From f2ee389e5d3fe9a9f18ab3635d6562bb7ab1ca52 Mon Sep 17 00:00:00 2001 From: Never Gude Date: Sun, 10 May 2026 18:45:27 +0200 Subject: [PATCH 1/2] Formatierung anpassen... Ich konnte es nicht lassen --- übung_3/aufgabe_1.tex | 37 ++++++++++++++++++++++++------------- 1 file changed, 24 insertions(+), 13 deletions(-) diff --git a/übung_3/aufgabe_1.tex b/übung_3/aufgabe_1.tex index f36a6d8..870076f 100644 --- a/übung_3/aufgabe_1.tex +++ b/übung_3/aufgabe_1.tex @@ -4,7 +4,8 @@ $$ T(P)=\begin{cases} 0 &\textnormal{falls } P \textnormal{ nur 2 Ecken hat}\\ - \min_{i\in \{2,...,n-1\}} [T(p_{1,i})+T(P_{i,n})+ \textnormal{Diagonalkosten}(i)] &\textnormal{sonst} + \min_{i\in \{2,...,n-1\}} [T(p_{1,i})+T(P_{i,n}) \\ + + \textnormal{Diagonalkosten}(i)] &\textnormal{sonst} \end{cases} $$ $$ @@ -14,14 +15,18 @@ d(p_1, p_i)+d(p_i, p_{n}) &\textnormal{sonst} \end{cases} $$ - Die Kosten der minimalen Triangulierung $T(P)$ lassen sich aus der minimalsten Summe der konstenminimalsten Triangulierung der entstehenden Teilpolygone $T(p_{1,i})$ und $T(p_{i,n})$ und den entstehenden Diagonalenkosten berechnen.\\ + Die Kosten der minimalen Triangulierung $T(P)$ lassen sich aus der minimalsten Summe der konstenminimalsten Triangulierung der entstehenden Teilpolygone $T(p_{1,i})$ und $T(p_{i,n})$ und den entstehenden Diagonalenkosten berechnen. + Die Diagonalenkosten unterscheiden sich, je nachdem ob eine oder zwei der drei Kanten Polygonkanten sind. Sobald ein (Teil-)Polygon nur noch zwei Ecken hat bricht die Rekursion ab. \points{2} \item - Man nutzt die Idee aus a.\\ - \textbf{Tabelle $A[i,j]$} speichert die kostenminimalen Triangulierung des Teilpolygons mit den Ecken $p_i,...,p_j$\\ - Für alle $i$ gilt $A[i,i+1]=0$, da diese Teilpolygone mit nur zwei Ecken darstellen, welche keine Triangulierung benötigen.\\ + Man nutzt die Idee aus a. + + \textbf{Tabelle $A[i,j]$} speichert die kostenminimalen Triangulierung des Teilpolygons mit den Ecken $p_i,...,p_j$. + + Für alle $i$ gilt $A[i,i+1]=0$, da diese Teilpolygone mit nur zwei Ecken darstellen, welche keine Triangulierung benötigen. + Für $j>i+1$ gilt: $$ A[i,j]=\min_{k\in\{i+1,...,j-1\}}[A[i,k]+A[k,j]+\textnormal{Diagonalkosten}(i,k,j)] @@ -33,21 +38,27 @@ d(p_i, p_k)+d(p_k, p_j) &\textnormal{sonst} \end{cases} $$ - Man berechnet dabei die Einträge nach nach wachsendem Abstand $r=j-i$, also von $r=2$ bis $r=n-1$. Dadurch sind die Einträge $A[i,k]$ und $A[k,j]$ immer bereits berechnet wenn man den $A[i,j]$ benötigt, da $k-i Date: Sun, 10 May 2026 18:46:23 +0200 Subject: [PATCH 2/2] Aufgabe 2 --- übung_3/agt_übung_3.pdf | Bin 34805 -> 38725 bytes übung_3/aufgabe_2.tex | 19 +++++++++++++++++++ 2 files changed, 19 insertions(+) diff --git a/übung_3/agt_übung_3.pdf b/übung_3/agt_übung_3.pdf index 2746b6e162e9d3ce142e5bbbbff94726e5c372d8..8e84eaea4d75f86a9a46dca5c654eded401bb8e5 100644 GIT binary patch delta 28411 zcmV)PK()X1j{?Q60th8gL`E$!E;o?~HUTh`krWkwy;{qT+cp&4&sXRN!jhNdB?$}+ zIDRa$D>}QNs}@}~i>~_nJ$y+NMN9SsCEo|AHA(!b zNpTRGd2*6P2x|KHF@1lRQeC7pK}wBJOH#7Jca6{UNm=}EB%VuI!$X%-UDo>ag`CGX z{WTtc%m>sJfNb4?&)XVUTx$^l%I_cFK(>-VED?}65vqUOQL@bPdvg5c;)FXlGLYtLrqaxM;Y;2V zKbaHM+sE5KGiYOjAQL9*g7DH$fBbm+{yTp86VJCv3h(svZ`%7~vQjvQx4);~-hS<1 zu(y+idW@l67}&2x&;`cVkD_%YMUePwHDSCHffc}dVZ*Emc8&f<$AS@(+~!ymao7rf zz{-$h`a1CgAp!=}@q!SO0D>JEq6bVksnrB2gvtidiJ~7_hL#;3kB73E8HUzvv@1oY zFECQPIj(Qoo>(TU!LImX&gJMmgGnH-Wu42$8CTj=d^mltxaMDNUBSQ7p35p_Z;U{b zI}~p;ys~iR9Lx_&Q;?u`m0PW{m0OvAuzyMD5iGFj%tF__+l7EZ7S!uDCM&fsbFBixs_%~(mjhyd((5%p z*6gc68$zVsfYL`4SS6GS8w&2(aIzI8Cz{`gi{V}hl`98G=1egy)HJ4eY&TV8up3~X zF;^SDSAO;61Z(`QPJ0-D2D=7H(D-uNa*$Ax=GT;;_5_&R{GZDqNOMTn;-7ZDGeE=jJ3(_NsnHGh{3*6x=^(ilSZk9Os$dV$=d&agV2=fuS3UOURMm;;^P1`a4HT79eM~h9?pKlyD(s>1oCHkuS?$4%opmp3Z;kYI z^#QHdcFBcDE~bQa8(v4L`APmY+8>Wn>_tMfLYQU$Y5p~#_0wj5gZ8Kf&{k+k1OA_~ z+x4ku(j+?67y&g}N0PKjld0>A7E4Hs;c;RtyNqqyCATU-%jd0er1`8bJ*25E*c0tz z7bBSD1wB-l(@_F{rUyZ$Ef<;Uq)Hrjo z@O+PiHePG$NjP$il&j=MjLjV9AnTwa_5SA=j|Br~#tplFSGzC@Xx>mdzsNX(HaZpF zVZ5`_#ftW<^s)Wv2i?pgyN;tsYgSQW6^0LcpE{Ay)yv8+b?A0qAj$iX1`0^-G)yu% zryh1^3#Do=8I=s($hA_u9upR9tCQPU-Ddqb1kd!kR*Ds3g>;)C$viMGr@4uayxP;m zuCf|0ApA*xhxy!Crp}45F6kFITvldXohx*@EK$~O_(vwR_Wg-C_7DoUQY^MB7x=X> z(T#5HEY(>`btPrzL9CUxGDdic-U!Wh)3`;CX;040Lpd`l2wMC)Ysbh%JFm|38h@Je zUa_O**Hs~wM(sL#X@YyHoGj9=yq5E2d|y0rcs+xE#v4&||9VDi)R(+-KNDwa)Z+DI~S^@)uQZb*tQtxju}xK__#Hfr5vp*vJSrDWzuN2SbYS!&(Bkw=&`P~LBmV` zd{hB{DKs<+siFf(l&8h199{+Gqe-H2@meDE08_25nyAv`hU8T#Z>wH}scPNNmru4n z3HHy|ztqNl)4(0X%yE2!(DXdBeyWOXjHF(|tqpD!`5wf@{aTEW+|X!kh}$m!wL!%T z+mT+(mzz%%ybg_ek7_Y8d2gQUoTZP3FS;jxXexuMtFP^& z?Z#HeZs!rBd=JVq9xPnTlGX!Lnr@SF9--`<3)CJZ^+}Su$*rEE3DmXV>Pb5do2t~ z)*_+{W7l=zoyC%ZUR(TJS9k9<1hkHRZketBW5B);@|5gj-l`jkt5@9+e@?rWN@?4b zpb<|0heIhAZn;}3!&j6F{{dtkmA{kY2s;EbFgG)kVIvfOy<5w!Be@OT_gDA_Mv+KS z58%RppNrWAxx2xv63i;S$SS`d>RBqOTq=8#pmE`HS)wRD4=MHa`^R6NXirKCFZti; z`;Q;$B>A7>cU~aj$!a64hST@Y({Eo=f;}tApLZuE;raLPUzvo1Z4%&w2i=p<*Yhu6 zEkCJecyi%?-G!e3_(|Tv6NX!*`}r4TOyr&4J_^_Bkx46MwrP7QwDUb}{m3jn3u`QAVUYi=H>ia-_GA@*s?PJi~j^XGLGh2()RXy}f^QP8c)npNDPi zJAJcxU-A<7wr{TBg)-`7SgX?b|HqC%YC+ESOCH-%XXKTp=D5ICVw@F@Y^DkB{$dmf zX1k1k@^X8WaSeaqUaV+HfH5;#q=kcpujhIc8G(|RFE5;29Fme$NbNc#aKv#zo@^;B zs>LBEYOq##ulhw7@z0j!c|hZ`m&vjogy#6zFMFAI9(mzu6j2WR)h_SR9w#0Jyql5K zttNoSfdnw<&T_!k^r`NwVn$sRqMzxG7v*4o&@K9g?)c@f=yk3+E5}8TYOWK|pV3@L zYD;t1tT|40GtH3|;LN9*BN9gYw>7t3^j*z$iyqZnw`gbGaD4a3S=loKZ!&_YIPl`f zyGIQI)wt{==Ab5_joaA&G0R;~BfaFqCHJjNtH4x)R!CK6!Xw*zK$tR^q{fspDSv8z zrmcO>wI*zwB#)H$GcVyeIHH6IyVBZ$?-f#jGGkwNJdbr}dr|V17N6e~Jz$*I!