From a5a398d72bd762c45d69551e63f717dff785dbef Mon Sep 17 00:00:00 2001 From: lcw Date: Thu, 30 Nov 2023 00:31:12 +0800 Subject: [PATCH] =?UTF-8?q?=E5=AE=8C=E5=96=84=E4=B9=A0=E9=A2=98=E7=AB=A0?= =?UTF-8?q?=E4=B8=AD=E5=92=8C=E4=B8=89=E8=A7=92=E5=87=BD=E6=95=B0=E6=9C=89?= =?UTF-8?q?=E5=85=B3=E7=9A=84=E5=86=85=E5=AE=B9=EF=BC=8C=E5=8A=A0=E5=85=A5?= =?UTF-8?q?=2010.8=20=E4=B8=8D=E5=AE=9A=E7=A7=AF=E5=88=86=EF=BC=8C?= =?UTF-8?q?=E5=AE=8C=E5=96=84=E7=AC=AC11=E7=AB=A0=EF=BC=8C=E5=8A=A0?= =?UTF-8?q?=E5=85=A5=2011.11=20=E9=BB=8E=E6=9B=BC=E7=A7=AF=E5=88=86?= =?UTF-8?q?=E7=9A=84=E5=BA=94=E7=94=A8?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- src/pic/~9.1.1.png | Bin 0 -> 212057 bytes src/~10.md | 275 ++++++++++++++++++++++++++++++++++++++- src/~7.md | 35 ++--- src/~9.md | 148 ++++++++++++++++++++- src/第10章 函数的微分.md | 138 +++++++++++++++++++- src/第11章 黎曼积分.md | 222 ++++++++++++++++++++++++++----- 6 files changed, 752 insertions(+), 66 deletions(-) create mode 100644 src/pic/~9.1.1.png diff --git a/src/pic/~9.1.1.png b/src/pic/~9.1.1.png new file mode 100644 index 0000000000000000000000000000000000000000..911200921255b3c015286fa2a115a095ef1b7282 GIT binary patch literal 212057 zcmeFZc|6o@8#eB~+iq=&q>@w;LQ)}wyCgdaV;M^kVhka~7~0F8J=x067-N|QV{1Y7 z>}JMN_GQK-%?zgDy~h1KPo8)C{qy_tozJHj#&@pob)DCF9mjDV=Y-xc(%!T4$W9&} zo;|uc*KYFg@X~mAwj}+v9sH!+WceKU@`uk&?W;V+9Y<%uldUdS46pF;lt%CRb$c6l z&U;VC%7=&Na3A;IAGo{o4|#ajb9Ap=F?(P~9p()hHcwk$H!i0mQZB-)=)2-?zLj;7 z)+gQBfBln_S^eSb995Ml_H*LN{0I#ZK@tCLf_Ln(@dx#!a^@lZd(T#PMY2id zE|i!1#Z=<><0T1xG;7tMSs?MyA?R;OlD~ z5A$Oizkkjj%l!8XANpT#>7e4t>G(_=f=8O5kPs2h*!bn4GtWhwh6Dcf!iU2?J|ktPazHLazUMVWdCuiblSPQB zhN;F4dlO}KNB;p^f6`K?hNtM-_ZPIX*0W0oHQIT@(&jSH2etFsQgoK0qgTw}S*!W> zsNMD-1j`Ex&nOAypUt`+S+>0VK+dVa9;F`ma~NYDHI}C``<*n}E85%HD;ktOZzf?v z4YHNUkI;Ov*UHxy7kN~<`~3OySJgY8sXD*W2EhcD5QQnQb4yw4;9cbeHT=o*@X_;Z zwSUi~h2GN{ns%3-$4(C!w!vj-8JYXd)&T(liLtR`3NcrdN)zJWeY8-%;%)ls+T_x6 zRx>sxR$Me-Vn5hA{&nSdDK_G|Qo6bG^HLrvK@vF0M>kL$aR~`11d^CEA%-)2^>$qP z_Em6C$9b>$E++q#{kq_2O>N7fvc!;2ryAa^?+kG=5$e7;)?l~#Xe&H>fMxzXKN9SR z!C8hv(<}qYBor^@cfRiH@2{%-d-AUN4f{~Dxq-sCW9Fh6K36Lo^1ScoXA~UG@OeBZ zRv3pFEI2DJE?#UrQ~m1An{yIxjo6Cd!uo z`0=A-q7H_s>F-dUKB}*yGqYU$9X;kd@p-@MgYR$WcU;Ld$}c!Ow=0mgcKZC!=lnzW z^Z91JYx&N;!A_&G%X`3o@KAJQb^hWGFLS`*bn%^2o=Z^xBor zv}#j-t`k5{1y?uw9qeZid+HQPo$CxW ziTvH-tbyL%3PDTX;J+A`l?ELSp4w4Z{kD$rqSKOx=iHayC-9+j@z^}!I=#g2zK&Md z?i7#D#%U^jaK!Zd_EL{q(#?iS?~tSM7Rq{OZaBQ|%vOU(qkhC=2Qu!&ao8*hhc)U+ z!NYyvves~V)qHWe*Lb7v+JfHwo_F2{RPFWj_2Hwn$YRlnsi{C+@-Bxd)jv#lkB23< zEFLaDepo?AaWNU27c6_G$;G=T&40vI8d6k3@vIw8l(8C<4SpkVK$Wp2;Tz28FR~6i z%R8toFA&VoC`a~XGTGi~B`g^--0Sw%O&I;5@RWn-KYPUt8N`I)qNDEpREjibTxchO z1QwPi=~r7UaNvSCOFG7MdK(%qG#79-Ro)aC&;Rv;^IYc&1!#z+s4V$9PjT;q~j+Q7&zGk72hL ze4?lSdBr)&O_MdE7#bStw>q2W4~5gezJF4L-vEh+u$#w-fLqmu_usg@1g$2V!ZdgW&#QJ@ojdo1i&&q|QQy^!4<-Q5B&OiYdP( zzyWN}-MigH#i>&7%ZiITf)~T>2Q#(8sp0m&GAE~}VnI1+Isa0v)vqH*j<`>Eq;b^X-=-MKd$vo6tR-Z7N66;h zBmJk+ny?oO~_m1l6;I#lVGRcY8BDmXEGHT>6BrYRH6al`Y!#)Rtb>BiZ{ zvFs2u1>$UOiVXq@)DU=D&ehFjQpJ=3ph1CT5__-7U#PEmxx;k0Eb?oc28&VD@G z<7a!gF=&jchYyxK>SG$ct*98RW!2D0dFl))LYbY7O=^3Z>cH8`3I3#@ByjliPe<7^ zjHG9g;5Pi4q%qZFcyaaVR3B=$z8o%KY0B#Q_2=Piq1x};*o)C2RJ_#bHSW9K`>`ps zx3mnFIu5%b08$x-PRxYGCV|CZb$w}rD(O>oG3V%kQ1uAUhthW6P92{j!X`S$UJE_wc~IXym=HBh(K2lqkDqX|`g z%y`MXYsA0Z+zKgc5c$5Put|V`==gF$@hJ|wZk-q@s!@C4y^+^I*o%ziPZCrS`hyqd z5D3}SSj~w-@C^AFhUC8a!`e-`X!j*@Hv`*aRNmIs=7FNY$=K#X6iRmpmS?^I!PvpK zZQJHImFz-}71wv4_#AU^|Kb!OB>rn2?H=FJOJDKtYrcQjMHJWZ%jsLewiolS{#aUq zH${mQ`TfOxD~ZtG8~5CC!{qY~&-p}0WRu;OrrIGkHU{06s%VvpU{0V=v};dpCHz@d zR+egQpu?(iLuqbqBge+WV}VzIlbM-0H1F)>WTmScN*k>k75^vuuSRdax@&?O`gjue zoTwnc2F_9{ys{|8zWEXhQriKhRdnl>Ot~CT27r`*&}92Ijl64@(QQJaqNC$y5Pygp z+b8v8|P7wR%Ce~p1Vy^u5$L-Ln z`>up*HM`DM)OTpC2k9FdYZR=y^(n*UQ08;kA2y!&B$_lANBf3yAv`|h=aKjGmpMOs zm<&wF@ZMvW?`Ev_=253oJn<0`y9eliE){`&GM?Agr>~J0T;WbS&+=h2Y30U2V*<={ zR&^8FE&sv%^iSd(`zL3$lA8;r)mh4j)&S)!bL&UDCHp0KK0i1>F7NFXH{za}IU zk*oLFzos=jLE6Dfn__YXsB)ZRfqQV6V7?3v4J61?a}W;a!MF6Qr9FqUg?xj9;lL70~jV|nL?%?%2ZBuHh ztkTFIQ9A#r2L70G2Q zlRv}opUlffM`{qmkjid`OVw$A$pEcp!WlUo=RoN*(q{5|%&8;Pzs8Ofj;^4i?)5ga z-l=TWHn!*M>%tw)aN36aTl>;{Z_j|H?|oT`qfU&UL6Xt;`g36R-_7kR=EjH-U;k=R zN&ayF=vL2nLjD6vb|2C^)?Ii`PqN$4-X82r+t{Ao0@LA^JGCDCFkfM`flyJ@6zV9t zFvmOo{upB0W%1_)TpsTKWLOAol&3i<>Bl`@wMCJ=O!_E&^`*`IE-gQjQ&Q!%vb9D$ z7Tb%ylo$LeC53`|imlxV_&4OdO}^yp0&$d6%mH~7zp^w<;U;X=`J(cXvfT_0J!GBD zY|>ck;u67NBh)zKr;oM5?E4*}SXFv;4~GC5B94Vg%bYmzzTww3Y1*?)&-}DLj25!q zCB&2iDYCpx7!4-MT9su(AK#U9HM&s;DMEJex)F*|o~y5o8LQU3CLFRw^{L-LRz_0t z9z5&Rx3|$R-mK#0vb6h}TUV8UvhMA z$?cM3?y97Cy-Qnfh62PlKb4@u2Y}7*Ddx$0$i-6Gx^Xt%nzsOf@lb6&9_pEYSUsph z|CO+UTRhsTyb+#+dRk2gdl9^l>eEr$m8DH-m8)|%R%67AsNBzQ%IN8@Fjim5<^lup zN~844l~7^HZ#vQ}srLn$nIF)>`PqB8aatd`IU!vZ4{J|Xqm-4Gt6E&X`C$Ycm<|9G z`l0^XqhPHJ1MJVE;mXRaamXCx3&@3z({5(gPP$Ou^(mz~uTZ45mu{#Z7al<6jWLTT zdrnL6_a~wi89f79(Q>uRnZsU9BFyg}`G`+zLROMOymS#^bz^8vl%kZYv9z?*drvUh zVztNS**agjAo!uuCcK);j|FX6Cuwn#?b+3n<9 zzm8O8ML78)wBp`7{W8@g;E1~bd? zj!jV~D2m)!ym#_n+<`l4)5rXu04#MCyB;xPK$e!4_JLNP@$!`Ph(leH>@t$3BIlu_ zWtBeDRpz{`h2eQf3s>H1YcojE2&vWoWV(9`*<)FFbon{kN}TK(PC>Gnm4Yh=jK!H! zC%#W>tXJBGa2Q;juPP-wp!Vu&8h zB6={?;4YMeU?b@TKtbBXmt7H1&d|azak!IHx6WFp7L|8+Q%1LAKcw?Bv5(W&&@}H( z00!Cf_Umqdah5aY2Z#gRel>2G@m8+l{P11W??d*UUY8rfdfQnYau2=;Q~jgml`R~D zdj0wkH`3FPOcMUq`#*&>f~%odj6;1ruSlz1z{|j{dPp^wSrbeFXNP~TR!AHlF zxr!V*H~0CcjXSJ=cy05#w!fDD2$=GIFKXfoenxzSg_+sEet+xl&AX^9zQmsky|{Xy z1%*=T_=0kpP*@oD?~7_~x@Zm9wwHIR!{~@nw)@zpP$1gMuqWk0 zTrst)g-9?MY;&9h1#l6##;2E<15%~W7YikSDASb)IxyeXNw*u80u$$W=_Pny_FFAKa;gmuk z>;W03YhGJRD?nP?EULv+S)HPT`Z{|<*_KeFwjUkO1l;xm7ljF&Hn`Uu7#Iep+u(kiaSg#9AR zKDwFs7#!AMYeOX^*d*>M>aM6On})!qG87pQlU zm9(MnnKfm8k@I5K3G_STM?M*0#xM9?Q4ZwX_*5+6sU2c!RqN0{I5;!4rBBP}d55NY z%gs6n@`G~pbFR|8>XCKaZ|s8K8O^0f#yD!tvR`zDgcPG%rDz* z|Hi&NPv3(SM4Qda@N0f8WcT2mtWCuiz+sJEZ+$1Ye75eFx3H2&>ahPPk_pIO$?C+78Ec3MPRwhsqYjW^Z(&X6_X1p75 zbgyg^8_dIUuL9H(6@r!rcwiv>VUdwIkj}~ZCRy&2EeUu)6!^=wm*(gvkp+w|-%ePJ zll3F_9ZXOpyIabw>atml5vl{n5MxpZz>#$qxEXOD|KP`4d1j4TgXIzjKal>gMewsN=eN=g^s0v{{HRbaHrsb1D0N1r9i^9wzaj@ ziC$e@J(i)75Ph#t>cHg0^fU!`0BR@9fSeicRCKs?l?a&P2b z_j3{Wz@jHN$hnWJ9zavQ-K*#EAwm_PgnA`>^Ix#ufb#ZY~r1N=tECPGR z;?A9H=pP*xX$LMe7&+z3WR&hAOP)DXXpAB=%z>(-I#QSl7<7t9LN&lg6`yKq*No1L zKNGSmDJwe<4ui)zIXTZR2VYrdkVC3tZFIq8J`RtI#xUh(Tj8{I z)@t48@@Rr~7`nQmK2yRT?p5xA{ru@$;1yP2O>a$r~L`Y-i;3!gfckX5nrM&Kf$AoX7R zwpvFJ@ppmzQoI}ep77H2+4a;K=taXw)-c{@+DH|UF*r~u zIeI#lL_ah%65g9{0?wmv3ZdI2a#bO+aOZXva$ZD7Q&b26t8s=GgE`W|XXyy96i*F6 zH5k@(Ki6u!AC$v7!jd6W4XoWEnNC4Fs{O6ag522UHFSxt7-y+cXV*oV_E2fl&nRt? zRciw?d%OKS+cSJRl$*xJ$P(IsEb#nJx^}LUnIpjm&~PJ0O=)SVorT9485t}{K9<~y zmxKhu7OgGaQr$gF{9qw>nnImAb)H-3-x9kd~gV z!S4RW{B@7=L?*`9u*GNHOgStCksC6n$HGNNpVq&$qmyn+M9lke}K~P{@a-vsu zf(p^g|7`5~hb9&l(;nwwt=1W#yRFR)LlLHVMvSVmHy-hzG7##rQ6I_jzMn<$KW_`_ zY0}2h-+r=kgFGd9Om)=*Jz{EP>J+=x(L0BdE*ERAk_d>LeZ(^fUtVdgU^(L z`NT)Hs}Ju|XKt|B)GdYKbJuEj;KB*yp^L*iUL7nG%4lgJ3TTi zU$U%9j4jK=rpN|QF%IsJ8(K^lfekKV72MZQks54kVI*_U!To}i#e`ZD>SM(@n7z)+ zP;62BUE#F-FoE)Mc=zXPDX9XUhjrx-1`O#-dF8@RVn87dGuqobF_o$$oF$>Zl;6@F zG%g)u6o1R^#*MH1QSo1Bj{0UMY*3H`MTU+nH&KzoxK5u}t0^5<=3L&CBNMU$v`YmV zItF|nJNSLA{{yHrWuWMrR3S8{tiY`{Tx2arB(Ih?7Vb^RQU`+f$kG2u{SW_ml3lab zWw`S04VDG?=V&lz-kt)4dRuQT`}yJuuCli&b!wcW@t ztqwYEuvPbXp}wR3Q$Y&_$|JEo_`0I^d*c?^M+_bg%!OlA1hBA9cl_LTMQ1DLy`{Kt*8qtP4mOl zkKAS$!XcwW!B`DNtf*|wAdz(^mT7cKOo}YNXm~97R-8|ii0k71{%(VAJNsAIfsj)) zh6wi_A8rb&E8TYMGr7NR7?O$WYit^2bPcbs^I8%9M*Q??rc{SsnsNRdDk=X5&;QU6sNKvWU3*jPcZiBV8YVCrEts<7prD@#mnN2=lQc_EzymF@5CUi^40`}8%^VB6i4cmdCz>p6qHL)U}|Gvi4U zs=RZsIiK29=tHpNrtF#Ht{Be)7h;*K8^zhx-$bVVA$P8JPiEJEVjJ-ek$e0PRr=VL z8G6p!L!mIanxC=rK6<}Q$I|(IuhPr_H7sx|8-6hlw}^>Sp;%c?L%zV^s)=t84%y9l z+J}c8ah6&%Nlf7HNq(txS-grf+O;qmXb>4*f=|q4diAVvXbk1#H9vX{iwsZ>oITeg zvw&q;-e(pu?Q8vg42EGL_*^s}scD^NPZP*keozOwzk4h1-58p$t6QX7bV2M&l=x4n zDe?Dp($Q*|PjzcUpXUoA<3B3}UrROYP{yN+AydLJWOXGe)iO~tK1St@p9CdMaFYed z`ygJF!a(s0xj`6^zd7cudN4yF&%L|Tx1wkXiHYP?Wgl+wtR{@{MgisyU<^}k{f8VA z$n8T$8l3wUcKK;LbrH`d4e`OA2{qMuEsAsuF09H~wM!&Bo&Q5%>>+{M0m)v9u6G_s zc0}O5NtLGQ2DmPo928+p!Lv6U7#VT1o`jHrfMla6^8@YJTQO~w zg!Nx2GGR8z1=Tj0GgnXQ{5@~TpK#TNGB^jBGd(%_t#FFz=Z5_i8%VJ-bJ2D)ss+=K z*SFkpG{eEgSP$2AxKyneGAPiei7eLOpyhPP^BSORIr5Vb2Nr#Fg9!e{h`SGgoz!{5 zm@FVZ%wZDhd`D3e#27K{^mDFnfdFlXWS9fxJVXBn`|A#kyMSyL==YlZx(Yvjn&v7! zFx7fSLng2^W(Y}|RvJ@KEhm&>Q>&Ku`gM>PUA(4is z7^xJL%jqIKwWJrfp^h(naZI{an@*lV&sdlUr>jY|i+?xlh$1{4)L{h~bC>^Lx657r zr-wT!x{fsd>yjtR4sd9Y-oOgdj?)SVsMK#G;b2K@ z7MJ&NRbBYcnJ&ek<$Fn~@0OpD|JEf-W8ip0HVodrpa&)7k@X4_K6foPsOv;UmYB?T zomKWE=if;=f4<8*{;iM*Iap{eTg_zj#@LAcI#UUzdlV)g-~u(9x)a`(dh6p!M>KBk z70&E{CFN0Hzs+)CyBabVIVo-Lr1=XQ^(k(KDh~f%aBR*;V$Sm&|EGxTnp%(zzW0s(`F~2Audpl?@d*yl ztNnR{cJLje+Q5rYfR&{vz!LSTs_Va&;9N56F?5NmbcEaI*QDtpwmI#=pRH>VpM|Sg z!V(y=NWHJ!%mT;qG540wPaRP+I8m$6{r&yq39|j<@|>r7Ec2RI;P>}CXk2dsS7*U1 z+c`Vu)=aC>OS#4Qc7b#&&kLYi0O;e{_@h%o#7XBS*CnYr(o zBCh!M9l~&AFm5vGqNS!OiotY#h1XVd3<_&Mnl=OZBAnhm;-6K;q8vYA;AjRPN7b$9 zk$1%>B#;tip*ErcUmxvo2MQYg!J-54M~gIkVW`p$uOAFXXV$T}w<3KTz;*@0T3=Soq#a#-cx(KH}L;T9Ew3;$vH7CC; z_RT?s}C2-SyZNjXz{Ut7+Fr)EA+!cf33e-S>{s!rXmfg|SVcS@2 z5qG6O0B025D+GronL7#ZEVR98Pk|0y+1+StWL=b|uGlaYp^xurJVkoh%T(Y0!7b*W zvm1;MnYU)Z-Hga_x~=Lzg9qXhPuA8NAa?lcx7_?QFZO~_j_=+Uw>LCW`y`Y0;s;Hv zj_ffSbT3-1cI~A|;oY)+$4WDa__QOANo^e^ayCjGYjoyeziCA7Ao1YD;OnAgg2CX& zuNNRDNVbuhe#@521;{yofFpLO)~%D9DSAWo`S7Z4b5w|sLH7xO$Yr_*ql}N#B-)5P~utt*B zg$ptO?_8Gs{?yd$szG*pi+)*%T1Yl$S+j>KMB_}FT11yNTzB=MWvqVmOZvffn)b7=~B0F3gG+wT<5quCO1_=0e4_YVZFw;3OS#v>(}$xoeNFmV-ZL zCM88*WaKa#*#4xD_1k$IKdpDPOJ**SvT727*R{AC#gR6r?8=;+Zz36cra9XOPj4mq zjr=8?u-_#{Chx^Q9mAJp0U&SS8?vayEQ1ny4Wfv{9*e=>@-B2bmHwcwaf|j5+9QP* zv|TjLiciRh6AN>u44Jd1zj3XSJExhO=d=Us+T#vny2RJ7?|xJ{9|^1g&d;7b>nD@v z)>Mbi%)Nn6GItW^OOedxQ8)pSE>ogFEG(+3&1o`c{Dc~}MG?3G7`(hD<;Oxukl{kk zl*i4@iEF2M&Hk4BbWLk;`CF+Uty+e?N<2+A_DFNisBtbz(@<;gHZGxg1KI*tz5%NX zWWItT>97!rqcK_zH`a1mEQD*3)C6Xh-?17R7FNb}=Kv8!HI4}?uI`|A0WmW>fQNgh zSVxg_ISPLCvMpesv=UGCil+2nbekS3#khh4H?oef^}U`5mNk^gVHx@9B6_ZiTL&53 zaj|`PuP3ohsIvttXR9%?;6_g(*v7+pw8bsm%{q}~WyK8;S`n6*Az5O~@gRa4sTU(k zkM)bklFAQ8wpnaFcghu~CSnT|-YQ=d*U|bWC1p5-or%7(UR5=y&dy6?K4be)?CmbQ z?`S!KW^Ao|48W$xu5M#ng~s6T7*nbS=8&U{p&o96Io;gz@$byii>IYKMsUZQY7t9! z*sF#Dw5sywl>DET;g_zs$QHZdCG2H!81)j0ItLVaLR$IA{ZDWnPPLCpY!$%Z_PPC* zFCLzNQ3p$b`a?>_S^$-CegMNNBik8jqGU&H7Vuj+pfFg1ND{e^qV_2Q*-AD<_U7trSIQoxVf*K5>YjaZgX@WhAz8{3bOkX_911PjOgBG7dp6Dzta= zBa9ULUbSir-D087;5#|4Nyyo?Vdh}fc~u+Ir#bF&9x~e;fDoWd=nsWQN7D_4dfX7e z2ZIMTRMw~jDzmsDon&*{9&vnhAYpS(d?p{O#~O5TG$k7+*hZ>(v3$UbII&I@V^pJ>UB zfke{#AJ<`G2yUo7;h`^pFB^~gSBWVpFdzentUE#M?LC30iS?cDCyhsIc&r1128>UA z`7MY&lyPWKPM;xjri!24sL7_~>4(F69;v|GXO+K6%F2^FGSZzhh|a0QoHZ#Ar?Lx; z640AA*`@i%whO>xRQ(>L)*x=|pUQmmfP)98t)v&mW z(4Rx&A}6>7h}5dh6K4&4G=}MyN!>j?=$xDeuAy#pxlxIl8Gg15g{dX0|A>hm+@mz~ zwbrF2UTUFE3Ao+x|Yb>AKF(-}H z0V(FQd5OV>a&9(%L-UkBb*k|?IeFZa>Zl(D&tMmz8V5f}6(lBpSz=bQTaQrrq{FGL zAtV|;X~fD*`v*7?d5m;72cR);0Qsapu%6+8PedByTJo~3An_dAHqrarw5;n|h$VG- ziFV5h&7pS&JBu#Y@1Q2Tq|LNOFnCN`A#|hr#EU9fXu;OZ|qe z#D@9_qqVNFHLxrA$d;El9e&2Sr+bV;@vTOkSj^D5_qD8%X6D+`b@KB5#e;_z8y}gN zb=~2szCT#IIxx%}&tp>hx8P23)A-l;tN+2(JcoY7=d)(AqN`-@iTyZeJ!j6coKp>U z4_(r5D2+?9{6$TXnT*9i=LG$&hO%3!I5d$~HIE@^aArI4OE(fY%t}pW4#@JJiK1m3 zr^tTOwHtQMsWsC>N7+oG1S!Nuh3p)yTedv-ISTXVKJi(@L;LBmOswxhoqa0I)H}X< zU~!LayqN-Jd|sc10;$no4d2;6X#v&r;Y%(9(_7C2iU7o@kbj#O_j%h|oJ2^2`cQ5( zdVFk5=6tvPdDAOb9s!<40;TPt#Qcw!Xre;?&zRcUVB~9ZxOVDkF+6*vsmaou zlCORw>&!=?1QRnm7h$H-pbrHFVmJ_XcUDab$E2YsEh`v}@5-VFqrDGk^y$9nT+3a18=SlLb;%}ACDdVh{%H33y&@`i z`uh45y(e@C&jRzOEAKTK0MTnv@B+hyq0pxf?-^CTQkQ}GpB%&A^+Na6a3rlmUEW7J zWrVtb)AXzrD9?2QkAL;)^E0RMvFCv=NJ7VBXKa4Z$oIV)!YeR{10Q2kEfa?!aSeJg zrWnFtG9CN*sSJ$Ip~*kh@?*btk;k~bj8EHcVd9LvtUTf-JG$mrTr;WE?>+WF$_16i zZh`n4vvSSXetXIfoKl))m`8Q4`E{zX1`Ewm)I_L9X+yXWOZD3X`u}7qzv~El3Rk(| z(&>RNlie|o#+SASst`YEX%Av!y!^gJn5D!e-I7|=+d8*A#@h>O7odb8?E(~s5&nW+ zjJbr`89(*ur^Tg9q*1e|y^IS9<32_=kk@>F2&(qwWM_Y3gccRafJ)h(fV2-H7t#nw zrczDt4T%IWp(m7;N%J;*pnUs#E7nVk$1xxk5OR;3o?gf6f65L4M62SIfx0_gTY_$xfYQTJdd?@Ws=id{5Y5W4|TC=srO0#j%^2}f18B15fJJN6Wi!Uy;AB7ha z$VqhE^R)Gn>VN_3kzfAMpunj1Lut2?+S*D21ma}XPP71*ysiBW+trlMUxfAU^}JJm z`%$Pb2iBdASvz=&23#w^N=+crYblUo8&|@xUkcQ<(;~w(1CsW0m1{LG>P^im3j#$s z%xeBI^`^V~%7HG8uOAM~??@lEah+#DpaHh}2#wk0M`ts|UXZe>mxvD_Z`xB{IV9`S zIE<}5CH!r;syB0)eSJX~U<5~(1$FS+vQzeEOsgbh1s}x5@Lf4yNLRk%Bw1MpWDbDh zhkUPsNPT~>{J8Rs$!#38Mo{B_w>8v1e3z{@ylh_f6eHXkn~_2P-#gm*rkNFIjCB#} zafZME&-D=12CepF;O*BJjQh{eL&6V-JhHkrI@f#u78=Nakxow2WCnfx_3(q0KT}js zwBH=Vm5r6sdH*k#_7LJyhbp`wOwf-_BT#@bvAV(7=dnXx@LO*0#}(lMxLFiebH=Do z6YI9go3c?w#qvO|b5jkUbDwP#!w0(LB$z2!u}wYSiYBL~-LgoJaoTk{&pI%ce^8}% z@LgG1H$1Hv-*u*lmzUR$to{Gl>LXQYADUWOS?PgO6V*k03j>`#@jMywyJDH#($=&J zFskngp_4Z}9$cib{hYYaQT3ofH;O}h<~Su|7SVm}PK!?XOMTpalLTfI$;)p9dr{x; zf!b}phZ-^aKe}6cWFp;l(~;x3p@3f;ZEcMxe>uMWZQ?nSiJ6NAXZjEJNEX|@uVW_) z=1%j1*@8DYesuGx-wi~qp}DC2i-#3uR7y3J5eJjcx15aAwqE?^fGU#oM;-p-ue!yL z7?liNK5DA-QytifqERen`ltAB_`S>#^3gd-K~4>2PTwIp8A=FuwAX zgHiXS7e$hYE&#~TYWoD4D03hP)`GBTarll+2q1Qjok5e^;BFg0KG)59r(_LpnO=#n| z@oE z9oP^j0vGSDq)H|)rg@@s+>_Xq&6T=-?W)CiUV+mk-N(+=yQU09+a+NFE7oaF)zo^vY=hxHr%;r-KUfbv~xslCPDil(no-uPIEcGpL<$zn9$YjhW6 z?F+5Hgrmz|R}Ul(2Q9U`NA5~}+|8c_xcvp%u7RlX6rsHYlUWl#n}u`{z@K*5ohhYX z#ty78Z_0e@eH~>VkknVa`cA<;7s?Pp};<72oM)S*; zkm@JD7pWs$RhmZRqvPu8Y#eg>+WmfguoSrdi9`c?X1&_IqP;a7|LOJZ4cR{!nC2-~ zKF*ds3po(ZP@0EUP1&fui}pfDhB;?E9I{T%aJPiN%gH?j1$9c`p6}W#sy?)~dg?n* zUR6x9GhJDgv^F1Rqw23$DBgH|aB<$nW5nK(b=m4xUC6>KnjE}D5#I)UH-Bqva&>Kw zS;J@_IAEt!8|9$_rYD;8Idj9;!o=tw|K1|7@6@1$k0iPKvb|3CG>ZsP-=6 zOba@?L+oO;LYZgx$1jNJ@INyDE5lW*$ z<%qLlVjsn+%}g2v4!ll&-@je~0NSVXk4p^kCT%hh#Hi&U%RuFhI0jTYLZbSQjTN=sl#3I4o+d&ISCwo$M!O)C~PsyRAMP`?N)1Y?Z z1gSSB^q^qZIz^1@#Nm4KPpa5yQpVJQ%FQ(=#4;aVkyI6L^hnkCpzhUo2zp7p&mpVI zg?-RMk(6N}NQq7#^qgm!m2XT-;IrSG?_Nuwt3?iy-c`e_fAbM?v#%HKtA-Bq{T6Yb z{ZqA(9IJddF>zlXTzY8j5@_sjfB$$}VtV>WC3z%W4M7F&Abbsi6zfQ0$(?Vg?TLEGyZX*9`_+REeEx|};NarzcsHumV zCHr|Fx^ZuGIYmwczV6k0H|5;P_a}`Mp_pCp7?kXNv5odGD9$Z`Hd2$4t#)f)E6@S_ z+dJ{bHp-3Mijqmp@N`0E%W3xbE-k-Kfo*v8409HD${jXQRMVDLYg>8@k~xqxQc;yI zlN#%sfo!@&oNAM4)rnG{?PEmw16hysYh_9H!i91l9JlPq6{nqngY%>p-=PWTX>n4M zTxU5@MN4B`ONV10Ln%?@)tV;AFwxUIMx^joAD75i@Bf|SzsA4qV+7aydJ9eh4u0kD zNRa4^qk!566Rmv^k8}q&8!tfSzV*sv5{29A1pGOm+p7;{K}35)fmbj6k8_rj*$sn; zgU%Ff%5(~lscUcd)qDtZL@jVSC0(x<;bfcu^`)-~g`>Zqs|FUez)kOV-89vI=<^2FAr@Y7 zW}5$`RMa)TfmUIPlhTgBL@SODs0XhcN>M*Ey9Z^va=$^)q5|#B?I%f>2OT?mP_#cZ z+g`U_Vt;)mMq}zPk*D8X3y+vl=My>OiPb2Q!HN>iS%p@Uda7$Y$o$aN@HuC*OqA3pYCZ40TDF5nl5k>!nA<(`9x+pt<*XFjN zp`l18&!ID????>R$sU6fY%jH(c512v%liamRykM;)l)8s{D>JsD6zxfd7{E;1JYqKb=f0Poi55q_gKz=xg&Mz8A@Tpwav*!5@kvQZ1C?YuCt&9N z`9%}&+H)F0+4B5t{8LGyw?`uKSD3utLcCdc3WBMtz)#tT19yDr=})K$l7!WSz*9toO}(Q-30o&SiYjY0|4zalF;9)u(s|&#mLX zd&0h&+uEiPlPSV_QQfS@hK7I|;HR$tLt0iA2ilMWDi4c(X@`l6Y~vMB_iT~&GQeP- z%4U?B-h9(ydR1T2bInuD%rnHw)*)qYFVs;#Wq!vQZQtZ`Cp$)zNFbapu% zkUn$9hCeS>DIq`0Zzt%ys|(QV9$^gFdjhLIQZqsnL6s-6MiB6UV%r7QL3j%4Qw_HT z3(xD@7L`|2cK`7YbN*lP`B~;IL8p~Kdn@r88Z@F-(F~Ep$NTrV zi&xG*ucoK`IHRq!j>O!|->R69_w=Cn%kvH|O zgY4`NxPqcR3ryeT(q<-_mKD@!u!Q6Ky~dYpc7PV$Z<~v#DRU)nG z$$?@G>DK2GFs-U6Ijl6w1OKA`D1KB%2h_xMAI^-7Z8(gzvggkx_6^FDkFlPCxQ%?M04<@Q2e-Mo*`w9QL*iY)ggh(ua9@RgM!6D&{v@tfp0MH9x1jZ0^IVY9q9MW_q)7l zx!XvIamOg|HC3BocfM*f_c~-Ph>t!f>NNPED4yLrf6pur2D_~o60u72dFJ=lK>E6G z(7WN!KP`#0%r0iFkB}ua{61X#`hrUo)C(N^Sw1*5bQ$ZDfN_c8*@pse zJyX&!5!uu{GA5>{)`@l!s{MPJ>*t# z;kL|=h7sY|kmL-wXzd-W;h~sY`=7W5)QsBzEuZ_bKOKF{J7BBeT{@3(+s#2!PnB?- zpbK49ZeXNblJeuc1F=2sMN106XyMct1#t)jP!9%oO;c4iA=eW)XO|p~H|YxSH};dO z?!-?xHITUQNJ+L0m>OSS!HIYn=NhHC?GieR<#zq_F?a6TMT^lsRtoB}0Lp!R+AWYp zC1234*gBmYzGp6EyT|1?h5c|;^v=%gXZBMoBE;m@wY09f_TOS7Xz&1Ao&q(*rE?s8r zk~aBqvn%lL1&-Ni`lP7!sMFVqkt4%)mil9W71v8~wU_$0<`xz%z&Ss%=3ph754usT zG&P@yFseBZ*H!~Ls|;YQA6zuJ3;GBut7f`fY!8&r&ADOZQ5cNB?;__B!6By#7nS)p3-pNeH15%9=2;jLDLH$R1;8 z5g}BvWDVJwv2VjTDn!;S!`O=K#?Dy6|NT|n*SYWCegDtnI*;qR&ZA?-%=i2KyqDMO z`Lg!~V|fMet2FD62~{=d)IWB7N1OUSm|D>DX-J$W;hW6nu0c@XQi6x(weDNZ8-^9_{pKjR(s#4}=l=TV=1O;@@!I;lJUqO-vRh|ONy_Ht zRA0eQ1+!d7_>C=wCnSJu;sT7FJK&3fa{-ZLetp7ND%&^v=AQ$1XHLle)z?Sjse#j> zsCaa$$c-|cRoE}1V_`j?k@;q;aNlOvsS&5_&A`yCtXKJ0TmA+AjoT8!!Yw{-%Y3%@ zi1Z8K+UGxWrdpZhk!qBfE;vS1qc63D9=FnyR>&~&MR)kWdOU z?NbTvlf5KL;LYA<4g59L#apsV(o;_&()L$1DAu=CfH|C*6MyNelv%nWlq4BXsJ$b_ zjIQ+;mq-MjBfRNP>JEi|bL^uSq&a$>pZ2AK&CH_W$B+F@f(GU(5%!>(krpt@fdO+7@3l zNhtG0Gchqy!Luy@tycG9dG#|w#YF{V2e=%4ZP38v<4D2FzP!}S##|Ky0d>ZzW15*c=f_@|PrK zDV-IAU$r8r9E)YD?#L2LHo?RfE4{HiNXWYG*a3D{H{6I+zva!FH>XNM;@xfwYqCQf z=9pX8azYzf$__t1h2pIl5$*clkwY;e+CD^y(-vF>fpxROapQ~aBOdgkQ)X6Pp+kIT zCllQd-pYy!Ecl_dWY2jB}iTn5>Co4s(mg=jyP_4~W>{Lv2$X$41yXcSUb>~dv z|8GE|EgLsGvyw)ItoC2FqJO<5 z;l9wm;U60GkXULFJ^IAB0aN;DFme5f#1|dXF2(bxk2-6+XdKUL1}iwyxh%XeL#e%s zM%km)52+O?)BCCpPerW6V%mrvO+x9uO~Q!+_LMCB5!+);K8kp+MU)C-K!ccj^%25iK(|v?R-Vv&zBoVLs?^+Bjw|XugBI5E z(vfZBwBr%}Zo1}CY@7^h_=Pne#03fTvofeV1>GF`%G|^(zx-`CyU#d59~jFSQ%ci!|ep|JAG#kHgY5bZ11BggD2m7!EMgmWda4NB$5 zp`f~b5+-xMeOH{jCT%bd|x51^EV6Me~62`ACG_sb+q|&rGL*p5> zuBp-pE*dx#{4!jxIaQ~yqx{3*g#%X2c z+AhDYbZsWFyW;gWp7kRDzXT7TYNI8%=wvRW-ifIjG;|E7$`2aS1|~}X zViVTP^?7w=!BgJvBzgFJm5TFWjPSmZVv0xR(u_Uc`w>?$c^)d$yGi96t#|mdZ1dx! zHEoEKS$Q3WQ$;K?_cv~k9H#Cot3S^TNy{2$Vvnrwh}QYzo1UdQ_MOBeV$_$O`DZ(U z7*MzN@vMvyGKJT7qnobYIDd9R6kp9>%+v~xGMT2@aiqgHtjPw)008q0*ZzbJACg*qrt~bqf)sJo9g}_5#qa|AFaD>)d1zQGYhbrIAAAj0aD{Ku`Er+_!0Eb; z`MS%b9}E1-L1&Go8w{M=wPA?+*fzt*7QjG;9<%aA1T|M2E zMV93o*nst+q}w>B-ow@wX135CpSba_(%a5*a6=EqsB5%>$5VWhFm|STVWc|*BVT?) zb$`&8qW3sr=f2m*fOkLYBaoT8Ku>xH%Xp>2;JkFN%!8{0)jGB8PlA3p?Zqq*byY2e zGY4dn)07Jl!D1h(4EK9}$Y5s$Rr}hQ>{55(6VZ+iZX>%N&n~SIL3UQ=cdqx<^_gKN zA;U>jH*m;ujo7<&!SvdT7{CG3XcH{#C(5vD`>jn2RyYPxq2Z<)FNsaH@IcrSl95Ij zbW!LCMMlWE(y)`{#x$8dSIQ5@$W*IwhFpJdC>!nC=Y|;b0-jxR z$xz^%L;zvj)6n6*t$-DSO_9N+FO88ej9bu0==n)2azf#qAWDX{031;a|Dt~_jE4T; z4gZ=$Dkkf{?;CU5ZlP5tA=J_5SHT0a4KcSTFRFT)PpXBEXyep4v8A z#F7}&dU^VM9i%5)viz zLSb?@z19uD5CwuSCRWz&m2c^c(2nJdj#@;)UW<>f4Pghx$5##v3>Zj|#}gvb&{{sk zh;|BvUYs(oV}z9p-?so8k%%risGZIeC-YCL-``k!|hNS@VsgqMbD=ZnMaY z;6q!X&2S^^FF;6<>RzjwMPKT&iu$a8L4tVtt5gOtNX^G(Rw;3zSYb{cYCb2!S!Yj; z%!|P*R`e?fjtT_37eqv`aA=*jV=f>WCn;8qYjMycNo|5B=~m2`-<<&sR9fYjH<#=a ziX>EoHPIh+>fcLDiE?I0dl+z53ZW+!mJ%%r9Pbn6RyMu?=>r8+F+vIHjOx?KRYJAj zDxvW#xo*#}U^%(kgvYpO=x+J?(u#4nVW+f_U0>%V(rl(vRCJVS3r7>5e^g@?xd{U` zy{$488JPoHtZ05?3u(60Wsa_RjevPz);dk-T03G=5IAhwo-`4?Nwp?+Nz;1jYy#Z^lZ|x9Exei ztMe*i6HAw$#ZVRSSAn=$;T-s;X#<5uBL-DMG*BvBIp#FNezJH{h=XN92gBOC`#WBD zI!ak(m3$s>*R9oXSuax|*`Ok;6yiMkZ^_<@xmdAcllT@n=$#K_UGNVG=rwne6dIL0 z-Dbk`?2Vz0V`UnL2%3}@9TIbNfu-Q5xNaHe`dj39MXL878ZAERv!wf~9#8Nozw>Nh zIaiasrriP0i6zoVfK4~ZS+P>%14)AmWe-Th&yTT&GFd8iQ{8`b-D3adA60j&_w^OW zAC!fjSw%0elvqz&08>J{eEIXIPopZgn|X1Yz^UosT-p!Sn0jZu1`=>{n%H(BXukWq!WV?UL_xQ)0qZHnHSI;qjZ4&Y*pl)c55GH z?b+R+{Z%FQn43@5zjLl(<*o)QckWYRe{*-!1y+ z*gAHV)BCJpitRif%n$Mq+p<{&x?z@(@IgZ5BDDsiW7AvOzQq#+=IzL^WXtp{U`DzG zNt3xUXx|;slmH6#s~&ifhL$g%%|I@kuKuaAc{TkUe)p(xkMWllq4JOs-0{3B6_K zyBps`ShZ-Z6EjwS9r_^ps#1djm$C<7s^7EH(;epRQ7F`>U%ki(12D}tGIP>_mf^v8 z02yG9pb_KB)?b%~j-f76n_?wqe7wuSY`gXk%=sOi666(@Z}Oi=U#M~aJ)n9Q2$13~ zWRr~eZ}u=V+`pi3?;};J>7?z5s&XFkv}c^Yq-D)mZeYwx*MVu{L>at<_tAe%8xeoe zh%zJ98ka%hp1gOaslQz_8C7{>VN%08eVsFEjBxE znQ4RlSyXxuy)T#cn1v;bjrm??4zrAop<7an+wdE}T_OZozykLIG6{D34?|q5i%oHq zA2vmEhFan6T9{4^BQJf&&V$+)L1O_Q+rPvF`>%ST(Kg_r$(y5^O+<#yhhM|*abCoQIC zQBg+fWw))8w0oP7YvJFssT0N=_@s{<`Z`v=8BwL&rUn=IKJ-c06~ml@+h`i=0MN{C zfcWx@i4_jAfKmob6i$0Q6l>pZJ9G^Z8n8C97=g!9>L@*(Rgd`VUn0Pkoj57Z+9Mm?vU*mGLr%daIYh1*_W0F zgS&kWux|ZM=QQjpziW|P48!1^S;lP!$1nuJ8a9L&)|J~ZgzElO2H(`btup7Y^Y`o7 zdg*K0>&EXn7lEdw`W)3ikT(0dTSJVX}Ko5ZYbA*f&Pu zabcF0dx&SJKmp;@okpZ;z|HgXY6qA1e_enM;B$rbOjRMNxQ|+z`Nf4A@%I`92E*^7 zy&DA%3!g`3mxA^}AkgHVt%bUM65+f6lo$EU9L8>HxU59;gFe}Z`y+?)38omS*TqFS zZ>#n6-XO1W?etvG*82Y|7K$-rEEaoO8j8xE2?cri5=LR%YHWza0&@ee9A~7$_3IDL zab1FuJemdmn#$Q4(s-q1!JuY!IbHdX2uSSPr#^C~uWYP_|T z?maLniF$|pD_k%`WaCu~=2Z;ZT&?Bs522#5Q;wMz#l%W!L2YMXZ)Hf8H84RYb5v=z zLBqv8)p+%O#|ysH^0Km?@a_pt6QzhKZSZgeucUJM#Rv zw2w)qw@J^MjVp}m7H3%Uz*LcunwkxWH9$bk-u4MPWwu&GjCg9Dxnt0RYw=! zI>DEZSTVbqf^)|bkF34UPI1tRg>zCN@`F=q^jFDx-_lY^S3#8QZbH>|1O*At%3{gS zpop-kehyNuu#S|%$&-2Hj(Y$&21DI{|}qWry%ai3M|3?=~m-sFXff9yMo6*JlY9nJY0yB=Z^r#|lW*{)XN3I~tp}Vc)<>BVHQYnLzE)AqChDOasTZo$Kt`8fl+Mn7~;Ov~*>< zG3(0fDvl9NrKvRMC_{H-ipz%m5Yxty9zew)mmRE1+?Pi`Y~!{H2W$=N z6TsCmx^ZgaG6dbV&?o420&vg3An>Jvv2j8a9bW)970doX!=coJb}smLtQj&*duG)4 zXpNIfIp!qH5eb9rDMoPu+#f%pbO8~hg;>d?W*TFIoZY= z2z4{-+oH-=$1@1gKytyYFz_#bp8VUA{gixfWC>i1;ncLF# zR$Ra}x!9*2RP9EYC3{$xtlQsw5F?ba5rVG-17?7S&N#4zIX7joRg9Qiwi^*Sblf3$&6c%jvoT}GDw zm8f+`v3Lp9Q~uu5$iDoE?SJ4e!IH`I%3BxkyBQ}lR<=(mbu27y^X4&IeaN%S@Lmz! zLBveUOh(AyOX=U)+ZFFEFTc3;U*qFX%v1c7?_NI$V?HlpQ zE;{HoqLxpS8)j&9`{Gvv7Arm-LOwE5Kt^Gt#SZ=61AlQI6AAQ++tc`SyplAbdIK}U zT%|N0L4*fls5JLpQ!}$t0s6IGK`YlPrC|T|w98YXu4(9tQ|*Fe0^j??B3M7d-}rJ& z3#a9BeE`%F??tF!>yYU(RSzm9+txbE_Y`oc8 zUwtb4Q}edK8Q%Ac|4W<(ylaJZT@!8Jy4e+uldx2H-$dg1U69QbN<4T6?8~ui+Bw2> zShnjFj4Q{Vt9%|af6vj!!Hjl#xn|NxsAbB~A-Z@iCwlK^m^sbs5COVX`@hIvfpau$u?gok$Bs5$Fm18 zYMg$30hpd!16wfe#bgMxUw+UW`(R*C(QPR|9D~PA7`_9h0bBX{Vt}8=ddFP#Nk>~WMX#rW#UDnw*szp*>&b7O;UG!Rs0%SS>aA6c_gY(GCj z7^B|pj(5k6hF;*~vCbz*9T$|4Zf%T;HA>r~QGF7ZQiuo?fvB`#3zA(lsbguf>jPBg zWx$qrh4$1-hVi%yf$9z_ve>@+A3KIAcO3aXBh34Sf0=xup_z@My<8kBEP97~-?!4* zN=ujcARr}L-Fcke2D;o4R5#FSw4eh(5+;yPEhNAM*gjJda7Bpmz8_Xq%5h9d*1I-2 zQS`=@NxV~&mDfhm=t+T-^d6+I_Wn-`|Mgh1z@9jdf;KVs)Pm|^ijKY%R^?UigU0); zQU-i~IbZhE>_Z{~0P6w<;a+HQRu?C*P!zGysr<%AZ3Kqx!~zGAWZ4{@(1w%-ap%)&BO`1h=a z!dFN&Aw&b-(zSczZ!KWX_WG8(V?zfs1iw9dGal~}?B_T3Bft?JE$lKTNKtB>>@vN2 z)g$$sS$aU-%wduCtM^6=@WICyg=V#x7X{kok>Wp<14O`rhLA&LNUg9YWeCEq4AOHz z3$iFu#m6>?2u2vQUc^hL_KF6>Zi~^p{&C5Lw#O^->vc%sznVuZJ$CF^Cj$0{9oN)O z8xXG4=v?D__68o9%~Sp%bu-)%n8!&7 zQodx2FxX=Y*0aZj*r8DIfp-nR0-9j|&iVj4%9?F) z0e=>kiq+y=*LR*{A>GYX;`w~jpWW=7{f8d6k^9H&{tm{pmd+c}u&e-1UrK4xO#$jXi zdf{|H-}5s-yDZt3EdFBkmd?%Ney5%7QSINsSF zOO=Ud$|o7><2#vuow{#^j|UzHO?kq@aYzrV*9u0HTuR7NfJ1jZ+6)Ky@0D%8;*o@Z zZ8#DcW1l$QSBOy7V|HEB7XSarer93}Gslexao>k7nj|5?$CuIV zw)tDhZ@cjl*>pHl&?Ajq_%z&oLk;vb;gJdaAlkL}Ua<61gf(MJ&vH&MzMfD#u-DFu zfvI^#e!gNHmcN0Vu-6~`Up?@+01RA0tK{w*KcgxfqYe8=RFqB6FQZCl>){{i*piaWTPHRi7}gYIQGu8zj7F{ZUcph6G7O`jKl2A`2i6 z;2W@ynEY2ER&GO7CtXm+m?@g;iS^%@V_cz$^Zvy70OKS#el40OAomwzs{{VE=ihp3 z|F!)he(mXCEft(|BkZ-17s$FV1Nse!HKDuUr{^Od;EZC{2j0jPE`ph}ut~SFW?eis z1WRfBoO}2jZ3+gC57jQ>cIka#^3TEpqp1L**9$hNu1IsoOj_DNC37`z$;O37^#J#6BMRIEo_ zNP7{Kd=n?QuOb$?rEiR0ov>!OV24*jT<4|U?rNjy)~uErv%;u$vGm~8f~JX~`&BA? zhGCS!oRyv?{QZ~KguDjO?jKrb+2aZ7Xw3|P-aEDkPo?TO&Dn}GW86{G@#tjo3fE+& z-#I3BmeLENlr%MH4%QxJge>>GQ>+@wDH$srGJz7E1TeMT)N`Sqi`bQb9v#`Zz5*! zPh7__0~vzj`Yux>ZkrLOGAuV;qxcj-SYRvO*i_h}3o2a*ij19%U%m0d z<_j_hY-UT&eH^ukXtNGB)S{cJD$VywF6?sFJ1lW&lSkLCBU9IQYD!sur=xu{Bb-rW zj?%EU>Ew6iU)QtyG%Xfypf!1gdt4zz#5Whi>BTe5tGJ1h0KEsQtCjP1G{hj-4q0RH zg3r*+%pOHA4f}N_FDf|ia30$dVmWKDUzEXDsracX^|Ve*;N4z)ZEK~+)*oK5hUp(i zJKUhv3W~aBO3&Lb=IenxzIE(IQ+Rv+orxABvC~qOUqYx8ClVY;jeBHFQjq5?{#wTD zI3u4NJLxTE!WqA0T?Jyd3VgN7(6hQN0`X(YHio-Ams}7t9sE_c)=@;hhlE}A?%E7s z5^&gqt2t{v@d1midPn4Yqb`1TQ3T1#lClE=1Vd)0o{`WrA%EP5X1{7orn|5~cd+940e=S+~qKpMIscpfhx4lJn{kF(?tv_R3#lfhX;BNo^w3CH9> zcBu~R+80*pV+8$(3N@gq-#;TmHQDq{ZGNxlDlXzbRqQbTln% zNHX^0i~Cb0Bc(KhClktOKKLv*5ig))@9tAJXNuyU467>@KL427IN!V^SFqHyka)yspec_Zz!yK=^y=bCKTVr$>LxH@W)ZfJX(g8ZfwaBQh5xMYEtFN0ggkbHL=U z$@ z!CNNQuD;d=9quXQBx=76`FdLb1Rwv>o!9`}_XFJnvEtIbXM$C-M|rRT${l^ToI&Rd zX^ar!D!KLug);<;2CbJAF1yNbNDO#xoe61{VK0|g$B6(4=>fjg&Fw!wgWuwtCM9KM zbOKsMMWwhTP0nPu}4#D;V`7f5rv67&k{ zK(kT_o!$F0r_X!=@0;78Sjp3Z!ou~-9nBwcy6|=Xw%s8jl3re%sw%aP;FYo0B8dzY zJpj{lpwrR6zQb+|K4xCP?dGIl`10QSi`xcBnLUV>f05(s0vOp+Bv2tYH&=4=)_2g3 zEVXH>cR|PpY!eTOx#`;5b)G3IORkFTM}0d&?>qxR1HZY^WvzSNlyX6ylMmzkAak6$ z_#L2Y^TRGjA@Jlq&|I@)pc8z8c9siRHyJ$4$Air-6s+AGX}VM>U`x?{{%}yII|MAn z-Jl@6lg4u8PI;GD$%^kp7xE(e-O8e1(Fity?OCZQQHiq4m5h_|z8tv#$Z>6>P+UC} zr_UJ?OG~K^j*hzbkh{vPDr_&#*{+~nw4AI&l?b^#`TnlH0jf)m8MKD>8MJ%m=B|W7 z9RmZKV42lau+2YhUt;i9%~qZ2*<;sphCU>%jiP+=0N8<#n9R`Di=Xm-omm9V5hOLx z1`+xr`l~EL3e6sPq}HHG!IO2};bKOjmXW7Vbug^xkeh2#Y>JrUWy6z~Fj!O-69N}> zClj+Yu;xU}>a$Z*Qz417gMgkOXz0QY^b%k*0?eHH&lDvTRvC7pEQ#NB@{lag6JLIH z(WiF2&P;h%hJ+kB*SaIh2EOk%-Q7#|xrHEO5W%p)4L`AXK(l-p3CnoAPcR$FScF!R zLTiN2@T(ROFw`qhW@~EM0=5^s2L^UPS}u~{SOAeyu7qX-6w1tNbFClA;Dp@IQzik?qI2+ZyB!