From b74be29ee651a4291da93cbd50f65de55991f15f Mon Sep 17 00:00:00 2001 From: Antonio De Lucreziis Date: Wed, 9 Jul 2025 23:00:30 +0200 Subject: [PATCH] fwejifjewpfep --- out/tesi-triennale.pdf | Bin 2834807 -> 2834044 bytes src/main.typ | 42 ++++++++++++++++++++--------------------- 2 files changed, 20 insertions(+), 22 deletions(-) diff --git a/out/tesi-triennale.pdf b/out/tesi-triennale.pdf index 96466f48628aad047718790296bd65bfecf27b2d..283963cedb0b7aff00211e627993af5ea17607a9 100644 GIT binary patch delta 40809 zcmV(>K-jGgaw2Kga?EOgb9QSgbRcWgbjoagb#!egb{=i zgcF1mgcXDqgcpPugc*bygd2n$gdKz)gdc<;gdv0?gd>C`ge8O~geQb3gekNtlw5zS z9LEv=e?P_gNNnXvt-cQ|izLRvF(lz3;RO8rM=T>lh#tf?I0-nPJ-?paneC(cm?zl? zB7}C|&Qy0-SJz!NBaR&Z9teDREtvPgAD_QGJp9I*Z@>H7zmLzqKk(!C&u zlh1MqThPv|dyzW-=IggPf6Hx*+xBlZ zj3fWm=orN$_Z3c<pct@u{a8u?$D}jcS z@4!oeO}1Iq1?9pZSA(HGetdtFqb%3`%+upM^foymNt}>Wn#o|5Di29!13lB#NG+MR zUSU?jL^ATT0aHjLmC zV`2d+O|buk84KndpYZ*HLruxKByt?b$3n4RnUk-@>?v`5rW{Kt5#)bBTBdH3&B#KG zRW7*;Xr`9S6F})h&cqLwI78hp9>eTO0*%=!`QtuWF*l)4C7=yA0LNPPpGsHC}l$ z-QZ1EB^OZUa`iVkr<8vSC^54Ds~Nf^LM53)g=zyck}|_Xh3X75#+K^zKO=SO0<#h$ zT3k@b+iDmlzjXrKK}7=!9e)q%Y(D<%$F_r<3A2hvz47=8u#2viMZ&ek0~4xS88sw z&58Ec5$gqLIIa=LI3`k6_g|6_-ZCc)pmFZO)2cC>onvjbo~5CuXXZcG7A#}C3{$3aw6H#CfZ zQX;@#P^^FGA{GIl0!!#VD`M7-V6+mDI2d?5DWIUW1(HxWq!n;LDuKAvr?WQ1K;W<> z+@^e5TFHYic~Ej@Q-W#fbp}bV57t8bT&#c58#!x9XaVgE&-KN(4eQCF_YJrE?79?D zzqq(W*S6O(B4HCmhyx+^3f7pGcPfbh@qZI|P>D|WFwHX#F1om~hX06$NBYUB zXyo=%!XiVVRUEjN5{Ss)!$TZWN_^4qc|f(OkH&tC^dMg-K!;{l286l_>0jh{gcfq% z%TqiGm6LN?O@UE$DE9nQ0~9(qh}nsu>qSDLsE29QqM{Uvfs$71H zwtExn5vr5%Z9Q-zyVSsq5B4+Cq>dqP;|-BOXvA133)x`m5!Vf!2-}ZPi&&uHSV-fR z5mknm^ev+5v>^ccK}-+7buE5Y*P@XT3I>01mEnfWJh#-wEpeKPgRnRNzMf-WS4ExY zhp~ZV7RndJEEDX!Ndnb;Ogv1>g@vP4*PecAWfTy^%})-;1(^b0Y@KFJBx`)oz9T&u zH2eoEd(gQwzsoKqkWGDsoY`_tPx7%B&1o+M<7Q z&GZ^&aZgXFR0xCf$~xQCcr-Bt7mdLox2~JI&vrFmcx+L$oy4REUGlM8dcTn=KOv!K zCY80dtbr_btSj1jpAn1}CqyrCN_eG(LJLO79l8O5hgI2#M@<2iE@oPk=o!FvYF-3E zjHHP;b;gQQ;vg!gOwXQgU3zTk4i$f;LGREVL|Jx`bk|^(!da@BdE>_0oCrl>yyae& z1tnhaV=ns$)rqRGN=bT^D6h24`SGHIk(uo2n3A_Btk=Os6-`%L_sJ9yM=&HSU(qY>U?*xR zp91(C!P+73ZL586vJXSiy*PhxjuvLGD%p3@x6F|kC&g#{=gtnlpUT`w>z*!slDBS*Htfxg=l}u|C0v6>|o%V zJL`h3Y4F9UZekGd(Ls(E!MqLy&5xs z@%l)wD%Vn(ND`tvr?CSvz`rUup^}Jtyc{f1^e0lQnzq)pLj-<7|E5^GscUN@?U$Jz zsYM^5krY+qCaWTM-+q5(aSM>UTU?ZZqiOV$7I)cg{Al!ct5_GVW+T}yvEC1de6D0u zAuGxAB6i_=jZz;Y)rB|_;eWMC){IC8OBzZKfo45)(Zioz{+xa)f>h|W4x!nYGDG<} z&?f6Oc`;OLai%_qbrO&_v=y5xMJA1y@?OBwDDY1_{7&-dZFhg_FVvlS>GXWf?WtLh zY0*%6X;-B>O8L@lI@3{#2u5o;?x%DfQ<^unos#OJoa%-Yo_XVEn<3B8TQ8)F(SS|5 zA&bsNE`f^RZlbdh%wtl}zAy<9Gi9LwZ-l8x*cxG~sau_mv0q1&eQyw9?I*BOHuMRNtd^MKTIo(9+JB4jIcSR+ebAfFYVNp*isLMp`AR zOdZrrucNjn^*Yh(XyB>a0(9K#XyAX~9QXG+N{8%FFq3}_5Mys0g<|6Ty^8(jvlIL1 zfIB;J`a#9^^tr!1*AW#xS3s)At-wXY8+Lg}u@+G;K`hc7+B+p0 zPr2?&`A(vq{bQW$JI0D@9hav@*-dcizlVWu9U; z&f10f_37f;8MA$_4Lm9W2ZT|Gw$DtOA^!3DV~~HVL4sPjpoq-X1A%0+yG*~hFu8TYoH_)-yJtp zVMen+Lm1n;*d?01w^QU@SFa|uz!QF<3R+)YUQ^&wgY*=s>dc#&(mZ3Gdlm(JXG)%) zSkZqxrzXZ{r*?k~UvWl*G{XWyF>bPe(A>ald1*k*1h2B(LiGKdPq*(fTdN!6$tu!m zmIjs`pMvS$lRy*^iw>5Vw->ysZBGqjo*F?l)H){Xs>?N%Q5MYFXr=VHcu73|$I|4m-E!0kE!J5_lu|~(n0bG^%VxA@e^l2jU)%>pCfMB)BdYQ+_!`m4 zOvKN$h;JRM5nkDJd;QJ&N*&!Bb>3F?S{+VZb2GE$FZJ0lqF3fQzGBrvC%k{?j7?t; zL}9+}J%3q{UGEK?I)&_t3?dY#!X}MtRqENaUZcQN1#W^;9z$l*a!Ke_wqDXlk`RA# z>4_qaT4u0q1}ot9vXtbb=SEOQ(J||iZ*5VuPf3Z+UT%~g$t4CPqu#2F*X>xCY!AI5 z^;7(uf3MwomIWHTxs!fYp+xdJezc0^G5sHUb^f;HK`waQjaX%`9-uzQO?(8Uok-df zCs#AxG`pe*(A-0y9#Lr2C3tLKx7vTUHr$!8#NyHd_m{@&Dv)f98J9w3wKui1kD@VA zqxZ9-wrC?V$WK&5?v$*ca4NO!?ii>&<*YMW>gvveX4_lmT8{8kBPcLd-fKg3ZWs4j z%1w4AlM@Sy2CW1o-C~4g8N7&^y>H4)D3xf~L71CH@{r6VXVNWRjdXLOl8%4b-yzh+ zk@tu@#Ta@rDr>g*R8f9AyR#`jI7U{8_&${~0U(+ncYivfUaiWE)F5|cC_S99wr>UK zTo2&%0t7oW$iF`?S7Tl`eqEx!dfC#3$?Y{{sXQZzb24VWBA%w-9S8X#$r&C@ChFpKU4%e{z9jvzyww zUxcxQg{=*577IMEkpf2M$%{x3BEZLUs;6hV>eM-1)xB%kB8t-Eovz!tUu)Ds!hc^Y zctop2j42-8yt}yhi+6wh{!c$1-u!SO4?nzlxVU*G59x6C_Tt6eg*r`A)(IO;JVYm? zNhTcb-d+6h%X=y1y)^##f2qy%`7k}-&hJ9?ZXSCmUw%@rGS8S+`Lud9ef3#>e1801 zs{Hx0^W&5AyVC~ciRR&l@~h%FKfgREBM)B|>+4XCDi>DMH(#ut^!(QeP2uvO=MC}- zL1|2J zc?cpFR6gO*0-D?zh?%NV7svm80nnZR{6__PSk_v;o!6MD1dz!2Q=Ngytl6H_N8!E2 z$GwDCMo2G}PV*LTFAuIcg!b%sX--G5{1~mv_1rwsoz9*=ZTSbh)b*hGB&(~>bLmsM zdfn5U`EO!Q#fUR-f6JL|4gBiy<}pSwYw7xX?aS}QV=#Y>R-8_7)u-1HD{;XF{#DLYN3*@{FA2>`Qm_4 zSmSImEZNrO-Wy?6w9YgK?#aIo!a11PLP{P>QjGYrKVFqG>sZ#ph$2~>+hj$%(DPKq zFXRwJK5U{2fAQxicm_z05_^XL)+_$@p3^P$xUIUSp3P`D4uzCWExZ;+{y=a|EL^eK z4CUunScGe+G4wU6D_%KKadqNZsenydlYGWod3bW|K?63ZFjR05wb=&0J$0d?6tHtM z?{$7?hKLa6sdDhAHRX;_(d3-mAq(z_Pg>Wk8qSZte{F7;(4*VcK8U?1^qN@Nr}Af* zG1$+y9}no5H?LZ;!J$W^y326mQLqo{`DUV#3k@NTOl`D+)Ox+BVAxtoB~r=Pr=uwZ z6APpAAWTsg{H52G*+MHc6-f^UY#~9rr9`YkrMlPE*9xGGT%aKa7IyT)SHo!3 zRrDXJf3yKs*M0wEJ1iV=&=!l(Hd~0Jm3~^w^)+-0kEHOw1$07TqNy7U z*1Bu1J-Ew&36Ht(Kh;Foy_p$|NX`R8D7REt|2u=8m9BpKT!zAFVfx{RHB_y4I2y2I7@MV+}S_Ne=zCP*T%V;Qh zK$NTTu7*COfh3FdG7dpxtN=GvhFuVW>#LHL9zz7&7doMxu}OIAd`nkS?kOXE-r;qv zW*zV)1e;TNh{PwLX9PEL4^EVvqR$l)f0Kc(6W*i-7h+6=t#C5rl=_G~Nr+Zpu-nJN zLOGXr+CgwHfX!SA6u}{ig4(Q3E+RWazgvqb(O9m+#IL`p!nAr!+HD)GFi~r+d8^$V zOf(`GsLzgYNlv_|1RSwT1d?;IGwZY3Si{a3WZZkJ0g6rO^Dpy1c+H<{1MNO=Mj`| z;7msVBuCzIG#25%J^DG}pv^wldFN=sN7mTh>HvSB zkmUngP(5xz|H-(B0#edr_A;;Qe|E`k#$P^?5%IXqGYB&EbJ7jViqEW@)z^%egM$pf zMBiHUrV3H$$ufQz)Ow)sz_BvX57AypE37qf7wQy{(}D{aMv$jK>b+4gc)N~N;13y< zVxWEa9@%7s zD30=0gy17?bvyS~9*Mxzf19ffe>q`2KmI`L9TmU_Fc4<9U3Jw$q$sw-n1nBZhqf~b zxK{3aefElkZQ$SZlf}T_7#P;8_JDC0Ic<5V89p_;hH;2S*>LU_yrt# zud3c)94aC?l1QDXMuFTnDL_g+75QVfVuG!}1BpUT8*XdxSOuO;f3ElVIzNXKmZaIF zgS{p^c_0}YVSVlnDw-l{bTNdO-qMNvoXa|L&uD62b8+aHF*in7D4(SvTb@MpI>xxi zmRkvvA;nubvD4fa}>*OtKsORS2DR1hVT9G&v|20#0{% zJU+o(tH+S!qe%MLf62bpI|>$Di4^@9mdeyr^KPe#SX4v=y;eB=8~yo5r&KkO#1!wf1HGLHl^E)8_P^F-d@L@7$A0xq)0< zblR99z#Y_vls5aa-=I(&STegS`wg+PQ_0|sHIs@m9SowWJ7dJkXrp>{^bevp5 z870c7yJ9)af1Qvf160O!?nHw=7@TG0PU7U z8vq_t1AX0x<9rR=uZ$U=KYy|lKIdL+Y@uuyxF)%)m`J8UKu%_9>AS4DxIcYEiEQhA z2JoP@3XzS%YEEkcu(hQW|LW0^a-O)j~5L<(J_25<<zjD|doLfflE^su7SNZa zJbtuIgg?y|2qt^1gj0$w8J8uK!8>MamksVex>7`qMK6L6scG=}eK(B;3_(qNRmjL| z`Zrk|B&OjX(j3J_jdV`oQkHa=hm&AFkQt--fAi#Mo_?=n@sGgqIAO|lSjHKlC7HhP z0F|}zbd>6MS4`y#EL!k8WG871LkdC}7xd;HvZO`OA#86WgJ>6$wPvXPk$`Vf9=k5( zlIaTyDH!eg2)$+S{N9y6-f!`X>Njldm|dueB$^SAsTdQ>J-&L(qN8w1n-NW@*}=qk ze_%|v&=mS5<)qVWjOB=S*07XzMC2OtMFQv7QjLLk!5@4SLPqe}_vV+1TpUZzy_tFLVOQJACbgj>}D50;8F*I%kE> zD}F~e)rn-HZ3f>l9pVrcPgpsRekSFwUOX@9+ z&3|@U;eRXziJ_A*ZxffndMc>`I5L+p@F^yLTaRS55q_Uv(F79M?Bcb{cR^5sShVoA z(!f4skO&)Xp4cc5B_YX=&*#&pyL~Ai`}9l*QV`l6x{ojAa^3t@`KW`$fA1@N1fxU< zF&tifd-L><&i?7UKm2fb_5F=JeE;gr&C^fiAs%jD-+X*~qfVWavBCr$4#5hkqxOe? z+i!1v|K6RH@=j`Z{7ZWI`)2uky*~5Bv$gFZfB058%GzTY;&9XwFSxVKKkl#`}xg(v)h}$tb2$pR9fg@1G)TvlL&l@hg9!4#6+m* z@_i=t2v5{X^EWF~ef8I@>(gj#osdDrc}fE^uw0unnbNm!oNaV{j^# z&JCVR-O3qBuAD;od}>p%aXjyNz~exse7G*)ys#4$GYecP8|@|8D7<#T9$>aEJMxcn zx3aNI8y9@L_1g12ycAX&73v=EGkQnCfR<=AzCqjaakPNcOi(DNDN{;--;4}vzPT07 zQ{DXU{GyF;?ZDFUjiZR#ZR%2g!3gYtZRogreQx}sqk5XGur}I<(!EUGs1$8Y%--Uk zUnZ_Lw%IVxsa>N0vJ&!x34***?%Y$Bs?v-^ykZ}Jr_Qj~*~=(}vuIo|^@oAAj8KQj z^kdhn3eGewo>a?Rnm?}1NO#nQYXN@$A|WpC99Y9O9C64xg(ymC9k(ri4$nTcM_W27sB18t!vjB%S*#>@uh zhDRrg=or7zAb$H$%HOGvw&}FOJ5HoPzNO^qx;C_FQJFKXINfS{PK!s`jWw;*n9_#I z|4zulF6rz`_~km&KBKScAAGC3p?haSyN8?-NRVof!ZoW z=F)||E=p61%-VkKsyIe(sK#j-=D2tbjRd)FFd5blFc9hns^aPq$vG;!JUScaPBDJ z~8Fr?f(Isj?2A?ilE-e#M_L;!psH${ua z`YDjV#)RRhYc!>adPeL;3A!C%^I{DF&TTNc)3JDRmx*028nssE8-AC(kW)4i*r%P} zOCxM+CSUP;Ljn+`bIs^qGHfzwU^o@q8vCCzZ#ts2vT2`xbEF__G+~mtUI3?4TS}E1 zD}W4!5WtO@`#C$E6)h5c+leUzV;uM`BMI0&%sfiIvsx0D94iw0{o%d6XrmNXHID6%x8@rW^APtCc9|2 zLZ_e83G?ZM!s_5?XBXyHJ;b^nXe5QSKIy{$49rk}(jZk~WZa8pC<)<>Oh;~I&-+Vm z;oZ8;92{TwdRm2+vYM{Wb*RyRzrHIDO%*uLB}v=0mY~SGq-PTyRKCNuVn_~e^v-e@ z$dZ|*O<;8?;SYWb1@S(qtosN$O!3+@+dT3R&y*is9=y{ES=nF4z zTt%IIc0hEYk734vpJ@`P<|%FtUk9T-2_ z8}z(cY+fwh*VM2su~~er-ilLiuCJ=ZR(1T2jSDo9d-*{cH=h%y9g5Oql{VM$gBy&I z^F@F8r2hbUXNm16TPHftrq{M9sMVJ^HkL|I4RVF0ZP()XHT24jwi$D#;3DE|%A}5e z&1&y*{JlTbFF2j9*pVF+^N`ntMe2V}MjU>6$%syw3PNep()m8Vm*6OuvbE8YJN84C zU3=vbgh#-ahKvEv!E|fAU3UMoZ#5l0`SW&P6%wkPBGRU_K6O3=(C2y3-<+D}vUfQy zs74+f=CKybOVdn%_Hd>aWO-qcYMu~(3N6TawnyjufS}A8$MoQj5D4`>HmM!HbBZt$ zDy^bs=;@%!Dd!)V4zF3DIM~aUZgJgdV{ww3%rQ2feTc3|k>Cyopv)cC^U@mk)crrjr#tEg*MvH`rLUuC&_rRjh z-M;Qw6AI2Wt#5mIM5MhyB$ya~Myx|h&4ccGMlwGDMJFS~VTLvU``I5Mg6`P}5qmd^5Ib9#ZdqBj3OHo~Q<r=1F@kwi1W%Beb2jZ|GUmc!?VN~l$; zJ&Dpxs9`6DY4M9K5ETx*1ESVSb;rggRo(Dq&P=Im)bs(>tg4=@WS{+YC4)^BJ&IRnyxZ&Kh;HFv$pwOad)e_sU`W1_3}*tcm!dSFh)MJ8%#D zu>w0f#R#CTPR}ua0*NFX)T^dL*xY%M%5`DHoip=x*c(K1OZmYB+r0wR(5#}%_kdkW zg|0J<4{%f}A390jGgkUy0=`W&)wpkW(0;^c(hx(m?Q{rihmL#`vVIZSfvWY3j)z6= zL8_J(sXFa_r@iacs1Q(NKS_Ej{Y3)7SFOL~TO&;^!F4@kI7T8<0-hxlZ1K$tqZAr;4 zpgiR?c;|KZupkz#)(jI5Dj?dkL}9nPg4>O$#(YZokg7Avx7XbI`X`q(H_@C@vW8^5xvKP! z5EV(E-gC0o1~0{bUN*D-ty9ZztQEYDNDtV};%In{4fe3#FqeKd#7f-Pen(PH2v$0GW+KoMC-}DOq?4;K0yO)|(&D!2n<_5Xhzl?-` zJX4g{c;WyK1nK4$lE1LEc(fD8X~tzw?3H8ZZxb-7g86$h4IMj=`l-yzkiF_vO$2mB zdTI4u*`rkDO4Pos={~ZTOr?xr2;g)~r3ZrJg1g2F!CGpZ(c5=Z^p-TLpzH{3e%5Qu z&LypLP9n9&s5l4ZNx+U2^$Hz|m!*||mXuN%x67}KtzC*Mx?FlJ5dv#wJPtJ*6+CsD zR~@@coaq+*nV1V_Ej2|f{g`KFcMZyq)^f+cm8uGa&in`c=*9gTnt0G%nHVDaI5J&%e2P_?35G zfBVP3AD(}Ar4HXce{uEju{xx~)7z`}pI+&uk+yEK(ZoY^lQPMK!_#lBK7IQ$rPOE2 z_~R#;`SZnmy*)h(#j_LbA%A$U?B&#A?&W92qxq}X`11Pkd!_mFjeqmy-uc-wKt7`r z`62%*o6eip2W`~h?W}(aIaS`Vp1*l(b*AULWt+nFfldQ(5Bc3`(YMWbOIOFK90$CX zwzin^Ti2f-o<6zy=;_s8PCNt)wV6zGk$nCqMBqZgSC$D#fTmgmNKf7$;-r($nNR98 z8{*IV=L??L;{vV^4}W5sNO|p!%eAK+Smy8Z9t8S#isy=EHb%a@%a<=Y%|Pi+E#1b9 z@QBJu8C8CszF%v)jCLknc<}JC5%yC@J=qYWZT9pe1&Ydbv&7g%V*Z*@etY~T8&Bq+ zpOTTrlNMzZ)Zui8ano5+PkVUTAYF3t_`Ju;MHh~Hq&pi|w|~0uTHIX{R%?