From 8a3d612d4ac04ed2ce5242b61e732a96d224e3ff Mon Sep 17 00:00:00 2001 From: Russ Tedrake Date: Tue, 23 Apr 2024 09:47:55 -0400 Subject: [PATCH] initial pass at randomized smoothing section --- .../figures/stochastic_force_field_pang22.png | Bin 0 -> 140103 bytes book/figures/vanderpol_particles.svg | 5198 +++++++++++++++++ book/index.html | 3 +- book/stochastic.html | 199 +- 4 files changed, 5346 insertions(+), 54 deletions(-) create mode 100644 book/figures/stochastic_force_field_pang22.png create mode 100644 book/figures/vanderpol_particles.svg diff --git a/book/figures/stochastic_force_field_pang22.png b/book/figures/stochastic_force_field_pang22.png new file mode 100644 index 0000000000000000000000000000000000000000..007a18bf0545f15b5a29b26fdcfb23673bfc5c0a GIT binary patch literal 140103 zcmeFZg;&*E+cgX-pdg}B0s<-^4N6O^bPJm z+v9nj_rAaJ{Q=(?pJO)$`4q3wC`6aUZOgaz*OpdRj@UkZ4ww&?%<1#RHs|Nl0$|8H%{ou^l>T(O#{b3a(u zc5~w=L>=bWp0|GwJk{UV_mSsW&8JWOVf0FF?(SIxsKfT4n63PC=y%4#8CA~?XM%3h zNQE(L?zerSMWEsxO$hIABn02%;IP}CZNtRG6w68wa1|p&{qN14e}jlVf<;@S-s9Ad zkdc&(jOtHlDctxQRFhbGg@=7<(iXo<9zJ}SrBTX||IZ7^|K|miLLRFV^`7Aj%C~Rd zb~#wLFgE`1=i!A#|9*wnInK3f<7F1H$;mJJ(`CzHu`YY2?(XjYtbyTzGYjgG(2x^L z{TXIIbJf$N!fRa*1YP&d=i0+vTwMP7F2tq3E4ssNIl4GhkeHRV^yNhZ5{Z2C<_#>u z@1JkA|My!9>fDaljJj{@>(AVmjp29N^oqQMiOHf~B=XwXQc4Qj9hF2$3iQYcZb@Is z?>?lMf1ksxRKMk;%iglOhKA*@FOL31yIp47S%{gxkMYBSo}OMlQP5(f%)%R+FfK0c`}gnEbHg3B zM?c{chbpXRxF&x6{@oqJxzhVtd;nFNgs)f@YSy~Bkg#&IsO10pR*S{C_xADM9WNP+ zWYxvIdP@OzNvGDu*~v-4=7vcSM(FP9QqG$dhjG}{qIf-W*b~5Gx zsZ#$Q`47{(ckl8!tY+%eR;8uQeS3?Q#i3lbGYXGG$!quFpN~-I@OQwovEokCF0C3o z<2%xo321&_dHe4XO9XAq}Zw2Y|oDt zC|yuREs5g>(=_G2{78mH;Ms$s(&DiSM}2d1ra=?Bzj6F~WiUszKSO?KXsAFr=jVJ^ ztN=ehi&n)eLBjLn&8Y?|@sGI*$!`h^3;q2&<~kw^v?{-=CWo{CQy6W&WrWFZF^xwa z{q)e$91u6){?$F$HOSf=l+8)}_mS7^ryG5_EPf+$)q308v+Y-YuEBAh$W}Y7X_T3( z7w8B;pfD(B!&#J>4raR^tjBU$gt|N4`16EG<{?ZrxSGX6mgj9Nw4!n;^USgJ?)wqT z9OVD=`SYF8mSa`Qun8KarbJ6ov9Yny(aMrd_4DT=zkV_4)ZF?LU`UZRrXwCc%g%s~ zcqXHX#yW?+-#4ai)Mz;ni|YRyH9C-1{O-rQXQwB4sXIMF=jOjlvOLev-oJm}+}zBl zn$K^y_@hw2WqqPvp3w;H&j-^fvq=j!$*HfG5|myaTvle}Ws6}b`L`pig-1o*A|WBU zFN;8gWn?VWIPdK4?F9w|z%vsP6BFOK5wav87Q6rf=*5CHOdJ7Z*j7m;by?G4+cv(J9?lZ$iB5ZtT)XQ2F`E@C56y zboSu?yqVY2^PEOHLSlQ=s3+mszwZpy3aTI9FcuQPsSS0Ps;YH7(MTm!nm_wzVQ6R) z2Le5LT9s^n_WIB_RIQJF-yAu<<;{#uY)@Bp*QSAZ-+Q^_>ff^n?(XTa`t}B+$)9+r zzu)zEmp=UEKiN&E!X~ZrJp!Sld{k~)|7hRNjdX`2!jLVw9`k7e4umQiT3=I3i|66y z)bd~s6q*lyekpyO{~U{VPFaP9FA+_;Oyc%dgE&K<%D-E}LQiiatKjpe0uj*h(ET!u zmCm}K7B|mxkn!~x`iH?J@}gqNfLiP zSorRn`bz~4Iu_%dH4WLo^L21i=6m#| z2w_4Eyua0q?&hCOX-)q1OHEv}WjfEFm`5Q=);v~?NSg3pTtR^I=hX)CO#bfO36z@x z4^k(tKO=iqT-(JZV#U+Yt-zW3EVsP2dhB+XNQ87jV9u{timULj{lqqzdrYsWbCb2ql1OxAQ)x?fjiOpP$^rVL^5!~Z;mJ4*CS zG`=)ldr_J-Mq3y5aO|ok=y^z9_qHT<)mC4$H@7}#a-s`R#%GBD@u-|zhwYT^q)=dOT#Qnd?J)L z_GQ1^r5-m{uyf_JswsxSzaa7Nw%k#^AYFm)VbokkLc~RMT)USjCUC0Zmt#}>UppPV z?9gXX&FMfB6JgAoy+m4eKhB$~vkUXT7G5h%#Pe!axH$VIyHU?99=`g$`<-3?B9Ff@ zI(e=b73EuSUn@^A-9>cA&rCHxFyKQfLo3mLewbIPj+g7)PB^A5DbjR*C1uVZV%w8h z?pt`}@IQHjhDLDZPe4f2JZJrgMZQs7Bj3v_Y9yOTNJ-X%b7Ow~`hRZXrZVD3h;@sMUXefn% z3kp2~BC13ewww~OMlP&x&9vwhMtP8;3)|M}ZzN>!Z`joMx5^C^TDLfEj6cJm!{5Gu zc6f#Ei;Spfu%Ckz0|PV_1#X7Wh4(%_jw?U&XW8hrt#Ih_uNCY<*Ugy>g%SStPAS^Kt{)i$jZE|*efR~3R5B4vY7q0 z7CU<}H2z+F_$+{_`G9vJ<~B_j!z!uwYO5Wn0e+vlwW>BXoHL zN!Y@ua!iWuoWFk=4-fD1<-<5X&l@*x+>I9G9Qx3t=aGbukH7TL;KsQL?zL+l{rx|; zkjya8%*?!f^QMl{`ixUIBvJ_n9pW~IHbzvusDS&C8^vkObe&&HS&H6M|3Qh|kVc!m zAwh{dtY}`NVkT*5%4n$k`*FF|wzOq?uEWB@f-lWhxp*lRmZPDV`kJUALI;{?8YP@oQP}W1<lUuj$|R{a~Q30w%y+z4Gs=IIoR+#-u0#EXzA+8d-hqZxS>-g9d!HA^l=viJKjsL^1twnn)zsGC|~>20{fo&V3~y`71iglYR8>5-AbFe zu2^oExe&CJ{~)HTw|QQTR#<w)S)&OX=dpi&>Y8Xkgfb z35uN8?$?(W7YQXl#l^u`=C<;a*&}IVth)SV7wNdJy|wk!0&VGa2%)4GHPPj#e6GEA zA%;{P->|Se<&elyjvd{>B&I*xE%{yQZZ;aKyd~WTUSLqLu_*%Zm@4^+*J0Jz$Y>}< z)L$%+R9#bZM_{zXq(5J~nm4@xr`m3*FI_ekHAJbabDID9(bs2#JluNm;>GrCs`~dt z?|KSWR#uldQMabyVk0tA(*2bo7$ltYG|O33^G9K1ozw zn@QN5&tieo3vDnhH0eDIZ*TN0a`Loa=#H-tBo;1C`w~V+RJuM_MT&10RmP@W?U2X4 zbH;1L@_jTB+Zi2gmP=BNUgUqH2jixHQ%|ChZkhS;uR?t+7^*Vl$d~Cphzw>c$MRTD zr`p|@iTX+gMQv(pj41Q@ueVfhky!NK!HI+FzjD(LrYS%awLO8;l5Xv534@0Vu8pI4o zLX_`0&QXCw&+l+E6`fKS!tn1s?@?i;xg0f(^?$_`Pn&(|w{PEIJYi7#a%Y1U4&P{F zyf%~}%SqYJZnrz053;al#BuHS-pYFdW?JWU$UrhqQ$(i1U0Pb&vp0|!iN7!2B&1iI zh2gKQtZGOwpz7r-`qf9Sb)By21uV59L@8I!#`KO;XszpSi`N-Q9$1v`9= zAJVVT{bV0WR`}&hh2sVVtMlgMH`v|tvy+XMAW9=UYZjq&MwQ%2GYgo3#jf;=&yJ4Q zy23-{#;Dt-r=+B4X=z~-GH@8ShskWP0m>0BcGpWx7mCT}(<*<}@g4UgM@7i188iC% zPGyo0&!D(%CFqhOP>cequ!m~ZIBgB-dWPF2{>;-9Pm8W}-kFEgfI0JN5FvxBbN=jo zD=1cT6B4y9d$aY=$b@2`^<=9RPQS&%%amx6iQ&kCKbmr9=Ej3(yZV((1(gh%Xy7Z(J&Q5~iWzwKUP@j?c^ zJgdi-3iY0s@7Hk2R;|8-=B1h{(EQmZcXDs!2L^bgKXn$9m9-#CDMRX5?%K6$Lj}4S z*ywc&Gt<+3GAgh3SJi20Gk|C5*Y|GMNg$)76tbO{(bgV&;*A|hDFi&l&hAn_OxY`o zi>o8$toQD{ky7qV^gJ^$Gph!c$|cwGkRIw_V~dPH*2`xXY8O{~G~dm<>7?N7yQfFV?~+!A(7Hc@bFWF(fM&ez|+8qN)l zvaj(K3kwUhu(OT&^Tom^h9}3PkKbYvGO2xWJKEmX`YCcmTOW5tl^%})_^ z?IgIZwltqK5ZQ<&cw4%n3BWhwDB{(o%Ut*B#XX)`JS%@R)-5PR7JpmTKFQ_!XEb5U zPXSNgWunL>RM#~8RqI;*`t|G74PX)OG7xU=?4UqP(&M)fzv7}

FYtM>|PLcU*E6 z)Z1;3%r^J;&tRi+R0|-$n(9MHIZc6)Xq%WgpMg{mbPIMLT!UVE#1Ih?0VEBAy1b&I z0(w306P_pgYtTxiWn@zQ29D?si~HZ+R&q$_I7p6-g(5ma!S8hEh$Z!YFLdE0tH_pv z5s0543IPVbmjJnVhYxr#=f7Zo`FpSi=v z1Uz4#HG@XU;^_%T9}!eB6#$;x7QYE@-ZZ`-2$3 zZ9_?qFG?nm#WLK#f1iP&9hef}@Z^hKe6}7%E{Ha9#}$K#l^*ym64H( zWI63%t>3iDKx8R$nhrdWRZf259Z1IAhrI+WRSD!d1`bgio1qji*x@hlQ&Z2vMnEVa zoy7xgS#M1@tqc|PL_KWi?zV(&z@y;*QdBhEvob#~#yA_b{f7(MvijEByEO}~N-mD> zS&B%LA0gBh(ZLB3ad9gkzl2|3fJ}09a7gbP=qLv)7yEmU$bRw16of3|Zr5m~?aq8x zM-W0y?G|Ag(C5NqG({p0@rCqzj$3wF?eh@m{ue%B%46g7Y-Ug({**QvNP&x(SA*^D z^(PVio3EolJ+H2=Iu+1+o*@B)O#sVQ2~0$~jlKO?iHQ<`k?r{|O(2&S7q#NoACT=V zh>3|ooYw)@cHp!>rP!Ubj-eJqpc=+ve4))=1XG z=x7ol`Am*dMnV1Nt996_1v<6R?3KJZV1tLG?e|xQ1Nv+Mtu3#UxbCx_ILdX#+0eH8 zZu>`c>V}?$dMc=+0)%^W+@LL#hDM-uH}eK8997w|%iT{LBoA8&=@gOxy#c`oTr8_n zdMA{a{Lh~oI&cUXW+x}_oR{WchXnF-^YA$Jrig|f5vk;BNv1^)S6F`rejiRZ2+C?$ zm`ECle?Wj%wSxulaGpnVkxmuiFMghpeXCl&s-rt=I7@@V2R>$w6v5f`)Wwl zv$wy$4o?GNa1|F9I-+b^w0eng2tbJF=x84w@nb&sw3c#nbMwxFsL!822L<7Ud(5n? zbU2!r3L$3K*IDF+nP?4XD*+MeOYG7nZ$fS^qYQ9!m zEH`UG3}jb~qzz1PLF9bR^2sptX85}F^Vlsa0Fv}LKRqC1R1pyqQ(Ovyc92=EvsEk7 zA(9f4(yT;waw+vx;0nXFhuCOzy-)(`9X_!?%>$hAr+@NbVPQ!Yv~_j{_<3*`v<8C` zM8W4ElaQyDO!bTa zP6-AmDbKEL7*nW+7KoTNIHXwxmEfe!hKteye7%bA($Qr)to@E;(GKOmiicNTUfu(G z2B=46mSYU`VUr6;fPXZ$_*TEZyq3ZMaVJ|jhs*fKovFOOzUo&~7le4>7yf;jR%2{! zh;!35nN^a0i*yW4;?>^;Ic6Ws*re0374RX-h3TCryPKQeJ8sWDUP066#P~a)KTnAL zdJ`Enp}&84!!`9@$J6~yPFM1FwktJ<-H@EKC!ZXn{Rrs$pbh|Io{b;HX6P3l9v&G< zY$Y$6wbBftkGD6y)y?76g=E&YinunCTg6OQbewtO`q(ov?Piu(rp3VarfzasG2_9JPxb3!m$D7 zK~a1GJAQU{hM>k364S1-Yl~!^01<_~-5>-)f|Zqs2PU`983%W!v{KHm{wjRDI3eJaKmLB{e<$ z5_~<9Y|8zjyZb4WXlYz@K$v5xlK3v0vU+;cFw;3~jGt;HMN z0Ce{E^EJ!Y0WGq{5UNhQ0t!Ltq_Q^~-*91CF_kB44YwP{tMYUl;ao>t2X;n*+R@Q* z+yR zx!-)asK)AReLQ4Cdg3bQ-McRUgFtcl+%oab$LC;e#1Q~c5o>d&Z|;00lEwnm#=gPf zdQYM7_Q&1)ksE$c2uVpuw$?yMI)#jDYf}^y;eXkAYdi@Wam{0~ord%q1Oz1j4@KFS zb?a)>i(f)Pw4A6r1<@7;5g9_Efi2RER=?rm>8XkSFb4;AFJ$) zLT>?~RJw2Qk?s7|@b(wb?*O@Qa&y-^ti=TIbF;D8td9cvsd78v;^KnoTeiOX!i5Xe zJ2wDj)w}FTnNG%1OtiU)dPYBa`m`mG%*et*0Eh=rwBW_hM0soc921JIDY@|Qf+jrA z_{ z8V!w$L&A2$^adldU0D}EZO%wj4oY6u`;ayhsnvwm0ZL72$?nPAVCIr36(GZLyCGO(ms5+wLVr26m*_q zniP;ws_p~tXC^BA;PQAs&DkHgJm>iB{F{#bUSYs#(AzH#7~ z_@GmYh+HB}+uqsP+28ko6M%8%oymRA{4Za=z~1hh)6iI3TSLQzLH~6Cf+fd!-ShlZ z6@rxCc^f9B$7iJ#$~h`q{h^6*01d*eDc-+(x0!DOSon~FjNj=&_?a^MHhj~ln^ z^qxGqKxp_JMy8i9UxHLRT51+KaI#?y9MQm&3(}YM9w%%F#O_+^srTE=PEeiepJNnH z65QXISQF;F3ta80t%C!LLXxm)q+%72tR6stYIr`i|I18H(n?B6xxiEjI2K|;0meSy zK;(g-f}wAwInZpREbm!1l+?E9z}6Pe^(46333x+k3}|$ zjEIN}2%TuyXL8c7zN&I?b1y8=3Kba0D1EI*9XO2SVRX;*;P?>7pV2R3LS5Ij zv3+z@AQJIOac2}zU?3?cfI?)oEAsGRxQFfJ*VoVwcicyy_Mw;t!dKSTS;{#P{1a?K z_#o{gV1oZsipw8^=fq2+qRsM}J73AO9x>cpveC-;{SD!yx?o~7VTaLb#~?@L`u876 zGJ#E*YVgV03(EBV%YYwBes5?v*0kAYJFJL__A{o0|6tf_8-)U~57Y5uz z^c2NMTJ;{a&;>;O2%-gC%K|#2kDU3OHYeX;;HYFOynr-7Fnk@#)2`<7#03gMz;&M~ zoZ%zvCRAFfb=6)Na6IfXcVnRhsemN{MxfKVu-$!6?$wS7=xCKh-p z^8!lY`r31yn0R4o>KVXS$m>7~fnz8;h%H=JlcD^0C`$mF`47H4Nywo~NJt1}WN~hJ z4kZ!6pk!{ITU=aRS0|{u1EeM9f}FD!NCvgml0>R1Wan1P|Ve1s`sIkz^=?z>#hDO zWK#+7^*uV-sJFMb_dHoEuRlBXm#Uv)eGa(-NN1rS89>{FQG~*sH0a-#<)R+Eu6I&W z>fd!<2Qmacso?Wxsy%!g_!A}1tH}f3FNU@@Hq$+NFJ6T7HvMta42HGd{Pb%`sDa4< zr)#VWr-b>(*RpS2D;&C&--W`^g#JiGZ-61v(9qb<*AzRvb*JBzPDu$p8!f!Y_K1$| z!Gl-lXQwd6PF}pyR$F#7Sr0mhrKP1Cn&jH0Cr_RL=KPr=ii7guWYf~o8ABOI%GLld zg<&&Q@pWcqCQuJh)dI_hK`{t_dDYqS8aN<)e0+8een4lC9Ji>19{a4+%b-v5EdKcL z5V+h{7;K^ULZz#5k7;`WCxsFhph3@mSXd3nyz z|4x)l7|yf{)Qg)N8)qYRJ*G-w^V6`s6-^U5T=kIR;q^{u%yInAU_}ye+I$WU4%EaAeKU)~TTp z>g0}(kCCqY(8l0Rp#3=!dwZGz;0pbssj8}KDwtp^)n)t0lKR72Z0M4fNaK?p>NGqsqpj~_#Jz0lW0gbHz#4x}K6GoC5p_<2!A0svCRC0fz zWI6;XfCz>~s*?&|3)7C@qypSGId53r5G9mWU9QJdLe& z!P4%lc~ruLN!iXUlvg(kwR~^VP_yQOKg;cMqYqZ-@7dW|C~TY77Ya;&eVKwZqn?9e z15GhB_q#Z8=o8Sb#Q|x-Bm(WJytEYH8|$AODXaB3tpZaYlmtf41BeVO)KucuP=7|F zAKHAhv#`K?RE5&2tR_l&?Ot|9eVh0RQ`><%*ZU0lL>P$T3!G+}aV32lp?U7Z82LFi zGL7F6{E=`vp;yrRMl)q8;CPIGmzY2Y1ixEo@D@SU?ejX2_Zosc!2JiA%>}@GTy#p_ zWq0veoj0JAfgIJ1))1-zjpVTS1)CbY<`ZoE4V>tN_TUR zxN^cF1N#RLYQ`plJ}W5~83O%f``W$I2)sN{XOlvm*8w!daGEuX3nFQ@3iT2N-N)

