From 9ccff75dea40250720fd405ecf6ac33d582861a3 Mon Sep 17 00:00:00 2001 From: Yu Cong Date: Tue, 13 May 2025 17:33:37 +0800 Subject: [PATCH] commit for dinner --- main.pdf | Bin 97060 -> 97948 bytes main.tex | 6 +++++- 2 files changed, 5 insertions(+), 1 deletion(-) diff --git a/main.pdf b/main.pdf index c4d05980df5a417da190b175218daed27a95a461..c254a5414a629cc28008bb246f65402d5f8cd5a8 100644 GIT binary patch delta 15929 zcmai*Q zbMuHX#y5NW@GT$}Co@8mmw`oNHb9_R#*N0d|eOh1fNk1WgRk_khr(UJ(^o zAckkZW!fhh84>aDjSpIp|6sz6xmCA`mMPLiBJC*Hh-ocr8m?Z+0;3WwUl8onU-Srm z|JfTW7Q)Sg7QDf1D?q7$)@PgSNZKesDTg*NU&?klkM98NYRB}@y5;oJGBXr{3gVUMHELVthQT220 znQ@PnvOsy8B4c59yc4Nn~v@G0&5aC4I2SwYA*|r#^cXr>OeP5 zm$Ou*vInm=rxeQ`V_s|#oG$Gp%w2Z<8<04mFI<@Xrn*s3&I@<1Pl6!zCRy<~l0?-~ zHY+`0Ra6CyH#Kp7L3us`m*&$P7q*EJ^9&aE?Dkdi>-&g|`Px)K*-oGyEoHUr^>omc zTtVjNog@$IfpBRo)Lt$y4uZrkH7YbrF}U8fH{pG=-@!$OG+JC6R2-K%9_F@rygNDr zM8q^%E=U)xr8KxmjOJDDRWpc737g%wGB#c&(66YH#I#T3y16?_PuCL{0+K(vnm-Fw zuiWbC$=`lCmf&Fh5u|kF2z0hX>15!{eQ|+>!RNYnZS(dpeA5URX8Pj_){Pw%W@%*C zn|%`DPpHC8HbKB1Dv#I-bH-k41?pggE%nb)N7grF7c_8vax|BIT-H53FWuOqTO&Q< za7Yl|gJC0>12dI&t{?Sbd$l_r4+)l({-r%MDA2E9VvOO5`DFT1mcUL19vtVvF@7wY%TS4dp#=H1k-f9@UcgPZR9IOjLE#)n({d*T#YNLeFTm3waK_0DsD0;H#33lVS z0ZJS*UH#GCUX%z9J{kV%%%^3bZC_Yn7pQT~=UR7iA%R%}ajs=bq|wY5bbLZH46QrV z!u-DU;YSK142vVGQO2-+JES;p4s9A} z9H}Bpn0>?nZ%uGOA0P+#W-igrAXlk9U3kvzUEeZv}s?rguPHD2v!WH53 z_ZFitLwkJDLkk`hwhSW#nGZ}{Z%)IgfJ^pps?Jd{>pva z=1AQ2)i8wbLHxk|ZhA>hTg58cuk3WfX8o0G;pWr^ocz?&WANC>r~TY&z6&BcDTI3R zM~e}JX1J%PE%Pz2k_3?%rC1Y2e9^v3bRatl_nJ{YAe4k`HVYR+vOY553j; z`M6dbXsKoV!j@2Af~qy&{IPRMMe4Obmho$FY@NXLDu1~4WuNC+bve%swfZ?Aup{-G zr|ZZz)f6r|D*m9ho6{hyS7#=0he(<-swCyq3w=gL1JYV2NwP0`d&_-XH4&r;1G#cSwt&JxUoURIkC9x`St!nPRXI7NoGJ| z_@rWD>#^P`HPS%CtXWs}YwDtM+rHckSf`7%=a%P+``tPDk%SA^*j_Dt0<`^@VAZMN zTuL)e(ZfPa01R+?#faoRsfeTsvouX}xam859=zIbu;a^plp1y%X`(TM1M`4ZlQqja zk_J3^Wu98eUd^|w(;S(Vo#Pr_Yqni>Q$s`ENi+B2grrc9x@yK&xRha_j~_fhgG=J8 zaR!L4sfjYi-k8+pG9%*CPI`|j1}1|}&%NAfd-aQQM)wNBuR1J`9P)J1GTsmyEcDrz z&)b`Yr5{HwNR{GE`J3y{)iU)wOiFSz*a~RMwbQuD z+{e@Ei+O4a(cK4nWDU^GxDH0=G(FMR-_Ezp3&}|F~kpw+@8by5>@SXo(Ui`of+WWiJ2J z2d97rKka}88twq!QUa>I{39T>?lw~nFms=`z<)zrYj<|Y7#R~q$HiF|#e|5KK+%8| zf#dx3(bQAw5O8Xi@+Am2Xzg-v(sXx%IGXp2<7>;;(K}2iMk886Mpg~5oPP=V4j4xX zVc18($#MzfV$}3}R`~+1^}IeJ2y560G|vFVAqVk`JYOd+`S^fMbfPfe>WRU`5TH|0 z^p3oQo}qm=CoNIdIX%sh6(36ef=n;VA3Bz%)+m`rx8kX&Ds-_Mg7m&MvdcT zv}5D8ino)wpvu@PJ~g?Coy;b|3jF4BJGSdzmMK^b^T(PS_rrV7$^CwcWNvKoTE8xR zq}dNL8or*Bp?83l&GUg()r*?y8Y(A#+QUbB7ufyZ`rNvLnLH5#-B~SHQ*q)AJUSk{9!!i-1>0V3usG+vvslLfMREuYifsQ?sbWJ~?s{SfOG03sG0`XfME7stdT7IS>9M9<_IY zb}^uOq$HqPj`KjP2&$VP1Q(@@SZcdU)pWV8Q3EPbTGsc=JyF~?)%5JNCo&r#^5s+| zHIE;C_8PCV6AiqYE}1!s&qXrSl*`q1>C2(QnMgxRfZ|``4$0YvWc5-@-=}A8FzM&s zCIbi%&Gsl{R5S_!=e{pG)kMKBpml~=N`E3Ux#gXclch1T%P_wOAUC_Dt__{2Bz#%~ z9f5nXd@02N;X7G0?DQQ)g7j}lh}X0}=MG<~elTI)J9g#14ZzztwgIgrUO%^z`k6%CU;FAK1noDA`9L_b)x7)4r$_w}^$ z5@7N(8Y0IG9e0YFPtd0VLN|U5YG2hv&I7-{lkFm{u?gP@=i_wE-Lh9y`ivX5eum>; zBe;KmD=*&5Z4b5-^m3e@pZOdNasT^_O9d&F#w)*6rqDis`JM`6 zDrSr4ty_%Hq}@>fZnJJLX|qlo%j%~v=toS1g&RPCP`2@@j(50?DxY`{9lB6Y9Uzrh zaj``)mge?VHp)5G1`4Y9*Xn&ZoA5CA&PQGcd&p#zx~SAgbcf%@Bk0eOh?ZE~h|M6k zGTed^DZ}2C$FEP~pV)Uq!V%RdX`u3;=t+MW*uXgf-2b`SO=a3SY;vHD>|B@ZPCN}c zaUb5CpBq>nz`Nj89Pv zolFYGALE4-7ll`+P!Gr(gwW$Tr5FC4r6|#fnx2SaUgHQGmvpKs9@McG-hKs<5y!Z{ zS$_KG`%*Pof2`72q-Ad{{dSw%9~8MjA!