yIpyIr<K_Tn^T^;FZ;BR<`:rpH^IV[Ff[FN[If[Ff[K>\\IN\\Qn^Sv\\Of\\Qv_\\^^Vn^rF`uNaqF`pf`wfbRWcwFbNObon`GGgH_dUoe]_f]_aD_gn_gZWhRGf]weyYU@JB@kBXKDXkP`kFplixMUxmixoi::::::::yIj@K>@jZLZ=FZ\\b:]R:AR>=ryCpIR:ER:=R:=Z:>:;:@J;HJ<PJ=XJ>`J?hjyMfo@<?R:Ar:?B;AR;EB;CZ;fi;NZ=>Z>F\\?N\\[F`;oZMFd[wZ\\FhNN`;Hl[@[]NbkHrONdKAx^V`\\Oh<H[Dn\\Q>]SN]_n^a>_cN_nf`pv`rFatVb>gb@wbBGcDWdNgdPwdRGeTWf^gf`wfbGgdWhnghpwhrGitWj>hj@xjBHkDPlM`lOplQ@mSPm\\Xn^hn`xnbHodPpm`poppq@qsPq<Yr>ir@yrBIsDQtMatOqtQAuSQu[Qv]av_qvaAwcQwkQxmaxoqxqAysQyyaRyR:Hj:FZ;:<:;Z;N:C::PuBNZ;NZ>^Z=^ZAfZ>^:=b:im:Dj;@K<PjJ@M=DkZ@o=@prHKKDm:]JDDnBAtRAv>HlSDOrQKkDqbeJELLT@xL@yE\\kFn^a>?PMUX=:::::bZAF[E>:::::::g@DxkMHJsIYt;NUSr:=J;@k;@K:x]hAo\\@lOQ\\SVnnNtcG[ZXfCXnrnnMfcg>bCx`KOq\\huBOe:p^WqbdYjwW]wAw<fiNqgbx`Kqq:x^Wqbd]bQZw;qinYEbQr@KWqetw]xiwHZpJ]dhygqUfYr`OWAwIwWEbMrg]dh=wqYiKyQwVmoW]dh[nygZH[qIdt@nYqbtuaeu@O?iIbMrwtUJywq]nitW:mlqHtxXoiyX]xIxchNyixqXykl>jafUfIKAWMXdVXdfYt@tUwmM_GpthkOyeFinmA_<fIdtwqynYQbMjw]thsx_XxcV:wctiCOwRSwRSxNWqrdYjFanYuW:og]hh;ovKovJ_ZuMb`QDaQDA::ZYgiiFm:W\\hYno;::::Ij]`SZH;bNYEb::PoxLYYQ@::FD::^dX::::::JMdik<:::vgZ\\ttvKsvKc:BdZY<yQwxOS<BBmAGm;W<iA:ZG_x;VfoW]dh[xaxs_L:w:rQtkl>eWqbdMLyWZTkU@OW;:l=n_dyoxxlygq:>E>jo>aorLovFSd;iFGdyNLUogioFo@AmbGZ^XtCgn]GdMhs:fZchjc@]NagNevcXqeY>oURaEMiDEYubyUigtqYQy]P;TVwYmdqQtisnArmpqGdXUeYXdVPPjHMyqdtg]XQhqb<PP`QDypDhoypuG>phHeYqbtioxXlFQn;QhPIxeAc^wxdXucy`KAfsXgFanYywOwpqYnFisPV[PxhuIt`YiOyelfknAehNemiacaaIQigpvLGiN@eh:::\\xsqMoytFYnFQN;QxQIMiyrStWOaYDuslTk?TSxyVwpNyQyelVJav\\DBvKdtvFIklgHyX\\HXtFaNmAWj`uslvuIT`YYOuslt[P:lmaeqNUxbTxb<pVyP`YyKKyPpQ`s\\DbyX`XyKdtF`LXdVPXKQ`QIMyvtstIO`Mts]LRmoVUxw@WmsI_sZEc?Qr_ssmoEIvn`QdsalR;:FdZsVVNdTmdniDm?Qj_uqmpUIXpXIosaLxdVPf_sqmn=Hd\\liasqYnFyxdlM_m=:vcFqvQ`s\\HR:cDyOHIbE:NvI@`KAfs\\]LOucaFmGq\\EvlvJXbcCubShbvvSxwAkdLJDusl:l=Igs::kf^YfFQ^Xxfwp=HosqJI@PKAVsj]BOHv]\\Sn<Uh:BF]hsoBEi::cSXGv\\ErlbAVdmi;:X>c<::::::wZMWxG:j]BOR`E\\IY`XyK`tvYRV`tkUrvTJ[<kXpNJPlsqMnStQiSoUlKcxUCIIxT[rliWycIoud=SxZSxbUxwMWMeh\\cUFyFjovIcWUifuaIwotOATfir`YyKqvu_TAgt=WyiuyvyqeQTGPsSQQ^eyPiLAMViPPIxpXiNuiuEdX^uMJeRbTssxjBUrxdsH=WPINmiybUxwMw@QPIIpE=YoxTLHkM=YqtkOqN>XS`YyKKi@P<HrZMkvtUtmxOXSxxVwl=Egsqinmi[Q>n=uwNaY=@@_=I\\N;RjISisSLcD[svnghLSs?XrMUROervatd`t@DM^ePBmkdQPo`s`@LCIra\\tZat<^aMQ]XPiMQ]:P^dGkG@cOY[TtRoR[qVemS]CTucdCASGGdQoVmUhKUhMCh^WIcyHNWisUFokT<QVNwWbuxuMdhQV:gcxicxcxHMwGGEZIsqMdi=WqKtP_HZIsqJ?ENt=vIQQMlYdimXapU<O<hyrU^ipqGpunQ[^Yycy``AnWQmqNv:Hqx^yLygbx`mobtQZ^UtsclAVWGCy[x?Ss?AGmerQyuRMdi;VhAEmGiZ?ydYymoTMkIr[x?SSX?nSPuepL^tK:aumlv\\Y\\OwpkisUvYocWQb_SD_wVSitq]vuGdymstEdZEy]_sZTohQvGpYN<UhDuLLtselRuPkyrSLMftlfHyRhnYELOyXkArLTk?TsuLxbTxsPou=xwEoEDtZEqaasoYnFQ_^ihcqbvakqQn;Unaf\\YdFOWxcfU?Wj_uomFJ_fdIFuUTDsU>EdZEya_s_ShdEVhEwq;HGktOSSxcV@OSdwUTiUsaUKIfViPNHYOtTyMyEDx?QZ`NcYW`D@oY?jcWbkib?PhHqynHiO@ey`@;H?kdEDmrhNmQohlYI]ps]LRuxfDks@nCeSOyKGEOxeRPXKPRXeFOuW:KIfWgP\\mKmVOiUvQv:\\XRmOTMPmIS`etgaYKpbKAfsXG;Wl_hdiVbCgsQf=EyeaKX@vdhNj=Oihr<hViPPIPpdxw\\QjvET[aUn`n\\YlFWkLyg\\HrlwuSxBetG]hiQV;tqlt[Nwu@OyfVaP`yDaAMwiwX]cIPiTELsvVdwW=txgHYNHYOTTwGtZsUHT`etGqYnyw\\PRsxwF;n[_yqlvklNoiWnwo\\OVsx;xxepXPLLFYjG]l=YtNMTt]LkTkBUUJmlxPjiTrZuRGXqguY^iX\\XWudSwpPbHJuAo_eK^audYPH=sGhV@UYiXtr]TspL\\pwohrO@M@qRi]s_Qo^PQC]Q=EmXhJGAvsqMnstqc]Gx^yHQKdYmuPwrZOF[Qx^ovcGyX]hsqEn_suqfuyeHssqouLquKgvEwsSkTUyQYqWyErKmSgel;xPrtXimRFMT<tuqpuMhsqMO\\YrrMyDPTIxsVEwFXtfimN=p:Iq:yXZ@kvLUI=pqqVeXStDOXuP]PXV\\MMaQIMy:<tEIS]tq^poylkyOasp\\mP^yUe;dyAyZkdYIUiwZjNa?hqk`q;^f:ygA?]yfmAo`WHlUHimnyCqoi_sqYoPNyGhrqPysP`yhuhgboF^nVeQ`s?ppDijIgqnVcQgwoY_EGv^aubvdyNrWy[JatQNmeorFnl>QqoQutOkoX_LhtB`aDyelFos?qZixWFo>omoafQ^aDaAQwiwx^uuHErl?gMOUKoebYwNAgnQr_]fteeT?W]atb_T@ee@GwNeDNeX[eSCgbOEW??BoQHLCUe]TGOToqBW;G<oBboUaEHJcIBCu=[tIOdaSdRQWioDCMf`?wRMiNgS=?DjOfRSbx_x>OfIcWaWRK?r?eU@cic]iq[FnArwoenobUkesYvkckWqUnXL@er[\\VtMMiMcgIu^x^N>htgx`xx;qn=vpK?qDHgcyrDgcRQv;`ekga?q^dYbJP`cN`IntR`epgicv`HfmG>`aaaKwtaPe:^eKpbfYtm?uLq]b>\\wiuc`n\\Yls>]^`aoov:h]u`aKWqkpnVNykIcX@nJYZCIa]phhIZ`ImV@hs_nv^hnjhqR<tSTyWX]MLYJHukh]LRyjhiuMeOZ`wqqvRDuV@tVakHPn:@q\\iUA]lP@sB]ycAjkqmygm`nhVpxZp_CWqFPthGrpAoCyvqWfcqbAObrgacfjCy`gaana`>@vMyZqYeg@ZpiabOZ:GuX^x>XyNwf;XqvNdLPiJYZ=aftOd@hs=OlGvaixtw@ZunhB^xnng=I\\KWlIHn_x^_q]\\@jWVqwH_f?jmGdMxswf[SV^=XuT@Zs_gTv`^gicfkBqZKxcrfxZH[q_fINi:_uMGaai]s`\\=vuoTLqgDUR:_GccDJeiw;GAgSIUT:_UMyHDEWq_i`MfhiScOrYoD:[fggT]yXDoyncRvWVpCGu?HZCSEaXtOtQEVGiBOmBbyr^wC_=bCyQFEWqaY>]tftukdRytQspN:\\mULMq`y\\<MrpNM\\Qx]P;DnhuMDUJNavvot?@aiOr:`^IFr^huMYwKWjlym<IjNiibOZWwrk_nWacAVlnqn`AjafumIZGguGwsHatVQX;W<iUA;hYcu`mgcgvj]cwGg]Ul`hUHeqcXqspnaIOvIoZXXT@jNtq`TLoiRX@WG=jEQqGdtXDVAMu:TLoYMdLqF=t>XqbdUKqvFHxV<t>NfGhtXvwX_pSxsnFZhNwq^dSWnnFZhJdaoKILG=jEKRpwSTns<NCtpMUNIXo>dKqIPbeJp<k^IQNdRJDQwXxTqpAEunUogiR;XX;qw^MyDDmn@l\\Um\\UuSer`mjUmjPEL@ys\\ltwqynPTMhmkPuw`UouQIQsGqQNiNvXvsDPR\\qZHwywoNwxuwtuflGatL__SFc^NlCgamgcYAdhYnq_`Dp^YywAGmJog]hh<v^mI_jApcOvPWy_@jy^cOicNInHAiv>tAVedXe>Ihg^s`Yabwl;V\\hPg?hs_HnMi[gYpD_mvGnuitm^oSHnKnuTyrxnuFPhdfnOaxQAeLn`Knidy_D^p;nf`Yg\\Ofe?dbIrx?huw]KOetVfnFcpFon_s:OdJFp_yqIQcailNA`hV[hFi:Vv\\fp_yt^@_kXrgO\\\\FjnxaGakJgZcf]EylKPcQHyjhicYmcypqVhW_s`gmqIaRvso`bCNf:Fs^>VaCJaRxcfiIU?gRlsckYvluuteXVKhcWws;EdQr>[X:aFJarUiybuEKOYv]WLeR^IFNGDDeTX=BDSgJSf^GBVKc:uTxAYgKEpQu>oD>YW`?cuMBsuU=IUy_vsiyKOxUyXY;h;MtcsTPsxP?xfKdd[DaWeOSR:cirQVZ_xLEbeUw=yv:Ev^cx=[h\\AXaGSgcVkoS?YuscidguoadPOXCEFfquZ[XyQUc?fsahPgWFOxhESNOxs]fuusdkDlWXN]c?StnAvnYSUGUfqvliF^wut=rjOR\\ydqegKETkOUaoTdAWOCFI[X;CHUeH`UxNSfvOCoGEcCGQSVoCGIeHHOIqueTmDL_W__CoMbOgBc?gOer>cTm]TG;BJ?IboEfey:OF>_shSFwOWu]fOkFOUCwUhPCCeAhIex<?bIeVSaXIOc>]CMCtP=RtEhCKRd[w=wUTusJ?RK?bB;HI_EDOsKSEoqGHAyAOTJ]Vk;RKignaF;cutaTUYhLST:Ah<;r\\KUIkCGAUfsBOEFXWHXCgwOYD=V@yTdCWtIXNaTUAyD_x^=rh;Un]U>UuBefsafUuU]ODOAVtMDgyrRSD<[UJMi\\gsZkx:atRag<QeCuSyKy<]rrSVGeC_YwnghcQI^ItrMtgKus]FJKfheIyMCFIT=KXdOvZOHwCGjYin;VBQsqegCGBFyeHyv@GtKOTTSD]YWs;T>AuUIRbcyuUtD=F^_UIOURGhKast=dNywGeDbKRV[v:gEc=HAicBEwDuhXoeX[t;Aen;VBOsOkBs_T_sxFwXcGxqefheeceVpYxRoyn?RFKYTgC_AUmWtN[ElQYM;BfoxjMIJ]bF]YiEdCsx]=DqoEO;G?kSjoiX[XlAV^KHbCtBSVdMYMqx]evhcydEr:WbHgicEF=[cX=fkKe:[ShqRXSbHobJMRxIfqeBBsBZwEvMiMArikRIKc:]BjYHvwFg;FRAIIoEoEgGwB[AfKSXaIveAEJ]bfCE>IbLOEwMXt[HokIHMIlQYMOs:WuAcEnAbG_fXeytwIGQfmiDhMiNOWZIHNIrQ]TL?CRGF?=b?wH<sYKKr=AyNAyDmwXaUNeFBYFm[t:;BsIwRUdkYrJEhMOIFyBv=woysGYgPTpi]sAeVFUjZto=ytkEokQXhyM<=w_]vj<Ws]l:hsy`qtMtFTvw`tNiOFToF<TQykMUJ:]kELlAeNkxT`elphuhxnQeonlOU\\l:lrYilIdO?XXYLTd\\w^QQtUXCQM_ASAMs:\\KhPrH\\RT<lvYneMKpAPDlstqxadwZ\\vneU:=ljHYGHQA]owIoHuqsPV^HvlIpnQV:<n_ivx`\\sActadUqi:giAXx`PojYrWvqg@ZAwkNhic?dvOrYxpqIis>vpin;WxJaZ:_]o>^VGlLOo[OeOpZRgibOZ_neTfjVNkJx[KxkV?t]xZaHbYPt:X^EVrJyZFQ_W?qMomgQbHvnWfZ:vbItsgH^WR<gYdmDH]Dx[x?EQAXTG=j>UR:LkpDvxeQdmRSxnlen_URgUJnDJH@O?Isp\\kn=RnDJXdkRDoppVFpXZ@kpITF`tRTNVXJD@JIhmberCyPNIT:dZEx]Op_dNbsXnRNv:X^UqbTYlN>fgosr^\\;n\\c>hdgcapobvrX?_<^_N?l:yxL^oK_kmXd<P\\:WZ^^xOvpi_[tggcHiknvKplxnmNin_^\\NWfpo^ZNtg@cVFpuyruxmDoviq__GqNXqY>nWBweRGUylsHmkd^IBJuS;etDsd]idHcFUKFlUhPwYmqgFmeRys`Qxv]sa=YwKGJmy_OyIuVWacFUWomQ;TuhqQ=pJ>XNPTYSQVHDK_TMLmwNuVvhtnHPoXY[QVg@XmYjG<RbpuSPyNQuAeseqNb@mw=sylMdTW@xj>MTpXP=qYE\\sD@lc=xFqWk`OuItvQPgQn\\plcIJ?EPfYTgMp:qxlxONTp]`QZ]jX`N;tTfiw^pmj=S^yvntPmqPJYXmyVZpMoXjTmUXQWLTRZ<w>]VCQnaAjWXPrqX^LneTqBeo`Mk`hpWqV]YvCDkMym<INNio]PPuTWieoVeJAlXIQyK]TPXxdPUBQvl=VSMlbTjK@q;`t]UwNipMem\\YVUAWwIoFpS?AMaPVFPYLIjrTnN\\gN>rhO_hqkZPwpHqfIywi[NWoTPdmPgpOvpN_UQy]ya_dUMXACHVMhCwFZsHQsDYYx]owFshx]EOYGC_cTUe;kV\\GIM;wLOc=svvANhEwPHrSqo^pmsiwgMu\\YkCIyRqm]QTE@u^Pt`<MG]nKmn:`UdHm^us_qXZ<kolleYmvAj\\mUjXNmqXVXyVhT_UYmTWw]nhLX=]K<hOdppkiXoIqdPq^ttPulLIrpyNO`VF\\kjdv;]wkdrKHWminw\\T\\EWq=k=]pCAtklYM<RPxo]Lm_apHHUT\\pptyxXtMXpHhUdeML=o[MtgYn:LQc`Y>Hx<xY:dwTPLlAkgaVlXpVESK<SqXp@HyITyeDWOeXrEtxuSrDwEqsUPkBEuedSZTpcDtvDlDQp>eVWDQLUQTXqL=vL=QWhq_hsxTp^=tVAJmHJByjaTYE=Uqpxl@UV=M`ymhypqyJgdrE\\qL`NkPlHtj[djnYnCqTfEQ;lnIesU]YGdwCHMHmJFxV_PUFdt:ukFlNctlHtN>PMsdLfMVSErPUvAPK<<NH=PGXUGdQyMsF]NGAMeHTHLwRxrqtVPUTo`K^`s<tNKETg`SodnLpMoTmDhLdpPZ\\VfLoQHoTMN[ArD\\SdlLOhV?Pr=modajDawxdMdYpxytcqTaHVcItKLm^IlNLWAaPWljttKtEYTauaAO`\\JuuXX<qx\\LVtYJtqTULaaJiPNJXX=aKwEW;DLFako]x\\\\Lc\\WFtvx`uNEnyHqMdWIYYB\\ogaslakC]yc`UT`mflONAv`EyP]VqMXUIwJUoEylKpQdYJGuV;UyWheG`\\hpZGgfV_uIYinwsFQlq`v]XtcQeThfC@jSn^y^qhWvoxfCNcHgyHNonAwMQjFhe_atp`dhxZF_h]Tw;IoqHLmBIYfnaFR=E^yc<chr]g?]sjSbncrmQcnCGACU>]VtOnsDymtMDQJ>quGAs^XUHxT_hSnpM]dkFErMEWF]oA]pYXqAePZ@mZYXdeKHelCAs[EOjtkF@a;AnBnhaglyfj`VZjiqdgeupcyOeDVooW]TGjJ>jNomYhkUvZFFqANt_@rcA^?I^LwnqptEHjP>t:iwRfacAZZVxIipG_ppVao^[sHvxXdeib<ar_Fh<xqqOtK@lXVdlIop^liOcVGhsP`IfnQV[Jn[;VdBa`uphkak=Pdfa[lnZIfno>hxNdrnyNOr>AeTYhG@rkQtOxlqwaOXc<hqqI_^X^[GwOxrTOZ>YfHn`KpjN>tpNl>HhcYdlng;a]X`tRpuH>i[ou;H\\O>uXQob?i@y`HfpdbKIH@CwpEiiYrJ_HZ?ck=YhwExUIL<p^dYG`SDITqDor\\n_mRWtrA@OZ@Kj=kktpXqrUfbbybD?mZhf?Nipyy:N[FwgSVZaQeZ?`F>luOtN>ZJxuoWpIInc@ZAnv@yZkYitO]p?tZIn@ybeAbJfg]NjsneXQnV@b]nm@`nJ?emgkeQbZxZ[wZAnnbG\\D^iFxdNNaFvfXxaOPcJ_mV`idIgEqj:aw@wbo@ZPGbY`lVXZ:qanivWVbHFZciwH?_=omyN]J@o^>aWniqQt:@^DN`BYiaa\\[xh[xZ<PaN_nV>fooeYPcN>Zai]IVb:?\\Z@senkugic?]<>ntyhcHpohtII]_@grifVVxKPKCF]Gx@kwtQdDSfuIHUaTnie?STWyReqcU[d=CiAwE_=B>ABXIrA[cs_VGCXZYt:EgLwCuSEHHxtQTthWNlpw<W<LJxxs[tnKLQjtsXexepnWAVIDhAnwRYiD@ZGxt`ysgH_VfaE?_uynAnkcnhmw^NFZ@valOiHNiLO^lAbcYjLgjwIsAAoGa^dWcHxvT@ZFx_Bqi\\`j:>q]ykDGl:G`pPi^GdRV]yAZ=>bBQjvikIHdDWkmqkmOd]yxaWjCa\\B@n@far>nBFxla[kWl<w_DAunqsdObjVkMQlI_\\]wx^gxCqrbF\\SveOHbnqsbVulIZdQgSwbFqbx>w<B?GRJaHTMHbOBu_CkWBqad\\;IayMyQUK\\TPDmWLXb=ng]V]IXw=o;DL@iujUN^htUhloXT\\mmjUxaXl\\tkDel_TjHepm<QGTowiRGUXQuLmiUVUp^ESmlmUQtjDOqlyRiMRMyJxpnPOgymFEqWPSIUObLtppk@xn:=vDPjDAT:ImYtl[UlPqXHxQg`WidWHIsUIml]wA]paMkp@VlmSwMOFYvX\\tgqX?MpBpxveQu<TAHQiQtgMYu=tNqMnEjPLUB@M?YSF<v]Yx^LuktW:ILgeM?UMjmrCMyNAM@uSYMy:tSd=JZmUcppxiMd\\sH\\m\\al=tSnDjPlUmmrkhXc<p:HwCiXchwghs>UWXPQXxsZdnk]nSUtgLjIhPBMQ<TlypsbLwqdKmEPOyQtXrsQmKeThaybpLXmkSlJ@TqDlRBvZ_PhNimHAm@_r_Fg_hidHrTGgTOs`ajUviDFmiqgWovp_l`ifB^yHfbn^k`WmpPo\\ApSifL@f<xbgfvGHofiacVk^FlCqv]NpyHaZGiaiovFjTQm@GgBPmPIiN^`cV^`fv<QpV`]ayn]Id_frNi^Oq_^NbAqv[FqyVdFors^]V^vwOgS_lBOjoww=yk=wbJW_mXaJ^s>AphIc`NmlGc^NlIWhHww@G_VqZDH`Hwro@]\\@VgxAcWqEd=KdqkHCgudoTc?VtYI>mt<mi\\YtBGWFwIGKUlqGOAFpafxorg?yQkYx=VYarImvy;rtaT>av>?CH_CKESNsIC]vaOheMug[bcQG;WfB=F?wV`cyuofbIbL]W;eHkKbOmb<MSH;x:UGBcSseHEIEZIDI_SLCIlmTOwut_YVyfmqfTiDNwwXuYJef>ychkFIiy:ixAWHdufJ[iaWuA[YkyrUswByBTyemQVZgerkccovTEHh]vskRVkfM_xV;h:evUWGCaxuAC`QdwMVFEYuYV?ATuiV`YhpGumYu`EWFYiUMfsGyReyV;TmqU_OfuGYpIYL_bqKcK_YnyF`Wvjqho;Gi]cTitIKicIt^GwPEILcxXet<QUXWisqXhMftSxMTOPEw\\Yt\\LXZYM``QLTyuymjeNj=OYMU=]W]AU^aO^ay:uYyPweppYTXutL\\IUI`nXpNV@lq=NfxrplORaUCUWjeN:AS@EMweR>el:EWH]M]aLAXwUPqg\\MqAtg\\X^XLqhoILvTis;<tuiTwqLiajTmQpxPWqmwyR]itiioGiM]Qny=JexWSXW\\PLt@PV\\wRik;mR;^tv_xaFxd@dZqojW`ThqQVZoGe^Ftpqvgh^Q_kkodJdDkTn_SwUhLugTeSdgDc?wNSdTmutUDI_X@QBOUuNicXMV[]C>[SlKwcofqsX[sFfCCSsucerHORmiHV_R:yx^aTHksdAGUuCHcHdAWBCCoSSvCxakYtEW]gHOWr[;coCBZeBBiY?yEKqFYYt:wBN]yuOTaITEmbgYC=MWPIhSKurgHcWVGkhnKhWGxZCsx]DggidoIqywSah_EBHme]YBn_eTIiEkDqGYbMToKWbsXTcHgsHY_w>MivyFvGwpwXjiuDCSP=sXixHYVsod@;b;qDZoeocedOdMSXuGXrMUnOFVOiUSdwgYfSw_YBZWT:OrMycnMGqwXTiRNSY`MVAKvN]Fxchx?wZAglYDvevkGyIGXhmEAOcuIXHEXMOd^_TsETR[GwIWLcXaeX]QYTcuXedBgrtihDmXGOcqoHQsDC[siWXy_CFQSa_yUgS<ErferICX;QTSGYyoW<sscwrPEEhOG]OwQcTSgdaiR^oWUsXtIcaOhlYdDIeBSDSUvc=GdyEgcCm[IuYrxIFyQc?yqpIoidnoaJrxNgDK[yqRavs\\LsEVjQJqaq]QYLQxbpOGIoKQrDEtgiUUxUTMqcYYLYliaPMisxMM;HNHyitXgUHlFYgJX`UqZWhvWGZYXppP_]Od^hlKinVoaL^ls`FUHtYYUWiUSRFsV^yX?;gg=yB_CQkCLIVv]Ceug?ShPIhIEgXOBDybDoVbKgtabQKdQGtDkrxMFpObneDQiT`UxJMRuGgpge\\eSceHGKIhEf@AetGR;ATyigUkuTIukKwBOvj?vDQfcEHgseXegMoXWoyamvOaYduwOMwdoI_uUqmtfuRucwcKBxICxkdRwFN]bvsbxWN;UysMnWqsAtUO\\oqLl?mKtYTGpVY`O?UU?tLITw?euUDpd<Px@vDAOIUj`LnqLuZUVuIlxIv\\qnMevU=JSlSC`mKpusXwOQXitv;=TuXvmuNPmWUHmZApNYwpxnJEuqLMaitJxMrIJyMK;uxZ=VITqADPddrmIpsUxM\\v=uQWHWUuvGhPZeVo`QOyxkxolDrqXsFqsJdJd<pOYTmlKdmP?lkmuR]AUC`NJtp?xJqPWwdWvUjgUL>tmTQTWdTaxvslJadJdXOWXq>YqGTve@jXqMo\\ppdKj`OR]Soep_hprhlqqWsQqMTtOXldPWG`X@=mHTUoyq=qRyUXOQt\\LjmTr[eNXmTUul_iQMewlEmm@pfUn]XXcity=johwAaytppMUu\\@pNEsmDYjyrrPypIoGpjZtQrmOwUpRqufdPAYUHPkUdVqaWQYUeEUHlJJqMFMOQATRQoVqmXhxClxceTqLQVxx_lkqyJ:psYeVHip^hM`HoZIoOuJxhmvikJlqb=vvYvoUO\\@k\\XjFmQkQmpIs^]TtXsgTVClkldqwUW]PTuXyUypOxKDEKBtJ:QOdiT_MuV<YFyoqhlXDKTxod@uAaLHtjkMwrAOQqTp`jhmPjyK[hLGtwOhR[MN?\\MqaPmEWsuML<niOm>PwoXh_hy?oaUW`AgwJIm>Ihai[MQ^f@s_pckqrH>cGQfSablyu@geSOboAsiYeZiglwkrqfqXjgWgsxvQak]n`[HpSVZXNfly[FF?AE@Ci]cdxOF^GuCQivoVVUTe;FVacvyfLAG>cVpqHu_fVOHQeepKtIKfdaiqkT?uypuBjCYAGwaWG:gfGAyAmexwBqgd?qcWWWPgH_EuRmxj;UTehbGwwGEo_T\\]tSYV^]XdEI<qYiYrBQYPoFG=GS_v;ySDUiP=YV_IasyiOhhafhmGsODIUWkWf\\mhUYB`KD<GBPoIOysTaX?Kd>aRw_dDUxxQVIECjkSTWXnkYwuyDkfkKbxiXGode_cfuCIgb;eRRYxFiTu[Ul[E;ICHsBoSHb;SjKXAYRfSWi=SOYwCATlqX_UG`GVwKupWGHeRnIRWgUXehRAwGeBnOeciipys\\eVdGg^GHqkfumB[kfmgsa_x\\kdpmtR;XjGdsaWGMhoUL[IXp\\Obpqy`vTpsf\\uPuJHqK>TwGIofyjohwdPSXDTZXlH@MedNlPx]<qytjDyVh@lRDSWtr\\LQGLQ[iptlQlQraIx\\dLHixbHPRdV<qxH`sX<VSQU;hmFuMuhK:ewaTJKiqXAm=yWYxUtxY:PrldPclOhtoWlt`TL:<JuO[fo\\qO\\<WxDWmK^\\YXhKG_NOe]Pin?pGh^`nwGylvXtBwayvghymjqngpuVXZG>yBaxd?rKPk[V^TPgENjupqHar]_aD>kNYo_^hgwdG^j]p_SwpmoiSfohpnbWf[Gl@pv^Xgg``ufkaIa;IyGvfbotLik>OsZqnQO[GV`N?bThl<qkUHjvAroVhc@_^`sj?udg`dPcwn\\@ylTapIa_hXxCqy[yy:N[Cxofv\\FfkHyitXgC^[LqlRGnivpsbCGeOQBCSRhMYkEcHqg_KIravgaShpPOxn;LmmHL?]uOyP<DpoDS_YT:EnCaOwMo@pkCiLrPVOQYrawKmssES:ptMUlKIQ;MRDdXNuMLEoh\\WPXn_mQHYY=DT=MNGamF<MZndQgbAqedgco^sM_qS?r]GlRGtf`vgY^qh]<hkRFo=WfO?r;vZo@eoxpm^qbWaai`VVomA\\soReRVyFuoDWaxsWr>OuAauyhXQaR_dvmqS>`m^Qntdl^tMGutoUXlURJlYMitXlXCtnbQv^uPHUQPAttQTSyY:<SCIjnmOteT_EoSqM`TP?pSGlobmwfQO[AUoyn_INQXxd<JIDVMiJTalYDvUxkPUkbYSFIkaam`MQIQN=eXB\\wjIPXUQcTN]LKteYeuqxumf=nUMLjQYKXtrmjKqx^\\J]ElahSoaQPaPDlMltQK`uhTpLup=IU@ljMXNGuytqrJeVlukXelgYnqxPqDshAm:trbARGqVcQXChWNIPEuo@TlSmMSMM^\\RaMKr<jqio`eViaXmAO@mkpAofYk@UwFmsqmYdEwxht`tyy=JyemyDVSqlPtLqTLgAWptOlMW`<q>PkaelDIlVeXcDvjePMEXiUrmeWtxwqyY:HxMmYO@lsXpLDV]XrqmS@lRedkG`rCDQ[`o]`K;ltfhw`QMlulbEUOts^PKLQPcdYHQuJQRlupGYQUPxGun>]sW<mr@vGpjchQ^ekddRBDqxPNMLu:ypZtYt=Py]UPiYLxWNEkyPrnDNLmShaot<UdIt=qr\\hUUTmCurVLyOiRm@s]Yxh\\nRYtVaTBHnmlpqtL=xQVyUiYLJuTstYwioFmncyuIDVJ=iOXdePsfypkVr[gadPhM`pK_otqjWH\\Ua\\GG^W>xNniox[pinup]g?sX^rM>ekibqGhFIcohiGcpyhBCIb]Uu]txuhmYfweRcmfbiIfcc\\OG<IccETUktc]fTGeUmbkIDfWgPWhoQuhkHNGxlGv@aWtuT_AYkUEUEE_sE\\;r<QYugdsmYYAi_cDrOipgFdQxPAtDuSsAI\\[Fv_cXObZQTyosBgGDwFMiuBABywY?pqxpLdUr^hSoxL?HRKeRMERmIxG]Qvmx`@qsaMxXlLQYwLOcPQIquButthKuxY:XSsXJNQVThvqxLh]MYLRkdt@uMsikrPQWHT]tNDXpPeMo]w[MKclXltJYhXu@tsYvrDVFdoaUsElnBYbKNrlAsKnZCgwN_kGA]VQh:ooHhrZ`pLYmJWa_glA@sxhmsXoFpohHhOEDYT^WiOgfpWXkIdpCImIfb=r^etQLUHXNp@Qo]NOeoFAK_DWClV`IJHlSseP?qLhitXEJOesDalaLotdVAuK;enLiWmhthiWVymVelydJ;eWkUmD=Wrqr[yjadQ;in`Tn<pRMUum`ovDo;QmHlTpHU_lVLMpuitAYMgamoiy?Xl_DQdAUFmwKQQDlvrTO^IkZXWSXNwqTeDlNmkPmjZQtpiN^dqc@ky@NhdXoxQWmRoxoBlSo]jYqW@yQgxo@xRtaWFxrWyksELKYWaQqv@MxelKMyIHXdHLVlJ?eOb\\LZaTFHRiYSDLU<Ak\\=jRhssaTpmtLmuEEP@@ju]StyOyqu_HPkXYs<XHdlxUXpyMwQyNIqttjI]kTIU]=yVpMupyapT:PL\\ASfHNuiPjlM`IqpuxxhxOxPLlSEYLLtStMRCEQfDswdSRXnsxRgHNHTJf\\LHDs<hphqY;UvrtPplQker>DQvMLGIt<lugAXmpR;IM:mt[=jseOSio?pSuHPJ^c:_`AxpH_l>yfUXkafuE@ZypwsPvd@lmVtOFQArLCGqeF[?buSDRSVVqXeAUu;CaWvV_XccVZMrKkBH;cZYRicu>;GocUkevIgHDWXIIXNkT:aePoYAWXpoVqWvJSRZYyOUTpaVG=gQaBjcYAIReyt\\SsKDYOYWExWmpUrLv<YlOLyO=QUYN:PjPuxjDPdyQNXVgpsxxNIPW<\\qpavtaTdEoFDMdivb<lNUSBav@<MdURFeQcINllNOTMHLwPuWFYNDLV\\^_?VfeioUhnXOsYpsp@jsirmOy=YZqGaHqhjya;FeOOuAqfGNehgeKpmKy]kxbr>wCWdgysOfZ^xq`wqGxy:fjxYdUo`PovgG\\]pwCgfxih;@h^H^wF]s?ox_vwqcRpiyAZFVvPy^YO[i?l;fxfh[pwvHatYFgDYbly[ixiPqpfpop?gyAZfOh;F[KhxgQy\\IqsvpBWwRfv^qgdOouhpM^_TnxkglaWtiOdcGfkFbfwrfHlhwaCh`p^jpwuFoqexdoAqvVqu?^]hj<wqDYpnWpmpdHWnjgrbFgKWnDoyxQ\\Lv`oq_nGgyAZZyatA\\hhd\\HipxrRf^SAjRnomXdaibYpy=vy:FnDfv>hkK^uVvnt`mTNmhXtFwt?n[v_`]Xiy?ceQ^@@c[AbH?`ZpiN@mGXp:aZtwdhvg`GfIhpDWhRIqghgG^nuwdlNlHowC^xgHnxfgfFiRakt^nMPdFWtdVd^VfX`jNOaXp[Kx_jamIhyBfd:@cYn_yo]@HnNQrWp]VgmsXuIygvP_d`if^kyFx]OwlwhS>[;^]agoo?lAQqnFuIQc^qwOFl@?iSfxBqo@AtcNxsPujwaTnsA@rnovynrx?kFIxWvsGi\\ZXydx`qxtqHwRGh<wtQGchO`JOxYQcLqtHhhCwxF`h=yi:ib=On<PqF`oIF^rg`Jvxdp`HQmyAZtPr@G`dqgAOZ@Gj[?Z:NaLoK[u=yWV_DYSWYqBocEbSvYUWAYFmQCd]i[KVo=fJAbKAH;itFeuUCIQMx?EEIuuHwU_chD_GhOcVaCogdGswduYbkh>;vsiwY[ieoutQdaGWPgcdkCWKuUGfsEHmgVusV:mgTWgb]CdstwwrRyuF_DtIe@KXq[FYaWNOYHudKAynShUyu>]TOwX<qFrAylwdbwygECncTxadFwV]oDkCsb_R:yfPUHvYixMglIeWWY_YGgmCHmIPgUIURWUs]orP_WaUi`QHUkHQKDaMWAQYaavHie=KBsquoIEUMBEYflAYbWWJcpxYWGYxPMtCYnQ=RyDW@ax_IPyDymaVbATftyelS:xWaxY:DwVaUshwkxNXYxDPTxhWpMYxmk:uJy`s\\EOUAjTikrlSHPYLqYoUujXKp=UhhvNYumppHLu?HKAdQEYyOMjmhlQ<XdqyJuRF@prIwRMt=\\YhDkKUuYdooYN?=m@tr;tjY]TPqRclwglWq@Ns]nUtqXhXplYJUjWLStAPgWwcqpEnfqAaAqc<HphxoMvqhVmG`fuHmTi`BipxH`qPysxq=gda@kAYa[PwIvvJ?l>?xOXwuh\\k@oUSN_CRYgVqcOsee[UMubTcGVkX`Iwf;cnCHLKrKoHs_iceg\\MBZEuB?Sh_GFaEyuTiOYouGy[X^WPqyJg<qPqPMpNppuaxWKux@qQKMnZ=J^`LZDKQIv[yl[hXbhRfYp[At[eyBTO?`SD\\NH]Mo=jqqOO`nOIT^MShpoL]ubIyNUnjYRwDl^umgPq=lY?uQ<HR`yntIR;QjV<K`\\x_ERdLxcQK?uMK@PWeWY\\Qc\\nxymLIP[hspmnHUQ^YOtqtPtQZdw>YXqUn:tyyTwGItgaYwMpbIxqmkQqkoDShux]HupqQ<]lF]TkiJVQtKPxMpjhlMNLPlXviuoMQwo\\sDYmKHltxKaeuptjrpYGuPMILR`T<dY?eUSXyP\\w[=MJQwoXvn^a=?augp;x[CQZxyni`xfXtKVyO^qAao_xseIdX?clYakFsLpdIatPiqvq]HWl^oZr>vwAcaIyPgcXO`MXaNgyWPgnwdI_tEYtCieBWfMayyeDuH^UUBaHxmwy;rtgT;mW>OIVmwxIwZudD=WWkEJ;SdOh^Qccavw]Ds?yrQhPQDmwfGqDTWcEKxrWuKiHfsyt]VxIgakcxcw]aVQWRhIs^EU=oVwAEiYVRyI:iHeugEwxIgWEcxw]bKMwwADHMHeqfNMGteuNAvcEVUUSSmY>yxpmyGSBh;ivwc[iVKiFSUw<wrIGHgeWkgWSOFPIc\\ADaerOCbr[WnSvGMCBYYjEw;QpKmO\\pOhlLmTWN]XkqoCEMu`xa<skXnVqKZIlvIoixx]DLHuhDplZy[fYsGAn]qgfqyO_qxq\\s_lQvw]NwlwlYVhUi`uPfmNZFvfqAiwY_@VvBH[nQ^tXa:Ob@YaOv]b`ojxy:F[UQmyG]twiSPfKnyQX\\]?ofhgaoy<wlrfxYgy>ndGqqvWupgw=@etytvijhnaexy:>nD@eGHlSOewYvny][PuDoraor=Vl<Xikydp?