From e1a6e5ccef2e65dd6f1d4429c8d4a9011c936708 Mon Sep 17 00:00:00 2001 From: "Claudio Maggioni (maggicl)" Date: Tue, 26 May 2020 16:51:10 +0200 Subject: [PATCH] hw5: done 1 --- hw5/hw5.pdf | Bin 0 -> 74368 bytes hw5/hw5.tex | 75 ++++++++++++++++++++++++++++++++++++++++++++++++++++ 2 files changed, 75 insertions(+) create mode 100644 hw5/hw5.pdf create mode 100644 hw5/hw5.tex diff --git a/hw5/hw5.pdf b/hw5/hw5.pdf new file mode 100644 index 0000000000000000000000000000000000000000..75d0a2a9d2c3aa17b4c12bd1c78883d649bf55ba GIT binary patch literal 74368 zcmb5UQ?M=oucrAe+qS)zZSG~;wz-#W+qP}nwr$($zq{s4P1QLUJ-JG%a+%6oZ}O1I zi-^)P(y>C5%`FYDK{FFF5ZW19Li6xI(@UG!nmL;jGIFwV68@inrWduab~bS&q!+a| za5fP!F|so@f#&0bc5-$!F|dJl+t}8Sa3X2N>b_Kas#n1$UP~=H(eE@It$FA-Q7NWA zGX2jvc=XkKe4z--K^2sYFWLt^9f?8LC&DEA%h~RGSfV_EP!1UB)90vX5X|B zd+IwXJ^8_J;_~Q3j*zgb40oRLO#Jt|q%Eb!U%I`}lkZ=7++5av6i%^(8Y5xAa-S83 znD$tZf!R*+_}HRjW|LJutgGH1z^I@OKaw*36MftHi+Gx%TVJy?rHTFK0ljivt9|x2 z70S@jJ@uc==BLVLi9^Pt%V&N2_MeSsE*W1x2f-GttO5&e<)Lz@k>Xh}vL-9jr2>VZ9{fA^CnLcd0~o-sui4MVFKxws{N`IC^mqyS`k_ z&8G>wP16obwoMhO7{sm~tr|+`JVaw@a4p`_^wBc&S|M2U%&34<2i_voC@Eh>gvo&2 z>#+o$kvbRDmTRs_k(6A1ikR^k%&N@L7D@y1pyIIb^kSL$*VGh3XMkuH zD#9{z*IzeOrpPMEleAwXP>PluJ@>_?MxB7)}MSgno3inMo5K-o}8&Kb3U)r{ViF z*8}so!!RtVIS8rvD{71B*s!cU6NfPI)n9jp9ZVELDjdjf+|*`dqPtYNi(XnCHA+Hu zQ;%Oe*WAl-16KBUK+fB_;iL6+!m~!8f}reVm$j{<^7Q2$#lBvO4%gGHP^hqDD})Q*n6 zWM1Z7swBqTT>GYOvxu&OQMhu0h7lco26$No{U*(4JbG;NIy-e-X%zq7FTh*Krr_V8ID0~Fy8?xh-8kX8KdJI7&YN!wJgEdT@&IFIc8OPEoWS_#8XzydmZaG|W|Ne-Qf4ygSW9^9}(aMF|ZfY( zk!DERK6vXGRf2Gm^ebV&)7V4f`b6Lx;y;{NB>y(_oV%&oB&7GMNzG z@Dvi0S@+2dDZzRCFci;4&iXr(i5%mD6ZG~AJD6lyLCZ*7l6rp7XJhiyc<0l-)aEtu z)=zjxz|-d|!)b|t@X^Yh_={l!}0rQ3K9Sc7S5SX=J=$g%VE*k#rJh)=t zM1E7wSf2aCBB8ti*Ujg<$T7#xv=TX|BUP?~W()$XPs_O3P{nz6l7sM$lc{~y^IstF z!lP_x6Iuvdka43 zmmpj&{{i9F*$(-=ZrU1peb>>YJ3K7WPI~nEmO_2|X^XD4Q@eb#SK6wMB>stLUMX|> zxpi!&d~~mVJn!ksng9HJyLIV_ihOwI>3P?styJNyp1f`;V?4^#BcWliQC$$X?Iy8} z;nv$c%ui9Ca`zl;faNIR`;uaqenJ@!AbM>GY!kz46BsR8W9CL0xe&n=3oW}Jd`rs6 zEW)>Fn=6TzFa-+V@-vQsF`JzMP28;^_mvy4K$m8+k8$QSts*p!(4i;S>xKF!%n;(++D)(-B`bczy~ zIuv&m1~i2^B(JzkScYfXW_A+7$b8D22xV&dM|HwphH=#Z%DgbeN2r{vSQLs%F z^CfC8?lL}Vt_*t-vc@dPcKE&?7Bj#UM+b23c+qW;URdbyCL#~(MEH&rRj;(n242Jg zD&_&6f&7yr+#ow&NSt0Z{i=gfE;HdAx=z*5i95W^t-^oTHL05_{hprT;X43HIp7>* zglSMpZ36nZFw9M&Jy$WT+f3#%_8TrQRzx=&E!?e;ocBX4qyqV8f!?*0dtI9|CW)sE zq=?7SfIm)q?#{Jayr4&ap$198a@ibt+0oD%;Wo zHJ=r-a87XvEtFQTWZQqoV>pgN@w6w0in20uTONo>C!Lgb8j@q}UnbgSzNIX%*s>IX zt#Q*q!c_t7H<+gelASZw296C)!==2fOW^1Tsn_!JP@FM)$mE_)Yoc9eHV5C)L7f!2 z5T25vb-4=8;NS2Q{=e znt9^>2gBPFg{N7bGwrXxs~&bH)ug*q?2TrozK!W;P0sDcgfXh}f5qBpFzDH1F$H9G zR>D#d`UVGQrw0c^hlh$FoSH*_Mq`GJ0e{>2aQ6*=4abP`2v;F8dB&do%Wfbc%G%aJ z+}?q@gbcd|40(6}eE9hDzleB9h5+|CZdhRXQ}8m5fqXi3X~!5@UC1>loYhdLpGS;7 zXj728hzMw>A0+rV2R~wceMH(BNMQ)z8E}s5dJPfUfOM@8UPwH#ZXOj~D|a z>_2CF;Qns?yHtQx8ZT;IdD+PI#rXsjpr5EWoX`_vG}JAQ8`2b^!GrKifeSK^vJeiy z>-?tXOQ#PyHNG6Y31<4+DYkdZf?%ZTCwzp9hnr`whEcWqJU)mhe>b?*?dPjggSRyg za`Q-F3>PR|<=YD6-~@azXfR_dZ}Q&Dfk0m6YfYbD0}#Z=$2TBS04!kvocB7+DNwY{JFl|KR5>W55R;Bbu@j@ zAIRXN9~7T~SeD-uK5f3BQz-fqkA(cXfZ5yG-QOt!RB(r&P0w%P-@^!h4{}ZN5OQ4K z=C4*I)s=aay+N`uguMflBe1)Nhe+TcFn55@Z?+f==w~H-j;~?z{z?pBo`2FiZP8cq z->(!%l`kzM&R(yR1qUA`2DJXS*qJF$0MA}1{m!ph`!CYNZ|TFX#!s!#?`{O@_SN<8 zUE`0$+wYqoJcDO#FDAl-i<9>nu*+zuj^8i+GUCVS#RS)e@Xu=L6|~117}lHAXYVMa zlR}WY5RoQ>THSQ6+55P(c zbmbNY4ILb??3?)`K->k$d*Kfw04#k&K=FuQ*^z!ALVVzS*Wg0FV|a~$d}E-30t|iw zhyi)uy?K;?vpa+%Z*j0+3@`EHH+EFFJ-)8eU&luvKiS^^gulc;UF~Fn=}Yq-qH5WVreoq?qE48Qk7U&zAhd;oz-Zwq+JDt=DaDHohAmQ7rr)8 z+i}!=`ShI3zB0bgV0f}#cdJ*7o-PRXiyH{Z20Dszu*_VMbS75`y)2j35z3PBbo6D6 z7?$WZpb;GXk(XHIqtNBy=wK4>vB4r$i|S>=$A?(aHA%SMZCRbRCZU+BK>y)z7_~}| zJTBO7aTmM5(_wptM$18tct$8fCjYSh zyv2|@+kQ!KIg=8cZ#zq_B)oI`)}$J;I7D(eJ`hj1GKdCRFt6)q3>SSOBrLU*fWFCm zNYrv9l3droPMF%5$j*B-Idb%6Fh|R+OL3H*9xIq>Y?9!vhkl=3dh9yv2p^lSUN%5SRJ@b^6S ziVd96SM01&r72Aa_Lk#&6*!711U3%Nl18--+?U+lT#0c}%rz~PHdo}*VDkliME#~= zca=*ww3_Kgbq_z*&zI0r^axeUskT)!{ZC>Dj$w$5%)oRBJ+_rG^p+l!(kQF{tShm5>C_SexYJ=~qhY0Aq!F;Vvr+zGBerd~mu zqy-BdtN>4#DF~dBps~`I9R<_~!cbW4%cr`GeT)#cXvE_@pY%*~xn2`zE>g)noWfEK z4y5Xsc_4AfOx#bjZmlr()3xW2ka!&Zv=TU;5)s$3V@o4F-OD#Rd4Va8RC7YR0hRbI zjT|-;j@pbXWi9{4+(r4+>)O+Q@xB~|?OM}P4<$)A)L|P0N&SER#9=gqqc?Ul%8f$`)3(Y@gz;zw@HV%HX4cmP-GN??N z`on#L)G=Fd*ta+4% zPy3JwEl?%t;gB3l#9oxgY+O7KvsxoAjP3?;RGbdvJ8?iM`Ef0w#RIr;oyw`u+VG*| zsFd{>tJUe{3QkE_*>Gg3Svz4#_Iuz|0?tx~owd7>oWSGwtJ3p&wq{1M5Hgd5rkJ+_X)b|C@~N)g62Z-97(wX{2Cjy6c-Hmp+&jKV*l}E(**(&*B93fN81-d% zTnob7tvP!1xs9_7(YQRSMIm!fKT#gGna|Y10&gT-h5_w4Tx{febbG ze`Ny(Cw{C#Qq@8ZBqDrsCSro9+=qyylCd@ZAZ|qb^A;N(kZTP{4|nnX5Rp=Uk~=?5 zVE3(v#*gWZWb4GW2IXL&g9W<=w$b73S><3 z*}BII>kALFd}Lpvb=r1iWExFG2B`Jde1BIQ6^`$-wd)#^+V&Lquv_qBS|>*{c=_3z zF~%<%{fBLy1_+cl$?Fwf=-D!3eS_#D+$?|#yklYyAH5p4^y+x84^j|HOHO8UHpLZ9 zqzedVwmq^|fcK6N$|U7-)SchIbaSfSKZ|C(jfH$t@ojbX5ZjOogKkeV5liy4=-rv0 zGblO=X3Y?q^;)HS#nf}Dy_?!tQBb4A4b?N9C>Y_G@v99;)=5>q^E2%Pbq*2iq-m5& zSvvMn4Q9~5_g@4seT)B)8)&rw!$Ad_c8hL;Z1l$Y4)IW-na`;{8)PP8ib69d+4+mJ zaVrYBp2#p|og`2iE0K{Lq=^rK+- zyb5|+OB-7@R;*-ry+s}iR_+2-VJoqI+@oo;&V8zi2$)XQ9AqfEY5 zoO&j5NEICRYlmB_U9;OJtK-??4!y9(H4*?fZ^G^T)n`o&16`2fMRQhSY*Kthn%Jz1 z#-th)kDfGlL4G0MlEXHy3-o5aM6nvC+7qL?(k{vu5etYXlA2@CSpmMOxQeNKPj{`; zpwR%=JXb7$XMiJ$Ywc{7s_@ZClje#}x>uPe$-4zmk0D$6;K~~<<@vyqA%$+)>o}rqXK%8qRctOFa%> z%QX7(VmW=Xn>9z#aGK!9m1 zQ*KznV_AGMjUq_(cW+L@I8>u+yKZbMjkEbgOSfi*X|}9$d(G^we*2iDfdffh;>1=J7qayXCYGxhUzQc`!!P|@Ga9xUD3aI-N&Gdq};`!EgD@DVdZ zcIWyQH*K8i5=7BG3#naw)}%o%NtBwE)e!tL>8r35f>M!N*(+?l4WRC%Dyse4=zOC5 zhmq*^;JG;=9X1Ak=)w)ci|QmDV80Oqo_R9nG0w%p%}Gb@gxHx?N7)80HW?_HuljVj zPFX1Gbk^lIqqF}_oK>mlOS&g0nkYlBj zhL+x4r>T)?$|EM;R1YUL3<5(*FJd&zj2mwJ4E68dY0zYQBWUExn91dea}ton@_PZH zha(7A0jnwYEJYVRJKs$TSLp_s1Zn7R)IM<9T}x1Jjk$)Gt%rQhk1$fuLeV81Z#>Lq z&Es0uonc#G(Juc5HV-6)z9W|U%PfPizwTdM*^I^!{3)aGYJ$MGjEAC;aCCI9frgdU zBqlRHeMzMk(WL4-)4e*ovE*BK=P&L&oq9>$^m zg;m~^W;!ea59i9U9lLq^0Bx9V{jp@RL*X#JXld5bh%eMudZ-8H$JBy!r=@SxUbL5c zvx&{;^)5G?lyLh%aXJFtPCwQOd5xB9u>^fiYR#BZ|LYkRrji1Bi+y^>n(f{M>BjqF z3U4XT&%k&C1hq5Eta(ipq>UTLO<_8 zj%!M!Fi&>7nrrKmDtK=D?6eFDzXc{ZMggl>vNS!5pu|X(C`IncU{5G=HXpfZ9IZEK z(~AR1P6Gj$Figkb&rEB)!V#U*b`k7}>#`OG>0@Ixz~ort;NnUr@R#v|;ECdPC#-hJ z0l<^9nrphm{XVRQc+3vGiu1SQOwB(I!^`7YR#el+iFFpJc4k8SSL4+ZV|^4Cs-snXW933mrUadM@F z0dI#~3jzd}IyUVjy~tw%5T?7UPQUA{BF}6(U=ae3Iwx*l8ctEosx?O6y84|Tq@iFi zX4E@9ab$Oy`LWYi_P>Js430eBW@G;vHCOEpR&ykS*k9VD+?JfTW6P4Uv>HZ(rIvqo zuq^pzm`ugFP}riZ=M8tTJE$!qb(dPu33^ChdWy^c#@y!nOt9s%pYWGh1`rE7Ru2cF zV?@;y{Jof^KBw=P_~P^(?{-=~$iZg@t&Xl{9T2xqlpFy6YebA$B*>tpGW3*zVdFA_ zm+iV=+__|$=O^E6Klk{^UexK_D{ILrd&_0xq{<3r4y_e_x>1FGyZVT&N789ZgYSuF zr(Bzh$4Ky&nI0UXe0@BgBh$K4a?a$8>C;PPj~`~t7)T*5N3^kF&^ytqBacN=eCo32B<(Xw}eM1z>qXR_YNMIGS%>u-(^ z-Y)TfnTZP;L)?lA!y(y#k0gzZhdyK43j!t1WaOivbSYk0Jl7{y#W+v;#hPO%NjW#X zLZQ+dB=qyfBEAKoW@_|SorRpG@PjpOfJLaJ-Xm?~Agem`BhSsDSD)Y|56$V;_uJ^6_#PIRJPT@)t~QkFbh)7dhMrDZ&@Cq2=`qh?}%z@ zrJfz)+{uvqXSiIYNz02e2#3vHJH~5$UMU@UN*$O;-%;&C$=3EJn&)yCU8CN>B6H_!ZsUL=U6j0V72wYt(5s5_gu|y!cWw!k8sOYPy?PGHThzs zXR5}SbK|T7GV%ong5n;e#_2nn{5Os1mg&UHTcr>ZuVnPcqtyE`w;f3|&sIR1=*p1z z_;z-xOJ(s5?|0S_-0LL9X;OobWTv{ScV~lyoZTm(=;wX&kXe1SD724w^6ksO09#&2 z&~%Dc`pe74UlAeKGltQDxxChhgXR0AFC~jsa>`zGHP$ro)TVh_9?>xj;R60oV+NX} z;jrU13BVmmYkAB6&<$|F3+eB(c60Aw z4ql2ZotlrpH+I3h`*DrbgV)hl_4w%Xf}ySQqh9ujG3SA^3n`nmu-|MC)=J5&M8q}5 zz6{g9~*^}t>6gBlS=Ws$QnM`D9 z#C?rbucrifR5qsR0irO`k+l#+>;_2I$}!X(%ItCgLLJukvAN;7rRsNs{VK4+vPxyW z$%V|&Oe5t6m&0zC!xITUwc65*E^_2bG?7f%YQy|6A>MkLt6i7W>TIwINn}#oEWr|F zx|TL6J~e{3EtL$U!ytl@+$z$oHlJ>FAwS}w==w8(MCZ_d?j}&VmCK%4VMU_FM4Ht{ z^!-5C7GNeIwY?$ijVt=wM$Lt=(mNy~kv7<(pKRu;PW#m;(rXnz2QYy-<(0O&gm57w zHVo-wm|qc$>q`xUZIxB$sbX$LJr<>0#!hx>owV1h2`)0EBkI+mYX`)Gg!ql`DISZB zurD6@>}IW%=odODy6lp1Bh0K9u|m!