$hFfB;R$6=^Rt4St?_4x%ee-H($MK`gP3 z7JZ!@NOm`;5{xvC;LaM4qj{be5gchMh9Q&fPEL*seOKy+RNnw&g-JQ%2^udWkf)MAa-QZ&Q?{ER;)PCh zjr?FPv5|>vUYlt}ta!pXM!bDAt!1b+|1M$`n0|0LM+WfwQ!L2Ngb(n`?_OKJ->TQL zc~kd$-a5?G@D%(Q))-DFI;u?_kVnGjW_Q*cHDU^Tb@brg)C0a-k-c+@^5)u<`MoG3 zX#}ND5x3)Utsh%+ce2{r@91oH^7RzsB0UNla@)o!ZYY#-1}!f6*W*`j?R$B=H*IeN zi^QL;qNeily+N)sTidsOIzUx>EB-yvzRY-^y!d3dJbNqRXfbdF>LBuu-|vk(1VukR zY#D)gfb6bO#eD?U43?f)zqz*gFd*}Lv;Xe?a8#=}YdG)BktO21(CgZ^WATz28hh~S zvU|$(>PjiA>bi63(p2B!yk260!Uj7A)~8=xz(UyG6vCCM^6J#!kG_gyL0O^g`C_(-4wwTQ4dy2I*G$!)94mDCZLUj>jpca4vXV>JV!D!_KSF^o4%1QVE?Y6 zYH3{Po-%zi{x)C9`EJzh$(HSL;E3{GIPdGs`LcUEcwmty-fg0`?+)q?T7kj?Ixe5X z=vLOQ7kJ4QufIimTbv)*XES*;bz5dkg=u|$m1`G7{02}qcKM>wT1Y`_QTxy$Wz-eN z%9s_b=&L8%vZrccC&{ZslQYxf2!*jEpGt-sFKQ+m5uZUs#VDr&joi{Le<^k8sIdiTt!z|1WC;?aP!$BxFA`veD&3ff zYEAeD*ay1iYsN_M)`2ijI)C*O@6@Dy+i|4vFE5yP18#$LaaBaxkDZrK$+O5@`XpB_ z2SGX=)B+6VT!^fF3O zs0i@&SN!+{lr_ut!ON#O%TqMT3fv*aUbyL5Ms_0-&a758JvU=&{~GWfLW!aSW*n}D%A<iV+)yi5exyD{S%KKm1K&l^ zH&`hPuA+LeK&k{;yD+b}I`#p>j6ZwcKI1c}%UDVZgNjP=mWR0_?Wn+)m7ec{8?T?8 zo`DB#+coMn$Z8G17nYH72xn&Wg*xkP3p+5PieofegP$YiTJYF_jsn|s%YmOwIUE;y z6$2$`Ru6yRCr~<_c1A3Ba-vgz2dv?2K&Ye_7?h~Y-Xr}2LmQr!Eyg+eY%cu~h-fDLq3lOd$V()25* zJVYw}HboYl{M~QL5`UMy^sr=Ho{m9wnHfvdM-T&S$)saCeP&B;8_}Jdg}%o6 z4x9%8E>yOpEg`_)EtUUbqGN5nq=Cll)bO7qY%{qNMwyw#Dc= zyF5GeHfymW5HUm{F&iIS`WQOOzENKnHXQ|nU22&KVFBg-6kilagS*&<4-0uf0E2H$ zJathL9#4v{kCpOGLDf%Y z7z#>1>R4|&S8uvfZ{}EUY9SuKb5s0;mxa=EqL}PEDp)tw`IWEl)w09E<~{L^5HdUL z*hW3B`Y1t_H1D5!e+k^iJQmG%lz?f!e(HS@xWRfZn(Zp31^(1SB6O4bXY46Sp?w_e z$yqCe3e&(+sk1i6P)bRbB=U~T8UOkID6Ir;X>d9_Dh%x9rv~2>25l6!b{MTL7_DC3 zyzx15y$B~-0(Z_GgJ;s6J3u6&{)Ug`GIL^17n)WqP|E8df`| z-cP4W8@&&eQ|Gze>0bx0ad+=iL-rm`pBJv}mZ|M)SqesteeAc?a<27f%c)-*U~jyF znq5EO%M^10lFFG+W^6_T(Bbj=ro=jni?=nhqQ>dZmZw<+B{6To8S@jSg~O09Nm;8roIuHg8*CCN8%Er ztl>W3m@-y5%|`pz)B57>uCn`<^2Bn=_C&YmRl7Z>t~!s-Tk5^Gxr|3e%@^F5M?F{0?cwW>;rIiu%yQN`*^@SI;whEVCR{gdr+s-NtuMF;0@u7onV} zh$OR4RmPisTK&Qj*m1tqY_;h^c{3XYs;M9Fq}=T&N8AtFJx1As=Q_1|CO@IV>>|UV z$(2bziODX7PFo=Og(+R$0gz1n=adz<_e;AW5TJalE|gVNK4V@6yBF- zuF1GWR5_!-IlsbUZIHP^(8>#{BHh4&md!YQtbh3O2Z0aV;q=F4!UuXJhBJ` zIFOk495BDMJdY9 z75Vn6ruqi{U7gdtqN-cM1Ix#tKVkEeASh53x>|*YA&OpnGy~1yZ9ZeOu!0Pw!kN*1 zPSZuNXLI!=axfP}$zN?tHX zY}$)AiMI3dzp6I$tso9wPp^YaEQp{-E*gfUk4H&l8ZKseDmAXl?NW^fuh~v^ah?RS z^RNfIexCc&4YwTTXX%JvfkQJJPO`ak1gjU@HMvV&2~rU9II`h&j*<`wjBt8O?J=s` zM5Xdt@cU!ym%T=u^I0#zUSXoi79L00KlP4y%H7MMvwpdD?|qthx9J^mChTS@JC{nQ zTB!kg>TNBPDL(q+(9fiuTVV%vMEA1MH{n$JEb=aDh}~uJW>gJ*ymGL}=Qc~O3Z7*N z9j~jS>Thzt5~GSb)u4o*P(FA`p|g+iNiEb{#A11uI54k&*u3ilTdH1!yi6{KEV3|B zNx7=uX*r!)A@j_gm~Vtu#UjI<03?un`e4GT)f>8il-m(QrOAjGXqLNLx!x?^ysBo* zaA%VDpBwj?9?g3 z2R>HEyBQy^54>A|_*@5L96bOv!5SWZ*Erp!@Zj}3?^Xa8t&aLzPnUP(pZ<*L&#Pb5 z7OiEwySu@hn{_U+!5ax&T+lPRwab4$@n1AV_>_W=2p*ko|%P*3XIo z`kMRT1l@r+B-G9cXwmwkY8`BQ;UB_diGr5XZs4&puL8gLkc4n+;MJOa$jDbmyc#Lx zeRUdWLM+{Yj?ySUua@W=Fk}#9q7a4e6HXB@`f}l6;%i5S1@>94U`X&-BkLU2jI^P{ zKyXq|0>%E0b*AT<>AZy4UJT7m6X%~HNtLtuWyG|#fsEZ^_tEeYrW#F(R#vl)LMxj*xVm%_p8Q14Np2%mkxyQA{9zPlk*H_MY1P zuXoDsi0G=GW$&N)7d)lb8U$%#h{RUhDd9Hd$&Hz=T*6y*(i%SxlUlH)xk);Jj)>Og zDYm?8=j+c|HpJJD<$t5v0aB&pu-j$h!!