`+oVUT$ ztNne^Fiy5@nI`RguuzjpXD#n-4XMLK!PNskJ2xwc2`dc2$Nlp&VTwL^U(b(~e`|`? zPu|%^jbD@J=+b1!B)c|8Nz{xFQ*t^rn@{36N6SKXN|k8|g~DG1a*?uk^5+*(G?bGr zg1S&0o8B*NPJd-#d}%K#Nq5z7x)|VvbhpryHt&8le^=cb!HgR{K>~uJgQa=HW`iv; zTjM#Dp2Z{#us|hK(|#$_rYU*NGL)3P5dTdk_LFTVF&~Da$OVwQn*6y)3t3iB1Y;^{ zS(sg%g7XB0E2)3IrElI%T3H;GVKO#b?-$}QfhH!-sej*t>^^=Z635Af5Pj44J%RCR z-pdtsPi~0SY4U-F7_I9Lf4Q|+M3Z6eStxY2oPTVXrB@QQPoie(cdzd#Qa6QAIhtZ$ zsLVv(4v7_L?4SXGBNCck|Mg0?ej3>-*&pDB^x3b5SdT+~)S{TiNd5B_-v{{qwMgyl zz()W*@C{BO1U4T7|t6MI2y4Lc4wQ zOn!nlZbLQA^x?)dp*m9xiH3Nk;qN;eo$2x_3%&^vw_;kFto5_SEfo!V=nU=AbnHkx zV7@8P@Wwy^37kjcrB%y4VJxgPS}I2Cdo^(6O@G)uGxlqBJ+q8qH`NhhCLMhv`5jIL zH^oL@Wu4-%-0R&Mr6WQfOn+5Q1%XR!pF$Y34g?~c?u{C~-l0aYXYZhN1e2R$QiBc( zv8knC$9!Hgu(h7n9F&ehx3G2*QA)KOIlhK@2DRDENAg%Z1aWZbKEYm$d1e%_aOG(C zx_=>%5Z?Mkctai}LVrlr#J8P5jwIqI@|mX~d&D-iq`r}<`J_h^+PnWo^NvPs*BqD| z0Y1?1d`ylXNT3m49|Cthg99}Nc?`W>2X8n>^Eo(H#_SD_=tPj0UKNC-H$G^^XDzHs6J^32ZAh5o&+ zt*~)2-WcPW?zfZ%+HWJYxLS~GD?C<)<1Or7e!%h#q2bu-p~x`az9p9pM#Sosi(&WT zQvjF)wXT-aIU50Y2CsC({3n@6DPRT;{?0*70pOEX@Ejjxf1jUgfKI`1ZyK|Awtq-5 zeeelVOrL!4TXg3R-{bEm`1hx)Pd~>@zPhr9-{984$hhRAKYW9`2bbGFUwu;h0NPCf zAhNO9)FDj2Qja7D%mYzA5<_Om)*hHf9E5Ys7{5mV*a74@1IgXuJ^~oau2)9Aa!LY^ zz9CHs>03ZAh7)Ng*$&2lhN zK^IN~8((@PLD!ZYg*NCdox=}0C^Qlt{NGq21AZrrQbYY^CkuyAb?$o%CWwkS1+7viAa8w&&c~20gL@T`Le0ai>5 za13z*(2ir5V2l$8s-w{NW`2XAAe&~mW-rvOfH5cUN5O7IlXI;(=yHNMnD@$$DICG` zk1;mXzv~9@$ZQ4#hB;W6RaX7{6zaMvVz25?@=Sg#N~i+`!rqmPy(RkITMdZ(PraoFlhswxyRfI?OaBxPVM1CIWNd(XBU zbf~tLn?CO3so=)Xgx&Hq)s|6RA6z2^3xDY4RE6x~{^heEP{-qwjy>Z&33V)7#<85auwF1a;e43(YH>9H4zS{K$JnJ8oZMj-*F)^7+zFw)lS~rHB zB#fF2Npd26&OOgU(m^Kptnj^Eu9vsA+m#J8t4_eVsg-wx?6nl}B4w(Np!=56?6~Qj%u?voYE%uL|YspH^d<>(Ka!WyMx6wIG7Ev+FJ&KoiN7cac_ZTIunLANHArUGXRhv z(XcU_*M9>v<=B5Gfa`jw-D7Prl(iRp|9o&XP3jP8R~fdIt*>}2Y?>paGf2~2tPx}U zg2Q)=bonAAxtjw!_sHurytBZ1VHbfQ;HC~URcnQ#juSVVV1!y#{t|8jh-rtF4d5Kt zIge@@@hfp_UUijaL)x2R-HQH!s6Sl!0Vf~$%zyvihJAnCDe)5gWaWFil_a;iXY)J^ z7p-vOraB3@7?aVgs>LJ-^ME@mau6VQ)I^+^NA;0Z0%f|%*->fyTfL-kgxF4B0QpT92^>qU|K0rWd+>(kY zx_?(%Zjj~%p}*8j0xT!w=d@d}=eIBfmMSjHJWIewa&{k(J48Gu)FL7BHb&Vq;f4Yu zHH@TP)@urnWUPE5>wMMiZ3oVVr8hLPC|FP%Z9&;7Za^l0OY@5H<@Xab!yPkLjc8xl zO%H@NQFdrB=gIMDvSP(#JNrLZwi7m1hJS&oZS{sRqnfRNlAbdxj40N2ES*xY_7sYeEz7vrp^Jw^|y@{s(f?ch3I zvZ1E`p+g)&Y{on1%E@-Gx;9lOppeu|rsrNL0|W0?sBfB62RV33RCopdJwQbC+JFD| zAmtwPX)V8sx+ELS5cawJ#DLAi6Mg#8gA+)SzpY)p%`I&Y_jUPpc^mu;5iYx}w{X&< zlOcqG#1V;0z|>w=!ldo9+4>SBxL+>0MS-gR#5cj)L2FTz=Jg{ZRjJDcgzJnt7{jg% z@lpfYwWW+jw}zAZTHOU~GjQ@8zki7|AfSQ}{y6Nl-p2Z;C0Yuj*Y~n9cG>S@3?oqi zAx(=F$VV3vRl#aw`mglo-W1>@&53+9vN`hE$HfV;%%>&wsN;}EDYey!6Zz*8gm_hl zPMiXAJKj4(7Q$~|bhF!0B+rlF4qOA=*?ZcGM@!YbYoSA(e!ir1q?3(bQGW_ahl4c> zocAh>9SmbHyLbs=r@2Z_c$2TJq~6e^n*63yJ~e|mZQq^PmXu6?yIq?)!$5V-^}jpW zXaHL@SkunsvL>w6wCBQ_xVkL93jFRA`0?AONsR`6hTohrgMlC04rBHQeiqv9<6Qzj zfNtLF@z{)C1fw(<_#qQw$bXG@jwm!GGamRw7T+`&_;ICS3}H3!%l(|_SiOhxGWAdC zwDoak2vjUg5Gtd#-5kj`?S*+qs`>}Jw0!n$i40C}ev5mzjj(H*I(MW zRhm%6y~`#FMO~`1+|q_1FO;NOqdS&YXhs`jcNJB7sYVy{pwv`ePA6HfCVM$`+}`|b zSW#KpbIf2nS-IjNcpPyquao`7d|7(=4=;N#gp)CE6PK!*DyIZ9GB+@nK`1FCf8AV5 zj~urVzR#~{MTu=iYc5%Q!;X-|mLLm=frSLafY*mW#s&x?1&I%d56N%O$DWyPK8oEO zX=6Z!p&3tiku28xL9Uu4{`*wnBN!z@h+%sD=5YOkvw!*LpMRQO|9FtokFVbzuAj*% zPOt6`e|&XN=RwL?VS)}*utMsnfBp38&EdOGZl#pBQoG|f>G}KZ{CRhJ=ZkkI*eQSc zpq%A2VxHw!#jE+z!}Rg%<8!If_ivVu2g|$j0y#z}@F{bkRbXp+IkpDVu`mR~;Jk=4EFIS?88fwdOSniBX04;h7x73A$53u-(-ozkWN z{*;AvT0mrtvmlTN-W52jf1M!|1!*dVtkheS{)?AT`j=mPeUQ-Z>0kKq0{{Mc`0jhm z_rt+Ve>!AXgz3$}#q8(b4lj%4y%dC({=B)*rHoIXaEJyaj4|X3GJMNOtq+*erYRv@ z(wyazku*732(>ZG%Fo!9jj#k-X0Y?x4_SIDC8UEKRx^8cX61xbe?YMUc06zpP{97g zXSQhVz?T!W6c+QpIY6C)wC?mfap9(%ToO=GGH1jeB##GV%jTflx~8C+%Et=)hKD7G zsckcLM|PE_8Qk^sC^KamSOg7F1qzvMsc=G{X%Ki}Bv9E>0jPMXh3^Bw&wzWR5(FQc z&DxPjWkn!xvz(TDY%N^ey6t4+c(o-bMT`}JItoV43g^@qEVMyWEHEG*gCL>fC8U1R z8a6o@TkF&sGC-hJE@-^Za!`B(F3wHR>qsL}!!iOQtq}^ZN?*e=b)&B2yTGw8%On*{(02>_wUg1EWuC!A6F0agItTLMUvgiG1T2K-Io_2AX~f2)O9W*{GpYMtRwhp;j2{0yg#tEN% zIkeARAapSLF=d7oz56l;+i$((26PnF0kPoP0e2Z{lFeCRA5+3u4}6=;z{;P~?{j`n zxddDle=JyrESlHg1S7X<yO9~3mo zf7{<}6*}ybI5Xw8Cq3*mg*ewUuX1%=u+VT~k;xZtChNtoSX(d(__(BT>E8@1Rx7R4 z5aC0q`PswI_6gewMdTdr_*{&bIB{#oi$PN5cOLWco}D$#Cl#%>S_u_zujvt&?JA^u zX@7fVq}xwe>Di4Uh2DzF4{q1oN<##d1DxlIByjPnMe20wzDI@x1O;xhbN|$ebKgdw2t|RAu zLKYq3uSfT)pVyTkl+|LjdtFGz*7NZ%qBe@E%B}@| zFC|8;*`USX-bIPg7ILVzu~HUM$uS|Q+RzNuU6|prq~4J=Pj|ud2w-uCMYdJ@<0=x_ zK*?4Hsf$IymvZ&^zWTNXcho~;f3=)NB)BFU8+mkhYw9v#isQF}~% zWl$c$x-wTZ`Dj6evJRdTG}#S257z7 zP@B$jkV?F26P<^${>XtqcTE}s_hw&Ri3FLFW@X=s*}PoD?C*1))k$B3fBZJhL{C!k z5NkN*$FkvuYpuOWF_|T;_!_`#?e9JT+v|D)W}-JYxn1+m@$@-YB#^<0T&sK%TnH z2{8oS%+p<13M;5-@l^%;TpQg@oLx(K24N$$LBYR=1fv0lEj{FXbp37A;a8lJqe&3E zXZq$(1`UoC1v9(D5f5$65VQs~ZazD*j8=x-i6&X}CQ5{rW|JfA7S&y@pAK_rOD{X2 zsmfeK{#y~sK`pA(HWx?CJ~v~r0BOEM5i`J?^IAG=;tcrn^&CxXN3%6}SQTKd4!Dja(B5U; z=b<61Jfjk5<*#O8A$>Jsm6PJM5<%ieWE9{KDGk^KS+& z3}?)9rlyT$=jV)UCym|ipeQSOTR61Hb6|hW<_<;fYeCI-zof-i6glZpP%IV`n326q zO1Ii~^&nf9ES%iHS1rLv0pV*Z-zv`5kg#b>i8kYX6u;*b=tYnJ>k8A;8dW9u zQzO|uKw>SEHkMpETIbsOS%gSTCE^_{u4&31bFJ!ZJn|;^A-i5|7v;=bmdTawt5|{} zL)DMA%E%N7*1nj;4#>!?Qt1%@vyj4hQ zsYr9RKyXl`;MH{0G=&QfbLyKMZ+Gqt3UzFi$Zx8L+NE3)%zooRP*jK~8~P(ckT)2( zeV&`BfoTCkTg|j0qxL1~s2dz$VJd|B^UY8J4^S3@x0aYz1jeq_m=E-@)K2GCZrJx< z7OJ(o4<0LTg6FhbuaH*G?Z9PkfS8-`;#TH=WDC zSGP`Mw!tnb2t+Gaqo^usE#xsJ1f|iWnwC0KM}M)YsedJ`_3k}#JL10Tb#25TQS#NK z5+LfJrPZZ7fB=#PCE5IL5r!1^EdK3k!QJ}82DLy#a?*=rNBR=D~BEd)=nO z{V*<(vbk`(p5}fQG+-<{#nP!?ceqb_VG$|J(K;(vR^cWiXURsmsuV8;4;tK&De=LeQt8)K@wb_aKK?}lmc_!B-q=*$$#dQIBT7H{h zzft%|HGC;k3Gi!DA3oMX#@Yq2!>LlpxMJP)sL!`yc6)~v3=RplyL%xI@S*;)6?oyX zzJVifY$&N=wuZA309=^28G5iOPn7}eYE;6Wv?olj^SSG#G7rx}sVNPqZ=0$5nLEjd z$NcE%%P|i-a%$*5puW|Tlm+g)Q2E@nFclJQ`MKB>gJO=$K_0$azz>=A+n&LlY{KoO${5U%f+0M zLK0MJnM|_G0D?9WD3ID3`=g+gTdAXh_`I?8&^kjirn_M^pPW&HiuI5;6;wuZWMjgn zZ8d76s4tOq3V5ksn0%jRxY!|FBeHMmK+Rk}Sm6-GEP+tYtXjYc_ug>7`_l-c)eomY z*4}JLowQK~mow2Ws{V}w$v-z5E5$;;)etkZ11U`X3cFYJ)@#_k`?PDftg~2jMvsw0kNhP$ zfP(<@?9>*sD@aQcqRH2M2emke2B*;?^Iyp3-|UK=?}0Rp#-b>F_+;5oOns5C)>b6+ zS#&n8fRmCa)77N2ztQBM)AWztSkP-IBiEV$F^I8n8*!D$0iU`$Y!yodA9*DId?bAb zQlAdh#Q*EhmHYYu=v>5cQZeu#rR+yUQbbsV$Z_|sIHs`TUT-U#zqbJr67*C!ooV~= zMj9Zo&b$K@1L2PLBRE3QBNZz~Y-R$XD$%%oV2Vs1$@Nr^8O*1=8POJy$cCwiOux)* z>lGG+*bst=lwvL?oZ9lif{$2tbP|e=Mo@?hKc>hc0Flq{1lr1pjU+m%D2Y7{`F}(T z&4HKIZw{w(le6h(?95C7PL@5yk~TzozlOywes$!wVb}BM`l3sCUni(o6IDy<^ICO#t5{dN_5msr;UZ>EOs!g z%QvQMonMEBCrK9C+8!|sxb>J!OVU9H%H-gtpdf-mz&fOxiae1Kt~f}HH* z0g{qfUV%Y5lt+b?5iz1U{)Gr61P3;wN^J)67tc_8k~ykc)=km&?K>*(s7o_3Pzw9W3@{(JKy~DXS`_+H;Fi)c_ zb+h23Y{w+-IX=H#&ZdidQi%p@5DE5ipRX0bmSh`aYMI*cC@BmvI$N>*sY$hpWH}ud zH7~Xh+?iAL$O*(gvcKDT$__6Ad{We(7ngL1+JWTsJ4&1h6GQEkl>E8tyxR|hm*XOheNuQI zE(ePh5}&A0+T&lwWyb(d@*q2ygT{a`^&KzuvdP^N_A3vt)4khlWO%y@m|gFppxTpk zY)lU>gxG%{#6^%FMgy31S6r;+M|3eZ z$jzwqXCQT?tmkFpW_XHO$*P=vg#ofW)dez`oA8Ify{irU`xEj2e8~HgYKDw~zg13_ zz`ztMvY$jpU3|^W`jMFT@44ZFSigwDvKA%?cnpLyLWIZLC$#_zDsyB(7JrX#lC++R zdhUxKs4`m|*FxhKJ)5va@i#`>Jrm!gV?PSS!!%G+$P1d=eL%osn{rF+4L;g#xtqn0yVS*W@OW_w8%F||QWA=BgwTTp!c$cBp$5kKT|1a(g*>)+S^d&B#>70)aU*} zzkOM~kRfsRLH)RpjH*~j$vsme+WYGCW9GunE`VCJB8q5m@*tXjy7fi=cDWV&PZ$#m zzNZg9HMk8k!5x;{h(T%{jv2QJ<*(Xj@FN_(JjxF9B~hb? zEVHsJNFa@IF-Li4UL#BR+RUz#;F5$UYI~h9UWOF#nBk?%#Z{o`>6Bb0Phj>tSpM!u zHb7nDZ9Wl7gn6NVLi6tP!2f)}@{5nahG~nrpkrXYfy1%McP>P=_{Se-yO%=u2?&U_ zFg{RK?E_^v5<(UCMueV>5qR3Xf@TC*6rF+tnNHEc>iNdWr2`u=hF!@BVq4aboCZxl5d@}rePV;;tdRro zMIVuNXC$>MwD5tP^$IbTm+D2WyB6L~TDoccm^C~P1eAuJ zvc1@+ztY9m!SS3CR|)Nw$|oCv<)O)qanA3-k)Jkok6nRAa_?A1>t*SiK*cao)m_vseoy$pZ#COYiP(j?C0C#JLhrrD9r0LXoY8m<2h6>lo0;r(9AH5Pa+&QkY zwDPtxu}bx0)cT|M)B+*TwciL~3gm4|g>@oVUJJv6Z1dME|Mv6JM&F8=(T(bdnO`Zq zVk~$OWP~#yPeak@P7M<5NDVTW=&L>0x%2^f? z9yR#aFbCnfZZcB?@UQ6KF8t>8F^TuP)Xhr~EZv!5xy_sJblo$Z z3wKR6d%Ljr%R0W1yDh`8U_n74{4JVjqdq#3$Ar$G!uO~AlO%O0dE8u<4^z58={G8g zDKL<7R?2G&4+nNwnEe-cfQjK3)EtspKy^k;X1VDa)P*qP`5DxVTR!V~wP}T@Hoh83 zHUg=NSIz7)nJU=2$wb2(&umt#VyKMbIT>J?mP3dEV4>nHfM*SW&e}YZpBI?y?(T*b zw(~)PZ-{{4$cNyj&pijv%~VX5z{tpC+*8QR9W)@w-%p4EC+L;G@h;k$E~#@i~h z^uD1M+rpAK?BB8Nw(bjl4o{OIZx-KJeo4PD(}{i0NfMlZI~?|WE~<(LV!uD_q8ofqB@nAc%xNo0inWC z(sep^BBb*lm}!~F`yxfl`q_HBfoxTcX<5kR{_)WF{jhLZR5$x(-_Rd8_`~-?pGQZ9 z$f;4X5aObPL7H&`c|(^OvYV)z3m%%ic>Oq%XO1t6Y(#*WSk~F2+{)ewv={DkT8W)| zMaCDR)vE+f-w8B?*v z_`>6TvJr-H6@;7zSrBnKm;UF&hgvBM0{<=VoPLXXN7IPGf4iGW59{q4=HFTTe#s*9N{l5S2fi@=~|6`TE4eO~|`FN9+*>C&!-rlum@7|qW98PF(S)CO}V^AJ5L(vt- zt|`_6TU-AguB~YftbcCa$a}rNd%bt*0JlT-*6TDM*F}k+Hp|kR?%lHIxuU!4>l@vQ zySKNA5y`ae7VsOK>Z!7S%A7fhxpFcSCyo+%K3lX@Rfkl07t?n)E5no@riHHlVk95d zdUtwkTM||o=7Mp4|

