From 89a285ba9e8eee785facc9248d8addc99d0b2091 Mon Sep 17 00:00:00 2001 From: Never Gude Date: Sun, 7 Jun 2026 13:59:57 +0200 Subject: [PATCH] Aufgabe 1 --- übung_7/agt_übung_7.pdf | Bin 0 -> 66857 bytes übung_7/{agt_übung_6.tex => agt_übung_7.tex} | 4 +- übung_7/aufgabe_1.tex | 82 +++++++------------ übung_7/ngutils.sty | 2 +- 4 files changed, 31 insertions(+), 57 deletions(-) create mode 100644 übung_7/agt_übung_7.pdf rename übung_7/{agt_übung_6.tex => agt_übung_7.tex} (81%) diff --git a/übung_7/agt_übung_7.pdf b/übung_7/agt_übung_7.pdf new file mode 100644 index 0000000000000000000000000000000000000000..3eb87ce63c8eb43794105bce9f9c1ceab07562ef GIT binary patch literal 66857 zcmeFZ1#lc&mMtolEwY%InVFfH87yXIi^;N>nJi{T3oK@4W@aYKdS%~xyKhf>X8QM= zAM-k*9gb3}>SQ`|`<%7*T6>=&krx)FVW4G$A{m+OoatSd=;?!E#iz%&eQyE9&5chd zYHsCZ>;U*_W#D8iY;0(2WQfqx!N+A-uQea$smQ@zjGAqHHjoi6d|N`p}~4 z);rd|U#5K97{GT&Z~y+h2SG*0#%>Gy6~2s(qIvVU|Kixyay6trzD&g3v}%s4SX5$HLkwPP4-xnth;f^t_=!Llssy5w6jX5npY%kP*??%XkHhjGC#cllLwX5~5?<`aU#qPJ31G@J%ALdLYut z?q_p{d??kMsz)xY=z@9M-bVLnB}o4>HFv|LZ}4Z%R@U4dyl#`HjBC*=dim(4paSq> z&Sh1fKx=d1?SS(<0^N23QrMF=uNtVh%`2MEYXcyzya)0rJ-Y9tYI_fe>J{X_5fchbd4!1=}KW7pQENvV1XD1Rk%eIe; zs)^NBONpVWOi!J5J`}U<>=DOWNeQr;dztWQEpB~iccYj+D$O?ro3-67_FT_Q;YYQ= zHq9gfEBB#{kl7M|az%o`2YzF3EW0v}o{b+R*Ot6QK3GwW#goF=Y#WBAy4j@Wq09rH z&c8c^>Ph#N1c=o?LX^yh7x;bo(t)@9mB7TZb8YvF55-natYG8}NA&ftl- zu2-~C$O{-EK;GK&WWlB!YB><|z;pr+BchGr2DR4srl2;`7U5%y#3{CXtR#t(q86;T z4<0AA15_M8Dp)CsMH#ZfW0_`mzvp|A;&ineo|BEvcARNT@WHC<4y&E{t& z)*#*8M;ih+l-O5|N}wPPLMso^Q6@~DZKPF@nvw)l_kN_}DX=U4q{}4L+?3$$S+%WG6$sY;HsE0m~da&M5?8r>(0i zfVW=Uo94?0NAJiYmg@SZbWwWvjv|#cJzbLoC_F9dcHdIXaUm^rT6$@`;wBC(q05oSjWesi@VL^N&T}ndkX^JrlVOS010kdiDHGcN>Yv~QdOJo?g;l%q~P)naMN27}yLutxInjpO?GlDyAAh7FMQ)WqmYA&NNNy6Ib+n;BTLt*Mkl{0Q`ff zuNT1DpG{4dbw4@0j+wceKZ5oSPzlhJyU>FxE#!d|5hV-A;{1kA+LLEZNRnQ6jm}Zh zXlht?Dt_Uly$oR;M%wqW-!TgHOFarGRgD?l>F|?9mi33my{ThfmB2WK?8_Ob*I*n> zXWGr>la_^hSEDQFzA(@(oq=@|E^2%fH=wu)`x3{Mc2B-m-2%T*mS#uXbON|H^jjFv zWIbt5MmJJ?CN!96X~)B0Agk9ZP-u(J!e@xsi3H@CHO!hYClVT!opB!<6hcultb~#l zn*C>|=k`@7*V>KCcluS0n5W-JeU`U7Y1JXediboAEwQ)&qbEtcgIJu+GFY$Oq$M?I za&bD^Fu`CF#8c0njvfe*;sB9M`40{Y_oKbrHDz)WRMQ2(; zMU{&TB@4II#bjNbg*0c<-uomO)f}WBW1!3lln_L*a;tMH`9skl_(btzR)UVnLk0x~ zuaL&PPzX(qcrfME&nMO07SlK|ho6Yz9C=o$<}{5g%5qnP=0=O165A7c)lh8}luN5k zVj^C1FBayjDr|an`*EW}47D`us~T-Me#{l^W3i#&rm2z1t3Do&{GyX!)ST(=pus+- zkL$(SEe$=H(ugFd70JG^|ENNGe-$)xOGM*%Yw4j!!2`YQ*1CN|l{u=hG6Y?!gNUnL zmB`pf;hP;306pKnc~!+xo?1$lDuMa<(18>YH{BT`mSt93Wy?Edavj|iX1WB)&9_e< zKtG*3#w~06h_SNOyTNoQU;nOKOzjyli zj;O7JH9!&oUVn~Yz^9W}7Ez~_H!wApb+&#F&hQCqeR@C#FU(V+y@f_AUukI zC$Y7%bx^W1Ff{({L?NZ0CmA>a#F7m@ov^WsxuLP5m>}TnANL~v`v**nzn%U^NPj9U zYX*F#A5aLmtf)03KH$cFKW4&bV)^5k86Nj{*NA zFE13Gn1ije9XB_f5}mSxfsLb`frGJ)p*x)vzKMaAqcNStZ$AMe|Dx#F05|wc$p;wp z7kQVEz!Qbc02BQDh*DAc=Fu)aPvi}8O8}w*EJ&bwPVVNpVgKcalhLs?7Ot_8;|GZ= z&f`rYum=_%0Xu~6GHWUi^xzK+z0$twn^Q!B4?JF(xVCQ|uZ9?p8!wXy$wICd@ zf){s`!fS$2A}HSIA7?=lI#+c;ofoNmFE8#aJWkL^EjxLex#2#fr>ilvo#D0WYvq z->A%vAFVN$MMB##M#77~!!-I(3b77J0wVnTI)ySVU z(weuBiqj5YNY{kF*&+Uqtg<7EZHaJa{ci3|Ki$>~(wsOiyLI(Cm&AUZIL?-Vsga#{YjgtzxHA3lV zFOQmGVlWK-kH%Hsmmr5wrWZTBNvrA2b8&hv!CYuIlB8K0pgzR@K{FnnVpT4LU3ClpE`fAxvbsnO1oIE|=!+;tB0D!Jx3YK_TmeXH{&} zy?qgK_BrEh$ zF(r20RvZ~Jdzd4thOOgRdqKyfwJ$1r5fWB{^@6rf28crFdYo&q`MKUjsK@qn8mmwq zp*=V)UV~V1Wgj3fN`2_0tj2INb+`*AxpltC;e2r{))tTJ-LrCRx%Cw-TXyZwUT{Sy zzjy_X!G^E=dpP{LF#qsE{&6_`9eZdP@Bx2WXgSy!0C2~~!tw)5WDJ}f%zq%$4=ADk z{q^slNYvKmH_Q}e=D=tE4K{uv$*&>m$4CE_Rl~;k0}=kRgqbF4<>`I5K0C1^1qQ4% zrwcaStV&a(P~TFIhL1=i3r;n`puqUT3kL5{3NNFhqhl`i2D{l~kOSRPH90m1+W`X| z5hE!7B3wVP>)+wRT>iUou^_1YB3wV<{eLK29Be-c?SE%>vHdf%OZo@{Lz6P__bHaT z@O#Wg$m@wuMMoRKuBL-NQ zO+e;MUl!o$XhFfVHK5M4D+siK`UsG|{332YQilJbxyAy>Oa4WXEOqJcmZlnl+AqTO zBdhwq4A<||jGdMZfdBtn@%o>cYMB4YRO3Wy{YC74WTF3;vHOEG|K(xr4=VU8tQjB@ z{e8@s|6X_fAsYTr4}Z~G2Ie+SKYsxv>&oU<<~F8({Pug^@iVWWr^o-v2;aQTzd@zF%b=f0Jg& z)63H{1HBLWtQ^El3xuiy3iXR8|B(m%?QHp9dh)+K^v@9d`RV_Edh$PKOTUWcAF*co z4~sY`R>!i79y$2@nre&|tgT4q80{mnNk$o(x4!X71F0BVm4t*=@T>RZ#9Kp~Ak@qq z9*%R*sj+F+cbUzc`t%1%3kKzyqx9lxA|jj_LGP_YYcz-)b{bbbptQ=>BVnDUtzsl5 zZ^GH*PF5URi@niCFNt?_-aqrZMx6^Zq;^!Wbz<^OtLP4Je(r>mJ8hl-t`G8@Oqc2G z(4+@(qXu$az&g?-=Ljm2qhNuii!CgvQ?NwTJr#6=wnL6RE;VIe03-h72R)}f=%rz9 zViI;OwW^;om`hlT5m-=Lgym(w=1II_7O6Ra=!!lWt1FA)pWpUbg2VyP4V zCMOM)?aSxpZw%3%i{BLqdLoHz(%K^p2_Q! z=)zN{*k!0is&fT)%r_|Rm~WUbn6Ch@cYxPRW*4}MwlXxXmGhgj*(G6DwvDbub-}HB z5|xq~l{4o?&*xog>%<-C4^xMCznH>*=GMQsBtjCxKeG5AYm;8+*Nf$k|6mR_mcK~| zoRzGlmDJFAlNxShD-uAAY2SO=k5wmo^LIf6z5{6x-}(s)V@Z9 z$aW^yI@~0EvLNQ&eDKtkT%mc?0V|O(&Pw(eS$Gzs7P6RQ&|*oS&Iq)4C4Mzp()XTM zZk%%ztpXaR+#M3u;g}T5Q3oTAg$!VcHxI&dBv9Ttqhyc5SjQF$h&X~(2`Y2==liRK z=f*<7ba+PjsF^gCt}P3U1o+jSA0j^R?`V`J7>i_@Y7rOnjN2p$jqdm?Xid7ubu!vhrTp%SF@NgeIy$)kdsGXR@jeXFs&;APjef*VTH$%6x zTg~IqcP9>xuy-z(I6ho4`fdJaQ$chilDq?dBix1H`%$GZSj5JiS88N z*;v?#EYzjPU8nGhha+V(@hkIUW}Ii+J%1J*lZ!yyMw-c~+;wPKW0yUj&4ShY_<@PP z@)mwuw+$H8=or{4E0>h)qS+XBtx6vg_vv;C&GgBmknGu`u)w4v2<7WjtC$f{w3{93 z$HkjKsrlFEiQ6xBcm=Nfz^&S9YFa{QXM~}|2qioFz^G2a@-SIZo36PM50?(N89Sa1 zpcV9;t5bMGkOw>c9WvqC!FZdhV;>-p1?_Xc#N(FFXFTo}PNI)|?PVH>5ksEa6lUW`9h9tzx5(3$q#b zoXNoOuDg6sbmJZP-Sk3$+-S_QWsAGl_(O9w`GnrM#~Y!mkHC@Yl)hNdBU82<&PdLD zo;Kuxh`2mG5~#N;9fs^wk}?$=7d4{pf!S{hmEWJbI8q_Eji0iI)}ke;ZgRum;T-05 zOn1zk`^jcYa7rkOQepIlu6)|{e7L$Fum+bIZ@%FruPlQcrk_(CW<7Kt-Scfl0F00--L-p&^@ z`mOGb!?vcGq4dYT5+BR4UWv=p^SH1Ll8@ge$%?jonPnd-dqs;^Z`%F^Ui>+^{I7tY z;YWYPUuClH6PaEmv$bvv74yL1C zTZ`j%qBuF|>eR@>MAdi5_~d*(h!@{#Ao;|_AkyeX(v6~B7>}K&67#9Jd6QvyYbbdi zdSXg^LyMsspAV|66b`Byk##-p;D1S^b5%8PhACaYcFi$((%_U2Z2de`nvdY~{UL)5 z_AW2)B9`x^q76B6SDyu{xafpaJ|>C%`up~&k8@qD0DEwVmVjc`_uK2!D89$Rj>o5$ zo}D(17rw|BcaV#&68h_oLZ9}R?bGXi2DF3<#gWL$t`4bu8&e|$@+M&ga+>kW;j7(; z22M+i?^xeYanDs^(E66_Q4X(}3-1dtkb`G>(hV22uN|sYDJo`df>G$!4{UB77ppsR56K_xf4z9pwL2b zM#dXnk<1wk53HBnlZ=Md&SFSr(D@_~H|lC++5@>fH_~QI5fQeqCu0w3Lg2KOrW$2L zZ=33llYZJazh6)E;VYi_=-GR+!!^$5Y^{RMf>t?UjZGji!jt0Ro&!;HUOXwpxCyxat6#mFYmjdik z_fsx{>T{F16^m!*TA^qqCvu9@oHMY3SgH_f35rKV&q>8|?B!