From e68b2248f634729e4367d669a401ab66781da279 Mon Sep 17 00:00:00 2001 From: Never Gude Date: Mon, 25 May 2026 18:06:24 +0200 Subject: [PATCH] aufgabe 1 --- übung_5/agt_übung_5.pdf | Bin 32274 -> 41766 bytes übung_5/aufgabe_1.tex | 64 +++++++++++++++++++++++++++++----------- 2 files changed, 46 insertions(+), 18 deletions(-) diff --git a/übung_5/agt_übung_5.pdf b/übung_5/agt_übung_5.pdf index d9498c3aa86805a00ba3dfdaafb9a45999e828e5..cbf3b40acd9acd162809800006ca705f1ce4acfb 100644 GIT binary patch delta 30333 zcmZs>Q*fY7*tHvHf=MQ}lZkEH#>BR5J+W=uwr$(aWMbRNe!s8&+Eu&u-}lKn=%eng z>T9i92_K*(BVchn5KIglOz{HfK&LGYJN)G*+C8``sgiu3x_);f-2$Y8n?of;xnrct z>!(6N(YzIb9GDS94p#WJaQxQuY-%oFz;+UP8Lf3L&{Zb8kh_tT45sh25bDB1{ z>34C5M0sG6gd4b$rs%B1GxIi?PU?pYhV~2I-&3@#((M;~w=7-Rq9znbKv{L}(^DaQ zme!@<=JVbR9j&MiU54JOP6*U?1$#daHj=aqCY@8{ufWn}a=Iv5LR!Y32(V$+r>u0! z@|BQVA<0$^6`?@7siqmyxW@=C5gnXql0`#A9GY&n3^Wxl4f8|FuK7kT%2!ngLjyQb zyxm682pJGna|?EALCjcD;I|i66yYPcba|!xUu?Id&gSs5$NR%tDa}kmfzatT!mfu+ zJAU0BpHlkX#mD>K!ESAz*(+abQK&QX0ASnO^T9M%w__dhQOLSgEO@R6F~zbY?I(pq z`q>;aw-c_9ruaAzboS$1^Sk;9l9sg1LXT<18iYi+;dC`v4>R5zh~w_j7h&_$fGi-- z2$B)*QEMWu1ho$cqc<9#jG>dquurp))@5g`LHz}5@-e%9M^J$>;-x8@8qTOB=_8^< zj+X1_9hb0u4~g3k2w>9644mt%shZ(7_usF^N4CC9rN4 zLd3&Wg179G3Lhl_MKW0@)l>_ZK1xWcBSXzSC+e>E9cgzrF9~($Z*I48rj7BLTX3}Z zGdzn3W16b6>zeam!z26EuclPX1;O(2k~>AwhOl>Y_ZriU|L!)(P(&$rEu>!(2GSy8 zNk7wlvREQo8eE%_UFH%8Olj7eh&>69ix>y; zYnSgQPg%?~3pit_1-{{$NyfFvO+6BJ3rHBNlgRu!A9Co;bp5?UmHhtRl`L3V3NKCO z;kOo2-X*PQiI1`}m*H+!yAcfC1Z;d|CvXJJq0m}0j0?`;n->@d;^7q^>IzCUhMtkA zIs0)UJ9UXbi?i;M6Rsw|q}!~#<6WZn9=T?`;l8Ini$+Xi9|`i@aTmRW&e@Rj*@;Vn5t0^RY0} z*}ddx!R8Y6wb9|8XvdQsi;MO;0_AtyYRM$9;!@7gW2ay*24UF=MSIqQGXh~3)XZU% zs3X;VE#+xpelGFXA4k!{pxjzFy&D(tn2kpbJ!`P$6MM47efM_E-)%xpgubt{MV6^p zK*T!Vk=Cvx#DBHfZz~;8!xaNacp!{JbTz{{alp@7cZkJRXRf&sbQb#;d~nwl-QIxd zbvg`-uGoyW?PJ5x;<4!={d}k3Z)1bGf&AQtzkE;IVbhXpIT7y;s-|*YYQ*$rOkqJk z1KmbpRPNgKui;I8B{3w~ewF4&6{3&!na7U`W62kn-!1k$2S0%ZC4cGt=&2)|S8)Cg zfJ}U9Jx1Pxc~gR`j+rNPbqa59p&JM0odTrDMm(lkR-u|*LK2OjLYX>9?*hU^C3lug zr$}vM{Co+#oKtT5gO0^u#8!SWJ!EUI=t#fYIj=S+TUN5s$|hpKeQ)!VgHYlxmr-XxA43c$r+99ynDmuk=a^XgjC=BE6w=`xp42Ud7UBcTwXKr@ zEaMx}+>A3+cR1Oxe`_8w!C7j3T5fzRa{5a_16?}8-^vi$S2Q!{hH|AW-J&bzKNkEM zrYZ0LpnNN2pl;zQD<`gcJ2z<`6*!6VK0kpXr`cSb)thp1ndMv8D@nRJ+00LI7H*KJ z*Bha}KM@GG%!xq$o@y5l^&g6>XId}0cG+wkS>iujczo36;yU4TUbFy-Q7D*V<;;8me{Qmu!1y6_} ziACA8g4m-BK>=lIm-Oc;&Xis&0;e}*(z$Jw`qJZLpjnO3XB+F6NVz*@b9gU4Hq&bOV)%R}63=8yKnBbQiRh#al8 zz3_dRW?+>?Bm(yWNM!T|`#NFXcpH`lQhD0u%wyw>QR5&je%v zDWBs>Ny!BIfA4VL3$MyZh;uo$(EJSEr}yM>|4JiD%dK7kMC}as<8x2AM2{Im9tOyt zuhBCq9$267(y5B4lG%exwp7))96wNBFYWYtFC-`hDP$8NX{(B;4uz>)_^r?-_78C( zj9_MNM?=(UgL9Zh}5pj9Ckv1Pc*UHajFDayRcw2XAJx zFZHeC{D)J4RG%Y1f`Vr1qY0K`^GxpGfNEBa;-CU9`Eh3Al1%wIK6}CCU+XgSJmXP$ z^6NM2kxhJoQ*uN2$ybvXB8ZJfA|z@Vt2ad*!4_F2j91yLyBho*S{sm^s-i~0iqzfl z6C(9At8tzt;Ixu?uGE^M-4?!fj0fr97A-U_*RdeLz@6px$M6okfxjlDn67cx+=*9) zAWo3vE9v=Fk4g7f8{X=X1{X%RBUDM&ZXP$uA*cWGo`}PPkG=>N{z8P!6p|u713nmx z$&^&~aHBTPfFov?3aFplJvS$;!|R44bO-6!4v~u8$VQ&1e^K`T$gYOyj zriZ@8Dq<*lTNZ+pw*ADo=ui$f0)~rRL+1LZ)B2 zci>E!j26outOS-=CKBw;-Kels-Twwd;&l=+Q@yqcfe9V3IHo)iW-Zwh(`71KGG*NYpG zDvwgJq71_k2ItB4c#LU3b5!Qi9Nii4>svL!lar{_zL!c(!gNPDB%V&*w$l%tGIsvVX+v{7Z0`o@)lj_jk+yHL|!!qa`-WJ}V#G+aJCrGV9vk9rqu>;H;-~eZrQ{ON~*mgiKK#soQtf;(c=RMJI_}bCzPGT>W(=<;qW|AuSnD z3We1lO`wkRYW7#+OF3r6{R@__N*f*TYFmXE3z;CpSCd5Ion6zs|hnOd4ki-;w zb*|GaBePo2ic?#V9tfhu6q9V`oh7Q=eY~Hu`*GcV6nBLaWk(TbVNc;L9=MvF2v_65 zI=eIhW0ilY0+l7q^!x?yB7iMf`xd-UiIxW{o5EH&pmi_2%8XX zalFSZSCF$PwJcEJo-Mz1zSJGs3^Kk%e}+UfR&`R+LlrbQ)=Uy_$x!n-=8BksDD0Q( zVAn?Jg?!yL{Vtc4HZZ5uxQNA>@I=$$)%+zh44N-l`BOxL?N)L6bKnQj$r43joV&Hj zIw!MTo+)HqBv2Vwl_t*xZVjKcS2hDyqt$h3YL}u4&K89xcODZ*_ukItZ{MKpal6|9 zUBsywG~RHk5YM{M06G@H(k}(|>ges!W9xnT5_3-1gCB@Wt!R$03iovb3&##a9+7gc z&tf3lPIp5#Mt4~4=k~mn49ns`Ltau6RGJV6_AE(t4}_@HE+ODnkQJWB926dj55xR= zTW7NSGXHuu7W@12_ovj+BzHDgDlHWNcK>7tb8c(V+=l8+xJ19zxz!v;j>W zI>u}(VkKTn^z=?S1=|@}I0&7KBDy6&{G;yV>h81>Z9gsjb5IaFTg(gJ)dZG`*`rf7^o5^hk zvu6yWt*kt|z^BRHZ0GHr-)v}g>gG`+#-_{BED%-?ZPK#g8Ha{ludQm1FAayQv9qQe z7zc|leP9CaaJJR~Nb4~xnllouJ@SpS1WFlo7WI*BbBpF1$X#k@# zNd8cq$Q{{eS)#3uPMJ=7eX&Gq{tVuVL+W1Cs?HR--SJ)-abU$mSupH3zLOoc{N>75 zA0({*(JAmDk^9@5M&D+1mHmw+->pxw6-czJl?M-sTAJFmS^|OYv8T9q!ePxu4aH&I z?&=nsevh&Vb@Yv3s97$0P~|y;SpogHV`-&XUVVAnlrF zt2^V9iE#gOhTZuj4XY@3W#b_ILS$c>ffJ~~j@ntq9@~%Y%1MGPeQZus{j>889-qY4 z@&D&K=Ktk7fR&AtkdKe>|18-5!+!1?)ydPgn+))y*B-Fl0vt*o34Z+oYAm5UA+M?r zO$Mb$af`Y@6o10+`>YN|c+eK(FVQ=3snDNfQK1Ru!8EMxRCSVX?YmuFBNMflvoQG_ zrTp8y??dpqw7Rz_C`>dlQU;AO*&pr7yn84sc5Z z4bX+9tHnt*k^7@&9|UTl3^rk%#_&|pBMJPfV`Yk<2tw;AEtg%DQ)2BdLy z&NO?LnDgb~e& zSNg|Nq+6o{nnd*NFQZkvDyFaX*_@uXTt)1Q*i9GR^SZpjlukNuqakI~WTm-8^w6o} zv{bH2{`1s~4a06qnB`^w1oy@{Cf?|1$70~9Qt9G=Q; z=_n}dQpR{e?RukMie!L&@LT<4CY(p#|2C6Y+0k(7%#2WgsV1!Rguy(UFOSOA%`q|s>3wV zf)J5mAcXM!;>E#;#{EfuUusSeGo^Gop)Ex= zD>0i0#aq7R%nHDvE=*6ra~9L3h)pb=eeBX}mo1(aEIPpzCRbdPolt&f)1>`QqoGrM zOQ+EhG?7xHhPz)|%UYE{hoCOA4*vcA9W**jt3O=uy71@J!%>PzR%Pryd0}j7m4b^p zOx3uYf{IHT?J;Bdyt`&fLfjGl5)AUO$&f#V#1$E&4hA#K9z4zwiY>X77Rjv z!^WF>m63&mp0*Tz3gKwLM5O&o!#Od>F~-X_$}Q$!xBMKjpEjoJfJzvQg|QtC#G= zH!%N6g|DpdQ}#|g$~n@-AxD#UUmY_u3~{4-N;bxVnZ>5X0zBwl6e{HdEsMfHgpN#IXZ&wK1czgWUUssd%E}}kh31C;i~YP zh}Je=fAs~$iTA+-Z|*G2py@0YR||@gs^4hRz&A!q7Spnby_XjB-TH{MQTWPy`+ty0 z?*S;UEzwxqlPiNzJS!w20-xnQi8hxybo@ z0)E2DonFVk7n1g9z5Jb@$Sm5cH{aqVLd~r?DXU;^`_oJ_Nv8fFPko;fo^ESQ>=5`R zhqD%Mj*Hv;k85osvzOBWsV2~heMr#tQ5>j)OyDkKt~%W8b#*o}r?M3yd;b?9GZqMo zSa)$oLyBZ+V7@9q^&eGKCt<5?BE=oD9^0hW?GxTRgx4d(V9K7#|C^5%H|~hjABgp& z!giW(9L@pz$H}s11HSb$a|tO~1~g!styz4v;ub4*Ab0<~vghEUL6j~@>@-TMuLCG3 zx%GN9h7!@HIg^Sn60%nE;6(5K2u=zsFRa)(un~{VooiA=mQqebBhue;{x>GfBrG8m zPI2XL9yAVLUF&*gCEE+t)4Aa=x(>eEc<}}LFM2}IDK_5@&dWm0TE)_#5%yJkGzQmS z*RQ&-NGKycUAF=M9651e;g7m=ZV({nO`r0PI{LoJ9s5khshd40u5wGE2 zndcv4YV}qA<}!W%%$ryH;1qsiwj=3^!)MjFth}viQX911=BNaMo}`3wuYEV?dYiu) z`WX7?x6tTvh%M2o5eupTLa+S~YAvudt%w;jelO-roQaK?w7@L#OAb|Dv=#S(r=A_d zg|*d7GY`kIMTitVx}U3ZWelhqpba62A)cq5WIYKG@8{x@NNatSC+{(|y3#}>5OiQ2 z3{;W0nj!