From 479336a7ddf0f67a28dcc236d01c646582a829d7 Mon Sep 17 00:00:00 2001 From: Leon Vatthauer Date: Fri, 29 Mar 2024 16:31:28 +0100 Subject: [PATCH] Work on limits --- tex/main.pdf | Bin 168091 -> 175925 bytes tex/sections/02_categories.tex | 136 ++++++++++++++++++++++++++++++++- 2 files changed, 135 insertions(+), 1 deletion(-) diff --git a/tex/main.pdf b/tex/main.pdf index a5504139bff3d98b9dcddb427baab79f0fd5e5ea..14344e88c910462335ce9a52ade323bcdd61f567 100644 GIT binary patch delta 42894 zcmY&;Ly#p56J*=AZQHhOO`Fp;U)#pKw%yaVZA{y?ZSME)Y4?(ss;H=_Lq%m}W);9S zZ^I=@0os*@L=djt;C@89gpO0SXcKiP_=?>kO+CfSX)~T;a`>MC^sG0jv%_9>J38Gs8u}v?g-64`)tps)oDv z%YQS(?;;32O;aFVIjI?o$Et2F=gY)Tj}^FG;`@)FPlnSH`!{&b6GQFT3mqE{ws+Fn zInZenDlc5slRJqZR#fa~vqA-tHso8kvtJG1MZG#Nuwe<+EM8$SS)Dy?POFm-Cr9fd zQPH>yAGSLt6TAM7?BMZm`~5>`sTZ*JH{~L;d0T(&{$dbWNH4YpNQwoDp5hOh1mNNl z5`uGebFnb7hx1y$%9?gK;6fR_@rUaUT-%$vg@^H@sngGI1?#~STphPm7JU3-rleFw zlhsG--gamp1siN&NFl!)6}Adbx!zIo*!?lLs$*Y=z34ard`9hjU0e)q1Nhy01O5;O z&*Eu%`aD@7PrzImc>26uz=He(0my;f!UuYQgg(@d9PE?{cPN+XU&)~$WfN>XRl^)z zuGS44^w&Q~GbBL2HCbbc0Y|~ZQeMxMUzu;&{Kj#v#y^-o%(cMcW_*`VG#jTIU@IVP zo*8AZlC3trCXrr9Ktpnh6R`52^xrDGCr>mz4x2zCB&DCdR6vL?WqJgw05$cNF3SuP zejxJ8S~!C&cM2ovJqodV*dT8LPLz3H5TtO1tK@h;4xe4Begcog1005fieT^-F+%tb zHxLcxtIr}MYISPgz;6&;>_kQgMVG$lJge2Kezo*ftjJM z1~`wTuznyhn3ojD*#?mOfaoyib1439mAK1vlf8v>emHu$RIY8QpBx%hw%>Y7-k~F~ z8W;e-C?e8a=meH?WfY8#MeZ7D|eZT0MN&s9wcoGZH>0b3R=I2m{S#5Ndd@_<~bKTQ>nSY?WE0Qj31G}OLY+-d3e?F&OY~?%~!q08zKiE@r0(7G@|zWn=9MN zxdHtz0V;%dnp|j$_#Tly+ceY$v81Uu8>KyDttvO3NV;;e`yMl>v=?3=X?3myRkRj@ zwPT8@|0g(|o$w|hfdA#s0}P|1OG^Eb%smipNasUl{wQ`WidE88sUEvlpzM_L?05p_ zAy0Io1+Tr@4hm9#%HF<9D3kJ5CVijPSCO>_j0RE687URnzQv{6c}-v31g)kxMQXrT zqee!bFLl-T;KPQU!FW3>vgz*fpCi?N;fs*}16!NExg}Ky-~v;Bt&^Jd=u{0qi~sp6 zNsgH3dU8Qg1~SPcr8crjz0b6qnmI%ni;cOvSDD@P!bkwdc;d>su8VM34jQVK^4g&+ z2(~y;3EL}8A0{gU=3anx>Kedlt6HFzl_}=$8QK6H|1mHCOFBM~>P(8s4{Kq1p0y-P zTOe}6#i8;Ikp3Dc61;|grSh7EbK~CQRlcRcLxUAWQ?-yXFfD+6iTVq(MDDqogBlO- zn#HlDtoTk+&!i|qL_C?TdZ1tK8f_}HdyPq7%A@X!hb6p9IT2o@mHb&K77y132ZX_1 zyR$htq%1{DzHgaM)!58mV@je&l&0u6cAXR^@xzP+V1yW;pQN+|2=^wC84g<8`7Bte~Z$hzZW=3f5OC0&SI*`Az7-8j#lt{OqcEN$e2U^ce%Koy$o7CGXCvw@(x64W=@ zX(wGZ=}>P$@K2I-p8r~@0Vd-#4XpF3x;bLQ0KV^uF&&E%Lr|fCsL-G?08U=E|8FB2 z$R`|fA@$tU-V)PDl08A-`Rf>?8$0yRFpim2R?+vFHi{^HyZ{#mlYh6b*VN=f#EitM zI_M)ue@dv49i1h}DkgtdjQ1b@MiEkA?p+AUJAJo*`go~bKo$Qp(K&o}z`iVjKR1z9KO5`onBD(cI)c)#K_<8MEJ5kg#kdMx8 z61ieWjQ8oIH{47)+*$pvB;C?nt;DScrxx49l9-ZCQ|6=&sF5-?3Rk+pY&Vkr1DHa3 zX7CQj{B1L7uzBM9d7d)TTf*dntnR4czys|5ha;f9ctPcY=BPaWPFdqk!Cl3(8MNJW zW!nj+ALi`J6k#Qf)yvZkhT>l?l;n+QuOmc8vQn-POtpJboCb3vi84;c7>FEMZk_>* z9uR`r^|-eptE>eg@?1p#gc($69A(B3%+e%#+h&UDCzRIL`8@@Abzjz*ab|Nu z2tNQ+F$shR6*_c|Gy#rHu!5r5MTwDBzl}4%ArdeIdp*i6NS+WeiZUv;7zB`uE6DoQ z3aFq*qO1{tb!u^1CyyUWa*!u=Un)r$>bb{8ra^+J9NSgfE~LK%giuiz31!I6N663_ zSl~*Gvq@W7sK~jyC_J&@r91tRNCKI}FaktZR_dYm&0;((jLVxSF6ICfR3#+|Ic0ms1yjXTV=)Ct_)U!i!eXB5Dg2h|G0r!ty7DyUh}* zJ<2mrjOa%xylK@2ZF_-WTa5K}jZPQt%s?WpnC%4ud~2i5*)H9Nv>JQUW$;hlA3)X* zGMzVb>YShz_XJsfzS47=dv0p94{&JNUO>teY6&Td(Z`WOYI*3?$n?FuZrN;ulp#)U z)$nrVkWKeK<2jY`JZ$0Guu!k{4o20cAbX9pQt~FQe06l=5f&-ZPOwMNm0nrqTm^^N zLB2p?$S`bD;S!!W$LK2Z@pA8DjaDsPC(dATezotG>2kCGP#JYI zcGPp@>(y2G4Rg!+c4pA)iNg?mE9;L*-x2W+rUFw`!XD>O@Zk{Bedl@BIor?z$yRqlN_0FcDGB3 zloy1}>?zCh{O$ySlISopuDa*Ra^GxUc<}WCJ+n{DMj63~a9&3h0tyVOdvRRh`twNE zE{PB-_k5Bh)xJ}kOY;8ibT`NAW$iv^d#RmXq?I;{-iLr5J0*D{Wr!3rhgkfOI;K+~ zMKNXfsCe$BJg{dfWSFufsQ5w`@moYq{L?k31*Yn18ig~sL43is^@-x00og! zmov&=a1uqzK5|x0TNuR#&aN$q1j>7=83fn?9-3+$rV&}=jI^E4U_+56uBB4TPiiR# z+BlNnA}K;|kUc{=@;{tn`1VDO%&7=T

8XEH~!co~bMU##D5PFqbi zR;6LJrGZdhyG3dT2d`-n^hNgm<@N-qnbuLTi0>b(Jt@yUN{jbbG~WA63|T7a!sPk0 z4)H19JDZD-x6pYmKoHAUWNiAVUoP7^rFWe9(+JIy|u8ife zTKTi8P>6I_Kisr)9-VpY512_Gt$1+X+&RJe~4Hok4AuB_)+BepU($D`BU8(TvV34>jJdMQ0sq zCMj6$cWO-C0FbdIBNx#JKe%K&)G|yb#NlM`3CXro-d}!zg304}k&}p)XNDtpo*XT8 zY?M%XRz=ua+)c&4#1i$uncL!zeheb$Q2|D`<}94a%=| zvZ;8#i*b^S^>-x1!oL>eEd<=7yJjd1v8sc(Af;IxfJ|!q(LiB1)ZfFWS)=>|d*IQ! zMT489#z-4dX(+T(^ZBtCf=MPLSke)3;nu_xIQ8mM*1?IkxLzZa0*<1tJZNmwoSvqr zP?i^|fTF*{a+|hoz-Y>!v44%@GDybql6sTtf13+aNz(r|fU*eUC)$i5a-gE~}zC;Ew4{YpNDE5D4; zS7VPOVJ~&xux56KUsdT7O#C*#R_(#0V^?1A2hC#h3VLJihT*zmZbGDp20TtKLCxCw zpZKTuiAssrdAF>c>i3BL-Yyqq1foN^0a%y>flRtibn5&R#X(=aJxsid|=gp#UMJRWk40M9Eg*%yGFc5H7 zMf@?J3bqw&^t@(Ho74AR#&yTSvG8}6!)juha{JgyRAQ#J@nUi87O<#bs@rRwD1@#$ zPe57)osxz|zbEmaPfR){=r#@{J%RXxtm}k-c7UFR6WF&i{@;7$oOf=nH7fpH?f`+$ zY8v7s2(U9#je&sfQQ=|6X!RadU5-BOWUU!)p;^|6dW z4bg?0wD09Xqw=%94*-IzWLc4I;1uF+r%)74Mt%A({1c~UT|&j}htiMC;v};@NJZHD z?bl5M2H)>zHrtecf)7+)jOnA?M*Q_gy=8NZmPs>Y&7pPyy3OOY$snGD`!KJs$?{^y zOCICqxhXZ~Z(@_AlUA!inxpJP15)8QZ+jsUT&EAc@%UHwM}VS3p{|^!C@^nB+rH#c zqx7eJk5#g5LCUjd%{Ma<`4E+~{*kg^YsTR15dtesV~Y_RpMjBbb;fp++i}X80n_gG zJoHRp{56wOlV+8EFmC}bpXr+Edo~ceku{~-jdiVYd{Mp@`qL#G8GkAJHsq2|5+Sbf zn+IQ8IoRBTAMl{ALiM62Q{nCB|>nVroRSo0ctK=-%# ziT+c_+IY9-&5`Ex(5As*Y?BuZZxMs>VAY}TaxX?cj zNL!?gD#{g~bm=s;&}`0V=mdSg;(OELW8o((k%iSW2{0xe_aGN190&d5#2}u7#oWK| zVy;wDLO+A&B?P~x-*fKQM#&73rOY=xeEn%r>ENuNzmKI-@!F)avNpXSisZWEJhiQT z5&KO=|B}2;tFtp&R18(k30C0eGThg*E{Xo!%-t~LomQS{@o+A$^H1uJjT;eDMjFhB zyOtZ*HUQ;)8ls`KQLwxxQXk`fqSq!BnQzkkJVbp-_ZTu<`wBDyvciZ)o0b!Q(uvM| zDFcBDK+WxM51Lk9R@E$*{_e!`nPy$>+oh3U7`GS^A_vAC>s;<;>0`ph!{ zh^@XiwbDOWphXYq?@JyC-8a3sv4O#j&(Dq3e3pY>_zKQ&Vd0t=Pu2i05IRSXfHYS| z`D*VynSgk3<%<+7xaW;-;*ZZa#~<)Vw0a;Y1}Oi3Z#3@zk2M;O#}l-pc7M>{Lr054 zd5X;T2U>w_K`kq$i#u`#?y<5^|MZZ{PyrQ=*VnE@i%8Qd`D5&cCUuC&X$kteP(q%suCQG zl!=lOp|vxP2M0Ztx`s0;U$uWt0k3E)2=^C=1mA@kn=k_NErX}RUknn0`3+ON*$lBI z*GQvtG}Y1%!Dc#m62fKiyMT-M{B&;1%Qq4YPp^NWlW`L&)42%jQYTzZ%XO64zf8Vf z{t^jST4gJ7b>2;RC5;w3H@(Z@!yV`>Wf6PscRBD?oUojg@+D(Aim{t~ISaNB4lk5T z+AQ#?;J_7Vrj-l-6S-?4)mPQ!fa(&V*H3&t19s{+lGneun%ygXibt0daC)&Uf!6{SC|0K>v2L6Tdhpe!C@ARrcMH+E=J$wS7#g+sv_ zMURw;Q>%~Q{g1Y67yB3_+KYlqulWALS|?gwy11J(0ke$TRsGjNh)`k1OguJcqx^zv zidKSjX$q}PF=dRm`stiNx~MTmA0gOb!udX8Egk7B`uDVI&y znMg$dLT?yUF(BRX^&PuiyiWyuYy(zWeNRS-zS@Sv!UknAOrlj$icqi-iG22=!p{v~ zc(U8E{ex$aQSmNxazwE#?gvsJ#Mrr8>0Ag8zOIx$QfV^^Ol&$;iweT|)KL>>Wo=RA zP5jw}kkfTnMk4|kSO7oT-mMZ!fB>I%++XM0MUTNT25=TDiV%IWu@l^me-jJ{%t7SA zO`^a6o}H}0!almbdS<&)SvNF{1nfF0jcHcH8SQHwA55zhL9$+Rdb~GXk+fB zBTva66BmSctQncN;sg=ryMui)eX(C`V0q|-;=fZ`Z2WR$@UHmufBQUp!&u<97VeSq zc?C=b&tJ34fam|awLVZoF%XY& znlRB#prK=nQocVLSEfhm(zGy$ERAVSdob`+say1E?n*TkUYQU~*;FTr3BJu_B+3r9 z>upsVLOc?Z7)Josc3_tlmkJ}&c5q47$VO<)m(43>O_|l}f$-Ag_V1tuc4Xb6^A7EtktyLln934x8}Bx?X16MVGB=i&wiB(9XL zv3~byw*7S{0Gm7DJ=u{RNf=;$M%|#5ojCYATLS5rqTx_~ zzc@dLADTwl!=!EX(4*c@6L=mGA%xo7OKr#t}3J0z$ zt~3)O6qQ&F9?{Ci+xaT2luh}rmV1HV!m7sf?4_ieri|Nw69eE2BXw<{^G~+>?efon zO+yjVxr0?#nb0)(8s44rK5-U9)LM0=Y|-D05dIK%A~KAFrZK)MF`->s8=_u%d=-xt zUJ$cUTOkDJp$jOXtg$!<(CEwjP*KEsV^Xa4|6CJzW|K`QNUx#G-OU#5`3#a$D7$LM1uSH$znD#3c8~Pz?SUB7Bf(vawJN6 zfrrtCu%pw(J1tVXVOQ0qS`j>QRoHD5wkT8&X9}ksk0Uq$m?~ErIp->`OUd+>aw18) z#~x)B(A#qt*4G{x7762}G19`$gU0f|nmvqEtjnH4HLG`B?dNQxJEm5n<)4S$Eldb~ zKug2m?}8;gGdb)49e%kc%ZM6tr2IscL>laI9i5tr_Uig8W;ZOS8kK~Ef22HF2n~4=2OiCnG2?CWvgT-pxY~iZj*hGmkEHEQ<@>r&I_* zbV|DnS2*!BDxm2YqAWEd%Ya5aVpG0ZprDVs+xU8L;qj6);Fo+AX&S?{f8L-L*yw>YL5qv&xQS#r$B2o%YCH*>w<35uS{1{q z5uYoF>(~?A)!^QpdF@7xHg4;c52Gi1jdq*cHyU8wt+ZfiDkB<&=nZ3ERG_p}Uk+9u z(q2?wU`rd|ClJWc%0RBig@cC5B>;%`qmo__TLR-7}6I4fI``?2a)*5 znbO2xLK$Y>*M5ziN^&fMTI{_;mHNWJ<{g2IoCA!^+(5$cTF z3)eSfM98FezF75xt%Q_#Go;d$#c}QV;Ty{M<@5aNhL!)tQM9#=KCEcR9LAYfrvv{u zP-M(aMXv7)hVgu4FA93f+>IFkl1c|CwV=a=3!$ZsT34kFwU6m5j!A&?#kA{7od(vI z6^VDwF5p%P-PIQ|^{0aR*v{rO<30zl3OpxchdH@2OpNEUY_WIT_VqKd^;tJz-b$H^aK1v8VlAD78j*oxuv;THm7xQ= zpRPEF7=fE>c=jm%qXSJ(a}ZVR6a4oGjc5OE5xNC0_i+myW<}T?xoyH1+xm~9T(-wa zRs@QXJ9)xA?kUb9ik{k25HA7m(WRjmT3-5X0cqvFMP1a+EI9$x&iTryeBIO6Z)DVA z>&0~zc}4^*N(q0vl$di=x7C>!&XCWKND3C#E;&PI1_D2l-ISGkBL*g-XIRrSZTM{0 zL{E(M9ZyM9668({;FRcY9`|W-7C;^uavEbhLu4w(vx8IZ*~&5 z86uE15ppT53*4OrI`~XhU2QQF75D%NsuR5xDs!KSER%2_By{9|%w=!c-EDQTM2)s% z1YK`A9Ge8xt_VxiFnn-t`Q|gtmLWZ_YXs)5dPUC3(`)t|v6ky_%w|Et#sZRB;xrhn z>F4K#j3~VQ%Y(KoV5>}JYM(Zlv{4d;faTRusA}00LVLzRX5U8d?=|% z1UeD2g&3?lFRlhwONywSwR8ClWj9c{uJ=(X?Ao~G2V(ZURZ~3<_xoaokI<)OXbV|b zu?MjTN!{=B2T|m1^%gUc?*|&X%?R);O!NBm9|0w{VJ?TWZ~#(ZfuaI~FhD5*tQ_1d z|1TAt)|F4#;6mwn(LO~^C$$P^?pqZPDiv`QebIWXGqQ5ELE=5Sv3f<5jB28^0>^+C z*VCiueLKEGJUZJbrWyy>Hn8X(ggq==XcN7r2>;?**~u$ICKgqegJbT_%-x}KQ=&Pc zdK{q3&aM5)F5v)R(>5O+Z9 zjm4zfHE4C;cbgMsAD5NiI!&+0ci@d{?`JsT8XU`Hb-4rVa=_3gHagn%)p2NTZo#}r zyKTHwfw-$jFm)`G*^@GF$V}s#r{=)&z*bWbE+`T>Sq}U@1RHlG^?Ub8<55U!NH0NV zwAuU|#%Q5yaz+}(M}Wb5=r+8VU=9YHVh_t>W+8c)bDfNpbz=#sT0?VEbr19Mp10}k zh`KY$@i>5Pc6y_q_W}9KT9P|fi+g1DU4$=4hMr;!Uq^SkKAd}j=|d{_1{Ec@MSkGG z;6F(P30f~V&(ewKC`m-di;Lv!3Y|=DJH9;l(S?QjC20)kO?{Sfb&8d5zGeFLS*YZtxs9x1IMsiM~l>2tk(IB$=<}k$$CEar@UxO zRr)wdAYYN_u$!ImP%fyjvYuOON{TBKgiqAAraayN2)}!