&BqwCylnO^p7`RfQo z>0iYSfNI>xVbo;RNMPzsokQsHDC3RD;#fN86#pisv%C_cY~aQJ^Lae^)#dIb6Z$ zpGb`S4zJ)g0_bT(@jwYx>Ta**a4zG9AV*bZ=8jN{3Li4tI>7H0rAPM+&K-X>ND)oj z0VMv1KL3@JZhi`Y5S+;kql&or`zB92t2y!T-j*N?HSeo{Fvx>S|MijU_E;c}d^nlv!84||O zd4_Qq97^^C6f%d)6~f8IWupbT?7huYUwcQ*-8Z=`qe4Rd68Mb+r@BG3*{QSQ_&j>W zA?bc1XzoF8Kfc{J;j7!4w3OOe*5Q^)dGJ|@JqzPHN$`kE5v^%WqwNbfVhqVDn_AQ^o{~w^aDLgP^9IoDl*hC%lqQDjlwY9B5Nf3 zs@KtPq98YODyd$)qhQNXVsDD*m8wc(EqpRT$8Ky=@0)8qU7(0o+0fTx@Td9jy?{kA zTfvGu3c)UNR)geDg09z~HKVl=-L6|ugWcy1X+8v8YXp8R>MKdQxhQJx)K}t)OpPtn z=Zf_^l5y5QItH@EaxPt?-z{{40#_$^+S&nHgjo@{TD$?Oz{j|W;C4cQ`uRXhby)g1gGR%OoVU=bpRfjxD@J=OV z^VF&vqbc-D3Dmj8k-+a{F9+`{^HcZfVFZ5qUbEUA^$v<>+4)=Y+2_X{j<1sgOO&=i zWNhZ70yAt>PcCnq1-@&3;%8zWb=4wl8v@7m+J&a`his}GKn159Cg)nAx zS&JrvFL4^FEgpniFHQkCo^Gf}6Mk5-0cmY&@zdSqqQ<@Rw8~dprkM-og%?y47uO=u zoE4o@IK8QlD+A%0EwC>*m6qupBd;WUA>BikboYG&2rxOd}~^F#y;iJ zs&|1Zd246KyySL0xchV1bBdM$@2WUf0ndR+``BINx8z{PBenWTU)WIYOk^<~s!~fT z>Msw_>-09Rf1if}oX)?xIsa82%FfL6*EIA`O+BM(gP)f9;oHUm&BH6x^|v6R8_byuY`O8lx@A4s$X5a-FXzOYKDP9+4lJYxE~J4 z`$gY7AiQ_f>f+qB;`-I*x8JefDthIgR zmvWckW%25?($RUPu2Q$24d3fsjAUs`@LplsJ}DBP63PB+{1BK(M7|JDO}q89jyO+Z zdw!<`&s2LK=0LdyTrO@Z*PN5aGsVA@Qhe4` z7&K;x?@!M(g&S|f*3~>MXp&A;F$Ue_^?z3ELuNjoHUt~?$WLGB$W>(g4DHJlyvwvm zxH2pFk;0lrhjOK*4|QQ<|0OT*N`wG8VgM0&4IINvgsaFx0|6IX!UKQ5E@S6?D~7%1 z4vvWi_UE0ccHvCj{$-WPmAtaaeZG`cFB&Sp$~8VwZ*{r^q-QoMVZ=Y zDTH;(qrk}5O0xYO->7~RWEaBgl@%EVD$rH>2~VusyvSGPhFYj@s}nj!H-@tdhZPLS z&@O|CkAh_GW~?F193dyv^hNz+CWfy-FQjgi?Na-E0*ihL@1nw@!aL*KnRTAIG5EM4 zx~Nu`=xYg6Oa+b>MZhtgKfU3FT}8H*Cj8>Empo#^NCc`3vKDN&hwyQ-jUnAK3kUM! z6Zcm3svPm4e^y^gl_P~~ZW#6cyIwJk_vIO!_vU+x!@f5HuXxBDpcsF@Hd+4OWB#KN z<^NM}&;Nt1Jxo7ad)WTn+Vh{b_OLLs{Mv*3v%wG%KUy(E4-<6n^{GrFu*ZJIDT@Dn zh+AL`zaS2QYAbJ~&y43&+oMAn&2& zB22=!U$Z^Ueju8$p!kV(Bh*1(c zXGR}K-jLKe?e?gEOD9w+v+V0EFXp#9fA#d`g}|IgPJ(C!k*OG<@~Z*HyjAM5j9Ye# zBRs9yk%d^>raX%2)o;ncbk1;|ViPse2smeWdH8x@yLtQ7LcC2L4hN$MghE-j8F@bh+R^mu~TQFOr!wjpE{+3lDDN%tAc{~1l zHfJ_sto66wSUbiMo{g4AA~B{97}{jBWKRqvpCQe!7RZ*#R>uMTF>&Jqsax>hkn-Pk3$n2P1Kon7DqkX3=wVJ?P)d}@ zJ>=_FAm2ux(PmZggMjIR6<0- z5Lq}r^-ofp=z{hsh2^qik8YTK7p-kn(^nhRanX2pAJg_+q4?=GkQ`-aCP}Ai=-Aj$ zrrV?Va_E5eswmFy`x1)7m7^pa{Zq8r)!EtgJXaH)&zgc#2``WXWljQ-Can?c9Ft_u zXPRkIsgODnPaq4A!2ninYA8RZzGk;Iu7bVpGI2x2L@G=mbLqudI~PR5-MlilK1v2S z#ywoQWsJ(MmoDx(LrA`kY?t>q$BD(a$<#$*DnjuX-Cc!oCs6E z1R@F(b|NUJiYm@oU%m-XWpUiTUZ*T9Q}=?s=W;ls-Tq9GQcE{*Ln0?2I8nVuFGh$!9o{toSD<3W&8tHp0m)CIh(8{HdjU~E;BCkWy+6k&pfIq&tCm9->`5Vddz-- zJ3l(&{N{u+j}soIvk0_0N*;U_Ap{_k-M7NOcdP&oK=M= zPEG}e=AGpoRVy948?5??OSbuo_E`;EVN`M6`S7^%T&g#n`|4Ckex5C~jTXqlRIMoJ zoGv2a6%ZF`AocdNA{VA2p~xJA>H_#ABl;B4ka;N`-BDdCQe^6oZaxSI&2!BMPND${ zBLW|X!(kj^k|!*6HF*5^%qz`h*{o!(r*B1FRH&J#+(;U}HLj}RvB?7>EVQ)M8|-%J z657g}TOerjjZLiz0?H)LBF4)rH13sh35wchK=uA-Pn#5OyTjc9&TvT~*m!Soh{t6a zr}3gDjyNr3e2qsFIL|rSyk21rSED+z>uoF{;+3I}0XtHb2Zrxono2xB?NKPlELjn{RV=763~nEarSt3_ zZ=KroGh{w4a3S+2I z={z@odMm>|Oyx;NcE-?pM4d#YbYHi!=$X#TVn1O0?PIt3IKmgm zQJqbQh|I(!UIkm7$I$bYUc>ur&#BcCgv|;sE9#1uNYkCeOMR?F?OjK?jsuKNTs3Hs z3@4164mcBxoOfSTgPAEh2)~SVu}@$hI}<7(DQ7QNaF`JXn(k>7Tbpfne#8t{pQ~x; z(poYOJVVP!4I^HjFu4vK>jxJ@ctbfM|KflYX#CsQOG$#5SGKx>H6hGABicOHn`qWk z0^$aTY>oy|S^}AD3C2MJK~a;G)pvE5`d|=5Fy_&Aw0Vq*0S0d*NI559;Vgrg{eq7g zVm)XAXO@B?zNrzMist%SF){{6=1K@)!lAfF?m&_E>tjwWB7zBauiZi%$N4ih;>nj+ zK4Bn0L7bLHMB5$+33e0Uj>kv>Tf@(re{LWXhdz8VQ9C3~AK3&3Z?z9vW31uP<*Bo4 zj39-jt7)clk37MYkL=_=(PU2~j_ogzgWKbvL;+m$I}0I8on2gvupqJAUP3dsfMaWV zPLScVN#&lAcILJs-0Ty8va?M z0t~`PEH?PId$o%bp){%Lfp)C78)d~YR z9y(GUW}S8@-=%t6xn~`Ym*?4HjimsYc&J!@U6T?N*4_9T7;WseXdx!_DSv>o4=w~> z6GEs(g!lAjmsGZtW3#9jTZIsRqPnAz?*2^;G{-;|_R|%RM5H(P91hr<{KD3GmkF}H z#P1%cn>dho5M|+&0ld&{Wf_{BHBjG`k6Kl>a*`~ktOXrxzdehOb0pO5_|=Nh8NH=T zJ>NP+#m0)PbwV3;ximr>cfM2>0~@5DObo}`Z!FSLLvL>42C@KCIWZS;+ZmoFbc9PP z#Lh}EjBZuKN%3|IQoUEO1flk-yh#F;lqhsRBzpPU!ZafubN)NQ9u9f;YnZ{nCB9tIjq&q}$ z!Y;JVf@@>h?WjxPzJXrvxfZ1%(LzBL9hluli`s}5s%i2;h(NAzM}o8Wl=gsK#5RzX zYvFym$dqk(Oa_!U-SYf9;TIm;msbp=c}7cmmKeR}pdq*9f%nuA)>%Q?VmogI4bD0k zMaiXURrDDW+gmC(Up`)Q79Xd_C<5^YJcTkTX8PBT{DJ*sV|RJv?Dls|T@hXwrcnmZ zFFhP?ZG(%nmi6WIt2wCUJA*@u6bo#Ebh3wWMl;qlBkUw1rS6q#GcRf0l>5EsaF4U* zl?I;gG+jm5if(IG??Uh9RQN7OR#)zDZ!&LeRKo1$e}Mlp&UsAXaKLia4rP|ulkEJP zJ9HW&=PBcfb)976AYQ977z)L95xCW$>Iti3c7)QmloO}&cy)+fJl7RHtN@S}h83l@ zT-4fB<1`973y@6@)$T~`85XIABtHS&&HpAyp^gN)|z{bg7|8^San8BJYZ)e zXvQB`v4AJAM-?^Inra7e3M`cv36IdoEpgQ_Cjyd)9^F7ZAkdK@A%+z_IC@4HdR4z( zRUFBzXiXKdGAJ5zdBV4YDo=))u}DU=Z^EAWt@yBF%)NMpZw+h#!EPcxJmy^mQdt&q ze4C*FOZ$?@M&RVxoFg>Tl3r-;`EbEe~@+t!F3Cx zFRdPCo2#s;$gKl=UW1-96~M+=Wg$Ay{jtIh8n;T2*SJAYMSb%>!T*93>q#zfVDFUN z^AT*+-Z2<8@^so}RB8JPH^iZ+@73~9cq%x( zvI@gPhxut%%%*=Uo*~j`Pl_^XCS8RS&y0A@s%cd^WRGWt zv_7Ff41%{mCqY4mbMjoI9u)!UpX~$&)r9EPuv@g+KXwjcv=sb2dXj$4V_5BH` z2t~QN5N9(14_IwiY@qj2g9~C%Yc=K&Z#`$$YbF(FIFl-4iNx#r1$@fYrz2p_;{@a8 z1InE34_v==13OfXXQEMWdz%Kpbs<334r_}VM2#_gFoQQ%xjOP`hSZBU;Acu7gVz?C ztI4A59(a_WJ`~AxBecCayvD!CT7d3^>%?PrJ-_gcrY-*-<9p8M^79DnP_J`(u0}hO zQF72RFSvt~T26LkX}SQ_@6zkugeF-*t8^DsZLhY=<-plJ#F$^l8iBta4Lr-@0T;5V z8*xgrMb-=;lS5Q*?}VZ~+`qdcVR8*l;dNIJcjE4ZrNdwi8%woIu{4j!mn5i~xc zN73-luP(2RwhZGIARjR-3rB!bl0;GW&#$bobYI_Ul|AA#%_9QB+kNT5I867iy-9Eo zouX$q3_vpVR76f^f5!b?Lfm?9VYi++utJ(yMI64ZH{VS!%gFG5A-s8?#5)-3Q5J#m zCC~hJ~{ql=|H^(VrwdceNip|7<@$(efQ8^XgWufKu0?$FFQ=^4&lO-Nj zm}SQ{%@yi?)7GzqLfEAX>oU`1>GPO*4)$O;$EX`%n2` zpf?(4?;at=p?n--^$P4rdz<_V{qWCisr$(mf7-v!`fmdH7c_<#=mG5q{{VpuN1ial zukKT|wuiwl?>e*s_OH93C4N*Pq7|GL><(TpT$3G_;akX=Bu3d^aQ>iOIHmQ(uzRzA z1@LgD_=X$K4ns%^>7ct3f$p4i9yBov8h7`1uW^XG-d2_2^AFHiTNVdYG|k>j*TT?A ze@L#PZ+B|h)BS)7%A!M~bycW+XLPKitFfEtv`X-3@y$ma+&F^QD4}}VxzLMysngR# zPH+6-c^HJI(l^4_*t-6*4#HAw=&dzQ{j`(WbBjTKjDSCI#J8CC7h!4MtgOX$DquJZ zJ%i}hk4+8fjGqXdzEC$5mx4u7Wq?A=z#^M=I#;LIHexVZLrDnF4WYEIP!zh$CVo2w zmS-wTl{=nh;sY5QiHeTfW^x1@tkqmSh&q=aUXqgVbzg;=onQgb4+?;OyufLK#xUxZ zkmttq>thz0`23kAhp1%KIf5cu0FF|l$3}3Wgh3pNqpdQ4eljaQDU(`r|DYem>2{u_ z&|C`!W$!=>4!o&5qMLk^+iF%^%$NKE$N2~KWzE5ug*k|Th^QduTok*qTp`1(gs~ib z%`?1+SLkn&&#%@TmOzrypW#kESOS$rp18U}v!7_k%z>bH&Z*^z?bU5s>+d1FD&a+Y z+buhOM=ZR5*CQpr`)>@-55#b)ND!TTiK z=Dbbz-H8VG3*>6tnQFuv*JDFN`(sybBDuCm>*Pj4HS?k%ZxMIPoR8je5wfE&Y|TQ) zbE+-K6h7f0k%C!fk@Xqk%HSvmoKCPUNL^}s3WGnbDnx)))jBt#h3QbZ?%pRpDiV8Y zmb(nxHVW~ZSJm45woCQ5!Iz(-2S(RFc?2?xhc!oQPUsBP1x2f03p-i`r3wU~gbV(Wme?wZ)C|AiCjWrI{yD3hD(@`GxGYB-$|rEo_89zpD|H=K{#) z5Gy#cO;WH$2E{%6&sNo3T|j++KO-xt@^z`VXrRBWXDQFl@ei^=j_L=Hjp|32)S{EO zib5?7T2wr5$PC$Yd|fqvBby)q+34nP{2-gCzmiQu0bZ$#9etESiLZtCZ6yLlPEcCe zu^eyA=qb73GH^?85>uU>)$(bnJ3VcbJ!Oc+_vlkS^|uK3zu=mGZY%PCul7#=(tO9&R)eiHIuc&%x4cUlt;ApRyAhgF~CzOo<$}!K`>{?