[_Ad>yf]f\\@xpIp]OngW>a@YZKfbvPtwfyx`^agZsxvwNw[Xd_WfvncKFbsFoa`vhgj<yqQQyMi``H[]_Z=Go\\wi[vy:RdevYgh>]e_IxIhTkYjxMyRxrjyrYttYPTWxxhIlQproITI\\L`ASaIVPMpIHvXQnJ@MXEqQPOqhp[Hna@MQYMsmRUdsOMMYhOTmnVDo\\HpQ@qNqKtQptert`lXxxJQuAdy[`ti`YnLWvTRp`QedTwpjpqyNtuEhV]aoaOltotHGoowvEa`aAalGhdyZiOtnhoenoO_t^Ar<Ytog^n`bHP^Pi_kgycqpI>nNVsxg`EoiUqke^dUA]vXaRV^`qdH>ihyiwihIhmq@\\rPwRFZsatinh\\pblYlePjgwxtvb^Q\\Anuhoa<hoSOoAI]OpsOFb`g`RoosidAfbRNyqwndOtEhijnrHN]]OjwVo\\PhnXevNsNfq_hbMFmyHmaPlCW]iQsWyAoDiigvorIGDJyEAaEMaWgMdugTLGi]Ksoqim=bCeWw=uSEc^cwO]CG]FaEf=MRH?YhSWiyV`Qid_GPuw>EIpGxnydlqg^aswsDSgTjsb=[sTyF^kFsWVOOycoFt]vj?Gfmc;iWcWCTAWmEhngYOoTEkt]wxGsrAih`EIcyQe\\WtQmd]o;UXHQy]enlyOqYMbUwdXy]tpg<YdtyWeSG\\ny=J[xoNqT>LwvhrtQk]\\nF@UaAq^uyt@TFtKoDKsHmgaTQIS^UuLqkutyYH_Dy]FitwF^qOw?yc<O_pQqyVtNwiMI^visP?tkgyhpuByi_Xh=?yFhxky]hAhsq\\oWwIp`bAbyPhOvr\\QiPid^P^dyxHnaBSMmdi?uoiI;yqaUNyUp@MkQ`SYdQCAmvEwLmtgQpkxmuXR<YkclNNhw:=Wc@SiysUYL:trNXTF`kXdmeaokYKt\\u:UqCutiMsxhpSLvutolDxgyTh]R;pq^qTVymrdp=ASB]oeYLwPvqUPP`QQhp?AkPLmXlPSesttLwQkp=xwQPw=NfdLA\\OIERWUlTQu:UmLuVkiMO@QfdSZTJoEqxxmPmPjLoPDK]POLYXcDOm`RDaWfEV@URkpiZyh^@qHH[Fx[jOjsVe<`kl?ZtidkVhjGk_ao^x_[GwJwrM@afFc^NxIg`hwdJir?goFWwlY^s?fmnZ;qrP^a=VdbGhUVmE>oIN^=>q;ftu`tTOr?^t^WZJy]LQoR_uIi[mA[__fUva@Hp`hlVycMg\\vA_NWeIPqF`s`YeZHd^ngA>hxflho`MqlQYs@H[FgmVHsHpiOPb^QasphCyZw`b^hhMGyJWm@hmEflt>enPmpOLuhDqs]SygSFhWBrmY:og]msIStoiCCYt>ccUEWQWD<wCgESw?HlWVSUEt[scus;EWGWG=_yfqc__UXCSwUwreSC=gsetjWx\\iy[CdycTZIhIAGo_DqGtB[VUmcKmrQEwGeBIkc_gSZKF;sUlyvQOdG_CqMgq[FwIG^_eV]c]cw`Qd=IR??dGseFmg^EYv;HNyCQghYWWLehuYvbAiv;bOYh[=SmuwjoEhytnyqQ]oe]wpDnlYrvhovIWlPS[IS?eQ]imcEU:\\th]YkAS[DSD@Q@MWeUQspwV=VgIrOysnyx`<uRESumOIEl=lJfuYiPyLYQvTUNqLp\\YO<m]iyYqYwLjPpWlUqrpQCMW:<VjxsaXVeAe;ixIa`ZXZMynlGgGG^:Xvg`a^GZAIa^HdIiqu^uogx^X`ywbrXy<g`v`vuX^sGjChyd^oQYt?ihpGlfgdso[H_uMpkd^kI^^LF[]NhHPaK>cE?c>QlCw^^Nmi>ngHok`^gq^:`[lpwJxplW`PQpOWiMPk:VZHpnYpkxWfYhn`nwLodH>c:qn?I_<`hOHa^?^Mys[`y?@bVqmrvnPF_Wn`dPokiblwqp>`yVZOGn^VvonaVxudGtFxfQ@dNgyAOccHZvvd<?``_kw?aeHcOGf]Nkp`l;N_NWSUcLcG=cvnoDaMecCGSCeXaH@cd[kFoCXGGbQmWYMTZMupqImyUaeU@mx@yGbUhViuZ;s=YyGOdlIGk]VoADLWdKwhawWQsvJIcuOVjcXuSv?WEb?B]iE=YfPMY>?dkQf];brKwT[TXgwt_ss_EAsbXorDQgkQYbkdDsV_SewEu<mV^cu\\QDTWXJmCUquSyre_idoEI?RY=tamBL=FyOYDYx_mBU[vXGegcyHYeCEXPIVmICmueTKsgicmUXfgVcEbLwsbeGsuXTQBwOBxuyIoYoYHjsUiGTpMxuAVQwCemgnkfa?dfoVsEwHEU[oYU;UMUbp_G<qIpgshubMGw=gIIsy]=yy;BnEfViC:miQmheyGNmIgMtMAugyI:?T?SH@SDu]g;eT;GVPWV;erIOf\\AxTEf`GDmpn?EV@=wAdu>tMMyt\\DK[huKhk\\`NC<vBElxUtS<R=XQ?LpuUSEhX`ivOHPKqK\\yY:dnhW_cpvdXdPHkHnr:VZy^eNQ]Zxy:FkvFuoyewA[NohqNrsamdhlNOwdfeNwi>qmVwx]vy:NbNfcuaoLQjd_pQGmCasB?bmnrfQvuX]w_oBxbDqhZytW>asyZPQqbAp[_cy_hn?o[@xWF]IHxFhklw`H@ym@ZLgbWysIOc_xnDA^NIt]QsA@];i`JQgj^ppynao_Vhjwfy?WhDIlSx\\YV_cXyfxiK`o_Xytxlug]Kvy:Fg=QhgPvowZcWwlypVwv=Hc@`c<HZA>noqnS?smpbd@choacQwdNv:Ac[qjXAvDHwGg`mGskGgSQnu^hWA_lISsX>sds]gDsdT_EUSU;mYJSYVyI:iXeQVyGt<KeqwXlcHq]bZAhboIroyoUCEUFkSTcufhCEAiXImtvwGPwfcWra[w\\UWIUrAWrbgScCS[_edCgYecA;wI?YR_uNGiAAESyReWETgvQEUZID=kTSaGogd?;W`yWhkUlICmWMA]PPqTDXR:IsDan^QYM<YsUR;=XA]oU=LIQwSIvrxlMXwXYPn=o]QkWaqcUVQYXVlJShLeho?ijjtUkQQkdmp`mY<SQQRLTsmesnqN_avRPPBaOfpNXXTKAxAHQIQS]qNFIXPtJwlReusN]t^XQJ<vgupYAQwXXhiydiK^pjp]VfXRqYWEYjXIqUqxmTt]aTFpYaHrqDxlhWFaNcmpl@O;iRTatuaXxitRTrfETBQQeLxeXoLLusdWTijDIxJmxxPnsDoJYNnTX<DMIMUdXyMlVPHmd<YqirhqKHDq><oEXxXxjL]M@Axl`xfQrdHWltR^TsNpodXV[@q`apPHuQev[iLqyMg`X@MSUmmFIWDQl_QlNuoT@QJ@NaeqmQtb@yGdt_QJWEyKDo`qxIuyTaPhtwg`PRmSVtscXYbHQTiYwejlulMUqBYxDYuSlsxqnkTontTddQfdKQxjgyN\\TrgUNcePBdLsYKmqVthWD@TOlsp`yCewSMy_TM?uwwDxGMXO\\N@eyd\\WqpTQ]KXtNbxY:PQRujyptnhkZ\\LHQsViX_QOC<W;EX[aks<l=`PpyM<QwVLuVIp:UTc\\Ja\\ntukTuUUmxiMMjljtuodujKQmXurIMlZXu^]LJ<LoIM]]PNETeIT[uNLepLIjCISOPRB=XAIqhpj?MUUASh@TlyRFeayF`<a]vgrr@riieO^jygfm@k=Px]?luodnw_Dah`_ihPoppx`V^?nfIX]mojRFwMWeZXxP@e;QuSAsnqnKHpv`t^Vnj_dXF`Pg_]F\\u@a^^rAg`uPiXNgAW_fpqeYUurG]Rx;eOGG]SbG[uZ?HhKxUADPit]swh]Glev\\IetaUQuBe?u@kdbsEu;EF]En?YfAWowf[=EcAgAKpd_rQ^o[AhL`yRYZ[xwLW]Nxk<Wcnwau>sqwkZWhxi\\u_dAxsl`^Ipu=?sXVoXIq`igDXhOyiTorcorGo_apiSnro@]Hyia_x_>p;poipbYIy]WxlW`nioWid=Gw[?j<IyD@bniayfoM?tZH`UIyrIyVPlxXvrhowNbjNuFgvl^d[yjk`ZQWbGHn]WsaxdYP\\`XyVXmFvc;fwrPZewonPbmY^Z?jV@`xflBQsmN]kAtQydaY]WG]hY]CHe<n[unm?fccVi@@uTqgRWmhnpjfhUHnhFnnvnNXdjXfJyiMHYIB^;yaUSvYDPwwn]U?kgumeeOG@[fjMWfGdIWTKUdHOuLmf`?YFaubYsSYDS_egQYEAX:sRMIhNquNGEMSvWeRoqT;qT]CVY=yg=FPoWciWpYYA]ujUrlwiYeWG;SbMuBSdEGCPWfTedH?guqvEoHG=XycIBoRi[cmYVFmRjSvees\\=WmEYQQt<uuo=riYxtqd^WWq?CuyRrIBbWW\\qcjIy_KbvgTNaYHQr]eYESYJWgashYGYoaWoiTZsDo;H?EEuWtDEggGilGbyOYdYXtmDnkiMsWmwUxou>;xiOYvYV_KFeUtTwiJiuA[yAuI;iTJ;RlEEwoEjgxKsIMIwy;BZyI:=cLwGlSwfky][XeCwp=TV[ejcTqAvkiWGIwUEU;sGbIhAkbGMDCov\\CtgKTvCs^GX@YXqScFmSe_DEAy^cug]cdIIHKXeAUCCUVctcicG_v@Or^AcxiRAQsAwt^icvAVn]BJsyfuyT?epoipqujUBhCs>uvkSVyErVoHewVSUxnAFamw:[IHwY_eVPutDuB`KcLsFsCigETaebLqhuIHCeyy;rIOt^qt[UElkf=sR;kSAExLGGDgBfKcuyUasdiQVugs>=rwiw?yDdUgDGTvmCveUYuFSoyFWcleeg_hU?vAwhL=x;?YHyS_GUk[Rhyg\\sRSiUSwG_=ij?vMuRViDWkr<muoITdqrOOyTOjCiUneQFPXGLMhIPuasQ]qWMuvpyvyk:ExVaPyQOepkdHuhHRJESgExLXXpLPyPS^mO@Lvr`VXPWdTQNaSIYKiEVdaRd]_nQdHvhZoiOxli`uAnqbFaBw\\iWvYayuqdphmdFb_X[`HwNFeAIoyAZrnoP?vnpsM^^vhoMHyOidqOg`>aeVdFXoxVmtGlCXpBikIQt^HkTHeON\\a^_HwZo`hJ>bK`bbxZ;?rrFoOohj`^bvx:ynfQfIoxGpiay`fvfH^kjnb?GgcW\\igpEvmXpaC^x^ptZNxhXj;`rExm>ihdPimGyqfnIguxwiTNkIolHw^@GauOeK_oHPmBIfRqgHybtgv^Vyi`xovtSGZ`IanYwgaeEhy@yr[Pnx@wlfvhadxYqTPi:Wd]?sIy^y^cPajyWwNGlJx[:FhN_`jg[Jxvs`yeOcoVaQIjCy]?`h]HsdyfewukQyyhxByim^dnqfUQoYxxkwdo_yE^vyAZhXfsQm[pnZOgGomuxcOfsINvmnt>yopAavGko_`cviqveVxwaqu[XtUNsw`frN[wisdOgJHyKIkQwwZHwdY_\\^afNoaAyGW_uIasY`Cw_gHvLxk>ikvyfLHa^FlMYx^P[UNg;NxkAr\\ymhGovNgKWxAAa]NxephPabH_o^iZ@Nqssr_ULqCGIddMTsSWVWv:[CQgd;Cw`YUQqgIkbOGwhyuSaBdGtvuVHqsMARvOwF]RYKeC;tJYSJuyDOvdGyKQwZWU]Cts?WSQr;_yUWHXWrDce\\=HQIB;WVKYePSia]Sf=HHMiaOuRQSb?IdkSMMHUGX^ghc_G[MHH;HjwtVaTEavAwWjIdVOee=Wd=TUAbPkHfiURGv^[gxqUoKUgGE?MilQWsOfFeSLgTU?tSadvARgwuZOvdIgCqY\\CGukCdEwRCXV_YuGxDGeqkBucCtuxnmeSAxrKwwMg[ivSGeEsdmcSBUG\\mxJSrG?SdMdSicUYVsecc?VDyI:eHHMw^Wd^GTs[gikWe]rseGDwCmAh^IR\\eD`[EXUxNkF`CY]ixBIc;oWAWuP]EAgDf[cVIfEAhcuuD=rkmFI]ueWWMCTOIGSoU_CSsCViuTmEbN;DjUiLKWO=vm;Csctc=VkisZqdAmCG]ydOcmuvAYyXobd;hwQgGWXbSvMiIAAEtqUOqT[KEs]sgCrAWh^SI=MIycshSU@qGgCgykdewTTisMAc=SyPeieagJ?HT=xm?UmwyYOsrqurMWGSE[KtkArBWgTgxa;uwSUQ_GfAfZwhi?xaIWTUHX=Iq_GjIg^oShcyAAiOew<cYKqYCgV?iRsSSiIBfyI:ob^CviyGLaFugEX[d;mr_iGfyaEAZHxZTgdW_qKyTKHbABA;RD=I:EyiOBN?r]aDJuBqwI?kFjEe]EBI;uXofMKtkuxAWHaAWAGRIUXBQfy]yIODVsBR[yH@n:yVZhquITudMc@jximkhwVYtm<YMeJips`@LAumTiJdXVFhXbxUg\\tCIluHVSIQTxQ]LtNPXh]v;IUHPoxpJuyo:pYtElQyWQhWmyMiAjO]qFEMnHq\\mOaPW_tJ;utMeOlHsLenTEKdEt:EsB\\nnTVGaP@lrc]KdNm??ZL_t_OxgApIF]ai\\Hqc<yiKH\\Eyf]NZtxpOGfBqZ]@_s@S]cN=YXae?OWLIT_SuJ[bBer;Wg;KE_QCKOyOOCOCIOCGWGGfcyy;RweX`IwR]f?_GquHCwsPOsDEYlMiooW_;ddcBVErI;UAcBN;tuOTF]dOEDoMgDYf`GdYmWHQT:ojLURpQq\\CLaWdUVNQhAkVAQIgCU=iI_]BwCW>;sIOsEEYNOSTQH`_H@Mfjsr\\AeCgYsahKMfG;IrYus]f\\?xxStRCWUOyTaGS_D:;sAKgcmYFcivahv?GOAwGgUOsSOOTNEY\\GX@[v^_yIODIuHjKV^QX>IX?mXx]trkfoaflETHKR:gY?wcjGrayTeUEmuiA[hpoXU=u[au^GthmsLeS\\GtO;CfuRYygP_H:cy:OvTGTeeXJoi\\eHceh]otV[e^_FHGgIkUFSwUkwrsrOmdSSgg]u[qIr;EowiN;EyQva=eMox;kRckBDKe\\UgPeTaCYFiVH?IfeyDIcO_cKmWA]yPkIHGW_KHs;eA?VdEWEmBGOiLsVh?gmEdESvYMCEkckah`qEqAscib>YbwmR\\uyTEg^Whpsdu=v@[IdywfSsk?SqaCwSWQKBwqsIcgDeELGYnGWh?CH;iEqeGocOGYaEG<aCGki`AtytReMSo@u@et?YUbeJr@nHavuquAxOaMU<MKu`mOYoHYoq=mhQxOanIXLq<nMPK^iNrxtO`sdTshLvEAOAiPQ]MX\\nKuMKAsJyR<lUoHvYpq]LMadjwPRHLNnyWDIX@]viixBDUW<mFDtUXsDurE<qw@jZutYavdTXLXoiXyndX?ujkDvUXyaHnblXjtprQYAEpiinWeuY<MsIPXPsXhXudWaiLvDVZhUfTqXxQWPUTUk]mwr\\WtyM_`pHL^IGniQe?i^kHssNs]`qWpr^?`<>b;wvFNaDhsOa_TycYx]qnfeQe^a]_orN_xogwKGvJ`]g?gtyvop`iHqk^lZHy]HqBImFf_lhd_G]iyucycuyeDybXxwS^wCOvtxhqxpNxidHe;ny<FZov[pifaxuHh\\Zah]FlROqk>wHixR`dpHom>mLN\\RIjT^ckQto``wI_Whr?AsMwuDioRHfGHa;P\\mfu:GvchwX^elPjRviIvnLqoNVvWnkt?uThlnWlJQg[Y^g>\\_NiK`uwWgOHmLH_B?^<x[kGrh`oWfsXP\\IwvoAo_ipHPh=_bXxfjwi_X\\<pl[YbKNaQfvdQhyAZdOusHcS@bxA\\I_\\KI`KXpDv\\m_t;ntth`kPp]oy[pdH_uZO]S`g\\qc[?k>WrdxkaAdbxrc@tmQ[GHe^^kGXaG?h<Qw^Q\\mNry_hPIuWWnnOgDvmvXaYfnDFeHiv[^fbIbbQrV@au^l`oaeiuegf_Onrf^av^pG`ko\\BGy[HfUAobhpSfsXpm\\yaoQhjwrwvZo@eevpaik;_kwivWfycAZJ_dlvj?@qLWiJgxP?[CirWa]e?lZyro@kiOqkoutXq_vgmxb>>v@@djfidwe`^^wYtd@mUqwxH_[A]Ih_lI]I?sXipkNk<@tLipcodvOtSnlb>dIpubVvI`qe>mLPuSgvlIv?@jGnsuw[DOwD`p:hlrflHv[wFgbPbOhl:?ZjAvpoan@a`pwb^dNX\\DHuK@rC`\\k_ns?eRihAnwohbd`c\\Wt^IkQ?gJXxMxxwwqTvp\\fZr>rKvaMom@`la`m_`^Jgejo[yWbNgtOIk>`m^^nt`]]?ch@[d^ukaxofndPwG^`pFrK`jd?nOf]mwuo^q[_kFPphnieAvngaGP_>OleV_ZF]R^aqgxvYgyffU>ecAitpkdogQybqnn>_fNq\\W_oKnjLAciYwWO\\ag^kpjh?qfYrvIg]_kO>i:GZQHl<_m:XiqxZSijVgdOpkdWlmWlMH]bFdnNhbVy>Y\\Soi[vmnGpJFqJ_qKFsvYg[?tRNuj>ZAqsmFwXQl?vdFxZ:Wimoyx_pDO_D_sdhd_OcVGts>_Rapkap;Vj@nrkorG^htfmEq_T@dcfyZY]kytHhtcOfYg_NPnhqern]VxkeycRQpK^l>^fqV^QYjCGb_Nf_qeLGogq]ai]]njM@g@wvRNvthgxv`E_^HhbsQrKxkah`nFxZF\\l>nIYb@IaAfoSGh<xnOIqvibJNkDPpONilaoiI^k@`FPsVQ\\sWwgQm^ywh_[M@clI_hvr^nkWXgdP[;Nu:_^?XwsQdRvdfyn^Ib;`k]quN@va@qbytWX]r`]sgmjwmen]ywoyAZXOm`Fd`NZXfq?hh@a^uaa>nb@vc:GanftDX`l_d@_nQvvIPiYXfMVnuqbyxlVYhPY`G_[L`e@gnj_ncV^[hxdpn:GvQWgLxrMIahho]q]@?`l^fwViMYvGxZQhlXG\\UHjGWtTGiS^oWgbGiygQsTNblVui@mx^f>VxQ?]\\AaQi]@wiMVcLfgGXui_^gwvVYtjPEKEtsGVuU;KeVsbs=w:uickTbMFfKt:[xWUwlKb?ohnCCwQHAiUkQdB?RdIHEiEAWRLcSxWDk=cVaevYFbQYLETEUNdPs_`MtDLEIpDLrlAMmanDMJIaSQMO`mR`UQU<jneRpqK\\@QxIvLTNRpq`DnbeL]\\rdDqvlMyDNM=OcXQmLsrHmLYKFPYRTtYIswel?DOP]tXUnVPMcPW@XwrDmKAPatn\\LQ;MKlMUoXNpdrdlNHdT:xnMAna@si\\si\\oEIUuqQ=<xmLLyLUXmjIHNa@vV<x:lwuMTFHxFXLritVAr[loIYyrtLiMKyQM>yO`=pBxOy\\QVtTNUVLEjZequxY:tMtErTlOH\\l=DwSMqcYsRHWHlndymm<Wolo^TJI]NF<SMamXpyo`ssYSMYWwEPWUT@AmWXsKLYMayolS>YwHdmb\\lNpm\\XnCdmN\\ttIMTFmZfgZAogflIine_bO_]kFwGW[HPZbXvMHwA_]oi`bwvWau<ithNuUwts_\\nArAIfTYnMYrwPwBAkRYZF>chXjCYb<Pswxc[obWYne^pDfj>fmHIm\\yftNgUHu=>_^WuHXauqtofwmprFAsUxlih\\rxdkG]VFZBwdvfZRv]gXdCWomN_Ow^D_eJqhsffW`doI`YPsaPjfI];HiW?jWFsonppAhBobrY^`gAQtR=uSIIh_I>=y=]tqOVk]x]augqiKAgPCgV_f;mGaAd@gwH]WeqISMb@;GA=bnQVgQBY=IO;B:;i<sUOaVLKE]IiNetAcsgaceUiq_SQarBoXdQR[aTo]viASQoSJSSdcV]mVY;dd_ip;HsIV[MTA_UHCgrow`aXkcx[qghaIFwDt_SrEgSwB[GI`UGEIGU]RfUi^QsXqiIshV;SJkQKMkZ<VFLYHDOTAOsTvdDSSEUtEmpmL<xMXxSTXrYQtgdUL`WT]QwQo;YvZdr@aYkqSqEqNLmvUsmumMPNk`JNxQO@qWiKrTPkpMShPspOX`nqTy=AR``O]uXOdun@wWEpOpPlmJrimb\\VAyuQMWoIsRHRXyUP\\jahy]<tOUSUuU]`OamotQmOulHqMXukr<R>Ty;EYueTatn=HJrqTC@OfQxOeotxOXAV>=JwMw\\xRq`Lp=MYPUIDWvLK`=rt`vpUOHpQK]w^TWfTrGlWwLwXTjWxQWxsatrnxXe\\lC@QjHNAhWn@kXEPxxu@tx]umcXusyiTNrLappHqK_^Ya_=Vonw_fiawXw^hkghrBPpeajTYseYwROuw`uKHspa`YG_OnbfIhJXiIFbNgupq^PY]bPw:voSagxAe:QuFamFNiDVsJ?\\;^tLakK`jRn]n@vkVt`qanpj`Nts_aDnhm?rRn=aeawuRQt]wTYaCL?u=gIXeiCcf=syScXnaxeGCZuXI_sF;t?=IfwCLmghcvP?XqmbiGuU?GoGDDCg^kCuwTLudmKBS=XeugPqSOWVDEi]MD\\[TfCtcOfa_x@KdUaBSQU=CX^CIbmcBuV[qE@_ePoxp[wLQw[MuYMfRsD[oi`oFCSvPADsAx@iv`QXEOCSwYPQWLUbbyx`]UTuWH_SmMCIabqmv@?tfqt\\SUxGDteftaUZwIGoVAMhc_GPShegTCGVBMhv_GkexWSbw]yMOEdAdg?H=QE^MuEWySAvNyVl?Uh;hpmc;YgsUdgggnOh?gtHkHdGH:UiK=Vd]rgYFXewvyen?fuGU>UvbqXc;UluVu_V<WX<ebnswugY`_tXee\\yH;cC[;Y^sDq?xIeC[mDpYrlyfLoU<iFGAw\\ky=wwIAtPoraiBTYDWyBmghCwFLsG[yI:gwDYuNyqA]ssqyaeXoDx[Tk;XvDTQWPt=dpXyKcmTCQqNQJ]PUK<WSHo`LmkqNLIj`<MdURFQN:TnnLtrDOG`pn=nB@k`DLLMMheqc]UPIM=lrc\\r]UwCuKDmOPLMAqMnIjPimAAXmmrb<QRmvrTnWhycuUDIpH\\PV]om`mKUJHQNFXXDPJ=AseqUJ\\KxaThujvqMnUTE`KAItTALHTpIuRwDOjHyn]NPLmtUYLAvN]JoiqcxnX=MRmwkxTVlKc\\LZakkmsc=u=Ho`=jCHwy=jd=N@xMc=SNeykPTXtRw@o;QYw=O;xPV<J:AnHdYcQrVpwCtq=dRUXxMMmcAs;IWi=RH\\jP\\VfuwYIX^dV>PLZmOIakwDWqqKLHvu`ky=JG<oA\\Of<MyaXLIJfDMj]MA`Sw=wOaURxUWdYIxu<mmDxvIhLwTQLMp_mJxqrgurAHX`\\J[Ass=nvtxAdODLxluJ]]x]HpapM<ojW>]ogn__[l>UIuQQIJ]B?MxkKsy;RquS=Cbu?ESqBAcuUYTescZAg=AdkouAwYiCb;wdIcu:igqyrr;D=]V:;HYQcAIVfCwRWXlauhagxadw_G=;feuvy;rmOE:KH:selmcpoUe;RFcV?mIlIBIysReicCysSUimG=oc\\]FO?g^IgXieAcvh=dNIbmAfdiiP?tBeUqEfV=rBEiUUXLehjKdG_GwOUXqb;aeharoaxypT_DNSxjGEQtpwhaP@qrcAqmaR:<Xudp\\hmwqxEUtaHncqTXlY>UKbdjIdeiGhD?wV?fJ@]wytYfr:g[VobS?ljGa_gaQ_tLil:n\\JO]`VyEIwD_nMxjuffVNZuWyTfd?>]lHo@QhcIWGv=[F;weRYehwH_GWIkhZWD@uuoeyceVOUtjUr<uErys[wx^;B:SVpgty;rOEC:acsScM]cDwRJyCX[dJXXJlLLAPDejCiPR@VZaSY`xtUtO=jU\\t:`n[uRvLM@dP:XJDYVw<uWxJN=TqXJQqo=Xjwiva`LR=XHILHhTwdKu`J]=jeXjAytM=WbEJU@JC\\L_Ym@xVqTvGELpLX@YX:xSq^nXw[=^vf?lIVfVYd<poLImIa]uOk>vdV@\\>OsxGf=Q[S^dkPuxGcxgfyAZtonGpivyg=pkIvq[@o]Od[@nbYsDYl:?rlWoiFnsyjmAoNagWXnBYrwwumOu`xkCHa[i^wy[t_fbPbAxrII]TyclAnAfiSitAhuJpin@tRH^B?wDghfIiNFyN>mrAvcp[kFwYix_@lcVs=VsbHfoa\\;^]Ba[a^tJ>utqkyOeqg[hW`RI_IAtyAZoIohYqNAl;nuAXxdI_jhkJQ`;xsyNvb>\\H@`?yy:FuxqbWP^\\I_QvpvninF\\x``f_vlF\\K`xyAZeYdUqZpvwOx^ny]]AcD>yynfBxxVI_dxqcaiF@jYqt_Hrua_sWv`y]HAmDxqeGayn``iwMiojN^eVyR@qZNlUG]yAZxft]v[wxsE>]AvmTWgcH_J>r>FneQUkF:Csk_DjYBj[t:=SJewFsv?YhI?f^]C^ShH]VZki`iF=cry;bfsvrch`kD_KBoWFVQrScI?=B>mR`sv=ev;yr[ARw=w__cDiGm]G]iWwuYT[Y]]w_WEs]gxYbyuGEQUgmDsAsaqva=tyXWJIphXm^=UuimGaYGEr[`s?HPHAyimKdXfv^kP>lkymIwemIwK?\\lnZANc:W`b_atwhHYhAgbsqh`qm;_^n_ys`\\uHbWFsnqn\\>^uFx;hru^ZjIitqmYqsW`pxI]AAp]@ZZIp:qaNa[`O`CWunXfSf]cXexfyrXwDob;GwFxfeQcEakhWZsvvTAjRvdqo]vXlX@_:>Zr_\\lI[]yk`Ha]@g@I[vA_Kn]C^aZIlQquQ`m]wm[wcdFiAA]W>_ZfhafvcIl:orgWsF>_:vfT`e[OiXHZa@\\m^pKnkmGbVw^Z>d[>mIYfMPyx_\\?V[Aa]wGg^a]ZWfUiabY[Ramxg]bG]XF[:YvyMelLf`yp]WDlMyLo?ijVik=pKohqoHQHdTltQ^HLD\\SFXqKYKpqMexsq<S_UQ==jmaPneph\\NOxoQ=JExooqn:UYWhUM<xApwtut^tPtpt@iPFTXGQPIUnJXkJPowhY?lPnTlYyqR@M@EsYeNK`U;YlsUom<pS\\R>=VcdPFtL@YQ]`QYhxm<qyO[eXo\\^ghIs\\fkinmAolLWqtgZWn\\exu:qllQo@_wSI]^nkXTUodmMBckesESS?DFGbLexTMibgFKkU\\=IJ;c]?i[ef[qVh[tjQc:gtCwCcMCdKvBASbQgNOyGUco_UIif\\YGC]GGKSOObl_S@MfmYiXqfEAVGsS^gS_Ie:[Y@GxVkhVUdIEsAox>QXigBDAiveHOCyrchostwOEWKYEcFFcUHAuniHyMe_iRLUU??hf_RSsd:wc[cgh?Cm]wbpvrplRMsXuT[uQyPWAyY:`lX`YZeyd\\xqQjPAT?qwRhL@mM@aq]=UOim^`MTxTJqxNAKctNwHsZDvrMWdMR:=MXeSj@JaxNM<rKdlgHSZQkPPs[iohLlNiUn@xRaX^XNulY:<tKHu<dJsdQOlrCm^VYHMVO=I^KdXAIhSwLmhA?ivMtaMGHqXt_dk_wK[U?AuY]sY;f=UtLmE<miSeTBqDdGHFOeOAfXcFZkss_I?;yIYhT?DJYy^MDhiWg[t[_r;odJmhwGgn?I^EBDMILEBH[dFCxWiWV;CLWYAadesHwKWoqvYmFhIvCqsfWXTAFq_hnkg?EchkWa?TMachWFmMedWi:UiRgCAYWIUbKocnSvsUw:IsLMf?yEI[fnIUH=e`Cc_MDS_CLEIaiIdEvEouJ[wsgu^EBpgGHmi]OuBghameciedMf>WSTAyG[V:uYvqdPiFysUkyI:stkaYGaVcWsU=G@WyMMiPoX^Uhn;bXKSe?eSEHZ]uOAgd[e=OCwsEWOW>OCoQWN\\NTAjPLmcaTM=RGTnnLtc`XM=RFPNTtRtIy`DL:ILJhyc\\N^QmJDJBYxL=jS`uMPUMdm:UwIIr]qTFPV:XMfMQLQvWtKTIPG=JmxjceW;EmaLKp=oxhMbHZHyZFO[:?`CwwI?^\\Yl>fibGZy`h:n[IOtMH]nQvWpkWiZ`V`D@ZFghAa\\MytN^yH>g@Qax_h:Nrt^[\\Wl=voankc>y]yoNfjuomyAZ?@ZnFhYQlmOk<G[yAZwFgrqarxZPakpo]r@n@FlHyZx_xMYugxa[xx^@ZbxxoAn@f\\:Y^RFsNfgS^ZmykiPexo[HW]XYlWVxYHbD@Z`wZuvkavp=NkHFcannc_vxo]shs[>r]qobFZqWj:PsUvur@n@fdu>cKXhBan@A[Ca`:h\\uVpIio:>aZ_v;VuhIp]Xs=aiFHbhyjD`eiQvHwcFokn@q\\_qKP^IngyOyNAZJAbfwmWypGgqGH^Y?mg_rgoksVvXftanuRv]j^xv>\\cFnBGvxfh=nwX`p:^u?xgUH[avo:oin`kSHauakt?\\rwn:@]]wwInwXvq;`nTqbD_yeiuRNhbFZZ`ysifbfyH@iyveTWbPFhnHylWf:XauQkr_r=`kjnwa@oXnrMHg:Vx`ybVq]\\@jTfnEWhuQptnkGIyLigZGuFHfAhdyUIOGMIbQ_ulkxwyTvCwAOS]UYhasjMGs[t:crDABZWbXIxachN[rNUsw?YIIvU[YdurG;rp[wXoCvUbEwEYyclAI]wR]eIbKb\\QgDIis;ByYga=DwcC=Gf<CydCYu?eHyI:KvcUYSmcM]swAGIuyMugEAbKGbYYToycxcHj?eZmfp[s;yxQyTVYTx?DasEnicIOYTAgV[ReIHSwuqwid[U;QbF=vaAIMwfYsfN=BekgDWwj[uy;bOwiimxc[rmqIj;R^kESSYT;XDAtvGu>[xy;BW_X?;uOIssuR<wYBwIG;hR;vOMeNKXxGxYev@WtrsVs;D;]vwiNoTnd<pfXN_uQsyY:xO[mRITjq]SspTAyjY]YbEj<LJRlMqMXRqy@\\MCtJian=trWxY:@rKupVHJHHYpyNtMmpAtcamX`mtYf:Ne:H]dvkPHfviax_lCAtJPp[F]Y_tO_j^A\\ugidafe_pnx^avZenm\\Yk;heQAiggqUvvXOiXNvV`dEgpmhjKp`YVfTal`nrjFoAIx[nyNPo^xlFH\\AHZNPiT>ZH@\\:>fSa^WfqtVZyAZQinIX[Tnoq_`IWjnaaTFhYfqGvy:fa@>]H@`??a<nfaykoFieatLGZDxapGZ]YsvWhcQmEGhlpbK?rHVaaQu^HbvPpIXvHwnNIhGG]mYmMxlFwy:vmDAjBvtqAgRXyhxdsyy:fk:nfO>];AuywlyA:Cw:Mu^YE@[UT]TF]RAwWRIxccCjWgdwsmir@mG@scxax>QBGCFAiGmGhcedCwHEeiEIrcoE]?bPWEjAvouSm;RGcFg]WBAB:WRIqe`ESx?V;IhmkTwIYeQtyxLQXNrYXtMK:qpHANL`ynHSvmjb=qG@qc]k^YPZmYVxkeEYLasrtk\\Io_QJF`VaaljUQ_ItwiTVqYwxY:dodHomAjHuWfxvkyY:hXT<jf=K:\\TYlpHItFpxeQYKQN@DtPHVS@q:aw\\pmeDMEuV[pJOymPAMvuj[QxhEYQHqcqUJ@lDYuVqm=lPIMWZEjxmwmTtsDWIYNhtKvxX]DW>LJC]p:\\S[mYhIyCeWBut;lQ<AQdIQcPj]mf^FtnXlCaZX`qygju>j=A]@Y]vF\\JP`kVc:@]k@a]>jAfohF[HycAnmANeVG\\Ui]cAZFih=FjFhhgAb:>f:H[eakkyc:AZFnxfIhC_p;pl^>t=>hjGusv^LAjxfg;I__qi\\wcJAd;ga@ycf_hNnw>Vix^c^wkQxnZNy`ylEFlYhlN^hWvcaQdBFuU@gaat\\onEwb@Aega\\:XoMpmWYyqa`eX\\yN[uxkhOgtYb:^eaAhIQdrgn>^gf^oNNiKHJ[D;QBTIys[V[YHHcRwWF@cxGgVVsVSowy;R]KD?[VAqDByI:arY=TMsxjkig?bXiGCuY;[s=aCA[FO]SB=dtyXJ]dc_ROEBLIYI_ukQYtaT?CSVcvCWgI]yA_XbeuBgUnIHbyCm_x:acPUtfGxrSf>UBOSvrerdSwKwwokUjGx@Yfo_wBCYW?YhCyUiRbQEI]htMu`]gKAyocIeQFAUxmuGKUIoWRiMYLqhyiivGGRyVc[c@mEscecwVhAcaAhnwfMksrwC_UXiqXc]C==XIME]mEjmRdWBPoe<YeMar]oUbSbDIbEmEcWeVqTZoXaYVJyvVKtKmctuUxGgCaCb=bY]tugx`SvXuUXecEwHwIFTsBN=C`Qi]ySaUDTQHA=I`eF@;C^]e]oCoERiMSbmH@[sBAspcCjyWi[ERuhC[xiQyJ?BqyRsUIMUVomFbgeSidmsH^kedyI:OE`?rJ=Bw]TNsgeEYPYvD_X_IVVYW@MfpgctMSggUNgy`]eH;iHSvIuGOIxsUtHOVjcybIRiWCDoIN=b\\]DniEc;boGw]Kug?brmdBmDIcWxABViCNGBTIHIOfWKrtoTfoxmaEXgv_gBf?TFugpkCjkcAGvcqu<qSkmwLECTCwgmyVwF@yI:]VKkFQCxAEF:;iVED:gd]Mf>QXdWSwgd<CFrOvP=FJ]UmMswUXUkFRegZqutKf_?dv[R\\WVFsf<yewUDiawj_cEkHaWETuYvoFY=wVAb]oeYcbqeii?UgchbmWD?Bj=ECSsZygo[GJGi`?dXofx_bScygCeJyuFgtuWrUCwy;rSQRM[iv=eScf];IO=EiMXqYXv]cBegKSuh;Br]uO[VVYIO=y;Ofh;vn]bDOF^at?EGIOB:[fn_d`OD:MEccctADJSBIaPXHw`<JUdsrdWIaPL=o;xqC\\ybeRupMNQV:XMHDP@EPEuRnnqnAZ?VaoH^N>ZMytw`ZMGpCwkd?Z<Oa;`tLYf_XaWFow>_;^quGtFXhXimIpsF@d=V]ipibnrc^uLiiA^\\:^uZwmXGuZ`[]OkqGvT`ckOm:ngAVZyNekfwF`hNvwgp^uNm:Fg^q[\\XlYfoyvnKgc@Yh;hx`>jM^ymAcu_v<FcapinXfyhn:v`:HhXXhPYliwp=fnvvfZ>\\cF`XHcZpZX`do_nSvZjOfk>tMIqcapuIdFXl;xslAn?NsKXy:IZIqu<^m=giaIy:EFOiD_C:EW;=V;wuNSfx[t:kHEAvxsXYEIrYFdCWH;iiutYwWi=Db[cRiS=Iwx?Ha_e=qtciy_oInABLSR<MHIuYwQIx_hVKbEMtkIdPwUniy_YfwiVboYn_f=OBr]FouuneIbGJn=v<qMFMqYXRopo]UQFPJV`xAMsbYUH@tgqXxULDAP:mokpy;UVyLS:pvWIMRUqlaJayQ]=rDXWqDWZ<x;QWyLsqas]`KtpkAMJb<v^Dr>HXvYrqpT:XMq=JFpsKIt:]VuMTgiN;XtAXWAqraXj@DRRxny@xqHyo]NdxthmOA]xyPT:PMr<V;muyDky@OZ`Y[`lV<NsttWHO?YrFpJ^]x[]TuMMOaNPdj@YVN]xGxY:xTZpjZEOaetUPqlhxWuwDUQT\\QXTv]Ljy=j:Ltl=MSdnmDRW`tLelZlWVavw=Vs\\KbHJ:elxivkxSuqUyMUjtK<qXXHrxIWyMKQDWJmjBiXIYOgmSwls;ux=xqy@YJUJtmpkHjJykcmyNXvuYPuDqMyxk`YcArIMskmyy=JIalclsKuJZ<T<@QTay;=umuKDES;=nBaml`yEuWHyuJDyaILOysqdn\\PJa@VhQxyDV:ElBINO`nIXlqAJxaxP]ViasYTvIMWd@TutMb]msPSuuMD=W?DSJ=Q]LxaeXN@JSUTl=pXuytdyuyY:tMdIMyxXwtsshUxapo=VZykuljKiwXMLjXJnxRJlkAYy`<jNdwHtN:@vxyjy=JidSvYo[HS:iyaHyL=jv=pt@pDymbhNRplB@qeAj=YXZ@Jh`KS`MlXJsatExxBtvUXpsYXwEwkLSqPX^lynIpaaK<xsywdyAZX?jZFkk_[VWhyPyMQ^VFqWFcKOyNIpIhuatsOiXaHBsRysdY;dS;f@QVhCwukWwoi`edACe^sBrargayIuiTcEJCVEyxCYFbyI:Qi\\abVEx^SFryFtySe;RGwcSgfOIr^oYWEgOChSsT^wVVYypeYmWcn=SOCCsSvYyfnsvOWS^=fj;vMaXg;BFMCL?fZiUiEdCiS=kgjWbFoc`mvpYYLaxAKsCiXigDB=bmoEV[CT=RFcHaubkSF]SfAaEaaHl;ssuCDqrg;BJ;g;Uu;SFVosX[hYKikqewcRumwCIcx]DwaDuoCnARVwfVuUHEw:GwYodWicAIrIKxN_h;kSIIrikINCBI_FmkXtAvLSFy;GSwFZet]=C?;FmMdyKY?gSwYf<MwvwrjsIT?BfggS=IhYHCwfcEg?Kyd]x`_i:yfCQr=]CpAbnssy;R[ecksx;qrN_wEmCbIR]=XVob;cyp[xNMBEOBF_rA]EZMCLKI@UuNiYNoeycsiqeDIiAOVhuIT=BF_GH;P_]My]XLIlPHss=UyUlwETDatjDr=pkB\\q;dxnpVCaQ:<RW@SsyrMqT:Xn:ivtmhuii?