~py}^KRXD$oXZ_S!T~Fcq z)eKPbimCWMN5d3O0>H)91>U3wS`14<(P?Qe2BfR*`BrD8(uoh!cEubc=qZhh4{{ig zWJTbax1y^$XNIsrca+qBvf+~Q51F0kTOvAU3ooj6$vO&T zd}Grv6KQT^!L2#Cb|v;ndXMj0U{$DN1Lb&Vi-6I49=&KS@# z&6_5*K9PE+SeEfRzK6Xl1(}BXUV?+ZaJX)99vV(hawa7+63T0-d3!H8x!quQTx5sw z;ycwK zebHIE8W?xzlW1zaG+0UKu}7Dulp#@kJmHcYzMgv#kLUI7zH8iMqabRIK_R0ub+_Dr zP*uj?i{-%*!2}}&LLNnVa$_O;E1w{1W@ah$5?JI#I^+{z8Cxp1=)C z#ao56L^QldQM9jwoNE$wrzKOg#=w1|46Xfj6oyNC^G4$0(!uy!umGCWM)}ukXGkD$^48TL-;SKiJS; zv&Ip=jV};5%}VQ>1P94`&0&D}QQ;*T8N9j+AO9lcU)q~GHWrAMQx_0sd+x}7&uJ?K zS@i>FE*uMW>Sz6MFcD{#?}$N&o*Su6FKAV&G5k@@3r1Fu(jpIb1E{{h1<&=3!~VWw z(~Ij|v5h>HM|kacRVXQxKTTqQ z)W)O72wDBE>gT1WlEe9CkCqI$v<=$IpeFl{?F^x7CLK`3!+oU@7;5R>XJ_HZ>)vO3 zU+k7&#ylfBP7J<2pio;y!c+n8SI|}?f>Qr;>|p>WFhLW6r5K=m0GoM*ZQrXtew2LX z;HktVF;<=JuG?LnPu(tiCx7KW91UJk->36b7ZrBvj}v@}ttHthztJA@geVk?8|q6I zXg+}x@9D6AzUT73p`Fi!?6Q%Ce&$rE#$mnX{wmH+IcWQ35dR9nTjS!e*v^M_az=G{ zD=~$5^M}nU)E6%awK-l8SbbsxChAANEnbx5Z{|sFR$3dU#r}{aF)?0-LozPCAGkT^ zs2!(O%Jb^-Vz+DkjLs+Y{(>4XwqC4`Hom2gpml{UDK=?SA78#B7c%q*;cRJ?{=ddV zP@a?|dP?98Ca5GR4=~9djIvb^3p5=J@$*%G_2A_pE6)<8+xGva0?}|m#R2TB|DTI- z$v`)OfY&A9rFKlZ8PqBz7KUiVw9eJo1KJ2bW=>!g>$re&$r`^%Xx4VE^Jn`Pi*DLq zg@($d%K2E(3i=Gu5yF0wl#FFW%env==epOE>D|lSV1yaO)X!aO6nv=B5G%ZF1k(H% zVp9nqi;meW02-VTj|p+vnE(c7ye#O_m^UMc07d_E-Wc2gE#wbKF9H|jBQ%_yIZ3_~ zTmlLGt71Mp551%rl-5iiHh&@nn*|Ll@)QZ|A6yy+uVWB3tk@6={7p#9 zIG8M0o(ht+?-JUz7r48K9PFj@9&}xy=RS#Sv*W-nV_O3iqS2Cd0h@B4U4IHTcqqz* zuO{>FBkUh0cm8duyAt-l2aaC3k9;rKr9B~;;Ala;+v(7 zS!#(Vu1DE5dJR-4pC-B*=Lx+rpO9AFw23+&R0c52O53zh)aKZ8wn}Q+_E6wIgx-#2Vh+#e&z_ecY2~UX?T)Md2q||u=>N)?nM4IT<=D?aPIiz+h zKqr6vJ(4S5&1}#Y7ApM9Kb{0<#rn6m7BYzTnw(gqG@Px^%u8Q)Uy*YOxxgVwa~{MT z{S&6wLOx!7;k#K;j|s;FhenrP!qQDw2%v773BuP&NdwFl1ymbUY3iI61zT2ZkQ}E< z+ei?efHfO0WAp-Z1gig+Hu;^dJVx_Jv5zv-KTfX3=o%rU zraS`gi~gLJDnG&6fddv-`IcCg{!k-?eyOaSxZl7htX|8V`Me4SEmkv6O4^(RFny%N zNH<&Ont2IvPxie#iR3YeiI!=JDgpH=O^&Bsh^uulB5qggZ$kDOu5CTLD)W|W+8oVG zQBt8(C|9)ES>7g5A^95iz$fI67D&aJ3gv2d@ zcF6Ye^w5HHpEDQ*g-_K6LHy$uKspZtjU|QEhgnyr$$$qqbYqy^m1|#G%@-h3w#%fB zOjdI9QMP}K5H<+#efhrLJNjD6LUc*S4e0v(zJ5l1>5UjE<3cp)5cyt+sqN|bycpcd z0%nbB0|8&xACq}p06^F0-tqa?@y6Ln*4ar!UhjX-IXw&^n@8oJwjBdNfWNQri`U!z z!G*N_*U|g)%B15p(Y6DT5w0cp1_@MuZPyEkJ0Ht zYv#U}ge>la+Fjc1k2#s#lhHt$+qwAdPV}Tt5V{r5)}rdj5gyz9yM3v-U33&n3yS!3 zMkS@yY8Z9AxMSr!sc8v-j0E{;3hMW3N1H$uq zvXYKgC}V@P(p|u!jh>8@!U;9?rFLi>v1?e&Ws+Ni^g0E=rNcxPJ8iA}!E1(CCnHjH zJ+_RRKsz)fQwyGmr*UOIQo4Y>SaH^&SdrmJiVp8UB_BLcRp9PENz-Ffz=lGLfR0(PF1xa>CWhGn?c}; zc~qi_lfp!qEgfa5EbN?KvY84tm5r@sCYD&RNrbFZaK(2t}f{z20*!QA)(u~Sq zI}7uy6lw>(f73e6u^mYV!86lF*w;nbe=iySe4Wg>*z1?c>aCol=hdq$eTAXY&uzPy zH}B3Z-Td^1&Ex^vJAH>v6^}g4AxWz@oNitJDlZYBLWW3FVLxPNTS9em4RS_i3UBXp z102=mv~P9*_C~@6SLwz)_%?IQdT?dgqu|-986p_jf1;{dwYjr?^@q3neC^%solhT3 zNsAGAdK`nh`oIMAk1lK--1~05rq{Ru3jZcIgE2Z)$tSqr)4xqc+rz@bdJ*V0Z@mQU_!$P3J zL4a)KTuU?1U9ql=@@sMwS;mWgJs4MGWmT^YXW8EwBkn9)jlGm5!Q zBhm989jElvaw_+zR8c^4N!+_=@)ui^Dx)YgyZztGxLKe|`!GWa%~Ub#WMo=n^wnQ! z$r^sZgbu}7BZ#xvHl9@Ymg0%BEQ}^zxr;dY6rgC;C=(x^xSr3Pwav}O6pSjs(nCa=o8%^*5gphljK)G7q_@ff3b1}oV#J0EFZgfZ)<6kN9t!e zGVH|BQ#S7!m0e!Lv8n%V9j3u%6QhUG_=zByVQs@&)D6MvF1x&N)|TkGL`VK2qI(rG z3M=^8SzzeL*`?6GSWM0`!msM*motE=!(TL0P39Tdd?nS+QHc`;6->v@&j(lqtqKN! zFeY$Ed^=N+=L4bgE_A6~2$04jHS*UC_v}(v@BHw(bi%{ueID*ixHX7uRcT{NNM&2_ z_AMQo3>c^XS3oS^%O$OnqPT!a1pS91g^W*QY(mRNOv#4&I`-$bk z1}CG0Nt1T>hVD=#d;fJ&)*H;xvvk;F*8#tH-of0v{64opsAhSgaIR#cU=zdncXl*P z@*<*1XAEh_ff^s@vComoG6^xWBah!gQ)OclUjCnb4N7#qAzw9L1Eg9dt#PP;F!05+ z&-5;bkK(ygSRQz3_md3jyuzjj%CzXRq6aIp^>rGkw`Cu zcNj@+_3--<_1(~^-Q3pZS*8X2k}sg1T+>&lO*^6EznVXJ(;JSv^V47XWlWI0mu8JS z7YAL+>z}^YTI*k(zpjb5yQNM5Rni#gt-u}o@00iG<56LMb-vG|_v81w!7A)uKOge` z`@&!I!~cLk&hCvFHyi2Iyqt`g&JKJW3!BC8SseABtN9|>%mH4ToB1}vRO5= zW?KyTx=PT2Za4?!1LW4OOV8FT`w&h3OYznb@mf}Qsh7Qmyt&|7Y=GptzZoBz*`e%Kj5nLMfr?Xlu z;9}g63MmdWZsQDRVk%>pPpnl0e^HEe{pXJXaje=h(0Wf%i1loqu7Ut~XV zzQQ1hL`YK$M9jb9G@X-u>k|FlNah*TYN9qTVBEd^MW4ZDTrgF!87p6+GFDoJOmhSr zOu9hY3ZJ_xRynPG9#nkA;4H8}yhdSkmQ=eGTxir#`;c(Wq74AH-r=nu%hfYn~@^ z*@fz>0rd!Oc0 zUcCx-8o3BI2FbesCbBa_WX2!3|DD4j7h!)TUsKSTujPrjH7p>u9GD8)1F7OYz;58Z z&p!&Ii0L0t#Py>@=@^jp46`4q(6*7?@&<^@YGG?4Ps?<_u6695(`dgond@|L$L1>0 z!Ylu{m2B3YG1Jt%dMQ*Zn8|Vd{KMzob8){_*CzkwV6b`Q$4$7a;=i^;@IF_|o9%)9WZz63Db z#r%*BXti*0Ikurq{`H(25ThQ$Ptzi#U6CmplM%kT9%o*$QofF*yCtcVR3dFLMX^W1 zExRT0uT}8`7C+V+Ik`y;NvcbC3zA&jKPTxAx+@2!7bf9-^{d+J#|836hzIj^?Y8~7 ztR-lfnzN&$qw2@j*4r$R;?c|ZnJgd^Ziex{(^PIvp`>^oC(HU}hfz zYuZ;yTwNC3>wLK5ke)hB-)V=NTEW3)GLmhKjtvSN)9~wJsA#EaSCdI%10bbsSeo^D ztfRW}qPmbVRE;t|Wbc3QTEQlOqEg6|qjJjd1q&kA%rmQ2IUMv@fhOHv*`<>qCvDHo zFTwzoF#MmEDe@g40X>d2I{)d?Uy8Q#tFB^G$e^y`H`ZJ#5oGh{wm1o66VNCzu%Nu) zoS$%QPwk9}bi!0ml@QrmBu(p z$p|*YP3qUrMUWP_3^uk+X1|qVZ;J-;Gs8i88`|*DUI>AosyGXUetDWG-_kb2G_#;a z3wSht&taqH7pg=NCmT(HAJ7q&p6 zXe_dcs9Z;7qTI?bDr;h;AJV+2PQTQ(xBI-htC2qOBxJPplkrF+(&PWh?$yQzK#%?(p>y6Lnmt-zrG-t_X}9is1lX$B}D)M`P+sBWxx}k1s|jrj3awE3~#t#uXghQxa&G`WH*L5YX2! zhBO%PF}0}Mr3#{L-|pN=Bp1a{O2S=PPx@tQN$pr0?&lA=SxiFT);8$j)T^TDzaQ=y?-Naw|QsptD8<;5y3dqIOEF`02g34{jBGPFgG~PBi?eHvypJv3?t8= zVL{guP-n3Ya%n)^@2&h9^4XOXcH$2~t~Zi2f&l@sDBzpOXtz|y72a}rOs&@ssBfQP ztKe8LAjB-95N*Wd5D)7Cu_8Vniwwhr)F$ahwizZ|Yz6$){3Iy3yRwsHs>hTTXH2I!FdFU+EE6qvxoLf3; z4Rw7$RYeD0%<`}SO|qSK;)#TYzHsgUx1`t5u#qtWoNI40=I%q2tO|#LgnN-Leeq7D zXQPo3@Up^E7%%FL8m9_cdt>Hd&Sd`Z5IlvCj3~xNJIF~O5AOkyf!ue>is}UiM`w|K zx2QXPob89Qrc*iSZy6F4xH<){IsRqcvG);LqEypX$7_)|tX4dHQ_&lI)I*!bpa8pN1fi2&>rG%`XPv%r zzQ0nCTZ{VY0@p_9u&i&syp*uq0#SM1^Tj}6e`N!7Xl%i#lJOb1e{AFzl8SHwe))m= z@_8$!d!@uY_xncakc5_WpID=4?}mQh5Aop5{RAZdu(0s_zdB%?u57~*7t-bjh5)Fd0zu7QTEs0PLHEUnXK6V6P;nG?TeySz2UoB`t1t<536y)k5bo)jr^@|ztrGcU6j>@n(1^Q zy_|M-x6j$^0;gP_OAaRv$ZzCRog0f=1Rz`f!E8n}j{@qS{TBvTGV9mQd@D-}(SN8n z!8N+6l7d~#iq&KL;w0~3#P)b!(=6HGlbt(h;ass0B~~ z=8F&>iCXP05{gvgPzY@D;R^7E&8P~(99TbWHqcgKBJip*Bnskq6y@;(aw>$QGACy_ z$SN;L{5kGnu(&*1Dl!6oAT-4*_V!Yiod+JgF7 z<3=Enx^n~KuCe(Y*=W3*6z1omPq1(qPh&xKEoV8adkB!lJ#N=JpG5#hhceUIis+1@ ze$%;;_hUX5Bg7Q{*nQF9l}yjrlF4JFAh@9k2C|F9$XkVfXSBEz_BHUM|0cT`Y*O}m zh76!*oH}ztf}QAX8+%10iSX=d_8WK4a-UOPF#|DIvx=>LB#XzE5DU^p# zG^;TccmFM(D^#7&t(O%>@6F_UJte}sWlVppI$4AgBb+hT4t~&dY_=0dYeNSL-k;wE zwbfrzS~;Qu5p2*jpy0>OAupF>zM~rSqd0(s7(B5ie;NE0yoJJuU{NPl8QI$mf@6b3 z{MU2nf+)kV(2NVm{*y@}-cImDasdul5aAu5*cG+ZseKKUcjITG?}yTIn&%_Pf5F1- zO5F~4e~%ZOG!ngoHTpd2`+U27WCRpAa^PI{!>;-#!!QKNL-T2->~$dnI<)U$PhTiP zM7Pat)dyYTaA}!iW~xz7{`{8TPO1P#aYyG7 z8n1ugo-C8yvoPqd`TLI_!F2U+s-c-QJ`0Z8h(=>Fvnl--pQWufqd+|BdH{_zo{F0I znbws{PtY4Zm|RWXD#Hv^cYX}JvUr?{F&UGY+h?@u0)yU+qj$LP9TDwARRJzVZ6RZe z_@6?rmvN4l*-{}?3t+JtlOce1tX0Bzu91`m)6-h$q;(s=AJ|53!vHE!$2^5i#9?;P zga-m$Qb6jfmb=9&F6aUHRJ&!Rq>4feHv1b0KUxkeQ&K=shbHcc?rc6>eeg?Bt`TPI zX@>IVv-;Z_jYD1aykYg_>I)4Xqlj$>lO=RR8(2*rbWab=_SEH@Gc4dr9u-cXdNyLD zTdhWL{%8el+vWGY{F6m%Uk1LT1@mwp^ij0a&#b@Oq?pNy__@%`3Cj%xJGU*rI_Q4$ z*>i6oy{`B)NZ?aUq3Jc$vNw;Sre0W#m@=EmJMPgPDJ?wfvy zT>7LDNak3QT`+SYJ(J$6l#!lXZqck8_mlnt1Ba!I?r7rx5CNx zw_k3#xFC5P_$PTF>)26?f(SSjE#$7giy`44zhtcb9z7Q2pwridcQqhMl6PxF|IW3? z86?RHd$xMiipd8EAxhy`(EnEAm6Sm{>q>`{M$HPbLEsL%At3r&nnB2H!^HD14eo{n z1-Rw;9Ns2(tN#=7>8dK=r&EiTMEqq|(~-${vT@6ixWJL7Hzx>b){V8l8Pzp8F-YlB z8xFsNqZ3!?-8~E96P>QzTb`D6%aASDv(~^jNz-7Mk$f!x8g7(9s$Q0p!2?%kgFR$+ zMbBhvN}S`N3;mG2U9E+5NhnJBre+j_RXJ=2L-!=$Y`UYxMqBuQAK@CaRxBcaDW%Wi z`3z5(8))7P6pFfTn8b0_Tn&n{GObU^QCX$M?7&M!ri3x&#MtpD6TW&zzP2*B>Q*a? zZ^F?wMcG>c!taS=#@`b?vQ)3w+$1lF&uSz_?cXq)^}ju;+!{Pr7q`)CJ(sxWy}w~! z6u$fvaChR6iyzL%op@Semb9Pp#LBD|Q+0Od_&}1`=nc;m01;y(q;l`8RVZ8MSQ^Pu z+NtBC-)8wH+toY!_9SyJD5yUy_%9szZ`pNRP!9vJk zS07RQr71gOrw*XPQfz@j3u&1`brO^n3Du36q96Y5+XdmUu<@+7Gb^=u7q>mukbeN{ ztu$81z|qCDmj`27RLf3|Q8-fNFCx6(yVP^eC&-(!7p*pXoOE9WZDMLQlVIPD2qt-edX75J^{z7VQ)yU_RXk0s_*~lqH$IZRS6!dr z-;B8wMh>qino0x}N3lbZ8XRp7lMl)V6sEVZ1sA`0b#nEz|0)1SPT zMzp+tjywFEj{_A~h=)!xggV^9G?LE_y|xD*avl}wYbif769O};tAzL+?T{pqQP}(% zG2|yY8cp)5Xb^QQNSsocg@`!{3ze14xs)*LfCf4nJDM7q1xKx@5eR_A`JBycG<3G&5(4O9zaMS?q^-;6X&`w5eNB`yoU{bQe=>G9&7 zm)AZ|5RqK7=ZfC2D~nH~?a(vi;Gp}Fl%k;Y$E`jXoCTJ*_Z5^CoVq8SG~VbYV^$x4 za4LtswXtf)I+GU{rc_z8wcU(-CZ%YZ(@Gd&%5@%n;n_`ePWqS~%c#9GDA~)Sm~L$& zktct@&)t_3zRKo$Xu5f8_S|DO`pr$HUbJSVTwTbPn3_Vo{Jy)DxF>;SKCN-TID6Tn z{1@egG_BfkB9*KVFDViR6j@Xg2o(CQsM#C;N>1%} z_~r5Qk3bbKcWp@5d8qT|In@;KIIyE^x1RAUJ;YmX!Hv96ImIqbOqC2u6Sw;!VsZ zfaW#R&mmGnN5ank)<_)0rY`PwQcOWpo<0_G%ctQjrl+hCisCC?r7V0k>0~6y8>m#C zPR|zKH~&sNQl*Hr(eUv&pKe|_8~Af#y`zWA18;MFPhsHJ9NRvP?(O5-jZz-?e_ncc z1VRB|=lov-r|3s#384#Z-_jmB%W4|N zxNS#AtKKqpZ5tW}_4;9EM%s~?C;%=uTHI1TO=Q?abM>&YwNO_e0&s<0`{HGI*~k`r}Kl>d@c;J3N>3( zyFA2CUJALp)@ZQvT67NfnsPfzUmSlkta|XJ0-^$R2pq-^zTQ6oTg3`WFmV)Dl;R9D z9WR;IU#LIx5nkEEz)8ixdjeS$_wvi|Urnei35!J!QK4B$Loy76!crj{tI-E_CIzZn z#E@;_B3lyDrNNnlcYm-tJ!tU(6TD!*Dw-dz(*qQsZAAr4t4(iEP3=R5Rd*xHkk?