%clJy{4p`gJby(D~8by*WUb9e57q zr}Z?)dWhyI#m6&z;TQT2NwsfYpu<=>tCwG9-a^(}?I_WzZCFgTnPin!ydCouPgOv} zP+G&-=H|;JuN4ZJcf_q5wCy2HTh`S(66>bBxwmf|^39zqYGE;Rrp@@Lt64&`VcoA< zzNPT`5K_{OAErZjB*EU)fVhCD8iL}?`4Iy<4a0hAF|lH%^qmKfenDJfCHV?$4Mdv3 zN_g6m=kLJp)J$D)sq$AXlzoM|HZBt^m?p@n#LLO&JDhQ}HryB6!3$&op>kcU6Djt3 zHQ_h5c}vl6stX%yIyZRJuV&_qQ&0M}W>1pDOJ?1xS@7xmx$A`HVY)z=p1}*u9A{|6 zGLd*;Uh5R#Yr3iyRe?Bf*5Fnym??}js>5Y(H@__%mH=$7eI|4u`!X8q$4Oc2*^-pCU+JGa)bQ9q|*(kVET_YWzo{pq$TTaB$$$!(Ui${!B)| ze~^*Ke;}hnYyEMe?}fbhFB^9x8*{}wz!!m-_pM{)u^wsKev}BxQlZI&vnGpMZwK9y zNnEGwxX=6}HI&iKOuG@bspEJVL|LgGbQ0J3QijGq?Y~Z2+ZxXqVG`N`yfbA3${MgQ zeXL`GXG%M8f(AB*#^LhGiOPN?3%9fOGUrO^^8z~i;Z9&1<*j(^L>WqUi7kp_;+PPo zR(2a!uAlrtO|ytr+-SB>III8zAS=J5j{;+A89e!G);Y+kj>&drzG+L&cXjxTYiZC& zO`*wi?;*6BbtA-a{!Mn^T=t9T2`;m15EgR__4;pYQu#vh$f}VL1if0|_rvpz5 zI17{HT_`VgEeyrHZ;Y9oP=;cTWv9ZQNsIU!i!CP-;M*CaByEJS-iglW_tYfTqpVHE zQ+e%U5V4?1G~`6=fpVV1%C>7@pa86{6)*#;>!KZi&-Rf08yN-vPDVmQbs^CULy>z6 zP|bnNex!p&un3H*iIdH_f8(8D!U&1)$hnEJEtI27fnk;`OJ3E(D>`CfUUWd2<3xbe z3=W`kMv}fgtSKEZBv#|+fS8UR`^`MVDZ@jKuWlA%=>V8#1P z=;+V8Q2%-F3}C_h+dKQ$^UfGp0C~iJOGj#7BB_7#&epRpbG2;>)!q=-1i>Q!zPigL zFfkCId{&vb=op=x`)AL#OSZR59BgIz@?yVh^D1gsKA8?4C${TJK6wcYyw#W55Aw0> zziIzg*Sab|xB~RIY{VOO(bW|KOtpQSz0O!t`93??l7-BN(phTn{N_`V)Rc9=&f3Fk zC-kQ%hTh?o1J_)yWHd5wIG@&_sGAsGy2mtsR&CE?Ffa^rjf`Wf0Fwh|%n1i88EP}3 zwN^Txyh^=~L(7hwY~XFf5FQ%9T)?H(esIV9u|O@o!R_T3SfkS0uAO^IP}XUP`T?v! zak5x3E;@<=9Qc^BVdfuDyX~E;I(-ub>`jVVgYF#>awZC*$Ks>L-fcLMeYvlz-Z+2f zizzVsL6f#W*T+*GKt?YBGOEWUuJn_;-Zr0FA5B{7U-Im-7Fl4|p-gm!6A!3qo|nW% zR-FFIq9$2h>a_W301|%wwpVHeO&tMLhJ9q^w^8p*vi>th$=g954PZ9Ez z|w_j>G5 z%07k{G; z{m!S>mA`^1EwfYJD4)hC(~D|2zqF?@;S~z->PAliUY%r|6pCiJj%mjHMSG7sjA#E)`6G1*ZAsaaX<&a7i4+RTd#U*7H5ImBbz)|i1Ojb?&~N|Cc>#j%Lx z$>)j(D6N${&6}m05DG#x_88YTrZBVL_y=vZwO5OU5rpwR?PV7PYlt3nFAYZ% z?@GBJQHSGN7P!Jw9+C>iYA>PPI-VQ z=&l_Z!vVN}ew}ZGFp1Nli^J=_(gzBE=jxt>y_fy96RgZ9XkS_Vh6}$NN{7DGx>-g1%Jlh3;rU4-L$_K{7;z`mXPv-oV;pP zJ>X^c>_R}+%yaIc7HKPSHQnkXNZ-=cxa(YDCs^_?LX`f-TgJ2RP(~b)DYG&4j^{tl zOmu}=9Ta8_?Cp{}J_7w-^GRDx4e8qDfZLUiz^i$IHuIO$_yuqMc{lVw&s!Y-=B2MRr>o?cGuFq#YtY8f6AzFfQ<6$h`)LM8yRKp?(Qqx z1X@P*23}Imz1(_=ZZFZBJM1DfNDlOO8Ku|D4-1e{fD(S<$oejmu8l+^Y^>+@Da(eIA?vp@I#Sh3ff5iw)NzBS~k%|#^=ykUXSKeDK_e`HZ(wam4@ zv#7ha-!(fg0!rE=hfB!UnEy`}75;BoRNB8~QNhUn$fCgh%%YeyQRkj1gZ55!{Q+tG zcgJO2p{|Zd1#+bbGAZyf@wyNAovzFbdUSa0yIF-~rd0SXY3gz+L*ge9PF@nTnj0Gt zr(_%>YMky0`=7gO# zhD}44nr)|16+Us6wo)0s4iPo9!K#Do6RSY}&ci&M1Me?%@NydE34G!dReyn7Ah+y1 zLeEl=yRYg!eE->$Xh&g-d$E3PB|E(PI}Zche_#DAH*lOk`VUC^`Ts&1#=k?FjMn!n zq^AZe8QM@X&$jAFb=1ekzI&btTpPP4Tltwt!qA}>ae#uj;W**wX&~-3FRX z0yUhKt9xA6qO^GeYj~$uyfW5y48g#5gOzMGUIKp}*TtKeduV{!taI{6|%=nf6MNML*{+6)G`E0R% z{4NW2_|@+x|9k)GKgxo?C2U<0^+Po;Ufb9mxOPqAvTKO*IOeyb>}u+qpzcKX`iZ~$ zPi>VDnB~N-zxz)xj^1-{W}SEKf?m}v7R%b<%0_Z1=2}Tl4|&W^3Mw9fG*<33ZkBEf zWx_3MZY-$Hj?quU3R8Ow)UBh{+FQ%{12MvQS@yCDebhwvdKX4wakqtBj;MoC#u{s3 zs#3DPRtlceV&9&|>k-%f(JEp_udOh$3~XjHDuB~BC>Riqvox)L@tJhbkB@d20mUq1 zW#>;Z$x2)fV!_S+8>YQL&HqcFrZMz?3)FZ_bEE%HgPIH7?Po}GYyv$U&4P_$0pQ~aWG!{X5m z3h#3?t&82@flcSmt-3^;_mJa2r{q<LnxWMR8T?WcAFn7vLZ8A=F8A$FBg1b8*}o;8h8-QH#lp-w=5=wpcQ@|dqwKy=?A zLg*VyKDoF+fzbL-`z=%pf5m}G)D0I8=FL9J)V%F@#dv9UC;z3qiljC*1%}i*a@41j zFp{;SQdIS(z6O!^;Wnd+ioVVRd4ejX-tyQEMCLnGJFl~N3AN<1p@rf@b*4m|oe3{6 zeZ^J#D@Em$JOP5O!1H4-k7ZS(mHV>e60l`*%lBhc^(C&?Gu=J&N8%1^i zrEvP-4h%|^rqovUO1zb(Ob6R?bKX%-HQ7B7<4?988GX*sC^zG#_tqZw z1M3okmhyLybH^(PUOs&9MMvP>xwqysNxp&BT) za4Lho_Ns!4$sEF3R7 z7f0<&f8)2>ix*pV#eIUGxcuw>WGs@%q{F)YqQmE5OgvN#?*36J#$9s*XBxl=&^Q{=J( zF6cYJiKs+w)(xf*IJ$i;tMkYlNVj&#YjWIi*^_PIvWff|k;f+G)tBR=<)<45^H8R1s%M5DB-N8F$T z*Tb9BY~bbtBree1Q4YqP-dtXaX&Mm|YgHl3eaEkls*|sHuMcT8x4j&`;>9?@L9RM$8fIl<)njYf4)nDP4W0hcj_)?uO7inwF#UkqXdE_SPDgJwH$+#|AE*!lvv!kkk7 z@Av+14bvZ!DgX1u|Ice5|BnH916_2`0sue&Kz;y(zrFuYh1~zfYmVu+dHjFk&7a>j z)Ya3|H8e!FgMhh%gjjT=gx-izNz&e%;P)K8?Y$S=3Burr3rNh!+)5uJCO#iNBReBi zUA{CYR!&}Cx3F4ATe~VbMWZ5FC!wlzD9{{z7(GT$BnWa7Bb2?A0uuLSz?H9aMOPav zWG^NyOCc>vust^Rdko!zoXwB%G06!zo3RnTWAX z$q^ax2gx53R3p@-hPt}jKaGubL1v*Pp(P_CMnAS*!PUKmia_i~0T*9{(!uU}XA-2l2ntjz7Y{F?PekpANoz>rQ1I7xKcN zxsg@_LGKKl?HIhC%Dr)91&k>c9q;`r*>JVD4Fciv()qQ0?D!-Gv|2NhK1GJYLpT4o zwWO-mU0Q?))xaub;R=D>zF?zTH$PQUuI~+lR-t@KXrRK#Xwn|v2TbRV@G$4@C-5GT z7ijs^+#5aAqGc$@^5G$->=0fc1vbjBe59-$U_C|QJn3Q_t4U35Lrh`Cl=V3`;NB48j zq;h>zm4pN7zxhe_dd*+zC#!tR#bP;VqLh4Md&uN*ViwrnTZtxCz)t5dDY19uM_lVM z1G*XHf#4tUUU;jr@2P5Sx*xk+pGC+N&APm+nu_#9GOS!&oV*$gX9Fd;Y3fp6s2aoj z^|Ujn)vy&~t%W~U^|zDy(w`ZOhoOZ2V zbZ(4UJ>{%ro=ir$Ppyx4vVOgMUA;}de0^P)42y*g?a|0Ax3F676)Cl!+$S?ba;Pct zNfhQ4H&F`9|G3QH2cj~>1M;G7kI+xPTV8fO5Bv7mBZlL>$vZh!r4iJnipuVrq<}2b zWOKRH`TX=AJksYk_nv5frR;@`BHYX6@t9xz*}qP;oc7#Up1ny|WVC(vP&PTnk5^_?b;i((!1Yt3cHsWr`m zz`8-6JZ=yQFMce5y+M_D0&Vo}>iLJ%N(Ytj^KBJQ=?F#i5Y&^HX`!T|Wb$mUW~~^( zsM2hhd~O{zw9^I}X#CG{Vr#oNc5V#%7l8ISnrtn0Z#x#b?m@a@6N9|pCaV~S#{JMw0XZwD zbxi(HX%pYQu;-pW$Y;}`jk(eJtm&`!@{9(%t_<86O^XbfS4~AA=A6H~U zm97G$ZB)5XIe7+M5bi*p1Y{p+p2Vgx8$f)a?UNz!hfJ@z9csPMkHD?-?OCg63 zqKil$I>O#xll84!H-OL`yCz=?rv7wt{)G~)3L)0|!zu|FBMH$<)3xi@6Z@r{fcK;8 zCB);Z%op>hAnCoEK`<<=KxgZuVsLAV8hDv_dBw_xPkt-uh5NZ5MAir7-TA_|H(~xJ zmECBVZW~>f?d9tkBn3QujAmqJb4e6g2yvChtK$CTORcftU$LG|kEI#HT@VX~br7wfZ`Xm=w;u?_fHvN&rWKlKrt78`h4_ zlJLc!g9b`Qy|)d$_Zw$%O=to%^UVUZ{A@+s1K+c^A2dx){Smmw8G6cU?^Bmqw+)XJ z(Pg4AIm#VO_q^H!pegV)%dN;(_{qI4DSK#yvu3QTE#77-w^ zggRerG$wn21oVHYT|hk6(q}z!2ztZs7!iVE4Z>-Lasw-P>S*?Xd7FW*3SOz8b$i9Y z^)Urha7TH)+mhX`2wuh3C+zhZzhl&^ZexmETsh&M zUEDZBH$3w3J}=0EsO?5D1$GqWuqcQE+&|UQ151A1T=tN>9KCH?e{8RXW2hv3@*UVu zePii#_SvBa0@G?mff6jsJtuM*0*Sj{eC~n!9=vweyh4Lo4nzA<{OI)b*1XLaXZbxJ zE#1=J$78z*#Bv#hg(Idz+EP4lG-k5UraTQrigMVu^FS?-f^bE883d~r+zP-749_1PmGK!hU-`aTFq>rz46g9rnmW(ew?L^fm& zQTWWe)8Z$`WAwRkk4o`(%}A2&%~RUt2D`7riM4PM>#C4N9oyf7rLI=x-KCxD zQLCxsTMl0*H_=@$ZqVvIg~6E9^K-v{hRH%APksZ81i{kcQ8)s0$n~x;M;vgfn2HX` za(|8zXM}kxiTZq~Y!l641al5(p5xgjGd`d-sQAYaqr?LY&RTWbbZ*%*elu{Wd#p2? z{8Qo_D`%|%NPLnJ&0t|o7|I>x13TKXIGg)(dl2%sO=v+HcILf~#;dWybNsiQ?o!-u zIbOfkE`eCt9t_hlF_j{fT&Prn?}Z~FWxu{Tw49w$Is2lPE46(Ax%spEpYxQbS0qhs zm-#S|%l?W9OZFNYH<$&1v^JXB(fty0PLx5>pr%czzz;3UHZBc!cC={vrrGA~$#0Bc zmw65g2djO^0H%FOFzeVHg*P|^4*hv9uV`7qh#{uG$bQdr^HRrpn-bVk2_q$gca;iK zH%qER^w{ao1RGh2+SL0Bv#xJN^cl6VDVYDE39!