%6hWSF~U=Ew~9`>7n_d=zb^Pe%f)ygzLrEB;J=2rdOq^q;J0}deq8K&<qVUmR`E;aDCnwxxEAW-cv+=6=DlT1U*Rji;ayl@Iok zayW&+>@-QDIKM8bV`tkdtCnP9f= zN`_}sWKAA1yx(3Q@WCqaNDMp?@W}3mq%*Gy{B2(5jFs)4AdW~}xTvlN>seOj=ScJ8 zYj5#%_ioqh+dxhss25ev-E^)ujI|nNJlbFi->l7e+VENE3&-Vy5?mQd+xx3;$zS&? z^BW3Hq@f$uB=M7m3t;5AqzOdJz;rI(2ltC>*5^({j7Wvx&s-2_y zh)c-zB%_=+Pgb)6)U=)P$mf}_hN{jIGwOlq!(`b&DR)*>eFfgfc$aj}u1gc!s$5+nsk^J(TX4-)^4$b$$Ac?Jq?7`h0VqGS`P zCb6tzQ5_+gh-i@^Ssa(6ik#TIbPn8>57SJ116XF4Gs=i$Fif|cCqK-_8-~(3ztlg{oUTZA#BDL2cfJ^7de zC{2mdAo%n=Ib^28fu?`GSHE>-p`RBLjR*q^jE}|_JYI%#)36Faels_c`Vb_F&J&MM z;qdc(*n9xxcdT$u_p0jHnbjqlh1t`y(>g5t{Oq-Utm;)&KMcs=C$H=8O*6+0Tk1PZ zUE6^W+C$4T8U(Fu3w*5#jY@+_T7-FG%dYIhGgj-C;i)rs5;Z%0+7RHcb%lC)wZ3%I zIa_sYTA=}Zrh8|))t(KHmeIc|?da^*4RvVx1P4#v+EjN{2UFL=cno$kHp`sc@80Uk z2Xwq%&DqS$-(JjQG1^qIni9076Xn&8QojKW^9VWQVyq?Gv+^odN|MuhZ~6#03kMCJ z81aL<7Zrn)I&wy8vK$Ik7z=lncrj{UH<8g&ag%QOpdRu&U2i>6cz3q+$W|k6Up)H$ z=rsX#o@n)Pe5P3AM6t(212kQ)XGCqkNPHB?`NUSoF^B|VSeQQMn@vm6eCB`y;TK>r z7KgapeE}Tz?ayo7YI%eQpTlSzhYsU!IMEgl!RA(8KU=|lQXe||k^`E6v^VebuCD)1 zm??A4ceVzEM-@)4*{yxx@1K#}XNLRx1^O^1We=@Lsw_>Fn3eX)VfCLRatwdraYZKe z4N;UE&|1g3&&GdEwJfPTi? zcjU|NXZS01-kptID$kR=!eal@-U*ND(vF+&$ADVE*W?Kwm)*_Lz=f&6LiGk!6G)6p z`JDZW_CMp@@JgLsNTPHxYGKoDY~5JPI0sCf09b9Z6te-p1F^G0?lwV9i_?j*{eLQ|UR_E8cy-9pV(wup8*#=`bLUfR0PY4B0p@(K0<&U2!w?#Br?Jeu>c_o!w_jVC1##HhsQV_S zEo;qXVC8|+GH6*A2coQ0;_3|9eYkfaLOG~+@wuw>2&Otd6EZis|MhQ*PSCL$U_cGIzNem{gXk`k{oMFXZ0#FG ztX#^pWg;7+lP4>+q5H5)FIhc+*&rmHd&J9m?6bHs=z864?;=#YTUL$FYZBf?tB;cgNN) zJG9?Toof|4;0&jc#S$s4obeAqw zeVp}@+TL%Ml@ zJ);nvDdcHeGTKqkR3pHZD$ke;GRADN&$u;431Sxt*|Cu-;>?$+bwW6q=m8h{@kYjB zsxd4-#yHB@5G-Fgjb@sajN-NSQBlW*tMOVw%VoEM5)ZSvxNkmgg{8`3&wS2_1=dn? ziN%e@+x6k)pQo;C>$Xjq+GN$z#)}K?I5+o7Se!d=mW)Zu#P*d+CNQ&LD(MU2je8TE zxGu?)=>3xbVGaQF{6NuIKtP13xn5YPcHZDq9XHzOA zS{u9Om5OS)&D&4>iWdk$QT%-@WO)CZ-}HC-huOafgMR&h`9Vxbh&WuaY`LtdRjpaC zS=zn0%E8=v;5^E?v)Nf#{k*f&^1Pe*k+3^H&SwQ!`TRH8gQn4VlZK7!i)^)8Eo`2H zRn;GDtbnMYuZ$9x9-)M%K{lymTspFL9q}(LcUTT2e{v0fiwl9Fw7!S9J`|(FEXHr& ztFHm_c?|g&-hh&Nb?fTqz+0ELG&|`Nq48FlI7(eOM84)i9zvN%r6g#q*H14 ziNMYG@wiEOf$>*|N{>PUC8go~D(Q;x3hIiCD(X4biuH>33h|2Liqs0#iscISislN} zil-{e`Og)o6){zKD-FY5P9#!w;H z5kCGW5|se4QBENM%@fltYM1BhDd+*|018u`dDOC~52P5pK` z37k1sSL9YJn-Y7yAJS6(%b-*K`(S$4hf+qYaiD>-vI_J`4e7%=`A zr+DO%Gp)b6*@w_V#Z4a3v~w;Do82Gzty6ae6*+I&A70&WiYn=9?Gj* z*dCS7_wmMX4V1fy8^j6Hp-#AW5b$d*Fyi`G?MRXTV}fP<47Y2q2j3!c;*TVijPGV2 zx75xD#2h<`BwUG;R*r7Z#rhA*ACDR%Qa-^wBC+xb@*d)01P;fq{bo<#J@c78&La)x zrV|f!vCZJ&JziOaFJ6m$$2B&^bDJBK53U@D$IZu_im7{H2eJg|+;6Pukifq`ZHf0^ zA;O(cvyQYutaW0YAz;zcA;vy;v!Kfojx52Ju+IF5mJg~%;9p$!xDJ~LLb0!eagX*+ zFbt7?ShKnHrjISvlcI2hNPnlTDj1_}frQwsbMmh*edo(BCVKY&;&`{Eo02bzJ!*SV zFG$iNCp4?7m`Xa-r-*;lBUI-2Q;Hxwz?c=v7u=JiWR!UfY0P7W=kV|k=k5Xdg}1B5 zhj(n2ZLMY(-}(LJ*%m{%oUN4U9f?1j3itO?%TDH**{Y=ncnIhx2=E}N_lJOdVh!6) zq#Y_44ZFX0$P!7_BLju`cYe>QIG~^~F)2zsC1Zjw9^RR__+1B%n4oEVS+Cg{-L`9PE$WTe z8-d7eQ0hxgE=7&~1<=nl4NTB{grn4t8JBATo;J4 zjB0BlpK0O0t4~B+v}9ASRe*OG4)9hzT+N3v!VUtoAuaw1ps`qR%E@Kpni1u*d%c>? zfoAVK}z-E>CP$MbhI6 z&IhYX;P{~V*$mC7fy_V@IjON|+!qaHF1p@PRbf3AK;y$kE=9{#CT#PERf;0e(MHh( z$uy@sH>%AGNb~TI6#X?BWkUMw1`8G}(K@TKYS5=G?=~k9LDx0sJH!ZUYydd0D{&F%e{gvPi{Lb-@K1UYVPGK+=zO_Sdjv64sP zkH(+k731R+Dk(t(OPr-Zm?%$@FCGRB+gU21@);pzfG$j+Vum&r-S{}{0Oc4aE&K+% zM}+z=D>ewX?UeV>hC?X2gEds@o&?UQ@ox)V)J_~Ent}$LFYd_0WDHaZoBumk(H+aW^yQ)RZ4iTMZ!Uk4~_Py>4HP{7&O=_Ri;e|QDdy{?kM?rr2q zVbjA3Xx%2SnQgc=V6U25>oU4W_>u`5GC=$wXUy@X+;j==av&RW$!y(8-$vgLwN)$q ze(C!P#P|v!bBd=?%>L<>-=}*7hT(qBrF9d%=;&4ek~}W0BB)c-B#fu9-qK`%jQ^q> z3_g4%t5&68Alq*suw(h>);SMWw|Icq6k(zsIL;WZ!`4-=xANCdbY`O&O0{$s7ziEP zBH?Xbwyj77pHpq`#Z(*0D|o%V-whidlNzTk5}`QD3l2GIvgWwa=HK*4zTt;=NT}}` z2JfU3%?d)P*3<5na?@qpn30bw5e5tEun>EPr$yZujUF?(`}2;Q`+$oZZ?uIc&>mV^Ygt zV+O8=OWv?(eS|hL*jSmZ2~9h9a0wkct9_^a5x2$Ky7r{;bkG~i++IDM!c|pY;Y=Y< z7U7_<6aKL$n6{rDTR*!^WxyFmNl@%bL%CVbQIE{DPY4SbLb|f| zEsiz$%RX(q@cSYBN#OI1Lk>>u)H6MfQxI>t{O>XZ&brx>`r)(Jy zo`FbC-@>k=@BOkbQEbMYE8&$<*?!sz)pl%#?|CZ$B2?wJI7u)6Tpe8eWv%J*7J3UA z7_Foe>`|(Mh66imKwJF5aXqu9#L0@8s0ayLC(fu+!XS$+z_KW*WP(w>Yhs{ze?oJ8 z@X0GbDw6l02U4u%JG;>t@2@Qbl99fx?cXv(dSI3AdU(75X8;)Ya!SwLY0#faHsfcV zT>KIa`LEZVLGK#2o2rJ$$FiKDj+rJroVMF%{%2v@H8ceT(PVE?^cbVRal|@_h{18k z6fS{?9XxJyMjnGZhNLu8spEoZQe>V07ZLTa6 z@hbW&@~HBbP|c-oxx|7|*RdHT0FaIChhu3(|04;wfBayc(ODwDQ}Z(#4wW_{i3k>o zrCSWHbeKYh?uKR(Ql5^07JR$%N}=`w;(gFF2* zGm%p>F|4#K&O00at~^Wm&e!9@CQ`|Ak}mQlifv3YhXnFui4Hn=Tu!ECCJ+>hT&Yl< zGX=!b@%3OU{RP8QMpLjKHUdv@j8ghMW!@IIXX+u}3?lvj6sQXj9pZd>0Erj-qA_X} z%{qcD(Os(u8>BxG=KxsZWwEiAe}XGg`_a`( z+7+|?M-Rbm#->_K%qTb}*PNMOKRqPFzAsTq-$S9En*-2fq%vf%Ag9_$&$P!i8!rkL z?`bP~=RHjJ#=-$+5@;@SiYZts4Ua!29&k7KM`T5)<-A-waQ%uIjP4t$KUnOL#2QG>N~mBBdcr~xY_!;&WbPw%eW5A5`_pK@HD z?P#nf3LqZ=CY$BBB7BbT-#4pN!n7*&88WuWJI=m0f5QPSf*xiG3=LFg#rPJ1^k}1W z_#%l#i88O=i|E(>v`0D%;T1MzYT8^=jcU{ceO7)`YJTA)tWMnLxYYRaegSgP8wx8a z%DttJ!+MUjd@nHi=Qbqy5KI-^}0b z^;+AFPk4aA;KdT{lI(;q-MgrDW#0N$>2tRi2YrC1Upag;681^;hdzoi!hlOhaJ3%` zJai7n@Nc8q#O+ie6&dDP&2XL-F{e)muYCa9V|$Z-KK z7ZNtN_nM>!Fb7Zgr-bmalmGCy_&{+>bOGAm)&{Uo>#e4tUkM9Wwx>>3*R zJM+?UttnJe&Y5Rzu2(TC*8e&NgL5RK8XP_y=C>}sVi?# zdIy5*pC3}#E$+p;%>XtEX(N4pgO9UuLg74L<8GaIjhanH|12o4=tH-&fosX7f5#nD z(jnSH6Bhh)An2vLor$q%Fy-mOZSr;wJG%}IWU#SI;cv=<~H|x^0Z>>9cch)rVUQUNS6BL!d@%xC3!!)8*e(P%C%fwy?cI&&vuB zg8Z|xH>L{SlM%Zy?$q{_ZP(8j@RA{eM{w5bjBCLWV4>g0jKX+l@?fDR*lPYVqeYF_>sf?VL> zMIn2}&K|7_-m-b?onU*ZWU6i9;x-_mKQPQLHc+ce{PVai5Z^I%6{5!1*oBp=YYxO# z2i!eR_nMiB2%g*mi3ct+v?V9dcOx+L?dB$b5MzU$ExL_Pfc{9AySAYJ0K#&VqLiQg_mK zm1N{wDw7q-TZ6eH)%E=Qcq*}--}0fKk3bOG4>I;!w2L1eSPr0pj z0DPnTxxiy#M8My_Xyw%acM&Qdsg|oi&U+Ng?oft|BWxl_-Mo1BABoQJFBu< ztOswR1CzVCB+R<>`;fmN-D3tnm_hA^{Ith%83!(h^Z2M=YP`#)YHufVE5tOhGfKI* zs7H1tMl}>8NJiDLE&d%X+F|DRb?v8sY`$DIdv?S44DM54PseL+*LY`25w(lyfp}m> z-)Hf;WrHvya5ZfzvoOBI-eWTnvNqJADB+~}b2YTZ`!