From ad420868e8fbffb3c5d1ea38eb26735cffcb7bd8 Mon Sep 17 00:00:00 2001 From: flavis Date: Sun, 1 Dec 2019 12:35:34 +0100 Subject: [PATCH] remove la notes from ana folder --- ws2019/ana/lectures/linear4.pdf | Bin 131858 -> 0 bytes ws2019/ana/lectures/linear4.tex | 233 ---------------------------- ws2019/ana/lectures/linear5.pdf | Bin 118241 -> 0 bytes ws2019/ana/lectures/linear5.tex | 259 -------------------------------- 4 files changed, 492 deletions(-) delete mode 100644 ws2019/ana/lectures/linear4.pdf delete mode 100644 ws2019/ana/lectures/linear4.tex delete mode 100644 ws2019/ana/lectures/linear5.pdf delete mode 100644 ws2019/ana/lectures/linear5.tex diff --git a/ws2019/ana/lectures/linear4.pdf b/ws2019/ana/lectures/linear4.pdf deleted file mode 100644 index 885b40f16fedf14c0ef09d028a7a013e40aead84..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 131858 zcmb5WV{~QRx`i9twr$(CZQEAGPAax-+ZEfkjjB}a-1_#}=eFDKPHU(3{I!10@r)O} zzhlfrsvsgp%SguxMLN4Uv|ZLBPz+&Q9>J2Z~*de3vTP!}w`U z--tp&FnGu_bz)6juvMKb#6_BDW6qzD_-vJI_g)d#;!Qlo_QA~QnccrJ6hpEaAGnHA zQrEcg+clUn4xDum2nOHi}nAQ06bmB)+aa6)DCu~KV13bZ-j|KTP zH^Z~QCPqP&M3dv>UCJ6k3HWCstUlp-%F#)BNZVwIU`py#9peCE6O8%$Gd+3pK-rui zry{CYETtkCN+RG$5+b;e@N$Zt+-ZTGvlEur0jdwT#Gi4E?=5RB-vkj8B_iVie|lvB zl8;O2yKx8y6%lg9hZ4$xy-5cRuK|MxjRLqBu~@TRy&gRVFhbQEXOgiCX9cus5=o7b zbNC7&I9%UhG53tQt?{;@ssa&-3Xjo3#{)TPVjjy| zs)@#j%0maEUbtE!q?h6R(hLq25V_{tVTHhE63I8(CmIG36jCF}^42C~IC$e0LV$~< zj%0_=mI=D5yt!SVkPeJ!(eW5X5(e5V)%YE&aSZ@&ET1Axx^^_6Oc74)bVs>8C?^<) z=5Y)Tvpz0;3Oe1WS@OV~n!EiviX~tO$3Tm@pukgT%SIQ0SOyQWf_ZszBl@ zw$;*YDk%^}t~{M4tGag}L{{(d0-i2&>%_DuNS?1lK9b+=ElT?G!7$?OV!}U$>a>h3 zyOWY2@VVs4nwK8$*gKa!>W5mp-?gEc9#Jt64+Y8kdHOFxmPXH<(#(ajSj)j+OW#tq z^AcfdJ2CFN1pr8RK*&coYHq-YNPvXvxVp;adn_5^&UJD(ljEIWi*urW9?@X<8#+$R zt7Cm2FulQIJDE&pYmsrGbj&V{VYuI)>3K)K@%})wTXjJs#bBbS&{t6XY}gQ2Xj|iC z2c?Pv8{jseiK7F5p3PUFkgPaIox z>Za|PcAF8KkwVCb2BLk+BosaIA^5Z^nLj-|!tIUCg8Rmg1b%>2=IJ+#@|mBxop@{d z$9pKQ+Z*#DM`F~Jna^3sZe&=M7{_?Cf?_n%b;OyU7YE5dP`=k*^!rz2@!>3V+4T3G zWIj*l7<5uC9q#zXzo&0=N}$!Ngfv@QGwKbH*f?gz6c7Tr1}cinP1cq$uhvK;)e=Ww z8tta>NNR@z^`Ky-hX~;yDivLK<;^d~<}c@h{I>o;=FE|9W!9j2CJe7#xf}}DAQ~P< zay-;PYB25$EgFK0@gfTAT5^9Wm_Vc`a_-cuqu}r@t$U4^UZGx%vI?dLc4h13%lxG} zhvXISE7jP=ZZ6brbS~wUi53!L3x86oT*h{EI4-u;UE5*P>VX>J2BJs{7jSeD9{sKQ z>9MuWtg^t?sQRVHP~@S5=v)6sX|+|(#Ba` zE4EVtpi*;HMnPrFmIZ!QB`${#geQKR4GqDds+x5BQgH5r4ox^TqmR!#?dtMuT8HgG zL+0jHHF>zg8Qd0dIFE_m+6Qx637|%I68+V7&A85&Fh=X7=}mclx#E3tvT-w*^})KxvS{J`n&Bh#2i=6jXXz z>ZaZe?b?8X#Fo0>wK24vI8|>fV7wS21lY5J-Wf5&)*Z!tp*Gmxo&{%L+(ms%%|+Z< z#d>T89tePcjn?)cbCUfy54yFk#08-y9;+*Nel-Vm{EQ6(R~)w_L7T*o7-QI@qEX(Y zn*OGGZ0+CykSbK)(-@2^v*Db%B5-djgJGUW)&yFBEw+l5`Np)gnG#*E2ml&a>^4=4 zc@(5}VnAYbH*36xVH92?4w<7DgMLc~KthGGw*xr)yUHsPK!^dAEUYoK>{hwO5%pF4 zFcFm1pmu!u48u`zb&i@p&XDZ&o~gUBL*BkM{^}|ZTrIZE<-CFfZ{^WSjDQB;LtmI4 zONue1jml}WlOs6Pcq&j8yg4O<{ZS$l3WfqYz=NbX8AD}ep_4id?C zilp?nu4Yr=Jt{bztMTI;yI?Cz#B?tQ^YAdUfC{#)YV4?UDBw+h8aQa+XJ72WfaT;r zEd=%+H4G+bt(O5th0cHGEm=@P2*7SZ07wqbus94vBNyBIluU37VcS^3f*X4no?qfb zgg|+fwX2eF*of$Q0DPmKjt8sigK2|iVgK1^eDp9wvb{M&e~T2fNvo^sLO&N9;3#=v#mbP+>t%N6 z^0nG%cg!=bho9N*SC}8JIM6>DpFf8AQ3}f*>aF#XFrvd#fZ1L8S-{1l_dm+dcL&Yb z2oNFF3ug#!({3tmu#6uT^S__wA+ENd5SNgjB90{UnDD;oZNU*p@EDwm2n3s&*c9bK z(ZtjjibeX*FeqtEgV?Y#sl@d^#$Zy#5cExJ2=?82dh*Uiqt?9#4;g`qmtfLFf*1js ziwEywP?n2{Lcr#$u@Hlhn;~5yQX=PRag|AN_~E%zYpKgL-?m7ZE4$x9fn*F5Fs4`; zP-u5rZZYhy29*rOyFT7=11w<4=8Tl?IPxwUm@iS!Ys{a>7GTtDSM(=dpWd;zTg~yL8FdiI9%7>lU z2dgD2n-e>nrK7B(JNm9-!v3 zybE)FxB6{8$NM~X4!%zh<9>d0zm6B!s7^)Eolw=*!ml1CT9d!lGxI%n&FBuk=u9W0 ze!sS9wkEZ!bKHMf)aSE>Kc?9-O&sXpDUrm*0pY$;g|X4Tn}Bz2UR_MIQQ1=wumt4{ z7qX?Us4u1Yj4P(zgkBs?B?a5afNS7{a{P{4{4M zEMSRHyc@@9Wdu(Z|Dfy!LcH4NKwtm7Y~=U%^Qt%qbmMH}p!J`9EJi=gYT^BHM|eHd zrDxyMz7N;jZc0*D??L2?A)Bntky?f|qJhc{vOU@V794<09-w22zgd_y(_zsqTzWf9P--Xlh zFA|-w(+A1m`FZv8>f_-c<>UB%h&n??o!pX1cK-0~uycicr|XccevqmpVWl;~K%`+% zL9T3h>>~5Q`Ol$)Xo=l0$pxnsv`rPvnW!L*er8>Q@uM^jC zRxDl5=kr^L-}?co`T71*RMdjL{-?vu{{7ewc?yO&vZif@=3woVw-yf1SL=+;UU7aB z$}ZD{$D@8xA`Y6lYo{EYoVRX7LZpy!0Tjycz+cw1kOu_`qHzg9FVZ_*Fs7x^7G}Fa zPG_oA%B>hEgF&KM7_=9x=u1EuWRV)Mk-?xD3e<^=r2Q|lpE}j^eMF)d3#_O=V2k%S z5%O)25T2Lmk$xA%?IaNe3y>{c9!8|`VW9-qM2u=Mt5kZa_Gqb(aJ7R`GZfnNyj-E= zxNF|K*^*sLif`zEii~iP3Mnfj6RM0wKDe(DX-~5ap-2R1&i(WhwP{aW`tHDQI<)BQ zkVxB&XjXY|!>3u@un(h{S1$tLu90GKKK1UlA%;0RgCXA(*ISO)q+|qZ8{Nb*uCM`1 zS_28*iO=C@t>I#Wn}R_a*=Ss+q70>3(5ZwwLc#?h|*Pd~#@d*b2i48KAlR9mS0F)xv}I z<6!Z6?tR|cCw<4ubX(7nHYItxMrpVwlt0@;d6)tW3nPdu>1O?$&Wk%G4yU_)Uubjc zy__SkG-=+-efEP%+g!R8n5g}T1oiuxOjkxNBCE0}%L;g<=7XS~EzbszpaPr99qu=i zyK5!3&DZE(p_}o1K~|e?fq`yNH-kXK<4~YJq1T0kl?JrjY5Bz^bA%?E;ASlO2#T&;h z-Q0(gwQ3|$*U}VBmk|Q)Z^ww-{pF?Wr35Lkc^?fOvs2@d`FwJN6e`^(WKqe~S|?~~ z`N|9Ek4$@9p6$}rsi)7`za2V&Mp2=w*Axh^CK9w;5Usqvc6uVDA#xH*+_GJ#tckU6 z^xJl8R=@oq6D5^ne4a|)asRpS_)|Vb80>m53id>u65>NO;|@b-WqiGiyz*Q@pQd!p zHNLi@kp4!Q%c{I4-lVX+A;(tjs3x(~^Ioi{OwC_x#g)uSb7aR=nRmNAPE%&Zq)bMp z6V#~3E7jbN7^2Fijt_+PoXy)$k6ga;Q{bja@7NHItp6CyYy-j5^n%Gxcuz>wlpjrX zgeByT>!?_!1_39JOgH8DbSymQOof95ayg542#AGzl0{+lFixd20Fj zS830La?Y=NRLV26xuOE)bdf$aq%rKtwjrtjDqj35=`&wf%V#n*DyCVI zX4`CVGXpVwRrp|Xb(Jz*o_gZjCgB_A!^07s4i#bhm2Z`=mTD;e_|vW3s9jVuKAMJ; zUi)>7)PYjsgL;@~2nxEl?~w-_+211%DwC*KQui$jC-9{Kv{bH&UsYjubuECRLMAPN z!D74!K_JRiqJuE8YLu3aavyGTcb-Uju8o1uf`oMns=wRt*nmTgO0=#c5MnuaEUiDS zt*y0!Hl$X<6?t|>52I#DV!lkv$sFKcZiHT>6f4ZhwjDqoVsl4sVyze%xH?cv<7aJK4h6W7*S2y(IylkCs%TP;!2fjdKbdxdip*Py_a$EsxdqypZTkbcke=ifW-LB-)EqD#04)jafyo)|Ev{Lx{|u)H2$X68NSHzK(ut6R zsR`uEBx!Bqf zy6c)N>87Qf;a+k6WRkXz@7STp1E7KC)MgAlmuD+|#{^A5enxlCyOz%nj6u8>--R$4 zt-XH2Q3eqS3PrE!I!d~L7vK|9tE#yn>aa*nl#Gx%89;0Eq;f7pSr7Jz!vN^KPWqka^3ELrmIwtS<>nV zk8L%sUHGvcX|2?`8o`ETAVy_awY?HS;Q&C&sdUwc`|&EWI)=tA(HLLw@@8%Tz0e=~ z(%*S!Y87`l4Gp3uJSH_Ad>nqL1Bxo0uw6Qje|OV+N(lDE3MHDsbJfOp7X!E5%G zIZ2%OnUJS|y{;r1kRwmxVlh9ok(j|rpqT?#r8QsV<#oL$ru_#|8_jEy|K7q+Q(~nS zReYOB>?W>6h0$=pN@i2%7Y0afQYxGH^}5n+Gtcf@Mig5RYv6K$)vVfAtsgWM(WiEt z<(&XUPgS`N6!ikpjEVv}S zy}j!)#X`5O%g}t@oBeljqKgw7yDq1~^RH8_$|M{)FidP^3f!du3w_j;E8AI4pNJXB zBr-U~l{7U|4m372-87E(STy&n!%CXz#TqNTZ0Gjf1DkYr(`?sxl@j2ZbqPk>p?|bp zD7k^B`8j=}grCkMZDk;9(TFb4`hHWvTzs89xD;=-Zp^_83a4u_S^M^VUFCa_?eoe{ zx0D6y&nmC0^F-bRJ?;-tWvq*PLfL-$5iQRVEB^N8pKFLwN`eF9!{MC+N|(@K0W+pG zpT8KcC9bI+Ljk+dVNQ9g?{6uZFWxWXlh&hvxC8>K<6nQ`{3u!0ZSM>=F@OL=vzAnn z`1M=xBfO}X%n-+l&_BIz2TZ_Hsio9710@HgaIN8NyXJ=+>tXC9*#u2H?lH_bv*{UP zQMGRX;xxAem}PDzXRAo@b~`=!1^iO)z_kERt3n?uWm6?ge3Mf0$@xlFpeNm4kI7ua)Mq%Ahg?b?aZ%-ZH_*c-|mz)=4u9 z$8;x7mZ;gY)V)*=Bq@q+VXej=P0USd%yYD7`nN_c8ObTnhRQP5(}9id%0V(W4VsJo z+^;*_ubAVZCHnzWN*vxLLp6=9;Mwm3*zvDf@1kf)XO-!%5xpOwd2qRnype=FK5=G| z`r+a$6H}`NuOpk!;mQ*6w#yTeyuteV^A}z|_3uX+__tLKe(6JvG1T&4iuH%Sbo36a z0S~6+nW%2siGiqd#(CL1crf>;nXGh<`k`_@=c$Ywn9hsdtzq0NauNLsxktWMlj(wb zKBJ|WZZ6}9tB(1oEQ0uW2k$x$=iBDwkIuXHk)$n!H-4CuwS13UZ#?%;> z+kB~(RZ~QoZy85=Fe6Zh+G4a`@QZ07GMc(GwGXY|*o7{gx0HB>hot36yo+4a_=b74 z?zwLjnzzOSu{lgP#^_M7ZgTbrV?&O%(2)q3Pzb8t!s8x8Kz?T<3BCygflDC2DV=+) z4W2Nn0|4|J{9-)pC%P|`_oC*q1t%9)GVPpnT}M#@Yyg9fr9Dq6x>k>@{@e)=FFZIR z;RY@l%zsV4s@wC;rNj@kQ%t$ni0`3S&!;4<8KL6X+XO)wz&rK>v`#Nf{K5~h{ih#d zV*KNh{_;R-Nn6`~K?22hruMp!INtClx*88nfyxBYBCYNf@DX7F+4prYHcQa`73X2M z{f*Ta-o&OZ7E9jrtk=gW&V>{76LS(R8!`?p5e}~Gu8uSwzX2DMxOf#YbbTVZ_`LXk zPNE8;Do>4N5Ywk2hB^3j`F&p5vK3LusXg+664T_&htro4}D(F_OA{Pjcz`J{Q)?LHs}Yz7=;UG+!JGS9b7>CdYZUBW+1?r6%*cgYS(}QB$`rAPWrf$!Iu6FqH??5CoeO)=rC|EAsn(Oxg zRz&d)gD(V@N0R@MP;-5#E;MNwA%a1DgEh(rl)hRaT(L#hA%fBQvH*e6sPmXhTOr2E z0cCmPgkIOkfTWk2aHwqzJ&BfR_NSv&yM&7B(XZDIr!tzSYt^ zsMl0{HZBZ8do7+9s63$zA=DoL>k^W_LY6@a!R&4p4lNudel3Ae!Jz4($-f$(7^u9Y z210QdEPPHWfT4Ve0PHB+T01HZk;wb*#LD;8^>=@E$9Ng>Pz#5MO-W3+9_iGlMJWy%YWMSMH+Rs*(~2$%^4Mq%7mu z_%tj-5R{$_jtqFc`Vt&X(yR)K>%^V%_mQJq$Ii{kJ*m2JcUa>f`9Hptj@QF+ z*_IRWP!IH~%zg91=Txo97SWdCh+hs3{azkreOfU83fG4{`*#Z_{cVGuqU2}3>Ioh^-fV(MjvIuY5R?Ee0Pczg zwcddpy>4?!aHi!BRVCsY&t^8B_z#`7u~c<*v%P4rG4H~@;PBA=Y*6>-!*zmVRo-?) z3F)88ywwPSp0L$n=X2^j?SrET;@Et@`svlx#|GY=9204NHIlnsX7RK9SR-xKA;Spt3`@y^V3YlwS{BQU zqAsm>vo4O@)vg@ozb4(4C`c{oEu@CI3#tmDna3g0(qP;7tZiR+RBkymIVPx?k3yBC z!v!dD(21M1#LxK7^y}yQlcU5uwIoZ04xt+=;!5IOeXSbYm67Px+1+ZCDu`wpRB5l4 zFo{tty}3vGP?g@%yrfMCdsM zCwrF^fK95{B=$+-Nr94%n$S5As8WKMHXw-~Xn%HOq^%X4>kI)*fg$Cc6RikHN=OVF zWtV<@KUV`6cp{9{4L{hZl5ismsDm-I;}F{Gp4xJRw8S3f8E39N! zc5MH}>|1r@Eu81*U6Rh7jw48wyk4txC4LfuP7Op-*Ij%rHd1rgJdx(Wpx)2cwOf^y zI=#S}b*|4rG^*EdB1|+olTtC0LX$*0#&KeGQZ5mVDa8BXhXLDm-16)0WYms-RJCt} zL>Ca~qxb6jNLiTtp*~8G3~0YuB>f#JeFq#9bGUI{(*wvDD}kU~lEx9U0H+_Ixn|w$ z7s`b5Ka~k1Gu!_N6N3NysthyJ5;LPRg93x{EGvsL1Cv6XiUi{!)gcoL7!(!-M!Jw` zf^&NoPy5{fD$MuxJ6`{NotK;*C{oela-A1Bz-g#ZofkT&xlkyudYv3Ps7dfu{%gOu zPl8Wi82&nY0|o;M0||hBa2Rk5cm{R`<~rtU#!&_hfRF$o7@e9Nod6wxiB!Tb*2T>5 zpX=ge{`a!}i*?n37zs-gBpZ#Yj)Lw73<|h7(WNGmr~0-9lBV{6hhN{RQczOK9?iQ$ zIjAul&bupyv#BtIAKkbp?*2K(Ewg`u4}funVf){gRdK;s_|HvXX8g~WW#VA`>rHT- z>y{c6Kmgcj=1LE0gSbuf*L z8@ z0zyDTe|o!fg5R@ojARUU?uudT2r!BXRNKzjy6~0-aaBN+@@|HNw3kilXKx}}-Dl;W zm5zMXS~WKY5`X8PS9}+HXmUGk#9EbI7w4Iszo>@JjAaqvd z0d!M|m4{O~UZhTKixlH=QqRz=kPweAb3OJ{jXUx3s~(~plhs82cfQM^jJpwMOBd5r zg64Yd*oC1K2lXye4`5?i2=5o5zc`m*VqyJj(5kcCasvVgV7v87A{oQt*I5MC(lkX; zNnt4H5(%1AkEG!_(S3j=|tl&@vmN=Zu9Nlo9d;umi4Hqcbc{{CWRr;BZ8F+P{+I}y=KSW zaMA;Sbcir5Nju@H;#l^Q*pR0nZm=R$A*{e6a3%1S=cLI@?aTXB#QaapF&d?t>Jb_N zv9CW_=ZYH2oQQuNM1$b2S{GsTA&MZY5x0Rs!48JsvJaGf)~1q2{`?i-KsBIzTU;+V z4T-X%TRrmv&9@tu{sqJ@ZrA-c5Ort!q=FSthJVZJK$ssui#X@zRl=@l4T3Cyv_n`e z5oxJT7(@o53BOp}Qt$;zqYtb;*Tk3wezZa5y#Ao$PM?uA%GzElcQijHO?G!ouR*4J z-g}l!X0JFBSYn8il>~&BiX|guBG=WphHZ8s^CK7zcyOm z@IG;r*WJ;pgU@W|A}^7B4qxuaZ9^JTlii!XRtd z#?kwk>!IGz6R$e`0%W{=RNU3m#oMs0n=Lu+Mc-OZ;;!>EBzzHI(ho@d7bLnb@0`#{ z1Ui=d9wwBI9D$v6fvrJ!g+afL>?y$Yl1ZaDHZ&J2(Pghc1bD_0Tqj?U+3(63 zk2`by!N|>avO~NDG|%-TOJ40k6AVh$@@j*+*F?_zp6g#?JwZ5{wF-f z|F^pT-%ZPQninom00m^15QU_6526eD^hOy1mLxI)g-lBmgSxqC)}kRK{>aQDkr#** z6cL@)hNj1iEL{dAR``K)PqA0Ae=ZmvFq=|F=F}O*FY`U31T+FR3^F1lLJ~!~N6$_i zX<;cE7>Uy!_`zM}5GKigYsDcK3locnU`|krwrER$3u_*C(V`nmwuEM2F8xMD^Pb{$ zSz!Rm>)>Ae@n9!lH4Z*c((nw$?W#|ePKiU+y5@8SVG3Gn0lNT32>c5mU(FZ(i!LrY z{X+_b5drL4vjsvX5gmbvK5wnf+pnY7Gf*2sOP5g1t2m^9fWrIL0#KhM7NM@4sA`&~ zbNww+@;I|rFE?9R6gIm9l{MxZm6ywB*lTPd5^d`4?m9RV?JDM+be%e<(6;vM{>V1g z&DmKH?keRcj_Tv89i#v#z;(pf1%xOQ)a1OkO z0T-dOPM>6MgMqJ?9JU7}y>{1-ewm7i`WNij|1+4Fm^lBwC(P9UX}&0+v+P9(dWrZ5 zH@*Vq2WE!BLjkU!$`E#@glbllRRspglch(>L>~gQoq*0QqUQ}{QXcx>7(Dp7n5no~OcD+7`v}CZ zD1vKcubh^JtId|(3NRcnu8OAMeV;y90dJu-eQyB_nh&bAlRxG*xDbi4kn~Z#4fO+P zIx`{q0vgAELSy9k`|=es#R%0efB-s+uS6rWrzf!4?r(<_U4mQ?NC{F+Gblw1ifYTc zKeR9V070n?;>gbF&s_U7iNYTVK7a_$bL=~+*zY(Q7DtByddY^@ockUzAAJ{E=zrIr zBWW((qx(yI{>*Be@C?&l7|tze3PTUjkU&aeqV4kJiJSBds~{{!s5M>#IZInU2_EAD zdNIaa^;)~w8d)}(MGQ^MH~IzTe97Zvd?wj{A>dL-B!XD-8+8;bM(3lv`{XeJhp zzmK2kf8ys)CD&}xNZY>wa!N;^m8IK86x896X9&ql4$&wt&MUYwJ%ZA|@JZBI6SGmG ziC{(yvF+K%Py3`F@5VG`Dc#C?FlV7ZV;d2tLBnzKx%O^vA2AJiNQeYoSB{xeGr#+z z*}~jBePuY;QFV`!bd8&dW@-JghkKr(-ko=c`)qQQr`mh|JkPQ=NSKSJmVF|D|i|b0Ds(gz>6;^Rvn_{z!W=D#P@CM zqkeDDwhOrQld;FlV=772pZd(v~!Y zTLu~E$2A{60tRO$SFhgkf>l*Ub5>+?Hv4T>!n0go;O8UmG6rv1=Q4;DY;wGyTc|i> zK>Il031!W1Xp9=surJpBl>uP-FLdcly;Z*g3fM0H=3YPMK6E%Iy@D|V38E0NRX!#N zw<|^VdQ6BK3X??FZq$+DPht}ngsb*31KpmzA19xC!($v{9{rU3A~-W188_x4KTyPx zG5}1=qY`UI0~*cji4q_?b$o&p-wJ9r8^GU&$^V`O=k9iP7^z@o}LBRF?f&1 zjWARyMAe#d79v&W!uj_lS+e6YA9kDWWfy1nLDzv!xWUnKRt3(x1#1J&Z5468E4x|| zD}!I1-}`-IZ+_ew^`qFg3T0Zf^dSeuyZQkVMT2Vgy_xe_lY;>1e+>_2H@d#0&cT= zGrb;~6uMPYT#>vz)3d5TYm0ygY$x4*JwnRcDF3Q-ezhjL%D;q7i5i@CKL|JV| zcn(uAZkS3)6x`ubhKA4D1N6uAzT_@+f~n;VVha@L$Bl)So0WKmpxFWKY@*6!pf%%>lAqhFJmZj6MSWU&&j{8x2~OoaaJ)^(zILHdEO3^mA$Bbmy$g1| z+uGx*H?(VRCsdvlq|a>Nn90#F96W|m%A&mS(^xN%(oQ(S3855I8g2s9y+VEc9bU2V zt|aw#03Uh@lP|b@rIy+MzCr2!Phka}h5To_02(|A>XIlcgfbX{(MS8g%^H-tQG7zt zDL4sD2*(Bb_ie@JUZqdmcZ!0n7e>-ZCec@nnKC6h;_-xE4ctbC3N@0&6el``EYKZ# zcHl`vPEw5H32cm_+AO32_Jn1EZxHFOEWo8e9s*0Q(ZKXiH>(T3H7`J_97S&3cV029 zxfdN)9Oh@OESl8i-?(6^5D>0yp*fh_`q>Bbh2Xv*@RdAf{QDsn>lovo7L5_QXP-uN zjn0h@G4>}xgbLC_LjKWsG#3BXcy-B{*dE24<2Z)nltK;(-=~zj>=$(Obe+d&^;I^T zbXwoE=D?ROFr;hlpS!viS_=2$FIZ9C8I|X*o-b}+zeirZ!>X%XK9%p^q<7#F1H=&r z%lZ;-N!>?Gkj+C@dmXvpaf)3U4&SxkgSETHZ)X!d1!!Uz`tMCb8j%g&&p>bp1N$4Rx;#p{95enV=yj^KyL1&yua2L-Tk4zA zEO+`9k~7Cn{mNdFA={g zt5H>TaK3xz)4RYWJGEK6$owl5S{FpDC=}SZDu5m8f$=V;cf>d50&c{ZIDH=^s5bC)Wx_5`fFk1Z? z!ioM+sAmv;0P4?xCZT3bTQx9pz^RKAP-!=0Z^?xS5tce-?cM1qUsc#{g6NP9E75xU*{R1jQTtn$ldRoT zXGSG2tF_qn32qfT?zn;fkww796TsjOBti-?lRZ!aAf9HdU_N(K=`30vs6j%VgavZf zw4YXd6Om<9(Ntb+(->?W;VnfW=CzVo_r_{rbN#@ai0u(^+y`Jc>z$;Z04e_$dXV)? zE&TTd%Xa$T_6ia$!14|(9l1?XrdK84|5LDSWn)sXJwkB$=7n^~f5Ne$!5@Df%Ok-j z1`Ca^QWUZj>jslYcjCC!bGLxguvDN9VOC(amfdC1om}9l)~6{1R}{I5?18yT0x-D6 zTmtUaS$&Xf9_|f~Ysu6rlsOB(E%s>+D5 z(COoZrzg$Sc%C~$m8{!nt!Rq1`^Pt)OczgQ!FEY?mt5rsgA7zaMS!?V%*<6FL2e3k zPmvT{SX2bz`!t9c&?weIt0g$yVGB^fUGb(lxo6i!YW9BUte;D<3xeO)ILhp?z3-z2 z%XzKB;8;JSX!%EB>^}92yJe6Y(VWST%eX_MhuTlE0mE=I4_rcV@@a|Col|-Dqq8N< z`a;UQ={DhhBJ1*AgEA7I=7*^Z`;Y8mKpN0tJ6ppk37Bqu0r?9J&BXHe9^Q7QPwHR8 zaQ;g|hSV-W?mv(>f{zsttU#R+?hXZm1HDixDDDVYV_RYydinxWafB}T!4`wUp3&UG z()}jR95t=-oAG3uv#eFm-bHdu)NUJQt@ye&dB+>#-?Yq|4^O&My4q(`PgcOkQd3L0 z;(dzQk!kIUH7R$!01kjXrFju_{cj~j))Qb(8JN(-VDDDF8X$+c&Jb55!>*+raQV8T zo@~ar=X(J$$>F25o%;J@hVWSG%^YTb4V4q!>3 z!N_44A1<(=9q)gLUJY0*AZd}F#%fQXUs5u@_yXe>;+yHen7!G~OhxuHAb?*7<3Tz9 z1`VEuuCleQPBlg4H}KY&O$0{-xjz+DTn$3OuilNiLv*6in4Av&uEjEoFWb-0jNGd2 z7!4@)gh++~zIwLH6^ttanGLoI`&p}|jZw5a!ywiBS>k-XfX{Ooi+v5ANI35se2WkS zT11S}1oeWWI>3s;iWR!Kk2#%^BdF29l`NW)QW{wzVrRLzbH{P-dNP|n35vVczN^-?h?X|;6nX+)_bJJt5$y6MjR1N$xD zEWIPd5lZ<9*d#*}{tI?rNp_aMH!h|#eO7Uj_v89;X)Iidu(6~t>sh_Wn{-~V#BTjtwZ?gUC_y)`YV6kiG#cS#xfxmRh z4Cn}r3e*XLJ|u5LHY&3ZT-9BeT+S$dZsZX?5+T3c?!W_Ko@7V z!oMK+g}7(>(?0&^`M*cuva^i;oM?g0+PBxSe2?922UwN6EE-UPK%$GwD+n+1XA(tl z38!Iq9-)mRrK>B3raqpb3PgF0T-)Mr)SjBIl!B&(=FPNhUhG&dRdQp}uhX*V=CR|o zGhLGMt-TF7T&a@Y-afsU*l0Yg+>oXv)xRiN+!tJL2I6oSN(7!S2hWga>LFK-47s3pH0pCOU@y4OjH5qZQk=>BJ?kEL51URy)J!-GU*eL!KkBd|nfn=( zUefmL3zA=%g#RLsb!WP*2L8!oWGs-@Q&1rv`q^*9Zk&}O5l zu}b|pNvoAo?@#UkQ5OTq*kN4h&R7w+O(Eh=oCgjYCj`YlP^8J5M40&i^aD<V+z!y+*g#R*xmiZQy-c6j5;&n|32PXB3gWGXD zzP<#(ZN9AzIu7*7jh9k-+Us+9GT-v6;ncJ%fYLePrI-#56CjcK{?uxwC700@nJMUr zp#-5R0XoE9%^IpBI2RE3-ksgVZviZEX_ATEW$D(#Ik*q21Y0VyHa8O+D;%lkTTNc#mf0=3_*E` zK^*0UK?Tm2E4C(dQ-&DsbO49v=1YOTXi$D&omwP3WnEe%P}ra>s}>jk7<< zqv77K%=4T((k*8#s%t>64uHEVEgyct=L;*x$ocpBo0)x?ndwhF0~j(xgDN}!PdGCp z6YKyCf=ZH{IB|M9orO`Sr8}H?1Bm{K>Tjr0ky6U-ciBK$s4(q!x+n#(s4zzDJh~_! zK?1Hj|y4X6K`2{7OvCTfxS zAK(KFMXT5lN^c60fY79|LTiNz_Xy|wX-2^clL(QY_-PfN;BZ@?929iw@-+f<09YVV zq5rwte^UNG{w|1#?SC%|{og&*bf*4K4~6+N_Bclv1NICWrU$T;B1$ffmx>?t7a<25 z1c`HIvOh*F)Ru6gb{v>Lb%)tB-rwW^l2)qj`C z*|Atr`rW&f5vgsfJoi7&9rYjQUcP#3JXT3=^%$+<0LC&;4;b$l6(Yewl#K*A3U&zS z8B3FQR;R$50B{0`+9*Ccc2$+DE7W0ukLv=HE@Mv1Dq=eyj#@!?Y!xPB6IW4a+9;Y1 zU(N=WP=?B*K66aeBn(w?5qm#j1V+B$^~@ZfqKhP;7nu zq_EYT7e{xBofg+DJ34qi+ZR~BFma5We}Ay*I^F%J$oy%j)R@8AHxTXQ4Ap43z`p*t zAlW#BlDN1i*;kqA;%9$~3<2-2io7VoXTgtloYdHtXMZKE@iB20oCU%GW;e|W^>3@W z4oZ1D3VZ@T;!wWT7hN2=iSTR6QVR1I+KQdQMPUkB0QNGd1EjPAIy5I!EQSt|?J0r8 z=>J+0SFdbQk}V&9Vf4v}bZ6ZYyTMC+seFHc)XjZ7Zv9@XKcsJ@^@dg5u8ReiF>O*G~oID_tc|1(CkMhJx4D$r^7ZaD#_D=D)OZ*ma ztd*oH5@jZDt(j+^j!Q~Rda^7^_b;}Jhz>MfJirhHaJKRGHXf>;*hr8e);l>#laWDcB z14A6&!Fm+iM0W|1;Q7a}XBk~K2^kSZ`qp3m;NNfIKjW?_%RlHSZ7DrY!n5)jZb7sc z)ol&_nd`uu*InEq=uPR{G=SRu=ORqOmQJqncQ@(Ij0$d?77!;XfJA>_kB@x?hFf=* zv1@OgD`+}n&VW_9Crn+CPsAjm*v}o!c87T~EnAT4D%)blsIE@Pp=ozN1 zNyZs$Cg=Z$wKtEaa&6nk7t1`$JT5b3TFX3Undf;(6f#Cariif2WRA>{DJmICgOp_+ zGKUZu6H=K&Sif6az0b4v{k#wF_qX?F@BY~Pk9D2bb)V;Po#$~J*ByfgrwfNE(E|}GEV**WnY~TdC?`_lrq8!T@u7R8oFmNe-e6Ui}S9O?2 z@TRmP8wGEMf27JVu~;xG{htqJ!R6-DH>ip}^@R-fjjr6VFd4>n{Odn>!|fe&3L0W2 zofFO{{KU~qa(p9kVa?`xcs1VZRxzmjkBfbq*utN`V0pjHvBj=!)D3kc_KCp44eBRX zHr#&~U0ZRc&3H(=#BNsBvb`*O!Q5fA(ys7Me2bdQ;H?z)A6p2GkM&BV>^s@`+zF+d zc!M$WAEF~1?0CssH&XVjM?;tI!yjJ4)i;QWs{)A%7F*YU;jH20R}hX0;0HW6Jr zk9^hpMqgJkc7iAc9p?s^g)#30ThZMr@$6ryTIm5&ecE^(z%413#MLEh<0U5YZk+| zJ=-i~|AGA*%7guzJr1KMWIkvI6CA=dVtoXi1)bd<{`1I7fdI^t@Dd8WZ47QR* z#`S!K;3M&6ODqOW3M$!*g*ls?!G6U;(X)(+jht{1iXQ%~%Y(X62a!K_KWi7-lyVMA zHKG{oiV)G)oTdmabs5JSu0%h>*AOhFiA0n#^eT=@-_=i-FZD(!LeDhSD89zZzL(E> z5jR<%CflIt8EX{{eu|c2#2kzNY0c<5PoB+pLFgHqAG*@OvJ z01i0j$210O9z%|7#**qcn1paGGlbxfN83P7k%;jgU@%dN9!EKjPU_q+$ojxA-U;Y& z+;KpTGoT0uD22~f2}Y?h!lPP+rpS+oOaPg`lHzuue=75Inq_$0PmR@vp01u3wj%so zRCF1!{BtSmxfk7Jh(&NdGYOy3BcJiqlbrXoxcX_w@1pd@-+8bR`_ow z&~1%95;VF+E1cvX3`53LV&2ny-yt8wxkLvN3J`pUI6;F_RN}p;nBiYr&53J#)EeUa z`@NC=JlMDY?{{hXZ3cRHr5xk4sF@pV2jmTL$S$(xH4H{!J25;HWoyz%gR?^3iXnvo zIWNd&J9rx_Y##$fwuv2Ph$+v_IifjiNRNjR*eb!$me}#{I{&{Wa#8pQY#Wo;aG*e& zvabN0#X!4|;!rISj^r+Q%BliXHrjOxgMpNGkuA*Z0_m%04?~VoJi~Z^`Fym?F_9AxY;=1R4!cHetJWO`e%c9r*RkJ?g_7AeDA?dD^5S1JQpZ=l7uLrtsJ=?T zA{)J0EJU`0wAxNNM}mKNbD55lhOM41eS5t{CbT? z^h1|4=aZ?Mt&6A!xal7QeyBgJ6TB*b4A8l!kiq6Z8&iE>IlhD@u$S0pj>Ux=`2a$3 zhHcTG*a%DaevSz$-P7pw{h*N%O&ZyWb<{H>XMPyZvqgiklK8r`&4YUms+POhPd_>8 zfy4z2iv1RMA19mrE^qj@RLZ!?ss+P#~EpkZ?>Y|&)ydMkWDBqyGzX zh$1J^P@L8#PCAe3YpIJosfgzWX_phM4~jgL~HS51{#mfGJPq2m_XHDueKWKw}? z5O^Z$l}VI|brCY5U`u@Mp^`4L!Z|Gl_&dVg<&t{_wq?j=tqaTA2Q3!*u|Z~~A1kW& z;_KMi9XDIJT`~s~eZQHQbKVzJRWYu4Is6`emAn?VkQoF)o=T?tXYiy!Qm4oXxUca& zzveEGDdJE9vat6$tFMv#{0Z76^cU!s*!%QYluEelBExZHsOQwz3l}KmZczB@yVX*Y z%g4CCP;e`Qy~Axu?F%dU6grSf#@L(jNQ%LDcf)uz4=!wY)1X>uv(wq+Q{?0H50s_{ zTRM!Uik7;oWN$;!YgFZz6=fFH7#=83)^o1CehsCNfF@Cx?G;Cq(vs5Q^L!PaVtd4J z9>L5>ueKYJ=^(RmZl@|TX3upV5rjg?D*j0C$Yl*DCTXugo4nf;c=-9t`O6B0Y8$$j z{o^047B^qt!*i&0JOdIi&@_DfVN1N8EWo{|&Ph`8(@jXajy3U!XYBMgmN9|F`RFtY zqBCQfUHzV^%0&2*+X*_xTx7j7$~&x8AgZb47%$v#IUjW8$;@&7rm}SW!jmz@h&Kt{Zwvc zo_<(5@s=wsq7G}>z%mUaGGK{V^7xHhQN%k@u|rsC)F*BNM;OAzP5%7x4xkEDv56&ym@vjC*BV}Bded7`iZe5 z=R5yfe8%)S$DB`dLgGBk^&}LnW^d72_Ni(b??P4^{6X%fKqKiN&3}Z{ z@sV3@;xDR|YH%fi&OJ%E7uLiwQ3|p$nsWS5br2q6VZld4ODk=WkiuzhA){%Q?cMnB zfJF4We%DAdvu86WRdtM?%XaCaQmr1hq?@;tv5V%_^KC_UQf^oC140&Fqs1FNSthNr z-P3nnTajcYD_R>w+ejEaHsQ);zlMh{Hyq-Hsp$zy39~L<+WIs)y-znGTTl134br1% zuhJo$d+7@QSdW79v*J{f+o49rogDWgib-!m)E^>gK+X`@Mg0W5ncu;vFCx&P6lRm5 z>+623$Puj?H%0pw`!h5)G(t7uPT?E@YeP3zRiB>UP?yvE{yl~aL=^M2$#7Q=R)({e zYmxeN`$ z6Bc%UIic-Gpl^e%gL>R|+gsCY_Vc7)i^AT=ox0MqTZ~a;to}Y=K(kR9H}m^k z=Wgl`JlY8g$kC+D#^q1p{!Y_|FTx$Q($D6ppZ(lj=z9<&ozJ~>JE=WNvYN_Lyt}Gj zuzI3AI0=~0Pnw)!A>v9V^kH`*pKV}=#34ZD_y{=I#rz~)MbUoI8UrAMn)Zns!$l3? zRR(`$P;o3G>pk&c%a^zL5Rokn5-w{!U7;zI)?ldR6-@6=O|Y}$*z7f@U+wV`tf0l0K*I4&vzvFYo7q$i9;Bv*`3gZl^3^!U@gz;?CAjfrX7pa+L#Ik~eh+Tz7zGjVA3Y z8eT5#vpmds?WxR->S67#uYL@AS@+ZV!eB&C;`EBT)L>%)qaSTKz7(ucm(3N@OP0ro zB$1NxQx(K!9M~Hwe85AcSf60Gv5{@ku)t})I)!&B)8T9{ocz`-%cSvubr{4~S zLlpNF*c!IOUZYT`eXLn5JiHyeNPH5KEhH;cnFWf$r{BR>6gdb&9gyabZCslo-05mj! z&DTd&`SSO<9!Q$;hiEK z_N8X(P})lMRB6}#veP<&_Id8-KS<%<<#He?X z-XbiXNSRL&Ip;{#!lCdYB$osZ z5t;$4mo&9fZr^$|JyX7U-@2Dd&CPn&vHx_HCJ$4txynF8o@!O%SkAnW4w=!ccuJQ&%0uhBh*1Y2&9Yeh$C_17{0VHnm#wZ_Efi@YJn;RWEFE>ofPK zQnQUaw}aX|RUrmQ^Y_a?r8e0vkXKhzYMKV%t!KR2X%OwQZ9PBBP>fK$v9Z84&+9DD z#9;h3sf?DgF;b^dDICW`!oY`wKH-kkXBnf&LQ<^i1j--TmSU6AAFHPqzeY6SCh+vM z^XyrS?edn-n)l>BZfHAYy#nK|yjlkmI|K+g5`iBdHm4<39gZ|26X8kYGn^j!Hi}p6 zMHO}I;r$&AhXgV;r`^kPM2YBjWNE}hyi;^zPpuz+o!H-Z5Q}%D?i&|)$@a47N;G*Y zR?WNcuPvVvuEox1h#;%P@AD0?yuSOLDb}yPghEy6ep0At38AwnQ3$QLGE~Y!@lG}c zT3AM>lgw(Uq5P*u7S@Kj$K4MbSH{$ymD5z&YN|0;j>8}#L&1yJ?!Gn6LFx4=my%_w zo~3VG(7 z#{b}uW&QWj-T|}$$f*>YP^Eo4AkR!fRFFc@uze`J1%su7z(9=Sg3;7XfcYLkpprzE zLT$8Iwd5hjdj?BT+Sq-3)+KUMKDn)X(iAPL1{Fwoy!ES4Pl`QdGVaS6ipmu9ck}ac z*(s2O{x)*Iry}z3R1hH|0s)56PU3U)*CZd(N6bR>e1ob^7+y}#LR=Hd05F17C>{W` z!zcS<3N6CUI$qbJ<54Rqub4IUx?3OQ=kWMGI9(>4OH@~I>(l--eKER6Vx25y*q=Jp z441?w+!IARU7oNpl{>p@la*c(*YA>kd& zttu-ozjssydNd(gKfHb?biiS|jqx7{i94O?^riO7i}&?YMzgdErgak&xc)zF-P=A1#FVHRiJ@fVYTemnP-upSVg! zP>{M@(q{UKuG1p_9BJKJ?CkJpHxHY6*1Wc3O80X8#ei||3+tz0xqx;wpp~3d-k2%Y zr?k0eKE_Pm^!d22$wimU2M4j%)*o5REH36fIa{&wczXBlt~hiBio>@jVf<(kf6pc! zy__6O5G&Y~p3jVOM-4rrdVw`P`~|z%J}UZ61+nHE<28nTM!4vu8h{y=f_0&9F+%=w>Z@nhq3(w2i#M%jP9q}ex zG`SPASa6?d7wa2s>IblJg27h!2~JV<;FG5&z%jzUr2Xdphzg06dSkoiAx zcoZ$YlJE|NN6WyR!9||PaKmNmSHqlHUZd@67p5=OVXLjWt1C#LLYOX1c+WJ>VUbQU z$a)Q5{gxC*Tl|D<1yfJnY}Pt{ZnipRb7#MGXLqqDJ;!}dd-2veHwi11_71tWxXh@dd&|)SH#k3ojK|jB*~!Nd{;)hq z95zHtMpy5WcTk39F z!68@#2cjenM%cp6SUjZgc5IS0XsA8T?Jk=Xm`PdSP;_+t0d_z@ zAgag-=m9?c3Ri&fIbr+O+@yQcZC~|DhCG>!a(HX$%otE>s>iG8uAdflt#vK zaiUATeSsqIb*VY0Kl!)q33(|pAtKA5Y&jySf)E+X*FRr0SH7(|m)g=6h}x$gN^KN+ zfVghh(z~(wau+!i%#f7mqET_y-<_VkgMR9BMj?W*>2=r(HhiheYO{V(7dr{gtY#zT z)3&Fj?lZmduN^T_%7YXMTp~4ilAn&gjjKz#DKbtiN1Q|A=-@Fx8-0O`7OmL`9Tw-m z@j+eehuMqs;wnUX7D&f)D_@K7c=7F?4h~Sa?c=+5q7CDy_Mjy+jqG4S1Vgtc_{vOy ze(<3$&5AIN5Io{1o?{+bS8rG$9<`2ROyG1Vc?T2@SB!QpP%3J}8cc@ExKu}cu5ZQa zBKEc&ZDPOMynHT~5;1UD1Ulwl#dv%5`Sq2(?{=ZvlxeRk7+@FuBOU-(Cn zS+?={6pOcCjA$iIDvE26j`1~D^ViX+lBln!x|UuD0i1X$!2V5126+~Y)`#KziAQ6)7fOYjX^Xv+oQbI zPN8$oaXnVgVPm16KGP%=_cN|8dV`EV(v zYL#-IPkn4YjshCz?uQa@6ua&@;xl~t{D`miMzO=@{o$aWd-ESl5=S=fzqB^YLT0XZ zf7z56;MaL9k+GUc)x!J-8MYemG5Uy1?SghL85-c)@j#c6HUdqG&21LVIoD;3QqErj5_BaJ4c zXFyi6TYT(FJQYK?pvG+w?{z)DI#6p_>e=U8O%F;^=Dp#CJ8=mKi;q1MA6vOp7OB>} z9Y6cRbT*cBNc&vQl@Xe5TzQ4p&Bv??7i&nfJ zYZc&C;(vYk1^*AId|o6cSU|xL@<}*DHG@yYfWGG;ME*?=!(9c~VQPQeTgwoDeXBvL z_T;;B_lioz(zGW}qt7=aX-}%Mj~O(u-Ff>?72wYh$RP{K;25W*V4F7db|Pv=ku=(N z&j71{{w#G!8Met8EFA`$V%Ct;w}49%Hh&AGgkFuL<)9u*qcbd&F@ENVPIIouvl48X zAc*)RN`Oy&hXV!*+$lO7I=ud2rS=O*$(Tp2S}XWEe@W0zmtKA-ou%GEDPSD^#TBPT z)LdY4%`s!fr@)Nb3w_m1&Gm+BZ5`nvvQ>lrMN!71>tY%j!XxwpR56;o#%Ec2EeFCz zlavQItssM`Ag+dlJC^{*Oa_&V2$`)ss)P&2&5G`0j9ay2N*-Z z0b@}o9E6-wog=~A#r!l^jR7IjqSJ%Q`MDygO8H;SHI!sOsJ}Dx#z|y|8{)lEN*za` z(D!_=zxsvXHw{BYNnAl1K{KEsLwLT$>Du@7MECJjz8`gkf%8tOpAv$4>aF=Cg%eW? z#|JF+mRQ~jp8tSt^6ZV-2qW7S_9{pcV?`gNCtUJ5@tZU%?3(M{2}-2s@Z2YMPP5%3 z&I>Ks)n`&)B|JvS_s5Nb*Wa@}g?XGpl}9 zTiJKn-ZIsg4t9R}t?ACuq-~QK{sSzculCts0R#coqCmg%xS-IdAEDiRDC;|iO&UI1 z>nqj%6FRohW1CC#nb4QQ+mm7%c__PK!bB+W&cIF+^yC&PzuZnKoWa%A*w(OW)V4am zEKFuF&HQ8DT&Pm2`NIXdXrp^yTKauI&szyxNxo=XrsAvhmg8aX%Hrydp8eZ(yDrsd zjSrcJYD&*t{)#UD%5epA>N(>a9&#&gz6gKns>%$PV^9&NERlw5K30A4Ybj)5LvHMK zdo@!$`rNGLQWkDYkDVf`YgBxTHd>OWD>P}MQ?mPYuT+@e70elpqE?MG*|hYyZx+2C zmZOlrt&-?1;!04gIbP=9-_Jv~p_V0M`kh*qa6>UmxEoL8LXWscxzrzO!l{y^@HsJ2rw5BJ$`T9wC~Vs2sp&T zMFe#`>Lb^&ZzGiintz!|0z*T#Qosz*CLJKjjdHp=Q~Cx@-eMX@@7XxE=Vdx~-hMW0 z#Kh$DQ1@YPTAlXA(Ym=*CjE-)Z$&TO)uzmJniVfR-dvykq8hu|9Wl0~_Wf%*{-Ok9 z!A&VorD}Eh8uky71qjDU( zulCOg$-YdpuF3LV2MZh+=!YM_KXA3{kk)e8jU^T$K|M8d6w1$zr+kW-f*xf<=X-qS z1lfT9UjSfJ)gbkykTU%f({|Jj)x=^8wPE^LR!TAXv0XCmH-pc z1VaZenLMEYlfsq^u?K|Z;;KwtJUI7oLu#=pByf``<^al1B?Y&zwcih614RS4h|~6d z1AKs{U7&^D{Z9kAFy|#HfiORV~GM7I~x<=9!PrgK-!Ek_q$Xq;t z{2uzY+g(uv2@9CZ`$>%N;(LJEoefYyc@_9blIaL?h*S6XsB2GkvC%1(Tc|vAVK5&Q z>MHc7PMjKuFtPIqp`Dy3O_X$$Aremv3v>WYyQzbCyGeX&*`r~>p{R4E5=&?oR-|BGN6WhY zPQ|+zi0m1g0Nh=xn7fv?QziuVlDGGXuHR1$hTO;MHU`{(abC$&fQ11BuK%A-huIPD z>Hq0;08=~+1PWabrVed5fS82dz*#3}W5>WW2CIGm3X_KI1IRjld2o8m1N(BaTsUOx3c076e7oXz1^9uD947Bx-BB_8Pa2~e0tYa-PGxNk*1Pkw*;4H zx=5yd!~3^ik&e|lo=Begc$}-JV;IJ;a!U6$BbB+lDbl zs|SX|`Ul(T!>r;RhW%7po;Ayt7f5t-3%}CPH%^C}eDX}xsY5;qH`~B^U5F$Giv}2| z7CZi(?(n4ti9=A0V`~TfGxy{qW`lM8i>96a{C}QD{F(VK(bH#OB;hNtKs4LrK}f@0 z3^3=V#-MCkVO{w2K)y(d1)56Gwz-A-)S{S6HUM`SnsC%ID&Voi0b3mimOcpuH$L%~ z19odY1soo+O6qHcd?NjQF19IR9q0L<&9;1T^XZ}WqeEDhVyDJpWU9{=gnF zd&enoIbH5YVC@{QzB|`-ey3|&Pi_R>^U?pNhcowhF84xkH|%>}@7%B?-Ezm(?T=nR zk^7NY3pm-XYLew-%{2lymoM$l6Z^Pj2!AM0U zWxiApdJi?NKvES9xmK1i5)9u1y6T}vj88sgRU5FSfMCrNX={!?={|8o;PsYs@TUfF zapS*mfd~!}6JG{X)7&3ML)nTu1!{fgg4Xsd;Wf;Kd$Y;wZFklAyy$vg{$dTZX z7aOV)aSBWH!Fx`7D|rl|tb29}22DZe$UGDV23;q|JJSDR?w__pRh^|X6_%sRy#4&BW zfUR}jXTfEi)re{JRKBKlqZOrogR7$G9Rjx1Ccfw=Vw30H=#}>xx0ui}!l-j^2J%JW zsm^A6?L1^cbR?8%-m{?-hv~{yicqT3a9O{>M$uDC8j;#`Ok}<+MI*>l+!Z)9GfYBD z`|g8Dgl=x>XU@cR#P1-RQcE_lRaiW6!S)^u5uU)ptuVZ}l#s1%pu>yQAiv56` zq$`ZP3Ij+;F%X>J65!TQLm`kK5AOAS{EMpSlflCgC}6MR^+yi+f3jD}0A3pcNZ7zw zB5WTPxeG(?hRM%{$wXof^Nr+)=*nTn>0z4$at;c^9DUG+4#rmjDiWpv9SqUK*w|n~ z;tv4ns0~3Mn|=uP%wH)85XI{K#wMJT(bQlO0E28NFyH(4jQdCV`+v!}+X`?X+5B6g z{k81>kZ9qM*Q*#z0|vvCq zB$C*8+%6TQMN}DS6UY1FNi(WX6Qr8V*q_#T)TL+Tc<}9DC;4ty3G+&7TUKF6lXRZ= z1YewL>b3sKoX4pQMge4YMpu$GGf5S`^%9r4zOvUn^EqsON`uEq3I?${haF=KEzdCw zqqEnTGFzEWGkTN1#;$dyRFDYm9K`0P_ft61-F@{6p3|%DZ<}0-i^Ce9C}YpUh!