-v+so&{oA>}elYaI~OYyRE~mkwICg5cf! zI|zINu-%ua>Fw9aOWuWOg{DaXi1<@Rm{?Ov4?f#;mD zbqSx&NDi(|rf>pCR4Dqd>G-sAw$c3<`@FXG`6RgAl{jW33sSOD5HhVmxl9%=S!S$F zawHLK`CEeKu(3Z7Fute?b=la(kS(ci5#Q|ICF-AU_)XfWOw!>OX}Sgk)T!Bq%(3Ew zCPbb4}%dL?4C^JrSx)rH@ZfdQLANEz&4l|4a)@PNB z6FeR(Y_rs&k2ys-8kTb0STU&ZnxLmHA)rZPt(Zcss^dVs1G3 z?>Ii7S5PrDLKZQ5pAm738eXH#-=ei|x$Cw>eZM++js$o}+aj-Wq>Y`#Tty&@rIr7_#1k*(HI#CAyI zOokE}Z9mNhTQG#Y?Xb50)I&#%224S(b5crHh^W^)p;wLp=d5xuc{Jv03~#^}M;*+N zdp-o@U?lKif#nR_Qq;~E_&Kr01Mn|A-U~FuIWlR&$vMs$!|tN2SG(i<9$!a><;#vh z(v&m=pe8doj0lu81VwWUbefR$L&oIX6sSRlK)?VTSdua`{~ z+aJ$;9n1?#2sv}#7JW%lr7nZDu3ypCQXrDPC(xPYISl{LZJ7cU@Yt{JtCm+;9x9(mPv6?%zwaa!%M6Brl^XN$EAX!$?j zNHru{%D9FwGIRI+Jc-*x`-dyIgG zIKwIg-$gj$jl@&ip&6+fpXMw_B)PIjG`PA(V8i{)^%Pwpf&H-(N+tZxZzP7s_ZR;+ zOzgjQDro{wf*uBJ?$^8&AtgU)90;`v#^Uo z8cUk(e8dJosQKGco?a`( zaxa`P+fp1M0NIWl1(s`{v3M~R95t4V%L8e|@JT4kJrV~f27aOzsMMIo2uiemP}UHE z1O|@t16E=WeSo_-9*qhQK|3f3#Cvub#^DJFY2F_Oj#I*$CxZhVlP#BebP=*vH;}G6EFvK5{5>cSf zGw={ZNpujHczXPUHC{JqQM4Dg-SOZhr;w(t#D_hIcq%~=B5Rfq2IeM`4Gn%!I?_;z z4&k;MW&nh`H&e9`M@UXmSx(0LAb6APw+u3UxXe%=do6n83$eHgoGz;5xF#4Rm3%=A zxf!-UF)dze;(R<>J{w71QL;}VvUXxdg0uudd|@V#k9>|pvf311`VS|dZdC>bPuCbs zD%Au=pN6GoE;w+%FkktS-?Mf^zFXlwm_U}&tYHLc!a7-li0d)|XsWQr_Jo3+{&7I) zlZ2dk2o5C+X=MXb2Hr6{%-+x7=t_7MYhi&nY&sJ)X5oIbE1dOD$;-^osx^6fnqpi3 z)ouyQI0LezDp**!X=AUMX{(>us$$9BU=;7;JZHIzgna@(Opw1l{-lO2qMJjRh&Tn9 zO0(9pHmP4r*dkgB>yx|4@3Wlr;bQ9cj#7HMc_{B;&I?&jdr8l;XOxh{x0fa3*YQ@F zu+veVU^g_d6Ro_ikk-r_d5x8KmPLNpOcw*i`(ppVZ0cM<9EVulbg=D;m+ujGDs)jT zq?Uym!0tv~e1km3B_cEbh<~Rvy8eEl@{+dDm6l-n9Wz42*@UiJ1X^w!BW2{!!l^D@ za=6}XjWCmer&%*cTXgFBK3Yo`=u$BZ!?vy!e+Ar>ACND4b>baUxfr;*YLq9?Mcf2x z!_Cy|=^*g{gH>1513jSI>=v+$NQ+uK)O3Cz=HH2I6gbb5BNLKehR=f>tn2^0Svwrq zfRAW}GT7lKISYOjM>+iHFz<~Kk$eu%C+O*B#(-^);!vE03^%N)aQ4g^NJM*jn^WqS zzpJ2pZMBT4X}I@|4~2 ztDVXSQ*lH+>6s{xyM<#&yY0_47Aoa0=x_Yhc3r9NNZo3>j@1M564lsTyL$XH98n1J ziLOsQqW#s#9(ZyC1KTzlg$r+{ct;B6)Y^9sn~X-M3scUwbLO;@oZ%M2rGNo2?z1A_ zEqRJ0#5|*YaGE7aoYaBpR|9|lc8uPCSo1Je@D(jEHX~c4De^3U_;MX1gCO2Eb`lGlB;V!CMx>ZKdKYP(BKU0AKie^-YL#CN3o_$<^i@z)> z8u}RTHy)2^^Hgtpml1Qnmj}!-U#!7Ju#n>+@N4J%fD%?%)08U;m7Nj!)Ajv5ifUGe z6w$Cu+0>^u0fUQR>ain+iWLc=+Aj1bEB1JM)n=&}x>Qz~j;7MawDH(MtTd5Q+^VQk zo_idbe5|!G0*<3;b30CPnxFy_dlRu$b+vUl$S1v26|Ne`tre+E7#A2Of|a99afs#B z3SOt>rsf-SXl?;0NJJ4&a({LrmE2I=p=DG?hj$If5AHv5YVtvNeY(=g&|6OE7c}xq zvgPBN$;=;P`i72p1QLn9^kTYA`EP(K+gL$=3G6|VWR%-e3!`xEi7O}iKx2E#%u%EC z@F^pqX6+-@zWZ$8r2spxc#(v^5OsIgzx~Fr2>0T*d5OuCb*Z$&7hQy})s>m96{TW_ ztvGb^f7c_0^oy0;8eR)mBbLEEbO)CxCyfYAqwc>WACg;JY!#2QRF$aVOP88wbwm%4 z$uoT@LTw8^-q3V4sQiFKe2(gnO#9|BHwOs zu+CfXmmy$g&#u<-5=0D|tz{?}FfnzSLSpV}2^_}nlO29miwGDdua;LKAeGk{PWu+^}a+eq?#%$U*y!85Kv`Q1LtMy|jF_Q0fsn%FKk=(94t4u_(~ z81qKEx06O}k9icc2pLE!+xAb=5IjPI#N&J+$|=32DS*%XoqZ3NcF)p&lE5=ee9of1 z+{%y-JkYzgIw|jYPe6&9)Dlr7K8t=c`s_(yHrt)ZfN-dzYTETAft2aTm^zBOAK~dz zXmHBxr{Qk*E*aR>A7MwHhhoZGN^9KX8(0RRIb7EP) zoZ3d7D8eAJSz1#fPHr7%gNuzIZrd{@;b&REa-8|pX#BG}c-wu}8@CL1crjHSi-b+P z7npqd6Ox{rR69CY7c*xrgQDcwiIbrho^{;YBk0+9cG?=>sCgv84r^QsfH4Htna- zCA0Ae_14oBBNOV@3f4}k1%vy8v{Pe5S# z8EvC>^=Ol@1`L%5X8TDv$8Hgz%Yvc{f?#w{GA=9s^#G5nQ-f2(^1UyLT-aUH3%><1 z1Bu~h=?DVHI_#K&6lznB02VQQ5k*YsFj?EPwm5&@zk^x2-s{UPXqBz_M!t0PvLOPM zUvK&YB$!eFhimkFp1AeOoRGWZ1n@g+2WE1xhTfD8z5Eu;=)i8H9DuoIW=?Bwx?Q*8 zi^HVTUfMz>rA@?