>c@?`@?vBWwIXmyAZgXc=pmapa^XhyAZPinUakbfu;xtavorAt=NZ<`krvrqhxwFwH@api]AvcByiG`cRAZa?ldn\\J@\\BGsJOa]yorAt>VhZplJInsVvcooc?e`Xdr`^TFwJ?lfqoxwfVNiDNrxxjDaq^n[YNm@AgPYZMFlMPTqTAosydLmhQ?TQ;lJsy^fhchFZm_tjIgCFs:^hgXgCpg\\?qEWeLO`J^i;pbIg]bQlsWvuf^NQfS?ZuYkH^wxg`VOn`I`CidsIb?FoBvvX@epWoeiafIw:Hb@gg>`lRFscisOOmPNjPgjkalr>acAbV?jVhxai]ANghgasGoRVdS>jqqn<NfT@h@F_SFkcir@GgCPkY?tMw[aNmpG_^PiJOZXFgwVyMIoGF`G^`\\olF@d<NjQG^HGZdyZtwgmin\\@m>hntQtKqks^nkVaogoWN`Wq_=^nlPs\\^[EnrWX]eIe]qmNiZAvo`qbk?bW^[QwhkNwGVh_>qRopfG[`qoNo[WPwCnwvVoaoj;YfC`]MX^nVowhqcoxpOy^orrOd:>x?A\\`NfHVcuodZV[M@jkNuU@qOhkUg]on_godpGi;`^[IdwgaGq_RPfnhtROcF?gN>j^W^Uio`G[_@uM^swwmWIs?a`qGsoV^qfjJYekg\\<YeB?o>IomyrcX^\\FmPVnjNqmfcmogNgkxpe]Ajw>q]Xcq`pXxsHYgjofq`^jXZiyxvYg`FeTGeTnbR^_m_xpqn?Qf_quZt?mXueVR;VWMBywTgwVIKYGuC_GbsOIHqWFIYtwXdOE=KYEiHuofEYd=QhxyfyeGOiWAIrsgTWmTVCIjkcy_sIOd\\uxTCDSwt[=fO[XOku[krdQCMMbOwVDQvMcB:oYDMED=R=csnUVC;BG_xNMGg;Bq_dRsVTKS:MSFWdkMCD=bcifqiF??EZqRLOvW_h^;f>WVYMSVED:GSFMd]Gy_LMk<b@G_Ran?AZ_v^x^lfQiKyw:g[AIyN>m^yfPimoQn:@]tGtIPipG`Cws_@Z[nx^`yrvn\\Ok:ngjvbYfla>asfstVj:g[]>lwGwp^v]_`liacwnx^l:vjFP]H_m]Okp?a\\@jSnkYhlANltWvXiMsUNoix[x:Kdrcf?SbWgwFODJcIcsc=sFNArZYCQcfIAWbEWlyRX;t;MGAAFMXNaTTDUK`Hx:=NAdj]lWjeQILobIvHpRBYNmxM^=wLaNVDvCYwXpjW\\WAqUWeR:tPFtJpYjxMyN@MVuPeLxuyKdIO?yS[pQS`QxqJQXmlMSxqWfyJm]\\:xiEnkwXplymjYn`YZ:PcHhuPaMybG]snkxy;R[qbLAY@ASwAbp;V@;vP_uRwCh;YyMEVmbW[BjiY@MIwEgkwES;cAwyaUvECBr?F@wb;muAOD:KElqys?FVkBwACn_XUkXhqbZouWIByMSqKFY;UvwVmGdGcemosSoGnAbW[vWYCCWvOawN=HqmgQ[uXwf[av@oU:igeIrvcBRMw=yrCwgHisy;Z^V^v^kh_nyNa^gfRo]mNuN@\\QOhHfawFgUQhqW_nWwhA_;>mXanH>]xoj\\ThGVp=B`GyJKXJch`IwYSGCWSnmTZCSqmry;R[yek]gAgEEWhuwdKOImouoEdHWbPaW@ehgGH]oViwxrqy\\UUhiymaicufUwuGqtJixIMcB_gQAutedqYUccuxKbw[cw_guYu][BFmcGMW^sxIyI:oT`yI:Mb>MRNoTpctRCRxsGDeYHeBmYhV[RVUFpYXI;RwesXATnCIoCw>sdUkT:Kx;QwAadykEeOgjsv?mVemcMYtVaW\\Cx\\uWHWrhIFoct`=dNuw]cB^WCpcFDGhmMctgcyGBhWhZkcyKEnoYVuYDAiZuSlwIg]F]aSbMyhcCu_r?QymEIJ[b]irCaGawmG=K\\ioX]srywT]n]dv]qwAaX`@VB@jpYvmyY:TWJUJA=lHDq]Pyy=joIOFEqReyuMy;xY:Xwa<puDTuyVn]l]yxFxr\\\\ky=JG<Jqhj_lSrIrQquFDVEHJmuqIEwEMJJ]kZIq`EkHlUAUQ@yLe=rO`vAeuVPOjyq@Ym;`mKHjNejN\\wnYVD<PlIyAiXZljZQlAqmrpvWxKSxY:tOOpNFQx^ijgMWdeTFak]UsKaUleS:ttJ@S:=jBdYdDrLDn;<u=<wsxn<hS>Ys;hy]qt;`JsUvUxms<nAdjRIx<AoqMwcuNsEQ^`ry`Wo]Pg=klYRFuYDux]DMUIqb]p:hshIYRmX@yJXqwnevZtvbQRqqyNloylQlAK[eR[`j]]sAhYN\\l:TMBAmILJ@YST`dJfnHxaGHoBOsIhlCg]Axc@ilkGsWYleAuw?_;>j]ov=>gw>elycLilQwZ:>ZIFfCyaT?hLo[@WhVyxyFvHgd@AcAYtvAg;>mVAbvFjsQd]amIxsvaxaXvMIa`pwJgaAgo:>]oYvTYnLxcifj;yi_Ic]FlM`ttyf;hcBWk__uZy]PAjRNolimFAiIy]wQgQ_gv?olVrahiox^Fyvfwib>wUWuTij;>iBpZxwvj@nDVyv>nlHauVpVpfdPwPqvb_bb@`xfxY_fdIumY]NaxNftYO`pfklarlG[xidmvd?gbdYhbobl>AeybIwpETVmG?[WaKDRYdJaStedE;KaHoUQ_TqspYtfHoCa]ZwxONjVIufqg:Wo_ftxY]e_vh^wlqZdfnwhn>PpEOZf`k]F]mV\\;Pm[pxCQd[yvA?_hQhkOtUha^YxcpdZ_\\oQ[jv[Qqtd@wUX`HG]fNmEWeROmA?[uAqRfZwhcaOwMX^YiskPZgagVv]vhidOnBGxBOp@?uo?w?g`WimSYmPXfLPgigh[gn`G`C`aMQiMYm_h^=N]cgkIwrtOc\\WfcG_BgrN>ZDI`Hgr`>_;>__hr_VA_dRiF?kGb?TNOFQ?e\\;TCKC;[w:sBaSRnOVNof;YU>AuTIWycfqOW`WbSCu@mVioeOCcb]sDmICkvv_i_Qi\\IUtEd:OrH_tw?GZcSueUJMUAsGFGdWMCmmgtCYoqSt;e_MiqmhLAwV?vHiId]SK;RCWEtgBxmdEyVZUFbyfMGYf=W\\IW`?cMSWVuT?qYeef\\otJ=XVYFxUBQeeCStbSsiKehmeX?FXoiWQggQIjOgOMIlUGLidcEbTGePKFRctt]dkkSdcDNARkoc`Mcr;vAMtLED:EcGuFLED:cKGPqL<JUHSDDxN\\l:\\l\\qLF<T=@s\\dMC=rGtRNPt\\]KJMjKuKT]UK=rGnmnPfN`xonrUgn=@y<pwe>v<V`t@naywi?rciydWvX^fBalsPeuv_ZhsantshutW^vFlSgrPquPflx`eVHZ:xaDwlH_tvxqH^avI]gorFqivni>XdpygPPvOg\\fqg]onbvwGAfcOinOeOxnTixM^^lAcHO`^igaqpeVcJGlf^`soc\\id]>u[pkCWv<VlDxcPXVoWhcE]eUAUTBmbeAEKYrcQeCOhJyCYAvg]yRysrutM_X\\IX^kXBwSS]EF=TtUdIAY?QHToUYUGqifbKev]DZ_Dc?FiwV_YeKsg_qslqw@MwGCw@OvhwFJad]egMufeifJetLoXyUDu]ELIDMwV_IHe_xPyXjOgfUYLEgSArAAHayBniXSqxC]FpoinsVHOD[mi[AydwB_AuekbeaDQ]frgh`?qy=jAyQP@m]uQXEWvDrmqxSTnrIY@dnVuMpYmy@Ld`TiLVW`ThhxRDr=HO^@nHTn@XpoEMpDwfAkZ`qrmkotRLUWuDRgHwbducUxt]vpEsYLVd\\TiplDyvnLLt\\K]]qX\\LO@Q?QxtirG\\pThJddRXllPaSSLVqMlAAyNQuw]mplLKiNvDvNLsImVwPYMatMqpuHKNQWt]WnUUlMx:=rW@wAmPkHUT]VpDT?aop@Pt\\k:Hv;MW@XxIqTk\\xcpYCiYp<VPXqBTs=tkFamx]JLaTiUYnYMcTwYIOOeWv\\MMFMKTpAw\\SxY=Y@ExVoEKUgCsGSkV=_hZAXI=V@yRcytoehuEg[WXCSbtUwD]En;BVys>YTpoXLQbpwXEofW?HRQfwgfOcVwkHFeGD_tNwSgUvbSui_hYQhIkdKqXP=tBLXtxY:lmdpkWtnTiSeluUESPXVEpxKAqkqj[TRQqy:xn\\TXtVaXvZLgcd^mXFaWvrd?rthbYW\\UAZZPZQ>^;>wcg_m_odYdwGoUawkykP@^>q[wHwuiai>hpiqgFoKQjwFhXxr_@ah@c_NcKXtwviDvnewfONnl>bpFnunp^amwW_T`tSOukixR^lBNlyg_xneupby_eNOrVnsBQhYP_uXaXNhtvprx]HAl=^k[@sYvl[ic<hfT@_^qcHXZ:vcoIok>s^I_fhs@VvankUFqwvitax>`[gGfIxcIOrYXu`y]<G_jGhIY^s@n@>\\@whlA[eqyn>fFXfuFhrykka\\fA`cAs]xg=vgxvrD@Z`?`lFq]>tyOcVOhSOAKxy;RIMIkeuDiHhuCtIXHAri;sy;bP;BT;y_Yf_usKStyPyoyjilUVQoRPVJ\\nAAOGlsIqtqHPHurK]TM]kBavxdralQAQubXsO\\UGuu=UjU=N:dRD@jgUxIlVdxrHTXZyY:LPDaTlQKJXWolppiOSLmRPr;LlBmRePJaUTLDS]TrhUkhaQexwUQxtILHTorQvfhY]uJ=Ys>yv^ll>qSrmvYMOOqVr\\opmRCXxR]k]UwUqLqulTTkYLpSAsc]MAtn:Tt_YThmVi=oVQU?uNFIy:@phxkfDrSTYSTPq`SnXsuDtF\\oDTOA`NyILihR@`N<@PK<OD@J:il?qnGToc=spQoHIMCyjcLyTxTLexmep]aLk`UZqwuMSwekseh`imTAtfynIolpv`kyjIqfYfocnyhFa@Iglf]xWdXPvWxun>jcOvGguBpyn@fgAZawwygks^dZq[wY`DwZhf[:F`QI\\kpaNprK_jM_uI@sDNlYgxrgxZNdZG]k>uD>ZawdlOibFrxapupiO?]CYfMXcFxnuyvTphxnfiocP>jM>a_fqrf\\XWb;HjVp[lNgqGyQnkWqaoP[eX\\Uyom?bG>[RGjT@hDF[UYxqNxadIctBOyHahicDQ=b_uCD=bGOWsqh_yScqrL=IckcQ?Haar:suiev@mdmIyH[dW;g;simgseOXiUx:kRDKRHucPAwiug[GxqSX_ktc?W^sfYcc_iUVwtpSGfuVf]v^wFgmYQWgL_fUKH`UrbOEAigWcYc;bUmILCs=sWTIhaqx>eiT]Ca?RHwItMIx_HD;RxGdoKIFstn?Tusr:YXycYoWcnourASi?CZYD;sRw=Hs[x?qrZiG^IrgOEQ[UHYHoadjaYmCBZmuDyFM[x:gEvIdLITSwT<MyJmSuWVTwfOWTtkD=giT?rr_evwVJQrqcRFSY`KHrquN[y@;FtAftMcJsubQhD;wy;R@YIw;wOCTReb=yd_Oi?cfeIi;?TY[vN?HDqIcYBYaiMKrbkI_YreGSakVQ]BZkDR[y;[y]QyLagDiB]uEXyI:QIo;g=AFAoENOte_T;=S^cF@KiDIcNUGieU?ASMuYnki`UgEIimYD?=rP_DZQD>_fIYtUOyDYRVwSo[xKEVyqXYgXyQsF[Tg]SHEuAMCI?IfovfgsZoWfOt]IYKYtREy\\kh`iDOETH?UYOGE]tA]fGUhyaTuQyhsBOIdcqeXgXa[I=QfWaWlCc>]w@qBZIDxcdfsT@cs`MVSeDOgu<OrREv:aXwOWfiSFkd@SDS;fHaFZOskmhEgu?gbvUYwqh\\eWEuffkTc?yLIc_kH@kBlWEwCsHcfC?FPmdOcDDKDlYXcCtKeCdywSyWiSvHkbbUfJEvVQxR;GyMeQOHnOueKenkS=iIV[S>qw=oUE]EQMHwIWkCrfmGLAeE;xSArngHgaDMWvLMXegxOwbLSfgsh_esUQtggroih<scjsEaUvtgWaEvVEbR]VomvBgUOySFABHGgRoW[Qt\\cEfgwfyT^wWTqtUkrkmCeXO^uYbYSpyY:HQ@IXMiQkir<dVVLt]qtWLKk@s[\\pMEP@=OK\\opQTCajM=N@<qxEyadNBapeUrAXM_iKZlW]@xWuKViTUYPqHRxdqHHvB]yd\\Sjlu`dmn`Kiho?mS:\\kxMw;`UwQOfXoR<XSUS^luuQP=yjvaxJ<vYtNmMTAEWhmlqmLmMn>INmtkSHSqiLqtX>toGTPAmWhQR[etO@pELWGaTK\\o]mloupedVKPMBIjBESdeoZEaRwr^NbOokRWvvnZThdJwuH?_DHsCnfbop@yn@nbUhvvAa`ipiioggnxHkaoksWkGPod@hKxoghdIxc?p_NFnPPwSyeEN]v?rqvqop\\Efl`Wt^Yx?`pPwjGifVa]Egl=^t^ideVksggU`gkalh?nM>lAottHivynuaej_u\\^utfjfVe;vbo`fdwpj^qJNe>ouc_jmG_W>icIc^@[CAn`amdovU`fio_xFfuan_iqIin[NmTf`\\HrMneIgj:ywRQiOIa`WgEqlR`kagjXNjgPgqAfjXp:`yexxBqyOoeXQaTQ_@acq`gRpreOc[FjLYo:wjDhqTNvb`bDPaN?jM?bGaaH>g;NrWhcVVd?@ZxNkb>n>^`Kgb:F^^hn^@n>NnPPl:X\\NNfPPopFndwp\\@sCqyJPi`VtcqmrxrDOZpi_\\OleHcbPu?ohpxkcV\\q`bBvrs^ycn[[@gifbSXmMnmB`dIHwH_sQgbd@Zdxptfj_`nKhrko_Ca^uYjcGavQocwvHpuPNm`W_T^kM`pVpiNgpSf^_VbeGiiGiSNlPIb\\VZ<pbt_tlPa?Y]BwvBVn^VvZPnGqgBVdMinZGgpw`JXgqwlm>bLG]qgwgOst?p]>jeoeLqxTixENuBafO?aaFgVny\\>mTilTheEp`NhyZXv^A[Ayox>mehceXoJNtpwhmFnLqdpQxdyvNopsvhX>eiFtAw]<qiOPe=QcsPkeWsc?n[wfj?[GFqC_eY^loisggrbHuEqhPIlFa[dAcb^d=xrNYdGhvrXqPnn=wvj`uQVfngxHQ_spvnx^L`_>apxAtKylfio<^e>ysuqpL^ZaYlHpiWtXkwEYUmSwOgbisdAGUt;D^sR:;X@KXypqdlXZ`lwtQbUJ:LMoXN`uMFMLy\\kOyMgUM[lvh`rAaWwyPg]NyMoVxM?eW;eRvioRPqPdK^ttpXTcqPAMxWhsuqsZMjxHxhDkl@sfLsOuKOAq]QU[xpPQrIiW@xSnyY:xWgqqrHgch_hQ^s`jGWZh_kVpZ;I]vQw^_vPin@G_wn[u_c=XdMqmbqoX`fmn`NGmJWfixqwp`wn^tY_EGqpHiQxlyn_JYslIos^^XhZhOudsW_FggtnYU^GDLoxjurhOf_mUrgw]UHhevRWT`Oug_tOkX_WdGsxjyGn=c?;RPqtAcgZywkixoMWkOUtQgHkHKiVVcV_Grn_f=]uqYvvgh_aXN_WiGuLMEkSvbCS;As]CXOaeeMIRUyGkTHIhxgwy;b<gFseH`_h\\iUKaucUhVoI`oVI?VYwwPas:aHHscYyRa]t^GdhoBB=fRyhVaxu;E@SB=[RHIStqtgidwgWSEDoqx<cUxYtIUVLeUWEBa?tLMf:=sH=TjscycRoMTECVriRhaVCcvw_GpATXSUKsWNwywIIAwWFkxseWJ]UcQTTOwPYhcox^_BRkwvIrCsSwmStuD=_DC]Ic]WA]HhsxckBlsiTswwgigaIcaRLgWPwcrEvRwVVkhX_XOESYGRrqbTGuTgrOisGgg^=X:eu]Eb];YFaySmWdsSJIuVquUobPEHiGVlmB:cuwUw<qvxQTP_rHMfWssacUUIsI[FcQuxCdhgregSpWFFSG[eUtWHD_d^gw`AB]uTwshc_hT_spMX>aHmIel;sGovcIC@Ary;rocdUcYPIynSI[Ke?kuNAUd=unQIayexQiVQEd;c`KSS_eAaD[uDcCYy;DdaXNcwXIvgMT<eV:Ss`qrByR[ecGeGLWT>oeGGUL=UVwrhCBv=t`cUO?lilNttvxdL\\HWY`wyPQY@TqDNCMJJxUrmry=JtTw@qtpQUmIxp\\lCApG<U>XVmelVPmWLMStXDyrLDrYuxgQxMTTvHTGyn_DJ@UoUIMthvGhsHDox<URHUsDnHeVrhmrlscMugiLNQqwhu>ApOlkWUUU=XwlSwUw<UuMQpu`L?uwy@MZaVbprcEyu]tgeocQO?QUaUw=LJDtpYQsU`lW\\xL\\kOepc`uSeuxtqGLT<]sC<JUAXxIuqqNyuvW=UduOoUvTdsNHMWqlj]naqUpltb]Kx@YO`QftVrmWk<t;IoRauGaV;AXitn[ySoalN\\Nq@MqENmLWI`kRQplUu[=uFPo>yPlQJbtY[Mrn\\QEXxpusiXyy=j?Iy\\iphdPETSqDKmqo<Ur]dVaxqBHo`El[`KEENePmFXL<<XyLKDesfqj\\qmfIN]dRkijBPJdiOGDM[DSZMxmpm@]P=pMVPmDPU`Ymr`QUEy=lnkUQcaMxuqTAM;TTatXp]tOql=htmXTyTVDmJrluu@VNAYalJyPuLxjKtSVLmIuOGLSRlMHpqAdOh@QoqMnAJVYXIyjPMJHHY:iQGTqYxKo@mpySb\\p:\\uauwjqUnXvMqjqqvWxK>YypUnXDyX\\p;Xli`UsqTCaWVHmmxqwIty=jQermAxSqpa<oglMk]JRIyIIOdyLbUOI=U`dsRIN^Qo\\lyATLJQukhpJyVR\\]lQdlfaHviZ`oiwwpNyTVu>_jyPqLVZaof@Y_bnyM?pgQ`KxwNy_maoRpg\\ByQwDaDDubL;s:[ymod^kea?IPSURqCMIH;WflQcf_wnUIgqYMMG@[t\\Mhb]csgHJuXa]vlssmSS<qrfkBnCyDgEcqDXgHpYd>EBJgegqsvgxbhS;`qxqOFyJi<qOdNntq_AXNIpqtuoISvEXDQocaUuXYP]PnXSMlPZYXmAOetlTiqW`Px`TXpv[MjD<o\\HPnDyDPWZyksqvSaYeUKWuo`HNk<k?ppbdsoIvZtnPhvJIV>]tkMlKMWpyN>MqbiVT<RwlxOUweUouaRmeW`EuNpkAeqkqXxiLvVaFA`@OiNOafWxcOqnX^^F[BvdXnqOxom`j\\autF]uQcJPlFPyWhjpincofDYlQHssfZ@OiOwcrAcnGrLPe:w[S>uHW_VHxMoV;urYyYycyewJ]ERggHuDiSieYiBaVhou=UgNEWMmtLMg=UwOmuKCuWgvusRvSG^kGTKH;[swKgEeu@QdJCBeCy]Etukd?ireGGxuTQWbC]F\\;tXCeaQe@qR>uuxqYeETNqx^kg^OuBMdUgIGefSyhD]XaSdhgy`=XEKSAIrlyI:ixdiwOghg]ucmviQuw]d`AimMVTmg:OYV_Fm;bNoSoYv>Af>Eh?_uOAsI;T;cTT?hNgGcOHeAy@uxFsuTogVYVxQuy;BYyUwOyTucKGhvADsSh@EtsAU=Iwy;resd[aVrQyhKhbkWX[U]cxNES[SYGQSWgtHAXwYhiKCNIGGmyW?TWOcJQt`MwqCFEQrl;htEbNkWoSiRueeYX_uc:gxSMVwmUEUi^wh;OcuwcWuBJMi\\IIGUx?[DoyI:se=kXlOyTkcj]S]IIo_XOISDotaAtUCxogxogSVcc>GfSIyS[e;oeyeuIGfQQSQkBqStYKFagdCewcIxc;S]YBmWt=ysM]YeqVEEsEsSHcrVkw]IBVCsreReWTOkbeGFOmGaCgxovBytnoguavCwwqwYiOsToxPowbSTnaFnoG^ycHGy`?dfGdpoHdYhcoxPugAkBEwunEbnQH>myMmgw=wNIwCQEG_rd_dDiIMSyE`JnpO^<LyILMipaIxWesFHXVqRRAWHAXv\\VqilopNWASxmM^mX^\\RRMJwqPPqQY`Wq=TWeWS@Wx<xy@mepNNPnMQWfeRQIoHIxbmoqmPQPVlaJLpQ>`vTXvoYYSxY:`P\\]VyPPJxrststYQ[YQ@uTemPf=oUxLcIuqxY:`qPEvXaQg\\s]@s^EmmuMyTNWqSxXsnXtnDPmMXCiy]tNPyNoDXQQuOqW[DQKXRrLydtvYHKgtQNxS`USNHM<=n]ykLQnkttgaO]TkW\\oZtxvxY:dJrXTNPNVtx^QS^tvphNlTpDLW>yMnyty=JxDPQmMGAUc=t;aV`AQrMkQqvIqtnxm?=U<qTTQlR=v^yIwXfwg\\oYpEU]IrB]vu]dNeuBIuBODVEwHKGa=uguwLYeIeUOstSCrX?IdEWmch]QH=EdwoYEeeqMCUmT_MI^IrtyI:gHeyI:KbKSw^mW@MXksddMxN_dtIe@[SWsdX[BX[uqEwx?F]MFBqrfUya]ieqw^gH_?c]AF?kWGMXDmsHagg]SNgtJgEwyRaGSIoeSyF]cybQiN]dOCDlCGNawKCYliYf=XwQgEsWYOEg]V_my[CrWCWoGXaSvTQwVQrrgGXKwbue^QSUitk[IfKXGoGliFTeDZay;QIPiiGUy<;e]qsAodj]TVgSM[caEiuCsJgc:WbGIC:YbTegIMw>OGcguTCF@?tsqsYObm?w\\EF^_wMcCiMDGSVIQBAeTccXFSeoUhUGVEkFNYrJQYwOgSqVLSBMqyv_tj]ECaR@iV=WCFmRxIXiITLOV;?UoeHyig>MB?muEiwT_WFqbyeWAUGqgVeQCDSBSUD[]GIcD;]DMSsLgylyFB=tsMXscikOe:CwR;CZoeSiV@AyoSfxaePoIxORUAUA?r>IhokF]OuHAyiEgEQcRgHLWD`ASgovHqE]Eip=tlYrR?t:kbZCgZKrB]G?MG?WV<KTq;htct>OVtCun_fuqtKuVn]wAYqyxkLYOEqLeTQKpw<Lt>psBYr?lsc<UQAPqASdTTm=OadnmmkweRxXsEDK@mMs=Utul`pL`Iq]imP]VKxOkaVaepJDWL=pFLwptJ_YTNYZLYfGHqZqxaPd\\?j^VxaQxvyqtvciVyupkyN_\\_qKxvEIlMyhWgoFPtK?bBnbtWxoQnQhpEwggg^FQnrvrNQY?rPqTLaEFWvIChxOrpoWacshedZYRwSHHgywIwF=tboH:;RTkFVqSfeixgTB_CQOdnOXksvweCc?EKCGE]c_;s^_fXyfPexgQfiOs<keXIUcMujyR?=G;]gE[S=mTNEXGIrBOF^eUk;RHMej[F=aDZ;W;cRrUD?OI:eE?]DJEB?]l>\\nn\\PJUJkertTLN@jOlSDyKvqNKxY:ttyhyNttCQkDyQLisG]vqqlm=Ma\\uG@UIQSr`pX\\NGqpO`ku=ry=J[APnxQfyk^itYdoCxQoloiENvTUEQLxAqy=JeQVqTl@=MdEPYUSriVKxkGEqtdXVXvZpV`dScLsXani]QWqQhmjpLyqeoNPtkXM=@W`epsquheVoajBEKRMNx=jkdyIEwUmq^PQGdo[tpaQUqLlG\\SA\\R>Lly=JOLQg=kCmN=aVMhwlaUsPvslsmYukUokIWlYKbmw^=mjLKidONmoshXeaR_dmg<TNhviHm=HvSLTWps\\Mu]LQCPxK]moIr]UxYPStXqy=jrIxsxY:loIaYG`tuPTXdWKyo[EM]aXAejmxmQQTnlO\\HwghVB<lEDnVILMQN\\LXLMW?ErnLMk\\Y`@kLaVIIyIpy<dpSIry=j>Lt]hwy=JlPmJYpLuofDNkDrvUOUpp]YYJlSyQqK`PqPq<MW<HvlIXmtWfYVgttllVfauidl]pmNiOhpK_dYumWjiW^ltrLwrXWtiTeYqyogOIft@d=fn]X_bx]>q[yO_Tqpl@`WEMWieiG;urhouROveQubETTweU;eRcRdwRPur=iHvGgtETeETlCCwKCXuDK]FqwhLiCqcC`UCyutFIxsUdiwggyGnYUMSwE[rO@VDmJCIVbQWtIWqllMget>e<IcEibb>aYNbs>ofah=g\\?hsgXr=xvZS`mYVEtrwEROdOEqjxY:LK;urYPwApY?hrWHrm@xd\\SH\\MedjxhVHxqYDWMqOALxfPuKeP@@Po]TB<qxhYyQKO`XQplppL@evkDr`LXphYxMXAlutLmGqrPuqJaPiTYnIQglQbaOoTwQMjgIXlPOD=X@IkZixqeOcyTgmUeDLVAjKARS\\rvpkSHwoeOGUuFqYLASN=S]<oC]U@uyDpKaUSsav<lvs`qu@Q:hj<AXYEtIeMwDr;eOAdm<YUueUf]SlhyZ\\KCpPhHpFhXHMYIPs?AxqympYk^lk>lLadvLlLfeWShqupT^Lq_IvOUlJQQLhKDAKUqMhmYLujYeo_pOKtX`eVeYYNuujXXRXXwiYcmUc\\PGHsnLSX`n?pwhPNGPQ?YjE=Y^yVsetUXQSdPGLP>DMyhVE`xRlWqejYlNyQUdQnkdLiqYMaO\\yuVAKjUtSlwIyvTtoXDKVpPqpxj=sAymG`nFdw=HYOqR^LTXQRN`nUUx_HtRpQMLwuajUEykeYetORyJxMLGXpdyQteLgIwPuK_AWj`p;PrMLJQ\\MayqPAnNaX[`ykQSL@m_xkhmPmHUcdnpdSVXU<lr`mqCdtnysqyrxmjdpQudvopUgxOJPpjMRYhMIiQelSWqL\\Iw[lmeuUl@UBDqkHX;]JZUjQqlGqj`xXX@V=yRjlOs`mtqVgds@mt[XrTtxsTyeUXyYx_Dkytt>qsixw:IRwMOUijy=jDpnjYVdxPmiL^\\XRutLqKpmlk@lUEmk<lxaLbapAujOqlnQS^HSJTTi=rkuux\\tstRUmX?DKcqY`iQp`PyHLIYlvAPDEkSHwHXnl]vL]u@iw[YqUxluuxLEkB]x?ljAhvvUWYaTLYVNmXsPxL@N:Ynr`XwMwUUYKTX\\eW]DvT<x;lRrqJI@wh<MlUQnhtJaSiUvBLM?\\TNMJahKLdyximelMqtqaUMQUTKtysLMydv_tk`LQuUsUTqoMK]lXT@mkQxB<J^LYaeP>LQbxTuTpEeQhIRBYK<lKlyQWLKKiSjHXMPS?=snypQTRyqVDdvqYlqANaMKHYxIPt[@PNivmLLUdmD=UcLR<HSHxtqDy\\dpgapSiwfiSvtX_AxUIL<QxxpunEunEQhyVHXuEEnihlDAOI@wIeqVHWWiq=hlbIt?hOEij?ivRMlGuo<Lo>=QaHxIisLaPguVqlmR@mMlLBmmm<YHtQFqtWhkQDUgMUPDX]TQPpV@MpBuwNeWnEyghOhhw?QSlpS^hyHyjadoVDxdiU;LrCyUsxm@HjxUsYhxKyQOXwZmtoqNStXcyLMhLZIlMXluINxeP^EUBep`PQuURsevpAKu\\tHmsGaurdU?UOP@ktITHDpSUvE=qPtpjhYtPrLam@DRUxY:xSo<W;UL?]jkaQ@lROAjkLWdMmEEocyPJEPHaJDhUnhwo]NkDrGdwEyKyeUqtWt=X^lMbAjqyS]mRyLQpIr_dR:TxTLsRdXKENR`Kbty]TJJ]U<`ofPvfqkZmyOypfTus=lf<r^yrQ=wtmt;Yr;iVXlS;YThyQ>mTllTguXotS>Mm_DMwYSg]jLLNZxloescYwQLJUTVgUmxmxHYrj\\oWYPFTmuEMZiXZaLx]rTXj^IjIUmuTselmSEqydYdIqwTu[`nNHQATr]qxQdkRiJ;<MQLVj=Pddy@eXiqVUuLjxr:pQZyY:HKbhVnXyg@omxQNlJFHWFxpPQmk]pKaJn\\R`imR<l:lwmauNaXkHsTewM<YwMmeYmEqmbHLNxjYyQeIUipWQQykUrd\\jvQL>qkOHtbmk@dLf`wBLPcHNpLLAQu`mOPpTvDXDlWpMVy?wJIdNOuaWmXow^PeAwiV>lB@qK@[KGsAFjV_^HxpXX^IW^R`rVx][ouNHudQtanlL>bappfYZUO]XFjg^p@PwZykmv]b^xcPd>X\\KWiGproO]lodkXjihvoiZYwneyy:VwhPtE>a`Xt[Qk^_[<nkGNhmIwqOtdA^DYm:uv=f]wS_qhJqfR=DtKSeecCSWOKBHIwVYVv_SXaREswTCfpuB:wBa]ByQgEiXLwWhKVLeBm=uM?ExEhWofooVGKBOYc>YSqeclwS`KgJSi?[RY;HAgX^OGacrUAU@]d^qV_YGVAfJywPKWPIY]gGhysDCinkubUcHYcbsfycuxqTQEdU=y_MxBAUWEXLMWTiynuX]Qis?BX;sRABGOS\\gspwwZefG_XLqtNCGnAivcIlieAQFjWwKetCqiS?sYEf_qw\\Ke`qSCSFV=XFcie?TM_cxuTLSDdyD=_CrAe\\OHacHOWwT_d=_T]OfPwWSswDWcMGhpwxrusYASQwf_UeR[W\\gBX[w;IU?QTP]h@CIEgyy;rt;TjuB\\WwYqyI]D[sIf;uZkh<_hNEFOWGu]HaAeNafWiDM]gr;XMSiTqEswySOVgQgT_sPMYfodpwck;b;EetGrD_sLubLGINahkSiVmsRovocHwMEcOVD=yQsFBgtQstNIy[_si?TOOCaWWqmT]Wr[MGqYW`gI_=RhmbYyWeUDdKum=ESGc^yDFsV:WhKOUFEEdKGjiwI[vcMTUOWM_RkCcMKXiiB]OBdchLidsGCOEGDqh^ChoQVskiVATqiwY]sNkeGsRl[EkWRiMY=EFx_hN[CHurNYuCugTkiROxPkDCacC_xkkSGcfssFEqw`atcESNiGpCHh;FtoivkG@MvP[E@Oy[Kgd_fLWCYADA]g:]Gg;GdcY?eHxGFlwxPIV[aEEuUIIXVsdwufcuXA?tCgfBOwcCSooWfcVGsXm]d^MGsitoAuVKwLqr:_ygwbtWdTey_IFWQx\\EuYeG=]fmytAghgeS]ASuOgfCTVOC]uuTppY<o>]RBtQDmsjAoOhUTDO<ax^EyOUtnxk?`x;yknenxlU_mWREu_hkrLjyLqetKpPU=PP`Yl;usDeWfmtYQpaXmqIXGEVudoMHQv`mXLPP=PvQuYMqOuxY@sy=JGxO>LvexNmPYoxP>qtQXLVev@@YH=p:HWAipc@nTipppmBLW=yXgLOC=Q?MncHrcLsIEovItDTLgqNVmt@TvBTVN@vZaTUdYbUK:Il]W]AOmjpdMpgbWZt>cBYaQ@^D@]_NsfAl\\WbsQ]vHtOIg[^nOqRSvTXM>us>tkTIonxxh\\KjTn^AvKHU?`tsXtmYX>MxIdvR=Qn@W_TxRHO]tJohW[LOBYNTxWPLwDEQMqjGpQOAWAyRQpS;Qx`XtXAj`hOsaXXdTu@kg`PYHTIGne`cqXd<GfFFr]GrsicRGpUGo^Q_hn]r^t_OkkirCohXhgk@qqPqVPoW>qp_awI_UIbYWdJFb]>`<v`^^xRVwM?uTI[`arFIp<yjaaujoiRHoOfnSo\\?Glqy_<ockObn>o`abp_[Aa^H`x@XE[deIwsCCUghtqG:ArgKgbQD`wcoYCNstM;CQGD]CW;QG>AxFkvbwfwYeG;eLEFIKskoemuvCOvSSFmUIgAYBYFGei?EvHMVCwvWgvRmF@aYuUYN;YoYGE_VLMxCgx]Qcp[flkGG;UoyFD]Xs]HRQCR]pdAsBXL:tqDItnPtqaYqumdhX?mlEHmPlpLiur<ujHm_AkgDk^TjDYjDeK=]StmouQYThx?Qv<mqG=n>\\xilkAPTmlT@txfDU\\Ey^xXg\\lu@L^mTxhw>mnSAmmtPmqtZupxdL`UMiQWw\\lRdWPERN@P]eLoYTT`TIdLjLU:<wN\\wLiw_dR:<jMAJZLKV=T;lsN`Ln@JdMST=O;@o_`NZPJD@OZPJM`Ln<T<PVFPTK=rCLKkNk:^cKOkT?_;F`?g_N>ZNPdKAbGfrRvnK?bG::ZL?d<NfLxmC?bCNk<G_NQf:H]DH`IgrR>n@NfFXdkqbbFZRXnN^yKC:GUDtn\\]KJ;r`KupYTkkZg_`\\wm@?_<^aKOkM`\\\\?j]frRFoknbbN:oRFUyM?s_cR:wBDIXgdRR\\p:<RkLsmpUQ\\l\\=j<HNQxJw@vWEUsqKSMT\\Yv;qO=`lFPkEmJJer`lonlsKQVODQKhN>yY:du]qjvIwjqSjxvEMtjxVctnodp`Pm>pwCLKuqXbhs?lry=JPyowUXEAtJAsQhWQDM?PLXYPRqKoxMJtuppdPpgSvy:NyoAqtHdmWySI[XfltW[Rgg@Y^JgacQhYQhsPkCNfPQm[OkYQZHGqwVwiVcl@mdW_fFlJHZvFlWoc?>Z;>tP_qHqtl^vQ?q:HZ?OaDPl@@vKOuWHc:_[;iwPakHfmc?YcB:ux\\GTniXioc_;f@GBD;HwIgN[Lb<NtqvPpL:HMq`q\\ulX`PdMS:hs]PtJHJcMScEP:=kcUQd=rbdR:NuG?nng\\`Nuk>bFfr`FtoIokFcD@Z`GtcYc=xcAa`K>bFNum>s]`\\wap\\?jSvkdo`MAxcG`:spMDgaXvOTK;rFUu@MExAG@;G<gyxadPscwMWfMd\\\\TrYxTMNOAyIYsMAQgPjnpRF<T?xPDHO@Ak;yxdPLRQPLxtKPyPUL<Eo@hx]AObDXc@S@ApKDrNlmIePgalGpyjer@mtZQx`tLc`U@ySMxROLUgPw]mpcmN<PqcPN;ExnAUTanSxT`]WZyNghOHiNnPN[MJrDQ?UTG=kN]V^MM=mLHQYTdy?`t[`vKaVuiTyYoTuke@X_HVVixGTo<eKjaTQTnBHQbQoNptHMlJ\\VmlMCuJoHyvlR:tl]qkNuu^LYT\\O]xQCqQNDyO]NghuytJYPUO\\WAuTvDt[aUBAl^UvYdNIqLY`NW<r;ywPap<UrIduVMm]ESe@XrHTges>mM\\EpGhpZlSqxqQQMe`Qm\\uvuQoyQtPoBUjapU_<UwdRLmtO`s^qpcerSqkYQUh\\OoPO@IoBpOKXVo`skXVoLSNfr:V@qSUkc<sDNARFOT;qC??EZaJTEObEJc@w\\<jPLkb<^Nj>PnPLK:ZC::::::::::::::::j@PF]DJM:ZC:::::::sXNOVWcB:c>ZN@maHDUjPpLD<ZL[COko_<shN_Xn;l\\ZR<\\;rGEULMDJ]B?CGpItJadRSf<;r\\URwAgyAbN;YN=FJ]R?ADo_TXMUtoIOqXKqRK;rJEyKKID]bkqcYefG]hK]HJWYK]w;kSyMSJIXKMgGOfGOF;?tWwBpcbnCVwGIeUE?;ENERViRgKc]IGjAg:;fBMbMQrMEH?;r`KUkoc\\;bLStNKGbGbrgf_OF:OTDKEbDdD@ZbNnD@Zb:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::rym5@\"\{\}LSUlUk9PVEc2Jy0lKUJPVU5EU19YRzYjJCIiISEiIi0lKUJPVU5EU19ZR0YnLSUtQk9VTkRTX1dJRFRIRzYjJCImUy0iRiotJS5CT1VORFNfSEVJR0hURzYjJCIlNUtGKi0lKUNISUxEUkVORzYi 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

