC9Tk4lMtU-aTC4u970Z6!*6|xs-&lF$aaJ7p@^j*@vfi6U1Cc zFy+PJjD;g09vMImi&3M00iOxPBG2teNB