br4@zA_UL2q*Gjqej!ob=FkBgd|AiH4%XHhnQic|)$ z)Z+|!1XIEI_&D+$=78;T#FaBnR+%8~6S=+w&l{wq#{xOBR1Y5f0KMbu*XMvbkP?#E zU?XH=W(J#EUuS#OtEulw8FE*wvLnPIwnssEBxcqqfk_G|v>;#KWW`F1OP7#G3yC$l zh0wl%{$}VBHaA~|iuI9Fs15)qqz5Vj1O*d39Yf_w_tr)ZfUq1uB-`BWnG=sVC_P+R zm>An%8$oGAfRwl5sfhfYEwr?5pC3aEBdh02kuAZVLm?p{B=LAAn@W1k0VEJYW`On# zedYn;Aw;mx4`dU=1nX}fH&vurcUf{~ILqz4w7YW6n4*ymEjSrYoq$E_(2O+lHH>nb z=od>P$nuzA*Y%uPHV%M`udtbG4;=!alK{`wam)SaS>W~D-CsQa63NSFRrhQt2e0q%^*x5F`AezfzrmE3L8CAhlK||wSt1Yh* z&tshedy7Pb9S_azrhNV^lU4})A9g)TVf_LliD4=+)k9h2cj~oZe1J&qY?r^ zaK0|+c@_s;oKObjV~thB(kOum%IDw`#-h#JAFYfcy{-w(4@KLLM-=6??=yH;6FQJC z*sW|aQ_kb}Ok=!YH70-!ywe0j)kulS4yRv-S6y9QK=gpYXIU6FG8Gd##J54S_}Sn8 zS(WOhY}A9hU~J81pIlzn0Oc%{M*3`j#Hu7lVgM*%rm?T2;KQ!k+}wn=CmYQ+7bJ9+ z378a2zEEE5C%>Y%8O^eH892WMh2Sa)TVqp`p+3rX8qe?CH#8KfF^fH0sR(pM=dWKC z@XxzEgCL$CYH|rpyJbj9Imv$=8F2;fw5Xsp0vOW!_XPpQL5&Qp339}Y;kN2d^cJ!& zD;|Ks1$DZP>@d8EirUO%OaPLkabAbE(g&0B5-$(W58jDfAaAzOg`sQ`!`^~Q&kb#Xn;Ye1U}s;M zs6PkMU=}&xASET`Ps9uoOE1i}^I5=?LWvA9d6EiJcp5Ln6VU(A8l;1iSldw44{JS= z4d(O>?x!=lxw`ddP@sxfH#_Ni=0-q(umjEr#$XSqf;!)W1chjTzheW2Nix>_!^e*f z_V$Clz0n*dp$Fwz$hqCwHvI9#DFJ*BshuIQG(U%>J{qX)9Q`Vp{=fr3+uhMGao%~! z(0&W3A>~)m+BywCulnD*&r8iPTDbYEOesWbS4YCTd-J;yY2azdp4M~Iky1p(gVF7^-v!$ zHB`E@gk_ir5zX3Vb<&dYLaLGnv7waPT3HD~p5x%Rz{DkWa&?tHn{-*~OM}E;Tv<6- z>KC`cT@UV+D^m*rskC=0iGDRTrD;{#plFJz8&~k~P%aA? zAZ9B$6Mq1NJ<>q#@$mA_ZzmEBU`#NlNk=-odKJ7N)`BWU-{`oqCG>8LHB=pm9;vcu zM=y;|Cp|2ah>D6*Q&WTS;!Zy|hGc>(h>|YIPj`B{ zT44-4LZ3q+96+hiRd>!|Xw=HrdNe-42Tcz^1Q1w2JVYgCwUY_ zX1mZm=N-@I2ttf@#jE60*|M!jJCL=Y$nCC=jR4G*n)_ndK_t2G&eL&%_38VK@p{i5 zpNl9t40uX@av{JR*-3aSR2ui&HTkU~!?oSs+Sn^n9adidY#iP=)Y4MMHF)kKJ!EAk zMG{>`QN8ivGUu}^zJd!x_W4E#DIc9#RncAL4SUmT<7Vd`J&ai~To&yoT?4!=#-Cv% zXSl=5>jFK%?z!S%uDa5hzxNTEN8^VZB`>o<2R59+{E3#NgDCcSefI7`Q*$#Ap*1fW z-h&jeI9j;_>6LZwVkrLs=+((BLRYp&1Kz!R2XJl&)HmcUV2nJ0|G9km@?`Z2(8_?- zAQc1vwLt}(yRt{^ybeUr;ubd`aIi@;s(qP+R{^jDj)%o#8*qVG_eoS+v+gfI=0`hn z(QMv+Y}ZLid9B9z&uaGf_W=cl>Rtl%3uZ)sdc(f>w1<^avZdod;p1Mt3hX~MXCh3% zEMMhsG`@MFCUFO6^m`fqRZlfX#F&k2hlS1fF8`u4_PTqzENmx!z55!qcGPYhe`cW6 zX6q(f?=oY8frq$Z>xFU0g)#NtwSBW)v5o*g2Q(fV_oH_2YeU0Ro5bLaLt~%i*-aoa z0PXk2WP$I3t+oUUZ6MBX|G|$$goeu0~9-BLltISqZI@UG1jkMMLl@&9T*YA#J1lvhg&la4h|5D^Pev=v|l}M zo357!Hh#9q!h8gc>-iHf|l5dt}Jc&4R{DcIGA5^a$2MoNVXMtt`UCs@^^xm=@Yz43kDUSFV^$)CrJ> zBLL;8$2=Sc$Ona>#D>9nUiTteX?l^s)m_@z$k5QxurLC+$U#g@I}`MZ-KabFA9E5^ zB`Q9QnNqO(i9jg^U{(VK4WN>%lT(eysm5Vt9HbYh1?~{9z}YDs=6-}hg9I)vY*g{P z?gu1(MI2L|>E**711m-bPC$Z5nsUoAxX*F1v|kUIu?Gc6K&kCag6MqiE8aAa3P-Q! zg;W4;&DYCmYiXs*>AZ#(MFPHRtDl;UBF?8feky+0VXO~&oOOiX)Ofx}mwj_f)a+fw zd9t8BsXA4I*vP~)##X^`vXx(jRBMVRAY6By%nfMtE+cW)PZTBu6k~ zjTfKKMd}(GhO~bF{^Tr&A5B;w>lNO`(<_ybY_M+$FeLvjH3OX(5z`G;x7^%Z@IP=m zu4~O!-s!D&v^vAzJ8cjE>wvV-!JBO$dSny$D*^4aS6q55O@05q!}_Q*L`rmb0USRg6MWnBkLT?#qF^Or9jrW>!ACUfi>K$;5;0v)yJaV zYPorNCUXd^Yqx_JR2a~b$`Ey^BIyS0jU5_;R5$|(DQQ(jg~C!049r77)Bwj+YSQ04 zI7sNsBGK5~EG8l%l0K~qxNPoB^IYCpQT8S!rMzxiqh~(&p259EEv~igsi&7RFo6l( zFf93{glsSMv(uk@<@pnSv2tdQ8tF71HzTd@^%KfxhWmv)L{lm~@)*RYoLXF7?xTFGUbnTeJBbpKhY8_bzc&C*e}#rk@oL3FSCivARs$M`nbSFfVLMs&0~ zWHlBpsU6S^c$9*N&q8C>^P&7P;7(2A|5)^FU=s;wJ~nw5Z~9nK zIK=jKrH6FouT`h$r(|6#xur+IylLr5MOvDg(Ki!y`9NsVFkRJjoZJ-Sk)D-Rz1@4n{bhHr z?~MIqAuH7AeC_n%)qbY0svn+lBnI%k&OA1xXTy44;qS`})(~0G8+77>n>(9#xyb{p zIy*Z7%ZUuyRCt~XQX>1?vp!M?NZF$$g$$&l!n6jg(m?K@U+#`ZZM zCH*T!ahUYMpgWgngb%|v7s~x~-RxIP_D~MdqSn`vx}}Oq>qI3%B@APMMmo}sHf$x* z!qki++XWA*6{^r%URjX)mHqHevaX?Vgplq*vuwQyt|%ybTEJ(3h)6*}f%II5&Z?uM1EzmcL%2uf6#>r_ zEU?8S7%F-{gBq(a>9M)O(bGA&wv%^TQ^0BaYpgRZ`{>Dy%X$Q|jz&7~%i~pidTzCo zdM)udKSxWy@38voS&@Mx@2frqzRCJ9)B|3n6pTyQiv@7=EdKW4Wlsnqz(6n&q4bMv zbm5Cx%8(kqTBu-0IpkXtWX=2i!Uzj~<=i2n=B2q=O898sre@CCKO4R7aX`wHfi~Y~ zBBkcGm>9f^4>%{6mQ0L{#KoEP2Q(Prrs5;8uK=2+=%bLNp>HDx3r3QWtTJ#_OtQJ) z$T9bull*I>X~or6y;uR2=xl7a1RQ^D=pW`G< zXNwQoUaRy=P3(;BW{T$D5^&)VFv|u>1rUYz^6V>^b~V_;;X*FTcnYBuOp3x?t=g@& zwx87xMfMY zied=ABT&=3xmh4r?d-1&_3X7$fi4WP00b1w!dMs>&p6SHDePBKM_L`cF#i!|=pYjI zbYPr-BqIT)9vq+RqaiB=_<(xM2eZRLZqUmR|KRJZ4q*%R4v0Ak(WE@!91Iw|)7}+t zlC6qy_+OK`qSZ?D`(gFAS^LUhFWI0~7`R4CF9u^e=VN}d-@vo4x+yxJRM@-kIB*r= zRb9=uQQlh^k`728M8{;T3ng_bp&<*{3xmpKz>@taPDeSM0Jg*M2oo+F=jqhjPC!~6 z%Nc^`!hxAae=@?GpPLvcd1G)-0UroF9%M|^Zcv^ z|B0yI%*MvX>@1?z#eSTbz`qHB{Ts`fML1ngJ(tgxvi-fKp{D8=!f-_f^^L-xR{284 zvq?S&l!{bd;2Iv(@}-a?@%*B&>*IQ2Oa#C?d!^m7drUW(_bAw=nV~i zSDovQj9J$Ec5a82Lt5Mir!o;48J|fX_1U>wxnSsXWMvopadd-$jPfW@ctbLMsh(7 zmpFFb9t`1_QP)31XM4l1YTI_Z)L^4H*zJ|Q$w@$WXN`p%EeIf*Q8Awlh9aKaXB6{z!JKkO)K*-k~e=+4A&#eNcALZKM14 zfTc{RbGBh_0@BzY9Q`A~cb^_Q1BQXCCe~-KU@Aer00NCxCh9tI{42iWD3qcp z8>fNPbyG^p9<(w5|B^j-Z^FD2#E|M67&r!eqE-DV2()*nL~us|4uC7u_#VdogEQ8L zo69vC!{^0?uRm$k;_TAez*X3^X{%uvFsCx|!ovqqH-W}IAg+KN0kRuaX9N47?uU$) z?1SeE&^aReHjj{|1>5cJ$)QI*o2pPoBQH@hCTu4g5(!Pd?g`tGu1!&ro zAv!W?QKs@q*X*XAg}sLCLp$^G`tD^~QeCTjaWmC4<6> zU1kVsk>H8D*)Cy!gz4O)S>z5zHo=>p{V2Cy0vp{8zfo?3?s&!;k#g{#f>&|?1v{o8 zmZ^^`@VJt24I=wfzNK8cynYj0-``g1y5ahmRvfd2F$B~<7!;? z{QSZoC**;IK-yD);OHkD3nv-em3YL8r;%V~EVyF%)74?)3SI-&?Ym~MI=X13M#H81 z-E13}@v?)e{B0U3j3;kMM?dj8b|nbJ?z>@vvl8qB@_A{=4oR1>4qQ_;0V1ME z{gW21qZe~jUqOD`On#og@BF*W!gZmW95_x%eP6&y^&at`+t|^COX>4{9zWravmu>N z4>d}`f};bg+1!*>3k+6l92~Po7GQD*H>F!17&kYSfd&iXv;Dnon*`1pAZcTGtnU%N z<^qK>ID~t(3&Y_>N>5{`zm&!;jn&~YT41J^(PrQCt3GY3ak?*UJ3>#@L%4KRFuXKY zmvQ~%^=%&4{oJ%Pnl*b97+PneX#zFgPSbG>x^K@)g8343@o(k8qg4Xndc?;E1fmA2YW%!a+a{?7iRrkXjdI19)E@GI#H5f!pG|)TCD=T1);9_D5@C#!CYy*h` zO$KEn0dGR)-*wl0VQo_1IAvWr}j^s zp31jaCyxj9m{X42IStg9!_n_eY-Mh>CF}-I9w^K(*MlY<>86zqLNl1&+`)SQcGshm z($z^B8(I!CvlVj#EC?PjAEK`DK`jIRCnh*pm@oi@55;EMcZVilU44f2j6JF>RDECOt?#6_WH0W_@AXFFu z9EVF~Y9+?KK+WEli>m;|2qxxD4V}R(C0aZ@b)mzHSl4EII{27(Z=n(cE!lQ;RDr8x ztE2gde4E>3e6}$epI#%js8= zq8j3NoM=mECZ-HVpcG=z3ZonfIbgyG-kmS@`$?RHofj6!e~>|2c@tC_w_S+>dP2(8 zD+S{iXkDMbQoLW)c_U#kIeX)YEc?v^y@>;v@_`yY1OxstekI)OyWrb24bTE^qkaK& z0UH3LJ}Q3>ub7#ekAj_T1o89dPcWCI5cXBV@N1<6%LWtRW*+>o4*)pO9*>IQ;vE!- z1C)wr$OIQEzkPcFLI4Ps9Gsk-Y;3$>D$2Xl1r;A~Sxe9bA)-ZUV?t(P^IE!|SPP9bo=g(lpvH?j3H?0B|&-ck!>XCD+jfEbcbo_vRdhN}>bJwv-z)g&0{@YK25)ny3@;}9fsowh=5hY#Qm#~Bk` z82}>#Tvvd=gXWNOUoL;#&o z>+*#m4MYU>B;nUkIN-XCuM~SR$jFes+uGL0yC%+-soe*$)Sb*)6`KGw`g6CzE(ILJ zrp7q#q~;k?{U<*SlmlRxi(n@JX~8`ODDrTh&&z0a_zqWV!f<5ev-^qKb!E&W;}sqk zU$D?&!dkpZNfQrqmdaNl&enC>>eQ?L-L=RQc&7KPMz(- zM=+dODS%)KRa(gevpZ49%FIj?cn#2I<~J|uB) z{`=b%ylMPR5)9Oj5{Z%6SHN&)K`t)#eg>asx&XZ_U}fi)cn!u27OGHILkIX(!#`T4dn;87H({c+t*dERUkaDoRu&^+A z9*ilaP;OJOxji#$O3uSk@K%xfw2YoHD8CIyA-;V)kT(*W7l+uIABesY9W zyJ{DJPu8wD4lxT;s3|ZH(dqU;ojlZUhWVMH)%GzC+*B7Pa*Byx|6X;g`j%>@X0rB< z1A@lZl+?={t|R%{Q1!?LT-~m5|7mfe+n>H?WzkL&9?Hq_3DbGKrxa*B(Di$-g{1@5 z0=sD1Pi#^7J1|ZyxhCYWNal-xrHY1C69fyQC;~iT9J)-OEq2=XPvAH*pC_!$&2d_e zR=|z*aLOgO?AP_7;KqRqY`WW~>`nFYfYQa&%Y6$qvi`yJ_dnl%YL-vIMx#Nk zDJ*KC`AA5x*xlUh^j=9`oN&TP@rNc9Eb7buln(6_fN{!CDPegqY-!LlG0D`1YOU7; z=msHkX)+C53mLpj3T6xtZZ2k*}ITY zL_<=^-jR^4>@rizibTkYl#w0Eh`5ip`h36l@4EE4fA{t0^|&tQdA{GT*K-`t<2arJ zw^?x5Wavm>eP!44(0HQ5Y8NtdPE%C&wY6~4;v9~IEQZ*^z8c8E!2jX`Z414NjlMnsFW}78JcvaF45IJGRQ!V` z!1f)uxAKXfd!3(VqlUq;fCmAecy%0DGuKSyx))X8MHD#PlM`hAOKY*yp!hJ?h+3*e z`fK~Gb91xq);G=RB+M~QVDjwG_ZA=B>ysrCbu7WJe?gL%*XXjAR;-3J0#A6rIhaX+6b{iT2xIr2(u+8- z(N+OjbOdmMoHYt1w;VtD^#Wjt+j#;`bQ(B?WEu$W@7Z%z_9!Jzu8-4IU9&fBbo%5q z;j;`=<;KZ!xhYMn!Q)Oo5k^^kbK8l%?7VeUsGp{ zAD?-IKSB=*$_9>F6bJ>HoCysMGo#z#!uaI*f;N8EsYoH^WC=4fGmuecEX^9?z3&%S zpb-w@)Czd=x z?m3muT=|Mujh7yE|GrVpO&UnS(NZE4qUAm0wv`Xi8ra9re@!vCQxSEy{lpEh04Ap{ z4mQ4cWYGp(%`C+zWcYPaUZ(X&t!a8IsmesZsxSMVW>|L*52p>!y(6vN!}Cu1_D{}- zT_uh=_tZpk6VUgx2CANkj;wmO@e2=a9@vOrq&4_glLX088ppKJG?w}8Na3)5Nn|d{ zi8G#HC#wTum@(Iej|Atbyxn|`!Fh(E?PPfLBZks9Nq&brrNhARDt(ERh8H^k#^ z66&xI7*G0h9C(j{zH!%#xl1Ey$=NecYSCq^TC-+S zdwzt%j%tF;=lkq~Cr%}`(#bAPNxJ)tY|Bfl_P#$N&dy!;+QDhC^8NewZ{ObA5FnpJ zhEqyvN{HDhwQmdeq4~-1?Hr81+l-eGq@-XDIWI~$_dw|rTy2dO8@LDupz?%JU+dPa z*RNj11KY&F*$s~y(F6Sifh)n}5k`mOTVoOvS?hZ8=NZ3^k9Q{?Md(FMas1KmA9ATY zn%4Nl$&AgBde++u&s(L^rDF!SnV!BXbyMFln`3%0;WU#5$HH~|hsykJzp)>y2^1W^ zPQB)epDyr=#In6>wAY|_^|-Anzj5z)#|K3pQ+XGDZq(B{sHZzHXM~x65(H2ffL4^3 zt0Z^8%~Bt=7}_EHfr^R>lxNVqYC~ng&(FVb=Dv>);1fe4q@!({*cAkHaslJ_MghZf znJpl0BZ{E2!l)uqo-o0dHUN z`;gQAk3WhZu}Iec)Bhg4@c9*L1@*IM-2u(Qo9%ci zMzBU7`z$}-<+6L!_BnLE_%~mUuwj_#{_AIMeE52xk>Ju)Jvg#BU08hmG{CLxeN>mT z@1--8u3m3&e6<(V!pDi}(>^+ozhUZUw_}2=mie;dA>kt%l4V`E#djtP5tAM-mX(B# z=gBHFW5NcDLt&5D`cce5wNHv%cX8?|YE_N(ojY`gN#vqXaSWLjssuqm7zzixg5h_H znTS!%)&19D&xz2Mo14r0pjHhr4-7QPS0CQ=ZlR{$z<6l)tjq;R#}ENOQ1L^?T;WiI zmO^DSft|(}Ol62sX&v8@pgONQK5sHRGBT|AKqRWTtDHn}wMgQ4)y{oY(|l6lhC78v z)u|`Wd#0xq>YK9E1-l)wKBEvv-SP3GOQO#`ZvluRK-Q(OmGLG2U%jN#p4(pyT!Xb@ z_J0ul1tM8OW9-grBMQRQ9Jtq16CI4VeS8RE4(c@K_aEV?HhG2Sh#X264s$;$j4uY? zC)OdzUP9N#5fB*~`T>>mEM+C0x&PjikQbo9fWZVb<+i|Xdh^4!3ILaUM>|y_knaXT?=*vqg(JTBk*mOFnz2b?NOn*zd-m zZ_G>?x387wM2YR1AXZLJD@Z{d4jsrqpJw4Bs3UQ|TV4m!B!+<@6J)YL5b?Ne+Ve&*5vY}WeD=A`xpOKB^5N)% z&#Pu$z8$x!Cj>Gj=l zXGo#{q3&~jO%h&_utf;izcNlq=%S5>E zIG4{o$X28&MK|kpDvKx4e`sY$%qma>og5tE%XXiF=>sN-#~^~y_TV7=S(8LheCK7R zMu7ZM_uTGH(b=mDlHA9lBdyU7;er)yd0kfxVT;J&!*^bP1}E_Az<_nfGymvuxCb9)C-r;FJ(ie^68U)N@XcpUgRfDbhIdGl{cI1!u>0u)_f_O zXScHbyti&!b>8+z+oIgJRj7#wc;N z?y0Nw20Vao9t=Su5((HRD8!60T%!Y4zG;&Lm)&k*;qd9tgU#tfJw1{q=szhQ1RjH8 z8xUV23Zw6VDk*A!#Sp%(fZl2`z4yvjz(aLs7oir2i+is3adjK)FO!}yhZvPvrG;M< zJe|HewcDX0+0}C*&g*W8`WA(Q27dl*LZ6mp{!S7(5dd)$y+kD_~w@uP-gOnJ?GP!R_g0#P1lZ8a4 zZH@PnMSs)gUp3n}FG(=etVQ8K;bQX^y@NHNwxXe2^v1x$IMg>OD#Ac{J{#mes2uOz z39N|$5etTzusR3$h0KH0w!SYEo+vT*#Ix(XS{^>M`pPCW zC{^RLsIYL*tTKi>s-TkJ_K*bkalM!qMs?Jzi^gnwcB=M7QBSWCk=pywjk>jPM7YM@ zxYPNy!|N>;t7RQwL?tID*EZIGu>&!2gpO?gABFS9n53QM2Z_EayQyg=K{|4TCw`3z z0Y7sPBvm`XQMBLvHQ|#LyWGF=F!u`6?Aq0Z@*ny2x!YXGZHYVRpnfprA97-CPpGOpy zawApfBLVoBhnf=d#zyT8IrkuVHS}FY1n(xc?qcD$L*MVNK4G>+E5@+#@?3GLWZUia z_?Fx~`4-@EOd*QRyI;D`kLQRs4@w_^*$fkBlz6Vp?=qxpA=6DL-0$+?>zBCwI_lBG z0>VsW@A@p5_vZ?ES^`k(HbWc9;(YS^N~M4qls|pOl+ia{fe=id1^VPIs<~ zPj@mw3p3+lcepRw)3(;A3q>{6dLy?@d1&TwJ>#1v9)j!yOP9v$0go^GOcvyvzE>i} z(b>JN@K?h|u?<8aU|eb6bmG{tYdvt1@bq#w)yDc}>{Zulnn-gU3+g;w zBYQ;3z4vD@t^9r~`&K$y`V%80wT-|<|Y7s*2?Jtfw$)crN|D^<}MaABuZ{fy!(W*nckJcol|uuz%npl>q|lsK)fQv^vzmFhbReW zwWM{gr+HU>J|<>cXuX&U8ij%Bab}KK+v-AwxaQ&K6D_Okt;vh*_C#i2d{%dXv9B{xPo`51BRXp-L>ibrxaDb8! zj1|0EWIu?m#^5!8|8DThmr0y1IJ0O^vMNW3eyFJ#hDhN1Hj>>Nlng1S)3FCYO^Zpc zqf{uzz}hiWx327g)30pHrUdoS+Otwkq!ch~%L9e4DgPMwte2Lqz#}O3D!&>KDOuZd zdT|@<`*zuykQ(jOG_?uQFiN0csP;B0o&{z|h z!uYkifL72(H&!1!JJ%TL%Nh~Dr|~l*wENdvD=$4KpQKY8kL%8DK{{QWpY)B3GXz9s z2^KsO5FA$;x`H;x#5Tgt;y9GYP>JN&c3lA%2%#>awwD_&zGY=)u+y>C)lfIWLZ*t z96P?Ij8JOu|JHrv81nPNM$aOBZH_Y142g6xcAstI;QI$N;)-Ws1%eR?vNdptA&_oi zGbyR4_yidps!uJ{Xn;kCNjfmz#lXSRt1F8LPk+2_jHNBWy8+`iH5F}=^6}$k;QuKA zG{T4keMf*#{|5XV7uJ4Y9iY#&gEpbCKYYm4;p52Q%Jn=8q1mlN0%Qdyxt>Kzxv8tTYVCX8135=##GN!p12)N-)#z(rZygH zTY3YbfkQv}AEg0_WO0J)(zd~-2cOC+G4On%^Yk&;M4pseALA!tFbKf#FrYYuWk6MX z0GPzhMPpP3$e0ief=mKk0mxwLA3 z=0Upn9fXppBmp3yy15p#xu@AKkuANQAF->&)?XY{1Ros{C>OaML@`h?EMVRXIw1h$ zQ%zd%#dF26fwBl25F)U+0M0u2erPCUWvhKQ27<{=A_Y^wV0xUff3kJ{sMWhm<3E$W zC5@MXR@&V7`n9JvDTx-0?mgpgMOSVwh>we%Ug3Wsl(u6XS3hk2&|UMjJ#6^4rwfHe za&BzBJ<=ayAARtcL6W-rwTpIs06J zwtC4yU(GAbn>D-2N9)TAt8d9Ys$-o+*-x`=>tkPo=$%CFQGn;fW#r1FLi?ruRV2S$ z{TsP8s{MVpG&x5JVSpSV3@C=m#Uh>YyF3`?c)cedUEXHV{6G`_3HZd+RASi&OZE)A zth4hB8g}Bu;w@alx{YLlAx!dku-|iWZr?3(TEo}P8G;u$M}J-)(q$~b&6Ww)khCmx5QBBrzMae z5>FDK9W_YOasP~1h(^u(-o1p1+jNk(LWH?`)v9-f#!IH~M?MNV)`kn$>GNO8?sTjf zrM>)PeqyqIuM~=!1qg5gc(>a3U5h|^Jz*rjJMrApm9qo^Ji`IwP5sB7_qPj}Z5mNn z0mo}l4V5Ta;u2vhJ#(R73HaV^)ux>{Fa2N@uoCqq4(64|hv*L8skL|+;b0OqmsRqi z^@mu+)cV0AW@z=0d4qC}hEWbux?C0VzYr`NSzOX6P3wH9{*COKt^FJ?5s4fwUNjF) zfQ1=FQ!mA((|=0S5VahTpQ-=p3grQ-$82NF-7B8`)xr{4OKM8&V+&xhG znpRTg$W@lP8R|rC52jvUaQkZ{p|^V2aOB(r+TVh!&?)2Qp`x$%H=4XvUr%t{@8#y@ zl{k)U5ALI@Ql(U0a@iJq6hJ6n(Cfj}_}dniY$MaY;aB%DNaFM)MBT9Q1GoTmj~^du z5C7PlAUG`Jl@1&ojXeq~*OCpkQpuSaXLe*oQl;@rh8QtpMb=Ci%9d-X-Wne_77h&# zF8ug#7HkPMs+a}BQp6@MN9A|FM4D$qhl_bP1azwQCe=ag^NYYwXMXmT(`*A6N!mSa zZPtS{a=YA9Q`?L>uqMz%(za}C$ba%($DKI%3*TT0APA_MA2M1+g%-yuK2Vh3o z!666n89ckkk8Q%$fDdph$G*a;(d&uCC}@IOkK4Rd2V>B?TPK9N#=VN(wY1EjpwBT6 zr>3Sxf&(gg#C?Hr=gw&4eA)@1GbBmHgOeQD)lB=c&Yd37nkygoIcz)7k>&Dc z=f}(6p7L9)iD4&xA$PZJEPBwGqzP=X0W?M`^@R)tDsy!}T&R6v&98;G_Fng-cX2X=@JaA2s&xW1+`HJ`-VVQ}+d^EY(4v4F4by4VyU?!XLm3Pa zDIoqaoN~~dq4{g%=3jbnA6yO2PG!0oYtpNlSX2y~WVgP^e6dD>G08+LUBg!o!r{gZ z64#du%`<-Erz#5J8wAOgPC^{i=dfDS(D;BD2<+|!NcLq}`%#5}{gGpCUQ}ERUAY=8KV<~Yumopj^0{|nK=!P#@T8=q zk}6@gPm&m2Yw`ki=Lu;8vUv?&v)=-qwLC+^uaT~O5x;TXN2OuCL>ay*sdwW0_nhqP zxElvnHq!iltO0?6#CjP0QV*QUgBFcn0o3C`Kva&`&)&t%!g4}V5_${-D<~^bc-4jT zSJc%ha?(wj977^460`n!vWW0%Cw%1Almd3|X(y^e$Oa+kXe6fonB4%SN74pPw1JB1 z(ZvJh4=@wPa-k-5$BW=*2cO#UTI!;)ZdayL5wGYW*Y`J1!9xJx+QPT)>+vieeMe#a zBAWwlMfE=8*yg28BUhN|?!X>iHCcrPN^>;-6JBb2PJvSaS~i1#nG(DokU&+EU16{T zWQXvi1(3Q3JMGcYQ4rysLk5xhp(IN~F9&Q97W9B&Xs8?s&&1x+~q?u62t)pD0ljSUfE*gjA1_oU9y~}nYHMz++fp6E1#6^j)YJj> z!xZM*8e`BT`X`7b(x4q zdjNY^od1WI<=;P~j264To{yJT>8&WFr1p?WqHwnc*$=gPvOpAW6fvmt4RIQ7fus+n z=2{es6)k(G%+@o!zc09zuihpvG87J-jo7fY(CLKnUgJ$t#70ADlG0tca}lx-k>IPC zuuO)0mypOJkNM9V+l3+vILe1qjk?N8!YK)450Lw4VC;YrbUs}RK6+1!V73Gda7MbN zqJOCN#iP&dU>#Xu5CW0m(rx6nH-7A<`Jf>!hmXJH&FDQj`u-|WH@%tl!$&f}&PRP0 zFsZvyVx>M_6-5T1M)A@(Gua5#pfEs^ZwR}+in&*!aAnTMD3lTdt_$<|ctH3EZ2Y^# z0-?K*i9=J+2czqu)@)YVs-v8AAeF#K($mX}m6=&7nY3#Ugb6ZzI$s-;--E64J4oCz z;M>)*2CfESf{$xBbof#sw4s&*b=RwI$LMHFF?<8&M-&^j`E#4CySrz_?vs!&kA3|r z{V+%XRo=%eW6E5G6SN?n{4jI!n0m-hBJGZXF*Bl35U@kwmndbYCnjQVJ2<~V^nswf zqNXMdF&j?BF%&1zAh+e)n*t}ojqqAePrYrMG%fw7vH|=T@Tne0d88$su3?*D~F^E>B zi~Sqnk&JBHhE4(H+4gPQ?!re3NJP%M6V40sF6gu2{bA9ZmXFasNA0#<$~rnagqh0o zV=ISEXn?hCF2alQ4&j~}KrVdGOHIw_T!*jDFG4__Ns zu63P!+rU$W3s^FWX9*J~%^PCbJg+EPc_WKB$6STFd}qh)Y;DI7CUus8rlSqi679sX z)e-`jCj0OJFQ^}ARV|`62vUOzc(U;L?o%6Xo#6k^gE#Vco=UiZAk0Atz%L*maNxiJ z(DL~Czp%_xLPCe1GcYiq4mUCI8d3boD<~ug+7E+;jY2YLRTiuaN-lg^tzH=v5YT{| zi*$}-J{$jYX53IoNeNykx#$=x?{2XltQ4^^iM+1)PTf&3jC}HCq0^|4ZD&Vy^&s*= zfC))^E$)BiAM-1fRV+TD?t334Ec>kQlCN0+e@hkVl@tqwj!) z0_;#g+_?f+7^ee%ZI;lDnbQS%VvSoM@ zLHb85Co{K`;Ec$8S5F&5T)&lFYf_P=!G-ukj|C!549;PcK-dytB!h(%p*h`l;?D>d zZX{qNWkh!lxF7*Jh5QxT+ti-cXUuiK;A8fc4+o8r+2C=QH%|s7hRIr1&4;HHRD$mZ zxemARAZ`DUhX6$-E3)T!J}(w zZACL!57#XWf)BxXv#AP$c@oJ;5jz5nAM0vqtm)hI@))z{yw3oJ;F#PFqLx6l#^On8 zTaQ=h2S2eyXjp@UWmJK)AZRID&c2IS?nS<{VNd>g)vhx87x;5<w18QAz%cl zequg_S-80Cj6`~`)P4}akkj_~?OXFImY#Bl?h28WB#ApP8M>JeTTu;5RT^TGj?mE* z1WQyT&B!inga{0Bt|nvhrSEXlz4f`Zmd@ra=>MRbiYH8?;me?zZ};fQlPB@3NJK7W z|AT+sj)<@S4-=KC?Z$E^BM0+H9b#OcBq+Wx)GK}abww#GQU*JV=MX`Y*rMQJfSd}3 zne=Zo1z`k6mT?7~OYPud zAg+}3o#)0Xl|ffA4}@+)WhgBUrY_4okirqTnu7%jCvselBQ6t0LgFj-Hi6_06VyW& z2i2hWg55C&@XD`!skdxFEoNzG7?+qxY=uFQF9q79ZZpv=lY~99l(zOY+!f3=&O@FM z)8S#?NJ&ZfgCVQ~-hMFhoQKSe11I#;qNu1S#tU-m0tpHz?12RSpmG1cO*!rOUI2DL zHZjCb2b94;TE3!O$9!fT6;&|b@oQ=X$NB3VfPIh<;n$>bL>&+mG3rMy^SSbh0rhhd zARIx^m!H34N>ht4`?>=3Gv@*T)E;(|U-yvFOp zYI1V?(8s7RkTI3YD^8OdcOV>mQwNF_7`Vk)jy_D-e%~L1lx2RvPWQtlFdBiyowv6P z0v3`L)Rsb4E#L5slakoaY@)5n~3aTI1gs%`w03^PnI^3RRZ{a znmux-C3at$_ey)`Dm@i)LqPW!zSah^)&bO-Y2Ou0=0U=bDg`=Ly~c-zQ|3Kt8Aybc zh8W{~D3&=nBo)?7pIf(DV32?~B7Xi8$vyJ1(!-bNw;!jbTA~KGu+Rp2f%p!Cohg|nJd8DKyim`CM@B-v z1ViFbHsxzipXTJ;hc^kqA48!peFDW&LGFQ;9AyTK4V2hP@z?p7J*L2tX4n;`9L;oYi0M3UC_W^E3xIRY~X0H3%?gzUcQ+E)JCY-)? zJ!jV|dWMm1Ny!zkws21IV}NqFgP8N?{rfE-v0NG&5s!4<&r%Q7N4>G{kP>c+^-D45;aG@>BwtPl2vA zd&p0F|8_C2<$~sJL#%1jLry`G#5wPT@he8?b87QiU!I6>Xz^YrP#^vR_a zxE^=cpSzwG{=;-Cd}ktBdX&j`a&vJrQVq|YOQIni@W7K3vV+maHkto{=vZPBmrIf! zj$7`$1_A+6MOD?