{8 zk=NKovW54OjPQ>D$jcJYw(=NcTJhicjO{~FXA~$z_G)B=Y|^I%fV znVLk>$<^WqreG&}l39Z@4oBfFGJQEsB=|^MCVReD_QNLX)1%Zc?*_Sx++#P|64NdZ zH<`pnW7rZ;5OFtoQS49cT8I8^R*OirA;0w?b$>6n=j}LD*{A@M>RCJA#+AU-x@-@1 zt8BD-nUaKkZzF^#5cE#Br3y8n3P!a8!Ld5|9_N-;aWBVzJI6AqyB&`(#i_B4TgITl zc{%6X)tcq;ylr@1A;s{ob0wpcQGl_qGXWL&L9hWTL4^Llf|=2~AQy_|_x8cetS?|q zq^l2tKYP>cT#g4}E!dl;?9>*`Yf^)c#U$8{^Hp_F<19!5f0@*=$*LsCv?GLS!f!T~ zbGf{ZK!qId-D%?o5Fm{;;j{;AVTCYZw$ z>6qEuxUmgg>StmSzMW^0CC&4n*NUT2Oq*RGKrJGgq#YUSH+G^)>{@jQ?RHA0jmRD( zsLLL}x4b>()mFBm^=0$Dt~Kp((YwYQ%>T$u%HProh*kt3F;Wzc$Z{!5ogh%hKGN!# z_R!oB5?Z@^{QvK-YiCe$02dqk|4r=u)7ES@gwVsT-qAbls7IP?!3UV4AwlKaijneH zWo)d>iny@6UuBLo*&7*b>Zc!PGn%GJ?1${TFXDhEuRVenR~xd|Zs&;puRcC!kM`HA z0)$-%SR;Sh`{cy>UV(?*Yhhi7Z!O-|(HHt}%CA>|yk0h-si!ATv%lwxUI5@@O`z}H z`en9{0F`s3z<)41{Lxi6BGPg1{q?NGzvCiTVPtx`l&W>8dGD+Qz$nl@bkgw7WwZS< zaMs|W%PSt5FcAhk$CZO>CxEGo>7hwOz!D)<3MWc2DUl@AFV?4gU2OGk5e8{s zFck30=8~wvwuL^W1=ZAm>$*%m{vhYbDHK&j93r<9N-R~`r%G}WvSLN)Nb59oF>DChM;DV8QxznWoD(MN{mzwC8e@V!kUO&_oty&z?(}`i8h+ zjO)dwVmA@Nkub&;g{=oEiOL&f(*c|tlq?W)kcES-auXo;jbRvJA4SB#bC@7+Qp%kE z?m8!O>nLG?Cg!i}n?+CxM=;!EU?*y@emS9Yxj#%k)!0 z=#43lpGj&P*BPMPGBoKd>V|`hBH#^)Ps`5o{#=n3zSf3O644+@;h~L0?=;etmX;H8 z*1rC_WkbbG``6T513TrJsFd3BYMJ}Bd4@Z}J*>ds2u=Q>`omKYDKf5fC~sO|YN-Q{ zaAj{}^sTW0aQ6DAK(UVOj)z&`IbNT)uO(aY$QjfB6STY;JNuttLkD3>L?Hw6tAZc_ z^piJi_L#ol@>hVJt3)X_rU)?=JL|*qQ_!Cq@Z6BumYe?@V(TyA=r&S23o(az!4#Wn z;^rI5A&#}2ytpF;EwM$a0FSWY+_)NqT`{&AoQ$`=lT%`7&e{9FDxPG6H}Bhf+hZGL zNA}xG9C4SG4IehsTSt;Ov~#~e05gQZK(RqRjIK%R;@ZY=gKCXHo7GtX zih#o=&6Nb(3*}8e2agXkPl7PU)A2YG*qhDp=)|0p?>q=C#F`tV5LH$$E)6tgj7Z}g zedjKLwy(j@hFxp?y?L8OQllMZv6K)pDoUU_L#z;ga!m$%+z@E^iSR8iqkyIWS8yi$vsha^rGa!3h~+{w^Tj z(T)avjzfI@rU>h&5|x)7yF=d7feP!hnwNuMn2(bSFXJqtY5eGvkPBUBKP<~HV`dKZ z#d)dtr9T~VS$ZCsPAw@cE{Th_Q2hhP`m3LrZRJNbd*kxBj;MZ7m(O%^uYxX?Af@bQ z!t=w?LX|2-|IqonOg=e(%kRNLFt_vHFJ|9_7a$oU3B4nz_IK?TGG zF(HRuc}E#^u3-m?R7Dai|EiAc?E2vQHh7#QMU27d_ZpfzVL%5%W@vfX?3%7HFW<_n zPDx?dN*%WtX=^Sc8-HjGhl#$+&n`T7 zp$~B3EryyD*m^7?a!%n<$#)7&2d@!Av5J*TfJcrNCN`0qPs|QNXTh+F!UkB*2>puD za)mUJrzkHcmm+0_5LRU_5KImHW!MaA9`W@v65r&!cA4m$;g4)goCzU1_q^OHe~1M< z@Z}~jC0>rg%BH<4pM;$Xa)2Ddkj+o|i8kr%SDu-?Tk)T=!{h;Pgju$ig>!a=nl%`R z@YjJqFgOxc*l&FujJeAX!I;Mm;oq-~acM;XSmpNX1z%*xd}PJx-&6W3|D^z4ih~dX zmKdP7T8|wH#?txhjpRjQpg#TONqmok!4J(X(&g0H-AO}3k0+^?3qpmZ9GoA`_{zRBP-#S2;D>?POmmL6kp#0te3>h1MHmjE*J3}S6q|8#)uQ@swAX5 zHy5{fbhB}}si~YD;gx{zNX$#eXl>D|{;Zj@~ zDS~aqZX&-8eHQHU64@*| z>)OCy8E1_hNThcyb{G>Z@yMUPEQAuSl+m$DmR=2(h7vzc_Cx6u#P<|3vz9fFh2zNn z-fXUgrW0s_LQZpGQ!wtB4>Y?ZsW1HGPuSi5bn5kRcxGhPP^jU9E@bgc;fkVGi9#pt zAtslyEk>^pTjz>OK-Dg8cS*sFOF}*YizHE(3N2b%FA+Gx7Gw#~keXu>DZ}lo^F!HJjsPSEJ$@Er3>eR2*QD?;GN7?=P zA#fJHMg!??V`Y3Aa{LgiD(_fCo{EqWWyLho=2cmYVHoI%t>EJWFjiqLybSIJ5Mn;g zZFyI3e(N&Z($OLfpV#1bH%owrZ&%ti0l0^OQx1a2&CaRPY|&7GN=_IZ+_yn-3Q0@L zRX^CR-ANr@-9U{>0*#9o7N;OPGf)5C> zwW!>SgIlwR9#Ea|=Bmn<3`t+<$>R_YvB^|IJ3G?D>`?pOT!FMoSD703MLKo(a>*tgV>V7H7|_QFld>fTaA3Yi|E$7L}L)#L~brv zDM5VlwFp3Zt8rm_@;F?m8U_I?_ciMqI(Y?n9sP%Vd@4}lGT;xBMIk%}0TtKwCn^3c zYY`hnAic{=6(aW$ro5Dg5d9p_*pS}5RJ>Qt0n53$v;nV*g3PpHDW^2!(2YY){z~J7 z0RzqZJBVR#-9IB_&_FrZ{*x!zn3?}?c(0$V=oln~JaXk1#lOxLCKw$}5jGq|!O>zb zhQwdXq=TwG9tG9sZ@fJ$Doyl!G37fXXYp>A?mwxRvmCyD#eP=bF*$;AwFEbTuj_j z3Nb!TY`A+mdaS0*!gl6sz9B#Ho3O^V&nt4W`cm$(Ip1p|#@f2x@P0bRWpTUbRw^z_ z4|F%1y9e<{gB@+BdnZ}dbZECZ6JLdvLm1`#xZ3Bg3*y>|-iHluX}F`P5Av|_DV1xn zP$IZ^J_fK(4g?ZHf)3Ii8Q3WY!i-QS%xxlftTE^s=3@f}e3AnZ!=K$^yjn(-J$8uD zy>dpg6`hq`Y}qPzxgtzgTzmf4fk8MEQ78ca^8r*paU*K*9~k$F?t0QFg=7<@1Y7G+ zFnJoa1Qju{h_Fgld_UN>O`+Po8VKGyAs9Y2yy2s1%P!>SCc(xfRMqUZniY-)t=UbD zUxFh=9u_%B&*MoHzRRzLU$eA>}&4dG+dynlsOtuHP#Emkr7GYPEoXDDo#u zv22B?G1)^JoSWV@6HU^b3{~aaPv|cWnX6#DqVeW(bfC@tGdYA_RxvupN_-fUUOV4h zrkNr$1??h20IWuebD~lxCgnNEN?z<9d*nckvCQY0r&-|sSnv5qQPe{?)G?}|18Lrh(ZnoR|G)@4A_J)p?{^7-(TvD-im{@FnAS4u^oM^ z?z*X5u7go5@n|r>FxI313Dqk(!@kI3o;|Jv^ac8+@Zs+uX z){aVEXi?A|d6qR@)gu<&tZ2LsgcKex=-Ko8&+IPaCrA?(WN`Bck%rl4m3i++ z2CX_zMpG&CsYf4zlBuw50q$j%sl0vQ3r@a||Ja24|7|qVpZ`}n{I=r>5GUZ3U~W+V z(hiqk20I;^-a(kTbCgUYUVZ@tr$Ytgl%8BXnSY;Hnj2I)kbD4f#30bDdB_oBhU~x- zaMu;Q>4+N9l9TF!1Zk&}C$C-s?_8RCu`v#S{G6*zJAmU#khqvg@We_u zBq|rs`yQL}Sau1XOqx&Rt)%)pd72u!}P^#pR$FTH=c|9)q38vp9b?Ov}J* z95?>-`r1$N{5s+rv74GV;C1J1ZyC!8I*KoV>d{zxMLHSC)%nMuXrSz0G>aVY|LBE@ z^3h*{>_5ra^}G?iPiF%HC90OF`BnMCIG!12OGsX1G59lpotoc{DA3a4x7lGVFx8uS z1o}5nxq1*qhqz-vSU!xHZ52j32)W&8FZg`Ir!o?#U;dHL9|Q!f2(H|oJ*y~lOl{Z#%ifZg>d z=3T!2Ug&uwQbPYmOy{VkscE=O@H)^c%>$=c^2kRY?4|>C0xxGNIlrdIQ}DN;f;I_& z5C9;^f&50}2_7tHn&hp0!*31fgOebplker{vT5;<3)<=*?cGCj5mn=Fi;cYUVz_Dj z#eq0QKZ}siBD=mSdBt2 zK|r4+WIA8s`|RPIOjT$YzW~YV*zO)+`WXNf1-C-{v1_%M(+qCP z62!80FdY6UaVoV%^sxk+THT0&F=Ldu$H6j*X^YrNO-7-K-!C{QpN2BqcN4=iLVupc zd*W@2?a@!reDLYE{}TdiKv-1}Rsbv4|Kxpng;`lpVeA~~1!>M#VN~S`tS<13@RDNP zzF)`4)ki`$suL_4(tKFw=Wz-pWegblpo;Fd^X$-y?#Bk7!h%K`P=(sWr>_K8d;WjD zkU-1OgrK2zzyGu`vF}vcl(jzaer30m2c`X1V-%0!rd6Z>5a760KlN+f_Mrs%#wp5S zh_vd*Y;~JLLwpwtg^B6f5u8$biN$I|toy4OK*Gb?l_E%GyXIDk9W`olTVQ5G zOBi*uw53v6Zqr9D7VQq5kI3vKw3_UHt*xw3$8&=EX4RmyFwnam9v~tgRRuYMA(wE; z0?mPtEZOc0$e<0Ogvjj}3@IIjX#i?mR49qe9rg%LCHyp-AHh%F#t{K9BgtdhaT9c$ zl)Y5glMiYdqZ|g9z#2;jVw5@++*c|v&0RRzVN+0G`#W|;QmL~e%W91U3?AS!gma7F z?*tqjr%mpL`h~QE5*%%oENUk6VN7h?v2{=T)C5o>R*+ zYY?6`R!tB@R8aPRGot?6*Q5n+YY=i!4yLxRr%KQu9RKoFEEf>Ae?Z*VJzh{|CSa5c z2rj?|ZJ`7w8^>-1Bc)8e>K+{;HR=cLV5Qo?w?73;fqc*c$jH#r0WgfpleB*d%>IV* zsp+5>XlUvc*T^`xv=ex`-&b!rY+Zgp0`AT!j#~kCpR2A9k7JI9n;o}Zj{%1PM|uQ@ zmvPr#e9~rWF*LFR;1I7PR10nyuq~6FX}5sg!*3`PiP)0YTeFpoJ#W+cv-@acXFbq#jjg+_?%)nO|#PZN;Mvhj?iW66dQz`QjL>Fc7YE!JD;$y<*LOl zt0VQADK#3lpXfSc#Z*hp9QxAXWA;%cE0x&v_!)`SW^6L+v+ZTXwD`?nr3KwZuSlB;4LmwnX zn`LrJ#)q>f;dFmI8xO3q(1F8^koILH!#zYC z4OQ*)yKI~+Pkyq0roCD`Hh~fb8vIqmW;h=M<^v)T&Oh|D9C&#G6dAeQ(I@~2@$9k} zc(;^m=35ke5~|sC;9%}#@Iz3-o+en{B>V*&iCUOASOcp!x;o!+b$sXh1y1c`4NW<( zuhq?wQ)7xQMiWY|CQE2F-?aTNBpf~SVpDip)$tU0CE4^VdL#=Jp8PEUPWsn*-;)r?on3e#t_)vfQECU%B@R;9+Ov~u zh8H^GOfYPjPf+ zPhi+SpQUdV8a7IrjSG-LVPxb_lxsr+OMV~oYuyEl3wn&-$fiJxpTL68EzBpT&eXhI z4tlaZ1N7Rj-^IWqeSl>PH3DI1-}uD7_8I|myAtxk0#;&I@rS5y(78$L*Rez=ld{}W zv%V=%`G=K@fCK{q>dA65?FP|cg~2CwmQ90aew-6A;TLK7`2#?XON`h)-m!q;VK!}I z$>lpocq176`MX+~vFT}ngA=l7qn&2=~W{>XLtaU&w0dfU2p!qdb{k|kwIr1JBdru=mbEPK;v=F@JlQbYA=>-%l8q%lA)-l|UhSdA zdvfyYGy`z%@Xv@ha5q+kcUe8E9+1uBp=2K>M#QH#b@*qglOLD`fY6>l^QVruZ-fd% ze=|4-bbSNB{<*W<7J|W1A(e$v=H3`bQs1~u5wj6_hY0(5$!^F`dj-A{_n35qcXXzR zrf=z4)~r0%7Cf%jfxW~{9q-23N%i^ev$loiS<>`JkgKAaf1|+^1}#BTCX?8Z$~^Jy zsGLUt;zDd=n!0Ca9<@ga7sZBWQ+R;rP5W_=7pex(uP2NNyr7>>W2Fzh_jr}GS9o9H zwoPhcQepHKsJ0C=n4Z7-qt7M#kime7WQtDxXGa4 z06sas_GTU<>9@-CdvqD04p4-#p^@9@POf-|-;<^LiuYz-&i4?oE?hSskt$rhWXAVD z&BGKSrJlky6-R$Cr;GG@p-b6rOCL5rpx>bZ5GcR-Mw#fI@_ywyEJ4T)G#AYJq|rz! z>m9M(VLhB^sC4i(-9UADX0N^ug%ThTRMlD_l0y!&phhoPsB_*4TkRXSFA5%ciKW(N zF$@TN0c>6pzknK2(iv4dz(pm&(3*V_wI%H)%m&t`{W`M<;RxX9t$H4VTX}RJGY||g zt)=Lr?{a+Nv5)D_Ltn;Iw9}jJ&XTDhi7rH@c&tIZ(2@^x^DpQS6otwP*>`)?O0~j8o;E5&nyuHaPQ{c}4;@+8 zr$l9MThghbnXFlks)U`BbND=uG#vjxfJ~&S`WG95aQrI?0g-({(2sUyvPqP)?>~;%IVUR0fDBC@0H*Phc`Z7(qce|0x6m8f1ge zgL3{KR5O+hLMRK$`Gso8fbhp4RiIo<|Ni4^1rF2y)Qi<WXN<({|^tIY!u$`0Qc>c1|*5?Cz=OhG7Hc_p;DrS1mA?UaYB?R=0xU$ z@YkA&{W44Ysj1yaEs^c1qg7fh=rC z_7j_d#an6UwJzqU@m^<0O&2O=RB_>x zT`!XWt8B{X1f$;5?6=Rqj~c!8MD&COgj}(cVB@6YMdM$K@61pd!M*Xc!{{V6NU9Pj z6D<=g6WPag%mDZ|csG2F1ZzL+BwC4h6LQ8G$WYc|yCcqpABZcYc#@)>68J)*(TPCC zA|jBPNyKH4xs${40_cR(#L$>gDvbDsk8|p+g8T<8&lVplu zN+8)$mI?3zn-MBVIVjR7ND?uxlz}P!>0(66(`B!ZA08X-WXTPku;{8ZTiU4QMC*qX zs~SoIClVv5Zy_P_7o=4atXZb1LrU^IN!D;@2TE8q6i%%pb7Ha{q($>v6<8I$b9skO z+;6!%nGSWmY!emL^0D%cNl4UM{L3o--}0CD?oj~VzccG$PUJYpG=fk}Ha#iROLp3+ z5mzhO_V}=ygq_y#{VTK6^@ zxl9h8UHbcmwemcVSy<>fqOR|*)qx4V+FDDq2h zIFg-%#s4Hi7(@E)n;wowCN9}UZ|ydl_MfYx3BmnT8-}y}MO(pJndD59v#TPWlB9Fp z21N{#Oayj_e_I)7PzHfZDqZtiRDQb~)UX$D2cPX)0K(vnq(CIt^|sc}`{Wr;=pV#a zeuT^1g2m;>A={FJEeh(5J0J_2SI*Vh(y%rs#Bzr^nt`A}0JON%{bM z0DfE%eRkm>hr$b(O?88WVyzKt)8}PrCU`O_&3jR8{+8)R0*uurFa3?o*x-KN^ixhP zepYIym!mu-Tx>FFf8~Yr=TC+a4?g$sCgl`OpWIunu(hr9^MF!*al1Ku$6=PqRDhha zTId9I!tDlAAm4Q$$0@L0d5CVVa$5!@{|y{J*pPchlnD%zg^;&y8yiP3@#wWUOBNiG z^32H~BZB4;Q%bb4`0wmwx;q@FjB#WlWzL0CjkgYTBW6X_>o#33}aO!4>kN` zg;*tq5QV{@#0t-5{>=)$ge)|+wFoa(p@{%kVMYJ<2MvqLcx8hYjs89%5n+p#{oVW6 z8U^$KrFCaRt&so9?7V&Q={+ex|95~Uns><3OD4Tnj9(i<_vs*HW4v9iC_fWWM$5%+ z4Y&s`8|v`zz9^F*8KLbYezn5E_*AXC?Vn?;cBzbYP$9~#hK`4IGNi$Z36shXo5 z{=)550e^I>g(4%5?$;z7xt6k!{?ad{1>x`(3HX(8+rdOZ8EpT=mMQ4Epo?FrK$QM( zi;yC^bj3~O?BAku&x2=+9%PJKjAKJFO#?5DA_Jw0G-~Y6mH&1Fn*7$t^Px2}e`pI2 z@>qQjyZXVrc61^JN}nhxFDNu3AUVP(zIE>vG=N>i?jmcJK2YMsOFOwGFnDp@KC>H$ zn}13)8`W6xTwZ{l4xiqxbA|BY@2*gYHX}Z*!0EI*UH4Ko-tHJZs6-IQ=ca1Q|7+Ic zJD$0iz}UFFd_&1D02czGC_Zd%`bINrI-qg+m}8O|Okd5f@Yp%I@&{pZMrQfcAffKF zE|+aP0fRpw3qagtRus(VyURzG<7K$3fUj$QQz+eCh>KtQq|6GVH~gi@S+<5F;pO8T zeQGUHCW@0Q6$@qMYICK$cOU{zqP!