&(sC-PSv|e`(t3g1E(v@pkL*dOcP?0dnAA|o zYVP-j>dA;km{57;)W>R!Uh5e6yGOYvLUG85T}XMMhcRQMm043riun}Pa|t|$FJdu? zYT2Ur+V-$)RG6MAmj=h~3k_1(LasO)CXmkJ7ue>v`H~86I|G*<0+N5kPHba_399+L z#|(&^8M!?S9`ie+Yed-v-a9jNg@H8gSaa1FQsKyvMDLZsTv;z@oGKk%hZaqu8DNB+GtXKQe>SiIH2$QcPO_T)5No2H@cigfIei@}r>5Fa*{ zYpg>QS8AngB(i|Q_riU`eh6-aNJi#-4kNVPPlv%4?jBC~z=_l2XxxN`OlPQbRjJidq8IWiVrTDmk)EM(U~-S9&&Y(Y5nLu8OlXX59_Z;R*eqnPof+M&*C$1FG9k~jeB7cCrdxB^Jlnc658(>#Xx?EMIN2kv(CPTlrv~;;3rrd z77DB7H-P}nH9A*p&-al8C}@dUM1cFwTkLWaX0yBNNG7bU&9t}GDp~%=3~MAvfLS%V zJ{TE>qkDC!EuHgD0#Wb6KM&Atmw4+wHH7D?A2-hghn(uBQ$hT}hAE^^RU_2JzHD*z zhNM$6o|InFGkbE9J<;`Wxsz;hx<-DVIK^t(dlAzMMiT>@hqr4gWDjkUm?5_k*CNNN z0GI2?qVrlYZ?hQX5Kh{HN9?b0M~6z2ANp*2OfwD&4uc!XPeeYSlFF)Q3BzKgmP~KT zOPLy$dcL^f)#GG4!ikBlqac zs1SJN;=4W+T#2Yqw=lXjX%4q|uN%^87TC$QwS{kYN%kKvN-s`rG0JMbL?gR4z{h*o z>%q%-4$QykURj*GFl4${zNyx;>#g?anvxRHL|9uP{c{k(zl)WPhh!ots~3CNketKk zUt0Q?h6{&|wJK$yO7fiS+7PSsk`cUGk|71*rPD0SIBrTh&x-D$Uop=*fF*_BqMmCmRZ|B@s3H-U;z=*}K|{ znP@FpH<`?KaW(7HY>?HWFeCRxv=N^b9Yk!VB~kz%rwFUpi({*kd2{EqXVY(l>y&96 z6wTzGPfn%qlT{YtkQt@F08>hsI*26|D(RQbM}fCKZFy~-=WAQ`+@7pMLqpflLN1f* zbpsOXw+_WJv91|fe~p^rNmrk=Eva*)BuZe#0k_kbE{u03FqYSwrfhd-e_en8+AnSqSbycbawqtir_EK9Mbjhg@_Gb=+w$Ef#a2zI1|0E{hmJ;aDUlG5 zf(9NvJO_7acd*!G)yL(K;3sSEC(oj?T)w;O#^yL7J0a>;y`IXrkSz_~%*)n(-gN-O zdUe}h&-(bda^~SL5I5Gm(qyRPu=dVQjqOVbx{Br6D_H*uhl3>-97joP(j1w{QM?}# zb}&C$;aZ9Xf}T9*{iVAR`1&wCp3GMCFi{AvqMU{EVb6w-=INAH*yl1|Y1^?I6klc1 z$}-}tRr$Zt#o%~Z{oK(L)nG!JY`lDC;)HDtmx^-rW>A}$L*P5KOr8OZ=c8If4&jA~pp2gsj!!$=s-8I`3 z=Kb(YVW8N$3@Z=|Uu)Z;1e%kE4L6Z=^71Us3f__<;n<8{-9(ze+44wj_UvXW`Z5>wW?#;I#$~iM2aKNycK+W_>^22R{mh7 zkO;dE%vi?Mqr7kla54!@g8Py?=wd{sbqQM;F^;JNMWx*`AXE_PqB;r`V}TImpP6q&x?jJK2fCgCU5kbTJ2QM9|Kv&|GW> zRW9%4Oo-FUs5~Ukq8v_Z3Mu}yz02&J6I3a?2J}#5`iv#yf+*-F`+77BZ!k4(Js&iu8HYb;N6@CWWM65(2rb3aO$(<0kgfa%ZxF#CYe zE4Ab}o8dHwNz(oHFjJ+!}jV1si6K1T7t!SRgYaY@nF?*Xg;lT>xXb1B(d@ zv2oxXedYM>-XBWQ;x1wRvCQW9-qLwI_u+N5VGJS1H!m8Qp!v3F4`FHm=h>r`5qmpb zKn1imQm2P8TEMs+{hPx?#ZVWSI(6yBS_Fz1Qgvy~=IJfdnS~_r(A;?7y93$ZsA7sz zherpS%$!K;!eWV}O5+hs%81Juo$Ju&sF0Bp${?0B&#bh-O$IRa-14?!lS;EWcc4g%4;Mfkwn+D`?_vN|hE)`v z@6MmwV#YGfwmG3G_h4Dv{=ZD2VlAZK$Ja>E>X{VrzOA4l!movm z+8rczH51S1W=usJ?CamG?1Ri)KW^Da=0U<6A#Q52iM;?L3=^W6iPZ1g2cc z3D9w3Tx~E33G5%y#BTiw*?8gL0;2Ee%ozj~m%@pmY#kX)$9pkPM`4XY-?p`UTgOGg zlIsS+>o;&eMA17to!Q|e(UTAv>b+!veKDeMR94arVqj{&=BIsKVn(sMo_R91;t;pR zwW56d$p7IaqLMbdFN*Mf8lyEyyCLQdF!lbVnkCZ#QbCwtJ|7%?D%xy{UMGv}ws5}_ zi;pGfY;Z&8bfHbshO#*~7jNWuISH9dRe?zekGM=lEjv$7TsP58Y6B-bO(3svy%86o zoNJHmGJMEi&V^(f>7Xk{O#np@O|B%GRZ@b4<7}2uL0@@3x<4i}=9Rkt9r1V!ZyC<4 zg*=gxJ3r_NUH3!Y60sl2IaI%hQ@Y%=vAPQ&GdUhhk!?vUb>4y>HoHU`Vn0 z-tP=e^5HTQ+Yc^SW~%uI(25bgSY-7Jwa4H45E^MH#erzBmhKTop*Jmz`M`AP9$jt7 zjMw>H82vlNB#Ix*x7l4CXSselcy4XV;t*VvKBTgT2K7C&5X~&ZyD!re< z6tgg9hZ~9ZZ!~&0`FsHw5fLe5f#@x%xX33d`>Xe@_pfjDtybg8RMt0-XYOOx_toIA ztvPWS=wHr(B?a*)LUBk+5czqfMo=IifxI$AL`tENVH4<4LVe%S@wO=gb9xSFsz-zn zXl(Ei?P2BqG@1f@XsEdtQGh@JAT9`2ToD`+Gz{Rs;ESSQj^#(a1_2Lt1_jilAfASS zl?pvENC4;huV4H6@l_9i5QG6pNJ&9`%Z8VC49(w1WI)b?7-{Rh0>)xm%r5f)WnTU}Lyyt*L^65^hGga&x+V`BI*PQiq{_zME{l7c+--_-Fh1dX); zO6crsdjTj(C?gnAAwV_2kQ|^PPaTr?qCy7deaklh6j~iWe+bxj42@U%0KnetF+e~l z?>Ff)@w*Zc_njLH)<18Hw@=)cV*zUqRICpGe$gR>$sYv(LUZ1F z0F743+r;RHKj9aInx^mzpe~5S=$9AP1d0eiM!^6Pmy7@e{OF7!!u~qN`I1@@Wy=H3 zduKdd6nt~nPh+9nexxDk_ja3~6x3FNf!uyBowf2f5FMYvK73z3Z%f6L_?DyB^_r?7fCqba{?b_!a_cR25NXA6_h3l`KeE*!k;>mBn z$ueKOeH!wvN#_l#o&&@m#@+g?i_62*C>CwVtwhnkNHSatUF#+;(>K`p3??H^b7JZ# zxZSlaDc5i_LkzaMa_u9TG2?K61@uC#gDR3Cl9*eP75bitB3w@>6TIQp>q_;!A6snk zRVvN|UBc}4#dhnPnT8!dloi_$02^UTLu6Vk0jDry?}LABJR%G6CCDRQP8i0v?pNsR zlyu3LLlpFAuzT(}uTS#dks~R}qYM9*+Y(BjnNC**s2!lc5at~a!)x5nNUuA+t) zE6wv~-Aa=xXJlV5+*hhG8PsRHHxUP6!DO32{p|0t@w#6$mqe7`>i8$H~cU>#_Z*%jkU*83PWq&pLo(ZZ;0 zZL+r?+is@aPLtS%OgJB5_ZSv@s%V#}cZ%|6v!j*A4=eWM;r48JBJdi-xYf+UQJ;~I zPhoTm(&PmeLH0Jiqdog=DtiMEBs@oHMfx~Xe49bYfH%pGZPetYVSW))>e%LkeF>jVgZHh<5%dYVTW{y=`hG-q5ibIb*#X#hxmBTF}NT zjtGSnA`fH~TbZDVb@Qnj#E8t!fout8UB^tYM7{qP{1Zn~N3kiT3CV!(-8{iNc2Yqq zXHhB3;_#+Qv)5_5)TsHpsS(^dA9NJWUK$j1`K29NBtoEsMBu%nlN1XXXQpe@OZTng z`xG9#_oS9v3e#m)QX;4FuCCea9Qcsqxl{42__98KoA~u=gl;#H_p)@sjl(pk{aS~x z1#dZ*!$F-(CYO{T8Ioq)Y;w!B$uI@*ec_mJCu1I0u=`ZoUII-qXY zpb<~ES*EY?&x2}i929$BdE1?pOo8I&o;ObLClN(ps-OlD0ogPE;|sK5j9cW5N}0v| zR;I*aV>=(h+uV=ih zS(;OJS+5=9N@>?@ndI!!8_s4C>^U?IW!=aE53&m8%dQo`>yBQo7a+0M-K$_1H~E9= z5JJWTYSVR=X|5=IZZllyCy8w@vn{SOa#!j)r}uHZI>(-(<)=q0i(lZUE#z9cW_w_3 z_~HZa5XKsaRihHZZnLSHqXERqPi zV}=Hwm}hVB3m?5ThpMKcEf*4iAZD`}e|g<@*gXSFYavP5&w9?z>s-TDAKYx1xVG_> zK@yrQKV~%S#<|&3dhi!WsZAMx>(42~8*9fTb(FGld?`^rdLCv<^r2%dK@r~!d#!iJ zWrBm#X2}24aygB}QaPk(&CqvD5{o=uHd@{3Gto~hxM6=hO75m578RAkf&abEKgnFK zSGXHB+L-Tvi6ZcIEH+^<82vVDykBxio8d4XtDq2MW5(e1Ex3%9 zKUKRfN0`R_l1|;->Xho(bfrwu_(?s{4x>bTi*SoqX*raJ*v;1QO|%5^YWnVG3{gL{ zJ=sjq+&}b*TY-Z&bJ$MU0S3N=>Ce!+)Ou0(_Z_P;>&2eObdut0`Bse0sxpROq&vcM zne5QHa3Ddm*2*-qfiNqygauO=^(ytv;~Pz_naMd>qqL*;{}mJM8` z+^1?*ZX-XHJfnZD+>3Exmgq;e-4F?8w~2hg`%n5G)6d4>+!vdE_aIoEhM>(Y1oVR} zYE%pY{-^XWMJ!(fZ{0%=8NK!$x`H%Yy|G`iuQ8#f(pMeX5!a?wN5w;1_8b)VOLWON-=@AC+H|J-DRmAO`! zMz=U}b}&o|wS<;w9h`l(P7 z(R9AYW?XIPUeD?y6y0sXTPt<^x6aFB)c@=gP1a;6#%e2U*G*~h1~S_3LijjM0%aB> zi}`DyyWXMdIq?{6#05F0xOi1>>nm7kS&QgLgIw-;f^mg_M$P(vc;w$6F=z(0+64vE z#<&Q%Y1scS#@;DL7v>Mb9NV^S+dO02o-?*>+wa(CY}>YN+n)V4n@u*^f3kbqH+|LV z?yCAd1-;u>CXd&f-XSwDc%&uL#@1I8>U@Oqx_Aaiwr}(6pV!RhcUx#x0EM{GKEx|X z3T2A>o{*=X`jnW(4049-gtcxLP{kRA*hr!sbbWhje+h2Yq@t~RA-v&|Kjta8-O-jf z4BhR4c4LwEo%{W;_-51MQxdidXA8K(q11VpJQ00@8Zf3!DX1O>858qhz}5E7+RV?- zEcQPHcPsF>K;Jz!*UwX5fujW3X=}aNz1tf>8^4xeyZ+jifLlEDXd`E6qx3)J$4~sT zv;7!0#isdtD!E@E>PW3UsZ@kEiy<&iNl~+gTrbPI;s(7}>Ho=~QmMt1$q`srs5raC z2EASqzU$?j$K8`GMIjnIV|9MV*Kk}Z0czKWAdj~)fHMka+W7Us{f}G{+qL-oiO6?R z0o!tPlE+Q6QQz*ZEGMfUhfoh>(VASA4I95@X|mv-?9TufF6%DGG(V*x2JlJ(WB-Bh z)g_`Fwssco6X1{3(!xaYXluno;`pHHmpuxpD*L!ISZx!sorpg10OtSPCyY{!`$)mjJb01fcNLQB;f+sTFhvUa%-MJx$CAt zO%Gkb;fm86AM2zSEp20ig^7#dm!r7XLmDo^liE|Hy~RlWHqKVMThMv*5q*Nurzbuo zn+_q*_EU>Wfilb2-)bkrm38xzoi(90dq7g_E3RkN-`a{C)5+tNJ^>d;+|Rw@s3XwD zB=E2w>yTVXTNeQzo|y2KJ>K5xK6n^JYuoE1E=C-!`hu+kNe6rhala}k7B^-G@-O6JArx2RPk!$|>x2g~nfQGPqU)Sz zF!@33?7m;+?^49g?!l#rY=d;cWEnFihdJ7B)t8r(h!vPb#xw4e9NPAD z{^~n6-1R#R*L^Cb7S$0b?$EQsg7G~w#V>4vNd#W;Evv0vyae_zJ5K}nic~T_WFj+T z1#_KJ=BI`Rqjys{eShf8#-gk{nSIUx-yxh=>LG0DE&|W7_VERY6ez?dvT0HSi0ax9_w;@(`=k>p(hu44REzCymIO{K?+KaRD7nF5CceznD-_l_af#&D5_* zPsKOKQmA#Bps9T1{jnlDa`s~3Z|5F6$tv~obP#h9sUQ`54Y$@Bf!G-(qI3RSQ&QxI9i1X8RG!ssDuw4C z^p(dmiQXdubY~;*-~%JLAA%H9f|jxJ-~n0EUpL2CG`4W@1~ZTvH9up^<3^-UBgL7z zJMMLHnsZEUhV0W07~3mXC^}Q`L;Ns{%%u)gdC<<2`~FJIqfK0r;@3EBYjoVf+Lp^p zoMaEhkuoJKZUn?ApGXaj^>=9A1Bq>6WeQG0e3jjt{M1d3cd_w4YHzkT-U0UFeeB%pZdmmyRU8UFAd#`f_Nxb2pD5QyNyPXcjQcH6NgtH zmVZd*xVVGTkq2d~%~x3wpkNGnb&@R%0FK3l=)0J+yK{M1 z|FFR4dmjJu+jYcs=6P;cRxijoabEqA<@1ZzuSj^CTJbXQ^zD3`LtjqRvtIAQ<{x^^ z-0DcuUSl9MeVUgnlLKys{rt`3QYGdc`xJ$ti#!@caGj-4a{XNH9wYxg#t#JM@PB5M z+pT&-2UQkrag31^3w8%St6&EoM>B&r9z8uIEG%gh0ykV(-WhYF3;$KDsN)|t=?_I- z=Cf1f|D+E#BfSaf=h@yj8Mb+_NEW#=_aik3t{sfgJDxfUi&o>;xO9;|S-d&&lCjT5 zf%6m~Q17N?MYODt%GY0VwZTNOpcrcvGM0=TNGo$>?CNWd5sK3TDT%6{DE%SD`q)2sWD{fQY4~}5^Kr>lojJ3q zUe;#XFyQGYFVHYTJzz-%jQ_AE!HY;(h}WfInI-&L{&}Y?jySQT7<>GnbsXrblHEKN zWcAek8ePX$o{_on&D*b%gq$PHN~UDUPo@Qd^FfPAVP*4PvSLYd2hC-5V z;>YWTZzR;O4O-eA-v1CfnqWm(Olzi|N8v`tda>S!eW~_7o#E5|@KF$%CDt{hK7V=0 zbia3d>1)0O%L^Bgut&Ebt2KWFC^^>Z$`h-Qs3D~?GdXeeG{~Pkz1Sf6gJszlO_1=D zz1}k$o#{4bnvA0A@HVp$G9L61fa`Ip`YJUDyUwqHcNy?gGwd*$L`c#w05y4tAjY1( zQya?7-K9AjVkR`^@^LK3#D#pBq7o zn$}ikjIym6UOLha-~p)zG0oJv6hB5?8G7-zSdP|Ox%LHD)Qox%Mognw*#Jk!sf!bC zwi^F;?V+_Jn&U&yKk>dX`yS^N!}}8*{G}J&>rmBb2&|tov8i3APQOmBIHy(e61i#i z9etd_IM!N8vbmAA1ltSJi0%k2+24{N@Z~i=D!ojUQ9V4mByMElq_m%1)n;N#+AxOW z*X0>aC)9xoOpcFc=IKawQ^9N>R1j4sfbYRUXK^WS1wx2*iuQ?ysF9!AgZs?>APKoL zgpLR&-6!Uyqim$>zFJn-(gKdB-q!O{68(ncPJ732W+R z%8k1>4`G=`R)!llG)L24veQY;Ap7N`M{21PW5Tj2R#e|~HJa2_8RxmoZeTIKKI8*g z)ZjR-f+u)=yt+@%_2@P9sC;| zsBE1u7q+TKDzpEBY$5iD(`U+}1KP`d4KmF~?(@kMuTWHkD14-VOdwb;w&H`~?