}}ButVz** z9~-f?DyMo{?ry!YZ%M@{`O_;`rE8A)Krlqd7_*zcThZ+EV;FjeIJzc(80GfJ zehI!m=m5A;arV zBhzyLX3iMLI#AW{bpqvVYi$pv<~C9pRou@I(OAiIvgzKLrJhPNBdvROj_|AH&ubgU zE1tQnjXb>#P1Pm3*RcbCcc`1Fe_!Z_N>A5#znX871Ln-lZ&20WOQ?118RCnb5lF5zHt%6)Ak3F57G%ue&Y4re3KPpkPJOTlZt4)Vc~-Jt6TzNbAY zdww_w>1sz%Wxa2IN8p6hwkNgG)V>~RJV@S_8sxMp{Y?sLvDB%J2irE-*=)@)aQZ-}M*EEr0+wq*56^14~_43fOb1Kb$I@PY97P3CM642i>7xc*4 z1qM!LrtBF#vS0L^94tUIR|p!1>H50Ass_vZH^a0y5<|7bkRYu2B(x~hj5~W065ZL* zS8FS~2|;TVY+p-oDptqd>0Ne?LZfs$qNV2KSWMAOiz_T--XE$t`y^;%N0%F?x2mLZg;^rIi}ru0nsoH#Rr64KAIlLZwfR zxEg2XcWw}+=(m1YO`4GvYMyQ4!EsU3?5vPjyS^9qG*lQFYmaUk+k~qi0Q(}laouUS zsM{TX>>_N_n>JOon#;#yw1oDc#Ynpi%$IgX+qf;5zaF(x8Bqa2EsE=EOOh_sn#y6h zmC@QpOd1L3wuvT=J$fva=U;Moj^AK780hTy+15$NQaf@LgStXfe|;~tTP}b)65FZ$ zMXfyv!0Gx}x4;beDbIx&=waHH^k(oi@jP#To3!25CGo6q{%4gryP#69wX`2K9A`=& zX0xtqbu$m{T+4?tu3L280^ke}W|;QE)s+>fXq5s=Sgk#zpq?618k`g?L03K!! zowfJ|TU9sxvL+Fl*{&0K;E^(~wg*nv}V=+g6 zG)%kKjhEC%LzgqjlFrt@Oa(kj`>*CiIL;y4^=7wmVvwUX3p6;0KMT@pYT9KdmsM}_ zgT@9Z4n(Y$j=9eo8^GQe&O$n3x;D8cypR*p>3(|bR>lMA2dr*xb;nW59e`%sb7n6j zh6O8dqWxnR3|C~`pF4J86>$lx|LezpF5Q-n9=r6@Zm*ABKHz*qgiJ)a_m5pXomlu7 zi=|~3;mV>9&1%abr#Xr{Luu*y_yraU2~U>%MvvePZ5T%67|&QDDc z_e)t;k(OHy31*h*QE;XSEmb3Z3mcacBsAIILur(wSIaOA3_}7jQ5+-FIp%DCGu{H+ zyxMZ&RA@uFSwKxwyz4|I5CH?XYN@jG@6_bM2yd=y7*j#Yz1?k$k|8&3UmOZIVdUzv zS3S5wx5mr-#;-3a zl!{j$jiiTk`VLkP7?XwFZCdGBkJbv{Ak>NKR*rOsOZ635H?DSXN4x}_;bc%-H?)ni zGodW?7Pax|GPVO5N%tNQ-wa2@@om@WE^mViVx#BF(1^|>I}J6yF}v=6$!QmLzwOYx zqI8!o++|Dm8S{yE17mRYpALd)P3~i8$;B? z2-`F?E6)LUPl2ps2x10*vZZRG(uD)rUkF{Ux>x^>fd1LURF@+ysCtWOyMvQPw4JBu zXKCK1_iWpem0ZBJ&4OAtDEmK%-;=XtC0qcnYoWN%_>3Nn)~9Vr4aGLw-M6@QgiyN>HP4DIJD z`~$0zL{SeQFpx>&;@0UF+iti2-!4UoGUYgT=3-z>B2y%Fba=>oJwHA-NQ<+kSo&L@ z|9-f|(x0QXVgO-DA(|BY^89c4`(kZCdam@u^)DYXt@s;#^Ym=iBFdXmZ6D1RajfwB zYCBenwRfQZp?$`%I)A)~C$VgCR$q6}i{Dt)Ofa&=G3H}<%Jd#q7sTGR*v%8U-(zC8 zn7rM2KYdQ!$CLr)eri}_-C^(RKhIyUxB?hgV8Ydt59f|3J5MV>D?k{5TR9K=ShMBz zm9iIDB8Po(QV*b=onBenvmFBqDD@HH|t zl2g!YPiOKEd5r_}Jkst_1GJppVeX2FAxxNe$iTDLo80coS>e}<#Z|MfuEM1O&$;5T z>j?1^$0~N_@cCqwucJb28)h2S=Ku5(Zf?H>%cdxlol-uh`*01Cq=r!TRsc}=<6B7+ z^-jUH(b%$s`+wNe9@%buY2Kd{BrtDRU_ILN{>9xDzVw$n=mr+;YFbI4HR#3aZAi#FqM%4 zZMMWQWO?ucYzaqTOE@ZXK}8!pRmrhWDg--OaJ=bCOn)jVD`!>Bv4kur^>IBr_{bji zD`$|ul+eMHgJ=~f@a`k(ZFN8Qum|96|WK+W_y?6kody>7?^WMIC z!)~@(mmy5J%k(jO(!<<)RDB?68v>+9=OQZ9#@?X!Uu8^{c z(H*9)A7BvzIq>cevA`27?s~fJ8aB<6bis)GkEYgH;!j`*E*Z4pdl;YuQ*t?hVHgHu z^8(3}Uzk*KwgZ}^ktS*9B8}rCv}*G~e^8T08cqn`#};Gc664Kz7=ooYP&Fd0rRx2G zRZ#4;9^TnfZ!Cu70|J4Bkk0_}O9BYI0fWS1X!sGJQNRF_8(Zh@Q_xb|qdIB1cC^;k zN*x)lJ*Bh5kjfev z%chsK*1XVY8Xv=}L8{`TMf^H3uL|Q;68`7mqH{4epM(o z{VY0SzjVFOrSC}NLLrTBXn@QI*MOK5gOe7Lf&rr`&TPc47l}{B=MfBh4 zNAzQQiT*JnHR5H7NGxQCR*6=H3B4yp1){6s{o?Ck+rzF&awP4NpyW|_R(Oz#rV`f! z$ER{)j>8k2gj>VM@qpCjO%nu3kir)MDf^wGjLRYDSby(m9 zID`}vKwfMhNsZf)r|y62vy`H@>2mX@fd2@1y>q^07}-6}?-jw0Nu{fj8Zl263L<~c0T$sEfFl8~BWrt7 zPX#(Icn8lR#XY~j^AcQwvFb6iuW(S?u7ll>w9{0Ax(lhZT~lKhU;$c^;W&_$4`>JuSYzr)F$Gzz)-Icu_1OpD19*4ZH;SOM)J+{>Y<3eMTWRMv zciZu5h?y)Md_|QBTlUn{AjRVaT&`pWEF+`+1Eb??KciyUlAIVB@$m7%`*^h+hhs(3 zSBfCfhqs^TsAy^UCwFuD>}MT*_yj(J?*Knhcd^l5J9d8%UWb$n(^1rIp?vQ1y}d93 z@G6i@IMPU>%J(B%+MXj?q1JmieDM>d!Dk%3@YcD}5#!kcRbG)PFGgmse!yQDk>jv$ zp1ZFI`W9Cz-OZjRUtM3l+Xh4_Frlb=X)iP&SIw-KQUqJD0^Xmr$0i3S#GZ*19 zOyBD9p<;g@RaVNfjIiG&9hGM`&AoiR!E@5-?LFUrdurz5P!|GE<}g)Um7Pa^Pf}1l zxOh$NY4U>AUPsA3tGI*bf^w{w-})ssK2+Rt@=q!I3aP>Fx4L>@2pq3MJW|ZTOU*~^ zWH;)m{d9m*+-kZ3gD@Ma+KK7D?rYPPH_zU;WMO5u8 z1FE_<+h_qB*xXIS&D}5qlgJSPpEut<+Gp#}KV^heNII0uqQ+LLvB%Es1H?dP?m<10 z;ivI2PK>|jBmsO(iKodl&A9+y#n<5!M{WY(>DTN)u92&uJM=l;cvJGh10~e7);R0X zN6&v#?KLMWp%VU(b)dwEd^T!!q32zpvKyIqPMoZLqttaASkT%a9|>d|juX$|ILXWv zrEa(&5Evc~1PX?Ax`G0oN=D8Q#?NmU_8$A}E&PXOM>4(g1 z^*9QU)89aA!2V{vD`)aNuE@Gk>9u*vT^@f|kH_tO`$j&l7@KT!wZA#{pHvbB_4P*c zVf_%9Fzd=KY-2_<`ibAbvflvNr8GDr1c$b^A>XBOBcAXDJOkd=DF+&j$Z)W&!^|kh68bE)t z_YZTpIMl?quLy3pajTN-z)un--l4*297&_eS|F17DlA9*UT$eGeFn?1WFD^t^xyd% zL`Ww)Vq|y&W;t;Hv&zLpXy^X5SvZ`~2NuQuQu-_58xn;A{YbvpwOV)=S?^-{8Jc8w zM5y*9dp1j-Xp=?;A_H!zG_WEtB3%agZ^hO{-IE?0JpnM2&m9$ib&^4Eqc9MK@BS6; zAyRsv7)YD8ijWclD-La=CaSu7BlaY<6l`S7A^*O%CuyZ-iv;NNyn*+|9$l^0(Ol>) zMA;3auh8qkaEOYhrX!=#QuCn&WuE~Ah;y}nq${KO8Y~?b^|DsdUOREE_+b!mR{dYJ zfW1`T68|4M-oSf*^j81-`)3uE!vRe6)Yy-RdHqJ(gVX&cp>CaCtkcl?2Bw!+T&&FZ}sNb z0ZjuZXp(CIeb;a>joJg5x!^3Pv&vmL0VRIalL@wMcl@I}C9+>lVG+h9cez2>Ne%wYJ?sbR)VS>|Y60VQDw98)vEWVcHS1Z>|0!cA4w z?c-$b%2Qh+OdXzd=9%JHl?g+g$P7tf0-+%UTXTg3CI3~Qb*f9sz7uWP&kMt*^yM{l zXw#u}hqfKsxK3A%?P;UBEy5bD%@!_CXVTge5^s^0s$lixBIE6A;2H|jdeWoH?|#lXS<0s;(p024z4oT-2$?f_%3H!zF>1_llQ6}klA zlL{kK1T`@^Gm~K>6n}kK30PCtwoZ(PY!Oo>#tzR0wASKS$EvmUI#$uPj&+_uKt`Df zgc&lgOiVHp=1C@rqKF7otm3RtwQ8w#s#bm4-rKHlH}`#S$NRn8cfWV<3w--KJ2`vp zwb%LA`qzK>yrDyRd_LcK)#{DzUoM-nA~MiBY}ywd5x(|sKYz2i*j&L$Y8%V5z00>r zhuEY7+nYn_WGBIY%@|AH9XtHh*x|>ycX>R%*Bkb+chp$NGfv~#<(Mv~3HEO;IK9tv zVD`uKKY8)n|Jh{5^m#Lu1&73h`R(_OaCO@^$#v#}1@or5&YCe}f$NeW?=Zi89tT|Q zcX|hTM6gMq>wm`JeSY2%F|KaD5fLFDfB2zHCY$aN6h1vTZ2zR`j{j`TZpLnG)=bwm zz8-+hyb-)Nc%yjEJTY%H z?_Hjh=fWG$dyhAf=f<1Lo6eiTo5`EQo6DQW`-HcMx0JVxx16_v_Ze?BZw>Er-df&z z-bUUg-cH_bUJx&zui~5e{rvkwmJBfrF%B^eF*|k(czpX_b9i%xu&eiYA-t2kr~HZh z75qH@kAFjE4ml-o5KIVSSD}9D9e)8-CX5 zbEj`dtQ~Pv6!pf0H?l@Lj*J@la1=MHX4G%a!<<8$QT&$pOL2|3U;Jux%6MqEt!U@B zw_|6!pnZ&Of~{t7fQ_|0jg@AS-ZE&=csp^ znv@A;rl5SeB|d-CCBSolzID$^PUP3u)f~zol|oO&o`5jlz+F2jA7~``!x(Pq5OmX3 zl5k;L+VT3TrrMUnKLM%$OD-SjkYB6=5Rb_*^)l0dRC z$)qCJ=5v{erZ|X$ZM)XVLP=3P*V2COdpHFbH{aFiQ?p_+Qb7h@G6-f~-;Kj}__y#K z!L1I7Pfbu$Q%y}%Q&5eMPf(DLR5ULB(tm)fj9-5l+j|7{cv?dD_EPQ@&U}XR(NhYz zcJA-aq&;K-zEJHZ+nHBwO`EB_}S{+yvYXI2Iln9)Fo1 z5@j|GT*`^Y!H>3+SNM4UCqecYn>&<#r^=u`z{P_;(_la&wp9NNR{?n+pI8C2VadAf zUlB_*ck9AoC;=P-M(PBKKpnqur8%^ah{nmSc%uS~&pYF_?{_{GKPfyZNl)UA`*z8? z0q4M9a2TMFxk1Mke3nKsgh#TQOMhx>i1^i^LwU#HI5Z|UhL#6cduDjSMp(9e^KOzG z$<kh+jV4MZXKu6Md0yZQNT`2bgx?(Cqi11BnjsD9H|+y%{ghr)`x|V zJ=lj9E+H+!%*=v1felG{noKpZ>1h(A4(e$fm!ghSK{7+_g5+<4qOhtNpH@1HL&`HG z#^lFEI1Kfi!Nfj5Fw(&YX@4q%nsm{1oVY1HG;eJql`#{lhH-guCwCV2DBUwFLTDXzkkPsds`oiZ?