{5##p^-6dNDd90?X1plo+h%m$S`z7w#v^I}Ws z`ynG70o@GH(!veX@blqfyZ37X6I0}6 zsjepFZkN2{Yh26VL`(4gNm%a(=@a*?3xah@ks#{YcT3PC$BAmtbQy#YA=30dFsv+E zTHNl~OP|I=fErRZSB!rG_IejFXB$zT7uv&i>AA|SgrLMUMH8$MjiPn^vf)J&N{>@4 z>3+3)h=n(zZgpU5dTZwIXw7Q@+bFL|5SvQAU^S;0bCYu+*O`V{q=9F|%pTxQD{D-A zelkqmkiT8k0#2jp+&V=$S=ul-I^=xug6w_zAOa{jK+X&TKYvp~6o4HfiETVen|LAj zWSyX23z9_Ne*o5RUPnema3Z#`sW6Mty)0`RiieTqS5&NP`0hC;s@eP)EBuPT#dpQS`gAkpdF%v$r&lEP za)YV`BtMHe=pu8halcgEcc&fOab* zA)@SvMsv}l--!vRXMPB6#$Bzm^iAD86MzLdcFxl70EwahjbG}|^Q zAhIyQ7ymG~NSR8`3_y?}l00gl9*BT>cbWM}a$oOpUf!>AK*qq~X2=!EsTCb%E-!E|xj%^;8@sLi`X}JUkeNjWfYstcX%M=zi~o`WmyGC0-6+5 zo~#}})1hZl3iCwg4$FQrpf|8B%Y9q#bakY zysc`Q_R&6>CgSsJ+2FUd)3o%Ls1IAm&q}WN@bC8|2bviul<-Y`n*j%rSAf`&V5~Mj z=&KMruJBeZ7|GQNaU_>El*n#=YTxUr^S|FkV-waqGWoW>tM8!$x}WIk9v! zN77U0}({ngaK^LU#5;ZjzFE*(!>{&~%DzHp-@Vxxh0~p1$?4Rdkf;@-DuG|CwOtjz>TC zf#!yZ-!HWtcV2O~SvCjuXyAE2-tQXm9-%GvYd93*ApSA&W2mR$M=N|we*F73Y%e+{*Af0p>H8m|djw$o{6Sc)+^~G#TXdBQL<~*60 zu~uILXfm|#xIUh0I|^M}&wGqL%)>EL5oArXY5H^oBnD`uh?CAa1NmV6J1WU#nw>y$ zqs8-!qGT%iRGIOE=3OJ5uDO%o1yy zJ}w?>WnbiZcr@y$MvPAW@hI-o2jq%fD*rigFd2b)Fc9Z2*pR`W6DvPmY}NuHm8(*c ziI6qT44cVru22+hcUIrhM##|`TN0!P7XAUTCk;}E9dP47KArg7Jdz+;+MwugbHJaM ztVc$wP{9)H{Rv1zZtm3C)Yw(mid?6APk2YUw1T|BWzjU>KON&SBGPjX>FqMa@Hyab z|9gXsFgM8RG)g-)?(YQiy0;YQhBV-L*zVi#vOamm?q13255AI*QqG*(RNULy(Cta| zJ}zP7@=_$N*hk~IjN*S9aPJU9>-E)QhaZQ=vKs<+2Lhlg{~Im-mXuO6#9cQe*=e-- z4TTeW5G9HO^h~0ZMY56v;#{LWmtZMy?~se@)Lc3yUrW-VY`Mq>!rp;Nox6VRqThnF zS|fU70~_p$(5^Pr?hUyL5xZGOHA5PUJt_RxW+ThJiXKNT%0a(yE|)p4^G)-$*rLqx z(_(%KojG9QrbZ&$abbg&Nw>KjCPJJ?ug0NjgJtroPj2an)BT3tt)!wYnL?fIn>e~> z6}?dr^J@s^q_%OoSh6?GmKf=_B3Zv)HSq(6C0`dB){n5t>y~w0C+HsL-*)V3q6ZO$)Vv~L^G=9*Pq07k?9WF__o^x?T#x7`5pH;Rp?JcAD(h9s zR?cEDljSA9wRNNKIX&}5GGKc>E-?0<@@aG{l$N%t(!!wF9x|z@Kn~k*mQ!SD4;U|0 z?luCvr8lGyKgo?@bF(*J(jw20--DdM{xF9T0nk zSS?-von7&MMG)GcAJ_;$6u%>D*3*&;QMJ~jVm5eq*G;vNyscW< z@xWeTrP31SzZ<^s-iSmO)-l#mksEYba@{LYb!eGCELp?n+Kg&rmzBXC-yL;Q=0v1K z=x-6wDZT7jgT~6K;~R>B|2!SNLs$*g$-xXqxV5GshtSC#6{{|JxgY6QD@`8(-oOG7 zcc{(%FOD_@t=r`~ZSgUL?Wh>DJDGr)WnJbdgO{a@MVJF#^-A;!mPt@(h_%v#x!8v} z0`BE4ExD`s$4d}^#`Twg_@6(bXEn0}lRx`o%1Il}5zW&nQKQ6Qfy))-r%3DVCNX_^ zjjG8WRblJl8v+hK!A@%2w2rhHY@$aX4RuxcifwNYLp>`mOptDQ$ttBN zmv8E($wy%pWtr_#w*46uQBnqow080%q-qtdRv^QUcxOn8gN?0s=~PALu#c(7KCMs^ zX^1X3ySknIwL^cz0SJIuDa^dlG%k*RsD=p9E1U^3J0c%gv$op*e}$b@P#s&hwqfCt z;O-vWW#PfyA-KD1umuYX?(PuW-Q5-v+}&Lgf&_>B?EQTg=bW4WZg!298dbAqcaQfO z@BG{A;z+K4d5^X5qlz0L@yhR-1))yc0GH$9lT*cjtwoQiX^D77`FhI2p!Z{za_^g) zcvEX73;3~s`?6EwIkSC2Mhtt=#i)=CeGKxxrg?7iXGF@;T3u7aW1 zaL!0^xNmO2Syp-0R#9KyUl~>s62V^!CAg)!Dg^ z=8lg--m+%_Q7d=Q9)ns@n%p-tmt|gfH1K?h1!_F+NXI(NWpniB>&NyaUPprTJiLL{ zT}D;@4ydE~Ak3h-IzV0_xa!I%#Kr3-Uv)*4^b-uh4#KftOeP>iV-AXYg(;q_;{uk!x0^D4O6AST^rg3k?y3G*l{3;wK5e7 zirEJN_#Y&M?_Y|5zjgWrS_A#v0{fq~)qg|)j5OU309pXwe{23-9{_wX0N}r!DufsS zmZbQ1Y~B$Azz6_xwq{`f*72c%|JrA#WitR606?DBQ3k;FM*#5O>jhd5fB*&*7+yBE zGz>|A@%!Mvib0JeU>EZrE#V)@;NQoNXai{8f3j(D0C2s>{+kJ%BVZH;hL_{tRB&AZ ztkAq^X3WsE?`XvpG!dAa0|@+|Ol-5>dg3}yi(g*t&iYD{E%N<1eOe_*QLWyL?oL6l za8`VsdA-866{LHX{ct(03-u|%zJRKEpJhA*(bQmkBVJib`5J53JN!<7~q1%&0EN$~aUVU@004qwzz$9OWd;{S=P*7L{7s zBp{3}m~{?Dp1_-=j|&qI!7G1v+HB|(4e~lYYVV? zC?*NAp&G?UWL?E(Cd$tYSAm9v2DZ))=nXAMHN=^SwIU&A#zchG0e7gZDYQ*fz~T91 z_LQ~R!1oW7-Kv-)R`u;n3T& zHZ$#XnIWX_SraOo?>?cPfP*%p9ca%Kf~A|yaWv^7;6UydPR(pp(?_e1QnO> ze3fYzHSvehnS$lo;XO9{&4oiHu96HhM!^QKmYCv?=aiTZg|Qs{@UbW|5$q4-0UU>l zh31z#bJ!YF_0Nr(ONkbK)^bS?P2fu2@o1VzAa`;{<+6_yZV!$k5JoUJ6E$Y16(hll zp`~0=^cVQN5VI7qJm5tuW^7m z#=u@~tfauqcOna5Mx_s~2WQ$$a)JX(?b+#O0nJn6Y+&~99Hj>YsjgWi%@ zr(=6S9&$ShZfrzjPjEM>@*7S;Cv0?}GFD?{#Tl%=;_|HM}3oGJMaYyD()6&Fdd zuh&ozt1PfqEJKw58_b?%YWy@{bgx!F7e*T%URzo#Pmt&C$J-z_u6U7yRMaY5`{P%_ZB5PZW z1U4%x#TE5FuXR_eVC%b7c!7lqzw?sepi}Ldx|>rh((v102QfQa*TYHIdVP9>gvw-_ zL*at2$tC7?U_b7#a>KRk06@|@BvRL2@kyc~SbyK)q!MS)yf6$N?S?3|%9@c%HLlh0 z3x1$$Lrk+$aCDV`<#s2pZ`X!BulCrS71aIFE#CsLyPO(B(~wwgp5aob<1fV4PX z8B>N(aa=#^Qf}CIcvQbG5IbgMR-fkR;nuWuTSUBGhyM|8?s0TE(IJNXJYsOsuo9|y zx`2 zUX0}C`m#K!IWqt1_4}^m7PmY|!?1`$ZIiN?5%yvky}m{Jg!Hv@p{`OpbbhCVt5J{Z zqd_=A`Ur;XB(uq{=ysBgdbHM`gAUKm<2G$!oa3AN4IbwgdCYGGnTDp|^2oQNlMbrI zA04`$!6lAcs{p^W-)6Nlh{fRLFZ46;;O4?#2!m)r6eBpg^rX+{lBgbq4i%0JDkm7M zzVtc0>>Dh_+oDs@5oz5&3`zJazlK&K4ay^$ZKHUvV6y38ld^5TiN(237W#aORTE^V z;paH>w+#2?z`3Gp_OOXk?T=kOlN|akB9jafx-FPwDd+3r26_*ty#C62f1{cCyGdMgoA(Q&roM9 z1g;I*?J(*JEF;KtFg-EqbP6UP4tzDK5W4wQs?w+s24_EJ5@QM|);GB2)ltVXAqgPd z#DvpM&(PL#DsI8?c-t)4$-Bo%PT3)*UPnLO!(-!a?E1(&n;C& zPxQ@~sbC;9&X9R-^b2z-8d%rAK);oSoV5O4I z{_xU+5T=}hcge!{h6U?8`SaEf;nkrk?u#bJet|l0`Bz7>6GO-a)8|dIR zU;8>cIHzZCSlqeWpVeI|bSgm^pkyXe8M#|9PoE!t#+)#*Huu5d`Vnd1&oJS#q<;G4 zOjkRZkcdOB&z4`3z@to*%4uI`j7sW4h;y?&QSS#O-8jd4nY`9d9UdI(CTn=A`02X&?>J^)C1$<5wn%zR{0)!A$%~(#IR| zXeA?c@XP3o$y$aMR*3}xONV50R$T${xX(4nyM^Dc?agfJhGz|zq<@rWi1KOn@Y=nz zr|ah8_RsY@?pgVBsBon`8^>A*u7zsbv78=iHOX*~2V2=jv^f5DdQCv3+*& zTkZX89oFhzeg0}Yw^@*M$RgVT=MKKRcJ=%E$I;vSIIeN~OWyPr_^I&ml7uE1(=hVy zR(IB>el;s;o@1IP>0h*t=otpnCj^=vtm{j$msdxr1IY0qB-mY@&Pl;i`OCVb*x$z| zd*Ji2<>Q{MZ%+qUl+EjU^>qF45q{sl=cy?p%6)zR>h-z84(fPyx-_qCa8e=9WAL6= z6n~Y3RjrOJ$5DBDnJnG<5uaB$s&{f;y+^IESny5{6fn!uG^R+0CpGzqSkey}p7c|Q z3umoL*AtGjhYVx_GYaO-E-CXO-AJ=@Z(Ll3xoWw|;@rR}ct;Fv-_mYwqq(QNIOEcb zq498bWhKyczNDt-0*bfLk96B4-Q99>p_5}&Z3Fuz1vXb;sMqJsUOL?pQkm+|(y7`| zG>*nZ`C~Yp`8u^WbhQP-1W=BT#>BX{i8_7@M^p7<_7b7FTfyYD!Q%=(eE z`|;o*2E$b(3JWh>-!bnQ|3D6G0jsrlqBxU3=$?Kqe(xGX=^FntZOkT&a8wz0bTc}9 zJTWS+S{l5)%!h9}HQYpqe4lT5O6ZzlJ|DVmeG2g-_aeRNcNPm;M0LLf;pY8@pOVQ4 zz1~75Q+Ey|QJtm_dxW8Tn1Z3zJJ?qTVHAMbKXsrQ6^q6U=$FM97<)p(gQ77qLZ{zg zaFY0I;n9=775BI zqUBX7M?hrsKY<#E0@+5BSi0-X%BSM#L7I{yw>(KV8b#^k#^RzqCJ$LJd9r9d0_4OW zICJQVVcKZ$hwF^@Ys0n;NkFnNL7n@K7W6@Zv?m81vXgB3!x-ilc_7i? z0iL^Vf}%OvT;3nz6BD8qSg9M1-wl9O!i{wN~gI0#RFh)ciw_A%BUlMb_#Sr_0 z+EmI)rCL2MydJg`Xr2YiiKO0;O~-=#(KZpOT$_%H!#paP1jI6dF6GV^Etp>h8_1_x z%&J|Ne5mcbK){k!oW7UIh*?$cZz5Zzepn)>Ntgt+aR0(b#z_OV)@dCBMOOd5SX^9p zSPOZ1NZ($iutZbl9bb5UnXEjHGXmdVJXX#}#bDE+EgxHT-7cn0etkS0iMl^;dVZ^0 zvuEwy@OEzT@9Yxrb@6WL(l-FL-Ru+G^;P~%>zuiMym`FFY8?s^F%rMqKRntzJmb78 zJdI)d6-xSdsf-+K*;|aa66$#sN@a=0bNPu8apbsO{TUYJ-~y-W32&Qau;lCpZG15- z?y&%&7yRJh5&By5hjz?o)bARp@gO1+RGPxrJhTRU#>lE)>_osLn@WpG7ZMVAt+S~^ zm187-MQItmuM6wcc1pdMxW^mXx%9t^7wETvU43@<=s5t7J0C718Fy^#*`+&!@QPpx z+~xxPuLm#2Af0~*0PN>EjxIchi%-Fkmdy+cT2ZPyFqMC z2axrf#lMEky>JG5;Ver2I0n%o@hr1A9kA?@X;|fVA*yp5k!-x5SN9crl)Lt0)TMtP z!Q+g~(dmOrPx7+nICuR%K_1KPLn)yZ@9c~8~yWn zp&#H;@W3F{+OHk@>R#faIkiH>rw*xA#^zOImJGt zx?h=f4AmCMSIt3&gbmzv)7$b_4c~5W zS6Op_yF?AeF9A(fQOibyxJImIL1&GS5|0R{CCCfuU!$>9LXc2HGD7WFb9U+YV#+t| zn&j;S1bw6tx5LMMqg+AI<7VUh&$A#AXnjLLkxl=X)MSFRp0`RlBP!eEe!xs2DvzRe zd>z;f3m@Ym#F zZ?9FPC`z)0MB;eVPj{cA31Dw-oT{!^gehzr^$+KPath?|b~y|P5)@ld zT3^UiZr~1|ET+ovo&*4XLq3R24tynsHC#lQi8&nO8vvuWry!sHJ<(b=9S55ZYPT=I z`ZJ$2a}%vTM<5#YZsuM9<@=1*!hkL-C`m;O<*cR_;{X|ltCZElD~0UxZ@}~6^-2mYvs4$P4el&eGw7<$e(0_y^zHB0le0mr|!8g zW$jEDTWH_r|JUp4X7A*wB&92ieMXMz1Hx;XTp=FBMkGgrCHUrn=Je10GC8kS)G({+ z2Fm_|EWuwjY=c=JWd5PaC{lbgAnEbPrEKKpmktKCCXvQEO+eOLR@Es;%L#fy0*3+Uhky^A@ z!>7=LdWEG^o9oNkNVZ6gbdMR;m|B-NY=sYoF-8a&-#`1I_rxNpqk^d=Pm?}}5ONRl z5lD}?-*Gnm7I<9Qb$B36NuLp_xktcA3}ox<7ATaW->Oh_TpJeIs;bk}>dQ;fy&rir zvnz?JAjj!N*tI5WIut6BC4(wB%v z7Lyhwhu>RDRy7Q?n1jDDH$A>NYj$_@cPP#kkqqx=Q7hqYOKvUV9_ekxP=rXTp22z~ zMoImoC7x=1ly(eY=!6Q>5k}#ZI~pCcWS+s`2#ejrx8gHJ#%EwVWbdGu>eKbd_Z#Lj zD;JG~-C}1zeo4-BkCi_v1uCb5nD3#=G~TpU$~5iUM0h+mFTtCRjb-9*0`&1zZzBiz z-OPM-u(1Ycu`Cu+j>eWrLdPqkIQAfpg%X+;%8{x>s+T17`wnmat=w-Sog)Y4X-P?& z^gtcm)NFGKAks@NI@{3?r7x)*Hz{M~6QK43bCfYz^}GWO$}L{tDYsBsBqAA`jEGO7cMk_=%v~`mQUU$hQjse z_qP){9R09HyBzsUt3N(JpJ(~}(4?{Q8DZI4R>8X{;JJ(&Jc4g5-VSomNpAPd`X8Cj zgNph~bmc;VMGk$jA5~2Xo=y^jjoI)+-}f_OCcGc%w@&U9n7|={Ogh-`_Y|M9Wc~En zKNIiJX(s;bI_{!v1r%=9zl$S~k5-W!kC@i3Y2)1(0@r}Z+5hiy4foG_&6U;@0l*jI zF|pt=voJH`~h(yM{C@_V?k*JSi*3wYHR#C0@{EXhY z!p*}p#%CtAeI5UhI%YmBNRyNyIFx;3w4SyNy24|h37-(()t`-!QQUQuNy-Ls|Jdz$E>SZ3@Sc;fw-rPp zGbngdbe?`=`$&ovRPlOXs0j+{NGg6{!pe{Co9&C7)+1rOs4F|WEFLcJ2V|p}R>&uN z>A&#j1|n-#*Qpy&aDKB0MBmBaP0dh;$?r)ce+o4nZ>G-jf(J|RL%*Affm<01b=reA zpv~&2z79;Sz;#AOOx4xK95&mHx|r_C*^?>fP4_Nh>KQXeqtEj$)?5t#@GwnGbePYv zglR{(8`@eyc{Vn>ptDp6@^b(iK9l^F)3ax`46W_v52(xPIuo=dNzf=gEEOQ;8U#I3(Z0PBZ&WVt%W#3338EB^Ser0kyC>$Dk`WcLK$ex8Qy zBP#SKn4V>=eJQ@KP`m!bo+rHS&-Loho@Zyz8G00uE@HJ}$uw!