$VjK zG=_$4za2gK&W{XFIL2OX;TcL(%{$uHunL~k#v;6+^XY&6)oRMS{Xpv}ojkncX|H1v zLDaolQuPab$Tz*i+WmgW{`05RKmP%){^7oEK7SzLwiM{^SZhn&rmBG5r`&K+n51^| zgmOSxoX{D2b<}5ZJO7aMtJ)rRmZ;r!nuk!x^C=tf_YU#Cqt7**iN9Ta4#rV-ved3JZro_&Vh?n$Z(Yrk%qtpfm)`h03q z*e-Vpbsb-juvlFJ)`;E-6P9vbACVA^h&>7WhaheNz(3S2w z;d;U`!vOKV3-3|eSAT}$9aR;`)sxX^zSYGs>+;(5W0uN&X|00*25u(?9WTCgm46xJ zIDK&XD{d_w&)zn6##oPxpqlr~{vyGaf!{|c+?$a9Ye$F#vFr;@=kDNz#ER9EbR2BN zGXO5genFEzRWFPxABskH&HOi`_vKsfjBT%N_IMk$rvpKYO)?A|pKztOipQs&Bj?+n zh{KwMdEV%R7KaNA&^I9!zZTC_k3yH44ZaJ!*F0xE){EQ>)-ow^Uq4KC&t;^4nk<=Q z5M#;$6LkuMPf4?&KdqE!hvPvEYY3i#mex5ccii$hl0-S8g}_cQc7n?eG-EjJr*y_P zHi(V9I<^w1>LN88&zNG%G@cib8dIuLEG*p4XVT>9Fk#e4GI^cRUJ)i`zDsUcy+~M8 z&yX8Td(B^;0B|{!>7JbN0P&L!{I+wI4>iuQFFyNPRchI-_6SN}Q#qU!A=@!zQ`i@u zspF8kU3+CObp#0Y^WMkj9onlu(jX!zp!qGO3`338-l%EV_nZ@7AvQ#kp_JYtpM`7dNT+07l|HEymx^gd^E6K6&bCtYT*mQ@Z@jXS86qn) z&#@>%W--J-*)!X%iv|=Tkd^wd*~SZ5-zzNVhQcTqXorDdvZtC7vS*>X94h$3LlE#1 z!R_D6NtVEs?otIH--=;ER0C+@xJ%-AIUEG7cAQ`ygh`4@S3B){WkRT@%r0Urd>jt^ z7Oi-o`vYE=E?!$;*2lEUPNDw^l7tj_O*oE;P>GJt(3c`rw*z4`mku!oN(F^saP(C3X>oOf0-p|X-P`I{&UZ%L zLgcG*;XtaX!3lwiVQnW=P@I#}A$+iN;^GEEz?;84+lqTb6yW+w+2 zeTmsQrC?CPu!U55#JKejmwX?jN_ce^{-czpL5p)KW~UzV4SGCSJ1xzIv3(iSz6+O`8U^OIXM zv}Ehn$1}AnkkOraSu30N^>Z8wP!`=4;^)}OHNsF4M9kr5ZySZr|7GrP3czw1XfMsz zuA8r3MJ0&e>Hvyw!34;;P3}Gyb_6X&7HOaTRGYOofE8+w64ob7EG8d$EOpo_es#kW z0{G){E{~^uZ0%pR#!)I*ZmN~4FLCcIxMA{1V0EnTUGTMW{Zb`i6|BC?ddCdX1bN&f z=D@P0tgm z(PCA;pp3D2p@d{7pP;5K^+h$Ixi%o4NbYR&q~{b<7HWY$ zsM()JDGQ(-i<6yE#&`0asdH)AA1~y7zB|Q%N7(8DFfXonyYQ)`@;j zNw;Q_!39L5wvS6BjY_o5FN4{{CE1a@X$47*Yy(BlHhb~db9$%>KqYh6H1m3I9VYOn z{2Z)75or*0bANSgo@ZM@8DgyhBj_L|(|;k`nMV=-hqui6|Ke8tpWZUp|C8Lp!p-`> zyk%|{?*HFZ%UBn1)urth4*LA2KZ6Mia5*IOf6|H0nc$e9So`3%^+2Ra>9=D8QizDj ziMO}m7w#l?Uw?MJZ(pmQeXUnMrq{g%z4N}aAFl>wYYV2yZ4o$wsrromFzDOmV+pCN zsYRwE0)ag^g9iGvO-=DA7Q-JI`01W#AVGqmA)tP8hE#!qg>=1+2PV7S8~}j_8v>~zEx;Ii_mX0ng3g5n7a$d1`llGC)`^f@4|#ZG=j5~t zw?Nso1(%TFQubj-HGx?EXC*>XMsV+Ong!sDVLWiM+v%DI#G#|zYY5@m1-d|R3jw_% z;8J0Mh;Ef}4NMUu1bl7-Z%ESsx$;6?G1g5O0Ll05hJ)@MpM38+`CI%lfQ5cbK?L?Y z=K~g9OKl(vj#Rql@0!l!LLsEG4NBk-aot%Va3J*#IVvQh2 z3;R@f_U0TqVEp{~!Ov#^65Z?m@&NAJ?fuom-ld(wLuhpThWt5=@?6j3vwIh=itr37r zb(c;Ur5Mm5G{v6(r*7Gx;eE39(|gY*pD6+Y5BU3gXv+dP@E5%^kL7Oj(*n$~cDh%D zXy|*4_*eJH9@j}w^>;m-4-Ss=m*3YXNCYS$7<3H%_2=Q1UO0gF_B$g>RQIPGw{H+W znDkZ!=rx-k7{dW_YZsHA25t}d+wHp^OdOc+71Z`K{?t95@8s9~0oa4?hxwL$5cHGt zQNZdoe%zhV_1)x0a@J51GTd9)f5=VY%-|*O6cofUFu;*=bkFb}=yD=p-kh8BqO`r{`jcNE--MMj-o7F^$Q^CLyr#?99B?de8=VMd*y~%4TO^206pn`R(Y9U%^j|qhOIa7HPTY_)>Iw0s5r#nb3SbG^Ne3r=8t;!L;n&eN%%k$w=n0 zV^7fCWS>Oy$;!hQS}NsIVXa$QQ^K?PHcw>`<&nZ-x=qnn`Yv`TMY*r3Vwz=7U#uGg zsqWduc`osX#3TFGYf19%1+WTI(jWaUfVTXe@OovY!rSV(r~D>i??3H=0hbf}P9so6s%~`4SC;J0Ls%d~x&{kG4%=0KC@_(ECT^Lm|v?lF8jUQVX0u z@8sitFW0D{QEDnQ7ab5@9c-Yfg2i7I^%&pP?N!n|SdA*v523r|g`L2hG-W?@HDkCp z*!Y3j1&zY+7k^zcayrnsV{U&O%dvE2_V`*Am$ofdPVF-bHJ`sVPeM&iJK&Yb7|^N* z-Imr-sr+JO3@ScgfK*tIXnbfqp7v76=OJsAH!7yJUtGdBL?EIVl3i#pFBU5Sw1)al@wwz^Zb~ zBM)(Z&N`@iIOn`pY}r0g`5xf)0lOglt^LaGg(?$|QkKlE@7^nc`D0nwV9#9Y*1WINiEzpt!rUNqE9mU_Oc{e?xOY+)auM4BPEUBjWSW1vPnkIhJW$w zv%GohmZfXT6{#H>;%jWQToi}%1TSfYF=5-+pn%T5{L26<4Zd;=V?yvmfPTOCTFm*9 z6ou-aCige8sZuSSAWyM4L<*l-zReVKp2UUbN-xSu?fc4+&`@Jl%q|Lz-3HvJkDPL5 zxcMi;l32H71UQ0Wl-F+P)SfXa)BPk)k0hz*rIY5cOPQs3{~<6j&~YSS@V zhhu)d0J$Xk>286TY;rP_M?eKHFZIJEF*ClTS|#8wm@{I+XoW>;$FLKW1qn@H_I_|87PU=g#7KfPmQH|}AmGe(vkO)(dtoxVSfeRC2FFY`b&omymJ?*Zfw;GQ3=m50l5+%l7@N>{Kw^Ta)hUqIcn z_2w-VpxI|6|Gj;;fNP}UeNV!2(>r4qq>ovUo2AYsCG4l)2!YGl4;%59p0W%A4$|+a zR#G_XG9VhY1~)sfl!GH4C)e$$?H|iTk|tuAU1u*&Ag0r>)6z zB%+I>a+PGuBb#qo2qI<;1Q9%$m`wz*Q;VH?meS%Fqe^TpH{%b#j5CcTPbu9*e~+p{}8qMOg>`hRBI_J4LX3Y)mo%S z6f^kkHCC`6`HT{qs<-Y+Y%BSlZU6FD@785p@;X=FvsU(Zl@d-o9kSxQ<0~Qw=yWmpYxCI5qBX6M6PyOY#F&0 z-}cqM>x(O&Fyv{SNXw70xJvw9r^f@-xv$`P6rYhUBj+;_v3LK2SRSOxgbtZT?ogG2 zrV58LJKNkQzY^5ucw(b+uIN+w!K^6?YGx`Ttl~5KCy1q zab*t{UaX7~*D**BrT?}=;FSw@Td~TC@I=?BaEUXnN}@Nyc4z0!gTS%OumIhu5atdC z-9>qT!T-)0G=)tH2H99h+(bAW-8ys|{9V8dizN9)M$Oow{KCA2ca)I|^F#Em; zpHqKcWt%<*Z=n_3*+P^a0^R0GC9=t67$}jW`ZUaQ=W3MmY?*a z!bcjd=7{=ZRKJ&CnEU4?Y7vyjp_AocwS;vTurCU|0M3ifTJYNbcDq?C?tI%*K&ugD zxhmJC4NGRzXB@lo%E?wYd#|aEJb4{e!zfkleUXcsk4jKk>@y>se}fW>X-xe@w~ic+ zYR!M?v|ur+t^!N7+)idzS|qDxm%LPmvBs;8ij+-1C_K)7I{OMQUmaYd-wK`#;d2~nn z@l;Au7@O4iUtSn@+%GC0&Lt@Ys~EVFZF@_?#gqz5xcv$yFO%Rb@)nG?DbxRSHk{Xh z6;QRoyUNlvv}0k^Sr)|HTsCoyP(xKeA#d%>jDV~lsm`xU=%l;|qjILuap|LSJC15c zv76l4S@#&zZXb5`jh7syY+QRlA&;cYhOByv!ttM}n$$+{#nX&1)WyE{z9V>;ag|EA zrW3dje^>%hUy3h1)bHny>sBcn91`F1P~CVhJahWs+64KRM}ziv%MV1hlBS*wuB-wY z6FwX?3ZIp`@4!!{EYfqBofL|f^8jW?(}*fLL59H$3#qiahqDz)Atxm3r2TSt5vIj# zJLQBAnJASmX6-J5(HvaNqbyuzkcB@Nn`!SI5`hvqd--6Qbc}x)T9{ZdzYCJT14Gp% zvWH}7h)F^R7ACR=Cnp^T+`m)eGqUZ#z}^X{y#3Y>xnkipUB_q3_s=qu2uNl1CM5c^ zxH6|=n@1Eo>jz&|4415GZ&e^(6m0^W>x*CI)zR_-O1JXIzQN$@au*Ii?neT#RB1B< z^($*QdX*0-qfT$O4_v!VGhr%>1d!xUE5DtBPZ`oJ$qI45IZvx-NYO(avBZd`%i1JA zsWk|b2P3vZYi)tnhX*p?3(9xpTK`?;MGt*~@o!?};?KNp-W!un9?K(em0KyjuNN*nBy#bB*-+87l?k$J^EAUBHmP8 zMCm#l8m}z{)Bn}xMOzA4J#n#QjT@Q#HW>e7WUhBOu{3ZmyL5o+Q1lwUn8U75ukpfX zZco!oA8qn^kXN_k2D3XEk^Hn)HVCTmTtJo_gU>thKASEIAb_!V*DcF=lo z%?t`=@G%da*N6B>p>n;~;c|2#%|@5q_Ad;ckbQ;kd*8JGki#KWGSuxnqLmajgs>jrVQ zz$?D}$CTx#dwD55y$`P$_&FsiPQXRgTm|j7&%U*O4JNPaWTuKzpehRwsUi`-8YIe+ zo*^f_dc^o$nK=`TtdLz+Q`T2rB_hE%^{(1E$NxHe9^Jb(a(;c6Mi#z%$JCuUZqe`ewWVf7FVVBEqirXoj#@0mTV9;%jvd0OQU z)$sYk`zpIqXWlNg_%h0l12<-o>(b^DK$TZBH-T@v^e;f;;nMf{>VzK_T28wdcSO>M z5ph94{aD#jisImkBw@2jZf^ydE>h(8X6L9^B6GJX?3g1Eew6i0{X0q zi!HD9O(JF&>tCi=l;vd*y$6G%BDtAcQ;Wp}K_2%n&`t(b?C*@TUNcT5B_5LgwO7G+WjF!K>p&IR%%dP zNLFsz>GMUVe;By3r7g-uSq&7)uAF*Uvd*Wr*mAcQbX*=pp8OIO8fy}ScVcMt4D62b zW63%(3Z0k0Xk@6cG)gsNVLWe{)?5fJ=2P) zPO>tZ7dH{f7>DN@0-?r*QNtTkxaE+;`~k_dpu>i5f-FIo|AjNVYb%zw!-&?;{&f$^ zs~KgwHXC+^4_;Z%K2qh2p!A7wj6bE3t9#*1wBc+Ny>gc5T2wwW$VHOEYmRWR6w?qo zN?4>6M0qSql&7?Pj}Ht&`1iSa#}NPCh7V2Zvf?0u5I;wItnzv%>tv}`NzYSNc~|yS zREy(ie8vbO5pWO85T?#@!}CqoQ-sFn@+(4D!2ZvIMW}fpBo)px)G_H&Hu~b-R0Q*` zrWzxOj*8G;K-o{!fbnAWNi<&M!dB5Ibi0jnQ~m(wG6^%5c5uvU2Fz?CP?EB+ou0NV zL8Z3CQ=AcFk?5dt-~p3_7MH?^D-qJl*4xyrFDgt*yvP47r3X2DY7s8OnKHO61uT7* zjC%>-T(qi`Ov>S9-7~hIoM+z>@L0_*&Me@`q0g}Bl!U0XNN+XaT{PD@IGaQ@c#u7BQl=YF z+Z+`?nJx(rb+CBFtD5gM{5r0ADj#V68W{`=!}A&H1qM1jiiv}yy$Ltb`0x*e<6DWx_QLIvmk zk#&-+OTpplA$PB)AqD*I$R`yYlJVm=q*0{RvnRE!NkfWwaZt(<%{YC)h9HX+K9}s= z(SB7^3*7R|zhsP`a|C)=gXFhb`{M(pud zgqWS`e6J}zxH`xsAI5Q?G|0^E8FqWvxZMN|xkFj(Ns1zJi^pwrc6Vp}7R(Hh(UvLQ z3?N0vXze<8#O*g7ZqF#=2Ia0h&qDp7IW{x~r${wA8~1zaUzQz=Z!e-Y4;8U4bAizv z!^qh$hJq8z#_tlmREi4@a7O{$MU$!4n}2f5*!mOFe`=ZfB)sVugtPV7=GX!lgCdQuy=3pcMm0D z($~f}i29<=CU}3^>YtX_V{F7BwOAZk+2h-xf7DmMlV;%?5EH!)$f1Pcq;8f(3k9B& z%&G7itQ_nI6t1Bar-cIf_poixVo}0+R3~!FXZlFmA9a;av>~B3%0*b^2R9X+6+qgR z9*TQjBA=&0(n~s5C#lBWrUWfu5Q_9BOLna|gYoOgcq>Hn;7;$8qEYY^G$IQzqz1`5}7&KqV*~uD2n{%_D1;7yde*41#f**wA;LV zk$SgVx-4!KiCD@9!{tB)ANIGRYe?7ei_o6K+#EM>7U9Wr%xR4lDRc74Q{%~5-4e zuKaU~2ZGq^_i3qX89n>lPDGJO&k&<{V&*q~lhcBg!mn(Sk*CB4l7o5JU`~~gNa09Eh+OPd)7r)C; z-zl+G-$on`gng7QP#;slZtVa}1a(={iI$2nze}|@gkl%qHjLXUpS`Lj_PYd!qBckl zeGPSZ>mc~*?uJX#i+lZ3K{AJckXNp~!^z95>&s6#cSr@d(a}Rol?X-7=a#`E2XFo%$wzyKyeW1|@lj z&0z0YuxkDahwMD6On5?dsLDl^&r-;7sXqDh!XFgH=DAH%x1~sOvH!htz zSG(%@0&nDRlb2IIs`*qIK5f4cm;TPTQOkR`S}4nO2cypwSpp=G`P{@=Nd#l_>(`c6 zBfH zMO`L0Ic$lYOyv+wb)OssC!SeF1l}c4#H>AN_q*LrEgjLn6&btOs~Q|10Bw-;TUj?wyFmJ z2J`fv;cvpem2KIm_F#Y1B7`H^I9?^GJfC>E93AxHi7 zE>t<0XOzAx%Fm=lOd2`YR_LqJe}c@ELRv;dbE?v=oO}m)@c&~PTHmo0l>L{%)~Y38yG;H;{60lVJaqN-aNoQ_Lh(*h zL*3(sw^ZCnf2OH-K6ST>6pn6;Ihw{>W^bV`3Go70oPHbRV#Hnl$N-Hvh5M7cKSTp)s z4a3PI#kby#nm43EB9I|Qf}?&hg{}K$v+xs9{7BS&>cWIv;yB_R;T5#<{$2o3`p1Is zHN=PLF~U-ke*!kHXh5w?cbfH_(ng#z|4M7i=o~eZwtUDAhXSs{l4 z-J*2ychqz<6x_TJPo8yhbYFmhNcgJUgy)c!=Ebb|gt}j9TG|3M)$fumRC>Iyt@kmR zUWt=oXS2h`CzgoRomU%0<|NDa-UG6~JGr+|GZ-Ppu~Shpa7pjkSNTQhJOmA;|Hp&qQjI)#c-I94>TmUWUZu$E5}P-FAR-Cm}F!y5IVj&RTj?Q zVhT5@?JWL0wOwL*YN~1BfmXRKaaWhlsq%@(BBTtEcc#T!f9|^8|0ZZ}NBKL&DCmD& zb?m_#dH$R_^9R*MRlps<&g-oBRfUuhA~{=KVIS7}j7Sj4kra$YxAsMsHk^iOPBLH! zW(5=+*=mXaH=E?an_t{Q&;^f76Vz_xV?Gmu4di+jL>l*8@9}i7_@+a%W!oGrS#LdH zh{U}^2*hv^JgXP>Tuu%|(P?9$EgK9mbn*0Tv`G5riRZz*PTnhwIkn}Zh|%^<;kKHc z7EJhFW?L1yle+c=Rz8_b@%Sj>SKp3W@HMr>-r}0P(3x@WpDiWb76H2I%xaX~P0oai zIpP^Mb|t;=PNb-LbS{n%71r{Cyeq)Z{)GTI4ZQ_6A*nSFOda-z&ORn@@G*I_E=uiHPX zo4`1zlmoYy8w4U}*s@l(-$$5y<^u4#hX*ItuVVzHW?