&@> z)41NSU>NJCBhb_y0}BQi{5nAr%k2SN3=U0ZG$NH~VfXy8Uf(VEp?1NQ{mY7uCoGNdLitk={fk1M&UZfTJEzA4=b@uO0mSx zEIbvXz3d-!8`JdzwN+ibUotU?C+A@2%^&yz>4U)YW;bMz{GsjfDtOBI7UC1HSodX3 z;fgQrAjUfgV5axa%zlE7pQyxusQ9l$V5j^i5de_%-+h+;H%$7w7LUN%MfZXYf~PP| zZR7_EZWuHsXCJyQ$`*v*?4ALGV=i5`IcPwKgen-&J%M%ux_2n^?@!!iR4p8A$H73A z^zlKJ{O^Y$V8Fu=j+5vvV!wcF8xsobRbT*jeTXLNP^?3Aj^G=>E^F?Tu({14)x)hG zo0z$Saf}VT7SyUOv@PawZ#@(SeQjjrQu_JRpq!lXMAD?ERZ9I(Mxa+4U?itM_hnNY ze~temuGL55C$`b3WY`NnDa8nW`;n$;T-u4QdqA04XbL14HW6M-HobQu3dp%d5j0z{$n@6XMVoFXBiAHgO($2JWE=r71FlICTk06?N_ z3g&YR?=-}Mv4t}nz(YNt%A{Vv9YquxCNB$k1SnKG9;H4yAB{U;>jXt+$EP^_N$yi;gf%^vjuvP|Y38S7gc#c^}TvN~sWbP_UJPfitP& zuhg`w>hL9o)>TfrQ)J0kEI;EeJvgVu+d$$;;Nk+bJ6j_Qo<;w>d^R@GCfne0dTqMP z4k?EG4U$AD@4{Nycf+aM^aDLjoUt0J>CFpIT*))++tax?=8V&lokS12c5@wpI;?A{ zW~?u-bQ!rYGQ79WA<7vLY7jCf6mX(}JD;8+mAhA5b`RP2YoNAbj$ zZ+-{+2G!fIZ*B9-ZSVknG$qlnVW6U9S#n@iNMBIAPA<-OzbKnJNz-?F3Q|rx52vRq zd)Z;Dip?(Q3D#bY8(hW9^q$Y_gWSGdPED$_FV?s_mTB+V3JlzzbE$u}OVH5UJ~OkD zl|p#V)PQF7hr}C2+{ve6^DD99FYjL?Nj~5pvGp6lk>`OkH4Xf$cPw00l_%``2^jOMzVlUn&S<3V z*Hoh0fEJ&(2Jw|Uys-SE2#5gu(&P3vbq@`(kR#t>Eh|@4 zZO|lsV=k#~-Jo8Yoxh>8G!XVPIsAf<;m9|ikkP7c$bKLsP+r<&pW_Bg2MtesEUyk49ZG+=0ZZdkL03< zsFeG}Fm-L9DI>R7A*_j0uL$IDf%;)1j?cC=?K$$v1*AxL&W~A%dWaX?sx1JfGQgM` zGbUFhC{=HueH}C3zhxL0?ngxu^Q2mH@ssRc)83x^1dCb`UxA)fzLm;u{4o1LKI^py zr4OEX zbQFQS@ECqYMe4tvrcxm|9KhsKB+eVk0nZ589pGAAiR}H zcG<#p8N0Qvqz_5cw;mY|Cx>q2Ven3CU_NT43wXV94a=>-1re0(N z9e^L$=LmjLnf?sb9M&$M)nc9QVP47eGb`t*(5ki~$SyGyxS@dv(6!H^*A(9sa7XPjDA zJ%-D0<#D?R`1B4P{kL|NE;@Yc-MqW+7#gs?lW)sRdTr_LUHVMDm+8r6-4kjlNOzX- z30j~sT7Za_JIX5@i+3)}l@h;~<4JqhDsyq>B}I#YY~9NG_Vc{w)<{kA>;l0)0}%9i z5^;kMU1X@=&Dr#X3AJxB&fon<2r>mJ%SGCy4Qpzsh6q)uzOb+uY^q9xIu_}4Z;+e4;z@3u zTInJi#AUJNalnxX4Y}X%czbgwVLf^6JRzSy^^CByqbWTxG44LBvc>uo0im7J-e4)6 z?%5%RTl=9e@-i#^i!mXg2{kW7tVsf!Cfl-IE`!Am45gkx2AlS~BJtxAD|!p^W$>;% zepZuv1=sy>hiB zT7lJM_tX7cbj#{oyd~O3`a9lI?ixH#C9~4YA%?;jwK=_jwqeY2l}E zVH4uV@}u^msg;~g^=nQ`?*4pdd?oop7~9Pn&vyrr`Kk5W!B5kS2uTlwWoW&%%OCkH ze$z9tE9L!=RL2q%-^{yq&t;j?*(6mY?6FGm`_PYz_|*L7U>pE(5KMd$g7ekH!}px2 zBlJf&JhJN=dTwIn+CK>!`|BN;v0y@@1dave|cj zL0HkmnZ6AqEk0W!l|i^yLM`)lC>GC~CzNk2NmR~qQm7)s3ffLZdS;MmZjuM#of2XE zDd!ul{b1Hvg6)m1$~b}zPp#!{5Ftx&H+&xkXJ-yoz&WF|ek&+avxH}q?sW85`4M~a zyW;Fj{v2C%WOrF?7UFSb-#YL=UnAAsbqDbpLWqOlX@vCgTZCzU`XvoYcsH^7>q0(W z+$_2s@!%IKq{Q(7-lljl3Z$=Zl!0McfFtD8RPxVA1+MFyqLoWS5qIYN08q>C#hx=3DRq1*UUWU9O9Pr`kU?O0_w(bPFXvMT zld#1uk@uaFQ6eBiHW9yQlR^!;ZQcL)9e=x4 zfwdflJ*C2XXGX3;JP6{tYbXfvF#_`Qf0RPRN%YwggQ8+U!=w^o%SnZ+d{orgu0q0* zL|n-^Z$Hg-6vN2o0O?4G=KrDz-h!^dmV*Z|fL9>HFs2H_jzR51j*9qn7GEydF9$2) zC$PPZ@Bc;a3c18U8v1;jV1Uqt$%yy7t%h-FloIg3VdkN^{#g0Q8_mZvhwcLM8FgCU zHLt}qnAmJ{31e=X-FoMOz-JOkik;FwR7dfR!z1X}Ox~|?L6pzQ= z&z3c0P}eJLF4z)ax>s5Lu<&}zxBAczr&y=yS{pi3z+w)90Ypz=*wsDo`tXry{FMoV z3nHY69_!dd%>?GjIZhlAF=n*$XKKU@3&nr%{5S(B^(sHn(6wf=*u2~}48Yx~5?CJZ zsu$3I=cR*ayG`;|v`cv9beJTcr{av{?=m(K=thbm`u2@ADy=h4N(d(pP_B=g9 zvAQ*i=)Kn)W1<^x7)9G=kQtDD!CFZJA%VrC=-c_$kp+{X@f1>$$h< z+y~_1QRvx*Sss@%sucm&`{Bc;fWH{ z?HO>>$>>efpI~Ray%5O5om;NybTRZH%*6Bj!67?s(?LKigGXd zO=D2wE)#QZ*h1F}isCr_WXJIot5&w@aR!Df4jIj(91d9mk7-lq^Jt=nh`kd&s@p4| z--g@nW^&LLYCODfG$|ECkxJHjGv+u9{v;0?kKfYBdS)1do)5_>*SkF`r zkxGWca(k(S&-hvrq9&N^eTQCM5VltLy_Hz(=gU8O?{e>uR&?jxXpx~vzH?vMO4SN# z^&_8csi|eVB5`2V&}N=`Zd#iO+MBjS=@acY?DrgW1PacIysjspo4`~C*#|rMJLy=) ziy_*cl{|@sz9OL;8@{aVe|t%bgd7j0M04qFz65D$13~4a*n@TJdSja$dg~$ms zsA76^O9Jr@UsH2JaP9ytHP1;n<0Y&Ka^JuxQky{ik zv|KH`y}bdwn(y<(1;xD;?|&BbxngmBV|+~VgLskqB+Np;!dG-;_ik4ySv|+Ct<52hT`icT3}JL0rqW)HW8;*)qnME|E>*^?Dv&`mkNx@zik_jT zfWg>z>b$G=6E-?yE1MYZGn`H86D{;&_68x)S-M%u)Q;*9#F9*%m5_t;6Lj&ObNoTF z@}1JVUEKR;`4=0kNVj@|pc4!2t00jEdsYE)0!J3nBdh|)vgOpq^@1KXApT~w5T|q4 z=Ks6V!r$8b;(+ll13)>d#3(>i_AoFu&S*9R+ETpI6iBIp0S1PP0J;zw0UI!y-wNi@ zm0%UHHGz$7Pr$JLmo)(-D$yhJ2u|a_k*G5NyX=mBi5!^PCdOoKvV=Uz5u4~Yz_~SY}-xS9bAa!!e0K1>8`Qye>dG#z6t%Q z0Jx%In3ge;Apo}v1}SSj)R2~Kk#7Zum;{II!SLoW>kQi%1pFWm|K1j|6h^X)K@H+l zFJS?cNrM7Fb2tf%;1mLX>zHOOA2NY083Znih#dbCQPW@b>+U*rULYLEkDqb9zi;S0 zJrx&v4#yTy!0|Z5Mh|~36x@cKRSFCjtT1QBq^X2An^c*f9T|1_ocGmdELZ2$q82}k z#>aGl^!KR>Qi-o(HmWNImU7i`KfIh{_;7k_l(x6}y!+%xg4JCv2iZHSXF5`DRT(TY z(j-4Ho@U zK!7?z;`kL<6fyM2tlJKk>gbAL_jk=3z2$MvI1}LHgK^)(00(>?1H9|>9hkdnYykI; z;5T~;^O&D=7{tLOlp_coLv9m_A)m$IFDr!L%tG0KQLPShzT_%Kq0iP8=jdwUmV}}M zTQLYsK8YZIsFR=U7xUctj0D3wfT$4iRbpa{r^# z(dAcOWW1<51yv#GVxOOEW@fu2jc*XFIbhdUXdfah=yx{Ey-@c06m02CY8M^*B{QY2 z38odvO`II53sb};b4B)G%LeOmod7%>iW}j;EVdGG0V2i~{k_ruXb@ZeXC~Z{xDjX$ z!)$=R@F~~W3RpGZ82nRP$QewqK=U*P&dnJIxd9}JKf5@Bmz4*$95Cc~0$YWveZVU| zhtEXZl2fVWPNY!4(kv=@So}=G9vK>gg}}1Ir_f+YngL8iw<&?<$Bn(~1tB=fXIr+u zKk1#_Er11nSKr60XWf5?7Ooq(R-wG_Kfdlb^R1^s?b~Dc+X?TllU9>?FF%aC?xQDq zCJVcu`m*|5nbC~W4Q!_n>=~Xb8k;kfefC)qW6_)RV%d%bj64~iLp|;&rBS;|2ZV3r zwKpXVNt8+L2n;`M6yEgxrd@Q+_UX@o=U)r(_$j=px<_NV`Sa`bUMWjH>)N0CkzDtA5OQY$uq6JIM$K9>2-8MZXdl?6v=~RbeI%6zfAc{QP1{)1P;BZK?iF;{12C1o)HADZocCmrC&qf&q8@CPOIBP+0Ol25$#L zy4=e|KXNG=7EPb8aTleSfNCI%b3rfQ6Ci?YY=Y2`r=b`~SRmAdh8+4^y8-Eu2K!zC zj=(<-mFNj9(}!;VQq4wQ^eIg(PBf^8JT*;zoXf!yrGn3uK~F&i7YVU(^M5j{t2cx7 zVm0zXtLFHtr>bZz{2#YxrF>@;dShn`8cFEMKb)<=3-bA@M=uJ z={~Lnw5doDY^3CK{RS^HVNIqZx#fpCwlZvd2l13S?uG1z;y#Kg(Se7_-E5y>%jrY*j!g-!HD^w= zWOH7@X|e%5^}0I3h4?K->WTALeG7C8N6Q!9k2?~xNAp~8UwUMAZi!f-ggpr?1%RLe z(GyrQq`j*;Y$f4MaZ_`BSRq)ZA{b}zGU581squ@<2e`M0Su_={^2uSxL{Nuc8)euY zUDIHL5${|dVOev%ZaSXPb>YJksf?zcx=*{tbO8Z*-Oty<)}zjv$=sA^vAX}m*W~_C z*v`SO|NF(&)!{iA`ONfj`-)l_hO9)jh^?`UE;NP}%ak8bEe)k+QBdX|9s>;y#P5mj z+R&Z$O`a)@nk57Ns6}a(&ud7iS4*dKCodO89RAVMfTLaXL`CM;ztXc;8NcJ>M1^-n zw+J^=aUD=BJOKHHh)%r;ljLilf{07$38i^RDJ& zk3D)x-Ed`r;U~B1N>)Itl{RIab@)dD`NH5Lf<>%e(%taBs0%o#qDy8TmC>vUSAEo1SRDMWZt3I};!{B0&_(L|ZL_~Tw_V!W9M8!Ym0`NF zc;mw8s*Ghut3Y8uQGk2L&c@t$yFZUa_)Zso3UOX~lCZm~0O!}vKzy}%>00iWzU&xl z$%}J0H+@m$OkMFW{Q%l~}osorRZtWg}Zb!0@?VcZx`G++k-Vb2Jy@w6x^;GF9pETtRAW%7YZ$ zj_()fLN5*>*4J7e-dR^KBkpk*?D7xb&4XE2WAifh}xg&TKwcXxLW5*&iNLvV-S?(PsgSa1s-+}(pa z1b4Uo$hr6Y-m7=1diT7qx~gmUf4%13d#yRgoMR075|EVyAykrsP^o8U`Qi>IL%Rz? zS%n$~3S;tlq0hrzDrDZ|mANzarB}E|W4gz9lmto>UMmH~={yG!gyyay=7hi^zT!D9 z2_dJT0>%xX-73UUD!y~0+mbmHo_JB0OR0c0a+Cr69*9o~4l_0yQJ9^U&jwM>`gs0( z;e9W$dz)_fZ|8&N-cannjCoaXNLRNc2Y&)w@_lSm9!cUsU?~4(&X~5!wNH1W^ay#f zKr)DRo>_A9mZ#1m~Rf(gu4am6FUiv0z=7j?YYI_{TTBB)d-_RBP2=P@x$C8tFZJF@{N2fzh6Cx%+t-RL zabD-UsY1_N2b&)i;CS-`v$t6Kq>uyzja8Zzjrr~rn((Vz^A?QVNN`&>6ZGB$xN5ZZ zvf>voR)^F1@YTRKxC5i&g-mSH%oPVL!5Vb{%E1l@yon~gL9|^kUcqWcwhesvf#%3{ z;)qv>2)|9zZdvB-s9_iU?+mw*EIx<=jh`{<||=qb{b`l`S9k)P-sR|w?GQN?>u%9}p;f95W%|2WMY1TYV=wzXUFAI@j9;J^77u{HIBA`b?vI1o$(na&2$lO8?AH5BmP;&&<_p;0W0? z2s@mzubmoLM_uym`ukP$%(0V#|>j~tZw{T_^&GZW&wl%A_5t^z|nh(qL)(`9+ z2w~sx?`C;B%w}(}1zpHc z;B3IP-%SGC&L4JHY&ed8nqk-<=+0Mo;NP09V~d4+@4U2cebWD2+CPFF|5YQrEe#C< z?*EsE((%9k`y1?Nh`!wm^!E??o0<6|yyqReQx=~0>KpF={#`kldQ%GhLwtDSM(VnQ zKZ38JpsYwCqv6OpJ2L<%zye4<#!9zHnp%^`X@H1M%icvgT0d4>!AnnKZ z=`Q0+e6PJF62-gzO~}u18#R?A26&$Ph#2>bKoz34VMG9!8s~c6i^vSv4UvBJm$6Rv zIVf&A`(Qh`t^17kZsI!y59>c5S&k)i{IMDCe=B%)f+b7z0gNPaqQz2$$r&IpMTi)G z3ZDH;e%#mu$wBwzQtahs31~>(JjUXj_N#}9-y?}-`yr&#`Vln%z zXQkmz7kFJ?)a5$CQH+^%rGcF{ds{rCwL%32 zBb83oaHM;P9|nZE@5S?-l7!{WrTV|l3nuswyP4qulg>BOWV2Mn(Ftlsr7960ApckS z7~8Mp5u^fdQev6O%6tRRxJ`W4%sfcXHjc=k+h%uHwueY`5^6AXXcPV{ayq#~tj-Vd z`Imc#z&P>97%0Xd>>cb3*aEEhX1*SBa~dvZUP{GKjo4N=ul{`)ulm(g8G$$C`j`T$ zJ{*$;ayVSSO7UV^8VMVhVX<+NHNT^_PP(TrUkopI6x{3Fc91x}g_@-vwh zCbEWK;Qcn;^91x-9QRJuAVC7`#%++>Za3#CF{3SfPHfjumwe9+KcSOqk8334ElwAJ zo1ME4Drxlmz2y6iLiL|p<3I3TVq<%QtN+m2*#W3Ud$4<$urwh$!8(*?u*4|DSoDei zo{6b6FzPQn13}-LzPnbXrlFPFopyt@S7Y9pc2f%DRACO=y>wQ3gD~Ta0U&(L4@e)F z13&sOYa)>@0^ht_fW((Vln-D9dq^L4sXt=X5@KHifg7a%rnIYl%ujmnF29ravi$=& zeeWqb={{y;zy^&bcb1xNbAD`r&kN{?WCCz#HslidDG%9415z zxm5MptSHfWJqKRQq9?nG6TWz}#)+wNeM+aO?fm>0@tc*cSclUX#ZQ+pcZ{_+KvT!5 zNf0T^DrU11?&K$4EJ&xF@HbKV57AAiC@55ZA563|NEtFP=oywonK(<>0Hp5W8ToJH zIlq(AGchYuXNJ)$t-?>>0!Mu9*SH)|yii8T?YAW!_cA&LiCZ5`AWvk|g_j^iT#=qJ zaJ5kDr3x1%X3C2+<;pnLti0&8Oy-Y2)|ncyPg)wt`CsqUA)Ax<3rDLsHE%5CL5ub%|@u_C!jwMJyV?;Idh$Yc{@M76MfeAoG@75u)6bPzgAb7=Fly-*#6v_-w3-t<%ub?R0-76i)|{aaVI^iX)?x%e9RUUYDd&K zCbTW-Hd2_tNM_PFg8{UE0ZX$W?V&-85JD-yzz-6AY23oBSKLXd>}wj0vLOAY*|kg%gf(ndJ`WNBZDetL zEU*({4D~1J=svn!ncQfaaD1oBG^Nxp{!;g$Z?#yC5aol%_>>{wV<=9GY%YU8P$3?O zgF9tE0x82n8aV{FnDBej<^Js=Ci(O)F?TgV5nTO{N-A%75XB4&I8{?3KB&r0WbXMg7aagRZlA^_Fw zZ!^e=0g`w2XV!OpJN}-S{cj8b|LxoHHl-&9_y26%!Sk1KhvMLQY*&c?$Xp^_92`Iw z1m_*$FxEGjrT^GOS>MEU{@aJ$=5MV~7&t8Kpn6QBJ(!gb3t`0ge?SawIye;YKUygq zU;e0PY!0JK&fC>u-MrGncRZLGMmY3^k5D9jO5($EqnzOBsH2Nxi+;Sg9fF^SxqNIOUXKG&jfO424gjBIy70;85MXZoaAVSY zjqQ(->)VS*-eN00AT7BbareSVK=V-&Yd9h1)`7VQrcj3WgZwfB^cdwQif^B<2DCR= zCSz2HEkhI2&4>{T{7Yl(CAW_@r^)I=s-)X@iC8p!-l65Nz71afXW0G$@Dn^KB;Bj{ zHX8k=^#yOlSbaPW!5$u09q?z+x9?wuNthAcn6*Q18Z!c-!{{Uv=^u5%h}-uhDX(5f zQwxhf_OmcO>_pWi%{ckU??)>$^k-7^-%mSoCa$ztVG4f~TBuN#* zfqDVaJ?@2vX<4hkDf2Y$CU~=o8b8G^xSe>k;Ya-ysT(}1k$ng|;pLMP(;KeJS{mQZ zFbexlBc5Di4>3p7bV?EsOU3~{IJbtn_y$y$g@-ZOrOdL}YjQZG6nI@MXUTQNo*@4B z_J#M3_J7ie{vU~JBjf)ip>O%ZVd84pe~4H znGLA0yLyH2!P(O80|O19(1h%fpAELa5Jd@P`8!1xzC9v|_zAofc_7diL?8YhFKIW_ z%6o6c?;QE8T>pKoq&xLzaQyAahtUQvVrH_B^9D`KO@-3{AO9D!pk_(a+rj&#{zh&K zPscnc&c%%F>$Wodm0XIUIord-LCfTK!EXx%9zUlhaM}&CKb=Smx_k851P}cjcap6< zprf3Ne)R%+beVX1erJ<)eI%JVAXDQ*i2eb|4SoV5j5ACKz@;_X7Qwl9-xXGJpC!x^ z#t|9hAqx1R#k6TE#1p|>n;DviQ=0Qj|a zpH=24s_4fO=icggXBq6-InljE#yj(0tZxz-|M|{x|M#qH(|AYt^*3o0n% z&Ij=CcuTIR4G5Rjip7XB$SMN{k-U7~b>WBvPq0@Am-}6=9urx*eFFQ>5{A!wi3;+R zpV9|EwOl%-XAKRY>oZSSWS=ML^Yd?)_ui}R;qe`!_>3*xHv_+ULRWr}w?JLXo;b#HOGmOPphk z0~CW70nm~J`5sZ#2P_aVa7&1SWCz6a#_sbV^yRscbrB*E$t`Y^h<%9tB&_w~_*irB zw9r;3lic8Z^@v-sA`acGC7pGa;0uy{8a7=J5b#}87#HI?FSiUTuwVpv$c@BOJ+F|EKl2J+BJ2JDV@{#iHh5Z4 zc+YY4T#tq6&OJrR?8E%RX@_d;9d?pVpk9aq1U&~miQW3c@NcN$BsruvsexNKJky~s z-JA|t+k`^xP~Hmf#OGZbm4DC#jh_4q+Xfg&64I{<6XxB4Zg8tEv5M1*lY*hj!k3^q zA1i`8JzMxB@rw??t3^#>LaLm?z>VyA_s)U@=ticf>ZIlNdYhP2|Lh9 zzbV#~($~%aQ)=|h1SY6H+fCP0n0m&0d{1^AiMKgmoAXM|mpMJjR+e`lvVS5T>pj^e{bnivx#0`b#4P1>qqyJZXNxK&s}QW!g%2+9B~DaC z;7x8}ZS>o&(j_#{ts?KZE7o-`k9Q9|Je#j-CI*LjCYG0$J;(3MOd=m0ke3$gVzCPjSswqFM;F%>kFMqZ>NyU>kZh9 zFhW7gBU|q81rUic6X7i^8$%BLx~oOY@d_jmxC#{b+Mki>oG-N-&~9_#qol%yZ#vH85O1kM7ZW(m=RJ)N_{3dOcSlQ z$0GDKe_%7#j+QUTStwn2eSJEX#UrE z@dU%4$uNkG&$Jm)o6w^$3$GwC|1%gSOiH`~eXTJ_f$s-Lya7o^m%+$a;MnJt-gq@y z6sVV^C{>eHuP_wXfI`T;i|@E&S~sARuc3_lEp161-BF@=`%5TkPArY6(j;xZeRM7H zeu=EVUD6bCT5)MPQxm|%t_jrn%$FmooM^DT^u~;jLSMVf5KPDFwZ`>mPRGFNoVL-Y z52687pRc}HIFLo(SZMl@xu`e17vdGL5u%;?-hTC7q3{pPn!U$6-XxmeGTsRb=9T=n zUYsx;9M!2Za{>|G@MlPenV>hfQ<1|C z|HYvAR0|fMpSsn50QuR^RZ(CXvougk?4jaGW-C5I*SaZx?SPSX6AX(DYAgrUQ?dPw z{_6s!P5uSESv;3pG_-bwdTwh!7eC<$Z_wVwF@dgWQg9xJr zpuk+h!(Sq4`1QWIML~KpPXVZ~6~jD`l|m!$p-5jhh~M&DB-sEQ@;CV>D3gGHSClP# zeCqEl`@P)#AIO53{$b(&;c=+*g0CguEx3WmiIus~&BB`fq0myfI4h#BWPH1!<`M0O zpT^e0qCsjWdiDMCU_{9#{XO@4ftS3d2v)coe0s=8N{?f^VWA>^cZ?C5CAy`|#K2KR z{!)che#rqfjX+*0jU)1MzklPJxKJ9Htufqa)Mm&H_QpwC!L9%UxrglcL_!3L=PCFk zTrcWexDN#6U=G4;NID8_#(M(KpYx`OI)8Kv_<-mVYxunvhj%jie=<$`R~+7UkV#Et z=r^c#9A@R%l3ABn!XECA=}|-qX2kr^)a_dsq~V5m!9XGz2%mvv9juWn$`TOTl{6Cv zmgoLz9+ax0P6NYvg7FNBXYS%Bx7Qx+b|qy!A@GM8;~}+hEg67LFmig+LMROWph+5* z6au?MHDUT{mZDy+lrRNr$`B3O#|54HH?YZO;#Uvzfy2>xn2?>glIMFXelNjh`y2iE zzxzC?{>9cuhnVD(WjTkv0^4e5vPb>cDXQ~U6bI+dy;-rov0tedPP~@9qy@WJ#Ru;z zTQO1hnA1I}m~5O@vMeeX)QfeC6{6cdYSR&Unx5a2mg#LtENg8gXGtGd-E6;HX>J|v ziQ?L^)`qTtdWzQBukjA39dMoh|n>7|< z+;{&I(#KQ*8(59wC&$L>OM;`Vy#ayfXFOJisZq9|!OTwuParnIY{H)#;P7GGFN(>? z&=rUA2|P!XhCF-NoF3!KbiU030j;@DLLD$0Kl$9nUkcKDD5({;9P|P^l?thylpx$Z_{yp(Uk2lZ5pY`TRJEguxI4-8brJyH~wX z6rm({P6T~{5cYmNAi^*(EZOS^fG_IMpsX60{kYH%pqc&Lg^~4;`8t_~00eP#JF)D7UTS{vWV72$ zoyfMa*N`N{e#?Gv=Pfh`1E)0H^c;L5Knnz5aNE;KI06(uzVA50K zOBpiyEgudzWRLEuFta}OD2M@)i$B0wwf;U%P>K)$ZFUz4?Req0z8BagtcVqN!m#Of zMC=#QCJ1mYJC7AaVg@}7x!$<)Yk8g?1eT4Su+a4!qi%YWNL|BxDQ#AXq#I#Ky*`$2`#4K3mP}{M=hkh6X^iWl8acP1uov-9H%E@7Ta@sObSZ z31d2eF2$e#pT=c#z#eFgk7?KIzte@U8OgphFHr0*?}6gMpF>=9>#@%v2v* zzuVI#N_ib^vCSACip&tH_jo1l|G4Ruh|?0povd(hMw+g#y2l;=)$}=h>2rBcxTQzs zy4Qj4&3$^;z6aauHT2w*LNMRukDu4>&TSHoc&|dMFLI)pEO=AP92!om0)62(mqQaj zJypCdJ!O6iO2}6p*|nj}kvGv2Y)5m&)WLoc7|$^O$|2I@1vMlSJ0kA7@8tHpbIqnX zUW_LZZN733(t05(P91656%+~65$s4N5{tM5RgcMjoknFsB)O;v`}I5S?5C2g{JsE( zB5=<}JXOt+Pv4LW>dYxyp_3W&2m$W=CPV7qC#&LW%K%tXgrtuapaTLb$*?rsx8sY= zzRHy)HpSs$p*TZkrnW&w7qnE4Cs6e(N|-2C$_P5cWIKo$wZ{w*?lhQGvtPw2hW5TE znpaeZ6oZgZP~*4Xwj6H}KcPmG6!{m)m*+H%54#xV*=g2agk!8BWm8}}OBMLw zP-RX!L9jq+JQ7`XOVgB0E4v%%k(%0Xg>$?A>yh%h)~f(kqXI>{({reU^iw+UIwR zxg-HX^rULf=mTLkn;K|euUZv!oH7lcphx`P&)r;_l`+#Blz}yW^xZVK{b8}0oEEby za`!$J+paw(kWII}lD4bIBDI}t@5#|en&5e@G*aSykLxW!5s}Ue;&Z$(bXtR+~qFR8gsAs804Ce zSm8buXFKUkeAz2%_(C!8KaJYMslI<(85Y(cRxQ7?aJvJW~{Qi3)ulzeuC6ny2^sy6G+&NFDaXcd50hu(Div zD#ffNXpKG9M#ze>DkH{Z+MorM=Jtc}!=(AZY>N)`DDoUe_YBe_I`)Uw?N43c+`TlD z@qkfYuOUe&LDwd$EVC4}v<6hAXsFGF6IkJLw*FF;Cpk=Qn+o}%alObEv>8?Xql)N7 zN!*~{!c)J>-Ozt{q>{jjX_b2MTd)RPt%3riv&QTl-QrXQ`QFbbrdG0RT9(yppVofc z+C|%7wPPcPau~!zgPHuNMXX(-j_^b~9CtICC;EM(4N78${kpVqd~+tI%b>b*rSw|f zfo~7wHY2Svel_!Md=j^PDK>m3cTg{w4T{ZI;LxajAG?NKuk1FMB7O#YFNpu#g~!0g zx;+y5&eR5Jh#~QWC;^Me7JK})+l2;JZUlx@YAJ{v3%`9{Q~-&qI7iInG)HfrU4mS` zFf%c^!-(IB2~r;K5eW z$RddLVjYxHNfaVWD@JliA;F(s{4?KRwU{ka2kOO%!f;TlsnvulF!oRuh=bCSX!*SR(<23HgOL%lor@2fQV(@?C3z0%ATGT~^0V~juJ;9ph78^)fJ#AsxNH%<&M z@_yEl3LplXO39lZwjtT9fVS2vm=u4GTXKK_VMksMymx`e*`07aD~Y_n571ieo;OH5 z8QzDs=x>rJm}edPO;rAoroIGbJ=hr@gMEq4?BnzB=iJ?AmphSpT^Z7a0!eUk&%O-x z&sj`2+yZD(CZ3t43s1zJ95Sm~pLt)rHEBFwXU@%gpo*nSl|tM+u8E=`TJzSKvY_n- zP`ur*ZrW&(f5&NlE?YGu#gnR$g&-Q(`i%)x!>J`@v&){tjc}NtPi(!M8FW?cJJ9&B zoY)}$(esd%P5ET}L3gW75wZ4{{~({gpo75I^{&2^LQcyKb1Oac(exFvG+8{vGMKb$ zMsjxL^6{@d(I4pZ9GHH(reBDz*NlHobv7KL3YV8S%ncwFtmZ7#7?`2fonMf$87w)g zpS4AA(|5Bl7#{t^9%L);R@`$U`G{X)tYg7Xu_@Zz{{6Z?6z<_us9G+*b*VhfvF`2f z5ryNC9W_=xcR630*ye`&hyHM3$-I8v^02MAi93SpUX_w3R0VJhg1b!+Hr(dfmkOFI zx}#d~uR4^}=g=;ypKMU{AX<-r2o?M*y>SCa(feL!SnYywM_@ozwFsQ_sTwBFObL;Q z6a7yES?O@uFf7XD-BvqI@KMF?sFdR0ei5#jqnx7l{|LWQ^6*^qB zW1W@h+?GqpdVb2&EhjU<+3z-Wg|Frg{__OZkMn}X*w+-TVks%1_v(8E$HFIpVvnV^_`MPorHQCoh}5EJ~!* z9Sv7eo`Vm(rO9(9%3h5;$W4}2DrDAwd1Y%m(D;G5YKL?JGdv4AhHTM1KjUZKuOo|V z%g!gP2^5>Ie9`4VD^TL&bGAGi>%?PXpeGAZuQ#DNQ7f?O3a@W}w$Q#>Z;)G|+AQ+H z++gx21(E&A6jhReYvpoyVV|5RjYbJAyP`*a3g7DUG~OE0$eQ*Q6~oszT8pRDmcLSz z)FGf$OW%OQ-=E$uR49k1dCA$Qx33|%nmKfI%}t-r;wPnwH`j zqkkfY7iG7>qGmuU{qX^r953JW6Q)& zlB+cdwmfr@6oLshq@RmMp7NpI%_WNPs=9I=iRjN8KcZtK_yLKZl2ggWCqZsBSZkF`cX12(Upx3-g5uiv}x z=TRY4rg=Q=a%^@4#b+|oCkj`J{ybCJ@Cm8^N$jWgj(~vBU~ZI0a(Q2dt?MJwiJGg@ z1QV_OfQ7nTeA0m7lI>1>^W-8j;$<6~EghjHDHoj8MdQipLo~*kLF&NpoojIw?-~MB znNjshM;b0rXLWH-xIyEkk>FrQgKs4Mz)e29E!poOkR*i+t z%^fwio2ATd*O}nH7*)OyPzo{4pfF<#%zTnd#tKIfTkgVDvP-?Q=}PP<9E%rib>VjO z@o-`iggWap&h{T;+m@xMZ~%muCPJ{5x%qRqvuoLL%s6U1 zYjx#=(kVgmioXZk<1ya1xG*;0)9!7Fl@oE-Ft)+hx9gCaLo51m02ZFTkk3o zJ;CkbOg+GV3x7N@-P#~1)`B>@`Y>~k)!snmc9(Eesw%pp4*RY8u^p){PKx)WYWr6> z3c5?!{CXjq{t@;UlMV6MlI4WH%5U>LIqW!}h_Wug<~uIGBo$J1aPT|Sp=-1|WLKp3 zg`I@UvbKFOGe&7Bw>0Q6NZKNn1uBFLBav0z8(Qc4xt(6iz-07I6 z=0wuBRhyY=-Il*4k5}n2+=)5Ym|UB81UU@gIi(9hJVhA~=I`d6qEn3M{MuTKDRry!Gu(I2Uht51VNi+Mti_zD(oFrJ#dS&T=8(!jg zAd3>@*=3kAB41lbxV)QOj(}^fmesuqV^+0EM(ogn`40CvV{hljB@K@zsUh!gT32(* zsM-z1z4H|Fai0Cv(_%vu!Y^MnrZE_n)dcfWzJ1NLKVRbDJSvZMS)4_qDIbm)CzS0L zJDhi!)Dvs*w=+SU%IquO`QX(!QWw-PBT0f)O(TSAR3zflo9wVc7ZtAl)SdY=ro}F? z-l6`)BSZ?9D`l=JngP#XT){*=t-V942uroBO^>2EU%lf zBMQ%!<~KOiJ$*2gcGQ}fnxD1H1_SBGDn&$_Q3hVHPUTe&C@l`;6;48(!6sB!Ag6B2 zAF7?El`C+43LM!V(CDMTyq{2vxo<6fmLcs%FM+vsyT1o%dHNc+0d^9 zw@-W$PnR@-hj;%-q4_vgudzH&@xXTUZTAFlNo?kZZ-9{{VdaPj4oax{Os`9*PFBFWtltZ|C zbM8UZ8L3aYTYSSjw>K_KSNZA@%*M-&=6b!sF~av#_EoNh>WY5dw}gl=Wd06uK8!x_ zDN4(HC86aZcZKdK-dby-B{R7i;uT`^1ECArO#`+27z6X+`xy3T&vG3GdzGnlf0htq z`lo)_Y9lMX`(_uaLs^0HNf+XipxE+>{?OYr&kX+S=G@j`@{}3Nn=*!i@0@a0$!6bY zJukS<^oPt*J&tRe^)(*Tlut^N{Ej29hpJArqhdcsU!8Usrq@}$FQTLj zs%SnO@p#Z4>5cZeKA>jO<(>3xx(NsLFnZpRA#m{U1d;>FjjfxTe2fLrj5`K%hh3@^3>LM8%CjLH0+Z`JAxkpl?m#JF% z{5O>dKj)8dYy}Ug88Qmk3Rk=q=^-xG(`e%z&VFf62!t!bIy;*0aoh{it&=`YvxUo@ zSA^$@9*>GnXUU6X&+)=rOx6lxbBy;-``E*2mBy9po~2$(47w+xK-Wgf!32kr)I?!{ z*Tn8mdhlO3m%)<)B%#(ZZ=dr&tGHoFGgwWjGshK}8UbDUipRgS55YC|HiY0^&nP@k zc(zPK9OT7*@sE&<$ZB1s9j?*y2I;vu6A_u%x?PXB{Thd0m$Rj0Gan9-MmjQIr9Tka z>?4$Q!KD_V>4kD>Nso-XuXO9(A-EmRJ?Jq?0S~OP=!p7*aa(qKl2CMc%rDM4KOJ!m_?$HqrhffFzaBh%nR(3%HDv!=jhU~zTYRG#o51wSFDud! z^O6ov=Y>ve@ffwXc%4E}pNB~jM{VORnP3=%t>=UNv>)4x$HSx+l~q=KK%X>1zIr!rW9$^&7k#b3F`Amy)YwAB{IdFN4x7U5m$W&UG6~HnM|)?#azq+hhyN;btn3= zam%A*NKW!Jdgf`O&kk3g>IfrHQ;*LeeL|2OU#RXK&0YmBdVe)PQ z;?;v^6j9$3JNqjZy9V*lD|wk*v)YK|Oj>svPgn$%7qrqW8Pze@k^N|p0~4B*7qGmU z<2YX*Nj}MT>-8Ku<~Y~RI$}o~5_4N=sQcJ-S%2SBR&Ct2pcd!^KXOTAr^%>G9hEAV zT?AmrYGg$8bu3(%Z}b^OoY!<^4NTkh&kJo$-6+)|T`tX|=`IJC%s{($YV@xZ75#JGUWT_a!~qK)Ilic&t8^kNttp^n|~i;E9G+i!eZ zra7#9t|L@P)V|#19^ZdfrC-dOBadRjmaAqPxshhXvWy3MS_mS2HH@x=RqEqEH zd~+p2A&yfh8 zyA*bXYDzY{8i!@hP$x`@y*T@;h{gr;`ro=V1D9umv;E_-$V4-lblH6= zmy#tmLqUyp0iuJNaGfx6evhvwIQS>{NJc+b1`aagx2-NfIw%*u-Bz?8zb= zMXZkeF-#p3&tNe&N&%E;4z2K5>H6x!8#_4nn~yypXD4|-dtX1G)s8TRQ%n@P*v(hc zH9C)d#hefx5#B4hS>}J0A*4Sx;~+FI5ZP1F5l8xYT?)4xgiEu=hKuA8gKOJP-@|b0 zy=<;kFX5BXyCe|^b=I9m8-Fm2dCsIJ78DUQYs*?>vb`J9qH!?%s07svl{ick zGpBeOg(SF^+(+hY=lhA2qN+T_NV0+k#fardO3+d^3IVp<)Lm)Ysp?YeMaJajZEbU1yGK)SZBfMNasaX z(YUnxVIxR0t~(z1WExGISkw49 z+rdj=lOB5PXy>xxEO51rc{7#pG6&??^QZ8(!jCG>BHpqm{jk!J@Gffn-(V6~%Zas@ zeLvWjd->1}zSC^4eGjJ;>-_|Xibwl;95nE|6WXoyB2&iNa6S@t<9akUXr=(w*25^rR#f34b_(^QdG4ab#uliDv8=>e zjTpqH);Azn2F&lMcY5@1ROSD32==Yb%*D<1cQ=`pn1zLnll||X|9hXAg_Yyqg2Vqs zpZN|#WqJ7)0(QGkx<)xOS3Clo>6EdrP{R+<6#(v5Eal*qx^=3&5{c=im5J#_D0wRI z`?bR^>Q16x%ExIj+v=>@6;*2($#OKmNYS_&eHODH-o$VlER2qJ7<3U}ZH-TFZGF67 zUw??4#&Iv?>Z~PK9Y_XlIr8S4>Hx(IeQTWv=*kAe$ZG)bP+0-uzyLdYV3+4LH6RO% z3u{0sJ{FwrVB1Cq~a z02Kx^h?xr=py_9mtQ!FO$jC@fj3Z=L)_Cp-hDFr51bu+<)v9eBu2{LD^0LZIt2lPDA@ND(p`b||W~icM1$lb6u_7G5P&|=sNN}@&bsw?p;*rXlk=jZ^Rn;o_nvA0PS60wZX4_6`;X3 zd?RT@ath%fCxPFb1vnWw6Mu7U0L^~_(=UMvd%h|UzN(KvQ}SICo0sC8*D60CkF(qpJv+>MQUlIrvRiN@RBaS#x?+SRRveyyF;I zk|vC9;TjCw%;+N3`nA^TnZ>W z*|gBUfS>9^$Nq~G`99G#{^w`?-W&V}udIdVZJ=?eh8z$g2ge@>u?SLb1`L>h9|J=0 zfRtmtT}F|-eSIi@g~<8U@Bk$^0a|t<)SLZzNk9hs5eeh=x1}qP7RswX2I!s>$tOAr zoP)VzbCR@*+wOn{$>GAgWxCJYzNUK40poOVw0BqQ%t?IkdIWa)uKh5mrdt5_Hbk`S zCbG~(TX5B-klyNUV`KF5O7N-}8|Tlq^MgG~%w$~&Qyr1gPhv{e+J}(F(Qu^=U(`3R z^bxvRs4OgT+HNx`id*6+W{%1BYzfKi8@wv)!Xv^Bq=LZDI|Jce3&UUo8H+#JBY{x(`Q$KW9< z*z&-Z*$&4~yY<#ImTIe1;{CB8C@@)E5PP;&!yLgC2_S4)kK0^e*p8&&Gx_}j&89mH zpC@dMj~vnJID7ojf6z;pVV%4#0S+d?P5X_JtkdC^ppfvwJw+r1lxI;pud#lbEX!^X zm|mpE&fB$7B^_@dM-$=gX;0M@wiSwY>A$4#o{YkLl3X*1J>AwC*4%Df|FHPp5dwGW3rRqG!k{8BT5R5Mvq~LC%-k zj7YBSSjm1uiMkP6-r%0hihLopMOq<3L{LejFhY z1brYX+1#jp>&YF_mnr*FadC$aLDj2q@wYAn&Mi=L$&M;9hR{(H#R4p*LN>19ik1vH zDJU&*=PmcaElDUd#fg4%t}5yX^|KYw%uM~F2jIAF?8PI=0sPUt^rVqd-qi?PqV{WV6>1^`tQEM=Rhe>_Xf-fR`EE>eh}9*?O+RIj*)xW6`YQO z?Z$@LVn-KSTpAGT*KI!{>VU{*mSfzK?djm1Ev+&nY6vWnSt;~=2wK>rWw*Z7ExNrW z3vO@OF>N$0Jv2z;qMIS;zvb)_B<8?*>;1Vc>w5CcSMKrCF^GjIUs*0r)ce`Wa_p(HLpzh!0@u9p6|HV{KM(ePuuLZKUQzl#0d=2A&{1n~n<`-Yv zIJSMc;4IR;VOOWl5|H;~HiiJ&LBD$@q%fnwp{ZXvjhnqZxo=$Dwr+HaFu3-`7(yBQ zf<&+Vqgu{A;QD?qR5Hr$>&wBFbH{}cqTN33k;^WJi&ue@#;U2a2MB`K$d~N)S1`OsG)u)Px~$W-qM(hf-ze#; zI**YTV#QBZ{4i+=*FSk`Y_u#^sAHYR4!MVv8t9R8%zZuqZ{%tMJ&18RPJtPQw7~;m zSg6-cQ^Lhz5IG_gWs5IgG)<=1;+*_J(BQDdT7}M-Asw~e3js#^8tc#i(Iw2ZDueW^%AXyZsFG2LU0hTtq)NP03_qKUbhkux@H#Ec3T`6GdT3k7+RX z7n6J%8I|BcIlKK_DVG-*Oq0VSylUlAXXMdJJ5UfC9mi||nC!S{o`QPbRt8lqY-ZPy zK_(T?!>oxTFUPJjDmDJWZTA60XDHQWoM&q+VRT1Py0(3Za^Ygk(VzunZt$sCv7ws#gq$(yJOC6uw*@@1!< zHK4P};i_h^2vT_eY)uY|C}oN2a0OURuy%as>VY-Z4&P6x^TG|jqTKbWaD5n3PGT7w z^rHPxSl4#bei8Y2f2H$FRg-+iGt(tzdNmWN(14KED_1TH>Zx5<$ zRW$n+hbg#3j+W*=_@+*{Kgf|2GHXgND)MGekCeksEtwrGPkz-6O|DE@>9m!;n3`x<;e57BjY2Em zqCImdUCpgr$EBx>Nz}QroLx#pxmh{Hv0jI6G_gE=9N|EYU(aP$f=|%!52zJFZDNYe zpiqC>qV(oUG}U>qkRT7s4U_3)853TUSiVlo7G-(OJT5it)LTpYH<3zXYg$Mv0^Tfq-LTOPu_|5rLjt-=dDLVfJu{rdp%urhOhf)LkU#*N7Kq zW5jkEsaW@DiU{^Mz9(w*WPeq0aH=rE(wyh6AES)Ficf?s({0(@f zD{ZS7xV3I`XD#ts5i-G)FRg)Ct(Q43uizG3rK{7O{C3o1rQk1{K>z46p&B$%;9z#T z4@$!ntbTAKhiBfrdN%2kC9b)s9Qob(F+~0szJAsg@_0aY5UXu%WWa5P)-)(f8lX$|+&N*URXVZM)l7htfT!e0ytJG0jy});s z?;ZGoF}~wpm)L5Z1w?FYD=*!<7BkXL-}#Efy8yop+5*dtOUl`F0ej^4TBL3)GS<%S zJCd+zgq8Nq=5p`p0w}CW2wJ@e&BL*bB@6DYCD1hvxIbwxo~OGG3tecp%ltE7z-;K% zFc)q&vAm&3*6s>OCt{wDXm5vp3T=obI9Db){yPeCww{hannIm;W!0|WQRF-Z3d4U$ zIVCH8R4PXb(=CVK+6u_6_n)wM{e=~otZAtkiTxhd%1+IRD^W)Oikc^p^$MF^bDc&i z;sLcE;Py2DC!V#xOz`*`_6Q7f}Yy%`MA}Qad$pQ0VGmAqsjq)`rz{6;q=+gPrfE-&Zdk| zpn|wqa3#^Ni~LnIR&iiAN^`B?c@A9A>JWeIr1W`~jFh|ilAhh~nb2pWTNPY1F4vS( z2TyKy4VqA4N=>aSXF58eSE7<3%XUQs&$G>*T>buqxWozje>`wjtRbb&DzV2rjl;W^h`lQ$W)Nv(#$;b^Y{Ev~vxb#8ZUoNZa&ifM?%2f|@(^G$5U%!aC3{h`Q-}wBHXJSz;WNq&a zgD1{e>Dt@oLObu`5J56iF&fe~d^KYHz781UvCz}h~OY}^vme-lH9ZElEtgD@=xYWc}GR!rcUnw5#`?GBFv-4Y3 zcz$yd^A~w!E~j8i(w~55w>hCu(E0^|7Kf7qvr9R=tc%GMS4*$O@MBU0y%HyvmFtH{ zs&%(RM22(|NdUq(FiHUSOZ49t9OKKGP8?Lft!v44L~za1RHLQtQhy7qyGK4+=1Za2 ze?m?oTMwbj|8YyBI1@W&d~Ei7xQt9THH6NW4MCdO7^f-QUYm2mfyD=ofb%fj&4_w7 z3L5|S zFh>tWKv(Zx0^3r8t?OOD&mujl=6e*nN5Z^o>mw8*GTvLapOG4AVFI|e2Tyw|HH8ZxL%)K*vLbDv#h^*_` z*ZxnwH`OVh90W7h1-_|9vD(GGs`3r{WGYpXQKrmr@5UOe)l=5kpSfnu;^OdQD#M(V z)MA;dw36&YcacRC+E3{H@uC*X%}q`7Q=z4YBdJRe19BhhmN&Wp-n~Y! zdb|6n=s*r6%*h?7-P!?6J?F@LHW|KQ#kN+)a?4f2b2(*@6tl70k*4Kjd>Bmmbzs!` z08=b6iUO1U-Vx@Hz1kNsVyfN;GCJ=^(R?!cxVrT7E7kl^0(f4W>Cs!{nmShxJbWj} z93C8Q^B3T;=U6C-b%dZ~TIJXWF8H0FU;!((;yhA{^J&@f5Lw%55>sSd^s*-9faOf6 z&8aoTD+kp6G_YV;c!Q(bt_R=8hwKaBB}1<$P7)T>E3$VUy+5ohl+a}IPRs|5J`+A* z=8P`_=>JuhZ=C2=3nh1c?YQk2i7R*U!)!C{W~wp?`=mtTjaeNdTrsA~*Bb|lMB2VB z7zdtv+Px-8k~6|)rxe3V-_!%lIq!)N47c0uL+_7LXLx%E$XmU<<-*6p#G(hW=Kl~c zd!qUqht1B|m5uLQdi0~~H&%s%&~}vaZiB&zb3|k5i`}YLRZVEMPh5>9TJ6(+BsS}9 z`7T&+il;0-Qe;$b2Db<0x$I%&U|4>VD2h*yiv$k|s5*iFP36|zNC)EfoyUv*v6WLV zUr$r--g1JCkUb{fGgBvftg*Q&nL%MYptzBg5Q-1(8Nxkn!J&vax+#Lf+9fNoWFIVc zG)Ml!lJp1*kP}Tdc(`{y9X?TZZ77DVD||O||Hn_!7_MWOiHD%_1pl4=22tSC4sqq3 z;pd>&A)Ox*46O>apI2ici-Yi-o4IqVL}97b^xGOrp9Ule=}~5UFkRPgOT02#9yc2mWT3 z_7Tg{bp;oMxcFH>dsH(avYoiqN(=SqB`0wD_`fUkaZU*ZyYk~Aa?@^N_(k(HzW(Q z#4~Fh!o59gm8YffP-hB832O4Q6_v=0^n#2nA*-$R@~T2AZK-j=Qxv`r%#=M!o#WiU zqaHsWTRc#eJ=P<+>$}+i`^>uZrMq}fTRlp&d#h(qVU9rJ)p6%&)Y5>~+Q$F|{PAPU zsAB&}AMJ>6!M4GJpGpxt{DO1^Ek|7$IHSpKwqApNHL3$usF1Ii<_r=~ye6Mf8yUZD zZf`Kh>7*B!RVDT?P3%@nwK!|aTZ}^FIKX(9i18L3nZ0oK=@o+&`5# zJ1?D5w8hXUD=lcvV}P5KDO>Gm5~7})WpX36flwv=6~*$am9L`bUY2^(c{mK#sN;ND zG$Q1BhY0HsCcH5trA)T&RIfz zy9P8ox#)4S1se*1YMKgNK*!GECl{{`;Mse(Zqm*fz8~Wrxh}Mt@NJ@*u9y2n3h)Z_ zS`5;uo5HV?r=kb;u9zZZ(66cn=o+%JlHlZ0 z^^YAH4k&(2oQG?L`HU!dF;#?a-A)`$Rbz|o9hK%wBFV!nf?g-8Yx zFe9xc?b=K>?d^}xgY_1ce{;O)O>OU3PsB+BO&&K|wK9fU_Ehgv1OGa!;FIg3M(d!{ zp}36v?DgEP*DRY@F-Tn3p>3TEqX;bj1#g)_ae$(L%~BrYDI9IEO*EW*#WFJ7 ztahYkZ%omX-Z8#YwW%IO6B)l2IGyv0F9 z&IU#2?LPF5jJri*ZnucPBHwCPiEMIx{ooi?Jd^JYPI{EIEBAWelq=Qo@u+{iDXi>? zbEqTf{sikKtbZ)SwO#_o&XGF9e;1$jEW(AX$#~1W`?NCiB=@OAL-l&XpC=iEKv~g5 zN;%OdG8Q|zGRyn_2&MJ>>>&aYnrlWgxByWzv{W;7gr4%E0b!fdsL02cS<+lb2w0wa zfGrhV8wMI2wek0Xmx)ls`F~H-#lILdyY0AH5}PL#CCnWEI8E(FYXYuEEt%-}Qp4+u zp7QdH_?9#S(@$ZJ^6{PoI>pip{*k&T2f)};V!VFV?pF!R_{7Xg6R_Fz#i{t6G_M5C zGYDxqpXneRQO^fHealmZiJ{O(@<{gNZm{XMyqG(Dxfw^-FWJmwQ(Lg3^Vs$d$=`a< zpG=yw`vE@dp4+M&M|y$erC7N1YU1&^13(vecd?TOIvj=qrJOyZ}QLo zq4gk&KFYWS-j|Es-srptSpJE9x{_+ z;QS)VbqZ{U&WESi@K|Ga389I$WoMQ=w{z7%!5Xsv6n6@AsWltJ5k3hki@?;XaI2cu zqSdPUb!}9}O0kQAmJCmC8|va-^zS(>)r&CV#9RX+nnpH(B|S+VehP?sSnw(>y^NXn&Uhe1yX;!TP-Bet$KR$2@l&`=GI$=F+ezkc|Z1r=Keb0vGaF z!j{v8xf9sD_6`7wf%$jh;OE!!y%U*ROEvZ+Esjv6*}=xK^w&Fw6y9$>W-TS-#PuZe zp$Fx&cCk0wXg69OF71!iN`tvkrWVk!dfBTL7V-=MkG0tG2BTgKbbi&>;j|DdgNTWH;GG zh1Js!eJojc2m>KMdJ&rLzSMtOhHBqz@*ZmWAGyV9#9`n9QOvLkWz^~va+#Gjf3cN- zT(_`T3cBzYbG|-QRa^Q zr_k}bOWMttwHsLc>NrxXo-@Mj=Z)B1$!20Xi}MfouH)^tVbnO9<18GH3*o;v{RohS z?SZ8294?+*2x-*6e#i+A!t@-=EAAG{`BqdZdn#P@%eFQ*cF@V4Jm_rr3n1A`wRJo0 zIo|AjI#+r=tDcF+=sZ@hD7gFuoWthO4L(SLH7#)MFq9ni{KplqeAbwK8`Jb187|FF zKK#WZ@armO6Jb(U()Je`Z8KKj=5B3y=1EooYVSLf*K5P}PrOm!PB9U0`I^dxfT7$c z77J^q1mo=KBCRCs8}KtJT5I*;bhEo`K+;?ibw$c!)hpD?-`Z6<21@(xh3V4n{SQ>8 zWGwCwHdj^MAPt$VOmY}gH(Plg{}49yCO1aVc*Rq`@NJv$r;DOM=_5TjI?*BXEVB|l zJ@2=*TMwdrTtbHADQ4N5qf{P#UWq{@T-RrEr)u`#8CJm zFaY8-5;OY%+UhMN3H$KIH`ijemf4WYibKWI9Cd$T7hh~4r*=y(h=_pPoEAPuDbXth z$Lsl`-crUiV|0@B*GV;Qfc7#o<(T@njHer#hfB^ZfLETu)Q`@3dT$VOqZT)11Eydi zUIL22QJ8V(+T36L7vF|Gz1&M;EmWsutxy48a#{pNu>M+4i&by55aVve+qdva#e%Tm zkn8rIHRF?