JSFH A declara\303\247\303\243o do teorema de Marden na Tabela 1 \303\251 retirada de [1] onde Dan Kalman fornece coment\303\241rios inteligentes e uma prova geom\303\251trica eficiente. JSFH Seja LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEicEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRInpGJ0YvRjIvRjNRJ25vcm1hbEYnRj1GPQ== um polin\303\264mio de terceiro grau com coeficientes complexos, e cujas ra\303\255zes 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, e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiekYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiM0YnL0Y2USdub3JtYWxGJ0YyRjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0Y+ n\303\243o s\303\243o pontos colineares no plano complexo. Seja LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiVEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= um tri\303\242ngulo com v\303\251rtices em 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, e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiekYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiM0YnL0Y2USdub3JtYWxGJ0YyRjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0Y+. H\303\241 uma \303\272nica elipse inscrita em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiVEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= e tangente ao lados em seus pontos m\303\251dios. Os focos desta elipse s\303\243o as ra\303\255zes de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEicEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKCZwcmltZTtGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4xMTExMTExZW1GJy8lJ3JzcGFjZUdRJjAuMGVtRictSShtZmVuY2VkR0YkNiQtRiM2JC1GLDYlUSJ6RidGL0YyRjlGOUY5. Tabela 1 A declara\303\247\303\243o de Dan Kalman do teorema de Marden \303\211 bastante natural no Maple come\303\247ar com tr\303\252s pontos complexos, fazer uma interpola\303\247\303\243o com um polin\303\264mio c\303\272bico, e para encontrar os zeros de suas derivadas. Ent\303\243o, a partir destes dois focos e os pontos m\303\251dios dos lados do tri\303\242ngulo cujos v\303\251rtices s\303\243o os tr\303\252s pontos originais, \303\251 poss\303\255vel obter a equa\303\247\303\243o da elipse inscrita. No entanto, se os tr\303\252s primeiros pontos s\303\243o tomados como pontos complexos arbitr\303\241rios, as express\303\265es que surgem se tornam excessivamente grandes e pesadas. Kalman sugere a simplifica\303\247\303\243o inteligente de selecionar os tr\303\252s primeiros pontos como 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, e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkobWZlbmNlZEdGJDYkLUYjNiYtSSNtaUdGJDYlUSJ1RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiLEYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GMTYlUSJ2RidGNEY3Rj5GPkY+, com o terceiro ponto no semi-plano superior. N\303\243o h\303\241 perda de generalidade por este dispositivo, uma vez que Kalman mostra que sob uma transforma\303\247\303\243o linear usando transla\303\247\303\243o, rota\303\247\303\243o e escala, o teorema de Marden \303\251 v\303\241lido para uma tripla 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 se e somente se ela vale para a tripla transformada. Depois de observar como complexo podem se tornar express\303\265es gen\303\251ricas, n\303\263s adotamos prontamente as consequ\303\252ncias de uma vis\303\243o Kalman. No Exemplo 1, come\303\247amos com tr\303\252s pontos fixos e usamos o pacote do Maple geometry para obter a elipse inscrita. Isso \303\251 seguido por uma anima\303\247\303\243o interativa que mostra a depend\303\252ncia din\303\242mica do tri\303\242ngulo, seus pontos m\303\251dios, a elipse inscrita, e dos seus focos. No exemplo 2, come\303\247amos com tr\303\252s pontos sugeridos por Kalman, o polin\303\263mio de interpola\303\247\303\243o, e os zeros dos suas derivadas como os focos. As inc\303\263gnitas LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEidUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEidkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIn5GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTEY5apresentam graves problemas para o pacote geometry, assim obtemos a equa\303\247\303\243o da elipse inscrita interpolando uma quadr\303\241tica geral pelos pontos m\303\251dios dos lados do tri\303\242ngulo e possuindo seus centros no ponto m\303\251dio do segmento de reta conectando os focos. Tang\303\252ncia no ponto m\303\251dio \303\251, ent\303\243o, prontamente mostrada. Finalmente, para uma abordagem construtiva para o teorema de Marden, come\303\247amos com o tri\303\242ngulo, e construimos a tangente \303\240 elipse para seus lados nos pontos m\303\251dios. As coordenadas dos focos s\303\243o obtidas ap\303\263s a transforma\303\247\303\243o da elipse para a forma padr\303\243o. Os focos determinados s\303\243o mostrados a ser os mesmos que os zeros da derivada do polin\303\264mio de interpola\303\247\303\243o dos v\303\251rtices do tri\303\242ngulo.

