From 1508eb7e77e8960e01e668a07096aaef9ed0d774 Mon Sep 17 00:00:00 2001 From: Sergej Jaskiewicz Date: Sun, 19 Jun 2016 23:51:43 +0300 Subject: [PATCH] =?UTF-8?q?Corrected=20errata=20in=2010.5=E2=80=9310.10=20?= =?UTF-8?q?subsections?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- algebra.pdf | Bin 1296494 -> 1296559 bytes group-theory.tex | 13 +++++++------ 2 files changed, 7 insertions(+), 6 deletions(-) diff --git a/algebra.pdf b/algebra.pdf index b26f5df159d48db28dcb8e4039ea55b053bc4684..d804cd418c94c931c7879a0519b06938505d83c5 100644 GIT binary patch delta 46596 zcmV({K+?bNkWa6XPq1?umlA6eDYKj!;{_k?20g;EiBqqmrdf=ge8xEwCOa%ECBMIX z`w!`Hj@N^rAcvqJ0f(R<0*9a=1Baj>1c#s?1&5#@28W;^2Zx{_2#25`35TE{3WuN| z3x}W}42Pf~4Y!~m4!jfsG&GlSMF}cxTaO(%5q{6FIB$DKn&Y+02oU?@Dc>(`clVh|c6o>>8NA`{;$TXNo5*ZJb+2G!U!E{_M;Re8a&M) z(yXwnUHX-wIIOD0Pie z^_r1MGj>-q@)?@ZhRLw_d-frj0o!o>36y}9oELvvH)2NE8cD0Y)E$ za~I?^11@?(|Cnl6g@H+V-=`rYG%4QD0~%o%ZDO)pX0qM>bxH{t(5g1WrhbOx(`CMY z&gOsf9KmcpXPQxDL&YwBKO=(-buqHv#1U)7`!xry2h~UKD|zRP;zFQ~D?U0U72XK` z8sd{MLKQkDdhyMs3{S)MT5U*q;Hn}GuDEvu_1(ZZ?`BBGr1Z_}#VaD~Asn&V08^rz zf0ztD5_){Np;SpDw13iXSr!ykKF_D086|&SBZuitNIK-nv18`PQ!S$gP1UEk(A4n$ zL{qd+8|r?ohPhPbCa!A3DMY=-{hs!^&iq6$+@EmDbx%BkoN_E5zbsJ?2VvJ|pUHgAck_<45RD^3Ox7$8FJ!`tEQjQ!Y^tq=bRLGo@ zy}Zj)Gah2{=+JbRX4uyU8b_m;)zEXmvMAAJM;mIa5+CzWZ~f5;%#9L|0)lFkDiIUe zZS3I>OYj4rr*Q&)eEt38pck63HISm5NGf{ExrhU;Y6gVMNSY?A!hB#a8< zcX3I4cZo|L+ey9KHp%jO0@Ixz-pfa|?451c=MOhgfI~pZnPFZ*di<+N(5SWf&fvLa zMpe+GTCnY9kaDwYw&qO0NxOdmPIu-I(eycMR>#(?X4X7dj|vvkSaZg;@&NhR9pn=c zrJUkiT-j1o;V#B~M$ieGv_6EKg9->y$a4WFc^e~!fU_soMKBRDcw^$s*-j8{HH_oH#Jj1t<4nNDMah35YC~stRosXV zWO0_lhi+FDg89IPJ@0q_;J{m_L4@TvC z?^tp?#%oaxv6bDAt#*G?iT(&uMl)-$%hE2nRE`<)L)|-JZDq>^gk@Le+$IwonYFGb z`fjp7^qBk2A@T0L(c6q=T*=F=r9@_P17oirRu0-3_48ZL5n}u}VGNm4;`3?kc(Wbl z_vE?!UK;j(3U5&A&m!W9gX!}JV(lrX$-w%Z63#deenj!XGKGKZ$=Eg2E*EEE2@Ok>+kWx?=yf zjNE0Ul++ArRi2xg>dx8RoOTcPtd3GC;8Q88r|a7Wm|T^$Yncv0(x!X$u*z57COvyw z9R$kxW)vk+-NoiLLLBqUC_-R}NdeFz(A(TEn0e`HclVoEFzeWUJ+JWzESvhji@YB< zZa2(s6efS2W7=*kU@z&Fl$erUQ9-NHTO7NSme}Nq6!2g=C1ZbAz5=}z@;G53K1;@; zrn1_45lo!pWM#?jg)D*dk5h&u1GVW8Ay7D=QeDXWVqqbUkCp$OQu2>6XsF@CoH-zX zfO_C=YrXo|dhI>DO%|n7)95?;zNZ`bJ_rJ)Lq~rCz=Lr)v#+bK$bC?l`k)vdxkAZl zgSiVjlB`z0{r2(c8rYjdLhi!iweFN1ad9==C(6?K&*z;=hFLYRaNN693Q>x-0a<1* z!M&|pl9ORd+f#XcbQ;hs3~{49pJT<^UNk8@dM$ZCj?eDzLf^Kau%CL~-$jwVIMLrl zF{*z)?(ZtqC=1NkanVSi+}#D+?yjA>k&<*IJLu`1_cA-D5V;5RS&$SbQ()-`^!O&9 zrXTCXOy?XCfXBNS|2L;f({im(xJmtq-Q;XVcYM+1rYzI6F@x_>pSu~V39w@?6cRYK zTDM8`jIwQ0;B;+)6N1^bFhBkUH@~%Yi}-)n6-Y=lcWM{u{aM!u&oE-Wk%eVa^wJ*X z*^#`q@h-Dh(H>SPZbMU8js2TP2@j<85X#P{+s3cH>K0Y9Zdb@}uxSYzC7pVpmw-P7 zuCb=A`54)SztmQZ)McRDK?Bl>WG(pYJUP>j!BtA!rw(>A96oJcYlep%7sx}ZaZrCw zn|5wnux2eOxNnM*5TzWYo1ZD3eqsQ>%^xbuS^QxbkjVf`Ou|X%Cz#Z zI~nAB9hXwXjYpBOv(>itvqHZ5O0j=X_tN1a8#+`dfbL#m8BIQ`QW{?^{a*5rZ=eO^ zW@LPBH7>y8!^)OV@XOI+`ox%Gf=kg{yLC<-hb0BBryqFye7+#0cvl9UZW|&l)ww+LjHM*+5Y`4ta%C z5oKcNTZkF;Fz>@?+VlA69k;cF44>%X>Rb3nIXWVE4VuocqG#+HK)xSPkLZ z_x(jN!_+}avUS`@77c%O!nVqjj&YMpxjJRwt=h>JhQIkc02ZIu;SWwT?R{>`(LBZ1 zdTN5nK=J7yM+8YAy_6h=6W{ke?TIGM)6^ag>mp|-EC?|_l zt`3E#b)hi0;L1Q@W^l#Gw>L0-Oo>0?4NUI3tfTbzTEMiMHecZ?7m(_uJ=ykE^fz4) zCwN|#D8SSv>D+@64ds`47{a8Vu)ikz zGgQ&hct6u_3?v>*RmVnkw5#76B ziHX%+eSk?E9d@do3ny!$=r1mvIda;(nC`wCuv79(XT`MSS&nWW+~T5uxJlNM9=IE9 zbhl^u$62=-Fk*cWdT4N!c8EbnevdM z6Wzg$E;R4~AumGwZ6`=X!QF{Av<}U{$i{J1A~}DL7ZX!8mz(MyC1PI7=SM)34%EE) z2oOCD@8mFhu;&YoAyN=ct^k!O(ucaVWap@J$YdTrYhG))yxE642Go{6Ns#TSjHt4roq{pkAc0-Yo>S>+e=14$JsA7)g#+}qQ%U}Izf z2p{K-`u>Xyw}ut6w0T{pJJiIY221d1V0nbxsw(&C@4l1Z`okQW8ph=)-Db&~rTREs z&Thg@2MqV6VDl5Uz{oBd^(6r7JySdxfmeU;yN$!z)6aWBd!5%iLXBC^_GA5ehYzq! zKm9jz^QeY=qGR%DI%~H|->fi$EUkJXBzrsNSQc0;uR_dQo^jFf49x05{~u<|cjoic zs%SmU>I&L$aZewqn)WjT5ThA}V?L*Tq`htnnzcixz2P0dV3MLz*$1i9Bz>;x^<{rO zp)7f6*EYc5Hbp;4!q=c9OuHp{coX!Hmre|sjD zBc?HWQ*$ZObhTZvm9fh$E(;6$-C~Z8d4yi$Uo2WK>+$Kzb|HVeIS(DLmHIj>;vU1lE67MR~Ggf|s<8W#NM3*;L%Nxe#Ftvx0Uu%`Z0B zZP2t?2!Ay*XCdMxnehX8iB^`P!4lgYjpgG2J`#jc_Tw*09eiw3FeP+P^^g}(z>FDL z$yX;?q0v1X&5~!S-`W^kZu}KZ4zBC^AAE0jX*QF#ZdJY=!q%8>Nw+CB>NENZY!k{#R{R&p+E(33NvWh}&# z-0Uez(e$=gRBw@mR;wp5T8)3?UOd|y&SSBNwvE`9kB^0CUFAd-6xn?0tc)zR&vJsN z-WwB9k19m9Zkig)_g7sPj^`1Dd?CFx!@dk7NIkqJ*7A1=yJojf({zw$dVY3a2pf`t zFUanDCSae5qwM~@a!l+nB{eNsbO{(${P1j5_V!D5<7b%^?>*(}GlN6T0`BH0<*CbB z8JfbT7FBGKk8|VnQ&4j-+TO^|m9Vxou!a@;1*^jE<|DoUE;RSv=%@9z@0S3$>qe0c z{|`mhRm+zl^bHi3v_}pWmw^cnDwjK^1`L)+4haXX6JH!e2P2mdNDdZ%Bq%`+i|N_n zqgedv$zt=4U_~tcmSq~44bD*DS&Jze^x}NJ}mQ*9>r)ToM}h7PhB=9cbtI`-Q*lKEyhYBLt$L1QgNx;_~%>j zT%gq(lN(AA`Qd3+CjJGU#9>V65}9^;_Rl8%OUn4wPekpv)<~l;WpzvJ<8+NeOKRTs zx~s{Se*4t+)J`&|#nGuH*GzM>!Cn)&78sLu+CLLH)I!`OhI_t$!Yx|g!}C|OJODv5 zGz*>bTDI9pUzt>D4^+;IBjeQe42n6K<-pS;JzYA{B+J$+Rv673-OP+Wa@gMo>KRps?y=BjhTo58LVxZMA$a@&-Eal2EanhC) z6USP?C=WytHV9YLng^ml-(DmF)5iGcu*n1hbCWhZv<%x7;Shc?CWv`lN?2;1H7v{{ z7ZwCZn*2CM#TE-KaYl{(j3clZu_*0>I@Pl=+OI-x!mh+>gLqM`JfktT zhm{|DuB>WIG$ECsRBLL}rL!v#xbjn2Ft?ii^jUR;QOt_YXQ#>UVW+0C5PZKqJ9 zaqxzJMiuvL+cXIJ9}(M({Wv2Cq@Yc)Jw@w4Py13)c9$O``O$95WIdt{%`IAc*>sGf z=Do{1UWtEdIT19HA8Z$MKVyL)S4!)SaV*csO>um~Vv6%lUb-YJx+x|=h(~jf9!cIL zXt)5$)Zbn>Z%pCsBI%2BFLmXJs4Od;aG+#=T?P~1O$QZ zJlq@=XUDP@n($jrF_246vpDV`NHax*l2M43F%6x!?Gv+?hc#^GYIhFQX6Re3rN?L{-+7wyRv^&#eoOYh8cBK2+^ZH|+v!9C8St)G$`=Wp9T?0yOs|H%fwSJ@LB1&Zz$2*C8Yb`t2fCR;wI)J;^V*tc zCA%#EQH>6SAoolPb+I$)Q`L!%X$)_S8}4T3%29j*#k4$dzA`XbAYHOR)9q4(3xho@ zqfH8|#DO*#NB)X-p2FQcL{6S@eY50V!yfSxykv8p;@NESjec1=nw*m;zEv^lY122{ zUgTcMiiWhu6~|Xi>~;gCjy|-ey?SG8q*G% zs8Jp9K9Np_ltUa(vO4Ph&=q5wf!Q4nK`JL1t6B1Dv3^pF$#efD;tiF~F90A4aTypms*tC-7oI zu_Q%-wiCya-xDFe-&}xJA#SY)m`Q~2*%Leh7@~r4ZAY{0fo>m^0=k+>YncS;wlfLU zk|gcCLU&+Ek_3?q*GLA|XF)+5d}tPQRI}P&p;Sv*l5|%~1J&7l&Y4ck)g<2Vx|znqv_l2qk%DYV!!puyCZmL@qgQTA8zeP-?XmTkw7arivkcg9B%Lg&5L1kQ;X!TyMWIbDJ$WbE z9;RsNRi1|VIQp(8P63hSWxpbCmfu9u7e1rbEonP_i9#_ns_8TXC`!pRxgvF+yS(7y z&cPzdF$0$NLM4XE++#;Rg<6)gm>d#`#nTH(F`dt3vP-|6_LPRC%(RPG_y0<$`F@t! zwcaYLjyIc1o1$}nu^$z^JBw~~kwQ0Cd=X%D8cOf4<8)u_#yAuwWgY|=A@ zf)vE#Oli!0Rwq`m3@kFaEjOw1Y_S~CGMtqoauTcx z(R+&zr6AR!H+ksDuh(;H)3dK9F#2sp;$i`v*i3(ahM$oyLK7YDu41iEftF&rlJ111 zt}Td&ZW+Cj4MMx@ z=zXGpSK64~@ib=;j#=8dGuU9J4nPX82B~jXAf+wtgOvPAA@yMeQbw7lLuwcac{G^M z?|$!s6zOkYF4sWnfs2uwX&74gqKaxi7W5pR@HBYNZJAuh)Q(vBiv?)$1Rx`LnEuCL zsh+6~2~%GG;1e;0Uk#=%^ve}=-fm6xKMJaU595NBYRrkBN*=9X(z@hVrF%IS0p#Tg zpI8pI4tZgt*uHAD!y`Cmq1)vWG<>PZ(yVrTRjT(jxylJIQ^+B-Q+LHzUWs2kQ)ML< z#|*&pd30Dk9AJ}o`b{d~nzL%T6_l8V@Ys zD1=5CvaK~->NS0F7kMijpNx_0$!IqLAojwjO40Sa}N z9r^f}!_xYp?eRQ#;ggi$(XAQ4%kF`H7kmzQ!QnN~lUo4=898?Z5&>VUUJY`JP3$Dk zQr!h`l7Uby9-?NIBIgk6TLDUrkFi3sSJa1)YgPDOb;hwLbzjEUU=wNDA5e)&+1FDY zzDp~!K&DsZ(lOMX9v6q)k`08-0cMyWr>L=je0+Lpnd0sWTHl7dkgd%f%A?PJH!W$I zpMOkLk!q@Hc{t-vHz4JWDO`P~`&jqtQS5^16S=~Z|Fi^H#&Qr51wcq4xc>&vT zC)J#q+!WV!nLB*5{i1l6B(oil0j2iWmil+u__O&r z&Ec^Mve!(MU>e-s0yQKZE(n>;^!|pp)%kXZU9{O<`$N7#lVh9sMvI(V+I@dDj5E8x zY9MI(hR*d|1RTjlh+~0&XC2Mjn_tF27X%r%7wA&@S2>6yNS7*xgH4w`C$fR)@7E6W zjGpItU{5g+ipe>upzx+N`S)-bL*$t4b8rI1g7xorRIJ>O4;`wru3smc<*#F^USL^c zV6r|`{@|qO3#hK=j`9Z=HPAwoBG+6C6E#l02e{k-uP^j2C6-Hn4NdkS`>RpQII+Z| zysau<8YYF!@&uqSZ?cDiXkNXKqAq@p*CcuM9tp9Oa>?qZ_KJV$ofbTpXo!8Tk!ZL` z_I_a(b-xAOc<;ie`a;zFCe)P~_PA1v035$`DatNBJo`wPVpp!O5(WPsea~jte=Yh} zYiaCqc0AC@W(Sr@pM z;ZQ}g?L~k9k%X)gM2iQ+S-m(?f*7!XJUr*`Q=Eq;o83ppij6FUd)&>Ts#tRs+x+(7 z#&2(5@%Z;Q?_d4ujpR2W*oG)?@Bez^Y_s%^p53&er`yfQjcLH!`|odmdi|}E^2s9o z1^%rd34De<|H>_sn?m=fh~uC>{aSkmpERShDnu%jaL$kW3>_|q=e?L|2bYzGbu2Q z{%*7&(gB$?;{O&W0@ip;yAwfvOsCB-ORt()?-7nURx zurXrOcE7g^2nAY(Bz(=JV`&yzF>AXiD@q7s7=qamgD1p2vO16hU`dEXE_tkYjAqJ+ zAxU;z#fucokDq=Tb@up4lQ1LO-B|*iV^U9ne;@L1S!sIoL}^GA4GUH?d0K&(H<=o* z)Sldbx?u+VYfoKcp7V+_Jn}PCMf{4uWse9A;q2votC?Jr{2E=(wKHMftYLhPU(@PJ z$Ng=!zpeN8BS7X~P*iwY3Wa-XW^#ka%%SMaNtHIBznN*bE!#4BuJ;H-U|)}cu1+rC ze;LgV#xq9VVC89?FiC=74+LRlbhul9foSILLVtzOs`0 z>oq^9JgP{z+c!xcKXij2;dc!XL9r=0C7^@j`2D?dT<| zSvu)e4774iMDcZ_Z>wYM0ZECcy|Rr>l&{zd#UTYyk*lOzWIiLNsHFygZT-^6f5$=p z$xy>R&X=>sX#bWC;g&ST?eW3QT51WH^)7Nd839a*4sb$I6+bS`Ltj$SwIe*$#bs zk;EcgCE`&?Y;xqPi>HFg#tZXWe{g1*>Q@(ZX05K?AZa(U+ggxNDH2HXL!(d$69q{m zm*-eVl4~f$)~*um#L?!YS~Yoq?dDv%leK#4z_axFB9wAdj8kaUY&Q)bO$quWz%+bR zIeuB=tE3`Hf);>|maTa+`QO%$kBU=l)F3sCK&ilcZY@9IiC?e>ma*ORkp` zSJ?_IflTt#Oe;(iy=f1jDek1R88OS0obtvEk-#`)0r3{53K!rwg=E3U#myprALv)& z550}Fy->PdS2M0@qcZI4;r8UYXmgz2aEX#Ugp|z0Y9ZN|HP_gzRcJi9LJhu)Ko}H7 zm)kugk`E)%JVzoQPNI#Ne-v@YSCKPuXPjD}q&7Urll0;1DjTO`TBJ>MiXaJ?)F&@? zvi2eC6@pYer)k>6NH_(^?ghl1jT)?j1&ZK*7RSSj7AI2hiUeh90&R@0O732C?=sLb zq5E}X3Efd{!nTH0?5yQ3rAN}e$`M+gIplw4UcbTZ3Zrq!ACQdee^ZSeM{dm6DpTW+ z+Vq)__}8?|RL&qfa88Zpr^jX>F^y+zUXsTclN{bf%#k5MCcbIU^2G-9n!}XW4s&=6 z()qxqIfiNO_=3EXoGUsn3a6ReQcxTS9+^8?C7+1#uAaeK6hh`5E00z$GIo;q9ZkFE zk1I$eg;|;+)E3fve^MvJyv%}bS6Wg^+Kox&1@~SPYsqEWM@Q z!9vVaX~VtFQH)S-RF1l&az2c~Hw^J4%Vdgw{4m5pkj%--U1=D^rVK__>SJa=QUO~A z=)dLog_CgDTf;>#Guq8iAYQ_(x3lexET=v#Ns0PEPeC4KKN=56+0n{M^Wsy{GvahM zOuo8M3Sq0OfAaEm$-$)Z0+?ypU{PjsfdUupK4S|}*S|nBL-BbBT}d!UcQ7ZJpU^w5 zkfOZ=ampN(+)^Q#OD4CY9*|6?Rhi+oh5YRbUqyCQYqiJsc(08ZhoqvJ^=`EnaKWVL zAp9mDv1na;PXbJD+a%tzd#qC~RmCJ3?&BE9o=h7Te}IwRlID^|RnACmQt&jZgSVxA z6q4UOI0J2~!9>s~$}A@Nt6^A4ss=FIh!Zj8o3V=^t-csi&O;A%rslAZK8}pvbB?b{ zr6_vrJKbWcWQr4ieb`m=LQbg>&WIXjogWhbS7H$B8zPeku|72Ekd_FBDe_mVQA7uv zniAU`fAEf=rgShIE|lrHNK?SMOb$FClcVoTQ|y`3Jd8Qzea!iQ9L!j+zPOYsZZa~U zPD>h7awo>LS(oBFWfiB3?w>Uq_*@8NC6yFX)0CDXm3^)TQtSs=@X*II6O$^fs~X6) zx21P7?yCn6k!>M)5ZP^1$# z#QKEkW?jtc@+k&V)G8BEcxs%GrH3|k7eSSG3f)e1HM|daca`Yu-6H{ZQwn{XUsYPn zm3P^C)}AQxe8=db+()jO>GuC>Qamq{HsT;`C$R(-mqi^KsB&?~kSMg|G(x-RI(2j+ ze~x{#Ku1~QL-6hleBX#1<<3klD(4Yc)!W^ZCM-@I0w(kcr?wm~T7HetO%b~*vg`gb z3^!d{h_Fx>Lv~FVBw0RSbw4pB^MbgYPv!