9QFd1A^ZMMz8G;)+v=#CT_e>w9)jn zD^*Y!$vOL!N~&(07cf%Hga$4=d3ADVk{0@3Eyfsh8&oW6yEu{(pMEe8%WZu<>uPOm zc;BrqJvjn;Jlof~{6`cdw=cbwcP9YmfQHg8eCR*uYWm2sq~dpVTdPJ!ixNt+TNy@< z>?-Nl?OK~G5_C^=Gqj!JD`DI zQc8q1n`)bfe&WFx$)TZuK-b)D;A#?(?^LbeZjByDQ{JO9{LL`x95nT1)s=2nDHjwD^;4 zEaGdc)qaieE%F_0UscG}ZH^b>_|xx|u5&B+ey%wE3IoHt#w* z`2PF9jAX&@dG35{p7(x*=;tQ5ZuBzGNH+zsO0c39+N2AcPx~0PECdTcLRC&HX}lV9 zVYQ>o_3#qM31Nb7++OmmLZ<^Kq@%i~m`+~mFP@&-rs5Em?RJ%YwDsyoXhgqT?8SUgey>u`&DPcMugCSmr)T5d$AiNd{uS3Wc;5%u)L{o>}5i4 z^HYRipHu-q!9gAdqZMOdqMa;c4)us`${{<$g1U~YLu#NV(DaXvS#A|->Rr9(DWVQ_ z&Vz_{)IC3AN>ROF(>SQT79%Fwc3cr;xQnevoJ7CPhfI@*~E)KoGV-Xy#R5c0sh0X8nvc9ES%gG9L0g+1(`F_zdZ`5v0IzLr!}=gTVNaER3xStpQ?tuF1z%(GuDHq0Ab*6 z`)cZ|W_JX@fYuo;d?)b8&EhMhO!@l{1{h4flu2g=y%;O*(eRPINvq_K_i5sbG&>(4 zMH1OwL8=E%MT%mT@H5_I<$Ml@?286ltRBeK>q#MwSKuQ43z!X>E3C<8I?cU>%w8!v zbheD@9H_&$u8^qe_#*=&M3<-G2eiMg#E6v04=`Au)ZJ)Sj#tDMSIL`ScjcH? z{adFwPktD`nTY5hWgFXBc+2{Ls{_;5ofL)ili=iQ{+DMGa?Kq9iP&(4$a1i~kmC|Y z#nt*N!IF|fs84UX-Wa@FD`=t=dI8FgCb(qNd63G zj*?k`qdWnA%bLy@!>@XIk^p|=cZc~nl$=oz7h51A*{XH>qMV?3)`knVB8Fu~T^*X4 zDNS17YTgW{<>wEKJdeSu4Wx;Tkc_*$I#STl<#Gz$MliDaGvG8){aS7qPsux4JnqM) zhdkaO4yQz8)-~ffCNZKWyP1y5MCzL>nmf*%=J==1BdIB*d+yqDHzXYCwo+@)*)kub7~j3x6Y;9je9u1A#IgapF@9os zDn9!+p+o!$5!vF2r>7YR#5x7dgCu7`5IH`XlL*btF|t+@3>7(Ki{(2GkuYz8tAj0Y z8;696o_wXO(n5GVljfro*E_5!dcTH9Bx#)vC;5En?^H)`mJQpT;*wbjM`I=SW3lG- zGRK0yxM4%7NpZnzn&?Wc!!$^9I`^=$|EFv0?Bodt2?;hr`yY;zXN4~@k&*L1i$80F z4T;8{qzqxf6nbiKeG@E}!jrH`_;m9Cfu*!z6r57&LY1qM0fAX%a2`IxCf!bb0}Drp zI0Ib?@q2|Z!(HTQEcPYN4mQ`$FygvBmC7>rkqZ;(tQK$`22F+Lj*^}Fu+ z3EmI!H*(=s)Ezv0p1M%)RWFDN+97p`hcJ-p3}dB1By8qpw<&Er`Fn?{HWvEgJ$>4d z+MC_;o~I{C08RybLX#>_SUmgNt;?gC@n4}wN$HLW0U=_w3SPUJ?67$lb_0)wC`6|& z3ZsP+&89e;d$XZfea;-CbF zOnrPw!tXab6r}XU(Z`JR7y3QiuN`PeL*yHqh@0|4S5j90)Y)44;$8Qk5(u$%9j#xq zh>A!8T!PnyEg}t3@>|6Fi+)Z4$>;7z5``F$z?mfWzN)LZ74LX~&{q-wq$)uk);39ER}jKI~4V`7eUo>uh|8iG{~Q}6W%Z`3!O*z zsiNVg#v6zxqs1BcuBSZl?P9CAW!+{I?b++3({xt7BoiYE11e=QUNG04(w9$`Nbrm@ zzL!c5k(!5{$UK;r&(i?N2+Qn9U5ULIL(lR~!uq8fuC}wxN=dr8Hk9i}9yW10a$Oy? zZX;Oko_E5NzIbN%8rh%IosOipK+fn z<8GF!jGW&?E%Ew+A#mHyl8t2$7I^a@3cznzCvJ`lPEkv8o<3z8|7I(BRh5%;ZK})x zCM#~%N^!H1p>>~|RMgokMCc-)f9Pv%<|mTZKx6b_e}xwJt`S)A$A8wNb#slSc36HeK$L_N zYl@_P=I^J;J!f-&fz*ifo2p)ONRDo-`JFzBf1y*o@7Tt=&9WS?oFf=BvB+O4xVg zbNCRL-NCWxL}q^??Q2ea+lMmUr$Yd4@?F|Vu)TZw<+x3=w6}-Z#AocC7P8OIa|RE& z+E41;IW%dC=Uxa8+@*XyOW04oUHna{ZJ6BmujrW43t~jOK&B)Bc0^%fQ|6eA@#l=O;$;`~i z`iZ5n3{lIbWsT4}z%l{9%i;wzbcRxpI_0q0& zXerb9#%KxBh=xBW2+dGoAlNyXlfDVzq$x?#AOYTS_(T8O27?D>$Jl%0GR&b0tnUk5 zyk-kN`6N-_F{*e=iBNGc`F`V(23sfFTY2sYXgyvmY$(^hrK6*)W9$27s$_s*D}_K{ zg6LdPVE6(z8hn+q>3 z2nYZh>A!dt<7&&!5%iDZ)q0;j7=}W}9{g*5c)Ka$lB6{tbq86? z;RuW{eF=7~-+L+0ov(`sLDJ{Ma~Gy}gy5+NH<0t~EUo}*W-sl_-F}-e>=1H%AxAz7 z#M44#G|2_rw;_H^&7Xbntq`4XLCh6soe!drwa)@u3D8|kDeRkzY0I3F?8}$?`ErI5 zP25sm(c$r<@1U-rFL3v;`u(QBY><)1@mFL5BgW=h%Qf;u)CQK_#JPhnSE5akO-`jz zB<^;t0+g2DU+?RuKsKU8ox;+}4*M`STOS3C!xFeiU1O2UhytH+quY=Q$f=rok6)|8 zN+Woa&Egq6{O-XIb))>uh`=x1X-qgQXkHA!>Z-vR%&Pj(?BY7&K8HYvO(=E;2J57) z5^tSo(E5fzts#{gbnAVEHy$|QL%H{lEHdp1O$7Z6{!;{4-8!2CL*WR> z{Fc=AHcafZNUq3X0YvrG?O{)%eb_}l*NoVv5F1|_qxqo_u#^sjlK}g&t6i+J+1_0K zorTL?bji^L#U*TjjtHnd?{O@~%0mI&$42w2!xNMfgl*RT2s*!#oL9zY< zF`Lc!e7-xNX*6AGqVou9JJmrd+kKWq!{ixN_(6XRx;~rhmk}^LhrbrAqhUCmoW=b@ z$s}=W$|!CzpD;meD+_Khqh0sSkMZ&^++C{96@%ZlrysNT7UB9|tKO*3@v*Tb~0NxlsnL~>ELMcX+nKNbqql#$jf?1acb-|AWM&cM^g=D9@+ z{_xTqoCTb@a8dveE`JjYn}h=-E>=$m5e{kn{|P7b$d#!V&Co+|of-F?6-9rh67mws z^S>n_KFnU_lMCMY-6Z~eND9Azb(n0AkeFszpIyDPW^QqVrK~B3iMrmz3?gzDUoar< z4AN`#EV)w6|KMykX%=MOZ8B2Sox`n z9g;BnK%SLiqGpm5GCBdR%OG&DWv)Mkn_Id{lR9oK0U4$}Av5qsFRtxy*_3W4t5x-s zwzs@6qWAK|U(3|XHaA|r&ZipQ<(S-?DW?Ar{;!-|IwTkN`TkDnX}1itUbtUUmgW;C zFr9+h*_Q~6@=#Y=`QZz0?+tpX*2P{7f4{Vl&>EpF*aW?3!G? zn;ffTqm3o3`sK!kf!fGlfVm+X!RSSo{FQG{T*=HT=NOK~xB5NRwR-pg|Rd&BA>3<1;BJcri~9Rja2b%wUv_^B>ISww=h%E@-P5^gpW{3tC@ zB?1xYBZVxN`O+TJpA2DIEGX}A3TQrYGgNJ+JJ=!8SrZ%8kV(K5k7|TQOUvX^ z`TJK$=xJ{U0MD=#kaJ_JEbXpDDo8^gJ*`MX|FQNkHzNH22R|OOc8P*H_($SF6_?kt z+W`KF2s5Cb*J_iU3=dAP-7%A^a0wV_E-VM;(z;@Jh$^6XyfU?8HzlFB4f)Wy$1Tc5 zY21Ah1jH!#pwYQvXOPuI;`+5$y}Tr@vIk!NU6lJR({O5ghdGull;Pojs@HUjApkU&U_p}bJ`w=3i@@lForN6D3>`S%&5opux; zMk#o%2(l7NI+dlIqq0as8q&ZL{*2x*ABA|wzWlHENdh*1n=m&Z|{i8g%29vuCQ zN)Ym@(9W>?8t$Ov*N9w#UCoZ~d!mb$BIM}WB=(#F-=;OAB+FS8$`1qLgwP7VHBnfQ z3l~`z;#&>(txMtJsumI}xXLJhmWU$(2_ujgcidNHY;|8ZA!f@!VUM<1NEg=8k^UBX zu>vy^MQW$Q{EidfCILpV0ZlYcQsa3ic zN=$=6ThJtSVOzgg@rXY-Fz;i_gD1{wdN&9CBTjISP?Zf?Z*e0kC^YO#?#*vpO9H;i zz2ggMEQa?(T`@h9@6i)%^LB=^;4xi%#j!HdKAk(V;s?=YdZ{10%Nh|WWlJF~y3KHB z;AgY_YLk5Eo>Am-EdJ<=oy0Z38`Umq_t5+br{nCFzRu7*z{57(EIZ~r&Y`u{_K|GH z6pt^A@x!3ycHz7TdH?$f3AwG#C6_jI7_+SyoVQ7(I!^qT%lmbdhdi%YE{53BK`Noz zoL1|j^B5j`XbM`YVEx<8Qb8@QE@47zo*6fT#=y)p?rE5QIql|zGBPWmtbf@B^K5;= z{o>2lzi9gg?TlFc&3ycSG$Z|-SM4e%BT>e1?Ap0bW1CXU>zbkAU%H0Wn|?=Hszgrm zv~a>54MnY2VLvpa_fk&KSK8>g{;pi|Fldlv!hDul((UP1RtDX}rL>Vko$G>x@cdLO zhO;ELCn>kpg0W~wGwdG#iPamkZjDfb8awuRPg3xkt%$;>>_+{3)Ny?LrL&eu-5Rc} zpq*1GIgK;t(jw0z@XKlI$-+1vn8g3qiz-T)kPkeeeF}* zQ{Syez%&uqWxO(?4ldPO*T;QvVNfs)Fp%nSFTEuLQ-$64Edqdw%hAJ1;mDz;bX+*L`-^dg9BQXbIxQ;uERN{s67!WM z(zWXOV_j1|f}K?@*%CXGxM4Z>oM)tXD>Ti4Im8{#ZzyF#j zzIc%!)c-nC?8SA@bpxx-43U-n&~y=Hqas>$u3j^?;(qWQ!LUgDdzNq>ubQ}I z{E}1U^DU&Icda!Mh3i+`slVsWq9`~#=PJz2WjXaAUl z+$fW(!d1&dohoK~7azd`WIT?CLV?C%rE&sdwRc&&kpaW*m`vo#@jR<7BY_=}L^K>* z9SO?;^Y7BL(o@(;3-{KY)9#pQQ+R`f7ZLmu28xwj+BCf@MRb z|6);gvU{i9U06j32) zr!d%flJC~n&D;ve-}?=3qpU&Qfez)Gg_X_^XcC!WMo?h(Ug#IGq#)67e4F8*;4clN zve>^5AmWf*#3|2me|hsvNh6r4k*=U%z`GXS3k_hQO7yRp$i(MmHUZyii}9DioL4W` z(f9^fa0GUy;!_+DdMHx+C<}w3v!3Y&&`xJS2mFxWNiqEnJ-Y3RIvg5=;}E3=>nal2 z+?P<7FKoo++>{nmiKHaHP;pdJK8h^|JvI}UPS2w^2^2XNC)EH#v$|4tMN6>#XZ(DL z2oGlxMV#|NUR{^b#nDs3_Ak+t$^` z7x`lMn|hxC$Metu42+-mX2y_^!4Q+X?Y^htWH1 zZ^r`W$;b}Mv&^>({~gHXt%fan>fsKCu0A$dE!aPtcmU0@EvsQLq`Jq=Q>^7a2e#+Y z%udX6_p9bOKTV3*_Ys|=oWh$H4~wNb=>A=T`|hU zrX(m%e6pMqSHz^`Lpj@z%UxwtZQ@Q&C=H=|a>*-bhQD*b91;w165LeXo;Tm_>)@Pw zy~iMUXPJJlNbAHY6Yq~4Yxm+HkFLOfl;t zYoc65&{`%msJD@(CQW!KdA}nj9|7KBy;L=3p{sdV6eV$}826DQbm?}YzyrD{m>V80 z;{T4J#=h?n;r2IyNpS_3nPs@I7wtk2A^j<1u|?M4Qa}i$qjSL^gG^0NO1>>jpomvI z5)Kq7gtgq}*2I@^L)sS(Ah}9vFozlU*PQ3)(pVm?=xoPI)wk66;~B-}TNjKB4m`L? zeft&|VIzq93|aEoA*74uZxFOiKJOrJMvT)(A6C^W&#y?$?ZR;&naoa)4SblrMW|~P zM`Erf)#byXy)3I+8B={ylrL(DO*rY=StK`kInqNV7sdOn%#YgG&z*6A+*!Pb8(gh-(=;3`p2aWHQmu3IMU|ktY`pk z(=YMqP(_!jK$}fY0p9A47#TZyix1b;=OfK`V&I#ri2j zU}ghx5wmfBN)xzQxQV$~Kg9~4P#VbvjYiszCM{K(|0b;fJ|`#lC(Z@p_|z_NGP1CI z24r!5>KZ_w5a)l_GH=mtLNGIP|JO*}jc;v_KXU&17WsXXQk^31@XcSRK;CMAWfna& zBwr{Q`6mPvH7$lb9OT#de-921paBy1$0}#Tr)l?*KMqfXiPlTfPq%V?vQ09B>Bf&2 z?+*7dpDoTF@8dQ*FOeHw-!}*ToR<7mad&oq+CR)M6(8p@DvHo^5y>p-p1!p5 zX?=bx{6bkL@6W$1s}%q2P%45wkrzra(e7!CGf~Y#H%oq;P{RR5~Su5LAF_nH9>-pZCqZFjpUk0fgFE9|n{78tq@sy4_!{ab# zTIOk$GMoTsg|dL$xIT`DVex~qiNJds3D`kVc&?_D(ybNKfK>cAk9Douswg>PiU_FQ z9tp)w=h!Z2k1DZTJs7cndzP)8rB@Ydh{7a*LmD!v=#J(Ko`?kC@UspxT7|8+(Glrf zT}(Ers$iO>T52uSVb>$YmX4CZ7_SyrWR*>K_U{ihk1VSCt8nY+v&Vq|<@&4J_smp+ z*y^g#Dmq(5us^V=nlI2=u)3fxkqkc2y~?)nqzHKi`&ca5L4`?b4>)3%bwq(Xw~S+< z{0+=%#o$$aP7w$|pwmRF3*$z`{tNVuB`j812oiXI#F_3X)Up8#u`$hO5+m-sY^#)- z1_@)hzXqfc+TVP!o1y#b?*uqmzR5vPlxSOs)1M|@88|Z)hz}gZzhX`aLP%dI8%1ae zgW%Kp==2wM^pE$O9H*e&$-6lE&(Mu~uV$niYJ*+IfBO^wXv&$VV3E4JLX4gf0rZ4; z#l<+Mi1C4G|D?ysYk!Q%iw7%ii+uZYUY18hoY%aGeD#Op-`nG#iCVA~E|~SVw>qW# zE{DxGa62>>fW_y1=8tVPJ1TiGEz)7Pfv#$CD78!UFz3Jbqf|Qyvg~Wek&Gd>@Kci0m! z9}}q&#Nq8Da@Zlo!7>N$B8M^zamo*a`a4d7p;-YnA(1}d>L~)lGq+e6jI1A2T==z- zN5Z$8!~`RxDL>WXQ_<1(?b2o^BI|Br6gE;IAZQE140wcbpohDIU^jiDtmJUcM#y{` zSPW3>3z_glGqFVmQuaxDEBvE>zo0F9)1n1zq2S#csnFp;LKb3Xy9$j5(8SYSlxLA zMHOm1+38>;tZPwd87v^j4XJv45k)vAXyWdAKTsz^{guOs&f}_?(esK1`yGU6-)m^B z^oReq5ph_fayJZb6&CG&#TVldEIC}L$K7}*Gr&_(yZDcYx!#qeq~#7PH?n5#UZH~i zxgwb>Bt-N0!~vZ`k0^R%hFN!}9Ul{U2yewb|8~F&1kZ&W@?7mQo04 zDwflIv*6jc^+GhsHHi31)$kdgu7`oTKjNVb z5!p?&t^kI0(ZRcV>6aQsMOI!QLPq{fQLb|ZKYqB(JuIV7F9DMQrM zc7uE`>QRg3UpAPjWMV#tLC%6oR9Lq9!kc)g=HG^F!B+5U;)P{ph_R<%E^;-0KKcwL z2Kv}0wWoCV|B)2lTRX7SzHxj7F+R6q3BK9HUY|^4&)wh6H6TEwT6F`>6Ga_m9VI zbqEH^>1*|SU0`jIeb9Ri_gB~q8a@o2pg~EFXp2AZ&Hz^P=2p2qJWfF8Y)$}f)MWy zThb1@50TcklHt63a)f2iwIsj42>sNZEGH^Ns+g{$%k^I-Q^ZS>*K&3v7{l6qy!Ij_k!*` zP+U%S8AL1pVCf^w6Og~+BZy;_zs=-Yxooq7(a&cDJ?UT=jAR?#8MBto2eH`8Rum9{ zq&;b9ILg1sM;^A57tg3`IqDxhb}RL(KHMh@!Jp_HL>SG;x4eRv2*reDI{Qiizu7T6 z45{4^e-34P=QjpTqL(!{o7jx2GKSd}Pmf#m)pJ(M8G4apbz~%5ZUovZ%>Gg+N662nB4}l{+iHX~bP6A)Q-V`cw;=vzs3#8+p z8mh0Qn+N07M{l#7lHY@7cPBE1&B(sm-#nEr(_SCf2n9^*@RAZQ>z1}!{lHvSZ0{r# zDKMVtdQ|9KLk6nzt~)p1V8H|qi|mlg|JD~O(H#wAbY^tUtY1D?;8)upGbeAc<6tLw zkqt{*t@B4}3G^$C(6qg-#Hnp@z6I=Ng!Sl)32JG9O4)9NQ3qcO9ZIUC8uCbUmObw5 z)D3M-FcBwXX`q_S*K7*={GPpZnb zO_73Yx@=2A@9}*y_svWx(@~|?yboKj8c|6SQoq=(+hReMHk6#xrq}QZB!1>>LX>v) zYcA3)bjZ-3Do~i9qAAGjqen7*?OK? zEsgt${HfU-iGoc(xv|!>bJOm_e^hy~^<3?=T`5?ec3lE@WJ4(T-?b_S94nINUH`b; zPYfwDLU(ZVN&ENGA#(>+oD743e^)T`BIpnh$iG$$bTBxS8v^C$h0~!H5U7;_EYU=V zL*aMk8k*?7%Taa*hJw)jpY6om#6C+#kjMA!t?QbK?IvGm-NCt&AZ}*z3qy!WidDr- zkU=O5*T=i{OM3dw?#AMV4zV9r<#5KrZ0m&j^igrj@9o6*2n}bby3^b}ulIkhZ!O>a z%51xG^Ss^>Q(6)MT-*<%GsX_LcYk(N`6HE}L!jOS)?>Ljvu}sM_S#CATkC`_P-w${ z#o~2&wR!4^04T!tzE`MSuRUDjI0*m7VMlI6&C|ln(}pydmh!oA_3$t~+igaj^&;fm z&ttxNxw~jqlCjt~m7f&ZPr=sv{O*&utOqhLdxeDQ*$29A6 zz|R*vyAm20MtHEO437_u7Ybkb{HkGT6!Ff^KO%(7Zj?ioNS+W}?rVI)TP_uTUdDNN zQvb1gblmaBz5T6Kxd%gL+?fV7g-g#8N)@{|_fMLig-M%M+T z=7|)^c@qRTR>3W^z$P2lZqVd(<+YJYwqER=ZBBTC02T{LF-}grbT|E#5rGBXBIo0+ zg-5d8q_yEYg41_bwt286V6?i$^5%=0o|0S4G^+XA3NY27u zmCDy@KuJUhNrROK&*(NQ4`g-t<_+(U@3^8V8tnxiY$BP+MkWiN`!1@O4Je~nAt1;Ntw7930SqOGj!6R?Xk(}d{FwL^={6w2mPH|i(_i21P9Z;J;m($@LYch zb&sce&Y&0U4QY^!>-z3;X?y646&sKkZX=hWqzwtffJqBHF3#c^;-kVhUa6qT^$g^j zz@rY*OYdS~((GJDqqL3K<4?;gWX%X>ydJ<6D#b;U{b(VZud~Q>f7_DK z``mc{iEYu`RSgEyH$%bB?aL{m>5L4x&tGp61`Bn(V=7+o{X}9N?H5f&;!!E)p~iLD zMGos5ZSFO+jY)d8S50l2|2*76m}Q^T*NRyyqV?r_<@)?wMyVK`UfNVnk!~7Oa>=j2 zTZ1XH5Txt=5vfDC{iJwEEZ!3#$(>FXX}>!23CuM``gqS-Lo%GT6{;Qy(zl%5QO8u~ z{P36TrC82%o?*nJ^#`ugZ)6gUv#xw1d=2(L@R;J8RG(gbc(71WbiWvD?=`JG#vP#{ z0UCP@85aHo#tRWN`ci2N&@$uI54lS;Iad+yJ-ydA-@zT59R+z|B>zLUcw-0 z)$L$`opDQXXDQM#Ld7A5#}V5&>1nZ9DVJHXPQg@!7a6f$y3BDOj;7k(W0H~q66h(7 zg}3jG@AA>N6E9>$TCBkuF9pH8X~(BvFF}m}#~2|1BOAHmsOF8|*_=nEl<&`P$mV6G9~;=(~7emhYtpJmi;Ve zDXi)|Kp4ZssG9a8lz;{|m|eE#=`;pD+nb?y3%3FDugapa|pDE(xi} zooL@)34aSxU|{TYmWf_cU;;4YYE>?ZC0t3-qC_zA!Ys2lv)BgHm7>HqpMHpZ%s)P9jFL_g&4rjEny5Q~Ba74In=%BMSpDTBxdF9^L-JWkd4K>AmN*`6Y zlO&on&`UtcF-#}P*%UI&-7ene!Kw8hn~B96tT7A za}%EGiE+8`AcsKiNT)t)Bdv%!Nqd@0HcdwpPMLn`Gxsc)t7oadCYNie6V8uDaf)4* z-M^JK+XdIY18~xp)PE-vqNyi8ekkbMRN#u+WoMkKr6}F1FcUuQ9s2=&bH+kXM-Asi zKBw}&d(jAHuhZ0KgLov6Mgr;+rqjYYl#DgYw(p?0Kn9`hhe}Xx675~q!CP2mRok=tj@uC zBZM1(ABXtFH@>F3K_IuA(_9&qZghhOnn?YCD->W|S!F2ywZI0TETi~mkNwSxCK?Jx zrX4S$8pAzCgdP7E-0YC(cw+U4?