JSFH Seja a tripla de n\303\272meros complexos 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 dada por 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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

L0kiTEc2IjclXiQiIyMqIiMqKl4kISNKIiNIXiQiI24iI1c=

O polin\303\264mio LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEicEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRInpGJ0YvRjIvRjNRJ25vcm1hbEYnRj1GPQ==que interpola estes tr\303\252s pontos \303\251 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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

Ly1JInBHNiI2I0kiekdGJSooLCZGJyIiIl4kISMjKiEjKipGKkYqLCZGJ0YqXiQiI0ohI0hGKkYqLCZGJ0YqXiQhI24hI1dGKkYq

ou 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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

Ly1JInBHNiI2I0kiekdGJSwqXiQiJyh6bCQiJ3oneSMiIiIqJEYnIiIkRiwqJl4kISRHIiEkcyJGLEYnIiIjRiwqJl4kISVvcyImZjMiRixGJ0YsRiw=

e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEicEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKCZwcmltZTtGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4xMTExMTExZW1GJy8lJ3JzcGFjZUdRJjAuMGVtRictSShtZmVuY2VkR0YkNiQtRiM2JC1GLDYlUSJ6RidGL0YyRjlGOUY5 \303\251 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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

L0lOI21yb3cobWkoInAiKSxtbygiJnByaW1lOyIpLG1mZW5jZWQobWkoInoiKSkpRzYiLCoqJEkiekdGJCIiIyIiJEYnISRjIyomXiMhJFckIiIiRidGLkYuXiQhJW9zIiZmMyJGLg==

JSFH Os zeros de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEicEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKCZwcmltZTtGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4xMTExMTExZW1GJy8lJ3JzcGFjZUdRJjAuMGVtRictSShtZmVuY2VkR0YkNiQtRiM2JC1GLDYlUSJ6RidGL0YyRjlGOUY5, ou seja, os focos da elipse inscrita s\303\243o 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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LyZJImZHNiI2IyIiIjckLCYjIiRHIiIiJEYnKiQsJiImM3MiRicqJCIqVGVDMCMjRiciIiNGM0YyI0YnIiInLCYjIiRzIkYsRicqJCwmISYzcyJGJ0YwRjNGMkY0

LyZJImZHNiI2IyIiIzckLCYjIiRHIiIiJCIiIiokLCYiJjNzIkYtKiQiKlRlQzAjI0YtRidGJ0YzIyEiIiIiJywmIyIkcyJGLEYtKiQsJiEmM3MiRi1GMUYnRjNGNA==

JSFH Agora se torna conveniente usar o pacote do Maple geometry para a constru\303\247\303\243o da elipse circunscrita. No entanto, isso requer que os v\303\251rtices do tri\303\242ngulo, e os focos, sejam expressos como pontos no pacote. JSFH Defina os tr\303\252s v\303\251rtices interpolados, como LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIixGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRiw2JVEiQkYnRi9GMkY1LUYsNiVRIkNGJ0YvRjJGOQ==. 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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder Defina os focos LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiMUYnL0Y2USdub3JtYWxGJ0YyRjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0Y+ e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiMkYnL0Y2USdub3JtYWxGJ0YyRjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0Y+ como pontos geom\303\251tricos LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiRkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiMUYnL0Y2USdub3JtYWxGJ0YyRjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0Y+ e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiRkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiMkYnL0Y2USdub3JtYWxGJ0YyRjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0Y+. 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 Obter 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, respectivamente os pontos m\303\251dios dos lados LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEjQUJGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSIsRicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0YxLyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnLUYsNiVRI0JDRidGL0YyRjUtRiw2JVEjQUNGJ0YvRjJGOQ== do tri\303\242ngulo formado pelos tr\303\252s v\303\251rtices interpolados LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIixGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRiw2JVEiQkYnRi9GMkY1LUYsNiVRIkNGJ0YvRjJGOQ==. 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 As coordenadas dos tr\303\252s pontos m\303\251dios s\303\243o encontradas, e a eles atribu\303\255dos os respectivos nomes LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUklbXN1YkdGJDYlLUkmbW92ZXJHRiQ2JS1JI21pR0YkNiVRIk1GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2JS1JI21vR0YkNi1RIl5GJy9GOVEnbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkUvJSlzdHJldGNoeUdGRS8lKnN5bW1ldHJpY0dGRS8lKGxhcmdlb3BHRkUvJS5tb3ZhYmxlbGltaXRzR0ZFLyUnYWNjZW50R0ZFLyUnbHNwYWNlR1EsMC4xMTExMTExZW1GJy8lJ3JzcGFjZUdGVEY1RjgvRlFGNy1GIzYlLUYyNiVRI2FiRidGNUY4RjVGOC8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnLUY+Ni1RIixGJ0ZBRkMvRkdGN0ZIRkpGTEZORlAvRlNRJjAuMGVtRicvRlZRLDAuMzMzMzMzM2VtRictRiw2JUYuLUYjNiUtRjI2JVEjYmNGJ0Y1RjhGNUY4RmduRmpuLUYsNiVGLi1GIzYlLUYyNiVRI2FjRidGNUY4RjVGOEZnbkZB. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYyLUklbXN1YkdGJDYmLUkmbW92ZXJHRiQ2JS1JI21pR0YkNiVRIk1GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Iy1JI21vR0YkNi1RIl5GJy9GOVEnbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkUvJSlzdHJldGNoeUdGRS8lKnN5bW1ldHJpY0dGRS8lKGxhcmdlb3BHRkUvJS5tb3ZhYmxlbGltaXRzR0ZFLyUnYWNjZW50R0ZFLyUnbHNwYWNlR1EsMC4xMTExMTExZW1GJy8lJ3JzcGFjZUdGVC9GUUY3LUYjNiMtRjI2JVEjYWJGJ0Y1RjgvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy9JK21zZW1hbnRpY3NHRiRRJ2F0b21pY0YnLUY+Ni1RKiZjb2xvbmVxO0YnRkFGQ0ZGRkhGSkZMRk5GUC9GU1EsMC4yNzc3Nzc4ZW1GJy9GVkZhby1GMjYlUSxjb29yZGluYXRlc0YnRjVGOC1JKG1mZW5jZWRHRiQ2JC1GIzYjLUYsNiZGMUZYRmduRmpuRkEtRj42LVEiO0YnRkFGQy9GR0Y3RkhGSkZMRk5GUC9GU1EmMC4wZW1GJ0Ziby1JJ21zcGFjZUdGJDYmLyUnaGVpZ2h0R1EmMC4wZXhGJy8lJndpZHRoR0ZicC8lJmRlcHRoR0ZocC8lKmxpbmVicmVha0dRKG5ld2xpbmVGJy1GLDYmRi4tRiM2Iy1GMjYlUSNiY0YnRjVGOEZnbkZqbkZdb0Zjby1GZ282JC1GIzYjLUYsNiZGMUZicUZnbkZqbkZBRl1wRmNwLUYsNiZGLi1GIzYjLUYyNiVRI2FjRidGNUY4RmduRmpuRl1vRmNvLUZnbzYkLUYjNiMtRiw2JkYxRl9yRmduRmpuRkE=

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

NyQjIiNoIiIjIiNr

NyQiIz0jIiN0IiIj

NyQjIiRmIiIiIyMiJFYiRiU=

Definir LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiVEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=, o tri\303\242ngulo formado pelos v\303\251rticesLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbW9HRiQ2LVEifGZyRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSV0cnVlRicvJSpzZXBhcmF0b3JHUSZmYWxzZUYnLyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjcvJShsYXJnZW9wR0Y3LyUubW92YWJsZWxpbWl0c0dGNy8lJ2FjY2VudEdGNy8lJ2xzcGFjZUdRLDAuMTY2NjY2N2VtRicvJSdyc3BhY2VHRkQtSSNtaUdGJDYlUSJBRicvJSdpdGFsaWNHRjQvRjBRJ2l0YWxpY0YnLUYsNi1RIixGJ0YvL0YzRjcvRjZGNC9GOUY3RjpGPEY+RkAvRkNRJjAuMGVtRicvRkZRLDAuMzMzMzMzM2VtRictRkg2JVEiQkYnRktGTUZPLUZINiVRIkNGJ0ZLRk1GLw==}, como um objeto no pacote geometry. 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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

%; O comando ellipse no pacote geometry vai definir uma elipse dos focos e a dist\303\242ncia de um foco a um ponto na elipse para outro foco. Esta dist\303\242ncia \303\251 realmente o comprimento do eixo principal. Tomamos como ponto sobre a elipse no ponto m\303\251dio de um lado do tri\303\242ngulo LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiVEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiZEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKiZjb2xvbmVxO0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZMLUYsNiVRKXNpbXBsaWZ5RidGL0YyLUkobWZlbmNlZEdGJDYkLUYjNictRiw2JVEpZGlzdGFuY2VGJ0YvRjItRlM2JC1GIzYlLUklbXN1YkdGJDYmLUYsNiVRIk1GJ0YvRjItRiM2Iy1GLDYlUSNhYkYnRi9GMi8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnL0krbXNlbWFudGljc0dGJFEnYXRvbWljRictRjY2LVEiLEYnRjlGOy9GP0YxRkBGQkZERkZGSC9GS1EmMC4wZW1GJy9GTlEsMC4zMzMzMzMzZW1GJy1GaW42Ji1GLDYlUSJGRidGL0YyLUYjNiMtSSNtbkdGJDYkUSIxRidGOUZjb0Zmb0Y5LUY2Ni1RIitGJ0Y5RjtGPkZARkJGREZGRkgvRktRLDAuMjIyMjIyMmVtRicvRk5GYHFGVy1GUzYkLUYjNiVGaG5GaW8tRmluNiZGY3AtRiM2Iy1GaXA2JFEiMkYnRjlGY29GZm9GOUY5

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LCYqJCwqIiVIcCIiIiokLCYiJjNzIkYmKiQiKlRlQzAjI0YmIiIjRi1GLCIkWSJGKiIiJSokLCYhJjNzIkYmRipGLUYsISMhKUYsI0YmIiInKiQsKkYlRiZGJyEkWSJGKkYvRjAiIyEpRixGNA==

Definir (como um objeto no pacote geometry) a elipse LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiRUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= \303\251 a elipse cujos focos s\303\243oLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiRkYnLyUnaXRhbGljR1EldHJ1ZUYnL0YwUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiMUYnRi9GTUZQLyUvc3Vic2NyaXB0c2hpZnRHUSIwRidGLw== e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiRkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYjLUkjbW5HRiQ2JFEiMkYnL0Y2USdub3JtYWxGJy8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYn

JkkiRkc2IjYjIiIj

, cujo maior eixo tem comprimento LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEiZEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw==, e que cont\303\251m os pontos LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiTUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYjLUYvNiVRI2FiRidGMkY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRic=

Error, `,` unexpected

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 Obter a equa\303\247\303\243o cartesiana da elipse LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiRUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=, e atribuir a esta equa\303\247\303\243o, o nome LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjZXFGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEjZXFGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSomY29sb25lcTtGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GLDYlUSlFcXVhdGlvbkYnRi9GMi1JKG1mZW5jZWRHRiQ2JC1GIzYjLUYsNiVRIkVGJ0YvRjJGOQ==

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LywuSSJ5RzYiIyEoa3M5JiIiJEkieEdGJSMiKD9WJVwiIioqJEYkIiIjIyIna0c/RiwqJkYpIiIiRiRGMiMhJyFHJD1GLCokRilGLiMiJitfJ0YsIyIqV0FsLiRGLEYyIiIh

Seja LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiSEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= o centro da elipse LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiRUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=. Suas coordenadas s\303\243o exibidas \303\240 direita. Observe a divis\303\243o por 3, para cada coordenada. A inspe\303\247\303\243o cuidadosa das coordenadas dos pontos LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIixGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRiw2JVEiQkYnRi9GMkY1LUYsNiVRIkNGJ0YvRjJGOQ==, leva \303\240 suspeita de que o centro de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiRUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= recai sobre o centr\303\263ide do tri\303\242ngulo LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiVEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=. 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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

NyQjIiRHIiIiJCMiJHMiRiU=

Essa suspeita \303\251 confirmada por encontrar as coordenadas do centr\303\263ide do tri\303\242ngulo LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiVEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=. 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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

NyQjIiRHIiIiJCMiJHMiRiU=

Tabela 2 A elipse do teorema de Marden, obtida com o pacote geometria do Maple JSFH Figura 1, feita com o comando draw a partir do pacote geometria, mostra o tri\303\242ngulo LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiVEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= e a elipse LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiRUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=. Os focos LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiRkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiMUYnL0Y2USdub3JtYWxGJ0YyRjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0Y+ e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiRkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiMkYnL0Y2USdub3JtYWxGJ0YyRjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0Y+ s\303\243o mostrados como pontos verdes, o centro LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiSEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= como ponto vermelho, e os pontos m\303\251dios como pontos azuis. Os vertices de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiVEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= s\303\243o desenhados como quadrados pretos. JSFHJSFH 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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

%;