{|KUj3Yd-@GVw`L&c_hl<%< z$p`|U(PH!K6pzwf?R^-@r8{!3^yNV6@2q=S5cafcsL0*n-pWO=wv z_NYYkg1Qf26S(PyDGMN|fyBSKicWqN3P&I~KuHOf0qHxIJpsA`PIJ^h5{uJlLY`1J z4$#bD0#GQkB=$sL$rJh%M+E0m1@*vwVzH3U#R&@kzoG$T8jm*LJiAl6YdfV|uCtJU znv_m6^V1>n;%U%UtoX!ewX>yBD;r-p})aUXO6sMZr@c+|*N^IAn17l(QpNh)w zu|N8ThWaLR??84eD2BceLog;cCMNcrs3asT{2-n^2*`0H_)Q{~_J64sD>KXgmR8hZ zv=h}@G)1ZP1=k^os{DVg1YK~#NJ_-{AifhL z7ullXDk7;ZtrVx6MOC|6mQFhFe5Oh7+Sz(vKWDP{KI``UJIbNo?KXSOb-Lo*zb}zH zynXfFMdaT?ed$kGT`?maDeCUw1%$AVdpiB^4?g;}rl$8D=Y!vXu_>K0X5280l<+V-ZUK!>^Yr#Sy|vlKuGKRISZRwG$~1kK{CgnnVEeCt zdi;AQmNPERVeea`$NTl%S-pJ>&=FDcmMQoS8G1=F{(ha8FCVVAJ^Ng1N=qBAw}8vB zd{kNSJNY-3Ha*WMx!_(7WQps|-gLR|be-}L~mZuV^sZBA_t zY))*BY|gyLJtNsc+mYL0TpR7+>;9ro!Wh{c)tgegZT5!Sop8I+dOZlxtu+9Rz20#n zvfD@H@=8w~;2wUD;g9XjvHSZhv(9l?)F(g3vutGvc`%xFzjl2KtT8X#)1PFU>3W$i zS*5S8F1pHaU*lc+n7zH7zL)4B!v+`xo(^-kfub`&3p*n>D=mh_-W-J73RQN>M0_WMp z79$;6-pfyMe9#rJ7KmtaeEIX3i!d57${f7lOUdNh$9&#v&~eB+Ck0JixfU8a@e*O7 zu3yyJ-c#)mqxC{T;^SqZm6$hJRKd%lbl`jQ6hGq(9HB4)qV~|#pKvwaBw!}-0|lZ+ zc8oD#(sciXB-Ri#s4B*d-k`;L0%rFXa=gS6D@1J7{NW2s;$(_@QX}>Dc1P%c*dj(4 zZj$oy+Su^&CbX=nhm)$(c$f1mVi0`z4*RrRAw3fmI3SWQnPx1=Sk$3E5xf2f>&RjHm{GP#bz!9f+)d`4YDJ8Whf81KRx4_Z6+{z!U7la4vJAJl*V6y7I z(F>UeHFEP0=RO(@+MkTSnCkJoBj9*>|CNoG9MPt$qV#*7FB(7@sBpy79AdL?%(s@X zGFc1!SIt8i1m^iiF);UW&^M=eg_uWp3y#jG7Jpq1u#8CO?Eo3X7ts1yqQw8vVixF9 zCU$YBpQ@b6SKD49oMLznGDtVYei(qe($6#PDPT>LZdbHof?y)Y0~pLI>S=S$=vrmC z%NeUNtLwLGE&Wif!xS(}NE@TB!~Ri8Ruxegvv9`x?=`A<*Y zlW3^K8SA>LK`qyV*n(R+SnOAU@gKC17@WDbz*lZ>zeg_IR}?>bJg<5l2MvDk`KV^4 zVsK2o6t3jw9B65$cC^Iym~jQ^1P=$un`+jw4#%(YyVOgKtJXz|vwQCXjoign;@s$gHdkG&QesqM#Jucadn zz<^6XB@L1w<}gRsCnER){T|U4kBy)K^;E5S~DZAk>o|f4}~?LThDlV}21F zo$z5r0lZ2vC+`piL2c87K1o$_2-GE9yiJI#gn69ak*V{(i|hw9Fc9Gt0PUU__Cv1g zw$c5+N*SIVbh68&g?Ug;MdfIGg@1fGfQ%*;2K~usga&pMFd?Wq-o&L0r40QTqG?mQ zK$9O6yTtW-INne?AXYz=#_+o)yMeV1>a$!hD6y`r?QD&bY(LzE)L&9^oh-5t>Mw?2 zEk6IgG^84*9>(_uhnx>#TL`mgT`Nc1?<&%2i^bhNP##QP=AgSuG}GVuW^qhdz)`?O zZAak`HzOkDV-UEtee;p$A)K8+M1-rKQ9EjN;I98&7*ZA$--=gLO?h<#ie;XRUWM&+ z1wtUrm|`Uhl*m){yas0Bv^h8q@<>7#UzbPH{plSZ;P(enb;lII8{HHUaW=Y_bs%@f z_;keQT#8~;MN>+nAX46;lPTT0x-wkOXVn8y_S-FXww^L45vn=^TuHNmcL^ z-|0vi#KGS-FU)*oWC@y!4M-jS{78j!*XgFuaWp$Oq3IsxvnXL)tKzHx8ZefMG7SA_ zgf42un6!jVE61&km3PX_*2w)lOnD%0P|Y64=9%rmC!Pl!Ir6-~`9f%?Z@ZVQ#OPa_ zh&Yn;22d#whQt+ylB1omwphGjSNDwn#WT1Qr1*Fff|p;w^91y2UXjQ$YUETe&v)r7 zY!C5AefaTu->O_ZzC}+1xs8aEoPc6_mPOS`MFsTIPc7!pwNdPZi9TN^v3A^g#Q&b~ zQnWpcn628<7smCRL^)lcso$uDMzj3KTBs}TB)kdxCCYUm8Ntb8*yky97KxO()a5TX z0p-AUlnrCrTR+mcID@cKq@^iZu5SphS3^GEqin4URuaiye~uUc^0WHA3nZT6CY(C{ zB_YH;)-zw9)Cy*Z0)s_z2gi;V2fx;fioWEd$F-CWt5U0g_4rH5cB%VB&6em$mcL6SorU6oK@G#|m}DK_8Q6A6TlAR&kd zs0mpUwU?3ajFt2Nx>h6QWW!UBZum;8kY)wSJFuS&JR9DaCd*7%N)|JM6n+m2U3bC! zP&uKn6#Y4|jQ>wx-xwT7&~_VJ8{4*R+qP|cVr*<|?2Vm`ooqJT*tTulec!r&?!8~# zs_Cld={hq%W~REjPxm=bhinb{;vZ@F)_~OH_}}nDktTHqp`m(`h2CPX=x{B&m|Tkk zqdi^_0qWm%&2k$gm&!Qgb~sA%&{>HF@rVf>|>rVORovR1(`@@3`gGq^$K_x56X;n-D)xuIs!y@Y-Dgua%AOnvQuD>@hafeEK>v zO?u&&zu}|e)cRB>QTI^QYddCt*R#Nx<=;@_m)hJ){zZ&**#8at3p`z+9-|=%j+jt( zKorcB44ncu!a>=8bD$njfZND4K^WN%JNb2@Eob5NKqIRT(a(ocP|7(TT=BZR7gXDq z7Nek8QacV#slYf^Fol+(wsjS0YjGF%{X_Ud-@Jk(1zO7xM(h_j0Ov5 zDiNS-R>IoBNMW3^RPH(q3LJ;uF>AA13#u3itP6p(71*;?L$t@k5M#G;ma5rI4=hXD z!P8ccm(N;Kn9GX5;b=rKnjyxG%{hO|`;EK*ki1L23_%yN$F^~MV%J>W3i>^~?>7uA zs^tEI3)9o>G=Cq!fedNoTpv~a!t?%3(QP+~Y1ob}4TVvD`~4_&ryd}^Br8+(;q6V&6HP*9DqW;fLeB2D7y?@H1BQMjIV3@#&_vTDnB#;ERI~X6D^JUvW4xOVzS^f z`i9%oDSbH$*P*5dvnPmYs*T&O3eUjeBCR`KjR}BmlnSGiiTfw zJUO7Af}I0xhq+N1BJ#WA-}?ze-oJBNQcZi)l(%KU&*uSq6uqH|+DV4Ul!Hvy7>I8{ zr}B>dr5j{GkN2fV>uCQZMw%tt)NN}e6kH4i%x|_4jt;K*GZl#)Z2~iIh^+xLYOV!c zIhz)h)%E2Kslht#BI?L=$8sf>2;Yrs-KbCl5gpf(W@h_@9!-vCk^*b(Ha-POoJ;zy zDB$>Uc-JXo%cM@j1zuc}ArFp|BT*RY_tk`s2h9R-a&Zcktt-^KuAMNC0ck0j>_JS1 zsO;^E_xK3jHD@_E*Js(nWy4@jX>ASawdKC}n&pB0v!*K9+Wvlj;-fzC zIq^s%RsF|(d=8q;)=_TUaNwUjW?^V!Du+AjIabuo-!=BTnw+Qng-1I_3cG8`Fd@r>WVC+TZtIis|uO zsWy#L-lj@+R|Q{9PurnZPgQSX@fvkt3=0g^HP9oA`-i8v31c?McX5K`y7ZQmqr`Et z3nvjTGsS{v&4ll8b`lb`97|VinhAM(VqUquMbru6tab~kuorIEF>40vG+18=mnzp% z`tm=zakyZwocgK5yjgimX|d)DoUO-?O{`n~67z&g$VV2*xnW=H_PO1xmv3zXct9?I zn>!j9TRLP2I_z9AlZ^~FW7`aA&89Onls1em1+D{c&X^_Fn{>w01v6c+MCyVifV+ks zRU(hcG9K>)$j2atfy;!$P`Oba1|F}J&Zmr#vW6PQ2!qKiqC=y`i+4E3zfBTd6?=Me zRqivKD`|J>#)9jU_k~6Udw&8IeN8BBD;(`BdnkF~0>F@|@Ylzittb(d(+g}nvFg3~ z?j6e~PBPOUnn>H5A&69=mm2VE=C(u{&rF8qzUC8qUwBfA9PeEXYNEHeyiA<}hycM5 zW`B2As+Ti!^kPQ#xMWre`&Gsvf#?O(mAb;g5VF``2_Gc@7{bW3g)uf4`A}$-RCXnf_1gr1u zIw~nm{6?e`l(vLKyDkS;mwI{XAgB0WwoERtL$$BHAOwAc&s?-5FOapnrN0&gYC;B$ z)W~DLpp$vIlKrBgU-*EE;%g&gG96jlpNbiWC@xR@5njhU~BhcNKHrX7T>9R;Jxssb6zg__zWddHc$`_kjlP% zJ`ON~3|Aiyix$e=<5yQ_d4;IiQZabVTXZ~T;0y@Jo~$+IN-ENgHWBJ(=ln%58@{a? zMha^itnVOdHG6B7zOnDMnSJJVQrD%9X`0jBx@y%4O7mCXkruugwc)H^bscs8BRs|5W5J>mQ1c$_WhXX=*Us1dbeD9NfC5`T2F0wRd!vf1%-mXHTU(nDYS~ z9L)dYi8GH>ql6-6^x>@+^bKgVqu_6{G~6tdFxeg{E|j*MZ{L*(P$5;f`<;3(1bCZt zycF199zOZX+db|t0*)vx+>{-!&l_q^vqiA}C>Y%>;>0zUVKY`=Guc1d+&J=Xp( zE%)VATmn`)YG0{Rx@u$Ylq>xfds8q^)fbFtJdyCO7MQ%6UV0ROU*kK~&2QOHM736T zPZ|KH&zGFZVU9o!8|}wWcP)+w_`7_8X*THb4*4H34|6;zKPWldtN1lNemV^-_y2MC zpZZgI>?GbhJggtfuxZd~Xt4Ou;9|+fxsq+XbOzAT1h`TvX@ z4DeeCT9xugFY z%bH$S@p#eFU;l$Nx=Xf{D#&q?H@e580+t=3Is=v(tU3eNOn%FwvK^XU5E~^&`VAG5 zLz;H>3PBB0s92;}P%f_Y?H_@NFT;)MOui#cFANLwN&XJ|oN`UIEiw=q zqzBtp2(26JU-TOsk{BuE6sA(FBEEn(>!mL^ISRC zds#m>}=Dh5!}*WYi|ACbFX~`prvnWPB~$N^2(%OS@D6fasHzgv5DJI znAfn_`ai!ukP%?|cKV2CKrEW%?Om0XK|rRpVGvS6tkfVlx!M1#glo}-_EukL72K<5 z(}PuU!$uD$FX{&)r3Od1q)L~Rh3~)5&W4Vlb_{bNtq%k>YFQ1*{ua5-2h@L zqLQf16czQ*fc&)I^Y#c!eJXMFvH7-%&q{9fxM^1dv;eu{1F<-R(&VV+3TH+xTOB^D zm|G5XW`hA--Y;)Z0JNV#_t=sU?J}LdenY0$4iTsyRUqo1Qu?)`*UgmbXFto=FLqWh z)DC`|36SgwX4Hf3-M5FgvB*cYW3L3vH6hB)UzS&YepjSQ8TEQUMB)K7XDc|<(>X2j zIJkI($3!S6x91aCZh3*8ht)oefq$H_I))|I_jd8nPO73{0CieY{Vp?u^eJbZixw{F zpWk8NaxNQvN2=KL7il!^kv_(_W{2s#BgWBW!