yIpyIr<K_Tn^T^;FZ;NZROZRkyig=c:=R:=R:Dj:@:?b:?J<HJ;DJ;Dj<LJ<HJ<Tj<TJ=Tj<T:IR<Kb;IR<Ib;GB<QB<Mb<Ob<OJ=\\j?lj?dJ@`J?dZyYU@J;DZ<j<Hj;PJ?XJ=XJ?dJ?d::::::::vy:U>KJKIJnIj:@[<F\\;VZKFZyaRwj:FZ?FZ;FZ;>:<:B<Eb;IR<OB;Ab:=ryCPj<[;VZ=VZ<NZ@^ZCvZ?F[FV;=b:AB;PJ=XJ>@k>DkC@L?DlR@oEMWDdkZXoD`kKDmV\\ouLuTUkU\\mjPqSIwEHM[@Qu\\KLTM]DOs@rBIsLTlM\\LWHNkPP<QREQv\\XN^TOmXPvPsJAuZyY\\_];F:?r:=R:=J:<J::HJ<Dj<Tj=@J>xY\\wbKF:=r:?r:CR;Mr;?r:IR;R:?jBLj<DkJ@M=@nb@qCDlj@rRYjSPMcDqBATSAVDHLSTM[@WrEsjMMkDrDTkELLdHQ[IncDWkAyyegFVZ;b:]r:]B:ykiQX;@RZ<Tb\\LDdj<Dj:?NK;Bb\\<JJ??ZZDD:;ON:<db:>NK;Bb\\<JJ??ZZDD:;ON:<db:>NK;Fbailoop=igaafIIfnprB_d?h_JYZ:ok;wdyNmyvtYOfTpn\\O^tFpTHoFpvtg_qh`IIcT@dDWpbP_L_mbNcUOeNHcX>v;vvwqi=qdyGfPiiCGbuqfQ@a]ijeo]EaoS>cnGuavjEG^_^rcfp[FcD^]^pxfXZ;q]=awofZpWwqpanp^\\hvqV^QHyqQoOWjlFj:?NK;>bZDDf[JowqPtYIuhOtqG_VhwIp`Uqfb`eh@uXvclFskwmegbrxrJ`xqWcdWewOxLpo<yb]>q=vrn@d]wYWwm[wQexLitylxpyqU<NwmxwQjxMoTyQyuveIYtxJQyVR;:::HkgMtuUoPhKoYxKaSMLUnutGMXvQwYak^yU;dn?MS>AxmuOwimaXyK=vtLVuUQXASmANlyKO`jb<NJQrwYpoiPJiSJexb\\tHDmRplLlvP`YmpsGYujinxMv\\lyHXLnEKgtrmQRfEyHQYDeX_hQBmm:YX?yJmaWwiWnTLneMDep=lN@Yn^DuwuqgXTmlXQXqw]r?]YWxNjayPXnsDVpaQadY_MQD>^sWZIqZ<@gJA_[niWntQIbmncfx`XGlPhy`VsTisgo^:Wi_>i?_yPvqDNuhvZqxjEpugWonPiYhmwqenW\\<Gj:?nJ?_NR;Bb\\<JJ??ZZDD:;ON:<db:>NK;Bb\\<JJ??ZZDD:;ONlkAqQ;@RZ<TvyNVMVUIVwlq]EW=ITUYtI`osmX_@nbXlAeX<DWKTPkHlXqrdHo\\HmSlmJeJRtrTemAdtvqvLmx<Xrb`rNDx\\eyh@wQuJhXODDTCXXj@o>pPXPjs`VqaNX<qcPVuXkWqKQIwndxGyuVTWKdmaHUYxm=pJKqXmawVuOMmpyXJ_HU_EPxluWpYRmVWHYdiK]Ly==OpeqJxrEEMpxwNLRhmRy@wnPq?PPZeX[aOQdu>lx?PX_xn:Pn^@NYlO;QQWpkAYoOIwdatOMwUMNkatIMPm@qH\\ynYxPtvYMuWuq?aO]trFIxXmO\\HW`hqmTsmhuXtWVHoupwYmrSPPgTOgypsAt`yVQUYsmLu\\K_QYxtOiQW_@QLDS>]xilmsTXSim]XLVYtXHSlpUXeXM]l>iRtxvVpYXXXrex=MuxPtcmXGxNiDpqPOIptYlty=j_yk?eoGAodqmiuxo<qulj]`nqEkQXS``Ttmv_UlhlOrDvj\\JL`JCeN>lx@PRD@tKhW^En]<uATNhMuguneATMiurIVDDQMILPiyKxvYyxEUSpiUIQyWupdeocynHPosutmlmRxKglqRpwA]L=iWUHxUiJ]XRkpr\\hUiunZ@SW=rOUt[TLRlPVYXLTYSyWL<MbYL:=S_\\R:`T_tmtPxGUrjIqhHqRlKTXycxKPYyaayAXpgUQoMQU\\QohTAuUwYtEqwH@Wymn_YLepuS]LDdj<ZJ?_N:<dkgbPYpnqphY`pIrvgygahKNj;@bZDWyGtSty<npXox=uO\\Yhdl@HvmaSUaMM]u`HxbHmGdrJdWPTmNYkGltUMO;\\O@IV_PqeaJY<nL\\jbHyu=OnhPnhYvMY;eyjuxA<otYVjdqmernTkF=psdSqxVAMXEUvhHrNdPqiOBpStHvv`wQpTTQJXuUbLr=HKgEKD@sZtrXpK@HWgPqEDwYTWXhwr\\WHiOApqrTVsXuShLXTKehwBtlyLrJUl[ppLePcDr;@RhDqLaqrTxxLUCXyMyscpYcexuMtQxtWMmdmlOikyw^RVaSWdPpn]OvJO^DIfJvv@ig_Haknp=ps>npoxhO^oqYiI_^JGfw>]dy`QY\\hpboihGfejfxqI]KiycVtC?cFW^vwpjVymF]Uok`N`^i_K_^gvx^iiWVcgvnoppJ@imay_ijWYtI_oahdgygeaoHpmuYsWpkRigPophAxl^gtVsHxrGn^fW[Lgtnqj_F_y`]lXxGii_^]fpkAQlKPsr?nBQiA_tAqhsv__H]M`xqQq^?etapHyunyu]Hbi?\\<Hk=YrAIlg^aGYc<Oby`_CWxY?moiiX`dKveONwsitAXoH^xoxZGoxWatiNcpIrZ_r`YaYV\\@Y`AOf>OijYjc^cp>uk?yiqoFwqKg^:QlN@nr@l>HimIbmpoDPqYptpfw;hfRxrQgcmNp?icOprHh]b@`hn`HYwuH_hy[QVu>Hw;wbioj]yg>@^gf^wouZO\\JVfANwWntypoxWwoVcOFwcwornmGHgpvlGOyv^_<xveWbHpeunmw?qdhhOqrLHvo_xpvpv_`_f[ppjMysd^abX`AwbxXqThvSxYiVucWWMdgqXBOeSsHuisHehuMySOFoIuE[RUWiHMVlaTRKtRIXT=E_=WMgYBChh_FJ;CdCVWqhYSYiCceeG@wDbYy<GuPAFkcsaCRkYe>=grkeRUSFAx_Iv`KuITmhUqOdxvLWJ=uDeMoiWp\\uraj>pkZAlSuV@iK=exG\\u`Xt?XTcpXVyVZQQ?PwrLOmPX`ER>yQ_]JxDq>URKxnRpK?xxppPB=swDKTMtL<`Q`hDf:>NK;Bb\\<JJ??ZZDD:;ON:<db:>NK;Bb\\<JJ??ZZdKKe`qDooYmofikvXqvnqgawSSmGweeQ]wCwc^GFOwGrOT@KR;Mu;cw=iBg=vsuyPyQgimUpOFqV?EXXYqdhVYHQIuUadOTpUPYUNusHPnVITX\\uNmskevRtvW`UOYNTdxZTtnDQaXNLemv`TBdolmOkYseqtCTWIQXrDKdMuPQtOXUTAYkYlpmKNMwrhpSeYAMOhtTdyVe]ROuMwAqYLRLitbdw@ML`XWmpWnyrNMobMoweT`YPiytntYxMqSdL_]ocmpviYEqSmyjOQUHinb@LyijDMlvaY]eo^UPglqAejlPvwuMaQn\\\\tfQQeqPwhpbXkppYoXL?IlauuImQ[pnQ`PUivuyY:XpXIMmxXdaUHHkYTpmPsbpXMQphpWUxXTXKmdswhkcXy;dSMpVnhSr<kjtuK\\UsuSCaorLWUEKgMoQMMTAthYV:@y^mksQOTiKuVhy@wn`x`IhSxvFpb\\W`Iisy_hWaxun`UXtdQo?Y`DIaaW`C`m\\_aTpaVyaSg[q_siP]YHlZwlmifIHoJYtfohE^efVr:Hj[qpPxsvf^YYZsP[jWivgbkwrdxbjHwuG_qHwf@e``vkgccpsvoftWymPtYvmoiathuqg[@wnKabKy\\]W\\RHwFOhBxkCnr\\_iaAuB@m@gnYAhEAktXfqi^jvviOgLy[cNey_vbhi\\Pqe_lUiqIg[jWvgnc]xbqOtT_mIwrGieC`oS`lvGpS^uVNm^WauP`L^ye_jsVcc?why^Hhrp^pX`vp?j:>vsuDYIb]gGuE?ax>YD[IxEyuaoUcqh`oXgyEgExVirFsFkSHMAecsSFshmqILqhGSiHsvTCC`kXsWYr[eUqC]svfksiOtPUwPmFCCsWUsSmwoqUJSYSIChgy^OIceR=gssoWuuCa_hKME\\oIgaD\\mvwiuKgwYmHnSYyyVuYBUiS<yVLaCAkwdOWXCdYaWr]Bxae_miwqFguxBmhi_vJ_XMACgkEUcs:ivDCG[AfEMICYfQAttAbo]txIbsCGVcFZEBXGWtogTiYYstqygI]Tq]RryrsiStUu\\=upqYI;W]Wc^svKsumotcGxSsI\\MI=qfPGIs;GNK[?ZZDD:;grQVeIUtUEqIUu?VxqipKyBEb:=^cyiJImxAjTyouAfQ?xr`dUVfVqyRhuovpgOi?PnpIcgprUxlZyte__Co_aHqgVadV]fH^^OhsFZHOZAW^SiwNN]>^xeOachwE`nxX]gXijNw_vhrHg_py@^fi_[dvv_?mtiuL`ungrOHZG?`LatUAskVuLWaAp[AvcAftVvjEItaqt`yxeFwdVgX?VEhSkXpSXvSifYi@]hVSebCdOyTh?XVcGHeF:_di?h^IdACDnuTaSCUUVswR_WGu]ScODEGwrIrHOfQOtXQVYiIDKfuAYuAyaIUw[tRWw[qiwaxUItdaehqifwGckeoID]mgVmgjudhYy;ybWkTVKxYOtLQUu=duad>oRXeGg?I>CgaselITaIrcEgwwwQiULMYTUHqUswWdekC`Qh`uGQUcWQsjEShSuPid]]R;YEBaFpQY^Ab=MGIoid[u]_wZACtquuIDwixFIwrEtEkg[WYSgg>cGckWbMfG?TJ]lCXVIXP?mja\\ugYxKivYqWkep\\ITvdmo`tgdMdim\\@X\\mWqDRgLpRiqV]Y_IkdTlC@KlIUI<NrHk_iP>\\QVlOqeLJmuXMkVeowUQiULWqpmMnTyqMlVUIxCDkVIn?=SiqtqYn;My[AL@hwlXmDXVDDL^PQ;eYDevdlWbxsgHYC<N\\tOIiUl`xb=tWyReqkLQyKUwHhNcmjAuJIURpXU@TOqmXnDUEeVhIn`eMFAYLaLodOEhV`]uXPNUPO[muc]V`tvAisL\\WQqYTIQt`OyDVtIOg@YHERyXsi=Qn`OeTTm<OQUq_itEUL;aS[lQVlXVMLCIvo<QILXSYsCdVEUOVXjKyTeIrmpORTm_`tW<OiQYuax<UPfUsoHqXENRevRenrhyQMQnpXOekWhkNdP^dQW@SfAXZ@x^XoupKhUj^eQAPQ\\pwaPoXAk^QykqOUXvl<vrivxLxg@ygpVMmqDULx=UexON`PtusGLPvplEEOkERhuL:HKfEO;`Qb\\LDf:BNK;Bb\\<JJ??ZZDD:;ON:<db:>NK;Bb\\<JJ??ZZdPowj?g@MDhSRGUiIgXaqCgCegMeAWEJqgjQTlOrraInYDeoxkkHg[VbgY>gDGoWigd\\YIc]GQaxOSfMcRwqgYQfV]gGeeO?ihseCaswkuMgWHeWAexS?gE?Iu]WBCuxkSiEYhWY==bMoWaoShyXqmvCyRPgI`KSXye_MEJ]ipwVQsrYGw=QGtqv;QEGieCMeoaXMirCoir?CHwgoAs_=y=MSuYSReig?eDqhsQg_AgxGSdwvAaw>scruEaoxomWuIfVgvPsHMGuuiGeOYEGhXgFBqDs?u>[Dw_VZQIxKUEiUHIxpox=eBqaDhKuT?wTGWuaS>gHXAwiwxvogwUglofrOFeix>ucBMEaYH_YSe[StIwiUiQuFwSs=KUxqHaosPct\\UV\\KH==SJ=CKMSlwd@IR^iYxqy;IclOwqyhguUEmShwuaceswEtOhsqvfqbu_WVYuMydiGsBYIa?DXSuq]XccxPChw_SadxoTkodQDPSHynADsFEKimk;dWpQuMHVlHQlInjDVvDYbDyT`VqqqXQu`HM]dR@yVeiTDiqKmtwAYlqXUyrCeLoetOlwOLvxdomHmqusBux_qPgOnTfdqhkwFj_Pik^j;yrkYyegijhwJYe[A^MPsPhnL^d\\atCg^dg^>GyLXgHihTgoHopvquy`dOadoImtosEXb^XunHx]gc>Wd>_hBxy:FasysovtOotDiZ>F\\dyrQyg=Oqbwe[?whX`:hsNiqQGq;QyU?aOolQojU`glGa=WtWOcVVd;WfOh^nHnEOdL_d<Od<_kphwOwex>lDhvRQnkouqaxhNwuWowQdny\\qftw_fMaeqw\\Y`kaWckprqXv@ybc?g>Gfxiekqt_xZ<fmLwcWVnOq]<wlggrs@kC`ioPhh_bFqnwabR@nJ??P:<dbJA\\LWUWyTc@qiRy_YhqhPjj>dbZQhyCvmbi[dxYgW;yu<EVJmgpSrLKw@URpwtdQICusjOeWcHwqIBWHRkeSGsOkEk?IlsfZkXr_WQod<cFNsc^YTCsc=kCr[u?WTHiWY?rjeg=gee?i@=C\\odfQHbcEQ_y\\WuF]r\\SFf?iZsVvCUb[gtqI_cV_iED_iNMrsOf;msgUv:AXggbYYgrotBKfP_ypYw\\kyNKsgAUNkDhSXvcD?Iy\\ES=IFQYiN_TOsxbsHJIc^KCGeHdmwwyTeifUwfuGIsoWVktWmF]qhu_c=gvsSUrgywWcOgH;efHaHdaf=OsqOfiEHBMscqDAMSf=IeCV_KcDui?oeVeI>ghMSWPifPWVboCHuFFwEuCxu;H@auq]f_cY`]rnMBIGXCWDGAXF[Dc_YvQd]SSb;T>sHTgsxabUoY<ABOutoKb@EC\\]c`yWqAisSrr]s>cuVmwiKrwQT=kykgFj=TswTTsrXsCdUS=sUt]YfuwnCI=EyhYfpWdaGyoGu@SiTQY^?YVCelKBrWbnOIngDbkCA?BLyRSERt?gpQbbqUV?hPaXU?bnSuVSBf_cigIukYkmF`]sxqiN_ffGf^[VccVc;Cd_ib_RHwCOgb]=iGabfUWpwTRCyPmfpww;uFQUUugRbsdFseRcShSbgkUs=Rk;wdiwlaYX;INydX=UcoST?G`STAecnSb:Ux\\AioGxJgttEcZoHoKTf[fIChG_hJITwwVHwsn=d]eskIgMAxW]S`AWNiW;aWumCmYEt;r@gXJKVkaVD;E;EWBWUdubm;B>[vHMFrCS:@nDAQHxMD<vR\\Uvtp?lrgmTUiqs@j?QQMIw>\\ubETTqM>qPM=V_DkX<v:@Nc<Tb\\<E:;ON:<db:>NK;Bb\\<JJ??ZZDD:;ON:<dsowq@apXgmwxcOscNfmV[sgv>Nl<O\\LPnro]YA^e_w>gtkF\\PAeOadK_cOiaBaewF^Hol>QZonnoyvyAZZYoI@yoVty_uwyy:vYewAOycqIhyI:qYymH\\yI:OymoiTwImMxfWybqYMyXSoxxAupgUW_SuICAWvjiiOGYPCsj[ypmuLOd<sESIsiUXgauksSXaUueReshgUtkMecoVgccrOStWxCIG_gwxYDTgUeWidMgniTkcsrsccoSx]gYUuoYfcggaGu_UvIOXw_UvwRt?ehKxgsD`WtA[EPWuJWRdIg>cb_KFNQbJIvBKxxEdQeWpucvuidWUNWeCOC\\kVwMWtwcwgwyppwiMMqudhtEUPOTTmXldiTPEQIQxbUUa=uGLkhuTQ=NbqW@LwOqsaMlV=mwAwJ\\V]UP]DNbiV_PQ[motLUL=Q<ISmmqxQS=huSiUYqWMisu]x\\AMA]YIIUAaxfhwWaoRuXW]tcaXQmneamlIvRDwSxw>dmXPsKMq<Ej:?NAUIghuIyJgWPGWEQi;;iVMcGqw<igOUElef>oHwEWY=CoUGLYtRMcNkWBeWx]IjAixOiuAfUehuiUyWjSToSTwKXsYqVQmwuqOExVMMYwetRunrlS`HyIyLMHKcuQVqOWPyWIOpdmZXTWpTu`Sy`VqlrgqtBpO\\YTTYSldMQMWLptpLJJEkxLT:iln\\TpUutQtRQooUSkaLMIMXHXLiQgqpQppWxmPMwcEp`aVGeTF]rtYPPEYreNlPXRtMAMpXujw`napmZivslWAyMNMLeYrbYWHUNY\\YttWCAmIEwi`vVQoV]ro@sBtQSDW;=obEncqwxmOuusYdXLiOQeP>]SMpXFLxJmwTemweJ`MXveqhdqIMlMDyB@tLmMWxqmmtMMuy`OHxiOwcHOmDXoAanBxkiwhWaloNwennVhrMnaFWgv_uHAvR>me`hW>pVYnrPpEW[PPvV@cBWyO?UgyYMiOOX]iwUOwFoC\\yfCggsAyeMFkkD`ayy;rUWIg_WYGiUOUjErUGxpcXTYt:OIGiFAurjYfmCIEmy=YcxOYkuwaWeemuq?Xguxq_ugSDmkdl]X^cx?ee^Ue^EWk[xDAsYED:KdNyD^egFMtr_f^It_yI:ixpgtb=up?EdMVisCyevCwUqkcC?Em_uvqUVUBtWuu[SX]ReoYFmrL]T:uDfch]yUewcB_H?mcyogkWymcWpSVo_eYgiWiUYgHw?YEwuAuXW;DqwsuCgmsy@[UnmVNsf<;IhQg:gFnsrVYhXwTDASysToOeguicASFiuIeyY_WooSygxSarTyBwyI:ogvaguiRPAWEYXsGB\\KH^qHSiuhEr[qxxuCZMcDCYxAfwmUOOdwuyAciQqYvwylcuTeYVsiWIWqyvwwDpwhgoxU]vpgUrKvQUi\\]UQMGKqxLwvSoyh=tIyI:?RdsTnihUIU?adI_thYUPETVmfcAemyRiIeoswMCDwyTDgHqufrUC`GwGgsvcsE_iTaTNkvPOxMYwkORBsB:kuv;SOKecaU[WFHGHNaUn[xkScHmXgQts]T]AtfIDhOeeawsiylwvM]flWV_KH]AxViR@QFYiE<YiTQSM_G^gVZAi^yudMvESTksTF_H@mD\\oFXIGegW<AEk]CMGEQqi[qC]qHbKdhMh>Wu]=hZqxLkFvKDJ]en;v<QVuOtNsheYT<ABpOC?kG\\ETAsstmUfUXVwXcYfRqHWOhEmcueDW]VIirDeg\\kRMOgoKV^sXXEidQTk?RJEii;H@WbXsXx;fDMTguDG]yLKrhSToAX<yUNCGDcb<JJ?_Nj=LkhhpYhNqHxYlpExViYwZ\\KNLK?rLwI[YHwGRoyup?riEfj;GqUi:=FJ;ONJ;Bb\\<JJ??ZZDD:;ON:<db:>NK;Bb\\<JJ??ZZDDLkxHny?jqvsfIiYgud^nmXxNIy<i]A_sQgvyvZ]f_yAZUxcvItYWnYVlaXo[o]Gptb`rMiukafpGmdAfoFiMYcIPgPnoWfhkomIx^=YgMHrKWbhO\\I>u<`irpomvpPN_whpK_dqwdY^kFgaA^v]idGgk\\ivmvu>oyMV\\EiuBf\\Q`vHfvshfQQ_wwtVieHyv\\NfVQl[YeDp_rhnlipLFcQgo`IivNmeiwUWkPGo\\Xa\\X^hAhTXmmPiwidIaiFqnaVn]QyL?pi`wEwujyxeXmgykJy\\vFwvAteqqIwy:FmgHiOGy_WqwvwoA\\Uqg:AhRHuXWq^wgwQa`qdUp]sFg^wax^v^p[N?dSA^_>prgZ?alZh\\;vs^VZ_YiPwshpuhfsPV^NhhSHwYvwfyjnxgunyWIpSOkoi`momNxrs^mygma?