LSUlUExPVEc2My0lJ0NVUlZFU0c2JTdVNyQkIitAOSlSKXohIikkIitwb0whZighIik3JCQiKyl5QScqKXkhIikkIispby1mcSghIik3JCQiK3d6N1F4ISIpJCIrNipmLnooISIpNyQkIiteaCk9YCghIikkIisoZndCJXkhIik3JCQiK2MpXFRGKCEiKSQiKzRDOGh5ISIpNyQkIithUCkqb3AhIikkIipjSmoleSEiKDckJCIrKlwrN2knISIpJCIrbnU/KXooISIpNyQkIitUW0dPaSEiKSQiK3UhPnZyKCEiKTckJCIrRXJJP2UhIikkIispKSlRYmcoISIpNyQkIit0diMpemAhIikkIissSC5rdSEiKTckJCIrMEd6QFwhIikkIitcRkImSCghIik3JCQiKkpFTVglISIoJCIrNDAhPTUoISIpNyQkIisuWDYjKVIhIikkIitEbnknKW8hIik3JCQiK2ItSDpOISIpJCIrJEgjZWBtISIpNyQkIitpY0pnSSEiKSQiKyYpXCdlUychIik3JCQiK1ZmT0NFISIpJCIrXjlhWmghIik3JCQiKyZHO1ZAIyEiKSQiKy9jbyMpZSEiKTckJCIrQU1qTz0hIikkIisnUXVhaCYhIik3JCQiK05PRihcIiEiKSQiK3U9N11gISIpNyQkIitIKSllLDchIikkIitPRyIzNCYhIik3JCQiKktAQ2EqISIpJCIrSG5qVFshIik3JCQiKU5NImYoISIoJCIqQEJsZyUhIig3JCQiKllDTT4nISIpJCIraCw9KlElISIpNyQkIipENTJQJiEiKSQiKzRfLiQ+JSEiKTckJCIqY3ZoOCYhIikkIipvIj1AUyEiKDckJCIqNj5OXCYhIikkIiswKUhqKFEhIik3JCQiKlUwclYnISIpJCIrJilSd2dQISIpNyQkIipiYD8meiEiKSQiK2luSXdPISIpNyQkIisnPVo5KyIhIikkIit4K0hDTyEiKTckJCIqWyQ9ZjchIigkIitqVWAwTyEiKTckJCIreiZcVmMiISIpJCIrN15MP08hIik3JCQiK01HODc+ISIpJCIrMSNmJW9PISIpNyQkIiskXFtxSCMhIikkIisqZloiXFAhIik3JCQiKzNpLThGISIpJCIrJnlGNidRISIpNyQkIitoZF1gSiEiKSQiK3JQai1TISIpNyQkIitIMGE2TyEiKSQiK0NSVnJUISIpNyQkIitDcSEqelMhIikkIitraCdbTyUhIik3JCQiK0opPTdiJSEiKSQiK1sqeil6WCEiKTckJCIrekkvPV0hIikkIipRJTM4WyEiKDckJCIrc3csdGEhIikkIispbywzMSYhIik3JCQiKyJSbiozZiEiKSQiK0FfNz5gISIpNyQkIitccSw+aiEiKSQiK281KVJlJiEiKTckJCIrNyoqcCdwJyEiKSQiKyhHIz5eZSEiKTckJCIrKnBmZy4oISIpJCIrKnpXbDYnISIpNyQkIisvWHVKdCEiKSQiK1BRJmVQJyEiKTckJCIrLDc0enYhIikkIitWKkhdaSchIik3JCQiKycpKik+dXghIikkIitpTTlnbyEiKTckJCIrIiozKlIieiEiKSQiKzhsW3hxISIpNyQkIisxQkUnKnohIikkIitrOWp0cyEiKTckJCIrdWRyPiEpISIpJCIrJCpcW1h1ISIpNyQkIitAOSlSKXohIikkIitwb0whZighIiktJSZDT0xPUkc2JiUkUkdCRyQiIzUhIiIkIiIhISIiJCIiISEiIi0lJlNUWUxFRzYjJSVMSU5FRy0lJ1BPSU5UU0c2JTckJCIkMCQhIiIkIiRTJyEiIi0lJkNPTE9SRzYmJSRSR0JHJCIiISEiIiQiIiEhIiIkIiM1ISIiLSUnU1lNQk9MRzYkJS1fU09MSURDSVJDTEVHIiM6LSUnUE9JTlRTRzYlNyQkIiQhPSEiIiQiJGwkISIiLSUmQ09MT1JHNiYlJFJHQkckIiIhISIiJCIiISEiIiQiIzUhIiItJSdTWU1CT0xHNiQlLV9TT0xJRENJUkNMRUciIzotJSdQT0lOVFNHNiU3JCQiJCZ6ISIiJCIkOighIiItJSZDT0xPUkc2JiUkUkdCRyQiIiEhIiIkIiIhISIiJCIjNSEiIi0lJ1NZTUJPTEc2JCUtX1NPTElEQ0lSQ0xFRyIjOi0lJ1BPSU5UU0c2JTckJCIrKjNjZSR5ISIpJCIpLE07diEiJy0lJkNPTE9SRzYmJSRSR0JHJCIiISEiIiQiIzUhIiIkIiIhISIiLSUnU1lNQk9MRzYjJS1fU09MSURDSVJDTEVHLSUnUE9JTlRTRzYlNyQkIipYc1oocCEiKSQiK21sS11SISIpLSUmQ09MT1JHNiYlJFJHQkckIiIhISIiJCIjNSEiIiQiIiEhIiItJSdTWU1CT0xHNiMlLV9TT0xJRENJUkNMRUctJSdQT0lOVFNHNiU3JCQiJD8qISIiJCIkISoqISIiLSUmQ09MT1JHNiYlJFJHQkckIiIhISIiJCIiISEiIiQiIiEhIiItJSdTWU1CT0xHNiQlKl9TT0xJREJPWEciIzotJSdQT0lOVFNHNiU3JCQhJDUkISIiJCIkIUghIiItJSZDT0xPUkc2JiUkUkdCRyQiIiEhIiIkIiIhISIiJCIiISEiIi0lJ1NZTUJPTEc2JCUqX1NPTElEQk9YRyIjOi0lJ1BPSU5UU0c2JTckJCIkcSchIiIkIiRTJSEiIi0lJkNPTE9SRzYmJSRSR0JHJCIiISEiIiQiIiEhIiIkIiIhISIiLSUnU1lNQk9MRzYkJSpfU09MSURCT1hHIiM6LSUnUE9JTlRTRzYlNyQkIitubW1tVSEiKSQiK0xMTExkISIpLSUmQ09MT1JHNiYlJFJHQkckIiM1ISIiJCIiISEiIiQiIiEhIiItJSdTWU1CT0xHNiMlLV9TT0xJRENJUkNMRUctJSdDVVJWRVNHNiU3JDckJCIkPyohIiIkIiQhKiohIiI3JCQhJDUkISIiJCIkIUghIiItJSZDT0xPUkc2JiUkUkdCRyQiIiEhIiIkIiIhISIiJCIiISEiIi0lJlNUWUxFRzYjJSVMSU5FRy0lJ0NVUlZFU0c2JTckNyQkISQ1JCEiIiQiJCFIISIiNyQkIiRxJyEiIiQiJFMlISIiLSUmQ09MT1JHNiYlJFJHQkckIiIhISIiJCIiISEiIiQiIiEhIiItJSZTVFlMRUc2IyUlTElORUctJSdDVVJWRVNHNiU3JDckJCIkcSchIiIkIiRTJSEiIjckJCIkPyohIiIkIiQhKiohIiItJSZDT0xPUkc2JiUkUkdCRyQiIiEhIiIkIiIhISIiJCIiISEiIi0lJlNUWUxFRzYjJSVMSU5FRy0lJVZJRVdHNiQ7JCEkNSQhIiIkIiQ/KiEiIjskIis8JnBpdyMhIikkIiQhKiohIiItJSpBWEVTU1RZTEVHNiMlJU5PTkVHLSUoU0NBTElOR0c2IyUsQ09OU1RSQUlORURHLSUlUk9PVEc2Jy0lKUJPVU5EU19YRzYjJCIkKyIhIiItJSlCT1VORFNfWUc2IyQiJCEqKSEiIi0lLUJPVU5EU19XSURUSEc2IyQiJTVRISIiLSUuQk9VTkRTX0hFSUdIVEc2IyQiJT9BISIiLSUpQ0hJTERSRU5HNiI=

Figura 1 Elipse circunscrita do teorema de Marden JSFH O fato da elipse LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiRUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= tocar o tri\303\242ngulo nos pontos m\303\251dios dos lados \303\251 demonstrado pelo resultado da substitui\303\247\303\243o das coordenadas dos pontos m\303\251dios na equa\303\247\303\243o cartesiana da elipse LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiRUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=. A elipse E cont\303\251m cada ponto m\303\251dio, desde que a sua equa\303\247\303\243o seja satisfeita por cada ponto. JSFH 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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LyIiIUYj

LyIiIUYj

LyIiIUYj

JSFHJSFH Para mostrar que a elipse LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVEiRUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw== \303\251 tangente aos lados do tri\303\242ngulo nos pontos m\303\251dios, temos a derivada ao longo da elipse. Isto \303\251 obtido pelo comando do Maple implicitdiff. 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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LyomSSNkeUc2IiIiIkkjZHhHRiUhIiIsJComLCghJi89J0YmSSJ5R0YlIiUiSCNJInhHRiUhJUk7RiYsKCEnN14nKkYmRi0iJmVgI0YvISZiOSJGKCIiJg==

JSFH A Tabela 3 compara a inclina\303\247\303\243o de cada lado do tri\303\242ngulo LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiVEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= e a inclina\303\247\303\243o da elipse LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVEiRUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw== no ponto m\303\251dio do lado correspondente. JSFH 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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

= print(); # input placeholder

IyIjcSIkQiI=

JSFH LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEmc2xvcGVGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiQtRiM2JS1GLDYlUSJBRidGL0YyLUkjbW9HRiQ2LVEiLEYnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0ZFLyUqc3ltbWV0cmljR0ZFLyUobGFyZ2VvcEdGRS8lLm1vdmFibGVsaW1pdHNHRkUvJSdhY2NlbnRHRkUvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GLDYlUSJCRidGL0YyRkE=

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

= print(); # input placeholder

IyIjcSIkQiI=

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

= print(); # input placeholder

IyIjOiIjKSo=

JSFH LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEmc2xvcGVGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiQtRiM2JS1GLDYlUSJCRidGL0YyLUkjbW9HRiQ2LVEiLEYnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0ZFLyUqc3ltbWV0cmljR0ZFLyUobGFyZ2VvcEdGRS8lLm1vdmFibGVsaW1pdHNHRkUvJSdhY2NlbnRHRkUvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GLDYlUSJDRidGL0YyRkE=

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

= print(); # input placeholder

IyIjOiIjKSo=

JSFH 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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

= print(); # input placeholder

IyIjNiIiJg==

JSFH LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEmc2xvcGVGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiQtRiM2JS1GLDYlUSJBRidGL0YyLUkjbW9HRiQ2LVEiLEYnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0ZFLyUqc3ltbWV0cmljR0ZFLyUobGFyZ2VvcEdGRS8lLm1vdmFibGVsaW1pdHNHRkUvJSdhY2NlbnRHRkUvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GLDYlUSJDRidGL0YyRkE=

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

= print(); # input placeholder

IyIjNiIiJg==

JSFH Tabela 3 Verifica\303\247\303\243o se a elipse LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiRUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= \303\251 tangente ao tri\303\242ngulo LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiVEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= no ponto m\303\251dio de seus lados JSFH Aparentemente, tendo como focos de uma elipse os zeros do polin\303\263mio c\303\272bico de interpola\303\247\303\243o dos tr\303\252s v\303\251rtices de um tri\303\242ngulo no plano complexo, e for\303\247ando a elipse a passar pelo ponto m\303\251dio de um dos lados do tri\303\242ngulo, \303\251 o suficiente para determinar se uma elipse \303\251 tangente aos tr\303\252s lados do tri\303\242ngulo nos pontos m\303\251dios dos lados. JSFH