(-ZuWr@CbK`Zc7Kc{Qdm{#ChtxY4lqmo@beuB>H0c z{s|g8<@{4Ofu1UVe~hHyqy~h5jmh=FSTp=gKOCtDixDcerOO|PtrmUkZp9wHanx+;9DJXh(wV zFNOI;08-xlY>8Ql0c8Sru4~|*_CFS_a%*I2#)(8i)HwL$VxhDBu55RGDZ z-OhfbyKy(5gqIDKbyAgdqxbmkvD1D?q2A|}WZuig$W-vtg`x*NxJ#xhLqz4Jh}7@1 z1O2meVz-I97P*tEdQKX;A!4FwB#KD7bVeHwak8SK5v5embhqaMKEnH>vH1TeD$*P& zQ;T|yVwbtyNnIEbDFmrsWX>=V_mSrY{T&NYt=K7dJ19_}RYUa6yw?YbSt83KetB)V zDa{K>*>xonx-U9|(Ca$SC{rgw&0Y&>fEXdVDCoY%awptU@|f*zMD3@w02mQS5`(Xn zu?dcM1%K-vw}~nN`h8K6+2lg`4jcC_l$&wG5-KR{qqet-b~wH|!M-}#nBawXL3$Mx zwBXIJiO&xZA6>&9#?h^=0P0r07Raf=(mb+qJihOpg~+cOxt|L=6iGa5ZY+GRz$c;| z6MiI920m6vJ*wyM`EoGEK){3YE$$yD|E3$1?G&*~J1i&dH`mI9Z#gOJO>-)CE;gDB z#*bH6ZyQz}wSE>6cZ%17D5lXB%334%BV3?V4e0l3|1K|(Tz|g9MFG2yy7*s3Ey)HK z@2qM2L7JQP);rmS1ibebq*H-_B)YM>mDo3Qbk8(o({Y%*I5ulpa7JU2P$3)$7-6(yK4^FoGT#!-p&`kW`h3hJ>SU7g zn}9@aIOwE7RtKt=is;NWvFdmT0}`1f&G+Ad`fhtPK24Yp7TL4LB!nu!?>;6DRu=F` z3NiAIpDxhuwtVLX(*tA4c@cZL3QmK3&dLirdS`a969Iqu6ScDJXok-hJ|j*UaV3rH z&#^}OeU}Rilt4e030hq*q2x8c%!+cl80^^gMQMz0uYV9SCRA(F#d>H8myoQ-jydszpoVvZuukK)zR?|mI(#wM28R+Nue1b-fFco7Knp>skL?vE;t zAtfP3CnE2Vc0hi^h@be)_ebOWwUJ}9?AMIqpq{{%2G4R3-%!rZ>Yhd)egQSE%B_{y z0%MpNX=z>Qj93N*`g&qB=le1z1nLPiT{`13Q^!u5V%pi9(GADzON~82)zT~{!lb)8 zWT2=TU++2_ob$h_q#4aK%=W_I84I-aZ!YX~Ri;qabjg*Q4SQ^UC0hxMYbDklFt?nn za2W=Hbp*28912 zUkyV2_58lgORrB(B|{@4)}pZh$$@{#t}GzxVe+aBz<@$xnO@=2hPr#``}1R-hSL(i z&3u8u;O=mh6u&0-u9N^Ur(5Ovp@qSAK?&PAk7T-4$-(lhmR?!*K3Xm)qKrB#CV$r`ZJAPjl)xCpu*f&0_@l}2&@Oxka zZ&qJSRkN}!kx1fc4S22gu(RTm5(^=rhdz1%iYsG918_d9Z>KY&Ke%Gz;j7vFOwjBX z9YZ|WRhFW&@2yo5IHeHfKDRp|zUQA~alrMMO@H8V;JQ^8;R+F~u^eTU;z6EQN3~T& z{r-zCVbZ7>gv6z8Q?X532v>Qp@mQ;=lgP4J%{Y=ug;=lzXLpN7i`=3OwS(>7^jgmh z>?{$^G=1ZA!9&CrX;eX-h8e) zb;~X*$*#z*_>jF0*NM>*f`d0!(UXL>+)@%y@FT{8zez;m^H4eIjE^8vBLZ(kkJ_6S z)-P1rD5!?DzNSSP!S6e_=r6QZ0%zz32A%Sr!Bz_>S~v?y7=`*P`VJL1R}~`V<9s5q zmOT#~3L%eVf_-$o`&LYNC^X2rlTUpc-{4jZmF z33O9k)#IxvBM%EDVosYOPjiIj%VOW3hzs=f6g6y!DCJ%}_5*iNZM_#WSIMQXiRS~A z@(zC}Yq|s)hJ&sRp&-vd9)kxN>IY$qHYa%6x}~tGYkNDBt7MM)k$Ae?M^EI;OX8bj zeb~M;dhL*`QiZh<9c?JvRuy&tlTkX8)~((rUH68<|1=er4qdGYUp;!RJxK{R8LEqS zDLYh`RL`J2OJBl}0V5n11pUE@J+P%UvhrAYWiU%1M5AA9O-TLj7acl!Rx3*14C~pR zU1ZpoLhfY(A8X@`1F>+{Y~7;3hq*==*Xcxej-tcK$dHSMGJTY0HIEYkcXsww?NK4- zee1Va?|iEm2XR`X`L;8&a#U(gODhxCEvu-9iOf)2Yl)g*Til_AA|jN|nb9E9UlaJ) zedcko@(;ME^>c*FRX1@%mm>8Ylr;r}X%7chPXkLchgLb!`B4%BCD#gh%y@w2KOVA? z($3}~m@J&=Q0?8^zF`3HtEodi4-djTE|L!vofR>3O}1}nt{^XukXbmI4Z~CVW7I@9 zwiw2p@I1b)5n#RQs-L>K8M``|of2uSzG$97)VI|g+2NpowG%+>eKRc8hsJL@IB=al zDI6$0Cepe0Sjs3rupgc@?utqtI?$C|geqsC=K{UGQ<%m$kof?_9NHV0Rux>ZYIsCt z5GBw1i`>%B;_{NhA{%8X61wt25Tzax^c}SBga1~-NEOvdA~tx%@wtB8j;_n;q-ke_ z9bGx2XUFwx;&uJ;qzSq2H;A;1-?ZuV;@Ep|jbADvBjv?@o$@Nl;BNn#5H!xy!(%Hd<=k{D{wWuxC%upexM6|J;wjNj8a8D04ai85ljuKN5 z#?XZha}V;gy8C;WM~L_JRi!a)xDmpCPJx@!m|W7fj490k6Ahs(Pc?&k({pQkFTp#g zg*pQd0Y%Hp0VE|Gqn-LuAxBRVjh`{cuLT-tQ`}kl4zo=87Cvx;5w;h7k_`B_lY*vw za1(^*e!>>7A^5yE!*Hpav{2V$HVyRoR4=cEM=|jE3OP}_#{-&e4Eor=MY$*=?H194 zgcrB~5itu;PX5I~Uo-!Qk4E6U#G!eQ@}L(H(T4JAtTA%N@q+Nfu`mBmRCS;0{7+2T z*~+4uK(-vQzdSOM913|szbc%&TrgD6)viJ`u)8!N#O86(U?yP}ZRfx|yvw!ybPC(^ zO1kbm$Xtki+qgFe91C{ckgl*#1Wd#utU$E;A7kXv7s` zKvadFKV{hEz5456=?#y@h12dgu3{3KLL^=eNQ~}gXo9xC*SYYy3VXs|8lYc(!>XLv zNJm;YxWey!xy&+oJi6_@=1c_2GG|(kYoaetv{y*&xJqkWF^kOGK1OeeuAP31{ZZGn z)5&U4)Tnia)BGu#Lm;^xcDRU#<|NB2KxV)yd>YMcowAc(skia7& z&~c=wB!1RtR6^*#V?u~>U#JUwX&GzfK(y7jX%()YhF)Eq@}fh)9#sRl#BQO%{fwt| z=a@+MCkiJOQk%Wsn2fg18~y6b7k?Jed6c2tB)T!_d+g(v+jhP>!j)4W!xb7q|m4D;O61nV9%p*k>^3lkom(P98ye^qLkmPB&5_%afZ6m^>gl%*f zKNM;|#bX^F+kq_nE31l}3}}-o@_ssG-uq7({{AL^i?Wix*R5h1*HZc*Ofa7rbIaVo z7qe>j8W`4g-263h1XdRHN;OIaY-3>#auwldeHo9yyqiMdNY#!-BRh2Hyg&|Tb}KK< zs_?=*pP^L|VvKaLI;G!XUNhdD6tr}QEP7se+9X>&BJepiiq`*+J^{j8qE|MQYG5Lgq8i>xi`Du0>#g9R65gv-ut$CqlJNK z2WNX9tF*M^X~wqtj2g<9!e6b;hQ!Ey2VUEH6-qVgY2gd!<3R0mc+m{&@o=a@`cm#P zlM)fawR?Q??_Xy6X$_m*LqcnK)cj0N!8-NDr1e}KoHo>-7Z4M9XEKa&WyKw9o?96i zjt;o)r!YzVa1PR^hPE$2TnX2hbMO9|i4Eix@mFGN9#V4&$#D)E0cqpJ$}d3LAa(!^ zjnx$7Z72hgI|bali~gyenTJ64n>+3gx6J{W7iv-xae^FsgdJ02h{0P4(BCE^vuApE z-h8^7LkJ5q18M_8luiwuutTCa^jy#xVOn9$l=$I<)=bqkBjsB_K{zz}t9MO#I8^h2 zrSRFc6Zq>Cq*pCM5o%gestf{knn<)@DmUHTo*Y`t>}lbT%ah*jQITJfMwUsLFBZ3w z1hjwg)NVP(=sXLz=>yJ5;Pve?N%P` z5rr|mZR?>%%JSlE6(VHGqt+^qDp3j%k9UTLyQ5TmLtc}zxC#wWe-u>VTxd72LQ-0f zX@h6vqu$9#V&sJ*=PXMrUEGyM$-_&Upzxp`&em9$#S1M14EW8N7Oa^LItAAaE0gLA z$XB(;JLiYuPg{Q34_JAEtfYxu?KW+ZYKl?9>8WHD=Fo+@QqN_qbvEMl;W~=T=&Qyb zf?(zm=b6K0B}}Zml$rL0r(>O0P>vgtVmELXimIV3M?qGLp66B9yTUcrisoiSMR(Vy z#@jI!H=}z1zO38aohpuQzGu)}Bii^Yw;$+vs05XZnAULM;iw zQIpYpK?^7i*bN7zV-h%}&bS@fdP1Y-Ttq>uUz)Z*IgMkiFR$_;sO{W$uTxXE6T%xr zk-yt2)W+iU+5HwpUvi*!VB22&VR-iuw^R_Fzf8^pm{2TL&lZ`s>x3iWBDq5Epz6;W z6-8>|R!w{?uVaBVz^hnRYpt^X87G2r%?85a>G?eP9{5ZMyZR=ZycQhhs7mYlG?%|P zS<^Dib4z;y=NWyC{7YC9BglTt9#|a^9h0dD#BU)0E(6`^+}(#B$qF;d*(kJzWj6ZX=?l+KVt8L63dE|LhfPu7WY8)1^>L}Z& z*Wbi>+)WWBuYpOxl|x) z;%ODwH(wdwZVrQ@o}ilDd79908grg{$+|mMs3eLRe^jX0WUTal$+Wq5tT5(&RT}`= zzn6Mbh~b<~rGCf5dL{aG{!+d4cHoZsj#P%Bd6%E2J^9r#V*6>3WO2l1PMYOK)n#OS zX^&dEVQ$|PHuA2(swSnQnS1P83i`9%8|k*7pkA;JKch8;LAe({YoVPb5$Z(d)m#8+ zMg@0?`!%SEu=>^4#ccVwc)6?um!2Ltq!0<3EkX-fFwypw^d>5$u%5s1t)3@oOynmM zQZjtk_D*`-Z$Bjrbd4!_MddMKs-gTgpC-qB^_YtkkfWGZxqu}U#(y2fUPI6%AaCyUtL5vjk+ zl~b9q>SzvOfM4L5=jA>FNrdnzKgUiAReaBxvfsxyEd%C=9#yR?Cpj(!C0E7%7bi+FH2yK9h@YH(V*Hnb|*@I+|AhkrZ!a4yL~DmX@Zs z_{(rED5JwTEHC@h9Jm31ByYRotp(LfgPd+@njQkCE@8_%`()DcDQ1pRuF1xjw*YzNF?n84_B}g2IDmh#VP7TbO8ut`Ll<} zC6jbmX_&<6jo`Ov`I@-iUIkTEB}#u$%H@)`mm1fU{C=!=X8~*=ftZnLD+l@6k53Fi zY7ZA4!_+ZM@{2?{I}kC|n$cmN#ogfF9t3r%-rZ9<6(3&PGRTP@LQNSa{lqM+YQb!G zK^oB-txrvozI~eO!EKQ=swr_ZW#5^8_)kP=(L=-3o!n|5mhugbSnDO4MI%IeB}BYW)zPx@@qt%4%x7 zxQHBGb)5)5On#?-bNK@AF~;HeKMv%ZJEa&n(F2?uZ2#ltYh3E&KPxKq@FyR*X|QNU z)!iY_RX7q6FgE&CQsLZ{i2VWa5OUXnkT#+^0lEnkZ@T18f!^iE?f2^Aw{qG*$B<5)OW^OWH?09n$vL3A6vH_Qc}@vFRHJfviSpYjR@r?%9L>hFJ5QI*PniNc(XL#QkA$Scgu#DjM$`wWO&R zk1tp9ohQ?lz9?ZzXys+f)5bg_z22<=)4D`cNTh1&XY&gfd&jPc@QLh*Qyd z*!gf&Sz#J#*arvujorKe>i_IJKAcR`m%xS{|3TU!gkELs>;XZGfKu^=#NUou;JtoT@{<~$;#5A zz<;yH_wj9_<416O41Tgg8M|Zdk;!