}Vo$PKk+GT@mQZM(KY!lY`5A@Yt0i=+WXt5i$BhFQ0=2Rj?D6{2 zOov$1seun6Y$T~AHvl}~t0nUgMbdbuLXaw%WlAyG0FAiunEBVLRY}K&>PI(82d+F< zf7kQgV-os|80@6#fVK;cvJlC!ed#prdK4eKh6D66l(YRWL>G(~CwPRid@$AOwtB`o zw|G|qBL2XAr&3fNRRemwuu^~|OdR(|kop62mordFf!~BuR6zaYx@B&)L?Iq%D&R4s zAvZw9(=kHg;#YucV~j3#W&T;bB-heiTX&@Ipa<1E%e^_ zj0FKp;ef&WKa_?{B7yk9df0&zz*+Sl#-S08SO6<+tjNELQxC^>>=}T&6UID02b=bD zoa5ZLue_l_<>X0I?6Xjd->}p+QOI2|9Tn5`U7dDSFx#fC?TJaMp%&*8Kd`YtyFHG! z9Sof0wWJ>6ik!}V`V{y8yO>heZ`%YV*B^T=mO7IEqnv+7&`UrjiHA=o$n=Cih$pZV zfL0I^V9Q5HP!hqzBYnGB%x9c%N#2$&^2ZIa*-9)hG(_;m;lviCIGi)g44kW`Hztsl z-nK^vkf;sfQjdl?c38v{eb7HX75xsjaNJE!Hb*spVF*3MRkXCdV@uAUz<*#GtjS5| zRgEr^8KS_vIey|Lyt5OpG2NpR=G$BNW>m$$6o?thG6LB_#s1A}E$j*?h~}DGQBm>m z;lr}&2P97A?i|^0RX}(*U9INVuN3d-Nu)M{ev=LdWmK&2`@rjGh=(LSIysr0Ck?ZH zU@9!0Sxo@u(VwB3jvHB6PXKW_t!|F)n;49$<)<^mHgjH+ecp<`9)%%VmrXP@k|#)h zC$=3Y^Pq-j{rw3J)XM*^#tKiIJc)JG(r3@Y`=bH9G>Zxv!3LD1;MbOx#vr8yyp)Ha z4WP&4oR1Gy;MjWz&E5HBT$`pFZh0t9=f2x>GAF=DV9fy&MZX&qM3N99dLdabQ>hSx zDN+v{A6h0WhZ)5%U?CccZ&b00@LmS{0r!TmG)I^~P;5m1hGO%SUmfHn7*jH}PAC$% zhQwje-$OH4fF;mck<+ew*?}xK?&O7@v8&*soC+DK6=#mb)(Q0tdqTj*^n_*Jc$Zfp zA__Fv*n5IyLI}p)$Gd)SW;-G(+Myv1@DDcecZ@8LER~|^0WVd~X$_y8x@%sVX#s(621S`-76CAV{f=KtT%SMWaO^m6b zp=yd6yQ!%uhYG=zCFMvSkW)A(Q`b7VcewIEp1jwm;QS|4! zfFuRTaQ<~)0mKu3K5uS#VXe^1+giD%BfGM^AO!Hbik{XMc05R{fH;w8X;u-v^*v`k=mvn5zCgKzyI#3M-|^OAM0fDfo9NLUyf z`zn$#0SYu|XXvl+l>bBaX!C8U^vz>ht|op*Lxj9WH3~U@`LIGCYs-qZkA~BF*&h)8 zcwSBs!1@`B-U84YX&4B$00mEY!;Sc0Q2tODdNw&W(j$%XP|L2V~>lL-sWAQy!8@7 zyuTPJsnOpj!9u8}PX$I{-BgggdS#?KB1@Cey-v_RhkwSe3Fj52a;J~1~K`JZVykS9n0fVw$VQ=iWWNY?D*44a2&pfsv74 z#f&7oT}X9p(wuadZYWbT%cz5`3L2ua<%zg{@Jj#o*iyzA51ZBvkA&&6oHiGU9DQBH z-1~y_(Crf}*}M8wZr#3ZhxHZOxr1=$LqF=g?&TSe2Lya$-2?UjUw{B$p$#zeO8BFg z`&UQzpI>!4FIQl{ShUacmycg%J9E^QLSKLax-C(07qG-#faYiN|9|uye=@m54QjdA*!3_N`_R$hiewBb))gVd>YT>kgMW5;SwZ7!niSOom&E@|P_iiLB5~dI zOgFH+l&RONHG3&7I$r4}!P^8Zih$I6T$+Q-;{g$^M|wYhW~vH+1K<Gx#pI?37uVjNKjBasl+{3nng?T~$tVZZ))Cd3!(qo^HmxjXat-i@|8{JTd^|j5!==;i^<$v!rw;F(OsnB7 zQ#S?=fTChyY}^F+z{zPE&=m(ciFTgrs+*@4RD_1L+ zzE8|FpI;mrF1Xuj#{x0;$fr+)ei4;4aAZ|>QqoR5LJ6%9p0f%D>LzC7fBm8#wDa<~ zEDwj){(2>jMfI_oeHv{TkYWAWI3@&yQSiCXA9_HOAxk2P3yE>yPX>mD$7O;U%>@7U zSMz!NS){VRZll}sf@wJHBT4Af_Cl$P;qW>rDK0KXqXg9v?FtVHBGJ%Tf!ZFVT;_C<21K zhe#=Yx!r&C5oeaBq?AYUk3af*(X)H2WM-1n@JBJnF{VQ2=qTHo?Y`&Yk`y*T?X>HF zku-{82oMxckYe@`Cw}H}Ia- zf=i<5@4rIA<(2&K8`q~<>0DZGsMBuHW{cFleXh^*QtMD|WesEi=pQ?P7K1LLvKd@C zA`rYmw}Sb*+|eKburQz-g|a81)@8|hC2XZ|xcTw6{mtPQrwp&~aZ1&^3TV6g zt*d5!5j!mqFHw_Qf=~;5EJSUEN88fu(genMG)Il~Vf6!zaijKj3&MlzFNq`Q#T}O& z1}77;2NG%=R_J6zSwAluRf>`i;62F1bPk0H?2iGz13t~yyf3qAJ&A*osH6#6Iu{og zyL&)626-60G>X7;@$bbnTbW8;V}w>aUtx4wKf{!i%FM3<-BwVM07PQ^`Ub;%5L%RR z?OBNjW)B)HaPNd3_W!Z>`Fpz}@s?%Mz3WDX-<#nqs_f*7L0w~w+2bjGimtBnz%;QK z0&AT1viqOOq$F7ocu3_d^aZf4W^)Wk0Lq1iD8AV)rs=Mv@-^}grx!2FWSd&LALF0Dt0n@(7R+HJlGYZsw6XR`wA7PXMYHc6Z9E|mn zVn&JUm-A<+RUQ7nL#^NTD*qaH{w~rhg%I4Mtj|`5MDW|M>Epfav;Ea-nSFYd0YJ_b z9*Cnr9t5~0tFRzK%kvTze*{xt9xQqCAYNnro=Om#{2N7d%#Qz;Cv}-gtA{C1`jzAf zO@F$y*Xtawab&UW+h_9f#ySvHup=%pew6{Y$3Eg7+`@iVkdxW<0uu1axQ+?U!V;1H zC4RI{Zk(&QDty-@?rf&UI?k)I*#!LuQ3-J5R=nNXYxu$$OO79`6d?zexY1FDIVb-9 z$ag2wEbyo^-*GSJAln55j#@0!V%!Je^73Uf71&S3-qE!kBB>QFgG zI;?apIIKEB!SH=_R-#(OMZ}(HA!}_k-N0K}Sk~IF5THewp>2WDCE$iQUYQ8M^n`{* zdq0iX)#U(wi68KIv%uhj@XUi;gGrd^`uz5IK5~7a(9LpL__j|<4Ts!LyVhriLKm9} zSQ;*XtJiNkk44?6Kx#b!@it=#9TsiG1I`Cvy8q&5*Gt=%eKohc-EM+6Ll2*L>o$R< zJ>N^9(9LahU&>r(wmxau&)Nre$i1w%b0M|)HnUGU5F&!ObU@B}O9TrQ(mOL;K{LV* zuG%l2ppQvQuN73^aB1K2AE*VO$Hxcu0>%*n=GO=SO1U%B$+6}!pXC`Jb<5Y<)&@EO znsnkT{mW6Z&GHPQCMb3uXA%~UbW&bP`hkPzAw*DlUrUq07UKWq!tn2~u0)T30YZ!= zwrOKx0bWF;pyf?`=I(y{AZR~L(zGs~Ew6ffIf_?$=-znkn?vgdz(ldj}}I|g2p?>4?zY&=UyAQsnQ;PwjE>m=dLb)S!GB^{Y`uj^#sy}r(h zOua|K)wKu=5dhuT7Wr+~UWjLmob-b@LsP(w{?9RiWAFyShJTfHrFBA3(PNgRk)l?G z0S%TBVFL$vOF*y*Fd>UIjQp%gs76-sN6n{2oVF`Y>+f%uz1SM;=XV}WH~14cM;&!_ zzQEBUm$2%mf0(N0S*UXV-G!9anb_JcVntnhOA8jGbi$?$^KaCL9LljUjRHSwphhIr zuy=LV)yFj#8QS~acKp)1*Cz#Pmk1;rfV07#TZG>NE(_QHMY%rH3dy}7c?G7Vw!0va8`(?Xerx$iyv zz&YXvR%d}DN+9w3|Bb|dG6i}Q{VhR+2)B;WI$#pxW?`3IjNmyZ`}FkW@d=v%7Wwi|5e*3h28JT$DjbO3sm1HDp(K>KXceA zD}gw9il*W-=;5g?DOasx#NYG0kR3KU9H&X6-Y)^z5CIkIgs^f@dSNICKT3z-b5aO_ z&sm++BV}pv@1*#;hq(^iNOj!6R96f^4`Jyx2JXuED4)Pm>J8atwVM2!w*;H^;+WXB zL^6j+HVJRqu>()dW}(mlaK73qQXA0;D{TWI2u7(CN%7|IVu*#XU$2tVpZsg6K%xx{ z6nzRL2{7;?Mh6-xU;(UIwF)-)D)>|?>bEa_v%l=ns&M7(0v|ch<%-d+y_$gf6X;rB zx`$3IcEQ^p&_1|du=5ZS7CyUWxEllZ;*mo1{Y6o;3^XCTufp7Eb!tlyuHWlD6KMP->`}P z+LjZmPWZ8_u4v72GMAdR$&Ow$pJ;I3E+W$qpI;X`{XX)(J^!<5zaG(!&Q0Xo`tl_u z2Zjf8PyHe(eEGg&*ELGLkNN zm|udrA-yR$oSH>;{#)6`tSLbwmaPpBU9yDFJnQvH`^45-$ZfQ0)8^lwp|Lpvm64bHVc zYSZ`k52~6iHeGW*hL>U}=JI-9u9r-vp*-;k2@8{TM-bO7u{k`1OHbjpHyhgpymu`i znJS=lv7E22!AFT>^N-fy4?X37eIwG5Li%Nwou3@MbmZ2W%P|$KGd+jy$vxPJ;^85l zJ1S4rCj||Xl0jT=_jt3}KX9F>igM~?H&-RLa$W*gUF$GU&(!jN9zFoh7I+oaLuU#Z;3JkVQk#?Hh$&<_czV=?2zU)!QvopiqsOEBQyB5-)c8b{b z+!ENlx%Y;>G?SeZ>O{~VW!?sbpWNl(wM_a}fM${SAGMlC?L@o>A|&&Jg}E z?hn@cQ}g#GpuwY*581~Qdxm&j2b`xrIJSiClM~ysM#~0kdIDyxk_MSP`z=M>~YgS(vJK;BiV@fwqg8H8qcM z0$6*f^a69mc02X|^%KbMQwdRWrrbaI>B`Nz!59TWwaA<1?w{*4Ux{c;!j2&fkVMD% zGAjIRZ=W9{hMSd@h)bj|6p0ZK*9#T8PS?p(TJ45*zRSKaIy@z|QtPrj|82tCu4@?n zc<=m^s%V^Nf$F3)<7X9rj{UPz=gxhG&F5&r&|?hx;AJAWf3vb4B2N585KqDTj*piO zH^-K^F89lmPknl>=t_I_RrQ_k4q2IXEzW4Hz;CmJBn@X+Keh7ixt(24j~B+W{Uq&l zCQ~fBHDlEp`oxX(Zci%+!icWk;NzM#MzG5y;Mxl&;nSE`w}8;etwPfHL@P_ zzwESUM+9qRnWxT%N{V{{#Y4xWNSl>2^rPh@ud;9UzMPS`@#ptrPwKactvX&1J4AcN z-)7gHJ9l7BWrv~*gs9$bjet%5<-{i_gWU6MtYnT^zFHo(U#{P|QYT1%e^exTea)N3 zWqht|H%DJ`?@t@QrFbmBVGd0iv9kvYv-#oXd*j9`yzc^Tgc$RCO%~QzmHbLN+-0WQ ztLY?_R{NSBgEN19L=u^)M@p$VT~_(7e;Jdj$>3vVsr>-!#Zd zIusxBVs5yP`zmuYC>$=IGe0F2CZzxV&13GD4;=g^Whk)oUN_$@zOrF?=gA6)HCRtY zpw9OMxA`08yIYm}i9Z_)cAwnco>)*OLEZ}ybd}jzw_NyraSh>jR(BQC%RSu#I?kzk zMM}I6PM>>{&C+$I$oT@04b-k!@U9>!c_W8(({$ z$umq7l>5`Ro;Nt07b-PiI&O8)VgFTXvHI+dKN(*g)nY%J6iO_ZB`kF@F+B3?dm!<9 z*5O0inm~#GvHnf4EAzS#%D?^jYQ@u<))~o^i0d1Fc6cx(7_{**@|XHusrGcm7UDgE z?U&}qD^T(AoRXC6EE8tl+(YPso=RRf8wzWRZ z`aYAIy6#%o>;xh(IHj)NV(xbzEoK(s*|gb(lK7*Fccl!arEk5`ps(8gmz!DQ$XMb2 z%D0R+ZJ$NS-O#R5hFzb_E^2PQx>jrNu1BoIl3q)s9zt?${(he+=AxJ8TMv)0jP~3q)u|S=oT#q}_%HASH%3XV<@#fAy*@Nq7Bgk(lF* zpX2M?t%TYE0yh;JfGP_cl@x7fO&t6U_~|`5U`D%-=Jzv(tA`k=|1&iuNhojmfaVap zxYo~K7(h+}9#8ebgsKt*p>>u{*3`cZo(jkN5%=GSK?zP?QS1?%(f zgIZNju)&^? zoH|_+w|5@wIDZ_JH&8~09p?^qx!OnXsPe?iaamou zu=-^5zF&Vphx|Y5V2-slCX)cQ#`624q1m+Uc&4n)4`Lca|JvsxdF`EU)4GCh+^ z?sT6Y$Bd_P`vw4aghXc`A@ctI!#}>(A1_GOKZnz~Q{*~-==lLT*VZj!IuDz;p7q+h zmM|2ez^Sk7S={^!zFgg?5FuoaUvJJS)&P+y@0U+Fd;m~>-K&yPJD)m`QlvHV&|1P>wyvr$ZR)?!8$S5 zfv039)fNVxqV?2VhabL25*8#ojx-6u&x6aO`3Rbj z2P#mkz-B8%ssT0}VMNUl-D2>xG~foa*!RMWA>E?O3^wnNP9M-K z@u2j-74(Bl3cI86fn7<;gj1=}rOrJ}Ob>_(sz@KaW?#{XTQx8FCx^4^b_(0Q%FhzW zKc5%)k1pgYm$0x4D7F@_ursUP28pJb;2lKtcRIFPKPjGy_@1vc?Sd;(DZ2q+na|zz z&yo-KuEQ~_4&47NYkMj~+y#39_YHNyCt5d-ceCC7xy3z2ukhy<{l>#>$2W?hYlwv{ z2JUb5Nt6`+C&903hvYB(nrR;n{_Ol@ow4H z(|-+U!_(Y?zvutEbZ7HmVPyq-^90og^x`tA3JuRU)+VDsZn!{|-Ae3HtrMTK0t7Ia zm7{XB9Oo;`)KhT7g(uy)_rA7}>o(R2hXoGM+pQe@bVe}Or8igu7%jFCi>5Xa9oXzW z1dxKAm>sG=Ff_Us{XdPdqg2+-WpXu{CcMo7^zKB)Nz-fp*kY9jOtNazhXI@X-Vj7U zt)J2>iBl!?_Ve&D&iPHdLQb@99sj)AYVC=n@8lVPn2WKn0>HTr%zMiaNO*`Is;=|W z5LbAN>CsbdOZ~ECrR*|=8ihUx2u>d_YT#*d(cKX+9)eo!Y3HTX^%tU`S~y0OV&V-X zpaVVSt990&qxL($J+bRmq{xq|tp(m;n!5we^di2D6-~b7dfGA3Zu|UELIO%@{|8I( zKn9>4%nPcAMTxe$X1wTjR?4!EKt-hiH{v-~?&e1a;%0yDi?j{dGdlCghX~|*sfaq; zM&XNt0nHT}-%g*xH?hMNGc(3Tu4Jt7hcm+E6HtxPu&Wqhd^1R;j2k}hg||>0400x5 z&o@P)l*ra0x!Ek1h07d>TMnZgvq*kHdmg_R#2#T0X$CxSbFH8Bw$>THypJU6%d$Ff zc-gttJBjx#-hJR?=)}y#(;Yxh{^|a}>gxvYVveEZRA771gQ_!E14gr7F5A-SKwf4R>N$Gvy^FNl+~drP0WE|^|lz>!h{sl++U zRZK?3*UC(?cVK}ic)h5#bu!P9*M-YTuJ9zDcmwMLSG)cwr)mdLenjqKQ0vp8EbR=J zL4?TffSUEu?hV(0l8XfuJ1^JRgmx9P_~2E?Z+2{{apbwVL;PK&bq^djAu(G|h1w8$|`~QuobF6tV=qvJcG4mK62<;kQit>QC;{h5Roq z>ZIM)Hg}hX@8m3e9g1=Wku^ zx04s^f#PUD-y!nR`sv3hSQ*IeGGC4O>=Sk;pXc-I#Bm3n?`_w`(AJB!DVDCF2b7~u{4<`7OT6_d_C(7+;>LCDU67gJ3{Zt*!x6Z`9gmC_ooiJeXl>6l^0s6yG*c2`ZR|l zi$B7#S0}L$F9F5j9yeja0IHx0N2*tZ)(8N}H7Ul=eFl0AIp$aCY`fEWZ_vInw6zxi z2U^Eky~Iu5`Fff5fjp zd((t>TRe{rj59b@;-%4%f4@{LpiHE^q)!wlzFtb(b<;pl*`9ax!DD-WOdfW1Vyxi# zl9fh7)8Jc*`(gns6;S5e>D^2mY(x*wl-h(r&f#!t)4p!6U3%~zO&hVE*tXo&(+498 zvki5AXtP4M`$(A=OQAwG);tV{m7^kd2hM+z$X!4k-?&m{%hCg(2)TY}X6wRF2KTy( z`As*zOV(}p`i|z*T->7BUA;TGFPyHCn}%U*fO`CFz8w)7XJJ_VmYXTIv_hEKpAJAz zweb75gj5h~^o-Sa`FUMfrh19Nk{K)Xgto-}uqhZoR!Gx%I*Ofb@pUI4-b1}^tU2UB zRQZ@+ulVK%z1OKe?~=sY zd@E*b$47P!&r-T4H}$MOigCGeu{^=afm0j~p(@wF$zjBjLx?2;DVRqb=yp^FfeHo9 zo9*IzH!g$V#(H2&H!%UDPt%~LUbfuUPBS)S`&{q(K6n+lXKncH>@AaFGk4wUOS>9%M8y%ULXHLZS(3Db`zH|t>x$CYMF?j-- z0>Nz1~&=h?Ow<+ZNd+v#RKL?M>t9+JtO2Mzq zjNK-Si=r{sUQ&E#~2-n#;!$8;B3 zG%qY6v`J{_iS<|pneCnyk-nkHD3z#g6PcS@ZJj{ZBK}TD^9st@<7f@VBs7f-PH-t= z_yy*G)xY&H4i64|;QM;)qc~YkrNI|ge_Fqw^_<-##he>XF&j=^oBQn%Lc7IA7sJBr zz}-Rf{W4sPW4#U&+k4{fTO9Bu;r@rvZXe=N$gyZ{YyQ3T!^5&Y7cMryehq>)_=MboLX-&oxbggg2L`QZ$42`QzscW5;C#6*E-aZ(EyHSW-ekp zAa&w8&Uxw6SF{0hg0IKQ?n#VSF@o?oJl>{r@T}u%3lP6Q(`%U;-VHs1xZqc+LP7R|LpeF^iJ=eb2N`oqZ`s62wTA=EbS_vcWnIDYpDzJ`iF$Rd`y#AGA_J7fasbLd(Uc$(bnd zL#AK|`J=KxAy6rh&4od&#rgXAF}WMJPW82|oQpRkj18}v=Vp4FxxF_zTA45XOPOYx z$6eenn6mqt>m?fu=9%`M#xyLe_S`eL0!ay9$@)@gGHvTW)dPuYLvgj!^|2H5i#smV zzkXL3{)@bGkAJytV;;wX;+y8^kMk_cqPOFX!=nWr+XI;clHr8fBY1`^z(q+ISKj?# zx!r%?7OMq-zWpMjVK%0lt{$zL{1je7n|7gUq~pCpi;Vvw?FA1{Ym{fqqVGIsEqH7` zibh$?Z71p{rEV{PkCKqAJp7rP{r_*(m?7bh`gcyJZ(&})^;fnvzj49IG@ps_lII1Y zZ)cAO{21>zHmc>xXSe=sD`XpR@>HSEhzizOC3Ze@{weMAzfmhjNvs{6|bw!*cS#&DGq7ygGQb+`#>26iZq z6Djv(vMrKw*rSxa^Igd=sMznxF3v;L|44Rgf82F zPb0R>Zz|;QZ1YG1v}p)F5r#%1nc{kPDDKhg{|k~Xls*3HkdE-p13$iY=ne60Ute`` zbn82sdp%j*A+r<9yX2L1kw8d{`>fqacGTbY=i7+SS{bb%`v^dG0M-d;^7i0A)n$YSgO~zH>Qi z$U5J=Q02-)$@)alE7tU5Syc-G}FTyu|%_~Kt|iS!N?8rN@$VSU0V@%8>6 zPk;FG#}-Cvlrz@u-un8u`tU21dxajh9lu+7`OD_Jq53t>>0P%oHrbw~aNBX8X}f_J z7p0$_%Ou<2H`@%2kq3uWan~&&V?%$h2=a-WbpO}6BYC*i`-7mRSEJLk;6094aVg;o z$2#}keq7S{i?4WQt@zLlhLZOqZpAO@Ydy*+BzltWJg*+&?-H!gDbbU#{VF+qlLt*q zn2k4e6-!4Ts{dc*50w)JK1*xJM=MIno^SW0nZCj>;N~Cj@^x5jckr8Yi<_3`wlmJ0 zdf7Q7w%f4E;EU@!iQDncLoE+4^p2c+{nkyn^ux$Bf}RveL7?u4UchuMoTDJAm4bu9 zj-&sOB$`&BUVQ50$!4WO#kDn71xZhyFpHq6+q8~vpm5jOquB{eE%OUtaRwtTJdv!A$YQ{terc>Bwk4m54t_iqNKfBHODw!aXu>K#S8DxLVH*} zlG~EE>|{pF-4mjzXPeLY?hw-$QIh_DG1De*u;xUh#Z^15U&_-0?G(36XxCn(<3{|E zi5%C$2UU*GQ~$QA$agqbut6@=;L~M)cTy!W@2cBz$>c>nG~yc#+vDBHavkZcBlT4T zo|YTmYFT&Zr`)?yv$H(8+c@F5j$J5S#O24{=I5JB6y@Jq*P9mq!@ZNcU#!95Vk+Hb zR2;+*p@M%V_VXQ&lEjidP#`+oG=Q@)@gXT8A(_hV$_7NeZ#}qtKi$%m=pCF7m)H`# zQU7|X=D4g_bDIC#OUg6nMSrpBS>Ara*xSo@?kDv!+{&+~61yH7Y!>mkl4PqzQSxOk zNj450@@~wMu}7#$#M82p35Qm0^x!?k|B!Iymb0%s=DyZU-On#Qexm{p(UN2UW1#$7 z0Xah71u6A0V!AVS8_I7rsh9IwP-dNyRzN;T$1zoj6pgbDac6F7`3rJ*J}2C?VQBgmgo}?^A?6Y^P)Iw&|u^ z=w?IWtL1*=Z=<+ zu)uvRwrV~{&}FmFRl`}uQMGfS0056QM@7Yl(S69mAUw?$G50SN zN%~2ZrHpgt0k6a4!*wWxS1oV8Xw~u(#86w#-Crfz=9gk6&O@^mr4@FK^zimcw1Th>)^S zAG@)m|7_-#hrGu<8)=qE^^}h!hqP>ysH}SVwXJL7m*(6s#Ukac+~0=T<)O=CM)h{$ zp}ky(KN8#{;Qkua&2qAkJ^?a>DPyi(zq zl(|#2W04pHfz+Rvidr3dJgT4JJ4b!*HFQT%(ljzIT__{deV<5IPbqon`hK_#q9_T^p%`8YR(*dP;{(bS$CQd158Vr7+qOl6Mh}vb+ymC2mZys7-9hA3GTZ6$!eQhpfkxD=`}xH+_`27f=QIJi z*0)sNai$gBJc5XC-7znwsU63FZNtBqXB+crWW7qw8gEIOv*+5K_4+NzInKQwE|eef z8*EIf4d$V5NEs%KaWBs)bj(yjumWN5~K7G|huwWs@uY7~g@Bm6@#2Vzbgt3LC6dQJs z4}M^Ns|HXE$fiBIlMo8djIC{LKC#Wmo95~o&y)e_>dOCG*DS~1##De4kg_eV~Y zlfT$z+SQeKPT%izI+f{#ZDF_72G?fPr%m|2^pbnL`L2{b{nuBN?j)K~J}+Xb=HmsO zNt4umY>Aqq_`SDkVoF7`p(iTUV?3a!c)bY7ZM!X$HIZ%eTWH_O!>LgCm|(W8HT_j; z?D&VaIcM?#*XtCa7rzzEU1c_Qzt=#0u?L67&~@=xXY}1q!CX#TD~oSxcD~X^XenCx z^0sEnEvN9LcAtyMsXa8`(}QSI%r;2*R}Q6wr+zotZCqEjb^7?r-fPqJYD>3XDt9j6q`2%-8fmHR384wX_sN&v1Q)~GR^#yt!V|m27{!;O|J9O2-w+5#0mMYF1 zV*-UDmH0^Z5`{tQoUHrb1Su&S9SmYd*g@qYrn&&{!WB?#C>`n}Uy8wAW_$TOV))E8 z?m1bF73Gx_w3LLE7$qi~Y6L94##pOus+wF0^#&oAe9X+2!YIV$k>M zQc&%HWPJp!kb`aCMThy8YRzAgGkbOmS=jaUl?Qol3g5VucN_h7q2n#bd&`z9mwWH_ zUf?Tk7tWo2^!~(jRx^joV~e^RzRx$WOOk(@#V^mI@Q{``|+0vYczMi@k^&);e z;#Et%TAJ+>@9+MKEtV!$suDkht|$fbDCmj)yja3B%^>*mcnFXB#+W@ccFYMQ5t)V! z{?Sgx13o6=I=lZt+mpM+*(6|1_yjOB){i#ADLX*9Y#G^gVil9sx9k0CGdB-=JN&SrB~& ze$FXb2sBaPK>^(cn&ml?T5nyOwNZqwtC=>lMo74fwjA1x^;e#6H+G8GJTp_!HS^U{;BM(R z?*eNX^F6LVEu*bo;${C?TJ zN-X3@VbWW%Ynm^9m9l(y8DHKM&2ZL(Tdz9!B*ku(Lz=ExfzG*UIvhI_Ro9;)P}c82 z<3N8-)?|q@4>_zVb&T>-LZuWOGr>9lPptOu+Dbj?m6VihyXBNwKtKT?$smCvB+CIX z9mr?{B*5=<->qtDOys*+ZFR282v4a}*M!@LVJc}M zjtef+X1Dw)Y)hitTbzW_h6PGv*$T&HU%DGMWzNvGWpxd?FGC_L7R`qTf#Lsw$bz2ynp2Gxp7)4t$bY@A}Wv7Daufl%_cvlNOCA`tW5^6~;c@pZhX0$?{m6gU%S9wp{7gNO(B;eqKQ zN=%lyf1im_;U+o3iJ^MP_iewU0ABk0KxKe_J~ zlNKdxJ3L-qAx*(p_n2Jh?O3XL{Lh=_FH$}4sZeK*sU#MW>*x-)%U^^L1<9qcdpd5fGPNttOVfM!-fRS>Le3~26&SdWgB2Thq)O>1 z$*%u+uxIE!Ku|Kk-9XHww3^g`@;B2YB`S$(*-OA`xicCrL;v8JcLU8Nx_nyEGmGVy8R2`P7_9}^9BN?iqJ)CM!=R)LdI^At zNg{dR&&bOlB%m=L<{=POK#Bfr;3*#-Zjy zCoXn!n@rzoU8m<9%3}XfC6+mNsQtqvL)+YC3T~l+LV3HNUEo1V-=$T@O_nzSRl$83 zZG`SUq!obSy)dq$B{~}VlHb` z<aIFS&TLmK%WCkcZo z6FhzKnIx|9$@LMXA~L~Y7FfdX0`ZWbsiqb04Y60U>fNUxG@+R~^k4SC`(;vxxp3_( zBW?&!V?5(mB+dw-(sK2vsHmog)3P*>qoQC6rb&p#ig9lu2qBxe{jLQv{{Tm`@QZ^K z2!|nju9ZLWL*4rn3cJJ9Cba&`G6G{@c-vT!HbeO)OF6z0*?~CvhoFZpvkA>HFEJak zWxD!6z*a`_MO;2jCsy{Zj9AMuq2O!xnX?}9TR!~aB85U|5Pq)0Ua9qJ;FB*~0@rU` z%IjZxUPbj%(nYJYmzHttL^rfjEAhD<_vAWlgTH5v5P4*#yI7 z3F!F>*5>CI*Rt?aZPDLroMD#KYwcFdgmL!y*Rab2v_>W1p3euk9#WCh zAWpYq$0X=@k#)v->jH3m;fgp`cI&>ApiD5u>o;%IGqlthDo^85-?q^crr#F!y+#(l zA^kt5_~$ojJ+2Yk&D3;sYLa8%AQ*S};ou~Dr3LzgZ_XtD?ZB?at$S^j z$BfURLlbf>)giPrW@-lo53;a)w&4G^FGGcc^4lpU;0;=SI?2?e({?@d2hDQF9Xy{U zZS-5%5Z7td=Ul#e{7(|UToM?#-Kp9i{eUdybMoImh<$@eQOq4uFAl}Q|6eG7$Fj9Vc`z1L8uZ9Do^g-C8UF?dh(d~oUUh(kk?IcsNHSK zZt?b$d6u7rc65!Vjv7?-QGL~zjQE1ns*J;B_)q2?SB6T!QNDh6Q;r`!KKp%mqyvv3KQWB~=X!r;C@SnC4$V z3tZa%M#R;`wM)?u4!=YZddpt8SR2Xj7&0`^8vSL*&oXxbs#?3$2I%Z*?&z{ZsWC2b3QK*f_2Z*O`tOVtF8Ob!J1{xsng3%1W zf9z?N1=%QY1sso&vlD}?v2j1)#Cb2j?*?mj9`HtV79E<VSTP4MKEFUiI%CJndYvm8fB@%(Y?l-$-4F97e17l^N` zQ2Q|dpKfj)s*JBUF}j`wz=~}FPW(dBZ^yeUe8+@^ov}t{GNNd#{82I+^HaM~CuMhh zBNP<}H!(OqLZ2k&z~rAh+9Z8Kc5DKcNldB2zC(W^ELRW3_D9~bu)gNBDg@YxA-M;+ zxNLFl5vU;UL5vmWc2hW;#SWxNBa04XxH&ZQ%}rmXHQ|p0^*VXuDFjF(Eop=^W0fJ^ z>{W7Q^oZtnZ2lhb1TiTme9$ba{TEUpkFS0# zP*$G+B>>?d;=n%9?LTmB^=5tCQ~{C2Q%r;H~szkNf6fL%>{~O1o*s>K3^9xAm zplW3ymcqn^;+bqKQY(Z*1UU!qJ6IPv3$g+6E`VthWP*?5KN?ng#mkifGAp-GyB|8>}rV3n_JEu600F?yQq9i&3}ZlBFg(PS^TZYk7Ctl zMl~3$#{d`|VG<%B6dg3u_}JKFw*^2Qf#@fzW98$^Lxb-vQYy3d+;8v{)~ND$-fTq3 zjj1mx;3Yu~9a?J|T3L-~XarhLAif|1z-u(gwm+J2#ON{Sj0x8>{n7QxBv1YlKZ)Q!*ezx6k`5zbl zuVC44@jJpD&ER2Tshl3rjv+{gEbqH3ho!H+a06@(6%L}82lwVYn!k98$*jz%3B73) zLjW8v!=V8x#Ep97LTRzHdd*bSR!QUpu06M?NvYVHVRlG&$5lg(GtTEcfk#mipYOwA zijRv!BX9Gj9f*u1%Z*`2J2H(>j-^ImvKaDxe#Ew8?mrLu;v1_1LcIbVQUPK!A7L+j zqR%H07UE$ApmPq4CGp8uVqBDfRaCCZIB4?cuna^3g*46l4yf!r+W>IlYB9 z4YOC8XzMMS_)oi^KMl!!NUPl0b+`$c0DfASE@Du{D%o!qRazYF8QgIg31otVr|Crb z2>FZw@&B-Sp$mycONoU2PCB$vTC0f-{} zV%I?7g9D!BkMwpRz9E_qkOeQ}Nku>0+>QH7yX5EtHg&dN8@l#M2G=Jrp8 zDyL`7ko!q#y9;AZs}=3dH)e<0*{!BKPT;?Kuc)XoU+Nd&g-hFF8wU(hzb*bprX;EN z6l(_Kc8hKVK+%kmSu%OApznfH9%rlyBM^s<`%ewU$B!Rdzg)`aX;4SJck|vugnVrW{9PsC#)XON_1fPoB5&~;%j9j%3vSa0dp(%q!7`Uu2qya9unEYb zQ|48WpP{?%;e!W8PtU3BMbjO0Q=4^aBL-7zhdbXH^PGz4{s{z~2#mP}GgS`sAv#*d zHEERS55;8oa2+JaIBWu@O_B=5LY%z)h;Pvfp!~xVFNj&RKDm0m=nh1-D}`tQeQ@QJ zakf`qh(Rn3W--hY;@pu8hA9pK1Zxr_d6^+UjRNaodZRD4gu8DZJd89)V`nN&P(}O9rWm$i$aB zdY5k#snyD&e8E$KL}ux0p@dKnYtNR^b~cNxJ}eBb)r&==RdD*=2dG6(AI5D#+$Z=Z zqFGWLo{g&%fg(;j(RT?ftP5rBK@*D8Zi_Tfjc~TKeNqB5b6c8jLx*ufrThtxtW|?) zB-UmJU%>;GFlF?N!m~`uw2eCy{bSlGnhP0tz}xR?FQeUV*aV_*AlS7fD<9x{p`rSO zWiKY`{V0BvT#HCb^>^zohx2vmwEPx=APyIrlkNtC3?A^w6^rLY?