(i8k;gW!}et(*QB*L+4>k{){O>3({?d~==4W8=5Mr>s%2 zdl)WuKT0FDI=0#ET=J3MW3h*%Fc&Wh_HB`ryOgK!@O0M1mgR|wVHgV*aRm8k6G2%; z0YJxqG<3SjX}7=lPSFqAbmH;6K(f|FhmfbATJ%vmJvrz4Or0_p9X8KKU`giC;0_&LrZ zsy+@~gCat=s}Y2mv-$hCcBg=&_DLqq=xcfzNLh#QB!I>E)zxFZuaIq4i;*xUP zC^O`0J?Y?uN`Qaw816%NqGoHM`;-^*th~kF)K1inN5x(k6XQSnubIUi#pBO z=M7MIi^1tHoY1WZ0HTG!No(fQfZ*IS%xft*5oIdM?ej(FuFgf8>E(7g2((0}4zn?n zUE6b?B44DRnHGSaD)w}ZZ2)QEz#G=LE#AJRyX@5UetGnGW7O9HdI14Ouu-~X_raTai34}*u z>*#Ko((yL0j)QkR=muMHnz&m|JQE;!q(zE3vr#T>3aW}X=GLO#0WH430{(XX|7!k6 z|7ZI5$N3xR`T#Tz0098b0j&P*{eNm+|2GK*Ju}^3mxg;LLj6=wLie#&yK)0_+`TL# zjd~oVLU)i9^2kMs>A{6w*1-06YA-bK)YVX-tlDPDz1LZ*^yk*i7hbg77#nS)9}GjG z&k2!^9%1%!o zLZ)fPOkEg_j8HE3AP-)7j#D;6CX`o8>%=RtV+qwQ4pn_2Rz~RCr2720?Kk+bpGbUz z&K`*`^vW4%d!!|I;^2koF3F*wY8^jGNX%t8SX%A%eDZ23cNdQ*b0AA1-*-HVa7qHla(WaqyrR9}Jj zZhjnHsv&SkZ?uk~NOHSE_Vk1crq5fvll0}+$5(56%Xp6d>==4y>-tZUXA_9p2r(jM zcnl$y+OXkB0-;_jYy{TOY$>u{!p!5r0txz5{Z=- ztSqtk+E6xzSn|*bQG;L@)4goEV_ zA;1eQwGP`AZvbBr>5`RUjXcm=m#Hbl%r}x~a%>?19i5?!$ zOXw1`&6D-zHOqKYc_V>Y0+Z?})x(&>lg0B5R;gGTXIYbLm(zgVi!Fk32_sBd)(BnS zeLS!5#C}0meUJ`D!!Qh+Ph9E4qIeW=L-BuO30mb$_n^51+rMbOAYjC>e*hcydAI6Y zPU>2%(z+t#;&j3e(%O@9taNP8#i%j7QIm!?U)EJf%_84yKs3&|iW;LBK+uJT7ayFHWR61BCy-#(45e%$k`9sCT~vA1tv-aEokUn z;$CpojW5(~VO@HYJ2s85x-u@c^`i_JD}AZgjl4`g75+hkxLM#AYMtIqY~Galbl%T6 znYU9a&Y#zi=&Q}Rl>$&!W%*OBI|YKm&AO4pbSASC{ms}7(~aUgZ)jR)=19GpLDO;(-^IjTwEuibz* zP_wnG8dV*_Tr@q94A~QHXu=$O(^G^ZFOYQmxPHRJvV(!9+*+eAiiu1{WO{I_CQu$F zZRz_&z3cRNXF!O*Pfn&+u78+Np>2gJ{HUsQwa(H6elGaj))BRJOu#g&855YyZG#Wc9Y#R(A^Ae&eAwAJ%5EiD1kH^4P9W{b zSOq9eltJ5L>q^E}s|l0Xn5dkP2Ad3$c=uH<-&<}&;0~bkD`qkAS|S1S34)M7d!Ial zBMQ<-08MRo^}vtu8!r_*J34MWc(+PpHPDMLYf{`Aw{kNIJjy)(z@j+Os8n$F4|C0J zFzYv{0CzJ=_iP6i?-BTDD6~m3hzjl-x3ckFqp>G_l9tugjM{Z9+|c)tBDEoFu|2NY z5i&Axt_PS0+)^fv!sgoC#@x=C~WEIXfsfspAU;IfW`8hIGu!oHv+#soyG;EsJWNraeUxq2%a zpiFH2UA4?jrA||RvhvqJ>@xqo1_vleB@^?YtNaYHk}8MzhmV03Sju^mS|I!?pS)FB z-bFQ;{R!7SbMLV2{siMdZ7E|AM?7fUGKc_D$kJgle8Rhm=V5yk``c)Pl8lIm)Nek) zmgbh`()Pskz;t)NZFYGwGdDUnJGVMFI^%GDthfK3L8@WGa-GelTHH9&n;E9D@STGA z6I-*=eC^=7^X}2r%FoQ{g_k_slsSB2}3>GNfkO8LvmMj{^9bP9?Q zyEQom#~DDq@TCU=P&9$7sIDQSZv8VGBUPY-zSN5V0&&Kj1WKwLf+YUz7seFj^`9Pln2Ow`c`V6j?Et7I z$$laT-`mN)`}zLF`=vlkOioQKpB`VWU_|~fYZS(3cKrIFM^#uZD6lBeY)YOfPB4|^ zMnn;*c?D>GVpS<1d~#Pfmf+?&8MM9K(b0k5dZ-(toQ#0Zbg^ZqjY+$5Dr*)YUsW_) zu+{)x&)uqa6*~(>SOVQhu;)FiQmuV}V4*DDJX)`mppIFnd|+BQHoKXh<3JlGwj`%0 z+xGqXL-EReBd&;>&r&A8?t#*iXRJN|j3KB%4A_j=f~}gZy46b)BVE{qi<&nnJ6cqu zw+^wVUn#qj=V|5SoaZsYI>dTL-)5G9Y{y|&k8F)S7&eEq7>I4Mlna5TuTO#Ddv>aC zB&-wJrz#UUQFU}%kOg(PS6PZ1gRKsYIb!z<0Ovp0A0eY^PfsSCS)*hmf$_e;mT ze$E1cE}5*7n#h%P8Uyl-y91|?z?6P3*RM~04Y9sCdU-0(#l|UiI{6@9LUP8g!xzj=K4pQ@BM&v zHbBu$yQzrXh&6GK=2%%IT_Bx@dPrrRanL0Yh)C})vQ2spbOlBdij_&R z#jeM=^FSi`{BXHD3%o1I=`0D0h>{@}4<^xlFWrUg^-mGas%T!xMNn%^e($zTA2kU%Pp-deHZw=K_>Ufs|ynkr*^iGcKBYWN+Ts3 z`8*YlE5zM5h3mR_k7%(8`c8;lGbb;Xp472uJ8BiIU4!E%9Al{tnF{afGzHZHwO1u! zBFijVQq3@b`GIQH4QJq~b!_t%Yc8)6Q#KZ?Sfd%-F6M%A-O=XUL`D9~5k?piyrMP7 zFH_r{>1R#9Ig~+ynGZ`6%pPc*`uCRY+84tE6%>C?fI@+N+)BWkz6%kKb3lGkE~B~J zE~(W0lcM;@i)jGIgU2}1J$AJ_?fVe33y`|aAgUYwZmMZPC1>B|UV48B$wYFwA4$pX zij2rlWUlHOXu~#*;BrPJWZ+W_by65Q8uI*Y%ZHw5)mBx!*@<)OKq9rh+m<5m=G)sPc zgUe|@55s8GB9kgoZzoN>L-K?>p7#mi`Hu4^TD?-i z?q+5Cx#`tu+w2$CHe~l>0GgU0`^W9&K4!vXr?N+oIbD|YWh4M8Udj+fX<*>M0GNNr zeBS|&5ivIUaulo_|4^;6E%)--MWhQj&c(~;#B}9}EI;Z#hQz|R6byyhLd4GtPw9*^ z&weB{_eZEJE=e}+-VmD>bW!$Ha#%(@^hY6jRD8E|dvmN}3@AExpegYCXx@yQ0LC4} zuBYdz0<`NSH)*ypDmE&Rc+2{eX2QOck&6lJLp~&x_aDnQx|`t49cEExQK-06J4Y?U z>7T6Nd%gL8gN}c-SdSxqyU)9xW6f+E?u3z<9cC}(8^{ym+CS}>zL zK;Ph#&D|xkBMvoc?%T+(BuFk`!XyS{GJV2Nt!EIU#C4-j+oJ7ua z*8hl0fE=-u`5d!=9%QzjstjyX1eZdE!sIomZ9F{B+>CKC06{N}VtbcyR^4!tvIjZ} zV2C?X>;_~VpvEo7G(8WZ0aY&K{>pmQ=;UPOQ<(ZeH`3_SRLYhjj^j&hW0N#D0L;S< zNa8h*gu40&{war%Kz0W)I>(fHC>DQ%7+QPNufTGX0GbAt_Lu-V$~A!`nt!k?*96&K zP|qiv)0$6V-=U>hJE{17ff;Fg8oViuNu*@zdTP4)5z>i!_zdeJ2B@*0yvu#B(Q9 zoAJ@jeL}0jbcec{^*4RrZ=~i>#H@9eiC7v=&z*5cG$R_dus`1nneJDt#@GoBwYBd0 zY?CDYU5en)bEZu?UH0Mh&xpme_E` z3+=rZxn#P-IA(E>l@c;dUacgDU|XxrD3H}?930t@6!b$-&?NXrXLjW&#-b5HZBOne zK`wnLLTD-1E5-y?pZ#9sp45KpT|XDZR6J|u6QnhmHOo|Rvrlu(6N@#3HTzU_b69g) zb5L_sb5?U|b6|5KTKC%ETF=@5)V}91)B(<+$xWgMjLsPCHs|xhyVK{=yL*08q#M_1 zu$&CYD}5&ruD2lzUe*-3dir4aUgoanQ1+zEQ8vy2k9kiCH6WF#L+a5jFcP(4U}>-V z4$KmqCSGpKOuVSdZ|zBh(RoR2T`g}*58Gyoeyr?11w)AW&@W~l{ay*AT~g_+7BBt# z{<2Wk4gYn#5Ul~u0jYRYsk)lEA_20arID-i{*6q($)lF!mY|*FfXqIIq`SV2KCddm zS-wTmuhIEi@OBXY8?+tZ9|FIi`qtV&It`iAx7}v#I$En5YxjnmeVBcu*1+nbcg`B*TSVNRv2UQtTn6b=kvdW1s{~c(!rF zde4cI0j>i(&G9=6z|j#}Baa>-zi*ik43V>%O*88h;jbkCV$=}X_*3I18ZqExdg}C; zJu_`PWofIWm@D}~3mC$O3(*>DW8TKyq|@$A-uW4?_r>LS^>Pi^`Qg^rSS=Pnq~ES$By z8+DUyx=d|fq@@p*zGB6{4xF;Zuk${Yi_O07N|ZV%NEGKa)Y9{fP;FK5cg z6yq=CYGbuW@6iT)=H{FkQQ|nHU=`LU4Nar_z;GCsM~#(~r`Jjal4OW%8q*S%4)kah znTl{l)|DDs12s)`%fK~*3pTmlq-n@rI%xvbFy;X0vv_*XBJ*Bkk=WWU zxr-dOm4kWP@mhwOdJB^o;bNS`11zscBB}BQh!`A;;p!kU7I)*%$f;rLsPQwC6Zh`I zPh)qmDHr2>g}O+{9bYipIAT#$kZBeHPee1HXzw;8Jt;zP3zcz~@?wtb98!jWcgwJd za7sJa-F2w}xhs{Bx14t%WKDU0Qi&QI)U;9;tYb>ml#(GCS?zop?gQfk)38y1mB>o7 zil~RL2uQy4IBQDgtk*2^Ia%TT?TI~F!|%<-hXld}62pHhVLb<2)4duJAFXow`{XJof%L`N+7~EMHNsHMRylY2o~G)rBM%?~RzrovZF3^UP?U1TcDdj1HwpghuQ1D47YTBQ`{%{8C&DH%%_v(*Em~>gJR-du-}s zy$5-xki^9dMLTbbHBFKaFH+9lSMoKgz)M;=AFSJQ-E7d51uN2FMg)Z%=2JNiTwZ9g zCG4WEF2Vqj%pnn%Q_NGmOj?}T1kSMOM0~ck8ul01GTP+nSveg3nnYEB*Ye15gLx!s zLk`7!sz>dXh07A^xqttTAxVj1TLBe?WZ`NY*vhv$7FZb=!nM*TJy>EmZf~CL63!-= zuxgH=EQ3l)FephK%yJ6yc-V$lQ*KuXR6qoa5Y-?3C44spNo8Mb%wA~MY%N9}WwZjj z%HcCVV-@)VVSiN$Eqe6*Fydj9;S}slzBE5i^A zcJOQ?$XB%V7irP9eZ^-uvXDSe{jNmg&n8v`Yt4e#45*zmlsljrGXHYdi-Dt-Ph{a+ zv4PpjV}%n#5p&--8#`BF>5EES)vON=Op;U#)>guk7)V`oxM3xYo3^A#Zja`y0z;$s zU^`w6Sw31uJz3(_Y);WT7ZeYrq=G$9vO}>>%mo~L@98^l#A7yosD=>U@xy#Q=tIKJ z-m$ecCcSvh0)}Hwyu%nu8_$nbVMs)IU)I|r&_kB{J}1q4jG{%@Z~41DYX%_5f?)+t z5YIqEg>jP~Z$Qe-74060bdOn`pGYL*G>jJJeR;A)$RJ+RY%GM!Pt^BE3L*w0o&CY) z>#L2S)NF{$ol0tmZlD*v5zrQ|jxJ;r3k-V)eo1g_KgNkk^MW$txWpOu)EYRuGheG0 zm_8T<-q{r3yp-WGd<|m!xCG&XHSQ~wy20W`?gf;nG}1S{65q7(*#v(xc(|L8f>zSP ztEd$ytnCed9~}`wty2;!0Y>eU?X3^YF>9#H-34j{52i2CAGDg*yffd#@6s4$VJb;f zr16bVh!jLd?D2u@qK^{sw)`a?ID@L# zGC*_(A&V5&e{g zh7~DSHXBwA;ddTW{e5|_L@B~*n)1RNm%lrj%iQRQg<9yJ9;Wbx1cu!97gf~Ve=jM7 zELPa;j()>6$mMkEG0;AH`jUK?LO2>&RY*PEJ&Y6Qqp4w8QFxb?