-HG*%%w(2MKu$AwX*kg~SSw z8ZRo+-1v8|$Q+a=7x(%jGizr@2MhK(7t1<#2JAcwkgl*i1`v8a>0JMRgyA5YkzkvXy5iPgMgD|m(w4G} z+Hzvy=T^p%_uYL_h#>RFbvCy%e+9H?b$B&&X8i-O$5xiEIH6T6yv<#8<|r-lV}=AN z>`6idS)B7x1Cm2SLjmcaKwn@$9hsU;zX-J_c8Fgx;~zR-BYm5TJ2M1^FA^YU@GPJ` z-^3m~IPE~d@(43R_Ot%9Ke)to4Ir|@6!JhO`P^d|`wCB-%yU=vUv6&*M4SN(lbcud zAew%^KaZuq9QvhhEh{(vQ@=b0=J>I%JO{>4{;WUo^0HGi@O$H9Gr)$Xho=8^P~8Ew zaccqX{Njs`Lp>>=)A{R~*-T#nb@^j{u9W;zuN~(-mc3hWS_1##%k|+?^rl(LJzLh{&T3VVv={L5GvQ;~F2&1k4jf{c&=w$!OQ~$L#w)pTKT;pm7l0ZO^ zxPhXx4;~sBhrToQ)e%?8-!x!_Gc<2#cJ^`x?wWsu$XMql`VvrLkOyi!v!CCM!0n^^ zAsm{9F--diUIU(D@t*^feEB2I0_2|&4}h2|zlH77vVMiT?8nX!4}h6)e}(PeWAI~S zs{-sX>oXS#xj+4n{1q1c(Yk=llYfb3S`8`OR_t@W2%#ZI?IUBS^Fn%crffbK-_lUt zC_z?nKWgE0d!O^NcSj!LVQ~Z2uModth5Sjr!rW#Mep&o!cfJhns>!1L`&(avf53OC zzIc~$1p$Hy&(&_5|1EA@{W$nG`hJdm$$YCveG@(dYQHzd?LQ52j{mC%``Gn8_P7lG z-n85JK1UnHh4;3$81*0aPxkr1^dWs=+^Di2`oVJUp~l~>X%xI@h4X*t)`Ojr$3W=w z&l%Ebm#=aAb@Bk?_j>oH@?2ayf0D}MMPpuw{qnn3y z=%PXE_GaNX;?LzGI9La;98wzQmF!zE-DMEZjkOrGF7|5=^o;V&-_m&&F9u#09>Kys zibZt`a2uYjD2n)(Zk^4<;&x;$V$YYa^$j50jkNNupUKN}ldg#;ecpiuw3oS~)4amx zV6nT97%P%b{n@-Owy$a;o&HWU>PG?Y$9yVu!>vw)KkdtiY1MJzbXU~38qVXy0;$tX z5|xtY@0hbnC%6`~he`ch%qacy1$mtXGuvA;g{Sg8Nn<06q#lHljhLPnHub}NQ{Gh? z<@MYzdrEufdnm#?`SA)Wo>BP4V+V9zX=t`QF=aC*?(#O9WcAvFa~@aJn+`A7gC_;yl$&?mmN6ihKG{gx0OSPMyk$(VMzHa*3%9}qB6?_nb2YH1&{uF(A-0&1hbIQ{z@`59+iPSdB zSpU}&MtB#3D2~Yv zB<2G{LAjF#*L)Lym(A6ko`+2aw+zaiUOhR3w2a!EFqYaZkBPloqiiIo14aa-OUFK~7Wr*OmKYyC zur+b&)Cs|lwgY^;AaUV?yf}J^k{I)rtTh6v+eF%lYS354s51K<0pm*`xmieS!96kK z#LuNg1f@>3&(O4G{|!tz3BjGgP0g3~_>_(!wki?ikL(?9=qK%mQ8OK^7p08_Wl)gL z8&h{-S&w_<3udwDtzz=Z_Gb%Y5XdtzayZ%ZpnfZJ+SYCAnnR&_4@T$okGnugmmwL0E(T z@OK&9VQ+lX;iNx8ObVQLiIZ!5*Bqk+TV<3KRfCZ-1n`79(l$25L6UlINS&xH#oBcx z7z13Uv&FzsG&U5_W9qUEN;E*P#C#`jH8YkzWSYL5hS>nzVF&#*sOEJWK<*?rCdrqk zg^bk>w5Ew%Tju&vVayb*{qB`h*$cQ@KQO4KV4=BW9kfTsmed2ejCrkT-7KglACZGg zg1uR?sZ%To_^tg++85mEAM^t=MW@Xu&&v%ZQHhO+qP}nRi|v*)+yVzZQFe3zKFh)?m_2ZNA5k|gZwkTwZ10d z+te$jf@54IavaWBvX;JBGQpuVEQ2|e&2;`OY;p1B2}i@;qq}X|56diM2+3@8YlFZ{ zOH!wT4@VxeIFYT5J^-^V?~=%SdKPCRLuT>Hi6|C3ZgchHYW%5zTrc7kqCsz=I>?TezH$PIm?#M1 zMBYyalq~^J)nZCrrAjG_7>b$*N4-HevA7JuF*9&&>$4Q~S)Y z;C(idDAEx`dG+^gpkx=KZOPas!=6YkT36-^T}}4g;XvF5#d7D`+f#_QuI?Y;kB@^)3Ayp8tbflvE4X?PqBZq1=u3yjM zbk)=sC|!BVSJq)_E>;qytEu$2SUIqfZO>(H~SY#))$$#GqtrYk2n#uIS_~Zkj+kwshzZXG~CLFJo4l&s2n~c zk6@0AOTT%OzG$Mz?atZ!!ziM!iyVbg>L&rhS_jy@)|U!$tYQS|DtV#~r}Q0xB5uya zk6y~%lUU_si8_rP7TwXrB+sF_f2htaM<)lQB6;96YogfDYM< zQ3r6qim6SbFi^4#+spq(-L;a>S3_S&3NaxD=?SBt#5t&sZO8QOjiM|&?XkRIY+7bY znqp_Uc5Jn5^8Y7ePu{ij-Xr%6NSAUt{Dd}?0Wi?kq_8Wm&b4?LA~myFWd%RQ|hof>RtY?}D>C$*k)$s*wD&vffHR~Tvt z29|#nB|0joKonh{zRe98JBY}B zJ`;~JDW?6+cJpKPEjka14;&8@BUwe@iY}gsM;;twCIiE>1wBJUI)hdqsi@1IK5iEM z6aqLvJoG8p#D|h{-E6!@Av{m{0wpYXqFPD?FYZfj*W_ihXwbc36k4J~9_W~*uP55A zbV9vpx!tw%$dS16-*K~=8X?oVCj1_QI!ni8a4mnN@nRB{S~HZ$Mr>ay)3=JcjX}^C zeYWUs5Pb~cGEwAItGh_;j36?}&wSPABq6AnAH=VW(ca9VGWaG?Q|615qwCZL-|^US zeqQjO7cz+p9t>gy>;w5MMWu<3MWY|Bc@zwqDrb1#u+a}|2~qHvS*XbKN)C_9Ad?~! zr{Z@9MFX>`PM|izfTCxC)g*}L>#bedM{~$KPHi$d|5atE?*H47^VfT}NWU~12(cQ<{P2QQl=^B#CNuAJMfIx3~o(Ho|y1cgJTCx=q)Z}@)k zWPys;qn<#!TeDd{%f-8vXziIu# zA;tud(gu$Cj%rW+Q3~HoIuYqmO1Q--#^t*&1boZA|wX?zxhRFQm1Vx(`Q!pXU4( zx_J(gi5b#RP!iJeaQ75Llw_~)$GM>x0&B+4=wbI*^q#uu&wVqMWQA!(#72z=_)6mg zcO$k*-Omdy9x~fS4uj9%BvxrEXKCPJg+S}8G*IL3AxbN-fkk0wDl4_lBzPmfZ6Kp_ zJn0yHTta3bZlUe7XueiK*QZDS`=b8=Zqi%C>~Z@?UWhKHSfn0*@n96<(d8s5$bRwG z*fTdd<)67MRKXZR0Ey1MXXpt|El#U*&yC_li=2Q6oj8+%$EM#JKPL@}t;!j}bZ{yV z+qH9CzI|}CH3RW3kXZ-Q_clb69jGt~L7knkPhN2tQzPb)q?w$RAyVTA@I}M6;;ALG zU+FR2AE|XhDuvm7ko@TI#akNNIwU><=0#_r#hFJhJS0EwZJyw5&^>Ghn5Wn^8|Cep zOo0^s;^JIB%J_?Kr;4P~$ zA{j3T7=`r0U~dL!TBA{iN~z+nF|74r0UaB5=QBq#JN)-``!jR;2WpVi!H%H3HU9ca z*lBgHJp*I8ADkco-UG08NgFzHezb|wO%a!7^0ZgR=7Ie_v0uWTZLaAFfTU`#cf&AA zPu@YCUPROIgYju+LSqbcchPf$)C`7xY8l!e8a-7+ByyY0WcEA1C3wbff|D(w!%Q|N z3DESk#1diNtV^XoX7>X;2=3U8mvlgsBJbmo6cNRu-$OE;%vE@6y8aL*o8|9Y;93r2 zr@3Kp1tc_m4$@mLsZ$(5ISRY&%x7xJ6s$gPNIN@nPVmN`aktdqExJG{M3#7Bl|wV?_30 zx9!Pym%QAFK1MG2l~v6(-G4=BCn2v6XRTkebcvg01N}%f3$F$e|1!!@-8u~`^syJb zekm8ok}Y?m&`Y0bFGo^f;go`=2@f7tLf9PUV*5E@#gd~l+1N7A=3sN&IYS*j#?s~# zK~b7h(ny^L7ywhV-8LRfD+^zN@(P>r7seJhO-af_%=_3ntXyT&KHN>HVB4?F$0zJo zuoZ36z#Lo*2H~>5E4COB#AlWaaPAMBX^H+NkLy6eesM?{z{*#=1BFDP>e5Capf*Fx z4o~||k~oG2p&4^l&+G~u1WF*o;EC(=nJWVhEQ@v|G`pv0a|TjA${qRSKz^n4!PlmR z7K2sfW2Kg;Xk_cVoARTh*_|VvcnsxYrk;YO{DO(*BL>{3j_s=mSTq8v6B=>4eJgE= zVNu-aFm~(R%OFN*G5h-DK$)qzHCJ1=H!X3Qk7nI2!FO5A0x!fpmzlB`N%gU*p3;#T z@?04WV+<0CPw-s6auqRxodX&TCx{My5ZHQ|KDLn^2b{p4xNN`V+k7QpH_nRs%2%Dg z^=(1Wn{R<^MJMBTqn0r>3~<^;Z+$H9owCsjPI|woCLsGGrrkLVZnt;jUGb1Zha&U}uk;mD z{7VUqCT=Cqs%cb=FFO&yirl^nn@t#As=3qM>MLuPLX=;_Wew#2)ez0 z^AE|6ERi8TdDf+yUV(HS3uA>}@|;i-zmN7))p&%~n`mB~FeBDzEBr^g9#!h~K9H-K zL^-`5N433>|K2G-?lRgEfGj%4%bZ3FxqRQk2BK41Z#g^T1CTMhNTV03v*}`Kpu&Vg zap|TbsB&AE0g8(l?-@eVLd({dY&>7w`P{kjAq;TKZWM~K!ZaNwSb)p#7|jD*Aoy3vGA~Cojmt`spZ@|_U7&y{5_%h=O#sK zTzXxX*^w$<7A9;FL~CV&)O-8OF@86g^XIfL-S-lgeoCol(Lsc@IQ+K2{MXXiY4#>N}0HE`S#KzEiQ<_mc?Mk^1oc#;Euvqhwi>E#jgW=JM^n0py2` zwdP=GzZgPacD9sUcoQ~gmo#L?|HaqJ#tg{93{z2B_;*eHX3ZcKQ(1aaf9x=Lw1=}uodL`uNO@1RBWJj7D6en!@4P~MhhQmS@pIW%*{j(Hq1kA){AZ76{FOylGOLPR* z5g4)f2t`Z5$w&33N08G}nLSZ;E6&He?**}!2sFj?P`lRv9h|nRisj8IFkv!n>k)B3 zlMrDX=*7H+9ph}V4Q({uXaXqM@|LOxQmt$I9ks%_ahbvUB^VM zVyCa%jEn@Tc7U)RU#{?g+RWls z^8+W@vX?{)m%RhH6YjiOC@C91cN*6L{Zc)jjfas zY+|CX10W5~(e4su{I~O!0`aO^1OoQ7Ge6f7?4`xTAFWbq11MX_WmL-@rX90$%STS~Jan-V-oDG_{75aGn+~euh(iQq$9)oNP zFQ3!dFy02^s}Y{>Z=@7k^b z8K0hD((CES4JM{4{mYT>?l$}4b?-EF1`AS9cXgkiEhqV$#8MuEB4o{Dlx<{86W!`4IJV+E2)}E*#cGwIQc3@%u%ttCH2dEwk!=JTso?9|6M`Z9DaiC;als-?sdiKh?US2ftKyZQ2? zUwQrW82u_%K3a+?@P$Po@}>nGpiYk=Z6`vnP>-5X!bo=^Uktk;(z8c7YUp!5*P18T z^ucBEU?;k}h&CFnC^W(p(9+lRQk|1NEgrqK?X=Q2m{qh0)N{Yjfg&s8Pr^N{5b8V* zsWM@ClyPTJg4Qr@or|`VItmFz32YIlxFX&qk~ewi_i)oyXXC`=5DvYRmegu&H#>XV zbR9r9#pCGv?0_B>mx{L7InF=gMxb{#x=^_xJO#LpOZKFo6Cx08EW$9vSs=t+PdJKb z(z%i=XQjdzL6Nu`UR`U8ER-FE>;e~dzyP9}^#}R@+$*7glal{^I}?->)6rY$v10!s zNG*jG8e=JRv}2~P7Z=2M^g7lPmi@GE4YH}n{-AO{;d}^UX2LDml`P;2GkACdlpx zjp&C}bPsu$g$0WwQ?E1QrjYj&m@8u{d0Ee{Iy>*pljXV?V@Vwh4YCDyw0KCtnRZ<+ z&H@6g7+TC`gxl(;UbD^qUYN4m3SX6N4GkJYPt!^IVgf32h>x}1T=OkCRll@R#Bo@| zsrQYrc?vPZup*}?(`-R}R@Rt-6mz&Nam@7YIHhfQi^RepiRp$EIx4&@)=^O_+lTB{ zKCiwGUqSUf!(}E{&a}D$=p>FB*LGjXn28UEw9((0K^bPSy6!8tDehPbhPc9i9-^_0 z-t9|QKo!z$LGL!fpuAX`vV97ZsA$F<-1$!uVRG?l{2d`+>+88-?eXh^+J1>TR2EQF zBvaJ_cVM-gF$fDT z3d|$^f?*AI+IY|4?E6hka=UkVv#4+kZ`9_%J*?!4?U@hE>5`>L=FWR)KcS3ql?xhy zwj`bf?!yoQ*OoixXG%TU#5cu&J&XRh&UxsQsIlmh`^(2i?Y*3sU}$&w-_h7u)9F6?Ye( zhC`Gx9}uifaW8jG=~q75Y2a%b*jqTgj6?^?j?D8?ajylV#v4Skn%*M@Z!rvH&~YcN zbrdOLQ11_hUajTXT5G%P1?S+0L0N88C~1{tuc#EK&{-~$I5m+Kn_;OwM z@>2J#bV^34$YKQX)A+5hC>t zrGEcnQKpL-C@pn{X#@;%l9zK)IeypFL}tEzMkOb{!Hk)JKdgbx9AAq$Ll3dFFG`?E z%kjN`NO66*l!s}%FiHnl6EI=0d*#&J&@UG{-op)UAGHFdIg?1Bf$6|RxF%MyVDs!z zfAsi+tR^89C7jUyWY=(=*^<{Ao-I>)38c_Wgp$lLT*-5qn4;ZILu47Bs4Fe2VC9ht zO~E<5>>%UHe9M$BZZB{{m9Sis>l<%v3yp(cxV!GiecoI9aZ9FV#!nEhqLH9)7W7cV z#N35MWYZ6Pl8h-;CalyVleu#52gyNBr-+yjklQOD{`pf+Ouc%%w5ON7=qwa*KiH&Z zhoBxap+ZS@uK+{o!AGs)KuvNrsDykoY{o5ifh5mKfZ84-c}-n}0jwv(9>xuDH5mQGIAm)1nZZzzVk&|HuV)^%4%hi5tKv9fs7)MX z`-q1i=FT#gJSLKJxc0yreo}R?TKQZk7(g10R}~GjS`o!puBaZAINf>`&-4i96Xy$; zdqws8QLX5w5VBVC5J@3pt8*WsYorzzOeRv;|br8R|_%WYK7U|{xmE^R7|gp49ShwAdIY^H1!zpQi7lCGz`f`0b7AF6{0Dx_NgQY zGOrcvz-x;)DP6?0pBOR$yG;{?)f;t+V`qxEyo-~Q)jcSZM5kUsnpa2k69Os5WsFuM z$2>ypyR$sv{x%&_VD^6^J%C z6h9qjbu***$5>* zOWGm4*_4Td*;U6df_&7(KkEb{^dW>toqB3u0i64F#pj1!U!euVc9RVxIy`~kt`fa@ zoS8A0AL@ZEsla|frg0!x7_KMTep+ieJqYEE|GFC2KS~4kfTUqub5tND`efU`-Qr0^ z_mX=?9`%;?JhSVN_Nh%s$)>q1J`>OM+W30$EML3bk}Tj({93&%VBTMFs?U84?CNX_B!