$cyhG;3F#}^j;@o(5M$5esI7&)&cY5xT19hUDjdt(t)+z^-~%l(2%{JC z5PdyxkA&)d}9`t%`j zeR3|49F1Br6FCxiLwmo<3{S5OL!zHdmAd@K&-i&vnPF-r4m|ih?OEMllLQrvw!Di_ zXaBF1A2cNnld@}%;`Lz-Plw7Mo7%gs6z&9_>X@?cKg|g~&m!tgqHO~RKT7|ABj%W- z+K&7y#?L>wcj+$s=2GeOE_|~er?now6t8(qdDmBci>5AA$oAYHHs#VDLO8T5|C;@Y z%N4t{V7_&Wk`aa%D3a&ioa9yYxzWFpGG_+{b1R~c@y}WtcG6s~ylH*WpYYb_i&4)L z7H(eC0D(q0Gz431nfg3_7C#Vl0;heD%EQzVn%ITw$2j1jvLqK3`kAy zY6BT@&>UT7n@%p(m~mPkYY6MN)+oEiy|CjpcdbA|J@$9+bDvmzhp zlyHJA$8-~}t~IxZy!AjKeUG9^x_a#&Eu*14){Vj28ZQOgwv@SoNc|-gIFkADnU3b1 zV_RJFe!8^E>8?%qViX4Ds%!jdY^Z;(=rPN|Ly(RVVEl6<#6vCPt_Wq>{7e!vrV+=c z7E*s?rY;@ZsCenY2)hCSdsH&=Sg}lMvgv-9nD_gGzhGpb(ENxt0^pW4W}ON1@v93+ z-xp9d6h4g~h{aBr?=fK$Mx>@5wUnaYD=5({p|boGJJ0j-W0>yH7=)LgOngnG*lY-FS&Ypl)?= z%OlHDh;WxQXFmfn~}K z`}Aht;yeLYHBvJua6wFoJhxMVvG!NLTKR%Mi+hw_zK&z5Xg<^e0gdzlpssq6%9WaY zEn7=X-KYrhnfN=`ouCvdnaCZ*M9Owgk&oV$6@C~E)LUh9$s9#=-CYVKgePPeGz(El zQjjsDvLR2uYHMqOML8D<>YZtf`jf2>%zL~0IzAhjyr5tfa9uajA9&Gf8<>H4vU)wW zOz+{w(>4&o_jbyuSlH$hIS~sBc+gfW%hsy(fQjPC1x920c$85aJ;}TwC**~H8vvOb zy$q&s;sW@Qt-<4x^S_^{1{@Tqh1r|XAKp3lP4&hX+3$xgsLo8HF|wyMDvbwxG^?iU ze;CKK|N-2`Gx+2&dCmd66xDHA3DfeRIT5MRZ{vA1GUodMkzoe84P?PEoU; zk^tmid%jzW!*%SW#%3W^Bx^QI zO3x?$3nq>%lA`)msj_eC3ruVlNJRclqC5et5Y!FU=X~zc`)232bAO0f+F4V6qC{_c zyR(d?e!HW`-99?9qNH7)roP(y6AU(9$@@JYuw^kH)}3X!usDTI5jzI{lnp7H*B{QM zm0Xw;tmh^|_GygyfoC$PKy$xKH?X(ZyGNxQ4XBI_Kz~MarGRfO$M3s++*(<0CjruLWqlkrdjR>Ff`-Lr%Xo?y_ddvBa1Kde4r6r2{ouNuJ zyMAs2980LgMwUTv{)NeZ%QR+ZU`+>0W%xV#az@{3C>Pv@^iZ1l-^oH5tb=4n+1hC$0 ze|i?14&29!76;!)3?SBnOSkN(DMTyuldoTht}`5o^q}*pfL|W;GTd1_tQ*oj@fTz5WN(vc~JFY*Vf&Trj+u{7(A0%BavMbKN|1u zb2*J0acN@M9(bQA3-Z=NcsB2e8W_Ly|9p8#Lwg-p9743vJ>zU{p%UGF6BRpJjxe-p z!>#Rf^#Dk-Gex<+&p~v#Do5nUP4wy7Yb0_TYC5~_42nS<8Yqnms?doCi^$^8RysSL+jxbmz`1aVrv3r{q+QFE(;r7Rzo-V)#m z9Nw*gGBwxiQ&rFR_6j+<6El<(DFu-3B)9ivfS)-b9Lb>jkhN|Rh;RD09}?a}(D^R2 zRQIX6z05z^k|ma0PC@!Ko-F_zZH7^DId047eMZaTD2nZkawex%@SG=887qmtg1ea2 zPKsUKz#`S?D^Q%7miY{rbEqrGP*-=|5oRJbmV#l2-3X#~?Z(f((v*dU$RU#?AI2t$ zfhFXfva`|3BnXijqCHk|JA)9Jp#dkhd$b5bD=mAoU9i#dUYA$sR^Y6v+@@2~< zUc`VA7|?<<8e*3GWqXsF=QMz%uBWkj3Gy8nxo{3awV^2RF)oImZGIgV-g>uWg0}Oj zuG{5!5Z0m|Csf}7^VC6g{qe`-pPPQA!2`zVfD?aPNL-Q=wAPt+stplS4;2?SU0#Fm z`-)MizoGT=0pZv~9PksSDPN(4kOa7tZ@yFI2~c>B z(5RwIV>1mi6_;a3?sjY#u^lO!C`UTHVOD06^yLPlijBTfH5X{Za&*D3eN1L19D?wVIp_Dc(9(vcT5oGt-qwPH`D2x}&e-*%Q{v}|6yrvS6Y+~|_ucmw2 zAiSlzhN|DqgsL;3>*Qn`&kwtI^fw-K`gB2y@E=$q51J0v)H!-ull9b#b?bL*e9xWo zk; zAHOCYv-IA!u(4lBtD3zB0wEfSdi{STD*oTz<^O{FIR0;hf`y2ajhXxZp8lVK3NALb z|HF^}{|HpLfvYWTuLw{_f-FFV!ZEwSZ*OlC$CZ%4%ScH< zLy=5#UijYn?tcDnx9?+m-B-}J;5+y63bbf`$vC4iSXcOHp9zdNGgKCfs<^C-4Cv_K zV1Mu6U<5eWtq_WG%+LWZQDA5qA0`6&7gA^h-Xu!s!;BtTDi;S2LhZ!~B*Z(&D8RTO zhzS!jF(*d$%uuL3he>H=0o4Xn?GT7&&=|=RFA;8Qcog2oGC|1Uv7S6}JR2Jd0|mwC zGY=uv8JUi1ZRcuoLph(bL1jL4%veX;9aC z6l)W3&tE9tzZ^sO2Pe?~fPYBf)Y{zsd>M}fgMwUah;IMBx$m_?G0Jj6A)Pyg=!hEK zjKLvh!VkemZsAoFm%uDJ1^4{~ss9441qJ58BTWJScy{zQ2BL=y1W@Yg=nm%T(-{jW zW#Z3aTz~=Fj8(f3btBse$!1P7{w+=6#mjO$w}y6aY!(3t@N|Gq%~$}@A%Xr8pWWVo zzX)+Ub&BBmE*g8UhI>doHsWA$vb2PP+mC;&7Syi59m4Ux637j7SV4w(4SD}IUlTFr zXzi6+^J;gx=>JUVFs9y-Tf*r&P{9ovR(@$Nz zo2cFI+SsILs1ImdN8$!3Xh*>JPY;Xu#3TfQ>%%+l&u0KPx_hb{+LHD!(~qZ|4$cky zlPM(VddGWvkWm8=7FCcQ*jH0@8TnH^L;H_{ddT`fuu+}hHc7&{A-?YqIZ#>epHS?# zS(6K=5*uQnvi~+L4h)Z)$9?_h_Nn|&w@>x0p5`}a?6-^98BH}SnG7TwxOgJ%Qop^W(;pBMl;QKJ5b5gX2 zm?K*$tmT_<{OkVm8;6~e3a$v+GvdcbH&I(p?-yNkCZmP);oC{_;z4n20iWA0a(DG@ z@(`DdZBw!MEz0sndAh@s8^-g8{VQfndMm@({=5TPg zzE+exQMzmVWc)cr;tBlfNei=2r5=V;zKd?7@%4gm%70||{_gMy$(^D=U!#w8w=Z1=f?!lNL$Z^hgkY1ErHh*jrC${qM4oTA~BE@7*5q32c=e)k*S@Kqa#y4>u7)6pODl#b!m4 z&IQ~&y7ZkmN=NtDwwG*9LS9M#F~xJ3VVnv_Ii3gk%_CyQtocWq(qpX^9+SW=bRtwO z9u3(X;Ga%*y15hgaA^&z#pnXN>Mlm4mIk2LCinjD2*D+L-ep*TClh)&T0D%gW1%6d zF813(r=cJ}auqg)l-XNl__CZxe~?EP`#CgM?+KgYzQkh}$Q>O-8ewdJO;kM5p3zm4 z)E`)h_`^R0Zo64bF$DFQ3t$uS@*WVgyLVp#DydMVt9R#-NPj= z4iB_R#i;Scg%FoxW(k-ksw@iuBF^doxl|uR%Z>r2cO+-N)_!-umOf}fiD0D6v0U=U z7Z!>QyOw62`5w+nx69Z5E4hWu;`>!I4SgV{CeW$2A$q@_GbBZ{Hn}lP9_iAb5$#T& zdbxDQptJu*JSUqy>o4!K@L3Gyt=+GN^fMHF+0A>4f}6!hquGq6Cv8z4X;-R^hq-C_ z*t<~|9>kiQd$utWnHf&;XZ($gWOR+vK;p;$8$OR$?%W6a7w8MDCES5BYHKxVjKyzz zV>Qc8px7azNzX6o$c7X6nqG!$m{ts{=m2kGK=f#`HvJ(M<&hLWJ4_uyP;XjHnLM-C znZV|9d*bHsw^OJfJd$KJ_PesE$NFGcK2@h+noP7dgPzZ=_}n_Q!&9S4LU?i16}&xQ z0tbqR^33)=M9Yn;h%`jXGR^L6EMeR@SyX)U>^%MTMX5c}t6 zEIrU`dyNX9m=y6A90XpyEiGbmgB@a+B_s~&Q+va{=x%+~k~?%;KZrv13F+FNrV zSV1f>xoiJpY~sP*z8&uaQP5<_tt{)ftMAixvD8;UA^$=EFe-t-8blGOLBrBd{!7r7w~YUuuox_SSOD^hB8i|1dH^5wZv+Do%E%BoGw8vWHhgbg}4 z^J4Q{c-)Bwan}V@awSzl?qpAaT(soVoHIye8GC>}{5#${K9$nOkAr(>=?u7|>cg^* zIoZJt@THrdwV&H@(+z4jqeXYScTNs}#ZqY0A&JYj7%>_y5|tYTnN zIilI=u4hA}NKF`ly~wupOmzkdrge%Nxi85rvTRK%YG9469&Ob!#EPJ_T-!(NjP(@d z6K0abEdMM<&JkE+(IH9rIU~-(S&Uiav^Ei`#s7q=b8|V2W?(1o{I;tmZRSRI0A1JE zN^jlA$LuUmbRQ_b^$6>ioVv*a%bJUZu!h*Wd6!>q-euT|33)WfRuaurrPPYX&!|8c z99)9UW{1T^RTqHOJ1>kOvb;&+F?TCh3;3%VPQGOmM7_aDj~B`a*DD9HiyE7yKI!KT zZl3znzc`-Y^+@wlJZv-BLK+j66`!U>tHWa5?{lvSGI7A!7H>Bd0v@(R7$H$c;K1pV zHQ8(=prMGAzro^z0pAE*#3WO&U%(%&wKYW!!Ws5Jn6Fj<8)v;5kUF+qaPRi)C3MBO z%(8m2DNq6+*Oi@;6tR}j^Kj>=Tfzt_yJPY7MSh6K>#BEVUn1$TU~o<5b42pNL?zLa zbKmGVnoJ-VT+Qoz?#A=&KJbq@gU%*(_{rt?xl6k1&q=LMpFl97-$(U+WC5EYq_TGz zL1X_{o|9KAD*F_;W983{fE-+;A#}a|u}whi!kexk<_@0aIkHHrY&)|xY^YH3l$*xi z1To}r<;=fbQ0{A*hVFZ=a{96sPdT+8ls@E7p$uc^M1jI8(B49S06<5%@-wuoV;-*eYH_)qY5 zRLd0nZG!f{t2Jf`%rQyK3$3EORglc&=R1^JcX^y=%JZ!M*ppFXf8Cldu^ozVKa{0q zBvonlR(d*)uVn=VdJoXjnL`EI_5YavrEuXstugl~A=tX7>yu7tL3~o-xXqfSA9o_xC6Qmv# zK?X!xr4VFW-j%vd&-|rI03G?mmsQ5~F~zYMsJ^YVM~+%kte?6@XVPPgQxoK8@+^0x z%*nRpCMx1EwY{|*@T2Pl7-PA>1fNQKdcIMT(tQOws_zLB@X$ODT+8&a+-ZjBSR+uO3L#p<&T67B0tCU#$DM3lF zJRF7c-0BFhN<_VuCRcS4Z|@`8u`eog3@MOESb;Yva|>%8&zzzOjR2!`!WGCU%|37$ z)7uDjBlAr%DVlKdmPwy^SrJx3SuQ>9qJea%etei2g9AiFJs|#=lCGN~$N1#Fa@Sp4 zS^dOn^XEY6pyDD2vyy^7yAy%}IQH7lE3_*iNHpd@n$Q~>XLEQ6Y>2NFGHjix9)srMUbQY2!}f~b1t@*ur_En-Q9B2O#&;Yz36Y{@ar)Q zKzQbwx%ZVY^Bi?SQFlG!%_`%e+&ix#M+@ywN~(TjYN9s%H6AdoEmua{QjRn>%Rj9N zZqH8e-EoqdyY}I88chwvog$I^lOAt?WqpSA!enhdc9IX?)zzOdLKcG$mr|)U(!ZHE zAF7b;{yvh0sNL!wvQXR93cLS3St>V01<$VCtm9lwRE?N?1X@=!Zjnv@rE<&3S3&y$ zs=++K7LK0D#Dp(`iLRXrN@q>qj9EVYn1keX3$cN&qyXGOzUCWXLmRTxNcX&9cZy5& zGO=j`a=kv=6nv5bo(%xiF^$im#j1NPTh4q&4(VfPvR~LPXn&?qpn-mOwo)gC0_Ita z>j{AoaeQW@_Scq&6f4n4QL_gLz6sfDK2}zH0poB8XY1Iq(|s%JaAz;`_$tP8P;?&< zrhK2}_F0Op#TEF`C3T?+w-kfrOI=lSmw33#!00JsxZz@MpSS)Szv!6*kZo+&|Efq5 zCp7Gx+%lB+kA7Jhst5Qhrf-WM=2?A3yxiR>0&Cx@19=YW!1*A?aQumozI7I`%R#=U zmZ9xF{{ z+M6&od%(Q%8~GHz#l*8|T{eQ>!t8Gt{KGV5gfi~rAY`fbQlPin z=VVZJq1>+Z3}=rRzN^B2-Z^=9x_$yFo?yek$fS14gOmMM|-Qf{t zPhdwmbom6dfU6k~HxeaoZ`oRigKr9XF#Lz+zA9p?8T3Ge{b}A?ZJ;2&N(=zDGYO(Y z#&a-szdy11@)u;R6hGGm>dQRzltG-952s5FgBp?Wb}?GN7zU=% z|2Jid;oD%SC#332}NmCB@S){yc3spxaQmvq54&_g{Pd^>l4uM{_d3oqNs0;$+Z zp@ZydSq3SNJ%r>D5HPoM z_Ph?=2Hk(drYrUJz8IKJ&^~D-r-Y4^FQ;JmxmE#K#lvEAFOf6H<Tip)amHplW7*0kNGHwEkxWHtoAExRW@IWZB zBAn0l--oE`6iw%Vp**N_Pec!nxwlV0ITcD79eOTTCf&nz-R#x+m|pavBZh5CFR$WE ze8CNmB67XA8*udd!Fs)>T^%#Q(A8D-Fvte2;kqn^(_)W7xIlq{TDzLVca~WPkmF)^ zn#$|8T-pEx^C$Jo=_IZ`fD<0mzKbU5Q+bH@Fhi`uq_k8nC-evTQG*}MZ4C2J?JO;@Vc6HcZ&z&a_!Mmq%cU^{1Oi`XMLd6H4p#eKC zH{qi9T+48U4qcno-*g%E$O4ft=ZcY1yxS#7uW^Lz$>mY$gt1NhT6VqJg2j; zCR+L%3R#NYfcI{!(JbkjsmzSk7V^30bJT<+c?NmcnUe4Y{wQ&sgw)p1yOS9b0YA+8C=K?X1^c@?S-{651n^w zgJhy}*q@)6h5j==i{n;QIxiAx`~+J$T5#4r+yW~?ROxW#zka;UwiHt+q{$1DM+gSc z!lmXa4LT^rp4T^3N}!_u^s&?0{Hj)5f{1$y27?bP8&QV*`W^k;U30PjH;T2uy~|tw zeqzz}!}YMrO=J*FQ2P!cPUo4SYbbyH&t)+Ty|(H@F2FK5WHwX9+Oa@k`|LRB?%Aw*u1Mj2{9-46Pl%O; zpK8mBB==|?FJ8{cVx*S@)!saKEX0O^Ay)WN86Y@@{Hal-N2F8Vdtp0INm6edptwZzq6RpcKh@ zBQRlChZfKh;zWm`>W&`bL-0fD_m|+&&#IsmS5w#8VrF)^zmpb#n9>ws$Cs7mJJ?^G zt7zk~;l12W-<@Fug9HL?j@R~Jsak~QB0R0Pnxs%Qpy11LBPpBQrtd=`kxxQUaXn*$ z3&3rkWL0m`;`M8VO!3_!uqy02HL%!Pl4Ap8{t^V~*BdmkqyRf>ohE+s$ebxhe+KD_ z(%KC?IR8|JwkVXr>uVo^Z>>EAwVqlr5_M3wGeWC+F@7Z;2c@=;N5Fd4^X}=M?DY3+ zx@fC%m|2WwEW@#K?}M^iisA$JA;Clwh_VM+u~x7_`WN($2OM^nDO zHPPFQz=TIQVygMK8Jo=K)A8Lhr7Y_#lPA?{YIxcB*-?5EnMQO`remAt5(JwjyEj+N z>0471WWsV5KO@l=KUi8aXO})s$$NkrTncwwF)4bl-Du}5(;Qjeu34Pk7?l@6^0guoeLOeva0tiEs2AhOACmp- zd`Pc}*suCi3o+CNyHWm4gI)9??_I<&?+v+1G|4D`R}{fr{>MNuWbD;yCSaxkboJI0 zR3^ES;xpJ(*Eb)mKV}P)XBQ!aQr{|cpvw#G)|h`zdDMP!;bE-4C#u=!?{)M6!E1g~ z9JE*6OI*5y=I&1Lr z`{ej2qK>Yrj}HZTr($xO1s2u6vvrut@ZHo$J?O%BLVs+3562B!la5%^S`A{CA$%I@ zrksn2iD}G6Km8ZIFuWe;j%;5ui9%6D>4r#pcB)|-Q{joNzP=^|T~75wkd+>|FJC&2 zf|S*_`M2&{INsKTwv2w#x&PchbyynE)Wiml?o9$VIecI)7!?sC3*QfH!>>iH5L1el zsD5wsB{1?NalS_+i|H&*BprKQej^8-jYV4vG&a3s^O;_Q~J=6*^-{TzWxVe=g=ewv?kHAZQHhO+je!?wrv|-wr$(CZM&vp zB4%P1Z!x?37rvV(Pcp(LYcQqGO``QWZv*?VSn_X1CVMwMOa;1{p8zgqo8Vl+xwa!! z=aR-g@Nq=)%}&O967ok(QcaWeyQz{F@GDCb>KOMX8~tYHCR{mU=MTp+tf_PU0m^@t zS`wj>vGqFC>%}KN$1q?Ry5eqdIj%5I_IMLs%uj7JuB%`=MedOalbPD`%0n;YfL%80 zZ$Uw*&%ysH3W)9zq|2q6Uw1Ty-k_b53Ub0Q>~GxXvrq;Uu!BI2LB0 zXQc2=hL{9*kwv-9&XaeH1nj_i;CXg%B{($To7jQ>_?IL%!_V7t82rS-?Ww)VVNxK; zfm4D7tF#+w1Prm@ZQ_J(`2u-T#fZ!kEKh0#f?ug5XvNTV9}adJqt9bxXUN-c|BGe-hlZSKe* zWDlZ+9Xg(3FaS4!ZX0zbSPr6dcwaj z^M)u$^~#89KD!r09U(|46|sY+J{3A}3~yHxH1P%d=twIv%;r~}$|H_dqJNk$C~CW! z8!2XFH)Ur&##zeHReRUu3v9feIi^m(&zA4Mg0H%?oKO`xcY`0}Q=c8K%K;fpT(GLT znghYGhsI2Ap2%X69&HEd-8UnxLVpIp3z$8)#YL48i9BzpdgCTa+RmTOCDvu^lvQ~( zDiloUfK@v_60}FBG`<2#4-G7kGR$cFnAAKw;1!1@uzjMQ)MC`3+*pNE6W`{MD=xBV z)F?7bJ2GyAa=^t*sG61X#Yf+EvOs=2k$h=#kEp5@=~#6_ThiHRVm_0co&cjWjn z3w<&3!h;BPQT?8B-2TjCcE4Y(RIdTQ>fr}$P({(aQXG|W)03!iiLY+;wRku3w98zG zoJuBfz6b^ym93XZ z^$&fq8P}dH4Lh*TMXzuxQ-hVY67bLHv&T4Gemmc-uyYvSoLVsB%8VQ|o2rUx_#wLT z%~RacSs^xWkc(S+j@#r-0RJi0f_cyY+oF%# zT;vDw*Bk`31F4{UYh6b|;{+jH+s!qou9OhCun-xD6XMeLm>%co)Jobzfw`_L6)<*O zT?FwWqS|a$NA|Rg{uD>`KRFEI11(OPlI~yZaT_Yyz=GHJGJ#T0YUZN=Q3b#^?I~aS z7|{3|*pl%8vSYBAhGn-&{rf&Ius%To{~MqZjwbCDS?CpPN1!Dx@n{*Zxy!MuK^BRr z3@{;mNSE3wiEH(q99Qod)}deGZAXJg21k^9ErTj8EujGE-Gx&BCNBNVaLKEk|z+T%E8HG zCIY=$H=gXgiNRMJIs6UJwk4ACpP&nl|D>^G<>2@q%z}x4lbz*1TPztk7#RP1#`pgT zU3jh1(ZViF&*2J7Nw~R5i~lxG^k&om8Gu-{ai)kroiQ!0=vE=uR7NSc4Tn|0nGa2t^t8Kc)Zw$Xar^h&W;0SK1czm ziX$A!8yEA#Y5@98g8`U;|B!F#@ALu(5c+XsX=-q+ac2th^dngLqprb$D5NMFg?S2S z0-7QGJ44J|>ELF6%xujJxS1c#gZQb~fycrtfv0k@zbbjrq0Q@vmqNBdtzSDuV|NX6 zOKD*1lb!2Y!3Fc_%6c!8fVhKbaz}5*?@!Hkg>beAcl;pL48n_-Z^>wMaXFg^4an8w zyO#9HW)Uv<(^(;)_KuH^j?nkO{IdZF;GwZ&clVola0UG+0($pP;k>(Xad80EW@Y`o z`_=MK{mORe%xnn&mex^^F28$Ge^V6#1pGGtentF31=ai}W+&aiyZ~T0 z^4h^c?0IjzIwY zlA?d#2VZv$m!|ssQto@bj|tV_00Q_ceef1{Q9Hjy0Y-XbgCOs2HK^cbt3UxUehJ$N z$>~dnAK~wQvo8GFzIHKwxF>$2j(&CHqbqZ^@hwOApMJwOrtqv!-_!b;Ep!WJ!Sk=~ zyusps*_J`SJ(?y6r0Xib{j81)%x1#~;ObjGXEFNem<-_Ki?J{)4Ijz1e}Ei}7)e7SUTDc{4Op1e7K%3}C z?1JGT_5e8B`RM;WvpzBJ>*|;re@A1W`wWlwF23Sm>HUEZEbV@>C{}(!4iN$DdH6$q z$Fc$7Mo(YCjldfMe}aI1g?^7_{Ps?}VqI(KeocH@f;KpUej;9ZNa4yl2l?q{uiXQ( ze?fj&*`d`>PeJDR)4zF^dXM>cC=tehO#(U?E)57#jI@y#Je5i1E@oPoKRhFC#b1e$ zvt9$8vMzB?qDV?6qVri#sqc&W>8_4xEk>m4MJK>-gHAfoZ+l3}TE8CJ*&`Oy*DM5c z@X61xC;1U-uSvxTjTezVZyxuK{vyAj^2GDJeKckjt(cQ#&#Z`&h*qtxfuU*A{ zyh`zjHhnHgw*0xK80;&w=)ifL!X&aJp}^*3VxB1nUwJxSMwuzCCzlH0KvUTr{Br|z z%YLbYZ)@JAHqqRs!xe53v5Sx}sDA(>Kj$TVMM{k@4VkIJk)mgb6irxd%+L#1D2vg+Kwh6gR8sknjvsCexLQ9s=HfMR$O7PHKtA<2f zt|?!ZNU3iNh8@L}1;w3s>wH+|E zzy^jmDIIuzL>XQ@hu8+E8_$Esc3G&sQ0XPos9<=T&m6&xv}eXgeww8ozFjwHGTODy zXO8bpeIc*fQzPG--RLyR2;~cPqU^zBC(p?{P2RGf$~FyQJSCZS~xo z&Ad%G}rReRea#szh|{qGtmKEr@QOZGy24cUFC!I+jtbw*YP4M*(i zwT9WNuu$$c3>KX2(|Z?4yZ3?29VxP@Q#`#&5D8RKz9joMD~Vg;W$S1Xb+I{wR^6%_ zVu&a&k1P<*PKCNd7n^HoOHFX?ea&jDGW1tfWU->9(|wyr)8)e%|If9(0fu1Ui6}NZ zdG6R*0S-ZLFrl$(xj*Qw1sma{>ms%CRV-7<`Lj9tV5Vx9^!{AKYAEhUU6Ykk;r<4{ z!btD#BdJg3Q~b1I*i%|Ui70|y5cRnka%0&EnLC)qNrxb1t_8R zRd=*V=sHraVIOu`ge2c$pXy=iOaYW3a+UA+o#VHI4vsQlWg@OaL8+LMA&MBF7L@Sr z^>iG{qGMM+@AlI?mcf4Nmx&a4J*6Q}MpoMz=3yg*HDZG{v%E(sed@2NZ= zfdDh+j2Mf=hv(0PuxvUwhp_Jt7MCkAcw=}7;ZWMf*3o6v8PwM4Pf7_bWDtZLaamH3 z+LDaSyPgM<;uPP9rotR%4QCDrhVT1Bj(Eyw%ml&qk=Bp2?XslJF|Y5gTa*OS4C_Nf z-UL+ZMBWqUWSH?**ZWF1k~yqh2cZ2-UN+cbS$l-O{vf%TrR)WD13fj;H-^cD328E} z(i0nWnl~|F)^ezn;7$8bIA*~Z!pd~<1ZQ#5Lx#LwOzO(b>W{7mvNq6uhamWTKg%Bz zhKG_okPHn6_t@O18Ls)Rh0E>c0R{)E%F3WTM^1J4gw+ZwZ_AfX3%-*kv=gD|9lGd- z2=aiJ`2*JZT%KVOAZW5eJL6UC(9)H>eAK5xQf>SZPdZ=0_$IimO{AXI1vBjm3@Nta z(>S^cz3JEp)H6p9g_~~2LZyc6uP)IG`@L4!rTuWMcz0Sg9|t#)Va(m~yu&>gX)kAP z-)($>Rpog;#_-#o`i_3nBZZA_us7=m0xG*l*hv?9@qr%=un2`ZyzmH~JnIM@roC}D z+@<<9sDIWo3OGWgz&pzy=Tdq@?(~X^sl?|FO0+k@Cr^Ju-z0@a@#vEv%s6)$a6 zaQ}Bih}t7FM&r0Rh#LBy6o8SaAFon5Xu42zzrOF|)& z_=EBUVne=x;I4<2bhmK7_4U7^V{JBtUQp(AKWDXPhxyTFf!y3Fg`bYs2{bjZgHGBW zw-NODG@To5*BdaIq7gJDP&{M%W5EfWe`T!qUW)Q1w;TGD)N--Yu6-Wsi~#KPf1ZY| zXrxB)AwfrLo?4+dAq@4ziNw?cr`*)TDA5cxoeUslrZSz7+O(Vt1BB;96y{cl zkhkIWH%d~+dsa(=84&jzf)pf7j2J3Pk$)2Fe!qlxJCTH?ug@1~IX=-)S%$D~-`XUQ zuCDBo>{pZbr0mhKkxVCyPGtkVVU>DwV^|RziH;7*610_>owDwTR`B}S%Rg8GS6@qD zB>Htaw((<>G5=02*xg_tkR5d^aYZ9(6wJuhmHs7W$y?+?;tPogc+^bMWwpYc+W5Fo zU8fPfGj!7^doEoKtz8{1GhMkwF|}=SobvOD{;WWL>yMqE`EW8nDSS5(eS%V5)H|1X zm|`D{3DaiAb0IKXuEWolF<6u=%`gAc27qvD^z}lqI{YBa1+qw8gZwTkx?|h3N0XtH zie5h-mR4Fk^9K>My|~|&N=ctM#q=HY&v8m$+!N%%<4O@W0ym%hni~`aBU8mQe+a6g zE8LRUgDQV`6f$gk2iAH`mX zq&mtYO(LD-lKMBV-hm@1b6%UFBJa8%mWdaOU5!A%K@Dng##!uv@f8@4N9Lo>$xQ?e z8o(dPpL(e9;IU8{%QiF6>NKvD$N{@fnedR^d4}EXAPjLoWwd4Y5cQA8u?IaMKDc%A zq~jBl^^eP##cu#HC{PPED^%p1g)Wd4fi%uuR0%bM7+WrnmE|sv-#RK8YCsJyX05{$_C27XY%L8?WLp#+SS#c`0elvNw{4Y0*( zD5z-RQ_*d0!IYuELBO=~$)6!HDMpe?gC`hc$L$maPdYreY$R^_rrV}PoeuIg)*I>q zpRfv`6L}BrrHYU|`!F%*&J0ugXf+NfSzhVCOO=WP;K;DcNgWcV>C$QaS|H~0UL#cg z)Y3^jri*)D46-6|y7BnFAmSxbDIQ{D(q``)oORRPJFoj3wprv-R+IWYrw=4L0Q?Id zhg_Rc{J5PY`!3HpzrkIaLFRHc9=eXaM~)sB@v-J~C%C7aQK2%Vl#-a|vVQ`mYA%0E z_V0oZxXB4YY__);mo`MN|B}*f2JfpLpE+}NC)OEr1IZz$;?i}(Pi)Y^{&S=7v)kh3v>XI z#g*V`-c@WtBy&aD-%~e9@MN!c+V|m$vuH5uCA;rcHW~?u!tmMkU`fWioZCR56fNbW zG8_#4h3{>A{h9))A&<4k-fF$>SfGtnxtNbphui#`d)^7bq1shl96AK1^we$e4_LU?bm=zJB57|f)U7fs z^Y#^`j{NO|`3&S+&sgID>7C-l+&nr!Xuw$uiN05T_JyXZ2^=d429%7IK@?@tBxPWO z)NL4vs(qa#I*US#WGgPi;-^wec5n5Z0Kc#}(+-kH^cZ-H5rks4vGrEAV z8tba2e;Y@neG*Da2i$IZSF*>B%vZ3XegU5STg9f4nV{?{@#hKpC$R&0D=hJ6s8tJQ zx>R#bNOPcGt|ugpCy|6fuok?JTPQK`0)>6`kVO-Lq63%n1~hrevd156*^T20SJfT$-OvSJ0Fh5-Tl%rm4AF5M z_0lf0l*&WrZ?n&)mzQfNePqI26Ckq6ZsKzioL}FTlI-9FvHayNio6ezTG3`BMSP7l zSJ7L_kCu_4#!fhk05YUIY(8h+$HM}c)0zOU%y@}Po(=h!{NnrkVl;YwRSCT|6EmF% zp+ADGS+D|=U>UqH0w&c6HbQR$Tfao0XA&ZLVCp*V76%2X`6nH^*CgmJCjXc*C+0J^ zSK8RYo3*Lw%-Ux1Y?Ldn(9?Jd%Rpz8g(|;by^I?2CX?QINz8XlVY~JN8iP@$bpG*b;(;#imh0@KAQzMiEmHg}qZGR&rS{Ds;1y7vv&=J8SjZ=&z9BrIruKrXKR_MbfUi66_W;Kr%YFR$-$vZ? z(!@_sq;jg)U>=T#fQ6$LLZv^qy3=R!ziqN1WUV+;nF4=Ju~arf(2F&sVG`L21G>rw z2s1_Ck7&hrE4XHdkf_3$6c?r@E`iqWl!m`)i3VP-ahwe=lQI292sj5>(B^3}W@3b& zx^2>A+I_C}w#N9gd=2AUCw=eqYfCoDJ7?Rol`gTkp5&%P6KlTQA3T@lt!FW4?RQQD zo@u)*%nltsQV*wbJ%_2)XHB(E^Tw%9C2PvmdeG#yX}WT9eO2J8#h5ePir8_((l@G5 z>+}oOWp?`m9r+u3D?(pr7=76Q%fW7vCeOTmoUz1-5GdWYwQmiRP+@jCF7Kgcpk&j$ zj3vS zetRBQZlR z^KX*L!I3*W<8k}m8Y-ZlhhLL2*1S(=>rGENf%mOn$3bRD zr*rfXTG=8+Qivvp^H~2|tYK6l-g#}yn?9G1WnBk(iYR%pgr9vHK`@*CwPYDJU8$l% zwQHz&duc2@FNl3g+8j~IyMlVTQ;0vk@S^Y|X8&Z;YEIM34!ri$xHIDixFom%Z*}2G z3?_aMq~I$N!QY9~qn@^6-ZdufIhAnCc|W;y#R6Vx4?sMS@5lnQ>HKh6=d7le#w|&H zP=EBi~bc+SPs$GRFhsa$-?>SUhFehtnw7K*_z5{ zJox!Kb^q1~e<6%LOm(7GKqFnPuP)qxQ>Ivm9@(U*)lD{2?WYl!ZsQm3Qk^uOD}j15 zvfTNoV?jlWAJ%F7FN3Y?@jO6WK4iLxJf=*Q#vYf=`^+%g;=CyWaV#5uEAw%_3G>xO zz~`T#cN|+v^UI|IkC+bpRMH`wk?+2xMJ*wm>Id~vxVi3ab6KZ^d3#n9(7Pqtp{gY@ z2J(HhxY|dDz7ZM|5qH!Z?16gWmIk zI;S?=?q5&Sj&VeB)Y2!ZI=cRO-?C(pYR!Pi8bpQe|b_QN4vl_rQ|I{dUv}sKvjKppd9aK!{U=+^mAGW;IcJ}4e6ac68Hk4yk|$GvN-As?9@anE zP#z&P`;uih$@6ybO*~Y_hNCAgg2S1d z^T%>l+aY%EQj2~UY3Mb$T(#~E938@%X=@x*BHxkF}UNUcpijdj`BkoixGpO4idY}WK zhEKsWltKro4~a!3IQs!TW!5bK8hrGFcCP&Oq4-2hC>|2&;y|eD;iqcO&@66CMB;o= zX%kE!uLw^xyND~X@^I35_S12b<@at#YDzfgc9(Ds%VW+ZShf;WJH;LkyEXk)78?|x z7}}`xuqt_>s_~_8?I+8#zVTAOg4aG@^K7u1Ghd8fd==9qq@hT`OQIuKSl=&aDW~o)ieFP2^ugqJwo4!K2OIAupeGh?mH?QQT+Nvp-r_pW9j&9Lai4Lc8S-YFjyY_MG)A)arUj?JiK?KsjI+az;GkmU~Tc`c$4V-^vVpoJ@t<7&U+fFT0Y5qRLuDv>Hxvs6*QbSE1yaXTorx_}p3 zntO{Qx5lj>BGKJs^8Xeu4d!We_Me<9xd~Uu5(n2C76yM->YXi0G(@S^AJ+ecAne83 zwbx`p7Pt}Wn#x+be0_Hp;W(#>x14-Lg`M1^bJ^d{rFp8D!Fi0$Y4By7cah3WAS>yA zxWV4!ESRtQ+=1iF@sW5dlbVfRQ)%cwwCsyQGR45{d|;&4Om?4+!)jz=K`%Kvp$mh9 zL9!HD#^q&-aEm#-cEt3$JdX+&`~GHG%jVFzbz5gUG25zFn6Drrc-rux^!i>dQ8w!E3=V9aVZ7CyBcy17L*vC6>Z57g@sA9GEwh%Y=lVH&ei z4m%7EWeF+Plk4-88_Y2+&AwTNRpjYX>_jwcV71A|Se2?}P?sZSv9qV46u2;e(#ZgR z<6}wbNIKeL4n_8UyJvK^!nXJP-jV*UT0agQ$@yamJ<4y7WOH`a6uUwrimW|)xvXbU z)ti0igT@)kq!UM1KL{>B59$Nqurf2QV;cc9iPd?7xAL*I)|{oskqK}cCtEdVN{-Uz zU!gRR(phT&BB8o0Aa5}AEY`kg#EF}Zs46fkW#Ica?2oQm4VK{pp%%9QZ~(KR1;!5^ zYOJj6F;RJ)FIkp5z+bNlH<2+6#8v_8F8x&ra4%OVi-B!BJhzA(OzB-ew6$-&9RwZX4Mrk2+y?CaUIateMIdy%u6B4|TCtn)I zCxL9$T{=GXkDgZ!Fx?*)QU_ix9+w+s+Ake$chT;yPg-@)Cdin0;^Q!*`X>5jFjkH? zx29bkd}#gd__aab&7VfwM{^X*zHhHgeL>`JtnUX*Ef>6r*4tgCA-Gp$1EosnF!J{N zVA>QEcoQ1&qY6HI>Tw;TQtv0Ae=9;;XlRoE?v7AD1T=M*eWF_* zCK<}@Q-I$G(f z!>bs0Yrp5@d!==kR!WDH5Dr&vhZ@Oenq9468v+3xfe%1%JliKcI=B z-jfJ#a-Ho^c2#<-kCc}u+*aOCrH*c$W0PY5uS9?^AGn4F9D;Xb2hU<${eZ$IyD4K< zA9ofWqDR?AknRo6(yB(lGjZJFEUz&~IP1mlne#Ju8Or4jPxsm%H8FG3~;2?)E9~pjF{1eH3tLr|g zdfg|U*q;8{IV!a&wFE6EV?@_+2~V{485c~Ci-?#3&YVNj4Pm7)#C8dWt#^2>=IG+i zf;F9*LoI6a}3ay^TEJMy}y~8N4Lt_}o9Vu)| z^QFh+Xc967k5SsH11YVp{fsqIX?2j=4-GkbnR5PY)~hQkqw4_J!)Bo}$lq_dF@__P zeTAGUofhB3p5yXf%7)u3@YL?5uBTzDM3=7mZr^zdoBhQJ>CV9qj1pRkmD>}OyE?)B zZC+dU*%NT!=)%$3jQZg{A}tmyP!M-DD-lQjhx)$T0LPnv`qHGW$fxj?OLeDq)I~en z*__#Ivb(%g2eMo+keI6)Pveq=AP{2sV;VgW`;1|p^XJ$UfjHBqTZ-P$;{7iaJ=YVPv683I1O(!GS>UH;P_+g;w zDff7&%)sk;CA|8YV3_``-w*NnkRWOw9&^S z+#8BDFjNOUo5)RM-5Z_-_R~>|TpD^~sux-Vr8T?i(-Q=oV3Fb+2}|@P8lUKI+ikXO zN5p&8clxcgEf6OW(aT|@fvnQ9#6v5i@;8J}OIkN`6^{;aVsdw9ZL}Jc9ZGo+u2^i znWOM$3CUpaLq599=F}xy2~V4)m7fr!YJ|~6*j*tuS zwac=U+1;wqGr0WCqw28H6k!A(XKcjJGjOz&(cmf{an5QS(VnD{jh=v47w%~|aC7mv zrAXCRB47`3R_ad#!=z1iJUlzSY^0kk-QEXcRhV$gK41v2sgQy9Ar-h@aGgRK2G`aq z`IiE0kRtCWkhVU2TWHM8NMs8w``MDQYP9Kff}f1YJmB!tx_&9A@|PfTQn2KLO;M*Z>Mzx zGG#ga2x?lq61=B zs9fhcI<@*Lu)5zrYxi(2{R_PZNa+Rb_ihU)Gj5TV?$he&a$TpNy8OB_?o+CldnbzQ z$!BIzAKl=iC#fv5tq^@+8 ztU^TFt%xpu8CjVKMgj{)2zrSSv21G&tvB|7XnJF)%-`bW6tt4o6uh|M1PIHfRWz>8 z#VWbFxD^pmv4b61olX3mUIVw=ys@H7964{xg~2lPN}|%CK(`55VC@F-+erMk#L!$1 zFvyual}#*g8*$oKmvnGh%q_Tt3RUdijup%9{Tm0LLWxA=fGpUu9Jy1tJxhte-(=Hz z28E%e7p@wKxIkg#f8X2q+GPj*zJre?Ea=dS&$LB82A{z;j16Vap7ruaU2`h5w4M?d zMt55so`M6}^n>(bk<6LS>XCV$LW>IiIwgH`T;~bVkjpy*~-!Ks1(7>kx5|z@PeJqCoRl-IPI~u0`n5_ zl2L=V-n6-#f}Fi96>qk*-nqhet22@Gs3i6g>2smtLMh<{fuk1&!u}Mo?%J=|jPy{R zWMF?IiU%S@{%K8jJMq6(!j!)k?V>2ug?_P-$RUyos0-mH?bz1N#JsV%-J{8Kqx~Y* z4Kg$+{4>LlJRq(^cC7IUJD=L9myTQJs2NK_WgFDou;eojN0O^W?MZPQvt(u`#wcra zE52Dv>-@KZyeSjH%d`+xRGJANaNQe=Ykn#+)Q9O8c$Nso?LUC3%nbhtRApxWUo@48 zfQ^BZ;eW8z|7!Va59^}@KG0@ z(%KX?^DyGs`@mq)!zKV$0=Z08rTjBOWy4_5KqH_wiynOM`BeeTQ`_qRAO)#?+qJ>L z!3`%_cPQ|TPs0R(VS#@D5;_Wm7gC8xqQZbp1ol(?Iu7lr1a!<16p_!#fc=RU90Ud^ z-?2wI7r|J9{}U8Ixc@fi zSA@`c6*FqADww~wXMjmTB>)!msDz#d1V((nBVgqYfP)V53i4x#{s&I9-;bRP7y)#{ zlNk6X-G%|en*jwJJQ2oM0s{wE0186HYrsKZVO;>5SUDdQE%xWo`eRfO>TPuyfRHKP zuk@4pL!F4^!;Jw2Y%sr0!I=W-8dQYfdrtt`M;X%_LJtZ;)a%DF_yg2H;(m^RVgdd_ z(D6-|1Es9i6f`*T$b;M>;);v*&0dEE1lJT43rsQ4i;K<~w(=)oSt zLUmZ6Z`?9^45S$HPZgp>6ZwHUbZ&q~JTBHbJ_P&1_hgU>(3j0);9&ri0fUAlC`|At z@IE1f-CXTaOM%9l9m2z;Oa*_S|FA&-gc9@}1PPGb2Ot7azMwq;9y&xE!I#@!9yb68 z(38l(odA3rIuh&~_rED&@vrqHvN+*TfZ9OGp&)?%UcO(w_V~8r2*J;gpX(p5HUcML zZewia@m<(o?1hz)U;xO41}OmxO;82|poA1qssuE|-zg(V(H~XNw_6Qj79e1icV(LM z)E`y*IsHZSPic&UKED&D(Rd7K@W^jjd-FOV46%>EuU?BE?jt|r*IJri@c!RMyl(;i z-rce_`ZvFP1(XH)C;IH6RRNxePcw`}pt;|3OZZ=6b>=p5CWPm_GDJM71%I@S$=ltu zaF{vq&^}(;1o!k;{EDyo&2OZ1d?eV`ArJyTUJ3yV2#ha$3`tc6{e{1X0tbh75OPS< z{BcXdgABR7OQeFjzt4Apnxsq5y~(ID4x+ z$EyAW3yn{cZ|1cyAR+w@>ARtR*&xtE`x0EA(;!NizZ<`3tT=c;VSr>K40Y10KDqjS z-RjlD=rr9+wQMvUCVuidnG69|P&@{O;|PA4$jnij%M)i7=I?D~yq*J3 z%!D&l4-MZEv@4$Hl!y(y@2;`}#I3YgMF6>cEwrbP?~H%%s8_uy^%Gh#qE0@+shBm< z8g4<|u!5Hms7rQ+V`w#L`Bhm8_$%D$eKzUF-?h%e{{)Naf{`R2$rBT!bwQ!YK2iQi3b*4|_JVNGbvk(-Q-SMTtg0_`ds;~fkz}>29=}-saa*dOp&g*a zh^x;J#e`$%T7TEL19$2N^Y8*x1jt@#^fUuEdspF(7C536i7%hNS@sY@>XpIfX_Gkf z_x`i|bhR1-d1vIW_QGJS3Yj@)FcFbFUnY4EG z0%lnm06yO*>=YWa`w>f%zUf1@UtCRj0UqxCnuPj^yVz;>Zj3P~GcpaLFbnb-nTL96 zjUTfp+2LD*54}*~0o!->oQn|*p$2kaYsb;W0ySTF_HO%2bc-na+F#~5RwU;oI+;0u zplbaQSN+%zI#`ppi1ETX!W}glv@lHJ2Qw}$i9X!7+1rC>OH;TEph-?sV{WlEUwt3; z*=pL-$k(MiF0W0j8?P^hUD#R=iL(Cge*3bXECk6pb@^W5#TZMRXb@P`KGpAF!=mUz z!1q(A_0ycDD>f4Lg$oco*_p*91gPOGD5e0v@wJZ_YxgGe#IUsxO~|4{@OgQkO&e?T#C=%AtaTHwcUxPyl5v=hea zJ7`)9A5MG%C)o_OGFQE5^;W#&#z|-4m?wXByD17|1P9HMbk?J9%9QR3NqM2B;PI1B z2NXdY@{`XwwHt-vxe1hQ@=CH$-_d>q*UtGwuN>~{tJnH-y@WIjT@AO;rQJ3h zZ2pbub&*Gv0eVb7hlRjuKRmM^xo#@++9^A{-+xWIRgTYnV zu&(KJs?VbaiVWl-19-{>1>QU}FY_*f@O6Bp+dMu&&zFtHZFcHPLw5Nh7BqUrU9FyE zbHX|XwEi+q#*GTh3!-7ZQTqJwTQ}n<|-|livkUfC5*%qCML@GQ; z94Rekb&gW|p%#*}efAM7ANh=T7i!tD{py%XcY&DD$t~@7bJdIvqDkldOv%Gpv(76H zY#_C>^w`miqe&5L)3tI~N_V$D?JJpAhndI5HA@!dmAB8#wt zv9qT|cbwGY+6TF&s=NPMH+FdEj=#d z!DZP*oi@57^~Qr|Yw&D_#Vpk^M&MYY>7;~8N{kHtFpE^(_W{`aSI|3pCVW;pV5H7T zQ&xt|LwXawYtaroq%EIf0TqKyjU?DU%PWIkJCTl)+Kv)L%$8196*ZY^ujH$#68 zHkg@{S^}}98;w`1Gx*mS-#3G4^RO#tPd^s@4b$CFXTMn$UWM&U;(L*g9!-`iE-%1~ z`pF4-UDXR0by)?+8Z4j>5@l7Rd3UgG3&qv9l~YUh#iSBC_Fw#_=fbdm#c>M!8ru-4 zW3ss#-dDubE3LB&*B*W`iA(7?sA-MzF?&pFqn0)5{T!&3pxxmGJvBbq`@)E<{h9c3JKr0$_Krk#_kxxMSgQJN|kGLI?X(_YkArhrPd z)uR`R@1U{yb3b%XGtv`I zGlkRPC(o+<)GDpYm!1)``Aas!OZOE^fvhy`I2DuaeR)63ZhHc(M_YnPwR*XAXUB`v8^|l)4?^s@wtS`tQkiR#klcEx}ag)9SI6mnP%%6HwC~xvrw7a*dZSCsk$4ImU|=9Z1e;- zP18SUV9nWauuaQ*YL$bm8kTqnB$Z*eeTH4_yAV38#JwVE(riHmg}}x}(GT6vl<7dblhUzcKzd8sjnk z20f}Ri#wo)JNdyDF;H2zec%|zWccQU_8#2eQ7RK7Rg68Scocaf4Sk8KdqsvOogg3h z&*FQ`BfI#*&{m9Bp7)+&Li@U@?vgedRKa}#<@-h03{&;{xv&2kJ_oig;^4OlO+zhF z9pn64hJ4)(0K153=jPC|-uP3pPSuM~RPBBRQ!K`Ca}BT**QV&TnAhKj$GHO!*U*wn z2ZUNUdbhpFS3LdMB~Y`4Wn4O)`=PZS$I2z-2fDQ!AqfrVsZcZzwrQ4(z~oD=86(h!S>_+FTFQZAZNXUo{5n3J?JmNb!& zomO>YP6IdcWejFF&tgt_H&|yR4}IZIVy)Gi!w6MJ^cVzFSkRbx%cK@KvVY#3vpHRR-9eWzZSej1vPv)x2C}JOL;;!J) zHm~BtwQ<;++O<-|bZ`3EyLvM_*yTASWS_5%C88&tl-~{Pi$WM|qBC z;hN6fn`f3CHO1mw0^xRjI6*S++gDS!n+wC-uCj&E5R%I26X*D;%!@j1^}L*qkOZ1W z^~^ip%It%xiw>$F&Xhdm=d7@Ymw~SU)8Mz+PcfK%jWDN9SZ0; zJhSwRIz*I}$-jlB1QfN4xnFeZndm)N2{ zuoFs@`$m7XWrW30(KsSa&AHsQPe}EkwBWL+U`sIjvN%869Tv$w5FK3P!d@H-!VUGqy{kg%S(E@ZgJB* zG9z?mLCf+g=0@Be zap2mz1guf)-M-vp^VJ>n06srGLiN;7OySLaQ5QV#2@jFk(cMcn@{<3Ial&GIa4>-` zrpZfd?!+j2m%L*4+4Z~P-9W3)&A>3w!=ZBgvD&|nQgqY5XRKtsI!gz=sWcuV1}02(XJW)$x8NU7<@=$tV0V1PIc-WZ|DP2Um z!1{vj0U;G9>;rZYRs5-CFJgWwWec8pyG*+PgxWF!Ya0rO<`G0e5Uns}nFMuM!}^Q6 zv$vv;VF!7W(Y|K;qzkoHg8Gz4sIp4#?c=h6NygqiMpu^2omi)Djl5`4S%#>1^gemx zFliPgN_TdhZh4Vqs-Hj&f~a0WQYyq(-1!4UpQEyIsv%_&+&+bYXw3$e^g&Y3Q_z^w zY8S@yfFG^c_JQ@higYG%{#nH1R)~r9CTX+eY_(L+MGM<&F%@K-)En5v7DAZCg!w<) zy~f72_9~x<;JZ?oKHs)6Zt|aPALjR&{1pzggR!RG7LRsv#n!+IOpg zIqH%Rjv_fBKWG(#0l#>E#bKMcy2fLWmVHVg zlfxYTJ$JWp-Q`QWiMXUWH~+Io7h+}}S_(TxHzl-1qFk9gZy(~hCdou8G0DCGb#qJ> zaWG7Fwfkwk)37rP7anPj{n-B^$VnemS`K+M6yquOEv_uZFy9Pe9`UodfV-Q<{A>d1OKsle%Zi*QCd|K7P1w)EuZ zg8`|pD3&LN8ohxO>vY>^>eyC@KB{Z-2@w@<0H{{?Fnu#Rd$u$G3d4n^Fo}m zNp+&38P^8+Mw<^?)EtpMJUFby0gbo_kGv>*LnlwpJpy*v_}QbYU4=$d}BlTAqYzfOXolKZ!p! zr0!_;VLjSKF=2{`B1Y+g6oZ`*UtFy;4S5LdHpaTsg2KHT>2hbW-a&(d!Rw{!KN}=+ z1t&$6_w!ly8Rkk^h+7YK0@(G zvMu7e;qcPv*b%~0oXYL&T|hI>(6tmJd`=|MZ_WJMKn3qFA^`zsoRi@SE0r4d*{Ldm z&+QQrRZ^?Er5z25H2*e(bYDFCIz}n6Z~Rh?vvAPe%8hXCkR4!8&=nnkO)H`mso@RIR@y(^1VJ+QwktA1K4f}3n$Qs=kbWqn< zrHa7ukwLiKu?dc%xE*NMjs_~egRQ|o^G{Up_jXv(isVmDIM)BOrj3+E_Dt(v~s84$!r%1w}82qTZ%=dv>&0iaD3Ygz|^xwpP%ZGhP2KEcRP+|AecOIWO&Dcl+v{_fIkW zg;kf32R}+pI1HMnYRL^fD>+LPrT33!KR!>6PaDfyuDoq#$L2-yWT!l}+`LBrVIp4M zk^8ipj7fCWc;V;1T376Y2iN6R>)j_`H~JNl$XJ5RZ=ik0S0V+op_h+fU8f8m$`9XM zMM<)`yDJV4ZcmBsg0*hGT*YkBGAlp%iyr$mGT?to{Fwfy#E+eU@qcA}|M`G8IsbS5 z_kSmToQzEWe>2VhOXAlKs>09GLx>EbRS#W@-yPGd2jCNFYl?>{LH5B?(FjJrK9#HCRX!o0$9^J1XTnQP@EUx z7}*0PVa>;ghynls0pJl50s^tI;X+uEVSJB+FpF>)6H>Gv|3_MQ7ZXURfDse{s-`?L z0C-u)06>sHK;bws|C|^QFd!iy;C(L&;!GR>G=X{XBsrXUc@-`+ z?&*y<0C^e|0RX8v>hv33%051fR;SE$H*mqSX0qA3h4`nQTLTrIOxTtUGdl185 zCtyxt01E&xP~m-v=1AymtV0+9ac~~R6#xrv!F_*9>+h0&=yzvM071TizxFTVpD9F? z-z^LfFk+k>0S9=BZ8QVmP(grADJ&lfcNBU6khb3vh#*2l3-1JK2q<990#v^;I3S9N zOCW)BsK4cK5N_cd1qnV9l-DY;UwymzwQ7jARB;Y2p?wOHgSu~&{8IhmCx%YT?7MO;QtC-t9=4D(1s({iw0)hRtD}MP?i!e>%eTI1dW&gJHJqdX|&7FiZ z`H4To$qB-3Kt1@7VLSU-iy&?