>x>|Bk!sdEr-BD8iZyH->TC^FJs?RaxzXeE~l)x zN+%t={^$^7LD!R@+W*0VZUo;`9Y%CVM>vlv)A|=98~RCfoH_sZCTee5A+*4?8HGQK{?t!$4SV1AtO0|=k_B@}B*K72O&Ovmn3 zV!&*spFp+-$jpDq?<>XU>Rc zdhe%msLXbJ@iuIq(umZ|%+GD!hASARdUV+~{kW;KDKu)vP7#=i#x3~dgv&UHBSR<5 zDmdo7?0b+i1ex*nH6!`LJmjFnik3yFwD{#J9j$cnJvUEwADc9jV2`5IGrZa0xl-Z2 zu%mmJ>B0aJY@a>c<=Ao~j8kvOQ=uN$Lbb(O>o8ZVN#7NP5_Rg`MQGzRmhq8omymCn z0e1fpP;x_FK|}Qxvy@Lv;8_~&#`C)+?R^^MGC_&azN;GP)|krDX(uy-3NwFC&3^V8p#CS%#(cAjy%ezx0AN=J*n}D5ps%s zv@~*w*Wqjuz5_Os5tq_?VRAmh7(!*KBK1DTPa(3Jjq%WTE!0$1o=*DGzsmqv% zMbIMvA}3>bp(0ISF88&j*Ni;W?_ITN0tTg?)jLtUUy^BBIJy__PXNG)=#r+}-AZs| zjL3hzL;fC*UDaO1r3Tt(HMZ;K!EgV(_&SG{%u9*UP3MPh^mV-Jb1#Lo{5yh1ldD+u z$}yKur0ucJm5<>*!qd}V^@+W*KT=pR$%&J00IF2VDu`Wr_v4OW)JB2=UH4@nl{$GLshd3RfHCw9<&uYz z7PZ;oVfg{2Q;akQgFj4he?7ck^wa0DpFc$(swoEl3l~@a9EFPuLBe4FN#{KHZ2L&^ zXR8r}t?iOVv8M zj>0y6SbHL%GRzO!Qx8=bh7u_v#ww9Y>;6jFs+~n%`;IDO8@B4PZI;HyBdRicZzM&D zd>9K2<1$vT^1sNhCQ`J)>qK`J7k5SO@=1{V2Ej$wKj&#|CjfFVk}isRN>C1jvoUEO$PxHTQEYB73HI}o=4UKp-xUF6 z>~X{1hlwK1X+AxyGEVBpM}o%Ac_pNyeu1iPOBTUml%Z4snjN)0B>nFpI6e`@DA-;_Vj51U6{)bxTZCK^|IS{K5n9zts~!`>m%agdu&T-C;v7 z6^0adQT$VW`&AE?WY!Qax$nl4INtu`aAm(!z&>B2A;#vx37Vke1R#PQN=t%iM zMjZC0S-l;o>q{99LDbXb*d@zz%L{Sg%w`BXHPaSxva0K$R|HxXDdJCwg>q_>@w3O$ z5zc53YQ!EtBZ?X;0=PHFlJzq-@Fl}1R_DvLp-&|mX1BidlV`rq>GYQE(Q)Z#2W0rP z&6@03Oe$L}u()1Bpm%$Ywre@8@CQd_$jyxVKllM~okoWBV!{#~r_%QC#NF+>Q~7Vn zo!WA>SzOea_poNQgqt6iB<9CGp;9y_s|nB}y=%UHKR^K+uJ0}HqaJc+K3hTa(2jG} z{rQ+A)#wx255;z%ryLDDbJU`{X~g7@3Bz`Di!Cc&-94SxmLI`)Dg2qd>-mG0Hsa;t zC;O&$b;7o%j!AK{ucfb2p;(j_mS-1vTc7*K>2ze0=TWSZ5Tktb=M%c$N{T6KF;beO3-_Jh*Y+)r30ma0{m7UWail zi-~yq&L=iwXjX2086cp;4NgkHR|B}#US19Ev*A^nI1E$pY8lv0<+m7QeIQyvZo|Zz zEf-&Q_~||2^f&eL1zGdAVA?2AEXOfz#B=B)Bw=BqsnzaB%~SrYnjcjcg9da>Q2=k1 zgue(Z#dGkzu6c87``;W<<5SG6#ORN%BzV&@l8cbPd=#^HVhxl~3Lb8&tq8d=FYY$f z#hXNb4~aiajM1LZ%n2kO|m@_T7H#b{Dr zof|mN&vLDg&3Be(K%+xyt$i9T{Y)cf3#O?U?hz3`kmYchGr~hXNFW`UXN=+VWuVE$ z{y3Rv8-1u{w-veFe^@1B-`Yq zo&89y$y@#^;|Ml66^&))qSoAr3|9NHZ0qu=Ogm@6A+{xkcQ5=ABrg_ZT&px)m@8ca z)v(%n;?_SapV6%SICf*GC!%o(i1n&diUthrgVhK&wiqh)Y*$pSUXrl#kPqhJZCOogWszQ-S2;suo=_B|G8VPZB^GCX_Q&)Ld#7i|jz(Z{ z+=+f#VK-O!%>fU~j_QC?H-wHbti$fWH&r3Zue(6TJO@lO>>w9TAy4WHbhQldmtVBJ zgy6fo;;x!hVUUu~ulyW#w3nG0;=Ox)9~Z<#-7J_ypVIfR-(d$tCq$|_+G+7Eg&f?O zV^y44#>SpaRD{2Ezm#CgmR83ij23a&c*Mv%O&^=J7z-m&KKGBJJQ0@BzW-l>r)7Dah zNW@dDQo^%d<{FYoAK$`GtD-UurwK|$*Ax9YtuAr86`f1|b+2b*d5tk40ZkH19p6iKrh_M{Wd<$Mq@dj*0RvmF-cYeqN+lQ8>;I zfAho#o|C6x8N|>SKIZ9ocIb%rR%$fN!~@w!MSHAu;0Vd=MzfLsd$*VTx58dFr0F?PY0V*Of8d$~9B-rK20*+H#= z`l=h%BrI2Ml;}(L-1~1YAlc2Zr$VV-LDn=b9PH_AND%3;q3!O!VFlLZI z5&jddf@e}*waOWkK5_(*uQFYQ37X&0pAwKOMY)TQ-qmLDb$@_Wf6VR}jdcM26;A!2 z(#)!MU*pB|0c^}H-N00ba*y5~@O0AIU`LYrBw-_CN=^3qE5Lb@7G^uS9Zjxwq^C&!9$`V@5I7`}j|D{g@3(cjEFd#X@|RC+O>_}Rd&o0u@C$28O}D37_Bw8L z6YQXS=r~XTI0W@f+~fek{`;Yh2?XLmr-Y#@m*~L1A9S{a_^1~sKa>{&b9 zP}rYeB2dUIe7v`4NGPh+Z5kZG3;C1Aj}p#zyE8B^42HbThvb9&o6qQfwSvIFs1@&@ znnL&xh+E2_3bl~1+k8+k@~@7eFkT3MT_+C+4;K>(M$`=fOyhy&=PD5P{z<=?Ggaw2Kga?EOgb9QSgbRcWgbjoagb#!egb{=i zgcF1mgcXDqgcpPugc*bygd2n$gdKz)gdc<;gdv0?gd>C`ge8O~geQb3gekNtlw5y{ z9LE*^e?G;*!^3a9`}VuP{rmX*`-41w|NQpw@QFO8 zAW@Z={qr()iQ2Hq-a*^!eg^FI4x=u*dS| zJM}E*5z{R1R=1{0@8ys8PuHc&-@jTu-dXO=3zQh0!H?yo0-ayqJ1QfO9~SfLP(qax ztLe%ItC%joW-^6)M}1x(&rtq4Z~8^I-aOR_mD7UvDAHCae{k=se`XPQf}6VKIK)J#E`quqQ*W|=T zVqyg<4T%3m7#rc-=J5SSLR~AlBytk$6RFv+uF1y*~OC&`0i%$5_U%J2Z}^_uFKW) z9A{TosJYruB_Dp}$VGIcvU;eNlgcuqCrr|$l~I(4Y`E%$Cj^282VG@ZmhV!kD#LYJ=Bl6wBao{U z+Uba`QdHt@JdYo-A(VGXs_4*v~t2^#)iBv^kC(s`3O2Vta+)l%6Q z(!N!R6l4wj2gVBvqhdQPEDY&cjquLaz@O8Q(8bh1-n<||ExdK|@Us>00}|GI;ia-r zRV`wu)Lbfhgb^~2a7UelHWjlaO+46|2RCYRt`Z}+zT@$@}i$Urf@`DX{EEi zCfZ-OL@&X@NsBlp2vwT8|B{4=UIgU;4Zf#Ho5pH(iP>WWQr&>}=mB7-wbBzSytAba zFxK9B9~c4@ft<7=7?Y_Aib#7pfRN;oM;L@??Lzz~B=LVO{0xMzfL+-m@RS~U+sqsu zm;3YG_Pmfl9DK4aEfN^@;|&HYxTI*i)jYWmt%Wn%@~F+Coo(fhhZ$T72h3g`bjUJ) z`jsV_+{g)t-Nto|y>ZC2gy;(e_?;wihXw)b0(9LVDuh1Lxdxn$AC$+Alj^2sER2Ft zBEVlzq8NWN773sVOW1W$#H%B%#2h8E}JC3UO&HXJyntfms^I zrg~c1$U`n=GJ0fFN?09j1xc?D(L(&(tbef^wPRDv1E~gG=6vsfm9uiNUU6T4x+WKH};g{v#S5>8D__ zliN!Pj|_!1dEj13AR@yV9_mn1;tS@?1FB_vw0(}z5#&n^=%$<138Ah*`WHDKWtAR3 z1WArNB(jDZJ{&8fr+tD7V^pUBd!^n2;YxTi&%g;SZEif z5nYCuJX>Vb=~DvqgPb0Id$jmjj}}ZuC^>(`RZcoG^URrzTY{TLg0NtKocXwJtFq0D zo3Viw9>y2NESLPaO9ItmPCN|jg~vgwuRZ<5WfTy^jZcn)3o-?<**YznNY=z;Y%zqnH}YCUwY(hhsl51V0YLKqAWXUdSHa5IV|O@u8lq9_>j8|Fa{CKj#`Qx`tA_%cIVdihCZBPepT3~8o6lIO8Mh=LB zTlRrDt@hT{zcH@9ZKW}C{9vGwWH)Ofwh^c_n&K|i?@$;=OE9+bJH2Nje;g>vF$!zt>r9NBW*%C);1IOxN{bjfjc4cXPywRvzdb8#b_fYc|OSJ zRu_}6sq$_)o*bj1ue;a(9o5GH`Z{anR#VyUia=Z@0;H;chlk>AH+HZ$Q#;ifxD800+QXQpo>NXweC`ANgt={gZ3=vbhH@2OU>Y^O#hE!2R7e|{R&(KRRq{-2M zFS;R{&PJ($ijrZVvk}7MO3-y>QYvT4QUlI}sYuv5<+`c4&c@uYquM?=y0g&$i)iHA z&c;W-bZ4W2jw63gX*8FPuoRRx1h}LM_G=n82I0;0{A?<#c4RyA;nxoy#%pHbJ!S+ zVxDr{mGT`<+ck?eC*{+)CK#t4n`9?!gX1gyJl+r9m*wWez8_ovmmD^H~Mx$c%(ELppUL?t!7rp2U}{5JJB>y;rZS=P9T^DA%W=rT{a z8)xpq{Q7ip?u=Q!=LQ~=ffK?gMB8T}tq}is{;_|Nt3iU=gk*@!)dPiOa=1)C*PV%q zqijU6<)qffYxyi&nrhgqb@^GHoQ0`USA5o)nA(wIO~X!vU2C8u4Bs6$ z)L}-80HcijE_SKr+S@7WuB%tmTHuLup-I+WUS8AS(u1rSQnNB|bZTLBZMN1jQ|#5#Oufm>c=Grt_it_(VFs(L?;q^^a5$?BK$EclS?${JZU8z9=bSZ7`+{au6BB>I zQeDCFa@4@>6&)=%AM}7t%8#YiTbnH7Q&MfKw-J@RxCCuvnA+9dR$B}P`#En&8GBgJeBNhI zSli8b!!|JyptVD%o+x0-2r_q@d+UF>4X;etVsYtM`wR1S3FHQIf`qe8-KKW7Junk7 zt(qOR6_3b9I-whKr`!UCQ)^^*hb;V*qi4s~Qm;H0w!9>cJGTz?Z31Hx;iITV>*gM3 z+Vsj~dSF4t&`MF-t+udiV-3}d_f4C)r1Ang2y?^a`pCp@rQPb)NH?Y`<(Pl{4Lz$k z$~EE+35FdEqS%g{E-2@dF^lobUP!6@`ja+ZS1icgA7k=6~$Q=dBZqC^Iw+3{q zWp8)^LL32Jm-wzmtl-5C6}LVDhhv`1d`2e zYU_Rx#u65`HoUD^;DL=4WMrOfM1l|jKAuxOJ=0aE&grV|UCS0IO0Q?SZs&fjQ3nbC zeWTzJtr9V&czE;f;^xoZ{pE*0{d9Qq~~t~c$DLYmlSHNBY%1M-QoT>7q9Lw{x;JPNT`f3(M5ml%YSATcx?_! zV~Wc|5V4^035OQY;F?2d&yJVobOg(f(YjpE%@f_}?D?-PKfp^}51LQ1y81kq zKBcSIJCLX2;p0;$BV4nYJP&zwqu)9e%e$*=Evo3YUbH*35^vWxj_))oe-*ktISf zvM0b3Vrw^Jb5Rec@iWdzF`zatSPs8B6G+y7YjM7*w>qBps;5_ zt}`lBcLPG^J45DO6h);gS}xF$DI~57Mh^>xQtZC&oY5mrU(OmpC#{QDrBgPAR)l@k?LC!UoG*rYYdXS|j7Pp&;^zy=kD3J#(++u*mSE>x5P zc5dd~<%ed72w|Qo2Y*&m?g$l4&dD9J;GX!Tb_p} zqM`_;xKIuReL8mUt9IN?%{Zm@Zp6Hp#veu_8JZ45dQOs*D7=iTzD2<^#ZlX%V1ns- z9&CQz4xFs7gC8BqF9g&?<`MokeqtoZHX=U*BA95~`T_uilnX3Foy92bWhpP5URQe|3nU-?eSdHrk4`{@wZky@GRg_9f-)Fi&pP-r8VVHlAGB`ED zB?>fj@WJg8fCSN{b8fQ;qyV|@pa%IvE?(EkC%8d)v}1H=EP6-UT!0i3DDok316_X< ztya6lO?%MIMyfsHrae>+q6%>kotE}L_{f+LwY}L2v&Qfv4j<1RC^^7ci~#tJyuoM; z!GC(BbHYJQVxwOKy>Kf+gFJ6+h|5`jfbklVJrPqg3zG`06u2l#*@m5*#V^|;~u z2jdwE$RGPL!G(35-(@BJ@km+nrnNbd`h+1jkTPj`%jgI^55MBgguresj4 z$TDmgRCr1T@TW}lL$p`Y3TsW=g*pY~wBY%L5#%Xl0nrKuZ&!~>OJP)sfkxhKiN~{{ zRiwRW)1^d)qOtaUbDf0K8I42c+D#M+`|Py`MpAK)6R#nY?6t8B8g~@bJ%fK+f|naB zMJAz`IuqJyusNxGdtE??`!Q-)Lz8AlNl>RQNjG^uCQMyu@OtS=n~)6Nl(jOG2dY=g zhit39eP`6+*MEgoYjb8K_}a?rHqlgfhY?L?<+0n645%xgr0S>5@yI4=L~${AJ0bXp zd)UrRlSd*jh2(0(Urt!hk3WCV@}dGbRuIS#?Q+#ZBm=j@aDRYe@zAy$VVw5c*s2+O zo7nKdIzIA9tWvIc%WYI9*}kUGc0;**2!ORF3k(>;B3#!-DXX>Y0KW*UysDahaX5+O zNFsHj8U^yuWCx$28>ZCK0`kaaWXTB}|4aaN+Py zb6=8M!D#7Z+@2w`5K;jyBAq`{&I=bzvKxI{uZ504c0Gb72X#Qe=`PO}!tr3O9z&9k zBI#p``c{uDSa2m$^kaWmDmxsScRN+Y+LD%g$6L^L5v)|PT#(%GA*{~oDLrKhkUxPV z3id3cJ%+tHf)^>+G*%dZoPhOkpOP&e9k$O{NF)lx=`J5>0h zqzW%1Dd^mimYmsauC;@dto4b`KR0;9ooAKpxu&(>ScQH=dp16lrp>{^bevp9F!D0$ zu2_z9XHIn`AL4&%uLd6V(fCs-4f%K{(^$eVdpmjXu7n|^bQRR_cjW*rRQ|1}S+vC^ z)e&2b+1xHiY~mP%uMl^C35;C!Dats_qCAs6(%vvw8OqC%CT4{sY-+#)3qx^xH8rs3 zb`qooU37u=eEB}&W*%|T4G$ToExWoxa#B&yo*xfva%q2U6N1;<(7u^Cu3(!DiR))* zNDc6H7l!lIZqE-Hp1rmTz75D-*R1D}jkAG5cV$>{(gR;Z^CEM7k!Ahjv_ELc?ad2Q`J z#KR|73aQcOb8}&8nvs6rP2&M4P!nGlXuqR>?8SdUVjTV<%~4L&NS7CuLg_9K@vtbN zHe)saJ^5OvA3~9f>0JCd*9lLZ5n7V5sRyX6ji;kjKj>mAM`6*7-y;P=V;E8(%DA96 z_q!!6f(~JO%bSz}lEr4I{*r)iQXac5-jeBI3Mm-v`Ut&c@chAR*Lc6hZ>rz0wQF{v zCYXO|Mm(lsO)U5L>NSgw!ewnnG=Xjh6XQWS-NIAom!w1pa}TK;(JuR|-8oAE4ib33 zA#M(k+nKmAjT-X=#z1h(KQ;r@9M+))R+2r<+~#&09y8XGOkcf#!V*-Q8=XEO@s6IO zCFI{3JHXSjjl_zaUJ2#=JNU>WK|2G*csQ;a%nWni6yIF)~7 z6P{=us^+&M*d!N$5lbl9YD{Gt8#CD5f-8@4EW{t=JDRJHN9gWwyRtP^RiJf%&i&aN zRKSx-E1Qk@~mm0`yE8ofA6e6~Cw3@^-9NDfTh{m)M;{1>4mkb{#kZxffZdMc>`IWw0r@F^yLS&v-B6@H&z z(JTo#W6HHJf}jLpWO%bQ#t#`Jf+Oc8b`*$`5c1>m)$QB2YdN*to{58mh1|{bt>sjm zwZ3!eiUY@g9|?STEtvPgA6~q=dh{o2{`~zPe>}YS;ff!Ac=7t`(HHy>4mU5aKD)UR zr%pl}roHk9Zx~lWxx>wWtE)eJc*{Az<;otvrCPpUFP|^hXD)lTwmqZ|-^oW=dn}{8 zn>|{7dM|#wfBc<``2DNxz#e&qq>x!t?m_-NX4Y$Uulx^g$-+FC%o$z-*m4@~^F1-q=RQc~`SuIl71A%qT5<+2bQZ@1)nDB^ZUjpl#_mia}~7 zDCEQc6U5#WHS=(v5kHGbMqJtYk@ zCYbxuy+qw)F4{^Gyv0AaOk6OwVwj`Uu2KMA2>C&KCY=y=>&bIfsYa5tVjq8(jbSgd zmw_{D(70Ucj{|ENpbmlPN3K_7J5#lISS)jCeqEZ8=BUfAdHDUagxIvRCk@wd#NpNn zL{UPi(6=~$^!A}W`Z}U-M_!JC?+Rka%aUn}hts<-;MUNwwdgpzwPN7AJGDN;l-5jz zATJ0Gl!2ZQ#%)>|6C0Qs9u+B)$M{VS;(>%1c zuwfpmHKnxQ-j5|7sI5R`&aL0;qLhr0S>3N*6}8bF)i|;79833E($Rk-nDKrXc+^67 z5~*#bf~I>=58=|G(!U-y^eGEHu6Hq6NXry{o`|D`l*~Cf@VfE2u4YjRT`fX(pG@=F zh&CX9EfTncnmH&4gC%gI-7or}@JZ&Ya!<-^uooN>M2OBUXxH$;@$>!C&K8#2)=Kgy zGgq0@Yv_fNsa}-fey)zkUqx;W@)#y@t)fz~+OM5yFPjXq3%SEHw z+I&ZI$uT}<8-aP6d0uK}YV-Jl=8a^4CatYT|C-n)9S4RpF}0EZIqywFwAO9f=M<%X zXC`Prxw(!3pA$W$N{to31uYS{jW_ozayr9m1o);AOEAJX&@7W2aJ!%5S+pYcxIc|J zf#aZoSnRZhT0)rItOc^l&09lQ9johw&|EeSgIn2Cp_I$QY6i^CsW+lTgl_z27%m3J z!)|uKdfG6@4xCVg*})FThp@BkQ1BRkz7DmXCCoVfM`o9##*SIx)zJ+o(hcN+!zn?h z(~wH6DZ@2PJLbl|U!URdt4{~7zh`+hcOL8f>pI3cpgJ9T#3;8D4Fde3-4o_Ohi6V^ zTgJ0Q4U=t^F+8@x^g^e%X@vPSLS}Vvq%+Ir7CqR?4>aP88y9uq{{~_Ru92dD&^+u# zF$9P32BIUivM22&*RXEcW)6lgdp#;bOI}P@<~YP?z~9_vhou6Pr;?-fT5~XDUDD%; z4kG2SDK;d9HCku5GgL{;QYWsOl+Xvhg@SOG6xLk?9j16~nlMi~h-b`;E)U+Xg)DE- zgW4*Lxk`W$q_EaZoqSGenc>@iy$k-WWxhLZlaXwJY#Ko)xN26td4nwBl${7Qfg^*A z^8ze+m|NMCeM>f(`V_zrVT$uH@4*!3172W?i{&?