[[v_LinMalDghJnhaoio?j\\YjhVaR@p?HoVnmLanBPwC^^k?s>>js_]Yhgo_tvymYAmaAoFhySpyhQ^i`lwa`Ig_nVvgybyAZDHefwZfpbPQy:`uOIj[IgrXvsVojft_^uI?^DWZIppX`a?ors_Z[`xapmBgxPwZf@d:n^shs]YpUpjGa]qG`Ow]TwaYw[AhpOagWgoUy`TiqW^qMYhdysciayeAsYREitYboLNWQQoppCintIn_DuOMxWqx==YPaQExJKUsgyp]AQIQVvtVJYYs`WY<NA]JPUYqpVoYyOQmhPuh@MDtvVXX[YLWQL=yiTiuYvfoa\\SiqhOo`@oIa_r_sq_srG`HwmtQcuv^Eawsh]mI^:YpFGiPV]JglSVk>@ihhaogiH_Z\\^_nO`lyqbFidN_YOgL^lLhnIn_pw\\uH\\tPuhPkcOoT@qaXuDaaaG`jqvOIwxIdpVgpYwdPodwn@X`II]S@xFxcYGr_GwAhnMvpVYnuvjIPwX_ul^c\\WscvwGVumy\\`x^R^qXP\\qH]GnpuwZohbdFd=>uOhdgxcZgxp`oGqhhirOwbpo^mfvsvmmqqO^`YH_ugigabKOiFItFwx`y^XFhB`vvhy^VcGyo[FwcHgxHuh^[Egjq>dfww=ylS>t]ygn@qLalA@\\^HycN_C_ZK^v;oZdpx\\N_aXidp^kF`F_y[Wg_Q\\tXgfiwoVdsFkhHmI`gj_tNyeFw[LY_\\xinXmQwxcyoCwuxojNiiDpqIf^fyqmq[UhwMIxAxbU>pWqXSudOTqeXyyEmatTeWc;IkkCugWQefI=DAGvBcGIsXP;r^SY<;R_cBZUDXWvqiwTiSMCTPaxNmvu[I\\]Y`WiYMVqiSUWrmEw`oid]wMiEYSHxCtWyI:mvTGXyMYNMEIQEkGVFuvaCyV;SCsUKevHMs]mroaBjayNMTS;xZYhI=dT_yrYHuuRcuBZcXmwSikY\\gIKYxtyr;yFqmiM_XKaE?MesAupctK=Y\\kIcgWjoGpUuMuU`QbPMU;MFxwdU_YXMF]CiM=gJ;iJOd_?ciYVO?I^YBd;W[]fsXNX\\putR`upWPNYDsxhqydoWlukiUjaXUtLfqxwPxaINa\\pVQymxU_iqy=j>TyLtv\\<SfAyOLK`ItMlU\\XugppbmoC=QVuNBUsflR[EKdXUhdO>eNBLS;en>=j:`VQAQeQXQmxYEWddwPxWWxS?qxipPWHWQAQpuTulOsqlT@vETlCdLXTQu`t\\Ql\\QJwlWN@TJTYsej:UJMirTHPemSJhSdYXDQPi`wuLt<@uPpxoLxh@U_EWpix=Lw?qrZ]WR@M`YwAtxrXxgDNHeODLXsxX:MtLeJOxJ=DVvXxIyP?\\tWuPIIo_awQ@sdhsDEpnXXluSaiSaxm:`W?AkJQvlDukuXNPTUiW[XnLdNY<N:@JLxSjPKDpvdPQDAyBpKBHpgpmJpX@=PwmTtHKqTYXHXiHYitxcUpbmtw<yOAnZ@POxNceNcewwANL`TSMUA\\MOTJLirTlVmvbo`]Xynrnkdo^sGw>>unQ_UFa@?wt_fhwgHGh?hl`nbKgi;A]V?e>IhAIihGbgaZcX^LxbqXsThbcpmMx[MxhWNfLWwdWeMQuhyxjx[lImohs`Wp_otpXy>^rUyucVl;Ng>nj^yrRWckptrwdCFhcvv<xb]nsjPoT@oV`c^nndPgF`roHqQYjgp\\HQxWfnewy:vcvye\\NsRBLYvgWfLewgEEW]SsWcDuFXQXTODS[ccOfn_TcEwS_fpqF;gIogWeeXkerW=sh_eamrcuw[oW?eynkhoChxWupcwEeU@uesaHY]Wsir_USFUEHcVt?EWIUa_r^AHt=tSEhEscrqsXahp?b<kwskwsgUoeuokvROUucSnMFUYwOoGmSuS;dg=hcqDigH]iGB[WRovg=RhkD]iVVMf>wTISYCcigoyBECnOHyasmCB^qmZmMd@KqdUMEpWHs`dvnFmiYhqItiYhuYeTylSojqG[bPunXmp>m=?q_Gcqhvq>kIOZrPpTNlBXgoopUX_D_uEvgK@urN_mYZDHqpOmdhpBPwcPgdHgsHmngclp]dXi_NweVl_?i`PtoobPWca^[=o[Y_]pWrhV]CggoQq@plTanp>jZId__fpgy:X\\AQ^cxthOq]ntVOn_i\\nydffy;ohMQiGaeMqplW[ex`>`fyAZ:P]Ap^?I^?Fy\\`vgipc_gpAxnPnEo_?^oX^tZhZLP\\;warN_@qctVh@hgfHeNP[?ZZ@db^\\Dn[bNqPqiPhU\\wQbe?FF[<XCf;yAyu<EVJmgpEb:>nsicUp[UI\\Uij@YeK?u_gZioamIjBfg]^sc`bsAZwnv=`ZdwbNoyUP];ghPfaDwu@PlTqfQf]fgrKpm;q_[fgehp>Ioc^hNH_d^aJnoI^aI@pJQdkoskhadNxeauvWhVNwSVnlq^DIdE_[VPxLVaBhZ>whc>rA>lxVt;omjfg@WtwqclxpLHg@Yh`?sgvsnvjSwm]Oqmf_Q@\\kPsNglnhn^NjvFrAVjpAdP?oNN[?ZZ@db:>NK;Bb\\<JJ??ZZDD:;ONn[:oxThZ<Jlyjn<Tb\\\\D:;ONr;Asq;Db[TNey=wI:yxI]WsyEWOg^YxmatsKRWyRFyD_sIAUfFmcJItI;ue]x]MxnsIMeggusPsWuYsQIUsiC[KX[_c;uC^mhC[gj;VWYBlgwLKF_ESTWIu[TYUe]cyxkss[FIQYPkWtMGqcUVEDI?iSOvbOhDMFxis@wdeUwcuTOeeSGSDWW`ai`OucAyDAC@=xnkunSw_gsVMIBktOYUUORUyWleBleETUiPkgvuCd]DLCy>oxeKe;UWquONEtiylgxM=yMWqsPyMLIWhiuaQWFEymusNYPnaYyLSPilwEkumyXdxmiylLy@xVWxQTdMA=vyHMgDyOEY_aseYtbtpFYWdpJZHrtpqjlsrhstTTieVlQ;]T<IwMKuIkF?AimKCcuedISuSwh=cRQvPURhIWemT`qiswC>AxgieuyTuEcpIUckC\\_IkYdkGeQswMMe`]B^cUIMxWquDsREOY;ifOqtgEXi?wTsvhUbKAcKMCUQwfaw[gxs=SIuXlwBY_uDqb`uYQuBeAWLebYWidGSVUysmSvWYMQuT[xokhdeYoatxohUCtSucqYGEcuuYh]ktTIgK;GqcsgweHEd`qHQ[f?GHbqtBkG\\YHxOTWIGsGsHKfDyI:_FcoCc]fw?vKqxPucvShTgs\\cyMexa?xFoIGuEachMiVYaHqYveSdV[Y`CXyyQ<lVtIt:hKYIWZuqpYrrajTlVuYJnixYyPtYrjDyHMyLysRyY:dVMMKniVTqNJtW=HToutMhTvHyeHJmDw_LRpQQclKrXM?DXh`PUQTDTULQSEiy>ajMHrm]vTLupumletgmpftT`IxTLvatnrXWHlYgtP]O]GouxQnWAyHi_OI`QallAkXhek_lnvbh@thYyMwvWWaHpmOw`M^teA^thvXwkhwj^w\\qPtfIoAV\\kqdPPr;gwq@cBOxXVbBQ[mic@hupVq]?o`pmXxq`yjjphPhvQWiA^ndpoyXqvilofuMYZnQkbymgq^OiytYgpxuxoJu=qCuywvhspGx>PpnimoVa\\nqiw]KNtCO\\Wgc]X];YeUP\\yfkDi\\\\^eQXjhpxkav\\plTvcvvm^v[awmvvtZ_ppAwUqgXokohdI`h>Wf]q_ihvmVdlgqPiuCxmPOmmwwS`mvY^hybxymuiiJioZWuXovmgyS_pmP_oYjcOlaFfDoh\\qnFFidPy<WsbPcNwmKVf:Qbr_aHp\\ZHbha]hwhWpfihchHtUYprNkeirVOqAy_hItpYi;GnOigtXwqXvoFd@GgaakIGaqax@_wAVaCapuHamPgPw\\lOhWvuYNqkFhpPcc_ecvnSAhrfjHvanQly>wghvua`d__OQgxhl>_ruYvHvgEoi`uNUtpae\\MG`kvvMvl_eYefIAyFsx@EgiaS\\Ae>wE[wHdEioqiWCdguRDOc[kveWtP;BVMdJsXR[GYIhd_v=;S^ytaUUncrqkFvQXwUsWGshcrmWf>yRnyI:eGTUueCgm[VH=WMoDiMBPOiQOhQgWZwXukIdMvy;BLssWMCssG?AVqSiL[r>OI;cxOkWiCSsUCaoEHAXGUDpGGqGsUwSqyg_[IcGDokF@CGamulSGOgC[Ud\\_i`=skaXpOhqUUEgFnYIV[TUEHbiIC;Faked=YrWySAxMir?quOwd_IeNsunQTVsuXIgg]FsYsputlUg<ugtsBp_d<wbVkHQqTN;iVef:[bvqXXWeZuCSgC[aipEwZwcaKV`?I_ob\\GYIkDMweZuYH[S=GFUqD?oGAwdDes<wSfEXiIyGAH@GgLchxscS;cv[G?GvrggrqDvsy[kePKXsGdbqwQubYChgKGrEGGYIxuy]OSfSdk_sTssPUfg=Y?KxoKr>AWcgHS_GgcVeiG>;gNcWdCcZ_F<;C^OEGaVmUhQ]Yumw_AwfgXcSwvSefWcGuYIuwG_bxgHHqhl[iEkCyIFomf_eV;_EAQdMccvodNmwNseFWWXGieax\\gYheiNQgGWevKYpIHcquFYdfWi\\me]OGR[SUQy\\_fmEhu]be]vBgW?_sHiIHYfG=iPItDObL_ve_SYeiQYhmCxCuwvatDIUnsck]EiaVcceo_IEwE=cyfQwO?glGEkATbCrkEvmuBj]YmEUdYHciYFahkUuxqxAYhwyI:=g@]WUiWpeyOETVSc`EscqGvcDQAv@QVFkWQ;X;kULmUgGRxMBLuCiaepuSoSBMIXLYTFaRoYxkCT]YRnUVLcIZeu^YTWIRL]udGyIOeQWuhEe\\YyRYfCcRKicXMecQFUkcZoxHqbP[faabtEGKWbDEYtkvfyVCqSNabWueu?FGIxUoX=?wUSX_AgPIC\\?iMsHNCFQubk]Eh[W?ECD<TV\\opPljPL_<XI\\QqmmwdPHmvaaOhdRkdMY@KUHXJ=WSxklmpX@l]iOWij?IucAq\\`TR]YCmxKql]ERvMxNDo>\\qBqxftXYLQ`mSTxTg\\Yw=ONLK?PZ;HblYmtf\\pX^qX[Fpr]xr[gZioAfG`T_tMZFiZPrTHnNYraplD@slo]dxwyOcfOhTNmbxk?gmX@BcCxCRdeggubD?t[IB^;trmXJeFgQYN[UQsTjUgHqfcmDSQbwuSY;FqqXGOyoEsEGt`mBkiYBghoyVCEGJ?F<gIn]UXgxfcigWyFgYjsUyUIW]bZ>NcuiKqy=JZppepYRiLvm_GnsJA_Nn]ufyxIsDHu__vsh_\\i^xhu<V`Lx^Vy^CWcfnb_G[dVeH@alP\\>h^ZNl\\@B_ETcSeexP_Xx_XeeBisHWidcwXESEoQBu;ecEeteCumGx_rDwgj?cFwVoWXDySx?HceclmuMOv^Uh;QvGUEoiWYqusKXQKxGIThSwcKsLCFxgu[Wc;eSg=vtWr@CFjAD<_iNIVBsB^sUl;Wjce<QrlGtGYbeqgVOxpWHgABP_CUOCvmxMiBEwDxsy?cT:CY;MScIShsSZOiaITw[TUagciic]bhUDBwGj;hxGvRUbtGEBqU@qeD_gJGUCwi<?tH?dl_DNCXnKH;Ef;sHIKGxOfvMd=EfwMwhuTiYyRGTEovxgWUUtgEEHUXn;rG_s<;heaSqMgNAIlSexShIWVrshn;hNmeAwDR[HSoU;?JZ<db^\\D:;ON:<db:>nNqxehfwibqyhQyfSopeFnw@clgcTVrjfenVp^odBqpfO`SahDgms?mcfhx`^[P_;VcJxpsV_xni:GZfQ[xvy:voWnet@`cgdqhiQogbXbW?`eo\\Ewg=hmcqyownPWy]Ol[IsJpjuPnwV\\Oxj;wdw`a<fdeaZN@\\Uih<hxI^^kPbBio[Qfv>yGHsZ?aXh\\Rap?x^KpxX>[ZPruNqdIijhm@`ugptwVuhWhVVrhvd^g\\UiwLotfIkho`yVx_@kGAq\\Y]lAvgFcCv^Bq]v?oln[Yy`a>nupoMAeTXrqh[TGp`?iFQtLgs\\IrjWbgyj:fZG__IFeaP\\NVaU@eDWtBavDv[xWoeogK@g_OpQQiPi_BWp]G`ivhbqpE_bU`unyb>WsFPlL_rPOsBQ[oOrLP\\Kpvr_`RveGOqx`xFitwaiu_gtfgw`]TfwVh`kFdUNpmXhb^ccH^;g^BPxP>l>yls^ap_`\\atB?^=FrZa^B`aJqbWqbeiZMy]CWxEpbUxfuwt;Q^YwgQxdgApg^oWa[Q`Z`hfhV^GhqZin\\w`fojVYgQPkAVhd?Ztyn:PldNdJOlo@o:vZ^Vl^A_\\np?otyAZ^puafoHhw]Y^YqeEV\\dvklo`sI`VOmiItR_lCfZap^@pyDhj?NZOxhtVaNWaIO[lAnN@paObsPr`gvholNAklQ]E_kxVr;@gkO[VfnC?dlEB?F<_IB[XRuRqeUEkh_AHcqTuqIhshoeS[WdhegrqXeadq]UtYWgMxMSF`SXBIHYWCsMgIIsUYEBWVX;gigstmWmygUyXMAutGbpegXEh`AiNutNKthktCEcw[ht;dDMEjucSsFL_TLUUROsMLX?dJUytoTlD]PAtShPymdotejbirkTOuhjeimlEYsHL]ur:yY:`lo<Lspq:ILCy^<vcN>]]OgwWetGhiYinvhHo`sXqVWec>sT?gt`_BGhbYhY^g<fncnl_o`LyuC>ZOp\\<YqAOmr@nK`lKvjQOyIaxn@tVPeCQmdoeqApbotfikSA_lhahomuPj_hiWftlPx=HhJNw<A\\eYgfgoCG[iIbI_aH@_mnoFXwp?lhw^I?^dos?PgWWlhnrh@khIjvwrhi_Dakiq]NyxZ@lNfa?x^?`^sA\\G^Z;OwCgtYycphbwhmxhwXxxf@uXVabgsivdSNaiX`\\^mNHslPeT^joPrmotRWcG>sL`\\YAkjHijQkMGr^>tH??=Gq;yf_ugMtJ]Hscs_kTXegViF>=glct=oH<;CnGTiWXWYVtYvfUfJgt^WuIkEhGWI_Fg?VdgdGQxvCGkgYXwC\\UfHkTNCI>ivHctKkF;[dSuw=iXekBqgGa=TouI:cxxGSRQFqOFkqbuyCVCD`WXdOBDodJ[xMObL=f<MDr?FH;CNCdUCWauDwqISqTpqhumxuoUm=vrgG]_Xw]u^Owv_SDMHMqVC=GdQDQISIEE[[GqMVBUDxQv;yF<EGI_RMCbrAfHubmQrGQCWcVIwrJMTWIv`iTD]e<sJZpYJEr@TjGdw\\PxWutkhT`ItvlRo`v>atcakd@TFAQg\\mF\\jqtYj]TRanrpnspWhyXAtky=jR@nyhThLm>eK\\UMuqU]HuM`mdHRrExRPmaEnmttgEXvULg`oM`u`XjXDNR]J?DYTxK`YThLqA]JdmroXNSqx\\HugEUX]V_\\MMiMOdqCDMoILUlKBUTGXxVMVUERDDu=`J<DQntlWPTcyWlXuYXqWuVklL^pvN`WSLPXUsgaPTuRdPuNLN<<r:LlC=VJiRgiPeyXLuyQix;dqAXtw\\xZutFhMsYWELl[@Me]KEEydhwjIuNTwcq[bnmL>\\\\YqyAZKqwZhlnN[?vZ@Ivxf^hX\\qX_>plRxkWfnrVyiAqJnjJHlDal_x]ZB;_FY;F?]bQexoLtDIYfTn;ewUiX:iMCelvLR=qv\\aP<Yuy=JlULs<SK\\lCMX>LQ;yTdDKx\\tLdPdPSLqL?LjB\\VJ`yB@NNmoW]TmqNYuYQaQEXWTIKPUpRHTwyp>In]Exj@qrhjpttlYLbtpcQohulOxp_eLIHm_`nkPURiqw@WoIKhMoGhQJ=obbyxwYfVced_vmY@xkRZF@nN`pNv[RxcOpiFpiIoy`HgdI^ahocqgpi`Uf[IH\\B`w]@^mV^mh]<ap[HqGw`cn]awsXxt;Y^faaIPpoXe_FwNigPWoY`[w_uypbeapt?gLywqfoAqkxoyyOoypnrQdRHwAPotQl^IacN\\oWfMfplPyy`ssHv?Cicw]YSGIWk=dIwUJMevaIdeu?auiktgwF_itIsunyjPaPPmVuTpxaWAYuPXvhqnsdy[YLwumYPtOdJyMvXyY:xJw`TuXVniJIMQy]pi`yYtYmPulYolMsgixCLwUupWDOeaMWQM:mpounSqQ_TqGDKsmmE=m\\ET^yrAPvqTSButBDx^iq[]jelTLQtN`LHht`ILCmXaYvQmWt@WwTXKeuPTPkDlFmSayM>lrWupeUqCqPgQysDPies?YsRIkTPO`lN]HpEUum\\Kxek^MW@YUvhmVAW`iShDMtLUemSjYQ>TTxhjL@u?qNCmknupJTrcuKHLpJPt^=OgdnEeWhpJAMOQejZtXpAwTqXWeVTLYxqxrlMmUPOAUHXxS`MFyRAlXtYRHeXQxpGtU=qu`lQPiWFmV\\PNTLV`MVsTtRHkYtRWdv_awuMYVEwYew`hRvIrDHqsdYWXYfiTsivgHux@mMiYttYntny=J_XMwy_iawUyy:>mDooE?pyvbWWyy_nuvmNxw_`_wykxidbnyGxomiyfx]kHwYgqkVdpwuxq[Aqy^ai_v\\Cyrvqh]xy:bYcSg;xqmIgyI:UX?oHiGiXgwxcpyw^IObyvtDpy[q^vxu_oyn_tyAZQIy[XwWInxAbLyiKIydWgeqnAFwOFtyNuGWouaxQyfxhyG>oui\\vo]wGuyovWv`Uyn]I[YFwfniK@kYXpeweiY\\efbRye[xfgys<i]YNsIWtniyDpioV^pYrtohaWqrqbiw`JftfVeMvj:PeRGqYo_SNdYYccnkaakDOrThgWGn;fjchbV?ZyFwgpsiiqRIuwa]VOndpns@mH`]ogv]I`\\Atfi]XxqxXtp?gshcKng\\nfdwsHoiKfajfqOOt]IcNQjAfdGqpjybqHyPwYkYGidyyHoyEtYwYGwIoGyguPMt>yqIXpxIoxisNexLHwYAJoQnRYPUPUEQxYHrl\\JbYTkaYTTMxMoZau]xP=yOpmMvlRNaLndOx`rpPVrDNVIL]ULlIWydPuiviaxUQkn`xMqmbqvJiwayNAxuxlKShRAAPJAqsLmf=ky=JthUqMsaPOiYwX`JlQl^WaNoorVyXoku^ivhy@`okGuuhtAfZeiiLvi`xk_HhdxtWWek@wyGdfn^@iwhHxjofRi`En]@@fyfgJhprIfSItDXkdWgv@jop`Uf_linp?lrF\\QynFpfN`lY_m\\anJ_xRpf>_qownEAf^yxAhkcXohN`=qor_vBHtOfZOHq[Yyuwb_a]Y?ZkOsC@vLHiP`rxGwOvy:^mnGyCh`cWfNnpk>fLxnZPnXQs[_amHsUGbnpxbFyIN`Xx[jhd?