>GwMhmPn@gV0a{ z@d+?Eoxlypc(78-&-~upwDySi2@F2$7D6E-hwTMTaJMM>K8O9A?Hwr8dZNeLtbcYr z5qhHOsS7TuB}wGl0R@#)ad=hY$ReO>E(5>t=E7k{aqeGp%D5bmEtNcCd|$VMLD`XQ zG9~3i4`JY7SR*3vL*{edqVmQ!e{r_h6L#UO!}2f8L^9^=7328E%WwUMJHYh9V`rc% zZ1zW%dy$IjcSNTA$mfh|?we^r!=wN?CdR5cV;$;Uo;-SNTpdBaqa_?^-Vvd6-4`=B zHsF=}KGaVu&qiBd%(O~m^LRL>aUq}}IE=s&5n~7o7vW6+pk+B960-fe!RNNI<)>$f zpiTvdFC^2lV>2>uETK;qy#K&&RR|`WdBN0!2Q_NZ3fD+@y)2-T*yLce&d?USQ{Upu#vp>Y1#aI)-rTeGJ+b7xhvW3DN62P=QYDl4=NO1-mUAn78k3)c&{psg1xae;mpY|dxB5+fj z766-P7GzvhR8)Y+XdtaX&Q*eXNgD&N$qFG9Nyif(;u!9gqD0IxP?(Km6uK7Ttpb)9WT-1`k-3zaj*v8`#?M zXLJ0H;JMEt+mVk+zC#4|MI{OhW#t^-V!mcoIRrOoi%0*jtx*;ShKIOrXS7ph(b0?q zvHBDTg7Dm2glG!!(1|#f^+uI|IaIS}Niq18u^7 z4X!2dMC{#vwxC%Xro^^4;SkUVL|UjG>mgr3%{W6mHKolbT~B}isT*(gIU)F_5tCM-AkZ-dg2tJGf*M1?~ayk+qg@fB8nv#Pry+KtOC9T6v|1s+PB+e44cOZcTQ-ju*5jVA;uZz zJDApX7tsRRdwY>|-3bT?qYKU_V4z9b6-&B4*70H%+~aHF+SB}KEmZtAzIHHPP)Ix1 zDLhrx-O5Rma2Njr@AW4UGHP@Jirc2~q-juzXeZEVc(6Hmtiw3{MKKKD!)f;`=|vsKpH?xb zX3-$_0hscs*y@XI)n2oA@I1oER;=XPjd^K_#0d~f=amLA0!~;(OR6cNB5noqlH?OH zo0$4^L{r<~uPatNSxoL2Q>Z$~c1_MN@*V!){%>AtN&DAiEeCF__YlH%IInfa@aXPZ z%tz1zCmap=v+s!U8Q$c3i!Qz)Wr$7Ni(^aZ9>MFjBOF1{nSZ(QWXWZJ8m^0og3ZR0 zsT}pxwms9zK&&u|iaM(AeJ%UV&Bh_@V6)00vvX<6hpYd&;>etl`4udLZW2E3QvaT7;5PxjS1cWA`R^ItI$dyzqqWL5xE> zGCPH;i84|1B9{q(d6RT2dKBK>BPh8 z6a2S5!Es*w=)Nhw?z`B1oy?SJ(c&CP1lAJ9IIzJx;kfBMZPfA}T~ zM6$@Fp}BX@*EbL)AiHv6Gmo!Baqi!CGhr>fCwkV6fQuq{|ANd66>f*2_Xg0sC5{O) zMKw)84dUn?JRj*RQ}K`Qe^U$n@wit|ic|wg;ltpZjIbB^g!6Dp(ruuah<$P060NWB zm_=xafb%$5u%D@k^Pd(vuA2&kY=VZCp*2k)cgu zVXz%>nd9QVOE08iB_)|)@Q&;s487bOc|6cJ_7P5$Uoai~n~keLI}%1>S~Z>-6h+`? z;V_h-SO2t9yAr^}qdt0W{G(w2GB>*~&ut0R{azZTC8F<5#F+mUd%ek+2P!$Pj^;c0< z#q1@5en+f?;=lbhqNz57wP^Bc$<+M?B(3QoF-#lVMbJo*Xb>goAfi;f`dREoeHDY^ zoZcBA$US`ca8nNxH}@n~9<$P9(E&%S)Zu^o0sJ)DQ$NG7kVK^dK0uThbT2JkV+8QG zE>=J9Bx2NvKmQl&%Y*AA)@7~fxGr`4e7BW!$XeQUx_foaNb(-;{yVyqb&_yqyL50T?cT9NrM(A_gUt`K#{y+PM%=K{)S}(dmv1j%$ZTeXsvsqgcCl#g?fqUwyFz zq;UkXGTs+Zof_a$lNcvLx)~4Rf}qD`YG?x0>(&(2!SYRvMuhDR8J&^rJFOu-;CQXl zW@bUQ!>{OwgAd6)=X&bv+satVj(+USKkt1`#pTJ9T!k}cF%RZ0Uc?lUp@6vf-BPDB z{rz=z?wL0?nwuGy1@O#PntYLT)~AkZNV;ia{dyi3daHMmh+s2&|FMDgx92N;5{BY~0@Hi<&@}E`hwu zG}hert=67d8^Ue;EGDezltTf@&Al=XQHllW3ftWuEfMO8oCuW&EZW~dT!?6Ja0>!=c zD~C+@JhZ9akamaqE2kI8c4QR&ETi6Zbggi?Mt$g{tL&Fwwm~l?y?>Ak?B&{{M0X3UUeoxA=Z*H&yPh6m8mJ9_UG6s{J(|3x zc#Fl_9esY=iEExp5`Eyr=+nc8>(hqU5m&nA$`e?rRBmXcPGn%xx3oK$xE+-Ma98Ay-Qd(gENca`0xuAid|=!Zmch3`?%>7 zJKxcoZNa@#m8aA1y=NKvP@lFvGwhW470n&}!p|KpsTkZJORat4_GIXE;~C4~cbDF^ zw%^Mcv08I%{cfj+D-j9_CGjo-EAMjAwz9gVEs^2a_H%3Fdq+vf^xfV){Bl&t*vh}> z{(km~x|w}nEM((!HWg&j%UW}K(aQVC2bnYVvQ%ozo*&H{4c|<^sZXF~#gmaTn8XlO zVwWE!VT6l|3qAy%=jR7p7Im@hM=8DwXkPzhdZF1kz>4=X?z>wqFUXu847gU=Clqak!lddYB7SrFFeJX~JSRUo_SH18$Ux-6y@3!MQ z)1Khg#lzE&mKVNqxiHy|+dn(V^fs+xPrSNEh%;^J)!pG_ z+6vmT6%WEqxx9~Tbjzhy42d+wsq1caSfYBkTO=vEM?i&f-q6VIv(XjC9Jhyi>8=aT zANdndE8lnoV^P*C3FFe7)=Ww25veJ&)!&frknZQUqvD#6&mnK85w*gIP{~4aD_uR- zl5(4x?WG)|&WiT3A9g(;alay2#6Lgs_uH-$`^1_RQy-qTkk&e?$KtIScSXi zw;Ku@$=;E?+vb&^$L?ph_e)W+2H_FBllzrx8d#E|T?|;W<(4ZKV|Z6zHf~K4@n|to zwKS;<170;UW6>8@z;gx1FL)Dlrgmt{?D)o)jJT|cctE8AV|leD?co~7AgVcva8h$ObCt9NUj<5H1-+E& zLtQLaRLDk#hoe3E zs!#sce6R8?l-dWH>J=ZoWTu!tZ}}ygtK>_OtBSMd#7(Z@Bv!feWDnQNt-WKh@$VNM zU-_alK7YQ5A~Dvu$NUjVdP}-;ZJhijg~~gXxz-Xt`>7wz7dBt0yUZEGE0y6ZYZ`o0 ztL)@H9sZ3g9tD#rCe&n*9Z1FH?;DITz7+M4Zao<1Wn zH|6j#E#X!nW#oaVO=(3{(ONJj$4;83d`w&i8)qJD<5)j<>F3G?fPK3D{QE91-(2>~ z_Zmtz%gd5o2^KzddU=QG^Na7LzvVd?SvlVlx;c9GR9{xmmIFIst~3;j2R{3;pf7gi zL%LygL2aTW1lHk*2x;3@^;I)6Rot)GDs?y7xI7~&D6@R~)BQ~Q50+2*ll0OD3H)8c zjjKy|YIO^E{7)}(AJAR>)wtu2 zS4?(mU3fBKvNdU&_4ixcweTz1q3}z=bpMlyhv!st`bA}DpY3;*cKo7k8(Oqmegpa2 z&|W|4KkK$A!y?BNCmIpSr95q&!V=74TPAQ^_aM2P|D4!K#-z3d)7_cuCJE-eUe;Rz z=on2b_1|pn4z!T?V@Z?LD^K62v-Ge&v9Ej<&k#Re>?~}UJe;MXbYNEHddYFQg9Y;ZI-Elaq9#^~RH0Y< zo_&*0U7T~&=A!dn?_#9=_wX;T9{$eS)x%$Xh-_TsEal;bL`inPCh4K+o`vHgbte;V zhcwk@)LK&w2u{4p9Dkl-JCk~~c#GuQ-G8!zIM*jDE@|%{CsLirc;lW-#(i2bj&{d- z)-#FbHhb12Ug>G=Z)l>MqICX1sj3otP+OW#eBH%M@qZu2ojB-2!c%oL83P_EEP-_V zRYF%kztU-@FBEQaET_pf(F!EugW85fFWOhLUM$`R<4CjD$^>Tog(2pph_x885jHG( z_&YJ?_)OG=PO5EFl9Pdb)jtk=xc9DQ)7PNF`jzXm_ID!x!_Mu6{M@$ZnAp~IiR82Y zv8Mh5#C~KpjO}?smw=Ro<1pI zc2m0^W4yoQ;9Ccq5z;`}&)(Eq8_D8SA0|HHvr){%hjLHoj?k-WrbB#>jk-ft?w=d#&Yt2r zjHM!??&pg0ZcrUq8*JhJ*YNieFC{8)7;)Pj6^ft(BH2`qYeP?l4jpQ&MmoE!92C9b3bjMYcHHNId?0bnV~opd`Md_#%mo93oBa#P1p%PF5eU^UGL9(B^R? zm^imjF(*)OCBh)N`0WFmnYx-v*TDyC^J^LYI36a(KLLGWbRPeyT_a8@B5Kzn=}fL~ z;Vj^-D&1-R{6T2{?njSYea$xt|hI|%FTkEQbtC3Tb3pc3-Qdi$jUyd?SCH(7r^&x%n_q(6(H`It!NC|0CXx?_E zVJrQ*)H0nq`lsTrY|8aH^>&Kv_F8?kM@Qc2KR4RkwUgnuVsXjSy+?lTc>VWc&Rls> zbHB2HJy$-b4+}@FUl3G`6gkwoU8}4Hc(;*xOjpnjn4p9PWBv)zkZKWLK<9-j?EUV0h1}r5qC@`a zi&?nrID)pE+A*pyIww0r_4j#?DG@(gwequJaW`&dcUc8^9O|_HXlrA2L(I}DJLJ^d zJsUYoGQD+*YcxKYN}_QAQ^P@X8-N-hf26_+E?J#r#~20iT~BkXNcH}vr0l$BZX@%$ga<8%T8b;i7Sp_k!_ZE zAc5xt`RCQ|9WA@seL8{n%$6>yn5*Y98^x52<_o7xCGIBqPgHyzyEJ-^G~DP1F8mX= zsFq;t*B4Y{iOvz!gjd<I(-fmD)Ks2yPx9y#t+)aw0#5{su5f0{-LBi$bD>$L_A? z65P);$=3FTKkaQNMfSDaDy4fAT|4SO9Npmltz!C#;gjdrdXH{9I&}Eg_NzED%8wv^ zyNn_X8nh;X1nxefF$%h;_(mHmw* z_V?18HO1@Xj>xq~?5^K~6l8WNkSaV;V90Pfs7sQ0TK-wV(_V^Cv4Ej2JI{V!Lj6Nx z;`L6HgxyCn3cz3#L31`Jje&ocfSFi=wJS@Y=HE+}_xOXkegfnU73{pLt0hhC}01hG%r~+0i{7c=BX7#0Z9_)tnY?Eb&buQW%d zb}~%oYwb5ullh@s!V>T>-K;zLMzpkphNiSXEtf@e_TzZ(d-QzIekU*2N%5(MiTDq{ zcU0^3j;Gbwqn=nFDD1)bOIuIlW_=#vA~*`+B0|y*>WhrC-v7)(S1)q!-L}qu-Hclk zXQDgxMa}%9>CDqiD#Gp^$nx`LJ?nITa0XaBc&H%U3=fS%Nf!-zFTm2h&*$s=%$Wb( ziSadSeovi|JfX%PS%6|aig(~LETZXJ&W~09sCLolNa6(%Ib99*+OT84jlT)hFI@dr za3nPIti;O;3nga1&Aw@Nu`emMe8n~%)s3TVxfLO2Qh#39q_ydMaH!(LV*AN2iC2=? zqxlWKd9{U=W@@RWkj01Iqb;%@3QRn;@#x<7wx(4kq2j97OgpHbnZvS6-_(;^u9jE3eKaLeNvv?HW`~^IE-kGgKaSXs3`M$Fs(act zCnfs~GYc&>`iEIL=?`-xNV5Bq%5COhecYDdbwX|RVpRC1u;80PdB!u?V$5<*a)w7K z0YupAqBU2{TT-XN>8^1=T+bOvsI6N-b_^xhBMOqcl1H+`YqYcZ&ex+KxElVQPzA~} zk~o2O(%45j`yC4`PHnd1VHtgU9>MNN7GMYUJAz8uyUdg-g>cw>_xue zFQQs6wa|4bg_O!-n{%`Q#zP^Apt+{Qonfm}S3c+DRxuUV93;87maBzR~s%f`)u zGnQZAPvHKf$!BDn^QlF-iB>6%;^3Lb*WoF*13R1~g9FnuXy~v$5u@R8ok#E|f2aEv z4$D_h-kd9@P4jq@g?9baWZ^BrC$~@X#$@`xUC||^DBnJvv)e51)Qh%>g}cB|uK$wqUCFIo3wK(RV$ZfbAw2fC6$ zgH9U%6mPSB&|?!K~?(PoSnt77jhq0#7u7jC(E%yWnw)5M`qhF=eeJtK7!lHlD zt@-z^SakhEP$JUt=b_?e+KkWfZqoLnp5jaIv#7KjP9~Mpi0(FQA?4vT+!DHYugjy1 zf-d_+$KZuIa}o`~hRow@U+qEg)lW@ap(?EvdKC=6ja}#JZ9E%o1qb;|_0O)tZ{?Z` zn@f<34cwuTb0h1N`DM8WE6VzJMK4tl(*4ncw-rvRFzu+IET#BG-t&I9MTEDhTjT7u zVr43I#;RV5p2u;l?KF3PypFbfKfqqhM|}k<5yS2fM5WSErk;BL`|iseiJY}0v?lO8 z4=$`+lDkHCjt#UARI3LqTvmwsSBCkjiEb?o;;Og8OJ4%(Rah z&-Lv7b*~)37aPsJFAnWEI=?GcvCQk((By`g%f8-;XH$0yr_69n^c&FY-RswW%D3xr zZ10r={wXr*m%KkYac`irsNXr78mlEvX}LC$zyy|8qH+QK42!#wJ4}R)F2>OHQ5kc_ za7iuiiV$VplX1h4TORS>cA^UT5{v@cYa66XE8AFXRdmI@PVMBH*j60m`+B|L`#sS| z;w~P^WxE}R#}Fw>>vRe)*yN)2!)kPy;`ix&uQmizwbHy!*mt_a&&>7<7YPNC7*6^S z=970)cKX4%SdVutt?-ANIjg2qPb&BM&4P{FJ87=gVGY-ytCh%0Nw@#mn)@4JlaSF^ z&m(0xb;U80y?y3*0MtqLc6@$R_tVjx)qCb-R_Tz)mS8ApLHhcX>vPhy8H29VIuBg- z*S#koOOKU!THv*O02j?x=iq$udi6ufnV#C3+rz|V8B4iD-Q|ljJhvS&O4v>r)J2q7 ziT5vmOKQ%vgQItHOO&9`73ZPf1j)>(o z^zGfQ8&iradJVm}tKh+deYlp*KW6WT-+C(m68z?m`f?|3@0~F^D9yx8s{GVf%{89_28{T-i6Zc?a6oP_@9JnYjSFam+SL}lSl5@$Z}5m{Dd$)qkdEUJ0*nt$OImP z#omD!8N4z%*|!yKdIW1;iL)VbpACs-Y1ORrP?*7aRbES9Z%C(6X^GvddJ#7w>f(tfgV3RfaJA&B3<$x4-i@iR_N>-ncncd<+u zoqv#VgI1NxVeM}FlSvwv^GMT(JBj{fNF|cpNTa;r~kW~q8se%X%9s4Mkk5x@4 zQ8{Q_2&XVS>Tr~1{b=z1Q%G7?n35ZQ>aej!RW(6&_2tBD(p)Z;7KFkugMvzTli~Qj zt*PE-y`0|#?@8~w2%VS;;Uh}y(w!?sf#sFALaUON!A7^|ol{wdXX4MfP>F~K{jYB) zJ*RQbkaDCro8s5N#qU4nmc)t$b{vSUxN_+1S0~X6jMI?qgTAyUPg*wHuE+JCpU6qX zuWNKz0Si5h{H=J{!Gt~L<|Xc`=_nh#>ldd;er@u8WS6(#d7Us2h=le?dWuZTsh8V6 zW1pyPZKmBVd5vPMKAf!vocTL zQuAN))u?+rrSe)L9}>l=t#x&WqZZamOi5YqwSS{ryq5NX^t{I9X_jT^R_VSzEi!5h zh6l;pm1y@f?C(olNi}~^-E5n$7J!HpXCw_{Liuii6*mCcwQTF{hzmxU%|9ari)a0!A`zP zq&z30xF!p#o3Ew}t&^%PzPzYx8rc~FtDnLS%nRHS?9StoFD zS*ZX15IEY5tL-mCRGwitc%|mJQ~XR3q>v+*jb}QIHz@dxH#xVc7gBYkwJz)B-=VCmZxDXFN2F@_ z7z-=wjLQFJ@xPB*y)*3v3oI;W-I7m5*Ea=`Lm>e{|NH6qdR?7X`(2g?RC8=atwJ-%q7*;-@dMGt z%8OJ+BfFlayj4z&xqB2s-2v_>!-5bgOd3jQx zR-^PNEZ#Vj)!)CHF$I6mbbzqF(e^FIk-jIl3C)e%1KKP=)-Xk4tcyua(ac6uq}4L77bEcBTdB_sn=28kf}(JXy+Zn#D9#%d#sk%9Q5 zzIdzu#Ma2?0}ys7#7_s=T>ULq7dU%-BT5{bBYJ25^ei0-r2h(z1X~1=$UGHZY8KNe zawi2_^h4)r=d1wmuRyR5dST6S6WUG09)!d2Y1vZYhK%sf)yuFHQwZonmR6*ht92$~ zbd*s1V)n*>ho0dF(!IA7L62gBm1Uj2jU5G7AZ46Bqpb1mWRx_1hnVmeG(Q}cpwn8B zfnP7jxT_{3F7l~85!#;rYFOw^nLFC{Pe?9*EhW~gi`t8tYP))gBCPCj*y) zch#lujTdGK)n^Ps<+sPIkw&c+mF3QY^jt`pYQsj_WWh7|nddFiQ&RpttP#My{r4OD zRkQXg_PUHuBj9PVktPl5fQp85>#WELgRfYSGbl`kH-(k$dy4r{I&g%Q1N0wepeIH1 z=l+-9lQl18K1fgL{QFmbpIQizsZnP8hAS4u*<_f=X@C22^S`zUwwK`iRa{W;%V^Y6 zn+lP&(xz&0?fV{}zmk0dx}OQbtmtWz_f-%mzs4mJ=IIcL28pDrr=5?6F$W~Hj@mqw zf-$!TeA!?o@IR0HllSum$)ru74)_qFus(wDTT7l6ufU(Q(2RUH$`3(KFxDpS6EcBJKP#N=tz6-(Y%`J&W!x+dz8X<$~;xviH`x; z;2(^-n-wJ#y}+SLdIB7-@4wV8{Nd-9lW8&|0w%z*H!Ad>5Vy-GN`NmWdWr+kmnf@0 zs>>q1bITY0ipIf4_w;5-%lPV8nPMvq$m*aKRnBcsOznz)atwYRH5GF@?WbP`(hsaW z=m(;qw0jhMt+7okX?`5%+7eJK-S~+(B+6&Z%+C?v$N2r*{Ffbm%pML~eZSN_`I*vd z2@Ym&-9jRKz3g+=H1N|=k5`4#vJwEz7DMg6i$VXvr$ z7f!5q2?e8Otj^Kfl`071&j%t4Z)6rINV92r{(gFAM-)E=(sQjcXo}{%qA5*^fdfCM z|NacuQWq}^!#$NtT%{mo3&@R zpLht%#Y}ZM7pll<>OQHOkhc5Cp789#eJnPk!fW{WH75G;-tJ&Qh1|)qTD>3nZpkQ- zPXQtT@k)h6R&{ecI0761>DhtC0g-kcySiseK=T_RN1$T9bnyl;OmH>10>b2^P5g>P zsi}HEWf(DS=L<%9bcck5ss0oQC(~}u%GzlsNj9)#^R7^OXEXb^%d1M^)bE71t)hb= z922}*Ee-^&mXTMi1&#)I4h>1UT(OjZUsLz0gM*L$C2xnRcLkETpbb1L@`*@EKg;5p zz-j~e1;-@- zHI9Dcn+S`L-u;p!wFPqYKOVo#shIbRMvdw7C7vw%+xGiJ!3lJVfDqAceDJ7Oozt!9 zE}3rg)nn>`C?xb8o~iD;1R5tu8@uFn&on|N$4ky#$*}~!%JsyaKz&kF=I2 z|8r+AU8hMc2>qXw$5Dk~b@E2{z!b`t`1EIC+OUOo;)4zE?|SLW+iWkkc(8pc>a)Sr zd0~p=4LM{L4U<3{-2_LPY}=qD9zAs~oJg9?5jGHFbX6`FuE?X#>g17SpzlCS2ti6d zt3s5uYtnm*lPcot_da{7R%oxHHe!;ozL~&MveKe4zPsBfVe}NqH%l!@Zk*`Zx~?Z{ zwp7T8fM~7~PCB;Q;%%Au-hY(|i%4);KY*#OuYh}H_-4fSQR*k>ml^0KkfJV^(f8 zI1zyS+PTYc46N{DqJ$o8H9LQ|*gFA1j~8cJE|l?k>Vh zz*(BrqCYiEZ`Z<|d+J}&i2E2vGn^Nya#f#DidlNf{dQjWhpT4um4F=K07%yZzV|Ca z;VP7sGIMYG=I!U0Rw(f5syjy|6v?(S9Qy{Xy!*do$hs8H#p4?JPA6Fv&iiiAa)xJvJZzAmRNlb2RocZMHy^enuZ`7HkSgFm8olMX~ZOf78SmKfaF z&I$46IfK7i>Hw7O=Wwu+r5^Oe;Q9DOIA@$`8+aaoC;`T9&M$>Jr7enVUq(DGSv4VB z7ZDoCAe8IStW)n!sFsRHu_M2UIv&wt=OG8W#^Nvw- z*f!tkIaOWL1VO;WfJvozoK)6V4-K2_XWymPTKMsXyPNNYrDY3myE7g$V6tfh*EEWa zU^8WpHxz}rio;gDg&awG#&>}guMm^KoQzPz$YMJ&mFH10i>HH|TKb~F1}4(Dgusz? zVE09VUxFD%9P^eCr5%Yb%wH^Xjz<=}3LPUC=GA`*eteHpFlf+Q&5VzEHI0*P)bR8X zTe@=k$A%x+XEm73@F}13Ruu{fBY7>h?B~>QOU((+H5r~zp(?>~Vt4>V_Ybj(MDXv;+gU)U-Mq7)9bac_N=h_FNC9dwz6eDrImbciefCY_3Eq{@v_?bQBLCd zAIdcb(e6r(anH9CHy%B}+tCfHv@Kn@vEiDMZvx3a;GSE(>5FX)wv%4xC-p3c$1kpG zu9dRTDc~Ld4y=BQe(h4^wP_N*nuuD4J{IrU%3}JdiZzNvh9mz3`N8ehvz9p#SS``l)6DK@zj=mI$cgT(;J*4 zp|IQPHrJ~}s!`g;eZD)-dGYn;K7)c=o`K1$Rl|P?)5r9BV*OKhi3S$&zFD0KJyO@Z zrbAeEA26%d8o6(*mDAu8!y!b?jgDWdN>0u-AN<>#-(7b3!^QlEiDuJl={x;5F=FUc zY-gWGEYA{C|{&l*!l<(gUF(UIewUddSVJ>hEC9ZRg5 zNksV!(9Z~IO{Tsn5zRBHSw3I!;UM}!EPav2`Y(H8B1!q5p;!dyxJg+>F7~JplEEfI zo<4<#vs8v|r6#J&6)3XA3?;|&KgenJd{gU^sf{~FnX{tt+NoTK> z7F2mMgaf+4tfc}VQW{@2b>}MQ&ug6c7Chr3RXq<_EGoUHBBB__jwOZFs;B;@8jz-K zJJWd~)#CzB;8pXpLh>B=#1CO1qdVM&V{1#CaO1^<=eO=qHH?BwPV^nO+>8Sg$9oBkW)h+p$6K*Gj9EVX7e-ldPo`yXC0~L( zu6Ooh1%UfVI~2l%Td62+GvvR4>nY;c=w8Kj=R4H2_r-r7F$(TfY8d-%+_fq0?1&?KK% z&XBJeFRW_ly(!lfCh4?b{+RE}kz0q|BR6Oj%5MZZocNYru=y94B~gaQ)hkNgorqnJgX>zO7#zzRNWw;WpH(xx8@UTBi2;Yw zVWt2_#`~igch2p$S%LDc#o@ii?d*GTB~%md&3Z~zT{{xISdV$9YH7Ld<_$ax^rQM1 z%UN)N$A|GkPOzxQzeTQd05ht^jR}_h9IB2XsWfnPBlYoXDY4uj+LV#H&7y>J>-oB9 z#{?r`wWPEGYQB2xq=%(G;TtsEEcAR-)9JKmlv8-~O=$%oj||*?c|7=>$Ko^LSHbdQ z&grjXB(c3kDSb<)*Cx8Y>%INbSl7CPz1a^bqxZw-C_{$6S5t&(}!_N%k0_)yZd zyS0Au@xiGiY?PXde8%URZA{>8d#qb6&wIm0Fg`i@fPp* zrS5XQ9w$N1&?9%#q?!K2i#^saXA?c+ewN5@5!FmuJim^kfo@uHU_5psrWh`^ls%?T zMxCBv@*J&TO2P^xLW1+sQPJO0_JyvR1#cW5M8)=Yg>y?cCrTy5K@nk)Cta zf=Ne5T9DeMYIgS^|CHZIs1ZaDiNamVb4=onGg&-e2F$-$H2M)ERHL8LbtJ4w!?0JL z_GB~sqESMyjHAzGJum2WF?GmccqU=#rfgHI?cyp^BQr-o{v))#^YrqK76;0Vpwq+d zf{%06V}6Pqo#Glg|1E{=!Jmg!_aB2pPvkTquPHtWbz|nXh-2W;n39YXoXW)!8dGi9 za+y=u_54*4IICp17b8?9bkBo7N^aSUC-1dg?o}p&7$Y(Mk$V8c3KfYta+CB)I}hhY zWJX*@iS~S{6wh*491+Gy?*=U{2>up06(0+-cA&|KN{X|oflQ6CN)ra6PY5rTJ!F&x zD;oRJ*USbsG%P+cM1!yfS7%$;bl-axe@Xwt85QF29(&0NYeDd9@a_RRC;(x^Bc)b? z-6uz4D^FhOa+pszb?tlx3V)u+3wJy^Pk7_LGe_rTI8#UKP<|Y6hvwDl<$npq*_y;s z{OJQ2;mX=oG%y#*B z*D`PI1FO1aN3A1{&EeNN9~n+@f?0!%L)yo$M*& z3->4XqV6sAFVgdhy8}w;QX}`-k{4%=F{H|<5xoL~vaciN(FZKpUVOelpc;_b( zk-PtAm4b4YE+ecgu3Gc8&pLldrE;u|4tZk+zE&qZpy{BajGPb?{j#pvc^_-FJ4!Jg z23F{))l1Qc0ib3W6@i*zw&Ew&Qk#z7!H;Q0&>7QVh}NWPRdlUbl}FNg`HgZ*m31nD z?;n*LMb2(#iZqj(x?D7^(?z!|ZP2oC((1gJU1XA8OVxesdBgIIm`Ies`q5pLxfa%I z^OiKRzn$Wb{hAkct6Xl?uf8~b0MGE`-}tbY+D%YU>Gs>zs#KNF&q7}8bA7r~d4^*j z(@I7U$SX|Zk`n^c9#4nedgkTm0Y|-sd8#W%#0th5wCCxsOlLDV1EU2^!jm;<61H67 zNayr;(=1ENIM(Rr^8o_AwvJU}8C6mvk5#yPvoe~bYCMln(Z}y*@-9UEixCysE!zG2 zw7V_zKkfN3+1|((1?sI&i{Du5aSfL5gs<|d+}_(QsC3S2W-eYUUEh0WLH?c~V4-^x0I$a zlC7;bjN?&^@KB%C2qnM{2EmQOI2sJRS;AhYVSZ|}J3ymHd=*`?y#KyXO6J?YCBZe_ zb=UDedOy+Kl=C&V{bB5#zTodZLyOQsGN3fEF<71)y}xH_g|;WoAcuE6Z*_VWZ@b`3pNB$5d@Iw^O6dGkS(9f6 z)f5E`F=57$O!Su#Xr!>KMdUYMef?dUGx7QGDV35Hm(s@8@`(LwMC34)F& zIQ5c=HDIcB)VaA!;C6(=*d|FxU$m*2o^l)%`_V^^&g+4LiptCN{et^5`09X)ZO$6MfMen`VGRROIr|exSjM_GT=;oq-ak9Gef|IY0TUc^qxw>CUzkZoR!Ug3DF69#D@PE9 zxxj6~NH4j=*)Xa~MXCd*&;z&ERYq>{4KXlKQ6AU2dWeIAQz3v&2=YB0a9IpY(pT|F zbm_0)Kj$^hxQ;G$oaBE$69?S&Y9QN`lW`g_A7`aJQ98`~zd!P=-8s$l7ai3~c+V`~ zCwvO=VC;gd74I&0U|!Cu zV`~?iD(z>eM_VP&^5E|sVnxTD3Ux+G_}uju*-w9Ah^gZf4+Y}nZ_u91dOC%$ z0(q**3sPd$aiN1&GR6%FN7w)6zyDgZj*B36k< z^CApUkY)l$6J`^S4wkCFE|6FrYTn@Pl%%4M5IMa===q?#t7z8wkKvQCA1afRmD@bM z^Fja8iWOaNWkX`Px$88X>!NDWf7KH4Ve=~P+eEV8LBXv0@J8xLY#rt$tV+9lB)({y zhMCAJGd~U&mdw&S*>&L>L(|@~FLksJN-V#OY&izWb9~&fra!FRoWu_KIA4wQ`#zMFI-ZI(S z)o8erxI`uW(ht{oeGB#x_xW67)R53`d^+4mvScq8%XP=@=za?!g|3h{N$|edl|(mI z%ov>`@jrB)j@`;%)-RPC;o^34vIw^iLNj*S>Hsq5N4(Rv=#Z4kSp3!WX>#eOn7#w; z&h;mR7vx2rUh6@;!qLw`T%xM^QOL8y*XYHev}t(;nG;ST$KPJD=nv$gdzi&Ld|tDD zt0tdqa*kOY^&#auPQ>r@vG`%-G1$d{h`j_}o<7Wa%}qj&;`;+c@|8*;VB zx#`O84d3;!PwvyjQe*-&vsL$Ncdl1H7nYUl3mwoUKEBm9I;;P}m+zu*)qxtJDNpl$Z91{LV`XNkdmw}3F=2W(@L zBSk7C>0RGV1+S;t)9uweE)SLJrNEYr+~D{C4N*%+bz{yJx1NY%o zp^-18$w2uCh16BcguxLJgZhrm%uPTRXHmr zHgXY-$piR%Rc^0{gx8Ypt-P`gelAPqX@f~$;{bvGu-$hd9sxNW&d$!!4r>cv$I@>I z^ThFRmA(W!7BKGuVXj=vT=tbYu2lzV~m>WQ|5P6XAOUA zm@U-5yj|1&CDFZI79P-Ms1f>FTj}4J1#_SA`2o z!qBE*Dp5j*_7js>rRrOs3h|#;3~5xQD58CEQ-VgX?e1ZWWgH2qY$mQBdv9o_&dxr& z-s9rk*%+htgUhEnItlQyA0@@9<0$3dC1UHne0xc4-&*APh*a9$%@ym^$i?0nI53{-95*q+SXC|Q&~waAFM&xJXY<%Zq05>4kmhlE z!M^K^y7=i(*9GNR;>F}KOr?XeTQ8&2ci1%*L($KFx{1HS zuC=-=ZNo|*Ls>2U`pd`hQukKBvnY89{EUDig`yI9X7S#Ln5yCYq9kK1a^&^0tI`JtJNF^_#-iJ%5dqW;hFze;G`k!0g=Iz9T`&cvGPxT=cS@ z9bK=WK5@t0V6JR#?bak2`os`voxuF@f;ZS-8BP|?lp4N1r4(FdxfYQrvL4qjBP=&t zwCJZYSCOyK>#TzJJ-$%t%~g&6*2w3U+NZqr+l=hDZii}ZhH5{;=L*eYoxF^S=7+D9 z5@&OR!#ZVgVacztnXPD6q5HU_>$WsZzj{71I0xQJw|&1KHugFHV#20{h|JwxZIbuA z;T`yfi|afnN=v8az_}C2w|_8xtF(_h9ok;58&B>R8`<&myk8Nh9Uw-E(rm=qnizK( z4>U;Zi~U`3axTq7+A)W*h3q0KT2ICs=RHg1C*>Db>8snT84BWyE@o?Aj1*OqQ<8ri zcG=xxl~FdEt4=gN8nQDP3@nc(;AjqQ3SD~p^3MtJz*6(sc^$tJrZx{$lj5-SMAKKxWtF{cQPrV#o zqfVkZV^X%3>#_;eA=6<+eMye|NtDg)P0`ak678D~*H7@G16UQDyXlYCg@>MP{$F ze43sc25G9KR8&WBO$RhWPwY32{y2xo5KvQhFP0jjzgQthZ^YxlpFei?9*KT>>K2}* z5s{CNrHk?xKtf3B^%rLOt>BBVw+v*r|1?LJh$spNZTGf|2_#(*|C(VePDi%EZTgjn zS}`;6;X`hY|9#v<&FAm3+Sl6zBLoHo7wkxLW*vo5`ti(u-giDJT(_{nU39zHyHAlO zD!cixz+GiA>rrt^cD{3WPeI(iUo$hUYGhebEZ=LtMi9b3bM~wS|H~`0i1;9bTqL3% z2138d!j2MfD-2``L0kF|Y}ijuPH+P0#l#Fssv1gu(4)6V4V>;~4fwfSdYtxru$2E! zv68FYz|!3v#h|DVRJ0Hh5v;C}H~HcgTjdvGgs!I^u6dpiv+OD#OF!ceWDO;V6LH8- zeiA4)Vz)W+?uiCzM}Q&);j-)zQKtRt+*}!