From 665902822406cd590c95584b64af0d922eda1dbb Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Petr=20Veli=C4=8Dka?= Date: Sun, 20 Apr 2025 22:08:16 +0200 Subject: [PATCH] prednaska 15.4.2025 --- parametricka-inference.tex | 28 ++++++++ skripta.pdf | Bin 324474 -> 339968 bytes skripta.tex | 1 + statisticke-funkcionaly.tex | 128 +++++++++++++++++++++++++++++++++++- 4 files changed, 156 insertions(+), 1 deletion(-) create mode 100644 parametricka-inference.tex diff --git a/parametricka-inference.tex b/parametricka-inference.tex new file mode 100644 index 0000000..77c1558 --- /dev/null +++ b/parametricka-inference.tex @@ -0,0 +1,28 @@ +\section{Parametrická inference} + +V této kapitole se budeme věnovat problému odhadování parametru tak, aby získané rozdělení co nejvhodněji pasovalo na experimentální data. Hlavním objektem zkoumání bude rodina parametrických modelů +$$ \mathcal{F} := \{f(\cdot, \vec \theta): \vec \theta \in \vec \Theta \subseteq \R^d\}, $$ +kde $\vec \Theta$ je parametrický prostor a $\vec \theta = (\theta_1, \dots, \theta_d)$ je parametr. + +Je zřejmé, že ne každý model je schopen pokrýt všechna možná rozdělení vyskytující se v přírodě. Musíme proto aproximovat a umět dobře odhadnout, kdy máme ``dost dobrý" odhad. +Budeme se zajímat o odhad nějaké funkce $T(\vec \theta)$. Například pro $X_i \sim N(\mu, \sigma^2)$, pokud naším parametrem zájmu je $\mu$, stačí volit $T(\vec \theta) = \mu$ a $\sigma^2$ se potom nazývá \textit{nežádoucí/rušivý parametr}. + +\begin{example} + Připomeňme si, že náhodná veličina $X$ má rozdělení $\Gamma(a, p)$, jestliže + $$ f_X(x; a, p) = \frac{a^p}{\Gamma(p)} x^{p - 1} \exp\{-ax\}.$$ + kde $a, p > 0$ a + $$ \Gamma(p) = \int_0^\infty y^{p-1}e^{-y} dy. $$ + + Parametrem ve smyslu úvodu je tedy vektor $\vec \theta = (a, p)$. Chceme-li spočítat průměrnou délku života (což je jedna z věcí, k modelování kterých se používá Gamma rozdělení), dostáváme + $$ T(a, p) = \E_{\vec\theta} X = \int_0^\infty \frac{a^px^p}{\Gamma(p)} e^{-ax} dx = \frac{1}{a\Gamma(p)} \int_0^\infty y^p e^{-y}dy = \frac{\Gamma(p + 1)}{a\Gamma(p)} = \frac{p}{a}. $$ +\end{example} + +V dalším textu uvažujme náhodný výběr $X_1, \dots, X_n \overset{IID}\sim F \in \mathcal{F}$. + +\begin{example} + Uvažujme $\mathcal{F} = \{F(\mu): \E_{F(\mu)} = \mu \land |\mu| < \infty$ rodinu modelů s konečnou střední hodnotou. Potom $\bar X_n$ je konzistentní a nestranný odhad $\mu$ a $X_1$ je nestranný, ale ne konzistentní odhad $\mu$. + + Dále uvažujme $\mathcal{F} = \{F(\sigma^2): \Var_{F(\sigma^2)} = \sigma^2 < \infty\}$ rodinu modelů s konečným rozptylem. Potom $\hat\sigma_n^2 = n^{-1}\sum_{i=1}^n (X_i - \bar X_n)^2$ je konzistentní, ale ne nestranný odhad $\sigma^2$ a $S_n^2 = (n - 1)^{-1} \sum_{i=1}^n (X_i - \bar X_n)^2)$ je konzistentní a nestranný odhad $\sigma^2$. +\end{example} + +\hfill \textit{konec 17. přednášky (15.4.2025)} diff --git a/skripta.pdf b/skripta.pdf index fe859fbb062d042114d3ec3f45c0413fe1cc4118..c0276db7d2f69df3aae16035267118cd5a9c2c9d 100644 GIT binary patch delta 46662 zcmZs>LzE_3w5*$~th8<0wr$(CjX!PMW~FW0wr$&YkN0lp+;MudvAT0bd^6(X1lfNN z#XlIh2?YBvE#VQE6u`{E#LmYD&qoSXr$NW zug~9Pl|%qsEnukm_HK6<9^mcxcKPT+P#OK4{Ix%Pz9$Ke50K@+;jJu&eC_dge6C*E z*};{xrq#bcPg;5E@X;C}x8HsLnHl4_yoK3+bOE@t^dDqFVm$xp?V{|Rpy;7@=cHOC z#xuI_-Mj7ayoaBPKl2~=eo-SUhZiS9g-y^jGh>8R#+wwxbLu$ssLYThMbHAtR#`fN zrP%)=*WacI0xa}bqR2EUiir--1iNq~HjHPck1k9{=c}%eJ5=GmuTLj*0Uj!Rf*l#0ju1@B`&DhQeg=N0n682i^(JTK{9={)0Lb-3r!J;XkMBqt>#ocqEi0bh zx+X+JM7l(_Oq%Of-umL#Q?f%gT$LCpG4pGtO3po8SK?Be#X42i$Lgj?L`|kd8OuUP z7A({m|3+65q-OTVC%*@FsjEoo`w{QFiY9p|K`u0&cRKJDhv zIF60qK314oEfkx2-eev5$J$!r!jY~{FxuECZT7x?551)?w_}kpuq668!wp51@o*>8 z#*{nlxR)p1v`tf#Zf?)VN#`ihk^PwrOkM;K)Ve7jwnWIK!g+T{is4`Zz z0N&uYGEf*MGkf@7Zic8x2>Ju->IEBGe7~V%{~S2F=Cohux6}P7QE)GaB?QMmJ?vzw z^@awRn8!Xt4sQ;z0qyu(lKt~W;OpKFsoiVuZ2@&q1AABU8A|tM@;!Ny0do{pt3KSaMNRHYpuKmrZ0SO2doNB2tNv=KCMA0ItVZ;bgzpQZ1|eobHs?0 z1c3&7^=J^7w}l!ej`($p>sV2M`tfW^-yc$Hzd84r)y{^~H0~?c9s^9>^Hv9Y0IqGM zqo;1Jw5iw)&I2lY+uE~`vc+*3XljXiQNh1Q6ny%fQgN^0rifh#oh>mlpp1RXkdo!` z8iwXK8w35dRF|8ERcseSdC?MA$It`q`l6t+$!+c`%dkO~D2s&$0JaFpB%3as4<9VuY!=s$Jc4kH!8ag9Fxg;pGUgnc zrJ^KJ!!v12AIONogL1D@5zQ^|V&|>PFSh=w@0?FKMbse}p3vDwFc?*2G8$li8+ zC1ZgsFv4xQ{$_o_vg_{KMUmnCs0dr2(_pG0peR(kdrulF+?yyoW*`$0u-?r8#%0hL z@7g9_bMiNzA%c;Qxi$cJ(sy+Y-hauo>91afDP~GD-!GBR%#txa*`MvTFdlM6MCRoM z&!;~YAkO$-7(LGhe?gKCLW8Nb07RxVOUj`}Vz!4GWp zu4@KRNeq2-hW>Y1YD(rH03KId1!n0f;-LcFaN^GQQlg&=(h2luTCHmsB|qEhq&ouU+Q_q0OeLtfeSCOF!4(ZOaF50XpFf80+-suVTXM2irsI9?Nd8U-KK*-fQ4ldza3T8pTzLy0^WMP-+($Dn{+^r}&omiLwZ5o)?9x zzXGuNX11_s-&t3?rnl)$8gC`utQ^oIMj zl8#?5&}|uo0Lf7*u<;e)FsW=x!ZI_kYn1kOFGy*SSmJOOCak#`D1r--#zn2zL=Z6I zkNC%iQtaRg8hHj7$GHHrOh3U*%*sCEEws8Wsxq6<(v6vcgJ9ij5|ln=`D4sFLao_2 zs60;*ZXT$3;>YqQe7*B-wUIIml0#s22?ZL8?mpmrfYqu_cm9*&!Y*V!EY&%R=H37_ zVlm;dzh65vA%DgMWIvH=|026{{EZE|;Tl|td;uI!Y%^U6u`L0>20q}T$DjHvHn2Vn&F3FW}>H zvwDH|HAF*|&UB#DU4~Kaye7Bl?Dq6|R+_cDmc+Q;BvdQg-T;>QoOmFPq7Zv;&pD_lnw1(>$T zE(4!r>g1RHtx>}|%Fy)fL=$gHH+eq>1XK~kcN_D3AqI3MRpm?H(Q#K?)}zg48GLD* z+wU@B1zf8sc9N`cj`xQH+eVZWG>VCD>h%~LvQr_z@Nk#Bg^T@ES&$I${CU2d3r7_X zV}vh66wyt5st+p0%0UsGQFTz4uo5;ES5oezf15!2!9nyoAiW$^hVvY%MDqax5D=AJ zhap;eNfeuhnvLm=XQ({g&=O4Lb$BiEt8_!Yfem$$|B4UlUFa2hco8@kItW4(@Ba}j z{7cVC**5Oav**|^{bSMDQ40(UOLityk^V+;ly~~j+h)xDF~vs?B!3>>)~YpIdJu=( zD4Xhq{M*>&@!zknZtgSMT`x5T5GO`Wyq+VY=0Cwdrp`IuoaO`a+6;l|tF1B)-nN`; zd+1xY61P{{D7ZVXYK9+f;Ul@NeI)DSCBUgI7m6w#J3{JGOOY_rwk9?9h@op%;bSw! z+5*8t&Z+0+>-ggZ$d7kWpuaQFHL6rM=8bq21neDsJZrIXY?B*89ZNgEkvd}v#TNqAsV2EOr$^=~JE1CEM5#m% ziMabL)f>4eR;h*7HGmR8$-9UY|Dcj#htrYYu^lA}pmD1gWs&`{WTIaOY0?#)Ce4>o zw&FZ^u~{f-aWgqPHS@W8uimqU)80M7UTyWp&QhaZ2cIbpH_#|h{FYVbLp(7SFm$+k z3G=!_5gyl;^S(HzYzK2*?N5$QQk(LssUa7|kc@J441$l5@K+D8J_?ezTi$2BAl;do z%crK_bIWsyzz;@SU9>I6n&Br#g4;b=v1T-+^GFn4fE%&Vll$31d@?0bo5RQn+?%+@ z1rz0cxH-+a1Xs2}zuN>tOI#`Zq9a}l0ZG@&SS4p>X?!-};)Q+4>JXn2XhbauoQk#F zaJMCiXgxYiibV(*JI8~W#Dr~KFWtEDC=kr1F<}C7;B^a+gH;G`BN`7Vmxa7H*1^hm z=$&P-@9x+n*qL+C!lL5fV+#jVWxVAgu+4c+sYaH65zY4&*IZQ*l~z-Gw;ZN#xXg#i z!M={CtoO|C^bBLHfAc8~8orur54N5+SG<9e64N1kG_eEhFZK@z4#?*VA zy*W9UP5(kj#50ZAK)s{c$O5&sW3ZnGwZ5Yr2N$&Ijs63hgUTxlwvm((;d zz}f)?yUhhWU9UjSPIg*b33NXJ-MaR3D_VB9%=D~H5|f2exG=fo)-=vn=?2f*`-^yt z+C@lcbn-n-=9sND%JrL8WH^?g4Gjf&-D#KH-h5Wn5q54(6?{}&2h-b6YWQ{Q3qNNQ z)#-fJpi^AJvN$Jxt^t^bmTT3W6b+n=+^0WNoa_OB6xE~`Q`D@{f^!DIo2mmUZY^*9 zKDxA9AdHwTxp%>0ZM+S&?m~pvI9_mcK)fxz$$P~!E{&O|yOi8k{Enxocm&r)_zSA} zyC_NHMO7pR}=G&*_%TggFE)Pi`+gu=inr6tFF$7O3MzU8+2-y_1EWf5Ve- z79mSdJ@l`&5&QrWxPX)+T3-R2ZPS2ic<8VHO zYLDsa!W79M7}3JEYLDK`N6zeN!>1zzH|=jw&R|YZzR;KX>sz>e>XB;2s z+PFFz?X4cZ`wSI?MAN1=KxL+(Wc#wLch`D)*P=XUu*k;> z{_N=XQ22}NCv=o&hj+a7p*DbL;5?}Q^_>#?!s4CfTZVd#rxy6V;xVZw`hFYh$V4Qg z_Xfxm5dD7s)^4NS_?6cPA%Fi__R%!#`Wq*YWs>9c?~P``u=mRl;QAdIYbpF*=`rHd z;+5)<#~58eghQlNEE#C;XBa#>oKjLvzd?ES*rgFdSydZU%#UDO0Ft9eAf6Ar5)Ucb#j zx+1C(>g&Y*pfoq(zuW`!@nqMOj~WN6KI+4%BjckJJs);$#h^1y9fO3};a|sDOcc{F z)Pwu+xTrq@m

9QpG^grARG5oV{A2JRIwxDhh@-L-N;g6;|ZwF$=fOy+PQ6mov71{0b z3qp-EU=qwW*XV~k`UI7m;IK``I~zmoPQXX4La&8R$*=pu4jEnpqMRAeOt~3T3&zkR zGPng?FU4?IHs86Z_OsHFSVQo1{)eC>G zCs{@wG6wDtlHz*nAg|V3QX0Fn{3UbjDK`4{#*SVCklI@4k>kxq^I?f3nXL`F#{GBF zob02S3|$dSOGh>_&B<5ZVv{SuJJEnrY%ZCHxCrUyR4G`YA`HzxPb`oAebggDf^$#@ zKs+FitZv_w#~GMR7SRj_b$`-BLmx&fjzvc;$?EZ-9mXxmB+xXRYU>IL&#J;(mZvPga0$Y3}x-u(BjB*RmjXQz8pyx@%X z&-oyJ?ov9E-i(6W@p?0RxXOsnKPf$p$ZMh|1X%yy87l}KiK>wYx*oG>7;~5BfS?7{ zcLtJiQor?*9@T4ELlUcViTNyJwdZMC`U(@x?+N{*-LZu>8yCMf;kijLfT0VYQkz2M zHNDp2hQ`V6e9fiNFNulm6{Gy_?wBlC3Jz0h^wN#^6zH1EDfPh;#tg91a_u z6kT~CdVHTwPxUBc2ZKz!z_wyr(E%%!Jb~P$Z97JXZG+3}CE0y8R3N}LZimkMH{%)@6hx4!yz$+X#rDvw_cruI) z%ORboR*U&{Xvl|LIXt#{!U({TJ36|%@||t}HVsWu2yEo8xcjEO*B|-vV@oKa6*zCS zfmi5Bx9J{lP>xx{Fbp$6Xfi- zwOnyFw7JqkG6D7hoGHl3CWKgCt;21))BnvUj%F7D>GUVbD8BwOZaeKx$NK|%j~>A! z!hX1dPnL~p-1WC31H_xP;DFS*W>vm~%`+nkIoXN!5C3{z(VQ8!WIg|l$zlUw=i3{C zv1nw%4*i|ll$2|I`}LtdWzLwGz1{Dtc3a;)FAc2QFlj{+Fh)sB9VUmc85nEQMsO`5 zT;Lx5y@!_yt&^YJs{nqR!;cO%>>)bDgo2bH+>Q8(iJ6jyq9i;>j{KkRnufqH#OE9w zS*F%t?-6Q%ijZM~Anz=>=`d~7Of`TBVDHayA$(z+H8^T~68vI&-A^%xic=WYv4mb} z){Z2JZYVWWO*X%D9}Kuzjop+=U+qR$D`H}9hi2bXV8L#0(>`9fAxX=0?b#q%kBerR znV>GQ+o5Sx5Er2;;?hsN7j~aWT3PUEc$pdjth74`NGPq84Q!*`wWEL3$)n3os}5Td zTQ53pjadn&z*L^52Zi&4MVbH|+*XP!=+Cp~g^M8%V`@h^V-%cxly}Qb=&>icP3~3G z=z7CykNpcBJqv+Bq86M2BjE;*e#KYDA*+{*@HVOf4pd+9k`&y%CCVZ^gQ)v%>o?Q} z?AJ8bnVAY%I%7nsOGz(Pz{Xavi0JID4+Pf#C8^O_To2ThW@&yhK(DTjuwCh?$fxx7 zd^+@C9P?^F*-RSwe3CMNc_0x?&RCXt2Lg#&@F7p=7t9d$aBvj|?*7#Ua2rQ8(#3D@u*=tUx)5Z*m9)WS&N}`LJfbCs zGQ{2Z`w3R0Z9d3K5(t!?uROlY;DP)cufjAms}Sc=K!!it{(yfAtnQ=>Z7CWOToJN# zS7$z`S)p7%xk`S`pI&&m{t^uX;faSxa-Bmmb@-pQ$~HW4BFO8_J7QZX=4OcjqTRgh zQGc>~@2uvHesje)d^{~l6z`8i5+ZC;JB}vK?1PxXbM5>HLwmb_LejCmrG=5IP|L2* z!$c78Qs_jk*yx_tr$RKeor9p?-B%n}n}kH%mbqbWwfj8yGlSXHZTf>-EMLh^jJ`UA zc9XwXxFPAda@{Aeu4~(qT?_63+{oe~ln+igi`QEFNZH4fNOfi}C0m&g$4XT7y|Diz zTNLOR;9XnI9n_o3jul(Gl`!%edb_^u;0f7+#~|5i9e!49zO@^lH!WLkI41DK?did* z!L1i;aRQ#d`hk|LWmt7thltqu9$Os`B39jt59K!cZws2`Tt*rQ{ciUFeE?-9`rDfE zoY0_#9S|COb-ce;+)|dN#)DbKmJaC!FqG3^u;exi(Fr(_5hRO$wEKSFlG}SH#Fg4q z7Q@l#mRU?CK1W0|Uz7r;X16m59=BS%K5SFPfH!uqGJ(j4kI*vT-XgOCYN*Or(VGPd z*BT9oo9n9M>2%tTvhghdaPm~2-uJALDJ&E6I`3Sf;_SycIsp$>dpfuyXqTSm+m7n=SzaBV-T!YW4p3Bp3l}s+1+$ z!#mKBT1PrVW@HwmeEGzuaYOgt`xbvMM;~{h+>qwshtQY!