^)|R=WhUlcQ?-YlHWwmDZM~kdTPdkoSXj)QgoWFpUqHZosq@`K z$p4c`V4k4AM4mz(=6C!f119?q2ps73W)R;p6QCVXHn@EuQB(m{LF3tc5;aDYnoE07~m(D=ZU)OKy~ zRMyG z1YeIv-IbLU2uB@7Bvtl4&=XFH*Mi5jxOevv-mEUJKy!CZHIv|0dj z@O2t^2J?^ep*oScD&;W#*^ZHmXL($#o{;PJ;E(6Oq$&(8BYA7%j^h;a0Qc{hbSFFt zkp5JKS|a&>u1OkPf90*=JtWqYSto^r*bB|Y*>kFc+81vhO_+=n$(t;7+H8<8_n0wpYf1gl zl{9gyY~gB7U9;-(_LP)qsW*emGCfGax!XAT!j=aF-@*Ot4bef15q~1{L|QLCcnzEh zSYqPVBHOunVxphCssq}4haV9wfg6Yj1{Pd0MUP``IY#N@?xSmG)S@krXr)OAan00s zR__iucbW*!DDJO5gEKqeEs%juwwIx7vS_EjpuH56_wMCTv$7AEN! z*t9TXa`qnV{iuU!R=vt?v1-K}2Rm_cH)dfK*2_Qr01cU7(h}bgonEs7`wh9qziI2= z_ivAC@Rjr(XiJ_wyl}1{O-L!92;?X60cUc11pVrWOK${axwR$AK@2ADh$aZ16iCat zv=m)fg>Nd6fLXHf2-6evxvibF{Xm9Hg2Ut4(Y(L~4s|5j!b2k=weLw9C(o?T(4S7K z$+D%lwj2SrLxcJG`7%|-*7Y99r|2o$uFNL}Q%+K@b5=T?E&T)Br0VH3z{mv|CKj!i z%0B+Np+QXH26MwmE;Jx1`l#og#TfRRPd;{7SS1@XFNpWAms)S-9VH9HiqN@b@y-8? zJBm#W1bR6$yOA&N$*j!euKZ#{;Lo;;73wM6&PT|RpA08gI6kU*RIA;yAZtPHWToOC zBl=bRTJMjGz@q@7pJYbhMB2Fz2@c$^w|e(B=faxay{mRk&W_sR0Zy8qC{b1r^%l7H z;s)p5wc>3_75S~0#WA0FB4grpVNFu%evELdsvWqU_-9utAHs?UtHp>BMg%`=FHE*( zOs9X&n3{L-BD)t-s`N1-4Cj77WXOci`V_yl*qN9SMZpv^KUFxbomDID);`$lWXVjz z6e}m;0xVAM_{q=C!TK%T_u#))JDn;@O5@8)qkm?2cypPJo1a{>+PtL+Bhqml-VY;X zM27_<_xl8XUfx`UXCEennJPRv;pZuo^$OP@N-1XbQmWp||F1zpZ&}hrD6rKjf=FE9 z{KN5-xHTlL54E~metjYG_V5{auKX&HbvI$!15Merb6g1*>MXDnV196G{Xkh*6-x$% z5SG%wYO7o89vF0%w0rnQ+(`A6OT@FV9ON7c{pYTMrTUNs|5hrXFQ;ec;(-?2rjWVOennkW8v zSKgVV&NZgM{4}nkeHZMB69rj-lmrXBNfI#Ke|eW;C!na{|50weRo&cup>eGj33ywZ z3$L(YygYLycn@y%En3`OcC{tA)SCp%Mpxy|qtf&boEy!(=e3PvWv=Vw5>VG(f^d?O ze}04LwLbBJdlI}Wnjhx%`D|J@PG;D7N*k$n4;WtJ>b;=;B74`ubpTM;-Upge3?)SA zJ8m@Iw`cETr4!p8-oFU}Fd{WcojrTbF&$l86&Ppt9iN2tXNH|*;d=ml{B!H-FE*;( z)mk^CKA~k`*3-N978Ms45AyX|hF;IAkJny6Mk+-~U;LsG`1~3fVoEx-bdd?}QPue9ig-B2vjhnw zv~5rP2NYdB@wE7^=XOiF53CMVK<$s;k$!CwU~)yZ;*NCl^*hdAz+lvNsfUr^Q0C zdz1N+mqIBL+0ydTBRZI@nH!6;k43!qoKGyGJ|Y7rBvYbjK!m}&HD6;7z)>zLD?ghu zkalskk15a3_)?c1l^IwDAKdxtGlB?ZkKy5*$N-hZ{2{aE*~;eA&iOy_cRU;Cu?N1fXv#mAyPVs2=8bi#vvIsotZB;6d1Ed zi@MhpLF=mq-#cy?eQYuA&wWhLoaLwI!SlTn0^8J~M&m->4+$!uLJPgfK$T$2xbUEu z!8zq|>`BeN|XJF`|T zPX5NB2-)?sU`Btq(Hiy;ak2uB+|k5J zZ5)KWXJ!S4W-)jNo5cf5OU&BomAoR^GprkJU>CK|DzhXMe9#Q%mwz?yCvwNf$87-W zC8#@{BDf$>S%SDX1JiJ zOLEjR;fOo;eDMJ(YHKgp{C95a^|rIME&Trddm|&4+)Yli4gjx0a(PwtYHzw3aFr3F zFSIoG?>*H6a4*Eo-7zqT=Bv>`9}_8njoEQTghrWy3YUq6rEAt^^qd)Bc?cY2V+6=d z51(pHQ7`iL_C|~zSRj@@-)fEI6o0KcWU5WBnA{F8g7i4U|2Bk%)x~`i2MBQ`{9n5c zMb3k%9FiU|&+3E}k_i%!VG7>8dj|@q*y?xHW|zSKmz+afViYYPjVE{}U0A&^wdg2W zA+tJ~2+@{PNBiEXfaL`;()-z!+V+8Q?cKYp*s3)ci;(6i$Uqoj#lV8V*F#XV{^HLO z_Hf-V`yVa93A+{R>pp+R zHpNO$t=E0@J6ir+QR6?mkN%&#j|^zjYd$W=?ik_4%;Vky*(iuj!We`_w*0H5WS#!@ zmFsw&n%SYtMOoC1!lh@x6tE)Fb4K8)Wjqbz5{Fi&1Nh03q9gTa|2IVI=_|$58(PdD z7rbZHsBu}l|CYukvb!ejY^tjpcj?>go%S^U94_QKA3S=J1`ZGBkx6o!^d({{G&~*} zHX!tiZN%tluR;opBOWuWC0p{%hjkJ$KC|vC&kAW2vf9@UWkGxYF{ouIIxy$#-u%(D zSsc1cb|Idz3t&d&=*>T|?ON45ksurM!A zVU%5bgu5?CMK0-AOYRUJLWTtd{jtm0pLPgjJu#5<-!CS2k*Rh%#%<_05_66&TQqV| zUwHH*K|Wv-LAZ#UY6p?UFX{LkK_XQ^!So-iV?Is?`Fa1%Dxm;{fMt)h3 z1e^#Sow~8EfqO82zFW6L#!$+kIhWeMftLMjbIs?#nD)}^zl9;PUR>QJhO0do22e=) zZ_M;Iy!&KMP0ymq`EVpA7b}_}J36x%+kAGtvaWw)NgRf2)*}&G4qqUH+crwdl~6R_ zl6J+u3))^Zh9Yu@tSWcy95FBWS7IZ@)pK5x?$fvI-YnkC&QKu2^jA`UZ zhSrpCeRj#eY$nKO_cGtrs`WAjvMELB<2X_JYUywoES@u<@t7wz$t0CrU)KRce71GW zMoCgfY@dO7Qb88YS!StcNaW~b?i;_bmxsDG%4=dL4pgatHk9`>bO2&s9xMnGEd*PX zq$(Hv2U6tl*EX|CRIxf}G%Z$Ex0H!uh2vG9cc8doGQOM}(;DG?BW@QeBaon#Bt}HglHT6RfqEpfqcAm0})__|chO3jlk9r5N)F#1t5QSK^51eQiV!>2I#Q_<^^(d(+tw`E5qeU}u_ z^BVf(^2S)ImbLaGHd*&v>ADX3;<-M8q(E)%5sWOS4-!o|!m_vrFO%4$Du?c<{g^4V z)qs$b6&DNO&PY@YUOEYK{D0pWQ8ueH62+%!8G=YcSh?cXXHCIfC9Nr4+4tKnj3}G_ zvta(0CwKvbSi3M#&maXMGQOIkkNFK`{aunlBvWCIw&_DocUU;>dY`Z#@_kno|6?g? z^Y!@meUkdG@A~I`vaFK*zFX+0-S<;dldJxBHJHu82)7K~A2*8sI5ptD=A}MeB(TdW zD{IhX6$H$a2o5M;!;h(@rXNIK_*mBM-%4X&BdkRL5{#kBTEz&Pvz(jX2$XBOvfRWm zgUqe;daR)4Uld>-HR+7r8cY8jUpF zD2fOgS}HZ{=5-+xjvf=q8r9R*9%|gDw=UW?-&0$iSp<4G#klPNMfn+x_#2h=+i7IS zgr7i26 zQ$0*(v8JUJtn`$G1FT}5pp!a<;rN_7~?l`Q1q-LQL3}1NP*3vRnzdY-W z?JjKKe!y_$5(4~%zA*0*`(aoP&)IO-PlZWcE4DwK6QIe%5*Pke08k5^9> zRjgwXZSM$5;K0V-3cjo!$3C}_E_T-*BTlf~A;#gp4JwGQzCK{xYc*K~(i+1=0nK1( z*N%_Jq;R*>lg?acIfo-63Km41p5<^6By2?kFQ?nrePGU7{15lEbKsD&P`Rm;>y%Rl z_qHpSB1ER#Rxk&c9pphMT zI%4!AoRb9f5Vs7nen!&#yh+>YRWaZeQPblet%`wGp|A5zcK9Jy%YfvhuGEFj#^XNs zpKlZo=v1sCB+_mu5(UA$@v126j_(m{1EGBhrt$48O#qg_eSfLg!`qI`cYCT$tGZx! zA!ZAU0GH_f0en$5?Lm7HxRKu0{^ZI2X&Y!yfW4Fn_dXRFZ7LT-s12&$wBdCuMym=0^I2H3r&`K)Rl8VhF#CPpB8^ zOF`_Y9w=*G$`3@+sJQ#ldg9G z)X)#4v^t6)wxJF-C3^Pi4quEX2fD_<6j1GxQ)eh%I=t@){g69SOGWj-{MiLI1rT2h zP4PqJJ_z`>Z`yXHc)z+|&YvNg*wxhQMfV6=z@+?4%D|dzLsmWyD}T{!|2Zcoj&+^t zu|%5aEp9-TLCF^we@l{AC9{|ufEU-zOrH63t!G5W9Ar)Q`h!r*m&J5UW;*Hra7GJ^ zM&C>e3um#@khA!#gKix=X^Z4xLgm>#H}n|`MK{X8phrMM#m`i47Tke#*xq#6FQcV@ zL>s1%$$d~oqH}d&E{`)L<^WU-H(SNrYh3|iZ^SWVZEX^oJc#y~t(wv+nc!_BmM=yA zjHS2Rl~w4v8etj`?6zK3Oe$_Pq-tB<6K&{FxF8NggTH@mBKAKhJ)OboizFOOPGB}m z5$NUAFl`p`K`~+CHh+wu-}fP`;;sD;^0}`ehD4F5;LdpeYE z(bIW#hEN-?&-ltZWt^S}=5LhU^dOBU1WZOdHX?ejE|BA(0r%)Y@q)#r9Rghdm1UK|W&Zfodcw&Rk}mWo>}D!oobpIjpLt#?=Fw z#;-K`c;89BOpDyYyOG=nEslq$qxG7!F z`3!>#8@Quvx#eE5ZS(H-o_rvMGtRwtMqdAV%{d3m&GM{Xv}F?VEP(rJ*RT6(`)yzx z_2Q<>U251}JCSKWN?sz?_P#oRo+0sGy-SBYcU(XF?juNrb@5o-G@riw^?PPIebZ*T z+*DbtoF04V%Omf<%Eb@=bux04adYqOcMzcUm;cjK+Wv1JI^Dc+?dGW$eYmEjKI@J7 zo)}jVRwnxSxvZS*9yZnz<8 z7IZvs?fS_NAoO7tT45uQAT7fUH5=9cW9Rmr`_I>W_xv$ibLLfCP@VMd#RiL~0FxGb znXxDMq~}CdQ8skrW{OAlo%R;meQ=@XE#c*fF9LfXZ42z~nv|h`r`%OWagQIvs_%xk z9m60&+k?D)_&=k!K!ZL2$BeK2`#~RT_-xlgo;2$Qv*s4{IP62da>s=(zky7h{`(Ba zMHhMaiSj57Q3qwKTYBveB`XfKvF*No^ImyZbCXL_g1@9z$Hj<>!|;PY`h6ak9wK;F z?2JXPj>c+?9%1+R!WQtEOK0Vl0^Cj#OyMtInwXeGCG4LIRm?xgars0`ON%N+e;*fp z){dnln0WQ-)nRu?F%vBQ`bT}V#8GI_J9F;^u-Mfd&XO>Xw%-ZMf@d=`GiQ25zHo3I zyYQtT0e&kF)!=vMpHH&~3JO=wxE3kn_GaXG+DRy-k4Hs+eTw|bYFa-GjtU&Ggx{ad z^}%FJQCdcZ$iD2#N&^P^#@6m{ptY^>XuH@< z8_Q5Ak%r35}Sy`fzCWba0xZx)&Iibu7 zZ{LO-nULbT)tN0jU-{#f&jFIu^81aTUhGJfB_FodNXEjoFUrMS%4{E|tG`9py1NeI zpO5Z&s)3rDpYPR)`f#BwOJ7_iPKF&;pVpFpguCT*k+mpoC(TP=S;-zliM`D(+jg&g z*DY9-VKqcbPn!w<`Cz^w^Yv&tw5-Jin{Z545|#(xm_E z)8>Ein!Moq5Y%_@)Ia@AeVth+X=$0OGh3WFd9!H-F9A;br$h>{aOipL6@malF0}hXu27 zUfRsPfPN)5x{jJ6W8y>b;M%NjDS{`p2&BOV zmS1vphb>AyKEU6qxZvPL1~un)fs9(g>)`Vr z_0RD2B1YFsLGHdo+I_(yB#1p`wohzixoyw9vII6p^ZeYmqw1H9*cO-dYoWiL4T<}) z1ESEeX4Zu@uRlmCNfg$xcK;D(eN7@uz>fB)ModUAe>a@B!b2ZAqMtj;jt31rykJux z9TaH6T9?xjJGa5_NIPeTt!!bTsp}RxRp+q81XxBrfBxJ|Ewj&iD01Z+-@HklL92`k zna3_OgWuf7yqwz{r^aoFeihgx##A!g78o)nQ(IYV<8efd<;BD1yHcfzjZ2^uU~A|S z%ErvPNSP~}`@Ua_Uint`aHyf9(|_oVbEuz#&5|?RJlD;ys^Q?jC3hGcI*Q!pwR^#o!6~T_t%%u7o<@^rI;Kpsw+dN=uASN;BHV67BW=83S z7c1;e)IoZ*a8mTr!8yno?-+e;;#A|d4yX4=IM!p%lpmF#6>!#UYhYH>dM(#|D=2X3 zHQoG;wVj)_Kv3iNe2R+&=NZgvan^$tmv_4MQUCZcpU40G7|F?nfw01Rzwy%!0~z7t z!r$sc);=40ONO)>cE4zig{M=C%lG`V-iH$8{&{-E?!!|?H4m%+;ePG}Ka>3*R@S#w z0bXZurq$s8tbhi;@BL_&~m6r>#*qNw2zj_dl=MF8iU%u5%6{cepKkYg~<`jwAJ!e0r& zr4bhkQ*i5F` z3xwbX6vqKriA8dz6YR>=AgPoiSF$=A8)*>{+!#3WS)u{mT8FsP+Rx=s>Q7zI6ox5j z4<4Uy3V4D0s2hQBF}P#_V(ktv;J}ulyuG8Nwp0kt!)d^&$!QQ$bnJW|>x1^Ih|3_s zZk{3;eakd=L9||&!Vo{hOspZQRaSe3yX&@Cll;o(Kgo)o*Gt4@nN1%!PiTiCC^iW# z2gRy{AX!pZp%K_mq~B&f4U3gh3|%>zRLN-!fNW?o=aoyKr(p~KM$*e&Lq;qxA;Wbe2N6o)5EtrB{ zU!czT2{dQZU6o}6yDMIWwp<$@xmcy(_VHR;>uSUAD!+m>7pju_Z76Y1lu4tEud7ws zkw`E=BI~2n^^|M^Q;*(Yb^QjZ>mp58XIA^3Pct5SKd+KN_MUE8pQqI}eY*-O<1(ye zfp?PQIUudX8YKI4J^OU5U{3Pq>WN%wJ(i`HWew#e6{+s1>o!VeqWbzDqj;)GQfkEx zg>tQKm87SJ$4ZzyZ+Ewo!Te#HA#Q}%hyQmgbLlSqzQqT!=6hS|S?hr{!>qh*#h6eV z$jFkH@TeYjckcScj%o^ciI;4sKxnM~rF2nQ>!v?NE=GHHh~beQJAa z(tgHa6XA){mCZqDX|lB?B2ty7;kFcT(v^UoL_|^y$o>CZ0nAZglzcuHvc3nYQOJ`h zFy@V%^+TM2u#k2@R$9=I;$sP$3_>?JpMzS^I+G4(3(-)fs}`(|c2s&-E?7xJeVkyT zp089onZQJgb8cWY(Dk%83$r* zPX>Lj0$4LZdDXUFr50Ip41kU9$Ui_$n6f$ira(eJXM`@t20n@fR>0u}P>HpJgD~Ra z!b`yA?c>tg6{>zv(D%PSu`}oF{NGoSP#53dMb|t~o)M5EfXt|{UVEKWj0yf}aMLB%U43TM;?h|S{w6i&U~$p&c$3Of%uNBsJu=$@ zU;imPv8JxM1D|rg*}5d?gW8~*u(m^R&rLE@ z^Sr~@M34JLN-pW~10u=hD%SK`OWyRenJ43}=Zmi6M~;^^kSX7%JX7vI_~R1w^DD`E zdi+1_x0YV%u6%UAN@5zfQ~Ytz0!y0Uxs&55mu2@(#JKflqtB>~lr~qQ4HusR$@F>Y zx0>F($;(H~(Bg@i&e%>#R-I#Erlwv~bH$;fxEV@1JUH8!xQCkw6m;Ys?{p z^mI>0jjIT)7Wa31K)eqK^*y%)bwQtO)=+Id$v*{Be>#(65b=nBJFUm54!!IYyoOKW zOt5JAPKE}6a3*p;1l*oP^8V)WNS_jt)$}Q{gmI%^B`>Xe9tvN6!xYEuVWFu<|2!fB zX|15)S2MnUyg`R5!Sb>Pq*qR5JPJ|xj6vGnz@T^KgO9nnOvkKIuf~N8bu@0z7^H{H zHdo?0uGqF8`p){-8=!)GIeS}KQ^I4_-&kc&(BMX^&&-t&Ch>{jX{LYnN15f%`$h2Y z92{fKeS_e4aa7}X5YMimU2-?3mlR$5`tL0kD=0vrXj-S-2;pca@Q95R<(ba%f^$5L z*oW{PlLAK^X5NYE;&|q&}p(Gy;BWNg3 z4lq<*d~i|(9(@n>ow-BE{Wj{7*$eQ`&(HUHE+&qs!-kXGo^L~) zvhERg?ckDe@)AB=YX^lu6H}X@FI^Iy5zR>|os+ANApEUH_O=%J^}o+3n%Dt}*;|3SZ1ZDHNO-92{qgmvwwz)m6K zhKLdB-HG%1-I=dm)`MSUmBmtj;5ql!uaA;ktZv$#9KQD6-Bb=pN!`1$*YllnmQtPK z<+@)P++pNaZJ*n5hmmQuJ>^*l7FMQ?vB}#Efsn3wF|g~laXlAQ$MJtyNm2z1Ppf!0 z*JR`S*qa51O$j?2Zt{s9zW(*dP{-`{j9zTSY-2s{tmiw45+CFHJ{Ld9#07mJkEgZX zM)Q+l&J7MHWFJ?FO?bt)AUz53xf~-Ovc78}eRT)B5u9Tv8qdC*a9kXm{^4DOn$NO2ls0 zvCATob!-7CS=u3ExB0`$V8!q-oj+dlySF1RI~1GvtYZPCKC&~n+(@0acV*yM(6CXE zH@_JhM)6AkXKk0BHCKJ6oM>f!)OCB6iMSS>9^v8L_66M%;W>|rd&!%n`iO|(#xlN**gXHt3x>awjYH@P}2`!79vl{K0sxf##O8e66P* z-xxd1sAm%QAx@~5E~j#MvM3Lh)!Z!U9}o}~K%s7Em|43b>rUKczB-hZ1khvm%wYHf zarg<4u|R-gx7Y%FG#PQR1mR8M48n7Bsor){q+kWEhWz}IHB zk;LPA%#Us2sj%4ll>Ov1uW{$+mdx(LH<{fJ8<*cptO^doES-8CA#xmVVireTd*5s6 ziV5Dw*PFrOsXsU$)CrkuQSz8yS6AmP(R{SfhT86~mTbncX*hpZ8Th43*4bGQ*sdI>TxY#cF44Yr z40csjVdS*5QDN$cAEM(|6nT~cuvy;-`w_5F$77C7PD{Yzs`gooi8y4eQ&`C6+dc7} zebyyuOBMRbmfByTWHo>~Ki}wOvlf%wo$ni3n!`|vQx;Jcih_ff4%hs=d2-DozUYsG zKBbb|P#)S(QA+JebZVivR*j4XPfcl?X4L$f`%w|p8E<0HSKbooCx$$aQCg7=FKP2Q zz}3`lc-iE@Iji=Lp&z<^Q-;6w14&+a4^VXPf)RBTAj7u>OtXXmUz8E>lY)Q?CJgqO zyt{ybx@bBmY%rgk?rxRk$OkYQjl?EKfxH=vI|Y-=xd1@eFGwG_Lpn_)JtWM0&yS9F zJ>CDI^}yFB-~PFjVE*(4;4{WtRDlFr*>E@+keLg1&0TG~Hn(*~Q8&*6oa)->X%Id9 z*ex)!j!p^hdFND~vzxE!GC zU5_`<_ufxqf5Hd&jf;3TA84o}?>6SxPlKcIr)kb7Uy)H7B`t?BXAi3umr?q8fQMDTQiUetB5ikzIh0Q9lg;ta0c zALs{C**oIkE9sxMV^*_~PfAZo9v`l9lMcx5F?C zh1w!uEn5TdABQS{+JRb42+S_+huPOhT$D*V@%Ek>1oQ_Al-Kj)k(LZb%R6a3=sXDP zJT`afh?}Ji)%4*dX>Kl&v=zyo7A@zT8DfC0D@6hFKm$PyrEmt|e+ z=>S@nKLVc5r~pG**}!vR7*m}qIvR{B%GRm2RUXDn#n=UdfJ{KJOE{c0a7T1g{hSF) z_^{~kK2{lHHIWWK$BQmjtbgD{g1;U6-zAy-n)e2duqFg#$1N6jDc1oXNF}|V#_Je~ z(_dQk1vDEK@6;$nv11oY6n=Iq5m2EL%)iv3_mof6N|$(by`GVaJ2)GNd+r-v?Cm|S zd27vo=5kj?@k4$|T2$sWUngbk4(+x$dvs9aZVdW(hLp<1zv zQ@qAH!0{tW76AqqH$}MS1xRVCBh&K_eD>`p> zj>$%~fm5p|gewhpJvCw$$nq}abFbS;qXZ=5=iR5Gsxzl8$&mqP6>1P#EmqNn`?$E3 z#=ePM>k)_PJsNsOk1-~c^|vu}63=}aqD)+8P>zcos2AqN9Pvg<=GK~8nuR>nrW1ar zh81}ND*+16%QyKy-)4-R@OS>`T=^ZE<3p*82Kl+Ip9QU+pVGhnexL0j&@^as^%iZw zen?{TQ3iYvF~n(IsH3(Mzv9}s%z~>%IviS2#!~#^paSFoJu{TTMq)bg*i7He4$dQl z^6oVvAuK38U=b&?1)@9_daGcUp<^n5CM)tCYx>u#Sug)B}S;J|nks<_}(TstWza2UY_hVNj5lzmuJl z6XRZ7SDi`atM?(`{`td{=-(+rtT#SIhsivP&nV)#`)GN*Gbu^LhTPfAu}K>Fj`4~N z?zpM?<>p{B?9A!PXUy@a(F^UhQpMGP^=CjRWR|`GLW~|5OcjbLP2Uk~7@Thc?x;wh z#T;Q7$r`Gh^#yE7IT%wkazzk547dV+v)JEnZZ7i~AkbyEo!ewZXEvJwn@%gf-!Cu_ z-I2G*oWlx+q{5RC4R=k4SE?jUC#;F-d@o>}`VADqQ}#E_`jd>fRHLKZe0BJ-`-GP# zMrqN59)0I13La4ro13N+qm<(&6J#$`zqOQJw;d6qC} z>Ln+czq|Q5Q<7P8$~o(q6rdypNyuZOxukO#Lr!r1dqXu^MbdUSbjkqVYpv*L7+Mk9z}asZkXh#t5*iD?lmM{Fgg-QgCIy<)q=hKtF&OpK0k4UJ zgY%ru!WC`;&%D$DctDIolmxIIxm_NPN2#lU_|EW$>t&^7cRcsLMz!e=_+68Arj0By z;gL1|^94IP)UHBsdB@x0Lo+NF>aBI7NrIVlTve%UO=e-3hj~gw`+I?f$QCZz4s{hT zQ_ z#F*OeRmq_Hrh`t75VESC z)d`tbd5w0pmhvsw7f-F$FUuDuW)l&3-;UGa$1F`ll(hP*HC?CAyu2C&>qY)oIek-ZEp&+r3t+ zLrZ6uepe#qvN!JJ2hn%`Vyf^FG3iOXy3!(c?t~5=3oY}OKYmHKEV8vUOaxo!>uO35 z8@F)1@|hVwrPep`>}htq8tY+<8|iePY1>Dq$wq_06+s|hk@B}06qnZkVIIjn04v)U zrYYLZdX|_1UrlOG5J5O$-cp!DQWDmn7md|3Wo5y|F;JOP(h?n+jCQ=ge)BU;TVqPSJ1=Hc&TnpB~zJhU65nrk4mGEb~P7lnvWFJTYq(GWGH zmSW|a$v{lO&*%$u_kZ=ME6wi9?QVz09s0!*VrW=v$>8 zeC?O7vXWkdgcep^SELi6oPP@RpSJqwI$5mGtkVhy(H*P$w0%= zx2-;L4q7VgUGkp2=O~(UQ4wg)C3{~Y;^e`7NPf1>YG&Vee(DM@zA>jv?<6m^87)n1 z#Dp2@|6n8Z?RRgJ+Y8$u1H0%v@8L^c@UC#3+(I3b8!uitSWjq1 zU*7)JX%vHSSF^l1Y;|Vsl;K6oPa-q0%q!LG~OB00#IQRJmR31*t## zVVEIfphfx?rn{zn6-3Y~q(>~xm#=y6Wxt1viFwLv-2lDX*DTNKF`bdDg2G>l?r%~3 zv2EZxNI97U`M8WeS3d&W_NU#oz6)Y)9K{Dsim}JJH)`?7x}pA)3)wywNUJGa!LhkB3iQdgc3RSm!prwJzh(S zd%cF}@^as`+-(Wb+hO}s-1Z3-zB}PrzvKI7Dza;KI-nGum|2z0_a+j&#bLTJG>0%@ z7_HropXEG7Je^Ur7kPH&kM5_DcLs7y(iD{=3)``$fk478ya@w>`8zhJ>$Rq2ubYzo zG8{oA5Ue;izWZMjIY{!L^-yjmdmq^Q6lUylSbYsw`0wQ_!+f00C z-Q~jW^>rZqn4ZPFBfP=7%RDx=B3M)wm4aHVksrkv7ZEJh4@#x!1iiStd;g^GqiG6)+dM~-RiVw~T2V+6MC9gE>lSZh(ysCQ(aZvL_a1JkcFirH#Sh|J5~5@}D20yE6V9;ZHerd7msw zUIiqi2&6LlH5?2Jlf4CE%V`a~c5j0agkcbW zRsyav9>pkJd3@+rZO&Fg-I}nmDJ$? zcRv=!UbWfF-8OUatl|7B#0{wTVUwnxk_ROL+BrHd?8>*WGP&sMPNnIM#=Dqb8!z)w z!27y^r`K>Kqa`iul;OnOX<#qF{rK2v%6Iv}#R{^i2IfI^Cr|EyR@ZDeaeUd_wR;1h zt*Ik*3)Py(ZE56(KdM^F6+<6;<#y|dzIHnrv7S24pmp1g-I@GLq7965M zzY2j|KljlCE~4F7sqhL`s31VL1&5Dr+@OL4W#-HPxm!7KB z44mAw-UYgT5hZ^lr!Frec21%gVZUo70Qkdc+~#!gZB>^^_O=o7huf656py&eYj7?k zM`ukl68I!7Iv%gQp6^gSUfdpsFF^K>jI3NptBx513H*y^4Wj+`0@RLv8q4q&domd_ z-k{Hr7*3uitOd!7(jZ$zy$Un9W)YlFEdcVtXtCx6CT`_*1Z66`WVwk4z)X>~i8zBG!TMgc=LHhS-><+SN=|r7vUW2p?!8RT7OjZ=HIT%^ zk59{vOebjl#EaCA$qi6g;%}Wvzj$Xo_)Rt~x|+{W zV&BNnyVXA=89FZ4gm-c8NuBKU5jd_eVs8uK^)6Aic5|eSkfzWwTSWBk{k^Wa14S=8dCiNxipMA0l$NV0M8WULzRKFd?$79_ zN1Pj=!e<*BaXDNPa_Tgwr2sNj(UJqh?R{sT*<*@N@qwx&2iEblt<0#6*M09T6DzB* z917L!+w4AP0mO_BQ^e9I_vCA6Cj@U$-c27q`dY?O@KRw3gZO5*WlvLJ9xUeK%EXLw z!wCH5XAenku^hSRS+XCE3*U`I2Mt}3UnBfd_z)rOt(7Gxs+E2Cw(0j13!BGuSI0sZXW!Da zD)MeEzs6|`>GKG;rwr_i335ZSaVi-g9Dv8#RXpp7( z00XwF@(mw-#Ft0)xgHKXmCYJx1$oG!Fr&gB#Ot!!{^ovn_P%78WCv@20w{B-Zg1A66w#Qs{NP96~x{KubG!9tF9~d+Hp{ zJdKxe7wVk^7)d#xTsJ2xu>dl*iu}$YA4%a?RrRQ}&jI;%Ob%s}$5k)Z6T7(7A%9LZ zrx~-oE0r`MOy@nq@IoE+zBL?aM1cO>`PyRecrli)jY8s4^f^HmW1+!^Z+VT+(IXKi_y$Uph1MQ^7TV7G< zBIwjBZCqJJ57TKZy_P1Pr`CuZre0<%dsg7_SHO&o8CqLgpP$-rZ5+Ke1iGXp5>4Tb zNwM#~obt!vQm-sBH}tn7xV5;oeY9dI2OLWK7*DD~b^5 zzXKA2@_Ece=d`AhA#uxnpHgA7h;`*`4Kx%SM-k5Ol(Zy4$$c%*Sgo`Yao0V36?G95IK&?bd)xH7)%J z<#Ub~%b#;%e_ZngQlZb-UVhuyUf=xq0d(~|*|3>_j&A!<-1%0TJ8`d3dJ*QVQGBfVh-5ksucg#0v``12Mp3 z(YM?t3t|?XA-aCtt-*!~3j>;Z0SISXg5dp$_}5{#HzGi%dpo>OC;BTn$y~_H)2yV& zB6o7?6&}#9ce~`~xY*j3Oj0a$!mGDbJOy~XO!Z%(V*sSwDM|qO85$bOyVb;1F9Kyu z%bHQg+qci%B^1`MIl9~W*y+S*GVf->fRI&JH0=s~EzpCege)O{erl*=!nN~Bi@11s zRP;nERMN*y2vADzG2NtV1DybmdqnGBmS3K@%9LxMiC2lEDUm|l&6wDi{2jCyKn4INB!RCi& zIA|$|`d$JmI0A^cg%3qXmjTld1+2G!l6cA3Nw0 z@~blu&Ag{$<8Q*4sQ!is0nD;R@mY`jd3~Az*6zUV) zYFmof>#XZ_=oCVk87NE>u5S-HGy=$1|4JOU$R!~ges!%?*Lx309bp~q+@W~*(pJ8t z&TwF+Sgh&t@x!~C+1B*_BCrzTn3CwU!ljj-cKTp>VsisiUm^VemK9FesbO&8d1E%# zrm0(%qjeX4`er4W8u3-cT?bLMW0(v|`#h`PjIY1xT+NfaYs! z=L#_~nAjBhzcgGS%Tdn1C<`VxHwwk1r)l4m0EOIcMxLmfxw|c>Q|G4{VTZY|Kp$WY zg&teHF#kW~Tz|>MVas_2N!Cz!Hm7|>Urv9`gpp%;D5qZC=yM163mj8-Y87PdlOG+| zd&_H|JgI*X45%BzRF{Iv{BO6hrPE-3-P-TVVn2Z(rlgK&AlvvXC#^Gd)Q@jEp~aN@ zA2O#F)(-8N|MqP_;xCgkvm(v9-=Y{%95;nsF<-Sdk#-EP4V6zTFTuRJXiDAaCmx}D zHfxcmm=P!J^^s*ySxW$!dd#-!b65I&z+qqp*>wHor{??12A8D2qtHQ~=u1jqMKLQm zcZf?^j&#mAIu@!D+i!J{qr{w*^Zs=snjUdLrAguV8_@w4)w?qcNn;FB%{$!(QSR9Y ztv@zU5i##v0r`rc-z>R6wh4ee7p8i2@3;1g@24kk)d?&1tcKiHUpPt!T<|sMkZ@CE zgw9j)VMB9~e7$skWrO{(om&lT~%%2O|O6Qh`4@#vOq{5Bi~6CgWkOxn+g%qcij0U-fGEc za}w0BHh0dXvYPizSZjAeX`n+lTwhz>|u--ki&n)4SeyJn+LVf!T^{%~BzNc0S zTggckr|teo{X(qL`JC9u%V7@DTOoJs38G z-V2E24JvEFD=|^%ge)>5#&GGZ(@Hwkn)mB55L=~)3V=w!1u%2vM}=u$q+>Xc#`%v< z7#=9%DP)Qr*l552(`FQS@Hrp57E`bj&|d%7H3LdtX66pre2YT1AAU%O<6m$!^cgDn zvjcH$gvxtqY|mWgzy%=K+}$zthK&@L0A4Qmy^Mz5o|4r7pK`O8BbL5?YLxeF!4GKA zJ*R3}_Y}7WUy`yF+1h&@@jj5Cfe{{MkKw|ye=OR&lW;R~iWUQVo-D~HpipYnbPBsK zUz+>kmZ!LK!s}O2v;ZY4!u$?+mrx)R{*NFm6z^7yf)Bdw^aSNtYP5l9EaVxKk$Ihb zJ_09vr5-vlbnResni@pVZx=~pr!aNgTD%zUIXUfU+`Swb87@#-6;3@qTGpHg4|FHu z&*l$>qJ6a&Gj7Et@EGvy7AtLi*>QT`>DnB%Xm~z(b8CU&=Jiw1?$JDEYq#)h^f-J6 z^@;7efpJ=N0`Kv14WQBQ#?t$({$5Y%t=y6VH~*#9Cj91ArxC zCthwE)NNP&A!73Ar_v73Gl84Qx`(?fLvkvDRT9y%aw#a1d7laNUqkV)$BYgU{3P+e zT153qH9zs*dlvKLt;Kt3r{eJM+Q*Q=Qw39TW^YWsuBI}c&irA=mYUBfEMbW z-?oKkUdiLsSO?`QiGg~|G9H%tN5hZl@Msi3hRn|C?~Fx11)mUuKd0JW71qSzyG^S|se4}}B zaFL!gDv4)AKcEMFXtiGc&h@_j8|@fP%~vKmw#@6!W?<1fDUNM%bY1zs8+Cs)dQ&;R z@xe)tsVcS%=-n|+DWHxJ8ju1O&mD}*0hrno{@SIa-&tedagBP?P!!{Wg_6-wyYI5B zk){8ihBe@C3;4HT6~VJ#T#w*s`f-W>he)#a&$!!S4)a9D?36aE2m@Xg-_s|ij~@y* zh1I1-ZL8u9`h7Ky_uVCbWuyH*#qNw7lYT@S#nBF90Vbn1{_LH$N&$ORG9>_iqh&5F zB8uMQkCQCM`l35IA}Y&EGxP7;)`9ix)pE3nL!vn*NE=B_v>HNBNf;V~?VkZ2k;OvQ zh)Ua+g7kMZCl^x*Ccu8GRqMbEf^0CriV>}lge8oAHI`)kv!@_jrnW;)AD z>^wiX9=Z487M5kQ9=7U@n>PmtYa`*m(X(2TBKRJEE|1GW)-0wIKM9PVAOPp1Os3c< zUE1N%lBSV?l;FCvELaoZM7VbSxZb{*9P=$Hupfg^%O_xF*ob=LOrYv*^*b?VbH=&% zDe-_LUBKbv$B&VmcIpNOc4W`p?RtTA&0sb1G;=y2ARvV-*yc$Z-{h#ahDIWAAJLJJ zEH$lr7YeKd@msG(x@X?|KRD%BV23^Ez_t|HL|eM9bdX`ZbEA}p9S-u|r`a>rn&zV* zM}T7o$ek8WKk2vm=WUb;m(qNv>#E>|T$eIZL`&jm8tmIl`ED#H31&gKMUFYa-ndy0 zFX=k!u*)=FJTII)6kT^1%Q8d1d{yF0oY0pp|0@xn;FV@LP%9gQ33VcXp(Z3HU2Zy; zvhX!n@3-V=j2dYw)15@%E)NBR4h_sTt8}jgEc1x3>D#x4qlIdqn=cyQUs{cv_?c|t zx*o=FJzvEWeQ8t01K*^hBn!=&&gK-!-sm_c}l^Itj)z_94_(33M!-v z441Jar0W%*P74Qywntx^7axO*-78CgE=FHV%VLECLagX^+}!r6o~*1a zd0&J%23ZF%M#>89+S=Occxgr$!+2uDh)`2E?lQ0F-&YxQ7;q}&7Rg_(yTiCyu0kw7 z2|Djb`w3-bWoEOIy2he8oK37keW>3VzP6o9jPj9BK>JiY*`q1s;G~fD{Vk&%(@Fq; zC{M4TDS&Slqh0~GI`T%eU~5~OvbW8eXV+&7>Xi_5GHXhm`&{+jOA9=0@6YwP#08$EJ*wk0Tsdrn%w;-XDK z@yOys?6QqW^2&{etx~BQmG%J8~ya{zGW*YRk_Ij*i2;nb-9>Vyw*&L0ijkY(4MFpD_tlN zm*0)r!8TI=DObz&jP$aatf4r(kmp;&lV4vK?F=hGjCy{SmYb?R2IWGE=muf)55qv_ zg7GJx z0Nzpgk05M878paQ|3`>4=9@^p(gD;XkAG4!PWm5Z(j0LB^UHepRuZtYz8V`{-2bla zc3LShk&J&*{X&z-#2<#7bL*!`e1C9DQ`^`6HeFx+T__S5XG6KtPAg{qRU6gpP9yUy3Q8+}HHiVU^5+oKRo(X8k=V|! z`(p`nk_O}ticT^|W>P8jcx!!0S_5J(sI^@tGs-skCn<=D3%0Tm)=`bLUZ#xeQDLX$ zlfJ`#0%BsQsvf6@`< z4oO-Fwk{2bED#X|x z0MmMc*=7=g&f%=;3 zm~)yJpI0?kXH6%QCvxV2>k*B9M{Y>e$EcG6ui*NJk(D);*S58}LXjS>-Xp zZQXmn{cD5aX79IFdY{JNmbKU#kC*)Nhmp>c2=8)IaL$q%d?_NXovGZ)*3&{;lItwu z7_0)jl1<2A`WD|7eL*8JKC<+?y_b1qsl!}NSnLmwD;fYY8X2Qs|9K1?2XE9vE53S^ zg>9!(grm&zOkRv*pFm6_HzN4>U`WLj@0^<(3@AmEP{nkq$dJ1u06kcKx&t_|621wX zkDY+qQcl0y^^V-Yt30{ryIfb*eVeyM2C&Sgq(Yt)s7YEr&H8%>yaHV47MMZrXx7l? zF@VN6Y0Mf>R9y-Msw=ZE!79NFWfL^nqqb`x6fj3rM(+*$z~ zhRp+e{S}>F!$Mm$$0YhWz}u3Ai_d>?wV3|x+n=P`sPDO{aUviG*@GR3&*G6Lh19?;Y&m)jap(w!Ufq@TW(bos5BQ;S;$N?z;L z4?~IVyUI%AjmfF^=W}{`c}iWQmfyWlTclF2y$bdn=U}GURm;N0v5sVNtXhh=IDzu1 zHg$h0eMxiSuGEV(fhyjVm{P!h7oujddTc-ld1j zQ;Ca<7%%*SOS><2I~scl2(RR5LCMit@TtKn{##h@5P=cU?HJvH!Jo776_Kg5^ZhdB zq8rJ8PW@)(l)AsaukZ@_LC8^f*=_QnPxEv7~wgk+fMh!^Rd^LJWyVQiEWqCFh;`1L0F2J!aD&Z zU5wMPSrP#&-qn>4#grgUb^0XfY+7RQOivcJNN(DTQ9xGh(4rh4zIge1e5rz*m@KsE zi%}>Z?uWs2f^UX^+%ijVT~!K<{o#HO70w$P{b^$4m~kGvAhbF=GxM4p>Gz4x(-eB8owRy96-p4G8WKEH zZpI_`-Ef+6-+h3AKCDkXi0Kmg6v+S+=z^Y!0#*@eU`G z@lj2!RjB!BqiJ{@VCggpORRo$dM^WgaohFkas7-@`}Sb0ha&3`RURk2&B z>O~NO(*lB5{Q*4I3?#h5)ODV?U&|!waq(iBR>j-9mgwtoonqpEK|9Ls<|Gxg2S1WSEfUtA;}$JreEpy)4F4D9SYR8{M*q?@=&D@ zUFifirWm<@;Z$bk1MmWCKl3K4EaNb5PGer?#TQr$_Kw|VbKlqXGN9%TGIjni`xjw~ zCjalQX#0WfT-vaQ* zww6NAdQ!{-i1thUNVN%zI(%q__xNC_8jKQT@SiJag9TX#OxHQL0Zeb8h}fnyH}{rZ z^QDkRv6deg@9n6JP2ZsW(uuc@B~VCoD>ilE&B!1JP$6J;`2YG@WHL=q7(Ed%l2d>w z3ok28Ou+_9VtnOBW2|Z{Oe1A)Uk0Ej(Bgw!A33#_AcC>bdv~9V*ATQT+-coK^>Kaa z)Q4{U>ifrl*M;>jHW`>wT+Dg#Tk=nf48BAl@GH(!tF1kJM+JN)`$iU|ft7Cg(=THKHNo{I zUW}hMbP*&Z{4FxTu9T>)tvx~e{)qsCJ_!avrd!1DYK>8fHg(L9k9pSl=%gZ*2&vRO z-%927)2tdxjXSo^dHQOK`PjAO3o$%-FFFE($Rh zPH7o@Fc`j6KMJJoWq~m--g02E^<^n6?Y)}XWS|Q&_{IoMY;f@E?ugB`UIOh~polGS zztqpV#{j~3-^o^1_SOX_XW{txI5j0uO|X291z3#Lc!{7Y1n`3Ole_dY7@HeVRbbz} z%XeCSn^qP;E**)8ni{40kf5NJ+1Z)>yU`&1W4&KqADp1q@P3^fi0+%Tm{R7`?C)a_Zdc zaOiBP`hM^C@82mFco5$UK0tPu^bTh2ys=RvdX{sC@qwv`G{a)bUdyLl?;QJ%8YbXE z;~Pif?zdpO_21m`$@Lfp%4K@%3peg8&xPR_> z6f3m3{lxPH-j<5C5R!Z*1JjLqe#EpMMx7lUS)lFcvi@{Gnbd77!mD^nedX*jYTUx} zBN4>EGNi)<`GcZe!EN>m2o*fg6KO~J_jC@^odX>Tg?mAz4Pt$xhy`Q#%*QX44rbCjVjPMw}8YmP~km*(*% z>gLvQ>>(mh zEzhex6e#co=lh1ya@g#)KX4pBO@w=RG-N(MYy;-{wHn(=GEygY7-Y5>$kIG z&rzZE|HD?7a4mnnJoV(*+c{|UW-GF`cBPOy{&}}23Ce~??}vrrTek+cE*m>L-=#G0 zo{gWsHdv25ou?`I2DQTde{v)K1u&zjb!(P#5h-DDGAfFqcb5aJ^3XI&3ytgnah5F9 z{Hg8OFX9P_iB0~>i%846@OVGbwn`mRPv;{v`ll%?BeC2f%lr`b%*0t#(%`l*T@J$w^AG5sYb z#AoK^LpCx?&KN}O*J*YXC9eta6y*cn|2OqlnB$W`ftkVe`npD&@I=&rZdHz>G6>BnbrJ^&Lc$6m*hG2g_HDOQVqI0Hir7kUd?M_}W14B1{ZQggb z(s#UIKuONtR}bsH5?Ld6S|Uch%jbn0c3e|AjbTDY6_d>q@cKC9NOKi446i-plNN|A zL4BBKT8}J+JGqFjU&fyCq)`8C6&AS^+Xxv+pU5mM#0Im6%^1_SO3iDvEAp`W;GZ&! z&*o|u$RnRhXT+D~V@rGsTK;JIX;F+tXE_dddl+b+SdZN-;06sbb@_|{Mz(=_)Rr1h zPBWB@9Pu+d-CLe$@~-a@m{0N?%9IL?in57|mT)!`;A#5*D0}O$D%W@W*8~(KM7ksd z6cCVZrBy-sl_a z8P9y)JI45oZi-gEnQuqSR|k3-;|BIDiRL7|HhG1m@X5Inn?345Y-D8`QG`6#1T6q` zjs=G0+*AoU`!aWDn}NsFLS>a4V>BTfvH;hTMRB3Td=_(-{x_vjx9ZqB3rYCEQ(qJD z@6_(P58O|D%&msLt-VZlO zhZAd?=b@$is4@zf`<_85W*F)hP!m35RxEf&4*$B}@Z&&+fBcXQ?aIS(!AksOSm`|1 zhXs`{3^%pH484t^5%^*;{8nZ+5jSM@SrQAWf5|&~e#hh;HU{ig(ye+Y3u~SzAdoxe ze+(PVv7{C(^9LtnjKLsG=NHc#40cnDko1!*EE*X^1*{^PWx&ldnvN7^8h35no9FFw zom5}KrS*!tq6a;S(PNiq6tv@F=Yi(&ifD|Hh;p)1N2=NQr5 zQ?EnSY0S&FRAGLfB16M9JPtHkudT&_7W zqcpsro6c6K4^M}4bl)bixZ_MqJeE01dwXfBz?!f&Oja^joL%>5hl(a$(aKf)6N)!W zn2*A^eQ+U&$ z9ObOwJV;LGAMD9fkZUFzKV|0VMuhBL-T5eW=?smGy(I#&HCE;|G zUhg$pnGwkKOl?vQ6y2KgrK4;VtALH2#YMo|^cFvn_E}G#Y%uZ8a=fR64*F9PPg(zM zh39S7=C9K7-9eQjJ}vcpL&X518HcjwlDYT*1jd2Vao`gl#3}n}%)Cv)_uCxm@=-3a zvyp-Ra*;;Pjs1hqpnoA3bK;$zo*q?uVY}ELok9_pVgOxCWN*|HEphs4YTpqt`ZMua z&e3Q491PI>pftf1*}QfyyZjmq06UJ7pNFdr2$U?L^(*h1;z)WH#9sF*iWYUek*XNe zzvTCvR{Idt>+dk19Y>Q1B^|w^88T%zVRrbFz|fQpj>W4*K*M1IY8N_j{ zS%~-O(W4b*f{RpC0X&_e!~g*iFfUt|{khPGn_$7-kRUz^&Z)@ce#Wv(k><)&q#-ee zhEFVIrF)*P_~XTGlbeMo1>gr37QvTBx^=~C-i0fwE=q?x%379^c{@PrwJ(PD^j()P z<>c;%MiLc+_x*&ILviVq?gNk{rEK=e`|{pmLTRrvQR_*BHT!{70{9S=auYE&7l?_g z|3omfa~*MrrrqJKY+Cu{GY(5{$leYxsQnozP3iwVgo1i{XM8}%HMvvyTkHr}$>fb< zv_a0SDk>_-3U(a=-S8#=a;|X6_mlACm-?aI{R7v*_?}Tc4*F|26VdTLLm)d5Z-43C%aykUR#wzs%)O#XKP&ZsEQX|f{PuHSPtekb{na zZ`qs2#I9P%&#Ff4KZjAWS{}D@e{8i)r5M?Q1q2)F>FGrY+g?NP?4ywJ!2DI~-o2F5 zcWV9Oxh=7axG%jOm>M$>a(M2>%)iRvx!vLo8`}MVPbw;X-(XrxLHeS& z>GB!uCVgd`5rrtOlR$SceN`w&%Bf>Yd*clve2Q7~8-1UCdAGED8+?neAAFKWOjurP z9DgTLv4k1grTx-<`&-%WK{5fP(fZm1SD2X2fXeq8f-)X;TFfNpHzf!B(OAN%yC5C2 z*xY$C({Y2>fxXV>%-)oyei+wWAl^^KbCBFwh6vH6M_}b`qk9tI^1hG+K#naA%+tni zfvjypVi(dbC`vmt-D(W~g*6$#A+y_9qmVKFhyiR|(rGOD>69~lSq&Xx4;4aiZ!v{5 zJc<&d&yeyhH||NL7ZWSLI;`X7CO+Gl5CTz_Ey(xAH(xO4C~XdGz4Lb#?*TUC^v1E% z!YkyjTqRkmHvK$=4V-b?`m8&J36YRBHvR}2C$3ktDK`#)v{Mg(mcgNna+KKO%Hm`9 z{L&=GeHHg(=u%=R$zDYA~IW8w*uwR`*ezFh4RO8c-lu7EvSx)GnZJ@Y8~ z!amjj>Y(hd0+-||?TPi>(rqT)?~McgjvF!+E>}Exd3jwhJUaRsmiL|ALsB?(XORD2 ziT}H$PNVz}509)@bA}Kn)nE)kSE==t>#E6_w^8|_W*QZ*tG|CPqc+jDFx!xEi~Y`~ z!SW{7?}XUsPb)BG$nmZ2%`roYzF1z1#^(=amZ8O_yld+f7fshlz&Pu2? zro|su++K}W`oA&{!kwh3Jm*BLBu)|JM-)3xK8;%cxc}j9B&BaSm=|1Y&(%{|c7=6N zB1(zi%(8o^0$eDJHDHR8>ntrTosW4~cEMIvTia{{xFN^XOG%e*QBl!R*S`H@`KrV9 zSI)S@adt^!Kor^P^00kVt4SO5y!MD)vzKg9EG+YD%^&z>Gp(3Y)PVz4<4T!8YYs;` zPd`bE(dUlht5PiGSMEk678eh?ei16zd`&NfWX(r6p-ne6p8~6`tV|HM6!+7Z8YM+I zt;c8P4^JOKao5AQ3Qj_^BesJAh>HtF!QpV{Q^pTFCo$*uwtLZ7%Gp zb4>=WGchqGLYJWWkKpyOh>G^e3(mqz)4IB|dYX16pUW-XCzI{11hZnJ0{u@S6wW8Ov6%O^ecow^x={5a%WAGT9}O?sv1uCbNa)z4ZHG#5Qh7{FD6Gx*Wk0O zeN$T-uSyw&tPlcUtLBxH=#d^XEZ4n=!}q$;=LD_Q@unG0b&YpPv|isQj?iWX1vVld zP^U9%rmx5&+G?mf7&Ho?5u5<(Ex*}~6cy*~eP|^`kuZ#5x*G1`vt(LNek~P#AN!#e zMHYim)%_88h&$pw>-}rP(9szaB(S!W-}w|Csj?_9{qHc%+$R@zDdsywlmoMZ<5cFw z)oq!kLBFY~){pobqY8*-zVV0ar(|vXpJ@jSbsG-|XFryI{cO$0L6>#4=I-5%dn#jt z9Y61!ulClT=FU=MI#98gHD)JXB7>~FviM^JN#XxFf@Eo=sI%$6F-TBJwW>NGcAE9H zo0~3ZZx*v{c=iCLp`js*Dkxo+;XBrgwQ1x`m75Kapt?F#b<_)^$PgQso_MjNylZ_! z!{gk_G>`^pg7>J0G_Ff;eQQ9s5lJtJ?WUGHt?ZDXk|I0xbup_J>Ju~mwqnPLH)9h= z*T}NjJ8H(0DRtT83Rn0WKrcs8{yEVz5-!C*Q5ivrVe?GEBxxuuEtcZ=R8rPn+{Y1w*j&16iS zn@^zi&UxL?KDW)3=9WL2*RlEK!zzu*##?G;NykDnX(Q}e-;anBuWK)msCUI@RlgO6K}fn$WA`KFlR)~;vk~T@~$H|B9`BGgVi(dG0eW+ zJb;E2VT&BMR5p(VlV&9)SbX`J9Y+t6@swoEl$mBg6%*TTdmT>@myX|(pV@5TSW+?