From 624017b9875640fdef8c3fb83ba4caa2cbeb338b Mon Sep 17 00:00:00 2001 From: hearot Date: Tue, 2 Dec 2025 10:18:17 +0100 Subject: [PATCH] gtd(scheda): aggiunge theorema egregium di Gauss --- .../Scheda riassuntiva/main.pdf | Bin 509102 -> 522394 bytes .../sections/3-curve_su_superfici.tex | 149 ++++++++++++++++++ 2 files changed, 149 insertions(+) diff --git a/Corsi/Geometria e topologia differenziale/Scheda riassuntiva/main.pdf b/Corsi/Geometria e topologia differenziale/Scheda riassuntiva/main.pdf index 6d816bf07df9100aad17bb9498ad630834821afd..24ec3c1977d56b9077cf0f6a93b541538d0d96eb 100644 GIT binary patch delta 74810 zcmV)bK&ij3i65Hr9}*={L`E$!E;kA#(A34)3NkP;u@bfdlgkP;128!;li>m=f9+ds zZ`(Ey{_bDFZ)=Od;;SSML9sM#w*cK%B-yYn$p^(&5@C+y$#Ssu*YBt{lqr#-{FZdU z0)&<&@%Y?x$K&xNbA(Zh7(o&djuD}VL~f}Q;CrX5oG{CjT)-qF?<5NkN^r9qL2d&#zrBGOky|>>QN$5 zC;^a+5Dd*Y<0xXF4q%Q#fCSegfWj1V44-gw3{Zp=DCUTVjE-V~1cCA5e;7Vt@K^#Q z01K)K1{Z-EAwW5RAOr}5p+p>k5*RQ`ppsw$AVZ)5b2yOEh+u%vfJuUZKPJ>Y0F;9? z0+t9B&%hZ9;SUZ#w+M&;_TT{2Bw&#+g7FB@7RpE+fL@rekpdchHfRh70EZ~s@S1cA z2cSIx`+yke1s00JSe*g2e{jfZSBMpG0v%!+fl0tjF~jkQa776LgrIxOIYV3z#y_d1P)((pL^YpOlj#e&{(6Zy)?e;bGuK~J z)!b?swY2nQ2g@Rze^gnKzZ$bHmLok{En=o+FFFYBTLW3n)%Q>8b3HJ47smHmVxh&R zT5PFhTf}OnMOW-c-8(gp{!-1-qHMLD+F6g<;j^;;g{Cp-qBu9nUtxO{z*OHg(@na1 z!$fmhOL*w_#xb!$d8?(~XcWy{@J^DsY2}$YaWa$b(q*vafAtDR8_Hvwrm8tu1=F~0 zqUo7*STnvnn9z&Hue88R#<3T(CFp$6m~$O9?(}eOoFdyg?A{4T)(5=h!UnA?Z8HCB zso$7te#YN7N!hT7nV6xZaiMM$ZJ1iDWuj^^$-WKg_ok+K4a9Eh(X`!2qLWp)H{{I4H%D%M-DXnqKyHxRgZR;9P z-JH4Qe;BvA$vUbw8X4}h_R8(0!LmfXx5V|OeZD$Wo|r03T)Al4i3Z7T0$W$sR{o!L ztnmahA~$#0L;PUK1nG-7y|pR-j%A0-lsgQ0Z0K=#;jAoe>Kk*j4wZL|QfQeIb0#Gg zo&5M+yFPD7*=6ETn#S*@=82A?wovL$;8Sx0e|KkBWyh4VVa3K)G4m13jp->JRQpmdXp7~~ zhMLT?%uwgHcxK6zvK>q{&t7jEUtDF)>X2)(=EhhKd>EH{F;d54t8clXs_HdLC z=Fc2S9sXyl!=+vW(RHh*+3zNwa*v3hPvtPgzlTH1}>O{(5mp0<>(&8kVD*z$Ry z;oM7CEhaISkb}(r+7Q&F984iM;c2i{egy;9Z)NsCTcyc2oswrBRK`-TN}N z%-k#Xho`&#Sa5FM<1L3bd2%alf6g=q_a0Yf{X3Vu*-~3Pdzg>(C7naxLEF{7_1SFh zHG`}EzlJ-!8{iI|II=L)oNIH}<*E4{YlN+hW|NCG52m`$R~;3smeVycGBr09T~aU9 zPckq%MZx>5x>AH59*%VN5N^jD3;|Ue^saO=TkqX z(=2&Y{EaTuiI7kfNqRK`5he6Rlzi!Wl;;JAx~PBup@zL08AI0BN5Pw-oTg-eqc2wlp)R_J&YyXcecE)KxXhE%l{0H4iD=Q zf}`4hg0tY4(-Zao;y%e{IaTrP?f4;^rd5@Y?-tc^3ZS#`GSBAOIICU)#4jjU3H$B$ zKM*Hl0lLP~m~o2oQeekcJ_i|wqsAN~UTt2uGk`%oB-uKpYygTmV z-J2J&8~=Ux;-9Zmwxc{s(uC~p{@igI3A&Raiv&w{cZc2Y!Q1Mf3$_2_?mw`Y@3JV9 zRN~rr7fKp2>el_Y?tk*nx~}v-WGM^u>8#Z;@6X1LlMW{VF1|&+;+dimQrbVG|t9uA9fpWRDDuiqd{;U zCpUhJXW6sd+d}i9*Bhk~Pn`bWHL6j6^`N@WQD9IW+!MyLIDcUGao|Uz0Q+K?$Ue-d z2=4Zo3{-9Sfx9}WvQ&7+toI>| zh3-DUzV|2t;D4FY7A>G-}tWg}Pv)86YPOlqdRbAJOA)TiODJ~vuTk-Pl7xQ{V( zV9fh9RV2iGJs~tGEVt|C09M<%$;0HTER6&^Mxr#GtErr`@$iql!Pg}`c|3!+D!YZW z0`iOOg0#$$*4VocLEiOog(^JsGS4O{qgu+na;7&tC6SBsToEQk|Vb zLn!jL-hbq=r7c4%V<0*XhLua{q>?sHUv}nUG7sF0YQt`Xe{vhN1`P zMjhmK7SYAAuTUvlL^H7p0EZuCS@OJM^8%{Si$7=KV2@+m2?g*E_m87v7f=g`DM{)g zj{_E0RCRO8OLwETkou^{b?J|S4RhGsAqb;EqJN7#xbd%k3NQfuhK541;hzIF}7&!6v03#@)b%jK{I}xxFaOf;ea{ zB8WDxjMuyk*b|6+aPT<0GS_XV+Sd8%sYRs^SG2sz7xVAwi@__Y1`NY`W19X5Zdl%v zWPk9%53l9oCa|l<-Q}SB<5Aa^3wh~yfRIg7tfd%fOt-`srSQ(}wKd=q`mWv-8k8G3 z5-SJX6?s{J-Y_R|&r75v^^`QMz(`?O0V(5l`Z3`PC5A7+Ee*dd?d3=vYV8!q(b3xb zN|p9vAWyu`n1!tKeti-=)*;vKDKc21*C(W|JwTyYSm*5nSF2HpIz(K z_)Yj$&C3$Pz9YoKEPX2Np0>kg0e^2#NBMOI_obW|upgTyOYEl+3*xss1VEpd&?mt; zULriu~ld#CKsUhEHN4|=oJqFpNzdy#1@o=*)N16CxS zO)tkCB`lIM*~v^sS(bVXeQ)NS59e%XA0(!IFbVkpr>E{^9me^$-O#+Ckbi^xqYtw? zkRn|)K%_`)nU@B|Miq%mu;d#wPZnj}MeS#8V4#(?4Bs$7ynuyYv&(Sp^K{a@7`r|0 zv$olwXZ_4;nqovgTpP>a%aSM+7<@r$;>g8p@O?QRa$xLj`^~`1iO2$S_4IH83L7Ht zE!;h*M!V)f?!9iKP?uQ!Vt+Qk8M&uTeThrr#NA-&DCv0SvF!DV#5FKr?5o^fOj-kY z+vwK0s;;Z;)HYYmOKiEh+VXa!MT^)zJz1pyy+&0z?se>Ym;S?oFxyiR1nR@mj;@3- z&t?{j58aPSwYkx22SZlnYZ)x(^wCZ#z8s|qBiOWH?Cw||AQmu+v-b$jWn z_#qXdrVVL^k>BAaVBJu3TIN4ZMST-Urg|1jkbDaDKOd-F5oS{$ldT)o=%k z-%ggTCSPa(jNK^Ux>=98(x!wn$CV`6J(Ore<8mbXY1FKutkh`t&U$sev=wl3xb zH&6bz&Q~{QEZNnNQhz2Qo*$pW{lS;6vDr@of47+Kw#Z|;vPGPA!>nU$ry!h$Ydt8} z(5LCM`%fHekZ*V$I`q?jc0K^J-o&QFFii1qQ^3-y&}YanFt;WGvE6ntuI;$!ZoTSD zg-yVln?sL-3BM^`QPZRw&V?o&xL5|q9*eiUGM6lM(qGccENcn1@+_aSx zGzu?FWo~D5Xdp5*GBcCm0w{mQT1}4}w-LS1ui!E9fx}{bkOTw+wiP)662P!@NV3pj zEe~SB!mh9y0m{G6s~&Q9R?_ZttnLv6ZFf(TRj;cai&Z3Z;*dg4DM$|4@IRN3i9;j& zOcE%G;zk2e^h}G zh8wg~flh1w+TWvH&3G!%*UaTuU`lD@Jvj?aAek$qmK<1JSgwI>YTN?X1Q~?`H-U;G zK~jYZ_OJBsD;k6iy_f<%qHQwgASO^)EJ&$PQA&{Jz?p-lsj&pb_uxi@^3=En6>rQI z)Vy(NLCe&*1Z_zmxdwkr_>;K>BVfUI2b*k&FEMdL!S*)UP&ioe&w;J2x;sQdNeL?8 zhC(g}`U>7}GQO>dD~0)rx>Bj3SVJ2)rc|B`8A`*aWKE$GT$C$^nhoHULY0K>Pz-mW zyXH`>>Lx4NRCo`b3AMRoRcC|?#EmP=)k5P6fr=Z2Au~+etayK8+*JQSxD)<&?I1}? zZfNwNjmz)3AoQ93TNAe!cnVA!e>{q1? zc#9ivfPTcTsb#-|-8g}@Wbh~_XeZb)IDe^3oOF(pzjIktoplhC@h`Z)2!yr`$cP(& z2b&0#!aMOBIEsILbim;trw_`0n{U7MmSOwD^_%OP=Wj1x?E)V<{B*hB?{2O_ zK0N;A!~VzT`^)_<(DcJ*`|SE^AD%o3+h@R>lN{PT^KpL;5BCR{4QA*M@E|OAc<>>d z>UiT1ZM^YlkfsNq+x~QO{p$H{A1(mt>9eqXvHP$O1NipEf8XvL>wk6|e8bg#ceQ^9 z4^Q8)+5WtHcm4k6)$ZNo^y#O6?0$WH`Tg~WaN#P9oY?s#)Lh=6FEsad-(6i@L)66- z#T<)AvBQ5=`_=lj^lR=cb$IS_bC+wQUzcA-|E{MDIbC1r^74?^ z`GJD%-}Ok> zQ%C!*N4k9J@}G|)kuYTWbzrViub$2sSl3s5Ay8YYshYRnXUOI_if&D_! zCn#+a-D8+EBTaLHMobH6_T4lVpNH*_*DtOE#{QpP{dV~lL-?DR|Lh}a5g2Mw40BTD z*s^~I$BZihR*t2#&%$_zj<2t;zKOg%j6%`FFeZT5z%Q){p{+g+LzaUvoFXMod5cl3 zaJy=W?SxNsd1J7}YIf%n(O5D)ZVX%A7$ngrbb?VD#v*=$ariN7L|Wb$DMj*$zSLNf zqe?&{j~OGo+?N!v3gcO3QFL))o6eAd276T|H~1SHNX^&>Io1db|5dU7P-vA zvU~&)L&U&T!YRjuDOHL@Yjnavd2zamQe;eVgezuvhef%Z55{l}x0pPSs*nyiC?{g& za@sd}4W49+1=HlMZ@5Gin*(MA2O*x6<_R{!8RlTgAn`*)Sq;o!Z6XgNca|YcJg0w1 z%Zu9t@in&Qg%3hL%Yb!09GxhP=<3z}Fo)wxs;7O!OR{zt#Q+9FhEJhm4nqz&4E~|kVmdPznb+RVU3ji)fwOL?RATX6E zQ$^q1l)<4nQzEaBMly1FMfGPF>0gxk?+j&WEG379}Z)KJgMfCSR2^B$;_evLGu&I)vO<RAobM2Yc+6rPX4kA7}OuWwn(THTj43)Ob--C zV|`=!;YWmWC^Lrj<8^=Q8l@toH0jSsoLcg&5`?dIGREaq);DU6;#)14fefB% z4XMj4D9if?wFgbxl{HjDiKr($v-}7)#^mGi74!rOUtY<2+8Aq)L@{#YF3HBgVU{^i z)>utA3}VKx0Tk3AT-uqTFs9&^TPTPezFjLYlW*u1DL`{-3@;eb7z%$Ya)Oeb9KPk8 zq9C6vtWk14ZI(qVXHG4)>f6)E?u!IPNJ(xcgfxb8@cdMl)=~38?N&gUDCPEYqw(T$DndXbT*a99(X( zQav}CVH&SF%AIN8uWGYQ!^@jS8^E9-5=m3`;yb!6m2;!%L)$lYF%>Dm7~!#@CeeIi zWUt^N-`VvuCCVt^eN0tCzB|Jzd5y88sD`Lo5SXJPt#jri$#Z|utYI79Zbt4u_^T*~ zQk`X+HTcVAI+1XTMv(e){#s~Io%wMn!L&_nI$#&6*tyXRPkA+Tlvt^+re>OhMpm#* z0vht8iWV8c*!RS<*}2hl+xX77(%l5*JL62VY@^HDX4)Dzo=_kL9`?r7&W)x=VL|a` z>Bu&y-Xzh9FuZ@laPr;pX&DHKCZ+}P11@T3#4*UihZUe(gP?GecG^3u6eyBQEPmPu zNsTXM3W`Z(JvW+R8uESdyKKfc@3qbWvqGLH>9Fb`K7IRf3YxX-@Clly;llToS3kL0 zeN$%~R`rw9c6(UW&#{*;I)&QglT)ZI|6iw2kF3%7$Qpk%Spxx-0rS`#pEiBSa1XRp zaJ!K{-jw|?l`k>*>4&@3`UT?&*vCOrMN*rawB~nP!jo`%NG9 z^QSGP`SG_htEnH2YxATE#{`ScXv)n`V6<6Hk&Lu5OR67nlrjrzMmC(7=QO3_ms!Rl zD#+lDKI?xbiTzs&Wo~41baG{3Z3<;>WN%_>3NrySlQDx6vyelh69O|emr-;F6SH1m z$qth+gA}tnZ}bxbG%zumLkFHB`_XLM*F zF*h|hli>m=f5ll{Z(BDEefO`>FShgsjc2Py^_c5o<%I00Yf(B@V?~Hg2&uPXecx@7Q{23;Xo zQ}P)U9jpOYL#M(L5TyhovU>mx6Stt5FjY(Ff51QtnaZwKgB)KlhDPc@ZUVpYm1&SH z#a}@(z90Dv3WK;5BS&B+a}{7+Ey;O8Zh<&Sz_^hG94$c)h&8wn1{fXlHyFV}k0dEN za0p3;4v0XUxwpDEnd{E21#{C#LdX1T%n!G5hs6Xnxi91E>fQ)@TZJV~PDbMw;hf30 zf7zQbe)r3-uylks)f5{v@RBYt3>2$& za?WTw8B?i|;TwHmmgvE!3v3o;n?x8tpM9Lo&pusVO~UGn*O!aMWIhdf`S`<^#mlqB zx@4mRdwM>jPV{$cG58!H9;jlupWs%`qXHbb*m7VB%hI(%svA z3tYi<$aNMy9`6OKN~BDE;57{te+w~lCpa4xy>u=LwFD2bKF$PpDy?%-2)@CsPcRaU zR}4oCes_Y>X29DHg?#~UE0Ar4xUKNH8RG5);Ej;^*x;w-Uhq@x3VvMj68CgEok7(3 zP&PUjuNs$aUbVbxm#W{PG<-iApI!g97@mLrF#U5hem0xGpUj7;>0v(2~j;BiE)J9}?Ihm2UT{JshuP}3T%OXv{I zNV=e@!mCOTG{bRg>yk>9qt(_0H9>y0E@-k?5XbgHZz_Tw!`@T`NNX*%KCl*)|5W?H z0*?^w1moz2@}U!qvvJfzi+qy%474(xu)vuQX_Z$JX653`)f85S{59G7GCxzSe z_}H{p@7Mg59-H>cD!mn1wYq9;)s|ITSM5?OKUE(w9a8Z~h1iFd{I&;&W>m%k-=efT z22TFIzFd5mO_7f1h*`04)Q0`S3?d#u{CLaQKiCqj9Ac7>$0XxCRMVrYjfaIhNM0%wZWhTB-!mii-N)oNWrmDt93y| zaKgMr{tI_P>3Neu#uEWDmr-;F6SGdLpBMo&mr-;F6PIj72Q0HK!zTj)HJ1@=2NSbs z#={T+Hjxn%vp?6Y6_;590Ti?U>{=EAGBB464goX*F*uXq0w{mYS<7x)HxS+HE4XYo z6ge{-asVSh9(7uv0fIVCsRD=ZLcmgBs}soNj zs}#$HA)XrKVc@FZ2*wfBwey+AX(E`-tztvL7Dj0hKAZXs2TIvz1cTx-7Yq!F35>zj zwZczg88Z!LA=lk7sDzyXuCSgIU@SrSl3_CP8Q3bT&uD*Of`l1|GW*HcnYp=gDPRHy zgV9*3YbmgF=7|(Hx!Y$LxPrw3tJ_DhO5Hw+v#Q$%$8d!MvtsAw9`u>!E-Va}!H1%Q zpJ8VecLP)&^mkFQ3Q_{>9vX}ZTTAt`s(<_}50B=tQpJ4^LpsSQy%+-4JygtB83j%53u6pi3=<4mb1?(L$AxbgxCc#x65?L0VgQQ@e6O5*#xQ_C zp%Vt?%H^OQLrG;3ykoH1aI|$sYL`& z7nZC=tI`L~twr!eC%9-tNOpp`Mo!zl3)AO|_lw($57#%dz^gT{ub0c&?L5%x@w?B< zmluD_>*XxuVPY~pU(A=`>?};r5$%MlIN;9V6fn#B0ii?)yY+*4G^`&G;!Y{+UkZMa zy9W@F-mh`~PV0w^5!wCT)lGW;6KE%|M1xM#*SCwCi`g<B#pX_x78wM`QX&EvxTk|_F2eNX;>{u;8opWnF`o@H{=NS@|#gFM`_fmU)k zW)j_$#P1I220>*fsM>II#yDpSI&fKqRXpKzK($d!sSgT<^iw*#puXaI^ zi=!6nfueGV+=T?$!eLzopdvB#?TUXelp}lIF`^nmwzNJl3WAtK`oJiWU(lqQ(MVsE6Z$U zrtFn9-z}kCG>GzUG?aDyQRtLWL8v?2Hf*Rf zz$gU&7_1@*Nw>&r@u+ilmw+?HTpN~cSEYI{Vd^|3^!D+Oe2 zBw5?%RB6x&PW%m>#)?iq7f*j7*AkVFu#BCK?g~h$wK{YF>NKYacSC2JyFHX!k5ot+D(&i})SV*3G+H(8EpEK2$Y9+S&sx)rQu(14?MJ3TqEE zL)JFNPa{wi;Qp%bAoPxKx@>UY=y+3?A`f)(dd6{G5LW;XM>`5637PqKbE{(+avF$k0tMR(w;>a6f$IC6otc| z1#&cJYXfVxQEqzr>SBi;Jpx+orll?Dia>D7a;iO0uGzCm50W|7u?w~jMes!CJ}9V$ zbC*{87hn%~&q)u|!=u;Z4S)k(S28eU2l>Qpcj!x|^;pdVF#c9xvme*@TLu+0}ThbinI!NuB5 zm$9)169F)nQFI3r12#A}lVM;ff89N6lOwlr-|tsU{KeeLag6ul9J|V~b+#O*BKc1F zBB{#M?&vfTA9s9QT>ACtZeSi50z>X{WlOo*t08AF0J_odZh)+MSF!4kFWBVz?{8oH z>a|mque}kbdi!mqM6E?-rLQ%2)!T>a%f)B=-TS+x6pP)V{h{4$8~Ebne?r#6-+le| z&%b)D#HfQW>ETyQv)6aX|q@zPy2Z5 z-Rg8Ww5#n3y5eD+WTIa#YP{Qn@~hXJji0k>$$9Oy4nVwVSFsb5P8MeIS$LAZ|K(Cy zxj1d(v`^dPE_^(k!u7OWe|0zB-)RmoeZ{!CZ<{<)py5}Hne0#i%2H{u`0qPw7ppZQ zSZerix3p%l-tDpb)fi(iXoEN3oto{D2JGQA0p4!`@qqMK8K9kqmDANyu-Zr&nt#QF z%FUY=GKaVhX%jHH^b1-rSY@~PP3BF-YRP?NYM`+&_TRR#nM=A7e?lO}vZK?(4Xytt zZ(n?P!2x_$@roN;Ya=V;ZLN%|?l&*K{F+q{@DMOmOYf@xrKTI42Zyh$T32sgd>%Pr zJV@V{b2V3Cs-N5~wOjo0Y4d#@pJ)KyTj}tL)U_3^61B6D+eGGlT^pk-Ijruh4Cunu z3c9jD1y0OC?o4f*f9xSoyD-86#H!|k&-KA7VQT|7rhN#mYR~yieRQB)(Z>XqM6RVw z76hAtMO8AQ`VZ}9cQ^*_BEdG5C<$>-1xf?V7ev)VyKj!i)u!2^s5^FdSL=>hg9HV+ zHskRCW|0jXC-nJxdB8Eie`JiP8FO=8XrNk`A)CGn zn1z`qy;2vFK|3iP56C4&1_G{jTwG9OlFcfz-;;LIW9_tQ9@-ySGbvuwOd50rY9?$F zH4}bB&4gFdOyNeO1EL7)QrpG*eY?GHX^mIw_GM_d z`}nb;MnL6R{clvQ0S`;zK?g_u|9FI6(EsPE4urjQe-=c5by5C4G~Z@A;k9rWQaPXZjVKF=KA)qX*`4A5&m1+EkjH#fahmIvg61 zQ$fAvB!mW40veZ>bj|e^*k3??3gb~Qf_@uoe`o=sxAz}IqkX$sp~A;UE!b&x5gg8a zyE=CLtjJaU23~sDg_i61=oj1FewmZb8}il^sXnss?%~ES!kzc~=CA^xtU3594UKu+ zQ){#MaB9dp#CBv$#8*zFsfD=Hj4gKI<}j~)91FBYU<#L)7rG#cGF&MD$cqbr5J`~1$C^M z3n2_>@gDGX3RH+V1*)b<20RIo47!m5)r8w<8Up=jEf-%Qw z(b@SXw2nx+Z;HXEKNVo`7hssBaSf(cwUi*(U4h2Ik^vf*c__%t(d@HRU{Dk#jx9hG zv`3H{ZIl>oM*-i^b+;ZKA(xKs#`kkV>-`!;^!`WY4_J*nf1qd@h4={CC~!LJ7=`(O zoX`0qQVq&ir5C?jgA4SOSsbE#e|vyI+WY3!nFl#`p}45IH2^%^5}j!yIGZC06b8c@ z?y~OCD`0Y=g3c&N8u|R8!t6jwEq>suZ3sdT-(WCeJ+mB~xuOI#fBGM^7!C}W ze=9hM92diAMFTd6_HZOz;+=bBm?3h~l(63|PSo>^20OSm`Qlu)mNcz))P zxpEdfHM+2u7z*Kw&8j$l)-N((k!Ss)M89x+?#7Oh$wJai<}L!F_%xM1xjw9=qe>msUedZ4k*tdeVi0dnm%yZAaA_^LwWcHpJCrtv z(oE=CDIhdaDXD9v?3_O-w5X-ZMSY zTnaveBVKcHDT^xA)5675BSQL740mEqDxrceMi2euO`#Wm&4jd+tF7RbtWD?K%be5h zYKIZFQL_+#mi|05N_X!uM7-OCuqBz^cz3(oh7TW4yW^@34E4J^2~PMBTE;YJ9(Y#_ zU@tZ1@kENn)drl%e`AcSk_8CYF3GDw=)^(ESfXHRx=6SxV-NCinWWlzUoAaY=VIh1 zM<<$|0sUCn=NzR%TmljeAaQV-@$T{T5aI&(ja*=dF7PI879eDajjKYC0Iwt$!bb`s z6ha*%3-xYDXh&};xJHPDFda0e(AoTMaEGYn5mN=^E068%e`zUz&XxjP9cKt;I&j*t z4Ki>hdB%ZRtrfQ<&oHbj{7uO-oQ1bHCC?rW$R+v31+O{dm*kgzo-zy9!KuT_J{cv$-xZQfp6oncV1@?afb`iQ=TWiDc;vktK_+CR{rp;N!WV!T1AM zL92<_3$3Fqe>Co_g}(ON*xf_>=y@uRn9QPziLzAfa5PTk(fqf^W_u#=9CH1!2`NF4 zNJsEz2o+8Qap2Isjx8UWHawv?Bi=bQoA&TN%G9pAhu!fQzdYo_pvTp_bsI^fLx(@7 zfvmm z%5^F3DGG3wgaXl{Km=n39&{+^0G;vNmi=%J_`qM%Wad$t><^SV(mZM){1Bv76b2zn zfwBvwVon=zOu>V-XMtF3Z^@VppE3|kq8hdPdp_Q8+~QT1&GE?>S>M0_$No!JOlo7Z ze_~RDn3U$CV}Q(+_ys5>P;a*ZS>NRi0etkg*}zIF7qrrdM58^3<=M=p0f%>{;IHpU zj+cYyW8^BvY!I)x`UKz~RXgTW4LJ`Nrp1ALi5$$8fXovG(QYG64xM@KRY{^>Tj!K?MLFBc=P zxYtg*b@MW3Xxf?^dker*+|syV5>yxxX0nbm8W{={{2wae`dC2xco=8ZWgu_@-}qXx zNp$B>w!%Nj^PSYAbnCS0%N9$%f32I((iS8gPNY1=*ZB}0x0kZoS5(xH4P&T0>={a+ zi}_Yl%ydRi9$F;v9~)h@%86P?{}W(2n$$g+ZUrE12}mJg!5w%kj9tx6{03l7c^NBg znqJ7g3}%{1Bsu9VtdBbH($_-UT#v~-&w30wgrx#=1ZZZvD^d+$M`rjK5@pS=k4C&JtC=z!uti%+zI|@VvHI)_Xe?eNR_GLA=1C z5zZ9m#5B{7;}B(P&3%$Ce=Tr`9Vbh#V-S4}gN*A^3H?pRRtMV$D{VFSU2;Cke92bt zdt$ZaYKmg#N03lg7z6NSI0X1h8eP1;)o4+|2C%3j3yXsM9?j%|k25v;kuPm6xQLcc zAC@M&BGht{C+~v!;A~=DI2*DZ@OT%jMdy+Vh0x~XX}1o~a8pmXf4ABWi3~?&oy#aD zKuAn0Nz%EnSd`+Exy15JyvDh}r9Wa z(22$8r{+L98z$Ip-mlyHRYv@R2*tf!D#gzCIpWsvlB_gFXr#S~xVxS}erWj=;!Z#~ zC+_bHw$~5=I5!W!e=pE|c3Q&2%#*;%?8N$3-xqXdFsgU44$&^km6XMG7mi0`M$1}* zU;K>G2`V$pMJJSi1p=bEohXK$vP6*~^1#_#)(Ur_j780xoNUH=dyx2`fokqt;Vu(4{=Jk_0NQI)5Re-ny+qQi^jm$?Wi=uV5& zi;;4DSvJ6GcERr%#W!korua&pWWmIh80G*|Bvez(an}+&Bp7wn@b8&Gj*ilIurYG$ z3LXM;6GP;Q+r5FAXE#mdl)H>kpeuj|Edmzqqk;aIwZ3rM+cN-t?e1Nmct;WQKz$K_ zzx;Bw|E9%qe~Gp^_AUh`61*wpakaNaABi3|h1bgV6}{Fea%$OIJNRWyH|=7xdjCE? zFQRJ|nfsedA|cfSmfMBRMLj3shFs~7$F2E9KiBfiRn()dVHtHJ%Sc<`7?}?mOTdNT z*FZZk%VVIO=apNb6Ry(m4=wAoYH)nxpXIDwNpXy!j>U%)-s; z!w$KAdmP-}H}7b>Unp==7yuB@7iOg)!X6gd`Bm6G1&u~bPkwQqEFZr)-vJgydbaKsi(dOu71AotwaaZA ztCVB?E!HcKZk)R`;JORv#&HE`m~$-AOigPxLN#72t|Z7YWYz<(ZMnuSUp!)6%~-Cg ze>|hQ#uLHt6E}-DWI~iu2-;@%yWoZyyC`hvJBf~EXFs^CueQV9KVXbBu{5Y zJ5I8?qErH=Bp;W6iC6-5j!c+#8_mZ3e>P@|od#3DXZ?z^t&XC!shSrh}!My&Wz*W2}S2^pA_tYb@CW+<6V&x*{ zqd6~KG!;OJfZeEkR3hS%SA<(D&THsWQAuvm<(0CvV(Cidk%zg)Jo2QM1>^}Qe@mPO zlq9a=G%N^BMNV!JWHHh(N^hrfh=D($o-~2`nM``Y%poc&nK^)^Pck!9w${o&MN+;j zPOo702suB!*SQtcHI`^xo*qbSS$j%P>RQ`qA(cb;*O+`Wmg0oUjQ8U@`0^q%o>amY zGRru@vPC>!cDq!nHqmjAIWPeA3)k#C>Z3M??rk_{wub+u? zwU!7DXiIPNp!(X{Cxa^Se~eT~+p0~?!w~17cCETb1nPYGteq>L9b;$OcZ!`6aA(*_ zN#l$Fyi!jl06b$hoYRqFB~4MrRtZ+V$nn&;)pYgyX`Zis01%WZXc6~ptf6b?ZeR^Y zd)n#n0KVg1PbWW?LER=SbB5?%KITAS&35N}Fe@Bv6D6WhjUi}cI zoWii<3qmo2w*|B|97f)ZZi1pmkgcfJ)r&XrT@bdDOs`or8!#O{~X*VNzv=JIFw z|38@PU>36-uza3*4r4)A#!GFWrPp}oGj20h9*-BqEmd9)OEx@OcF+2^m;LMA5X)|i z`|3^gdDVf=ak0Crf8ywOVn4bT3T!6ua-bXLv4~tbMA5#fUVJ;e+||d`j`sP2@2s9m zW(tfg7Z}j1K?0|n@M5d3Q8+*QoOaSyDH$x|Z2QUf6qHf|xcImU%uy~%V3`|C9t}KY z5hDVt6dZ271pplwfOrg~GFEt`Fe{KTP>5s1{(c}95C0V6e}WlJ3l~0g58zcVw2H4v z&VM$v10SrLp98Df6M*%Hz7ryt>V+!pOcjySCMkSt{T@{1o^b&bl4KWUgQeuQ+{ zgIW|F$ODFjeD_#(7$-4U3Zx~ZLmP z!V$^R@~27=g)$3m9O#AHk^~8@x<-@AB&)(PyE4S4kXj|}DJa`GlMYj23vdl!6=;p4 z>4(*5SRk#HL`nlK;+RJ=HaGyFZe*@l&jl_qP@BTFqHA{>^^dX4kog1Z$Nfx%5LO@J z*+KvZ(fm`0K!3+Go&*QYrOZGCNgcYzksSSa0yF2u9bpk%nNUC+b2Q}V zsboc{mIGKNBH(Cf;N)@H4AB7C$O^3&GD87*iOp&){Qsar;y{zjE^&G&H#+7`A6Q89r(;iCLA)!zb^J|75&yhWX!Go)(3r>$XQO_6sKchH-0#n5EO?