@w;i zHGZ7^Z)O6WfWOz0PyuFip#AUgb2FepAcNN(&|Dx{5HGa-zbY$`4{H}z!c_(IvA>kcLVWJ_iaV$V<3})xg4jH~)rH`tAL-?ty%V2sj|fpBBS;H6WlrVqtj9b-*6c1PiNQ zG{Jf1=RHT%1A~y4Izwb6G{AuD96`L0bG;(@K>&KeXB92sZU1D<{yA{*{CP3}msmak z>=5RIx=}t9ko%$<1iMwW`aZ5Ow7*nzMi6~V{z->%sYPuMV3=IQSi{Be2d)gSm*-fwx1SP z!r6o~x<90R=`(i_PC~_qKLLxjIE8lTM|@+JeIQ}MocXu+ykb0{cf|7%^Uzb6WBm@G z_ndi4qUwdNTXmW%f1pT!cisJYedP!8Z~qst>%;39whvyB^U)vQ-yT##1b2vZ2QwtV zRESo8G8rlj;zwo^C~Qu zzkVOcSiUst*y5kt1|zJT)xVRevFY4flzqiqFZC1&QwY!-U3u2i>%ezCt;u$o7BCX9 zuI&2^A4??~Xxjo~h%ca3=7rFzhwj|ecD?*5ZEf0*fUV8m;1{|Uhy%%q>)B9Zu&EW8 zpS$m2me_{_x9%0nY9|}jRSff=iZ4|G4LNi+RAhj*R^QvQQ;x#+<82XO=T<(XId%w( z20kI@2O26~IfZc^NhGq>FIIgy5%AGt76W4z?;j3G0l_h`f}*IB5u3haCWpMVJC;6d zEju52K)=R~_lA}}=4XI`&M^s2Gz9DI)ZQOM>RLh7_iN@3!nQ()N-PKy^U&%)4ot|N;7k8s^D>b_-H@~rlh!!Wlee}ULg*i)qtGDX^Mn~8e1~jccT<;!A zb0#zg0r`W8S5)6l$458*F^yKXYf2iP2IFb_5hnkHh8s(H7U9dT z#GG2TxMEoMl(sbUb#N55pUHSH%^+yQlNZLpnMZvuiXm7TZvm_t^4Ry;oM5&W^1Vn9 z**Q|YS}+bxo8Fa8_f9Hrx-x)v;Yr3HA)I!lii|ht-k$(87+eK>eCEWS=-yjB*mUlS<(1ze)RQ z+Q$W9v<1bcv#uUPyXR~@LWL$s_UYpTqX$O`V$WR3>0yK1hPcDPQTPH>>4MU&6xkAp z6cTzNL8~{$%`RVU9NZeZ=3QEd!{{by;u`N5uZyTianUYIS;nJua`o#->WX@ADgKJ- zZ)5d5KPR5$`;iN-byi4|kotF_^4VHeFd} zR;zl;vq_t>3Xo8eZO`ufA;g+geulF%EcSt|A+0eZbA@V3U!^YEo`3tpyqGkXQcR+> zoMprj&zg#4vI&&)QRuB40A!(8bt_RDEa3p>JTB2f!I{k+L01vfAR=RHW9t%n2q4tR zs5+xpo~Oz<_**_tP`C{Q>h)Rtp52*eDXFbAX)N`u7tSBG=49BECPRe&*A4YLwi{nw z-z_nm>5?=BU~=T2*~AfUKdD~pFT&uql9xMKP8pKG0zMNwF>lduLJucEFP*@rXDoI| zir;4%rA^cA+-GU9!b@34W)Z0Z(UhxTuj4I8#LiBP8cNevz>Sf-9PhmT*N=^$>Re5~ zo8bNk4~(ZuBfHZQH%O`iTga(8k?AwV*67eN)c<&z`p|P*e6UQ;+Pu(UG;Yr({icny%oC9B{YL}yZavmv&)+t~{ z*INyQeQCbj<6s6Xvb2_{3ZS*Msu;7ia4%r40a8md@@ysK9+3?0@zn|)^&u+UOo{Dz zn})SHsUz)PdtlZh#(4lV|4A1!Tyth2cmG>avvWpgxAmq`RQqOjZ!9!ja?Oz33LFdK z$-bzO?hZ)?$radJfhHKpcTuNvKAsEEuXi6xhozJ?cC$ch=d&M67hpe`$v%=NmIn&) z=E$zTgq4c(Z}B<5w1`sg=IzonpO&9%UFG}FtH?hqLImgaV)wgY+#qu;3F33|%F7;e z+!tP6uG^QD&og;hKia8Vem<0D%iBJ(hi`V!b&K}s&Td2+LKj%FF#*bKT;X%a4bWmF3K#Dg z?8XU3Jj8RCz+1YmWl~ZHJM%VDbR!#?>E7*ZoIS+SjvIa^l)t0l{Cv#7sCApoy`uP^ zU=pveS$%@8wm^~anuv+_-ey&;?t(=(M!+jBz&+sU$+doH59nxKuDd5j^6X--WLL?C zA%{mJPLiTBEC{$_dlhx%LeFxhb|tA#(&*us!h;LNumXx^VvJ!qZ=YBu6yfEh) zW9iBV_hb#C+A+TH_y~OZN(wlxRqzGfUL;SA8gJ~D%tL+GZ^lbEFU2-iMatf7Db&Aa z5~kpHlwy1W-i{N_@Qk8!9c;VS5hN_86J-^;!LWyKC}5RBqYBa~ekWm2NH0sQ`4LnB z96iel=z69Vur&X7(CRRE1ly2ncNZr_d6oBy_j#cRsA~_4>%FF&YLSNyzd8A~G>SWR zBj0B&*GGCAxzt#SPu90T_6K;fg|n7}6{H+vaJ(yv7=P`Em#g5L5nW%$w64luzWgwAdN}?O9Je?k|Xx zL5zhkQA6RwKf?7~4}h3+ZAzz4HsTdrBC>Be#e+1O6K^q!G1d_O{w;7tW$>naP$o5; zs3FtVnN@p}Mo}hXCkPFdB+xq%QD0p!dxJ#;JLIsJ9M4}zj}v(}C?Gt1YUA$yt`U_x z()v%Uchxq4>3yMwtB3n4&g^n*NO;s3%KIJ@e8hk;#@B1cwS6|BEUznC(Z!6mJU97F zL5~l^@NcA!2R;vvZeLQj^gGk>V)yAjEZtV2BJq};ZEoKYtA$;5X%y7OGe_WGWq5!1 zs}JAx!`H!1DdZb8Mlj0le|Ci!cc)6FLpplS8chk;9rsndHoTzdL3{Lsc*Bhda7Xop zI}Cm<+r5NKTUr0%A4|dD1+XV&6w@>h9&UObwK6f_nZZ{!*)s$BbTVE zzZ1fcJ%?2<2&%2{{EOCl3R(c*Y516(AjQIhkQk{i?$fu<%qMchXK1_ znql=8&U-r=DYy;#_vBWp*tv7b&EIA=>47vrlJff!@9fLVf#aSKzXa0@8o|w|-D-?> z)jFG7>x5!yO0jlBe^4xyXyBIS<7IBI=ML@%!;-2r_3|%Qas4H2xzoe3Y6ePf8sp?8 zdvh{GIm%Ql#{0?CdyhOE34R~ci1QH07;oPnr?zoX5~patb=$>IZ(n{{3}3p#_GeO> zF}Ja={;EW~ALd30ixZ!^zkd zI@f+=U*C{r;U@tb((CohMecADuASn=i zT8<@gt5x5LT6!PPZy;aF*C0NB9M!}0L=Re<&!USVGfDk%91hn7E$uc7a0k$8YK zRs{Q%x!R$8Z#C($K{7a(SbKRSP}BE#>t&oyS}T{__wrdxHxug^dcdMGqhd*>_~{-# z=7Q8Vse2FlR}c;An1?11xyG#?kDx~bqbN+?Y*J;23tW?*AV$EQ8*q{p_|L)+R z{>7QdB(y#?_ZA)Yz8?WHo=GgEY^2FsZJg&8V&GlYvuKBns}>EnX*5S0l=_mZZQ@cc zmMTtjBLo2-&TKILtywyJhWnKf9M(ejd~RG3v@^*;^mKeJ55YXMZ5f`Vs0D9pUtgU6 z5Muj7fogq{QRZ<@$QgtoTwwI@U!KIw3WR{1P5hMfgUTQJR}QnoFu( zg3`E%*`+!O5E+MnIgJhPqN4N6a4An$Z2eF!*8h#*OL=#lCD3%4Qe`&IXU?X)mOz?8 z)Ji^X%BkH6(3HCr_f;D*&-hkH4=q)n!CIf%99+^ zxEMD}BM0npx1ZPnTL!m3!pUNs}xBD@ncS~X@Yn%J$q(eMN2hO~C z3};Ha#v-J#9O(2wcEFc~pDWdk31%PqmGB1H2zAk`U7qx#A(`W2%Ibo3wp6S8a8p`F zM9f0Zfa8fSc9YA);N?Xg24XD{8&*{C*{$Db;<_tqOs3J8UEYLsy=uyd zR7-&{P~8gvgO6#@pn?5k_w_BNlRqlf5UxBJDf*xH8H{Hn?I1s9J0}5u9Zn;XVE)&y z{pVVa->*U0r&9gMD6$fw#i#KT-jl|!?UH7!%j4wfN1m^#ceTd|D`kyif;-N-*h$`% z_e&BF}lSLCuK?*eyYp%~iv|#Ig-}Tg}c)_h@sVh4>k;jqONw$+9{(k2dfdK5b^?S?y z0!Ge2%)CXBN}j>`@)!u(BAjl~sk-1Mznu6Ho|Cn=9_v#ecKppi(hv$G zw|3H2p*xbS#p2~G9Uq>}!z9$umnwP+QPMkeNgX)xVrs;UphPbh?JxF6B$^Bo%F8!= z3i{+A&@CT=7`5Z~Kl0}5J!b0rK2V5i&NhEqb!s!Ehxj2#j)CP$maBwTkMV}I4olU| zH71`s+%e*p26H>PeM8@`n9Pe5I!h`4;G?3_VbB5)F23YFU?nfsksNlZv(;c#7-v zWf$Ft6OQxg#(FFM9aC(S3msqJ?P{f?!DQIx62GCMJx>(9SG&4*pd!{{{z=TG=s8q?|8n)!yZ zf61oHU&dn8e{l$3(iw-^5gNb6MHePc*8#03N#lzpfU2F8CzSoVK)s4UJ&ok(Yga&V zR$X3Kv$Y?`pzeJ<*QmBfeCcf88XsKbOyvYiv_t0W*-Bh4ev?vfBQG-&+TAp=9@-g>OS+*QQRlhJzw zEhp7my`McX%+OzWb6yu7VxD5sx~?t3ad%bmy`^K>MM(Jr`8t9e%FJ4*x6y6dALCo38bL!RiZ_k z;vUF2)||U*{MPhW4+YEw41!lkU%p^`$!lmGSFJbt2nT9i(saTcE_7=L%>_RPzf{}m z*XN)yFX{0$rNQiy)8gT75GxT6RwT8>tBptHOl3SBsTMTpLtnDCKon+1F|Sf>-fk|C z%(F3je+K_-deqX(MH=w#ee#A*=n8e|^t{tAZC|&YFt7G}Q^jYdnQo%^{@Fu+8Eh>%a;ivlX zKtLx;Xbw~ka~x5W7c1Z=URU$rz6-7{YX8&my=hpj!YAz(z~(ck^>_Pg`%mtF)<)u?9l3 z9$ zxNK5yvHkZotZboTfM{yfAVSPm=<$wS+C0ijm8WT_8l^W84=xJLA1p7K&!5r{adV_d zlQw?DU6(A5B5frvb0+xy=J2zdhn25kDq&dxswducqA{}!s?TPN z7SkcKeff=q31Y3-Ak&70ZFr~jYJf4(`(?AoE0}a+`J89PO!5ZhO46+P4X|XXeNsOC z18<*w%RlJ5_#3XSgk0oikq^IFk$jNDXAVm|IrXI!gnK_3Q z#?Ww?F1cKAVQo1GcI{is3z*d2f)Of2jJekY#4oSgjZ8-hQGGy|&I-1XUIydk`n$1> zub{kJyHg{DujkuVz^4s0(@R?$(T(shqVT&t5;Mhc<~{c4POJH93#*=9nL!f_i>^~k z0RH#Y;~w7gTu!nt-9>0-f!0=y6_8M5lGCmrW6>k+j22ylFIGKN^Id+3?*6O`%rzYV z*g{E98d5U&`Vh}uW0FP+b0bWya{&fv$%@=NEW^nfKev(ie^qK926k^rr)&W4%tAeEBzrvQE=LUmb5%FQ+lHwGSMZHU&Kv#)Rmu_B&Y{%7*h1o6wlnd!9qu zN)c#1E8=O669w&GfwoNuR|&QPsQs0*-9niF4 zMLz{1%YF!La`98N!6~$3*zdxlt#05rRT?LGY%*C*bNcD2z4rFn6{PvxX38*@RzCB= z^?c+X8;S$3M6^=#6#QIz=`2m9o*&kXOpzMr&oSb6P2j;-)2np(2Ys}43?#Y7Dgrb~ z%g(C5(7^*m)#sZAS6ePukJzP_gMegnc&ekhH>1!<`q?>zHJ}P>=vY7KT5u7v-H$c$ zRHsMkk0|8_=`6ZHX>?#nFptJT&YtEWRO{Jy zUo^YgK6`Gp2E%lqa)tTcww0`(s1^F|<~+}acO!7?KyDrK!b7|bYfMgcri!^u|O>>|!&nHrBK zvJt;+AyVD1WmOb|_KH(1GJ{&}HcZq~;LBUf}g0NmV28w|9$9V?7V_!#FWk zjRIDvDNJiyvNIb?&`^`44}53;$j@&=?Zz-SEBmmZ zO&>jdM|)M(S>GR_CU-qBB4Gw_v1UB6rkk+~>3wigK@&&Ip0tWBP5N_E`nVl2z&6`{s{ro?-3uy)}UV-8M@C6DJq?jpsd zn<=Q2A#$8Y6feS=#AZXlH43V`_;s$uVgY0VD3vh&z}p4~>;ES(h~<9*gIHME{tp<$ z#>&X~zh3`07{t!X$n^hQ1>gdz^6&1IZiixLKR+OZ0frW7aR)bOh@l^WnE_^JN5Y+w z6euYO0%$Qd#3i`6m>>w~k8zgsZ?D6>#(S;$W#*0VYvXI@%Qx@L*nDO6D5XJ6Ll70w z0fjyyULS{`tiYTIYX1!V_~;Csz{q?pya1=b-;l^n_`f@@uz=`4`XC%6D6s-YPX?%& zC4qjxO1n6K1OfmOA~+<}vommr`zQWybi_au@bTas!&LxSz5ps9I9F1mG+_>JLc>-! zif6VzFHi@ec7XhFcv1XsIq-1~!9)fK47hoKqU(IQb6i3L@c=v^py0ypU&SEhLAX#S zG;knZ9-jApxmq8H;u@4S-~ezKQ}FrFPNBqG1?&F0K)_4`^7Fij_lR}CPdA1&{&u`U zuoFNrAwY|MM6kd?-33fL2WtwXfL)yYvO>6dr?A1lgq1%8Jb>R^Sb$;hPxp?#jXtP> z{l4S@1c<>2OqjQz0b4*e25|}jX~i7)lSnTBfT0?H#DTb42p7I}To`8%?E=U?Zg5}} zQx^b(=K%jP=THK}SqgPN_4K1U#K6AEe0fbkJKAsur=UT_T9LlbdnbXpWpgj0VCA|ev7fKGt?Tm^SJfKVProh6#2p^q+TLl293$T}`kG(+u+6V!H09KeF zAPqrVLx;jY74ad3EPm_f6Jo<$0A|1DR{?-u{XYLbUcsp;EI{|?Pxzm=AE1?!=H}*Q zk6)SZyYyaR7DS5`A;9cE#176r27ZtqfFFP9pZ|(oWe@r)zxzaf_h2bIIk|q} zoPXo~@D1ycrx&j10co|^Q8odvAev$K|72N%ei>`Pma$GxpZ63|Q7~*lFxzRhrn?CU z`TPp_Ii^(+Pa#`Y!wLx8{7Ig`+22iB#W8RyV;w?&K3nsf-ar1R!(P#c0e^lRM6Vv* zA);F6_}^3mgb`Nze8>oBfB=XS4d{vdnzKPdLIL>*nh9$Pa{E$X03HVrDO{icc#H7+ z!2(G>U26#Z00HKqAj1T33)sr_8~W<^_21`6f1$y6eQhnK-mEai;CJVSJf^B@ z6d}oW5(g>bE`ad4UB78c9MLz*R#RMpFE*J?4~&(2W46Kf#Cc};k3nclD9?%*P&(I4 z<2~};^nHE|piLXZ7}n#WO2uoE@yRY3_WZ2EjNSM*EH2H{EyDL#uVxDWI}fB?3ik#e z7nopYT4fPa$(GT(!c&WZq~4;k>L1Rg$px}ZJt(a+V(J)rY#Q05pzYE`}= ziHMA(?TyaegH)I_;imwO9+nZZ+EK%;vA4s-M%q75Hu$-?303c>&c$xAC!-Vq0S>nF46Sn%o*cM1Ob&;9-(J<3QYKH0|7LRX~T z%4b5x!7e>0mb<;+NlU|T##P2%rzd?_McfDxOZ#c^=DMU4_lpS%nzOAtW_&brK~r+n zLpz;MsVNWO3B|XRtH@@z;tLZ>+oTFRC2bm;JU$?o$b<)RQn`}tyxUlz8ayce*cza- zJtPP{95gTXGdnH-C|Rx4vJ3SW^w9$9aBww-EGia;e#!X@LE!gJ3@A3vT_K^^JL9Wa zrM9C{jg?n2R|ka3U>*5V-uZrszjz3u07Ce)DQf~X!;-e? z-S_6EiD~R9P!yD=watLRqb_mOqkYohB^zOxGVmp={DBE-%QVwZ2->casT0@55oW^( zaCEjTjiL6Vav6N})wN=WNxs3pSd#4>s)zC~(*7!yoG!p-R)5e*w+lU?DAE1-m<|EQ zzJlBtR-x;us$xNcn*qtYntQ$E`!RQaI>Q$7q zN<)RrQ~bzR&b}Che=?8okTJFT{9RSg*ECw?1pun;`}`%pq3c-1`4%CH8(3(5eMHD_ zyQ?)yeb4J>@OHq-RO7T<-3b26whA3x7O!fLUrP`O6ez+(VQerok6kDG)-tkc^N5!0 zM9f8SR)#+ggk?IX5t6daq6;1A9uG6qanU|l)H^N2HsA6x+3|^W1}HVRRXf2UI_)yg zCyfSD)Ra(v7d$YR-hIctGomaD=Jr?QJ#!=C+!GfF!J?#eM~%&%xu2-0CE;CVG#OF6 z-`i+D@pvdmVnC?8EbmlE)_!+)TLEi$$7YJ?nSQL$}5vzpci(+Xi zf;pe%UEBaS`F2RD{C1lNq|WkxM(;yBMErx}L}#)`rO;@|DB~yz2>{_PCT^MAV_lsd z^tzIfiml}EJj%l1y92locYd466N@?X1YG31Hv+;%dYdS=s6F%Z0oty9bp$k3{RaK1 zMlAaJd);u!t(gD(r}b(AXa_)^Nz<$7*^> zF6}jrGxPRnK+7r1Z{wqD9-(!x#tVMfi2b=M{rUg4(C99+AIyl$-&S^c1lQ%%x8~7T zDUZU5px#K`G?d)AvmrRz;SN=`C&FHMEJ8Fu#V`A=)vMw9jH&b|s;~zzv1*{9<=JgE zRb{`f9|=fy^B0?$T^4AxUzWUaS-l3=dF)xYtK$?AAG+m zQLS??>-^j}WJ-Ke$r2K|b9Z=f*N`1mJn27Y5v1+@;>uLtmJpKj$3jkiJRL&hcaQ&L z>cHN&f5I7Q3dp7dY1`rpvBKi1BmMR1Okcp`S_gZtZgk*)D!j8av4ls7QlNyZk0U3` z20^%S8WD2ud}M0#g=gI*VOSG8;U$}8^)G3whT|qgkd9cWmGPZK-#vISw#sJ;wcA^k z?ir3;ospDZho>4JZi4n>Zir(d-vxd|u_mR~e6qvcAka&0U`d|m<$7U}lS&1z#)Os);Cm32Y1@@_x0vlmABme; zV=PY0Zd`cy+l+XTc(r!K8}bPKfquoND5=;Js6aSgc)A^rzM4Rizxt87OcJQ15BKok zix~mHBacV1+!fc_C8KaM!C@Ba$|`J|!>2d(Hs$E57mRa#dVC}R?#nB8kcA^}R=pZETb)xGr*qC=j9i(Ix6-bc z->R~hYd=~Jw%-GN{eZO0A1+fUSuW9--8%eK^({Q~lR*AQp|psQZ(Koq2w~7pZZmav zzK`-3!)m1B=WwVX`8!bekx&Z&OlQRVTTn2p6-pA&kos5t?qs^n(@HC|z=&_>^}J=& z&9{&Q(%mmLJ|LlEpSDhxJ+tZ=fz((g1^d%=0a+Hl#~WfYMU82YVi#RkP3@Dk$d~Fsf zDUA+`UQT`|+8o%tA!zynQNES8UZuW&&>e&~kFGk=hlkVv9hH@E@Lnv8PSduC>hN9A zsoAZfM_gn3Xd_QYOY%dyf`l%lp8BXZIc)X{mYyPJ@!zliR5ObLR*r z@iU?D_u&$4ql|_~Q?ckcvhfi22-K||rKqZTI;t^d`eE`g`BAq+M*=J`bB!bEE0i%D zBJ4-SMk^2J|7t>_BZGda7|Fdb*$j^TRH_4MdrB?V4YnUic8Yo&$s@L76~eShNRTNPhq3D5`Rk1=P8%jyA*dStKE zh4(YW6AEAMnWB06et9`XR?38W%DW#i1Ek=j9+TW-6Ft@wM)?wVPWO3I-Cs*T8nEBs zLzZZrX;0otd1B-o6ii$UR^EcCB)f3PAhNLxGUpl8!+C#csN$F;%6GT%klCd-q6^$T zgp=*wJGYXs6e+fe0iePL@*4CsB)ZG6dz8S{0zzg#zRQl7?jBDn7NiO&R{X*3TKYCm zz4TCQ3w2`bnDD60a3wNvfphzBh^Y5HTRP0b)Mw>UEMU}w&86S_L=kTMHzb?BXd7A7 zg`;XQ7^hlCx!s3G_-H!#C~X}nOXVgCvKX_gDUaD)KgP_&B4%-}rHZ$%y6mUdAzK7| z{Tjp-E+h6R10aKr6ms+~i>)3cFRHGCdoNYa=qu1NsGR65Ns<~li^2Qyu}dCeZ+YVu zpP}bwnWS<`s$3hF=*A^8X-dgLFNh+?k__B!x;1JV_juK8yAEIU+BAt~H^liNGj?oi$I#|-`t zX{CG2gybYLK&^w|0MhrN6;?Ni@h6KN%Y15z{~igoIf{WAXyQnJ6;YgK#A@z{EDd~& z!dQ#9lYaX9;=KBD2jt|JB+?-~X7r_J_9R|I75|0d<(f;48Ol1D3gDJ;hOYbZUXg5R zP(1JI6boprFTQv2J!A-JUCF@4Q&g>rNlm-@BwLkc`xoasiABdPzQ_FZUGK^aX}c2 zkZ0S`OfFnaXQM7{0WB6{=fVCFdd-Hj6s0Omq9~Q4=$pk^)v#Vd@;~jx`FF>cyS-ab?OI&va27!2ADe z>>YzMjheO5*mg3(6HaW~$;6!4cAnVA#Gcr;ZQFJxw#}3Gd}mkfst%v7AMzoZr`~Db+A4MZ1&Z4QLpjCFd~l^ZYUz(b5|H_~=^;wk#O3=4hKY zOk{Q7jxlU`4fXK;&#)R1E2#l6u(Mx@y^JiiPq*~JBN)n{d3 zEaHuqI=4)O5HO(IR!|poo5X*d(nAv|!_EueZ* zV@A^5;&BxVdLSY@ZZ(UhNSiT=T|qP=(_rZ{?%(sQoQJ_n>Clj|U!r3E3Df7eYb@X- z!oA}P9U{huXIsU>V?#uCr@|vx#=A?ndUt_^$A*e(HgUn(j6qgn*j^6%x|dS=8G0eC zy2VIKz2(MzmQl!W?q^}%#k z-*|pM5I*O*bo7H9d&|q!h@-QcY*;_C&z>LUgri9Muz`G%W7%->TP~4~jN!KSBYDqM z_amE0LBS!2&a|bBS#P`6H}9ydPCoI~!|y+@K*Xcwu9?C_cxX79YIs&3mwCa;T?Yr2K({Ugfjprb01vFjJ4WAR0iW}W^9Zit{pMUTZi7!XAZ`d4?J zyl`{V8)apU>Ky91nscrk^A`NHs=HM_ilv4ddWhgdxJ9V#u`Y$LD}x$-n%0jox%FjQ zP{N9_X!z5p=KV>WRv^1zFhR;hx54NZBcCwnMXh88<^;H}rX;uu8uj zvG>PSpp7X)c_jW9kGyo*TyA?Ayp}9)L#yX~9DORdq#d~3RpEY zI*&ueGGkLMch-m8@PZa5Fg>4c44=QcsD(>H*j|J+2g|nBJLltJ zB|KWvF98Qq@(D{I6LU8&#RKQRQ?xS#ZsGj~x>#tmsYal~1&!mXl&$Zz#wY(HMfXWq zLqNBWpa|sA>cdS1kZkbd^|<&o*~Y3I{DcAi$_4Fll(z^v0`j!>#HRAL>IX)nQyuz+ zSg$(A8UuWz2twzaY-!1etG!M!Wx~dYv)X$8M->u-DHm0$BJ9<%t8~FUiNW7>c>UKl z>h0qhsa<&�G;qen;8rX%#!~%7e_(w_DcL`XPl+Gf3#)hssAHh7?)Ve$~xwmP>0pokxu8fesW*(#Ik63d3IoC{crfn+>bvc4j^VD{y7TuxgK0HkFpq64Nl`gyV`}u)4CeU3%Z~M78JFh*aSMvXm#})pwzJDOcM@w~K zF24;{o(Y*dCYXeus`jB>laCbYDX@iyBGBujIqILovy1P5;>8dQo#kX5HaMyOa_cR_ zOs$T1#5c=)EqDzKoRHY&rX|lJ_g+oO)ZU!TKS5Cvsw_21bzW_bCNSbpuZni1l86>M z%JX|b4fO{?jekF#!(kYd4UlUw4bGEu+4<=)VV##4*pSa@t8SINFGu?OyHd{z_T}1< z3e9;uUQ(o-`o9a)!v5)O{V;ZF=ui+>ir4G0)Eug$o&|A9!@53hv~g{iLI9g=CCLnJ zlX|hdB@4>~n{ei{HvP+1iVjv>=($?J`sTq>>c}ka_SFM_D~|VTc5wC?01Hy{N$bg> zuu-}>BPWhXrBU#7v4BruEM?au#%p0(PCm; zvwJ*2f&x0~*?|=aL&3pUT3xN@xBVb|>9x{C;6GJ`<)Wf4Tl3(Uqy)3CigDI~ojz?c zYx3vC>$y>WOLNMNH@!r+)>CcOvn8_ZSU*_5#hyTbWM_h+E<{I5HMGN!KZxoD*Q)x2 z*K`4r3S2;>`6(chydM@2HM2)Ebm0RZw|wjdm^n@JbuQJesQ*`}Vs zvpmfC##0N8VSPi{Z3K%&VzMDEXgms&rIsI-h^V)w$e=L?OtrnzREJz_=Xo><@~JLy zA3$pP#^drylIGrBC(zLOm_lv9ShdTy~g;m?W&u`6eM|4i|4mqwCpie`} z&ZbzNl9`$|*^5}APGfXRs`*X%<#fhlhOCjcW)_q9@jrehqg=Dcuz{u&LR;%mwK7LkM>u)e(tc!{C9^?(|w{FtquOqrO-EHSUR+YpEe;NQFZVf^%>Gc`a{B3BkH$XrQ~`RSv;mqLRv62rLia8u0qZ zL&!R#6rW*WsJka!)Nbx^uQBf*S7mmbZZW91$rvY{NnF9+=JE;fss+1r9pM+koE4*e zxSkcO0CqKHsuDprNubnZrP(xpnnJ3hgt53?72wP+`LC=)lB=y4|7V?B+b`C0$0q+U zay?STtiU(dzojy0NA0((ms@`mrG|{5^f&jabzE;Slc5=|@X1}Nnl{!a@cQH&QvX@$F%e9G4@`<_)TA%z)ED&4ZpMUglMaCC9A&gJyU{}f|`ys-y z38%3W!`P8q@3P)4RTM+y0bnIbZRb?>-RJSLBZnQy)Pj3ATNUqF_*58<>NN{PgM zeVI%b>U%cBR|C!C!A?H_>0F{1;SPiLynK0>JQ$j+2k8RT6U4|&l-HG{6bEPIL>YA* zg}Usl*5Ag*d|2{06;t~pIn0$uO3$s|GVqi>rW47NHww`K;&MojOH`6FmFF4MHtg@dhk_0y{ z`hSSN6a|-dj#JGSp9fH>Bd-j^5Dp|5i|?g|vZ+iNyQFoId(@5J+xB(mGrciE>i-om zE!Uf&ZrS)Q-`mycM?z%{MN{lQ+&DcN&mJ2oHzlYgS(d|LhWf*EbcoB@$9H8%R?7hP zS6aZpMnvJP`%52wqX-nFsEGP++KVNG5Lpen5eqoBn%)`cW??921dx?Dh zbnr=<#g<@H`T`i8P^R}^Bd;e^0ZCvf^&=okh=P{p#7`E)C?IhDGw+}UbB!RR9Rj1^ zH36W9DsUryBSs~x?3w#w#+IN0F@9h|sDhT3m&zLX;80zFOwk@?5E|YDm{$iovYpW$ zVrqW~=GE>(g&7LwR8~4pUH||jeV5TB|6mZ z2x?Wh2WkYa1u}hc?dgjEmMLn)tdD@^-YD^GiFe6jL`8^GR?Q%3zzisVz>PZw_`h9R zKR^9@RVV>X>>>L5Gi>)?>sknO1eAab@k^~BOa2v375we^5hOFHa}b`AqW~Pp2go(2 zKa5^yPqZxfa=?fxM|0?oAYKxbo5MOt;IAye6EfOJ&s!i!!W38__!sW;W&j}04?3&| zVnc`l4f2+TXBpAMr@r;BI3XHb0#*Bk7S#2$oDrEic;XXM?*|k9nX$2{Rr!18 zLAH>H$SDw@psGWlAeP_4ttwIunzkWwedTU_U2x_69%vWi--5(ckD~bXQ>suTgUzT<==UT@g;qq1 z8WDjESF|lvd`N=WzKsim+Hc59ql5NjE>Zcwt&E(t3qQ?xdbJ#8$6t~n+BoVs(+ zkVM_E#S-biDe6&kxHlq&;TI=o}g0)=DyR!%|7!~epEGe;fP|kOA3-fJ>DThy)w^Q3F z+U4Neh+{I%>pbE&`$usD{(_-uE(20`{(|3}D1JBu2boarP_8vG_NrMH5Fw%TO%rWr$9ME8+o ziK~*2S^9S(k*V2zQHL&iv&z?0eXarm8`$A|n9$#rVm;ax$qCsGqxXjx{-lGSV_+vW z>dv6)!YQ@i%vnm49qT-%IfXv6%G6w9j?}Ym4b{p2R=d&YN6Wt{CQM$0I)6T?!!s0& z4L9(d)AO`hHqqMc7}&Tvd&fKd)7>i?nt&@b(-pw@wpVP zbP&L|E#yiroaJ?&tVY6hs60FSWdy5z8r8++Wv~&*JxX)(RJ523KXeI?(J!3gGAV&L z4Sle}rr&4z%3NHq7%GJTPPLZ})}TKwfs`@K#SZ_QKC}@}l1s6EJm_FyeHqr=su+td zZOG(Vk1Ol(xFU@xF0D{kTt)|YLer)_!ChLyPGz0Y>$x)zo<7+=Sx2Pm*}ix^(D2v_ z3pu@$7@2P~DYwsT=Gs!ouH7PrvkDQ@cJp|)i{%$m9`sv`-Mm?>i-xGphGF5yH2icV zQ{12I>SsL>=u2=h=0T+_s=qm7$;?D&Si1cn$O3$Kc3=+mOiJL6~D`X81 zlon?|j0uBidR4aVyqE#Uxo(dTq@E5<_7-gEgICim#b_9cvs`?RlLU2}6Ssb626`YyS>JYaf5s^ws3p2UBv_-gYG(mKsger2=UI-KS@d?YiOwuu|xX%N!F=zl)w_Vjp%F(_^gtXCn}I9S%^Ul9{%;iaVJ(i*N0G`$FGd9ExZR zInJhJ!l9swY&vEfEA&j&C#;O5k;^KNj2@H`54SeQ6EO+dZH^7=ji(q=rEKkXGI26|1iXYo z^VFO{_8U^IC{;6-`C2L$8n1;O2@JdT&yzM8$mFgs5W@?91*=&%d?+b567iyTh-m1{ zS)FaaAamcLnarAnXI;UlpyQksd!Bq5Xm=G~G-+W9y<2++AWkQi*#hbWDpUlBfIF28JX0{ljBXL_O=@?Q zP%(dD>#-ojK2tbg#w-^Qt?PxhETST~s0PZVI{t1ab(9yJjiQ?EOJ|n-cJ~~p$#nLt zld+Ici1sda@*j~L2lF7AGhBh{ESEmFKFOduSHdH8_~Q`DvA^nsuR@Q*4Wu^w7=se> zZy0cY!x${l$zXVx`{_*F=U$_r7zUSBt+tNtczn|o%+#mE=P4n2mM8uCgvcz$4DG^s z2}^obRP{}^h(fFxTxvN0-pI2}OQ^Yl^itM#hd+IZJ&FgOL>h#D?&Q8^1zP{th zP*QUT*D-r$OZvBF*=RAl@nv-QoAz)5Sd#N$7&M6Z!I+ALh>Hzu$!S9z1LzG$JW8+RsqQE#VVK%TKml z`_$~s4o(i%8VQTYCd=QuB@l$=M{N-gPYP0*Qw?}*rZcjsp%$y1!-e@1u3y`5_&XaG zE7b(Q!@lttK-lAcf+aZWX|%)Rz5O%rk29}5Z+-pOWOOseGberjJIxldHWqb^id=2* zlRJWL%>Jyhb^?7ee(|?!Izm33_N2G?MCg9;TH@y2xmszB*aMA*wNfX?oUdNPQ9f059~V8f zo$cgKL2xN{kG6euibwZ$G?fz5hANCUR8FKFwKd5^`q%bs+oPLa2(hH3Z6K!Lh} z@78ePzNB=B!q>uq*2|4W6PzpV3SCrxM!h5D6a5}c$=3iX@EP5iU`wNObRW@>bTR}i z$(C)~j%Y+hOtf*BU~Dd{38YUJ|vXw7PU5f#3Dn&N5jE^8pM$pX{HIU2=Q?cz

V6SM%Q;P|M;!SHa)E4#;Bgt^A^T?T_T)&iRc?T7xv+OqaI(N|Onqq1M?K zk@!;%u~U+rY8bZtu@A!2Rr}-d#F|PzS1cuYUEy)$23~3EJO>T7{t(Sv7fYd=@HF{< z)Hf`WqYTA`Xch&LzBB~3mC#!&-&6EQLG_nHn^HwERDKB-cK}2rs$w2UlAHvQ%o-NO z1YD?pZq2bZLU=AiWVX{>KYE(EayXeb-TYfC9-)=pd~YT0g;qF{SB^=qCRoC?9vs#O$<#9N%TVaiMu z|DV=b=Oj>a$j-Qw_W0=cknwz$7-@aAeLIQ=s*sD0{gAqVs5!lTk)j}|dd$9EetnM$ zE7b_=gflEhihlOkA%iH1>3{#43n5f1ZYx;u?gW+vYf~Gs^ZS&KLBpy7t1d zTx^)ssA5>M^txQeKFNVhjyLV9t+tN-5NzFeCl{7j{y(nKDw6MTJp6~H+H<>axME#SD8hJL4 zotEi+%{&5Q#*z=?mP_k_s*Ap+y-5d?Vc1U&yLcrewP!05V)q4dV%@(4K+i)?wvetm zsQfvE1*`T}3EoUxSI0-9uH?|+T+hpmb8G5DIDX3aznA4lV;TvNC*H@{NZ)D7mnoGZ zKl3~|jXgU{jJ@1c@vjz?*}gE)SMy*4u@?V?%OmeQA9>*=QA^J&FiX?tkG3i!1<-=> zYaqmg%+{pNEiTw5Sqmh|p*OynSzc|9C|;|@EQ((NC&zKgwJ1x5hMNZRt~OuSJffJ% zUsn|`8Ho14U%%s^cn8CTr(waVm{|mrO{;1R9fc`^`eLxZZ0B*QF}H7TdV3LHU;};t zt0dsGU37e^D++a(YR|ioQ))LICfBBNi5|l@Xjtm=OcTlcJdKyyVog3ZOLk)ZmRF+B zC!@M5*}6ISRU6FJATK10OcUdcP~dblzuUiX#<2+PT6Kg9&5*ILw3v7pJB_-~MiSj4 z$FbRQ^YJ^7JRsG*j)9vO)XXg!RPQQiU+>objoxtqRrFq&tM995yOCP0G)s*A<(MQ7 zN0ObNRCE{0Vgo`O$p;}O;rIzY9T;l+Kl$pM|D&(Y_}_A`nV2|O{>yX!@445^j7)6* z>)dN)SQTY8JeO+)GUyB`I&rNGX-G)KQE31GR2Uqr4#K2ff0J+&(H&(=T2~i_Dnb}o z2&W98ZBG>~Hq%yPZe@atQf5Ajsz4P0p99dO?rX_$(M4M@JjzH-aMZp0_`3SK?Dp#J zyqJUe8JGAc_!B~o3%L3R$2EgE#;XZZ+DM=Ut9i%|E z@cjb^Q0+H2H`PPz0a8I^6hc6NI2D&nfnH(`9Ey-6qvQ#N0;k&;l@!&EeS;?54_TFZ zSZ2B75irfj_(1!T5M#7NFz;RfhHTK#*b0It3f1s}xF-a0egh>esEvX?+Mn_h7)1JD zvK%64RDWXqFtlB9`#-2XV0)dQ+U!q=n{EwRF#U+VC8EM))QZ}n|A2xaQ~>o|qQ0Vd zDl9=@Dd8XL1qgx|irf^is6xntSpivq|u{-yNN4*Oz-0T;O5yYrRsLv{dz zo3uwh-*3O&Z#oC4HmDG8fwuhsr9}CiyiQo`HqR?_5koF=q7)fF5=FwaLR|SCR_oIe z6nm-`H0%mV`74hbN|?rf_$UyAzEfH$#Ttcprv@01C*r3hQV5DG#C#9_&*8-{f9UvL zQR&J+MnBnHGF}&@|M|FBZyRwP#(+7Ik-G{FEvDl6`=1~m6Tv^n{m^)=O`9Il94Yfs zv215L*I6T@H*FS^iEONgz1X-p>EkkP8S8rdqzpT|B-vM%UdmGsxkQj;CSy{|SFteu zTX!0Ikr;1lb7yVsz$yc1k?}C|^zW#FG`op=O23rwp%EJq!foo~^ElyZU&QoIj$dCZ zrNMfV-H2ZM*xDdom5#cM|I|@SGHT1WAKa`L(^@Pl ze6<8$Zi5rNoOtNQFFMEP3Jg}c^<``ZS>w+2Q^$=r?k3AsGTrK(RGMQ%o6084uMSV+ zEp_*^`+OPROx>I4;?zA0j}pb){RGV%HF(H+&a{+vjEyL!DhJgvlL;NC?TzEs8dj4- z>3HklEQ2u&zV4%^@E5Iz4`t2~5`EDJ6PA`Z(US7D0V*p_cR!1OmuvO@t(zHi@_BIK zomN4%^Da7fXRT&)TJvePHmDuV7a^|+FVboc^#t*<4%!EAZ))4w)$5O}n>t7=xHngMSY(o!ZXqyK*BuQSjd)>v>qrr^*!!Vw8`qy!@y zzu+r%K64%~Qxn;3_guE8f8iDWnRsekY&t+$nixFr9)|vW5p&(^>)Z&Kgro?rPe1Sf z(m7t=*iUvLi_y_vzLN~fdiC(oR2cQo{q1%jd9iOnoc!9UCstWWLGyHj#CCP9v?WsR zMflEo@s#3p7KdAIhp21WV8wp2sm|6t4BYD(=8SKiY}nOnV{2r{x{NLkA_yQ=zFb^M zNtV0i$Mz-XT;H{$@tDv>82W2accE3!8sKgKDq%@mRnYLR{c5yXD+^8J72$g)*(L~F ztAEzqF}>mTbv&uyH|2F)vx~Y7jWb*Cl#)|-O*$V%O>Wb5;?eZEPcaz?sf!yUNgs99 zlsM-Vz)AC|YhN+_x)!P(881eYecKmqJ=*5LNMVV-42*Vsj9GEN2{7#1z-3{d=F*F` z;v&zPO%L|9S|_?x?7q1ludKHluo_axjrJjJ6;wv zHD7G;o$H{zjaoi*8^w!oF4moj?KAXIx}5ekJtS9aNRTN=1Yv@!2c)Bf);K*O70gM!8o;He~OlhV7&aY%uPQgCQnQY=U2mRf18xmQ|0cU+7&{ft&$_lV0m+gW)s5> zJ3}2u!)Yj&?tsPD95M3WNp+}r0ro4e$-C%<()Je5W8y)%WrC|UqfWI!l>?XU9Wgf1 zP*&HmfUWK{{{D|nw1D3x4vybT16b&pSee+knAzFrnCaR7OV|HbLx7BhiwWRcDGmlv z6GICFTPlE+y@8Xtqlp2)<^P+`PR~rwLIuaq|DRp4Gqi+b`tKH&io3lDfI;5SQrXD{ zjzJE<_KkvwTR1p60oWLs|I5e%u(GoJughH@Xjvru;E4a2(o-aIH58`ZkO=BSRT}5E zmabbQj2VXW&S|3x``7i?_-f?s?1?X@%x`y=#FG`hzTFZPLZO8@Zp15QJoF=PW zUZ`VKzkP4|(22MfDx-aVpstn+kAve4vaumc)btX(GqU2L8DUmJzQR6j zoHblpFmyM9xpP?*{8m`dPBQ2OfY9qmaCsO)UKrBC3I&u+jodw2pMSteusT99V=zYV z8`Sg-vavL80-m&renjGyKj}__ic*~%X>n#MrCebP8Km4V%vtd`!EZ8W^ZOZb2?t0n zXe{a|LUBn4IKIfb9ePbkqY*KFrxb(;R{jClQg+luFA4-tV$xoPuv)s7NMIZjts$?~ z{PPGWV}y!&3_BcOA)>e}A%8}Lz!#9kZjH!{=qTZF|J9POTeBJu5$MKZu|1)-+&o_Y z0#_GDtvfZ1T|c~>o!$(F$-Y*4yVDdmkFqVxIEJ>#g|6j$C!4mjK7D3Ze75TGd2R4^ zmrg|9HDwxQEloXJc9jvz_)tYx6n33T%8UC8TpWX|u?}#U#~-XtR1N=F+5e6)Cpos8 zBMhCq9=*1il{GKP=`43;!D=e8YAJV@v&U?tHxxHtEtif+@mc6i(jSFIq;@ixogDYq4UF)WwTF(B>s`cw{S0{Hnzn-?Ywe<+5^=PkJMiY8Y^N_60$oS@4@%ci_ z=?@nfSp#?tYjBlI1?pOpxyt^kf%lB5Ys#0+@Yo94^U9$wzTp{&h} zL+IF$*s7Si7DN|zj3D{Zh=OB=puOpkM`q@78Biro&Ss_uhaz&J&^D*qAc~brPQy%1 zq!7??6#tbCXC+Y)dr^u?j?Ov+5Sy?S>Xr5(zePY!9~20VxXR_k(wQt%gD!pxXDr#7!nheuPa zWXevGYmHY!golzWhpc3}Xo>kVwR}uXXMo*IxVg(Q=w%V`j_Hf)q|v zD#0du?}MbsPhmY|g{`u~NOVl1$-hPSTl4Q%RPETZxXD|}{c}ctB^R*Q5Gp|}k3x@8 z3_)YSS$uhOG1$*w#Kp@A2N;3$VxvZ>ga2gSNePGWmFbgVE@ncvZf}(&l{ZvKJ8H{w zmCyvvRy3N4Qj);=Uq)3X_LTUVUL`mi*(MypnBT<7%e*zn8^(#Jf z>)I(q8QoySDS0H&V>c)cdI`2pSF&zBJxB(xA`OrF#)!U1d>|#rz)nIFV>1~r$tAx(a{ZvG?1I!gfi5y+yBY9Cm zRx=&69j6)I7#ns=U8U!isFa^4ztfeHhe6j|{nL^5Xjepm%ijB3E=(H5#-ZRy0B&;W zK~NmMIty4h3j}xS&Cw9KxleK})%poCt+vd^jcNMda*F_N7kyrbP)~_V!YxIY=z!;9 zP6=XLP6@8uzW}x%O8sfvEGN+!6Lo0KP9v)!Uq9&MSJ5 zjQcU9Kt*xI44kzyz1vFM3}RaP1G)mZ$Y9T{TajS?UTHnJvw-U{{1o!koX!-|P$2lx zm>Z!DZ-bKs`py=_u|3Ozs2eM4Q}wN6(8d)3s_pNjNBC&81oaM5itx5iPHc;0(tT~9 zPX^tTy#3${Y!{~hF^1XD!-KJ!9W4P2DZ9qs$Axnx=UueXR1P$-&AC z7_2YueX#ee@WSb1A53Pnmeh}Kd~gk+%Ec?Bh9u9Jq=kNNuOh*%r5Y_=cx3gQu9`k& z*~H8rI9s2m6!~yWE0N1QG7o{6v`UA^BCqV=T&_91HfCFBws`A8XT2?9Q`zS_vgN@& z$|yUkj+^<;LfX=nLJNNmZyl5bYefBuJXKf>n@}cLIc@%jbapC@-?}Nz+F_@wd>c}y zqG)o$hd8PxxxoW8gyS}v40Ji@SKt{V+YI(SPBVY5kci3&7_rVhtO(pBkXd#nou8t` zOqr)N0VFl3YH_Dl+=x3`P@|~!c_HeNr8t;owY}*Wys;RjHA;?@;>`{pat5Mm!R<0G z-!8M0b7g&FN+=jj3o3*B=P_hT>`dOwXdcfc%_H&yECU*W;j|z2MQ@Yl+M6h|?46)u zAMQj)b?x6S=B2TX!#V#Cy9`;jY)zJiRo%-A>X9G ztl$Py-y*7z<8ZB5Y@F=9mPv}8GH&_%Uf+O{Of=V2tuuLEIB8Ai{>cn?+dQ}Dta zGzz*WW`^igNbQ=yV+7NepkzAsV=G1mk}eUk+wWXu6@y{D5Gwksg z#k_*^`XP9)E`Ku$qS0GU_$1V{i!v-P6oIw_T@5!vzJagsU31@a>oh&U(Ijk#rVC7= z?|tqS?I`)96I)Di%?HveUF1Ih1`(X8$29LO6nC8;^6bjwJLE@$`@uleR7n zw1V}d_h7V!A$I!ZPF-)9iAfKwKu>j}b!blL980jTdfITyNh+$dFU z1C3Y2{!ukwx5?BsWh!rzSeSaMspo$g9?3e_ep`9yL9*_n@Z@m26e(4TAOuN`wQ4eO z>79{dTgvVmR(f`nJV?WO#_|iy5&IN~NbLuD^sO7opEbFX2e^D#T->b}Co$YJ9RsiC zEiI42&6))&foBavmGfny&YJ(MF^)j_!=H3Kj#K+xWSsHgEb%sv-S3sJF8Le#y$Efg zZ}wRSqh4R@hWL}$lk9kCbE{vzK9ady|2(ew#F-R7t}UtJ#<8gI3~eARZeiwsJS~~! zKieQz(~yULKkrJAqF<7tf0e36yphctAny7#fNdQ-+b6jf95)0{8ig&6#}Lh`i*M1v zIp+o}xY?E5!`v5sAlQ$4l@EOrO(y%igZqnmQk@S{h>MXEpYAFoWupT{rD_{^84XF` zuoB`nIRz4fLn4wMm-#xX2|0_8y8sozrPv-a|b z<@E=^aPX`}VdA_FCSH*a~yj+;ttpz}o z8`PSUua2b8Z&W?K*%*q8xJfT22QSKWd^M+zE?%#eFMOwymyNc9jNI-{SM|DhKKwgY zNg>9bl>E@2*wpu)>O)xVX7dLXJwFcjSD(85vgW%lRQ+q+V_5;Dc3bPhs3Yy!+RDzC zxfV^@x?dmfA7Wb_DyMZcFwce$ZwJ;NrQQNOZ+t|jPvfhrych0c2Tdg{10(>N2u$CO zdcO@P2{QQEgLBiyE?Wj{HI(S_^@xYv!`+z2S5u#d&&OTEu1h3TDxu`N$4AQ>J(Pyk z!IVXblLaC<-EN-`Z^H+ENW)%>kg=qL%$8TYj4cK}R|k5>L(|rljF?~iQf5AH>j~Hb zANNPe#W8x93H0!3Q6#(^ZDD2H3_~^<$?E1?R(e*w4s8@q1>c&^f3g=HQg%MyHtThJ zeo!mcn}H+#sST*Mym|U9oD!bqhHSa3Yxz53d~nd3tB3-Be@h64aQgS%{aqa$3@Zu$ zM+$3h`EE+s7y~I{rq`Mz)pfBDb#cX{EsGTjYy=4q02v@RVLEz$dD|HH}&Sr*k7wNAoH5 zh~?-nz0EN70%!3`Y!ThZ`U0?fZ+SF^igNt`#zU9*;J*nRHMS!BPm!$u&RX_=!Z+$l zCZ=!z8jV7?3}(E8NY*JO8=Q* zYWFSuCp7jSNfe;PE5a-$!ph9V!OqMk&c-Ir%+4XkCH5a+O<0_Tk%gI!AMk%4^1Y6X ziLIHFIe>$S{r>=R{|lNlf;kO^7)2bYYey+XvO-}rsdc@#GLj-n=A`pF={hol@Pc4i zOsXVuY1ma^xZt!rJQKtu?-r)LqDT|wc}Vvx$Gddbt~>7|@98@N;-KSYv_5q-;$TLM zii%Nn=CnwF?LZ(7D#NZ^$0*sZ6cj2Em1o_;?=I1F^IrzB#aZrX1k8ePcS;X3$q0#k zYuH9Ij3kIXOGqn&pl{SW*97LT{`ms-QXo@QJ%zX}>|o7AJs(8Z_#hp$e$C|9uuuui z{#R@}%Si8|81g7RIz>wX7Ty3xN!db)`%!)7Ae`9TfmnnD5=sI+nI|w7Z9#hom@p`o zVm}QrKm*uB7jj>U(YP>$WsFdpm}kj_Rpu^as~X5tE?7y}GX8$) z4dJ}e#ZSn39m;-zG!IqCoj!NHZAv`(Z*ZoZn1! zRl0OkAt^Ai-cz+Oj=5A+6}^ylL@g;lkxfnIfXu|Kt}LVQ-7=pVd-taa2T9yV@2-Hb ie*gIY|Ij)*88|q(Ieec|CKg6cPIfqQaxr;vxc>)gfvxBO diff --git a/ws2019/ana/lectures/linear4.tex b/ws2019/ana/lectures/linear4.tex deleted file mode 100644 index 196f6eb..0000000 --- a/ws2019/ana/lectures/linear4.tex +++ /dev/null @@ -1,233 +0,0 @@ -\documentclass{lecture} - -\begin{document} -\section{Grundlagen} - -\subsection{Abbildungen} - -Die Gesamtheit aller Abbildungen einer Menge $M$ in eine Menge $N$ ist wieder eine Menge und wird mit $Abb(M, N)$ bezeichnet. - -\begin{definition}[] - Seien $M$, $N$, $K$ Mengen - und $f: M \to N$, $g: N \to K$. Die Abb $g \circ f: M \to K, m \mapsto g(f(m))$ - heißt die Komposition von f und g. Die Komposition kann man auch als - Mengenabbildung auffassen: - \[ - \circ: Abb(M, N) \times Abb(N, K) \to Abb(M, K) - \] - \[ - (f, g) \mapsto g \circ f - .\] -\end{definition} - -\begin{lemma}[] - Seien $I$ und $M$ Mengen und es sei: $(M_{i})_{i \in I}$ die - Familie von (immergleichen) Mengen $M_{i} = M$ indiziert - über $i \in I$. Dann existiert eine natürliche Bijektion - \[ - \Phi: Abb(I, M) \to^{\thicksim} \prod_{}^{} (M_{i})_{i \in I} (= M^I) - .