* zFxV21uc8n$lEK#2*gRiQWH!Q2tTI(krpt?OY-4ETPsAuY32AioS0c4u>XbW0o3NvL z2a@dEVgIi4`v&&VhaiJmJ)3N!w)l8+fPIjrjgNFwEU%cPiOJ$8#+Pu{*BjO3HQMn}-#oRvchV8~vBB zwY7Z9x}OhB2%d?N{tg-xyX^7#Da|o0 z;LjcH?y!kX&eZ%BEO2o|M;K+PP?vt)WLxz~UzSz4YHr6a{WVcSRIq|<$a|cDRii!H z%-b3EZN!WFxu#F(I8;zdr7~cdnj7@9GBrEm0n&dk!TDTKt_8G~mKKi&;w{4P6NyI`E)rOmd&)OI>6U6^SqFMg?5}O8=pzhNGsSZa$ox&t3S;sWb+1+(a zrtq>5|5IAi$g?A6FFg?#RohjIW4;XrPu6F~Ik~;4apCER6MjNW|`!G%!Wd($WMtrmezW zc1a@){v!@A!4ir-M#=%Dm6ualYCGe}^l3SioGuYTMU^eLf=1{Spmng>CVQ9?i|=gC zGV>GKH=klk2{T&UDeF{)=$Bn7a#W23zKElyX{qBhRLE%dIxlPn?rY>nD{d88D<{sk zF5c5p@x^jlM^uuM>azbjuKh5l7|BH;)v7@wglL=GAnS_5K^KAhuGDc|2~v=@P$s$L zPldGZzbpmD)!zjqx6B4JrEMcr$@fXR&!hHVJ$Zj#_RSM73SVT1;Ku+v(G@l*!J?1jh}=VXxn)`|^^l<1Vy_`u%@jexj@3?FN@F}NRILz(LL`a}~b*C%Qj ztymP_dBLMSW?s>Yh-fbni7{)hl||kZuki9&`YQdRvL?R9W{!`yqmg7gD2e|yrk ztD>*o%1w&zPI@Acs&aYM>4t@8!XGGv+s+l&@tO2TmD~X$o{;K&9QxtA3hJBk z&hLwpX@#zQNw>JS&ww1T|BMW#i04mi!@Y@t0KTfqqxe{YmJ=s_|GX`I>){sX_u1L6 z62?luj}Fm2iULzWny;Zi#d^%o8||>jG3TdaRXUoQQwpgQz#y zYQkWhfQ(P)yFUc%pKp^Lgxn?qXRTbq>F@eCpEG5}#RmExP7}>f)!v87tf-=;c0yv@ zA~>RVJA!ap`kA{5UyBL(hrK6k5u{{+e&0^S1%tT%Wrq_0A7rw1%HPp)O?MT87(N(r z83adHosfW39EOIs2V<_TXakN7a${ws>f`q9@4WSl72!WOpr|MV8|WR9u8Y31BaEWV zz^^NR^@QHbDA^(sM@u3T*AVZvwB=1}&WMl!(x)pm>`PW(nz!1OS;zo5p{%OMckR>S zJFRVo+EavN6hDIsm2jpskq)~#j3uUNQK_IDcD#BsEpJ(`UF+78!9gqhmu~dh0x)Jg zooGT3d<72Of3#gBdHMP4z-*Wfm80eEa5}KR`*UTCYT|Ik9+_WFYEJwj1whDHLP2oQ zJ{!pe=g`E9Yg4AFRot^&(t^Qx3hu1C^#k$^Z$NNjMLO0G; zpKOnes2Ej!MJCbN7_oF-2sAfJtmIb<$^by~O~*+Khry9It7hpOTI(DhUY#Ei<2#uV zeXnvvjRpLf{IE) z{ZE3F2v*aG<92R!v7OcV>+imuO}f=SGL&r>KJBe+o$F-pPYqut3tqGgAF#A7UKK?C zy%zj1o#6U-1!{sQp%h{>3viV0E_}{ztJS;kGml8p&+glN0oj>OR4B{{C_|dw4jfB8 z*ctzfciBBft02k0e~)MmE!M=+0!A3Lv@Xfr4q(e31;jy zqkH=~#_k{X?=aGPxb1dnj9DHPGfDFZzcS*p8I0l5lgu}A1_>W85&Lmk56B=w2iIH{@&q6WT0+j&N~^m74Nig z)ml{LE)jlrcef>EjK=6&a)PZWzuAgCV?;AJk`$$9ZD{RV4#VY9M;&DaN^p zr8q$0gU-loxS*L@4AH6i)uKDn&x{IYvO%#FLvy9%x&2ig-FG31(FVw@(?%UghAN6_ zVxYV;dY$0UOqt<(6Oyu!y47`m+svuTFW3ngBmzQKMNJKrb&g(I)BpUro3WoK?30%t zsR|@!e9Eft0W1uBQDy!KCRIs9fZq4RC;`88KW-;IBZC*$j)(|0LOT@+!ZZ(98Ch9z zs;jFNmG_2U1cZdwdfx`V0N8aJu;}UOaq#d8BFGjpAV;q$=L64pf*kQRmsr{z%LQxqDln#X2?2Gjnx5G9+RNJ>fh{0b)sK$K!e@9)Ljf6!=i@Taw-y(KyJ5+fIxVaI&RCbX;JV>hxx>TLELlp`W#aMmq(x|Dn z=MIOqH;(}KC#9o9yS+ML5sZr(F|J+72yii=DAcp}RqiL7uCEtrVz+GGG}>g@4yf-- zW4g@P#Wya9^`L8|4foi_oj*PObZNYt3I;~Zl$ji*z!j;Y$ z{(%xaTY<_0R36s96eCWzy34~D0s6Yv^C z25zyrsqJ>*+j<)^j{4fR4aSAvb7(%S;MmRuS(Tex9ODRD?ZaXI{_rU9mWp8M?~~N& zAG!XBI!1(`jy8Bkat%MJ>B6=6%!!cA^BMm$u=S&6E-!!CwNTTpmH37O}2)@kMZ)- z<`4uy@VEd?%HU`*V(UHAs_`OE&warkSNWJfU_QI%KsW2zVGbvLIag$>6aX&ydiCi} zWpZ}`<3p8}(xWUfM(xqM>R5ZEQU7Ik|D|ch;G?OEZu$EUPnbtt3dt=`$qd)SMoo38 zYTiEFzLEYMdQzTBAi;H;V%%j@acQh{ z!1b&k2%69xLURSekCV;*JCkF=ohj~1Bv3i(OvT+G5z}x~5>*bGL{g}!w!X5Xh~oZN zB1aev5IK;ee(Tmrn64oLn1#r{xDC^yw+W`KH72chUTfYb=p_EYycN_yL7|^x5IA zOk9^as0BLPZvHOtOHJ7bJ`1j`#a#U1g?yYvoEbRbhGH>20U8_ZU=6R`|8J)dum%4l8x7grO!?=$iKSiq{rF9g zvH)pPY8D!cCs&!taNF!=u`Wq>4>anO>hT(C(SUN%MU=KSq{q(?NYXm@sR)5w_<da4$MT#>E1Xg=iksyP)d}jlliDTA+iiOCLi z3Icf-oMJf#R+uQq#IYZBXu)EYdULRxsQBk=2>r|%)p@5oqC~^hg0tJ z&UjVVP+CmuT1%vN)730A9sf|1vDEb1@@?(c)Qgn3U$eiQMTG?)`UCL;%wc3RL){uG zDxv;4cd&Vc-3Fi60_>?!55yV;I~D0WrnTvx8G}MhBhXV+aL9Isj^x?LtWR7a*-CAv z1fr>cg0dX!tA&Eh~h*+s-GDY1US0SCaWRlms6 z6{{|SOUwUE&_6WN;rDgzujCrX|6!}{Hs5Od!C(unt!(LFFPKYFm_%gCrh*lw7zZLL z3W@>|GU3O_=*3J~sDnZ8?u1Z;bm;@ERkPBp9Hsm5nPr5t-uy)xYU;rhw*EJYji1#* zjAYymm*Q0i7d+(?So&kcB1=;=aC0imAvVQay(7nZXI!n5A$%D!Uzp z(K?h^O8)i5N;rFTFi2%;(Oa0{!wS{A1@s{U{tDI@V>xq@YYSQlX|fDAM*BDmEJGNt zjC&%iE<2RfcW@gEPz`0}>FVh|Z@u1j+N@@$(53+pVTijhE0|aOB8&Lwl0k{pu#RR9 zK7g|IY$GJLBa3HuF9ex4NPU%k>JY*zUD^$Mv@z z>cCIl-jM-9ikXVdja48r0Snm@ikOi9Dp0Fb922r~aF??m zpLGZqKu&RR=O8H;XW+|rwi978OOV|JwN}Rh}ZNF+P`*h zPMlWYI>QNLl?#6O#y1sg3P`X!h&50gw}je=fedU)3|A(Afyz}9j|*_ZX)mt;6Hw3A zBlZvkpJEu+;%_>6PT(VX`y?dT@u*Zggy$EL9Rd4(J#x=E#}t+&&bLmw6`LJv_m?Xe zOsiN)3fKg$Q9Cek((I`#!H-40jWXVkjoI$jGxg0TdfWk$=`SBNSg)DvMcKk4m#?10 zR5A>RCyY<7Xb$-pHKf~Bc3A(&~Leiy>^w%#8yKLD^ z7F2X(8t?3!MaEe;xJEO#kiHd~rZY4@-S%2_r*j)=c~rJz852dPdS*eY+2MqA;9dDB zWj5tb)dBv=Xz%^CnbfDfUlVNXz+Pbi&}t|_zFCVy7i>dKD<8uT|SW(5oXa7 zw{B&jQ+?h+e}U-NK$6bqT;)fQU^bYOboE98cmjMTZ@No+ef*odmT0;K-qrif+u2e!AGTH~CwhIpt9WwZLLQ37Bb4CcS zNIN(z9c40p@duGvcHZ`hmgmQMM=wIVzmo(OZc*WRNWJGkq&*1T5lrp?jkril8w~N( zRH$;OT@&4ZAGIe_3{F<+&P=)^@R2T;lo^o+J?P;a2kA2=*D!3LSAq_6*YK~k>J+S* zVBm;@c1W%{Wm%nmCRTv?T(t)_&CbSM;9ijIspq5;@@-k2B9)}3Yx(T)6-z=eX&clM zZK-0q-h?zUFznF>0sv_3(YhyrujT_opC8~ol8(W#-Z~6T@>sJ@n7{X^XOfbUck)Hq zu{lAHXxZj?l8S@ASi|TU@3L{5SYs9ZeB4Cm@UQUlUV4zKP>s;SVk{~s;3{}dYSvC_ z;r`ZBprS>_&UllNI6Er*r3NF0h-&sQ#i2elX&JV*W2QU`h{(o_{`w6ZvY78@xH(pjtw}qpjdh5N46Kz)02C2FqMc=f!_4*>`IAYK4Yg*;wZOS zBO8GBht0Rt{7E@S*&6 z39?+B-r8a-Ts$6*c&pMOcK}T7&rPo149wVRVhni#PC1aAqus3tWtk@p8#~>$d4M7& zQ3Z)bKylGsuYBtWJ^|Auw&yE3_S^H)u@cM_+R00Dd&IuJUE6>}8_7`M8m5igvH2Me zAL9FZZ_38~damq8 z>;d5_;AE)KC@6<;n6ks|ky-kb;o(`LQE$TJD>W}q6B1Dl!dvO>-B0?|L2%(+JaU)S z{7v#nCeAl#B|Xk0<8)icb%7K<*6Y{p;2nv}h}tcwgH#F9A8}G-gCt=Vu>WA9N}ot~ zp8?zXe2ko=psSJSb=rZmKXR=GMaF>>9%I%0#YAm~lQ)`$WN)G%GMT-`dBiIrO5W%P&wH==(r83{?> zr7HoU+d#h4Pj03AwihAkmqIxEE{a!n*jm?8ukb>9y0 zRw7(>M2c{Ugrr2mxC1U0^nkYgRItbj7rsV?T|Z-h0LfHe{m@{v?hKr@aF1Ld(_XR( z*lF)7o1Xti<@J_Wc4VZ~J{uW34@)OpCn`45y4dhD*jt1(SkD?XnTH0ns-~QFU)WY) zil!HuM=3#U+?llQpj86%Q3fJvYSY<55QTeGx?>8-7?)tI=?s{NtN(;k2~z9Pi_%7h zZsP}^{G`1}gehRjK87}{*Q~yv<%YA@b^Bv_Iv1{uOH02-&L*>s5-TUC0InyDaTJv| zhF{Esq}~$hULGwWhH$~EWSM|__wG$r z{8B{nr{Kzs(f4wQeSIuH=?{yrDMafE9r3$!_OD!pNzXHv1S2g04jR`|YO&S-nv#<& z7DZ=K>tYH@lkhRbo^azv_hGYuUN15nJ_$o9Tiuh0=9^eAnNRph+_N#$kPam1w(MY| zmHAalZSThiXy6?op-aF9xTkBX`$zi?ea63X6Z35$kelr7VnTw#mj4@iZMOKi#hkye zzDUErdJ~%l`Qr)D;j2FYHY8aAHY87Bpb4{2uB|4Yv5#yO_tgqVS_*sjAC=x++n5tl zFZujFI&8dHJh#~J{*7NBq`&^0s+j+i*sAso6n;OI-Z&1nVPR(GUpz)r@H9T%mlBjMoqUO_kT4ceCUSUw^Qrad0$W_J zyWW0h8Dv_3-(l@2+*&Yh(^*+;>yi$nUH3HRxoi|^J1>7Jo_%NXIyTm&cVZVl!x;H# zNVxHg)*PbzEyO>4Xx4lgBqr2~_Kl}jJNbimiZsSWM^s{jF-~|Rr&{!)^{7xOruk(z zlwAzmObgFdbkjgaNh}O;_&xUM+rk8F1uV3=lG?F2*U;sYax4mBYjL+On2yd0v|1-;nFD-h?yR^cu3COvs1S5rx ziR^P(eh)PB>E%)XhLP{(?{aCmR#&QZj7?xB_d)P^@6i%?#$ z46Q9Ed`PkEtlhA}@KXu^nE8rKLWrFqV+Tn*kr`eb6~u^WVw`;UbS>&f&ki+x#N(&hp#CK8U~Cb% zOk>8sRPLQUOQb|)oNr+x*uVbFL=S?*h0K1a4WFO8zZ8JMU_y@rPV|2kI&RKJ|HZp< zW5x^T2fHX%&8)Si3Yrnm987b;GH1Ho%nsI|VAb)XUjvoX0Q8VmQVOQn+_2~F9tTDs zi0A?tk2)YZueU9Gt}WVABi~S?XJTr$dAz~8OySroH!&OASq*3`W$+F)q{n~~qfpOr z>T&c1jS6xT;cwy!6|5E+pV?8S`DWX;y);QHWg1zPqmKjUAijRvbl{+};-m-mbMA6o zuB><6BtNt-mXCMr-AA#XHYG041lbk87W8Pg z=YKkmm=z%#;Tw%p-Q0AZ|4c{c|o57w2-*BRdb5Ns)%rgSO(L*G7AJZr;EE1cqgDkdNIf^Dx68jV&O2mVbrBp)b zhv#f(iv^EL%pbUZf4ePPTaWM+1E-&O*Dquuh40T0&ZaQp)xsp$WY?Q!v*NztF z=H^~e7RJ)dzqXcLuQB+h&!Hf^HiO7NN{IcWKhdi;+vF<7NMAgPZg!`X*wQ;?e5+Yq_RFWZB9vYaOnt5WT#zq6x5I` z@cuqX7|VBqHVr>e#cae&%e%x3-ADRC~VEGK7IF@fpIS)lhE5;n=-Txn@AA0{e*5o494pnBCCmCzdAlt zkkkNYd4~T}$+>nZ17vBM%HHJhpx~{}?I}UjGf^MAke6~*Vi{u(UY(^nukug@7L1VL zs${V2VW=Xi&p6tM`T83qJls=*cEbh6@`{RPua4T%w~(3(3?qE9B$5U4M)D^>WH7nP zP54AwM|LFa54rO{jhFCc*mxRBO(pr#)_^BOKRNP?O`tL;6w$R81fprCX)%~{5*8^cXK?9iQz`~^ zxLRg`P^8Cjx%-^OY+H1cAUb&{=e=U=g*$~THlOyJmEB$<;l0cY<8TKC!}t(WgUiXQ zBI5b-frdGyu)@dgCq4mM3=u^M!3huZ?Nk!ntiez76*G{d+U8WW@4Cu(QpYTKaJ#;z0NJcXtw6k48ufS)24E zKptuQp&5^dr6+xA`3AH+v1uKus3nHF;Qob@{sxJ>Msb6N4O z(lZC%Yat06;4gAJbOMizrt`Pk4+cGib&4(Nk(Czl?bQfP^J=ghnDbx#Q6)EjFZ%WC zC&4*0U0(wE-$Y0I!?rw{-%HN-0s!-<9hV4U1=`h0)Ua{DxR*dfe~2TDTqqR+kuJ~~JDSfj{1j=>X`zQUuj(uDfvs%uEniNmc0 zt=l{VNbNazvs52>03oPWNKt6#F1G34hurj60P8E7pNFghA9$p8yR7E5UguHbW;s>5 z@o8;#12WP-+d)gz?w1?Lmm=Ons-D~dplp~PgWBcI5A5m5SMfkk2h|z>VPK9$`q%A zk|N{*b_0Xp9kP%PhC6PRxrI-nrIjbtG#L}b=!FR&vX8fG8zd|c zsEiD2r2TYCtUe$Tns%Y8<7^Ye9gfQDH+Q%2=EV-lluzwld4S7U1ept1aa3uPnwXghcH~y zTe4-66KO#v;Qmc=&YMx@sLdW?VcH&gjhMt5Dv+x;3Nd21Gn~Uen+oXYC*;A?8C)%1 zc`X*(aqw$-yg*6GI4^kS?5`MB5tv`s*7*~2Kdtjio$vY%f`S{?mSWEsyw;eiI_W%o z+t5Nvlb(_rL&sF73kUer%PLOD^@4qgj0}(*1j6Sm^94mk%dT#O2u#(`8m!F=(dO$( z`J5)ZSaPzH#Y-&Y=Nf4*ah!MYxmD^9C{G_BtcQ;tY4lNSRv&zGOu8a>%3=z5sZZQY zzk3r62tLFRPqiUCY4pjF25z4Mk;U`JdmI-P6vD1}pllZW#D zrA7x<0fl3ZPei;ghKqo`m0c4I#gJw=xHH0vN^sdY7w^0xWc`q=kpp(OwO*>rRZjEE30P!z^CT3}m1 z)NcP3TNW4O??v2lb3Z!RlT}q!C3S;GO-yeP4gE-Rc)=YU;noe2FjICi4!CL*+B3*UT$ctv@TaD>;2Itc4hLjrerpZKl8G{Dh> zYj4Z&k7Se{mCz<+cFNt8PY<=i<%U9w>_$%v!Yle{ehYf!omt$iqR> z9MEzYD?2*FrdRRVK8&9!s9vvQ8Zi(@-3U+1cPo1cwS#-({};7GQw0PaXqQ4HLzPOL z(7;4H8i53|!K{JigKI4M-SWnN%b4hhnR!QmU0%dMpv*ZMlGoC}R~0DeuEleerpGt! zGE-BjZBwMMKE>o{!-(*v*G#mqKB!h)Qk*4w<{RMe_tu@^yq{Y5lyw~xYo4BEZ>Tn+RcCXF7=w1u5N@QS8>=+W9WWzAM zUKE_s_gO6lQ&uwA>31c(e!@AOJuPd^o=a$;JdS#Qa|b?`Fo8ciQ%;yT#=Ja^1mfoG zjb1Jr%yTzoYNZU(&XzH-6%$ie(dl_H{pz&5AKpzTmtr&8i5|872#T?(_SPoR?is^q7 z;Gj;rmF3oOC}vTGKC^$nUxK-i17?`4zB?$f+$+BKf*;VC4f$CHHy-~^=2=^E*%~u! z4nBxtcVNgvqa2w7`9+PsT?Tw@;qAtF;rwVaa8J#=vjS{$xQV3D@>Pr2&z5DaIDOQu z7qh->0ijVeqo&Zu1@fO89IZjk&3x?($Dz;kW zw=A+BcyQjWqF9(gZpDmL4RL2>5I7*jU%X@^`(-AhF)1Ax^LdngI`wttZ9WZzE6g;V zoD+0`^}71TM{#rV|BCQXv>1*fx@&qJ?;c94NgoEhfx+Zj-^m3n6Nl=G&O(6gJuEVC z82(EY_NGUu!kL+V)PLNA4@{Piz!8Nx+?i+uj$uqP5B2#to*!qd`!!I}-cu0n8!h}p zP{i>cQ=x!Hc`2Ut9PEeM&g&DPTF`yryvSn1pJRSwy}bGWzi8Zv4N|eYuF(jph?iyZ9A!ZZK?JBXlgH^Z%!5!(>i^=h z7;qm?aMaU&w*U0lCzy)(1d+ilH>lFApYiW=7M?|Hf+`Zh;Vgx>11W3#E`#JjF?2il zp&j@hZx7cP*E$5nL|K$?ks?FP42}GT?~xmzAy*Aen;k7#;in7$0e8NvOXKNh4d5Qqkaet~GO=uZ2KO(JqKU_5;I1_*`*X zc^0q1a{u4dpK^`kfLIV#3k5cu=BMxeqQ}svjc2?{Q?54b&W;&BZ)X-gZQV!iccu9 za0>tEG8STCX%rNqzJMYcL&FiF6^L_R^Q4;uIcSJ+2of!n{JU!^is(d%<7Zxvdx6v7_-Dp;k zg?iu}fV{X}I(pWjpW^cdJ*)7#5W$J_^k+POoc&cgjI;CPg}yfy*0>rmQt0F0{`J0d zO39IlC;g6@IB1~e8+xOUo3gNmGm6a5U?9Qhw7ujgDY7VpWQmyAMMmpOQ_Jr7Rh2Ma z{KnU>^PQ#({Y1L_=g*(1@>DMGVw64yY9$A8t=6WSiq_acv&Q_1C4|L}!MEUy04qhk z$8vj8unf>yYf$8IB`saMC+QWy>#M2&dGj=`$*-s3u66tEE-z9!VGrzFNcz->x zqOxPz2HCvDG?>ivZS6icp@>*!l`%W4K9Ym&skGVQNo(mWmRq8RnzYW6Hg^QYX+-QY z{LL5J9_?OkMIxIyD-XJ*%Pva#ofx=z`SRrClf-d8)pU{GR$b)!s=520k0KYcIu2Is zD|zspL8=(-`1todho3XXX>o?JTNS?#S5uS|#8pFXtzQ9d6S9a8eRLmFamq#+r+QC+ zx=Ta@-&;Cd3@GZth!)9%l5l zUcth=k9PJB!&c)!mkN<@kiVO>bYz@a(!XZi!|@^83q;)Q8uQV=`s- zuhgQBy9Q%}z$_*QDv$V(WG^r!?yz7doyH5nl)wZJnI|QIP@#b$HUG8RV^0FL8GV%7 zm;F1K+YDh?4Zv|hTS1lx46V#wJ*iG70p>p7Aq&1OYde$;AOjXOrXjlhS)q&#?Rbu! zRFB~e-65s&-RS^kO1ikMK~=HsLH#J8@7%e2w|xhPk+EA9whg>;PCReuXt<2;w!DMT zr-l%^kb?u4gY^)1-n{wO&6SMd_3jV)!6_9&zJ{9VoZg=#x;Dhz&6 z9GO0kDe3FF(lbRSDIx=jLK?iYK$TxRFK&9IyzedcpuDGMY?n{0fQ71g|W)@8h;0jhjq?Eg8h@$(#o1NYm3IrNaY4Ebjmu+T&S?kGfj?< zsph}O)Xy#tjgdttFor#|fITpu-JPz&(6cDV2O_eUqEV{=wBbUaob2_-YJRrPE%zSS zTTWRGPYQwyz;ke|gXs3Xf_S&XU(qRP7cX8MRijK<23MDA*EV}qlRd(62T3k95QgNe ztvwyrCaVPjxYxcuBIScujmuf~gnAuEfX4CCAUu=WCVGBYfPa408Df$`{rPLso#x`~ zY41OH5W^5^>A8t5v3s&&E7KyHmB(h7itqWuunh2j>dk*kasY|;V^K;i919{k5--q9 za-~{adO7Om{OHRC^@>dD*21?@IFF%#W?E=lFJ5skKDRx$Uc50ZGNdOxg#f|9uXCB- zZ1`Dn9*`*70)qq%7rIh>9bZgkyC1T_Oip-{&?{I~44p_raVXBjR2PV9kKz+OmsGAS z)%&rC@%cg=4waqIa|Y)pdkYtKJxpR@cx4~s`}BL_Rq46!U`9`HtlI8$KjN`7B&APW zJR=<#<2i3^Pw&!eYa~w{cwuCFddk;bkGe3DT_f4=^YI@4{J*1wqQ-fgw>8nxf77|W|sjE@+=xFNBtdFWpg@zWJjNRGpT&+;bn{SNty)d^l zg=mEw4S>)1S3r#{Gm?LTW?}w)W0PaxMaeO1j060DW}~uUtds;AnN-DO#oa>)-OS&M zjg2*BXy$s}1_IZ%i8b=kgoE!a4SON(7z&bbcaf)cIE(>im*cirO`vR%?T1Zn5Z;lt ztgO#|wpUK=i(dIQYD!=8+fz7}*_O+kpK2NxU%@8eV{kKxBz5RxOo9D3laMT@zyg+p z@~{~A;dcs}uT5bIFRmx~AfjI1OS@~Q8pQ)e+e{7wXiBb^tw|zFZpBbvnMUvzl^X_X z&C&VfBt_ECW=t?V|22j~V?!^wALrk+EJe+YbT;mt7K^A0oI!DcN#AqqF#@fBK>mTXD)Z z$FXN`6~aTTmO9}$TMPY1X%F|BpQ>b9I4a(;LArnc|Dx+HqpA$Iwoy6+36bswDFNw4 zBOr}RH%NEK0;Hrn1VoS$kOt{4DMh-wOS=2qi@o3P{mvQV{BXz*2R`drcg%UsD*zy< zqO1GwevQgSWd&Ez``NdMYZp88r+ZD&*3-XuE)7j7+}0>{3os8)I>*Evw=(ELniGhn z?MZ<>5MTD*k!Ho`?6=`2fqz|GJ~ysL3q?BTu1fWUdO})4RE>S_PrjuUKyC83rY=DJ zX9A90;MNBnb>Dv9cfeJN8H2Q1VHC2$e^(K;s@l+mO8fNiz#YW?k)=_3Ecxe|^aPdn z`Hi7PZsSK~wgsx{@tJ)#8V*L#pj7*A0_;>ne(~>B#5vsTAtPV654H|_Du4ZYnDSn5 zkyG#$Z7#R5*W0)8#5ZJey1HMlzQ$b;y-CM@_42xbtU*xZ>uBrM25CW9?@QG)njRl) zcuqaNq=&Rw)Ao5rYO8Buv^^g36A}H;i^Y$NQd(oG^%5>vB3Em8qx*!Duc?f0FK~IT zu#gy@!ritC#611SHFb9NAUQQ8Utv6ea^mj2rHIQ9o5}rO?>wg*(jXV)Bt3Ezld<33bF8OW~&YD%FaHQvIDXYK8{#4Z6nc$M) z#qd7kK*;*N>M&#wn5KW!m7lpMee9OB1?mKHC_f=&exef?$h zdrq*G#V!wva70$DysMU+ofQPhTh@CY1HjK|{zt8cg-9L&1EJ|L!e~Lw79y=^;M@Ur_-G#w4K$@CG7J zU6Zz^Ri>Si4S*Bu%)nct`>B0s)?6IjHXisUjKf z@WTF9GHMD z3=-!MTH7Y7Z+zS1(EjoxyT0kv`zT5Yo1Xz0((?U#*u|J_`+qJ*$t8y0uq!G$er-hu zG%q&^8!r($VG8uy)`yD+g~UQ&)_TF1{td*ld)RwYxNUfnMeH7gfcs}y_-f5T`*}$Y zs9+XDYidCu_h&P08)J}#Kffzcz-zd5Wr;)7Q-K!)6e%$HrC zNeZ}J8EtmI1MGAj8*(HH5cHEoyGiskA1LX_*53%gSQNwTiNM4sDJiLYAJWZ0)#fAp z1-XD*kPa61Qv<_k(EjAO*$4&>!(u6sP`n=a-~E4#eWV+#WA5rhTY+8iEwFUqj<^cx zfO3m=hG6%=>IKKTM;pv$)RPL32K)txyMq!kaPj>-s{(CP61_5Y_~bH*`-Kg$VFCptd9N&ZR( zz?P;Bx1CCFSYdHpkML3!U`1RAwk6!_@KSE{nDLQ!6VTWD8u2UbiR$k8h$GlU zt8W#a&P5Vcml_{1cVF%SNea~SG|LC;oGdrbYV?X}Yr4C-{@<~epN2$W)b9b0By2NI zD}5bT4Q*|!2|NDe)!_ypQe7abA`Od{bFb*kD*v)4F#nWU4 zP}t22Law)RJe>QmF0t###QPAn$vsE2+!iO949>~^e&a&J7WNQ@5mPr7SLD+xFw2E) z%l>L3{{`%2JG|NIzayEPN z2^L)B2Hb}!Mq!{#2Rn>O@T0Y)otUG%X@PbZ3jIg+;XXV^Nu=IVHTY4 z;eNcpjb07opNJ^It)*USURN1!BifGJmlaV}^dal)U2q_!sKULGYGFMEsc_ z8*d=_xU+Hn3XrM_ zzDGZ@k+}485EZgKNcpcj9F|I4#KP2u4fAE>4q>Dbtg2stS>Xu&9HrR32V|3@Zx6RU zQdKT>fSBk25Li-~@8@Fw7jF|h2UdQ}>8BH{^>TxX@m3WLSb}iIS%zubZ25l@nvx~= z^xvyT@O@ri9w>8CRh{=xNNO$GO?~x}03dQ8ERi2UTlGC)hJoKjF0hwA^)i6CM~M8> zOr3bao3wynm1xOZ9F^3Nq4|T3R&NgXTGCcJr6*I9KRGr6wOI52#msWsYk@JSfL)wV z$bjPy3(9{*Bmt{9B4)f2UW0xHVzWJN)zB8Ht8hYGt+cSI6s97R7t}$*b^F~pf9|~g zh+R${w2Qt1q?Fws9KWU4XD0p0PjCpy&DdV7_MuJ65}m1otC*ko(VGv@^S+*IV-vF1 zUv1mS&H{xO$h)1O1=6!o?fmAZCWtqnxG+>w(E6zkvJJO>{P@*v#3?jGYxokuz(|my7N!-&HWn~Rvz3qDoci2gtz56);w|6{ z=A5gYJD(b?XR6+iT&&5hef*XHjZbr!m2TPOQQSACy4O^;uOpEm@G_9UQ%_DHp6w`*Pl zv*HAxzA0*{%dcVK;Lr$p2jY0v!N^#}xxaL9=E6>{4K_Vr(?MQo>P0kuaH{Nbt0&MvOv@^z!g>dL=TTxf zd*a0x00xq`P1*Je^~!JFJFA+PZlPsk(g^MR&=})Uo>_V$#{#}ccMp4sFFOW?ELA29 z$MdA%d%&K-TEo~8K3>!HW!TDqlUvxiCMP@f= z1bW4s6I~e@drMto-{b6+3>L+;Hl;H*MpuQMzg_8AHz$mVwd^!up4mmYCsU@OqQJWg z-vA7|#8v<%$AA8u2U#~_T}bfmxP5AJQs%wR0^><(0z~aZ;Kn+Q+Fl`=#U;(AkYi%2 zf@p_ng;Q-|h#*rJv1@ep7-di!I3(A4m*4vZDcv^&nGf#A$>#sqDSu^ing54qgwFkT z#k|tvXhnZBM|7jF4cZjxp-`3Y(b8A(O?npdDyB|h8hnI>z~kVCaHnA2+4qnI6P>A2 zzV(Kh8g-Z$&2ww`qx|UM37zpDfoC5g4x6CHUv}lk$AJQyWldEh&5{!z1{?pvU)ue^c+dtg`77z` zXOJYHcTK`0i8Q+Hz15!?1RPpdxSm|Y_|xb&2@HL}Nasag`}oS#QFvW=Z6k}%MGxX% zNtQ0Psy7Ugq&Zj=sn5Vf{|}=7JeZ@K%GniGtu?d!z2zC1`F9F?GvT#iCreL=xt;2~ zqTjTG%M(Weh4-t#qXH`y9u-35eYqUs1g2as?9oAAsFAPHh+r?RVc=8!>`V_>TEwTM zYj} zke->j?*wZ*{O1p~iGPKO0sUAUQ0jK^N<-s#O!;NA=i35@m8ka6!-jl+Lu`$Wm2eda zw2Js);$bdYKBbPPQZgaU87iG)tK8u$PjOM|4~IBb82c_y?Gk!MDNLb(gk){0ed+Ym#R&e=opP!IOOr{48nPKXh>@cv`)uE zlGuGFF~WHeTK@EJqSR@rsmumZRK{R@ZbWXFA`X_p*pDYvs-)ZORSn#v)qyP^3+RsebD+SxhYaGOGErv0 z0buBajt&WWghs%|{Qzv#PFo1z#8R#r7w?qV8@6aH`)*{dl7*R`l4iWs(BqvXkdv3J zuZy-z>ejQD+Z%y?_nlv)qs~>LxE>F58sM26N}!=e3Z`YNZ8G2i3Z zu@b0)=Y&luWXlfwMVDHG&Ohj4!nIm!@-=>ITx7YG=V9{2Z{WvO(Dd_h+npl+rFx`Y z%eEmnV)MSG>VN{|aST80ux2vp^wj05U!x^k#Qhh(hAdztZjw7e`ge6Jz0JRqfn(It z`+X=YQ8JSxUMHjsXT({BadYrnSrC-OgUeqAPxrMn8nt?S8VP-VWN1Rr*2|KCxTX>5 zt5dP4#xmzn`$fT^SpR4?x`Kp!;Uz1(ICZ9r-pmc?;!OrDI3gL?UibMUqK?5=Od5RD z%kVkZ@&ujY8W`pP+IkJs;4pAL$$fUUzP6@PPAIm7gWGhn2v9#RNXr`%K4G@;gGF}y zL0`rGZ&#J?oA330=-gX7lIhZGS%z_$pW9T-?#bo$NlFJ{vVx8?Z{`R{HQwi~<%L^s z%J=W;|9WWIw!?0rQ!De9w@SW$OXA+j_A@U!N%Ub`8Rn`n+6k_090^wcpR%xn9Oqdq zuq{%e@K}Ps>ZH76c}#Y~Dt!Q9fMeH_XE@q<0#-kIPLH{_ze(qo&Jjzkp(tJZpbcRIm``t zeGW(t8l^4QR>WK%(D+ondO=C!T~{LUq)@Pw_^$$HGB+cGe9g_KA(AQD0=MSpVt7)6 z!x}z7nElPsstcPs(T{n6uWJp=Th$k)VRJHYJz`>?BJuaO0_`J< zDnn_*El74Q_LaF`@V(iSYXU6h%nd(HC@f@XZF5sz9s?CC2=kRgCeGgVE%#t@S&09mx=*Sm=E{R|IJ%^<+z zt5Uufc`L0RP*(27bb9;8-k zX}AbTLRyYn3k&7+p?f^*Z0{Zv4?W;xU?7r+QR?tI#w9IV=%5s&j^GkDV{9;c>M3g4 z|9qYPIVpmA?ZbWfblCCyi`(Irlt1qFLp7P?{xZsm@OYOjY+Fy_*EBOg<=c~ z$-6zC9A)~pVZ`=bhn`~`Wi4`PEs|k{JPAdu;eHJ`-p7}iWuB?2snShMmTAk=7B`Ci zj>tB_9ttzXKYqOV71$66unfK`WUrP_9txjpL8hc8IO7=j=3Nq4wJN2^nY?cHYQNXj zY2K0d);bRgYy5?rD1=2s?7Henr@_rGdos)-rOWh^c9~=g|2k3KP)O#p(g=2=@R3JNu@6B$5ZX#?f)%nEo6*@;AXY-N(~Gu-ua$waXT5# zYC8(-J+s4zw=S)d^*z3`f1_&?x%qBlNjWVG(~#A+!;B=+d`t~ASe0ck=Q@-p&-Xxb z_%@-TcqH%utoZogOK$-LA<8!rJ{skrPaJ;(4k{fR+rZSys3CRP+qHponvf!4j=H{R z!mAaeI9&7$LKOJJf|oW^FI^SofO$R)$~*?Zk&I_ZBe2X(qRMP((YM`Kd;h-R*PD<2 z{NT9vaebYz5iidk2ev4Z?$sh7hO_E5ybli#hm?grTV&U+k{#b{Zv(CZ>tLpo3|KD( zpKLu`>j4b)VXn^6W)Q6+CEb*U@*gg<(}m+T&Hiv7O@vGYrs8v>C{m)YUOPXY?;-Pp zwuMLV%X;*t+wU*)>wDSF_TSRk%$47KP6@@SaGL!JS_DKR6a>)2g@7MN)v7e~^-CeF z#!b7ta_EpD{mjkB z#m2boW<0-R1z2Z@Gs4X@1Kuu|VLOc|Luf@sg){*c=kzB{#0YW*!U#B}bL033Meila)w5DE_0h~R*`mWwUS=(4-Iv6!jSo(=~M2;5;aUddqbW!QFE_bE{r<@ABtfHQ+P?WLL zF2)fgvUC|$&dWeFRVIDDCwZR^%N&EiahQRZ+5@r?Q|a0lA@|aC%YXru2i3_q0zBSP zpIi#s)D9?KCF7mEvR}zibZW1=J)qGfslZJ(O0wF}EE=)g29+qeH6LJDG{$liT=XVq zY(TZD-`!tW{%C4xQTVE8d#5WAsmLxsuh#O4MUAFo)&?A$;y74GJR2-PW%z0$xZO+^ zV=HO^KpDHjGbU>xVMn;zqL-3YlVfu)L?2qyfnFiR;vks2@1E-ppuBb;TFYGNaR7&AjIJFiU!q0IQ0bynh40hr{wRu)c zl@7#gpPl~-$atC_DEgfDK!`nJl5u0g&YutR37n5wq)|Wo50s&@prWDrcgQR)ya#H7 z@pu&I*Xa3PZJMtgmMSM%aE!=T5y}rQIEs5p>%A6(Fx&`&o9jcSq1^<`p%2_$9Deyf zWGFnPD7+8F*L{8`8)8S~;V=TJm7W!+4-l-LOv~-Z=YQO1;3M4y!tPCQ?3jBl`J=9ZTKSN9qLX<5 zbbbBg?sL?9i{3w8ijA#N(U{jTyY4C z7>sUnI+N7iUns0r*;p?ARgv60d^0*M`3J2rz2Kiec_Sz8Rv(m!3 z?!Kb~1~Pw8EPLB5MN=8nfEnE$no@Kai%X3dVs=3Umo0pd1s9AC`S}L+@b6Tr0C^Ft zETt!hn&&Wl1n`d-0p0iW*w~oI!Zuv~)aF1MBT%H|dmn%<2Uz^N9Cy7g&dKbcrnF^A zrcJ^EHDMShuYiw4{0GL7jV=f|48_11U+hg_ z@thvL49i}JdPr=$KU?n43o@Ir8;5d9G~%_T*kO?HljNWbo$Z7mFP!)H_j@R^QzIgI z%-Zfd`N`|XJ~o;P&-f1dodA3!?mpbQR~1J8bZy;~*^y28!$ziqn&klj1L6iftd zj_b2yoL#M-`EpPC$ihhqI3A=5)cnWbj>6~>=n_nN1hkkeXdoi6(z z3Pmt+nMPo_8P*C zw~n6GDYA{ojZ;u}q4FChrlrkpQ&D5lN;LHdP*5WVn&`(wRCKiIk-&<8-Zw%2ZO&H+ z%VR+s_n_lB00q@_H1kB7fOFm)sFxq{J6M)`_}OjS-vF#~S^NX)zc^qm?J2_cR#%r5__L=0r(J27 zs;DtOz&I+zAdeJ`KCUj=p+VOfb|C%v2gwZc>U zz=z~SF0EEL^!yP4;1T$t>NJyr)F&4ni!=B{%P2`t{ojwcI~mfT+O=m~hZV@EZ_1Oc zuqRD^g7V!Pmz1<CL==kFQe@wb}Wr?(T`|2U80Qz0*r zp*WHEfN-szK_+_hj~i$PE00|@m70MQ$e zh{XzMSSlH7SY-T}Qc(Mrs}0WG4nqb825EHn3S5FUE&Pyl0EFlZg4JN<6e7iB52Xf7 zivvKO5U**UrMOr?Cq5J_C;eBAdtkMER`fGOB|J*E-x zT6%_$zwQ}w8Tb^{YJK!>{O$PEn&;~e5^hzjMBkWxaAsv_pkU#w_}m`#90M|qyopH; z_Bp|^(K+ty)M%W|Y)Yg_Uxvg4;dFfrKF zW9>ruvA9gk0g``DtS$gKD*^Bw*Q@P;$CN^y^ME1b(c zg%)_%+`QK=v;u0RqVPDxxnRhy5-iM!NAL_ zZo9v9tv814VVr3($OpSO+8cc`YlS63nV*?RnyTAHD*Oqzx~S0rVCnqQCK*=8ufQF(#w@W~fJcuC|QYV-40%-J%@U~=CNainVpa||S zx&o4V!Cw*I1Ox<}0I$3cusRUE6k<+02mq^MZ{gfQ6L;a9X%6-h9eCwSn(Ifs7zza- zCyzi(ieD$@-<7Vv|75@tEvbw%V|EgO< zX%`zm^EaUShk#=|1>ei&fAG3^$b-Q94!siaP5?&hOH1i{nKh$ZiQqBZdE%pY5*fwn zaTMr*o%SBBW#@_IZ$_KvUiLxMF-zNslNh6RK{!Rk8PAzbxO0R&XNBIbC*H}BkNg>M zmq1~yz@>ghGO{d`U)fF{&2YgVDEahRTiY%vWO31RGrbb%j>BSNlIxu}`+?q`?PPN> z8N?m%5FQaE8+kYT-g#XuV}E4Ah8+5N0o~~5XLoG+O`4v}Jw!e*xOnv2{riDCc{w@A zq8%b?Hta|(tcLf-a{dPNLPbtMcTva#x3}y~6}is28CZZ@Gam5z&$}hXq3wVF`Z92y z@lU0fyv>(_+P3C+K@D;q&54Y8sNEZnZqvZxBvxs2envp$NN+T0Em#Z}5gCd&={IG= zOY3Oy;83( z7k~s+RM8nzn3HM}|4ye&V)}qLN4D=p^`(f}AEJ6No?W*#xcQT-8&Rk@vkZ z6SQc(&Izu_+kWOqi5#K771kbFa?Xxt%uSu@M#eL+bf0>(GyjNBCo1)=MVP`||D8Kv z$dM>K1rVUIR#Tx^`sqonO84K3|BR2CKTit1_aMQO%$lfU_I0NlFF zFr^7YYmW7Y(<@_~=Je9eK9$;;-y|>O zu1kR%|Ho6cT>Pu(B7eu%<+T>WFRBLonA5hsL(*|Vm|bqNPZp(ajJXz@+wonQ7IAKk zPbQ^WI@Rx*7u-Wi&p-xV44V6e>Ie;T5*BlrbHgg`kJ`rH6>L&YqcrrKf^)WfgCT4P z3+j%S@Fz*RxpXF1*(a1Kg)D-Lcd7?*59LXqS>uf8T(;m~VSG|Rc^P(GI19zgsw;lW zOKugbZC)P!dwlE#w{!LfS)0(teN94+Zcn1YOc4ZwZxu9K9){e8BW}IQ^Au^(sM`{d z24QYo2Xa=3V~*m4v%0~zU3syE6j_WmZrt+dLtu5OsPD0i%u^bad;@E#d{1*I`}kUp zp3-MZwxtNt(n?0v9|`}7I;;m;1f8%ms-_#*^clugTLq#?uQ5rUbI{YUx67a6L8B**T$~fDJ**5l=5IG5-gCsKZ@)9T^_XwyK#B3 z?SrQd;KPt4D5vo%4hTdiDK|vp6A~8H6N`jYhEFCWB&c0SU$|$pZV6x=o)NPI)R5m3 z+(t3jYubuVr^PfOZZ0hUf;5SH9m8~EDQ_#Gc%raAMky9Uw?Skyb$bf$bFFco5%P3 zyRM0ne*>&Nz(n~UfJEv!o=W(+5+*}uio)tN1LLpza^ewx?|d*yZv%bz%2xCMmHsv8 zBi6$hGgKmur);_xr}4i+TEQf3y`QD*eTT4(cS

lR;*qkz$ky<2TTxpH3BW{>wH$&Eid7s8Cy$f&81_zvW8puxgdUmm&@uJ_Hrq6X5t{h8 z=hXF*G<03YjewH?0|sii1Vk9j#B@S#ca??^ME$rdeghrzd>G#1OTma~>d-?u#s`H(Va;qc(s@lc@vXw{pz zi%Js5ATLqCxL2wQv-oJl=+XWW++|~}Fu5L6*4K-aXFhPATEZaV4u+G!ruUly^x>tTl*K}mB1xikmzZ}8X*a-qtK`w z7hC{cbOHZiZ4RcTW6u#nM#=B${ZVh9zd&hmX2ru0VlJM$>ah-Y@_Gu(nh$K9CR}F$ zTOor*NwEgpLvK7&Mbs&*qc*cVoBUZm!^&tHETmChN&Rd#v3pMp4ROkIP7n*H)lbwMdR_fxo`sNq1*iOMRMEN+2 zDSD^1;6;i(@!I79mi2|{^50cBjHeIQV5B}y+fUq>A61u~X0oWq>DkTuh-uVpp{pLe zft&EGZK5E*@fa8)Fsl;V%qIa<;A$kfg>Lb7gKwNh_!z-)X*zHBNk1XKst7CFm;C+lL3P*3N)*j{6MRqogYdWsfk16l=q`%rJlX}CT=!3*$H}f{sBncyvhRL$<{w-HUEi5d2 zFIZhGoQu5P@1l)^-S2Ea>I7k$*(GoA8NRa5_TfxDSjZdzoDk?17XZX^Xe4sS(-*Hy zv0Pu9$;%gw&7{#oST(yb!#;1x*6y*gnmyk;BNHYFEK!J#2_se!85(qDgiEB4Oi+>W z_UR5cEGtXk@jQFGhvt}ER8z5Y`A?HLjhxYu6IY~lG|jJSby^l5+Z70R6!~UW{Er`}D3U4BW?Cr5wwPAi&o~N$Z`+n)It3@>)-uYXcU8sO)p9^m zzyur6j^C2mGF&4(6^U3p!V?P$*|h^*F(b$Zi35gD3h1Xzts#Rnh8Y2zzf1KR-;45s z1P%JNPAKr1Oadg!0yi&EJ?~Ia-iwf9x19`qUgf!+Zy6cmSt7pFIrN+wcrknR1h`kK zoezaHHN3+rcSFQpmQCBwc^Mrd({3{UG!fAo>mW@bCK@a^2*b{c<7bXbR}8xatv10& zkpzdv-oZ!pWrJrtmp^rBDbi&aR)=kI?`D4>tfD1rojw#a>K&$E1zaThzhp31Z)mXFGzKl5QS=;o7=GZg5ssC z)Yse|aveHem3HHGU;;YEqXZ-iO)nZXFF!fh1CI}@ij1$2Si(c6Wj1}uG$alRi-;yZ zO3+3=3C@%1pZa5gj=qCKM#1dbzn|@8X?JyNge)O@(JpPLjKJ&d(`;voR*fuQ1x2&L zu*0LH9-Gn0{m!FlL*3FkI=d8edMQMucrTmWx&o&?W=LZJ)k>v+$YYQ$Wsy*HQA5Bq zA@5kJq-UtXdv|c>8ysq~Lme6_iX$7VuiIS)$_XP`W;=d4zeRAMGSN555B`!o9^@;+ zy44sQ8#tGqG1EuI3%QGOY2+MRF7A9HQ^p`CA>GDpsSTb-!yo6=WAI4h3r@^-9g4QL zOZ|n6ZrD5x$`q}mVj29jlrSGQ;!QF7!D$q zZ%gnW9)~O;)t^9f;m|Xnh-@uLIBn_jIz)2?^VdEYoOM_pl5mmx@OFNP?%Q6`=lCzt zO@H1*B-Vo-kKXLitJt6aA8-RoIPkq_?9V}f(6^ZcobO93QLOgFXrzUJc>qAi-S+2x z@OGBt!p7}fbkw?L8(sZFYYyl~TRomqq)L4vr4UZ~iCQBhG=O;3-AAra&lXv~MHb#?sJB5>^)=YALm zUYdA*?xG%Zjo@-y55Qno33;Gm>e@u1IjoF!#bul6Bzty(?=c+ggHG))o>Qc@^KW2e zg$Kz3@1LhH3>-t_gbN{o{Y{;VSN8--znE&`=H%N0>ujz41#@J(tAN4H%;ehr%|SAZ z>-BsW84aAWh1L&Wn$)TDqe7Fa#8*tQ)3lgYTOd_NIp`WeOYh4rlE~K90`O+Q1aZF# zHyEV5`L+iFdv{GmH>g#0|Pu@_*46lFuT>>XIICHe0k1!Pz^Qb zr5R9%rL7nL{2RY`e_o6DwihKP_z){2BV$3tz`v&x44Z(Xn_|qK9GZZ@E5WoRi^0Zz z6v--?eEY}ufaabF+maHpLi|rZ0@71I<^3TlxB?@TIZS|%G!8b74m)eP9xszKHqPE8 zA6azdt?ti5IG$*t<&B1lW%9ht&i7$~ zm(57HTq&xPtHGgL!dLylX7m$hy0J2{Vwt6mm{{srjFV4RPOg{UDz~5l@;LH*E9$)9Q3Ks0F^pOAL#?@YZ)`HaW1eH7UFI|F3_C>I=~a7*=tfp4EFz?gQl z=YZT@$F{HyN+)FuBDFH?;}Xz$;QWU@QL0zel{|+=3tKXa%gkb zb^eo4d&p6hjj;>oXv7v$A>mU2LcCi=BwxCscO8FB)50S)&4^2d6xnhv`V%(oliB%e zVxyWkXrfQ`~)^(h5U!)9+QD8Wh^N&M$u0#^Cg+ma1(5BxL1m36c&W&C zJCE7fW+-1XfU{W5EsTQ{NC{ZpRAlW%n1`@bS;Q0y1AYkSGL4Z#(RS*}7!PmQ{4@>Q z*i$yB+K)xEx^WFUQcrLVQ(9ptc%Z`C(n>O3VjrL1rIk|X%yr}@JSmdgkuO$mfVIg9Wu6)Y7 zKphM&8h&1GJy}fa8h{cqz?n^lZu!<$Lq_E`;?>b*^M$XfH-uyit3E3sYVNeIZ$}eoE z2UQn4wLfBaUjzZ$TM0prs!j;-rCJHnU!Zy=1SX^77mg{G+aupaT0<5=+%SWE(^2pj zA;na#*Pa|9FR>4dAp7$FP{k>+l-o(E5bnvdg#ht$LIoJNWOXHYwFG!lHtmV8$=XAM zPVE!(g+m(2PsY?drZM~rK=cFv2&t&uSMM3YPiu66Ec@l<=B5sU={xmaM?;h5*U!p{ z!uZQCLx1t(Id1ul4u>LQ_+4)Aa{HjOC(9#4NVhqY2yD3x`(f3w9tYgbbtHZ}B`*s* zySk-c0qXYAS!xCfT6l){ttTXXI)ct;y1`QI&lvN_Aip3hFHy(bw@>^eLl&f?+uD% zs%;MN_U#E@!Uh0>sA@B6!`Gb1B|*ke)rudVb|ViP*@Z5J&K94XUc9>YL0a1NIjD=d z5I`CO^!HMw4)fT9-j4_79;mu+J`GUn8hlR$#fTin;TidXVMFPb->r-oL^io>@RTl- zva4F}>gsA|hJ6Z4q8~8o0BoyQ`N*O^KBXM+gSC~Ilq_SDlSP$LMQb3~ly#7Bt&zPm?^q9Yly}q; zROe`+jI4EPR-|9n#Zo0n$oFdisF8froM@32DTm>lUuN&tl@(T4_=29P=koXa7K^my zMSpz_muA!+Qp#;7B?Lmf!C{Usf0W1CyRQYOwMb~x+}!UDn?%@Iw59W8=V&rBQs4jq$wQ<&K5qp+6!nOjBEd6=7Zd(y%P|H0WsQ_UahdmPZ}nAMZahnW zA}o#h4m=*L=ODa9JnDw3zjL>j@irP!{-EWi^qO=j6??I>p)-zFW~Mcy6@O9kA?Tp} z=NV8RQ2{_HQ!pr~Isk@gkQa)38MXpe&|)R%0r3d~lxUHx%bJeEn*hSU1CT-YjBASP z*8N0Py;ArL%gUw_-TJradoODPHk&dw@UZNS*iaX+RPEsJ&m$u-dCZ4D3e6xj#ca~1 z6c!0mKo%4CZq;O5wPR7bO#97Jl5^O^v{j;qu~S1a)=9RH%!PJhj)RZw1Y@f9{M2d! z-RH?=c1-u~tt=g4Fi7OE<(%hL!=6}vcF>6hnGH%|PCk053xo*MW-VYf;32GVPBXxE z4&o;&chtg38gM|xCZG^V7NbP4rkqk7e2H%H3u9ktLmC@Hh(?)wFp4iiMps7^GFm3U zz?O|+erePrQT8T{np_r}w^@7O!eZel@!r>CD_1eeicoKIpzOHYrH zj|@4T_UGyW!`+yksG^W{>8gN*sq?Y590^cF#k-2}?m?lkF?q2F&wE6@ATCJtqI0mN zyljeH*;kjQaZZ%yL|VH47x&7C4_=YOuU}Oq6|gXzP_ARFW7xZ63>*N!Q9%(&YkkQ{6TyAU_=-5>8U9LcIq*|;n@?aej zfsKI*?X2zUmQl3o9I~!KVwtkd1fih}63Y#tF6SAjvS66D8VL?CiDrWldQDfl!n$XC z)AJc@f};lWGrZ(HdE4udHA3}3Jq?