}3I zlLl^2YWd7gwCbEIk$09l@ylE~tn^u;>K`_&cC7h`Ya9PA;Lbwi z=~9!d)3kF@x32I+YF}Q}vEHz_!BIY$9>zh}=fR9&ajv+koxsKkEe?ZIr$N0;lg}E?6VTYZjGbYqI~2mJk-1dA3>@rD$n{#=7eV zZxVuO*L@nerV=)3w(burL-|=phsh(SxS(S4<=y`j?DE8P6-xV+hJRKwvnZ&H_y7b0 z&XH9W?WE0ZImQLn-Zws>s?+9AuPkH-Tdu%>@rU5=6o^haPVjr0NYSe2-tBl{wqko< ziDmNyJ<)sBq8k=@>ax3rEjnTxvqR(uE(@!av73|`-7wQK6vX~icUE~*K$11m8-6z^ zNe~wr-_LV>p<|#UsLf9C{HiMHZ7t6UraG67*Vi2CSPjGj-E?$IU2R|RQbL4>4aJI#5VBnL`P#WkR;3@;i#cY z6x?06gro?UBoZROhCf>@H>>|`C*u%gw3sL<9U*($jF}PWnDA&dM~9u>>o;!IwxD^J z-$vUV*htqc&-u8RGa3qg!_P|UaV|)NO0%+97Iz49!QA^)mm)Gx5BdT__6>#x zvMPV=%kqsMLSVw2ZHB^&nizMY=V*=skP!lVY7!)>+#mw(iPoq?zbVVWGQ;&)>{Nsb z8FP{rL~E{6zLYwrLl%FGx>?CTy*u1H*tRp+DED`cRug?ScOFPP#L3XwODcEGU61=c zh z!s$w_mPS8H0kT%!=l;@VaTBKswH?XNUB{3(-ddr|Q`a~WH_L-u)9Z;*(amaiS6l3J$4 z?QC=@HIxs}BQ`}c2MPq1cl5~Z!nPeBoaz2oV}NRjzI)U2QEF{9S6&XZoRQ2sB53rsxH~TDAL=NAzL>HjH-t* zf%^y8m=}lCXHK#0aTWbVAacgq1vZ7Z3RXr|e}L#ooTK?6I6LK1ut`}BkqA!`@QT?f zH>s2I6p&a|2jQ7W5kl?3Bgh;^1og!7NX6gohYKkX`pPU9ig)@>8I)#gQtnWlI>|+;QFRsY;gyn>XY<-z zapE4sTw{tN!VAtdq(oRL-4Mvv=DRf1sXKFAUr9aq`~`1`EyB0ztiXbz!=*XpCg0%N zb5+UQwS*|e)B_y7H5>VQomr3M60e74mbFuR0vNZos7+pNUwD=FG%{7emVJWd;N~qO zoQURv6C0I;ku+EP*$WgL!!vCiAewxJThl_Ls}uG$TRg3kLu(Xo#(hBz;V;U4x-2}B zBqylz5A%K*%`M+3|90L+3QXAqpj*hcyZAKegD;v4(~V){%$t}5T%j`CBWr03``^i= zSf#AVZrq+PA~tx*Hfdo&qb^&zOqLH%^llV*bK_YCJi_^Vok_m(+z~=7R(~_K-1yT` zVrR#ljF)+qX#h$#O8=A;gA283c7k;sBcW$ECwqu#7U-DL^2R~@aATlKzUh4>FLY9e z0yCxub#by%axKkcJGaLriO9E7m+yu9Ht(YlY$mg|I#;fNpC-WG=L`gnfpOZ7k}L*D zvS-^qtI=Xl%R@WcC2p_C+xy3-VKlb(${3pI?>!HrFYm7d}5 zBB;?Y@PZ-7hAy+B)z#>n)dMiEkLk@_5Wd)9?G4}fEPk!c&CeJ+B)$Bo9||}7iZHvv zKW_eaQL!}&=TcmwV8e3pUlNIHgL|)R>CYcwF`^Spy8H130X-P@ylNgUR9Fx3_TUGF~rn^j*`?-UHt?wHi5$ukc zke0#Ahn#3|twd7!AVG~qz6Lh@yc*A_k8A&#&;mwFgZNIIeJWMw1h+!{7C zJeQvv@Dr&4P0>8L5de5-3Ueb>mgixP~;D z->H8x5@a$KRz}ue^8$`+M^3z9Mn02`*G`-CF|(l8`$9TKW;>`c5}-96(!t^vqtUov zeNqGB`Qujm0Ozgl!gQY=vs}K!;F4P@zkA9$s{Q6*5#=%e?d=wm?~8O$%_hIvaz~>x zxeFq(>Wpt)!JLN$VMKev*fA3SqFufGhOkRvYv? zwj7e+HF+U{BP(MLx2^XVxpFGa2hEU!ixHn*P;RhjXSiRRXbVTo<}>&n7OYbinH@^u(U7IWHsb;CRC93*_kt=1Yho)hCcQwIW7WN;VpLsEM# z&l(trk%f|z3TFoydX;N5-VeY3e(P^dTG<=}Oa^rQkzSOJv$kfO!zGRRUQ)SA0X1UE zi<@VEJ7_krD0%G~1dFFbsb<`%GGGcSbH2PSiSyn{}*~c!Rnrm+k!85BS}9T;+Or-I>wG55BWs)Pq&L z;)%4w>*dh1_K%!x8Rm0@rJXRX4qnBw0&7dxDfKfbP3t6ce*ryqw+HUk<=1|*ekrAP z<*uisED=WjHILg^vN0-);)K@B7kTY#<4PZPkEyjAfq3UeQsXS0 zh6NdTVd^;5RCl;{n53`qb6wxMLAB#J%(dXo`53?^ny^9P{bPa}Eyk*Ul@|u-X}8pr z(Oz$GP@$MPepD*Z`1pAHBmR)>o2!ek_1d3^rO@+<`Y!~?3Z@$(T^oftmCtoy_90br zjB9t&ytifPxb*JIXNA94h9oHQNdy#5_Lxi>)-7WjjPS=Z^BSZGy}bHy!l_WbyXsqA zg$Wjt*hgxG2!Q9L$U!hXtf19(0j6HBh<>9Ba^Mk(x{|@Rp)g?(x=Fi41=@~n*$BWZ z0h%xpG378$P*ZtRF2@qWB>Y0Mukvct?$L4{YCj({t=)tT0{bz65`@3cu>j$-Wb6WC z3g{+F9Bu(S+q^L$z93@ef5*6P~3;hBt ze!!3`I^fsJdaM>*3(ty03PX0iYK(LLngL9o#ThA}y>yEc&3jRKDr{s{!zW{oUQ*GD_zD8WP#>D;jx!z^WW1p)-fX)_^VZapFk->yqx zax0j<_WsDbR@}9%ZU8mYXBK`|ssnDie0DFSXf;n^n-XH5+BlV}_@t(fv(|4H;%plU z!gGA4lPl|^*}=8fInnmF`+gHhdk#*?!PEj5Ax|FYOpTPdWhYF1tdNKS-bF~M0U5{M6-UHRe_7eBck1cQ>V0tBH(W=bN-IHUb6*1tR^SY6D{iSuA9 zPuJ!jy1Sa7T;EhH%gRMdMWf~~ODfJ?d!c!^jp{)S z%Gw-b3Zqxb#;yhOw1*Wz!jHw$p6@?hXyAHAoVO6tz&zFg>F9t+YxStA8Q%TZkR$=&U>d)= z=4(j2oop|hbj;e?gqH7gb}I^B+#WTHM9e(7*{)xWB+oXn}9#bRWt0 z>!}T9Cq(6bKREY2kHyF{4{JofU*t66PqhTS>NS@&nFiC|j~2*!NA^oU51VyGhCvEE z?zqCyW##8E(yqWpzK=y8uQ0(NHA^jT)gRpgcQ-W%Svzb!Jk%oy<`kyu%2r(`MmZ|= zR7~;zU6?J~&2nshdQMHw-2{ZA5oTI$X5c=1&p2^@80B>w>+)UKaCi!BsrlO6{=0G5 zP8Czx#br(B&!Q(Iner?bk)V~G{AeOcn`6r_Hgv;YC$)nh`Z#O&+t{5M=I0goDL9FQXT_S)q(fedOJBFNYQ zhVYD){HmGARiA^NkNjbj9H6rxA-%Q`W0My>clZWOJV9Lq15Zz3FU$0;G;XVVl)Sp+ zLw5}vDpMr;DI;C4!|&Po9)U&jP4cm4aYr%GVwnEkVMcU_kX6srDAavoSfeW=M{%=i zuT5AX)|6Ml$YXo?MQ%~T;mAcuVO!?3`QE_q(RwRMBbFlaPk+1Fn@P_uGNHNR%}b$- zFYTv7X79*lEZoDswMSz2(F?d@3+}<39;lJBM=>v)qMfKDAf6ZHIFPluu)mFE-@U2k zZSIaA1bd=ejkFso+g>WSV)oJ@fs-GhEgj$_Wn+`}hh#_U6XF0D#QY>6z42f221&7% zVP+JkA`$3x(k*<6xe02<5^QW@cGOqWK}|28Ja{;}XXW*ev za7?8FV9zrqjQg{m1mQ*%Dm0-p!%Qo5hmBh<#c%Y7Y+;89Oupz#1*`8((te$Vm8-1| z$Z(Vg8kXB8iD|8v8e|33REIFti`AuPK1g+iD=VBd!?$gx3IXGR6i4HL01#O6W-5AaoYFvN0Pr|TjLP`~HAnv5a zFr0T`^`wG9Fyt&n?1o{0;fCzPkj^h|(q9?AcKFlj|AZ8hiNPNy*7A~$tC>&b(nr?gW#74IuP_>&*p5@&UZQ5HYL zBIfj%No*TThHa)-bzWFhh;by=^x3J^wDE89%YReT&tJjx+mmE zf*C)4W6rGO9fY*#>eU|TeB|_+TW20Ll|$l7-8C*#1&^B$kQV%%D~rY}eoyAw7gvz$ z7%{of3^>@pA|ClQ-;C=qN)a&ZivwTt7;qzzwXjL2CeB92ZX8KfWP9U~t3pTmwOohuDm9a;KOgQ|RMR z+k((!c;~j23i<`Hw6&+w+nNn{NzPQCA%`p?^LXQ?XgnY2YmXPP7)z07MldWd??aR` zSlf!UNr^Dor_UR}TqK${MreXeQ8?G=g#G+H{!i2H1y5G#`df&R+i{#EA;h4ZC5 zxWOpRF^+O{(J1QUmCAuRu-f=|Fl%vi)_Pw9sK}E|@AolSr93u+&%5R&GaMlUli637 zr*QFIvi)$k=F@)*K*;XK{(Ea70A28W2zui8XK5l<3{g;cLvi@h))LJJzIyTt6oC;t z*JU-ci@$IzPcW|`;&qlQ`vO0oU$G8UP&)F;hoDY3uPEx9zYpL8|Nn-cnHm2d@G~PD z+ka_iCIU`2hX1}X6EOTADw=?ifsLJ=;6LmCgMI${k9}UpqK)Ykjt3}c_=h>)*!7dP zvCK)Z-`w1U0Q5utBcQh-Z)yqKtUXN3Zl<{l(VoJdu{5S1es z6_9}3ObiT7PCz3l%j+Eg(=*mFGBPw3%PW=zVpsZlrzn=N1iZl!K&C$H02saV6Aq(g zx5n;Cx~8T8)XdCse?f$Lre;y(J7k|FHbC~~4fJ0~i+z6J5=>q^I7KhHCmKH}Qwho{g0s(Px`K&`? z`9h10ZS9hgp`-hcIRY*Q!P{9-%PRnSY#t~d$OT}78(0>w7ZModk4=C-ld(tvSh;2Z z&QEid&=iht%vE3jdNAu42!xx*xC2lY&@~|aG+-suLjZiMz+GPdgFo0D@XrP|05tLB z?(xsWk1hnr5Apig5QvenHHaH<;548afi=Nia4}C&Q57+7AB4>Z_uSY9;6tMQkqt;A z83sfhPX@$^Fe>9YC%r`VC`1hTosB@8VY?dS!^U zjqAKS{+TpMNgX9+?eFirnBSMkC?Op{JQy1r05CN;GXQvQ@POzX@V)0<)#Mlf|C*rp zJQd7(Opw0EQzL!1bAD*IpUW@HpG;V-KL1svkgf6+givG`z;F;t665GR&~H)R_Cjb(rM3|0sjl^~7)zg;Q-Ff_B1 z-}`Qv)X3$@>HWLHF@BxCwEp+oR3roBi1S-WS8S;oK4323En?E9`G z%qFtVJnO{&%0GU32f=lTFbUZOQH2+NwJsC5CQ-4rKXMl8p-yr(y>L1W{ zK$(^QY;Au6Y3Q%}|Fb3h_rS6J1ziV}dHD^>1|S>t?@#NI`}g&a&QHLvD+HO`%M1PL z9KP|xz!m>n95+0K3utCO&6JSL8xU<3khUGQNQ5qi+XzT$xjPI0B9jNr+F!11V*;}I zRR4SZrd~8jtg8X7oy7chBs~)EhqrZ&V2p+2{H?FOcMF6vriR5BreEA%d!E}e30Hbb zCdlB-yV}#FoU*VyR2yQKP8!$L9Ax$|CAga!>9}NTSNr(|iMy-V2RqI(oD1W565(X8 z;#&QF7S~qC4;VtwAYx!jB;1(_>XWDCXB4@UH|7kREpL>%L5kKoJp5J7qFb{qb*Uu{ zT&{@n2tK650lobgnXYGq?OzgUhEv6K{J`Ztj;YK?lB`;Hj4&p8X}O}_!_8|$PO{ZV z3O|o-yq^_Rj4iG%@59T`0GA88bt1K3l!hwIV%p;k$~luF86ZiVAv2c1{tu7s8&B>- z7ZPs8_$YX$7g2meJMDkvqkg7&G2udkRricV6f4m?; z*oOwPmQoawR*dA((0-DXp;fTXq&3d$nsW>T0OwsL84%=A@Pi|HziduwO0tHJhB}AV z1wkxRV8<_8A)DeAD72pHGht<>7A*$b6qTPf`nbZ+Nk3e$jK1n=Cu1a4N~%p zxVz+a?fu{ghFW5xGa1^Omc*9hioz!=-pu*J~CLdEgP- zE>h$n%t_R3KZl|!?SqSM7w&S3kv5&Ha>keFjfA8DFFJKv_q>*>p5M_98S)hNZ{G6g z^nGXHX;NNI#5{{;+u>gS!3d2&Cc>FY{%V2`z#z)okqL-AkLetsnL zDLs;pTBJ(1UVu)j#OS{u?K&FCi^OoY#mA9LAs_hUA1Y#G7XRb9-Oz^rbWvSyBNVez zzk#egGUY@-BI{QB!G0`5&6r4M52v&qNyoUj5FskUs62bM;2u5FhAZ&HcVLbNbFW8u zbqxvB4j2T=f{a7(sb}9t@1**v$WsL7tI9QdwUqUl>ah(Gl==^kZ-0m2IQFDK7&8a6 zFP1I)A2F=NhoEG!=E5x$ein&@r=V>w?}Jlf*be zGUb?4`%e{0g~b`O@edbkhD4I`LlhS3m3J>zRrBYX{IGPjX-pO|MMt+h-6l342zM$H9;fRj)2**Q$M6RAZ4>U`D7d_S-pn08fm-+(redSPt4ULe)#$+_ zfAIM!Ph{QA6DaDS5@}0CpP+)+#00;{at8lXs=0+uUV_TI-rp@JA7nsu%oBI) zgf7lVlB#F5#z1|tgV(VUwT)&phb=|uIkr@SL@{yh7qo9#HGFJ)Si@P0r~qXGJ=xO? z34))p=3MvDn^^gTa(%Yb*xH-5ikNI1^&C(&WvlY^)qG&HTkG`0$p@>j$yt5+d7i?> z*$j$3@F@2Xi_OuN|E2~uL|AdVDIk$g_ABZH8r;B5qF$QQk?LY`(TN?RcQZWKYakDe z#nVpr%7w5)KJ50kR zqKdB8v>(~1H9_LlMtf5W4>~8_aIfifw7F8i3Q?rI$hL-8SH<1>arBE)+8e*(f$&cv zQmObeiZbF!T3#PjgxEPqK{zWc`ZdRo>%Mv#BNv-@EDY<1jl_lrYkz!Ko>7qr?Wx-x zx`rtit)vG)9T{!Z1322VcFP>vojj`xQ|XWizH%AYhQ^e+r+PDqKs*_$hei@>Kub&*-`ewxb@>o>H1Quo&hpIiEDS>VOTr zjz5Z7C@C<~zY+?C(22x<`4mRePtb`WXR%M(VHdbe z`v`LDa$_q3?~&j-+Axf?^QzM>;QDe_eiGw#CDN*7)8T!rGa}tXOeUjRR`awYMCWSD zUl5-o))W53ai7ofZ&*xf$PWn$h~`}6T30gWX|`;HqIeXz~Jv5 zQkdLO*fmHQ2+exH#EV}i{xone!HsWL=&->E@tO>0OtAX?kcL`SmjhM<1(Xf?>%^y$ zyL-CB$P!0~f(tF=t5^}j;bcsl7c@p|yT5C{`j>ft^$bPB_-@8qXNqRyru4wtXS3D{<(9nSEnW ziw5Y3i>q0IFo*5Y?cx?v8WF|tG(gn8+2OLGM9JNAYu3069uAbOh8zikdmO0Sjv`k9 zKaU@wTb~|#y%ZVvq!>%V41&wkH|$XJq+#uCr05Hi{O}m=HxNX<;#bQ%J9-68vBrA( ze;7N5AW@<%iC2TuJmP2bH z2kvwm1!=RgU?qwIk8@AHA^P8VP+Bz7rB64PfAAKvRy8_4h?NP^yC$2CRVQR|Ejk=s z69o#-0U`&JHO)oZBtWk$BLeZj$1)i-!Tz@o2OQqv7fDftV2+ucIkB+h5;l6X}#t@~IvRxT^3> zfS}92>n$=XfBF+j{TD@WW-gwZt}6vGtm6>GoV#0>g>#WufV!ndNV%G1(jrib zkuQA`vgi4@pckUkDh?IQ4!g)CuC~q>&Ta5dViDp@)&MIT#g|Pc3Ufl@;JuTyeHBqS z&+xs?h=eTxv`U!