}5O*pdM@W)x2W5ac7Mo}DV`z+5v2Pa8} z>JWa;h}7MCi@rN<$)uTfp;^AhtayvYe{kFPL(hAYfRIMfpV}fUl?Y7At)2C8Vq)k_ zuRy%)rn2ZeQ=7e6B0I0TVxcN&gxXg~A=J@Oh$~~)XNXLz4p2;Uuqm^}CMD6%Ox9^v zUkNN8W`=TG>Q|k1xPCnrE!Wuv`H+%v3w`^?wQC|VxiQTGGf^?toDmgWJcr1uf27iC z&rna(jAfyIHhl! zbSk_q-LtxGun$5cN}%J@0dm+YMIol|6OGE#wFhM5cD{PO87A7L-Y#xSe+jM$W!+A4 z94&Rqas-Pj)3a=wc}EEMHZ-~Uad)ENO6jP#7NB>lTX-PZre;Xwji8bb{xCJsv=fld zurOh>Ui<5F+8^DGJ}rj)fAN6xx?n)3cq6(*lJ0fX!Uqm&jYy{SVZ_qZp&!9KxPf@5)Q!VaGsqvp%n`Dq?A=3$d%agnRbRm!SCE+HRAtRuP4^42V80WWj*? z%|W%fyn~z`%@D(G0+trLI}N9qCUesO`LBtuD7aW=9z+RF-mIK$OCsIVCwNwYK1X@D zK#w{P7v{+F>vZM|e}(HezD|TAhgtk=!+AvK40qT*C#TitQHy#f#~G|D{f?)TaNaJ6 zc7e~aRT(ZDIyjnzkK=T*YN7|_0wH@~jw8zRq#)9x&QBEA<~HBobWxe`oUmaJ*7&DTiBg-*tM_ z5!jf>6XyHlh!7$aDo%jEwcxL}yO&lwF}TP!Lo|VeMqEFo6YTZzz&nQ ziPa@ZP69ICfBZAu;IXDttWrx)FMwNQT)?RxOk1B}+$#xnSHC7dsX=>@YqpMAJCgt8 zTwQ09x%DZu4(1n7@iQs(3rbEoKX32ky3T^|2HP6Z@df;iqWGVJNoKLqT|A-=W2M^f z)yPoTE61-~@ATG9xig$Prquj77XA<8v9$C#(r467w%2 ztF~kIBNqE|eEPr)i(F?|;6jFF?k$}QSeMzit;xQfPYaz&_RYj14ZDx@herJ;K={~h zUq<=ff1H^hU9L$y2P(rgWdMUjeFw!jS{~~YR@pTT*6CzBv5^~tE#OX z-=H+iSlvRu@>u0Ygws97HGX~jNxmXz%H7I{&p~c6W_#nvlNWjGk98!=8Wf3?AE8(!p(is7|>7(tE%0Jhuzob%b= z&4M^xl_{lLp~h(O6;fpx_EXlE&_69fp|f>8(=8+^hCI>3Vcgf+I^Ou)Te_uSIK+^& znKb(1h2Q0&C`pQoyqN}*%)Pb#3QxLQosqB8mmW1ALSB8XZnLu8>jcAoSRp~QBjv5H ze{dE^%XB~GjQj89;rFv|B`CeE`q|BPuAd#&$4i8sT|=5)RMuwMpzK-%PS!=N@oips+#d_6!%{ZK0n^3rDQLY?T#}S%55@fM)95o# zFlc?LMx9{Ghw%2LPgB958SfO#a#>BtBR+kqg=vxq(RD}WFOlr)s>+fKXA60)|3&r{aakzqs z<&xUoNc(NdY;*d6B4s00wct`Hb z%Y6A>b#+gVKs2kTI@j1Twv42gzg_6%pWo5=`TGy=e)p}R7Y0Ot;+GG9y+}&nqPZms zAQb_W#8w&c0<9Hbwi1($@Au+_`E-C`txmn@lD*+@Bi~}JKJKLZ2>6&W5i17N#Y3% zQJi0%m?Rch!iJ*-hXu(Z-W_IGh6_@M7J2TBG5m{+{lK^PYtlOR<9R#S7IegDq$}6g zeXmu4(3YNX-at=+)%)Pw5Tj+n{GVbYuoq2#tfqlDh(daMVnkaJn*BTiiNX$-s*#6V zW~;zc6#%)Sgerl*Z~~NPdRAe*ZvAd|5IIVUcDEoOo`74=iG=lYwJT!;$EWxoZe1eY zq(Xw%gaNMfr!cE7xJbOJkXLo&RX?i=IFtGNAw*f6i3>}#w%trru+R(IPMlbkvGB)# z@xY82#g1YMb}&`JgBwAVFg-jxJw{s7BGM|YWE%@GKpOSqx42CpKsF$f_8<^SMS;l! zS{+~|1at<3%P7>`GA4wpEs-)q?8n76L1>~GYgdA-4&eDENoPN8{uaU>-M5Yx!?&4J zBNe#CJBavC8la`5Th0Y3)5Q7x38D~x9NbZQ1OqKFP8)VS9X6dtnbH?yf^Z?*QGbZ& zkQGtjIYyyjUp9hPwOWQO$u(<-e)N0FvvW-(Gi?);p-k!Up#uLm!-60n&0yI1CQ;04 zI^JYU`rBRpIASzQ+(f0(A0M8$HrHQQ5Yd{@e!Hv#i7|w6aS9}yf)|1(K*Fhi-$T>m z=h0RXHo_zZ`MlU5=ZXl?lc-~RoemKd$y8Q?SnV$rA;NjL)|m*@gcl9uzlP%ivV3lG ziqxSSM+;t4!7qUdK2koG>6{X7)w!AZ0^&j#0-T*eJ;EI!puQwL`76RxG&748Jgp?U z2aea~m}fstyN`WX1IOXi%fkA9paes;sEKlQnq?8SSr-(F=+Dth>oW_{EZT(Y} zfk9Drh5^7T0s`IwQrfxD2(Zrv=QB@j37Qzoh792K8h=<7ohaxeLK3cu!0&V(6jJdR zP|>nkX(f~s$#pyK-^b{YOcagx2?fIV7_PNFgox+V#z=_j= z>n;nu1no+#+8zfE;s5(}JSsA^VRxX0dQTQfjLE^K$|g`^N-Ix+isNij$TP6w3@yWc zCC_9w({S78m63xaA-UZU`}4FLLERJ`sqYD+wJgeleaJBaY2T(6zXXoilQ0_k@umcS`bNuQMhAkh(P0)j(YwR|Kkc=DcF{zajM~FIN4t|b zRjyvkSP~=kQ+B6gIe~)XSpl@8y;c$<%Mqnu1FfOyn8($IsNuLf2ALqHpXZ)*@j2=} zXxA$D4jf=V#nE~z`xQG+2MPl5*}2od%acu<58)z9+`+d3~rS)x%CG~*s~vYDlm z4fSCs#|LA3mlSJ%!vook3adps<=m*vz`gTs;RTh>uh5Bsaz@T)mqL)9WwZF8kbsrc z6V^J~C`wCn>ynKj6nUW?WU}OXYSg9#@A@sYNQ#HF!(BHOAA7EhG5a23TdUO1apl+B zV$OBSRS(n|@oII(L(D1KEY7bs7+i+I{Ukh6aTRLwnj0j4!)9*>+)y-#Rgak`5zds( z`5V6Vvq|?ayWpm(j|^dn_^&}op>`aPfkjex8n<3Y6vNi@%AHE2^6A$qI?~{w15*|V z8d>Y*eqh(e>mFirIR=$B7vfN=jXwpAOk7)KI-xKg;ju;Xd;0^N#U0W%W}2ueXnXI| zv_(tEgYjB_J19zJtsP{2URHtE7#$pkeas~66Ta_*O$<-Uv05Eap(LTGTSruE5UZ=X zLSSoU1XJ$=YR2_puqZd?>tT|i0FZ6hvd-)=~Z*@oCX zx*7K-UbD7UR7h|akYN3Wyi`$7bp6wcbQU)^Tv-Xv;YBQCXGKbPn1DUQzWf%c0_HLQ+-H9MgJzT2&e| zCQt<({e2oRsEH*?BKM6+?2eLFb{m;nlNkbk!T{l_>$q@Vpv5jxs`qov%t@`6<|O5} znUg!H1+ED*J!&ae3BvLelEo0oj{}PciO|J|lm5h~4t~xEm!dG8U^5`1KF8{o6JI{OwH{f2 zvh>0oGV|J6@7Z&$VAKv})E+bMpPp-UxF$8;D{^O^2-+fOnf5AUG z=by0V@;|=mPxxa9s@k6}e|qrg>54!9pog9P?*=ic5VX; zpLX&(t)N_xp!uMc;W9w+m+B^e22{=gFQ$`I*ePQpw0LK|sJ40ntl1y60d0LJrgrFW zlqkT{6plcI9W-LVI+f7&`V{96Iz^dNT6cyQ4XFqItdz$+!N?+L2Pm)oD&)U(TE>%7 ztCSlN?{Qc?C8aSLseS(_M=I55S+?`f4_R7rM`p%BB?+Hv9PsKibgFlM2PGL5+{PK3 zAylh3k=eY*7*WNpmHChoM{G!GOG9L0g{TQxQw=Otxpb41T7d52jow-tfE!dwpABfK zsZA4b{g|!SVMMCv`kvJcWIK0wNue667*q4ORUfm8krY3R8Zsk(?SuP~OrELO@FS;b zIR{6yw&UWsJh=>FhCK3rTIN-)O1nf@XTNhaEK*!$k}Cy5)wjo3a#^Imq!3;TrubW6 zyik;rFR^8i+wotmHJ17=6DB0*?aF_cxEnxK+94=dYlj*~HMSjnqaIS9rroqz>4#3| zrd^+ff`}$OHC>k*GeeqdNt8%{9`kKhTM9-$)`;41UzB8NiOA`H#(qsb)ZrK>q_aSR z7QGL83MdI^(^=c2ECHmltGeJTiaH{AhHT9-8vFpJFv2QV1B_?~{CRSER^rV2Y@awD zD!&c)i1bqIs@Jvrep>~amG%j)&6bISnNPy$FU@&K))D&f%}A_Nf2GxdDAQl;m1f+u zqsjYU)O1lmnXt@iPeE<1_vTSvCb?DXMIdGrR`c}1FeP-lO~W_0~rf{Bwz&Ei^l_ZSxT$s#lT9F z>0x&4+U2z4e#1jt^LAx_7<+iQZk*j-uKhamf4EH3z4OAgXm5a+rB1+IqB>dz&0;&9 zfJ^Rqq-nFd*Pslsyz8?_rq$uVYq}ir8daykHep+8_C>r#Zc+2o+GYNT`+1E7ILEi@ zxuJF_^jsl-)i+t1$dZDSGR9;y-+ZUrCtVPy=|FAk; zj3$h208~J$zi2pcKC)i+C)H_m$<8Z48OtD!WJU|r>%<^Y0y_Fy&Qj>I9yPQ!=n*%+ zQbZ!dH?!aAvXgcQLL#Cy;{rw}fA;P!ak)gk$=;h~hpoF> zILiybPo>pcgAsC(6$21ecSN+iRo}E&9vOmgx#be2#^hjVpsC}W6>Q#sWz}-Ay69jTvH1LIpt&p5G!gRHePqXOi2Tl-%C(5c#;x22}D^LUH}+M_x`H=Ezpd zQ>CScW?ne_Jvcb#190ZenAep*PpFY`VR-q=wEFaMN27;=x6at$A~yI`tn@KvZW^e{3eVY$(Bxct1+WBc@SQ#RxpD z!u!udyLz{>31}nKOa#g8xQOlkcPkm><;44e{J^SG5`e>JNUm5^OTc7l{u%oh>p_`OL`_A$3Y z+$U0$rx5ef#L1q(Hy;QBHgY&`F^f?Fq_Dpt#Dj{Gq$5;;sadf*1sM1BBIOHlq-&K0~U>3-Q_B+tj#!S&D2Fn2UDi$fUJ9$<4{0V6 zq+BJ)#pb#^(o{(&rw>8hI^Wo4qg&kX7rsR4-w(SRw(*!lE%M9eei@Tc3d8cM$5E(w`10)X`V?wd8Gh*^AHb#-mU<%YHkI3*C~&k7pq zD;0H{O9hBcUx1kLogA^I$VJm~FGHk%R-?J$8Q@c0pR~j4f0K@5-)B5P^#pFM%T2S7 zyJCILacet--~VFtZGyb90yZ+ZeMe-nc-{uK(^n_^hxO5O%hp?~JT% zdHsbG>nt!7)h?TJ6l`@C25VbPp7bcg3itH&VAP#-KT81RbJOLnb(23YVIjdE0Ntwb z)RQa2IJAiVe{pX)ZExJwt&Ux=-pQ>O&Y{n{wa#D4;fw3NmCd<$XEj61UuH+;wpl@6 z^FyIRVaz$&arIPPf%p@|F8J!53%=CCQE?>fA$gRV-R&x{-oFaG)ydCZ z1+FmzDtJ2^Fz2&;*H4Ppr|l8+<8nSLP-nB7`Ra6Qe+ajWKxRhGMd0$4TH3rh<789y z{LYGLb9I4y$EdDx(B&~S^%VH*>i@K!LVQ-cQMy+b+o@*lmUc=Omv>fNP_6Ap(){T{ zWL*D=+||K_$TZ5bu){w2NLPGCPxg6Uv8!PL8rc)ZWHC_e0*aO|OKct3?i4lULBoe9 z2&L<~f1+k!==q{%ajY}7%fdYK+8vL1DT^0%;?(<(tTzj+H+kmWo%q65S~_c$QTGzM zRSlf?R5<>Mx~OS&(Sr`YY9sFt`1dIHQ#{wb=Pp;PV;*!t6sutbL)SP1xweHB(Of?3 z&BQW)U)!)>z<(b|1$SPM8lpZ8*~h+h$o5smfBzAmzzONLs=Mlw4+A5w_2E(|d{AgL zwtmL@HSV?*w==5P7HT$jT^ik?yN;JksLc6CUXaMdgwXu6oBHdbH1NL54ok5hWJ3Vm zdri3}TA;VaQ4;8EM`ow ze^&d~j^j)(`)24UGVm36?)awuaQ9T)&UtLEZD9eB<$;ZKE{9Q6e28v#_yQxQAnKkD zlpPOGYYN@Jy6HXif|N%Iu{2l}(pHvTj`eEO$P|Ngt*3nki}MA}AxWY&mb zAFgDa1>GdioRv83(_g|M$>&Q;22#~wc`c`JcqYpQ4Kj>IzX)c%iUY-TF<@57TQltP zdTCUTV8g70b~*O^B8-hc4E~rNNHY)Ocpw3OfIxH*{5pf6xnd~=<3fLrcdYs8jY%aK zaC^8hnBN!}bM3~UIUr0iEC4Rvm>OLb{A22zB&Roz< z$aY@bLBo89=CXA=5|XSABW*$ru)K)U>0?uYNi-FJhya*;>@a`&*~zDSfx?yrPRYV~ zCP>G$nErJpMjZ3pUlAj^2%9M{wRbF#Ufki9c{y^zOSsK|$v`DUd8Q>3<1H$%y1*lR zB=d$gsnd87c~qK}uCyrEe64|00*6D(Tw5upm{a-y)lMQ`hRQo8+ytt4Ep$=V1jHw- zmTR5xwQKm=5XQ@00HjYzql2m{?~^4)nQQV$RJCPlL9u zyS;QHn6ql^MOI0uq6uuxCG%mJ}X`9dULCp+VP^DBM{-n10m-q%)} zlMpb;A9hQmLWwn;rKk4e_J5n95#1XU9nGlkJ7IsRQMVG)w^vEb4Uy;RH+QsgL8-j1MyZ>;>V`kbHxl%o~4|rn~USwblMn zH2rNx(~892`;)YCni<@oyGfSGL1ee8@xpCm&FgbA0Tg@=j$|?=0L!Gy82Duo6QN%= zLQH?{N$n6@`5x(P>5?HA3H3TsJJB_QX*kG|b2UP?rnrtyvB#%)Oex3}KIK0epF0~w zYl^Gt2|n96OVq@GHUuj1BCR{Q1Isz4Ixn&WN11=8A=1z|k@3^&gXF)ou`yD;F(#J6`zn4$ zZf1mmf>UXqG0c?I;?5a2ifQW(_kYcxle_3Bda6>`VfB500R2|52bkUvGHzi)Czs2C zaqba~fn&r&`~wn!adw5kw7fG!!xC?r3fii$|%z`htt<(p)32T4C zy%1{?*@}~D^dkokhG2;T{8KrGZbwMosQS7bm0_GL^MOUyoSuyKV4PMCPdMXCsAO>^`O&MQS zxE8aO95sU;pe#~8x%cdmk;watzZ}e(fL&wN=PIMCq z8qrlqXv>)d)mP@YX^9Jc;%iM&8uv=8NZ{_ujQhV;z?8EIgN#cDu3vtWXErEd#A_jv zTZkwC;%5+52%JJ`q5B~V>aOdem1DSm*q_34q1tf`@N z++L0+**ZLM(U{SeIs9L@`i22fZwn`13DC|1lNK1)egaU#L_X@;cF4~BLEWpYf8?AB ztw=jUa=pIm*9*le-pj)&BC&LZl98BTDBRQSr$$sFETw#1DPCM(q%A$18v3dDtI)40 z+*0Q9rgA72i-kbRl>L-LMJY>-ziPaK;?2+ovdeSVfNO$XjQ(Mm5X)f8|AxG1$TFl@ zNE9$-qY_0)Cr+GcH{PVPND$+pRy9!QPjcARK)LsqDVz>N0(rcbZk!HQf5vLMcWDZO zxxY>{Qx1zGKK$#a58pqO`_`yc$$U;%{^y@Q{P9ox_80t+;%*9!@Ba%!f5Lx`aeMpk z+aEss=deO>N)+Xg)!7P`2}=+!mp~wl6t7wW-E6Du!{_K)#{^2w!9wlS3V6#j8m);h z4w*XJ)VT7TjGNiLrHG75fA&!scMAu3C$ivKgG3c*#`JUJ4d+9hZf#<*&u}JD{8Zl- zX`7+;*H$&3)jsL*903eDeO^rNJgP~f6akMT@W9XF3C}FbzKu$b2FJZD)~e&;S|1FH z6dtwZD328;m%#674UUfF+M{q0=k16|qe2^Te?Q7$aDr)DOYo=hm%^P6Cw~|!buZaG zDeC5JMFuq!kkXb#Tj*^wF>LpH1crTioTUt85+-qdDF%NLoBq4TQiPA$hYo&S2IBLHSa&HiU< zQJGoFrB|vtK}t;JtD|MmB!3JFBkCq?s>k-RBT7aA<~k;NK}qh+?L}(jpKMeqDW9!> zTGNXJorJ2|RV*ng|3rid)apWHj;2G)Kt?B<7?sksIc|WnxK6U5KZa;xKB%|*?M4g? z8ldZTRSZabbkL%=6VXqM1>#v}2^W}4#0#2VPCx2+Ia`T{^oi#70DsZPsV3{noB%Bz zGoB-pVD>&Emk>MO6i=kaOwgcN_NZ@tR-b0OXQxld8*pNLZcnkI{8U;;I;c?4*y_# zx0Fs?t(Z}XyJbEehkq>RXSPReA{*@ww2pShP_?8yQ?b(qE%fGLfHCCi9tgQoIz$eu zPSYW1$P4E>d;bLy{`B|x`ba9(!T&h-9~ztg@7qWm<(x$iXGn*s*2L9`(xF;WxsRtb zfLXb%Hp%Ngz&*7jgetTKKtFCPJ*bOkyjs(is`SO42|k@W9Dnglq5utTI{L&c#J?#s zz4>j)ayRLReJ2r~0T;0yHU{znbeVKdULZwIEsl#LC#b^2U#78D3fw-Dx%Qd?$R5-o ziNiT_au~AfibPJZX144)TZPV{7$NyGm&a}>v!1f9p+<~m&@P!NC?10b|9DPhz@{R) zjh419O0n)C&wuFqF`K|n6TASy4{RAt*OoOmeV9s#5X_ok?$CtklspeW;;)jML58h^ zi^ek!1F64zrzrqcO%Eq*VmTdo#1vUe9xGf3RCmp=EBJV)m@GXb0bGx0GlLsu2RE#$ zwosa6J7EKw@oEAE?1~|!7AWtBQtZ=od0V?-PR)>r`+rSVkwj&7k;E2wREMbJhNZ{G zY>K8>-;bGzpl)F+nGwUJjSRAQsbm+lQ-0o_z@d83>Tm;XUInVLXPQ2WRMV#0I<}M4 z=6M}3m3Z_(e3{Bmp+bIr8>?>5s1)+K*5etWRJW}S^)DE+rE&2TB{Lz73BU_PtWi{1}#@l-`)7suc~=8xL~ zI&^wcA}9XVmM>dqjtXVAEVGIccI{Eud*a4!H&t!% zZF{9cBgdQmBrGFKhPvuV)vQwx?2#Lw(X9y0k|^gmw6|f^kbJ@w~S&|UAkRAgzS0t(Qdp5RH z)kKKc@cCn9Il5eNH_K4Os20l`iZsm1rplmgWYMi>v3<%g5Q_AONn`fNp2^+yV~i%$ zz4wbxD(^>AZ$s-~kEm;*koQ27x@H$#MiOwxG_E=dlue_raG?mUoApTb$|(hWyMNG} zjLN#(oaKAvW3kw|7;ji){$A}M)G1gm%_=AmbF($PYszzurM5Iai#YZm9$KpA;SOM? zeW&U{Sv#0N=;3)drbK2cJ3sVW&jg)stTx%pnk|K=*}I0#>J$HF2o8Db=aHwcJ8HB; z#9OPO^pKKyv>5|UN!MtV{KRJ4k$+Zdj0F%- ztzHU748C)alv;_%+39zAlc9mf6y`#Rw8O@Gg-8`Dn&C7*j^uXw=Altbp?`ZXA9vF5 z5Xm8%2cQ?lrt0MeADh4lMN}!M)$h=hCz`(f%+wcYe^^v7HUevPo2I@a^I0iF zX^qv3(%ReiQUXnm#p%#9G~o5j7qi(H(>csoo~<=)-9f53$nh6w6oS@^a+dUw(6w{~ z(w4IxkWykq;!DR;g(QSd{ePl+-sqw$ttDj#+>$nSmyn|`u8Gl5>Id0K#=e5(lUpXl zzh5{*-{;(%dZFM7_asHa^W#@31x_fG@|(A2&}Yu|qDr3IiH*_)iX6%=Lr$9V{iAXn zWO!7E4(5vuai>c}?C@4B$_AyF=G8P*-X>ZK^x@4U(iHzXQ+nm06@RrQ58;7%p?d&U z;lO<|rfXwH$AhS(U3tjGNa@icR)^!CHyV?