+7evPL*%f)KDTJPTBIX&I> z7DvCKlpd~w30M^>SMWOUM)*!=nyZBO@b>O_41a|Yr(?WxIIX+3`Ga+_Q6bhN@TVlM z%F?+SoyRl@wQ2IlHDG9l3jVba*K8ii<@}RE2RbVdPwJIV__+(TQ@y_`!8=N9nkOYT z6ZvDPjBc4U%$^{Dza#+K9JfkfN!1PP-u1-5yLIZ?JsJwkVPQjFi1Xnm0jSWZK>`(C zq<`80OPfBN+OXkkJu1}^RCtY-(Ft~9I21o$4#gMW=C8~{qALVbRmkl_Eom9$59ov8-GqSden|D9u6D9jU?)-?IxGXu#bP_4#-A}nQA2qcAiD*?OXjOBP8%Z357qqR&%Xxkr7=-tUf=QC%=8?AB4~8YQpqJ z{r)!3J|Z1GS7#m)dS_+klZ|o=EOza0$8X=!PYA!mMylz?c}GaO9q6v3|JOw2&wq$2 znPRUBk{|>6{My?;yfEfPP5hZEx&b{dRB5JC6? zlW>*ZeJGndFsVyZJ~5hT%93S9U}v2f^UmJ&aCXA5+F;y&qVju>85j{(_J0rrmqEO-WiEkt>rR3sN)C&P3#X2#ZuW$S>! z+s5MJrl?E*UTxPF{PrD2ubt5WmZ0S98+(k^0LwekL>fdmK!B}ZcF7rzIX7dhzc1j& zO9_pwD?fQYo?Jqs{|d6HfuSJe8d!=AN@1#a=*k51p(~84wtl(hVOuTS?0+4$H)OHQ z@bC|Je!G1Un*I1<8{o(55GQMx^mc##U?ovHPmbe0WA$Ow;Skvko|t#YFzQ)2P@-~m znJfb8xLTH{h%5**8P!8!f@V0$48Kemnv1K2d4gf-G$zrKOYkoXwUkI5Fvhy1NuPGb zc59=E5NW&GRo+E+t&Q$NI)9t6UB4a5);SBFtzk}sm64NRg*P4$=tXG>$+qf3f)O?f z^0>pG^Bq<67SSCBcyE~tqI=_|akK{#JV$8n12~3Bd=GlEa5GkQY{%$QmKTNiihsT6OpW(x=@JhL zRm>|?(Xm3~`=FU+e>7r=Ic#gll|Ob&P`fDUvE|p8qX5|<7&3&;geyzOsO4dv%|ajz zCOe>}Dxjg|=$eTO13&$O==w1taRvg(hS7Ch28q4j?Drt7PCUhlu*icwvOGI4pCF87 z$#CRl5=NDp5$J3v;(xOcW0dlU4|oC`j4+@N%crypUiUsCGZy~=EM4pLSDaMpp0iG6 z(>WOU0sJ_GXZIAJ^AP5IiqE6tJmbXC$IQAzBYho97hliPZv$L4ZpnqxE{%dl+rxde z51`w{PWOUAD)lS{Z*>4%pOW-GV2`BPZCsLB7k~D0V$FdKGrLUw#TD!Q%MjW z%X?UMDSf^wLPm}<1N!q}d<3wtcy^uV!G-k2E~Kv!FX}?zV?F%`g)CUtUq^Uuj7Qfs7quzw&B;4_oZL_h~xp3K3yA~fS) zHAlah&(AU4j4N!8Q)pM$lp@EJED}r|OuzBmV3d{ixbD00YQend9=GeFE5-G3z>{z} z9JncLajwFUitF&3Ck|S_B0#AY%vt%c3A60_e>UTKZs?~j3Pru_!$t}C?$}v?R-=M zwj3S_{*Mb`Qn15J+p3losPKZ+y_lh4bpRpRA25b@V;-zRtDdbw5`Whr1Qh$P^g^J^hHtE z-+v9bXm^I-)sMS!RjxaZ`OGGvIBwgQxk5Xd?_Eab3hnlbb?AL=0b-IoCJtyPnP(gB z3)+<}#o0Oo5_?y9pv)s2I**oRTi4}7U4_z#B!d3|+1`YZNi(XY&JZ&2S#2&)^~|?Q z^=$qeh;$eRi`rD(9ZnrCZQcaky6EBYM1M)5Xf{5eY3!MJfhEOM@UbsAgPXTFNB0te z-J1N8x>tX6*KpO3(F}u!D){H9G-u}jkYQjNg>W$#=G+62(%0a;Z=mI{uWEavvR#J; zM+*=t)}?bjpEJ5c_Z6KONZPKK@pN|%j0G^_RrC{?)4p7wC%0lkO#J?JG-ZG0fqyRW zq~8vq(B)r`1!Yfv0zQsQg4LOl;ECx97s^ku@|^A3!j7?UxZ70QGOi-@|9c%RR&Zs8 z{9jKx^K^4RrxkwD^ra*vO7wemL2_GXcYae#kw2<<%qByQ#CmPN=$c(m6T*kpJL^_9sgJlZtW-B zoXJ^$%+wixMA9^)5IdzkC4ace5D#3tOHlBC?|ug36y@IMQWSK}1jTGN*^o0qQ7JwH zyLOq^vwL}T@eBexRPB^MIM*S^LSiYqpgBO7VKf!M!FItI^Ld^y?&_KPE*Dv|a8(<{ z$vMDto&9f&!q8&`C8xC`o(p%G&4h+K>+>ZWO)?nUN!2Hpgh3BXa(@`(*@}$<)R;)| zshe%%wTj z=9wN%fi3?J;2QG4m$9)16ag`}K@|bZ5CS(dmq8T)6SpBI0i2fgJp{V!sFi(>k=u79jq znBORv{R6($1^fqmqh$UEvc5$#xB4&UVEYZ-{@8Q;HV3&n{UgAeiNzl_Z@ev>jNSg3 z;f<2zAA)a(e`D$CUL2i}KHGo5H%fMYAj?}h|L|pbD+lx^`kO7t{vXL% z-uOEFQNQ^*7{A@Xwm@^2KT?+elm5Na{}sQL;sA8A0{x?TEN{g+{(-+u99=;!!2k7R zVRp#Eg z|4#zSKUeoZyhTMp9$pOWZyUnE%FP2{;o#!>-8L?t|M4~b`#Jd6-TQV){0IMj2mydV z51=W+f6_e2l<%{3N<(mouSDKtDKsSyl36YT;4Mz2V4EaUB(hf4(1DTv$ z?IQN+jFz|-5`g;1p%_nF=Y16G_$&HlGMQd!f6MAuX!n9ymPRZmTMUmyG=g@*#mRPX zm)Co&m`LMpktMnrqugMe5g8bVu1+*<;w$nv@^?$+=PA8D=S|)nl)`x$*E#1jMJ7mB>G7?Bn@pL2if7vne#MrFdk7JA^A;O(%gma{meSOG%mR4;) zjPf{^?G&q}|9-w+A?W)d&l#^d$xagkC`u(ud{DhXbbY7X0*;~>1ViJq9TNX3_&h!} znc`J*J3urCE0&MjH@(@zdpZAz59UgW*R+-h*B0__h^3&hzSsN57L1?MnF=z8e>$@f zG7XfreDs%BJ4^_cRyZ;*xpFs6&v#*JIq?JECw(!XWUrQvL=Jpl9UUB$3Ki${<$=f1~$aOIB_? zW>st+mL`~Ej+jYEevKbxf%BwZVwZLpJv-r}f}(ppJa=^7bIw=Tl=|GYM_gHwcWVwh z=TzKPED?vSRkJuXUP(}cVO>wmdDfRT?u3@Q^1jb$W}*{P>e1)B=F7;Z7~a{bs|SO8 zJGQs8)yugRyNpMQuy>Hbe}hi-8nvd%Zg8U1#Di^vMHQ2;dB<=()ljuFJX!ptPBY!t zxrJ+x0@lbjoQ&5A1^oPkT)shbQsI5r~ zXw&IJ2$o&l(sYPpuS>?f-+Ms<(4XqBeHqs7>uou4Uvl@Jp;b`Qe{2zjgib32ddy&u z>;3msL^Dzi$&bDah3HJGFIL|QPa!v5BX+_tNtwr;loCVtX_K6EHL56g-f4n}GW)*o zlJd|oAsYtggy);ohVokQrkK)fo-gOV_ZxBNTBqdNt5-C@5!(in-1okUN|z{ccJ=DA z?SqDbWTBic3@1t%e}>o7sGX+{OosKV#Yxb%w0gL)qAPwd7kgT`F>p$ZV(8O(Qo?zp zm#)kT!Y5DY4`}2$5*uFZc@|c!nd84l=U{wa{1JGUn1Setcj)A^^CfD-%aKzzh6Rm9 z`&OU1C=ag-+UAyf4A82v2qHTX{MHL{MHM!zOs0zV%ZDEef8V&Wu`G==oZi@XT$wfr zKZdie96Fa9Vi(>luKL!sTHfdp=xoH6PWe5W4{6Vm0u?3l;58vzmcSHfE>mXZM))z) zE2*8fDkA|AIpDGUu59mm{~0xj0V= zQqXGjpRq;T-mOrrY=@0cC2WP`k7u@+JsnB)E)9g?ifnu(f9yyhSrYQ}hByp_@nCUL zk$%@0_3~V!!zoeD<2ij@irY^yT&o+D%x`x>MR%fqe?aDOMaZZrv}m5Z6bdFT#5!T6 z+Xb2TtuW-V_L}Z~FphixA52SJE7+oEnWnOUyyftR*U39ReQo_4M>S+P^#?AW2TQ*j z%8)2)0eruKDQI<>QGM8Nha||<=8ATY_OBsP2$n_?z{yV6=ZFpR2hJ(8#tzE+JM?_> zaj5Qbe;s#)ZJKZjO{>Ne=BEcVa)kMzeRy`ln_UB~E1DRm)OkRBJQFO0vr3zHGRDM+ z170nU%&$`iHy#6vo{0>{4w&?x{k<4>)*tM>-En!5mJvrKE&0h)z$Pd&Z!Mc|hGN%Q zlAC1r;%`WBwS;DiSv*pcx$`_yO5L(tHfnRzf7TLfvF=+QoN&K6EG|t_iWf-ShN7IX z^P~r=V~sX@a$jv=RLWa+3HOhaqhT-cpY@SVXq*&YVR>;I$0~M4oZ8h+?_qh4@j`S! z_NiC-MF}^nP9JN87`c7LIra4qGw{n%;W4J@?F@Xczex1zpc)h0iM%{MK ze-Z`vAwi4GDx2j7-M~XFmq{{-K>1RF>K8sDUM=RTRw-kpDS>p^cA|MCi0GiA{80lP z^vK;4dT%V&5(3RN8X;)N@HTDqC_c_Z{&gKNJi0dOsN z?-hF*gnS6HbQ_PK-;7nX%p;!Jt;Wnbf8skauy)Ug&~4@Gy!;H9jNH*JCp;(6RvC&f zI}(G_3mksX6$FuD_7Ob=b?so|jEm6Mp|wMpux!y~PTra=*m3K1;X=7pdyVDmnIUNj z;Vc6jXppot5t2;J!Rg#y((^H4c;R z03C0~>oaRR!9vMc9Mk*Pz}#L39jd3+Ptg)1OiQJVCDGgj;4N|rEG~}Zf0qadPPpdx zONDMZcZkA>Br8wfOvkZl1f7n>y~^j>wW?IV5-vFKWV1Z-2?T-KZpn4a-yw5v*>d2$ zn4w=5JWIoW5BkPn^uR(qlo1EkRgifm7vi9bL#S=}{^oMgkfG=h^(W-4`|UpR;l`zs zKjEmEUF24htw&Qz0T{A#e>rP=S~H`)X=jwDyNC8M>Zb~+n=iv5{xCOcCNmH|huGWJ z-@fm$XGR;%Uy5ZjD6KXx+1di8FwB3&@i+_wp4n-AG7aRJ+E17EIHBIfewmyGo&HRQ zsA<=llKk%eFz{|pM=f?RPW1A#T;orU_u%=`v+W;Y7LQTEex`jse^%e93wb`O{q-ay zoG@yS+2rtf$9RiZ-qPg!H23rJVW8McoL~uJ`l=6v-uvi0%PiMY?s_s(^IoYYMpu<} zXh%ZsKpxqW`M@sYd_V0kl6<&VKlY3GBo8o~v*@_@p872cn$Q}6%GthHN*jpHlhjFE zZoI>WnAl4D>`+i!e{jv;tG?o0L$bEFiV+mS`|o`$*xdt(?J+OSOiE4G9-E&LbH$ma zK1Lp>Z!(03l^+poo=n8Gdql-h;hWTPJIuvL;XvT!rnJs<87a1$Q7P|2(2xrF!8hlw^^9fUmZcEde&J2 zOQm7ReBdjOj~@<92!)E(x z8BQ#3zhcr5fkJDLbTpL#{aqy=?cIBG67L{Lb7RQJ%OSoqHE7vb4U(AQ48rs6VGGz0 z2Mc^@e=8K1Qkq;hFw&w#AGpzcMD0c(q5XYLc7Dv6sbY>4u~u6*c3P^k^!24>EC*$X zlPEafAN~6mqY&$ z?iw>g+WeH}MBl-v2np7UF`Hp&CEgEO_7APabYJHqjKd*O4LSd~hP1r?r1pIBIltJH z{wLWnQm-A9dn#M|*RP-Q9jz(G?p;R_u!jgoR=t~Z43G#Q(o*GhFi>80m{L_W-IJ#{ zfBTw_-SBms1luJa_Otz@%6*)xZ5A;Hu2l17^=d1`p0VK_ssd|=1P`|+GyseJL^#iydJnY=UowVdxUF%&0(9U{_h^j z%lPp?yYFG08_O^&r;%0gi?B^Fit2rqf0A{vE3R^Uk$FPpf+#lEUG zcOtUVLzH54BlO8tR$m`>&JF&v<67X)I%$eW0tIq4Ey+hm0d_LD1&~D*s!i5Df7vOv zB}xjzK#k8XD9I+sDXwif!vgxe%A_dz3Ap8}5*1n+Q;-)<=XK(JKu{ZqXbG^u!&yu# z$g0_aIP#qq{J^hS*VRWgFU;EAc=FjKj&kK*ijr1W5Asc|hHQM+AxT0f9u@KD|sT>(ak*2k; z7N1e zk73c0wY<8J+{MZF4XU1Gf0P&Q7ete^ls6Ccy2#`Uj2*A{k1REwSOM~~XEff8A!j$)!F5G+fB2cvF=;uRzSePP zzxuJ*$vj%t?5YaPg?u_ocLReL3TNkJ;mu4puNn+Io2^)jAmBP81!T^Uxe((@QMlx%^De}bb*U) zqz(f=W3#P8h&mH`e|{~de>(W-tx_{NA_7wl-9+g`M}XQAP3pb!Fxw<7O|GciR(LJm z9jl{2K|qx~_wI@===)+cq~#}pZ-;Z~?Ha84dEu8e}5UZkVNnbXsko2^r@7} zHEU$yysu>EfyBQp5SyD_cwW1_L~bLn+;_Ds7C-$GElbS{Hlpu8L0mKr{s-k;^?clnBi1q<%!N-Sj}hcGGxzosBT z1p^7HkmYvBf9qtUEL6)>_QD>wu(!Lf;On((y}v^J%J5uR8rB#`ex>@{D3#XBOKl;< z+CbDc7SSXI@$I0402bv;878|Y^RLS-w_gHf!dW;K`qSD)qu~=b7{RC*C>5&B^w~vm5mYAf8Yah_U(mXk)!J63>(JyTx^eA zb~i!VQ3)ow<%2z}A6IL7pDmg@Af`TN#eMaBMI1Yej|gs6>t!CyIZR&|7)?eG^$Nte z?4O}SN4FLh9y34ZF5mdr1}v~kwDos!uUDYHIKY;+4LHmcki27Zp*LRZ@o_mYEF zp$Qh5<>!;p-9R#7iK)r3JBdK^N?sLB_5I5tgT}qQ1bYrZjL^E$eDbw0eBnzSR_|2KP-K ze|`6qY^rXk9gQcq#WBk{V?M8}eg` z+B`e?FmPU6F9~D5T>Gzji`4B5H&d7s`t}{s3)t-$z)L{17(3-eyD9hyTl%zc}w%{0kzA!W4 zP<@#c-uXJbP3rn(L1g=LEg<2&Qc+F|5D%)cy!aJXb91wKsYUvTd0i-KjWt*JfB8ej z0o*_eT}?iqRCN`?m|xhB5t;Q2`R)b8pg`kyB!k6RyiaF|h;d-pYqHuWC$8n&ouZM# za#K@L??wsfyvQwZZ$kOy|uPl(}v+kBojS`i00iu zz_+bRucsJOzbz9IZdmu|oc38tgIah%+7hw#*|bBhIsq%5NAk~1$9{jn0|E0eyx z)hG53ni?pZgbDRs?=l1Irt0Rty76nEs+CEQ9#+e+mFfE;axmLW;~`C@Vupvy1X8av zFsG^s!G)S@Dfu|+=w?`yfAAPCm}uTXfQ|MVef-|4~Z&1j{il z{^EUd77UQJ^K{_PJxqToUqg>^%a>oPy4f(uFp(xeguKN+Vu(ti+UbH_3BR{f%v{K} z;E_2t<8sjqAX?$WE`>ScSCd(s*+wv>5X|xEASV*oejkt*p7D*he>GfXh&_{&X)Y;0 z65R>2QHi1ABb}+6fQrP2FWJ9#`H$bXB0{}>w6Vd`A-T97oCpdzsS1&iP~LztnNXb! zz<6ChCRkD&v*Tiw^ph>P#3jvpw{whwi+eU$>6WlG1*Ycx=*M)~G7e_5M}t;< zo}9x^RLaJ$f1|T_zon#>2EZXA@_(uNbquj^XN~xk*wnnz(lB%>ht;eF z)ok|RI@VeKyDOp~Kpu1z`ObdyheAR%B=LV%iVRkZf`g^>0SJSs#U&zvf=%aI8Xi>*FnDjno@6;{S zkD1&8fB0FJhHJ3R_uIZuk3S!qb42iPcbM#@drZg2oPxNI7Z-3Aa4W(x(r=`_J{|tp zYMfWD%BhI{VnjhFqj1`vqz3ydji21ThHK6P%_Rs}Oh*jHDk_H3@JiefDUf{G^7K=y zYnIcsP#Qr#k9sp3o~oaf^fMYq8oTao1l|ULe}GZvRai$#qtci#ZkHOzyu~bfRbh0O ze7mOAskjlt$s>!4=pS1GO5>nO4|OCL=yQhz{M1pA_)o_&OeZ z>-$~6ep+XnVzwOd;tPDk>rVy^&O*;dRlfbLhDeWLl9Fx!H%`RINP*k#_Qvfq2#?*hqYkbcRq-fdu3+ayp@ z9^{0@D*71GP(eIPpSq^6lk09ES05br800;O-Xf9K0-w&h#l z%tQ8s7vT*|e<78g0jI{c-J~Gollzpw?Udx#WRhsbb8p9ey4b$$Z^iHU2)0|20xs;3 z^riymsX_(x5vGj`b2a0D{pFbS4)fS92i9Ls)Gd)Nj(@4?`zV<(fj{MwPE|y|bNmpfAlxz|` zr&X&lk3O1+RU*5W&E)G(&O?Ju-(_`?9$y~!s$OjJV zV*1^w60sKI=Y0$n(wElSK>A6bdO=lduv4npiaHEXf|K!QYDG<=e|g7}A62=9x7C@k zCq}|t$9J)2<31+gNF@1nf;?O191kALB6;-p!X=`frCRTLpQ|aV2~B+PcoIB<1$q0Q zS>nB8I^dCCD_)KKGGxwpe9h~Ny$xu+vK$;y37i&tSc2Vc`IclGU|Smb5YgtLGSS-_ zzuMx425x^r;j@MnfA$j_d05J8S$ncvov_%rq|F;+KL$}Ao$T!4GTgaQkCfq5_E6&ps91bhb}H!k zc~U|$af~v7s4Bd%HucfezdqWE;s_@5y@}(qvzcfmcL8I4xb{LJqlW1>AKt`oa2&Fw zAu2Sy3kx##f8o$4dONf(*28GL>^H8PFtzfA#o&Fs-V!3{!*rgX2oaJ5hic zscmUsHxL-keK<(^>P62f1O|4y0RLB(@=GO$Sz+$Fp1!jqRw*WQoP*g!W2SUuc?gGCWw6SBuUQ;75Tbi$mo=B?1b~B zhorPayzZyYcU^q!Ll-v=P#i^gy-+hl^K#^i%vr9}=jPI)5jKYd)IC|XXxjLd!C`CL9RmVDvfkodNL5)4P^}M|VACSh?J#uo z6p&^*T4~#>qk2kR0@6&^^1;@e@rwhNQN3~ZNA7B#MN7^^HHszho1#2&kE@E&Bj4&S ze>W3jd#u@6cn89BWt$IaqPzBw#yrYV0Swtokw{NlGANouz?gt0?K1|3vW%*)ae{ytV)FPH(06J^J=Aj$P^w4^Ak{XybzMKfG zPYt?>yWg_L6y`2K^{c6$J2UhAqe;pQL zjDy;?ZF8Xy$0zQ$V-%wn9ydW|{=sb^pu_frT4zycxsx6YG4`H`?fbS)N6qEy8 zWEx=TKO50z=8bzBM<*w48$8||jwxP$2bbMi@Q0WFhLt~|Wz_|8MU@I|sO{-?x07F| z2>U5>bHqJTtgF@QrEwO({UW3nf4b(z9kE2ugYT**UH1!}i*CEI6)pDQ)P~2~ne5Y}J9&dMV0q;U^{Z_K7PHj+yMsCx)`M*q|JNjh(TNJ{`zGe5hY_t6FX0QN+}nt?%Xq9a>iug|2bH&rf%1Os8jeMT*fO9KnjC@{UFx_#-%0gYqrxTsssAC zV)2vI`#mqj*N>OjOFS?4cC2M zq-92}eR@_NC8fph=L|X?cB#_|yin0Kde@zn=k}ODg=!W+~>Y<(z<0LoB`0!Wl>Nb(HZW<@_ZT>d6eBe+K z2U9!sGHnps%Db#22It2kZTuR`lA1kzfykbq!21JqdqX`Y$^ymRkX=1U-yd=rT}%3o zG}Rh5eBGwf!t7loKO6^DBOoX60-W3bAD`r-?^Cpf&}Y~VHU2e`T=v0x{}DyJ$9C}8ghExAl;4}FV_T$QAfNfHdM9_hkmI6yVc_QCda}e*jO~=1qFXQr`kmB(x(x<||Es2Yg)eb0d0IzK zWz@dde_%IizA)M8?rn3sh=5#|Zje%nQl+&1{_6hxjT&!=r%W>$RqwKp0~QobQxl7? zg3{AgFH#foXO-(|@s_XKH384GKj{Lv^AG3`}Y5SqPV=NVo9jloZ(QSF4b0PGB^#_u<%Js zDc#t6aZPc*FAl_J4BN{fKz-6DkV_cNJ+?7eC8;yQ4-7$R?Eq6WDGPsh=YUBaxE%UZ z@bMi2-NH)fklD>&W%7&?B}x{n2UEWEf0ZzmuqT2okkYsC_U?%>UpHlt)k~%Xx^OzJ zIj_xS1P;V(8v~QHmm-~b+`jy3-_gzXj#B`0>AjuFOU>hzZLO|6RozmVE>olJblWVN z3~$R9=k2^earRc;^nn|Io8r*EfjO@67o(4rW-E={f*skXNXP2&QtOkO&nl~oY} zxJqRFAeqjhjDKElZ<%3k(@Epre^q{pyeoOi&*|d_it}bAx^8x|S^E5VMFSc`6D@|v z=*EvwdqmG{BXD0F3yb1;O}A@065o|;HPHje1axNSPI?cd%II&F&$M~_pb}V_)z^AP zmgPk!Zz73$=KAG{nCs9WegbmwX!lGQrW>EBJSRUp+DJ+r;|*S(k7o#-e{Cn)7IRg- zFs3wo$>c0S_?W>7cM^epd@#m&b)IQmg^XRPHBNS#eLafFlm8?BmzV+i*ZsQA`@{O5 z`>OgB6x((Rt};Y4lLE_*yZi!risMx>i80{&h`*ee=JazP0scZ!xEf? zz6PYyC_Rw#6;g2JfvJUyD0znb>U*%k0ab}%*#a=Zv|RJ_I|)(OB#>NS9Dslb%k(@b z{fVqhV3~LM6FZBmTe{t%qwVJ=joge$y@6Aw6|O*a@iU3+nB}|%GZswOvy^;lqq=_C zv)dpT8%9+HRhqX!Q%&di$`z!k8g@y%b>;MJ)@Fgw2@njrW?G&4O_j_ zmf>6)*l1JE9F;9eCw?EKDXZ@6#oJ+cgz6oH>8xS|Z+Ke~gZxm5PI&Q&-hA@5%^eFe z>y6q3;Dlt(;=%f-({6F=aTg*6n2FR>tzMltU6JqHYO%~1`rXWXiFG-MBh^jxw#gc&1#1N`taCN4wo&_4{uQY;G!LNg?)B2Wn! zDX7A~^Ge}vIVJ2DxIZ1@bGLoWO2{l(6JLy`#kX?tv@Eg^mi8siOL-~G-)^3XOt;+P z8`HlZUAO!4%()XcTMOyJ9xH#2X1O zjp)q2KE#be^M58l{YnQD_K!yuoJz` zS$Y-Oe^0Kf*d-qnLX4sAB}mSk%XRGr%+QEtM|z&<6w%N|iMJDq7Dv4-I}R&jF#*rz zGk)xgR|+lJMLQJwB}zpMQkl~89ysSRliRCl0^KrHU$U+ug!)lEDwVRl#KV#E=?x^T zaAr-PtH=3&QO$o~>k#yc58MCLdRFy)To=y^f6tu^?=(QXp3ETSrFb~dwR~0cak|7y zp1!&Y|4E?$g9R;dE6cFuXh@J|AA}YhCVi^pC56l2rBanj0~Px{9t2H{vU@TgD%_8$ z(3JMM@B+?4nAfJmF)dJy@kD6WE7JWc`B45UP+2f4#ZmeMZc;ZczWG_DA#B4@C zkjAMYtwz7moFC~}UVOa%*tU957+Hj!9eo-Aia>S0$tFlDPb?zulq_^F_u8qY=DK3c z4nMkuidmz+;^cXsFaGt$e6O(l4q1!oe zSt$zQXMqK{J$2dQGspPc|dFtNW|WWvKNe5}Dz_?+>U7? z=6}w{Bg8N;Y9c8!BmPH(*)j(LXK5CLDA8wFg7I1;eE^P`3O{R-?hwjW))Cj*jeBPi zVK|TodcOqLg=}M4eJP?yyH*HXtL@tmGYj&%<&%-K*_={PoI~9(53!>VFIb+X6KeMb z&AMcL{%Ilphhk^<43gePO<1u=XZ)0(tAA8YoWK>w@^gWD;0UY7O}(%Hq2U*Pw`KrT zx#G>%mj*;|m9>M@!K;bOPS}(_EAFHcQ?dQB)Q`&t8_P+31=qVHuq;*D+DA*D%VkvM zBcd5Dne3~nvi$jPAO-q2UWpnxUgStcpDHB2h*T#YgH4VJ?GWCBPB8S zt`cm%a%*Qm8u1-thJ%ah-I+m3$bW}<4%TV`hBRE!hyG#nUM!ad4a#xCp37e@#-0wmgk-Rp9>xM5BUUi#tuDt1 zQMcT~7jnNS$BKwmH(dPV>jYUl^~dR4@k4j7qJ5EC)e+ylQ{xF2-y87Gd4I^Y3paL9V`i7&P)V!8hZL3ci5dE6){Q7uCt`BeA&m6c_PuC; zhpkwvCJoGmr`is20Uy&b|A%jsikT(U5&@wXTYaJKuwx%kwO$}!T-ErQ3iAhTWC)~c zvXx6KBUJlrD%E9Sj3N^flYeAYCyN#DWN#93B8^;qA9os()mtb*1v{3U61B zq&BotryraBsBdT)+%o(kKmG9#=hr4R&LB>e44C68#6YkjJq9A>x<#;g>WW*?s_KW2 zy0KC;o4z0Vs7xXfIOm`Vx~N^!SIDm@_5joGPNo`dvn_u)_!PK_FXvOBF`h$*D7E?8 zPrK+B!AnG@iziLPFn@eqytR~vxBe=n4L=TwVEq8{EjE#Zlw(hG{)Rz4Wo33>fw|R) zXsCqPA)eJGMSrYzOF?%zwQl$$xsPVcI4vL?F`Q z2r@!KWEOvH(-B=}>S0x*W=WeDGj#4ZdPH$CUEmJs$V$D9-fvXp3uNhmlzKfYw}|hPuS@Gh z4YIuX{S(0CZ-1+{#DV1D3F2Y-xzx8{)DkJA8+&sdUEjC$6b1AXM=`QXzycY>}t{6TnMnE&^Szk#s=C`KP@TZ_N8!{V{zc+LfGnm zy-Y!+F>1fpTP)#@C0!sc*$JZ!6$!=WV>~{;be}sJYJWeQgLXW@U7{U}M3JLxPbB_W z7kp#oXn8!`=8?jqtLiUnOu9vei@E*`sK-T*vN-Q;v>-sQVt!L&B` z5f`7VGn~3%iql)U8?{s77v@>>auJIMPOS!)F`IrzdzRRgYwL$37r?P>7>P5YTr#^S zgLkwUlz-oO?L?b$(~W*fVMQ5&aQ+^4QrG2HC6U^TjYLGTfrOrvS}J8YgM1=a82t`M zNPzUYZU9*4(ZnY=JDyj;6 z&G727bd7M2}xC6v?a_7X#^e3$q*w^?xNd4bBdG6IZ%TB6@_e&&M^IW{dcH%wus} znsSk|Y4=9~J7$KUI7Pqr-iz-MiJa?NZ~Mr_OYdSH_C7+Nk~*lgj3cwvs67hzIrRJ} zQ2mT2l&FDU3?G>8cQG+i{Z;#i6C+k#7sH`)VFq?mb?U&vgmS+`%NXx4Ut@GnI)C0q zBEl1^3wjh{6bUjmm$tyYTKwLJK(X{j-GSV9WQKvg=5|}WtoZ~X=^{g@&vAJ$loj6D zBpl#vaKHewuRzUp{+KUbe+PpG~!W+S{X_P@q*$WNk7#^w|kp z*?skPAN4;yKj=)$v#y(7pmiRNfq!o940)~Osp9RuWHgHMJftWoLY9@(ClYT{vRKv` z#2+@Z@%E+WfLk1Nj)?~kIH3SP!2kL| z`<7#hBW_3{EWl$YB*n3Byh^u#(0t#{gkN(fomdh2BYx0%&ib)ftj@A%4}bUrKt+Ry z%n1qUZfss@U;!@@KEA5NAE(7-wX$%JWq5M!u12OyXAgS+V>opbB1W!;du z&SsJdK!(Sk8R;zku2=Q}3)6CE{9UV|z}IB|9CykQt-)MwrA-7V>02IZ)h)CcZH<7^-Oo!4SyDs6Up)e>+vGF=ahwC%SU(c?}@YSXktYy*wEVvtSnQsO*%)>fGJMP;kmTe<2C%Y+)5&681*a1yh^atA7ovbA?LP#qYBA zdl=Q)euGor7T@}X$0(QA%z3EqxWZD=b(dgEpe2~eLEo_Leu{tDoS;XSg5%EIb6pn89NaYykBuZGy=A>8>^rn=30HVNBK z<5)lM?N3BK{IfnfS5dADsqYGqz$mZe4@qN7t~=&YJhN`G`pQBZQO-2+#Y6G6Jd zN`M$xDt#OW>(c~e49G$;Lup!e0e!hogRG-#cxan#)TprdvQyVGQl)>HnMCe6qougD zcie0sczi2V?3K&Els1Mr{JkuAi~3{TZpQb?nF33!