_I9EKTTfulV1 z3u4b}t%7|gL_Lnv7@@T{Jop9(FY7d3HV34E_ahXjtN)YIY40t2@l$Sj%Fac#`*qc~ z4Mu7SAt%lZJAeC)-*tK8n`};-97R@DZ%6Cx{mt&%UQ3bSixY~8Ik*HCtYGf zdY22p*Tv)Dtn)HUeYV<_UmLx#8K=6Wbw#Ryt+*1u_P4-!&IN9kEO5d&hAUO@7Wc%% z`55f?rIR`>SNrsfL$CBumnmW>lq>uz%5R`u3+F6Xvt*o=19U{u8|h8_{1FH*|VA>3Z!qT|LrQ`q#8a!=;)jdd-d zYC2FqHgw~%B&WWR@YThaB5#_Yi`vUKn&s#u=gOq3g|6ggY?_gLJQzG-vvlm7Q-)Jf zdApW+c*czF#5qz!&cq3pEtfJW;gf8B>(W|y1=|pwqIFzQltSpMZ;}~mo2+Q3-Wv;m zA=4I*?1t)?W-63&m9+O^*r|8L9Wn(eZ_ECCF0>1GWZQF`i-{6Kfz`}YI+e*kin`GM za%pc;yN!0{jOW9#_~o4AimGUM8>;Z1c*6;3%!PTHFBAHlB+~9@IGNr~eh8Zk=;lN= z3QoGiA)gMO4~`#-`|Rqv${8DuN|*`0YkMO@uVJj%CH%&vOUhvpGme z&}-`(9!@2iJo2CJ3f4WG)?<(Jx-m%zi|=>d&E`!OAyT^M{ve44(g>4sQ89A}-DqZ^ zOE?R|N_%SCy4!3A*9&a%QF1Zf#^iBCL6`y{KG89`qVQsyqG)T5O9T#L+fOhGLU_hu z0@7co4w+*N18>Om55^nvUo-^(s>3C=S@-a3_E;yd_721qbU#`u_sBm8oWc@2q4w1= zOi%*STl@8Qo*zA7m`(waZuQ1Q{i z`74Av3P}>;1On03k+fwa;kO1Hpaeiq#^7ra=a;H~Wym1~a7&VNsldztBOby2!c!_+ zo2#bLtNn1_K&i(tFG<Ntxb@b8$8vjt#&}v*hU$5 zEW^YiXVi)8kyXBYM^j}1V|?RJ&-3*RIDBmk_}o3YajHb)xjKVRk1eL{ApP{{))b}` zGBp?fSV8SAUt7q2wd&`2I#Xe5J_IzKJy)du{8-d{n>D8rE7)Rm3EPrbfd|)qB&Me= z1kb#@l$u=`rwCu-;hY6`h>w5Tk0=U*3%n{&i+9$i*XOyjS4KwzjxkMzrQx+o_w!A` z{d~>O`!vtegS*MJ&{siF3_IzuyEMe_3)ozRzV|so<;F?$YiO{Bpr`*qr}0W_jBj|o z2^|KBGHrS%No!hcf06?Y8;2|Q|qJ`_Yt+BYj4 z=i#g9KFb}vq5Wc5ICI)pNRUX3e7vxzHTYSBh;}AE&pHIja@wmVl?~yiUNRM*Fn<3; zy2c?JaGLBD2Ryq#C^NI}I)LaIb?z%~{nAH0uE3U=4SKr+e3k_JvC@O*#Mn3}^1ikN zyY*ZZ?sDcZ^KSR^srYW)6joA%0R3ftxC+{0Lp;glVZ6yF0-_BvR|8(o`5Q^xX1vK` zDT^8OmqlbmiV2quhLSkqiZIiG7U(&6fo{+^VVW)+L6{jPx)YK!z^!zr~~Ghd}iyU?F&`MHhZj0@szRPvY} zlNfg`=+w)k*C7KXM{g}3 zElT*yX=@s2a7Ae9z=R9Wc)`2}?)B$<1rte-uIg5RCg%34^m{6b7`naEusvtZ(ZZHQ z>Gl*EIgjii7-w}j^s@TDU&ayEIYEc(VbJPD{AGkcbP0o5!)F-dbxG;El*D02)i|(m zLFRDyhaF~N+r)-Qp;-O&(k8ux@nRzwx-W4!68xdvZwp?f`u?yVT8ky4Y&KEAR>rHL zVyKV+IFcb8X%V@EVf=FyPd3bR;Mgtk+7RJ1sj`VonPO)gy;}EwWJ%$J0+RYJjW5R! z(d!!U{q_y>@$nxe6)}FTNEpsAF(EzJ8}J)5Wm5!h9P?tr@uCL^Id^QZ88Q#7mSdFN zvF+y=Ubv8mfie3U{BkfYvgGTqKx%)pajyOV*bWSe9z*G{R)je+%%K8KQJStgLk@2s9 z@2cBXhd>nS>v@$))Y{aTDv0VAOtI{z8C{;vE6Rys_oznhO7Idy4SqW7iXBGuQYTfy zx3$zevl>)R)GJMX!tGa+Cx?;FS#0`@SG+xHc8E;vnM|M>%o~{MWaW!|c)jSZl*Aij zdl7_+$lK-2V%@(}VUI-~_g9_Ao{(sO0EvUEtBpxT=vot+g$Dt!BQo3ltOPG^ys(q{pRFKi%L-40$mhe5&#o#9 zhhdt+0z96r{^{J5!*nN>lts+3kqJxFz2``IXGSF+(b!e%?m$(jcR|ombK=skK<^w#zyRyr69_dd6>5O>^b_I*O z|1G%$HsInoa^Gvn=qh=54MFN`h>YkDw7LBETK|esmKNW|&r0N6sq8#Cd9$o<6k*@H zE$8>UR#UL8%Y($`;)Z06)yxVX`-FZQ(6qlaBg>oTM1P@Rpe z*WnFL_V2HNjScvHCR0A+Yh{CKT8i*g#3%l;3(l;){znCcyNwS|U)CqwjNbRbUtrm) z=)?cbA`&2ikpmc582?Aopd}rLGYZ@Dss5zsovxHn1u?lZMd*)8P=>J+6g2jShZ}P+ z6j#DO;4OInxo zGIxuk0U&Eh=->8seRev03TLK;dFLcXNA{DRkhgO~7(jDoL+gIzb@s`dI`?G)xZftV z<8yfpeLYW4&uIT1&_9E1>=cbN2$^tNuZPTe;wSOQ!2}P#uaMCT(lF8^aYGZ;90X^~ z%R^7BBCQ#t1`0;V>xu5nPKL%{^CtUp&LY|6?a11b3rlizocAIZn*im!nW9(qOHj)3 z%bX2AoQ=`v`tken`KnO^(epL}On}Agv}wQ1NZ@T*$ITct0L!_tz+Af`k;i>eymF?a2-{vc}O|J-r)Jv%OyW_MZ<7H zTvPQxYkW6h*gHv;D=;&)Q|LE2F?`#q&G@DYTI~iRiZQ_gJh+nqE7!Cs6Q9cna1zfz zyZ#vtI4#c$}(gPOKFfK#<~J&mcNWOj0Q1bK#`PHE=ZH$R6g9va-jru zXi+4pgSxSVy%^BuLAgd3_fs^P-g_70Ql}SpQ|(SKULaVhRQam&pvbCLFvf$>&2cDC zgBf2~DZh;Y&A3K@15~ihI(3%$h~aQ-`%*8CIzW2VIf*@6XmT) z>v;B2It+s6YXl6RvqwH+@8<$U|$@uUA4{*5HvlhecN3a|tf1*Hc zH3LF~iZFf6$`P+YN*#cCFij2n{e86W%^>tePGLe&;@=1f?sEWDQz%F-8Usar3sXRr zx3&SRfyFNXJSwtCSk(#({dslp`ePAgj=|SK7|2zz2pbbQ*+v7w(&nkujFb^=rf?7= ziB_cJbT~{ZMmC!WX`KqPzj7Iqad4PC&|dj*;RfwvnuHTUq5<=Ey_0D4eN7-shnSm( z-3TOS37>Vf(ieeQ0oz%Iv62$QODA27chXF|r2d`&NAobo2_+g|8Y9L{2z5kyj{Cn6&A!~M_Eneql-+tnDziy+rZ*xDz1nFtW)%3KS9S`WIYBx#1 zi_s-uO4~%Et-r^!i8-k zT#=!F8nTt%4R;j};W)up`6nx8d3HeI^neyHCn^-^{~h$MzY41)u#uQA_j0QsQpmDk zkrN1>0H)PnBO?!N&Zc=&H?FRok33v32b!d=t<7Z~^m+>J%f19i z3;Kpp6=<_}21gMo*RvJYmdgRz2Y5JNLrSe+=)lz-Vi|BF-N=t{ot-gh=vCZ%nG6|# zIC(?sxW655?9kCHw&Zm@skW3QB@S0!dbqz9*TNS==`aV-)OwX8*_;cEajAPm!*eNU z8=A-AhK0`E)g#gigzGL5V_tq+1>FOn(azn0ZQ@icBaX>YEIlHyi9rfA@QQ8+!?(X0 z4E;2f^j2`5w6)$CRv24@?Z@d^0d~ywzd?B!mPWAFN{-y_--U;otw3MkaN=RaAbM0O4I<&S)NHwkPuw`-5Gz8#=s~!Inf~zMGj~ zK_MMvzuzyW?xOlL_rXxB-9OZW#1B%S*&CZ)v>Fw(Cj6ggzu(XA{r`(yU}60Ks|g%z zEdRqW=t#$rw8HkBsy{jY5mXmZlDEIb3G@g$LRh=UiymTRV7_KU8VdD|^c}Z{uMkfu zPA&B|bGIcA2Q9Pyr&1`Qcr+?cbKA4qFL(cIaO!YMKqL6G&g(b$+H(Q`^nPA%Zrkq! zq!^uPOL&+KBhuGVMKFTgl7d&m;JptkZTC&ed-Wua0l*?SIFJLD%l{X|-rUl{ z!mrNlYJuS;&&~OFY(C29P8ElbLRMB4oO#)e~Rx@LlDWbe_3eOmI9_W3|xO z5HgmL@RmJ*^ID6)3u2Qbi$~bDB8+8A0>+-UIjp&t6mT=>gmlmWqYpLV&RQR1Mv;hC zTT5keo-smd9kr+X4|@w<=G2ds{MeGRVb)gI!x7F!%2~VYN6AGT}6m8B0c`6ml#FfF>KOX zXZ>4e16G9i(Y9Ss4*0_OEcVv+W?L<4OQD1F;(75}`!L^yz}%+UYPphxO6+q|4}$Gh z%b^U?GXxpC$Kh!OEZQB*m;81_YI_R!^?5E`u^+0I`6##CJPjDB(a+!5*ViZ}DHbK( zcOgOm9K<*>qsgk^&d!aer5zs@9EgKplh3zL#&q`ffr6upB$FeJG;P-fnno(Hyvq1R zS)D!&2XRAdYSmc1&CRO6s-Nl`msm0R#& zTPB2N^VbK|q?aoA;l2AdW1Ustg1 zEPs4-g@F;m7W6Z$jqIfHD^*U?vfqs~ zP0Notitl;#PqJjBrC|e1lu6DZ3>E#Tl-eiUaC<~@6d@fbUp4?AcrnVgmUPOB;Sy+Z z?l^+rn5BhUKvjv68$&jFch(^bNud?6&z4po0tU@Rh%{mhNu!}$VAx;@avZ6ytwvtZ zhsQP6M)Vb-d-h4<-#HOqcGIx_jagGh4*u`-2H9l+nR4!i2Z7w=*U1=gyj3o6G?{*-f#gSxIeM7y7+6@d)X5lU$ ztB{<_-RHQI$VE|^xzQ0UtDH6ra}-iIzeFRoT{Cl>wqqThixizr$}0h_i6i-Z(16og zX8UiIL&9ip^u3f0@$q^ns)$J~&#=Cwk~E*~rd#-5La&X(uHmD9F=nyV-2RpWo_eFc zdm4uF1YTlngiNDtC{`m*NxU=Qji+yR)Nz2`V$7BC;#Szf7+pYQI}}pX>d#fQVOm!xeB_%hbe9AzP;*gVXKj{Vdpc6+gwj*&uSTtk z)6M+7J?3slsJ!SDZU5vwLug=wH1>u+`zTsxsI-yceQKCSg%gK-=iT0af@O80S(gFx z>^My!D;k8tM4CW7=y=6=x1$Kc_L>-i$oW=sbN&}pKaO?_a>VT?kqy*d*mUaOG-Tp& z3`WPp zw{61Iu?PWizdfw$Xdn~dZ39h{hO__Pu*9pnKrqSS7hgIbnn-f0S;!0p){rjrA zw-S;aow1~Na|Q)gb_z)^XVG}Z%c6?Src7TyIchxk4pY68KKus&2c)aPIf>kCsNT5V zFPspw8nnh-8seO3&_Y|dL?fsSO+jJp=bQ&R;%?j#zN)DyI}3dz`KjXQG|Y}>YKCMl zPpQizd|+G5*vj3kqQ=@J z$ejleTerhn>0X-JzCmW0`#^HgtvD8j4#u{B@=A{1(Pef(ivCy6n(_+Qp;{L5O!yG z3pNeEi1wX{fE7n!2+`1=EwhG(*aV24Z*aKl0uMsZ3|u|HaYKHryc8)Tmb%(`ZimQ`zJ zMC+-y^v{&EGfS5Gb2P$c^t)Z`<$hE<)U@%s??W>@u}DY9!EaC=(!Ne`U_UarEM69~ zc*#U%+)E8>@)Slwi(qtv3VWO<=W1waXr;=ODC_|ss8wL?HNWYoU0OUE-TCG-82S`T z`S(_zddHEpFyao9DD#^gyFYA@Gh#5xX5Dun`AuO_GSC_7L=$x*aNXxVJ&s%YC%sX) z1-TIed9A~XiUb)4Ls8Z6Rz-H8UL-EW(P!+i?ikWEJ_RZALWjk~j-kg|hSNWF<-L1a z#3u%DUuR^sh}_zvhz^px^k)^(s`G`F^ULSKpx32A)4Cv)9jU!Z3z-LyyN6pOcCgl= za+5t!{An9SMpeg4;Rn_G=&T(M%Jqa|j^f3)%K16kAEsMtLr4y(!dL1=-jn~Q^%hL3 z6LdHg_08kN8#f>E$9O+_-gRbxk~2PN*jg0ea6-!kVT%Ill^Z9fZ~}QW8#T$@|V9WIigVRcWD(=uE$#%i&5(^X{ zW^i{clmt4!P*41yJQ6lt2CF$5K^S((*^X$sE>taki+ql=EQjexUpZ0B`ORHC$k(I_=Yp@$8j$^jpkyP7b7^u&a0lrRK1O^p} zW2``%_dL1;$;9E67alsmCCOQ&V|<1J1UJf?%;WnHz{lRSg&En=iERo`OHzOzHnx|p zaa4Q0Ki*mshDYQ0cCXP;$G_jxw`8LJBZY4YY*5$H?GAze*1c;yuBV%(ra2my*F;S| z%%;Y8MBn^hB7+cm)NzB?!rleLHJko4=1i=OZs3FvVQ3!Joy^dJ;q-Zl zuIHjQX{#|%LJo&i(L6nq7T5#KhD`z%S59-S;Xke5jEx@(Xsh9hr1>!Doxgh1eKcV2 zZ34n54LdR<qS1|$MM1+wto0GThKp}W(@od8?P|&eWBszOOz8- ztul1y;@vvPjv$0A+fHq;qh3=bbO<~dYe}h{tw?-#bK9yFU{_^=&0$e0rv^vXNO{Ir zw$vu+RYUzyT1oxjY!L^;z-1}%G2#=RNL~R=ZpqgvrD_;Aja504(HcwaX={qu8NMwE zRz!AL^5X$OZfXKHrS8dfX6@≫@eEOsAiFal}uC<7;|qJjM^)+`3P54u;+}$1BQV zcXcKIv6mltQ|}Matr2jv=8gckPYPl5!(t`;Zaf*_Cdi|&XpEf=$H@;Z$+_@lr0+`- z{%!Bvr=r|6QNG(k3=u>isv2hK4PFItA9_x=HH*0Uc2@#?=|#u;EiNJx*}q?oaBdwh z0Zzedj+$7QAhLX|oX&ZQx@ncXzDEQ3wJ$oori4C>M&tNf2(IZ8tLYS+c(%vhJqD$@ zr$j2Sv%_LDv{)bu-c{MpLb=vguAJaaf|^wAd*;mhE65#}*{GjXZp5n`)GAA#|9G?Z zn+*JIdb#s_@QenGLd`ci7iDwO%bZH%Dg7Utnk^~c z^dDT|)h7qNX>1~2CL#3!7 z0jRy=-);Ba-_lp|?^gZ15wD}-c^-PYKGr=H2gb2gvF+?3dv|uMe>W^|Xv)IBX5v^* zecUeHjD}fd zB%WlL$8K6M}a~g!Zc^wuxN;Ju}+8D`CFO-Q#8xu?*vn zc56J_K`g3=nOZhA;X1gD6lT6?a~7{-RVX&6X$43hmCKF&LrsCjcwbU*tVUCZBJ~!F(&3488JpNgYg)1bEUhXuD3>sKN5c!nq-*zJvyP zR4CKVy2+S2fNX;8>cCrFi}uLKIu5wvfibdRHDXLEt}4eGooPqhUUCzId(<@h>Xxac z18BJ@$DNyDCD;DPXN*?lsPK*muyIQSNdZ=bIrg1hu^Ug)j++Kr&MlsRZd{99NKnkV zI)iB7w?agN2T6{P1rn~Q@`^G^F{;_QjcG;QQV5zEVB+nZM&#YQ*#j=!&M}YgWz`i* z>W4S>M$0(hv1lh7UIGu`y_s66PNlqO+NA>$nl_*jUPp-hT53o_ z|Ak-$U<}=*c^cL9njlxW>EI%M>-)&|LjE6m6d~FMV`(wzw0!-U-4ypNMfl0t7%4g9aS?=uirnM)8j& zy7c(;n?`vu_+fmV>b!>6BC_@)37q1AbhttQyjc6XN6G@PY)jvkan_t7t_iIiA|OZC zRtlHd)ZiL_ZYe`wgrVrQ1;$QkNxS4ADED!nugF>ZrrPp~4An z{a&Fueyp}t;izMnALG3Y5tV#*HRN+iDj|e)ACDV`#~c!WB0dD-4j4&6CheOA2s+E8 zN*sx1$qA%jX2qFk5=Rp>fbPzo;!d~^f`%|ef??5jNV9|1W^PB--d8e>H12~R-vwhc zjG!6f`s;OfdFkP!rmx~gr0=OQtMYH1;9=%y%uMF)^*T-9(sUyV^ik;PLovA)bIff&zovF-+Fx4MD zg`EoEu$04H;QXiiVzBoafjHt$Q?WN`88qhLpSIgGLHuYYeptuTb{w?R0HPBRCyf&d z8TBE5+asj%`)Kwq`|4Q4wE+T+A(>M*plMOuF!S7SlkaKe_PFAlu`<})E|lNhb~ z<*yDn&Ow)0_G(U{;dF0xz+I9rI`=~}CIX!-%IDQsTOOHYuf2ex*hm$z#tMrhMC(Ob z*T?iJae1y}gzm4UU&W)6)EtmZ*s!>JIf)U065`oYBA0jhh7whUtP%UpM<#X%Z1?^k zvJ5R4J8>y-vTw5iQ^Bgz&P9c8QtH};WgctS+Rbp5>XEE1wpWPJ0P%1&{u`ORVFu0- z5_kVtZ%HiH?YUY`gf!mmI=w)?`hSNgV3mlUtRjM@trrOFurS|;?cIJXG|s}VcC&_x$rA z!PANBx+8sQ1~%Uxw?~aRbLxE}NQ;X%f)HrYPk;`_7CPyv%3pF@K2j)esc>_julP~- z>)^c%?j;B;>>zx;ndR2Iu~2Cm@dpvLP6mIbe!tI{F}pamYxuKCCHVD}NT^3a(;oh% zuW@9N(>?XV&>uI77!q!saWp`A)WU*WtY9F$DB0DAd;1lXW2~lC|1SWY)QvmxBW-uj*Qpr&OA z{oztA9f91n>kIn*ku%yVBr#y~_ml8?-VG($CC4Ts(>zWU&(27n zEyE_0B0g{@K?))PW(%IEPz0Q?D=hZ>{fq~>LUq;_fOajMIFO2YxJ*bU$|(A1S;K-J z@9qTU`}_AOwd(Ct0O>s^cs!-6Nb>X_F-C#3rnjhAf~O~*wuMznCWLIJ{w&jyG&i>W zzn`AziC21I3FJArk}2h>a~f%U)^qc0@w3cWj@WOzfevb<)-scpV20BcZE!