>yN?_s>ynAsgAqtw`aNnq@clWeOGyvQ]`isCykVfl`N]`np]?_]@uJ`el?eDvy:VcnxknibUWty_[<qma@y[`mtIjVq^WiiLfmx>qVwnwf^qA`fW\\>IiqQcPqo_Vr=flLFclAZyGtRWdYFyYXitvy:FvSXdKI^v^xj@qYxy:n`iwauPriPmI`mqqacqqiouTIZla]Ne=cUYqBQOhY?WwkHoUHJoWKGEIqfuqs_sHC]sAyV=igAqWk]ULYTVICgeB>mCI[iDEyy;R`atfmchKihMgecb<Eb:>nJ?iiyxuq_g^fQPl^ylroluahBnsBwmjgm[^_kH]N`^cpgrNvBQcJJ_`R:FsZPtI`dIacANcnQieQhKqmU@mn_[lYyKvr]WcNae:@aU`_aOd\\Pj\\?`LhlHAv<Xb_hcn@i?nadfc@nkqGgOy[yWq^ammYuZhu@WeMPbsOtZApdPv]OeTa^kOw<okJNrv_qs`waYuCaaXXb;>tpWqKycnAcgWspIb]gyKa\\V>noaowi_u`kwApYwauge>>fZ@db^\\Wv_tY\\y>tUfdyAZfO[xy\\DVjm_pDv[wntcyglXe^oehVtSgkLV^ENiNGmH^Z[nlLQ[NhpbFy>>jC^^uAZZhv=QtS^x@XhWNy`y`G`ngY]kni@fj:?lUydCFxRYdLVhCf_gfbH?q\\po[yZu@ppHsCV_bn[fn]L_l@nnb`\\Df:@NLdYkPQ[lwAinhHv[TwhijXel`@ulQLHYU@hsL`n:yq<]VqaPduR[pK:Dqg=vuTuQeQ_<SJmxG@pwDXbuYKiOkXvupNJYQspXIeyZmnWmpE=kldWm<LrMyV`L[\\r[\\te`WpEO_TKIEOTEsFtr:=NJK?JZ<db:>NK;Bb`pk@mgUwkYyF`xUtxKTkguNtyXg@LuHrK]KxatuiYMhLAlXl]YyQjRyk\\HOs\\R_HKiMtQ]uvDY:qM<=wfdoVYuXXpSQQif]QhxOqupAndoiN`fqnjiOaM^h\\_]Uncuviw@pjX\\@NxEig:xl<hl[aZ_VcdNy=?fcF_v?jUVu<?d>`Zp>lN`nj_l;@r<VjAWmO^sthjYyx;GqWAsbyy:VcfwZUOxuojxxefy\\VWxp^trqhUikh`]Q>\\FYe=G`_op]Il]pp:Ig=Oj=Fjcox@Xt:AcHyktX^vh]_NwcnosnechgUgZJawe>a>igqXcPxl[OqQPZlatFgjqXjc?q\\^^O_^=acRhvLQpTG[TGu>>_xAgDvm_H[=PvTYmlhedVtfovnivpXsJpgY?\\phuhi_CWcdVkOfxDGgQYbDPx;OcPfnqw][vraFu;weeihlhqQHvW_]oi]rPamNk\\iwcofPVqXXmVioPnr[>ck`e]Io@F]FPxJ^\\Tamro`TAjvFq\\A\\s_^JV\\QFgSqia?oU_eMagyAZKWng`o@Hy:deibosXRUTDacQ?vlYfZEfVCG>?Y_Oya]CuwCW[rA]hvqhMGVQ]YMUhTWYJGgOqde=DYuhgoDkqX]oHoCx_ABVGcgCIK=sL=TDUbh?YqYtaOWgeb=UB;Evt]WdoWaAWqASG<OtdqjEmHtYMDKMIp`XUvARvmtYALFEYIDnGAL^DOFPqlQj;eXuXyILLG]j]HTGQoY]xWmKSqxiPKtaQtemtUtelk^TrWmseiK[Pwt`Pf]xYLRE<yAmwNuJ;pkrAvqejJ`Nb<XrHkm@TQYKVqlT`xBYTGxpVio\\EUyHNjDPl\\JsptVlnwHWMTWhYU<Mk>@UhAqUiyK\\q`DrD=Q;DKIYJH<O]pVrqpAuQgxMdyWTdxKHwy=J`LmCyOLuWrho\\XRUDWPUWmevQ\\okmPsLTODJeMU>qV^INOXonXOQEXEEtgARJLTSxk[pwshWMyPIiXMYSkis@tupHveptvqKYAyOeus@QCYtJtT\\\\SoMnv<S;iqfHnOhN_xmCaPRuTtytEEJ;]tRXqi`KWqWHyxg]PWAj:qP[yvOUunHWslp>emjLSl]VTeOShKT]KPqyG`xQtMDhv\\URhaQl=ULESYMoIEP>AL@Yy\\YtHXotUwkUTw`sULTiyRnUtlXTgQRnps=ep<YuhpL@`v?iWJPLuDV;\\OS\\KCeWEawAEXADxQ=la<L=]xa=uyOo=xdXcO]hgEy<IGuUiXeFcgvLGVQsvSmyDmU;_ytUeTQduGt]ceYqSN[tg_bLkR<Qui?x;cGheGd_YOCy?iFJSsAabnSvikexAtcgbKSGxwWGqw@SIIoujSB_ExgIT>?EvaHDIi[]HueyKABlYBf[tNoEhKiaUvsuEPgGCaUeEckYsS;Cm_kUHXu<U]DSq@OfHu=`KkXN>IrkUMgMwLAt?PxNDo>=jCpV=XVlxMpXvpenxPvRDKD\\llenMLRUHV^xnFYyL@lKpYZdj@lMpHUext@HpVurlDwEDtXXxc@yH<NauleaRgqvPamxEUiEq=mnE=KwaSsdOHDStupraYIHy]mtu=qqiJLDmiItftPaAq_ULo=yhAn[AMHuomePhQyhaTVUSBdxDMpS]NRDxEHtZMZPPdx@bZy[GqxDv[ywdWV\\KaqiYoP^rHhh^@q?aw^I]@He@^yhotBNtGOsen\\ZWvf>ckA\\vofUQeN`p[^i_P_K?^<FiZHuV>gkQvA_bB_k[nnT@b=gcp>lNHnZ>h:VZBAZv>qZ@jwG\\yvmWGxyexwwiwutgrZUho?FGUfdQesuhHYWpWM[HRMaMgAqHDot`Jjqm>yWE\\Ra]urMjuXMIXN==x^Xj<iMhyMTDyIpSKMuXqxtyTeqWkimslNxyLZ@UuMmQun]YXSitSaX\\hV`UuAgZ^`lAW_=vt<Ot;Fva>lvQiGGq`_nSQqh?b<ahpqu^AqSqsgXfRotMG[qVhh_bEaeSP_hfBIUI[WpmekmXRYUHOh:uTB;tw[tKuepKuq]TiGUpUtwSUHIEJuG=?XfQbYkcvSs_KhP=iSMFy]VVGGoGgeSsH;yb;xNObA=sOoeJ;FNmTrODsgSX]g;eYauF`MEUUUkstrUdmmHjUWUEuf=Gq]XGmwF]V@MRW]XBeWeYswKS?ib>EW;_rMIc`Srf;Db?fi_fGMu_=UYyRwqSxMcW]vUOUwGsmEuistRESQ]XeadE]vbSxO_uY]SCeVeOcDeyXgTJsb@SRZYWyucGGbesVHWCqIItGw?UunQgQuvLcTLUFP?IbqdNSXCMwGcsHmhlytKwrGWvM]uOOCC_YXYr==Tq?DouSNMY<;W`gVdySBQyjkwD]uO?cNgBAommtw@ak\\YQCQtDXnnPsuhyDxVrDYKHr:lpKqpwPqUQyyguNXepGj[IdTirkh]y>q]g_mPk=?cn`cpW]HIa`>_Gvy:fqWQeAQhPxud_lZH[^NkGNmJA_bNyAxy:>ZiwmRQxyPqOGcawvcXx>PaI@miPsxo[@W\\xAfy_syAZvyoKyKyI:gh`uUX[ES?uH]YMMyaSrCCsnQX;KXcKWysFDEdx_shYfxOeCySVidy[vAIUGQhW?tuCgpGuaQWO]DxIYwgUQswfKygkwdQYNCdykRyeRlobX]sQIT[msb[HYicVUgjiWDWBxuiqQCEEhWOsMYeIIg<EUjIX^ssVgi\\OvEoiQmHvIExUuRYI`yfogrcYDtqW:iRFsyWaguOfSwSFOsKAwroiN[weSyLyHviidwDpuy:aemyVmOrqIsy;BmgHiOGy_GgoipAx_YbdGTemVVstTGxh?TVYW>_gacy@ceQcRHgyZ=Hrqy=erR_W_EtPEB]kuMGY_WupaXOucccxSGxISsESt>aePYrSKYLqVU?fWmU>sfyIid]isCxkQtD]yqUfrAtWIH;IcZkHMiUJiDIEB:aVj_TJQwXADeQWggWw]tMWirMF]iySgXskYysxoSgUod@qS>iuKeskEw`]FHYI`eYXmiVyfZcCUqixsTTyTuGSksYJOfqWyYIdQqY?wUPau@isnorYiwMGI[YIwAwYEgwwfyUximI[OGsqw:cYWyxgoyJmWxWdx_tmkxy;Rsad=cINuhWYVUaCOewOOSosY]qvViUM=ShIdfGwJuV\\qVGegg_iBEBvqEQ[EBEgAIt^EYu;YAifTgWygTrIwfEd`au\\]vaCuVSvx_GogyCcUnUiXuVKietGXUex]SevsVXWXH=cNYtR;tdSyMuVWWcEAUG_eUicdgRG_ujuwAuC>GheEyf?SDCHy?dlqy^QyPyDP;IvwSkOrvuc[EyGquRKgdwfaygsIFfge`uhOqw;CgbWWfKyy;BCeWoax:ci\\xspUldqYwipUyWyTRdqQ?uuAjsuZgYtkaji`xW`h\\Yy[ou@X^cPxJgcuX^:QmEH\\:qkLvl\\HcugrA_asqmQQuQ?ps?_u_irqvuiZxOmpQsgybTOgIyuKfYeHyGWTQybiugqehOgBuSvasaSVFIHLUEnKeOwHGAvVkbw]gTCrTCCmygLiv>obRAtLGSrCSG]se=bi[XX[edQDQIcp=TNgYCCtQUiEAvOUGoKit]wKcrNytICeSIsFSYsUsYCuWuc?IVKWwb]DQaTGqXkwSpChkAspWH>YgAIxemSQ?i?Qs]qTaiVVkWlOEEkB];SdYEI?iZ[B[=fsMTNAblowXiFDeGKiHQ?iBacI]ToGXpeWQQYnET>mV`CXXYxKad`iXhUy<mh?MvRmiwIYwOjNTPhhxlHRrMSiQXT`SciMgpP?\\l=PUJPrNhNYdTBPrPLnLLleYXoHYspxcxNUyOOqXyex`AmeLQ\\DMDalBuLRdWViolUmwyJUYSFpqDQrJLVNDQDPsADL><L;mm@UnFyvMQt>Pu@qLduqLeoXTtWhP]qlkMoTEohMYPDueYP[DNlmUlUuFIRQHnn<j=Lk;IlVEvvpl]QJhLJ;qPfas?IqSDWDxxcOv]NowHw^_hqasfx[coxsApeQiaIe[WfK>hFqvFohIYyGqvNWpDNdMIs[ypvvbTw^HP\\^p`CfxMicwFiShnqIdAgx=GgWuwmw[Yyi;E`wrdotEUwI[vPSS^SYhcW;KdJyv[ee\\ohPcEhcVZoXAUy=AGl?r[_DJOwwKc`QC`YdUKgeKF_?gN_FZcTg;B:Ci^QE;WvSoUiGUPIbPWfg[eGuXgIsnqUZMeUws?EuhEXWWBk[Ip]uoWyO;CgmUYuRgosuUWlQR>=XLEIkAfWshXQSPevDyViqg\\qDIci\\cwpwRnwH[iUiCCkqHDewrOCkUiGCId_vJ]rsCXSsbvMtCew:wvMgGb]gmWyNwTwUEDwX\\iBt]GhwioYuIqoQeuIqsuekqhsp<jvuROLJqmpxekf@YTyY:pTyAo=UpLUo_mTXYqOPu]IrPPJQ`sPqnlXWFHlAQonLnuLsZHXxaWIxWOhuypsLiLFLYQIs:XjfMoEen<DZ:?nJ?ilY[wylOFpFIslXcf@gPVunwd_^eafSUsFmb[_hOiGQoD\\KbJ_d<OV\\;B:MDbEyT_x;ciZesIKgEIgqgymgGYgXQifJSensx[yI:aECUScGidAtZuYxQSlOSFqG^QRFKxr;f?[GO;DJOen=FJ;WuiebyFt[vpiFu?vkqibKSH=ttmdxqtWmrx;eiwewoG<=HJ;GNKcHyDwGsY;gGQgykX?siEeb;IITcb@AEwsgHGgQgSu;gOwvaouG]fCWsMOgOIYCIe>krVIVbAUjEEf;HBWvnUCkUw;qXxGSQYtAcF;IrFIyp;Db[LDdZ<VjaouExlNWep@sqws=ngtIjMplnvsRwnmNgsHp_vuBYeiP_oA^Gyca^jO^_`XaAXsNPaOX_vQtro[i@oNN;@bZDD:;ON:<dbZ>FgMq]VpdWg`dijcheF?eOIilwvdo`CVZSViJfe_@[`O[]>[:paSHZ<ynDnqDhaLGjAIimaaJ_dtNmnwvLqi`XybWlZP]KHiKHfrhrsH`o_rmV_eGZmGheYmdfvLFmWFshiv_>cLWa:PdP_i<QjNWZi>gpH^X@fTvcIHftvmcxbl>Sgc[=Sq_WcoDkESQuVU=cCODpWBHqRVsU;KS;[BOcDJKTB;cBGUroYIEU@grr_YIiHUQUYmfowhVsXuUtD[dbAe?KvWQSIuioqHuCTc;H^_B[Oty;B_yI:CsdefA=bPcvJ?CWsYtYfcqs=iF`OyHoW^_fTwCdOYK=x>eu;ctfIDNqW]mHTyr^=U<SE;ID]mxC]G_YrO[f<cf>;F^YfYafIwvrorgcWEubnsUpIGaaWSqrbAXEicSAiioTV]EcmWCifJgDI[hbEvdEv=[CYwilObgECnAgDyGq]IyYsWuxLesXoDWqv=owfiSA_H]EWFAGkeFrKcdqsWmDEYf@Oi[ch@[tLuV\\Eyi]cpODTgC<cVcMB<?DJ;BV;bA;DN;U]=FU_uo[GyASI?XuoS]ASCWTWQwGsXrmh>UUdSVRmgV]u<cDN_RgiYcwgm?RlEBQwIT;wloY\\IGhgDe;y_UVFcHYWUCGYj[vPyrgwXUaTpWrFWsDKXEkgn_HYOFOeV>yq`TjXaWnykP]YqAjSlPG@QeIlglTw@KQhLBAKMyWZ@RMlpghp>qXdTKqtvMTvnxRtEn;lQ=`y]XJVEsCXtphUsfw^@gxGaqhc=^rSFp\\?eghqj^wpqtN`dLomDolohoVGoAq\\oH_eOeCP_L_tIGmZXkuaobixv_tgatHqup`sqYpThwmIdlVce?`mFuRhphha@yuM``=qiUn[Cij[FcfoqTYaL_]vFy^Ni[`efpjH?uQvcFVh^_c_GmxhcfHqpFodoi[hsIX_Jg`yN`ToiWhhkVugvrHXubgx]fb_O_JggNPhM^uv?sCF[DnkyAZt`icy^JggpVp\\GeXIdJPfSp\\_^i?ww=vsjIucXkswrh>cCG[xW`?a^>pmAOiwVkCvcjhndFZ:@hhFkSomg_orneehxNNwQnmhq^p^mWgbQI[=ywPA]PWkvVgD@bBvl_>kvHmHpp<_d<hp:v[Zfj?>_JnmaaskGb;Pyi_GixniwT[cGEhScXTmrN[rEixTkFiOdgGgBgxSWdXmtKGV_SG:?vuYUIwHYaEjIi\\GrlgWHQUpWxUUWXEwg]Dcyt_SghawHks^urxOuRQvN_vPMe;OCLoDictcAxssG[avmGi\\QrRMw?UTpqdvefcmhy=Rhss\\MTWYRL_W@iCUIcGIXeSYmcTSMDSaSCIwBsgJubLqhLIT`sBV=TsOcNKDLQf;mcVQU<EF]XMEytSIKotpPTXw<T=AorHQ[]jvDW^Eo;Ap[mWQuV^\\nelKIaMJYWmYKbYsiLUSllpALgyTfplkHwHekDEqx\\XgpPpLuZLsxusStxNXVK=vVqm_AuClwTMsN\\jlQjhXvXqO_=omtkEqmO<YIPSeqQ^@VtXsdxlFTjRpSm`L^=PZ\\vKPR`QUXIpJYSbLXYEylXYv]pe@Q[\\jJlouIQ^yjeDOQhSSYulil`HUxIJs`QEDSoukCMPStPfunpxrg`WG]T_ES^Up_tn]\\Q<emDUUDyRS\\MjIR_MOL=sB]w<EuwUp\\qTEmtMAl`twneKiivUhLOAL>EXpLRUMSV]Yn`lZtutEJQ=V^xnulKIsjqbEkXsYwSmciegsgVqGT^weQ_gtSHu?IMiUuMg]UcMMTUCG@MWBOUv_taYba_i>YtIoFDWSy=YUQF;whYixvUGeOyMMrfII@Cy\\CU\\wr=KFdWVEssfESDEYIQXTchgOyKAcoSUXOv<IccWVj]gQqv`HRUmywtmGUS`YmWQrmEl_uTrDW\\isdUvkdxt`VA@TOXO?pXriwsEoAqJApn<hYWqtQ]XqIYtHJMhW]pukyq<AMxdTiEPhakZ`jtPSsLKhURe@NruwnLvLUveAvNdOCtQ_]j_DQnqLPeyFarRYuXivtXQeqrZ@WFDWFxxcaObAP]Hsr\\r[avr\\tstpPIRKhNhXlTuo^dlt]NN\\la@JRmqK`J\\MygyjTaPyYJjhrnDUfpXPiOpUYVqL<HMChLNpJTEWCpm>eNCLs:uXDPKgPj<pSVql<DwpAWnTt`XuXiP]AsuPVshx[TugqwXiPNtLS<XuQt^HY[DWZdOelMcMtLIN`eJ>xkO<Ti@ui=Y]Uyamst@reiLYARUMjbTTAHm@`uQOdXH\\hohhIl]IaVv[J?nqPuUGZ:n[;FZjhcjVtFw]@_h`ir^Pq_okk@gAIhU`bugeHxtRv]H^_@W]EggpFa^nmJ>ls^^Mxr^NlC?n>QmyFpEe^YumktWYxA]LaXsOUSPtqfILHfpbngRi_fg_NhoifZLHwmwqLP[MWuAa]T`[kAbZHx^q\\NxufXdfWkv_p`^boOjZyc_f]bI_aykqpkecD;ieOCv=eVYVLWUT]I]eCKuS?ss;awfuipiueIuA[YDyf`YWJyI:Cx<yhxkuy;rOqIIqwy;r<cYxYXuacyyvy;BSOftUSnaT>OY=ofrmRiiHViBImDyaD?ED\\ac@?HocgLUe=MCkqwtocZEfVeg:sSj_iw[UX_HuuGdmwfoThCdPOFhOgrQI]we>KyXADpQyHuypieDqGG[yNAxnmCyAUkKimoGF;UxyeMssPIG]UBUqfUIf]CeJ[iucTqMf=qSHyI:_rLOfu;Ei_b]YIc]IsagySUXmUxAuScwoUuUeduasUaCOAU@MynygAYh;itx=cSiySUYu]uW]RKsDQkttsYQmhwkywUSECFWaBkgyDmwhgCsUyPkVhCy]mXrUh]qFKsVRKGlcELWfgMdEESw]vpyxmawmWfDgxuoxtqfgGVecSpOvVWVXYXLYhZGWkkxPqcAEiMWw`aIOahasDHQy>urVwsDIVdYGKUfCyhwGUaOukeg>gt?uVyMB`_fuMBZmFNWWEeCs?vxuClyD\\cfA;HgSgXMGLMKshLppoNMWpUwxqJd@ygYXV`xRxs>XXFTyjHPTqS@EwqXwY]PMaUKUXKHM@MvkUVXpqVaXAmnDXTIiRaYsgMYciYmLwhdVa\\ulXKJDvPXmWuQWdk@aP_xk?