=nwbu^a}bGr3lBHy zau}W`#z9)Q&qCrFkuV*w=S(;Xk+CmwpqWCg#KUZL7qCQa`F1(m^JRh|N2RhPA|23=wII-GdNvx0qL4~S%L+*s#cTKt?u z`DkbM;0elSGc(ja(S=pMyecd;tF|ew95eoA+#RvZPYXze^Ww)+JV1DXLZxV5^VjC1 z_~-9$q*$t8>9Hyu3DQ9NbUC9aG&VfEeawa9JM_H#UnJfSsCk9LLYrCc6-+d(d#f#d z&I@C`(N#%Cd4E9*?e`zk_K}~O+deKADmA7YfMZ_t_`ht=NEj1OGPrs!T+ZoF4A?JK z(HcR{yYvK}d_XZiPLB_%DZ(qb9#bcNU;D(lmd7UR8Drj9)m*TD4RQ#M626L%9x1uw z&2M&5ob^;G8&erV?7V`P&vM^LfQVTp_)FjY(|C3jGqt+FoVUdUlbShDn{{+|16yUj z;1S%7$n}$F6EJZAlKx^lJNn3uF>#P=)oeKjc9;pr8TGOaCqUX1ITqqlwHncBO}j&# z9dxSCOnqL(SvK8HbtcFpCgjv5AryE*%A0Pij+Vhh} z+6?uKt_|)_Ysq%1&%(SCnL>fhWF{sd_;nLvhPD7at&_SJcwOQa&56k zq=$`by9Izg{OK&+E|wr3$_zd*M(tO*i1vAx7hV^MOOyw%_%P_)H1p0h7P=Mg3sJMj zGLaj8vHGV6x0l^0ihL_>BlcK3(a?cpnt5eQl}ZRd75ekK|6PmmRS~gx<&xJ17k28= zpQ$e%YsEfAEp=Z442R^kBQ&dkF;>%1`j2Afn!Y%Zgim_p573RLMCJffoNEuUKmV?zb=G-BC3s|+emYt0yksC0+ z1xnv(%kJF>D(m5E!=v3x%lIt7Bo|C1-%wPhZG7hB#fA1y+Z{iijVUVI`H0P{XXFmu z-WJo<5R`%Y6$elGusEG@r=*1BCm`PG5kCHWag}U%9<|He9!NDqhix#+d$tQXE<%p| zirN8s^~5Ok_)&GJ_XSf)!CoI3f1{I*sC#LdZ_r*k%^@)g(!K2i+h;hzLVa$!nO4KK zxs7kXvu}cryF{la=5uw71o4u+EpLQ@Rnswl^g)yUv1t<5FZMOqI=BuuLJ5c9Rec(@ z-wtSgCr9c$M!58ErZ-p#-GvS{xb%M^M^=op1V-K3?q9oN~I<0^=)iA@VB2?osZo=ogx~6lXtt0H4U#0F33D< z!gG@%t8cMKptVcIU!EiIUhEHso&Wo`vqg4uH*t0M Wa<#BTX6NN%;{hVm&`2svA^$(V&y;Hb delta 35091 zcmY(qQ+O^s&@Nna)wXThwr$(y({|PNQ@5+OZQEM4ZLJ#ryZ8Sc?C&6Rc0iIRXW#UbTi+i!3`!umotYL%?SD&(BS_K|-aV9>yS`iytCAT|&*w9*4| z9-a5`u*U;`=@6Gimkj=!f|`34{4pS+;?BViWu}N?X6RQ}q3-W*F+~rv3FJe)52HpW zZK)I`=cQfePcr%IGM`!&^Iuqm%(4z}qduii}<1|Aktwdeceb zCGgX`k*!6TrZ9q|KcKQJzqp1-1<5&zJz|CseY6#eFMHa1Z^heSpYyPg6p;K){pvWy za!WWXprB*t*75G0<(NPa3~nnugK-+m0`n^gQew)$nrl^jI3YW|;m#$^vCNrI?)H>0 zFN-=|o!*sFxZ;CkE+FMI!^~`Xq@&2~W7qaH(TF4aXd}s&$fBwaNr-JS_IHXcXfc3` zMNkmV&E3_)!~xEG<2qX|;gA}6?Dmo76LJt!;yziIr<%QKaYu8~p(Uc&&sWhc;})RP zKgx+LG;UsMRE{y?f=``I1gMO@xRDy;a|U!Tt=U*)Hf$eyc^xplynD922q|q78F@$a zr;4uU=54S4UY6I{%+31_0O@B7Is$+^K@`vj^`C3+-}f!;Zl5lxcHw70PDOYc(8=qv zvD4ps*PCyn+#d!DO=m&w9^Vsx%J_RyZDDzz_mRgw9|ZsdP-Vh(j|Hk8E7yH@AhhJE zT^XEBb0{~rr=DK=L3?sV2@nLIS{F6^PUotw#%ZB2W8$api9rR|Pyhj%1^_dK(`uZf zH<0w|8s_l8gY#Gx4;-AKI*`wX(`cbiSklnjL41`iuj`Yz;zJVuyCru7F2vztns@v5 z9+dH9lTC0O7fIDlqfT&g4Pj0+c11!u-yGw|!V`^k043VMqZUL**Aqx##t<|f2<iol%u}rBTUKUhPs+sWy2fqi>pw4qMkTi zru?;DI9r6QC*iD2hPKKP*_Y-Y5Jds#I7@ycAMTT-y;!Thl=R7aOC<4)qT@m^f3GUtJy2S(*=lHfLty8S>?_hT3#RvbINC_%#-g%xLB!TUT8fM z^YMK%4%qmcBW3NAA~AYGCSyd0Om<8vlg(x+Ia-|I8ZFZOkW-jaJd(z8 zBGi-Wz|mN3hl_(V?cmV8lTG0)eRjaYr?AipMhz*iikJ%T(CXUbvaTm)f?ivkA~~q1 zUMsD~n~L3i|J7_`%6zRLzG3}v%7x~#;78QwbFt0vhl;Z25`dw%-bKZ7a;A!x&G&qn zBum77Gqn^a?UO{3TNi0s7Br%qVC0)WZDknJ$3!{2+T(33Oxjj7@ZgJ1M}Xa(-ma$z z4!;+xr?IEuNMdhE8hRLI?D|us5(AgEv5bBJBuf==-onC+hjB6OjD?qINKvLN4b;so zHb+%=6azoz0$eCPpSc+Ia}E9u|6>q(%0EaZkuMD+EuMzs92G{1j;e!F>337FH$#tc z!fDf)oAo4OYLF$&?f*+fGS2SLEKT%VP_|Ze#)15`jdpjvTq=T84S9!zgtkh*M!Puo zRD1#-l@g0XVrrX1Y4HKnjAxX-4R@h21ZCSN_@Gv>G=OEC!=+bwv<6z+9w}mLS>*Z8 zw=x$>+ivSa^aks!$BySx@=LHDsJsHpALjA#2fB72jtdvOu;FDBEVm3BB8G^!bQ3z~ z_44FdIUgAGZ2t#0!wI$$JgUEX4(T#=%hxcQf3J(b3Q_)JP) zLBKVKu>l#P*<7pSuem;;ICNT3dL#HJbtF!wnC&P|wIgOA?-PsZY5d1>Qz%5Gp{RpNB~63`A;h-q~BgDVcgxH16+ZJhc7E{x4Yp+fslOIHHGn( zubza=zQ;+g)!hU8o0otW=$h@ORn9w5-H%sqQHWl-JfvQ+xwk7)qPy3_P2fJ!F6U1{0V()B1a(U!{i^bKQ3@!2vo|98=_~s zoh^`%oQQ0LRH8S6I+oH>3a5A857a`2L`tJRHmHP3iFra8vPuBvG?q~}96ZAIJ2s$* ztt`0gKxwZdR-p!Oy9CiJUI5IuDwcLW15$WCcuyU4Sc+sm2`y=5=fa7F`VnjjGNiE1 z$YHKl_^MqvFd%(*YkDY0wBJghc0!dgzh67(9JQoAqu~7=rnlKVjz3tVOZ^tTK*JlJ zXpk*zxdZJEISLR2E+?!LU81G@I+3bB*OxiLLF!f+2Bh6>B$|?&eMyg<%CJ2qt z$9ccM{{-@wX&pkvg56dYgPST5yfva`vaN77zFsh$D__9K)BgVZjvj#VgOS&*_-t+- zh1j58Ldz?ig%K4$TA<3|JADj?8|tzkz7lkXZdh57RSlpFIwrvkSDT-7fnM|c<{?K* zvtKU27&VUgL3Hi<&UZa`m6hm?x4bsp#*(|(pSt^k&NuA1bMpV(sdzG{uN)Wq5Kpp8 z=typm5yfEN^inr2csilptm3^H;GlJ71m+cI>kGqYOI-TIdeGPDY3~%SN7Xr4t`dCe zevker{sADTHZ03}{>BWBf_YhZ@0T3umNUELy(waev5XkSteImU-5FM`V&Sc<_Sp5L zj!8`2qzF8qNjc8t4Q< zqZtRVMH%{l@qiaq@1SVN&R~KdRTA!rFqc732_XB(X3RxLb%@$(_UCe(z{@`?Ppso3InaL>ClTi z2v0}wx7Hoew@ych%cQ~XqA^c(_A;fSiq!qgV$}EG=B`@qw-r}eyIWGY(2=M5s$as= zHUNM$B&23j)Sl})-ZEbp_p3N5J==Wpb|^ud{QY%stk2v6jgh~9KdwZ{?0#dgg8hC_->pt=?&rONhsg(wZ5qwZE`TU> zDI{=0)Nm1+pFO4LR|E!Wtcz^A6a#T=1|Ztn&zpM&G%1j|m=vcuKd2oMW~{fr2My_l z?A|#!?)Mo#h#oB@s80EWDDvg%q$k?$Ds?tD89DZ$@!C*>Vf9~P-m23F;nJWpea4xU zP^DOXR$LW{xinu4eShGBbhBm>1(5P%@+^aVFnT)Fg6guU8vgeLMCRA@0Qse~6QG$! zyAg)%ku)PXvHs}Qw*2%x2%e0rftcoiDzPMON2`VKXF7p^{7KOnuLy zD>J+JBB!z}D-y?THcM$sKZ64tX`c8O->ncXx6%tF;?Iv2OPu4N+-U1PMcz0Xc%l63 zg7vk{261}LYxm=qx9GK{3$yQ(6+p^{4S;g5E7b^A2gyO7#YVvk+L*B?dAZ_Rhc~t+ z)tmltm$MGGo`drntmD%ki+{I*1(N34BdRn*zX;E+0)6pc=fd1nSo1oPNExzzeBM!( z!#+pUWlO6DI2b86PxXWaKmD7W!>|QU*@ub147hdduhe5~)=+bvaAb)PCxAW>m>6ZR z8AhE{+vZQAo=cpCAPbG3c*O1}c+Zig(5IHNrb$4YXx64qBLC2&HK9SZERSP>GhOd)cIwtVA z4teilX_^geKW7#c0-+u;1i<|X;Fn-1(O!fq4n>*aM@JFqr<84&x6OJR)dI{_T`4BF4H#4gkwJZz!=Ez2Y8k zW&_$GMSo&1q#(PrDMHaNdgcbISP1_Wk4$MX<2G&N;y~^gK<)CvDjgl=MzNPTvug8# z7~;ck60tHe#Dkz0*)&H*9UI3~ckZELq+d&3tEZ6u{_~82XBNsy>yU0@r9b$H%HAbl zGRAMANFUOFkSiP80`QHJ!)ViW;pc-pv~JWL{JT-V;##X+Q%n)rnqdzz{laUnn+LHW zbFgRx#5Z+OIJGqZI$EwLUBaCg8S1Tw(tE&Q>ir&pb1ZfVq!_R&3b+XpstNwuEw1+1ar!=uKn z(>aqaauJZ+Ohuo~D>|VUyTsDILJ&xz@ z-S{+J39N$8`F9ctZ!h74aC(dCUzh#?BX}KnvxsK}E?Ry2HmR}@cx&iHchG1~z;#=Km(NHkJA{`_Uk?csE#AbB z6yMEDm`*CB#0IX{k*8A!mvI#nGyb;h?&umV3^;b?1Qhx|OVuX$RU^bf`C;@Nul$Vm z0^+bltTHcbFj*Jj)ogH+GuyT1Eie-;%a(} zK>t_>RlR6G`#h|o5B&5OF3;4oIAxq6^kY;uK|6_h@j2DNXyD!OaDi*LBnu7NFz9in z3Vn9WMdX-t74yQ0Bk)rv-)0mCLa6bQ;p>9${Zk%Aa;GqVai+p zlkU8;cA9 zoYZL(Mqz)!N2iO{LTd4K8*F%AfNUvfG`n!^27BSvm}-Jyzf2Eir z_lbLNn`aC8`G&q852=e2oUh{A?|+R1qD=Zq78y($W=xwx?R+I^rlKf*!Wd{XxJ6_MmXC6yW0>RIx5@mDHyB%?K8P}WV`g+jom=^(Jx!>*`)7$ z-yi{MOhm~Aqb)8->S>zUEVq_wb}>HQ+kQazwV;637@&N>XF5=EASO8|C9s+nlowDZ z!#3e}-OqFybY*m%`A#Sy0`&a~9hfiI!x-4pLR33Jm6aKC#?onRCHi## z2g-5NBn^b21ubqfrU%UcLx}ppe1848>_Op}zhzQT%R58`lpyoqf2k}*8!={ORl%~+WYVVb72eX-({({M2W1V$2#G`p!*}csC)BtOF<#5t1f{K~T>cu$m;s@R-Exob;I_rrATA z1icpiFB5`Y4zBuM4$5T$Mt3EXGPm3trB=T;nZ*xTxgcsG67)BuY!3lhv>dtIaE(^{ zZU7q0!&rm~ml+mbm^lkdGg?*HCwga*8XL_R8-8XC!c4cE-|}og^zTH!Cg!9Ml_+S}`W{>>3cTmBh{X~Y+Jh*QCXDa+7sF`R%n~A*q6KCwi z2wgc0xSC$H9X-7x*}oHN`Vv;gA=+i~X87BITv1`U^tgy=&L$>dajP{f6Jag&yfdXE zqKAQ@0(ompSx;xba!g(i_H>WdS0X@*d;+~;jk}Ypb%ik16+C7}nq^e~-kt|Dbp9Q? z{0Um>CI)WmUku#fRa*8ll-l`%3;jPRVO}|2%OQ_xw_ zV)U7qEtyS00fQA9(+YWE53)gZaK~xVbzWCf>0ZrM`)D~Owrsb;TIW2XJ{kZKvDARP zl(f8xq`Ad5c9&HZ!ZE`YpYw6ngja`%5F0w z_Fp1baunDLGpzb@)J_Fj)W-RoG~#nXpq-$IycqegIJ)YRWzyf& z`EfZeaHmqCU{10=MG<3k3h)LdXD) zy{PftGaR0^2%KQPcP6SF)gAiadkB1U2Cu6_f0`63s`;nzJp2BNGAA5yF>(C&j#R#9 zAM5PL0TNPEeD*8(a76y2FtSn9Y-g>!Fm=RPP?1_<6BkBh$LmQqQAX3!irHN2-=&OVeXd`q}8h`&V*ODxSK-?Ylw z%tJgU6~Nr`;34d+zaD^KG?eQsAm2S?Jtr~eqWHa!1T@<2?d(ZxyQ^%V` zfXfJkBzFDtnitK;lB=qRTBVBZcC&QAw4sbf32?ST1tHxuhZ z!IK-WhG`mj17xzvUR}wlTAt9K+mv@Pc-V>5LMUbs92w+L9JBdl*a`g7S)3M6B_~_` zGB%g2bhZ@hs)=}`cC+LKfvTquPWq*@y$!&~D^$X=7B-eNoG!H#=WTNx_5;Br25>e&%xE$ygniG3dDVo5h&M<% zO)(_#)K7XuFjyMev=nF8InH#lXZtCf9vo}RdHxx?6z*JX!?yIq!$LC2>*o_v54(|D zAC>d#h`2Q~twLXPP5wVkoQ6t$LuZElVFPC_SjFp;^259BC*-m+Z%9@01TM{(9@j&j zgWY%509)rdsPK)-8`&(kfSPScpyOdaj|FI`}4# zCbUTLIe9`sn=@GyGALvGG1cp2Aw}w0V(DykbBncegAlPEo70uEX8YW2(H32t@S2s4 zVKD^Hibgmi;aOCNYHn}zdFdEV~6;M_=7V>~kN`1Xz{hRa8+9En;Y%VO5 z0WRcmZ!{&E^ahi|+9(hH>*M(y7Q;EPE-x}AtD!4dc$SD0++Vg*cyGVwo|on&TZa`U z1sv3$N2kh^J4R?zC&s&s}K)NQR{8-OFz2_7$b)-=w_EU^Q!K|Gm+p*E*7?`7lI? za;d@Lcb^N6_ddKxG<`$tk^Z2I@@MT~gjka}4{`i#PU+^cvb%#nX_?}5i&XVQ0!u&^H*Yb`C!Kp!2oD2r@W<2Y3*C{jTx(_L^rr#ev5t_08~^7OM}x-wVrCo3?to4YuHfy+z}j zuYi5Y);W2<)vDX=?Y!v*1n=$BDm19KVrGWH^D{=cUfTP?f^Yb5l2lw_JT{Y5*%3CO zruv)a-xYvxDJJpa%z@kQQR}Kd(Ax~5q5d148+cT(%<=)T0`_o=2cms`Oou8Sd)f*d zMJd+IJ^uUs?x6feaOFing;*ie;~*=I@14##oq3v?_=F?D-QcVacwxUhGE04S7b)34 zKYCx+X%*DTu_LHWv2F1i>jTC%d(eyb@t6oo_KKQtSQOjyOUy+6x*2N4e7EtXYWYzw z5#R0WO6LR02`xY^-lo+htWo-YJSsWe27aUbuDeO%@9Fq_e+M`k>H}WNm@b3*wz_*e z056|SOy6HPyOvAaY51 zMfcVi(C=55n^->&SKk*mgaQ>$&D8dj1iHIBMtxBAhTFl)kar+-EDQ>fK!YVp{VYz1 zY2IQ|K2{S2DAeQmJ(Xs&rSMoDj%()uCYblEA_qkC@9Pu5an~t7Y{I}X{->+K20yrv zDW@hqUfM9cl`a8!vmSwY^S^mdEPgD$f&-$*~0DeeiSFi4cGlEW!y48 zUKa(adwsI_M{BNw_8?C>#NjqGAJq~vPX%b(#u|R*6o(^{k2r3y`&^q1ByL!3Ns{CrJDcKxN5$~PGe^zKjTR7>Md_k~syKEy z1{<C0IdwSKnmYSiAV!jB#Kg$^b_nI2a0y_u%jA^d#nA2QD z@akO&?K(QvAnsl20kQR7m5>P305+mvkdev6_}v8=JKnv&TnFCNn{5Ze>%D2v2Okam z9gDDbyI{j%l7xw{aonJ`aQ}&eh*7NIIY_{wZrGKnTVJSqpuBqRpH?yM7D0Atc?8s2 z-gv-GBEq)d)s|p27MrlX^_F12X@koLh}^KIn6e7K;z2#UgWYeiJ<}>4Y~YDb{IGAFZcaq9S@PwtQUObj^&gKXa4~AM60=elXAU>;uHH^z4RyO z+5Pq`GKBK>rvitFZU#iOs-j_B6IBN$pT7XO^Qp^x$DON5!Xf+1aw)wMr_oLdD;}tJ zuzI~9^q@_!W{@LvufQRL42%9;ChD*B^s)e3!M4E>DpRC>D#Z&%;tRr;VIAl#mul># zA`H;8GsX};mRe|K5XFmls>+ux`&R$>B`XFDQG$_UFc<-luqXlH&crM%!W7IDqGLd` zT{zZ{VdLw=0(o7ddGqn_35G>*xWA_4!InPUgcKa-_I}5rwioNqqAwhv0+RIG>`%<$ zPTpCixA%>)$yphMz9mnk8g=PA-4_(5E+-;}{3#7$Y}0?n;H9G6=sy4K0Tr0WE=suy zUQBu*+U1vGuP0skWw&&h8t#%gd+Gr>Q`v@hs!e~*TuGk;x~=!?UrUzh4bycC{4?}w zx9MNK$GU7RDM1PT@W}t4T7t%3h>mLs>P+k5r50>&6|;FN%8=xsqi zzkiSa7FLH)w9~6Q<2w^6cB>T5Iw|MmvYr1n{}E>@6FBT2IIw7OOe}e)CUOH_a^EBB z(KD{B>Ch=xXhgm4eCiYKnAsc*A(C!J@=$+B+JyhB*kVX*dtK z|3|bQ2!DES@H!f~$dL@k(VN(%VbQZP)1w0U%0>x59*lI9PU2lkJu6 z+H6_WV$rQ?y_loGB-h=9pepX}ltCmS~> zt9JZ>F}!i;gA2CuT0tO@*P;hus}O#2(p@;uzWTju-IA_mglzTCPekx9f8a?H8o)_N zILiKIwE9lF0SNEM7i<-PgiqFfzSGWNEw%8$!