+QnG56r&Uu-nABw zD_2~&rnrYeP9|cDQ5rsnl%6M*OTLy(lmF~2e#WALHE5f|#uMiWSW?+PB)pj$V#|zl z=*Nr01`f0}F)deD}O zS4K=m`!3K~y9+VMtEa3pOq4zW1ojkdbI&;RjETpyU&%Dzx9*iL4OD`zD=sDt&LcA? zD9V8pS@MY-brxn;-wF4d!^p z#l7z}FyB`yEd<=?FNfywuNTFUcFT}?>uyoX_W4;>Un!|w*g@FIR!caG40G2*25=}~ zX!cWyVPoJ<O7)giGE@FzDoMo`{LkO4r0ly)?fuD}1l7@&S zW?r_U-jg1y>*0!rf%Fm2Wdyj3y-o$nGQf>#2#tsLmMy+`+BQQ-U^ed`t*iqVt{G$& z$@EH(hjE0a;0j!l{^%DD%WzcXP2R%EY0nT`$5y|Af@?5FAG+n6*7ZRm7JYaRmfSk*(4Xg$Q0b4F9&< zb&-o$sVP`Oe6M|c5foB;sJG{gC1!qxCk~AmKDk77sva;$Sdv##I z3;)OjcEXvpmF&GM_ZQYE2_@2f_9<`7Qh51o&1+sN!g?_$R|e@{edhfv#5Z&-iHCA1WyZvz{yORu$y;s~Ow5^4EUB^ws12SYMflc6uIT(Jy&I%-(Hc2YLfGx$^59x=& zN^K=ut6s8K}+3YOOz8$2R{kL`~((R)dG3KWqUaK814Hy^p2!uE{j-9>xK< z8PFDrK>KmcK&D1YjEG+)v+u&N`<~hN*$eE#;N$Ierr`mum7!U_l15DnL1d)8WqnU=xS$;y34A)c7(TPWClZ^^B0s-TjUi z_^LpdoWphmsrYz!`%?l&cUxJht{y5?5RP4ihcnv zGE_*8=z2LOHPZ@PCKhoVx!9WF!|z?MAaM2TF!F=T z3oMbT-}^O%!h50Xdjo_}Uk+aE-JxyC_*;9YKEs`Cb zW~Kw5 z$`M?);iBVk()xO;E-HniwVB?Vw!HfM8jupu;$lWEd{Zl{j&>AMDw3D0(Ff=f5j-{n z=rwgs$JaQ5+kH}1)tzdbg8AFmDKy0%5_1!s<)I4j*ej{pp5rf=)S~rU0d-{`&ESt z!31ktE@wW~PS#eTtBVs!8}-%NL-l zb0F*AYV7~&oD0kE(YgPeH2I?)?3kbvokxc}u=Rqx0giO!8{3qy+n<83zuWh|GP7|` zCEzHA{B7HR%WKWuffU18itc4*&3&r%!0CR^a*xcYp0UdVdb#~1-ChNq*K<BKB`0SvqDhM2_qbhu_m8rSJ8=Pi5x9pdICJxJH8n0K= z^TVCdp2<=E$@`JV^EEKqugakO$TyvD^;at!?jjoA=~dNfuc0?X_}|XME56Si?!Vt} z?w5s1Sy4VIX*sFr{X8;s)2ykZ45FIxwyle_O=nH^qAPanwC-4mklMV^=XF4nf8CbS zZl85f^3>hqbaZmGw_3}$6<6J!II3WBPoIC>CE>+ju{B;Q)T#^`>pZJIz9?jtgtrf& zPMf{A)K2+c4L6vsw%3y}q5R1DB&p@4p#rq#^tMZMMebqV=g-$~p9jJOT9^ZB3LzfK zMivJs=EElD2SN@^!%rnELQI$^>&rwAG=L8ykOZ$*Kqyb}O%1tD%usHaaEHIgU+A~D zIDw+5EDoVbKn8)G$S{V01PBd58*;7$!7E}eEy26+b@4Prq_k?Q5MqEE<^%Gn*}TGa z&JO=h1kK~dVc@spcNc1YNMv9A7_e9k9+*%z zioH-mL`-CV#5_UwB;T5$Jr~zP>$uzWh19fIzBEtRUY3008zO zL;m*d|G$%+Y>X^_)iDgXfqN(ptUjqF$Kx;yP3YD3kmdm*6n>kP3%l1w#19C#&yphI zPR}~OtZyGFijC1`O_#dL^g&KE2W-s|`e_3=@W=p8_VkdBBs&kK>Am&#*2OB3w0}O% z^;P_3LP}^nPcA}?IKo1s(Pn;7N3pi&8yu%hPzYQ|IV2I>1gCK$@X~KBIkMT5`-|4opTi(;SQP2lFjGsHZl56veScZ zk0l~d*ztT>h{e0^RZ_83+(qv>$l$7LSkqjrQu1&%S3Ko)@o>U;sO~=OUwMLTp%>NY zE>z;q7t+jy-@i&S>vp1e#ynZob$bo3bEQ(bB&o%_;O5Vj!IS%|HCUbVO{&pL4OjPK z_wwNUNRQ?TU2Vwe?3PBOQpIY;wB77%zjV=Q^D-B3^7E45aH`Y5%jpSmmz=_wQAsK!+Fk+nwWDHr3g#$*Ol=lU5KtfVOr zdc7$OMd>F7unc(gN5Xr;i+K=vXu>Rcp?N>@l7$(C7=`VH?1k?JBEog@zt`LsSVYolb=fo9^#&PlJ+dKN* zwp)v+sztZ9Jq~@5$?&v0ipP<0fkvT<5RGgyo=i~Al|Hpmgtd3#?jSN*rFVZuk)Xa761Mo$|O#L`$jjep`s2{(!U+ zDjW|)isQYqb5J&7E#37zDt&x3bRYiucBA{N#hdyI5s&^oPVMU&l7bfu4mLVgHRk^z z?VN%{Yql+2Rl984wr$(CZPzZlcGRMhm18JRz$w!T9Gqz zjBnU~9y&1mmFJ54Pht`-)J2XuzduIC)i`%W+ox^>>49)V=p@d*6uhcP;}xAME+{c6 zGR-q4dI*+G5-gl~5m%~tXn$hdC7dTc3ULzisH6m#sIvx@{K{sjAFbs0&6yXINMTV% zq-Q}PIf-yh?v64_+{iDu!xpCo;T=RBl9FK2s;caVGX!!-V&UVZ#qe=9Gj)SCU9jrK zO3%PJL`(Wswab!GB7eqbxDz8B+^VJ>`l|?|j2$krM3G4xu+}+CIa0WU9x(?q@m+1g zN;>3RvtV=g1dseBMI$x~?GEHlXETWH_tlf~jV8@qR&h!dt_g)~GRMod!Q z)2p)z(MBbJ&r{q}+zA}EH}~DI4F&|9 z(tc@WAE@ZD@;URE+6(ApDJONKRFVMfo&e5qe9~sr4dORUvx(iOIXCbLfE22?IJ-LN z^WHO;0y2i$FZV6$zPRCWC3_6mwSH^$%g&(MLF_oTG0SDbPMDm^k+c%(7d0!(yYHFH z8poc?ks1jpHe>g5H&{_uQkFiE)_IpxWp6D5vPXWq-yLQq_6p|9)7FD9dR{ZDFk*WZ zBw}IcssToW)jH&U+!|0KH??g~H!FAm&W5wLTl+E>+p>-e{wkR|rjQ%j>X`~Kp&v(z zHCxUZFcrm`SD-0h-yyM#BJP6%<(&v}JkuMB3Cl2HO}}H9*^pBJs7(!wyehjOtI(j` z|0Wl6fd8V;#f67%lNwpS*nikX=Op8REV2wl^d<-NEUKY~*GdD_&FjjX3)yE(2CgTz z|J{xJv7h7rDGf6l?8_TyraKDW!o9LL7q#bft%-|EN3&Bu!?rU9zmUEPSh72iF4T2{ z%bXR`;J5aM7KU*NBsb&%H|U)ZwRIP_7zwSa0_?F02a-#dAF9X%psQ}dYj6bh_(z#O zCzs?v;~H~PSyqKJFCMwMq=d5vZuZHD3PNbmY6U(niRO|zyh^ZxuLJ9xJwD_^0`r>e z2I=~BL%}Tv!^&6A-)hk{y6Usue$J<;QDLLdB1qL-sRfesezs1RQ-l;GHDyO(JqEhO z9?KaCLhCfM+D|w%Miy3;0IaWdYaLgHtx@PtyH4s^l~G{h-=;B#Fn&De76cW4d&8TR zP+-7P6#*WhO)Z!^k$O8qsi?6YT3?E>SCd+)`M{T1-@Bq`4zXdye$$Q0=a5!;%SU9r z)Yx-=KEZ$h6E@aQOwrt$5>nDn{uy?k)m*JPZ6h-nNkqp*Yy(Sn0E`}f`&jqN_IBDw zX(vS~+lE|pGitki95!82&-R+6;O`l#qHUpoOCM~r)ny}i&D%_~74A%111l#yQw6!aUk<8iiufy4 zQ{w)7gbiTg>nK@4pSeX=H?Mgp?{Qtth2h?(cDQM;M*}j`UDREeM${P6Y(Lfk(<4)L zKq?lh(^8lp56yACIQx?dMoi}~zoA=~*Ib>O>U$GzyT6&r_0vLBlgn_5Q7K;sL8++XE zJYG2wy4gB=VPE6OR%*6?Xvq zqD(3Y?GWj?A`5@bdIxr(0K8=g659wCp88~!%j{?Hv~i23sFu^c2EWOc5<^=-q($m! zVFc&WK_RdwPN%Mf4<&G<2ztsi3w@AS`$VTmHJ>0#J}WF8h95y;Qz(kO*L7v^W>ea4 zY&q7dq^1I(kc%#Sg(1o|G>Y8p(~(vc72NPKnIf3Q$~v|s%4EuOtDa|WsmVJtCX^=@ zC&=5UfH-e|B5afrT&d=0Nvs?gI&mhVI$b(QU_@r9V4JY@LVhTM!(eK9TD}95TD0i{ z;P#|(aaSU51tAtK8#&HONy)0>T@>0%b$UUxS!e@-q{gg^D7g>>XN4hxO84jE4~STY ztBdEX_L1X%{s$lueB%QGLeRvTSFd(l-t5t!1y=Q+03R|zob@@$?7JV5J zLNwRo?@&awHZ+nz=p_Sa zxzkU`uLs{kZs$KRLUYx-DJ^S>uff`M6#sg+0K58ellvkf$^f!P19&g{T=dz6^1;*_ zXM2W&ix>2XeJYak_VtAP&UzU~&FUg&iR*Vo)bH^^doH!*ZPC(xm0zvy{JEW7nWH`= zhav#G^X}O@MYeA(*IugL1--^>;gbq7*xBp)WTSp1AHYtYSN+guhq3@UW!v*V?s(Jt zozQVNn@f|-Y`j#svH;qTz4mq<33Fkp5iAhNN)C1OyB?+N?Huua?lq^z@ZlmN8gV-O z!x_q2#nvCD5#AbJ-<4vG)+8Ay`Ew|TVUad|NB?l^aQX)f{YgUvbt=2rnMptu zaL&|(K;sU?6G2xjcPg1?CD~#;4~TLR<(O48tcF&zhFmyt>ZR`HQ0-_r3D2DIaR8yU z`xqbN!?Wjd9a@VyqY3j>1d7(bA)v1)RoZ%Rn!Rz2)t`lm1V;ctJN}9Zd2R2E0y_38cjC!Kudxzpo+55 zDOPzk8KwnyD?tM|OkI09v2j8X`JGbk&Hc%=2@$bryTim?l4 zyLrOJvP!PQV&$ZaS~`F|nE_hsE3J>t=Z$=yhW(f4r6nEV-xPc?G<=CIJ>n6Og6f{- z+)LT~dYEzqy0GMHq)D>47r~?J2EO$Pa%M^o4Upw5r#J?U3F8V^z_Pog4*57RzWha| z!CH=Y0mgyxRSL%x^_>XW^q)Ily`~xUl;NJhaagxXhmcw??X+e7q4IpnzA<_SSgVo! zo0*I>j1W|wWu1$w~-P zdIzICtuH1xfWHq(q_Ms~Uq!yhboq-KQ~0d0V4?0T-=sJCfPR25&Q4nvLK3@(s^Od- z*eu3<#H(*lKBu-8$ig&0y~IY`-SZpG+cR5T4Q)%XNN5h_!bUHy*vr9fWY!s`MQam8 zLX|>$V%LpD5y+!u`n5+!*N`c6ZrvQ7{7hL|n5IO*o^yoSZm|Y0qlx-R(5V_g#tDZ= zyz#60?mBOD8f{sbsHSEZdOK&PORQo`xX@}HJJ89DzB`tPhGq1NB*0v zZP5p@n!eX0s{^YwKn=-xR_1!O6;Rh1$c~9QI6@Y7FPv_Wp@mFphkB9z6nb8{bewuC#@1)hH64?-Z^UnIUy9D}*QyvONS=)r;7@Go5U0o+ zF-@e<@9kTa_Mtd_A6W%~xV++`TA10{T}dlO%Y*#2jg-`J^Bq}8zFsM~(DLp<4p0Y_ z=h*m@ny&Di1ROu7A&w7)G71B}3xw+oaSaj#x~|Bawk6+7s|wlnU(}GIX;{$AAni=+ z^;kMoosK%EKIT?~qAy3XxDy7XMR5*)+?MVRJVcortzUuMpdG?NFUf*ImMT895!mGM zW((K>N#wJ$$FBZtdi1hd2L_^UKSI2h%gwCHK^7! z31;pC_`xM0RCCih)@Z(Qr3_f#^JT+Dz+!x9tU^>pgv2c_c|nK?2$Om-RRRbT$5Xgg zKR5u=+pe8H*;$6OZv{FVaOtX%RCI>M^b|Zti)v|imUp)e-PUigk33{FY($pYirmjU zloe}64OZI!kY4+<=xY((M3hRgmPX@q&s{=0pH3fI-m|RL##|4lWD*th{(2_Y7Ch#7 zt^9*F*91uMSeSC8lH}^D{33{>Oc4$=;pGUVk3v|GcxekhziJA8g5Rj}HUEc5HvHR4 zT)R54S;=Ed_Qlx7?b-N6IuPqFA%0R|S)%PvGU#I)u+%;DACo2dL~VqS=d(R-tYnlD zrP;%~@O7+6)*91aUdYk4nEnrte5;CuhH>X?K2qxcs(IByz5In+JCc~9a_Lz{#;fx2Xt0$mNR;X zsAgnm7c5sa&ix)SPu4Y!AY}PU)-a z27GSxq&?eqV1=OB?4373GE_u?