+=M(IP; zoKk_5fI@fwsuDe}gOehq(IQnpXnZ;04}!hjjBqTP>PrLkf}TJngJr1{9PdOU^N>;m zHm*H{-gx6DnZ!a#vTX?YPtXM6I-nZ2rQ!6ReCI!3EHhL>J^SelNW5kvUCy54iu;Sh zw1vEe>?K<)@2ky&?A7M!rE~$kc~K=aiHX}?z|yo1@WG8uNXr~t$|G|2i(WFf-9&6y zKEWK_`6!3k6-_J0-F}=);S-L9`fLwvsXO}8kzZvg+$ikv8YbE1@8dP)vTW9z1l&vA zxpLJ`bpNUQZ#u)}2SP;;zby-#`@e)-TCZSALq+-1*1s9C??wGaQ_AgJoIL5MBPph9 z0N$n8ZzGi7Mj{w-ooQ#$nQ+5*1=qFTg0736a}+AOx|F;0e=N-Rd9;Gf@%Ulc;;oQx z7KrB;qI9I$f0`OE1AG2@Y(kG`B*VeR$J+13q=21{)2vy&y zcEzRTrk;}qmBJU`V{wpd#GK1i6TOTP=M@Hfs4Wzl>g|jANYC{*69#JUaij2bPt1%U z4~U9Rfkbl&<9@gGjHlct0dpeyZZzukXJy0bM{iZU8Ll!R3KK>HZfTW5-r6cJ0Pj?9 z)Y*%fFb+8T)nb0^jeA4H$6;1gRZaBqL=xmAm8r&Cz^E-|g(O`QCywvb29PsN-4^2@$a& zzB13S+j&1qqEU>gh29r0<=VYt0E7}^JD#d^h}bjM27@hjweaXkbx4s2{+B3*F;GNr zAkrZ2#;y%_)$QsC=^?5lxLMoa(!>3~t6I5`-;&C^U1V|gi>-wjQ4vr?k|mGLfqPwT zGu9m;oM^vHQ$-e^f=|!Rv8wz$&h~3I+BkHI=u`x$pmFP@2Nj!lG+K~=MEAGz#GlYL z-XAmnX}18(?**r9-i8C8MkXoo&dB{b?_Q2*Qut4)T>lf}WBq^R$CGh{&4}Gk)t*xL zgGrPsMMW0%;b3;bIe05HVC({BovUPuE+b`M{xW_O()Afn7QZYBhwV^3JtX^?eqy{7 zHk9TnU78(yU1Drw=&{Otd3e7i@xKAzpMdkkTUiDltFtl&EHy%%UfiK(zOJKmxl;&K zHJ1FHtzW}2jh7b}xRoin9nDxfsrQzi@mp7w2XBw5BA;?g0v(OO9DHyNz}CAu2V!Rl zV@)Ir+HYF%L2Q7Jw$zOgGP>w*y^M2-s3AbgcbBm4CdEA!6V{F5sH?U zzPC7cE5s%8vw3^crT+WPOoln6A=rjZOmo7U62T$y`|A)rjDWq{6`@X^4`0?avm&97 zBZx=@?IqkMsBgN%s|?W?pd*}_|KsW8;pFU;oV-330zaMWh>g#_0Fg*yhy@z0mmjV5 zR1pIhIdF<<&Bt%G7Q_)a@Q~BR7Iaj_jP)AI1xpTE!Av5Su_)4oFB3&>z zF^pxdWX25pP6iYq0&fN-Zhj#G-vtG&25yjmy8~WlIA3fOf8ay{d&-fg!Me2+$pSJP zNu9F-u4FL++p&V%V5D~}RwryG=uuDYCbM-Wk~(dE6j0QQ;P6dJaw5#OgAP3lMST83 z43yF#&E28*Clm28+ca_4obbo%%(oknj3h;n`52Vyj~u|qKsO>yP&p=kDt_cfmZfOR zI{}bOnD&AJl9vjR;Hc0jGe}VCNMI@&If|LPetZzvlc1pT``!P6l6hN3ZH-+sV2B)y-U*-s`~@Z=?I ztH)PJBAlf^J_Jlyo(p6N#>I-zj7%+xO&kyj`_0l>qWpTmBU&oO4tPirpSuL7Bw*gO zLn7xel%@@=VX0LkZOsR*F|`oiM_7+i?w!ADY@fwTecy-~5@E&QxpLBsnNPxrzRS9> zS7Jp&i?)eRiP+vr!y}BeR5lgFPo~Ik^e=>x!-NvuiT}PSg4i{~oU(@QzEPQn4Vcw; zX^ESqS=C}np&v=98_ zCT+0NPKFWCaJ+4}%X*%mT{Kq9>K+QLX}0VC-PmqtD!eJ{EUCm@YD!U50}#3xMuT`r zSox+s6^zjnTr$>X28I2iE9UUFJ4fm(?^zS2kBM5ZFV~XV>95EOGxVnbhT56Uxc4XTQhrh_1Y_<8m<&u>H4jzAUY4 z+gPu!<4S9v>f+~|A5|e&42Z@9j{QcmJm-!h(e2#tV%z!*bQm6ONh2d*WG`}!e1^z- z4`=$S7>YW~zI|Q~in2uCKSPBQ?5orf!4! zheq3*sbzP^YHLg(^(yzvVULg^B`>_(h0M<0I)P7LzS4y&*oD4|Orzm^bkWRDjt8?QHg}1v#11Vcc@=IY|iXt{f4&c_v6k+=d##=WJ8^RsJ zN%|D7ljO=BBJ$7X2{kMkUBo;M%oHTgulJ?CR^a|{8O1-(DETJ6{#AQ>bZnB(HpF8f z>K1&8n@EXWamuQIrY?-1eWVn4elpc6p3r|^7l52DDZ)XS^K@+gBE3R2FPK-n8W~}Q zcYBg-K4ymyXc_`pp3nwiw2%glbFTdWr5-#f2RX?s^<;#<`rd(QRN&GO#J1r6zJ+9f-IxfYmuZFs3YbC~Sh^@Tc~ZVTPn^KSfQ+xxzd zw$FEqmeZa2Nf#9p_hf&T+Kr{+1eP7(JGYophKI7rUuzEc!v<4$WHR8v-J}aF=Oqjg zh*1=Dn{;;)QCIzU89y21_*XRlI6?t$;eMzxp_BFnps06J=Oy7jETsrBBl$=OWKJOE zRh3od7F$t9dnwA!J0pce`cMi<(8UASPQGqkMwUnl-$SXC^Pf08?T4PLF8*?Zlh18S z0}>WN2~}9HV&^cn(Oq!vzEB#7U>(rlp`KDe*@x0nwQK7)>(*%aiqJoyb+W^hEMivF z4;M}rKvCO4wwu$K2E`XxcMT9bbUCvjWL-T_abvWvScsUER8)gQX!i^5yerOD+dZzj zKHA%2;f$exVO-hk_gKb*7PRS#cE#>r^$qj#KTaY+n?paM_QNMc6Uz#Hb%Z0!El#|q zD%^S*cezssT=8=*)om?i-DuO*)>xt{Eds|a0LF-97#ljGYC#+l!iy_f$-`xn>_ynf$*_*3L$ z0kTAcQ8hFE0GC9h2<&YZ{cDM4_;~=hwC9BUPx&G2%I{Qsm&lFyXEtvUTlWXDd8T4zD zM;RIO2`2^;TMS>A)#O;4ZXmfoEgvNptv3&pRJHkBwhRZ%q7BMvWUJC+MI}?sp@h+h z?XwTCD_4P^_3$9*L8%i`An`1Tn9+nni&W;B$FmM-?dAbO3~fXe*b{G}erqT*?R4c; zszJduB3Q-I%*I=jFg}-q(-Ivg z(nlT?o1zR5WiK*1O+uihY7n!Qt_X;|ji*>Ar>Vfqb|z4PLP!9WKxFISkracMO;S%~ zHftI)aRf<&iFOIHK;7I|i3YMJgK(3P(4dY<+-p*-LG}a^1n?mU;}wAYQ>j!0L!$DO z2Z;z?q!mV(8=L?)5*t^pE6~)-i)F#A4-EZsG$#S1_o2E5Ac7a+l$fYsl|%bEnLpH# zYF8R?(98Sgg$u?&f&}uqLm!YRb3|j_COn|Sn-v;Cs2NF@&_D*#;+SAeT7kWiru7IL z(IpmOvf|KYHU_mwL&hhjGpof@iDr@$i&}Mt5wjRZKOl$-b(A1l3t2BmuT|b5G$jpW zqd`$(hD^kI{eQYNh=4YcNun7i4-N>2M^{t)F(s#=!l9~~aUN@dMrrwL3qE?xK2F8f zNf4#4P=r6Vn1)$bZl<{%gy@vks*hO@ay$q?We}rjuk*$%8BAgbG1L5`X}ixRcG$O_ zU_4q2v#QQ62TH}iDg}3_uwol_4p)~9mT7@QRYARqd8&?I#J`$=OJiA2-XCj+pr+_< zjzu{WHMwL{XQNvj`3d zZDGZ4NR?Qjk2@c;ZQM49-cv5rPd|WsS48--3RX?j&RNY!Ta-N0k5a?Sz_ef!diwgk*6Om0?7ubF{`Dkw^kOg%CN;#njlZWVS`gN+ME%o*Jkav zvto(DzArL@(i6ddmZ^7%1`qXzfV{!5ON3%MvUaz(r^RK1yKzdHe4K1FK|s@E;xA(f zj>VW-JjJXr%E@IG-1dq|XXnwmLmw@Y9g;`8>*I|<(DGrmPzf5O!bdLaK`RB^Wc(;n z;tXQ#fUUCKNb8p2Jgkc$XnJHNfS#!-wP@zl+!0>rY=EAM;mRU2PvXS6?`WUwhXt zN19uD-CcgLQTT<3CbETr&^~xcJhDxNakHN*293Rnd{uGt&Y#f z*T;j!-0t_&)AqCOO#{D=$HgzbFXPX!weV2<9X zmEEIFFKCO`Fk@X8FW9c%>_~2aR<1n{1brA9=5lZobAr}MWpebG@+#sjnw59p8&WgF zC0thA=!#a1OlrXoA_Ty8Ar!^oraN_|OC5Iq^Yw6fIIwK~^6|U-e7(RKrtv6@myx`C ziWrk@F`bxZH~G=@y-1V#!(@J-E)bI-(Mmn3Mt&$4eLn9^PBQrW2@LV&F;~Xw+5Vt4 zt%U{lTfq~^lbil%ggj-5?K`}M=FQVDb#@J#5?b>eBwiE|Gyxd-lw>nfLvp^yPv!w{ z#T18<_WfaUDYmdHNVK#WQDv0L84t??Xby5N1>6DX*l#f9w{Sw3pW`nTzHkKWaZNZQ zrjt$Fu%;kVFkey??9)c`Pg2xroaeJ5-e3cnBa!OU570`oam*`SbdGcPgPTt?Qc?bb z(DEJ)@D?TPk$@~IOgaAIpSAxQT7F6sK^OwKpN{SYEs)%fu)bYw|8T!N_!zwGh5qn? zJJ*Rn`hr;gxeCumdz9`DT|i!OH7Mv$u#(HzW^Zgd#kX^wJ$M%$Lj5#Wu$OGu!%e4^ zZ=x=wBPmH4+o%$iUf+yvfs~z-@oS>(**;p3Ymhfe;1=*m+e3{8k}0f6@35LE8ZC_H zM7Du_51c^vYKR5WjT$9Hn)tgSJQ@`Mt_=ZuHlY{ zT{Ba1LMh@r%XNQ&$*{y$xEq?mucz%}K_NIH$U1s&cuHi}&@OP(JWM{80@$7dHgt_; z3ITxG=0;)ovc%wrbyp_UO&;KSV-fixd*2V;QI_9R_oQ{?5OWoFcB~rw7&U7`^x93lu^U&`so^wfz z&HQb#`YN9jhU(nuCbISw?CpKCBLvA>HbMZTBKCNM$`A%|C%4O(0|I@x7?($V?$57n zzj-N&*Y}o_*!a(mI%0MAC(fKM`qP-tu6Uo=9;TNKkYm-^#peS2^>(?kOGQh7nSaHG z1%UU|9_?Z%`a`%@sG>ulHRc=eT8&&^6KLDl8cz$}Xf^xIj`f?E1?eg8DTzNj;TjN4 z#M4U866gMUg%eS4?x~e2{7&0DgQNo79Ju5|=KAsK)$vIsCsg7JOUdVpE0`kAVf;bn zp1ST_QG!b9IPU(JCno)bJeG@5YspcKe9TXo*S`P$wd}T&@GHAAtdw;FS*}x%5$QZ}^V@%t zxzF;kUCzIobVex2h4ubu`soZOn9s4qv`KZ=QDt!|#B`|9Wf2yzw;8)|umRY&Zj|7O zo#(MABUiYB>+vb?5fTf^`{p4H{or1egVdAa)3F;yPcH>h4yjFLU9Jjs>}APQPu>O0 z3-BeptfjX7yehRYUW{d2OZUSl?=(soIx+i{E;Hyb#rEo%F6*2LJ!tRL7UhU0fb>VX zX}TTsVJywzi8i@P@2R7kGzE+qILokx)!%)QPsQ5V=3i7MUCKWcX3uTJ*t}8KzR?Mn zrsFFBC%n(I+ny4yrhJZ;wWm4o=C$;>kyN7}=f16dI;A1{F@1KRdqobTp3YXse_mx# z=!ADpJ5ZNyvtZSvpgMV=giJ2v0?&xp*2m^GLUr<-;jVx}itqO(LqAm)3wN1u>JX8A6rin{2vWBBRCbG0F zUe}24T*4eX++3EJy&ZLJTD@!|PWmr(F}?hIe3Y!YnD|rA|H0tA^#*8*HvQ|#cahpDBoH-zT_lCf zRAKes6I9@xc3Av=E$Y-zlPz|*RHvAuh*H+Gk(c-P+yHlgV|i=I)O7^YP5(ulI|K@~7tT>8>sgHl*;Y>d%kG z^|M8`sQ1~?(-aHYR@%Z~zx;u*!xE&&o!|3z+%p{xs}TTZp%^L9dy1YL*s!=?(3@uN zPrfxuY}uCwM!6Wgn`ga(5emj*bcDKD<25xOk&_8-NH8+Om1&Zh!7U@Dw ztLI#!sMWGKAugik!zwoSFZ2CIFNxNGb0^J|-ls2H|K6{oC{HUt?*nsB9Ci*IHj@qG zDi<{T^Yj4%2m!Uck1)&{!$hD%rw@?P>dmhQ#kz+jx_Qcka0nRX(eW>I4}Ig#WujNjPKyTaLrVcK4(VS*3a9%p1q~#>Wv)ih18@kv zz)%V`u}Bh^u}J2qyqqC^uA|0M%OgR$%Ej_QM(nq!21v*9H4Hb5W)mr>yUa7>F!Q)! zoYt#KkwWv`emBUG5pT~w+doo^w=mZILD7Bu@&x((D)5IzgI>?IgncI5fSYCOqmpS@ z>wvsLPOZc4Iv!XG-ljynotu!sz<7`X?n^Xb3@HP!h}~p~VD~Po@~w{hOtE#Q9;`U9 z|Iu+eBIf3{kuR_`sZBzB)Uh$;eM&7Q7WO(iYZRBgVg=ah3TzsFq!_YgV^tF22iTasmaN}%6@TlGO5M+Y zxz-EmyeAJ7XHSCa#+oIkBJdj%k6^?n5K2RunL(?7;tCpx1ZQzU+wvsNP8E6f2*%QG zlkrW#_e{m!fie2_m^5eZH4=fxuR)P`_6f$8&2(|w{b*o{y@k8*>j{Ety$5gu9`2@> zulzmlnr{Yo>T^*eb&Ncg8+}IPxLq{w2Lq2HEM8Uvk9y2nLp#{kJu01Jj-3#7l6%Yu*9g7%O^N+G`IFBymP zO+l`E<8Kr-S|_ivkhfo+zbiY*-{fPf0Ik``m`BP({ic`w(nBNXSEBuUkJzRX2NC;* zJ}Hz|NK~Z|0uLC)(ElE?>R@<7v+Asrt&;c!gJ|rUd*by;a(E3rA-2M*Il<9*-dbe8dk40(dLs z5ck#W*KAvHt6D?@ThrL8l4^i`gENLfD=JZ4R6j_5Swtby{|fV%7m*8-1_vv4)_``% zrBh~Ms~@K=V*fh?7qqQ9=)X?dH3#Tq^DafrLnV~`F-0ORr5Gj%k#;Iq4H@qKuT7E5 z-Q~Z4fSOTSaMDz*!)Nd_DNV{AuhD1%xq$mbY#ulAvMl3`C^q~l0%b+wpzO~n)a85B z6}I`cPIpfOOQqc6YyhG|&T&y@D9`5x#p?r;2VAUuqM&*LWfxCsz_+`n3q2^TR}9g% zeqVZt--(5#M#^@ee$FDpeuhpRgm4w>n2jzJxQ+@}6$%Hi#d0ylwVt~QuG-9{spBuX zTy(>lV*+J;{TS(Z;yV3+g1s9d!2oqjSkMt|6i$lf@vbua z&x%E3UVA!n?D+4Ao{5w<6y_`|_GBa7q1y&HkCAeQ5;jo;2(?WXLA?gc7AC1>qz&df zd7I)1LEo zEKQ-9p$izI)qoL8$a>#D?Pn%oym-14C;>LM2_$FC&7mNysZA)tLmIlS)fhzfUP&!U zq-Tjp^OS@oE(pAS%5N2~bOtTu0-pIxCMb_T8nJ>`G*5^Ww?lQZ0${Saa13tx=8_QH zl64SJk!hQ;f_pSt8*#*&$0`T&s1NR_`rFVd-6g=2HUOf5Et)Sx7{ZCVNg@yx8yN`R zbM{0Ne)hw1RQkO6xed}JtQyt{!k!g#x3M_d#Rr6hWyj>_=gCuxloF+KzZH*!Jzp!{ zv?Z1^QmaZzY~aa)oKlu7P!h_UID>2S9*9&(Bu_f57Nbh^4a0f=GDOGAe;4YgT+2WR zvR_;>1I#4Y@X)2#0V{qr|0yVw06Q+if(b~{i2~&;KBJdd_TIyZA-<=w+Ae;Qd6F1V zyoqsCX402v%+04UigJSfS2;J$)DsHS@C#8NfP`mD42S;6TZ8>J5%q}zTtNY6VtzsQ z4+F$_=(^}z>$eiM_1LRdBgB1j`tWoP%-F@vIvXg1peOo1^5K zs6w5TEu#0K3oZP!;GsTKkfY*YNMB%w23*f~Z#XNSIcw!=Uj0El{?nNJyRI>xqMqi5 z9WMP}So>0YwA}h6_Jin6eajnxMHz+tOe%acd-z@$Ib9gpjBWQ*S|?t*HQBl|%#x_$r)Me&GK`e?TKqkgAE^H@c?Z-;rsM8{6 zM6J-0OC})xDB!+26lkAO6nkn=S)vyM%WLpx8)14VRNz76$tov{(q!0sE8G(2TFah7 zpY#pymrj^U+?QXwYuqzQo&cf7z-4}barfjx@~T5CZT;3*u!0?yYtsg0VODCib4KC) zNp6+5)xb{1yg4>K10SKaj9#g_sK=B9lfbC+k~~mhIr$0%fO}L|{`Fq{MN|@ZBL9`R z5&`?MSuON&FYtr@h)N&QMR;B5qL@`{L_gH$!c>;%V8TVlt)djJmCMhbslIpP3a>>| z1ZKX-o=f;~moVEp0H<~dHSi01`s4CHFgG~4c!2)G;N(C_O>hzb=l^BtlA7cH z?Sokh7Twju$$xv~2`wma_VLuYc?cfem{>Lq; z9OsQNQb!f81}dgX-$AHNhm}q59sx5|xs4jGsbd5RUl*hux{eO-@eXDYT8%)=*6!`64eT*R;OTh-A0@)^$n6UF0A{M>wBFy3` zmVrc1Qrhbw$zvzX5)ohJMM0lRq?|+b1S+IKz=Bc~(vKp)f)qCrGxrM z4WdOfbfB79zebuKrCj`7JXI zzW0jJ&;;o4$9*uVd(d!jkN{=^gGlq|RaASzV8xzZ%)=5V(2A1Y6U+c50#i{T@+zu( zHaE1_)pU62yn7=RBR+9+uwcV{ZdhbBc1$B_Or@n{xJf+f74+u}s^gQ4jm zC@opmP%AJlv9RE%L(xto^L0t#Fhj&#LF=U9uk3kq>G^~zA0bHh59kIE4CtO}M6$%a zvZePTGb+JwgI|ktpOdyY0bj{SsMFUl4Fm4Q&H*`eUxAxdM`7*|y)gmC#%chhRrxwl zT1#1GkKkcu4bU&{W+?Q?SE!BMSd{JU|LtbY^T%4b3*M1YqVs|cur|aA7z{%D&<^ksITwTvn58sCF#7Noj%tTh z0{zno+5MRt$o064UIzr!48o#9S~sF>D?3s4kQh}!L;#!6NPgCw)q^aQX96)budty4 zDiQRVNgUv6zS4We;baG+@`aMm3tOsjic&J*q146;xagz9F_l$@f=G23K8k}$6uMZs zMQ5=P{@ih~QRX-XVLF+M-&-n5jB2r{G3jIbD>sq>3v*;GnhF5$yf*(5W9dpm=y4Dt zs({#zxct``zc7oJ(c0nz+*_jkWjr-v#Z~r2!MuTq@Ssx_+GRbv993f|O59#d4{+v! zvBIMaRPeA?RKL4%&P6oIUL`#A$vn2*5rm$ zRokYHg~+mtyTLd_g7#AV)6MvytvhRZ) z{=qBa*f0R>M2218EyQ#6vn=4DBE5GhtSHL- z+L{Kger`T0^sP`C`=U#2d5&=1nrfnYAUzVwyW@>14nCEckJa$)+R>!5>`(pPAgpcY zEwYPGd$A=gicq*JS)ODWvTSS8Eq|gIU(edgsiXjm?