_Lj zmXs^bBtifgtQ10$E=;Ggx=UDBZjig5}{CwzBG{-k`O&)~$*FIC-d zvV-bSVohYJ%(AtLjszmUO#u`N4(AUJNU&U(UZ5|;p*TWC-=@>(*w_tQBJ>qf{B9_w z2*uCyYmG;xmC&OpkAFQBmFEvZ;E~`F6tv%WZ``Lq;-VqTMWll>>yP277Swj{Z1byh z#<#u``?L;xB+<*bODRQ(u$T-c31L@3T&9YMOKopKPN&MuiT&yP_z2huM_R(Rf4UR4uQx}lvD zPfpOsK@2R1iOLo1gg(?w#}G6}-huL3{QV^V(IeZ~JAy}eOG3l(E$WCLOZ!+3Rz4^N z(BK;FV?wKwAT&+Ib!jiCk7=s35Wuo?sU}gb4panc0^n0vQog5S{gv=uct8N(>-fI9 zy5;CMx!(m6mCxY?ydar+4tbQ1L&yJx4kh<$^#{2x zyXXR(@A|viq%#1+k=blC5@nWmKJ~qo2~48*~+^0c^IN z;$H6rW-uxs)!?2%br44AYN0qsRup$kYK4x%WBH7iVzgl_6FnflSz8c`^R+k)a6Wvk zuP!@CvVSKCY4xC$)2fv!HK;+Ar8UjR71MC%CY(#ezH~W5q&D(OG*_ZblS3kbg!O~t z_tLE_f44^;8F04pd!N|$|19XmGZGqvPOdnUVYa9e|B7oC;S?H7bKDquRnjNb5?tJa z({UBL-J)~oN7Tn{9DR2J9sMhMOGO9rq6Xe+4u30Wr2J_9P1HOS*L^)OUecy4OEUPF z*6G*5IwI}^I!;B$X{jp_UrbkU;=cYWPJB`KN{P-;4(TRyh92L~1~{IFqg%7k5gMUQ z-sWBFRX5wbo#C&JX1&g^59tpQxNktt^nh718`9FHryZ)GN?WP88m_GwL!I8+;pz4^SE!95x zyDY9J;4wV;uDlM&Q?PuJ;ZJfj=TCEiXZJVKAux>*$qu07VOQbqI{#B!|03^MT@;lc z0O3ISA9`;E;tzhg;boB}Nwq08M6PGN&3_$?8hE>B^HFEa?iXLJ7#JhTU?&lnZX3%O z225H|>x1-k0xSS3R#9;(6_d=AmzAt~k5J-Dz!7lA_)4Ek#7${NbDFdminaJjD#=JU zw56tVv(;|O#VkTs=?Z|1sYb%WBsyY_8kk*|C36;cmJTeE=tH=RDH)24)V#Q|m4Bs+ z3BETNm8G~+!8jM+vW-SJ^g4HwD2wLGxs6l(7EGcsA?y4XX*61m1~fXYUTx5tmgDM8 zxYi3dGUleslG(Yg&>dw1kIVRXtb#jqucX7=30**-j1JF%fs4q-GVUvI2QM@E<7QlB z6`Z2WSl84AozS5oe{~glsodc!wtq4lhbO?_E^;DM;sx6q4g3d>F#cP?1N=%tH=`h_ zQFXcSCrS~G&1Cs#}`KD%OMm(36%>YWA_}`2kT&EK7Zi*L?lmc zvkmRR#T9%U(TBQzLFK?`$+Z-&P@5JHv1BkrxU_NYUFkiz*>dJ=X=%$fKmj9%P3Pvq zN?7l=c^^qJvjXB^zMlDnDAVbuF-jGO3kR1=pxJQTP~TjCyu1_0g(L2iqvIFuTs1GQ z2PG~dIz0N4?d@j%$$kvDE`KN!V}3R4W+9`9{|>wpf2 zNOXYv(2>>IV6Cbv&8mk>kU!5DNeYx*om}#hxn>!2X=%jHExWhL++h_FX=5(gM%Lr< z3jUAxG3l=0M_eVLf)jIok#@uNBdxWNYF^z1WzbY`rIn`a1I=+=0RdZ2 zY9^g0Q>pclTrrerEvmX?LlA4|h(gVUWQL?2fVHqr=CNnvdf7r)NbZ+P@Bm8E3yz;m zraY;d25=!E8)d%i!SGYivB^a=F7b+u)ugNa82Y2&Dn?0Qd-~R*U0GojtNsi>!jI=q zcans{Bm=i({g&ilMt=vg|5P6($l6b?IFr@c3^*G3jCFc{f@S{OH+bz%TnFn(f4u}w zrXO!UT3k_+Uk62yqsdlOM;GpbXoyv$Dz${}UZ^&4x-?xHq%o9gQ~U76xfkf*%xat}L&{76Jzo zvbdd|5$Z^mluyEQn*>y%gQmhOfRmuWPtmwbV-l7NcPL()S~QEI4z8d;Se zkRS+%)cP?;Ds5BGK1WAqle}b1zTif)zAXn=PMgYw1ta|h<}LnXT5iLc6{#SmmAKq4loOa zPmo+;QQB3_MI?T{HYA+Tcjz08rxPI4Hj`z^oCuYg6Md6>4S)T{8Asjw)3+FWM|{g{ zn;ImBJjJy#PJByy7n=I03k@=zypQh=9lfZN07tdRYm(0MBKmF(pCi2VfP< z-s%@cQqwq1k?Q2r$-PG#U@#8jy;>tI3w@zM>kOWgSalyHc^rr&6VX=I zGJG2CLPLd&`ZnmOhiW~^O1fLiI8WK3d9G_^lz*6&!4;`28VlTj8)vJ^Ern&)oZ9^6 z%nmpPIGYMHB4G!tOIY+JW4}}rr)f$#%-XiyuzF``6v16|vIGtqZ!*}5FP>;RQhW-? zFM9fsmcFrl&Nvr;2+RvF0loHD_@2RONnw<2(#1{ZoN@ehaZ{#kyd+!BmFLzJl(Kl4 zwtoN}rdz0@v?c29rQi!2 zw?xN~WE1P~HI~$lFM)W$@=akfw&7&?VcYZu=SRKx!R0Ud#7{adNsi6G0afrE9(S{T ztUSInrf_p7buEH#;p?LnR+cQU&VlhOeSbK~R(##W=}MA{WAh@41580M2j*^unGjGI zTpGomdCylkA{FL?$1XoFhWgK{l=n%zooI9D-ZI#Zh3YM~-)e|s&ac$}A4gcrr66{M9H6;vEOABZW9?de$=g@4cO zH_|r&QbWS``qa?QU{85iq-ukX{L@}FulK5X{VISNhm6XymZl)=tU6LqUSjUnlM3Mm zeWY1l9(<$*JNGt)ltBiwO2UQDAtNR|xp7+{O*#5`L1=k&figxJ9xV^`_`H^;?BAwH zPK}uicJ+>0Cf|FReDB4JcKzOX_sUL%DTpc5K@g@-fS}_4%GHWXzU&PS)=t{-7K#EJObcq9% z0u{bY!Z(S{-8$&*a1h@_;Y*Y<@BjY$0?KZu^Ihz6S8nCEqFgdC(JpV_x69ip#ZmuD z1Y;KX%;VI_sd1oyq)b%~D}RXQGzRE)bilu{Mf6v=f-|t%epvvGKX9h3^gKw1gDGYv zeu4GXiDWxzGT} z-~h}SJZtVUpT$u%4BHKMY*VM?keTs2l=L*v!^FO7psb#c&6fr317(tKEe<_U@I~IH z26`Llr-Zs*Mv)M(d_Q_d_sTDBXp6}!$or8Q$Np+^hl3nZqIoh0*OqnIR7^RXeHint z^FZNf+b@#Hk^%P|2kMzEl&+pv@S)SNG$%)^qczvb$vWKH;56dD0fyaOWeR0(WOHulZB!-FYaH|1%p)UE2@MbGM3H(w=Ie}_zW>W}~P z*LJ;0{d_zr?Y|Vmhfi(&t{zUN?tdl3jFY=@;+Fnay06>ji3E?7QZtY@Rob3yp5B{X zJ(1bX<)LmWeKkh*)}|LQQq|>fCHG&R&BoZp+e<&F^SU{--eN&!?`EN zQo3%AWP0b$%x=f7J1Ogge^76^B$Yatre-fT#aWS=4ZE()Y&~4=Q-4+OE}bIGaR8HL zTdBS)N~MeDsJw*HJl!8{E z+))rX;uOR{0f>VbNPsv9Jvn*?IVb}`fkT0zr$A4Jo&r5t2$G-}e-wd`K_CNzf`9_2 zpcM!iBr(VNPr?x2!euy0*8Wxf`ID~t_56&a4nz^LP0rx_m6Q3XCTaC$$cE-`?BL8&-~5o9pE+x4TL94%LnNy#HO>*;VdwACB86%hK!0`wPBgRhW~aGFTX2 z7vEt2|NaLCC~#n4;Ba6NXaE3nYzB#w5;If*IFnx^7JtQA2Xs``x<2FNWVR9`<}hM` zNkjt{M4A)1D7GnI=)D$vl(j36nM7^t{>MZj8>KM2}1|>!T-A z6i@OD_x{bZSZpzc{AMk;c$HhYY+*|Yh?G}8xcuFZcONTj_KbIC&RQV}iVXJi@eQ?^ zJ#*%~w`R|rwZO((5^O_`*l=fTydpxq0z>>Hfqx-3?vXajXV|QB^YE8QL;U@w+pL?h zafZz%iIl96zq~?i+yZ9Uye0{>arg3d3-Gp)c#qvE+4ES?d;Pv%}Ym{C5lVo$+Y=53ersl(>7@ zd4GBZhWdp@Qsn1J>M81J%9479vZ5Gj0`(F#g|ellQq!o{s5hwT)LYaHY8EwznoGSy z&7_ids#rq1IA%)H-TCwSn45ZK5_)Td1wnc4`M@PdQLKsa@1=%8}Yb zl~R4wA?j0Vh)?l2nG2`|PmtfHP{Gtu>VF5G1@BFsocHY$u}`$|m-0U|YodM3&CNXp z69js+8l8PI>Z!?3m5iG)uH0g+#kHq>o<3?B`i%KA@#8(m|M2YYX9uj-TV*r*nE#sa z?u4sCN8zRC7Cd)u;`W|TMY=S7>e!DyO~*2r*@CA7o`x<8 z$op|T9h0SGokFijRivh*D$`hUWIj8SoJZV!B`5iRVFQF|O7bDuqF3mWu?UNX@l3#T z$1a&WAJ1gTk}^3(G4_*^ti%k<9Dir013L{Z5|H;T>~xkaA-LJc$j~}bW@nVH-8hb@R&|R zr)d*HtVbgSuv0F#SEB7o5YvaXhc$=cAPlMxTG)bdr;gsCi_e0C2uxqcrqb*DR*Gl( zBTMB)Q|%D1r5aa$&Cgc~&ucGe&co+0r2gE(R#gI-kPA7GS!!X+-j2uXus!|VPsYP= z0kB}nCoBUiz)|YB8%42`s(&G;o6bMhSaAlfz+ros2TR?Su{3Le*!NgF+EUtvPuJu0 zGgf(3ni`z<7snCi*F5}|uw+w)PulLm$j-zjxCl484xg!SE9itC=#{qnR0J1>X6!zI zn9++L8oS{*Twiva<-;0qiP*CT1+wF7pzsKtRsT`_K|rSl9X2f8vVUP^qNfh5;~dhH z>E?o>)G9#Cua|orX4-CAJHy%;-1EeSkWyJ$#36Lg;5d>P{WLN9=|>nHe{Xhw%~y;-ZR%Fe&fYrOS0_t{e8|b|DCtLrGq?@9Spi+(rk6ni z$fJ{jRmh3+P`9>6(|--^(4lVUPWtKS{aSgE?~d~;(GvFu>-W_H_A>EZVED5VfvD@PktxCFEnVJAg&}g6l0u#cb z6H!1kgx(j~3w_F73tKz^Zq=PT`{^g0n1WvbZz2KzH0uLsD}QWNZiUsbMzfmi+Vr=H zLemWaGgO({pz8 zVy|{Ff%f!G+}@Db%7n`~biHHf5@9hKwHLtRlq9DV5;c-+ca%31Yf9!i0DN+ z8jhtM$~=gCL4V;#C-0R7#45s*mMdn#PKeY7rXj#}c&?7_grb!6efltsHvlr4tD4kJ z&;%`-<`xTEu{i+jQ$!^CMWpP7-C(D2)gfFgs7Wu-oQ0!sL{Xc7m_<~1k}d^8(Ygi! zoJj4>>O|~#9Zev=r&^+Z54ON&%@zw=OO{doUbQ%*zJ;7+P##gYrGq;`LvVL@5AN>n z?(WjK`->CY-QC>@?(Pl&f&{zy?yZ`dnwhHk*Qa{d{?&cz?6cN-fWZD@X`|d0jRly) z;_Cyv4had~3k>Yre{<(=Mx`KQ%IXIMc_%0zl5+x46Yuv81bAh}MpGe(MBTzU4Gatwerq#UVHVAIon zn(_L3KcyoFjDoc|;9390nr&T{zhXwVJa0?w+S7Voh$zKdVPtmj?~)he{6lv(9{8G~ z@}`ONOesh$Ev62%u^ze1cM;q#@vKFWRDaB@#aog8ocBrc0u^{mal5cSY;o}_JqJ6T zcy&7FJRgDG;u==8>}rbecBPy=s*DcO~{Yu$9s3rbw?