\] -\end{lemma} -\begin{proof} - rechts: Tupel $(m_{i})_{i \in I}, m_{i} \in M_{i} = M$ - links: Abbildung $f: I \to M$. - Eine solche Abbildung ist dadurch gegeben, dass man jedem $i \in I$ - ein $m_{i} = f(i) \in M$ zuordnet. Wir definieren $\Phi$ durch die - Zuordnung: - \[ - \Phi: f \in Abb(I, M) \mapsto (f(i))_{i \in I} \in \prod_{}^{} (M_{i})_{i \in I} - .\] - Da die Abb. $f$ durch ihre Werte $f(i) \in M, i \in I$, gegeben ist, - ist $\Phi$ injektiv. - - Ist umgekehrt $(m_{i}) \in \prod M_{i}$ gegeben, so ist die Abbildung - $f: I \to M, i \mapsto m_{i} \in M$ ein Urbild unter $\Phi$. Daher - ist $\Phi$ surjektiv. -\end{proof} - -\section{Gruppen, Ringe, Körper} - -\subsection{Gruppen} - -\begin{definition}[Verknüpfung] - Eine (binäre) Verknüpfung auf einer Menge $M$ ist eine Abbildung: - \[ - *: M \times M \to M - .\] -\end{definition} - -\begin{definition}[Gruppe] - Eine Gruppe $(G, *, e)$ ist eine Menge $G$ mit einer Verknüfung $*$ und - einem (ausgezeichneten) Element $e \in G$, so dass: - \begin{enumerate} - \item $g*(h*k) = (g*h*)*k$ $\forall g,h,k \in G$ (Assoziativität) - \item $e * g = g$ $\forall g \in G$ ((Links)neutrales Element) - \item $\forall g \in G$: $\exists h \in G$: $h * g = e$ (Linksinverses) - \end{enumerate} - Eine Gruppe heißt kommutativ oder abelsch wenn zusätzlich gilt: - \begin{enumerate} - \item $g * h = h * g$ $\forall g, h \in G$ - \end{enumerate} -\end{definition} - -\begin{bsp}[] - \begin{enumerate} - \item $(\Z, +, 0)$ ist abelsche Gruppe - \item $(\Q, +, 0)$, $(\R, +, 0)$, $(\C, +, 0)$ sind abelsche Gruppen. - \item $(\Q \setminus{\{0\}}, \cdot, 1)$ ist eine abelsche Gruppe - \item $(\R_{>0}, \cdot, 1)$ ist abelsche Gruppe - \end{enumerate} -\end{bsp} - -\begin{bem}[] - Menge der Restklassen: - \[ - \{\overline{0}, \overline{1}, \ldots, \overline{n-1}\} = \Z / n\Z - .\] - $(\Z / n\Z, +, \overline{0})$ ist eine abelsche Gruppe. - Wie ist die Summe von Restklassen definiert? - - Seien $A, B \in \Z / n\Z$. Vorschrift für ,,+''. - \begin{enumerate} - \item Wähle ,,Vertreter'' $a,b \in \Z$ von $A,B$, d.h. $a \in A$, - $b \in B$. - \item bilde $a+b$ in $\Z$ - \item $A+B =^{def} \overline{a+b}$, d.h. die Restklasse zu der - $a+b$ gehört. - \end{enumerate} - Damit diese Definition widerspruchsfrei ist (Sprich: ,,+'' - ist \textit{wohldefiniert}) muss man nachweisen, dass das Ergebnis nicht - von der Auswahl im ersten Schritt abhängt. -\end{bem} - -\begin{bsp}[] - Die symmetrische Gruppe $O_{n}$ - \[ - O_{n} := \text{die Menge aller bijektiven Abb.}\\ - \pi: \{1, \ldots, n\} \to \{1, \ldots, n\} - .\] - (sogennante Permutationen) - - $* = \circ$ Komposition von Abbildungen\\ - $e = id_{\{1, \ldots, n\}}$\\ - Wir schreiben Permutationen in der Form: - \[ - \pi = - \begin{pmatrix} - 1 & 2 & 3 & \ldots & n \\ - \pi(1) & \pi(2) & \pi(3) & \ldots & \pi(n) - \end{pmatrix} - .\] - Elementare Kombinationen: $n$ Möglichkeiten für $\pi(1)$, $(n-1)$ - Möglichkeiten, für $\pi(2)\ldots$, 1 Möglichkeit für $\pi(n)$. - \[ - \#O_{n} = n! \text{ (Fakultät)} - .\] - Verifikation der Gruppenaxiome - \begin{enumerate} - \item $g*(h*k) = g \circ (h \circ k) = (g \circ h) \circ k = (g * h) * k$ - \item $e * g = id * g = g$ - \item Sei g eine Permutation und $h = g^{-1}$ die Umkehrabbildung. - Dann gilt $h*g = g^{-1} \circ g = id = e$. - \end{enumerate} - Für $n \ge 3$ ist $\sigma_{n}$ nicht kommutativ. - \[ - \begin{pmatrix} - 1 & 2 & 3 & 4 & \ldots \\ - 2 & 1 & 3 & 4 & \ldots - \end{pmatrix} - \circ - \begin{pmatrix} - 1 & 2 & 3 & 4 & \ldots \\ - 1 & 3 & 2 & 4 & \ldots - \end{pmatrix} - = - \begin{pmatrix} - 1 & 2 & 3 & 4 & \ldots \\ - 2 & 3 & 1 & 4 & \ldots - \end{pmatrix} - .\] - \[ - \begin{pmatrix} - 1 & 2 & 3 & 4 & \ldots \\ - 1 & 3 & 2 & 4 & \ldots - \end{pmatrix} - \circ - \begin{pmatrix} - 1 & 2 & 3 & 4 & \ldots \\ - 2 & 1 & 3 & 4 & \ldots - \end{pmatrix} - = - \begin{pmatrix} - 1 & 2 & 3 & 4 & \ldots \\ - 3 & 1 & 2 & 4 & \ldots - \end{pmatrix} - .\] - -\end{bsp} - -\begin{satz}[] - Sei $G = (G, *, e)$ eine Gruppe. Dann gilt für alle $g, h, k \in G$. - \begin{enumerate} - \item $g * h = g * k \implies h = k$ (Linkskürzung) - \item $g * h = k * h \implies g = k$ (Rechtskürzung) - \item $g * e = g$ (das (links)neutrale Element ist auch rechtsneutral) - \item aus $g*h=g$ oder $h*g=g$ für ein einziges $g\in G$, so folgt $h=e$ - \item $\forall g \in G$: existiert ein eindeutig bestimmtes Element - $g^{-1} \in G$ mit $g^{-1} * g = e = g * g^{-1}$. - \item Aus $h * g = e$ oder $g*h=e$ folgt $h=g^{-1}$. - \item $\left(g^{-1}\right)^{-1} = g$ $\forall g \in G$ - \end{enumerate} -\end{satz} - -\begin{proof}[Beweis 1] - Sei $g * h = g * k$. - - Nach (G3) $\exists s \in G$, sodass $s * g = e$. - Daher gilt $s*(g*h) = (s*g)*h = e*h = k$.\\ - Analog: $s*(g*k) = (s*g)*k = e*k = k$ - Daraus folgt: $h = k$. -\end{proof} - -\begin{proof}[Beweis 3] - Nach (G3) existiert $h\in G$ und $h*g=e$. - - Es folgt $h*(g*e)=(h*g)*e=e*e=e=h*g$\\ - Nach (1) folgt $g*e=g$ -\end{proof} - -\begin{proof}[Beweis 5, Existenz] - Sei $h\in G$ mit $h*g = e$ (ex. nach G3) - - $h*(g*h) = (h*g)*h = e * h = h = h * e$\\ - Durch Linkskürzung erhalten wir $g * h = e$. -\end{proof} - -\begin{proof}[Beweis 2] - Sei $g*k=h*k$. Sei $s \in G$ so dass $k*s=e$ (existenz nach 5). - - $\implies (g*k)*s = g*(k*s) = g*e = g$, analog\\ - $\implies (h*k) * s = h*(k*s) = h*e = h$\\ - Daraus folgt $g = h$. -\end{proof} - -\begin{proof}[Beweis 4] - $g * h = g = g * e \implies h = e$, analog\\ - $h*g = g = e*g \implies h=e$ -\end{proof} - -\begin{proof}[Beweis 5 Eindeutigkeit und 6] - Seien $h, h' \in G$ mit $h*g=e=h'*g$ Nach Rechtskürzung folgt - $h = h'$. Daher ist $g^{-1} eindeutig$. Sei $h \in G$ mit - $g * h = e$. Wegen $g^{-1}*g = e$ folgt mit Linkskürzung, dass $h = g^{-1}$. -\end{proof} - -\begin{proof}[Beweis 7] - aus $g * g^{-1} = e$ folgt $\left(g^{-1}\right)^{-1} = g$ -\end{proof} - -\begin{bem}[] - $g, h \in G$, so gilt $(g * h)^{-1} = h^{-1} * g^{-1}$\\ - Grund: $(h^{-1} * g^{-1}) * (g *h) = h^{-1} * (g*g^{-1}) * h = h^{-1}* e * h = h * h^{-1} = e.$ -\end{bem} -\end{document} diff --git a/ws2019/ana/lectures/linear5.pdf b/ws2019/ana/lectures/linear5.pdf deleted file mode 100644 index d23ba7e6a36cf9859544184e74aa9aaec1667941..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 118241 zcmb5WRaBhavbK%8(`ayacY?dSyGw8g?he77;O;?#ySux)yE}j0z1P~`KgME=o!v)$ z&m z5Jg^flZug+>K(h^5{VT&^60`j!U6~qOOzkaw_o}7JAt7T>)KR?L;^bn@`{RHPAWZu z`E;Z=;;h=ax|Y87ERDq1{)o@=HsxX-6sM~Fkrts41Xqws28Ucw^W)_7Ei{50%;>8- zC$19D^V`|V4Le^Hc|`Tp?Oa;&!PfJFl<3|qZ3J$H+<=evtAm5L{q+SZh;2945QhlJ zu3&Cb=A-Ubl!$W{lLWd@ z`DF!7h2%Us+}AB3&?l1IoNJ|6tI`q$4dz2CorH49#IYUVVBH@qnp?BQzr|5XBJX#3 z>Fy?{T-B&!Anv(#!$XERL;>^4^HFwfH9}OMr%KUOeTRC43&>lLk4#~h(+9Z8Nd1C% zlVH7Wt-|&N)mjpOp2i&I%r(sGosBkcPw8xhs)YDj+a00AMi>EQ98n%5b9-265mt(Q zDkJOd)g^x*Sk_cj&rqByqu*U1T>0Si^@CY^Q?xh7RZBXpN-9bff!ADXm$zi)$U5{|J? zC0vUI1u{~)SSU<{{Q zy!p5Kfh@NK^Pzop;nE5Zdhczzm zsUIlgQA+r=t!u6svJbb>QM;k}^WhM%K?2__aFtyi4-j#m0?zGZe>#i{;{jVC9aFcE zjEY^PBXRqqXuVT43*HYTB&nBqO?O&pi7HKGP%j|2I`Cf}lXoYBpqN>freDHFfGwFb zNreJ&6~f{2F3rYCQv|0EsH9iukOHxSRV5jE4RPoRHo>sh$+Q|PM+`wxfw6bf&5#z( z&cU6JdsW|KfSsdWyxuEh-EVs9N_14=+%l3h^xcC|q8Eq7wFo_#w{Bhv3jPi}q{HIq z;_}2P!o)o)V{mQ@cWMpC`LQAV<1$ZAX8?I?#-TUR8VnBQ1lqL$y6&c-Kbug3J9e1GPNiNfTwH3?LyE)KHr7wPrzP3bkOf4A41i~x zn;K&Eu;9U_y|&*+sx+)3@9AV#RuJ;y@p9FeS@A=zOM^FBrwhz&m`ei70|Gio$=0uV zOlpkrX-Xvy<&tNwuRyaTq=I?X%x$4Go(6fsglHm$pC|#$ENWDe|XoShjso5bHWa~y&6x==0 zDp!VuWKzKSC5OLOZLt!e0gcTMo|F^jNu|wqW{L1u zVu&1Kc8v;(-cAmA#Y0PNge=6;liaELAs%o>;i;IGQ}@;ZRmDFnW}jpEXle^Kl{=sRfK!vTjm#VB7s5@Y%WB zG1T$Y2DlgziqYj%tmYvS7#(rcK*pNbqh_v}JD%Brp09qT+2;&=E9v;C4Qe#$9z_-M zTPVR~$by8iOFE{|-0#(*48Nj-v8yXMJC$VemCM1M0H`dq21zZwgmt>!(!(Y+{O~O| z=&@=WU2q#_(&ReeOF%ng3p=zty=8!kbjlFOa@qZ8K3xF>S0|X7xF)R*^?rv${oN42 zBDyJ!fEKYmWF4-5S!QUTv3zA*uR+!U@?vApp%C9lbY#lUal}9$FAoNTPBsS7&@SUq zVOSZXc`9^1fuh38P|JlQmsOw*Lh!3FP)YpN<;RjGT6ZV0)bLXNs){ilmt3%i@U|u+XT*74y6;1?2tRCDFSwfZcNh{1=}k>E9&}eEvM7WTIqM$6 zKdjo+4!9{RLhXQ3A;~n>1z#)`P}77Dw@h z^{JRM+}^Kp+34Z6oFi&rPfuB6K}wk&?!m2BAWuH;eh&Wa`4ZqI04Kwl#)Vw_yrOvX zH==q3oA%qG`d>zVwta#JTYhUEc^lo$a`#P9N(6IXER<9Iifc`^Jgzp|_da%1KVUk^!^%do4*rQ7|yAsy#v~t#4bA3#_}`p|{)@oVLbq zXTzcHc`)BWD`Uj5?*XfcaM#uDFsJ?q%^wTZE%GiK8p7FMmLg#S0INCKN_#q2s>~@@ z9nfnj_b?_l#{XjCKi~f0X-3Zf1Z!qiPL{s~>o#pI#}zho?}y6G_MsWHaPCg0>q#3O zxs&>|=A|>~lk*708MZGH5|nN;LzNq#C?vqwm$_08q=v#!92^|U7uuV0dK>MALp$gG zWYN$vzv$aty{?Yby2&UdSQmy)LWCW1T@6zSMpJh0ysk(5k)4~26Q=vD+r38VlC{+f zFz%8U8j@G(-tUg*<{o@Hv|$J_8uWa8yi|C9^o?a~KHtyHo$Xatb~H7*dtD8H2NYOz z9~YQQ3J=F`uwit(O2&J*-pL4VQKxxQK-!>C>WBIbe81l5LxjJ&B9pd7?WgDtDrdVA zxhEWP;g7F@6_7MM-tc)wQ`(AVoni@M-@9mEKP!t|RrT;#-+$pIG}(G+@HpVBeG}tz zs9jbyx{<2Cj9#sPg00pkBx7M%ny0QPCEPMl7xeS~cqe68SJ(GoMU`QZfKSgzlR!@W zX*{&qbMY{b2B~pK&>}e&6GBOj~Mhtmi&Z7P3 z2wNl{=#Yjv5~|>A1p}ToJ2pkE)L8`BE~eD~F1xq&B@8V3;r9TA2v}$gMyuxo@5Fqv z)XBhf!cyZclL%E96c3rQMz}$+ zX(%J#ytZ+owW^0XbZ+2visz(nAK~3g`=Eo9_zH~72pR76q2N2wgY${*IyCVH-`9Yk zC8944I7!yd@6du6r`prO4&+mBWA>69I5GH+Vw6H;)52^*nKd|vOj~3>j>&ZbjEsBk zFS54k(6q{7tC9yn1d)xtpvPI-JSs5rYJ|`FO8bj4$5E-kkA72{Ek0Y3vO&LK`!dje z@Mf9yvA|;z)SzxtuNcWbj^dVRIyb^yO3`g<0iDeA1Z6ElieFHo5a0lF|1+Efb0-p` zf_L}>Yc>H|AYy;Mgd0k4 zK~fD$u;73V4zl+~Me7y`6?F~8{ZaaE7j1kuR3FaPv&~YFoH=(6_eyR{E!>}^6?j6| z?e}^O(1k=)`pxiR2I9U!4j6krszsN5CvC)+lxqLAYHBjEyKR|aT{ErWE_a!LR(62v zDs2an>H>p*y}eE?_SVwxxXS>C%z)4-RGa6@sh?z=pZ~BMMi8<6Q{Hkwxww}b-XJk+ z2%7iAa!}WJmxMR_J6_!a8Z)=PGR!#*~XO z%kK(tL*NKu+dR-7W-Rw!H(t1UK z#=qYjIWP4JslO!Dem%#tKMQa1X58k8jAShtP1~u>)*0`xTLpxh-#K8Oy&2zb*9o;; z2kmu!Q@-5kqLCV5AN_E54+5#sFzF9mq*&u<(N!s zfUN-~zU8T9`5S~2So`B)r`nebLSV~b$rTQ?0ELyotC?ZB_KLS5OSKn1{7k~lVc)~a zC?8xd1qQP~#wi|!6~0M*9Bl8FnbZCaWF6#DF8s@cfc}$*Vb_9`)9OizGv0tp9HJ>6 zHd6j9wkw9@QiC7iT?Q)Hi9b_7e&@9I!74EZy-8&s*MRAHL1@@EkI*H!|a zY$eLq6WE^CoPB8|=ad_VSMmW6SuI%^G>eMjML95dU|YT`0i!Pz#*Sg=XoB@t+yFW- zM(ziGYSBBmge<>DinE$#OTY<=kviyiDa>VqpIMRx`S&RYwTp(*Bp}LDejv)F;xu+R zJ)5zR!EF;{Mq#N#q}Kf@yW}vgvm7W^Yk+L_6rBS298(ry6yXAAt3CHp{Ue@m(sWjM zl=;vgfUw;@Z6)U-=u`LJkqNw~kdgj@I2Z|0`_ zvJKXnY)2-meg7ToIoY{i95I*JI}Rbdpk&%rwUZ0db2*i@M7`|=yTHENNm)d_W6E9O zLMR}QKWqg+>C_7)g%46Oc4jw&n5EW;F&H^aS&U)4(|9yF)=VqMKN0Qn^Vq}D8vIkjSE=h$s@-qhaWS-TKw z!)Qt+#yCS~=cp#yC9kzB^a+Oqthyz#mO%Q@uTD^I zSz)FUPV1L$+SMznm4A??vvWPOTS-FotSFzbRx))FDYQ!j}sz$fZcXXL`IqzZu z==2Arc4aSVU8vKP-m25hS&NN2?&0JtMa9CQD~eZlI#`sKS}b_Umo=Y^gv}%`;i5UD zUEH`d$~R4uqOBfS}J{Kx@Y}7Q))9;`i(nJguE_e z9%X3yS9mF5?|yA_)d3a12&&DwRO65zl3hhYUPm zqAizJpYIbct}>Qc=j5sWPEMpkf7$HNPZV2T5pe0eDp6Wq2|_KunolXYcNPmWzD~Hm z4`64STc-m`5Xx3kb79lCx^Fry6`%3`78S|!m3_aFjhR!mk;i4MAniID*8T>}u_QrM zLApG`tc*NzZaIV-n>zAqW1fAp#9e3$)tWP9z}$X|wA{;lCj!~v_&TY(=S|lsysRm- zprZ@F_EKH%LRFRpoYF%VsqT6N%$S)`<~7v}@v8CDc>(^n z2;u|V#0)xTF|AVbB{Yn+uhMo*lxuiu27mJ+Di?O(wC3d*@Vp;)xr&_SntdwSrTyx@SJ=-+uf~7(u zy5Vo#QuR<3q6_B05LWaodBtScWOOcb^&JJLE#*1uriDNHx@2k@*s}r2JO_ab`um%O zOA`%awEV(M{KqAycJ*4+=Ja>p%0VQfoABHM9vmu zsTml|)iv}FPidXLh1)^Z8#e48vBy5_oXwfF_Ks}r7KXbh*qCZoh+S{{%w=w$1C`8} z%N@KilhlHB9voFV%c$VVz95UdOSd==vD7;-qq&;am{Lf?P-g1dmrhwd%IB@8=LpTA zhFIp}WpUc*Q>}BxZvFx+w<8hB$nS(TfBAX??Rs(evbw|Q;F|TN61&j@{b<&D@v0OU z^kMH@Gee$L-=vF%r@+$gQj};E?TA|qA&=6)Z8GzCGWbj^foG z^6+=cD!MTyO=dR~6-8G@U)4S=Tr8T`bLQnOg+~1v&+OpyxUZ>5awQJwYC!$mQLpS&n{S)vDQpu`}=jm&txU<&{deH6&@#Peaqu%zNPc zy5Mr5+xB+tNfd~q=ksuXtnyCNZ)*d#uyCQPllAfZ{!*)UG4XES?@P&L2#(4^NVJs~ z{i9aTyC9GIvFJh!&|Z_baUJv{7EsmOx#M{|vlP8o|1%5Oq$e(RDqOv^MZCxI!F^tk zizt zF}ATo>#M`q&i65;bamMLNP=1QN_W2eAANw?zVK?2rc6MG&poZu9llhqFaEL5{hH|s zdJnd$Ru4&f8}0npV6^X4Nxp{Yu+vtl?lN8t#G3X^9`B;SEq4d9ilgVDzD$ z{Ew5uBMx2c(U_61o?l3mTlsIW^SW}=o7SKz7NQSOU8NVQN0)iG&I(06yGx9wBFOwv z#{zw%lwOg0lH_xuHfnKN&B$LoClC)-BOHtB?BrU`oYLNIzHYSY*=5k0y<5auw_zB* zUwkP&B$K-6p{%rNn@qao8F7IHi4hJE^%V|Pme{mDSn!dp)o5;oN}q2af>)Ralxqs( zgcnQdCPP7sLSsl&`{!N9mCJ3P+J!aXEvs$L{_aWzr#y1#SgtHiW21dqe7KW_H3Tg3 zu=hI59~FulY8(|fAS(JuiG-oRj1%|}_l>2Wf1B1xI(HnP3`iy;-~5%Uyc6}?P7P1H z{&JLOV&BD2rgG82)6L^#`{LE6Azg={h}|HZ;nD?l{91py^jomFQut1=V!e;Ate%ug z6TcIs;vp)RZ*c$2G|79Qygt%u-^Hfei`6!#DQdW#3LT42_qIaDnv_$|^6^_hSSUa< zxzf#>SD}t0OT2_^mA@C_Np$(rvHsUf4N>b@;R(|5c_C-(ivFsSWZm&@he$P1KTA%1 z#8BGW^TknsEy#qUz#f7q znAeXpoSGn~Hk~3ZNMGQdu&ap!)u#gsJdYFeKW@jtgV(q`qxrQNtk>eLB@{|G*v9r7 zW|rN;>Tjm?uUeY7lX$>LfcJCI#7aWPBKi_{U&ggd!B9P;3nwzC$= zGq{!xq}j$FJ|hYeX`BzIuQb;DEgL&G6biXbR&eiKT7v;Jv<8<%-*1YPf?pg6Lz6Ge z-y~4U?U8p`sxX0Q^g7ssZitaS*3v+h3*6}Wi0w8oXk<5Np z^&4lO7R{sB@^efwYD-yHO$D|Ulo6zIK(e|LX?_pZ11tgo4bW=F4x2NtXyogHxv zJ?t!4-bFds!%f#YvU8nfkvDTzV#j~D|h2GaGsxrnv z26ElRcQLXshws*eP{~i##dsFtlKg1Ex6Q9fga8(SO8dys1)L>us*4`h$5_R%p25SV zzFKwv2XTefNO?${Mqoqt{H3NBrrx=dK0Pb65Jevc(} zn#S`CV4c{jOu*i!Wi^#W^aO;3^F4J0PEYDIuN1Dx>-oR-V4`2gAc6aK?;G+ZG%EsF ziA8{M{WdP(4DmJ=9Cj8Xct}$hwc(IUt=LL;QJLMSLsg@+WB{yU#@BxGy);RKVt1+Z z4_J~ULr;uuLOJpHHqH45&?2v^xvYcOgOWm zMOi-Zm}WPP>xmgikJmTjKJS}Ah4{<99hiO*qkOvKj`?u2cE$bR0UXpmw&iTG-H8g; z+T7s5kZku?)+N z)x?gACfc*TeWfWB7bNW>FKZJXThccStVq8H1F*)%if_vsofX&b!m*A|n_rwd>p7i11FO zkbEeJtjjhZhZLFn-DZboxi2zTyeEQ8q$-io3BLzZS)^uSwa#v~ult~d;6GgWE#oJW z@K2PW8KH9b%6PoA?=IL_XdjvS*Xa}GUldAqWI zluTX2R@s@|ue45Ua`<{iSe|6!wFWgF>+hhk*dbYxf$VMeFn{C@=yyHLEI%4X1}zSK z-433_X?Dq$u}kj0exI^Qg9En~WCHr~nx9?KzrSw&DnGh!4n-;(z7&O_M{SDwbtp{@ z4^O5c>rMab$**Cd?9$DJc9*NRABsXkz3R{Hw66o)K@Nur!5T-47HA?{MUiPEU8tIX4>#&#=l$aFZ^Sit)*gCJbpm1Su!uTjSa4wE+`2J5I;>2LKVem z{OnKPoUp;O%h-muD4XLSWGK%|dLMDCa*CA0ZuYZcEf$bh&J7;Jtp5(BEEm%0{2eNn z_jy6LsL+7qeEtKgU4$Df210eNdmaIJfd?K$;mo12Mx?+fQ^V>yhV$X!*>q|W_`9lhv#6M zlXaLZSqz1;Khf2+MJwPklg}Xw`$n-cxGYpX>n=6p4GWdeRboYh1Lc>zzG(+&m09Zl z{z6+HyL1VR+FM}O@eDH}=(@gLW|xVnEZicvl1)Zu6tYV$LP6#xEI_fGq7N${c@mV6 zWS^UkVJn@4Wj|SU_sy=^eU+#(f0&$mw=Zw4O*Eb!y!xc%+C5Sv7NUy~rA6}sPY461 z^--9K)jQFw^L%J+Z;bxh&?2=ALk;^8TIR9@S>_a@Oghm>+hF>>7V~Otd4G|%;@Ps2 zaTfSq>+WJiG!!4kksaEhYyPLu_psH4^cq-KaH_k#BBH)mWw?U9#3Z+H-62MTia3P@ zsL4J*jA=AR8@rD(Pyv>2+9j6Swh)s{B^AdR)a~7VSY@K8rYiL~8?3Xx2&Wot9-v!p z;);bLtb-92py&|lYp7d;pc20QV6bTUa>S3=EkJTI7>2aNrT1IpdqnVhm*KFp`T%Ml zAYLEPax`ntvjydoh=lsIgNpZNF`j#1f+6(N1{K`-I8K4xL!Bg#=$SOT$_I4xT5<6c z&&vLvo|TjNzh|KY1poVEhRjTJ%#2D5@>O7lLQ({YhJz}D;M;z^{7w#Z$?@dL-i`jG z$?cG#m$xbulvFZ%(=IS}stmi+E()P+$_$}<*G>wXMpd@OwvUK@aNptB;Iw~bYWrye zDLY}#e6m=M|6D8+%fB9p{ENk^OmfTi@FPKNRx1ks>=(OCC-^2slm87nM(trm!orPoF zQIGE)r=?~1XD^R8IW})~)sk!Ty42Jgb?ZMzg`hCP0+n*nhCC?UCx>2fQvE=*iLfk4 zTM)`)Shf<_P{*LIvBOlLEFr>h#qpJfZ;BF%g5|O7DiPiZiIk=?+v|S?QTBWs1_K91}x}QOgzK# zZpNg3BH}0WZzfL0e{K2yzT-MmU6O(F0EkUuI=b|}N06RTFaKGJ?~DY}sJlePDnHCs zXagu=w85Uu$I~#|d?)*ZT)7Xl#c1VU&)a^Sd}L944U_wxJ#k2yKJZN0s}^CX3E8?E zFo3aYdbn{!A^H*SJT>v_?qy|w`FSM`7B{zJ<{<|Gk732aP6k$Ann%nGI6T`NLm6?C zO>7d{H6q*qf(AyAbD)$$09p~m%YZYdX0e?5lEzY<0p)_vq0%prpS8;Pl)Mf-a;3XJ zHy}_U+KwiD`G^pMAJIdUwF`nADLiJ|3#8nF$TT%Dseji^n%4xy?wPvA z^MH_oBV*87(X^YArAh;$h3+}G6gm~UrvedyGbp8{4;=wMX>VbL;9>9~&|yJg5&)@o zT^li!nYjp16i!>vdl%(hxCGy|1-mS4EbOlYQv#Z_`D^@K*weVP=55$Ag)}`=sn^OH zcN8!4@;xx_J9lCaI~#tBF^Jg`21fwrvn~}nMGlp3zYZsm#$YvPzU0CQLVh9$<9`am z#LV{BIVdvTAqmEa1aYZR4<#Lsfy6|gz0~O8)7rXNjD;ukQq8-zJYRAaI{@2^CN*z z;w#cfZ|U-{Hu>71L=>Xt`cr~c(DX{uf}>fpZuf1=+(S_+f!VWj`Z8BOjsp0?A$yP^ zzwUbvDsK(c6!GE)#GlL5iP+@D+N?up|J`)}%q)(x@OEm%MyPn4D=`ox1ZgmgPTx zr-%Q}V82O^dy?()|9HTi$K)w)nFq6kPmC3C4i?xcR z8#^JLH4W+Ov~P7Bd~Ed(aSXY3Q}PMpOt}8MHWTguh@r^3{=B2d-(aDq^xWgfz0@#- z89}pUZ=r`dI02Vx-eo^(RcbPx*akU_Z^nLn;%CR?*&jBL- zh)KKOth4)Zb_^Jd3Jo~?2;MU^EgBp!f;$>|9d zzW#<_HcDDU3+-oBVr1+f(s1$?NTW9qMoev96mm}idyQQQ+5x-4P_BsYFLorv^^G~v zII>VRwUkAEULQK!1BCyDvGv0@$IOk>HEBG@)&kd4Y6nR(LCBOb8Wfa{#O4zA>f@`@ zCn~W0rwU9A41ZlRJY#>-MjrsaiOK{xk7GAKhds>N9bnTz35795I-SjNnvM#hLgNxg z^Q`_ViAQJ@9J7Jihp>TrzL#lq_GpqD%X>tj%B}EHo~B+Om#-~qIkRH&Mk+$NFB7jk z>i>;#PtnKuMUJu0va~uSwS55FOPo_F8xn67x~oYr7#ou1v5#GoMfZeV_oi~c{1yF@ z+X3zC0?J1QXw>Ln2o4^@AZ32`@L{w&SWycC;fP?82@N-a$yT18-Ug58aBG5E6Obpp zxbY{te8Ry@jDO#eSce!Td-*Ygw`^00E-|<|nua3vaZ6GBx>%JST* z#I!H21)Re;2E&wsc5#toO0Bjt+PXT9L$rFzt99B9ubNYkb0?TmzwVw|TW9L?wqs9N z(Oejnrp}&DZeAk8&)(qGlusW^wy#s0afyLqhy!K33D+d=!bZrZp)1_?obWhBPYwES zo9-Z*zQ?X-5Iy>7U>f*tjY1oe_1;ZDaqcjdqxZ(hYi4a<)Gn6X8z^1ZNcKm=1n5+_fo0 zEIfnRPt^N_y&2j6KFh4f|JA#p(furLAyQErC8Rr*{V=;||EG1!L?wN34Z`V~7Stv` zM_@xo-2d2@LqUuW6dYcp$YUwc2_%nb!EvtUu7{*yDMjnUD#dCjzD=h)IKfk?PLU5R z&HpaE1@T=1h`~AP6nL{5??%g)cO=!KiyeN~1)YUKA8A&VuCp{f?Z#O*i9AzPZm`_k zhu)J_mEe6;jTO_#(oZQ;>J^AiOI++f<7fEX2~+8^h05s) z8q-QPx?|;rjCl_42VdJ$OpK@w< z5@9$d^K3_Ch?{l=6?@RFBAlb@@LYm35+CM-s0sNFY+^#|(|vLLhM>rAvi6C{pTRZD z--~QL(Ixp`E}8F?kRiEMfcuZgD}np+NS5G^NVmHJf&T7*Qi@vw*68}^n)WXLWE{a0 zK8V?XkSBEKkW`nE97;|u;)?YwU`M63DbS$YbO+i2b(7*j((%2K5MGXhJ7i!&7lprFbgzN#=Q=`O zkO;Yyvcu(V{qblu#68^!j75$Zq2c%jk z_t>!R9O%aqM}wKkFx;POMLXPmAF=2+n@dtJHICgBM?a@%bn>4vvVNAU{|CT|9B;Gi zVL$@fg!P9)2w0H5YU8J-j*=?G)W$d_oRq~CEF>`s4g})@?26sw9U^~qM{<_4X$Bzj zgxNOo*_7bVfcGU#1{Ci3PbVN?Po$J{U@1M{DlKI(&?|V!*9hJXTPW`Z|4Lp#R(Zdd z##Rx~lDR?{@$bAwtuPnhIugYy724<^zHVy+MPdVuK~jA!2r5R0$ABa|qu(Sb$I@WL zA;uJa4oWrQx>S3r4i0;@+Gq6k^WzqHNFK_-3xtImtn5^txuYpNIMFcY%M-noF?WkB zzbfc;d4(`(Hl_MRu+Q?2;qL(}QkMIVF#)8<2)fEd#kc^km6I(~J_0L2X=;QfYQj)0 zON>rAB;XMK38beGskhr}ps76bU%>%2@FlqTH zEVYJ~EaT|OX( zzX*OL2%&#E9|?eP5erEY5^HG=Lw>B|0~UWd(tS>BNypIzlxy${DTKD5>Wff6&Q@9R z+6YNvP%H4MyjJ2T%6w+o*#CXY_P_goX2uz27F7m$2E|EMWd=qC238eu#$BpiCPpwA zY>Jeh0>*KUP3d2oZhO$A;hJuFe7m)uGuvTEMG8u^pJjo^VfYm=g3Pls)#>Cgz#*^* zjP;8l1tEez;6J|D#UrsI-5CS#Bf^~`V!r$6zeY=5`{>8`043tu#o-5lHAf-~zUx={ zbaq|_{PFs>OWXQL(}hr6^w}P1%wizj0uh^N{w0c`F-WvQ6ya)t%+b!#4$%xIFhg9_ z3P^QTPiPwqJ}F8*OoxucUcC3|k**Be+;Y(gd)S5P7t|w=*vY%5>3h3$tYm7sS2r^w zJWW@3oE{FS?N{mRikt>1xW2NBKtUG1*tC~XXrt&o;uxZn0cbd{X%qG57+j;0(?sHs z!v?!>KjDez^vXL*h;3s9iMaPDDBRm+5hBl_Dr~5UBznUWo1UN(=IE6tqlW9krol9{ z3S`*?ba#HBYfXwsC_MvRb-5vYBHJhaj*)}&uR$v#`oB;?#HR{MI)|OX5qRwsCXT-< z6nXU@Ya8gRsYwBYj?SqW6-TVD$t9th=G0yG4##{UH@eu1wZ2v6>D}^xx$9^NwiU<#j*StA~u844;Q1?tOL0$37ypbX-JGn`+XUlqY ze%xFHYe_=G&mP>R1jlTkaeg=_Um$Z(ZwPvNi>5UxS137s5NW?(lkrXxsyhc8u6=y3 z>rbu4y!Y54B@{eggsQ(UCw9^3D_-0$2G_ePFQKO(8@liX?{Z zv%)0R&C;(VrV?+9W@|4TTICJI&((`a)V$=T%b&bG(k0N-z^UU%FVF@cnMgw}rwAP6 z(i&{(F1)cZzUSN+al9fU{H`j7$P_sN9uKi2hWgT3+hZ0E#44za8ITlQe+%Lp!KnF3 z$e)-q#{a_+LOb+NEdWHO_`m?VTQG&LUnW!W!@{g1Hve%PL{L+T@>5*3bxWyaNU|=r z?b?rVnWP8JxvJVXg{}fTkZz2b_kLWR8O3-u3oeaS2M2F$J#!)OXuq~Jj_9G_E1a%> zw6Pq<$uKbu38U7g3@MW_p;9M)-J@EBz`24HTp_OeB&1J#)W6?B`@6ZzJTrqDgFKLd zkR!NM5J2dcAe|J!1kfOG7}LfbSe`4urFKTP@R9Xk|J}@4lLH$)okOZ)bM?yb%D15g zJBc@QoLw2%UCuUVp++bKUT@+7t$CS_^4nOzS6pOEssi^ZdAQta%rM22Lps?hIZv&O z{-QbS!PN<4r6Xy!#BmeUBW<=sSz|O+VD497*IBCm{|uDv6X;`P`1@wX%=G`;79-|= z@5=&EFK8I~|9@YA!2k4VFEq(;Nu{RS43KoRKYd#VkPD9nXV~;r2VjhOjP=gmsm~Jt z2g(SfgppiEu10_XWNJs$_{pL_0WU^|zXyJ1<|*di@_+C`g@Hwxfmxn`P5Hm^f))4= zUSJBC{6D&oY5asPg0-LNV5Wj$AgZ-9>0s_Y1U4a4UOz(o#(^wpXOaIk(ennSS^Z?` zpOF#U-!r4ir~r&V|DQ`ab|~nN?(eW&A7GJD>NAoI0j9{ar6OR0zu{;s&v2}xwvk%} zET)O@Huia3Eg93kMZM%xmXVtMq=#OUh%6ZH-}B7tj`> zBE?IFlQo!t(=8S-*k--%-PHPGp*0{X|U(~!R*hk}jw(!_sVpDiefAjwXY(0Xx# zU+Rm1IB7xfAFwB#8f4ZtCuZell%l`wTkR z|9;xcTs_JBht=g7zzmg){wH=Nq<=zZ{C_0{{|~U|ehTcv{|)RA@Az;&n3$NyAGIH5 z`ueY3-W^Xspf8~PAFq&@yI&SRhWPZW%r-wj^N%-Y5ee=fWxe!m|NN};9XLPDFLim= z2kFsIbgDZSI5*{kq3Qz&{GagovK9Un{w8EL{3l!g31=`d|9$w@lU(7+fF zN4h*v+;Wq~w6S+2#X;u+=5jm<{*(9W#nbD7V|izJk5C@BRVlJWjS6f?yrzO=e5tbM zTNh zD9H;DHG4My3KQKq$X^^(27!XHT&MTzZ0+sMgeB4xFu6+8M9`G~Efg^U`1efUS>Ili zefYLG6Mr>p5ydoaTjs@=aMzAPBoV=)7=PwMXbWZ-UvyR>P!3Ijq%@>XdM@c<1l_r= ziWj?|z_;plnJc&7mPP9;(5ek3L~*KC@qw7;e2(lhM^w`NWG97+5mH5X(M$D$t{#l= zeq2&JHyBsmRPLSG%x;tQfqDa}f@H~mBG4!F!}O>3{`cp9H^dcF|Gq^AgOfJUgx%T) zX9-&^)uK%&|DVa-)ck1LBUO8t8`ubS?|0`KGr}anP2%{m(esY+i)T=qrK@o~?t$?e z88Jkb2Td!tj+ThyhvjB}XTS45QKdvutb+@viF5(!&^#*o15lgsQY3yW9g2LxPv(7N`rG-n}R0wlF=kvt4scWti5?W)oK4fevV_` zWnYh-vL5^H*!Nvg%1#lHP$K)DJ+eghHL?@Q8X&wD#1s`q`}1b`=a>o#jtU~cCIiI601w09&L7alfb_4KI>q_FX6j$yg0Ej_^PcvDYEcV4{`EgNX0nA*TL0uYRaHzWs zqX<93Vpt|3;FQ|Q6en(9*DXa#V{SUaT!;@92-$8V$te(1Jy) zy6;_OUe0ZZj*qY2@g6fuYaw-`Qm-kwEi50?8Wpr@4p`lQB>ei)v@}ro^H`AH`RlPry7SM+BA}VbI&R$u7H~)u4B+EOn8(c!B^5&-iJ0qS zhRwIgZTP8)h;@zmY6_UMCC93|^PeYT1^^WfrdeI#&U&gaMmb+~);R!%Z>~a*WUKq5 z>7)hRdyit(C~&2K@aZJhZ?NP4N-z#2N$k-v9#Ac2cJpfIr{=hFTzKUYJUnD2qUJL< zwXQF5%@Z_igwKtR_p&n@rz~jL#`Uf=UGto9y}EfGp62}C*|UR)K-z#d+^yhs-$K|W z>5H`!?uOUwlZ%eS&CEVA6kfTOUMW+$|9s})>47k84TjEnC}L1Ng>`5i*}M|#gB{M( zlbAv0=j1n1L;3sA9OX$`Cw6XciiOo*@>&znmeeU5~F^w8**h^b;{yV!d*#${z@rYwmh zE&(SC3=^@W=c13y^Q`;KF}cQCTZXr8&}eEsv~|Yt$w(q(xAd^P?q7Y4)(bfU`QXZE$nK3@^QaKzkVT&91oS2qw)vr=^(;V8(hFNPZZ2XTNcV z2Y?BOC!n~iLB#tvBT58FrW61341eQ`LvB5^<#$e>5v?53j*EBjKtV1MKT3x(U0?8#nd$uad}Vz*`JQ3t5%M z-0tp#YatHzY|X>Jo7dG!#RW~=&5q8MiNDJx9XHBLDRa>F4OU{WZ=`=y|I00nqQ;nh z9lqV1OHT|g$6a~*Ri8rCur#+CX&YJXn6cUHmlyKQuc5skg3XUN?P=YZmqgUo@G+@R zdRyq4=7``vF%>mQXP&Rc5Yn=?iowCI9@%f`=Vkty>XDYFz2&*L&5i9s>6+WLj{rpL zYimDO<#WxcMy$_OQW@!~W-hexdc7Y@E{CLzxT*mniosSWLWl|u3;uq+P!jt`z0fa~ zG||ekWr~Et6gkcfD`JwS(M3FxkhtMW&Jd|GLqbQ5eb49vRjOl(_tNCl&Vd=3W-GM^ z+0Z?8k~`Yh;Z9VTbX%MoFMF24)xuYwwn8R_Lk6`(w_eEdEwX>aSoc=LN^fAv(?FxD zVN|Hj&7dA`AiQu7q0Cl5*L>buKDBL;AZ9%_JgB%x?iuYMEImf-i&DEiOl9?Aklzp| z`4pBm_05JKokB(2iMZYa_QO6w4_c%?Dl`e0co9V%+giw$@N`C!jy@&q5d504{-}i5 zDdK%_yNgiLAaH4hPQ1dS(;Cj)#HZHGzcx|bMv3Z~OZ>ovBs`vjxdUE`xwo?yKycJDrOfqP_D#{a zuRUK3<@FSmoAr857r}Z*Z*d@SNXDKy#9gt=k;MJZFyRq8OMqq>VOx`>ciZ94zV+se zO2m)#8k0|#+@9L(y#g%kN0mGxJ1em;-Jy+_3niL^*)GVgcUKQms;}mFE1KWVrhu>f z@I_v|z4lEWvSKyUlj6K=UPBnU7&UN=lYGwJfAd3a1%*^TZ0z;}(ZHcNT6^s8N4vsuk1xaS!o^fvZ(n+_$at+rPfwQiEqkByL0}ZU z`rNn%UN19y5PV+M1#rz$zVI6IMhyRU7Jtg@Cyz3eKV)7M=C2pSw7~O2SRgLof@wRdu4sEfhzkVs^tiPXYvz& zw<#ShJkXY&jU%svJwtb2gCkh4NvLS z*YY`YF^j(F?+8M1sHl-;OjkbjM4t4;$3=(8<@JFv)%3ts7yL?=Y{ark}_ZC<^Hf$#IZi#-Cu-uYPDQJjP{;G8~xB2%Uc z-#H7V@5+i?O02I2BQUEgw2Z@=d;(3oNM$TScn&%aW3@to#UIjn?GWV06!Aob%R$}BZ$q={;YuNpL^>(%?hvd0 zloVjBw=gp*|2e%=hycfTbmKLq-Wg@)6bL0~Or3AO+!CWPrNs0>w}tWX+jmMW$FkT` z$ZSG>;ChUY`J3jwXuo|qf>6stU1%1S44H2sn&AbgCbfAkgYWr=V6l(J)egy{QpRsT zZi1?I2l&%O&bn;RcDV0Q-+;4(>`S4dTrZ;Wb)G)#@dK!(2GWGG-fMq!A>G?=cKle)Z`qFcsi-2wNipfSYzimrm( zesrNahrE)itdQ?kO#Kv8^_V4PpISa9m@9hUj3!X@VLMk@VMgu0@Njub*x`UM@Y#x*kaFL%Sdog9pWX(IX|qBktPr? zpYhFDRbKL=$~!$*^l0jc5ssS$WD&%&1GR^P6)$*JRrTaVF?h&%E`g0%oXhRkZ+}mW zcAALi+-=DATDTtnIm)}Q$&6E!FFHPZV#q{$nf@)$<&S8FHI0|XXc%uYl|y1^N(Uf) zfugl|jR~Y^)pvWNbajZIy=2DVYMltTe4sEVu^j? z?)NLvmXUXFb(HrOi{8wOT~cbVF&$*ElzjKZRiXmuV&bCOndu&n*)yEwI)>tYvwngi zekd@%;2GF5w?Tx)Yko4wv=JIX;9R}CSmzJehpj%#G~6#Z?!>Mx#52f~tW669$#TrX z&tvzc zthU}cERwjY4jIs<+*e}A?3T3fyVlAVF{#p0Rto6ZOq};~OmCBNE}5%~o-b7+4~=^= zsCBc{5Ho9Df81|fUyV^+o9#i)t5GRp=|_sut^y9&xoQ)I9)pAIgj>of5*NRdN#bnD zrHFUwgg+qI626exR8kMT#sb31N@DO|r$$gJariNFd{Y{fBCcx8drob3otUHg1@Y8i zN8uofEkIQ=2%drU8$f`_1w6uhIoJ*CDr0xi9wFtqU!N$gPZSJ{1-Thn=81GXD&s5; zb|mgzQx9n;nh(uwJJXZxx*yey>eJG?J=1#DpU|LjZMr%{Vm0T*yZX4#8fsxxk}`yOU1g%j3~ zLHadp#S}&ED-qhDKC@iu;UEve^L7dzWwluWcjqXZH|5rQ?<`$&UfnDocQx;scsFe0 zAhK!P@s@dav*gga<(o8x$G8;p!OJ5fUdg%yv+5MrO%!oMRVVQOe!1${bE2?2p=9uQ z@%^eU+45#Qi6p5)Ov6qyAqe=4v7dnRE}nt$6fI(3vq=&^)9!`rlTI$Rlj$XXNQq0T zfAGOhin+hDJz&??vso|LzTMMMFiOwnjzl`Ir(t$`l28#&iLerF4?B7$hHpI@u?R*C z@jR$LEF)&)GrPCTrz@w+FK~VDsD*!sJnylGGyCdlv9fhqDg~lMoPJoD~iwTsf~wud$K*qqNj&~46WRJDW(<(qD5^baD}7C*K{kB z%W(EGmNfJ5*a({vkHTi-4+&_sj^!;k-m#hS)w1lb+jqpVHzf2$4FzUiY4#-Vyl5lb zX&Bj2SUk!z5@J*!vfOOXfaDqIYTwk^FMSsVk-T8;iE&^W_SD33+7R1X^wAOS-TZhT zNItaJ030_&e<@9jA_^!#I^ush8<$S?m;X;^1LUp&2n@FAL+0Od3^DY-kG@I7$OOPu zhs$^2=6fxB$B<2|-~-qSk#CJ(4r8DfOt)M*31aswgw&037T%>uUvz%Q8SO@_R3PNT zO(GX%=}x)tvi!&9Qb2lU@GC$z;86A$z+XXz+&QI3oQ!X%p@<3!G=3I^;k94G2ylw4 zN%DM*Vw3|~6`UWa2C(ypt15`OszI-yM~gotyPqj6>C|v<&$I{#9#Ts#MxyPA&);gU z>38q^;oE1eaQ?tS<>K|bIcoB@y&|lFi2}*iE$`ocL)uoPx**vXBGDbshf#lkrk#6H zE6`tfmE1J*PJgw)i$2obQf$@sJ-smf^<%wJo#Va4Q3l~Iy+KlSm+F-pi}+e;+26>i zT4w?cKf6S0HXthlFKt0zWh3!W1OpY67W(}XB>P$L7~wttrgNaW z{NLHLKXnevR8&cTDE}JVtC?}?*tg{=0BRe^06+5%cn=m8m@8t!0RVu#nP1E&69g>G z3&4MgI&E`iv74ZySR4ujEg<;&4U)*{pX0V2O~m~CLF)wWrpQY1@AKhpL7V8ce{QwO ziw9LFBVRV*?PB7Au=1E@K81xJ3Jb^9h`Gnty;c&XcD?H7Idq&@?{Zzgy;FJLE7MJ9 zRU3W&`Fz?{pI-R)^#1u#QOcDr$GuN?ejty6p^NBG9F#>%E_L>P&4`N(h+@ZQU%Y3n zaM4gGyBlcvqzBW@&S{StsDo;XLa{`kAw$Qs?