@gU2&V1irV;^HlU#CjWL@U_gdi zD(BkBeck2^-GM)R!fF-idU|463`35%**QxsQBTlba%2#cIEbMIJd6%D^*!U9dCUVf0iP3OdE zM+UBw3Y*LJgBpyG^F@E@Wd8thCy8w*StmNrrq%isleP7y zptpI@U!R($vUff%h)NzT<}n7#i_=Vi_Hd>KWI1M#VxABR#iVtAWRJ%A0YRD3mgqqr zArR_2FsUBCaf;9!DlLK{=xLzJG1ni64lhZd*qbv;d%JFxHaN*m?z-|}=dNpKcka3~ ziyX}EdQc%QV8_0D#j|bvq^lPPpC;erA%jKmmE+60yaejNy`I`Tl8dC%w-CCMzfF%(7xCk@G<*Ql*Y1+29 znHGVlx>%PF_)00QPoftzDS9vs$Q26A6w_@X^{r1vr*v)skQwFL4loru&z#giO2!GL zFGq`ni9&WW0{6h8w{G9ItcmniSFLYac|@eWKqNNNkG2kfDK!VW%aNbZBgdj*U(@ky zSX?9F(S!6#bU^eWpN50E$jVh{Fu62llf+LImBj5h8duiVzzt zjJK-{S^XO`fw4SM(Rg>d$#v5zZ%{Pxa7htrF7WsjwPnybM82n#@QW!4GwX}noiA4b|f=Q zI34;`agB%q=ncZ5`tIuU5pa(f$~naS?LaRV8v;t^h0@fKT0TU1e@5iu`0Ze3w|(pt z`P*)PF+&gJt;QkloR&>4Pa?GJd%R$n!up+B_0p7{4R7OgJGem7z;%bYH^QR0czs95 z!=hT2(=jVhWVhiMpOYsd2S@JD4LjyXM8v}uO>bH_Yf#a`L?bjZ339ozmk--E2mqQw zNyM{Oy`FXTz%B5{FmQBgBY?VEHMbE+B;lZcUNjxT=GL)Tt_ve>t)92TP9vII$`2;C z-3dSq)he3%?!l#4=sL6U9*#<+Lr3X*OiEvfz_$*%827yf+K>2*Ye^7o8XY{@p&{QA zS-*hnK+*bX!^0x?z(q|97mfC=(cU&{R3uPiH%WRd{Y3)76|KLfTO&=)vFmD@c5t76 z?w~A*F!RNs&fUaIW8+7wRhFh%x^VU>4v`hWDZpj9#~_}4L)+k^nJr^DYUF)&08jwH zSIEjtL`3jON@{z_rS||#4LBKHI8&`*7RKa|)4CXEXtRWf1(_>2dhq(K|CdW%| zi)}S?$%UT!HcA?Zwgd33W$cVO-35GO2Rx{tp1Z|F9tC?T^1%Jvfh(TQgj3V$bhPre zwpY(vp_BH@ov`NZmm;3g#G9~Emqu%Yb5zGBtG!@h?A8vXz>Qy2Fn&7(jH}Xr625*H zT3qysP0x1f5v57j;~|=$Y)#|+LCCC0&xL`+sI1j8DNHSe!_0<+CUGawb1$5tVA)+P z4xRy2;MEXohdq}#W9D7UFsHQ3d%(1^7rh@q+L+lCwz~86&S(#Cmf=3sZy);$O=NtV znB~S^L}bu0RISrc5SAf64T0o;OIY9XrG=P2B&Bg)XEIEnFikj2A++D~@{8_G{F8nk zX)ST?qUN$dOL+b304$mgPX)8}ZKj{b;VEb4c)oAxA{jJ_c!QLX7|pD!q#KvWJ>S#x!aSF2cm7qkC{uLL$E z9b&DiJEgIFtB%V$5fp5KBVKRPFt9cr^ojRyOxZ3c0gyZG_8VBwke1-ptp8{j*x1}~ zf0==G%xhI^-;{w>3>rg8|i*8rB9ciI)HLs3Wb(~hil8XM8>ljJcI!*h0w0{OC zYaa8v9UhbKhvk3~xl-hR8=I1KgZGz( zc>rJoVD(GFJPF8O;e=nm*`l?iQT=5@Xj5pSGCSv_(3XO#jZt=gdP`G?4Jm4sNo22B z%PnbiaLT5a&DJj21z#$;wp5+LEa7mYLk9&a+PrAkT}hd4)}D#Fu2xZ##m3k4W;WL# z+-NPg^t-HzxO!re>Mm2K;~nlFReLBJ&aY~F@0DXC(dnM|lk()WKD(jsK_Hdp{J|ly zVojP&`)&OA^fbl>e*xT&nQ@n4p(z!&_lYVJ0U0zgH#jvQF*!FbF*i3gG$1oGFfKVY zH#j!8A&V+M0h16w8kZ0?DGis0j4BcV#Fv_kDkFakveE3@-Rhq1y1MFDHLDK_|3A>U zM60J5Q#?HX`s(4A-hK7WpZ;-p{_T}IeEa;x)x*c?kPc68uikrlrI$h4y2(Zp57AA^ zBohu#zrOn9?N60bpDN>zuVm)e7xVS@^j#>vJJBBUFYlGJoJP#E{H*wD{^&Knyng&# zX?}lw<9xYy{%*NJzM>QPA^#{_&YRZzkRX(wvKY43)rRR4Go5J;hPB-8g z@^`0A-!}JKraCU=c*ARnwZ)R(y8i6&^vTtSPp|%Zk|9K>&19mBHgvh$nRJoS!^cM8w@zuY)?l8B=ZlsoD)-GA zWfzV5TSocK@ssR+qI`{=5|qj{_mehd6wJjP-{HRLtjQ-HUKpfHDGu)9tD40 zFp`9g8KoxYZ7}u5{!k2zlWj+)Njs0*Yb+xhd2j2MI!x4Z^4WPjUGhvE8 zd0(%O{lL}|t)INJjYYpEuhFH+kV$rJjgnRwAExAVYM4*reU46spoyv4PGQ>@-CMNf zokAtfT4yLHU37AxIu5;Gx|hnCRBC@)DYdI^r%TP0-Yqnxd%It)-&OC8;L%|l(14)m zU}pQB{ zO`%kdrr1|1Gm*DLY6TiQ=s>ieLNn{XU+LD5qg$o;1HzEL_|=f;ambH)6w^4Vf4!3X zfZV?lslAFuEeQ%CB(#6T_0@z&`eqzLPsA>`A<`5b|)k;se7j_yg6?f}LH3;NQ*u652YjuCUvP@t%)e&Nl zBKk)2JCX`+ijBR>Hl-u75xv`@kgvku*mXUX@_qJCA&hwk0ufI4#*AL?P$Sv1cQ87F z%S|zSmzen{2Cx1B_eB;qIXnWvz8#6Gp8zLBZTellj8>$EbxN9@%14f*fTg#!;Qz(+ja1Ub2gvjU}etUK!#2P2~O`n z6cB^c5R)(SjIZg=Y!Xs{=zx-kx!~|MYd`@ZXRtaTL?JaLyGMUomTL+D=ay!3+q4(1 zK|r557`o8E+w~PTPR1K!Tr>Ta(ZKp`gcVmCl6{58&Tzbi-P;e?z99@8+dT{!&fB-- zvcrhjy>c<^-h2uGb70ohb~YXjBP49nyjB3-z@Ba?dxx;t(`w9O2`RbF;u#zvY?BTa~>)>Qu^3fl@#=8fX zw|}|%xQ+p|n*!=P#%4>0GW}XTk^(S4(TNy3OSX={H1Z&vW5)PB3cvv%uNg@0mh_Rp zSPs21>XlOxcpN7r_0*e(1+Z(A;vArtdwJF~NNwl9bN7GVEs~(5c<9*v9rjN#3G}l1 zd&L123v4eF46++DV<0T_m>&vvQfgz6^_# z?KpfqeI%GkVqZwEF>v|hMmzv=geiNSA!+u8t49Iz+<~=lHwVr@i4@|A2bVuDUlTTD zJpusD34wp!&+;_6WF6|=Gsn;GP7IfghX9^v!~$c-1_1_uzf1d%O|k}?Q^~$0ULi78 zfcnjk$}9&L6?73au=Axy5_D}jP-v6hGB|v{gF>U=!T*gFG7xvdDK*qzbgFPjRp+_K zV4}zxZj2oUiV}OGc0dOz3LH)hr8kZzw%&&!rXYX7L7>_Y%RE7vg4!!%Z9_Z>2rhXg zYb@!3I{*qy^iBTs-iCiiU}PyZnTX8PB^VmQ3C^+5NJf;!A0_!ynH*<&3SOJBGL6P5 zrV+!ADKciAEGD;m(N%3(2*d+-0<0PiAej&bZAWu3pF$Y69St3~$fL}Vm^DhyCN))s zXB~e$2(V&efMZA!fOZ^*1Y?pwQXPf4H|rY=1=%#iHG83M1&ld)KMHm$nw)FhL01yQ z$-Gy7%-{%-e~huA{(U!rM`bf0G0efjtjX%S{;`RzMQp6 z+h0^vMfOic%Td`#&@8KLC9qZ6UM#J?`)GgnQMD>zu6N3{9B*5FNL7bI22jXmfuanY zWx&zjNblKJfDY5v^3cbfIu*kBnXucbrrM6F>w{~wV37~KoUV{v(!ac~)vOCA8Fzt! z9twa|Bfc|IcS>W7gdF4l?HSoN`-|HMM2vyOA~vtfXrA9 zgt{$RrNIFMpOinf2IwJ!gG{)4PoD(&#qmQGs@J8{(_|WYRE{^#ms#`IH-rihIcobB z=j+>|Rct8>06OE_Z55HMv=kiq#@m0+QfdQ`_4u?z(QioovwgGc-SBLGRF36txy8j~ zCi!}0_G;Z3c8V}+G9>AV^g7QxD@g~L;IqQ_xLj{-nfM2HGlFqID?xJUHS7v=uW-ZnA7OQ{bU@JWV z#*&4~}L?okHzu!?v>b6_15Y zcZ6~VX}XIyVvJu1_>P$_UxXreb71EYd3}a=Hdt@$q7Ve!)M2G+t#Q+z_+6&;&P;maidk%j%S#0#`pmB znH=idN-(imz$Wo>uXUN?M6;d*^3bbq_z)ZN+n$_!T+r{$HUkU9)t)f>k(Hxbj8$4+ z50Fy>V}_}b=qtM!e9$Jq4h!ZIIbKcHrZ{B5*en7-!~H7bu-(6L!^vy#oF97NQ$^*rg;Wl;RBiT}9Cei*4o@tQZ|tfoCq z4^{Gz{HX8X7GAQUrvJV}96@ZxC+DWgmRDV$%1`uaY8KOrER=zRcPrF4&8dU(J0&Ut zg8v;BA_naLe`tSl5B0Q`pF&;g3}y)STz+W4=9!5;{q(^JAIYD|uAbSJ*u!&OK3$&q zKBI#RxAhi8dJHmz43Ib(aS3qR%c_;Mb2h9m@qzp0mRkU*nomk~gqzl?D6Q)UCaKbt z4gS`->tOo2a*LOm%dTx@EU`6Q*VpPUIGaI`=lCI{0R?{*l<O1c9^xyTs5dOBCco))PR%$@J9j6yB_-3} zZnve*2vFT_{hv-D8kiOhwzG4mtO;xF?76ZgZY+zh62Choe*B#&AAVC&3U`}Ln>rCueeMfgVXDK8(i3@Lj6fV-T7w2Z z5FcAe(bx{Net?JbW$nStuJ%c}S4-0U&9|0Rwab&T%0VNjN^VBXFPmgewwND=0qFtT z7Glw|p-_%RYjmahp{!!%z2F(=8#};w2p(aG%iEZLIbW7J{tLO&iT;x@ZxfeXnkuIR zGB`3cmq92gB!Aso+m0N!5q+PpXvIk^MJq1J;uUfPB$fnOKnyIjFbsJ85Xjg7K~_QH zhr|#0_Z;^0bn{Z|?pbXFC@?hR=`NDRx*XPps|Jbxo+*3;qeKWX4Das_mp?iCmw*2G zm*M@-2RZ!w{=?z&wH)GbeS7%h^+BBmDPx5R6oz1hq<=_$xV}65@c2ebc_Yakzcr2D zAI8ty>76g$O|(P)@=-a-3oy6py40>81&5-|^HhtTycbe+R%5lLboM;P{zkKrJ zaQ*i1>VNw1k4cA6p&~)S2JQ0yg$XPq6h$Bl<;u}CUh6^W+7jfT)uMboFO;Z*Fg1A) z%IiUsh|Vm--W0>yMU)pLbtsmC$Y>sx6Kf@+mnHExJY^81LOrc?EHROA)|A9=dCDkk ztSE18SyJOc>J*uR_!&#EC_*?Lor3 zhkxP6Tm1X$;fEhF-%kfK{OOQ!5r(^ii`mb=9o`kodnq(t`qSpVk}|$}!7&83f)KHKc5HL8y4E z#n}gep9r@^B{a_1Y}SrNDl3A9Hp^*w{C`kzzesw|rr=>Zn1YgDUweQvRqH>Rm%qvd z4-dC7z;6>I9o?~%Ht;^WGtLJn&{}^~BxRmpItoaq3D(w8Iqo>A{LvB4g@(MZGMs-A zGRsHw^`;FZ?3n3qGuagbq)Hsw68yjG9BMdz2%6qLel%2VeMS2Hmf$tKQ%WBOGJirD zrS~7snu3T@>7A#uAz@uCssF>1S{Q?~dndLQN8GaQgmJvvY9~dEm4G@9rkxeeseQEY z2GX(MK=T{~2_G*h=|u}{axk{`sU>89L95)*_%qAF@e#N-V-&0tnI~%aDX!FJEj$ng|1zuX<^znSTA?X2U!2dJlrV#cj z1abStrT_&&X|pc1nF`axXYUS(34}~X+3`VbWAp31g0)7tl#Q&=UlpewPJcB&`o$P# zNH!^|&b=ue)OJeM#_!*i4^@`vhUt}B9u?W5Hq*D9CRD}qalq5*mF|$bYAV-Z<9Ydf z(+se6*v%qm@g!-UX8FuKTSd!&;MLj+ZMJd8p1J&v>nT=j>X1+`? zZFSq6j~wXC|9XCwV9uMO`egFOo>s;?;9#P$)-kWGO8GY=7qx$&Ff?&qiEVkYh^N$< zDJ9uktM=LXyU;}G;O%7h1b|uXy?F_{wx#NL`>D*dJ0WX@Guw{Er+)^owxU!NE~0nd zGA5I`K5u6!vQtrWgSp+1?KqNzg-nt|xi7Z%?|NeB3+?1?*(g>Uye(bkx?Edp1``$~ z<%s){GMua2=D1vAvd@ebPFfp?_s6hEEVIyYc&O;t<}57mq8hLf4BC{_ZChNs7SS;8} z__UO9dA=FetQJ|RU4jp#=VuR}Zws~)ipVkC@wpi>apKyJXFyWrcOLWcCp!zxlZ#ec zt&EDtYyE`Fb`{dSw7;z~(#>PmdNyNIMEK6&zk0r3w(uW`y?^8ej{1XdOAEAQ{UV3? zTKrwBXcUxrLcLlOXvhxfPC#zv|9Cv^v3wsmRw32MrPZqud;ce4AueRxP$e;1A2(KesKgYj_S|q9%TZmT!xa9#nF=>QH zeRVnPZDqj>iDdk-;{V}fwR!GtU6!QtOc!$guood$+Pf zvKOUSrT74fxh(1G43z4)ZHJ;i0`*CwT#9O`zX$3QT7SjpQM6dM=pP3sUF28||?cV`?S!tF1Y>0_aD@7Y1Aw`0yeI4F#l6HI+mcqUyFZEV|~ zIB#q_lZkClZ2OIE+qP{^l8J5GP9{3}&VMe>RqtnY_3pmws#UetUJ=pMRO-;wdthDH z3-)V0sHjlQKP-j%^SbDi@=UnV+`oVOD#_Zm(o3yI+KDdeZHz;(}LtL#d&4 z276#z2%ON2U@$Dh+9gAOc`Aiz0|?Gq6@wgk&TWF1L}_dRtPED+}-9PDE`CFG%OE%u7CD z$&9=0&Cv1AQYI4I9yZ`ERV zYQytVD@j^}mzdsPZLce|3EVW85350cPk0=(X6eL{2|XtPHva59mu`D$i{MRO8Dt9z z9-z%SfRBpu7Hf?R`kkj$diIC(F-(?%&SFAM@jdOH0wfyWcGQE$**nPJw0|F;XNb=aOAc18!hD`dNkPsoUb}^<4h$5~q-J`i1IhKS--VH)#~9&W|Jhigt84+A zti7=MJO18I<%ri%;MgL{<}q-_d#Rb|UpRQPX_M?2B{FaA5}16jA3zt0LzJS(e%3=- zJcrI9AI=_HG7O%1h4-!nAItPyEFb;!%R?h9;Euit4qz}pt7wEJXV`kyp6iC93G^$K z5H_(+vD-KE*d}wz8!z?x$eXmT2bNvmj)ev#!J%}UzB9%w>2dX924CeZ)<>r%E7U6ZOx>>tNDZBtP1D@I1 z&l9fHdPPbE?CqQIKYkYX7RlB$V1LmJ<1>MGpTm$u$228gz3=gD5Jkg30nY{ji>bZ~ zjHgif(b0R+uyiLC+g*I*n+VgAxz3z`=ds>!!ZMccH!%Lst=FbODJK5f@D7?ygy;-gg z7mUshu^VekVspkP7-Ms_sjhoFy7=0?-F$`k3ld-QKg;l@pr?^yE_VwnfYQw>oAsFj zul6oQsl8JZNjZck4>(Uq-Q(Zp0?iCQ48ey z;26Z?IGUv|Ow7IzUQ1U#ywp8Xe08JlRk2bxH-arz7*>48oEJX)gy9xkcsu~HhX)YA zXweCts>b71dKw!4w^lyDaB0;-#oYbMPlC`{LXW*Px&HOMq=(A~<6MzX|G{Ca1iQAp z6*}Esfj4vKWzG=@$d!TVNdW$~sc+R?O^BkxpKo~XjJb+qKry9!hm02j^?#=8P!nr><+VKtP=N!NZYUBuGC zj;v-Sr5d%0T%;ecGoxajV42dU7!>xKZ>v}YzQOxvPtGz1>pulYjvZv=pLFe*e{ z1Et*)M*+j4@OW3c9V8&2TBW1ACx#3xKQJ*mO%Q?Ko*(Mx%KzoaNl59hiX zfWA!l&WR_Q^dK&Q<^}_8rlpqXIQQIqx*yQ9&EJS-#2b8GLmBQxe96fAgOWI++4pq< zT9$!x1x&S_p}~guI7$;Wxd<2X4mjR17WGs<1+Y#=S&dZg)kD3wVP?uoIWJ!InN8E0 z_JdOzYAgC|TgpR*$`!5P)#q{sWxFv#l{aBU^A4jL(|g7`VZDS>qAn~+W~3jBe%;dB zO>sV~ahSzA-oAg0JSIVC@IL{e`_uYx{}W~OZqrgs)xk?*k8MPDQA9`*}91Ke`$ z^*PT#hC-6dOo}6R$L4RAuvGF3+`1ehlG*rESPz`Rc%6Wy^_oiXo2j&7P zAKYoSIWZK_#bi<&7$s}$(L!BlK1@tb0t#EMXSod%SwMQx^y@X2>fjxIQ@FviD$aPt zOahRsv2YZ^TV~_@$3#wkByO3+bIoPfN7-O`p@>CzmIZav?Z;*$o_2ADSFLG{IZRX! z6KYg~D5q&!RUcd&lr^eZurzd5t6~9N&54bx;riGv>S)s7PihxBslt@jgkP$#4uIPP^ks;D_ z*gy0^R()S+k zI!ms^V~Y|iGp8C-IVu1*M?TGCVlBwyGmwiYjIbGk-q@C-mgPB< zSKd@rqvY+cP^Q+z<&sF_NO-7jbdItaPWZ9^?F`NNq3KqVj^_9`U+x6|48&5J%c^qsH@pny(`i zsM^E&;PRRH6$wPITNhZwp~_hh;fT@d3K3#7V2ajI^f#W>2hKK~rEB=8 ztsdi}SDX0$qDabkvc24X+(GXhCIY$JNGrR{=OXqTEOeGUwc+8Ki&|9t zq?jA#Q5QgptP`ho8k%?jBmQf=9`f<~IG@E_XWa}Nf8>fk%yOeS&z7f9>sAxtFpFZ- zMQ_I)b6THP?ft^c{qRuW6Y6p#d3A6WniqwKkk8~rsmDFZ+)!us!qf%z$B;%tF`;TB z(^YwO?580{!rfkhIWIIgIL7HO$K4>uy0rwIqH$ogGWJb?d^W9Yh`PEZPTYMiOYipl zB|l-J22SV(-L5ZAF_LJl-<#nMa>EMIvCngbj8n|?&549X0r?dxSOE;Y%BIV;3*oLo zJacaTDNCdeXr_40`r=E|Ul09%S~{2tj}AV2?{e$K*XKifU;#GB0iEstj!gBbM8LqX zf4l(0|3)XnGhZVwe4$HivB!(jp7ij;6z<&LZuBKLu-=~4Sm?JN9~)X+k3y0;>CMVg z8PbE?fDc+^K(Q}zA$+D8xp;mR6X5^6jNRTDrBV!ET4YCD-&iSfj>_kPWH6-xD^;$V zu=%ae*Wb{teAJroIbCue(MB)7xbJn0?x+gHR^)fQU&21&mE)-9cQ{HS%L;P8QTfA~ z3gm`6Smg?~$J)~lZ=@ehe#0tHGpd{uFQe5!V+Za{?x*k|*WtONA+F^PCnN zbc0#6H|=#Pn5P|zsJiiIWtLK}8rQk=yhk{RykVG62TgDy(b`xnmlb4el$<++)i@Ur z2 z03k%u86!