>}{$34euEIgER8s!Az5nK6UPldM-O@>Cwh>V1JM zoaM!Y#<6VB$=X>Z&H@bR4CRl1c?BgodC82=yQ^$l6cmYO8HjA>QMU}vT*?d5E>SVK zpvs7&*gjs21usY0{f|N&rW#u1bzf$??Fa`HlH@mY<-NSq#A?ej^|~~%U5DO(LspT& zi7BOJ*oEI<4aIg=OYouVEUv~S~9)V=r(geN+JpUTFb&@4} zF0BO$-%F$QES$+JcCE@>4O6U;BAB78>r2$Dr%Qb}#;<(>;r|6VML8K(DvCWsdf+gw za1LjzTy3SPf{f>~{cPLdThK#+hL;#CjM|<`m#4Zk(kbeH*=YO&E}oKluLUG$4J*rF zni})h_1z`U%Y4-t21`U<;D3Mpwqe!85#Khk>t()FW7@7fd%Y%l(iuEU(P9383d&Hh zjw!c6CM2g6C`b}c5WqhBkSX>kuJQHHu+Tv#kmNl2#gG#A$x6WuH)IKrGf;R9My046)y?Sv2E<00q!R#DnTe zg>7c?KP;(Z@{U*-kA0_Kxrp$IYm13Enqz7)%ghM@L4yLT*fz5LTKx}iR9RGl%Q!4F zrZZ_-drwQ-RFJf++rKjd8I=k`>Epq8XX>kz+x1I|M2~EOms{&#n83tn=zWWIEY_G$ zmq~}2Y!BcOsFB1TSoB0AH<`mssO9SNuFh*)OL&JGPHMB1vh8-<7N2`Lx9$AW*6lk3 zW6+`j(KTT|3+z3jAQFa`mfWF*z@hWadMeTt7W^6TV9V)(swZ1E3m~a50vFK(k!S7C zd$GH6_^1_6Z#+b1I3bJuTyyv~0iCoMK?sLk#x#qnghzO$Qy+9J3m2?o4?IM~$nv_O zGiI*m3|AiJB~49P+J&SuO}Cg~*vax{^nC*Fp3!4on4LXqW{z~jNbATu{zb`qqR~9L z`ebUyW0f{H0g3mXV9&?l5L-IuPQ|`lDSZtB1-aygj2Hf_qIsyrP zv`Jw4nxX|x7vLW2hL*d*NbcnrT{*SB*L;}`GqX3Kk-v|ti z*J~Ahzi8mv@fqstM35Y{o-*udQnjtXt#E>c>@7|P_S$QQHKDFAc?48&Ho?d=&2UCE zY;~VeBFF)DAX@6tLx^)KR$OcRE8HafEOrsh&@^Z$S*1D}W5QlbtO*?>U%^9D=lCVk zyACJDHYoZDcAo4s_kB{zMa&qBm7$f6+^V*~BV(`qO}W^gJa9$6zBI;pN7{z5@BK&*X?LWK-<}B=dw#{ z_M@NP*7t>4aXy{bskq6+o@cyriC}Q*1!3&3{#Kvcq2=o z;ho{ah6*oDxj#-ot9qC^eTad8F@|C>m1NSo%HrVXh=&#sufEt_hS&PAb4YYGp*79r zB%6q&^V0il5+YF>$8aMZ^?wwN#Io7K_J%@an11FOiKt{)emz1{Cmxx4J(oy}zv_l3 zFAfD~Od%SR@5W|lX0%<$*&*mA>G0=4DrL3nNP|-KC`^b9ztixuh2h$1u}Jpj8#UGi zQn<~dj~!BylExSK(!Rnpj9mXYlo@(_Nt$awkqQoEFo-x1|If**WAwi#@60rYwftI+ zE&f}*1%{b~_4_6no|EuEuEb^gp$RjLyEa8B)N+X& zi9&+fVZ=}plcw7QJqevUw-!?|Jdrb%bN}dVkC~Nt>br9S9$9DWkWCuU4n3p9r&+Fv zjym26HgkNH<$Ka3gbtzV9};`z&tm6DgtV|vB_SARh%GjS=t$f>*KkiQcIbgWV!|)+~KF--D%*>NJw})Af=FJj0^%LYS7l3ze28E{0iE!PQDal`2 zZ(LMShve~mg`$IR8$R0CGE;>wD68CY(GIs3(&K!S{@A`X;-yYX0?oBpS}+ad z>?2DLaJKeVMhjP(8~6#}E0=Ug2Xzk_tMlBsd1hF1shmLl4uj52>wZwoGck#Kc>&{s zon4xH#eDs=yq-+w`qODnZm)?*2XX^KfC z;$j@kWMZmOeurgz+;lgWnypncc$ry3?p!>PP5kB;qIdFy1<*lRvI64@##Mch8R9?w zN4)?pX5!*1{x(VbofCvI1Am_8HVS$M=Qhs7(3jPsBOf=!@@(KDfsG?p+WmWXP_++u zpIksOEWf9%?K!oCS6o&Lps58!E2i}7PMS%hc;~vGAp5~~IsYvIi5!B+*nqrNXI|nf zHHX_(SQ})!RkGM+FBWR9r^Jw5OTjT-8#SYO>mWxf<$2B878}Qj#8iS=&wXNL>@{~@ zB{T<8+C(JeN?NGRfh4uNexOA_XR6>Od zPW1e|_IHOgv@SNStt7OR5i5#d@Iuym^52svAm-d_@FSeb*gD!(Uw+!Z(69tIOVRiT zwvC$L>t_UrO}cBhk?HSQXf;Xr`MdFQU5SaH;#VmzFBf#5oP>VN1a{WJMd(6icS*~s zcq9Y_xm5DYa=us)v-iK{+28;nDoI5h*r69!Y8a|Zd)fE)$*n-u>W$V0OKfl_5jMhc zFx*fJI7sR0>JB}IYD!kwv?5`+ZlZDZnOdq`^0nmjGa0N2^*?ghUpD~Uvkk&Cjxt)| z)x@ME#m6f@sv~n$(m4KX{5cUlT2l4pK-468d2FAB%u36#wC6`$L-y_7Oy{B0NuI^G z1>n)!iL3*s2XQj&gvo(t)_SVpC>iY`Yzp`{h*3OGLBXTPc%Fp18ZTu2|U z$V|?pW+6vfA>_BH8q6bvaH$qwldR__VWZ9~SeOJzd3sLxKO#)u&l_h9*o}n-+^S1G zQhZ*-#YOtK@k+}6U4!Yl&C#V73fl!ysC%ntS~uZ;7X2>c4B0Z`!VubM&@k}c8#eVA zNxg3D=LO|_5+XGMU?vk#sMB4siN~F@4SH8*$g(4|lhsoA7^1Z2*k8+w_H*6Y5` z)&msxCf-c-BQmm>JF(!O9?VhJm}>R+pOhimtf~g^xwC$8i8Gx}CCYks} z%1^?+X7Lh?>)&JL#aF(xPejsU#uOy)F6gheNFy zbZxCpf}uGrATTtZnw>eq9F;S&UwlVUSc)XmdcAJh{VY?cgPt1RELcA;rIuG#79nU< z)1;9#-Ay8`a-W&&3J_kreosz67h128M3jQCJ8U&b$~{E({7jDETPvO-Un4$-5*F|zYNSs<$oz_{Kj zE*=+4#1(5yqxd~g^HUY4g9z+7a<d1AjmNOT zzL=6*X@~5@P|Z{1^LPAfFMWwYNkz2?GX0qP^*Tjb&(#~_&A!dIc%Ahg7Cgg71ffYt z#~(4Wghod0HAsfoy1*fCEJ8gCO9FrIr*RLCgyh z5E76n6F5Lf!uI5PUP2>a-(wPMnOkw@^xwCBGfzoE#}S($ zzU&;}cd`E7sL(e@zUk==`Au1mW11Ki-|Rj^`*V64%PZcX>lqa*yV52WE^Daqn4{_N z&@Ba`kX}?jnx%cBHwODSGS%2a8BT+SNmps|^Q*-cI?I0Vr{F)M2_`rVuQk*6m2`rX2Omt@%wO^*P^N{H7_~AsCuIsz+>){?F)LySmchx9WbH4ZGkq7xC3> zinbz*cvU?cN^)|R+1c6ko`%|aNCbZy|K*EX3hW+XeOB~LAb%$zCeE0HuJRb(5mI#E z(XPg9z-E#reC@45_XO)qZ)STh_9kw_QeexVZQ2NjNaY@oVWN;M)AWo|wp%{O zZlPge+g@!RF$ag9M8O{|b{ec`Hh~vB%JbV4Z~hhvm}BvIZjyCMcUCFDNYt zSqHu<)ubQw9D01l0C_)DGbhDYQLnp@_Hl9h!**7$Bv!X_WL)3(++M$}P;gvM?@5D| zk8;DfiN|3#{ksdN13cTd1n;$??afSj#tIa~ctRW%o4rH_nGlNVA`C_Nt^C(4#mp@F^ePeF0< zbD*XTv*c!HUtT(JZuYB8w%U0Hf{W7&YoY^ao+(#HL$E%}3bXW0f;&U@{yVEgJ&3=w zdSaeQ{ko_T$llv9j>`8!yX_Q!o=VE9QdwzDA59c2KRJ8!XnxZxe(_^H4R0(rWl`7b zYhuDMkSvJ2sa~aC9LsVn<)KuCb6QR_CoTp~SFmR4yT;@+jjgw@4R7xj@Z>*v^gyUv z;bQ#wQsmu6*A%Zhm&Bowkpho^Nma!7%xhRp0s^Cxs-EqjA1k*|=~GoWIs1;tiGM2B z{mpI%*}U<@t`olx7#fE=s*?KhYr6$DE3C8zXr427B7DrD9HOStM6g-a{>%(V=28iW@ECs>#&882jMK{8 z1+%si)GXFH6xN&8gU-_26DbO~z2pOa!upp+&UY<$N6CC^ZtF+Q zBc@RB3YgxF%kK0sxHX%$Ar}sdzQgoPCwFCaG1|ix20yaW(t!%-+caxqWo#f*N2HWN!8w;6U{lYBVk)6a#?)6REC?%b{9{9x2=`{6`q0;wyexkL^hRm03 z=;5JW!EZ558u?>4W?=mWVuV)od>grU`%UG@?CHypidyLbJLe}Zl>y@_)~477^k3V( z5ZH!J)6dFt8hnFC>(L(3$H8ywZr))yAxwx~$5`O)CH*d~>t@Cv_VU@eSaJfT4(Y(Y zi4$jsN=$F_m;&x`d14+ePA!s5d!xPsN0m!XCo;9tX#U@R&xm-8gu2o|G?%+l=b+0nP$~cReQ5BKWSC_4ly``JI*Ur+g^TXbQvzwt7{)q=w=H!2D0)h-tL>@5;q_-z$-?O$OUHggz(Fs}dWyG+UO_Rf zvGUkX6}&?4ZoCHJ*^k#==QS+*sowt;IRDIlWIGuvcx0p)cxkk9{M<_c_WKri(VDae zb#wn8s}4)rQv_6%Y}!+nt(_MG?4S-?zIl#nd(-HrH<_lYm@wOCmH`Q9ihNlM|Kv-$ z7T)7^5Cr|W!FN-s-L79~QfCvhhPlQ)hl(+FiY?rVv14c1XX8lFKWo^$5+eVX;O%T( z;3h<_VGTxzJPPb$vVPc*-sXla* zaYak_zm?H+V2=J<>O9}z8u{D}OQAH`kglQcqG+4JYcm%J7tb3cfCWFYBarU{9sDm1 zFbTSLZV?Z0gZ_M=hPg@Va??_Xx-Q^g9>UTtldhqRK47W#=^XT%IwlZC{2?w<$a>~6vk_AT3p&)2J0e}S5pmi2cb&4rNm?6rp9^rUSMX`F;h zQ3HdM4*KI?7^nz_`%dR%4s@E7EBRqOm}4=Xec0{8D>_Ph*Zy}Tdw+VfHRdm?3epS0 z)AfYQHnk(4>0vcsqFZR8pQ$@AZ@lvPm5*S0w}CmKg-AU3%NK)(W9Jj)avSAGyahH}#XLx)-@L069BY|#$GfSM%ioHGKAJ-!#2Rfb$fHWKS;v`JuPI0fPjQA7u9auK z*5X)x5iq$HfWdMFhnR$H>V}V6rif>F<=qPCUBrNBz8mbViLCsMTmiMcFieFONeAK3 zty_xs-zo~f5Mdru499njUa3`4gd>FLFMAC1M|97y7a*DIc`&Vqoc^1Ev9X`-x#)WN z_C3r=Y=mCg`p$`UKJtdjVseJ#KG`Y?kM+~Md?P+aJzu!&G0x~uQCWfXj@v}=i^+nj zMcm5ZL33Uv0kokdG0B|$yWpmpyf)_F;Z)hRDHrJ^&|-_S?Lu*?p84_t&cfLr5B8Fc&2s)boVuOn zGK%+ff`eg6G6Fut>(H)jTo9v(NSE%m-BYNcP|t}dEaUC3#PTqZwKZ0aUM!@E(;oQw zqV@Nkoj#u?X@77ABxik^Vj_FT zWnZT|S?{uF$sP5#9WiHEW2%HafdR?C;?iYmI<0dCL73szE@N{ZAumh~GLl48y=4UuQ_tuaanJ^zGT_|isu!NZ3Yo*Fhj zz9v>=L*tsJmR2v66;NWof*<3C)LC0)*6M3iIt^H~M7Tcdo?%N~+5J4zI1VVgtWCTD zUE_-b5H%lNT9KBO?E`mGg3bow$D>VW8)0N=-Sey&kTk``iMx?Pv=-=L0KQ;<<G#u?Ak#H2~uAxNn;|YxwV11=se%ZM9>`sbCrhHF9@&Ca#<^_m*dIXP}WNN>Iuq zOTtZr3+W#oU;L+xXEj3PPDmNH-gsbuNY}EPnx^0}Km!XIobRPTl!E%TIuFAxxe#`O z=VNc`G9-zgt{j#2T&8T3mXQzxemtDLx$)JFAgw@RB&qLsjh$6vv~Kg1%j=#uzly&a zW_#-_FaAbSHxFEG^gVJBF+WSA+O-ubu~a>WpigoYCdt5aVz>4D_2nUWgrTW)-+gjk zoKd1EHz(tM@7Hhxt`Y7us4oC<{4- zTvj(57#twfwi|qX^?TL$mr_yqY=&&wY=&J02bUiTgQ^+9K_t2mQBbfVdN+jM@vZ#) zoVYum@y%Uc#1RU&6`9Bf7N66vA^X~g7rcGjHAXiVa3&P8-`{(HI|l2~ zAGz?*ed!-U1IC$nkL_$6EiLmQrccqzs$lUb>R3j1lhpDG-dOfk}C&+5!G5>Zh-F0v;2 zbFSn&Tm5Ci6zhuXKag6k%(ROmqj_DC;Q6gyx@m!{LQzB2hH0*get5M;9$`%Hjg$%v zmiZo0+!&Fhxi$Ro{19!07l5(t^Sps7|_MikH5pM^;gzlkb%OPwLEYl!+H+8PhhVgo4IOFWaabp$~%y zOCRsHZ1kX$`_1z(4&~^*GGVQ;^_nIS!DkLSMDA7a^C$F(J||ab%u>E2B*>`HB*?A* zJt`_`V2%L+f0;qQq(GQn9|C&H>eQLRyzD*2acp@r;e6$_#{ zkwY&a2re6Xdw&*cv1pM>Yt8wRqnvv0kH2v1_b-4q7*;KuAK+_OCAAd4p0*+Qvyz@J zI_Zx$jvFlA1A?)RU{=EfO>70_MYtG`wmO}n3)B7KOWY9L?XakNZNy&W(vxmt-4wPx zK}<%>A&?&%M-m=6_SqN9^aHf(c@4$uZ8;3#cNry%KPvWD!L@cS+9F2#rA9LL+UF-v zpfK-+&I`9+C&tBPV)*6l(4z$J-I+9Gyg;@txOOTeW~NiB)E%Y1;eKbt=6Y01r|>eJ zUsRVB)Rz7~veJ{ou;^*^>6E_{e|P(YTJ-8Jy!z%>awVLbGTu zFAz-ns0fb48sLhow0QC<;iPhH)5}KaSlDAX4_r!l2hKvt>FLEIfgbTsXrg_Za3<3t zwu5Q_)D+VCg`ED{=r7yoMszz{Z6!&lh3BciaSIs3@b`xkYQ!~ zk8`UvA0FMmeMg<-o41#~{##wbJ8qjs^`#D9YwUSUJMnl=E91nFMf|^XVi!FALI3!1 zlGiA?-*1tkNG(h*GS%oF%BGyTD0-DdIr(~PH|C`P+}p#!_>vmo>LAH$LLjg0IsDr+ zw2B^e*U$BLbkX@<-Dv*PMDpnn&36YF3TK*i#A6xhtid-~W1pqFa9Px+VWNZo!Zxk> zIeR1V_g0{Aq*w?hN2Q=Sle9n3pcMdRCHIggh6Z9RW#t``PpB|;*YouD&TlBK(+Mk> zZ1~Z#(xu8pjRLk}!E|)+Cs$!A^RY`XuooZ>W>2+Ly;_c&_<>P(K2oZ>cv&_w|qw7m)l`?O{(v{}<|G-{2ALastgT^)=yM(Wj9m zjr+O+kTRt*WpN#Hvp{xlHwRa7FK1A?sDG2Px=8ARDZq{2VU8Tyz zZpVd2!2O^dJ#+g~lKdaIE%lcc%o`ZlHNE4Aar6-9!3Bp#*~vgJ@kZIEWJ>MbP76BQ z!Z_cn*J9$V4i3IH6RJif^nHKRn<*bk@|{tY6O7a?&(N*@?@pI#WOR3nSoDTc5c1sTXLC#A>4 zih#$}Ai*#Yh4lQhU$YJl(ms8(3BaGb>29%48iJeAcZ7>X_h2d0a?jsqna~iPUKmr& z`m4U0P=~)mgv~auknQ243g!3nB2|HF9=gTV-$#4?ycOmEz(4`jRqHDHqq&GnN1aP4 zBs8>{1i$+S4L1H6`TsZchlJkf2ByJTRFgZTMMSfYwe!{>djI1YEYTPMvgEzTl2Bm@ zR-k-SQ1)^DT(^8=ObweOZesuj&)9-r7oK&)&pzPq`1{C30WPph3KsAROzKQAShJUY)L z#fQkV0F%sl0}qwGkuYo$@kD!c!LM@c`jr=#P$-d03&^!K;9n5JE0rx-Z6GE!WFCRZ z_m616{3OP^ezgxi1~AJ#Z4^`uztEvj6wt9sl6lzGcCxuE7n=JhI>r?3^PA0Vf6~<# z5UjzWs{IuM24aZ|hu3?QE+!Ej_`a?xyT9GHc2{>k!GiBb00wndkd%Ui8Qa&lo(9C@ z+C%i3do^=IJ7}nr%d`qO!aO`YW?;Bp&Lv+rE-v@}?XtKP?yev=omasxZ~R6B?(Xli z#^Z--)Or-6h^YSFTLp0bO50<^W#wV@EuG9!G{+z~YklSK;gD-Cjq?jZ52x@x)?$st zLb0ZbNaNof|1xV%s2H9#kjWGZf}$v#;&SoH^|eN{(T%tFD}s=T_AB{NocN5f&7C@% zg33C1oP!s&Jt}f7#83?x=M$6AjFbg5<<^K7Q0fgVpF$<3^pta_qM~B*2WQQQ!{>C7 z-bvb1W$YypW?n7w*nw_}d+7gaq&XLrwFJ~8n?Nki(kE4L6N0t5$TcX+@U{0}QI zQ}3v+aQS$ebus z#G{x#U^me2L8%#QfPBux?qkoll~Zqu2dy&-MI_MT`Xw`&P!l8T*0z88W!}wB4}G|S zj_SYzq@tC6?}M5o@TfefvQ`gP5qJm#S(qPpeP4{)FSMV}wC>e#Q8EjuHq}Sg4N>zy z7!yokoguHiVeLenjp;w9)!+{Ly_<6jVH9d^JQV$%g4{bvu3TAi4~{tv%*xl?r?ZKn zB>7&mTE86Pw z35=k#P@9pI6XW3!xjUC7!7O+5?#aBEeU>Nn)YYMn@Bm^{Qwya$Q7D>q&x4I=RYb2J zyRDmhNz*xG|E{SdGiRv5*$~`e`}JP{4f=DSUbxRk@-IXQt;ZnQ-gk9$eriPA0NW$N zO~@;569JqI`v~Jnx=7&O-TTw1G4w1R26reuzF|!5Lsk?$-Clp0fL*^h%3SIWV@hq=6ZuHo_>3Onzk}n2?0^02)O&k-+i(r#ESmyD zG2y$?r4=R~465nhQwIrHO*cQ?&Wd;Qk2(D?mFbb6=j!f5Dj!lV57ONZDW{ihtO3+i zAr>!5(c0yY%>yM6XB8oMFm<<+2sI6)={M;GQWaoi?_ zJa*XvVd=z#2`2rp`dT#|Z)y!~4jK5TkQ$TY@5g4EvA<0XG+Pkb_X3Ew7=r@bj4&&B zj`)Mt>sCMI0-pDA(sZC;fW>rXs70@gza5c)yVdGE-P@7=m z#a|a-)r4KdKZ07|?pt$dDXE&&*HwHW(5hGx!2e_+aCbIgKsTw`zszg|B|qz ze|#g5iMWh{Af2~gfuy?)%->iO5gz*6YD4s7o6EDtZdL)=9b1Bg5+0I|9{v1L{Iacc z6gXjt)glJ*ilAVrilKjpGv@M5Yx41XXBFm&$A7m_^(ErvFuk`ELTX>xWP8` z(tkd`+RQ{7GM7I+>=Nw-6%%yrpwqQTHGLR#*8PR+grc=|(GMC4G%CH4ByEc%LC>zX z<75WDQNRwBNOpelj`mz&TCvA}6&;ZcA{?Q!_V( zggOTPylJyLC&o3^vo?tdZ0z;X`(7WqPcDIE$oMJ#sf_M}X^EQA-nxPYo zcYA2K#yL$|it#40b9%R0RP+GL4Awq6()zArNt%M4vr$|>HkE{{6-7h!O!jf=0#R|d zd4+^r%MAuziGewZL{?>G1AG4;VS1oEQGD{GSn0(rdB|CsY+R$cZ6^jh=$rifc2ZH) z!Va8UX1-B9-v=nj{Bza{9AUhh^AUhw-|XA~@Z^LS#A@ECX6oYbZLO@V z42ON-y}s4*7~#jU=$@w8g6-z_U%bhNC-9=U<_I;x+yyP^;5kem1Y}(t3jiB zcpBzYz&Qk8_yR(B2JEk_tgI`Ep$@(^<}CdHOt`@X(6I}Bb!HBZ-kpNImSQ==xu@2UF>hR)iUnPtZw%bq1!5GxInWuu#*5+3U9MC?8ty~CMEp+(Wx|ALP& z9;iSLlgza|H>-c3Y5xCA)Bg<<_4&%#_^)xg^<))@wz@%Y%mB%j7S+~I1w-qW2vec= zw9feFE#^^FQ;*5fk~u0^&Is!@6VYK+2+kUSL|X6f^ZrbWOmj1KV+u4A zNT(9!>PL=fcR9uWuX;nrxPq`st2dsG4i5Arl07`du!NEiiitN_Srw9nqWhNt-T{t}<@p?Npr3_pWOT_g*&#iG6IItQ-ii79`WpA{WeaPy`fKXxeYNi@;4Udi zsOHmDaQB|f@zpa6@%r-;FGWyTp`p_2j`+B=uU~n%kriM^xyC*WjXjtz5%&8=6hj+- zq79u%xa}132>@SAuDRql8FbB336ITh?s6j$D`S0TwKCudLvW;ah3x>JUYK}XqUp$~ zF)x}X>*nJ+|5OY*tWz4at;U{Do!j1rQxqO$ao5i{hIC~^`CVxb*&Ey6zeT<1rFgn` zx$;5?>$Pjj@9bH6`FeQ=0$#~Q_wcnE0to_}?O{llS?bf>bJ#ifKh7_n)mrquQSeA0_%Y2x6w}>g>)SIndH! zc)m!q3RYBjoVL#QW(|l}RAV)3PsDs9W>!Qv{imomRP+Qa)k!FZ_h|xjJ;PVIo#p)d zPQ2+}ZBQO3vS9eWUyOD;hGr>eXJFG*H3zV-PfJrp=QasWLvW8aq8(mKst#a4@&i%S zJMM2TvtO_}ypl@}e?^Ja1uYjg$R4+#GS@T;2g_jKzjC@>Q*}YpReba6}=|bku%lkX*#ks;_3Xf zEcrdt!6Riq5gvhT7_3m@Mtj^Az$5hB%$&t_%RoF{f{V#7UQDq2ZqY0ViL5!(Er<+A zs(P|wn&a++k?OjpcGRNfMlr>HUxCQ*^7PE{61&6EF)A+Qi=(QH;Pevw6ZACLyOpEf z0Ia$>OPV+khMu-mXj?NR3l}_`udD(6OF;U*2i7+F)@#EX z!_6&PkGhl=>iLns=!*-=P;Da?QU7a=T`j2;Pk*4#(dT+E3?u-J`+=4{+ixo>n0X@L z&!aDkOn5I~iLBvU?;d^{sxbg_dv3#8B;eU#3KJ!yb* z^qf6%@Ki(Xe6<@FNdMnO{R_wkAEwAc8nl#_eTcy;e*U6w^m{c~;-sECR~9M3%e07( zC7bjg8hD3J%F3GX6|_b;G9QbiaQQz|9P?CeM$pyDd)i4>6SZYH@rn66SE;uZq7JAJo}B zszSps2*9H}Lhag3m{=SuCUI#lo?og%0Aw)X5nUHlwmq|9l@i!7r0!k#FEIFbi#1p) zklb;uEglM{gKfwY=IBQwuc-GM>_AM?$cewK;0Ny5tW=_aUDk^n)OV-H#(7m`Olmr0 zN(qQe$UuX0{1OnI-9WQ1B!2}ec~&Nw00mvWJPc18Of676W_PmF;?tp+p2|fNCdDqn zeT(*Loz@1oWx@+gy=NaCw*rWEX6(A){y9wc$wR~%2Cd~F_+)m;i6)Q`)PPW!b}|Cz zYsDmb;JNpyy^lAAoTQ>P05L0hT(Gd83cdk3I4Wy57OH*M!#X$9r+c zMlQ@~Q=JF?uD5A#F=XGAEqv)vieaEK>9Hhra45{mdpFKRBJjl-9AFo#W>Oj6QmDRF z&Wi$7-QlyyK{pJnXEXo+j0Q{>FXo?!sX9`RLRRjzn$A*!pllbKmxot!hx9np*q7le z0eD(=jrT@RWdMGg$b(#VXBrt%4EN$ptTWTrG)MX6Eh80mvs2Ju!W&bT(jRx3ltbLW z;cMCj=ezeurEYMcI=E-(S1K(B%^)OrtxZI4FVbJ;-Me>CkAwuj2x1vmSL1en6FD$6 zpv4`;6wtR>iCv~%h7i7DeEzw|Y;j@{P{%+wQ*XWL_Y-#rBliy51I(OxPaHE8B`15M zeIdk*Fl+Qr&x8S?fFOosiu`W5YzPh*NZ&%BhJp(|TzFZMOYVddNkqv?IK@EGR9(`d zDWqpJI-jZdBV7=6UiOJ@wh|@fwX#^$T6tqyApYHZYcVWSp32x;q%dlXOH2F4H37)T z@`s;kJti4D!ZSI77h3z$WlMv7gcwmu?i0BEtX9bBA)&(aw`}U*7Arb{8jk}t1={C% zjYA?@S}sI%I65=sHXpg%OPKocyE_~h%Es^Xmm8%#$K_{9NRg_S1^TkbKN{9-U>pd# zSXrpElB~+2kd5y+eqz-!6>I{t;-D3haOtnHU8`XhwU~HI-ZqKR>^rwsaUg z@Xdrp!I(xp-E9sB2D^%^sVFXt5C#>Iy?f3V*6%+|V}|V1##14sAN2$i77*inXK)na z#f#GE=;%teI}t6)X#rz~bm>>rS$GvYYy#3OeT=$!@6v7($ zj#R0rSWO4p-={sk^U6N+sS~{j%W|XZ7d}bq7WlA~PFIlO1ni=G?K{w(9o{iDF}atv zyC)D37e~U((5`xX4IALNF>n=gS+O1DLuVPtMBk=uP52mt36qT~o{|;ke zgOjzqcsFmLWGI-euXr}%j~P8^_Gv^M2ojQ#!`~+p*foX{wZT?tb5oci`3dJUWDIm1 zOD;T3=X^ms1qDePY|-G@rx8`IP7J|nz1JvvB+=6REWc96;-+>5b#ZB5F@yExs>I<1 zC_I#L5@VjrK$|MIwDkJ$bgDvlar`0wb>ise<;Ey1bKIl3m7CbYhopz}C9$7>QruwS zxzKU#=Z?nRyZ3&FJ2*3#Fxr$0G^<2u)n~sy;pgzvO~kr0WNY|YtWna_Z%ahNb#4j2 zH04RP8llpAbRxnz5G(F<*Bf}!<&{!WUo9#w)>@?J;~S9^nzOkXZ`lvODa$}c{|V0a zG~M5m$p+N4Rs`ohPiDzP@;q0aaB=gowF$O21;+0sa`J*7=f^HOh5(q;oRx+!-L}`I zt|5hMbZQabK83?JnGU;iU1YR15|KsGS{*`<#M~J^Ot^UYd@T?H!x?KH0-nTr34A5CP z=eLrrNs;~InM6!I`eG~ zC{*y?gL7>kV4~d`sv^vfM~c+vpF>nfpQg4xbA`pna$#R^KEq6WAw0k8?m;a0=$q)T zb^F2>`0eKeziqqJl@YN^;JPW`!z}Bua&BU5jwL^q(uH0`L?WN3>*IIA?=qDr(`=~B zNpEH?^i`0W>3GE_BqgxHu=0O8=g~W_ccJ-FX_)&TVqxd0x!j=T8Mnx24*rQq8J9P8 zTz|(=jFR^$zIv`;i9ZoqHQMC(N$tL{Ku<2eb!GVFl?;Lx%N6IAvFG}oJIq8{US8NT zF19L)V(+qA&*+wB00Kx^cfaR@CF=NYb_o z!xxs<#hEWNKJtx^wz{0F+R-fLUl{Ja$r)w_y8Z1+3L07licds4WFPXslCMv&q$`X zvX$2I@8RMjxqfu3RtE#Jz+aQwmc~A5B1tIcbrE6m6IBi_6(qDS^5jj`~OfLdhQD5A?F_rX!V zO_1PH^vCnxv~=+YUh{7f1rHznfj)5`XGue*FeL+5C3ljZL#S@4Dimv81sh&~5btGN zgYxv=17X`K;YDv3fImOa?E#={@j>2>*8Y}0h)jQKEA4T+-5D?~z8TEt#4}Jz zGeVQ#Fl#EcDrG8L($@so8PI(N|;g~5j%%) z5rzdgrmx?ndscNtjLxFXqOS2kwsDjywTrYm_3C_w=&ox&t<*VR?>`}{>_tiBpO=57 z#FH$pjXNX`AwievJO6XJ0&%qK71}NR zDdYO$#k#5ft0mrmUnt>vE+{*h-rl{-R_kT(;-w&;c$;;XZ6W-dB5a@Y3R!;mBi98n z|Iv9sOGEz8R`>GL9yXRtkJxGC!f-vbvqP8LEjdII>ni!o5nM?)xB%9u_%!W$erH8& z`c(FXDdQ=Rm22+sSQ5L5!dXjWUC$x@dOa8=ZolF7mcQnMx?}ix#pcUVF+TyKkA8Za z=$8qoOZCDdZpUos{6zS(Xxp?~Kcyv*zZ$}A2!tn{^u^PpymAK6V#pB)gRGc9&?s}q zGv%yA&t-FMWBDsb%VtL(b0G*N%BIhQHV= zrMszQJvLM4(1Bk1`VJCp6!=zi%h=xy1|J+;9icz6nmber2QgAnhDsw>^tEGtgtQ|U zpmX+1$Nc?GKY1d4q_VXO8j;dbNf51Mo`MKDyWOm5<*6Hy(un5*?x_vOG;vW8CvTL6 zfSO5?$zp8ZH;Z75p3(%lD=Cy5&hLf`3|og^=4?y<5Iwa4xJ6Sll(D7=fWegH(5OPY znwe#%k{^_eLp9e0pt~E~N3%A%E}-|8$408C&ZT6b9u6$dir#(n>gHiNX0EfOpZ3@&t(u`|2`jvs@s9 z9eG`R<6`lz-$?o$GAJ?w&ZAX)B+-CK7{}Ujb}0)dyPk=+UcEGS8M&Tf^eOIWqSXvO zJ}m*Nlqn!)JqCQrl{MFK?EhfF95%b5^G(A#F&I;E?t_)m|Kp#kXKfQxzBebM$!;D8h;ND=gHDWaS9i^X%jr8y&w< z#$7_)n1w$)M`)KxOS{pa8q%J%nl9p5gChe5b$jBBUe2WItWYb@_=J($7YORu*3ZfW znrop%Yqfs{SFh&9hY7j?{!|Pb74(e15h7llUsTLYY(Vf+;j5;RW$Y_?2_rRTle2;X zx{FRpCsm(rGotilvSk#oFPu$rmxBM9LeoCuWI)o~m`8pi?EMcH#M}md_o(_Xh@LE| zo^khj2_)n`v*(p6re&>h&=XN#VoKSXC6R_2$Hy2h)V-4iy1FlZkb!DBs(a+^gGAT+ z64(O7Tk3rBQMel3H92(|(!Gz<7%t0be1&N!8gWbI?2Wj~{wu2!29x*4=r1I?*!L$w zTR*yGa0-wS&~h#~@%RWQkD`yy9YV@j@e2)8v{#ol%PFjIA*knNrCgc%-;uNr_TQ28 z5;4rO*3q_UxYQ?THzM2|hY8DEnGSLb3Fw(Hu#Yiz zyn;lV4o_qnG1ZuwY7`LjB=#~fgXI=dq=gpd+s45>>Xt?sAQW%j5YmmKpV&Dzu(f@D zEqEE6vqW>+c7^YuPo7xaI5Sh#DuYDERcY(!0DR3%&B&D(r1l;HYF4hF2Zb6|BR_`R zt=4o)dxcb(*h~EXJb`)8ZL=ZJ1(Fq!qlI{fpI=a~&;k*{0in+(`r@+<@W>}2nRh~9 zSyWS7it&(@P3u!wfU@t9%G&4SO9736!9kIdN_~L~0HwoY42U5mrl4W4geNn(F-)L6 zxmVLmMUe=0a*p|O6Ehu$Y=96vA9p1iR%Dj)ESdycV_bYZBSa;{jE#-KOa+UOHUY#K zJFkhaT)LzwV7{SVe@jp>>b)6LKu-u%_kn7E%lp%R9JO1a?XximKR$F1ad8UR%{)b1 zoc;N&^2ns6-l2=e6*0oem(ilg9V;^{9&t0WE159dj$rMWo~g@+vl;5~fZecwN2%Ez zfeJB|?@+^=mD=<7KqrdKNy{@6YwiSSBZnL+`&HYwJIH?Hgx1!8bb>-R zPk)Uz_d?VR^dumhnh}YK`U=@s4lpuNymv1F23aARmqu^N`xjOOM}1&&o2YR2VGKA7 zkBEr)40As&E*OGU$$^;T2bl!+ma<*|kQ&o}?d3fBV)y128MZtV|R0hoz`7@&imXl++YMT9hhyN*-)Umha)DGP2LG80Vfe3gSa#%VN}jpW8F;&MjuspRbO zK{E9#?sE0kw%X5NoQ3G+eJ~^%zkdCy;`kg)U5J&RWZnLg1SW@U;f#5S`imEnzw~#z zmaV=HVS~>A7Q0+?P`x*@=wpWqwfg}6NgsXZSDtS74)aJKWZ@uyI0WX1aIl!qGE*RD zWzqSg$-#DIQsO19{#XMp5BOIhx(NXkKprEs;UL7x44NXnD=_D#j+SzzODCroS+^-^ zs?~%^nos%*S_!oDE$C-mvU%LhaPTNmgO8>lvG*4XveXU}5zhrQ6q%Ws-<-VoijGCl z4GF2)Wo5A@COk8CwOvEOy{itdJEna8)nNJow)_c?mh1k0dohn$I0a5XgI_8e-yuG4cRqpS`m=A)@oR4- z5qkqNwcnAfACaug_BNM*24>k2iYxZ_9$<^NqI%G=^bV$OWD=^Nh(JFR8}%crJDXK1 z=z^k>TL^~x^Le`qK8>TihXFAy7G5r}tpwDqxKTw$ksmqvzJ*iM4S72^7QTOX*{%wn zH;{)(!FnAKmUWEnTO>YF(!)<6h z^g)UoQ=xVV2ow|*72^>kun+J>d(D&dS+=&e0F{7ZMb~zmv}iJL!YEVEAVHdjtTb*# zPpd_&{VW0LZU*js0H+DLD3}~_;}U;Aze&XDHjwL!jXlCz1>G$o}1U+N82se0de;Y zlu7VnqRyZHyHL*K6)*pWM3}4qH%_f0qWW*^?z#R6373w5fqm6=+Pj)$1ti=GF-@O? zi5v#Uea!TZOr zVu6XEL`BS*zh%6pz3_Zg(0ni53dkoH3k6Ue(-D_%NPwPTQra^)cXhH_6}%KL12F`F z_B;-J*L_->M-*%3tbu*(5M~og^quQKPxNey`NNu**kuXN0#6OHaXS_rinfu26 z0STC3$^OfA{v{}dt(`I(9cgnCSigR~DuL(Hu+sCdDfxEX>)OTV4;DV${Ji=cUyW6r z|HSy_|DLy@~m;LPmBGsi>dy+mM&zgMsCCjK64PR_dS5IHMNMxz4z$0fj@&G$hSev1L-D> zHy!o4uwjK@t)=$3sTC7{-uIJnH#d#^l`rjC;b6KDR+}Fe|NY5BPxcA_gJb?FH_1Ck z3#6K~F~tb8a2sAwjgO;mr6%##C@0XM``t~Y;Z4-}BqX=Q25lrydE5`VVcI6AenZ~v zj*ZoccZ#RL8SjA+ej&!Wv7bLL@-ZN}0cS~>5Im!WtHwehjDu>-`ounG{XkVaV8U-m z^MMvNyu%~cfjI;4+oj5xNaY*5T{@S*a%S81)!SVvsp)G!)4n{cAhB`|z?|v7&shLPajLLA>rxkZ!xa|Z(aiX|izf@F_LHOVtO>|F< z(-pDJhcCPuZ8bNey6EhWJihfly>0as{pT9cT~*cnYhFxjUu9;IVtFXt9dl@8X|wcu zI-~FW^>LO%PQ&9^er&^~n6a#o&LVA==IAquol~ihe8LH%#1tYn;_Qt}o$j zfJ1}c%WZ8*B_%hvaq8KznD8S;Mcr$*H z;R|zRa?1!j?e39!kYf|{FqK;S&=b+WBQ37~!>n!u`Vm?$Cl3@FZ`BHB3s0_@ZA|83J8RbjzQ5PijV!Am#hWtW_;|t$8v8T{pAXnAd z_FzyvpAY^v%;6cfR{r__q3gZlvHbu3|0E!d+)tN8QIB-tb`(a zW|h4a*?VX26ItKq(ffUUzn|;+{jUD0TerG7&*MDK*YO;W$NfRIS5^sesfoP8Du8?5 ze^iLH3IwyZ|B%)$61eRm0g4NdX8o#WyX6Le`1#+v0wgHM(hlI_Exp=PAYYz>y=y3H zmfo6(qG3je?)0jgVIl$|jK~pro~9dU*E@C$rS^;9AG9H;og7nJB6BAX2!_DDp0&^f zsTEraa|d67Ze*4YzLIqmDS)fx`@*#lCKI0oLUnGujQ@#vvs05xqVCViywY~L_6z0- zRkhMopzr?>Bw2N=eFZ7=2#D0|hLDv#Hm%)76hy$ppFlew4@K%gwi=2o>rSm+qxmL*s*+ybX+W zeS_ITTJ-xMX>WVMz$y5AF+w4#v=Y$~dPa^K?|%3Aly94XWCc!r_cGr5{c~m1-W!7{ z|8lFwhdQqKC`jK~U5MrVdi?95y?f1Cv*gRROnpu+UhcOmuo}WAVqd&40EIiT>a*N?UnPZCBVSiCC%qiw_hQNvdlMD4 zC1C66Qmu`Q`FR_DSNRiUgy7=D{k~jEY<=T3yDO+6%3t?S91uUiBt`0MSodGD97su$ zKPm&$H4-)uJmsfm3(#dQtKmYFfGjkpI|MpUo_rI)!M=(iA-rYCP2ar8Q}-9}h<)wBhRfXFJYR=CGYbnPCc!Vbu;dmY zn_MhZ-#|$AYF!T~)#e+pm09M#JyLZWJchT)j*y8~RxFH}E~D*bP$Y=?*8Lq~zvA!` zhw;jQXI+YG#Rs@vNaJ(hsbkH>#~ zgf**Iw)PY2F8R(^;{{`h5#s;;ol35LRwT`?NixO2O}R>eKCaxpSI{^v3w z5s{I6GAz;03KM%=eSdjoN)LG=gK;~4N+c&Zg$gojS27EF>5xhb1`p4D(-DOI&K{Tsg24<+Q*r`^`TGdH zp$=!p8?1#$WCft91`fQvvn#|a+7C5>WRD=~sUj7?PTTBMJA{VCeRnc6IQU6Yj>=MK zKFi^9t?ao4xDn9IawbZfH4+d+QU@ib0e5P@nHkH2)rM!17yQW9 z+)euQR1~EZ!B|I;i2D!7@`$`qC12}y5FVA1BMW64XDqV&u6s1L?6&3A^kM9I9v^T9 zZ;$cv@_z0$&?a<@OBq%Df75Q>#u`d%G@uZDGhv+dUyr8tE&p(a*s`*AeuLS4a!Q46 zZ2a_d?x${UBL$7O$pV~DA6_lmuoy>(hgFW*l)`RLVzDwU|1l4SDFp51eJkz0_q7HM z#A4gD@|O{5B+PVQ;$HI~r((w62MnLUvf0yjv3g43k8EKW6^+fo_%#@v_(?9QU158@ z*O9{!NV0y-k~3CbNV@DMN*c-eDTT)}F4=idy(2e;Bow2Nn0ITNHM8}a41PWik})MN z7)5R6k)*ZN2Tb26YGQNPA4h7ey||3E%=xNZ-Oa5sy7}6?(8`q**ii5=>p~Wv0sXl? zlNBv}ul$0LT5a~@v$9f|i06D2V{6h&rX45IKZy)}w(IvF<%?^ERLU*Z>qtu7FyUfr z1Jj}PtqzX-TMtHFwc%Kw72QAHS}W=8h@cV@E(jjCYrI-)H`8EqYK`7(B7@#R)$=2DEC%h9^gepa|VWYd3XkPyrg{? z*bYNV3nx>rKjU@espzO4`@C?j5-Y3y;n|3Vl1rGDy~R5@DvG&?)?IO&|LXxqGfXf< z`ySpd>X(3Z@y=WAupqf|^{uhxNC>gxlWi3M&nw@VcX|3B;+@>egr*qg9 z7;$KMc{Ain1+R4u!}Vt?f(FIZdU*kdcU5^tqz%Ra8x0NKMa#Pcmg$t!(@oo>36sEI zH%+o)`Ki!g0xnD^vmYo1>R(Tvo#NcreBp3aE}Y}ue_Fr)DW!tWXv!r7?o%?3Qm5@+ zhK*sADsuph?@3V&;IS-lUl-xEq>*Xa`6WY;ya+qDn`j4RooR;-Xd#d<$_TFIuPx!= z8gfCWoFZrAx0ab$V$rZ+r#Sl1YM#~kuLV4JPQ5H!r+rxRTPcFOg3 z*I!a6lH|P6n-u-~)JG9Z=rQ|~ncZ+q-8xtEcz(xX{Z7Qw<)1rc{oD(`im-`HqJs!* zPxRr0_7us#?~^7bN-D#IZH4*9Y!iHI!aE9eR$^LAY#UWqR;K;8u^smP<;YX~uX^-i zv0d1wG9-m}6n;tLg^7o#pI{_-U&}cVtkNbgxqaeV%+r5PUrYdzrmcH|suGqR8(oL z&`!Uf2z6BPWje#Z#psj^MEC(*A}B{9CpEEydbiV1%9|(7xL#e$mdJ&(&xk zZA%t9Z9{`|0a>|><}`DAqeZe1ta&fX>MAW4QOJ!J-G9-HCYL48PC%;*HxdRft3SgO z-Qc~l3ut=Wtoh3rmmwBq3;n-n?AZmho6*!w`UcSiM-g7)KJfVEi+IAsS;JFS6;zDj znLe4M_4}l^&&%D%*zfu1n6UmwCdoF$ZrvZKS-}snhvi&V!I(+u`H20yKk4h)=-qq9 z!1s8-@mAYySa{OlZoY*(*sRBzYo`%FDR-}Mi6-yX5+h3o`HJYy6qqt(a5_k4?~ZIR zP_yQ&*6paJQTdZK9ZdP^F5JFfjYUXZqk8z~2FOSM@mE)9@9F;e;~9LAr$B5K_{Uah zI`3F!USOvg@j9R%zx&5l&D3#Fcag)B;L1%VCWPM__WuxqrP^&|zdS)=WdG_>l6Ub3 zjT9{nT8stfz8}A%)-uhG{$yAQ*jg07e5Ikwr2jugIb3!>=c@f^N72tKGM?z1=1F#} z+BsVn!t!C>bIGK0{3kY%e)^C5|AVrQ5X62LU0-3I&h?=XUKdJ8vPWc>L z^WZg)U)YU8;*7tD%}z~V^zsRy`ay?sP8feX38Ga!pG-bcecJQGM3cNX``BV$45T`) zPXq2%lxlzXSV?d@YH5%ok0v!9`Eu<=M(t#Pm$=HAg6Xl_C$fejyHf;HXc_LkfABKuyHuv93=J_M>+JIAjq&vd)`l@|&ZjS< z&{}>G7QLY$%gU|&yt|4Tlrg`WpLb9rgKS`^_iOM&r?&|4UWpgB2;eL$A~vGNbPZ=V z_Di06GF}OCRMcPco6D5`doy@)S>Z|D!KA0dm~}-v;sneW-zy^sWVwwb6@Th|508Wu zBMLgBttS)1tUZhzKXr_NSf`YFZZzU;zx{ap9WOduQA7rJksalV$-U8{&&EBKd6x$8D-&r8#oQ3@yQWh zJzcl;jX?xTLtnYvpj; zH47e|W9X|x1=&cO^pfSL4lD&Sg(9+4KDpjQUOQUP+coA#5oIBDNBO0Lw{s7kBLv;X&|udt2L+pzy6{I0rjBJ8)X^@bCyfxvwBtN#uGQ{YL>yv*ZoE z(R`Flk$w7KJR16izdIKK30A<4hU_Dg!%tT|bPZ}b4O`l}`KDN5A{Chop0W;Ze7MeY z7B+Dv1<@{Ep4@*Cxtaw7;KBB>N%+kOr2p482)Tl>{mk&GooZDUK!Nx% zB!lV!rZCdKT4SQ#1JT5Zofd)7G|-Dge>P>+Vtrq3q5f1r2Ok zu(qxM6V=ex+ML7;INEeZdfeWU$z2`c&oa;_uH;Q_SG2_FY=->F)0U-+l92qWnE)|bJMl{ z_`TI=Y5S7N3FzYI5qBDN;qi!#4bTRck0|*?#`}z)j+@|QWy2I93RK3oMsJ9E9fIH- zaaDq|n>=&ae^hwg-F2N{O&|B0wfzH3QOAd^?NKiQ&`>#M=~UkKdO}(0$;{!nFkqQa z(D2ASJue46*#r*8o7B`^0UUwbly^!xJG7PG=vuf&#*F=G*@J#gj8PmAZ2g^o-Nl%= z|BOAnjZXjU?|ehYZ-b4T<-Top|1tuiq-_^7 zG#dC>L zko@Z8T`(^Auof;C`Sy{7;lDgO^eYio$myBm<8-7AOp5UAYnRN^xV*grmNumJ@2H&l}J1@A> zuco7VJx48VtYaB*FXRl+89lkndP}M2-CJ66$Wxd^xsdU+6~9+jQd<9KI2IBa84rvQ zCqb*{YHG|$yw-03ly&7GSQo$-?SVBKBQBLHU>6f?ysKF#*A)@>sL`P5A;(|g5xJh7 z6Oy~_6k|PBe!JHLs+4*-WyY6cU66241RYsK?PKtrC3vz3@g1r9mO71mEE(~?l>pI{ z7vrX<^%D8*Gj_CQ)~z=|&W+f9G3n~^Tdi%(l_y=W=>mcTAcB`qL@9*uo+V1`PzT55`GSPjW|>ZD?|SWqn;c$pqb41 zslYXViOc`biK6fgPF^q(QAdM8TUGSz&@k1Y7Wj}=NDTdVESk40`IQe~gaJMl(6W@T z+6&qC=^Liv#Js%3i=5)*+$PN8^(Nq6f(5vQL_lfZM?AU!%p3464RN|4yw1}faFs6L z^?brz^?P)mK+%$M2M)w953b}={`G_iK{tflX@D$`pceUDv;KXRx^|r~=IwysKv|_w zb_PppKE_b!ACA?bXmU)SL$zP+28>R|IFZ{3C#dm(p&j<)gO7XW`g{if- zdbw31cr|)+snT$o%PLHh?F0X!%=h;8bej9AK+wgMo}SJH)?#dY`~zTWSI&}|H$Bp5 zGJI?o{HzMx#ePl+!B|7M^ixGYey?}80o3U-e>9Y`fAK^FRN%M=&Az)%88vtY1Ng0Y zla`cM@7FQtM$r_;fAY8pEPLe%kkZ_HbIz<;2->NHD~vnd5<20+s7d{icedG*#Glo4ZUq?wGJ4m0gqY!iXK7{&Y8Ul{v^O`}-yqjvS z#P59&PqAV~qo&6dphp_m010gS+i0b&9$M?*u3V;bl5YHF)cONQ^%o~t>X!KGW*)v)( z0{qd((4Skqa>?U3nxuLxE4u*TiWSRNt`hxFJmtsuQxzIN0dN9kr6BmCC$uj~HZ za^bZ+XB`Z~SJ9S>irF@zQm>;5=nV1tir2ewAk!ZZkVj=waN z^9V^KTU5zv@fD2R@_J@}VV-byIb>aL^`mS&f;ku+QUfHzLb78|G|+7p9F4E^O5X@t zN@BI0T+e|}#O_MG>)X>0NlO3!y~5eqE}FiDIy!2qbjPxk9XLD*T=yQczkh#oj*I?n zg~f#=I3vu9M_n*5F#ak4J7QTrmY1sxeAw*~Qq2FlatEl~Z|X+#s?CzpMd63K)hQ6q zE?Xx7Y0$Lv3$oSuL;Uw4Ms5cf%XXw#fhVX1y4TKpyTwy%CMkO!DpIyctV_fMtKV~} zNz=Xknop3GAVk#X@TwH)8(An_1wpmwa8o1wB`MDdEceL0C#9|i2z9HJ;WFII6Ll8u zvjL68r*^T$B(q1$%~dc3l9W{>S@p^``)iD4(kxYl2`G)vVfqQg+$vGy>pk0(MOY9! zf3BbnhphdF+dVbseElkDi7|L#zyo(}z$?=URa6{eD%J5hGQJJ!=K2rpvzx6g7bG>^ zct=mcS*yWbHBVIb)aX_r`K;vse!CVN`OqV8#jM(?Rvh7GC6tc{Y2KMHu%&rhyyAgv zFXs6tN3v?A6cxG(u8$ExU1{=QW$A_ zFo~<@5Q>7XNf>fN&JppJ1HhY(ujO1NrPXK@XK)*7RJ*Jf_L@f}OjW*XwS77(Pr*n% zrLBdYFy1sLYMy%KeF}ra<8qmVs!wN2-^Q(ub{2{uqL+tE(mfTKd3tVCS+L4?ahvu~ zj=lpiPTIfWYnaKwKEKn0=8IaXW4;O=$W38A%T|cJVN)qyw;gWlrGSf8GzFf@w2Qp{ zUT9B=g;(|8q(n!j^WyHeylux|0oXPEPDDm+ieHVi2lJ>9=NZBJm+@z}&JVYO*980M zMypRd85Z{Jv55?3sHy~~Zo?&%!D?u~wq6U%HV1G!vek|P=T2Gn2)A1(0NupIvd3QT|zC|{td4PylLgU5lq@$9_ z4P`Wp&<3(y+5VHLNGl;Ix=LKrWDDi=&|4t~1%DK?;ozCbJ7Me}- zsL>Xcg>Yi8g|}+z{ESKl^y8@qH7@j!+>2*V%N|qS@BZ?S*=IIP7|P4F25euiSxj}jy{DHvgcm#cmc=83-OZ&sZ&;NK*&j=Nw zFS2gk3lzRzt5&Gz2kVJ1&ra`8(x&(+<#VQpYrf#0UhjNPzGYg4ieGoq4RV;)eyDIM zdF4xINoQ`-%Dh>4wXnNj19@Y^!mK$b*S*`%YvLQ_#_$XVK*gjQ3lSE<_$hoG)oWax zL#CdVB`LE7JArOb2DgZfzf@R1fQ`sgNLq&&G3>v+5bk9=B2-qAjgpQft(ENK$4Y3k z7{P9Z!~TV^WJHFMIJO)$TmE1BNRt)_R`j_duF~r2{d9rB-{ZWXt4?x)oM_D@$ormoCD;nSdMt?zB0#9oL#6fa%Fq`H1?;%=&+lsR|>xR ziyl|xfA;y=aY=d-#7X2Ko9s{FV3Cp=Xr)U_)?@fsT&!drDA9zsX@xXsUJER`PXWcg za&sk1%qq|!@N48r1;xBjpTEN^e!24FV64#buLWy3!?;c20kBqDGsX8T2qJEj`L`v7KKC!*(pZ^L?4)H;BKHU{P7K7P zkM}Q=Pi6jiI}OgZwEs~3j9D$C?i`IBV|`4^Q}Oq=<}#P8@ml|dn<#Qeyn%Hu59hzD zexy9nZ-~@!^W+cdg}q{NXpNxC9VCEf+xL(~LP$nhDA*)x%lG#vaCC3`^#aKJz z*q&L2$;PpAsw|#xDq>E~88`LEpsqQRP*MP}EXe~8^2~79EALY=_w_dH%14~u8#QV3 zMKXug#9A~scQ9464Zn0rYGt*)o22z6IC+Z9op^tkxbmfVOW&9u8E7u{P%Pt58Wk2= z%zW5kyxX_1x4ltR^u=*(7Ge73Q8RtR5gpXAlfU;LRx#hM8-yORw$_8s^njY0hYr;S z<^s7hIOP)7R*~Mt&%a7t2rArJCZC;{)HdXaOe)q3AwUcHKCs2M=qCUj7uU<(( zhGTPh0F}(Ir9%C){?xPQI_?W3`=|MO2JWDD{;SOewUJ@A)NN2#i$8O;JpN?xqQ9w< zbm+%dD(nl>%J`v;TRoVZG%uHiS;c)Z{kV8b==vH>xFxl>3b6_}4|_m5H&pli!5^%) zRzwzyNAgzYS847om+!r|9A@Kh-P^r}9U=2}I_D;K_dCYu81}f~XST6hKTX>^oNv6n zyo=RY_2fUoRI5z*W?ZoTMD za><(@xsl}?OeqWUc`|Jeo&)KH zn7HOk0M+ZH&CGZsB57i(rG%y{sQ7ywe;||2+RB0~CsHob;UHxD4dsoN{kwnr1h>C! z4$+Sj(8H_Ptjsv)Fby$?mj^WCW;!NX^u|GGcMJj0!)