From c7b83c1a42dcfb3af106fb51a8c8437d3a0c1119 Mon Sep 17 00:00:00 2001 From: Never Gude Date: Sat, 2 May 2026 00:33:07 +0200 Subject: [PATCH] aufgabe 2 --- übung_2/agt_übung_2.pdf | Bin 34352 -> 56594 bytes übung_2/aufgabe_2.tex | 97 +++- übung_2/figures.pdf | Bin 17153 -> 28274 bytes übung_2/figures.pdf.autosave.ipe | 811 +++++++++++++++++++++++++++++++ übung_2/ngutils.sty | 3 + 5 files changed, 910 insertions(+), 1 deletion(-) create mode 100644 übung_2/figures.pdf.autosave.ipe diff --git a/übung_2/agt_übung_2.pdf b/übung_2/agt_übung_2.pdf index d0ddadf6e753758fe00381bec2774b00525d2d5f..879ae2491a9eac0b5521da9a360b45652917f3af 100644 GIT binary patch delta 38610 zcmeFZWmH_-wl#{oYw#k$-Q696YjAh>poIi?3J9*jEx1DcwKF1tuuCeNKBt(2OWGogqJ1C2e8iI)pr09SJEZ1zZV{1Ym zy~cWi$Q|H$57q_dOg%sRxw=P!gX4mP>*BB_T%)Ga($WwP^7`{Yb4(>yLuEsUPXQM< zixhD|rQq7K$@ZAsC}rTPLZ>GvKCRtXt^@e)@MKoG8fRNDux@q0J>kb(gt3Q$y1;ES z1xcg+BFn}$kw}95`>DWfpr02UsU7du4`*rFISC1o?U>3nF&pz0sM+_Ztyp{>n_!fu z3s8FjUf5h}@L%-B*+@^bg7Qj0J^8trGWlL&@m=&mK5xV~ZIbzTM1`VomGb?>IcJ2g zi0U*lM<@h5G|gxbnkAR^j>&!c-K!FwEH1D#3B)I_jp8UUv)Pm1121rpB$sE_Cd;Ly zRw(ZUbcTSZtUbGPOF$mY4HLh~ZqgKs&8sne`;H%^_Rr*5YZTT-U-mmZPAkL8;e|7w z`JXnAPigT5F1k1Hjl88rZ}OxW)Lu7K9ypoHRbOy6`x`M0@a7O87oNb7!0a9qy)~ix zFv47iWk>&o!!+<28o2L1OeI!!Dad48@Auu65-D#y0m~GMS=7oCOh>3DwCy{0Kjk2- zOl%x(M~y^c;84qlB0lJ~Od-s7d7=t3vg79PW9fxYCad}OHeM?2f<~J;ZV5k*i4rHj zxRUf75HGtcObxkx}vQgyu!8`8JQ^MDs#aWDef*{v*$(B`>; zB&oO!JK{9ka#2ahWQBIO3x3OyyMrzDl&517w$pVk#eo-TW@hw7(-~LEy2)!@LO@L} z9k}=fVG%63NI5x|Z9h*!d;5=0UW;d=!42@!PlO>#+GcFfjj#NAdy z1x)`><)_dnMnHbzh`dWyxA;@3M`os`gYX}(0$a~N7p)TrR98=3ze&l5q(1dt9 z-=~+C>&dF+!?n=BJ8lLpm5^ZzY%_V*Qa4ywz}?3l4T-_%y}4g>=r@_~N{zsv z?#&5edFVx7b>tX?u8|!x1+c?%mpeLZw0Dg%m>OXS=Cb_O+Q-m2EZz%&UMiU_bP${lsXaT>REOn-#V`EhPn3Oe{&czFkO*# zsI{w^&}nR;cY2)7m33}Nxc#cD2StrM&UmvJD-&>zlW^V z!9UCYwCK!%kGix;Ie{X7KEIR9|2Ykb%CWa$d=sdGPCvtuhQhB-pYCpjxU?^Fk+jRB z%A?Py?wf*OYE8?29l9ALT0@gaein)&BV58}0oNg~iQfBW7DZcKU0Pi|CP9E|qJP8U zC`Ui=&Q)rl477Z2GAa{Z*St;XxGkMFCYT+W&B_?eeT_(9!a z#u120NOM;wRKH9)7)=_$B&54O`{+z@%Xx?&M=ey;YwzKd<*|L@9A8dWQ!lDRAm*cI z?uu)#c|YgzahpO;uzuTDJ^}MCXgTXmEgb&diQYuPP>2i&c^e4##Aai4hr? zO+-U{kQJ5?XkOdyV z2{%5{U8OlgW!~)pG45S`TNvKXmduc|VNs+gM@9IY49`6BjKv4ebU?x}Ne8sBPoTh| z3_^Nv_h5>p5Egm(JxR}UB~|rKrfLdX`ieop+O)AN#a<~a3}#2ObTTX?VVOQkFv|wO zicTa=DnLMd@*DE2yP40e8jsOhb^s=Jy>$?fP`5Oy9Xn)9akQZwPoq&^8aEQL!@%kQmO5;GsE{uqJAICI`c#6 zhcx33L*L*`WftmB*Hv`1({|tAi6{(Ta^52-XHimRg8J)B&ze>JaFI4=5=?-~7i%M$ zaGsD5)@ExA*l0mTfui-2@U+y#x3c{!b;v`7;6}A?gHcQdM{`0@MD=}^`b2D^=a2J( zCewRb3~BZ)LndGu<|(5NeB0?;fPu1a{pftCy6&AA*66~T`ranH&s7q9?DuM)xI5~; zk1~8y&w4l4X52*MHRf!$5&@#KIf3bAXJh%tMB~?!j6^T zSMJ3zx*SGQ1o;xyO*lPO?+2ypfu@W^zsHAZ={U4Kn>jJ&RsD~_V6Ve~wdAy{D5Hs; zFy{zU#~;jPAz&=Z`!%s;_2l8*Fh7KzEUBTD0|Xj&Oiwq~B0njF19%c=h@AKj$k@qr zOfZjh)J4u!I^3v8VJ`U(EzR?&8sEz`=%{}P?;os;Db#>g&I!CFP-aJe%P-*g3ChF( zUL78`FQP?3JEE@Zz{cXEmJMrDJFj!S;xwXu#)pNT(}q?udd4#7`}zjbFnXrvg!1QE zFo>F2o5~Sd1q(gL6R0!zr0hE18t;wZdA%f)qUqvGUH|G=GX za@fK<)lCgbA`(yf6V=70W4NwykA>e;aD^PIEIx?)+&#M8 zU8~8+Dd+Bt@dE9XF?50B>K6oErCn!&kxY*sLs@4}dC^Wl4`RB@Nlc_4KKNtyQM>LJ z<&j-pGF)zkOf410$iJGSe>*XFqeg?<(PSW(hP&we=J10nTUmlzplSl5TV9xQ z>YRg_&fz=Aa_QJpbMeZ%{#{q?C9Vv+30cAFeF61d-y-S{A$qrcPQ0^N37EL6t$0w)BfC!-K@dEBb_MdrhtIQp%(# z7tw=2Dk?X82$Rojxegy@#Btt|f6v$TV_k$RR7-(BvD$NmUx4e5zfVBR5`sT>GO7p9 zmYlsyQjyTKQ1|*uVdIu zf2p<{BF7eanI$jXT_+-VOU~)679pjzq2Y)eI5Sx>>i8ByFQX@UXH`)DS$jtOLL|>z zL&$$r$M?t0#i9M<4(juxOI(*`<0E7AliNC!Roi;ykEX|q3+IN=b#IebXbA#3fgyq4 z=+cuKVJkj;S`@=DQH@8E%pjMOj`k(+8+XjquuFDZn{S=#lDchOCAa}~LY+lEoxqC4 z0kILevP22lqQPA3R61DztQc*fs)Rw*Bc~ub(kR{AP$(6>A8Ol( zTLg#^n%gMSys3pB5D((=%p$|4gw_{KMVCH(iKd5_O^??6xrs%8<^^4oI74JG&pDM0f1PrmyhLt%%Lh#LBXv=!z=8 z&b;*U$uWRgJDTPdbZSZqmvAKEO09Zehzwb*vK!rrC?dV>(N(6V;0~eg?Jn=*sCwngE=Uc*y`SqVQyxYhs5U}$>wSMpY+TQlbA5UQ^%f zXg*pPrypG%1cys^lQUiQ@kqx6QUh;57dwmLcO2gQ0p&^CLif>`>Db-Ai{)1t{M=Yu zPen7IC}BnL56qrM___C?@MlPdYAGeF=8xEXV8EM_oZxT`Hf*h7jZ>@fJdt_PxhiZQ zFZsEZAyPh;1&tccA@rDF0r^N!aR&+waW~K8lRZj5Yo|I1UG%JCW;>^>Tfp@e+$+wt;r#ouJ+1czi=7%D$x7Dt=K#C5)s?V^o2{mGk$GGYnuH5N*(|hP& z^JR2`T~Ja=exg@UZQd1(2wvQwEFjIcJo1`tfxXbiUDMp89o%kKn`nwq9hqJmh`;}o zznaAEWM58>^O|Sf0T}$=V=iK#JQlJSCLrRo?;^t2$vd~=*9&A>2X1(pM|I;J1JF8+ zY4u-GC|rH$%9Aa|+{fSisMvWhmm)h7L2hQHTamGJ4>OsHq=z2xk^bm^U+Eb#c`eA7 zT+RB1kDx@wWd}MnLlQ(%K%ScE{vpuJRv2dp$1{K}Z(}(oPzva^d@tNP!-W_Wux;l) zxeS4mYsyIHx;0h4_~|paJgiNS-V%e5wy3FtY%tF^3y?OVZ_ztCtDLmS+|OFPO>N%@ zd($MS`xk2JmH7xW4o&43Se<5>%#!OdrBcVnN;icjC47|tmU)>dWEf};j^%sZ8)eMq z3rufWb2>Y>TGoMmu-n%Fx)A+pNR$Wec2zFS0G?GO7o!PT(eYUPoA+r!fQOJi`FBXd zu?J$#ST@<@dG)-v7z-A+jU;RN$6AK&xX|Rw@7gV?&Yiep-#IWl(0rOswUs?_GI=DG zr_4#H!knTt`2XtBA)1tLq5VCF_sT3R}HQTUL@*_%S$x ztHQB*mVMVPyNG{-w#+`o5T_Wa6IiBYJ5yr^#s?86Z5fA_DhP0BqaGo{9RFwZf7B|2%38R*;FxqsX}DQ zi`oz(1Apjg&JCaT%C`{D$Yhu4#>9#;vMOU3&nkc|;FWg*OV{9iARBZ(C0Ugkh+yVcl(4W`hfWB6j=r|19O?2~=40*BKeAX&v% zFs5`qL5trQmI*%qDqO8>d!|&Gq@qOu*9jE=TI#XjP@k7w`Vnh308lW1N1Hw|b?th8 zPe*=-JJd)Jafng*k+R%WcVP}Y2wUJ=cqt`y48jpDDdqs)nw4yn3 z)PB-*Ddn!!es0X6`%q1?wyrB4kI0b0$o+9H8p?}3d_<3e#B59y7qen)q|*5O8wTph z8pYbT>w&T79-@os)eE{M@g-c|qNeJ8!Z<~L&mk2)&1m2G<`T#IFqtFU%j!WaUX}I> znJU}ax6ETofy4FNK<{-POgXGRd z{lqP2ZVYAkW`US84^}CGZZ;J!m$TmzoE?L9VkMs7;#kJ;Zun(4nl!uUTq3EJM*I9y zb*OX(eJ4?dOt1&|nvHPz@VG$U{V3tR6rZ`l3WEj?&*r%N=8+>9i z=a19TU&S*lG}`u9O<~plyr4Mr+|!?er7|q*ev<)FodiwL5;diqSuhRlPWdI`Yn5hO z7~M7m(?;(bN8lHn>I6;*zv?8kmEh7RjtbS-uAprt{(U_elvH5xwu=(mgId=T*-0<& ztrYJe;x;}1XpCb(;=(8@`4xt%ZPn|tA(cUG30V5~cKL%+^ar2VbS9k)K9Um?e~vWI zS=n2Gq}oeXJE{*3a(`|!7zg08`0^o%8Jb99afj|ufB|!YD~7R7NyF*tQ2ZV~`TG*k zH3&WW=5pz~+mFaXW=a?f!PP0kt>4bA%-O%cgq+)zeoeskly=iDf7T5h(brKZ=&lb# zKAR_LK}q-^M?Oz-$d5%H!ev8KtbU0oj~*|K4n>rMURh2=TlTffuQ2f<@71x!GOE_Q zePHiJ;wzvCyybP=t5FL>a1=j&2@6#m)z)K0jLwDHJTKYGl4X!c6SE!8C!_e~LP5P5 zmwVX34wt3y=fV@euf6G~>q?>Ufc0W=#X|@hnz{Bbpg9;(RX^2`-n1vE!s{Kycka{Y zzDb(C2wTdFuNX+Bjpv3I4_8GXFTa;tr}SZb^e_WzqwF2$kxz*67w(R-?ViWuzrxz5 zwD@ZKic*VyN&cKKezo?PuXpsS)xzjw+*@MK`(BJ9hRg);k}^F}nBL3rWS-Ze&g@Hx zsByEf1g~X}9Y^c!G+0svNDm4PK%cFIzorq9qQS(4jmwv*ML8RWF3&*@3_qr%vm9wu<}0J{6^Hne#~+d@#;Z4 zP^fkZQUfaBlW@uSQm>Rn(AO`V>DPOeN!d(Ntf@Vk?$4-$gbQY$df%@Is>sF&#t#^w zeKzD`uVbmRWt67n`l1JIZ%QDMSS)@)(i3sv6ptzm!iPcwX93YdIWe;{u`n^QGP7_{ z0|W#Bj3OfT?*ZBXW-fLHb^tR6Hv=mh3xJ)A<>k}Mh=HAr6*LOP2EoPzf`aA;vM~dg z0LlQycM3*Urp7J+K0W}Wge^1RBLnSPCdKf#y)?0;JE@_`w^{uea!i{XD^GqVEN{{m-b z1F-*v&dd&A{|la(1Hk?lJ~QVF^S^;Ia{<`@vVfTz!0}=N@F({dj!XcKzf53Z25|gk z0t*X(<1Z6fSOFY=nZUvZ;P}e~7Ipx~Una0{066|KfrS&m@s|lKTmX*0Okm*#a3cTV zh8Gi9nE;%i*Dyj5tehZ4WE_wu3=*(SeJC1>8L9PFW2+T|G&*Arn-pakEsF^Q(2YQk z>r2vCHMOrab~Fkd<;H8dR7|rZP1!hxvOIR&;~#T!3Ul%xp-R;IEwe$jI)b`Ie@Wx! zy`z75vEP{Dcc1I=Y_IL3Dt25}PlTX06^a<4qbcw1=bey;vs$0HHFj0lMr0tg*)F-T z5V|nwJ)zI&u>e@@_Y#~dcD5kA;XFn>XsH>c>*96WA{5rfo2}~(Yy?txEDf057_A>Gmg#iV+a>VlD-%1_5|UxL%ptS2(6U6eE*;RaotH-~*x_)M zlM=}&Q7e^jr|->ntW| zC2Gp^jdxp57`dogQ5ys|J4HHK-XvBwBhEz?;>TTW?n@=mR$gL5n$^*}$=4IU(VCSj zTzwSpXfxSPIV##`sL~%;&CbZIdiSbbZ@^15t!_MGCN*(7m?h3Lm4MV|OI2?lLZ6VN z=>vl#OWGvJ@2sOgk`a|h*C9A!9Lb=4x`I-G11Ml_bH(Xa z=-uJZ+F_PBa>wRX=Qrs0M1`xyq^HMbNmhbg(AOe`REZc*R^k~_iQV>;kS6N&MTQkN zlYSfI=8FoCzx1`&1r5j+F2JG54W}G2o~gtWp%PoS7#S~-aBWhH$P)4SbJ4)5SZt_e zVgo5Hsl5MnYE)lyci5trZF*7OT-En?*7Fq|UBfijD^A ziA{~Z>ui(S_;iUylimS3M@yEp?c(l5QweF>s405Fgd%axZ@IuN2~Y;r#8-_z7ey9N z3&Q2?>~1>8eTKB2;_iDB32D>;&qZBK%Xct{5vh;z37-&ZkT{6pKrJENPq@}Mw=w$iu8 z`D8?K`PEslz2F*1$a<%mdpDWFNNS!OlT6f--Xy#oWA@|y$@u!JQ;R;oJ1y~dl~ugg zcwgOi7AudiH4Nrg{A9M&ys5k&98PTvg6A1&brJ?!_;P#uYJ1Jwze?$JSk6x&q2D!1 z>+rUFs>`=BIHczE4;Ejr!d?zZX1_-ay+u6D>0UV2pxP;9IKLhdQTaBc^45tq&?vF{ z5`$Tt-jaNAw57J~=3Uf<41B)WG_+C@EBuJ2FK>-c|X%oT(2Mk58yjvBi zo(>EGVC6)of>a00bPaVF6iV{P)Gs;xC0DXBa5A&~W@^dbObvtc=hVTycBB6?wK)Rn z>c5`}vax{-aYPW=8Q3^qlH?2E?^sCu4oZUJ4;C*_4F3XU28%lL8z_(gjwr$lotMo1 z^3DMoM`!;Rcl~#qD*gq?oDTKdZ-6-dnbnX;8qx{L9=X@~HK{p~3Zw1{VVx_fLUwyzJ%wATVJFZuXxF zlleCualxKRW=Ver=T9)SnF67iodTTxlBjDsIw6}-t2fTLpRFLFV|D)!9?=w@6)5~Q z3CISA6Y+lwQque%A&K4aoIw$EzaWvAnHZRUZlw$y+|2(%lk+D{{ePz^;RzFL_Md3_ z+3-VRA~vERenxpA>hlLt?^t}yfA=*z$RGWuHd$C-Dw_W{+N6N_S8bZspbq^8h~-yM z*8Brz|J{av64Y<~fQ590Bui(&gGATKgM=k?)8yO~>;Mkt-SS&a z{Ypa!+zd=V!@3!}G}?*WA+3!sgSTo5Rb}l`t##Q`5l` zIKlE262UMPW`D~UD$7keqK#mO(C8o~8B7TFKXTE3Kv4J}Aq4+jQGX&FRG@qQ#p0D-{Z;tXFM3Y-{Kw4qX+*6?^o9Ozn}*rAN^an<1_Tk-@yIK zJ^w}c{zvYFk^d#he{<)N8+zn#@L2zQcm6lwgGu@=zx{f2o8RF5N(sK#WHJ3Phrr=T1SvOCa)p1tLE)sEWB- zQ-~FCkBlY6;P^)vJRV6pK>lo);D6*P=Knn-eg)(AM!24kl>Rj0C3lG-vN61ztp6qw zFKYZR9r5>2{KgMKzx?nk91cAaFVXOaNznq}!Lq>^eej3qr~jjftKkPA{<0y5_zs*C zltyv~!O8j3+&~Frdl80!0K%V*5APSFly$8)nb5rFD#!VuCSm8QGj2S4USR(jFI@I##Jo2E`b3BuRn-F7ox5#1k zjrcCl@<_jr%c*l~kC0@TkP41@Q#GpJ*D?>p+B1`{F`lq7pUc(T-kx$RqgVC=cFUd| za-atYKX!^Y(`B{S%=$_tIh(8#DZ061)K-Pl&j%zia7C^0v875jsO2pzS1p&rtmRPl zsTD#s4y904bRZcQ!xadCcC_Sy)>Qp9&UZ$62zNqe=quA0CKl}asq7n(+%LJN2Z|Po zs;?5-#1u4}`-wnuvg^r@y?p3>SeV8w3}u}XaqvW!EX;5F9#fJNjSEJ{x|vmW&F8q` zC@88oW1Ld~!)t9p3b53!7jDot)f6fW-|ESAmr`gR7O$J_+J%=Oo*+4pkm`QL)>MWH z$o6t>_fO#j=|~=Ay+VLh{6EofKSo5Ao z7*bYOe81XCxx1Cl^>D6tM-7rZ8(@_n86OZYca|c73x2^LMJ(Zb6 z@MIes%Ef90PVOj=4*|b?+qrL`4rIjz^=t`WLVDjn@GYITKN3BTHmK1z+pYi~NF0b6 z>Mp9_`OltnMW4S$)k5=E16tM@6^TA>AP0@TGNvzs9x^pXS@!6B$A)0n$K}{L{f?U_ z)%m^QhgXG9Qa5i2R=6>BbX$m1mD4{pXypi*@90)m)IU=)&eH;6!XsEy1!+_XN^@)( z4Z=m{-(qxs`*b_!vowR8{lz8E#53`BF2ptk0(A~Y(S+M2Uu7WM+8Ut*$NWsanTSic zG|CqP73#s7KT>!8T&%;|^tf^{+7XK~Nm;ToRV1B(E^b~KhgXZsN&aGL(sQ4R4QpfK zZlm86@K%yQvRfI*Wfn>&ZcNA_HYuWl4ib-RNheb{9qf{beVv*xO>LsgQrIdx*h{^j ztGUQi?YcF3oXX+WS39;G_RznVosjvljmwSL3`6J3lU-dkyV6bF$BUbeSBv(of*EGm zzbW0hejd2~Y*qSsGOglj1VUqH1~PNLoKOFw2olwN6hV^sK>aR6?X+MS46D=c?