^i}F=l>DEjueSj9 z&XjlkS;*Kc$uH>GbGHvHe9W5wZB7;GB|SS37CR(|wW2esV`8IhKzQK3Z) z>qZWL0~KA?4ns^osWj{&-*1^5lu6DeC{@?Ogp`|fmi}6AGOBUo8nS${$de`P&`qpl zpdgg{@PgFY)OP-9R+S;MVc6-6YfIAJ9w{eCrkzx%)YaKiMo7w9}^Wix|3QlpX5PtLZgRCs@~~E6e(8IO}bY z0AL_!pwlL_e4{C+4tXiyLq=OA$E{CL_fJdvi~>5m&)jJN3{TSOtIGn&PcKth58q?? zixylaN|AxCNW#zgmLdW%+km8OIj%Livv3b;215HxbNBm3!U?f&pzm~>bC+x9A5zcw z&u}xTu5M2c$!P9F5^e9Tx7UXQ8zM*fz~dK%+j-9)cw?6q;EzY_?p5?Q-7iczL<2kg z6#P2ZJw}ISC@8Vg9il0ix%d&csY)Il$M3c~d_Ic~`VU6#dRt;4X<6Uq&B9&o;G4(B z^bQK|lwK3ycME^-4H2r&%h6<$Eo0SRNDN=vgL2dl%?~xKW>M{1D<{OR;A?gZ0H-7C z0d5j@5$oYG?r~^xz3Qn%vu9#HvxnZ-z#ocPO8Sd~k((j8W)8D%jc$=hbYK67EPZ{Z zSAodZPDs(J5NqC??x8VgW=u#MNgEW3knX$_>=KSzJ&`b3gQDQf)WY#6At$XTc*zQP zh;er^G$4yjfA`EB&ylxXR&P2*0Z0jHzuVJrHsk(l5E~G~i-S>9$svc=RM8!@#mEBH zoX)5_e{fe^h63+;Rt_8AE6ge%<>g9FeVw8xbXOjP0GFwCSzau{MvXlie(MdEbIvhF zGN*r=;1fy$188bwB&&#EJ((7J47SehS7$})M;EP0^>6$%Wavnu4Jp|NpiPv-w)ZxF zHAWDCmk`bR1*cJZ1~{O*qD*}1ZU#hpz~3;jNqLoqJH4p+Pi?J)N=zXv92s9I5rWyO z!jM-Bzl>MMx?X&YJPRcerJRv_oz9fHTG$PmJtHz{d%u`Df{%{9zs|*71pu;Rd3uG9 zZ2;!y7~Bm_z8|WlFf*3S1YK0@W<|KS-+09s<3SNQ0O~>Mx)+ zCdsjTP#}rN`&rmVGqx!n^^xyqmw1Se@p)dF%doZ0kci3a*H|P)s}#RnsQzwHBr(`O z{JslmITKcU%Vit`bk7TQbrLXEAE?Fc7F`Sxpb^`SHFJ74bNS*q1|~F=#Iy`lR3+j0 z;n38inay8x3!^^{@YL0&K8P)nW2=s$eP^)7GtKXCvXbaVc&_f{;1UFuSVo*`|;FPe>U-&+HwLYQB5l| zwPNY~PsTZ$8?%Yw_r=!YeR7AeK@Y7!yq0Gj5&jgucO zj7ah%fGuO6!Zp`KW@HyJA2lCZw*!plVZ0M>CS{w0J(lsc5-#|$lt`BAVcb$RuftbX zfi%96jeyUbyi$+Qn;17q@gxeN${*u1nMmk-w}d7ghJO{Q7*cU!hlfY3t)%j(1ZgmJ zbmG<E^(q-Ozky-sr&YRHP)?v+TI~A}$^W$K#8p_$wT`F-VPEla# zZfk{1Z9P*TtrAW|F-hs(0`hk>xG28d9i%nXY2@1!!A9Y=Pv~NT?cLG2>9w8%9H`7Y~KG)_P~0#HG4Tb+V#!S z#UAax=<)mkxEUS72pf(JSjojF4NQ$QpcwXn0iOnWX=;^irG#JW4*3*&Yg4Z|*5msw zM>oWJi{87-c`H*3jLMsr%KN4G>9Hv@4t?t`t=W3^#Nmy^ywv`Eec|4Ei;;LF+_D{k z4s*MMNL*UggFT|Bks*U!rBC(kt-ZSyJ|?kQN>33f#p)#kHY>MOht|hG2ozEebo-@< z4Hf+OJ;!Xhr`$GN{(I|Y@q6gbVxPjnhVZ3SroFYgJeVTc_4eNeMzs5z_pOZcEE3J)EhJx9 z-IF}8!S?M1Ny9sx#of` z{W-5m`8FqC{nHJs8!-IkwH0u?t7ZU6(c_H8Cf7w?D%!kY6B7*70KUTL*D5E193n2q zi0q$;(`-!_IIQvoZFD?j;&ccRE0OG|MB;VUk&JfjRM)}TZWJ!c+ii#`paB(2Z?#oZ z|6eH4P<1r)c}#7pn|Ll5Kt~>XYXx}rO9BP~tf~ZUHX>Ob(i6CL=m&Qmp`POj0uh}$ znsmBouIN7Dg%oTR8Epp@hd?IE8$NTi8GDQd}2 z^)w9?+2g}fM`S&Y1dv9R5W6;0!rV%3OpodF5@bR^LR0yvHYOxAP%UK7=wNEM>eLpS zii;7ZjdXs{;#0x5l+zoFmijD5!U!@s`6(M5#Zl&5K(j3-(6HjO>w_nT)v}TcF;7of z&l!0@c|d42NZH;VlAz(7c17Co)c=FThmbPM&|a+=YScS#t7@7+xC^Q+Sn+Q4Z_)k` z4F>$>Po-^NT{+6{fC@sUlu1IXbDAfLC_%`Lw>4jzglRPVpqm;+*2EaIu1s`pr!jJZ zKF2d0&nN%%*l&bO`3_B;0_rd{D)ltYRTiDT?^T5dY);sBd_z59*|!*P4B4qU#f)E) zZ8RBOppkJ)2nYR??3DPJ*>S zooFxRfTsU}w#!+;gfJ zN$7oB_4hA6f%;~LCpK5*r+_C(oz4|Py~W-S zJ^4o!5`eH^yee8)Hpy820ERT}ug4UsP@S=Xa|EmBWRcOB3!|Lim@$Zy2tyZskkQls zQUz6VghRssus}1LQ$-OqgG?#BCK7t)gPZktA|I_LoT|y)B3`ih?ldpW(l)(wSU!yFzRUye~&!O`$}G&uyRD#M@fix+8S>wrxG8X|rjdN;SIl6NVL)>JO+zk{^uwzxA5f zWCe$Hrtjf5FBseT%07~CkylNa!a-d^c?0wUl~s1vU&EVV|Q&itC%&ESwrw?GPEL}_4uJi0<>Tgn1 zx~iqTXXERuz3i!`Uo7^9ADbJf=aK@!aczFAy>EYxPcH5^TMc@1bsEPXj~&O}G#Ul) z8!x~ovXk768wm%%1IEe!=@UqZ;hcOxZCDL*_GkL}ZaotPRacQdsn ztowbxi2Ya*rDQLF_$heF)i5pG-bur*7mzu>< z`8blbDjZavPIqNB2^qetD+eRH>?bumJC<%tsVRYijJ6jeGOQd^L^Ddbz+NPeLu zqL?DA6jjji?3B{jkMSNwAv9ng7|}RNl2B6rI=&{ZCx`B*=46Neni4G^p61|5;)|<>Vf}NM+8l z5ua%6we)`OZca%CQrA5tTENzxjb@KX1XpSkj1%I&Ux zyJCg%`VF?z(%w6zvAMBcIy-p4>D7(}>ZfiK;%K=S{-1K8H9RLL5fjmW67K&1VKQVW z;7pwV9Rq3CK>@f7^QsFZsikO;H^ily&Qo@!zQG}~93}w0Ee7+_OYT_IRA2A^%y{y> z)Nj4YtPzaIUvqCL?dbp8KOP%TyT(nIQq#f~Z>7nkwyWOJH_lr&7y3%HdM4D^H?dE2 zQ~rp}PhZ@~|8lKaERC)nEP?TU+A+90GCIlXWz>+{*au|Y^qzm&(fip$d|gt^3i$lX za-ZUN)2G{DQ1n`%reN#-i<^^hS=!vrMCYp8FnKaa2clG3ir?B?Vk3|fA){)-i0p|0 zmz5Q_tM?Ity`86d+jk}?oB1)ghv&*e|F(quOgek*!6#$H4mj(`tRfrf9uAV?$+$Gv zuN4!as{>rditE(}{}4jFAoA++8s{Hio2FG4{Syr5LwP`)oQ1mx96RY2dx=Q~mr4imKQ$|VtG&IZ14m-A9cRmPO3gvw9~g+u6= z8$`e6EhY+fL;iturI@8oAQ$=;NC(#t0f`Z;tO$S$hniO1!g_z97m6oxP0k|?j6-uJ zG5KE)stQW{%`LM8am9$}x(FV92U6>WEuF9Rx<_I*jav5o zTi2`A6Mj<+Il!_J#47A++@+HIy z{0c;&uMWoiA9fljQ6C+sjff&5=JUNpQ51qiO-UQRbkV zHqo<7)EsO4DN29+#^tfW(gPE=cYF*FtvqV?kW%S`RoYQNp5 zeW^i7X|+bKG;Uyn)z)J9Br1goti#gn!qb-b7_zq3&hU-O#fvO(FKe5P@FTzCjo9F! zK&4CeU;jL~Y9#+ta{nX80JhqWxw)Zq-p@T)}7p`Zb!_x^AGpVdMrGt_gp0BUgq)3fD zGTf*WmW{j`@bUV&)4mtgu8mzcjBNPTiCRA}w-I$CdE;jT_CEK0kQaFuZx`{#aEtSX zd=I0+i~umoiC`LJ{UDsI_!#l$dUPX3QDDlXcOIlSlz$hj217Qn^~ohQ2sMD`gPkbZ z<%;giCCHDuS^oa`5OC;}MU%}yaVI^oPeaAlUG-qtuiq)^wwJnOk8n-V+q<&0`2mrl z=b`@6eQ4R;^N109EKG-u+0M*|D}9e*_8zDTPg8I+$Rmw#E~88w{5wYUIpmKLc#BsymXj>y_~1m2jhO} zt8c&(jg;e?8wx?eo-?7Anp@o+N+<*TRI`8^f8zHJV-ZVQ`R{mNMj{%GepQzUPy{CS z2wtD9`9wFAnQKmm%ZNwE5={%=0;o*@aD2)>zFIB%i~C~vRovDJpC&&T(sKDM-_$X+ z@A9|P?OqH=s^Ab&r&{=6LgXkxD6I1=XbZqm$Qw;1>%pigfJGNY5eg<#Mi4~O^F@VB z!O0u=Vt{*lZ|+_j$eD3HkaQ{zTjmDo{2NJ>RVjiI)`)zl2ZAyI+<~gUHV_9r;0f83 zH)?=PGI;1GR*+61r;*{{ z;9c2BLmiWG(?n#z*4Rd_ONt*$If6`a8%9Ev>ugNoFq{M(0er0G%clmIX+vM@7o%bm zmh6N5h)9?N2GH3>q;SZ^M8YdWCnRj$Dcl@+T%A0`BKEBkYfRU1J>e=TnI{nPNXiKR z{+vICn5{_jWe-%kEBLyYU}TjAL7fckmO%0SY!z=rDQ;edC^-71CIsxnX3%k%%H0@u zmkDkTVTY85r`$01Ct5E-%v+t!_ZgJ(lMQx$w1k*9+<{X={>V#oQd6M|!XQ$vZ9JCl zHq1bCMUsaGYj95aTcS0y2`ix2iRlJAZzLdVx@(*%je_Jxba;GXC0tO`o8v7ed#|&$ z7O^wX<=KxdOPExB^U1KcZ#ENOQA%S(QN7|7+!wlyW0{s(r~Q34QF~EjieN4gjwF3#^gxpa3W*?6nMWCXJsC z@H!L}zqn*9uRC~KWla9Gb?S7zHsF7np;38Amb%q3yOcX55-PZb%uV3n=E9tV;C|RSmUo{_xWLg5{fl{-H@BVbiLInf1?1M*+jFg7!nfK%T?HnD znm;3&8pXDdkp3!UwFjx1nQpXMV+`c~jo}v!QnVJfx18BGqXN#qJekzh+V$EdBW_7Y z$!@oB6Q@1y1ax6J=&1#ovaSginq}r)A8XK$&>jeM^qjTLTexObta9^o`Fyu-GuASe z`@Sg7G|t@bl(FNcbo+{iAOh(@*?Zw2;MSWBPhP_2&Ar1H{ta0Ssf#S%nK~i?<0X`o zQZJIw_oQ*;cn+p; zG1ooaqw^iSg42u2f)AcZ5nV@OIz-+ zZrK90+O@Sc6#Ql&g{Oxs}U_rVPGa7O~dgs0i zn-^rz>DRV<4r}DCFwX00J&QPSWU~bgk}6)E4Y+Lmg7@s!>_f&|y-MKCqGw+bi}9X~ z>Oj_sh*whqMCa_%9mWqW6E8pjz9F4g_oI_Hvu}O`>|Fusde6uwd&(CH+9yH}SO?F& z>FJ|~VL@$I9|6}PN%3SorOBBvwBu`QHR{|1_8)Y#J=dZ4K@T#SG(A z#1w3?2|UakCYc83WRr7cI-w|~Gq@)@ovYoaM>EH$e_WQ zS^s;K;B`O&3j18==*Z&iCW2j@CfR!GAMH7?