=EP&+*DBcP9w8fwk$h& z%kGz`nO`O45ciDW0mwyrbD1zF326CSdB%E0kMm&b(zJ^wpgw)Y*G*Kb#3cM>xUgbF zAltXwXuZ{~Ob&U+y9}gl02QSFn_mbV>q$DWE7(yGWeEqBI`4qMxF+;Tf<&9%Eg=CV zQbmO~U6-`9hf$+5T-DGbDP766`=~u;3Euz?+TliuJBt~AqVDCBOu=UJYfG}fK_A(j z6|G_u#j@5;9ZmJuNR#vwX_Dl!(b)8Id`Rz-_(s;t|Ukp)OK-I$;fAX1|;hn2x>e=y*K9 z0m^ciI8j%MlBrUN?_t?q-g{~1;HQTFJ@Kx3gCp5vJExkZ_r%24NLdK0mSmip?gFQ1 zXjvpW3hl*CsVPoh#hizv=f+v8=hRDFi^Z^r_-KiYUjr}Rm3abj@F%AI4=N_Q`I~9A z>&wnVEiDg6Kn|{<_z}ylj|@e|*HO;kY;CBA&(P0cyz=9E$mInT51bD$#uEP`dHDkw2$SBN#%93*;vxeOTFLyMln}5?2>!x5r z$ak7?AMhycCJ3tAX?lDD+bCA*MiXFkp9H;++Jx@1W#_b(ZDD5{<#79p#S?Rx@W{8e ztQ~JSB{GCl3o$d%7luK604DarBU+fLA!@+-6FuHl6wzUT{)KH=YS)-gKzyT zOD=kNSgn_-8h@0~Do4xdrxX{oY_V7uK*GCK4GqURpJHsbzu(LZOCSs4Bz zw;JShZ$2evk4bCW2u0lw{qS%_%v-5A$)(f#VDc6y%*_ir(rsd#HO=XDpVa-RNb8pN z=EUeAorNqXYT_e&O}b5e7Hwa-C*Z8k7gbPD*l@x~RHg;_>x9ZXs{=y(4#@ZAv>7n8 z+hfZ5W))_hj=QdR2_vGZRnZ5lhhXemq9G0CMS!wlV@Z)0OWfdTLWA9sS;|Aw*oYpo7S zLD1s=?w5Jd{_dBvMyZi#+GT6c*HyTKPjDa{#bl zkCT%X$T#ctw89xv7g1nlW{!eSj7@Q`|o9=fodEcp7cSzi}+i7?}9sZ&9|k61@Zdb zXCq5tYaDK#bd>Am=NA>%l6KwxlGG#F+~cDS{s)ExoGFC1 zJL%Dpq)i$UQULkU*cOE17HAdOX{qBi?j;&#yc2Oza{)E40+JI(rrrc^$2%QcXxUPf zi*od=_jdj&V)(V+DneC#;Vn07Cc4#RA~Ug@=*1LUCDycl|9c7JHy;XTS$+JD`I^*m zFDu^_%lBim)7kL{TuZspJVySfSNvNaDL;8rTIqS5LtBk&KFML;jWtoPzWNAeAb?1x zcu$%+WVV2XR(Lz-≻dCNNHXsDv`D^z6O*H%rSEvYVMbvAQ9yTyYybx<>m z5ynS=zkOv-CVg@~9V<$=}4RY#c{^cp@!y z1sF#?EB1hssm1!I^7+R+mwf$ialVHGd$l?EK>hgW<<3BtS)=2rK3u3Duyg-q$mdV( zcOYQzWn8e4Ikuu*Bm^;MrkP}4;-hpvw;Ic&4ZvcZG_wqvywK2e74FC-w;`&NWQhbHIf6v*GF7_<2D z>E~X22NhYhWz&tq$UD~tI5DqAh3OaH(JOvSyA2P%PL23g)t0@hj&vRP)mp(*eEhkdwQ|M!~R)B`$i z{u%^LBWfDaP!tkgo6oS?-gJ0g;z~2^OyxZKO*i*o(z^YPXT{u`**$)dn>XJ+A-Z_` zKI!l)3{n^M6(Z5N!nfauXm1woMPbq@JovgkY(G9bX{;VM;JNvx{y1WzO*O(wcIW+# zM?SvpJq*%czkc|%lq_&A)cB0q)=l8if&+ar4F0;OS{~gcGv5w;=RR|_y0d1O%TPy4 z0q^cr1(&LKziG1?8;wsL4TAaU=0Df8IVWOdOtLAs5cb{I>zy`pK% z#7KYb8Fz-T?y07WpIPIzV6M4iZYtG%n<{qh#Sb4pHqZMl@hDtdT3Rv$%m#ywa=4}q zms#WzVg6&wselD3_Ri3Y(RlrK@9_ouYwqz?q)|l&>v-@rWNY&@q}8g*|Cn6b^x&ui zEEz3?#~#O|8{SxyKwAvL$IuGv^z(Vrb=KyjwI>@#Lc?E}rzL9l163)}TJ&bWp{~ut z-r2@p+vK=YV=HLjqno!YiHC@L`{UQmY)c=fCuEff2^XjSm?m;^%zy5>II>B;*YM~1 zvPfFkRa4I&)FQQ2M2a>!lJ4j<#RuND%Wu`j-PK96+&A$3G2QWn9)1<()3^eQAB^>I z+}4ZbmIi|CV@dufg$VC?uv>C!F6?Y(kB@7W$g`^kE}drO?$B$R6AFp~9SgX67)hRsr zG1*omQc|#^C&=FGOixcg_o}+u1w1mXphYyX;dOTuQW|%OilI+db8vpfO3y{fgeRr- zzEd83ki$JlLX^gw9dB+ zXox>H3R~S+mdai#^bdGJ(93WC`u#V_c~-}fx*HlEtc_O@!=RM$y3G9ZcVpGti{Cx0ZkyeY?{(hl%423tqOcXs z`z)&uuU}xy?4t-FA$bY4$8S0>aBA_6VVanjMEoYM1$B_rxbU&XslYbYMU0AzM?-hvC=)cSCH#bVU@^9wb(i}?1OXViX3%ipNhMC zl|ZjOMgn9A)3USo9CxIT)%%L!Q3<|87DR3b)l(C?qUBw~Oz7JoK0+#gZtUu*PUumv zucj_<1zgNKkA6D>iY2}iNQ9QqZxfd6I=$eZ5mO^Z{%&%R;-2jpk3#^C{ZvI=2=oEQ zl1F96iw=24?@Q_ndrNe*^u6y=Ma1U!aG)rcKTm0DnA`q#1BJ!R(aZhWm9GuXiR-Ku z4YoQg-{Vd+D0k;?@v-4;iinX6vB^DD%kf=JHEyYi%H_f_s;@X8hX3r<|Jc*peN zYQfv-7rneyk2up0=U=mG-DS|ff1hTAvu~m5r-81K2SY6{#hnN?;e?3L-Pa#uQGvZW zp+%8gZ1GD*|9&Y{Mum9t1zQGCI=-jQF<1t^`s!@z#ZAlOv25IfVq;~wT=26PT2U=^ z9WE`L$4ySWR2EG%L$Uh4k66AQVJk-@7OhO6exk(nIkmyj={vHOHg={L`hZioK?>&+ff4(blt;T%m5*ia$LPRI_ z#Ua0l0E9px$k~rzJ;JJgLr+haVT;i6y-j zQ&Z!-Zx?9|f<&K9i;Ng?&&UFf#-E=VpQ$W|{568t&qok zRn^#pW(9M_FFlvbP_&YYeQX0Dxbiw@>r-b}k%Uw7^P{^){KK1-SA|uLj(c3|0>I>0 zQ?GkzhmK{8{8)5#YD#Uh3ula^-%enIn@S;P%yGf4cB=uW67>6pM^C64$R_;?*FL6f z;+<};3;$u%C_h7s=V)sHY-egE{5$Elx^d*k_5P^9K;ve6tIU1T=Wy5wMrh}ep*#me zb62kn8JF+dq5GU_V3*V6qcdL8fBaB*(%0uszDCr`LW1)_vCc4eI#pxRHlN<@g#Gli z+HHAp&(<&FO5v@1&(rei8XeCzjwdtPiz=61v&!{SR?6p7F=(gU_;O!I5jo*{SmNNP z|9@^KIAJ4MR=;Rf^?6N)ttTG(t$>4>I)+i+VGz$MvFL0hUpqF@AN4R|J={BXJ2Br{$G#n`LaBJyS#2@b(1CO;O6!a;*zh z3X+mWHFmB;?DX`r!?1q#Kd3vXHMx}mBjI;Rppc(Zk}3$P|^v(uVmRiQ{xtP9g3~segWnh4bqvNM}s_2D1I z+zvUkFk5fAfwi)&BK~3N&ycC+c$XRLdy1gncGjUR@H8>y_~+Y$I^Fc0^19*yX4=IV zTM6y^ak+cj#69EeQ7rF*gTqMaz7tOqmjvaf=Y66i^m7j(il1Lkdw(;#Ven1Z1swhG zzlf4-5yhN$MQxo-x<)Kz+>;n5l#}e?0(fzyhYyj15<=2b$UbMv^z} z3=9o9ea}wNawSxsKTjYzJQU~7FTFKu>H7$WcabmSQ*HJ+I!ixShF$E^IPWbshi_P_ zKs}f2;eCg9jWC)sTr&;$2vakenOk6&IKO7+F~qpH<`H#%sa7D()KOOtf%L3qtL3I4&Tp2$ zOPNgV5MtxzCWetWAA9YdQmO4Z)w{v*$dr|UlvLa^y->|r-kL2Mv#Dd&$@7$hcNe-K zBzjX(%7~SlWj*nu({ao0SuCowCpZ|_K*t3)UneT8>ynM-@PSCa)?VZ~55LkxgwDj> zV3`ZR;ns&D9KAeZA(>@Kvurfwu%p1NQMP*3u5Guh_1N!M({BPTVHPym>?S(7R1J9K zMwcY#2f|I>Reg#YD>CjREm39{8)(1(3I>qqfQ))zZhjj$+1oIfm;qo`E6~p6(;E5e zkK~1cgefB{yIU6;-1eKmqv5e&(!Pr(5rqrs^feEP4-y&aXYSmfq$#-!b=E5<1ZT?vL?VG1@*OcS&surH9(H z@kiC1lM<3QEjSX{E9g*Wc$c?NxR;W1Y~+Z$duNOOW}rtSCMOSp?4pDLlz*jGp|r9x zNxAJ*1SlxJlruflmgUo#QjP4!xcYlCC69s$@3R>%7FnAo`h`ovo>7qv!HSShrUkrpU}y&0T-L zem$p|b{}#WA`ib|iN1)4z;hIxbJ@iGH3ki-yG%n`K4_+bOqA8FKL~nkYbe(GdzLTB*eP9D;c)M4jxmrp1wPIujvZ4BgjZViUEkm{xwh zY2G%`1=8{K4tE@xny25rLa%7Iw%Ke66|%I?{Mwz@$3{w_!f#FVU-&9W(u&-9Hw&&w+xane<~xm=7h)6_z~4nAM+5D`Y(hk$8Ht>|JZaBQ|W zTChxXik4i+e5O$tUnI>eF%s+ z$mSZndFz(`V4nJ--w>P--RXa>k=GxN7iYIR+8mrTrc4|q(u;1Y{74B-?lE>GDsp>F zY0waG+!`j*%y!s{qIf&#?ACI9f-hJ`&#tT%$ms7p$*MB?me{PU1(kw_;EYzb=ALkMqwW2coNc@}L$^J~=~X3-m`zNjX1+>2YI`hPCvT%EjjuD(ZS62-FZa}w zo`@D6K|`l`>Q{D-*0jMHsDL>Ex1u{UUgO zgwfU4oJD6?J?PCJ_AkHK=+R=5l0w(k*3Je{8k(9#fU5mc?i%;WYOQIdHhkD4)A?K3 zMqb`^*7i_|N_b$wugQn1GRQ@z{~%+wb*W@DfD(tR*~cDS1k7Q&ZrwD zeJQgjNuyx;M*kuMAFkqOST-@$9=gOjlgg1RSvJ-&Ec9s6iHRXd=O7|7VU;Kgl*<;N zqWtLV%NP*rz4+z5$gtXvd4YFWT1!1$uUleq-rOB=%JxXV0>5#c|3=028yBqGVu!ZPK`roSa~t zJbP_v30@K&Pe#=T({E}F^s^lyx$DkOP6=tX(9OY>ARSi!6{ae@l(NE@zc+e-#5@2k z9!++~pd0Hsas$k-Gg9_TYr$hBc~%8iTU$FgJlvT`uMwNcN8=tVEAGt947%vZhAl85 zCC$v3fhS|ww^Py6qflB=!9Y*nkU4jUgOz&_r{7N5#M;_AYx2W~564VbwDl70FTOc~ zzl2I#%GQdx*YIe#Y5DW%#0m?$=JA{34myHLhR6PgC*KE!I$v84lc1zgBw63L`=qMuwe)po zt}kX>)$GE;S2b?&nqOK4l4(VW+8vw{~YUy4D2xbQr1{{^$u(#%RCS zRa2pC)f%W)R#rAH$Cp)5c&MNdF}3ns*C8^BTl4M5g1-9yca|YQUDD+y8dvnOsK~x8muR7XuG z{||m=*z(qCVninj19_T>gsdv1v@u6X~j`Zr5aLB`7ZUm zcLV+5Qym?fmGE_2P?uD$6?aBOMcF;HZgQn`RyRpjomKnh)YsS7b$uzry2LAi$;a47 z3(~kcZG6>lq>O8YetE_Adu@YffrOOkWoTCGw1{j>bnG=u-;_W#lP-Kt#WVJ5;1}m< zRT05jPU6|Km}Ti9ZC9#|$~iplsWrvC8`Nt_c{j+c!>tmxYk*?CeQKSOfVXOTQ%j^5 zzFg$t{`Jc;yJim4B*L_9Ky|H& zVJtqB*J{LP^K(}MemVA{AO1c52)H%zjS@$S`li+n8(bCyIpl)YN0fE=QHUn`k~N!7 z&2>QNOr{>jvvE5p!ze{vL9UTRsBZX=D`#D0zH6v>H7@D2z)R=NO%MIrlDrnfde^6$ z^Tk~hV_%C(axkzuHGYhY7*BdWRAG&i50!qqq_w$8IfBd{O7^LPeR^RaS5+fQ$~XK_ z%~e9+P@`P=#`wKq%M<%8ec{&W%*@QQ)x+;Pu31h&B#4HUn43`F_&Z~`@(Uz;R~hTb><=i#Pz$o zyBRAJzhCSc(kl>(2{@u1axXG&5w2_t5(!?eG#jeJ8YAzYsn^bGG;9pK$`650ajfe8 z=KWa$EMlE;6M6;Pt@^!3tlX-`rei$24fbz$DR|8yv3z^19my}aGOnj=8jjt-S6zQ` zumFYDF?Yh)fO}iHrB9hV#hUXOzgC>Kxi??R*v}W?7;GlD%q{g5?%8O(^S@0Vy(r8x zycw}ayBKtCQjKyQDLNDAZS{0YxiK7J+LLU)(Z7zRcj7!;Q>dU7VarQ(HYSyLL@gJT z&?3{yhY}LXX)E`n% z;qgz~E*^9Lh^RkkB34Yx&+j=VPH?iVS|Ig8m83Q!j?vMUki%mrz#4mfP~5@*(Lnb} z6N`jN&OrVUtAjkG0#~I#X8{zMjb;Vbpo$ ztwGzkvm3=Im+@>Z{ zbB$ysvo+@1m#=R7jvVQX6|bF4iRq57T#}v?4O#Dj&UE~!Oxo8(PDyXLZ`AS6jsb|Ha7FC@52Uf78cv3iE;{Za`(Qw zAk(()I5IDp#z)o)CP%a9^$?bD2&>|Vsgp%M6NhlkMY~l>n}de-90YiI2w{xDJeGqA z*qpj@@qRw3hfPddV^e2?m)5!=ak{1z7Kg?c9gkAH5)AwC-rYqLsr5Dw4dY3+TWrKq zC2p9vP|}oaBFXn380e0vKDa?G{+*a$MF1*c3sjR?&1TI#I1X@!1Ghd>@wl0LvVBgf z6f8SPqNk4l@o6G{`q3o1gDDzjgFQ@Ef>I_8hc$*@mK{_4_|-G;>9{U6k>Ir@*-e9y zU;IqSzy}KIaR0wG;Cx<*?UbnS-VX^AAuY`DT2Q1jCTsxj10%(AL!d-^z5e{To`IXY z|M-SC#EOStQM-Nfa!CH}jW|yQsNLrYYhZlh254$~i0Re??}Xc0QEOMZAZftH^|scj zrN^F-_CW~N`4C{gO~F-`Y1#CV^#H%dn2pNthsriRt$QMvojV45 z`qz-MlTHb`8Tgg#TzOSRN(#fl(a|1~9+TJ*VA;;u@bnjZqPG^wVV`VuLS zUJE3sT~Te~hV4I-f_dAN(w|3v_%t+nM;E;~ZNTie$7lyRUBb8LHr%@qvXb;oy?S6k z@A_ItT?L2*iT66DknjQb--fEiM)mr3X|^;dXM?XyXLZ3cY0fUFjH+6!+LUwVJFJ(B zqBm4-l0=tuk~k9Eec!v@Bz37VQ0`Zm(_A7O55LyWK^iSO`q?W>8UT{y(zBH7X*{$^ zWHD6rkzz@iPzj%CW;4Mszk>blg;dN3`=4QMO;YYXVy{Ptk*^C8GHQcDLOpb>e{g6h ziOpOwD5evTb-ZYjxO+*QhJor6on!%lhao%QKcf>9o5~v=8XdLpX`!vVdV`mii;Dv<=(0mda5C^WBxBbaPG$E^^(zBAV}ZK!GyHJLn?FVcBNNkV4JS|S8zlk=SBbS4 z=p7gvBp9bhUp-1lq6#nkG1q^7wD85v$y)$Vxm?`dlYUkS7+_UFyV}+Td3m^F6}Hl_ zMA`V>QrOX=P*Ye-YD=9Xo!uKGyR;-Z_f@Jr;Vq@8UMRBjA{5~HuWK0O_uypSRaO=U z$v~Y2Nvkw~zp$?flIOo`ZC?PKQrCMSvZA6QnD}2KCN@;r_yF^s7);ea1{Y`oLiz2x zzul_aFxu&S_f)Arf_;-I?uJJ7kCBg$tjRqq8zy|umV9R|b&ubT;Du=3;xvo!D**pK znv#-|+z%^7MMdB9IaM3+)1zKrY9xQM%fbtcMT~8mpL6rMPJ_@2v_5Uh>i!`@MvduN zSuH2|1H;3?$o%ARMYY~Sr&XC-Y|9US8c3GBex88&W|S9UC5m=^p!-9IuLftG?hfm9 z`)E4;cK>vG`o_3ef{26Uq`*(hPcQEr*)_JDJUsE1C3(CmC_JP!Y5O{u|6437OEEP9 zrW2d4e^ka;SXu8K7;vFVT~K93MSr!?q=apGxHN!)myc)=Ei(ET*B|7>30~}6d*0Z#maT{bbu@SbMx?&42blaXD}(lsEb%n&E2wJ z)kF!1{-VRI1b5GAR-{5QKVd2uIJYMc>V__j5{_L{T|7n#DL4-&FZFS`ZMNL7z4yJ) zYl=+A4Gn=6$e$z0juDXK8^fqwyzJ1q5*CK*Sa@0}tU%JV^tme!8PDR2>_uVUIU8;j zH5q+@)5S2xwI9xLw#i+$BtxBFD4KvbM%+K6>I{zZ-DJEBQ$tan{7IAD`K6kH#)n)urmC zF2N=*fhKAJn!?K_ndR@=gxnkID7W2z1HvdtzS@K;ax6F7_V?cRnO{` zm_v6JcS+`>m@bu`1<924RKUjVwI7qiOZs2e)EHM4h*|Wf*%GOs29pg}!`x7=x>314 z{s>7#C1p<}Pg*g=7hQgDmjxB?z>xc*ps|f33THZmK1eAq_pj!8@fS_C^HO| z=rmWxC@JDz1c*1Cwx@Ya9e}Q~l#(F*)$G-85Gx7d@M==b4Fe<7^b#o@CM2CO&hI-_ zD{AiwF9sdXDuosho0I{RLO`BxyTy=FKVR_s+e4?e#FT=^4AK-``|gt(BMoZ=zruI> zT@QVw6}pD)CTpqXakFGwAgD4qp(ZRq0fI2M!qt3Q{zx{Eot+xs=4cix)9abI87h=X z$xX?xa~;`!XYR@HFVCn)h%F9d#ETO?eQU^VM9abKIQdc+8`XI0;2u4yq_u_qLuBJA z1)=1L8J@19>Ser+&dGK$0j7LGZh9Z+rbE}m%}~zXe|{+UD)R5~?gfwA*Yy?_dT{&P z>z`34JT7IVjp}%Vgm@61qmnZrN5EEY2;+JC^a5+8S@{*t@o|>31LXmOlqr8)hkx?m z?m<;X7#7u-(CA_;FB9h*UEsb43fMVd6cki|k+PaMeI{|gp5bMouba-}+aD(b(d7J$ z8p$*?n8+fJMbv`mbq!cie!h^MEC{8++C}a5)^GCc2qktrK^QFtgFjVUqJTW4dh&!s znqhM}P1MqURm4n`U;0Ls!G{np%52%+o(9Xx2(+clA6O1bhExo$gKK(QfVdd|IL|mE z79%M{?B=S0`0Kg6=!9>UGs#2ywI4&FgpU+q0&>H6;eNpX%K- zW><7P`D{8-fA?ya;HS(jUPnC3yVAy^hjn^9mJahHnWGwB0!&FuQlN6%x~~9=St0IC z!og_?x^4!gDV4fpiTPeWmRp;P0}G}UPHFd4r#2NX0+EIECmV+xJyr4&pc5)_`W&>| z_gGYek{l?0pgiOhmDwwiaE%FPt$*|tl!vbQ3439?t*Cv6ndy$E5va;PuWf_qV;-j~ znSY!FV^GmBIWQ*D{G$BLn|RQ%=mdO8S?=56hYLaN5fN8>cG9Lru>J$j#II^v#Zqc> z>A%Oy{S``-$=e#x-C(GFip;8ZW`n0>g)LLay^^LF=N}h5lS_(6+3Ki7nk}pt5scIH zY?38aiyx^b-5>G_Ie zLhxuT(KN{Kp!Pj}V0j6zfB?8(1XoHnPW1Q-Jr>)hPy7VnJyA<`InAX_uaT5J5hij2 zI~FOT6`&X`s`NBA;Yigv?&DeNkLuu3pJ(Gw7&e}wIf~;Io&!)OKzEn}miPCX7xMzg z^$yImSbAVfRvh8}XU3yA3A2zPYH7P3g4|9?p$k{jm+Z2&plw~)4+$TRSLq+D zjBDG9BpPs%Y`AUdaIjWMdwhGq*-I5MTnzQFFTYQ1Zk>!Sjtmj<@K0f!Dv`k9oZJ{H z(cc2A08!;P&z>RBnrA9KuT$<=V%KAaDlnzuJey;1DOb;`wgoFpOA2xIdJE}%j#uAc zro(}Lt`pk*-&?9ScrZG^j=8e!_Z(v7om^-*z=~B#Pu|>bPE%tJIzbzRuI^V6ZRPlu zWF4+vex-l$1y?|Kb2fYX?14HDMheze9Rqj;q&RRe6nasPUy0~=$C_MBPzw|c+d3l0a0!we{rY%Yu#U;f^ zXTfA*wLQy?Ueh;(_K4U@USeZ`$KG2AvKl#J0avi@ zsAnHgnAF_hfV`LVKqrbEVHJ^2O`ePDI6?16RLI*ubt6uTTplRlq656rU1k|0kb6c=u7G_?p^5teK?=p|@U|oTtIKP@ zNk*~{B?ZmXcDwR?|L%!}grL(5ytZcM1vRRVfRZVannykPY$?}9M_U`+U-L{*Lk^RR z5_g!g4Ll5q2zWZN{k|DS$~FgcObCwedKA(A-s%ZB=Hms zKvj-l0KyFD1UvZs51&#}byfh@hS*LIX=#PsBK7X*|2=Ee92R|f=vGFUgzz27i`Y6= zrk6k2Ddw-HeiA1WGhWacyj`%msf+Szyu&u9Oq!D=<(8lF(r89@%g+g9R9u;0Sn!q^ zF3=%KD{(i#Pn8)i-jfj&mAxXK9v@gU`r|UOdK1(fccy&zIj6_c-DpQ#%04m?5<5MR zfxEZbF|Mr`P6(|6N0}(k8{~F350qjxs%D8R>t(= zXA~!^63>UQFcT6Nv7@o{?Xeuskga-D(~qn&m;_0v=oTkL+x)_{=5N8Ge% zV%D&z8c*+D-Wi(Z1no(}D09{DaX>tXu+Xi#P26K~ixq9Ls}3y_Iy$`cKQz#xi( zrl9O}*-tk~6XFC|W1D5cwDHA(8PK~eS^&wG`By$TJ;LwA8#)wP!Aw+-av|EFKVb^W zV8mt9aKoM`4)jz)c-}*RK->hzooSz1A24n2;Ac|9+oep{H30UWH1-c3L!m0WzKwZ! zHFdC}?${b`)cUM|>f=!&A9Yrvq?Nbbr?yi9H z?!)h4pv=itIpe*3y9q?%yA6catbA3Uq>Q__vbH9w0CS%Yzl_HgD!&#U76meYDV^3^ zOu@`dFF5k3p+hGw7t{hQIyTP-etm6{rEm%ifHf4XJMozg!}TPb=fl*;8G;eiVzXP~ zJSD{ymnNs)Ad|xY;KGBqq^3q&GFb~DEm7(4e29RYFGR6s0IL@P2u>FY@X}R?EpXVH z21Qaw?-kvuDQ_M~r&4ZABlr=dfbg|I4O4ma26P;eLo)?>v0&dhJq4TMW(L-W2+#`n zfdLYNz56({g`5dzfku&bFqml3h3gBZ(YHLkK}aplg53LYK(j|BVdUQ{7np= z)Brul;_@Zh%!yY4G#*1A;ST};jNlJ~jWnwrZ~pc2<+1#X8;FNmn{J#g{An+b2J>Aq zl+!jx(x^w=D(EINcY-Qexd=7T&+b35U4BEY12LDT^Hdc8&;%kVCc^ICEcs~yYQbuI z06S_Ty+uKafFNwo7PlEH-wL&#J5qISBu)$Pafil90-Wz=5Q~VyecTBcd(H$os1Dys zRQ*`s_9NZs>F(Y>HO~U`W6EWhfX6XvzkW&9oLZic$!S3je$>G#Z@*9jb~l^v zz52$v4C$xX?r#D;M5*f&Mz)qC_4?0Dv+p2oG^%R&>hwe6X zKLsKNP&vb84gJJo)_j^Xc?7*dB=;y%$p~(D}ZkQ^312d6%_28{*fTOP}c8QV6~S9 zD0f2;I+WwTW#Ka;tXYyZ8JL9U#OlIGRN33R? zAs9s(bHnC&+P8X+taO9pg7@4sEU@Ri}13bUeovbvw_%*DPXb6N<7#wzMs0gqI;p_p^L%FOxp&eeJ zB_wNK`D=30u0d@ge;>@xLp28x#igg)`i1fsMu7VWv*6brhoL1WBQ9sY`Bp+4F-95p zrsr97lQLglE0B^99QtVHA!gy>-7m1k46YdCgS}cF0$+U(Z66)?#m(1tQ1%Ba=q9>34384AaK4 z0&ZY`?=5uiqUNgc{R15`l)t*Cfz4$HKz*c_eE@3>wJd2O)$2tLO|~vB!pxpCcst^N z{znnu3H1U2&l~_vg|xM`9YHx_45)3+=g*aHkxNOzzPEgo#h$(N{4S{UmJvnJ`#ro< z+R)sbYNP%xiEud~;l^tb*SY4Th~B+0AYh{Kp9^I={G{ynrrVYJz56qhC|{KwI?pRSBR#hBCmmx0jU#)fKYl4a)OdSCNd({)+! zZKh-8)W}fqHSpBXHV@vSQvt{CapO5Gi6}O6WUi8%8>%AhOq27i9krL@;VJO{dg*iu z)FN9LmNQxqt&l~$X5x>*+D%mdC`{~Vk|W%4q6Q*Pr!*Y^JE99eN&?7_@?FR4qv~G1 zf%(Lzx?1sA2q>K*xBynf6CE{&>7i=5B=Vb6>rSEyTx{46mm~!bIyq9369okvi@zY4 z(&AU2 z=C<&;$bNWK;pb-y{2XLos%7@t!)4IEmZ)}72qjV>^=wBwfiPjiWDF?-cO z5di322534nnAbpJaP%_?oeyg`fRTPX9`--cp!^0Buwwz{?$U%k0Y6C6ddz?8Rx82o z=sj(C^*-DK*<<^ur^u^jmk(_I>h<6xHHS@rA!0%1($*Al_pDdf6kfu}Y=7w|UmY26 zc~0RK%A0mQl#EwRSzo*Ljo|M`ucev2YiR3Y#IiM@1C0v|eK4;?rl+T$HpvpMZB0e9 z{4^%ds@51B32p=uke)j0A3xmc(K~;!Z%w%jI5tOl_V4ENo$GLP|Fwy9-lnFcd;7iN z&_;0_)2)fAW8=_3VXR>j@AoEL`b7i0b*Ztgv~N3xoo#fFVGTU1PIW7AIJ~OJud66= z4uk1M)Pf11#5eA08ZuuK>{L^l&-gwz8kx9f&!{+EBf|#D!UgmBA@byF(ZNZo z5aVr|2gUFjrB<>7JRUe=iJ@BKufL4d9~FQ5_IxH&F}i5d)7ynw-M;8yom!K=vC8GC z%3GH-det6!eq&|<@!Mepf$&;zm4H>uYxs!7sP$Ou)Drnz)Hba!VP(SK*S)kJ7r3ir zT4?$E0{yrQ=99h4oi z-HlvU4l&nzGgD(HyPnoBsh`N~b7(uMDfPWlQ6UBUptxZra(mkuOccid`t_@}U4Oq+ z9bJh=IG5Om>|QRzSa@>U+q9${HcqzIVm)z{rXmI3ZUN#L0bqa_ z8X7WRk(H9F^>69Fl&Gbw9NHCHAT(a>BT^1$=N`d<6UHNm>!u|U=dC3lM3uK9$ zras?McAH#R&p0T%xON??j!YYuX7h^$SU`_(Pe<+cX?-QlF?StO9#76`@Rn{PE8PzY zi$r-H>|Gv&k%p%E8qc{Z;{PcF+qr!@;@K*BFMkwTz~IhaXJBl66o}iW6lf`;*VCIW zUoXolS>N`V<7Sd}2S5%>f5qBqeZ!T0?6>_Wqe=I;=a`(f$JO4dRPVEcWZmZX=%W_e zT}oGXG<(~kbjfa1>`^^Cap)R41!o2J6_rk)H^Rc8Q>gcPA&$F03OTnNC(=d zTz*u@WO`mxK)nZTd}bzPA;d|(^i3}z7&P#fn2n8x&||06_sG~)z?eOVg3;CIbABO$ zDVhlgs6iWXH_rk4&`gob8+O#9e?O3mRZi%#;H)<-hXt8j6Vpm_Xpaoxaf&<{gA#36 z#l-|J=F=yuCq37lexqrXLW#B>*Wcl1R&&T}j+9;n?IBGeX8ZE18o{fJ(Rd<3CldzB zAAz3CnM8@cL7DZZ@d?pqrV;jc3ri~{>xN&vj7r9U<3j+1)SZ58Nlm3MAJc#F;)Vb7 zj}B7o&ungo+TqLS=AhWg4`+WYNS-!S-iUQ5d|+cSt!WYa)Vvj_<*vV@m2BSeAU!=s zN$M^ID}U_nO{Az{q`VlHbnlB1S=vy_7mFS}&~w^;OaRIU(}|x?V2T~Y0)AzKa5l{L zOJB%y22?wn(Nzh1BU}c2m)r7BcrE|fN5WL~@5(h8U(dM9dPyefXg6R`@4Q6)XQ+TQZT{L8I2o3F^5#*Is!=%epX zV3;&ygNvJ<0~4g}fr|ll8!%#$bq!>{eBUy$pZMD2rfFj4zGhTf?jCNEuP!ZeJocQv zl+yVq><%-3T7oc1z~t6OP2;xuXugYz21^@(`N#flqTgaUp{!rB`TaqnerZBv{^-tmIj8jSAw*SxSN2Hjm&>hhS6r z>(u=y$TbE(H@UBd75r7@@d;7GFg57}=CDHJnX9!h_mx`D8aClwnsV%?cFjyc6BR69 z#G~v~ba5Ya{y?l!3I@~P;^f>b7HfZl1iH)JVscJ!v`&Z17v4b)WD3?IdyexcifiJH zH#ffKC5sBu-~79@_ENqBMAYDAO4aj(R8i%isb}w}6!4OO`=c&W>6%?zO4$&bO8J?S zm4lOtG7wL>&M-XeU{b@r3w3qr7W>NE<9Hgx@XUU3(&v)=tH_7~ia3gy8x0^yqZv5< zjy1+@Y;9Y?9G8l*DFLQD>kjPDhglYB>+eqYo2CNSXeaz$glJjui)hjSbpRV1R^)F@ zL|ByZ9Ver($SZUupC4%H5v7h1sn&y9xO4f{@KkVjJKrDgq)`&$%r^&}&u=M(S{nn& zQ@VeH7!jxp6pdXw-}E94#`Qwabo3$uBh)W#gm;EH!X|=AXxKP7+6cBN@c&We7a_z6 zfV~>6S#PbzD^*9-$H1F%Ju+55G5mp7>7w^5=+;bmQOeNN)OJ$?Bb6?Q-rP4h9r*Dh zU}M7`WK-@s6wIjM-f|6GCMH$@^JL>i3W1t6RV`%^XtFAB(F?6boM3#Qil6T9^>xvB zTfUyCLqk9CQIEI|bW8q4d^&?1YvG$+YIMT#@DU*rGBWI$NV$CJ)TqY66#O_Mqt#4b z_m_N6UO_?6ubKkyTm(W4B3S0x+1c^cZ0%b~>ga#`n%eK$_KIiQDt-DB%%_;Zojroo ztR@@-&RS=-2DTQADBZ;1X4jq$s2RujR%L~RejZbvG4KPyXo+vBUa4;l<9^Du z@$v#8*iNtbRwsL`;aG(gBy@yO39K3}(yU!-RbB& ztjsjeh#&es;{bAv-fC>VzHQ16&*goUP_G$LbXRM8yObduXYgt#0I4 zJiOUSb~x|GLpDWOzNVW8hqr^l(<;zLD78Q<{8xRy3DXu*50GA5TIP58X%0&y_Jo=C zUI1zfNVnae0b`};=*j+cEJ%66Ou?{iAS(+~*z2TXI9kdCN4GLOxnTS?|>=(-lr&BpR(38W-(}F-T$Y zuUK7w@XXUy?-GK^>VDNeimi2Z)XYn;dVP)*ol3Q2`&4%b)PLi2t6d8$?!w#ddSC&DTxV(3Q*i4w}f^l~zOXC?3^8)0{Gn`i9D&mT719W}#W2j<=-2yDAM83Q@H z=&1xSsb5VxnHoAzcyLL$w$r@sulcahWB5ewomqSBlHiC<-@GC7!6~k)V9$&!k*;P% z*hioQU~$5W{6Optu%@7f4HYsSbKD9yKYVqPSqxB;8oT}b9$MJF8AV)T;*Fi>0>JLB zg{&_0fK|i&=Z<%#;VYBOr`+YZ?rZg4-!AdmWjeL)_@y|_Y6@`>YL!yT>`vKkXh>|- z<%(yWgPT6#`5eo!)uxHFW;v%9-%X>Tu9ASHP3o$u5oedWz& znPV0*jo&5c%$fsmUN`$)S)zI-~|2$t#>Q%fV9eS5zKN|kr=2Q1zJ-1BHoUe&x?3?unHgVyK+7XLOD6g>~~x3po3ap zcPNfmdRuukBWyjI<>L}}tXPRN`9uO>FH- zPn7TZTh?7C>FIgEfB;l9NM|_g?C%%1OX9ITI;NaxSmS2-m!ZaA&7N{K!^^17n4Yi0 zHwV?_3WNWts9M}M5Bm>oxPO9{M!%p;T_t^^UlEmEhA&z7 zjm7ran8<-R=D`4CHRO(;*~+iHzIK5`x}E#*?z`_!GBJXyK}#ldjcdCZ1*_gqdDf%T zk(oXP-TyeRp&iRtwN(WHAPimmMh6UXq!r-#cF0KAKwHVm&28rb8 zUEZS$3zF5_?mq1D#Qs#erM#6nx-JP8%->G;9v7yb7)|$6`(aRsLoyGG|B`vMOzPD^ zpi0=m19fBC&+LTywMj#j*`sxOz#|tHr5eqv_sx1uX<9qO_c|z6M8&8!THXPG!QwEA zU;?&q3yqFoE@9d@ExUnRYcsY*JKR%F!rs2k=4=h1X+XSuBK}y}{E_qvX2n7`L*FKj zvFc_cMWeyX5LqsQwFhqrXBWTzuHN~1*OWsjZ2Xx(GIS~FbpKQ<&i_;^_aAuaai#hq zJ^@vE+>hJ_B*W`yJ&DE1oV&L?FV3+m#*z2(%2R{#3WI9tDm}<8;56#{vWypS6QC%Y zks41*-Th^?-LMeUsYg_O5vfNJ#S`o#iq2M!O&zQ!(DeVSsJ4U4ke^S8fJHYm zCRX=-fT_IgOJMb9W7~i{aZou&I>VKnjf$0@;D=i&$20ptN-b+({Ve+g@RZ8ExzCF4 z=xMIVN>RscnFDpX&rz!FT?r%UiJxQcGTYX7fUghuPwXvy?^4i3fLxUFv8gYQY>l7Y?ltK@vAu0yCxMTZ<@ar31X=0OSMx7M zoep1!5=Ft_hucPef#dVqo&T7wcSSoUW!)*(OKp^R_S2*2tBTJz32r;9DYd6r{f;|W zvMDdMbY6SYgv`%T#ksrDWx@&w-Fo%D_a(9kQF(cJErPmh%a2IH=Rn{J2}y4^%p!ZJ zkGZ}io6uiZCj|9+9U!Y^*HMngZFJSM=~U&Ar4n3}U#;~y%}??Ny;x#V(^1>jzO!?N{__{>BjTaILPctxY}qKWp79Dr_pj z#l`&y)4`~_*yv_8eQ5ng4DMMQ!MZvp8%ERoK7pLqf|73CZ93u~H%}D0*Y%K|w!W86 zs}YPGl}rGFj~jr36~N3Z3VQmLlfKcKG3KBQx<9!2_9q_(Jw6UwT*%0z2$tsSYBej5 zC(k+Obm9abXg~&B(4c@hw6t@d?-SYzzXp9&4nW?ab@kBAZgLTir@o-+ErHrSAJf~{ zKP!sf1Z!O1S%p^4`2{E3;6v0cLLQid39aQe4q=VMEf_Q2b)X~nWMgyw3}7}8BiL^n zZ=*5J!_O~XunxxPWl$HaQ@=vY4HqXsed6;U-+$AIBjq=N3_B=RKQ){rhl^E2X;lJ( zG^0dQ*&!J}1syy1swtTKe5^8mrn-xGxWdk$r{Q6IPNMxQ=dZGVWVNCruL&v~c&Br- zSwxO>lKWVC5!!3N|5?@jt^Y!`U?ZNqAL26L4?lfH#e4w1)Q-WuoM&kv0E+9E_$mGl zilSu1_*NpJ5^Z_mFEC5QL7ivUP1XLcocCkS#QC=l3e^Z+C@KdstMfV`~UY z<6HSxgCQaRYCh>-d-wg|aAPXze^1$>7)MVN!7BR-i1i;SX$r_WDiGQuS(#FZXYnuY zUsJD`UE)uiaY!owV|Bi+J3lae4selVQJWji&d%gizr?w~a7Qa3mFDAPP6~kau1_8i zX>j&rBL&qctzHPGR%++`XZNB2858fwsaH2P4{!ag)wIZ z2;Si&5a$O<7?^PRXY>L0`Rz+GCx)H`aQlAKy?7LLm99jp?Ngc9F9bKV!oUN^ljR#77+%&x^O^v!~(Pl3({T8d`|yRE^jZslp3`inYWN#> ze#*G=$u$s`gBFc%dUgj_D2e6dbudDGkbrfa$vL-kmfl^mA*sIVh|S$yj$#?Yy`Dmpw&;u@-GR1 zP>4!@go5#(EnXnMmhS!G)$$hF^y-Djq+l9ii;vqSu=hw9VC&Zn58F z^e~X40E*Cn!q!c^09f$rbaN^)cCJUd>X5C z|Ib#!-m;??&x&?k{TU=*zD`6dhNiLZcw!-Ms$uw-Vb=8#KYXZxO(3$XKCX;%0f4WV=R_w@-F^7C_C|1sNJ^!)q9OF}1H#)& zUmwi%^>EG&?F_`F(8{rv{Qal`VZh(Vf#85p_Pcp-8sibJi~hadM7~+BDZBvK*y{0F z#fX54YV^GlgfJxq-7l5?lipl-=G(LzTUmDN@hWj5^N^2$aV0}=gJXZ{si$q6AtXZyz@0oS&xh&C`E2PXVK2s{4Co0s|8=a zw0?NIv z{tz8t1sd4J0IN-;-aa*g-#LK>!3*GwjWR%tfQeK&_1CXopHe@YxNZhBqU2^c-tHlu z>avPUPQME=;H+^73C@-jYe46_#O)SMO^9H|u)Oo%Qt_Sp(+`@ow;mVnfU^1{hsiQT}9j+T3 z8;b}DAq1FEO6|VKIrV`lov!=lL2s2ZDC%Z}`t)#(TkiCN`(o>DT_I`W@E@70FSF#U zkVqzwGPmf*apz8#7INf2jl^0Rp1!xTS*my|>=s;!j)@w}kYig@ZOx@gc+8Bj(VX-C zT7SvS-97d6(Rl;@EY$2FUr)@gRfmcH7s?GfsYUPhp5zi%s$ut!c^M{-)3ie%N+9C_ zujTskLvLLHHko3kHCfO=OIzC7ikLVnDZRbZ2;9k>M5`fgt>AW)M*@ncs3lA?$_=$>(4{ON+gT3u&DOz`sVy9W;;FNF2xCfnsvIzij#;-uQ zk&j@p4^wfTL{4nQhNoU%=^JdnjmzF}v%dIG05RhC+ZVMP3~7A)`1z`=-1zK6ulB~L z=54b7Q+;3&a{w04OnvJ>7J+7kui%cp}64 zfcY}B0|5&wIz_nS%Ys9F%Az8LstSmM^fF2*)lUZQARx#Q-em?8zW&Tg z^+ZvMqyHiGlu~42h?Lu|0As@mT%{q?(!v(f3=x5@(Z6DiD<5EW8NcMmZ}dc-WQG}s@?PdjF`%H> zfEw=ddwZ~$jzS=ld+@*>RDUUCJ)89mG&DOOyybX86xi z6Ph0MU}e=pSxoizF9WexnCE7p#Fj=Y8DR>AG|0 zj%wfWUVTfglh%;p6saCX9NSg(36f+tBR+qX{i5aQELzY<4*!fSK8hd-?}ef_PxPJ@pmZKyu8v+)z0=Zd|8ySA80eV>Ko^Y zf)X-FR6-$}{+32fMwnYKj(lexyY+!3)1b!rEAgBiKxj^u!5lXflgEV7V%o`_?`G{g zcLto?uFV~f%Lpw($0Hn{VEfeyyUDs%cHt(k{%TWm|`xlWJrU2 z&&)B+aIWb>C9{{)xnH?Bf-x@G)TrQ5MUp>dyYP?5PbPAnKqJ4bsc&nsc3kN1Z-Nx& zx7AQVEmZfrN^IEzau_mqn1HaxOby+C=YM!E0T_|0_Tod-@=HB`6Kvnbg& z8%TaS4hAZ{&3Il6<&K_z``}=UmMv`jH0KuAii)edFH4w>ahb`N z9+&L4hEBnsubG(gZBdxa zb@fQ0XGUDytm$2o$ākxV7m@b)-A>H&y-aV@vlzY3YZdSY`C$N#2?aQC-$a{jJ zvRlB~#;9T7TUox1Np31Lfu484=BgNp)9U4dLWadq5aFUPqM5Qqe*`QZ9YAh_?gt}t z`Uy0F+Q31{E*Ni-kwjCUl1o)&n889@o@o*};#^JaKlv&c*;cf?N65bO(TeUz^)Aj; zS3vgK?59%)lDp!GWIL@WGnfg?P#Pn##LX0wjixN+J*d+Yw!}L4A2X;I>)TzdO__Qo zK4}{0bt0=qxh!OoW+KJcesRvT7t!uhYCkgdFwj4%po|<;fp!ydoPGk6iBb2MODg^_J3Gw%{MC3c zt32*1nn?xDjU>V6A2NHw@DKG*U_TSCd*a3*1&w zZ~VK4091&c<=OpKva%!cuGblUX>Ci+$r;T4NDv^Bs6;Bth;e?EHf27Q<}XU{!iAFn zqN-kBI}hH|rIh=Sqj$Gxa+6P+gUy0sL$xU=K&~~R^%{$u?KL>xp6V>^?$GQ*+#i+) zp3Wv5+zisQhw6rIqC*k zdHwo#TTsPR*(J4h_nt?EMfpE|{20;`L*=^q{%3$6K`qWVI9zPpjgTJy52W0Y_np0s zxFME3zJ$;8A&ov9^wj~ey6GVk9~=pO-+uv`uld5SK%xX*af009yv9v8YKVGtUJQJr z<^+FvFQ!1=?@Um7`2)OS8ssxkRCW1ssgIApoCwT1&8GGDM3T0NGG*GdVzOVn(i8y0 zy598bB?U3`Jy!U3ID#o?L~@CGoo|j3pPR4M9|m$?(ZkBHe&t zO%2Fl;zvOL4Ff_qiEifw;DffCygf#-_fE7%(58ZrA#Fghav(wYC`Dh3bhulonN14*rqXC#zvBr~UpyT|Fd4 z*dlc>RTpSecy%_xUR`u0-oBi9vk+laskMgYBIlbGbKfw*#T(-^`yP0I4d_nUsAm`}6({-E>T?eQ&q|;qP zhzlu0P68t{q=DZ+?(6Hi^opL?^-W7~maL6jJKx-gC{{y$SJSE;p4z(D+Q7Rbp$OKL zp>Q(<&^$v)OJLBW$VpV6?7nXOsvcIz*ZbRg{IEqmzr`fbM6q*oTR+-;IX)3B3R~Tr zKv+|~u1Z^X@_nWn-30V$b8}k6k0P$^>e}q3;!1pl<@v@%S3{Lq#~2{~uEQ2M7!#RF zq5Kjr-%}7qXat7N=Ew>d0F|cjM$Hm46xe03zyj0_2)rrGIf0krn*eNVUT^?j(((U0 z&Ph6iGO0dqXQ??&aq8VR=LhjGLC8gwYYpN9Grb~YG*%X~TQZI6 z^^x#^a|%zDyc)9N{&p1VGs{TVH0S%756og%P<&Zz3q!F*2Z?l7pi zDA(86y%OJG-ND8pk8u_?TutLOoiq4PBc!;PSnB>_5Z=(4Vew7}#j=o#Y(t4&4YNTq zS(0yvjsy}Uur4ZWLB2QC8z?v_bUhw$eWgEhnx$p|`-gKHan&7aWa0shAz|+3Owd(^ z66ulEzIj@HP-(AvS9LgcuRXGp7Gt*F7-z0ZQeaoml#;yu)FqpI?oLFrU+Dfl+~#!_ zbEgS;J$ei05;XXDDM-qbOgr0>;Z4WGd)gOKnbV{4Yo2rWfnF>%EiLZ-d*gNkjrEZA z_jXCc9x}RLQ9|Xuad@nJ#{uh+pk8Duo!&8&x-0!8mJIc|UbFw?IXU-=^p6QA8OP#+ zCE9BrDgj(h{bRQIQ8Hw#udy~mp}XqW&3pYUbf<&Rsu!f7-#5b+5p=n;6zwN-iY zzkRg``$;LvddPACX}Yy!N6RqBb$6xHu1!zB9v$6VtkpXPiZnOllu|5^AASa9P`YB+ zIwvo$ohD0+p+Is*?5xb)e#P7ZmJRRC6zGl-`?{tRWA0+~br8zA}Q ze~5qR`W6SS{=Cz|pwxz>@iTN)NlVZYPA2lA%m0e1W-Pbp-|&C8dT}-L5bX2MxBips zJI|}GWFtE7w5AqNhKm>gXym9lN767f2_`o>z*{h@JkO^_s>U=`pAg8w6tCS-k=o7m zw?pnAM?>^LpH~dYH`|?peS<-U)c?-WYxEBsPtsdp2QoqT_697r%g*>eYvdIB|BHaK zJU@u!|EHeh^}82D78V~L9~U2w**^~-J4i4SO#~uHz9Euh+10i|w>HO~wdj+p05kfF zv1l)<7@4`_^w+H^e+6!Ma@O0Dc-vSV4UN#iz>6-8Ew9D&{)dvXBMKL&I@jF!qO^6bZs=C+uM)pY*$piJjBmzZuIoalZwR8y{;I2wS zwq45PB?j#G?_<%qV(N3s{Y=d{in|UZE0l3t!7SdU*wwsh1PccS82e_{#WmjYC z)gwX;c-sTEhX5B&@kycD(OgCjrgsex2@xMg0`UG;c_o@(`y0S6sjql+3wVgq4aNe; z5*yYHLG9F9l;5sO^|~@UHy3NftKr-oM$)bXUzxWL0QKqClL+EAqQqQ`%kYvRP?0IU zz3Q`8ig_gL_h;<|sEx0D7iO|y${1~pFZYamF+l69DN!?qG)gZVTqB6R5pj2f;ip9*`zlg z#-g7YfPNcLurVm&G26e|y@gqdG3=RrSm9x1<{Y;bh6i(5>U*H8t9u3%{8uJf0MGNw z9WrmvHq%6w9$O06`l=6;kP)|B5y zZC6uHQr)fmhDs8i>HHS)EQz=Bg}jPdzC=`YTta>zSNCvdiT%!2$#|VJ=uT3SKTw?_5=!=xD(5t8thdIWt&iwU1tC-~VZ)=` z{>za0jGP5z0)XiJ&!D^==pe$*f8Cw*1aldgy|Sro_QbOrDlM8k$tfwKo?39t?TD+i zANM^~)~;6{j-UMvB-f806Yp(I+92$&5fi_d0gqFsmWpr~xa}Z=t?AdF+mzKE#HLW{ zJFsFP&v}s3S1-l`PzmeH3dM(K2g~H>zKHwof4xPtQ&Z5HRj*7H(R{%aU{eCq62Gu< zB;sA4V)17Bc9Geq=tiSwCF3DANGjJgjlzi40AsG8rURI24G8kharN;6>$Mgr%0rp| z114Cu=$pMH;q*;b3CoL%X3CiI;f0xUu;ut6per|-Sq8%tUPB35z{ltp0QMKkd-)I} z99N$754Rbv6>t1*1@IA5?{BzNxTpKAg7%w&t~O-Ie(jDOYBnFEgE4PYHoT%S`Vv|z z-$X@auV*!IG8oj}p`k&CDZ45O_$YE{OT)Id`?P&_!Y|^?U*CzaktQVA2E4q@g?A4F5h_lU2N2P}=`e5HPtvKJ@!1o~`2s5U7Z=y)3 z!t7FsT)ANv2L=kvsZmEW-7d6NEZ)!K>qn+MzUixjS&>WzpTYwWz70Mme5Z%0w&>0X zAs+L?DdpEr8Uxn#uUAx6Gz)+>%5@ z#)IBvxtsTsbfz2jaU!^mUax91EqbBrQw>N&r)JZ~dxRTS59A@fU-@510Y>SGEp1;{ zw4!rGzcs9__nXzv8^H3;cKS+xJQ|f?ccR0U(-Caa*GhY<@cGbPigFc6X*;q~}n z47R;FyKtv7jEt#dg_&tPYL~3Rlj`hbALZ$5z?3>x`)Ncrt~97%4XpHVO0K zwIld;*!lU%SdPAjmN;P^)`RrP>f?>NQrl4>UEn%iL?-g-MWi`2(D7)%l>i>GUj-KR zt?#ZiAO;Oo-ZAJ*s^~nrxUkEzetC_>)t3f)|Grr)PgbP?^&Z2FRh(MhG(@Y!-qX)N z-&=ZwOaR@T9L7H(0AdbW*`?S#o4R2@MWTtU0_kuzHvtJv5X!Cn!?z{>5u4BvBT2NP zXSaybEmPx`w+%J#zxQz~A*k7^>%xog*=rNX`L!weoQ~bS+Y^1y^zsy9JLl0yDr)Lk zu&+=<3Dd7MG|~pyfK^(3!tZ#U(=b-SJy!1M8}XlUB+TQ?+M8=`RUeEc_rWksH-RZB z=L)|!$ln9GY1D@YNGP5Y*bT&0Yn`*e5mo)~1L4*!%ZujE=JtF#Gyt&lGw^f1SP|h( zAT6hTBv zx~02I1f)Sk=@3Lv>FzFRk!I*2qec1X;5qXyUA?r2&ep*;DOT_L5KV^=(ABjd+eR^SV$K4 zmAFEn)G~yg52p@nE||Jrj);iRy;qJ*CDTlCYhITlj%LK>h%}1dtg8YKrW6<)^zT?1 z8JqVA2Q9*sHVsmc`E{ktAIjwqZVo-oyYD{>l^){e+F~_(J9J+ZygHH=aYzsUblc08 z%eA2*ZhIs}Q1_wh%*nXIuml*GDJqLt1AN?RA7x*-mMtOi_^hka6)BY`6sm*Lei?