%G|bsG8Y2z5Vam@}+K2TpY2B6pi;%X& z1Im7p3o(K(v!Ewh)8HpW*l#UEnfgmJ?E8iNR?gYt3 zw-;HDITcktWQ9a{TYtF4*$@Wi5;bCI%RG-JtM`f~E3fd+19$wGnL50s@3X4Nnx^P0 zQO8Yc-_lzcr%D0UH&uUhyD!2+g5uMR3ee;8x2~Tw(T-OoqE@S|w0W~rsn^E5r z(v~_1JVGEK=^$|}xZ{kzl+TcdQ*~rYb&=`ObdV-d%otpLaBIr`oHz($zG(IqgDz<#C(*4d!4V-^LpJ=Y`7k ztDTRxNBbY%vO}$5((2y`vvUh_Q{^F50-k_-kLIgmQ^-vV-Txd0o*RiEeo<6QM&8{9%^- z>n^T@{)^9#>Vr)-a4q)KAV&!T=>^1 z71Dn0p-ORqdRb8#kzS&AjhG6-RMUx|@)aQ>Jphfezm1>DS}kS8HGF2AD9DkAmF?RV0qA^t9mXBPB(M900hr;RxjsS!1cyo`)fTYws&y4*KFLPce`7xK#2f z)mZW=)wJTUFPFB|-ZU)tZ$B+gOh@bDa}vAc z-G2_9kqeh`}ngUPYQ$qr%x~cavkiY+C1D>vNu; zKhy8dl;6#Htg9tm);Xbq!qxMtFAy+e&aeJxzIaG~LWc2PhXlP5<*9lopRcv?We~Jq z5P>?#im{s#f6>}ZM_R5{-TOhU2U*q)%f3Dh94T!%wT)j7)bkM&up!z4qjL+Sy7vqaANvuOD-P#+$r; zIYpxw0V?vi1Cl~>?7u%EnXyqs;FB)ploKaqya*f_e=gmib{%8r9D`#UJu7c!TFYJ7 zAtE1o&%yXjnG);?kJZb}TTy5gP8TJ7G*xPjFtjoVrKhzY(yYF{RYu?wHUgPWIbS~9 zS(Nc~SrlD^41c}sCYIKK@Cue#Du@%Bo}qbokk*0-UeC;52%krWP7u^Q&Ku!mALd*+ zzjS6@etWNvnTs3fp`gdV(~`Mr(?;GE&wnzCt~Jlc;HaLql6YUFuk9LMJK zEmAcCXorNIXCVwqGz3&*cUQr16#+Yhw}|~9PkE9@3_^IWA{tp6s)VRjW%x;Dge#Tt zK&LdB1KR=Wl=k@CtE$m$V*|~&0F|qAoeR7rf2W{#Der^OZdzcAN86Uc37r%aopXz> z0oC{q6qYAL#X%*!RqEy(1M zn5i*T-cH#DK->1-LX!wv8L97+DPhYArWrn4!-BkTN7N>aL(4~uc9;t~AhT;G=!LMu zf0#KxIJ*m8b1Eb-YN0wjQ^(>(ACgEb?U^oduj837-vlS?iZXh6WVpF2+?%zM>Z5@Q zC81q~q0Aq2>+?1Rv5jzjk6m5ZaNV_LC>+)VPWq)*B8LSL2g@*@S9e7UXiQWJIQy_z zT+X18;LA!=%_gu(Ug+Vt{b#wZ71D<`f8_fEoC*VKD}3k(Wj@J#(K)?)N`+s*aW9nV zgmw;Ph2~+*-jf+8n3-MH87P}Sef#B)-~2o6_|3n{uRnhK-P`iln{U4S{%w=nyo0LT znR&+#+ZQTdcfT=@p7iI0=aTohgfva=_s>+Nvvi!YKOdci3PP&sI0l|o;u@~Sf7iUW z7czbaxY8wqkbmOR9MI=X~w;{5BlG+Oh z(?0L!^7r!wD?qv#g#)dvtQBawf0qDVd*>XYza2s3C3^mruPquibrzQ@N@h?I_Jbyk zQA_agHVX1+LLb1ZjS}IC1*StspR)4&)xjfT_L$;EqW6xF-9~Z0qImRV6rOt2%{IN3 zQZ8uWgvIajHbycULq{+iz=tjbvf=4!Y!6Lw^pwqrjjGR+o@Dp3J6wjXf24+8p{our zFfYx#K)o&e#alyVv6OI+WN|}0S}13$R}5ptrsRRDpJJ?+=A5y`dobq@eTt-$%W{NE zLpqe%4T9M{hVI%G<^4l}NSMGGp2k*Gk zd1Ac;*JMkMU1Ble;FlaMO-u17Mzg5 z(2TXeHDeu{HpnWH*y!X%f|N~rS*ns-cI_&iRd7XHx8WEdpbB--1n`{w0tn3j)`JH( z>F`6_3n?e-=AE|kWPX_^i}CS!vNo$#R%EB*W{&>Sj#XKvV~x!20}17C$m4tDJy3k| zmZ|9b1r*c3=iCzDe@rI)I>6}xqOr5daeBp2ebHqZ>XU9yH{xo)jH`$D^n_^HM4tm+ zMx5WRHF-$#dPCN|(;boz9yDK^We<7+r&E~nUaPVN<|wg~F>=bO`R$zA(#=zVZUh$~ z3c=!_yvaJ4CeDhM9e_6AttGCPYO}m0UK{XqTJ`yMBO8Z+f9uFW|M@6pL8a}{qOnOG zkK?>&OFOn1n;GJXE`=sZiR1vNJMH@^LJU!z=dd36gJ4s+VnR?ffE3GAwrY$$lVU^G z1f3$#?WMIn%~~_akung(laumy@21zLTBM~$Xj5XdHmU_hP2aceiVHCiXx}bB+;PBO$4Tq-xKl|I16DZtc6F8!v_dj7=6IFvS~?-H4q>^ zY0xHTyNYW^iVsD}kgS?&b+5({`^Qe*MXJ0~)*@_We=Ukrcx_+mldTL}Q46NUqYO&6 z5-jKVsW2!>Pr)Kb&TAiyGUiNbCDpm*qSdQPW-bwyH8Ks08p9xAUxa$fyHU82Jl z$;y)*lI-2L_6Sn!}Dl%&S)W)c7>TY`@S_!4sh$U|XLk90% zo`G_ve=vd*+Vik7kU=1Vg+*BD$QX-ZWn|&^-KQ__ez@x(8I{Xb;H*GoPhY*cd-a7p zeT@$jmn5C^Qy%&z^)Jbor26ltKi~bSwl&ecj6oxe0S%x9N6($bl`}SWLcL++}?{jdW9lGyRx zkLr66f>3b+Su}vC^_kSfQ!GyUAM`;yq>05*j!)v+tCMGB{&p3TjKZPjS%EPZQKN}d z5p^3-rM2+r;<0sEKz4AZB%qp|j_s@~O>$BXHtmu8D`y{g#B!|(bJXmn$eAp9Y|s3{ zf1Y*cuEsx`)vqbiX%@_Yu<}tBZ1>Pra>+Db_EA=7T6iSW%(2Q-sE4S|)eJ0JSZD&TKP zZ_))eB{LjJrY0Up1k0Dz4W^p})7hs8f2MOpF#S?6o!u48TJ>?cL%7Ii_4F;ByyfHM z;tqi#Z8I`lo+)J&(1>^a`V?s|dLwLlRQ2hGEZ0bYdZc5qUDtbO%VQ@Ff`DY-Df*A9 zMQrK?*iYE|+Hw({e$*f0Ncr zT{PMy+Mqk94zylKS`Xr*)!yQq&ElLFl+Z_%Fvx@W{5dFLBC6nU8ztgnDRIc8)?y5x zW@VBqNvnJ&NG+UJjhAK8$v*TtEa_o__N3I=Yv$C9u4TyDG!LN_jOvoMWgU5Z;Kd)#GlXD+}~QPn`!|+BK>5 z3x>L4DOn%|nLuuN_3{`Gl3VS8v`IH6ZK>_dImhNe`SK_tw}{W&1DA|6~t9_o5Bd%3pEp9bPG|%?mVgJCI|!2 z8gccdy1vU^@$jMzwP@*@L6Bp&soe=$#u~OPXR8>{e?eP}qRc8~dSQZ>hu=CUXe(4(p=Z=I?;V(L+;oGZfi&`5wS~^+ zNdw8+^UxFZ@@dWjq>Q+a zj6|EhLb$1|re|{vez9?)e$HBWNh|rCa#z;bO`d(hQd6q%W)xm+&=DaRtE}S(e=xKoLmN+5r5ibl$Inu(6Zoo@Ko5zcJ{T_?(QNYz9C#fqy%51O&SU6p%QYo)mf4Jn%03FjGLZ=sneBIkFxNcln z^rbR%Dqq)1uP`y%-O#HYjc2{uv(7Zgs~0ltxfQ4RUntHcuF9Zu>EFM++^#y+v&+ji z;^Dn0Pa{Q2r$4Xqe141aLCNwy_2=^mLinH>)I45;j+f6k((Yh!2j@@+x_)iM)ch@J zn;cohf6)%sSGmM`n~w0ORcywhh&e zD{15UEaYxK%{tf!qcQE*8?nk{sx+o+Td?1gH(<%NNw!?@z!?*oos$NSetxr5#t ze_WPhM=o-=9NUBKel45aSzyg<=7uZmMG%qAop!gCOJFYrQWDAhey6*>4oT}FbMA~J z8|YiOprv-l^^1OeqUmHyHD62JvkNXP-#EJP!G1DV2@hYGk`ZVqjb`|x1N3gEO@G;P zAyI6gdkep;D|t%l@xsE@GMDtWh1B=JQnD|ygTPQcEmM)+~XzOWZ*{Dxn-u)NL zLu?qALAwqqlW`g=mw%NH1%J2kuCM504=_WM#a+4uv1J4~B#sUVET8Pe4s6+R93wMG zK0d{LdF12k>6R@7kkCCdT#B`CBt3n7qNmp{X#D)mn-?E_0`$Zfu~Ne6&EHOv5^>UC zi4yYk=Bv}^=eL~lw_H*DkDpS9|AO9q@#c3QeZn}arwdLrSGc&J`hVLvM%a@kR#WDN zSYoU_Juspz55v9>!&*QXbze`_Fa!YZz?|LY2n67#ia*P{2hN52CcN{dt~*>@N0s#zuCGO!rDa^tea2aCT|bKF-SH<$aA3@c63;-t_;CcV!%!jRPk$eCg&>Bp<-uWn zaQ(p?90@Lo0TgG3fQeh2|HCExgE4$6&4A)r*!sQm{x8V_wqt=-Nd$nwpaF#h65|tv zC(txL)cSAtHpS0wAIiiLHn`}JrV=^>=~n<{&{ z@yVXMT_o+H69YF!@gY4~#GydsDNqd(r%sItPL0@cYJY0_2yKW!>(&xTHZD#^tjL6D z9TgcI8h23dd?;^gGyLA0Q-TprZQ3C?KxJN9QzJSwi-^n)m3L=!a)Uf!XiFHS#wcW# zP?;Tsp`mq__>h|;S~o|IeJgYq6r%qIt`%wqTW@)v5FmK%IgTAHLpbPLJ6QC?aj?9q z$uY!7pMRLvl7U8cL*L~AEt;j-cSp^m?YYQ!lG(sgh+n492#)*LZ@{Q%z#){`$l#0{ zOHg84IoTC^K>K1vx9Upn`97WjIkOIC9Mut5=KQZQC{FR{=Sa`i zN#!*w|942?3ZF`u(hEW9R*bxCR7=Ia_%<;8a$w#rv$JUv%w_37yb$AqT zBGLXfM`3%1=K^D8l+$L$&q!K;^IzNtpHLXkjRUsUR_}qtf?}ACdmksUKu8z{_WuVY z7Mdc$x?ljDD; z3054Dn_3JTyLNM>|9<+Bki zhA1w&;H+cx1{N&|*U(V}`IaOsU63)&c7#jx5xPY$OQ7z6j8r6A^&n^ZhM+AnZhw{D z^p07ey9lC~SlzR<=O0}OP!^^xMJl4sllwT3&iXT^jQVJp%+Z>J_P;nR~OS7xu zaHkZqVWcLJ2F;{bd-9+nP3s9i{PU}!sn>+7HiWFG?^6{jCK52_$6?IM9lI!rktaaV zZ6jcPy1q`5JdV~0PG(8nIFGeNEPuUA{rmT`K0cG-RygKB%Q>or(5r1jaex^xb z)NDF@E}<66Zsp-s2Bj%}`QPN=yVBFNb$$Y%otl&^q#6TO1kCa;7S_c-bAU3+g$LEB zHYMPa4E}Fjj)97J=+569`FU+Rpien$9g*baGIXYqO>ko^c+NNIf>TFy8374-G*vmd z-if4zxrHJLRUi#nn2!fl^Kwdg#p|rYQ#F;!ke( zV=(l1d<2@t?P#=&Np8W%M-3P(qhKK~u0m$IGem`pin<)Z>04GG0mdF6Rr2B!2!SVe z9%gfbSDEIlDn!egzJW+7jJWT~Ub9kD(S`#a4MiD43sVzyYE=~V*ner}#MB&(oaXs+ zcU#Mea7d^Z`F^o6?uwzkY$u^*LT|~7(;YjHC7_6N5@k1uohyO%rHvQ@W$9Yv`%s-| zb{Xyfb&zmTK!-dSS62d%v+7FttAHv#)g?kq3Zjl4!Iw=W>3GQHyAp;f-JX+U zJ}3!lOzScNcIu%_jk*iAkst3&vFx4UTf+EYdlfX0u!>5Um3pmKUVo4t}CQuK4 zMWJt3I$Qxda(|talZ5gVE^1lC+X?-mgf3CKjj{((ZC1q&bkq1;_29}>$6=`@3*9)T?FITxLALw_`OglO_8(U=m%TtYN&ghWTR zYvfH?ewb+dG89g!#;>5-?G)wqfQ^p7MyFhN#6?TXcLPLl3~RwcZOW!LcC_L z-+9ZhMkZ^yNd{jB~mGioDBWG=Dhuq7Sh#Fx=OHohVY$RPDJ>Lo3-# zzu|3PuI~DB+pIq1#$||!KA+D|tG44*YThX6zOL~kC1;w{uMi47{KASUh`JB`xkK-{ma_tObRA9 zV72PKAvzO;Db`;UNd?BfGojM64`9XO4y)fAmWc)Ga;7yLt0EbCNT_$z2KasD&wnh= za=ukP>uI%>HRxOMcGA5&ynMb^2Z?3~+BGjLyA10*!;1iqvx@*=`xtAUWVh(<;!hnC z_9c+{dmZrGu4&Kce_h{6k_f?xRUY;9RmfaE>vBGsb$;p!N zF^w#_3^T}O?CLj;Qi>wbtb9d&Oc2G)p^O~vYsK~Vn-qqI+oFQ2#E)eY-GAD0C+@0) z0-~+jcQ>pSH;bypEraS6CG8Cv8O8J?=J)GD}B3w;;8pN!u~B=SJc+*!+O;C3t&FvtOCsBl7uT;+%#?6 z;}-5Z?GfHT&^y(L%J)m_)AB7{|JUcPCsC9}9TCU7lofh{aWbBUyIWB&_wQCx|CGl; zy57Qf)H&gUTcgS8*|R!akCy0Ii4w?rB(iPCJbGSUFvB&C^m@P~!hg2-)!d@1FSpI- z;8Moh^dG-@@#Bm79w}2Y0r};-7oUGYPha8Rob;kdpZ@JfzQh0Mdg#-4r$4>;W48cT zcuMV(o@{Rg3>vjlh|?ty1}UDk0;(YGyyDAF(L8=OxK$<^G79E%tC2UTE_c~HZ&Vjr zV-A1OGVYokB_5|)IDfo*Ful!F-8~RK#nDW@;Oc@xtEzZ^D5grQy3qL&NMLQ9ZcGCx~52V3gK4>7ylW=1bp1BO~CJW7fIv+)1Ln8 zZ&rCqa6R>^oqu(ox37g|vAw%ut)bg~A_c4j3G+sOvr=sN3`Y9uQg?=3XsxTN*>=h| z6KJ*6YiRXKSLF;PxQ8M-E+q-$<2wcX!aD^>Q4~Dc?(uqfJch1N4vhXhdCLk3#=7%u zuAeB=_TH~v_sP-SUnhMVB>?{U;1!Mzr9<67EkWNadw(>eJ8H}h@2CMi@81-jJieI+a5jJ$I_~f36GB)A$g?L&m<_B#;hxE_i2HgUTy>9 zv{`+lH&E%qB(|SL>zfwC$GC7eC-=m7tvsqhgXKgqURCrS1jutKh$iUM`lWq!R2QB$GUDZ{!J=K-%#=_PFW$|kgk=MX|owniJ>K&dEcNATu4vUV$3jY(UUPVpk7UK`C zI^X%WwsOFS>7_0^&YfVhM7o^v0^VOYV@4xr$BQkD`+(KXtYeCdeT* ze~m`>w!TK9O~=s6t8JP4n2sJ8nv~Q;gi48trSqfq;%PTb6|2;DDw;JYX>v|KS9a~0?uBnHW7*VqGDqfhs7rYuTFtZpI zx1(lAG~gD`nsUfH_Lyj~DEi90Q%W&r$j@lK`NBx5XY%6UZ0~G>HDNPV6_pjnc&0Wf zwb8G6e`Gr5msVS2;O&m>aQ6Z5wVm{yyueMyxbF)MstzxRpCZT)S>LV4ce20$n-J!^ z+>(Wuy$jma3{4BvY?uMbQY_?UL9&gf`hvXUB?nm}1NnA14grK^>n~MMGy58P_kKJm z$!nj!A}$wl!+47+<`t4r4sYpKOFXt|2R*jqjmF}@)f}QfvZuYSzjlLZY zrWPo9J%QeG7#QUEIeV7x-$z{(dClJhUTp(v4h4w+q~4R5#NdM#NWyLarA^7>Wb=M)prGM+0dI0BjLfwXtRB2Dj-rk( zD1nb7rVcc^j?xpR!Qr@-gN?7TtAKEWiuhgitNw~GmI};h#O7<6%bb)G36mkZXE-tX zELa!V&l1#3N%zJ6R&x>8#GuY0r-hCWjMYM_FZ~M*F6g}1oat0iDs!{o-BevFk5|Q? z6rWzBrrf(D`?5S~AK1G3qjh7{Ks$Zz$yF`Tw9yLAN^CQ&2zEtezL2rvX9UnH*s)Yq zS4h=lr^*=617BfaB9wc+(y=Raf;XZu8{xs5kw>f)R5ea0g)%uZH%ajp=|B_fSJ!9EpWf_&qfPgE~^ zwbukU@huJWedKlU7uK?TA7@N#;{aWj_o{_#a;ki-A^7iDpUI&r?s3C;=2~P-J{2F^ z+EiRyQ>TQKG%moX_g&|&j*^?Nz`#HS{-l)ZG)1o2&!%SAzfIYq4Zj2`Qphg4kEwNI zqha5+kc2p2Zx7o&8Mc8i7{c-f?)Q72L|mdHU#ivW$Gy(iyL>+1AHC8>KXz_)Zn<6R zUF%u@&;e|I`LX8Y1`v)v@8qqY_w=r>o$*oMvcEg7I$dMy^2YwA9VB_mF|CC_T(6Wj zDmuCaTM9~FeU`Ys6Cwh7?VL>S=?7mSWn$h8?N~PMGq~R)CrPL(xq7J{*J7jGcQ|dNBFl6gI`^`Gf^KonP|kj9_2_0bW3B*yk*fGNIh*3dCRr z(_RxytZQrS<72Ov@^k&el9gZYZ0t_0E0u5*ESQpx^PMhkNFIY*Es?XF*nuWNK(K znlZ%(l3azEdMqBJc2+U6W%OfLXxCFd9@5U-MmZX1A9aBJ6CcHN6)P#<5BP_I)l7&O z)s8qPRH~UDgpqN><|GRw6}T8_iD!iiTA|qU&#_-3N+swDNg-w+Z|a^+hhAv!%=fI4(uOd8&!mreeGKe3!H4zi4dd3Hu2zVo!&qQ3$a zYoT@rWTUPw8@VyEfR{^Xg^JBLuVeNi$b&Su;U|y{LgmBBHF(^|iA{HM5crs8?b>&< zr3gQu63`tZvP?30EE{|@wM9yS*N=avsvO`I)e&FY)Ti5n?c#6{%?^)}xtk=Uu;Yu=O z-Jj4^QN&RT^z7h4`OoiQhEyEm@}h>n9``#V6$eZW8jWCLH||2_TO5LDe{m{@K{(fH z-_a%@USky2vJJy8N}Q)qUY=6!T4NDKzDDBRE3$)qKiJA)xDUd`haT_3^9g>vmxElZ z@%@DgGq-{(Ph&XNs%u0g{F=BE)V{xFm|(ohJp!GB;xBV4zliLLzE zV?};9u&UyVmbteSHZc)6tg*;k$G}~`95A3tH7`?piC$W6J2DPcaVd6vsYKkyAIU93 zV|smA=)pswW_c~q!B>p3U4xnaa+R|(?F~_;gI}6ux~?pQY+dCUW8cIo$7utfFI~`h z-W;yGC1Xp8-7}!Q$sb40>HPkQIVDh1AYb0*`}ZKVc>BWWa1~Kw!K}qXZfq~GgFV5= zCRa}~Km~)#uh?pZ+b(sH9#uo?;rO)oP7GGw7GIjPPtV6ogN?#-`Ej!(A~=@2VC;h8 zMiXBtW$u$!g#QJD)@em4q9Dx7HY%he$l*3I=v2S=Fqgmpiu zzSUv|>0wYL)i{{~PS-u=`*|%S-htEKT8{Qc+8*jAn&!7FBtb=v9;nY`l%km)ESJ&1 z&pU+MGT;cMVASZS8GBNvC%`RBwE;)#z?GRp=`pj_$e%8_KV(sWj9UPX0rHuxlqU@H2B5Se8EkW6Z=t6-E0OQ2Ut8G)TwHF!gt@A8HVJhup!f3>Po_X-sMKMa;h&eYpU?jC=Sb% zZTR3Udz56t_zEAWTz=4d3Im$Wu4)v>D(?