JSFH Durante as investiga\303\247\303\265es detalhadas neste artigo, tentamos ignorar a tarefa de codifica\303\247\303\243o interativa Figura 2. A atra\303\247\303\243o era muito forte, por\303\251m, ent\303\243o tentou-se uma codifica\303\247\303\243o baseada no pacote geometry. Infelizmente, o diagrama resultante respondeu devagar demais para ser \303\272til. Ent\303\243o codificou-se uma solu\303\247\303\243o baseada em interpola\303\247\303\243o: interpolou-se uma quadr\303\241tica geral, atrav\303\251s dos pontos m\303\251dios do tri\303\242ngulo formado por tr\303\252s pontos dados, utilizando tang\303\252ncia para obter as condi\303\247\303\265es adicionais necess\303\241rias para determinar os seis coeficientes na quadr\303\241tica geral. Mas o quadr\303\241tica geral \303\251 determinada por apenas cinco coeficientes - \303\251 sempre poss\303\255vel dividir atrav\303\251s de um dos coeficientes diferentes de zero. Esta distin\303\247\303\243o dos comandos do Maple solve e fsolv d\303\241 algum problema. Desde que os pontos sejam lidos a partir de um gr\303\241fico como n\303\272meros de ponto flutuante, o comando solve encontra apenas a solu\303\247\303\243o zero de seis em seis inc\303\263gnitas de equa\303\247\303\265es que n\303\243o s\303\243o independentes. O comando fsolve n\303\243o encontra nenhuma solu\303\247\303\243o. No entanto, se os pontos flutuantes s\303\243o convertidos para n\303\272meros racionais, solve ir\303\241 obter a solu\303\247\303\243o das seis equa\303\247\303\265es em termos de uma das inc\303\263gnitas. Normalizando, podemos obter a equa\303\247\303\243o da elipse, e seu gr\303\241fico pode ser adicionado a um gr\303\241fico dos pontos e retas relevantes. O c\303\263digo da Figura 2 \303\251 escrito como um m\303\263dulo contendo os procedimentos que s\303\243o chamados pelos campos "clicar e arrastar" no componente gr\303\241fico. Inicialize este c\303\263digo (e figura), clicando no bot\303\243o no topo na Figura 2. Ela pode ser visualizada atrav\303\251s do Componente de Propriedades do Menu de Contexto. O c\303\263digo \303\251 similar ao que foi utilizado para o modelo de tarefa Curvas de B\303\251zier. JSFHuse DocumentTools, plots, Student[Precalculus] in NEDRAM := module() local L,N,dragIndex,q,a,b,c,d,e,f,qp; export CL, DrawFig, DR, DragEnds; q := a*x^2+b*x*y+c*y^2+d*x+e*y+f: qp := implicitdiff(q,y,x): Do(%Plot0 = plot([[0,0]], x=-5..5,y=0..10, style=point, axes=none, view=[-5..5,0..10], color=white)): L := []: N := 2; dragIndex := -2; ############ CL := proc() local cx,cy,G; Do(cx = %Plot0(clickx)); Do(cy = %Plot0(clicky)); if nops(L)<N then L := [L[],[cx,cy]]; G := plot(L,style=point, symbol=solidcircle, color=blue, symbolsize=15, view=[-5..5,0..10], axes=none); Do(%Plot0 = G); elif nops(L)=N then L := [L[],[cx,cy]]; DrawFig(L); dragIndex := -2; else return; end if; end proc: ################ DrawFig := proc(L) local LL,P,k,z,PP,F1,F2,H,M12,M23,M13,S12,S23,S13,eq,p,R,S,q1,q2,temp; LL := convert(L,rational): P := mul(z-(LL[k][1]+sqrt(-1)*LL[k][2]),k=1..3): PP := evalc([solve(diff(P,z),z)]): F1 := [Re(PP[1]),Im(PP[1])]: F2 := [Re(PP[2]),Im(PP[2])]: H := Midpoint(F1,F2): M12 := Midpoint(LL[1],LL[2]): M23 := Midpoint(LL[2],LL[3]): M13 := Midpoint(LL[1],LL[3]): S12 := Slope(LL[1],LL[2]): S23 := Slope(LL[2],LL[3]): S13 := Slope(LL[1],LL[3]): eq[1] := eval(q,Equate([x,y],M12)): eq[2] := eval(q,Equate([x,y],M23)): eq[3] := eval(q,Equate([x,y],M13)): eq[4] := numer(normal(eval(qp,Equate([x,y],M12))-S12)): eq[5] := numer(normal(eval(qp,Equate([x,y],M23))-S23)): eq[6] := numer(normal(eval(qp,Equate([x,y],M13))-S13)): S := solve({seq(eq[k],k=1..6)},{a,b,c,d,e,f}): q1 := eval(q,S): temp := coeff(q1,x,2): q2 := simplify(q1/temp): p[1] := implicitplot(q2,x=-5..5,y=0..10,gridrefine=3,rangeasview): p[2] := plot([[LL[1],LL[2]],[LL[2],LL[3]],[LL[1],LL[3]]],color=black): p[3] := plot([M12,M23,M13],style=point,symbol=solidcircle,color=blue,symbolsize=15): p[4] := plot(LL,style=point,symbol=solidbox,color=black,symbolsize=15): p[5] := plot([H],style=point,symbol=solidcircle,color=red,symbolsize=15): p[6] := plot([F1,F2],style=point,symbol=solidcircle,color=green,symbolsize=15): R := display([seq(p[k],k=1..6)],axes=none,scaling=constrained): Do(%Plot0 = R); end proc: ################## DR := proc() local x0,y0, x1,y1,j; Do(x0 = %Plot0(startx)); Do(y0 = %Plot0(starty)); Do(x1 = %Plot0(endx)); Do(y1 = %Plot0(endy)); if abs(x1)>5 then x1:=5*signum(x1);end if; if y1>10 then y1:=10;end if; if y1<0 then y1:=0;end if; if dragIndex < 0 then for j to nops(L) do if Student[Precalculus][Distance](L[j],[x0,y0])<.8 then dragIndex := j; end if; end do; else L := eval(L,L[dragIndex]=[x1,y1]); DrawFig(L); end if; end proc: ######################## DragEnds := proc() dragIndex := -2; end proc: end module: end use: JSFHuse DocumentTools in if type(NEDRAM,`module`) then NEDRAM:-DragEnds() end if; end use; use DocumentTools in if type(NEDRAM,`module`) then NEDRAM:-CL() end if; end use; use DocumentTools in if type(NEDRAM,`module`) then NEDRAM:-DR() end if; end use; -%%PLOTG60-%'CURVESG6$7ail7$$!2tCnii&*zo#!#;$"#b!""7$$!1W3Gd&yQm#!#:$"1X3Gd&yQY&!#:7$$!2L\6I$)eXl#!#;$"$X&!"#7$$!$l#!"#$"1(=g#30`Va!#:7$$!1K9)=>F*=E!#:$"#a!""7$$!#E!""$"1K7"puvYP&!#:7$$!2w'G;h[J"e#!#;$"$N&!"#7$$!$b#!"#$"1By$>MB/J&!#:7$$!1)3NDiU;a#!#:$"#`!""7$$!#D!""$"1pV*>9/-D&!#:7$$!2wQ8h(p#)*\#!#;$"$D&!"#7$$!1*R<(*RF&)\#!#:$"1*R<(*RF&[_!#:7$$!2vibp!HjbC!#;$"#_!""7$$!$X#!"#$"1rH*=(o'Q>&!#:7$$!1/#*fZe;4C!#:$"$:&!"#7$$!#C!""$"1u^Ie+^S^!#:7$$!1.#4ezO.O#!#:$"#^!""7$$!$N#!"#$"2&)*z(4`6)*3&!#;7$$!2U)Qb;s/4B!#;$"$0&!"#7$$!#B!""$"1TLe\>]T]!#:7$$!2=TVn,$>bA!#;$"#]!""7$$!$D#!"#$"1)R$\rrM&*\!#:7$$!2k)*4)p_65A!#;$"1')*4)p_6g\!#:7$$!#A!""$"1%GAul$>^\!#:7$$!2wvs'Qni)>#!#;$"$&\!"#7$$!$:#!"#$"1<'*oI^34\!#:7$$!1viR:8/R@!#:$"#\!""7$$!#@!""$"1"\]fsO'o[!#:7$$!1tz;i$\k2#!#:$"$&[!"#7$$!$0#!"#$"1N]])p)pH[!#:7$$!2O#fyM@r5?!#;$"#[!""7$$!#?!""$"0HnuyQ@z%!#97$$!1F">)oRmr>!#:$"1F">)oRmrZ!#:7$$!$&>!"#$"1oR&f>sgv%!#:7$$!2y,UG9F9%>!#;$"$v%!"#7$$!#>!""$"1sP!z](\@Z!#:7$$!2_M=*[HCo=!#;$"#Z!""7$$!$&=!"#$"1Qf:&e%*zo%!#:7$$!1H#*H=*ff"=!#:$"2&H#*H=*ffm%!#;7$$!#=!""$"1_]x!>%obY!#:7$$!2dDu3")>5z"!#;$"$l%!"#7$$!$v"!"#$"1a"[G)euCY!#:7$$!2GCsW+."4<!#;$"#Y!""7$$!#<!""$"2Nm(H='QYf%!#;7$$!1*)oS]]F(o"!#:$"1))oS]]F(e%!#:7$$!$l"!"#$"1R`#zn_ec%!#:7$$!2M-Ut@3>i"!#;$"$b%!"#7$$!#;!""$"1K;$oPgz`%!#:7$$!2_^)fz%fQd"!#;$"1:&)fz%fQ_%!#:7$$!$b"!"#$"1([!*3d!46X!#:7$$!2/76XMt)G:!#;$"#X!""7$$!#:!""$"1LmB0GB&[%!#:7$$!2$ylXEqPq9!#;$"1ylXEqPqW!#:7$$!$X"!"#$"0VEqJ]-Y%!#97$$!2X61b&)[*G9!#;$"$X%!"#7$$!#9!""$"1COOi3EOW!#:7$$!22i;"*QGVP"!#;$"1@m6*QGVU%!#:7$$!$N"!"#$"1>JHol88W!#:7$$!1(H1:r<3K"!#:$"#W!""7$$!#8!""$"1V$*)y8i3R%!#:7$$!2%4p^fy)RG"!#;$"2&4p^fy)RQ%!#;7$$!$D"!"#$"1`/^QncpV!#:7$$!18uQNV!G?"!#:$"$N%!"#7$$!#7!""$"1$*R9Ye')[V!#:7$$!1VkM8b7)>"!#:$"1VkM8b7[V!#:7$$!$:"!"#$"/&ez(*p$HV!#87$$!2N<?!Gqr;6!#;$"1t,-Gqr;V!#:7$$!#6!""$"1fv&4?_/J%!#:7$$!2t[g**)GPr5!#;$"#V!""7$$!$0"!"#$"1O;GXiQ#H%!#:7$$!2$RY?LMMQ5!#;$"1RY?LMM)G%!#:7$$!#5!""$"1-&=$H)f_F%!#:7$$!1BaOKeyH'*!#;$"1UlB$eyHE%!#:7$$!#&*!"#$"1[mbG#[(eU!#:7$$!1J$Qzy)[B#*!#;$"$D%!"#7$$!"*!""$"1LqmK+5VU!#:7$$!1CWOsM^,*)!#;$"1UkBZ8:SU!#:7$$!#&)!"#$"1OLF$op$GU!#:7$$!1v-s+_*y>)!#;$"1G?2?&*y>U!#:7$$!")!""$"1(GM&)y!H9U!#:7$$!0Vn6LG>^(!#:$"2Du;J$G>,U!#;7$$!#v!"#$"1*R*f'G!)3?%!#:7$$!1.e2u'G^Y(!#;$"#U!""7$$!"(!""$"10!ztBU&)=%!#:7$$!1O(=ckN)\o!#;$"1u=ckN)\=%!#:7$$!#l!"#$"1Q/"Ql?p<%!#:7$$!0ZXm:8P?'!#:$"1[Xm:8PqT!#:7$$!"'!""$"1bF*\![+mT!#:7$$!1$zvq?wCd&!#;$"2&zvq?wCdT!#;7$$!#b!"#$"1#)G)G18e:%!#:7$$!1t"RW5b8>&!#;$"$:%!"#7$$!"&!""$"1dmGGK[YT!#:7$$!1l"*f^BSd\!#;$"1;*f^BSd9%!#:7$$!#X!"#$"1nP!)[Y3QT!#:7$$!2x=%)RL*\eV!#<$"1=%)RL*\e8%!#:7$$!"%!""$"1`q@%=[/8%!#:7$$!2NHp>!yMsP!#<$"1Hp>!yMs7%!#:7$$!#N!"#$"0UZ&)p$fBT!#97$$!1'[eWDG&)>$!#;$"1[eWDG&)>T!#:7$$!"$!""$"1w$*=_<a<T!#:7$$!2/4s=RRmj#!#<$"14s=RRm8T!#:7$$!#D!"#$"1KopKOJ7T!#:7$$!0op&RrH'3#!#:$"1op&RrH'3T!#:7$$!"#!""$"1'o;sQJz5%!#:7$$!18:[LP8Z:!#;$"1^"[LP8Z5%!#:7$$!#:!"#$"1sRncyT/T!#:7$$!1fUPjoz=5!#;$"1DuL'oz=5%!#:7$$!""!""$"1/+#=r'z,T!#:7$$!1W^c&p)[4]!#<$"2:lbp)[4+T!#;7$$!"&!"#$"1jHE"\#4+T!#:7$$!1=9O#4a!)Q%!#<$"#T!""7$$""!!""$"1h>R6PN*4%!#:7$$"1-voHpS%\'!#>$"0.2$f0N*4%!#97$$""&!"#$"0FM<k`&*4%!#97$$"1YC)p7;S/&!#<$"1v,tQ)f&*4%!#:7$$"04Cg*[,Lp!#;$"#T!""7$$"1Z7x:?MG**!#<$"1'GU)zlr+T!#:7$$"""!""$"1l$p"Q1u+T!#:7$$"2[Mb7rN=Z"!#<$"2bYu)Gk"G5%!#;7$$"#:!"#$"1$*fC6$oH5%!#:7$$"1K_5><%=%>!#;$"1x%*3Ge"e5%!#:7$$""#!""$"1`'pj5]i5%!#:7$$"2:odeI;JS#!#<$"1KUTp$)o4T!#:7$$"#D!"#$"1"\1kp;16%!#:7$$"1Z.g:L"f&G!#;$"1l*R%o'3W6%!#:7$$""$!""$"2&pW!f&**4;T!#;7$$"1`Z-ZoZ+L!#;$"1DvH:B&*>T!#:7$$"#N!"#$"1WQ_?ItAT!#:7$$"2&[Hl;</PP!#<$"2bqM$GeHET!#;7$$""%!""$"0$*H+N]08%!#97$$"1,3*e*Q$e;%!#;$"20#4T5mTLT!#;7$$"#X!"#$"2:t*4&z(eRT!#;7$$"2(*><O#42(e%!#<$"0GQw!HHTT!#97$$""&!""$"1dY@oE))\T!#:7$$"1B=*eHi4+&!#;$"1=3TqP!*\T!#:7$$"1<c)p&G60]!#;$"$:%!"#7$$"1Qa_(=wXS&!#;$"1duC"QU&fT!#:7$$"#b!"#$"1xws`'[>;%!#:7$$"13#elTL5!e!#;$"1zTMem*)pT!#:7$$""'!""$"1*z9r]Aa<%!#:7$$"16^Pwbc!>'!#;$"1*[iBWV4=%!#:7$$"#l!"#$"1Eu%obX.>%!#:7$$"1T;2fROtl!#;$"1OG4/Om#>%!#:7$$"1%[adI5`z'!#;$"#U!""7$$"1<,#>q3z%p!#;$"1*)z!)H"4_?%!#:7$$""(!""$"1ktG<#oq?%!#:7$$"1:J!)y=W8t!#;$"1*o>@"el=U!#:7$$"#v!"#$"1kc))H>&eA%!#:7$$"1:)fE6\En(!#;$"1=St)3NFB%!#:7$$"")!""$"2v0'o$[GjC%!#;7$$"1Wi#=[/d-)!#;$"1wt"=bHuC%!#:7$$"1=%\*eUS$3)!#;$"$D%!"#7$$"1r\\a&*[o$)!#;$"2D]]X/^JE%!#;7$$"#&)!"#$"0_,&3$f%pU!#97$$"1KR?c(zWq)!#;$"12'zV-_&zU!#:7$$""*!""$"1N)Q0U+ZH%!#:7$$"1.1")*38Z.*!#;$"1R*=5pGlH%!#:7$$"1e7/:nC)4*!#;$"#V!""7$$"1"3;*pDea$*!#;$"1#R3IuTXJ%!#:7$$"#&*!"#$"1k.^b05BV!#:7$$"0v9vaYxm*!#:$"2X_[_MDKL%!#;7$$"1RfzVW'e$**!#;$"$N%!"#7$$"1\oUtYqu**!#;$"1:tlK&HDN%!#:7$$"#5!""$"1[HLPwBaV!#:7$$"27"H#G)p0F5!#;$"1*3xr,VHP%!#:7$$"$0"!"#$"-HflP*Q%!#67$$"2)p%)\o:8c5!#;$"1J:]J%oQR%!#:7$$"229N&4_@k5!#;$"#W!""7$$"2$QMHt'zT3"!#;$"1ilqE.#eT%!#:7$$"#6!""$"1:+V?s!)GW!#:7$$"2yq1oWF:6"!#;$"1$H$>`DZQW!#:7$$"2)3+6pd![7"!#;$"$X%!"#7$$"2sdNP\&*z8"!#;$"1BWE1X+iW!#:7$$"$:"!"#$"1$>rA/DLZ%!#:7$$"2GK4!4afj6!#;$"1x1*4f/k[%!#:7$$"2bPe#*fRs<"!#;$"#X!""7$$"17sw>zM)="!#:$"1)yK-3_;^%!#:7$$"#7!""$"1.i0`IKCX!#:7$$"2A$eS'[z@@"!#;$"1oTf80#y`%!#:7$$"2'fwrpMyA7!#;$"$b%!"#7$$"2JWs-Rq]B"!#;$"1dvs4'H\c%!#:7$$"$D"!"#$"1`K\wRv$e%!#:7$$"2d&fG4Q6d7!#;$"1WSr!>')Gf%!#:7$$"2t<c#\ZXi7!#;$"#Y!""7$$"1U(>)*[&)zF"!#:$"1e-=5X,AY!#:7$$"2u)))oxR)pH"!#;$"$l%!"#7$$"2w:JE^a")H"!#;$"1V)ot[X=l%!#:7$$"#8!""$"0[yD.v[l%!#97$$"2#ys$)\S!pJ"!#;$"1AF;]f4$o%!#:7$$"1/jT$>FmK"!#:$"#Z!""7$$"2$)QUg8]ZL"!#;$"17w&R')\_r%!#:7$$"$N"!"#$"1wVFg29XZ!#:7$$"1.#o*eTi^8!#:$"1'zJ5%eP[Z!#:7$$"2mK*fi[S_8!#;$"$v%!"#7$$"2KiaLJ[pO"!#;$"2lPXmo^Iy%!#;7$$"2oGl!pO1u8!#;$"#[!""7$$"2uIC*p>?"Q"!#;$"1#pv+.)z=[!#:7$$"2sLVk6bCR"!#;$"$&[!"#7$$"2.pT=-*G%R"!#;$"0Je"y4rb[!#97$$"#9!""$"2bGnD-`X([!#;7$$"2(=xR">^eS"!#;$"2:G-'3)[T*[!#;7$$"2;'3]nv\29!#;$"#\!""7$$"2"37/6%>eT"!#;$"1#ze*)e!=M\!#:7$$"2.k8W[8%>9!#;$"$&\!"#7$$"2;BI]M#HC9!#;$"1p(p\l2d(\!#:7$$"0"fxY#H&G9!#9$"#]!""7$$"1>g)4OC6V"!#:$"1")R,Rc()=]!#:7$$"2dzdh)>&\V"!#;$"$0&!"#7$$"2Ohp-G]hV"!#;$"1(QI(>(\Q1&!#:7$$"2RZGzV$yQ9!#;$"#^!""7$$"2D5T[)>=R9!#;$"1(*)e^,=36&!#:7$$"2@J)yw-7S9!#;$"$:&!"#7$$"2u)\&=H/+W"!#;$"18]93d**f^!#:7$$"2\msvUa!R9!#;$"#_!""7$$"2`KZZ!*p$Q9!#;$"1vED&4I;@&!#:7$$"20$yU`LnN9!#;$"$D&!"#7$$"2)edF!>$*RV"!#;$"1TUs4o+m_!#:7$$"2'R!eKKg+V"!#;$"#`!""7$$"2#eH;]CaE9!#;$"1Tq$)\vXB`!#:7$$"1ZC;gYHA9!#:$"$N&!"#7$$"1.$GYCIcT"!#:$"1(pr`vpVQ&!#:7$$"1L,Us>X79!#:$"#a!""7$$"2#)or(p6!3S"!#;$"17$G-$))>\a!#:7$$"2&*yO%oVg+9!#;$"$X&!"#7$$"#9!""$"1xkyN$o@X&!#:7$$"2fUO3O&\'Q"!#;$"#b!""7$$"1wP0t2E!Q"!#:$"1Di%pAR(>b!#:7$$"2ZJMS5j/P"!#;$"$b&!"#7$$"2)pyBu72a8!#;$"1H@wD(Gff&!#:7$$"2wOB#f#)e_8!#;$"#c!""7$$"$N"!"#$"1MAqT%>lg&!#:7$$"1p!)[_l^K8!#:$"$l&!"#7$$"2Bq\d`T!>8!#;$"1)H]UYe4o&!#:7$$"2K7er<I1J"!#;$"#d!""7$$"#8!""$"1,AW[>SAd!#:7$$"2))>c7+OnG"!#;$"$v&!"#7$$"2V>*)R2=FF"!#;$"103,E>Gxd!#:7$$"2UkItJ=4E"!#;$"#e!""7$$"$D"!"#$"1c'[ogr(>e!#:7$$"2=j%z'f#4L7!#;$"$&e!"#7$$"2%ekwrE]37!#;$"1UNBGt\"*e!#:7$$"2x*R&*\WU.7!#;$"#f!""7$$"#7!""$"1mBQkYV0f!#:7$$"1C/pVtbr6!#:$"$&f!"#7$$"$:"!"#$"1_kxGG5#)f!#:7$$"1y=:i^#y8"!#:$"#g!""7$$"2li1ZzKu5"!#;$"1tLH0scUg!#:7$$"2e!))y.65-6!#;$"$0'!"#7$$"#6!""$"1pK8g!*z_g!#:7$$"1uU#[<1T1"!#:$"#h!""7$$"$0"!"#$"2:97NHhx6'!#;7$$"2_'*zI+dS-"!#;$"$:'!"#7$$"#5!""$"1"[(>Bgnyh!#:7$$"1L7,^'4(=)*!#;$"#i!""7$$"#&*!"#$"1/Gdw*=gB'!#:7$$"0TIIY4YP*!#:$"$D'!"#7$$""*!""$"1,sMQT>!H'!#:7$$"0mRhJ]t!*)!#:$"#j!""7$$"#&)!"#$"1A)eKyY:M'!#:7$$"0w**=qhfT)!#:$"$N'!"#7$$"")!""$"13!ptwt.R'!#:7$$"0:0j6=%**y!#:$"#k!""7$$"#v!"#$"1&4?zsJpV'!#:7$$"1#ey#3^jct!#;$"1************\k!#:7$$""(!""$"1K)z8nV9['!#:7$$"1)R$\#)\Y'y'!#;$"#l!""7$$"#l!"#$"13$zvI/T_'!#:7$$"1;As?@p(='!#;$"$b'!"#7$$""'!""$"1Cl")*R%3ll!#:7$$"1V0h")y-fb!#;$"#m!""7$$"#b!"#$"1^pROV`/m!#:7$$"1:nK+Oo8`!#;$"1Gt'*R;j=m!#:7$$""&!""$"1A_shaGUm!#:7$$"1>m)zo(3'*[!#;$"$l'!"#7$$"#X!"#$"2l2&4=aaym!#;7$$"1@fcHMb(>%!#;$"1*************p'!#:7$$""%!""$"1Q7@"R:Or'!#:7$$"1mA4#o"*od$!#;$"1t2zJ3JUn!#:7$$"#N!"#$"1@='Q"3]Zn!#:7$$"1'pC$fTNiM!#;$"$v'!"#7$$""$!""$"2:WV'4u$)zn!#;7$$"2$oG?r$\Ao#!#<$"#o!""7$$"#D!"#$"1ZF]K/D6o!#:7$$"06sN_pQ@#!#:$"1)yUw/8'Go!#:7$$""#!""$"1j1Gl,^To!#:7$$"2PZZ%Rcpc=!#<$"$&o!"#7$$"#:!"#$"0H`$ezcqo!#97$$"2)4'pns]d-"!#<$"0/Bt#\U(*o!#97$$"""!""$"1nWh!os))*o!#:7$$"1,)R_*=q&z*!#<$"#p!""7$$""&!"#$"1(GHKjod#p!#:7$$"1ev+Vv>OS!#=$"1************\p!#:7$$""!!""$"1.8>KM2_p!#:7$$!1Lf&=$*G)yT!#=$"1b=$*G)yT&p!#:7$$!"&!"#$"1*Qd[bfq(p!#:7$$!1U]:/zq(o*!#<$"#q!""7$$!""!""$"1*zGZ&)*[,q!#:7$$!1Clr'\qz-"!#;$"1_;n\qz-q!#:7$$!#:!"#$"1eCMfTjCq!#:7$$!2'yof*y&>]>!#<$"1(of*y&>]/(!#:7$$!"#!""$"1W8Ny.DZq!#:7$$!1%p]2PuF1#!#;$"$0(!"#7$$!#D!"#$"1`9THLnoq!#:7$$!10_Uis`?G!#;$"20_Uis`?3(!#;7$$!"$!""$"2u"R_&4`%*3(!#;7$$!1FZ<e$))>E$!#;$"#r!""7$$!#N!"#$"1'\(\'RY$4r!#:7$$!2v&o.^!G:l$!#<$"1&o.^!G::r!#:7$$!"%!""$"1WZ.$p>$Gr!#:7$$!1n$)f"['G[W!#;$"1P)f"['G[9(!#:7$$!#X!"#$"1(p],a/n9(!#:7$$!2&QaJ#RLLf%!#<$"$:(!"#7$$!"&!""$"13Y7'y3S;(!#:7$$!0")*fI[n5_!#:$"0)*fI[n5<(!#97$$!#b!"#$"1m&*QCff!=(!#:7$$!1CB&[oC)\f!#;$"1K_[oC)\>(!#:7$$!"'!""$"1hPN*fdl>(!#:7$$!1n:x>@68h!#;$"1*************>(!#:7$$!#l!"#$"1)*=&4X*[6s!#:7$$!0p"y;5Ghm!#:$"2v;y;5Gh@(!#;7$$!"(!""$"1y]/1TmDs!#:7$$!1Py$><uDN(!#;$"1%y$><uDNs!#:7$$!#v!"#$"1(fozPw"Rs!#:7$$!0"e)o!>HAz!#:$"$D(!"#7$$!")!""$"1(=)=jQ%>D(!#:7$$!1R3X"31c-)!#;$"1%3X"31c_s!#:7$$!#&)!"#$"1=S]-;ojs!#:7$$!1:hjd&\ln)!#;$"2Dhjd&\lns!#;7$$!"*!""$"1W"pI;?ZF(!#:7$$!1$\H(f6^7$*!#;$"1\H(f6^7G(!#:7$$!#&*!"#$"1KX[i9/&G(!#:7$$!1Q^2m9-M**!#;$"19vgY@S$H(!#:7$$!#5!""$"1u9R*yEYH(!#:7$$!1Mg5e)H0."!#:$"#t!""7$$!$0"!"#$"1L%y%*fVLI(!#:7$$!2Q3yzj"*R0"!#;$"1%3yzj"*RI(!#:7$$!#6!""$"19I'eDJ6J(!#:7$$!1&\cd)*HI6"!#:$"1%\cd)*HIJ(!#:7$$!$:"!"#$"2&4ZNdY9=t!#;7$$!24y))fHF3<"!#;$"2:y))fHF3K(!#;7$$!#7!""$"1#*)Q4ejVK(!#:7$$!1t.N2RUF7!#:$"1s.N2RUFt!#:7$$!$D"!"#$"14L8$4n(Ht!#:7$$!203J!H%eGG"!#;$"03J!H%eGL(!#97$$!#8!""$"1$z6&=NLMt!#:7$$!2<))RC$y;P8!#;$"2:))RC$y;Pt!#;7$$!$N"!"#$"0`RlSS!Qt!#97$$!2Q'e8PvQ!R"!#;$"1ke8PvQSt!#:7$$!#9!""$"12Mh'\k3M(!#:7$$!2'))\S"\^DW"!#;$"1))\S"\^DM(!#:7$$!$X"!"#$"1HH>"o"yUt!#:7$$!2=#z'yC#p$\"!#;$"1Az'yC#pVt!#:7$$!#:!""$"2v/**o'pwVt!#;7$$!2%oFZM5%Qa"!#;$"1oFZM5%QM(!#:7$$!$b"!"#$"20"*[MV%zVt!#;7$$!2i.)>@y-$f"!#;$"1O!)>@y-Vt!#:7$$!#;!""$"1O[G!>PGM(!#:7$$!2KGlFQ"GT;!#;$"1$GlFQ"GTt!#:7$$!$l"!"#$"1E]uIt'3M(!#:7$$!1Lrjd$H')o"!#:$"1Krjd$H'Qt!#:7$$!#<!""$"0*=h$)e&yL(!#97$$!1#)[b.$)4N<!#:$"1")[b.$)4Nt!#:7$$!$v"!"#$"1U7'=wsPL(!#:7$$!2P>])\Pr!y"!#;$"1%>])\PrIt!#:7$$!#=!""$"1/>U3neGt!#:7$$!2FPZnC+b#=!#;$"1ttuY-]Dt!#:7$$!$&=!"#$"1#>S(Q_EAt!#:7$$!2hIc=T"[p=!#;$"10j&=T"[>t!#:7$$!#>!""$"13w#*zXx9t!#:7$$!2X1TS(*zE">!#;$"1l5/u*zEJ(!#:7$$!$&>!"#$"2l:_igzgI(!#;7$$!2sON["y6b>!#;$"1n`$["y60t!#:7$$!1G2H7Pr!)>!#:$"#t!""7$$!2&G%QV(pq'*>!#;$"1G%QV(pq'H(!#:7$$!#?!""$"1KX[Or)fH(!#:7$$!2$*H=G&3QP?!#;$"1*H=G&3Q(G(!#:7$$!$0#!"#$"1RD)*f.J%G(!#:7$$!2lFhE:Pt2#!#;$"1x7m_rLxs!#:7$$!#@!""$"1pncC/Drs!#:7$$!19)e,'ef;@!#:$"19)e,'efms!#:7$$!$:#!"#$"1M<jEAwcs!#:7$$!2(G"3iAw^:#!#;$"1G"3iAw^D(!#:7$$!0Tr)\PJr@!#9$"$D(!"#7$$!2d0pcbjG>#!#;$"2b0pcbjGC(!#;7$$!#A!""$"1z;?I7RSs!#:7$$!2dn7*y&=(HA!#;$"1uE"*y&=(Hs!#:7$$!$D#!"#$"1,wqM]6As!#:7$$!1t)ys/OfE#!#:$"1t)ys/Of@(!#:7$$!#B!""$"1wsA&)H<-s!#:7$$!2'>m1)[L:I#!#;$"2&>m1)[L:?(!#;7$$!2Fd30*z10B!#;$"1*************>(!#:7$$!2vbd_OugL#!#;$"1dvDlV2'=(!#:7$$!$N#!"#$"2bu)y&po&zr!#;7$$!1M[R@h'*pB!#:$"1M[R@h'*pr!#:7$$!#C!""$"20LT]]g\:(!#;7$$!1jsyetF.C!#:$"1ksyetF`r!#:7$$!2b.b.PF%4C!#;$"$:(!"#7$$!1=)zE*4bNC!#:$"1=)zE*4bNr!#:7$$!$X#!"#$"1AQq(pds7(!#:7$$!28z#G#)e:nC!#;$"1"z#G#)e:<r!#:7$$!2N()oV()e_\#!#;$"#r!""7$$!2CTIzHe")\#!#;$"2DTIzHe")4(!#;7$$!#D!""$"1$3FX;Xp4(!#:7$$!2Y+O#RP.GD!#;$"10gBRP.yq!#:7$$!$b#!"#$"1>y:0*yE1(!#:7$$!1)ep#GBRdD!#:$"2&)ep#GBRdq!#;7$$!1`'>E#[PnD!#:$"$0(!"#7$$!2jNyTQtde#!#;$"2lNyTQtd.(!#;7$$!#E!""$"2Xtn)3nPCq!#;7$$!1Gd!yJ0Mh#!#:$"1Fd!yJ0M,(!#:7$$!16hT1SAHE!#:$"#q!""7$$!1pRtM(G-k#!#:$"1pRtM(G-*p!#:7$$!$l#!"#$"10s>)>R7)p!#:7$$!1%HZXx7hm#!#:$"1$HZXx7h'p!#:7$$!2&GW6zXo#o#!#;$"1************\p!#:7$$!2MUl))\W7p#!#;$"1Ba'))\W7%p!#:7$$!#F!""$"2'y3@"*3'>$p!#;7$$!2BBE/%*f`r#!#;$"1KiUS*f`"p!#:7$$!19>T#Qt!HF!#:$"#p!""7$$!2<z![PalQF!#;$"1"z![Pal))o!#:7$$!$v#!"#$"1&=)fu)>Z(o!#:7$$!1FniVA)4w#!#:$"1GniVA)4'o!#:7$$!2XOX+MX%pF!#;$"$&o!"#7$$!1i$Q]b&G#y#!#:$"1h$Q]b&GKo!#:7$$!#G!""$"1Y"G-T%*o!o!#:7$$!0C\"3X!G!G!#9$"0C\"3X!G!o!#97$$!2`W^?\bY!G!#;$"#o!""7$$!2E%4")4s%>#G!#;$"1V4")4s%>x'!#:7$$!1ku_vC%\$G!#:$"$v'!"#7$$!1>Z2Q-GSG!#:$"1=Z2Q-GSn!#:7$$!$&G!"#$"0o&o#*)4=s'!#97$$!0n\V8Su&G!#9$"1p'\V8Suq'!#:7$$!2xv"er-8hG!#;$"1*************p'!#:7$$!2&f)GWO%GtG!#;$"1f)GWO%Gtm!#:7$$!1D#pc-)R$)G!#:$"$l'!"#7$$!2jN[sb*3))G!#;$"1d$[sb*3Qm!#:7$$!#H!""$"0[i&)z"G1m!#97$$!2Q'*>tR#p,H!#;$"1k*>tR#p,m!#:7$$!2[77()3&G-H!#;$"#m!""7$$!16*Gt)oh8H!#:$"20"*Gt)ohjl!#;7$$!2&y)**)Q">w"H!#;$"$b'!"#7$$!2(p#*y6E@CH!#;$"0F*y6E@Cl!#97$$!2mX"*y=-+$H!#;$"#l!""7$$!2$*[)3(QaL$H!#;$"1*[)3(QaL['!#:7$$!2NG/6b\&RH!#;$"1************\k!#:7$$!1)[#)\z+4%H!#:$"1([#)\z+4W'!#:7$$!1`N,81PYH!#:$"#k!""7$$!2o`VEY"pYH!#;$"2l`VEY"p'R'!#;7$$!$&H!"#$"1L7g>P&oN'!#:7$$!1CvbK)=0&H!#:$"1BvbK)=0N'!#:7$$!2dx^\Qa0&H!#;$"$N'!"#7$$!2(HF?*>U@&H!#;$"0t-#*>U@I'!#97$$!2`'H4Ti=_H!#;$"#j!""7$$!2m7Y*o)*[^H!#;$"1Fh%*o)*[^i!#:7$$!20fCHw]9&H!#;$"$D'!"#7$$!$&H!"#$"1RO]<c6Ei!#:7$$!2_t(eiAR[H!#;$"#i!""7$$!1viM-0A[H!#:$"1uiM-0A)>'!#:7$$!1Z;kN)RI%H!#:$"$:'!"#7$$!2n.f];))=%H!#;$"1P!f];))=9'!#:7$$!2;`q^47b$H!#;$"#h!""7$$!2<=IZ7%>KH!#;$"1"=IZ7%>#3'!#:7$$!2LgtL-')e#H!#;$"$0'!"#7$$!0p=i*op=H!#9$"0p=i*op=g!#97$$!1GyO7]B9H!#:$"#g!""7$$!1-"='\T(3!H!#:$"1."='\T(3&f!#:7$$!2CSc52H1!H!#;$"$&f!"#7$$!#H!""$"10(\%f@*z%f!#:7$$!0D&*flpZ)G!#9$"#f!""7$$!2D1PpoUl(G!#;$"2D1PpoUl(e!#;7$$!2%[g8jZ.nG!#;$"$&e!"#7$$!$&G!"#$"1M*f$\[X1e!#:7$$!1Ri\\AWZG!#:$"#e!""7$$!18Tni`^XG!#:$"18Tni`^&z&!#:7$$!1k,Ug"fc#G!#:$"$v&!"#7$$!1J"=YNOT!G!#:$"1K"=YNOTq&!#:7$$!1G_p#=q@!G!#:$"#d!""7$$!#G!""$"1s$*z")ys&p&!#:7$$!2(ogkdPZwF!#;$"$l&!"#7$$!$v#!"#$"1;#pLX];g&!#:7$$!1,FX*e%3\F!#:$"#c!""7$$!2xrXmRxxu#!#;$"1<dk'Rxxf&!#:7$$!28^\,"*\%>F!#;$"$b&!"#7$$!#F!""$"02k(Q/$*=b!#97$$!2tCnii&*zo#!#;$"#b!""-%&COLORG6&%$RGBG$"#5!""$""!!""$""!!""-%'CURVESG6$7$7$$!1,nb=1-MO!#:$"1X"Qzf')Gw)!#:7$$"1Ny#4.,nb$!#:$"1@S8rBT!=&!#:-%&COLORG6&%$RGBG$""!!""$""!!""$""!!""-%'CURVESG6$7$7$$"1Ny#4.,nb$!#:$"1@S8rBT!=&!#:7$$!2j`%[\;s!>#!#;$"2E3OX[\;A$!#;-%&COLORG6&%$RGBG$""!!""$""!!""$""!!""-%'CURVESG6$7$7$$!1,nb=1-MO!#:$"1X"Qzf')Gw)!#:7$$!2j`%[\;s!>#!#;$"2E3OX[\;A$!#;-%&COLORG6&%$RGBG$""!!""$""!!""$""!!""-%'CURVESG6&7%7$$!1*HV9Qzf'Q!#<$"1$3OX[\;(p!#:7$$"1&\;s!p*)Ho!#;$"1_]$y#4.,U!#:7$$!2%=1-M6P7H!#;$"18rBT!oA*f!#:-%&COLORG6&%$RGBG$""!!""$""!!""$"#5!""-%'SYMBOLG6$%-_SOLIDCIRCLEG"#:-%&STYLEG6#%&POINTG-%'CURVESG6&7%7$$!1,nb=1-MO!#:$"1X"Qzf')Gw)!#:7$$"1Ny#4.,nb$!#:$"1@S8rBT!=&!#:7$$!2j`%[\;s!>#!#;$"2E3OX[\;A$!#;-%&COLORG6&%$RGBG$""!!""$""!!""$""!!""-%'SYMBOLG6$%*_SOLIDBOXG"#:-%&STYLEG6#%&POINTG-%'CURVESG6&7#7$$!1tY/du8gv!#;$"1$3OX[\;s&!#:-%&COLORG6&%$RGBG$"#5!""$""!!""$""!!""-%'SYMBOLG6$%-_SOLIDCIRCLEG"#:-%&STYLEG6#%&POINTG-%'CURVESG6&7$7$$"1^!QZhBr/*!#;$"1"=TwL`*o\!#:7$$!2(RF)G&)RnT#!#;$"1%)4VJcMuk!#:-%&COLORG6&%$RGBG$""!!""$"#5!""$""!!""-%'SYMBOLG6$%-_SOLIDCIRCLEG"#:-%&STYLEG6#%&POINTG-%%VIEWG6$;$!#]!""$"#]!"";$""!!""$"$+"!""-&%&_AXISG6#"""6&-%&COLORG6&%$RGBG$""!!""$""!!""$""!!""-%*LINESTYLEG6#""!-%*THICKNESSG6#"""-%-TRANSPARENCYG6#$""!!""-&%&_AXISG6#""#6&-%&COLORG6&%$RGBG$""!!""$""!!""$""!!""-%*LINESTYLEG6#""!-%*THICKNESSG6#"""-%-TRANSPARENCYG6#$""!!""-%*AXESSTYLEG6#%%NONEG-%(SCALINGG6#%,CONSTRAINEDG-%%ROOTG6'-%)BOUNDS_XG6#$"#]!""-%)BOUNDS_YG6#$"#]!""-%-BOUNDS_WIDTHG6#$"%]Q!""-%.BOUNDS_HEIGHTG6#$"%]Q!""-%)CHILDRENG6" Figura 2 Investiga\303\247\303\243o interativa do teorema de Marden. Clique para colocar tr\303\252s pontos. O terceiro clique gera o diagrama completo de elipse e tri\303\242ngulo. Arraste para redimensionar qualquer v\303\251rtice do tri\303\242ngulo e a elipse inscrita. JSFH Se o cursor no gr\303\241fico n\303\243o retorna de forma padr\303\243o \303\240 forma "clicar e arrastar", selecione-o a partir da barra de tarefas.