_4$-o8!cKGK6burd`=R(+auZ- zxpYOsG_7W`P=CcVzlf;?glOdyO>E|&y0CzE7J!3u-@{G8L7oGXTUY5Mg}^?Q_WsEoW z#rw|kn15kqh1mO+p!Y)pa>SRop%?XZ;;tQhNQOMYtE|Z-BvrTrp|4XPMdVn%x2{GX zEfj3tijZWy8VVmTI1k=$S6;6zL@ft)b5&|6gvdnpgULe?mYX_E*9iRQA5+5T*;wqq z;#jBqC+NoJi*hUxm_L+%viPCRp?NVDI2?OLR)0DC>GXiKmnP(~Yf;nbaq7738)lf) zF`;?t(pkMGJ^4I@btHGqXgzMzT5UZ4xfg{nH33urc0sLumr^Q@iV|}A;$jF7xW2oO z4WTfpc32xY(varQVA8U+TdeGnMwY_c`Se4O^r0~j)6-2Ug++@BYTe0lf zmM|Vl?FLhWt)=@(%=y8AR02ceZCM7IZD?)nQKP~+xDlaP@>07{1@3Q0Ucd=&Py)6m z3YcMWg~7kX!)d*#YU&59fECmih#X4bKqb^#Xy$P{;7KDZJ@W2vH#27XrPfJ zE4mz0okq*xLJj0s?m=4ph%J!_TTTRgf0D0sVSyalZDJL^E|G2tIDn(Uj>J$sKUJeQ zM0D}gzH)HG336R>COa>Gw&S<0R^yy7dYDw#OE}zt z$YP4|g+}K_?JF)1TKhe`s|Tq0pntPPTO8(-YVvzIO%M-%3C7^lMuk16Fje}iEv?xE z-fOpVL#8<7bg7RX!cYE6TU!RlOR0Cu|A;4HF*x`hJHa3$D%0FZW*`XdPCs8^=3^Kl~ zY43|8)jft#QS;Uq5XQ>);hXT(gz*6ac8~?APmMW>ykU?g2w|O_xxM9eTfhVraUqBC zHNB2W9glGgUoj>OTGwIb-#qzk94_cf+H$*fVUgs2bO^DO@Wr60Vl=bA=a<{Xa@QUx z#tIlB!S{Y${H<;T$LpZq=BKwLFxTGBzv$72lGIN*>}_-A3docacXbvm1UUGDgj@9|dEVM-9x!)2C~F(24Dpo(q&#^# z$b{&Bv?f3^jIHxp|H$DSH3RldoAO*)NAW=?+_y&r}!I#+;FVjYu0_W0ia0R$3HEMWl?+0EWwXClBeN0m=WAH65E=^BLm=QGe~^)BB)+N( z#3k4jqe71;%5TV7yV5e7b>kd!1m|2USWm>8^7Y%ZY+003)M%&5D$YeW^*P1g?)yG} z1oW~R`nK(=NGF*t#40Kx)k8Ue7y4nsrkX~DaX&Qc|V;J=gJ+98?VFy#)zcYcis6o19WFSyMQ0I^5tA6sg9 zM_T;-)qDIA1*6wf`=}DFv?@xT~EUsizgQf$8ybZB2~UZz|?68qu7%8IwEAm z{=IPBik`OkuYd=$@_JdwA#`Jptlp_;!lh?1p(U9t zXlOFp831}wDpIn;{zVab3_+~CLw8C+5HpfY^Fx7nuqetK!|wY&SA0mdREqPLi%e6~!Sgv0M_z@ZNvU z5)>zhEm4vLKeDgue#kUQ+~n;9MiV9W63-MN^9h{Id7L6I47KJY zJ17DEXizi9;n*$J8z{}#%68mQ;6fG3B@29LG4)h6<|v|-=#{=cPg>dh+ly9H+`cWB z|4-a9{OnS`nhLvruD%_V*+t8Zl;p(k0irkSH%&AjBzn%a$vHlPj-;Foxc^j9I3lHnlPwz(8NO0lVgKtvgYQT~yiQ8p`>%}31*DKU8S89T zIx!CT*W{6v495p-?&ls_o2Pt3N8?*I)1CW|*i*!Xfj%h2y$M-Wth}iRsdgib^7fk0 z$$z|DeF*7)_i3a%+BkRD+VA~vVpO11WEwkY z7FXK4Qo9ZF+qj2c^d1Dz%oK%_U(@=X>o;FQ$zo|1nl<%B<=|NZ5Kjy(wm>9o=>r6c z%?yo}bN(RnXK>LWb{e|9duDit8>{fvez++BPDhPnUDiC@Gdc9>T?`o>MQ zz8=?q#OrFJB{l|7zrD7=b3}1E2yhDLIQ<=q`cl;KgcDeUaMMQ?|6Sy8%Dk} z7mcCv9WuJ^a0q-a=~jTa46?EJdwMUocUhW$La}>sFTR<`>E`p(EIq^I|K~@5lO|q*3hH)2p^}6mTCTiZR0j4B9IRKCRf%KN zD!9NMs71Y%rI#0JH&X85JX<&TI~4CkeSQg{EM9xqUa$5m7#Cb_>EOwG#)?as5gR0a z890PAQ(@t~)AgoBP=~Q6EtSq-z<-B-;PDw>F=IQ`@&DkfbJK~ImgbDjAN+c5Fz=v6 z{<1}QV}(vOyLrYU$6GknX)hxZ+`T*YKu+3UH@{1g5(~k30W9Jx=KQ zf6-YmTBys%vNB1O`+C1=g8pCMOizg4(%L>l`9w(ccXkQ?vE-!VD8{RFOG@Oeh z&!n}Su$L8L!f2tyCi%rr)_+3iJ0+jRUfzI|bpg50{wyJXDfOcM9LLsJdlnoSi;cJy} z$O!fR{C%bh;?d$y=C^9-!~_%rKS6EHqGs8HUBYb(8V57JP*(eY^uFtVF?Qwa6wbgy z1kSTZWcV(E>J(wNyUv`rzmAV_k;NGF3&3hvzknmHj zL8%JC^m&17Kuy1YHQXF91~)ZQU~L#$lF)_B2d8I)U$9fZ%b-dSsv2f05VaS31%`iB z@PS$R@_u0Gp)9=B+8Z_vhgpM~sgV(szGb8kp_Y~c795YGu&9whn>?{M2zm1_Vlf{8 zmks!}i1-DwL4qZ$D|Bz9Ffr#6ON?8qC`E}JjL6Xy73C6tlgb|Ly$ZY-$>hobZq?K$ zbenA3RR-7t96L?_-HMAyp>u$#n7qv!0HdjFBh2pHajra$;$zKywej0HK2Xf{XefPqT znMMBLQvJVwgPPvc?zK_$B&}$3)6ufocr^L2E0i{>&w)~_p--v)#iee1C>$8*VSZnf zC+Di=#9gfGNn@*%nW8zTPR?IphKQB;X(ttI8$JwM6Pd(ZRDbb3pgGKw9iUD%{bANx zCQ^Ot8;L%f6{P51cOuUpsKZl^HS|aP;?|l5TB#a;|251~Af(f4U3cG6w^d`v&k&tk z)9)Zs$ldx;C!h97faBw3o2qfhw6nEn^Xsh@vEUveRt3Lat6WCqIezLwwcN9&Xr?&1 zfdI(#)_}?Lm?hI@*@HvTUToOzl2gX-=zad+J)B0=T7X7o zAv1s-M_h%4;WDI1@8dW}P%HGI1iT1E-*=sR3W*7UJSy!LWhun0%s7q>H)T;CsBg2a zYQZ3v=(kn!$MU*4Pkq)8uwjTl1P1A7QWCh&#A9kOW@J=poWI!+bA zVUcy*mibc#TXpPlG-hZY7p8Jt+k`jdv)8}NSdC1 z7ll|ww@oXk6G|IFj5uE|%HD=NmtRx*TtiY=act_hfmcU+BVTGL_zdou;(aq81zAUx z;?bl$U6jnvM+e(IzJtE|5A-)`)ouytam)(Lqg6P|SPE}th`Zn83;7XdN1M=CA$b(^@q_cr|kcPP+R3z%v;FX#FgCgmn( zi1jKRIyq>Xfq~^ypK4~wc!(biV$a;Ykn#1Q9^yM_3zP2npWyJ>^zMQ*xf_aqXfx68 zBlUgcDN zPv18>CVn5MBFRZQ(A|lKy#Fu+5=@WXFl%PHHC~%?(rR#!=RPAoZ*<52o+f6}4Rl~U z>GPibs>NtoPOwe`&-&Iv>*nEqJRxc<>V*JC604dDqdg&Gq1fn87mj4*&%uJ}w%6kw zE{Fn@#}}Zia&Ai3*Q3ID+@vlf5bESEe36aWgSj$>Y6nO-Emi)?^W1@BW>sU;J9YCU zP4xe6EZNH4$awHhf1L`=48=L_^hQoT+7S;eii~64K0>CDu3_zmhdeiba-;0)?EdS7-J}eF%4qZ7mh=FTnyC-*JP0pWAQkr zC7;`tRSLpfZlY7rpZ0TijA@Jm2?e$*KUIi%jV3cc3WyH%N8)#i?X86p?GWZj+9-#6 zYle0cYktbz*#TcWEq6sYMH;?g%54?CfpaRS)Qo|DLccNB=-pxMqKFC8lH$*Z zfT_{3><7do#42i{H&=l&&Ag4|=t4_jjYCC-RW=kt`ueYz99DWD+RstN*pZW`WNc8l zM6_a3O#8$^DUkqh5kW0TVG18}n9c5%8hv*kBJvo38p|Hg9WDVcLtMoJ0>Ic~S8V(>HfOf08B zee3czwAS>6PNIta+3mi0k@gI{O6#+YPPQhBW?E<>J^55)kW(iJ7`2gWPDJb7?vbrx z#_0jAcfP{bFVA(Ni;`v}57Zg^Wanu_zN&*JdYQQzJ3d-jHlC~J*9k8a<;mIj)MK?+ z9ceo>Qy4@bQS8>`O+>GbNh@i~UtXlz4wiQ>`B%W@st3nevs`lhohij4vgrtz-b{e! z+OqIcm$9)16ahDv5gY{-w+96RpE?3JIhR2d0TU83F)=v`FHB`_XLM*XAT%;CG?(E` z0~7)^G?P%ODu1pfA7a<%-rWX=XDOz0;&_}v>V*Lo7C;*9Z1@t8ml7JD`4>FSVj%wR;((Dkgp=|>j-+sembsd_jj|0M<$f=D_O{oNfPfZ#7_JdlKgSVLoD zL%<7(!a%)7Vq73cB9iDs0GtkN&)QLN~KR2ZbR0 zet+*665~S%{HZp-UfTr=NsT}xd_NHc+)!wc#GXLv847b?L#P?)X=|C8OBh1h!$=^o zP<1epM1SIeH|abzO+zI>PVqDVgFYmkYGGV8uwGseYXUW?e3~ezPDCs|KHgG4|Y0KEaw-^D|UMBqR_Br}X; zh6)oBgu~(hHzb+>hM?R)=!-gtfb<0cBHjlK3HllM^@$oL54fUSh>-N5@u5CAT@T}i z1r)!VAtwJoe~Us`MiQDT5omN>u^4m!;0n4?OBrE_kVJ(4e4icE{O=*ZxmtlF_QFP3ycZJv8-^liqx?ZvV-(TF<9n&U+x3V@Xg<_1?r0Ed z(}Br?G;(N2+t7YOkv1G40Xr@C8wSbN#S;S(2*By@VIWkP-D&e zyPOXEwJYfPY#V(uj<#ED!{P2EY~cKM)ZhC5gcjp%4J)Lkt1j zuy|@xqvhd%lrtXb0&NaAqB_dmodh2svWh<;&Oak^(tjfdeg6fLfhhn|q@Cc7N1|O( z1RNR}@FPwZkisFMP4FMN;P9Ui=)fN&V7~%C5JmZ)5#qmgg`XpcxF5;o{(rU~kp4CM z>7Sur(#!mY{FGne7w9Jfzr_5+00x6@N$~OVI(PvRLH{2ykWipmBemGo73<>+sp?-u z_Fsg6I?x*l`BgH;q_ujmAEbY1=;Fvt%5 z{qxKImjnVo_R>$$>grhkAb$y&(}0AGBBTh|Y1z|&yu3`vFQG2qH~+z2fv)h+GimJt zAm|UeP>+vcU6dm)X55Xw6{=M@Tt+FNDEY2}O~qP2g<|~ra4Q#wX5IoHc&;d{@luvx z5!O&w$v!ka40F?3Ad(gRZKf%$a%judM0F7viU{SR(^BitwUo37&woO^xK!58C$g-c zTVPXi`bk!EN;5ZL(f?LMv9;q%qRiuc#?7mIc4f^|`ILUeqp$`RJetY>1p{Xr*Nfpc zGUEOhmcJ5^_teHkpE?ypv-RsA!F6>o*zTM#D7zYTJ>>IYf{xsWF$Th3(wNw66%fkc z5xAbpqgiS3<^CkQwtsvfA{zfkM&b>wFFo)}hyqW;iOth;8=v3uQ}r*pU6?JiDNrSM za~WSvb4cL3Tet2?vK=~V$_(y*Fgoqsj7b_33z>p7)Y!~;=UA_?|XYp-0vK~lo zN%Rc;Jo%w!nD4H&v+Nz=Ym~}IIp#grLRl{An2jy&p$$C8%YSx7SFLpCQ=cS!ELCJ- zQOn>~dl2T5*wHZ~sBqVw;hW=t?8-x6(UhK=u6M80%;wKCl2T5Mv!k#{TlTAjpyhyG z-nIJp0pVK`V|44jp>L4B_EbTAlY%!0#Mf@4_hgd1dH5UL`|Nd2F(`gec|-eXSo|a+ zrHszzDv-P#Nq>b9S#Ywfq!Z(L&?OMEL0(NvTw5rlUQ&8{YVU#4M^U%t85&uuFI#x_yTDmNCr%MReM&;kvlTWli zTHo>fx%$*xhJwmxv|G?!lguz{ow~IahZE#>uMsV0&wo7{rhWP(u`}xI#O$4(SL(We zPFc*lrQ(ELdHY(w9Ft;tW32Yb^D5ovy%_H#MzhaF$Ib<4`5o$B3iNEGEKs;OF-|A3 zo@(CfZ_hYkjL_^?MsoBRaRss)6u22-1>VIqa zsod8pe}B{EJPwELOP^$)ip}JwNeJMe%Epa=+rfo$3>^DcW_F#9sBoeL8~mw#hP>w| z*B-~$h&Y}y3T&jJe@ffl_j#u6fm~fxW`Rt6Xp^>E82f+%MgSKPOgAGc^>Hm^&D*0+ zE)RYxJ3?^#-5NSwa@R|U*}tkJxv&Buer;1}IDa9-?75kQ0aqbA^%wr>XGyI|aYJnP z?%RvQI47b$cmwMAMJ=Bi zBInt0erjDG4&zM6`EytWF|UhrpUA0`uern*iEL=Q1sBE7+PltM2xr4iXm z;$CZVBX@1yz1fdmI+9fL=rE%@7K~Z3S$~>uIxHcnb7*@j)-!HLr;Y-iI~xJhDsvj8 zxWf@rTc0ML!+&kULLVD=uO`VeN<+W&u$D)RuF(;OLFx2SW=$bRf@vzgV#*_kVXff( zlPy`LksxxBLm2(7i;)T5JAe43qgBtItZ#cV#Yzvjm9Y%&)rOr@36ow_M1Hf0aDU{T zVru4%i8edkQJ4ML6{%uM98Wqg#y_Rgidkm7HC(>i!}yV+HpiE2UG^*1Tbibci#)L~ zswQ-h;`K?ht2JydKS}!BmYWatFJ}hZ66nc~nYsGQ4DSuLf(sPAg?U@w4u4)GF)Jv&@v|umvIq<@-|lVO9aoNNp@%Z;kGZ#>cveRJVsm*xsZUKPB@BaMPo&x8dROnEZ2bZ^^E@{isae z=JWTwaKr_qy`d)b#F%9{FF{OW_?2(1-M&VcQs7@3}z zt880hhj3)O7y67scW+#Iw0~TR>@*tl^Y)!j<&B~AOOE&GdFXvazAD(Mdr%P(Y@h<;dNeeYc}XAb=5hx$V@=7% zw((Xhxs$PCDSl?%n}5bDE-bH>%VOh|E@u8(%k@Mp{-XmP{Dsu5iOX+L2 z#doXRK9p+1H4PSUMR322yWblgXZbBtJ28^%5O)-nGpUln%-)h$riQtuGy92NcD7` zj`m&d5qWyG_wZ2)M`|{Qc#lG3R6^`vNi@wLVV0&Haev(}a&x)3W^FPq9XtFqB1cnT zB`h}efkOda#Bab7eOM`MjZS?Z5koI_1}SePcD{~-7pEpxHvN*PJ|sLKwJ_l?&nJO> zl?YjSSm)Y81IOxD`=x$)R|av!*~RvPdxUtnhn@d83hbG5vwCrupJ2QbDSpB=b9wEv_xRWA4cogD z(X?4l3i~%}Rx^b1nU-S9gxq!;M@`%Px;v-?6kkf_3KS7y)$^ann0sWhinBA0I?qQ|ILQ~;&-M3foJxucj3``PM*U}d8j}R|3^hO#IQ|CbT zjgG7ReC88m_Sob)tXbv7d$Ma%x%o%2CVyAPL}L>Wql##+&b-`Y^6W3F-Km>>x5GCC zJa4aYstmrR7w|(HJkHo${}3mc4yR1ncR10#z!pHYM!Sx3zLRvFOmX+Df`>x6Ash$$vje z287^@kAd-@2zxBimFW#8ArQbNxdLRa|2UF7QPVf&dze)Kfs@l4^&?F!K1)fq~qR=qm0WNZ5t)s6VPJ0o;84H)F@_!y1)vXyDCSD5qW&0v^$`27Yn;IKD z@%vBZ$0Xiv3Wh(jvSuag*QhHJa?Dp;JN~xOtLBw^WXDJp%w)ssRCMeFS%2PLp-6#5L$0}HbW76XJQ$epY^JT=`QpO<-6b&GATV`n5=cjK?i^1F?pRaA^tOS zk>6Ze+n@Z^JJpA*Gcs&9Ie*9SPX;eXDO1g*NNB zsnnxH31{PYOV!fA|XS#Ayo>*UFpGpfqqknu#j+*V->rgl8PrIi~ z`#ODR^wy7F?=txGMPglmPtLn*$L0^S%EVg9ysfJ(>RC*JgWR_Ys|lBy;jDU1rSb7? z7J=l>t8>A_Rb*y%H`2}(6K)3aj_J#_W=)DI52AspK16ZHMpmH{J`jdJZIX)S?G>_o;UuKv*zvIGmH`|JezuV%_DO=F$ zZdSilR@I;OMHBd)!Rd|V0Y@1oy71YwdL!o?i>MhuTrrn$6xWDmzuESbGY zbil4oe~Qj2TN+x?l52{X^jI`|%!z+oQ=lq7;a!^ySF7}VE9ze=-g|S0eSmRU!H`0f zQ^9B*m))L+^c9+{NnszkT+I`CTl1pWh54_Nnt@S=sb0_GO@x#KdhjAwo?Q^kqF>}r zZ%)6~dVj*S`dFaF?DRrNqz+zDV1!$#ivw3E+x<3OK9_TJwSPh--~0GCb5yKx+{Wz& z)(m6I>H9`pCzqT{?#s11K5g=m+t3%JGS^N_FE;!{;O&epr^Uq4(KXQ?E?ItWs@(VP zal9Qh`G}njA~Rn9JYpS<{6H%h`o*-WzP;teXKLdMv9`_JPB~4(Wo9(BTL}g%WSv}f z9J?D?(H%St3#?UswcQ`I9m}cVSO1*0-^pCHbE|`ET^n3E+S8&G*uC91ccn~LKa+Q@ zqJ^32!TTv6hZDzGPE?2t&-yni@ksIb&)obUdy@1Rmk~?{6qjQ=2NJj1Qvv}ymkK}! z6SwY;0*?@vSVadDw~(I#LnD_YOa~LU=E4HgikC=J2NRc&p8^H9(MPGQ3SC$mr!&E6PJ*!0|mFjiv;^q zmymo16SvUc1U@{M(S!#Sw;~(`HC>k#jRzFBYk36*RhJZ%2Nai(tpfzNiOvO~Hv={> zHm=f3iV6y>Qd0UPe-KT<67U9S3a9}f zRVluJJxHX00iGZUfJ9KNQh+gt2T2f*0X#zhOOS$g2qA(PY5FWV*xZC1DL@r;eZt(2m-Ny3;_># zg1%^+H$dT;38a5w(YJRvVk{3B=vp}#0-&Qj zV0^^hf%ek@#6$7>$OBdm5Kr?13DVRp4IOkHoNWw|2-+P0Bya*Gk+C$lf5j#ZMF#u| z4N~W)f`C4iM56hy{FfsA=jPwg^$5_-j^V;0 z&_RD!42`Ffe?x!E&7aryBH+nbGKKupA_#b6aUd;vGOcD<{5EE(Yh`L=Xzu{CfO-!P zvm`*-!NV!Rlx=C6JzWC}4L}v83?QLzTAv!?G5Umn04QoQD=mEnSSU{v0x1OXzdGC> zPYA+?{ZHB(i^q7=>VTmV5l8UYKq_cz@Q)G%vHrq*e?SVL0Dyr280_VXpgG^}9U6?J z!BA2n!iWSS;El$S!3eB32z{`Ik!x^b z0)YAnLy`PT{nHRKig0M6WTCOe5b(GV00VlnBCH4$s6Ax<|4iLqzKp0ioE16%l=&Z- z{aYLze}Kh>{J#|b5_AG-k;_;SNC9ZvUmTWfgbfBUHdu<6@6R;<#7!w^XfAZ|J~$A7 zA(i0@N~(%KnIp7`!$GYLttTvP!O?itzc{FCz5MYYnG7f^Y*QeVo4>+`3PKAWK$stO zv2n7N`(OREEp3SRB4Dt1A3#w>6+n|n=nz%~f2c_mRaAg5B-H&FFnGI*00bOQpg<}B zkxGdGya^;$TBTLh0E9jb`gu|Z5C;F9kSK_ROcH`Ho;V!nP5F&c|Hb?)|1V16AL=h$ zQ5isZLQ($8D5B#T1MFl88NR&3Czl2p$5Ew|soVbLnd(XY z-H#fSPBIpnsNZXcgq&0HSlWX4CoO;Wunld^Z|^LHUrqhb`?r0zr;rH#pc57Yz5c(6 zK#fkq2D>Ui3kM0|(AU4ex&7fl>esIPOt0wyi6w*tS`*lZtKIw(UQv*tTukwo$S3$2M>6 zeNMagzOB*L>uPO{IeY(lH!*|jc_~x5;M+VFF%~=OGmomCf#Y6aRtj5GXl0m1_B%Wj zoiv{}rQ2_~H}iy;A)gS&yeUgT#s^_)0H34Z{Fl2Z}>)y;Y| zuMyh2v!8EuQd(MQ)`h$|F|I0JrG*(i1IxU>Hj&HCJuV^S|8!-MT*dBlIEoG48TC5N zK+%VqT({?#>AXo8n)rSOEiC4NnBPI)?uNI9tK1S(haB%|Oy>}DCAdwDB-02kACUgZ zi{2dpPQtmzs%}~Jj>ZG{GWxfZ4^rm6vbkzfU8WnWBxP6|0Q3#Ni7Kihf$^xVGOe#{ z#MM9MPd5u`*=_mcR}-GXBxcTCC8BdPPLJ-rue2yD4^#aAwQuwI{eT3b=p<*ya9+RW z%n2#vXi_xFKII_9`On*vHwEhoF;Tt#J0)G4vyXdes%iY3?K}Z+%+$c;Cc!wBpy>=# z+``~tEY^)(YGA+G0MZ&*Pm=0;j3ltUxEffj53R>zS;FeIJB~SLF8W^F@1_pBm_U~1 zKqQG0MtO)_LJS$)4J_Es!&dSm^X;;N%N6-}nGS9R(kS~Ex%10b{*Eo{F|q32dBeg@ z9mFQKdHv~hP9OzjdqfIP_6v;Kq~_G!Kq)i6vvdX)a(^;-l@ip%q^AAUg+>=F4&~@M z_)SF9M*L3!mt!4y@381;g{EXQ|Y*a z#{2He%a@y!E}?sX59`A_nqB?Se)Pt&mxBX(0sEb}K@JC)?*HX0VupD93l$TkCkiss z&APGgyvbk((nvT*N-UU}emL1|UDB*Dq0T4-c}kc%{NUUOB0cOV)VNdH_)vFuVAg%W ziL`^?)x>nrtXAs8Z2L!{5O*_P6L;|OQAs$2uF;q>B~Br=2}Yp&`X}jo%m|Y;41QV~ zEK2(3i^CS+j-q|BR(kSD*r@KfU$Z1+|DI-Xv@x5t*EMtgcOR>KJL_vttJ#qvK1ceq zk{mJTx(Dh)~0rK8mWoY1&kzriw{0K(?Y?6-q((5W!{ zlU!F^p0ADp3kho{J#~yRn-_O^a|U(VMpgbM=>436icHqk^Y&g zRmo5Q7*DwC7v2}lZ|KX z*4nz`5SZhZO^*BbX@~_E?xfmUjq-3V{pPC3ssomV_m@ndX7#I>sXJ>DM1?bU26B#G z9!ar$Tqnz&JV`vEyox0~Th zD-@yWmPOxiP}@HcZUgkmKDdP#u`s_+?0S zt;(cG-H3brcy6vL>Vmv9FK;%3|JmYpb!S=Z#!eiK>^YoSgZu|VkEyJB*DRGjH0S&n zz|Xp1)f%FHff4SO56h;cH0%Ot0_*O<%sPzwh=%EWSPQZAh9>KH+{m7o@G_%1cqX~o`iqlKV8=_}D2ivb_Sg{d`8)YM_u=yGTL zDdf?ZZ_)d}^ps^6L!a+_2b}&OIH$Y^9Am^Ei9fjUp*J+s;*_Oz-|-wk8%0qs-!G4@ z+`~&T%(MVqFz#R}%{{37UEUKjUp7P=<&=_NH-8PV2g=GrY-?87hy5nwfaJNt<#8XV z+MYMoQ2ic1a_eEVdq|d^{^c)Hso&`oIImkOoiXpj_uBeO*mx&44<=hs;-No<}OeNlRRfxycYHqH}R4nKG6fP ze-V0@cr$tH$%Fr88*a*z=+yEx%vczBC(!1D=m}QexB#q`b$(DwX;znM6>* zilc3Lw@a1S=F^X> zJ4Hj~;{1WD-3l>NysC4J>YTk@8j_xB6h<5Tv0O3z3jInUUXr2b;}HdNc`KB-R3X{- zCTw%&&u5n;)zct{8mmwhfPPKw^5`#lv0It`)wX5Mn_t~DUC1`+SgebCR&ew=ys+xs_M^htiELqaTvPQACL)voF3Env)+8hx)%v(e-EIM*4uyt$I$eU`$)rlWBkKQ zvse63bpbzHB$^2sKyX;ns{taOJAr?SNfPbAEm{FEIH6;2&xq>YhkqW|=GrmWmYaNP z;(v=m!i@2AzI;y!t&VNUUxp7T#7wZg3LP4@&%xWfsf$_YuXC92QleF)lYD>eSwHS~ z4Euw;({t}pPj3BH3&f&<$8d)(H#_w8(q3w^#Lrs*-3S57vqqs>H2me~0m3&auswzI2koX4uPDGq zUr>BAhwI;^0~?d%t0$X{jh%?exh)YtuV+`lxh#1Ne#tp@sbhzPdH370l4L2yrNo*S z8|`<5dRG<#7}01B;-%oJZ#inwyyv{tQ1$DWoAwG)ik)zM1D9$$^j|z$fv4(j`Nfkd zxm-&>8zDS`#egvK%Vv`XMvbwx_^hy6XWf7e;js<|)fcy#FI$AYxjn;@1QJA_)V&p> zKlp`V&^b=81*s8Lh46(3tCa@cN_%QSv_2d$N2*SMTvBykqnCw`AB0=$zvMX{9Ig>! zitzRY0vi@973&=-X;#w;&N#w#`b@r`Jbl+#5qCC#(i-pc6Be)Ol zujPjUvCPPqk_~VZn(8yN^?KO`nel41I2NvVqTh&MKX(4G6mV z9;~8=S*cC)96v{Po#B{qQFDP2XYSN^&KthJKXg{sCs>|{G)o#p-R^0|A2+nva3rHh z1GJ208n5L>ULyE?%(IS(Vx$e5W(eRT50iZ-HK1v#d?a~YI7)|gR)vfeJ9bI-721XX zow!H&Tugc`dGAt9;XA({K21}8?93nF(Z(oG$sN5{=Q9@iu$(^$F+ zAIKhkeXuMe`sl$=8FXxj^V`QL;CW!K3G*`(^oCqea*J?h1vYLfuf2}eGS}N}&Z6*OM9I(Jil(2GC->XzB78ad&*Uu4F0otb))lODdM^Xq zjeL3A$Gv$y^kQwE_<0OziU2df*fg3ZStB~5ikj{r!LU82(LW23%7mvH6{FRaC>x`OiQ!?vE6Eh}4v55OvUbzU3& z*D^|?lT15)2F@2jIX_v~rF_q^%AUKRo;}+-VHepY>=R!<<_zu@jj`JSwios*Lq?s0 zr@v}DYHxAc(qqRN@s+Yp%cFYk<220x*T0==N0hcPYs3I%(&h*F^`@s|@TRsh&p~#r zi63De$4*Q?SK~NVVJ^AZWmNu7o{|5)3d4|x8zJk+r5UGnlgd-k$=-gJE2~Ys?H0&7 z5)MAZMynz432-SxgfT@En8@LoR1@RzoxiX3pkT_ zZ*VACobua-{V=<`GUo_YU6`rDvK(gt)b$zG;3Z>GZ!1zbBVO=klS}1d-rk6Aafpak z`aEaOhgu(9@Pu`Ht0T1kyiXBVo1@fowD0t+*E=iG+LF!pdj$mrd{V}G@}`w&42hWn zTK$a|3O8)jS}svA0%7w_n`@>Wk7oG-AMGsROEcs2nOO|%sxP8^w^%}%LDhP=Vi-#B zlrT5<<~&V3&>oL|dSh~%MhJbM<+R|)kTl1?vaL2L0;PYtaN?Byu1x&y*1$SG^p$=waF z|62FbJbd?U(nYOv(g)Hy#0X39RLbE!d!J8y7)-_rW2zT^W^K9eiiu;RwkoH-3}UAw zx?U)j{auW>dp*b=pOMjD{2ANTyUeebR~?Cl!yyws8%*~v4*gn(ig}p)8O?=VtqYS0 z`sHWm$~lwn86K`qB3Lf%(K+lMHWaME?ZLN%n5qWAm5ZwReHpnl8d{U7cenLj>?=Z!a+?9 zi*Pe`+v&m#pmMf_FPILR!CW|xOimb-iJ0IZ1j?7cOI2P+>CIWfBQ?>hRB8;dLGZG< z0G|O=Y;CE2C(|kTiI!gR`?|mU?uLfN=zUz8eh$U}9~R1M*G4%n+wa!Eo?jqlw14~l z;qCmxKkOcODC^2yx=N3qC9E`Jo!WgPLfg#= z(zm$lCTi$;Qu5z2VvbH|&>jE`naoEoA~3yctJm|qS1<}1lbTzq z`RW*A^+UQe^=_=_fJ(J!@jiV8=9ao@>)w*PFW+m3Yk23Xpt*COv zbz@cptXA}(BzsRNZ>e(%nN__Ho&>z^((QHtm5rhJWsqu}IpY`A(6?R*r=$5+yDm+n z-R9W*7^)cVt4*u3DUx?0XTnt|!y#BsES&diXi`%FSc@>~!afN-lrXJ;w~PZ7=I4(D ztG@{f7%_XF?P>?<>q|$O?qzvx*_)rW(?@%|p<3A|ABoAi8tjD#8~C_ahYY(Xb5))I z@-wE3*1%Y=-J^xPQ1ACAFIvQrPlu6e-M8TW!Ft~6$;%{C$5LJ9e}RaiUe3vPl5Mz= zJ3W^qx|NIaLy|pnwY?RC3M)+wy~z)ni;~;ZW_pYo1eT|teTl9C0c7af4)=!AfUhxJ=4jHhQpL`aCmk}N`%gP>dM&)2prRd zX?