*?5SJ1z*#Pq$VxR9&W04h7l! zXYS;>%1wyXc~TnXT6cMe_lR>i_mU8-X&|GXtJr_U2|!D=Bl9OA$=$kpjbA?IWc9Q< z-Ixq=svP;9KJDK%4r4*rM9SxSv~BVA7X71?&y;Uv#}T?Bmnc7vf~Jmr!q#`!A5#s$ z#R~w?Ee}6ygN|wVPGlx;Hs0U~R8vPkLG9>*5ui_ADA;*?oLwGfQrM=bT(A+!Zb9K? z-oHNi=0t}&*sYlfIkW8EeS*jqFg%*NPAyg#*ZFF3VDRf7J9KWHzU<$SzjMkdSj;&A zf-}ygL^@0U9gX1iJH+8n|FqvA=BHjqEL_vxwHs!!(nHqsyJa=jBpr`@x>8C{T1SK3 zCYGGV^>6%;$4zH_jy3iOxspx4I&FN)P1h<#$W*yQNOqqAi0=ZNp*3y)e+-?IoB6-5 z@!(wSY(UTzFe1SJMbcc<`Nqkc5dE&IXH4Ieaw>~m z*wZ1v9CCA>09~GSQqwzn!IsE}7=z=91e7rF1ey$G370UnqmbwhgxbFTj)L%mYzx}P z(U+eM)yjI^2eY-g=9Vmlby3s51s&c;vxS~y+~KEiFT)@hH1|YNanvS7*8i3(xrff% z7N*%B)Ao!|^4%Uv!*B;u!`bam68<4K=~Et%!Jz)PN0G@nVd6q99Cj1uS;yUL3`jx^ zl5a=?c@hw%I;7j7*v`cvCCF3Xh7Ap=0mYLDVi<@^p13=0KMx1f@8b1qjOcQ0Ch7J*-N%vk zJ{lhmT#7Z_RQh$Z{OG)%iO2{e5kLYuch3Y2{3R>-gh^TB2K|jv5T4fFmq;mNf3D*IdlJSCr}K|G)ZiYYZV;tZ%?cRZtY!RN5#Av zGWslIy!hv)1 zQmbu|KkzjTkrD7%azhgi}T`7y#TK5G%1iJz$}5N`-?`JJx0*?!sWoxH7bo8(uK~EGRTC z`g9rP%eb1fbc7Y7N+6*!yoiPo%Nab&HGVp3fWOPp@P-QXu&@?#c$(7hnzsho%QvEv zG{Y$wRXwC2y#C1#i^C!%2}=Gz_NQtI%v`e2BLh)VPJ*G8wGyGBg$95)X3RQ}^vfB_ zs!T}eK`fvbq*VAPH8UPmV(v&ottg_vzUN}eF(;$=r8(0EOI>qlL(7?E+g&QUgB4J- zu8&|Dt30}RkO4$BT*n=i`v3E{xo-2 znMp{15}l`Yd0$aP;D_sk_+>sKR{Jk4phl|}+3`_6*{QmK@^>IkV%(-`rq1q8cZny5lfDU*U%!-R;?~UnyNw^ES zC!SvB?+xvLAuWLo;m(RPclZJRek_mv`@>W4jTYg&5U!NJCvIwS$bm~SG~>k@NK9Lc z%hc{v5s?&qSjt^SG>yDVO(-A78>l+G7k#}svEJ7NR|A{JCI4v=pgsgf6GzxP=enn~ zuv3G1?MT4EN(5l)cY;z4-{TLPHjZ}4C8`KT=Y4eZt#Z9(_~ zID37-wLVMJprFL5Wrm?@S~GpQ8RLPlqNQ6LI2cB_Fd_1)t?Dg}U;5F-w6g+(HPq?i zP*^oi>C#eI(s;2R^o}+rEA`u6W8}m&Nm(j_O(`+kH7V>1xHWNRakvyh`e zP}|?sowPNS&QcILyFFl>RjSDeVC>0_izl&Vo~&u_cn8dvkbgUMWPtMGGSaHYGNGp%uXzw6xe1xg=SD;Br@4O(wb&x zWRj9)#sPme4DRXI6)!rrX=kJZ0!R@cL`M;qZ3~-pJsPcbvz_iYxzz%?w8QXdI9yL* zwrQ(kRHcL)SA8BJf|{I8VL*bTAz+MW8V`BjnAl6)0E_bhf9>()q`)~*=300R3d+ub z(gTsG*)Ex z?HjLxz@Rk0bt68o$z%U=tlF@YUe6I`Ar+L42DMfAZP-?82SU&~^W>$?*!KZeo-4$HVZu4jp>q+LyeO~1$&K>OSL-q~<_HQ>$F z>*@XG#<*as)7$N7GE)f{e)RGXEAn~P8qj#W=UsX0?@K8@$8qsZ!+ogyj4F`cwl2E{m6Y8 zAk6K0aeaAu*SW$j{yH*l1!KVhyg#3uyx2TnGCAbfCv?7@-mrmu<}@dlDHl%yBu@8Y zS%;HN%AT7#R-a9eTyl;<>RoB{ZaTIliFUPZWgC@J;8V_YTL0Y|F)~y=H}raEdIWG0 z>?tt(yQSOp(>-9KW3o6eJKR<|8UUZT!Ev!?X2OpIwa{USy)NLy?i!-wLUKG|shZm@ zFoXu4&T$=jc2@40$6V;eT|qqnQjl(z1hfXnp*{Tu$HssDiblBdtsa!ebgA^RyYr_y zdcmP<)H(q9rRP+{MF$-N(6n_25E*)3X5G;>8;-mb3r&3RX>@NfvKYNf)s0Bl?W)>D zGyaNIpt5}%$t3n~;qUl*-n&1j?Z4>L>ibIX_uaoHjwQ5D^wviz(nd-J;4B;j@I%zz z)$7`Oy=Ol$Z5iYc2?4x4yqp^GdRV^Xd`X!*Mb06lW;y@F2~ z3?9IBCn4a9!Udu?Bj}QL}?`G;uDLmHhbSi8{@MJ8{ zph9dN0>J8P>mJp?wNjR>7f%x3JAVtXob7bI58)E3I+4WY)GJHX9XhBD)Q@sb|L#Pe z*8ODYd@VS5#0`Z9H04&rW0#dRROJ@vedO$&zP(>PS|O2RH(BilhB@o>+m*F63yEer zIXV2KK(chJvkfA0crmM_Qdu6bUgYG?8vg!ao+f>et(-B^E{x$r><2eRIksxmQ5`p z%Mjw6zzj7Rn11~XTF6~eUgEa~X5&qr&N1*ULlx`85nTE{{cXnJUQROz5n8%tTKCla znz8sqZ@>$J`~oX&VgT-Zf@1&$h#;t%VSa%}fP%6&C)k3oe_w$Kcc4_wN%r9Vpuk+p z?|xrLa2ilB4wi2!DuA7XL)4u+G9ouyZXfBb=Q`q2S~$0i0!SQtk?rfcf1MWKZ69w=hl9Eei>r2WFV8t&snR4RQx{v^2Cdp75tS0Y2G zn;4au(m;-BjZwF=T{KjvK|G>HUw8Je>$#r<+=#2XcP#+u+Ka|FvxveXCkPH=F)$;PP?qxi9yB`QN%%b=9g~qr1oIIjUx%^a+PrL-a=2Y*($ZWQ15w55C+lC&)RjtbwuI5%nwr2N5p>Cx) z;_9Yf)g@PqY>Mv(SUv95URr`P05y$<5(uAwi_tT(SpX7%c6a6$qd7 z$vD^)To>rR00XeJLrx%CDjSfvsl*RJ0Qaf&xs1r0&cgvYU|<|+iYP#~ zrmjf93Mn`TOPUf2khN)|0x*Y~CZ!6bY#QnTD1fEatNz!5Odp^e8l2;k(}S!DZyeA7 z2F}6tuMXrSpcfB}^IvmsrvP`9v>%qAE~LMGCQzl_S^n1m%?H333Y_zwpy{R>NFW^; zI44J%5c;PJsL;T|PYLHgl1)UQ2pAY=6EQN79t@1D>C?wDu(a*W&l&PJ<1`VW0SW$j zEQk&?fdJ?FkFg;fAO;vX7stQepx^;%!PB0{J{>S601|~WJeL@g*c{X> zne6VJ#ZnDjv<8{zU7-PDv3O+?W9SHID%Dz4Br}xcm0_glAYeE~jfQV_gT_{csC|de zMZ^3it>#iL@55#jz~j<(>!IVN!_TnDb#l|T3RLyC3S^Ibuq_0N6w3pX^-s0sfRd2U zVY&V)Zx;VHD`MQt1kUXYE(y~vrF4(H-rs8kb$&qBxxa6;7Ni?4Ye;a3M2{`3oc9QJ zKh+i-!dINIzcd}Hkbi;c!1X=%SRgqfQTdIUyYSb$%(n<18m7LVRUtWKsO5}2sSMes4ODxKWYC#=#>sS=Wv zVbmM!$};XwRz~|2g%(LJ;?-R&3=~?p`S3F~yN&(re9|o>Y;+Q(b5^9u`?|Pz*mzi| zcm*-hu&|3XrlP?qaGK8*NlZn9sY6#_0$@snXEI ztEdXAF`-L!Ni9D zDyG;>3#jee45883=H@Pp%*8CT!y1v$7ZHhg4ISIE*Tz9CGSLTv)77b(mp65gPqcXt zYSQp=eA>LJgAZNCaxY4Cp5TRVC1e^a;h0qftd@;i7tkB_43!AkbKMUOlV<; zKNl=Xf(;zE>*|^u=V-tY9V#mL^juyUKt;D2CRY$zVb*-FHBjxqBwV4?Def&1johR_ zE*vc5X8e8(FRE}aJ}^il!%2=?2p87EYVdWK=^Z`-hvdD^HI4AfgT+t=*q`IO&LWgC zNt<05jn7Di#SDhQ2T=sWjam?r;2G)*mnIKHas9(TdND=I>lJxy4k5l-lnaW$fvSqf z_BiIf>%8`tOSK{;`Mn{+{GHm@XUD6GGQ6kov2Jz0y|0OC@gae^o^bheoic%1ckB$< zeGBNFgG0O3vuA(-?td}|3coGmzCiPvyp#1KkIOXW#*m5L-@{){91mQB(Gi$_xo1Nx zE*Ka5eXC^e|2*M7^t33{m1s_P5ArjI_vjfd&S4@LB=m1gdk8dkX&1HOF|n((OJq;& z(ls~#iD^{q8Po166aD9xwA(9(pPMcnT8|2M#Jkh_$Croq_qlKZb-uq=eI$H#@9WOA z6OLQZyVd*Iz^esVInW+d<#xaa$8am`;{*E0N-0%)<@ErE-=O!`{^tR` zlnH48-^RtUjjFvxO3AovCfDu`ni?`K(^vG#MshNk&IXYfabRL46cH+1T?lA2E~I|) zp?}v%?l3^#9RND3$dg~-oB?aRM3`OrvuOQ?UaF#bOSSb(C8KcIZ2HJ~ZPvr?yQZC; z+`8d{+Ug*3mq3`X>?hfVEU5XwkqF!RWVYptJ3QO=XmbH9g%%~$5%$A%#CI@WQZ>AG zIaY-E$zTh$Q5KWmhoWx#EL%zeH&zWMm^2DIN*pp{`{}ay(r1eW&oyI!sQbzT`ID6* zI}V6K`vYg(>_8P-Soy);jrE+}qQ9Q zW<58b^F_VxTrS}d)lpBuBotG;Cxw%gZ~FA4Bm@x(+#&IzGtotTEUH1V?bnu7G5*!m z-W`RtH57EbUKKi$<#~Q#`STu1DaXSaoW)V*MDUW5b8Jwj^0Iy3E{M`wy~c* zxKlTmEG#ls=n`YLC?H&b`sri8SFCfc&Ac$gJKdp1dm~Y;(gx0;qr4RSSLKr5oaz+L z<4dK?*a9_U=$)9DJu2z$SMw8sjAe5euIym4(`p)RVA!nQ>H(uWE&~px*2*xL{=00# zD9woPZWa8$sSD$)Xv;=6Y!l5bEiCOd`>&*zyFiNGP9LQ_GCL@^?5QK3Mb~?0pr&J>X&%+F_OC~< zH_3mCr%u(J8DL-Gtz)UZ^C9Sp9FhT|PhbTg(6Cl5xfjj){e`H8Z7pxEFR&rJ8_KC1 zZ-31uO9P?F*<{9|t>%3GFP{Tc)*gubZ5d}nW-febPD~JlSyv_Np>rOkAMr3gK*Wt%jLnB2XK}*d=Ze4g zivF3FL^WoS>-qrdahO^r}#q&}LYe(nq|10O6N zA9nyA6sPk84Y54Je8|+b+$2Y?CcBip`xHza2fySq&*mv);UAo@bzQHo)NvbObP{tl zP~qOkUkqe=9S=o#sdv;hute)q)#vtS#fc_JWo(VAW_Kz0yUVM(7)(e#6D@c^c%aEP z5X=!QPi3S03o;yO4hYgTavvvX$m@wwx%79eq>D!>`(uA@Y^}xpuD0R%Y7#q>jvJyx zH1SUBtCW|hl9E?}j(wz^Ln9j=G5jAx{#S92*0M9|;fUuSw9_~D3sB$&UvClWRSUFa zRO|+)njR_DALKKgoA&$Ej>pK0i$IR@Y9;i#wzl-X7q^PiHNASY_mn;8;{2t#6&NQtao}KE^74WbS9MleSv{Lj`S=<6eI-0jmBS#={xapg zn{*uiL6>SJ!7zX{2q0O_TN^4x3_GZxOQxsxX*&+t-36$@?6yPbpf+tZJVfU# zSRBv9+Usd}*!Wm9mdn*qGlD`kVupzM%*fzlY=`$*CsJed8qFo6Ih3w5DWe_?brwr^ zXjtF}D;P0k9vJ3BMroSg4icyHi>C$d0a$AAeO^aFUOW0uc4XHVmY-ERH!5B5NaTkY zuUHEItm^qEbShy`eI1gTr6KR#TiqnlHt4Y|i6O@a8zE@AkWT1iF$B@AF?)YEQRZFM zZ!0Df{7FkKI$#f*-VB8|xwUVEN0*F-Mv^2hEQV?{M(xBmz3+mDHU4Erif9WO{+50w z%!Zq4XruehO?H|Vmz(u%D9aT}!MQ^HVghsJrpV6zD`8ej!Ac%9^AN{n)4BbN)gGbb zuCUi6Ub`i7Z(;l(vn8ne@0p_Ti0L4er(~TZ{Y=hk_5iu=^aVJ?KVkj%Fqv;CkwsN7 zy3-ne=2~9y#lBTcccq-5;TivGCv{@)@N!k#UpsbThk`P$M~{Q-5?b9R*uKo6hodBO zgW{ChxEwU-n(=rJ(}&^!Krvix2KQ8WRINJ^9@oLGXXYY49e@V6)pl1zo_tq_mixxv zR$hl(o6tBrCQS)=$M3TLD!9(Rw|b7nsTbqx{g}eH?g+YBh8p(0JuG)G(2YWfUW7VR zh364XHAqePK3j*Td#eQDDFTaNrPl4UA6EJ}zzqfPvK6)#?bwx4%g!{NJ%W%Bhw$;M zOLQY;b$mO(B>}y3BQtbYdz2ls!2=Aj=qR4qLPO)dgW9 z1lwlcQ^4_32u(HVu$#6}mw;-KH9NMFPq2cUw~I3F%VBqRo;S>J&alTvMfgcao%_ukw)+-4J|{c7uQjV`(f$QpfmH zt@s#TK*reg2U7dBw${ryOPx#)WpJ4iafX!r1qxOBdkYOKKC!isTc*So#4D9lTLf^JR)1=~kH|^Kj>=&-3JCQ2g8fJd zx>4~?s_A^J?nO~;;bx%_u(Q|Qmh@EIuqxXol7mh@9~s;5|F-NXA}=DSk`bC=(nGiy zU+oH7!#)bv*HWaOhf|RjMrJvn9-UJH5C0&SAGn2H;hQY80WiNPMd8}jn@Q5l7Sp;x zkllp_%n~YSI1Kd3Y&;Cn9)7G}M?GBOS20yC0TI1BiUM5iZWiz0XPb6+4xO+-iYkeQ z`YOebmu9;@e0K9K?OZuV4DUx%lvq<_JHJ7EHL!}#L#jE)yGCI539ltHSE0u*4j<=N z?k|WRiW>rZI#fh)AiH6-kaSUXX$%s%^C9r zk28+)pya8on>XG_x4NOfThr2n@0|)bPiH)l&I>(5U4P~R3-QJt#4fO&}o z%F5Ji>wdwdfsHQA%I|~yu4=eHKXnS77vRo4n1z==(#+d+T$H40ds(xqUljC;rz%{j z3fjr<*`z?uJpb@4Qb`T((sz`2anPlIm<0vljeDUgY9M-Cr1-C5?M#ypWj-AqcBw? zllv|C*uapi*jl?fzZ8(_kKc@!rE{lAJJy!4V7s8PU-GE(?3PZsIj~ll7XkP^Gl~M3 zr{JHxD_B6$0W7EEJg3F1mO>0czcoutA)^CiEWpembeIvF!|6<9s%AJjy@<$RjrwhW zN?Y^klytM%Q>5fdrc2Q}6?K2(V7bMj{%Qm3Cj+oR!%ERWd4Pn7BR`IpwxrXU9#XZ$ zIS}o3(n(;q$|XnbQj0Ls!j6eT$TG!A!M&@&qDBYF!|EJ=$Dk35!;r)?(&otfGCGP3 zg;dQcm#ra8RxqkpKaVIY!5CL)KDu{EZx!<8=2xzC&Zh9;V*UU&G=Df*_7r^SaBywS zbQaVU#o;kLN@`&!xvo=+cgYw{XlkHj6jd;@EwKh6IqbZM%`I}?cQ3T+$N1nrz6Yx2 zacU_L+b|xD_)jAFL%L)vvthk2*}t^S$R%Z< zKuF-NsNHPNh27w4lJaUUNUX^afjEiqDZ^fD-_q2OumRJgGtiH2Fp;`nN~~u2OC_rmp~g>; zDyl|UrIkrAlo#L}IU?Mfhb4Kqepra?tT+BGUzTYfCdSlY*iVQE=_8@=VC3C3=Iw&h zS%uEBDLUF@Ub$Hy>j_sI{0nHE%ez%C{es`<*MuBtGTSXj+Xb) zq$TKVI#zcMfzRMvzPN57af9SE{kJ@bsl*C<*7f$a5qY0mzXly7UOPKXkJyGx0-5{%UkE;Ht01j7*bv1$##hAZ|*g96WNPTkhg%yZO|^P z>NShnU)&VSx4?==--;SmFLm?5G)SEn&M-Y8y%yL|2r+4F*(U#7=ByN>s>xYm(XIONpdyRZ8vZkkQ;FEIut3 znEt3Ad3pUd>!TZ_^EX)5v11ifP+7MzudEYIQz3Sug1>5KWSKO?Ry(F}Tx>Moh$eSI zk|MoW9&<7G<63vl4ZmZda^_AaJY_Ah5&w+I$MbBu5J&E$NZuO8BADrdLNa@QVZRa~ zEIH}Eg3V684An4ECB1&^MT)n9-kOrPK)*_#yNzA=7NB7)TUK3IS4$1*`$a$5M3Q(G zCpE%E8(k5vdfghCnPlB8yCQUWds8{OQy3YwXTnAxkmHXXe~jN775AI0wTmjOY-P7+ z=1=`&`Ww4}zU5N7WepVrVboIe%JF@k7T+VwGha>|gJY-JhhO}M==<$XADa{34*~4T zC@95uOzWVDuK`EP%OR2=?{~q+597?eh4%DIeWfE|7Z0et1?;MQFAkdiHuLLK4|Z(D zn(DMZT&k%;Hf6O5E2%%*3svSr;46fcVM#0K!ecd@4_SAI?a`XqTmFI^SB{#tJSUQ* zJ#$(63#`-2_KbOHR?i3r8v!U^pF1LNFF-;&@Gik)jdqM-VBx$VBy%on2|}_FhGP6r zieQs2kv8+ypj*}Bp#4j_iwasjUvmR-n9P0g5ur*RBe5~o>i?(mHEb+n4La^(}g|5(>Rq^$5a%eviA1YFg z?C(63cESNNo^mCELNYs}bqzC7XAh4FpQP1} zA3XFxbM^XUf!HjN98}sFu3Bf^-*hp*0#f!rb6Mx8q;fT`MxzIzTfrSY<{ZQMm3{$m z1$?5k_qUVpjgYUWW@m7Un+1*=0F1=39VL4mzR&mxH#|Im{o6>$)Ck>X8rl(NWBqeT zx&V=gWpRd#wwMtUwJVysOJkPm(qW3OjLOg5@7WN%IBF&JUk&Jdd zG36DZuQBwPx$X^E(fpkH^%pX_RblD&tu|$eCw#R9V#PrU#RFmOaDTrjocxw6^@WJl z;qMxA-cl(XH@@3vlXj_Q?;Mph%S;3$6!r=8l&7kIJhCME28Z!|+=p&#CFfm44v5xT zhv&hHarCxcat(g?