(? zb(vF#N#7oH+M%moMUf)d7~`|Ee=D;mufzU;)2@;U@LO#IbS$e{qV8Fi&kZ9HB+&`kE~ zvS}Z$Jc4&-jsu_KZzo=+z#Fw^fbMFql1X4s&P%}a&SPgQG2x*n-;3>~6Zv{-Vj&5J zA_!%=fnyk)&L1ld*X=wILueX^3l^xASu3j9-w3q4ZL&lQ%})w??N&q-9%?+hNZ3M$j8teeC%9|SbUl~_c|vC z=7Tlbs9B1604$lZCeB4`fHvKY8baz@(x%^4i>_-M=lCYZTWlTcRcJb{4=?y+wY$yT zmCv#i?5kl1Hv|4Ceq?a++(9kv;s&P7@xCX4)_$}8;ZsyyUmmZYj@G7N5Mg(Wdr+?U zV^oe^UJD;DdG)ecdH>k+Z7>k^);Uc2o$#jm&3doCFyJtt(tA5I%zl2}V;F!!4i95p zP_wCHys>8991-29c7o*FHz0D?E&@4SUZa02$9BPNt(_H)3rU32RwvEZo*wLx>T?xZ z&~VZr$sG*}ytSfJ!^17kyU0wb zUNeVV&Y;0n{rR9hw_IvO+GL)lrMX?9^~#j~3m2VEgnUhrSa(&2$HAx#&5mL(Q7uB* z>ko4jx=A+I#KIV$FF-rhry&~F=-aE2UtsLmr@f*9U)W(zZx~t zIhHAjg}{+SlwO9@ff`BJ|A@Tik#{N^y~o z0JzOmUnD2U`v&@R1gnWnj&iJPGiic#gvocGQQ%+IpOF7Cjmt8eylr#znaI@Hz74Ilw+p|eg``uWFux-)YF3n{Cp~JBN6h<75}%y)dj##8_HiJmj;DoG zkq1}BhE-5%g86@nQuHj&9mrDI&`#=aQr;OhM%|lSlMvEqBdRq61O+ zKR#%7yN#(ochMb=tz^Qo(whGIbaa?m4*af1Dsz?Uu-cJxeE3zh5)c!s#u`?bwm5?& zKmChcn)A%Tsg3acjok*hukq9m&tlilo+8dll!ro&$olAGhW)ji+cL-(n`*)6W2_AA zP>OLLLeZKQtk3w&S!Fo_xr&?NzzkqNn#h*IgLfK4%Nh$Ftvw2}@yyR0E96ibOPD48 z26YZ=l~WOT6SBf4=jroa?5+P!eGk>FkRZJyK&Z!S&WV_v#Ny)bXNh&AO^ zqbRXGD*1x@(>~fxB#-7=F#r#^aT&hz7{VQOlAK9^GJ-wk7Ku2 z!SNWu_e@Phfr5`fc(_sV%XQv~-NYTwf;hIOYXg~}?ZCoQcdZnck)nf!$t&*v3F1KbzEW-_chU1WQB-J#;cGOwHha^;O92+5pk%LL) zUagF-%^J=lxazouzmgNtbhYLbCwP}?;!t#zL?NH1s3{wE?>k_dpetQrRa{Z>QSJ0} zNA1{8dQ|4OTY0q7;#%rP-Z0Dg_q2W(EW8NmPE5#&1v#->r8{v1_CQ?R9K4)@uQ<3F zIXDnk7g8#6zmgVDS!>Mu!N^uK_ONjGvi1TxcOL9o_ zadAlTaBxa<@$>KqO7g#<68>LV3{lt>EuF00ZKwnU(y;AunbW#UaM1uB5pL)8tk&ML z*7Jv+zX$gREV1x@8W1CUvCDu7JR)qrq5;Syxe-Oe0SSwWC;|#P5r={r4<^b58brmy zrbtKFB7x17clEHZAE2_~Bp1-LHh0*gZ3y`T=GRj22?l6%R@W96mr^=9q&qu0J5OL{RY)X33c$@?LSU@X>g_ z7A7M6!PKJd_J#%PHFb-O8w^3TA>NOgb|iwBZmb_A?Qp4{ zUf1q>L!NeQp?hXB!=5&^K`CaK!!7m%CMnCf4UU;rrc;1Hb(^t66e1PC{3E^$kUISIykVAxdn07J>-6VnK!$Nrw{fdjaYe zeHM&;IRSv)Q`w;%Y%4%}^NvORJps7m*E@vaRJ+^=RI@Fo;!7F>oYxElamL}V%x;Io zgR5L>{HBWpN>O?12GJV~%?f6e+UN<+eS*P`ZM2>SEDN2ew?or0vG(f`h;9vsdu9cv z65ezz8V-tAoWj^Y7zxHj!>r9Nb7gq)2D4iNPMv@T0YjsKR}BI;gPC<(u{vG*0*l}{ zi=~s*u{SQ=6VU=Df}D&G4z0@pocl-BNdcZ`7UuvbHDCFmMcyePs&3AHQ?OXWa*Hvy zCr9i4vu`AEmJednpc%DQU8$GoYnpdhF=@ZXtiKGkM0?l^*){E$QOkB2%J_Q*FS|9c zDXjpRISM;{D}szo6?a`+BAq%Xk;|k?sgrE@oeW@|DJ}=k_GQ`z?aY(xoO#duqbDW7 z>88nCLwbU`OYwPK&Q9r%Xd13O#~(8d8NovtzNLo_**UM35E;QyW9QY}KAuVGG2a$& zl^7pR2pT%gR?|HiXPj{T=x=1_$KJg5YQzLm&4I2=Na-1ln^>-IKIF01Xu(6d+q-`r zHt$bskw2{=|BhwqCA>WAoRg-Ap>5tX8=)2J_{ib+@7X5*P*JB?oh6XQBGi!FNIpEr z5Q_dr^CY}9Dd6T~dQ!l+pa7&SN8$FXf-#@Q5)TB1aHx%M4|vRhbZ&$b<5>3xaX&TO z&LAt=%DsodQ|2Vms_X0O>(NtP$ast9_fcT+Z_g*DyogI@52^4beeZG>6~?~Lv(qICL3W(BVbIK)hqgdvD0^As@=_vPP~m3)Wc2b#6cd`UHEX;-5FgMs%NkO) z3GZ_rq5<~bFYm`m-#@n}1uVvU=x)(v2r;CZu=V~{H##Y|!u%DD9z#BR5*pZ`cv26B zLW};*kSkOy2q(z7;jZylGzl1opr_EJhs2Nmh-O-mf0gk+!g-}6{Q0kRX0iX3PKX*n zQ!oLsgznYDyc36h*Kel-YY&)`S4W`NWApV}EyL)Wk~&0?*W-HjJ4LEcL|6bvB)S`x zp!Eu4RrnEtZHdl4!fbbVW6m&HO|mtClZ1HLh4%u`j9Ylw;oL3+)BQeeP=s4J2H~$< z@N4@$+MxNj2v);iyAYoB2Y5qaZea_DGhX23_P_FmMpR!4sk!vAeFu0uf-Vr&@9Bv| z*>Q*B$0;K75(BVAsSv3G`7nYhV;HYC8MnvK9yx>sQ35e?vk?Q~az(NYIdbdce7;Ezp2K9I6&EX|c&j%b(FzNE*O{9jL(Q_tt&_|)5wVQ9~3G@pDfhDjR&5{)Hk7OS|nM$0Yf7Q(nw8;uaB^oZ&5n1&%anb~%r|T`OAZ=&jB}Fr*I2;(FQ6V*Q{q-44 zbVPiE^~5w&EGmY;&*9}%D{h{wf|W_V^rl0gYJ=QD0*Oa*>|K+W-4I9PvaSC8CZbJ5OnRh{$9uO43B;2Gi2$^t!uN~lRLvG#VTMh1X z!8{vuYfG53Civp#0~No?DI8{fq3*#FD+PK5ro!`1nA`8+ZV7;|qlWVVs$%e^obcM! z+zp~vnQltX7>(mTHyS5D(TGLEfu@mvMu_6r6RTNBCSXfR&Dp|f%0)Z44o@Fo7gVYN9c%WLav4xzPc#Jxrzna={^}}pN{)vV* z+Jb51d|rSA$2j?}aENfPk?HerQH9^|>2fNX6a}7->aJJ}PjX&8I_ehw+R1s}L|rT-T{2X!AOHFA2?9;Yn~dKHY^6 z@zeECU!q4j%le1DiKVA{KwohlH8Iyc3cM{?#wRARu=!LV7LM?TkoBhxbhy<`yb5n> zX#jZuOSQ{ltN1iZv}f=M1=wCeqhBK*-dNZS0c#XoJlhoU$6~Z+Cv6lwOkY2Bg)8#Y zHNU6x0Q@1_zNl@ghLWN?@wCluiVaE?^oNGK_4cQQyYo+%ol(|}U=YokNQPp^9;1}u zVmL4|Bw5^edG_C>lB!&*)e0Gv$Q&cFwfjjb|5k23ZI&;KZ{U z!*Wq_`EH+0_G^ys^U9vhjhHA}AJt^&`odF*@kcg^PoctS5(q_DdsZhV&>zckpHCZB z{B@9Cnb2H+eCpL{KuR6p(!r=QwLH@G6Y9V-!LJT;tY^4B34};?zwa^>sVS~QIBPw= zXP>eF@(+!fmDYw(!+OM{Pqp=^H{Ct z(*r&(X=h)h+IBgHse4dvx8#q0f4^;XL9ZP||DW+rF+l5$rm_hVcB`xVF&DaU73_Z^ z$l?RdzJ=cv&M$PVZYpWXbKUd1$mS-*UE5cE=C(GTNP#)g;1a-Q{#bsIPZOKsfAo9E zOIlPw14>WRTU8fL;qCOR3H6y7gGj^K!h!5@c`8{;bdEytU=(=f zpZY5pRq8W!k7>)P1o(QIHfjY@VSk7gIr!OE!sVkrmNG}ba{#O#X9)k+BBq2^?8g{K zv8|Q^vaWlwN2m7{k=Vrpu_*k^AFA4V_5UJ3(zEuk(lWam38wkVJikAoa#~lf#A$WV zRi~B+LrXz~tQn~Noq90&r`2k?OObd*w4yde>3Tpf-jj~HsazO6eyZj`VjDl#ZjYnI zwdGN_CtnMdY#3Dv)@}`(Q%)SC%b+{ZMR>2iF|Axp^kI3?Uk3`80~100eCb8<*Mt~F zICUsCQ5dHVQjCe<$FgH-HS_iZga z9K+6@Gm(XIyKr4UpE-Yt)^H(V8(3L*7^ZL7CNl_XlK?>1CFl*?Tn52aShv6GLOZv2 z_%${Ld}i65wl~7tJOIM&@TUNmtiVU=HbK#6qSZu70L5u2{!72-LxAwv(fFqOTaq%` z%Q}sXj)zM-r{4G^D?PVNo_U}+;|v8C_n;dOi8(B*$a+_t!&bKdkU1*!bi2_oJXuwyR>J2@jx-tHdV1sIbh==C6d!R zlYPEXR4Mb&qvBlu!JO5$RE`_+X(~>d3>K_-9#T_r-ucWVbPjb7C?=WudL2~>$Km@0 zGtX;gSdINESh(GZ)$t=z9++LYy%Htk>`|mdZ)0u(ls*u99NQr8sjqpAkJhnPD}};|8f9pYh!8pDJ3|xF(#9 z7o5M`3}>DPR5V`hW`{LfAlh5|MrY&a4Ga^9odQ&w^!ZGu+VI8E1 zUGeE$AKOr1fk7#Y{-F=IhT6xyzZAOVBJ3@uXw>Vj$`AocPl^5oM%walKs

UT1`tIAW?`BDh9V`Ve(?3;{x;HQ@vFlozOHkHli_8rZ>69aPkdwThe3N*mG zeV?@LTx}j(>_PrzdsQ-(#%KJ!mdCND*=Nx+!B(T>X=ta(`}v0Dn*YV{B!l_X`|B;v z_9cbFchfO_eRnZ=*o|J!)NSh3Y-Zy-9iE*PL&_oCPUs88GbsvTB|pyne&gE6X^P42 z(Y~EF!lF&;)fn#sT!jhKKoX+I4WJ=R#+m((FZ_=YoKg?{t~hwF7ds0dqDRAd>j}O= zR45$8`ZN(ZTgwLDM&RL=CIE%Fg+&%7V!Js+Ib?(}i2c_-_+t`4 z$CU(k{$Ae3%MNbS_Wd#kF&4BpnGHgZU0|ICSiPYL=lgy*194Al;mZ?-k!506EFvLa zE>MgHNxh*l=lfdyg*>sqe@q9mHnr9k3Y0EI*q2|g3p4Ubedjipp45lh)Z%462iR^R z(th@+Tv*Yh4Dq&^i0yd%c4fPnlr+npyXxC{?alX^ay#k-&ZTHNR*3)TW4T*7+rxE< z?WXAC;PM0tkT0Ku=E1cvrfRJm;6ZY?+8Y(<6sZKK64(S|7bKK}IX-cfPM!cA)q;_(yAEsaz0>3Af%tJ)h|5 zWFqv|;Qb&l;q^WV^yIEq2;Jyr{Z{*rJM(TC;fE>W$%m(Udh~bCG7g=no`V$2sJX+6 z!w;{KA~uQ0WJ5)7fPjV-QvsB;EpL*?#oI5@xGp%#{k8(I)>~xR5vVTMY+?s)^yn=k z=Iq*ALaRYpE~rj}zELI5zRNxdJ$-YCJ|9T%k(&At7 zvt&GynYQxd1y(@*cqns1C9W-G{aZ`EREm;Ts6gdzB~EdNFnSIqV-=@eDAgiSTK^w* zS0lr;aEh+TKsX58c)<}tzI+O^R;6Zzx}{_awib$}S4lw~@kes3;ttG6O%W)Iatdf^ zP0L19)>v|P37plBl9TUP-D$VeEan=^ z+>=lImpW>WCi-JYNx z%}Rc_asK%E7syKj^H=F3P!rJ*BDg24S~8jF3XDH(s(jG{C)=t~D78~Qg+>n7=tw6= zX~vcO2HmbGGRQUDfV4_AGw3Z-labZmr2V`i7$ztN zT~+$eb9#iNRH*l$3Nvje|K59H6`C*er!?vxOy2l?sUueWQ^Q0qLvWAq?I-2Bk|hw( zL6oxrWxJ{cke+-koKFhx>=DdlV2^hHIeCfou<+A{H1}=$-Qm19eMJwE!7=qj#@SXn_SwRXg1+$I-4NxrC_<=+$G@f zYawncV3tNYwLkvVC*!B_{>!G{iqZ7x|hMu0R=&56gk{$IT6br0Bn^IN*X4 z93AAa;D9OOK)5m?0}q-lL*YWUc6l(<{u|lx-g#w0|Hm)*@A)jt6xAWj(S-T2wT!H*cN!QTfTt=iv*+-cN=EcAy9;@NxL@73#fnngA(d2 z9KGWu|J3l_8y|-o6eCzxVNa6E*+S_U5>~tJuW8}EkJkNrL9Ith2VfhgQTnP{XCCN zlyNzY#UqK|IX8`Csdz*F14^^V2E%V>QN9*5Z+q9vXAW>arjmXpa-WF(&id);`xMWr z@A+VTvGgZMs_NTdG+wTSQB_)rShUakxkNI7`@(lSd6DF*l?16Ag(H!AM1Q?M(8IyL zc?IFU2^JXW(Rc>mnoEhIy~X&+@$bwBLnObloVn~t@loQDnN>#*;uUbR1nY1nG%oU+ zHI>wpz3Y?z*B_Xw$9`AhFcV?+%+Aa1LhpjzB3x$2-KsH;1#E4UrN1*Zdcesg?RIZ00m>JPUqxYdd}Wza6~1nZ$oXO8 zyk)ghTA=*!DUhBU^IWzsueM=gBc&l>r&-)@1VMU7Ww|Vk3veZzS`T=kKv2uBwu9QT z_fCM%JT8&1tau7!>n8s_8$#ktYY`W~O;xD7EsB61t|{XjkqiG;SFRhRP#t~G?%*o} zK22p@e$to%YZeQp*ema4YP5qjYXv=QoNC*q0$&^;W+)1ToB1C^$UR!QE#Bco#WT+@ z>VqEU{0`gES=8phnoaF?Xl;xVyx|K;VvxtH16OkTzj1wLibZQSXJ1tv1TWOLAN}C@ zX+O^?--Gxul)sME*+_q#4ruCHvHsn2#?yE!XMYCBM@W-YNr^V8s{-z^@`DK1| zNhEq2643lNpexme&c7v2^81@}%oJO{WgCq47KuRw=^w#2_lCiQ2>$QfvE>PoHcZS- z&<7Z|m6u&j_b536&d_b%p{}S_FujhxJk~rd%>(=V=*)AsPJgWWWWs?$k?8XTc1#5p z9>6pOE69#soUrl8*ucjiH8hDX$99>|lPdkZ`L=pbD~gI=sWqMyx%uE z{fY1LLU-z04T$wZZJTdabSBbL?IkB1(%&fp#L7jz+*tO43(*y9S91q>kY$~d;ii9@ zS2i06>%rM#7Y|1g(CTU0wo5m+&2CG_ps{i_TU6nnkB1dPYTWc{30R$)N59fY{H?j0 zbNy^H3lvI05cGs?+MSvW`1M$9+f|#1X3ZpHU|3O_<6y<~7=y7{r6EOyZ~qoCeT5Lr ztlHrO#CjGsa{db2`ZybfQpW`K#q|5Egwd%(t#m!~m#k6F4aLKW-y}(%#s>t3ENsHi z8aEQ3Qcqefdg&inSDdE|nZjeG$euY({t5Sn1`-8{5rvTLn*K2XA%>q12ga2tv|^vQ z4qS{WGE11{U#$lTgro^p;*uMgu%G-#uc66oGLeO9U`6Gbugn!{X2#I zClb##h~I{?wD~_4JnHS{8{wdc3nYp`TyK<_O~J09w7(wNr+~dFm$d#tT->zUL0pDE z7iy^~*~c*+zI*na!E|xa&(yJwCov4fnHDyQ1#;p4JK;m7+$Xmwou)Q~i=W0Z1aW#$ zc&4~`ZE0WK(T0XZHNww-LG9iwG`=9KHqlh>7rq|AN}tf-*lIM9cc;c%&K`Le0P^I` z25)3W(zn*2A{gR5zKDs5>2g4KawLx2Sj}2O--Q`OUIL}H1d43z)lmF&sHJ-ZlPYX~ z&45Sfx74L+L>fk)?m~Qu;bGfQ0R6e;p7Y2hj=R!&ax?JvX`YrB*an)?$_!2QNZr_n zx#i&34Fk@>Auqg4>2>-7*&`S|t-}dCo#a7UszYFzeF;v*;y6&)-ex2QSkANM}N%2WAN`KotiCi%qhQReLrDnm$6gVFkES1~8M zBB?1|vPNfG^IHaDPe!Al2A}mf_%C-;dI6=z&y>*&96=2lYx!M8ksP1rEKuE_4uqyP zzhoQSHy8IzAr7G7QUZaSk4#_&>*r#*-CVQIpzg6(z<*6 z7^r5xtUUeOHMfUrsq!@5$p6u#qWTY%&~%~DJ56hfGb_7oMWyVDsHSxFT8=-QFhW-b z{QulfR5mDqo8Glla(desWnm~IQ^4&t!A)zM60=0$*W;knqr4j=(Lsg$hUf54bdz8i<%h}Zlc1dX zf4uj9gPBNwqAw_4HU+Z(+gSa7k#w_vMg4B9edxuW_j0s&NJakf|L3yX$n&!E0AByf i_|EGIc%2cG)=!3roAz!L7XyWdmmh_mUP?t8<-Y)5geac? delta 46570 zcmV)3K+C_ckx%ZBPq1?umtnmMDYKj!;{_qQV1Fd}u#9l(Wz;l_v6Ig`XToHSWxeG0 zmv8?8I8Be?gPtIVo*)5-o*)8;o*)Bo*)K?o*)N@o*)Q^o*)T_o*)W` zo*)Z{o*)c|o*)gko*)jq6qiaw4Jv=l9LtU!Idz|}xI1o3eLeQ^@e6iHOag2`WHpmn zj2Mw1(ISyRfS8Zx`28rms&02O!y@W*m+SbveBLg8d4J)T*RS~S^Ve@*ef72F7a^Ea z3NCN|a#5V&#eicP)#dFEmv67{q>%3T_ z*l}|Xn&`2D&_Is@kEkdU{~>?e#RX6^D`XG!O?(CWH-Ks9=%vV4zy*;&w28dzm@2UJ zo3lLv%##E}62OC%^i%0b9%g?527-e~ReGwUn6nHJ@=6a!B_;5GHJ(i>!_eXZOoA0w z=m@i4r69rJX$O&ZgQmoxGioY98KApAZ3kj#K>u>K58zzWWjts8%`qY70u@aP+n ziS;(3vk;dX={_^o(ti{KbQvyB?JO=64xT_t8pZytIzReCf*z=z`^AR7VYn7n9f zNw0Koe z>L~HiD5>y9u-6cugcYj5G0}=|4rO>6j@Rly$^%msVQ|I0A*k;L%z3v%QYNKuo-dve znGeCmY6DD(;{Pxyd<69Pa6_pQN9g>d-!d&IDt#VLzcWg_Mht(`n~-?OlVQh=xJG5!yi$Fdd9>MbK z!gL&&Xh=Or8HdWH0GLM&@$e`fl?