-}M>@IvyeAgf%qKJ- zDLz5uyHX1FaHus0p3V=No%pAYViNOPIH!aCGS?m2p1P`!?=EalM>N|L{O)U&8a1xq zuaKW!Vvql?fA?RR1a8*jJO7!T)v5z$UJ zpx`XbtSSC3L9`q!+|0}@taQw*RLsm&G{j5_PUhk!?iR$<;=HWPtengotp6L5Lg^Zc z$i+s?Bx&R7=1$DP$(-UuObEfs$;Fk7gaPQ-<;q)>?l+c9I%k%N4Oh{YXSXP@2u+R;~TP$KzQn-z<{mkMDmYD)ulGnvVuwt!8`3>Nr z>5HL1KPFNjh)NXlQEVV}eETC)M(-Qs63*BhexAjQ&x+41$(o5mDI7siMY6Zn?}Ipv z|Grp{)x7n$9u5E9>w46+Y^<&i$EU;^0qjy#X21cy+y*^9Z%?!D8KGm_S$9_tx7!S| z4CW(QZp3UklQjV+8H!N^R-w5*cm?3LNMy0Wd>tsV>(3fYb>%*rX+aMh#c{W=ah`Y% zdJ$8Lm$}9_m=TAw^vFTCWXKsv)xo-ss|}Sh$9Ds}qy0^O4(X2<8!FEeOGljz*)$jJt^Dw+f^4&cAow+X!s(oONe) z<=1c8d4gU$dye=*4<;KlZUx4`T>nOFoGGL8F$2C7dWDx zEb6A02h_W8V;w2yOkOTp>3FZJ1aOqR!hbMslg6DxDY9=HAo)t$b$U0irW7}7I~RTX zsg(Z}y6s6}0_8>!baC@xtuE!H!lm9Z;z6*bxYQ>DAM033S3uX=1XPs>V`F+C2i0>! zLK{bI!zP4jlO&^%rd8VgVW2cXldvE77Q~sWpNqwQ((P4;jMBcl6)DWHKw4SqjarSj zCn>lgsH|Y|(;cf>vSJ2W3)#AyXW@@0&(j)>97G>%TW;fZhh3O1Ud=+V@IFL;fW-b{ z1eP6a>8ZJ_itbl*CQwYG z)T5PKN(<^M{<$Hpf|wpDwl$H#R?_d4?25Nde`Gplmm;woc(8P4BVGL&Yfe^zZu53^e_t9qnllRQ zCBm57ND+BKM3xHufm2yl(V|7syb;vltR+of_q}*u{A7@(^ubCib(X(m^K<*M9(&WD zP9+>Stg9mLLe|$?9Z7Pq>hsxBJt(BxZJwB@g7_jp7I3gGXc!IMspxYrW$y&;v$bu_ z*{l{rZRh3P(b54TBZbx3`8rMmr_Cwb~5TUxd5j*uUK6xBTO~UK`2-gv;x)gIQ#PiS2)iu zMY=M$bMkO=C7!P)`Pwkm9Oh(cNQcJ`6U$)x_8J2eR597A{PC`1Ki( zi8RA<2Vpa6P%yipY=+dW!AOuzqI7RdD)%5(&Xgu}I5My2H)kE{s!gVl+Q8wjU$&<$ z!Qd@ocGnMHhQ4=XAef`!)yqy1p*sZz)Ua^t6C$mGZR3PTQX{SkI0B4DnuK`0qx@9_ zQFYYr)Vqgd#lw|z6_?qmC(r(f%jIHt=)2SA7VP!mlBK#!$6 zQt@jjQGl0!nl3RzK12zXG245Q-jqY~DUR}cOqX|X&JZaD-65Xxni^YTo8d&*lMf`C z$N{esoa^dPp?VemN}q>3$jC78rlE)PFjtAa>(LT5hto5;Qs4{4d(fCX_4gz&#}&t8 zced+5_Vw|4aP;o$%yzb&v+AOWq2$MCPsol5d(QXgS#5fFvQs97DyKCK^%FR!1olp>CutkH~OH`ac9!(B<4CdmNEXiArMFf^7s zoI14A2z_1Gez~wf_@(@P;5|26?sS(VJ`R{ceO#l%E$ki2Y$J`nYqL;zIDp zc@7+A-1r(|44A8KGdsBR-01!7X%La~%OiJiPdA0pAOHsyl=kmPDH0CX#fieMSct7S zWA|X}AD16S7g?h8Z8Nn%NB|5+pxJk&ahSHB68e^vej!WK7By8hKKoF%SI_6y`w2b} zNHHhokHWKDnKb)OzACXA8ZZ}leF>)EFGznTtLv5)Tx%{;97%cuBDV7{5KQ)FG75<_ zbBM#r^NH>Ao*~bV?!doDkDzC%h&6w!a9Uk>%hqFHsHQJ@40z!H$BGLXoP^%tFDqKI zCyhPTO7z+4E;L8eHpvw#c(vB5EI*5+T*W4!+ZZS|pSF5Wh+4>+Oh}lQ&n{@~v-_ac zMM(*Qk~TchPQ89_GUIiSC_w^QGA41^Cba7c~dec$KStups;rzI*oiz zJoMiJa#;=X11Zt!X3xeGb-RCHewF4&u$Q;n+PKMe7h2rzr*3xI^bW-Su^f_R(-=<& zAHvDb(yF7<>O49y*7elph<~qwF2rj*pGiow)$uqkmuaa6_}rP*#>>PaGh6KWQuA$B zJgmiZ#(Tudd0Oy!@6Af7+X9hE)u_Cp*vEQE2Bd!CvHGjaICf>BHwMJ$hCec}&-+iM z?(JOE>*rLK*?!2jW{R+cSqNSrCo)iSxdlxDAt@{w;26cCy_m8lT{Mb)e>b<9ibjss zI!)ITy4hIpuTBB5xv#qacQ(z!%$6eTPx7yLAv>`FF_W5&uLbdcVkRwOJz^GO)_?6^ zx2ltq`@e1$VrF7hVkQ|!OQ(Ms>;KNg{~`IsIaqnbxJ4x-#W-0x*jQLZng7AXB*i%; zIeFMwB-sT2{}71(U{bdINdXS_|8ZT4F*(jCrh*=M^B}}n<3}KH>Ct>zaJi(a(bhqc z+!HA-ATpOFodpYp8r{G{R%gseI0$}y(eH%VQ{B>*_2F}vMJOk)WG%|JY9X_vJM-PZ zo-BfYS9_RrwH_JS;8-GZcj>YRt?76KK&PAug^1W0uWRoXB>z@G1dcs~BIz8aQldP9 zEsAf7Z)1)=B;TJ#<8in-VT$@sluP5!VzFhAKZ4-;9k=XwDfP=W0O?L!xt|N;QvS%P zmdON%uF_mSjcRVV{LD^!G=ec-LF2Qw)L?4}6RuKA;elvwGV)B~yr5*H?WENnqeJOe oPb4`09z?nC?<_;MN8}V~j3b(5BnAZQHhOW4CSF{j_cFwyoW^ZQHi(^L~>vnM^Wk{i&=}*00K4x$3Uc z5s;)W-~>JpX0GIYLJUBSR(l*NC(`sO?FVEUMU^K=5KwGfU&j782JX7!5j@`etDb57 znkgrF>`HWCz7>boXjPW?ujl7++Lv*)$feQy+vPM}=FgOImj;mRoPLRETKw(gYVgWQ zb+f!SsUPp$2ClcnhroPm>1?~eBIHb0nCBM=@q(4_EM=U5ZYjW(7)HT;?$xa%DbMFZ zY=3jKj*iCin7>VV?p za^mctC)-32y7`I*%9ytqenV}}Nk+xqesYj{S4(EoHt97)b^8)_`EqnqFt*7}I#50uR$3fCU9hLu z?_0v*r+Bt5T7!A-!D0Q=&q+H}==Zz(>*r-NEG*vM$&}D$pBR24p2n!;o&lj!ec@>p zcVHwxiBpW7COwnb_w1UJH@$iR$^DdN$OVu{3{V zp_3bm)?c-+9nXajf~WXGR<<_#EUj>d>ji>xWlNK8Q#8Xd#KdkyG6of6D_xY;X#vfG zsR8LbDh()`sF2d)ny*B*%I43+)0jE#R(4HU>|!kA)7?#3gFn>%p;+@hDP}H*H z2B}PwSCyb8CBiBbeVt*iEEK0x6yGU~HG=V8er(Lt9DjC`q6ky*|Cf6pOM9yAi*~MP zdswJEGVw{TA%IsY*JF%YS>0nyg|ptp`?+Xxiwwx*HH{LGhtRC=zAwu+*lF_|+TXI{ za;Y>@*2q^G`#`tWN|H^^Zxz>~CTF-^JrE53y+L{|21ba zP6j-yF>2$7?OAFScUQ_ir>X|eVjcV;>gu*-rDTe10kO#gj8M9n5)j5s7 z8>8~uqwv$_XgzI3TZ)+>W&S=hbG#DU_S|jNYK|k?nUxmUkeiR$^IGFSxEC5>LLVd= z=Rx|LOgW8yN%{n-@;1uMR0^64My7J8RnNH?!KLiaCIqe5QrLE0*ONv%^HQ5qJrJV2%~gw)H*4ra;_FfrxAf6ZjiL_tzSvyuQUR+g z%o)2E@TzhZ!NX_arG_XcW5@U5dTs{yw{7sZS2kZ$c5}Bbd>(RtyqkLl^5c_kizm3e zP|XnzMOX3JO=Kg`t(WIig>sY=H*}pAEaDDzS0_z>s%_~j`8V(${TJ!(Ca{F<(82Os z4tTQCQhlyZC!Ek6W6}R;&aFe>BHto&ictn3EXj|Fm za-UV2cOJPjAsOoHvKG>7(ZXtzlXJJ#VqPHXWwZTI^te|pD8uS19C-$cN~ARea}6s* zq1YUD^Y)SPpOJ1XrtboIj3IS4`SbQk-B>7YX1W!d6!W{{1c~0jgqtSHo&YdG;-8-; zbYh+PT z4@@T066&t;jC@Ej4fZaUV*p3J!zN5e&Ry{Cin_&f^WiUdk5VE?4exHE9eGnEonA&o z#4_fc-PwrP38qI89x2+^41Plo0O)-xFLc`ddJdS&yBrz1^dmj?#&cSP>4qJ70~qu|tBUOjvxV&jnX?kiY2wGywGAyoTp z<&CRmU$?g~53>!%03a}(*z-9rWJGXK*p7Y7X@bW|Eu|5JapBqY2ELKS5}4Wt(%@#( z@ssgq?OwD$ zsc+V^KWX!5J|D3%>lVY&$@bUIXkVXOab1k$l{;Bf+-8#h1lU&orBO0??ftMN603<6 zY@a2#emv*!;p6yBmFu`#9nRe=%aNJ?;_}akkd{`S{rrtFEN{Pmu|VXdfH?T zf-$ouQr>04Cnsk^z?O7ztof@ z8+Ii_Xd{OY<#BYTpD^uJ?*$g&YJ&VoQ>?Hpov#JcQ2o$^%OFq%J=$GwD*1jVHyXN- zj`<{jVBbAL96dLD+a~4f6qM;L!7t$TsmCt61Yk+^5$Yr#qqSNyIJk$*VGatJg}106 zHj<@zslvf^Gt|9o3nb7{*XEmT=t2$QhMpI6f3!(Mv;LS+f5v?FGifx%&b@OM6hD&? zM$2$?`B#B`e*)JBE05~BjjMuJ*3UeTe0e)_CWBh_gXEaIJJx~4vnXcK$=|>syN>1KnOo%-nYW-E#o;u=HkDC5eC@XKV?>GgA54wjC%9>H2k(DA> zP!#6b0U|?GgoaBseCkN9MTdKDM669K%b=M-wQgMe`d5gO%-CnRfruh9yNdCTN|krn z^NI0JzXD;tRJU{{$HR<2_;r$Lqs#`WBY>|a*>2~l$w-aHzT7j{e1tm;R|pL<2TO8W z_%gkkeztnJ@#q5oyZ|8somB^aJsxe=f!u+`3@sSrQYYm_pUpWCNin*RxOnoogtj{y z(GLAZ;&0i8T5xGB5qFmZ=Ms-CD$aq(E(y+0i{+Nm+t`71D~y53O+i}gJn_tWA)q#` zZjO~PrrFT-U8S98eRwlhaN2mO!pUXdHUt<%q8qUgSbQ#WKO8zPK5P%-r#j_I#Z+Kgoi{A|zhsBWDh`b87Dk|cHao<