}AqhU_C$8Q#2JR%bBdJKQR5*D1w*{G6 zGnvV-)kQ$2JUQUoqi)Rn0NxSMED`$bxb^Gh2hyhGu7diE5;l;j-ps7QKP7e<*R0{I z?owScOswMK*P~9XQMupxc_%1n_6anwbeN*6*E=UR&}7cDu5o=YHd zEwBWpKpZTgMtq?MYqHQVpr4K3@K*Byt)!o>VMnc5hCr|1 zpl3=68eV#f{(KG_gJ+roxMq)#gEwWp-x@HclL9FXk=YGV_;Vj#3|Ug3YeFI`2cMei z2CHdW`XkRw2IdsIz!+qyK({Z*KHbEY-PD#O)f5aZiR@#q;tKuO zJW;=8To}7@R@F`2P2>f!X7I|`Io+F3y_?`4!l=GKu09uXfkZw0zerxZd;M7RYNo-u zn!~Rbc^k2#$DO=_06T_Cu{*obtUYlL7vhAIjC>z&UoU431-Z!gw7k=lk5&3$Rt6{5 zG)~FXPNq2NtJpCu71xJG)b$NLA3aozyVud^(=VxncX95{pd(s(W-3ECL ziaIJ2u$%{<39K!N$oKi-=4Oqu>n&~_P57SMq1xz8)__hTj}!uRN_^PkE=l3vTfMzF zf*)kZebjaQP_&%QzfZHaARa_SD~=1kCi_<+BFC`;&oRw7BY}(GB3m_J#Od&MdK6W# z(lQwJWN)Jajql{hh^sh7H`)Wk=z}By-D9W@9Nv*(+Rn<(X1JkS=9(W#B0<|2<2I)i z@CyXUo%(bm$2JrUx;)`M^6*7e7a+meYx#m0ig(+&ZbfSFgAvd7^*aGgsWV<}@cNGE&=o z)QNm_-j$Y~hhmWYA^-GR?s)0K0bsj{TsYR9Nxix&3uP4&;)6}tLD-EWrNQ1$1h+x< zyT;YVhP5RQ?MPR~mwQmTE${}JDZjD;%i0yn^Jp#QD?BC|-vEsnTUJ{%oO-50cbHIv zVBmffHx-NPTV-2}GrE*2+mQ{J{OOOhzwJF(J;o5yB9>b4Qc>!EG8hysU&~)DM{KZ` z(Fq7KCax#-XjBx2Zb@y?0<xO1W}>D`2nPrphEPokDvI?Ux#ifK)F=enk(94Jzj;DZX3>b znYToXh<7g8lSM0>F6QXJh@^)ZvFGh%JF9cg<_3|@PVvk{1J(HXSIy>sZ59W;r*-V# zhq+3~BMS=((Z_bRDOFvB9t8Pm!-5W=u$ppR1!G>%aM8Y1FGq-ob~fXIuA&e2rJpY@ zhn^;y>|St1KTej+^ip#b&I+DB3m+@*M=0iR`uZ%BW8@7!WSkzEtgenuJ|6V+W6V#? zR(>}2ODx@Ww$f)%;CbMlAF$TcUEdokn;tBj9GR-h%kP+43>AK8BQVK}!!x_ULoWlb`;vLC)X)0jtaXc<&|P&M_$$Dd`l!C zN)Ef!2cj-FxOhX1;tcfwQ;^Q>xfD~Gd55<3dsZCT>PKqAOpcT%_cU9qwi~tY2LUSu zo&uR1xH%QCGnk6rSt+WU(RdiDJEII&RMl}u;#%rE*tL!C5mz?A(cA{7f7$7q8*z>< z(jUx1M1P!ea&u0SwD?a}8TksG5$W}(hvkG*h&H+NpfZgFor-rboV^p}kj-Ic{$=(K z;*M90S_qOZp!JY-Qc_B0LvC9OWJbF|r%Jeo_)5^<#7BSazr##Y4wclmXI+dcaaXo& zD75dCe~Mk3l=8&<9Ilv}mz(FhO0`c!wdqNHH`9L4R&VY2C4p7R`$rztE*z`CXGJVj zu?s&T_!m50zk3F_8y|kl-_gqWwcN%PRaiwXS zf)f50{Y*hq!C2Xnt{8q`v%@h-SUJ1660`kpI*yf8wpwb*Bo*1%(Qt16O)uptuJ6GM*R%JfWxdO0 zw$#+h+^vM&zTJCm=KEQzk%TT3ZLMsuvb80c?Wbj$K}7q>p;Ec{x`^%n_S1e1zEaNZ z z7Srrb#`~*fEWbjK2-0yRJiju>m^z-Ha(rgACMIp!*d`{cp1WA|Bul3c2Nw|-Zv1T&(%t(RJx7~HWIKRH$d@60vvAy&LGG)_(7VJx0+CLG z2OJ?{`&mu{(Pt5<_AnlLt+>D~{>)5io4lXw^6g*~dBx>o|2{UtGv7m<>_e!Xxa2x~ zZ3DT*xrk_q(2GQjtfHM}LQ4Io0Q&IZ8@Sss6_rK+M#nRLoZY#CN9n^&LU1V4G&E zX(`@Fs*PF|t}aHGk2x2qIEWe*4>(o-By_-c_IU*q8@0>;O=#ObUr`srH-@!k3;sUQ z7T5bkjj$i*=!BQ;Z?`p#xBC3DIV$(r(~t!`2c)D^Zccc))L@`B85=uOvOMzgvV4-T zywk8eGu6GY)IBgL)ljNm)PektQWY;JRZA$BY)bfgE)Mzzgf|N}#w1T(FC7lsAJpg*fvg_?%1}SOy7U*otK%asa>^e?e*>2 zFW<}B$o_yTeuSzA5`(j`Cj}8>K(KLeCl$O<1DEs++}1d;{h#W#^-l0GhPnEt&OvPz zYYMAPD`O}2R3{J&EZE3u*c{PDQR9=5)M_+0?Mk)MmB9V0#a%WgfA49Ftu0k!v&5?xL3za*A zIm`+oh=O->Cx>k{`P-(HOCG#Jy(4bzFP%vqUZP_4*CCHROyzArk&#j9(|5p_^&8Kb zt7%4bQ;WC@M(h#QRY1`kWDXOVEc^1?A`m%8N))XW($H$|cz^3N(DS?{u{3J?kz{hk zxP1|Y9-3Z?!-)YW+<%Qq2_uKLSI15I8@;{8BA(|TCm!f50eS|NRAy}klT2xX$F=*8 ztaZtG|S&?F02{GelPEC z&PGZNuQJh>W$7`9LE`>RzHa{}(})+Lz-Q!!khs{#V?xohcglSc%dJTMx0LO)`iq-) zv!NN0TN0&aeuGm6%2`;gyL+O=r59ygs{zgJTsYP%$A*gKX-T$7IknSfukC@?fO6^1kNtA{RpaXF!50EDu z`OahJ>C%R1ALgvrbF-5EE(<63q$V#J4J#%iQ+*vKMRzrzohKumKN=-_`NE0s>k7G%uGvdW85@d= zm68f4`=QVM3uYkk1g3x&b^r(@1S4^1jR}rW7S`b%P0ac`aAhV(`cpz1Ac4o60PCG) z)!I!Ph>B-1sK^+#raqurnEYPoS1pn~hM+5`2{T5~->$lh-e6qdsmDLWh-?U*pZ|8e z+Qv3pvTEwIH+!+^VyfTy4eX_D-R++7lt24YD(9i5;WzTnX#%Cku?=8N!p|as0%U0L zf);=0IRrMb@*N02E8q2NFoHtc<5=hQ1K3?