>wgwU6+5gy!z;Gz_4ul&UV~9`6Yp$ z@AKL4Vlj&wyZG~2f^AG&EtGQ%1TAkair&-uF7`E$k&GG&Z(qr-*OWU_`2>UkQ$4_c z){(2lA7@1(H9TG)2%W33T@n@B{#{@3A7^TZh|qBO0GBWr}u?IIh5ecn;`6zyJA+y)#rCkIx{8H7l`fm^Dv}N!_cSG>>3thY9 zZjx$SrH`rf%@Jt3hCgy|s(~nF`dv}af)?0+Qrcq{R!Zy?inaxAXHKW`w|}nxeGwUb zzrX(z0vK-X&K#eVSFiK`;c(jZN2})WxHavb@4OT!DBFOK+8*%icW(+~^H#K5-Gv;g zY=JooA@Qz(g&JvE zgZd#4*T4#D?i(-@lR)l6K@y4M{+mf=|8GWSaSaUYaTV36Kb!I=DMkF*qJeS5_e}uM z=Bm)L%|O`Iu9_d7g(e$HRto(KR;n7(0_!8}#3d2j;aW3&d*Jtoq7uEQx8mbkJe<;{C- zFfKDRZ}7V{h#f<3wsZLuPo%riB zj6Ik7$N2^VXg=hZ=LVVVgaBAYSP-dZq&1XyYodBG{qgv}cn?3?@DOZ!MueCkb3R0R*W3=Dwu$fKWtEl?GPRU&Am9E=KLzb=5X%S-&Jv>bT%J~ec4iWyma!ly4T`oG zF(6cp6;Npl5)*U|a&jFzT!{og8_Sd9&-30H$j3fDej>`+e_Cah5;l$TCov`mo>08^o*o$)ba0Uh~ z<2b}NfNhK;K?8Ecb)!8=(fehY9ZhQMpNxE@Uj@*p7Ok zx?5LuZJn7#bKGJ5WR%lpKtcIYosXAHdAa`u{!y ziOW!EJ??}J`@jj4+Jk|3&y>_<@}Xn%rt6s&+I_B^Obe({TPg1plq818MsTfpq?UT; z_9sN)=M0=NgXp_rek^)e^^PAO^5v>cL zdOefTCpdqn0bIqQ?7m>^#T&@tyhakl>vTu52b{hY-5KIN&yN=x3B$KJ?_8dWnmFrs z?;9lXdz#u@e%Y_@Ii(5t#17~EGaD~!HZxsn5C9LD<={J2aEF`Ka8QMjJa*SquK8>l z4CM4?PDz>&D_Dt4_BaIf0Q!n;m+XW{dfYweI^wW5s*Z|5BvG5}p>{_4xOc`a^h7KjOvMD`g;6;RA*!8+ z6y$*>1As=}{r(k%NwqDgb9h9b^T`bliQPZC9z~DJUP{RA$1Q}OjEo(Y9t};10T>UH zN+F;hGe?lQcW+cM7f`diW9BJA@6KE`u7^bloy(q;@a(3eHy`7x6e;a76GZmQj~quV zAzsjc&gn7s39`?w&P)we$gPnr2B&^g1Az#p1cYMsfld4l5%AEZ5FfEz1esBX#N{n^ zVbm&huvKf$d4<%eRSf@qq=CHKd~l#krUwTf(@?^p(E4Nq1QWTtthuAmgIMJ8yP(!u#&1>z*piB({r7f& zL)*V4vJ$#PZ@UDJA&0K65=W)qfVf6`&8CHG|fJ4RG41x3QR}miV27= ztGS8ceqfVCgZIuHbB=ftvfdN-U$Hu4uHO-)-cxUlBr6Pwt)rz5OcDEY4MUn-sa(dT z68TBl?xI0fqwu~^X-f$m_$Q^%9=VSM?mX}3_mx&-Ag2v%ve3K?J2jmj0LG==>e{t; z#w()Gma8zo@cMU~p$$QpB7f9C)~<&!HE*Wm9QBeOvQ~>650>|dzn|!jC;6fI)2&LD zA5=~9{Y0UMZ7xzvf`0a)@1s`_>j(gbx z)OXZijTDwgbC~NV%9HUKWsqa17ln;G>+FE0Sjfz((gg_*lXHj*KyINy(Gzd^dfV&E z_NSHG_5SW?MnkDT%3y-k(sf6E1D=+o0ow<*OnF%cn(lqmyIy3+Q;z&x+`#lh3-FvY zTMp2kAk*`E|Bcb^7kQIYEUt!{8JnMkUh;Qh(qo;>$&&Y5;=fLUQ@Y1FN%NR9ofq0D z0yAoYUa~Mu3&?+B0O_dohTJ5Xk?h!y(&t0T7JUf9NjQ;rP3_h73q`!G##Q*a-xbtp z8(yN7&H^*PP*6-LM3#%VietmtehJttptBD9WlVoScJIIsQ`-kH3+v8Ogthdv56VZW+o}xaGEC z=%UU$c*+<%jFvVJNq6Vlt* zGwW~`#5jj{16ZZ$4Z>YUFuUC%4XyB+ZrPm0Z$(t6v3YHkI+4qPx0mS#9A8#?b`gYZ z;9s(1B$&|5WppWlWVN>HvA!Q$7TCyB!ar_@t(-_M+2k4%FtHok`-6#3Nu{4g@EL8c zELAj4%lJ^Cf3~#ARd^Wd)ZJp%IPeT#s= zkP9fY|E)5e;e=)D@6V|*hkN_yA8h}qB+KomC)R3jbMX(T5b^NF{|^Cp*ns=mpcDYM z|5Y(GNHK^B5k?Qc{laitZxp{clNW)pfE;M;s)qEi@wE-ZwP=p{{<`RnVANFh=0EK| zwX;li)Y4P)Fnw^iBrQ_Zr&ZIny^LUx&Nr| zRE@FOpg#G-NICsRkaDJ}s0FHDBuj~4Kgz|jd^x>16r@5N0gd(OT69RMWk~e!^t%TP zegDuI1ga0VU_y+U=xwsbeAkixnWmW(?&k8D=HsZp7ya8O0r-d0!uBtfn=kNQvUBJE>q}6cl>J32AW#vM6i~&$z2Py9`CK`%4$EPwLiBzO z+>#-}RDPxCkn3KWiSACk9^X>hengdAZC16$ewT4G=Gf9be+5NjAhO!e_DXZzx>B!5 zs02T`=}YK(xxBnr*L1z>Ij-%CaSLz)P-z=7K?|9J;lj1^qt_dICIJ&nLTeKh=8}g^ zroUL<01+xeYo>JXxQ16-I`H!~-3=ogbS|YishwibuI70ur5Uqjcn^mC1+<8r$z0B; zbFrxu&}^#E#jkCSH{m88LjYQbwvWv98=s_nT}Z!W-#A^!X3S($)ll6zJG@0a8ZrkO zImJmEhXlBQ#o%VqFv6%th-S72Wf$Q>ZnU66#-&3YJk)L8!p8$-cxFHaLzu&1Q;h%O z20FT5Tuq~f0|h?-dW8-zY>r4?BA4lZ%m;K<1f>G7|Gya6Alb<7H#2ho?iaex6}ChX zrz5dw6P}_KsLN6cyVW|VTOZPxo2QRJ9%BF%$4eWQb!kNN<|csSG(jAE&>J0=&Kthu8JxijeLTVF7Ed*S8v#X`UaoP8BuYexx%?c_uTw0nWn z36D(3Id@ChI~)`lhIR#>v#C>h=*Sy=6nN*m)hSBYw%tFn>x0>)_3cLpCCmpTaZr`; zqcZ7WrB(u!AoOmO9<(rV9v`J-hS)^WNz|JtR?p-YAIAg)gv^Out-{%3pQD2svP^Lg<6;O0= z4j#@V6mkFu7svmyZmNM@kubXO?ia@6ngxxDlocvWus9h+>-A!@Q2!Y@9XstP|Iu#U zY=^r^7{si<_uN*;j)dnpk^@`i$nBr1ct`cq(i&*5%Nw!dTmBS#gV~?&)4?2 z8(-_WT-`eG63nI66HY{=f6X;rDIY8eJqRs$SUh zm9?I2z13UFtyoyqL+9(|9xMXc{Vo3hkDe2)OC9fOh>s7}TntD<|K}X228q8d1lhW9eo2WM4L#ApT|+jXa?o=2%ukJpdDL;9 z-uMY^%;}te;W*&K1^X>UDlD9pI@pyuEIlz;vv*(GDpPN6i>*)3(t{|xBKU3eLho>E zBx^O`WvBP@)ZqIC%O6e}=YQ@nE}%#dD5VU~|Jqy1Q?^6Q$laH8&l#v8L^g6rqssPR z;p7YrVsnkno{$aXs}BPJBRNhUcN55_EFDWu+RDboNs%W7$z@=GIw%gH-P!LLTvRByOpi>fQZ_awl$4OvhA#~`grDC?rudqg)Q7XzI`f8!X+i^l++3lkUdRB`jQnn!&#&V=~&JQDs# zfA0SiTioni|F8Z5=~Iq}oao^%fp83E)KL2d=*ZZ65)feQxrLcJ?iFkDqy6HX=vGN> zb?$*0sV(K8o3DX{d3a2V2HufKU+22pUmQ6|N^iP7Iq!#wyK_WCBwBNC|CVpt%j3(2 zJSg7vKWDXN-}nC0Vn1sJfWR-lzQE6m@H(MhD#uE* zz=53Ge4u_*Cegvt=?6!jz!THy#dn~VhSy>9(uc=ub#MFO8_y4?&2IR@Wd)$7_Y+2` zm_IVXt5^-XECjLw^k@?s(NMRIL+p*QtNLI@GvUkvS* znu3KGR?5x`qo(V8%jV{+2?xt*V`B{b8RI0V_VtsA^F3=7IKaGnVRK>0YGwQ4uaza1 zWl1MI!=;@S%~Wi+n(@hZhhH(()?BmT=axj)P3zDt2g@Vjt`%t@u*e?minztX%iFk8 zseH->WRn6l9ckK`{G-l(BxV1}f%{E`Ij4D>kkdZ2|cc_bkua!kx~%KT2hk~j+1saEzbBj3;HePXIH z{1?9{PWUFf>I=^r#9qxOI&_`^+34s-sUQ^S6rwgU$)?hOy3$gIA<(tZktonh!cb$t zgfub3M05~Mv)rB?vzwGQbAGQ`VsAJIE}+j{{M?+fEKIn6HjPAd@Bo(%eSJ5z4LK2s zhL{DP&eK8-sYG%K86>n?cI|J#HjkzTp_u zWbftDbz#Dn9n1g7$SpEJ^37Shsf#*=Iv`UO+RTg}{U~T5iD=tjnCN+t4>o#l2KMdrId}$WZF2jT14iH5 zIFO9;FSVn>no=rP`g~E8L-8`Pvnl{+JgKy7R-PV%)-AK{) z$M6F*_Wc@S@-UY|f%Lgq8Y!QBLdcESNUXY!3b9}h=+Le$V?r9|{JCNkS=+Y`wB_m= zn@jOSpWuE`_f{<+homUL;8#OF0HC8CEMk;Du@m^}4ypOdnwd`s!`jQkaY8QEvov%< zHSnU*@%tvDEXyHZ3IuB>z<$Z7Gf>#eD+A9&1P4clFRFtaS7OS3`Pw3c7)JY8&QFmd zKe4NYS1yQ!%aE6|{q`M%Q~o<%F<&!EKyzlZ6)mbCKB1)Ghlkc!j2}VB&T}K;rYLXd zrZ}xz#2Por{!+`lbUtuDm6gBK&Ds{nf^}L7ef2U~H~JZ^C)c)u_ihsZ&?m%*a7YgX z#R5YEWd`nPgHi&R|JTnqgOu&)L1yHz+Yj`PEsLb@Vg>Z#f|`)}&VxDdWlwi_PKE}< z*XPZXUxxO7!kF0Hl6i7p*C}^1I>+5>J^j{J2aWYygzF3wkyA~U$&?*E-ttY_HK zowzB%{4i4s`F@}h#Z>mppSC}n(KWVoL?yU+y3>tW{oSr0S&HeGQ=`HH%)Oqh9Lq_3#r*^%BCMzAz=oJa`alEFKPPovx{EFYp-fZZ%fDGdmZ zq$q%4p*)vX6oJcxW0#0!vm&-0t>*cU^q{FPqZTJ+1{YLh%;!&voG}>&yAJ=?9Y%!p z)UreN1m01INXdXi6WCB*5sI({%Za^7(+X3fv2$!`C@0~j2JIz>FyZ!6e_~8{oGCR@ z@-E(~Jx=U(hg;!(**xQxtzLzOPz??3-G#=Iu_J!_-At9W3=wy3?o0aTjBd<-fO$A@ zX?DCIX(Ii#`yZbrAyWeH^g&4g9w^1zt<^UcPAonf{aK;dNZ%h>;?MKYu+vl1%$eo3 zvvKH{g+xW#F_=&!9RoTH;UrJoa5Bm0?Z%!`-vH@g^m|SU^naWbA`?G7Rw64%S3umcKshc? zd@GrAhiaR`XuwA1f>+X@AekG*4Q!TUNT?#6_k!bexb8 z=EYN4(?ed-k7DIQ%wXgK;BJ4A19PSl&}~QTzTbLtlM>dD)MV`5WO%;k?x?tDu1k)=_MPbKalvyjFs#;=h4|G4)5t!+qP}nwmY`% zNiwmWiEZ09CZ36tH|IRhkMDf{s;cY0x_WorwRf$x_uBB0Nn|N*zSBt6%x}c9ju1=2 zDV|vLIaD=tkt4(wq%F3}EKrT^fwsu6W@f`kEJch;KruyAv(TE!X6T>WX_=aS<+cf6 zwQ%SHAO#fHzJ-LI=FH1<>IQrP6Wo_y{%hlJD8w9?0+=gf#1NPWprs1J{TNcRJriGJ z7Cyoe?>g3NND@Ink+`4qN9F)N=0c15oTy7@+SYAOhMW$;rx~xXU!jsnK}hOaqbTEP z3e4Eq3Aijc%=J^V{+r!~#W z{fAm-ac=kto#XVbOqRgF?TTgk3d2OG$sfvFw-}rK#_rN42%R2 zwha;bJ{dow`Abs^YDdV3L@JSs<#kLJI<+NfhtxIrk9IYm==t4*_cybiyr$yuEu|@P zlGY6?QMu!)ZOkgH&M3$uw<{cqk6ko4OxTLQis*eN;}yjL3_2!%eLwxVDC-EzWLGg< zdV7@k`C(dm^i?^H$knZS1bj`loYDbDv&O|7De9vGb0$;y=F?1-l)Cs6*9wf2+hsJ; z?2Q&xy1AD*eiv_$Eo71>TFS-0^@>sTr9};)RKlvqVe($Y=;TgOwaF#{?$^Q|bwi4U z=^jt^4xV_sacslcAV^O_c%d_Wpe00xDW?PGpa$OVp=U9te05RYmZQkt-ck{9T6IC!X{clvUZ8Pv6t3ROm zT2m+gh{FYkwklF9w`YC@vSrx_Tn}ac_DAx6;SAUk``TDf`-=o~OUm6jhb{i<@45?f>JH zqQ|Lex1{gRI&j&|e2~4YFRn!1P1iNtZrr3ba%jCLjl5JEwh$CAk}5ujkMSBGO5T?} zr~7z@j7hm zS=Wu|)k_`|MOD%i%T|cif+K`GH_PQQ)1=JPP+iVfLZx|mDVEi%j(%nSxvwTTmQH4* zRg8(X5>JKHISERqp3k;YQD`Rjfoa~iS(=54-RjQ_0W)@ZzPwL3m; zq>(&0VMmSylGKl}4iRzAV%+V-2Xbue%Jcge({Cej++kqsNv zn>(Ww_g@4+rwBXFK_(Dbirn9s_P~ z^ZCx&*LA@4u`(=Sb)L%W{rlHxxyt@e!=KaD_otX(DOSEi|5}7AW1jXKDrf$md$#_9 z@_!IQpgm83I02^wbA!4jQsE+WygRP!TVop=cb<}I?IY+?C@I0Y zJ2#_g%n3ME9Y!fC=s#MV28!ysOx_)Ve%0Xw9d8UwbfUf-8Q&Qj6o$w2(pwd%0ogoH z=gWn?)_As?Lid?NEfmi0{Ed~bfB+*wN~Tq)3&ql*$30$oJOMg)VVGN@}(OQD;G)TS0$-|eOCy%hpaoNK{w>?xh&Ye87L z{C~na5GL*0T@-g3L4ZnFocfD#v>(%LmB|)pHp1Wpf>As?;_=#K2Jmht| zTSu`l2!Y~daUyTAx$yeu4iId^47q#xAw6>{()pM;r<)WHUQe7vJe)ld(M0=2d zmic4^I8}BS_o^{2cRJPn{dneYacgd##6M>6Y-~ovLyym8fWZ?_|Jzftc8oxl^xMea z_T0ST_M8Z}C7-fUK({WvA#~_ev)q85rt=F(YBsp*pN+`OoB?A4EDliI6hiAEEp;~G z1Y3fOG^A9o2_yj%bylV{sz9SDEUu|^sO2`P>X)!YP3;BZ#q>1_0S_<7RSmzkFVoo8 zK3@Y?u2^Uni2BPQI_djEVEd`N%=bpPfC@-NE1=t;#=)NdK14sIIU}R^iH$zQO$PFu zP0liWAxn>^_BLtUkPLA7^~uBs4x}al9wJDZ?5%z8Zw(*>9Yji}*ul$V%kib?cQ7*D zy@PHi=iqA#i@Nb*xc8W2K$yaxg->iz)LD~s+&p{fvnkNFMWC;%6_8*bZIo|}tBki@ z$K5f=;ezMIS~AQ`kI46a-VVYxY9xC5L08mbfeP>ACsv;@JPO#1`9eU$bPxeTG=_3P zLTJYG1e2TFO0DU?;wpi@hqR`ZfEyW|{KCMew;wrt}ox@;etdwGN7F z%d3yQYAB5gBwtN}(y^L}g_P&Uz|$h_$hGq#gweaI4Eg5Ui6V2zEa`1n<+u8!dRJG%-q?#TzADNPPj znuhcENqc*g<3~zMQReL&O0e=6FLKiKv^fK0BQdC<3ZR*9h1Svm(7%`!7hYq`;**~J$l-3K zNrYQ0HT_7hG3|9tV?R%WHic~nq-l`_BIKENQ74ho(WM&UFgL2R!BADhO(z?f`_F8b zCB-T#!`6a*k;wFP4>zDB%fbEN;~joc7*GjG`L5Ls%`V5IF5i^rxqrD^c6+GsB5EvO zF8aPP$AlQ%+65+(Y&amhbPvNwj5=Ht2m_98(_(_GOE_#(Lg2Z&+~lEIv%R}F z*OXIk|F!nnaC&ut$564BS%-HR4(jM`^AV}xWHQ@V^bSlih@>gcRrp< zlNGIE_tOn0Oh>e&T)jhXn$M7iM!ll&k;Wb8*sl`(JlZRcBx+$^8iu_@UR{ZJUbm>+ zokmACj2acaSwi^bSt(Vbut23{1282dC|JWVtXZOPC+qQQ^}b-pYyGbG^-{fwhJ1|L zD%`_iGO1%|-*fr*n59+H?i&1Cf7#z?DDDqr1caK1n4Ewyj8;@ z?ux8E`lRPzYS*q`@;KVj?