>8Wq~T3dm1iV-n1Sb^*Iqs;~6n&qtB zz)F7T@rVK1<%%W5;LG;1F+(PeDtaXjTG6;S-Rc{oYRnBoh(WsC6J@p)@t-p8*4#O2 zK(x6h#+`)mC&VCq56sQQ(&z>QQ*C_q2<2i0viUhM1Yy0=QoxPw}M*Sal*0fAL@HqNhQHQz9uRbyW_btIH{ zhB2U_QiZ$4y|Y5*JBQbtAn{$F#p<62twP=s35?td9`CEU9cZC~3RO5ua7IpzZEKjy zKeGkU3q|3L>oP0hT2|{<#JY$P^dxdzVYf6!DAuWC2kft9t zQK&B@yJvG^>$y+%()QHm>iFHfx?s0&ndF)Iygt7WTpPTI>)fr8k>u&G3DYfl%yq&1GS)chaV(4#<=2{_I-AFu_f>T4_K$?qM6Drd84)mpt>MrE^$oW6$*`H=QWx|J;a+Hh^CaM(b2PNgE%5{CkQZk{vL zj&^|Iyy8jkRm>wBK;GH&BGS*YIR@Fe(C69MAeX3H5ZPcsO`dw6)Wig!eJ+B?|NV6z zr5yS>hw?M4eB3`(^JSu$tVK7Hg*V7&$kY-zeo*t@tZ*$8 zNv;yU1*+2}*f1$Zh45C@{W@ZRnCF9J%2|}y`@GV5?&2IFCxj+4y--Pk-!?B=s`d!w zMO<;)=fCneWaPepssL4adq}ddFfdUQF^c@7)45tX*ozvunh{Zn@~|+ma4@kmGcj|q zv9Yn!GO+C=wB0d(5w$T7d~T8PQ&*DG0>LS!4TC8$UQhdVGx=Q%Dph?vPNG1)6%(0tXx z&xr_Tl@hbHRde0(ps}RJ5#&^ot~|w(Pv#=a)dUGjG6|5X%(#_x`o*Rq&O)7z{8MUJ z7DY#ywUQ1LrWMbf%KgT)!2Q5?A6U|W0j80Ku;GnaCv~Z)@Ofyvfh| zw#b>TR9_jFO$aB6!QH@J6#Bl8pkR*#!2DvxU~M-B3AyA%g=5tsO%T;0cXjuj%0lC^ zb%&(?<-l(Qx^z%ScSnxWi(~v`3L_-9;pLx&A$vNoip%lmR!o@B0#N^LRKRkh6#q{9 zpQSgQyLs@lnKv~vz;@U^KL$hK@h zhY_qrsAkK*DbmgJ`wFUG?SuY1-_wMdZwpZtq+xfL*HBGz8^zH_BFm2DIP!THNb-PH z65?dBaM4H??)ne7^0eAJZkayc-*_|{j{E1rCjg+J1 z2K8*&ZjRM%+lEkEEit9_F zdbN2D#rDFG`?CIlePdpCb#qvv4Wdgbmxl2o-`(-;3dcoO3yMI}>Ou3!22r+l>NS_# z)CO+bM96(f5mGlt-Qpyjz>r$MzC@bPEnJuaB-bK#v%>vpDFW#lxWhtWW z(C&5Z&6}g+S7~Dbz|u7cVwBkV;Nf~ddJ1>q*x)8O7Pxif>ng6IP`<+4bEhPFzJiT> zLw_M7Pm!!far8J@!EogF4)z#)9kg|QC6#DmV{%mI+em!4r6L64Bvv{>8&1%<1V4|~ zwy?r>+1jX1EKPG04_@cEM7;IGLOdj1431ZqwlIJwDn~4JutpZ&t_~YJ9=8WO;O6D$gJ9eAq_Ai0um?5m#u5chDj^b0+r06YqEAIH^GSTj4TlRCt+xFJU9W*VuawWY&AmsuG%v_H> z{1m2y>@h`EnMY5>BOX5>@*CvEBwQ7fMIGb{Ac^5kD=x`~B9nZauz^w+`$Bps`??~#oYmlQ_{EKILY>gbU5FZaMbdH7Kgx7%t%um}kS9;cmod9%!1q%s@lp%;ltNB}dB}co6u4T5Fzyh+(aSiX zh=P@$rYpgUFpk3iSP!M5{arX1J;Mr@U#5^E?pB5^7e`04qdF$e)|~|k1#tVu7TA)T zoq+N&r6InGS@|K`Nep%P3Jj-1C%twUKq~c{h0b&A;u?JgoMPv9>^ASVT5rf*qa_t$^pc%! ze*FlxM^H0ep;$wzv&q!*)+3;N+l~h8uiq~vm~9UtLmCSNvslN~NK8rFgj5RJ#(>VT zQsJp6rrH2MSa#3$Dxqn+Ok&RiJQSqe$xMA6(E3&Y;O*?_^lZ@#6~1Q61MFikF=2vt zlsHH|>`A>s-mi*kR8B)b_;o%%)~fqDsQN)YY9#M{9GN|v54Ju{ zmIiG`b3*qvQ0I-(6kGD77=E`21dN;DPGC zcmzEles8a>bjQEiMSqjjficP6r%}Y<{x-U4ITZSxpd-;Jkm3>wL4Pp=E6<@%J4YErc`wx*czR z|8rYjOh^E+Tm=)}NiW+x4sbT?OHS@gJ{?kj$!AG!l($&>JndFrm~|>~w<=jmUHmB7i!XkrkxKXI}n7P}dyQvp0zaq6|@GC*D zSUchOhSK~xMzAE~X7DF{F}CM=&ft2{Z=tYvx%{<70;pDb(u;?$20CthT)|h~XA941 zA8)|Eq0Mr1ph#4R6YiG{{IeX#3pa&ZrdoZS6I~++qM1-7cs6q7oWP=AA*&YXGIv3l zC+wu-KJO&nwDZ>4>v?0+7vZ+k-6a28WMF?`=Z<(n=$m7~ekrhR0ooeNDL%OR%rqRq z`rp+6&|#>xh^V+YH!};XFx$V=rHBw06B8?o7`v!At2hUXFf)q~*AF7T|6d6xF^mM9 z{eP5B%;`=R5haZ9-+u&9_vL>QIYpE0w++ANIBsVA{=(p3ND(_AYBG;~#tvVoQihoW z`74j9aPjtP|6kmu)qI(wQQ#M!%2o6k91_b;H@|3Iq#Io!@_mFc4*GYoZ+}*WX^o@! z+i_zpg;}*{qd8s#>{sHDT}k2?o+a~e`6Z1B0qO^%ukYXc7@(O$@QavZVv-n3R0onj z+&&MPg1T6CN-pcEKX<(Ym}6+U*r5nZl&Akl$>!(P8Nw6FQKGI`Fhz4`cW2Hlltgo` zVAVyCrxcdl6`#=@{e@SrFOi;8_2Sq%)MYFPK~g&?Id49DT=;{s!PQ3`=lW#d!MH9! Z4pByC2AU4XN8n;%VuL3q7gG?2|1VMaB}4!K delta 24387 zcmV)MK)Aoft^)Os0th8gL`E$!E;W$|HUc>_kw6xIxsL3(70vrA^aGDWUS4iMqk-yL zg2@bbHkinUBfr3re}4{FQItwjy@rj3P%0LA_nrOu_4eB%_(`$QY-#%X*PEIo{?w#w z5Zch@0mos~js<;P~WNg803&{&5-DI^AOk8m>7YI7@7I^@_J@*l3m5B`&%Z4+9 z>Q*;e`4Qgn9g>pom7Yv%g~)L|OQh07S_&P1%w#1A<8|ZTbo@*H%oK9di3L=5$)DCH zi1)9z|1_{{f*=l)aY1`{Pgi@=rX!Pf~cNr~jtCKPMxFb9npr^!K;F4KS=X zlYwfOX%`0eYY}vT@%dFWuA~SOf4vsiI}xk`ST9UyTClFu-PWy7 zl0080enW_W0d>3}#3TS{b;AffV8TI-CP*PvHi$kb`jD~Evcu!?P&P5P(7K5>rRd`a z3tLp=gtrvP#(#Bhcgu z#S_^stXnw;^Mle9B&c2GR;x$`9+|Lz|48WLLIZo>r#D-Q-nNvW1v{8oKtO3e4#2WT z2Tz;l6ih}N4YgYVQ8!{C03Z36F_5OX@ScF-CBCV9aZ3HkOXiId%Jall3#%IQO6`-+ zQp0H6c#K_+D@jDR{21Qnh{-0O89?bH3Ut(#Us3SLI>-u1_SoLY78|%0Di^kYlq`c{ zbgkJy*=-e6k+Fj+e8XJL;Zgb3lM`0sZ*kg5_!ih@BP`cgYV1QgNXsEX8GVuVfh76x z-Q%QjEFE|=I$)pOmntDz5W>YkWD4}Xtr)dSEyW1HBe5VL5o8|+L@)`hRzxJTB#Lj> z`ZgNyE>X?^Y!;y->O@$?bU>AVM>d!HRPCCcMjCY1i~wTjX>rY$!13su;rfwcUtEV% zkJP)&pU?a3|{F@+c60>`d2VxeEpz z$bznb*w*qcn{&QuQJtZTioEMqIU<@Ih}v4=EssbgYDQ&K6?x>1(KIA7P&66>5& z4zS011-}j0&njyvr|;;0Y6)pWRVkszFs|T&C7`1u-BO=MA~171_oDuyD^-0lC3F$FBPmg66o4&#Di#oG>-aA)+YG*^~y0|tiCmOD> z)xSJdCnF%N*nHZD>`PlaVU!<%CHkmHokz)}l}qjFD$i-ZO%mOdVCW<$@7tO)h%u7- zj$)MaroNnx0^lOU+8{=KJ09uCE9gV21uQM9LfzN)HWl=J%|EBO?1>m7cJ8o0lco+r znKm=Z{deu!d%A6ZraLq|m%^ng61tV?!{tM#NkCt6p6G@cJ?22nOPvtnPspaq+P~Zh z0WtZNG>#l2W-5<-HyrE69tSzc!%6+O*haVwuDYmuxz`G4(TsbQ@7Q6%4R`o12D3CF zcVME=jn6#kXPy}~p&ypK2oZ}AeAxZep@Xh2R(`1?s>cj}Nj|n|P$U3xE5YQ1df1=M zl&ZZ%RMK-N*Glnns8+BoPP$c~?o)mo8E1N3FU1P6Lb^9dGLM(bY1@THyV%nOuCf|O z_5MSLc5YLq6g+A>(^rHuoN8}PSC${BtwN_3}N z)1=y@R98}eYTgL6@?HiBr|6B)%rJ19^_ceL#Jnlz7*&jIex0?$a@NkPBfHL@TGA_a z)cv|B!qQ+`XD>}~ua%Qo+LhOGz6`sIM{ZtbP`oR0yJL8*g$s7)G9wo4UYQg30Vlczy$Q0No9CnIN1>Tf zL?cL|JP%H#@FFH3jS`guKy*g~z*MKJE~s>=Avsk_+iDbHs#y2a<;kum!Tx^jOMU3) z4(>*O$lMNZvFYU2L7b^zJ0qz#R!f6h1imL>alaHJ2QPMO;tnnVSZF|`=y3D2{K2A{Ro&3DqCd? z>S(n(=DUXHpsH7n1re`U+IHtO=y7e(lZIt~lwAA=1zAUD`Ar>lBk}5L#2axH@kKkO z#kcBbTm$1byF5VPm5-R!y`SAK`O4|ed&1IrR#qcDG7>N9L8=wP5TtI)syd4$g|xo1 zxh<}ttAqD$eCe63m*?h%fTrXa(H5;nT)pXz_)FR~mqE{44i#9~V4gV9zR{8w0Y*E2 zfZ)$I!F{v|?#67gOmKHH5~ad@1ix@AfcZS2Qpam2lP+nMcc(ICy&||DT^k39W;~3r zPhT6O2D5%rsA7CKzgP3Maq7u!n@Oy%kL3&3$7pcle>@GuMj<>A#lV;_~q$<=fZC&rh@`C54y#cl!GKL!Bi5sgnXPl);llDYVn4uOFx1 z&r*VxlCJy$emN=mqoim4{NUI90`i=mYq}^M-iJ9RjJy2t^$UM5>0on7ki<*5aY-H) zmz0moPs*5cSfqTi;nR&jT`xa@b^J+v#zm@3@&bWQmPnw*EEC-0#V94TErYz=9t6~F z58R6dK?%zToyby3Ahm5hm!q^1C=G9m{})k`bkd1dMV)LVVUYh8+O!~C&?cYUxUz({ zYGMRyh4(P5*>rzDTh)01tio|sIa$?%AZf={uX)xBA4Tnj*Lu{Cy{O=V)g>R%6?fN1 z2Yi;5qZ%2Qe0)|fWw&j+KzH7PVqK7Rv zEV|*{2TzZng(v^+Mi7;d8ozydBoL@pN}mA^k``p##`%wV?sA%@mI+(dTey~zjQD&` z<5B1aG4PrF{mJT<7}Sj^Tk8CuST^~bWlfaJBPkmu&MhOaRYu9uri=xXpFC4O)_76j z`CWxPo^pS78Xf1Cj2_p1{WM6>Jlmi9Z<0Pz#?N~R??WKU;7|Z*?Xd3!M}RV8-*!BY zZD&VS@{wB1Z>rw1@oG*=co4=XJg_FA`>y>Jd#iG46cxM`mFlo7c|>>`POR+({kiza z{^?je?{-`v9FC&a0-#aUnZo_eLI?