_6SuRa3e1FkMAUt654QH#hB43Tf2dA4 zICVUnHk%4S(m-y5!e0+k22LxsD|i&MJAfwEojNlE;)5RAJ(zgHTe8dRHB0Vxm$j;T_s-ePtr#@Y;F=U% z>8pclVpCHlzRtsVp4_OMXTx2$Skkc7!=hp-FgEj(BXf3A7tiibkQAs?mP{7f2-yXYK%!?BjJIJct{TZD)IKDyZ zu#h4)*-I?q`yhmt2ZgcuL>k$r=+cuDH~Ize9JrcrD0Gf#q;_ z9E%$0Xnp_w9qcCfz)=GP%;42bL3j>~PJe)0>|r$sVHx`!BO;+7dydGi2L%PCr6E_` z5U(GQ-G&>VAkfIc%d7t3Q2|X52Kqf+sWT3PX@0+g zC~Mq<-1o&859}X2;1_3;H>HzXz(L1aQUwxg{feBVosMlyi_ccEmaS<01~5h$h*pmD^c2HAHISGGi^eXHSc22v$Mc<}MMBer z$?x0}6yc)l8xYh~0VQU*JZJ?{TLlHSAR1iv@gw-FI3FLl3Z2au7o|h*o?@{*mV-AW zLpBOr1)4)=U9LX6<$;a5nT!vQ{#M}7$kgjvHAjeuumtroJ)5SYrsUQ&oIBS_qZgC8 zPLhRqS8m-iXlLxN(rn=ie4X~3S*t6POk@^w^ljgOGy$#Vo8L5k5-EY#eye26rQxU) z40V|E)6&x3y*mQ(e1f1049C_%{P?s6gHV8?8-)Bvi^|49+B5X&Q)yUewN#N9T`D`` zXjn`|U5)h4-AC-|fs=!W*Tp3jSR}u)TzZc}E#GX;GkK@%`;M1bbv9L1`IkI>kBWct zpi?Zi`ppRu!KRCz#bYx(HfOWB<69C;2QkO)zjVsiym3>h{>!CDXH2q{)8)Dp&lqYw za`?Jj6}ug?1fuvL#pdMV;^OLh3<-%CCr~!~>++|QdY4hx-(EhTSsp^j0-ELbiVdp4 z!=wj%$=vnn=BiQA1jDh5D++$`k?&s*uUd=O<}*+~zlZYQp@U3o`1+Ini>|t)@cT}} z1bMf@f_%c&W4A8)l;t;&=pqIB=#D*7lbT~&!?P$|uF4Cl-{uPT{`2_C=UpoY6}2Nu zNge#9%Cb{X-}$lEt9YP)hF(b3VcTz&^TA;zlq z6cGy`H4auW(@8~FwhU167dm^LN50mWX%}80CWy&r6ReX-Lc*)&3WOK`sd&+!6GiX8 zFI8l7Wojpr!SH-wu!3EDuHG&5iUgupWCADpoIPHs4Q(!MW?sQj+If@5N2hD?OBwgW zXb;+&_qFy}V@Uo6iAOpI!x$MwT#8d|Ty3ySUH*u8&6h(Isy`4?=fBGk|BUsL!nvXRtf7`t zWE6q*8T7ViTC8T*q|TDovg$aa_b@(E=ymJ1^@+Y$XD!CxUwd!;tEX)7G1sQL!wjv^XoA2p;)XLe=R+Z!~OS z)h|Ych!{|P6w)0q$o}z$Me?Ne93bf4MN+roWgT{&)5l$NtSbiZwi~xIxLiJCnuer> zwO%h5ab&Bi(47JK&~i#1gAWhO{K|e@Bw~%`!F4MG>zu*@5Sd;}0{zeVC>Br`2T!7V z@4G^==VZ})Pvgs?Q0{A$d<9Ayt&Eku+)rvt3IflE&-jNk&uFz>QudZBpLgg~rXirs z!^2*rxSzouz}jXO)kTcs$=&f@iIcE%y{(BPXqjVq+5KeloPXDS@UKCHBK0cYLRtrP ze**&pP`cEGlRa3cZ=u$K#}X8|dpxtt%lE(@2(%4{j(MipK_Ysp$~N%tCsa*8d?GO# zV@T7X^#Z3V_r0R#7B0&F5)(WU6%pQExXrYsx4&YT#$y`xeX2xRU9;@_{+wPR*Pf^E zm=ZBFv27U;u`_U7U6`Tcx7K_5|x3=l3c$%RZRg zHbcx4WEheHFfY3Ons|9kLrzXkOu(6s^+vp260gV;Nbpru%NW?c z=rYYGzTksGk*hT4p-d`A~i?u{h;=t_<5x270k^lcGT#{ z&Dk%D?QwY^nr~B?Ec~(pAOo1sf`<67?>F>sv~wW2I%KEUnK;KoIjVQykF<*wzY2}~ z*;Vy4p~2^Z^sShvi;Oc`s8UtY{y_EMdD@p8L|X>huUX4vs2FvqbYyU&a%g1S|I`wr z?DRc6_CX>Y^cMup+pbKS_rQ-E8X7`Ou79u18(H-%P`Qb0jhGY9UraS~DwC0Ox~ZX6 zuZP9+<>XdG!Ynr(P^gOx$gkb<>gP~kW4R9D)=|!W)p9EEm9$h1zvwrzZ6i!n3QJOF z&}B-U*UB%!ZGw?672LW$0Aj1HJp@&W3cVBxM@l49%N#6L*MD_PpL>~5E|hJ#xBTh3 zK%qv^wed6lxq#46x^%l27^2Ta@M|e?&sFDlX+alu^j@r7Kc_f5a(Hu(6E(^kcx!rg z_Wpwh!X}?llkp;S8^=FRPwp1#^5Nk{fx$85m&G%vX2nx6cYYO;7*>{f^ZIk96`ZJ2 z4`_%{w%H76yiUcHRH>b?tJ$~Xb(s@C#bN!#>lYYMch6Ek>A^(l=Z>s?iJ(l9^g98) z4d4BZCsoXm-Pb@W7=&T3-?(xA$N=U4L7ROD8X>SVcnJP{lkt{2Ie>%4HER2{Ypx6a zP&*7He1(D1nRAui-SL=dAg*GB{~YEa1kvdBtT8$6*97r|KrUPcmQeEBBg2uO&!X-_M&QxNdRFixEKCXH zVOPOR1NJI-MpQtb0G$AsDiL}?GU@aM^A6_v*Y;9KSmV>sNcf!`T_9whfF4#jSLlKQ zJ!@lLVh)xl+n?~BwZ)G$C+l*yd{HWB|b;r*JOXbwQG8Vgp3gR9Jd%0r0v?c;dg ziu9hXDqhqmdy&p#aGQcmK1MEb{dzUnJ=E4d_V6gpxD{^e=m<_a)1XqkK3>HmCYEYE z@E(m3+ucV8G-l3jLYUhL4mCzEx+m? zXI8Cyph)rYhVH-}>4D(EqlinW_i`nR3Js7J!BI^ZZoC4xOk~q)g(d_tHj`2!pk&0c z1@UWiob-ln>eba0@jy{@Mya?Vk@QnmB_{;7HcbZuy@uf1_i=7GXBS#k9%G<5Q-jqo zJ}X+u6Us=L5$Jz6xmbt<3C%nObf|@u%>*GCGQM|U6}Eucoc z17GMrP)I<98iE7lJX3`oCqa}2>hr6ChPlJ1EjY2r6!UW_ED9{|=$(&;ZntZf@lfplBBLL#e~PO? zBO-f8>Gw`}eF?_rl_i&&;NbJs20c7^mvc4AiHLG^^jD+D(Iu*%zE}K~-1Gjv>jK!O z+^A6$^2IF%;*3;m$lD8d+6*%P&pOvNJ3Z>6t8s30C3X==tFMIj@j2MBhISJO7^p|o zj*54{AH$-m9_(j)$Nm;%dAO|bQ}(vzoW9q1)WPp8qtiY~XemA?hrq&erX*I-5t-%w z|1VO&(`rm#PZ#x;JeM|y<#rbh7D_i8)UNLo=yZ2?+XLu>{RVvm+qyitq+~sG>kgA2 ztAT)k&@=kz!M9%exBhDK^+x2h{jBg2xy+-$g#9J;3kvm_1o@zxDWTc~v1BdTI(HFR z{V%4CPYB9xapEgAG6z~?Sy?e?u=+hc>+gC256>7(8&ibr!NU`&xe(gG1Jpm>Q{_%# zaesCWd<4~5!NY1FIvSu45F2qYnt(k|DQGhY_~ehW&UtioffMX%%hrN#brRl|XB1cq zI%1+qose8}@int6FQ#86kB-kj-t6xu)n_f6zVcn)Xga=;T^T6tXftFs8&K^(Q$thmTgZgV_Kfy_GO%_oxulMyKB_(xZSbG3c z<58gPjgQ|@azAY}TN*NvG1t6j@#KbJ{@#u+K9`MhgyUB(>g8wLC=?~&byTSdJ`o+$ z8x0|w2s9nRI)d;j*O+jLf;jQMdf8ZW#7O$3ob?|9Whq=dyn4t!Abzd{wk+U-2;Su& zk(~!g&>md=!1EGxolC)21W?Vv;UV_9bHOb$zy=}BGq8D7ye2n+A_5y`Jt!;iW{|{) zId!9tKUohj3*{;1&g_|1{@t!(y>+T1*aK4}gJ$$92GX_xtikRm)aW@Rf^$P(TkZa7 zVkN8WN0^|0yX++acG&#g`RTZ(-_*ZdqU#6v61n{oLO~7-B(b4P2my@+dR<`jSz^)< z0J`5!j~;FA>=c4&3z*SigM;PhD+oid{M*^ua)RN`!-uSzIr6}ljCDb0`vZ>3Lrt;Z zC$Bf;K+|;e^Pa!F^wyPo=m~t(eq_8J&>(67;@2(!*~0Y8@}#QMnz4F^|6gJmQ^k~L z)C@U_G?>lJd}NmtSpNgr!?WSJ8#~Jb@Y~9eKY@$_Lqk_rS1vHh0hbT3U()@26>7=a z15mS9Oypdio6`oVFsPF%;1CDS)OU*w;Oi_1n-l)Gden;27d7bcLvS=3uy?K|+u2ZF zM4`X7JVpO#>%V6r?J-6M0r6Z3(CGSbMeMWP8rM@Acw{DkN|{+)tOCRVhP7`16F{M} z2f;7M>iXoR#=1&CE`YO>BqRv%quyE_r9xL<iFVGG0m|-I?K~MnJca3{pxx<8vx8 z>%Ey*r(jTds!#@2n&laqZ{mLx|K)sQcEs+g*zkqm^-Ixiy}U{I zx_=O}!ha6~HOh@_rIx-J?f`nbWdWAl~#Vu+kBs{X(p6O9l&Z$@CYks z1At8qj2*D>+y6B|u?WjWDW<}0XK9Rc>XgDi|ak~ zWa_O-qEG+BnVESL+Id;PZYt^JpIHMb^+E6fP(^<=^f+FBwemP<>h5%mB$ZKX1<7rw^(JX3Rd?17`4=s@rgSMB1)7<=v^4_EKaPD zTeiB#&cRq+NY%c{;4}9fg?j0a?AbG=QOszbN|rCb8=5^L_A-K?P>Vf_nD6wiPhBfA z90^gMYbHK=I)C=ZfV7HSD}ti!VM`D09HbC002Dzl@NSXL_V65df5oz=iS8zOusWA)B$HvKHukrn6-x>ivwlleRftJVOsgT+$CijVf~z)904u zBboA_-KbW}QqU})ah5-WVoZXky_#*UKq-Z9Mlin8Pz@+DOFe{S`yPEgSCkFqZNq&_ z3{+t!_@IL2#|X?_{QZ$0E=Jw5*%9&Qga4y^uGOBW*-b;(ajNr{V#3zGtR zWprH zywH~lZM5XidfAcqoH=I{%KQxMYX5MO+Zz0_Wq7P@&expN^)tN#NBLK7jrsDKDeSjB zv{&Myro)+`#733k*i?D}DuOnBX{01WHE*_vnfkg@4pdnfBt_9mE~qHD!9W8_oR^13 zJhx#DtSQ*U9YQGURai|gEiJ9BO+b;JvwVXSh&X>cI5@14to{56oq3DHm^>I+yRA=l z|L?Q^0x*|WLz}vM>9@OZ6PQCnkRDP(J$pP7?K5&=VrV|09GO^F4Pc& z-AD`}_G72_3k|<6GZNbS>|8WC8&T+VQ_u}j(S!Z{4Q6N6bTOEJ!2rznaM!*_r&B*} z3hFT-i>k}RhbAM2WoDSQ2LQf+yz+sX4E{QIpce&qv&qTHLcWl8eukvZf;$D4j^G#P za|jZnFp05r6$1-5Pr!@y0Sai;YqmXcqv}^FHIrZHAA+VEUcw>F)ks>3%;c+DBI)tP zLcL5xLS^=Ro>W}i#B(&q29p7eV&J;jwY2?ZW>_waQDnLI4=`t`e@Z~1I$7e{pI@eg z-<1S+xW7yWH8r)km>9GmaXV89_o^HW!3GFUIE?v_M+|-DjwHX<+R~B>0S?lW!&U+x zn;7eiPB*5d)zo@naE1&Dz6Tp{KZt4zmZ1*`51$+1yMQK>qZcDHcu&TP9+WKqR;Tca z;a1JIHhg32z9R9|QjGbe5{oMFBI+g5C0v!p)O^()ghcs&y%N7d2(j6pJJn9nn!-2b z9`7@sL2()brIoLd4F>55rM0o~a57n>&Zr&`8+7}%)z#43hgUH_k?NqwRj7_lo!xv>~~h8Bu}P_*x*0|N)r${i|UL0 zso|&M6>>6J2io=Gm6EsfbR8KFu~E_0NEP4@j&xZg40*=rJNF>o_nQ&I>i_M!En@$k z(RfuSm5fV4ahq?^MzvMyF)BI+4AFF8umSyChR7p&PEL5xnZ8VEFl&7H@L@hQo0>ft z%zeu)(DQ-MjCgG} zX1*OpZSf58HAc^+U5LG%F;FB90FXdvv&3?PpPoK_8uG+zr0|{=xX=JXr51U3RbcR_j|)g-)2fAqg<<$`DZ=-A zc;f$dKF`G58=he{IbJTgN&HM~kCl38+OHY|bqNT66ggdTmNc8dweX6okgMOdWE;RF zLz|g>Ax!4c=tHv#OPTh48X=T<4)}D#)`NO6J~{abkRM7P`v%1L0NN^w}7kT(fmveYEPV^*OHv1*`E8Tetz5m9r2c*O4wKW46k-{|F z&(!Zpx98FRBdC|1;QI=FIpp_G9-9H*8{v9o4U8=TOB>g?urV?|>rECw?_02`13)_J zc1yoX-vQ3K+^}Jx|9YpU1JEPCIDnO#vca#;leb4NQa~e)Y*oSpkp))6F~WOGAJy$G zxQ?Ub+l47mCS}i*cL5ARRw;x=4Gg~!gP(G91ya%^p!HgL86XH)kBNzk0}G`OC=DAMTTV`H7sl3dP-X$U*TR4T8l4Mwl|?J{#KDHw z-F=T)B^h>28oVQT3W1Yk>6q`qGK;aX@nrG`DB$15#(-e*@boNWGM9v2xA|9=Y18wy zJut5-n_nM$w+L@Mnms$h7g7`od4gNFbPA?5)%QOachWdIMQvmHcPWq;8;JQm%DfQx zcJgga!ut~yzo<+;+GU3SeN`oq%gOOMFQ?G}6b@dXyU&C%MNUE`pWINw(50=fJ7+aC zqe9Q3!mbb#{|28e#DHDuDHiNAALzot2k9P|(?A5njDww*H@Y`TnLXhxH1xP|#4|43<=+RE-N|M1JCHwxP41pThwkv>Q}-eYC2s(ck@Y8xT{)k3Y53KlO9oJD zpX7SV(;U&3(+_^AOX+_{w z&e`3Iwonj=BIk~A)`Z~Xf<06_aI^y>G}vXpzk-L>4ZwG>0x!Frp#wvlY@wt;Mz(>x z4V5t>G7>7zTAp6fuuUa&hVWm*3JMCIK5YWX3KNEU%bC%$g)kb1m>uJ4J0+%|NN#R= zjBz#YknH3Ugl0BN_$QB5ddD*;e-ZSH$jjB74?X`1mHlC00X-l6TPm+53M}N!L?ees zB7)Pm?a!mk^ih~^<1Rkt979NeAP%pSZc|%QyoO61x%H!wfH%SpBn{6t* zw7hKn;K2x#Nys;lqnCg4ElS_;-si2qgo+lhlUpXEwxyV?m^|{5AoQl0Yy>$@)CHIt zqjIw4L*wHnGDan|m_^YOmjANdYpyb7s&aanyZ7YAg9+sIP*({DaHf1aJbhQguy@PKl8Z!1s@Wk8Y(OLV?@rM4=Qmo=9+J-7d<%6Su)Uw)kNE zM&|lceLN3Z6sj49_$YZf98L4Lrq1{O&w>mj>e3~iGDVRQX0E=?mfW{IhvJWx%?8Ef zc1W+kChIzVU!SWDgo6%pw{LHz2+0-c0M4ui=!vioj2+$AaOM`m_oS2b3($L;^=xkMx1}kZ^e)Q$o$ivKVE7}5m1b;N+A%<1t#bs zfl3O=W9WwGf8fn_qBgw`!(~w_qVEF9uL*n_tG}Z7U&zo~_q}?Oot<4*S0{Z-H_6{P zlI1;|FX?G%VQSF8CCK?|W!al<2(=Vk0E=KEP}TYl3|=7&0ZBuZU@B5lR-wbC_LMD`ihn8=J6m%fGKq+N=spsXRNdeFRaE<& z90N5aiHlFoUK+CI|M? zXQOYm!6Xq`8q!v6Of}8lnwpv(^k#_rHtxg5z2JNXb<+U(7!{-{Uo(jg0zaAept%V_ z{eR4h_G|8!GH?!5Qkf0p@l%(Bo2l(aI7EM=NT>O`2 zw*#sT9tn7OcW{_`ij4=k$frL?!N|y{5IGbCEG4w2;%;lY=H{BGNwNh)z?+rAK&kEo?-{SbqD{K~PM= z?|lZEMIbuAVgV`i|JZu-crM%Rdt8HxG!QDJ%yY^-D`ciZ6v;dlsZ1e5MIy7znTJSZ z2$>~{kf}tXNTf){GJn^t=Q*Eqey`v8>zwC2^}g@xzOKF3UTf`rVcz&BAUMRaYFt1` z?7au#UGLxPE z!aOjony~_GKcAPmRmmJV^6Q1)E(CtEZQDNQD!>Dj2u>Btc7TDQr>=g2suJ`FY7^o> zXlJ$nK+DU^yDAYo*PHC3mRDw*=kTcJPkEcHBiHl1CqxU95Ku_e2|^;B?ZB8EmyTSx z&;gs{W4Y#&Hg@}S8#2q`+sLAh6awHP9A1@oUQ$-c$80w~mw7TN5n3h6BfvYkhh0%h=ELrdJ&ug({whhVFJQK=nOtiOJ#1 zfK$(uRuxa2n7~!Uv)?+f6)+a$+{Zi!J35cgb~H3JG&f%YSbP5bxvgcSYQyCjtR(2s zE6&c&4i08|l@6mjYl7Fyz~ge~m%=Xur-w;rKa}pZPu?M?cmBU#a)(W)NjfQ08_jD0 zZNuR*P91VJ2G*$R`*%Wigj}XPuxE^WL2(O-z3d>c-W}A5;I~^#qSd^ zzpFU2wzZyg%a)%#1ux#cD<&BJ=4ku(c?T+pt002ugdf4U_c(#iDors6(8faKAuT~$ zZuULZDDNf~Jwp3%=p3ioe(s`>`Kf9#d{&Ye*hol}1?f6{w5&-;)8}m3hepce&gnn8 z2g*>@=4cYzbl11MU9m8!rMKNWcXFg}_WQatt``QF1V zms{Vxd)LuXpd7{w)E$EY&Y&?Xi&LgloIv}>_l~9RTA0nKRfQ zfzUj;;h@J=d>@h{g!3a*L@51qXdPVL#KYH5pHJasdUqo6o?M0;sdBvlVeGa&9rH#l zx;>hD!=X(O(E;E0a-K>?+&+H%II_Ebt~0hiT#(q*YM1rnsNFmicjgnxJ#sb`b-&kLTV0)Qr?kJQ7WDeda zG83~9A~BDF(18-XtG5@W*d>q-NwQue2iDjaV*7CME>nvklDf4u=VTELwo0usr>|}@ zd4+X!fKDYBfqec6R3bZUZgFxRAWUUQ?!KyPI(tFZM_z2$tZd$9@%nAE4iM17U+yF}Mh_Hmg0}y%o}q)2T6~Z(|gnN;Vw3qn+~(1~gm^q(sO` zZ?lPSK`_K9XMl7Pg)c?b)W{~aDPnOOTRhV~z3dReJWp52bhb-VKH@I(pAk609zaUv zj-=c&xMh5AcdAylqr`!vruAQa8r(HSr<2Bfrt(B-Pn+FSJ|DTa={qw{%?qwtQ;-q5 zy>T3}zre$_mv>{!IwhLm(EAr&lSf|hXQPt!A5Y;mJ*ME;_AN%<(QZO&fyCGY$J1Qj z!1~@^SDIA0x$Nq@3J=GGCY5(WI3vjfL3YSt(LOLnoW~>lzg78D{!vVwJEUl`81mBN z6!;ftcan78l}qVC^aA`ds&Z?H|6H^FSIc&_9mskSGMmQX`XOS4Z!zu|?Y}$3`|a-I zlmg)k5jCfSV`VaCbzf?nXw`LN|8MI{3RNzNd^-IhvUB@Wd2-W)6*k;R+e~6Jh_H#Q z4XHF%%5@s%nE$>9V4_}u zr~!)#z=V^Sr(gUXul*)bdI^F1^XJdN4nd0GU+xpnAUB@o$#Zdz&qFe4WG3?o#H@ev z$ZKmAdPNhe@Uzzw<4>#Pts8CsIs!Nap+?E5ZG1wi_&y->jlysL)IVFuNwlH?Nw;l# z<~SA}5^@qLabjX3;lYFRhK9Y9&||ZK?2!+U;pr&DTu+|5E4BAfkx9}F_Gr1zZ>fY) zjde=&ZxVa0aQeOvtKyV}MD&=Hs9D7SeA*FcpPr$24wJo`ZEru4daU~9M(?M|TG@z4 zvmh@~B|-~!0}O(h8~!5&aQsNEut*YQKK>>3m?I_t{x@&N{@CGmohc?sg6rL zOqIQ0NlwyvU-KbR5<^|UeLpp*{oG)*0q??t2nHz!PZTF)BLI6u!@a#v&J~RybBrgv zeqvdHuhJvMXJgdaETQvI(kbbQ@jAiTQn)N(s`}Yi$)}d=?}L zu!9dCJQyDz?>X5mfKmj~VwMiKOldCsj>a=RjO}jvvbPk+Qw{sG-ANzS%6uQgd z_)luPfo`2%rC1X3{0CC+1^#!}5Dx&BK{_H^KWA2Y){)op)IO3%P80>8m$|uBvvppZ z7uKvU=78luL1?k#K|%u0nMaOaUhW8bnK_V!AF&;9cax3T@+70UZES(|gFqPjbnsh( z$N#%&r(s<HAR9myLEtedsnzMr_@Zu8_8H4}B6%=ejCtxf-lAx$t-P=(jG@|@26KfZ-LGLSq} zdD%?SaNEH>dFU^=%-kotLUn9$0j+Of*-;og18w(Ad^}dr%JR*F1#DopqkU(%BjNLq zhR-LO-{`46pM5bIu_)n*vpm)(q#wNx(05AJ?B(nemw2dhdve2n(tM~on%@+T(_S;r zEB-%jotnFsErK(c>%J`a+?hF_Q>2IHfJL9bc#(Exunrach{hH|nIDO_$H{$AFZKQo z{=$3}ZY`Ll_Sg)y%{oXw((`>(nW|UGk3#uh49Vcu>8F+D!`kQ&0foQyU$4Hes~$HTi5jntqEN(9@0!q}jvBSZ(}#Baw&v3G)N%)}_z4j{N3gjx6KDM2P_3+`_>laHWTjGpv}p*dyP+Yjo_g1mjGqTjzzf~6Q z3CUe~0=f&q)=bn-``9A0($~fAP29)oHm}h#yyFO1q+Dq&wIuoV4nj4ESUouH;r6HD z(qgSS4&4KaDykz;q9MLISv3)UGJP|~R)?-R>mag21|mQD|*9Sgz=KQc1DDqO2R zzRCMZ^4jn7Rv^Hq=I4JRB--DGDvAsA`kI=up*W43B7gWecOe!Yg7RBvFM?S*zq6BHj6B<@@?$==i^= zFLW<#bPg-u3G;Q4_$KfBKy>KF#0htw83{^C`gE6)g%BHo>F`K3UTcZMaWHJif_z)x z`#`vKyLo=rKI7JEeYkKUOIiNn^?RN6oCg2GAd(jU%x_1?_eAV_G2-b&P$>eBV?x4f zn{R&Cy?9ZB^{ashi89klP0wWALOV)tjt4`5F03~Pqio6Dk=r*srtbSR#b#9UC5@$@ zrhMqc1%RTY*@sdGYChloH^O;~t7@q#n^K=j4aeC!ofXJ?wWY0{EhX+JUEF?$%!?$- zhR_7yv~WZ`TllI@fzKx#kbHNoV@=|epN)_mTkg1uw3_zV%eQ|d3`ZT(_ad_bnvFYU4f@=7CmE3*u9h=B+fpk=4CH9E#a?vd3`wxH=3$`=h^XLe|la{ z_sRB$OC2I4q33`S@)eI$KaHVv4<9X^op6~o6 zuSOpxdD014@3!CQ-4bBurC(y(B(nX6Ht80k6jT7*I!>t-Zrbzl{$9c?@`dLZGd8Zo zZt8xixH~T?*fxVS+-`TzK&pSH8gh5DrXlo1k^mH9K@Xe_Ud_;U=*t8%AiyyF@ecvF$;dKJfjE&yHP{bDSB5S*^YBBlU1uhS^9f0@Q zc^&-iU9vaQwvwn&($bb7MUrl(ZGk0WC9v3WtP=oc?q`1=*c+65ore zmP9R!(wj!?A{U_j=ULY>SP}ws>Xf%&5QB=2cdhpNTpC?x<>0K|E|C*bt!s`)NhN9Gg zw{o;Csjt>+nsn<{_^Ak4KsS1#kPZJmPcdyUnkg2o7+~rnRcA)O8S^ZlUwGW2?ZVnP zhr`Y-!k#uunza?`Ql$pxSUQl_qCr$Mgz$m+xBr zWkPz20`tc`_$T@m;^nyRxA{ql8p4_1+0|8qnjfDG{Odg0g^3oiC91t>Zlb1Ujc7{O zvN1L`=3YI}aj}>?lG|5&9Ax)H_1L=ATDGJ6EL`?dQl^~Z^jTxJ*cHULX;MwewBR~k z5#Xk@YO*z*ets6{_ZzA<@br~jlwc2E1s}N7nNH?DRg^^N;$4}o`0=+Fg_BrN^-d9{ zkfHVnnOn@uO$SXbf2aMAU4fc=4yDl_HR?5Og`L6aFH!f3>?Wz+*+<3?LoS5wpPy=y zJ`X6Lw-vPn%p(d9o$SuN^GcmW$3wok-?w%%x5|)t;q*I2*1CsC$tP?%IGuNI!6tM( zf|e?{hMd2(n}CpBS)A)bO^Kaz-H4f)g#~JyIPxhj3MSxeoevp$tGAJ>`f7hHl)V7s zx0L(*W7$3$&71oLE#Xs~>?vUJcg@q`w(t^wnqIGa3)Z}rSixQag%cS+3bsJewcP+v z1h2`S+^AhlJDM`IvT?I(O9?%GWl)2-(fHZ5ujKAKimYzH^-C0b`cJ>1yrT-74jX;R zfe3z=}&Dy^nFgl8tX8G?T31TySDwo>HR7!Us*?U$qHhn^iocZ!*vB001%}9U%zD( z{ql4(|6>aixwA_^1-%q?E#pG~J@RsLTGu~cyaBXuyQ*phD%#5OGQdwA?K_1nbciMv z&9w9Bj^E$<^9_SoguZsf>}4SA6yWc}_^zm~-u{IJ0&D-op!8?*@!KCt>?E%a)z_@8 z#)C63xC4O%h2?Qx+IT}lDt~kM;ISy^7yAt*qnAY=c1xIBq@7pD zSMmTWKVLYi@#_ql4k6Ov>=&3fQ4QSRjhPtm!e8K{aF4=4PJ&@&xJ-pu*CXv{gZO@o zT!@_cbhg(28GEvxa(nqNr%Ksc##HAe((dtnWlO%{P}!|pw{G0H0q=D$NNza5K!p&a z0scDK=q0Jq0^rRy!`har^ORCJPP5BZo7tAV%>zA`Pi?yJI34h?(g|Ng$IgAi-@(rx9r9j@4fY1j@hDU>zTgMuT zh0)QU&+*&e(Z_^3+Ebj;R>N~)+5%3O@yQY3w$;TSPhetQTv+f}{xb#t9^pcGn-vxv z{hq&OnFNrWZj=yL$TV9rg3Kk7Um;2Ibh7>_vCS;`30EI!uW>5u7zp0p2bJ?hU* zsm#)SpZ<3psUOK|dB||#(={hSVJGGfC-0}TY~S!%7Qwxb%c5chdijXPNPg86){PkN zFCdhG^~}?NQuaE_>GNn0!TUbO2pQd z5`pjcq*ap4o-5!=pgxO>ix-UE63y5!|NA!p|9D$LNJtwJ%ypjh9vpTs?{FYg@f(FZ zwure$g^jY`1FG@1d#ysRIcW54d)-GNB0KW1zgmfgM>z5hTconA>TMU$B7v!N3RKl+ zHhZU=EoFebj>#M=N{eFABT?z$m>iT*?lN|G zQq8AzxUAr*{sbf2*z`1LUcYI_4Po$Br}?kt97_FbQ9?r z8GjBAc2s+~7g;$~c&&Nf+(N!fqRAtgZJ(eTImmljY3B=;r*( zM+}QaW1Q6%p5J65;bPeGT*C6riwz`XF)(@c3FpEC10uRru^j$1!b1fC6|`1py}aJz zZGht2XTvY7D$52a&q{kF-M%)su9q<#0*5JJFaI0b3K-t}gR*|%?s4Rnd{HXGr2K zqN~?TtEg>uxVtfLMK%hNJ?JHL0ws z>f-DsI)!nyy(mH{xQ!`xwYn%(_J{%wU!xLku$7n4K?U5Pb!X4<#CXDz(D-pSJtUQr zlxrhrE$1zT3{zss#y4s3rX8l{wgY6}NwYPPTxXHf>44KyeoGQMiuCQFytaDve;HZW zW)M+!Pz*l|44K5?nS?77nHW5i5C*EGGnASdf^s;Uyz*3b>(_nCn@T&o;~ljX1qQ;z z`kEbNZ~Unhc`FwvX5D^h;Nlwy`dF9uuo`%ZpJ8Kbi){W1-&Gqzh=J{VAb<)-!Ig-W zIg^>;mRPvl<13pON;J`|)tcAvvkvgM_|MXkETkJGil&trYD!8}yWaQ=@KJh;vfYxt zz@%W=6Cix`h&|v+uN2(RHd9_n;02-cxFG2rl)7FU&)b6SrxZlzG&OX>v-eT{`!@TU zm6wUth;OkTi=m_Jgu7gz)H>j0SlJjsB1a9f?67+4E0^KAKe%&8B~{ktwC<4hE;eSt z7tc1-dTrjk8F`MF128{7k0Namma&nxq#7taCHJO(JgK=%>+eOMzuFRIG{@KL=5Bd&tmFDzrEZ?*X0u@m1b3-k~i>i?c;|FiA&fCn2S(&@`L!b zVPgYZtmF&7U0xWRRABaM`tKHmh-UDC8IuTjbZrre*iE}ZR2ud~_LSHeXm$29Ha0?8 zr{>nVYuNDWm0zhRAADKxNc!hT*BcODJmh~v)F^&b&Gneo7COfiw@7z!&rFgbNvJ|yiWX=DMj`9a_;>@r z@!p?TAqT+fh}!Kuupk6oXz$NKd4O-TO?uGU1m_5q!W|YC2HpI1obV5v=+?wx zK`E(aY;fCL*mU}5!{XDFLM)qglaJkm4w!NI`|Hbg5F+sn&%zFCaDCvS2?TkfyA}^L z-Q3MCCiYDGp{6a{ld}c4MA=joQ+`!tCEoJYJkt}y z3ik6I^T5%KXZ1T(m8WAEpQJf4Q;CPlGjSshu5FE#UC}!)5;Y3S|0>#E>NqAKorBc% zcUit?SE0il`Q(ZH_3L8x0?*JFe4k63=mPn>q8hsm^zRt`d5?4FyA^h~X4F$t-SrC# z3v&~Fzd_D|#s5@dM~^kMtqR(A^pWj9hn2N#Izu$H1iG? zi>eVR9z{i*@fv7%iVYw)~@89FgBb>d7tDO+$m2}nt zHQSA4D)bni8q+cL7dy*a!@DbqF7MLgH0h)CswB#J5Sb913j4>f$)L`b<3D9(=n@gW z{PB8A%u(#ilB%P$L#C3$*l7aoYHq#v<7hKd2ZsCa(&eU}k+gorCBc^B(JX?Eysq4H-vbf}io zZJ^BI;V%-P8Mo0l2Vl1`*@GcJGxVZne42j0tp><;TO+p2ND+N&6Es^vKtZqLOt;UW zHVvXd%v@EXbCAJ$jBvh3{hCrkJF{Gd5vg)|QhERj`5Cjw%Q3-kOb;1)KcR&4&sn4Q z@`RrkP-911+sVVx@hi-aiqV1^%Jj3NO7ktIOFcR+tg1cs`2IWp2lHK?`ir;oN=K*H?iSEtJXQ=F;m;fgfiWGS%nII&xIF}6hWAB?Yo zXoT(O0e#PG(|qW{N0k>pJ;2@K9Ev%NsNZruZwhKo2vQst=?r?)0HTrfZMz@$BG&;O z^0(A7vKUl?BOs=PIVLtULYZ_2mr@L?^|M#(MXw6skWBj=Kh~W~U-1?HA8tc>z8Y6_ zhOnW)Z(xLGuK6~JrJ2%8?