@q^@paDSwmwp@LYUOJ=KDDTC`N<pPqUyuIOeDTGqTg]RKeM\\yvVPxkuRftsxdk`xm^UTEqrTLqhquSlokIKDDyMySY`omImmavbDwQTnaXJcqqePvtqn@ywhXxVlRl=OqpV[uOIhvnlQ]=s=IrlDn^pX?lxkusAlksAVPQqXduW]tcYwo<W\\@Q\\Xvr]Q]mmF\\XyqNpapTTqqUVKYP=]TH=qtMvmixKXyLmKTqjiaXjEO:yMliWfyNy=uDiOA=vsiWQqyYEWGxJD]wFqWPHXoYNmat=eqNlpGUnUHyNeyDETgLVhUSGUN:`SUip\\aUZaSe`unpsH`lvtTjEovdNDQsL<nLanbtk]DRUpqNqwThmXhrelxxmP`xn^lra`LohqEDunYmXQnxuMKymKAmRTwMdRI=qEew]\\xVEPEqL`hrvTwhxvV=Sk@wlXrh@UgAqTInBaMLyTBivAYseAxLaNsAOZtxsqMLaqBlVoiqxDqXmmcUpaqjc\\K`uvrpX>Mvm\\woMqIULupPoDtOYYv]t>aXDDxm`WHuvXxu=eRsxpy=jMuuOtu@EugTU]uVslUOXwolU[iS?PNUEw>AJEIXShx`Xv_PNn@jXtT:xJY@N:@QhttamUhdwtHWOAxkas>urstrSIKHIYrmyhttw=UguWUeWt@qiPjR@mR\\ra]NFUvStKNxTUyS]hy?hW==XRqVxPrWilTaWpymKhRudPfuXLHwNLsf\\OflPP]nb\\NX@Q^YjAQQtdMqiwhTWnuxnTX\\YNHlnmhRMqQayop`YX@uUippexk@oSLmdHKAuKVmsxMpfuWEhVtxJxdWdLqCyoRYRMDvnHYM`WYLK;mvWmPIEW:iYAtjwPOgET><OcLoAPJM`uhhUsPwpeqAqnMitCxwHHWIDkpYmpxs[punpQ=dTHYVftsCIkkyKmekbmvxPknuriqKitsqQLUqx=qVEyXv`PhLRIHXoat``N_POZqxsaJHtsaHJ^YoshplIjdQv`ymYPPhxUFLxsiqy=JM`kViyPynQpPXxY:`j^tqIqm=TmqEUPuYIPul`YHmxy=jSTUAiX\\hU<MJ]Hro\\QLEjsAM[USd\\xXpWQqlmLuO<SBAtheoHXxTeshUWd]WK]SKaroAKaYPamqX<snUQALvphyP\\YdYoeLtVqkS\\K>ySFtrVUY`iYSivh@OwTpnXRdpW:PRJeyJatFtLRpVOUyGqUQuQXhXlpqPlJWEWxTqh`n_pX<euKiW_y^J>ne?mq`eUYoj^weypQF_>In`Iknocdixp`c_fq_VuiaeUgkaX\\qPq^HugxdGNa>ww[@pv>lUqfNwjEGcCVZlAg[>psGv\\^nUppd`mGA_\\huDIi?GcWVteYn`fkfYnOwgu_nNiiM?soyjTOPMwGUUMWxHeTBcFdgUe]c@EyQIdu;dLcbeeyd]WB=RLIDDSwDmWGGxBcFC?GqaTHwfVgVXWx<GfTWUB_unuIKEXeiylebrqR^WcoQFeCtIorRQBAUsgqBPMcPKdw?fDsCmaC`MF]eskgEwkeu@qdiWQUUtysiUoi<tCxP>ajWIPAhobhqSuu;psZumGhV_hUCLKYMvVEXuIKoat;dVMMYhAO?IXNpqAlJmaR[YuOqSRdQZupm`kwhnUPJeaQV]stdvSlviDlnUyBUVTmVHevcEvFI_Jh\\[Il^ybZ^\\c@b<x[NVkPHoX`dxhsQN_Hhh^v\\Io]MXqoFwS@kyffUqk@fpXowff^epvc_ikO`hwtNn[InjaPjLO]aGqZnjTOcU^ZmOuIgm[geDYwVXstf_Kabl_dtImfq_QNdWooBQuwxwPwf[otEpl;wgWHirXeggcDoiF?ii@iYybAOKKUdMEUkiaseW]ep;GLEghGYqmdE]tkWd?YhLWc_kxYOTQMslcwXAboQbkytTMxVErq?shqEZax==TLSvl=bZoTIWgamb<QS<ITCyd`kScOhsCis\\LjmrLPNjpVPqQreyVTs@UPi=kiur_YuePqbqR]HSxXk>uxSUpCDPy=kpAJs\\w>@qLEmTayE=KKMUVloi<l<`LMdpQ<qcIVdTPBXomPmrHOVLsIaWMeWwUrnuQjDm`LxtujAeTE\\YEYtj<v]mLgaP?dv[urQ@vpYsJLxNtPWex[tP:@SgyS_EsvDy;dJMarlmnSDtGASxIODaSPEKDdj<DZ;_nI_cMNo?XtA_`hhsMYh@Oh?grxxfJhbQId_FrN`nuN]Fa]cNfK>_ZFj_^rf^omovMia^`\\wHbGix<Fj:?ngyH\\HiFu?nw?_sFBmdxqlFhixpIJJ=ONdmiLYMxAQgykX?tlDvVcBAWTwSVqewpqUaMTwQuQGEqafCCBa_WKaGA[YjKRKOg>ww\\[BC[r=qVMEsS[V<_DoKDA]YJmBTcb<JJgi\\NsxW]bilOfvpXwdO[gorPQd^@_XFb>ViBnang]o`hHhufgsfax[QtgFsXqogNcvxejpxT>sW@g:f[HI`NGea_pcfev`qDit;aajAnr_]kuBKG?O:<db^<JJ??ZZDD:;obHyXlMZQQILLVdk;MrfxXPiOQmNhqPpuoppR_LnnpRCdOBewhdN;qkZLlLAV[IsaASDPK?QJ;Bb\\<JJ??ZZDD:;ONj;@sq=TspMH=wVtKwQj;Jb\\lNXWHHoFlUXMLimXBTPVLSuAt^=ObEXCusv<xDHjlYxfHOsduVHOVXndhtttVo\\rIEmherkTk]PSMpvAAV=ExCewMEl[INo<Ou=Y_<NLHQuEOOuxetKTmVDewUMNm]S>YyX@WLUvFqKC@T^InP]MI=okiP?dn=muBLxo`k>OdHq^d^k=yxAOt=dAcTTMeN?IlATZQcNcrPkDIKcAOrMwbjYR^cB`kftmy>aRncIsqEtoINwECMX]UR[OX`=S=cCpEiUkCfcFcqUlwclqY>aCHIVlkfcasEuHYuEDyCDmUcUWM=CoevBWFwEfVatmawaeuHSfk[eyecCacmkwl_C>eGg;WA?dOMRJ;C>KrxsC\\ycteswaB>my>aBHor^mrssTSmF<odp[d==wDCBb[F<CRYwFKyRwobR?E<kV`AHxcHdYghAI=MTUQUS=tE=s<CBb:xMRIwClrBAmS\\rx`MIdYveisn=IBBqY=AR^YAcZAnsNon[vbVGqIG^pPm;Weh@qj`l[@^l_dCOx:v[x>grFkdymuXk@Iyt@jdql`qgm_mtg_uY_Jhu;p[Nxm<ftVfyXV\\]wpEQsufcmwrvnMIcaKtKoX;?jZdwqQnY@wJXuQ`w<xruMNbDq;UwSMYUuhpIrvgygaH@RZ<dnwqbuy;BJUuOuIf\\Yhdl@tVbIpH=xmXkP<MgUPNephTsOxN`YVttxuIQ>ivlANAdM\\YjHenddwZ<XD=Rv<lrmXTlkLplo@qlXVELoLuKdDtvLlw]xYLS?P:;Db\\\\WFctO]tYmvApcYfw?rX?qFiiFybOogK?tVykpVnmP^nFccfgixaGywkgtK@roql]pxJigdHj:?NN;Bb\\<JJ??ZZDD:;ON:<db:>NK;Bb\\<RJSDmEIQ;griVDghSOXc]wUuElMwLuEsog_cHN?bYyHPYrEggf?WDofrOStcvWGedUUOcSwCHfwhj_esaWAyshsXEoxdiVs[y^oSDUtkYcZGGqGeP;yksdkoRVsUE=eFctuqUSKS>shE[C_EWE;bGqTgPNy\\sGMqb]MIMoaUqmHKYlwkxstUNOxxnTyOtWGQvcXKOttSlKouRy]KGEtMltsasa]ljmscAk^QPgPqKTOa]Yl@p?ivQeVDmuj]xaExaTmJqpo<k\\pRQPur\\NpaL_pv\\qOI=mXhVr\\YO`L:LlatoIqnGLoeHVFdssPviaXV@y[uYIuXnUxNUnKYoWLwgIXHAykYRwqqILJ`PocixuYXHeyS=xYYM@qSb`Ui=MXhN;`VShqddumAqWyY:\\LLEPoIOq`TMmpcukjhjv\\Lc`s^DS=]qN\\LcPSg=sxtP@hkqlXdAWshuBIkRLKrAYvpVdLVsyxlImrqohyY:`POiUUpxdLO\\pVhloX@QDPoRxvWmS[`RRiRIIUupwPdkTYQ_uP_pS=ExfWllxmJfouhn<Y]@IvO>l^h^f^pUak[veA?c;flvFn<IbD_buhptneMofc^kOgervn<ImHH]Y`g>ixiQrWnkwpedonvitsnnWIeeHa\\QoaNk]Nr\\NfsvbFgoW_i?xoSqgjQv]ohFwY[TEkS^owrgwskfkuFQke[CCdiugIEhstLCtwkY^;kWqWhyVr\\jcdpuPs`HtOQnqpPGeTMasQQkaumVaRKallys>`s]yqftvDPqrytWiu\\MkeqOUHY\\dQXItCXKMtTv@Y?IpXpWfivRppSPLdiL=MWrmtKQoBTqEAsQQklhW^ySBDtoxtLYjWqUSEKxHn]Iu:avYXWgpW[iRTtxE`lSuRHDy]yny=j@uucIqbTodepWaYG]yk`moysQTKN`xZqtvusNQXGIrjtUl`y<DwdUjPTsjiPednwEsLTnBaLCtqFakqTsFxpXYuFDNhtRcinrpWQLuD=KIUj_eQcaocioTQoR@Kdpvb\\M\\MN\\IpClra]OIIoSdsKEkdUyy`oyHOwPyTpvcln\\HKH`oFmvmerS\\R@UvK@MH`THMVtpqtE]i@wYia_pdvVkgnbaN<YVJudeAc<si?CYT[tUWfM]eqqRrEx;?upIhXcFY?cNarp?iaSIEadbufcWGDIw]ebmIExaw>CtNYFWexlyweaUEUdXyI:qiTkfbOErMfb]sAAX\\Qv^gTXkUkssxuW`IYXYye]ch=EHWsA]eOauXGXViXwGr:mRcwyjwx_=yPQdFcb<sfJgbcqDOCGkUuLABmmCpKt<esQMugUtpewkSROiD=[IkcY`SXXGUVmvwEuUquhut`grsWFTAg]kcdWVfWtCyw>Kf`]w>Ii]iyhIWqGWt;UpWD`mtUgTt]WCGtj=UbkywKcd?eJcR>SYVeWcOcJwin_F^=dI=HuSwGOVtmghwddmV\\MfdoEWiyFkHTWgqUhRofb?eRkvtihqQxu]wrgwP]I?wVJuBlsS>uiReWmswvGV?MyxOUhkhgeIxgRx_cvSItmg[CT\\McikiaqCYwhCMSfmIK?fNGG_oXjgI>IIB[YKSuwoUdYWQoVVMfcWVayc[asnqxlsxnSEOetU=tjgtVerOiXHwiH]womX\\iYfWGn]U]WtjiuPgVyocSkdqqS^sxfQF[QVUQXkgboCuG_fFkf][KL@lL]m[EWHtx=XS[drVEObtsgisDqvTpWYmRrpVdPVVmvk\\MjmsmYvC@KIxVxPugqnXQoHEWlmndAVdpWHyN`dY^@x]ulf`rFUyvAptyWEUtoTwGxTGqoAaXYUpter]QMcMyUeK\\PSyDKGuLuTXy]RE]wlxvL]L\\Eqj<YhpLUMSvxrNyOBqkPYtaHtWMtXQOfqvbPX_]MoXxF]s]uMI@qFaS\\YQSywTdmoempqMEdtjUTx`yaQkBlR\\xND<yrEQHUnSTovPlD]pHHnDxpytkqlLgUpwlrYMYrMWxQQmukhtT;Px^HNo`l?hO`<tDdMTYtDMj:`vKdrXUUhhsgPROIXHXTYAQI`YIAo@TpsupQppe\\THIYMeQ]XphqKsEYpxTL\\VsqrQdU`aUlYkOpvHmRYYxGpJYuWHdolmOP]xwTRI@qoPYHAJidLB`XOtLTiWqHK_]vFtPthoUaT>]R>iT=ULNurBYoyXSuHPWIqHlVuhrEulneTGeTGaTkiT=YPPIWIIOYpmrIki]KIYygep[IOQeRaEy@=O_yxcqku@oq<QPUsgmTm`WkpJSmmmiO?]K_hoZdOD\\W?@YeTOe\\jjmo:xoTxY:HucUmnIU`XnNmN`YvxHoBlswiYJewkIoePTQQyctmXAqB@M>eRk`T>YVNxVQtyv@yh\\UotxMIOsMy_dRLQna<xy=jJ]UkLr<tYZXYr=u:Hq;yxMxrmPsetTNLYDDpvHY_qWQyLguLm`MsXVhIUtekaYqUuxKlOQHqpEkkTVVQPUXQJ`VwdMCaRNpN=IJoHOoHl<=RTaTLtRv`lKdWOTWQeUo@wn`x>YXDPwIYpQEOIUR?aXhQmtlNkTLOAqpQyNtRilm`UjSqwpiY>Yw?lswMNFAYQak`pS^EMitRLET_Hkj<RgMSg]rj=pPdl^HLIeJ^NkdWw`hoPnmRpmkgcSoxtgxTN]evnjgtOI`BPmcxrq`t`HarWxu_`O_ucPigaoGnegqkmvgiW^oX[]NwphnKH^]pf@`eJ_hZF]VNaVwclOkDPcuGZ;F^]f[IOnwQlAa[mirSwvyAZnVvQxhinwIybqvih_tkybhN_kWsSfxcvsvVhaYsyXru`[u>leqbuw[chmMhcgFaO_vSwmo?uQVsfFoIo_jnkeP^`A`eIdKy];igoHcCwcLamn_qq@d]I_XN]Bv\\gIwgocAidTIoFhxChvVHx\\Yfs^slqyR`k>OftgpQg`QXvn`hSonc`r`q^sVvV^]KG`R^rt_urpnronmG\\DI]=FiKixHwxynZ<axua_Daojp_MyoC>saOfD?x^qZTQpGQirv?gXPyRLADA]bpcDbcfvqe\\UTUgGWcxN_uh]GMSXKkcrMimOgRmuSyFEqYhYgUchtWWOOUoMgd?SdQg\\MUskc\\OC`IYqQyRyXlmtgGePUXWmxLor\\?bm?YgObMefcCImERjKSNugDkXAUb?etkMex=TuSII]EueC;oxnadhoUHyVq]yrycv]yRycVOuUQuDmhbcyKYiSwXVYft=im]sssxbSuGisgIi`YUWowRoxgafsgg_WIU?WCIIDQvjMVX[tbWwNUCI;W_KXU_b?YYIKxKCVr]E_Wfo;v>WigGUkoiRQWVEtNsbrsssaRF_XHAEcWxRyfXUb]syQaXocCqOghaE@ovbGH`mF\\wvf]RHWI]WTTWyRUiBcX=;PwDSm\\WqpNDiNyiN\\ePoHPfUSlQrL]U^pRpLoNtk>lpR`K?`qfAvA@tl`V?tjJIN>aXkUWMUV=qRCQWtXnQ]M`EyoesSakomMVIQFLVsXvf@OcexTPYuTrpeTOQyKlmVMy\\mkSlRk`m`]OHUxNmva<yL=TuUo<MWDe:AV=ee>ex=_yD[WiGUoCfQutgqCR_xtSIlaWpAEkstWaX:YY<=EIwBL[EcmiZtYdlKT<ONL;IrTuG?yI:Cd[sxiCe?ySq]RJOx=otm_xpkwmqX;ayweGnGd<Eb:=VJ_xy;RbaSy=Rgydwxtj=QNYmW@nahvRlnshm\\uXfTokPp@IQTuOJpM=hxpdS^AqFAQIAnpTWHaNsEODPrNLlI\\PL<OkhrqtNaxSehRthq`xukdMZlWvltJTsGdkphpX\\R^@jKDs]YL:=js=twuyQpO;uyKeyZ<YeYWyQj;@YwlxEPyIDwATRUyUr]lIhre=pY]Ty=SxPmTyY:@RZlYihu<py]Ly;AxPyTxej=Dxt]wQdxYLtIpjpxQj=oYXKQAvy@ox=LvipoxY:Dj:]yXUq?dyAax=HvgxOvMkAPvo=uiLwy\\NYdKgyY:<VJuqQp?:fZminTh^]PeU>gKxkbqoLXvr^iCNhxGlhn[i>fGxg_wvuPbvgb[`j[N_YOgLWaBx^:xZSIbm?tb^<DZ:?NK;Bb\\<JJ??ZZDD:;ON:<db:>NK;Bb\\<JJ??ZZDD:;ON:<dbB@YbdHJyIOwapouw>LyeIpGUrBMp>hNPIUk]LD<vv<P<DyVLlMyRw]PVxQJ=?Ob=ihXMcyMV=mgYKHEyeh?sZcfAewaEwg]uagw<IyuQEbSF?OZ=pnYQbaX]wPutyhdob;OaXqn[aeoiiyAZZ@cd^ZwFvUAf_`i:FiV>_kqv?b:cqthSthSylWuurldkS`U@hvBHUl\\MD\\WQewRmOSQQXuL``oLipxLWRDXBDTLinn@LidPxas=\\VMHr`xY:lrOxqixT=xTxeNWyqA=NxApgdyx]qTxQkQocmYwXjkejiYwoAvOyY:DKQysk=wY\\KetyYuo@xOvQStxY:tk:]Y[YuteYrepy=J\\itM]YtyJ]QkYyteIretyLpoYXVJuQRptxuQXekYAYO`Xyqm;@y<ypoQYjQwy=j>Yoa@YnyK@ilyx?:=d`oUVYu>yehqGoABKcYnqcjexLOwUosd;e]uigwEcsDOChcUTj_vtWUCIxxcT[;CDcrdKxZIxacSAmFnKSDmRu?iQuC[whFQBXSui?RoGsL=Bo_iacIGEwC]NA=NJUXKXvnqqtTs^Uwo]Qemsnpq\\mN:uOB<qFxVDHjaMJumNXHqZUyw]TOxmgxLQYKhUr:<YcQxsMqAptEYw?tx[<JvaPs`YWYJeivoQruAL:mQT`Uxpw;hxlPY[iYB=VYdKhtUq@rtEUwAxx\\Vjxk@tliXMZdyfqQrtUl=mATrEylG=txlPY]uiDQFXj[inEqVbuMUyOhxlVmj;@xLiVm]xIhoQ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::cux;Db_iqSIv_w<CtduRlERNGgK]U\\KbLOfL[FgcFd_EIIX^wcRAV[UwsUym?cpgCues>UU@STSiwFMrlIiP=fNOBYgtPmUJiFJCcaih@UChYrC[VfGYYcG@OXZ;\\pWqKycnAcgWspIb]gyKa\\V>noaowi_u`kwApYwauge>>fZDDcRAOfXks@mdOchXATTGuIaUgWSCAYF?fuytXAt\\EcLgerYW?_VJABgKfZOCXAIlIWuaIC?sqGwVgwTwFcSy@KBqEf]?cqaEMay]Obt_DbABVWSMGF?_GHCYv=CdMfwmIXIFlaIlWrRYhg=FJ;?OR;VfXPkpyt`ngmVo@I]PXckP_OWlFggmQ`uXoEYgsppWGgl`sxFcCg]YQcwgl^PhI^vDHj_a`W>hJ?_gfwToyeOhYoxxwgqY[Z@tY>ngaycqw^vida[mWyuijAVbvx[j?njga<Ij:yxDvZ=^ub^]I>H::::::::::::::::::::::::::::::::::::::::::::::::::::::::PJ;@rZtvQUtZHW_tnM`TfYYcpxPTVeppfHmp\\otplrHLC]reUKCIK?hP<yJdlMbmjDtk=lQuXvm]mVpJE<WNL[H:FQJKbA:h::CRhKY]aheUIoyGdgRB=w^UwEmg[qHCQbq=WmUu;]w\\CTSEBH]HNsYowciKXtqYXiuhkx^=TpuhdexU_wPkvfoXBec@CcO[BmkDegC>GvPKT<Od>]Fs_B:;R:Si:?vjuhesHfueqUybkspgrbEgJUHaAiNUwFubJ?r_yRkSE[wCZsuhqxQAU\\ycR[V=IR>qDfqhAMGUiXVmeYkXg?Go?CSkVUEIliB;Ag^qHj[ecyHUyfmUekcx[[reewDMDbIH_OR;?JZ<dbNao`xNOad_epickxZoVxNG`QAfaOmJYvQFiK_nZhnRq``Ot[xg[?bua\\n@q^YjpIx[F[]^lJggXFj;wgdwtme^yI:awvyEhud;;VyIrUIyN]uIkH@Iywii<Wr[KE?OR;Bb\\LD:;ON:<db:>NK;Bb\\<JJ??ZZDD:;ON:<db:>NK;Bb\\<JJ??gbS=IgAbLiuM?WXWcqewjgbTei\\EegIWUiydaedMsDMuRaI^=gsqX\\it<?tn?h^CWc;dZEr;wRQ?eXIttIWLuwkOxnshnuhCEYZwXswgyufsMwKauGKTRsd[<O:Dlg`nNtjU=vsAxnPj?