lHK5yqGJ*cxax}`#|RQ*0*8>GLUdJHfqx^z55L{(#F&J%k|+l( zi*U0of)}=pQfQgH#nn?GjQ~sa>i!%t7YaIun@-u2b`SUdlbXg6v0TuC@KRTu31YB7 z@cj5LlK-H|Iu4KCg^A`5ycfzqsn6iHF`>BAH^CnMCm)LZYOyh3NdF3bgI>Xt$0na6 zu*p(T#T!WqhJwe7C*j>}=`--Z-$A^3k7=1hP+}-qlKxo*2aYHJxISpPj9Zc+dGRB6 zlzhF*NZaMJb=$E=S=;IHdJW%M!cd%E9A__G4RKneprLQSTp@UEZW!H{NeXmtFDthj zsxWpUdvfqJD{{d|-fHF^?- zB-=Z4HF%?z=ef2oz5`mRMH~OOxc(n)WlKg*rb=$4AR_r^AZQQ(jLrrG#Pa~E{Qt=0 zOm;#S1Y=|3X8B(#JpIQ@H(9d-VYo;#tB}03cScUUvgBILrbgCnBhGEOgh5RiNzD}6 zh6oG9h?0zWGmD>C2#Od9g(Fc9BM@fU`cg$lyIG}K!KZBVdTL9*jB+R5$4BvsrI)w$ z`ujDB@GB|aW#+Z(_OWO7(I47y`fooB6x5%8cBi@Jnyn0xfFp4SdZY)E165C7|F6bP z@%yhPvELy19;MyGK7@Pzkq3IHyHLJ89jr4SR|)RVz~3&W?i1#xcN12LIS>q5A*R*e z)>EUTaec8}r?xA~FU*ZKqiU@uf#?~(r(=Whx^27RhULk;U9vF-q|%b&C=pFMgP(y$ z+BCsl4mK?!09*;L$hVG&*E@;6hC(J0EhSq4k?Uc@9R7VIHi(mg#KyuL{-irS>^42p zBJC5ZA{x%D0merY5iMI_I?k*j0y^2Qpv7+wz0Yf?{dT7XV5n!85tct;1l4TV;=$Ro zAhP0q;7tr!@h>XP$$Zu@CHZ~Q*Xue)9y(6OL{aZOK&xWXALHk@tBqJXp>H#HXcDC) z66Vj-De;Q#3g3#c2G*tYipq-2iuQ`c3dM@~3Wf%k4Xq8X4WtdF4W<4yt1=5o8uGmE^5!$Ii-1= zLb!|Hp~p+sOm!^4T{4+q>=%B29yFHpwi13w>a0$Wl&| zX6!0p(F0WR)uj;+eCKfbT2H@T_HS-ZKP_Cg7Q$y+lnH{}sZn9@|rA8l7EVZXe*)9i5?vN{j6H$hCmcf3S5TmfOtYPGa^`x%Q3Qb&Sh9;r$F zYu+ljBg*iE>d-6Lso@ZrmAq7W5O=P>8VB41qp7aBj}YO;f5jw9$?~G}LGQ-}z>Rt# zvZ`#NQ%tN|t6l?zPN>gHIgx*iMZ?-(?@BcCgd<_g(I}{AjgBq@!ii*j5 zi%dSur&E9Ie%}eOM)wfn%*PJ^2%IfG)ek;RGkd4hBxe>7$Z2P-2nDVqdxd$GFkdn> zwkfZc+kt&7u$4Pid8R=Pse2JjS&o5WlM$%dc&PILb#}3eU+Bg{i6vA`n}wTAgJ^kG z2nA%kPmxmHNQq2TLEaNpNSxR=w#&wUK7W`GsXnstae;+5g|8XW^xp{rxKz#5iw|QL z_sh??n|YK&QPs`_ejs_j&(i?|?Z)4sOmu8;RV$Sqd+~naEBY?1*38S7mNnm2R91rv zg7#WnObBWyV*Zn2&BOX;T=G1vEs-})*4frqIjNR(jZh!Vjmd09krQc^3bX4!Ezn$u z9=W*MpQ@s+-%CgiU#dBPnpYG3T8;0349i=3yOxOH@i^tU%Wfapb~o##vVSSqF9$E@ zv14s|m{qX@MXWXoOV3Mg#v~8o3D}GA#6BtXrQVzbppB60-qSl51akWK*a_oCb=GtH z-uP@qaBdwGpbNx$S^WsAP~J=B;;Q7qC{*g`YG{Th73W|>+!NJ+J3ZZgyc@i?w29As&v`+_rx>CTvA&33?U>)TC!J7EFYN;J;BEeWOZ|vXcIA4##YQJ!2=-8hCtmK@q&-j z^sS|s`D8vl#JFGpA`R2@n1T!UNczwK~6sa)3_*`=2T7M^@RrSIwxGSDnd7e}O-m z5J7G~7%R1WF!Y{{$xsT>#^y=xV}a#OK-b}O8pfSaGnDb(a@TSO@4_G|>kFs=o$ZwY z*3gseh%c-JNM>zf)JPx21D1z0;7M(aE4wleYpBSt;p4!$i8@X5FU%)V6{daPE^iO_ z@?oV-LlY=~;A(1CtF6o_?YOXg@&b9KRL9d1jHB#^zwMRCfjQ(L|8vNfu*D?lssrb& zZE)LY))M+&B)w>mSHQ9B^kMg(C3n&gHOn5>k(Mmp9*~E;BNLSR-sZh`H{}!6_q?SuZjZy3wY_V-R|k3 zm@`9wSD=$q4NT{RM5;+wjm6tn@#O^MQEmPBf;CUvuU~1ul|9?CVTo3)1h+FZIWA^k z^psGuM`mYuK6=;i3!bi(WtVMJk%(*>Gb9;6sW^$+g$%GpKQTT{KbdkhJj_@GR{w`0 z#aR4Cl4v{pO->D_k(ZNCkR&=!M7?23cP&6RWhq6*7+oc^IL&LEoZG}Q~EfH~fKq5rGx$?smP zuHXC*r{^1wA?#XT=`b{(ni^ff1jMnqwEQ})h`$pHVHxy8G7+*t`M!w9cBFgV=&};G z`RFPs5;$+l!Bm(l9y&qq3!=~GZ1@*oxHa_icy0JqloxC1`W%Yo81jMXi`tR%fzlB^Y5i?iORp z>%rPEK+e#y+bE23DOX(=-qBA-%e)eODTHrMwlG9^ZBl7JaU+HZLve(`dOSD4V;qz$ zina-py_vnmwKE#ui#Q|biEX1t;@peya^V%;eBQa{I2}LMl%OHk8PVNU*9f86!7j+! zQ4_Igzra1?(Gr0saeSGj($zV6DbbtQgD-Mwn4SIX>%E{Owx?g3Q z@=#t^63#VYC!PS_6|^nsK_D$33q4w63e2)}d5sp@*i{L|vhQeb>Z_Z{cCVjC;;J9q0^XB&U7O#*Ed1mBeU^}fHmRfJ+M+u|SKw}umPOzsWW*XeFb zn+ql!Cf>B`Z6lE~5PD#hO|4iN@js>2v9n=oulPqG2x4Oh{d?aA3hp&J@pgw(3_k$h zEA)8+z-RK^W_yOnKs|eBrk!@Afd6 z8nC(yt~hr-@|sc_f`wg-c#nGP=`q0^ex*ILzmMsnLYDTc(`J2$Ci7E z(UKFkH}mO7hKV0Fady87mFk4)+a9rwK;c$awKuJyLk(4;*9W%w^aPgw?{KJN>*=gP zG7$g=^#Craq=W{zxfV<`s7H=gT^g;8OeaYN$E(+1XFopqHH@_u%w@%Q1Gwx&tHnnqD^C4(n9phJcJQVeGM-B~q?kVk%OKvkd$3oGwu> zQ6*;FqQ_9RbBP9pSi#cEtGxkifoK9nCl%w5K z&^T;bY1}x=zoz5Bf(?g(`dRP`5uq$%^Z%F~aQ!#I6$S{$XE7m#-hRQnB2oJof`Z9; zpc9jmtrxarS)w*~qxd9|AP2*7AMLKbkanu5i;IKY?{nsI9vVGabv~Xpa3=`*!L8xC zO^d@mJl>jJ#!5^|=*|>>Xp%@jv~2J<*4Pild2`G}n-x_4^hdywUqlyYUF;Tu=g>S8 z*L$sbDgt`H77eLfNJo?RVAIkWQ3R_f>D$Zw7D`#7=*W;SgG7hIU0vVky7wv8k>u#q29S3 zh5=)viHr)ucp-4UV@#0zfqOB7S}_~k*72J8qiz`XsESdo7o7_I@{}m*I zTi#eguU>B9Z#oLR09~u~AjY;?+EI+e)@DKR!lo9!p4(@wNVIQ$W3&pcESO(^1M}<9 zz5idOkPL#(0K&?dEU$<~tZb-aY+L=2tm z^A|69d|2)zH**S~;;4uCh{!Z)EKvw)ETz|tEHt7k!yS${|Sq?(qo z_@_dE%acrp^6-Psp2x=nczJ!a$TK7;q2hV&2eS3D^q&(q;#x)bXYeIqa+Z1{8$NxT z&G|ZU5d4i#C?BRR)Spo;PsRQ`0&fWQAvKjPD$*32ND~(qpEPz}NWu0=b}<8MTEOfT0RPp^PzShbjH zWfi@ciu~%~2B=}K@S?VIs<3JY#|F2KqHQcEx&Q#vge0l#FM(KdHwS5pcZ&_HT$VpC zL0q`eT&sn|I>y2Z0W3LBM_M~%EwTYvkZAtwUmbtv_YVy~ zIY8XW?$@?*MR? zH>npKiIBXJ$1ko4#k|2sGS%q5<6m|VEdIC;c;tP{>rQU*w>zMp7FMxp%U7wZjXIor zI$M)UJYC=r*mrkF>?*l4y!D}o&+Si}T`q`bB^~ukAwhR7-oMT^86|i!M3c%Z#Due* zI-azsupaxT6BNknrF#Ia5l?z|P{3cLl;o}RP%$xglIl@HsXhn>9rOXHEbOdp`}B=| z`+BXp|LnOH8hoi~jAUgQj{9kfaDF+{(CDn)5sR?;>Ogx9m<2JWYt+&TbdIY zvqRuNv8C)FQk9I4IEihkIgsoo5|pGfWQ-}8eF{Q~Ryg;fMqF}xE*nn&Tme8|C%~-E zIUH>ncBNR8974Es90pka%5xWZHYp$P2WIwth`6;`34?m<6A_r|YZF57Hb#NO7ztcC zbWJQI19)_q-f!P_qQq;Q)IB@Q?3xGjtbb42tQJH_$&B%lNga;6 z6=qNnvF>OC2m=(acQ+A;odCU)H?GoI1?xeY=Lw^FZrZ2jx$N|8)h8i(l=VQlQoIY7 z*z@^~mKW=}*6ItdGjr zpQYK)l&i#Sx43?8p*acj)xIUOseXJ0PT)0Qj?KMpmOdhC+vU5sp5M!X&`8CqTaP zX!|}(oz{r_qf0%=rG7{cU@Rs}RS{{*3?tqpgAg&7%2h5X_p}yhV;hmzBM|wzyRSDY zjO56ofoFY9qIB7UX{ZN2e9kK0tuZIJ0{X2oVl_hg{^1 zv@5&aME0TmrC$Q27*ymUw~hL*&Nt+faXQ`bazLtm{jPq z!#H}m#B|f@6Z>+%uw#G!Lx+kKa09S=mbBxzgj#N!hvt+$Sx>Bm+;);_^U3p*o9nat zY4ed(Bid)) z6{sUbDFEH7P>NBc8#GUG=f+6HBHN1aB@$e}q&nvnXIJh0Vc8z4V|6&ZRCXcoz$yx} zDX~*S=|*3K4m*HnDuS1-6nYX&u8(?CdNXp+%@3XwPbCYeifCjkqYLe&r8p1F6}{Gf zZa(g5`nZp3nL9Kz;HZRt(1=T|kK0@}xU{{R70}9qePE>C&;XLE!92W;Eq|U(uP-;H zMw%17@9w1QV%zD;Yb!U!c!Gw%s5B&@yTd~eG$@Gn>a*?`Sr=j@xTL-d1G*;##4_2j z@RTipv8Z>aHFD&LwFq9O*n_T<@qiN3e^~X@u;Rz*l{!)IEJg&tKA|3(pOLBPgUxSfK;M*wHY zW(3g-?(yC|Q`XJ!ttck#RlctDXy#n;fYX~8Ngb8gUd|1>1qmTT6Dk|qP2Le7c~Fr_ z2_2zd*`2)TV63|IPdWV?T-IpUCI}giPf+dP;H3Yr0HGg4r=YQz-{Bu@{PnqJ6Cg1B zFzNw(H&F6=g+O+SB2~0*`PPB4ma`oGeVF_+*??Du=9T=Sndg~Ah=ilM9V-3JD*Hbn zI(1II$(~IkAa_a3tNUW!H{YOUa|!e-EK(s)~vO`?xA7+OW zx&BrqF6f_exLP48%WYsBt?yc+~E&j8L7a z(ou>;es1F5DEoBjOk;#cf@EkP7N4IXh+mKdV>yzFRCx-h9k}JPO#~zkboQ7u!q;cBMSg19wp8Sk z=T3%~ogziAfV+R`2I$*9tA)Y)8SFvNPg#ZcWmu^GLocni*{NY~cM$Dy5(#q93L!B3oFeX%d`R>SyW zsQYlUf#^v6T>p##i(zZ`k8lb-N5HGUQyE~0<7d1G>A}%~+j#>w1AVyTJdTEEr|g5_ zunhiZk3)wB*DmbxuokfNX#*)o0?VS+3iDB0*{}8iwliR#&A5KBEFg>6^g+vjD#MF+ zSvQgIYk!r8ZP`U>PBbknSqcKgq8h&;E<3Li75+n(D3(n2OI)y&(RRcGN3_= zf`y3+2&lpmLOD5xP!)`w`+uP!8lYJV`j6^ri+~lEX)8%HUQzS1kX`-tGS8~krBZ#q z8w9$OAq4gS-Ut%0P?B2`5)xR385HqUa!izljm{{7cBMeYhJJO0y z#?GhTs}D3-gUiZ}&9_YrpvH|Pzq*<#P>4vY)hT%rqHH|NueCNR`cCim9B_+^clACZ zVeorqI1BX?Re}LIDQietA5%t$3WhPRis4gm>{XTLfG~}(h#1#;Q9!AbBJ@G`>;28` zJ7Z4ru2|UQ6>89CdMFh+M$HIte4cql{CTL(P~FWIFbQR&V<4FmB$_Zfc{+F5`OED$ z!Urj66#|Ovv}cCrYf|JZ3Lph7DM&=ncS4vf<7xBshLko-6b@9y(=F}cT{fywlh7FB z-KBz@-K#*TlNQDA@&)A!