}w&G zuX&(^%}eqRl%{d+4&Z`nYOTopp^O8h(S*A~#Nha(0)zy{L!FZKo=3qq4JQz2#Xc%Gc+_=+BgZSkQ=;ig>-=1+|QzZ-j#o{GnaY z9U7<*0NIY{djd=GA=d)#EE;kskleq^!FOMu#(SY|aTO>$jx7Z^*k9cbM zhv$Q(P9j6y)?f;WC(5pJv52F8-qe!Dw@|2X?dwI2 zUa`_3vJ7-ur5e?BnNq&VnlB@J)JpCY{(_imlCrg8H9C5kaIuM+gz+jtTwL!XVTybf zX39v*tJmy5ZkWY9E5&W3rR5`}B4d`))0;KT_zX;HfUchEIc$S7_<_R_S`D0xYemzP z``_nke~f%9MyWzru`_KIDP}K;3c?b<>xD{%c<2@kBZ&aw{16q9j@`lwlfnRKGJM0{ zObf;EsJqNJnYOb^PMYBG?4%qrml@w9*k1bDI-35vL40d;hr4xUX}@C_p6vFFS0~KH z?pW&wH*oTnq-KxPA&9n_MN?=q7dF5?fT>+XZ>wKGFp8puYge&?yMdltLqV=<8n7P$<4fqYY0dWoBz|`ib2$Vq>+-94 zBx4p0^^c;&dxT6V$F3vD=Gq;$_+00lSkU?VvX1t4eXxF^$>gQd-%Hl#^FOnWpB~t_ z@@nbOkBlA}mpEDknw7SJqeD~1XFh&17}0`;4;_qa!6im9HWQGo9l9XTOzGZk1%t%d zcL#pH`U>WobEw3PgARokn=>{j%6XPz0dS0IU=T7!ol^F+`T>{irBigpF)eXu`oLL) zG23aUSUZiBtCT)C&24QfCr2rN)dCA1*3URt;P^PQG<9_Z>HR&}@A515WPW|vdRW=S z%+{QkY?nt~dt@hLP==q|;WYL1`@n_j(juS?>|R}2oc3FN1Hs|QM$}hb*|jYCYJp-N zd_3JWr#cs6LbTtnLPIMgb%fMZ*GNY zYZnRKra60Fy&X71=*%pREEJFKFm&JiY#$z>GZ?t}Yr6yfaED&5n~>~$qc?-d0)wWfSPe`)uR9Zy0u zH+Y5y7h=&HZi#lzsaWu;SPx>e?BZG9?(?Rd$R<=p+*z417i(-18ms|B{P~H5l?mYH zML)D2KcT*(cv}`?x=aev*0Z;M6Tl7loUBWF+|rv|f-9 z9Y!i3GW|&R2jf{UrQhYZk}Qa5lO)}*5gPlarz4|YHJ7K8nTN8yjvj$90$>-9-~c2l zo#vgcUS+SQnl6uiOSj|LrXZE zZ@C9sqjq)XEwG~^4PJW?S6^Z+rN+!BJfDqa6-<25Lj!kurj|V!#15JVsbpLdt(b(B zY;&+(jUAEp`kf^B-r2BE;|W18UbX=5M@FHY`aRq>zS zRp33{kh|Ov*HI?zp=IuJA|!&zNQy!6iBx}JKP_5;g+({i0PP{Cc5P+_i&zucOL-3o z_}U;bbhX{`A5gyDT7NSQ1S5996{5h>L{TRa+vthEjdGHbwAUGKC8oJhpWSWJN6=r7 zcynFQpvVFByqDw<^XZOAM~8Mc;K|+B#JwE2H_ImX=`6)_odr#Rx3(;A!mN(R=2~QZ zyhikzp|pI}s=N|c;8sDIBn#=^ulcyx0iX~aTC%?vw8jRnu!Q^!v5;WDKu~aps*kNX z%!7kbL4#L<)^t>XOfUC%|7ovOw^qc`z&UZ;OF@i=t2Jh$VZ~p$sPY3)f9awND9X-; zIJj`YPG8^dM>7M1K36L8gB6d=tpI%XLsd0^gu;RjD-AgJXGO>rR+{K30w;ODsAF6& zsghW(YFc{pym!*P%e(8n_S9S&6UxkLECzf%kqoVuiTD^;_`MX=_6YHH)5UlF-l7G} zRW+A_@1^;2J@N5f?7~GJo^NDm15r0^_ahu@vnEAFQc9a3+dVcB|JC*$Y2^Yl(wl&s z0_(QxJtb7r%@2}J(j2R`D&%Qjq+pp}n<24ATbi6O^Ig`2KIymV9uXZAQF_WL^T+{R zU22?D54MWZ@e1d9d-f89dCDbPcqB;jYBaQ<#1VN17C)%TtY>D=7JYTKN@QV{&zDy` z$eS7Dj(`kIsHt=G+JmAXEvNSK8E}j{*XcO>l4h$4v9@I-i+eV`nazROrd6f}J zJz{qQ@dMCuC!n|b?7w<*&+cjZi9;AztbF*@n2pB^)B5<}yI31frvj}@#6w$vAk?s` z<(p{%8rO6IiH;=nByM9vH8VAP*TI7-_9~7BVk`QF%>ImT4303P{jLt~68vb0=9F~N z>#~Iwy^YM&!`e!pEn@c4_X>s6dLrM4HLeUVmBr7zEh96Gcavs3uKkp1ov~pJY!pSQ zh3uP(LmrZjAglFvqJljFvk`s!xOJqt!3eJ_AJho;Mg+smCH%aA8ku+RJt3YJB>-O} zF0ViYEm?ZxO_4YhIXI$`aZq?)w4N<@m}u$R5xyTmx084-dPHQAZB4Pq_LV)|d%k1r zTd)|)LC4`C^M0yt?YBXirXRd+fP3%6Y1!fmFKl z6utj~BDvU3WYf!kXa}dsf6NFCm}G!|6RL+tHlau8qBm zO|sa4@95Mr(njgF(ukvZ!oCB)Vymo#K=321=iGF+aWuPNYPUf;7MpdpA3@@c+d+-?Tw`@gWGqHp4zCt=^{p^8q(6#4Zv85+=fyJv#e$dFsi zq}WBtdSjFQS!e_REorU_CtEM7SHJG^APR_b5Ys1oI!rV8@|}agciykmK#Va7QG!aJ z518i%tB1?~7JhC`Q`;3!E8Bb$doTdAvF!0s)~WYn`B9_q22FY(tJXWHh$Ps%im~OF zZmR~{<)m6$O_&r{eHx(Z8}h7>VI;l1f-|t)P4EV(5?C+b#g_sQMOt>mZoGq5OK8@k zmbV!f$*Q=Lvd{3ivYwWzLwi9{_IcW@*?Talqx=0V|7b9M_i{|`-LFafbew!axM$^@ z!yon$A1Q^_fbsti% znXz}$b0JAKkdQVVhrs9wBNNI~OI3spBMxdx&@p3FY!JUG(8E4o+hn}h4IyURC3u^u zToA#7IGPBNab5#t%!I|!1?#&_xWZmdb9Lrq_Cp8t6QC_C3tG3AHXi zYjWKMBXKpw{|y#y_V$-Jqv~690z!f^Z6tl6e#=JimKt}U`Kjf^Y`z8ZCzE%?;5%_2DoOQ^i{~uMI+l`(i#GRNQb*OZBI11&)0GsmWN5U``JO) z9*WS35Ar9KYijA*tu?U@U!4%$vA(RW*ETO8Kaz^&&EykC(I7+Vzawm632-R6Dj0_> zH9#h_ms=77suCZa2k0(cW+UC$`iVg-v9Mw>)E1JYDvmh`!=7@iScTXFPTzK>B5NM9 zaH4Z+&7rP*52fdJs{NLwXdiA#O7E;YOMxM8{&~55xVFqSR-#KrL!hRP?bs7<@OJoyU^SYe@T9Rq&=Nbb@J;O&KXB`CZNee5_1SIe(qAep^9f zC(ecY7I2pkuw33I*JGZI*NpqI$naP)#R~N%8E{FP^LAb99Sn8KA&WBnTpCVpgkOI5 zv4~Vl`8JpD^b)<({j*Q=*~9&Iq08(f+oyNuc_u)N9i-kBHs|F!4=;yTKSVO$4SQ`H z6K)YDjfdJ4m)pno3Y%rp)_^U1vx?YQ;dOSpIl&!H94LX+*gY9rNJ#^M(r5`TNK%j# z_CUF&ylkx8|5O?nOBuX^&I5z~%)~?oHX#ex0L0D-`5?Z+LV}j?c|BYua4Q~IRZ9L;-`Lpp11vpZ1#fG$U zOWiDSFY*ZLpckQ=CnYu{6WY_uvF|zDoR?2cSwfkiJ79|*8#tHdas1&L@^pIq@az-f z_s~I5i}AiM;dTsfZk*<1{9RVE@Tv&GgmK`a$Oj%XE0nu;+j(UkI3TkzHR?g_^1`?+ zWU?$~oOY`VFB{DeKp>xCymSfOmSlPz7U`mj&^En93^9T5M3(?0U959r4BeQ~ z=cB5U>F4^nDX9yX__0@r`s{bQ@vvneK1J`>sABS~xq+=?R6R|D63X_mu*J>su*KF} z^gR7Bc*Y4h7wV^o9`bCqtVXP0g^lyUP4Y`jg*_a@jq_%a)jR7(X}~6#k(}#g4$J|w z^q|U@-lqOSgei_U9FU)sahE>D7uqW4^l%h+_iz}ScsN##=;ZH=d)lRinXry_X~_9f zZoRcpxkJ}3#<q}6~7By%fHz1h*@b9 zMRj)5uzK%n!DY6w;Q=HmmXu7-OyD%P=D&RutHv`=z}eR4JH_38-ZlHEJ_|`uCrq+* z+T2D}1I0}yb0Kh`QY{uCA)cxOp*%(bh?3g7PKi0Le4>Q(gq^|55C(@|D^t{aRTP|D zEXvJ=77~BSK0QAKouDV^B)7*0^E$RFVRj`U);Vnx5sbI?V>OU;pBQI>iFQ+zEZ+B4 zmq?_2A!5PWuR?LS3@v#)CplaMz{xm_grBp_YtQS_Z+6>#S)uF?W-L(CtJ(9AY^-?B z04}i*(MD#?U$BGo&7{09a@9e8)^m74?z}_MZ8$4OCX!*vZ*b(^0c&)`)77uTzZ#`2 z1fM81$UKDNdj=5YPIog~pLgqWG0wNNjOd`DYYBy@S02!(hN3lUsxXlG1c&;q50eR2 z-m{2>)0C3&6V~TO!WO_2!=aMk2=zJjDY+;Sp@6kih|JV6WoPT0$x<*T zhex#TZ1j91cO zvv1JQtgIeVjd#?%)n3miQteYmw};G69`$>K`vGg6JK_587m?hc%$LVL*Np<1E+N7`(fZug09kq-cG1FT-(o2@jHRfFF0``1-8cCKm6<$;*a6Xitb>>H zX8=iwg-d7=ANTP<(Q{e!7?=sTfwuiCA@yExrWpdn^wEGw+ayC`cXwA=K@F4^meUHW zYnZ7I;+2ULN7YhVxDzVCSgAnG$m!(lj66$V5ym_92XbNKayJUu8H0|E5l`FYVZ2JN zmkXrcCRYDF@*Z_r9fKY4V<|}~P?I)!IKy$Ha%>#^*!-$8DtmNdXy8_Sk~B2aUBX=j zoTvbtl6L(dqFAI`_cv>qC{meHQ&B{GM?0e+G6dk^rs$Y0sf?=~-NN#^T>a9rYw$WS z$w0#jfU&%VGm1f2eY~8ou#=d|HJoztaA1uD;<6Gg{`LvJ)st7F50u_I#6>mUseSDe z$4@)ZElD}0aIMuQ8`=0Jp4P&^+d^!sJo;5c9EGkel#YqiY6L&4>7KVR$;Sy5G)E-X zD>qUf4*|jtKg8O#lhky-cRn4tlOJ_&XS}75l=zg7&XOWqSMO3< zpjzXAsI3Xys;){))~c_F)>Q4CJt;A^Q5FYRxEzBl-l&1|jgHjFKU*k%JgV(Dm1|26 z@*R{R5OszVG4oJvM&-MHlkx^eN`5r)bHp$?R&GC{#_8kz!`91XRME#BdOhov{pu8} zC=^d=z13>*w--2!g~;jz^vV`tqBSi@2P@i&oz&$JCFTS?G0D)tg;GZvLqZoK+}@Dr1Y9&At8e z$@s9=HB<8HSjJbL>Wuqk=5$v$Z)k~ojZ_5}fBdK^y;dh`5gyYbqzH*Xo5MHa&mpbt zPAmQZl4s8I&SR6QagtAX3lz&dC(j`zl%o@RP6Hfr6-G?xdtc z>gv#U?{g*LC%#F>fgt-BZSA4&+(=R-ek zmrg~AFKrUM$h zvWcUGf zdJC3LN7)J( z5OC1^iNL4zq|^ubSvV7=B{-Ug6A2-ZnTbn?W14p)E`QBjLBPut&kbDOVKZeDr1#0Zp_sI3p=*;N$3b%_eAoxwM zuo&nn5b*OMJxEqArk@)W@a2~M%N-sppVP`lFQy6DPY3CvXz?R4K_NLx4M*5ZwAK*x z)MsBh^tBa1rp#}s*RL|CyvC^8LRLDx)(<|cnn)SOeS7kYtDUa6;gYwCD?n($BU$;7~p#Xubs>CiN?3e z!`0nO##-iKH$^kV;)!@8z&!&5hmVja{R-3hica8pr1{e}W#sxLFNfP1LYC9EDfnmw*i3^w$i~8b%!9s4>vrE#OSV1&%78?>D zK^bp#ZjU4WN4yNOjApsg69E*bN%103wNq>%Ow~RMBAs^Tbide}NJa zh2z+PhnIOS6|hw+WPOmYH5H6TPMa)L+8b{bufZwTu645DakSvDn{bZUsd($2d2DXn znrc!v+nY1Ai1#@UF>LOTO4U%!uF0$Q(G71jn@s~qSevcP1C5teM*O$IwN(Dz!TcfC@B?Ddx7{6%C*D1kLMC+TO#uZMY~4*KVI+q`!cxQ{ms@K$ z7F`UfEKIH~GaTpz+T<-}shuO}!5am~pq<5GjlDeiADcxYrH6_5BQypOhn}PGT12q$ z4KxJJEwtcC8UZN{8skNfOD5N17ITJI^&K#^yRSSHD5+t>Y;iFoVJa(M z#$q^Af*p|*Qp;bV%CCc?~wY$Ii6;b zG&@cbp)97A1N6Hvh3*Xa2BwciPL-pVTLzx%_XIxnp)`mS*FQwzT#*=+_!5r)^1H?J z2Tq>;P4=NXEWRB%bZMNVwE~!vZxd-<;NH^m)pqf*yIhv|9YM~oz9f=eDCxyCzivx5 z1tlH7#sD~vXTWnW6LjYY>bK{nQ78$i?nNo*lEr6KVFHtl$sn2Hc%sLm*Q>*>B9tFD zYUysfhGjg;^PrMXOL$5R=`T(&h1I<*y|Cl2&)~}eOaJ8wfpS$WTWI#cI zg!q$&OA}BO8BD4`7jiK5rBOFy`Q))J+EYS=rKuBd9WF>i5KDekY>4PAYDRa?&{-WK zC89s;bp;liPJa2k&O;`4v13P(?>Gz_Y)W|&jJ0Tfgmqn3^`=WBj63+4yPgA~9nZ9K z%>QBQn}d57MuJz>OedfeR#*Q~D8zn@{ z*~ZA~U1F>*Ej3O!2j!qN3bA>$wXy&&05tH-zU7w3m0IEvAsC1y0srI>O%{ zX)^1@0J~i~g~*ibl`*S;zy%P9*z-|k9da{ISdsoszJ4>=P1^qS@H^VPtW-Hn9y+w%p6Fe+}#oH6}U*Rk*qSnmQUXQPQ zat7%BD|w^hOwxTy;^9$PHTO{JP}(2FURHxj1I6wg7DAO8;XyGsz=D7r3KV@VDK$wu z@Gu;}aM_K&z0Vzn((1!7r=X2B?S(;l@8-%{;PZM5Oy9k(NS_(ih6n~} zWe~~e!NoKpU)k4S*bOh{oDsY{*KGue+l*y=I**%w;Pbs&_h*fC)}P}MX_wOC+H zBRWX4rUHzd{pLCd9S(+nJ447+u3*DCnVpJI2emfssnmH--juv*JH_x2O(VO)JF&b& zZt(-UvvcZpYPSmD(OX~OOXkh`&MPkkpjMn)G$6KLquY?Bw}iSSs2X8n;-^)1Z&gUG z_=Mb?TG8UqmN2a{<>q31VNA7d_0?8-TaF&`m^J=5luP1@wA2lbodmdg$n~jDD#Ek| zTn6!I>n@wLN*seyN+IvGG-j-6b{v2SpY#EWHq?T+bc*=P>qWv4-7h)F)AlryxJ0tX z@#0s&i=hS_-$+5pzEr!d+t{@qvnV4J{vRF7)<{>pI8z--duL{~?h4)VVrB&PLzg{!=K9%vK z^^Ol9R3x@}|Laq+|LdiFLu_NDF}O#h43M>YMtTMaa|V0*e8Cuj?Ljh!K}{WfSD|5z zf587>bOsUquU0tzojh5XnVJ5bJk_C8R3zFin_4%?jD}}i7GT-&pqg%3 zPxF{fWx8Kwd;VR}Z~j}}{rUP?c6IBHkI&1WbJc0T-X;KQtA&|a6{<%63Lqt>o7%*l zc&&4|j<4nCb)nBmk~1^`c1ebSyGDL*S_qkXNPCQ!ZkV6Y!H?;_0&{i09@N*rNgrM; zigD}wYh(WC5k+yZqmK=^pWptnjxLN)r_;^Ij4zCgiIPcRSUG0UZ}NC3TRt35q1UC; zPe84V+{UQYzr4iCLX8{30zkhs9eCf&T4>&a*;`mp+0tp|tCeF&kd~rT(ER$q@cg7n z#TkNY@=Eg((Fr8xmi{!X`z^r1e$$F}%7wbb&<^Hqbxq%k{2_Spue%s+T@6K@B z;m*9}l}%s^#NgW;-kjYW)tvQ&#Sn-w2D2Y@=W^?E7yn%UEb{{1m9;(oC1ikh{cHoO zpM8Z|#h#PWcXs@dbTvG^3+M%K77En}@7!vf82&P4_Bc{EER&?2i*Nk{`0HN^QIvgq ze;0Xo{(yV)KFr$R0Jw4AF$&Q2N`ZmU1zwgpFR%D@tD0x2L}wCUZ^x`bS_I!lw69*2 zAiz(EIgCuD&>v>9>Dg}dnm>&tl_6;@Q#NihR=&;;%?XU@`fNYG+C~zB7cwSQOsUjN zp@>zy(wK1TSCjzoH$3q*NcEvq4Vy~J=AT=f_r86O@dX#u2As6)Mc$epJv$6e^~D2c_~{@RQ?oYdj0Dx_W-ONeVT$28#eRXG>Q9QbrBkyu zQENqCKr9S41`zv@**XbV9TBvKS4H@faFP~!+A17j=saSAFe!mQpNH|| zv`}U$9)Zn*m{Bs1j6PO3_8u4mEPtu?=m|2X_<_h)?Ug z08j$CYkjG^Nh}?Q4Z8;SGMF>QLE{dhLfQ&qyYK{W(ox>@eFL@o>~V!a$Uc9oJCdP) z-_cRYk}jjg2u|~VjUB#cONF>Y6%y+0J@wg{CR45`jQXf#XdTDdeiNT_G&AZ_VO}!g zR5cD#6S0S%!GQb-8Hoo9O9uW`H&&x50#K?IQrQ^NAk3%U%r+aZZdgcz&#;5h2~zf5 zmr1WsJ%lKe8CldaHznnJRT5_wmk}&B8|ZwD4C8=TFY6==s6@Gvs-&7o%6HIhZDMb} zK&TV~J(f3B`CH{|Cpx%#F013KNCF^!9ZFiAXj2JpYLA5K&+7c@%zCf2m;KOV48~G|WLTeVDOXy(*#-1JU4Inj3B_+K zd@tIsB5S2i1c`j)4DtKxBr{E-83Z_-$N*$Jcf2(+5WCoZH=D9p5$#L-nbCK771ehP zDY#^06>cn*c4e$L#4r|){#nj}0%&`)E{Lj4)RN9iggHwOhF$s^dqlF$e3Foo2jh{~ zN}6m~=KQO@3%Vlg_p`CXS|<;Nyisg91M4p48WCS8s&Q0LjP#dkmbHZEE@`4z;(=Y- zo4dd-8zy+b5BnNAR+b3VwU(On^ahX&U(w#S3u!hEL%~OTmm9?^2#)I~b$~!Cl{+gV zH6NNAOxq3=FK%#7E?+fUIgxSf7|yQcbAEOIsQpa}66MQ88L?^`g9oOJjF96`Yc0oo zIw-ZCF+>gUFu2i5EYaJOJu^;S7(c{X8h+?}1MieihM z?8LQk9$0p6lzW}W&3e6>oMr@+Ebm31XuiSH8XyY#@tweqy3za$TAGcZjmsR(aTKCwT}v|PQ0>DVr4+&EX}g#lx9vi7D@BPN)> zwpCo*l0pSdsiRBhveE%|z6=I|l0W-nnj{WmBtQM0_Ao86&ku`|@B2I;8@%!-J~+9N z)dG^oD^s{4?Hv*V)f{UFrBNZU9BW@%n@wv{pUzisao-3;ZA~5##I{DvC#zLg>$u9Q z)~l$9jo>EF2BT7LPQm!0yTli*h1lQH?*+-{wH9^N5km5~@z90J?5SK8Upai-5X5(8 zXW~rz@LXRxWB?