@&SU{|?#R!N^r3Ag^dO!c#Kh|YZpOFW zXGcTg$S?@ck%vx_L6{t~_;zMbi8G$^y=wO66iiGyMtL)DP z1{5j69MT?mtw!c$8rz}La+Yh!vuJxv;fR=THrwn{m>k!Ai!Akn`Ect!ydKCN3s=g= zcpxGsABAa}Dasr%IREF$xSI>I&1G{vTiIt#1-_H%0kltbyJ27eRUiC^$BDA+fW1%M z%%!ZdhrjxpN7`KRv^G795&M{&ILic)hWkoU72^Yyx@R4*aF`Fq%byo{WXByV-$lnYCoM!~TpXlSR-5dX zQGTQ4;lI6F2g*PsNsD*6FOHvmx3Ff;wi&lbX5$=)oJ8p8H1%$_Mdto)ps~v`=wY4r zT@P!C@VwnT^+6lK*zLksd^zB~7WOX67FkHP) zM)2E3SLs{=IhO33=_{G7bzY8+E?PYnH9=+d6Wn@4dyhab!Zdyrx-~ke&QIgpL-lm- zuY^B8ctBYU;{-96**pbPp-cp@xadI{?a4OCKW552=IE=27f(p{?p~H`dF`;&Z>lP% zER!alx+XF$45p)3s$n;Dcy0`YW>~jagGI7RX>)>VB8`$)OjWd6hxt2cEr)MGD0O$1 z9D1Aq6A{45$C_!n)OS-+ zjjW(kUb?!wABK!Gesx+nOfkGfM;KN@Lhkx0e|5vhO@!HU50kKp4LV~31q=~)reae) zc^-m6ldjFn2gAd|VNL`a(>NMx)rURm8|T9o_5(oO~)@rGoIy1LWHSe~vfJS%91EkD+8%(mXGKk1^9vd1?H!Fx*v<*L5LUlcc!wJ*OGFATA=ZIF^!|15<7GUl+sYb-BI1UoZD5Tq2@_m z+Co?5)q7X-yUUrm_EW;!UvKxQkPR^!cybytb6D|U&(&CK+&(sQr$cQTzCf z=4;aC=6aFHFhX02(#aC#}#pr>Vb`U9=nqL|g z?nXU$pEJuOWzU1r3Xu+;u7J4+IFLA&59e(okf=dtGq1Z&DL14zW6;&>B+plEIIfmo z15C6-z%B{t>T_B+onl>s5?(jx+^Cpjg5mMYRHRKwvmASad+@oSS9{x8AJpS=c1G58)ukT3ZxeVvUT7Z zyrv#G4aU@!T`5GSiv+4M2a_51(&Kzcz}ni_tU00Ee^^}fhe&|r)M+D-J^P|Cz4FXG zEmQn)q@BNC3PLfP{n;`jnwQRZ-8)Gv^*k}ADlw&X5Lll#uAWpAE=fNUqo@H(i!;pb zz0FviwADxxTs}rs>rnS41_qRC7lZ64Y+irj*%)y5xjOI%Hl^VerlTmpW1_&7UF zmbOCbVaq=n2J~fjKoU_C`IA0s;}E2xwsAWWDdy;T{=>shC)wPa{;O{A`0wK&daG9NX9#_6Y zM!f*~)k!$-I}1J0f|VuS#`k3-rEM=g2%RT|_;FYC2`IF>3Gftg)Fner!~%dc@kD4x zbN8I{C`vuYXASko9c5LFE!H=Gv=b>%L+N-HNfWLE7plu%&cNl1!`#oaE~vJ>K918& zlObtKGs?UI;HM2)oxIrEQPTk|Q=<+hoUttK*^*f>GRC0l)otKyKbO-)? zW(%QIMnLiChhjjUIiwG>_s`BaL|3A~r2Y3O=S(b$u6>`54$_zEai{1mMz2ihY4l0;=gOc){R&B1hHSr+@$D*d!bXo~B{-f4_Hl;>Nlv~NFAA%X- z2b-zG2Al{2fD`&p>>HuH4I?Rcbp2#C#FbWa61L9+%qbizAU7pyp`Lq_aaxNn9*y4d zt7U{f@F`m(@0Uf+QC_r+?;a^c!1pbGHS

LN^WKL;&glavr;BY|bW};O!>sxhXa&VJ!uIk09B#$- zPRqIIaD07gK-VPuoO1hx3E(<)gr;nP>)N@*! zKpWk9pn1I6FPQ8$g5LuZg!9WJ1q5?5tWt&x%T-THqI*!&y7YX!%-rtE6^{K*nGc-C z8b3IXZ=77oSV@s*o@_FXlOfSDS6yH#4IWV{wJ@G%CJ;!<#jC+()TYV!HT8{0C7LH> zHI*lRfCa~8hOLfWTsR?8UIbX)l=v<2+mWtlu|yH-;cTg-+~!0Sr@SOddW$?<6|QhH zy7f9+NkxD#-v9s_NoTZtgP5JonuT{5kuY)FwY)Gp3wQf_lNIrRXl@X!(oq|c^7wWb zB(Z#8B&^&_$uCly4Y8-gH&O03QJOq%iqX?$h;<*t$ zKHr3n%rM2#dJLZ0fITVjd%rETgcw3J)L?cfI)r;gK_i$&X5jo@Y#(MMvu?PYxBf51 z44k&_P!)O#`9JCeKv;L!uko2bPE)MYQI0wJ&&W3Uc$v3N?roI4ZMwvm;d97b2Irw{ z)hFP5P-<2k&0!;xMSlaS=Snfji3BL-MCJkw;HBNePxGS!qg4~A#XRPvVcC(7RZ2L_ zrO1v{MTc@++(_1k&7vUVo`<^Z1g9CeH}56#s|!AfbH?DF3Cu6`{Vjb2$sZf-b5lI9GQcFmUrr;zGTq8O%K^i zYo^E1+*h#at|oPUP>#16hUI~nmxx={4T?YzmdtT0YpaXDvlI_`Skai*{!zKAuHsDO z)Ku6e+^*GIa4P^<6aQqR0^Bg=C@;tDd!t-#eLMEsriDHTs2Z+qck0@#5|R7Eq_Gt+ zcj3TsPwf;zmj{h^a)0Lt)(x>etrg!jszv%&FEuB58c)F8oqc@MUk8WYH^~Sy>HJ5t zZL~&X&`n`<(z(O$ik64!zX>*ST821xtY0-9rdLpm+<#etL`y4>;I{nZ`qothb(&cF zU1d>0nM1A8Vb~5NYog6zjtC3bEe!g4O+y_ig?colDWru z^-M*u1`5*+3ple3y2c!u$n(%6pAs~7Zt&7&1siEpB{uL+fcL@ zMKzSM#(kfv`1hMm?IjuH@NqVpZ+#)8SHf=cV4Ve@tp>?2Tk(0lpg&q^KLmvGbAu0| z+1#WcpMvRb)kerzp?OJ3uXrdexTX2~%m&G&fP=PNbLXsIU1MdCjkKKKPkDT~Y3ZQ6 z*j2pLaV0@6#h`jNRu$jV9tvLChaQm; zs6_bGrY-BEsL1R$zUVt)hsz|_L*7LBWU|3taF{@exiHyR9JXU?Pp%-jupT&Y?WK5C zri*znY@t?DI(bn@W3}X}Gd+1YslH3bvt5qEY`}@=EonkqjJs#Etpj+<_=#w(W97frAMN+$ED&QQKcFOGhD7`1*1|rFM-%?LPV)RHp4t