{>CfzAN*{y*KT)89;}SL)LnJ(_Nxrm$#+mIw}@~kt_$`E zum~yhNO2G=4xUQKJ2^i*yd2DXjI$^oJOMIzxWvX`dLIAy^>@pN2P{plu8(rE(J;}( zk;Io(Sd=HG&_C0eNir`*FNs~4O(bTDbxX*XmMS?Ysa9Yw(OGjmQ#5C53wO)c6la&K zFY%_Z9*fkJt|;BA*i^VJd0T@vM{dZqtJp7TSmQS5TolBq%Ffr6HP6O) zkMJ39K&_Z3POm4&;I4)~?=AcjB0ns4{2bcorU5uw#4N@cc;yF2kq!@tY{Ehd_5gixnLz2(nKBo4=ck&Ohrm9C(fqJ7DqQ@>jJz*$htvX!&yv@DMB}ymy zkQ3XtTuI{JzGW1lf5TxhaMg}Pog)SG(!}9oQQYBcNK89`Z5e$j=_Z1Wnzhmu0k8Bm%nFa$b;%OQ%iR8C^J^yatYX!_IBDMd0` zGB#lDxty)~+8>rPgyM~b^NmqAIvw5I3^S~y_B;lkW9fp?X@5bF_Q5!&w>ya5Z@pQM zT^7SC0NB*BLv0+V&`p0x&F>o9;N?&(DBz_+Vj(7<;>$FtKM3G|rC1Tnozd5vcQ}lqAX% zA>$>=TB5H*I4oD2?vny}cyz0%5ZZ#;Tqn}miI1i}UzG`oQ8__0q)nMr-I){NTquMd(C9r63#yX9DNYW5RO6W z)u`>(*Rv+WX;~zty)2FTtFV8d3?@IeI$8;Jf$Kml(BDcMFL_?w?(yJxBP8}AhD0uL28O6SuRFqm$rVI6yDOqooid=2u~Mds8XL)F?<(t(x7 zO7y`fSvy@2iS1M3C}N+_a5v-H;eqJQP%aYj_adXWc< zKQah=KJP0(^|AUX9R(2M9Yj16p{)Pd#Sy5VnySs|TQkODdIoY{iXX5aRVLLc-O2_^ zu}Om^UL3)dkhtq5u@cSXG!D+15MD)5+lH>L69$S}$&W|8pNrXwqrH)|0&tM=I9!hj zk3&vsJ~2=tb(7+g+n{_z#1VhYQTEClpi#NWW_+u3#aGRIm*%z>U0CAZ?8zEz(fdoL zt`zVuRstj4H9Kv#`te&DZ@LtEou<|2w~CbtKvO7YOR zy0~hB_JKxgsg&G1q+*cW2nnRXHX_#KFVw=(Jv4Mg)&2zVZNV>V?7N|i;&y?^ruv}Q zw-8q~<4>p7Tll|EKb0kGn|19skPmeOB#w1h&n|{4J%^e0;2kH=6Bid7lQ1(XWC`)b02;ymTA>M|@#BF~j0%dx5!WOU^d!|=HY4F#1ZKAT{3kO8?U{y3 zd3rT<>50-@g*E9k!@-Bk`0ifZ2=|U(oO?QPk>5l16m! zd8oSm{N+@Ea(WX)5$+V52|GObLL$8&Vf_fH)j84Lbb|~XpF63ddQ62ryY!;1zXnnA=X@HN%&|Jt(#kUuiFr zX^Uu!US<0+0p@gWUf37|2PaP&L%wO=X=>CQ2q;AG?&U>`?ga5%#Dc({+=iWbK)fR9 zT^ichN|za4;#I@1yk`y?qHgjm^1HON;+PAM)#5{-&7mO2Ie^k(KmPja}k zpvk*tlpP#RuI)6FFigr-m6U@$wg)<`LyAt(`8_4G0qx3{pbX^@PwAE|d>(m;ZPuC1 z3<8(z{XV4)q=av_p>McDCA+^*!ru`=aE{*`<2g&E=k+B`|q zV_^g#0L|z-vRMHHY4_mP0Zy29@IcuTmbx&8^NHz;5QqGAMNa%~3`v(mQV#DvTUUAm zxLES%(t{|_(Feg<@vTRaQl=%F*g8Z{Q6bW%W_vk%6`M=KOG*UKJ`8or*FE7Y@0NO?w#C)H;h486o&3)EB%k$;*KG3bh zfx-C``G8)<@lucBTWP(Nn7gk6VP*srVSfc>;l%om_J8PeLc27OGuGP&+&XC)lTa3A z6LEirB*9WS9pjY$NP8RK4C|=g!6uP9)^nW#(Xik03w@3UsYqF!giO}$pWeRaer^09 z0bD1eNR(EzNrAgq8{G_oJ-mc!F>S-;>o0vZZyt1@8>Q$K1bVtxSbA*ML^?k%+x!9& zR}T%D>8hP??j@%7JLVYPt*8QnKjioa281&c%M?j-%ZYNCgkwjBe2l~65SA(%_DDsv zMB}HEdnj=rqIBpt)EK4_0+=G?q7#a=0K8|h#Qu{;2p#&gBSA%FJ!x#h(Om)!Y*xK^ zD#(-=fzjS|d{Nnq&yI*MKx{VC>7HP~Cau+o4poD)HsGnjf8NpiMQOs=-)kjy&0Agi zF{QN}rtIk}C+Mdaah0TV_`>zCaZ?*`b^DsNH&At|*eVr?_{Kl@nl5Kf8{V%30Bedo zn`W5Yw0FVV&UIt&1U@^V>GL&%#%BxZ$LeVW)^!(Q+T|&jp{dv7(4ihk7A1uqLR^=b z;~uXeSikeZCjUW$hmfZdxjiYr3~mKl4dUm_=-eIzpG?ZKG4T2&F;u^XDKi%Wf2dQ%xhuF5{h?WCXx={ zT69rKGg(<>;WTBB+yv-tyyJ(H!e!KJi#lH4{#;v46D`skhbu0(T9-vU%-I|p^4lxE z1qTP-$hk!qLcXb9Tu?4EfRLq9q>gmA%`va7JZ=2l%qSFO1kcQquj9*H3pq-yvRXwA ziLiADO>AQCjLjPlXtv0jdPv@mZ+2tSn{W&Z1w!{Roaddvq5E0D8S)k{^p+@sSVmcF zO+&wrd+V({uAx88H>?Bbk404O4o)NaI6b^Ht~kASNh3cdz4w(MV8nU;p@6Gc%$y}P zfzO+TS;={?(!FSISw4bV#s)L`!Jatb-!;rv!$R&xr z@Y(`=l3GF|wf4}T8^N~&>2SxGiKf?lGrWxEx20dFfOBk)ve>_iGTMnNk~L#>CsK~c z>C&u`tyTL(_|OHR0AcnB*TUKPpXaEqH?FyETAdH3Hq!? z-E|JTj)ro8UFD~H(fTckE3y4SGms@4d=LY^3~2HGHx+c%Oa0?l4P5}b4Z1;lazH!K z3+WXOW|~WEs{3i#lx{@zUiI~U_b$3_cb~#BnWB53n*qBT)grKQU_mJ%_}?>l zM@hpaB$v3vjMXZ)7}E1@Rzk!HW9ViVw#Sd*2-24^1VQ9&R6QbfM@G9>Xhgfp_L}w< z>{(Xw45N$2?NpXgFLqayuQqgRD~dhft|U28G5)axz<2TWwGOYBc_ZoZ$Ngf7hb#C_ zWqv$uhaeJKCK)D3iTY}gqltu8flv}>cmxSbCL&TOD|;U@lY7=?^)3D9N|10Pp%9&XA^9Ul@l%@qD zr01F>09*VDxP~#}?7#u9Om2(hoO&?ZdH=L4Dl>0m6vTbCbI4KAi_gJ&CHLH zpeQ08&o2-l8U2EPOi?V13UAjDcBM+iogOC#fJ=nDT@L+Mj}&Bhd;qlJZu9`DV@I*>yfbVg={c24G9ypT^u2nA$iFXE&U*Z_fmoN+VC(&E`*7RoGXK1v0bhHhL0 z$mFPeJfOwMziqGU*wevN#B5&ngDduqJ+()clhYq$BS%oqVNgTCqj})t)&#^vQuW&v1&?nplMP{D8wj z&C9%J^3P)UGesjw>pv<9O*5zR7~B;bfYtb4n-w4}$WH-b%$^c#aDq|00@IaZZq;ONV z#{aL7tBi_*>$(mylpsh6NDLhk!!QgpG)RZkkb-olfP>@!4vo~1B1khdNQfvUNS8<| zNQZQX)W`FF&!2CtcdhToIqTlL_Wi%lIeQ-okuONihb8^X2vwqA9{s(TJy?ZCV(~VR z+THcuaq5fXP%Kx#BnLka^&^`j%Wbsf33vvR`8Kn2=5>?j6ETQ)nCuLjIQx(uBEvgh z2v6GCHwwBTF(v_(uwWjrUz>)PesoIu@h*Y*2EqCBBz-CL@WNd!qf*1A8h zG*WBK;7uJnCv9)AZu&+C*=vqmI&yEzxFCFDa#Ra@T#vc~9{k7$bL$sps7j*gPMP@S zx$l231Og+7gqVrlOeY$<81Senop-6bLzBmClbc{n*i)sb5^XGr9clw+bqo0edVlJsZC zJd7l-0BxRyz0QE*d#`Jn+yeCM91TU?>*XLk8iM_4%N3l62DOMXiMNI4pNo@t`|RPJ z#1ihmzi0j3vF*zH%e~6`o!^!B=LVz)?v3%PA5s0q%Tt(6xM?L-BJXBfW*V7t8;;H2 zQ;WHw%8ZT}4-s?H){51=54kzRGO+p@actd`tE}&fwMvA@$bKbV*tSMzd+b=Nu`>Ob z4FP$2gBNJNp_TZfZ&Hn^Z{keSfz-?qYf{9!=VMq+wm~lD?;w!yO*O_4`#bNgPcu@z ze;S|G^S1B6RZLCuaeh#{HVM{q`Yn`lG)dH7lt)(cZCcZUgrTU#=-6K9LdWUUE$@Et zag2=!&x9UJ$4{<214ZwMm}KA*xE&IZnoEkW-kw38dqzEz=lgEz8(}M-pR>r-V#;3L zme`qM1O*DEzQeR!HLu{x!q_}jh3SZCY+KqF?4*>(Q1#nLCz}SHYsfE(n>Vy0rYo5 zOfYMaeMkBnyJ)A}r+S%hD~5EF&b^hJi5Tk0KE0H4sfN*+w(HktEc@ZUQlV8z5 z-mU$_tfd1x%fFV%=c}1kRoHKaNQ#nu5xK1QhGr_ElwO76f(7uu4!z12z4<8nx{|jmvTCqV+?}pGAPctm{L#!g%rR(UO`qpqm$zU|uynBvRI0d{NMkYqyP!kM1 za#y?@2WZjKD_td$aNLI=?fSh2L-QCUSJ8WPwH~duF-E(^$3Pk6-6m^jCf2zJc$8HS zOXUn^uZ;CEF&bdu$K8yF(itFJ0G}!`0^ez=zRz4a`ftC?9F%otsMq|f)H$f_C7toFPv0~(Tt^S%7o<%^;nUng{rvgJ%|yE{eY9TsNdT*<1=VVtn}YU@2r%YItY z>wsR*pomqZzst@7gZP!;&eJzoM}LlXn<|{cE^tv{KXUM(VPM#QoyELK){6fLruepd zPQ3$&lCtS#`893E%Aum7SSaW%r(eZN@4%tL#*Nt9cD?}8>eKL1^2kUo`MST`U+=fu z9E$PNay#3qA$Qt*zOvjkSKCGZCP{pE82NHn0Z21Be)7f@ndM$$y@Y<1QeOJOf3&@f zPv#hCmVeDumt$=l7@jWf@+IGV=dbm}w(`bCchy71%q^8-z15(R8X4QZV~w54t*7E^ z=&u>iEy%6YXAihb8p_MWR%QINi*Jk!6iwg1S)0fpZJJ)*Sk^WOW9Y1Hu30<-JnsAQ zsONgsepV9urMZqN%Wxc>iz?ECeNX9c(0jN!-BW{G?K|Ys zMIyeA*W|N1oiWu3wb5T6|L|FIXTW}SXO!X|{{_YSNnpKZDz>kb9icZ%;oenLay`IU z8r?df7+H74dXvTb=(@B+O6XOF@!QwW<%oF*1a1>hK;S&2a0E>lmUE}>&Y%D=aygQe zqW1wk5e1=Y!ky+|Hj0zwj%;BEK&aFGaRAZ_H-Se+Ope*W8-H@2L~evFC+tZ*#wkuR zO7edLvE2R|Ln!b&3BNrN!yf0A04MxUx_`@H5Ho6xD;|#*QadUz&*DUq;Oq+_x)kCM za;eaGacpo(59;>B;C!Mud`3kNj(OHlLIC*#Ng`Zajvrv0xU?JB(wR+MTD-0vDy6sC zbBg^ubP?h+>5P8mKVl{mxg)+FahT~OMbL5KM(}mu+?C|;Ij>ac38b3J&aSL{9c2!E zY5ieq@;P+Ud1OTV<@Ft^oFrNtIR#6BRehh|igTdUqAR$e68wE>mTM&u5ugPE#kdTt2 zrq6V36rD#ELf5CKD4yn$MSLC>Y zUzsQ$Fy<%r4} zz8`&)6SFjoFOqcIOc6c+i09f918sbh=gj#@a9Bx{@Dlz=UQyJfV|OSIiT|!lS`9i$ zsO7`HT+NrER4N9cqNV)({j+0*kr}-YJEa)b;69Zfsl=iO9#(to&UkvGZ{RMOai{eD z^HGMi=bAO>fqtQn?83puf##BPlx|8>>W;l2BdaqN0(o?