>+6M$WXX(%zhobdCiK>cdN3!CE8DmBgqESj@6!p)lRF6@PL5%T;yK8?)k^+Bbk_vGx9KFyKTLUr5iNvCJoQt^7s%9Zs3tPfKF_XzH zF1c9-!gYUA8ORWfI7uOfq=;ZYP!Tg3e}O=y1c*quaTvvuqkyd7svI&BceGIv!Xl`0g?;d2BcJX4@pq>j6wpet0jtYS|mxaLylYq67{hO3n!L8l=a+ zniLwfI^QWgx6G&-^r$x2_B2SjIW=2#roc(NA)J5i)FDRG=d@WJYqOeZ^PoK{XiTHc zIj)rlk&oSpd}2f?r*ST>bSbiMH^zNN(g~WlKBSxj3n-$H=Mqk`Hbx8yXAi8)U}D7J zm5DQFlRi-r?3BAG2h0l08pX4x7DL7`#+2AZGJyF6_zciq&sU+WVH^h}-cPL^X96}R zN)CTn8#=qo;)Z-6jkA2`6!fBq{d_?Ptt?O^q9}*c0SKRZCEHd zu@KCtLR~tfs>xS;RGrN2;tZm7B+eJ5IxuA=(Ei7@6;_W2x~N&qX!lR(3zP+AV)2dKaXOX4YU=rCnmF95ZBxx_5$XWs3y_ zu`6@#kO_{=TGs=8KM@c;=KgR^yL$=*2`&9u>Pb3ALoM~QEaeG>3V-M zwCOLc9WTlIP(+L?bNHlkVkaAuqehrx{G4EH442%*(R~pptw=?zoWXk&=TZc6U`V1l z)5I>Bcr!gVhUqh&dOtg&O^Q$qFz~*r-TASEq=|=B9>p*28bvUq6{-jN{siRGUs@C22DC7#)56*;zfwSGY_#o=}Iq6i^yPX1O4Xht52_L2az%pU3Kfv zPp`iHj$eMDhd!f_MA5&((kJ>yCed8}cKOq*KMoM2_J_@qPu_)Km)y9a$%N2L_-r4-e}^(G8Z z@9_yNhx)&Zx*s=gH_dJsCY^s{+HN#pujrMSn2KJJL95nVT)R`2*wl&?@Sr-SVt-e? z0zDP-xL_f^NX4R-vf6$TOpN11vZVJymc;qTDMFHg+DwR0P&h=Tx`6rRLPH!MJO4Ya zH)j0_UdEpwfEpQ5lY9V(RTE6PdD&$5EPgW6A6C+560!nzOJ?+ z&p~0DgJO7O3MHol<}T=nvfBOj$H$jzU~dlzc?yfyzEd{D#nfb zB<0DJSUL)N{E$yGk9A_FbA|}O$GaH+H-}2wa;;C8N&T74PFw&-$GmT5Ye!S<*x zJq*<(*l`vLDLA!Sw?*_EW!t8~>DmS-1hs3!{P-8#{MPm@;$MGPK|+GL)4NFT&!$dz z4kOkFSy(1TPwi2i9m#4NZ!&up?ZpbkY-mcWv48WZ;DIC$q3nFSZT{-JZjmMHafSQ_ zo3@})lGg*h4ER&x8hhHBkC|QgOC8lnQwGW%3?Q8-)`G9jlQHcOT$RLq>0r0Q;mhW= zXLvYqfjpEN2j+jYW#@JTYc`UC`>H4@qLd?bbDu&cR5g>AAXcVMS0=najP@x#@(qV> z|9v+oHJJ)-`&T|J3bokIo=UxscCo(iKO7BakQ{v=KA@fTFexvlBn|VpPJAk|WK#O3 zo8ckNhbi6Crj>`&$sp%)Tv8Da9%aVPR^8gK3i<9UE(?63dw7X^LFO{4UO_LoVb@* zqBk)@_uH-0z2mg(MDa?!ut3y?-lRBUuF0!Gs>qm~p}b8|(|0I*FQQES*Kw?Fm{eRR z)}epQk}cekA+|c$FZfb4SqpFH(uTCLD5?=+CTPYTnxV7JOkf>HlfwXuL1{*-9LIW7rDE4yv5 z7^ETm@V&q0WtciBD7I!7Nn@dI*!F0W6E=UT5vx=E+^U^gU-+A!;J5g^`FwDiX>T!G zjOGQp*3MFp3zS_Bbi}ZzmTBrhezL0p%VbwGWxKTJnNOo@<22H%(h&*5=paQ`I^zV( zAURA7l>~}43oW_vS7Hk_w1xbYrFtv!fP{_s9`X&EXG;*kGGp|8mm<$fD4Jtl{;+>b zp_~Y*T>J@7tDrEL;EF&&W-!IbxA!M~MuK0L^RJ&5VC8zk1xsvB-6bVZh6gVJb1wzZXMUww{}5fz1yh zmSprlv#_Fr@z~>Cr5(>oH^tFJKdZscU=DoSG+w&Q_Y|bOtAQU{W6cy$j2hy>&KDfi z3~_sH4mm6fLO`q*0~dQ9#c|HA{yz;%vPwKZECJujSLP*QiATa&{gSZcUOIn{!V=J$ zDS~@fSYl#tRv*M9j+~vUe&J+C6aBTLGcKpCYU%FQ|4zd)`HE@7vbb)an&P7Uw<)y} zAGjNIba&$T$JwkHFhYGGdKgcYc1XHLdm@aOPu31zryHyla|ZLanVQb2Y+1N)#xovi zNBW4n#_;Z&4|Bcf1|Zl$YMOuUx&R6W)|OsPFrWFZw~HYPbe3`S<-D^gi!HOb(vEhgp0I}8RM3$Dd$w>JeUwJVHt!APbm zc(x`jFMx#2MCZ5Bh3Pw>z>5O@c8nti!JR`J=6+_e$i{9}Ah`$^t4e>h5SyA7C1GCE z=T|^e%hSC1f)70n^g+2`wVaOOjN5xBV}kW1%)J3N2L_lDY1I_}pJ#!e<_1EM+rX&> zRy8;dn>F8Z>02K;UeC7^L!uy>#6d55XHt^|gJE`lV^DOxo|_B`SEbq-^VpS;rxp1l2Kp3x85>E&j`F)-)$P!dOv?}1?_d-tOyNaJv)!} z(;Gg&GX3`7%+;eR@`-WBr|GVpl)hQT46@AGkrw%)dW#&(1dHW8hWWfQF2$V$N$7|Z_+41uuDJhkGjykQ; z=ayXGlM~94m3Dva^a^e(^phHV%{kJhwZ_m_BytEM_wL0EpK0kb`E3{)VfrAO<=tpC z`UoX|I3{)@rYU;UFe%h@jajj!u`4Yu`wIJ`UXI*6LeKGEEaoMv`~A46$F!FHw7Fhi z)KTD=a&pjzP6ja`y_ME3c6x-A9qXz`<%UiQ)>j>M(qn%LFG-F?aKZ3w+GX2Ph%km( zK_{E`7n{2>Xxbu#zgL-y5b=h~_;tGkD^twnNdYa}o{&c$Fa9#_!3yuDn1op!6 zJHp^K-H3k_if$x1Ifywly62!-vMlvO8RNW+zhBA0btC(O?d@*7X3*BHy0=5x8p|!| zDum8&4wHDBgAPcVz!l|5$b@^@K`*c}sRx&_F%-LYvj%;bHOQA`4VFpLgIj}2E`<$z zawg1sg?y5mJw_?o-u8^@HL}2J`6NcIk=&DKd&PfwEE>_y0Ne8Au<)#FoTw5-Hs2{L zD@*IMcxe$uhZv7SUcBO(~A9mRl#@j1zrFbCUbA}(|X_+Z;hi*sUC#V4?^?wEa{Wqo&}g2;LI?~Zr{KC zeVO2^uYt>Ycwn3ZfBi&roRS8PqQ-dFYqJ|V?vk6wA-_P zHt}Cl#;<-NYQMEc8igsVTVfxlYZO{i^S0MrO}6ygr?#hdf08*Zj!rGPW}2G~_L|7G zz?iht{+Y<37UCu`-18M~(fS^qznbL%2$G>$=#MJ7QCDwsj;F~n2aBw?F%S>Ad0X-xT4lP5C!`7A`zH2#y^Km zCJ>mLwArC$*schN@QX1)%;QqRQuC}~VIH}#AUM+Gf5$N@wpeJ1GivN-9D&7%O(~G1 zFp<=5!<8fj>ztI9IH`M9Hj5J#O9H`#Nbp3}+Wf?svso%RBVr6NtE+L-7+GR)`5u|F zZ4<~ANl@*mkE114bO0D8wQDcme}!h&sh*9|eid>Pb|qFD#EWX>8I7?$to*obrvx*A$7m z5m_j-S;W!PXfpAfk^RYI(2i{igd?DL^WRU1R$MTPaKZ4zE5ifQGa7Wnhevh5OVH+C zys(i0MfwrTSQ|>6sTC2me}p%E52F^e`mqD1V+)md4U2sGmfk+c zIdaPl%D2%2B()tMei#`w+Fqq(wm07mM|CuY%}v(STjsy8ilJ5g7L3^#*q8P2Ca{F} zopd|uepprO*Z^da6iJt6^S6f>BGImr){B2+;$OO5M(56aj}y>;$2A|R$E+JIdy48w2p#$LUBi<;GA=)y2Le2 zOf!r@d`xwP5X4SH5ZTSrGUze_`R&_RpIbA{h=Fym_dM}Ny*9C7{M?wUfZn>K}4W@(g@yJ66WwSN~T9L!gbE{ z$djTFGDT#B3VVBYisu{*iLy>cFXJH~2z2M+=BPM3mbK7?-*Sq9TymPlaR)(~DI%1N zLbQx&=)8ST0Y)<$K7+R*;{Qcue||j>mSMGKU?D@{b%gl4uixKg@sL^J3KoC-(_NAS z6ec#3cSSOSp-c_ofuq7S(7SKN`_il%Q{F%~rbuJP+(#NuvNbKI(tc}#H8Ds@%aB8x zB1@WfXPS)D&U4j{bU&LOK#+7p+v{!;ds$|rZM%Fkok$=9-t|iPBB8Sbe}h?v>DACT zaMpV~$QMN)cm$PN!vx;oKsQsU)t9zM2#b0Oo}X~J+>Z` zc30MGmH``%q?08TVu~?5$PJ(??l_f6fM2V(=Z=L-_^t^AhNvdSLDs|n@IY? zXVkhSZKp3$D27Hgon`<~!O@n%zLQ*;it-L?-S$`$EvyZC<- zIvho4AXfG$9ZKq2IG267NPtO8u8};D|H^SSF41tcFKV3b_a~9EOAsA)#dSEjOfBwK z5>W!mJbOIt!8DesrNy=ywOKO+M$C>)dZtj2f_R)Me~r11JRw6aTrpJ1{)WE5+l~WU2>~U&ROSKf6c$FrxK0j&fbwnH=>SY-d_8rM;kTuQr z%j}Ue{b=j6r@`8CJ!C?^?Gh?diM1MM!&5{ zTr8jyo9WN+Gx9}fqT}6Fto13-QcPFUov_rk1rgCLqgV0)~r7AAC9+(yC+98*S3eI;=Ky-)N?8`C?U<_y9yOFMT48_d)JNa58W z_00;Tw8edplD|+$eO!T*QReB88b(4M4d%?>Y3V*Fy-|RJ`q#+i^0@|ez}6q+pVeo zM?v**T(DA&Iq_4;qZLeAm;9=9FXtkFygcC(%fZ$mFKiUsSFLt<1jj6NyIg{XFBMsu z)sC-9^}Z%oIpJjrIfQoVuK3C;@r!4wtiZK~AxWo#a`ny8uoy5URyP)T~nE9AbSdK*{kjR!H`W z`Vexh3g4^FIQFFO%lH~>B2D`PDlsYhdaA>BX=N73^om?MhPu<^;*eXie}S+$zzh@Q z6g3u*k55l6Q`}ua>)UV_vbDKGdGz_FB`x#g_lYV}O;s%qXWZ##()*R`m6i}ZbuRoO zuVfjHan@cz;T_|w+`(DZOgct4%_)emkIFaxs^xo~S9VQx zBH0SW5(Q@QH?=&CLY7F+%n(8iQo2IFUxaPRd1WM zEi?!NW!vREHMdfGO}>&BupM_&%c;ppab1_WyEoe}igrmddqOg!f7&}-!U;zE+cti2 z-x;rhQz;zdS|11M0y@19bQ|zW4k~ENG+qx~{)RT#cGzujIUO!TH9ekqqR{99Ql7RO zwy#h~{Eg`+wZF2|zsbg*%+F~Kk5!1h608%k8ri=0{7e|>v3j5E8vY9MI(hR*d&1RTjkh+|=A9n0FApTO_x3Av4QCC){gUxo@aSrPbmy7Ce|{h<&b+X1GZ8zOakB--2$ub>VY;9cq3L>dFjzTq#8WjxSw^vWpMT zJ`kqRmFuenPr?63-?JI^t3}^xC5>H9jt4r~Z0KbBES)@jse*ssmVMSs6~e7?fakna z0fh(^fCL39XU`4lTN31Ywk62$)d6!)dcX7|&x zA|nT3p1ZkJ6>G0zn_iwT^z!tI#=pOR_v-66oL(3sR!V+(_qPir*5EsQc2OFi+Kc9v zD3F(TKVH7OdoMV@HxmB>eJ>=(f9@~bKMH?p@TpYzhP@Yxh7q8{GYJoFh>b%O9}HFZ z+`R{h?_^k5>-+ED{qgHJOt2bA79r#a8t1$P@$X@Zkr#wtQ|2ZB5fmLG=!QYq5(ua7vVg7QUx21=<;$fKoWgVYHyc1JY^4zZWM0Mte-V6OnYEPF53xubNqJCv;MVHFSF9 z+RU&+VE7t4Q?T=-@alX?pLkbi&kO4CbE zl!ipnu*hmAO)DVtCR5{;+P(WvH%x=B_soV~o;n#mQ) zuU6$;I}_&3nvBooYg}EZxWB3PH}(F01n~R|iV9ClN#@?_ncT>I<`8)1s7f2q-^{d| z&9)4mt1ZG1*wAOWj3r@H3^6lv%+ zKH4W@&`P9L9ON_!Us=ih^_m|<9#tgV?VF?zp!5FrX~2v^r7l`HX0CsN75s?W^Q1bY z^*BQlj&5DE`$I;P)(CGIJ*cn~%r2-PT*)D_bIt7BD8_miclSZGJlED!mKHz=f)57_ z;g4A)^B>r|c%ikncJ$)aES2=C4774iMDcZ_Z>wVL0ZECcy|Rr>l&{!IvRw*Dfv%Ej zk@EKr@Uf9wk-ifEyeMgrTPrBqCGSMGO8c1h`X?Rj4MC zsuz{8n@-rvC^#$Z`gdt@rdl7thb#U~vX12`M3!)Xhh-z1h`?l;MTXO9jpR=xEteR~ zd#sc=s^tI~iQJNpqU}(ZM~*B)MIs)C#5zZ=s(30g*?6Y!7$tv(h<aY`aRd6MLJZYE|d~wwqJ#PS&WY15eWHlTdOi z2*uE<*=`y>>Js#EfNA(Ba{RK!S8#!n1T6pyMTzGFvV(aV%2{@Mm=y+T&i$F5QSEg3 zCrP*NI9zG&e#CzP23;@C&axF41R3S0nO2x4dea_4UEE1$Gh&u0IpvKT!hul80^%)9 z6)wPj3dw+viSCKR2#yGV;No{x}P0}at zs%)H!X^}S3$$})vq&{h}leG_7uMni-Ax%>{M#3pTb}u0Ati@m*S)d61XK_5dXi+2u ztw>O&CeX&{isbG^_bvm?6S}V(OX!Z$GSeDXwy~C*lpad=Do1E&=8(V4ynZe18AhX= z-XIy*ry74dj;DxbuN^a}3km@dS!KKj|XRM_TusIDksrFin~a8XOZnof6aG!TQVfyO?9 z%c_58z4$VLMN7SgrML7OSde)tZMfArf*{I`$`Pkj&hr?2O{6@?GMVBp&qEv-${erU zm4-n~%3x%rK4u1qD!^ud{$GxtISGfYHCzNUqun$H;w8*_nr)|fIrV8tiq!{t2=XZV z(Re`0j#gHh7M}{AA*YjJ^3{b>5^PVnMVZY73Y4|`j4ec6{{lrc z#^)V$CBYos!JK5im)>!O6zwI5Q|74TmI}#SGPxafgJd$UN;EYs-i#1`NE zy(}^gN<}m4?P@QejBwUL_)R`y*1Gnd1TwvClXwsAu}ZmA5tC$c8^=KQWZJj@H1~g& zG?z50az=8Kf~Q#>yeajgko=~>8E9J#CW3}hW--ZM4Z})QH6XK%I1p358M_GFsFNY( zJoFGpY7X1zW6$_KqC;ZpQ)0RU-VlFOmkx&Ag)%)CX$m-&$$=YWa@2KciY;^Mn=vQ9 zjyZ3TgBk19N0(BSmPZCuX-Tb1?nLW0>r#BDtm0JB{j+8Rp9_Jkq>@5vn$l9Fvdz^% ziv1u9p7im|#H4cLss?=RZK;in`|80>WSemsME0C;w~4%&aEmWdxR*J|V<~?~vu1zx zTa|5fd)(fBF`^B_UejMqtPhxO(#5PUpQ0f}tvnHhrp5_gdT3L35mb4n(Ct)L!~1}D zQ;E*ry+pt+LP+1{SCtlX<(;>lwI>Qc-Z8o;_o1t%yZyhK6wk{fiyS1|NhCo zIzVNbBbzc?Y*J$F%w(N5^_9TlVP+_|rGC|EhwJOHXt~ZV$cL1STj<;0uU#XF(T!;q zn2Cxu`iQ8g;yFZKMU{V6dxpvw*K5>APOW7`2Lzq4GVEorlp*L)Y?qn~ra&avmRwLO zjEmbMOiE%nYgagd<;MF(wNfED6$4fLtYx1%T1F*o3*w?YZ&A;%Zpw_{{0LV1ELKb5 z7Pua|=^a+7YQ64u<<4EfNA1atRTEM}n9s`U<_N3v6Ra)}I>CR;gkIUF^+~#rK#l3% zWr9;*!~GaSjG{#2<4C$k9l*2THFch6)`aqtM|MJ`T%(=PIm3XljG52?14Pr)V0x?| zEHTdQtxw>a(jAfyIHhl!bSm7H?pakg*asnECD8Hd06y%M!VuHK$Jc1~o2iMWod9))feD-S+Fu>h{?gs(Q*6i|H#mQ<69#mOx0EiCq!q(b5S9|GM49ZHO`=^OEkfr)Ij6%=^nCzK-3>|c(mu|c&2V$xojS;O? zU1uBn$`XIwDY4t95Cl2HHrS@YZ&QL6Pq16FjRxpS?U>phumD3v+n+bvW}Snd^TyK2L-_hnan`;k=a28Sb!sNMglW zuN56)V<%0>{H2;>mgl-AxM zmVi>j&SQCiyIx+#RCS)|f&J`&s&jD`26Z2pPI-1gsBVJL`y}8Y4lP{~B^K4Lt2Rz# zd71Qa1KHhM0l7_{FZ%F;!si&B!$A)RHH?3uvYk`i@~rMmtnNxu6qE7hpXd#b^_?KX zR_-uJ8~GRH)E&mHkMQrAyt*r6qr23gy+}D5$Fm*D=ge)cRT=YyGBrMv*1`M;B7Q9e ze?dtt=jZL!T-RU_-pIC8w0{rZVle+}Fv%=rx{61{Zpc)-ze*Cx%$egCu7%omQ?7rE zsv1We`M}6ikod1)=!2)hP8h&n#^_XT_jMBc3BG4eBTMc(vro_or0dmU!xOuSgR+2F z3qlp2h^wRzSzepsYcNOUgAPfIS-dUdQyLEktO*Ui_h*n*(=q!Vi+w&my%L!u2KIL5Z<@jr%}E(b;eMaD^wEEf1}mq zC@`k3^sCljx9xG`);NE$#IKUNG&C=F@lrbpRG;svN^JWVDK*hXwa~9TR&J4Ss>is- zukS+1HwAUMVj1z-NioKxZyb5>K5zZajzsw?!4;nPUQI|9x>RcPL1_3o6|sM49GFHn z;=I36oBXf*c@)(B?(zmP;kr{ygR}f?F?p^nhM^+?AlvP~Z5hm@OG~Q4Ewx70%?cJTbau&pRJUvhoq|*59-kS`dbok24HYr zJKep;cR=)9#Ns_?I`_vy>abML<$&qpXBCuMDK3smw1;AT1#0xQCm3|VRHF{CYCTh`eO|43-saue;v5lc#VwQB%O2WO5@cqvlAJb^$A)ctoe=8 z{RkmWaq_L{aG<(43|JazyiIe|AwuYG!4|4!!EkBu5AR-md{tt;dMgN1(tmo;0Kfe8 z$5-EdPcJ{2-TN=UjF>*Pu&WxBalg?BHLX-$8yPZ2?*Z-yk-f7 zx=ZNOckt|*r<%~5KKarOI1(*z3-IozF3KN%EXbu>c;l=|ke`Ggu z_x_4JW&u?kG8o)iw*f3;?2C-)!x(CvJeYw-t+55GVZ+eJJGefQk93%~sHJDxs&|KZ*5zP0=!kV({V`S6#E;tVea9Mh;SAO3v#{wg?g4^K|< z>qiOVqg0%JF#e$WC^gUzkKb#Pf4=kW-~lxCLHgd9hbJk*zhrE!=~J2bgZ$x#5C8JJ zZ-r17KO1+#FNI&80GUuOuH&N=GR*>M7XAPbW{96*B{F_5ugkc=>tVHK!U`HajQXAy zCgt_}Z-037zhPM716cZ0lEpv%=`ntO1ZiR;mA|3&r$+cq{L}aUDt;(`f9;0CtLTQ3 zS6k*SL&3a1uKL5ezx*a`>i7To*Ntt7)wYl=029n96-eROYpLU%FD86Js)e`%t(C&7%9vDx28Akoy}QZ)*2D{K{cssbQr&bXHJ3oztR z=vl}0`t|$WVd5wy+ufpictUW26Pf7eYF8#0jnC;n+PWgVDNO`#m_S;3D&? zCSEm(SHrA2;!KtAhY%HMCXkL9{j{@9l!h50+LaKiBL;rS(m709zQwpl|E=f6_-*0TLL>W>K>sv-(H$2d0ZD@M?&Rx5}l z!H9O~$FQd|I~b;fZJUq`723oP9r?c*79~Sv2gA-cNn+OU@g`f+U+?m#5u-WgCt4bP z_wWS9UVq(#h%t=!+Z7#1tYre^DUbliAOuf<1bEm()8p@>f2|U1q|FTSd1r$Fnn~G{ zsAqeV4-uWnR8@jlZ!eV~0?