$M0=xq;#M*SaYU&)dWoqN{yWR;yfU z@V0;q6N*3ls-x-l^4&$16;>(raC$98EaCGc4jM&ikZU`x8dC#m_O&R2hXQXSgnwTL z@#n>Y_EQ3b_Xn{`s_@tD5*4cMl5ZBMtU~hq6jt@XseGqpF}sM^lkK$qS1gXr0W3xD zGORc_QKu+)yWE!J9kbRP!Nztm8hu{$GI;$%p8liWefd2R(|V zqJYK-f#1I^eyQI;o(JR#Pt|VopUNEnWI<<3WSL`OJ#ieIS&Zy4G4oJa+NN>u)!aAKmZ+= zmNSXAZT?RQPsC5n{W+8pp67o^csgMCD{xT3l);#RtxE^;6D@1-;4vTH7h6gq5wgov zK8M#2*V3u|84j&vb=$m~gVX&0IBb&$lh;V+Ig%FwSta3+n6;r;jN=Q85nK^L-U;&OhaP6=7YWvKNyR;A#k=%QOIuV)19)(iMX zcRoD^!<=eZhl|2(_4^%uD)(7SbKW7~J8y)S?g^NuySCm*e}$2YV-lp_eK-sGDqE$w z9a+BsnG_uJr(JMq=|-o$=}7EPS`a9CZ@5+P+_Gx01|=<_JAKX=@*G&BirKhw$K#mT`*AWJSrT>e+C?Qs^I+N44;0j|Jxas3jsOR7|GuGTn2!^z96llIAr^vnFsx1`9D;w7a3uf6 z_b0n{G6VvWXaPs?-~%}FAV7L9Kq448$u**5f@>$)rjKz7%r|}jUFh+fW*;m?@Gb&c zntdSJfVnx~8+qK^d~A+Az^LPkHv32V0f1=jUzmhtDwGUW1W-Y>GYqf&XSV$nga0Yp z?#c3lndU!|?9XNYmn6#%d9@AzEdW3pqjvh$`h?i9p;{wK;Pv}QG%^YS+JO)&HDxj; z2ea@~4%lD>h{Q0m-?GR`2rAdtz>9Rp6sJ*{!HzeawLY&}+@o!3d%SwQAN#Z?k8Umg zO-i$Mnm*A}bAaezt8|}8wp1zl3 zKGQ(k8=_;`TR=0AdIZ}PWc0>*?UV%P2P|%wAGb97`pfE4R>FD@K`cu5>l3#hR}MtA zI8=a2{PzKsbl<7?4_;%OWINT|gLlvKiMb&$+B!%W-yIyGdKO=uvhw~_61))4@*fIOvX&Pn8r1YBzfI=^W6!q zGyip47;A&;6Nc$0gG$R#zgYMSPBFP4F6*(j84QZao(x%Sfs!wxe2>M6@BXZ8HH=TVYO1F-6$*b~h9NUj>z1R53w?yoAqCet;WZ zaYA7lo>Zt6AX+(<@C(3BCIo5zZ9*`j=bttF_~-EPsm9Q7j2LI&pim3hga3L3$qj0T z+k7}}1H1L0aK=FDV}5^Um;%8ausRWh1xQQ6V1R6y?P=Vy_FHwCd)& zyfhg$;x94O-R#k~r=fmtmWrD?#M{DajKh7MoZs&JG=WrRZeb?OIiQ9;__E;2>;ij1boq`s%U_39Va<=R;syLv)V*-L_h(n*WMw>2G`}!Rm z<9o!F?wkwzX!l9qetT<~QDTlM$ALwHJF4d;Ct4WmRqi|B9jTdy{{3Evd4uT1ciOUI z*Y}^z%#`&r!Pn(p+c!@#^fTXQ&0V2#scrJUwR$5yrolQ__34LXYnKjCAX3Y!^2I7j zReSHk>{?13j?qP3^7UPjMmdbBDxrn7aN)ZA+xW4^%=nh~#xU7tUEkbpYN0dRe{Qv} zf)(0caYM2qWml8Pm+`IZBC#;MRSI&9W_zG>Gf1G;Yqq+DYyI&R2PK6`>p^UqjPmcC zWnYq7DF)T#DYsy`m(5W4v>^~Ez@Py5o4?EMY4w5BG7=wa&F4HPdgil$0VzL6N0M59 zxH%RWw%htDa!M^~c#X!QDrPMz1y3@zG?#}0e#8b|<<%QobsPJFyhY|R_Sp^T87{Od zJYrs*>n;B&HQTqL+^|c7-AgJ}WPUpz_INpla;PrHy0at4D4@vQPb}nOvlf)38G{F* zY~X5O*6W`2NV@$%(73%#0|Kb_tuJ$V(iv#>j z#b>WZb-IZzISYz8O^%Y)dtIbq6Uv6Sv1sR@I9v!+Xz>gm8Qaem7Fpm-EHW^Jm6F(t zgFlQ*PLAvkFDymu6CxpvIC?=(3iN+6PmOFhTUn_sV_zj?A*g<%X{J>iqRMNzLh&K{ z)mS>K8rxVw7^|^!0^_yiZ}(-@V~X>--SSLi#?>U=sa;HP)5)i6JFk4h8*^=nNius= z!fK-@=3~sv!(zSBSpThb0Q0;m@Yz}ItLioV+RM!>+o~oxjnZ1QEkO!4p50 zrIjFtfx#aQoBs(tQBe``^Yg!5HMurOx0AYxc{1PeX@Z_{S})8>6+nl>tI zj6eYc1q6P-P;mSMDRrznjWhFWnNGiW0#^9DXhzsSwRL|oWi}f(WYigEy1AkvHkX9` zmAuO&fy))e(J59Xu1jX7cJCGyc=+Nf)43SLU--niaV%ZA^VoH@Hm)A;f#(CC_^L*! zkt;*WPWC0YazAo*^Z0tB`H%aG)v&0W_UWzgD@<4g@z3m2Qmu9>_E2J(9i%^fN8JMb zPP8X6b!SKW(Bcc(VX_OWS)acN52XxFWixkKC^s$zTgaV2D93z&0|{0?b7g1GI$dtE zh1`{)Ct77qotHU`HV6#Ut-MfeKMHtxmboRj0R$*A0sZm9^o>){rpyH?Asn>a8CUEs zv+6U-Dft!np2H!o8dKQ>=cD6IiurvS0@1>lb-E)q-#nUI?c~c%FeOYJN)OxJ7+dGs zWoW;2*wwhX*7MbGvSjP&BwP1NFqenVk9(H2jWUT*lgg_ScHce5u#XeV9`--&NoU{BzM_TeSHx+87Lgl*4ggq^3(WLu=jdk#4}?T-txD)1xn)`dgRy`MlJo2{RFs6f$es zG4To~eRh+c{j~>&%#xQi#aSfhY&w?0!>QjilSaJ3UKpxx4IFURyU@->Y|qHc1-(ah zhrC{NCjQ>*gxKCMk0;h*uLdwasCIdG9Gnr~wC7WmppQdv%qKzNs!>wxwzR5kXjQ=R zF{Xh&Eb=wSMyCA=iJf7*K)`dw-1q*UmaxdUj8Rb82mutgG~x`dCxQZ?_z)bs0kaK@ z0)~RsAK6ABCJ7pf7pL0y*=1vXhzM%~91?8K$uE^x)3dvf*l6He>Ccqd_)xwo(_fA| zG5;Z&Pry;Y0ns-681R)N?mve5{Ne?fVp&nR2O_|H_;(-<4$S;6xEKL%3^X}>C7|LO zO=%3NnB;P^JM1g2_8*EGP_g^Wvr0T1++yN6>vFx>T`Tv0bQ z`7oHF`5?1|@RCUpTCzBiy1?9g91f|>N;Iv&h->F#&0f5>?Q!zGNM4fW%g---CUiw7 zYMz>Y^uSLjCQ0qltAga49ajgIMddT3s$cWn56fB)`u4QR;vnUHrL0;uQt&?7=16@T zibD=IwEwnrfirXn(*{93(TM;=J*3sd1$_!fQ=>4~AoCJ`K*pnhlkvQ)JDx((LoBW< zx-^e=a;a|HGkVR3?6#S7JY-dbZ<_{Fwco>;Ce+L7Ym`|I*(4Bv9{TE`d1c@7d&naL zFXdWusBMMZi+Te&A`PX>HFbKk%~ZHu6?c3YNe z4D9{CbLIw!NbI&fq9w1IjYnPFirX%fwwUkAMz7h@CofLT;>j zY^Sdx2j*+^2z*9k&)pjy@lx^~_=D6x7;Vh=SwDVx2`s;Tc(Ir3`F_K^ecN`hnfm>F z`w}fjvm?!?Q#ao0uQ!jRgqt`T41QYw^5#7k`O6Ozb0RQ15WRXpR9SEM_AEuD3rX2 zcfmeH(;=oP+on<}nW#_%Gp>MK#`LpQX6bTxvZ8Q^^y=~Wp~Uf0{-eG(Uh8JO$DCtk zaX1ueeF<0sR+@%V`>w0zg%SW zU@YBPKVwQ)2H6xt_MkimMC6LHm$l9-$Ywh#FA+YZmb(FM<~M>ou7f&PCvXl2x3kaa zqeq#2A5k%SR->;~*nNQTN(sL!Jfpn9ka+OyXb0z7`tCyQdTFt+no(YGJ%_@}d{5`9 z35lp++Ghcmf?4|TuFm0!@p@pRiVLbH&=~}s*M7zY^dL2mz`onXGB4xjSU6CgLB7Jc zIM1lPyqLlHB6s@Xw%!IdwIJDC3GVULPAm?;CxYD}N-gKVxF}P9!T2s9q5o+r_rVIh z28-r>d@-wmfajI|eXshJ^VEFose1bB5_7H!ZtbB8u*GQzsf6N;yNXwc9VUIZvPXQ$ z&cG$fOjq62uyUsc{}-wfl4Maq=3IS#P5weWgS}Tr4T+P| zwc5bdbZ5bgSGhHEp69)*+Q?ruHb`epUQIWMbk}&9QY1-NgYKdZdE^VbcRZ`hzj;@v zYt8fOH#}Y|albL`J?d-d07*P^G%$6!&UuLaiX(bSv12ZxIB8eDpTxX`(Dyq%voP%d_&vkQpq#^(5qw#(D3U#eZwM46L)$+H+a|?oEcn=aO z=pDTatuMXs#$ZGv&uUK6q_gnJqOr|*nN{}V$aZCk;fHZdyE_QgPfhX!O#4r;*rE!y zF^9vXKZXX`SaA?KY{ea#jr*_U^FOn|(9sQvC`T0*R4|tR_ql{$=o{Q&u+%?gds+T! zPeMig&y%TC$AX6{@+$y!5*9UB+Y{0KqI$b&jP_Ce+zc zQ00d9^n2zHxc>i<1gnQyZhF9+7^Pc9CE^?N+Phj{Vu4coOgIPMZgD9bSm;}Y~t0p%<%+dLW)H$ z5HyzrPbJ%sOTvs3`tRcmOtFbv%!awEf#TekYIP0q9Jm~43*@}c2Uc0zub zNQHT{I2Gtuqso9_KlpD51aTJnLwHmWbT9fj$iVU^;YIpa!Yj%6pP6r}W5h71!ULlB zL4%ks0D#BDUq2>db)*7B%YbK)xE?@;AJPSYUWst?V;@ME1Cp5;VSmEAVFIOA zBPNwhTAVje9Uhd+7L=ihZe`&YAnxNzxiPF2avc2Q;EP7Kc>&9?82I##RSqKb_VsCO ziynhWy|vI9ELENY@?b;(b-&!W_*0!k=>k`T9PC0{wcIP{lgtc;YZ$RQ%ivZKhqjC4nb^{)LwB zf;Q2ti?-;3%N57Zpu?B=wUx(~tLjmg#BW!hyKp3>Txx}UG-a$2zO51K9a=?uZx<7d zfTRa4H@~iyL3{$Me$>uk$eIn#qIcqFLAN71cD2BZ! z|GrN&jBY`RDi$b^-kD@+BJTx-PAsLs%?2k`Pn$(7f1OmNx{L~u{HMbl)gCn!f0-0b zO~~wh#$%!ukmMzNy#Y3*_o4%n{VWYz$pXpqXe+<3{q=Qpx6mdtgFwj4w2Pq6w7hsO<;g4IFg-M1w zOoP&_f*!)f*#j_#_;B!`IJebA7gW z9DMVhnCXp6vE#Q*V=i~aYgRA(_;#CJ@MDiSOXc)~jwQb$jKoi#yDHBbcpSNro|>7m zNsJzIVHNobk$L1^{djKk^!9AXA_(yX#w8CteW+G`s-a(^i~jk1@3Ap8a>>a}zZ!iz zE;xJ5lJ1AR$cBXN<4hYRlLNG>&$imA0)q;aokd3a>z2c^Bn5S(q<^$Tt*rhkU!nbH z&lxJJc`Dy#Ld8Rvr8}`65$iFa!ge5c?yxNsR80duFq)QA`w;nrtJJ8Lf&!(T#k|=Ouedvmi=cami}Zb6_m+SdnJWxz(J@v;59dU)uxFW? z_zx&gSc1}%A3jH+Q(=YzycwCREoeIv~jvdBJ_9g$0Tu>GW@9Dq6 z8`~ucmkK_WRvbn)FfrL~x3k$N4@bMN8XB|Y^C&4ARM(BZ=XWHkhc703Ly+fUNl=|S zR50-jwLwDvsV43*E$-z5Oc5P(lZK&O!vgXKxq&XZ6PTp8s9P32deS>`eU|7`jG8ih1HVCMD@?M@m#Q}A=KGi*cYj>1z3a$= zXE$FHUmutE_)FZ>3wu4qy8We8Q;*5=DUFeesjQwx&-m!we#)J%`JU&;o#u7BXFDgA zZ-sK!KMh}0#vLrQ_X%pY_M+~hieS)0KZk7gnHO1EaU6)9Fl6NW92!kcv7JM5hvvF@ zv)7B5=Mha}R^-s&)&j~Qc$_f47IeLBd^R!O?yBA`F1%b17gF+YA{%!Kj8vsN#WNvM zcMl1Mg#uBSL?gi4_HQ2`;w*)+$grRgs30tZShA2}D4deujE;~%Bra=g>f6urUAb_= zc`yU}s{J1h!#l7I_=?Xk02Wi!qd+;p1o$06PHUu@6wWjh`;F?|g%i5!clW!J|Gi-K zi4+cMiARbdcv{on`Av8JCS8~ z+EE&81u1DyL}G3&wj1Sl6uQl-3tIce-+YGEcv-F~*QgLP_glt(VFj+O+YzN!lay#A zht|kE!_$|!-)}wrKr`tp7in;GR|`vjdWR7AszFn2RnG*A;BJEBH%V*lKJxM^pP7pL!|2?5?p))U zH~L4^L%W}b3XBAE8hv9dP|m8?39i{uR(|4uM2ABW1KT23&rI; zj~qBRWnMZDn&zLc4VCH{dq~_)!P?Hz-|yM4_C8&hN7z*^{|k@X%`11eCO(LM6wYy) zf?v@obr&2vcv{~v`d+_w+gSme`{JwlG-0ZL^DB>Z=x{cD4f+a*pqZ-`ST|zR&|nrutKf-IfY8{Dl4`6(FtSKK zmP^VI7AvGv;!eU{Kznu5kBYi4i`u|_`m%#YB_pMQsd*UN1(r6I$#yCsYh7R19OWEI zd{>1pVp*cWl-I_tvN`wAF7h~5;c>y!9=0PHuB8@Jf}K8Z*yLj8I;u#cy06b-KqNRM zC;*mq;M@jd#V_w|jE$D7F^Ydq9T%SeMLY%ng%fO=gZISg|c_RCZRJ6TQp;Qzk& zi#SyO{N54Ox=~!sXYu71JiTPVRL!D+aR+v)wEBxfa)joIVEL~O$^U6OjxP*$v_L@` z*rSt$C>{cEMwU=UU5WzCf;dQltS$h@K!9>9RnILr`LA}x_?nL*sx_hL$DGBx_uC*? z)#>76u7Q2ox03RA(9FKVugGy5{%ars_m&KYic<#V?M1!&C$>ITMFB6cR|);560LuH zh`f@mL?~?Y!Ogzr#?mb21Dy(kj*T*7E2_+=ao;l;x+&a*vL@Y|dtT( zPe3nj@Jcl#bs1b(e^kitfgtIaqQdJ!}YXSAr6 zjG}KNfcSk8bMA@0QWrm%g;4%6LuQ?CBZbL{Vq}fLUz>0?CyFq)LvR9BY+QyK8v6vg|Kl8@vZ}@6xs2#d z-q1S_Z+f9!Ymc@?6(tmyQ$XPN$Be57%YUlJrY~~`f_L;64A<{l+EwQw{Eg5pK_5VN zoAA)lFWEeM5E*%|K%P=#Iv_zY@U>yNvCP=G&6o6VZXeP#&n>BQ(W`z+#nl2GiH8yM7@*h5s!^qy2YN4w@*K?vNCkb;nTHj!_E+M zKN`fs`Ct($Icf;zEVP5P)Y6#D?f_3QT5c}=kU$6b={hxb?gWbWCJ-neoDlhav@3`h z`I8Z_!XQ1x=~jR12%7vxM{t=Id~^bEIt0Le*a84b$-aZrJgQqDc=u^MlwAOR%mawy zDHyYNa~P4iKR`4GV6DjdqR+t?!2uvmx(v~EKz6{=0sR!;--_`=)f@yD_qWPKK;ZYk zC8cOkpNYg*l1;H>6BTdWL*tkHu)8FlBZp&viP# z=j(NQ!U!=8zvXE3iwWH%AsPA-ROm`q7`tn&FpEepWdX!0M932VOIRTZ;r3ssh%a)C z?NKuX3KF?QzZk1~NBo%jRdpgp_GgJAjCVMV%GYt$i5d&tY6lQK?lHMqMJ&OV_Duqk zlR{g_rVD94I4Hg5aHS-$8BGVMFx zEBogTvfy6dRgN&57>?dG^EC|JE>$@4nAo(PUF|DXUVYC0cGC6Rl<8D@-Ny-sqvpxJ zsq7w@j-(E2awv^>3*$KiQh^5efOSgHhtO>*p(nOkH0()V{GA`mCy+Uadj@W$ zcecfhh!l$LbB|WF@@>1XYUJFutokuj`z;HTi`bR4cRZYpE2ByKrGjWp7jub{e3jUs z-(t?Chs(Nny)60#Y8O&MZZLRf*tba3>CYtOESji2@9l8tHSfziOgipPB%RvezzTcK zjw-Y$E@lCd-=~zTV`a75bn!bP1r#^pScWNm6Ul~LJ@wC@qXuOp1xXoTXnVQ_#nhu> z5DMg0O_VCwh37O_l$tu%oBF4U8j3D-F9q}BUE#5Nl~ap0RX%L4{q^hKmu=rCG?Rh} zhTCmc_UT*>J*zZ?8?!S?-Y2k~(;={!u7xW(b7lvq zlK5)%z%i;<`s1CJDZi(0kha(G&RKBuy!bp*`-x#F!(b;)v1C*fCq*bv{8~@!1h;P0 zjS{#e(O0%Dzie-R%t$T9bXJv`FSCVpn@?+YUpLj;PLjTJPWNtnG}*fV zeqc_jlHHTfIu>wOSZ0PO`T1uQ7BUDhj(`6Q&w}wqKrP7$bt9xZAPlM_!5KZFQ%3s)luL-Ausq`-@GjU7+_I=mE{96cWrtw^pSwrBLH(BAXw?A zr5dvcg@;mQs6O?Ri}GtBjIeKB#KJ~+o11$#L#q4%NPrj2kemqiODGKK6G!>IqPWxr z&%ou3Jo@R`7<|pGAU-!*w+T{pG4^>HGku667Hbj}F)6=*ulX&H$~i6VS?G)P;Gzz- ziI-JM&FWaYkLJYOXJz}t=dxPyDeuKwRX0~O|F|k$I3y;>tuxU*nSEvS!mEx7{U!02 z7q6I2zuo*ApbkDKn)J*yNL1Xmw#bxejdF;B5$%VtBBZ=MG*l$Uc(g}y;4yV!NXNGv zH&tY?6(QtEo7by1ipXV#H^vc}R^3~Qwsh{9`dHcKx=A1R-0$EG zdF&~YdgvEY`($Hn)Zj6qiZ0@Xd)D7(Dz>GN?Z0irxaRP5Lw{uaq7MC4OK=s z-u~S&`VEJ>7blW>u70c(OKR(D_FJr?Te}&s86tB@;(vy}H)!;_GW~73ctA?-xLn?~^ zn)=Pi_u5*0g5?2W+Jqfy^jgD<6P`j0xzWvIGtBxK6H}d$Z0GlJq27C$$iN}vWQxG2;5h<2TRgA#m$T{ue+- z%A>vg*;}bEIG!1o&P7j4)3U54E?9L|&tI6mN))z1)H{*ux+ZeDJ6AM)c^|RE9zLF| z^UAZ6CEy7m!!(hbWF)F~Eck5I-!izs8NQ96n4d04A=giasTi0x(dui>6`wVG{PApJ z0{EcjhkB2y2k}y^2^1D@lI!NSbP+LLYo8Nk4`-KV)O7G9vI3sYBHC4nq-CrO>vXLo zcXeLSmA%Xyv%1Sf^KvH66nqV$+{833c8q+oJ6V$M68f}QKt!ypwPVtC-8c5I+N%)# zpxXozkE~w@UTDGb3c6%@t45M8;5u=o65%Ex!58bK9mJ>;C+?WvuEiYD4Mlmt>X5vW z=}6H8&8LOjDXAFIq;xA62fMC3Z=TI=d2;nukqEZ7#OBqZD<91X+VZZcJ~10tlY+0& z$U;57mZYLOw zcX0H{JZ7FIi9p}Vb7BT;|FW4ktA{@tyPk_XnQ)hPR6fMKD=Z=`bMfG!D1Fo8F?Yn) zUe@j_-qrFY*W10{>ldBYj=s%Zru^|yquBL!a|rI+>{TM{m{N$>xh%aw2=!pxBbb8X zW970+W_>GpFLud1x^wD9X#}LrJsmc!Y_i##RovBc{X~E2T_xAz2js2X5AF*I0uACGJ$q zECT%RH;YXk_&oPZHP|=vOFrZ;`-D#L^gO}5h~{y#G3D15?MAc3(oz2CkRLqjtu|9} zte!h~wk37kV~TT^%jO7Pl#$deKQo;qW*wqOa#72Fjt?7!u^9fvo6V%`)TM(vkm5einBfDiJ`sbH*k zJXaFc(onS+#eV<1eH#R=@lR$GK=ZI`_s|c}Kar43s1lP>Yr4AdpJ>GgFM3pYk}=Fg z1mFkWze_?%$?NPKGo( zKpZw7q*7o8;bqd2&sWV&NP*(y5t5(au*Fm!{&U*<(R3Gb9>aYG{0L3=6Usg+k7H@R?@6p@im=?l(5M^25w5+xO*PlIoMtYS>g9zV8p z)%egsCT&^A$|+^Y1L6OHbBD-aK_?)*?jqg zC|O`cM}uul;Ol+6q~Xv#rzCYefG}TZ$Mdm26iK19Si2OdS{Qq(G zj=_Po>DqQ|cWkFSw$ZU|+qP}nb~?6gyJI^Y+sT(__RQ?6J*oQUc`JXCpXpl+dZh|s0$~4})kY6~Hh2|a3`)#0=xOf&RPN(nRWpuL zv-HE#D0UfLTE_T4L%!jOB4?!{C80K6 z0-9+RTzvK9UsW=HV|@*$4l152_7KnlHN|uR0V# zM74zm;)j7(yT5Mtbw{^lR!bAyl~jCJLcTL8v6g^?nT@JghHilE}-|F}!>It8&2!@5^Bj1vd7bsylo z-^+ZCPi+O09o;k1Bh`1uiEFRe=M)ZhkI@6b%E&qZo-ls-Wlr!#bwl?z$cPLKpY6B5 zu#b!YNJR%w2dGd#f;0j(NR6QI5%JL|P4#xPq_T?>9GERf6YVs1YB?cFR=ez z6s;B){r2Nyi}0VwM}u%y#|;`86=M>n~BsAdX?lUSTxCXWho7d9D-o zPf^KF37cJ5{FoFIyo%`0>~o1gtVS{zE`!?pHokKy>CLdN^Hy15mPxbRWY@GUuL){% z#vN6BrSd~dE4sO?#)a^rrdb~&{5gx8rxQ-)6xXVxS5JBhC6Pwu0urFp6*$F&u#Yrd zick#}<80W+_aQY=c!04XE%_nOF%1`B?@BltL$O+8x*_Hci3FV0A5_*)#|I2~Wzxi` zU(jB*EIs9i95>~*(XDs@s0CDJ9veIkd3bSb^hY=B1X2g#_z|*XndErN&)9CqSyGWj z&Qh0={8}_S(DLC^Y|0WyO8<-eQC_rC_bF#m81-T4wVSo9Cn;62zA@I5?24394$ z2p%oA4rlk$=g(UAWcOhA5PqLdj|>2k(ZBXLr-lf=Iw4rUxOD%m|NJl9)Bg29pUWfs z(Ercw)NKE7r%EBi%6DfzUCMc=-el zG-uK&wyrvg7>3B_tJ~4KxU&9H|zYMdXU!f2y$QTMjA zMUaK!>;h7&R1g!S@+A4DH$&=Mbkk7^_-4WJsYdv41-_+GHp06n+p|RVK~-X%`*?J! zUSHu;J`er>JR|;w2t06_N337wbGz}A!w#cIU41(FX~P*)?T4gc{b1 zT08Oy0p{WxMJAX^71apA?>rDDy?Gx`E-V%uq@#J-i>OPOv-grZij<=o%pmE@E>>1U zL0-2{lXW063=4zxZujn#sc-Gjd(yh$@4X^IF$Y7qy$oDa1l(e4f^Rrzu-BQ{+ClnG zG4AYx<;Fo|0@x+IG@Jz&-jOj)Pz8IeT!8n8dF5tU*5+$SJBzsu(xRZmNwNsN7yE7W zS$j?74vTE;2-N!L>e-p$9ZO~H5AW^}5}R&4wj6yoemkU8QUX9T>LCtj=f=9&MkL3j zrwNIbjI!ukVrcjz7)>+>;Z2#o0M4(@g)c5zdb3456|<%C zycA3S+TxpOc{cJy#_O5kjSvmw2XEQ->fEbcBe`&D1r{qIBg2zhD7Fj(A7}XWjp|OX zZb&xJNz^sSiCnY(cZAf?4cwUtcM-CsXjwuWlM)H<#2W3*J~$d6fDNz^CO|^~Gjb6q z2S7?Po^LO!2#7QfpWqfgBKKDBxrTW(0lrMut6A79{v4w zz`ya>AiV1A0K@U&N^o}bF6BSN^ZIao7BzqnS9k*dS~KX>Rm=V2-S`U3PS5h+*EO0m z9eFKz2`WJWpQh{5?%oIkaZkGI+7`KbtfMwuF$E3YPC$qbH_wV9I%lMV5}f#fIl%taRD&N^>%qN9$of-%DT+sX8y$B9cIJNV2zla_|9p@ zs{>MMSYrDJj7efWB2oCP1`VWxpY=O09-QCOt{$?7%d1N8(S`cuNtOsY7nsSKj_gHE z@GKW&)=Ujrh|#TZPLgTuEOyQy36MKT=L&3pS;|ZbiN(-IdfO4b_(?=j!wU1k`eb(* z)Ws#oP%`lXJJc|551xV^H}PdDo8MuYnV7mZtVF@@|Vp5q(Ra9d&LkWm|(J}slzRLn2WqD3`T^KKDVyp8s+yLAl0e!t7Hrj6(atQOYX;u)9dbpiv zUfW*!lI}V)kR{;(70Vt_P?#Pvl&eWgULGl&b`Ts>_%8nq02=Z39`BN17yqwb=&!nK zpSZvOHrk(Sy8lpiZ4trzrR-Y!rb7E;a72JEwnu;reD`xl0yA@a#swMIcg9zyN?6o^ z7G@&3t#Pr7J@Y6)FYS8PewLw?*hM(g4rg`ND#N;YToy;9xP*C4Fwy$>Q|lv3fvj*NZ;qGkuqW)U6;huaShn%y)TU1nD*QN!>UHXV_wEMP$Fk&~iHcNpb1U zM`RP?6G}c(V`ICQa0dQ{=f~|n?2hj|7=nHG9a@-4Z2SAi4hGw7@LMmlZRRd6Pbavi z^jGouDj)wFbCk&Gj=$!f06N0BlU@9{)n|rX>_!)ikM`3QtaOLQ21b*|I0K4Uf z@ju7C`gA=3aC>nG2D^pRhE;Mua{B&^;1?3jIpqcgLdN##WwkW$)0RT)6Tw`L>3!@? zSv&WURHJRgHAQA>JzG;@=pO6#E755z*7BI)w?}f?RH!X^@iJqOQ8IAZWE~Mj-F)*f zTrx&-@r}B3s^{#?#hZC-gJ2H3>8_%Z+mB&AIl@mxR_LwT)S&-Xr@!$dSXf><@K=%i zBHjKw21uUMJz}4pu3%fT&^*Eyj-6E(T(x^{ZE7d z+r13?q!Ze04x48m3=D&}Vg?G6aR!=)nhn$8bq1cjTVd_2)!;s76mFL3a!lK9EunLv zr`-foSC=PetonwAjg-~E1DmnAnGz*o1!~}CPu;p1eZ~)*75t0gNguq;hR6P-{w-c?B^}y_VF)JbbkZD>KOG` z0{~fotN`M*w;q-6{ZpNRDu@+`-h=!>iz-}J9BmPM6X&*yx53WGuc=IU{ z1(u62qP|h(t4(@1lQq1o+#-cvOh%_4H-;g}bdT z_${_xZ@+u8fFp4?l~cv*pi;Oo@!deV)q7`PctWf-D;;{T1%qb)ZvQMcec*ShidB-G zeqqPH?T-LOSHfLM{Inf6NkMcEf!St}yJB14h_ZDY*btK;SjAMg4I{6MLR)W-A5nNo~lpy{4bJ#c#K%1PmnEzZT`hWKxm92>gL0;LNg1b7l<{jtPy9A>>CN z@xryi438V|vg-*vXL2fkIbkN{hN&uhVq^{-5^3MSy9wI@e)XAtRa|@m8~@u2!SgQ> z%U_Eg6mXx!0+0(xiLwe-)oG}Icx;h5I>=b|R@#;p*xeEB^KHTQR6J!TUma)0)?_H*Fj~8|vnJM&5T|V|rfGw|jm#r=YMS{B+Z@K^AZ4}L`dH$bo_ zFk}OG0hsS4S-!b&C~x{YkN$q>zDM9dbpHoy?{dKT@YQ2}k>39u6w-RH-J{^{Un zSba;=!TXX8K&Aj|NFb+9Os|k958khU9t+T;RLHAQnlB6A4T|0i%jp*Kyht58s^D0C z%k{!#oNRoUVZ*u{^MdvoGYf49oE?wQ*S8ZY1bWP73_Q#7p5#Ec-?aE3Je$8tS6o2m zk!)utJrFQM*V0qUM=4}M%#>geA&78`6QTF!`0*eeB4s@(`Y^2B?yf$Gr zVa|!4Q9bZtQ4s5Y#*O|!--jBm_iVE%@&WEPtX%X8HrO=+X)r#x&{+wNB`iHohHw-iLAvxDv|KDPMASRDK0IiX$CN`ZU%C=@MelA z#~Us$y))t<(N^!#1=cWsuW>s0t)XLnN#5i&0NMzo%~4`2vw;8>fN zd3udv?Ub7QN2+QJ@}aqc?bD5{ebIq%E}2%B;Z?#(81t}T!Q#2#04aVH&4W!FzF=?+ z(p*k{!$hhvK^kM29N&cvzZ42T$sec!Ny@JqN;k4PiW3EhBENgk@5bQK?!y+C@8Q)S zh4AH34w_2(&LXDEcG(AU&qxyM*Iq%KHId+}QTra79`rP2F-iv@l%~YyS7G@o_x_}M z{ntnBWY?!9XBDbA^ zscZl7$0uK^RLChxV`~LT^w32rnU`8%Kkek5!DBE}A14{ES=3U0HU6iH7xA6gFinf* zyp3aO@@-%=2Jne&BzKw43(E8*RLi_8*7=ZoJ&N6&_qdko)?|fp2cPeuggbwvPv2SC ze&Z>wCL^pcn5xY{zX3UuS&n@bu`jZ5y1%i7$nd{_eTIK?IR4)h%6nL5fB8MV8|!>* zZfthHcS(2p_IO2k0{gdvhI|J=guI4o$rThl-KN&#qddbYZuf(sC7Kl$mvYx z4o3|8oU)<%X|^CJFBC!x=7!7I$KW2|kZj;jTOK*+{er>k`y% z&6@RX-*tLDx~N^BBPMIpyBMBqAWf%vbl|)gmP(SB8kuy-tX-Ai)=$ZXLwf3EHIvB? zB}XRRQZ=-7U9@yYveM81w#_f_ixq;zm)ju(P{3@(jv`Ax!yISiVY#|3>@C@Lx`7s&WvY6R}CiwNo=%O?)96XkH5F zny}9%=)%a%{dYD#G3XI?V8C!H+}Dq?F8c5_IU!K>${$n5W|zK7ZlsEQ_Cuq&+_6+L z7cPQl_qT4H)+J?qK`?*PCWC6BThjo#fr%*%3&Bx11Ezn_CE-}dEB&ObrYq`aNeYp+ zAPrI>e_qmf{G6y*PA&G)9^0N=hVWPm%6=iLrKkNW-DUXiL9dGcAPXadPIE}mT|(Ue z?{w1GAc=PKX?%8m19N_(5<-~$DEYp0=CR@-#@$0NIQ&@IhKh7Ro9a$RV`;yZX;ML@ zT&!6v9oa6bPJ!occ=U3zBm=!S z0fxHz7ATyL{zM(BO4*VMEhiZa4*wLb0cVb%t-z#D1dX1q69)AQNH*UO5=8@39r4jD z*I~#2aEKF=rG!lkZ#ttU*_@71xtn~l-^Yg6v*RS|=pU%bq zQ&m9G2$@JuV7g{xM%-6!~35A&3}toNPvQ!+E2pr=|0s<`%(O>3~!CkSxK0$Rx_@1-A8S154mg zdVP~T(}@vwmp7KL&iu7Zv>iPy2}r;52Viap=3^Az=o})bSGSzDdi?@>*{jW!vaa4g zkhp&XcMl*~_ccly>J)yQwrEHv<0Nw zr*)XmXV3v`gvnx(hq_QcB59YF0a11AS-W8jK%KfDhhFm04W7unPP>SfP;>x1uz8#S zE*}mr$nu9E>wH+3THg3S@&_!`Fw^8#)T-Xao~#Q4K>AU(dU{6yb+)&_fR=nUJODO^ zz^gv)^Npb1DWbfWM>$mZ0J<{Yq8@5wK0=qDst9ym&G}ORKF%aSuUT910d{%ftswTm z(s;aTK6s{H@JK(r_1{;=J{)I1SO_u5INEq_BfOE`dEDgPt20-%BZg)i{dg*U>Gy0g zu-}tQp`Y!Y6M0c}$X-5vkM>F8E%L7Q{IM-iU20MB)$ktep~a}C80Le8VQG4|w|Gx5 z|IlLPs0J2+1p@x))Wfat>He7EvPx|^+hqcB&zRs*EUF$#^#7O{-bBA`R`|dPuJ>o_ z-+8#VwYdS1z`>DRr^QYG2x$hyJ&iUu1GIb7Zw0g{heLSGhuoqwrtu-^N8EMJcWnl= z*y$4VCd36u@8=0Y>n43-*)asK9(ng?1+cLD$PuOq`@rW0NFU`1!Rs!1X4!GCpL@i* z;>pr^hIgxHcmd~HN&Sdy_Rb$l-@;>l+0Cl3U>@@B8KQsPjXI>`PRaZ+{;VA^ z^xXU5^YL52o=kXXi29?(GaBa|{(YAl)K`P|0G+1@|G@9UvUIaaODQbArP=}pIv1N* z`;Tok%wde%a%Ub3tCTqWVvIlaB@bH9E^Q0YSCNk*WU(OB5% zY2SR`Q+z0EG_+mXj|`yz>~#T1F<-tRD-fnIn>9EGS?Dq=NjL1N>JIShL_cMUzh(Wocj{UY=X8k<(31iV7dwJQ0uT~{?KWu3O6i6 zZiMRb4YR8ImYF}+Bo!ul4MxOufuT(?1htu5dExqd#yiTP5r)sgOEop5iTW+Vw3@R13F`@r#mqmK+Mf@wr}?-MQ*^t6sspIsA`Ha(nBB z!}kWxNHi2cL;x8>uN6~xcRbPY6>Kqi=B5P{J0aDu#~z?u5t6pO=lN)p67bou?$B+G zJv7^n6R)Q56eyV_5atLJTz0yfd#%D!V-*sLzaJ*qsv z`z4kRXYR?9OI&fX@vKP@PV4FNu)8YBgY?e^_-KdF1J9&OHqfeZuyAI`J3UqsP$n6* z1evd(%Nj(M;3E@1=B94f<)tX-XX72VjTOKw2NmFr;1PBYgOT>wpTrlr-hri0q8&|3 zykhYy7mW)%HJQ0Kf{w@(v6(P|Q>fblah zN16!g)&N7sqwzT68e59mpI7%eo=Bh*VoAkGZkxOxN%9{YvEvA|B^D{q3&NOLXP_hH zMH^q~<{3u*ogPPuSb)(0vWp!W)i~kx#@tKEd^hcx137_gj~_Fp0_12J3;^o=US#~3 z_O|u=h;rlcTL#y9t67xScVf*yq#eY_za|t5Htp0Z4_16eMZ}+9!zD|Fv{P7C%dp1p z9P@B~n$e&8;cT|HZFo@DKQmHL@kgm0>TOKrWwmZ7Py11@NS6T|f;V-aG?*Lnso4*h z96bH#Q9dV{%Kjs$u+^r&3Z%7H7EROQ5T4R`LbtoD6P?gyg{jnU2!RahncW_O2)A5g zQHsW1FWVl8SzKpX&!Jtw!rf5J&?~vEt$z$Pyy2p2Udp(|&+eUA&XhNJezhL$lQ2!d z!DvP=Z?w=SadM+mMq)Por|OhGTBfi@GbknsF2bt==Dp!PdTbHx#ZjCv&kLmPq(N<& z!867aHhKOE1u#Nqlu>355Nwss&Ey6Z^a)Lmuqj^u__y5>aY?78CZx&da#VNN!lVhD#yvu6h`|_j z#UrsPyy^-7++4ET{?9`#mDk&9(j6qoK6v-%1;IbNx#%Kq^E;|&vr#{mb|#Ki4QuY% zWf{MtrpU*%uSn;$iDm#f*z+&Dy9EU@ipdw5bat3V_}Y@&y__jQ)01aRNk~mUT5hdS zZ9afgB>*H+3%aMQ-R4_2Sc5gO2Xhw#*a`uwW=~@+%fjD}f!pJ_#)%Q*3h4_Qrj5zC zbPQy(cdtQ3yY%*uO%?3ZUr`HxfVnl|_E3;KoAz&dg)v?|gB7T~;5j9=9mOea+YoKiWIt8NDc|uR=V9ID}6fhs*c-|=Y z2h+%=CvC%cmH8=B6QeQZgq-+L!*I7mL-|LsIMWS0^Uk;_sgi!rp8>_+M-h15P;ifm zrTXUb9mxS{maw6aT25kwm;Q|y1~BM-bavLjRooh$$T*}?4gwG_iEAqs9%{Ic$kyX> zD3Z=s96M^VO0jb&Hrs@xvq@Bq8M%HhFej@jGm7hbFs<4sV{x-sIB$A&T+|&B{=7MJ zIk2%Iw*i(7)=Ujr&cU<6jn88l8|Y^Rqc`S|~rZN-P%sHoqg zIJ0rVAomI|?-}!e6wnLHt>ao)o~TL^7>HvA$E3{a!heI-)Ls!m-A9e`EMvslMi;*< z9h7nP6@`Qtuvm`lK3lP+1Fgg6uMCupYD+~`1f{;aO;YwSSMJKd1 zCSHZI4y7KcM{_6c4t7vbS1B6`n6enm6i4Cbj;|>m^~dNFIxFye$Oz|7dS)Hw3tANI z4Up20TZVTDdk~bL$CbHFiT8VA@rjeh(7v%NucnBIN-`EzHhlz!89WsgT|W^&>L9r* z5pQE?O$`eUgDngqlHJt9R#+Ja&BJXfv94b=AKH>S`b#Xyedws{avk57%Vp%$zy}4o z<@s@HdfMw9rgINs=n=X{I;(@Axk7>U*K8!oH;cSheG_*vQ_@DS(>{!JZv&uJcjAdP z?-W8bj7Ek1*~giRlzpUSSEqlgE$=qV2xL7{#K%7U?$g!P6u7}Fr$@s)DB*C!8y@q~ zm*MbD&$qG^Wz1q{J{clIti|$(^ol{AO+gHkk^kYft*Y5Ve>dTx(9%JMlYWU`dI=o3 zz7)wJ;e4=p-2sJb-E&B4Ar6kq_+(r9#*&z_5!f+cY~9;t(#b^fhf9+crb5&2b!oe_ zH8$f-ejIGz`kDkshw!;cRd1wrU0>@$Vr%6jMf+xB3EY8pnx7DZ2(x>>b&Jc6R4Mf- zg;qfXpPKmL3#3RnbOytt;tUCNf1AQ=)7~2B`iYi@AY$eI-Zz5vwdRgWF**LToe|wT zZs&D!ydRzBIe-bh-i7M-%~p0IbfnMl>;}qHQiW5#heYARLOg=q)g0dSLSW@ub?nr6 ziiEORB3K@JyyP9`OC0WvC^CD8?`*b2D>c}l#>TD@l|S>)Y$e8B* zefQLuy;d+i41dBcjD_xxiG?hd!>>EeV^^Zkg3}@6PFwQLI`aJ1Bu-GkFzE+Z8;<^D zYEm~ziG@`QkR@6~ZTzD}ffw#IbMFG<&I1C547Oj%OB$i+k%)gbmu13p{0Wy6o}6wi z+8la;wSB`;d-k882EL`jHhuG%S^-@L4z8|XnZRK7)oMWx(%!a<1%km}&#!TuEb%1hd6Eq|$&<#P@wycIRUi&yLh zBr^wuHd>IQSen_bOsaRe90CdUG#;|~^ zVC#Ot-lhF~skFRg>-WRyoX~IT^J_la+*cOl8iRO3qbJ03F04n*0f#qu8_$W6Ql+E{ z%Ty5_&fiFRsN7B_sc^Q1cch#zcy!*)5m|N0Fu)?;DZN5WG>;(qU|zBH{PJj#ovpDp zRv5oiSaS7LlRR_cBg6<-Ye*Tz#ng}v;z?z~&>_o*G5i*zpY_o{-)?SFZYMT;x67qM z?FWb0m90}*28#lV4mu+~UP#*;=SCI_ zEL`!D)%>fN`fUrphZ%k@5p#D?kJ?+8-0AHF>ozXfQDLB6$VE73?c;GKPv?>5U*Y-; z>AsMj3!7X$RUeI~U>TPr9(x60< zkvnQQ9e5uqV*`o-wLR8!9MX+0#5`A{YJyB8+MYz;x?AE94vIP4-R9fGC6Wi%y1&^w zts9?(*bCwKNP&{0tYNwwa1^ahs2OZ~61c-BNNHgR2@h){>uXohggAgI2OT4K^@U+r zlz$JU>C5zcuOC%*-Ptj!XEaRVhTnBD?((Kd8)28vQStVqKC*Qx`rW@DjWr*8$J8oA z@}L9cjL|URxa%FRk6^ zn^Y5^n<3JmL3zturh0s1Q1%)9Z150ET z3?5;}((cqcuxPmnTf_pnQZP|{x=7IN#&6-2rWhO=$hU!kci-s+mBD`yt0Y5rm5OHL zhn5-9C4u*Jsw&MeOm6-RE9<7>*v@Bq(;b#jD*!=sw0Q6AKX(*a-iZxMubT%UQ z5QFT^f=3RLl7ey030H9%n$ z#tiW);^i?Pb{(ZudR1`~*0nDNR3BkiZxS_YQymrKH+vaxNBZw2h~KtjFtA3qnUNHD zZ{LMG&*C&ppzcG(|hm&YGsFW*#*@TLbZCMA8c`%<#^rP0ypdzG?D^Ppep9Pk>FmSKo>Eg zZqMcG$Y^F4h9H3(oCcoo?RV$5oYbZ&eA(SZtiSc_ExKMr6m9W03>)WG(v{uotdzy9 z551rynC^n!BI4!Z6}IIV%e7fIkQ0lzW^K^hL~@o@YYH`o*&|Wr#yjs7x((b|6Bz_Z z`AKfwaCi>NsmMwC_c&r)bP}?ilDo2}?av@o`8h0;sv+S`;h_k{V6fA5Ql=WSkuur>$qk$mW3qnVg6LC)v+ki3=FmD} z)}CfWM|0p&R}~Q@5R{}*&)-{kideu_oa@^)|EjefUhGE;sDJy7Kb5{GUl*o0iY!6d zEJwR(f7x(!p<K$1w<0UlOcm{4k+!c4smDh7JPARpP z_gRQfV_OwHCx+%)a?I0EQ1l6`piXe!%}gImk)hcSqbR!kA>L{aab0l=k*mC)UgYU~ zlMp%=hKNc^yA#_nIgh0OOU`U3ty1x^nCu~{uh&A6^$g~eUQKIONVp<{O*}B|b`NGW z(kj-~n)qgSW}xhP73<9ALG?gr!NnE6xE}GbtEgZ}l$XkL{j*JkzAnR1fv5Bp&u)VH zYTHHIyU7;U8bayA;B~M@gu2o$Aj{@AHLUnvEYp?SIkip@qy=-Qelja#+^F8M`~wmw zRQyOb8U1qeY|8e5hr4jwa7Pp=G{0)T3-%`7hqfIX9}(YX^Pc?}@4A&W(?bDWpstpv zoG?oh(Ia@g=>#?{JottJm5QRnmwWjqXrM-{IjOQ#6ya%!0IjT)BGbJ5M7lk{M7%>N z?sOKAf?H6PZ`V@?wqX-_Z~iUcs(X72KqUuFvFYwNon4%sr1{HP0&4BplytRok6NMS z!aHYF9mkNEEeuerb#JShydHqL(!i6W7%CxRZcj*<^j!6T6)PF+1Ct`iquq6gmKuSz zw+7!Fs-}Tj_B3riUPo%60OKR6b!fnqPL<=G8v{vx*`Qv6$DiN!+qio97%Erwl0Wo7 zVy9~mX~+}mNA#Gfhh*=wJV%JZ$+LM)DsuDHR&OT+CANRP=+KkWNsR1b*?&ia6#z*ltH+5(Pz9HOTO*ZZRMWz#m1Z^UcN(KdfV_ElWr zxK#)Ub7>YYiO0owWm%f7uNy{e!!OQGow)C%!?{pvZw{M#=0Zoc<2i}HAhzQ@2v8$J zS*>_X(=|;p5;p3msE@`TYap0Bhn1yuNeZu`1qo4+$OIrn1tW+|1w1B9C%8~aE;F51 zRwWOr{5V!icr63vzG?V*iG1nP7qXaWTa^kOrdm0;I4Ut2b~-K@3yDShjXk`SPEHOU z2$xoSf#O{(#p^ddDUhCFY9Mm7u=TolTtfU7KH0(TLmQs*w?NPfsU){vFUo;g=E|1&X z;A*KEXO58tO>wKP5PZEVat%snTEcqSg5m~bE5LZ%vsO`yQ5kTdaKpKc=t-7BoXF4A zXR(okMP&qB{n739R?*je{V4^8bWW|5$?W}nO%sw~;^Qs$7s{>(gYpe47;*K`YdurR zjAK2nvDF^;bdNpHf$9-lJDNMR7su|a7j<*+*lH=?ISvEvp9H1OAS(!%t5xBbi5Epj zFPO1oMG$r(jj_?dW&ckYEI>CLghvb(Crms@S!w8_H*Ac)@#aF4-DB9@t2 zuuA*Mr(VWsmpX3*qGSuo+rvao>jI)gZt(*#l2AIbhsRRzN6P7@S<0;;J6weT!K^pR zyoy+kG3yEm1%4R8S6nDVg(MFfFUN9j+i~f>{;VQz5qdX@4!V|6&-B~oZW-DJJ-Ix< zpTaMQjFaIu{GkcKPV5gRHsbTr<~hF^ut-4b9H69YlS@QaB;rBX7+%p5fvVfqIOPsu z21!V$_H%)ZGUoBvj4d=Ygo#1^{9d$R>7DGNF>jVbX`r79@5PEATQxy*1$BaJG)oU^E~`f3l;PH)d(;@iYbI2;p|1=%cN}?rl}8{R~@bNle}Xy7*oUY zxw^np3jL;iV}8~Fzka!vyBVqS*!JRs35Uv>yDeWs;Q#0w%wWlLImD!7QY2xK~X zNZ>SI)<7B|?y_))D3hGaUvwLB8=4%RJL$z4U(D%sit4EOWDT{uv;P|GCfBGqu#zHy z=M-Rc3YJvaYZF*W(LMvN-h}st*Aan%->Ih^A3fop)+F0PI6<^nNbHmGAiRy!Cg>Fn zzR?K~${3ylGTYfFIi^~rq>VZNqDdUPtK^nBkz4$wm!V`bbj~PX)BB_|ju3ygXVZ;V zcmBYTYlE@OZ(da4DtRU@xr-x-)F8%DNvxz7+ws)RH+t4o9pQyo+DMVUZCiT9xA-#J zya9Itro4xg{ze;@>coQ4Xo+_&I%u7@qNB){q{N{RMV&0^9ZWV8hkMxR-{bFmjmJ68 zF@HWp6Y0XzyzV`iy3TyuUnO*;*eE;3F$^vaKX>DCVlcI6*vJ!ZmIV7M;X@jl-d+sF zvOKEd9j@|T4piwHQ;H7f7JQJEkGlSk=_#%fH}HgL(mhI0jt2Ko~yHjA&e~Q zE=8WdFCjKgshe9Yp^qy)S9gkFIAmYlm>6KaBtb)>`f8tFPmrQ6Uc!l&Lucm;;_%5_ zN7^l}$g`fM4LuqF{^Cyxg^9mb!-#1AGTObhWy zNrFNo89AZeH;0(te1QwOZjDd}cdCw1j|!~H+H_^#MKPkX9%F$oPUehs81F7lh|Eg& zVqoi};j&ShJ6XvZz+6xiqjsZ1a4uW2x(du=%Mv!E%mR;F@Gjlao0h+5z`xVA8G` z2}A87z^KOSaEDgdSZkEsQZ#|>WroTzmeEgN7WYD(d49(AlSMfZe=WL2rYNNu70}}- zq>_lsEM3Wlb|Hf3r1=-55kS9XR(0NoV{VAPmLT45xmQbi7@X~12r6ig<%J4mzeX2> z7MF1yosIg+&XJmvn20?5TBHi!VSL?V%bZLTXV%y5SnGb;R%r{Pq+}F*_{*AzTyuB} z$5`K{<)2Cj>4Ay66Qwr~yD)Ld!9qP4HNb*Q7%Y~6tnr;ezm-mJPZOHVPBh+_VO8yR zmUaQOC8>lQh#}q6Qfkt0xKZ;eL&MxP`yH)llsI<&wvMCFB!uU z`3zrVpx>1?t)OXo({3_VkhIriXL+`DAXSfLN!ifK1uQVkw)-&EX8wSGK393iCV77H zp&wHMi02hC7!Ur!Ls_%EQW%A$Oy!e#H6xYKOiz2Bf&dtl#6#Q7xZLp)FB!RPf#olc zoL$Dv5;Jdbf22fGm91x4B95v=#V*L@2(0*>Gr>{WBwn+*^OC|Yk&aul@DXzlpOq%b zL)6jiC4WnzRzbQ0ibkON1cP>~Od2^ow{|z3ayB^MANq{|4biu@jS2{gW?Jb72}cRf z%`0Iu9z_Gejo@yQ;-y)rEFx)JFF@fk!z{3;aAK3O{Y5XFhwZeMPR(Z3EpQukp?*4~ zM~P@74QX;DM%)rc>1*GfdkWxowMON1GTPmk;58#LwfWL%I#+v)Qu|hbn$c!>AcNy| z7A?c0r=r~oB@7Q^aDSObyMPZn{(Jl?Ew}7+ud@@vegB%QGuijc_doSzTGO8$&dIec zga`!b?aBlAU)WaQsG+sP79&Q zA+0WAQH5pI?73ZnH{y-Gm*^a>23BDA)E$uadQ+yu-MmQ`UccQr*|WQ#r(T+2m>ig9 zGKgQ&>O4BZUFcHeGi$u{QQQx{10W)Z#onr~Tq6zc^fy*7WAo45&`7}#)+pBH`( z`TT+%0F4va;Gqt4(7b}Mt?~1yMotQEBIqG9{|`M-Fbjd?_6t)Od5Q-LO0)Db()8FG zSn00R;0#d|65X^wU6N5fp0hh5Q7pMt&y`Fv zv1^+{>DOvU)HHk66Zd2tv7v`&IJB#;91E~Lvg51=h|pVGgFq_+WF8UO^?u`IHCZz+ zO{aJ)G!2padznf`=W(5hS$Na6!{1q8BwQBLre6}h*!2C>k#fwABY?wRf`P<>3c3>u zz)iq@wb>ROkM)kU<9ZUn4(!OP`L&-*N;b`7P1I@hs9R7-9}&2}WCG(jd)vz`hmxuA zwn3Uxvw89jmrQ#+pil4A5RsZA2|2DoVOrY2f`T!4gEkpH!aZ2FSyIIk!Zz=2U@r73 z@0?g9Y&Ewe`zU*}LS9J^F*x4x1|pkGFK2;=mg%ZXQ(Q{Bwe+?X>QSk5yvqjHr>WqB zq`IyjA9VHL1gLMlt@#$xwgTpP`E-j$It=o53b%cgrG!6WQdB#tAlFIYcwNu-{^=WvpzpRxbd)aTj^*YoN4xdPf7z(BRJ3{+DHjd~Hv^9(szpH~5N3 z>?Hd%?ns>DI(W!HyNXPOnNQv1nfB35sK)^Gybr(+N&@+pEIiF)F}2=^&Fw$S6t?;v zar(@yjyotjoZmR4KM8Q`4P~iF?G2kK8 zdNa2=hMy(NCjVS}+srEBa2aOLi}RYhEX98jWbe{r>frU@-3uDRlxB3=y%$KU?W}r` zY)#D3uHxQ5UtM{trfi$5+>?e4?QO&q7vaqyZbiScC4aV%gLwh zgN=N7%Mckp#SB-WJ!jtCG=`o#0>-fmeXN{Z*7Z|Bf{xn^NoK~zNy$NcT)JI=TL_=V z^>ZjzoBuF;5#*-XZ(m@FN#Ew*9qy*+=Q`fr?Z{AJ#?Bjt{#IpuQDaZR+Q6;J~&uhO@R|EcLb?D#&UCw%Qu~=@aR57?H2u9en*Y7MBwBna2 zEiM;hQL}6xh`x{9N|?