~`8->j{`SQlN6fZSq+V(*6X}qZ}=vBQ0>r+`*1m-w(d#3bwOs)5x z`L&%WlPk;L#BPmY*7m3vxwh3FS{XlHiVA>yl$9b;X0oRKg;*5{RbLI5#h{v6+m6Bp& zw&!bMoDafyd#S2#p4wYC`#NK#*t*s||5OUCp0_zTm_v4AcIBDg4zYy_2fk9yi~Jj4C;OY{+H{TQLc(Tl>} zMIklAa^wLmMwFXr_~UlivvsG{nG{ZxD{1F9R+ar6n=my9^=s=7Go(k7;{%C45Kb5| zfdT;R$d`}4TeK-)9JFGDa2HGv@Ulf|KFNcEtEYr( zbDcr+={Ha+X82dhE_Nx{irXW9dS9t^7AR$vp4P$IrH^LzfRC&cf~WaGM~wOIhipOf z)X`75^eyHa#l~21wJ>9X>N5R3w#J3=`P0*in_GvUj`$Dhp8~6S9TWfM&2T0NXi8zUEGDpr*|P%agZs; zPEUcm*%6*Q@5@8e1A%High0#jIbNG7Bii$+%&JF%)RIa+mQy#7LT=UUrC(=S(VFmd zkwqL@+vQb7%gmyMf}QGzc0=&5%5JhMgp5nTPW6{(2H!D`0Krd#_msM?>(=?Jzn{j= zUkQw!Q#MmrMV~LyuEM6r{?|i!p&; zi>rE(GFy6W_)|grtXmGFrdRAM4@dq#uR2!C6%BrS8_(movbW)_J%Ua_?Qi`aM8&lN zD0*UK+`?KN1=A%)Eqxri{Iz|!oC8i6@t0ML@~@(!VJzhLZ*B;E|271Wao$vFp{71nx2Pc{s1QUbg1-HJLb*Uc05IT>|5yG0YP0<7A+xi5BmMqS zNodr9(okM*;%CLJTOVpTOl?wwTL`bT&eE!0EOW-U>w{7eO~f)zq#{I&Wg3<4BOT!t zfxJUJ5?Uy;&RQ>TEL8s;Qm$Uv)HLmVe$@5$DCF7Mw6uP;`2=|okWl~hy4=0=xvX{E zAIZdFHZd`AAaik{wqEV=tA2P1Ev^^;44~V=`~I#|WOaWHedh>;eyK5{ea8?WIu-Nl z`Np*49coK@pxgZOiKhQ5@>g{<%azG6OQhxwOW)hYaZR@|@P~C@4k=0y%rYr^WU7|? zVSo&WPs^KzwyoU9{5_ToZ~$?DcSnav<#sy1_fleW(R8Zy1s0~2T#5#aWd$FxFn|wO z*b5j$xI&kt5<|XG?{M!3rv&om!F}FiaiLMUav6;J1no6NqNFimTjgvS7^Fg%uS55p zw-SU;;<0wS!D^rU3=QYveAzagcX6$En1r=waGPYHe{FJ|Y-NycfrN8FYgZ_$wWZy& z1;$0K4OGMS@iA9`9%xIMAnI$k91yVqqRVHs`TZE)!X#L)52!5R-?V^?$*{wbrp6N* zroea5EOE7l6-l&CQD2%6CS1@^j-fAsfL2PQ3DCDI zrYk-nKt@j>GueHCQ2nWCtGui`@l}{(KHky(WKsp0=X}0W2dX9s+3WpiVsW-x+1Y85 z{IQG`shK#K43@*nksGwFD|uFuwepFak&zSrGg zI8(yVKsW0n877ZUh2eLk@xE!y8J0eEOf10G8T9pe*4xzE+bvgq;fYruE(SB(e3qj_ zXDDU}q`zQLDZht|LKHycQ|F|rC9UP4c-^o_@jJ1<2=ifWWZ zpGt~)0_hUd9c854yehS;n!*;@14=3+CC;K{h?amS;&xP2(MvN<=NAaD*YQGX68%{pUBlpy5Ygcm%eqKiOB}00n%Kn(G z*bDWl`zF|h`!g#2Z~ml}5*b1m2O@|%X)^YMBmNHP^?D8)9E5(bp1l_W6!>J{fEwr^rwP zFir`p?P%bUdNu{Oz{#qwl25|i1Q2*j^eX*&)?Qr%wOV*ADJw@IMJ+VK%VQZn_<8H4 z%FN%5AUb#N063z;vAR%^1$UBc5C7)k#3i^eC$|(@9#jkvTH{`N`XR-rC1_FnIXH6! zA%T0#S1{t{GffF^9e7*`jDg`?(O(LAF@rlLw@DC&G%!8m&MEVko#8?SNbeV?<{|pDJ75906t-TwDM$@3v3oRd1$ifYCsXi z*$+!JEQACO4(l?nvAeA7LKsN(VDzQZp&>0L0|smk$Q>th&X(=DaBFPVebNMc?GhO3 z2OnU>qwiAs20(jWyrx8TW*Ys}AjHJ|3nR*ddyJX1{kWII$$xT^=oK4xr?Krk%DZQg z>zD1$0h5Q#tVT=fH5TU&+M6Bdk7po9?=X?X?=E`ZL?8m#thGv_! zO~EX7@ULj(G1LeF)1Oasp7mpoIN^w{1;thQSx4u~I36REH31LQJlLJncm@$mLLt{> z-7#^yEPLpiK9s6@C2G9)Pu{$0|?z>P z+~0Y(f|m_oXa`}s-?k<{|Ku2E+Urp4zUFwv>AXLhEmf1_IBwKAzlDE;!-+ zX>4hGY~GwwQxnkEL4gM)Sc;t)3mS$x@erROgN&=k=cGlpHpGn-3mAa8-pv7lF)cYL75l@myGMsydcL&#{5ImJl8&2Hgz2e2g-2LaqFtGO zJG!N;^^RSs^iuiR>?5$Zg~wISI^OGn>~m(m(_1qokvmNJE!59dsKJ3igh{cvM}c7M8W}b4&up(rwNvUwRRw7nl~OyImguM@ zag#Sy5(lW90Wr?FO6uy7(uI6>yg{TtTLn3b_Gf2No5HEmv6QL9KaI|Gvb{vlQ?W*CsO4;dysv zszD23h9k>jEq1dQHUVI|m|oH3#l&`9w6RSihVq{IcrhRh<&C2BNqb5Cn|iC`2w$?uvGhC-C3tZdp0g#xcDIC+?sW`W6GrU=`L-%su#eTTX16d{KfWyC;l#YP}5G#TH8)(G@BNwa*Cck z8t2n8H1Tq&D+6Q&u)pS2X666R7|K1XRGU2(v|2w z!NjNNF88|q6mu+44c^_H-YP62I1r7|5KR=ZVC{B7NqdSYp3a|yVQ)%KuGMqmWdp^09@F!Z~z7cE&=d<-KTks?-98jg(od< z!WkwnGjm#A_3U<`Z$+6gv3|dz)twbO_0<>P4hLI;SH^0_YC!yUfLPG0Jiw0n-jj_{ z_C7Q1(p_BEBt!j4SMuOx9DD?xOKvH527T!Oz*ZoeV{JXsSKKMMM%f`P<)Z1`< z^Qmq=2m+q7zr{~98ygo}=MTw5;{e*D;`AO>sLedCevP^D*&(Of|=s|u3uZ5P$0&g<4RpWmwOPm zF>2F|lBY#SNspUFC+Ho7s#Ss(0p@Go@oWT=Ex*9fy&o_w^fgT5z zNL}n>t9~7#86*xzs$1D|=1Zy#CrB6^`4aTMF`{5*QkH`JBbA)*wp~-6>nfipN3^AH;eA02bmI$zx zD0?F2)`%(ZfJG?T1+%foD;yWVP*Em3QEC{`UeD6DV>`1~niH)TVLaNh6ZMl3MRzJm zNZCH1wuJb~?y`6_QGiJuai?vlA8(_l9ct~A@zcvnz}5xXmYtPq;wRkhZMEpEE5&%U z2CC`6i#D8Rm|-P3r9IY|{BLVx?I!^1B~ET}K63#n!sct>MTvC_C;&VXUC#q6vxmuH z8o$9EWrtvoWi`vwm0}`7%x&sgmHS6H5l1;=_l&}(k^wL)YfWEz>iT3(qluz*X;LC7 zCH!q&fN7HcK5ak=vgg>yilyyd$^pc#u%a41b?Iixum`o*{wbxPXavJP#ueZm?`x?n zU}`w1m-1KEw@FaNI{zu&>~LkJz5<^?e9oJEajyezJHI9H_;KO<-g1eAK!?-ScOjBl z2lO^-V3TBBjkEW92GW*9k%u{^G_Qn&u4}?&a?6Sx28|6xvS1!5OzLu?NsvVi!k=Gg z_Uz~BCow=G8n?J7cj%Y4g$Mv8lIoSde}s1_=sq?|4eBaOFsv7$=t|-cDX$~?Lwe+k zjEoo;W|-uW!<@K=;N)=c2z>vT&TuoI7^xc$)KQ7gP{C5(5suQG=LI@uAXnAdTQImA zxed0K%VClZU0x^Spfs;&-^m=Idx3=A4Ws7g?QCExs+%w5jk+s^ZU)HH1+Z&ply4$H z{D{ENB|O@JYEP^pa?Et84pN_K^ucl}PCimec4|<65X4iVh6#{%H3RFB7M)N%hhHgZ zlt;;4o+*29WQgW8dDIulXHKe!ni92cP-NP~`9q)(fOAv77YXE2{2L<){Jsz~!V&gr zygZk&mKPUKG9<#v%@k0fCxsC6v{hr!(3=dmQt1S)4N5=$L3nOO9V?E$RD$fiU>=hD zfooCGdvpA$7K7)(azKR?g~# zYA1fTS!r%5lLJ7`+s@X@n+N1DLfD)tGm3SyY##|ol$62B3sC>o-js4DLFVPkV|FHM z7>%ZjVAq37I+m+J(dOtA!QD^laRFN7y+W9y&R>b&ynz?tzoq?nrP zq|^?a2D<=Wpu{ydyuD{0R{_sNBtzyc^`RIhBeUI;FV2C7=$3i$O{Q<9HmB~w_hKFg z9mzS3?+6JGw!~T@M1>vgfD_0U+_Oc*l=@~&!__A%*I%ma7Xgvg;p){cYp0hX=+zKD z!~3C!9znAB_!2nurHBUvA)+xR4~n<91{{VA=d8%&gAmCaAvN9Cd>**V84OlyKRK*} zl07f##;fO!p7V+-VGfK313JykzTQG!^q1e`e~SZ3x{5=7B3wG6ZEsxfvbJ($nG+Yx z_@h-^Q7xAps#pRCb*EGZGgu(DGT^6Bk`x;Z6vUDAIDZ1N{Hj4IF#s6hc90`(Vt4}0 zQx%WYmz~sQgP+W|w;Z+xSlQt@Edlz&zbLi|_ecLop^O^8EP7xi-)FwRj-{!OauRQ~ z9c%(do0e}tTbX7|Jqa z#k_q#T{a%kjJg~iVaq3Xv`%dD*S=4mC&2h2_^w+f9g+q{w(EmnbJ6i9i=$bm7D6$i z9wq~S3zIEEV*{eq=OlllUz&`2Uo87-gard z6}Oq?K>FP{?1t*Evh$s-&r&uLsf|@xZdNn4EOc|ddY=R?ZInSfy^2utBIbrEabcMY<6M$8 zV1HN&3uxJGBZ+9p8c<%4dVqj<|JtzF$4$jkMNP=j0Ks#Tn+{-8x<&0CFaRV^F~lvF zuL?);^V1}PyF9C|Pin zsCGD;96(kD4NmJf{TQLddB)88iay-C#;gmXTS_vI$O8>$BSXfq;R9d>JXlq*v$N16 z#4XpLWF2ms%(K)f!~8hJKGIMil|eTcaG-2sr5`TFNBU#Xs%zmXO*#5k$wUpd54kQi zIznc3z|CZiU(l28&rDB@1tX8m07q2*JFsS(|Hbly<=ZZ_&a6(}W%B9xyr+Ukvw-N- zFJ)p~ROIlBcHbDtlJ)o&@oHTSU-8uZ=v z0$~tu^O>B}eTsCrTNJSX4F;0<-c}8NvVefTw+$g;qWD(FFj1c`_u(6D(?Zv4mS&r+ z*Xpl=V*F<;p9_%(P0DG9j*pjZodPnRuFd(8?wP25Zn|m&Z*Rax9`txjOXflTzWMfQ zh2;{v2n(I*I=c4dxNIt@iFd>KV)>q*aQi$b@FgwjcRRNo-2^APcxj z>e1?Y6oJl1zAfNx-2w9FRu*a<2yaq2<3U$MAz>nu6cQrzRM0NQ#?Y<7J$(;Rb*i-GPCL z;<-kmK^9f?v}W1XbjTBh#Np27ck|v5qZ`)M!-&tB-Yx(&vn^dZOS)t1qGBDw$S}4<9sI=ki_zI!LOjbCcA}uTUhi_axnD4G#T|KFUE1XT}uB%A27VL8nfpK ze`lT&2!L=;CZI`U%{EM3?dx`5(Yh_0b;TG#9qf?DcLDMi@|*H!H4QzyGF`|03^^Eu z9aSFAVWv0zQ&?;wNh%`0Y+7_&gkf4NCH{d>n-?thUwbG2BFRAhVVnLJVUegPzs`s% zzI{j20YU0UDTlHSq@tQH#p68xLoxLc8@V}Rfm|`2|9*S=QA#MCoRt)@xV7skTi%(z zi?>qZ$>h#d{KlCwdoqv9B?zlf;Fi6mWh8yCg~R#FK-OaHZoWUu?Qgn~wTFFLRh_Et zgL;#jDn|P+iz(GF`t%HIfGQxdg=_D2@ckQu8MCe59d+KVFQ4T;)@<55E-`KDxpBBj z>13u~=3_SfF5g;%Fi_0a*ZgkLCbGETYUF?yocCd%m|{`yIu&BTdrmiGmLR8^vRTvN z=1AR3ifp2K5AxDIxD|X1Uo9W9b*}zU1XZNW)Ra&zvYpk@tIFsDIG3JReNfZ!X)CSN zAy{`Y+fXBhHDysukHRyk_Z)c=kJKeBpX0B5oj)G+%JkxD6c^2=pw(wBK-m)Q3GBDttqf>;fK=-K3P#csfZ3ZPPy z!KkEpTuxV1`4N8rGNKq#DWUZ7^hmm-y2Nl)lzyyEAY?OiP9TOfwNWc#@a=zQaEYO$ zkddS$<3lBd<3(|WWz6@af)K@_3ouE76e9!rh=zoA5%+WLLRXb*i%D7JOyi-_q5e%1 ztZ7n57DxY^nCFejM`aVzj4}Amg-z2ZNC9aU%n8Otqq6a7@} zFsUMuBT>bnzB>Z_?#Mr`kFr;CH+CnsB|Gkonme6^uV5UvJCaZNQHPPQz(LAnsKexM z^`>3-2AI=T(v!A6Zu^v;``7Ia$J*v$8T-{$ag)U+)z_K6)$wvw!LZ3SMAa)s@cDm@ zQO@r;TFQiIX;I*B?$9h^!Fm)KY6K7_7RGu3EivHl%s+#eGNDQbo7TY4Ak~0~h;ZL- zG+fBf&wS^{4-YBe&i`ojoBKbTSn%J<|7;q1t68WhOQHM3#PTL0#!l=L`aR)?h7ub( z8^(zV1&XV%51Pc1(E>w}1BuoSqvN2B%!m{)&r`!T?WHwIq~q%#Cc0RlDT?;OGv<;D zLNsogPkYM_&foRDrx7?7`KTDFx&#)?y5>mRhAHYojsG0_zj8WbQOP9ZAt|Ba0OyNCehqJ0hXfOg7LQ$aRwwl5++r>r8b}OO2(`5-L?t(aO-J(*`ni(3JBPj+iz|5)a4cRO)1l zB(tfMng8Nqp(G{7j#Q|PEXrEhfV);k-rO5wCdm#Rlq?4M>FNE=w<;A*yGQ~IW+}QK zejUe-jT;}gdg$upn_1nLjkE+xmU^Uk9O0!gJ8Ri=NxybuK3_Fn%Zjzpax0UoAD786 zRdE?^r4pcrf*JO%P}2gxfy(qC*OJnLtw$FcVrif^fsFUxGI2HGTksBSv&#~k0)r3RIiH8=7C!ClmT4@TL zRSm8?DF}@H>Yk0=9N7JUD5oa9E`~{x>eXUtsw&8XJ^k+H;h}V&E0WBM z2+iE9J8^)Xq^IFaeJT~pWCom3z(-tBc)88YZ`h}emGCfpg&eqb7Ci!Bqc#Y`VPQ6r zF-a`j+&d2!H24YyT=I)rxBNvIN7`V8y`X%wAeK214_)TL#%HPWX(;lzl>BkMbrlf9 z7g~Mq_NQ3*Qce(!1QrrTev6dksAr;!61Ej&VRmB$R!~l*p%Z)bYDd)f{^EUvJf{G> zzDsM;Jn(XytO-Lo+=&7(p+yW)?hJt-B|HUK=f*+H7q!tWNk5r51l>}Dr-16p{u&$_ zLN~&|HVU{1Bt<$&fX(Eu3>iUU88xTuFjgGb4ig39Iv6$&Bc6mYWitd>Qi>uF1#TmT zB?2o5bLfNm6p|?L10RcDM}R-hBW*c_iP_@cV? z*Ji^lzyP&ei5{U)O8TovP5>p7uyGP0NV@agKjld{B|zw-MjUuEs*ksA>6SP0l?T9A zt|V=~Wg7ny7KXYJxGJ*dZWs4IdL?v3^#_K9)!6Rd@cQD;5+UT~cUQbGQhwquNQT}x zYdGuG0v>;RHADb(qV`F#QdlJAxEcwB_C5~vthlLDA}bRYIR0W<*SPf9FeL%7Ocb!5lsFg$=7RwqVFdod z0Qytg!vSm<|BE|lelIl}!uGsKnH}*3l7UJjx}DCbcesQ|RGqW;GFosGlHbs`R-N~e z#4{4KSdh-4a0Y<@2G$Nk8jR5E6}I9;jLlf#7F{2jOazYmit(_qirVkh7v%v?wjVy)1qtb~S8~Fh()X*I)nru(B z<%5GCz^1W{z4Yb913H-}YF_sndRgvBFEJpA*r$Mrb z4y(nD3*Pzi&5DYKAbe5N)LS|<_h`(k^ye~q2o1*P(%Vi4ucF8)*cDBI4G|3#GT1OZ zwD~vyGy~Yf4&!TSt7wxsWHRHBrho1y>{Y=#=tx-+2UI4h!Poti_FCe_%%I5|q0cUu z7l)1XtT6Jq_fRY+bFE!Lr2q9_9ENS_OTCfESC&c)-@(h75XgkwANryN)D3qOtT4&` z2a7Vf7C9h)uG(69d>fz0@0)G^W;>J7v)_0Ea&w$dz?PBUv7WBA+WGfpy5wn|Br3^0t zXs!f`xq!W5;Kh5qpjzbq_W1qEl^$-gf1vX9d`~$yL=IHqa}c~s2`Z?8o}$uNa&h`g z+TXk{g5qKoHd)lkPW)uDzMM#M)oRr>#VMoUdX|B{xyT`~(tX*+o$Hudx~oa%Hch!; zcUZrYm{JmDfK2>RFyD1mw9|Yj9(;WTka8=&;Jm8|fF?DiedUB2$_o-v1W6!OsrrEw zPdsg49Pn6hYiJA?VK@tk(e6o=!ywgQoiQzZx+EnTeDD~C!LZh;@GjeWNL+NBb>Xgi zH&76kziwS@+Oa!onRd57)O6{ACjZXpr`VXR# zMxv1!#AmNzUZyXDD?{LR7Qf9A75pRuIs@y= z0+T!I;gS)`*wX)gAK;U#Pc zP)JJz!phF}ZH1!)5_)Y4{t1iY4SGVP;!}VHRVas~3NjuyT&EOm_au8HwWPu{-sxGd zzOdIS)iQ|_^m-OJ1%Qf(EDrhtIl(560 zRYC$)9}Gz!7!KYlg{AYltQ{W$NkbB^>z0QcaF!-)L3-sI1cRG8ZelD(UB|xi+27Ku zY6D)RzlU6aUAv|Av+Pbby4aqE{5=oV$h*#LuOYl+d`V+2(fx{j#(OxB#Ss`c%T3ty zgomH{tq}15%@`wCo~+dzaV&R@-&}mZs8E(8HNmKz13$yq z25eI3sB0f57Hv8M$&S_wn+B^=idId1_@`3jq)+=BMNH+VGc#hZnL@mmGblaRfx134 zg120^^ojU!{tL&)`u||mLLf}6|H7l|gUuPhz6<|`!qsnC4*`7_{y~sYCQRA#edqth zfz`{}5kPzw{xOLu>Jwd;fPmRp6Rg~QX#cceaZ0lpVkh)Kq&4aW7!;Pg4!gAVA94MbCV|DSYR{qRD80Gl zVvyMyNFkQWB||9We$1;=IIVn= zFi}I6V)j2MYVNU;bQN)=I3yKtq_i|vgccg1*!78s$;yb0q@_5p#6(8NrOoL4`{3q+ z=`}=oAk|U_m|NNqn!?T5E#^>UaY}@tg1DsALU*iUH3|iRBmVtuWX9;g#;;fsLFu^~V`e2{De^gPX5=UmCWTRhbIF2qLJnf^QQ8G! zI@3h13dwJ)TavSZmWhPJ=SA#ZUhM1PU|;n9X^<;7BMc!Qz(_j~^!%Vs{`|bpj`5Mu z%a-k#U>_F~kyb;t8{);@nxS{Z(vya>b*$bG=)F9!y&k)s7GGD+{z2=h&xMHsv9Tz3;APn^qx8= z8>O}5r2CZM@oCBedlhW*JYMZj!