%9Qqb(yS#fcFv=QVO7;FJIFtSnuFU}u@G&U6`7U(-Rz^@| z<>#UX>bep>wATIm+!!Hyu&N>QCMP# z>`&}%d2_IUf)n;UfO6}1u;ZKaFe>C@^)YhswBTE^n`A$-a`Zb?4mSO3fn=w{__ZiN z7$HJpdiWa9V1|RY%@ge)G%$}gwOv^f+jfKuiiep?rcsWk`Gfz$k(1#iCOe+N96~J4 zNb{JD87_UOw8nY{nbnn>KL_v;;`4Ps>=hc2Dp%Ez^QE;ZB>y6@`PB+hV#68&OO7`1 zud}QX_zZ$oS5eJDu10q_?~O>199(W|vKTFW$SL_6>|2Cz1%FbV_qKC{S+gb_S=*8i z2r1c=KY2{ta~5DzFM|{FNsER)D^k;IWgR*%MeBAmPU~>zfh47F&4nS!YUG>~MAZPi zguK9lA^)Z+J<1$>*Qk(>=S@W&aV t52>`pfb%~!Fo+Qrarv=G zJx&IdxoSP)M(q@sCx>$2E9IGI)WIzaaw6Z?-kV}$laglAKu}h0bXX^vUKByT2J4Uy zb*>(!5_LC6FYBE^R-%_yGOZvJE=eWB`YIidL);@(H6)T5B9?CDRI*dljV~P*%d5-) ze}DU%GPplbik*dPGlp5qi#R*HHMJ+GA6z<6O;cmmL@Uq_F)U3esNh5!6wkmo zASw;}J;=*Xfl1QozJ7PlMNcw-KWD2H%dT6dQ^RZ-^?fF3=hKz_3< zue2yejpN?5{HE+Fb8i(c5hTRBqE)a|ajf%|l!lnlX)2LxVhXJWGdH?*?l|2@bg_7D z&G!<0js)lBK17EuUZP4{0hOW*RBwF*J@ysPqR_QWB?45}c>T z$HL5}kM=T+L?}AR!d|oQ?TKty+(jdx&0EkONY!|DJ8Sg<}r^k z2C8Nw$+`bn)dn+)OE^Q3=^@QeZnjLeNl}6oz$$cul414~u_h?{1q#EjB%W|40MmgN zDny+pq8ZSK)|8UK(#-4-Y+&(-p-|b+(Knje!SK$ov^+yy3SMy|-`vcpdaS?x1G8`< z%s_yc1|i7r*Xj9q^0pNht7yU5S9%wx5LLD|;v~GW6`)@k^`r0PAZDt#YH(~}_bj+$ z=DgjD%79*Cz=W^E2js*>Q&e_+dL}x~_ERwmmxpu`^pR}|QlVqS*n6^R+-8(GKE53Z zmkZVN+rCY^=MA}su4!r~(phGQwJE$I#jfyztK76?iFn(2^=9sDRq($TF!aZY(^&eW zkt5At<$_#LyVlsP5Gf?{cfYzrsZSFu|37`t2n`m7UhTV)cDPVB`cVgRTTQl zNDS4yffWoLJrIDtH5B6!{}+TW3T%l`^hb)-3RM>lJ#m_ReTd#wV5Ox!QI5kZBl*|w&zbJ82pmqSIb{0cN8UDmLMFZnpqUJ$GHVV#1#2mTM_cc zUnBDXyv>aRbv>*Zhhs%Y4z7hT$d5MR>$-QnmOow)QB> zDiOwCbRDQkKBCYn3erCu`(+;?4W7l9g=C){$|RyU!00>rJqJhiyG#x)wN`wu{XXWR z*%_bsK|B~Itxhn4Db;pj(d;#m81g6f1)eys#(%5iwKztrBGI=7M;T5oD4yGT#s4;A zH1O(e3VMH>-xc&s^0#0t$U7`3k~gVjeyNrywv%8d0@27QIk#D zYh&8uq}GgQO`hk_==)~Rnxf=agG8b$0R6@}NaIb-!| z5D}B9E8kc+SvS?s#D9Ax_aO01E$^*Qmt(BECFz+DS+h4#%Fc8bMh7+=`$W z^aU-|&`WZ3Yci7(zY!in3vB*Qh!1yj9e&`%y#^<$X^%G9&@gVG?8mMRl|vY2^okmq zAp=DpE_1OX9Ob|PO$tVTb-JQMnh7^HL)8E%YCvwhC{*i>9kuLCTsdNFWss*dTm7lu(NW)~qZ#Rct z{Oq>&irXEt0DiQif*WP#9!HuAEO4c}C+N&B^f_H-!svm&@U5g;<6zNndbbB!pm8h$ zh^PV%z62A5IBs0wLSV6Ujb0S(b6A}gl8(mSju~5LJDTrq%`&E9zp67)PUO+9(kpRn ze~lNlLFCe|SUY<0ZnhVrKt$ZG;LX%m03u{PP(oH4v^6LZ8ghsH2eK^fH)QXa=8!LCmC(z@Pk$k3!7m|x zUxWQvA>}s1!O-g@XRh0Pd~(g#u$1iK*JFyS*9+J)E49!_OZ;nbrYH?p%2g3rcz~U! zU~+D+-dxm0n4wx|X3=A7x8^lEnnDS`Ljuhv$>CMZxjV5{9eA>)FzXmgL0`#nl84n& zATxffMcXp#(OH1VIlBkeyj$ZeK=P{AJi1?cl~jK-ST;?Z9{cqo6#izD%JmS?1=F1y zyGC;sN28vOrWR7zLZ^K2V9jFGWOe2Z<<+I@@w|qR285E(Y>jIgMjC@Zf{8vSxAyW3 zlC7Ed7*a)#oZI*@XTcYff}FWCCNRcP(_}C;V<=5$9}Zfx2;xcU78z=&aEV7;xrY0< zO}I!_zaBSjw>0R=5oRn68nrq&tHS$TKkvST`J9Pjd^V3 z+W!!tUEa`4ez{&=L^`|YakIyNwijJ%o9lQ>yIRrRRL>i^Vy}f*0Ua%v6-qyo)s>C> z>H9_x(V#%IMjeJt9y0TU+&PqN@KvzUTxkSwI!osU$GvnsAwPnf}2$oybqxz zZCY@6?=VtdDZ2J=w6>ZOaULb&elTcIJLPQ|T_u^$SkdY z=IyoVA?}_+&`Zcpn7WWBTyHhKeKX;eOmnO^R&}DNti9PgNJSPzCiymVF%UI|##n{X z2cyXqQu(8dY4octZ2q;20Cqq{gxW%sg1V*3L^yiG?+c&iXOJx)4bSMwX%YEb*lekW z#P)6LvIG5#A!$lpdm+M+x-99U>fA;9#(~EqKF(yG`HZe46r=78@!R(gjFZbG#VLbx zd?$e!RJ{2P^R}8#GA*;VJ4dGJpHk1$*Cak^cAlRFfrq(?y`)}vu}!jZa^AH%7n85< zN7?MnS7TYSD?km{IHP{|L)W*MaUTJ%_t(ybOw((&a}M|jH#ts5xssxw+X7}wwTmx5 z-%BHP;?R75-UM7Xc#$gL)Y{TpHktNPDkA(0cvQj{*w}ku7k1yWJN@ZXcf#3KsZ#4+ zR6drreb<2@xB5DYiS(m?i4VuFYh}KzePvxJ;Hb*>vJ({WC!jcAcuRocW}_U=!N%T- zYAGBTUi{*?rSwj4nVHejWS?+W!+!BwmE`A^bdf0KZ7)S}OIo>RO+&v3?_`KWmh;!h zfw0jn{(#rRJMuLb#jKi#oeZBT<(&*W2NrQd@=-ocduMkMITu;VT~*dJM>;d#(gu8= zYF&w={3TFT4!?ijOy6coW?R*C`mSJC==efM3lAN^ICY7(W5)`^|U% z5EZ zE9Qf`=KDY3wjMhZ(PwV3i480tAETPLlR2Z7in#@&w3sfRnJJ3}2d6nZlc^~ao2dnh zF&i6`u>}h&lL-@xDYFTS!2fqdTEH2Q@H1K<=L|>=Vqs$XAF^NeC2uA5Bka#ro8?-` zOLIvQ#Tx||1nWQtOEbC)4(-q!Dz!ck`YTYvge_7+d@m6Rog_~}RL?06#>V7Fsv8015fPU>ucRvvtsrP*Kg1Y+$8P3 zHWwLq`GZ@2Qs8*n?6Lw{{x>iKl zHH2RD*?@D?8tCpZ?q%Qv#rC`6Z6+6hwH#);ok2k^ioL=LAyGFv>Gk_x`(wmwLykR( z=f-^#=R=MaGhT|gX-9O*j|9-)i<7eBroHH9(X2eWA1B@8%FZ%?#gOTC=}W4~O~Udk zF_1{s-j?=U#vvNFTGlgT`IX2=Dp!+f`H9SJBUhK7jXY=O+^*l#c;+RWc zi3HNNa%^eWXg-;OXVx>xxh-PJXg!&R0Qk4?eXIoDhQ*;-L8Pbh1NPX$C#n6Drp1_i zYm_HlknP|cADXwva3+W=b7ezccTfl%*B1{-NX0ZXS8RIU5rKTB$>HbK77kT^GMEtvg2G2Hskm{zf17^}lI0vbXO2MV{g|{eJnGb7T9U zYnwWIhgxMjX7JnB6m-L)$FSL*>M8v&@@+q5cR*98iucIqS|z}A!j(;QBy`stWd3%0 z*Ed`?po{L{kNgI5y5`Vtq-cIvOE#lDLhxk^}yuQCD{44f?wkL%pfw+BD`5zuu1 zTWLxTce+{G=4op;Htw@7l>bt3`Lk6wEHB^^*V`{#;sJYuGwfIAy}a4m<=F!dc~FAc6dq^PDq9QEuge$+`$D?i@3Kl{q@2VxOC@XtNGKi zgcqe>P3zHjk2PtAooWi%&iKv9Gt>-%M68SB*0*HXnsSY7bEM$Dlj!}aAQL!@@8=YG8`MH-FI&$;QUp& zZ$fA8LU>s`qbRm@%R)B*}4nV;^R#D|mb3_oZ@$NC&_x-adAtC*kDsqo97 zV!+ia$C5ouZzLvwp>@+u{3LTF{3XLXy8LHbK<)Di{`QOnOa9aji9zq!qd-95QhNEI zrsr|ia-4zp`mIi)?n_?dSz>FK3&YI$){XGyUnKlZ72 z6{M~8T{~u^a!HrNAk!^_wxXU-QDzu*`sg_K4SdW{Bo_=NtE!}d_#*py2;w#JX)Ax6 z56a@z0O}^TFe0F&xG0+M#+7ZO2I^i+zvCH%{dbUQ9$h!0wXa>$;5*~C&V1YNO-{!A z%~GgsBD|mkt}JYQn53sQyYT_OdH@*igxJcQS&Po!1cm>KziSv*KtP5l(s%Z_=aznRIlaR#ghUf(?do; zB~yl7$gOoJn}uz2$b5q_IerSi0u;A)kV%xToIOwewlgDB?(mHd>QP+f=KQ+z90FV; zd~iR)z3p#Z@M;Ay=3mD1DqsEOt%e_~0r%W-nD;#(DBt%h>593_=!){aW;zwPg(Mg< z)%s3(O>pX|`VfLM&tASIx$(xZ&F)7C5)|6-uH2JvpKzVa-v6xB*-FaatC$WW_3M`P z#heT)s6q*J)ii{>j4xV48)k}l9vaL94rPRf&?9v{IRGh`)>;*`xP|C*?KdsE1=T?! zjGF`OSjD=N$mH*{y2b(F+hvlJW0P+7RnZScJX{C{Yl5CPr|4z zp3xhwYbZo$gYPdX?0W-0IPcUDNCd{tWG<9-F-k(o;%5XnS%YQI zx#T@U+0a==f|&YU5+4_^Q;*m|M^LFr1A;Fd2YA=EEcA-#AJ6(@-n&~7^?dTLTPeB* zWbaq_W7NAK)av$nZcJT;6rnPvu^*YPDF-Jg$A1LJ+Q^U+9la%PVfpO6xhuuqI*Pg` z@0ylz^ulqS;2io;=mxU27`_c3ZascL5$Jv;_GQAv3Lpyy8;hVItc$C&xv@R0=SHcvf&)Gme9x=al#`#f zMoDkQ(7IS)nXrSkAM{+au$^TvxI$pgM*gmp6FVQ-Y$t=w-@Iq|@FK$TQ7R=vsx1Cq zYg&Gcs@jXyr#pyO!GqKA^RBM*%~iLeGtnvaM^}$L){Z2Kl=F;r4JFUl8{mDq-mMEi z!MINyk<;|Dk9WPTng07j=B<**wTU3a;Il7~Hw^Wj23=d=V7ypBgRZx&4RzgbfE1-q zR`ARFm5h`;3)%MspF>!PATtNNh*=5~MY7(!7I70JQD zqL|lQOD=)hh9XXl+Ko3U8pr`@-RjzO%G{Yjhpea9+s&go6OQFg2mjDCF7etaMZIf+jzj|(#(su<4L6T8I z0dPZV{RY=JXy+cL^YX!cZn{3489`8b#5Y&>+Sbp=I6k+bdoZ(O11yTrNY~7U{8JhC zx_u#Qr)$xr64_3TdVs$qSPS!B@rg8&!t>&EHq| zmKMg8b+)2^<`3_%S^gqX+a*GE8&H;hnn*4M5}jUA1HX}~>tc-usbCe)KiuKN8knq~aD!O6~-5LHjz@MUsw51{m zkBSSZboh72$P!SeD(jTm64EyAywYt7uqH`WP$%Juq)Bxfd0jzPca6pRGpDkC3*w{! zPHtlT`KMf=m2selzs`405jOj-D!LbSnp4Q&Fi5;xRw#cp0H_;<`#M5Z3TNnbeThBR zP!~DSG7S2au{qIq{ji%z5UwpPM2Zn zW;z9%YN79ODrHtpFa9n6@)}c=mX*3){w7yvO{dl9s3^&Z5{Yft1?&}KbA!``1z9l! zJo?uMXjHuJG#2mO7r;Vr0%5-Ey{rh1_n-a4N&&n)K%XqlwA+L>TZze>Cir6x&lu|O z1$)6?DzKFmka`ZU!@s$R)~Vje7-*=2P?;M}KxwE{Bvs2-k4GE0v^P9)h?$J87@8;VQqWxH%ut9VXqZ zEPfUimbJiyUHz?gHZ{0bQ|4i*;oEtZVY?&w0H>s3VYM#@Np&QJM6@vhO%JK+S=*Wvn600n{b7onaN{Ml=yK&l+lE`ioM zV1zSRPQt?BzAZo68M^_^dTlEa9u&WQ`3SpHoH-AycE+*0{6A4#cjxvtLKZ2nSk3k; zFZ!nKZQ~cHIyLh-5?76Is}n-3wM$ZpM0YENqrAMM9&9+ARKoz3q@C;g2$gb^Ln6MM z?mV;5Vp_0UR*R-6yax$*1LW6NZR)Dp2jp}n?PJ>o_xn;^U;yZ5mMEWUlp zzUDA8KD*omQyCJiJyMoJ&TjKEA5Mpd8 zfBbU8V--BSl;Bcc=^5Hq?Ph*KG3UBYLbFs3l7*eXt0gwMG3=nhFff`};=g}ljfd?- z5m--veoiUG{ym#~p;KuDXNvyrxdVw&I}lt~5BYKncQc{1u|hpJlWD1uc9#{~LCQz{ zP{yU1)Wk<|qBsh*82ZWs?S6YY5hf~`304u=S`KN5SV=hPpDW>;*io@{>}*L|j9nLz z%yvnC5Gfi~Qi-WM(~WSuL*zGBLR1E?1*<23XfAEDC}MZ`dBUyF*UCHeX*yT(J803< zFu%1HRA<-@ue|kGNBl(89&=}9?5 zBD`rBn~!$FD6ncI z*GMG4@+QWP+WC1Emz5^Zna}SL-txU#2k%hzxM_RL8J{V!f&33-7Sg=fGY3C(8Enzo zz~BTm`Zc24v%_pt=^v0Y+6u~SAs77I6hTBvZMAjzn z+@BkHgz4PQqU>ZB(|(6d=LMDTPL{V}N*3<-lJKW{Q=xXR9O%2!n&WOAY1zo4!%177 zd@NB)nAu+y$5Z-^E6#aXH{Ci8cCr|rPi@x3g-6wfAcXc0h2Y-yf!N|sap9iw1}Tl8 zKu$+15ki=TUg)RO-mDa08{s*Kljb?OjK+xn)hVK;wP~!J4%fc2I4z%9l?L3GjqX7bP;d&Ftt{NB7X9^$& zFn^$D)LGp1*$wi~2wq+Z!e1)Lp0RYoFIFp1jsH}7(dN-5$GQ?|r9X;LY~ftb%ITK_63r{+K#@DG$~d3Wh8t$Kts;6khra)(Q0*(%lT5R z7ur-M4x#_@3MmOJ606F4BcD68z-uOU_mA?1#7uHJSH^>spKh;K-(*CudG|? zyA?Yx(hz-(I}go`2AR}NuP}gCu`i)rY7D{42aDMHT^p9a20K;-H9S6hdWX&WJ8bfs z&Y)+F5B5Ool0DC>FOa{FGYk8lChPp_7$b`%n(XdY9LQyYJH^`w36SEy3Lh(l=@%NvZ7QHiqP>6(oVjRV0O}LX1&>-u@Mf zfa2!X#kHnM?$=l@lh+K1ntUgYtOl@Mp2maG>nOnTp~8DvbrV*OO2OM3k`;FZ>}HUO z@J$jUDQ(G@^6q&hMr$96BQrArcjlqdYza6!JDqY_%b)v1lj&M@YxEa<$-y+o;BgNA zxMkZ`6y2_#s_wE_7SlV)$ULO{D6`8c%xJ9slYCr-3}p>m{u?w=xG`Owo61n>P`+!& z71IobK;L>c3mlirR1e?CmENz5g3^upTGX}`!~1soICs5mb|o{n&bp8)lGMWA=@Lj) zGx^b(O{DEqKW||2BosZLUb|LrR5sQK)8V3ojftwA>25R0W$+ElLiOT=cxfo zLXxpXNEoQ9ut+F)syklhnkd>k#h0STeOS*M?{s|G+57jr_I492_}BAcSZZ&7G7HTs zPwf10(60)nQsR#YnwBJ#ZZay$-v^3)~1`lp@vFNTrGN0+I{|cFs z$LY}5;v5^>dk)=DcPutESG)t_(*oh@OO%d893++?*GCL7W9Rh87gQQ~{A1#WiXi`M zNAbA2RYR!_4g}KC^QwW(fPA4<_+QViKLafL{1n}bsl$xu=Zqlw%C8Gu4O<|Kx%F;k zU;g^lRY}eE1vZnt`wcD_SZ5P@UnDomLK54z+5IBPa}Zfr@J53E#gf@Coxh%HiSI)t zOA1PEd(;0D}tsfrcAkJn##8#S^noaar)=U`K~IXpnxUBi!!mwOoMoV8TZcH zvSOK4@wH)iN&QjX7bzw=Ttgs}Y8`3kw7qul-ig74+Cc2jvJsG;jnmDofga|8nI=`A z?k7FQ$H+bHi8kXpjlja`(Q4gT5(IMsF`cumwX0^jMsiKU@#bJAISW}BAu36JJ{|3W zY#M4OlapX7iYDkh7rg zB&hv-C4FQhj%2-#7>s65w@TE%#Dp0ZQ9nqHm**?qm>vJzpzopUv&#HMtOfKkkh(WQLKBVBANBpb zc#c8O!sZX-J#$D$(EwlqZ_DN93l62r{g2w}4D(4sv$u?U}cUUDuff=;mrJBujiMGhJWH?rg%~9%yx2Sui7Iy zJ<)MS@uk5ZrH`ukRP-rP|Cp9M)b-gqh`I-Vw_V}uk8XP?!c-UnKM#06PWBmZ%W{{AEI~wh3|NWWGW@C!e$KUo&O%Ua(>QS*ywMqM6 zykvbO%;Xs&9uc=SVVi&KIMh-T9bYpuwFzP5!wL{VBveFC3ExArl{Fvz%p>A#Mse%vyscxugnf)$MatTh{2$5NFD~63!c>YHY4+^7jWu ze16~g%Sv&D>}|uPYik0m36QwP#1V3;L{ub&5%+osV<@>xg1ueEDWj&qf9%tDGy!a& z^y#Qt06I|EbU`fu=6@{>EkGOSZ5x6%-~beqDg90d;12Zuo$bp(g%L9(x3?T_8E8mP zh0;I0fy|@W??DmOZxAhF0AAwQWM{!)kp}%-d!op2GX9GLLnUdQIEKKI3@_|#8^rV< zk@!z(SU*`!!mJ~vP-1~V<8PKOIt!uLojFdk;vwX)lJA4!eenZ?D46;LX_}|_PgS2B zC<;`AxhG&^QG-#SknE)j6a-o%ssb{!4swVl*r`SVxwJ_g_s9r!q}yZEd4>uvDbY6d zu)*I5ir$Zu?9gmsP6K?OvxZZ0XTR=|^Vw3d0l@IKG(XdbXVQkWGuHw0;M6`!MlZQ! z{*&+DI-}nFqQ4o&(xRZmWq2UAAw129tSD8(I7PrAaA!fX%cLJ~1fn$oY(e0Bj+;k zBVOa~ZB#fgFp?Z&vf_7+^09G4a1|{12(n3Yx_v6arLcfPN9q4M3m^@xGGwn|_--`k zqJd|%JX@nyDYmn;`HE*Tp_)k;_q$>)JIUBF&qekR70-%m6`&PRcULSNyr@hCBfgx< zt&PY=t_I>TA?Qdml2RrIotxO%6v^E{JQJs?