>>5V&t&4;2xYH-G%Ut+)18x&H;xB^TS8KbM+mO{rEs8S zW9N?7Lr2Gx+Iq~^wzS;hRu+gjraJBaN8js)d{~49`Pc&|B)x}rP^0EK=k+S}DOMC)w|VS&FR?u!Js{8<&ma6Rcw6l#~SASXOw(Yj(dYOGh{rvZIp|pu7D-HO1e5C8QB^j zAlrE1R_EE$UwL9t^L8{z*c0%_>Ob3vUMbr1IE+Gc|DcRg(cuj+G(F@&YhX=8!^%U1 zL}_(cc5@IU{4kBElE!r_&;q2OujNY!o|L)_h&wtj{>qx|A|_Ng50WCqMzEA={}B0g z+xO%0_j4}|7h_2nnkAs6AsEBTD#`81!gDbF`pSSVFD^J}!SX&o&3|aUHK%)bf`IO0 z%JF)_2yiT1qA!g%(URF4d)HU%JL+IaNcZ5=v5$Qu*zpt$6|^f$dSJp)hMYTE4rDu9 zBV+eF1K#kGp#APegL|GWNIGO^yCb)cOg1=Tr04T-qCO;4RTBWE^Yo`wa%?Ct2yD>i zk#Eg2ZI+_%Sj7V2jlc%DXXW+hcxkYah$3vwv}YiG+b(#iMe_Vl zm&1P4BT+X{(qoy>`p`TYq*-vd%XOeMxNY*FF(x^@5r@V8`waAyDztj>ZjdSq;x>%N#c9iRfRuO-0 zK?nMw@B^!5I&*UMru|iBka}2<230yh z0uH3>ix_AaUtHRWh8j9vNOg_rt7?h$W_on>a(?7~DRC)Z`h9y-w4V%1^?B|0y-9yH zx_&Z}P0s@K3-|#L(=G3S0@&;|cc1(wUA&)u90=FxBIjMFxsa4Pd&d{^fSCvpu9tC7 zB@r-nX;tCpeEcEb%DiEP~dE!-dEIAvElTp}|y$~3t5(^>`N z&#A|}MaZT2P{RzHIDalix-E|n{5==5-<2ENpq4jxmBO;SdsZmfkn`03QzRZB%j;C) ze+B^{hFIO7998O*dL`T?08Kz0tta7tt98OCb~ZFt>whD7iy;w)mkSn%1^)Ua`oC~?!%+ZI@w4OYDGd91k*lbfnZ90y>prZ@HzOkrV4+^1yB9% ztE8}g%x#w_$v_8Hbw=p7&!*aIZE^>(OWQ}H0%bX&;}S8V#9Atb24Sm(@m_X0Q=$h* zRTCRu4}}tyZP}EMRMD5Xr;#nyKUKyr<-Kg&`!=xJ)aS4A!ys}^(!uPc#$)$LW0Q}d z9LY03pRhmjju+EZ6XlAU?WFbN+eQ}5FtVNAL0ZllnvKQRRqyJjg5#&xLJGgkh#1Z_}cgpj)ZMNh+_X+0aoouxUwG zPmL;VY+oD&P<|j9jZzf<6P~cJ|A+f#N8K|*VsM*2AN9bDARw%)8S}9qz;qdo3czq}F-^dV zvKe8@z!d3Uz*QM?>cDUr-(ySwHZJb}xvbS_L%X4BrqdJ4U@=h$rD9h~r4fY+0f7ct z$VzD))I0VMAz2-6V>FU$8<^>)(`hHGFRU`irem&S?3f?oI~t`Ud7u!%o+C&Tx&6&| zn|0%PIc89tO|^q6rpzn!mEe(-#aCYjJZ*dK`WxbzT>-R02lwUHTR+sLb*jC_55jU- zO;yA0`a^inupd*1QVXC%DY%=B;P_KyXK`fxI>Ky=Nbm*~F{F2BUmyQrc*v3JtSHdJo-D9?60!Kh7Aw$H}kx0nI){$sQ#OsmClOi($C!`M{dkNw) z+={L~BXl^XxDOnhslGPVi15O@2jsCi{I!&1+{HHUM|UNt1V5B`kaMiy)fIL4q*>43 zm_Ck9DK{wrf7jMVvrG9{OH3|;DsJRm`2aolcR&5kQ5E^_rf(nXpM-&W2nrAPw1EA`3@e4J5hv3v z7Id^5y2R1-T(myrYj6gY7d331gxDFhwZNik7{1=5TV3`$Q8hZVN*q?sMirsdBV^$a zBQLxtH87J`u82YgH6yZytM!hb3nM;acEA$Kf~6^nkv1}FEn*TubN7ng!5$FGx1bG5 zXRc1HABQi=dn@o%Ris7Ds@# zQn+gBk#RGc#U(Lh#tc3+L1-ZgA|Z^x=eJb@EbfCpr$W|bLC9);DdRW1(B!mIqVwwr z15Y%-`}gGM?%rPW)y%*?hwKwVOh_ZR3b4DpYZPsx6>3nmT!b?ncrxeEx%64 zc=0?6>?*(I*x=K|>r7tlm+Q9kz0IbPE#dV!>quJC+aDqbBbbB(DgU_MLovBGjT7eZ z*{N^3hQIg4^Y%{hQ)|TFt8UMi>Lq|ij93zcd+}Om-Mq(8nI0KmfftZ_Jz2$zV`WVu z5ZrrAsH`R(Y26uGQM5GW;ypMoK*gRkspgtrEg(8P+22y5t4FH+KB}DFVQ%ZZ0AX@Y$uB(JoJyEI)0N0PgWYX zM8=u~e>Mq+iIXxLPd>mGYpfeSv$S8a?mot;QR=wS5~}gA-MImjA5I`GNUp3Xf9Im0uwvuKenY}mNY7B#4j!TEg#@UO_tmyhQ^qc?7*iWF z7zDK|vB;Sf!3#pR%2P*dyxTW3$cH%kmRGvKo5KJpU_VNMj0qq=dr*vyyXQSeIe1tI6F|`fgGbTm?PNatquQbCGEz+{oLY+r5~N-b z>QLoc2`z61Kotp^fD{U;HC}7FQu_&9iO9$RoJJldBy8h#88m4NilK|`jlD6i=%pF+ zP~r^{CM=BOPBBRJeG^mPkW6aJ`t3oNDV!EHK~G{ZqYfC;II#87G#d9m8hr@3E$c}Z zK32*qmJSjS;+Oi;0vyxxPy%6owrjC%5Tn89{_p{3xBVE1C-gjxZ>d%$ErMb~ z0*i77UbPdvIJ?|eLMVLAc(x>NB}6EU3iz`v#|5~Ye0tr)9gj5uG(vjntdS5U4Dz2L zM+|Sr`10Esnplqwz_h)dYYVTNmKYCk2prAnD(Pb9tS0rSCRU*1MoN@46GK>zupDN# zPfZty;>4E+USMhWP2F!SJaxPN=Ks2YJKNF1o6wLErsuZ~J=h z*98!&p}=4bw-)2ulH7HVAo7jo>^)xq-^mHZJIR=2eAP^K8S9<_`+QKlb)elate@c_IGgFY;h^jkqbI_$dv~rOwr`W=xOHQ}W~UJTRJAPPS|+RFoT zx~^?u5X3v{A`pha&;^fpOOFt-8x9T|YEeJ) zs1J#<&pTyjILuJ(Ubb1N2cL@{h|As_Z0OvhdHtBGCtkC2J$Mla6q`_Xcz9Ur&_qu!3R3xxXGpr1_hTCj@^JFMS|gdFP9BK7-)A0S&Qm1crw*1^sJ zfvqWWdgk8nBV7Z6%kV3Tm(9Y8S}>FLz=?%CR=|os6cb|$bq2*C3=+$~_(x6FyU{dO zDi|tDZfNbaH#-SRf^5a_m1K$-@b7}~ulWt0cFvp)aDy!`iqDBv!=3j5#R0&b8_mX^ zTgU4y%PbWX-R`*{gtAmSyedOIm6_OmZxLmEaYI^$38*!{?@7-H-%ng<^vp^8q2rBO z*|J+5S&iD@3F8v`PbR|U9F;8T%ex}Jy%};{{u2(S0grYrM)KF<#@{KIoQ@ie`=WkS z@0JG%`10@MuY8_XbZmF)7GePO%yK;ZyIiVpXk(0~-)F*#A*^Q(%`I#DpHQBVcja`- zO?r_6QXf1FD>w<4>U3HRO4#L=?MPygX1DvbU-Q8$_wN?2VIl88(R20tcUsI)Jq-vVsrnIiJxB;Eplb#xc*;wxWu7?lC@IzGeEVg24e zTRp9G>Z>CJyi*%{x;rn7hCW3j79uY<$|tP+PA?+>^kj->q4LaLjeM-~!Y4yj9zb@f z85X^HzxJ#6koztJwfM8ETc)g+$~n=MGdI!<)m8SZ-B9$M*1K_@@`2KmFB1Dl@?BT& z0_qvRd3;>har)RNLT%9h^x4%l)UxsG-81A zm_!CHTQ521uVzq)=iRH0o~xdeJb&*u%3J2Kh$byX!uj!p@of4HX|d=h@!oh!GVmSz z>X5Ay)}!IShw^#PQQ@MUV@&BMDaUxPn$@k=THH(bYTg!2(NloNi|LZgK^41JWW=P& zlD6|d6siHhcL!Hcd6_WOCeY~-4U4HYSD`=M1C1!)Vw96KsmHL{;ncy+PEY~f+Q+v>p78J6_u#s;J2u134LRYqJyZbfUum%+&xAdUML;xcXY(@9 z!gj{s1$NH=td%9~xl19Ay<=%#2aIR9?ga}oR2#eb0on0zHawaB&cnsZb>MvVd#iPK!b_>WprC`HPxkKWY+LCly(FchS z$^m7%hqN;*hfxs2yPj206$U(*f~?I$@@U00#jp4EBBn2zaPmSulWn^i9yDXfIA)<3f)RfKCpLcaQn z2Z1~}-romV(n%k*6sw9U9~ABH@B+xa0qMb9H45c??~2gEDNXa{#I*w~OE%Xb?~2a8 zph_A^)HX6h*+~bvJcb3$Dczl#zX1;zaJ?L3B4_~^3jQgwg3uYaH??=e=%^@?ja86U z6+HltsviB6Jz_D48nuuLd~bGicXIv@=e(S(JLiX=23?hQbEw_f0@DU^Wc~pjD-Lhc z;LZyOKEN6k_ZF5i_eGw$vH_3+o4|vwQT4z`1=uTWj#$}a_%vmU&+<;BwzfeZ`R+I# z4@YQY%PF0iaaKt%SXwC>Ak`eW^*Yco!*&3V)v&%SQ26D<1j1u{V2HdKEvqF+%8Z{@ zGRB1#)U{a4ktjx#iutYieD2{q*tz97%&-HF?J=H>{?r3LuVS6DU$~* zifz9xguy?zzftAZ1-4G9pFF>S)R8=6mMzVh-*V9>&w;Uqlf6kc#m?VA*_n=QqCf%d zceaMZB?Ya1ZiJ`)T#-B2_S^mK=iUaqxo>kL@p38C9-&|s)E$0qOKTCcYKI zg+qVahJL(0rI6y}xeuO4kO!=dpV+9Q!u=U6+u2_rcN+fiHZUeSNQKVf*iQz_kQeSq zMvYc=b}yVaBZCz5ujAc=4chnY{RIYi!NO}hnZmKSrlIhO*+O1?+Gobv*r&BqKaYtH z4zuDwi3iE41VW{p-cl}T;MD7e_Ux~}20oWLIX9<0xh5$pX~1q!CPt=RVoXSG95OMc zcMF+ZT?ysn9DA@C-|7(3z(g4RGx&!<1L*UQL5#Lr!xdeIz*9_);mv@<(g71-vnEqg zmqKwdszt(te^E0PHa4vCJQ>ehTh{o0xoudTJa%8i9qwV$0x<(PaBc=bsytzb=yNq%|b&?S7}ic6aD^ z-p?X}@3TB4)n_~W8G4WT-LA+E&#}DCA2(a<25hv9@sSfK!yh=ib!P$^cC~kp$)kI) z<%2iZjd6SAE7ICs2IekGc|)l+LrWF3hA}`lzOzf+gwL5y8XJW6d2d+&Y$E+=X#If> zIFW@dN%g(ynw=DRGZpQON4|i4ttVc2v&9w#tbpucdt0Y;J=|E+3&I%?j?u->I0Kox z-V*4gtNM3&3P_~}hJe%BFI|N1ePzJdUoE5OX(bpSv~CP(5wj=;SgU0qMOLl} zlkDtC%pG?3`8r1Mqc9x+hZ=iD+Qq5TqquE@w=VsBF;Kyah_^BOa0mKq!30Cu$H$W> z$)uBiL;LuozB9=L=ZIBc)^b!Rf`lj$y1cu0`DS8jj#N-Y?o$c z;ouajRfobK9TtRzpb5!$H^l=ZM}^DNZYKo4j-X#ayAu2T5syR~XEl;ovRkHhw~R@n zR(x(VDNw;(NbjzuznAC)yZb>|>5c;kn2qg<$=vv$^3HxZc@*v1w1WT0L+6mRvXTUU zTeqfW-=sain3Hb4yelMs|AOd9p?dx=UYBvH^Q~V?MFoO_f>bZh@y=c1Fc3@|qXk5R z1Ht&u40wZoak#cxOb|7sjBBHRp5V-IH2X&FY^gx3Kr?79zXxAvK^Q>Tng7A{6zD)` zGN5d}XN1y$%wwhOeJA$$ii6OAu(P+7iG%DSfUtA^g9i?%fzZN&aGThQ-l86OyND7$K@OhCzRY}! z>{X-1xte*%5OA&mt!i?M96;}>nT53aF->8k^AL(Lje1&w?<~Lf&2)8YwM$xgtXo=i z8cbtjp$dftFlTjjar3WA8Jv)++TztTj9-*!0*CqOzls30sK0z30}bZF($6R+WN^2d z8WsrbbE{*8asq){MhYrf>`s*|cr9sSJd#zg{#w&szG$l}{F3<@zj(H~e}Q*>IU%lk zPDO*ro;td$^H@bo2$!EjQ&3GT$%M6gc%f~mschw^p}qw3Lmr(tXP_yv2hA)^WMsky zjzms~xM&Z+H$+0VQwSv29NH%VglA85~s4G4VVuk_KKR~2Y=nFg4G7kc-YfZVf1$r1s3>AQuxDKQ)42}OA zml@-Z@_7Z=3)GCB&NTOwG&>N*#xUz_PSPCQ$JiGDoJ*IMF%;sC_U04{{+k;Oq9s0= zMy&)P-2c9m1)VB{=jGL3tIr0Em?<$k+&nl4L$3Erkp! z_6SWq0zFrRUkj=^5DR612NXxw>PT+t${9>{Ae$lTY8-!z2wlQOXxhZ@l)VIanr~F) z7pfEh1P(N~|H!Bc6C_Pop0OP1@lIuMA#uaiLrN5b1`bBn+hrF5c6;$i*gOu~{O%N( zD>9fTJUirPK1UPKFmEI@LLm|{YwRJvoVh5_5A=(~GvKAfU$D{jffGqy2M$PkS)tg$ zq2(wSU<#VDue2;!G~o1sSVqv_nyBzVt~my;y*^B~I2(DN#f}a?)mPv^PU;Dz2#<@dOc#3sN z0aafj@|Y-Xh|OfYeklH&Ahj6US-rX9h*kdZa6(yYFa_C-p2ma)7_X)PDm54^(@O#1 z%%S^?R8Y(>r0NGI{;mAf%tUSv+BTe};0fiyJKcU`v~6al6ON-*h(c;@E<90a6iCii zoXx|{481d7#FRM)h6wHjkAg)mPao9NlnZn=?w!oCiCMckk7_y;edZ-DX=SZ>7)1g@ zAQl>0&$j$?$Ouv7ia%ExMc}hEaXE`p&6RTcavTp92J%aaEl|-MBcA`qn#Wuiu)QhIIJq6Rs@oG%W%kFpK7js;M z6;IG*HQ@kCTtuH;qkUw>t`~$OOVG>*VhtOr;L-vZKd{dSBC-jk4Q+yhEsEHsac7AJ z>hok!go=FM*efyAT&hMVbeH0n=um0YRxC6MN588DO6z?l2gHD)(BfyrM&T+wL;%*G z)^?<6-J;esG!v8XA>iMXxUOMDXqy3Hxkn8CO#=0|s7qT|Sr!i5T{bE`V^vjD z3X5{X_D(~3N++|AkKhZ`_OR8~sDtAn2l9(4$T|vz-+>@U?#@P9as$$KaJag!Yjb!S znH-V!LAvz&&Xn^A&CSdTT?9s8DuL2?K2VJO^X$I?pWZ&rS~Z$`z9u7p5Xdffm!2N2 z_jlvF{ScugF)PW|LyTupKe07oyZ+q>zu8O3#Rw}`zK_v+Gj9HlHk~fRAB>EYE+jXC zUQGVpJ}tlW%D@su_zd4$6s(QEjPS%xgt^K!Uz&Uw!M3S>P#VwNj#`$?xD)sEY)%wz zB&W9Pktu^Fcg@GYv4G-$hBBSSP9@?!M+R=!-idIsRD^nHyOYF6o1)9Ddm*$fF zTsr-LE~s)l!C^nV#G#mYGUJ~{V}Ie+^NBZE&1ytfc+51wc7OV;(yLh^(8{^|7oA50}%@Y)a=jqi=GB?xAB^@_p>;lt$n zRNz=73yK8R;E8w#0h1a@;=i`c^*GZka+3|mUfN<6l03AqwLD*) zUqHT*7V7nC=j;*S^XuJqG9F*uJv{I;ZNBG09B&1 zL&xvet^o+Zl8~4_LVsP>rf20guY3O_AZ%3S=z85fLa+nrenFiD z3bVhIf9?mn3Aplj8kYv=_;QAFThXfGJ-@wi7tsSUzX&I zO4zYyFxG&O_DgDrh|yM4(~=gt%&=6&DNW|%`d-t1J4T%ipEanZ#l}E5ma?UY znK=h4O5-z#AoA5&62Ohv+k2erEObSW7J<`qJiA%+LZiWA8=88sQ|o0a_^+#(v(~e+ z2W~yy0&r8ET4Dl^)z zZDARoM+Mro@ZwTb2K+;`=Z8X<&rTpq|2>uf)j&vUZa_8xh#z8eO}Gli0}yyU`7N^* z9ykvt2>7(=G$5LgY1qq1_cpM|ELNV<>X{)NfKWs+YC=W>^W!L;kL#M7n%kZ`msr*7 zN(Yr7KlMZ?8Ucg_>=`G!cj5~>UvU^<)L2;dQ0xZOcBBWL=&g$WKIqryGBlMIZo4P! z@;;rGhS5QV!3V2;h{*Yoel$^NlTB}yIRS16gQI||06+{=y6D5F9PlN5z(<631%4Rk zo&}+XE5E0lVm!rzrI=Ph)5~J3WP?{Y7D+YFE!VrID|KdrHCK`3(eIbM6@UxFu_zYJ z!Ugp_3o!yt87)@*`y9Bl&!QE`lZ382G*Qe(*mXG@G6#Xwzc4-EdvhRZm+I1Obgwh)EZ-)|mZFPcI-H~5TpdbY-l zt7Uz-^s$A4m~zd6z})%(3!}x@$X#S!IlNZvhp_JvUQ8(|kw!wwEo(})JL{O3SjQY8 zt++ZpvmcK|F3chzOQ6HzP>wc5We8)DYkM1Q2OyUAv{b?490#ninQ8DAJF<#h;6mks z+VOedSCm;gDZ4?Zcld-EDX!Ufh>|h~1F2<3u}+Am2?j6D39ulYKeC4v8#zc)rb85% zl*bAUjU!G{)KrgWNn?|hfKo&$34jK4NQdIWWi`uara?$;+;Jxa(41&l?W@!dyD+nV zmt7IV%frKzbPZTMyxJKAY=U}P8EhGwgm17_onrdCO*o6pID0v_ORAN)i!~@D@ej{m zp{Pu;k*nQbh+Skg<<{_?OT?