|8<{#x~RrA848^tGP@7VCVZ75(!s*scK_nATX~P1e_)ED0rk_0}&cTB{ zy0!|KulkKrfAh$C5x#puAq$Ut6UrJ@+X-JZ-$)PH6CDH_rj%qP%U%&6W6!OY?Qbo3FR5D+q1ZblZBJ7klUPt|NT9}OWbX6&?KC8r$#a`q)a}l!)MjT zPiqdmK|+%JG@sRAwBY#<^Wald>4NN%ML}WB746xF4h{w_AqF*?Qy1v?8az1pW0ibtUSZP7I#nr#58Ft3x*R-Vkwo!06UTD8-Z*lx8k0m%qM6KoKPKQD z25(dF*Y5!z%n^lBUnFqNFQ#D(^NE`vEb>KkqXMg!)Ek;h4@B5t)Y;D<0*m?C5OWOX z+lH;Qr49#lme2!smb-JWTokSaGHgU_HSi8O%gjwEFTdVT>Xzu@6)KLWYu7<(MQm*v zoB0@k9_jho#e_YLhGJU*Z{p%h=q88d#wGLUdFY_NoDsz-tHv$Hcqtp-w)3!Erg2s_ z7yRWCdp+Ne`%RJKtZqiG$#)VOz<_$GC`b{e>P%MJUn`3n4?;?bc+R&w$d;oylVD{D zJJlU4n|kC-gXUL(^pqjjRx_h!BBf&rH^NDMZ=+zLM77igVyN9jYqb}IjN&e#?DkI< zHCVlC*F%@gQm|SphMmv+OOp?6d*ud};C8i2Whmk3AjK^;yy5W@$0an`P#eLc^f zLwqzcdVp2QzY?^|)NDt(V*YrD?7)Ui{DwLsYouwelREdBnK-Sc6v_$n07D73wzrnH z1jcVUjpwE6#EXeD#v?vZ%1sM))iGLjKu(zm8GNPsM0Ea62fr1o^@>BYs>8qDx^n5n zpy?8P3M~<-3-y&)H+CI?ha#!fzEMNgKHkB0LT}Gy>1jvI@`ynd0hbq}!hvR9gLaFT z3I0yCez5~}BCcgq#g){M&C$Nbx)7D<;$~}SZ^my!6rZ6>Sgu$l zY@%f#OXPI@jkv{gdhxuH>`d^9K5aAscK@7WE?!EL=q|)av|yf#i_aVH;@6@c7)AW@v3~82&ljoU(Vuag>wHeE$uK;+=v8PM+-+D zcRpOz5Y$?!tc^niD$CAY`UhSoD9mRAOumumXO@DtJo(a}hF|M|QvlljROeLAbB;Q} z-Dqc?p9GEs8K`HO+`-ov*C23Z+1?zdyQX2k|wKvQex|)d& z$?xwX4fHvu@@;JO>db;3JTN$k`H7j0pEU&7J`YI**N6{42>=I5-!BNmFoQqS8X-tb z8YNw>bs6zDCOV^d6zUL8ci-5Nogq-dzYaytzJsPApKnK|O3vwsME*h?tjGIfRXVnX zSB)+MdF#=$C++eUI&MiF&~EH=NKk_+QHP@sqC&x^rJwm+|nUwyv}!wMgGd>O0sH88eWo_De} zw4r=&SdF;l@*--wg!=w=FgG6yG@yNm>dK8(YgJ1}1GO2qM41#<=htTxTw)!3{a3y> zpK)H)1ay_!GS;C>!$Q9!p?7}Y#xXA&T-ybZX&e6e6X)9wc5_wV$@_T3&|yjKIr0XK zh9uXJr?F9K5n?*dnK5N^Pok~YNzqI?B-{~1(9sEwb7m|B1<6UF!@j%HSZI+&(HQBY ztfFZi07)**AWA?RU)GiCh73D!auL%FD`nt+FrBmw>(IR$qW=U*7s~U??SXJeD~!7g z%TznjP}9(iwcGP);oFAE1U~aT0kIy78+p$&ZUZ+tKz^`Tn4g>-H8{(O>q-Ly0CxBA zs3T*!(wr1NzaEH6-Yu8dx*1#jrggqR^+nc#x7)&^y)%XL>?%Ur;PY$7a{tCt9qEUU zqiQePDEh(kCZQZzc&+xN2j^&$V^pA8R|ZFQvjJLn+H;$2=H^yIpseCdx$LlFlMYV5 zsh+EG`COop73b$+hbRQ=TWWGM$uq`$mS@{ds9U)a&jjnvH^z4GNA6AZ)0Yr?(+iX@ z;$(Yf`yutCLbzq*^-dHa>WwQS8nYd%96_6Ir5;kI5!BIqt8D5o?WgKD)*`LhQ}`vg zct|3cI|2>Ym;r-NIKFUkT+G^G>Ti)o z%rO;e-Ov&Vx_vgfST+j2tb)`15w6g% zOBC0}7apz)C2RkwY3~3$9(PjeK})eJ;f36a(JNg&>l7QX3w@(X?^`djlB9lvw5Ix@ zs`wNZP2KJwuI@cT=ufY*I7T8Cm41jgA;eHgCE`L7Dy364$Ygt+0Ny8gu%~ekr;G~w zVy|4Q+>J*-FMw6Ud64^b`=b))JeCn%qZ*Od;Jq_NTnWe~lXXpYu$y6)*Tpw9_I?j_ zT+55otNok!ThvhkZKSG#NclW#SGIkYs^2~dJ#+WtB-}%VcA>UMK>Hy2QIyTnRd50N z!kWbJnb^q1`OW#Ptd>#fnEYUSvG=*P3oDQviOG-0m!^B5?4d`T7$!lC%5j*Poe0nT z=s`liIbovNeCKP2L4Ju7sFBQ%{QSe^#?LGuD%c-JZl*9hA+hYN$X70is zx9Ck%9yT7-nNU6Z37WA3-jQ9++myKT=5$n~)$U^kAD-$o+wAQU1X$Shl$;A1!E}&J zAc^WZ$hl^9@FIato?mZnTX5;U^V)@n=J$PmNdk``X+*Gc!BmbV&Nxr16ZQ@8V*YWr)fU7N1AzGxYh=+f1a`MUpGPhup zSd79b-aK|M!hNT4z6HG>v@*_58iKTx-7w|eAkH7A?j-g}CAs@8;a?0-E;Q^k74!qO z7#dlkSq!e}0ZH(p7&RnX%<*2gvHc}DpNdO_-s3ddTFAJlO@G(M> z?c2TeDuuig+^Y%QlgE620OEpMJ&|+wIW-ilRer~kU$cG}gR>7=w3y2>%lP5R@qmyl zR~bNw=}hXC{Q2&HT`{F_%n#eor{umC(8(#F+Z(EMgugNh;_gD(texc|_G5ZaF;ibx zuI@q&{CWHo2e{S)2q_5-sX~MYX&#;*)`CG{(bA0obtgQ$lO9R7&vuKH+DB)QHg)n> zg(fwqG%8h3g`#NfdI^kb=l)hr)+|wa@7V(0C}wE(|W|4kXV>v zE@hs_zT4w80h-gKN`PSc8!F5cswp^~F!xJWhj>$O*wU~utno;8;9^zM+r(AF$6LdN zr;3^^nS~a_%w7RfO_~-HjljVYPv6l{k@H z{D4myTbx3URvDSHKA+sKuE|XY&{bcpxKeoYEfII`T5}$Nv(*6g2;4#v=|?%Dv=lYw3p$1+?B#Bw=nPlW?UuhOmut|{(ebIxubXW_)ZDyD zxX`+gJm`x=2h&F`g4V1NH^faB9#>#>t-O^eCKE~hTN~>i9~NKch0i*p7z`$+ zM~t-NW1*Og`p38T{7vYGxgRhSjPdM$l1BWeR4cZBr`7(OEF&sOz;2%&KKSPCFV(E* znLi9?!-6UZSmMla6*bASNi7|n6_J=c=+}==f>(%Yg-TPB=H2<-q^I5Rz*5VQBmG!~ z8(XNY(A_!gQr+|>{#)HTn3|eJ5{_H7b#~T-jt?&ncc_StiPTEyg>m-uM1Gq^;E72y z&+#?((@k#K2J(@ZxSE)DPn%w#2;eQK)8Lw@3*0XFWuGFZR$~EkV%JI2Mn?qkI3o&-Y zT;&%ASoP!&XOEJ$r=D4lnhT!KPRO6UcB~h3pmwmLT;NA=Ndcx=qZniGbbsTReE33s zL}Y(t@j${@K#N!qj9FynvpB*M(vtssgbScLgM|yQ=Q#)}=zN?*m_zoXMbSa(F?S2I z8`u*Dl=zzg%l(=G&j!s#n1r4rOvOkQv1hQKV>fURRO(X{`0sHLGz1~TBgOMyV=73U zRQMob2n`19qHXu@bLvsOSnMEvh$Ko1H3fRXC=EBzj3FE2ap;ukG-A$d7Oh|=mrgWC zKrfOvup8YQ)SKZQ`rYvHf4@-Vc9y^63av~&hd>2y<^U|{Yb{`(6-(iNfecC!r=%_I zKtymKH;Vkl*^>`Efw-EeW&;|W>0em$-!^)HB(|nfq z_#l;2n4|YjTrgH7cNK7-QL3e~1=@W%a;d&@<#@T`-1E_1rIvVIKlZZJ-LdrZtOs~P zR|?xT8Ng>Y*faW1AI*O%ykq=#Z~MP}G)DTh@U`Yf=C!^)a=rcnVSu360K(wFJpV8k z^Z%4H&BVd-Z=j!ld7G=$A$}*AG=Cetro%-7V(qK+GB=_kG$~2N>Ez+7!>>tdtE+7qP&7qNZA!k7y(q5O82jJ3U>~eYyWR4wR;dLR4^KvW#U6 z>5@sv$SRD2K?NnA*v2uo{0bIQhG;k-s2gA9pm{>*+Btx*JS$B^Dk4?`akPoV7j>#810YjVlziTcy36Kisv3Zg3|25tr= zyakv0U<~)vUqY+|KB<}xc2w9U^}1SVRG`jp>n;GoB?(9z-8>KyPCKt1dtBK*iZ6;h zqSTeN*#6RLKTv62#NN_7XM!|8r3eJF^=XL13&mP-si4iln>Cu9HP|!>YIn^|wUQ)l zMqNhj0EE^`JOs{j%RFexykU7$?og-uSoJ9!sRa~7wtG%ax8+a3On)xglvavbKrfbz zPkX|a*~%?9Tol&FrKf(5(`|?fgS5}5A}NNJRIMQ4^n*e6_IpBv!JW4Z8<~jaq*8ES z-ZaAQcvYcH5|QrW)%u~Wuqh28{$rptNp$=LefDmuTYYI0uWmbBRNwwc=jP|Wj@z?~ zlFPndKuT;O`}WgiDDq1nP757=a&Ew$l}|A0HfYf2M<8qB+=M4TwL@yVbT%T52ivJhOUbk16pBNIoty zk73Kw$v9>y#J84B@va4Hv#?kC%Pm@KJC=fbqTWshFxR9=;Q*U%|&;tzVeyGaHfaFcxPrmrmWx=0^m6bX5w@gS<^@o;|AO zN@}p^ z;k4!A=NSwADu=zB1$fi!7g4Z-CD!o(qg8`9z$1MCk$k}lxu-4tJuI8+arg9OL z%#@meA=~p)j)5Py#J4cGyTPS{GOjkFHfkiFpXolo@TH{kvYu+!N@zxvdSW|%7h(Xx zD7^L4N{z_JQ&Czh(Ahh*4Q94b9FLSOfrE>pn5ERGuaREHX-oJE*v!Z#b~Lr|khoeQ zU4S4t4P6zp{+)fxQfZBC$#%;86^m@kagA-(U`K}Z`)YGS=xDmPfF28 z9%D-@ysra=Ck`UniAg@FQ9&Nyd7gltos4i0#1KYr)Q{EUonrcGlFw(gLyGe3~f(v5ayzjsluOg?4`JWgS>AHDpF zAQ)eT2mojFmzZFB=Z)ZXE~E?PB%J{UA#kj!Y?EF;^29 z=AOR6*Y@=K_ps0hjm{L2Gd%ov{ahOUpV3Br6dzBl*crwLwM)S`3<3?T2KqGyS6x9@ z2+Q=07gs>sGrgbAz?zPXEWV(tD9aJTYJR6UFYh?BVwl>ZC_BO+n)kV%nW zF0Ji+1?a(rm*dgE+@4?LX&wzGw~;!0&cvzv_I>ZH{BLIW=@A}x*^G?^jJ#~2$;p;- z){xJTVzk)?T765HmueA{mxD|Pd+V-9T9nCzcYC&o1bf)L&ZJ1bugdsEqJ^X)_>VRO!=gGO5yWfUKBj4pLzPzDz|AvfdQEXwy-Lv1GvAz?Nm)Ammsn!-t0Mt#rPm%e_Pi4ZV(du17ty2T>X$+2@HH98EmN{qm~ogkj`CVN-JY26@%U{&ZTml($c$g&s$YJ?KI~t@c zp3n1vf;79U)Qs9%wp)*VDWHL>iKUYyA2*jCu4bE;oc74$xlaHX@JyoVdLXi);3%re zENpQ1WTKZW*{i*^F0ZSxYKoaJ9f}#hTRPV8k}bsR|xJ=Ag6m~-0OBmM2rx)N@uF;1QvuY z-q9ssher0k89+ZN!DzYyFKwNI|-E7ZzE3lbk=~wei zeF;f;2zWzVUf(9_9C~4BD0qA{m+_6J`)fy1;2)GzKyzo3cQ|%jO9_NEZrPi7RxPTQ zh#Q`gX?VT2w0+ytIXA5+VGM;-h7;bQDV?e;GB}E4$+n_J2U*ip*grq}tts0J9~F(C zj&fPKapi7A%t8s>Z)z3<^SOX&%*d`L7L^bJ4rD-9YIC4%KN!5@<0Y6^@cHBSv->+o zw?2EDF_EfKzYk-QrVJ_Ec7Nnq4@%#^)s!>4Ok=YcMlXn&Liy7AZipQar_Yqs_QkdB zHVZAE=ld%*t!