@(SLep$3NwFb1!jQg?2(;B@9k7+8??UOopsE} zR+@YkO+xXA;H@Pdvgc*3QuAr{nf$c({VeI2@9+DZGW^hu+Xdbr-naNEeoj28IHfUy zkg9ggu^0%B=os#X>2*K%#eQxF_G3t}`9^_JZ=d;Pa*!q3J>t|gYnQ?ZcNEFuNX8IK zR>*(fKI|N9>*V7^r=FO$c!myi zf)}{6 znhF-K`JB5ZSQOyZC@^d3^Xuck4ak_maP@gIfP%C-{rThL_docXzxegbNeahB^8e!4 zAI!~!^@iX6=k(jhuY(Z7C9q+=ORsl@@OTuSktGSag`R_wY8z#__>>w>hBFsnDa3!J zvHAFZ`}pKgDCU5}G`wycpLwqdIR5_5H*_c+hmwCshqs-Ui)RFOC(RYKg;vQ>V&&{? zefy;*H?1_bpFz*SvHX9T_7`;=EOVNVM>udi+s-1Rbg$8zl{*n2BDo`zXr4}tt7%V!lf zU}LsQva!|tl=)nNxT6HpH~~tnR)4;%!(RiOH!&ziQPbpG_q^og`^>>GJad1{E*HDr zKXWhgd7w^oTnytVV&MoHJI*Ru3C3DaV!Suwx3!2!xl!RI)yjf>m@MCcr_N}9?% zmkqWl7!{We-U9D(I~|yzZDgqwe$O!g)LQ`%vy8p?a~}h8I|g$9V(kn?P)x>{krP|; z)zy{NSkpv_eaCa^Ru~%edejG#?R^I#!<@y9(?ZhMuHgB5?t-EJ0Zdo<~#7Bkc9H12#M}u^ttzy^!`OC5Hm$* z8_%s?$IYGRfK^#Tj;4(q%`{~h7n2A;238u> zQ0)-QrzxCGIg5YMNzxl#)HFZF)^=8>(BuO*!uYFB$qpGMV}-SD zRq_@(n+bj^Y76O1MMG;+ObMtXu4H&Y;##x$9$U}J^CAMq#4tuk;(S~L=XV?5>`RUHOI7Ts&c) zr+UlfyD{BxJy?G+%I;D5+Rx~_wuST8dsbaWR5nlx;<{SP&_!BTIkX>R^u7@@Mq;^r zmWgAJ-bv;8*Nn~a6Rd6p20woGb<(lCj$R34Dlhf7_wu?$KZ@AS>o4l;3HovYOfW7m zV|~gesy$BI(%y`_rajMFCVi{5Wt|1d|6WxNf|Pn~rG0?-z-sLu1@lx$=}3AsA$CDm0X)oJb=Be%>`mSE(kf#p zH$G{KT<4R0rAZX%%y6#5_#Oy41i)sC5gf*M;QEG{+@Q>Hc3PT;oBX^QSw=6URThzlUx^l$!~NuKrs+;{WNUu zdtD7cA1^`%VN{!3lf7uigpJ1Ou~Qjuqd#Hsv#stf$}N5X(2aY}{6!1&Znb0I67k-x z3sR{6+&{Z@i9XAb@o(R{3}-re>oQKezrJ<(#?F5?bjU(TnzwIVygn%s9O%%WBK%&_ zhX%71in?3k3zVLIh@_alYJ}I8IF@@EYsx#+39rMgMUK1X%_Z(!7yr7$ao@_aO150P zBbYg-N5Q!YtP-vjBGk&^Iu3;M`A4V<`XaOj?7p&8SP0%!7Oj;9^F4LvKnUyPbU=sP&Tl^;_m+kG-FJo3T19&b98cLVQmU! zZe(v_Y6>$mlkp-b0ys01kRug;Wsp4z!!Qhm_nbl(s4B^lY(p{hFGFW` z5D4O-2l^zQee1({tOl%@)CKx?V4x_5Qc)^HR>!O{`N8`_B+|s9n-ggcm5_u|$lFPb zV#?M|Mw83FI(ZP?IjC{jG7Z^&E0t!`ZJlnH#*1&C{)&((0~1z?+NZ2G2{l6&MipB_ zPJ!q;FK(P*iPv~77;WX!kyE4so*h%wjne~{$kBpej_;w3WSyyJAO5+!M-Y>l89bBU zS{W7?5}*J~GM*q&8*>8}jLE_T097yn&65KfRRJ}TKNXX18VG+#zGRCr(!_Xk9zwA6 z2C7Enu2SUwz$#R<)WJI|*Bgr=`5?##2_c^WsE z*P}XVxpuVH){}E&xORH9*Y3wGcXMC3`=@hrGdu6>v->{Jv+wTCu2>|Mio{~E>OkiH z%-xw=(pZMJZp(kv+f1R+bUvEbf+C8K6!DwHd{h`8CEqJS&n3`WwDj`1GDD-HP1@Zx;$(AYE`Ri-EB1I(iuj&*j8XG7l}kvGPR3Jq0E$p zDxqw$A7p=6#>=I0nLJbeszf9fGDPb{>%xTIGonJ#4e>$ot*~8THzj$JPDxPmjWkCZ zq#~(=&A{<#oS5VA6er;}@Ui^xO00}qv1|A=JhhT0SH`$bs4)F~{Gz)55x=CFmwBP5 z%*i^f@FKj1)KfqXG?K)oUC2}a*9(-ozxi6rr+|Nd4|sF?V(Tb!c!(_(PE*Pl_!~cY zPmCWdNzQKI55eG<^D8=J2(C3 z#sE2G|7at!>S!S0FUOEB;z7!o3XcEw&no=klSALBgI&`aR~0p8nJyAUb^;dRHGsnb zZz6vi`_j$^x-NT%FCz6rzrXt`T!o3635&02Sl?-Yy^y%uT#9;&s0%$a6PIBLT9e=u zkhSEeOjb2&F|`BrHC!(rv?6uzBGYSxT+n6he*rS!^*^was2ZApQWCcM3q1evJdRLd zgcb2m)C+DtM$=P5^}G=n7z8u|hiuXHq=bKhoHkpJ-OKtML+}B-KkFMu&|T)Hj?s39 z8IZlK`>O|?cs)cA;s}ujC4iclZ^K@5bYvT{xo!JYYb@|~F_z1oQ{8aswCV$<;VR#)8M1)BrACS9gxQXmiw4%FinAkWC_{xE*smo=oU$f>Mm6<0xcz`= z$j(1(L`wV|KFNvkcbp`EPipWinU!%az&G$MILnbc0C@Jd4j?zljnEzX9B;iN`QWhz zYTIht>(NIqP@T1Bs-OyfmveupltDf_HNVvNzEIii?E9zB)V)#WIt47~?Qk3kWIK)( z&*50f+;xp%v@j4D9SsBuM-7I;LPM02oF}xO-!jf`@r%3hjAZ@8Zd|FEY4J9BtUd!n zrmh-CEFBFv0#LiZQKkdOn+>kK=}WjW=XRCX?x}EjTzww5_wC!qapix+bcd_+&4vG@ zk_c#MU@S+CBV@{AsIan4SuN;CenYE%Lu8Mppj|FFbaagPu1+#|$`|kqdD~{3Xk4D< zWZNo+EP)X`b##*PHFOBFsIj13wg8u69+J>Sx$gX?w{L*!wG$05&X{-KNr3sQ7Fj1Q7!kZ7v4qI zyPR=eMsmC4QTvlT+Z9iBD8d8b0k=XCSQ8jito=6t(L>q_Wp0z}AUcx-h!%f!l231= zFc8J>{uJIrr1U^BB!#w$kV5`Q?25K(qSaoBJxMJE8yR!Rw_n>6TB+GZ0`c>_F>fB8 z{CL|%OQ8=C&F&d}hh7hcL$s=!j!Y(N&4(70eE|?4#%lje-;Cxvuyner)|Ha>&WS6< z&x3$b^>0xLC#k+9{yTKKhd+POuli@btfS3v1{2kd{fL;?@1;FE-Tx%it<#%z8d`sY z>7`cBG`VMtxrL1qE8Y5edJ|_xxG?&^4108n|GJqLR+b$ zCW{4)-(9h{<`SIVk@(dJFjAf9^v0d5?uM>AgLgt1DGDm!=r(m(yfl9;(AW=K30IZ& zay#{xdVlGFrhyYQ$+dvKYdDxjoq#Od;H;pFt-A^WN_?v`>^d9~onU-T=3|L}G{$Z8 zFne+vF*ZwzKue?)sYIFu%C>>Br$9MFS|TM#CDI&e<0;!_fzlEwM_M60A_Zm6urDu> zurFT+ny($DDSHg`kOeME(gLRo)A%6#fBa0G55~B-!_N-M`b?#Q&-2jf&Ub}79Hj9G zdwSiHzZ)j_m$Tg>=K}&aG?S1c6_eX0E(hdz&$;*9qmvLPOn;7Vt;R!=VV)=65wj*w zv`4M>BqhfqHUk&h3P}-%WLS+rbFuvZ9B9HyB1Dkr`Zs1E3!swv!6@a*|)}p z#M{RxRcTf3c3-jo$1K`!$q#x%@uUi6Ze(+Ga%Ev{3X@VOF#$7^;93_b$Sq)3U~u7L zu?%2<0s#iRpaITOKoWI;G1waz2m=m=VGo!9BMbv!lg21h0y8p`;XoFDbyo>kR9BXM zMe*Q@WhJ3fCgYf*bc|7BRN@xfbUK=l5seX-Xxs$>K~~uckR570wX#T6u~X~%-o5`hPr!M4asq+C zH*ooifR8_WJ0LkaEa9Dh)xk*-?yH};{9JMn$y}2;*Bb(t%)=!Ux?c07vqZxGm^Yce zF?sy8$>WdlZ*ZI-^d+}F^vYzPOQNalR2(jv=DyM>dXw{F_!CDSJo)4QddR#vix++r z7oV08xhEn?K4bSxx&M+Si)YKp*yNm20H^v1ozGv!FBt#H`0qq< zQ=!Kd&?D&S!BaiLo{6q$uI906UOi(9sVe|ajRkm%X)|4w@(bS}80i&`piv4`b=bdU zS7Z2>Vclxt@K%^&%F?Sc%Qg%F_5((=KB_rh*4Em5u!uBxhZO9LN{EQwzKsfiCX*Ln zxT#lohOUr*CVF>UjfgH5l{ta+B6c~mCzn?Fr<*gdmqeei7kt)+1BwJpcz1) zZA!@8pRS15uTT>)&cYn009{UD7v@OuYx=d9vk>q!V_|mEAprb(w-V?XdK!2!9Y+5% z!i(QaA=j8=Qjsg~@x|Gu49I}Z+k+JQNM$B}w5R`nJ2(l08;5oJ{F1byd{98B0^%6! z;S8K4xPg;|H+rSv%`qJv&CMMhG0oxOF)`sX@s!M=QMp3Ub`g69gl%|QN_SnO{7>lr z2;ajH8Q_|Qe_GtPGi^)a-o1+!?VuBYipa%FQn=HO;wJ+a;-Av#Kv$9lsdPG(Y@B%w zfq~k8Qhagmqxp9v)jzuaBpvapgQ^sLf<6J3!xkbr1yrt~auxL>rK;Nvyrf!l9dHZa zWVmnm-h7`ZOKJ3SUOWZvx=vgY;JqJ(r4wC&Q2TpT5ghNZ#rQV9?!W0&HVLXyvmkS!RX`sw`#-%9O=w;>x3c zX^=UVN7MN%Wp*AY8Q~?l=VDT@@i0DY@Rh{Z6-kY`KUCs4)bj=tJAh!amk}%~gPQcw zAYRf@xX-@k5ZJ+Pu$#!gH|y&8OkIXH6Vf5dlu;kiANMGEcrS`};DU@1LN~^HeV@S> zYmG`!6Ud~oV>76jZX;NL7o?yEi{3zgkf4Uw8;wSp5sX^BmRzA4UT4S$nMSKt$!L(5 zMr|_siDT_4qmvFN)cK<1`}eM+=8>fJtI?^_Zlxo~5N-<62SE^#d;@fficZl|Igtz& z7Vwg9MjCm^pzbFn`a&HPn#@Ide6tkbm>pm3DnTDO1l{S~VJ)Gp^UYg;NLp!s2^19Y zIG5g*!aW1>rav$wv%yj*JMGm7joOBS;gsU#5DnWEJNNG0vgI9BIH;k(2*pG^??B4v zKMidB(icldB$w+)CrXPLl+bk3=m0aAw4m0<=;<_A0#u@+l6)#5#d%K~*t?ye#D4{x z0Jn@k>1{;PVKJI5vTCT-;`{l3q^Qu)onOe$SI$S7W>0RTm_jfC+O(@S)#WAq1y z;FeQ(i|&&4nomI=5OC1(Ru~;bW*z+J5D1}W^5SOvz$rXQKVkyY2dAJ{MShWchpGbM za~7G14^~roS)M%?zt+|F6wlPV8nvXAzx5UC42vP*^ zT)$Sa6qb^EwNi{lX<_-X6SfWU=aFm*sBN}$SUEt zg(RtySs@=Jq*gulliV-DaQ;+!{SMgv!Tr*x`h5pw2cf>!