@ML8p`>1Sey-l}YSLM^+ij&QYcx@Xd z)1C_D7R19c&ePro({V#H77v9zyp^qi&%i6Ni3f;8#;2anu3oLvU4!#E(0GE*+Q(wQ zSi(CRG2398;I;nrEDv+v8yF1A2EW3DCLgW-=dHmGThm&1bSbZJ#H}yQEoROlOhPfV z8YiUW6`9|eDHdXgDOrBM`6#+wBVRVON*NwOum5Z_YW%+2PM?2U`n9+MZ@Vc=RRxUe zV3G{zB4rnx@=-CzMD$2sQxN&vlDdG~!|4vSuVG|Qk~T7Yy{$JM(e zQ@Nx*c);`rh}k=xQdkStzA9PYWsO^d@1n*BTs)~ExF%9k;==Wg;u~3cY0c)TBjj}W z{bF0f(7LhC$k2(-HQ6E9F(Yk2sF$$zbbPFU4>PW8_<$jN|oE4hr>=ogOC^kt4I>~;>8+Qr(6&&(g8 zVMfhXivoASWVv_r%QM(zz3@qzcTdUl?GaL^-;nN#q=r+JQR{2iL-g+A*H%Dz(SGY+ z#+y;QS16g`?NRa9-tsSZ4|*5bdA2@2sjYDQVt_3vj{%NNm-c)1o@Oqv!i6 zAFaMWXWTNjr0d@4$A7h?l1qS24%64iC6eVb(L;aAYRt`F^)wkYR~Vd zNKRUferaf8xpH+mG4YJ+vk=v&;cKEEr9;~NqK^Bm?B_mnXua2K&1%n_?tUrqaJfxm;yb_PLO37Vdq#AiQo`+96#ul{tZucf(x{ zN`j;z71L)Us)DQURy2Yn~7O7OXKTAw0e@8oGB#>3>-z6Kw> z`>z@~umtYA5?x?33jo&MXsSn?1uPA~(nXTn)&B10!Jj>Gsnz1k2U4L;in z3QT`91SEj=rAHb8G=Qs?qx4N~VOsB}^=iGcQy3e8X?KPb zfvraVHu4VyUNB6%3O}L4BcncTZj**^mE3`f!h+`)6Y2;Nzw_2uAuw8CiH|J$z4=%S zL1%schRMOIioB1%yNa)CEngzYf;@3Z=9xpPZYey8{>YENcEqd;gVPfK-@x zBmz0lll`K}B!7o1FQLC2<`kHgMJ9hFgUavdis7VOzb2=MFOKahSHp8C3Qh56?5v5k z-Dnr^($|H8LsUciYgE2-2v`4pMfHwE84!O}s`X_jgS7N(d_Cp1t!T>Qf#fCrb+$Fa zi{dm~Ui>FV0UlWS+so1*rx9bkufOi(jJ+G+ILSSV8+a2>yyA6iNI<1XB$;1nE0TQ-awAbv~x@ zL6weo9-FN}eKdC*1lj;nzzWvcs>$se7)MjfDbFf>FP%jEw|Vm{eiqX;?B zXnNweT;V-p#LM%XHnOUbFPT^0niNzIL(8h*IB(UqAAz@h&a|jdBZc zhtEnY3?b@arUwGR(9)B=0AfH+9tgkz7sdPah=0 zk25v0W`r^|1vZZRxaaBZ9=rDY?~M-m`?F8fLQmUJSxN8pWitY{RuOgM#Zsk7WXX~s z{O>z{&dF==yR9O{n12VzpdC&@c2GZN2Yf5kC5QV!H@(|<(uo?>K0q$KJMwH3rO z=?vROloxdE5$JU&^529(Wa>k$Fyi(M)J}18bp)Pr(Dbn`X0tKmCw`=%gK#h}($c~` zZ&9jHDB82Op+Ev$5iEREB#5K~u#hLfjU0EtoJ^`qMV5vj6pMj6#1?U{C;l99N{cv0 zpdBHuTvR)HfhiD%8pb$6aT$qUoM>J#LW~^Ll>{L%`B%`O>Kx5G31$Btj50dcKz6rQ zbAjvJ#8sHMZYBmI$YG#U)ZA2Yc1qI*1=2bwA`*0CxHI9G`HMG*BQeyTJ0KyfB7h64 z1}!ic_J$0EwA_sqIoMTj9%OBfHHH2R1FE7p?LlT>PzZ=mBVAP=&SQiCK~7gzt!hyN z<>yrLoJ6YA{7Z#i-M1iIa2XZ^%T(;d?-0n(JT@s zRh>pd+)wj%nDGwr5mDRH(W()^7s;=u2OOcD~ThFHXj=Dy>5E=Tlu$%8VG^SoP(qfQKm2UE6k6F7LULd zM3l}EZVS#fu+J*m<(O&ixJVx(mC#bwhe2(HvR->BPdNkSPf9vsO_Z|`buh=!z7`o% z2}JTh{zMcAFGD{YU(FS z3xuY)Wxqj6VM<_+6|^OkJOp;oCvBiNE}bbv1(aq^3H2)kX0`ucV%oT;o$A8n%N~iz z0_z0a-^=OZ#iH=M`UyL5wj|JILq;uW;?hLRKNO(r(%#{a?-d_GoqNhXu*G6>`VzoX zVFd>4WmeJ)YiJX0FkBU=@B+bcSIC>=+9A> zoy6n&!!CYQcs{as^?%-8U%6IicY3;dy1w^U`?k*4iGKBcUOscR5&8GN-whhGy9*io ze1E(@-#UWXe7k{51Rg)N8RBGQW}{_WQSBh_JDsy8leL&CI(p zTFSe!f*?_lj5)8k96MK71H@AfVq*E!HDqj7K509KhZb}3kPHV|acVc&4cdei@+Ri% zJS(mqp3^5QE`{PjEwnrHojH(LV3h4Y2iEJPZ};2N=j&R_VOO!<)a$(0e-YKjT6|JgRUJZHb$^e zdXSKKPu}6SpM3NgWL`q{NYWTR7ZH6g+Z6B9`C9#{1k+$yKSBFX`;7^!X@SNmfjvnO zK8E7_FdUD-PMjjfb78B$j3{1_x#n(O*c)s}^~g-a_EL#3Wro;J2p!w{3{afU z2oherjzgyAhYM}J6a&oViA(aE#^bpQ-n;B_0m|Q+S}1cF&zsSWpqID%GtmNj)y&k>qgo$D zLK}(@hU}R34AwWvvEh~RW(Z<<84bO{2 zZ@Ta<#ZipW!mM%x1AJ=()!b0T7Ym2LlF-#mmF;B)5e1(oI z=L!RHe6u5_Mg)`%cEei62=hqPg_(miN}l#ISbsCAe`1O0%tHl>l}TS#HMf`sI>Y8C zyxoLv_gEMCCjec|&Jo6Zl3ur`B5ck0b=-Mu+(ypfPEof{+2}e+N?{&+V4tD?S&e)2 z+~tfO`jg&i<1n3Sn}7+$ce;KEW(5h3S1w?UE~vWNqS%U>Vb&CL$Aep%S`zv3Ls33_6ue>P^O&567x#u|qgv zwKq)`Gd@rf5(v=Kakid~*3X2jvhriQIQZQg)IfIv&N!(G7osZC_Vmn5Og@1ob z&bvWmXSw~AyS@K7Z$BPC>IIQnJwUP3dHrJsZUEfYP8dC#_2*`rsN+r>DCF~K5-R>4 zzbvzqf70nY_m&3gug}tU+2X|m=`Xy1hGRX#Mnvy1fG36d<+mcZ&8~RW?bMlGOaI!A z>2Jp+1M-b&oX<#;-5UD*DbZ6krS%4#4S^6d!-tBlBSaFOH|CQ)AydNNBDYEpuKfEj zWI$*3rXlu=xPCEGMc%(+3*-m!GGXosomZspLY~-lXS0XTSUMj(rJ2eL_Q^MLnH7kh z{>IyrH7?avD#8b4J}a{LXrZ%b4k`D(a-E0FBpTp?6tOZskl~`8o}(w{^P?)SuB)Yg zdDpY=`xyYEA66cj3;?=@x~9L!sA97?T|nlK;){tT1E8Lm<-$kf;pqhW(9QRsn~IHW zY=7EWw5BA5&Q)0tDyc!2d;a8t&u}%-w9kU`c8rVX@`+c?e;#SLgtq(sx;D=&UPh~H zUtV6xl53e?H)MSV$Y;0XJSbo1r=R9eGj`m`ETEtU()5eH)sZTd)kksg+tmSB{GVSN-?wZ74_HsemiI6v~KxZ&C0VOMV;MikyS z+X3-|ePQ%#j*>t!Ugq<118W-dI}kmlCVJ+#%ReF0+qDVQjUAVT#HxJz^poG3o4b+Q zKrr?!9EZ-M>d~EAAG-IO_O`E_XZ0QIQIiEHWt1%E{f1tv0}*}6r0Q{zqUcw*N@p4{Gq^LuJkRRcL0W_~s7(05~`M4->nTE5Ed z6}fI%kJ4s~)d$zkE6oS;L!=f^V}Qo=G01o+fLSrwGP~JtsXZk7sjUPlJ`VN97#GTQmPe)#Wz&rr(Ya zA1@~r4ibFrZJW9dXW<*)N5E8>j!rqg&rfE}#*b0KHv9OfF7~Usrkk1Q7cN7g=Z9p* zvD_Cb-gbw%RqlbL3Z`z!JC$_JoQ0#NUR!e3k&6B8cvT@v5Xy__j~Hjz%QQYy!Ad-S=~N zS31#6ZLha~IeYKNIq*Zsu(wA?A9m3vGWwN47wFLhX$2_wYxj-EVt61uau5_ z%#BAkVDu6*o^ z3DpGuw@1R!(tmNC@qp$%^9N}I4+jiPFKgRH2Lg~mIdPClg~?63ppnP1kq}U8 zoLLCBT3Qeo&rC)uaf}o+39OVx+)*}?8*()b%}sbSC|gv(v?5|TVK$oPDMfrZ)#c~% zfUziZ1^yAXvl-{uR8|uV7gEI+OtVXSZviN0OL6`O)=^C6W$4q_)f@Z-kQYlMp!y`7 zoJ!1L*x6JCbeI&_VwyBLi2nI{eWMtt!Fimfc6r9|ES$6dGoV-?Y1uIg=|AxIKJ5BG z%D+~eedEePxW$$gM6vVp#KX&h0)K&HOuK!3UayareX+9}wS`3rPOQigk`w|Q^o+tr zGiLJ1?B;B?oCdCfiSib#WAbq{msN(CUAuGl-wyvNalEhQYk z8OnW9lL*@ecl{Ky)@sHY@mgiZcAIoR2dU&7Q>y~oEx}lo<$`#&fF?0xw$PtNQ#e@t zjfAttKeJ$)x-sNffak%R9!thQ~@OVCE1L@UnJlVESqpJOqNs;>rS@${oc(#bG>m)Qtjtow$WzM~gMsI!5E?}d5K=nD zmks#IIb*+WdMdgqLWPuK1K5~|sYRb|jj2oO{GRN8^lBVMFFMIVVdy+qlS7ur&>gct zt&t$eYbqaBg`QOtiC#CzI}Mg6>Ca&+lTg~q#o?VRL$LvxG)#pgX9lRnY4u5VmL7ot z&nuw|RHF%-^QbZv&6U0LtQrxVJsQu|$$n*O!TQw!g;R950+elxgE!05$Q(TigG=;#CWpvj|w)X5g(lqQOqE?;-oPkd<2Aqomu)9X6QdZBXBBuQ$F3z&n96s@7& zJ{xI)n4%@M$n|E{EaDfmwZq6dmF;P)(#k_EDI!V-R(j38ExvvoRJxLEul3Z_b`Ag0 zJuxCXG_~gNyr^y00?qaK!+B;EWWAwak$>JWVa-tGiy1a=u$D?CUR`#$Xyly8smTdj|6aNI5GSz;W%PH7czm9QkA3;HSwgZB6Mv4JjLNKehm;GXdPNik^5SD z6MtZDYgT9;7T#{5s2*XMG-CfP1DWjvX>!boZJp>1a90}i`6sQag&o8NV$LsCJ|{*Vr2KQyOAutgIS|J?;UJaL)I`1 zraXiR8&i!c_TL?4|7&w6-=-O2%pRlXfSonVIejwATTG_Tj@k&!!ic~C z?_MTfWwBy+$^^Bbjq4E>6Uo%$De+ZCYbH_(th|1bGl3@1s@qKpFH!!~Y)j7|QO?t^ zicg%Ylz$fnfAGyx$nHcPt5W$->zwXatt1}k>3|x;*pm>`EMbBr4{oZ8(?Pg}g0xHs zpbykIBS|Eb9+fF;P%Gd74J1xEk98A>Ux!SZ=ZlD`ZABuq=AG2ilvkW73?;C*%vtwY z87ax^QrF0bE4(latS7fLo@yDyrzx*%zQlVMHF4KFicQpx@M37YGav{5^?J!gKP4Iv~vC?ZofqrqZ*WK`nSvjak;O)N1eKt71II^KHx0u9qT*s<#!dk#4fJP4zcIX5%pfddT-Q9?m}7t-s&n36*-r>vAUSho#v{-31-Wn139` zO$(9~zSkjd(tSe?ZOKb#Z&V=q*;;=OEI#s&Sx;a=U2I4!B$zR}5+1@5)4d)09$VwT z?wx>mX#+(B`4^o4YU`=yd5|W5pnd1}&&%r=6Ri1fGZ*Cl{WtSp)xpFDmXn<&eK+Ah zR+{Vo^QR^?Q=t`~1~K%sCrTR>A?a;XGXCQ93Gw2o`qgk(p^No^M|zNupDGiY#J~V1 z(3U_-aBE}Ve<>|q6Di(#Y5?hx`q!I{l(oNSjZ`Ld7?H(Po0ImUFFt2x{D*>yyxDX3 zfwgZMSxkqG)Y6P4J_}_Ra9t%<$W_aA6;p~Jc-Eht&KI$Izl}4V^Fzf)u(PnKwODI? zFc3SF{KI<;+Vkx?veXNKP ze3UFs(z#T_K|2UN<~8&S-3nANX#p#M9j-P(^!5!VhoUh=1)I?r_#~d(aaM^lL?Eyn z3;Lq2$!?-@v2>#_XZk7LUfA1Ez+N=RI=CG`Nw&pOXwG@fhFyQotZa73ioV2;jT{}8 zYK|JCS??93Pj{A?eB5rouKf!a&~I;K=GBOgUW08+g&!6PkIV>8$Ie_-G?oSPU27QP zA~mD3lB0o`fv9}~3@PMc1i(Wq|v*g(oGWHJB*J93{|wVfzOo@t|H zfS3!wfup8aX8@r1 zfO4MIVSfiSNHOdw5+q_iX=v^)+MMA=j>7@Gf(S*0<5B|Q`k9gny+ ztbQ6pyFn$Z2_s;&8!|z2xCytU=7UYzwk`>p&2|L{VqR7R?eG>#Te0O`D1RnS3u180ii`+if^@Q|CajQAXoFG5ZHwj7?Ow5$Z) zRHZrw_f_jTQUBRzl zt!V+Q`bgD^l5JY>lzmk15Pxj5VTB+ESebh+9O%`u1)u^kO;Y23{(ZLX{uI#rsMg!c z^uP4|{5-D$f1atnznKkv6pSAI{0l+4Q2YF`nD@R!K)BFUKDxzfD%T`I!^MkId^Pu| zGw>jO$&xY%(ou7O?&}RqkMdeXt-++^Id1}?m7$WZ!Ke6Bqx-uD*1Q|1eQSDisr=L! zEQzu3rr=`WKtJNxcc{@}$K%07h(9C)aJ^x~D?QNr6Hy;9vAICc)-Du@rEvN1tu9m< z@j$b3)RhpNJenjf?8%T17A5}XI_+9tE2y{&OW*dY(9s^@TD`MCS^4QhP#u$*Ro3esCr!z=7)kH7(X;wH2bKKV2oJg z<=vo~Y%~3ay)(80H_^??_WEtPD&GNw)AoGmMcIRNrr<3 zrhm}R(?(w?RWy-ouXsQ zSM`P%752A5c<`?Y5l-PDfy_XCH3_xn-`Zn#_~&KAf#SZf`;jSEtX=bCK6*+AcL^V_ zbv*^a1?H&jPPu%391Lma>fYc5s#*{2fKhA`jwKN#Fd9w_s}kpd=e5@VBUdH@|0feH zgmeCN`e@$rZT&7b_$D?uB!&+>1TFNOGt8$wKguj@JoO%Magc`*V|Tn;mBiHHH_d zIlY#H_*4HusJY0j3(cB7y)e+8q>e>@&ZU2wHSBa$FU?-kaYb%$U3Rdw8YEvICrQI4 zC7ic5?2fjhHx8$EjT{3}8`@*0FE6J|1X7Q>Z?ZcTeEsqIhj81Wp8bC;{r}Ib0J*vUKdFq%x(feAp;5X|wazl| zi;O*z6;QRY9UG+)VS~Wb*6!DkPNT8$q?^a(A=+M8&;s~#USX8LOklfAy@E7|~W9)-UWi*}K5dS3N zdk58G>hsNIXRa1gz^{XBr`vDKuk3s?SiiXsE395K;$0BA(5dQ8cE)MsK?r%a5D68A zV1lp3r}c(l^dV#lhEE{ThCug#6o=$&H*?}9?EMTd+-OjSV0#Bf>%lBe%xA#};UY+g zLjy)ec!+!?*wJP&dh*QrEKH!l5@J1QcXW8De=26-eC|Qm>mX6kArOJ6pxF3ou$=g5 zYJ=c`Nvx94lB%uL#yh6=m#YUmUD z3sCBKuQz44wV@S~#j)u$ds7h)|`NQ;bA<*{LdC44Q(n%9)CO}Eba!E@HDzdFb zpf6NKGw4OsTD>7E)-%JDQ5pe>lA7+A`r>riMD>E^tuw&-YzICv2zGXVn;TAUZIGy{l{wl@7Z!fP8r zO{Mi2#PY85w0}(H)EfN9{I{C?4{FM^*VBw10i35!eoC$Nem<{leLnz_WUujb?#HLM z4FMdDxMS)G#2~y7X)1NyWr+ew8Ia?4S*OZ$u z-rV=4_`Zm(*@rt1Y#RED*Izz9HBfL9CiZ$kQAus!!8+;MP_^PVRfZ%|VU$URKg6e!R-~ z&jMma#8jwc@!)c4Wb-)UOFl?*?Y%aJ6D^gB5y9d8=LSxfhQ={_8Nw=tCcB_WObkl7h*eE+#fZQ3@^}dXL?j8I+0PW}J{O{<2d=)xz*vi9CgLE% z4|e5Uy5H6ijkNUtPKf~qrd6acK?eSx!oD)9jwM((zy^X7oZ#;6?hxFa;I6@)9o$_u z?(Xgq+}+*XEjT>RIrpvg?yvV_)=aOis_E{jSv~#rS2csafqyI}4D^L~VMVYss?mSj zCK`2#8``a*HDy8;n#R`uoS?6IO?T55QZfCG_2+LJom>W@>?zO()epLv3u(pM?Q!e8t^}C^x}6?C_YeGNEX+gtrH);T9;(j}x03bV zU1+1cDx^oa39)`XALobfyB{78gYui+tuN1u@}QSRhmC2i!Sxh=is2wHAQ}{p6Zxs%Yail)X9Cs$tJDzvJ6~>lXA_s(Hi6IJzq|G;jH&0Q28bW*p*1-RVrV)mY}s#XZpq}Fers~0RJv)| z066-Ty?|2p@~UvEr&2#kVuRBZL7&v~?E*V937ev88 zC-)K^2%mPTduNu-;LENq-p-e+-q&Zho*6mL*DTrOX!6&#T^J6bpVHRmQr7ERNhoR4NNH4U zEQu5&Cel~u`^U4ONjnC4w;Np#;6v6W!>@;`(Rnisn)_Xr%B*U8UGdEhAFo&A)zGQA zeP9|F48^!4SRGE*L{#+nqt!zZw@phVP1$4?e|vATaIeFl?#9EHxx*X2-_J8Uu-Vo{ ze|O)OuWO^a7*0pY8Tm8V(Db0h7yW>GmfZukUn$NpGT2;JbKA+*9$@rX4YNd&L@0yT z$SRLYf~DD;m0a6{;&&UWcxBB7Kj8Nh)q$qUIc_s$cNcl50hBl2&^}P4@?}GW87Pc6 zttK{q_2XB1EhwyP&EQu$xuk}QM?4g$XSSb_EIUxXQgASfMv~dkqIXxo)WRADwxB9; z=X)ym%yd6GxxA`|JhV{cjZq-%S47+p&f0-523@FdN+uq9i7aS4-Aw1Aa^bl@?KQD}&7K_SG0%tdfiMnd}|?^c=G#W~plyv+hPKS=8e;e@4<8OT6w< zPFy2Pd~la6;(kO`2O>1qE+1)3&0_TU270XsbF1fS3!m`3m2|r4@hemjlULfTX)A_C zFT5(beAlN<`_o@Wu2B}g<5g!zC>G1=vvkCs$^i>rCX+NV}MKaoTlUN+6Qy?3HfSec*QZgjWvC@Y$)z*n63 z9^q9v(nY9PhSCsM)KmdGzgE<$oqs`|jOf~Z4~>HGN0w@$l4rNq`)Xn6=3KIohCgf%Fv zqj$SSi<>QxvFud>W;DJgRq2<;Sv1y+C8As?