+^R4x~^R{mHY6u%=UB}fCc8CK=ORKbBJ>7k9BwW=TX{u zEfag@5@X9{Yk@#XrYJ(%9_8e9d}3&Jx_hkGh5J1s25Dy5!H+ zS=w2vee-+C#qX--DG%>rss>oHL-Gs{zq}b<7F;=>^gSe*GB>;Uu0q?G_@t%`HfyPE zFI9wNfC5Y?GA=(E?1R4Gks*Kf=9|cKk6g86JKDBm`*s8Py0B>I84*F=hea76Wf}}5 z5Rugc08BM#Xuv~wE7+u7BKBZ@S+tROa8_0pl#!Cl{c+MoD13}V^kQmY)hDBgz5*W4dZ31 ziHJFMZS+k)>X`b=%Mgq)E8^m(>J=P4J^210c$6H0N_I&>VY2~;?Ao#e60x~}C*83- zD`C^We?I{g~Yi`<8}KK||+>Z(5+?Pf&?qzS*6A6KEWT;aILLrC_sVN{Z@IJkA zMkgYTAwD2FJg}LFRI0TzQiIQO=6uNs4?GFR-w-YFU%wWklm;*uuu9h92BeoUsq;Z0 zgpyN;J%Pp_05nPV_~o{HAZA*55F84Ocu2OEQGxWLNq_x?YNi%6iqQQbmYaKZQM8T#6m zWkQ;@!?2#0GkddIboA=pHJ*7>PL}fEavI zZ5B^l=Wm&u?8eg=0oTyR=MtSE^-AV=G#&Jx`WR>vX zcY77^iLddI^^iL{JIjDV>a`B>_c(m$QZ)@N>d+SH+N)B-&0)GKvl zdsCqEUJ8I}QB`+8iv2@lW6)jSfR1?shxldl$L}tJwY0#T5_C%jcCwrFbuV6URJe=*`K zz$y?Zs)shXfUV6hg%Az7<>TB4>u@@Y&<|mcC$ye}y%#})W4>JOpVe2NP1g&p>pWa8aH^zNsQ5Y?(H~oa#brl@8Miz_BEl5 z53!4OTy6aj8^N#meB=gDgb>ILo(B#3X6mS*5 zIC|)aW@W9nC11w>z&|RIi%|I_@(5k+TrM3`vrV*V-X*>3&Kw~z&YlQ@g3j< z&f3G;*1KH!&YSNg;7pGZbN7#L-w68XS&n8}hkBfle=d*n9BVM|b4D|4tlnILulVHp zqlQuHI(q*kyW?T-#Q|e=nKjv?CEezMn2csZSm!u>zKp-CMu%0&u==u;3ud%EPRPvy z_44jp`v+uOVm8h1H%OSRBV|OTV_%ANU04B?ml)6+YLnk4iUA=JFGjelBFCk3`O=De z)=hjCPHa*4GA7fHZ@v9i`0d*c%;pgYen;Z1j&F2Kf?oZ$npV@0PURk_POV1?S39Dn zKO%yWajY&vW+zGwFRwK~q$**8phl)Bcb>-{G>>6*ngJJKD(875X`zClaFr_@q!K0tW9>F2DyqDvN3<`k3|H?OmKK2^U3f$ z)9&BjWblOynGjvq{#0x}N;)tsr`>i)OHK7jae{AXC?vLam7+jN=b`2Sk=tm<`uN;o ze~{vrFJB_Cq{xY=hC@r^>Z78hx1&&t6}7*xTssBo9dZpFFa^{fR)6VnAy20L(BDZ z?S_(HkE5L$4xYP}OHA%S%1Uf)2l5_R6L8VEYJj^iIpJw-q^l={#YM;Iw+({O2YA5Z8v?*15@ObalrNQdqGusP`T@L8?d>9 zR$qKZdqLf=1JLpm{baY}2fDyDg8pW64t3(4FEMSq4)+$2P>7UhF-FuJ+5`6a1g>$k zo!e}Ebp{S$zIDIsIg9%VR1PL#PTz)r7z zK1G^U%?Nj4#ed9UhyY--6htpLcn;Q|Gj&nW3ZiVA&P}2d|N12cTMNy2kz9ahP&p=- zZkMjArFC3)ceiQ^&j40O9RHf@k3k364yfzIdp+jHy8KF4-(&Ce+~aVcAICQoILfYg ze*DB7L9cvxs`6+5C!DX|HuNk-@*8=Awyjy2k8fxEgpYM@lE8%5-Xlz4&{^`Y3f&x} zMQ-==;~fc@{`c+57&aFfmx%i$YfJ&SniTwtaNa2soiYf2plreBcwtysqk}fV*4iFe zqJP3({9w3*Zlo|EX_VYTJo_*)uFeg81v@KuXE9{Gb^T^7^XVy062yXI64y^ohIDpV zJZ*_Quh$+>EA(fw`x(XtMChyE>-C^XGtJ1l&!%I-4RF4uSrgytfO!w>3>Et55e9GI z3kQC%7)qc9k@L%SH9g(qa0~)dSG!Cy+N;|6e=URlR+n81sM-m1ijol^6XMSORy5s? zA;__RrWV;~DCr_E7hLiM@~Ea!Rfv&8q+UDg+W5uH}3lx_;XmNSRsZia_Nf z;xM&o@PX{ichc|t@IAk*Ao6S?&waLZqL+n}=Ww>d^l_@|?57MhH0=B@*FR9BNADbg zxt=q`VQg&l!)ZaA5qY;P=9vYxLhU+4DKz4iw1C2XAmQ|=SN;&fPGrLs-BMII@hhv6Uw-_M z#6STNuV4o83)MH83?jIgnNv{$fe(~*o8`1uRWLUG4DQG`A|Cw1J2wK1 za&@eeZD7g>`NK?5=aG(otFh1>zvD)44UEwXRW#kD zkf2dSuk~U~$Pl{reglo~It-RfQP3_>Z?=T7_$jkuT9eupYWda}s)eY3(2K~-;Q4kmL0#dUi(xZIeZ)( zO@wERU`1*t>pW*q8|=N%3{Am^*d}b7@IRgN&X&>hhe{WiqLLnjO}H0NedLX)>gkzb zW9Ym9Eo46H%cp5n036VvyJc%^JE2hKz@h;F0k#Kp&iYBP!PHimfl931BkvQ9A*$<* zA>D=>j%HtODeJKG{r>u!HEmcde-@QsnX<(;5CEN&{T2h(Qc+1kZeJennexI*n+I z61Xaf21l&sVXgFS@nuMo2W42tJ{E(SfiRzWWr-|t;`L*UCjg)0@w?werT0UTQ=@M6 z5#?JUAt7UfZYwJ*@a(mYn0u}+Sfw>oc&@k+-7*8HNvFHTdOjFb-*5%=>7_u2!I#{t z=thHti9b<=xCydsIG4;7YA0w5WP`r?%c>b#m_XAoFaVGMIdmY-4Ha##LpkIrPw~k7 z=m;Hd8eKC`_<=9gjem?{qUqtohaZa;uw3blBYX`ASql~sJwLjdnwntRG2|)G6ZlKX zcn6stbYte~Eb(g%%1s|Flgsd0@5U3(o6YJt9!+F01VAKL zXc-ugVm8B-p!u6{S1JW>^Seb~bUaoEw8 zKk(@jF%!i04Kn*-gOb3~xFW!MMD4+fd6)w$g~d_!j!sM%qN?u-%kq}qju-`v7kleh zw*rXxVw^WyP0Uz8a+&V-!oQaRw&AfT_!8`5dn=#> zGuWLDk#0G444d>L#nCQZH=@U}Ro8c#h8T+NTX-KHvYV#8+s~QTC>w6Y_}~30Qi`cc zK_tgA2}DMN=1=B#25vu;JiXcvvSlgkd_5IjeXX|3yx^vksF2X?dm}HJV8h(A1w){C zultF^j2S2GUXqZIfPN~CJ3)PLodBMQ;@g2P8g7mbvHNDKWOFwlKp(XPG*sfD599U% zd|(V>xUn=*%3d9nXq-sTz(B}-NRasrAiy~6HSX%>NIQ%K9(nWlA6?l`d=I-iA#@uE zLX%x7k4Q1Ba(ma?OLU?Wy;d6j?yJkLs4IP?TtIGA3NzUX=OI0}Mgd9VXfznE-GabJ z=u@pkpAzEAOt%=$H)csUSz3bxMQkT9TZSE`WJs5R7*shz89X=rwHY8IpQeFv44lVv zgD=KyI-v7F%VX5m}?o`KQ*10T?I>x6DiwE>j=z~mWP;xJD_=L0kZ(HdU*@;Rdu z&hGnMgIE0Vg5UxHM2gNhuC00umt~)Tld42nK5jSpf}9bRq?qXCJ26c>9$IMPw7j=+ zJc!^t&z({sx^RX9nG4<1s|#gdG{7hW;(RfeXgeh2{dNCq{_N#iBB6ujZ|dh$^G&XK z3e5YD7<*rl$pL94bN!dMOH6v#7%l&W@z0-+fZlv|4kHy3q1=WtfsZHnbT~x8Px`hu zkAN3G2UrNlYun*MKBfwn!Ny(?5o9y<(Z)oq1S@gT%IZ~KADArYNZ?0_R>f9bFd_AC zx+4#njO%c4JOpcb0)qiCfXZ5ka8W=)!m$p&HV5lbOT6gGeb0=szwxzDdgIQ74e>#_ z<(nghkYeB$iE2FscOhsFe5oGhf(w?Aiph44H|x$3te3PjI-Uz|EL_8{V?z<(S-J(E z>!8eyn9`S1qdJrK|UfC~ z2tQ1i^eucAu0p*;6Ly&uX04W}3G7y+dCz6Bk($C? zj8cu49iX*>aIK?2B*OycXl1-ceDtNoOap0T4My>6tThZLZ$T*_22%|38h{}VkbES6 z9tJL;I*Xb6yyvD7x#F&Ktg43oItKLrGVj~q;1tg9GnWJf7#8Tz)Qj=JRIdgsTp-dU zfTAjtOu%N*${s$j*1%YNC8`9Po(!xE&q*Uxi4$ctBPJ&HK-MdY+(uI5cNKQa5``X#v@I_xwD)?8UWjbBT|%3$4OqMi;Vz{(mcIf|53Tgr3r=-8 zDoke%pvFb>6qF6BddKz_aw{-A&>any$AHbAPi1E@k@$Yb`j|-e9RqZav(uOk&QHbK z-^3unJOS`yZ>Mj{P^X!4j14=+T?kj*nZi`bGI7p6k)D#0iS{0>hE-rgiE1J#PbqNU z^NKI+)^3@-6rcTDa+P;&HP4<5MvJ61Bw=QZ7Cm;uaK{S|r zW{T6vd56lLXa|GvHIuZoE1Lcs&G zpR1qv_;C=o2Kx$=;iOhkzZo?Cp*ROwOGZY9EYqIMbi0&g%Rc9aXkS+Tb>i!fAH@AI zf4!k?vjs10ox~+13gbTzb2|jYFjEId*5@kswUHJZH(t{D<-%Td1_{1Df2Pt9m^&8Q zd#C`StH4!1<^ji1cf2?IaM1MmJ5|O#Y6*NdKyQ9wY-qVKP*-v6`j>qx{M!uZv1BMl z1(tk8V_*DieDQ(>Cl3YEhz8j|HjaEIiB2vRE=+HY*;g}Uc{jH5-+n|>F99>64U|@I z!%?;xj$QG)GslusrtV)*+P=X%gV5wKQ{7J+<^q?opIZ9gRr9Kc-4pUc9!_D7rM`@# zM_kcMDN!ibnDVs`g)i0^T#OEm-)gTu>-6j_0~E}+Vo=PPTZp0!g(H-I!+o(guR1vi z)7k1}Xe}%*;+B{BCI3AfXq(dlFNVXFqQ@P1_(Elj;Z?lwRX^+Ns9NAm!<_vl{#Rzq zZ7YaLC}q*5`( zPkul}K*Va=kp3~S8U$^0VUw*eisB+GA0wtS8HS0?`45u;v``a{_g9D-c$UzCJYHz# zugT{a`ZGoFkGRgo@!B<0e&cxsqFArJxe4oQ$zS>GRc`#t5+?lXCT-i?IS3PMDf{NX zet_CL3a5O~X{cg)i$+wwBHSanEsV_URD}w$i`k=lbYS?wAH^C1_3?x=kdPT7E5UYed zoSzYNrJu3Ay%#1I7Rhe~Vo5B;OOI5$q@uBt zRDrZmZ}b80%(uJk+qSl{o0j%vVjLkYKe>=l)p^z)I~Q}39@HPtA|0oxOALdKn(y+e zIXd&r&|N9fGO*>wdwd*fwrC}fnK;-L-yeAWEIX@Lwe4?no|^JCQX)e8Mh#*hn)bPG zi>DqPGndNWM`Er>)bpeK;!*Pa3&uO3gnd zF3Om=d}A)60gjRkHB~AlGw0Ech@zDpck+Js+WcNcQZ3{D}@`s~?2efbb zjfFxGynMuY+r@|Yk5DS$aeKVn_A9Qdu!1koKWLO*55*+TW{=0p+7HxGM(}dsc4gvTMhmoYs3CUP$!C;n1R3MhfqR^xqr^w)VsOBV9(3qvn96s z?NvAbQ>baQhq8xm+{8)Znm4Ap_RpIBId%xTLkchMjZsC@nwMv^@i z^*7_KN9HqtT?wBG{^{WVc#vurZIt(@ro@W0Sb$6rP5Y-&c5u_pb$B;SxVd&|HDLIg zuj(iDlOerIvej3&c&mf`tkpXeYD#Z+NlxRnR&UaTa91-Z5(+^zsn4CUb#`RpJk=)l5yfe%l6gziX65|rN5N8ZN zKy@UaVLf2b2u>dpF44?l@J#p~;nRRqq`*(N#I`p*u&-9v9e4>I0S~~n;k-3sIuC%p%ORd1X`)>?ELL^%Nxm{OR=M%L#!zqym7uRSe z5WE(E4}*l`-QxTtRA!cZMpwOa71J;nuPQ#i52hm52)5n=Gu(-ygqO$YTF$k}XB)^& z+d3c$;4c-2Z?s3dkF5iw5l&xI;w%7ZJY$w98~*>_$hft&#|T%Xp0I&920^McRs5qN zJw8ti84HjSz06H#5EVMSexu#~TjvQsU*RnI-6jW%ljbSSa%s&zz0R*sq8sYw)h4r|Az3Rdl9n9%e%1o7~QKcrMZm2Lk{Ti-Gb8PV9}$ zVO(6`kSOH}wrn(A>gnwB?s&yC%)|KMZr# zJfiJRGP0xe>;g6(H+~W(wy({j-@k*>?ZASd^*sL`PPpdKV9r%UO?dHyaUTKgTsY=D zXd(I1iP&;dkn?h$e|F>&psm!8uQP0#8Coa=(Jx3`J_ZvuzRCoEAV3B*k_Bmh1*o+4 z*pjfWOlkVlP*QfFe+TyfA^ET!9Z~#iHOSW_F3QS2Z5?By*66?|_%}oh9VB1h9y!@0 z{`IoB&nQ2`q`X{WG2z>#HxDRCbcvQzGXAlzCuh5Mlo$Am6sL&1%U(Q0_cmOAAVu=V z&U-hd-t(57zbqt`r5t~< zEB7w$ASBQIO;^tT|IHP+FMP&Zfw<(XSzgcgyTq9FVP-?`7IcswyXAA+0XJ4q`eRc6 zYn?LkGh-*Jy4&NnJ04eQlDQy|3z26l1Y?t=<=!?hff@-CbAZeRRyt}YkQ@k%f&@qy ziQaA9XjFEM4SNXe<5Iv)m#$#B6ryiK&t}{+&#^S%( zXtcPfVj?F7MuhGw*;}-J!$3p!b@z)k@y>qjYX`Y(gy`h&z)Z9g1Qjl$8~oc=Dg;&v z(t_p?Q^wdNf*6c~NOG#YKc6}iL*hUjqkRg4c3tK|7RpYVRiURippfM%)8_JRSqj~ znB9@u>fJ(u9ZWgc>^mN<@id$9oq-C^lXjYvhH&C@!9H1oI@;+r+;lLScbdLXK)E3m@g4(gICHX9Jt7E)5S>&s$)J4ubD zQ@JGW-Xgjgcofcgt~WaCk^VBewMwDobb5^EyAA!PaD$#fC6dtBh`sy#lkc*>HQ&-| ztsazfibi^@S98Z?k#VC#*G;%9>z^Oiw>5rE%NwNm!SeL(k<88RVXPjch0%Mw`swp` zXqxhS{_S6^Rjt2MM$EION#(5}hRw(3*OM1uJczYdC_vBq3rg|5R-!Mq90)t?J%PzV z#y%4b)X5vmIQ7nPOU5bA=-wmdo$;bCk?7nt-tjbjN7@mJBIBy{Cg#Ae2ltGrvW8%H{GX2)Lt2N*K1QGBw4Yrt*_ujb7LqAUrDG;d=_c5$TGij;MPyel)KSMlM#nNwk$t;6e=ifg`qS7CUm!Y2^IwTE&g3xCB4FLm8|$FMSt<1M8k2?o?L=(OWV7S+Eew%qbjU4Vf7>z;Vd(q-nj3N8`~}vw^?Q?fUP(ZaeP3L}+C4KP`5*5XLM_IruK{ zfKg*!nYNIb^^pg)6I=NS^VQ+f_2Ef!?4u`FbF-Z;zwW>7rjzlAEvx>V1g;vX>~n)x zokY!BN)&gpZ#>HlK*n`m-89X7w*~IAK`;0?Td;~#hJAWUkvuM_UL15Qe_lFIVvK8{ zEu~q!*9==dWdz9+T(XtTggLo!DBZj>3v5 z9ZhP#UHAQ&A60XX;r25dYAp}7`KsUZ7{b*n4%$Cu-dY`;*q(M|z$5`JNxRUh1~7T4 zSl?6J;@0ikz1oCxi2orY_C4qhWGEj$zZrIKM`#D@?~!O7K>M;Kh<;n@A0}usDDU%nCIIkf=<;mf?201s)R%K z*hjctzH;Rkavu@qfOi0jw~~@h1;4HBJ`0*qKOt}`9SO7q*cf6?{*UR*`@|!KGRecX z$sgV9s?BYZbE*C=B`VmNnVB!>$}64%*9N+$pm+uN5ZG{FL+HO@!nY$_B(UyC%dH?x z>BfvfHC~hSgBdAZa>B*JN6p3(S$`~ZbCa+lJeX6tbt-AAZ^4KCVzZ1vC`R8U!`Lrm z@OxYgg!R!eT;F2pl@BEE}@@5luhnz zpFr$5pe|JYeVA@w(1)gXqDcXyU+)LYoO^A!d-k7D$Yydd@D|rTle~%bcf|cLM332L zyXPGiso5+Y8&>sjlh*-!7K$F3d$*{q#>OwXtppE5W)ubwb26Xy`hF0+3OkRL8o{gJ z7V0p}iwCO0HG;(4SG?YvSV2F#$8g_Dqj?r@GJUS*HO%|a?gw#WI7Hz2?G@3$gt5Vn zEG#U&50I*!Io&(hnxK!-B*fGJxR0P5OlMMSb5etBTmV6KP};3No(ea_6J}8`H>k=l zLb9;6oBU9GZ$%5rER0pCJ%Bj%Zs>Zm{u@RVg-&cey}RywJYg%(ky{{Nx0UxAlh#vI z9`fMY@nLUz-owmtg$jS>Ke+QH|3ae!lVE$e^B%j4$9B+mq&hfiDx~gsY9h`jtMPDw zp}P%@o7p-rcV@w}F+NbW1YC&$BJlKHD_h1H0onKqqne$aL2#{sANoTRJ_Z2@PsWW= zrYZ7%J(EQDT?EH21E=x%1%|8JUJX8a_Z|Kgq%z`y7CHCtilr+#G;r8aRNIE+x^Dg9Vikc+lw1YxWIPeXsy)CYbhkP>J2)@<~~u*&u9 zXK^Y*!bgtCFIyFQ6^U-S^%-}ZeY`KumWQ{6hn`_NJ&~Hl)G?_bu&VSt&W~Yp<6DFn z_KrIrgp#*NXLBrNY&>J^el(1Fzh;TUBhL6H2f|d23LL!DRP)*#jwXsYAS)Ljc}mKr z)sU|sPblEB#s`E+&fK5|*4m;S$-i7zVF8qLyM&|(dbkiZDFBV2r1Nt<0*@P{gM?gK zSYUg$uc^@F#TEckl!S%8qZ$`7!ecyIhh>N5BP;8She0)xY$!X+^*vDPw*k( zvq44bK{3tYmBz5!f}ZFwB1>A{Oi)a%x+Eu^ZaZ(u=E<3}n|&H&Yi+dekRXzqNZ>@# zwwnC@s5l)57CVNMUuLuhNS_|FabS7gcPufdYmAT&ahU{U4T%5jBDO?BnJ$=NLfzXM z|M935dJaG$w&Y=0J+pHG$c{QcS13^RiZs{%{4&9(>@Du$ujH~LhW#A7xe;aHj$J1^ zlz8SxU zjOZ5>l9rp+1U)Wj63TYIE{Vj`4TG4XfHPKL(3Z$m=_ndN*Hr3Uss2pmJ8$6Fmo{vTcM9gp?? z|Bqjtwv<8{4YDaSR77Qu5J_c(?5vE)u24o~%ZQViy%mwl$Osv6NvN!>GRjPT_g8g3 z-`nr|`+fZLKIh%3uIu%BJ|FWwETNsd3S{sKM#L#U)@2f##GXQSodlxLPs_8%NEW?1 zO8P{AB$ZML)IAoqWQv*DSyy<2-dt?JLZ(7-?3W{JM{eDsBV})!)yYj054BXc^={M_EF zgK{=shn|P*Sq^2IfE6Ek(8<~#a0L|DV{ac-6A(a2y`$!DiT0v`H32ild>4F27YtDQ zjd%2RZQQs~1hH68-H+qC*hB4{sHS0|n8O8jTM-wC@jk{DD@(N%H`+DL&A-6cfc&}n zp?Gu-MSrY2itFri=`C2vEe*>cb1uM=662rA14O#O!ntP0$SO=3$S2-l`EY~g6oiin zF@>A=k~vCl)5^VMYUChf#Hb~^wh&*sm%sYOHi+`i+?9H#m1>!itnc@8iD?@tp9ODw z{zQ^IltMIP-^a&#$qx*t#7{l$+va+3U$JEt@s@Y&0Qt=Vb0HXAK>3`9#)umN-Tof` zw1%-aVO&Zsxsjy^xB{XR-hk-^unQ!6zt8Ll2lH76=o|zl87zI%ioYZIV44j*&>7s| z3hpIB>JQ~Qy4~p}|FapIXg{1C9S>vqfiE7}C?n5|xs8wEefeUm9wGF>I_s$ad$&79 zGECT3r1S+$ZA=N)z4GEkR$`bbr0j2`u^Q3im`Ws$$g8^!*)h~_n$-=Gn?pl^#t+r|8dfP-L%*^k40wLb%m7NT z-&RC1N6YrZ(>4MGQ-EH%;#~?*q|Vq3qo=S6C65p1Sa35l6MhSrzCamyy{*y?IGUnQ zMLNPG7_Gg@dK1&ZE?m3I`H6-64D{etTF`Mo8I)` z95Gv9chBBM5cy&r*9flXug`0W^p4PsG8b*L{B?IdDI3zQ`3#;z&Np`yKN1ZddK%Tm zmm~{CRi^LqN3J?W=4NucaJCeRiDGQ)XPx}{{sj2;Amdu}mH)sn1n&!! z8N~h3@(9^(RKW0=DEmX6JEnllscN5GL1ohWJJd2+5}_8ZEjX6cF>KQ}41CmNFh7bt zP3!i{>|W|N162CAt^JZ7s|#n6cJB;*%zAw&=T5Q)ToU#3ElMLsua>;WhziC5FJ8PL zZidH-C^IuNICROM%nEw(=vOu*U*jvlW9Jz=X>5^5)un+yP4T2s({x{ zFBR>`3z?c@IKvep4P>Ki zbiP>Fq3LXi3%i-Ku2jLw`VegZb^rytf5EoQ>713J&oBXD%5OS{+5^=XMYqz1zu=LKM@mvSzzdz3@xH#oJNU!bucrQr!j2CIj%x|jHwcgWeLjxryMK=;oCie`WF$o+;g?O$}6dQ z4dL!)^GR%;JdYnIuiD_x1kD0P%yX!T=9ACBO8{4U{rdI3fioGJJlHVd0`X}V`yFKu z>JlJJA^5{L25g)jIg%u#LliErUNinyMqogKTU0c@ zZ}KwEoAs{T_{#X$MC;Hx(%5DfzKi=y!>Q#AZNF^qJ#Sc5q#xBW8`U}M^}Wj5@f!b> z$0@4C>==LRp)#ivhgBZOaaG*XfQu|0;D$LKW z4Dx<)6m!bK$l*O~X27d``qa2NHd5~pFu>WqdWSK_Ko+Ckmw|R1ZA*J!UnPPFGX8Lm zVs(@gY!6Vr&d$sbBT~Ex!i& zcMJs+(k<++yNPjV`WW8-r2hkm@1s5qdv0Lx?r)}Xe8iq}oAwIz-dgv^X9#(jsObVZ zf<0?eM8Zz=Cgi3-;Z=dL<#GWB$oSOYxha2R6}hP+d`F?VuO9 zi7W&V5k`R2;!KRaPd)IvfJ=J_PAxhrpSgPlmPo9J~+jAi}m30TKijiw{o=u)wWS zJz*uW<$f-j6#KIHCmb*FN0X%?_}qaV;Ei*i$&H3{K(t5kUPZb_;m5Kk&?Rx54rM8M zQXTc(Jzl3bJMJsg>^b~v>8;NPcL;%?Dzai{!cq^bVyosv%;}rI5rz$qAU}ZGqT<@8 zf2wwnh5x39AXq5Nsvo4C^?kk=s{i30Riq1{&-ORtKYpWg#lJ?MWko*iSoT?`^W#@B zaBS20wXl(Ncqej&SeE&D(Z;Tuj88)X50#0g+}UPv@LN+&Hn>mIA8&;i70Ls?u)Cj8 z4Q+xLjBa2lB5H=s3Ze;Xc*BiEMYM6ql>E=Mehymqn1-y)^G7O`AWi@z`3??SfEHA| zV{>9fb|cDxXMs=!p_eUyl@m8argT06D1!^t#FZJWoZb<{bTXm2&So5szd~dy*?y!U zd=xKHMDT$$VP1=a7r>hdulqmbKJ3`>B2kZQj0?viO!X(*G8VdsTxOM4r9jifJz<=L zZ#GuX$Yy4h7#4cYeBStt6nE!O@lW_aBylO7reG_J`R&zSoz6&Xa~eBgg4$H`*}(2& z!>QCK8fJN{r2}vzggBBnlqx3d!);X4$BZl{J<8V}97s$FzwkwAi|_Q;GjB5IK49j6 zQFFY<NJa-EV&KH|}ku zphW>y2SQq{PV=t7TEx&Mgd_BOF6Tb~TwR5%Qp+B2#-1DQ^`c4VCXmBG9gtm(ju6m~ zd*av(eeDzflQ66*lzlX+5)-h*SaN4u~(!bMF$-wE_8(YZX~7(&=Yg>xi(k{&?@4OJ|V6M$nO zy(OTad(E`}wuCq~X0*9+*+xMxGylroS$KQUQzQ#~n#3AM{dXX2lOY1(ql^B-R|sc! zy#wXKni8i}`us&}7~Ix9>nBBFvwku3VQ~@T`7A{d=MJ0x4Qqw{Cl-)atPa&ksz-CF z6IdB6L@QViJXCc?cL<^bhFGBRgdHQl!Y6`4EV%@W&KuA@2KxnYa;!TFmQb{zVN!+z z7|J8yhx!QE_W+W}2AX$d`f?O4Gada;$)ZbmSYTOLSraN~74PDK9|0*6VBXujl;8p& z&5@-F*&A@00gF~)>T{o;ykxk+AABk7?Z!Zosi^*lzE@Eh4$LI&^pr=P#gKyiwO`3-AMU&+W5zM+G$ zpZ0))+8pqzRg%BQvbTN3mE^r1>F?rPIlN9Z5}hV38HA5Ic>sK!lEL3)-5>!^P|=lE~iwr!#)R683Ybt@a(XoHp$p6g2~v$1{Z+bREn(0&;w4lJq|{H@D_qhp8V}gezynK+t(c0hD||$j-TBUd}_U zsLA+rZiqSnz(C;Hbk+hTghjmr1Dh~sgdQB(=mZdSIDQZYE+sf8R|$>=;UW)iB2?HW zqu>OIR-rkH4LCoXp`&(O#UHVsG7Wq=Lg)e_oL`~(WpcDu@&njFg}In-AWH<6Y|*nT zaB`AIJWrHxbNVUh`x5>Kza=L#qZAZtL4B( z-GD)tuO(VMa13bo?CB~pQxmNMLy4LBX5S42^qx1EW-h|#&qaP80HA$+51Wzwy*HTo z1zLyqNWpxRL!uSPT526$Or!^+X;7{pQ?T3rHi%)2aMv$&Um zp$ypq533*-r6LymJTFf?@ml-!+ZGA~$GA%Ve1<<`zEeDHA#(IaFS+WaA6@)C>Cd<% zm2xPu-nL$v&Nox+v16rUal)3@S4qYwGz`=aw6V@}3*Y=_M~7i)qQ-5dpHhO-euWZr z`^T>JAEALO&ZI|zBrbn zyxPK$bocISm}EAJ6QhzTpRF|H5F5=t|UAr!m-%R>KdTbv8z zPG+cnLG+~@GcSR18@!Y^!FOLIJTneTY)T-ia16iEq20wY8*~XgY$?|kt&f-{s_g4~ z6E%m2@ycKu03Il`O`L01$giLL%gn@-NKEMZafnx-ZXA3JSOS*#e{vD)X4E1#iBkUU zG6d%hxdM{N^6Xx-3y`j6ri$FLTa@$g4f%ZaWZBJzJot*siajS=CQ?j2{a5FJukJ;c&~65?>QPcS9%YvlPvrbWH$U)? zETNAvyG^_6fZ@xp;b?sy$^tZ&iubo5fHm60>jmZ{qWzfG3ddsyKe`AcNYuj!XER+s zaFiyjPoxr{esi^-Q694;fEt0St}&&@-rrUwUNzll4jJYZN|WCfxBhRhmZ0E|#zjVl zgW44ulX!@}Sn4O&p>I9o(}ahKT{%&qjv&QC1p2kaKSu=w@-f3C;5e0&bp6ZvID|Q8 zAKkuoy@*?sO#Qb`HE~P{BwS4ev~4y;wd*wWcf1$U4*cWS^SJm>fo?Xu;dY!IfB2*G z&J~S5w(VYA2E`1$6v5nzHwluR>afr zxd=*MLWRgKXjJ5Aq*BDeb7u+D#K9az!pRDF0mu|!<<^bY4p3T@q%9YWvc0M0)|A7-}5t#YP+eF zloXINxRlO-6ZA(sMMZ+rm16Yh5sz76q?kRCIfA02IB5`sYZd=hoA4AB4k!zKEiE?4 zA|N=SqIjMAb$q!j`NH|zdfM8d&BUL)l;?K;|zYLisVuRh$%21WdARMc;KqO%qk ze^L9NVcCIwV%WzYFEev_ngxP93le@^SxNrcx`&j4Ep14PPshWp19X(>*R-;Sc`Nml zls)RrsHQF{Y;&%0w_6|fnsM#}Vm+cbL?Ct9sDFGL02p})9|+=ai-g$$1lwu^X|C`B zo7?A!@9edv)wmN;# zOOzOxfjG0_fVsH26)ioxK4I!=(Q^cA8ol|a&=rfWuUF`gJvRR@fP2jGR5=6@OynS; z><2bcSN2+WzXwUiF2|a5*(gxm$aafp05ccQp2J)AOa_p5i>-Z!cXe^;$C=t-t^8O@EVUk3@H8=lOUBvXHaW$n|6ALUPn6 zJwE2dfZGoJK?Lp(?d?K@dDin+mtSE#3gB_AXD9%7x$9S?B!P_*-&M8whWsnZbBw8q ziUIW93OsILBhUO{BX_>$Dv+6#qNdps{*+mLIGg2Yl0ec$$|}+{xHP`^4+novcpE-k zT(RR_jN062TZOmd^o8Z?$F@@?{Y$UJM0?)b>w}wf+JjLcYX6$HHgz^?cqp=qiN!v7 z9$cdKK;Txhk(t>-uAz;U6~?hfJ%#%2GqM*iKG2Fw@2Kp#6S}Ga_7TD$zg~I7ljn+3 zQm+ukC}_C|Uwhc>^e;CejA1lZ<0(E@*LJ16F8H4z_}2<6A`TQ zNnv4OK1Kd_W1PyPCzXJ!$>5g!%Do-gh3%2fx?Oz^*FmK9CiQ1qSVdgQ}MV>RJ0 zF0~7Zn{F;(wd^iTkQ)}SG4|hie=Nk?PbRTrly9g#K>K`Zrj{`~hhXCF{)he}WnvF) zP(h)Z|AjK2j#s-z=Lo!a_W|jSgxZt!3~5w*)n;ud&hFRYl_m8_u2DV0QG@rvoPYHj z42pa=I1wdIg8@obK*gwYPikR|glWul@V?rbnv2@nge@G^ho}2^m&-V8#N{u<4x7ojW7f-t$k4qYQVmz;rFf;S)9+0BtqDdXg?+?34j7swh3uBQCh*8^#8`D*5tKSd>0p%g)3P3xf`X6x0 zHE#iYU;zDjs6vg++%dA$9r%vXa%-2UrH~0kIK$ zP_RUpn3(qN-8KALv$yUZKbQJj zPM}ks&o29zhfH63*w9P^q}Fm0qnv2^Se1tLtx3}dafzw!?hmV1JfQR_yX9@nDGEnU zXSLbGvZ*KPS%W{baDjTMlyU#dE^&ihQMbKbJI?9K9p1BsQ;ED|1B@X)BnmLXmmNI= zlJdinpVQS;7?-$rITwQ$jLH_9O?wa=h;iFUGxp@;T{)I;sswoc=nj>T9^7aIS%3$g zU?)~MAOboqpy<}nu4-&lVxxxM;%B6M_pT>__wVat_Xu0Qo;a8)LNhqJY>hJG)`(gv#CETPYTf7=A5fmu=m?9UZSZmI`(EnOZL| zqKroufZpghEHvjcd-84!PCpB&Lhr6x^KG4dxS+NTo2=>9v9od-F0Br}%ZrfE_@LX= z(8iry==kXDW3NkXW9%MWK`RoflIpo7?=;k^{mQ>N{oF|UhD%@JJZT{F;BCkV*Zv&2 zcS>jd%Qc_ud6%j7XZ3sO%iMwNRTfr+Zpg_XDQV7_|&p3V;%ewK`JG+*hyK z*48{I4n{>q;aoK>3HMGK3-y5cgo#NJ8n*fQ*{&zyO~Y8Wo4jeg$w1T&V?BJ=J2no1^{4`0UOXyB1UCs`|$O1GoButHMh;N62Z4)X^FrrzX<9Xx1=0RzT$26@CGeMM=Y6*6kd`FVk4 z`*J=YjEg(?GaFljm(gM4mYvNNlB(d*AMK`gYT0lJ>)TGROmozKs!Zw&8N!lmlC>vg zMYL1ry4$pq%zhrCBK6ZbeGfiC*PmxV@l}4c{4AaR?9{3KxP^DWPmA`crWs3ab|)<{ zx2}G}%Mr!44BK}MXMkOSfkgQX9LgB6c8ib$^a~T2`5!8 z0nWc~*UG2Eo`!pdz4Bg4y?fLUMdWd5nS$lFzi&a{RGM*pJH}@HYKk32dOf_C+|Rme zrwe=Rm*8bD5B@|)>PMwJeL3Z9qeQv0Pw-D!uafln>yK5%uO1EARJg|}{*~Ens;w@- z3&#tY1SBULVen4OKedTjzqK`y!GV^bn5#IHqxB4!R(!f(rjwU>B4@iQdLVCy*&4W% zWbB!