-nj&Y339-zlo8(}XgdS?euGw_^<)yorl}=Q&Do&plG_ubeYvowb?p!9E&V? zt#-ToKDWJZ)dOq#*|o+sjB-g=q5C!0=CB*OZ@s^HM*cXVZ8B;w{|Lc~q^soyq=gmx zjI)gErD<@d>YMa>l`PAVmNl$ou?cK4Qr8>Mw-wh>mlBeexXIP=&Z;^iZY-&%WY>RP zSE$~dRuzBRW9wDo^a``Kh>p{!li4#~a5*2{2;JrcI;Mc?F*Wzs`KHja!RpjHnXFJ) z)e!O>m*tq^MzChlE4wl2yyxj!xI&K*cboP_T<_6`}cQf?N#rRQtiTq-krmnYd}-j{an&XbBeyy(<#S?$C@@0Z zfKj2x3D7~XVaNS&3G+V!AtCw+z0LrMEk+cAM#5%AOz1(fB8(@ebO9G!w1uQxfb~$I zEaX@nFOW_FWs z2#fmC{B15krbB}aT}pXh#E1SK!5^`KNU%U=1LSYX{8-;F3zv$(KDL#Aa+#>&IuX5k z?W%JUcf$T|a6+M~_N}BU74!pVJT%~h5@dN!DheTS(M5^oufBgeLYSB-5-D*aTFmor zHr8Yp6x-4-5HVCiCbs3zJ^$dFXm*<5rem?uVNo#nKqIsvBpESCC8%Oj!H#7yK)#O` zzW|hwD|r6{Qm+g0catYHFL>z=t*Y&W*aH}4hynLq;cA=beX}X2SOJ;nlR6++AfSRc zD96Ms#7Heu1B-=Uhb+FK(DKsIhDok5$dL-nG}`P8daxkKzgC|J2^>_cghYlQ!kU%U zB4M}=Gh~5Pk<;+7M|3A0t7cTj{+>obrp6$IXw|YE8mmJE5*XS&mM>eS&Q4zR1F^68 z2aX91{o*W^ymTM`^*71TU%OY0?Uv@EW}jvo-CJHXn)yl_KAX`?DDdhcy5P z4=d1lZE*LDkLI_jkt*%<{v=D| z_zxklr1}iM5z|K4lq7uWO+yUZ>K(2n;lB3H4M#gCmD{)y*+&4I9O?j{wPR3!E>QJI ztHd`(T>K{;bM5S43%NI1lrn$s*JB5-E8-FCaWjco{o1%38BZ^Hd}5qEvi|gz=fL#2 z+fvFz62m7B?eg$)qTs-5jDq0wIAx`e-&x~#;S!yz`D1fL{u=}RZ7es^8B<7QAtkvyBLEUDX(`+tUL)xpNT6^W#dZA@sjkd13)%Wjh zoO0===>EiL;1zZzig`)Li_bG7P^HB8DMLtnyvTIKngh^W!-YzsjP#TeNa|5uX`GxntI#%wI2Fdx5XVI6rS3%t+a8HKK*qsC@MWTJNaazFGQ~D+v~Nr7t0(( zH;Ovad0)9=fw=+9)jf79X_QfYDW{)$MjP=3n!jhXtiY4Zxs(1v-B@A$Xm9M?wv~%H zSOZ+4lx}g*qfd+K9Ojd%w|S8L?e4WWvVX$N`C11mKVY-DHXPIpS}f+`<=((578~2< zY-y`$vp)kY1u;ZZ)>4 zgm>)g%MWU~u03zByF1DJa@CT!{3+`<(yn#Sd_adq#>TpToo1GW%ndHjXtl88{eZjt zSJ4g8f9G%TR;irvY$faG3wOQ9&I;U8dCdZ!I2@m1xg4Iy?j97;g^CP8J>)^+&U@Xh z&Bbx?g}ah8ZZ)5qD`+K;7sCzFjdMHa#=e~KH-5hp0+ie(gKa>Utjz;ID9`vEA;W0L zHX*mw=XQxp=h&v%yhrxUQ(R~C06?BUOUGkK;UK?l>mQg+^Hf>P@0s11J@(bY(5v|) zzg z1^KAklpD`vjqiTBpW^)I`J$Db=i%J7?zCswr+*>2*-GS|vW~Mt=dq2n1wdR^=rQy3 zLAH^ma(L6SH9SMgKjYVt$6+4UIzi5!bhOp4&1kIDu9SbRM60c1=a=wpx@-?S$pDYr z$x}eN!EE(?WBkoURH@^8Lv4MY%Nx>r<-_mju-K-V&0m$#b4$9Gym-|KYl}KNZQZ%o zMRRu(5K+G4kAG~urQSfX4S1f8#=UJT&U^U$bx=Y3i_ni{Bqd{{#hN07Eh}f=qt(u} z$htHl`!t*LG0*vDd+z&dSv7fQ z-n1nxjme#2BvZa8entm zbbTw!e@I@61!TZ`doctGi2MWz$rR$`no81?dB#>at9IdjAV39j>S)Y8A=;cHoAk+B zNK_Dp4yRfFD1*H5upy;o=j6mXm<8T3(#G(I$mR};L;JT2Fajb`p@`%WL_&|l_E;>T zvb%m*^!OWa`;%V4GPTDMjfb#Zn-HmxNQPxUGcX22<>XQL^5N|Y&Dq<63S8;bkfvWi zF$$!O2c;1$VnQDV@bF>Yq&E`lhqV|I5P@slap4If?jvFXci8#!wCmy$ZA(MN{rdrO za3*){hP@8=?|^z=O&R*BBS+vbA%8-dQ1FxX!1VqpF5LMn6MN%JA;I4y>&6A)w88ik zA(#W1kr+!Xtxl|1dFgk;M1TmK*?$b%Q?1OZSDas2pY!CQ(KfKACrnj{k3 zsAhXfG`mb_VMe_sYD+8R$#!GTpG*gDU$!lsZopx_+OB!%*LR^(#T^#m?iz+ zjMK@2ei^`zTJawO2#|21mZUKK=cgchoFXr*R3-p9p&uB7Cbw~D{?kCwAAYn5QjBI< z`Rx9p3mX0Rq#{}OZbdj4A}OI@&S2OQ&j4NzeBK|@5L~P@pQW<6;UVc^9fo=*^1o(~ z`W6Ip1jujpbq zIDUXY0joMLMxm^}f6?hC{mCq?g6sT}UqJdCZ}&Y%jes~@8R3{WX(%BcNQB!3vBOy5 zi!tCR|Md<|+2`h_eghq?2JxQ7p^b$wFP{J4`5uTbn9q=Xde438{^mY$=-VxQTl^0w zm;fKe+1v)7Xk)kRHsnk~%j`uj%kT{1V_!f(Q+cQG-9GTN8vTx0&3vaOXv(Q@vVeI7 z*noE#)kUgYnC^LH#Z-B^(>bAB(-bw|Vs`~X8XkXFSv8&6&|;|bY>M=|fL^tFgYz&h z`O;DF*>Pn0FjLCkdad>ZVhU7D|u2Kun=dy#tun zYLDZ1SEV^+)G+_jDV(PKt=2Ivn5L^ucg$8?cci4XE3k0jnBD>2-TImet8JB9%lLj? z)_8B*UTLeCB;F4jTkg9iig9|+<#C)eG_Wd%&9|Xm1IxWAc`AKnc=kLEM_b)gR<77g zVHS%kXHjIoxLFg{%hJ+Hp}@0mQ3Ys<-29rG;jlUCW_BYW;{J7fUO~_vn@>r8muSnt zH|NL9^*SClk8}=r3p6XvQBEn^(tGJt2 zp2N||M(lS=FltSq`i%38ckb<0>Da)_zdQMP-o9GsbRYJ1`xwM!Lm_u369AaK#EpF3 zab!4-gH%Izp>sRb*n4-LD3Ll)$`IKrjUE`Bp_q+SXW;Jm?%pR?KAMPWyp?{Bt!C%+ zTIjKrc8PaPjgPku;+R@>{Z?z5B4re<2T(LsvaCjVrO_-Ty;OC)izFg+eWRU_fNnnUs$01cKdb% z;hC}VQyjj3%`beUhF)Q$0afc}fM%Pw51cRssq z$6j8A=Q~hG>F*PMpn5HGxn;+Zu7{@YJOTqyh1dI5lW;Hj>Y``s+PL;811q_j&jNb3 z4M@Jv%dKZmTk{9np91h}xt|~?Qg};Fy$8!80%SrkxiCDtmO`RmdV!PIszv%6hr`Mo#!7&wD6|DjN$<*KX_sh$31@ z2}^9tYw|YZx97Yceo{I4_;-bkZzOf;4bAl>2|rKSYrsDeR0KE{dW}yQWD-h%p#IS2 z?X=TAFJhfYi^Vme)%X#ihO5xM4+YWMaQ}yaViFu*TCu}PaivmSP)i)u+gJRBPbjox zkF3S?Bl&9OY^!pH&qj2ITdW$T1#!pcU=Or70nt#ir)v0t zyAu^t+?3DLT@~WB)2UBw9+_OKyeK;&yAQLtSF!hztX1v zOXg?)r9{r)sHQ@@py8N1_~);8#lCiqT2on7wf1`ht!x%jQAy|iN*woN8g|XayQSZB zD!HmkFJ-j3QTH=e?(WcotleH5JpGpBu!bKRDihNI@(duhI6hit7(tzRh$r0KPMpN`^J4rq1%a^#~~_bBsnCCi4pMPIXZ~k=|qw(6R{WZE`sTZnz`*qX($a&tTqQURqYxH!k53KwVuy1&kG@1Ac|s0o(qsG-vh;AvrYSZ&wt zW>^}0+P4~Rk#8@7-2?A@3{m#Shba*vn7HvletX^&twb(C6prUiL};tv^hZfYjM zaok8Y?fjVYwy_HEUPL+#wI>2WlOH+rI#TUxr zE0oH7$ycQ+p798&eG5_Vgv@p6)RIXSKXjB2xZYcGz-Emw_x2V*;=K}0$N?%M4ypNoI@6Y&3uGY&}qf_9Mnw4XYNr(P6*1yT=`y^d{FG-J*j$ci|}kqjN_?e2cAe;Nyw_%?Unl5WHT z0Nz#@&r1JQ>^cUBS#$OrZbqDRI!Vc)$O5Dj?8NZXrj_HRea(p@ z^jzfI&lA6h2M<#-@pam~q_MFF#hNtIPIx;+Z<&0*^M#fKxAp6&-gsavA3)S|Q~`)R z#gk-TE!?+?S1cY)mNnvdRjXe!>bj0hMkhK8r9^G)%b$Z3<6BQDwIRv@lj}x?GQ%O;nu0>ADAL! zu~@b#L&JaBR$?0tjTf!((9;cM@d3I?nZl0N`?CI-!)Xb+T#21|I#+DcEsFiF4p;fg zM^XREwBm~IEiwtmEE^eFlWkP*UIx7=kv4kE$B6v-_rE!&mgz=VM{wPpO4PkJB46sm z8wd&|OAeOxOr~&mw?L&RxbSIk4U{t<%L`p(GdVx_U<)%s)LS3Mv9g)Q=LPtg`2)O< zLTBv=nXT*v#FiJXX|MrWVFva-ec#YGi55RfDWn(^YJ%FPx zIm0G(1gIXWOXt#ZC_~;FiH?EiVyB|eA<&K0Tdo{pr_>xC223b~$-F>()-OErZ2lR&n7qf%3|F8A;b{$(zqmix~o>O|k)@DdZAA_59+<+Mf)l_;SSL zq)Bxn7tq%82Ng9K0i92oWYd&fEaIYU4ZLoH2kC7v`=`$>2rlz}YXRd-)$ydQa_n7H z8ASEw#wx+ET2igSh~TXD9XwVXRF|$qm#$mX-KmiSnFTQfZXlB99ODH<9-^|zwtjT zsEgW}4t{Jg5|FfU7oVoh`ly+a!H3{dVvT#+SykCd-^7TBQa{p1>D2>wFHd7}lk_Dc z)&Ee)QsvuWEW;hQHl6j2BRn3XuI<+mZjG`XFLi$Tb@QR=+`$d`VR3eJyldqe@4u&+O7o%Ns-kbThu!z zXmV9xO=b9VSdF(uPIN|Mrg!6IZ0A@0)>2^ap3EiXY|V`paiAFyVQ5fTUm%Fdj~6ol3~%>|hR@^47JHUG!$xc!Da z`|pJOkMe1C<%LWF{m(llhkp}+0AwO4C^J*y6buC-7t{aMeTdlESrS2DX#hH!&bX}& zeyg=CZpP~0Vx*g9BAcnDn`K7ov#iiVK{OnlZ$t^N*kmg zOWJM*q9YuAw&ds`sAkwK4Vj*qFEJ9=~)=Y6u$CWFyFI@SCQP3J1pgvyBU1W zBO3X8l?T;4PZ~DWyyomXRRAlzZwSp#o>3Z0o>Cf5FFT9x5O!x5sA7Gv{|@&g`1fi-Z0^>Iz^2)U(xzNXMS)(be>E3iugmts&^_mC8*G&_szxP<_gCea}m zVQrBdxnGnrtE|7~T~sY)o8}$_t+9LzZbk5EO>xgW3L+sy6d-3%WB@~JRn;=6VXQ0p zLGcRddGq1P%O5oP!lZJl>~r2gRtsrLN0RJ&`RzjY-;Aosf}@09*opW-PV^K#*2rvvO~_CfpGr zRwBmG9Z9P8`abtGSP4`}k$@*voIaY|Ig*x{DU|+XPtz6Xb`26(XaFlaP<0Pzig)ON zWrj28sEP?favPAs<*?Y7)1VfHBwB1nPg*jHDiRK3OL=4xof&4dN zv#;?I9AG0vc6Qm;VENGZVEAj{ZrsMti;V|YRjdRLF?Dj@N9rn+kkD6`k4qOJwNUD| zPw+Dh4lMHK0BSVb-3!kCP}onQXj`oO18sQ!5c2L$c9E}7e$5R9ugCH77qfwh$HwEB zOR<}4Lvw}+#b7+h{ZpfVL{G?p4oi9&rHXu7jLKJ#5G`8|>`Q+Sb>#Hi0&(=PT zulkwU7ecvdO*7RyZ^QMKqAb=DX-Te9>4TNgky1h2{Bh(O+$sa4AOc^2`0DV=-JjJY z|HBsJ3}bF2j%mYE^>UF&(WV}jD!pvvatI{i=BL)BiyDmH82^Qcn${BeBPn`YZ3!>@ z6~IzSf0W(YxxB%bobIv9oIPuZyp!s*qP*hmZ2x}wV_*3(f3Ve$^Uc|Zo!ist1zFk` zY6NjU0p2gb>?~g$O7kxZ^)4&-|K9On%c&4vM%m!oDWaNZmykcZMWb@YEF5 z1e%Xi4T&~EEls1K=p#?37`dH!Qjg%02w16asx8z|@B*czBqAqF+nmVgZk=$W-1b}1 zT}N@|%Dqq>7?XI|tU&KU8xPDu_{(+UaSCzS0u0 z@Q4?v=Mg9H>PvzXz-qV6pJ)!;t?rC&FK*;Eh-Uef!ZX_@Iu(T+IXslGT1V@Aj#VgY zD*`2FhlFN^t;pHigiW%K7G8$I10ZTL<^nd;okB~-41C43k?{shBGG~^On4n>AN=T@ z4B!pqoaog9bW6Uew^$wIbW%=>Y3qZu2K?4g>T>plnV zoW}178F0u>UZorZ#V=ivqS8Jt?-13#!h6)drNISRIM6!vD?T%jzAHx!A22GjGVIp! zTsMhEACMVui?=I*LT4>$w{~}^X7VC-P9klG_TG-e5i%-TsX6I1xlT&=J93kIC3O?S zI>pvMpXRGky#7*LqECI@DTQO|2-nuep(V3=!3gb;G-5?Ux+lmQnuJh$1IsfOe;qD& z_38;}GPxPYBTm|M1!gV14&W&Pz1Ygf#sk8>d_-=tEL+_Gmr*{qUY<8R!i_kJOsCuq zUH6l@K!ZkjY_^QQ|MAzp&Y)$&rL_| zMW(bTJhqYM{hV<v}jOBXuuo`ezfMA1nCiJQ!_ zu4+@@SP_h#Q^(I0<^b&?@^<6X)L0u=&{1^SBZ4Ey0fzeS(EFdUoPGt}NXmWooD0fi zLC9yA$gflr(oRiif2)Dyc)wiyQJ+8p_r`{VY|{L-9ITbBE2Bg}m@Hf7!%4XwbX{7X z+$~v(P1k!8-L<#@Hh#)iTY$yPbwXhuOQ%lL1VeaBV4TY6CLp2Okv8(9{}F`5d#bw6 z#7QB^WTQnu=t+*o0leQYi$uC133+?x7eYL`I6AT$4a8rFs@S{?TPuxMB2(HVer)!x zLoEp-90__c3DmZNVaeztM(IGhWN^dOXV93eYKuWPvp?5#wt|9Erfa#|7O*QCwVi53 zwLY1vdp%v#D}eNbpA!>fRvI3lCZIQP7nDQV5`@TyUiPUeXhnO}@3I?)igtE{w$Iwp zXnmEyg6Ti2G_ki3s*GUZnnSd24 zG0UoL%7{xnw2DYa*qV8k4qp)kONZSEFCZwM5y0;7P_kA`iGkZQd`y+U_X0~RYMVS1 zQiwf@6EP7zEp$TVQeWLHvOPPn*L4U42_&|f?-SJkb8Q-TuAxw6+5Y`Pe}5N@V`@Kc zX0f@qf2aF2k~VV5w%V+b+`A z%8;Ir6<*D$cP{Q{mMZ3U$Ms8rFDI+o6smXQ-tTF_Q z=SCoY&CSS14d*sL`l6D?B(pdLq6B4sYThsfN$OkC5ArDDwy7FWc}DW`7zjhvT)=KE9>jpdgSAEjvv5SK zWt6$ZM;nsIFtGBD);^V+&n$<`#t3BJJ+yq&K>EtDpqK*vp z;b*P7&Wqt^@XcTORl^kvcQHpWRRH{j-bk>4+)NpgcJ`Ie|(|uD`mdhi*i6 z{@VCYE!}v*K<4IZK;<_bhiTIxQ~T}*ZPwU5w?c3W zDK#1~s;8_~=-*Qx;@dETzO$j_fmLrz?;tS5@(OGJk#nJO_#4go&ZD!%Y@_@x29)j- zUFGQ=LZn`3b;EB!cfHHVk$L1t>tOql71;p}nHnljF~ZDa$y{B|-c@qmTI1e^wjzBZ zsJPHg9G}Y%2?Z3)9o;K&1VDBlLeV@D!=!`cRlduW)cHY#dY*}7GzzIXm&wuq;?#PTJ>95J5#b? ziXD`FJ5Uhjp1jl7?7wS&B?zE7gKDXr9zxf`>WZ#PHe5||s%We4Q2+-mm9TiN6?>Ka zPGk4`P9}JbqDK^3*t%MOr8*{g$6^&*Jbumbm=Uwx;dL5U6CHKivO=zy)M=)v+k=Cg zI!~%Q8PR9$!#U(W)d0WkzZtY|;HW{Q)={kNErJ9C4>|je&Dl-+D-lSXzA{i`3ZtwM zDv`W?m1nr5mXHVUO#teeJTI4j%RzcZSC?)S+sX%hzi#RQH~$_Z8=NMd%DBc^g_%=Y z3?W#D2swpUx(>3ig(kji3yfWx@}{S+rbN1LRKrvGoOf9IJnwR5Y9ibI@e-Hu8(n~`?<6KC+`ZqKH~7GUG4K9f8K9j9gY%yf2Nu^Vj4A4P(6rBmES>28sA>3o!jCzu_Y6(xId zWC-fCGhCw|Gd7W8|1!~o5OZV(kqDgN4E@U-n9006L$_*zwYf;Fm%<&VE4Y6-y8oW^ zQn5BTzi-3WqcwAUx7?^7n)+~j(|?}3)AKP4TzmB40c7lCPM5-Z@nY-I()@A=eVt5x zW}OlfzT&6;`g+)h)338ZID;IlEG@hp#`NoB_xxCM;>6C~%GHw*^Wf2qp$Cw{;4Rs! z?;`fV0bdH%de3@8?oU0uZtd3|Z__CH@iFzcyI@l>w!>=Ywy8pLKpZ{FS+@ zy(^=SmY)@0)dVZKXN_+*?CG-S_g*UZhi}fG>0i;OJGq58S>+68k*{$CJxlsMy1v-5 z=Z?JP4Cj`zXt>LbUSgN3zHAw>=Dhcl)O9-E;PvEN?QxbU#r^1P?t0NzBzag1Nx3tai!iIfE z++ErX^2P)6_{cqaA%g`C2vo1VXX$@#pFSGNRT? zhp`?`oS7~Mht)&v|4(6G6;#I-w2N=t9fAgThd>}W1P|^Gn?P{40YY%M4FnC&hTss~ zJ-9<~5AFoL3RC*FFzCG z9m(_|XNq?+QQw!x?ixKEY;BF)PkFo*>2}A_AW{4Bz8_1RcaIJCHmcxAONb>u(h{1? zBv||b+;dSDDVq)U5z20;Fm4m_)e_7uN9b0O8a(bgWWM!#_2dQ9*t?VR^n@}6Z}c4Y z_!K!j(Hn>C1w2?9P{tlW%G!%I(cppzX~~JR3^`*8h2XbzRJL3~aYkQiwfYEi}`7{Kfu`R4W_M zi!w&KK^Q2SR(~UMj4kNhARUtx_lw*k=&S_UJWL=>66)wUq^3l6Q68@$H{a(Y5LORq z_C4D;T{!5D0ehq}<+n-k#;zJ~G;l5^pJgprmHa9M3#UjOY&#Sg)`Dnxm$A1BS`Eh6 zzvlH90fsUS%lE&!9Trd4L#LTf9cJn{CXR;X6ou)D{PW^0+*&#(Y9SY1r^6Sa6)Jk@ zkFSWCK|B%JolB0NbDxnVPyOJ7ER65Mj<%^*MBYAL?d=j)HNQ?4;inEUe)h4-e6;WB zx*mVfx*uiotRG8jwX-ml(Uv)-@4w;pl|4~50z|zQap_mYiFbKS?e4_MvHU$^PAoHw z+I-J0YCvpe`@3-@>{Y#e9}pA z7*Hk=Q(lL&dT6P2BIa|ywGX9fnjbSb+lEJ2p0-%g=(#PFr$g6XT$i5F#aEBfyKu!n=u<7_wk z@uAkGN2yMz!DKT{1LW*s`{;gCfWsNr8@M|LG z5ohM!_7LEZw2>RJrPSOxi_ihSUT<|{D(F{#@1IUt=%_F?!~d9;w9?MAQJ(EN24GzD z9?4@bk9~cSs;jLb+dH%tE|CW+Xz4Y?#xZAi-tX6+e7Q0%iJ{l$DD7`OAC8x8va38& z)Dn7En&K*o;hn1aKKW_{$d^m^VUN{ans3B5!PURy3t@bqIm;z*<}&Q1Tgh zf7#9x^^8@`e%n>#Q6wt{vif@vaBL*cj!vn8E^XT>`R{BFt7Y5ykQ^Fgs${iv%?wW1 zy=mqF(dYgM6~n{92Qtfk1YZmcqeiS(<)zMgKjWuz;Rc~^x!m-+rPFT)goX1|BwiLd># zQS$R!rcj?h4hQSj@JjKE^Osnh@?W|3*K-}X)ME>+Yc9?%gX&3uCq*Qui1vbu+{W#M z+*WF;$3yM=djZ(whz7&=t~Y4G*R#X1Lwifd!cD_y8wStJ1=UX7hW+QI=hr)#a&1e+ zW>f7GIliWkJKLMe(;rHK@}6&5%x>D>uRjwSSd_a?Rs1$K(q82O`tM5?9YO-$a ztTr85Mab2Nq$} zznQzR@+K~4#0f1Duk3aRaqBeS*`2L);7pc?ATB2P>Dw+TGi3*LwLvQwX?3ifk5Qte z1UbV|n1#Yxd&s4=*}3?Wi)M2KquW$<<9TNL2TpN{m%oH&il}Q7CY(rhY%&!nbIeAc zz4tjqC#Z(V63V#!MIK z>d6nq)I_t|A5&9SFani$hKqOUl$=?sZr{K=aM5r`X)RF5gM<2AcEectlrid|UQUBE*`) z#3L{MNfk_>57@Flj9H+9Ebg>aH!AkfeboOEFJ@U&EGrbRD2UlOY@n7 zTCabymuD|5Q%Qgup3_c#kQ#|q8;Vscw9-O120lV)@2>}*(QaRF@&Ch7!E!^?{&tLe zVUwyF+$BNlf9a-p9J~fQY0w9FIDQ^TRlv*rA^|~2u0Dtv@+=1m2NF*+GOi!BJu>Br zSD{bD8V!gvl^Y-y@B-zkyQaDr$`xY)dQTzy+z5*B{V1pN zt;a6Ck40@!+CgSgA|W#YK~193?E-86o%gu0Rdx&6>%FS1kDEw zgga94(!H}N-$6p4t5g)k#*d9EK}Y>e9Ach-iUSS6+e+aE*1+-a;wvR+L!_z8Ht0C5 zs)Q68ql2-~(D+Twkl?N=U9j!pyE+qH45%!eZujD}6xiV7yDZ)}D;dgYQV!c*=^Ss^ zu3~0R=ygVFZ22PQeZU(nzc$W+O7Lp+rj9Joal0HV0A!vzyh%KFV2d~m#gcY5sqEoR}UtHD=L?^ z#D~M>Qz`{=r0$ENFzYeYC-d*&f%K-WeS&npalF?F!0E%-+JbXCxvyS7@e1p%TbM(r zV3>^%$1AyEFP<*4NrwDgz25mqvK>?k@)>46!8H3~f}MV+a$b=iskYp?W>k?Y!zhW^Q~gR^ZP0hJS#ms^sCz$0!d_i^y()0h zC}d9Xh_yFF@l1buogn)RW1v{5{x8?c!`09!2Qq_)=jY*u{7?Z6Hk>Ge`d;W#o)=yf zuVF|9to?*B#F@Pc#|9x_r5!hmG@f{+^&<3WS)5J>Bb-5LM_H83TE zZsA^tXu%f_nE_Maf2RdeaSQP!nwl^Ht$IuLWJ0)pbK0j|S>k4dCkROJJ)^Ik%zBCF zHU%TSRB@@f)^v3BjSe3kwfLH6TEc1fO)0sxh$4H{iy}l0`;bqFtrJ|3W_j378?J9z zQ&U1vPSOyg$I^wm(>Oz5cToW_k_m=7E+Dr(Zbkw&r4P!B?G1o??9h!Cz03jj#j;SS zU-xxmPj15f;?8Bmgng<(4TW*kt>lG&6ycQ5aqJA=y3N5KaaJT1zhzB~neEb@q@}Py zRL=+?8N{dNB~8WcTgM_#=;ApI9;7yk`kr)-7d)8MN4(~k0y|Na8`X=>2n!9Tbans1 zXi_*tEBQ{r^RuX2+KwQ6traPN-`6Q!2O|t?c?QBTwI{8j(cdd0zoT-~%OiRHhD?zN z;f?+Vme3?27ko~QZyq1f#)q-dM7rEWqGcetr z@!P5?B}G{Y-HlVgkkKLwXg(%7k9-x&#YzAx;{4ecb`AZ3u9%Z>lNzIz(h=zj-Sd6- z2WercdX|!)L5FrF%+=>dmrhJ$_7knd?uE@=%^NwHRC0e1bs$})F292rV?btuB?9=kLkLH{c^{=qLibz;daTEsOLKj~h z?AzUKfSdZ5`AzwRO$e4uW}3|(UH$o6Jt1eLqm!s++Ej!u6X~4PmK!AO++`omx_f6P z*{6d(s?>(lNbamzP6VlH{Z3?UxB$E2o$ZT)Wh^SK+%KEDPt>4+YGmI^%N#tkP zlT{oYO1_{)0O^n-$o0zm+WyW8X6ZNloCTq08KOT~txxgH<=y$l%mHlqQrT68gG%}G zOXvr8C#UP3El-#OGLuNQ!k>j?(1lXl8|<3c-8pRrq6w#FadPxkaqr|6q$3LF>xZpP z=-f%(raSGTVUGv2epzxzSvMWqdeO;lxNocojg50Tu=hW-a>8ne^;UF@mn)kj@NPTRiOhz zbLLkywsO;QEsNvNrtY)PZ}y)l=HI3KBqBM;o4iYf^^=1XMHbi6)VB`k;G}6vNwkEO zol*5i$mwRk@{Fq^9jHR0fx@bgV*4hTU=^sS-t92a^nC~~(~z963@bkJec`;``MJw+ z-oO4eMlp!E^gfP(O+a<7XbJvcil81yV~-*TETa)wpj8#deIZeAt`=Zvrkes|HCzl; z8nQEI@e&MSKWVO+OMBXChaptFZ$MV5ALzIVVe6XHytKi=ODo^sVw^~mDB{`7++ZQI zoc^s?idXO*me}o0q74o_F+OKpBDmIpLM>0i8t$zW`Z^0!^zV#tmv4Q1ToiSHVB*GW zy3AmCd}t`%`S2yPZM_1 zUGdA2nzP&IBdLo?`$?`P{$((;zU_#6;lSW0Da~`TZ9(--gw*fYA|LJOtK|K|Q}$oC zOWE<&HrXUCD%#-XmhT@j)}##q^c^2bh2Ps1Rt}z}X2pcJ)X%u#&nfEHkiDl#-glGk z>sNBu9sC}fN4%?NFeoxI4!Jy0uV z%x!K~{lIwnL$cEMtgF(tug^Mb%?F9QQwuz6pxYfXBQxR8Z*!hIEqvWCfx|xQ*s*n5 zIG=N~Kim6ueC@`sOsKn-o)Z&iHu`zqF-!nRf+DSdoN6NG$b6rMU=f9>QI{8dP$LLK zAs|oBcNVG^*zw|t)LCYXj9X!|Xqd`waw+uv>#s;QPP5S8+8Vcw0pAI4+Og5Pwqz9h zEa(x)+7t-J9oOf}-_6B-0g@AnYcU<;7vls}TR)wh^#A#7<#mJJ^pQz7HQap{wdQrr z*t(3|hg~=q-U!P?BWo79h}?TDF%|#OcDAO=5Q89Cg~H%Sw!J(JGx3M_U&+Bu4~umH zBuK?mc5q+x*z(16csrG}3a#+oR8!%vo5RNspyAHhzM#~QBI}vJ1_H^ODtL$&^SNFx z&ahv1U}~Wh%y**ZM1V&UIbh$iwqbv5cWs@)tE*@F-S9JHJXp@o4|M)Z?utdkDed%; zU54bdoUcG9MsEXiY>d>KL{h{+cq1JfAaJ<6Ma?H<`;~owU$HVcI7w)pWn=%=tp6i;zrL0#T+_uJs|WMTN9oQ-Wpfrhl_P|K zwVkJzZ--i5lpSfQdpH}93D(IEQfYw0x&SB*fN!TM^qXLeNWGTMV>D|LsnWQiSF?bI z*%-eF?o}{VSJGVrZl!B7d%U~AAuiK$jh7lb9CL(H{ytwQk&R7Lw$oCF0~Yr)l0S_k zzF>);6l`LXEWT&4msFqg52+x=vZMq%UX@?MnfEe#G%c5d&KTY0~mF!EC*VuJm3na+ZEP;`lD>oe@{L_f{?LlP#`lm7blkhH#Z9>7Xv3J0~0ET zl7oemsjDRwqtqL2PHsM~7x8Zh#JdI*^Kzzt`Rpen=6-48E@R{D;!5?B{Xfk^sQx?f z1JPPa4ojTqt-IQL^9E*-35+PnaQFwG9*Jj8uBwb#1(Yo|o(cas8Ur&4Z1+0d z={;SFG&Ta8)M#Dqn+-FJg=>ir;Nx)4Y*w|L`ch~P$%4*SAL%CN3m z^9sMug`?B$)Zr8V5+a*j2HA;o$wraT7xh5D@-_5%OjG7!H`H=*dPMyWwtFWnLx=jW zpHrrH#YVNDIFG@8oeWx|UTh>d|BP##BV z(|=c^1$+)7sr(4}Jf&4P+-U<{+&0m@;m_cJNxypthvQ@_W4&@rPg2Dyl1KSZxpLVy zO@sDd-E0%xCHWE`)v6L7C8_=tgNk?F)}-UL@TfVR8A+v&Q@q>*ybE?0;dU~^zIXAQ z>^=Dk>Dn59t4iLIA+DUlGn5u0#O`ps^yqk2<^PFLS@t-+kDHh^tLjG&YuW-9Z3FB? z$K&o)o0q7a`^kJL8q~S6*ivoyTS{WaH|kP(l3-E4lcO}V{BUwfzIZ zg-n{akxmP-qf-l~+9Pe1KlHt2Pv_cW`!rT(L$8*O-LxJVUDO40m4u+jqF4@JZwPZS z_n-WJEV;dUwz`?rXulbW{}nWMP_*-@-9W1$d+AZqko{(6hUBAVETli7z3Cpj!m)(H zY&>_ycp$cVj3ocx-V=hPwSuSs0ZvXsR1S3;Z%e8d6_rDqN}r30hl=aP`N6@#m5N_T zfQpmq11g8Sy_Lg@CHS8uMWrty%_}J_DZwW$$j>b$!zC##Atf!