zj*qpY-42lAyC;l&@aJ!wl<2X)U12w>J3Fn^KU8S%;AYOIG{W3;L5VowDb@av>64f? zfECDQ3A}X`S|9e@*cYD5@-TFYR$yD>JX*pIx8GcpxM|PkN{h%Q!zwe^P&y$1#?K4z zOn_yD(=-<0+m8rN9HqS!mZxP^zD90p9BylpQ9BmY4u!c`x8YbKX2Xsyo)Jn7s30!K zj}_G%A-}o=NkNvdO9WF%vpRJCc>T>jY@AuRW9l|GgSMHPERYx!jc-9l6y{F$bzKMi zirBe(^u7t~b89xB2YG6!J!8B9E4eFnD8v1is$=!J8|yNWul<|XwG?PV%T=x{LJB;* zY;)ABC{M0K8{(HeZ1AG2*B^Plg{n=Be1@_P6$(Wif8)u{hvQH$3U&1g7Ea+=*!sj0Ml&Z{02il*89uo>dLk zq$$vlvUcMvSc0)=s`yzWX-db?GXKAwR$~gbo(+q;X-8F#I!TABXUVDTMoKB2gH}iF zy}?S%#mpW_k_uT9yh){ zf}4zYOSIt-yitm7@igAVh4wk$QX*3`qmR(NCHSN|O}>)IQH#1Zu+k&=DTy)bUQasbfutD$1+q z{xZIb*5l{CK#2D)U5C^cOpIF}75%xNh>RX%B4Ni^Myp_l{IYC<={L-KO(vxfX9@#` z^?A7g`6<{AYPYNx^z-a}k`qGKB`}1UTI>wy@zCbm-}U@!NUCVWOrJ0`(uPl&M(=(I z=JkB$hkfQ}|C6VsU-YLhkA=MMLh#7(5(|Y^tH2=}pj#TbMP=C_Y^;tp)AJQ*K9^jk z%7+G5mG)=Sv`7;ohHYKJwamAg(J<1t{MpzERcZi^D6e8?EhfI&(cUqF7_Qb_gdM*a zTDT9bcT=>y9vPOkwH}-$jjZ(Cd2tU0!}1S~um>Z0WP+ZF1kDE@!nQEb-y84h*^5Z0 zAFn*tK&BZbLr%5GLzX*f@v`OlaIMLbRx|o6l48=T#hY2)l&JWfA0nEPn{@5IorDfF zkAZN$XENNO$w`|jQr#)M-6`rD8B!Z5#M6rG3}mu*9-0pY?F*i6Yc=Z?0o!rBs~B1H zF_m&sm5c-x9q#67z|@UpzLksaqzy@)6^DT&;D%;9Oc|90FCKKt^}1}dB9xM^he^R~ z!wvl1eJhN{%_wK@@32Q^+$IrnWK8p@&~BnIUVNw(t6Km0yFc_As zz!=1E@VpQSnyylDC)$ffn2`C^sN(5Q=Ge$s8w-s@iNbjOP$CE@tKXZsPS2%NX>d4y z85$llV1*^BzY_uINKsO;{e({l*aAnJ3daN#eG>?aG>CKI(FC#`Vb%Ia@`>W2g@dJ5 zN8%C>jr}8*w!qd11Moe9Y!6O%U420@z~Rzob!?6ZwWK8pwY1?fQoS?_Pud!sejX+k zM(d={!IzMI=*P@b@t}$f^MkNPVy+>Ega3=++8h99R3SAncBj$aBvbc6aN?D=Z9yKw{Wy_w8aa!j_516StZqVuf%7L2)F+z_Ui^#ciQSthCJf|D= zN;E8Ltv@!wu%Wz>H+ZW(X!vWOXV6oc-yTBoT=Td4-3;1I42AxREOX&(@5)V(mW8V^ z7p1b{mx=lbTb49wdrOfnwZN>{xb0ryDEBb02{gZk3%k$ z<91PE+iaV~r&h7K7<0muc6Cm}#&3>2xUxc?NV?1V2-E%SCpazc{PK8zM~g=|#1YkaYQo%Zx4Mc7>SG;Et@-{_fUa+H^UEg=%9Iul9hd4D`VpGp;XUS0gt zvE)(fFQ@i)WTRFSPUyL@xJOJ!`;c>T<^Ms4wts(r?<6i9wM*!^b&S(?aWnN60kS6N zxr;EY2y4MfOAK`V>y}T8| z|BHRj=ejTqY4!eovi|5VViMz7v_)xl@`2!+R{z;>rL|EdMn|AKVO?{jX|ZrRhFw%@ zfZx7SI36MU=R;-i*n5Lr7B-Ju2AgI4!()(u?N_^23p9CTj^*U`h2Q5+${*7|(7H*R@K&r`zehQLmz9 z!NAFmbu3~tmbkwi^j5HBsL$1XX}H>o4U@MOAUI4>N|Nt)NhfNlE#!Ydk%rAXJ+YsY zH?%$Bq}!~^OR&LJLT=(R1T;OFVWY!QuzR&QNR5NCHk&f>B@IyZ!aYzrMm~So zUYp74-;`;x#!5%E+lfRZRZA^(l*c(SYRx&`;|4K_~;XIG%VRALD$yjEC-=w>hS!gss$vRM72FKHP zBibza;^?-qyi5=x@|&s!891~VVW(T!z}4Yi!|rWVS#Za2rM_|U?cfqTyXmBd)tS6@ z_lQ;@tlQn>we-SJ@c5LF+lZ7blN@$qdV|ALLsB(8ucOn6_HM0Z{R$ccyLmaW2#?LN z4A7lZs@nXyLB_PI4P|76;`JzbG`afjrA@Z&dvv^fzv=WP@uQO=6c~vf4O8&@DVE-Y z%*MG;j~PPyrHnI-QDg_3IufpVlOa`@K=UH?CXfzG82pfm$i52JJTr`5-WwlW8Uv5@ ze5ae9D&wvpv{;IC1$34$bxsC%4&SLgB6iD7Dia;yt{3>J)AwnH;tcz1g_FGEXQ(jz zgCli~&xj6UI(~p2C-5m(#=AVoz4p|ox#wp7X}jDOhV7b)s4O^mb>mMyPTZ4lM4fZ& zv_m>yVE=KLu7@v%ql-{E&n3)sm`%Tv&3VY44cLUY#%W~?@+@a(yw_YNSBY_Bat z^b6B_MyY|}RlWsk%^!MDlw<9W9Pt4f&X~&A^GffN5{!m#(F#6&hWYXFCr4~e&l8=K4YY_$oNUsDN<%?1bk;5n}oB^BR7=wt*YQX0-278oBp}?$ONZQ4x3CRdudQs z13S#++EV+0F)Fb*J?C15lbz?i@^;zcyLMm>zkR`rl!uvqBGgx|=&^~<3{{3%C+V7H z*!Zz~KCp3+0hW_GYy!HZc4mM@5{J2DZR!y4INgs>LX(R~Q@t)1)YS2PqDODRZXzK; zsD#C{)XL_k?bXzD@<21cn9JhQ?;v;!apC;21uGhuNpDO9$SXe`P7O072$ati_KS~X z@GlQ0Aq2s|ewAh?el8AFj6cjH$iz7ccnFR^Yk;teF%ku9pgZ+zcq=cu<7&OF!Cq@2 zcL5k&j*tuEE4g~dAM_Ee_YK(~MeC^wpXWO=0?7a!G_cbgZ)EV>=14->kbq9bii`x{E3RJez3 z9OwcM5P4r$ctJHymnI?YA6(;@8zIjn!I0e>ifPz0c4e1!baE1q#B`qBbGfx+6CTrg z?PlD5cm~Q_g1?+kKY`*g8bu18_hyUfxoxrh3e)dX!i!!