{qkYW|3P#v2Y&j}WHNhE6lLpAR;M`Su;bYAOAwXH0vwT}9RcaA` z)NjSWR^xyrhb#?kBKaa|TWxA;TdQ?wCH}HXM|m~Me<%Ui3ffu~3ZR@4^`J!e70xj= zXL^1uqjT=75X;8!0Z($IZnhRIdIjtw&6*I|7XqRxx2kzs>NiIaz%7QR) z#_X{2P%MV`+yVn!ZJOY7eL4%DJzPvifV;w_^eWwsf-!==4@8d~>b$!CK&0(Fu!@X@wewjb)wE{pJ~(j$IRqPgu=T zUm7Q)he9s_Y4W1Kbw=h$(YC17RCNx*Ll{yC%U8%hMubW2^XVOLc0b)a1QN@pk(giO z#}H)4S+)x?o=~}<5~LUBwgV)nG!_LwZxXCLLe*bTDpc}U0+{`A2_e5MMCgYC*hfIl zg9DkiwqYh&4xK)I+)Lc_qvjY_gyQEpd(b zOjWP&^&Sm`Do&<1R^=5I)@g~7UpODS-EpTD{YGIOiVI>oOpMp#&Oz-DXQQtBo94=U zB;FnQjslN_3H{*)M)k$aQmf4ILMAn$3QBBgcYpy6=<@3$D;deU*CJ6Qks)1Ag-)R~ zEx(zlPWEkuctjGYMVQNn7^3z5KKM|FI0N@MS|J9) z)AV}BG>Y_ZuuvCEg{P0g(0vVp-xV|JoQhCtPDR2*3(OCfsIjfP#kssUw`skM zG|jKTIs;mSxCr+1$0Jf(3s~$Q9=q*`Asm4S9W@e#0LHWpucQYtI}oI)S@=@1pZ0>? z4!$1SNZIAv-m5tQ7H!~eM4jl)&@5|*5b!PqFQql~UNj*SHiCc^wun3aTmh>oGv?=; z$Z-0G$WB;pYvcg*d1X1aw=bhhf23j4l(XsO1`(XDdn3utlnc3$CL1@*GBeTux#kFiZU<9Tr;!BdpkZ0h70x@@4y4bWBxUHWvL#-^4TL7+8Y2~*p~m1@Kq;x{ zNuZK0M&$nK#C`@wIJwS1F?U%$d?M%Qx)c}2 zHhq3{tr@B(Zm*vMpS(+%cUX+#ah+8vBP!C$%sz-3PTF11q!<4NBd5)oG$kwjL!`SLS3rx5RV7eUpSW+thnLCI z2M!jv(STZe%IUf4n(r8)o3gllwH2&(#x-nbW;spAZKBGznbsK;GeAS4Efkxp-=Iik%XyN# zB72u>CDaO()rH~ex4`a_D4<5#%lrw4nGh0!wj-MR?1warfX}uq; z=uZ$iCxY%_d&O=2uPg_y5t)35c&LsJQ6(wxCNcFRijz;v3niBG9W>K3y})YC6 zyY)DeNqD%{9VK3s}I*s@cMVq>dgK4gap^GQW^Ek#AYp> zp3n>R$}uZGt_P@E5oJD@hT-mgO)+S)J~Q)M$}~f)$-Uq165Lnn~AwwC6=n*zC_X;4S8=?M+w|W zxD$x}wCzo0^LBS&0m!B41B)-qjsXI{`2VXLyEtVCGF|bS0E3hc#>UQWXH)nfXDZB3 zT8iucqVxncJz5wLgKIdvE;Qs>y*9S7ztT(dC1E$&m5}Dr8JF(*o2%n3LW=$c{SWCg zr|!XEX~XnmucLw=3c&ND;5%qz9)AM-^@?GITXMRft<=ire0Scn2wj~-xmWRN~PWb@t)jO&LX~6JVRWHmTz$wv7|^}=qiP|n@s?UE7^z9 zs#wdCPEzl}-BO8P3c-?4%qcln8J4c(4Jbwv=D9xmJ+gnm+35q#k!8WuhiN?b@8)UD z+K7U&yHI!H>f7*)H!mLaOC(K|9%0&RV;#`1T3JoIar{vEyP+y1@XUX0#h9o62#KHbB298L;CKr|Btm?KdBh!vhNpr^gtmkd5B&jJ6lBjS?0%{`t zc^G6kGjb^>Ie9)W46)84LTTk8zpe|Yc!(T^c!raW*78c&1|$nV;(3ZTP(2i(Yjb6c zFz#gp6h;$NTow2NNulPWOT_0u4U>lgY4e7M{iIh3*`61;;($ZT$>mf~PGT=!1S9G5y%co?y;c$M9ByoEUM9J(vol6YALo{HSVnPDTJ)F(}R^hZNUn4MSf zXs;MNohphBNlAwecM0*E#(C&0PRHborO2|8+Qk|*itw#E$GLG)LYEP?85JIf22dbwZNvk^B=tY5 ze^*ri6I*iWZRUt@e7hkTpo{iVgR>`4m1JyZEh9yV{jx2{I;gHmf68&0_eGXx&!-SF zJ`fW}fmnAz+kA`XB8>#hdfzM|p&Q?5KqG3u5m3b&ZaGHuUo*H%GG*&HQ+$%YGo4bF z!oad1V_sLy%4lZ0@-?l_xZGvI9nlt2(Yc1rEWg%}6D@^N)-{i!HM%DBbsAKSG*bh$ zboCzVD28s?ORB-YT)aDBbi6Rb|6c6W{E@|5?_YI8if2vYpDIEy-&*l0!9XC_XqIt4G72$n#$pt zA^HrQBVkFgYd~mx8Jzx7`fVa5NT6U4)+t)wMYmg(`ROY6eRU!tr;|;@lGi!M zg3?s%PDPnq_b>JseQO3s0mCu`{@@y1_sw7OQk{si(mj?{2~B(`OX%Vtftcs)3Qm@Z zhxBg3OzZ>9r1`#2CyiF8*Y>ifk~QG1x}eZ%1n1ZCa3Wl<;lHfw!{@==z%LUXtSSAR zua&FJsq0pfMb2XlS_ADNBvI>IiT*-FL=kV`j$CQS>ggxm`N2lL@Nu8`|3 z+C{Xkf(7g5KU0wv&{G$n&(EmD!%jrxAv(`4RKpgew;aC0bXhtQ%jQADR#al>=&kmFxI8xZ*O%r;B2u}u`YQz?xLYbm+6J*g`wGfdaBQj z%(q~7Kb0mi61EyW`kMRB#8Wn%Jqr0IQ){R5IK^#eD8PK`Z!_W(>XYyTGpVa;f7)1h z1dNZb7akM0$FQ*sWOk}*=&^NEiMrcDwNxY2vFB-4rs(v`4=H=5VW zf4L!3HCo2YdZb3XIo17cWw|RNzFP1#(6X5<>I$T;dt6^YL>b$7m*rfM&AW5o%ald` z8KyNO9487VAgZ0n0&)Aw*-mFHO2u<7bhf6FbU@@aS8zcMg_>W#Q8=Y)x?I9NZm1$E zWr1S!3G{!mfS1EYx*nrlU~YN^o|Izq##vUe_n&Q%CK?o`Z4LB~o3xm6%w|{*HF{l+ zgpv6YuS2Dt#e0GaeuD4Udj|oWmf$i=jsmn31aYLi-}=?lHAUZ|_{hpGQA2 zAmiN~s)m*MsyaM7&f^4{2VE*TSb{WKcJDnkGt1LW$WNES3<@H%1}K_7zYUY!4EhQ5 z$J@=>u>M(PBD-vzmu?#J%su{nF-x1Uscnd38TdRw^wc)r+h7k==46gv5W##toetcz zdlC3z)yGMDif=zkyzis42ZtdKN>JC8O?vjvNY#PJInV}X8*+N(Pw>S>@*mmjRK8v9 z&C~|3xITt<8@W!{uRPF)5?tj z9_!Y*)&oXhOfoh&mL(fUh9Lw3oAof;8n(jBOJl?y0XDJoZW7QY<2^2sb-f*(Nb={? z?UVqrWu*?pC8z2r=twC?ET-qFA({RFpYHmBq>Q(c#UdplkOp^4rqV<&n?w}y8_v4D zb&OoO0Ht5BrChKE)H{MlqXP{^B_Rm%=A97T@o~(PDur1$CNEuWvB}pPA!W84tglV{ z!50Cd0+!XnTPE$Z8wx2Dqv4lJ4S|GLSv4oS7h(JaciO<_dvg3YTBIrO`G#xy67gnP zBF;rDC0)9Rr2X4(w*8JRv=*{#b-}`3>@b6^jk@ztjOYO6Iy_a6>Y_D25#DqgP4S&X zaqUS#qVZn9D=yd(>0}r;99$=1t!pKFUq=r3bf47U zgfbaZt-3dz-mfW|hOkpxHF`xfm^w*$lh*5H7S3roQbb(WVO@HWoGBOwlD`jD=m^p} z7lhu!p*T9<1R7mv4ne&91*O``E2YHTJ7SN*FriZGK2b9Ozfzl*nfPV~-xKWE&xO=H z_har7)_-!1K9BMxdb;jK9Mt4Nb+Gb9a<(6NNX=VXF|?#AvO7Y^R)Rmx1kQOa9&s@d{qGM1hTt})gYAuRF@7r&z2SiKZJ`BcRXo8Bp=Ieg zq1)(j95W>LDDJ6^nML{I4Gi}lBq4z@dM``DYQ?!5oLrk!RqhA>bJ-9V%_%pDHdU$*^^xm>#E?6$XJM zaNimHe^q9Aa{E*l3?)qd%_AgX+Vf`)TYInVP%@2oji?_JOOfHL+1t%qBub~fzw%Lx z?B;~2Po9V>jys#{z+f9n5^&zW-3cm2$vs9U?mQ&xF%q0$p{;L`cil`?kaEDXH-}sv zdm_2Je=jdwdrhFiu)qZTTMpnAm~Hu8GR_2b(asj?0pd5$908!OHPsGT-+KW=gwYMQ{232gQKd5 zm;|MHw8yQMVVHC>wxV`u=}MVcu_EDyPN^a1eci-VM}=zkK0GJUd$*LROfBIodcLK=9>~CgRk5Cuw`ZP-pk* zWTZ%rKPzY)WUV7O;_^!jm=s7x5c3@YIF@y=n}?Zo$AcdF*1`#0CzM>vfdrmA)+cq4 zJ39Xwb|<%ommkaMa{8b*h6v9oBej2WRs7RFs|^M^-eox=Dz>DNTa6#$gMe~}9_R!c z?VgZnE>S%i_h>pE+D2yZ*4YWFqy3aR~-I+#XsH zGvhk0vdPqbl4dk5p9Fj$b3Ajr3;j^`FhT=Q!L{R6Z!q{G{`ZL z=ZQAc>FA2L)@LZje-bNs08(tPj6!m^uz*gx9GE&N?7ItfoKk}(d_V<{8RTG5#rH^( zoDGBp9P3DiG@Ds_TP`Mo45S?XSPbSWNpI}FWq1nTot6YGkzGG>+EgQM`(=}fMzNbw zJXGR}LHqjTHn*hS^I3JIunJeIaL0_?uKva1X*~FyGCOFy|1h!znp>jz_qK}W^rlA= zg@~v2`l4G;En}F3uB*I2w#JhKn5pNK<2oFtcOqDY(=X6%QMfu{Gw@Fv-0Iz2TV-k) z`2qzynWCSsY1pQ3Z%b|PmEk2so)ROD*QuIMk$ojWYK-|wCj#euEBenQB`||B!)+j2 zceq;+HX8Frn1G+AHYK~^U*o-6lBYKXNmtaL^YcNA)0x#BW6Yg=z&Lza6}N|_;@&k5 zT%Sy9`uS93QfEt1oZ%a5^i2aU`ZuBtkn#aL2E?~OgC37djKcY!sqJPKj~E#{FG3+d z=ARmUUZIrWdIAxSP)<~aWNRPBA>s}@&N+n`+H&_%WmlP*rJ(v0f<{-RMRt*GQ<+e` zOJmLG0Z^TuQu8vtN-T;=<9Lsc)$Jvu)nJpLCaLzxGwUebO>KD$UNvV>Qwx+EoM4=G6Qn=h~5Ahcm57{+MjH{6^6+{ zLcLflm=M}a$rIERTpG0C%`LM|#{mX(0Ri9NGjh2?X9D@+yJ?wlGX^iVn;Bfe#v zsI0rxJU8~%Jk<}VIl;QL_vk|jh#ksBEunC@Uuu7=e!;D1cR~IOEBcTAB(O8IgyQD@ z4+P5aPmROO_@5Ia0V^v9>wixFmlb7WW#jl?RP_JDiaLWTFKNB9ibn<)5fA_`@Q4#H zY*Ubk!_d=D^?_s)Z4(g1I70y~P|$1xEf5kANWS_leeQhr-o92p`&g}fOmoaOzVdqI zeqRj^lvR%s8v!>0Q4HjX;}OvHvh&LdsiE}E{)VUJ>iPSJh~P&D`~T#DP=^w*1HlAE z{?h5f!8HgMFnCD)*^mYX11&2c0N5i2kXOecCz_dsN7y?>|BNGqp@oZYbq3u8V0H(r zpeKhA=pzDmdhrjszDhV#`e_8I({cjvH#8*L>fHuplqFza+dzVvs}tS`%9ZI2NLi6w8!MF!s30f!Grrsw2!1DL67LW(o00eCY><2t+1oWi50H85Lc#5n4zz4SN z(^CTmcmVo^drf<-<<~#6Gn2BiN>6GeSptS>23`v!B=Aoy;G|o?9fz$8-uPl{3MSAu z_mfhSq90m-vbp1Okn%5xhU-Jp+0|PntlHN%`xA%`82VKaf2)S^L_)=HbEGdTOF)h! za7V@GL62h`)8hi)vuooLJg}9g>$lRPUlwy+i)1Z7;|(TX2Mtw3^qU5XMf3*V2uuhl z`1SQgWXKON1`6QV+H(4ds=Ygi`IPwuTln~T?-oz@Pr?LKCpla!atxu zfM5G7^W`N500Ly)w<7M3ItB+r@?H3<$wA2FUM==<5&Rx&L@ezLC1u+pzaL zss?Ha4IKV0f#xIiE3x)md(-&Kf`Q}jH@XmYq;r@UdGWC*U`t0&EN{%JI!s z8Q3H|>kqR8_wY&*h#0Bw79YckVPW$tM(JlCqz4QJC?v2!5AwDe1hfbE@c4@!mP2VJ z_EZ?ae|gUaDhNN_8>j5AIcV)Glja{!--iU(`b5CriqVY>~UWje-Plw>}_$r*~$@FAvif=3Dx+&IfeIAtWE(3+N2~9{*xL$47d$ z^%iei=cg?U=$%9GhQFt`u35Ne|5Wv(irkU>d*#OmLlDn3mZ5J7WlD3ukpEz^Xb}Qa zjXnDjf5bldvB-wQt;=+0y2QbtOC;v85he0gFKxIx+Nr0Cx)xVthFR0qv#fR)!u;oq zS=U`pbLc#_h7HLZFaH8>=9^S$S;Q|hR!q-x@N;5#lfDnJ60cDug=7+xM6xPd#`j{S z{783Mg_{k5ySb)Ofws!^w81@^Y=U5cI!{0FxLW1o4+}DFVi;a-lJ#!3@xhsU7PZq` zr~pfBRG%5yg+fl+cq0GPdeNzOc@IEAOz7W{;0(OWaBKbKWhvLk=8JBN+JP>SH~xh` zDvx^&i&O;0N!w03O0OtA&x=_pChA$)p&9T|f+R$a^#U9_<^BwKYVN|UB~-P2gh&&u!{BS%hfVKIpR~H$Wn_y#SD4WYTq*`a>NIn# zC(@rEB=ZNJR;`8{WQrD=RthWKR7sfB?3|u-S_W&~8~sE1cKB(0*0f@h2fmjqES)zM zVnlA(fk9Fp41$KskcY&lJms}=$%`3(1;Nyr3$aLq*Q?-6?^Eo@3#B=cHj%14ty9CN z`nje|Ts~pL>i0fV-2_H!5j2{!p(g_(aS$AG!P$=ER-z#e?8DDkwB_odG?JNLwMsf~ z9O91I9^ZNKA-N1BxBC@`+p#N2?!=v0(W0Tlk332Wo(4Rt*Hw*e2KfB;O8cJnzT4Ju z@O=R8pI2=Q3gFIzHmh!uQJ$2eRE!H=Kas|Sjvt3#TK2CK0ayxB+#f$W zX7uMH;zvetuuN3-VZ42C#n9yxPYO+dy-f?)gzujNl3eqy^Yn*> zfx*AA@nhE z4iCtJk_6R_MfZ(KX`FwixJIG*^WScX(xrNym)tW+F)>=tB2AIQ+#V$yJzxTlHpQ}w zYkv9^RdKJZO-QCiq+(K96&L=nqg?{j|AL=SQ(;E5yHglr7zCg}Z zTRa*~eqpSC%TCm7x5>rteevBa}nJU1ft&M37p*J_KaxXiN_)7NZpwVtCMx zvqnQeONtkL+ltnn7v{`oamSV)wjPdQbmA@Y7;Acs0=|0zJ7JZ#earb2wgBzBV1Dxn z%f=4keRSSp>07%pbFm1s;q$nSHQqQ?nTkfN?q8rOO@V|2q4r=gZ`ovdb2+m;-pejZ zPXDQGXSn=ibLw}luLIR&7)sJEX#9yCNo@;t33OBlLzBZwxo@Xw|AVG}_^;aCITB4d z`K7dGdvF!$;orU6f=ToSYN)=_5%dM$eKxw~kgAvj#ai~J#HUc*5hb%a3#y16z{7Z# ztef)a67}%lq~7yLmF|W4MfoUI?&IkN$3NZqHS_eyQI_lsk@e_F zM8|mzK59}Juz#R7b-*Zm;4QvZIl2v5v)n%nc<)^NB!se&T%{mWqOX~_ zxoQ~$O8A6J3&Zy1ZU}qJA-$lp+lsc|hZuyYW*c|{i;X6?eovg0`Nua9o51=J<)Lu( z7m)3V>r)HG4*YO~nZn-!abw?7Kq*EuSYq2GA_t;wHg(#ymUmd_*(YrqtCX9hk`#N~ zDlMTu;^%`uIWwcrgpPL?QWwQMvsp3!guC;3Y*$C41i2434*yt70~iX>-@H^}E=oa( zg`k&p8P7^1-;%rpD0Cm1DYJ_<(;pfT6h`3k(!