{1)IlGF#@RuNf=I+{hkmFSj}D@dl0<4J+wW!L!* zie^dfu**ab&=u~1!XiA@i`|?h;w8;P=I6rsJCZ z^yDnNONQwz_RqLEcS`wrRqX`@ig`9Hw0}c2YR{r?6oqqAAu<+UC6eMV^4IPt00V`3 z|4riwfu0ac|K9K;&dQQOa>{*<073W1`{SbGXLsjQalp;_NA9!Zn~0A$2evHGwwFs< zOf~qve~FnwJHsx7Dj?Gf8=;qXxavu#o@;BJkN@>GbTtsHK8(h!-nB)ZZt>3&8u;uC zYEl2X5p!Wln5u)gJxWT?WcEXd1Hcw#Wc>Md8Z@UkAv@{Ns-4e=b zcEH9~;ss9gXY$FXqN6^2+e>S?>E&zTaW?GuLqV@xm(oH(FWVr(hGDZ4=Q`?isI_P| zP$#KGkCM@?e0TPkX@)N^#JOLOk=+hBevdUWVHkr;Al-?@V9_+ z&FYuZ15@aR+epAJrNoG-)@n}x___yEpl-Sj&kr}h9%bdhzD7l`o)Q|hKHUOfbz7t) ztXDCN0LcJ7;#hK69xMEGoE`V+TF#KPmbzYL*MUroEWA6z)+*m#0gg&{e)s&HnaS1D00Z+ za`5zGAs;a`abU3rj1gGY(!|GD*DbSCf8X9#ayk%nL|?1mvvQWw0MJ3~zsl zgcCM}aA3Cnb#Mbo8p(mGGh!z&4!W*?Q3{Qju?=z49BR<2iZE%_Vx%%PL%g$NrU$u; zn%r)5eZK1^Vf2uRLE>}pfIVd@8ji#lyW4x3Foxqpk!=Ir0Iv%6>E@VJ_RwKll<{~M zi)k;Ke^?p{U{QNA19+`Pj(0#Dwye3DFP*Xv$CWXMYLOpDmY$z2zeRC(*$&<9ll=z_hB7*mSZ0brM@8n!v>N|8ri!(S z8zehoZnu8_v4ciq&5y734$<7zl%tx&8iDBcXlH3F=_y(O4}eF|`I-uF|M-=jK!F(r zPSbQ~P`FaG&l4u-2cJJDw_4sRr%9Gk=O3ZdLG=snq9{_AbT!e$l&76J-~TxLuX@F& zkA{4)`_rCBS}O&_WBI|hDsC3N+AdQTC%>ncYyyi@qi( zcs%+R33?uJu|-^X3B++=O$YaiG8Rc5&I5LIFn&ST4<#5&Kr%LeJ^Me+$h742II?w& zOTz@tav;uLky=X>8+My5y4h_aLKg<_4Sc3EbidKMQFt;N$-#0kt_{73rYVwW&Z~JU zj=P;wJW0czg2AX`)>wkc+UZjoh0g4$4QC9cfy9g!BaJa@Tg$uC{nx)8J-fAJKW{C5 z&RX1aS<8YYFS3?@xX4<PzEu16kXd)Q8VbdN3#p)N>rm_ocQ<*2*<|_Hm*=c=kbjBB|FJY(imYA3x?FtP9O=^&+vej_W zs;1Z&5F1W^Wk6J?)2J#R;EhQWV!f+6QZ<00w(pWzX+~%!MnqCJN8b!5WqVdsnoHSU znFW{EGmEqRlh>bK&#Ps3GP-)mCa{BV>llP|nD9ND=VyWckt--g};9kNSRD$=``|>7#QWfh~vV^jU&qft|RF(Qt3>S2h z?=qf2Qxb>RoOwsWDD6X~F~rzHIcw8r%Gt^uy#JJKyt!6o)zTVgoAP?FKYg=za`vGX z{+oO{nXT9hEJOsiPM=%Q2M^MO1ovD`fbT(^ZUzsYbSJ>K%5;FQ=aOpuY)SRf#Vo%d*>V=`NTkpv?0cFv**EPO%wJD%ug4&k2L~sdmnI$oeY420R4YsgF^+DKDuQgzc{UC*{najY&)uwsVxa}I*WzjX> z+qX~+t&a_@i{(IMf%A3^^w)#(?&;a?@qSmPCEgwavuS)VeUM0dVF%3a5k44+_BvkJ z%%#ZY*;3?Xt6v1@MY*zhdak@w_;ZjpZPIMaOJ4d@6f_fb)pdvW(8Sx})vWnCu1bf0 zsvRNJ0_ku#zAHwta>(GMz&$37c=6%-8qmsk(f63Czso&#b8=& ziIQOR5GtaJF`3rYmZ;LZvaYv86;_sib+aXON^iI57>VocH*i%Tp4=E$?r!rIS|kdW zRB1?))G=fg;FNU?8B6h}*LiZT30$gEoAh2sHy;+g8{Q0yc}b+C?KNgT10j9Sde4CN z1~7xkb&baQgR}-&ttMFP^d)SisO$Va%(DM!mbWlGzRkxwJichg`acyD1j`B(Wo~41 zbaG{3Z3<;>WN%_>3NbY`lL>?(e>FBBT_7)0X?kTKF*P zG(|=;Gcz?bL_;_*J|H|nG&eyoF*7kmL^(1zH$g@@LPIw+MMg6-Gc`0s217V7J|JC_ zz-=~v9nwi`O<@?u@#ncMEvl5drrz68dpqi+!_`r*(ke;8upS~1hB{sO^Mbu?TqZ}33h!Sja z>ZP3iAy=g2$_csZhFtwvuK6O@mdkbL<;+vL{+rxbBsWdT&3EON?{X_WZ71aRJ95V> zx$~#o)gX7Dk$dLk-ZyggkK9L3|08)&^3X|nnDs^q$u{Xah+fP)zGa#mjE&hPRfKZL_LhU1v>d;YPnSM(3& XeM_N}2!9pJHY-(WTa{UrHYzhKjjx{5?>XK5o~Os@@s0i! zbMJ^Tu6-}uv0|<@Bc&U>F%B#V1C$#mqCySM!^;I^wZR0`Y01apvm$&w)_y{kXd_B@ z)B&5I3VzVa)<3N(t6;KJet%6f2FkMKP?jN#vbPfz2u<8xDAgd3s_v)%EJdE@d zuVc74M+^ay8lPQkYinl+v(lU^l%eni`ECp4cF}yaM9eDiNERUs;D3HcO>#oa&RP?{ z(;2FADGS$D!Ne6`>^G{K0%ea4I78$=FHxgsxy{eg+$tP-IC#Z|LW=@-n0}^}LWYQ3wYBq`0 z8^1?=PRMV3C*N0!LUKIDiYwDMyEw5$fT_w7RQZ=woyxZk2#5muj>J%7k_Cst3}~5J zh=WFeM$&}CrYWMrs2GtcieqJNMPd4(4f#f4zGqu)q?)lzPFq@NpCqBPMzxi3se^+* zq^xigkSc!j*1RI{dg(^hrq%aC)*h{BO7?7H_wXXFG5`Wm-Hj$=+~MMN-KfE_vXK7R z!8TBP&Yxf3^T+(W>+*!4A0-(@DfH=~zMn2YuY|r-Gep7uF@TB%;kNM-F^kSvmT*-b zogTKDKlEr(&r)vjBX_7)#c-LGneGBgBUCo~Xk;K{~yO3anHn-H&!k;q!ozt^}lOSE`Dm*i9f4>Ahy zBY!E7s`5Kq3%bPn=)O?<`}c54s3sl3uiF_TH@@~bk9u(I68789+*Y%fA8*ci8!?kk zxAqY`m($UptcEqeyhz^^3WeU`Z}pL4QQ7c_e!B1pVGNv2qf$kwDfZT1Q7ZcBfDa*fO3Y&^Y^1semvVK=sProTOs~eLR>wysgm? zxg+AXcK&0(9%i3;=4z2r=Ai(TW-Y2#cU#a*!*1}dEnB#EpMh3l72kQ6&>1(l_`4s! zcfw|<<&NcCpiiyKrcGIwaR_jWd%juk;qvOMoBs3IYt+Waia6Id8_?IRGah;XBq%W0 z2@@#FfDRla@5F`xk=br{~7a;u(SO$<|Scg|3_^07mS63{lA{#&jl+9`@hhv zY$WXeVzaW7u>T9r%0a^ZFZv&S?Ek{Ea*=TSi_gkU!U5DU5CLQ30kXf=k>9aiVG$`rSwc;epWn-5ca zt=XG77l3LYs*$@i_7{$Abs~`*)%{jIah)z;l6Mfii0(@QcT1FaKyHq4Ob1vB3Kg(f zOB1j$roLW~4YJ5hW;p2kL4C`>;mB^r4I;1SFlR`YNnf3-<&{bJ)7cF1suu4v9@GnV;x6x*2+e>+|#m#U&0-!QmjKH zYqQ^&#xs`7Z^<9DC=Vr{Q+()*(HJI=wXhGz^r<<`s0FpNzOFK-7RV&q#@mP34 zp+@>g5?x)?FW6BBguQ@ySA`)}SPZWUNkB%hJ<6Jy;z{qN-Iw}KV9 z3Og=q9GPv?Nr=UYe*gvB5SP-*+}eYZX~0Pcm_DtQZ-7)iG?P?+(- zXUS}yl_1c2B?ke>oDXi`mTQSd=;>pjF!zS~TTYY7?m5@oAVD_H088;^L55~iuF(pa z(z~l3zVLu1?2a`M!=lU$5*3!h%otIU4x4ENtfC!$W@?YgqsMP|^`!%#9yOs+Q5Zk zRG8>>nUOR=yP0bft|vt%@-35?WbKHS^t_`d70Z^--EF;ft+?y5vDXqZ_^+@>*$1Zr zRgTB(ad$lZd9@DR0=6gT8^Ux~uO=JQh-1)t%IM^6`%=3KZYmOXZ?3PdOQzr~oh;lv z+$>EU|B9T=?BLiq{}`MYA}c2oF9!$7Uq;5x1}qZb1ZVj(#aSuDKzV?qqNECiCRNt9 zRu)#pC@G_sFzMjQQhw#55pbkka0^^eP!SO#4j|v8yqZXj44~jh)W3Hbhx`(RDTN)M&vKvWx#G-hUEQ z{8^P|7z^`VOX4ew72{xz?-m{_>k|9xJG z0_&K``Ts+IVR>~&jFLovW}@TojaU|fuubMoafZQzh#a6P0c%i+fzyQC|EZ7ulce;& zlXQ%VD)~2({$UkxTugt~3!F?`e-=Xjt52~0P)}+A zqD6|F@;8`&7{nh8D<>-n_a9pV77B3v%Z~m}7^uk2Ti6X|;dJq58MZ(L_!I))7(y@x+gTS48N4UcG^_5-vc0GDM)f z3ITwFgPTN12=2eW9eps$EEwTGUg_D8L+<8n{eH29!fevrixQTzAsp9H=~J5k zQ`!mM9)T7$;kzUi^FtlYUd=5jNclVPfWZ~ex2NzFWE+hN+^5s>+P*;&_1YSdc6|_} zH?GazWbZm1P)6Kx-*ou}A$)hHjV{2xi~IXlYZx%8Z=_y4!vEtFOIx%XaBMY*%)d2EJkEG6Yhyx z{yQRiy|w#Zc_TZ@ZyF={=sD-4GZv7vXVmFjlQD^KlT4;ea}b$!I2_-NHYL@HvS zf*r@7pJH6>|69)nYQbxuYvX-oMZi^z6G2#EO!>0vxds-q7aAgk0+C!Pz~BfePckkK zCQI{mzQ{%ufMFvVaI=i%&=dtWsWmbmQY<1F5TbJmx9YSlRC}q&&(z_4f5Gejkh{%G z&HXw3_UZlk`TA8>D$KzlNd`cXjYib?&G|Hkz3qkJbN*(XL*1s9cY#r%Ux=M^m4*UB ze?<#BiB~@_$unmBOklJcO`m$>hTmdODr?3jerc|EDU4cazkp301#J+*RM7F70x`X7 z(ZwLkA={@m1eJ__jm|0x@Ln^RZXtgv^+q!(@Jl@W|*r<K+5O1RJJhvL8cdPZxAf~ct1pbDQ!srSsuO+4 zJ9z6Z=+#lYm1oFcWddL=#~i4pcqO(Lfq0r_)yKLl;w}Gr4f|m|l;RVrL`=}2%ub!f zP3pH!>VNPB!-hiM{dn9ag?xT zH|>+gtCN!nv|YeGXw%AAQ)tI0qNS{sE%t?1 zjAG|*K92H<`s&I~_wz(k%{+D?6NuVl%owFgXr7Va>+FPk z7ZzZAK(sF*RWS{ol2_>I>Ct~cfnSJ8%Y@hfomxoAX%P%e=s)i2_gzpPjxvU3(tC^t zbt^fws2Vk4{n1Gyl(cUXeybM1^!pWDIR_SA1aVo@A^}syXc>_veR9I#1#(Si zDh7vbYxko2U7z7Hr*4a#zc+oum5=Oyl`QiSApW8CA}#sKtmj|f@%VisXBM2Xfmxe2 z|6<>n_7e{e9j)`_qC>f%z`_0MBtEA+1==03_Ulq;;U^)%UARwDVdw)MB`I-`v+XT8 zjob_`I)-0CsQV=*X4x-HScsYWB@j_BR4g7Hl{X>%ovDK()FI{$6gIm=nCG%ArUUKn zI1qaWG9T|Zs~IyE1}okd*2xr1jmAC>doccmGEHQgvmWRnW93I3t-i* z3thVES_>xhZCit2GeXP4E|81CldiA;5UNmtcw3Qk&tT%bH3#D-rDhV*{%>5{uNri6 zNK~bRb7c2{$GucnE+y5F(rl22&;GD@=Ze%sTOxyb{0trqX$FRrjvw_R2@jYM{zjAs zsNodSv8eRNeVt6bFPkbEmHoud=V<5)i%u4vMJ+uul4-iQbn6fKtiH(jB)D{db21w% z&XJXGF0citZf3ligC2Ol_IZ4%%8uAT0EaE10Az9F!IdSeCk7DMdlJMwF4kC+~&?X^XW6V2@jQMp-QZK zvMx^0H)8`K?gry^>}VGMCO|}-fs%>IZ(|0Ll)GV9z{6an}Xuma?|;vvD_O~R7zjMHuH`@1U@oR zqj{twt2EAroYXi%-8h+jj5n$s<^>NTM;5;8Z7~pfOC8UhHW(G`*v2uh>>5wh`Fq7= z61O=GtR+)O$=CWLlkJb+0O@n5jy!4`CVByQn+QxodCG%TOuH*1X8GQPcC6v5gWlwx zkOBjYcOUngh|IzYYlhX+)>m3lJf1W|XEWh5t5u@-&o4>Ppdox~!b|hQdGQ={oeZrT z9Em+iGD(Wi;elS^G1sSx)Nhlq{5|12eOh!fUX-xm7U*t|+MtEjfLbW7Wh?C_+^Nj$ z`_-9NGHo1oj~XZVt9y$cGg?7{F)%zd)OlwN|xc3{hsfq7IF**l&NXc}7KI&|5# z@3=4X87C0}Q@Q-+<4XEZPhXi3LClfN9#j}Gn{j__}=d`;PCF;`}q8F3BC z>z-slOoos&3aT&P5`ZTV((n&UgKx<5TFtOrI?W-!McpC87bOU)$+UTw&C+%J%{*+| z*uR>-b|{~lAzkV>K8iIl8mzF%Q{Ua$SXkKFC_`nR%7sP9K*K;sLqnGm{|SEBAhz>Y z79N!4&+ZrvDeM2XkTW-V0(>#Wn8#reHgNy}@ks!u_(#Sbksjf%B|SI?E9XD<((+Qf zoQ7EtM7#mvK_qmt$$VdiLWTBdRX;vLOgE*N|*0f)Q>|% z8)5I+-=)K$?!|%QqhVBy9l;a#(k%ce6KIfgKT42pGGr2i1_BwOSiV(BDU0vh%e0?w zF6)SQSH)TlEXoqU^$2ImqYi$P0Q^q8@oY;sWTK0I=U$;5Eh|8&4!?D`L)MfJwGJtO;C!|<)>srPLT|X6(kn3kP_LURa6VNBmrnu{+ z!iyYg9F)Tx2cV>Q?kT85Wqyw$UCzZ9Ps5suKw{Wi{stzi@xfFYnZFfG16V6-@^BB; z-l&&fOCI1HbgB%NlTp{}l#yX*msiKi!L~bVwCKL9X<$`Iw}^Hh++c&a^QwJ-7W7?f zVmC2&IeMk==g5|oF{&syYV+%2-z%}HHxa!lLQV7LGR2GIc(x<|$smp-dbuDdP7HN# zOC%_bImRP;ZMC>|JS_gEOme`EAj?|#7H)d?({d@+oU%!Dxd$dd34Dwr2&7m7E)Xax zK>SySfw6J`o6KEQA=lB1$Yd z+?UY@Igqgy!UlcA9*OU!VA6ds?GtBWoxQP&d)zI!H~;iZ7=tz??NKrMx#^O9F{F}JnlA>ab=2avjpcw|lU8s}7TRcEy! zTzc^LhM+sbhrP);ZV7a0R$>|Kc&&L))~$NRXrvZ0BK1q(6zerm*@B%s6uj+sCudQ#g3T1x=7k(i}1rc`O@M8;LK_v0}7{L~E(%EgN>{erP4i1T6N?enr6M-!n4^Q=A{aB^Q~84e18Rf^KcSAJGk0DD^^ohgk=?_S>P} zX=*as+x})VkuBa~ao2eD4)I|du*M#Ac9r?zbqL=H^*In3$%2^C14aIhNDg86<=Ex( zk>1wiIZN85T8PNZzvR)GjT$J6427@G79> zB6bOATQ_#lHn8nJUN;vItQ{UjUe$hEx@(p#I2qMViUWJj0&Om?V8^^be#asVWAzd8 zvi%aD&%ZeQ#AkR()(8!@#;OhCqs$iVPMXEzUiQkN3)ciOtUUUu@RsZ|E``n|JS=?4 z3&X#Q&4s0p*o0G}3HXM53s*1WyOBzlZMRM5@TvAJ9QZnL@zAnSTIF5j8hIH&+d(sN zSn9qQNRTnBi0tlb4AK*!-}Be>0pCqKFFE(Y*rWv*-pKcfPlUC? z$FZ6KtlDfa&&G)v&cXx$MtNiJCymMZjT*G@OL#Yy+$;&6nw+C4<+E7Ytg_-z4i(Hb z-JFcmHRsf?>sm16i6u%D>ICO>)|KwQqG5-+TKM)0S-hkEP3&G3L9qvC!03M)|z28y&(3!t-n2v-)!c z$K(m~aL|eHu#SbiA1(>b@qGAxWrANA2Y#&ptj$)VP`Aj1L2#zXfoSevf!Al<2uk+dNA-+Gx6-F{${n|$6@HfBAJ z0sxO^%_g3OW}1y;bW8$F$>xbo-^p{s{8QZzeXeMo*to-UCIzPy_w$d9epwZf5A^r|fqBLJE!A@Fu#ynPPQd9WF_clB%X?`4c zNl<|!Z6FjxagYp;CM^42BAdu7-2T$kL1g^llXgyDkN8IRarvudv_m$Qx{}%;G{`id zzp}po;hz7uGD*AptO{b>v-gwRNR59Y36nBIMvw$8msE$G+Xs3fhUe)ifi0>sH%v3d8qaBcivcF z$@%S>D*3#EtBw?^2>OeQ0rx&7L>ech&!wjn1d*WouGq+pj!lJ%>3xze1fe&ca!j{K z07XuIH2M1imWQUXOY z$XpZ1+%~z$?RMsteR~7|BGAy89P~0IL&`&h*^#v)Td$CiFYYoSQ;dOTx_Bm1jfUy8 z`eJPLt`xkx3MXyCy)_BRRyGU33UzTjF4fUBwv3oJZ+YSI9oI>;XWABeSZG9px)&Q3 zhJ?|8m3YaJT&gsFGY`jkfYeW7FIq{?$1SdN(OgEYhL`nCrlRtUnzU)KD#jo~jWSEV zB1L1v+NJBw48HxL0=u|Pl%7K#WQoxOEK8(4ne$tg%=qHbx1;%K$OGm7BXoBf+!P z<3C9zfj#mF$&IX_4W4CG!XLm@(<>Iw0nDdypOKMJhE@`uJn!Ng9wcx>p2^KB&GHj8 zHbGB!6L^a3l3SJ}DYiL4NW#G2#amRak2(xUJ1@RoeBC^pWBITn6A_&?NYwo0EXO@7?$})gC+7uJ1>zPGsAtV#v;CSz zq8*kx?_WtOMxRsjYL2`!0#%FhuhV_yLMF=Q1?JxE`bqtg+91RL_EgbNM!9)M(U+Ud z3&Nkn2HPPvQ_S3bh5|^u0w?_I`fd-3 zf6MuV7dVLBo)d5l7?swJLXU$T6_H}Cb0_(h!$GB>^=ALLLx|s3)PX3>hqn%1@}ix* z?bvs2%#I{sl&So+!nl~vy{-zWx^PkFu#;jiE=5sRa?(#hnEX09lmdN4a}8rH+od9_ zD2nTXO)3Uo5*FVqu-e|muhZjxvn7 z9XM}~HB|_4XTR+a{9xZP^Z9cu*sSM%Vc0;dopV2l8IZK$jT$NRuDdCPC8(WAtla@4m%!