&MO0#9m)eZs4U(ERLCMBJda+`FbTC3 zT&*(TzLG-z>ihS9nNC4nbX{5#9ECGqHyk3VReW+%(*C_nz7k6_ZL^-PJI^+C33@+3 za*0)GdlR3O{pp(cL_#Ogmw3tLEGTyQD+}p@B$b*MpUb_1KcDl(SML1gcNlj|a>MMJ zCM{3qn=0$ds#)H!4rZ|W!omV7(e5Jlf-4SQazi@|hv7Vb^cs5&$7?Fi9PNSYU=4(Y zkfx?W_yShdCw2ij3s?G^8cAMt7VrtFQ7K7~1j*&vHeDrLV@vx2JXX}E)x;FW!U~xG zMPv%exA2-u)rn7mgu}X!;20v_pW}4-3~W5>i`);3zD4bANo%%iy404+J8X^iY9Jkk zU#I%fecnueFV^X3uxc$S$r)~8LZR%{Jl1tF9Vsc|D^*pRD)<(@J>OVYRpD@2Tgna> z_rh-h=Tq;ZWY`KpSs#4HBqQI%YdZ2eHv-uKE4S@SA-J8+lEMMwb+9n;INouj`XrEN zdb&tUU)r)@ir-#{wkOtrUi&kA$ClHwiWJw(!43U?zBu)&q@&n1Ra%&! z`OWly>+nZFq2v1X+qbPai4_4`Xwa9`8|ZAHerwmhMRqOI2E*IrflUf0jVEp0EkEBK zL>{mJYH0{8g}1WkxJ{cjZ{8Tch;8&WWxI}&6&K?l!b38Go>DLd1_x^c!LLaNL%hvy zD3Ns;P8yuh4sDut-2pJ?=yUa{`cz0I>=xvI_#=ivki~%E3m)>6xjDKhZ5Ydu`a`Y( zY*4ALgi7LWo#{?N7p6-`r@LF_o6lP%o!Nz-btQJWw*1yta``EaNnPL2N_Tr!x!beZ z#!N|uInPAK^q9dGx*oGxd$t?dF14!vu06Y>98@orbU?0M4WRK)9mH;bKT{CgO%6XaX0&e;DkVL9rfdNbZsO(pRpl*HT8^L zr)ALaUu;H`*kIdfp{H$I8~jm}i?6xK%mVsyv+}&EkC9|l3AP7%vmiY6B8O9fUgE*Y zRMtM3Z)#&d26$mm`0AZonE8Tg)0jm+-$*+Rw7+^s!x|Lr{%?GdGq)$FPlp44&r4Ak zi~awYL@oB4SQ19e(BOcz&vp(;%RiJVkDk@gPTl<2G0Wd&_bl!3sHjzN^%B0?jruFX zt85~n2Asb1sq7})beul@@L>@yhObzEJeAR#_=kX@`9P+8x@h*26YAoss?usduxhP& z#fqxbYG{JCgZ;y7z^KouNE-@>wTe%}k{hx(&!?*j^oR=#z^oTz_r_*%u+_HsW;O(TZ1H&!ovUqk&d08dB;lTe-M= zu4tS^l+C(DfcxSt4!hZsGeju9)Wo~41baG{3Z3<;>WN%_>3N|;Bj6Em`4rv*5axF*>UKnuTYr&mt6IIV@Hq$qvydy9)>qq4>rL*S*ko{ds+81sW9(>cdLd`BD!V(m z-|}h>#%|u<+K#SUb*jDPl1)BLu zRFBco3>__;ideW43>WrdI1gPc%(){}=TYb=jUCPHNpO+OKsjg*+JKx-4o#6bpJE-M zy7QT&c3(CZahBS+yK8s1b}Z~vf6ZUnYi)+ljlP>RJ7JZguh-GkjoszG?pX{C58Be( z#`^;(t1XO^@mCX*FF-{Y*NbVe|9^i20~9zgFmO092s8iyV`>G)lkry*lb=9A12i)= zkw6rG#aRhhQ`fdWX*^`NQffJ-cF;g=(c5Yrs#U$fQ9(sOBZNT+L8gE}hzv1g zWnd6w9%Kk1%!C;fty8N~J6T$LOKWYV+G^X|*ByFt-+lX_y|&hR@AvNazL!8g*x7rp zwf;5zE8$V&#!);TPqby#a`&|!Gqy;!t%;9+lx!3SNy5U!FKm(o#e|6?xgATb&eo^F zUSyq2S*P%F3Ptf`k8rP_J&L9FQ^{XbR@y(yEnKvB zp#((AGiN^g_J`5?%6f6uOLOL~kVV8th6DviJHI$*&Vm@Jg&74n}X+F2Yn%lR*|aOd5U zU~yQWvn+7z9?#9IHf?rZvuT6p#?8;oa`p<5M2Cx|k|>F@f3P@G>>n+OjB=Jsh%j+L zfFyvEvsN7Lyd_vde#POzv+k|`?^l<91;}=>ZFWDgT3U&2$ib(k{mCdw~(nMVB5_Jj8pbX8f}8C+(-&zxQy!!@~~8A8~)A zbHd~arV0P`=o!b&j`_?|rfcG>6Z3?#g=LS;eeCR{`ICNpeCUa$C#OI83-ntj_VfDt z@jySn|1s;c);Qa1LhD3-JYbtBaA4(l!dX6^fCGiV&L3vyU=b_QXBjfb9)>JE z%V1_Bo(Xt5x+Ea4r|?WnmeTbqgDO*%c_34r#gZd0vvbIK#NAhZmj72aOqiu6Z;~wr zl|CJduxJ?10X%=~lKC&=IV@RHryo#_Jr1O+F~c&a*qOjiM~ejHbt5}}lO;>Y!M2K> zjq7+t*pFYtJ}WFxT1x3pe`4S~tOhB4Tz6c19FD?(=BT|3n6~QaE&Ba=a1?>{ ztE5cYEo7y1PAGCvU$UBqc&)X#`YV2sTKJ*vqV_}h2!=Et*}G(vLoO6RKIB%|yRbL* zV>j$cfBU29I9voQSn?jrzzXn|dv8bk*vYk!-%S^tY^oZBFW|U;CoF)a;$Y(IJIP1{O^lhjXBw4%REOp$PH|I?DTzaS&Ue zn-$Q-VuJ!wK$(yhnSp#b4|VH$wB67S9h!FTWQd;Lt5cSL27iiJmGxXG&;ZI1$pXag zwP|QYcwBr;1`1TuI0mbPB)*SeNA?Kq@U^mjthCo)pLXQhJ7pzz7VF{n}r-! zsN2ORJka}v9821zM74*n;r7PVHYQfdY1ccZT`DX_HctU8K9J^f00nV?Fg;3(&Z4!z z5PYl|BBB@RX*ij6EcYl122}{1zDp67q>4>ju9^#fTOnQ-o`nF{c3F@+owHM$7ys0v$AZ8I& znWjGg(a5b)0H-s1^EwebK~EEvU&~mcc?~wg2JJ?B7YCM6-)&m5$Hjaa1l3kr9TIt9CwLN3w^TG`muOEBcfFZjms&~c+3(eJ zAnM&*k+DLvf@tT#X$R7~uvMk{s?iQL?ZDnpn?@fo@rb_s`)O(=r#{Kd>DHrOJ(y_k z3~!A$c*72@_x*0~`1dXcEY8iw-?LxRHM(klZ4FdFxu$~K604&VwF!A)wTS%;pTng% zjjpMz%CFX)~S3d!5)lz_C@bd^FmKaCv^K@iQwzqRy# z&oOksMYplycU#}T#+BSwU5mDr6p*%C1!U(KTnFJ}QmFl~+4f}_&{fBBjOASjueLgL zegQT=`gYcYa9Pu#Yu9!_KOE8Y|IwEpXC5Sav~zldWrS(MAQZy1p`@A@+6LHS>i``} zRzrVX1!?D<%0W&qQKb;Xb`r!Elc?{1H{&BMw`0EeCiCrm$qz;l6ppA!r1V{(pjF@!46OktsCjl=9?D!L47wA#c%c_Ix#rf>G zLd1-)4n@1_N#z`V`}CL43eBlCiS_&P67}IIYm=EYlL13R?y*H?zuYZ=*ymX41$L5? z!z#ilY~8%7I=u55-dV?=xUgh&tuS+wE&$w69T+~LwUv1Xjl@;6?ermk+GyB?Y>V#L zNTTo0p(p#gv=#b#?yM2=QnXRXu(*zBa!%Kpc>=LvYW77!dholW&zo}Oj*K#g=Gy z;=vignqVMLZ7>%?qz$%zs}Js1$r1awEs0%d71PYp*wY7cQX5dHUF;hPeqQX8q|CGL zOt*T{sV%yyRy|^rW7#6k5NpIho?0=<+T;@vvHDu;qyb0s7kKw2rr3=6!X-U^pNLAJ zSf8DV@PsdD#z(b)t|pbO8mdSzRdIOG%;EqY9i=^x1APdu6X0oo;sF+kc7eZA5{<}=;;k(yM z0>B@Fo1udc%EywASb6907GtxVcYYXGUgjr`J|}$Bt|VJ2b+QEs;0;Yg+A36(-qu97 z?QPmWK%%2MySxy8-F%@MPFaH8R{&WB7ubesw$190{MA_~}5*6Kj$ua8h{J@isK&L=A2CN7!h00wpbQQh zG7SjxM`%W&noT@WMLc1GI*p0*gs+|s(W$fHZBkclcg&N$DHsEaT_@OFDa#3l2#89L zRG@jj^d@P4;Br`iF4qe&@7UR|L@m&!XpAaPI;4P9#0mxAma$(EP2|gbyu*9|&0GID z9#6p7B_F`s8}QP4UiAo0yF&1g31NMKr%}@C^-kDD((;>gEG0F0<@tszRMw!#rPoQK zQ+9zHc-G4L;_B0k87C2*W_JNP^cV891=@pfi16)yWf$3T5D2>zyQ5z5+4BZGgRUJB zLXV*$zq-7$qox`;&|=01NVsCqy++l2#du4rRd*9h;M^SCEDgye}pa zdAQPl;d>N*;EF)JIt*ei7=Ue}VZAynBm?Tt@t-!x#azMKX}^G9C89-rY& z!`e?6+klxB3g=u|PuT1XJpLMXcz;L#DiJ&1ju{=;8g;0~3G#FDsw=WGbvlC~SCgg5 zfesibwbXXiSG2(Zl&SMm%h6S+vK%2bzKodBaZFmb5#Hkp6+qq2b=7p)Bj( z_F*bo>`s$w_a~|pkO;Dpgx(}H--k|0O$vlCGG7dQq!U6{bz56WQMOTkfmA%YHQMc^ z#p|Xz&EIh3Lnm@woprr%sJZLxJKdWXxQYGTMQi{Z%VC@{%+FGP z3oWE6TfhSC8ViT8-yMX51zqR+&J1>Le@(o z7P~dcD;>$21#N~jS0^?`aL0d)^`iBEEupkbZZegXnQGd%EKbs*uB%x0lTFP7c8@o%+a*WR!cMl1d1?;O4OFcxXpwOo15M%v$^y7O8;kfqx z!`3Irw8f?V--emKF>~69ITpf~EVud6Kg|*05;l`&60g_7VLA%Ji$m)W>xdtJrGpxk z`TNQc7Jg6nG}Yu0K46+IShvn+XFwQQz7edx_XC#c<09EMnGg>L&dGlp=HD09dzF_v zw{dr2pD{Pd&p6%~Ceu9mnK+s0E8;HgAeXj5>n$!QzAJ1_A8X$Bx`v*cj;T5*Qgj0`y;J+KA&N+TP zjJqx~pXRUzp;YkaczXy;@#eHHsDu>guyxID4y<_vct|qMcaFvl6F&TtM_qC>V1D*sU z@4|ObmwH%Uwzqmu-n`;hiXzIO8}&CD&xn{SgGYjWoT7~a?MZEarM}LqBq)0~5O`K@ zfw{1wBBVRECV3#?okYY8b?q;W1qt%pE?K#JYh%C2A{D@DwKUbASU#HkHXiQfeK*Xn zusR4oBCW?lFRKq75)m?=nU#%t2NcD0WKyCk4p2ZsS)UUw#1jPvkFitIp@oKaeN)a^ zl$=LLB}x@x`}IrHaeaO1P$jh>>5H@7cB^rH7ZZvU!tZh1B%31Y=b!B8od^0)}DfkE4 z_+CK)A>`G6++}-+>^-oD$lk-rCOWreWJM^vLq zWn4?Am@U?EEFh^DY z675chz8v5qAu+ux0pfG^6(R*hEv1?A()~rMQW%7Pj;5B&2=BB8(`{du8mn~3$O-xV z94xEO;6{h!#300uXS?W_mi>q0`p`POnBLc^D{a-GmRnd!euEV>TAyg-oi^bcCVo+| zFiTD!(H+qqfva#;bCq0rSYMgdi?Vv85Wko{5HC)fLD=w9fCsHllR?2Z!&l=A3*i;* zLVK5gjBT3a^wr1&hu)zL?zi`|nDEek<+K7YJ&lZRC|Z`|bnzkd$N8mv9P zYvEi67vUX`{b7wbFr_2VWS!K5W4au#4}W>us|JhS6rW=fm4uqM=vuTb&_X(3i@i&M zfaz13lWNn=B%6!}50{{mopgCoQ77ptN5h(bmoeSI+ zw0*RI1Ku2xhX%-qFs@X^ZL#cwM83p_UziKbV}8k&K4SVA4%w=%Z5emi%GhFes*6>>76H$SP(H(wv5F?q2in2sJC*!9_A)?Wf5&LuY zky|GVP{Ay@dleeTT)Izps`yQU0W!m*t6$j%|RH8Q}W}}KeEM}wVZ^(2lPQ?i4q>8E= zn3{@ExuZjb3c-0Np8zKfM3YdC%NEQpAwVq$tG|;QOVoV_q7}w*M&Es(r~$NyU`6=S zW1(sqNz*809mkBPB~T%!xm8B37TPP<6Y-y!yz^Rt_mJMMc3f0gbaquO3?