%04qin1oNHMJW2!T4JP-(a4(A4lc z20i87AhUp&e{V&jUIabGkf{4-WbvpKe$kxh(_OzTLno7Rx`j+*FNPBpcv#YLvvc_r zFQWKg!lSoTmv#B48(k}1m$X{5V6P&3tDamXK?KyC`T7Ebw@M=pP#U-8JtrV=kc%N)pRdep$mu(!6o%iB&)jxm|)G<6H- z#E4B3>f08#V4U3>=A{o&K)j8&40oUCaxBN$k7|Q*@(gn zsSG}04&sYwjKW|YcSBvv_`2%^z3%JCzdFW1FV0T*%miDXyk%#{e+)`pOR^I&cj*7# za)wv&Nh-Y^S%zn3O~qzc+x3*XP9wtE-dF*VYCD4nO$^q zjY))Ol#47ryBabIm;Ou4>1^ivXplCE=Gbw7J9ma{};4(4`|{ z)z??qUr2p^NY)p=_uZP?KvWFSWb)w0A!$1T5+7OV1+EiyYj`aLEacs~O!)6kjadnD z5a+7KA1cC5>96jS=vbIySkpz@yQ3n9gE;?N&e*G+WMX_8*{>(ZH_uNwVH#wZSx=2M z{l*$;FrfM9VlL3wrx!s^MFw!YC=S*E5DgYLz|8{ko8t)9Hn2`7*GlCs!E{+AgRNr(+)c>3X^Amb%=4gd_ zfYW>5nI2esrGac`#L{N`Yca#67z%i!{4vxU!fcp84I8w)eXQp`buFMQ2Qs_b+Md(W z6aZjIWX|D-13P6ibefS-C1onNccYH4I44P_`og3BgfumIO0*Ol&V^y%AnG1h1pir2VG8#7Y4 zx3R6An~)r*qEF)I{nXQnQMUDx#iNp8E`K@lo{ewS)1Er)!odKviTlM zaOtuTWuc0apR))*>w9v_v=FTAew}0bV0O%J9tH$rSkBlf`vC72OHw)n`7#+ws{HH9 zw`#sY197&MH(9N#CBwE@=dQq*`SaE%8qu3AGP!4KN~qY_j+;$4EAPVQ>yK08l^?+Lxw8hXO_WC| z^Bs?xaeC)c`NK+uV83g2-CEMn{iGn`@!lt+MAFi9-uxhA?Q(*fhJs?~;dchd*38D} z2PAZS{uEb>D<%@<>U7j~gyOpNxKqQS(%}OhaZ2z77nU3Z%1L`CNcCgsMt3X3&F2te z7}8;tRE}SDUKyryX_Mk6a@$ttGK#N3PmkHp6UZk2i2PA@XDnU#!+uWSg+EO$LP-rj zV7}0WAiTpfi1J4&(YSCV6jgDIn-CHDhd?7E{EgKdwXxhP@DyhvUa_@zi95Fp@(*Kt z*-|edsQd-vM3_@+Dy8p!!jiMJTcjNo-V6$d2Q3Xz3sEW{j>EguJp9Ox>cx~?C-2R_ZN{Wr-T-4Bi)Ag$*($wLKcg(iJDS+U2ZQ1^E0g5U zk{J`MDunwpJhXPNti@&dsr8VEJL8^#d~w&5EzYzy&8;C<^?}dhMh`s^Y-^cLLxP?K z`9ZKr2378nJ!k&?N_Z}(L1-%-rvU!AlnO8C%Qg~}d|*J^X-9;t?U;jwS4?19{$W?# zO=^M{MKvSgf^?08SDW)VnQ}c$+v%D{w~&S9bg_~-iaDb=Wu5w^ZZonbm1h`ibrwH+ zvgQn$`U<4q6E1LB=G&YWha!&qQef&!r@TgSNV#Ni}9mm77 z1}Un=Z_j1e`9R?dA4FMFRZ*DV{QM`yhDCDK6MS7sGp~0B#aY5>Hzuw~4j^I@^=_RY zmhf`yJK0T6#;I7Q@aLyHRLAgTgU{H^F17sZ!VJtNg{p;FhTGWlV&O>K0LPEG3ccSl zh#Oqo*gVM!i6&X8=S*-mv#s+0B)m|g7X23HTZVZjJRNjH55+pG1~V8JZ4@ICzFjE; zvSAx)JSX>WVOnm;F^bhR#kMlRRJuq&3_z5}huzw=FV1n2F;x4L>h4ZJHGG;7g==|2@OrK4o&LD^N#Jt3OvC zs&!S3{gQ@Y?%f?OhY{?f>PM62ZDAFfFfFTNrcIrjLgtUS_IebN@XFJp8#|*tHWzQ( zmmYhIKa=O7E<~CJQY-u6Udmc6V^(UUB9u1sw>v2J+Uhwy8GtlS+KCOm23X2PWVS6~ z?qqVow5hd1L?P$sQeVcVO3KQ_YldC!#sn!-|Mti2u&Jcm@K=t<0Q z<-Ls=Wx25!_F=74uDwa?|6K^PM2he~@(K)=N=XcP^DI95q8{m48$%K0CcEU!qr{1N zW!&q%3Y3cZXc^ZdN;h>r_Ez4uN->7gEh+&-mDaAsWjZk0F)LT?+8q0^ePhbkwS5vw zNgCx9lV=q@O^-Ui$9TZSk%ueQ9`OHsQr9uw`3#s|^x6Xr;!9MAqdxbCjJ!-D<6U}q z(>F4nF%543TD3Z7Hd#P>iLPFl#8CLbu7QYAvz|WScl18SF7w?K{Uh0yxX?KYA0ukC zCxHAFr}a`k|LXm#9{K$$MQ}txagwz~6Pi?C)O1*I_E~e*BD)Js6oppA!s^(uNU1DX z){^CAoV{O1JlY$hBX-1p_^t^@-(8yIB6f~|bf0UY+lVXW+#p;x2}6|j%p5%dQn0io ztU)$oM52T?VoGG8}=Z zw&sa^UGs--lCjjto_kP&cyPy>hN+s;Y9|@Rv%&O*;?~Fhp8@p+R%fliUmt(bZ8)qQ z+S0=0f(e1s$00!oYbU z0Iz_SGu#T~b}m1?xV_WOJQ5LV(+4K(BBAc% z3XZ&@6skXfS2XiHMiFUng6BBuX+tv$Dv%oO@SpIR6VKqN%O8MNpUHIZhb%Y5pE#nQ zkg1yufd%w@L5}*>zSGeqo%C)64bD{q<`_P5K$5rsTahAYl=Xtg6;p`htsDv`=Mjxz ziPW|+H$uf%qrItpTKz6kkBIbyC6~g~Y^XmejJ6In^UUmAQ*OhagvWzj(pJ*a`b_Te zI!CZ8|L5%@DW%n~igJXUJgzw7U2x6ZE__sXy7 z$tGZB#9Mh01462Ish~Gp8W2}^=Fs>p4t&Vxl0La1>>SFYD>*~Xb^4-;sXf)Sa_7*} z>A{`2iS(O)i^C|o!O9PMw|IW9eUu=e59w#qN)Jo*yx&r$NLb%^<+=RNiu`c)cltW< zTI-9dQH^2qP5Y96y8Uo0t#P~=nO=2iO=0iuI+NTDjCj~uVO-U++f*T>6nTLyH!Y{e zrQ|fkPN;IH<8d3-zx@brp>fD8qw=mvqMiQdY3?pN^mLrKcy1FzH{DeWO7>z>(Q z@hai0DYa?6S75JPHC)d!@zP*1rj47`3UGWha)?vuBwje2gA6?vsY%KGMu@RP#szK& zRvg7$%SE*W#+z;NLIDmaCg;JlD=2Jgy^yUE!4C19?e7Xg4PP3U*bmAxD>}pTJZGh& zP>yF#_EtVK#`c2=$*0EFG1ai$lNL}9A`P;Vso5NOpm4H<&b!&z`Kqb8=ZJg+P4ji> z%SY(Q@O@Hj77v-tJnGN~7CwU?TfhFWn5qFtF_l2Ws9Ug++BmSZG1Zvl9Sh8@vlMKw zNK})$;yOxE-Yqr^-Bi|SZfn~xquc;y4zzesirnZ(aPS*E(dATw4V}O6m3Z-7Oz5k+)!|`K!toz{2+ADEch!5mbIaK-6P(UG}lb2~y!qDwnsE>D8vhj9XBL}Z_0Jl~XxvXRo4A<}o zYJvJb30q=m*yVX7mY#L?jCqwi>*4kiv)^W~JG}2D?=Pzdqqq6K6teR^JqDeohdHz4 zWrL4As=QR6e^z6!bW7jK!I!jUpXk&aU_mER&9CB*X#8;L(zTf<i8i5`9ft9`*f2gqgwrF4mfEv}PNYj3 z3%$W6T}ad#h=|&$0zUxQ@;{PX>f&%+2Wih=dvxDcv8l7r{nG7R$=(9EY#x%7d;)I$!eY zTtEY;-V(t=^1j%$8e*gG>LUg>AAjnJ z5F+0{3b_*yW)(PQ6V;a+Rl6I!@HX=?J*MKrfyxR48(`j}JJN8H9^c#&}trkN4G)zae-)oS+29?_Ug z(HcK(TWAGu{2eYlTl>ioi&>9FZ_h}c4@s^FZMHI>ZBSidiWqJYo)i z?xmLZ_$pk~$%=l`v*-MFyiPY?dp|RRT6iMtwmysI49htO1Nby^#+KIIW#3o0M_A{p z#SA&%oEGC;S928a{o!nnkyOKjKmrcbzr{M$rlq>{2%XU>M?%r#Pt`P-hoQT>1RGka zARaV0pynoUUbDH7WmC}x5?hM?#cl2BSXwoar~?41g!%faDGl)6;u0p11+bzNfgg@a zqM^z|Feksa#qPjzsP{Mok&fJ{++~P1y*l+p#qQUHY*JWIOE$C^(y^{E1SoZ^s|7qz zUbZvW6sEb>6J30zqbOI_mg=X9fe}>=0Sm^HYV4<92+#hx;Ay=m6J}0hvxIgwIag=a z!o#$LBc`O*r4pRPh+jSc?>CMAk~*{ex73-5o&7&KGa~^D2mOCdomtsg{{N}7JGipa zW(Nxp5K*@z3qdz2LAP7{jzCfHAAW*A;)3AkDxOKC5DNl;=Q`y;3&m98x8eT&5FZ7j zPPaU-zoYJU#?jf`J$Ak})f{e&tYn!1^?67rCh$sPgbaZMgn7*TBCBgiARqt%1%mu} z5Da9ckT^m9-!^0?%t7si`{YGWegw)}2Kq27B~T;!0UhLj_Hw|10FXfahl&M|7WfJH zK_HSpu)`hGz{&!7_T~L+5ccq(Acc^fD)P3xxAtRYF|4zD?EtwEbOFRAB?b4~*!jm% zPvFA*699DRM<7okt04f10Y=Cna6<3j#h~ys$Y4ffG}YH8C#4{+BGClfxh5W=0J`=t z$ovsuV4Yrr1ps?R!OjA74E#iqiB3S$+56}HIHDEcFzD*IVEkDK_7E_TVqow21r2Th ztX=%;Q{nh`VMD*5s~*w$0q)G400;=@dKbPUeo`P}zi?qf`Q>YD^^4$f&LQmmiS+?| zTyP1a*+c;VLPVIH#$?1xAcd5YHkuL76V9LTW>nMhy+u&Fjcu{2gBXLEpYh4|Ayu5g-6Ugy;dh(ur{-zHYD7nWpw@Szf-j_jdrO z2vU6s0Pa>#_1sp}Lj@GXgJ*mH4L9oQBAZKdf^omIW514+RE1rDzJWxF00I;a1ph+p z2;e_|h5!J6r;GqXf6ov344dQO$o-e}t_@$$Z&P`G?fp;V_}%|KFAf`EL&udDn~h*~KmQB0%W<=Jo^p!RK2;jlFvh>SJ654pIrAg{lNS z@)Mdi@RLwO2Mh6P`)O5!1|F#pfIJU3X(BkQLAblob7j}Wy@3tF>SI7C?NxtF+kQ&h zL9qWb1rQSY>p7rb=->DIU?2kK(9bI}r*8S<+FytDVWz|K2L$w+gcXs&0bp$#_v)YC z$?8fHW)FOz0txEzN5<5@4go2oKNO&j2@C*7{${8b4h;msbr25>DiW2^)%hybaC_*N z9Pr-WZIsi`2~g|z_Sw#1P=ALW;(m)6iU|4Si?ZsvOEY3z%HAhk-=dwEbH0I15@wL) zacWi~j9$vcqf)$x|%_9`q5s2e;QD zxL!~pI<^o=u0V}~j|{URep6##%b_$~PA^o-Il{JQi@fWC-)<*u1GEh&QjTJ6;V->| zWIJwWTO7?gdn!XvDm?i?`BpU}w{(-VSgk$&;NfiYrXgm}dzI#}8JzFe8*6FpYs8sC zfU8@|TNH#P7}lpXchHLKISF>g2U1w_%IUB-aM@<8 z-}^_A6_$T`Ou{BFq;&M8>x#iyjQ{NNQP(|W_!{MCTy=4?rN3rO2xSxy`dZk&K*Vds zc2-ugFm>(ROOlC~#X&me1*T##m5q?ifN_qT4t+PTSxD%lr(o#{!z=JFxknG=adgBC zsch&Dtkk)Eah?Peqh(qUV`|!C%E4{UcnI@&u>=?(K20>Pt`f_ZR9=}zx5e7?b%#tr z_h)_`L_&~1@}-aKr|yru1}eYE3=cLf zNympETe#E&eD0qKYWb9>%0H+S?p3_P##j`=hevb#U7_-GIi*x<%?IvVC_)-u`TMT! z8`ED29mS#l)7V!A#n~-ehY%7N+#QDC&fo(Cg1fs61Q{F#4^D!+OK^fa1O^BmLU0BG z1b27Wpdasd?x{Le_g39o_59e{Yv;)l2`zxRY}OqlQTea@Jb%c_&QuC(-R1 z%r99jo9|7Whd>pAn!7A?haX=`e+j|@j{i#xa^%~0V(nbhtq8N^qEv6Kw%pk)t_YvAY*u$ZWM{(%#>Jrb zlnO?)jK39iE{*OudpKo~Z)kA~S+=J>t>uSsP~~%3s)jLZF?DwDR8cH0KFl{DS)rm> zqAr^e+;yR6zAqTW+;^D{=Zm~PN#r_odH5XR$zPTEt%kwGZ@KMqGW;xz-E!QBq5ga^ zE!rPjI!Abuq~jy~pCke0+|8T6HU1B_Brk{{x}4H0MeY=e-s`&DxI`)+68R7*3a!SK z{eS8Zne4F-Ky4e+LNq?fNm2b1`+-G8ot<*!cJ`zUOs;`#pCiL!Q!jl34lP&tg<+8t+4!>g!A%mpamb)%HKX z)}LaaRC)02SyV#&4kuull}0|g@fi&xdigG?_|>i8-b}WVq8p)#?MK2?&4rudZaR?x z%biUkjQ2aAv@y>JdL-H{K$((baO8yh`lEM>6#5H$YE@N-87Fha3qgW>! zA2=CJSPUff=rwKQqw%ntB}w_KZDb)!?qg{M%TMZG1swo#91ovxZmd6P__WD&t_I$T zCdDZQ?$G2+ija3L%}THLA53i^YuSY(Fl1?U4{lEr_=@P>vYS@nE)EkCUC9VKLwiC6 zq7WACjHpW9(XB>aTmm|+O2i9}!#SKuwJ9FEra|Tu%9V5;$;{PkvdwBM5k~#I`t;rj z>1sT4y;P$9Ix-IIN?dFtBrC*xO9FXc1ky*IzJSqHJPyk-UQ#(rVzE_DDf?%fu`*7w zqIdm0_!aS})8Y38{fAAC{uFB=y1rozZ>9AJ+l&8{K^satoa!(GpP!} zn!MO$fk>;pB5HKw@}vSi8M6He#?>sw;)r9LyoHdR2eFu)53Qz_kCZSM=*dFR1-W|X9X`9QQt$NG!5qj;-nDoIFdB6~t!nD}<#dg}wr~YP@;+a|O z3%Y8_Rqbm|QXha@Kb@>e?r@KIXzaeMIZ6ws_thV-!^Tr7)1VB^fvm)`fwkXZeT zZx{0Wl#c9!Lme_o4i$GCSA!~Q-%@eppfXN9zx)z;40t>YLO~pqOmtx^zLnqddP=s? z8Za=A!LDOGHBG+lHKMGoMHFh89fumNzm>mRz(;w+_-tvphvbodX}7e^xnkP&L{QQ! z%iOev<})lGr7S|Zj9_2=a8r-Zljp?fO_$F3C#@c3BSO3?-<8>3#@}4mY@H;!-+5RC zn`G7fJ~XrJKIPyu)yH*x&Eh_v8yRJ#SyQlj)Z9;$m>typG;im_E$YWo1Uat8b|%y6!x7(2b%}oOzxh! zdEidzozNFuC*aO^rQWxb#EFho_QB;NR^4}=`CV3+uLI@&$j_?_HywO|-r*rBIbqZJ zst{!|;!+HiFnDaE@t!Htu!t^>8Wb7jtiQ>*#Way^{KnL=T}qTSus;GiM!D>GbBs-l z+4-JQp5emQhg8Tv+I46Zc~&hc1Xa0D>K*0oTouh2D9YdM>}q?nnUxvyrHF(rLcac4 z^VU9X#=!D!ycTzaqW}BW)h%2g$2~qCCp(&Ti`D`+<5Qmq=sxj!=(X!