`NJ]Rtdj<X:xi>[^khGBjg]uaiGiAPj<HXJes:ltgxsdiQY\\RnUmIqOSlQIiyP@kpUwOmn\\lUkeRDAjrpOJ]ypXTIUOk]U_DK?LSZLJbQqy=jbiNLuJFMy?iwcdsytpVIuyxVsQrSYMbDQdYN>lnNajZ\\j?yKBMKFmtumLJhl`eNglwJPlx`t>`SZfty_nA@tLxcLggvfksholPu[gpg@]oGpfooDvqa^ygpp]hl`H\\SG^b>lSY_ffo=gjqGoo@\\D^\\:hvA`^@ywrijxqgeflSgfUqgPHuhgbsXeaorMw_?iio`\\rXtB@eDNbLAnLOd:?^<h[Anj;@Br@SEwSehQBsqRseH@qTkuhEUcHuHckRYWHIQWIWwrUePGrT]s;uWEggOwVo?HUEWCeh]AD[Gv^wi`[VAITcMcJ?D>[F:sB:IB^crAoX;ERiQwQUhUQdyYXmwYrce@ABwuriuVMCxy;BRAuayHqKcHuBb[DDMSHGYVQVTgV>kEosesWYqwWlYfpCGQYwGIbNEgCScOorNWgh?TJ]T<?D?WG:IslKx>=T=IFcEVn[sy;bweIfyEvuypEIDCcMaxwMHgUvv?eFaYaEwtGYIsvpUguEwd]vfOdIcSCQwh]wE[GrQDeeB;KwcuWDWI:]Fl;glch<Eb:>NKC?O:=tRKiuCIgItQYWPgVICW@syXsXmwclyfkai?kb]OY=_GtOhNIwBKChCV[MSBMUIKhDYta]FbwGDcb<Vj=vwMFohprpFZl?pTy`?@qUnhKv^aNf=otPvfUonxffpPrJxlNoaHXs;ha_`rIVeIpslyvHQjAItXFqwh^qg\\XhrMi[_vupF]lVywFgh_ZENl^YeFwnN>bEgghVfGG^AI[Z^Z^flY>pJWcDfZ<Fj:?NKSEuGReXmsCnUtEywTGTeCYmmTVSfQcXwOXyiUYIg?KVVoTLad]cbgeVE;DCabj=dI=YJWIjaGaqtN[u`wsb;yogeugBM?VowRsGEhcS_EcF?gI_XQMEncb:;fNgR_[EJwcY;e@ORg?RZ<db^<FJ;GcEhm[WpmG]UwHQV_qDaygj?Fqmh_gds=gNkF]?I_GfqqDJiYBObNgb>?G:]dLkwsAVJgDb[DDxkGLRvUSVuNhuTCdOklMuLskyXY=X[dK[XNODODmQ:=JC`Ns=JbDN@xTcmMnqy>Up?IvIqwZ\\uSuKoDP``Vp\\sLuvpdsSPtxlSQHqRLwa]pLLlPelN@x^lMB]PMtp:\\TFtNOAXupv]HWpDuhuq]yXrhsFYpXeOMDL\\`pRUwW<souPJLsPMlvDr@PJk@RZ>dbb<NjAarqh^\\HaXIq_Wqf_rmAymYhFP\\FF[Spfx>khyjg^sGGblO_NipZn`iH\\c^^>Fo>Ghair?frLxfRofYNaOQgDQhehhthdpyiJagkpnFYbHwcM@u_@yffnAwlQ>u?Xoo`aX`tM`w>>tyW`VyvOVtFn]kIoSft[YqowkYfpCGqXqgHfnD_cR_knvnX_h>Pj\\P\\>H_>?ZIwlJ``Xf_ZftGYaQiqi>peqbK`vFquk`kX`tGQs=yh[gp[P\\\\QqXpVMRVMcP=TLIR[;RY?Ql=Tb\\<Fj;o]qGiOYgapv<YpuofUpweQhP_sdvxrgpEflpxupVuofxy>\\tpp=@nAIf>IjXQuMIrZNyaPs=X\\w_fhFkYxogXjyAZApwYI_;W_pgyrh_Yfup>lSi`iAbmAgsq][FljXvPYeVqdWggs@c=Wo__f_^t[Fg[qrPymSW^Ga`Qb:=nktpMDQwHLTqxRxqfXq?xS]Uvr\\rSEt[ASuTs[utJxJ^aQPDMAUWBQUsXTELssYv;N`Afm?VxIylnN[?fZGpnUYlKi]Y_tfyv@_hayaG`hCaxPahBGi?inPh]DgwIOs^oq<q\\_@n_ffgOjZ@dNwZX^fYN_Env;@bZ<DZ:?nAYm^PuX@jiYb@o_TYZshcovp_?]?Iv?H^bYhShZk_ucNdMG^AxasvjKauDg];O[CoaA_sJYhigtyGt<guxOt``eoYh^?krPw`im_fvt`_KXfqavPphrOdrHh>`^C>oBGZxV^=^qmIs_?^MFbc`sMH]BA`eavfXffFpGqpV?vxnnaWuhH`PVrkimCGvBGho@j^@_YB<CBNkETqSQKycoICgSsqIB]gyKi\\WBNogowe_uhkwEpYsauge?vE[HMWGauD<oI[eUEswKuVcodOwYFGVEKcVWTbGUfwV[QEvMfwIXCErVerksSCcFdquHcF^mEbMyhCwaETUSGwYvnMg_uhD_cFSdrsij]R_OU?GiFabE?uN=X>khJmU>AU;WruMRCCdaObo_G_gI[CHb\\\\TNueIabQvgwocPtaWgXwlGikaPaFqnuilMxrDhd@ny^hncVbqo\\MovBOcu^b@@yk_atIrJAlJ`]RygYhnPOytYh_Y_jpg]HbhqprO[rOn@fd;Vnlvsvfi?HoGPhYa^s?ye_wjWZ`Ij;g]BQv;@BoGwydJey^]U`sQO<wx<MYQxvQlZqQRmXVQyRaVclksIyehPjTYLqQOmMLxJS<NJuwY\\niMnCLLaHNqXWQdTc@pTEjYLP>eo^LPVYShDSQaJ;HxNPS<@tNpmMAvjhNqUyNLV:EOJyWqam@]WRhY<llcLKSMVUewpAuGhRqTUZuRE]O?Ivn\\jpTtg=n>DNC<SCDK:<J:Pj=Tu:=NJYuTipvqt^yqfayYmWQHRZtq;YusaTVySpmjshywsJcg<Eb;ybteRy=RWAhw=d^yI:Qr^=tdwf\\urQoUGUunEgo]FTGXsis<GVPayXeb`qtOqYUIh>mVBgIAedjaD\\QRVkw\\OT\\UETsS[ybBKcEWF_iV=iSqITQudRyhI;HWmGmauUIgLkxkYYHCCUUuluth]CleTDiGMKWeUCc?BcGfogBJIbv=uTsbiqcZeUwSsqWuJ_GmIb>IHwqeLGTYQg@AW_iC]MeUgRh?xFacUQRUQDQMfEqm>qKTYsH\\okiV:MOAuXrAkEuMiyrftYHAYPhO:ex\\TRntrrHtsxLBplvQxc]nGaU]`uj\\JDEyFlnlEte`lEqKA\\MD]LLHqvYTDEr`TjZQuoPOPdo]HtFu\\VYvy>hpXfr^sUau@hoZ@a^qj]vbVgj_vokPcL?d<oi<AcZhtxQkoG\\eiqshco@bdi]qhgrVuhwg>`uRv`N>g@Hal?qCIsKAZrnpEqZLo\\TOyb_w^npL?aQG_fqwCog=@gGQwVV]hwlGHdIi_IYfKWfRiZPixP^weIfEYdcWf@IiIF_DNduNm;Fb?O_cfvANjAgm@^qnxtqgimwxqAkuVqGXkcqm@@vTxbkOdWYtfXiPgjCYyhydCvnPFlkft@I_hO\\^nhxgcd>Z_X_AflH^]JOcXPmu?wuoiUpiQhm_QudoxIfm\\Ia>_wQOdjIgl^i_?ui@lPQ\\uIZHyZBHuD?l\\y\\AaZinkIGgn>]uWhuFmdIueXm;AsptnYxUkiYyr];igkxF_SA=eoQXUCxpYcEMXUOEMqtP]c^yFcCB?gYe[XcgUdOC;ASoQs=YwMUCwYyIAcqwDbcYsOY>KVtOYgQR=AXBEQpXu_LP^Um_QuNaYOtr[lv^@OsHmnaoqPWXDQCyN:LjNApmextLwM`qGTqhuv?mx?QPGqM=MxfTOVeoQDnf]Q`ySD]RUaKRPsFTpkDxVPX^qv]moDaTREJDMTUEjXaTb`nPds]tWlpnEtPQlYq\\Q<lvviTPMtVhl`HP_ePgMYJXxBlwpMS_HVOyNGYRBmk:YVJDSBDviuUIttx=nSmxsElnqQ;]P]qLL]WEPorTvpaOAqtWumg`y\\UVCHvqtlK>yFfbHfZ[p_X@vixgkG^C?bDo[TXm_`uxNwnp]xGbthwlhenVpJG`VpnpgaKHu^`bw?`afqOfiypcqPajivrqklWiQOsAH_JO[JGv>g`?IpFyy:No_vvsWyMAtxpmtGh`ptBighQhmAiCi`Egd^_cp_[a_]<O]hguT^]>gjvHyFf\\ghfW?o=Gk^QZ^PxMVf`p]typGgotHteXy`vuhGm\\opgFeKyhgWgrhejIgiGad?sgXtUihBYtSXbvHoH`vpH[gWcdfxvQt<P[bo^WOZ;@BexmetXEmsYwiYtxEuqyPklomTNmpkAQLD]u<yRJ=tvQTZHRm]lLxOctSHiqftWQ=wSqMNLwhLl]eOFmSwlP@iPKDP_evL`WQ\\JlptFmNWLs<It<AtH`x^@JnPjM\\Vb]OyyRm\\xspyhMyBEwpPodaLQmvYMvUaNRmWQDmHxXsXQjaYaLvpPyCUXeTTgmPNuS_PShItp=TUQyUiqxMnUH^vvtcgM[SmgsgqHwOvP[RgqSOeGQQhYyHxedssCOoHRGx[?HqeEgcv_sDCCV?gE^?v;kUQqe:yhOOiFuslEUauchOVtwUEWfTgYFSVf_Fp_C=orNQhfGeWECikDQkHdyevSVeiwh[dgcVLCi^?bJsejQioUhvGi`EBoAHLgy\\yfrgG[;e@UX\\up?MPnINkipfLM;XsePj[mWg<YhdRJMTI<wQIK^uSV<txYpG\\x`MltDo[eMu`PUh\\rPbegcaqvThotomUiveabyF\\kfwFyrfAdAOkmavOxh=Xrv?\\s^`Xni_XalatgqoDYtgqqgWgBG^aOuUaoQGkP_w=f]txsNWivo`]W`]actxckcfAuK=dLcF_gYdsE^aFlcC@?cWeiXeGwmIosgB]YoaR@]HaqGLlTKUkU@qaMqBYM>DQRhX@QuN\\UamNmXpJ\\WQimjATatJbuRqen:qX[HvYPyOqYChK@qYByoYLqhPjuIWwIOBduy\\PDaua@LUGtVighOq\\QrL_jE`dl_dCox:^asAn?Pu]oqHVpwNcgIy@>vthg[QqSVjbixtXyjgp[ydGFeOOrgWsmNy]Vs_WdL>mvo^]N[UgfcNcA@h_ybO@ZG^ZOHwmwqFynvOisOmRix]Pc]?ftgo_Han`mEWdk>[QGbl^ac_s:`nBokaipKouCg^>Vx`ij:hn>xxJ>rTwvNYsbpl__taYdtYefWk;_ppicaQ]@aoqXm`Gn`Qt`nnWYf?P^engFOil?]d^dA`AkhUqSECrVQYdCE[ov<aYSqFuwhkuCiIgx_UwesnsbCyXasTVmR@gcaOe;svlsUP_EpScIqB^?HPaVxGTC_C?eVDsRxCWDuTdubdkDOoUdeY?shUOXwYwUoWDgWuORfIuguEUMhegHGqteacQSVP[FmGUOmBjaISGVPWRIwxxOvJuFeggfDYN<MEpOdIlPUXgYuqXPfUwS]Xu\\RoujslTFmv?UR@uWr`vUhlxDsaelKlWauPnMputmkmj\\XO@MOgEoLMKUMrDYkd@X==pfUPtYuy=J>yXuyQatJLUmHPMWMxepOUTorHRmeYclWUAL^MRdMt\\uQPTsL\\tPuj=LK_TOVLJL`YI<Xc`kOaTU`YG]Wm@R[yvrpYTPSHUpvUpbXjD^gP^[ZXsQXu^irN>p;Ah=HvpPZPgpixk^VnIP^Z@g\\nidpGWgo=HVgwgaUiuGG[H]QYLUwm_gwAwRoXOkYMQfsMsUees_HsGx_;SdmWdWV_QWi;cA;i]meLmUV=cHeupudp=hWMF`WyWUdyAFXWUlIw?SrbyrEScdcCwewU_uPuRkCb>oxx]TlMt;egQGdZ=BtwBwouy;rUQIUkeq_iGmWboW=?vraUVgfcqXvsTwQy\\iII?hL]rlWiK[IaUBjOvtKwP]EyIe<cV[ESkKWC;DZkVQWsGSxs]T]efRqGdyvcQDkWyOIuc=TiAisydn]b=cUHWUkuUEmGjYIUUgbCg^=RrsdAkEsCF?kXoaIdaea]fSGi@KHfubDWUm?sqSvGKwUCthWdF?Cp]f=ktfqG<]rj_Fa;DTKxLwfbMtOIu_cr@YEb[DDdkhMYHQme@ophqT<VU`TMYy\\eWhlWADuf<mOPvfyjNEu\\uU_LwUAS_ANbhn<MuJlo;hfc?vqIh;o`ki]]hwyxZUYkUgbAahp?rPYmqHfpvfkf\\UWeNGaJVswWk=?o]vjNFpCQdOQsNPnNGcx^hPvZGo_X@ey_cgHZQppGi`OamQp^@yaNXphopbFm[^fxaZdOc<htHFagG[x>[YOhwQh_xhrXpIio?qZZnuphyqhmxou^peThym^peiZY@oj>pPQpfxy:VaNIiIqiBfrgnwBi[lFtIX]lQp^VqsIrZFy_>gw^nL^nAvjfWemyu@hkiWiUFwgitYVZMinXgpPVrjOqcoh`HwvGqGVein_<GZCq`aQnEiv@ye=OgdN[^i^:_^:NcsHZJPa@ihC^tHPmuYh>ihAacnNnhVgpvxdptVofX_adaeiFsEx_Aq_`>_<WtxIyx>\\EgiVynspiZ?t@guIygIpo`QrnQo@_yqHa\\P]GvhLYmf?uhqfTFfBhuaJN@mWMq==ScmKwiQXAmNTWdUUcyu@dJ_Lsjqxa<Pq]NphobPmEukcqt=pUqUjpdUpht`xrBPSBqUCHMZ\\VuhmBPOL@t>XX;AX[\\n;xsnLKGXvbuNKqmuXuNTUNqk[TupYtGpp`=yGIR=Dx@=k]ule`kVdMJXJE`WjdV[hvipnHLREev]djlqmHavP<wpTJa`PudM^TxJen\\MTgXtMmkUXKPXuTLlWAkqITvUtWPtTMkDALiDtWMo]<Lr]Nj=wjtYDiUXqvUixcYy`Xyt\\TfQVOqvwpvpDSlxVUaOXxOK=UMUT^uRByW?QtQDREEoadLYLpxMSDtvEiUfyvUavMemH]SoujLXpSyu;iXAiN<iWgEUvqUCAlguoppJYXX?QuIPkZXpWMU<aYA<JJIvWHmy=J_UJiyqwAjMyOVymZPRWqWiXusIjOuKayMhAX;ax@AvRxxFHJGePshWHUW`hU[qT?YK=XXvILsAqcmKSTTDyWPYT?DRX]UJaWILxtxLL@whUtmeS^qX?iWU@Y?axhEWsiTl<sLIvBULTXji<ydTXDTTDMUuxSRdnatU;ArcyVixpgLTfuWDupWHL]qLu`ovUu>tPXiNTaoGDoJHvrTYCDucalbdL>LJrAJL@Yu=wZpy<dxJTwa\\tPIYc<ypaSnuw@=PEqyPPwOuxRHQdqN\\XkF<KQ]v>IL[yRELLfhxcPRt=TvxRXEtGtkK`P[@Nq=TBqQNXmn]upTw`QwHquqik]lTVurP]XqHOEXVFyY:Plm`twqndEkkXskqn@uW_hWA@LOXO=QTNLrNYJBMOb<RKypglqwyV^YmyXkMYO`pQWDVq`OxmjdltEAosqU]@sK<YQxkq`QjmWeLS`yP_]ND]YA`lPDR?DOCttdEJd<r]eoFLwMaTmHkdIK`dYixxK=NtUVXluQQKXuoIMWxDklAM^YU^AuKmukuj\\APkQkB@P^ix[pVWUka<lKMUB\\NpTr:=NJ=OcxTVtmGDS^lNXIsCTUhpoppk@iUWHJq`tNLXIAJg`n;DSx\\tTxQbYv;nowabtqj;Oq[qhS`_=ytpH\\GFoPntPplMNvVgqNOZXP\\vvjJxxJocWqxegjMqfU>]Oi[?Ig`X_cGlqvcjXeGPwMyfPPsUpjeaolvnLOuLIs;?[dn]w_nYvagoZAFwuxoWWeqxep_rqicr`[ivbkf_IvskyfhoxfO`Pq_iffPnpVQbO>ZvXy?`_rfeDWkEHvxNoBwcbGdoQbeQwSNqWWyZOyiHjgWcaptSInYQxFqxNFuMhxmFaGH`rnn_n\\y>ZdXcKHtEQpQFsfafgv^maaOxu:a[CgnUPudyiohwrIgHostWlTapeG_nXgdogfHfsqgLhyt^_E`grIdx?l`hn??m\\`dDQlO@ZnHjey_UQwN>lHi]Zwh?hlfWd^wdGWr[Am@faMxs?`lRgobap_a[g>sE`bEYlK^llplNilqg^hfl^Vx^AnwnqDa[EQqG>du@w@PuoW[UG`uahcwlFva@VqX?v>YmWAvx`xRogxpjViw[fe?hc:@iZ>xI_ZJWgMAbqYnQYyyWe]orqIlohsG>tfw\\UVmFhppvuDxvi`eYGq`Q\\JokYOhq^jZqg>vdWObUyk]AaN_ncn_gFbd^Z>NrcIhxxft^kfWoOfu>gytneaNhuhatf[iy]lnyJ@kmGnEqheFwgosAVi_ggO^^Jx[D>vmyr^>_uG`Xq]OwoupuWq]WywtwiIPeZAg`IdIXugydeWdE^cuPp`VuOg^eol_@__Pg<wjdOc<?iIwpYhg@N_YyPudtKui]DQqscWfmgspOfsiYm;dnMv?qYKYHCkwi_RIwfTICHOXcWTW<KJLm[iNc<S<Y[ogcphlHFx;gbLiikih?OuXaynWq`geE?`WP_Da_t`uUXkrna[HgiVt\\n^YAh?h\\Lg]CP_ffpO^oNf^A^q>Fj\\qkDVyN_l>@K=eieEuYsU]vFSyOUTqUxvSwfKsZOVtGw=wrO;vdEiv?elmTSWDVseG_H_UWkYg];rKsb];IT=cAeiXIVWWYtqegQdiQygETbqiXYHeYbEac<UF[UdhGtWYb^qYlQtYOtLOxAWDRef;MTTMDNmdJmWDGyZOE@eduGTMGfp_ULSUbigUgbkCchqHYgYcWdGeF>msv;y>=tN;GNKK?N:=t[iSGaxqCuPOH]GwGATgswDcCXcwPEdk]yRSUmMEIKCVsHcCbiyX:IdZef]MBs[EYKYBwScoeBuIAaspOgUgE=qBICxN?iHigB`qWetntvtEq=HkB<LLYLf=SCysKXxaYs:<uXPUnUj?PupDj[UyjUtaxvstK[AMnUuoDMqESClxDUnj@J>tlP`L^DOvuKlLl;tXD<ke<QYhrEln`pVqXMOlWmetaMwVYKhivM@SxtuZYREEM`Ymi`QcIx@QtNpRkALSaNHPju=JxLsApS=TPgyY:@NiIsGINWAMCaPEpvRXsQAMHyx@iQ_mygLWMUODDtDUmNiVtLmJqWlMT<xsJXXl]m>@QEhLB\\S\\\\oPQLUiSZHn`@lJ`L[XNB=jA<L:hYNtMDej<BJ;WvCEXgXIkFPEgrmYSWVAWXpuS[]cHuXVOv[kh^_x[OrJUFecReCSX[RJGbZgrtiybeVnAXViSCyhFuU`mDUaCq[UeMHXsStgCN_wXMXCKg]=s^GifmEuCI^wFY;F?]ry;btUEw[vy;ruGseyI:]I_Yd^;gicuW]xHKYnEwFhYuurlak[uSKLs:aSmDQeLR;tRiuW^yq]@n;pVZ\\TC`JuAYZAJWLmEdpwyPgUWQlsQpPwiK?