^${CnZ9?kti})g6iXGf6F}D7qX@cc>+Ul2lG1@}8S@CFJel z2J9%MGGDz%T$FV5MjSqH(~Vgds}w#N7*Fpo{59`JwB%?O+n%7x+}I8m)0#3;B_&*? zW980Muf=&tR1H4g1cse}K5=&2aJ#ZKJmIYMdd&>~!>Ux1s?uLibg&J53cbTfx8lJh zw$=`SfBlzIm*o{+)e|Y`=%(_Gu3~X;;DcJ*?c_;D0h?-5YNc_j2~wefkQo@;ZVv7< z2P6Rou0$@~QRK;-yb({;l<55gnbVF3zNr^C0;vF7QQwH7)nd0xO2eZ@e^U(A>)h{K zo7S>BgU7&==@ZI2{dQwf{X*{5~}Z?Q>G+WSUQGe1wI@+U%+jf%OqtZ;YLVW ze4j4%bCqqqk^28*?3|iJ0fIE!wr$()+qP}nwr$(CZ`-zQ+qN}#BX)KtV&-8U>jzY2 zW!3pkex{9_+J19p$kLxu-BVbRSD78!%Fq34zLmj1d*9K@1xI6G2es)pjjoh+m$aIN z67E#Ff&NDFb@shE8W!(M={uXaVQEo6Bg<8^bM~;8+VEeok!5)1ip z{9JRA=6!bII?P6;E2P$1`o#D`3b{uX@?c~Th$eT-6oR5=TNOD;$;!j8+llL`FV(I6 z@RFn{QqpWcz;?{X+VTGJl{}+^)i<@?A&JoZ&Rwc7SN?eF4D&gSl6M)$yp9?4?oXiK zwy4G-2Vjkr6EBb}N;X~XPL*ig$<#)n$;Z0pf;gQhxw#*MP8gt|FxRlwl!}J|vS!Ir zCD2%v!$r%4!BB>Yn(a56Pc>Bmsh&X`Av`fr{&Y$Tc!E%*%wh7?vI# zaXWFUQY?j`hjQIPllMBmV0E1CEb$=Y)!0uP^f5n!&s3KHc@T1!BfT7la=OZO=$WJv z;-W1?kM6=eXPFkLD)CV=F&kc1R3CXX`F$Wr@y$1o8mw5_LvliMcwp*C?B`77TEx_g zdVpwskw-iJ33U3%D*qkGhuLI~eClGB$_7{&l4;!&w0knc+^*jmQNKm^V8gzsVzEx$ ziH^Gee7jORf0TS;w%6m+(5|ft)QSkpgbo7scXJKLdPu87@fSrZ;|E>Nj1pkNSKaG+93kcpBRC!73 zl?|4NFy=^{9Y$w?V4D&GW)J{)5Qed-n4rWtESO+hC(xN#JO~L%5h&34OX1e*_P1xZ zb>+2McLU8oumiyJ@%1m_@fk|xgn!7*TCgYdTHeHN(?%oH48cu2U-w+z@Amyk}L z0RnCgfbg0i){QGrfWaRR2quJ}`$r{EW&tk38R_)+`R;BHkfY;)K-;=xtsMYQz8IGu z{Q%0rAxs_E7Zzp?ghTL0dL(EPX0A1;Jg84UxCj~I1~g<7$U2_^f?rA^ z2mCzZ2*`hLrPrSzo%(W!xK(c`oU~b#rFXj}=HGq>)$3wfIPLKHE zhsw!qBGTTfl z#ufoJq?f>rZp+WR1%ZS=Tuxb-KN%mu0gRu!-?giE;?j#lz!yBAcgqd=?c)z&HUOKO z5WjZ;TYM*=4 zJO~6ryVl!JXCxcMhZ?%~Z*gUx4FUkcZl3LJ>^UE9=dTDrOYcxW+?yMt%n+^>AwY|t zxa|n}5O~igz;AEG57+VU$eo_bj~>bIZD{hAe%-D?%kKRzF^psIK-Uk@R>BIb2RQ)j zP!7!AFDz@|7h*No5Z1-X+pYpC$(bxfgZ(BKlM^tg#~aA+TS1Mayj*xQ8wzC0r%(o; zZ;+m1kib5IO)&M->ZW7b@aU^vJ(o`a?#&MTDwpmLWPtYVQ0SLWOt1A=PWI1s7!gi% z-A@UZFQEaz*f8i(h?m>5TPi{yxI4MLRrsl$DX_c89>kFj)Sj)Wo>B`{tJ#pFTT!T4$)=;#tl5?^-WDD8vvl z&`3^}s6T1obybkoER{(GPur>(DdVfsO!RxZ*yEH#JWnJt8nuIG2IiyXu%y#AKdIBF zs|?3!BfFkytoMrLnN>H4T-$j{&-#Mau=H+jzU;_n_5y=6GF#yh2I=^G1bW+3zWJgk z?^zqUjm>7!sPtQQbB7h%PEbgbyo4}ovC5;5n2A9sCr3>B{!Jxa!+52hpUzo&BCFLh zV%YgZ30@ z+XR*Ut_1N*y{8~i*_173Ki)rTE_cVMDQF*Glku$W-gEG}TG-70TlQWh^y+j^Q`11O z3`Qzvf9Ls@RYfcys&e$HH7NNkK)rhY7zmun?#%Vkm!kDyUb(MB3IYJEiY4xuZjb-| zu*r-0X$R~}Ax_c^jM{!REX({;{?RQW82we_B^qCYJRR**#C3hduO|D?Y@B$@wufht zoeZJQ<)i>6o!jwUMO~f-mA_E?HJp0pn&id8EmGW>bWkv@|xeQft5u@73Ii z4eD$Cb0a~ZSIMfBNhBE0(&{$aA&M_s-Z`_|AG#|!iOCtG`^LdPl#@+eQ_V<$X>Lt@Jcf)yHFJ8jUd4fOh8DujTLh!VdctrUMt}Q}z$zSF&Zl ziD9NNWy3H5_!xcTPa7odZjXz^?F}@5hw;&1L}yfbv6MZh^ zkBThgG-<~QX6_pYMXrFvWy1b{-5#23hiP8i1Su4TzPTjto6ahXT>QY1O8bN%i5cp- z(-$cKwmhApSQ@Cp2F8`0j;3|$N1^SwSi$@v6Fq ze{I{xJ6H$Iwz4hZ)Bd`TXwb%jm9W!Cawb^za^q>*vM$zEd z6835}RxTH7H}br#NP}zFI&v%v4f4gTi_vo=-U<~ydJMoySEO9~k;%!=PpC22ky1o{ zF?oi`S#ftG+kg|vFQP`*K2+C=iD~Y>JV!p~lqcW-YKTbfN2VA0O+3UPS78kDB{3r3 znURuthh7cT5C6wb;$)wYa@pRPyOJ~K1CIycz9No%A&WeUx>9X1J zk~fD(0Ar+sl#GgZ)oG2YmEd#pW9;*DXC8XW}l9x2j(HU8glX7v;H&@*2us zLC%S610sqt3X}$9sQ4ZGCll_1yu2&Ye&J*iM^aLTUxRSQ0L$O!rafJl0d+}Nrpt`k zULRZ+#E1Jn(Kf${0>q%ZB*SH^qLg>sra;rZ^3xl}FPvP@aNDid72a&|4kVgZ`HsY# zhei+loCkjSMdHW?7ZDK3vFnWdl9%kTN+lJJ3=a~O^wA#{Va!McZ=ZN#(8li>N9I$7 zcUwLhRn z$HH}VNsWp~kzL)h9GEHysJaKMzQT9Q+6cWNQA8%mgz1c+Kjk&oWLKuYBAn%+zlIAe=OsiW&q6->~^^lN$ULSl;USmSpb35 z^-de(WA8~y;k|dv=}CX@85PM?XNf5A>B=5P?VE&VFb%b=%ncaNnIg^YbEn2F@GWvf zuA_6LCPI;NAI`R5JQ)Fli>VjXL~6D((QXwTo^g1i3cA-D0F#` zOiTViUKg_NPviN_0bHNl>Yx$J1yYv$kHVENR*B#>4Pp{;qcooAdsB{%=r$*thfy}O zh@#6-_j^$WEWOMCKu}LDJqTDiCGDX{P>n~^KOPX32wh~Z<(sVPm`%nD*g==$t)vl* zrK#+Q3yqV7p+MxA4dxhKH8h!VnpPzch1b^ZU8~pPwH#$?p|m^Z!IbN)lz0LZv2EeN zh7qFDR>j78f*QxZP)(4;T8>0~8g%U19QNW_ml`~_!coMtI@7-=ATS^rxZszl$E2>kYOi7x7wY-Jy%bAezaoyQl^*DSy@oJc3XB^H__d*8B*1R*`;Ti!FcK2#r~s zRCC81vNt$=)HSfp8g>xB4s!O-n`c%B2_Pvf8JA+KHje?Bid+mN6!nsQtVk+Anh%Cl zsJvKy1|j&3 z4SoI8PEg^;J2h6%PttuTEwjXC%}vdeBO1tg$NAhHbB%P2EsuI$o@R$3JqFa8g%Kx+vMWz*-GUUaAwtNjeJ9N zmEQ;xZrmAFk3WgDawE0%ztue(CE6Ilsxx)-->$YF^Hf;TUpkzq!XcRmTf(Vwo?aQn zBBOvDGxG3%C%y%;sLD|v7NKd}v`AZPcp2+JKWCyNR>RxNRg@WHa8+D_dIh&9YU=yf zQq8W5VQvTr*bS6;?0p8;LIFve!@;)$y~FJ!_=wjk0m?)f9wl=}|EbL{i10Zt{?-^R zk?ld&%-rC+yqnUPiOVJZ1+`Frf6fAF1herWX4YFVB@EoT2KVprc&E9YG7mrE)mk)b zfRn~j3)||l3m3Z5tQYGyYg{PK?LQo^igbZ=fuE4xROnPa+{tFCl&q&=4xR+X-6>iE zE}Is{;VZ^|dPY}-&~{U15Vvg3+ERQ3x2)rO!kap%v&!3JaC#gF&n0$az*e&Dvq?kw zxu^bcM{~uMa#bl0tHt#t32SMk8(CNhgBx2_=?55{B%lC`0;bm6^p(_kpwoTwE$NiN z7!Zgyu~*$I4sFs7_giU`TROHJ^1IBqBa0VG0HTHbwkfX{V$i)3%wtU@ZLOML-B6#T zg=vfsU)jm3F6eF%tCDP1I;>z*DRhikWOE|ijsms5qF_a>fZ?o7%cvePq43J)IGk$6 z4mRPdX`e@T`=m1hv5Mj|80>5EW2~JjxPUgSTgu668mkmSf_Y-$6W}NvcMoekEUG7w ztnE{%o^)v$nbL7ok}c-?Hrd!Uq*2@K6f;{h@PQn}v{DS(Mxcapx9gGU@rl&40aJ>a z@r+SL3q~>UZfQxw~2#Uu1KnmCR@lu&H=#=$X4UQvx}iD?BONIM9%LcqGeJTJl1mMeR33u9e|%Zw&lrP zchjBk|Er6^%5tl8&OdSEIH1%7$DDU@f(vR(UJW>2et!}lKigA*zie*%>7ovE_ptKu zIbQF6pIJ)M^?lP@1wD+%33Z^awYjD$-Ir?iYYZ)3K(ulnY4_&$TpSi_x-iHG+@hk6iL*O;MJ zRNs4@cYC54Tib9}zwwBr$gr9oFHd@BD+^ia#+7aF*I}kR1V|dJ7uvj; zSH8SA?^WKnTj*7KOvgs(9?0_TcwXf2#6!s@CD@6`00)4;jO&NOV|J&u z(rLGEWvHFi-N%lZQ}PyAM)7(fU>>5PczTIUxyr>|j%rt(R?;UguRu)lZy+UilIqu^ zK*o@o-(O{alW5?YLWCa0V{m0GNe(Y{&UvShz6|Jb!`6*g%g3cpcsEQuy@JR{#|H>` z?N*koS)}_b2w(1!x+(Xz1cF=KQ+B+bND)*<57iEWxrm!V7JkFID>sdFD4o0mL}MI} z_FZ<(*@yHA#*>|N-{*56^plhRs{2vmoDforp@)p4llH2Yw>0cY$*Pv+uozylpwl|e zu_mtC(L|+Lsk}V!BCb>;+8)|-%0M8OCrSLuPLMS+#G=L z%~v?8g}2h)6}Z*?xnupz43IQkpY*&z@(X3ioZ-XRb6NN`t_3`N(>`G)@A&L-NoAV{ z$*rqn##Qlto>uMhKe@>fKLe1>6IBI{wh>JZcY>8^x0>x(YKSLyA?inzNw_agqVvP@ z2PJ512rrCD6=J>~z5=H(k7Ki*9@GLqgE3iA9!ExKWE|0%0^t34V=7(?_vKA2zn@yk z(IH;K?yD0P3PLhsoCkK`J9CK#K8IO9{~|1)Z5@?lJ3-U$Z;{vTY}QX?&IfU>L~@c9qR?4oB3PRFEEH=rMQSL?W;H_#Ou}cia7**`PZ)iRvdY~ zh7k}+Bz5`*YM6R)$&uAEzp3z76RsT!D)RH4f_fj7I9vN&cx|9}*4hJc&pp6e-%7jV zKU%mUGt`>>Bj+pDWB!I0+k;UXuuYe1=~)S(ok2cBp)!Lv%0r%O(d9nN{EiI}4*m(A zmVihXBf1?Ny^TS9wctPPNN&a; zU*E*JL_+;4UiiKHmr1NG)6dOMHC_N8P4VvmukPc;3b`H>RgmBo;o*B+;nkBvm>pD? z5{`*8MF9I87a9x5qLuh&e>ijJSW$_Dt`h6NN|fj?h%^4+7y>}|aMB)c3*Hh$Ph3Og z?cbrpjmSbv?zg7-b}a|QBj%SLN7Y&%zV$HyhAyN<3njWQISN9EwHY}aRJsN(W1_Y_ zc8^jE$mI*Q+}(|j1Pj5nXDrS7c30%(hDI5H)zR~w8k4Ehz*`!g;d?E{cB(?$g@IFc zzkhKSUNG#>qJr7l>%hXzOm`ieiRbvKkrWKH{thPjY44M%cV&q4;lCcCoICwYnZO2^ zmq2gr6*j(6hNYaP9^OcP%q~y4KS06}F*w>YUuN6yRqM*k(A>di z@H}X?Hq}fOw#KC^+R4E45kG|MEv>NPIju}%nKf`MTA z9J_tX$6bFxu~K3aC?gGjc4EPxA(?kiW`#{wG(8l8A06oE97IBYXHi<_@Gy`W(sK!Q zoy^|FPMXhB^Wb!_iI*UIB9w^%bP*I6 z_&tF@&&)m$J$^VNm5!MF;cpn&O;;QpQTnm6Dy)C|E`m9ctMeZUKszlMY0tXXai0lt z*S@%Zjk(UpPh7d)J~8T?kzRv`%)-9L%X|?oDGn#$9c||)w2L-m8~PZeM?ty@sxi8coTY+&IrDF1u+a3f`}5 z`_*e=25&_sVSu@&b84k_a{MInzzZvO#FL1{hk^o(=9q=#5)kzKtaHG{)ygb~joxrz zcC*|V$IEhypfp7XWS`#;?+|M9nIR+SYT7OYj&lMzlO(jdlN0^Amj5G2wXpmWE5@X< zN481!#|K{1^$&-|17*IJr`5IR3p$hGVufj*jYOOFAfmp zQ1R8Q>avXJxcjVOF_+wfUp7yzXUY<92F;0)`^8;)2MGh=l_a9j`^mtt!sT-AcPX zV$tSKqJ^9O4QE_qZ+i=iW$*HCS2&*lZUP`B$n0HDx2M!WPLexT3h|}@I(KvdVIykU z+cBC9Nsd#iMZO;9^&u0K!&uz{@@6!9RKqTs2dmyofio%|)xJ%cTDBz=kJiC=k49W~6X3TBobe2CyVGuvdt zwtcvEj3b4I&3JD6zerwyF0E&Inx>ScRWeEFxMNT__A?s8QkP{9xf~je&XNPoMSSxg zNpz>khIGLlEUJ9^bwsx#**f(h`)JWMSQG<|B5rm@@`u7vFyNjC2{dlvBKVeg zTHegG^0YJktv!sy1mg}(^V`B9fpRg>Ig;pN;g1*2k3sEQbUYcCgvLH0DN zb8I+691&4cPqs8!xhs+izL}MfvgWD|j_f8GDodJ5GEZ>ftd{$dBblDEW$v1wp>< zg*o#dtcde7Hu?2y_PXVNu9?4iR*-~ zInW&(K>O}4SdkoW?4g#meSV{V9TX;sXscurWg_yPlVBnNuY4(|?}9*xJ6J)HkS$Mv zTc->*-l}nhe6Ch6u!8zKbU=#yol&ZrTrF!{ei%OBamnqddaleQ;HI2iHD_)16Qn}v zGh(VvEle$#nCZ8iFuCtZ{v4q&77Bxy>?$(M%IZWTxZM|c5m0BF!liXHK&Hg=Nd+N+v(H! zD)v(y(r}WZTMKr1*+uL{(M>F2$WSNQ!e<*+i4nrY#h1u+KzbCVizX;E>?D7{Gaa4H zxs4w1W8ED?mK9|WdakZf;zTh-fQ_6z1Lx6x;f!`H3%lTNRe_vrX&MQ})Mw>q+pH7i zHDh4DNmYZBcwo&aL)OT1@0jprl4pR_HAEnMXJ_vlk(IH;wk@hdZ7Zy$b6{NW^t||89(!2rs{_Llz88m$>Z&FsLe2&sTy2xOidzw2wtSc`b zPSsg>8b6-}^kv|Ir6&{N4x2MT%a_v`K7CVhxoZ2YWif+Iw+7D*=PweRxm;9an0cPd z$#-X{dT)jq3DxuzH*j%MMp|u>N3Wzjj+37CZt~^QaqVm#5x7TB&HD*lA~JlJU!|W) zh0IIEtP{El-;O>=swO{wP&w;S*M#U2n|t6ft$l;L6xLEg zEpbj(R>#W?Bmd3qoVPGuvL>nFl4f%Fwne2nzIPNSax`B_DVQ8sl+FOPRIylHyUjW^ zOhJC}UVkc8E_)gkcj$I8wtAC<>)WVpWaY)!?s0^zxyH3;&eY{>uO+fW2&2byz%oYS zWAvPQ_St^wcQ$phZkcAsV?PGBniuASS@3n3a?)OQs@)*zINyPzaMjIQOa(D- zL9U!+3eI<-4ru7lReMXO1d(9rM z(qyNcAC!1_q_N`63*0n}RvNByjAZkcn*5%g8P4jKl)CRlK+R3D_96NbM->}m8=_rP zlvzywBQuRkEj4cElaLcNZJ(!zzytan6;xVtq2<>bi(|QNfBy*X2r1b@RLiGmJ2spT z)yw~WpBpc%VX;!wE5227Tp9@C$MMBUkT|pIQb~DAzHES%5@vp!6r`1BM|H{0=^TpF zC;P+EXw3HJ@BpQAw`q4_fD3l$UILi073rnEQKF$Fd-DC|bW{Ez&E%f(H7Q(GNwm3D zw)M?Qi~%H6xx%A|e2}|i$kVMxy>gDgdc3$4PL%$hQ($SaWn|-1Pf*}VkfkL!SbwzC z{MTS-pzH1ub8%KqR|idVNrkF7B^-3}MEmb_Hr=V}CiaEgYRq0tU*JQ&o96YC5!L>#8>=x zSLgrXD>&HxKVR{OorU#3SO1l-;9zI_zq612mwd(c2OTXT0fCN?8w@Gw_O=c%%rS!y z%r<49xLa8;i+H6oq_|s9Faf2G-_z&J`_JiC=SsKL%E$E1EcU0*%V$?sfT&QG&;phz zWa_`4X&io8TLb^5O0;J*S+g1`N1$YV`8sN{AeO1| z$>E(9xF7ea-c$fnYBT_O@iWlRJbV9Q;7hw6HL6^0E08B00Q#6 z-SeN=pPVtg4{{7+6Hq5-Ac5|yf))U5F9?i$y0QVt*WgBAe))eELV|GWD@ME{xP~x) z8hqRzWjLTQ2}>aUIFR4cQ_Ew+TM)Nn=jO1l(y?c*=|kE{!Riu&*jRmvE!0OhAEp;N z{i;!`*MpC$#@c)a`109ZY;3Rc=4m^m647k11lM`RU zA!qeK9a!URefm|7l{#y1Z`Kw|n@-QPd+ius)rwK40G7 z&AU7<>3?{IjU6bsdZ5j9LHe(;UvNL0-!*>Lt>G;s!-?+_9zx&u=j(0Cc~RG21Nrb( zz8k-fNm6Rkl48=q7xY8F&EjJHTmXEye~LqJcs_Q3H!Wj&JapgR3{ha?UpLHOYE?u_ zU|@)Em461m?<&LBUeLa;SNl4EALcZyD}`o#fJZ(e_WhI77SFGLctyz%`O$Cb-LA%u z9?|b@;L#RAJfGTD&wax86zCu;x z&zS=PNkL1zpI%XSRdzS|n&u#$t;uVe=FfnOpB&~89@L6|`^K-YDgaJg^*jCMp}9u4 zr#GiIKI!`?h;MfGFSjC^C1~Rhk0JLL5I}qs^ceJG{dgRguRr{q16p-|uAeZ>-a+ud zUL2vnn5QoQb~^OQZR`UyP}^Vq_|ZfBeZFu2gg#JLSFfv~UIbo3fYn3bm)TtGzT>Ai zOa6ajLf`l(?(CjwV}G$ve1ZvWYktA-GVJ?#^nd?wtM0+NzC*vk+p5~q#hvf@Exn3= z>3#CqL1J7%whUxvg=$0ub1sFp=%`91df9v9dvNsM>F}k544TaxCvCFMB$1?6PVJ$l zIgJ+w%$P-CH%yr!JubQNdQCse>9&%Xx9q&_WR6W@iu}g0i&vgQAQ6X-Il|pbi*1Q!O-@} zNn6DpydG}FyE2Jnf{_++s^ppIEUfi8l{Pbp>=3U4CJo=oW(9j#@>T3L7In{jw?4-e zI#~f?%6Tsf5bZwnVxn}k$(i)#yj2OV$++K#&8#)Te&UUXN_zF)mH|NgX|))O|09~2 z5!3gyn36VSM|^8Tl$GkjLvndaX~{(9)ldETEkvQ{EXRBA$cK)-t_FaT%49-Ug;LMs zmo7Wzs{T5Y*j5^A;i++Mso44TCC&2pt3;xckmx%y+CBINK6<`dE1)>rLGGPf#$1oX z!;|E^)CYCY*^q5|3ZoPX9>^ia!Ig8THl`2&Ewh!)0IdH^mCIe>34ln(jA*dz8dEk?1r|9Nu zX(?*y7_w|pn~W5^o-qr)Bs9 zU>Sv+-axMo6~WY@VH89$EBkvpMJJ$}huwlp38MVkE${Z z8TCw902wW$`*N6zN^5Ypma2mB7IpG5d8MRUB}eEMeyHJ=4~VKb zQke{0CxAE|#|-d!Q&%xPeLQlb^9XDT2YQNxFHD_t9r7eR)u%sEaZK@1BcFkyf+sD* zp)eJ5h}(U+liXQ}G8Bd7+@g@JYb_s(0|`PcR%_CgOkfyzA>HTLoJ2~PDTW7zH8O2g zm!2L4Y(i;$XaAQ9-<@-kJALPH*>O)UioT4U3GK+u`4Anx7s3aVVgu2RPJXty@vz{- z^X72oc!CXFSD-?d^Wk>ujUKx^OAb$*9Hf@bQ~Qb~*@6sa2=U{^>EbR)kV@wg z4dzl6_BIizh`4vi$r5H#Xn(bh1%#=5dRmMa7n`TB@&%9Q4lL%25EKywL4BG`4es4> zw>gKVvQ9q4#8VSr0VjGGRA`(6&m&NLx>CF%+vNT|wp4P#0|gwnvzq47@!wfnIzzhb z>EfxO1#U6A9Ej=CQ*|`KQfsR$XDGbm6?Kvt8IQul)9&ol*sWI(GLEBI=JcVd{qaRq2Mq_Y1haxMOMBjR04TfCYl8{P(Z4V*?rH&H5 zM{mNWh3=YNWSod1Je`X5hB369I)PIH-$+0%wqG$`osMiX&@_&7mN0^Tc65`XMwU9d zBQkdXk&AZX$y!a@nD2+s9$Mfw<`m;WpOHwG}--)2kFRpjH5HT6v*5wEDnL^e+dLCA@Coz18aVeBKLx)KxGfhX6;YgIm2XJ!OTvgk3? zeimMr+PM7?kh!#B-$LBOW1G%7giOQ@_DEM$&zLdedIf=y?pvl>KhnRc>P@@1oDM5# zYvQy4rpOO0i_waHl+g)cv%tM52QkeeeB(ua;_{dEC@Y<{bjI)UcR8xvf5Ph!dxX@(aI%cC>~SFu)m8N`kdTudHcfu=n*g*vRpSlR(DzRDL} zri}NH7}^s@Kv~1c2&pTM5Df~L$))sHY)^f0Wk&y+%NIQ_hPZR4&g7TiZHx!Vb9Y@hxv?SZhd`O}m3mm&E7aJD_;C-^+aJYJ7bHv1|&Q z%3S$qcru)OzJf@--%=bPpRvM%&JoqjpMIAAzVgdXGF1DUZ9*>Q6XN= z%r%-i>asLu3Q`bRI){exMWzehtFUYI6YbucVLjz{dk|yGO5nAtMS4ZJV13l2yq)M@ z<=F3aAKE70oSTpL&2Gt=?z&;(2SJ^KNR&n8G$f<%BCCH+FY*YC@O?k%#0f13PHU<7 zbx?;>)Eq_yA!F_SBm@lNihd44(z18MG2;(I@vvtz4MLzzA&n~Ytg1C%7T;H!CGr30115pmxoZ<*4; zWn+IV$Q%A;KKWI(lq8>o3r=UM-A?x>o8We15rss$T7=%1>Mon{U}L^2akwXdWx+>( zwct^^mqfBeOKKuoQ3?v=z2Q{DESJkDom6|W_M->N#N<+c|J~pSInb>dwGH+Nkd$2; zF2taU$H{}mcM>fE+>0st10~?wBx^AfZ2HL@iu$(IA#5))1l0xu@LMU{DHLTCsZoBw zG406gr1zyDN+9QKEpOS5eJ|0n9EWOc?x-BaLHW^yi21P&bo2Bc_GewVn~`W9O?kP9 zPb#@YmmVL|zmw0EMp12;)gY4ehQG(0b2ua^70kb3YQzqflnzY3c8~ zv^#Qaq4FWY{b9SAhfX*RbL&_Bm^k!)U@7xL=R(hr8mIKM*!rw+gNRYictK;9t$=-a zBnv}-K6W3UbZX!^4*TLYw=N1v4<_pcZ1T!K0UX5~fa|+b0C;?pM`*qKWJ;pSDY#G) z!PF=+?9-Vt?H=Itt#+)e<<|r~!t-rkLJy4&bmL^cc*s$tO3_IK6>qD#PA@&r_NGp+ z{t88+GVFMnHMhOn}59?O?5Q-VVYZb|3?qaQA z#`Z{AXD{CF4-lM5L*^FB(;S2OwN;AT-U9Owf`aP4bea$U4KzQ0AlEP=2qX}baZsgn z>$BzL`mk{u$fPJ^66E*xI zVOQOM?jVq%YHHT@)BPo|47vq_g;^fTK^^_X7G(GXIb_&nvi2hD@Au}8Lv^BpKoV$T z+@}KG_(P9OV}BLnH#(5gIQ7~IZ=|4;z`3_v+kQh+6w9;2I{p4jXaUEvzfI-_ior)a zpnq59ylZ=>xw7WYaJF70ro@t}C3(C#4nQ^-2ca^XH5tUxA!T zIMjK}(-dWIAG;qZuoBk5TXU9e;XL-kn-6Vo$CvUneQNGe#?v{3DwylYVYG3AW?*q#Cwy^KW!^%&U3kF-ZODoJRkx+Cj3 zTuShTp>ZT#?D0KRA#Sf$_<$U#EFJQ^5xCdUdsv;^YsHD|9OzNu zSuG`=c`8BOf5mp-KKI5UdANbkOv4T^1r@Got=bQnDcAe<#lNOohNu`v4l8oCx=0&} zDS!8=4p;oG9M7;T_6SqtW(!?$FQjlR`)lsxE?V!{C&RE)B`B{JSB1+byLE~);HGs( zJx+DdyhY9pKRQ?puC=ol^~D&dH=BhY=%nxZ$R`}lHVsMKxQ7D&r2?`Ho!Iqa(QEny zbPT?&p?k!ZhF{F%ZTNdFVMK*EVU}iu4}RPf-PtqVCI2R9Z zsui5X7K*6%^BKhbz!vwyPuM5%1@~j)S%-=}8FduA42sBB`N9V)g(V!Hbft;*Eomb{ z$RxVHcMt4ceq9hoUqNqR&LSb(ukOjDuUWcl_}j{=He>u6d&Pa=oNKzj8HrUYi=ic? zWp=V)ok27Dto^kE!)C{*tcA}yOyJ)e+V;h<&Qb2MKS!T*;ICMmP<5emA^rAMnwmo+;^TX%J67h55lI|IW4!0lK+S)adWb= zcu)TJa{}Zl((ysSZpF*fcZcJ*E{^-7r1<=vT9=G~#R-g*k zhu`1%ra0I61}a+f-ad;w_ToyxvNZu7XZ5~PW1PICEd|dB)gILQl6F*FKfK>#jRwsf zH&4JBdGI zbv*8Lj{@6fIcBhp2|0xrm|; zp+OQ~<^Fj!Ks9M;AE@KVBt2kENjTOUvYu0YvyAN#-Jt6Hfn(sjcYTJ1exW{7&8S=@ z3#UPXYog3@wD#Ji9QVRt_9>1TUi?mEvE68!>2P4%SEXDuu8$3`3_J)Pv-Ha)xqE?H zMZc#0Y6Q0b%P!=&dCZ$w*WmN_A=g=aygNxJV*?%Wu$cEsD{;rs+M3Mt!Y0(zy!-y3 zq1-ksfB{tU?klhjb(3Sz5_Uwcc}0ZM#<$>ZGCr1b=&Zqdqvrf(igOb;XS=0DhIvx) z8_&53^h8tDvrh}Y2|kUBCOE+knQdSyw`#sk*%{LlJpwI+8L6{4TwIe{GD*u`1mxYo z@ecq3XqQZnpsan^4H0w7`6^=g7?16j3q&du|IC8&YOrYz~)RH<=6?+Ha$Ad}5pb-uwz zj`Rq;W?qnTn6oqJ$GfR8A#+;+NU_okY68uHn(;_Yml@D(~&sVY`zZ|p%U!IuCq`8vJ)}$TW!bU_xHaBpA}bhj z2O!;RG@?H&m0~eBTBCVU@6c!BKA-!;@dd4pQFpHLNYzafMxm%#PT5IZgX~npzuoKw z0EHt!sz_bIpBHmixQ#v^*V_^Duf7-wN7$J2<-#pIOl`9Xtqf$Yv<#rMAEVnnKv0*7 zZl3(!2pu4!7Ny7BW+qE}q{nF`^B<3gaJneQ!mDRtxddRLWn|~<%g(87Ehdiq6aMGq zd{Rw+mbr}pS%oBVRF+O56noqkM;4>9&;nqK5-&-0DFA^en#?$`QcqGeiV_rDbTp={ z0f}!uw6ljVo$EcBt2NbF(hWxRCL#e%w`C&D1l|;^$1WQ!bL$!eb&2XGO zpUuUZsU(g(h45%9KhPHofDxy#%JB2Ox37eluS7D`biv=eJ0fxR^1pt7yY*xQfVdH^Pw^-x9_9jL@+szQp}>&aAc z?C%&5e#=1T}KatQmq}{}@$EdUt&*VWB z5PQB!x?i>&6mSgrx1ZM07y+kdEIeAt#h-QWOB&Dq9*)L>yL8?0IE- zptP}lX1fn>~8x7sE5M0N;Q~_HcS1v+~trcA>WZs{e2RYN+fF*RZQFk1-DmKfv#;yy z!5-A8enHi}p0!p+v#+8%kq&J!!AEdy=WlM<6QC^ zGp6{5*OoebU`ZC~rhVc&WglW?a-A8FoH!F7PYb0N5C>$sGlS4}!==P!q~t0TtWGh_ z0ZKl3h+I$09l5AWuPY?9O-rS!*mDV?>GQw4lTIsm&~0OgWDdAYFsv1O&XF|_rbd2S zbcN)c_*mDc?QKMK6))In;cO< zKY#3pqb<+o=R8fJhh(TO9%+oaJj!55QT@UrwEOLB;$!2bvRU*iIiZAN_jeB)X+-(q z5X^{-mfH0%Vkos)>|4~bXqItnl~U`Y$w6wcOsiq+WU6q#eL>vZY*U{U67wFQ6_>8v zX8?e!vO*E62rjOjNeMG1IR;5LNTAGGDCBjoeVLw3`+*+KA>*KbB*4zmEx)}yQ6a_? zSNqrVGEo0~dzxav7{BS(;a*yI+%=hIppUVqtznU^vMHwkK4%T(<=}ZMYpl*-sfqKO z=WUu)Q>!k4e{YZKh5)%+9YNkzaR6~4hOUUj9oHtN<%9IcLznS}WEA1WOb;*Bav>M+ z&9h|}+!x{9wq%0-0$wInTH1@I12vQI5RU7--6%@O+TShhGm`6;i8;Zc58{9rQ?#w?+{w% zV137wQMgOP9$p^CKG;yHk}b)o9AOpJb9*_?`0Yz75d6k6VGPehU^_d?WlOPLh(;8Y z+2hqCe`<-p5KVi437ykqS)dCpYwqqxfq>?mYK0LK*TmLqj*c>NEOwhI5kDG$v>9u6Qe zq%xoLyhLN<%xuj3w7#RCsNsRxhwmgsHE2RXzb_4X$T!q?ONK&!5aR(CM=qZ(t%AX6 zDen$%49OQ;S*WHd+R>4)_1&LZgK>jx_EnRaN=D9;_cx}ZH|_dX{DmI%Y>!LKyEMW zIFyvRq1HvKI>J+?be9Ep_2nY@6(bw>x>Q>Nklr}kUUs=a9<*jPU);NFN+G>FJXBQw znnvd{$*ivjZw}wCWr#p-~BxW)8z`Dh;56Xa><=v#adXt)z9(3qh3KSb0sUI%a z(H7fmBTJeR#{&t>$U45_<3#x8zBjJ!1M5`0Q@`CSUZEzeTftJXWq-|3Ko~*?MC+ZX zm5whk;3{X&C7lv^EqK6SHD{Bacb0Q zv@?c0@|10}siC_Cm%EbO1@jQ9R_)Or`yTu`>V#aTSRR-K%p`U?*L6nlq$~zl2$eO}JZOM>HQ~p<~s4CCl@9L~L36sII1K#ah4L@@t)s z-TU7+7^XvrWh1Ss5?qEG*8V*rFp5K#CM0iZ=nxA3rK8o3++q^zsS4=(@tf~>i2g{B zB{(B@?(4{)(Bh{V>L`nd(e2xDvl%}9r#|dUs$xN$O0{j9Z%@1hoy_$J=nbt_`-c`? zxKzi4v7a^umgmD`qeNznBj3ChF6qmSYaO%r3xe0QofE{LBMp?mB}aJLbXOlv@)4gJ z*J1QEFe+j@$;Mr*93`JJW-kHspNiVypH8xo@WbZbt=phhm#Kp+dJR6k*DnO)Kih76 zBhUqVbWeY$-|`phtSHR-WJV`bAZZ>HUhd^Lme1gR?Sg6WR@`X{g-#qZ;uO@B1Ypq&qp;nv)u-VH_dV!pSW)O#}X7}Z_VCEj0u|h4^ zEpN`oh<;AA&(*gSfD~E3Xf&sz;lA0hdm;4lTOSJvRoaqCYDKS6!w?JqzOkMp`cXRl zj1sCM2PG@W^qomt*>-vX1#hRDZit;Z*Yo~7t7sM$`t|G5qEfgi>>M*bR>{Htyg|%F$zgf=W)`&N#qiUuMxO; zBh!EXD6t$58F=eC+!{esjoQYd7&2o?X(J~?ZRm1C+(g_rU}#GbD)J}z2|eJOtw#x< z&>pcP_xOQ4O+h~WpSZODKOOv!OJiZ<_z#K3OvJ{;`hO|4|IVecb8>L~Z=2*XYLF^P zn~kNvp?f4He5s`5h0&9Ds#K^JgrSg#po0}aB^5KviDbbm7SI)or71v2WFyf^q!cS* zBu~ZoUUS`UysUcK8r2$Ky;+*fU%YqqkooN_i7Rd*9fZyd<~V@r(xN0Z$*st$*A1K@2s(1XFG)1o;|WKZ^?jyIWlbQlL8PTl_-*qCrOa;=zIlGgjbdbY?`kMrbGQLH?_X zPfDeOBnRSOpzFsq(EY_Y7A^2XR)O1~f z=vP9l*T}x1iW($LJjW?8SNGl=uK||re%ZgbYy2#13^ET8u;L)wSiV+=t^MXVpkZBD zB`m0WPJ^5Wd*3{X{R`}f1SKkj3_|1$EQ+)R`bpDaT90_Z0rh42YlSfMwI2XvJA{E` zD9HhK4;lO#1Wp8mw?c><`g8kNz>SC!&0cK4!5?-2KLX+_C+ClN``0=uMVuG}@G7zB zfe`Rm-E5yaf~akW(cDhIU)K)-y~d{C_P~PVr`zC9C@U+Y5Rjgd7I1uWY7mgZzss?k1gj8a?&sVx z20*HA989x7_?%bHk08F}&%Lqzv6~kDv?v5YtRtJi**;2G`PrcTg_6#J62mwQAok;< z^e00Dc|(jYr*6l*pT8r0xaSBaiag1auq@igTGhWuOih9`(4eKo62)V3pn%*f5XJ5! z3G`*b0+KFZ;xvL1v}S;_A2bl^JE5wA@{gEZU?4psjM)FypjA}sgOule*8kYW5hn^n zvY#8mg7AGSJ)O*|d!=6X03pZxNC^wUtRW1SI-sbR{f2~7u_&BvDm1I_y0GB8mLbG! z7IR(t^%i$u^;}nOgsU`#gD4W0oj4tafh%+vbY%yTTV1J+4EWt<9?KNpC0VrShWp5UX0~V{#vEpF4S|C1pYJ)FKL)Os_hE+?=$yI7TGi*_!HZ zC#DoXST8STe|^(LeYY%{o&#^V^xWNOy|8|ODrY}@H1{ZJYFIa2BAq>f=0++gb9B71 zY5^%4-h6whBo=3?`tHGgVf-47eYoQkWC*R3y?r0%VZoao9l`0bBDc(m2b+D#`9C2i z_H^nhctkQe#d3Jqt(@n<-YJ;UTxFNoSJ8?CRpC0-c~RS&rgq22+gQ|}8+Vst2J&LA zy4?mZwST$oonG^PVfifjm9k7VSr1SGsb?;i`OLjo3%MOheu86P?fZoic#m<={kByd zi;-~N_Vq;~n#!cK?pYj#SJzj?V5;qwm|>Kc`(ic1Vs*!yrqh$N74y@TsSEaNM;b-A z=aE&*OFAuic+|E{8|508`BJ{rh{I%fv0Fnq;Vk|1-1%34RY&7+^yC&>(a!YTUSpFz z>`PjS_BcJXWgeYndKNbGdY@xr5)}Tahd`b=%V|pKU#99j%{r1Pr)Cs(Z%|fW2g~_~ z{fa*p08L__{cq*n^^el`z<<9_XsJMHRs*}=u{VOCtSlGnBuX1KuFc?%_(<6Ersb)< z%H`E&p8ASZj4Y952HK;+S!J4pkfvWoKR2U2E{m@{!1yJlW+yW6+s~b1kaz=lc4I_6 z%<4waGw+_0Zi=D+2xnnxY^%OCcLuoDPMK=Ms$In>*8~*-#c>l=R3rnjsk^v?DidO_KG=%`)qwQ@cYiWv2`u1!Zty_-2}24cGx<9QaK{| zhwQh~5uXG5>h8o0S61dZW7-eXIvaqVD_4o4U2h|7k^D4)ZZ|q*YkcFmHD?ho)w$%$ zI}ycI1Ann?PHL$ghf)?Qw{grup1||?{w~-w$GxS+LzF}(-X%y(iKh)0Zuaxy+tLuM zfnkr+*O*l3sZu?Ty0ekCGxzl_%TDW*VrFOy=9cvG0Y%z)1MDGqDfOnqojmId2T^V! zJ3#4eiC*lra|h-#BVoEJa&a`aO7HH)w}Bp=+|jEk|DA=zSIwZo2QTTL#G|w#l=W1r zP8`39Ud!lCfk@!pWrD+mjkZ?cBi=UiYiuM=|EA^$6>f${O0Ax)jZT)fQ0s_kf#Y6P<*&fRiq=jAxUHcCqb)M$HUHzsc8uFUnP{wD&VL&LS zt0*aSFKLHH>GIOF#S%=6$G)+$-*g5qMMzrEN4ru;kp z;$Z1vJ3H5tg?+%EI^w87hBF5%q;X3;z(NR=jVfH7&!$YkS0j3!Hqr;CAJSQl-}|^x zt0{nC7dF!5R{e``*mTAKh_DX3>X8jTK?l?F!zEe>;Z;{iM+N1Bi4@aSZp~-P8Yfvu zbJN~1g2dzZ{D0su4s2G94tlB;KdY0AexF%VPsT6RU@Ons$5t*l9xYTIJKS9DyU0bG z#!d@+6@azdlOEL144v+wX44(=aaUqLuvCwnuF(WEgL++=JV&tL?a&Ef9Y^eE_9KRXnsrq_*^p zUJ(s*_pTY*vg8<^Ix_|Nvp4ejKp-~l=~#zw1#D=aVF-OC#1JB);Bh2 z6j|UUFxpv1heHnib4OjyX?9Pu`W#`2400#Ca!xxCs#O(+mhbak1l`(oCE`%4BmC## zuMiXUz7yjBT1(qO$}x5I=Da$MGfa|?>0f$#CHa%Q#zY;+{J3%`MW}`k(ZMD&N$*A{ zSwlKa!3ichU-Y-Vth11lznuZ0OP(IA_Dv;e6m-o~5%#ezQBJ=qZicJ`k1}ScV1o79 z$x?lWtfWbr7>JJLP`<@RgpEJX-+H5OeS8eW%1uD5v}uA6fTm@9_GAXKom-_ zMGgYeT&x_JbfWavjxSmgW=(8AFJ^36Z>c{kq@yjKVd^joflRYnMs2x)foN+OR&>ql zxX0A63$a?0Y$ z`uM8PW@vXg7>0NY@1AVGTt|1U!gN-sqWvmqwCj^&i|5vh$!~y+l;qHdm(Gei0M5dP z6Wxv-AC>#65R?F*6=&Zs?<>j3@Ft<#CPbY`r3T#-@E-Dh1#0=qLc5(axT4Cu8A#g? z&?{t9#q8OUfsct#TvRwccL+;(dtvmpPI&wp^k})?VwJmX?&mc+11Prk)fR!M>s^#N z<#s84*jk*kQmf7^5Enc9H*ib6Zf~xoBLX?4C-&c&G$V~W6*}6KrJN90Mof*1Ix)^~ z6O5Bfehd-H%^Gt*V2bq*7O9qES5o|_k%>qnA|9UfwBIi&xUO}U1#t3huM2o+mdqG) zG;Ohqsajac8Ape1>iherU^#h;2GKc}Pv!!X9#t%@9%hFG!rB#KvQS{xG zOD&TKTwL6xXJ8?j>eaMo-x>OtNUU1^Ssmh({f}S912DqcJLL~_lTVqvMBLUdrS{w! z4-6^t$*U`B>}2T(t-5e$*Rvh4X+#xUGrCWGsQpS~0FTR0<6`Z&QLW-AfgAerAcbC| zv6u7};*6E>dT#^XkxF#iSM6{Ag7Y`-?Zd95K}D*DOY<-&o6pm09UcSXMup~>A{a_f z;i0w@L&T*=M~B4ZL8ZfLy>XKoxAxMn6+W*({I+?2spx=nsOq~740(X{@I@E_ulWBm|*xY+1#>?-O1|5S%dDsZ-Bb9$G^gLG(|CB7o`B<#s)sBYqdiyGxGe%-Fzljl$Ki~I3hDuz!AZEnI1cAC zUhJ1JJ^wlKt&e4$M#q&Pm{+3ov$I;;OBKDV4_V7``)jwCLSZ{cU4GJ+jY^m4{IGNk zAHRh>2vA?M5##S-qcY}_ccu`M=docXSxg?r6r=gyyzhbWm<4zf+}9k==3L}v^peh> zcuk1f@YYY=U!F8S`4TJ^U#|M0;Hfd6i<)qJ@G*Vc$qp=H{wLC9pQ!bwaAxtk3tA9< zkE}km&Egqz>=^AdZ0Tnbe>n1zWKN@CLt7ElsVQN<}g_6B=4w ze0-|bJwRA#Sa9Y#)7-gm@_I)GvFY#Z(YYR+K=^w$Mk`K_`Cs=olbPGyaFoM5>e8a81!&_zdDAVn>u}>8mZ!~p|82ZZWa+QdID@m&E5;wl_TNDkY~YTp-0{{`~GesoAdfE!<7z!aV~p>@qB@k<0_IuLi%0sluwqgXGi*7E8OP{V(EzwIB*RDJD>klz4m$TjcO!0i><>~hFV<5|u*=-gU z8_iDUbEmIcCmr(c;aOAZFHRC^kt+r{z`yJ>;(^jS*FUhW9VQ!=+#Ix zPT^6q|CTbJqw*7#kgil>GNNJQ#qEhR#mB^xprz(2n_tMjE0{oAXa9qyp=KtHa?n2c z&Y*F%+(OS~#maK7X-w^iI*%4WAc>4tOQry+g!dW*UzVjAbmEP2fq6I?41m~1kT$2? zP|4yPWx+=eDgD^oPT) zwq^K4^*L;JyLDT|z)>qxM!4kR`Elpw_w=X*n^9xd9xu}hWH+qvNE7d|7)7~L`Ok4dkL*jJrz}4LyW@8Dab-!WGgfyC`T+Ca`G*jWwHeac;k4VanD>xd^Sz4b=g-KWPGrD} zsk|&TEbG5?L1_vsUt|Z4?8=RhGUcqO@vDW|dD8Z9b}#8W_s?OR=D5sG^)@oP`xnyH zw?$6TLNYkWg~}>eh0oG@d5`RIrldaa{&e_gCOV{Rbs3CKI$0Pzlfqn++vlAI=`@_u zYj87to(E1|d+}_bx1sqBLARb47g?7{r45S6HhbrqYCLF7Y(o3-;4Kveu;3%x=bG+{ zm^e26x}F6ws*q7NkOZ|WDCF9Gp5l08#xL5_1YoX5G&DY&pbVZDoyMwi{5dtzVGm(z zUk;v#*0ov*rjMw8FWF-Ev4Ur4*u{P8pcLjw_Ub3N0ZZdjAZxB1l0sI{nRb`#)@k{K9u~lw!j$b&BwnlYS8<}EPZ zL!-7xt`_1Oj%)N8l#UsSFQP0)qBoO*49Q@rxPO!)es5n?%fSznf=-*B8xwIyhKyzPaw0pyNK;dw)nuDL7KJw?c?*uQ$ z^N3JI+|u(bt{MXv-yk@)YJV$<)DePl5sRZRB;g^r7srNy@Pn8A%nFFWIHZV`#Oue^ zL!SY z9Stzn1rsk~k`>Xtn76Pp-PVRz(t6q1c_r{m_MRkj$3Kih9dHMkEen^+5MIU4W8_xj{xp9FCt3OEsh5gs^{bY)|wPkf5S$EO-Ud0LZm918Czk3J7tW$Nw~|aS|~S*%?{F@bdm=Nc%Udas0m_jhTp(iIeL;@BaI&#>K+I z^uM0f+QC&8Z*kdUC8gb<;EH*Qc}jT11hGINj78XSij_Nsz=Y0IZOOoslQH5GZ^RFB zd_P`)@*aE5Pp!RbyKX-^^JZt#v7Mhfj;#$=h)l82`ln|HDG(IqmN<@2LGSLNAO1ai zj4ZhR$VhYgoCr2L1$!Wk!bD7BG+;`Ks1V@g9l}7Lfk3{74!+0^{QUkv zgn4WFk&KuQ{)H*HYY_S4pb9}kLiTuO;OR|euxm2}0nv}E>Oi>h_+~zlIC^E~vf_1Hs&zJplrE0DfFw%bpn|49@I~X^4xI<-=05iMuxr@BrvX94 zeU?XG#}Mmgcd6quvlIXB3jX$d3aMjKA zL?{6vG?J?K^7v%IkBDZF!a%`*q2Q1Z0B}C$zt+cG?yEWwsJ!`{-M$@`W>8%l%M`Xj z6fNixY%4gifPMGAnk^B~z%cqhX4J0VPoDGh69|_P3Ai3&J)nT|$6aE8Xj5Qj?5)e6 z56H}0^8FqZ;M?>4Z5C^i4i5)&|0(hH8t&nu!X^u!%=JV2W>?V7I|aHoO-BT=hk<$m zdiVGU3o0ra4AlGcTx1OX%@XIgUMXy22-G03Aog-zm%ROb1hkn4JAeSFW1z!I>>vW# z6cF|MKOqg#-uoYc#jm#UAHqpLkGDRQFFzI~*APM9$@Omqz|UAs_Ftq~0k-%l7crtX zLDbMK@Ux#voS<(FUD-gxC6Thj!R{$a&oH~S;zqRvUsQfR& z>Nil1&lWo*Mzmtkpdi0(MoAj}-k${GG`O?yZm~T{%WsT;c%G--b}0p-sgu=4XeemV zY8{U^>tEHb0vefpjR8M`IxmoDB*k%cftm)eP>UXt#6xg zNdBwi6WFo-U+~05Tmc2OcYfX^!0J#SSJBp2yRMRM3h~>wkU)4w;6LguKzimTz>K&@ zU#~P#en!wln|oIvB2xRcEB14JkwP#!1$+85Pv#>(*kp6d!{FzauOq}|pQ~@L=rAB2 z{{EaSNsRfT^@Cx1sZml~IBqvB3|LXpHpmX8eEY&ssTFNIFF5Jg@*{d<0&P@9crwcw z^f352PX+sHU04t9FH9^3#A4*Q0fkFVBz}K$7X3Uv=MhBBL5o^(F@DEr5O2h-mXN#K zhMJ9J{^9k&Ct09s*ZV&FlEwA@s#s(H3mxw#J{B(=6rMV1xhd{rI`OwT7>m(I982WN zDD}iL-;&ci=p6>niGCMF%;mhp2qTG~QQ(KFsf|MQj#9m+O1PaiIXH4jI)>Pau^=vz zmS4GsAa;O+!MRi+8E;fF${ z-+O4->AevQ8bH`$NiPsDLcGTq!TG zMZ0m-Y&iDg+|<0_oVATF!JV3hoo@ikicB)zSdi5;zaciUG{lCQfaFv_E?oYgU0qb0 zUz_^#twzNlNTsn{V0W@3A;>GTlcynAl?Kt7hhd)XpjsEf9lV})scAEJL*SnaK~;n| z7If8SRM&1SD;69tT!!9cau?@aGZC%VJJkmFUmw%?tJqawQ?!=*lZuR_!e`2E_+i_8 zW2LNz32~8I+_h6nGijAi#jcS`_6Ya!noCI##vxZem4yRs+ zTVQh~N9W)nD@U4F58l3Yt$caI?OXFxSPxlH<}Wus$**>$((_r8lbBFk+oQ5@H)^S9 zb2cShN=E2op@z1aLCuh{^4Y{w+bpIY%W$&FUe5z>`;}+=+~SH0;ySH7%)3utz5K>A zc@F%3yIl|2<`4moiT;hM7d_j$EZn|)MYtvFAt(-?ZVh|94Z&n99G-iwRZ)p^!9#I_ zVWs?gAx&ds8S-`9u)G1|=*VWjsFt4Ll!-FzP&Wrx(`qsKsZDfu8M)!E#>Y&ovUcg8;JwKNvEz%qM7gt6JIOOrtu-!n5FVAz9Z{L-nV zt(}s(7rwADUNA@6V3wN{O~84|HzR{9j4t^n3_X+@!^#a|l%awT(zD^`;H=ApGGC## z^iX?)sOQJ&U^BnEW~;<7RO~D`*&!m_u9@dYb$0H>yB2gU6{heFMH_yUXMW0pK`)^Q zSvl4ux@#((vL33pY}8F?aeRWU^0Zzu5ATD0V5 zK4aRBYU!DLtmREHw?$>i+!>L{CDrE9f&s#`mZOOaQo<>+KQ3gy;#ylnswXS-&NT8d z)XTbNP2!I>%U`P8xf+3I!Gm~xN9M&|Ag|64u`bHhHa)8l(R~7x!}e}`m}>rvuODwa zd|>fdr!E4VGHZo`GLkksNdDVasM}hVqK?Su~DsGl40JW6a`f4Z?v3uFW>rv&6 z0pggWQFAg!mDq{0LKU-4M zfLG{SBi@=q!DJsVGl1#+i4X=*iG$_uOFoai3$2Rzs|y8vg)UXa(6{l>DKJd>i<<;C z63E1KGkHopzcT!r6$?%Og0{B~Em}E30|$NcG@;cuyboi%X^*0)JC8|;i0+FrD%|Uy zD%(Y8quBObQKq97YUtbcoWg34`$V%PsDdc<59)rh)x78Irc{CHO3{W4zM~@pg zTvaOl;3CM!CujC_-zAR7-4etY9V^h>_^9CSncoHU9rTugS2qov_!~nt&-l`k`6m*Uz(Mt zFg3H4odlIm`R^rQV_+&=s%Zp`M2t8(QRdyv+3$tDJ zaPXz3%W=q7I{(bNR>mZJPoR5iY#TU9&R?Q?+9`Qa_O1>;>gXeFSfa7NoR?Z&ihHD% zgd@;OLS&;VLe0TtMhO8-a7R3?vw@TY6`R>cq@ZZsYvYR>*>z}*MZO&ZBhUqfbh>8|kBmR3YIU^qO6n4EA=Yos z69QZbI0Ss1$CgHW8R?x(TS4r@!1{J?ho{Nj^H~&}fir5wZmTqu>!s~OFRODghQSQ# zKC_@8hGqXEu%?e@z|3CxOi3a{aOhIe7eQltamm}kgyXDR+z%a)(~8y7B$trU#$*!Q z;`!