~(Xo!KU#6~X?1tTU0M6hd9lCXnlyTs-wj4NkO-FmngUn6z_;V9~OPf!#e z2EqsYMK{!$=~?$XK>-!p9L6BGP4d+Ojbv`^q1UgfuS5#JQ8IO;MBC*9b!K2yDPGeO zr(8v_P02~KHr1&fsORO@Z>nW^>S_yHDj~!mrdcN{p=_C);L^>x?Fw+b=*sQaUB6f} z;%xDhRD=sMkh+~O1f)6w++{+++Kuit<@d=0uki`GZ{p3q>!5FF7=3H8yFBosku-~( zpEcKM9=khJpP`Nviv$S_ycCEypPczXctsB=ZdjO*5gaZU_sz_c^&U)vtYrM4$-YHG z22Z%D>P{nJj}=zm{?Up?u~C zI|)ctk8d>fv*S%|$nFLhT;_U2M*mY18D>;fRUdk2lCGDHb6>pFl{xSfZsZWm&`bN( z*B)U9pN0{R1ihR;lmvgm!-lsBG#^>t{ETFCinY+HNRCS z<`SMZk^~Fd+Da9G6lgfoQG)qcK0Pza4d)a!w@OSF!uk)i^tWBH<{e)X< z=c3)Bsyx5$V&j#;?KNR2@&C%l(&?HjAmQNk*InoJ_gG$cL#SP@uanCcxfgZldS~Uc zZSBUwpH~C#Bkw=`8bCl6QtNb0kNbIe^HcaC*C!>BFOc=Ui`O>=E0^#$@;&l3gBN!T zj_2#_Ug2)_^1nHF2)*2CokXB2(_H;yV-2iX)q|2Kl>utk(QWI#Rli*}R#` z#5VKvWG|=DB|hQudtd^(=sf7MZ!IixB|G$4$u>vQ^m=?80(YNg7eiasfdW^gEi?7I z1T4d^xlI0zVX>6SX!QHZDU(Y#Op<|yK2dbHqZLix`C*JjX@&?J z^8{C?DrVpqa0)A?dt7?yB?&%s7z4OVR537%BHAXezKVaBVx$q?TY_T}Ua}IPnMrXT z+|Mvsl{TQU@Z>3`-;TE23O(MuMCYSjsvWU-cwNK!l*m*m7HS|O-5BzOkRd~CXS z*jzx#Ehy0eq1uc$x14kMTr0!}KNkTT_SF82Nk6PL8a2x>dK1NWxmDC{BYE5zO*+8&t$SBPS-Ffuh!%TbwrF|tl^6`yVyUNgX1b0nPPQLrb>8C2HAt2|7?oDZa{v{sBRO* zE8vYM1KWCjV$67iB|q3<7&Jmhlz=s%Z)k$whiSiE(EBYzi+{!guFaDw57q^C3da1C zDG@J*8gu|>D2Oj&1lH`UVhW=y-JmBdn3$sY8~v;+eMVBk^LGl+d@CI#Em#MjK9EpL zd%c!^Ijkm5?AV>+&`^A$gR5)B*|x8VOy=45z)rT{6Qrx1W_fVdz`Rc6}*Op_>IjPdr6p>h8JYP=(uz-=&!UlR72C(VV7>dC@-% z1A_Dm1$R&z-B7Lz>Ar(!)fS2AUXYs(y7YdnC>aeXk-wYySg$!U?cnSeZA!YZ41y%1 zs|}+1d(f0zfop;aAER`(Q&Srt09+jv+c-MW-rA`1;ZixXQ!+XeRTmoZTP`H#JAQ-h*#vl$j( zp9>z-@U19cN^)>{9$QW21mBUe9{o?qw#1M=`BB)QC5eIJy-3C~SW_oG4(xvj#?ceQqMN{~| z%dU0UAQEKP?F+vrsbhNU?iaH)rYP3s-^I0``8|2#ac2hf(}LgpYe$#8MC@W-am>Oz z&7h;AmBWO_YruGQ*e2Awx}O2bIik|y-S_U?{yI6{XOt=&rx66-vuzPi-Ur$tn3ez{ zBi9v3j!hGE^XV=vzS3NY$KehCK{)Vgw4vl6-_qhB9G!*-i6oPVnj|8OlU|+mzFKoV z{bA7U<1`3t)BLxHCqj9>Gl4LXv)!$^cF(gn%_~(wtd)%Sce%xRMNz?w=_^$xxC*3( zw?4Wqu)J#BF|(Wm)(y*sIXOzMa2q|l(TqK(wa^I#3Z(LuB%bo@>2jPo(~WjeeFP+c7ISY_!9h=7^S=XWrT#?iQ&}VD5)+Xqz_m z6$u{c7z2j9uC1hy0n#V8l!RD8&Y$PBT^=K3X+kv8>+#ra*YX%e*XQD;jg-N<;nxVv zXgYM@WMnAVi3uV$p^3z{+D*`%CdpPv={HqXDjGdqz$aH~5d`(g6|7@^sn29w?7W)k zTb{9{k2HHg+r#awtmx%*rya58>OhxTO^}?!Mc;b)r-N_|>;O0h^{|zj;RbaaBOVED z!zYx^$U^sF2L_f9X`QVEp^$9JZuZZ9eQgkEno2d-(U5cdfjzaHBYFn8y=UPvd5=Px zst`w`PY|j{COO&^*YiV?%PD&PU)$~HWLK{~XApqIST=a+J%aX2|FP!P&^Sd=xV?V6 zX8{=rGi1kAeAWL_O9aefe*J1*lQ$!a$^H~2TUUSOlj>{GGKAv=Pkfmy@^u=~Cq)IQ zA+}5~!muJIm!kw0?cSs^eUGNN8F%dC7C))Uv-5Z^x|S}yf_tUX>l0rT*mChfn=OC9 z9p17*`zJNgruqW+rQosJav@SaI&@T7tG`Xy=ujA`dS;aNIY|;hcSJLzxa|V)TWm;o z{5|Hb_hG%?G1#8LGrxpiho@{<`7GbuvkghY^b}=6R(<%mPLd@H!-3RF@OBhK zMk(y((4%FoSWl}DS6I^gX|r%W26-UtLoi3S{;}UieCkfcVWXEVPhwYe((NFL%5AO7 z*K*ZP!?B~(VeeGk>0}l^Q9jgbm6pmnMJH{i<6O9V8mkp9JM7nu%-||RTuu$l6@7+_ zgU%E2>7SfF)b7~{+tbbUSH|$y@N56@eMufw2pRBvzgV9jG4rWW`?`7 z6sVxH)3K&6pWTx?CR`!`)viY(Ury=FV;ei1^QDILn@6M7QV-P2KcU0;FwCdEU{P9O z1-WPt8%Dze|6@GL>^9&`fnf%`AWD-!YF;Gc5MC~iSqVCg!ZO4TItq{t^IB3AX%x3U z=%z=jZ2~X(pOW4 z*`m#V)KJAQZ>9#ns{K;No5z4ClZyyV!7lDx1zNW3xwmAR^$R*vDOC;VSZHVM5>H}H z)7yC>X+Y&#Hu-Q6qIiL*Wl^GAkj#|*_DkIQ2X@OoUiyL()7!@)nX3?~*`uXm@#NH7 z-yfw3r<~$*y_~F$_zl3vnTbb5gzl>Ht?S+UcENBUrM@w84yyDmHr>{*4H0QkB2NSt zSGvWi^&Xl|XOiF}%2zdDNF46(S1zO#8In5O8rjZ*oix?A?bJBY+=d4EMo>=J7eM1bQOBwb@EZa80LssA#t6UI`##*(i2MfVP)S1gycmGnO&cr1AEA*rtrXN0@7%m;KK?vBf&pUYH z9uODmS$kW-1_XHX%f@8yf(a3gjr7>ZAJ9>~`Qy;`V*g$-b90lhaZQV0If@)NSLvjSLH*|}Ls*tnPhtgM`zoFr`j^+mri zw*Ox7D;0m7hAlN?j8>44g^dHi#QuHb{|jbeK`a9 zEF2_EBuXSK-=FZ`HT7wnmMC?#jTR{t#gh~ooQ;bkmFe4ZB~@3F1`dda-nT;Z>;p5p z2ZN;nI^1wbV)zLo!Ki4W4M+0h;NQjT;>DB<@ggh#wPAvke2Uxll$!pci@HlKAKZH< z-7Q)afk@cy%iiMdmfO_l?VI4cv-jAqIK7F?kN$hn|IR-5Y zeVF%{#a?t*Rxd5jg6bO1=g7S4Z0+F|@Ns^5INfDD<{!e6<_De_1UjDPlK4Xg=`}*n zA_ zU-JyuBna}-nbEB(b8kmr0~J9S%0tEIpko=B z$60Qa?r(fi6iaWOgI}Zsb_|;F0v27iv8|^iK-R=;e!XOlZQZ}zx+;)SZwHbvLLbAl zV2cVPPSG98aK?aftopg8L%pLYA}{fn%3&0tZN?k&HCRx)+x1zU_ zq%!`t&cn3MbEhq(^%6Zt=v~cEQ1MN`!Uigxd-vrp9xsYH!_%cIwMV|#x_uihpgrm7 zRP_cxI1a#VSSs;o8iP>vF<6EUl$jfA`ZTl(AjknTPUPue(r+uUC>mIgA7Y!+f^QU3 z>1bgJ1|RHk5S%^;jB!)&kbA4BG^vY#_Y*Q-$msqM`2;I$YYj={1R22zCEi|fJWo+`- zg2pKr`Pa=`X6PtoSarENFuf$!8ft?%ATXPq39=tn*H*ARYZ{fnyHsqcqgIygP%l*5 z_4EkGNO{4ywI~9+*EGDHE12yjwc;5wee45FwzbSei{wiu7PP%hmMkzsM!d7{F{7;-o zYIRy{$4Uh8-C)1Yj4;G@d*i;4ukUFc!YiPK!e)y$RBQji91341_u7Y;4U5RSZOakp ze1OtVU>%V&%>gbXibDI~^~aV;FUU3!My~uFmPK3|AL2 zY}D9NxwHR)Y5jA}%m=4!zlm3vEahITLR{9~m>^FpE#{vEH-z5GYn1YYnm}T2djf*`Z}S zS?$2HvTFFFgfD4^ZOg%bO!mF+gT1cR8rn0BN#YDt^-mSJjckX2KgQ5{#JkJQ&kS)- zV6}Q9|FGWG#gxb5<+c#5l?`tLHP0_hGvQKUH38BHk+r`{C2gBEhCH; z=l#5NH%;Dtb9aiH(NTiAp*g|waH-ac1`F^ zjjM-`-p91)cQgCj-5YeBUL>3WU@|{#q+c>+l^3KMjsJyo4VY&!YQGN!7{`)09iE7p z?!KVQi;7yOQaZ<2jbV8Zr@ zDx$mLYJnp#dGd5D0d0(87>F*RU2XQfp6Z4u5-v|jqqG4_-o%$ATI^zFR`bz5u&EV` z1~fh>1#z(3djauN zU^k*o#$;59!#ljK+C=EU){2k2l_QK6(pW+n14RXs!LB#K)ZrDWL4VGlvjZ0}PbL62 zgdJ)Yf5>xzkjFSShtN8N2FU4Y0ikTGS;ho>k#^O0#|iNc@gqR>h-Z9x|Mj5RdGDtb{bBl)fZJa1 zk=^CfNfd17Hbxs&(3sl}Q+Vd{RHa7Q=jF9Hz_D!KT#?(MtjdOIXG)$ZJ;XhtP^6HK zwsaIRB`mX5mJd9UDT~TrQMfkKP-rX$dnK$ zPmm;6E>XKW8`02IlqBh)iaDI_!}fSH-2x{;fB3vog1l-1pAyDK4EjW+Wx7}^yt39G z+*U+DzvgCz(6jkN6*#-v-DGK^JGv0jb7Iwe(Y?FF6B`Agdcg@FrM>FvuEV5It&dJ) zje{qwjtDdhsy5abmCMJF5L;)pQwvet)V}Zf1*+aC-`<+8+PEaIe2Jla_=8+Wr20JS zMcbkj@-c^UzM3Wy7yEI%_xKRfoKg$dMPISQuSh~;J=>|Wp|#8kBi~HS*UOXZx9-t1 z&1_+!crMl}Qn!rc&IQy@vZXxh>=3>~s;&JM&qQE7ST^mNwgfiHkon(&icUt?G{Zo8 zQFM(6_v}QA_|#oV6#@YbujooIEqn!dTg3wS?Fck3hYuZ@eLgI{*BRDO*`lbKJ*W8EuSc&u;j)XJ$SX96bY`RF+%_Q79{h-6;BHfyWtG+K zV-;ew=?iNvB>zx}rHS`q?(x$yVSIR{B(;E|&q%ZpJ8C;$D=ELF*3-MS%M5KJR(gX& z8hSf`@C?6!>8zg9D}+f{?UKJrfnSk-@1||=eF#h#8%f5>K9EfPiET{;OX?Gs-q=HX zqhLD=mt@%+NN19@k&wSOls;PjmMKNI9O#-n$C1y>&d)e@sSO~gFkF%Jp@N8g%Y%UX zl@FxZ@W@gY1o}kO4n)Dt4Uf)eJ3p4sCkAtouqV2)a{2lpa=h<;2o2uWLOXZ|eV;hy z{eejNzS&RE%jI{C_=q-_?(Zq%hlz8VuY{WJ9WkXX1^7AbY_A3fG%=yszQc|m)ntnF90eBBN>;{7Y`9r z6Yp3C3tgFyCy%LIL`_SnjxnSiR}e3UggRmzfDxjiPp~7CVNf7#FA})r=FF z7s*mMkP=S$^Jea&6DLA9Fc+7e6Ay-I9#gfa*)0ZUrv25*baO|T}|lKcV<@8T=sk^br2`Hb=4c0~+V>%&T*S2Fmgix?=bi*{M}F*9_{aRkg;7Jo>IqW)feqPT?UidR<=g0jwX@ z#NkPtS8!Y4Mo2B0NW_tM6gpa@pEQeuEV#Qqxe~#7qhj8+FjHL2=PYHOD+4SSq?==_ zCc2f=vJ1DUEDObR(v|mPqM>v)`tgdq^epDQtE5t({hYky@6zd9#P#%cyLOmCE-CO} zT&Jw|@YFkc7$YF_-c=juq4pv*Wk28DpDkjo7FeySF=Mq~5_&A-$~-1+`a>H({oZKz z^)a$G64aVyl4Wu!IjmbJ;hCNH(I`P(`nW~L$6OM^dQ)qw8itEkz1dtxT77wyZQO*T zyhx-`ig(S!x_JwCP+pz$S{DMzTBf$;UxKol0g(wiy+RA_yL%4M>GtUm5SUB^cf<12 zIhrZ_z%D!fV4T5BP4Lf+GEiULq}qRK)xE{CW3f&X^vyf^9ACBPVn~Z~%a$PpvfU_t zRINvntK)X&3ZR~U=gUBrNwxTq_LZ*bWz{T@zCsw5@;caL-P=~B`qq00*iJR96;nB3Q+`Z`8Zq+WD-5qroC~jnR zkscoYV>_|w_Syj&Q}lhBTmexLO?pdjW?T5T5Fdw=F7Z`q)O6KTDJKJI=T&X<*9aHfFi$HR4zo>Lf8S$f}pmeZJaN- z5U#{JHbgLWvg4lC@}$gXgai!|+`MLiZPR|fU1E>)5snf4CUNgCH)93!!!Mk8 zR9vSq&|H&{#~iegeO+7g(_uw*+Z<;Ns6-3<*J`Mvc3;vmOnqY9v8IrWx(DDj)FpFU zojB>~_o)<0_G7%I-rve7_yDw7H{jtX0USQgp(k5pfwpfpZRspn30otzpZ-l127}B=7LeXE}a;|imUGD+l-q}wvX^8^%>2k^q7e;PX1RczN<$!0M{gphUY2Q zHmSfdwkHOhz5qg$u9KMbFz|Z)9cF)Z4WPlm1}4ap>Awg32!oS`llt(Bw8Pa7Ir9(= zU2Z@k5T;_=L=rW#ZLmC{;Ex@NBo+jEPPyW;y0whD3cIsM2(_lz;xWc3RfLe#R;Lm! z!B;8TX)pcyXB-Na(#yXn1v}oU_FCZ16Vf!98se*531+98&H33Sv*~s($3^sMq`a1X z+w**Hk&|C4y#oD& z_vHij5>HT;-|2n(JkNdFey^KizEB49Y@zXGPdkC*W0wI*@8kt7-OKSy#_;S)B zAmCf(&~%b%+XJ~6pR^wo%eBNo(ff5$`B5qFO5D2!{Me@u#UR!AohVPa@D)jG4@HwZ z368JYu=~<<0*OmiCNmzY$6uJRX+@#%1_f)9wHT znF}e!mV@3W;`C?m4sFPO9&$b|#y_UOjU`w@AoJZ!u?wJ)9h-t+XR>&YU2zrV=(iQq zOS?xunc}BWK2ISF1&<7SKL{SW7x~)B9xs-g7l9NX*$6-53;mh*7K(GvM`w13!kfg+ zdnj(rO0c3>2Qb6(OnZ5OUfD5VA(H_qn_dbAd}vtd_C%Tw0#&6_kH6&iCF}3xE@5Ry zAWm~5uBN#F-CxNn=>YYon`zjGK$>d{)hSdTE#}&&pue5+m32O zG%iAg*WB=MmeiR}dCQ&zGUzXlTpepF2{O-AJ!@e)M8J!n_66Ho&QV)ZwuB@mP)2A! z!?3i!i(F$<_@0il1Vz+gTSYE+8iwf?%}=-^G47)KKl16aTQsSWZQ6`=IJ6^~&7mfA zb@^6U#SAfV%aj#20_*!Zd{~7X^MZ&BlJ`P zo*Dw+#cf7nn}ZNm-B`e{)*sM)M)sS-u-#@b7<+~0in*|xr{*E2B4`&aySNdWGfRb$ z-_soyOG3&zMrq{_yNR7B3AwAerkocWQge^mjKS#ZPm+#WWPY%703lyKpJir44=yh` zWKkz}b84^66y$g_hh>%TJDbcb{az3<0}#+IpdJ{k(_m=k-+q`B!H((l=npuvGJ)e- z>P@jkLAHlZq6u?{c@)fiK#gwOI`g^ZZOJ)TwF*+wRhb(jzYCBN2)ou29t-TmuhzUt zG^(Wj9T|3?_ODz~1CCREi~U@JBCOi>RvDZ1IXn_*W4Vkr3NmLC)6hyUg za~PFH$?PgeYZ-;-yD2~o8!K4|dhhcqNnLR=v=1G!qXiKwu=#-ng!i{DFDzZp5B^~| zCk$SZ88>96o>Lh!^mR%Jy1MqjFLLAy)u(Xb7%)?OKfH;FH3O%Fs2zL(4g=v0Hr=%1%nUFV=aMr^^EJIhac~Irm3l40XamYUcZgafL|x`*=kdlz#&0_{;$uLw>!F_$IGe9uO?n)5aHL4b6x7m{W(G2_mAhz z^ffcfjkh}UkD%oge_-8jz?wl|8w77Wq?y$;P&gldREt*{%jsiy1@|)#Tz&Ol z8{7^g9Y|?kA(2{LptzAHIDr;NKSAaZOABfmITtC^h5CLCHB>&$WECi{;aa{{!s~!j ze{|4XC|0=k!-i4n%jhOpjAv|8_g20!=mPRW+emH^XbOx zBg>8ySSVyaic{K6rE#GelE(9hszew1roQiGKMU$Fscay*VNWH(e<#kXBgD+bs-m#b zJeo`z?uJrgu0xX7_lEWxJPpn{(4h=g;03GM;Kw0CxmPBEfN(saBkQlpx-fO6u!Gh9jzmAtca9hsKdtH=Z$B9hWBjPuV+1Y?Fms~==r~$55sG>&YUoOJ+^`;5Z*S2J>?>E9*i52k!3Gh!kpWA zq#N;2eAtI)3+>umT+=)lgM^*~gs((qws9DAQgiyv4 zDQ6<});akn=W`!AAyJwhZL|69s;8~FdTxA|MePOL%inJN4tbvt9I{d(_e#mB&ZPiU z`5^k9awGc`w)M;_k)#>yM~%1>-8G+Pahj*rc>)aeM$AypI}SDbFQR}QM&fBo;7S|p zozn|2q^}89GupmU8+-7n65E#97RPzQC#U{SS_P-adTilHe!_h)b@u+(NN)HOsSKHP-Ir? z2G)^n_f1SC;;njAjI{HHS<)#}ZH!OREUqLw9zP*gjsf8~7q$8r02aX+m=>3aQfBBX zXJB*r5)-8IE}IpmIbiE_w(3VgWGZg=yKq64{KCaUqx^bvvejWh6=QqkhiXoRYPc;h zKzlF3-`|CczKQqj+JzBs7pLC6W8JWk>J-lAF(n$lmINlFqXK2O!OUe3kr95p+$H&$ zpl8H$ZBFe~gYi&;=?1NcgKQy&O^WY~io3(ZtTCNC>8zaZKnf?)~*>j`gmy&D2)okw* zE>61%*oNlT`*rgwOuZpZyXfXWLtdcB#D_t)hy!x@-=yf#M2n0qxX=ldLv#yn&*zaR&b^nSVsQC`Zpq5RU zvbJ`WM-7WR_0gd3B(Vzi*KwtwTT;>eDiJDtX7RcfhUIlK^}D4UwRuUkDT>lUp{ePV zazQmfT^7u(XaBQDg!v%4HY2Oj(x^(^W+5Na@^Zi~+Lh>6i%RDAMb{bmb0?poWjD%9 zzgO9Ea{1T}dW+GL`-&)KpD|NEnB*Jv9Z~}e>Hc`S-wls?0N0zQciVqX0+*>E+V$W_PE{u221*6ryiEQG^h>-vSdJI>Pz_aaJ-?m$gnY{NTWq>e zn1tAX>sa%&_sQ4dmW?b9X{NGQo>qeP;ZK$3Vb@uBvRJF>f(~?Ym*yF20Ui_mbNzEx zH*Sprz1x&}`1x=os)27P#koM$z~kz+q0u`07VU^;BY86t0b{hQH?1&<8H4Wy{R9bG zfXZ2^Iof3%y6&`%KNi@9`E6K|x`^e>!QSDguCh>BQ_JE(VcYtl#4+z?wu)k(7>Mc$ zwQA-m_Uf^Q@Y}2p*a?n4;WHw$pJeMuvuuq*cwb>>`7LK$TovN$7O+0~Q?c^6rL5$l zes$RkFX9f}b0$|8*TV6oo4c!psRQy;f@3BdRzl}CJCucw56p$&0rNtT`&$GTgcn); z^4|^n5M*f#lE%vgL(<^?tU6&%NZMg9Lti2Sw=yl=chpQq>?