@IrJNsYr z__Q5|hMgQZnTG0z%Nb=zYY6C;`^^|+kQktbL<3)hDuW<{8-qknEr2Q@<)~wPhs3MR zsgTIpy+~@plw`I@)sOWBZ-=CLq5+JxpA5Js8QZtSE?YmR@i-PkCNm z7`?^=U8jN}a6B@u_5XeC*Ei|1;UI8P2Z z(b1>%)tDd)+fJ^oQ5w3gMQ~vpL%tL7w<1SSN*9J5K5~J4pBKP1j#?EJFCP^U98!ei zgy2MFyKSx)n3~UPxi<*-32?z-?kmHgQjB4pLS%HKRpk&DfzLs6MK_gCkOnFSL0GBb z`||4V)A}Tebf>WnIV?J?u8$ac-EQ+zv7!g#4W-P|SytAC8+pTaT5SHc{h3W+`Z#on$z{g;pwOyNeyfyxKuBa> z#=23Y6XsR}Ayltq8ED&LHS3=io?jx33>CgYn>`wicWY!nXg4DEA7AJ0%IMxl6=}&C zdy{GG8A=I|(NuDhyY#RAJroG_+3~+Ge7&;HpWP7kY<1SlU>4<9=|y^c;>dQ$kW42p ziP~Z%jz*)|C`e?PeNYI^9AY&|mCtC2sYEa?oTlg0>BYYcQ|$A6RX~O^ zO^h&(8YP1@*rVp0Q!4X2gy9A6iAv*bn{v4aG;tuJ)20gcL1^%-`T$x!|TV+Sq-u_ar2BOd#cT-yPlKzgsAf z;rqR*7zH^A-!?oKvM#XawP zZzQ@UFmbId0@#H_5h3QP$A7sU_I^n%n}kK?o$W^06c^LcE--8!*w*#9OKeLfxLJwYN|lY7Ai_PAD)Yvz;M@k>~Da0z%Nb> znD_dZDi>k10IZxv=-P9(=?}Lt4HjcP$eh* zh@yS#er=*G6rsj@O}94f_x3uhHu@{7qCAMk%qszMX@V2HbJMv+l!GhxDRT5oiOyEz zFbfT)hu%(Q=6m8t4~Ck_-C>VmMg^B)u#J`e=o}3^GmQgITlAOrdfJdwvbFq0n1j zDSuY(pTGcCo(l+p7z&0j4^E*XIfciyY7I>G6X(B7n7?TkZ8w`{xG>Z84vZRqHIN$~ zHSZ&$&~kffa)~{9u_}alRj`1>5U5Vjd5e)5~IhYGKd&{xb= z)42P{R^gvFaC>K*NtT1Q8n=wCK#`SbiGEd#{-DSvSN5^*sNFu{o|CX@ zhCJNmwI}Oa1$AzWRNF!r^{A5M1uy)}ia&z-2z));fwOe@H;`CpAgr`k|EK6LyZMFW z6JpVQmi`Sr19nKxv&FY!+AWdL;g1ZWsEvQG55*z<`FIxbcOJ91eth?Vko{J~+`#*HJpeL* zTs~f&c7L@lqSa2@nnz(>vNd;=i@e!N>?PAL3=+aAw}@&ZBWuiScAVCH5t zUNII+9Q7yG)kXU=Iw_cgm)keMxm*n~!sK9c98uHbO-{7B?w!GRW0={&g{sL;ShB;b zL=IF*=+#t-&uu0C(|t_HEmIbxzdGN8)wUlP3H|9d9wz8FIh0eSO%LVCbs`(bPWxvauEa zZRHNuJSpr?$txW6+29`iU`zctVR~2GfA7jRfm1okZ7Kd)=!yv;;a{FWf8`F^6ly7qHb>$_rOK|L1r*9Sw%wzykVq)U zG>vySu6ASK(-zb6~9iBYk7LQUp zM0?s}!uu>grI<=(CMO^n$7A|O@J6eNxYx=>wCV~kZP6i(phd4)(dYfGxnH(0Spy&J ztU6Cf+ow>X2Zm{SOy%((?wLcxeJx;Md#2V^k0w3|7SQ{t+Y@Cao+ zCAoDilvudn;}LeLh?Ov}?Ad#`hCyu)y`($g{%OE#{0u-uMc@(mpFmWK&-yPAUkJ{q z)Ng+q4{Cc5P}u>kz^?VWg-zPVD(Z^eG6UrIca0*oELv-XXuGhh&fC$&(T~40r=XJ- z5rlU!of6-DdZ~uH=GZdE(8r!olKoI{fTfmqa^GV133LP}MhZ2j*TGKZ_fXj~E(c+GAD6IK>+-A;N(@V#6QOiv z>l-+CB1_`&K-zMm=clv*4S1sR5E7SCi*NAq>ddswG@%?0`V$?kq=Fbq~K^r{j)5qi<=@N>U zsRWM|E6cz)vEZjH8+Zdf7tY2ugr&C6wK4YCXG5rre`T`^j(x>lgRIgkzvH}Wk#(si zwTBYx(SOOOo+M@JU-ZVctP|6vI-P75Cry!447(<=x)uS70QcmIYQ&alP7$lrixH=p zC&Q4P(NGll5*@=a_gnoXbj@|V%4Ye8@*Y>}F4l=X=(nsxs-OH7ksX@9&sBMZ^6R%B ze!FlLPS~Ix$GV30M|%8MyMK%#L*?Y>;^pDyU!tup{1RtVX!C8IS$Z> z`a+*<8iy91WT@^8;J9%iOEJpM-(nMq%-@VM!0|>>RF>raOv|k@E+z*F= z>Ajn9lS&^3b`)~}fxp3FCB(qsA&_$G;N zOR7+%!INRhZv=g{(pct7Z>e^R;kp2x7a|Tofha#+j8N9PzA1*~f{>_i&%D{|$Hqi; z_VeOh(e@NLtEXSKuH%?iV7{3@?l~zqYjB~uZmH|;VASdA`nlhcwo6|gt7q(lATCQ< z)g`SWrbpFe@g9n}n59HdlrS;qfKUUlc+c56dDrztb zk533KYEutY93;mK&d2Ms`YigI2GJEDFgw9v6+q~q|0TbXzhLHgH99u8dF3s&MmHsDL)pbCh7xU%6;PO2M5qP;puFJ`**9&!q&j!PXaYIx_S$QiQZbfFaeC7 z`qJC0VyPzMgi2i+Qv;eZ#Go47h!EGCDOAD$Qq(8_s`;jeaglVN%jJDqSC{H7+nJ zN|@go7+C*rEw?z0A-dbs6;dzSN@20-dTyM!=4Tdh>aE>RjILGGS2QIc*`Vur?!gc) zyNNF9zNsw;d(QNP}8n7jA9z$&odDiCnO^l)wy zl_5_~=m~!2CNUa#4?hiM7W-n&1X^Ntv6B6?b738lrjJ=xweRT)6^}hX3$)YBxH#vi-e(56k{9LH0;sl~a7f{**gh#^ z`HMa|-;9{K-)uRhPI>Wvz`o6&>h-k+y^Dc?EPnCO4ET)nMCGgq1 zPwbS`Sb~Bpl^+-XD+Gf}rP7Z;z7v`Xbpz=LvRXr>kO5nJ9|RJKWi zzl1T8D({bTyj-t{mmaHQZ_UY&TO?t!6P2Q8gHj6v{K_Wk7?9U?R=u9fT zSq3akcBI2ax}*FVBr?TR1e?%`7t1fHK?J|>q$BLO@*TxG2tsa9zeuo3llnat{1JTA z@+NCw1Dk=lx*-vA=QJdEEAe*`As;orJ9Y|7 zzYqCBON2b6ng6W@q#qJX%PW?kT`UEx?q4cYHImlNy6E%_cUBGM^Ltc^9(Dq&FZMmT z1KNEdj_&^sUT<3WOoQ!|I|x^Db)J~7vcH<;YH*mZYe1SD>@#;FL$}y;S|qr87wSe> z5YkGo0*O^?X$}&BA!J_wRc=`VfL0C1!M;3iNh!WLEdUNS5wmwk#bWl%J0(!&*8^^R zJF(b?IC`b!sjZ{lp_jdbJvMN9TzFPXfQ!8f)dtS|q82+y<%0yI9~p^y;vmSux%(F( zQ4^bQ3IsK`hDySd3%5zvFA}-QG?2%kJBT=lfI)W8VP{DdU~pLAgv)VhPBuZqgwX(o zmTkKUYwJgD;uO(uYkc}bF|eC}U4Xz&#LJ}FY?Zv(=pr^7z+qO>##_FMbx--~`+9S) z*oq8WvK54E12{Pe$lC@2l_(`cZh3cM)|ii2kep*!z&gNnE?;Fs#(MH@EM%cex2N6h z(5AMF{^o{5#jlyHv-R6Yy6&$XT=ywTSR&@cUQ^{rz3FrZRc>5ZX6H9Jk| z9|dg-#cde;{BIYUYm}gNPE#me6S>>hTDagEvD`^G<_fYvg(6)z0t+$BvVshYC+(4X z2!D+aL5Y!46vfwEV+XDWJSh$L(+%48)Xps>6S=&n(YAOj=~4B2^PF{Begk7L$MSBK z!JfX~o{Ha|vLs15EBItsyczLtcYkxRO1M(=zT66uNzOkuWunb_J|o+_Er&$b=8Kks zjQuceMVIC(Kg{HX-S(}$hqKSU{LL)IkUstn@$Hp=!h9CjfhX|ibySd;u&e93miw0P z3Nrj*{@ywE7NYzILl1ti^8;GpM`Bhp4ahi>SvudG&jWvD}pe)N|E50c~-+DAfwNlef z*wmV3oo%c4!V#hcpRDX7OAq7!HvXx@>igPzu)CWDH8F?edX@g*FJ+h=q_)3P4J2SSBup7B zK*uNU2PTybkm};9|A9T1NmCq61;~I3NZ9^_aJJ3MdiLr%N~I0T3rY)Lvq>?eXN84DNT;@kZoUX6H(+$>kTj z-YC$)3Qr^E&Md5vY84|=9zkzDiUTEvyy^q4aIX|!jl*Tv$Kyxp)Y{5=hna`Y@_(C; n%=2|`IJDb?W!u9~WC-pFJt>qTjRFJ2Ex?UVM<=Z!gZ_U2Qgkj% diff --git a/übung_3/aufgabe_2.tex b/übung_3/aufgabe_2.tex index 0c7979c..7cb6279 100644 --- a/übung_3/aufgabe_2.tex +++ b/übung_3/aufgabe_2.tex @@ -2,5 +2,24 @@ \section{TSP mit Wiederholungen} \begin{tasks} \item + Um TSP mit Wiederholungen auf Metrisches TSP zu reduzieren, müssen wir den zugrundeliegenden Graphen + metrisch machen, d. h. die Dreiecksungleichung muss für jede Menge von $3$ Knoten gelten. + + Dazu iterieren wir über alle möglichen Mengen $T = \set{a, b, c}$ mit $a \neq b \neq c$ und $a, b, c \in V$ und $G(T, E)$ ist vollständig. + Erfüllt eine Menge die Dreiecksungleichung $c(a,b) \leq c(b,c) + c(a,c)$ nicht, so löschen wir + die Kante mit den höchsten Kosten aus dem Graphen. + Das dürfen wir, da die TSP-Tour diese Kante nie enthalten wird, weil es einen Weg gibt, der + kürzer ist und alle drei Knoten enthält. Der Graph bleibt zusammenhängend, da wir für jede + Menge $T$ nur eine Kante löschen. \item + Da wir den Graphen jetzt auf einen metrischen reduziert haben, können wir ähnlich wie in + der Vorlesung vorgehen. + + Dazu nehmen wir einen Minimalen Spannbaum des Metrischen Graphen. Durch verdoppeln der Kanten + entsteht ein Kreis für dessen Kosten gilt (siehe Vorlesung): + $$ + c(Kreis) = 2 \cdotp c(MSB) \leq 2 \cdotp OPT + $$ + Da wir Knoten und Kanten mehrfach benutzen dürfen, ist dieser Kreis eine 2-Approximation für + TSP mit Wiederholungen. \end{tasks}