@5>CIStEMFaV-;kZaFUz(gEb?nA55^5^=B~rmh4r7@P zoPpElW`-SzOKBN`ID>kEJ3&ByNqE95!c#Ug%RP8H#Y_*Jpv{TEeuj4++ptEU;q=SG z`k(|OwQ6ale;7K*<9y^?41lMZvY6XUIY6Gqn7VEKQnH)JddbpcjGP={zK)(lMZuWwWQ1a9|2dJMQ1c=utv0 z8t)Scgz+(4Ywu+HI)7Z&qxZ+KBpT^9HadkHqX3xKe}U^RJ9-J(l}5Kc4jjV&_v?66 zVrnbyKn?Yt9Fdq%gH0`)Ac?7*It41A*_2dgUVC&6dkE=38Q^kR0R8wVu}lxg-7v@`v;92xq>Il)jVqiHV=d&v*SO^QxdvbYL^|pj}or3OxIwM}A&v=M|lg;A& zYJytx>M z(rx@HYGm@-D$^N-=?G6Pvfn!#;3Dmiw=vU9O;Ou>pQl~4gfbY^+QFh!*4jbQf9F*d zcump4aoERB!ani)KG-Daq#Uc&5fxf7PP%nM#R{>enkxpj_KaX2d_c{(AqI4gCVpV5@WF;Hji!r!NhCUwigwW-~$q(-%yY$ zI&rD4$TzG!%cMZ)iHs}5WYc{me@NPKb8e9cmgKMN7r7TbN}@3%KrEc8#bRk?yeYnK zJ1O)ky}Os~gnPD=!AsTd*l1JRiFApo*%8|bh@dPSHJ)(WV=E4LY*pv6JqnV8Ynu5` zaP6@Szl|{r$Sj(3D2BVDSiTJu_q!p>Aw?GP2J)Z9Q)b8^GQzmC{F_O?f7R{G1c?fR zruqi<{dF@cya=P-MR@EI)ByaA2XZHSM;h;5PRTp6PDaaVOi``#DQ+feCvsnJ;(f4(4#U6EAp=bD+5#_XDt9BwlwH&BaUn6N!+Ip_>wbqdLH zh~&qCMMOmC2Ko2R&tei0666htw@YcuPu})B9NEC|75?r*R}3!KqtPDWy)Slz1YQ z(lABTm?vE_DYZ;7e;aYgEb?(kXxMA#^PCZXX_Vg#v{be1QT(f>9MjF8Ya+;&Pi0TzF$ zX<|UjIS|Bje|8FcWo(3&;H;O`R!@Mn_@h>!t?$It4*iu9g>;(Y5r~L`MhrTy61rZW z0(dYv%AC`>3%qztJqTx|I_?Q379l%82kloA|K-y%os>rB+=z6K!sLrxrV zF{LdJQHT|jCgf~2u+qz=o2=9#b{B8V+S)+cpw{MWKub?;nuzPiV!aL{Qj4x1Sj}Rw zbBC7{s<9ShY96=hV^%4W5@yjuW~8q}a6ggBGZh;+a+)sZ;E2{XTpX7tpFu2$M_$Ri zA_?M_e|$op3F{4bAj={LR#LK*UL{NE`udp2K8uoel`oWKqf90dq3ercx&-S=GF4-a z<-R)^>BPNOv@8E{j2jKAPWRkM4k=)v=?N369llo(4H?BmV@;b$a>z0;Nq#?H(`m=M zLeycUZoAx`9O9OskiYvSdgM1MLzWitiltt~e}3nRt&yY(cL01%64MV6>7D{T3q zB)FVVcThFGI$uv%UN$+PPvXp;5j!y10xUw0E;*p&8zZpXMAoDhb3#RZJeSFL&O!oF zZn~WF3;64`#-o>y=rC&md52gA&F(O}e{zSdr4gN_SlyC^#kk6od4yqPg_K&|XUCe2 z?AYmD2FsLI?fie3*#$y0?(Qc=Q~o*=?wYI3!$LGozH3ICd*Xy;*sr%!3INDHArq!) zvv;)tRTS=ZpPhVKf7M2JT@E>p{6>G9MIX4rFXA}zi<+O+-Zay@-y*JB_Tld9qc5eVbEv?=f zjEIYz9Du00Bx3xv`liL+fkDKdQ4ZT;L}hm+F1|mLU6x|$QI<1sS}1&~RdrLU7?tjPvEHzx z(3|SsaRzstT^s<+OQL>WNV+idz6{>jQVU=fyfg=XE12PI30*hlO6GIWw>L~ba~vnS>zAu zrpJvQ#9H^^{_gI2?L=<#e2nzh%44&wxmo612lXn4sfqja3d2VJ@gao)&VSVjIb81| z+$Eca$-RO!@ThHX_0xE6F#2_MBY8?UA|uwI>5yAlR@@?MMa<#5)rIG|qEDkn3&Cmq=z0+KxZNd8=hD+_k)p z?b#4QH!0etF&6~v7&vFJmVa?8=W0*IRxDn;y#h1JcU@0 zHnyET6l>$xR&~xEy?lqNzS%kxWl}M#-E3=X{$5M6o9gi#Nzne1_R|yUEpdo-y6{18 zeHwsE2D|eW!SzC?$6m4^QLxk#3a)R%q3qr7wSrq`pOjDv)SNIgDu3;DtY+24LenVA zDsb_a7x}|CRmDvSq9n5f?gj{Zx7~bZtRmbto!D4c_x{?YRvjM{3`y{^u%nncqFm7J zh!ffG>O^kfd%Br$%nE2n4yhUTx(h&oz<^BbcB8MPb-j=(LOU0m$%)3`O&q)79^*lF zHBe+31p=zTSIz(me}8F%S&s#0DXH3+N|&~_@!gbfpbVCc=B$Z_Yba*ObWQfsjl73O zFfCQP>D`;A#u5>A#QL~wrZQQ>H#@n6``QJ>3KMtq11rbS%iVh9ZPwRxvWc$8or*ZU zrZ3A^`||iczHvuJu~4&(|KquUMJVWK1|X_*L%{@g#IRR84u1{f)|`R7FE@vJN^^(g z`is?se8WC`66D;g1`XJDF2Z|vZm2CLc4~_)(XzRTC`oFGgK|smmrW&uSaRF?+F|Nz z*T$X6e|%%|Nm><(BcEWCkfX=tEysks2e|DT++T%Ml;>g~F5ENNkcy~$VIy@)Dti6H z-(Ed|ZZtZ)uYWN@_xk3v+^3TMt8s|s!@u%DBFwTNsU<$lFX)+ zz}^e0Nv+qpVB6=aWSls>osUa7p$@53o6AHR>;%%nkYS?lQrQHki@sN76U=XJoT-<9 zOjx|FUc#jMA0G8I`%+@iB8X*7i~Kr@HrM)$&IZO~A%BTuxzGMl7opbV@EURIv(-I3 zEGC2W`?MSq-`h-yl7fOWD+-u z#&5b+>cfb-c8DB@%!mOF#mu%%c7HQOwd>+z(D>KNcJI#C_L{Jv6mriX*@~8JVi4wB zB`nqEx;)ZcN~fd`Vcoi1*%qT~-0ydMi7GrGc7Hc)(=kU{0sY0EtWkG(0%$dJy0>4e?nQ$iV?g@Li*n7)FADXy^G?c5&(8ESFOOC7 znZ@Uvdu14(eE;D%+0{R&V5K znpL@QdqgaSV44en0v>3P+?Yb!oCv|Yd{fiQnp(DG2KsM}nw zKy3R8!~!;Q#F{D>P0Otek^Wtc=9*`OPk(iX(hcuWdX9Zx@PO4DxV0`f%|7m`^?Apw z>kxkbyV17^^2Q2S$>9EtV22^EBt8=SMJ{5%Ub&IYpQGZV@ zG{*{d=3~WT+LS}Q)9e4gnz1VVX5&}F3j@gNtqycpf5-@=SWwTq(EMuxGAHI zx0hs|TQZ?jskbxsk@OkSZfT<;@$!s{51F<7nmPy7`cGu04z4>MuHCS6&6^mCo5?=U zt8FzbkR*`BFwAjIBzLv@QRwIZ8gn%8+%*n0OS7({np!{Oc^ZG03fzn;)^(Vz+pm1? z(OpMFCRFCVA1_E`azbd~RZa7CQ5pu%WQV0x@3A3(?m4Dh2rbcD;|7Uzwjs0g`BV!J zs~MhrVow^z5!cbNZnJ_+kSZGsn(DPnnKzug5NZ#<5b8{L%s9>TvVTv4j{N>#fnN?* z<%PSK;5N=W`{2dW*0==(>=1`ziADf`xh_0hh8xACL_V? zACYQraVC%7kO<=I_6H=qYtKCA`3RcddpV!+dc>(6G*3r#bWUQ>SFlpFA^|CMDWEA{ zOCbDza)nF+3T19&bC(t~3J$k}e+~o_0y#35;l=|gf5kn?j$}7-_x_4JRsmHUF2PN@ z8Spf0Uu;a@)H=<;J*}|>HDtq=`FKZgCm;FvvMMz`G^)CiOE4Jw!sNFvH-7v0fv2DU z^y$MN{wVoP2RCGc-3a_A zKPwB*f3HfKr}#h6pOv=pr{Uq#A3y!;AO0wmXm=868v&A8BZhsrl5rMvlRR@);VEQ9XhUvl80n*z>C} zHvTa9V|pOXJc#3g1o#00(LwOr41(s0r4)<{e?8u@=BGC%m0-Z_;l^NoV_?j+8-wP6 zFvYL{xOih~xUtoG`r3`@H{ICrJmZCp0Q~pn!W6g6xbeccG=%|?;eh@j1M0-4+B{2- zKf%QR2L`2o#GE$IY*{w^49uNo@HE5V?=t?>l4k0sxDMD;k^$?OGlMYs(;O!Tg-(l; ze_u8@0dJTRW+Y;e?aAm=0qTSsNP-H0e!kKcc*R_%H8p2&vqCY;D_68AQ;_}=7O@HG zGL9hB(NB$wTZRAEG(*w#BoMTW*JGbDQp*TYRyXl;0#T<62p1vSd2t5~^BtPY*6m10 zvO0{k2{pj-B1)%^O$8>=Q~)9ZVDhoUf9Pi?pI!uGfpsvI<|<%NEm@c^(h8Xb_+Btx&^+@nN*00b++U{kKAtu z$iz#8K3j)^qe2)qpD5sVSs{_QfBZ1#<=hBGlg8U&%5NL+g|cY1$OCN1n22Dhs;CZ9 zvemwjN3EoVT}TUa&VtgSF)i(I*<6X)b>Xkv6`}g?(}g`!y3Rx1qp%yiDg3kLBar>E z3;n-jOkGqdIE8uT4j5P%r(UaxR_P9iO2rG*RZKxK=jMi|L0i||Ub~TUe}fFb<((7@ zBFf&D9lb5hJNb;95V(J;T8eJ(Ypcyk2$nM?`5GU+k~eqF>w=$DNUe^Yx>JH%GLMLJu$ zWXMHAy^YjPbd6vd4zlE2jgYM=uA@`z@hR?83UY-{`FrDYXM<=>aaBFRXB%gUni$ZA zfW{8DeE4yG4`iR>U%F);OVvkprY`aR!1}M!x|3VrOnSW&I>R;mZ4<~6QZw3T#IbZF zH>9YZKnbn$B1>?Te|Z`r4UH2SKdnAU{!1GhBh?#YVkx|@;%DS$Mi?kKmG&9KOi3;7 zoN=R=w(fBM*95s;=rjM|mvnZ&OSdbRA8<1y?8^!M5?^JZ_8`*BH^c zooP4)L;I6#IStM=aJ7!Dh~`PV{L3abVVN-SMu_AVB4lGAHaGYnY-ld6@6 zmV@Q)o|7t}CXwge>ZD61g%f`0KvJ9;a!qqFiw{Fz#?l-Peyw%PAi9T$%HJ^FNgs>6$5Y(1GLia-!)Lqv_E5~qs&q>kv3mNsrN#81!3P=(yBO~Mp zQYNe>_-^kHzDvZTA>JH-e@K@Yn+`31UgoBWj)B_21+0m+ou?JR2&0oADs$;KKP|f{ zpJZ7B?~pa5xV;=tvUPaiqA{Z_bNIh*^$i1}-WE>25ulw1CM__o{RE(fiG0+x?U0@M zgSuB)f6qA;T9I~yJ;+)bhJ{l8)8 z&-l+VZg2l}`_qU27*+^QiJ}~`I$OaqVF}{p5(tEm;!R7Sn{Ac7`y5^Cm_W%nSg4&^ z0Z%Czm-*t5sk2RuE6>TencZ88$f#r=f0c2!aFBN*3!XJdRDotpKR4cRKGf;fCKme) zXA;Fv^=*;18ESuRRr6WxlOE3zz>w4D#pKSTnlwrg@Hhew{4AdE%%beusN`sHyp+XS zbzEHQgJF@vqqZF7zQW`Z_&u$`(UDwx6fWYt9WiNCXd~`lj&c|rN;4$YtWKx#m%N=0 zCx4|(d@VGTqHf++WKc5!c|Fi|Z>?x1Qk5B^^uD3X5c-jQCy$Pvv^mg^d8)o+Hr(1U zc)&-T*YrT;M4U)~=HPsu9jUP~WWx$j%1;vTwN(w~O>L&Me39uGI6NNZkP=h*>S!4>34epah`LFe>al(7h>}r&xsHimQIb1zdzC8G z-bT%*qinDX-2^VpcYrcRt zo3>~u1GK`VeVflU8UO-)kG?iKis_uQaOwggN_xx{v?XmGYvi7_d8+EdLZcqlI{Qh5 z;I;i^4*y_$x1^42jdq|>iM>re9)E`{=x4@9?IIfu5Hyc=)=)L2JX0Z=;=E{I1{hNFpMmb`GTGx%Q-;ZJ{`uaBfsJ^YVz2cj|h|Go{yQPNrTaE5%CYHeJd zC>^R9l^c0V2bh)Ha+AF79o$oELa0P*0QBRw)Pvf1#;Y}Ltx8|*nc&m8#eWgcBnr^b z=A%#SLj0RD)0^McEO(Q>+qV)abU?lCu`!SrpwFax@&YMxZgE^3IYAXB{xS`&QsnlY zXs_33=E@$_A&bK~b8;B6Yl}oqux7UGI$ed{p%@|gGMC3L*I7d+&tUNBQ6V&gcG*lp z0U2Qq=R^i~EKA!@jO<*_ZBVky>lLuTTqTh^lcFZwwf@ni8m$s}lI{IZ4Kp<>W##C@Al zfokQMrh_6?v+1^i?IfvrUI9$S9UTl`rgBrLkXYXasoN7Oh5W7ca6%|mZEFL44X@{+ zpt4=^;}#C@(PA?r5r0G=R1+7j1$QUt962DRyZT3K$|Vg2{}!fsEu}1L;z7EGa_piA zhFl)t;;D+mE_lJe&mXr{bHHWF-o)S9nq>>kNukV^Wmb{EZDC>Bu8SdUvY=?S^yl4+ zVs#>lsav;eiMrkgH+HzGYJP89Dizu_-gF0H8C5crde`2jqJP>WBA3#2Q-`G_v#Q_n zUS1vD32v{Yu~g`1>21e_UFD29X~uKsTIDs{3?k?6(ptWmfhy}sJIY~t)9GQeU2*hS$2=!C9?@~ z7=(lox6?w}mw)_Gb_2UgfcVKG9NSj|aC=7;HL7hPbPxKyLSX$=9EGa99}rXO7{m}u zm?S&;^V?i~q|)!%u1*yaAvnY550m9ca>d*%8xbQ|EN>{%Fe{sig0^Wzw@$?N*}_OA z98vD~sGeEA>vtDTC~@!Bp48Zn*swoS|#TyY7-+$4^@YKZH)wZoqI0_%@%cs0x z;8(2z57jCcx^>%ffx9m1%_orWtoUoW4?JFl?XKb_U+ERuU^)8!zMH>Sa&TInprOOV z#kU#@V>#Hl@NSr6{vvHJ$|bsu$Ym?9KW1NR z{MM8Q8%yKHLm+KA>woenMMNaNbSy?lLg>^VddVAIbf2}P@V{Hq z#_keww8b?s8OrUTrjW67VEL$)2~qA>&M50}YE8XTFok=PBH@AYtCVu)(NF@jw^6xX z)WLH*u~E9fkVDyJ$U9TMe>Sdz43Fy2v3#{5&UA^0(L4i-vH=9zlhrg--X>ZK^nc;a zB(xO&I#YV(DHXLP58;7%p?d&U;lF*prE641r-P`ZU3tj2NQu^|QHSH7w-S@FG|btx z5+e<|VahL88ie&QY2A1Li}K zAY9iG?t5Ys5X{JC)VGARr49m*5D4gW&@QZVHGLruhw7-53Ln)4Dpi+=^nczI$LJ>t zK^)T@?OFuv5$sGE9CM!LF}G&Wo>BiX7xQrO@onC+#GPud=1SYr?B=u!DHVRVp|!CF z;Y2S5@@hE6JJcE`t^R+)>|BG<168#~bu8>j@iLI{Ngz?{%NAKr z%|jP5KPeIEpqhOXOYO^Rf`64It=T>=%KMiFNqbsYhN!q_y6K3Td`(S>8ise*EWgXA z+&nXZl2h0Lh;>g=(TwK)tLeh3JWb8!;7PsiqS_{BtL4P`!R)z2CzBk(}J!}g7(l6VmdSDLBk+8b)Azt!f7$-Z1AqD7wg!(3?{W3FTM~ou zjLR-!U9mvF$vcw*c|M{X)n-|%tJ3Ue=W^e;mx1O*`zDODNzQ47HnADb{BipR2$Hs0 zAu1QOcg2GA5S*2+ORPYBJ3ra__uy+&m_^^yAjGim$%Cn-Uzgs^MV;79e3|tjA37j) z`?Zldhh5Tchkwq;JKhOd_sup>^!s4tcW}Rtxx^Lb61)1WTDT&S)X;$*Na2jcFQ{5@ zj=6Ewk2_d`Q6|+9mW=TWwU>wb7-|Z!&JOHQAG4ZVVhO=!Uw3v?vf-_HglsRpWor9+ zOFqooUvClAdaK=gUT+~F{5cT2*IVvAM|ib`dh6*?9ete?Ms zb@$;XTAq{=(OP|a_1BXUQW|`SKc1Y&pX15vC>+?+t2d|5&aaJ@_d4Jw$k)cH@@D~m z{~Z3W@ehBu=@0HN#%OG5ZEBsqDg5TsH*9CqpDAqt%9v@4{0u*>YCWt^Ek}zyqrTUk zd`~l5NqZzZ5{-F0S?2OksPQI`|M{ywefWtoiV2`Hk29bsH0S=i(q&s@#zql=ce)@g zI3JkG7oj85r5n|*bDU@fTX^tIp0@CRlVvS;X@>|xdC$rCUFj0+376GNl{!SBRXAOg z@X?%JeTA*m5rm~8|cb5EigbzT|Ax%qTUR80WdpdvZw*3%Kd6HWUL3j=kO{|SoBGd{Qeu9i}1sN}Bm$v7?c7nR3JwErUNZi?` z2AXPti(YuwwZL1l3VK)aJ_zl9rUABev`rbD(D;S*xdm%LHT?s59%2Snc=i58Ym{ZG z2$UvRHDvAjAZfzXDovhcUs{%NiaKU9A^OmsT8bw5GMth^3DP+vWoinQr&G2O(5Ah& z&~}8aiqz-HlCWh3Qx6X>I`h6QQR^@kEibVYk!^Grln5H=MlXUL#?1MDq1k=oB_Q`W zhXf`qgv0ZY7|55sNfNEJXF9~aj%Pl6+c+63O6%p4;pDDpZ$>56TLaycM0S;i(tpUU z_uJfvt%d7z>|$Z#b=R8V=CCGk(JxVnEEYrrB^l=R>aIv3jct`e&OR*`P&3g;@L{E? zW)oN^FLX#9v&H%Ea$GBaqz|phcLzKb1$0(~&>6~llJ%l%diRuyzCcw`SA7bG32hz9 z2+hNoy(cqPFe|&PJ#cUS`1db<`1(I-#;^Zfe*NL^-@GmVz4`i!@7}h3n`cl}JG1Wi zVf#YW>+Uz^))RhCd@gm5?~sP%et%8zH?JL+>`zB)p@NWVT8_bgXWem)*Wznl+Y3nE z;!w_Q&VoKC%!>AbhU&n{RRN*acuvTX-BAHq_m+3M#qeb6q5rowJh9;TFx^@Eh{Is* zt%7J;pK+^BzV@rV=`-u&wl66G%^o&5#>tjTjn1l+W2s$bM7x_A*|UTx4?T&cjc=;%{coxfUmWXv8*+(`7^k+Rz)?pG3zp0vVMkGk2W*HX%b zES#|TUEZchMq}s*h7|S<<%dnBuuq$-b;RWWQ znHQ+HH-GWg5GceM-+`h$@7Q-dYMSf(qQdUBv*0N5W^RfJK3QUup z>=Tm~KkYq#Z61?@V0+F9@Q>MZ-0?&PtvQjYUQ4|Jep-MwZLoJp5rObV(<#?N^XNUh zX}V{TlYV|V=^N#AF~+d`SWlDnBnnis1|1b?jukfIzOsMo1PgaM|GMi==b@b*krZ zvSfalC5!RlS+drvnj$Z|6gM;Um$t0RQiQeW^Jy?NkiQ{|?@{w`&$G^3hN90GaFYh! z=a%q)W-{Q{;Y|+@jhzjS(<_DQgD$dbAV2EXbR(+v%cy$zPLGI{P4qeJWy1Nx8plK0 zt~cb|yWAmp;6d}jS?-{xZ@Pr3?$sRP$Yx2J6)4GJIc3!Rc1CUGm&z zThg)h*vt=4aw#%NAdk$BJmel?szWYjvtabE-|CbJ5BMvE#m%kp`ld7^XotZ{gH` zaOb<@PfcXbPnW41zMEc|YH^ktflZ0bTB{ZkHN0=r6$fH4(7tt*(qmhYTJNq(p#B;a zxwyCTtFb4VL1^oFC()>pP;uXPfwn4yFI=iKr?u$FaqwVu@-Fp3iMgSq(*g#lvLN2Z>?TaGIN>k(#k`Z=hH+q`m>8MVJ^qt&)_x4jXqFzQ}2mb?*vj2OIk zxd-kuh4Guvo(GkIGy)MUEP_f$+E@%KBMZLoK7Mug{aq)?s9dZ{DGC5Mefj3@v(M$} zD}0!