^g*v)=RLU%Qp{!Uj=4*mq~w2WRX!%ddM32#D`!Kz|PO zarOgf=UbYEE`KBgxBL5dwDZ1hQQdH-dE>M{dW5Fl9$uFx-=#TIVqp?KX8~{tR}*;4 zYp+Y-Xn9(re>!^iL|(|hjTV?6+BZCMG!on~o>$Bq6qI3Ymoo~F-0P)nPfb%K6$NT< z8|vE(9`3LuClFoB3cC8=n5c0CM|vIf?dt5J79aM>>il~%yF!Bxc^2~U3>XS-6Z~x; zrktaMO&hD5^6Af5K>2%}5$^QXraxZs^ng@>ZUsDT=XSaP?O{Wf;gXaDLXdwEt`4Z9 z3^2|-^nZ|Z}VVl(YgnuJZ9F)VWFD6-=nyYn-{D- z(NQIC{*FCq&-_yAk+tw<_DKUCYJV#-MBPT}LUI4KRO=Ia5TL5X za!u^0WTipz?0J7k&;h7Onk{5GTGqmpTWdr};Faa7wvRk#Kutx8&E!h^XI89cbKE5K zvLTrAo9a5xQAQcXUP_iA_xa6G^6bD!)Ga}zpLKamjJ`4D{HEy1U@e~Te2C%r+*LTANw2|)i^P9*B_QO zNpnU#r9Hi{aZ2!RAH-mE8bU}l|H&bm^ewV^6GK8k>1)FN`VQx zdZ{VreErf4)s8Bw_Z@)rOL&MEkT{wu&N4 zB@j(5e>L-1U0s%nQv5@A#e?dtqrjipc7I-a5Psxq6}y!W`a^74qp~znJvXdTRh$Z#$lpHgf0DbS+xSM|!+Am3$~QX4Kz}Yx{}=A9)VB4; z$te=?!c;p!5p*=W=XV}Hw{OR%amwW6M3O4oR6YkNS#$6QD=iRVraLRdx$Nhjlt{~f zgF)4Ki9gv2O&rJ+6lE^hnhic4t5=th8L_XLIo98brctuXC~cBGpmSoKD0p^`M;STnE>tCE zWX$|=?hr6MM%wrVA&#DZ#F}~Iu-Io|dMY0$rk)DzjNXUuN2{2zfMBAyPnOu!Q-OoV znz(gEb~I_h&)e#hq{W;PYmwky0O)76yY5!VPg%`=I`Ri!%0^dN)ml2Mox4Ko^53Xh z_KKk$iy>y6nsH(KIGl%Ej_mFxLa)l3FACk=uZ@`STaAru*SVo-0}dX!4iT~b$>DcD$b3$JHv9ywNYoE(yD7Fwi~ zwt*T{mC8bJ*h&S~Xq7Ql8)ef4Ltpi>saCB~tv3i*Q3(qL0k56a>ON-wCc#pks)tUR zkUh5lO=uph7JmA+*&90v(<(ruN9Kas6779z6!mP1+qcIxi<;Q#eDqc@Uwv0`h7U1Y zCwG;)cxM$&OPcDzQP3aB5h!mgeNA=+(NN5&pWd}`qtLZbD7QUB=^#SH1(eRlS!S|6 z_(_N&m-tT7>I}gA9MVcRbd*ZWUclu#Oc{-)q{BnArHMnNlUJxp-_ot`;2`@x=skx` zFEs^O&rAHV+L2Uw`5YdK-<~b%o?l%84njVeBPfRTAeq+8Rf{e1B+u{>PFMEHkZ2Uu zJnsBw)FfKzrESHrO!&oTtaSu|7`?n6Sinc>^d-@*^$B2MdMk;QMPw4(+=-Kj7HX}t zDLw*KartoKtke7AL6XPJxJnB5BItCf_zm8^K>kO0izM_r6lr6M3XXkwg+*N6+_pQI zo6t~Km~wu>@S5RaeD`=AiB893%A^j5M`_WX1dg96C zK>S#ahu8ph=3tfBM*<4%I{NThxpE@5da1~-y^|cwBH!hF=*D{HBc8XVNZ>Q^?4OUX z3AWiq6{wlLdSGv56E@@(xtFocGM-5k_7-`c>bt-=P7jxzgyn}yk!@0tTog-b*Q8VN zRX?u;)PU@c^l}Ud^un^%m^LTNZf54sAEsLk7eJhk{jH$(EzTv~w$P@w=~vNjT9cHe zN@^#zEj7WEbutaB?iSh%PUG4S1RNeDqRZ1VaH}drE(v+Jd~sEN-F$7>;=*VLSZ7iv zgI9(%BL$>_zDps zQ$~r7a6`Q48&1Q3{pqQN4rq-;t+rJIrk9Bl6(?1LC58lbgXPFILWw1giozfLCy(W) z;e|Z=emNkfDzkRX(m+5~Hi2+R)%+JEZk?aT6rsARZjPoQgl?-@(_|g;oF!|2O?Vxc zG3L^!4Qh@})cZ27Ht;6d_1Si$V7`mkHYtO23rWAegh%kH`jFSxh$!8?{=_-)&>o-G4TF&ufD&09c{ z4b+Uy)X3aThn@F6(yeZ!{5*4+LUPz2BkIEWKFX+fOupWNZmjE|ae{Bj3+-jPh41_l z*4o%cZZ^%&Q%=#sljG&@lKoRKgGm~6vfb;)DC{qDggI_y-{QDX(JYF*C#te;2b#u2 ziw`L+m(j*N4R2 z3RHZwGG7M;m+EAFmg@2;T_{_k`Dzl+H8Z$(C(UV0%ow~I2rlx3a(m>|q-ixhKFtKVw7Sl}Q%_&IT)K;43-bhkx&C9UM-L10Wu_XLFn;Mby#CNJMpkRpP$tzLrCzJ z*F}%HO*MW)GwC@xF~7V@#}?eLcrvp5*u*zc+H{0&0u>!>gxGz8D{zG`P_5u7DkC$` zDlSI>iDh8nnyi8un+AGt86397sve+|JvBl1>jKi9zv`jABUPZZWU6*b*Yg0l-t`&! z-mY@wQ|Kn`B*k%l0=?y69I_MVUR%U%65!1hsO)NB2`@JsHjvbojd_wuMjvO$%=9fR z!RT#YqiW%xOSp^kYLKQiBjHn7WV?x59Srj#=}DT4Ms4?F4!%x_=ob{mVgmCfQFI=t z{V}qt8S%Hdqv@3y`oz|13bk+`S6+e)cXaD3K5j)I|MJB`5~WY3;%qVl=?S@XpJ@4hw`6 zo8=PBS{iBEu_2--@L1nA=JKnPvZ(-kjNc&H2&Yu|BuNm1vqoIa?+9Ooe;;q-dW&t# zceHMoGKb!*>$+|u%6^c2vzakcK||$pw!?c0EtP_dn_1Uh>%<>tp`X!`4rDyP+T;4o zv(7%M9*Y7|EDMy73(I4D2DYos!nAY4G}m#!a*JsE)lrs81qNsY+8NsYsnQzqOiI{K zs7Mqr=?Q{vxd_-94=Jd(BC44m=Iqe%j;cH~J5p1oNINo;mF>MKmn^J#W%HWI%r)aIu%Q!m}~qBglqn}KgX?HCfgy)!*dDp=y`)8wGxAxr8Fzv;5=wSZSv*E#YE1SVc3 zvbgxn{L=H!q5iTK+-~H)<_j8;L8*vUc5QER1VmW}{s_6$HR4{mq$20413ROdJe$gxGC&ZPtiL%~6AI*ROv>~P)mR6#3f4!& zMwtFoW9#&YuxdsvFlC)++Lxq~9Zs^kcG7cg_SqUOTLPN4u zd0y~oh^4|m>Aex=HqvOaBz>M^HBnRPfcaD*Ye*wLRmqMiX{yvUe2u+9%FZ5}WKbC7{>BQ!UScG?Jo;^Q_^|!kqOI8K3`Wx*3zr4uQ1`JK3+_m-l! z>?4YTVhK__0vz+~eSj#|47d=^9jR>!$&=;#Qd!N60r{mOb(kKzCs9a;f7p}+4>XmW z9g1ZFd^+hPv?QgvUT7(1VJau!TW@o7%zixG&4}r4pJ_hPLVr+ym_{7yMMJaQ>OI?VV&_T~Ut=i!F3iBX|F6BrdTUS6?Xnm3!s(UpM3=P;_1yb zKKC@$c{(@4`0HtU-5p^y-m9dFr?3?Vz}MMIQcyjP;0l3f|64ggzLCj(|EkMHhrqnq zqo1d8ublYN<60f-FeXkNgwgNlcP=NZ__Xz%o0fVe!xdX~i)$6(dzO!8J}q-EY)36y z@k;vB=0tt)2vIo>Eg$9< z_W(*+m=0WPRlteuQ|ZFzrMRekZ|I#CaTiLLpzT5|N8X(f8Ry9 zp@Z@qw|AoHK1n4P7{*rpwHd21TEasUwo96Fj;4BtW!azuu^XN$zy?#w<74gcK z_I!IUpQhsCU)Aai(x6$p=J}Bk8mQbwv!-*1b|`r-zfjA<=i8&bePH1RF62AYx7gi1 zvFFYm?7}a)=P$IcWvMZRL#a%aMKT`7jK6-~Eb6$Rz_y^U3?x*;jxTLQMDnaMU&mVq zA1x|#GPw+D7->bW8F1%!>kRl6<{eLOFIxJ=lg5%U9c8vWPdpy-SCb*E5Avl}DAK4% z-f#I)OziT8RD%Qok4r-XNQPCN;Op zYMnC7S7{SLV6BzqQnDen!H%h+Tg6Q&hCJZ)qc)yL!lSgyag?Bvst~#J5|3{y1odQ# zy_ag*l-jnB6%w+`!7q$iPLa5lcTMUKr42TqXT1Wbw1Cr6RR4+`M5)MbwMU3;AUc?W zeR5-fzF^xoho3500wx}~L5O7f}bQ3r<>S~^4G++=d@hnwQs=&TwzvKMSB%xWXz7{SYx11sQk=aK*IlXq2)%M5U zK{(WV)fEgrcR}ZKt}(sx-HmXsyouN-bBvx!Ad@$XR!ONjQBJp)`ov_~{<#)}aBqc- z5Mp%YQDfIX64quq#(h&6YifYunGxC}$Bn*o{=zoAe6dvVxG=A1e~SJ!8Ky5YMwwS@ za7EBq9nIZ*_Y+49Z?UR*FVTaINB#qN^n{%Ti;LNdL6`ZP2Y&GfqR%_n>;GM9SdWDT z;--4Q%g2K}Ttx60i1xof)*C+qy+kL|lXZ5ox6{>!dur;!5sFe4U@Hi(c>OFhhzJ#n zSAdU404cT40s{ZfmwGl<5IZV41On%wkyy?5Xb3)D9%M`LKll((FdTfJhTugWnE4MrejYGC|2=*DJO~K*ziGz*=M^s) z3cJt93xn}M?kPmpR>JN%&CkaR|Bu4|)5izl<>#&M&w2Je5u7x=#<0E3Zby!RL($RPZi2K}24jQGni916RaBm8_&zJE?X4}i=*CS3qH5wimb} dBDikurmpVZt`?TK$l)WvP%thNleDVLe*s2pF%SR% diff --git a/src/main.typ b/src/main.typ index b33f027..98aa91b 100644 --- a/src/main.typ +++ b/src/main.typ @@ -1108,7 +1108,7 @@ La dimostrazione procede sempre mostrando l'indipendenza dalla scelta di punto b #lemma[ Consideriamo i due modi di fare uno splice di un nodo banale standard al primo incrocio subito dopo un punto base direzionato. Allora valgono le seguenti proprietà: - 1. Nei due casi, in uno otteniamo _due nodi banali in forma standard_, nell'altro _un solo nodo banale_ (non necessariamente in forma discendente). + 1. Ci sono due casi, in uno otteniamo _due nodi banali in forma standard_, nell'altro _un solo nodo banale_ (non necessariamente in forma discendente). 2. La proprietà del lemma @std-unknot-to-curls, ovvero che i nodi banali standard sono equivalenti a meno di isotopia regolare a diagrammi di nodi formati solo da riccioli, si estende al diagramma del caso dello splice con una sola componente. ] @@ -1116,15 +1116,15 @@ La dimostrazione procede sempre mostrando l'indipendenza dalla scelta di punto b #proof[ Per la definizione di nodo banale standard, la prima occorrenza di $i$ è un sopra-incrocio e osserviamo che la parte di diagramma percorsa tra le due occorrenze di $i$ sarà sicuramente sopra il resto del diagramma (la parte che rimane è quella dopo la seconda occorrenza di $i$). - Dunque abbiamo due casi, in una abbiamo due componenti una sopra l'altra, ognuna delle quali sarà ancora in forma discendente in quanto eredita la proprietà che la prima volta che si passa su un incrocio questo è un sopra-incrocio. + Dunque abbiamo due casi, in una abbiamo due componenti una sopra l'altra, ognuna delle quali sarà ancora in forma discendente in quanto eredita la proprietà secondo cui la prima volta che si passa su un incrocio questo è un sopra-incrocio. - Se assumiamo che il link del caso precedente sia della forma $E_i hat(K) = hat(K)_1 union hat(K)_2$ con $hat(K)_1$, $hat(K)_2$ i due nodi banali standard con $hat(K)_1$ sovrastante $hat(K)_2$ allora l'altro caso sarà $e_i hat(K) = hat(K)_1 hash hat(K)_2^*$ dove $hat(K)_2^*$ è ottenuto da $hat(K)_2$ percorrendolo in direzione opposta. + Se assumiamo che il link del caso precedente sia della forma $E_i hat(K) = hat(K)_1 union hat(K)_2$ con $hat(K)_1$, $hat(K)_2$ i due nodi banali standard con $hat(K)_1$ sovrastante $hat(K)_2$, allora l'altro caso sarà $e_i hat(K) = hat(K)_1 hash hat(K)_2^*$ dove $hat(K)_2^*$ è ottenuto percorrendo $hat(K)_2$ in direzione opposta. #figure(image("assets/splice-circuits.png", width: 4cm)) Usiamo ora il @std-unknot-to-curls per cui un nodo banale standard è equivalente a meno di isotopia regolare al diagramma di un nodo formato solo da riccioli. - Siano $hat(K)'_1$ e $hat(K)'_2$ i diagrammi a cui sono equivalenti rispettivamente $hat(K)_1$ e $hat(K)_2$. Ora possiamo applicare le mosse che semplificano $hat(K)_1$ indipendentemente dalle mosse che semplificano $hat(K)_2$ in quanto uno sovrasta l'altro e possiamo spostare un diagramma sopra un altro utilizzando solo mosse di tipo II o III senza problemi. A questo punto avremo ridotto i diagrammi ad uno della forma $hat(K)'_1 hash hat(K)'_2$ che sarà equivalente a $hat(K)_1 hash hat(K)_2^*$ e composto solo da riccioli. + Siano $hat(K)'_1$ e $hat(K)'_2$ i diagrammi a cui sono equivalenti rispettivamente $hat(K)_1$ e $hat(K)_2$. Ora possiamo applicare le mosse che semplificano $hat(K)_1$ indipendentemente dalle mosse che semplificano $hat(K)_2$, in quanto uno sovrasta l'altro e possiamo spostare un diagramma sopra un altro utilizzando solo mosse di tipo II o III. A questo punto avremo ridotto i diagrammi ad uno della forma $hat(K)'_1 hash hat(K)'_2$ che sarà equivalente a $hat(K)_1 hash hat(K)_2^*$ e composto solo da riccioli. ] // #grid( @@ -1161,12 +1161,12 @@ La dimostrazione procede sempre mostrando l'indipendenza dalla scelta di punto b // #todo[work in progress] // ] -*Corollario.* Poiché $e_i hat(K)$ è equivalente a meno di isotopia regolare ad un diagramma formato solo da riccioli, possiamo usare il caso @kauffman-inductive-hyp-c dell'ipotesi induttiva su $L_K$ che ci dà l'invarianza per isotopia regolare di $L_K$. Unito al fatto che il writhe è un invariante di isotopia regolare otteniamo che $L_(e_i hat(K)) = a^w(e_i hat(K))$. +*Corollario.