^#mvE(QSYdL>K9-y_zl7aoXt&XwjRU z8tC84Wn&SBPU}d*U1W=93wH-tKknS@6D^i6W1zLj;3?G5(v$rU|+bqVb@661(_RroFBmw}zhOw@B@mQgU`+qAN`b7b|LaTr zXS{THnILlD!+V(S#6Gk6%aI)6SJXV@=39Mc&9NDCGIcEN<7Bb-H}ed`Pw>G@ZLy?M zL{;O=)pJpn+Ur)tF zx_;QaeVJMW$_+-ZZkKuU`lzfFCrxlZ+Y?Ck_q?oc`(zYvw%um4rwNu^d8>8Gy;tIA zu560}lYmv7WScGF9-J7^?~cupyO{TTsoyNsxB*@f# zLoDA6e+>(g`Ab7lt9_-0c}_bw@MD0I)8J&{7+@L}K?+q7M8d{pJ?e(-u7giivn2XSMTxuyykOmJg7-{(uQ)< zEX%5}wB49AnrIt@s~__?JTl`OG|;Jie1j4JI|=^J9hjK^i8iCGfXD_1XJYy1`l1SA z==1Tj#(pDfTCahy2LF8gzOi6rO?LGVy8rlskUanuBmfN{Y65SBz=s24Y9i|X$77fo zLH4f@EKS(G5X&Us%*_9lC=MZJQ9(K8U=&S6FA#EIV9ZUwULm%=ex4N}0V|(soc{^x zLj!tn!CC&th&n0283l~xAIBqax@8CGfPLoFP~Ze4LW8q>HjT6iP7pu~2L8!-RWc{ZY{x1MA7-+l!0u5w?07=>8We=c$ z2gQ88a-d;v05=2&I}@lo9l+fr=mRi71U)@NP=bad0HPq<*H2#ezbaCZ0C1#F!GHP* za!dzEgLAMq{YeL~0zjke016OJ4uBaX#|ijP9Kg!T%m#|e0eqK$H;l?e9pqLKyqnKy z&{D*$;ncSO5i>;T%NQU8NT6DV`5GXkK=?bBD9jHKjA5pISn{lO`pfEm#i|6a_@@NN z!@4VYV?!_KItPFT1l!&c{0i{nhw}y%b5M~Cct)m`AR^W4rS>B1K#@=c8GVgH|8;}E zhD@}$3FgTI!@$MmB)*d*v@`9Gn=9%MBaFN_`2J)eKtE|g`7z2iX3_lC!&dYSu7xmxr%hS7k^@&r*^llmqMjO znkhCS$&+Xs1wjUjjy71zCZ~Ta6!)l(n5$;PTpImyW#N`ob2tYg}=Q1@zLf#fSB?JqgzNH5Ly{Fn4v?6%vym&@Tv z6E4xA(XnR+mu-ku1$yUY!dnG&$XBgocZkb1(CMP$rP!k7yCF=BT%dBLShVb^2bNjiLi(s}hm7 z4(`}npouYrJWi7wjoZe7rDsN8;ADna+l=#So<$@*3sFXY&;-G3e2iQMAES1Bpy4qf zaH;u4L`7PgU%ZuiL42T8AvSfKi71chfwQ?)sNj+JFIwbomX)~#^ij}dOl43%h)_8! zzJCf8F)ZEQGKg)a2cfZb&JP(}P!MkiF}WZSsIACcH}!j@)EHTgKhqr%Niz(Og@OtP zh1R(t5qf0Sl?;Q4+=`95s0vp_)_@~s2~J)kIxv%PTK8@5EolKZNvq)-Rj0{HUn1nt z*iPb^gt)O0>|ibVt+d1sSqQ3SRkw_cg3Pemm32C7a`7cxze#^0seNUCuLl-T(3j zW{^xjsXt~9^wy+jD=O-#hS^!7!9J-?j+(~C!OS$6*p}#UizhN&VD~Qmb~n89pq;Fj z#uqpV$=3yys(H~K#6<%`ap!Ztzh2P7tU_nUuX{9yeR!8lys6+^25eE zvm}QeQ*K}V7LhX8{(QlT0jhyQ@3=EE$0s&wHA$2&WXnr<6&&{H$#0X4vX(XcfRemN zq0sG6yQe~NlboC4?3EeN_M8f9gghbRS3h9wADxf<-;yV&7-G|igG?C1pt%$J{o$3? z9B)Uq*v3}2T5@(Rc!R8hnRcKTh1D+1tRP0zjY`VlYJcDy4vCm5*S9S34ec5k^FOqd zMc&Cu$kGnRCY+(tq!}EzNT1Zw-^|FOa*CNsd2G`_|GbRj#0j z?sk4HmX?@;K7cqYd9HI;z3W~GxL3okER7J?(1Nqm{(0i=NkWh}I7gvF8?AY4nh={m zxe?br7M+TDD8Kv7BU`@am$1y6LSnGx$&6hEUr!??D2cYP<`9RZ8ZHTV34}2+ILk5P z(L}W z9~wwaYarg9*Bq+%NcqEPo~}N)vcunLzTAem{YwqP!*k|Yvx+Gl^NF+j*g<_osC_L0 z0!-U@WI;uQqtvbQQByT`A&@Ots|#{k!76wGGNd;fierQQoxGneJXsdl#W_+A!|7Nr(S;!i4@I&d;T~;eBNL%*Q{?srk=0#GDgbXK zy=Uw1gsT|rQgpw@A0y=#G`1PfEaHs7ez0osuvjc)okMq18wfYP&iOB)2qzu%_pTsb z|CGs_3ndgktL-4^G9c>rgs|Vu0h~b&M5PemvSsFDw4RL%ka0S(OBl+;idpub@q1+x} z5-7>>SvpqX<}y^qR->hkuHVU)QS8 zC;rewW^{0f8Q%Hb-QhJjBI8p1wn9aSI-Jo`n#kb-osA|18ES6TBi8D=2Vdp$z%>Rb zhEXfm=MNxE_Tqm(*hj~fnb}C0-d#03svpm|7t-Y0UJ*4Er44u!1^{;Ib}|2|i_4o; z?{hq4@QAoO;sWiC9kDKYZjqCm6xgP=EN}M*;^r(~8@(^;ewMgZSe>aF=RD|C2h;5T z#eeX>)Bn*yO-ReisBib^>yNNN9u)1@+J@3_28f z|AVF*VGU+8wFq@SN-HdasoamYa$+MXF}7f~#*H7JY6p$9;DfGsF2Z)PL~3*%^k-zKc4r3Vmi{P` zZ@n1%X%+aW6Q@{Wq1CzMj8NQZOc1lu2yv{{8hfBQ-&vH4Xeq#Yz50|+R#Mir*>(EL zIeK6D28QGVq+L+Zj+Zq$j|#e9zkDZk-tP~&NOr?@gXf9RVWFT6ebSyupMktvO6+{M zFUR)?DN*A+$K>w#D{(FK6RbPK=@mUp#^3eg^*aHY z)AYO2>`7DWmr7zf@r0k_3#Qn2HMJ8QLlZeV^~IF3c2hH)VGQJ;{u&Q&6^uOTsT0&A zEL{T?Z%d9}ZB}4R#`%c*qIKU|Jp45WG$n1d4?(#J#QvQDmE!KIw64LdIPh(b*t?am zz4X9VoDzoY&11*v=+IKC+ITQ4{QEV2 z#NK`=4gPkArLV97Kgz_CiR4G#OEidW8gug5psDgGXxs0FQRnM5M?SR3DFlQ_F9Z<0 zd|Os_;o0A-@ZAh^@``6>`kL>DTLEhZNr4T`!($ivPF}roio#e?&)%kOe^u$OSKN1# z@nD##cu6@~d6^hU4OA=3a-Q>B&w?fWRs=P6fBCwtHIggOxtkxKQ*7CQfER&*5Q0DS zVz_upo!wbXgXUyolYoXlvMZEk9wIxVfpP0_Y`L|t zrmiiNk5e%9;ruXfVFrY!)?vWizrIEg1i{khQg!<+X=u=)v)4!G188dTWi&JBQVBZ> z5u$X4x`aBbnxw-l>mnwsRhdte1hr&TYw|n6WZHvON#iymkZe3sH@7Kq%qnZt{`Ne7 zwqNO>2L9m2mLOwSFzc>;Y0UgG$QMa3@w*4@N((9<=Xb8|FEM07$fsmrS~JK6%)ete$!WQ8N5Tg z*k$6|vs5&VdfY9$SU?vroL-%&8Z&71>X$|-=_ke_5jm0+aAR!$=`X=+kuCOh_j9ss zx>n#&I)B%L-|1Ycg0}FdjCkNJ{P16^h|uKr`O-+d^=<*48p#Z_1Q~5~ZTsH%bxQ_e zn{yATaW0D&pAc+fqpK{xWA#4lNFD)kmTX$>!cB&l%8vxO0%_p1)x9RSq&U0OWE|N+ z4(vfO7VZ?|hqL)t@|}bIvwJg}!kK68KDqkA8$CinZ6`C zzkO}kyQ#3g`b_B!oenXUD5c|pE}FPx<2r4=ugDl7F>QXkL-D=ZNNlV!-lFV^TCX-A z^IKG3VppH%P{Rk>!c@UenjmrzOjhI*G)-J(HumrccJIh)&`7O@IlX4< zHqw#SRRPP9{`8JC^D-elKd1vUw5>~GY6I<_-gZ-Lgi|o~_QWMYihB;0}=6nU?*o)!`K06CG z4UfM)Cy4xchI}C~QjD708jaafqn`xD@?%*#pDpFi#7UE=l(nWh{6$D54y5fCulKrB z%V`@S`{yTcM|_C_X(s2(vp~eFCGEkOQ-D*71?@#BTn*aaFu5DY!7=ezr#?gD2t)Kk z$>jNC;xGB*Vh`rq)4VFGI&#K@jh$r@_2S|4%jtA$Q) zY7>j--(Ni4M_5AJsAU`m*WLNQ_3}51shFhQv<&$)mQxhC#Tf&E4lk_J8>Xl^^826*8 zRp$dW!|A!od1gvrK{6o?qw-@y{w2jhFUsXRS2AHp(^+sI6+KmddKS!rIvPeewnVUr zWl`o(326Kqpu^G;o{I}AFNd(}C@Ef9`eJ+MTwK{FYC7R`F72iIUlTjZG_lw~m)Y$*k`NYn6 znvClK*o5F59RI+rWT5;xfDQx)=l@_oeDi=IBoIgrfDnuG{U7V%pLJ~i;X+mW04qXJ zlKLmmBLoGh2wKzlAE2jc5(<(Y3Y>%MUz`?1iU7$9!NJAypH?CQBn$-T!R}M59~qJX zoRRe(`UMs|7Yl>9g@dCLAtw_%sJjLN7s$l;zo?fTI-0JloV7k#dfiQF>0H>zJip|# z_y?uan{6nf&S~+Y35>%V-6fJ(wPq$>pPxzvrSg+RrFK?r!@hh)Q&82T`%*xOSI2wX zGM+w~pqS!X+#;hDO?`prnwEzMco(w=BZMf6c8m$ibyOKw~z}C8$>Be4b+?wP$@|uwO5eDL0Zq= zx{6psS)thkaM00ARKBMCerg@(vV;B>l7S^rZ>4D5PXy1WZ-Te)6oT! zRY*;p5_Lt~XMq0S2_d(^5C1^c2W&JG54`_P>O|UMMoCYz=NF&WkIS3$tBb#^cphYBSPSLZ9wXoKArkpN!(c z>@Pa2a&X96H_DtYZuX{^lkmT|E5zdSJoBLnUSAC!Jj{r*6 zOmPR}BtQ6zqy4oAZpc+xuG~?Md?Ts>#UJABcVCb80y_}l5n%nmI@hLJ-4TVo?zlXy zVaub&XGngNp!q@c35R8Gk$%sG#Kd#3wUUH5hl&m8;P#90m5~v|%NgI9!3zH|K8d#G zB?x@|?I=MIpg(541%ThvN9JY2?G!7|H{+5X?Gvq`a^KwHwaaq_BkMd_Y*%X-Z3ly^ zocmf{sv2y{rN=bF#u|G4gY8JG9uu~E7{7(wXg388EgVzOQWgh|RW{X%4?H#mPD1%O z*O=2*wU(6A*Wz^i8?#x;A317vZ5Xm8OqGAYD80EyNDX3qXBZSBSB$B4gN})dYC?A9 z>XxDS9JkQ>Vk@~OgD#YTclU9(yBJC44O|5yd&z$=+rYxFezap7D?z1m=W82hG6w_g zejG!<1@_6g*OMa&qOOdL#(tr5fm|3X=g|1N_=n?~3{Q_`8hTtEMQl7m>|F{}R4?1s zXtU}xULkd(s_d}$hiAcf^? z&zz-sp!_ao^iE)^iS&4sqP~ygd-k&E)t-AjtoSw}aH*cdY0lQmjPjB_Hp2+~o3^C) z1p6a1a?EnvHX4Pt_Y~<>vLk)}hhRzOtRqO&P;z_ChojCvFuU!hy@`ok*TU1Hpq=@7 zX76Iet#UctYQg|BNzZ+5OQWL&p8ZN6RH*cis|nqtjFl)*dd%J6tH=mV=h0VagE;l#^F(J*dRI=~Ea>j{!r6Qx z9Ee(6i`%5XzA0DD5RCEWV#cc1DFgzZ95G#*&KE}1Q}R%r`-d&0S2GC{WUmWJpo;_tD4N^)`Eq6oeJQO zD`%AQm8RIPQx<4w=#8(u%sQv#a|kwVO6zbLS%!TJU9^~g!s2FA#*04T&ty<)*j1wF zz_>3w(jXuxp}?cr7T_Ziw)4%}{RyGsz`Gj}0&v@EA+s zR>ODW3`d=eNFDea54w)Y)k_Ak@{LaICmK@<GOTFes}1;b?Q_M_KHr9@puhPCkwrdsOyXgO{+V3^Qmg>`0| zOhSWdo$Pzuo<+9qDY4HU<3h<4dcG_j8h({A@;Y4POi~4moC}@rCiUGnXtDU_%dc1Zv zwnm;JH!~x5pR`4or%h<2^64(4^iK=I9@%3^H$`y~QGK{PkTW{MF>5WLLSJ{#z}TeZP-51g1I>>?fQ5{S0ch{f53IQ^zh=qpAfl)Q%q5Bt zWe+5lxq7=l`xZ1Z!re-bzxfYK1CN>8`6Nh2L)D3eujKN-rS$7zQ;ndk{zKDcCDxQE?z$5Lz!^ zEuNAjYtByp^bPf~0esfzdw^+CT(-%6G*i$w8E0X}c^gYJNPYJR9gsp88?%(feS}g4 zic}4vIMuqZ(pZK<>L7Qffuq$A$8_P}7!V4_0Jab*dmv^H`VI0xqUoS~MFd`6D4M$& zriN3qnCb0_rOT2B#VMs==x+=6h(ip!H3HqiCNcuH|FPO>mr_J`podAJXda#jX|E5Yc+9{$D%OUX}eW*>vCJ6+0RJxkdtZDixV?fh99 zJC|qI4&u>%p(;m?3EU%}b99YSi_hdRm|gq#Kp?x_+k>GMY>^VfT`{XBqfYyqivpxHeuqs0 zp{Rwb{KFgz!O&^wgdo8}>j?$*}6`h@`EY0Yl((EVdoRx>%pP#F(Xv%43|x{QAk(y=If&RB`D7vSY4xZ`hw<( zt+V@2*|p9v%rzywtjcL$(5adRM<%9EJ0>OS8usLmG+qroPJ89aXsxCVWvz3?lz|>N z$Id}_UAzXGG+pFsE5{X^gbxIE}-0>L{DvX*{rLJUq+K&T-R${I=y}FgH|F zwaM#2StGXR&u0tuJIH?zhwG+%CxH$lH^QmFy_Ml&|B7F`w*)uLr=rWEvOKd0tH!NX zLw1pA`+W7Ro7zFv&hj$V)q}5m8+SIf({8n{o7mm2Q9P=O)Es78cfI}n*VCI1audd# z0a1^5jAPE{G39DgzXV0#zS}S`!U;K_nd29IK}*_nmf)7@w6v5|%lU#UC<~nIE1T#Q zk^~<>6tCB3I+GnVTsw`p z><5NT3&KAKCcm;F$G<2lhOBlwk=l+j1Y&`r4RySz1S1FUrJdTb?*x5xcoRxgUOiWi zLr)bC5A^y2%t}WrD$^XCSb*Nm=jhRfN`G4!=dgLxb~beub1F`ov#qEWDPN*9)FmW< zhK=#Psw;oHv{tPL>N2WQwQqC|wdT2ts)`woboOmBTs?YUqMFGQUBmJDOIQuQ3QjNn zH20x?R%W8@Kl1sq{*5;1cRxbqb~748ki_R=9zi}ItH%hjRe`FzL>(A0xD(acsTuK= zF1~j5G^we{P~t3%uZBT44B}d<9V2)L$(~lO59eAfJ&eVkp1#lXTF476t1oM(?hkc; z3|_|;ZC?4nqEJ!53~a%{J9NUP;O_GCoU|d zx}eda;z-!;?pf>j7Xw&7`Jn?Da0MYaWX3qOX!K{Vj4|8rFEO`|tUN=#H4a2+q;GI7 z(x|Lf-f@`Xbl{3-yu;GVh-rpL%rw!}Jd%FyK1i5X{+ajL}<)0~p>yANG4Uy$MX3zv5RXG>G?#4ld#5DS6}Yu16* za0yZbw6Nk=#&oX&NYp<_STmS&=nIN*)`O5hF3meA*L~Td#beig8#_j<>(pkImgd~E z#Qe)uO)fq{382Q9j-eu(aNOdr7z^J#IgmL=_NL$AfGrc5o}&?CxUKz9cwX)|r`Nv$ z>D79TfsZOgQ&q6OBkC6lGne`p>p3=Q!Zb^KstGUGOAE-S2i#6Jc+avTt1sah9UKHp z+VoURdr$G=jfCp%Y?@YaosliY!&kk&bdU{!f{m*1Jiz4sD&;6`f+WKQ!@d&G)Vmc7$_HN;&LjrWEzhXsJLQ z6VvF${hz(0B@2v&;tluB=KQp#(Vb|~S8MA`Z7WY`Z533e4PgU4cjqt|rp;F0erB&| zx!3VuG6LZcZ?!y~rpaX+hO3zns3Rp08qkrdRx8bQ3xcmC#)DNG%#rE7vo^mfxF|zr z9Nt(xE2|7BFJT3W#_SbuW^Bkb%Us{s&K=taiX4@vusIGu3E zTk@Be%-cL<4C|RRX(&wO+G@?%QD#`G0y;A>SAi9(AD;P22~A_Y?&~ul_j9axjcqc) zYdPDrS{NPnPE)n$c=aoc>+2t{C+3I0Z$r_$h4?fZanuJO!>vI+Y?57-w+7weM>e(V zY{Ql$hXGqe=a>?s5Rqvec-t{jJ@we;os@;Ni zl|b1xd(I*C00=m~nM?ab_B+Q7m*0z(6%t_`4DMZS)El97L1$WL)~+(mUBJhi-NEOp zW2!DaRE$mQfh>=@K&bs7Nhu!2}*An!)uvw|; z^OpUlCgI=et&@*gN8enMl9R(LK+4&^1mpoqJb7xcv)mf55;yfM)R)PJdUYnqqy>(_ zrKKO}I!yErps<{C8e!~4SpA@7S9$kweOT|uY1~J*AK(u(({hjcj7~q^B*?ZS8{y@! zv8M}2-b$YKE5%leyA*bSKF3fIDAZf z-;WlviiCS1<<4C?`Q;a%ZVJe7?5s(c?Gj^*ul>o(IbYa!X2m~hh_=Wl)6UN-bYslS zv4HT7_CDMzo)8iuFTc_8S>A6Vy)_btCHw6vkF$t!vSwZ&u~Qr2S9$&{R93BovWYJ4 z*|qImY#rT2-*VjEZ4c{$4fbCW_h&uRqg1!hH?fRg!cEx;maav;4`Yyiuy zg&DojNZO}WkyaFT-n+)VI;5JNn!I8HddEcLx0g|Mm>3Be3I7S%=H+EjasOq)pz)cf zj6qUVo0rkpz=+eBjm40I*_4Bmg`LURh|!4ilh?+=Vr;}@V#@#jl>pUHKoWd%45uj| zKmV`D#mxBsCMacFG*eJB`#x}e$bb3GNC?1FoE<`m(H8`X4A~D(4en=H)rWCLmK4Gy zZe$pt=#S1OHK%G60T~%89@!