=Bw^Bzx#^pe0wH7C)&DsCch*wjmZ)Er@x(=+Wt^|GrRfyWk3CxbQ=au*W!!wv{2V#jAc zs_sDuLdA(>(Fmf}XM%}GSR9C`FK}RSlqMEOIo^q*R~OI7`|SdfjKU%EtjL&4sL{l! zgt|?rLYwH(#be{Lfb3vRNkBC_9osoqn&PA$Y?>qaSI)lR5z93a=BU|!O_4Jh^w^&H zg+1%eU5$S>YhP2OQ!Q9>hg>oYw_C8?MOVos(|p(mS)pm*t5n(^`GxRM5Heq2sIq z{)WKG2H4!1;b?1W;(|nfuzXnEXu4@(THv6*WqKwZ)?*skxrGv%=t2SI>S zoc#xtB5nkR1C-gS;`T){Xw?nw)_I-OEn@1y#k+_q`9Rv*rKlc%0eco(IdmJ-a1ky1 zJHTE#M5A4j4G4v+vMfSp+=l=9NDvtD13rHWL70dL9Bvate4ro>Rn%Gx z0n`j7xs0?*X9D2-x@)pbi0nfz!jc0_(4Lecdrh30aby`XmgXk3fKfftHmoC0G=Z!! z^pP1TElCl*Lj8V!oQSTqHJsg}3}K4CWK_IU=P~Cd%6~8w=Pl#7fi^jP(DGp86oL=) zDTFSrl18JV?V@SvY9hdW^hh~Rr*9C$#Y&Sa>=$K4J0r4ND;%*Dw8RaZN1Bi3G)hu@ zoPhAG9yyeU)-AX4-`TnvIB%uiH|vqg_VV$&lrJ21pb#W~8quj*YnIhob5N~axLVN* zEndqqQz+EFj) zCJF=45^?pUI^JcUc=*tUS~QaajXu|O(g|9+8n*0c8!Kvzf*c*K*CD0sbwtSlsc2Xa z_WKDin92jP9n0ty*y;2UgFv}gU!hUHkq1{~#xXO0E3cCxlk-34|F0^p&JO&dISg_R zo83SUpg{nMj$vQ7%i`waA8t`1sA5gmn&ahhTr;NV3o`{3(}Zs)q<#@!=3 zl>xWp+HP+Y(%i%4i=m59UNcE-U8Cr-Gw4YAsZ%FA*J*VFVV(vI{Y1BEAwCa_Xz{me zsi$6lWAEJLK5DBBFIM+-P#DRTqt!9Ju)E8pZ>J^b;ioo2&!TC5USPgs)2)mKa(L(J zAn0t9G>}YPUQ@b{m#vxn)Y!TG@F_jjAVuq@Do}WKlAwk2)IzjlwI!9<2+Xjf25}&l z5eA~5kb$j(oU7<06)_!V9npiV2CaKb9SPfi(``RoG7T6l02ZgV=$(Pw^U(eD@^Kyl zq%63POhlUwLO6C1Xa?7)oP6Zc&xr~zY4yHK?#d*)$(=7;YAO|e0EJf=QXNd0Zi$ym zXS=t&y3c3l`+V%U;`M#La#qpP+k4ld_ehmJU5pedI40*2Cx=@&8Al1MdA{HmXF_#< zDognu!<*&OKu$tju!~1%&27K@=iAlP3ZqWho#lV6&yd>T>Ti48VKDHd_tSRLz~8UP zMFC0I=Xv|hau}3QQ2Hs@_Rq$4WNhQ=s&ofO@t|4Cb{eii{3#CA4$y^}R5OD*In`wH4D(5qk^e#*kTM$ETD5!jKnKfCxFp7=q zF|@V*K}-fM%-rRJmCG}8dCL_<^{BHulqDk(bgjFR!?^!v$hGz`uC@1nJAmWY@y@kT z<)C*3msQx2i`=ck_Gr6b#U?iu*bz2!!?pFi71KKQ#o{JiukWWL&POa29JiX)-`H-!-i#wL^JxENEAr%tc3q;Dq6pQMvkBgF(5xC%9fyli%5P zW4#z|+j0G%zCM<|UN!h8K!i=J0mk>~=lyus|#QY`+$NMC+IfA5H0(p)o47 z36WZgZ`WE8z0FsbTQed6vw2)vqjMd*Hf==R(S_@cGOZB1yq@5jSyp=Sd~HCD78dNT z3!g3^jF4<6a7z~&8YNpef&PG-abjQo?;|(i9*il!mefRemZYv5EBTvBP3$v{3y$8Q zw#;BWZ~pfA_`ifV2FC!`2Y7T%ylwCJ=}ylV#50?m{E;ny7lf5?NX(^ z!kt!@HT(G0-TwgIT;I)?5i<%Cmw37k76LLgmtnmMDVOi63l4vCDQ?m&h%F7yu5jT`QrLkaDHb5eu8`}qz<2oz7-no9)yti z7YX=Z-EreaDg1vf{m=2Q;O5|XU^qwMT%P8tYgo~(R>o`h6A!CNx0-O{!>Y=CS7|PY z2$c#jc*uBMkEW3xLYlv+vZoslah}`7&1s=?JGhZwAz)=sqJ%C8s7t7YOo~XF z`03EZ!cl>{zu&uk^9dv+aM4T<0g<5HPa?trv?YyF zV$H#{e+7#i&UVsP)gWiphW^p)N9?B@s1H&yTQ5MpUkHaky7h=7qL_*bD z-X{crxZ{8Nns{vp1vf-+ouG)z1M7~YOd9c)ayo*6aRNN!k0J<6=__#`DtzelaX$n^ za3YbhXv2`uV@z6EAfaps3Gy{6lQ@bIHzq5hPd+ov;0LZ55tic@#3B`mW~h6#y%s4? zQX5zb@yqlT!Eyik4H$(69736m499)gQ9nizk|6OXejFF}oMaPW9-gNKemdf{B`y|1+d;g;K8Z@WQr-r^8dF8AcJLV@CuI zFg}^%YqgS(eDs6s%-LHl*}FPC3OJF1w?|=nhZlhQ8|Ac_@gtI!^Xs48hnP^912LSf zwbg$|ATdz95peJ0BnE_p3H3`LF=&bilP5?FC=ozaPvQXaTsHxV1+yJ5y`}EX9N(kP zsM^&_QVN19qh0aC5)dgZkxIAI?)P_chJ!*)Zd4rqINb)4&B+PXx}6p6EgtR0Xg@mD zj7NPyo8uZ3va=?2xDlvi?k~wC@#=_YW-tW+(muYWrfE`@(a zMK;#{J~NjS3OM4xD%P&dBNGcV1O^$B8Qo6#!w42bl*pj`Fl6)w7A=X;yrT&6ElF6S z13UuVl{oZi&_?JMo!T5W*c{Mk#vPE6ibSg(lX7s@BMi3Uk9f@wvNwc?ac(<>7y%1Okk04o45DIDr?DVS6eLcS=4R`hyZ_&`f%@ zCl4ypw4U(&KfW4X^_mFPnvxau@nBjjHx6fja>E#2d-Hoy5+g4hceRaxb+`Z`CF_jL zcAa2kX3_8#Yw=imlg633y~i;}CqtH(+_vbs-@_+E1`*62N2vWN5&Ae!>0({ zD8Pg(PSFMt9V_t_hB;bLJ%XK*5>9a0Lh-}G=m)|&S@oti{vg+j(kG6J^o7hBBrbN+I7M&;atYE&B%a6txt z`*kq}3h~gLy*aY;+HgQ0a@ZOo$;xGDOpA-O2K^zE;|;pt)Dc}qKtdc%RYtBiB57nE z(VB^6bhf*yXrMccTLIGH{M~wIAVjC!G`F}~hc{5l2~(;)#5BZUD*u0T=7OQY(?saz z`Yhv7Snj=}1_+iBu#gtiYua=ti0T&AbUA?2wyZh;ADe$v$+PeS;IYxVY~g>E>CH;W zyF^sgH4!Me5cfUFYc@g+SYqdVZOusIaM}`ddZQ@nansC+VL2MP%=6~%wpI{uNT?V2 zZm}`$if+AZC*iGxmXd!Lr8{;VbAJ)#B*tzMyH>*N6C2U}$&$5*^`R=!>>Tbm>K{N4 zphq4b=T-ucv)oGfEAYxU)x|qZ%Axig!_*WusFQ^C@cB=D0$0cTYfwC+2v-- z3Gp5z#mmt9ILH-nX6ttYLQB;76~|CIqjBb!ZzuT=9?78vaTJy=31W_<0t|Ak;q8n? zwrW8?<+8)a=x0la_?UoB=%*P!Mn7jt2zxLqx1t<7LOFSqa!dg+XDH{dB-p0QQ>H))s~k2$My>2__fA<*$L+tlgV3#4LELD61O;tZ1t zG+ZQ=&#Pa4?p#`eokKR|)T{l2YzqGeYrW39Dhz!6HhwdoFrU_x|asMUf_AG74*d@g73JNlBNXEeHvOxWcrP0OLcWus@n$o zd9HtE<}v=~L;PvgcAQG}93=|a)uN=BO&bwL=L>mgXOigCE(J+_2RGUBR;|N707R#!7UIE zGA*nrBh6XTZSim^X}P5WC!VMCUbcDKC_)i`KZn8^nc&Q-*e0$c1PE zNpm;{e*(K`rf5pp%8Y0o`Jh`YBXHWp)ry4?x}M)u1nr9r1!6gCk914hMeU$)9XNlo zLsu$Htg^GAP%)hac=;BUa}0V1Y?kJi)H6|XXmv$ZDhG@>j8{2N1&6fcN%2W%-DtCs)5$YYa0e)ZkGmEnfYiB*Kwz3Az zD$!25cZZix*Xms2HN@LB&(-M-(?5UJu+kgwVb&YKZSPvmBkvXsUHqv-!oCDD-#Riv z_O_a-uXmb4B3LNzYnCO694vMk1KOH{W=gTe&rinqV(XmGCIp99UoB}N+0kmpW zb*%%eTlChv#^!O1nJp#q&HH+Je8Asxsar^2=9UZp1X0zik=sw67`c`d-8%)hAZC6R z$)(R|cVar}Dj0tSJA_4MFm@I6&L#pAxhFmT6uBd$@WN{@`7g304?U__Xv4@s=M(^! zF-_oi809u0(PvO|v(OySqCfxVyW%27(P9YzQ7?Bf*2ayL$*0+#$Fnkl^m_`c0na zJ?EbD&;8cAch=gyYPzeddapgxUG=NoU2rI|Q@g`(0sP-Uuq*F6CWckRDkk-fT8AR| z?$G7bVk}u4L}I#sdxX^MG9w{si+&s+=vLfv8Eq@}4o{`~IARHQOV~9r!8y@RcG7v5 zF`#Q)6;Df4z$A#CpQjZX$HGER2>^JlN4!J8nvg!BP>j60dHC>rqfUwZn@iY4-R-I` z^n{#TIHcWA^E99E@45O4|H$TmaRci<8?MltU02P1D_Ys~b2<{yG;L)*+?AlvUy4G= zhHRBZ%C3BX5hIB2t`KQ$gnIuYC3Bt>v)G3$pgGa$-0cJStj4{Tz6okN1b9!PAHFnk z&v61>-&u0Vz#?bztt1O7iW24!bEpAIeOJ@)z=sDVaXD^M_*ee76~97AP^LQF@sDIM ze4=%$gge_Prt$H}Il3W(sQ*tfO%?vH*sI8S>pg)=G8I-{IYKQ;iK!%mIju@okHaW= z8}c8Jt&zB`-I(XGA9OO?*;qMa9)A6ary+%-!PwlUSfgjkqI|a=@VQH5ZJZ3Wp0l3z z0m1KKX8?e{5kBJm7sLo3!{CP&{F`YHvhmN*IM#?C!|%3sYV#zDMG21)Ml#S}wYi&3 z!|h_~gbH(ZZjT@{CMp8f^7WbGM`!t|7l=7A^TtXg)|*j@1{1T`=!+CeD>fqA-59H- zJ=<3I7+aDCX=}G+!{H8zp?h{hPO}hhbulIhoYnluOTRThUAYOBwnN|QvS3l znlC<(t5){vjTAl*Py5c^_&MQ$D49A!eWs&$E2UE6K+k|W{o$1b?_}0$Pj|mdNXbMOx?BmD`XI(@x6pia(gT(1 z1g|{4RBe`;Wu>Q!w5EwF9CPY4RtfkKhGsek3X6kl@+tM7?wSjH^P;l(phUT zw^HbQsNS&9QSiehDf-!5%}D1pi7aj4+1XR)-ZvgpK~4{_0bR6n`@hHe|4>PE`9zAthN1F zc5(#>FJ2CRIeV_YKXvlVlz67Byq>>tBFqs*J!Ed_KjxUgheoSVT?H1phSyOy)H&9l zQ#a1tIsE6BdaqE;8?ks!k0ORfEhkm?u5jOkYt{KBQ@z4{eXfqle>c zOJ*Qb}=Q5)5xH0(W2sUmh+nGjP8i=C{X@+asJ_9 zT)pk(Ik#)&*|YHlzkhV{t>iJt16eFB39JdqHY{k z&AakmZ91%bv3~R=#bN;dJliyMtUeJi%0^syntqifljP_JX0YW8r8~PRSC^A4wxeq1 z3{qT+%^U_!$lpt@M?lR z1F=c#l^ejz{XZMuczCoQ^txtK0!%Z4d~BR_U`&%EiufGJhX zQ%s{uVnDJo!4YImz}`Y$f@y(Tp?!g#p~mS6Wuv!=@D@xfqnCB1c!!t!+s`EP_gVkEAmts$88$x)=XwDYBXgM|-fS5i!{WZ~5hu0aoNS5Qbvan24 z3SPzZW2|TA7R*sYL#J*S5slb8X6VesvRH#xLZ${a~3p@!nF6Fu11-9kRs!TEx{oyH%jA z=$Po$2b_Bmj|kTHIt~MvGz7T>HseryxEz7k znz0M4I^Ks*IMg{PQF`Y-k}>p!`?Q zya1R3XY-c3{H;4$KTfdd5h;wF>E+bu9W@NHED)Ec+zGB?fYNd#l8Dj8^uF;&^3MBG zEzKUEF0b?MUbNi5!Vs$5YWPDB!o&Sazz05PDondi*~!%U++Ob!AmvXKAE5%Jg}{Pi zcFFI=)#9)|4czgX3&IGa44XLzj3;*FeWKzqKH)w>@&4HgU1~+9g!IpQOz_nevx4F> z03Q|t+B+<%{!gI;yoMKEFvrs3muz`+p`c^ca>~1M?o(HjqV0CbWR#$Gv>59+?V6Sx zM_zqbMTn}!Us&cJpZ9{ymo69tLOgiXVTW}VhBiqyUlY|6g{sxLBJ-A53?!VJJ_!Gy zD_&$TT>-Un0d+6FoPLbPV6DLItK#z+5LOROd{YXZx$9fo^3pXTj|tRMUl5ih*2F7v z?p=eeXbfzvL@)n%BL5k-0&V6e!k16)xe2kvp53+`^r9wYmeL!l-*HU*Saf+36&yZ_ z&#A5`Zt2}yDsp@hZ0Tf2&LO#xbHlkwIil@-0mp6= z79&a$IBGsF>&j8f(0D}|1`g#RNYuWSO2zFVu>2s{hbVm$z-BG0h4V>UTBL`NDb+8Z z-mdUN)k{SP0hkuBgEHpW2qnoH0ghpv7ewS8B6~)WIJK7vnLt>{9`71cb3yfXr1i@0 zrV95>UF<|pGbZTwU4Bk7&u5V~O3?4Z*IIu0Z6}l{BA9&)?prZcUqJn~_w06lY34<< z@}W^9Lk4)1j+e~1o)qolZwXSnTti`?Ysk9Z0tY!OQ|K1fBp`@COCb_)0h&Bht12te z+49X7UKocG7_W-t{lp({O~h_Fln&M!S1Ku3^M6GVNeRCubgzy*jH4@D4g#X`nZtlUF}c5-yHt z{$sQ>hsFZb=Fmx{22)59)hha^FVh&{ayazQw z#>C)Pze$a@@|vP#+hcb$qQlly*AZ&(3E#K^IWnz0IUFueN!WB$diaSWDGZi*c$9=; z_YYVnsst5jsAOYv@K=f9gmY6y6F>GoOO@zQzlCe+{`}?xF>sJ2%~tHGORY5xRxv)cFTB< zfw=f+`Ecc)S^#zOQ8m8(;_%~2o8C%bXg8Ui}P zT!f!;We*7;@cK%W3s%n$&JvoLPla&P8-HwxwM?f&F&}XFDkZf|og4C!mILG@qwcWw zBv3=G@?=`2kspg4RybAWe#;MhD!V?Zd-(m3!iR2qH4h9u=*_TgYt$pMVbe{+7r~TY z>tQ56I&gxls4!0r%XqKZ>2&%IB&8-h=jij9N6VGrkoN*~sCv-$-f?Vv<_yrZ*gyTi z(Q~m$ZpfTOtZbp{Ten2Tdx~MeXQ5AvW^O>IK-7B=i!9B*^g8_hOHZ#R_b*VgXD;#T{N64OgpQa9tw_Mk)LFS6R+Z z@0*}Vrt4bhUFpoI>|+M(LT}$)cpKS@8FBcJfkk4QG$uG73YZ;4 zA6^()UTi_qn*BW+d-b|kQfqrJ#t&xS zyjSVeZoN zqoKbiJv$Mrw$+j0^}0(NbCOFfumOWdQFL0-6w5uD`#|4mp;>ID16TgO7M zh$PiULv`2Ez<##PFk2`N9Ds_@4Ess^)8~CH*LZp zGZa5^;3n~`Tm>vf5O$I;UwC4%|PKlP4d2}VUUDbCHey`M~7~< zH9D}l@1(}}P%a=G%MkaeWs)ZKv>_=hk6Gj}loS+2Xb#D4+WKSq>n~lTUY$wd5aI@9 zuhJuLKUf$|`9zu8OikG#!!4Yx{W{Ozy33*RjeGO+zYzCp@4})Ecf^G;Y!WFR7NIsaJu*8 zxw-{E+)P>;%2%hD2b@+oX%Bp!NjV6w*r?6D`%*?zd4(GWt-FrXI_#~hj*mn-oYI9t z&afpIZ>BOLIAV8;^W_y6oRd@lq)7Aq^c5tv&q(|{=5G)nDuWU~f_V_<-ph}zg{tz* zt+;@#Wk+<^R$&w_w5mj|nH-d6;4RY#juhNKbss)+qi}_3^8sg5d6RIc1k*ogfg5ST zjhZbP6ut8lLGq56LF1@vhR;uBPy#_{F_|_>3l|&ZoY}%?WepVF)Zlo)R4~tti!R7X z`+O7zJfii|PPf0fm;uX5Ykn1Xu%DsVby$Z~`cd+`^=46%--CTq5aaQQQm)IbZUOG?N-mrf1fbw{Yu?RTa`iOuMvP4i@z|n1e)RQ zP8z<{{2bqiWt~1g3pvsqcnj`xJ|p>B@j2YHx$Fb$S{7Lxnt@q-y#0NADWxUpM$I?8 zsGZfuGiX9hG0QIQ*bR9!m6E+Rfmd!qO<>~#De zF21Rs_|yASw?4wR|Cv2q-Q9BQ-Jyx|DPQj*J1;a;caF@969aVkoh@l2J1t_H>NviN zlQ$NV&AB}zqFKmf02N|OX9envySn7(@RrS5opLZ<$W`iDg70JQK84@0OiK7>ng3-#XP=&k&~DFY3{K7oM;vjrDhG0U{vL=^Hc7@YL5ElupD}R z2CL=+xt1@9qo;;Dm zVhs8g8#won%0qeQ5DN?@uhC<&z$>cJeern`daQkLifi83b1K0*Hw9i=ReBOgy4NA; zO&__p^7pP~k+Rio^8T-occ6|_*DcX;!$R9IAr}_p!fp<2!x7qMXHS9P|OF?X|~dMhKu#lgwP!N)21FH7@&9&Q$#rVNB#kWWrZMoLPCPf|)ihL=l# zpHqO7lUs&gfRj&3j7sGH%3_Sdu43h6<7P`GAi$HV8HB)?`dW;O23UWxUg2^E)SXvv z{c@X6A3JLYT_mVCp|Pb7*75L&v5>8srQWLONSbplY)gdDr_q^d$($p}Vi63q1V{v; zBGO`O4=TprXRV5_9{4Na_96&w~Z6`G>T}T9d2`4o*oi%gwyg%oc=S5pR z*=|l+41%2M{Xjzik58WdQQd;(xY!spmUUG zjZg@>9Kf)R>1kPztAEb8H0xY=Q}367YL>sCSl^L>Tc>bTus|_BP$zQ~vfwmcTvydr zS<1}Nr0gnKg(du^N!yja3diSdlQcJGojt7a(>Ji;+X4*0M`#qvU#Q4`!4BB@?GMd+87Le;TPT7`lh1vN`FU3UCqQs_^*z(Zrbe(2E%!9|<4fs-gfeVgo~23H23*C^zANmYhNhc1KR1Cd;Gw8(*`=ZyN` zR?*vE(qju_!fE8#sGL5$9gmBe_3Z}jMe1V0Y)z_FMzflk+3W;C{eRs1Z3rVp2@hwI zsuzJ)9*nGPSFX&MN#@xG<^Gt+j%mx0Bd&UTP|Q3_pS6CtD2`9@$i$+cBVxtM>bFgi z(WAwA&^ZY^Pd0vo{lG8>t9-*m+2S=wEoHn)F! zug*exPh=kjlYdmb^!_;_=3~HOvKdp7=yy|QKt{ORTLqz77S!sE{&r3T*$iaKH$W(D zkotg=Ekw#>xZq-GcJSZ2RyWL!D=Th4)mexb$uIV^6RW^q<@EInH<1vD9!_>;gN^&P za=Z2*&we($LDcb%;H8yqP<^FWVsn3QDr&|#^lA7#O`7g} zKD8nF@FEc$VHyuPZkz|1u?SIeN^#4y2FsRO<)b9)@GGgY5Dy^?V}&~z~Z6OfcR-Zu0Q6(jbxX>8xI**D1-rD zTy@HyWIogn! z7fi;H4d9~8ky%2l>d5rEl?