{x1SqbP04w523CAhf3?S?d8Yy*8qeqrx*xu3@d#y7?2Rn5Ku@yuY@re2!ue@W| ze~{lwV_!+Kwn}X4uG;c%a3uxp27(F1n=>yRBl%xfdf<5%W5k zE#MQ3e4aW?i=`fSKJSJ3E>+FooAWU_gQln7fvFJ76C~xYeISnZCN~j&yQf>lH$^4- znGM$E=3HthJ#Z};?$nWCMnO!RiYa~;XS+sxi;4PNwW=mG-27@%zvC>~2ph3TdR^+s z34~IW@4abt() zs<%c1NdkO2HUeO=+3Bn=9m+YH1`e;Ky~HqYqH6?As|JmLlHI&xGVN`+c17Cc2<@ty za)GA}{Ocm8+)3P}T8~9OPGE9=rqNjBbtaThMINh}4B4e*blL)r?x4!%me59vG7#2o z>H%?RKhdt24a%7rFOeQARQIi0{I^H21C!k2#oyOY&nbxudTP)&uTo{n zO^GsCW6)e;R}DeT!>-QMu>g@ti&NUuS=I4p#fi}ZQNeJ@0s)1i=W{UI0beOGn~NtA zVS!v(y<=gV%tZMPrMoTX8 zy_p9CY1=9JdIQZg>n7dYnX@DE#ej4rTU3wiAha18Cv3s-5nMaBCm3lE;{He8W4^BY zmy1!mqeTui{o670R3wI$UI3#vqoiQpS_9*II|fT4{guzw7=d3$EZwpC)q-*D@2_0z z{iGC(r!YI+9nAFMSwCm5Z~V5B)(dmi;on_(qi?9CUDla<-8F^;yV)ZJkawC0sA#F|D+FOWMJ?^vM6*9b=p9*_H^fwJJ?#fezO{(Wl6GTu55BfTYi`ZO0}$ znKD=p)ym&w_UfF-tb2a{J^hX1naRp;DZihF0Qrbxbk>j`(X17lHWhtP+n2l|HrAtN zMM+@O{0a;6&wOq%f~^=Eqi*x1j|a;K&R{T^fJwOv^gW79O_Sr^5P35hgL!iM<)CeG zFxG0b<4Hpv4}av+;=hwd#G8uHZnnFZ81sw)VE->FKLxa$0 zW(czSDPg)x=UE<_C@}1|sS9%-y4l(l)NjA>Z5vY}%Aq$01BmUlL?3QYR~}76%&BB& zuKt)_nPatOq&{Jbc3i2VTF0o@Jz5g}v1H$0QiD9~Idd_tsKVk@*U&*-60TTuhpBVr zm~(iJr3hNz#HU?0)NWCrH35PXk`cSeaHx-*sHN%q$lMJd4q!eGhFMo2BsI zLcHel^T968!%=(FXSc~rgy<`)pqa-;mz!qCG4e?$-e#;@Okc~$?*%}DgBh1E2yH=2qk|2wi1q5buf>7k-}NT6b5!?B5V z_GwEU5jThk$!Xx_$E{1SlZ8~9dLG2?V?>)Q0t@H#Cm_Mar z?VNCu@K(~!lmbSTfa{|JWr))`-U#Md&+7x?DjER&n>KDHu`*bOJ*fY~9%wemlk;un zi$&yd`5_;yLNRG<6Osd3m<>PSoBlf!%0j*(QXw`4$SUN+hJo%*3z?7AkzSPxX{9qN z_w(rT&}&w1rmX3M&=M@)7V`LvtTCJj39Q__R=%5T>6&1cAWnSo_fl6Qi>;cpj?bdJ z+_|$AK5sj}s=FrLVlBqfR95~JrS+KdI7Lrvfak!QtgahxdR(M~LAQyDCC?sGZ$~}u z5wJ3gekQdU;L4Y-ns4^-gL;y%f$xk$)H&X&nO8$)T2m@nU0-X(L6!zZ(*_E0iZYM( z;#o%@_e^exbu3m1snhqssLeWjUY7DHgNmJ&EpoVwxwVxK<Q?Hf7#Qa+M!Mm#Z`jz`(aXhBV^si_Pviq7o{8Or}5`Ajc znD4Qjxgkq1c3!qLLlv~ikW4rOg3R+zUYMO_y)=}eMXddT<$-xB8E13&6-XOcAX_XjWsYU$7|@?eUt5E6m2(y$e<3JL4mpvdoPno@^>` zE%G#t#ECS_baa)zMR5AXwJu{WseZBIL0U))T7-AwI!BD8%};IY{WVXo$p0X_q%a#j zqc;^1+#O%%!+O+a`qKX=YmL`0b_)nvi z{$2ik#T}F>R3z%^KzR>;+r9FE#^;BKWped%$|d~_v1bDq=^D!e(EbS%@r`8>uKdmW(qiIMPyoEK(LImV%yZmE!O3DgOx$ht zz>NgWz%N2Hs7>_c^JbZ;g+LPM&AdNVwfE+x$CZZmpb9`NMS4TM4O(`LBjph`B*#;hsLU@m16`z9nJuHhVJGXQRC1kfeHR0CfkfcYo`;S;9R|Ua@e?BERSZw~%e?ZhV z>Fo{=$Vf1emI&6+$Yr8X3Y`Tud6lB*-93e;;6yc7Htexpe{{OE-#}g@1xfipIkbw* zViUziZon?az=YWM`@NB~AVzeqvd}GLkL^8QrZ_p4(8<)I$0z*7N=W_%9vz&M%p(ZD zX8!cm1Hfw8kN*27$XUP-uv8{09_XrjSlTAE!BJLpAIH_)zgd2b$1z@xYGCSWgh0iLj!F{ST zt;0}vX_r@Kx1YL}|7B|%o6}k_5oPkuX66CmRfasK^ns+2$&;U%^&617!c!9Fz4EG7 zvVBeklKRAFYbb4!Uu?s~ugy_a*K0F^L;FSdSn=`!(%IIZ5Wz0XK7o2INQ8iD{Cfj5 z4;00Vn@yL4)Hannah=G0v&Twz@2kN+}FB933PPk+mjk z%IS_F_uPd{Y3HQ1I=Pd*I7_d^VVhr$Df{&v3u2&kMcmhlP@+9gNSu)0Kuvf#T_=Tk zVUE7H%Er2GTr==7>gn7Q>j_G8o3#y58BC@3s||dM%9vS;uWN-6#9u zPwwt?r&8Tj>5+P(pkWfKAc1$sf&gJODrK8%jrKlx(E;_K0sighBZ z&AP)4Le9lV;Y0qcYyV@CHb$d7QAcF$t}{)fLibpvNth*#uI)B3X=jX~jmmXLLuC$Y zR65<1sS(aSM>?frD3zCQ$t1YnuMM|xI8ZPpmC;z@j`TZxKO9?!`junvy>n;N{wV~N zv-EbEf?RIy&s`neQYoYcuC%QpQtV!Zei@2)B*M5af)OVvgd-j}vEmyRt6=**Ux0>_ z-h0K7URNQ-DCHKriF~sWoUW_6^Y8(r`s~o9dNxfB8|8ZWnu=k0X0s4w>o$2m*<2q0MQ?MbTRLx`qtpbL<5%`uKB}s! zFHFU?L({USd3 zZ&l6yezPv4cy|`o&c;dZU|4)22CWO!8S4+qRAR<8cmBK#;#685d$kSxMpGE=x!K;^ zLp2Ux>dU8;pO@vSsQhxqktEp!&(WLq``h7~a)Atyr0!&el1l~aZ{=MhoofcPP)=?p zMr(Dv*&Dlvsq`#98#4(>V#2$fC7ht+o11zd28V+u&w~xrBO2pmzCCG||1-XS>h47T#!`d&-zQO027lE_jD1^ z>ov~}VoOKh0FYNHn~Ab7>u>no5m$R=^LteZUGF+JNI&^1?^QQOg`$R%_awh*7s~j9 zh0Ig)7#Azr9b%+LyKF@EXI>F|_k(GR1$+5Lme)yUo9GXZ?=I*u0#uE2nbSMedfo5_ zxe>T_RDvc;Nr)GSVGLb#RE>!cE0*F{Mf3OKv5xb#)s72To{O-#JO8526?qKR_a70= z6Tt4vfWxUw?vW*OBJJ7917`5}ScgbfN~m*v^cMgpZX;#HYyoQR!{&X*Tq7LBypAx8+c>-Q%cJ^_VWGXGk}mokuJPsi`@Hd*#0- zoIxEIBj_BH9@Z#i*7?nrjVW(_Xi^4)4giL;YdPU=q`y%L(STuw3ZWn>n~T$C{C5uw zf!$yg&TkFC?WQ)!rES;KPNwqKVdy-&5=pZcd}_^H5ZoEqtbZcwrR)YPzGPhVWYsPU z+RtPFixNlT@hhA)a9i?|Ytv%Tl)z7|GD@Z*HvTL$oI%ii8;lBn44YOT8nb>}P$srv ze2V;x^MB5hR5rW{qCxHzD-f`<2vQVuUwGljGy1W-(F7GZpUADd zXMiIotJFF@2bVGydQ5&eSsI6*_iB~klq)Yhr<&GoHw`1bT@o%7dE5J@-Ys!zJG^ob zYYR9KDzMUR@oL|jH~~-*oz$3B{L(iLV%~yxjn;<&qqmQmhy21c!#}B`v{)4^jT9=s zDkXHM)O+|4uscEgXxTm=GAiq~e>)3AN06L{U@0=FO2;f3y!*+|*G|Zo8&`BO0h9U^ z$CF~^2Gs&l;5zt528qnrQK?PcN*ed|J}L==%iWT8ZA`rA9_2zmolQSl(`{gb=~$d@ zRp(H#?T~iL%t+7bZAS=_t(qpytG2gCkYxF+hWIaVao`D+H-EKt4jD{ zYa_G?TYIo_c_FcVynX~yk%!SfiB*+?Fp7;e6ejlyR}x>SqhM|C)!lw*G!+H?DA4t$3dL{L?#~cIdjQ;`s1tSOudfLjsE32fTq213qMYkQxF2 z0uuNF0tyhix&ot5Abg-n57|P9bPT}TkN+Oy#{~x}m`ejj3w~MAR(|@F(Ksh58HWM64Yn%;<`zRpUVEoZPAbpao+A{Edh2 z{N=*NzXTB(z}IKzM~ZF;;>@QK?285P0RaIM@%W|!O-;gqI;MsM@pN~;3(D4hM-bP- zxcLNtL!W@n19u4_+|FO|*8>J_>XV)0OT0&_2Zp}Vuko|@35J;fjt&Nz^CyA^3h68$ z+S*%@CkD{L&a15eoO2Bw_+_{Ha%h8lvtk2)=R4y&|B3ubh5-A;fez(|mz~jXLxZ;c zQy0J?2)H4M`9&_b0z`z*jiqg|3|-d-WeYuo?0CjvcF)5z_<5L>;5hoAv}aWOi&(xs=O9@)>-bAIlATJ zX>^Y_@f4Ciss9Ns1peLSYi=u;|eiG9NU||>d+6KKnG-u?10ly9T&!7(cetg>VU0*hV1;>xK9g+4B10Sg~ zAR@wm`oxG=BE9yUzU)9Duz-1HPrz&V@xr||DgXe^f&JUs ze)+wC0?d0S;ei~5f4*Y!p8=dj2j;jwLcS__hhQRvFYnl7=BB@WerP<&myn?LYRNb;!W=MJ~@M1+qSSV>=sZ60uSE47Di=(e?uPHqPCPS9XA4)v*~IFM@qag z++Td5y)s%&c(lY-#zhRsU8^T>?v9_c@mkjf)2k7lT8IoS5-N>9Av>hqax(VQ97r)_ zbV4JW|JZct&~;h5Zqp~P0kQ)|_9ixzFyy-}e7E?Jw9jf=aR%C!MFg6UkEI_gYN}^wb8yg^`MTlQ>SrW0p#25tyVs|T6 zrS9mu)2$bW*|HJBC^q%0@98qAbD$YdRu=K)dvw3kE4H6p9-Jb-?)Tx;L29`s`OX4f z_qDpxzHfmZnx_IMZ)$F!DM(@2VBF8ZEY$6jQFqvhAdg6!J(;mog!{ONoaQrx>;8TTzT2AtKdvWbk@-_&uW8wf&MfL_3E3{O!wnZw9r$aeoqz2;kKt zn#2Pfg7d;319&G#A{goYk(sH`paZL1Fx$V(Ce0sHPb@Vqy!WhuQl)UQB?9xdYNxN05JSaw9h6R~MmiMyjebnwD9cq$1{VXqj z$jTy(=LeL`m1?J8Dubjj$@nLbAeY%yN4Y5 z6jr@<4abYrFf@#|>DN~=L1%^%H-&FidwBF9IsuXQbv}q^Fdh-3cf6FuHlh4fXfFk~ z1B>1%CC6e6SKz)t0OFE8WgNysHR;YWz54F@iZ&_4B-(}8v3{$5oV)5p{fpil2m%EL zKVASU0@YK~&c3~vqTD!|DK`as8=RF93k$w9lT`;<$$Zg<27iZxp5ZWW6FBUNDr}us zj+t2Bm<$t`lGB0}Pama*nd^;44LN*--zhW8?-7-qC41`7lqjH+3$e?HfpDxs1Q4Kl z!AVnVX7iD5(tL`TGvUd&2jM9P&5qbQ9nq8Z=l*Fiqw;EeJsm?jq%G4%Js2nS0dISl zvp00FO^COSW^1x-JZr=64oG^0)Op@n^8ibVHtVF_xnoV(o5}w^w2V0Tibc)A+LQ4O z;V5%wk6L?a{bury5+|13ZDE+g#W!>-dFeUr8lm)z)iQh^d1~R0z(UH=H+@#xGeKY> z&yP|3w87;1DE!|mVHQb_21q#BeYo3Po-V>?C3YZFdl2}rrwmD~lHwBNTIg;Klu9M& z_`r|13?C2yE?R(Ys(=ln4yr%Hx6`}A!TTgAMQWAd5NAyosd#9?<$GLC@`|mu|QwSkR%>(t$bBd1-zMsEUCJ-(hajgX=8bL zyc6U%SUzkwmrmXy2n;bKpUG&dhjcXFY6fsNBQ0x*8j}J@R(z;3>~P3XY?1ZG5;9;gof0#x5F^{Po$#w)HB?E0ik^~n)moAv>~m((!73x z(OyLFn_g?oW@c*y&Q;H(^y{op7(ptC$d=QbBwf3b0m0sMvp1VA5ct4Z8mQ*)XKdS< zObX#)NToVfggJnTRR|3(Kwq{lEB1D5!Nq!M+ioB*+NG4gluM{($I_FAi4nfGBvim^>m|1Cd>Jx)QvZa1sD5p*ayqa9D%sJV!lm%moiZIFfIkqbf$Izg~n0E%u?ibeIbd7-Dh5A zTf+jSdtK5ogU5(WqJV3RBPz=ZL$t6T;dk-9Vdw~aYU3fDQxQE8hr3AYozqo}M30MZ z4OqzMZ=Axu-goe|s6Gd}-n^(*3x8~e3Xe=hsMU_L>46p7;p$5dfnrW6DJ6BD9Eh(G zXrnhKLifL_`UX-M6ynB*R4n7(N@2@rs^Zp} zlCwiv9>%JJY^sTllKn4vvc(po3>4885wmaUx{xf-CHbV#- zBg-=TsxLyfbCXA?0F_nO<{3JXlL}pSEJu%5!XbL8(=Cp>>%)Hky%U8T-Clf zhVQ*!c(Z_%b<<2@P%=^>XqC%|O3r-dAbbSdRZXI_&+=@iO4>A57j;f@8BH_3j;J;0 zU3Bx-u4JT(Z_j(mew%Jsa6R1%R`^&DBU5U+bPT7r7#2k}6GBbkaDA67M5DneY=x76 z(H$hRjP=kC2MxhuW=H&nViJZ12UN3G&$A7fs-0*{n^Go2^j(%0HG#D`aS%#I~88Qrl)Yo+oU~|9+x1QybDbbvobDszW*boiWf2NS_mp4v|VB7R?5#p6s*Rg0!q6kSXwX2B*C(f4`Z~1U@e=jEB$Vdx z?@Ihj@<~g(zKann&VD4#BS5Wkf!^t$ir21TAUKuA#twCKH4EyvtIjr6^*n|Mq>!K< z=9=*0aADGy4W6cAgkSF+2Zu}J=fOBHZC2d@)>_~!HCr#PZ(u9+AFIY+`u-X!+Z7iC z7bPxYQEe=fPNO|0TExSv-z~smX^u+<3;_q?G95}`cVV?A3!zMN>DQm`lk-vI+yYi|o{4-w5`PF0nn>#qXw zA{Mx>NMdQ*uw6dNlZh$sD(5@+h!E*N!TpH=p!(cm>SQg1?UahU; zpwVgJGtI=71I60E+P;xE*{}F(yz4&EEwg5~)^77=u8DM80cs+d&Umec_Y>x2Z=@IE zUh;|>@t(U>q9@f-7-%ZAp%T!ek6t7{(IaG z%k!i!Y_8yf(;Isvxow)Kdvxec(F7*BK&-;J0z4On=y*9yEIB5!R-e9Qo^>x(9L>#S z*5gtZu5MV)ccDl8f8Nsf$7!12I)5=2Y?r*Cf-ftgN`a;+l4ogK zk2E?OSGvqRHCd%fheTt63{5#fw$z@_rgK(S=|{D5rkx!|A6Ugdbh-Ut%)C<~3Cj%a zV;(X4!IIxP5#BFOk3=$_5c_g$WxR-zIlZrvQD~x-3wFbK4k??SqgJtVbBb7xDm_OZ z54Sc#9NQMGxhe(?gNYBEK+ZLZ!0b1oLQ9wej8hiz>k(B6OdgND#4LnTf!JF&l_`=v>FcXi?oUSw`Zj?8Wd zI5f}HY*T}Mm-w&BQW%&i%}uib&Y5|p-g)5-XtM^Ax(=5&Q>gp&$Hw96){)SXLS5~p zuYe`tiTYhfv@9fi6-$_4r+wH_EgMLPADFn`lGT;1ot{X3*Ru^xZJ{mgCa2^#a%~uE zGb%{vx)E8%^f%>~U!NW&*>Yw&N-18g3^FupVcBX3==9`qVd&Q|RcaN>$Rru`5^-6N zcdhwus8>Z9ZG4ZT4nFI1;|M1LoE!Q4OoOXm<)y_^x!dk5?^H(qCGavAoOYVe8z`|j zk+6%F-`Km5_=8;&W@;^Km&ZSJO7_7mQ}5x~NSP822a&6(;XyyD zEzuVD6kgsp%Qk0(#&%YTfSy!#ZGH{d=kc z2z&Jv)Qeh3e^p*fgt23Wa734;mL{@IWXfQQh=65^-aJfE!1JOjI0WReO2=g{#%|SK zoXkRJ_Y}TecK31cE{?C0KI*STqBy5)+%Wfg@;9h+u4v|5cZ+WBlBonlxfAV zamXh0U+0D_ss=~qFg?B%t7`G@_d-PYv`dmQnZyVUm(0j``Spd^U2}IXecBwl5#YBZ3a&%TU7-nrfdN75*8g>V1 zx#y-QURnU7J6#^K72Nk`uE9wfD72y@H$;eWL^rbcv1Z`mRVf?|`~&Hzv^RE?TP+Kj zHoQ@MBRi)nd>&^9f}Ga5+GOM3+-ChdIJD*fBA1G?*C&ieQKKCIs{ zCOyleAu%{t!dwaTE6poWK-v02waiMAk_|N4s}zyKY>eHxs}{0;Ku@Ri9H4BFDQ?>Ysu8w$Z9ubW)?3h96rme5O1+H&~HVR6uc zSJ0ZxnEZ?_+gubg1N>Y=N8B}$LYL}j9-iF85m-{vkI{k6W({X8z{q}5}-B9}2 z)1rZTAj3^Tc4a2R^GBHxlt;<4Ou5SBwOteF9PG};!`<}^{BFtu7Vzq0Im2Hf4g$|{ zwvO(XG28iOAjQEbid__Lg4jaxRHov((26OZ>eRrSq2^}XXr6BhTnkatzN2{QUj zo9(DP)QQ{|noCF5cUjB#%i3WC>|h-c^F^w~Dp4sZ%EWk!fMrS~_n>>mPXS-qqUcr$ zL*XtZ?wM3d7Hc1(t=5>?3r1P7RAo$h1(B+fB_T&|W0{Xqn}Cp^1ut0=K>UlWmY{wz zKrWI#t6cG~eCOjb7%{6}N$entZT2|XHddpTz!8C)w0&vi5+^Xn!|6 z{;USVZPNR7Yg3+&v)a$mZm5-qk;C+V*n`d{<&ID-#h=#{h)^ii`$1q?8$!x;mnG-% z3DY2q#GJ;Lv>8LuoW!|5b8a59qKTzLhm?|3`pgBx&VZcVfS4Z(#FS~x~JFq-GqJu`VKDRM{tL5&UBMt*2Bxm6g00O6&krR1hQRGF@ba* z!MW}&OxLbG>wVUhq+98zj-1wr(|o}AY}bz$VGC?qTf1ZImgpYH3>W6@#(pZg;Vwwr z1YNQ_oesYAc(>aURhl+x%H-XZ8x^WPQ4!`p>bH!QELPj-siCbY0hmOeG+xx{il<4q zXG5LQ5OMn2`D%z!ro%0iA7iBhM`Lp2XQA3BhH}n+zCmxQt)3eJHQVJx4&$jcnMH;t z){TEdXXrb|rnP3bmB-A)mS8~p9vUj!M)(Pn_v)6YfjF2$A&pq6# zPRsr;+{BN2P!t-b6<$#HI^*u9o>!Qx=D!rE35msyXK95qLNuXW)8A-zAUdy(gI*6IN8T(O$D0Cce9=2GFPyHE zEq;NEzLux|6OYLFpLj$jR>uEk4jJ*87+L;r?|-IDU}j)p{9p5kN|5YH*Q>2bCh!WB z#W|A37OI`&RyZ0)4XyN(L6A%-7*=D7ElCZqLfwKXm|A21Ed3G~tItzDGw*!%A<&+Ju@*{O-aO*5vdSuZs|f6}@nG4)>eHc&yAc{VIQV!VH!o?ls1Nu8VJMvkTWJw46WwbQl?ulix0H{wO zJYD>Rb?c1!fli=)Enp$oz*E`cIeb87OeN>mD`GGFCeGK@*E~QJ{6Tg2Ou*HoF22HVqGq9!tr5#HHJ~;UpsL_t> za*4!2k@v`hBN-6^wgKnD_CPkf`nFbKwx9@Ex2tf0zP8D2{edfC=>3lX8h-G9a@gtM z^E~JJ0Dk?zd|UA$K=_Ff$^dYki4zF?%*@&a!thwFesGEL_NcQ+_&@-5zrH!M%_yS9 z2|C|?V0JMXrX*+kG^O-j%qDvSH8qj(`hJ50f$Rlw#}_ChaY4)KU;%qi8HN*lSMK3z zc-I4f$iK-`pJn}$ub!2FNBwBSneV)4k)Wj7@$J9t@^gcz`XH;|4t{A~X(oP49;T^( zOXq%d5JFE58c_ItfbaMY*wy|<-NFUaPJ=$ZvGqZH)z^*SCkQ)zyD8^J8eRL7uFoH@ zJ|=K85aY$0OBNtz`HmS+!Zj@Ya;c?C=fShBf|Tb$>~VA3_rSAD{Sja3`$DMlAq?cz zVg%8bXAGGr0I+4Y1lZ%h_qUD}R)F-kulR?$K-TmDGxZXUot14hLE=0OhBTpK>9yGRzC{@x)Y-Hd+#ipecVajznE ze)W*a3^6ZMLsM`o{A9N3EG5NGnjfdUs3Q4SJ}$7H+oF#0+Fko z`N&*APzs&PUEeI05D{B|hij18oyy!%^g7l~C*5P%wJapXYv}8-_Y|O2VU0U6JCBMq z-L0m9F+7W)S~y;2V2NVk>cY2@diPZ{|3WK^{pgy!bBA3{zw*W@7n{v2xy#2zwP)Hk zl%^t=Q?7>0)N~8b5i7HFdGn3w#cf>9N&UvY)A&3k(fxWuB4_%uDCgC@f^x+hdpoPW zi}knJ+6e!y?X;P_Bx zYHBX8bnwoz4!x9c{I+5qJR|_S6INEd`?36I63&O{63xm{j4JaZmp6(_ojAn8CkI0` zxrfDt^KR*Ke^&J+OL?MaBiV`LoOb(^;@Le)-zd45dbs5s`qfleUvyU#!jz7c!Ot90 z&AGZj;|jLhT44Y3yEV>TGC!atETvYKRLmtSAzSDL2r##fF-@Gwrx*L;!1r?~B?)MNneWQ-XK5so zelN5dsl0a~(AVR5`|w^+Dxe=-R^2pdXD7|%$$z>k4}jrCd4SN#`hx%1h}u7i-b`|P zt+)s*<`6n_kkw>1ddDrq=_szn^Rox@QvYEYS0;jcxaUq0r@Zrf46O=cH#2(l4>-OI z>~&X(LrZXFy&*_C;{DhKsGX|_R!R1GMBk3ot@m-$MQGL`DQ@<0pJ~L;|4+E4>~irrK}!QD=gw6?9w?*!gCW><*PTup;OVH*>qqg}ud4@gkKUZy6)7siKxJ z39b;bo|uj^jGHmN&?D5Ueg93(R0!F;;6?6<+s7x_eF?Of(fzEMn9abBgU{(lSrr-j z+fKeBkP$}u(x5Ujjnn4<7G4=bM2Z&J-w@Fw@D6rFSr;|ArV}>^U18iyhp!L856IZGDM&4bcIzL>9Tl^x%mmzgAo-~i-4f-9w*dx78PL2Vd z5}g?5%PX0SNzoy#PS?o#Q?+}(TQO7CtMaZP17@Gc>*(kGcXL5AjYOl9_DL2`i`)As zn8v0}dX&i`l;Tc|Nti28O-2Zo?tTxxm!fN<*_zl;6{60xS=(g5_WX&;H?)ExT5l?% z=c}m}u*t;Txy62i@yW=gq{kFwEIFKgpyA>UhVG!xqgwk#xGwCjD?bJzxt9>Vajw%y zdowYP8nd_kPh2>=Yb~S=Jcifz#hlhH84HwaNlvG%%Vcf`SE3yYuVAWUw5TnJp!%n= zL8blNoJ6L-PFD1zeTifOADb0_an@J{(Z^-9I^IhFO$E`_1=S=-}xvl>v-h`>ph|k z-kD+C*MG&B8MrxVeCBu&TdQqfz0|o{aX$ZahY!>O2Wf+WHpIb&)-b*cGB7)ECciFQ zWKXJ9{Jj@xS;uOWvN0WHtQ0>uY>8)Ea`( zCy)1g$7(&~vqcWU=xNg>``d@$ZKiblUqNDAb1F08H*>iPRqVGz5cf>(*OekCJnF`P z0zfRqObYp|!qYxp1!qPW=}ywXN?mEO`Y?9CRI1FLnK5M=SS>7_+PObfeuU}4$1d$E zvo5|b1gI}z4pKvRd!q3eS6Lt&W3RUFfwLGpL1>~E?xhwWOZcA_JZ_X-D(&N*=P+!> zY6$Fa5@m;%*+u9a;vQWG?d?08&f9?H9b)^pU8rAWxv)hiM>@ji$`7+^Y|E++QtXI% z2~cBPKs=LXdf-Qi++49u*tT4OJ?HN2sR|S81cj+K{tUHv--nBkvyS8aN=saAA_Z9!c7%W>yX-Zl043IF&? zUGhP9MwaM47D$m;Q@5xl;6VP;Ai9nt+;syUGl}uO;USdDxS2Yb=<0A6$YIZ1M7S@}CA(R| z5N*Fh{iC$3rpF6m-+__ktpnrJ%^7wQZi^cs;6Y!-0xfvrP;~34zQ2Z^2ZR4=kYYzIOantG?W&y<@wY=wCUxr6O*f%zg4^FvwV@( z3yzF@TdoU|oE-~)uYF)KZ$22DxesiW5<{mDa2>30*R4KUn`ll3`71u( zbAV*{mYKj^O|+_ANN1s}!5dEJ(L@XOIkOuB6B=xq%>#pB9}Oj)n94dvSV)`0t+e%x zpmbB5wY7Zm&6%rL9%OW&Yv!Wsd>yS7`s|Zqqf^KLM)A+i=!7DAtn9TMuW((n<9JvV zV9GaIDa#B#cD%v0H<9MgMYIUntDHUoXI85vwp(Xk*(h*nweM}+gGNBJbB=AoO!s5J z;2Z2!E~b8;zltfWHWxxbys4V?xZj=C;(<%7VMbDoKdL>{iB$gjhfGXU` zL!kL3(>`PL9;myC-g4c&NsL0LKJ4zn&_Z?Hl{X-@N+K?e*Uuk6~An z{@P*(XI{u8OHa+dN?PN4%NXNKommYSWz{b~KyGQuum6Nsu>23aLf+BN*u}`i5ue=N z*i_j>orZyynVyz`odSwZ$kD{W+3w$yf4Bd;YhhKNYB8*K+pK^VqsyX zr=n*dqo*hPH%`XR`2TN+vZH~$y@@eCov4AelL-`^yt0Tot*DE&wV{En?SI9hY;NI% z|L^>NW1_}aHF0$M_iB75T84j+2?rx93k@SJ>wm}keOr0lw@1H=UK1k(P-9ikJ7lR^`8vTr&L6rBL>;H^HZqGqhB4wt=FP#s4qq zx2T1qlQTXuGs}NtIrvQM49x#q$mUo}%W0Dp)pxaa@9@T%5YbJabTNI+qQfGC)ym9k zT^bi%%YoTSOIKp2vo?Aw%2WEnI(OuxD(T}8Ri^#S396ZZo1IGk$g03TSQixKAQrY7C@?tU7xX|Q z&~D6PkQZRgnC88JKF^GQ$v=WfjBJ<~g~G>JtF$4cbS0wU`>mGf1xMEJt2v;s;zgY# zm8n%HW)?uV8W8z~3TiMxP4$})Q@n&jyb}>Wl_e+F4@Vn6o^REnDtwo7XiT5?FC07D zwrnXwlz1|h#iFJ!JbfD0_QH(@Cx_1)c+`EWc9_lS`=`cLYlpYO{-u~~7_nD0yshnx z1?hQj`+jlXv_*@hw-(yGSWc6k?jQwQ@f&>re)`;fiXXx9Vycoa&mmTbh0~zMbEHzJWAlVSDFWY#BOT zpT8WNd33tM7RCP1F76>FCk!G*_1FinzPj|-;xutX(-a`ML;;~_FjKNF;9VBX*UiuA zpvC0GD1R8r1{6bB_QH!4ni^4`?L=_|8xiqz(_sQ*4eGPDTdi}&r|_4$(XF`^XZ|x7 z-{3I1(fa7Q1?&4{XR1uw7XoC5VgWy6*!mYJcl4Vk;o36GI<)npb8P|Gx9@{RJp~nU zQV`(iK>-!-3goJ411PczH>B#p?a_wKlg+Rlaw=i=)XF?$N{Llae@O-zHjWKlYVLHn3) zN>C{_hLmsMBg4v`#@L#Y`wU_Mv8WAwebY8~xP4V=U!M-k6(I!!t-39#J%;X3$N@b= zS;XWbveF-|X%g|IezziJI<>oIMYzl@4OHsI3`W03>8;zPPO3t3fw~D+r8|xc;Nj*m zfw7lvV+JvThCEU}f)QoNG7jkqCT@7LF~B$>ek*4?RVv)n(&4*E&60e6Zd=^&)gkkh zMP`uIyiz;l)B2;jkQYMa!gcz3Ja-v*0bGq)+!3cy0>^2on!cg-x24#()npA`7jA zUO_tY>yfkgPzoh=(7tMxu*9;pOJ%lzh3I5 z?L;1X_o1q;JwB#~Wb+8LdsERf|H1o#e6#p!z>q_ea2p4Mte4KZESmNm=8s6 zCY(Ryb_5k7ApY%#!{PvsTG91sy9U1COgUbhQ@48$4_~l{2O;${2ttPg>T&hBNnJxB z3bZr7V4yX*o;q{i7KLisC#S=dKWzR(gr5v_5 zS~GXtBQz&bl;`(aSWQQiFc5BHrDzNIM!yj5D3>+Qxaeb`VDGPxhH_>$P^@4Argj=4 z4xS)Lgy$TUhBo}bI=FA*$LvBTSEvacgBr4lZLrovreviVVvNbUkk%~{hn^#xMk1kK zCh)TGsMDvdof=))!DAZGQvUTI2_?^_QXXINi*LeuHp7YyB@{A&pI` zxl|{XxzuS=K)@)QR~yraRQIQ&^Ka*b&LPbn&nQ>lJ%y`KTJ@++t|p3sqhk#Kwt^JW zca!4aSZAjLL0}cT#VQSgeh(S|KNjU4>xBz+b5IKbI7dOSy-gy#vOP zgzso?sC7;0A|G(bkzaT(io^i#ibE-^jpBe0(*<-kB~ZmAS4gR^b(XD1mze_lgjRDH*gQ#nVI%lo&S%gmC=V~%3GDfH}o2ZuUEK>>KA3ydtiYK9ATxcxRfa)|l5u<6ED#aQV zI`@>FPWm%ues4be8KzaxZI8I4St$DiZp)1faM3bU>2=ZKMT4WxH=&J{CVyW`4>x#G zNl6j(Q%O<5AgHv^9EjG~bmC3$EbU$ZNLqV=lR9DGyC=49L6qQi)hRBz=&F|BKRJG? z$d3FK+ZH6-6OtW?sE(B_QnP4j5}1mw9a@@rW|Dn=`5IyNd8q!Il{-46mGpGqfiQ^z8QluOzC?KJUNDT-f3P+bBXHLX;vB5CjA~snW}Zj?@T93n9EX?|pbP@6FuD-PxV}v>*Ok=I0eE z>!O@1<1$t56Z#C7_hq^*rF|&i>vBM&+?tM0u1K>ft@TN{LU?l{Ewl)nMQXabnH79& zKbF_kpFEzY7b0Mv4!UrSY~3zgUoLe^JZz_v4|I-aL1DA{Hb~3wD*D7(PK$m&5heS8 zJbMviT_a@t#$snQ^YU#K$by@4oQogdk+xiM%Eu(Dvtw8AeuqhJ*|)1;3nn>Y7-&su zk$GaOj3}3psRnPB==c?;>hP1LH(h4PT8Om#yUeoqkT>S$7E|3Hvp>s7cfixjYR#Xy ze2^9Xfh9v+)JS!eVLl=^jOp}m2P^s>abXABi=hKEt&!1nFR*@EQqoHt@v>6`1*Bh* zI)#BY2PN0V`**6F=#!q2d+ha>_Hs}M>zOlc%aeQf$nAygb$r74YZ7QtQT%x^M02fU zT;Rh_gk4M+jI?Im1VMwPRyW{{D!Q(BtIzhtIB&0ame2~DQ9;%t-dAy)ml;&sVXX*xB2z zY4#;)PddbqDfgV++zQb|r{xc$M8aEKqnkU$)M0T%0C{vGP_o~*6}#X8J@p5+ zKj{3H!W39y%J*oCq*P4%a`5*<58ISH|NdF#kU}%c(#<;c1}F+Vh??7DwktTsSx#A{ z?&xyQIie<*>@{ZI;g%EAKuO-g>nCFkw!T!tk0C3Y)MUji%w$VVBz2ROqwQ(r`k>J_ zpm6^+;q7e*=d9MzjB0RXf{xdGo4S1fjelfUfF54Gpk6ubRDI6icyd zu!!wWKvxh@69{5C?a*i}%Xy78qplOfCoGW$Tb2 z;$qIFA}y`Um)o=XW!q9OfD~j+4n=3B*zX{?%X{!#r+N%BBu_6*3At{c`SOyjC=yYp zf5^UsKZPs>Qp8NEsZ*-z=>#+GgbFeBIG&U=PQK5ER?5y1r<5%LtA+v^Nw9^|KkJ zKa!vCih!y>BSI>9rc~KpTQPdQgNcNC5D{1Rp>u;)e;0smHTK9zlk3kp^FGR8Km7YQ zt#7k_db6b~i>kI+t#3KM>+(^|M@E9>M7rgmF|`wKyJeEXV2g5ds4|CMnM^I%qD=8g zr9+j>{bShTWsF6+!)CkfpNILstnfll*t>4kbN+85hGLNzYy^hYc_0v26Qs#2FK=pl GllNc3Y(Ufi diff --git a/ws2019/ana/lectures/linear5.tex b/ws2019/ana/lectures/linear5.tex deleted file mode 100644 index 0016c25..0000000 --- a/ws2019/ana/lectures/linear5.tex +++ /dev/null @@ -1,259 +0,0 @@ -\documentclass{lecture} - -\begin{document} -\section{Gruppen, Ringe, Körper} - -\subsection{Ringe} - -\begin{definition}[Ring] - Ein Ring $R = (R, +, \cdot, O_{R})$ ist eine Menge $R$ und zwei - Verknüpfungen $+, \cdot: R \times R \to R$ und einem - Element $O_{R} \in R$ so dass: - \begin{enumerate} - \item $(R, +, O_{R})$ ist eine abelsche Gruppe - \item $a \cdot (b \cdot c) = (a \cdot b) \cdot c$ $\forall a,b,c \in R$ - \item $a \cdot (b + c) = a \cdot b + a \cdot c$, $(a + b) \cdot c = ac + bc$ - \end{enumerate} - - Ein unitärer Ring (,,Ring mit 1'') ist ein Tupel - $(R, +, \cdot, 0_{R}, 1_{R})$, so dass $(R, +, \cdot, 0_{R})$ ein - Ring ist und $1_R \in R$, so dass gilt: - \begin{enumerate} - \item $1_{R} \cdot a = a = a \cdot 1_{R}$ - \end{enumerate} - - Ein Ring heißt kommutativ, wenn - \begin{enumerate} - \item $a \cdot b = b \cdot a$ $\forall a, b \in R$ - \end{enumerate} -\end{definition} - -\begin{bem}[Notation] - Das inverse Element von $a \in R$ bezüglich $+$ bezeichnet man mit - $-a$. Ein Inverses bezüglich $\cdot$ existiert i.A. nicht. - - Die Eins in einem unitären Ring ist eindeutig bestimmt. -\end{bem} - -\begin{bsp} - $(\Z, +, \cdot, 0, 1)$ ist ein kommutativer Ring mit 1 -\end{bsp} - -\begin{bsp}[$\Z / n\Z$] - ist ein kommutativer Ring mit 1. Multiplikationsvorschrift ist die - folgende: Für $A, B \in \Z / n\Z$ - \begin{enumerate} - \item Wähle Vertreter $a, b \in \Z$ von $A$ und $B$. - \item bilde $a \cdot b$ in $\Z$ - \item $A \cdot B :=$ Restklasse von $a \cdot b$ - \end{enumerate} - Nachzuweisen: Unabhängigkeit der Definition von der Auswahl der Vertreter - im ersten Schritt. -\end{bsp} - -\begin{bsp}[Die Menge der geraden ganzen Zahlen] - ist ein kommutativer Ring ohne 1. -\end{bsp} - -\begin{lemma} - $R = (R, +, \cdot, 0_{R})$ Ring. Dann gilt - \begin{enumerate} - \item $0_{R} \cdot a = 0_R = a \cdot 0_R$ - \item $a \cdot (-b) = - ab = (-a) \cdot b$ - \end{enumerate} - Ist R unitär, so gilt: - \begin{enumerate} - \item $-b = (-1_{R}) \cdot b$ - \end{enumerate} -\end{lemma} - -\begin{proof}[Beweis 1] - \[ - 0_{R} \cdot a + 0_{R} = 0_{R} = 0_{R} a = (0_R + 0_R)a = 0_R a + 0_R a - .\] - Mit kürzen folgt: $0_R = 0_R a$ - Analog für $a \cdot 0_R = 0_R$ -\end{proof} - -\begin{proof}[Beweis 2] - \[ - 0_R = a 0_R = a \left((-b) + b\right) = a(-b) + a b - \] also $a(-b) = -ab$. -\end{proof} - -\begin{proof}[Beweis 3] - Ist R unitär, so setzt man in 2 $a = 1_{R}$ ein und erhält 3. -\end{proof} - -\begin{bsp} - $R = \{0\} $ mit den einzig möglichen Verknüpfungen $+$ und $\cdot$ - heißt der \textit{Nullring}. - Nullring ist ein kommutativer Ring mit 1 ($0_R = 0 = 1_R$). - Dies ist der einzige Ring mit $1_R = 0_R$. - - Begründung: Gelte $0_R = 1_R$, so folgt für jedes $r \in R$: - \[ - r = r \cdot 1_R = r \cdot 0_R = 0_R - .\] Egal welches Element herausgenommen wird, es ist immer $0_R$, d.h. - $R$ muss ein Nullring sein. -\end{bsp} - -\begin{lemma} - Sei $R = (R, +, \cdot, 0_R, 1_R)$ ein unitärer Ring und - $R^{\times } \subset R$ die Menge der Elemente die ein Links- und - ein Rechtsinverses bezüglich $\cdot$ haben, das heißt - \[ - R^{\times } = \{r \in R \mid \exists s, t \in R : s r = 1_R = r t\} - .\] - Dann ist $(R^{x}, \cdot, 1_R)$ eine Gruppe. - Man nennt $R^{x}$ die Einheitengruppe von $R$. -\end{lemma} - -\begin{proof} - Seien $r, \overline{r} \in R^{\times }$ und $s, \overline{s}, t, \overline{t}$ - mit - \[ - s r = 1 = r t - .\] und - \[ - \overline{s} \overline{r} = 1 = \overline{r} \overline{t} - .\] Dann - \[ - (s' s)(r r') = s'(s r) r' = s'1r' = s'r' = 1 - .\] - \[ - (r r') (t' t) = r (r' t') t = r 1 t = r t = 1 - .\] $\implies r \cdot r' \in R^{\times }$ - - Wir überprüfen die Gruppenaxiome: G1 folgt aus R2 - - $1 \in R$ ist neutral $\to$ G2 - - Bleibt zu zeigen: $\forall r \in R^{\times }: \exists r' \in R: r r' = 1$ - Nach Definition: $\exists s \in R: s r = 1$. Zu zeigen: $s \in R^{\times }$. - Offenbar hat das Rechtsinverse $r$. Aber $r$ ist auch linksinvers zu $s$: - - Wähle $t \in R$ mit $r t = 1$. Dann gilt $s = s (r t) = (s r) t = t$ - $\implies$ rs = rt = 1. -\end{proof} - -\begin{bem} - $0_R \in R^{\times } \implies \exists r \in R: 0_R r = 1_R \implies 0_R = 1_R \implies$ $R$ ist der Nullring. -\end{bem} - -\begin{definition}[Körper] - Ein Körper $K$ ist ein kommutativer Ring mit 1: $(K, +, 0_K, 1_K)$ - mit $K^{\times } = K \ \{0_K\}$ -\end{definition} - -\begin{bsp} - \begin{enumerate} - \item $\Q, \R, \C$ sind Körper - \item $\Z$ ist kein Körper ($\Z^{\times } = \{+1, -1\} $) - \end{enumerate} -\end{bsp} - -\begin{lemma}[] - In einem Körper $K$ gilt, dass - \[ - a b = 0_K \implies a = 0 \wedge b = 0 - .\] -\end{lemma} - -\begin{proof} - Angenommen $a \neq 0_K$: Dann existiert $a^{-1} \in K$ mit - $a^{-1} a = 1_K$. Es folgt - \[ - b = 1_K b = a^{-1} a b = a^{-1} 0_K = 0_K - .\] -\end{proof} - -\begin{lemma} - Ist $p$ eine Primzahl, so ist $\Z / p\Z$ ein Körper. -\end{lemma} - -\begin{proof}[] - $\Z / p \Z$ ist kommutativer Ring mit 1 (siehe oben). - - Zu zeigen: $\forall A \in \Z / p\Z, A \neq \overline{0}$ ist - die $\overline{1}$ im Bild der Abbildung: - \[ - A\cdot : \Z / p \Z \to \Z / p \Z, B \mapsto A \cdot B - .\] - Wir zeigen sogar, dass $A \cdot$ surjektiv ist. - Da $\Z / p \Z$ endlich ist, genügt es z.z., dass $A \cdot$ injektiv ist. - - Angenommen es gäbe Restklassen $B, C \in \Z / p \Z$ mit - \[ - A \cdot B = A \cdot C - .\] Seien $a, b, c \in \Z$ Vertreter. - Wegen $A \neq \overline{0}$ gilt $a$ nicht durch $p$ teilbar. - Wegen $AB = AC$ gilt $ab =- ac$ mod $p \implies p$ teilt $a (b -c)$. - - Weil $p$ eine Primzahl ist und $p$ teilt nicht $a$ folgt - $p / (b -c)$, also $b =- c$ mod $p \implies B = C$ -\end{proof} - -\begin{bem} - Ist $n \in N$ keine Primzahl, so ist $\Z / n \Z$ kein Körper. -\end{bem} - -\begin{proof} - Für $n=1$ ist $\Z / n\Z$ der Nullring (kein Körper). - - Nun sei $n > 1$ keine Primzahl - $\implies \exists a, b \in \N, 1 < a, b < n$ mit $a b = n$ Für die - Restklassen bedeutet dies: $\overline{a} \neq \overline{0}$, - $\overline{b} \neq \overline{0}$ aber - $\overline{a} \cdot \overline{b} = \overline{a \cdot b} = \overline{n} = \overline{0}$. Wir erhalten Widerspruch zu Lemma 1.15. Also - ist $\Z / n \Z$ kein Körper. -\end{proof} - -\begin{definition}[Charakteristik] - Sei $K$ Köper. Die kleinste natürliche Zahl $n$ mit n mal - $1_K + \ldots + 1_K = 0_K$ (in $K$) heißt die - Charakteristik von K. - - Notation: char(K). - Gibt es eine solche Zahl $n$ nicht, dann setzt man char(K) = 0. -\end{definition} - -\begin{bem} - - \begin{enumerate} - \item char(K) $=0$ oder char(K) $\ge 2$ (wegen $0_K \neq 1_K$). - \item \Q, \R, \C haben Charakteristik Null. - \item \Z / p \Z hat die Charakteristik p. - \end{enumerate} -\end{bem} - -\begin{satz} - char(K) ist entweder 0 oder Primzahl. -\end{satz} - -\begin{proof} - Sei char(K) $\neq 0$, also char(K) $= n \ge 2$. - - Wäre $n$ keine Primzahl, so existieren $a, b \in \N, 1 < a ,b < n$ - mit $ab = n$. Dann gilt: - \[ - (1_K + \ldots + 1_K) \cdot (1_K + \ldots + 1_K) - = (1_K + \ldots + 1_K) = 0 - .\] Aus dem Satz vom Nullprodukt folgt $(1_K + \ldots + 1_K)$ = $0_K$ - oder $(1_K + \ldots + 1_K) = 0_K$ - - Das Widerspricht der Minimalität von n. -\end{proof} - -\subsection{Homomorphismen} - -\begin{definition} - Seien $(G, *_G, e_G)$ und $(H, *_H, e_H)$ Gruppen. - Eine Abbildung $f: G \to H$ heißt Gruppenhomomorphismus wenn für alle - $g, g' \in G$ gilt: - \[ - f(g *_G g') = f(g) *_H f(g') - .\] -\end{definition} - -\end{document}