*m|Va&yq?F&MheX?9av{+c7SN{d+1a!Y3{d-{&_xX1~lq=q5V zz`(wK!eBlnNRe&PExr8mryaWmAFybJ*OgQyrh%8Wm9V<$t169!jDp)cZY8K)BA`NA zYsaXJ*Tx)4OrNKjO~+^&@!vQ|qCNTX>UOZ+{rUIrF?+PRTcSG-27zcdGGKaAR-+D@ z1?+-V&z}PUy*Z@zX62^N2)|4s;l^Y_N^f5}-5jtd1LU=87ed{X8ytB8T5M-? z4Zs#yf2e6F?DWnE+m&33=5_XURIo(t2OJS*kbz zM^+I|`$|MH!>m@~@z?@E-v%Sph%yxX+cuTQ$+(xpmBIbxPzZ)3v z3_x(umdv=DpUJ~)O}g7Nljo(J}Ghiog)QPnJfnZ7N>_J`*NX+ zC13S)t^99?gSG3<#}3Y(vu>?fC!>Nzw^{F~0p;eU9<@(s%iP zC*{B|>MhpX?LW#1;V$-)zt!{XU5!E2yK$yC5cJu27Fc zEM+FJM#wxsDhdK?pn<9D<<}OuuU-58{&xt%PCh2_!Qrk*qr!IS6>fR`*nUh-%{q)u z`x%UFpawrbZHo%7zXd3+zWv+Nn`&=J&EDH58VTy!WHHl>&Et~ z&{Ke0eIds>(fB^a9ua~k7}=0$RN_!`Nk3G=w?;}gzboab2DtqbD%}IQFSo%nbX0xn zyo@jYyzcwm=`EDwL3_3~$#*-z3i%j68zx?Tb^>|ETX^F~8KjbLZ964D1T;KK2Fp9; zH8teZZ$$N9u*G#>b&L*gafA`q{c9DfG})Qn*(;M11dlcHtD_zr*#GwaD$LEagE)&Ob+;hNiu!GZat$1c)+JP z0&rTrxB#{AY2dH`j8<+@zykoBnYEQk9Do3krj7cKQ;-5cLVz=~r}gOpFk7u;0WRQa z?YRFQ&g20Z;NZ-hiD($D8A<>w@U(vNe{{bJfa_mAck8P$5gs z1RR`&x%FS62=Fu$u7An8h5#rCa2D296BEEDM4F@_06A^P8{iGa$;QRZl4ke=K=|J< z=m#JboP|A2!~%f-jfWMUNz%sE&7Jt)GU5O9MeJPc%>R9%W#_h_-SUxZR1ja>QGFM% zVQNVW0C!IcR|Ho;5i7ye`0l;#Y5dGNX*TS+wP56|fEr%R+D${F3Xt81Lulxmpe z--((fouhPNy?I`YN+5BeMRSi#kls-q!myFp6)kL&3H=o{FNiim9{vVV;4G)>_aw8u zNOtOM>jVT}^|`Nb(Sp&}UT;a2ovo3Q0w<6GRfIw}E+R>)jS#@nVb~DoGLt4M7RHH0 zp&Tz!N1{hKNBugUg3Iof<5x;n<#(ahQXbvu#75OD3~ssYdlAQT#6Yk>40px0iaeAr ztQM6}*IX83h2!|%&CZA~6NlhbK!A)@OlII*fCw}n_7)K%KEs%1*np2p%}v;kYKdkH zY@+Z7Ye6G46A^~Masf~?AOT$DVcmB~NdLfqf8(K1!DHp2B1S=d;1@=8!eD~n6*nR* zm4?*yDVsG36o5da%-2nrRfEie#E>(lWcmmq*K>)>91!KL9m8idOq@=R(IjtX0e>PV zjRrzenZc`r6(^uQLDfr-l^csomveTgz(8U`21ln-Lta?p(r`3UnOaw%%W-FIqsvjc zD(k{y$(W(zjgOhQD&j0M@v7>NLy(*dL_pSH-o)*fr2c{o`CzDxtQe8h+?fz7leT0) z+>nq%0^g=ZH3Q@pyEJj!3J230Q%h4)r~nsv{I9Qf0KVB>Vn^xhR&c&=qe3G18M~II zO|ns0dn?xWpW9c!Ep0r>KcG@TXm4xoas@h>7^KUf+8wc4W z+p>-UQNw061Np7R>PTnRxU%uV2sl2Hc*xRWNh)TNo3a+O#G1)*U3$G?9Sd00iB=ItVOmj;`DG%)I3Qo$ih1=qFtI;wEhqv{cML za|O(1R>=JN-My7$AA{l=SUu{&$1+6Ki++3qe^E=k-B!Nv^W>07JC|Vj9E&3q{0UKC z^w~r`dY;`a=&Lvya(3db`h{X9k$cpdq@r^`V^C_rVII;T)CrK4w~qb62t+11eUdqo z$S%N^M+VcDPN9X3iLy?9uYyCc%8@LKZYQd5qOV_?9jN*kz6eS7Ff1FSr5hRSl8u=w z$4!&SISj!&`$PF0uwg~SI$mPgo4U|tS=6;vMTOU#_4wLo!;9zl?DD?j!Tw^B9ZP~_ z0AKSdWLvy*PeaeFU#b}v224a$7vpZ|l?`c#)^0`v)BH-$&*sxah?6cIEg9%c#~1BKv7w$qr5=FdyxNI#=ixImKKCV~v5FVjMl5;v`G+C+V%f6rak_FxelX1>7i zs^tVIpn}YNPKNJA*QHpNKf#WYRy1;!B|H~=&I(QHT@l}133qB>Bi#rBpM>~V$Tf$z zX{2$q2?R>$XpSD4fOMR{>eW?*5hJQ;M9@edU{NS2O|G~4kNT;nU+Gu}b*PnosV6=VJ_KnP#pH4vox{3Cm3LKRZ!3K3iQm-SuVUF2Sx;EUI%O&lh%jbzLp+^pTu=XmZ?81wA3CVL+2aAe`_q2}L0RdG4uG_AaagTgcDo7VWVI)l910?e7!yzapIc zba!MDo>!VEf7%d~9K-);mQzSxXca@XFu@qF_#KreO%7x@QjRI5bv{(#Vw&5uq35d4 z9c~Vzy{6_J;w+BWGDoW`my(yL9JEnyqc~-FG$w!8HeamLa9WV@sr=)|sks`4r;u~W z;U9fv3JWEl+47{i5Wpx`zOzZeq7^>2?&0Y8OrF}BH`(oB$FOx`tJG;I-if4;Hks;O zUxCKT5(i9D{q?wgx{?Sry`;PKcNS6Vin( zNIFY}3t1+X1=D0DOwML<;7ha~p^K970t7`do@K&~%Cj>*b2Q<3>ZF4V=16h({{ ztal13vRjS2SMhrmZ(?V!FG0?UX>-TixL)a3gaYDC_r6w$`2Gp-q#^ytuEoA{*_5LP zNOW-gkP8X7e@f~s;cAyETSH$>FY@gA=<3w{NNPH&InFL0R{G*W==I;>gYPATTD2#)QC2y8tZusub?6Xq~4>({7LsuBD0Q|QDDjmEjzu|{%T)JTM1Ca z1m#(@0l!fa?4*sd7T3V7F!>%p#?