&jHUC{YomuR>{g?6b( zuaSkF>E}CdZ6V{DwFIlzunTgJVqAom z1C^~{W@tKUD;p>On3y39dl>HU7ePhS1Vfv(5~cUAeSC=J{kXD4@DRLv8C1CwOyf2~ z$+NKbKrpVQAI)~k%mVaJg>l12*{ zfT4_yXrPCy^1xWL8%@i>vDxjq=C{|=qY^zW2)iPv>Ud5hDAFL+M%;Nyf)&6-qoktSw(Uuead9ujBsH zVj@zK0g2TZ3$s%S6+skb70ys0Nl``+Kozw^o>NVIc_BTeFSYONef{6uxN8P4qpaVzcz zy4gfcX0A#{#hi#BD_e>q2R9`@RrlM`lJE;Ov{v^Lt20A>zhze6q~czhpPhdRfThVA zBh3B|yVO2ujSIaD18cSJ41VaXsl1Zt(q9EM(#_4C#T8GiSBpEAvL=FZ3JOswhg|mq z3&Uykc$oj9Gyc11VUWB49=svrj!qpDOsGxNOw7U__WJ^qW)$`Gm@$W3^vSm#<0&NZ zo_5}LHp_l2HkP!Q!L3GZ{IRzhz?)a0`8O-A$TmLb5Dl-W9Yq zjMda99Zbg@W*X*}qwjk2sz%xxy1Bqe`s~(ln>I40Kx&^*<-TrbZ}ajM7d&9qEOyb9 zThq9P*(UUBR;htkRzfh!dKF?^;0Ci9qd;f_F;GldNz>KwFuA_l$Rj~73DUF`7{Fod+8jfNBZ+>huG7k3-(*;wm;UWU+XLuh98NOj(tgm89S zx`QDwhg@b+8ukT^oq;&J%%!!xudkQmhh5ir7?@q`-N$zE3UK?V&-Ee&pM8y_HrdEl z@Z~D}D*mqT5cJ%l0h*wHk1A{O{&U~j`PcoFXo}EDYDI=uBi|2D0O7ptg$oPGPhtcT z)4h`8m)U&b=1WanN6fYCa~$AbmR$^pE&2Z!M z4HN8cA_(^PS-VgK19F#9{NQ(uZQ|@6OTTk+TA-f$wa&`&6hge3gVtT;%|FrcCw?rs z&##6t(&n@@c58mm2LQV!<3~Ro=8Y45cAIbftE$D!TQoJ+&p6Xm*~+9!-0(Hy{gGjn zn@I;;IX>9NALISbEb{qua!xz9tv+^Tr6z5e_JI9Wk>WI1#gkQ=0;j|5Z>$Y9dt?|W47J8k2#`wu3f4fdcKXX#g)pHgk zS7pB@^V^jHHqF;xN7vR9Lz$DZ3PbW*#pCY5p7iUw8vH^HI*0`=ga^Wb^F#?~9vsE0 zUboVp{U^`i0PxAQS25Qcpwc1-96Y|{1L-37fdw@kZQx7Isf3(WN@Nh(9I&E1P@a0B zO1)y-ddeOYJ;u?&aW8_=(JZH;?N< z2o;k8fMd*>KnKU;6rYBfPLZ}HM3Ws~?h6v`1!f@ki3X)iDe)1=rN|T>dBZr8sHc;W z&=ui)dQoPo#kSMHpe$yf(*X!B^Nx3j(qzam3?CySr#!S!i`RcKn|(Jr$3$f@pkN zH_b7(5X`nf&@_C;({NV@bLo6bGP;IeBI1z1O>u}j zKpe^$5_mH{37sEhx^Q25_mXQVc$u!JRuAkWFB38s1b!$0s|$@S@0s2MhC5QZ22>Yu z#NW{v`{u#gSz_Idv;ZDZ&JBz{_6L38h-%qGOk39C)|^Oj08}nw zm7DB|31;O6B3hQ)w>*ID>@x&g?M_%N;No|gy3;WNk8I~z?^u^uJE7L%)^s`}8CHDz zcp9W3qhnRPiUr*H)W0c%@-hp|aFp~9{y0H~|C0s=!$uy~GPhfWa|nIMR#CF_y`oHC zu+Bv%OW9lAeR`O7IikwJ8!zE@27G^e{4ALW7ND!`t0~~!%!+d;xT)b>-COJta~MJw zr1+>j=MFW_-!PE2aGv>hx zoLpQaul+`(-OglhXr5SOX1t=6zEOlX+3euYQZUXLp!UX<8#1@{RS;Xi6ks~gp0*oQ zm5dT+x)Q@8(*+}W|eIPCLC?{!1o|8v^0KcRr12tD5|i!XY= z6EdNIwY&@N<=3!$X*L|`8%T0!S?%*ti{SK7*M!GFF}`FcX7i%O{kOv~Q(Rz#N&Z{-PR%mlwZv6@^jbA~ca z7=O^|Ide>AyYT?ejH4+gwrn1U+Pi7Jms@_Z&ADm*MlR>kwiJ}<)(kXkEmSWPlD`mg z=mk^=e^>#pkMVy5y!$S+GAe1Tg?}nl6fw0DuXnvxH_YT-r?RsTT&=Qn95^o;u2f=U z2|%87dze5aK)Y zS)#YNul#=5Llf`;ax=LIBuvTs=9G7*sFfB9=FvJ7gv(C1HbnUCJi0}Cai=xWUj<1oNB(Dh3IG0shjxsRlfzc4 zSGs>sP0%ZO^L_in2dKunP7v@|iXTXxFA2uO0wi@4X{pJlMF!(x{WGd)o9hX{fI=!v ze-f%#*gs88GEGQ#Y4%-YV?~35ZGM7)g!F(N0h3fTz**VbCR;Sg3UQ|hr1Y0Kw zos%kxXq*kW?Kdmg*aZAv-^VcWr|oa4g^v{8E34HtA6K;>U#|qi&CAPi684eki_Orv zOMOda*2Yq4N^1aRa9xY+vf26unN=)T(oG2G8nmT4&~cvMbSJ~gd@lmjDbQ}MlnSk& zgK9%N-F0_`^B(KFvHU#NGLG)( z_>_BIMUxD2%8&W=`vFPE>>@OipetmT0jC6(e7h)RGW8kYmX$I=XR0NW**VP!>DJav zQZSKf$?lrMiAE(_e}r|1%iR?>k#b~-b;NR;tBXA%S0y%aKzA^rpB780AZPS7MRf`j z5`mkpG<;E^j3b9O-BKPij!t>Ms?kwkx})Y zL9{{gdD<`_Pt_0eBS_}dvh~iOjf-@IUC7JQL(HvJqD`FhHNl~Zj=f)n_SqQqX^A+l~*dg7axE3zAEw?O(3L@x_ z`@u{CVGmicz?`0e-yRz9C0=cRNvXZkt2-(&3{2y(DC$$L5R#X87KVtN_XlQuQl$on z7|yQ#Xois4cB@Yf(OHD=g)QQSWa>4)j;{#A*6$8<4g(4VR&A7Mi79T9Sny@_!M<$w z3aD>@ME%2457y+4K92S{F?V@+B&-Woc@+$&m-V2D_k%~lZN(HJQ%`ymp$2+Ej^A$PUw#2E;pMv$p|`zEFXF|@n$hY<-5(Gen2M3qz*$=ob1N<@HK zLvqBZ6AIxY{wx3Yaw*97cG4wS3^FM>ian62BshX(=+b_?x8tAU-3y`SNE0suN>kk) z^$VN1i{d?62SZmuQq8WWyJ08Cv(vvT09vuhdB|*%rZnRNUsm4b6(61FeIbg0i{H)H zi2EOTF-cr%R)WB^%wR73A$m?gq9_)6m(zlFXcI*sxVT@(M)`-5qndMF?bc_xDvcF4 zzGvMMU~NMx>$j7-ln0~u3R@ck)#0&F(#Lx(Og5$CiP;CZz!MQe+bFikvYt~!07JF4 zl_wYNsMVUcu)#+U(k`=-p`j*sJ^QC*oICu};K<~^iDO_&Xh>{9>g|8I@4H+=23X|Hn|1Z|Nri53tXM*i77MG9Paalk@wv%bKxsK$ zt_sy76f*tNlp*i{?w<)UX2R%JH2)h}66z!jjVV4q;S1!Ykzz!t<9(S5-m+M>Nv*j# z3^i`*S3))(U+)p*_3t#3#zh^_RX{lQ-e3i{E@o|$pF71!wq_< zU+WDhVz2fx7WpVgml;p!I>9TKMGMAPVMV^Flzv9M;pY`TNe=w@_ud54M1&gWE}_BP zgl1bZ2ZYT0s=t~E!YHl9=Q2-&o<7bR1=qubMBr&StiEl7ze0AWGYVmPNE(b3*s-6* zTzpIuQD#_K^r%+iR2S*6tN>C5ZG+O?dK1md3k;`lQ5IO05 zv{Bvhb)%9kZF>Dx?74KX7r^ZeLZZLN0Mz-w*fhD31*p}_gDCS zS~!GKjz5p7cfWVCj&!83{IEudE>>@^2dbgydftuTyBYet$$r>SeyLZ4LDF+~HoKo?e3y})L^BU~6gIo`AC!zwbU|)tx+MQ- z_EsKYa=ki^%(nIURSWQ@?Svr9sLYIHUzOP0D872}o5@hjEvEbJK(Fl+!lPl_a!3I~ zSu#$hUCHwb(j4>@Aqpyuk_|%j%)OI(dayBt9hnoDyf4|zp@~Uys|H_TNm*A z_wVNhzWRsrOY2zo1iWja2)lYFCvGYNJIc%ho6q%W;%=HJMi)Q?>01x*huxO4kWEEM zv~H{r6W9LybWvr*F@**Lv^<4qe$hDIrMRW|I9&Rdo&@w2r^#b`w7{3DIkSoK<0L3s zM|2?2(TK*jJ;6=GtG|u6#yQ)E$5nyZZ+vxto8sF`zZ8*8asz#gm}*IVBMw%4e=y8s ze~g4ybh1%O>4r_WYt4_Fw<9UCwGG%RgFnLjV2?H6X8e!wrv0lqva8Rk&-`YpV2f_{lAXJJ)5_)4)frpA zSQ9t(Cx1ec=ZG`vp@F8NIHw^go0Pd*C?pRv(F3QjapijPosKh*?MZt~Tti5(#6Ev?H5 zdj~ufLe3GWnKIoRfhD*@e`*GN`1zXq9V^zXreA$=ifTq={c12_JuHRd?Ao_~_zt$1 z6?XCf595W}oP>YBLnnYiyVWrc_}+RV_+R zI+HyynXNX7bXS5`DRmd2>CTZgqUG4hOJA_Iafqn}-aCi0hP&hRu60Y6HgNf2a-)T# zVjMDHXVU0l)UyA9&)Aq5Y!SFo_?Iqt}xA42q7&5B|&xPBEQ=?B{@c5QQ4 za;S0aBdKO;Y{@!QnCN&7VU#D7KD;AnGjYoZ;7WzZnLj6+!eEQ;k^C0njV6 zqH5SbSBG$ZKH!>N-%)dM=}i%)ZEbcN!w>P|P@EvC-FknqsK}WC8+qtSm0W7YAmvnS zaKz^M+SK_0Z-XxxwSeYMy~Ynze6vvA*YTIJrI7gb^R?igXCGYV@39^s$Gc`m7I$RU z?G$gBhp~X3L(g>coS^|-uKaT7SO7`ve!)XGbtt9;GCfgpE+s_LLvRpF0W%5GnHn}b z(k|mNL3r2F#^qdUx3ZxPo`!td_^|=Dq#${v93~r-8MT)i7e84akhTIJ z`(O<54r)KGg8FcjkI`3!3C+#RN8Ug5SA}KnYKsBvJUlNiXW|b(hFhjQ@(apF=H3%G z4xG}NcG-1<@@B?Pdr8g+dJ*S0=qr`Ik)}&u+Pl6JR}UkPk9VTU)wb z;`NjIt4p=t%L)|_Q=HE)O9$bAy)6^{p-46ifrcGg7GPzIr5g?7KlCMCXC5-&nCPgil z8T=DcEM#2XPc8sC6=5+Y4u%=-vq?&-^EZQ+69!2PxUk$pVLM%xfv;`v*A;jDjhFD7 zF{HE^v9|gZTE13Ed+2H+#juV8j?-2%+ z1A8o2(f#Z493*>~KR;p`zXN6XuzpR7zdvs~tV#?-wtg*LX}5m%YUKlET;7V{8q}BX zA*>_ooAGKD`^}@!o~$K@Lh2}Y<%gxeMv0V(fTCx=Dar}^t`U0=>qQ(s+=VQW$i zj&bY8P1m2WT=4UQc+()o-w#}Wg!#``%?M}L3Cc`~`IFMaoVu@UO=PrethHr%x^L?n zr0^+zD`nlp=rC~w4!q%gErdM}n#%zDfE21RA#|8HR(EC1ffxKiamB`)i;GSkL z(pg|PSqO!p8^RPp4c!lrI4tiMXa1N?1X$Q-VpDwZB3jX@w+p~MMr>YkGqMEqWHXpQ z{(k{z2ABCZQZ@8N)L_|O+)Xq=(OujuTBIg@-?diOog`ZkeGx~3-6maqZo0EK>@6#` zr8UFj_V97kwcdz4K1$PUFtu7W^^@}IiGOshG44z_q_Q4Gf%oBWMCCBm2sk1j*K~8j z<5~6iWN`TA^3|KWS+?A#l=?_2^{B7+g?|L%6~}o%@sOpOOv<~Nl(#aeq>t+}scdCZ z6wj?pYFsCi8v9a3*O~>dR$7*?R$9hCyV6=`q63Tvt%$^p))@Cj!> zLIEvLAw4GWSVdaU$(2rpib^OV@uHdzE4MUPshn`Gl8Uxhk%o@A!%F&gpnCW2^lI?# z)m8T8==DteI7;S^aFRJ!Sjurde6z&WhiHJNKaK??TE)hfC^F^7|1TB!*QpV5V$F zoCI*tjSFEAeMMIuL5?LkgzO3=L_u8#iW;${uo5U3CP73}4tpD?6H)sb9Dn7w6ehN} z1H|W}i<3_$4>#ptF&jUIhJ@qbMwPIE!YgR#W*hSV1`XQ%IvO1BqQSou8a6F_6$(zS zLcxh=Lt&%UAK<`69N6E10~x%B?i5RJZz8Q0O|u>)9F#*Qq$0X;3tnhd)g3Y0U?+HT zaO^mNqpvc6%!j-sWrYgw8-JhXvI+RyL=M4Qi6CUosx2FOx@WB0+hO3~==5J-|Ezc8 zZMIzGPoxAbJw^9~E_3M?GjS~tgl-E37R2qGu+8m-mPrQ%rh@{fUkU{qm%auDZVe3V zvth8=@ZJ4#NsR-iehUs7uT@PDH9R&;4-al=n~2+XXW#N!)$&;r1AqUj|5nq4cy0rH zw)5GuuUDUs54xt?5VbW5J-TkIeti(3&}$qP-A5gkxVCUuq=lBldf9PUFJ8)FA7A&X zxB6t&TfKU=w{9?bcbhzquIm3EAv=k2vmLU1Rkl>&I*DImEnSKpg_2uWEdpBDCfj7qku-Cuy_XVngaz?kBcXT0%^TKqT$9q~`7hoNp^Sfd; zorA4^JYD7m{rVR)e4nCY>O2tys>nGlu=}P;Cj+*qaDUDi{qg|9^*2^hbJ1P)x$SS)>i|hT%B3%}Htkh!n6gxsUp2D^I zau1j-`^^smqT;xP$*J#JU1BJ0)4oL&syhTKVY)+VkFLEcCw)J?nHCTAY?C(E$5{?S zD)?4>`7nh?E-EIqYt+A<#!YYR6pTViw=&}-I|D%apYp8nkn`JYJ_z%(n2r7i`<7~G zlTm>a0x&j{aoQpdFgGAwATLvCdSxInFgKH-+7)6jG$1e_QXnr$Zf0*FF)%eCFd$MO zFG)loTOd3*IW#smH8?^sHa9gmH#9XiH#0FoHZ?aeLpec0FhVmvAUrrZG&VOiI6^Tt zH#ImnG&MFiGciFnH8(IrIYB}&LNh)fU6V0M9s@EtGLtcA6@L}bJuib%90l-mo>KHh z+o$c*R$tXyQ7zThTWqA!k04Df1d)bVghXQKXk!u*gO5NYK88t{BnB}^tQO84e)pbx zlAHYV2k>XX0#8nLT9iJzK1>b~5p#RQD-|ipg!p7s^5U0%2}n>fQWZ;F(nU`l^tM6Y z9q4}p12!031Ajwjp#2Djzrkn$bT+`)IT(Ke6Q5wx0aGhr`Vh?Ag4ruGPq(<4yEM5+ zdYQili#O&S6`RFhlfx1bN9H9aaha2Z3`kv)l9Dt_Utn2tRbI^htmI^n)eEo&u<>sC zAsLntHaEfMGq}EN`Y|cUI9naC^#g9*n|@M?GR5sza3p6HY(JR3EYmW>eeLDI3m)y6 mepYI-Ad9lZ<6W@h#y?qEDv*=v+#C!uGdDRn3MC~)PeuwT;%*ZF diff --git a/übung_2/aufgabe_2.tex b/übung_2/aufgabe_2.tex index d0e8cc4..7e69456 100644 --- a/übung_2/aufgabe_2.tex +++ b/übung_2/aufgabe_2.tex @@ -1 +1,96 @@ -\section{Straßenreparatur mittels Linearer Programmierung und Flüssen} \ No newline at end of file +% vim: ft=tex +\section{Straßenreparatur mittels Linearer Programmierung und Flüssen} +\begin{quote} +Gegeben sei ein ungerichteter Graph $G = \tup{V, E}$, der ein Verkehrsnetzwerk darstellt, +wobei jeder Knoten $v \in V$ eine Stadt repräsentiert und jede Kante $e = \set{u, v}$ eine Straße +zwischen den Städten $u$ und $v$. + +Die Straßen müssen erneuert werden. Dabei sind für jede Straße $e \in E$ Reparaturkosten + nötig, die durch eine Funktion $r: E \to~\RR_{\geq 0}$ gegeben sind. Zusätzlich hat jede Stadt $v \in V$ + nur ein begrenztes Budget, das durch eine Funktion $B: V \to \RR_{\geq 0}$ gegeben ist. +\end{quote} +\begin{tasks} +\item Seien $u_e, v_e \in \RR_{\geq 0}$ die Reparaturbeträge, die Stadt $u$ und $v$ für eine inzidente Straße + $e$ zahlen. Um $u_e, v_e$ zu erhalten gehen wir durch die Adjazenzliste und vermerken pro Kante die inzidenten Knoten. + Dann müssen wir folgendes lineares Programm lösen. + + Zielfunktion: + $$ + \argmax \sum_{e \in E} u_e + v_e + $$ + + Für alle $e \in E$ gilt + $$ + r(e) - (u_e + v_e) \leq 0 + $$ + Damit stellen wir sicher, dass die vollen Reparaturkosten bezahlt werden. + + Für alle $u \in V$ und zu $u$ inzidente Kanten $I$ gilt + $$ + \sum_{e \in I} u_e \leq B(u) + $$ + Damit stellen wir sicher, dass das Budget einer Stadt nicht überschritten wird. + + Wenn die Zielfunktion den Wert der Summe aller Reparaturkosten hat, haben + wir eine Lösung gefunden. + \points{3} + +\item Sei $x_e \in \set{0, 1}$ der Indikator, ob Stadt $x$ die Reparaturkosten der inzidenten Straße $e$ trägt. Dann müssen wir folgendes ganzahlig lineares Programm lösen. + + Zielfunktion: + $$ + \argmax \sum_{e \in E} x_e + $$ + + Für alle $e \in E$ und deren inzidente Knoten $x, y$ gilt + $$ + x_e + y_e \leq 1 + $$ + Damit Stellen wir sicher, dass nur eine Stadt die Reparaturkosten einer Staße trägt. + + Für alle $x \in V$ und zu $x$ inzidente Kanten $I$ gilt + $$ + \sum_{e \in I} x_e \cdotp r(x) \leq