&FUk9|m4yT)`6RhS zss6tqSfVd4`ghVV6&JtIzY`efAPQhZP5h7>(MAD*X8H7d`LDJ6EH+b@ne;Yya*Kst zmrjd?@)vu}N>e)cxjCK$j4N@V5t{lqI7pgTDep#$}Mn zI==P%na;z&;}4>*Mfeov$fXmcCAFk7kFGcVaRLbi5@ZQRo4CfQ584J}fPGN31CqfC zKt?6XI8IYu4}jj zQ_2nm^|T-gfOh)APox?l@{N|Hpf8qzuH}4#W%@VbOzSTY{!rTvF(sINX2< zE8HZpyt%=eU#{`oOwgBrBdmUY=C9>V!Mrlj?>~^qgI`194P*#x30Ry-1}*;@ zfXv^ld<`?Q9A}z^2;0{C-#(8>y3v`_-;DypUzVm17uJ>={F-8_i2q6FeM#UOcE4ct zMvrDlAmU4!-w<3|R^e+xYm7=)+~WR75e@U=c9%1nuB7%-qYc@T#voL}rFS0}o#Juo zY6g9bF8(9Vo>$n1K3*n>2=G$NnZJ%c6H#TC_su|DgfF9V+(0?>b6n9LGes3=58y!< z6@{fm)6p}r1MRq)U?UugncxS;WAh^88aL?`G}i`7zw~~UrhXZc!W|flROo497g}IK z0!AE$tr0FmfOdS$37mzU4Mcl~Vu-~L6Qd^H?TELAKtTK_(8bJT901Y#%p;}l=7KnT zyIJQk?>aEw%^_KNP@Uycfs8 zv$t@yBxd2^Vooj~p#f_DO3so*@BPp?!&Jq9?ipgaQ&%WSqOqXG;)9CWbk-nAKsnww z$b0F`l7ME<9AP^OF3T!~sOx*_!5FK$qSf#5L;1LC`-j!n{cAnyUYa7Rx>l%;I~H8; zSE6K4#mbZU6N#sWya`r+Rr@6P5X;_#3GG@%nebC#v;|w3`W<&{mp#hM_ zm-ZUL{zTMs1@`LEZ~SX)2e+0bc{^c8!Ya7Ek)=niT)V=z`X#&)6b=0!jh5P{HB8kt zPuR!FV4FctTqxirCE}+gx?x*bWc5%=)V_Dlq_9RRk!NKrBW$b+;j!JT4Ul^c`8IFRP|bZJZGZIVNeiLfA@*YlV4`?n(@|Hacc3+9~<05~C7#rA=jFy07~fF1?W zva1f^xDU-FLIF!3kb3Pw((9 r;S-6g5`*c}x`9qq_?GnC86+pAM<3sPmV>BAQK zi^$5s004xTsqL$LZdounRxn_)H-^8$dGJ@jh+1!>6Aj*W>Z;^2Y>744jxm=oqR?bP zrI={Qj56W0_n)-(%|5(1fZwgSL|ud(XIeyCWL4C*xe*1|S|Z)W+3Y44QCWeiLoqs^ zFhsJHak!Y&vyJI`G0!1xIA|-e-$un1%_XRmAO!Ml7M28bNxv;Y{Bdz-4zJ->WLi!B zAQG2Y3x`dB=>WfMbgs$~x~KCW*9own7dcf&(Zklppzl~V*?0m%2ko73YZm^CO1#V_CEyZ*zt#!3&Z1Exn*<-F;7rnleqMub^5;6}{S zu8BZAA%DAY$NpdhZ#gcA{dNE%gwadFb;@z~l2*%>nDy%fdUAwhH<-~SP1N=%GxWo5 z2R$_$A`L{tH6)^`KwQ`Cc5yx4VZLA_@u(nc?gOWxBJus`(9zZ8EK;l>es>+Aj;b?I zVk+8~1t?$H;n}C1i^6{l3!4|SnrQO1oJx2l)c>6o0$f5-1YxKohJ!sV9O0pnn=QASfTwFc~t z=Z>8&g0%$E8Ym*vye;A_!s?=WlHpHR-O_+Pv%5q-bKs5?9% z28Wd=yt(zZXNM)4<6TYCRQCLJ-k~q=5mBr5&=^pE1H-~H#rWsh1L?~M^adCgcW)2r zp`-A)jwGK<^L!Kmakm8o7tSj`E853bM7g%QZ=KDKNq=%dZSU?ZpTC~ZbDd%KDA{r3 z<{_%JpEj-h{K*tc9V}|RZ4FMQ5e*DvC{lguokia z2-IYoxgr3D;WRzdRKi^9%8E`$=CAJR+-4wMmgo4(Xe5unT38Tz5e_u-V$6d6y0 zZl(^%phkDay0ATYP^^S!{RQv?2j9niU_7`wIeU2$-1OU4%Vn$mS%7%^G28Q{f+G@M zPFR|}(!9P8>CfJw_XzOVTdXe0zimL6Y+P<@E3IhTny1x1kTvXQTe}6U7D!Y3a;KF8 za*HbQXL%ocqOV7SnAcQLz%PadV|zpDU*hO79o~sByzlb=3c~aJnKP@;UV{2icJfJ) zj4?b4>S5^7DL}QhZ~>0DWD#m-)pl8FjJ#AJx7bPZ!G9uRf!e$mF0uSL(OyIgH?B0L z2Q8N<0o?*Ov5Xl1fVI6eW%apW)_l;df7&AZbeLpBSxlAR_4s#Kp-kUF*X!=mZcS&IKB-ngeGVme_(5iE$VSzW{ z|3s~Co}M9Og`cj86t+#%i*evn=+vp(5;Z})Jv^NsG8|-z(pcs^f4>neLe!-Xwu>Io zQP)-!lm1VYjszVxv^62T0%5>yMeDlZczM?9)VppK5ib~}cDp20vHWwh{NjenLGX=jhjdC*+Ck4@)}hAxsp}JxGQ7ZyjV81;#^D{o zfB@FYesaUom;+nU_TMm|A;dnTJW7zVW~lJ;{i+$@e#rHIMhCY8u2?K5spZ;=`gJq2 zDC^VI!EOV{wao%>=pp%Irw!TK(U=u*A(R7S9n$%jv02txEJh7tM%%4eP!Fed2mJFT zz%D@HP(|72!SI4aGtv{(TSlwNZPaAsfmL^MBY~Biy%i02{A}uY*@h17fV$G|754O$ zL-mIK;2?RCrfvS<-h5)gj&|X51{nhl2fCDA(YaEh2Q!srA@WC__q(x)CcaYg&nmu{ zJA;`L*0fPwXP37bU759d#}&TmhALmyw2~^!)BAnP=H;lr0`yhJn<*=Y;UP~AKwVyY zhRBYho(q!K<`L@K>MJ3;JcRyzKkPb!k;y~`{Ef{8#00lYOuxo8d)I@#uQA}VCJ|?1~O8PvNMEFrNy4X47 zvU`&*z{8Z@)_>^(t2cRu@CCj&z@%keeSU~0r=9Hzi_N7>jkim&I!^x+=v|gLDHf=p zSti7XL5bM-xE+V=Wm__9k7`4vT>c6h-{@;aE9I{>ZRyV9}XMFk{$?%EuB9aIpaPk?A=@ zkp0+m2yId)HcON*GFqbIQ`XY*9BxpwF?;cZX(E12n&?7QICqMY)oqb#_bi}ZJFe3&%*=4$%L@mc!EZl- z3Vk2tDy&%vFnb*2NLW}uH_E&U;N937Acbp+3##LNaO5rLhcuM2sCBe+{?Xp zA36`)5(`Syu@3uiz#oto7W&CZwMlnbPJ0SAK4v0c#SDm6I=CNKHYA7l=s*{z2esrp zJ#+cVq3w=wz{<)oLF`K5$w>z^R0fx1V=pp%^B}s-{IoGS7?S_;5E=tXfeuu&E zpK2G!O8)F)pw64R-RDl1M=G|F_v+qj-0ts&+qjESgJgFA8cfI+`pA9tw}8-NO+Zt3 z^+8ppgtIo@9uC5n&P}@<)S>F}aO)c4sZTVSLI!Bv7YDJ*?KZ(~hXaGc?&!U|DuRRe z%KFcNOGzAox*tRo8Ib8Q+lOFk z69m7n|Ntx{d-CcvP6m9>3U)Q8^0`cv^9v}@!^3?m`4 z^Z}DlZbVPIiP)n{PfPq%>nFBd-;?J_zxDj+tRc!c`(u}0pF@B-@Ljg!)x+D%X~9{VNvBWNVX1GYo8@Ot z@Z_Ys;`=qhm(fCE>G)W&%3J_2Z`P=vGQ~=h^%rEJ(6_Q4`1xQEkt`liogsr=X4#NC zcT=Qiwe{y8_`cv(r0~c?Wv|}p5?I3+=$aRRY5}4!ekHGuz0M)4n?@Mwbb!1EtcutK zI7Ro+5Z?M#JB>w@>4pJ=v8#rz8d8%U59(^+@!%Grt{3g~yN{#tF7&apwzLi643D^{ zQ}lf6P`1ggiGiy?*RBiZtGlk=_5S{s)$@a;4o(L!mX1qMIWCSb3P6qDdl=TRtAI1EuGm#%=m#ps`;PcnpO5 z+8w1Z7&f0EIg4+44hAaO=s5ONz{AZ$Wl1iMm%AiEmkuO&`Nj;TL7z9hdg3u@1vz7; zH2P2KI^VYdO|E0b1oAf4g@zfLMm-w7)8ECeRrtUQKqvxtu0ouoNttc8{EKtbxkR^ZoyXB9<3*eJ9| z$Pt+gs$26x%J3bIrQomF$rwHcTDBvy4fV_R{PO7})ya7yWdd3oWt;wB$(BPNKpST? z-+n1N@o{QQ5XJQbfVIr@)bWf6>x5eyC>^CzmUx!9T_qF7ZxTV0_AvPxKsub%m$ zMR_0$R!+9}P^RKnLQQ7o2vpGHsV7H&3+{5k(du9j2A05jImZ*23g5SPD6KM*f+6rg z0ijbEOMu!WVWZ`lnS?!Li&_7ro`(HoL3JordtR??*=O9uvVQo5j}e;o4>F;ZULd>f zFx697m0_|^eAPuc#tOMA3K9f^bf9uHqP(>3K^FP30eS%V%K|^{$lt@lcbOttq=l4& z$)b&Zl>)Em=cZY_Y;{OI@yjPL09W%NJ!0 zu)TNpTK!*ieBX80y}_RTk44M3lh4D}>8aa*a0%Bxp}L>O?{kg2v`z zY^5HFMDO^S&c>E)-XG+`O%$`hzR2cFn$4^Y zg};)UwY=1NK;b%=OLv;0vn4%KDhM$R1{ow&!7|3)&L;PJ68X+VR11E(d{gv5@;aSl zf=Ys}$p!2u^MiS7@MNsGBiv08AF2Sln+_@YBR8&JZCYVV@>KOoItmDgkrYNyCY>$M zjXj$-lr)zcknS-V#mIk0XMR8;`Mohkp&BDD664|{#~2-mlW~x1GaaE$$_Ub)G(#1r zCETytH2Pyn85UM57n$Vd&xYa2*~-Tp@|LmL20EnYTpR$;r7b!Zaq+o5jNi@J79{=5 zsJ=hDu|?C?1wwVpOajz94ALx#Z=Vf6%GW+V?HFzZoh*@rjUrB_0*C7iC<~sNQM)M> z=PcLsg-w4GAaH&&Dd~UEDsljaWVITP{zV2ANdcIg{cCQHFIGYl2B&05JuNA4xQn*g zvT-81<3exJKwtu%p&fv_wv@?6H z!?aL#YwI4ia0!ka7>1 zYX-QP{|E64G4RwVw3|m+oX;rZO{yM_GViu7fl6uk9(K!$H5ED1==e-8AvTb#P$i$f zA+w%nILHVE-!6l1PJ5xm&EK4JTri&N0+_4a|4HRy+M?^5;9AypyX4RMXKa|dr zaUeSE!HSGDwC*NzQIEY%bV!|I)piAE?SqSeefO+hF6N?Nla4wqeT7Ylv|rzTUYVxS zKFkWXtwzRT1*$|!gyv5$Q@QYQWhUa$2)juk@Eg=5murc(ONWxqt7Dggb6oJ$rb8-FO5u22MYB!Fpmcb{_TyT>3aI zeZ1!)IE-&hg=B;WRsEoB422k{_)Kz8Tv$D0ib_gZzE)7yy1nG3(8XE;;vde)EQ&`u z;b7M%%vjP#jBjh1Lm#W*S(>yXM0;>`TZ8%?BDX%Eb9yht*VK=iYCBXL$)+@yp2} zihKDUIqFd)y79aB1Zt}IWN%d@SB_@n3f8Fo(d|DAsa!Pq*REJ;4XyvLSpCR0b@i7f z%iJ+3YYFYjYnC`B3C=z1d6PDd0tUa9%VYayA|6+UCJ*LdwL-Pr_#2&K6@ED4A@W`G zPT=uR7qOB&*H!c)q zaULHt$+svJCRL~+PyG)l$##o=GAIigDBJ&fNKL#(6Nq4(98D08km$)^ju=hEAxDS+ zHXha{$mB6(FgDizMjvWKw*Nc$uyAp({-41|bIM+a3wh@sUArw8diVn|3^wR}`4Sic z^00n0N4FzE0Yaus1u5Ws?`8VWrS3?hIJQjZ;mOH?qkcA227PfpYDn;^5(D!e;SQtf zKpDhTG0KtV(CXJ5m3?w-n)+9MD0@~G08E~9!o?Koa)l{^wy*ub_+N_jx9+ec-(8^S zz}+-WN*Iqy`5;;;zBNO7Fr4$CxZ%{B2_pG15vnxCSQBI;tp7Tg8dz`=7{?yP`U)*G z7>n}iuV2^*Ata8Jh6DJ=M@qD#kc~k^Uh7q_*w5PIjL@9omr;~wT&Mv?anp71N-}I_kkB({eyWct90JD1I^~tc4!%p^y zO;q;*&ZO){n><+6aH0%+<=X>s5t&B1Ra|&*2JW9hH7fXS=*#~4M(H~WY(+i#Y|;yS zbOdCizZltu^Ell7Qco00jLeX>q!7uFog7215L9Yd1&4}cf6-jCk^w+o>JA{{wMc=H zt5^_;FS-Fsdyx-pbsZQCPPj+`ua#hwiq)%Suc!#rNF$^aY?tB$t_;`2(l zDT3eIUzKVvJwtJbL0I}5{Stk$5nlCAYu(n%uSI(%^&w$xiAb+OQY+=N3jWXvpXc zI1KoJqX0>K^EqO8cOdYyF(cw{nh_XiSzTK6zordZUExZsG9z!nk7ig8Z{DAmq3Mw? z6V5=~)2a>MClo8Qe2$FX3_sm%`Z^1u@EG<_Zw{Z2>x+#;mG)aQ_=&b=-$;|%)b(gn za+~d?H(yX?EHPepeSW+;sg0OUoV7yWz+yd+RiNw5k7F9>&jtLkVfAa(?9E{aFFJRA zKYA=Xe}JRPW6asGk%nQa;$DDXqw!HnOE2)Iqc~jz@!?IsqL(vZoW%l-yWd&TuxRkR zndF6q8b*f@RM)n>o|IWYW5lK-=flzb;?beE07^w^#gB!1dP?M~_fbgmjItCE_UG6Q zBGDG&CxX&7^aCf`;8mma9|;We2@?Y=8%SJsS?9G?bz1@OwjDuZD78iGQn{xx3=4F{ zJ|q@!yr#oo4_z3%`P9&bZYTtWIM#85mX)`ai+~x&?aj_|Jg>9 zwxBt0@nPcRM;+>fPGagoV8jS@+0r#O_s8E;>nD2_Dc(Xd^O3>d3%)RH*muxiRN|qO z?HLt+#DLkyM@~r#if>0j8g)4CQ_zAKU!IKA7|I`*87LmanTr;f$XMMayJLgWIKIQ^ zk?IwstAFTk;T{6 zu7F^%f56%jE}JH^&rofR;pw+}J;~;K|DvZyavxeuC;o~N5%wD^=fyD(o1BI3G^|Ax zIq;m(V-#an{ijzCI+iXw+yEfiGG{`UJ^4bL%`tKfYf=2BGr@Z}h3V?x+Y!$`V;S8J zRe5GO-kBd{sjZAv6@#~5hv`!gPRQY5gm5ugX)q)2^Y6Cd!|yJ8<;7BhCeV{lpQ88q zjX}unyup97d`qz{-{aOrE(y2WREv;QU{K?9twdKWaq*?)8a|C&%P^eSUK{Lo8CJ z71PYycx=!?%{7K(v>_E^0hjh6>t+G zs{O_ijtcdYjM@DQE~Qx5?LT$qm}_n`8lgf9?WBW|7(vJer`rw3c64*IwixlLDb*V9 zwidEB#KIr%wt&Q6iw?-xRiWfk%TR{}()%h_DA+?3R+k*U0o6y3M-VaS(YvcxCI5Dn zO5BeqnbccF1|y9%UVnyBdATLLkWmw+d{dG%yBYF8Oc{;0*MAC}u#U8GnaVizEK(Y? z9ymKN*Ei1mq`WFClcrCxv#{EJ?eW$&lF4MdsA@X92z9)i{yblwrr|*@F2$GuX1)~Jw+6|nBcLsse%?xaOoIm$Gp`!AvVfz(%-hG}Q`*M5$4^@;+8du; zOeU{(*}sXq*#-||l!hI%oQ!>BZ--x^ENfVuo=>@8HaaL!rEx|h*{y%MS4FlSl7FO! zokE(X4rBL-2b*sr&p$vQ%#u3+V|pSanWoSz{vgP2{^(u)jXpVMN%=lB;Qi$CeR5`ZcnWXx;JK_eBS>Nd6re+m4UYqxswC0+|vm)av4W z!1yCb6K3}CcHzX>(~xlqMCw|mkPc-M8T(}pp2LyU+M)5gi3xxM5B0kJaU6U9mbb-9 z>ySNBF|P8?E<5TWurgNBc#3druBBpF}-Blu3phA$9Zy z+XDu|=t2PQV}uX_Vq)^SlS+gpj{Q5;?B75qdYoZ|&kZe*4?@l~5H4d7Q)r{D*bA+CO*nc1jMHJ^B3@Il-*-*h|-Eb<# z#hCdSh3;557^nTuz_RZmj;!Mu$V)qw6LjQmBL$?7avDCa;S3_q<))TYS8S1axt&-H zVb+u0X0@~FYM>1zFzH$xO%)kIT1HC@Ur(F_z7f8O5uzd>0>X`MraPKph(w;7drZPV z)LQOe+5$I>OU|fjdR4m2ulyRX`CB2xaMVLp>ADK&0^&c!%jr`bic*Ha@Yji!p?>H$ zyYvE{kX;o}9L$!L-u{qy6^woMi3fy4hM-s00Eyts02@E8?lg8G>p%iy8R=CoC{yC z6{gra#_d%OJTxVc`A9fz;-J`0XOY!MxAG)JaX1lzDFvH}zhxyg#nS;C(z`C1Txv#Q zF@Rjv)(8UipXvotM=bzyJ(l2e-ke4uQk;E}3Fh#yZ=}@S0?+VJrWm0h9v2W%zE@S9 zn;MFvQPCV@x>!T=8NSu!2=efnchInWkX+&=K{_8meaPt${V*bIIJGdN;jn#SnaIyQ ze;Qvly-wJ2aEr>@ZFM{$PnxIU|6Z4<=GFlf#1pxHlE*@nvQ7om-h{Hs;75O5*C$cD zJch5n=w#k$r%SPsy1b(q@A;hFRToRM?S%Y<$b!2_hYFMF`n3rUa7Y#f5tSf)b&E@G zxuq6>9%GK8EUB8AV)W&_(0FR_IBGYbM4wF?Ic2x$h>}My73ELu!Pq;!x4ybp_mLS7 zfelvk#}A965lcQ}`3q3jzFvZbYlZ=TXn(w+IOfwFogzT(;j&b-?q?)mc&ZDqsix1I zkbUNG^qgVfAuaGYC%n%P@SPdO7Skiy58E7on3P;etUoTBJVua6^)OD@NDesu*M~0a z3UOiyeI#lcppXE5%w*E4ilP-R`5vpynwK$+Xim)+*Llcy9?o)6tie3IOUX;j>4EZ` z*Z}RXyci?UflsGWQBzC!n&Q2Be%0{Vf2dNNo`$nE$<7KNJx<1jLcWopxo*(LuAQYo zpR3303p41sKBpyJZ9qvTa9(2_&giW-eMd+O+bZCAV$d?h0DE@J$gDUy>2bQcu)pjm zOvt3qcqYFTB*1fH6(?InyoQR63Y({48c~~u>u-P;~F-7$Obv*Oi=7k zoq;qt>;pKiicu{`K9BoGNY`pWs=+F2?jiI6q~A77VTx{;_q1Z?M4Il&k4!VLrI;eD z2_DuL^98eFa0fM7uXUhtJ{a@*-g`OTzFvO&QtaPikpq5B7H_vNFQ=Z!V8**QMLx1n zTiP8XJ41JlopBw;?&)0vX0!l$lHO&lH!}3xcd3TRc4U@!_c30j37J0(n9Sx}ARyymrYHeeE;nBY$&gEDfqxaZHILtK(2Llr33W3z6%^qb;$n7& zzP~gUc6-4G!}b*iDx;TE*J3h)K1sGLY6u02ftf9oCrjGbIP?K#z=Xu|@`waV`xYKR z#f1l^8eX)jMuNz=oo{5K4)c+O$6m@_pxt{6iO|73*nJFnwGpHXX9y1jOE*8%22oLj zGhD;PaRmGO9e40}Lef$o^YFI~y6o8sIHu%&H#h}Q17>uLe%R8y^X;*(rOY|cxIW5O z^%yK_It(_Yf$1}eA#jp_z+xo#W2s9Cvy-cX*0jbQx2`n3rNFCYEMuHJIJIaj_O}N9 zbkhAR!kRm5xS4chfhGY~1Q(804c;Ro(XXyMowQaD#@uioju&iegpXmX`Z#Zu{yU7f z>%`f_Km##zfI0v7|E`te%kDriZI_0M|9rx<&8@{!@uBy#`y6ysp2Zt_+>4XK$ zwc(V})tMpb^GT7nEQFsFA^{e7_U0dthbB#2gmcySO^Lc2JS>1^YTLTJ45%+JE4OA? zyr<00&RUA~-^UITifNMyp4^T&4K0r=km$V1OuLFK^2GIVOy#4EPE`@$>BSHYw8qV2 zCTD$OMqA(v&d?zWiWgaqkV9sd+>i2kXmrkI13?Kp5Flb`4)W=^i6DVM2%TWVn*Yb< zO8!oQ1Y_m=58qHBakKpY_|1Pv=YNc=87(~r9WHpkm%90*=R&$9QVLL!K!5t301WC( zep|TvgpyJ9>S(w%h)!VN&_D7g4dWS(C;{?b4Z%X`C|>fDY#C`1Dn#-SMHpLzJRD$H zA13=zhVs1j?Zf~%gfW~t_zfy7s1y&nU9ueR1vOo0CPp65vXedxf=Pz8%pOc2bZRbM2PS{q}M#)QRN5!FuU)ZyQx6bZ@a6{3zJBM@Uwt`=L&gAcc!m&k`q%sW+ zO~_J1_K{k{l%a#Df4t%;oy8@pB}ZTitP@4_ln+pau4{(HJLf1`D<`5I6Q%V1(ZUS; zzYwUfTEUs+(dU5^Gi5I~Ohh5~(4iWi5pKdY&T|3TX!8g5Vi>@sPLYO6@Tr{x;g4=~&p>K;Fu+kOIDxtbT|5ia+S!zXyI zjt|%oNay1#IO~Ya8~twU_Lb{qFX`P#v0vZ^9`{kek~XICyY19u!}nWn!7jn9pa{d8 z=q2WCMIj&)=ea-Ik>l1Rw=Uu=xA!u9vhrin_;P~LFx`OWZ&i}ApucuVIjjzgG;8*} zdclIyWn=KoPuyPQm#abM9FQ=0DJTC5MJCnRBitnb*26QF30s|FaoQft7l@Lfln8E+ z*r5$VCK7oGt{lKF+jw>I%C$d*(vjC6VYW98u5sRe~Iwc{A5jOplUH zJ96ACX+O~&=IfNGqRn!+s8Nd2q^|r-QtM4EU>ncRZFAv@ptDBRNA&~hDc_$Yz# zFA&wWrt8%T3LV0;^2zCp;K225zjxuTlp3f-m5xJTT4pMtCcRC=b9DRqq>8n!LrqtM zG|i3a)AlA?6l~t8asN}epk;C|g`0yBwJS|b_Xwo+N^6$bRY#(5XfjE1!&Dki5B-h) zu0}psz@x)eZ@x1juV|2CH(w+b&|# zfp*hs@dIfMc*%Yg7U)KkY_nkv9Yvf+T5_@Inq z6DT!6OVP*`DzLwzlOvw9d#kM7u_SC9$Q8FKLZk|GPtCTuY#%kO!eR|q*4*hmt8-@# z{Zqub4la2+sL)^l`xCHe`Y8{vQZn^2DA3@_sD9ovUi;R$v@1WsrSteDQHC8WgM=;? zp}h%!Fn>cM<(=9jOFe+G?tqfHX0O_#d~nd!cqS-(!kdg8odL245WgJl^@04nKm0%1 z_rDPj4mRdA&?<1WHVIbH_WyA*{?86o47Awke^RyoQ%jp_21N$^hZ53mFCa0%xwu(5 z(*`IYY1>FzK%D@P>?1Ja1UR^X{($aL zXZ!?KJ1k7sd`I)F`-`;+J>&Pyh}0_lK;N1h--XZMIlxhwv;oaMi%j3b_qTutn%=yc zU{^mzca%-$ykpOoK6wuP#mHC#6*4({t`G)d+ zcsH58OWhe+gn5l8>}zm!f&zXG9bCQY{de*Aqvv=sAG*6EgIl16{P_#pX&qh4+uZfn z-p~tE^~E80BdE1@Mo-V(Yj|XLLv-?=aK?wNud#bd;K%!%!~0Ki!2R6H7m~y8-wEMZ zfRC*(=6dG`5KZp(cK^26slPy9`5%A8Z?~6TJ=C9pJ|a;N;(35&6tJEhiS^{eHfIr8 z_mD1;OAA(hV#xCoK}t!M649E*uQ3)`@pB3jM~Ql`Z-Ob9mWZ5crs^i^*ukJ&;tgl( z*{p}B!S`@ePRny^U1K*5Swhs5Tq^jt0I`_=LS1uk%(E~hl}1;DA8!#wZ76uYpfmO8 z(yABH2=8~4e}-JC25__S9b>b{Ftr3_Y65e}1SK{<$I+>gVEg2WkdAV(UB@)iew3OE z+d>?2w4e%2KI=7#Kkjo!`OQnFZq6&&V~o2%=uf)?M5~sD2FsEbAd$q~D;71BvikE? zGD&-O(KsvhA60MopLfF?d>%ZAT3GPf^&WVfZ+#DX(;ba{AK(=MGwXN%Myw-jI>?BU z{-1BNwkC?1j+08V9&6XZ{z0_Z5d>TqsKK&PK#N8X&a1y7^w0xV6r4;oQMtvySimGW z?ajm7XzjM~+ScA{$yN1>F|kQgp+58&J9%?WiCu%;&0oP{nhY#8&%~z#A_rLy=XpdN z=7bpVMHT*?aiE`j3_lAe-OCX+*{=x4GTa0Fb5jE%=e!cNEu+`<6It}P| z|8bX58->QDVUQ^02~;9g2V}iHnzn!#(ji9;#b8TlH=Z$#W%bR|cLT(K-|*6)X<)&uZHOG8gn{VmWCal|s01T! zTDEpue(6CkU0dO^|K*nfJoQFZ30WfGKUNL;)4KzaP@pX(!Qqt`5Wz!)YDOAPIybGm zOF36|PGAZ!QM2pp{+E2%+-i)>Fn07(R1N}HjS<-m{?2{9Zn>bE&d-~s&z5aE2}gZx z;HaNA0Nfiwd}ElIsxxco-Zp1UE>g*dq;mlq*Ju#+ETb9S%dpt^qRyIY(b}yX(Ptt_ zG}O!u1britv0iAJ1Z7D!+b*NLw!JO-p5?*tz>pm#v00&4h}A${ zHq=~0bIE-&i{&dQsqMaT$;>zlN%4Mst9@g=rwQ|LzqlA6-iy1svVC&4A7MO7B)uds z1>WYX^hnlJG~#7bbKDtj8U7wQw%KLDSL9H=f>*>8s#ubHakD?bEe_ylM4&oy69p9# zBEj;BbFLCWqgxa9r{)5^c7Iz{vw`4KEpZePlWr*n2wK}Dfo-~WA_tjiw6PN$uK!D7 zxp~n~0C_BXw=oE7`S8|J*iPH-v9QEQ0kZ3elN2n$1`@JiAAA1@U@XL_irp76iIMOo zUqr984XTXGuSMiA%PF5aQI!nO`)!g_>BZ7c=6GZh7f$!ybQSZv%8iE&@Ep8RwiI+@ zcGHxyXZ@Y(xcQRY?pUSic)q|ua2#$OAb;tpD_o?I$=2)XwEf60Al9NTgByxe28JCx zv0MMG03;iISv#RNGt>~;SD!@@O^@Va+QVm~7Gb};=B79jo|n)y1>H`dy#sK);)cVp zd~!q8Y))Tq7I?7tuz=vZ6z0U(N(=} zHK|iBtCcJ{J!!JYb3_b20aCXBNxLFmo6Ulz6ttsZo$bX!J8 zDlj?+uSXdS=896vJ+c6!c2Ycp2_ima>C_PZ9uh==5x=IcYVjV2WDoz^nWId~gQtQ) z+TpVb{MrR1#lu#P(n8J|kSM`R7lqXtmLZdhDKsb&u0cWb++F0C^fv;I!dKwb-+{%OFjn$OZIC?&Ls)G+b5)|} zEfN^kmX5-mqAwe1^q`VNaL2}_Cm!SA&p?;S>W1L^Z$yDTU;IiRpzfHSQ5I#k=u+if z$lEz+EWVMyB~fn9t@)bpzbML48aF~@qB(H5gX+c8oER3C!vKvbvWI`m1F>WMg%+ek z4FJk73n0^I&J&c6gNLquvDxtNU$Xx9==Cs@(>hb9Sq1BEsmGKXJ+FAEx(o#y#+dQT zrq}%ODavj1X|bEzz~+`=?dp$ID5`A-#Aw;%ltT#AwgPIZOaAk~3(caL+-(g!>_7LZ zdV^m_$Cm4|pB8?mXt-3N8k+jsqYY6xC}r*~OFo*pCf&#c34Rx9{=WxjDwoD^NhIwJ zoD}@N05dz|LZQzGdo{XdFWA?}K63jYZ3a|q0{V4Uy}#RXfKB29e$w-#O_SywB3!ph zQ)WqWq)NRh`R}3e5gO4Qm1>ikRx-qTtvQy2Fr>WY)WBt7C;{h}kX^j!mJnf=SV?GH z*6vsxu*vd@6nmRuqfT(E<*;0^2-FpQ`CaI*)%{H-84z8#U7wL$ND`tT`km3Ezg#95 z3=a_&?o})oDEAZy6fQY~e2D2%|04d) z4!8z}T9uK_Qw$sW8C+o!DDQ%a#gRD2mB#k@N3{v%>DDyWx*;zg0Tzc+VXoiP1l=bU1!