#^FF?gh#oJ^b)d64HAQ9rY1i$6AQP?x9FXX!kmhP zWFuvi!V)G@kUEFOkW*jBz&rLtX{H`WF|CxUFMSWCu2aa$qQSP5!zTiq{&-+k1q3HA z$BY@)FXa&c{M!^_VksrxryxyyygGD>%j!P8-tK=B3iA7V`1!OaAM81KJC9V3?rK~P zpHgNJrdzvz-1)Wiyn5X1uitMUd_E2@uOD2z-ye2UT528U*Y$3XQW^H>(FwSY(>@1d z_!H7=+|-6$~;S7bxP5D5>jX6NELrn7wMT}4%p?CvDLfVyd;3~Lr zJZJ47E}7J;$uzRz5qkC96fm-QnlM;4n_wVZpgB2PmZ5?lNNUKaPH%p9ac7Gpan50U1vLQoM=+gUMXxLdUok^c z5y22oa5s|lI+>wXHp7XwV@S9obFDZ=A&A<4cm2z$1MXn8IL2|291veHsq|%fUgUFj zFtT|3e4dl?GmdK?VLjQflw+-E*?#RHVllHI+pd9{;jYt^xncNIsuiw(l_(~izR`+5 zm=1J1;aJ9ddgCCPa5gO?BEb-kq~tpuFm#Fey0~9Ie_hm9Db0Dk&@JhafK!Hmy@fEZ zw-ON=h?XyqmZBwO286S{Ove+DO?x`oxs>GrT{1)8UMowemQ!XyA5yzLo}E7k2H1P` z#$M<VKItwpGlmY2h>oZtE4u*V?+E1NIZyO zY<(lPs~>JoF=C~FzW(jUrm2=es}PA>%tomg@OC__gW(x*H|~aN4u9k`uFBRv{h(*e*z}%f zbLaL9@I?rs0~oRM@@Rh^j?XtOGUBrLPU2G6OKc!XitBe~t;p~$Z>Wr}LAYlMnr+kBaZ8t$6>=~ zzmxkO@O&?>8-BuP%`EvPXrXZXh9c<^iTW0G2+3{g32?H&%*Wlxv~9*lE%bnIz;qpO zKiM*3eQrD4B@_^>+&1hQ+%xO!AK#(j8txxXu?MFNVJoU`v)`D46=dOp?_Y&dXvNRH z%G_g{`&ipM8g{SUGCF*8 z^$@L>4M6WWoVV@7fpxUO%i%B;KRqKX@i1m^IuG9(YWSne|4*GD@Ayj|eV4xH;>fnm zB1OkOx*9Jv!dBCM!q#2JY4P2zzSr)7_!5Iuj-1WS?l0yyPTp{=X;MI*Bg1;Wb*ha;bjV^i+8-l~ElMmC;F-pD}Z3rRHP9|RJ>f%@H( zzW2pBq{G|y&pVR!9UMtmug5+Mpwl!_4EGD^J~%WaAozNi{cXF{c^G};u>P!Tzy8dG z)skw}-Hi6gc|OXuc!Qcl*a1ZtSl5rfyHk5-n!F!$E$Lc9N!in1dV5$Vneh4EBITM< z2Pp94B>&sCS%)ovW2~Fw8*WSaNmQM75TR-g)J>tff!#oug8cL(@Vec4bw{&{E~=1`vOa$S@q|qVwtAj+vu+En0YVy)9-!9-fq8_MVpV8$BP`aRV<_)RLR!AXf1bb z$l`9*>DmQXBYtt3QZzNe&#YY_lWGKC4vP3n)Yue55z^Q4j0`=+H+=p&)iaulRaGNp zZ@RLcshg-gEtGBvUw_b`CC~ZwBo#iLj+(DT6)ca~dcz5-jP!81{ZWrLI)tOXKu-~m z1pY%Z5CYV`)2SG>RLm_HrNwmlIE_u&|1YElTlq9FW@0lpFk)jdWMVa8IAJ+7G-709 zVlXl@VmCfKH(_HnG%#jjGdD0|V=-i6HDNemIW#n4WMg75GBaW~K3y+TZ*O!8F(5D? zQZGqvW^W)eATS_OFH>oHWgs>l5X>4?p_5l}vH8e9mJ_>Vma%Ev{ z3V7N**H=&$R~W|e^KMiWqJjc;?22GRKm-L*LBwuU>oI`e1wg#F*ZRTY>Lg$ z7ya;KY>q9kCHi9kw!+pJh(Q>PZLlr2!}i$0J@fDFnRnzolg0RSw@oLS6g+{I^dZ<8 zyU?G)YCMal@dBR18oY>C@iNw7E#AcI?m6tW=g^fV74P7GExd>IVp{)dkL*S>j@%u4 zU{CCYy)hK~i0L-Zem0EHP9lek3Eyw~zVwsvA>PNw_()9DID2G2nkixuM%$)8%{1}= z9EgK30wXaBqs64g+s_W>v(xbzJ`pp+&yL2>%p?yHlX<}QvGlXaabohSY(JEKo|vMq zY%`2zzL>Iq5ZlDlED%$<-Zlv|>Ez*JYW!`VNS`65{tMfTpjm>?@g@C8)OR5nlf=9V zvY#5wk;}*_V!r&=_G9R?#e7p|8~yfk#QZkbHe+d4k;jSo=Z5Xa)2|lsiLlKCnmm!f zK-)~DS>ravwwXkeFB0^bZS)&oClVZKn<+G{F$mj#Vn;@&x;dC8*n7WRdt)a?^%{HAfKTu#KI52$xQOOCzM#?B zKt+hYiJVRRW;XC$4A z?%-X_LY=`{qQe#G%&*UYFZ!XLVLfJJ4!y2fx;i|h(X7u&2zJHsIFV6(ex{&4dq?p& zqpSFvx*qAb^8g>Aeiy4Tmrn&?AO>R*qj`9LmBt4NywE_rzWp zihUR@B8Oo(_Qg0x^-2feK#V|LDT>LF7=_U|n9(h`m1Zc$<8U0osLl+dFd0+m8*n>+ z>WUVO?NH~g9puia&yt?c7Tn4)I?w0~I-4Cs-Sg}tS7ATwkNW27 zj;;dt;{p06sC%s!ry7pBJJp@1?luSDK#al&9E6dmd&_9lo#YVI9bg>lj!}1sx)0olx|>SEk*K>h z-OK6jOZR4TQTJN9PNm^goP#rea277dg{W)sBFw@})HQbluE1PeiEDAaNc1u9*I7)t zXKavX+-cAF9-avqo+JMD9QDpK`Hg3aujiOb&(xni$CY_b$o8E0wddqe&ndO`yDJo# z>SJ?}$nxv-yn3yL&e85cxOS=JReoX!A~SntwR|OKvWu$$Pd1l}^Z&hlfv?0VX)xwLBWY)!mkh50 R9Sk-$Gcz#?B_%~qMhXwUUPb@_ diff --git a/tex/sections/02_categories.tex b/tex/sections/02_categories.tex index 4c4d19c..a4aa6ff 100644 --- a/tex/sections/02_categories.tex +++ b/tex/sections/02_categories.tex @@ -980,4 +980,138 @@ Dual to F-algebras the \emph{initial F-coalgebra} is trivial: \end{example} \section{Limits} -\section{Colimits} \ No newline at end of file +Limits are an abstraction of products and many other categorical concepts. +\begin{definition}[Limit] We will need to introduce some related notions first. + \begin{enumerate} + \item A \emph{diagram} in $\CC$ is a functor $D : \CD \to \CC$, where $\CD$ is small. + \item A \emph{cone} of a diagram $D : \CD \to \CC$ consists of + \begin{itemize} + \item an object $C \in \obj{\CC}$ called the \emph{apex} and + \item a family of morphisms ${(f_d : C \to Dd)}_{d\in\obj{\CD}}$ such that + % https://q.uiver.app/#q=WzAsMyxbMCwwLCJDIl0sWzAsMiwiRGQiXSxbMiwyLCJEZCciXSxbMCwxLCJmX2QiLDJdLFswLDIsImZfe2QnfSJdLFsxLDIsInUiXV0= + \[\begin{tikzcd} + C \\ + \\ + Dd && {Dd'} + \arrow["{f_d}"', from=1-1, to=3-1] + \arrow["{f_{d'}}", from=1-1, to=3-3] + \arrow["u", from=3-1, to=3-3] + \end{tikzcd}\] + commutes for every $u : d \to d'$. + \end{itemize} + \item A \emph{limit} of a diagram $D$ is a universal cone, i.e.\ a cone $(L, out_d)$ such that for every cone $(C, f_d)$ there exists a unique morphism $h : C \to L$ such that $out_d \comp h = f_d$ for all $d \in \obj{\CD}$: + % https://q.uiver.app/#q=WzAsMyxbMiwwLCJMIl0sWzIsMiwiRGQiXSxbMCwwLCJDIl0sWzAsMSwib3V0X2QiXSxbMiwwLCJoIiwwLHsic3R5bGUiOnsiYm9keSI6eyJuYW1lIjoiZGFzaGVkIn19fV0sWzIsMSwiZl9kIiwyXV0= + \[\begin{tikzcd} + C && L \\ + \\ + && Dd + \arrow["{out_d}", from=1-3, to=3-3] + \arrow["h", dashed, from=1-1, to=1-3] + \arrow["{f_d}"', from=1-1, to=3-3] + \end{tikzcd}\] + \end{enumerate} +\end{definition} + +The notion of limit can be instantiated to many interesting notions: + +\begin{definition}[Products (as limits)] + Let $\CD$ be the discrete category with 2 elements. Diagrams $D$ are pairs $(A,B)$ of objects of $\CC$, cones are pairs of morphisms + \[A \overset{f}{\longleftarrow} C \overset{g}{\longrightarrow} B\] + and limits of such diagrams are exactly products: + \[A \overset{\fst}{\longleftarrow} A\times B \overset{\snd}{\longrightarrow} B.\] +\end{definition} + +\begin{definition}[Equalizer] + Let $\CD$ be a category with two non-trivial and parallel morphisms $u,v : 1 \to 2$. Diagrams are parallel morphisms + % https://q.uiver.app/#q=WzAsMixbMCwwLCJBXzEiXSxbMiwwLCJBXzIiXSxbMCwxLCJmIiwwLHsib2Zmc2V0IjotMX1dLFswLDEsImciLDIseyJvZmZzZXQiOjF9XV0= + \[\begin{tikzcd} + {A_1} && {A_2} + \arrow["f", shift left, from=1-1, to=1-3] + \arrow["g"', shift right, from=1-1, to=1-3] + \end{tikzcd}\] + and cones are pairs of morphisms $c : C \to A_1, d C \to A_2$, such that $f \comp c = d = g \comp c$: + % https://q.uiver.app/#q=WzAsMyxbMCwyLCJBXzEiXSxbMiwyLCJBXzIiXSxbMCwwLCJDIl0sWzAsMSwiZiIsMCx7Im9mZnNldCI6LTF9XSxbMCwxLCJnIiwyLHsib2Zmc2V0IjoxfV0sWzIsMCwiYyIsMl0sWzIsMSwiZCJdXQ== + \[\begin{tikzcd} + C \\ + \\ + {A_1} && {A_2} + \arrow["f", shift left, from=3-1, to=3-3] + \arrow["g"', shift right, from=3-1, to=3-3] + \arrow["c"', from=1-1, to=3-1] + \arrow["d", from=1-1, to=3-3] + \end{tikzcd}\] + A limit of such a diagram is called an \emph{equalizer} of $f$ and $g$: + % https://q.uiver.app/#q=WzAsNCxbMiwyLCJBXzEiXSxbNCwyLCJBXzIiXSxbMiwwLCJDIl0sWzAsMiwiRSJdLFswLDEsImYiLDAseyJvZmZzZXQiOi0xfV0sWzAsMSwiZyIsMix7Im9mZnNldCI6MX1dLFsyLDAsIlxcZm9yYWxsIGMiLDJdLFsyLDEsImQiXSxbMywwLCJlIl0sWzIsMywiXFxleGlzdHMhaCIsMix7InN0eWxlIjp7ImJvZHkiOnsibmFtZSI6ImRhc2hlZCJ9fX1dXQ== + \[\begin{tikzcd} + && C \\ + \\ + E && {A_1} && {A_2} + \arrow["f", shift left, from=3-3, to=3-5] + \arrow["g"', shift right, from=3-3, to=3-5] + \arrow["{\forall c}"', from=1-3, to=3-3] + \arrow["d", from=1-3, to=3-5] + \arrow["e", from=3-1, to=3-3] + \arrow["{\exists!h}"', dashed, from=1-3, to=3-1] + \end{tikzcd}\] +\end{definition} + +% TODO equalizer in Set +% \begin{example} +% In $\Set$... +% \end{example} + +\begin{definition}[Regular Monomorphism] + A monomorphism is called \emph{regular} if it is also an equalizer. +\end{definition} + +\begin{proposition} + Every equalizer is a monomorphism and thus a regular monomorphism. +\end{proposition} +\begin{proof} + % TODO prove that eq are mono. +\end{proof} + +\begin{proposition} + $e$ is a regular monomorphism and an epimorphism $\iff$ e is an isomorphism. +\end{proposition} +\begin{proof} + % TODO prove that regular mono + epi == iso +\end{proof} + +\begin{definition}[Pullback] + % TODO pullback +\end{definition} +% TODO pullback in Set +% \begin{example} +% In $\Set$... +% \end{example} + +\begin{proposition} + Limits are unique up to isomorphism. +\end{proposition} + +\begin{definition}[Complete Category] + A category $\CC$ is called \emph{complete} if every diagram in $\CC$ has a limit. +\end{definition} + +\begin{proposition} + $\CC$ is complete iff $\CC$ has all products and equalizers, i.e.\ using products and equalizer one can construct arbitrary limits. +\end{proposition} + +\begin{definition}[Finitely Complete Category] + A category $\CC$ is called \emph{finitely complete} if every finite diagram in $\CC$ has a limit. +\end{definition} + +\begin{proposition} + The following are equivalent: + \begin{enumerate} + \item $\CC$ is finitely complete + \item $\CC$ has finite products and equalizers + \item $\CC$ has finite products and pullbacks + \item $\CC$ has a terminal object and pullbacks + \end{enumerate} +\end{proposition} + + +\section{Colimits} +% TODO colimits \ No newline at end of file