B(x) + $$ + Damit stellen wir sicher, dass das Budget einer Stadt nicht überschritten wird. + + Wenn die Zielfunktion den Wert der Anzahl an Knoten hat, haben wir eine + Lösung gefunden. + \points{2} + +\item + Das Problem kann wie in \autoref{fig:flow} als Fluss modelliert werden. + + \begin{itemize} + \item Dabei ist $s$ der Startknoten und $t$ der Zielknoten. + + \item Die Kantenkapazitäten von $s$ zu den Städten $v_i \in V$ ist das Budget $B(v_i)$. + + \item Die Kantenkapazitäten von $v_i$ zu den Straßen $e_j \in E$ müssen jeweils + größer als $r(e_j)$ sein. Jede Straße $e_j$ hat genau zwei eingehende Kanten von + den beiden inzidenten Städten. + + \item Die Kantenkapazitäten von $e_j$ zu $t$ sind die Reparaturkosten $r(e_j)$ + \end{itemize} + Wenn ein zulässiger Fluss alle in $t$ eingehenden Kanten füllt, dann gibt es + eine Lösung für das Problem. + + Das Modell ist korrekt, da + \begin{itemize} + \item Die Beiträge, die eine Stadt $v_i$ leisten kann von den + eingehenden Kantenkapazitäten limitiert werden. + \item Die Straßen $e_j$ genau zwei eingehende Kanten haben. + \item Die Reparaturkosten einer Straße $e_j$ von den ausgehenden Kantenkapazitäten + limitiert werden. + \end{itemize} + + \points{4} + \begin{figure}[h] + \centering + \includegraphics[page=2, width=0.8\textwidth]{figures.pdf} + \caption{Das Problem als Flussproblem. Die blauen Knoten sind Städte und die orangenen Straßen.} + \label{fig:flow} + \end{figure} + + +\end{tasks} diff --git a/übung_2/figures.pdf b/übung_2/figures.pdf index e7e8946836231182c273637b8a8d4e5719f41275..2f9dc6cf889cfa66552dda1703ec4007f54756c4 100644 GIT binary patch literal 28274 zcmeIb2Ut|gvM7uoK{5)c#6gjuFif5yh-5{AWQh`ooRflz2!bd`R77%+jG%y$Q8JPd zk*wq(Q6v}u-g?f=gG&pmIxPwB4iUaPyhx~jUXy4EozDH(n!7)g!>K|pp! zmLL%k0aX_xXE%E+NI+6nO2*FCSq;cQBtZf)7S_&KN8qoup)*zrYiwr%)RD*9nmL<; zplAe4RFvGw*%51KLw>3Ep88d#u+vP}^eZWJqI}Qpx19fUsquBovd~^}vy9~T%C8we zzbEs_%eUmbzSr1GmR7v-rWBdT880!>Ph_Fwq-1{5{u0WsEhaKNyVDadd0jNZ22L+o z3m4egS~ zhn(E@%)~d+QaQH+jf|hl#Aw(UbWjT2vCZjCL)CX9bJ}qx{11s@muDQklHnt2a0hA9yFI6I)ePR z0+n*lk+znVRrEg-5Y!hPU94p)VqlWz;;xZ^Xy|0}Zt~YIKnuJ}d(A!dsVo0m^I$sl z6Y>FDY^g*#GUJX9z4YhWy^(}pt54lx_rJ#YO;SQOc=YhCGy6eW;6a9wD8Kz~Pd_G` zytcKB2yaKZS8z9)oo$uJ|~J{T4E!Kq+WJjkaCF&qxGVv?r@c0CX})T3xo=oj(wqd6UbULD08Z(o_s#$ zaJE^b=*io4jKs#`x-*noOTs;0JJsyYU+$~vn6*hVJH>qS6yb{g$MgHCISEwW_7{-c z;ey8&#YXurPz5|EW;UFCcCjEO(Iu*$eE$o-*Vw#I?ZUY?o!7W8 z$u`LXp`LYVrZUrcZo`E6fTkx-o|1R4v#lfb^oux_Df=m7s5|*FylwuywTrN}E`M{& zjB$p8xwmO%*&aG#?$Fq^hX&2s#QXdjLP`#@Q5&0z%I7yO9*ccYJyuFU#5i^F@lq9m zN5ZtSAS2!0!@&uy4U*`E2j(D$paQU%F-?bxyX7~s_{+L!OQ_c})7Y=*wEb@?Y?bm~ zQzj}$H@p_KvQbdrR$M9}-E*s6pdrO!t+}sbX@=;^CtuHxRSd6^pWPa|mDS!k+9f4l z>6TO;P$A$GPqRXFCAD*S*dMd#c%=(Hd@?Wpy*WtLJ3}ahpmKpVpaJSrtE#-^=3q z8eMZpt|^?nO)~qdIl7^;=oOQk0)twD$o^{jnf_wlea|X}-W4M7wG_STGpoOiyR*=`?gJM% zvq`Q9%9Nu!g7-WLc4IS*Pk-Z4{h??)pom84;G46p&Q=WU$LU`hGIh7#9caHcvRF@i z;UtT`gLGLOMfBMRl%pG0^ou~Q8xeXOvn90=8Pr{Bp44Zf7oe0vGSOy1uCFg!&z|9X z@=T}i1#w(PExNK~!EjErEdBhzG8<>5oq9venXI(p(j*redT~Rn#o^wM)Ez@2+7q6N z_TdY+3C`t`KjNlgG@xfb?4aGZ*3Dk-b?!wr5!GF_gE|duGO$vDiwlyq9evHGKS!_1 zQ`CfehdVw5F&}=?VUz(TIndi4vJ6sFTi?6yOSu;;d)j6=cnf9n_DjDeVl(4J1t-9;O0#tO0c-L2SmxE zTRdJ_t8%$0uhOmF!Zjks^y`oe+%bxUtN!NfJ}%;KItV?Vx)84Lsm=?>i}zkMv>;;~ zOng7uV*AvrgtSGX;PNEl(u-h=Gp%Or?i zPI!J;;p4Eht_nxZ323Dw3oA)Xco6l~0FAH6`LqF2QaZ!)VUtvml_PP!5>~8sXRb7g zdRS9}E6Y|-zUMwNI&}0k0h|3nF)n&7Y7JJY;hNCZJC0{g+vzryvK?R4cr#I?Pp&`Y ze{?yeKnb;XV=~-6=;3EpUELFJyw)#zm|T2xZSoC5;o-sq_aPXqsBnH(QoHF>A?sy{ zp|(89WpL)Bx0a7`4vMaxQ(=#zB*)sCYzj6IkOG7xIp&wJ{6|6&hS@3-jSUXbi+LK- zQ|j-_ZUH*22u(8H5r98spxKE8~aaaz7_o3=QAs9GF z2ZqMzfe>gokVL{ExFiPhJ&A-uQ9u$61tC!|paA%b#()qQv>pfvg<(KCXbcL3g1~WE zI0B@D07im8bDF3JE{(YKo(+G_G zJP1F^?>KOC0uUx^YiftnwSbAT0BFk%#3K$+7M2$zaL&;L>u6zX2I7%50dQ{N>;?c; zUF_|xu{O9lfQSOWpTmIt8pc1OLkTw4L1hinJ>?X2rec(Ee+l zys~FmCG=S>!pMz!>S3oh)~Bj&C9ourFqj zV9j2X=^)$ZB#RmSI*en*=p+k!6AKR+bVTh=y@y3o7`&!4`Fz{m;qF9CZF%{F)w36} zzLAdF9V2>Kv#)jjaA&3EWHJ1ZYD7F|1!Z9I^A;ObwCB|@nU_nv=kJ$1k@qQ)BgN!n z?B7^4#?M=l=Q47OJqh&Y#DJH=K(sS`ZnQSvtFa`Och_zY~x;pv;#wFmaijaM*A7N0ry0r%p_l#3oTC1U| z6J}k4WL#XiBSB7)pr&_aKIcezT^3!5t#i3l!Gq6^>GeH0{zYRV>KT630E8|BtWA86arFe09PNy8%s@u~*na?z!d`OL+d|dIU+p(X zrg_fD5^D@Bzn|+<#?H|O$7CFB@HGI2^MktqTnYpS!vJ1^0z+X)5YSbCCpuaHtPj_9 z2nhc_09C;{*||6xW1VmdakqZ{SKa)FJ0bLM`yjXygrG9f8G?w-uS}jdHB2$c zHnXrbFi)cmt;Lds6NR~_q%e|m6p^>1NVsYhU7v7V&?O-U4b16gbLbLa-_bPfGWn=q zDB7*-{}jbr_IrO1#Yiv`2?Zg*Xei>}0mUSY-%;#aYumC7#b)F*Z+AiQRw<9;{eP8; zcL?#nO2tSp0xbwoF%tQ2LB%98T$@x3pcuRj#ipb*ojXws`yu@Qiv{@4s2H|GivLv< z1N4hT;HVhTDENVf}9ry^K4FujxM`dQa<)17v@7lkBeqGac9k`F|)j zf%A($L_Puxg9GOm|9+YY7s+Dh(SrCb3t3sJvKaNa%axD)k=KNOsZKNg&V0PjZPHtvG| z@+}V(0vr(kvcvy%!MQ8h(^D={%JUfrQSwy?QPPX86gd_7+V3H_QnH)u1gr}`N%!Y@ z-Cyt}fI$$@tz)>SVWmWWo^j4$@&QF4S-vsiIGkx<@rfsh_eCY2S6X~L;rm5z6jyGqN!!DIsaMzd*=f~#kJPZ4 zD;tw@#S_94SKh4`X9oE};l@%&+9QZB#8Rwzr+&%|D_bM18gcd*`eI%};G&kuB~r0> zVd&nPW^m79(qWGPzXI0k6V+>E@M0~l?C=L=rx0HlSWhmEO>*S)Kq-%UC8SuDEl(=b zU`KA8c9ccE%~w4Z_2LXE^oS`XJkY{q4l437&u?A7OmBvDmX+IGK}ATx#W~L@^8IL9 z^x@R5+M3C`;zEyPN`z$Clk(1M@0F$ye%X6N{p?U|{F}5Y7t4DvsA96B()*;&20?!! z@4I*BseOu-_-f`hZJ5a;mJ!ZhqbvuOcEhUDH601 zvdu@+r1u`%Lt$j>bGt6^f{oxU$;@{%OrFfuj?#&A{sCz=dFgIrOLlyhL}nRQ34*vA z9GV)<>UjpsSADdwH!iPCYD%9#grpuQNn^No&f!U(Px3vFAPu^?G5!4VjX{~TOE0KT z_m;C-*PfiVCDVdj{BZklb_MtIui5DvfnIMOI0)$2$tXq&p|7;aKQE3g*I}4oVDBwp za&RnZF5`9`C}h-{Lyqqouu<;4$)bI3CKV=)Nkdh0?T-#h?Mv>@yBJrVHyKXfc}1^> z{Na!U{jt{}9)wZ!v4g4%ZXs(n;LEk&T%`oa7H@~P4e(TEry6;X6gMhcKQwy#Aa}p^ zdJEOK(NO}IYkOwsHxi>=+h{FD6j*M6)mMFV%}1Wv+z*p39P=r(!?ZqCK6dKy+2Mne zPq6M>5BMK7+xEWI6?X_IW+tFFYG^{wfK&V=tx8vOXPU@ZuAS*`wPt(?CifoI-|2U*uYn zC+UTQC*}5az0=ZhIjkLT_KKmw>p)@F+O)i5?fpkHg&xDlqrKtUntT1jNk3<|_JYA|;F~D&Bu0)Ly&9FK$iy ziYbQut+cYr)uuL;3)*V-Yt5DZqi!{0rHv4RmW`Vmuj}VNefI%Vw^1%Gm8bmR_x8c{qx1*k$6kaO<*w2(voL4rQ0j}-TNLgo$-8JaZ_)lH`8!aM1LjzUr|Lk^$u;Q3c-DD5ob@%GQtTZ7eIGET+S4 zrs92;-IR#$eN~*xd8Zz&Q<@iSU*$+~k^aTIq5R?=sx=O&q|RiPJIAT^>T9x;z`X1; zmQvb?G7YFW?G*aN)YxV|c9x5mq>*FJ2VENG(XZ;m$$x0 zFojP=d^Ewb=wXH=s?Z6!*uj4G8#E55i&4c)af8cl@$(wRqv{m$6jmH?I&6H9sVoT-!fRSv!Dm>VN8X+5XTs ziCE31%VWkYqpaa=e%9%a?1F2>O=C~w5%dgN`VS8XJ2|e*HQjreL3(~-uC?buR9INl z3Fbxi2bAX~cTw!NY^wi}wHq$DRedl%V{nK#iGcVq1j0wqE)N<81$T*Er8q=SNi5@z zIYB_68A;f_%geTGPd62C+zx7YAB=O766X}P{{QTQf!E1?Ibi^Yn7>(U5kL0QI)We_ zI7Scz`~!S1U??cyH-Q4YLl7{$8^-q}><1JM91nf307v2cG=Kx>&H8W@&gBAMACAU3 zb8IFBe>6oxfX$^228smSGaxA3Q=m9M4hR}>+`u3(AQXHv3-kwpfZ|GU-XTaN&=)im z4mf)tA&_709EdF&-CvWn#az5q{oHE&{wFi{`-~%SB!Tzmz~k%xflfg^xA^?s-}qQ*EA;7YQi4ZJu71oIm@D z+#S){m`GoG?bWzSTjPtt@h=6u-tdEAHKXDmiLQM4D$+M!zQ(%NQlQRXY%_4}E4w`# z`03)4eJ2+-5+ygP?&K4n%mtMU2`I7NAExqYJ!H(EMcjxrrtWvE&_s~i)?pkfUTX>p zMLJzFym2UX{mhCS^MK$1UA+>vNR{Y^1=X5)G}+0Qn(1-eg=-1dh@o;t3^oS9%F zU~pTaTW){#;KS9ft9_kR@h_Z{Ox*9ScHOjjKuFWYsAMAOoUHmX-pYzRgVAh3qnH&V zo_WV(Kh55+Rwo1Wx<5!gx5Ccm^aeW6bBC*(&WV(W2J?k{V;mJ1J6^d@@gV4j z+dmK2V?lDKnNL@%U`+k^q>WinQm-Ub>B6K#N}@T>%{Nra1RsgK`s?l66;__tENRkFa&qF1Oa?K{-W`AOE>?Pmj~vz9qKN-Y}{EWW|Bpj7Uia9+I%Zty0(L?4ABscNzp*&{Ly88(;I0%s^^DGX7exP|Fa-9{|EU!1 zOR_sfPX*BJ;?V>gO#DRD-(nsAxx$bnaCfa^x{2<_E)@NT!Vvw(!VrpcpMe8A#J}vK zzC{cDTl+&O^tS_=|E7LtYWmanG!RTe0`QMoup&;CwpV9#ALkkuW0bmgJ@fGGtb~ME zpOC}3;$o646=wm1Y>WMbBh?Tg0rNTb!#gJexGD8V6b~TdXZyb=EdMu7L_z}Ze?1Wg z`PqqgnTS6WroiFopH2i43!kxh5uEpV~O%Bx(i04rEOx?#*QUDH>jOS3vu|7|rxmsdy&=)FtF|flXe{x%6 zf4<99{Gmh!Zh`*kviM&*6?h)C`&78hv1jfw6@MtR0V~m;P6YxC#e3TSk8r5Jvo2(Q za;ROFg%5sN;JK82jSRq~u9G~_1|23vkQm*#PFT;s>4cnj5=60cGJrcBKafc-U}$Y` zZU}gH0oTxgyVT+!2pG8YXl#i83z$29mg8RZ%i@2BOy3k_&uK;Gs}l)?zcX4G2aqpk`qW+>pf=0lCeaq`;GayP`lx z0OgTfKohv;ZjZ~73uxh!2=d=9kmCFIN+d=Ov)Ms*_cT`1+3VgU>WA2Hy6X52rAj7PxMvH#y0 z_b-JAKfzEa8ic0-mG4;$2rwH1)+q8VH1bRE|C|UxK*jy1GjT_wIeQ5~Ik3uGEb~QT zE$lhJ1Yb7?n<1yzd~>2+-;+7nZR2r&ntLvkIGrA zex}n&-~Tc3$}N$50(6XHPMQ9T#;;}Xbf0Ne&&YY>G{zm;nlJs?`(5(lxLeRbnIw&q z>v_vd9_AR+;bAxS^wX!KWACEPtWK`3N#!0kyURGHFEW2{Y-7UozQ!9O=BMK9ee=a- zJb8NsInOSNzE{na@|Tg0)Fo7D0F-Q7rh_rfVhg-H>TBf(GZz8Sb1>=ZRZK_HxeKbK>Qjj;!EVnmWN)MHhT zRieDdzsJfmTd66FHli&d;(gQ^pwwO&-++ytP++R`S#Km>UwHImZ-_@`7VG;&n9#4WEQ?OEn0YQjL{Nl2pU|7FJ~;|Ly#|h>t3JI{$NA0PyFDK*FJmRz9STN z{MP#1dPq%+@x1Z$yDx?W<^=`4r}pRI?)*1L38(3JxY|XKm-GYHw(a#Y;vd zNmX0`giZN`3$o&BVT@HdEun{#CAcSlFTvoL9R2}6tS&gYDq{l$LGgXUrC~q>He4-S z8V-Wuv^abk0m9#r#;1`W{AFHz8U@1NI>o2aApG@6d>RA7U)aN^0WTn&0)kHi0Zi~$ znl>{)fQ6rL27*7}uZe7yz(M$n3!53>V)d^F02gg=0(G+l1;SgTH#2Aua0UBE2?p>V z`k4^~A@RNh_z^;Y*e*XxfI;C;@bM3T!9e&^=FJRn-1GARFa!wo>j6j*{zPfB8VZCz z)!59SLHM2ZW(EVoZ|ycSf*}0n0-pgc3)vDm@Wnm>VDcd$bL{YIsZWq_PQq>Q_8I~EyQ9|t8F@E#wLjKi|cStqTLMmd@iDTkobmAOeSgy9riW201%3xeV zB76=vB?%lRKGUhZoIYfeMh!1q8C`zPK+ds`UP76NQazqFSAt{jbqT*9F}=+9O5x9_ zb5okfa~{r;wV9b|$A>)ggx-9UPb|-x@BExtzT)Fd3Bzr&oL4dtz(37*;i$|;8y<+T z_macw{HbW!euchkd%DA1^giv0ch#~NC~f{gN8IJZeIyPdtIW&&VOVo?eSad2_MKto zmGLy)xGU_I*3C|7+0wI>Wf%K0h%GNmHEQJsPDCuXdjx9b3}EWGG*84L=26+@ojlQB z;ie0mmbH_)E-QO7v@BQLf?jDcK8MPDh*joY=zAjf)o-0rmfzb)M#1C$Y+nb%=RpoH zidgb*Cpd~uopjRGZ;rW>#P|GEvvB}eXMTV>g%OkjEpuV4K36+_GHx6yGjowaSmUHY zy*mwA?g4&&23UkLX^*}(2a&3OTZFPuqiXP&yNoPrtp^pUxT&n1kE;jGKBm5^T4!3s zZBdk#AeoAPTdcB>ziRN)-hfb!FU&zy?3^@U&N*uX9#{xtp`}kHuH>IZT10YSOE} zn8?V|ymar?J7A$nLg5dn4|gAu=TV~A_9-NTvB4Ax;T#OQ4Z&wM8w~RJJPdiO0zyrK zD8_lJq?j173CdybBt#c8Up(iDsS|%~N7|_uJMi^fEA2qtJM_8{*T*WSQ{^ekEbz~2 ziJxCR5a2M22#R1Wi7pZ!3o`w7X|8SPtz(J)$%`l0KB>MveB^MI>v(U@48wVY?g7uU zqv}_9u6(thw>I$Y7C51Mx1mHNv9>P1)~vkhjP7%b?hZ=2&xNwO!sYH7ilt!t$b|Za z^hG%7$Hvp~mni&JDdrQZduGq`jHiBBZkA9TY*dwVJmGD0ulnPDs0P2qvEG)FG<%x} zaA2X>J`zm75fD;b36@&8W-;e_A+lR-odxu2R+>(22h9Uf~!