>p$4bbh)SgV48>pEz@-Zu+qMrOtsdkUtxj-wAdB zQzMl2z-E8s!O2m$^TMx)8>N<%{g}hh;knV$YeO4b9Cr}{>4B7?i56?SYg-~`wBV1> zcl-Q;(EewtYzX3)Z&G`?3^16@=&OQ6szM=m(;J;yZofF|wP~;QtMseEZ=_5!Zim3? zI`pPKj0N~ZtzS*Aq?xU6cKq_UDeWnMfaP-g)lGv#W}#E9xGwm~{@#Sll$h=%YB8hO ziLf;RGF9VS3fVC$##0~aQ$oiTd`93;I*z@1U&P$?tr*UDA{d3OFMaO%M7zFMR_Jwb zMo<8gaE<1DP$ihMrl;(sOreD-= zAdB2yidcH3d>1?4-n)e{>1Fmp-(oT{+R;tdw=zlg*4@$drYa^h4QCr;#4N5ceQmRq z6YQ<~h)3;`UTB+6zkNP;{kTf{Y^!H&AQ*`nnp{|9W*~@y9GXn5_eRTG_Tb^NE7H+U zujF02^|m{Q&1`BH`_CHqd)8V&z5MhNd($-iz17F$5#2ZX{}7%qeLvdFF^@w0>L`iy z#E^U$DMKx~v$$w~$ZKZ+0wx!5Dln`+Y$U&r+Gzbg6P^yiwvtO?7f^AjD}UdaH50M2 z_YodR%UUM=Z#}W*|0Gnm5xb+gh=0V-GcX$akpn&@vWxFDF<9Sflt`q*Z1XeK`tK?2 zR}N3jCg+iU$|HQxdN@ip5Ju8GVht3O6ua}O2O));!*LOXa1w=ib5Ig=OQi+K))A#h z&qXs+R}6^AM7JRD^~@x7x~sO=NY&euzr}3h6Ck88)FSq9gl;tb#iw!ZejMOeCphk> zKLnU0`5CuK)cYP;u>eEqd^8SQ;~)z>tP?NJ{f_G+h%&Sem-Sgu0KRk`Ei1$o zOu^PI+X9!mj`BXl9*pbM$T-G&wk8al(vfh1a}=OHMniVN0Q zlU2&SuUWXkZx6-Vs%F!}YtdYj>v3TO7XnkM-*bHhfBx{7yg`Ly#46%o7|wlitFn>_ z#DX~?k>)~Mq144pf~uST~SEV%C6&%fd4k%WLee@0pi8KK!X=?x6!RffWpngKSPO4P+a#k|sW#-etCd;>H zdELP#MdGl>#ZF5|fUAQk@MDI%y8o(&68Op@jDM|SJNk$hk<3-L6HSs_>- zoq}hpT{3hKeDLzyG`bPbR>4<#gA`{q?k=>SpRSYo9Q}bOCFqFXvWq%6db|8_*>kXF zc#29o7!93^=Pv=_KDTI_OvvKTYK$H)f9&(IKy=X$=ZS71lnIqvf~JwCJ$a1F$M*CY zo(lI7sX>fxY1o7$smha(z98XRj++{so_j82-r$Xa4kKBz1sC>2BVdxSp+E+f^@!fd zQ`F`n<_=s8Ss;F~3wa;NcI5-4a4eh9VG?SlWts zmJaVPr72&W`U?o*7D0salbp!z+|PJbx)Ra>dupPq-nU= zJse*o5G=5^t&hy8$J9li+dvKQbx3->G6(6u@Rt}3 zNw26EQtTS1NMPyNSVyOmGN#rfzg7Ki-4=ZNXZ*xeV~Hf0fTc2Up;Sxc zV;jDqj;*G-4E@O;t^%6fWY==fDq*%zGPFJ&Z>a>@>}Uw zz9wTBW%G39->%A|=J;FYyj6jXbr?VU5Ef9FwNEjRzdSpBR;?p$>c&_|`2_4(x-DY( znA;pYFTP@N-qw_Ex{`(ZmEVd#n^Y}eBCb)91r>sEVv1H)$s+wBQFei>z>&Gf*40@2 z(lwsB7|+FXseD6`qhRc=)L z{-e|2KUbHOL7A7Al)*+9m$^Zt=a-viZO>xjCkH>)R3u1jXwGZ3S0BR8KR9(wGK_!O zL9>H|3T9!)()WY?0iuAOxvody0&ZGsB2MX|^!EqCSEThpRNQds`Ez5wW(#9V25Ap9 z{xlEMHlbqNzUk|uV_bPZ&?K$(iaU43DY6y0`x4T5%TFnv9Q)I_`%;M)bE(J29_DWI zdkmB_h-b#)tgWL8v4;W#x!cT*4j#{PWp}eBa*4Udjuicpfzo;qrG`}~6E{n`VAg}! z;+IBwGn|;>PSbmX{yQ#Lm<1l`&~)wcQ*QGK$ha4HTnQkx6l~DS)@j_XoY#IQUJjD~ zYT5Zdi9M9V#BG_DK3jTuJ)JJdJ(m7YuZ=}DkrwZyhqm9-v4Y&^YY=Vf+OJQhU+}Mh zbYxnSk{5SR8oBB8Us$pBw$mp{&ta>Cn05-YCyLL&SAmQg_T$buz~6``eU{=Zr+mhP zuW5fFC9-L9ItIVUF0n*4`9|XaI2%}i4*N~^VYce{(|n1NkLCejD)t>*rkcU0{CiaE z6>{=U$f#DPyCY!^pWp9F?bl|q=*AjA%n_rpIj~a6$M4|vq&A|l{ex@Scs^g)?=d@P z)o1Ys*lGIC^o{6K7{ZXItY*)W7s|(vZu##rr5%4|@x}j^`K#~i+>S=3zGG@8MDUfJ zcJX-ljpf1XqImc-XX$trpDRQbch#{FgzHano*(`7>+jbX*0fn`wLjZHiE7P_YMy!~ zyJP3K`x%d7yUXJ7%BColOr~Q7irj(AW}EV^`%}=Qj@?jjXDU|gt-%b2^2+Z5R4tOb z;S__&FtBUI(*UMCch2&)q)0s})Z~^4T5zcy`;N$+mY9$a$1M$P?54?=z%VfTM!q^r zbpX7b+1aE8YV3*$OV9vN2bc2KfUGp5tx|zy_GjiB?fYN=Yi~|o6^33%eADAE0Oez* zO|sA`cJmd!sh4j7L)eVrC}Y5iI97(GjGp^hu4SX` zhqRH;%71WSM5zWV&Po2fF;d-Z6l>FfN|iIL2E~7{ROVVZ5iS&V@YU2b1;Kwk(}JBj zkjb5EZbXAY8psyB=Cxbn7AJUK!pn>yq*2I*aZj1s{dRYxUw}$`U|E)!uNEpq3?W?0 zItkzE?#gA8x;sJormhNM9z4!U2u~CWNgj-qQzBN(sl#F(z?G|)^sG3?PT2I!zCIbp zCTuEj75H1MXS2Hp&D9q7j5AoU+8rQTmaVD;Bd(@iH{tRDXwt)HeCR95 zk%0|-F(S@vEhFWxJ^LH^d@ggl9M=l0@eSE5B8CKPX8z zh?6TXm0?JzlNde;V_V4Z=B)oPb4S|KE>=&b(hUN1khR?DDueB8r3IU|m6O?Z<#dQO ztv-kC!Rk`zMCfEINXv_n8ch}aD5;Pn)BUK6tYsV@IuVvQPt+(G_uk8mdViniG){cR8;T=@wijV>k(afN&!w(epr zg&H7j`ig0Rx}#%JC+{mEr$gWQi3#0r2=YUatbi-WDN>4KlC0ROFoBlSsfA{(5GgZJ zl7{5-tcOj}d8cKin5;TTf(D_`iBF31bMM#p#uAv6D`L9`3LnN4a8rX05_zsDCuPJT zBl*isubZN?dawkK{9XG5QJe?@KmlRU!;;P<57~u9$x08*btM7cjIWH6g{Z(;&8d2oli7l8DLOEAaw zjbr$@S~ndLC$|g9m&9}d)ZM@S+$b29t!QbHv_AMh|7Lj1HR~VC&pmsdq$k~?;p@CE zDwI9AUTGhlDP(rNbV!B0Fx0hAf`jX6ioDU;wN5f$-h$WzsX9jylttbu`YLWHQx9h* zJ=$p3r-&6h?FFvz0KSJVRc2~-L}gka#d7g&u?N)p6hV5!q(QBdO@O4n1%EUgCtj)k z8`ZY|y;4;+R7Uci_JyW$5o3Hwe*%uH(kNsTQWpqyCP_h?Mm2(mekKV?i$)=Wie4^h z=jy%>v)|g6@w~V{bp|6G+o*_fK!9~7$yT#KHi7`6L_i1lo%8YdG|G4Yij5{2v_N2| z^jESQ^sokvbOajxBD-d>8wdJrdvu3Jg{6vKgciM0@>^YyVgx;XP|`&4y0@|gM7Njj z_x&`X9wi;dWq67tr_y!&S6ZRjQa4JIo<5%TN*qX9v`;83jGU!cFi11|jaNeGxi7!> zo)8pff$5{Eg4sm5?~&7PlKUEYv#Ft!uOIup=GS$@^vOHj?q=4N!>Gs=Prekd*DBVB z*eizdWW#qSV6X~(+nXxbEcCFQj=!9k;dzRF6=||k45QE1#ZYvkmJZ_~7d+)CXn2DT z4BZYA90oFxbGZ#q#XnD!@VxINHcp#$x!$iU0;J<&vOKriX?Mw;+-{22bDtoKdz{*r zUxn%na{JQ-xSMB|-*F31y{7VIcWp^twohXnjdg`MF=An|iTrkhX3Vw2RLS|=ZKv~P zdV3bw8&dWEvl1iXfGpYqwGpH!)TD*38z*bC#BCf;TA|9WFa72VDZ0Z8V&Gzul6 zVR%vI!gUfae;4pv7&jMk_kCC@)6A0#%!oBDlyJmlQKl8YKutC7z$FL9?Y1nW>j_il z474m{qOp19=7==^n}~`}KM%zSru((k?(sJIX(P;{l%>4B$b;-opH?B7>c5y38l$?S zNr*r2uep)jN3X^_51bh}&4H#^`9CyE+}QKaDjarT_9c)=eh?{JM&z0s)}WP+M&sq0 z%kcp~WcS&ZYm@$L9unn-2EE}Vv>(j-jk4RQijNS*36(ph5Q8~xvoAaWGUf+!sE-_I zv~fLezw`*Oe9ljbu8nov?ePsaE%sLa`;-HVv6$azHSOp*G@<>2+5H39UDv_$^&BJ} zKTj-pz&d>X53YsmWA6H6;uwf!^?g7Ke) ztj8)`bIwNlrjvc3rlwoB1%VT;n?15UxG-+`IGXdPC$${p5cJLR+s@EGjLiOTJ+84R zf;H!Sa(lUvBu%=N!}BjHAxFkjXI8%13#ABm>rz~7K8b3C12o5XbQ%P$oNAPk4>U-O zT^PPkN%3ZCkMAVa3U1r0z00V?C_Rz~m>#D8t=8#iJ%F2%+Ro7awNrto(YJ$FEr@TY z){#-krn)%9KUkAy(J85>n5jLpgV)~5Bnc7YZmX7@QR$?z2>6p^a?1bHmh?@K-VwqE zXd~}de9;Kn(J5~|SV?-`83Gvvy|r^y`kht5uTLNTov*ZJoYB(NT4W0{Oo$?g;?^CV z8o^|HHS&y1W~T;m5lWwu$RK|G;>ZNP(xUNlYuAd!_q?4l8-+jIuJwMrJak+wA*4WL z{;ft>O3WvbJ{ZaK9WU2+ohJgsC{Y><)d|65cy_) zITboCM#}f-u#nYYp4c0zibBd~<o9NnpaqbI%$-U6I7o#>;lkFD$U@Rk>VM973&hKbpS=;v{j3cpndp8efJnH` zxAYm+?n;`we(`_cxhLJmUNGwG*h@-=?5{v!AD+7Ohm!jT{W{0{!YWg=H{ns z9S+{`B6;3qA2Kw-N7gEmjmI8{;CU!+u1}$tMZsg#NV?mY;o-ZwwP2-<{POl9Z#Zki zdbqS+mol7 z9BKJBp+q5LW1Ht@oHAGI2C^k?es?vK4scTE3ZsZKAmpPW45yQ7MO#%*FMlk=o4z33|D~n|00ai4BA8 zs&3Rltfq!F*sKlahMdnzZcGYh!@HHecml%Cb_TiMLVb6e~p**F4P z!!Nd)#oHv)z=m8DDJ$2v;i-gby>@28NJ!I|U8~`@mT4O4D71fCHk3!_3uL1RAQEiP z^R~ZFe_Xb$FWQ!x2FXNWv!Z-^J0%1SXQvADS14zJY~WuQ(N;4LLg*US{3{~iE~USj zu2VMZC##vF@`Mo^9&3cNqObA>V1%;@QjDUnj^MfB@4^pDL#vLHyfON^n(&-*)NI*B z|5)9MIxyVqAsGZQcue+!{fPo3iGuzg(BslfjO8yL^6>hnCWZVt`ypg;{BiUKQeA zN5S{6HIM2L;#f!S(XF-s|6edQMz^E@9LYbwY6~!#nk1e73Ckk@>++;lbRLo$Q=D2? zjf?m8e*#!7n3!wSf1z5qoL+7(4E8np_Ml&92$rj@;xnnweYj+)Ykjzae+zh7ZXEIS z!AmcC5$Wa<(v0Asu2@mFh(<8V-sT+w01q?)-0`# z+5CGnr>~e7C_mbf7w)HdI-3cM34%vr@S9A$Y?`(>hJneoM`uC^Qy}- z9&ukT9$u_%*M7M|DwI9gb@5^#l(@tC&}Sf&xl{cKM|pRq-IW=%?+awyuH_ESgz%is z`_y`Hjz4~%9GEHQIla6E?SIU;9Wae3X106zaT-%xY4`HH8eVK~_X4~!)Z@YS@)g6I zKKpR8^6xASnl)FO$*sDf>3pmzvDk6_62;Tt`bpjJ%ste>`gB7aW<#BE!<0)+QYAlD z+>|3_%XrKo_7$C@=KwH%G752-Ic4j^Z$YuH>bk61(Ok=hdB}bjd^&dPV-wIVd}+Tr zV2aS6^n{4@s%LJp)^_I{c2|gkTem72oF+vHgkry5hQ&9BX8^J7P4@n3EN?kfwWP8>mP8XKi8m58kJQtnBBd)xi5f}!*S z$i`cnicJ;wtnwJ{d6yEQ3B37q`L1*lVQnHCluZ@$EXFU~Aua@$ZMy$qJ_n%AtMt8r zY+ZVj#_WGom#9t5jimPq{Esfl?hsKrL+^BkA`iy;mQ_@<$|JaWT?n*);1B-gl(5M; zwEky2jPcy`A4_B=l7`BAy@>_vWAcTy7t&%pLzy&Y%w{u5RWZ Z-Ml_prREOfBA{>!a-z`F%c{$v{2!75KgIw6 diff --git a/group-theory.tex b/group-theory.tex index d034cc1..9115bcb 100644 --- a/group-theory.tex +++ b/group-theory.tex @@ -896,7 +896,7 @@ $h\mapsto gh$, задает биекцию между $H$ и $gH$. Действ $gh=gh'$, то $h=h'$, и в силу определения смежного класса это отображение сюръективно. Поэтому в каждом смежном классе столько же элементов, сколько в подгруппе $H$. Таким образом, элементы $G$ -разбиваются на $|G:H|$ смежных классов, в каждом по $H$ +разбиваются на $|G:H|$ смежных классов, в каждом по $|H|$ элементов. Отсюда сразу следует требуемое равенство. \end{proof} \begin{corollary}\label{cor:order_divides} @@ -911,7 +911,7 @@ $gh=gh'$, то $h=h'$, и в силу определения смежного к \end{proof} \begin{corollary}\label{cor:power_order} -Пусть $G$~--- конечная группа. Тогда $g^{|G|} = 1$ для любого $g\in G$. +Пусть $G$~--- конечная группа. Тогда $g^{|G|} = e$ для любого $g\in G$. \end{corollary} В качестве примера приложения теоремы Лагранжа выведем из нее теорему @@ -989,7 +989,7 @@ i_2\colon H\to G\times H,&\;\; h\mapsto (e,h),\\ $\Img(i_2)=\Ker(\pi_1)=\{e\}\times H$~--- нормальные подгруппы в $G\times H$; \item $\pi_1\circ i_1 = \id_G$, $\pi_2\circ i_2 = \id_H$; - $\pi_1\circ i_2 = 0$, $\pi_2\circ i_1 = 0$; + $\pi_1\circ i_2 = e$, $\pi_2\circ i_1 = e$; \end{enumerate} \end{proposition} \begin{proof} @@ -1052,7 +1052,7 @@ $g'^{-1}g = e = h'h^{-1}$, откуда $g=g'$ и $h=h'$. Проверим, что $\ph$~--- гомоморфизм групп. Возьмем $y\in F$ и запишем его в виде $y = g'h'$, где $g',h'\in H$. Тогда $xy = (gh)(g'h') = g(hg')h' = (gg')(hh')$ (по -свойству~\ref{item:they_commute}. По определению $\ph$ теперь +свойству~\ref{item:they_commute}). По определению $\ph$ теперь $\ph(xy) = (gg',hh')$, в то время как $\ph(x) = (g,h)$, $\ph(y) = (g',h')$, и, стало быть, $\ph(x)\ph(y) = (g,h)(g',h') = (gg', hh')$. @@ -1118,7 +1118,7 @@ $(i_1\;\;i_2\;\;\dots\;\;i_{k-1}\;\;i_k) = \end{theorem} \begin{proof} Будем вести индукцию по числу $i\in\{1,\dots,n\}$ таких, что -$\pi(i)\neq i$, то есть, по $n-\Fix(\pi)$. +$\pi(i)\neq i$, то есть, по $n-|\Fix(\pi)|$. Если это число равно $0$, то перестановка $\pi$ тождественна и, таким образом, есть произведение пустого множества циклов. Это база индукции. Докажем переход. @@ -1146,7 +1146,7 @@ $j\in\{1,\dots,n\}\setminus\{i_1,\dots,i_k\}$. Это значит, что к $\pi'$ можно применить предположение индукции: действительно, $\Fix(\pi') = \Fix(\pi)\cup\{i_1,\dots,i_k\}$, поэтому -мощность множества $\{i\in\{1,\dots,n\}\mid \pi'(i)\neq i$ на $k$ +мощность множества $\{i\in\{1,\dots,n\}\mid \pi'(i)\neq i\}$ на $k$ меньше, чем мощность аналогичного множества для $\pi$. По предположению индукции $\pi'$ можно записать в виде произведения независимых циклов, носители которых не пересекаются с $\Fix(\pi')$: @@ -1314,6 +1314,7 @@ $\Img(\pi)$ изоморфна $G$ и является подгруппой в $ \subsection{Диэдральная группа} \literature{[K3], гл. 1, \S~4, п. 5.} +\nopagebreak Рассмотрим на эвклидовой плоскости правильный $n$-угольник с вершинами $A_1,\dots,A_n$ и центром в начале координат (точке $O$).