+4mpbO z8%&+0D6xwTIBQhS3^|*xWM60XPHFFX55?q%jE(FNRVfZBO9>=e)~kFE(0}Gb%CYvVg5_%ZfbKG+%$4fvO+i%41pa$d6y;<$Ku~GMS&HLCh`Q?gjU9C1&a(-Rl7xP{rdT~1C7$Gzrn>hg=GDq^<`qXygbD6Oq`H*J30WVWE zBiq^ zViOOBkQWL%!H%=_vQl-0KE1l{fm82)XJc5?%Js`hIY!HW_v-1pKSFhL=R?+pYhEbj z8uN`VF*>ximV9H)SC=e3M0NaIuQ7B`Z4TaUDFhfQk2;aS_)A1S3zMY-j)P3keKLEL z>5Q)VglCSiZPkQHAWuo(g-uJvUZr+Da*xo*YtiMwlu8t!DVss41i?W2H z);v4@gjkyFqA?DO_B-c6qTVg+B849&1Q13T%w||xiT8t+{X=Up-PidD<8Vk+L(V_0AuX>zsXd>3&M!8l|4DX?)N2Rj zp32t#_3Nj6M{A0)d)H9}>>P8T(VXX4a8#NM^V;!xm(=g zHmVRalqq3fHvbox4Zf0#Hkvu=&U#b=uLo|~imM!7WS&sDV9F8vZ(tnukf_h^4x1wr4QzeC*`)ik z_wHXOXU1Fp%I$$6+MLkQFj-CsHcgeKhfLaawMFD~y_%STVn20zv9GGlortXT5TzL1 z2z_#u)z^oebA$ivxEA=cPMYG8K!IFMOY+fCfSn9(0c25yYLm5pPj-rJiIT!FP~)=; zO0o%ZifdcWuz)_VGAW9F0&e-LM1_{d6y$}|d7XG45Yz@DS^_Naa2C@FvTAl9j(n#D zKk#eTb@frr3$u1No_scmV_kQwDHVlu{8JI!_n2h~&O$6C67ixBHLal}m)iOlmyQo{O| zQXtrZUXd&{obe=e6G^qC={Brj!OCdv)@%h8w@#<+ARYKcw59{cD|;-4246+bq(hSD zQH84F@O<>;#JMhvr83mT7Hw`%Ux(y;GYFGMg<<-GXKfoIx+S;UDQYzAV_39gEw3&l zcX9H4gQ_Qg8Rdoh1<@oe<;_FAE;9K7qX!DZiQYu)gw&0#KB`+e=-Z>hHo)U^vCbL9 zPN$&|_C0<>fOQpJYEJ(65mKP7Yf_FouApIi5c6v0y7+1W!G;OT_&zu-A5M${4l=xA z@*2F9r7S*_WoKhckfg`0y3bS08I5;i$k|PHa9t699e!qXOj-`7uXWtnuYN3cGLM!u zyQ%_nA)n6D-N4|5!r3`lcr(+@s|EwlW-Hbr2)K?&!E%st0E=)mBYs!YYYFN(UOtun z(a+^yfz}?50X?bmVP<%)gLv_i3!~mpt9i`K7a{vGyrRNFvqr`#UEpFHsl&j}*lg<% zqRxbWo?naUpALR{tJF-6h`>}sH&Hs#5umn2lX|Z_%r*&2lPfB>6<&*X$Lc6h5Kv{$ zy}P0d`o0(qY57Uu+u>Y#yT`N0RwX`c=FHEgK8`R~#NBqFSVwb@h^P;O2<)1^)k_}X zrj_G|g_iLNasO50@iG^;+znKfwy(ENL%2zQ=U+xGBoVv<8tYIheJZ7L%^F!a?b~zMe%U5p$rI~s_0(f zJBs3%fBe8a%MX>W*1Z~1XPPB3_ob}!UA|&r!Ge3b5=)uLA&d&auPI1S!9ap4WVs!G z@;ccl3)M1}y|BkE?CtI=_9{OfYd?Uz8Aa28I5K6dqHztghJvInT6l=l-H_CErQC|~i3;Y-5r zU^u*OHQ=-JTv{*3HA>%G$p#2^Wn)BtHTZy>eS2Y8RDb556hs#XF0K^*KFYtpVqlKIEKsfj4&6hWuEfHqTBz44fC& zOTw5h*ZyoJ6hhizBfU?5`uU^}KJ9%is+uChKE?zB^|bKEz6lGxDIK>kJZhwP)iFHJH6Nv?gvF$}+h-C25b0EjWgsFU(9hR9_~AcfJm9 zle&Ic5ZV4*3rKjcRFu;K#Di)qFMfs9+}vzlYLPx-UKfg5W6c$Re*RE#05_0ASCbDY zRb7QJ<`?#3L}oohzIy>NDA4#F$zU-S@6%Z#VjLLunymK8iEH_Gr)Z?G+|*RmyHP?q zFLDdqn^3+y4?WC=sceX!UnK727aMy;M!^Fic$V)%wjfAcFQJc}68A-N0^`5#$bk@G?DRQlUsjP_}dg-aChZqa6DNB12f$BFU1Shjn-E!bFWA3Zz(pp2S@MiL! zC4&qC4$to^OTLF(^G_D?v|;!W$wZGKqIowEFzy2c5ouzl zp?38I>~C}Wk=dMlD%4in4~U*{Up=+LkvoE|^4&OpVjP=)`=V5HXPmbr)#PT!wn_sU zDz5OVZwSBAr5mt9g6XJl94B|&Aw2c#++x8YDU0a36L%A{{^^@;t1rUuF; zVM2Y^yUYN)sk*tZZu}akYGo3nht)D{W%|B|9LzS;ct}&JnBn0vfz;~^%&BTZaG~Z} zNGz1ao{k$cY5D-v{J{XME#-Z4Fl$V$bAcnoG)$M0dh$RAQ+3 zNN4IMpd#_%OZKl_{^R$ph)}N|ZEUb~NG`4iCxSvwszPKWlsBMECR8T_FkaV>36>Pc z?6_DZ{bUO+af$Ra8Z_w8zytzBJU^X(tsxi}dZZ;zR=~2<84E7${LoR>MyI#1S#ddv zQDD`7;#H6d0RbT1^|?nW$+B#!l}3rE9^r5r_NJqa2a*ZGqqP~u?}X+_N2z_M7@C?4 zyr|nXqS1R7jAZ+K^xa1Y3;W8S+)m4_ltWCyEk?#;%g*cK8(e#9pz^>?S3igjqrrc+ z>y;p90ZlO&pmyW$K>ONvT|Qjk{yh7oXGGn9L}CaCD-$)lt*j(wmK_MjTBL|Y9O7~4 z{48qJn40b+lT=iQU>aAo3j>XL8K3&WiP4Wl<}LyMwyMhq&h3okBmejHJAu7hr&{!F zO=K*^-D;{%ngI7wDIeI@?Hr@v;+_pwx+N@4fvI^v`Y~O$jDy+i(V$hIC+F}Jm9p`F z>*y@rZz-vz0dRW(v@w)e&3;$Q;kKF?`(ssrjGkSCzBCu8b zTP|mNBSdVhUn!oWcl*1AXU6!CHVfl_bW6aDTC&=ooqFeL9f#G*O#<8NpODh{fH;};a*!Y@xb{& zZy~@!ZDZ)(xk2ern4Jur{vPk$)$}db7qavq`siF2TGTNPCcTf@J9P{7VzwO>h8(V zaC~iW;9tmAHy)!BrBV2Ja0T|oK&?h|rWN*+$%s!6qC+?1Ck4DXzK#dq`hFL%pVrx? zm@P-V_yV6d7C<=bQTY5yL!cFtZrI17y~&>!(6qrWaiaH(41GG zCyQWr?MUyNM7)4Y-BZk7|E`tnG-g|lrns9iFqes1MFwb%4IaGGygS$ zuC8*>l)y1?ku{|KOF!=$-TS*@)`K#3(r6pXec^({KJHRKl_073p2}wYp>ArjvtygK z6|5Dv(BeF-4_Thp*ZnXRl^WO?PO=t9v|RO$9w~I=yRu1X=>{-=i4e@I3nwW^QJ(0l zV5<@tR^C;CF({fSk>?6QEjX>U7=jaAY(;cRi0&N*%DWEjm(snvX^Q{~}ab;wQgVI%bZYC`mhLMpnG_qBLK7OjOrDPW?e8Y-7&t@`) zW!8SLoxc0h!W5!^5*-^dY=3q+cA597?DyXGyFjuTq+c?ucN>`1HVKrJ2RUJ}iav%k zR1nY7r>^Pihy7T8u_z`FqNYdnb##JkFhK^N>B^MR)_# zUr42Az^SoqHz^4DEJ01fD1b$y{W)?s!#!a zglXf#T+KLOe>o<-!#uXjf%R9ISh4GN&5TiD%!az3316qQPEyTRb%%$8aa^*gvjQcU zX&oV5m(ERpYdKCQ0#UKdOb^n>G?Fxful-M=BR}_+i>269(p6a&C7VRgY1L}XqmL$H zmB{X8Gx_=xG{e0!^FBd@e<*T@gD)YEIXVVzlby1|^cehNGS@H@@`1y;n0|MvM68AQ zc^^ZC^rf{nkbV-VUQpE-LK7c6o&=9zLEipnmU!=&4tV6( zidQ4Q44E??U-SB6Zv$GdEC)wa0;k0umSA^Vz9rcP*p@~oeFw>o|KSG9HUGi zstRwcO?@==uaCB(ID*N1Z{qmuY$jUCUBFl$uDwvmsA2lehd1#X9EWUahzbqw!h(!{ zeK_=q-VUvc^)MPQdr!EpCER8U9Kh%_MISA)sdV>07g!5xQzRm^G}uS#P4m@_ zAM_4~_y%ntSgFHR+A6A3*9|gR^{^WwG8?t1MjhjK!rVc;EOm`WOo?yG58KvPzl4$` zphpI5;;1QfJs;_aZhKv8u#P%)1~dtOVLiSdOsi@w!_*-E;JDK9P8489YFirE4FraB z9}bfKxNujW<(i8CRv7vYr=JBQqVcIOwj zuB^u3G*q1*vdh;GOd`0XsI#286fZZrFolrTYieVIpRy=J%q1cgjpUk48krt^y)*$AAEkthaarYMixvF^_Uo0K<1vc>Q*djEI>f#=hYJ5qpKveZ*ZkclP&S;y=r_(AM=2 zVkHyqwLvULA~JM^=eOn4sXXBnYI(?0Vt=Q`RlnBt9ziWV#lb+;OJX?OSa4 zhdvXF`@uoJ4-@iES-zNmm>k_0wTLAcfXuU9SX`BUczX<7ng|4}AM=a6v;JfNc*Zo50qT6n4MTM zTXo>HUWzhY_(=)9ec}p)V^fd9C$pf2JRaTHuVm zg5X6FN)I9F(=SqVLPwh0>S+&?O+^{*%=D1Rv@f^M)@R*+rrjk55)-r1;>(5Zskrt} z^utFC8<0BzI+oekEeKs(xG|3}Q16pC>2*C3p3k14s$^;<(bJ$ zA|?#v#Lg3+QpyFZJNL|&oH1GWe-75|&HMpUtBc*MTjjAiIKRtVO3`ZM1ScxU=k(TR zD&O;V^928Y=_%&P`#hhPw5G$ zer#V{?f1SIZX@5HsoOOm>J)wmm+=Y&kiy_!KgczKacN2Wn(g$7>VQ73So|dQe$NZ> z_2VV>63@%M9jhJ7s?bR?`NB>S{Tu&4@v5^#91)TT6l?Y1hU+X{2r&uur5r{EUd#^elOy8*`xgNq2_*Qw zqAUP^Wz$53BnuKAy5YT$dZ?$wILXa2KKxa?x=rM)o5l%!o4*Y%A2?LR!PHK@OdG_u z@-8ch!TIq>8^6Y~q-IZFAhIVY@csbZ-cXN;vOsY+WLFQ;_lI0Y*OI;?O|^y%U$?2W zFnd?Y563~(2*?S%0O$7q$0zyd`xLDqGy>*-;d>J=+7~f8crL7HE<&(n3``~ZXb;8m zuLlSeDAz9ETC;7SWL%}SAKK}qV+CunzZoMegCYEWA`SQ}=)mdApM3qP5CboU!`8F= zwX0>~5ii*2R&LxM+^MWKLCBGf2yDDMNqTZAuhUtNh3PPzV1OoDR_yOjm@U@syA_dt zn0+PLlH@l(br!ZM>Qva-HHxg+p;Nv?j+hHpJ^&x>Z)YzM9z_iJ(IZ3*J|+E0n1w5= ze!v{0t|T&akDcYLhMb-^NVg-$%Qb;w)Ddrr4VA6Kp>0M=oZX@ekV1cZi4~g|Ej58;Y-|0p4O358MQBeHrS1t zFHCm2d)wSDA|ThL8>Ez?R4J{$zq&tvqsANJDbq|w)w?X@fCWX<)WqVep!BrWi`0bt zS><|Kyyfe5O~5nlPr3kZ`NQ?w83w3+|6T^{#irHuU!Ea@aGgl}1xrz2O~JrQB#el4V%P)1pqw+5k15;XiRs(u=pDQtwPrM=ad{kL0aY;bDC{JO7AI*kTvyl@* zT4tMDwUL1k@3mlk8tjGf7fA2w;mIg`{0mdLP7Jaj`9>@ur=Qj;Ft1!@cl z6x$)k>mz-CU>r|;>PgP{8C6lOIua_RSQ4r>XE>CoOSM&+3{Jx}EPT>ZN;mdiTvOcd zivzJ4!}c-=P@nV(Ibc!;E{FaUe0+yMx3CgA zWOnmcnLMLJiITzdjwmm(NEsAr@ilue}=fsJ_KqS&-i;`y8bgt`ZqPNT#zW z(~ z2;3LP!lHOy)9sp$#CPRdP4oaV0iD^olimZVGWwh4Gi}~Js03DK^|hXnWqHxbn@FOb zxqf*f<~lTppMYFE+C3A7>BeU&&&kh@Hj+}uc!QVc;~7GKXWNOk#avY{j42IYGC4~S zK4x&jokUY%zN$V2#kQS- zs|=apAsrEoH~0mGjeTJ*tjefq;vQvJ);X$A-3R}T7xXbv4P_jPYvERZ7%09lR+$(4 zVt>!9Lt~$Rr@LX_Q$^g;GurBXN%Zic^O_xcsO^0&f1JCOmrLX)5#8eO@bkX8>S#8h zq@P1d8a)&(xdU;TzUbz(2d3w!O;Na`E&M8yW)%ocS?9q9Sh-xXLw)c*<)vj~&>6^x z1&jqsYYfPpEoRgigRU(fc6qzGX(BPaI=%#~vps}=6bqDPle0aKviN`wg5~pE!RB#PD0c*2_zR72OuEAGCdDUe^2C-h9wHS zssf^as1ELQjd>_;@c4n=;?djwQeF!4x0`1o(=E3+Ilme<(Qm+i zP*92nnrqe3L9L8cK9)kSRpGQ2%n+XR05iMe#`Nz;*X_PM^SjU4!SK$?)eB--mLq?< zNJ0E0jUJ}t5qh-V-Yw=U+(>Hm0i@ZDWpTM>xqVrNWOAQnx=cWFBf}9^_CWy0xjNU` zHTKI_AAO!lm0L;$Yk59y^+=PDK?2Z!@Dh^7XU_f`8pWFSu9yuk@kYW+BRaFM4{@W= z{GSO>ztX|e2p0)o4d^g;)rfrgQ8Z;AG9(Mh(1Mzw?;U&EUuEZ0SKC3^HskQpP*L+K z>>6!wq% zcF6~Y5M!u&36eACa$UOtGc=;vk)9_yMKrWg;_ZZ@#ZfQIj>F1WOu%#bj34{rl|oB) z(GG=viBb`RRHpR22hO?7@o?mPdIJe7oLST7>T&*G zRP!I$It0Dq!}dS5o>hGx*TwUH!gD9XI}H%8Co@QSDIN}VEnn4qoG$T_r?0NUe^MyG zU_ndV$}(&@8WN=02cZRrNuMftN#QbhsZ^!XK*fHK2SF2~?4Hbr3io3wG^KqmynwS1 z=61}RD+^k$MmGOZ=z!#`{w@QyPL#3qBZmt9)+y%PJZBEjlJgY79bo@|xmbq$XxE2t zTKH3?dN+?kwLtjfqh{B(MIR8K$d~b6_BbQG8!H$;o_G@_*^7@jF`Lm3q;YCUtI=;X z=SMo07ay-bwyho%MiyabN1sNr36jbai^w}A3*F1Tc511)t{Ah!k8Yu2)~K&IdEV!X zf4wo^D=fc579+r%x^vin%iu={g<#*}9k;y0r!re!c0ul+uMz>j`xW1^^0OwyOCI{F zEN7G7tefW3)xq2pBfmccYtQJ4{UZ-GNiHun(?M00c2=C@iV9Iyih}rAU;%DVpX>W{ zrC^>X!LrOjs#x=9C%_L(?C%zt@GuJ>Yp@hPXMC`y>d@Gq4L6y8xwG*IF$|2FNXpEJ z{}Exf%z?mJn#CYW^cj|5ycS6xfMce@&zht=gtC=&#I<(g-dRK#4kUu!FM)L-+gMg# ziYU^q6$004`!>YPg1m0|WaMl%rxX?p(wmS^dN+I>N@E?J*{T8RIl*x5aU zq_BTFDyW4_=VrC830wTc(e7T0TEnf?cj9q zYT~jJHl@#sJE_D}Y`-k^|v(bDH~8CCg+XogEB`)aBzfBqXt zf&PtGqDGDvIa1N53W+Zw)rrSolVd_Vg!kaMrJBlfQjcJNRFq|K6-AV<2o7tV{PDXQ zq9IfCbIv>5BOk=Ko@1e>qi+8K~We8-sK z;G%kWW{?tp@?oBXwOW874OjG`f7rYi%Vj}>a-49e7p2&3nS;sb>63}L`(@i$k=Xsk z5rT~XiMC+(x?C=9nA3un{`q!}eY9y>J43V_x;MD@19Rc2wnJRN z$8^m9;Txr5W(l=KK?%YKX~CEnSucE#qTCD+q2)#Us#5==JDw z)jVVayO*pC=gO5Zx@ZFK?8-aRz~{MTa}@((2p%=|iSEsqp7rm}$_cth8XgwdY0BnR zqo@f01`Ws8G0_8-c2`_4803$x4AaB}wbwMmULh*Kp4=C}$m5Ufa#fk?S-5p15i;uf^3`r)H)tQ5_r?}t7rlZXV) zIcS0|YM1mC@+*ox!1TM5sYcsu%U=#Y1#aTY`4ni3=g=WaZNB!?F8W3A5|QcRNz*WY z3||*-E#={@ze;JtkAosuKY)CTP2?cu*wdW9VNg$5ncY`lZZ#qrDj{}=XLU)@AFExH zSLh1{5DnRgcQ1$Z@Z?^%iq>b6ctZ@xM!q}=nGAyBXMZ`rVBW5DcJ;vZlvfGzl2qZ5 zt40LculuVOZp)o3d+C0n(vUi4ZF(Aib8kuVpPp)%wh0Rnh_pC@jF1qS#UI;rM34%48qf%eo-ONzLCDO~1Q9C*19w)$T$Q&4G)+VAxiOSof6 z7l=!C!e~Q9Lb3T6kIygN=T3%y+Rx^o9ZztVXvZQ^S`XR{$a4Z`};*2Pl%1G<#%2?(WcyV zqhC^3QHCI#zlWXFb-7hZr1oMX5m9U)p(mx5N*T@|pU4$Pzrzs{AU$|bn&g%+1gWKL zb+jZLAA5jt5rN3%3R(7Kk8mEU=!4n!oXy}px^80~wB4N&6I3OF1nswJkfuK)1{I%K z5b}qC7-S;QRbRl#mZWhtO8H9*ZHVJ%Q@SKhq-CDjW1P$GX~j z-rMuVKziQ7EQdmWeaTIOv%}uRm2Q)W9%1bBagC!ufIokwGTpqo2GUMqR3czZ7yjiNjcDN2fvWhM2A#M_iCmURa4hs|ufeW^L%76+YU z;=uz>D8LW!zkbko`3xqT20MCY!%%(cdTN+Zf9w&_mA-!*;cV!><(T4#8NNvn<+w1O5O|(I6soLPEM5n^ziGz>9>B zuPX7!X>nPtEZk!mo?N@Dk?GRegWmrbP924ak?SFo+nlPZax%WNnWO@c;qhliI*Y&S zm3_d%wA>kg*J>#6HQ7JMopMBLFqd0t69G#4mWP`4kn$e=xEM3IU9-#SD#y`XA*pUX z(_MCdgT>@Tvi!h$yh!djW#QNI(H;DI;;ehxSF7TYDGj}=CTl45W(;CN&$?Qw?tHjs z-k6*rR~sYF%(`(Sf=oal&he_qc%PMwzqK!RFg64@b*u=wdi6j7INoqCPX@y*n8iCP zJ0-C?cXu%qoHEZ}NCG=sSjCrwy%BZ6)TZ`-YQySWp;C46yR7{lMzyxz;MBLpw|?O< z%H=h49_l-;uvB#2rCP2cTq#^gnNTZbkexX-B*=mX6i!UQe1Iu_7>u#Hxr2NH)Mte! z-lVv{0{CHgk1V3HusRN?-XCAwQT)QIA$EBPcfOUWZu6c^!nV^m*3WzU6H!ljT5!LA zz|Kib5v>p>ht&LYJ}7pzWq&2POBYWjye-*BpNV-Y)pkVlUEGrW;Eyi*lsqaRCeN3O zTw*$D11vC~XfgK%b(j(xo=;}Bb!nX|_LiR~10f#hU7a|l_P(d5jcb-gJ|a3L#q*pj zNrBITGx~Ep+5Z~N`+(3komcD3(OQvz5}i^Ml$>k#z!l|0kgl*2AO@C7AIHJ^Gyxd{ zvQW%WnwDKaU+&W&>*yLD+GZOyDlES2)U}LM>0f3hk$cW)DQ@i@Hya2Z-wG9b@!h&DzpU6C+NtC=i+R58sj zVrl^)S~*1%n|Y`%EZ`kRURR%w6D)HsZr2mCoJDBNZongry^u2_Ya6UZ^W(~w6)3Ar z+R*lMb_XQKVwetfjbTE{OWG(x_xK1(U`A|9jg7gla8q!Q=fLFFRXRx_uurAEKliB5ni1*ClClK*F)z-*6`zS3psfu; zi~IF{C7++Qn1cU9BA=Iu21PaH(dno`!5xFC1O1RZiecbQ=?+5izOy`kW>{Gv_P!

(oaPIhOCOtIV)O32BI&S-h876g1Xr8)sR+L zv~2AbD|@7orSNt>{SYL5XiHu^c+%WxxKR>cSt)DTv@?3rmF5yVVXS9#kIU$xy)$&b zUsKraE#cTNyBmD@V@|0s`2daI0A!kPzy*7e@ySwAMa`JSu2!Dp|P`I zk`{HYcpAS~$oIX5Lj(W#dL%Tmhk{;P;!DsPFdUtU+29Ni=-&&OB0=KoQnl_VZ8d`W0)O_oI}^nMjSn@j9|#bH*)F3B!b2VI&cfZK zX6=WEJU4Qq>`}3(7L)wW?4JA7-!kgW$qaa*MT3GQhHj<7DV>xcKlE+t)e%^tx+KZq z|7{&Ts zj?3F#Vp#)?TZy=?E9!yy!gGKAttN@Cd%e$|9Oez@T4uJEPJLY zjW}s_Bp^ecSq}3D*`i3IB{S%$T}hhFJ`;5jq}_9}a;&wqr}tNq&K zN&aXU)4Pg9MbEzDWjs+?OXpa422Noj?=HP8b;kqF^Uqxz?u&-!j(*Do3Kg}r-!>4UC{UVIDOd4M5RQ&;t)73ureJ8 z%w%;qr_R6Wm?V;s*?iD6lYd+~4fD)9Fqc0jtc>-ntGbZ1T1aFwOUpnKmeLJ@SVfMT zu((P@U*=5@JiZBZ_V*^f{zgD}py%7J_LDkwKBe{_6Vb6Veo3k-_~>)5lINrz1OUUY$87pe&?xn(a4=r#5Pvg79u&1q7+A5| z!v?i7_WRz1^1}dtb75P6-{x#g?1av}K8ZmQHfVs0y#H|<~BBuc3+ zsG``xs$}}Cc~Z}p!Mm7&Wiip1Iy0fZbCk3%*DLgHN80+{sRBtp767)MuM!uz-zEpJ zIdNm(dGddn7=PfnREzQS+brkK5g+mE!cdOw{7YEo%>lKXbD>SYvWK?;e`?_H!+}^w z#vlY;4b0Ea^21JWSsEG?*>7q%YnHy(;ZU%v!IW3bYz$yFu~Ke$J!0?{w*uJjV$sT@ zHghiJ^>{EKCjJegy@_HNZ>ql@C6fak2t!%0F3vS84S%A%!Oiq(EnphnU4s)o@TJiH z`J$R-5P9M_1~f?pWkbU5Q2YgnerqN!<(SH)Am7HV+Adg z2Deuls_hYs=awXCKt?_-1VdP?j2?i%NeK0ofn$ej#V`;t{Giwu3`xBiP*~y@Jy8+ zm2pRt)%IwM`i+CzXL)NrI~G(p0*j|nYUdPr*i*>u5ARd|xgH@hQpJrqQBIrnOobw; z4Ka#}1B64HIMzFqb#hV$E~H4%(89K>--ncvn}2A)Rd}C1oH7^-SFP9}of&B9-uZv` zL?Gc6o#zUUB|X6VV9K`VrAMX0l8DAA;Ey1#E!;uiBh)=y0p0?!!>Oq}`C&Pp&Kik# zh_bRi@sMDS6!r#znq(v(haUjIZqgmtgN+rpZL`R+@RY9po9U?d#rs_^AvQS~u|Umj zxqt5_79!8!LWA_YrO;0FVqYJGB^XrV&tBJxzGNaJ*eYdmMG#k4zJ#@z#y=`iRXjFj zQbUR79Pn3@%Fuxs6;hbGtX~>E1N;NQkn6U&IrBsZ?VD5R&Zb-n3ax`k+&7WW+1f8% zA)(Hh}XFh9^{mRXvIa{$R4`U0T`^CAI5l zEATKytI4J5{si#W`R}a|v>~f0+0M$X+f1yTGyF;DUdNVy3!tTT;wzVzC2MSqLh zpE2=>)xEy2V(<<&#dXOO257`$PtmA4_x!Oa?xcdEieD^awGG|ND~MUZ7$kDJ@GHxe zGBP|(Feotb;;}kswHoNLE?fTn<=HFeyk5hCdBS@PUT=RqLwlxLoTmSFcW4Vtl_B1~ z#!ZE`L@$I-FW1nyc%6_chBT}TkbmEey&tWms)p_d4*uUE+0C@)y)h-rubTq}a z+R9dioRKwZN9h5rTtU<)AZNuzG<)^)V$=iq8=>XDn3v(NR8(>qCt^1ewkGGu3XeLm zy^2jGR4SZuDnbPHx10lpAxZ=z8X)Z)GVm?sM|yv+Z_=YOcz!KS1H(dC-G9W>fEL`d zM`iw)zp2oO7_V*Ao)~vUO^s}5A^G1FnHn=8QP23X)S>?;uc!YQnt1ENz z(j=;|9m?Yg;IG5l@H{!eHWxizp7g|92z$d$j}-jvH>#r?xw9Lp8>0Y;2q?=4PuEDO&a$MlX%p?qz}^tA$}DX^)8QM1OioFy_skvfj$! zA3A2f1TyjTz2pGt`E0{Zennd2>NN*I`@XNB9$@p{G%LUu!zNqncTTwZt|9z}1V`L4 zR8?#9h!90_enDR++=uQmTyjqcf+R=~A@^w#b8|ZCG$10qN3Xr6-utJlQQIr#74Gjw zcrnL64)k;k{dM-GI)4I2jTJ-n0QxB%M$nAuI&l&lD#nFA249f>*BgCW|YBABN-}mmzh6;y8RC zUkYxC7ZU>3aewdcd9|i36T% za^_1-M4tRq555S@SudKi!v^?`8Yc*_1$Zj4QT3-Z4{P)6$-&<`lb85dBtl`njIwa* zz}iZCm%?(?D1-*^6FsO5=8jVB2mt{Tj-+w+7MV3d(byq~7KvsMJ&sZ^* z?$@MmHI0`(%rq?jK0e!u0b-PvMX=0I8J;D9{T7N4y4hIRw21I0c+wE-B!rrJ3Hq?a zhYXI@+VKG(*mOkt?JPFK#H5>!Ab{13g7Mn7rK2j}D8U#IUG2#Bo)i(MQXqrmbMZ`* zMf4p+-hbSc!9<5D!&ANOQr_U|8_14QFqxyw<=?^?YE6{KvA?%L!$mPY(d6In97b4+ zIz!fgNLrf`J_#<>xBNHuXe77~LH~ zO3oqOIN#d<_qOd9lKW zCHvXC%A+V-R)CpbVJ<W z@CqEC2FT#oSxo9yaad7<*?__o@;t-4k+#vP_0V|UigTF$cOJz8*(jKmPprR`GWZtXknrvfhOw)#`F*j2NseJyi#(!#z zCTaT9m{pGw`1V1HZr4d+h_62^pv~d7+*w6(K?==RvPNFIe{oq*lT(p7^!J0ar$|XJ zKmw-%X6^OLj=*3tl6+@1wYZ)x5hExO8%_1(>&T@04N#fCHBQLLe)ZCdz9ZcL*3F~B ztU5;8*Sf?!q6{T?>Vrjn=S1}aXnzHf`G>;D5$LbZoX-^6aClIbBN0mln}4MqSpCf9 zcLQz<9s_vgYD;SK6;LG-Vn)%Ebczq6yWz>Zm5P@T@gw>_NrFlTFu7Tvl@aq~N2h}B zX0VIw-{(UQZ{k#Jol|fi;o7akiJeSr+qONiZQJZjYb~mk^{#h47fi~bQwraH{s{iSvCbg#tQN&sQ*F83Mt09Np0u58*1Z(a)H}-BA*CWzj{*6r;SN#1sPO|}85!0yAt$Wg%Ewoa2_7&d!8g@GBD_>PkkAT__5MmKk zUv$T4rJg_p8(U8P1Vg^sIU_r>=I@LjZ47gR?-i#Xe5j6x0GCBSI18r!vB-vq`vj{@ zKSOh(c=H=b@eNC)t(_XRL#kjUWC8MA!pq!p{0EHTBP!SXgxe<;N*CaWN-<$Bn@f>J zx+8S3v2INM`{Md{d^|UnGFdjyO#=8pwHD_EKzv=}_>;(cqyuU%$l>XG88lVN%Uw7y zJ*Vaa$Dw7!1UF6k#OATW5$V`yZgKlmNUOrHOMkrgBHU4h!3TQmXw*hMG?l-eWijWv6$$gml z;%#!G!g7J(28?zOG43PGE&c^MlkQT84l~rPnMp}OzqZ3WWP=|bMKy_{M)!2J92?kA z=cz!V(L#RLSbl10J=oTgZyqhdoTF4ITDN)R3Nxd-4Idl&T!rtWuJhYC{D7J=MY`yL zv$}6SvZ8)C9t4iDQ?8!1o2X7Eulc&9Sl>9KY84x~14fB|=NN4#tF1GyAV{#zqN5>N zl@M%~tnQXo`_&?XOV)vMIU_~8p5c*A-_*G`2phm{3M|rDyd!H%gpfqr$o-`zCELBc zIryeENuB&g!SrNd$^$g~Lyg8WF&-AfHe|4~+-Q;rAOW(?SX{Ri&p{+KA*oHNsX5N< zrlb>gj6NdM)Zp^uN-&mh;{B z>3Zqtwp+OfNx$7OsX~(yZ`5_n5GOWq{-pgLZ>IfABurK5qSD%-k%*}HrH7m27g8sF zK^N3t*iuE;r4)PIqsTY08pIbT$^{FCqmJ`AiP{}PGBlql$NI&>B@1$Qa$-E->ZZocyUqui7e5!