(CHSY}XjWG)Xrz#?d^LwQK+j;@Kqv8S z#S#HC=NZD$yVLHEgKc^kwZlt8`{6M%69uWaUwc2~(RwzjaL)Dm;R1ONzBm4APtGo; zPSRVp8it>?Sj0HF7+r$fg!zbvmCPW zm4bdmN_x#D!JKRwnz-;YOs1MJ>epE_*@I)#9LMLXYtswwD=ztv+Mth59DnAUF@XvU z6ko~jm+Il7J~jFxNW(-tbpF-MA^O3o&m#e->KUD8TRGzw?Un7pneXk$_%(Wr?(usU z_Q-th7%ioYbgN5wOBH!JE_p&VinKJ5rTZA^v!?5j7QLY{#)HS?t&Vi1-r>Ws&Inq-#bNOCz6@^lRlI?npZ@X|dhLv|xR0@w|%)rBmwd zC%i0{fw5Aj0%?}9O=|%cnxh)4_*+)`A{_j}Y;zH*`&7NuJJVaFS>x1Er^5?V-P z?+fP%%a6GeiC>QAigXH|a|O5Agq1z?T@($8AN+8+FepWt@JW+!Y1oCj?yK|30jZd? zm7tQQkZP%u>miFrTTUu5_brvye*MI{PAvR54zWJ!&Z<{8Ia~1_(a)ANyH=dsT?eHi z3+!~&6OO*htlu$1*RhBgvTd)3c&Sl8s~u(fuJFLcut(J6>+a1_Eg#`8?_59bblb+v zNW5+b45 z5Oq^xoqAEL&?d~5W7VRRfz17o!!yIgPuX7LTF#QC>u|Rh@ad9~}K+p)w_VEDABKfjPvww7=Hj%e{_6oe!p;w#hE69Vtna5b}{t zPb%i5qvH|26*I3YGXuoM`#`4_KFhCV+jJ0qI~e`=ln&E%@uhF~ zDU8)ezSNQ}D8@^5wKb6!wvODxb38Y~kK#cMVea3LoiK zzAjticf#{lDAn*i0|R}r%g6I&k0a>XxRevpZ!|Y66F)go;fE=EbT@0blm2l)#}d7D z;&3vmHfZgv5=efJ;c?n$o{t&Gy2k0i-eMqC*Lg3~^g|R!mf0!?139D2nf zLMP)TjgEm{e?)Q%Do%Qgg9mc9OnhJBAmrL9r?5wpXyW&Ar`D(KuGtvOWRi0)lpE0q#Gns_klb5BRckAmFwRYD|n~H+2ov){xF~UFYkW zaLA|n7`R_MH*Q>tD)m5tNdBPoRco!nuDBt$+za%GgRsO^}755eGY064A-R6mB+J>arftt=6TbSyRG{mzd`gIV&48 zuQF*aKUwe-QGRyVN%Q1G37xL&N1(T*^ zb!p*9%E7%Gb=@`K>`2Ejwxs4Otnc#Mm8Ph?FO1H3iQP4kizN4bXD?XRGc%QvsNOlAA& z6dPwGG40*hXwxg03%uAiFmKY#7-Qwy!Z^rpv-OQvf$C&$4ut$QJq?J=LDpj7CyxDi4c^2ZU>#yNed?=KUTBACYr#DD6?~Ss# z)q_~-MQiP7cwZJzlnVN(Se_HxUcD;GKalF z+MQdcHTM*8f3OQ@apm54Ss6;p*V?5jY_3ic&2eu}QW65BFhRo$!Vr;@nQCbm_KfiH zp-9!K5<;I-9q=bRi4kwI)y?#4qdG}B0%61CJsh@;S2LU3b9*^jG1`ER?#;uhX=7Na z+L5uPA}~jeKz^pVqXoe&la8ZGqfzR69b$ZG+wvQzU2cj6TB)miWn`IBGvu|{yK`BzJZa!=XerVJ5LnxaTn$RrNM!RBTUmrGo9EZ zEI#gYt%@7EK+qC-#Z8ZN8sc%_i{qskrWyJdBuis1_qn9m7$?F!-4s^L(z-_NXlOF| z|j-z+Q3?hbt+khu(|$>V7{@7#Fxkz`H*`hnEQ(W6QA&sngGq%@ zZ)t8|jm|2Mh2|BZ((qaKuQIo)a_I?j)X%+hZmlegdp{NHaM$q=KgVKHKD)*=WVXEkC4WUs8TuK^aY-<`BTrpnrIK6oOVj;2)o;=&4579(UbJy_3aeJ^LkH)T@? z;)Qj6|Kd0egVBxUqPc?_A)d0Flrm3X=0~qX%L?Wp8E{8xmnc>jGfa8%<<~PXJ?X$8jcAj%s2#w{Kq*65W zrAelh%hS75a$qjnImwp@CQ_9&3tQRCbEA?`1e`Kfox2s-VhV{o& z$%6ZRjy|$E@Zt!&k(7Uk76Ty*Az8oyzBuoZ4nI#1{#P9{@K_(>-u!WDLWctteBtUL zd`Gh#8(>0=<_*M`qCG7*o8G65IFs?v4iDup%{FA3@^{m>=XrWvrX=b-G&b!e&mX~A z5Oe$8@r{g7W@m>^sgjow3%a3GTB^a&!H|p)6TZeM2_E|j-W!h4^KdG(xARfXQLQ`~ z{}-Pyr$1X)=dx^kPH-m3iia>S)+|6DdUo~6s+Y=(WjOot?#;R+_(qDG_VH3K0Nl$p zn8BegG>cJ@Kc6Ivw9N5S9He|KYjr~t`Lg+vI6uuN=Oy?3ft;~Y52Zvr-0xrLxr??4 zNgp1QYJEd1+Zp6sMA7A7&?#MT4pBWOL z%(@4gi+(y{hq!N`32!n#B(o&PAa9a0UhA&Kb1h-Iv}kVFFY4A_E8AtFEG(Zh^RX#s zDa!^2FPqfGDlY3oMzD^@wr_>OC5D)gr;&c|bLH7eUspW1U5*}>pYie024{H``6|X; zJdx9T(CI+F{NNqNK9V|zM=DZvUNIq)RV=Ucl^z`DFdS2chr=Q%%DOm)n(r*}#9rS! zRUfJwoO4bo?8SS}k9{n!z71aB;$~N0|8_ytZtBkCIEoz2>v9&1-A|x#3X_s&=EX%W zTLjSt8N6)v`uJ?leppKr;~KLHiY-TgXOA;pTxGfrsl zIipqe>oHmBb0>-762y`)Y;qr7SG;PYTA$l63G8X6A|nyuDU1xHvD?=hjeYyl)|M{@ zx+ti51#Re*N2w?(GFy6})#?6RM9DqH8m~$6IqmY7jjM_?T}3gOt0fiUvsa5;!R~rF z>bj}@^DO@U9M+dg7GpGPw6&jJX@vO*i*wyKJyNYUr=CvTe_rd2i5j7AW2C%zLp+Uj z5Z5s*_?9R``o1FAe)7i01R2o7&w~@; zg6*Z{N|TP^^PlfO)CXsU_gAs&U3#W*u;V@n;~ICq)}@#16FmKTx{fA>W`53}u_Xg$ zPuID^j}kpBX>>nIvev{HB5$TpI9#b8xSne`>Ts~}PGdIB6CE?#fsg!IL@&Zt!$-PB z*QK>w)mIObTra?oMKXBUymhvvZMzZ1vGz*DPWYWmp;OZQ9YOTQXQKWg(G@>)x)q%w zM*6)E9*;?PPDD~vd1EGJo~X+>e|w`&BK+{g zOY{SZM9;dQ`{*-QQAK8fd41BYQZMVN{QYA`Ns42s_My-9jzpyq#XgY&4;@{Blo56G(La^XH-G3R;hL2^znfY1$0ygflU?;Ld-^1>`JDoIpAtAW|~! zG#s;ea;>-3bh*Vl1K5cJ*JhL)EnIO%2K+g@fV`oTvjPz8+0+7S!XqUF1ERMMukQ!a0!kKGV=O*gIdCl)cSMaZ zmNzuQT5nq66_=N13@~Qkem|dw%K+vQ z-0wHok9TZs3!oTZ@5g%~P|S|LK!7OxKi>PZ9t;YE^WWAM1_K;vw!;uWOrmWtz&T{c z^WaeAj_1K)IAap-_Y*G=I1qY&Ck$sn*;WsO^Sj;#6T}&qeup7ofH`Le47Vh<)kE$a zF9Lbo z)eabL?f*Uw6dDKxy&Z5ko%sKF#i5>5NLXbP=7r+W~``7?u*$&(T{-e9VP&j{&-}(ZDVsL@)w!s8}-fn}z zpg?T8?J(Gmbq)lP#~B-ce;y14gg)2~6T}%+x78EGvCZFMaM%udhQi@E^XRsEDBP9n zZ7?)00RQhW1kU8R1BSD2ZmS1J?dS^vfwSvwtB1zL9^DQDKK-!`hJ*ldLAS%8K(O-d zFa*xpi~Ieg7oZkkFWnBq;NmK5t0xFt@!keQ!GHh|+hK6Xj(4C?JJtdeh1#(eplHaB z^$WlRci;v1#@P-Wpb`!6%^@D9*_K``9pW!0Bx}3>e%_*v@)@$I|vWf&n2l zw&Mi`#LCzK1HO^6qb}Uvl&c%^jM1)*G)xsT%lc54Cc6QDnyex4@c0!pV;vlRhUy{(k`3#_Cl7 literal 17153 zcmd^m1yof{yFZ;Oogy3ok@9f*fRuDer_ynNqm(o#Ag!c;gdi#P0us{F3MeQ_Cy8Te~w?uwDcSUOq(ZBAnxY+P+YFa!!N zAwl8d>WneBr|=x|(WBI%(`Rjj9$-<8ICbFpiP+2iZUY2iV}Swk)I>4)VuJR>Dxild z1WLS(-I=zUe)P6dmlmHf+Lc`)=+tZL4#+wscPYT&9Yw#xD~X~xRZ(!Y$MUSm#g&_{ zM2@4k96(aP>NU5phcjaB1+<382Ny-H#^i5w*+%v~t?vsuuJ$$^rcF)TLS!y(zrcMk zp|;n_=!RXgQ;x|BMQnr=CxW;(OV5?#Oiz>Sg>}Y+P+_v|T=UlQ(8U$ft z(no9+;f4C#ZSVR{dsn8U3}p`#(sfO`I#N-&OnQ3+UT9DtP=$JBH$H@VkzpMC1uAJA z1Ohe)D@O6>CnK%h0$TE;22w2Jv{dJ%2SN_MyJ6h`eRj%2Wo?0c)8<~RXP_DfTZuaS z_zmWKwR(d6X?>(a9#xb}g_u^Pnof>}^g3 znk$XWZxOlPk1q=k$)AUJUbc_5${n|+Vj?VpY-zb zYdI2E!f*F@o+2moinbtit0st+Z{a6X9Pr{#?rKL_*i!#w*iu3Qit+${g6CGVI>89zJs(vQJ8dFuue_?Q zqn9Xevn~dEnVT2t-3d=va<4xUWROR&ES}DhKHEAh%C;E&Svr&kLET zmk;jR8@ea&4^VnrH*+qAhaWUkmxVnjc1xcQqI7Z~47#jWt(?-}^3=iLZrt+~CHiPc zfxF**^hv82e(Fmz1IC!z_{RsU9i3VI+m=Y9(+kFnbr;^WrE*>x4SA6qz$74QW8h=0 z^d-wiBBN~rZ+#3OuRiI+d!412DyGKvb2sB&Kap@;aX4=B;uvdv)Z37@e#LsVt8)#F z>62`vUvFbs1p7zt8?Oi2oQ}>eDjU@yElsa{=gG3r^=Q;sm)cf6r?RYL^t84?NfduT zj^w52BRWt06-3KyLi4@Ire4!UnCXmNZFymx>p~&;o7 z&VUXZj0AgRq|dWKG`b^Nv0lv%V-BzC&@>rTI>neeg8& zC6Rm`XG*z_T4_9CMwu2Cx5iPrm1+LbtQ&b?Ab^CyZ>u^gRZ792?d_;#`pV_t4fhdH zv}Z~%rPxjLuDq7}*rKtkO&3-vk{&H(Ile4wWl;%jT9eE16ytcU_f&Umo%1TFD^L4gby(HbvWqvv`B{!DTW#Ge{M9-TeY#)O?uVnQ9;^I~A5}~8_P7idMV_?Ynz(7vaRosUs$1PRmzS8_kPkad&}l_ez}Xcv3}D2mcR7$Y zv|1lU6dqnM1^cHfD$WrPwPv(u6>?6W;BroQI`}+r!DH;DV2}6%U*2L%WfwJ8a%V{{ z*BbDZz?gJ$t%VGy+S?WB9fsHnU-HDjoS<2%EW&H^j6|9wKCHu`PgegK&%D#E0%8Ri@xa6kVayD6Nlq_TDqQI2P?PC^13d$_%kg0FILi^ zUQ~xcEd1{|ZLN`Q&s&|y(`lS7M08tRSwFn>)R*oR;n(bNSN(k6wZbBs(^i>3U@73y z!C6vMn7~_jCL|JP(m+i#KFb2amV|wP1?ns>_k(Vw@mp4~75LwF(9o&jY zV;OPIh3e+ad$F`txq*WTb(TzSr)qTE0QzH@lHG&m`i0Ha&iq}+0gMHkC!xrAD9$)Va7p)5(Y0%?WbU#KOY(?k%Ssy>c zricXf%v!&U^>wUC4z(fj6;M|!&Td4j{!mY&JdYG3`ON62$y;!=6? zl1JR^Xm#|04fvC>8!TVDAFlGA`?{&(SS@N6dN|Bvy;S~&N6g@&+L*g^NFKQ;)vM=t z9#{HBl!)hYnlc(lSB_Ym@Z@meUFZ`F`&!n#JdR|$&d|?hrXrd|58eNmhB5YGyaUINV+#o{I?prUd7&bFzwQzPv<-O&@JZjRCjyJsBxR< zAfz#Nu-sA|+|_m=AoXsi;K3LoITPRF++i_FHVK`JLGhF&sqX!Wn7(%@TuU?~oQK(b z3zKX&ly01{|0HxDTiVp0FfgHVGf^Si`(Zm{N4x*&A>rb?HKiFD6{U(i=dYs}j|lP# z^7HcY$3|`uPLxQGP+%Oab}Tgz@B~WH%@fwG#pJy4@9CnYU=RzMBoA)~5o?%<+o z?rM8N3uEJEXTD=~+PHuaI~}B@9X&yYC!i1n40HkxL8Czkh%gKUN1|cIAR#FiON@gn zNEm_wY*=$AMGV%)))j;j0XpMG#?_sG;z~-c=5|<1DF+)n3@}Y0ZC8xF9!LZZ5;FMK z2LXrf3<#itfrD^Hvevd;tc?NQk1I(?e8&(9`L40T zkWgS52*l1`6ckq_j0PFPh2g;JM2wAp3_nz&t?28rb8gmySXkh&MIL*ebU5&v90T!K0wO?t9gD-0zgf9!eXb^lN#Jzy2jSmdaKq zkLAm|+@gjSkakhwsVYOfL+hxa`WTPf2KXmfa=j8%dL$0JfCp>eI=O5NR|LgfYiKK$ z3Ay-XDg3#`jg1f0i|AMMId&+_+MHkWU!sXac~!1LL*;y{RA?yU(nIN&LFpNXGsh2; zoATz!8z`j}bUM_02sq!zU1R^2mwRB~Nk_~4eM+u-#OF)K8;f8agJWa86&e#u`SpVl zMAn#|imzi|{Z;}}Co_V@Vn%PtN0v>`d_7RbC*81m(@8jaRn=km4gu{8gtLRZ+(j>D z71NrgXQwzH9IbjnADRnhnbt~cPPrjGee-eu5CsINv*-_Xt2I`BNb-KO-t4f*EE!Zm`pzxnuurD*?h``>Ia{&BJ9BT=EXRQ;8|9#%x+4ffE4z9SJ z-~uv);`WdhAS-knbsezVt}GPCkGuCX;^)k^_Yc7G^1xo*o-wYSkcP9PB~B0+3ISd; z@G6X_tMM-WM*i%-voZs9i*p!D+(!JqQ{^3Z~~nnfjUo^rv!b zTxvs{@bM-YXhimbdbcg{H@F(MM+^P4pyt^ZYDpT=eW3nBwFvu%tHs=Xp~ljP?*sK8 zszum8TrFDf3w0cgjZDBp8K&|F3(C|6{I>^A7p$E2_0ye>bSR=8cMv8sX_3rHb7L z;6K!d062drIZ$9I5(+|ZyXF7e{`lWOn56xiH?G$H!)5u7@M)^+`yl*>Y7mHG{vpCh zFaj{fkzh3Be?Q{!HxS;%!;HW4u*`l4BmPkPA^uqV?eMTL7y^Wr{sVY8?>Jn1y`vXI9 z>1iAfXniXR0}1Z!;!hqy{?xrcK7pgwZ5H68~;?w)ffcE5^-+bv-ozHO7oYR}lEt1=8^|!`1eA++R zGI-e9sXxvz&5WEbld@L`I0-{?tQs*m4$g@26s8q&ztewj6Vrb%`=M~S0diHms>ye- zae9GUoi{nVQ`xt5@GMQ1B!fme^Crxh(0Y`2G5P1I26y;>B!Dk1zBn`C8qK5gc!LeSAp} zVGp-JoUSjmin5fTphn*MpMYsM7gA8K4jhMfXC-n z7I|IFo-3GfSWzk5zCC3irw!#2f8+kwV0)fen*h0@k5zI43FaN^ZRn$U}(?DMn5&lcCaoveDtRz2a- zQ3h$(J!}k{7T0B$PD5hlR;kjW!=1M-epC?{_E$w^RL>RK3tbbtGZ1Y; zm+&BvY}wdw*r7AVC1nAP=WFYTk+~x-c*h*oo~M}oalYH$3C%%nk(1|%aX zObS$O`}hE3=7^}!ao5ht&#fPevzzg`(g(-v#u~ajARip?<%d%mu0*rv1QQ!vT26wJ zJQ=(7;O2dL$)F|6%>%kx6oVu>4icf|7aSxC>DGy_t4|}JC3V}09Y?hISxa9SAex>c zmmA^fb&PkD-q7@tUX^QF=knVl~qQhmGinrED61D5NG z6gCjyZ=U84vRpnVD=TW_=S~v%_U$`1gneQ9CZ^FHa%baZM;3Qw7KS&uDo_aH*@aU8{06ZN>6XX<0r%!_HGqfy?FHYHI5;IMZ;wl;<7#lvFc2WkzC8nxz-_UHqa#4u zS-0&rND$zOertmQZRahv>1fb)V14^p7_=Sv-F_AUZHFeepMgU&+mW-K0u(rz^!-i1 zF@xK#)Ky4RdGQ5gnWW*P{3- z(RV9>9dAg<3HZ$4lq?)70-Uk>cWQRd$T0eS6^-xb66y#dMRq%tXV2RP35jfb7^k&O z--5-Dlcpz)vK>bm++4RHTklP;D2erzU3yeyN0;38PU58O ztCM%C#2%nJUh=-H4iyoV>2v(Z(AjCLX~K+*h2&Cwv^S6yoxN4lI(%I>$2=|XX(8nG zhKAK^-_{vHL3Me}$#+~jgziU+r`nHNoCbH;a#Fk@NKOvHww4EDl2nGP4u&L#fBlMB zyCdDxeP0>Utu6Ahd1945o?Xt<*Xic`s=tAS`3(OmtcoOnA zLX|EkeiRmL=?f1P5i%Pq&KxdhhMe^#xl_=@cU@Tbs&;&YMR|1CgO1vWnN`qTiHMoC zq`ax3r}!npgw+;r3Jxr1dnx%^HwWiNUNby>mhNuuC~9K`+&5zYzQ(?F#ir{R-T3PB ztOl{sNXx}&&we9VCUeu-ibSqg)n7ibO)j{-93! zR&@8lpo9(c1L1dI^>B-Er$fxQMT?@kA}1*CuaXFj>evS|kqxi5XBBw$U8;Oh{7g=N zRyuZ=X)S@JU`jS1to-#o7eplO6^w77dhhTRpV@L9CksvK`|I}d6jyWCl0L?)v122B zyhp}d)(JO=1xnK@K8?E{ekH%WY39aSb)mxaC5oX0I*Bi3Bs36tzxMNoWb4SJgubA{ zHaw`|<7;cTQC)XGNX_!39J#mF6_PSI0q+R(KkO2Qv9TyHcebjyvZ?KuLhj%4qVMfX zPl~}>{x@sq8L%m|hfvEWuXCxmEZ-43laQBKnV|WeB6wvk!yt(ROL%8FgCK#R|FY4E z+=y6}LiW&Et%S)>_=MNd&uu*msqp=k!q0dgY8OtJ3VX`#OC@EjF8KJ60@W+yd)bt7 zZy3Hnsf3JSY2tXdbQsTdMo1jY4-r#d7V0 z$PYlqX75{l@;NA_>!!jLBKJU>kE*x#BjL!2sCm{WxfS-~J!eU}+k3wpc))K&I7T(f zeNQE^u77BfrnbGU)x(a#z0_gUWjz;)A*_XQbd*yU52&H@CdiZe=|RtckB&?3LjZ8;e8=Dm1E4zE?THr=^3`!q@_gJx@OBC_hP`@oRmqErUw0Bn}k z`|&Lw8>!0ETmqDDL$`)%M56t4n6M1gmKANg#522kdX63x)Zzo z5821Ds&ZGTy4n_-uQ@%FdU+Pg>9KGQSy($ns|QgncVdc9w1zY;JRv%GFM+y>WK@|< zKXCCC_#P8AnN`7z%nLP!^Ger;=nkfHCVMbR6JM})dfdanDSKtw8p7lB2_(Y9e2tr! zSPz3%l)8T8vE-A~C#ZF`z^?