=Xe=VVLOhDP\\MVR`xwiN?qpJtnO\\VwdVLv[yN_ENy;@bZ@dbf_gQexYglwepqiiwX;oI<tpmYoupMhy;lKyuyjANbqX;@rZXRwQRBUm>tT<xSy]TSxojEQnDlYDnXLUnTJkeM?`PAlsouNBIxvQkIQL\\uLrxtBuPUTVdatPdlnQmMXS:hJ_XR:Ptn@l^DoZ`N<DJ;\\vninOeyQIwQlqVxk[pxgeXHhUUamPPsiUuX]siuKOpOauV_drpQJ[YJQDUCDUDIKlUTIena`plLmExJLqqTiOqtTkdwI`UXYY_DYHYxaLu;qMCUYNEPvINsekWikDPV=IxXeMSHtNxlDTngpPVLTJtRlQku`lNdJT<kwxmcyl]XpfHS?ax=xnXpJdqW^ePIxpwhr>lS?hwNao\\`u?mqd<kkEYqEmltYaHmpTMExTThTeYnIaJ_Ls;hQw@tW\\lcqK;puaHwHpLahOu<UkxTOYV=iJBYPrIUPYVYlKJhY>=o^<QLUMELtBev=El;ysPTOXMyLpVTDvl]u`LTmesZUuP\\Wyyjg@OtXq_Hxh\\WFuWd<KBqlnUREijlDsyg_IhZ@yZ]Ok_F[J_w;VqWIaLiw:YgQXcuqhCpg<pvBPeS@mbymZacPyfZGdIhhQXgfna\\QtvNkLYv>@oIN^Zpov>onvnohu^>wGFnto^@qjoAcnPgxwleos<VrP`oMi\\UXl_A_GOwFghrNu`Ve>fbrw_k>^pflpF\\TqmPOZswcd_tUVcbI\\^Pa[?jfOyiAothbm`gYhbfOe;HmDiqTagsom_o^iahuHrjYudg_LAbKPs\\I_`AlM@vqW_mYi<QkPOl<w[hykVo`Iamoi]QiadVwqoqggfLYmGVk`FgWX^Makhgwmgp\\wxFAejxuLndfqZV`dq`^MFyJ_d<PjP>liP^@XR[XkqeIcWWoGokvXOSnsxgMrnQi]sxrmw\\ysaWcVISsMy?gvLig_aFV]D^gw?wYUCry;RbsbAarmKU<UEi_v;Cw<_WvYxg;BoyDqmBbkX:aIA[dTiscISNUTfciR;xfWr`ufK_w<GX`wDvUfJKxC=UpUstmb`Uyg_cfSdaCIhaYRuWAif>etjEiDYUywB:CyduWDMriaxTmexqgiSyG]soSu]?TQAHWGiKgDsuEAkWq_rviBEgFloh:yU<Kd\\Ki;oCA[EDeGuOSJsIn;bPAX<cyJidHMii]smawWixuYSygVEAbSCUY;UYKi=suy;B^oRWqyZcx>iREsheMFrowrMVUaGEYxR?dmaChacs?EPqI]sCQ@u>@j^iN_DW;eWxLMNEKDLtCyVBMmE<WXtRnLK?pJ^PQ[Ywp=LgYXgpp?iPiqUmmxk\\SA]M]=ptextQl=qO\\LOQhl`LLDMu<mTsYUBxSLxSaYYs\\pQppoeY\\hsPxVuAYC]xuunX<nWiXIHUmTqfTOphkFDvrhj?uvRDm[tQ?PPXpOAMrJUUXynCpXq]l;<rWLS;<Ot\\qfQqkYtqunP<MguXfTrC<sfmP?QSD]j_uX[tPstWsLOEEvWMsD@xPEweEqadPXuMjYJTdkRmWILWwIppyqNUSXIUeel]uskTwXDo`QKGaPY`Tgyle\\VUambQXUQOO\\wu=x\\UqUal==WYim:EObMTC=o?@pZ@LW\\\\QvcVwlwG]@IqnWwTqio_y:hrkV^[GjiHuxwhpOigNy^wjTghuaiRv\\HfvrNsLojQaxHXdTQd;?cH>^b`^YweGv\\GYhWGku@qWX]mPnHGnboZMogNaqoFb=^qh@ubqhUge:ijpo_[^icH_ZVokpaLAZZPptp[ux_oO\\oVrep_M_fVGgtwxbXgGxjwG^mxuYn\\mXnbA`JPljp\\<^m=OwJG^Z^l^nxD`[uGwMfgawclio\\WupYxqv[_Hq@hf]Piyo_oafOAgR^]ShgVgwJnoF^pROq^XrLoeM_[vxrh^jKPwJ`auAqZPkh@wIYnqqothqaPiSVtuGbox\\kGmpgcNhrq>kkg`un^;Xg?ioG@AwRhYX^aC_CcGIbVqRuuct=DAAFpef[ghhgHVoCLWuFgYJsUy]HWibWIHuKdlowUMe;gShED_sHW?TjkBicvwgu;SCuAChYrgWVX?yZyTI[cHQWUAEcwhnAEWKited^uHWYGNceUueoqXAqfiICV_eIYTUaCcyc@uUigh@]MBDXhHx_YUCYj;Dr@TJv\\x:APdqPeLw`hvt\\k`MMoYY>awTiycDP_<VPamHpTrTxVEPUINwMlftVTEUdDRvaoXXt_Eyx`vlel`LjwxuttkbuoHuQBuVmypg]sUuoP]SEpo<=PrupFLyOlm>=SPIkgYuuQNq<pjhjcpNYQS^ajsHbRXvHP[N@lEQ]MNopqcfhaY?hgVwgQlgNtHGkgYx<nqTOmIqopv`[IpMxuhIwEWcE@[B_wU_om`][ftwFv:h\\dIyA@\\bo_HAodiwdirMywIqkm_yIAyL>_yVmCY^eQZfaqmwy:>\\ov\\qqZbwatpjAotcWtkxsYXyJpgyAZAYt;Ovnykpvns_u@Wtji_Bgk_xxvQwEantHpfOsm_geV\\JXxqVeo@k[>umYdG^gJ@vwg[xp\\u>[vf^AGlUIbiheMorwW]vwt:VjC`gmGcoVeYghUW_Qp]UAfKYu`?n_?d^goaykdoyX`wMHv?if[xsBXnXIZZqiiOhLY]Hhu@V[dOtXalThk`ppF_iT?^]YquWqUG^TajoQcJNmIPfo_nkXvbhZw>uN`Zraj<noXYvAa`NnkD`ne`nx_uvIyyAZ:iyIxx>?d[wy:nbZWjLYiX>^myy:visyhkIuNp\\XwkhY\\Co`_Iw[ng=fcoWrdnyGgeoxmBFr]Iw<p_JouEGa=Ft[_aAXm_?v<xujGebFZDwclOlLGaQgl>NyQiiCAw@HufopfvjWWhrAunaaUP_=hkRymLXrhH[qGeDPd]gbBGgDF^EG_Q_Z:HlAImNv\\GQZ;Hb@faZfiVXw`VwpYbiWspWt\\OhaIotgaXXem^ulFuS^aBamni\\efrH@sa^ptXekWcDOcO_u`Pj:f^\\GjapyKxjC_wYxgbwtFVvnodfOb_q\\XaeyHgpIbXqt;ogR@j=>pxYjUQvvPvPOc;^gcN[]AlhHZZn_HgktVxyh]QAgPxdthabAeTxrfGqHAfviyWVrXOpqp\\gwnRnakgl_Fg[qcQPZ;HcjwhNXnyPlQPdL>]QfeoYxRFwontE@dqhftXigOw@Vkhw[H__JFdc@\\kHwm>^]ytUIdN_f=AmbHv?_ntNsEIj__ZOh_ZNibHe;Fv?HqWyaeI[OyqiGmPYsUVq^QeKwpPOheny]OoHVflPnTivVwn<_brnxBqoBQcvvdAOlPQZAWZLH[ga`SV`LQ]Qog?hwkaekyy:fkpYZ;yy:NuY@nrha^N^A^bGQi^vy:^x?vqrapdF[gnhCY`VvacwjfVtWi`SfmlYu:p^OwnLNydWfxO]J@k[?c@h]Lo\\PXs^`Z<NdAO_VFyJ?gYfdihaCVhG?`spgMFgsnnjhgEphyVjPatWg]LAyQqh`v`O`Z^V[tGf_PjSafyXs]GrkGjRQvCPbNWa:vgaggpgo?yepX\\@@uqp^La]OI_theO^k;i]Cycqfh;I[r__I`difra>qIxduXqIP_GvgnGjeY]mhk>`hgYrpHatxtm^aQWenfsCqxsNyJowGfauitXQeaaqmI[<XtGG_ivZ=GwDO[NxkSO_a^jjQpSvsKinBygSohMixYX_CA`sAeoQsaQqvotWWrYnmdqdwIpqi]Fhp?IhCgxNopNQn<xbKH_^FiJgdpqfAotAnu:xvIIy;vnY?qwFbfgx>qtFvZfWaXIuPVwonqcQ^Eynrpf\\`fGivSwbZyv^xbpH]p_jmv]?AxJgnHfx?Hh:qaBGdyAZ>?tEgglafp`_AynXFp_?uwptvVyWWt>OxCnleajQObTYlWVu>gjpPwN^aNhl[Fb:gyZPkEva\\xmbAlUymfQjAYy\\@_jvy:VnDIbJio;Ahswy:nruqawIwDxZEOhyV]Q>d;wsvyi=ya;p_<PsQierWrtQcoikNi]WqwdHusWJqw[;HE[B@cHXgRPaRBAuWqGJctY=gm]BneGGIf`eeE=cnsSoOhJKdLcH^Gh?WrboxDcxL_H@qXEiIUgytexm=Bk[Ga?Y=ygIuvS]f=ebyae_wYtHvA@TO@QUEK>Ax_<XsXT^IX:MKJeWehUqyN\\Tm_UpRMPWhxIUv]ATlaWdlKqLVxUsH<q_dU`EoCeKSHN^@O?`O_\\ULLJAmM^=TY]PDfZ@votA\\JNiHhxP>Zui`wykiEW_r[UwSKI^sxUSiZmyx?GtYcuwv[qGRohA;WXIyK]yaySyihAAfQuETegpgsFcxWQRnUXwWyvgDwYCUiXA_cWut]CcnmgF;wguelCRgkUfIWMOvnWgGoRSUSEUbw]bsaFsgbb?dEKIvMYSGutUCgQuiUDMAcGyV]sboey?=coSghuUqQYWoyVgv_[VmWGAQVbwrDUFeMgTURc;ce_dNqS\\;i;CXIGcVIRLSI[avy;rA]yAAIfKICiINYWE=vt=vIGu]CIiyI:qIOov<IbbMgDMyAiwIwsY[yIAUy]H?krY]H`;CwwvkKFIyI:yhyuDygUSARcmwAUv\\KGBIiyySryFjiFJcXG]UtcStkxsqHgqriifyyq`HJOAn;htExNRyNxyQ`yY:@RKDrTYwclntTNaLSnuypMqOuNQauCiwwTwoUmvpQ\\mlRhvSuXuTt;lT_AKBaMQdM<eUH\\jwEoDuk]LKBxVQyphpX@upkQTayqUqWIywqey;IslTUVePYMv;eramR@en?HoKmUtiS?ywl`lmPrJlL<ERQmOrtJvHYJmWAIsyPMvxvwym?hY<=OhLK?>hy>]YpnAOysPwA>rBwmc>bvQfxGmYNwaAoYFZ\\^i_XZkIktafyWoX@nv_ZCPxNx[@y^cIlxqotGjjQ\\aNsJwaR::::ZC<::wA[A:::::M>::tI<I:::::`B::nY>X:::::FK::byBv:::::R\\::JyKr;::::j>;:Zx]j=muuqbycYkYcoMfOqccqxFiyBUD]Ai>]by=dbWBsUSCOCAKfiwDK[xSYIKQrRqvjoh=AwTEwkcuXMEm[I@iypES[qwHmXOEFtMe`ggaoFQQTS;xHOhJ[xMwbm=yu;gqUd:=nsYSClMmYKEhONPqM=KbHXa<lNhl^lKB@Ns=lAEu;YxoLugmPBAspLUZDPPTp=qj]lR_iopHJC]q>\\N:`qCyY:po=DvjmrkXyn@WQYqgllVDojxLYmk>AKbXuKhTBaQ[Ls>@NlyjRXVR=ow\\xNTYhxNETvhaQxiqG@r:DQVdY[@x[pPKyXH@YhEo=XQTiyxTX;AtZlNyQNkyo=yMDyY:`vGYqjulvlyKLYElYyhqw`qrimwxuUhvgmXs=tN=wctPfTrQ`QVAMuluk<sLdV@An@ULdTLhAQQyjKPU_LjMIRm]mw]POLODhWiqK?MP_qpvTmSxpVUkZljF=yG]QUyJHTyuIr]mMA\\qu=oxpVA=Wq\\lWiSlxqLGr_GqxOZv_dpvc_FZVOhMvsYXZDAjoQlQq^ZisTiCIVCIdLafA_DpMTV;Wb?hZctKMs;UIrmInoEtss?sxOkbl[rpmeEmc:?i_MTEGCWcCI[rMcg][IXIYZSIbiYCMcJ?\\:^]:vZJ`\\X>iPVkOgoCy[UggkXvhXd?IwdFf>@nvHvpio>w[SwePaibI\\fqxrxpQnwkiwKItdNcLGmL>d<YbH`jsa^c>bl?nxnsw_lRvwLoxpi`UFhTXghxdVFk@HncYrqvl\\PeKhg_IwMnv@ac@wulVa;YcgwrV_rPXiBOeYPbCiZ^@t^GtfAnJ?_cvlvx`LFsPXuSp`kngsH_JXbdvm?vpE@fuQbuGr]qmAfyNw]Eq`Knj]ychpdoNkUg_HAqHxrWFj;npN_nmys>fnZFlIIu;_dZHxXIxuq]Cw[jqh=ofCpar>eROff_ftpk[awwNo>Vh`aibqaJAf=op?og?Nqe^gAgf;^[jXs[?[gW^BaZ^Hi:fa<Yjoq_^FiFq_fnpJWwH?^[prV@bLodL@aZVj^IbYffAnsQQgqHe[w`gCJj@blbakU<K<Syw[XYsFUoc^EvXKBr?FIKFb[Ip]EMAe?ATeAIXSy<oeQ;chkFFqHSSs]IUI;vVIxCqXJOyaYU[cE\\EiiAY>IGpmU;YBFqYRKUVIcpcr^CyKei@YBoKT^;ykCDLSVbgg`;tJUdG[F_=GB[m;\\V:lMV=TruwRmjiHltXSsmKuLjtYvM\\xois>Xu_lOrynn<oXFrfyxDN[O`ZJ?tGIldqeMftYFhUHqIA]jXc;ixYg\\>igr`yjFytGcpWuSnr^ii[flqD_iIdgE>EgVsCxcb>GG=KbWKXe;xgETUKFu;WBgV@SUBUBcmE:cv];s;kGNweCoTEaUsItagkHNvcNcBXyfh^E_fb@hDG[V^nK`vr?nviq^gpCAqmnhKxg[GsKOl^xrLppL^eb?_j?nOH\\DIbuAix^h?FegVcsp^lYonWhk^[PHdj>pYh\\gVlCAbY_]>Xxayrv>DKYDgGuAt?aGQyjf@Uf=klaVL`vDUkCpPVyxMHShMT:Qo^IYXpYYMQI`xrHLauRVEsfIn@]M;YRG@qJ`Ng\\NjErA@S<pQ=IrsEjiejeQKVUKfqr]tR_EjF@P=EVBdw]<uLHL^yJoMkIhrhDteMP?=lfptbEXRLKdTSK<UE=w>lmCEVZlKCaNTxkOTrT@pWqn@EQWaOKanCajx<Wl]N?QrVqKhHR_Mk]`LX@Rm]Muej?HjthSxhMF=VPdyrhLLDphup?iSfyxEyQE^x?XsIpgX`siYnnnonAyEFh@Y]I_ksF_C?eCfaXIbM@gNN[?rIyWuysTmhQqeyedVUvg;yGSscIxJyhlmDxSu?WgA?s;KrQ_h?]xVmGIWr=iuB=VkEbycF[CWC;C:IB:Or=EfmihUugJudfYY;mVNuFAqcAATL]u<srv=hL=v;Sx:=TxcWPUeGKRDgGPUY^=ik=TCkWvktLUucaVl=YD;b=MdCAvx_EgoteUcgUhpqhA_T@muEcS`SSC;x[aRxQW:;Dv=gw]bsKsIiwLedgiY;QXSwx:_rboCHgEIgfNAyTsrv:Iiu;wx=G<UU:ggn_B_Wf>;Br=RJUdyEdry\\N\\U<JxWIVAX]U=\\qIPvraweTTSaMU\\LalofXnoHmeAk<Tyc_vQ@[hYZPqa=qxYhiANuSUgmx`]udeLXLPXEyHQqR\\s_@PqhlsUS[<nlYnpumc=nAYpTQVVyuuxRqtr>EOcLS^ES=EKHLqM`vJdn;Ps:TyslXJuYilLUmR;ejPYq_Mpv@SH=lVekg`jtPUr`QHPTZHrZ=JbyqyLjgQvY=Y^TraAw;tMBhrjyjAHvkYuSYufiw]YSItVXvajg_jiokWe;hgB`tr_wZd_kBU=S=hQ;DOX<RyAtZ\\YUaopUQmlWoPwpxrFxLXXtHmNmDKfiO?myl=SBambhyaLUbAlfqXu`YCYL[Yu]PpveP_PTXHw>dNiaLHDjTAJ_]RIHnIQP<hmiulfeyBIMV]wgatnAyO]ux@xN]yS]QyiPKew\\ULk@uWeRGpQaHUrdrKHRtaQnxXcTOv@X\\MJAmQVAL^`WQIvuxrCuPyywYuvKaWUps]`vRmJ[ToUPTgiPLAwIly?prRpLaaxSUKtMt=mKDEYcLSstRCLSC`je<LLLLYiXU\\yuHM:aOtEXeTn\\euhYkU@uiuLyqlUax?XSIpwX`siUnnpon=YEHX@UmI]kuL[f`ZXxwZFsnP[?NZ=Hsi?pSigl^nGipTQ^@Qi]om^vpRokNH_oIytYsZNZmpvvwsxXjeqaYQ[cI\\Eii@Y^I?plQ[XFfpQrJQvI_pcv^Bykda`Y>oKX^;qkBHlSVbg_`:pjThg[F_<?bZAZA>l:FikGbaiq]qxvNlY>vfqjGQ\\v?hj@p>AuCihWVrRYiN?[aassAtvWm>Ip`Pn>AjPya;F`ZQaWNj<IfpF\\WVfXp\\RYv>X_FIyHx[S@nniefoxu`v=OZkigIh_<@n\\`s`P\\\\I[A>lu_dB^vJ>[yUOIbocDLaybWGCgGNQa[ptV@bL[Z:EMmQJYQKQiLrplRekAqKDMJSHv@LrJLuA=P_XNByKd]lYTkWQNQaVD<nSioKMVj\\lNml\\@pP<TC`qMLR:aMLDSn<KpUyWmq^IkjioKEUxQuLDOIaP<QtqLKAAJg<rlM^[vslXjrYo_Foq_^Xylhok`GnLPt`n\\MNv_Pps?_EVvJpmv?yaQkI^wEibh`ibXx`Yu]PqvibcFdYfh>HofglHF[;W^NPlvvkN>]Y?o`VuoYqmOe@^kYggUwjsHwH@nRO`RvhvYc`njmym?_erPsQWyPYiGGyBqjmqgrvjTVxA^lbhjpoxJxjSnq?Qq?ygyAZSVggWmmyiiOekgnQVc^H_tVmevbS>QsulkH]_ISKRd_S^=yKUukoVLoT_sHJ[EveRjOtZGEV;sjgWJGupWE]GvRIXTUCFQXT=YE=wBCFcYBf;B:;gx[HDdZ<FJ;GNKC?ZZDD:;ON:<db:>NK;Bb\\<JJ??ZZDD:;ON:<db:>NK;Bb\\<JJ??ZZDD:;ON:=tym@:::::::5:\"\{\}-%%ROOTG6'-%)BOUNDS_XG6#$""!!""-%)BOUNDS_YGF'-%-BOUNDS_WIDTHG6#$"&++"F*-%.BOUNDS_HEIGHTG6#$"%?;F*-%)CHILDRENG6"%!G Author: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=Yuri Zlatsin 10-Oct-2011 Audit: Omer Yagel 104131 - Madar H Home Assignment #5 spring 2011 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