^oNh+OA^YJt3}AlP{qi2WmHo{B`F`CN3f1$8 z#%xVtuZN2o;}0fX98;R0_EM$g^ed`R|CSXpI-)HVcIeO7G^>nIs0ky77tC_o2bJ6r zOG#Xot-CHnadRsWkl$*rmrLFqIrHyUcxVYQmPSM!NRpQS;`cV|wbn}Yk+~Dm){Vdq z>4S7=I9h=gD4PIQWSd~p!>|8qC2L9o)B?-^kRCj{m5H~Pg^Q2D4WZMlan7Nv+)_!Y z5hmN@B0XS=bB~~?Ot5|e=}6)mVrWj0h)_%8Q` zZJ*U$WDm(HwF^eS8i=>we%&`f1J;-J_FjaeBMINTDd^gZE*Y8L2J!NOBiR6Ks~dQ*Zi zblKiNu}z#fRcW1pq-nrxa}ZJ-w-hBC-FCVAR?uLsV@&<&OK_%BM3 zdas0u2DMXjt4oFb6nh~Rh4&e2?GgW*JXIEzpU(2ysP zUxWELl=axSxcpi-kD$kLV)3LJQBiZ{wHRiLCc^NWgAL8mk>hc($9FfENSYF4hYz}e z-!kcq$FK)r%Jgx#ZbEJGRMm2IGpAs?erkG|hS#5p`!@ zs*dX)LiQ#kE1??$cnGm#!jzs+o>a+4(k+GCL|kjMziRpfraVYm^PnWg^#^-20_JEA zZ4i_PH^O)M1qJCncR%j-X|lGEuH~{wH3wv_m}qHz)E%3*|EV?KJh&rlAJ(J*`0l0l zqY)P8`{zE~Pb8Q>N4r0(=l;n+>kf%|9Mcos@#*bF5$yONjArh~w1ZA%4XZ>>xAJ7;&ZrsTI znOib8soD6kuEXQ_xesb_|JUmfq9N@~-d?4sQ7oYe7of`SwOw$tfn&(1l<5pDlgw%PFZFrf zC%71g?_5cu92~lG z)7Sk{%$%-~vb`@fM=fW#x|x;fD14WNck}Lg?N>W5giu?}8l6JDnHU4AilXc(j zN3S$Q@;oLm|}Ac^Ss35Lrr1`8I66UsZ^;z*WIza-jO*%YUSM8^G@f3yz$Bo zci)DD3fuFj^eODU)Gh5=AH6O)z0Dj(GHV1$_%(@?_zH+O!V!)M&TIqHo+-?-l(l{h z^bQi8cOTPM(I%_>U(e&a3BCG-SzQ+Yi27eq?5hzGBM;NAcWPKCjmaEcTHq%!w~8F) z(dbL-oyw>bx%4c|(&6f5pMd_`?6r4m=zWxA;&>D^TrBw-q6fD&uPsGz9G=m{JlUP+S# z9IRHrq!%)(qkL}o&w5OUXwq39#&#-cq@7jTS1YTo$tKHEC(8iL4j2bZ>6C-xa_KTf zV^3M_6dl4eR#G$HXB2xBFEjmcWb>F-2%E{XAUSxS=ytDHd>$Xw8)j{txnJQ{8|`XD zLc+f^lOZyv1B{ilLIYYUIQ&+H!l&& zLn!x*g(fdn$<=&&88N2VIv+)r3>PT==ZbDb8&;LH6p>VDHtKA$5nJkWo5IpLvvkk9 zT2^{KP4E<<%!!jqQCUmBK$-(E@nnPN)v5Ka`M0(1Jrb;Z+)ZK>2#{<3m!a3fjZOCR z3Edm~v=qMS>7zJ78XDwiE)vO@{qussZE}BDfTm&u8+*osnl{>p?Bddo?&bVmX8pW$ zN8tjCD$|7v%cmF}BsmPtq#BE9RW@%IVPTXlj{CB4ZF!Rb0^1xz={Dy(Ezmos`tov} zn7}O#$F!Ep#~0+skKMa7m83Tr;?qhoEm>1nhrini_0cg_D$>Uwq=7R5cZ4${Vio)g zXb&Cq7m(spZIWg9t=W8bsiI~~dLk_`YekdVfrZ1)<;wWc42yvj3pva0M&G|nwC#B% za_hxD9AFFA_6db(yEI<$?_~Lv4-J(EMfRQX?vb&)x_V^w9wnV5n7<^_aZDHlT&>ar zrj#=jQrXyhUBW^q*(+<9%eXoKN93Yy)a4nBwQx4JTNw;X=Qt$BCA?jvJXdU0NYJ0eWyJkH zFFH${^1OYbJ0&M2vN@xS(BN zyt4ME*!&q+?IqFUkq&=5DWrmhkvPB}U$$ z@Y;r&!oyQs5ofLX3@o?ks1+9PwcVOLQRmOTE9^m_;7sr5j@O3M>W?eV$F5_1SQWfy z?T5z%?_kX&*Ub{V0@u3tq9u2!igumHShTSS{ts<>VsgePmvMlYgxcbAD zDQ)dv>c5!XPn50n6H0xt<3~Y2&TgwdzZ=vqyJ$Leq?5LO*hU0lhr^f77cd@$0+THJ1JDewNFS($=};svC+M*wIGISxjCVJT5^OzPL_e zG59%6X#K5yjpvqC^P*qb}(f6b`#J!xoY*+Ynvon*G?vt6u+CwvfGnZV|xk|NktLz`<99*y& zFtSvRy4>;DT)M!2i~sjfO~wSt7dAhi-&k_CH*roa4UO98SH5fYRB?C6_&*O|6)0!I zo1=GXo9bJC9mg!*lKp4AEj3iMnk<&M#jYo`d`o#~b-Q)D!3J>INJD38zI|eC4-++# z@kI>~dPXYji@TVp4K=&@U=JV+tQIy6}RMr@mYJrJ#+b;O_`j( zCBQ&@TuCESp?1d^@&2wbh%GIVE}_0DDk{F?DP7vB2b~Z@hViiYSjd6jWBf z82BfvOiSEu%_n{c&vir#sf(9WKK))}yNOL?ScLsZXH4Dpy|z71*+q_vDDzX)b_MA5 zI+t}iANTxz{5GJyR2Q zFx>8YCKEdOqFaDt{mnL_*2-rM++O_2b~$dp3I4IK*ll|bOa$dS%$a8GSU7EGC1ul{ z+FLS&Bd?=IX`^kX+a!Pww~l1b@p)l--In!(_^wVx7i-VC{|dGlxM&}i*I)I%t8aeD zJA6{5zCBRr2~jEe3pM=xB459k?aAf6{bU1ctE>rssn%pqNxDnN2&a@tt7YM zsZDY`p^_1GzjnvbK8O(FVb5`h&CF1`peL{5FGrKZvK;h@3>;Pr_JT%4R=2H zs%>`pdKWFmPZh7kw2py}1<9c!cj`8rJ;l7SB_$?1mAB-fY*A^)yrS^f&i(Bna;GT- z{Y%DlHj`)wgY@6=?3;hEqm?apqz3xG&@)OJT2`Zq^n2-CZ2p`o^nUVXn=Y0Az6C=#5hs^!c%qqHh{{hG#GFm;dIeT2@o}QxVgi;U9D+z{e}N7^TDI9RCgcZwRo4J6^is{ z`a2JY^qcOuR>XE`1hzElG28y9B_l3_`tj(V;j$j|pZhj>9xO@u9)Dr^BI91hIQj=% zOo!CQqLZwWJGNS+GUY}I<=smmFYc}x|jn>-$ ziQ-YtWs8Hn6|zrkI;NT&8M+0%-M9W1`TJGn#Xf16zG8T4M+=~hI&H0u?^ewn$h?td z#02bjt!`pN{JX=!Ru5^+!C2VC=%^KCmUF(}5}voR`uS_ICdj`bFl@IzcRPP(*F}|5 znRkBUjGN3B{moCdxkzVjGq?scCBXjxdw|r|+tieWu_JWNz;4{Kefzty_E!4lCWdGA z4g(6uhNE0mTcJgb#*{_ngZzqIyMmeh0cE2e8LIJu2YdKad>t%ol&_9S@uh$1R4I1} zw2?h4Ls<(qvTUEk^&$FzfBs3gpD1;=TSTOsNfzG79mak97WI{$3tMXoB{&%x*w_ps z1u6Mjs+*OO)J*t>%F6cKx8Gjq7(>*z!@Bq&XI~jS)4&{e&+C958Q08}i#(N_k$Ta! z@%Q{CsP{fO%4cVCWp;8Xf}1Ka%xwzbN5X)MQ7?DBJM zZo=4P6;pQTmqru1_W+nfLu#PCy$~B_U|~-}KKIHMmP8SG)3{M01n)V}Ud=f+7`Icr z(BSp1>|sVdaYfDx9pk%;uk6lQj(rYlm$-U*RA*SE$R%vWn#_B2W5wf4_0uPI(Y_2m z?bOCs>Ng#}?oB|*s13BhRHk79UN2Mgt=T`Sn6dq_;zL0zDV|gm_CoBO8dvt!Ze_^z zVS{Tm<)fR1*VYK1^Z&m`;*i%psAqTkVtl;heD091jFZ|P2X2Xem5Xs9!s6UL{KwxN z63J1CEsWE6C!ad2o>8S`xmr@rAhxP2!OKCxrY&Fm&^+;PyVO=| zQTs)>6b|a1@ZK-ECEX+6|KykZiC<9T7(9VPUE=pqt@q`@T`Eb6gBBH>E?ueRC=6vY zpWfW_;gNWjdE{o7!zsR3sOR)URO+6VFKyM4#<;z6@+Rd+6`vE%SSIlI%p858!^XkE z6G`u|ssHeRSDW9Whvz|E3Fc&JoZd1IGqZQa_Q#HT#!l5)9Ua?h4(X72BNuc7UsUYUDG zbwDBS+rQl_Uw+K}ST1p0y(%%qA$Hm^oGW0z*Iu4mTn*Q>__JuMKUPeh4V+T8q^w>0 zu~$AmA3Ssrlp}Nvgs4sym|AsZG>Mt);o#L6?!1g_dJrR z^SLJch@IDM@#cY_a#hyJ)|_L;0vm19ns3n_3pZ^^y0p#W(f*$E$ybfc@9{4cTF}|g zFyH6vG?8pJ+ZLece)ns9(mA>>|A-6h@_g=cWiuHVGS{Drf?kx<Ouf*2M-kz>8#+vc{xu%m2$20Em zzL44kzn}p+rUf_MS1mp%`e8$J!vT4_8!s!FFr~gfmt&psu6I0xQvH0AoXkW2JG+*4 z1#!ko7k6FLvVCCq{f?I(OGm5i23A@+x^8r3*di^Abr9;y6+fU$@fdUx$n}7E;0SJS z#gC~of~_WQIg_ICuM*pe6ap$vA0^w>zy&%~)Kf*@IZ1VU#-nXzS9%oo8Nhjlc4EnjcmlMNKOS`T^HRd~lz7k<78a9%BiMrdw0q9_c|lHY zar5-OTf4}r_s=q1%GudXk=|3-mwY3@jGZ!)8AJGhDcP-d)+0qWMVfMNe3noBZ_k@K z(yl*OKt?+L;yzpYq|=Rg#T*`7k$BR&e*V2obWd3MY|M0j-dXh7z14pkO}Hr=yH|9) z&~f(bSFXPI5gvZhSZv!7VHBC!#?!ndXx=i%=5cW3uR{_`XI(v%g+tAS+Wtu*RY&%S z?!CIXjY)=X`=@W$rTaKt6~Eu+>c4g;uWZzS$ww&_gok*nk1(vH10*&gqDK63o4GKy z3l0trP#kXu#KU2AqV|5wXra*t$sZKr5e82t&$8Tmb)YSo^SjS}j{M|1o47bR0zgiPl5N;QBuV%sYj0?VRPWMzmP18=UT>AueTAq1}PY9MqXN9YEVp&QDhji zK3q%j$a;i2?86((KOd`IoJ`hrGtbF+HdXd|lx!B8N@rq|$}BtbVct42ES4oOG{)@r zpf9@YytelHrEQ~nab=rqskC?^|8zi;Jn{pek}Wl2tn82`f-o%D&E4yulcs;&w7u@33}vIt3=Z!AeYcl@{C zS?BJ(J$?C?DSh>Va2t2hHks({*A>ahK30M0Hg zE)Fes2f9}Fm)x4T^>Fjz;1e3vj~}UoTu$@Dg`~8apJN8oKy9+!%ah;LxO@*J8yV6% z-Tx|kcEdA3$51hO6x(u6Q6~Kh)#gx7-7|q+Nr`eDU)YO{MVl`xZ0l}+um6Rv>$AM4 z)txb654Ip(xh8Ur0ON>C|HBLi=W)q!)54gZ!o3!QV%kT2)7;et)Xr>t?ZOy*KL zW_4?gi=90c=nl-WM(?k?j6JB8H{xCm@xrfP?<=vS^CC@)`AWTfZVt?M9n+{d-gp9+ zBZXE*xn`Mag1TaPii}>;*{$V17xl6=Ih(l(RQII@q6bf!HDNzDo9U5d)n~2t;bf?S z|L>k_hBoo|6AvBsT6TZd+L23tD>inukVFZW(p1Z)kIgT+{ki{p>1F9I;UixASGQUE z?RwXA^nB+;Z3S)9uc!vTrYoswR%Em%!A^ueOT6^&CGgP`Z#>Sf(-c7=j(bT8w&IA6`yT%PVyC*k1WO_Oh+N-_%JL5W4^onVgyep4<_9 zi2hh$GChDrBx7j}Wz2JVtuqqc=Zx~|4*j~gOWrP&cF89pzgPbI7m)hWzeh+I?>@cj z!q~W>n0s(bU;4@@lI|cx1j*lA(Ni!P?_}`GNyo=J_hEY#|Pz#+<~xSy8Lnrn!4owf~*9EMX)!7I+&SAGPPZ z%x5L0%-{H-(Ido-xTYm}Kb}9#afiBIb{dP6^lJM4{+)4mZrw8{5eNrgcAav1 zU)gK3@RjkISI)ep>-nW0-AWbn5xqs}oe2`D3zOW>&D7c?+$0Aaipgz7wJiyJPRp8t zDN<_PF0$hvWhZO zklK2c^*TY;hg1&D=cksY-mR-vGCD7Fu0~~0OIj~Evph4kPUCUocq3~k>z$0d*EOBv zGZGp&PIMkv?Ogq*bDhpR9kndA*0ZhVc{T&ueX-X!W_W+i{PrvL*M!=SM8*=1i~D~* zTVB{ZzE`6pqBG^(gpg8JmuZ6O5wi&G=3fhI9n+@^MA!rcL-(6*^V-y;v+lB?rLPQ& z1&AL&3i-_J5hmps4V<1V1?3YeDz6#;=_x2-IexqcpaCYTNo2-v)t$2E(l?%Q>yAAj zus`y?<@+RyqUh$!-qi)spFGN7mBP9B)gav)lQv zF^z*im%8p;b@-**>yVxMOuwpQw#E8M?~@PLTqf3rz_bH2ssvcJnVB+ztlex1@d_~1 z&7lqp1vrO#haV~T-^y#Q6vTefQ4cMU4WK%Fxij6|F7dOk2L;_McTHL#C6C7Rv)i?< zbSocL=cKH+MVjj+`5+ZJu|GFolnrf>rPy)!V#Vc|fD(wUKEBxX$ZGdp9;>8#(lN6; zhO@*pbH1LfjFRTrD-4N_Ujb@0g!7+<#YWQtRm>KPxvk*yb%U|9V}*-!`E?hCj!rL@*u);ZuI`StgD&YZewEe9(!!!a>j78@ z+k!|j1(7KL_yEo^>c+Vg>^HEUo1?Rjvv)^id_4ISQmqgt&B>X% zpzm=VyZQduW-vN>+IAHIoEG2O8aXjsZAN8#v{*0NP_LYFy#4yw3r@Y(XOC)GiLHLB z=j+?#IPs~k`dPa3LPB4qxXZ%i+m2^hPcAU!ef2JPbDp0c|2X`vEld9Ofj)63Iu5e+ zliE`{xORjz5_Wa3T z1l5nFQeEVvjnj&??R#p^`Wt)3Maz?Zd+j4|#n|46ii(1UcYLS}$}GE7y#a>2oI5yr zSyw=gZ^L^gI@`{1-cLNS)SX2ge=Me-cxfbqT%c|2U}1?ua&~Gf>4jHF z(}BPSV#10agRYjullu5BCw}V$ypcd-O(NZ-f?g)^%Qr7!H)9Fm;h-RumO)-%9)yJ` zFFl2qDX~Am@{I!9K;oweWN{UKetx|B_`JKN*FH%>Mg`(B!1{0a{YSk>zl~`YeqLmQ zN$w19PH-1+kWM)Oa(y3Xh5tw zcFh31Nzm=+sj2_`$se)Q{`;MvJH@bbC!~|V4GjT3E7`v+mZ||Y!fu?@g^BKOz%>$M zLJ~<5BoN~7AepN0MFU#;wyg~|mH|~iXSdll%j9V3!({|^F@TOU9Je>dy8avSAK$#c zDiHzJ1Tve!2O}yb|{lW+VWVA3l6IeE2Z9Y4)F9ZR{t0A1M(^62$+K9I*Gaf!GCl zXW-hvY`6wg0%5+6L)998oTxtDqbnnXnBXD}?80+O;>5+7BZlXy-tyKZderl=%N{s$tk z|NT7J^!GhX3x4_GnzPP}(jcVZ$`-P8|GE*LIi5!yV>b?+;;>>joYnL4l*EM*C(%mOe>=s|SR5Py!OWP&vpndc>;d!}{s z41kuH*?53PS&AJ@peE1oeo_w?Z2&-ozP`Q%){xjI+#!gM_|ZEsIQVkO)$>r~C9Hac zZ8shPWD|rFK`*a0;3J&II~zI(nGs^%W!CZ&nDXLdk-a|wfpG&|n;}aEpqa{win`$a zZje(b(QY<QIXLFJmJ`WDUxr5b8 z0~e%DM}_I{aajBahsbe=qJsnu^;sxO+#Yy zHY02L`#s?hjK=94Po(=gf%S%lh7iI+B<4MrMybONbo@Kibm)8`tkKZaWQqUsm~-zN zbU2WXCm3v9U0uMIXAy!jHUd_+C5j6Qa1{x?o!t~0^+`9sfFuiRB=}uWtk^>+ztU{ObKui*H0nt!s^CC`M zcXZ4KHvl6>m{q@yzU8ix*WF}Xh+!j=i?=lk9PD?})6+w13_iewk5(q2@P)m2u5%k- z9NsVK4)?fu4RaA7O*T!+IeHe`!o{AfRyaO2=@dY@o z9@8O^fGeuM6EjEr+@#_X5xEX=I*8EYY1BL13ROx)L!P0P6PuM~dFs@usBM=O*{JpP z^-EvnGsppYS(SHmGlee;*jbp$OiD9}z^hA>_8YU3lG1w|5ZDOvT*y6v(*$hm%npGg z_GKS>dwUxj8*6J#04={%XQ)QJ*3CL0UuP?*mwwyJg}TLwze=!*Fu`drzRQ-pm!04Az#vuW)8A?khsA^BcdQEV2C>X zGXd};0+1ia<&frM0jJ4}@vatkU>cC7mS|&SRQ+59SD;R(2nw@GfLz83TNFY!sZ6&; z=jCAtJHvVt2htLxPh4JOn*Tni{Q{T<&=<1Xvu6+C zE`kCC>nYzSrbob#grB&uZNEE4i@*RJg*ph_ABuRrQ&WfW0d7o8fT;qE!({|uxM9Ht zl9YVyK^$Hj(CZ)q;7d;Z=5@s}c`n|vJ_<_t9zG@`z6~T2>mfy%)0(>VT@3vcBX>R8 zenJHU*Yq23cZdt*JB0NW7>crgk_;(?rc4)B=t_I{#^D$s$b1Fm5&;n@65Lq)oH!Am zLk)gKg~(pWA3=N>AjJ)vHy6p?I5Z@W3vd8d)|Hin%nspa^E=@(_ul-?at$|mV^Y5W zm0B4VG=T?uZGd8!?XrR?v@Vh-P<^?u>K=vdPO3&jDK)MMMu5H0dy|o=LG>5`t8`L4DB%brxaw&>Mt^Sk$})d7|1$0FMO1fFh8^ z0|g{M3iHyx*^X3pHtQV%@FY0{xr4#1w?G<_hau|?Wi;{na6(W)<)5$Z?Oj22A;mvr zghyhDP!kl?49W|rQ#Cq8OMnlP13m%PE20YGo%|rOyF4?k`w4ukLcdK z#Z@QU$N_UrP}lCgqoJYsFL!@z_8Ghi`XN|C5H7~r!V9;7p<0)v)mN9DlM`x4e7&G?MmE6OUnsJi428|!lWr1@y)7t7Wagub)(#3yP~r43b7Nx zeXMl7K3`b`e{tB#zUoe{Z!(yg#`sMn70BD zIYF5b_UeSM%D zp#*%<#Zqwb%?fiB!TrT$a@cQc2zrc_D9U40T*xUe(J_#_xA&sS)^Ub(Q_R|~U2g&) z()rxIEIBzjD{BHL+9hk<-?T4a3A`p`pwi|h;^X7VIoFgrQO)M$0N55eKN=yue5R zY85dPKi-l9ZcRKoy{SZ-;MgK^XG3&1n7CHF`=4}qA_fdp)If(S2>$k@=!p|24j;Bcs73Sw@!`05F`REqU^+^% zUQ_~TYLH>OENyLxU|Y!NI8%z)G5<*ZacfoW69T{#-O*%z03kzm*`OVvUU5%GUSp<$EL88vEzkVJ1 z8Z6KBP}va)dHozAV1YS*HxdpQ+g7y(6Vi2GH^*HD!WjyR**Q4?Mvsk-zSf4Ir5mch zPggC{w*9SfhZ;bZMS&;2be*`;qLPxopqX>s**Q-mHK4Mx5?)=neB{u`n-ci?xA1Q9 z*6<;*O_+F>)s5;OPh^g1`%*1b7Yg&(D8~Wv z)r?1SMfsj0u3=h$Dv-=WG&2xBGZ$v;-#j97cn?2f2>R+BJ9gj~Mso6$m6hjaXOUD1 zSucngrFKuaY<>`fbap1;L{EEr`}_ChD4OuX-^{-LVQ>fi(aWv?P-Lp?7QClyg{|Lr zc6CKf-FjM92K@?GH#dTAYJGljHjUVg6F(K3uM{le#u5(Cam^440!NytKXC%YjvdP% zgNzFz1iXOm@l%e-QWHtNXsEg8I@)*LSN zX!^$wqF{zv9FA>La`LXm2gfrs;TuLsmqF3!JLV_YYISyYqK*`Xf}FJkVXl4XK_YSb zb9ADukAf&pUfA;d^r?`!uXklwP~`+&lPJa_p>R)E0+rT*{~ETJvT}02Knw)tf?)1Z zjBp}2!*vYESkt>*1b!Sv9H=`G1O6@$H$6R#9EiijGS$2Qt!Bs_T!hO#$`r6MMdvuA zQZ*1>^AH-*0L=gR0bYsFH*-vn#=~LV|->raOZG zr=XzVE5%hJv~^`O#I+bc6SQbgL0mOs$lv>BkB-aj+qV%RiH71&gj}oviw5+P3Cx>U zlUi{gmtf3OgCbBF?MK%C)7`m;)tr89d=Hb55izM5G9)1#FymA*nuLU55JELNIAlWT zpwcLZMma_$?4ilwoza0&Qo9mGiY=#dXj3AMYIi`VDevdmnfd+oUf282`_J3uGS{H? z^Zh>0v(~!rwbs2B8uy4=#1~~W)oZ3AMc)%lk?!g#l=4faYK4F+03#CyN31EkG}yhW2wikyp#1P=v)_G z&9lp!jAo~N?SNn@FvKI~&TljNIKS8zOsu%Y&reKlA3i+PRP&Yb*s+^IgdQ`qlMR9U z|5;X4)OZF_43d{zTCeX3M!Vtt)=x&5KWo;4VSROaJ~+zYg5;j%bC)bRvgBND_Z5~K zCk|-6Mj^By#>iqYtrmka?2v6(s`INqml!`AR{mLg@2;a0J$ofDa9*SKq;v21eTOFt zpw$$i)u&Hp%U?!(nh+A`AgERV?hFhJq%Tb+5+$0o5Fh`T7m1`CRqp?rKQLP`;?RhR z6I<~AypQpK?X-Zmufa#>*TGXLdVEFWT-siZ}qqSZGh|n0EH}xeA3sE?3g$sW@_ID*2g2rLC=|3QBK%w6lb5jm&mtdYUcscC3$#K_P=$I>y2XCz140SlgT{``pfXTFCSVaV+zmprYpgDgG( z5wO}3@+0b~N^%mcEFC~F=pZ%h8P`oy)00rUcK4@Mt8|{6?$)ua+7p5XILJKnIPsk$ z7TE4;Xn9}V3gILAZGZaiaT>ZOAX7oi87=&y*B9_lHLqU}8#x+@&J%?`Q45coLnn$Z zuL%>NCB|D?E?=4Mtvntc9$u@(b$KhF{Gn_01oRGwHF_V`5{yuzEL19WB#3JMBf-W0 z=06+NNoMl5+V$h5l+v7pVSHnRlO^=Xp6PUC?AjxdgT#32 ztNqNJq($5%-)9bgESFs-hV}oX^FR2_=_m2Ib+$8SI$Yj3d~Zz;X7deafI;JvRbL;$ z?$x{Y-~|XiLb2A)Zm^uhusu2taKEE-3vQua;6=AtYOPijvbdsMu2Hsqc|zm6cP}+` zh+QHYU#^7zarCcKbL{fM_~UDD7BshwZEPXmKBl2tGT!TU`}KCu--_ORXnA9r5jBO4 z<(kRU!b9sSQb!!ZcPy-`WCW4>z*n>fj$D-ZtxtO=;%o$*)1GZJhKU=H5j0&4Zu87& z-qHAS`ssTYSKZrTI#jC}`K6v8k6VK%M-97=Yk;FK@G{?jW?gAE>4?&R)WXV*nIGEC z9q(r4ud6U`{Ly&rQLqC)|k2T6lc&CrlZ}v0$ts37| z5s>;Q#nX{%wOuWE+cx1|#Mj3&Hq68%o}k~#%@BI(ozPPB{^|becd$jx2f6?z%L8n3 zn;MonJB0uQ;^N}!PT6mqSRzIv8k#0vxM0p8K4oAU2f&|G;jg>@44jB>YRHkGfJ+{M z&R3SIZ|?Xw$qje0pM?~cF!ZWdC-W(|S{ebbrZs$f;(M12D>11p?7e0~xP^Syj2V=6 zILnPkjtm>;dSKtaJIq=v&C|ddtu z^m(~g zklON|xb=r~3&G9x+ozs1&1m|OvyrZx3>>nqlNk6H^;Bx-9?R%nb}^Du1E4Ck|Q%hrPY{N0T&Z_#WE(Yc6WeAlj7E8zRY zmlNvXoq~EZXc5P2bvN<^L8xuq0r`G)qPzTE8qokF@{19TvdQz#ZiHPBQc*zS>unAm zb!f9be)2?Pj>upAvAwa)h!ol_E+No@{_LhcZDz%WqZvF>x=I6x(waMJGlCOkQ@Mf7 zqj&r{iRNRL^~>i*mT)mx@63cz1|6%C*mWhMF&j)fH?pDSbEQ+z?I6CFr!}~dqVsp| zY-nh>qGvm`Yiz)p(z9LE)f*PZ8Xn9GnWFhA_O2OT#>a7wsE=}cwL8=rB3Xu7I7bxt zl%z&@ZGUX`^_Y*JhTx3&G%^)d1(7FENyM3zmH6IE^>WWhbpAA$@2Tq<8xa-N^uXS+ zn_To#r9ZetFaT8PE??}lVuhE;r5%ffk#pCxC{ifekL6}@dy|rri3HZUxD4?WiKrld z;>=2dPE2PeZD?Q4$@e)eo5r7uSWag@GiQ!B$jY8S&w5|Z5gcM@h+^9|(~(+9mD0eL z&_-PY0w5rt&}pj}3C{U`Sl@KEW1DX9Of!xf`ej3SL)W5AtsRZvmCov;P+ ztO`+Bron#;a#!!!|8+%03V5B73*do~jv0TWSsPIF!z78M-T?38WL>QH<=&R%s~F6{ zPlY0LvuwM7uSX>ZYna!!;VGE1AjyL%0c~w}@DCRaxW07RGOiz5DwSnr+3!1x%_YSc zq^r6oE`Z`4zwT|Vx**@tbHL5k`dqnuuW?RfzfgKL<>q0BhQCTB__}G)#pH?HazlAn zWqu)H5|4hnU!Tz8+bzUszK(i{(WEDT(Kc=o()+4wFm(3W`4B6~;1d{H+%t=TzrPEX zWt@SzQ53D!7+4gt5o*s+HsD@=rH`gdWT_1@`5m@M-HPK&F4|IC$s+M(V1 znTQ5xh4UX2a+c89T^pjd>96~Uvvgx=5ER8bvsu~EW5;}_DFl+iUgyc1S_+xg=QzHOvo*i%G1K;0D8qM0=LN4*CaN=RXuT*1~6B z&y#Swy$;t5xet(GQwxFf28-YTps>9oQsPd{JS?^>m24{x^bV|NQ z!pB$yA`?nZADebd6CtbcM`p4sM-n=ogaGnCM>*M&7XsL}HwX{cg!18o`O;Skq zC#=+9Et$~vabxyWSI;>*zVPPF|3WZEp zP0?QCi-B!^WKUJbA?un*>w!+N;z&|oMhn$5;F#43CT8lzoFGsWw6c!s+4Uv|j^x=f z;fONSXFLV?oy2AO&$#+L6(X=Kz^0(DTs{C=hL0y#P!=%Z?&^ykrbkUzGzGy3@ji<8 zWRMnSlskx~!+%Dp_WGOyCMA%12G6u1!Q`fVYJW{j+kzPti4HU2-FH!D2I$sn3bp10 zns05lQ0C7i-2(B~{9_jb+X&htUY4)|3MbYSnUr?Zs2{J$h7Y_MX)2E#6_(PgfB%Bk z4G|F$<%mjYJEyfWxggn<9E0|<|So~;zu zBbc^e+Pi|AM=U(X#uIB-bUOJ<&U{VX;c}yE9oiHXoJ{}XFt~ADwL#3+%;mFL) z$;#V>;B+AaPr&wK;Abj-smQ}saJb7~zaAg>w@*zikzJ7 z?ty~~QMd8A?(mdEG1x@-VhtURgGiwJ_k7{@i*LMbTuaNFgzXgtWO4NnZf%t1AThDK z?{H)_?O}_;M(r8UzyF3?PsvWL#5XV{8#vK%Fq@}3IXS_C4j3@tdia;nKVH;-h!?R~ zT*Fu|$Yc(w#(qb#M#wnaGCz-e{W`d#M;;y@OdE7#VF6)$drR{!aVhdC7l03*>GPOS zj_E~PNCqhLcgW%~Kn%-m$768z@q~S~N1~VuncHmVx#9JlLGK-kw_(VitE|Poy&jZq z;Kr|9aYhlwGY#q1xQQrBK;4Qr)Kz%;!ot-e2h&!z+cf09yriU!lta4w+t@-OK>mh+Rf!z@8oWsec!y#$Oyw7RXS@X~>u6#t&= zI<+EbJ7$`-RHL~$y1s>7LlDSi!pz9FeK-to{$WJZ@K7GE&j$z-vyb^oP25%#Pnh{q zkHtkyk81PGw)ZhHF<-{->>~L}wY$@Qf1o#E!?lMGlS$JLzB=#~9^^d)10GC~x%C4) zBxMc_IH8nP_g?Y-J=zgOzOd8E`Uax8%bF(S%AqN25{k&?$hgxyYh3N$kM=atWKVFV z?>`Ufn&H+t?$Q95upG;8!fo_Np1D_9d^*of+a`}Os);En<6?d`#>pL`%=#7rVgYZ3 z4%BXOrWbV=Pg5_&r-ti}IYqYAL%p3?Y4Plyy%Gnw!Ag-TihxVN*-J!XEUbtd0#o&> ztZW{nfPDFIJ^^fjTn%`3w8_;6XefVoGAbT%JQ9vpX?0^tEbR9kKAcSOK&(C9+}xg; zL~wCco4d4kn(IA^E54xgKnRsRjb_@q3)!Bk;1y}g?8?hkS6z4aHC_@C@KmHS!Mt{M zJ)~c%maI=I5Lkn6Pio6$mN~d-ueZwvDj`_ir9_EHCKqYLZFs>+8?sf*ew6&_97=L|?o3 z_y-~(AxY_W2DpwBkcgVHsC2+RN6coIbu{6>4P%HbVJe@7d!`uck{Y+SrV{2$|nO znx8|8hBZcSqbw`=;0TKbHnCx$cxK6%*!d&iBJpwF7zW61CBHB#GrDla93Z;?H4m#W z_F~djh(!cb$9-&VyDMpt{?MMrEI-mCoH@$R#aF?hr6!cM%$Yq~TaP()q>L`7rix&w zmoR|$Ug1U1lOaR1`r;CW`^2|?lccIrtROowDk^&|I_d2efie$Y@nRVCY1okt)+cKG zzlOAr_7`8Q<|gu^SVT;t3eg5tifC}3nsEA}w21pxIyZj$d@>;S@6T6=BO{TVGBq|{ zOYTI>t6#~B9@gCsT8RIOzwc1t9- zaGx+snHwv$Jk=y-D}>+vlp$Ftvz@4vN`;e|3Xy|6^TBkZ Vm%V?D+aR8A#?;x?@m5aT{u_iUAR_<( literal 0 HcmV?d00001 diff --git a/book/figures/vanderpol_particles.svg b/book/figures/vanderpol_particles.svg new file mode 100644 index 00000000..5ecf8e39 --- /dev/null +++ b/book/figures/vanderpol_particles.svg @@ -0,0 +1,5198 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/book/index.html b/book/index.html index c9d0068a..02b02f80 100644 --- a/book/index.html +++ b/book/index.html @@ -255,7 +255,8 @@