=9TbpaI&nDG8ALX7ue4()ANN>gI-aCZ1Rj9MiUx@Wg zBk}C48ZOP;3^!)S%qiNnZfLx|Q-&VX3yhm>81*<<0URg-Md=AdX2& zvIz70r{G2c5mUCNY0czob4&TtsB%)n+cVi`B>fWDC>iIl&}-5vQGK)d<{o4EDU9{D zRVP%oR>T>dl4qCAElm36mPxNvl3wtD-L%fz(wv=_5U?|7MWW-|JSkPnd^o1`vtl_O zx@nH9y;pTtTe>m(*_Bk3^08@=bJ)8mcDI+DtQLjbNgwATHG`iy=~yI_K%pNvoi9fn zRX%Mw_o2jzgvp?tTXusqe)KUT(}{b<=j^pJXvUl_z(SlN%&13l9lf&nri=6qX2t6$ zKE}Q-yL%=r;9|SX+ee@6jD6&K77Rwk#buR(647f24P(nO8j%Y_0c_S(wY^Vny9ii4 zKty+HizO%{K{W^M+^=#pQ=WXHrY|g&*m~LT1?DnSgemnGOM_!zhZ*O@_8x~ajK>Lt z(Zxq&Ou;oEjZqe<<^^$Is^f?1eK|`CZSXEWJy7#N{)4C;y=QzRfqC3z9n=^hh3S*6 z(8#5B`D@poa(Nm?+6*ol^gurZ&8Tm&-ZAd*uA<9*%ShzwH{|fb{R8QXc`BIAqZW}m z>bRBYdGB)}?HaJ7j4go>jO2$doi%T4{t<<{%lIWYC)cf-&)3zOv z?hwJZKy;9#Pp8<@vOhV={Lq|5tDi6yZzOq2^IFqF5$RC=JE{lwxQWZkZrjYzd4${q zQ&OM55#)Dh`Iaj2!SRx3nT+=tlWYsj#GlEtyf=Gg-Fe9dw3c(I>QSF8J_o&Oa={^$ ziR*)))9eoF)JsRw$XPkFBZMP3b7e2Ae-S-Tc(rPz`=h-7BNqd!(wLJg5{`N_m7#(s zs5VbJ1?9b&Iz{QjUYZ_upKU>8M49x1&k{yQxrm&@l9oE=RHO5vqyB+Vs?CmGP3p0m z3(E5ui7bolRwPCK&o1}A@;*(_ayaHxX<ft>`;vvdT@Lq?@ue0dddR+CRmT z-S6%b4zaU(8g@0*UpZ}*LgUHQfw63w81uOcp5>|`9Pzw1UsL(t8JY4Abj-35@^TKd zDp^z;9H*Y*3%;D2=x)o;eIZrrc7>z)V|`A!1m1*W&oL)OoGR!-3+PRFJMxuXY2RGt z70;*j%;e7G?@`KEe@4%uTgIKk_m+}k9mO|d;cMjr=FLWNm?PI&(um&_bqEO!JE;s7 z>gYG0AAqPG6+G2c&(@nQXzTTa`>~3%m`r1?XKEKpM0FZYln!#(y7Sl9cIy(M!_Z@k z*5%^#h-llgQI&ZWI`4+Y0?xA>EXRq{Q%W9Y3j}4Fpv#hcn(*aVRHG)yhx%m56{^g} zra!d>yf`!~a)p`D>+r{C{`siUnT%?}+~@XmlcT7ihAUwc@0|p4SRSbf>8?f(obBjZ zqQ?_*>#Cej%XXJUz7jVVu!pBf&sM=2hwaYXy(o5*Wo_QAMzx8iCjTMPgor%3{^8GO zWgM5!#pPu(me1$2zZpP749!lJYq@pJab2O_e9$p=V7gy2QC0kDbN;7c7j2;~PVzWj z<_HVjZZ&-K?gEP_CKhc~6iZw_^A!zU4e#qxoFHAz!CMjczLbZWQ-p-3@bkZZ#Crv- z`|w!&QO=t>nwa4u(bSpjRq718vHu!&t29>Lz~{HnFU;=|Kkg5Y}z{cfYjZ`}-K>#?xX3&qQ$ zCU{HKH}&R=80VX6OmbJ#n2AAbm&<&HMjqF6+l6y6x~;lyXXGBlo<`zFA0Z3xuD^Qn zj`l-;YAVUY^#%Fikxu&Z>a-MTP=aS>6_QN!)-5v51BI*oAM|}{T8`^;xf(ZEIvVIek(6tgmL}WpabcEdD&7bYAm9kMMI{CX}ho zEM_q%vJ0#+b)N-hh?@K0DQYJ`JUS5rL zDz8LS#_dXkKXvvwY{(~1o<5238T91LaoTl1a{AYIT8hCDC9=oHO~Zu*p1pY$RuO%* znxX7XQ|O|iKAq#cGt3N#%M!Ue<(jXnMkE?HX^thaWrL_(d`bWqc`om zS9@=0-UFLnD!mpRm*hpXmqc8BoilL%4_ZBQF7@jbky8@3#7iUY**%t{_o(nCy##N@_jQ}<=7o87e{oxpY@~&ms2dH-Z z84YtAj0?_jbpzZVD20#;)(SWv4npque#X0eA>^*S2jB$($2v8fvF+k-vj5%-{#nA@mi2)P( z=7?e+JiG%7$*aM8$$#aH~N(( z41?@L+dF4rBx=t(gi*M-(r@n*!NsY5r=j=YCjvw5rNMDwr(gSupm1@l-)X?rvfpVU zz&*NOX;27k4I*I{ySemk-|UZ0kGd( zoy~zedCnAKViZE!SZ@qY4hd;FI=X_kWh)SQ+>x5VYqkSgK-S0H*>ziHL4gefqd0a< JPF + + + + + + +0 0 m +-1 0.333 l +-1 -0.333 l +h + + + + +0 0 m +-1 0.333 l +-1 -0.333 l +h + + + + +0 0 m +-1 0.333 l +-0.8 0 l +-1 -0.333 l +h + + + + +0 0 m +-1 0.333 l +-0.8 0 l +-1 -0.333 l +h + + + + +0.6 0 0 0.6 0 0 e +0.4 0 0 0.4 0 0 e + + + + +0.6 0 0 0.6 0 0 e + + + + + +0.5 0 0 0.5 0 0 e + + +0.6 0 0 0.6 0 0 e +0.4 0 0 0.4 0 0 e + + + + + +-0.6 -0.6 m +0.6 -0.6 l +0.6 0.6 l +-0.6 0.6 l +h +-0.4 -0.4 m +0.4 -0.4 l +0.4 0.4 l +-0.4 0.4 l +h + + + + +-0.6 -0.6 m +0.6 -0.6 l +0.6 0.6 l +-0.6 0.6 l +h + + + + + +-0.5 -0.5 m +0.5 -0.5 l +0.5 0.5 l +-0.5 0.5 l +h + + +-0.6 -0.6 m +0.6 -0.6 l +0.6 0.6 l +-0.6 0.6 l +h +-0.4 -0.4 m +0.4 -0.4 l +0.4 0.4 l +-0.4 0.4 l +h + + + + + + +-0.43 -0.57 m +0.57 0.43 l +0.43 0.57 l +-0.57 -0.43 l +h + + +-0.43 0.57 m +0.57 -0.43 l +0.43 -0.57 l +-0.57 0.43 l +h + + + + + +0 0 m +-1 0.333 l +-1 -0.333 l +h + + + + +0 0 m +-1 0.333 l +-0.8 0 l +-1 -0.333 l +h + + + + +0 0 m +-1 0.333 l +-0.8 0 l +-1 -0.333 l +h + + + + +-1 0.333 m +0 0 l +-1 -0.333 l + + + + +0 0 m +-1 0.333 l +-1 -0.333 l +h +-1 0 m +-2 0.333 l +-2 -0.333 l +h + + + + +0 0 m +-1 0.333 l +-1 -0.333 l +h +-1 0 m +-2 0.333 l +-2 -0.333 l +h + + + + +0.5 0 m +-0.5 0.333 l +-0.5 -0.333 l +h + + + + +0.5 0 m +-0.5 0.333 l +-0.5 -0.333 l +h + + + + +0.5 0 m +-0.5 0.333 l +-0.3 0 l +-0.5 -0.333 l +h + + + + +0.5 0 m +-0.5 0.333 l +-0.3 0 l +-0.5 -0.333 l +h + + + + +1 0 m +0 0.333 l +0 -0.333 l +h +0 0 m +-1 0.333 l +-1 -0.333 l +h + + + + +1 0 m +0 0.333 l +0 -0.333 l +h +0 0 m +-1 0.333 l +-1 -0.333 l +h + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +-0.7 0 m +-1.7 0.333 l +-1.7 -0.333 l +h + + + + +-0.7 0 m +-1.7 0.333 l +-1.7 -0.333 l +h + + + + +-0.7 0 m +-1.7 0.333 l +-0.8 0 l +-1.7 -0.333 l +h + + + + +-0.7 0 m +-1.7 0.333 l +-0.8 0 l +-1.7 -0.333 l +h + + + + +-1.7 0.333 m +-0.7 0 l +-1.7 -0.333 l + + + + +-0.7 0 m +-1.7 0.333 l +-1.7 -0.333 l +h +-1.7 0 m +-2.7 0.333 l +-2.7 -0.333 l +h + + + + +-0.7 0 m +-1.7 0.333 l +-1.7 -0.333 l +h +-1.7 0 m +-2.7 0.333 l +-2.7 -0.333 l +h + + + + +100 204 m +4 0 0 4 100 200 96 200 a +96 100 l +4 0 0 4 100 100 100 96 a +300 96 l +4 0 0 4 300 100 304 100 a +304 200 l +4 0 0 4 300 200 300 204 a +h + + + + +100 204 m +4 0 0 4 100 200 96 200 a +96 100 l +4 0 0 4 100 100 100 96 a +300 96 l +4 0 0 4 300 100 304 100 a +304 200 l +4 0 0 4 300 200 300 204 a +h + + + + +100 204 m +4 0 0 4 100 200 96 200 a +96 100 l +4 0 0 4 100 100 100 96 a +300 96 l +4 0 0 4 300 100 304 100 a +304 200 l +4 0 0 4 300 200 300 204 a +h + + + + +96 96 m +304 96 l +304 204 l +96 204 l +h + + + + +96 96 m +304 96 l +304 204 l +96 204 l +h + + + + +92 92 m +308 92 l +308 208 l +92 208 l +h + + + + +100 96 m +110 96 s +110 92 +106 88 s +116 92 +118 96 s +300 96 l +4 0 0 4 300 100 304 100 a +304 200 l +4 0 0 4 300 200 300 204 a +100 204 l +4 0 0 4 100 200 96 200 a +96 100 l +4 0 0 4 100 100 100 96 a +h + + + + +100 96 m +186 96 s +186 92 +182 88 s +192 92 +194 96 s +300 96 l +4 0 0 4 300 100 304 100 a +304 200 l +4 0 0 4 300 200 300 204 a +100 204 l +4 0 0 4 100 200 96 200 a +96 100 l +4 0 0 4 100 100 100 96 a +h + + + + +100 96 m +110 96 s +110 92 +106 88 s +116 92 +118 96 s +300 96 l +4 0 0 4 300 100 304 100 a +304 200 l +4 0 0 4 300 200 300 204 a +100 204 l +4 0 0 4 100 200 96 200 a +96 100 l +4 0 0 4 100 100 100 96 a +h + + + + +100 96 m +110 96 s +110 92 +106 88 s +116 92 +118 96 s +300 96 l +4 0 0 4 300 100 304 100 a +304 200 l +4 0 0 4 300 200 300 204 a +100 204 l +4 0 0 4 100 200 96 200 a +96 100 l +4 0 0 4 100 100 100 96 a +h + + + + +100 96 m +186 96 s +186 92 +182 88 s +192 92 +194 96 s +300 96 l +4 0 0 4 300 100 304 100 a +304 200 l +4 0 0 4 300 200 300 204 a +100 204 l +4 0 0 4 100 200 96 200 a +96 100 l +4 0 0 4 100 100 100 96 a +h + + + + +100 96 m +110 96 s +110 92 +106 88 s +116 92 +118 96 s +300 96 l +4 0 0 4 300 100 304 100 a +304 200 l +4 0 0 4 300 200 300 204 a +100 204 l +4 0 0 4 100 200 96 200 a +96 100 l +4 0 0 4 100 100 100 96 a +h + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +\usepackage[ngerman]{babel} +\usepackage[sansdefault]{fontsetup} +\usepackage{ngutils} + +\renewcommand{\theoremfont}{\normalfont\bfseries\color{dark blue}} +\renewcommand{\definitionfont}{\normalfont\bfseries\color{dark gray}} + +\newcommand{\labelfont}{\normalfont\bfseries\color{dark blue}} + +%\setlength{\leftmargini}{1.33em} +%\setlength{\leftmarginii}{1.33em} +%\setlength{\leftmarginiii}{1.33em} +%\setlength{\leftmarginvi}{1.33em} + +\renewcommand{\labelenumi}{\labelfont\arabic{enumi}.} +\renewcommand{\labelenumii}{\labelfont\alph{enumii})} +\renewcommand{\labelenumiii}{\labelfont\roman{enumiii}.} +\renewcommand{\labelenumiv}{\labelfont\Alph{enumiv}.} + +\renewcommand{\labelitemi}{\labelfont $\blockfull$} +\renewcommand{\labelitemii}{\labelfont $\blackpointerright$} +\renewcommand{\labelitemiii}{\labelfont $\bullet$} +\renewcommand{\labelitemiv}{\labelfont $\bullet$} + +\setlength{\fboxsep}{1pt} + +\newcommand{\bk}{\color{black}} +\newcommand{\wt}{\color{white}} +\newcommand{\bu}{\color{dark blue}} +\newcommand{\bn}{\color{dark brown}} +\newcommand{\cn}{\color{dark cyan}} +\newcommand{\gy}{\color{dark gray}} +\newcommand{\gn}{\color{dark green}} +\newcommand{\og}{\color{dark orange}} +\newcommand{\pk}{\color{dark pink}} +\newcommand{\pl}{\color{dark purple}} +\newcommand{\rd}{\color{dark red}} +\newcommand{\yo}{\color{dark yellow}} +\newcommand{\tl}{\color{title}} + + + + + + + + + + + + + + + + +192 256 m +320 384 l + + +192 256 m +320 128 l + + +320 384 m +320 128 l + + +448 256 m +320 384 l + + +320 128 m +448 256 l + + +320 384 m +576 384 l + + +576 384 m +448 256 l + + +576 384 m +704 256 l + + +576 128 m +704 256 l + + +320 128 m +576 128 l + + +448 256 m +544 224 +576 128 c + + +576 128 m +480 160 +448 256 c + +s +b +a +c +d +e +t +2/2 +8/8 +5/5 +0/1 +3/3 +2/2 +0/3 +1/6 +7/7 +5/5 +6/6 +4/4 + + + + + +448 320 m +576 256 l + + +448 256 m +576 256 l + + +448 192 m +576 256 l + + +192 256 m +320 320 l + + +192 256 m +320 256 l + + +192 256 m +320 192 l + + +320 256 m +448 320 l + + +320 320 m +448 320 l + + +320 320 m +448 320 l + + +320 256 m +448 256 l + + +320 320 m +448 192 l + + +320 192 m +448 192 l + + +320 320 m +448 256 l + + + + + + + + + +v_1 +v_2 +v_n +e_1 +s +e_2 +e_m +t +B(v_1) +B(v_n) +B(v_2) +r(e_1) +r(e_m) +r(e_2) +\vdots +\vdots + + diff --git a/übung_2/ngutils.sty b/übung_2/ngutils.sty index 2dd431e..986bd5c 100644 --- a/übung_2/ngutils.sty +++ b/übung_2/ngutils.sty @@ -42,6 +42,8 @@ \newcommand\oh{\ensuremath{\scriptstyle{\mathcal{O}}}} \newcommand\Eh{\ensuremath{\mathrm{E}}} \newcommand\Var{\ensuremath{\mathrm{Var}}} +\newcommand\argmax{\ensuremath{\mathrm{arg\,max}}} +\newcommand\argmin{\ensuremath{\mathrm{arg\,min}}} \newcommand\parens[1]{\ensuremath{\left(#1\right)}} \newcommand\brackets[1]{\ensuremath{\left[#1\right]}} @@ -61,6 +63,7 @@ \newcommand\algt[1]{{\normalfont\scshape#1}} \newcommand\com[1]{{\normalfont\itshape/\!\!/ #1}} + \newenvironment{algorithmic}[1][1em]{ \begin{minipage}[t]{\dimexpr\linewidth} \bfseries