Given a system of equations: 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 Also given its solution 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 that follows the next condition: 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 Find LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiekYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRInRGJ0YvRjIvRjNRJ25vcm1hbEYnRj1GPQ==

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzY6LUkjbWlHRiQ2JVEocmVzdGFydEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIjpGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JJ21zcGFjZUdGJDYmLyUnaGVpZ2h0R1EmMC4wZXhGJy8lJndpZHRoR1EmMC4wZW1GJy8lJmRlcHRoR0ZULyUqbGluZWJyZWFrR1EobmV3bGluZUYnLUYsNiVRKmludGVyZmFjZUYnRi9GMi1JKG1mZW5jZWRHRiQ2JC1GIzYnLUYsNiVRLHR5cGVzZXR0aW5nRidGL0YyLUY2Ni1RIj1GJ0Y5RjtGPkZARkJGREZGRkhGSkZNLUYsNiVRKWV4dGVuZGVkRidGL0YyLyUrZXhlY3V0YWJsZUdGPUY5RjlGNUZPLUYsNiVRJXdpdGhGJ0YvRjItRltvNiQtRiM2JC1GLDYlUShERXRvb2xzRidGL0YyRjlGOUY1Rk8tRiw2I1EhRidGam8tRltvNiQtRiM2JC1GLDYlUS5MaW5lYXJBbGdlYnJhRidGL0YyRjlGOUY1LUY2Ni1RIn5GJ0Y5RjtGPkZARkJGREZGRkgvRktGVy9GTkZXRk9Gam8tRltvNiQtRiM2JC1GLDYlUSdsaW5hbGdGJ0YvRjJGOUY5RjUtRlA2JkZSRlVGWC9GZW5RJWF1dG9GJ0ZkcEZob0Y5 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= 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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder %; We write the matrix: 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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LywqKiQpSSdsYW1iZGFHNiIiIiQiIiJGKSomIiInRikpRiYiIiNGKSEiIiomIiIqRilGJkYpRikiIiVGLiIiIQ==