>qF*g%x9v$=ed&+i)U_2iY_os1^{Ku}ifSGk{i>thyu5vl<>rnic+3%#)7B&dYAzJ-{DgR?t zL=5^A9px3IlxEz-|Ho4+4QS@Jo>aKQUFm!5ytwPgU^u!GEoi=;bShfDA(vOiVXo&- zA)%7p8~F=$-Tr&Rw)fbUiL>ABhv}h>Lt@eOTiPtnPY$jpJpoQJk7^6H-j7|qKdG#i>sR())1%Kx?wyX`NpFJDE>{l4)Ytx!7d}(u2 zWmlVvUNDQLQ)FZ!;d4=Dx&%ufpTn)x2F&C)>OHlyJb7bE%Eu76yhyaG38E0~!YChn z9VuAI{(uM_jnB`0Nl#--Ou?0;ge@<$ge36C0ZQl>!TOu1BMf9X+3AuvOAx2pbob0i zME3FMw%NPz9Rh|TZ7e)QO=4FCNNS3oQnS)3Tdvc$+t=Sai=0@%#Dv zou4e7Yq{^PO?$o)f86Sl`xM;Z!V7R{n z?#3~D#Rl-Mx)|+=o5dOz$9x|y>gVD<_34ZZXAi&OiE|+7O~m81)P`455w@q~dD3JQ zs`D1E#_X;=m|ad(;V+2fW$NM9$;ZN^$r7K4*Kw3V$UeO8v^2tT4Wc`JYnGBp9CA=u z8X*Vjp@g^u>-VK%yZT?;!67SboEa8uOw@zJs-KJXeHnONuF5xE^Q=z(s*blMr)eIkt#%>1Kwn`L9NcTj=YzyfD*jl` zZKQp@w!SxaC*ULC>}0wPJ+^t({Gn8?IYkEV7*Y^i{%eX+PifZMRb&hw*95bB%$w;I zRdTNVM3gP<`J|F1%V-H_rxWoK-&DlNqFAcsOTYOB<_Cv5FSYhgKDpS|i_ZDRBH#!a z@vHjjkbD>8a&$J)UxIA;%c9BEo(y@1IY7`BDq$Bi^X9MLGu{b_&UL|qtaaA8{WSUO ze0B4P7QM|8pM&WU^vphaH4Ej*6?uD0RfrL*@-%h*5+abBZ%pU;N5EWtx7WB#$;B)0 zNabYlg8qi-7Lj$`Z{xzPxwqapgBOa}XjK|1ClQ6(Mzk64i%;ltx0}XRk$4Wgzv~br z{4kh2q(wA?nPp_QkC37ME=z)AQ@}dQ#%v7J#>XoEyYw)|_1Q!6qxi-zt(t;NtFz?r zfm8E|D!S&%)^0CkW$Vgh*^#XrEH_7N^(qiC{E!YNJ&;zGbpz-?y&R+byw36B^Gw?6{{ zf4E*S2TuQq00b_*x%!<3HzsfDpw*l6X{y$_9Z0XYkUso?jwvv`p{33DeiDVfgbA@U z6+QkL#N1;*ab%SRud*k)_f7M4=jt>2uSP%98}B`beMVukLSvR>42lFk4@x1JD=d9ATa2k?6D^Kk*>((mEO%utKCLS ztJ9f;eTFzsj&VFQ?;lM8-c10@GV7a;2pA`7#<(U2UOk?h=^b=i*WUsi zUZq`Xr@mhtIo0lH`NjF^O3=q7mt~R8-eG=b_Tl-l{7wHh-8uF;kC9YF7!HP!aB?bY HDUtjS?|UuP diff --git a/übung_5/aufgabe_1.tex b/übung_5/aufgabe_1.tex index 77ac72d..665e6d9 100644 --- a/übung_5/aufgabe_1.tex +++ b/übung_5/aufgabe_1.tex @@ -1,3 +1,5 @@ +\newcommand{\OPT}{\mathrm{OPT}} + \section{Paarungen (Matchings) in Bäumen} \begin{tasks} \item @@ -13,42 +15,68 @@ gematcht werden kann. Also ist ein perfektes Matching im Baum eindeutig, da jedes Blatt mit seinem - Elternknoten gematcht werden muss. Die Kante ist sicher im Matching enthalten - und kann aus dem Graphen entfernt werden. So entsteht ein neues Blatt, für das + Elternknoten gematcht werden muss. Diese Kante $uv$ ist sicher im Matching enthalten und alle zu $u$ oder $v$ inzidenten Kanten können aus dem Baum gelöscht werden. So entsteht ein neues Blatt, für das die selbe Regel gilt. \points{3} \item Der \autoref{alg:treematching} berechnet ein größtes Matching. - Der Algorithmus ist korrekt, da der Baum $T$ entweder eine gerade Anzahl an - Knoten hat, und somit ein perfektes Matching berechnet (Siehe \autoref{1a}) oder genau einen Knoten - zu wenig hat und somit das größte Matching um eins kleiner ist, als das perfekte - Matching des nächst größeren Baums. + Der Algorithmus ist korrekt, da der Baum $T$ entweder ein perfektes Matching + enthält und somit ein perfektes Matching berechnet (Siehe \autoref{1a}), + oder I dont fucking know. - Die Laufzeit liegt in $\Oh(E)$, da jede Kante maximal einmal zum Matching hinzugefügt - und dann aus dem Baum entfernt wird. + Die Laufzeit für \algt{Initialize} liegt in $\Oh(V)$, da sich der Baum in linearer Zeit augmentieren lässt und es $\abs{V} - 1$ viele Kanten gibt. + + Die Laufzeit für \algt{MatchaTeeRec} liegt in $\Oh(V)$. Der Algorithmus wird genau + einmal für jeden Knoten aufgerufen. Wenn eine Kante zum + Match\-ing hinzugefügt wird, werden die Knoten und Kanten aus dem Baum gelöscht + die nicht mehr zum Matching hinzugefügt werden können und somit + nicht mehr bearbeitet werden. + + Also liegt auch \algt{MatchaTee} in $\Oh(V)$. \begin{algorithm} \centering \caption{Größtes Matching in Bäumen} \label{alg:treematching} \begin{algorithmic} \alg{MatchaTee}{$T = \tup{V, E}$} \+ \\ - \com{Wurzeln} \\ - $r \gets V[1]$ \\ - \com{Wenn Knoten Blatt ist, dann die Kante zum Elternknoten zurückgeben.} \\ - if $deg(r) = 1$ then \+ \\ - \com{Die Kante aus dem Baum entfernen.} \\ - $E \gets E \setminus \set{\set{r, Adj[r]}}$ \\ - $V \gets V \setminus \set{r}$ \\ - return $\set{\set{r, Adj[r]}}$ \- \\ + \com{Den ungerichten Baum zu einem gerichteten Baum mit $parent$ und} \\ + \com{$children$ pro Knoten und einer Wurzel $root$ augmentieren.} \\ + \alg{Initialize}{$T$} \\ + return \alg{MatchaTeeRec}{$T$, $T.root$} \- \\ + \\ + \alg{MatchaTeeRec}{$T$, $r$} \+ \\ \com{Rekursiv für die Kinder aufrufen} \\ $m \gets \emptyset$ \\ - foreach $v \in Adj[r]$ do \+ \\ - $m \gets m \cup \text{\alg{MatchaTee}{T}}$ \- \\ + foreach $v \in r.children$ do \+ \\ + $m \gets m \cup \text{\alg{MatchaTeeRec}{T, v}}$ \- \\ + \com{Wenn Knoten Blatt ist, dann die Kante zum Elternknoten hinzufügen.} \\ + if $r \neq nil$ and $deg(r) = 1$ then \+ \\ + \com{Die Knoten und inzidente Kanten aus dem Baum entfernen.} \\ + $T \gets T \setminus \set{r.parent, r.parent.children}$ \\ + $m \gets m \cup \set{\set{r, r.parent}}$ \- \\ return $m$ \end{algorithmic} \end{algorithm} \points{5} \item + Wenn eine Kante $rv$ zu einem Matching hinzugefügt wird, kann keine zu $v$ + inzidente Kante hinzugefügt werden. Das müssen wir auch bei unserem dynamischen + Programm beachten. + \[ + \OPT(r) = \max_{v \in r.children} + \begin{cases} + rv + \sum_{i \in v.children} \OPT(i) + \sum_{j \in r.children \setminus v} \OPT(j) \\ + \sum_{k \in r.children} \OPT(k) + \end{cases} + \] + + Der Algorithmus hält sich an die Eigenschaften eines Matchings, also ist + er korrekt. + + Der Algorithmus probiert alle Kindknoten von $r$ aus. Geht man mit $r$ im Baum von + unten nach oben sind das also höchstens so viele Iterationen wie, Knoten im Baum + existieren (ohne die Blätter). Also läuft das Dynamische Programm in $\Oh(V)$. + \points{5} \end{tasks}