~g%MJ{E4T+uUX{<{7pNqa05jiJ%rR)*C&<>e8`jd2nkBD}3 zQ$GnPTsEax{58F<75_*pYt@8)b7um;1y;BbO-vVRBWR4FJp5LdQyBa_g#dx?siksSJ-05oq=FXB*QU2$=*j;?GSM#9Axn9+Bo~^+$sW&2eZ_e ze|Y1mdDnW}EH&GnEraXyIdj@$_f~G0eNuYvob5&i(FcnDzJ(`#W)|b@7y! zZ_+}v?k{vkXZkJ6WSpsC7;X*;Z1qej^jWlc4rsq9!1kt7AjI<>h4M+Z@YmA+)E^;4mm!-5Y6c0Y&a5MlfyYPU zz$0S)6pM%7<@!U9%miMJ^-G8l8B)ry8RNT z06H>sJ7s$l0V>mwA;0t|x&l}L@g9gt5jH9l<%_5Y7?Cgun0+495FAqcO#pykiL|0! zSXBv1T7lO5eJN3Dq^>D94k_Y2D5|?DrYZs6Fwe$5=$jBP_MefZwa`x+a8%;YE0%yZ zgy8vop-5L3*2b9Xm>@_Ta@ij60I;b*Q*ZN6LVIIm)*VXr5p)F#F9#?PGQKiZLN_ff z004?Q2ty*t5;hYA^w-~Q`2cA2Ke=L05P6i?4`3~5`;r5~r$ycY+xRnZ5b3D3ifTgb z3B;$oCkVx;EP)3LK!k8a-khJep9T~a(X$Q~61>^^(n4P!`ppn>xMCHv7+sOnpyCHr zz)ac<{J?2aXBY7jIu^g*HwY>PRa9=pr=EW_lY|3>q7Oz`PcW3Q(q*vYV^SMg zvgg;I!wCNA!XzsS833;osxVXw`4+>9azS9NDqb7WCsZ|s?s8b zQKTqcV4!&6VWXKzWr|T!@7r=)gmv&Aot+cRTX_S((A!tx(c{I5=36F`UO@*Ybc&UZsVpHkV_8f7hghBi7syX# z)lcxCweRQB5Y*^Gw;kBf&)B z9lZEk63Gkx!W;hL$%p<#>uz5NiIU}D^$*!QKZZPaq0tE$<#u}Vz|hB`!0iGF34lMMd56hc%I13{et`!b~ ztKIU^j6cW0*I)VNdn;-*D!sqHiU=9GiT#&x6A*-7X;wI`;J4J3jlbU5)0Dz=r|TBX zYMK|UfpUwBx^N@P%gyc)&g-c#f^xHop`|9c7xNH0YqD`i_vpA~$Q_QkDD5F&q5e^- zhoo;-ghkExRIkE;>QgK^{u9|fF0U<_^qX0;jY60wyqfbw!HBO0sy%FF6HON9_!Aqx zE}*EIV~~w%WR?3T7l+<`L|`m<7;&PAXBbYS&8c0$6c6WgX2mo?>-#Dpuv-E1R21f_ zcvArPHv=I%ijy?Oj+2tqI^f_HVmf{?e=w3^x8uoPMh$h@-TLAP|2_+0m&e3(leccy zY>!*9lY!mkZbehZ(A`kmW+I<}1TX2n% z;Bz&d9WA!H_`ON6PT)Kdg{?z%;wT=G42UpfPQvqOqBThpn0vq?;G1?0%Vgrs0l?q# z1jyTGi@NDTdcNFi=0=-}k8yWm*da;Fd71kr0)JGVw^y&3JjcwrFbBb`oQmr0@2{O4 zarpCIgr%|tija<;=Y?blcYF(NS=1#8A11?f_z|cuymaSmanr9= z^JjB9!K72(r~ZfFr!Kn2z}s(IIK8{my7d4sYuO+17F~B)r@S0&>)0B^rzF+{s^j%v?C1T*6%M$W$ra-@=HtU53)p-8 zo;<1%j=6BhD_b(74AbAHU%gdnEoj2GT8W;_yq9PZ+OFuQuod;=vsA1pTw*sQebj(U9* zYY3la;YjIyJH_8Qe@&yAczN9@(5r>&!{v3rYcSx&T)}W^b1l%+xd)c|ZVGUPHwB^+(CUEX%NEy>Zew*E4GT$_MomXE7(~H2E#^TF0wIX6do+=^Mc~=JUIOQ8PC`-$Z7WmLg*oIeDD0>}bz~_5c{G1fxQz0qNL+>cmI& zShJ%s9Se^MYCqDKvCAqnLz$6?N@%a%ccmGguE4hs*tu)Ql>CGo=}#y$!UHtdzQAEN zoFCfijhj=;#^$#<{(;kjbZXoC>2xhUD*u9M!znb=zP_dRw)z*Rvh|DyTZf*4onsrJ z^XwT*w8678Wq`kle*M5UjhFryl06Ls#&l1Tby&Wh%Yu33_4ExsJ&N~+MaC#S`nnV6 zX~jyzki)X+U&QWo+Pz*@o@TO5o;6=3bvlpvm-=1O*n1;Lw=dA#Mt>W7Xf=pT%nZEb zrF0URM9$w{2DIC}@LzxC>s!jTna|WWDwpbh_a(|FOaRMSOJbNvD0^aX!0!oG=A{h9 z?vu4Drk@wiVEaBGeb({M+us`}8MbXU|h2_>`%h-qbWyc8u1eJB7t7PI!wUlmn0Jjv%wHKFpuB!U%*xt$aW+N*=(b0U8Hlf~CI)&tv< z+IAqLdqDUPr^}VS{s>7~b-_Vyjc%yAQqpo_zb~jAeFtM5^Sl_zb&lKNE<4 zQ=tK;=4KOdj2q8MNhFIE17ez=zj--zE{RA++Oo&$&JD+l=*nI6Sz2lcf^FPNYNkTqm)S`p!i_Nt%Nn-vgi=uWOdd`BbT4lC}5EqqpJmGTPgSGuci| z94vSzvGnkfKDrOx$S)&j8qr#>?W$UuVbuuSbH?l>*>U@`KOQ0c+P&qa#Gpc-qfsY$ z?K|bg_w$oByXL#jArN50ShDKLVrq}vevtI#;7HIKMPsC|y+&Ldfo*=Vp)Xj?Y6i^J z?j#Tq;_&G%dsrq}up311>A1^-xAm~oQ?O4esP*F%YE5TqN2W&X_+Ex`em8roD;-CY z-M##YHP>4Vl~aETvL1Kx(we2xu-lgHlfXG5%}j;cUnuRe{|%Ma_5{)Dg*O_Rvr3;y zyj4xmt)Mw5Q82=xTbJRuUzsW~yA3e(htRYt6iVMbCfF+e+wMZBWIME_A1-XM>m{$U z=zkmc@ldld!`EEb9btG;MrF3Qp5=3De9Ovsv}xQp8MVCZ_+0k+ps5bKfo{#-{Rm*oB{+$c0QbO|xZQEzZIQeijRG4xYbJM|;BbZD0D9#eyWrr$7N+hzu;cZ_VL$$o_1_>rXlDeaaR}*L5P{RER*}?7^ zojUG1b$;pYSgo&T-*JD58Ud!ctlBpm%LA8E!MAH_Tp4_`KAmAh`y-Wh>?BqLbjh(@ z6Rq5CPUg%F>$(uoWz;dW9N9fOY;R-&jIJNG3R0_oQints@+z@g8ibmU?kS7`f4OGq z_cEV=;hP(awo-DNG=xMv!kW@49TtIU;IbptXJ$kJ!J{xB(WtAX8u(Z_Nsta><+piz z)@|L8!gx;;h{^Ihs1>Zzb06MF{^~Mq%RdTz3AdrJL#sf?jfg2`B4Ft9@k} z$ne=4Kd2WeSarW#7)pBN%Br|ZMxuI*wz>NCDdqg0-Wj*yz>*@xujwJ_l)uC0U=(Vq zbKusH0Uyl7Iw^Id2we56V}}$~;Rg9Y-o1*bf~A>TbmM>gZW5B~&Uowkui@3qWX#FxJN0kE&q@5*Eh(Dp;kM-OMr zt<6@}-iBG<5UH7Sn8*rJ3&&n7@NC(*5&RuF+@9JYF>%pMuBzTgaspe=m*(5Pwe4BWNpgq{Vg?k&y? zNfKaR>(%MYqtInv69y!i9S34+@Dh5D9p)x?RyWq%e-uf-!ASdepjW4FId-#@6q4sw z==#Dg8t?TgvdENCGOjS(zR+i-AIgo8T z!r^5;B;;zM>6_grI5XE&n~AF$8GhC%h-vvd0%JZe?{It>7y@fA^v!hLf38kcN|sbZ zrKqo`Uy@X8%qUKWGz_!rZh0<_nvA6+tu~i@V!dpPve*xsys@|H>M{b;o3r{tjuVw( zvl0-E=t!0dBVb=;A30)MSDP%*q11iiN$Q;A_%u?`%T9b?SE-XgI^=V@hE?#kqM%QS z0UJc>BebBSccpxfurzKKX}Ltoh~9Hzbcxi3&R?Z37O&5;OBL(kZzS}^qE+Anq7JFF zgPMJ82C8g^R=(X&$#vnds=X#Fn3KhkH1l9B6PPFp);=~9wGH6LDiUt3F=<)&Xk@db ztL1j41b8p-fp04fl)&;j_x(kO-pTK5pu+{v)0C~aWS-DWThMvtVBEhq2JPJ9w`9T3 z_q}P~vJ)gFO{Mjq+abiRmiYRcbm3(-?oeepGHP%^>C&hf0hz3QfsH+O7KCp2scu%?iUzj{f6a_5~gx|4do2Ht1r z7BAg0>gq=!tZv_3-XWP1m^!LU_2_A$?H=bU#JWmVXE(ievxrFp@0CX7SB3b*)fUBPQmiJ~vY-XmVkqdJ+E~*lZ*i+kfrD7E(L#8Urx)|EPR#Ihz2d)COb!uSy!#7X)GpJ0%3D z3>f==q|jUBoFE#w!Pq%k{-KXhRKeK)qk`V@?@C@iaCVOW$e_1)^Fp%d{X6~-FR3pb z5<>0Y@jn_EEnAn6`JDfb|G6LZmQ?a@e^mY*|3}Ks>sy5eI6LQmp9__Rg^lU|+nel6 zOdM%Kv)?elSUJ*=d%zfg%P&D{GFFzt7Jg?(Tj@l3GFH~G`=L=ML<>`Kv5_qwH4>SA zDpnTOdJ>cn)PxKE*Y3EhH+w$+TtNUS?w_go=o@qVsGUYslK>-!5a9;WREq@$&p_-3 z%jIAgK-8M<*}-i%>)DDvf#ph3fWigBKuk|APD)i43yuPT{=E?RNfb~D(#qEh$ppFy zllKce9GnP)97k9PcOZZZS`rL#D*#kVDBZgw$WaKQ4q)orgJFV#AP5wWW`zZh6rniN z^l-o%TMZGqBL)vj;7h2SmIm>Lmei=E+`@n)Vv-V4=o12C8t@hoK_?0v1VPM$1G|JU z%mz`pK{Yflu(JJUF5wz5v9h3~1mOKb-rTHf1zO8~rDs}2f#X<*mSlohG9X(1%1BTA z{1u25-qXNkXbHPp#1&66x*;^LI=L_>g~lM=4h{lU9mvHOiT=cBFY?dU#AF{?fC+P3 zM*<0NMTWjAB_rqO=O@pK@C=0beoVI;yLD`F7T5=#qnQQJg81zVv9;!6k$i(GPTB$c zbQPjOawIr}HohSmm4bUia}834!4`Jz0|xTMkfj7>1s6g2pg&QDAb)PR@H?2g5;%(H zF+m^){oxXcgn;-N4t4R@Yz9gU_KOS}>`V+V7QKJR0Q#>%I#8b5FT&X%{Ps%B_f?Gr zCOYu;p85+Atho#y+)?rb`z)12b`;4MM)lzaBDo)DT;)R3JYKzAoNy$RyQ;sKUexQ@J{T{UMKmNMp%b&Z4TD< z7YuJclN6;ge!Q56G%NgA5cHY#y9q>urT=J_Fc=X489)GXa(F@_4cooVOU9f<7Mi$s zd>-otm4$4{cM|3dmd}V|z_&*OjqE5kGyT_NXBrJb7gVSK4@Plav{1C+S`TwS7&6&E zl9=L4qz9$QZ3P(@$`+ z-VHt)YpNog21t~!EQGXw5D4u!LObA4mq`OfhX)`ATniskGd4X@Akr}KsUR63S7L#L zJHdmq@ig=`AX2}R!~_*01B!+K%2ree5r(=PDJV7^SCaQos!tLB)Gti3N2G@|UG4Aj zt^t}~wDGA4>zG0W{wj$-O}TT_D3;Y4Fn8-cv%HBn-s7n z^92eUk7+Tt557l)cS~EzMoniGvwJfWoJ8|?{F^a?9ol>DH%G{kKM0U^#RdX9@gAHc znE}pWurIl)-w~yZkr6Ei93sh3PCCE7?ae}Wjyo(If=XBNJ|qeuAbq-%i&JIsx_Z$i zHkJ{;j%>HeUYf*Xuyw!r-A0io6L~BgSt&npVL-^>ETG#RT}yab?6a@q&f*#2|a>5 z)}OP?ZFZiE9zNPbhUE+2^*5iTuGI(9>-K^&xaX%JW><-}WNcgTY7Bgk2dFsXvslmB z;YJ-@{N;FAWW^rn1dsVb3SfQ4QCQUB&qPmtzlyFFvmtQcRYUlh1sNuA_86Pckb17C zK+nB9Od%^rRv>IAbrJKCjl6`&FY`CeEqY03_%SL`uhjT;X$6<$fC83~@5(>=f z(wog*>{jP`pTw~-M^C$au9xv{EUGEb71Sv?w5gzLv0Nwi$2pMmRM2V4r<8y`dcONh z+uG2?MEI!6qJ{jECU-fkT#CdXmq^?WsCBm4md>)CaDO8G@iGqXm4|ZtB=cRoX|nJx z)Vuw;S8VNwZGE6!1Q?s)*w70rz|kl8sfBxV-DSoc6%E_C! z-d-KL(v;v>JOX9Y_<{nCBT-M;x7o559a}9i9@VkmPrS|F9BBs)Dzc2wj&?V`A1k&F zq7_2zGkL@Dmb>g;n7F)P|(Fk#eW{Qf}iv@IPScspmy-*)Mm%r=;|ty zImNh*?BBDg{GJ$#>hl=Zk*%$Dd*YmirLyiy<=LRVqy`!Ui^MA9yl)%J2vVt3eqOpl z`Sf7i+;ekbdJB$f5~)$c4py8>u41BbxA*!`N;`MEgx~t-wWbW*8qsLB8;m=fIMdkP zar9`tN9l$MH8*capMF!7Z^>1?2 zdIcY&8eBGi!t*^J4=gQ4wOockVPO_+_XazomHf(IhU({e1_mTFLAxI#Vhj&X|GYq;r(wt91zYYkeL3za+&wS43O3(zRj+$_e{*>m=$`b zF#DgiKSuCc3{KhU$j7`qy7dh1#;Mjb+2y_Tv5O>DO0gW=@~k*m2Wg@TO$?x!~zn z6q1LHoWUrvk2GuyIO`F^o17eX)eqyN+YL|S9s5{i5B(KOzgHWZ6oJ30x~FlUs$AXV zbBqBNSHFkTSao0jN)Tba`mQPKnXiKbk#|~%ILRIQTw~bkMTEjO+^A`bnnmk7SD4kA zlBOAUmrYcKnU1+ag2_yOBt`+pSm2C)Sv<&R6N$1R3~gHq5kJ!Hxm7bwk@#MqlDLXG z?!(iypb%ZkpQJss>nG*QH>K3ctNiQcH2ZkT#f|&OnR&|6pExyN^TX{E@{QVAQ!{s2TXx4l2~ zClxinA$E7-VaDka7+=yN>&RU3Gv})6@?X*(ak=sroaR05$NoblPJlOR6#7!7^)QTa zMlcsVo0fy!*cF>bAl!s~FAlrjh-To@)}Io0RWhWK{Y~gHX|Q+^oBDw>e0k%07cd2} z=g!dS7ZOEI4VRIls=kCP;szW_|8&S;Iwma+rw~1q84$VXMfonA#BgNOfB=4Lay!h| zf}r+t%p7K_vdF4WlJnfyW3a0MkG*iC%0ft0bzlt77t)(9)kqjzIMbZmbXjb_^>u4{Qt#Y1#REiVhbyZRRhOLL z-C2VLRmn25y1kMw^V^FEam4cj|5i`e;nevq2+7SkQPJ^GevV@s+AfCrA8p}0jyqmc zeglsg&v&ETLug69m_^BjKSEO{tBj>#HpQtMY0@}Spmuu^cVIU(ly3et`bvlRaPR|e z*It&qfA6Y!TbmZU01qgLs%Ld~xro%DC-JM$1}`sepIB!_x%81VS7>u>Xxbmg^&CF+ z7`I`mM?0-qP^VKBi*Y23i#>ae&Ep1xTk3<^?i8fIo806F{>8M_+pSF`zIVr9)pe&( z4b?%$mO^&Y)Gs@4xxzfbzTMG3{YLDQDV+VxER>FHj~#0Gl@FwSC}YrWcdOocGWisM zG0wOiW-gmhue{E#W^KY@>^NDIsuw-C7gs&fgn@ho;*g9Q&gP7zHSG^MDqOKv$+it2 z@R9wP0xQ)dzh>THxoACauwS=?{qr) zi=vXpdfuKO(hG2+bN65+3~K#*tqG_nl%qeCdhX6fT8S zdHPb#lqWuzA4`4~-)CDmKp#wFe%%;jo0+|Sig>dmDAWKUwl$vYamrn5?W?F=_6KCbdaCNBG z?1f&ttAX)I9zF)Zm~*mDt!;vC3%@+}wYW~+FW=G=b6r{a*3OlbHs)BzW(9;U}QhTgpWZVi%Bj4ZQ$0{ zG%LGhF1~$B;$xarsBu`vko0fdU~DbQ%&})RN%yy}avO;Z^x05S!sd`5Z-SvqTOXyc z>6kRRPsQco<;^Su^Wi2&6F)?wX6~lc;BQf*=P16LdMi8bhW>zMT#DBm3I^^jYCWDR zQxGtQ5gn|tJ#schV?bQ8AVwJJQuCybcRWU6bKpH9S9~>SwO(;Q+m7#WA1|tC|8tW; z`N?^myUH$ASwz*m=HXkX4Y|p`g}Ia|<@b*aJbc6$?o~sIHSK)3%!WB-Kh)~64q^8Q z(VDC{>8|e?kJY0vIDDbL9MYI^&$mYlyk0*n#IGT3PHf)y z0S>I7Ev1g|Tdlrgb*GCZR!P{=xH0=g4BHz&x&0ltJ894I3Xw`zUbpwAa&2Hf+>muR zV|48}PiId^Zk;5fq$Hw53Ts@(Q0JFmN6-w)TUu;GThhV3i9tHQP>eXjq+0De?H2%5 zOjMN|wz%I?rK%AF-j8Ux(T4$vJ9{J{C#5!55phG$=<&)9CGa_i?SCYN_4tP~Ogwj|Q%Rpe~r& z<^;mKuQ^H{MxDv0s>R%!Mi;nE{C)?0wUdwhy`Nh#+WCp|m^hMxv^fb)_;F9gwHP}W zg11uJC^N7!9#K_Xfkmg@Pj$3$p4p2g7)ia>tT)->M|O_eVtOH54RZ&3A*Y9O-wVRw zzj~7ge+NR1tzWLfsC+=Kvj7gfYDvZP4gF}7k3ZOL*I|a>T72aq?l60>(bes}7bmnP z#1^k?GPOsW9tk@FAHyHOdS_SHD%|dItl)P%cA?r|CQ+stV_a^keq8a5J@&Z7U_H0e zSt@1i-nr#aa~b%}u1Q#(I9}$p!7CSi&arUAg`f#?gJ~_6XYpWhk@|s@#ixgLg%}|Y&Op|8Tm%ule5v)j2Fi*hpTX+7U z_Vv_QO7{8pJ#eFZ)Z4Ub`jH*Y$X0HHL?fyyA4=lkYKsu^1P|c;Nrb|SL%r<&ZNJ%2 zvFqR6^h31xHg?tWA08~0Wc9AO&E^imAw1^@TipFDp?=O`%GM`H$!dbp%GT_mEz z@3XbbL^3*eI;%0>VnF1whJI-`amFKh=w(8$f*AvGIV(RtjIor*Q@h6Teka?H3%89} z&iJM0Os;AtdFKqq8@~~!_{y%rE%F7O{sxJ>=Z~)CuP-nt z|CEzLYO@1&ui8CuvAHT?ka@PK%nm#QDM;8yHq`m$=(Xu**`$ z;wGC!)ISOG8@gxMT1f)>rIeyqb<6Ncy)5VBXMG7z{;zQ=k9f)>$_FO#WvXopce2RoE}c|w&uyh z&B#C)!dOyF=d?|E+(+&1VdPaY=(afR?`?Z`w7o)}F>n22jIpx?%wn0A?>G%ptyAC~ zbJ#3tX$NjR1akIqzr!}(^V8M(?A-gLex8AQnJORGz3LJ_;n>-qW=ttuSP|l;{SY)s zKDe~1KDDy{0k>qKfTam?&hj;li7!AJIN`Cg%h*D83ws;gq*+cPZ z);{}|ysynO*IW_|lfrsPK7(KNB<{4v+j{ie#qaF+rFJW=|0!+$tyQ}9wjC8Z*65FJBj$5JYqEI7DVVQqU-40zosP0Ks#O3E zt&4#T!ml~?nH0&DNLoar6{>7XH0u(4LwOZ{xA7VMg+{hY(-ZZFxiI@}IKhD>qh$D8 zRES^L>VB;9!vn}Xgkj{XM>1M9tIfYdGCG@J&vc);OvW`UY{pe}S$}6JFEk9%8E(o@ zPyt(3j2>t~;cc4D1YAm!+u4MNa#XeYUon=ZDedJFm{^BWq(C zd%>mX#AG7GX8vTUTh8(NhZ9-(D7k|(Qp&PuG2`~%`Gg*k9Fyo%?=apxmy7%30Pm&9I}DZ6?g-tmZVN&O*MXV^ znuEho|I2KM^FQ+!3}g=G|35)t;b7tTzX5R! za87R4w0ymP`EXSmLIo{r?F(fS?!jboR`cjtXt+(U1jA^>#H=Ug8d%x};3+O1mPPq#% zXgFt)=Q5ZKOKX@`W-KC{3yfY9V%>z02ugIaqd<`WIiM&#a}OHAhZv%Osm}vMX#|yM ze#Y<*9BLkN93%`VT}Uh`NCmL~*}xuN00t-%5xS`aG!cs-$PWQeB9et*$jDlz0i?i} zcw%+qIB1e!M@1%@OCxh*l1s8GeQ^j~A$KZN2G|hL_-RnxaCnlP*kBVPcq}5{07%H7 z4IvO12p~NkY3K6ri?wIwkEXN7FTCKYqMXvQq*O7UXX*;7d)?M#Vox zf;rnj43VP?z+_RW`S`N1$iC-`iD8MMJ5s(d2LVPX$g$9(pcgvOPWjSC1HOn9lsNG6 z?D08>JKq|JyP*@ma}%ow6Ht(=2k)K$5k?|;b2%I3u0jyPg7j$ckrXzYe0&=q1km?N z;YfF@nk29V#wf^45k?N-4X%+y5Gzq3BBwaf4#c}a+KYrAM&P9_8Yc@Z{MX}vP`75| zApm9Pzr}&O8)b+>lX(UW`jZJWu^v-;8vaPZ7@pU|f>M&PBm(z{zZ(X;cVQPz35F+w z{?g)j#~em6Z62f^8zKI6Az`{s(vvT`37Rrx8g$521jPvA)Bv7fOtSAK;p;m>@Jp7^ zDYfGOSRyCk7F}o-{%3hF(S`>dvizsWY8*wg7powOc7pO{1fZ>1xB(Ngo_DxP%aJu(Z0TeRS+5UM1^VSK<9*z7fUgG zg%8_UbX@p(13Ca4a!=|CIx?ew=Zn>)r}B{O$azzk!1SgkjCYaoaYC$=63=76>>JMDZ26lJ$ z-nnsvs9&Er{dnVuhoU4Xh7#HE!s#qMwZpNZWB5dNx(?H(wrro6tnw7RcdO7)M^K>X zE;t~tA%+lB=q}KM8+hSlCPT+UiGVa5C>aT%a2=`;kwjsDkXU#U0c(amYzREI>iwqryi3Mwg8BGW~6@00gq%kC@Ed!6mQVM_h$r3opew#f@p+Gq;gG_ zob;$Zuqz~lGSh$oC@tL^Ua?+H7@~X-G$?Zg`zKzQ$}k~llRK&W+?4xxeSj{>#rRck z46xrAwO~{Y4;H~SM0^77MPVswkW-&Cj43EhxSn30#=lA-p|_9k!_L$ykfn=YnmN(h zxv_~TV?3@P7XA zRmwNo->=ts(w~ZP@stk>0^%@5o5kyznA>C{kz3ePKW8)Q-i--G0(t)0IOq+{K6zxh z(Z2OsO0fCo6mBlQKZ;$q>Pl$HdG#CjTQIzY`O22HI8R>)6oPvi;5V1%+PtTWv=+_CaQI`4)#Bq>zDw9zCo6o))MSK~gioD4`dE$A60ZSoh!0s*2CI2w8fkeE0r z?*dkBsTLsu(p~H&tBv#TPOAxHPjC%KE9%8w-uk+pm879wthyB0Hv$7DPlkV|A#jQ01nfSL(Mh z@)esV{dvVP$=;nO4fyvBdwsweNSan8U+U|5Pd-dNKZlcFD;v*zqV9X&H@!T76Ifh* zE*425U_a~G{XLTU*WRc0Q{y%*SOl@PtfOymCGUB>J$n>ZXY+?9r>^~Grhw;P+wDmi&3LlbzI1 zu542XpBlS8bp5=w-{CHuaW`M9gGOORPtV5Z>$7=vO)9Fq>FK)|U;2%IPamIUbmwEQ zi5if2`$XDmb!ax!lx)~ttotm&$8JMa4_ZV9&WEas_}FinFL^Vz-3(8OCAo0kobxQS z66I(&=UpeNlmfS@C)ME5+QngKN1=ak6TTQ!s(yN?eSC9XFL!;af~k|wJdr42IcPJ_EbGXIQMTa{#eX2Xb^ zE2sU~>L;Om#P2{$v&BwFiKcYNvr&Ik5#twFI4whYhXNRU_S=uVG2WhdIQM_+k#(|C zAk!Bf=085dddXH>@D%%SG#kmt_iJ4*EUDk8g{YX$_4_>2`Whqs zHV@q2Pq2BY=Rn8jo|9s2yp!CDB{Z2;y}J86M=3bL4z`@<@7}^OAuvg>=w(G5kZla& zZO$p;k^qWOXT`-2itI2Iq&(|$DaCWrqmivRUSa}I^I)I9fe|jw6-AZ+rZIU z?V5`ij#kO;q;t)lpq?Z<76%YI+N7!HCHZSJK}4N;cJ-Z{0AFCHiyDpR{gH8=fjoPC z-7-YDJk7XaJ4v51=*lkTc{WoIhESDOmO z{RICOsE4@WcCCqUHsa&IjwfSYj0QMIb`s_rt-)8a(rQ8pVA>qHl;zX z2YA1Rg?QRDnCNI@Si@W5LOs&eaH@8cJh!HD75m!xYzJs?mzAO072_W(CwgibtTx^2 zc5D@ti2t=|NVYP9ILm67hSxl8KKR!;J9xZ3&Rz?4-FQU)>d>@CD~E;Wf#FTZ=rBsQ z)}x+jXBRbx*fV}t+o-hWc6Ehfwi?@L3YdK04r|(%E_Du}n0V<{Vch0g2=ghyDp!E4 z4}{ghe7|=w=Zd)gBoJE5cMP_^f38Dh}TC*vfKf~so|IQu#HdM+h|Q1FsczGGI>yu zs>eb#Qtg*8!Ux;3$Tm6V%sg^f479^*@Le~BhAz)BG;ewt&(O@qT>Yr~hp6H1D&w&> zvwl3xk4Lhjla|&~EMTCTZ&X>?)T*{+${dVb(&!&t%qp|mXt#KHAZ3+qS>1yp^D8mm zZVKWl;m$D|t5^ZO*VXO%eJiQ?)S$xZr4e@k#AcmQVqPhoEzR7Vr+ zf#N5)ySuv++=KhUCAe#FI1mzCf*#y8xE|b{ph1GWyE{C-`|kbkRlVw}t(pGyOi%4@ z?aubLfS*_75ru2q+SZ1-?KVq(*LKdf@ZS2;i>S%HltpE#C)(+cCM?ak17pYCm!zs> zJhFvQoV-{_Xtd{0jtWrh>*_{O)b^rB%%9$1ztJu$*3;V^NLb6+fcuK^8Nd*O47>ZG zLaUv}an*Lu0LA-h=E#vR?oJMTH5|9>-KfhEr%j`+#7z8b!j(Dn2jcLSVQ!T77PJ$3MTKX zXDhI)D^wUN<(^WYfe;*c=O-dF42_Gu&9l1U3XfPlGdmKVlTDPD> z7GJ5cPia8!nA+XUqhI;+wLn_@YR5H|=mS3EZ?WmWf4h$`oW>Tu&}lX+JHq93EwmW% zi~nP`1%7$G@OqDoqTZc@hWiP1I+QWnUm1Thqw?9YD^hjxU)XK0$Axy`o6OQ@V0CRF zA6%qy6Iaajaiiyxok)5Y1-FyFgJ&>kdIb3dQb zRxa^PBI@$3=yx0Bo&?-N=W*03tO@_Gvhm_^z=yl>{icksEq``>vo()qf8Hp^u<|k? zp^`m(;3}4#`-s$G9aGdwD70#f@v}pdlk}i0^4|U=i;&)qrdtW4gcoLTb-63(dM`Vl zP*z`-39xtkk7kn@B1ts}gbj$qBVz3_Bn8O1h?BTq`+X={(F6*3Dx2T;!` zceZ-hR?mz&_Wce+2?1`O#qzhz5$wzN?saP5WIFLV!49GuSdiWNeOqq-956oGh?otO z`s2kD$9J~x0P1j`6+Cf!t^{F;${ZQj1^JUYNFp@vL-+RRwm0;ITYZvD&9HUxBN>Zx$3TtEyVvF zyY96`$1f(KzR7HT@s_FWQ{_%RIYa!n_ZiQ)?JZkC!pO_c;uHiWdTIUT|LY5xhk^qP zTMmZ}nSld1D1Epc@>g5?$9fM8hwN}$2S?l3rzaZA84^aqm* z(q;`Ph5@rz!Qg=X!vJ*iZb#6ApA2m_w({E()O1Zcwk=PP;n2Y?N^`~^^h z1=D}TXoL5`fMy74GGGwqV=e*6JQxrM3r2N>#ew)_0MOuIc?CJZ7&QPKNOleY2@X8{ z=L2ak0AT!waQ%l&Lb6K%DzIP-dN`b>3IOVV01xB?AcX_-y29arH%b5W6;8 z|McTRESdp`aNxJ!|A&fpe4roW1R%e<{~L$-{(nf|z{g5qI5;3v!vG36u*GM1Z1Bgz zxWGPh05XW?IH2nTcY zqP;^Ci#3+Q`Z+f13YK=7>s~EMQav^x@b$2om^)-sxiE9Jgw=oo0hZ?}v@Qb^LC4Q zsg$b9B52f3Zkb_89pC}u==do&|21*oN=p#`Q=Jo2b)~3F`mc!C4I3kP|%SQtZ-g#JX5*r5{~?%M?Cpyvb@uP-qNkG1~PmVhG02ZDk_PxiqO#-UqP|jx!m$!_r1;oxXZ~MdkF2#qD zaBb-2Gc7H_?MKvC6ktZ4%`Cy?!=#M$)as{-o<@?4*@M@Y82hA21ni9Hr_`@*k7xi$ z&`U>n;@kYR7Ltc!;#rBB<^EM`SGu21SNymA7lq%~n8=iM-y@0qd7B$Ufhoieag1=S zqXCfo6F*k&_gHR;cG zxO~tX(rj)pjrBYfv>_j+PCQ2lZn@tZeHn6vXJ5zVz5a z2uK@+HajB7T)yT9=ARy>VrUl9U&Fx?