=M2+cvc+(iEr&Al?PkQR0f(tDiI~y3jVg!HW@r1vT5gZ8cw8WBMpKoAkD$I2WxFH{4r}~0J zavb&j2RtHBayCOhBiG*Su@h_phO3WZEpRTSXkvz%hTMe%=AGQIl=wl;l|=xy+i%4&1OatA`s`l{D$lO)66!MSX;4P{n;RhHUYC+wob75Q^s9BN>3=@SIv_h~w zu?0uFyMuc?Y}23*`p4o#GqPUE{?%|?zwwuA08fo-om9Pqkkl^L3ZJ%$RU8#J1(v}c z!6m0)moOP3+SfQ>z-~r*Zh1ZM^x!tA*bY>$`3Mx~$_Z~C7^lA?Dpe*yV}d~k&dPCh z{P>uGVK_nVrn-PXfb7c_=awVP_8~sOa?yUrgpp8zN8JpsevCv**yW`g-{( zmGI5j3oGz)jtrq#RBjO|(luFjWtm$8egK{AEhUiq@N~#4W;r;{y*ipviu)R`G58B!3la+8~X{@!CQJ0jU7 zVg1*>H%IsLasATbb)7L%gC>))FYcoA`cRzA+cK=Pv@(2KmYmjd=?&lha@+_1MJro+rqbQ>%!BjjeD?PO zMMh`(Q1uF0%GY#8r@2JCq8O_WUvZqxjEz=8)L?6hiS&HmrS1EZc4nxIHJ+n|YQ^`x zfY7#ehm;hxGd8~Kn)vy8KCwI>h+?i_03;9!qB4AGY;HiP z08pZzp**A{e`zc<3a$WLF2*TBP$q;U(K#OR~xrUW>r&%ZBV^$Gfj5A3JH1^oTZ zcL4x?O8_G6g?_Vq1Th&5Yc?`uTCd8*yrob6j%-rk7Ka_mFl9sxj zJOX|Y0e*;Ne4aXBYkez}98(MjEq5TuK}s}uw>2{o35T>bxAcIKk~VZ)IuNi)qgde} zQaa(&YPZOEfZmhSMZaj4=cL0M4K$6uFx?i>=tVX-V?G0npzTE22j;R0Bw zTQgKIHl1|Pf(4YI3}35LmFD#wGC;Qq^&TcoS-V7 z=`4b^oAtq_d4qY4JFZn~S+ZGbvN^gLbVHL1tAoCSv*SgPu1s`2vS&PD92db3X-hxk zO9%13D$d5#)n-khPN!_`_JoK#(}em?W;EaM*wA@(nkR0%`uqEL$NdSY4XEDaVGWJc z>iFJh{X9-^#$|$wh?MUI=aKFCA5XVv9rh8E8{V?Fj{9C8qbCL2F8u7MaBal&(&`S^ zqs6`KFYTA^K$Vf_jR^4dFfp#e#96UPdkNsWC3pKJXzoevX*nL$zZc#7aL@zl4PdQ& z)|?(E)OdZ?{$JFblQGcuQmp>ihio$5T`T>w{zzGA_{AWfGRzP+aj`tL!Cyxa4<=8W z4FR=M35lmi5y+wj$~(ZR;PutXa7~}i7MTWRuF;I_ca)>9ce9Jbs>+w-J3|Hqi;7=L z4@f3vPF~=2a^*Tu2sp+f5HK+vB!>XPwK%xOB7}i_a7C+SyNIIBLcmCiefhGGoaW65 zLh=@5)>lDDS&tY{Yl{>ZllG+4x=?^R5P{RY{-*&1y!e6ap}tTB0wD1t65TADP87du z1U7h~mGW^>2=!qw^|9aihby9cT)1~Hye($nfJmlfuS)l-rN;xwX$kE60RHgXQUwB#GmWvX%~aC zvA69a9)NuTg)7h7~~(O)}bax?5$-kUON{-(Wavm zNWfeg5SX5W9U3V@o*dhUr{Kilt+@5MO$IQbJ<>?ZKX?A2=UpA$FFgeR$$f+CL%^=# zyZ(L>1&-c3T-9UX&j2HiJ?EBQ=R!E{k}W+iq(L3iPj$jc@cn%ecc0S1uj;}0$@MXf zC#!ww2vTzU!Ja*UOLgs8E3>YVgCjqkLYDkv`*QzPq3t6FTd$OI^4m!rT1B23r&N!2 z__Eg6*(wEieN^z7!f3O#%CW&wKy`1Dwc!Nia`?NpS>nn7yR zF?F<=t_JT12F-Pp_SC=B<8CbJ{;j4{HP)pdtYP#NcqV5;Y zvY$DxwiK&1F`Y4qh(bVdBaqq;P|za5T z)R&GXiJVT0<(MIJ>9Nv4!AVQKJZN})Z=rRHtL|<;qo?Kq*Z45ChFhzoN(8D;2o8?; zin!L{E4dU<$)@5)DQt+8(3igpCTP69ib@)vkCRBackT#2W_KG-t3J9Bh#co3%x|sq z@R)SJzK_(^(CS$;b-=ECY$Co#v#bysSF!x5^G8rL3PfV`H9y{6h$Qfb=uUWFcHTSv zg3=~uvYw-qoP{b8Mpl`f5qy)5Er9eMaA3CWtBRRJDDFL!Wte7j1k|f*wbtk*UYhq2 z|MNK9eKLdfMQ_r|95Lr|QneuQP}dFS{bw>9tPu0LJ{JBH)7#!K7j0Nyx+SIbYjB$l zeh5UZ{*;|>T`q}HJG{C{Q*^6>8I!7lvcfWQW3NbB9gzt2$%@;gh zZAt*jo#26sH|m<+bql4EOfayV5PQ0~YwWVf!e5v*JUv5&LHdR9t&&R?Cw9;wayV^& z)(z&@)+iJ(6cT9FsG%9J3PAi%Q?{|XD`&$_RP+6Bqr*g02NQ}SaSX-qL?RlTA|IP0 za;muHQsHs0EhNQ|aguq|mF8$i<>FS)=pV3 zO7d7p;>^;)Fvv{uCl_{wbI<$>!~}A0#A%JrzAd+4s7*4ff|i!EgT}SeCJsxtqfL!< zC1gZiTayw_t)uR1&K+GQshW;mIOzkNoqt#-e;L>R$^`!ZWv~3d?}hbu_jci9Q+JE@ z;VTFEG2{UN{%8ZC|I=Lm<7^HNhJT~N{A=g!q6(#qq=uO-AudW%JYkei&xk>ep9@GC z4ylPifbMRrmdi^%D-I-#-$#tNkRtw4`2{+CNcrGFUty8=|WRQq17||)cI6lOW_g9a&MVUj!Rp*`B{|Z+_7?gi{j8^zu zobxKDg8qgXTM3y0T3t>^E-E^w3_r90&65aQQgD{?tv9PscXwA%vRc6dYo*a9g^q%k z!>(vK0#)Sthkp@7La&zEUc*|pV(S?B_;=8vxb=e0p&+hrbB#| ztli|;f(b@(;mKj~NIPolyL~DRZ9>yL#s}Z+kCT4=8t;f9y_Pj?#e`6t6*`Jwuo6)j zFlAagf04Wr`L86ABl(3gFH2ODe92P9^2l_lHDjlvAUj8xyb$rp5BY;KQcY2_`HRz$ zdXD<2dfGLYH{ds~H-sECuYT`v?`bMs)k7*wH=KUAW9tf(baH@!Z=>+)cbuYkypvhcm&1da|3$3nw(Pcav+ zpaW*mql&VI#G_=n6Raot9Gj6}fi!)S<=oXJ@6~UoQkwwA&=w!Pzd<{Mu ziMe|QJ_NG8uI$0EmKD-psceM&qS0E;(i~{1vbEJ#>G|%$cd@~N4#K^cc3IGiZ*9UK z9qQ@#Ky?m-4>C}K!hTc5UCzI4gbac$w!c9bafe;i%{8b*4OX#!yrlMCuPDKLZg$Z= zzyQot;ak8lKzB|2sj$rFvRmf`Ah3b<;ZztcwI%LN#i0G$Y z+zI!eqdzR^0etXJX7_;Jq(Q$;MQ!2#1;xQBuMadF1ugVTwi^e86MfTjeH5eY8s2A>70DlXT!O_lN6g%Y4 zEL?o*tB6r#0XsJLJMUnx6c6A3YV0b2;%K&Y0t5&UG>dC+U0i~@yF-u#7KbIv5`2-x zB@i4!2n2UYfZ*-{f`lN!gS$Jt{r_99ZtC4z@7}7J>Ynazrq9frneMOqoNk%+A0tuS zW+s^WGBFrGJh@}Lbo>Z%$6`-tDOW)T2Qvj(iL=kT0NW;C=Ft}6T#UaC1C<$MG` zw4{ft-?5{MtM%m|K78CS)mS?cRfuiFU$wo!qrD_D{Vk2T8Ace3^ubKDWunFE?8e|A zh;Oo(G5tXzuaVTOpP;Gm?EN*fR6WrH>z(G3@Bvxu=BU`6vq8Ajp0PE{cO+*a_`{`3>{y?@ho}cWW*^% z=-I*J-$ugm;ymE3yfxSSK0srS)hB3!k?(8`^~JfT?v@T3pJTy_mSNgl8;5 z&MZxa#i75+q6%hfYa!^P0&U`)6OHGSGSsq3!uCC9&ZK=E{ReYFDUSGhRY~1A%)9%K zsoC3)^j}M}!?+Wb^#QZ9xo9Ty)xJzz2Vz@mQS}huF zkjAO+(1sOXT$zAY>}nI75^H7vv5g%u&HeUZ2ff|M7h=t%O~moqFo9!7H}FDa~gisy=h?kCjjoh9dcr_?D>|!R zyV9+JvvrVkfDP%_GVlBRlzSXFGqgkr+Nw*G|9N5aV3th~68ycKU5NE6Pk?Ae4>h&e zuLFXQ*}7PESp@R-UmXnVO%5<9erX`syx3^v;eU4wDAhwOn`9gI-ecnhF5CXQD*nHo zGE3l3JF|aQ<)Miku79sMD;9cz&nm7Jqnus-A`d;mOwYwcK)cq^O0y;!wyb zFWG>ClQ1Ig%I?-z>|1NgUYA`?96r-UQnPF!Mi(6ie9DFUeR2lgvm!VKt<#cNncOa{V@B)ENebB12~o3@it>hS(tCYG7A8 zm_02YukgQZ0uGz*=u#*WK8#rK(Cn$u4c}-ds{od!V zN^)budhz4+&BXl`K*^sM`RJ9T#(~B^7)-9*y~9nZ{m* z)QMJNe=gADaEDvM1cY+gN65s+{9-*4|Akc+!@L2S8B{0!jc%vAy;^W(UZ}n$b(u-> z;ZBIWY_4ZWDulYnEfcU#eE4kmL>BEwpJB( z)EhNy5{LIy*5)RTMvujVi5mrRC#*19dTOT4>`DCC%a-ZuD2dRNDO9g@aGNbr5s%fL z*YSlYX$2Ov=b(gq3eI|-rI5=F>|n8)tAZv(Dv9Ow$&(R&GA?giu&wUz7$>Sf^3+t53QSdELHVO z%KhaH&G$7a+33dzBDa?T)NjsO) z#pP!oC2wMBqAG}Tpw=k~RaL=&kdu;*|IrAfdXKDR*9H9z*L{}dy<=|&OK zCdzi-;^`%p!IkvuzV>T#R?K?)n`&WT0ZHywf<4Kj;9>iY^^e~cH2cyT19MvvQ(F** zutJ;S#T7YeoNs-GLo=BuOzcajp=z$6@l{AP_~^{?dLu?Zyn3|*jeH1(74=O%W)B>U=b~v_92FgBv3T*z&3YAA<4~Z?j7QS zl3+3+${PyXitKFR(6aXN?hOCf-QzlEppx7e5lc>6y{lXX5!VhLKX*j3Z{v)iCd+5hneP>hYI-8HS1@g zqJV(xqh5+$3Tl_;BZ*#$CUv#O$)RNd@}{k6Hv=wa$xBDKFBP)}!e+Hp8ngNoeGt>y z*C?L)6ya_bwOh32wbj^M5-L}&W>;fkCRgVYgY_4OnN;28`9VLbX{tYyvubKuIo-DB zPh+E&^KGsp*rt?@NBX^PnCjf)p12t>Q<(xK(wB}%B$i3fg1COd(kIp=VXT|HIYYr* zhA^@*u!)7l#9Cr?9rb-J^_8-T@uKZ^^!{Ax8NRu%TB>`aU(Qesys??*Y(H$x!qp|o zY%$5d(!A6-KpQBWJM{4k5uFh!zus9Ss3=-H!nM;eTsGvBUn$TRZJH(^lrCQ832G=Q zJSveOajD3#`|&{=>6qk!opI-c4iE}!D_$f2@%?f|_*zr)9tkpO%v;1C>^KMbpV0hJbJn5Lz2ZCa`xl959@m&e}?I|*X zzKSU_ZRIAYlHRzOK5LHb@Am*Sw$BSJbSzucuVgoMPPZ$xitEd$;@iBBS2|c5Br~_% z%wOg@VnPXNij+MQ^JUxYf`8?$)+fv1GXzD^t9&n)^_D0Mw^hsLd2EOg@!NE4(wg3y zsBoZl`q%u;UDrbCfkspuq;(iODk^cnUX1Sb0otJDvO<98z_05k%d)QAHDc^hS&I2XqgUP*e=zzg(AfHJ4F_13(m-^ zTj}2D)=%_Mgo@%<+z=-!+0fpI7I*ERN^%DkaqyyGql*Z4%oVT}%`WgdYZH!7c0ZrgViag(@ww4FC z%kHDOE){Buwo*d^^8Y|)lv@l{hV)f4%k?