* Poiché $e_i hat(K)$ è equivalente a meno di isotopia regolare ad un diagramma formato solo da riccioli, possiamo usare il caso @kauffman-inductive-hyp-c dell'ipotesi induttiva su $L_K$ che ci dà l'invarianza per isotopia regolare di $L_K$. Unito al fatto che il writhe è un invariante di isotopia regolare otteniamo che $L[e_i hat(K)] = a^w(e_i hat(K))$. // Utilizzando questi ultimi risultati identità per nodi banali standard che ci mostrano cosa succede quando facciamo avanzare il punto base di un incrocio. #lemma[ - Sia $p$ un punto di partenza direzionato e $hat(K) colon.eq hat(K)(cal(U), p)$ un nodo banale standard. Sia $i$ il primo incrocio in $K$ subito dopo il punto di partenza $p$. Sia $q$ un altro punto base direzionato posto nell'arco subito dopo l'incrocio $i$ con la sua stessa direzione e poniamo $hat(K)' colon.eq hat(K)(cal(U), q)$. Allora valgono le seguenti proprietà + Sia $p$ un punto di partenza direzionato e $hat(K) colon.eq hat(K)(cal(U), p)$ un nodo banale standard. Sia $i$ il primo incrocio in $K$ subito dopo il punto di partenza $p$. Sia $q$ un altro punto base direzionato posto nell'arco subito dopo l'incrocio $i$ con la sua stessa direzione e poniamo $hat(K)' colon.eq hat(K)(cal(U), q)$. Allora valgono le seguenti proprietà: 1. $S_i hat(K) = hat(K)'$ @@ -1201,9 +1201,9 @@ La dimostrazione procede sempre mostrando l'indipendenza dalla scelta di punto b ovvero i writhe di $hat(K)$ e $S_i hat(K)$ differiscono di $2$, assumiamo di essere nel caso $w(hat(K)) = w + 1$. - Nell'altro caso avremo due componenti, ovvero $E_i hat(K) = K_1 union.sq K_2$, per come sono definite le mosse $E_i$ e $e_i$ abbiamo anche che $e_i hat(K) = K_1 hash K_2$. + Nel caso con due componenti avremo $E_i hat(K) = K_1 union K_2$, e per come sono definite le mosse $E_i$ e $e_i$ abbiamo anche che $e_i hat(K) = K_1 hash K_2$. - Siano ora $w_1$ e $w_2$ i writhe rispettivamente di $K_1$ e $K_2$. Per il teorema della curva di Jordan, la somma dei segni degli incroci tra componenti diverse ha somma zero poiché una delle due _sovrasta_ l'altra da cui $w_1 + w_2 = w$. Ricapitoliamo ora tutti i termini: + Siano ora $w_1$ e $w_2$ i writhe rispettivamente di $K_1$ e $K_2$. Per il teorema della curva di Jordan, la somma dei segni degli incroci tra componenti diverse ha somma zero poiché una delle due _sovrasta_ l'altra. Segue che $w_1 + w_2 = w$. Ricapitoliamo ora tutti i termini: $ L[hat(K)] &= a^(w+1) \ @@ -1225,7 +1225,7 @@ La dimostrazione procede sempre mostrando l'indipendenza dalla scelta di punto b Possiamo ora mostrare l'invarianza per scelta di punto base di $Omega_K (p)$. #lemma[ - Sia $K$ un diagramma di un nodo. Allora @kauffman-rec-single-component non dipende dalla scelta di punto base. Inoltre se $p$ è un punto base direzionato su $K$ e $lambda(p)$ la sequenza di scambi determinata da $p$ che lo porta a $hat(K)(p) colon.eq hat(K)(cal(U), p)$ allora + Sia $K$ un diagramma di un nodo. Allora @kauffman-rec-single-component non dipende dalla scelta di punto base. Inoltre se $p$ è un punto base direzionato su $K$ e $lambda(p)$ la sequenza di scambi determinata da $p$ che lo porta a $hat(K)(p) colon.eq hat(K)(cal(U), p)$, allora $ Omega_K (p) = (-1)^(abs(lambda(p)) + 1) L_(hat(K)(p)) + z sum_K (lambda(p)) @@ -1241,7 +1241,7 @@ Possiamo ora mostrare l'invarianza per scelta di punto base di $Omega_K (p)$. Omega_K (p) = (-1)^(n+1) L_(hat(K)(p)) + z sum_K (lambda(p)) $ - Ricordiamo come era definito $L_K$ nel caso @kauffman-rec-single-component ovvero di una sola componente e notiamo quanto segue + Ricordiamo come era definito $L_K$ nel caso @kauffman-rec-single-component e notiamo quanto segue $ L_K (a, z) &colon.eq 1 / 2 [ @@ -1255,7 +1255,7 @@ Possiamo ora mostrare l'invarianza per scelta di punto base di $Omega_K (p)$. Come in precedenza possiamo mostrarlo facendo scorrere $p$ nell'arco successivo al primo incrocio dopo $p$, questo ci induce l'invarianza per permutazioni cicliche e ci permette di concludere. - Sia $i$ l'etichetta del primo incrocio dopo $p$. In $hat(K)(p)$ questo incrocio sarà sicuramente un sopra-incrocio in quanto $i$ è il primo incrocio visitato dopo $p$. Invece in $K(p)$ può essere sia un sopra-incrocio che un sotto-incrocio, abbiamo quindi due casi: + Sia $i$ l'etichetta del primo incrocio dopo $p$. In $hat(K)(p)$ l'incrocio $i$ è il primo visitato dopo $p$ dunque sarà sicuramente un sopra-incrocio. Invece in $K(p)$ può essere sia un sopra-incrocio che un sotto-incrocio, abbiamo quindi due casi: #{ set align(center) @@ -1309,26 +1309,24 @@ Possiamo ora mostrare l'invarianza per scelta di punto base di $Omega_K (p)$. ) } - come già detto prima l'ultimo incrocio è un sotto-incrocio dunque $K(q)$ è già in forma di nodo banale standard. Segue che $i$ non appartiene alla sequenza di scambi e in questo caso avremo $(n-1, dots, 0)$ e $hat(K)(q) = S_(n-1) dotss S_0 K$. Vorremo vedere che $Omega_K (p) = Omega_K (q)$, ovvero: + come già detto prima, l'ultimo incrocio è un sotto-incrocio dunque $K(q)$ è già in forma di nodo banale standard. Segue che $i$ non appartiene alla sequenza di scambi che sarà $(n-1, dots, 0)$ e quindi $hat(K)(q) = S_(n-1) dotss S_0 K$. Vorremo vedere che $Omega_K (p) = Omega_K (q)$, ovvero che queste due espressioni coincidano: $ Omega_K (p) &= (-1)^(n+1) L[hat(K)(p)] + z sum_K (lambda(p)) \ Omega_K (q) &= (-1)^((n-1)+1) L[hat(K)(q)] + z sum_K (lambda(q)) $ - come in precedenza studiamo la differenza: + Come in precedenza possiamo studiare la differenza: $ Omega_K (p) - Omega_K (q) =& (-1)^(n+1) L[hat(K)(p)] + z sum_K (lambda(p)) \ &+ underbrace((-1)^(n+1), = -(-1)^n) L[hat(K)(q)] - z sum_K (lambda(q)) \ - $ - $ =& (-1)^(n+1) (L[hat(K)(p)] + L[hat(K)(q)]) \ &+ z (-1)^n (L[A_n^lambda K] + L[B_n^lambda K]) $ - dove abbiamo usato il fatto che tutti i termini in $sum_K (lambda(p)) - sum_K (lambda(q))$ si cancellano tra loro tranne l'ultimo di $sum_K (lambda(p))$. + qui abbiamo usato il fatto che tutti i termini in $sum_K (lambda(p)) - sum_K (lambda(q))$ si cancellano tra loro tranne l'ultimo di $sum_K (lambda(p))$. Ora notiamo che @@ -1354,7 +1352,7 @@ Possiamo ora mostrare l'invarianza per scelta di punto base di $Omega_K (p)$. = & 0 $ - e quindi $Omega_K (p) = Omega_K (q)$. + Segue quindi che $Omega_K (p) = Omega_K (q)$. - Se $i$ è un sopra-incrocio in $K(p)$ siamo nella seguente situazione: @@ -1402,7 +1400,7 @@ Possiamo ora mostrare l'invarianza per scelta di punto base di $Omega_K (p)$. Dunque riordinando gli scambi ed applicando $S_i$ per ultimo, possiamo notare che $S_i hat(K)(q) = hat(K)(p)$. - Con un argomento simile al @lemma-slide-identities, possiamo applicare l'enunciato alla coppia $hat(K)(p), hat(K)(q)$ per l'indice $i$ anche se in questo caso l'indice $i$ è il primo _subito prima_ di $q$. Inoltre per il @lemma-sum-switches-rotation abbiamo anche che $sum_K (p), sum_K (q)$ sono invarianti a meno di permutazioni cicliche. Possiamo quindi sostituire $lambda(p)$ e $lambda(q)$ con le seguenti sequenze di scambi applicando le giuste rotazioni all'indietro. + Con un argomento simile al @lemma-slide-identities, possiamo applicare l'enunciato alla coppia $hat(K)(p), hat(K)(q)$ per l'indice $i$ anche se in questo caso l'indice $i$ è il primo _subito prima_ di $q$. Inoltre per il @lemma-sum-switches-rotation abbiamo che $sum_K (p), sum_K (q)$ sono invarianti a meno di permutazioni cicliche. Possiamo quindi sostituire $lambda(p)$ e $lambda(q)$ con le seguenti sequenze di scambi applicando le giuste rotazioni all'indietro. $ lambda'(p) &= (i-1, dots, 1, 0, n, n-1, dots, i+1) \ @@ -1482,13 +1480,13 @@ Come ultimo risultato vediamo che $L_K$ è un invariante di isotopia regolare. #proof[ Procediamo sempre per induzione sul numero di incroci e mostriamo l'invarianza per mosse che non ne aumentano il numero: - - Mossa II: Ci sono vari casi in base a se la mossa II riguarda una o più componenti: + 1. Mossa II: Ci sono vari casi in base a se la mossa II riguarda una o più componenti: - Se la mossa è su una sola componente, allora ci basta scegliere il punto base come segue #figure(image("assets/move-2-base-points.jpg", width: 6cm)) - in questo modo i due incroci non compariranno nella sequenza di scambi. Tutti i termini di @kauffman-rec-single-component saranno invarianti per mosse di tipo II e lo sarà anche $L_K$. + in questo modo i due incroci non compariranno nella sequenza di scambi. Per l'ipotesi induttiva, tutti i termini di @kauffman-rec-single-component sono invarianti per mosse di tipo II e dunque lo sarà anche $L_K$. - Se la mossa riguarda più componenti, allora il caso peggiore è il seguente @@ -1570,9 +1568,9 @@ Come ultimo risultato vediamo che $L_K$ è un invariante di isotopia regolare. A questo punto nel diagramma $S_2 S_1 K$, gli incroci della mossa II non compariranno nella sequenza di rialzo dunque l'invarianza segue per induzione come prima. - - Mossa III: + 2. Mossa III: - - Se la mossa è su fili di una sola componente, allora possiamo scegliere il punto base in modo che sia sul filo che passa sopra tra i tre, e saremo nella situazione seguente: + - Se la mossa è su fili di una sola componente, allora possiamo scegliere il punto base in modo che sia sul filo che passa sopra gli altri due, e saremo nella situazione seguente: $ #image("assets/derived/atlas-move-3-0.png", height: 2.25cm)