@8LT*BC5;r_CVY^~#CQv>sb7K(iJ^9i3bdzRPdH5G{ z!gInAKg01NT7dU(-9EBLaS2G>6q6nhx`fbXh;$a!QB!oNlkbQ!vT=l~+1Eljil3#~ zZT!8^5O@}T%=smFix4*~g%dv52r;UU7nfv0+em<^Pu@#MM@G-eE46=z`%ruKw`pi| zJ+2k8c~UG+*y#Jh^WYK96BQ(9ROdJM_U2Gmn_8xLnj?xZnl>|U)MsGgU3@hbMR*yO z9gA#=CYh}_gcY&HLR?zt>U-I};@xQ<-eY&_0V~eX^p2%K4S&$Pq&>$>xrI=j=9*q- zbs^a}hP@ttZ6W%&nuC?SfU(wQ(7T0$wtd&n+D^PTmOYIK)X>)%wbi<3+7<|)bIK2| zH@l74`Ja1kv2#G}EJ0wGHmOxCTZVZiCN{7qb%K>4WUSd*mUvv(0aFI0q_}3jviyRC z!iXbwesjsvRqY{OS+umY;!+4GXncubI&x+{^F5kM+@BqZBQTF`CkcEI!a!)mqSpfo@aSdM$J*qLHii zCKnE;^uF1>TUa?*RK`i{P>!M6oinFlkB>RuVBv=E_N}h3n%<<8pjNfMZ_sDAP;I0H zFGLi%hx39_7y@(L)RnDGQCRHa!>cvgU+#IdVai;G<7-sfCxJEd%xatHmjvhKDZ-9f zyy&C-FEwjwMK#a(?yYWJ>RJN+mt^gE?3Hz<|(==37LE#`t9rkwvzL30E@ zwll$xZv1k7p@pJO%#--cFz@6N(xO;`xclP;idKO)hg$xMXX}&rWM9p(@;`~J&oajx zWX2up>ajpL#mjkO+5r?(wRj36s-)@7z1cfkO%X%`2{AFo_IK|Jx4*qnYInC2+#+`ao?Xl-I0 zG>5vw3VbG?u_HpdCuM;eGyr2c9P;3w<}2lM5%o69pl}_aFSf(xLj@MH zID@9% zh~R<^*b&WCA0koGBMLNvl#{31T&a_GS?9dj5>v|d_>+V3>}d~J91-qG-62j%RZ@}D z8%zsVqw>ufpE%KrjJQrxY@jCkG=ZErhg&-7gV-`z;j+zNF|#wFlX5SDpBFYltbXyG zWGV#8Z#y<4H0>g;g|>#{_hDX>d0}q~dQ+EOGvbSRyWH9GMmD%%PwtYv(|e!TZKb&( zY!z{iIz+ZML@8H<8@BQTC;=0zxd(BIu~& zH*X94g^?w#w-=i_bJLeqhB;re;8GICM1(4HjnFL?DWIf^#)4HO4OtFqa^gh`o?e+^i z$dCH>3+S113B4knR7rL|5-jMg%IyGe8ulHo1!SAnxV(a`Ytwx-@scA+7%?Tb&2hs~ ptC7R20n+wij{?pP7ay^$$vL1!21q=3W@Z)^4p=fWF?n&={{x;j^s@i} diff --git a/skripta.tex b/skripta.tex index 81f305d..ee40c4a 100644 --- a/skripta.tex +++ b/skripta.tex @@ -55,6 +55,7 @@ \include{stochasticke-konvergence} \include{statisticke-uceni} \include{statisticke-funkcionaly} +\include{parametricka-inference} \include{ukazkove-pisemky} \end{document} diff --git a/statisticke-funkcionaly.tex b/statisticke-funkcionaly.tex index bb2983a..ba2e91c 100644 --- a/statisticke-funkcionaly.tex +++ b/statisticke-funkcionaly.tex @@ -7,6 +7,132 @@ Nechť $X_1, \dots, X_n$ je IID náhodný výběr z $F$ s rozsahem výběru $n$. $$ \hat F_n(x) = \frac{1}{n}\sum_{i = 1}^n \chi_{\{X_i \leq x\}}. $$ \end{definition} -Takto definovaná empirická distribuční funkce splňuje všechny vlastnosti normální distribučních funkcí a přiřazuje váhu $\frac{1}{n}$ každému pozorování $X_i$. Dále budeme používat relativní četnost $X$ menších nebo rovných pevnému $x$, to znamená $\frac{1}{n} |\{X_i \leq x\}|$. +Takto definovaná empirická distribuční funkce splňuje všechny vlastnosti normální distribučních funkcí a přiřazuje váhu $\frac{1}{n}$ každému pozorování $X_i$. Taktéž ECDF můžeme definovat jako relativní četnost $X$ menších nebo rovných pevnému $x$, to znamená $\frac{1}{n} |\{X_i \leq x\}|$. \hfill \textit{konec 16. přednášky (14.4.2025)} + +\begin{theorem}[Bodové vlastnosti ECDF] + \label{thm-pointwise-ecdf} + Pro libovolné pevné $x \in \R$, + \begin{enumerate}[(i)] + \item $\E\left[\hat F_n(x)\right] = F(x)$; + \item $\Var\left[\hat F_n(x)\right] = \frac{F(x)(1 - F(x))}{n}$; + \item $\MSE\left(\hat F_n(x)\right) = \frac{F(x)(1 - F(x))}{n} \to 0$ pro $n \to \infty$; + \item $\hat F_n(X) \overset P \to F(x)$ pro $n \to \infty$. + \end{enumerate} +\end{theorem} + +\begin{proof} + Platí $\E\left[\hat F_n(x)\right] = \E\left[\frac{1}{n}\sum_{i=1}^n \chi_{\{X_i \leq x\}}\right] = \frac{1}{n} \sum_{i=1}^n P[X_i \leq x] = F(x)$. Tím jsme dokázali první vlastnost. + + Dále platí $\Var\left[\hat F_n(x)\right] = \Var\left[\frac{1}{n}\sum_{i=1}^n \chi_{\{X_i \leq x\}}\right] = \frac{1}{n^2} \sum_{i=1}^n \Var[\chi_{\{X_i \leq x\}}] = \frac{1}{n^2} \sum_{i= 1}^n \left[\E \chi^2 - (\E \chi)^2\right] = \frac{1}{n^2} \sum_{i = 1}^n (F(x) - F(x)^2) = \frac{F(x)(1 - F(x))}{n}$, čímž jsme dokázali druhou vlastnost. + + K důkazu třetí rovnosti si uvědomíme, že díky již dokázané vlastnosti (i) je $\bias(\hat F_n(x)) = 0$ a tedy $\MSE\left(\hat F_n(x)\right) = \Var\left[\hat F_n(x)\right]$. + + Nakonec, díky zákonu velkých čísel (Věta \ref{thm-weak-lln}) máme + $$ \hat F_n(x) = \frac{1}{n} \sum_{i = 1}^n \chi_{\{X_i \leq x\}} \overset P \to \E[\chi_{\{X_1 \leq x\}}] = F(x). $$ +\end{proof} + +\begin{definition} + \textit{Funkcionál} je zobrazení $T: \mathcal{F} \to \R$, kde $\mathcal{F}$ je nějaká množina funkcí. +\end{definition} + +\begin{definition} + \textit{Statistický funkcionál} je zobrazení $T$, které přiřadí rozdělení $P_X$ reálné číslo. +\end{definition} + +Můžeme také definovat vektorové funkcionály, stačí obor hodnot nahradit $\R^d$. Uvedeme si několik příkladů statistických funkcionálů. + +\begin{example} + Následující operátory jsou statistické funkcionály: + \begin{itemize} + \item střední hodnota $\mu = \E X = \int x dP_X(x)$; + \item rozptyl $\sigma^2 = \Var X = \int (x - \mu)^2 dP_X(x)$; + \item medián $F^{-1}(1/2) \equiv \inf \{x : P_X((-\infty, x]) > 1/2\}$. + \end{itemize} +\end{example} + +\begin{definition} + Pokud $T(P_X) = \int r(x) dP_X(x)$ pro nějakou měřitelnou funkci $r$, pak $T$ nazýváme \textit{lineární statistický funkcionál}. +\end{definition} + +Motivací této definice je fakt, že takto definovaný funkcionál $T$ je lineární ve svých argumentech, jinými slovy, +$$ T(aP_X + bP_Y + c) = aT(P_X) + bT(P_Y) + c $$ +pro $a, b, c \in \R$. + +Z předchozího příkladu dostaneme, že střední hodnota a rozptyl jsou lineární a medián není (neexistuje vhodná měřitelná funkce $r$). + +\begin{definition} + Nechť $X_1, \dots, X_n$ je náhodný výběr z $F$ s rozsahem výběru $n$, kde + $X_i : (\Omega, \mathcal{A}, P) \to (\R, \mathcal{B}(\R))$ pro $i = 1, \dots, n$. Pak + $$ \hat P_n(B) := \frac{1}{n} \sum_{i=1}^n \chi_{\{X_i \in B\}} \equiv \frac{1}{n} \sum_{i=1}^n \delta_{X_i} (B) $$ + pro $B \in \mathcal{B}(\R)$ se nazývá \textit{empirická pravděpodobnostní míra}. +\end{definition} + +Právě definovaný objekt je \textit{náhodná} pravděpodobnostní míra, které má diskrétní rovnoměrné pravděpodobnostní rozdělení (součet Diracových měr) na náhodných bodech $X_1, \dots, X_n$, kde každý tento bod má váhu $\frac{1}{n}$. + +\begin{definition} + \textit{Plug-in odhad} neznámého parametru $\theta = T(P_X)$ je $\hat \theta_n := T(\hat P_n)$. +\end{definition} + +Myšlenkou definice plug-in odhadu je nahrazení neznámé pravděpodobnostní míry jejím odhadem. + +\begin{example} + Platí $\hat F_n(x) = \hat P_n((-\infty, x])$ pro $x \in \R$. +\end{example} + +\begin{definition} + \textit{Empirický (plug-in) odhad} pro lineární statistický funkcionál $T(P_X) = \int r(x) dP_X(x)$ je + $$ T(\hat P_n) = \int r(x) d\hat P_n(x). $$ +\end{definition} + +\begin{theorem}[Výpočet plug-in odhadu pro lineární statistický funkcionál] + Pro empirický odhad lineárního statistického funkcionálu $T(P_X) = \int r(x) dP_X(x)$ platí + $$ T(\hat P_n) = \frac{1}{n} \sum_{i=1}^n r(X_i). $$ +\end{theorem} + +\begin{proof} + Nechť $\omega \in \Omega$ je dáno. Z definice empirického odhadu lineárního statistického funkcionálu dostáváme + $$ T(\hat P_n)(\omega) = \int_\R r(x) d\hat P_n(\omega)(x) = \int_\R r(x) d\left(\frac{1}{n}\sum_{i=1}^n \delta_{X_i(\omega)}(x)\right) = $$ + $$ \frac{1}{n}\sum_{i=1}^n \int_\R r(x) d\delta_{X_i(\omega)}(x) = \frac{1}{n} \sum_{i=1}^n r(X_i(\omega)). $$ +\end{proof} + +\begin{example} + Spočteme empirickou střední hodnotu. Máme $\mu = T(P_X) = \int x dP_X(x)$ a tedy díky předchozí větě + $$ \hat \mu_n = \int xd\hat P_n(x) = \bar X_n. $$ +\end{example} + +\begin{example} + Spočteme empirický rozptyl. Z definice rozptylu máme + $$ \Var X = \sigma^2 = T(P_X) = \int (x - \mu)^2 dP_X(x) = \int x^2 dP_X(x) - \left(\int x dP_X(x)\right)^2. $$ + Potom + $$ \hat \sigma_n^2 = \int x^2d\hat P_n(x) - \left(\int x d\hat P_n(x) \right)^2 = $$ + $$ \frac{1}{n} \sum_{i=1}^n X_i^2 - \left(\frac{1}{n}\sum_{i=1}^n X_i\right)^2 = \frac{1}{n}\sum_{i=1}^n (X_i - \bar X_n)^2. $$ +\end{example} + +\begin{example} + Spočteme empirickou korelaci. Nechť tedy $Z = [X, Y]^T$ a nechť $\rho = T(P_{[X, Y]^T})$ označuje příslušnou korelaci. + Můžeme psát + $$ T(P_{[X, Y]^T}) = a(T_1(P_{[X, Y]^T}), T_2(P_{[X, Y]^T}) T_3(P_{[X, Y]^T}) T_4(P_{[X, Y]^T}) T_5(P_{[X, Y]^T})),$$ + kde + \begin{align*} + T_1(P_{[X, Y]^T}) &= \int xdP_{[X, Y]^T}(x, y),\\ + T_2(P_{[X, Y]^T}) &= \int ydP_{[X, Y]^T}(x, y),\\ + T_3(P_{[X, Y]^T}) &= \int xydP_{[X, Y]^T}(x, y),\\ + T_4(P_{[X, Y]^T}) &= \int x^2dP_{[X, Y]^T}(x, y),\\ + T_5(P_{[X, Y]^T}) &= \int y^2dP_{[X, Y]^T}(x, y) + \end{align*} + a zároveň $a(t_1, t_2, t_3, t_4, t_5) = \frac{t_3 - t_1 t_2}{\sqrt{(t_4 - t_1^2)(t_5 - t_2^2)}}$. Dosazením se snadno ověří, že tímto jsme opravdu získali vzorec pro daný funkcionál. Nahrazením distribuční funkce jejím empirickým protějškem nakonec dostáváme + $$ \hat \rho = \frac{\sum_i (X_i - \bar X_n)(Y_i - \bar Y_n)}{\sqrt{\sum_i (X_i - \bar X_n)^2 \sum_j (Y_j - \bar Y_n)^2}}.$$ + Tuto veličinu nazýváme \textit{výběrovou korelací}. +\end{example} + + +\begin{definition} + Připomínka: pro $p \in (0, 1)$ definujeme \textit{$p$-tý kvantil} jako + $T(F) = F^{-1}(p) = \inf \{ x : F(x) > p \}$. + + Nyní definujeme + $$ T(\hat F_n) = \hat F_n^{-1}(p) = \inf \{ x : \hat F_n (x) > p \} $$ + a tento objekt nazýváme \textit{$p$-tý výběrový kvantil}. Obdobně definujeme \textit{výběrový medián} jako $\hat F^{-1}_n(1/2)$. Navíc mezikvartilové rozpětí $\tilde T(F) = F^{-1}(3/4) - F^{-1}(1/4)$ lze odhadnout pomocí \textit{výběrového mezikvartilového rozpětí} $\tilde T(\hat F_n) = \hat F_n^{-1}(3/4) - \hat F_n^{-1}(1/4)$. +\end{definition}