(44l;mtJ_T336tY^l7$=6cec*IA~} zcWjeCp@^wv*^XF8sbDNNS$nQDfon-Hl7DS{7T0v}@EUge+kle>^5gYzNtdp%M|eM# zfmv&<+2`$3%hG+F(?9JSbR!gr-w!F9zogH{OO4D6eZwef;!!g!iblm z?x*nn*_YzE`4Omtoh&>PONrNdZN)WweI5pGSOLk>8aS-j{XqOuxO0}bK3l|#a;IAB4-zFdjy~nWC7=T%?d^k94NAZjh( zwBd7NvvDn&cW}&PX6JWu$aimcZE?a;Aad}2L*$^cO=fWkXxVNv`J9|}{D@$_@i;<1 z-Dl)^p7Y$xIWLEu$wGt#8R6N9vSc6pIuAFF&F*)Dlzu9@J^G7*`ot1WZVHh_7aZT= zB2)CaQ6;#<)oLMP{!D%LgF2U>G3J*Vm(3weyak9+zheyJdwUMFHvs|I)lPsXCpLi4 zIk^LFyg7Z%D!fYOUnN%_bM_@q*Nsb_zWkxFD0u(T+I*&L-{1-7QdX?u4k09mtk1~S z{zhwFMZhu<*kxN6nM8g$=-9z~uVm3vxt^7v?l-Pp+~s3feh% z;#j%Fxv^lTCP^zbTGu*Tk8E_0_fb`{jrHJ^cFiZYVjm1diy=m3oPp383XjQHfd;1`?qhy|m< zNuId!jj{QY-#Gy6hbMTkXTASQp?C!U^sAEgfZ0Q!EUZ912beP$86p>vbOc+&kTIl5 z2MC7DQv>ONjc7d`khIAjNx7gAxabUNbaCT1 zp8$NFam!cv;c_KxbUxB3QGr=ncuZ+5I_4^wr~#udl}q!FSuD;nRz!0^B##0WVk7w<0K#SUbVpWnl zoizopGWi+77yKEMS7P;J4XJO_fcnN@U3zAu6Eue^W&kC2QYuMDq% zG@q=Hw1Awfg2aCVL6-FYbw=>>|IrumhdmnO#Hg-1h_dhK-~v-QpGIh2MF&pwGfpc{ zE;QcsQ-o>^SuRgG|3s3yNg7jPz>-N?gRk?fDQQiAql3v0%L4g{h2JM|XLI+ggPY6^ z5xdvlzD?18?*BD)9m^i>H@#_F%^hutDi+uj|D-+#+qGTa9uZ#k4C@yZyOS%wYJk(1 zpCdY()Jh9wE(c#wR?zu1d)fF6z$0qK@Wr`u(k(&$Yk~s;FhuUkYgz=Ou2DZG6wLLz zLBDP*WjhsQu#;jmR#Ra-IT}&m`N_iscKh5c_R~eUQVXsoWyn{-OX3u;7A~L)l?}wK zCyl)u>{t{uUxjhrDKU+Qv4lwpEmaTW!X&Uq*KHmMxnONjv*OE;=UZiWFLm@Doc+g8*TMFpanBE`-clm1H?hs8!qb-KIGQp z^2rpm5}kHS;fV1HvE!;cga!E+jfa}^rc+(15qu2bOy)u#_{WVCkLG`zC+elyxB`Mc17Jf#|FmNz`lg euzyumcNho?^FsbPu>=Kq1bDF+8RazJ?!ToKLy literal 0 HcmV?d00001 diff --git a/übung_7/agt_übung_6.tex b/übung_7/agt_übung_7.tex similarity index 81% rename from übung_7/agt_übung_6.tex rename to übung_7/agt_übung_7.tex index 9eff193..5516d28 100644 --- a/übung_7/agt_übung_6.tex +++ b/übung_7/agt_übung_7.tex @@ -1,7 +1,7 @@ \documentclass[parskip=half]{ngexrcs} \usepackage{hyperref} \usepackage{subcaption} -\setkeys{Gin}{pagebox=artbox, width=0.2\textwidth} +\setkeys{Gin}{pagebox=artbox, width=0.8\textwidth} \subject{Algorithmische Graphentheorie} \title{6. Übungsblatt} @@ -9,7 +9,7 @@ \begin{document} \maketitle -\points[2em]{25} +\points[2em]{20} \input{aufgabe_1.tex} \input{aufgabe_2.tex} diff --git a/übung_7/aufgabe_1.tex b/übung_7/aufgabe_1.tex index eca2512..34222fe 100644 --- a/übung_7/aufgabe_1.tex +++ b/übung_7/aufgabe_1.tex @@ -1,58 +1,32 @@ -\section{LP-Runden} -\begin{tasks} - \item - Wir suchen in $U$ nach dem Knoten $v$ mit dem kleinsten $x_v$, unser $\epsilon$, - und setzen alle Knoten $u \in U$ auf $x_u - \epsilon$ und alle Knoten $w \in W$ - auf $\min(x_w~+~\epsilon, 1)$. +\newcommand{\indeg}{\mathrm{indeg}} +\newcommand{\outdeg}{\mathrm{outdeg}} - Das macht unsere Beschränkung $x_u + x_w \geq 1$ nicht kaputt, da ein Nachbar $w$ - von einem Knoten $u \in U$ mindestens den Wert $\frac{1}{2} + \epsilon$ hat, - also $1$ ist oder in $W$ liegt. +\section{Wurzelspannbäume und ungerichtete Bäume} +\begin{quote} + Sei $G = \tup{V, E}$ ein gerichteter Graph und $s$ ein ausgezeichneter Knoten. Zeigen Sie: - Somit hat sich $\abs{U} + \abs{W}$ um mindestens $1$ verkleinert, da - $x_v$ nun $0$ ist und somit nicht in $U \cup W$ liegt und zu $W$ keine - weiteren Knoten dazukommen können. + Der gerichtete Graph $G$ ist ein $s$-Wurzelspannbaum $\iff$ Der $G$ zugrunde + liegende ungerichtete Graph $G'$ ist ein Baum, für jedes + $v \in V \setminus \set{s} : \indeg(v) = 1$ und $\indeg(s) = 0$. +\end{quote} - Die Veränderungen der Variablen läuft in $\Oh(V)$, da im schlimmsten Fall - alle Knoten entweder in $U$ oder in $W$ liegen. +\begin{itemize} + \item[$\implies$] + Wenn der Graph $G$ ein $s$-Wurzelspannbaum ist, dann erfüllt er die + Eigenschaften eines $s$-Wurzelbaums, also $G$ azyklisch, $v \in V \setminus \set{s} : \indeg(v) = 1$ und $\indeg(s) = 0$. Der zugrunde liegende + ungerichtete Graph $G'$ muss also auch azyklisch, also ein Baum, sein. + \item[$\seilpmi$] + Fall 1: $G'$ ist kein Baum. + + Dann existiert in $G$ entweder ein gerichteter Kreis, was die erste $s$-\-Wurzel\-baum-\-Eigenschaft verletzt, oder ein Knoten $u$ + hat $indeg(u) > 1$. + + Fall 2: Es existiert ein Knoten $v \in V \setminus \set{s}$ mit $\indeg(v) > 1$. + + Das verletzt die zweite $s$-Wurzelbaum-Eigenschaft. Also kann $G$ kein $s$-\-Wurzel\-spann\-baum sein. + + Fall 3: Der Knoten $s$ hat $\indeg(s) > 0$. + + Das verletzt die dritte $s$-Wurzelbaum-Eigenschaft. Also kann $G$ kein $s$-\-Wurzel\-spann\-baum sein. \points{4} - \item - \label{1b} - Wir teilen die Knoten $v \in V$ in drei Mengen ein. - \begin{align*} - A = &\set{v \mid x_v \leq \frac{1}{2}-\epsilon} \\ - B = &\set{v \mid v \notin A \cup C} \\ - C = &\set{v \mid x_v \geq \frac{1}{2}+\epsilon} - \end{align*} - Für alle $v \in A$ setzen wir $x_v = 0$, für alle $v \in B$ setzen wir - $x_v = \frac{1}{2}$ und für alle $v \in C$ setzen wir $x_v = 1$. - Als $\epsilon$ wählen wir das das kleinste $x_v$. - - Das dürfen wir, da wir damit die LP-Beschränkungen aufrechterhalten. - \begin{enumerate} - \item Für alle Variablen $x_v$ gilt $0 \leq x_v \leq 1$. - \item Für alle Paare $v, u$ gilt $x_v + x_u \geq 1$, da - - Fall 1: O.B.d.A gilt: Wenn $x_v \leq \frac{1}{2} - \epsilon$, dann muss $x_u \geq \frac{1}{2} + \epsilon$, wird $x_v = 0$ und $x_u = 1$. - - Fall 2: Wenn $x_v$ oder $x_u \geq \frac{1}{2} + \epsilon$, werden - $x_v$ oder $x_u = 1$. - - Fall 3: Wenn $x_v, x_u \notin A \cup C$, werden $x_v = x_u = \frac{1}{2}$. - \end{enumerate} - Die Laufzeit beläuft sich auf $\Oh(V)$ da sich das $\min_{v \in V} x_v$ in - $\Oh(V)$ Zeit finden und sich jeder Knoten in $\Oh(V)$ in eine - der drei Mengen einteilen lassen kann. - \points{3} - \item - Wir nehmen als Basis den Algorithmus aus \autoref{1b}. Um nun eine - eindeutige 2-Approximation für die Knotenüberdeckung zu bekommen, - runden wir alle $x_v = \frac{1}{2}$ auf $1$ auf. - - Dadurch erhalten wir eine Lösung die maximal doppelt so viele Knoten - enthält, wie eine optimale Lösung, da für ein Knotenpaar $v, u$ für das - $x_v = x_u = \frac{1}{2}$ mindestens ein Knoten in der Knotenüberdeckung - enthalten sein muss. Wenn wir beide Knoten nehmen, haben wir doppelt so - viele. - \points{2} -\end{tasks} +\end{itemize} diff --git a/übung_7/ngutils.sty b/übung_7/ngutils.sty index 69cc21c..0bd7231 100644 --- a/übung_7/ngutils.sty +++ b/übung_7/ngutils.sty @@ -28,7 +28,7 @@ } {} -\newcommand{\seilpmi}{\Longleftarrow} +\newcommand{\seilpmi}{\mathrel{\Longleftarrow}} \newcommand{\NN}{\mathbb{N}} \newcommand{\ZZ}{\mathbb{Z}}