$& zua^W=yn8phND|pW7oucFNR2rLoDJhD3dT9tkfazbEg8cIgA?lz?*(ABy*rKT0SVo2vVd)na z^R5$RuQJMaVs1M_2C3K~c?ZGS=)3yok&wxp*}t%VPhc;tIly9s$MjEa!@+ZlMByE& zJNM%BcwT{r(u9ruAAL|lLOQ8eQ4`G$jqi;*&q(#{7GZ(k_ePLFh3m`$R0XQ<+%n2- z&jQ!j_dvGaUsXCwQP&s5-mDbN@BUP8x%B0fpYU<7l&hx9M%Bb|D9tw; zH0Wn;;{!zNJ65&n%P*`%wQ)!T+dm%3h|bEr@3_v(dkGq~XYldYT=cFS_@_*m>p-E> z+g)ebhL+-mNkT158cfSipE?y$DNr8h=14%$g4Cxo8QIwuKPzE%ATfW^>4RMF*Dya@ z#MvHg^j|B0F=|N==jU%Kq)3mHuH)yRC+bGp)UizGbUrqg<4|ytP$j0Bi%5DAdwN;k zd99hbw7Zr`TzDc_?#iz->s9;#VcA-jYF~R+xd`ywx)4`-ja04pDlX#`{gtb}m;<)X zxAPsHjs)nSyJNVF_$wa;X=_2z6Q3Aab)lgX^ya5-$G{9>iSF4<-|LSnayIFm4h(D0 z(OrSPHnNy<2I4U#DXMD0d|7aJcFKgE*kz#Th~j0#qhMC@o^K3k_0@Wzsv2mF&X4%? z1>pK?2m8*vIFnPngpMa~r>(pXBs9T1VBq5-m>eC^ADPzPI&g}4x+%P;Dkg^e`0?Ww zxgyrG_47a=*OKdF1Y*3U<=Ur;uy^m&^E)OVJ3G0a-t0GL0RSn2x%?EgU*!_FWSOMn zm{j3fyb7{SN-26fNhjVl2;wT#7StiXeA!Sye9E+R8$6(FadzO&;EH=@sRJ72sj0~3 zF%D)|OyUbiM`Q=`zwDneagTCI%~+s+p;+xycsnOesUQ+B1cb`aIc(ZhIn)~B5R{<1 zKCzV?un)}qKluN3F+b<`K$NtzkUso3&9XU|L^{F3e`<|G`6(z4JDTY1=qft+`4bTH za^RDkcVXu{)c)(p_*D)0S{0zO*=P|I*n(s%KPBXy0t20P_xi5xl_viMf9FH(xO0M} zskT#|3%>e=hz*1xXrbuWNKd+oAA;NA&~2#%>UF^UywM*Y$U%G7dwU=%W2y8rf{)VM z{(T^b1OmuyJ(85J_qmNY7;`w&5)oOcC}wuqawF)P+G zdehd+m$)B^sM&7<&0@^|-OhNF9yAeCx6u2Rm&~|bHoe}~kGR;-z@WvR3*`L$8z?kO zJA+XP^yjo1Sb!*KXv+A^y4C_ywO7dRdhhPt@U&w*^vQ{d(b&?8id5sR2F_@l-C?8w$|NM#D0eN)n>%j zygfBGKJsHFT*u<~&#Ol`7>;&+ccg-d+n?8KEu~$nwK8&1urZ2*d1ifxlz{%5b#ArV zRTRl#K8zyKx|fv?1ms&VgVjMU>vTvc>y+Mfw58;sg25rp=^fO;7G|r8*hO7#=!hei z->kF0Vx8~r<-XsTe_|?3Kfohpng_0v&(h0WC?x8Lgi_v4t1(JiK7_FpPv=r;@DxBJ zea?()AL|r<`jmR5b@7|o^VeLRPNsZpqYvRk-3F=7YSm;bs(HS)@q#NR*;!E+ydWV4 z{~1JpcLM|)XiZgxX_j43`+IpYvAW#0xxPV5bIGGPl;wh4Ui_EOOP$$ZyH^Om?3e0c zCKW@Q0iZfEzLnqEEy(bjDdYaSBa)xd)zcHnpE=9}$pSW1|3x7L1&s!%Pv~D6u8h}t z2L){&)K(Zp1S4?(Z5EoB()(8GdMf-@>a5F@2nKXAaZdbJ+&oC9fZz@Teyk(Kh9pBM zC8W;d!~c^6<#Kf;YB*zABP+!r3kjvuokN`i zGj)6RrN)im(zQN;w-%Y{{jnEc8Jq}GrgFN{=KkR2Ugb%2H)H~I)?iJ`1$Xxpq`Yw1 zP`%c|R0ZL*G>BRV_r!&Z(N&ggC%7Xrs#NuY{AGkX#?)uI)a{<1Ue1i` z9HiS`)>ocQWW-`5Vy{Ip{<-?y`*S`&&PeSOtd<{ehqGjMu&CQ?l9P>a>uyaXP#|;i>=3UWQe*AN@wKOwql2 zH&S}2WiH!oKTu4`s ziAgCx_3%V{4Qi`k)pRQFaA#w#71w$@cCa{f!Cw$FXGFQ`jsim0=1O;l3mM|9nr3jR z93A&#t%ooWZwRogQ!ZJyCfLz>XD%xGcH22$t&Q1CM8M^WRh=){l%DpI@z&-YQ{}WE zSK+*|6X=X$6d0uOeBvBSQ@h|?v7eH{jQeKzF{uXS%7=4 z+pdk4b-|$8RZuA~u1wiyK@8nt&2&=3y);=c@P7BxPw3ZkxkjHJT^WdO4QjRmN8*}h zCyd(@geFkWnt z5_J7kXyv)$xJ+XeTm3482zn;GlI&G8y_zjBB;MJWDyw<6zV?0lJA!UMLgs8* zEsvpJ8`Dx<7LBAilyfXIXU}hCL#2N}(i+0uX@Boz9PY3}95Kc2=2Anal%VmO?ZR1F z0BEMik2|hyaAq!QZ`nrcQ^(FM#mz1uL$iM=JSAHpg@~!0gv^CMTwPw8^m`=lpWcg* z^vjVz_sO*1D|=!q(pSS{$b1H0r1xl+1GP~v>z00S;aoP8({9hVLd-Z)1dIK=!iKAC zZ@Mw;u-6-Ms&Fael%0-Vn&Q>{zMnRM61+NLW2@4M+=(c)7yjC{T@<6f4S>?ch zw0ZC0zh4R1oEUq;C0Sq8Iew0e#-r+?>&0iauNg|dUo=0J3qAGEnVFfco|?h;F^}z( z$AZw~>~@QgYgZRzJFG9)vPSq5<2$4*9mFVtIAr^h{&pbEjizc}B?{B38Jn7lGjdYg zO^DAkb(DaLkteU|tt4E`Rq;(WeR_p6pi+JsAp9&dsRvrYg^jmJ3irn)oTlA7&3eg5 zgF~p;UM;KYZL&f5ZT04Xs<-QI%`yJHmw4EZ`JX;39lLl<%y3|3D~fEZ>GL*y*a>xhE1m==!F` zI|8e9KXB$D%Ia6UM&&7BQxKPYKbbP6#XdjBQnJ&ulGvC5^|W zx7FvaKk^_TFPnzYwG%;U8I=|LD_6=7`mXZld}%uAZ@7Wti2|aY#zHyo-e#v~66@Y< z_xX8deYRui?v0NLYH(Q|H58aE%xMkkSK1C^tRNjzRW+7p-oO!2Mi-dU`uh2i5!?W1 zifE*9L{T;-UdZd2nwqIx?`0#tJ|rZZkfYmJUw1#~oM&ldo0#;7Fb`OHj}3-NIzf zfc|iMbgX!IK?8Aqr6wd)m%2i>+qWoWwBQQf zYxco_SfAr|!Ou@xuOO8!_&ev_yv?V)Fy*{*&*pgc_?vSym-tO~%2FH(U}EnAnYn;V zw;T^$YL|MRBSnPeb*0L0`JuC)vuKY<6y28EU2zi*jQK2sDbi;%A*K;r>XBr$eVe$B zLlHDURh64?NKHI?SLf`5e?GtEp z4e_%&4tQiJxaq&HCe^G%eZ{-F(94-we~OPD{raqH09^;kRr()};4#y##r+)rrP)%g zhwnEw7P{rn^V_i#?@_)v< zQ91wV*fhTGoZHYza`yH>7R+n;S6|+WU2#Ia=y;poRwW;;trQ-8$w#T}X-!O+?%1z> zpGSd&LO;(m2d$;@k9_#>A)F1ww%g&*_ROhPw6MtLAujq#n^b3kKf!&;8_6s#y(7ia zaB|8^`2+P*Gt#J*Q<>n$S%V}KCMMO=KIMWqJkTh zKr=arLkyv#z1kpp$%WE;8Tf*P2x2mVYs$I>YIdOB$zK8fj`M% z=D`$_@glYbV2-@G(^MD`U>YZPuOHQsAJcPF-rviZ@@<^Rbvgf zLf5Ky0R8RHnm-&tOkv!o`N>9B_9I@G)YGRMj+eEZIav3aO23Z8#WLrp+(_Hn?Gc@4 z!Fc)axY!)5D-7DWoM$IR^-AjfoVO#c^)e>t!~BQ8p1XU4|YR_G)fD zR$1~5zSq-c?`jbaQnQZKlR0ljX5>gQ+>j+^U-ZMPE-P*(GpLxi;@m%3^yvTYv|ovC zysI35mmjFWCDBl4*R-h@rKNP)z+RTiMgtuznmRP{T170XqmOf|r=Z+IrrNBrMM0UL z50B^D-n%H*CjZURc7fegymy*q&m0_hk#Lr^Ha^pzY2y2CkP_68!NeD~5V@h1(WzX( zg_X_c2<(Tf`oHw?oTqngnt(`W$|2@oF8gq-8U2>3lNw)7roSESyO@{&B+uD)$U5vB zUD6?h$A#-1Z=rLavCH_uY`)FMHE8C3Yfg;Tx$7j_c^5rWU+szil<#|LYOOo5fHxxP zLei^uT}6#dod_FFp2ijUXHzw>CttowrVJfpp~VLGv0e1;gM%TKC49I}{^o{%t-LJf zn$z5X?)KdaAU)~yt};q$*rPbo`wEMF`(*=xM?f3bWw2Uk&21JZ>%m_e2Lypem4jYp zQnMGI+sz!HCxzqI@73N|!}!i2+m}sU`ywYZZ9&S`#s?Jk8a!FUDpFRfGFgN4?%Sia zF@kRj4)U|kN*RBD_{COf5RdyUAB$u?;dCM$OVdzI1_GF(U^uPPT~g@D#ebH?-eC)U`3L)x6Xh4gbJk`DVb9^hYics z+^;&_E*<21)yOOA9Q7N(0n)!Vl{R5IpTJEqwjWO%*ucaQ8s_JufPLxj{6W8np8-85 zkLc8H0hfI102{mXVzRrV+i!1GE|u?R@6?mILQU+q%gzSMH_0Uf>rQoI*f{8@g0G^^ ztbL&DT-A#(?#rw?xyW|KcOhV-T0Pk?qpZj2Q@zOk9qLf(3U*MO<&{a|3p?iY>Qm*Y z#Lg+$)Ml^Qme^22GD4`9<8Gsr%P(4{CY~#Sd=l=)fwZ$PL2@2Jmzkll&-^m?N9iJr zHyYFqRw?!%)`R9;c!NzMQeFmUi6A2>@bABmI>&>OXeWUG@V0$F#4-zNLM9``t$j{_a79#9l1He|YvC{(AN! zeKsgLbdQ2OW2f)C;Da4C2&ZjQa~`8 z+x#X~Q2*O~b8rE{$W^pHFqox1K<-Kg0~q5erpXw8K5#7WCCh77>2pc!Kgn*)Xe8>) zC@+FNSiVl5>=9*o{=`;NqR2J=bvqT@oqx`_92HWeX>}o&%gO0bMrHS7udQZh{OO$U z!!R(-au*v#(piU{c%zOB+7j=JL0_xA?`(zo628wDT;D zg))!$ZL9aQ5z6<<8MV&~@hfnZZzGj{RZ)o{GEau7y_SK)1tf0q`T7c84z)`@?Z{BfxpU)g( z8%}H?a4qKc!-ClB>a2I|j_Ya*18aeOMX=y$gKL@VZ4mz$y7`oUY>&qt+oq%D~A>8z9xnK4MmenCnF02bKNEzHB6s6A) zJ%=&7cOjxqf#Fk)tspny;r`eRLXVmFB64m0x>9z5Ep|MuntpG>^Yd0UEzzi>tDygM zL2r1Pn4<&b*D>dKZ>@kdRG-yXk_uJXH>}9UXhq>zZ2xm(xdFa@mO`*47wYTZE_a@L zvA1d5X}$}*(?}A}cj}vNFtIb(R90zEzh5ugSa^+HURx(KhCsSx+EHLO}`Mgz3^afT5WY@+L~|Xo9WJp%|ab)AT{4J8JW+o z8O+~Q#ShYip_5Yrz^fS@^VdphL9VDShsIw!plzv%db&;c^``;cIj_}sMB2=A|MGYn zx_H1mXwh=pvEz(1^3|PGkg&Vc7DXP^uEIqrSgdurd@H@N&`j?5`Gkj(mnOP~yAc#9 z0IbhCZLoSRH+pTtG=+RLBkH#Fi=nqB#=$q~p7joTauIi7!ZI#k;#_lx<90R#_LltW zU@wB#{Zxg4kRaeJem(Ff3OAd?x2nW+M;QwyH0w&QC)Rpi`%O*I#YZBK2DuydqHtX$ zlATPd480HdhaZcN&&Zcqk$Va? z{Q50W{ae}t*%@hWfsa>sSX|#+qtM|2d-?Y8t*yAAmP(YoMD5^w`EH3!oj~_pYt5kp z2mUQhHi4BC=dENov}BMl?YlXoRWmRk%ObR8>@%G1d21 zLcQX0oph%$hzP{JnPa((SgOWW;0_s(C|Zqx&mJ)-RFY{WLNX92KW zqmgoIFr59C%}jwAviDZRUu8?%wW|+EGw-kxQD(su8N)C>!mSYGd-{lsrdN;<$!WxF zB>Yr{YrbtIq%>vT)AQ}Rvk*v1E+CFmrFN-?ecD*JC1*Qc0SA3@@~45Q16l!=0 zIUesVuYV4ReR`t)3Kug~d{sl-gc0AMhpz)N82!<|@JbdJdO6sPYzi9oW1XEfY#fYD zmcw^p{z*b9Tg^ZH9r)hnXc5Y-gN4qO&wNQ^aT!gula}K^EpTYU5ioc)S3mVelz;s( z-r~WeD(Tma$~6&yIn!7(GmNahsP__;+D9g$rgCAC%%)3wbtX>J8D1+v3-@kjEb%Y+ z?lpoZ&Pf5es@{{c@J14#-52p;jKTX8u?vaobqbEy4XFyPFt3z ze9Oye5L;2QA{8{xVZAw+f9b-Dyw7EG>(*fxso(hN(T}R7H&+S8a;}p~DHTtzGBL%R z_wu+Y#kX2+QVPRwA?TecnzM2jntq!E!!UyEg{AXItRgJDC(03s+Fx5a57bfR_g**<$lm6kCB`vRLp0^ER4=L*?fRHfieg1 zGiE~x+I!Q?_FJujtyPDE0w-vT?@)Jg(2>xv=QfDMsFdCO`l`W?Z+3Z2zG;QEf=~NR zmB6O!?#ig2*h*9S%MV>PpPE^e7>`Mh40tkoMYZ_atGUjf6W9w;DO{U&TrSglyxiM* zuTOSRGryX;>9)__X!XR0Ge~r6PULWg02{8FC&F>;SGtWEs>uXA!^Yu$q#?x5@4noGKk zbT+s8;7rEGEmphk@z5gZ`VHJ!Y4qS1W9$9IJn&HS_cBX?WPab3wN@o|RrlR+#o^2q zmz)8aVcg5lFt?V5H9puXYo7^y8c>s*(N<3vo4@>%K^GGuFUg)VQzzz0kb?5Z1$z{b zgx@Nfx2NaJ%gDGxPdjQ9WgG$`I}opZ`rEM1=}Jtz!xTmC^&uSN<~T@h)*8$Ef>R&S zrSR~5=*q(cxIfkHzOuV_kM1ggAA=Yj<1MP;>0IQfFSR@OGD+0Sn?}4Dadlv!Db^!8 zSg2Pnb=1GDt0Mvtly(Z}Pd)io8o<#w$W5nGb1lW8wNqy>*{-q~T>GiIw;Q*%;;!en zTyjsx&P3@Rr@d;!$B`&L2lISW{-%!vjG!({E~HFBZB9vj3F>4aL#|VrNM4yD$FKYZIyc z>I>ei+RWcH5S7YkzwIba5*|w8Hs;9yr;R_c#?=Qup88dGPX$DsX(Pqt? z1(-Iq`Kqvk4?#tzA_r`q! zWVibL>b9mxPi?hiY>v4T&sUbXW>Oa%E}1xC3vkUw)QB+@tP~iClT*kkXiL>q=R&enVV?%g@? zzz`M{6#>Bo8Ri3F=Iq%Eg-0@MJ*I!)hW?BY5Al0pLB!6^?lAf4{tRS9&=X1yn4NDB zxg;kp?jz0sxp`pqkJg@DT;yD8wNjo$0MJgE!!^~_=PpbvuHi9p(6BV8LbLq?v` z)F=-gy(?iiG&L1dQHd#169>4a9BckTBdreSMWrR+Wu&@>er%r8vY+msJ5S_-*-1c>p;f%ZEDw`;N)tn`WpMX>}kz>cd!dGXhoPt0Ie{Ejpr`+nOj-$;SrPp zlN{$E=1*Ap9vAuaQ@^@g|5vqQo(_x5j!)GG%<^?mB=Y`-MsuR}&bUOfxe+)8PfxWf zeVS!>}M&}yW>JsL$Mb(27yFU<->0^T@VJ!EmUgpOZqbhzb7O9ySEU}^Y+y^R|OF_~FNOGut z!Z){E?D`EK*s0CxNlOlJ^QrtwG2CLSCgw8U`kC*t;?jY3c!rD6Yb)#BVVSBXg|&q$S%dN95<)j3;abGt3zHE$O|(RrGo(l8hOt!v`A`mlfU(UxwFDYdE8>h zm|w$6^SjpPg5-Cz?C!dNo2FJu5OdaAoKkt;5Wz5>M=*@^%&v3u^LL2}VWItZjZ?i3 zM~|bGRc@!xu~13|lW<~roqPnm*@(mqt(_YoJA&JD$B&z)+Vx?o4^-d0qaZMm(iB`b~H!I^v-lec9&kG#)TC8xL6 zdv;=4Z{yQJmt0Ll&|FrRO1=-SG?szPI;Umz2sXikdZ&r$>8N}@`&DhkJLx*^Iv+A0 z_5Z?Vto5hlFoQ%8IzB!$5OKkRc4&z-;y*;7#0Ctn%m1tC__yT)@}>yfT7rRz8o{GL zTAjKKrj)F~B_5kB)xIS~R=wv-1h?(X9ht#rO(h!;Gez|yr|X90d9z(l%0~ekdvP`F zS`ag)KlVSurXKtl{fHQeKg@eCzd1Te)E`Xa-11n>O-9BVV3IstPEDEHy+0(@$M$Qo zsN?L!#&tkyj+bi6f|Ayf4gEk)E;J;o1^SWbNo$c$8FhVP5uwJWgXCeyEO(zMwU~cO z?LJu?aQ9+BZyJ^@v;uv%z=x0+{~;6&3H)lri)hd9O}8Z?IH|=OBYywpc?&2#D;ruq zj5@Dc3vmPY)U-ssJ1B-H5{1=uWz7jZ%B&6RbqS488a+CL zKf}lY_j{k1y;OY>`{{WI9JaKZODkv@c|b5;Joff-%eK~aE%hrI?TUi@;S4>&DcM?% z7yv^0YvunB403OIPeuymDVrh}fvt2Ja$0LGge{^#c`!ESDO!<0P5~Lkl zBnf-4QZw7$BN`$QwdFLq)5D|uePT1n<*zE_Boozb#2jsn{8>+ZOw*N(EesS{fCU2qbkLq%y;h^bqp8kf|I_|vB;T=2Ev1(6U z27=4nO|pFuFK_y$#rPSF#NpC4)Bge$17!iXezlaf{+F^&48y|KHvyM~pqWB&RQ|!G zx>&?)q<_S|4FodHD|n0+TGJlLM0-{ipX3L$E>DFP3cAJv^^Pl?Ilx=#)KHG*wRDwm z|8PilW%zggDdV{mr#|*It|=kL1w!I~@0m(fp)J2u!0V5#sqobP55^P$>U00SBm{?28lIg)d2Lfwj(w2%jG)fH}7+dQcg)UA)DTe$b05uTP8)MCDBigH>-BbM`;Wtk&6s-iEK&}T0%dqHr3 z?BIlbd-+mp)CE6cC`@kHubhb-El1vx6Z|dOW^qt|r|Vhf(0O!9ilK?7qvq~p*}G=* z*lCri7<=;$T;?dEB9@Z-fNrXB2i}U+yfc0SMW7bTuS=#n%uh8zi=E}%dw>*kcl zT=vzFPq&=YmP#lrS%J@Sr`%$a|Mam{!=qo(+P@9+_<;vs_QU5d&YhBLsI_(C3aj|%*i#0^s7y)Rdhbr66*9? zbynr(&irVVyKZ3Uf`|Q-9h>PeKa*m1ZHo{Q!=W2h#tB&)w@akTVJadbrx3||4mEoQ z=}|;r$;iG*g_>(%82ehCRrqj3Voi}5#pZjssy`ng8MOzW{~Z3ga`hCg%K+{#B(DYX zUwO=CJah*y1uQrdfB0P!rae9cR@e*o_OKeXF3_gdIYQvXX^#*H zM`XohEtQ0u>HM1o7@p_uA62Y0Jag9n%0OX%?=VenCuQ`#x~brMMkq0dQ|@q&w-5db@vRPXfZ$6%RdHQ=2JthElv(M37 zSHa}S-UB>QO+9H+2ZtcsuTtUx)qBwwJ-8iSBfU*Gvh#P3NrNHZn+P#%0DAilGu>HB z`nu8RL2eL5(f~iRRu;5c>2=@imWuSlFU$CR=!xNGO{rNc(^f9ILmAdCUTe|ry!z{w zxx#3X92B^ogI#B|9TuZPv>uXR#NAV7itzG+J3P>1EXsvHPpjtn2p^sU{l2|b&eUNUztwulC0k_om-IQ$7@D~xVz*)B5zycK z=uE>ZWmb4_9T^049&LaiQQEilerWp)=={wd;zCZQxU4uW0x=jz$+l(IuG zIM}|_;aKifx&I($^D<4NbY;mjP0jiQ-kD$Lk6&{s00;*ES_?-wm@CqYrYqzqUL&pk1R>DF9`gfO3+|)I7LI&6|CL9cl`i_Ia8q41K4b+sz zL3~a&bFu*ExHka*_t{;l7-^9nc3di(iX4=U%26rJz7tF!>gk+Gz_k0_AxtHi> z5EU8OA}@KaI8x$juMWAlL&3cEtxn2jdkulDPw%a(#rY`oW73Cv$*sofoK?Q+XI&+% zv@eP;w6VGQOY`l)=E;N>Kml48v-8P7NbST*nc@=5uJfm6|Cz$CuITcc=j=5c(tnM) z$2HJ6wxkYJ;vWC@?HdU3<*zigfI!&oh$L8tdy_NVeSgFg-jnryocLvy^rbp{N4~7G zR5S+>)|r*#>Y3gaf*KxDp>r11nRCT0TX+000<^kpcN#x(+{%f!P+1CX#a}b~ZUwD{ zx%IJvLZE*IkKLo`)Hociu?X9je&ASh^rJtq2LB#`t^ASVp9`7u!zWbv6bz_1j6Llc z0xu&ME?CZZ6AwUqew5>qt+Hl1LE?=i|B7?>FUo`rumUi|OF=jgmN3rwVHb}yHK0Uk zY`;*}^O8bq$OA$iN!r=D`@lnv*{@G+;p7JrA;pVBdQbt1B5!xQ+I`>@6vA}ft zE8aTwc-Q!jjs0anPy+*kGsGi3b1~xoe`ws`b^=!-uBElrdiBak58sGmrg-ka6wBT` ztyq>o#W59>a{&Q>JPS9!8!2mR4!DgOhtSGRdJF=Y)>12EyBr-RT8iBI=Ipw(~D{NI@G z&Clk_@;>7t{THpvx1XWAHqAaxXERPSj0-h$yt}ldFEmx+d|X-=tfso2;NM{M?qP27%zqmayCNk$Ge?hLC(NXU z@CNA8KftR0n2O)-=eps`e4_|OW7F|kpX3E%x5A!W$i_O}G2AEL-^Q(50!7@sx6bsE zO&XklT8_GElT{$1m_u%2__nqSaOZ^!R`*7o$M~-zpYRWMdsn3_9f^AuQiRN%M<%|) z>7xJ@6qzX*C#Y9h)q|1}MaKret;AXmSH3=Kl?BU;;Ti*?S@(Dd)9GEnmtt{Oj!>!5 zfm7EJwt=wrvu3^P>gK9Un$7B@|kDZe$-JmWVET)Sn8nf6aa?evR_=FcAi#U1#wGaj= zPIStyNjw0sG5N_yA4>9HkN^qKHyD#5go*c`gK+Ob&#!)NclO!P;N*TFvUPubbnPL#e{vw%4Sp3Q3F4p%0xH_+KnIxyCU^e3K$1d%c(i*`5Ac5Q?z=ENg8+{!x@#<4N5jT0; zUM)urnZx`-K<_B1>c`%{e}6hPU;f#%*Xb;+N2kD# zM*X+Xj}AnV@#^i9^2`zsOe{P$`J8*^)9b+aZlxau_DaedyfC0&FvEvz+=P7H-O0<&`AIe=fDIXmmP{_@2Oj}y2=pVHC@8v!_DtPEC!2yHyP#vU{z{}uZ zT#`04WCZOf1S}tY;fZ%;j!ekcgvbGlz(@gP&Pfkri_I=g)2#ePBuOc-pS<7`nG#Wj zv(n&XC+Rs_Yo{*?$di(|!hDZCWkE+V< zkry%T|9-GK=K~FjYvDkGHqNKOYcDL=2fueq*a7fB93BrAr&+HE@&R4maJ z@6mh`%G94dL1xP2=5d4RSWDzPU_sx#dNL%m&6T(F`hr9GkzV zvq{c8@g~f_N)pEa23UP37ykmf}r&MBN{H~Nj zfL^|2VPUYS6JT4$ue@1#j^p5r61>O4!*C=9tQm6_d{>#8CG45$#wVL>93A9yx(n9A zm2qBY%!bnJ)(wZ`+jha2Gm&B7UNifGZyjam1zOuF5%}vXqU0>fuiz`96L)lATFlaF zmb(jpB(&JdHK=63HbMpexpy${7yHI96Q&I)h5dJ1;eZ%SqBM|!f6s5oR02p zKJ5x#rzRKKeu1g1!YBBh3)GW}q3>(8%#Y#VoO86CYRLlmw7>XZ%C~P>Agk;Hq(YxD zF+B6JKSvQA@@1`a9_zQ3dVM;tVIn{FQf9L4-TvUDMdX7L?sY+tZ{APIi=Mq~&$Re{ z&#J_}n@TCV{pk744qg?MWoNTLk#Jh@yY3*d2uQp?PwrOOIS@jL^O_P+49z>cyUZZG z)@}85i7h6V2P^|K5T@UUgfO$TEp;e?m>ZwmPA*-U@&lQ%v$JzgXQvk2F&^-!T1&Td zvD~g<)CHj8gOcRr>ax&_aX=&DyOw9;PQCjoWN{kTekW8 z)I{T@i~PnTg9?UH^G4bEi@oG=rWM=`iwa@-bwx8KY@MYESqXOb>tpZgO9Nlk&2PL2 zg6-v}B?EI;Pz?sV`UnJw2ec~GO6*H$sV&eN8`yS>>_67AYuml8r>?F(p-gEEZpM6I zGxS06YH*p;D06&#{6~dwm}b&SM$vQY6>mkmK!S|m(yyo&fo+Vc(-d`&Ei2?pye?h7 z?B1X=IW_eXJlb7ok%e@HnPkm-F%4x?EO}3?4KwyfKZaoU%0qf61jxDQIt0x0V~4E! zm7hEnDB!KXrVE*6a*B$SPO2S*Dj7TyY%(gs&iz`c046aMkaM(CrmYG~x2`X_kY+>F zE*l$13o2>|2fbA|)dtCoCFSxX-Q3b68#{Y9#|FP__S&uc$4rfz1+JH#mKn5S!3wy> z@Z0~IotcC-&HfD8K)cO3@b3PE{IT=OK_dW5Fjtm$nrz@ z?6=XJ@&TcqG$lQ*A*+zd$;p7+fayK*l)i7YU#VJ6V<$cKU%rscot9bf-s;l|>IVlu z#X4^H92RX_02z%83Z{WccXTgBMdBwJwmdAhk>Q!~keQLFlvsSbf401V!BP=GhtS~5vR<$>{t|2AYB2{4fLFeW3gpsFG zI3dZG3o$4wOT~u%1LjDvaN&!7*_yHp)LFL~$tP>GS!RhJpW{PUh|PJ+s%VlFD12bs z@fJ}uI8<17U-s77D-Fz~wd>Wf;)&JqbiOZkw<$u<)n(axu%poxy8JflzdNoJHI@kQ zRAcQfx4O9OGF^p<<@-nr?cfm0ac{-M!vL-)%W9+ zONI?`R_E}R{^CG(MR$2lUR5CHM&HjFj_Hp&r)IEo@~t_xERFfKH$7O%*^oc(EbMhk z#i}QlMKG6^uN9{g&yaWys2KNW>x2S)4mwOJ?If3$Za1tAUi6*ZNF@4*F;~UY2Z@AV zH!%cxs7z(w(RDCwpYv5v^V9eL&XjSGRCFKCfj~W1$5A(2Bd~hd9PV$T!B#o66FqgZ zPICXgj$JF>=ZrAfzy_!9o13Lrd`~u+-4v#baA<&>3d)p4|K?DPY1}ep1_?!g<};uVURqgB~^#i!3(2lkH{GvXb(+gvHT)-Hrt@!Xbr6W8;_{&^O z-}@U+-ZV_S<%`yDm_#{ZPX;x0v%G>|7T#I0Q^u+M@JZ}}XjFb^Zvojx_=}*l$-GYq z?CV>{+r{v`$<1@Wes0jU=Qnt$)Z-PDz3fCKwDpLzyN*%Uf&a~bN>J#s(}iajIl6_| z*1k3$?C-Yozs$|;+E`K3Xj#8_I;erJHepD}Ver}353wMud~~&#uU%frSDKyry!u3% z*2Ep*s96$$^lGg^#`y85_L$5Q8+rr6UGx>$wj!H`VxG_t@-p`Bimvt-6hQ)1tAP=- z@uuh$A_LoYbK1FZ{dq@zauMrilnLzo)6T6Qc{jb*Tyo2xfrQP=aAxN2bzKdK%Y~$D zxLwO%qROs&fqi{))1Y#**mz@y?7P%9++)aK(%KU6cn6YNWjXe zbRDQJ&^+g%!IXbX8!110oPsJ#sdLzAAMAS(rB-^UM!-oVKka5TN;zY6@~gK<%X%R* z%H>H=LwD&?H_MoUbSb>)B6c~9KqBly_ z2f->bya6lbXFBrzr&_Z65|;VXMUu`Bx+oHcGVJ*mC-lpE6uRRr_}i^`9O@}d zwBz7JbGv`N->A4q7xhWLO|QBkp~J!ikI zi0Zo^IbOA=Th6}Z-9R(9N)FxcUQHcu67`}=1$1e2Ai@E6DJmj@vTNF?f;2$Os%65c z!ji>nSV>EybO6QwBGAPluR`++-GnSf04Xzp!NITUG_hST%S8E-_SQ#dYy`jSFXn{| zWdwX22&HMJJ}7w8Vi!e55wqpFKoh#M;~LaMl3yXuW3Y+EVn@rYweByt=8yQ*lgx$N zx3gaI8(#C99pll>t*K_rC_O)TQ#H>(){JA+sKPegYxYy|?{-y79fh|8!VUc{441?d z0`=gfzicW!gUk_U?1$hQl0H)Hxv)y@e8PQ1khK2~1h zIgaohxAXe^=W9e8T5?!4T3);rLp_}By)Cvt>*vCJyCJ6n?z1-@4VTVmAE`>xVygRQ z_EB0Cp`SN5eO3BKN_RJYA0)wPlcb$#h7z62z%N zxC=&;!ky(-pFT0p9WDJTS^WK%MjKmKz7rQ0HzpC!#f~h00Qw5RYyd1p(B#X>e11mB zc}G+&m;7^^D4R^lSAvZ2nW^Lf6(7l1{1d(r*-#D3F}+{&I0!qbGDFwBpk4ix?znQTj_JQ2FY6PAQs*gMXkew{y zwR_fb_u!uVcNQ8p{B~%OzNg58D`Rln+C@6`?xtg&<0GymD|c?#vIANsVVK3hw(hYY zS;`FOq8fjn!N|a%`bUQ1x6|ny8xevG{Q?#`EoT6r@LVf{fA%gf@nP<#BMhOJW-M=EYdKg09bt%NdlGIf}e3OX2Ul zp@HmZyg6@Z&)_>8?WtsTekIvhcT(_ts62%O1rfeDvWDRdwn+LEM9H^j-Pqotcbcfv z_`4A1e(&KJ2|SH6x^eq*$$TB%?b6-N1ThBksZ94hX4KyxmoZh5mgFyXaBlS~kSGum@>;!rO z=XI83^n4yeenDU8K0})6a$Zze3Pnpkx<^;Z97t$X_OP+T38#l|xqd!Bx#9C|eW{X# z8MY+&X`$J>T%=s69QxwNG4H$-Zdljf7%bmrXCRhS_M$^~XkQ5Vm?(+^V;?vk+%GW} z_^G@9*+eUO`1Uq;yajMb8${9)9m2>b4e9J%*$F8%twa5VvHU-_xdwZ>l(@$AC_w znC|=7oWtzqfm9q4TA&ijhd8Gvj~<;l7#@LyfHoi%MG+4)ctf*Ga5Jcf&^d`xnK3 zZKTyBo0^+*K$8*BZ=3;iafGoC`+G)4eRG6#QOX_cp5^+vs+ zY-@`H{fL;5upim4{|Ki0&sUN72sa3?;Rw?wt1@&M(JK>y^o|C4IrprwV#sH9^Z)wZ zV?=r`==C|WHfGg9o~MN%+zN5RvET`qPw->OhVEZ*EovdZ;Qw&;-eFCpUE4S6sH3Qi z4J;JLhJt_yNQY5GR1idZZ_+!FP(r|tijYC23rO!JKtc&cL_oT9NC>@?LQ5zi;k`CE zbI&~Q{T#>peSh4Cw}v5m?`!XCuk~B!xt3M^Ax9^t1MgSC$5#tOw{CzllY^z_n<(Xv za)ly49P^oYmj)Lnh;U$x^oG)f!r9ow3=u0&obf|0Mu&NOk6Fvy`o zG%W2w3~hNS$Ac|$Mh3CRxpVLXy)WdpqcaubhN>vfK5tYdT%T(gYJGRXJyZ`ch$m5C z-cSwH5zgA$`rI1?2(iIk0A>+yUAn6^+vhV}{u&ij7}Gm}uMN6(MS28-y6DM|*vd@k z=XkDPUB;g~vV%=bb#vGrvG5>KVxT1Q`TL^s`x`_5g zAV2ddO-W9^WhyG`zfr;i#wG6Av*&Cc_|*L3*{z%6i;tLySi|5-h!6IWzr%Q#SY|YW z95308j~k1Ho+7aptP($YD8T1yW(>~RO*@3HTpI=N%p4ej-P+F%et<2q9aI6y&|-le zibglb*#-I4Km7_P0M;@hS_*zZ?1W=H_=BxA>$vg^d`03Vw*0CPpg1b(j|qAKrq(!A z{M+)K;05UKliyv51IdyEyni@7&EKTpQm2Ant+A2eRl-?~Um+4?BM$Bbr~Yezb%3cd zCBqm{rZF#;-&!pj;h&4<#T8-G=V~lJ6h4k3x>L=O#YiTX1hzPuXNAo?b+vosI-`|6 z7{2lD3ck>_L@jhtVUL#V8AtDf2Z^`F0ey9H)p*7Hk|#X9Qg(4a z_@+Le@)};BgmyTeE8mBFz4tK=d?kLlCZ%$OBj9S;6g_?VbRW+>bt%GJyPSHw0?$TO zZDO|m$HQ|(UG=A$m3PA8#NhCYC*AH24XqFGLqoU zXpkpj#oAZ{j|AxQYXv9Bde46bQ`AD%h;O)U1)IhqFHhJB|H^p!ZFIm58xWIQU)sa} zP8MwO&q_v)^4Th|eR2TGmkrS_#TlNr%JVgj!-?Ca+1*7|-b7bTZK#P9z{~dr-A+;kb0-aY3ebwxv9Uqst3l z!s~!}s<{ubRQQ2hqt^`WRfZ2YR`D9J2)y!`DS6b>CWq9}tp>z7!W zRg?9}jqE0#Q9R&qIzuP~wn(WK`^e0g8rRmy(e^#dB5p!OJXD>(}@@6W&0$kteNArS=cq zZcB<2?eu*&xid`6b+Ft#WNDf(+nf2pKT{!T>X+D3xOrx61?pky50JM!-_rdIwX{IcM~?)lM6HZWk<#jCqVHS|9B_}lb1m)1<|1dx znd>ah`@Wm`>H@X}uxGtYZZ@{mv(Szu#(5VpmR74FR1zqeTrry%8CoRie;xoT@XuUW zhPFEX169t7&-DHrZ^Jy87hsAuARPffFV znYMD!H;`=op<}WcWSO=1p%vEn2jU#Bu2h7pTo?++^fPWH>GVB^o1Us@L5u& z{Qzkcbg}>WSl^HbkM-%hh@)xr2huWm-mzxK1Y4{CO^MF9i^z#hBZoTklN!h^J(Av& z?y&cN@u6e?g9Iu!40= zI(Hk34w`KI@4wJR9BjJDPwSGNzClhyC}SwwNI@Y&SloU z$l)~dVy9u0ih-+FP6n)V45i4My)TQBXhL_XV$z2fN{^o0>%hl@o_0NzHESDPDBtG! zHue&{ozi;`k63P3aR!=|8vze0D4_52nJ7v8oH+Vj)cTX29blt-7@!;QA7JAjkB8pg zXZBw=uKF@qC`0IYU+3?)wvt1mFSl|!B22FFu?=rHN_V>|`j)oG4dn9BO;!71Vvo2| zE6%$<+y}iozr6edw*eZ53a_5L_)Q?nZIi`>&vs>;S=$dj>@?fhJjuBx#>O@kT&a`l zYN@>Rqqu&#a(yy^^I9uicFN<$(1T9N;Ue!*&D-A7gfIc6q1B#kCNv^BygZnR(gSz$ z8@*<24h&*7xO$5afno~k%bz3?>9YdhN_N~y^>06sy;>(;E8_w|cB~P0E^l)MCVz|{ zlzRqX+0&JoyDcZ6940 ze*)@7@0Q!!auWG`69PjjQv8lreA~jnJ;`e!ZDAre`H1Sy$BVbn!AaS9y>wf7RmdEC zgmTNCw!Kn!51|(?Prp~loY%W=b%g#NjNWWj^&s~O$2;Dw2~Z#eY{FIax!T}>;dIf# z{v4vpuMu|uF4xf9{P?nx$_X*1PZ=uAZJ^1>gzu&Es~JJ=DSSe0p}fSNu#G<>BDhGi zX{@;$%!f=prf#5~^xLS$cE+4xM;5oHw1CEhH#T(gDvtnv`JtuHL>^CJUBzGXYLlEF zH_OcdKxpmVbuQUI$D@mdp6*SA-X)*~__MjiCSlx_zV7C%|D6uCO+>S6M`UMb56g{f zhOc90mvooXO?yKIe2raC*z(BO&WH|n8y@5BNh&IE zCF8&N(9nI4RDj7nwE4lK2U72zI_gE{(j3%F6HS~UfET7(m!)~m+1CV!pI<>fW=ZhDjTJqX_sIuvW^fK*E zt7|%ZA{Nc%yr|FcUj23i0(G1wQmf{8t(SMs;+NmH_L*&8!3akMK5WXh{2od?Oh z9mW|2iS4Y4U1?-$d~RV*;BwC5_n?}t$<3K{V;m*XN%h`*RuJAau-7<)l~tdgPR%6B z^D(%D<+6n1$W$J&?i);1<~?Q;Y*0^nw#`%&0Xj{Q=gc;J-C*-$e48a8+EHd*C_5&G zc~ciWJ1U_kVCry`$Fz$#GYD_yxe)oG2CgSBx9)c54ZiI6wA0VQ6q8_IJ}pF+@Onm> zcL-x}#KV8tBMV8@sBc1ayP?WKCSpjk~&9qqEJezv>1%?|wMDB7SaR*L(eMRTGA zMYe1&*)={J%f;b&%T&7X(xvzcOkb{%MEw!lwW1)e=Ev&olBL~V-IVD1ayw8id$m*< zF+cgF*V5TLNePNZs60@+Wjtt_6n4g*8i%0lTYnPRF4`Hn94QD&2%g@Wi1bhM7n4;O zb4&>o0I<*s@5J9wdb88_7u_PL+>1_+pRM5~3*-0E+9RULIHTDd*Wu+z>CH)re)@vo zl%Y#qDQzDHH+wd2Oo3CB-F3fUwVLG13j765(V*@Ujy%C*S;b`v59LKGz{^=06x3A4 z24Eq_z}q$?xuT)n`13Xo1|I^lN0X*W}HTzuQFt%`Saal!J(d4IhQ#P1&R zdJi8SIZrkLo&U$8RhNfmwgBJ3yiQOY`1yJQFIcg2elLc+4N4Yj=c=mHzP=u6fc_wDW8U-lQSg zl>N8FNc*RkjGxS>H_^$2=d~fn1$9gKsp$#=HC78oaVr-wet*3N-its8CtkKWB`9#tP}FgDy0{8C8p&LIfSC6RKH84hjG$eB zch;7MNB_q3PxYOie;YMfzg^@HY_SvBgW_z8$%cxd4x4sbge+kP#Lr@AI#dkpydU|G z;{LBLzxhB+SN`ay8rUQ6;Bo8a`*-q|f-F;fnzM*Xcx#O}JArAm`hJOBaS+}F-Jwz2 zXf@zPJBVMwN`Rarqd0D`mlt(KGPePX%M&izAdSHHn?}jCm^g4%6ys~>%Fc3%cAjew zOU`Q(Tz~%xfZhL@Z>aHrg;1AL@r^sJgf5Tk0`;3*ekJg4#@<4yqL~G9Z4I+qJN;IG zwX(9&%(dStm9A%CDjMT(7f}Fa;vh)q`e(54Nzg@KcF5jq&?jwTYO0Fd_dmHV=@vQ& zUUkvlb+Id6Le~?7LomQ|#a<4j!9jGu=Jsbqs9hCO3vFT;e%NP1B4ATHj0t9m&P~e~ z{&|pXzPCrhe6tKw&D-B$j$~R*4LOQ5Vo{Y@UnX0mSGIuS@XaI<+Q;zlkh?{IeC&tM za(vh#V)AHHDE=_VUv5-C1nITKjDT&hbhAj5%OOoBA$mKfwmL!;5DA;gEI>C^()^yw<8Te@do)x`C7SN3=A+65+Z5=z#!YwRVPX)p z{!-fMf@lgCD(vdg4hoW8N>L_b^$ZLeT%hQ&^Vm=FQeoikPLGik$~OzptDH#Tzilc% z1_F3`&eR;qPD^9_INO&;Jn7UTSNUG^HmWO{rK#~PR+hh?Qd#yz!CSfV0{^_6G5CdN zqB}Y|oYod606bY(u&vDR>*{)hgOdv~GX+j_b9=fUfk22FTe`#RF z*HGfF5yb4QJC&7A4S@h$IM7jFW$=AZ zE&){%8f-g#r2fKs0I$ZsAKt=lslRX2x8_U5W-`6kjm;jV_*{ml{Ky|MNOHde0+T8T zF{N@-X}rtOfVL|ERn$Mtc-l0TMtC*1pY$qd@yg{m9tg{_i2#8Q_EE!oQ5+et1Uw*c zcLxBQi+uHykByZx5}g=bG-Yh^83}+-MEGX%MK;SD;XI1gX<%V~VJpu_7%5$hIL`l^ zhfde_e0R6csNzfw#oz0x3Hm(Y?8*V?=8zH)7RGjG=^4S{^hhFIKu|EJs!DMcfF-un zy+6<94%IOFIH{y~8(AVUWyq=;dIa`Be0G4_r9}ZyEAd?qbQ&A9VNBgW2+yZ?MZTyA z;hS?=H}A_sd`|CbwP8d|Y4o+PtDlY?^XnhI!WhRb zIeXr{xRss!@hO;2H7|;g^$P;tGK8)H%s0doO-t%7+wn^%`z9ra9*xYXDe~NclA?AO{ zHIlCHcyG$MBrf$B?~ko$s9eBD37q$z}9b{4AEnT;!iPT2uGfBO)t4Tc0{Hu3h*P*YT_9T;9` z%U9_UcYHGWl*Tvc;8XXI3yNKcW#+vV^P;7AXIC)&7``}ucl!)Sx38?*jfS>+1&BP6 z0+fk?`BLDf9Dd}L3u95Nn@+8gv*4FmKbN=jOS4XIhvO!8;sp|>^_<6^R8XDpUGad? zpC2r%+&wFi)3LjC|BPxrdjx#z)!JiRTzhfkmv=#xYFD*7LM4QIAL{^gp9ax%!4I%; zedmP-l@-{m%cRp24&lY;;gj}cJ0*e_n^#?KyxyFT|Pv_0%l){`6 z7Yo*AYGC7jI3!W7NzEbvs*srrK!q!y&ithTVKHh7+NnbOv!S7(lbu~xu?KWODciNU z;b)#LjZTcs9xfovI?1UhD7-j(^7KkkpQ3_+wJa*Op!#>-%e%}cPn?MBG)AYYN@`3*fm!V+oc<}LB#{y(YW@&xprsZ?_&DpyEIN?5n2OTImva=|BCQ%S;Dh=0yR*+=3Df@JNF&7B}S6) zue$yD|6aHEsh!(M)VJqda#(p_Wt9Y!x6K|f*z?ma?JisxoMlRU?5+i@k9RJD6vmn5 zJcDi*8zg=7#`!9TAcuKsHu*~JIThdh>5D=@(OxhD6V&TjI}O4+UYIrLO}<^s2kP{J z$*Ul1J)9R=`yVN%9s+@IW1U3(56BEEE@dV|S^uKU<+&9~e?w*>zNg1#i!x`MWXZKM zMtqb#7s_3Nb($ahw{PT?f$*AXI5ExCfuwcQ34u772oS!x zDoeW5Bc^Q%LJFBi;;8va?<jA`)z0ztT=>G0%vb+mlZf^S@9^XF9X#ml&VCj$QKf_s$KuWe1eZ4~>rtj%IL#(- zg)#T*+=z*8AICSC`fFtqOTf)uSjVdRSPbl7EBP(I69TZ7X%!2dlHoL=H8-x4V2x~m zHp3tM&mH>H0$12Mc-k4?X*twy=&EuG0Sa9Sm7Z&(;*4=jEjIhoI&K&UKE7rAL)M8j zl7oONP>FuRD@{z7Z|hG`J{ZI$PFXTp3hw~I^me$8=b=p`$vFFbg;_waG0wp!B;|Y@ zL5?g>`HQ%k_8xy5HJccp8B}lFpbq%$mevI9s$xdo$SF?~z7DHh7{Va1wm&m@U7ky| zqDi0qbWXl4I6>c3WA=eG?^GCQXQ<@{Al0QSR~|<-eT|%{kk1peME*NG) zq)A-BRAn0!UYu?-H0v;)?H>}??QWB6I*D}7>QlyP_ZZbq0hHU3Ml*5Jg(0hsz$Fy+R&)c(Nim(#IqsprKnTo81J zVj8WV(w2D{E|JFkO%K&K#3GscYwzp*clnrkrZLB~bbx~5bWUlOBJ^GI_nndS3ZQ6G zWG1!>%*xcCCtbMktzV)EMk;ps?`5;RrNP^NR2H=Mkt>KXgu$S4ph%yA zu51E`AkAlgGC89bl^AS8FXxgeO7z#_(cUrkqHbI-omLRA$udt!0SZoQBcIy4M&k%Y zoAZ9jZ)^eI?N%AOMEfcBq%EWe@meRSO2}W-qAeV$Yo1&9b>y7l^5CGAGE>m6>$wU; zP~G?2bNoOSQ5kg~O8sUvA3XSNVKof zys`O^=kfWv`u^@FF%mOkQs13ks<`J4QxDj&hIDWU1$vv9P0~x0@`6lN`k`5~8;Aod zB2XnUT@g`Bs^u~($_rr5>6)6l@NKTv=cK1!+A1Vw-0zCe;R0&?g@-ZI^NI8aK-&p! z@r@%`-0TP_TnY&ZRiE=HEGTfI43uilScL`4)1OBel2WW0NmWtFsp)>-P@2i5dq9#IZXS*tW$D*E|Nb&!(?$748JG zJH-XXkKD|f9X&24gij}W!s?gyDF2lB2ECW?%t(E7pE}M{s}`ih8+09QxALdUvr9Ia zLC~5zcnQh)KmuPC6z{>hWS0{e3hk-BFM{j<;d&R<_+UWJGL>~)_%T9A&IR9VgW4!) z50Qv1-6vDV+XNJWu@RGfvYaj0uH=Rl*={Atz1n**xTzA9a`Sl-BxVo7WIk{F4Wc)W zxm~4-pH`B{FS$(f^N?i6>QdH+_>E-8jyTIy$dzHY**T^xvtWREU=M#Gy zHC4hvFd^q$E3d1ld)=rxpdC`L-+uoO;xX-KQIp8LHL1UWonUOu;5&s~mcF2DX ze=scgaGT?~|0iUpb_ahncE}%$@x+6H9?$&GfVn{hvea@|v#?)#vWK`XZSX(Uq+GCr zd`M$uqcfEzyyJl0De^KDVK?g=j`!}pm1n}aY@yfi%J9!c<16nWH71{j-nLn1{YUQZ zokE8I>)E{%6VwReFV5<2N}1*qhVA!}v)(0aBbpIg8Uh~Q?3bMTD$>b1d|@N#)tsL? z%(l}ir#_UG)5=QIDpS1e2N1&9S-g0A%`IP!aDx$4LzL%gKPDD@JPgPY=2LS)op9Gw z#NKG~X~0|(*2Ug%B((rV-%54^1~(|$%h?N4;RjJpENz^1K{l6 z?gprSY#$+iVgLA+6{jJYFkz=v%p9)0Nbt+Q(0BQeT4413<# z^|u(4bc+UD3;!#$i@ebz6zyDvRC;QHyRvjpb~bkQWD%dUtObVxycr}IE)~qsoE)|@ zd&(HEoW@w;Bhu;kxPi{qS1;rZj6S)nRLZsuYKBjQZ$Yo&4Xq=eD~~0ndA->8^xhwx zt%&uG*Y6?2of~Ug1jaU2bV;P&pE0?cp5fJ2oG9%&plsfY*4oM<&9GfYCWNSZ?9L}? zvy;4xx;hy~M`t%SFSW)rVAGibn(>VYvXfXb`<;Ez@UtNs5Pf)ZQdM?0cmS^V-4Gwx zR|xR{9vSfhEl6qFDzeQv%y$-a93e6F#tBn{xbL|J;j~vKD~9Sc!a1W^GL=u!1xm1< zCUk}d?07Og!zbrlB{yIbz_^70BD6h@loPKvnocg%XmysoJV`G#dP|N2R8fk*;d?K1 z0Kx}+yBt7oKOxg{?{W8ZNWcxuB>f?9)Vy*KVt21lT^|*27I1txKMC4h`;NVm*E+A2+!1=@DZUH$||e=-Y8c zSfg=}u+nXZVZQm(9D~BT#l=M+B=rJA8|Nq#Y-ifq``HS0epmc3Lt}GD@zlyKaI{&ZO$& zpe+9htSHkPi=4#1q|eN~&0f8Nqf~h3xA3ku9EQ+K&p^XDJ2o|AEu(lQqeliYomTIp zVof*=?=|`}#xlM<_Xn%V`2rShaS=BMF|GWK4L>7{L)h_S$KLfjYoHpyxGCFWkZC_z zdcBRAUO(%{X95nis zG;|1(ae0NA;R>f?^U`<}hAOTQ6cF`08N=3V*G0tIN6&5ojK#*LtgH;QTXS=Bg<#fe zR(5vL(;b!izk)@m+)m)xG>Zx@5&c(sUeaTFxeV?O_L;0K@1{?!VDM&}wCk)xm}A*WP1HKLzLlTnNCe7SPVP7J#{3lXwDP^C{V%goZol6 zy9Uq@T+g#lQBKp@Y)IcxCEB-+l$#bS?`j<87>{s86VWbl6Rqm6H?~5<^7d!D*|WFg zqpoglKS1Yk8^B5|wlDUJ?ThVJP!3Lcs^GU% zHR!ilyT7~y)E9-MO?A`t6lENY4q**7hWe5RYhj%rBE3>HRB8VdSYui!zR;B()CKur zK4B0HD**`hr#7|-v~?Yp0H1z4w9S}@F9}^9bSXXG=D%5y0$+;eZc;lLW6}Ae$9A(a zWsr9jbfzw>YWhyxC9KwBVx#Cck<6^+2*Gm{OW@yN{ZGf{O7aU;yBL9TdahUJY-xDZ zZS0mt`1aycZZ?)&*1TblQS{XdpgOE;n#mY!B&WjXa%fcCb$aPQx!u4vM0_hNS?T9APf# z*_u*7h^+*))?a=B(%F7cn0WrJ!mYRh$c_lWtKZ$*TSx#$^~XDO^VXt>zJGtrRWh#$ zv&no~OGkT682R6}95*v9tjcZU-7pA~UtM)47!mDvJ-6Zu-e+zz&3B@J4CtRLudIvN zhH@;A%WQyB!S-$<@shsRD-4ejgb4|~v<7-DHntDN=G8lava)!5eEhqhEl{~a_xaPO zkWHBF^=@4R^bDSWEQ9fOTICI+f)x5>@&| z?O}hPwV7`jo;9nY;yjn|p@%4YU0PCBzS_kk#&&ZI8AKY>JFf5U@_ykeg!