Table of Contents

  • Stationary Distributions
  • Extended Example: The Rimless Wheel on Rough Terrain
  • -
  • Noise models for real robots/systems.
  • +
  • Randomized smoothing of contact dynamics
  • +
  • Noise models for real robots/systems.
  • Nonlinear Planning and Control

  • Chapter 7: Dynamic Programming
  • diff --git a/book/stochastic.html b/book/stochastic.html index ad055eb3..d5e01330 100644 --- a/book/stochastic.html +++ b/book/stochastic.html @@ -67,25 +67,23 @@

    Underactuated RoboticsMy goals for this chapter are to build intuition for the beautiful and rich behavior of nonlinear dynamical system that are subjected to random - (noise/disturbance) inputs. So far we have focused primarily on systems - described by \[ \dot{\bx}(t) = f(\bx(t),\bu(t)) \quad \text{or} \quad \bx[n+1] - = f(\bx[n],\bu[n]). \] In this chapter, I would like to broaden the scope to - think about \[ \dot{\bx}(t) = f(\bx(t),\bu(t),\bw(t)) \quad \text{or} \quad - \bx[n+1] = f(\bx[n],\bu[n],\bw[n]), \] where this additional input $\bw$ is - the (vector) output of some random process. In other words, we can begin - thinking about stochastic systems by simply understanding the dynamics of our - existing ODEs subjected to an additional random input.

    - -

    This form is extremely general as written. $\bw(t)$ can represent - time-varying random disturbances (e.g. gusts of wind), or even constant model - errors/uncertainty. One thing that we are not adding, yet, is measurement - uncertainty. There is a great deal of work on observability and state - estimation that study the question of how you can infer the true state of the - system given noise sensor readings. For this chapter we are assuming perfect - measurements of the full state, and are focused instead on the way that + (noise/disturbance) inputs. So far we have focused primarily on systems described by + \[ \dot{\bx}(t) = f(\bx(t),\bu(t)) \quad \text{or} \quad \bx[n+1] = f(\bx[n],\bu[n]). + \] In this chapter, I would like to broaden the scope to think about \[ \dot{\bx}(t) = + f(\bx(t),\bu(t),\bw(t)) \quad \text{or} \quad \bx[n+1] = f(\bx[n],\bu[n],\bw[n]), \] + where this additional input $\bw$ is the (vector) output of some random process. In + other words, we can begin thinking about stochastic systems by simply understanding + the dynamics of our existing ODEs subjected to an additional random input.

    + +

    This form is extremely general as written. $\bw(t)$ can represent time-varying + random disturbances (e.g. gusts of wind), or even constant model errors/uncertainty. + One thing that we are not adding, yet, is measurement uncertainty (this will come + later, when we discuss state estimation and output feedback). For this chapter we are assuming + perfect measurements of the full state, and are focused instead on the way that "process noise" shapes the long-term dynamics of the system.

    -

    I will also stick primarily to discrete time dynamics for this chapter, +

    I will also stick primarily to discrete-time dynamics for this chapter, simply because it is easier to think about the output of a discrete-time random process, $\bw[n]$, than a $\bw(t)$. But you should know that all of the ideas work in continuous time, too. Also, most of our examples will take the @@ -210,15 +208,15 @@

    Underactuated Robotics -

    Here's what's completely fascinating -- even though the dynamics of any - one initial condition for this system are extremely complex, if we study - the dynamics of a distribution of states through the system, they are - surprisingly simple and well-behaved. This system is one of the rare - cases when we can write the master equation in closed - formLasota13: $$p_{n+1}(x) = \frac{1}{4\sqrt{1-x}} \left[ - p_n\left(\frac{1}{2}-\frac{1}{2}\sqrt{1-x}\right) + p_n\left(\frac{1}{2} + - \frac{1}{2}\sqrt{1-x}\right) \right].$$ Moreover, this master equation - has a steady-state solution: $$p_*(x) = \frac{1}{\pi\sqrt{x(1-x)}}.$$

    +

    Here's what's completely fascinating -- even though the dynamics of any one + initial condition for this system are extremely complex, if we study the dynamics + of a distribution of states through the system, they are surprisingly simple and + well-behaved. This system is one of the rare cases when we can write the master + equation in closed formLasota13: $$p_{n+1}(x) = \frac{1}{4\sqrt{1-x}} + \left[ p_n\left(\frac{1}{2}-\frac{1}{2}\sqrt{1-x}\right) + p_n\left(\frac{1}{2} + + \frac{1}{2}\sqrt{1-x}\right) \right].$$ Moreover, this master equation has a + steady-state solution: $$p_*(x) = \frac{1}{\pi\sqrt{x(1-x)}}, \qquad x \in [0, + 1].$$

    Plotting the (closed-form) evolution of the master equation @@ -255,14 +253,13 @@

    Underactuated Robotics

    Stationary Distributions

    -

    In the example above, the histogram is our numerical approximation of - the probability density. The logistic map example had the remarkable - property that, although the individual trajectories of the system do - not converge, the probability distribution actually does - converge to what's known as a stationary distribution -- a fixed - point of the master equation. Instead of thinking about the dynamics of - the trajectories, we need to start thinking about the dynamics of the - distribution.

    +

    In the example above, the histogram is our numerical approximation of the + probability density. Each of those example systems had the remarkable property that, + although the individual trajectories of the system do not converge, the + probability distribution actually does converge to what's known as a + stationary distribution -- a fixed point of the master equation. Instead of + thinking about the dynamics of the trajectories, we need to start thinking about the + dynamics of the distribution.

    The most important example of this analysis is for systems with linear dynamics and additive Gaussian noise; for this case we have closed-form @@ -301,10 +298,11 @@

    Underactuated RoboticsKalman filter.

    -

    Taking it a step further, we can see that a stationary distribution for - this system is given by a mean-zero Gaussian with \[ \sigma_*^2 = - \frac{\sigma_w^2}{1-a^2}. \] Note that this distribution is well defined - when $-1 < a < 1$ (only when the system is stable).

    +

    Taking it a step further, we can see that a stationary distribution for this + system is given by a mean-zero Gaussian with \[ \sigma_*^2 = + \frac{\sigma_w^2}{1-a^2}. \] Note that this distribution is well defined when $-1 + < a < 1$. In this case, these are the same conditions we have for + deterministic stability of this system.

    @@ -317,11 +315,10 @@

    Underactuated Robotics -

    Given how rich the dynamics can be for deterministic nonlinear systems, - you can probably imagine that the possible long-term dynamics of the - probability are also extremely rich. If we simply flip the signs in the - cubic polynomial dynamics we examined above, we'll get our next - example:

    +

    Given how rich the dynamics can be for deterministic nonlinear systems, you can + probably imagine that the possible long-term dynamics of the probability density are + also extremely rich. If we simply flip the signs in the cubic polynomial dynamics + we examined above, we'll get our next example:

    The Cubic Example + Noise

    @@ -409,17 +406,16 @@

    Underactuated Robotics

    Extended Example: The Rimless Wheel on Rough Terrain

    -

    My favorite example of a meaningful source of randomness on a model +

    One of my favorite examples of a meaningful source of randomness on a model underactuated system is the rimless - wheel rolling down stochastically "rough" terrainByl08f. - Generating interesting/relevant probabilistic models of terrain in general - can be quite complex, but the rimless wheel makes it easy -- since the robot - only contacts that ground at the point foot, we can model almost arbitrary - rough terrain by simply taking the ramp angle, $\gamma$, to be a random - variable. If we restrict our analysis to rolling only in one direction (e.g. - only downhill), then we can even consider this ramp angle to be i.i.d.; - after each footstep we will independently draw a new ramp angle $\gamma[n]$ - for the next step.

    + wheel rolling down stochastically "rough" terrainByl08f. Generating + interesting/relevant probabilistic models of terrain in general can be quite + complex, but the rimless wheel makes it easy -- since the robot only contacts that + ground at the point foot, we can model almost arbitrary rough terrain by simply + taking the ramp angle, $\gamma$, to be a random variable. If we restrict our + analysis to rolling only in one direction (e.g. only downhill), then we can even + consider this ramp angle to be i.i.d.; after each footstep we will independently + draw a new ramp angle $\gamma[n]$ for the next step.

    @@ -435,6 +431,75 @@

    Underactuated Robotics +

    Randomized smoothing of contact dynamics

    + +

    It is interesting to think more generally about how stochastic dynamics interact + with the contact dynamics that we have begun to study in these notes. For the + stochastic rimless wheel we studied the dynamics on the apex-to-apex map, but now + we'd like to consider a more typical (discrete-time, with a small, fixed, time step) + model of contact dynamics.

    + +

    First we have to think about a simplest reasonable model for the process + noise/dynamics. In the multibody appendix, we develop the time-stepping dynamic + models of contact as the solution to an optimization problem, which strictly + enforces contact constraints (e.g. non-penetration) at the end of every time step. + Let's use that idea again here, following the ideas developed in + Suh22a+Pang22.

    + +

    A (stochastic) block near a wall

    + +

    Consider the dynamics of an unactuated 1D block with a wall occupying $q + \leq 0$, such that the physical dynamics is identity if the block is in a + non-penetrating configuration, $q[n+1] = f(q[n])=q[n]$ if $q[n]\geq 0$. The + dynamics within the penetrating regime is not well-defined physically; yet, + applying the quasi-dynamic equations of motions from + Pang20b gives us a model that defines a minimal projection $\delta q$ + which gets applied to the system to project it back out of collision via: + \begin{align} \underset{\delta q}{\minimize} \; &\frac{1}{2} m (\delta q)^2, \; + \text{subject to} \\ & q + \delta q \geq 0. \end{align} which leads to the + following deterministic dynamics: \begin{equation} + \label{eq:1d_projection_solution} f(q) = q + \delta q = \begin{cases} q & \text{ + if } q \geq 0, \text{ (no penetration) }\\ 0 & \text{ otherwise. } \text{ + (penetration) } \end{cases} \end{equation} This model extends naturally to more + complicated contact systems.

    + +

    This now gives us a natural model for adding noise while respecting the + non-penetration conditions. On each time step, we will apply a Gaussian + perturbation (e.g. Brownian motion), $w[n]$, and apply the dynamics $q[n+1] = + f(q[n] + w[n]).$ In this model, if we start the system from a known initial + condition, $p_0(q) = \delta(q-q_0),$ then after one step we obtain the + distribution pictured in the bottom left:

    + +
    + + +
    (a) The block near a wall. (b) The distribution $q+w$ (green) and + $f(q+w)$ (pink). (c) The expected value of the one-step stochastic dynamics + looks like a "smoothed" version of the deterministic dynamics. (d) This has + important implications for gradient-based optimization Suh22b.
    +
    + +

    In some stochastic optimal control frameworks (and almost all reinforcement + learning algorithms), the optimization objective is specified in terms of the + expected value of the cost/reward. So it is very interesting to think about the + effect that the stochasticity has on the expected value of simulation roll-outs. + Here we see that, even after a single step, the stochasticity has the effect of + "smoothing" the hard contact dynamics, and giving a form of "contact forces at a + distance". Suh22b studied the effect that this can have on the + optimization landscape.

    + + What is the stationary distribution of this system? +
    + +

    Interestingly, reinforcement learning (RL) algorithms often explicitly + inject random perturbations (typically in the policy outputs) as a mechanism for + exploring the policy parameters. When coupled with a deterministic contact + simulation engine, the resulting dynamics look like the simple stochastic example + illustrated above. This is one explanation for why RL has performed surprisingly + well in problems involving contact dynamics.

    + +
    +

    Noise models for real robots/systems.

    Sensor models. Beam model from probabilistic robotics. RGB-D @@ -468,6 +533,34 @@

    Underactuated Robotics"Chaos, fractals, and noise: stochastic aspects of dynamics", Springer Science \& Business Media , vol. 97, 2013. +
    +
  • +H.J. Terry Suh and Tao Pang and Russ Tedrake, +"Bundled Gradients through Contact via Randomized Smoothing", +IEEE Robotics and Automation Letters , vol. 7 (2), pp. 4000-4007, April, 2022. +[ link ] + +

  • +
  • +Tao Pang and H.J. Terry Suh and Lujie Yang and Russ Tedrake., +"Global Planning for Contact-Rich Manipulation via Local Smoothing of Quasi-dynamic Contact Models", +Transactions of Robotics, vol. 39, no. 6, pp. 4691--4711, December, 2023. +[ link ] + +

  • +
  • +H. J. Terry Suh and Max Simchowitz and Kaiqing Zhang and Russ Tedrake, +"Do Differentiable Simulators Give Better Policy Gradients?", +Proceedings of the 39th International Conference on Machine Learning , vol. 162, pp. 20668--20696, July, 2022. +[ link ] + +

  • +
  • +Tao Pang and Russ Tedrake, +"A Convex Quasistatic Time-stepping Scheme for Rigid Multibody Systems with Contact and Friction", +IEEE International Conference on Robotics and Automation (ICRA), May, 2021. +[ link ] +