|1nQA2p04%cL=-mH1x7n9EBHKEYGB-o^~(y z^)>I7cR2u%hEsD2_6pK<*Gfz`15qVF#g~yuNDj6z&D5F)rrMNOl1DOlKj|wGulV>< zN0t+AZS_%_i$dhxDB5~;`5Nq(O^TT`d$GnGIeUjX2uLe-T;sFk5rB zEl)6+!RHxx5xXlk3#p-I;@W3hFHz|Xelq2(-Q%qoTM;U@(Ik%fPS$rrJdX+gQZ&v@ zRU_ZuxWO5ciF%W1W*|ggD2Vjj$Ev8hw@X+7JA>4IRq2}Ag`C~iKsz@xYP?HAh&Yb{ z?jN;?{L;dhZu$z{5v9Mfi|G@dksd3d zfjIcMF$=ZNv<{~e4+P$A@8oc>m87fcIX!+gw47G!BOfsZ5#?=%;+wO?fcd6b&Z0VQXmk4U7u=jt;0K`b&n{gz(Qx?JO6l&A z$=~WHPq-rjm(A1u2rb_bK=jdHT}2Jbj_h7sA0ifUv?mal&P(U>Yb# z3tdkJITa}!&2fY3=%)?PW*M>ey{8aTTDIrZ>)nfHDK$Kx9cO1X>Yxw~{W-Ar)P9VZ z^K}7Xm#J6}N$tD*Ey}S4s!Un$@eC2^YCFQNL!$)(^E)s!yPefO#eC~07Yf9TM=vtt zlv4~|^+nix5C;gDfyi?SlFTK(v2d#)J0|T|7+BIEg@37!Q6U-0JI^;*UN0KYOtE}s zTSN4C`}b13;`d-x;~^0GFtg)1M%71OXe6ai>aN%{Sj%=LC-p8|E3&7vXW^-qWU<^t zA$h05KSB`wisDF?ZaY!6|6+iRF^dEX&Xg{Ks<3uTSw`-QEp- zcN;a;f$?d?UqR3Zma&n|$%INw8DT4U@}o`{f`uUy^)!0hFgHM|;@p3#v}4(T*k#va z_*l6s7}z2nLVf~en$d*o$Ns!Hnly(;!nve^(3X0 zO|18*_44|wWwFNuamHw4O2im$)u_q}#b2XUb2Hi3Yd|785wO}h&+##BYKjl8q|gmA zRv$_JQebr_uDnG%Xl1z#tMzbrtV~7yZ!&{6Qq?0TtO*WF1<=f#RAB>tT~x%HEC*jEcn%9Pi%TP*_R^FP zvDNEN%;hnET9`^_aaUwefC*tD9>f$NKs1Myb51w%{o44&K@*dfhXf>1n9`0^hAPJ$ ztIEK{&&QlsFg4ILkL4rA9Cn?M17HXxi9%rOB?6JiWeD%vY4C1$gq(A+s}}mq)?PbQ znV0{%A0!xWKwW5jV6Yzwj{JIFOjtLm&AvhOXsQ-{`p7`RXV~Pia?rch)*EzoRd9ZZ zyJ0=5M^<61mcnd`WnQl6~G7d!v+%GL_a@9IQdyjSk zD`3cdBg*`msg1u@{)a#&TQ+lus0_A~CK>b-a%_<;5Iynul~74u(VEM-?`PTfAMK8m zXh3iCKw$2@8ZT>dBa6GmUC=iye?&b8Dz`FKBsD66bnt-o6k;CDTm;35M-cqBwGF%o2_ zT7vCwGF9{Ww46tyF?qhUpVue(_+d;;{mN%<-*;M`wY~C1vu-4>B|-nY7LZ%Z(9+Cn zG3p$#88}ggr&hE}s`$xYsIUvIOfA9J-gnQKJrv7J;e}12^WxtsG0Fe>bJ`y zgSZS|OEoO;-N1I#hSA*6d8A&Rs`_|ut7CVx>f1`4;geS{?af7>pEdEYT-J#=H{{gSol+A^qpV{1IJrO?2-|wq3nX{RFQ##W*Lw(Wu`>6t9BZGH6gE}+gdQLfSy}H;jkVWUgL0tSP_}YFn$4S8GQp6mB!|` zRYM==EM4fc`}&707x||a%M4KQZf7v+8>9iI#DS7VNLE>vRVk9-*KslztmjPvni$#`r%Dhj6lfeO3oWa~hk*VMgVRJ4DkAa5H$mkB1 zDRTtdeXf}7;#TFKJx=7x`2Bx*bCXH;P17VAiDg!nXX~G!XZBOrxBEeA0s}4UqNf3q z@9S^QO}_{epmFMHhu5YMLS~0uZN?`ZM!y4BqleS%6*ywJsswW-rz#7LXNMOXeiooV{FLBDnR@T&H0lWKf=ci9h=s)FJ~HTTK8R z3Gd(^8M$*3w!T9Sj3$KmoGXhJKOj1#TEa6b$Xw1S-z{X<-fV%|uKDFt4SKA}&08pN z1*v7p@U zTu$ejKhfmT7m>>9BRypj;)R7<-bVi0ac|L<&eHda_x3hpHS(IhTgQOUZ%T?z^d?6# z9S=O@amNED3%5qEEpO#-`tNOT_uhdb7Hw-`r_P{t;m6a%sMu3q;$_%>WS8(W-45s? z%Tne52Xs&VCVpGw<(?bzh*MSWZ4-=R6IRamBfI`TfMxp6R~_b$Hlo?eL*)1~*xAkr zeO&kNA{MQyVTb3c#w1<-orTA}xwjQVkaTiFhR>if;G&w{%dcBk=3{b+>7S1y&O5Jh z{p+CXl|eq-S}SsD)#&S;peq(+g=X)Zq~QnQnJZehSau{{WkowXPc6-Lha@fgv;p}S zC95s)6R>IOE8W^JqPSxI98;Ew!6V7@}SW=-fg)?gR^b*${h(VwrkKYybjhG_FB<3-mVI%6p{5W`dZBLJ+WPZlV% z{2ohy)oYz%0sOh#4nT=y#DRtFcQTM<$Xb4|T!o|kZN(JZe5FpwMukrX^?03rnXEp{>GBOG$&hjEL(CAALP|T|9ZOhJIkV-b&KYf-y z@rgEP{qG2^axY_O8+q0`>)-~v-UcWJ|D?&?B=cr*)kDabf+6+K3HCP|c`JjEzst!ATOo(j=G_aU0LLUGZep1i(o zwBS51gPQ}!!|^XA1lBTzl69aFtRw19LI9hiE~H<>%#3)ZlEabR>v3yfb2_6h*7iP? zv9KxbVoWxvQ~K?-hO3Z!nI(A{M|mj0Hss}`0r|l6hZXUb00fLIw}pjD;TP6>)BvY24|5IX0b`QsaSc)|4#Z z#!AH!$ZclpjsudX>;Z8%sZ}zbW8XS78MyPJM7|jB9o;8-Ima2}NlZ8WSjO_ArQ_n5 zUZ+^1iuDLA**FM?$p`nxnXR~Y;{2I1dvH_n8KKbEBhK}gnl3;WYyykD7+c*w7p&*J zy|jk2H7R_*!Yvabgly5@Be5xbafm(0nQzJcky)cAy*2bT?FiK2a8`eR9@}-EIdbU1 zW3WP;);1-(H_r~xdA2n>@*lPO>&IE>#NOxgbhWy?(1ltW^|=lAHAb$2n(fdiVtLa0 z?c(m{K!854#H4znsswUBUoP+1Vp!yoOn|h-z!;!QX2-v*rW-fyANUH)_|kyxmh#A0 z@})p9@Ic#Si3v2S&x>kEDMJPP{3x6rYrVhS#6Y!%&s+U?`am*3Ull%lF=rtg`*7sc zn!2LYHD5oy=%F>qP}wKU_``5L+FDQ%I|McX@dTdiaCKmZ~H4tHd{rdO_q?Q#jJ0rSE9LPNGp#5fb`| ziysfIx(9t#xu}61|Muoiy~!I|s|k8wUpM86Wd%sY|MrIW`0e)OX-#QLKk_QM7p#3* zRJQedg!(gM>W`t=FZ#!?*b-MUSh&V+3f#@Idf?R`9e-{U3#`wLJ70z_4>xP=_@rM7 zF?IMKutBJyN~-F1b!$!yCT%N~dd><8CUezcNhg-+s(~Vb&wn{JvG^X-jxgU^!|sqw zqMRe4){6mZ34EGdh2}B1Z?2w!0i0<@Gkl40Wg4a#3=(l)ciEw@9l-nNRbJR4_om_ZNP4x!)tA|t`o7@{Zrs6|V@)W1VD zjCRubY<4xi7G;>7J{?uf;QbuP_)b{sF?TQ&Lj%)@+x+QjLP$@ z8xKl8??9H({;Bv|i{PPs<~As;qlCGG(mVZC!&1qtF^?yMl*=9i#oc+Xe!Vi2)K@uD z+cysAW0d|LTvY8JBtDFRYRJ>6(mDUPAW%aZwpkkoP{&-*5^f-fg%=6PdL*Y1cG9*N>j1Yt)$(%UaZ()QW)hWRQo!=?=j7bYsua0Mm z9{eK1MObyZT&Oi9cB((|$Sf3;;zq z2hU@_czXM(jhVL=Y;uX>ABk18vR{#VStAGbQwToyO`j4t^99UVZd^a0yZ7YGiYf0w zkOfGEW&yYL>X#RuZnX~{W1!;blFrURZfZo6=*wmCj!hSZx_aL*HdEgEbgi!;tXp>!co)eO+!1ZUT;v3w_Kp@)wPp7 z*+6#jB(`n|-m*(JKz#2eahf&*?6efyJnVRn2`Fho@g4nZ#&O(!S2CBE( z25YmT*@hs1+r;C~D@!C(*O}+eOH*$PBk)Lq3HMq{d#an3MYKPv8Xo?P%CFsTQu+}* zw)$G`pPuzQ&arq2mYl73I>R^sw$xpeo9k!_OiGUHi*X{P-ZdIilFx8hy=FvliZ(tDmBM zZpUW3b9Spo*4P-jT9cb9g^-Ha{e-h?G2=e5VQs)M(()18AUI0U=S4UvVIRFl{AXwxC5X{8M z$}(-z=3z;}AT7kj!NtqT#qqx);E!rEvCte~i46b=5kD^y zyR5C7y9Wgy_eWF7(#hJxhJuTmn>R6!k^z*Z-xEv1kJfPyJV-^uh?7=Nf+IkPCV!St-_clIXI0`O6Oa-=)8sq?{{UMTxCR-%$tS z_q!&bE_kK4gCDB-MQOJU`3U~4!()dJWpVe5PRL3zl4su1S=qbsE#{B(SY)$a_s@e0 zzHFuT(5P%Y(79=Jn^LLn&?da9Sy_k``eRT)S0bLsIiSPD)*+tYoAV3@MqqNogSn{x zAh6V%V(X$|VNJ;NK|zy{q{4Ya_0e=IV%k%~SYzB3N@^e&((+EkNdn>1ll;+}sVx&{?S zr?iouk>{|T7y>}TBcyXZ=j7RfSDyviedlOv?Xk$)Xf)20v21=+9-&(@3ARw)F9(T+B}NHB4|GhEos=8o7FKoo9d!!XiS`kKRvl#=$mG~DR!fOalW+v0&fXzbG-&>=<~+766i4$^`u0X7f+vS zBCYb&?gBSiUS@6%34ohr_@WIjHZ`}lxY@llb*s3pHI%lvsVi?hc>!3c(-n4M0-073 zB&DP}jeXLNC*B@&IQpPQ^R8)^M0;&wzsA}Covk49Dm!xmSv*rSii^sj4+o5)>SN2i z?FHWD4XZg1`^F5FW!@$AoQ}ptW$dpK(Vv&9F ztLp$HE@PG-QZv%THs6Ggp32|BuaeuyC4QfIu*7yVi3qX990zfhg3`Z{dU;6d68AGW zP21lXnv{DgIU=rjEH>?)-u#1|n^M{%G`op` z9tet|49^Soe*kUY+`0w6=x}sj4ckNu3p$z^)i)U_7>e1CNOwe(xa0W}U%Ti! z?t{c~*zVCyjGOaubGf2Wrk!e=IDDOdHWS`*fi)S`{>{&J^36D-c7qCK9b5_<*rCH*<*>r84MU@33ulh(N1G*xA(iyZP zc*Xq=M>)cs6^ptl*e+NcpJ`$~~sh z5|OgQ`zU>G1~_MDs*bsg-UP&iM@I@gPV9MkbeQAr^o(@E1ERNPqesnq;}vKoKjA0q zJvIETDO7E%_%jpU%~an&t+rY?XI!XEtBmwZO6 zj^OVzUQ@Pp>c%V;T=bluEhoN)io75fuYn}Rn}BG`Br{$ZN%{YCP&1Ccp`mI3K3MKs zErp>Et@*(iH#zETjadyV_%WVW6yonzY8d~3AT=MHorqo--$fja?Zb9KZ-cMU3jb`8 z=5s|IQ8KzelI8Ay#HkqFjH!bf+;e)sS9B$A@;=xM_2Ej!X)>0QmUwB54&#z|AIY3+ zy>hzQ=SXoUG*;C|On!f6dQ|)-M=O>T$F2~_U}8%50Izv2Mol3}U(}WPn}bnim*x8x zW+qANHeO^_EzPmZPxToa|8s#%RJ2p)V1~<(>X~o^BTaQ0cD#S+O@k7)F|8USx1wv} z*6(k{SV1E}NW~S1Oi6V#5|5*iaJ$UNSiPcyo&6brKkMfpYt`S5Nk>satmLg@?+SWv zPfuR&<=1!R`dKZ3V+Bv?vW?s7j;>mMM8R1g#N~jwN*_B&!4scMBfR>lpjHNoau>+~ z{?y%#@3WN zV{wcwD<)|jQ-0<_j&=K0P*p18X>W3 z+WJ~jd^C~RffNRu6xKXzO^0v}~DG?3W8I9WM=^aTI6Crx1>%p=1iz{4Xc zD9tIu!^OuZA;`tYAtS*jB_Jco&n>_uDN6DGD}pZiq3C}%betdA?fz#&M++Wv*4D-u zyzlHlUy>XPO|dr6S1?%8a8mS1UcxU*>J9x4&*m5`N`Qflnl3Ok+${}|Es(_~=f=hc zRP|f)*!iPOVPK;~s3@h{kO*+lG;fpV?%xYOT2@z|w(M7&8yv3)?XPqR?w{(1?gUK= z0$tYTR`O611;GYu5yj-7ovGNoMs=NF;Uye>W=m+CX{#wuwUln6hD00Iq`6##Qxtt} zOIF<|zNmTW7PQ&CESY5$J@om4EV*S_!fu2HpN7gLVhPwKm?gYX*&4)Cq$Mi_%IC5; zGDqwpwi;B{uwt>lVf=ZxQ$!5kwpnd>ZJy*sJec*7mk<VK+VuSm_laaA*ar1-Oi1-IxuyJOf_|grzqWYM9}FHm5e_N!%MW`hX>*T}F)Q)~OUm)evr* z4jaX!`VAJMaTOrrWN_HDjdZJ|AYh_EIoGJT9f~bKOV*&UB1q8&e+rLbKUn1n_w_Wv ztIAllY|LaAYz=jv;N4vqH4&^CM6CL826D4A&Ct`G(0M?AwZ#(+q0&uI9e7LOkHtkk zi5JX&;)5-wcL4m6vqAVQPTUqrgyL*q^UdI5AakN z1ex81aI(}O6zK0{@}2~@Ra~W?DSnvswuK%ujW}(oU`NQeirK=6#Ag;JaUe%v6n}X` zA?|DNas(YPaiyUv)F&}h`0`(*21Y(_l5F?}lfcO+5S1b0iqH2_HKTme(1jU8VG#*G z8vN~*IC(JogU&5dnieZrUV%y^=6@PmRI4#Nw4j+Sc^j&LSQ`3-%;xDfulM=eaMjtX zqEmHd;OC0zwq3$kq?X8~wjHK~@=|Su!hAf2_(=T>X(l_p4+d`8^zLN=ALWMx=m)di zaePgwk=&n;=>pbP4`xYiHf{UNyk?E5eKDD-s$~76nu$1hwk-SC!(-w(q$LSl=_Wwl z_l9~vD|nfc*i?MNf8mXoWBE&>`>V%BPnHSTAEoI-;DbUgk-7)NV_cJsdOe8$I_g?^ zEZ8(zR(la|`G&>}_R~8`qVTr!wDZu>+9q!mZT=6L6>tj3YDH_CX0%tA&nLT%HFk+!_!oBqtSeQ<*Sc;)R9Hp9pxnP`ImCXdB|147ZIzlClO1lVC0U~P6Utdj z0id&acA?WN?UJt9vOZwI#k=a~fXerCszc?q)7!dS1-8@MS-T{lbM~=BC8TrqJz3>B z!1e%nU$KvwP&S1-8fY!>I;-bGQJu<|~V4b7;w^1drTnS9UO{0ZV}UrF6;3?W>znR2Y5o@r+f&~fwUwga?@ z0}kMfO!*HGL~`*@paV?V8A1X%pzeYtYRE~T0KuJAWC&6lp9m1pgE2Xf2D=4Psi5S7 z-^QoB3jQukg@d0Hh)X Cv5><6 diff --git a/Corsi/Geometria e topologia differenziale/Scheda riassuntiva/sections/3-curve_su_superfici.tex b/Corsi/Geometria e topologia differenziale/Scheda riassuntiva/sections/3-curve_su_superfici.tex index 132e4b9..83a6764 100644 --- a/Corsi/Geometria e topologia differenziale/Scheda riassuntiva/sections/3-curve_su_superfici.tex +++ b/Corsi/Geometria e topologia differenziale/Scheda riassuntiva/sections/3-curve_su_superfici.tex @@ -464,4 +464,153 @@ \end{proposition} %TODO: idea di dimostrazione? + + \section{Superfici localmente isometriche e Theorema egregium} + + \subsection{Conservazione delle lunghezze su superfici localmente isometriche} + + \begin{proposition} + Data una parametrizzazione $\vec{x} : U \to \RR^3$, + si ha $\ell(\overline{\alpha}) = \ell(\vec{x} \circ \overline{\alpha})$ + per ogni curva $\overline{\alpha} : [a, b] \to U$ se e solo se + $\I_P = I_2$ per ogni punto $P$ in $\vec{x}(U)$. \smallskip + + In altre parole, $\vec{x}$ preserva le lunghezze delle curve se e solo se + $E \equiv G \equiv 1$ e $F \equiv 0$. + \end{proposition} + + \begin{proof} + Sia $P$ un punto di $\vec{x}(U)$ con $P = \vec{x}(u_0, v_0)$. Siano $\lambda$, + $\mu \in \RR$. Si può scegliere una curva $\overline{\alpha}$ su $U$ + con $\overline{\alpha}(0) = (u_0, v_0)$ e $\overline{\alpha}'(0) = (\lambda, \mu)$. \smallskip + + Preservare le lunghezze di ogni curva vuol dire anche + preservare le lunghezze di ogni porzione di $\overline{\alpha}$. Questo implica + $\norm{\overline{\alpha}'} = \norm{\alpha'}$, dove $\alpha = \vec{x} \circ \overline{\alpha}$. \smallskip + + Se $\overline{\alpha}(t) = (u(t), v(t))$, allora: + \[ + \alpha'(0) = \lambda \vec{x_u}(P) + \mu \vec{x_v}(P). + \] + L'arbitrarietà di $\lambda$ e $\mu$ implica + che la mappa $(a, b) \mapsto a \, \vec{x_u}(P) + b \, \vec{x_v}(P)$ sia + un'isometria per ogni punto $P$, + e quindi che $\I_P$ sia l'identità $I_2$. + \end{proof} + + \begin{definition}[Isometria locale] + Una parametrizzazione regolare $\vec{x}$ si dice + \textbf{isometria locale} se su tutti i punti di + $\vec{x}(U)$ si ha $E \equiv G \equiv 1$ e $F \equiv 0$ + tramite $\vec{x}$. + \end{definition} + + \begin{definition}[Superfici localmente isometriche] + Siano $\Sigma$ e $\Sigma^*$ due superfici di $\RR^3$. Siano + $P \in \Sigma$ e $P^* \in \Sigma^*$. Si dice che $\Sigma$ e + $\Sigma^*$ sono \textbf{localmente isometriche} intorno a + $P$ e $P^*$ se esistono + $\vec{x} : U \to \Sigma$ parametrizzazione di $P$, e $\vec{x^*} : U \to \Sigma^*$ + parametrizzazione di $P^*$ con $E \equiv E^*$, $F \equiv F^*$ e + $G \equiv G^*$ su $U$. + \end{definition} + + \begin{remark} + Passare da un intorno di una superficie a un intorno di una superficie ad essa + localmente isometrica conserva le lunghezze. \smallskip + + \[\begin{tikzcd} + && \Sigma \\ + {[a, b]} & U \\ + && {\Sigma^*} + \arrow["f"{description}, from=1-3, to=3-3] + \arrow["\alpha"{description}, curve={height=-12pt}, from=2-1, to=1-3] + \arrow["{\overline{\alpha}}", from=2-1, to=2-2] + \arrow["{\alpha^*}"{description}, curve={height=12pt}, from=2-1, to=3-3] + \arrow["{\vec{x}}", from=2-2, to=1-3] + \arrow["{\vec{x^*}}"', from=2-2, to=3-3] + \end{tikzcd}\] + + Se $\alpha$ è una curva su $\Sigma$, allora si può fattorizzare come $\vec{x} \circ \overline{\alpha}$ con + $\overline{\alpha}(t) = (u(t), v(t))$ + (vd. Proposizione \ref{prop:coordinate_curva_parametrizzazione}); analogamente si fattorizza la + curva ottenuta sulla superficie $\Sigma^*$ come $\alpha^* \defeq \vec{x^*} \circ \overline{\alpha}$. \smallskip + + La tesi è equivalente a mostrare che $f \defeq \vec{x^*} \circ \vec{x}$ conserva le velocità delle curve. + Ma questo è vero, infatti: + \[ + \norm{\alpha'(t)}^2 = \overline{\alpha}'(t)^\top \I_P \overline{\alpha}'(t) = \overline{\alpha}'(t)^\top \I_P^* \overline{\alpha}'(t) = \norm{(\alpha^*)'(t)}^2, + \] + e $\I_P = \I_P^*$. + \end{remark} + + \begin{remark} + Una superficie $\Sigma^*$ ottenuta come rototraslazione o riflessione di una superficie $\Sigma$ è + localmente isometrica a $\Sigma$ nei punti associati. + \end{remark} + + \subsection{Theorema Egregium, simboli di Christoffel e conseguenze} + + \begin{remark} + Osserviamo che, se $\vec{x}$ è una parametrizzazione regolare, + allora $\{\vec{x_u}, \vec{x_v}, \vec{n}\}$ -- dove $\vec{n}$ è la + normale indotta da $\vec{x}$ -- è una base di $\RR^3$ in ogni punto. + Pertanto anche $\vec{x_{uu}}$, $\vec{x_{uv}}$ e $\vec{x_{vv}}$ dovranno + scriversi in questa base. + \end{remark} + + \begin{definition}[Simbolo di Christoffel] + Sia $\vec{x}$ una parametrizzazione regolare. Si indica con + il \textbf{simbolo di Christoffel} $\Gamma_{ij}^k$ il coefficiente di $\vec{x_k}$ + del vettore $\vec{x_{ij}}$, dove + $\{i, j, k\} \subseteq \{u, v\}$. + \end{definition} + + \begin{remark} + Si osserva subito che vale la seguente formula: + \[ + \boxed{\begin{pmatrix} + \vec{x_u} \cdot \vec{x_{ij}} \\ + \vec{x_v} \cdot \vec{x_{ij}} + \end{pmatrix} = + \I \begin{pmatrix} + \vec{\Gamma_{ij}^u} \\ + \vec{\Gamma_{ij}^v}. + \end{pmatrix},} + \] + dove $\I$ è la I forma fondamentale in forma matriciale. + \end{remark} + + \begin{theorem}[Theorema Egregium di Gauss] + Sia $\Sigma$ una superficie di $\RR^3$. Allora la sua + curvatura gaussiana $\kappa$ è localmente esprimibile in funzione + di $E$, $F$, $G$ e le loro derivate. + \end{theorem} + + \begin{proof} + La dimostrazione segue questo schema: + \begin{enumerate}[(i.)] + \item Dall'osservazione precedente, i simboli di Christoffel si + scrivono in funzione degli $\vec{x_k} \cdot \vec{x_{ij}}$ tramite + la I forma fondamentale. + \item I $\vec{x_k} \cdot \vec{x_{ij}}$ si scrivono utilizzando le derivate + di $E$, $F$ e $G$, e quindi anche i simboli di Christoffel. + \item Il termine $\ell d - m b$, dove $b$ e $d$ sono gli elementi della + seconda riga della II forma fondamentale, si scrive come $E \cdot \kappa$. + \item Sviluppando $\vec{x_{uuv}}$ e $\vec{x_{uvu}}$ e applicando il teorema + di Schwarz, si ottiene un'espressione di $\ell d - m b$ in termini dei + simboli di Christoffel. + \item Allora $\ell d - m b$ si scrive in termini di $E$, $F$ e $G$ per (ii.) e (iv.), + e così anche $\kappa$ per (iii.). + \end{enumerate} + \end{proof} + + \begin{corollary} + Due superfici localmente isometriche hanno stessa curvatura gaussiana nei + punti associati. + \end{corollary} + + \begin{corollary} + Un piano e la sfera \underline{non} sono localmente isometrici. + \end{corollary} \end{multicols*}