(@?0*o{Y=yeFNi_59{(l`gJ_mYV2_kWIRZ5I?f!bG znRS+b9}{@Z7cv)AUiLdG)B)T?ECa}DB#*TsX-P}S-mP%=v$FlVAu&eRx1spqcR>_u z!p0x_CA@4x1zPJm8-^$p3Q=FF@sVHAgu5%@1d?j7MPzKI1j%-_S5TY{n17?WAOpP&s4`#Gu^SzkY)|V`;%KF34VSV?iL3F(cqKPrYB) zRdIK+7(eJNKtsONVrd_<*OII4?tb^5sCN<)=m1sP7!nxW$4$(HHlZ>@hTlm<8CcxKejc;X4dU&@`(5LvN;4Jp)Z| zMfCUK&$x%6CDhxP8832H$wUCNmP7h{{#qVKstud{R4>vc3YsLF}WFeGFATN-P_|^h-5Ixcp zA=1!c_!^g5FpgU=HVa><(TH>VCHw=l*&q~Xx16VN7wOoGpJL{>xo$4(qr9(Sh{HiV zlf~=8of;3Ltw{aQc?lvC=Oy zC6H^A9AWvz%H8N+KLKo^mkeo_u-X$bT>5C37;igI^|$!4`~p?Eu7FI4_=MWI{T~m@ z&5lM0vyhNNrjahFV|NL}V(QJUXVMU-(~ua32IgI<I8!lMd6efi{UB3=#Tfq-S-tHp&ZKvJ9X;tz0D%4?nXcE?-m;Ivfrb8 z^yo(mDof?rdVu7O!_Mz(mS?=83PzXgem{~>8ZD5XZm)s-eE(+KM-1P3x=^3WC960o z#z3cE(Y7yTI-IMlQc{gRIw#%h8!u<0PI)~Wh4)EoHiES~sjU^8Aw0gaF3~1v+0Yxm zs|^f~J1*llcUHcK(0<4Kuy@x$gsQT-c5O05jP_xj=mBnG$=|J=pyQh`;oLtTOl~O} zIRx#!pG|ABhai zqc!gbAdoi=HZ%Uk9e`1*mrn|bHf=Hdbep8KCFuXS?;W#S6aU`Qc|JFvFLB1Sv?(0P zM=p;8wFG5b>EA!U;ii zXq}7;nd@g#pxXmR;#g^EX-&R5Iu|RA_(Qhr0ZAlj1^xQ$zb)`tT;W?$MID`E-FkT5 z1e9?S2C*-SI;WP;#@2JT|JaXmu>K?Iq+ktAU^C6m$ z#BwQh*csUow9$$VH&jy94mq|G)t9uL`inD~z0(E&m65kvU5&vuf9C8EE#lP2vExsg z0<=v^5V!SBlj}0F+S(;?Ku6dSif`nNpIKN2pP*OHF=38Y;vAg00Nf5;$Sn5U+m!Mh=5{KLJvEqH$jr#3*Uze6#P{$7fsQ~w8j%y7L|?Yl&0rI^?Qi4=aLg6 zhHu#a7OpFdmQqpn7Ym=xfdPl}K)<@%nftZ$+P?~FEKaoV0t#z$z!I(>#fDdsZ4z8Q z72h{b%%NIJ3v}7{^}fG?jt6SJ&=39pDj2X&bN=iWRymV_S!8Dq34e;g}68?$F~wZgvoo8jpvoPX?Zc9 z4-~3!Zn(g9Pc5FR3EIvnCn~(K*|huborA?0J<=|Qm|Vl|5(O6*n{@-T6*|j#l_%x+ zaVi?ugT*&64pv$RZ9U_Rz(gH+$rlHf580G`lXr<7gPKo|M~h?w(_hHUYPR1nPPu=p zL!IogpBY&u$!Kh1H{r1nf+E~=G6z@8GYj;mx1Obvff}lWEa{|PFQSBC3LVM@X%-J2 zG8Vq+?1pU!O9HY^S5|E9K#-)wAiS|4m^b%bW0iESYbEpB?`(3k$^~HZfIGZ&@MEh3itv7w${ycpo}YlV z*HpPQLz?m*yPw%8s};?Zf8Vji6Ym7Av|@s+sap%UD;o;3*;%Vx-AA-*x)aI___9jK zKY1H@)*jDS8=Yo$1eKZ{P(vZg=?=o3PgKIM%kT-=V_tWUsJ!kT+8ag1w~O`Zi3i^? z(ZGETj=W-CCS?R24Hp#mO>bU}4j;ij|8o+XW@G|DN^|uEU;|k>4B(m6YL)e__;YHCB($Jc(}wk*~K`x zB)M4GnMFiJSXekE#MmVzMFolf|0(|(>HoPf;9zG>Q;`DD04WxDwA4&cM{Y8-pj=E? zXxqrz$VlbDP0+;2R3M8Yt%X&1@V^TNrlcJG6%4>;_yE`RT=vvt934US|4KUaqU0Ly zz60_9nL0OOl{;Mi8Z2kDxDT8l>9?reDEl|&D9E$ps5F>`)N1pLuf+3&Xq_k3KsXPg zsAW*T2=lKe0_qkZtrkEa3j>e`NVpMmW}&3EsqsVhoY56UxU$0ukHZ?BkwJrjS0Q$`S4sj*u8uJt7mQ$e*JsWSBxagA`CH1q^M=_nL+~=j$s~X z6WDMQ$Y|wY72FV3`95;_evb5TyhySs@C~XCr8!0zpgcZ_OUqCcdTd!I>RD9x@GqhP zjn>CFTnrQCb$9%95z`yfAyPC_G*j~ED4}31Z$zbhMBbxSqR4cvZQTs^E0H)~B zo7<{olz3&NsFwC5=)7g>eBp6P6Jtkfr7>IM{jK~T)7;?d+5hTsZ23CH^(gzl=h$xU ZCa&(@t`?T?Je;hYZ15Bm5=xTr{|liJEFAy< diff --git a/main.tex b/main.tex index 1d06154..9fb36aa 100644 --- a/main.tex +++ b/main.tex @@ -115,8 +115,12 @@ s.t.& & \sum_i D_i d(s_i,t_i)&=1 & &\\ \newcommand{\lp}{LP\ref{LP}} \newcommand{\ip}{IP\ref{IP}} +\newcommand{\dual}{LP\ref{dual}} +\newcommand{\metric}{LP\ref{metric}} \begin{enumerate} -\item \ip $\geq$ \lp. Given any feasible solution to \ip, we can +\item \ip{} $\geq$ \lp{}. Given any feasible solution to \ip{}, we can scale all $x_e$ and $y_i$ simultaneously with factor $1/\sum_i D_i y_i$. The scaled solution is feasible for \lp{} and gets the same objective value. +\item \lp{} $=$ \dual{}. by duality. +\item \metric{} $=$ \lp{}. It is easy to see \metric{} $\geq$ \lp{} since any feasible metric to \metric{} induces a feasible solution to \lp{}. In fact, any solution to \lp{} also induces a feasible metric. \end{enumerate} \bibliographystyle{plainnat}