-`A1QeQ)Ys~ zY~2+N^;3@CzvdsLk#O`rOHlWDed{Bg+bibJZTfQH&)Y!4 zLERp>70p9~xn@TvyJ7~+Q$4H)>7!t5qajN=de#A3_vo7JJRrKQOPIeV`CtZ8g=oUJ z|GF5``eEwFq43A2n{2!xkz>q_uH7BP9CK2m*5J|bFO=*A`Z}N1+_**ut!F_~ou069 z>)8_O45^lxj^AtxIiSHw>0Ujr&}VWcBC2fr2XsEi z^olfY5GF4+68bnu20X+L`Yv%WY|MqnC=;r}9h7HP+hC*HR1oBoP%6~3myvR@lG_+2 ztbqSHpPn@oKA$~UX~`HTh*k6lV6cOiy%|nz$ohh%G3V9`Qd37yjQ@^RL(D1bptAi= z3+!sg?xR`;543H5SgjcAra7BetRe0@p2F{~l_6q?rTk<}Cb-}oP;jRAVeY$t>b*t7 zq0l+c^-sKt!Z?`7p=bhpa@sepKx`M|LUdx~CcTe92hPJn5Wg(qat^UIXMPA9!@67@ z){=8q*3k%Gs3L|@%^whY;~xZcaRg?35%{58Y;M?|8)rYNCCNRG9Y(iM$hC zH@n!2^v=h5Tf>xLlnk$=_1bkG9Y7|JM(6i8C?2KRCzV`7MdijX{;u%Xeog;2={qM) zq~Hc?6Gt=In|o-Qj5m62mV0e1&ylX?!$LaiwrWUxJF0CwB4DHYuq7-N!Mli+>SA7h z_=6o}pZV0%3#m-2Qor{4>m4dW>ImCCv9sD2V%hjs8gk$6YZ3yUd;o&m&rj?QujDjR z1v|qou2MzL4qOv`4daAghe8zmo>kgeLED1VFU0%CGAba2XywMNi0!Emak@jL2zcvn zD}UPoc#!mBTzlX)Nh%L>h@dqhRUn%L1TN{|py1%3nELp!!uk}O221%bu{J>!%gxqq zq^xA$vUF~asB>!!SEYBV+4ls}7+9x~0_%Z?Z`I=sX}$blH`b-Iyze}eBXZH;T;g6S2U0L_SW2jekl zFyT8xR}hqB?t(VebE<~M%!1d=-Sr00KJc;bh?M%zDa-y0T8s?|PA`F6L3N zvB%2Bi&+4V=y7Qcg2L)1Ydvs1g#vTEBtD%Ygt9cBDLCz?0Xz$oZEqFn1qe%06?mW2 zoC$JmWzv;Fx%CCF-+pQ}6qe)*@BPc7nw^-C&jY}Vwd^W9v~$X>Dix7~Ij{EwbonTp z(Dq$<5J8b(2m;k}X%F=WWym7Y+U*?Ic$i;~5vF#K6^r72zPBKz(Dhh@F~e&re|fi^ z#?-Mr*Pw;I`#@Eb^f*Kj^cyhJRU;9~&q#mkdjn47%+2iRA!a10Q zIXI{1J;VF^Xvy{qzn0>?g#^-qzcLt4dth0DDvx6SmJ(w&nA#0-H@@k2dm4e=12Br5`0+ z3fQ>5CM8oCosU>0Af0B{v8WDXURLSAg_wzF11)MR=?mifEHy|_a9U==i|4zA`5KIU zNHf?39C6Rrx3uf@7WcmZuYr*0wm2j0SIf4w?EvFGTJmuZCC;QoA7#<`aB9r*?kaG+s?Qe6L$?ADc;KRvoX^`xj!DtN^JX1>!7+OE zwR@>(&KpA3%(s8$(OaE<{O;0q<76dh~Lu1-SMvG zJQbWUSCG(6dr@d2gC1{kRbM4r>4WLKoW2a0&Q&&xcA>|Q^rL!OI|)tDe)FLBT0wQ{ z@5t*h?4x)@4*zfTJ^i|AZltCG>~89v*P5uh?96eZ^%)miWz{NeDKk|9di26=a;7Sk^u!GJEf1!&nzNXBc);ILVQ zTU}^{p1dh{KVyx@2q%6s zuS$4}ch<$RMa&_M0zLdLNu<5-wFXNsa@VEbrqx1O(HODAF1MGLH-f%H%B>zL=ao1t ztQ2iB-UnJBvQaZ&_UDVpkZk9BnXhDBS!hyosa|P!uDL1~n(1f4OvbG;gGU)55397n*coZ5`*(9v*`^Z5vl zm<^_@LQpnYhC6ntXVOcnJ9`zrZNo#YC^hW^X1vyITir{3ddNz7-1`c)$5H2+VRtWR z8$0l2XyW%caX!hWcbL(XI40`!ukkY%fA^nC0`i*eA(_|LKJ0m3Csd~k9Rk%3woyBy zrdqL8xO&b`U#YGzI&fY0*hpdDmrZsyd)x5!k)URWfUE6r?M}(^LT{WDt{zz?S zuez^m%7PTXdrz2MxpR!m9+=wMGM{zhK4Nlv+-$Vde|oV#yI``tma_u{5h;+EUq?3TFWb7jp$m) zfUwE4NMfw498s>?f5I?Mli8;}HZ=EjhRwBf$d>VB%#ls*VV=JNvpKQUYBT1M@WFmG zf@SMXuMXmU2IVMX$sf&eyjLGp>TC3&cel|Ds?ICj?^Dn@G|g1=WE6ZnMA}y) z{Ucna{f0M%u?wa)I1|hH{RjlS1NbvJOmH5ad$d$BPhg)aiX~sFKT}O5Yn{Cq;S|QY zY*D^X;21fajJVFWrLY)9*1Gvd$CAHz1y z^g#cZTQtPv?Zk8INSPvt`^FNi$s@v1mh=iQ+ml&1mc9xOAvI~(vaBCXrmZ`~R`r8s z*m1*si>XQxMgcr<{KGBdy?n*-Qn|btly&b1C0=&qv3DdfAkq1qRSUGG?L|Bfo;@*> zEFZ{-zhdE1kf0=HDx1g1GLLQyM{~e0gq)P-gwYw_`b4o`@+xa@Qn#)7EA1TDV`gB& z=drZkNl0O4AnQ%s5}by{W8`-k_g`ueLz6s04U`g}wZEkIzbeY&co&(GCc||@Rk(bh z`Ss#e!ERQ+XVU!(Cfh9sfUsA|SFfRZwTFtDb@`8fFZ?>2P{lK1vuVl*Q;pITsV%K! z%kZx}HazG{HP~U$sqCE2cMG^`c#>GQ>}7q0XxmIi9Z>^D3=OXfLiR3h_)XH`e_r+$ z;RRp`F!iU`s&M(6ExSNo*6Iiu`)nEeZ=gMtZpZBEuRG(ZL3}fmC!mIN4V&^J2j?N_ z-r(-o0G|;fq!8>Bv~tgZg&!$V=ZzA(WjamS=upI8wDG`Yw(}8jHnieOf*#y?bUtSiQlcN$jm{QXk-p2{}2sT_PGd{!) z*e~$7AtThQN29xrwM>wLS{oXs;$s;%E%^GERm6=%NH1p*b$nI+eQh2cj#R^2_t~uA zMvXZ#CeD{1}@tmsC=Ou}WKe1?8+qeRszkkKV2GoJNxIP~Z4a0=cSx9sCMw{U?IM{&;4cp{llZWh_JokZRF;95iJD^?t0IVeDtQBn{n3Gu zT#h7`6gLS#S1W%7d zu(hF`jG)5sd8JmfW7>&1z0VGY;6!K2e3d>fT+JqbuA`c3-+vrWV!ZS{<7%zm{xnEg zvzMvvF6c#|3!oIe>xdAiE4gD1*byJX7#hGpJU;sHJH0Ae>p`c93#TCa${=E$(fd+< z0^==5CRT@l^6zP0_U=UxV8!6(s zBu@hzO8e3E<}>gWu1M-wXoq8=z_;8~?%57M37MLy#|D?`?qd9Ptt>NtMpgR@ zeZ@p*8X`8N&gBfcTV-TMpJ-mqcp4Y~;_r~)KPO*gCAa_9Z-Evzb-$KR^YUG*K?|HS zZhMJHyQ&Kn{Zgx?sh96hpMr?0a(u?E7@b@c%EJXBD<~g$dJPcbCFKh~<S0s1~uB z=A3WTD;AESL^fj+ftrj^(*;t#^*S9fP_KLq+b;c78}0H%KCM2u2i!}6S`}h^vx8QK z3}BQPDWoK$@Vx4ZFMd}vNx9o^HQ47!0hWa@P?>Uqba%RJxnkQxW|-%e(MYWMdnQ*8 zPSBc%hf$=E`XT@cO@zvF{Q|+{7dOS(_6%pvfSzBgSh3p)rd2^U8PcHyy2eS_#SJ0- z!h@U|dnqic%6}axr3;5kmgxPD5Com$Ne=dwaMz*l=NnbR$k z#p(VcfouaDrhe&EDhbj$$fl;7R@C4lRwG^1ram0MHYsH@C3K%b52lh{)KOPA=0I>r z*)*Qfcg~V)tp<@Q}QWdDYr*kxK(cZouLku^i!T{4GPfH&q<9qHZFV@S|cT z{doUhsaHqwy_=X3isX#U^w5N&uznf+3%CRF6$8Bva82p0hB}A(d(4z3?g_Gt^?XO( zAF?gBE7lzAF*?SJaQqb4(VjXzYx}z4oJixQFhG%G+fn|kjE;AtWeJmdt3yy=($p5O zouU{(+sFkU4O-t=k+l8WR92SCl>P9?T3l-`#$vy6TXLIQ_PUCC@9(8OFGR_5^YOB! zrMrK2Gjr%VZ5h*;GRH3Hvol{7x~?U~S=G@GL+1}7*(dNfB75P!;Lc)2NdFgbX|dRJ z!7974=8inKr1_hS*Kx#?o^B6k{({vZdjk{Fe%ItKqSqT<^{CsTZVNg*EkFEdO$M6I zv~mU%mii51H}sYUe834wcLpk(N+X*RqWzs6>{L`SdDAmTlV`avuwzG!sdHYO#BCeA z!z9riLB7xX5i;r}i)4!{Jc&{% z6BAZGa%&9i4=hqjKjE*5ro`FJtclKW1PHfKP`sQUP_eGI@aR=-efp&2hfxT^yluv`;;Ze4+o^P}zf1J-!^VPbVlA@;^--hFand97!FCITkDoU3KvZvv7H2^k#R z=5VaI?(%bX@jqQx{F&|X18c~EVDc%^9(16@uY#rW2H;7)f%rZ5z_QJGyp+@V`qxBM zb_!1vGDlVhhu2sW@bk^`B%u7e@Q2h&2ExnA4t?at0#u3J?mm=G4MsSn&Ur?sjD2>n zoyhMdhQ~Q)-V6ls#!G+t%Z(cC^L)(IHtIz-$L)(|TiAML$$02#t&LGw>}jP=qx;PA z)fQ>3sj$P`)&39R-t)&^fyj#%hl)n0OuqRRddM-%r$EPHhTrh}VTQx}9RJy@kFOwLySY4sgLkvOR3?IDn-x5fRoBH2K9$GDv#VP=~1i&SOqsWv{Ho{|ATy{tt-quj^S)18NE2ly|g%dIAl(fV^A~0H>ynH}rV~ z;M4^gf`B|g(DRxG4CV&p5qS33_{ZE52ITn%@BA~70vd`)Ny*4aaPy1v@C%Cb@Cfj7 z^UH8ch)c;x@pFT~61=>k!2jLk`ILWS0&bpvL4yB79}CLCcFe#JB+{#{;sg&;_rwSG zSwG|#K8^fbLQygb3!Ktk_+@=GF9L3Ee$k1Mh!IFOy>u`&-OxMl=5MXt#+LtDCv3p!<|!x26}4r4E)1lA6%d%a$v4REO6U#$ cJ-x1OrY>%tF3$-S-~ogA0QB_IsxpB82b~K+B>(^b literal 0 HcmV?d00001 diff --git a/hw5/hw5.tex b/hw5/hw5.tex new file mode 100644 index 0000000..080fece --- /dev/null +++ b/hw5/hw5.tex @@ -0,0 +1,75 @@ +% vim: set ts=2 sw=2 et tw=80: + +\documentclass[12pt,a4paper]{article} + +\usepackage[utf8]{inputenc} \usepackage[margin=2cm]{geometry} +\usepackage{amstext} \usepackage{amsmath} \usepackage{array} +\newcommand{\lra}{\Leftrightarrow} + +\title{Howework 5 -- Introduction to Computational Science} + +\author{Claudio Maggioni} + +\begin{document} \maketitle +\section*{Question 1} +Given the definition of degree of exactness being the highest polynomial degree +$n$ at which a quadrature, for every polynomial of degree $n$, produces exactly +the same polynomial, these are the proofs. + +\subsection*{Midpoint rule} +All polynomials of degree 1 can be expressed as: + +\[p_1(x) = a_1 \cdot x + a_0\] + +Therefore their integral is: + +\[\int_0^1 a_1 \cdot x + a_0 dx = \frac{a_1}{2} + a_0\] + +The midpoint rule for $p_1(x)$ is + +\[f\left(\frac{1}{2}\right) \cdot 1 = \frac{a_1}{2} + a_0 = \int_0^1 a_1 \cdot x ++ a_0 dx\] + +Therefore the midpoint rule has a degree of exactness of at least 1. + +It is easy to show that the degree of exactness is not higher than 1 by +considering the degree 2 +polynomial $x^2$, which has an integral in $[0, 1]$ of $\frac{1}{3}$ but a midpoint rule +quadrature of $\frac{1}{4}$. + +\subsection*{Trapezoidal rule} +The proof is similar to the one for the midpoint rule, but with this quadrature +for degree 1 polynomials: + +\[\frac{f(0)}{2} + \frac{f(1)}{2} = \frac{a_0 + a_1 + a_0}{2} = \frac{a_1}{2} + +a_0\] + +Which is again equal to the general integral for these polynomials. + +Again $x^2$ is a degree 2 polynomial with integral $\frac{1}{3}$ but a midpoint quadrature +of $\frac{0 + 1}{2} = \frac{1}{2}$, thus bounding the degree of exactness to 1. + +\subsection*{Simpson rule} +The proof is again similar, but for degree 3 polynomials which can all be +written as: + +\[p_3(x) = a_3 x^3 + a_2 x^2 + a_1 x + a_0\] + +The integral is: + +\[\int_0^1p_3(x) dx = \frac{a_3}{4} + \frac{a_2}{3} + \frac{a_1}{2} + a_0\] + +The Simpson rule gives: + +\[\frac{1}{6} \cdot f(0) + \frac{4}{6}\cdot f\left(\frac{1}{2}\right) + \frac{1}{6} \cdot f(1) = +\frac{1}{6} a_0 + \frac{4}{6} \left(\frac{a_3}{8} + \frac{a_2}{4} + +\frac{a_1}{2} + a_0\right) + \]\[\frac{1}{6} \left(a_3 + a_2 + a_1 + a_0\right) = +\frac{a_3}{4} + \frac{a_2}{3} + \frac{a_1}{2} + a_0 = \int_0^1 p_3(x)dx\] + +Which tells us that the degree of exactness is at least 1. + +We can bound the degree of exactness to 3 with the 4th degree polynomial $x^4$ +which has integral in $[0, 1]$ of $\frac{1}{5}$ but has a quadrature of +$\frac{1}{6} \cdot 0 + \frac{2}{3} \cdot \frac{1}{16} + \frac{1}{6} \cdot 1 = +\frac{5}{24}$. +\end{document}