|d19DvIf z-mc6A%tZa)tvob7NgXCZU3_b-JivEb{(Q)#G<1)*VcUqM-xa*-ZyIU6ciET6c+u0< z?y9&tv5)bA%7axgb;^G=Qnf3xa@NR~go|+`w^fHhEp!aO-3Og|ZgdQe)&>bFED9w6KxSTCVO1XzS_1Bt z-_C6#?k~qa*ISrk+`^IT(T{O3lkk?7JMT7{96?C{&&4Y%!$4hq-doMZ z#%A)n3j!Eax5WKcUcW$(1IN#I>wbejW9?Q<6o**#CMob5W!M!lYf_=;-aQ(Go?ZN8 z5r2Jqj?Hp>h&a8^-ecv-WotX{2fW$TqQLm77~c2P)QUhPB`73>dGSKbj9bQMF&Wr1g6hY?`}NzMff#!6xp(0-u4+`D=QV|W@gZ!%ll_; zh^jbnK>;X*LitSW?CezGr4HZtr%IOaDTyOcn}f#`Xc`0r1fEsmfT1Er9)YEC#9^HS)$uE4G8PQS zvS%+UdShau9z}>W6vgz6<2yFQRo?|LPB{L@y$cnr|A8~{&S(CA%4M$)!l_^**PB!C zZ}YI(KW}!x|Pclao4o&6uw+@S202Lyy;NelKcgyx8v}$mo(Dfy zeqLE2xh7dn_78z}9ogXixReHjK~fw(A5;8u)~C~E$E2$&bVyw)MU;)@PK~`&O0ft} zXJ4XcZ$Ib*NcqefOY#5gAztN!)$Getp1AcNpa}#arJohkO^b*8anQv1YG0W6OVQ50 zF5{~vR-6wvHUDK%|I2yVd};m33E?vczwhjdFJ_f;IpyUP?>M0Um}rib?X^Cv!Z$#( zFr?;ql+PXkdTCwqR&71{xSIbnH^aB;eEBYrZ*d{c& zXhPk}&J=0TB4KiJ@{B3yAmMJm*$yO`-kQz8Ro#3{geF!i$T>DBXp^Y|%m@!aUOkCk zHE`E`AK?%o)LH-xL)jyb;xV2mCKjPb{mhd&SCF$8pIwkq|M0_@5WoC_(1#VEF?(kq zrFYv%sw&;gr&k%GF5MHW3uE*SRgv9yjUtRa?*1t?{QJ8o@7gO)UbT0vz4uK;)CN)9*q?@G3^ah zV9)EH=R(5DvtcTVKSayS5Mc@DoX$ZUT_^zm}Ql8s6qm!+s~jX#eJfvQITF;$>vhLl)+m;1;u zObZ~bEWNx#xv)0+kQ)70tBXJt=AX&!!vviP9v~loQk9O|_YM?GB}l+)6p4Pkq!r{# zDq5izok)s#Wf-aZkH#E^c6tzFUd;fRJsgif{IpZ%6?V(F&T z={GJ2U)w_GfnEoG_1Mzi8NLns+_5g2uZSfV+k}N%^0Ry8P4&btN?f-(EJhOxMq&br z{>i3=JpNnD0kov!O8AKTYGXSbVPpG&oI@^%t1J{jj{{HIK|vU)PDfhzqvU|zxx7GN zXWS6~sR#yq8vXht#JTG#Cao}gWyvj0Bed9FPvjlcW+%k~=or}F+gAKnF#RVyvZGX= z`8hxThqW-fRq6_T;{fN}wolSWUAKxeY^;9>n#E2ivj0E~*koeCWXWO$uAsJtYwNxS z6W+~fK*;S_1?=uy604{q*pJyM*mm1%c|28??l~tPGN!$=So9_{R);?@p8sNYrf2g* zkB%$Q^W$bxW1cCZ`1j2I6a`n{?Upe)mRw~29FaD~_30$6`&b>cp+KYmh+acTTaz?t zu73!FhuZ()hPdolULXkg^V3Dh8--iMR=4u33s)NmwXcfQ+*pz--d z<1;^QzJM^#pc$Fh|8$Qkgz}unG$Wu^0E(VRdzVrloe;}AZ3%&!?s~cUw=NW)i;4e{ z*(JoRX4Zq$;aNODdFgx*-3hFT^a1{eTEi2|0I7L3YonlIkmmzjl}-VLlBtfc(aU1a z-U*ELBeo)bf9Y$j8EsPK5Moj()#=e`#t7&E7Jvg&NRg429eK6*`P+f%zz#AbYXeyz z^86+Qt0h-yeLS=s97$HGqBEj4xBrXaPGx1J4y%Ab7ZCl?E6F<3fW_q^G;G}VUk1vU{0PMQ|750<;kyW-$gQ3XVp`rodU zU(QaJCmy3aM1a3Qrv2Op*@Ls|cWB?1Z+8ri+m&Z=2gBN=AAbEsoZ5Eu)RK&L$kfJ7 zAe;}5`=ApJECAd6Db^FF?_bbg_pkE2p5S3gK0W)_{#W%9Va zgtgfPiWW6<;%%_lpUTQ@s>e$D7u8eSx6a1xygr}HQE3_^II{C8r_l0_t~n(P3CI^# zubLPd&MsQ$xp(aK5*qLpKJt=1CvHnQEA-fV@bj-$VA&LSJ=@hCfrvK5C=&%XHPfK$ zBR7)=35e|UfS2qKc*%KE_9J(lDczLB7-`@0sDI*m_UCbAKEP~=FMfT=jxvR%tmknC zLfXl(yFExuF5x=avDjHfCMRX7IVqzx^@?I`u4%Z1o^V6HPvKD;wPx+TG!dF0?Qc%6 zh8kU8@2%n;II#xC0=j@a9JJvPu2pkRgurdI;BgVmn?u0u)2&R-EAws^vA|{V&eqU! zkk~c1K>2{rH4f3QHiZ@ud6JTX?Ya8mgj|zQ`xIE@ z2z2jDZTkZ%lSaG~ry?-m8Hn09W;&66$kh`$jv>fc210_$6PnT^Cl*98~>74UYOqHP-HKv&G#G40&g|)fDi6@?gpO%?RRKt%NH93t4D)f&ZlSFv2#7H z;pmKG|HXl;ZTEGd$LT~&`Xu1B=-2%aDXu+6&R^A)b%_rxXSm*x zdT*XgYQYpeu4u|k-k!!|8{m}taXht8N3ejDS)d&g?_(nzQrq&>E%)7Z48nVthP5}g zs>t?SOa=s zfK-jIXsGkmjr`z5HN6hld#Lk;dp)P8KBnE;aluhg^N;N~0Enh%)1#E&swXC0No7Q zSbs8&X?mtW52zf`4DP*2Ip>*MqMbW6|AFU$#m`LxuZ7fp zRev@CFRyzS@h>i4)qQiS^x>9}HrZtqah?p_8Fb@YVEnhP_A9;SuQ6qB^{%*_@U2y& zrGud$>$&j0PtBI|?R72)f3qym1S6>XlU(6<|LZWZQF1}S0Z0ZT7_TU2*19;;^fqEW zs;&~Ri0`5Ruf<>ftqcKUn`2caWH)w$-?!Rmu&Ie?$2%Jvy-yHVD=%6&8L z{wG1(E=DFe0oiEM#F$A>7t4k*8x=O5f=B31^kJH&^lwny%-)qNnEoZY)ddP>+Ey^Q zo}us478W-K!hzYEQ!BGITXBH_@Quz(`5{d&3kt$w{;!$L|*wpZx#OWDlJ$}JPPGtg-p zR=n;C`YeFjv$!n+(?0EJR4a^UMuYFt3ivP8Wj0Zaol7Qi6n~Skgc3#%l~?}YoV-Zr z5BEEbUni&K74>bhQ1=*LkJdX+Eok*f&f6dYcW{MMDnayY2XcM%IXb_hl#K?-p|B1s zN!g#nxNN=D0T}vQa+{*D3ty?g(A$gKl2taXr*LKu#n<9t#QVnO3rBg@fzyXAF=(6h zMOwV|cu!W++kBp5u>9j*coD(0<^eqK8-%{N_W54f& zP}dXt`?wi^wlDTE71ai^a&xgjU!xC$!SX+VCJbzeffCl>54OmJN$ZRKu@NnWij40^ z7!?Fn(&)=VA?bx+zFj!RE7HU{9y&@ftDwz)=`*t`p1W|0Bd!SRQh65@l~bBDbe-ag zu3BwB%piGj;3MKP(ZqV097k`pa#KT(@(L^Wa3%|(N=7Ma+Z5+CVanC2>h&Q6_DA*% z`U~j4iy@!i&~Jvr&3?)$95_I@rio+GS(vjmnrm?>~(qjZhc+rVK+H5lnL*&KD0gq2(uEtQavz`~}~ z9qsG@z64kE(oc3N{2Tr?NLvci+WdNOdkHHK8hv18?gX?)2x+(_IBTtq2?gdZfA;jv8 z7^;dHpeW@KLys*A50TWk7Awi$;9?eG8?cz*!3f|pa;S2@|5PYC;%g#wa8KADYHEfG znUr-seE9H+Fr_&H7)b`ssf6Tj;oy(?kYo{*L*9M#M)Y<_Lv@{gE{ds56+#tVktBZ3 zJDCzA-P2_?6p&EO8kXHl=HSc7r-G^;##v5*Yf8lv*m)N%E11<)JO!JyyyNue&cV8! z1GcW=>d{fr=6WBk`=?xt>;jffH<79aO)VqBto3gTs9u1+RM-hPi?Duci^HO&K$G3G z8+0yoo@$M)PV(5hcklCF@FQ1!vTs54A-1|p&FWZ!NUUQ3tNjA~OMN4GOmC8qI3O9| z=Q8xgp5RIPh+La-V8rHCIRwlTmFVOaTJ<5n*orITHT8f15VSh&hma#Ln8hOsD`r)m zUn=QKh6FRBwR{b7(FqXPY$yL{B9i9E*l@jq*<6~lhBpCcha!KwH=8hY0OhGAC4FG- z`e8X?$pL4LeF$(nZgr*jZTB`qWoy0XxY)G6ll-9AONXvZ;eeb64Hw8v)5`C>ci@Xrq((_}GZ%xSD0}y6%gUNmR7b_K#VgT4^+EhXa zUd7`0Rv-u&T$satS zXk^K+_K7lX%pmgEWTV9 zw%-q5UL3RLC-6kHU=%m?OPSp&O=K%-WAV$Ilf?P+iP{ zPpc|#V^LQG$^3+v>^PIv-`d>@+T!p;C-97)qtE0~3fovszcVP4dkC=dPW6K;3B`#j zQW2cVc>dftR}Md?yYs6A0yxHt%Klro+Er7$g)4A%R3D~bdj|)3LD@i4^TsHso_vws z?hwOv^>X3psFROo8FKd3S;kjl6G_A08I7D?^ueB2?0$cAkTqtbrBdbWPfKPJ$Lh&i znO}sy&qfmmrh&}`#!97`C=ICe5YSCM!9LZjl3z^Kxh?Rb`&DBWYo9I^m$`vaRud5UFSluCGI*zsh;v#6@=vSV36L|LpHM1U6kPVjpVA-GLY}kJ)F4^t5!eL;I zES4`#>SwWR>&afMH62Eu5{|?Q@a<;Vln4b>;<`@}>WX6q3lf*jB`d1dzrP<*ze8<;>hklYx z55Go=RV{dCvdUZO`Vu+Q*+lkoH8AfLj?XimFwpZX{IPG#0c{!sNL)XO6)F_6iKY^q9T;FTlilEq912;A{Kr;OG>(@{s9Z3E_&q-`?@m9I>%P&90B2um& z(=j#{uZS>YD3kf>I9;O({2yS;>R;E9zOE?PFlt+?><{yk@!jL3p_9gRBkW@YD9Smk z_`ByJm#J_<0HgJHMn@ait;zT4jiHCK>}L+bU)30Oo_h^xgR#KA@FC*#^Is~47(F|n z`-)tdM=Gq^SkPp!RD-d&vQ9kzpP%{nEx7A`jBzT?ZYbQOv1-9#U>aEzN(y`hv*c{; zUY2s9;L+AuX}#h7fb(7$1*Zf$B0rC%Z~L%D^>=Koo!ZHzYe&i8*y#wW(W9aDwk#5% zras<3y;;Fs=P7t`*8p3^iWIRO)Qz_SA65`Qsk$CT2-u|jj++WXkdXluoeGOTTo^=G z-u$YKk;9CsV2ss=^>thSheLB87Ax1Cf|>nEVf6S-@Syy7jw9u^QHu_m4ccxl4GEB_ z{<_D{Pm{A}i?DHTE==F0kZ$41<(ep!sXtg7y-j4gwzF=7Aw_1PT$CgQ36bOJHM@lfQfGhBhW_`!+n|vO4-Ei+{Uw z&2hg@k#py)9^qJar?|O`T3gk@yq$va@kc>HF@5TP97Q`5uB(CyUzngC@OOhaES|Q! ztPgslJqXb=0Y+&^b!On@<@JLC0*`a-D!j)E2L}f~^O}khDv>yVY5GAEz$-wMx#+MA zLF%x>{;JobyC@EzyWZ%8D6bNf=z{L|p7sGWp<2~3VBXf(ln1V%6Ym<7gE)87-e9+U z!!@QqRcK-@f~N%EMyT)|%HRdvGyc1czy{zD|5S7y9rda@p;NaP@3_}d);ZvQ8aa!S zZ`FdA5Lsl`Og3RnCSTBJeLCNCA5{pdCQdg@%Z^W`8r;xLoUlG%w(FL?WXb>Z8%X|< zn2_cA;}n6BlaSMPN}aw34eSF2>myZ?o(Bw7+CCo)6wegrNV`zm|8+y$$Uuq^&Xr0i z7)dgh3OPC;wIF2AwU;Kk)vY&LPy+R`_l_wD(V#9*;W06epc<;F7-%1&oxQAuj&>RI z7l-Tzu^L^%TUl|Gi-Yb~8$rlvJnB2jhS!7V_dh2jVy!7zRkH;bXaV_1f0V?F#1Uu2s!mk7?92>(roO8d~?U zb6#-^22ZTkzHJ1n0hYl z-~j`T&6(jeIJ0xi4-vRI*r|BJhx~XPlklDTN-@w3wbA1_0TyQPI70VBM9WR=fWo2bSJ-PZpEBf0CB8~?g ziDjNQz9#iXM@b^DBUo!wTN#7xjqWiXs&^pKqe-Y5BffEY?SuXW}&7o+JCXH&f zQ&gIz(y$uLX)aBa>OHQt3d{RE@ArOxegAy@v46kK?e1Rpx~}Uy&*MDKgqflqI7w=a}JddnJ_QU)3pK1N) zBvwFBNA8t6OIE|($6GN%XnjZlceF9NAslp@bLA&t{s~>ZYZmqjGU;2T70+Ye;CIOl z9cGAdN;AeD=G8Jb3OBw|2;mGyh4~Ow_2UVxL&2@`DqGFW%~>5YYYz@?E%F&ns94>R zy^Y?uE-344lv)%gzOU(IjBI$D=#YkiPy5oQPQCTgi7_G+`+uGZnQY57o4}DLS_y@Y z!3iSXI^Ntm9%kK~RVzCbtHB~=>0&T>&idZSh>(1Zf>6;WM_12sBGWk`?#efGIp~$~ z(xpq!{5pjLfsMXPVX{wcnlh`1IQwPIDjPQlSBDumHXH*jJTO)^V%u&hM_>lS)wd@$ z#{_i596t%?%*NHS{TB^$B!g?jw`~?*3`BnahH4jDN^bl3(`~V#*eEKagP|bi1*(wp zM3vQbr5XdEb{L?&`_ChZlF{^NhT0TH<6W`GMvuUK&>^Ko}unWSDPVi^SDM(RO#MF(M!l ziRIKHPr2|m`jUwJ8XO#a#!=_(Ek)}4?vCr>(xoR%SI<U|MOWe21^uuq_cktC$4klYoKyP-5OZdg#Q3?xB`;j6>?^jNc&~IVlc@id z78f6v47l)dw?U`*pRQpkyQY;oo_*f49DO9Cw%u(<1YgAQFXH6PIyH;ln+#pIMMKC0 zF-vA=@YsQ?g)z`Q`#vtfF5L&A$kgJV+({38IOFNxt`5CJ)b#&Mlw4sYkane{KTu=n zmwAFs2Df?TJfzKd1W&rfuZuezCp#KD>I_wM4d*bY5P3gJ;w>xZ4;9RA-wT`tc z_uv~i^HFmO&5kdXMyGPe&WKU34hO8a2KSL>t|3vKj+`yIvGcZ7x={FI*gvIQQH1bR z<$r5-nC$?>@%mI}kA!8XqN*s1TYp{p|0tC>=;atT*<8~xl+ z={aHV_A$uxjKQ4Uz-vvjAPoKTz6P#8PEH~*2a=8kF1*Sovy==)$S2BPa~1YzmyaoV zksmNJ_ikfjW55lVs6)Ud|4YTXEzV6H9m9}>OS9JVg zImPkEPG6!Yq(3+IdGbuS4EAoh-IX-TQGP2p*obA|gs_ZY@j`ETNUfSGvp!XPZ))^q zL^JWqI9@c*c*4S=jasIQxgCK~!+P%Ep9%}gVW92L#Vki(+3lQpO{uRX>R3W z6Br0_4+t)j!N5R*!H$io3k&g=c8*gx9^=AQs@V%WST_U(1qoyqfUwAttzs!5iN6cw zWzdGF?#EhfycfhKFM(4viG0Fw&BOEfWmV~5QOFcn#JEsw?YVR3(qTUnvdOdp97s?> z!GVMnXI?7`J~1SIjO)mMPb**a^<_r^h*gOK5bU61*-pLbpo`OCk*#b~m=5D#_=$T? zoYGH$^asdXM9Y9J3x>7?kuWeY_>M?~G9;9ze#z_5MT-|VfE20-(d|d!H^@_4d3kx| zS>l4NUJM|PaqSaHn5rbDS=P;xdrGgbtsv$0s;UZ4j|(EFxZ{j#x0*u784*nU5siZC zi+9_}=RiuV3=Nk%&&3r?FF3*wGjF&FQsksBU%tFf3l3gNOEL9@JC=U@aL0Nn*TFT}I8bL?-bq(MVO#>j?THg72+ti-(sVE&E{XE{LjY01Xk)1>Om z*Hb71<1sD>LA3T>4y@dtuQNd^L>RyHn{r7r|L!fYnABb*z!{E#7okY5k@${TdD6(y^B+ zU1+Riye}Zbwd=g%Se)%z3Tj$v;iZn_eXsKjRYmkt*TiU~PB{ZWj_M(CA26p>!JdPN zveD%$f4BgoLV!$hLU8ndptI2(bZAtU6q#>*PxA!4#I5S*ckKkVxcUnu93Sz2ClfH1X`6q(O(^lJ z%zhmm)AI82JQoR+&E2CEcbzuSYI!Li&e{hUeRSyNy>x(QtYyUgG4v_)2_PO{1h*5pfJC3G=>3Qmdf zu~N}ot4iqsRlA8=mtB_pbriRF1N-tV@3OA$C$X5cY7yA4bHsuh5p2bDp#zpA2Gj=FEJ@izBmr@omh@BU?w@@FfNlRKg( zF|eN`1a8ju4v+Ywisad5f<#NkThGKbJ8)DEJau1^Vz;0vQe+AaF<_Pb=SV#xxMtyHx4;%q4$eEn@`jx$PwZ&u?{;h?jTaNwI70W1|QD0 zDPV%tK;wZlOhVlAE$u45!mU9t(65#~e^;29mO%{{RaWEdW{vaqkLHO+wjE8oqT}gP zFl70O?eLeKeaC_^bzf=o&sP(0DZ?eep0(aQx^(+7muFBl9(Ar0yc{$l{b1$*$+>00 z&|{YkaJ#uB>u}uqO35Q9J*(fqe?qdu)V5Y(+lcH?jaE8_CSFgfp~u^uPP0itlZ|S< zz9w;~)uo(u8`n25%F@+B#9797d}uyi#Jgi-B1!{iBgX_PXxX5S3yF5w`n}->1RAxJ zgaNHHHV1d>XD)fr{8U=@efv|>%uhX!U$0PUdFgE~Xsb5-v`3$n>yN>|>+P>A@i(O< z^>TwgIn=MxI0u|5x;Uj-^cI5$=0(E3_u@efO?=OrmR)#>!K_<5H5RRRYF~(3TJ{=q zcpV7ED8iJwbglp<;qf)=hIc1o)qH&1x5ff8+&{>5EyY=zR+v2S8Vwlr9}OV#$Thcf zjE3L(h&I;cP7J*^DS+zl@jA?nDrX+-otB-<=V7<-tSvD1V5J!h^?iD}LU0c3{y@7A zk#e%B84JW(snV!DM^Ech>~vN)f2;mgQgT7Iy{hLM^^z>U&!H)BWL=1~{C_H9KW*|U zsWv@OX@4(49};o}6+R0;rFF)`#U@rp)(fO~H@6D^;MI#a6_iHuttcNCQZ%mV{PtHc zTMa1n&chkA`J9(4)jXb@7_%N99kOv(w?AVP?Qv%#_2b#3D>dRmMaHtVV{w(Si7o|u z@&jYXQCyUrbdM6Pju3mj&Dcg?FYW5x!OO=RSt*vM|O4wP+Zq4T_&D%Mt3^j zz%WTx>6UwT^gJ`Z0}S!IS6O9|zOoiP5;lKMRkbX|)GCj^@|}$x6Y?$13R(nAR-_&K z;#(cq{?t}uqM3z4^%Tl*5A`r+qI65u!E#d{lHPjOBV@8)& z2LA1=rPF_@V6Hq-Oqb?!GOFo$;4|u9(ib{%;3{X$Q~P77{m}8``8oHWkK4%o(3Zg% zMj?JTL+1J^$nRP}&-^$lt`lakugREz^oJ5H&z4Lmg%4EXKzFz&9TIY zy#Q;j>)W&8;v60;xJVMS{d*FFi)U+1$-^zK^(#~uCAM#6v;eKv;EGLods&=`d}H`tR#q@cu%BF3WO^+hH*VZ$HPlfH z6${xLnL39L^CKJ7(J3N%zG2}dDVg=3O{d>=1$a~muV=YiSUe~wDpI6e`3IDenZ+}R zo?mF_G9;)z-}amw8X3{o(C|g0fCcixC@*$MrkIqYVe|fVbO4!;qGD!hgOtE-eOp^w zJF z$o?BnJzX=(c6ZU^LM!SbSo__diEQm2lZHY)-DPCz_1aPHMMu*S&h-c9uk2a-w`h}tx>PIrw_EG|u_+9rRxsVM<VjqRDg(Sc3 zC8pTZqZJ$JUD7~vrb;VR2P-}uPU)p(Wy?}%C=Thp$Fj{#tEnQ6cxS9zmx9q^tYk#d zGmr)pf`BB%!OGS!Un>PS631@6((>{&-IR)^l2=&MjhKLDo4})raWH?R-kUKxhYl_4 z%H--vcj~BFOUrgjL``sk%;=rwX0ASD#+4 zsHWDUB|BAU!Fd?6V5ub~Do}p>lLFF5U`n zA^3*9Z$70&$hiHJo1kEv!4qJGHb9=*%Zt9dPBQH-LzQCax1oxLDeFaSnc0Z|02%;6 zJxoihMcs6Uu$`hJGpoCJ>4Yr&pIuE$i)>F(J$jfkb3;Nyr9W?#X3uJG#bJRe`&Lkp zIc7@1U{Cn_@859fusgE8gu&ZFF4Rt5f!K48{RO7vx;T0sy}ygK4orVN40e>}E32wr z{{oF>buyL)8SprwQ2#=ny#em2-7RjtX*@QWdH4C1 z>J?l)6F2U%zIQ^}IC`XRSu}mptxdBs5Jn`k?EfwalCY(S6}b#r!z4gi?f`$K7KjvYJ1)a&B)xoTZ&YieM?Dnl6DtbBQKjHUs`QLNFZ zz216hUS;4F^hjmz45XWSR*!i*?345hho2PGP;Hm<6_xD0LXnQ=WAs|7@F@i{Sb8asQ+b+){$wvC@L6&Z|P!*r;sYE9sZ> zRgO>P56y+qHzfRHILc>UyVj^s%#X5V^fZ9+WMZHJyE`v-*(EDGtm>2UY^ePT8DC=E z^H&Ph7VkmBsYd+B8AzY;@NTM{h*}vxIy!o1nc%s0D4uHv?z)ex;kyrQ;;t6hoYxar zOA5&Si;Uf@ZW+yvAy8~ojQ8|bcB_;bIrM^meRCNhjw+#Lt!DG`il?B3uzq?OK$0e#`JJ=U zZ#12hZyAfCmQxv$x0jn@zq4N9$j)oTM)em- zaPzuyQnOe`8XU~I;a!t>fPZ{HOfAwH6&2Tyh7>*+4N`m*+4wOwI{cC8ZFlhtVP&`F zvf|Z)4#V9`! zto!>+hweAoG&MXp!LqfuDnpn6R05&N()&tKdjQMhd_|E+PU!0&g>wDIqg#gl1c+L+2}9 z3Z;c{+>)jcW~y1~@xh<@dBx#_4Xd7d!nQ@a)zy`Xam89_wLBxE{ZDQ(pSyZLqn9M# z0>Ny@@2v#Bq93_*YZ=CC#eb_SFmMI|lsX#C5=AkxKO*i)Kv6AbG|t?VfnKV#_yDS< z0Gop@WHM$!9+9MPTF-UrzN&kW%`jF00WY!3r*pa3OF!pwPf~A!S7G_;VKRAZ$iDRT zEwKnwqoP*vEL}Q>9;xUJ((li!s?Sgp(TborIBcN@r?pJz-jmcVrWMQdb6kf4>3R_7 z&(ES`ky^|P%G?^c;f|LSI=?yvkciZ&FJg?_c{4vDa+#k%%V>k)Q~yAcd#=f)K^mIr?r$r(U| zFl-A0T}M}2`_*%`aWkzG+ksURwye~Iv;U^en~&z?l*pMpRO=;qAM3 z0vOhROQ6P^kzZUSAsm1Ru4`fv1=fx2QPU{1eKa$t=z|5Ip+xfCJveOXFVHeRnm3z2 z6=!Ze?4`O2d2CPm+-_9#Hj3WnqUot6X~9!lAmC`hGsHs2wMeW01a$;?#12Vp+B}!% zk?Rpg6-gNVDvU5Hw^uT_Rl1aQEG;H9BUmFXuBBQ-&KfI^`>QQ+iSMjS%m754GLhkW zxrfBlUt&l2^54XQf$~^chy>2rAjLIpX&${R@gNR{+8>FST`fsI?#T$AZFll-dLMKr za%KF-k0$FxMCRQ{qjGTH6uS%aDKYcPv5&dW9$Z-@!HYt8A7-Zs+;rZL4}6 zPtP%YOkYyqKeckcpq0z&PiK|gTs`SSudbg~(6SujnqfcX_;jvB=HS0rX-d7l2hKnH z%Uq+Ef7K_H=~V+Ure%_Zh>wR5$@^6$y~lv-SE3%xUXp<_@xxq7lP z(PL;G>B2q)TC~*`W?;0I@gAqy-i;$e_*a5`@W_1kiKy9S_x?i@G#9&vgi~30p~1l&!O!jB0JQwL?X>B5${~po|MyWVg({D3 z6Xc9p*8FK$J*wK~f{;e`UbW$gizbiHXT=B zwYe1Z_JgMHwHq7vqu*Zgxx@BnjN*y7b>mUE1bHTL1nB&)`t5>!eAE5*?l04V13yKgcE!5&pJp;IVP_{szaJ;_J9TEn1;6Pb zlnu;Lu@K2XDzQOTZURP?K_;T`j9@^rBqB9&W(wnWJ4kpYLj_12;e6>^TucA_MC^aY zDW=$*xx5U!4QDg=%ARu|Km_CKPA2b;Auy&fI~SPf{JBh- zlgJXtctflo&Vxp%e21ZtLCeS;w;rqV^*D-kG>0$94K}1>Z@F^K5d72JU;m3gsfgdR z3AK*^p}pJLFujgLVrYp8qx7j))5z{LU!6mQ`G@Kb^RN8m{$7ATc_gRT-LX5ZP7esF zHONh})^Fvl^`NBx)r*-ZF%UlRW~P5cmVgEdq-wm(qu=N7L6{*LxVGQVOE#LqVhhG|3{U*>m^YI~uGpS> zilW{SB7A$UJ>=r&=l@!lyl~+{E98cbwFh)`9UaqizP$ArZnCfJkAc{cojUVP=2Kig zEGE`EMi(z$%u{z&DdF)Ylv^?uiR5SagQ#Z%(f>kbbKMj5Lf{gn3~v)fM<+mLtSel8xb@@NibZar9p_a?+@dJtUAw>AzZFQfl5?VMBEUdIaKQX zVDLaH|L|}=z*t*-pW}D>F?B2r3$Vn63 zS^Ito?;+32tz^>GOJ8NJ;KOTzGI*+#y1RQ0%6wu~aL=aESJ4yaCY!J0pt6d}iFKyf zEcHW*QnS`xH;j;)t#+1=W$Wh6?^_fufh&A?FF%2hw?07AxFS?CFLL1lN@^@BWLI0k zOU|0qlaREA4UaZ@0zyS`xv{rn`Qg1M8J;}$txe9hQf`v!4h7A0;=U*B5zMhjsutXg za@I(i(tvN#!2`4y*$3W$p0qa*^1{d83vhI-sn;z39^rc>cl2w8opc_S7@9q_soWmy zg<9oB*~NpFGD}B9C*F#7J-f(3Knbu7e7==_iA^NV5}yYKx<@=GN4iHl6L0rD7I?Lx zTKd5WY6Y#MvcvL0K%)XY_y#B27Ju(MFjjEFNqaZyo+=faIkxNFR)x1$Ijg)PE)Qj8 zs&%_&H9yndcYa>tiTw9bVi!vW&O1G9R61V$CamTqL-d=thq}19_^EGpUS|;^wxej> zk)1}1Q^Z(zIrOW}oZ}b5pd88!zK~CM=+w?0X>sd5&tqfPK6~MR*8N7`Hjg3v-F8a} zQEOW}k;z&8Ovq74(R(zAxWAK*-6{?#!M2H^!;=n4dnlW449gA#Rn{NSF<4xd&9Q*^ zM|L-~4o(~i+h1`M#*{uXZBT-Xnwr2PpFQDb(q>9>BW$wQu9Y+3(xYbBFcsKiY6lpXR*_=K`|Pile7+FY za(Jje0ipoCF8ePYbhUcWf$(-}By1QZ@U6B`v8>$oKIyvHWkZ`P#pn2GRvuHY&-Kie z`SRL}-i`r4D7<>LY5rtxmPdV>Wq<)x0frSl2Nj7Y2v z`vD4y9b03rA>rY_{*8mN?)PrXBjx5Ke$nP9+BZUMcDl9R)R9yP|J?GMhHudU7nQ~V zRdLOTka_-*^)BWX7LTU0nHR{RE(baN9xOZo&i#Sn&A2 z+i<&Mytb{Tj`~(`n());pyjKsLo?&j?tTLO?Vq|W%qH>Zr-Z2HYUhLC+T7Y8;48gw zWzV`D_7T02_Jsi0x+3|jkadADFycl&pq(C{rXP&M^a z<_xzblx&TGs4tJ@~CQy28WUfZnpD8m3q%%3i1$}8-4?9FeUE!+1Ss6khOgdHUF&S_THz zv*#`QV`5C>)LRa~@;$?ux(G!B%rV!niCCyY@L(3Jn<%yK46lr94Q56JCbwxrvn&U4 z4(Z2AIZK~EPh$7z^BN8xp%&fn^ApHLI1{7O5~n}&43Q-%rclH47)}{ZoE%Lg@_7v~ zm9eglQlqQOP~3+O5FtM(xYQF|Fvv7KxjEZO-^M1vy~~(Cg*qEDRG5CUec#xV*|PJcXN^3FOL(+LBIGHgL^W*AHHR-p$Vy&xWqV%iz>!Of4R<%lW@RXhb%}oM}TljB76$u zz30)t&{bD{j-xXwc1m>#>!q5N*|@>MAl<2#LMQLsWBT%+guJkE!+J|WSBdnKEG@f{ zUA>~wc<6WxGllB4+OvWJT}{m@jCi4-vIdW9$6E>_WFH3MpExt$SU*tC(<6x%?s2un zTH_+VBq{gNlZ*?QQr#ysJOOsrt-!z~-*Td(ivYwdS~iWEykkmZXV@A8HAzSEvD`&e zR#p}^Q{Ch{MDu{&HnFKv8nam$?YkAP7BC;0H zBNFf}j*pK|gHknZy3a-xW=fy}Pe(*Vphgih*SMMKgjq&_^S} z(D8E+YTPw3i|K3w@#`r2+_}3ahF|4}G-u`UlI_qS@8pyLq(WCuFBn@{fpSGwI4=&p z@6}U>lH$bBr?ve%uka&VhTZOJff*EK&T;(iF75R)B5{(yU2Z^ta`O`okMk7X) z+U#(~!-=G{afioC(EB+vSqUB$4RZWe&@7Yf^pvYMS_LEGusxE*m;Bznd(T^u?>79% zmsPp58sbC#fkvhcE5`{C^~ku%w70LCmEc*@e37{0;OrlHPs~4(=Yxt^pX!Xg`H>~n z>RZFJudj7c@Gj}6{+-Bs1D}O+@L%1RH;*pxu3A`VC0)$lw)3I@qqg50*mMsTdel)! zvJF{kN`{Yj|2>;8351b`@sUaRmLPHHu8`^_H68VCm@$|oifey^a+9Za&VTdbo7#^iTLnkp4_5+oNnv3h&YAd# zh`*Fxpqh7v`HGb-{3kc?p-W4>s@nuXN% z=jW(qPJ<2n)9pgNzI<`kPcqD#IEih;Dowy_NrBYr55egiui5O4Po8Wi2iy#%2iWzuV*?Ddtglg{6+fz2TgPMP zS2ogUbVsY1KUNa{-Ex(iNjlovCWv%-tz)C3B&2C;YGRAy@0bwp8JahU{cbwEF*p8O zc;HYb^PMlH(kL!2k4en*tefYCqs^E=`SY3bh|_CI5LZyuH$?3AQQ-5#YlU}`4G4f_ z^#2J96K`Nf#KV}F=eO4DZoHA|gt!|QAAgM8lKDBS&}QT&nk4VfUv$H62MKE4v=oSl zA=4{;4O~kM_JO2ZUlQ~z2klh?xV-+I`JkTnvbwrE!bb#FF1N0%?AanAK?|30dkDrd zf-`~SpPXYps6!VmT2xO`T_D6j{?F7A6(ra^(4SUhFY`0(Dt1MedoG_}2pFYQA{Od4 z(vyZnmEIZQx|3P`^e<1k3ippSc9p63jz2%Wbnwl8lL$t*S)om literal 0 HcmV?d00001 diff --git a/src/~10.md b/src/~10.md index 43f0ffb..3121e7d 100644 --- a/src/~10.md +++ b/src/~10.md @@ -1,3 +1,5 @@ +$\newcommand{\d}{\text{d}}$ + ## ~10.1 导数的计算和应用 - **例 ~10.1.1**:设 $a\in\mathbb R$ 是常数。在各自函数的定义域中: @@ -12,20 +14,46 @@ 5. $(e^x)'=e^x,(\ln x)'=\frac{1}{x}$。 - 6. $(\sin x)'=\cos x,(\cos x)'=-\sin x,(\tan x)'=\frac{1}{\cos^2 x}$。 + 6. $$ + \begin{aligned} + (\sin x)'&=\cos x\\ + (\cos x)'&=-\sin x\\ + (\tan x)'&=\frac{1}{\cos^2 x}=1+\tan^2x\\ + (\csc x)'&=-\frac{\cos x}{\sin^2x}=-\cot x\csc x\\ + (\sec x)'&=\frac{\sin x}{\cos^2x}=\tan x\sec x\\ + (\cot x)'&=-\frac{1}{\sin^2 x}=-1-\cot^2x + \end{aligned} + $$ **证明**:$\lim\limits_{h\to 0}\frac{\sin(x+h)-\sin x}{h}=\lim\limits_{h\to 0}\frac{\sin x(\cos h-1)+\cos x\sin h}{h}=\sin x\lim\limits_{h\to 0}\frac{\cos h-1}{h}+\cos x\lim\limits_{h\to 0}\frac{\sin h}{h}=\cos x$; $(\cos x)'=(\sin(\frac{\pi}2-x))'=-\cos(\frac\pi2-x)=-\sin x$; - $(\tan x)'=(\frac{\sin x}{\cos x})'=\frac{\cos^2x+\sin^2x}{\cos^2 x}=\frac 1{\cos^2x}$。 + $(\tan x)'=(\frac{\sin x}{\cos x})'=\frac{\cos^2x+\sin^2x}{\cos^2 x}=\frac 1{\cos^2x}$; - 7. $(\arcsin x)'=\frac{1}{\sqrt{1-x^2}},(\arccos x)'=-\frac{1}{\sqrt{1-x^2}},(\arctan x)'=\frac{1}{1+x^2}$。 + $(\csc x)'=(\frac{1}{\sin x})'=-\frac{\cos x}{\sin^2x}=-\cot x\csc x$; + + $(\sec x)'=(\frac{1}{\cos x})'=\frac{\sin x}{\cos^2x}=\tan x\sec x$; + + $(\cot x)'=(\frac{\cos x}{\sin x})'=\frac{-\sin^2 x-\cos^2 x}{\sin^2 x}=-\frac{1}{\sin^2 x}$。 + + 7. $$ + \begin{aligned} + (\arcsin x)'&=\frac{1}{\sqrt{1-x^2}}\\ + (\arccos x)'&=-\frac{1}{\sqrt{1-x^2}}\\ + (\arctan x)'&=\frac{1}{1+x^2}\\ + (\operatorname{arccsc} x)'&=-\frac{1}{\sqrt{1-\frac{1}{x^2}}x^2}\\ + (\operatorname{arcsec} x)'&=\frac{1}{\sqrt{1-\frac1{x^2}}x^2}\\ + (\operatorname{arccot} x)'&=-\frac{1}{1+x^2}\\ + \end{aligned} + $$ **证明**:$(\arcsin x)'=\frac{1}{\cos(\arcsin x)}=\frac{1}{\sqrt{1-\sin^2(\arcsin x)}}=\frac{1}{\sqrt{1-x^2}}$;$\arccos$ 同理; - $(\arctan x)'=\cos^2(\arctan x)=\frac{\cos^2(\arctan x)}{\cos^2(\arctan x)+\sin^2(\arctan x)}=\frac{1}{1+x^2}$。 - + $(\arctan x)'=\cos^2(\arctan x)=\frac{\cos^2(\arctan x)}{\cos^2(\arctan x)+\sin^2(\arctan x)}=\frac{1}{1+x^2}$; + + 对于后三者,根据引理 ~9.1.6.4,使用复合函数求导法则即可。 + - **例 ~10.1.2**:设 $a\in\mathbb R$,讨论由 $f(x):=(1+\frac 1x)^{x+a}$ 定义的函数 $f:(-\infty,-1)\cup (0,+\infty)\to\mathbb R$ 的单调性。 **解**:当 $x>0$ 时,$(1+\frac{1}{1-x})^{(1-x)+a}=(1+\frac{1}{x})^{x+1-a}$,所以 $(1+\frac 1x)^{x+a}$ 在 $(-\infty,-1)$ 上的图像与 $(1+\frac 1x)^{x+1-a}$ 在 $(0,+\infty)$ 上的图像是关于 $x=-\frac12$ 对称的。所以下面我们只考虑 $f$ 的定义域为 $(0,+\infty)$ 的情况。 @@ -73,6 +101,241 @@ $\arcsin x=x+\frac{x^3}{6}+\cdots+\frac{(2n-1)!!x^{2n+1}}{(2n)!!(2n+1)}+o(x^{2n+2})$,其中 $(2n)!!=\prod_{i=1}^n2i$,$(2n-1)!!=\prod_{i=1}^n(2i-1)$。 + +很多时候,在计算一点处的泰勒公式时,我们不采取逐次求导的方式,而是利用初等函数已知的展开先将该函数展开,再根据泰勒公式所证明的多项式展开的唯一性,说明得到的展开就是该点的泰勒展开。 + - **例 ~10.2.2**:设序列 $(x_n)_{n=0}^{\infty}$ 满足 $x_{n+1}=\sin x_n$。求 $n\to+\infty$ 时,$x_n$ 的渐近展开式。 - **解**: \ No newline at end of file + **解**:首先考虑计算 $(x_n)_{n=0}^{\infty}$ 的极限。由 $\sin|x|\leq |x|$ 知 $|x_n|$ 是单调不增的,那么 $(|x_n|)_{n=0}^{\infty}$ 收敛。设其收敛到 $L$,那么对同一个数列 $(x_{n+1})_{n=0}^{\infty}$ 和 $(\sin x_n)_{n=0}^{\infty}$ 的两种形式分别取极限,得 $L=\sin L$,于是 $L=0$。从而 $(x_n)_{n=0}^{\infty}$ 也收敛到 $0$。 + + 接下来我们猜测 $x_n$ 不是任意阶小的,且其渐近展开是 $x_n=\frac{A}{n^{a}}+o(\frac{1}{n^{a}}),n\to+\infty$($0 x$ 有 $g'_x(y)<0$,从而 $g_x(y)$ 在 $[x,+\infty)$ 上严格单调减。而 $g_x(x)=x^2\geq 0$,从而 $g_x(y)$ 在 $[x,+\infty)$ 存在唯一零点。 + + 2. $f\in\mathscr C^{\infty}(\mathbb R)$。 + + **证明**:先证明 $f$ 连续。设 $x_0\in\mathbb R$,$y_0=f(x_0)$。 + + 先不妨设 $x_0\neq 0$,那么 $y_0>x_0$,从而可以设 $0<\varepsilon0$。 + + 存在 $\delta>0$,使得 $[x_0-\delta,x_0+\delta]\subseteq V_1,V_2$ 且矩形 $[x_0-\delta,x_0+\delta]\times[y_0-\varepsilon,y_0+\varepsilon]$ 在 $y=x$ 上方,那么易证对任意 $x\in [x_0-\delta,x_0+\delta]$ 有 $f(x)\in[y_0-\varepsilon,y_0+\varepsilon]$。从而 $f$ 在 $x_0$ 处连续。 + + 对 $x_0=0$ 的情况,不需要考虑 $y_0-\varepsilon$ 那条界。 + + 再证明 $f$ 可微。设 $x\in\mathbb R$,记 $f(x+h)=f(x)+p(h)$,那么当 $h\to 0$ 时,$p(h)\to 0$,且: + + $$ + \begin{aligned} + 0&=(x+h)(f(x)+p(h))+e^{x+h}-e^{f(x)+p(h)}\\ + &=xf(x)+e^x-e^{f(x)}+hf(x)+(x+h)p(h)+e^{x}(e^h-1)-e^{f(x)}(e^{p(h)}-1)\\ + &=hf(x)+(x+h)p(h)+e^{x}(e^h-1)-e^{f(x)}(e^{p(h)}-1)\\ + &=hf(x)+(x+h)p(h)+e^x(h+o(h))-e^{f(x)}(p(h)+o(p(h)))\\ + (e^{f(x)}-x)p(h)&=(f(x)+e^x)h+o(h)+o(p(h))\\ + \end{aligned} + $$ + + 存在 $q(h)=o(p(h))$ 使得 $(e^{f(x)}-x)p(h)-q(h)=(f(x)+e^x)h+o(h)$,同时可知 $(e^{f(x)}-x)p(h)-q(h)=(e^{f(x)}-x)p(h)+o(p(h))$。那么根据引理 9.11.12,可得 $(e^{f(x)}-x)p(h)=(f(x)+e^x)h+o(h)$。 + + 同时可知 $e^{f(x)}-x=e^x+xf(x)-x\geq e^x-x+x^2>0$,从而 $p(h)=\frac{f(x)+e^x}{e^{f(x)}-x}h+o(h)$。 + + 再证明 $f\in\mathscr C^{\infty}(\mathbb R)$。我们知道: + + $$ + f'(x)=\frac{f(x)+e^x}{e^{f(x)}-x} + $$ + + 所以容易用归纳法证明 $f$ 是任意阶可微的。 + + 3. 讨论 $f$ 的单调性。 + + **解**:设 $x\in\mathbb R$ 使得 $f'(x)=0$,$y=f(x)$,等价于: + + $$ + \begin{cases}xy+e^x-e^y=0\\y+e^x=0\\y\geq x\end{cases} + $$ + + 等价于 $y\ln(-y)-y-e^y=0$(可以注意到当 $x<0$ 时恒有 $g_x'(y)<0$,于是 $y\geq x$ 的限制可以略去)。 + + 若 $y<1$,那么 $y\ln(-y)-y-e^y\leq (y-1)\ln(-y)-e^y<0$,矛盾。 + + 记 $s(y):=y\ln(-y)-y-e^y$。由于: + + $$ + s(-1)=1-e^{-1}>0\\ + \lim_{y\to0^-}s(y)=\lim_{y\to0^+}y-\ln y^y-e^{-y}=-1<0 + $$ + + 于是存在唯一的 $y\in(-1,0)$ 满足条件,记 $\xi=\ln(-y)<0$,那么 $f'(\xi)=0$。 + + 对于 $x<0$,由于 $g_x(0)=e^x-1<0$,所以 $f(x)<0$,$00$。由于 $\lim\limits_{x\to+\infty}g_x(x+\varepsilon)=\lim\limits_{x\to+\infty}x(x+\varepsilon)+e^x-e^{x+\varepsilon}=\lim\limits_{x\to+\infty}x^2+\varepsilon x-e^x(e^{\varepsilon}-1)=-\infty$。从而当 $x\to+\infty$ 时,$x\leq f(x)< x+\varepsilon$。那么容易证明 $f$ 在 $x\to+\infty$ 时的渐近线是 $y=x$。 + +## ~10.3 不定积分的计算 + +- **例 ~10.3.1**:换元法的应用。 + + 换元的时候,为了方便观察、避免写错,一般会形式上地添加一步:$\int g(F(x))f(x)\d x=\int g(F(x))\d F(x)=(\int g(y)\d y)|_{y=F(x)}$、以及 $\int g(y)\d y=(\int g(F(x))\d F(x))|_{x=F^{-1}(y)}=(\int g(F(x))f(x)\d x)|_{x=F^{-1}(y)}$。 + + 1. 求 $\int \frac{x}{1+x^2}\d x$。 + + **解**:凑微分: + + $$ + \int \frac{x}{1+x^2}\d x=\frac{1}{2}\int\frac{1}{1+x^2}\d(1+x^2)\overset{y=1+x^2}{=}\frac{1}{2}\int\frac{1}{y}\d y=\frac12\ln|y|+C=\frac12\ln(1+x^2)+C + $$ + + 2. 求 $\int \sin^nx\cos^mx\d x$,其中 $m,n$ 是整数,且其中至少一个是奇数。 + + **解**:不妨设 $m$ 为奇数,后面可以看到 $n$ 为奇数也是同理的。凑微分: + + $$ + \int \sin^nx\cos^mx=\int \sin^{n}x\cos^{m-1}x\d\sin x=\int\sin^nx(1-\sin^2)^{\frac{m-1}{2}}\d\sin x\overset{y=\sin x}{=}\int y^n(1-y^2)^{\frac{m-1}{2}}\d y + $$ + + 转化为有理分式的不定积分。 + + 3. 求 $\int \sin^{2n}x\cos^{2m}x\d x$,其中 $m,n$ 是整数。 + + **解**:凑微分: + + $$ + \begin{aligned} + \int \sin^{2n}x\cos^{2m}\d x&=\int \frac{\sin^{2n}x\cos^{2m+2}}{\cos^2x}\d x\\ + &=\int\sin^{2n}x\cos^{2m+2}x\d\tan x\\ + &=\int\frac{\left(1-\frac{1}{\tan^2x+1}\right)^n}{\left(1+\tan^2x\right)^{m+1}}\d\tan x\\ + &\overset{y=\tan x}{=}\int\frac{(1-\frac{1}{y^2+1})^n}{(1+y^2)^{m+1}}\d y + \end{aligned} + $$ + + 转化为有理分式的不定积分。 + + 4. 求 $\int\sqrt{1-x^2}\d x$。 + + **解**:主动换元: + + $$ + \begin{aligned} + \int\sqrt{1-x^2}\d x\overset{x=\sin y}{=}\int\sqrt{1-\sin^2y}\cos y\d y=\int \cos^2y\d y=\int\frac{1+\cos 2y}{2}\d y\overset{z=2y}{=}\int\frac{1+\cos z}{4}\d z\\ + =\frac14(z+\sin z)+C=\frac14(2y+\sin 2y)+C=\frac 12(y+\sin y\cos y)+C=\frac 12(\arcsin x+x\sqrt{1-x^2})+C + \end{aligned} + $$ + + 5. 求 $\int\tan^nx\d x$。 + + **解**:主动换元: + + $$ + \int \tan^nx\d x\overset{x=\arctan y}{=}\int \frac{y^n}{1+y^2}\d y + $$ + + 转化为有理分式的不定积分。 + +- **例 ~10.3.2**:分部积分的应用。 + + 分部积分同样有形式上的直观中间过程:$\int F(x)g(x)\d x=\int F(x)\d G(x)=F(x)G(x)-\int G(x)\d F(x)=F(x)G(x)-\int G(x)f(x)\d x$。 + + 1. 设 $P(x)$ 是多项式。求 $\int P(x)e^{\lambda x}\d x$($\lambda\neq 0$)和 $\int P(x)\sin x\d x$。 + + **解**:应用分部积分 $\int P(x)e^{\lambda x}\d x=P(x)\frac{e^{\lambda x}}{\lambda}-\int P'(x)\frac{e^{\lambda x}}{\lambda}\d x$ 将 $P$ 降幂,那么可以预见到,一定存在一个次数不超过 $P$ 的多项式 $Q$,使得 $\int P(x)e^{\lambda x}\d x=Q(x)e^{\lambda x}+C$。从而可以将 $Q$ 待定系数,然后对右侧求导并与左侧比较(应该得到形如 $P_i=(i+1)Q_{i+1}+\lambda Q_i$ 的方程),从而解出 $Q$ 的系数。 + + 对 $\int P(x)\sin x\d x$ 也能用类似的方法,此时待定系数后遇到的方程可能形如 $P(x)\sin x=Q(x)\sin x+H(x)\cos x$。取 $x=2k\pi$,总能得到 $H(2k\pi)=0$,于是多项式 $H$ 有无限个零点,从而 $H$ 只能为 $0$。那么就两侧消去 $\sin x$ 解 $P(x)=Q(x)$ 即可(如果觉得 $\sin x=0$ 时除法不严谨的话,可以变为 $(P(x)-Q(x))\sin x=0$,然后再用类似的方法得到 $P(x)-Q(x)$ 有无限个零点,从而 $P(x)=Q(x)$)。 + + 2. 求 $\int e^x\sin^nx\d x$。 + + **解**:应用分部积分: + + $$ + \begin{aligned} + \int e^x\sin^nx\d x&=e^x\sin^nx-n\int e^x\sin^{n-1}x\cos x\d x\\ + &=e^x\sin^nx-n\left(e^x\sin^{n-1}x\cos x-\int e^x\big((n-1)\sin^{n-2}x-n\sin^nx\big)\d x\right)\\ + &=e^x(\sin^nx-n\sin^{n-1}x\cos x)+n(n-1)\int e^x\sin^{n-2}x\d x-n^2\int e^x\sin^n x\d x\\ + (n^2+1)\int e^x\sin^nx\d x&=e^x(\sin^nx-n\sin^{n-1}x\cos x)+n(n-1)\int e^x\sin^{n-2}x\d x+0\int e^x\sin^n x\d x\\ + (n^2+1)\int e^x\sin^nx\d x&=e^x(\sin^nx-n\sin^{n-1}x\cos x)+n(n-1)\int e^x\sin^{n-2}x\d x+C\\ + (n^2+1)\int e^x\sin^nx\d x&=e^x(\sin^nx-n\sin^{n-1}x\cos x)+n(n-1)\int e^x\sin^{n-2}x\d x\\ + \int e^x\sin^n x\d x&=\frac{1}{n^2+1}\left(e^x(\sin^nx-n\sin^{n-1}x\cos x)+n(n-1)\int e^x\sin^{n-2}x\d x\right) + \end{aligned} + $$ + +- **例 ~10.3.3**:有理分式不定积分的应用。 + + 1. 三角有理分式的积分。 + + 求 $\int R(\cos\theta,\sin\theta)\d\theta$,其中 $R(x,y)$ 是关于 $x,y$ 的有理分式,$\theta\in(-\pi,\pi)$,那么可以使用万能公式 $\begin{cases}\cos\theta=\frac{1-t^2}{1+t^2}\\\sin \theta=\frac{2t}{1+t^2}\end{cases}$: + + $$ + \int R(\cos \theta,\sin\theta)\d\theta\overset{t=\tan\frac{\theta}{2}}{=}\int R\left(\frac{1-t^2}{1+t^2},\frac{2t}{1+t^2}\right)\d2\arctan t=2\int R\left(\frac{1-t^2}{1+t^2},\frac{2t}{1+t^2}\right)\frac{1}{1+t^2}\d t + $$ + + 特别地,对于 $\int R(\tan\theta)\d\theta$,可以直接换元: + + $$ + \int R(\tan \theta)\d \theta\overset{t=\tan \theta}{=}\int R(t)\d\arctan t=\int R(t)\frac{1}{1+t^2}\d t + $$ + + 都是转化为有理函数的不定积分。 + + 需要注意的是,这里我们没有对 $\theta$ 的取值范围作出限制,但是换元时我们却把 $R(\tan \theta)$ 当成了 $(-\frac\pi2,\frac\pi2)$ 上的函数。这是因为 $R(\tan \theta)$ 是以 $\pi$ 为周期的函数,而且换元后恰好还需要把 $t=\tan\theta$ 代回,所以直接用代回结果就确实是真正的 $R(\tan\theta)$ 的积分(注意此时 $\arctan(\tan \theta)\neq \theta$,因为 $\theta$ 可能在 $(-\frac\pi2,\frac\pi2)$ 外)。 + + 类似地,对于上面的 $R(\cos\theta,\sin\theta)$,若把 $\theta$ 的定义域改为 $\mathbb R\setminus\{(2k+1)\pi:k\in\mathbb Z\}$,也是可以正常用万能公式换元的,因为 $\cos\theta,\sin\theta$ 都能换成 $\tan\frac{\theta}{2}$ 的恒等表示,然后转为 $R(\tan\frac{\theta}{2})$ 变为上一段的类似讨论。 + + 1. 求 $\int R(x,\sqrt{1-x^2})\d x$。 + + **解**: + + $$ + \int R(x,\sqrt{1-x^2})\d x\overset{x=\sin \theta}{=}\int R(\sin\theta,\cos\theta)\d\sin\theta=\int R(\cos\theta,\sin\theta)\cos\theta\d\theta + $$ + + 这里 $\theta$ 的取值范围取为 $[-\frac\pi2,\frac\pi2]$,从而确实有 $\cos\theta=\sqrt{1-\sin^2\theta}$。 + + 转化为三角有理分式的不定积分。 + +基于上述例子,可以看到,在不定积分中,可以任意将被积变元进行换元,只需保证能通过新的变元反推出原来的变元即可。而且不论是换元、还是分部积分,都有着形式上非常 “合理” 且符合直觉的中间过程。这些的正确性确实被我们证明了,但其实很难不使人相信,其中有着非常简单明了的解释,只不过目前我们还未挖掘出来,因为这涉及到莱布尼茨记号的含义。 + +//实际上,可以定义 $\int \d f(x)=f(x)$,从而我们要做的只是对 $\int$ 后面的式子做恒等变换,变成 $\d f(x)$ 的形式。 \ No newline at end of file diff --git a/src/~7.md b/src/~7.md index 391748f..953b7cc 100644 --- a/src/~7.md +++ b/src/~7.md @@ -68,51 +68,40 @@ 3. $\sin 0=\sin \pi=\cos\frac{\pi}{2}=0$。 - 4. 设 $x\in\mathbb R$,那么: + 4. (诱导公式)设 $x\in\mathbb R$,那么: $$ \begin{aligned} \cos(-x)=\cos x,\quad\cos \left(\frac \pi2+x\right)=-\sin x,\quad\cos(\pi+x)=-\cos x,\quad\cos(2\pi+x)=\cos x\\ \sin(-x)=-\sin x,\quad\sin\left(\frac \pi 2+x\right)=\cos x,\quad\sin(\pi+x)=-\sin x,\quad\sin(2\pi+x)=\sin x \end{aligned} $$ - - 5. 设 $x,y\in\mathbb R$,那么: +从而 $\cos$ 是偶函数,$\sin$ 是奇函数。 + + 5. (和差角公式)设 $x,y\in\mathbb R$,那么: $$ \begin{aligned} \cos(x+y)&=\cos x\cos y-\sin x\sin y\\ \sin(x+y)&=\sin x\cos y+\cos x\sin y\\ - \sin x-\sin y&=2\sin \frac{x-y}{2}\cos\frac{x+y}{2}\\ - \cos x-\cos y&=-2\sin\frac{x-y}{2}\sin\frac{x+y}{2} \end{aligned} $$ - - 6. 设 $x\in\mathbb R$,那么: - $$ - \begin{aligned} - \sin 2x&=2\sin x\cos x\\ - \cos 2x&=\cos^2x-\sin^2x=2\cos^2x-1=1-2\sin^2x\\ - \sin 3x&=3\sin x-4\sin^3x\\ - \cos 3x&=4\cos^3x-3\cos x - \end{aligned} - $$ - + 7. 设 $x\in\mathbb R$ 满足 $00$,求 $\lim\limits_{x\to+\infty}x^{\frac 1{x^k}}$。 diff --git a/src/第10章 函数的微分.md b/src/第10章 函数的微分.md index 9530898..25878a8 100644 --- a/src/第10章 函数的微分.md +++ b/src/第10章 函数的微分.md @@ -1,4 +1,4 @@ -$\renewcommand{\overgroup}[1]{\overparen{#1}}$ +$\renewcommand{\overgroup}[1]{\overparen{#1}}\newcommand{\d}{\text{d}}$ ## 10.1 基本定义 @@ -297,6 +297,8 @@ $\renewcommand{\overgroup}[1]{\overparen{#1}}$ 注意,两个具有相同泰勒多项式的函数不一定相等。最典型的例子就是两个函数都比任意 $h^n$ 阶小,但一者可能恒为 $0$,一者可能是指数级趋向于 $0$ 的,比如由 $f(x):=\begin{cases}e^{-\frac{1}{x}}&x\neq 0\\0&x=0\end{cases}$ 定义的函数 $f:\mathbb R\to\mathbb R$ 在 $0$ 处的任意阶泰勒多项式都是恒零。那么对任意的函数 $g$,可以证明 $g$ 与 $g(1+f)$ 在 $0$ 处具有相同的泰勒多项式,从而这种情况是普遍存在的。 +还要注意的是,若没有高阶可微性的假设,那么即使 $f$ 在 $x_0$ 处有 $n$ 阶多项式逼近,也不意味着 $f$ 在 $x_0$ 处 $n$ 阶可微。例如由 $f(x):=\begin{cases}e^{-\frac{1}{x}}&x\in\mathbb R\setminus \mathbb Q\\0&x\in\mathbb Q\end{cases}$ 定义的函数 $f:\mathbb R\to\mathbb R$ 在 $0$ 处有任意阶多项式逼近 $f(x)=o(x^n),x\to 0$,但是 $f$ 在 $0$ 处没有二阶导数,因为 $f$ 只在 $0$ 处有一阶导数,没有一阶导函数。 + - **定理 10.6.6(泰勒公式-拉格朗日余项)**:设 $I\subseteq\mathbb R$ 是区间,$x_0\in I$,$n\in\mathbb N$,$f:I\to\mathbb R$ 是 $n+1$ 阶可微的函数。那么对于任意 $x \in I$ 且 $x\neq x_0$,都存在严格介于 $x_0,x$ 之间的 $\xi$ 使得 $f(x)=Tf_{x_0,n}(x-x_0)+\frac{f^{(n+1)}(\xi)}{(n+1)!}(x-x_0)^{n+1}$。 **证明**:不妨设 $x_00$ 使得对于任意 $|z|>R$ 有 $|A(z)|>|A(z_0)|$。考虑由 $z\mapsto |A(z)|$ 定义的 $\{z\in\mathbb C:|z|\leq R\}\to\mathbb R$ 的函数,由于是 “有界闭集” 上的连续函数,所以一定存在最小值点 $z_1$,那么对任意 $z\in\mathbb C$ 有 $|A(z)|\geq |A(z_1)|$。然后考虑设多项式 $B(z)=A(z+z_0)=b_0+b_1z+\cdots+b_{n-1}z^{n-1}+b_nz^n$(其中 $b_n=1$),从而对任意 $z\in\mathbb C$ 有 $|B(z)|\geq |B(0)|=|b_0|$。若 $b_0\neq 0$,找到最小的 $m\in \mathbb N^+$ 使得 $b_m\neq 0$,那么 $B(z)=b_0+b_mz^m(1+o(1)),z\to 0$,而 $b_0+b_mz^m$ 的含义是 $z$ 旋转 $m$ 倍再乘上一个系数加到 $b_0$ 上,从而当 $z$ 取遍 $0$ 附近的一个很小的圆时,$B(z)$ 也取遍 $b_0$ 附近的一个很小的圆,那么一定会存在 $z$ 使得 $|B(z)|<|b_0|$,矛盾。 + +- **引理 10.8.11**:设 $A(z)$ 是 $\mathbb C$ 上的次数为正的多项式,$z\in\mathbb C$ 使得 $A(z)=0$,那么 $A(\overline z)=0$。 + +接下来我们给出有理函数的不定积分定理,其中会不加证明地运用一些和有理函数展开有关的结论。 + +- **定理 10.8.12(有理函数的不定积分)**:设 $P(x),Q(x)$ 是 $\mathbb R$ 上的多项式且 $Q(x)\neq 0$,$\deg P<\deg Q$。 + + 不加证明地,能将 $Q(x)$ 展开为 $Q(x)=d(x-a_1)^{n_1}\cdots(x-a_A)^{n_A}((x-b_1)^2+c_1^2)^{m_1}\cdots((x-b_B)^2+c_B^2)^{m_B}$,其中 $d\neq 0$,$A,B\in\mathbb N$,$n_i,m_i\in\mathbb N^+$,$a_i\in\mathbb R$ 互不相同,$b_i\in\mathbb R,c_i\in\mathbb R\setminus\{0\}$ 且 $(b_i,c_i)$ 互不相同。 + + 那么,$\int\frac{P(x)}{Q(x)}$ 是下列函数的线性组合再加上任意常数: + + $$ + \begin{aligned} + &\ln|x-a_1|,\frac{1}{x-a_1},\cdots,\frac{1}{(x-a_1)^{n_1-1}},&&\ln|x-a_2|,\cdots\\ + &\arctan\frac{x-b_1}{c_1},\frac{1}{(x-b_1)^2+c_1^2},\cdots,\frac{1}{((x-b_1)^2+c_1^2)^{m_1-1}},&&\arctan\frac{x-b_2}{c_2},\cdots\\ + &\ln |(x-b_1)^2+c_1^2|,\frac{x}{(x-b_1)^2+c_1^2},\cdots,\frac{x}{((x-b_1)^2+c_1^2)^{m_1-1}},&&\ln |(x-b_2)^2+c_2^2|,\cdots\\ + \end{aligned} + $$ + + **证明**:不加证明地,$\frac{P(x)}{Q(x)}$ 是下列函数的线性组合: + + $$ + \begin{aligned} + &\frac{1}{x-a_1},\cdots,\frac{1}{(x-a_1)^{n_1}},&&\frac{1}{x-a_2},\cdots\\ + &\frac{1}{(x-b_1)^2+c_1^2},\cdots,\frac{1}{((x-b_1)^2+c_1^2)^{m_1}},&&\frac{1}{(x-b_2)^2+c_2^2},\cdots\\ + &\frac{x}{(x-b_1)^2+c_1^2},\cdots,\frac{x}{((x-b_1)^2+c_1^2)^{m_1}},&&\frac{x}{(x-b_2)^2+c_2^2},\cdots + \end{aligned} + $$ + + 接着只需研究上述每项的不定积分形式: + + 1. $$ + \int\frac{1}{(x-a)^n}\d x\overset{y=x-a}{=}\int\frac{1}{y^n}\d y + $$ + + 2. $$ + \int\frac{x}{(x^2+1)^n}\d x\overset{y=x^2+1}{=}\frac{1}{2}\int\frac{1}{y^n}\d y + $$ + + 3. $$ + \begin{aligned} + \int\frac{1}{x^2+1}\d x&=\arctan x+C\\ + \int\frac{1}{(x^2+1)^n}\d x&=\int\frac{1}{(x^2+1)^{n-1}}\d x-\int\frac{x^2}{(x^2+1)^n}\d x\\ + &=\int\frac{1}{(x^2+1)^{n-1}}\d x+\frac{1}{2(n-1)}\int\frac{-(n-1)2x}{(x^2+1)^n}x\d x\\ + &=\int\frac{1}{(x^2+1)^{n-1}}\d x+\frac{1}{2(n-1)}\left(\frac{x}{(x^2+1)^{n-1}}-\int\frac{1}{(x^2+1)^{n-1}}\d x\right)\\ + &=\frac{x}{2(n-1)(x^2+1)^{n-1}}+\frac{2n-3}{2n-2}\int\frac{1}{(x^2+1)^{n-1}}\d x\\ + \end{aligned} + $$ + + 所以可以预见到的是,$\int\frac{1}{(x^2+1)^n}\d x$ 一定是 $\frac{x}{(x^2+1)^{n-1}},\cdots,\frac{x}{x^2+1},\arctan x$ 的线性组合再加上任意常数 $C$ 的形式。 + + 4. $$ + \begin{aligned} + \int\frac{1}{((x-a)^2+b^2)^n}\d x&\overset{y=\frac{x-a}{b}}{=}\int\frac{1}{((by)^2+b^2)^n}\d y=\frac{1}{b^{2n}}\int\frac{1}{(y^2+1)^n}\d y\\ + \int\frac{x}{((x-a)^2+b^2)^n}\d x&\overset{y=\frac{x-a}{b}}{=}\int\frac{by+a}{((by)^2+b^2)^n}\d y=\frac{1}{b^{2n-1}}\int\frac{y}{(y^2+1)^n}\d y+\frac{a}{b^{2n}}\int\frac{1}{(y^2+1)^n}\d y + \end{aligned} + $$ + +在真实的应用中,一般会采用待定系数且取特殊值的方式求 $\frac{P(x)}{Q(x)}$ 展开后每一项的系数。 \ No newline at end of file diff --git a/src/第11章 黎曼积分.md b/src/第11章 黎曼积分.md index c1c446c..3550453 100644 --- a/src/第11章 黎曼积分.md +++ b/src/第11章 黎曼积分.md @@ -1,3 +1,5 @@ +$\newcommand{\d}{\text d}$ + ## 11.1 划分 - **定义 11.1.1**:设 $X\subseteq \mathbb R$,称 $X$ 是连通的,当且仅当对于任意 $x,y\in X$ 且 $x0$,存在 $I$ 的划分 $P$,使得 $U(f,P)-L(f,P)<\varepsilon$。 + + **证明**:存在 $I$ 的划分 $P,Q$ 使得 $U(f,P)-L(f,Q)<\varepsilon$,那么 $U(f,P\# Q)-L(f,P\# Q)<\varepsilon$。 + +- **命题 11.3.10**:设 $f:I\to\mathbb R$ 是有界区间 $I$ 上的函数,$S\in\mathbb R$,那么下列命题等价: + + 1. $f$ 在 $I$ 上有界且黎曼可积,且 $\int_If=S$。 + 2. 对任意 $\varepsilon>0$,存在 $\delta>0$,使得对任意 $I$ 的划分 $P$ 满足 $\max_{J\in P}|J|\leq\delta$,以及 $\xi:P\to\mathbb R$ 满足 $\xi_J\in J$(从而 $J$ 非空),都有 $\big|\sum_{J\in P}f(\xi_J)|J|-S\big|<\varepsilon$。 + + **证明**:2->1:若 $f$ 在 $I$ 上无界。存在 $\delta>0$,使得对任意 $I$ 的划分 $P$ 满足 $\max_{J\in P}|J|\leq\delta$,以及 $\xi:P\to\mathbb R$ 满足 $\xi_J\in J$,都有 $\big|\sum_{J\in P}f(\xi_J)|J|-S\big|<1$。那么先任意找一个 $I$ 的划分 $P$ 满足 $\max_{J\in P}|J|\leq\delta$,可证 $f$ 必定在某个 $J\in P$ 上无界,从而可以将 $\big|f(\xi_J)|J|\big|$ 无限放大,而 $\sum_{J'\in P,J\neq J'}f(\xi_{J'})|J'|$ 固定为常数。从而 $\sum_{J'\in P}f(\xi_{J'})|J'|$ 可以是无界的,矛盾。 + + 设 $\varepsilon>0$ 是任意正实数。那么存在 $I$ 的划分 $P$ 以及 $\xi:P\to\mathbb R$ 满足 $\xi(J)\in J$,满足 $f(\xi_J)>\sup_{x\in J} f(x)-\varepsilon$,以及 $\sum_{J\in P}f(\xi_J)|J|2:设 $f$ 有界 $M>0$。设 $\varepsilon>0$ 是任意正实数。根据命题 11.3.9,存在 $I$ 的划分 $P$,使得 $S-\varepsilon0$。设 $I$ 的划分 $Q$ 满足 $\max_{K\in Q}|K|\leq\delta$,以及 $\xi:Q\to\mathbb R$ 满足 $\xi_{K}\in K$。一方面,对任意 $J\in P$,满足 $K\cap J\neq\varnothing$ 且 $K\not\subseteq J$ 的 $K\in Q$ 至多有两个;一方面,任意 $K\in Q$ 必然和某个 $J\in P$ 有非空的交。设 $Q'=\{K\in Q:\text{不存在 }J\in P\text{ 使得 }K\subseteq J\}$,那么 $\operatorname{card}Q'\leq 2\operatorname{card} P$。 + + 存在 $\Phi:Q\setminus Q'\to P$ 使得 $K\subseteq \Phi(K)$ 对任意 $K\in Q\setminus Q'$ 成立。那么: + $$ + \begin{aligned} + \sum_{K\in Q}f(\xi_K)|K|=\sum_{K\in Q'}f(\xi_K)|K|+\sum_{K\in Q\setminus Q'}f(\xi_K)|K|<\sum_{K\in Q' + }M\delta+\sum_{K\in Q\setminus Q'}\sup_{x\in \Phi(K)}f(x)|K|\\ + \leq2\delta\operatorname{card} P+\sum_{J\in P}\sup_{x\in J}f(x)\sum_{K\in Q\setminus Q'}|K|\leq 2\delta\operatorname{card} P+\sum_{J\in P}\sup_{x\in J}f(x)|J|<2\delta\operatorname{card P}+S+\varepsilon + \end{aligned} + $$ + 另一侧同理,那么易得 2。 + ## 11.4 黎曼积分的基本性质 - **定理 11.4.1(黎曼积分算律)**:设 $f:I\to\mathbb R$ 和 $g:I\to\mathbb R$ 都是有界区间 $I$ 上的黎曼可积函数。 @@ -146,6 +189,8 @@ $$ 然后易证 $\underline\int_I \max(f,g)=\overline\int_I\max(f,g)$。 +定理 11.4.2 的证明关键是,证明 $\max(f,g)$ 仍然是夹在 $\max(\underline f,\underline g),\max(\overline f,\overline g)$ 之间的,而 $\max(\overline f,\overline g)-\max(\underline f,\underline g)\leq \max(\overline f-\underline f,\overline g-\underline g)\leq (\overline f-\underline f)+(\overline g-\underline g)$。 + - **推论 11.4.3**:设 $f:I\to\mathbb R$ 是有界区间 $I$ 上的黎曼可积函数,那么正部 $f_+:=\max(f,0)$ 和负部 $f_-:=\min(f,0)$ 是黎曼可积的,绝对值 $|f|:=f_+-f_-$ 也是黎曼可积的。 - **定理 11.4.4**:设 $f:I\to\mathbb R$ 和 $g:I\to\mathbb R$ 都是有界区间 $I$ 上的黎曼可积函数。那么 $fg$ 是黎曼可积的。 @@ -189,6 +234,8 @@ $$ 然后易证 $\underline\int_If=\overline\int_I f$。 +$f$ 一致连续意味着,只要划分的每段长度都足够小,就能使得每段的极差在 $\varepsilon$ 以内,从而总面积的差在 $\varepsilon|I|$ 以内。 + - **引理 11.5.2**:设 $f:I\to\mathbb R$ 是有界闭区间 $I$ 上的连续函数,那么 $f$ 是黎曼可积的。 **证明**:结合定理 9.9.6 和定理 11.5.1 可得。 @@ -209,8 +256,9 @@ $$ 然后易证 $\underline\int_If=\overline\int_I f$。 -- **定义 11.5.4**:设 $f:I\to\mathbb R$ 是有界区间 $I$ 上的函数。称 $f$ 是逐段连续的,当且仅当存在 $I$ 的划分 $P$,使得对于任意 $J\in P$ 有 $f|_J$ 是连续的。 +命题 11.5.3 表明,对于 $f(x):=\sin\frac{1}{x}$ 这样的函数 $f:(0,1]\to\mathbb R$,即使对于任意划分 $P$,$f$ 在 $P$ 上的任意上逐段常值函数在最左侧一段的函数值至少为 $1$、$f$ 在 $P$ 上的任意下逐段常值函数在最左侧一段的函数值至多为 $-1$,仍然能通过人为控制这一段的长度缩小,使得这一段对应的面积差缩小。而对于剩下的部分,上下黎曼积分的差是趋于 $0$ 的。 +- **定义 11.5.4**:设 $f:I\to\mathbb R$ 是有界区间 $I$ 上的函数。称 $f$ 是逐段连续的,当且仅当存在 $I$ 的划分 $P$,使得对于任意 $J\in P$ 有 $f|_J$ 是连续的。 - **命题 11.5.5**:设 $f:I\to\mathbb R$ 是有界区间 $I$ 上的有界逐段连续函数,那么 $f$ 是黎曼可积的。 ## 11.6 单调函数的黎曼可积性 @@ -219,7 +267,9 @@ **证明**:不妨设 $f$ 是单调不降的。设 $\varepsilon'>0$ 是任意正实数,那么存在正整数 $N>0$ 使得 $\frac{f(b)-f(a)}{\varepsilon'}0$ 的区间划分,然后可以证明上下黎曼积分的差不超过 $\delta(f(b)-f(a))$,然后易证。两种证明是非常对称的,这也得益于单调函数的对称性。 - **命题 11.6.2**:设 $f:I\to\mathbb R$ 是有界区间 $I$ 上的单调有界函数,那么 $f$ 是黎曼可积的。 @@ -233,18 +283,12 @@ 设 $N\geq 0$ 是任意自然数。考虑由 $g(x):=f(\lceil x\rceil)$ 定义的函数 $g:[0,+\infty)$,那么 $g$ 是逐段常值的且 $g\leq f$,那么 $\sum_{n=0}^{N}f(n)=f(0)+\int_{[0,N]}g\leq f(0)+\int_{[0,N]}f$。从而对于任意 $a\in A$,存在 $b\in B$ 使得 $a\leq f(0)+b$,那么 $\sup a\leq f(0)+\sup b$。 -- **推论 11.6.5**:设 $p$ 是实数,那么 $\sum_{n=1}^{\infty}\frac{1}{n^p}$ 当 $p>1$ 时绝对收敛,当 $p\leq 1$ 时发散。 - - **证明**:不太懂,感觉需要用积分和导数的关系。 - ## 11.7 一个非黎曼可积的函数 - **命题 11.7.1**:由 $f(x):=\begin{cases}1&x\in\mathbb Q\\0&x\not\in\mathbb Q\end{cases}$ 定义函数 $f:[0,1]\to\mathbb R$。那么 $f$ 有界但不黎曼可积。 **证明**:设 $P$ 是 $[0,1]$ 的划分,那么对于任意 $J\in P$ 且 $J\neq \varnothing$ 有 $\sup\limits_{x\in J}f(x)=1$,从而 $U(f,P)=1$,那么$\overline\int_{[0,1]}f=\inf\{U(f,P):P\text{ 是 }I\text{ 的划分}\}=1$。同理 $\underline\int_{[0,1]}f=0$,从而 $f$ 不是黎曼可积的。 -//无法用逐段常值函数拟合,从而不能用黎曼积分算积分(面积) - ## 11.8 黎曼-斯蒂尔杰斯积分 - **定义 11.8.1($\alpha$ 长度)**:设 $X\subseteq \mathbb R$,函数 $\alpha:X\to\mathbb R$,有界区间 $I$ 满足 $\overleftrightarrow I\subseteq X$。若存在 $a,b\in\mathbb R$ 且 $a0$ 是任意正实数。那么 $\{x\in (a,b):f(x)0$ 且对于任意 $x\in (a,a+\delta_1)$ 有 $M\leq f(x)0\\0&x=0\\-1&x<0\end{cases}$ 定义函数 $\operatorname{sgn}:\mathbb R\to\mathbb R$。设 $f:[-1,1]\to\mathbb R$ 是在 $0$ 处连续的有界函数。那么 $f$ 关于 $\operatorname{sgn}$ 是黎曼-斯蒂尔杰斯可积的,且 $\int_{[-1,1]}f\text{d}\operatorname{sgn}=2f(0)$。 - - **证明**:设 $M$ 是 $f$ 的界。设 $\varepsilon>0$ 是任意正实数,存在 $0<\delta<1$,使得对于任意 $x\in[-1,1]$ 且 $|x|<\delta$ 有 $|f(x)-f(0)|<\varepsilon$。那么考虑由 $g(x):=\begin{cases}M&x\in [-1,-\delta]\\f(0)+\varepsilon&x\in(-\delta,\delta)\\M&x\in[\delta,1]\end{cases}$ 定义的函数 $g:[-1,1]\to\mathbb R$,它是逐段常值函数且 $g\geq f$,从而: - $$ - \begin{aligned} - \overline\int_{[-1,1]}f\text{d}\operatorname{sgn}&\leq\int_{[-1,1]}g\text{d}\operatorname{sgn}\\ - &=M(\operatorname{sgn}(-\delta)-\operatorname{sgn}(-1))+(f(0)+\varepsilon)(\operatorname{sgn}(\delta)-\operatorname{sgn}(-\delta))+M(\operatorname{sgn}(1)-\operatorname{sgn}(\delta))\\ - &=2f(0)+2\varepsilon - \end{aligned} - $$ - 同理可证 $\underline\int_{[-1,1]}f\text d\operatorname{sgn}\geq 2f(0)-2\varepsilon$。从而可知 $\int_{[-1,1]}f\text{d}\operatorname{sgn}=2f(0)$。 ## 11.9 微积分基本定理 @@ -314,38 +349,50 @@ 由 $F(x):=\int_{[a,x]}f$ 定义函数 $F:[a,b]\to\mathbb R$。那么 $F$ 是一致连续的。 - 若 $f$ 在 $x_0\in [a,b]$ 处连续,那么 $F$ 在 $x_0$ 处可微且 $F'(x_0)=f(x_0)$。 + 若 $f$ 在 $x_0\in [a,b]$ 处有极限 $L$,那么 $F$ 在 $x_0$ 处可微且 $F'(x_0)=L$。 **证明**:根据定义 11.3.4,$f$ 是有界函数,设界为 $M$。 设 $\delta>0$ 是任意正实数,$x,y\in [a,b]$ 且 $0\leq y-x<\delta$,那么 $\left|\int_{[a,y]}f-\int_{[a,x]}f\right|=\left|\int_{(x,y]}f\right|0$ 是任意正实数,那么存在 $\delta>0$ 使得对于任意 $x\in [a,b]$ 且 $00$ 是任意正实数,那么存在 $\delta>0$ 使得对于任意 $x\in [a,b]$ 且 $00$ 使得对于任意 $\delta>0$ 都存在 $x\in [a,b]$ 使得 $|f(x)-f(x_0)|>\varepsilon$,又由于 $f$ 是单调不降的,那么对于任意 $x\in (x_0,b]$ 都有 $f(x)>f(x_0)+\varepsilon$ 或对于任意 $x\in [a,x_0)$ 都有 $f(x)\varepsilon$。从而 $F$ 在 $x_0$ 处不可微,矛盾。 + **证明**:不妨设 $f$ 单调不降。设 $F$ 在 $x_0$ 处可微,而 $f$ 在 $x_0\in (a,b)$ 处不连续。那么存在 $\varepsilon>0$ 使得对于任意 $\delta>0$ 都存在 $x\in [a,b]$ 使得 $|f(x)-f(x_0)|>\varepsilon$,又由于 $f$ 是单调不降的,那么对于任意 $x\in (x_0,b]$ 都有 $f(x)>f(x_0)+\varepsilon$ 或对于任意 $x\in [a,x_0)$ 都有 $f(x)f(x_0)+\varepsilon$;而对 $x\in[a,x_0)$,$\dfrac{\int_{[a,x]}f-\int_{[a,x_0]}f}{x-x_0}=\dfrac{\int_{[x,x_0)}f}{x-x_0}\leq f(x_0)$。从而 $F$ 在 $x_0$ 处不可微,矛盾。 + +接下来介绍一个微积分第二基本定理导出的结论。 + +- **引理 11.9.5**:设 $p$ 是实数,那么 $\sum_{n=1}^{\infty}\frac{1}{n^p}$ 当 $p>1$ 时绝对收敛,当 $p\leq 1$ 时发散。 + + **证明**:结合命题 11.6.3 和微积分第二基本定理。 ## 11.10 基本定理的推论 -- **命题 11.10.1(分部积分公式)**:设 $a,b\in\mathbb R$ 满足 $a0$ 是任意正实数,存在逐段常值函数 $g$ 使得 $g\geq f$ 且 $\int_{[a,b]}g\text d\alpha<\int_{[a,b]}f\text d\alpha+\varepsilon_1$,从而 $\int_{[a,b]}g\alpha'<\int_{[a,b]}f\text d\alpha+\varepsilon_1$。设 $\varepsilon_2>0$ 是任意正实数,存在逐段常值函数 $h$ 使得 $h\geq g\alpha'$ 且 $\int_{[a,b]}h<\int_{[a,b]}g\alpha'+\varepsilon_2<\int_{[a,b]}f\text d\alpha+\varepsilon_1+\varepsilon_2$。而 $g\geq f$ 和 $\alpha'$ 非负说明 $h\geq g\alpha'\geq f\alpha'$,从而可证 $\overline\int_{[a,b]}f\alpha'\leq \int_{[a,b]}f\text d\alpha$,对另一侧类似证明后可以得到 $\int_{[a,b]}f\alpha'=\int_{[a,b]}f\text d\alpha$。 + **证明**:由于 $\alpha$ 是单调不降的,可以证明 $\alpha'$ 是非负的。设 $\varepsilon>0$ 是任意正实数,存在逐段常值函数 $\overline f$ 使得 $\overline f\geq f$ 且 $\int_{[a,b]}\overline f\text d\alpha<\int_{[a,b]}f\text d\alpha+\varepsilon$,从而 $\int_{[a,b]}\overline f\alpha'<\int_{[a,b]}f\text d\alpha+\varepsilon$。而 $\overline f\geq f$ 和 $\alpha'$ 非负说明 $\overline f\alpha'\geq f\alpha'$,从而利用积分的保序性可证 $\overline\int_{[a,b]}f\alpha'\leq \int_{[a,b]}f\text d\alpha$,对另一侧类似证明后可以得到 $\int_{[a,b]}f\alpha'=\int_{[a,b]}f\text d\alpha$。 - **引理 11.10.4**:设 $\varphi:[a,b]\to[\varphi(a),\varphi(b)]$ 是单调不降的连续函数,$f:[\varphi(a),\varphi(b)]\to\mathbb R$ 是逐段常值函数。那么 $f\circ \varphi:[a,b]\to\mathbb R$ 也是逐段常值函数,且 $\int_{[a,b]}f\circ \varphi\text{d}\varphi=\int_{[\varphi(a),\varphi(b)]}f$。 **证明**:设 $[\varphi(a),\varphi(b)]$ 的划分 $P$ 使得 $f$ 关于 $P$ 是逐段常值的。考虑 $Q=\{\{x\in [a,b]:\varphi(x)\in J\}:J\in P\}$,可以证明 $Q$ 是 $[a,b]$ 的划分,且 $f\circ\varphi$ 是关于 $Q$ 逐段常值的,且 $P,Q$ 之间根据 $\varphi$ 构成双射关系,且: + $$ \int_{[a,b]}f\circ\varphi\text d\varphi=\sum_{K\in Q}d_{K}\varphi[K]=\sum_{K\in Q}c_{\varphi(K)}|\varphi(K)|=\sum_{J\in P}c_J|J|=\int_{[\varphi(a),\varphi(b)]}f $$ - **命题 11.10.5**:设 $\varphi:[a,b]\to[\varphi(a),\varphi(b)]$ 是单调不降的连续函数,$f:[\varphi(a),\varphi(b)]\to\mathbb R$ 是黎曼可积函数。那么 $f\circ \varphi:[a,b]\to\mathbb R$ 是关于 $\varphi$ 黎曼-斯蒂尔杰斯可积的,且 $\int_{[a,b]}f\circ \varphi\text{d}\varphi=\int_{[\varphi(a),\varphi(b)]}f$。 -- **命题 11.10.6(变量替换公式)**:设 $\varphi:[a,b]\to[\varphi(a),\varphi(b)]$ 是单调不降的可微函数,$\varphi'$ 是黎曼可积函数,$f:[\varphi(a),\varphi(b)]\to\mathbb R$ 是黎曼可积函数。那么 $(f\circ\varphi)\varphi':[a,b]\to\mathbb R$ 是黎曼可积函数,且 $\int_{[a,b]}(f\circ\varphi)\varphi'=\int_{[\varphi(a),\varphi(b)]}f$。 +命题 11.10.5 事实上和我们介绍黎曼-斯蒂尔杰斯积分时的 “伸缩” 理解一样,其证明是通过该理解在逐段常值函数上成立来证明的。 + +- **定理 11.10.6(换元公式)**:设 $\varphi:[a,b]\to[\varphi(a),\varphi(b)]$ 是单调不降的可微函数,$\varphi'$ 是黎曼可积函数,$f:[\varphi(a),\varphi(b)]\to\mathbb R$ 是黎曼可积函数。那么 $(f\circ\varphi)\varphi':[a,b]\to\mathbb R$ 是黎曼可积函数,且 $\int_{[a,b]}(f\circ\varphi)\varphi'=\int_{[\varphi(a),\varphi(b)]}f$。 **证明**:联合命题 11.10.3 和命题 11.10.5 可知。 -事实上,除命题 11.10.1 外,上述所有命题中的所有非 $\alpha,\varphi$ 这种函数,将它们的定义域由闭区间改为开区间都是成立的,但由于 $\alpha,\varphi$ 的定义域必须是闭区间,而且 $\int_{[a,b]}f=\int_{(a,b)}f$,所以也就无所谓了。 \ No newline at end of file +当 $f$ 连续时,我们也可以得到命题 11.10.6 的一个相似结论,此时不要求 $\varphi$ 是单调不降的。 + +- **定义 11.10.7(有向黎曼积分)**:设 $a,b\in\mathbb R$,$f:[\min\{a,b\},\max\{a,b\}]\to\mathbb R$ 是黎曼可积函数。若 $a\leq b$,定义 $\int_{a}^bf:=\int_{[a,b]}f$;若 $a>b$,定义 $\int_{a}^b f:=-\int_{[b,a]} f$。 + +我们介绍的(以及接下来介绍的)很多有关黎曼积分的性质都可以推广到有向黎曼积分上,特别是微积分的两个基本定理和分部积分公式(这也导致了它们推导出的换元公式等性质在有向黎曼积分上也成立),但为了方便我们一般不特意写出。 + +- **定理 11.10.8(换元公式)**:设 $\varphi:[a,b]\to \mathbb R$ 是可微函数,$\varphi'$ 是黎曼可积函数,$f:\varphi([a,b])\to\mathbb R$ 是连续函数。那么 $(f\circ\varphi)\varphi':[a,b]\to\mathbb R$ 是黎曼可积函数,且 $\int_{[a,b]}(f\circ\varphi)\varphi'=\int_{\varphi(a)}^{\varphi(b)}f$。 + + **证明**:$f$ 的定义域 $\varphi([a,b])$ 是有界闭区间且 $f$ 连续,从而 $f$ 是黎曼可积的且有原函数,设 $F$ 是 $f$ 的原函数。 + + 同理,由于 $f\circ \varphi$ 是有界闭区间 $[a,b]$ 上的连续函数,所以它黎曼可积,于是 $(f\circ \varphi)\varphi'$ 也黎曼可积,而 $F\circ \varphi$ 是其原函数,于是: + + $$ + \int_{[a,b]}(f\circ\varphi)\varphi'=F(\varphi(b))-F(\varphi(a))=\int_{\varphi(a)}^{\varphi(b)}f + $$ + +## 11.11 黎曼积分的应用 + +- **定理 11.11.1(泰勒公式-积分余项)**:设 $I\subseteq\mathbb R$ 是区间,$x_0\in I$,$n\in\mathbb N$,$f:I\to\mathbb R$ 是 $n+1$ 阶可微的函数,且 $f^{(n+1)}$ 是黎曼可积函数。那么对于任意 $x\in I$,$f(x)=Tf_{x_0,n}(x-x_0)+\int_{x_0}^x\frac{f^{(n+1)}(t)}{n!}(x-t)^n\text dt$。 + + **证明**:法一:根据微积分第二基本定理: + + $$ + \begin{aligned} + f(x)&=f(x_0)+\int_{x_0}^xf'(x_1)\d x_1\\ + &=f(x_0)+\int_{x_0}^{x}\left(f'(x_0)+\int_{x_0}^{x_1}f''(x_2)\d x_2\right)\d x_1\\ + &=f(x_0)+\int_{x_0}^{x}\left(f'(x_0)+\int_{x_0}^{x_1}\left(\cdots\left(f^{(n)}(x_0)+\int_{x_0}^{x_n}f^{(n+1)}(x_{n+1})\d x_{n+1}\right)\cdots\right)\d x_2\right)\d x_1\\ + \end{aligned} + $$ + + 接着可以将常数外提: + + $$ + \begin{aligned} + &\int_{x_0}^{x}\int_{x_0}^{x_1}\cdots\int_{x_0}^{x_{n-1}}f^{(n)}(x_0)\d x_n\cdots\d x_2\d x_1\\ + =&\int_{0}^{x-x_0}\int_{0}^{h_1}\cdots\int_{0}^{h_{n-1}}f^{(n)}(x_0)\d h_n\cdots\d h_2\d h_1\\ + =&\int_{0}^{x-x_0}\cdots\int_{0}^{h_{n-2}}f^{(n)}(x_0)h_{n-1}\d h_{n-1}\cdots\d h_1\\ + =&\int_{0}^{x-x_0}\cdots\int_{0}^{h_{n-3}}\frac{f^{(n)}(x_0)}{2}h_{n-2}^2\d h_{n-2}\cdots\d h_1\\ + =&\frac{f^{(n)}(x_0)}{n!}(x_0-x)^n + \end{aligned} + $$ + + 于是: + + $$ + f(x)=Tf_{x_0,n}(x-x_0)+\int_{x_0}^{x}\int_{x_0}^{x_1}\cdots\int_{x_0}^{x_n}f^{(n+1)}(x_{n+1})\d x_{n+1}\cdots\d x_2\d x_1 + $$ + + 而利用分部积分,若 $g$ 有原函数,我们可以证明: + + $$ + \begin{aligned} + &\int_{a}^{b}\frac{(b-x)^{n}}{n!}\int_{a}^{x}g(y)\d y\d x\\ + =&-\int_{a}^{b}-\frac{(b-x)^{n}}{n!}\int_{a}^{x}g(y)\d y\d x\\ + =&\left.\frac{(b-x)^{n+1}}{(n+1)!}\left(\int_{a}^{x}g(y)\d y\right)\right|_{x=a}^{x=b}+\int_{a}^{b}\frac{(b-x)^{n+1}}{(n+1)!}g(x)\d x\\ + =&\int_{a}^{b}\frac{(b-x)^{n+1}}{(n+1)!}g(x)\d x + \end{aligned} + $$ + + 而 $\int_{x_0}^{x_n}f^{(n+1)}(x_{n+1})\d x_{n+1}=f^{(n)}(x_n)-f^{(n)}(x_0)$ 是关于 $x_n$ 的连续函数,从而 $\int_{x_0}^{x_{n-1}}\int_{x_0}^{x_n}f^{(n+1)}(x_{n+1})\d x_{n+1}\d x_n$ 是关于 $x_{n-1}$ 的可微函数从而连续,……。于是就可以从外往内拆积分号,将原式化简为: + + $$ + f(x)=Tf_{x_0,n}(x-x_0)+\int_{x_0}^{x}\frac{(x-t)^n}{n!}f^{(n+1)}(t)\d t + $$ + + 法二:对 $n$ 归纳。假设 $n-1$ 时命题成立。 + + $$ + \begin{aligned} + f(x)&=T_{n-1,x_0}f(x-x_0)+\int_{x_0}^{x}\frac{f^{(n)}(t)}{(n-1)!}(x-t)^{n-1}\d t\\ + &=T_{n-1,x_0}f(x-x_0)-\int_{x_0}^{x}-\frac{(x-t)^{n-1}}{(n-1)!}f^{(n)}(t)\d t\\ + &=T_{n-1,x_0}f(x-x_0)-\left(\left.\frac{(x-t)^{n}}{n!}f^{(n)}(t)\right|_{t=x_0}^{t=x}-\int_{x_0}^{x}\frac{(x-t)^{n}}{n!}f^{(n+1)}(t)\d t\right)\\ + &=T_{n-1,x_0}f(x-x_0)+\frac{(x-x_0)^{n}}{n!}f^{(n)}(x_0)+\int_{x_0}^{x}\frac{(x-t)^{n}}{n!}f^{(n+1)}(t)\d t\\ + &=T_{n,x_0}f(x-x_0)+\int_{x_0}^{x}\frac{f^{(n+1)}(t)}{n!}(x-t)^{n}\d t + \end{aligned} + $$ + + 法三(若 $f^{(n+1)}$ 连续):要证 $f(x)=Tf_{x_0,n}(x-x_0)+\int_{x_0}^{x}\frac{f^{(n+1)}(t)}{n!}(x-t)^n\text dt$ 对任意 $x,x_0$ 成立。可以把 $x$ 固定,$Tf_{x_0,n}(x-x_0)+\int_{x_0}^{x}\frac{f^{(n+1)}(t)}{n!}(x-t)^n\text dt$ 看成是关于 $x_0$ 的函数 $g$,此时就转为证明 $g$ 是常值的(注意已经有 $g(x)=f(x)$),只需证明 $g'$ 恒为 $0$ 即可: + + $$ + \begin{aligned} + g(x_0)&=f(x_0)+f'(x_0)(x-x_0)+\cdots+\frac{f^{(n)}(x_0)}{n!}(x-x_0)^n+\int_{x_0}^{x}\frac{f^{(n+1)}(t)}{n!}(x-t)^n\text dt\\ + g'(x_0)&=f'(x_0)+(f''(x_0)(x-x_0)-f'(x_0))+\cdots+\left(\frac{f^{(n+1)}(x_0)}{n!}(x-x_0)^n-\frac{f^{(n)}(x_0)}{(n-1)!}(x-x_0)^{n-1}\right)-\frac{f^{(n+1)(x_0)}}{n!}(x-x_0)^n\\ + &=0 + \end{aligned} + $$ + + +积分余项的泰勒公式给出了函数多项式逼近余项的确切表达式。 + +- **定理 11.11.2(积分平均值定理)**:设 $a,b\in\mathbb R\land a0$,$f:[a,b]\to\mathbb R$ 是连续函数,那么 $fg$ 是黎曼可积函数。那么存在 $x \in (a,b)$ 使得 $\int_{[a,b]}fg=f(x)\int_{[a,b]}g$。 + + **证明**:排除掉 $\int_{[a,b]}g=0$ 的简单情况,式子变为 $f(x)=\frac{\int_{[a,b]}fg}{\int_{[a,b]}g}$。 + + $f$ 存在最小值 $A$ 和最大值 $B$,那么 $A=\frac{\int_{[a,b]}Ag}{\int_{[a,b]}g}\leq\frac{\int_{[a,b]}fg}{\int_{[a,b]}g}\leq\frac{\int_{[a,b]}Bg}{\int_{[a,b]}g}=B$,再根据连续函数的介值性可取得 $x\in[a,b]$。 + + 为取得 $x\in (a,b)$,发现 $\int_{[a,b]}Ag\neq \int_{[a,b]}fg\neq\int_{[a,b]}Bg$ 时肯定可以。否则,不妨设 $\int_{[a,b]}Ag=\int_{[a,b]}fg$,那么任取 $a0$(容易证明一定存在),那么 $f$ 在 $[c,b]$ 上的最小值 $A'$ 一定为 $A$,否则设 $A'>A$: + $$ + \int_{[a,b]}fg=\int_{[a,c]}fg+\int_{[c,b]}fg\geq\int_{[a,c]}Ag+\int_{[c,b]}A'g=\int_{[a,c]}Ag+A'\int_{[c,b]}g>\int_{[a,c]}Ag+A\int_{[c,b]}g=\int_{[a,b]}Ag + $$ + 矛盾。那么根据连续函数的介值性可以取到 $x\in [c,b]$ 且 $f(x)=A$。如果需要,类似地再把 $b$ 端点排掉即可。 + +定理 11.11.2 告诉我们,$\frac{\int_{[a,b]}fg}{\int_{[a,b]}g}$ 可以理解为某种意义上的加权平均,它的值在 $f$ 的值域范围内。 + +在定理积分余项的泰勒公式中,根据积分平均值定理,存在 $\xi\in(x,x_0)$ 使得积分余项 $\int_{[x_0,x]}\frac{f^{(n+1)}(t)}{n!}(x-t)^n\d t=f^{(n+1)}(\xi)\int_{[x_0,x]}\frac{1}{n!}(x-t)^n\d t=\frac{f^{(n+1)}(\xi)}{(n+1)!}(x-x_0)^{n+1}$ 变为拉格朗日余项(这里不需要要求 $f^{(n+1)}$ 连续,因为它满足介值性,而观察积分平均值定理,只要在知道 $\int_{[a,b]}fg$ 黎曼可积的前提下,其实也只要求 $f$ 满足介值性即可)。 \ No newline at end of file