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEsZWlnZW52YWx1ZXNGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiQtRiM2JS1GLDYlUSJBRidGL0YyLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvRjNRJ25vcm1hbEYnRkBGPUZA

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

NiUiIiUiIiJGJA==

Now that we found the Eigenvalue , we look for the suitable eigenvector: 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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEnJiM5NTU7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RIj1GJ0YyLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGSS1JI21uR0YkNiRRIjFGJ0YyLUY2Ni1RIjpGJ0YyRjlGO0Y9Rj9GQUZDRkVGR0ZKLyUrZXhlY3V0YWJsZUdGMUYy

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder 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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

PCQvSSNWMUc2IiIiIS9JI1YyR0YlRiY=

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder 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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder JSFH LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= JSFH JSFH LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEnJiM5NTU7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RIj1GJ0YyLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGSS1JI21uR0YkNiRRIjRGJ0YyLUY2Ni1RIjpGJ0YyRjlGO0Y9Rj9GQUZDRkVGR0ZKLyUrZXhlY3V0YWJsZUdGMUYy

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder 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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

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

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEmc29sdmVGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiQtRiM2Ji1GLDYlUTJHZW5lcmF0ZUVxdWF0aW9uc0YnRi9GMi1GNjYkLUYjNigtRiw2JVEiVkYnRi9GMi1JI21vR0YkNi1RIixGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGTC8lKnN5bW1ldHJpY0dGTC8lKGxhcmdlb3BHRkwvJS5tb3ZhYmxlbGltaXRzR0ZMLyUnYWNjZW50R0ZMLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRjY2Ji1GIzYoLUYsNiVRI1YxRidGL0YyRkQtRiw2JVEjVjJGJ0YvRjJGRC1GLDYlUSNWM0YnRi9GMkZIRkgvJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRidGRC1GNjYmLUYjNigtSSNtbkdGJDYkUSIwRidGSEZERmBwRkRGYHBGSEZIL0Znb1EzJkxlZnRBbmdsZUJyYWNrZXQ7RicvRmpvUTQmUmlnaHRBbmdsZUJyYWNrZXQ7RidGSEZILyUrZXhlY3V0YWJsZUdGTEZIRkhGaHBGSA==

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

PCUvSSNWMUc2IiwkSSNWMkdGJSEiIi9GJ0YnL0kjVjNHRiUiIiE=

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

PCQvSSNWMkc2IiEiIi9JI1YzR0YlIiIh

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 JSFH Instead, we can use LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVEtZWlnZW52ZWN0b3JzRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn function for easier solution:

SS1laWdlbnZlY3RvcnNHNiQlKnByb3RlY3RlZEcvSSttb2R1bGVuYW1lRzYiSSdsaW5hbGdHNiRGJEkoX3N5c2xpYkdGJw==

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2JVEtZWlnZW52ZWN0b3JzRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNiUtRiw2JVEiQUYnRi9GMi8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJ0ZALUYsNiNRIUYnLUknbXNwYWNlR0YkNiYvJSdoZWlnaHRHUSYwLjBleEYnLyUmd2lkdGhHUSYwLjBlbUYnLyUmZGVwdGhHRkovJSpsaW5lYnJlYWtHUSVhdXRvRidGQkY9RkA=

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

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

The solutions form is: 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JSFH 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 JSFH

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

PCcvSSNDMUc2IiwkKioiIiciIiJJImFHRiUhIiItSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiU2I0kidEdGJUYrRjJGKUYrL0kjQzJHRiUqJkYqRitGLEYrL0kjQzNHRiUiIiEvRipGKi9GMkYy

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

PCcvIiIhRiQvIiIiRiYvSSNDMUc2IkYkL0kjQzJHRilGJi9JI0MzR0YpRiQ=

We get that the equations private solution for our given ICS, is: 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 JSFHJSFH

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

Given a system of equations: 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 and LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiekYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRInRGJ0YvRjIvRjNRJ25vcm1hbEYnRj1GPQ== is bounded at LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkobWZlbmNlZEdGJDYlLUYjNictSSNtbkdGJDYkUSIwRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2LVEiLEYnRjQvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHUSV0cnVlRicvJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRiM2JC1JI21pR0YkNiVRKCYjODczNDtGJy8lJ2l0YWxpY0dGQC9GNVEnaXRhbGljRidGNC1GVDYjUSFGJ0Y0RjQvJSVvcGVuR1EiW0YnRjQ=. Show that 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.

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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= We write the matrix: 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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder 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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LywoKiQpSSdsYW1iZGFHNiIiIiQiIiJGKSokKUYmIiIjRilGKUYsISIiIiIh

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEsZWlnZW52YWx1ZXNGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiQtRiM2JS1GLDYlUSJBRidGL0YyLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvRjNRJ25vcm1hbEYnRkBGPUZA

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

NiUiIiIsJkYjISIiXiNGI0YlLCZGI0YlRiZGIw==

The General solution form is: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzY4LUkjbWlHRiQ2JVEiWEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKiZjb2xvbmVxO0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZMLUYsNiVRI0MxRidGL0YyLUY2Ni1RJyZzZG90O0YnRjlGO0Y+RkBGQkZERkZGSC9GS1EmMC4wZW1GJy9GTkZWLUYsNiVRI1YxRidGL0YyRlItSSVtc3VwR0YkNiUtRjY2LVEvJkV4cG9uZW50aWFsRTtGJ0Y5RjtGPkZARkJGREZGRkhGVS9GTlEsMC4xMTExMTExZW1GJy1GIzYpLUYsNiVRInRGJ0YvRjJGLy8lK2ZvcmVncm91bmRHUSxbMTI4LDAsMTI4XUYnLyUrZXhlY3V0YWJsZUdGPS8lLHBsYWNlaG9sZGVyR0YxLyUwZm9udF9zdHlsZV9uYW1lR1EoMkR+TWF0aEYnRjIvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnLUY2Ni1RIitGJ0Y5RjtGPkZARkJGREZGRkgvRktRLDAuMjIyMjIyMmVtRicvRk5GY3AtRiw2JVEjQzJGJ0YvRjJGUi1GLDYlUSNWMkYnRi9GMkZSLUZmbjYlRmhuLUYjNiotRjY2LVEqJnVtaW51czA7RidGOUY7Rj5GQEZCRkRGRkZIRmJwRmRwRl9vRi9GYm9GZW9GZ29GaW9GMkZccEZfcC1GLDYlUSNDM0YnRi9GMkZSLUYsNiVRI1YzRidGL0YyRlJGW3EtRjY2LVEiOkYnRjlGO0Y+RkBGQkZERkZGSEZKRk1GZW9GOQ==

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

%; We get our bounded solution when 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 Thus,LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiWEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJw==

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LCYqKEkjQzJHNiIiIiJJI1YyR0YlRiYtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiU2IywkSSJ0R0YlISIiRiZGJiooSSNDM0dGJUYmSSNWM0dGJUYmRihGJkYm

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRidGKy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

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

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVElZXZhbEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYmLUYsNiVRMkdlbmVyYXRlRXF1YXRpb25zRidGL0YyLUY2NiQtRiM2Ki1GLDYlUShjb252ZXJ0RidGL0YyLUY2NiQtRiM2Jy1GLDYlUSJYRidGL0YyLUkjbW9HRiQ2LVEiLEYnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0ZTLyUqc3ltbWV0cmljR0ZTLyUobGFyZ2VvcEdGUy8lLm1vdmFibGVsaW1pdHNHRlMvJSdhY2NlbnRHRlMvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GLDYlUSdNYXRyaXhGJ0YvRjIvJStleGVjdXRhYmxlR0ZTRk9GT0ZLLUY2NiYtRiM2JS1GLDYlUSJhRidGL0YyRmNvRk9GTy8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJ0ZLLUY2NiYtRiM2KS1GLDYlUSJ4RidGL0YyRkstRiw2JVEieUYnRi9GMkZLLUYsNiVRInpGJ0YvRjJGY29GT0ZPL0ZdcFEnJmxhbmc7RicvRmBwUScmcmFuZztGJ0Zjb0ZPRk9GY29GT0ZPRmNvRk8=

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

NyUvKigtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywkSSJ0R0YqISIiIiIiLCYqJkkjQzJHRipGLy1JJGNvc0dGJzYjRi1GL0YvKiZJI0MzR0YqRi8tSSRzaW5HRidGNUYvRi9GL0kiYUdGKkYvSSJ4R0YqLywkKihGJUYvLCYqJkYyRi9GOEYvRi8qJkY3Ri9GM0YvRi5GL0Y6Ri9GLkkieUdGKi9GPkkiekdGKg==

JSFH 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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LyIiISwmSSJ5RzYiIiIiSSJ6R0YmRic=

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

For 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 Given the next equation system: 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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder Also, ICS: 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 Find the limit 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= Homogeneous equation: 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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder 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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LywoKiQpSSdsYW1iZGFHNiIiIiMiIiJGKSomRihGKUYmRikhIiJGKEYpIiIh

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEsZWlnZW52YWx1ZXNGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiQtRiM2JS1GLDYlUSJBRidGL0YyLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvRjNRJ25vcm1hbEYnRkBGPUZA

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

NiQsJiIiIkYkXiNGJEYkLCZGJEYkRiUhIiI=

The homogeneous solution is:JSFH 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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder 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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEiWEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKSZBc3NpZ247RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkwtRiM2JS1GLDYlUSNDMkYnRi9GMi1GNjYtUTEmSW52aXNpYmxlVGltZXM7RidGOUY7Rj5GQEZCRkRGRkZIL0ZLUSYwLjBlbUYnL0ZORlgtRiM2JS1JKG1mZW5jZWRHRiQ2JC1JJW1zdXBHRiQ2JS1GNjYtUS8mRXhwb25lbnRpYWxFO0YnRjlGO0Y+RkBGQkZERkZGSEZXL0ZOUSwwLjExMTExMTFlbUYnLUYsNiVRInRGJ0YvRjIvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnRjktRjY2LVEwJkFwcGx5RnVuY3Rpb247RidGOUY7Rj5GQEZCRkRGRkZIRldGWS1GZ242JC1GZ242KC1JJ210YWJsZUdGJDY2LUkkbXRyR0YkNiYtSSRtdGRHRiQ2KC1GIzYlLUYsNiVRJGNvc0YnL0YwRj1GOUZnby1GZ242JEZhb0Y5LyUpcm93YWxpZ25HUSFGJy8lLGNvbHVtbmFsaWduR0ZhcS8lK2dyb3VwYWxpZ25HRmFxLyUocm93c3BhbkdRIjFGJy8lK2NvbHVtbnNwYW5HRmhxRl9xRmJxRmRxLUZicDYmLUZlcDYoLUYjNiUtRiw2JVEkc2luRidGXHFGOUZnb0ZdcUZfcUZicUZkcUZmcUZpcUZfcUZicUZkcS8lJmFsaWduR1ElYXhpc0YnL0ZgcVEpYmFzZWxpbmVGJy9GY3FRJ2NlbnRlckYnL0ZlcVEnfGZybGVmdHxockYnLyUvYWxpZ25tZW50c2NvcGVHRjEvJSxjb2x1bW53aWR0aEdRJWF1dG9GJy8lJndpZHRoR0Zhcy8lK3Jvd3NwYWNpbmdHUSYxLjBleEYnLyUuY29sdW1uc3BhY2luZ0dRJjAuOGVtRicvJSlyb3dsaW5lc0dRJW5vbmVGJy8lLGNvbHVtbmxpbmVzR0ZcdC8lJmZyYW1lR0ZcdC8lLWZyYW1lc3BhY2luZ0dRLDAuNGVtfjAuNWV4RicvJSplcXVhbHJvd3NHRj0vJS1lcXVhbGNvbHVtbnNHRj0vJS1kaXNwbGF5c3R5bGVHRj0vJSVzaWRlR1EmcmlnaHRGJy8lMG1pbmxhYmVsc3BhY2luZ0dGaXNGOS9JK21zZW1hbnRpY3NHRiRRJ01hdHJpeEYnLyUlb3BlbkdRJyZsc3FiO0YnLyUmY2xvc2VHUScmcnNxYjtGJ0ZfdUY5LUY2Ni1RJyZwbHVzO0YnRjlGO0Y+RkBGQkZERkZGSC9GS1EsMC4yMjIyMjIyZW1GJy9GTkZcdi1GZ242KC1GX3A2Ni1GYnA2Ji1GZXA2KC1GIzYkLUY2Ni1RKiZ1bWludXMwO0YnRjlGO0Y+RkBGQkZERkZGSEZbdkZddi1GIzYnLUYsNiVRI0MxRidGL0YyRlRGaW5GVEZfckZfcUZicUZkcUZmcUZpcUZfcUZicUZkcS1GYnA2Ji1GZXA2KC1GIzYnRl13RlRGaW5GVEZncEZfcUZicUZkcUZmcUZpcUZfcUZicUZkcUZkckZnckZpckZbc0Zdc0Zfc0Zic0Zkc0Znc0Zqc0ZddEZfdEZhdEZkdEZmdEZodEZqdEZddUY5Rl91RmJ1RmV1Rl91

Now for the private solution: 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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

NyQvKiYtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2I0kidEdGKiIiIiwmKiYtSSRjb3NHRidGK0YtSSNVMkdGKkYtRi0qJi1JJHNpbkdGJ0YrRi1JI1UxR0YqRi0hIiJGLSIiIS8qJkYlRi0sJiomRjBGLUY2Ri1GLSomRjRGLUYyRi1GLUYtKiZGJUYtRjBGNw==

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

PCUvSSNVMUc2IiIiIi9JI1UyR0YlKiYtSSRzaW5HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiU2I0kidEdGJUYmLUkkY29zR0YsRi8hIiIvRjBGMA==

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEjVTFGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GM1Enbm9ybWFsRic=

SSNVMUc2Ig==

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

SSJ0RzYi

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEjVTJGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GM1Enbm9ybWFsRic=

SSNVMkc2Ig==

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LCQtSSNsbkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjLUkkY29zR0YlNiNJInRHRighIiI=

JSFH 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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

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

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= After finding the private solution we add it to the homogeneous one:LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= 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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

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

Use our ICS: 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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

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

Thus, 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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder 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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

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

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=JSFH

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

For LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEidEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RLyZHcmVhdGVyRXF1YWw7RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkwtSSNtbkdGJDYkUSIwRidGOUY5 Given the next equation system: 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiWEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRInRGJ0YvRjIvRjNRJ25vcm1hbEYnRj1GPQ== is a solution for which 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 Find the value of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= for which the solution is bounded.

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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= Homogeneous equation: 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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder 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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LywqKiQpSSdsYW1iZGFHNiIiIiQiIiJGKSomIiIjRikpRiZGK0YpRilGJiEiIkYrRi0iIiE=

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEsZWlnZW52YWx1ZXNGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiQtRiM2Iy1GLDYlUSJBRidGL0YyL0YzUSdub3JtYWxGJw==

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

NiUhIiMiIiIhIiI=

Now that we found the Eigenvalue , we look for the suitable eigenvector:JSFH LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEtZWlnZW52ZWN0b3JzRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNiMtRiw2JVEiQUYnRi9GMi9GM1Enbm9ybWFsRictSSNtb0dGJDYtUSJ+RidGPS8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGRS8lKXN0cmV0Y2h5R0ZFLyUqc3ltbWV0cmljR0ZFLyUobGFyZ2VvcEdGRS8lLm1vdmFibGVsaW1pdHNHRkUvJSdhY2NlbnRHRkUvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZU

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

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 So the solution is: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= 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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJYR0YoZio2I0kidEdGKEYoNiRJKW9wZXJhdG9yR0YoSSZhcnJvd0dGKEYoLCgqKEkjQzFHRigiIiJJJ2VpZ2VuMUdGKEY3LUkkZXhwR0YlRi9GN0Y3KihJI0MyR0YoRjdJJ2VpZ2VuMkdGKEY3LUY6NiMsJEYwISIiRjdGNyooSSNDM0dGKEY3SSdlaWdlbjNHRihGNy1GOjYjLCQqJiIiI0Y3RjBGN0ZBRjdGN0YoRihGKDcjRi4=

Looking for LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiWEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYjLUkjbW5HRiQ2JFEiMEYnL0YzUSdub3JtYWxGJ0Y+

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

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

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVElZXZhbEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYoLUYsNiVRMkdlbmVyYXRlRXF1YXRpb25zRidGL0YyLUY2NiQtRiM2KC1GLDYlUShjb252ZXJ0RidGL0YyLUY2NiQtRiM2Ji1GLDYjUSFGJy1JKG1hY3Rpb25HRiQ2JS1JKm12ZXJiYXRpbUdGJDYjUWVvLSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HNiI2Iy9JJCVpZEc2IiI1dShRJHBWMlduVz1GJy8lK2FjdGlvbnR5cGVHUTttYXBsZXNvZnQuY29tOmxhYmVsKEwyMDI4KUYnLyUldmlld0dRJmxhYmVsRictSSNtb0dGJDYtUSIsRicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0YxLyUpc3RyZXRjaHlHRmpuLyUqc3ltbWV0cmljR0Zqbi8lKGxhcmdlb3BHRmpuLyUubW92YWJsZWxpbWl0c0dGam4vJSdhY2NlbnRHRmpuLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRiw2JVEnTWF0cml4RidGL0YyRmZuRlgtRjY2Ji1GIzYjLUYsNiVRImJGJ0YvRjJGZm4vJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRidGWC1GNjYmLUYjNictSSNtbkdGJDYkUSIxRidGZm5GWEZhcUZYLUYsNiVRImFGJ0YvRjJGZm4vRmhwUScmbGFuZztGJy9GW3FRJyZyYW5nO0YnRmZuRlhGZHAtRlk2LVEiPUYnRmZuRmhuL0Zcb0ZqbkZdb0Zfb0Zhb0Zjb0Zlby9GaG9RLDAuMjc3Nzc3OGVtRicvRltwRmFyRmFxRmZu

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

NyUvLCYqJiIiIyIiIkkjQzFHNiJGJ0YnSSNDM0dGKUYnRicvLCYqJiIiJEYnRihGJ0YnSSNDMkdGKSEiIkYnLywmRi1GJ0YvRidJImFHRik=

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

PCUvSSNDMUc2IiwmIyIiIiIiJ0YoKiZGJ0YoSSJhR0YlRihGKC9JI0MyR0YlLCYjRigiIiMhIiIqJkYvRihGK0YoRigvSSNDM0dGJSwmI0YwIiIkRigqJiNGKEY3RihGK0YoRjE=

JSFH Because the part with LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjQzFGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn is the only one that isn't bounded, we need LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjQzFGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn to be LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbW5HRiQ2JFEiMEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yv: 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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

L0kiYUc2IiEiIg==

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=