JSFH Se todos os tr\303\252s v\303\251rtices s\303\243o tomados como pontos complexos arbitr\303\241rios, h\303\241 seis inc\303\263gnitas em qualquer investiga\303\247\303\243o do teorema de Marden. Kalman mostrou que basta tomar os v\303\251rtices 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 como pontos complexos LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbW5HRiQ2JFEiMUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RIixGJ0YvLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR1EldHJ1ZUYnLyUpc3RyZXRjaHlHRjgvJSpzeW1tZXRyaWNHRjgvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnLUYzNi1RKiZ1bWludXMwO0YnRi9GNi9GOkY4RjxGPkZARkJGRC9GR1EsMC4yMjIyMjIyZW1GJy9GSkZRRitGMkYv e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEidUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIitGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yMjIyMjIyZW1GJy8lJ3JzcGFjZUdGTC1GLDYlUSJpRidGL0YyLUY2Ni1RIn5GJ0Y5RjtGPkZARkJGREZGRkgvRktRJjAuMGVtRicvRk5GVi1GLDYlUSJ2RidGL0YyRjk=, reduzindo assim o n\303\272mero de inc\303\263gnitas para dois. A interpola\303\247\303\243o polinomial LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEicEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRInpGJ0YvRjIvRjNRJ25vcm1hbEYnRj1GPQ== \303\251 em seguida 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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

Ly1JInBHNiI2I0kiekdGJSooLCZGJyIiIkYqRipGKiwmRidGKiEiIkYqRiosKEYnRipJInVHRiVGLComXiNGLEYqSSJ2R0YlRipGKkYq

ou 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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

Ly1JInBHNiI2I0kiekdGJSwsKiRGJyIiJCIiIiomLCZJInVHRiVGKyomXiNGK0YrSSJ2R0YlRitGK0YrRiciIiMhIiJGJ0YzRi5GKyomXiNGM0YrRjFGK0Yr

Sua derivada, 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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder 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 JSFH JSFH tem dois zeros 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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

NiQsKEkidUc2IiMiIiIiIiQqJl4jRiZGJ0kidkdGJUYnRicqJCwqKiRGJCIiI0YnKiheI0YvRidGJEYnRitGJ0YnKiRGK0YvISIiRihGJyNGJ0YvRiYsKEYkRiZGKUYnRiwjRjNGKA==

as coordenadas cartesianas s\303\243o 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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LyZJImZHNiI2IyIiIjckLCZJInVHRiUjRiciIiQqJCwqKiQsLiokRioiIiVGJyomRioiIiNJInZHRiVGNEY0KiRGKkY0IiInKiRGNUYyRicqJEY1RjQhIiciIipGJyNGJ0Y0RjRGNkY0RjkhIiNGN0YnRjwjRidGNywmRjVGKyokLCpGL0Y0RjZGPUY5RjRGOkYnRjxGPg==

LyZJImZHNiI2IyIiIzckLCZJInVHRiUjIiIiIiIkKiQsKiokLC4qJEYqIiIlRiwqJkYqRidJInZHRiVGJ0YnKiRGKkYnIiInKiRGNUYzRiwqJEY1RichIiciIipGLCNGLEYnRidGNkYnRjkhIiNGN0YsRjwjISIiRjcsJkY1RisqJCwqRjBGJ0Y2Rj1GOUYnRjpGLEY8Rj4=

JSFH Tabela 4 resume os c\303\241lculos do pacote geometry. JSFH Como foi feito anteriormente, definiu-se os tr\303\252s v\303\251rtices interpolados, como LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIixGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRiw2JVEiQkYnRi9GMkY1LUYsNiVRIkNGJ0YvRjJGOQ==. 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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder Defina os focos LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiMUYnL0Y2USdub3JtYWxGJ0YyRjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0Y+ e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiMkYnL0Y2USdub3JtYWxGJ0YyRjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0Y+ como pontos geom\303\251tricos LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiRkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiMUYnL0Y2USdub3JtYWxGJ0YyRjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0Y+ e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiRkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiMkYnL0Y2USdub3JtYWxGJ0YyRjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0Y+. 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 Obter 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, respectivamente os pontos m\303\251dios dos lados LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEjQUJGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSIsRicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0YxLyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnLUYsNiVRI0JDRidGL0YyRjUtRiw2JVEjQUNGJ0YvRjJGOQ== do tri\303\242ngulo formado pelos tr\303\252s v\303\251rtices interpolados LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIixGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRiw2JVEiQkYnRi9GMkY1LUYsNiVRIkNGJ0YvRjJGOQ==. 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 As coordenadas dos tr\303\252s pontos m\303\251dios s\303\243o encontradas, e atribu\303\255dos os respectivos nomes 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. 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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

NyQiIiFGIw==

NyQsJiMhIiIiIiMiIiJJInVHNiIjRidGJiwkSSJ2R0YpRio=

NyQsJiMiIiIiIiNGJUkidUc2IkYkLCRJInZHRihGJA==

O centro da elipse circunscrita estar\303\241 no ponto m\303\251dio do segmento que une os focos. Suas coordenadas s\303\243o novamente as do centr\303\263ide do tri\303\242ngulo cujos v\303\251rtices s\303\243o 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. 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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

NyQsJEkidUc2IiMiIiIiIiQsJEkidkdGJUYm

A dist\303\242ncia de um foco para um ponto sobre a elipse para outro foco \303\251 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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LCYqJCwsKiRJInVHNiIiIiMiIiIqJkYmRiksKiokLC4qJEYmIiIlRikqJkYmRihJInZHRidGKEYoRiUiIicqJEYxRi9GKSokRjFGKCEiJyIiKkYpI0YpRihGKEYlRihGNCEiI0YyRilGN0YpRixGKUY0RikqJkYxRiksKkYsRihGJUY4RjRGKEY1RilGN0YpRjcjRikiIiQqJCwsRiVGKUYqISIiRixGKUY0RilGOUY/RjdGOw==

Infelizmente, esta express\303\243o para o comprimento do eixo principal \303\251 complexa para o comando ellipse no pacote geometry. N\303\243o \303\251 poss\303\255vel construir uma elipse LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiRUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= como fizemos na Tabela 2. Somos obrigados a seguir um outro caminho. Tabela 4 Uso do pacote geometry do Maple para encontrar a elipse do teorema de Marden em termos dos par\303\242metros LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEidUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEidkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= JSFH A elipse com focos 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 tem o centro conhecido 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. As coordenadas do centro da c\303\264nica governada pela equa\303\247\303\243o quadr\303\241tica 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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LywuKiZJImFHNiIiIiJJInhHRiYiIiNGJyooSSJiR0YmRidGKEYnSSJ5R0YmRidGJyomSSJjR0YmRidGLEYpRicqJkkiZEdGJkYnRihGJ0YnKiZJImVHRiZGJ0YsRidGJ0kiZkdGJkYnIiIh

s\303\243o 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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LUkhRzYiNiQqJiwmKiZJImNHRiQiIiJJImRHRiRGKiIiIyomSSJiR0YkRipJImVHRiRGKiEiIkYqLCYqJEYuRixGKiomSSJhR0YkRipGKUYqISIlRjAqJiwmKiZGNEYqRi9GKkYsKiZGLkYqRitGKkYwRipGMUYw

JSFH Uma vez que pelo menos um dos seis coeficientes na quadr\303\241tica geral deve ser diferente de zero, a elipse no teorema de Marden \303\251 determinada por cinco constantes. A interpola\303\247\303\243o quadr\303\241tica atrav\303\251s dos tr\303\252s pontos m\303\251dios dos lados do tri\303\242ngulo circunscrito insere tr\303\252s condi\303\247\303\265es, e prescrevendo o centro insere mais dois. Assim, a solu\303\247\303\243o das cinco equa\303\247\303\265es 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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

L0kiZkc2IiIiIQ==

LywuKiZJImFHNiIiIiIsJiMhIiIiIiNGJ0kidUdGJiNGJ0YrRitGJyooSSJiR0YmRidGKEYnSSJ2R0YmRidGLSomSSJjR0YmRidGMEYrI0YnIiIlKiZJImRHRiZGJ0YoRidGJyomSSJlR0YmRidGMEYnRi1JImZHRiZGJyIiIQ==

LywuKiZJImFHNiIiIiIsJiNGJyIiI0YnSSJ1R0YmRilGKkYnKihJImJHRiZGJ0YoRidJInZHRiZGJ0YpKiZJImNHRiZGJ0YuRiojRiciIiUqJkkiZEdGJkYnRihGJ0YnKiZJImVHRiZGJ0YuRidGKUkiZkdGJkYnIiIh

LyomLCYqJkkiY0c2IiIiIkkiZEdGJ0YoIiIjKiZJImJHRidGKEkiZUdGJ0YoISIiRigsJiokRixGKkYoKiZJImFHRidGKEYmRighIiVGLiwkSSJ1R0YnI0YoIiIk

LyomLCYqJkkiYUc2IiIiIkkiZUdGJ0YoIiIjKiZJImJHRidGKEkiZEdGJ0YoISIiRigsJiokRixGKkYoKiZGJkYoSSJjR0YnRighIiVGLiwkSSJ2R0YnI0YoIiIk

JSFH \303\251 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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

PCcvSSJhRzYiLCQqJkkiZUdGJSIiIkkidkdGJUYpIyEiIiIiIy9JImJHRiUqJkkidUdGJUYpRihGKS9JImNHRiUsJCooRihGKUYqRiwsJiokRjFGLUYpIiIkRilGKUYrL0kiZEdGJSIiIS9JImZHRiVGOw==

JSFH assim que a elipse \303\251 descrita pela equa\303\247\303\243o 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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LywqKiZJInZHNiIiIiNJInhHRiZGJyIiIioqRiVGKUkidUdGJkYpSSJ5R0YmRilGKEYpISIjKiYsJiokRitGJ0YpIiIkRilGKUYsRidGKSomRiVGKUYsRilGLSIiIQ==

JSFH onde dividiu-se atrav\303\251s do par\303\242metro LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiZUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=. Para as verifica\303\247\303\265es paralelas na Tabela 3, primeiro obtemos LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKCZwcmltZTtGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4xMTExMTExZW1GJy8lJ3JzcGFjZUdRJjAuMGVtRictSShtZmVuY2VkR0YkNiQtRiM2JC1GLDYlUSJ4RidGL0YyRjlGOUY5 implicitamente como 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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LyomSSNkeUc2IiIiIkkjZHhHRiUhIiIqKEkidkdGJUYmLCYqJkkieEdGJUYmRipGJkYoKiZJInVHRiVGJkkieUdGJUYmRiZGJiwqKihGKkYmRi9GJkYtRiZGKComRjBGJkYvIiIjRiZGMCIiJEYqRihGKA==

JSFH em seguida construimos a tabela 5. JSFH 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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

= print(); # input placeholder

IiIh

JSFH 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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

= print(); # input placeholder

IiIh

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

= print(); # input placeholder

KiZJInZHNiIiIiIsJkYlRiVJInVHRiRGJSEiIg==

JSFH 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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

= print(); # input placeholder

KiZJInZHNiIiIiIsJkYlRiVJInVHRiRGJSEiIg==

JSFH 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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

= print(); # input placeholder

KiZJInZHNiIiIiIsJiEiIkYlSSJ1R0YkRiVGJw==

JSFH 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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

= print(); # input placeholder

KiZJInZHNiIiIiIsJiEiIkYlSSJ1R0YkRiVGJw==

JSFH Tabela 5 A verifica\303\247\303\243o de que os pontos m\303\251dios dos lados do tri\303\242ngulo externo, a elipse do teorema de Marden \303\251 tangente ao tri\303\242ngulo JSFH Executando o comando 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 gera (como uma janela pop-up) a ferramenta interativa de gr\303\241fico, cuja captura de tela \303\251 visto na Figura 3. %!GMFNWtKUb<ob<R=MDLCdNNZ]L;LO>D:;beOEhw^ZRLCTJcDXoHuuV<;EOeXiyymuwFMDPcVK=Tp_b>]B_gRTEWOOCDCFPKeB[ipITguUekTEobacRgegC_xwwtP;WeYWS]goOSwuYJUWeghi?gnoI?af\\GBN=hdUWUMc?EU^[GDqGemtSWYIyyhShamVlCS`mFqmVxsEAAXaqwqyXiaeiIywqsiqe]?SccRBKsFwhOcr_]SBuS;GyWifrqD^yxjsfE[U<iwLkUGAye?iVMTMOreWCOeDd?DtwYQkUO=B^_EQkNchRcer@<lT]ne\\qFUt<qlp@uyAMIIVx@WoQkvUS_UUOEliqPaIKiHykAUTdma=wrXuTEug\\QL]pV\\lUlOCduMXQjdnHayuHObYrhLTtuxvToAPUJYrVHuMATpqM\\xlkXlXLnahXHlOeUKolpTXwttXILTHPSwMLL]K?EM^xqbTPXPQGYWdaWZyWfLmvDlmmSSeP=XLGLvnIom]lLyYBXTa]vUyT>HOwHNmQSyIrhqUwhqsMUXPWPILTMm?HNpiST@OjQUoLkPDtduTx\\owxvuYWBdoXmwNBZWrreyx[iUiDvQwgmxIawKCgjOgQ=whADYwi_[I>;vYATkEG?sevAYEIf@evDyYBythCxcciLmxP?wu;SpkenaxJeRE?WkaEqwHQUxVQcdqDDmeussWQF_WSTgXIshdcccQB?QgG;UmcwskrQUV`_t>GxAYGj=i:;F=iYtqTCGDZchHcYxOVvkVl?rNMTGEC@CdNoFGExBer_IDTofu]uLATPucE]vcMre=ClgtvoWdegyoDZitGCVPKtgKEUgYGkwhUwiwhC]xJ]dCUi^YG][yOYBIIDKYwVCujmFRudj[BVutoeteovseITgFWQgsOhQQWF=hI?VuCy@ahdWYOsge;UsAtnkW[<sfQTRTL:MocEpXTpP@nXPKWQKUXwLuLL]PUhXGEocqrQUX`UnoipOAyYyUa<pa\\Pmmq\\HY_pVCLpoitN`yPtkrTtflxvXO>AK?]kUAO@dKOLsCEt]aWYqr?DY;DpqPv:LoF\\p^<osENoluZUO;PneQt]QKPy_^`]dWL[VdCYd_ytiDhibYMwq[vV_FasDyYylgIy_Y[AeAAtuqTc[IGovfgYugGYoyZyB\\wWIeRc]d?ci\\oWc?yMUT^?x>]snKgUKcN]s^[Y[WecyxpQetCTi>Z\\XxoIcsw[XWh\\av]xax^i\\AmXAuZfopnhci`Ondt_oQpafwZUY]vGZ>oj>Vs_Wgm?kQYfHytUWmwhsGwfta[VOhIYn<WaagvdYZ<GxBpv@Gvg?`wvhkOw=Fta?gUQ[A_]Cy`=H[`yaxFjQPrYfsI>gvpjLYbDHl>pk:xfFN`OxyqvgjIpYp_mw[d^d@plbyfHOgaxcROyggrkYeUgoaxsH`suWbnnuLndup`ZS^gTI;hqOTGCTi=IgkSXsYwqgigGvivUkfLYEnSg<eWOcGu_u\\aSX?w]mi>sgn?CS=DhWwLayI=Y_GyiWshwURuRL]bIycQYRXUfI;ykqU<Qg:<J\\InWPQhqMPMnr`U<ivP]uPxXgXUtioA@Othx<iqiXUUTOmiUdpTe`qnhugUSQhTelyiew>eXaims<y;Al;HyPek;ATnumeyMF=uQiTEuvGqRtaQedvYep?quxYW`txUeLDdrJTYqhwGYue@oKxoWPO^Lp:lyP<J:]ul\\o[apxmvNPvpUs`qRSQt^mskpUUXlpxSiIpyQUtuWepqWuKjXVuqlVTy`hPYQQ`XniPodXsLlyvaQ[It>puQ=oAQrNpM:BcMTtuSeoY`ab[IdEqf@CubmfHIwgcGsiFQchvWi?aUfEgroWeiiQQcdYyNuuTotoQbKydpsWwUG>iwKOTq[eletQkEBsByY]:pwaxsox`qyovqcIYs`fpupfiHcQa[vquinsSxpjFrwVvMy^FGeyGiewc[Nmdxqn_isnt:`hlNnIqwY`xcn`Xhqeqkkaw;^fExciIlGh[<inDqlPgu]IwmVgHwskW\\GHywwygqd[itTn`wIdrYhhajIYpqiboYiIomkosgxumnnuwlHA\\LWybIjiQmeAmWIucNbp?ecYiNiaTynNambGoXXhdqqHoeEwsoYouYkyIyjOcWonRvaPI[ux]xQbIWi?XuhHujwyEvmjanupjKFcwYxAXcxgmufiKvhYYjNohh`mQYpxIy=g^yPxn?fKOx_ouZwmtQwYXxhPmNIo=hxTwyNIa\\InwImmYc>>s[NxEo_lhfXqniawsQdma`xI_DysOalsyg>fesquMoaYAdqyjPxhxam:xciVx>PmiohcXn_YmwXuaYq>po@`royxbx_vi`iQmeha<G[^fvSflAfeKFrQ>w=^ZYyomwavYxmqgX^fHggVyxbwk]YhTXyu^uNIkY@xxwtAfrXHnwWqqahExfVx^a?[kqxkgvafcSgyM>kkweLilrIeX?gpNiOvkWidkIfyQmjYmXg`Xao;h\\qIyMwkIvbovnjIiJOr`XavGv[nZVyYYv>WxyEcHGb^QVBegIuu\\whpOGdOWrsxgWIXIIoatdoIQiT@kdpYikYU<MwGsgv?VxEhlEx>ovgiHcMysSxxwEtWdIoYxyEgSUXuHa_TQOfRUfDQu]YtTwgLIUWqvboVXkIIOX<?YiEy=IWeMVuyGxWXBIRaiHhwYwyiXCvpafHGH=]gTAXKiRQqDhICI]XcIIw]eWuvT;UPAX<SR;;RQ=WtYseuFY_Yb[XHuiUoiWYW\\ah:ytbOHi=InICOyxkwW\\_tWoTXGYxwtPiUD?E[gXEWRywXmaxEYwp;UHkelIelwXxuI[=ioSYrar@OcASxeMiukrJggKcbEwbRYDaqUWmYDixF?x>KELMst]dTYD?uDwEx\\yhPIw<Ybo?BZWRheYEUhSIuvGINegcihqciKuVrIxwugYwEREfyisqUeiWvg=yyoUQeTVWHqYiKOHyQtMqdAyWqiVaWei_tEAwgexWSTtyswEiyesaau\\AT=eRoUsoWSIIisayZWsuAsymEsgVqwyUiBauwxIsSirxyWMwwsqgikiv=xnerWsfeURqAEKACWqV?OxigeQUH=aICQyayCi?ElmulGX[sRvqs[YUXyDpUChEWbqIUqE_kt[abRAVqcy@yI[AvPuUkyWL[cBoWbUur]ERuI\\aSTYiRqxcYxcusasrTQcL]ygiUoyIWCVDgYKAbEmcvwyLATumYuqtBmcCUbsIcGYt=yTpODB[R:qI[mXhuxH_RV;GgwCL]TlqRryg\\=YSAhcSgHmBd]T_Yr<kExIi]kRvwwTQHp;UC;S:AbOuuSKVYWRwYxaWwa]eWKhluBMmIMgV:=BjMbauy`qBcGquQuqTR>qY;mybXStuUoeS>`sqlN`isUAo<ewimq\\uwo`TYiLLQKRtn=UumYYQayt\\T`isguWxyw;YM`lpq]pPyYbxYUQlQ\\OGtj>mvThKtTq`exJPyihRcxYNtsBdOWhjreVgyPYTy=uk`TRkUrE`TYqStaQvER>aubujMLnnqt<xRHYSjajw=O`UWk=NRxODuQpqTIXv[mnjyvhiMu]XXiyiPyptwRir`\\rxYXviPeXXiLyrIXYInMdp@MTFMWXutlhtKXOUHK>T_Caq_wv[fxyqvhwyH`^bWl^yaBGpn_pA?xdQr<>yhYgyf]VIikAsvFtVNx:^hfq_VheTFgLaZYPk^G]JNfZiv=y^_w]=i\\iogNfognvUOxXgcdQqsIdFq]cW]YaouFxriy[xc\\_jFy]YGxWqnGvqQ_skxvFyk\\@w`ybbOknQ_txdC@cXXtUgblWucy^YqhtPyrOjeqpkOi<?]xVvvh[YPaSvhmYfIpuqy[k>wLqvXpuqwaFPq<Ieqvi]Af?Wd<vjUYyXY`Iwy[xbewripphHwKVyJYlh`ek^fI?hxiZwvoX^vYYxeyvbw\\Snopw\\in`@v\\rhyxPukxxXwahQ`in`;Wg^fr^h]`?yfX\\Oy]V`cLYZJ`xAF_tQvJvrW?y<>yGGvqGux>t?vvCpr:IjL@f:Ivm^eI`xwblQr;XXc]Y]pw>YVqqRW]VBaY]qraUQtXrHypMyWvyoYdUmAo_YvHIyLImumRSUx@eSyvgyop]OpaiyMi^mvpvNp\\OvVPnjh`GilIqynh\\Dg[rI`Uy\\FNewAnWqxfvsyIyUhlpq^Mxql_q\\inxh`KFc<yovVuuYsyAxgybXXnWof@poQxqSahUYiI_ifYux`_s@vCa\\GvqpxxUw_cqfFWqdYa;Q`k^x^Ocy_aiqwWfhUVyvOeUy]qajeqkevsf?i^IlDVic?n:witiwPYmA`vUPZjffYwkaojUQgKgx_vej`h]yympxVYpmx\\UqkFyj>gfqq]WQ_tYgPItMFp@OdFO]ow[qhyhYqEo^?osIVivNcgxr]FxA>^Gx[L_dvGwrGb?w_Jv]W`\\=WyPxeSYpr^h;anKyhn^]UO_vGjwqcU>`^fy\\ausv`vihxQpxH`e@^CO`Z>ZnweJAs]VeThlv`im^lhwxmw^gqagisyhkyOeQxiKAuXwdFg[eHZvPxvWtexsTHlqgd@vtQ_yw_vSH\\;vi\\pil_lxilagk\\Vby`hhWhygeNYkdyp>QpEawjnvSvtUPr]_\\fhaAOsvAlrIrR@tqWito_RHvH^\\LW_>A[IidMhwlxw`QoInbfp]tFuH`lXXgPHk[nsqqvcyetyjl>wdqjKGv_QhWIx\\Yvagxr@vDwueocu^boYm\\Gu_Q^^hxNym]fwiFw<v^mQrEf_eqarvro^udFi]imj@\\wyaONqNqnpytGV]`_vUfZhAxUpasWydXlEasM>xYVgiqv_xkBfwLVt[xcvQfUIccQ_T@ppWinP_Qhd_@cRQ]\\F]`f[iosrvuqxj_x[XvoR`fQOopx_B^ws>qs?vkAwBhcLqxZfbexZuYtkqpi_i__t^Ic;fbyvtYNqqysQvvX_dlylvF`VYtkWZhIiyAh:Aj`HkxoiBou[g`FhcdNq]qkwVc]xm^OpF>;WRk[HxKR`isSWd`]hxWxa_htaxDAtceg=[bjOWISUISY=Wid]IcKyAis=sC@geAeGs;yWiFkoTeEYYivGCGZWwI?EtmtTchZYy\\yDToWGOwuaY^mhXoYVyYrSSwexEMrDMIIAti[X[cVtGWCYxwKSa]xF;YewTuiIgse=uuyWVQSwcIu[YHRYxRQGeowLKTE=ciecJiFWoHcMRaII\\;iaAta_sr]IxcXpMXfMdnyBcKXyIb@?e]WSyAueMx^GV@IbhGexYuuahkkisygfUUtqyZGsMOyRODxIh]qggCFSGyWCHZotuwUjYseEyUkwJktM]DXUYbaw?wX\\If<DW:MYvLqqhtV<l@aMVltqlSfHQYeLwtrQhxUhyg@oUexUxx]dRKdSouS?\\YtuurqpL=O@xPiHMyeqk\\lXmLB`qXmt[]o`UYc`JHDuhLoEetwHwRdkXAXw]RiHPgMSw@Yghl?YNIyLiMMyaJDhRmtXWUSdXRMUyeqvGTPtMMa<PsyuAxYpqVqyLwqoXYKxtjxdlrYnxPy?tUnytWMLjpRL]STHs>AqdAoQUwyMXFPs;YTlIlsYrhmM\\lNymoQXwilxvUpGxY]yniPxUmNIapFus^QMJaSy@v_iqhUjq=l[XQbUOmiSUPWtmSf@KvewuUwI`j`iWTAyuqXp]noAPAeooPYHIKymlodtyTr_YMlqtiArUPlXDoyqO?=meAqVILw@YcDkX=TBYK\\IT\\mJlaMkEUfutAQy[lRCMXH@rFYlDEWjPpcewUiyEurSHnoiJEpKGmM^UySYMQ=kKDlOMkHlUfMN`QKGPy`LWG@xjUSadSTyQCuwhyXWqNCIYJPnM<SAYpdtJaIyLQP`dkhhXUmWlhmkEULxTi=wqHyHluAisq=xtymUHl@\\J:pWjIwU]VeUkNeU`AroplBPScTYXmQ_xuoypApopMxQUSUpPwtuthyihYypyYHRkxmyYL=IPiMoUeWs=wPxViHWDpONtohPugax`UnWUXnPUemYx@OjpulXXohOsLuOtW_\\UcYxTatAXRl=mYylpEvb=o]iuqpmSuxIYSMlxT]u[Uys@nqxQyIyRYnyQyJiwyMxGqKEYKmlPcxKVlw\\xOHXyEQQwtOkPKvmU<XSQxoh]qg]UiTRiuNI]pYYQnTQKYt@]lt]woMQyEp;AqC=Xlxs_qmImrRYR<ptBPXWEYWPuCPMguNh@xMqsEpWaqkSaNoyKL]K<DwrexulKceqEUWYUxhImKxQV]kT`Q;QlyQqqmPpIqJUuY<QAHJQ`McxYcQo[iUwXK_eqviL?XViiqh@kEQx\\@UoDU@\\ZHPx`YnDayey_Tpa_YwoPbmaxwh^RYvwwmswaKNqPap[ImRXquVubn_t?[_xpO?h^ym_OiqIy@yhQ@tVQbt`sLhrgpv?_q:xvHydVIy<g[K_h=Iwqgv?GoC>]u?`whigiu=nqSVlyvhCH_yqrFQpXy[Y?gF_phhyexiKQncWwh@pPFuYfpZgyIYiQXo[Vh\\Nn?noJil=V[FP`kaewQxUW]Ewgg_mvwb?anjicdYeXoxWHssXhxyxlyyc^[SYbSwesy]?nyiHhH?eC`iUF`nacpa`x>yQ@vLVs[x]ch\\pyxi@tKXkGPyC@wpaaPQyCNe]F_`fkrV_ohw`IvmY^I@u[Vm>AqinvuHwgVgYq;YDt]WeuIWMyKiBLIxHgwtyfJcitIcqYUXMCxoIaetaqBP?Y>oheAfiIwlyxd=D\\=rIuyuUvOmra[u:GXbSw]sWg;xGuilgW??IAUcXQsXIfEsCxgxaMEJyXZouKuUhyB:_xsaxXqTMigqkydmUcWWwkIwCGLmvyeYiUtYoyb[svMYmYtvxLHeQlYjJiLtasYmtm`XPPVHPR]XOLuPdPJDptddqPesytSKlXhloqHR^ixCtoiYM_=oUAybPRthQDXOtXUSDjglxl\\OdxWuENUuQNar_ptHmNwmqciRY]unIlUyUiItrlWsYTGypWMu=qkutSxXX:=YutYmYy\\ywiTskmM_hW_LrOlvYaJvTMmtOc]TF`q^tlkXjUmmg=qsqtXqtQqYmmwOTX<qTrLXqYYAplX]TLty>XmuMq\\tXULrlyVTxWualwEQAqUxmxJpX[yV=eoQIlEhS>yqqeRYMlZhPFySQhSTDYHDjmPX_<Xdpv`iMlHSFYyLQPhEyMisqhkE\\wa=nvXPvuQdqlQhjyuQ[hkDMkUQWmMkEESZiksURmxJBHx@qN\\qlyYxy<S``KY]nOlKj\\WcmT>]sodo^`qgHKR<txLqyaX@xuNEunUTUilfxLwyjVUvkltNetjTodpvphMr@X=AjA\\PYiqj\\KrpOFAjGiqbtW;LqYpMQ`UXyWpiMg]VxeU>QWGUmQQKwhpIevIPR>qYs`Qo]o_isylpctVD\\sbiYemqb<pwMYSYS^Iq=QjvMtg@Oh`Q_\\qbtPNdurajoHrUdNHmmiYLdYwu`U`ER`QXQqyCUuMDYjYLDqyWlvLiqXPvODp@iVcIPaYM@xtaqpqMLp]RyqmwuMqpq^ij`AQpXMxUt^YugiSXUtOxmw=M]eo[xtN]qYxthIKuXr?UOnaPFYsKqUlhyH_qpwj[P[ai[BveT@x?qbwajP^xDP_VI`PWcVQ]CG`c_rSGypvd=QrIFjMg[ePerPadWlNxaBGdyFjn_aM_tA>gaWemveMw`RWxpnyky]\\?wBwkoGjUw[bqiIHij@gG_yh^ruIui_yixjFxZCW_XFgWWnSWij@]ogsGqiep^EAjvOvv_sPp[x^iL_xKnf]fqkIxRnmwxn_iqyXipyZufvxFxeYiUveyYnNpt:ah;xk_Iuq`qpyiaxd?Va:yxPyyMYxIhc@Xbi@wXftp?wgauuWb<Yxu?kXqlUwoP>e?WphWkvomcAtu`o?ngqxrWqeqIidXcthsI_n]iodPcXXsvawqq\\yGiUqrpf`GFfifymwg_ormV[XGgmXemfnvihQqytWiaFvgiZxiauyay_iDwsyxpxNtSNyQyfwyZWf`wQsqPxfilyquIGmkQt]XiUq\\cxatpvKUQIcpmSR]vcGDleDxmFDiGi[HsayjOfCgGwUFPoFtEhKuqWTVO]rXUP;UW^dr^HVaevqpjc=opxPttsOdykASVqNkpwEHXLLt_lPqqTxtLuuQuMwGiXFySBISbQoymVFySsATYipRHwrURiLxrqvEipyUxqmlj<VNhq`ew`uqHpLI\\Ou\\UYUyUdQyEUumJNpoRxQeTvnxJUhqx<WY@yTHMCMpHLq^eWExolDXIAuieMkym^MnQlwLtgPvsDhg:oakpa@ghPx[Y`\\wOrKYmTnkwawyfgkxa[Oimy_?ItXqf=_wyyf;h_my^PfiCo`XPkPVaf>[GnreNf>ya?AnXOnqHxK_bYPZe^scQ`Npufw[ogwlgyxI]=w\\NFa@WqhoniX]XhmI`vwiwjHqTiZQq`Ih][oskpr^xhwxyRouunvvgy\\YeTXkII[s>vHq]oVg<Nv\\@smapCy`?prFVxXIeTxpi^yFV[ag`v_y<AvDfxIhvwX]oSZlYguoy`qM\\uVaQ>il\\UniAntynhqWX<MR=yKukGyKeHv`EKYENHIKAtpgUpCxwnLYyIyB]rOiRJqw?qRAyY;PSYHsgXL@YYLTUslkoLl]Mt:IU?hU<xstMkvAYeernuSUXKiUY>ajgMltyJcLv`erRuur<TxIsjYMKAy@ukGXMGYoH\\uZpxF<YUiQsYsxDValXfPyRyYVLWqQx=tNMDVRaNT<L:LtQASyYsviuMmJuPyYxnpqQEEsiInRewCPWipUsYnxDtly`SQt^w``YmypdWYfwi`uhgQ_q`_tJGtTW[xfxSqtgvoBqrMQnoHuH@\\rWmwvnTfqiimNqayqo``ihAkjAw\\hpO_`gq\\uqyhydtqi?Nvfwpb>_j^fXgdNVrMwdvGwZorYvi=HiU`mvwoNgnoQ`w`pt^wQp]Qhd<@isXK]YhQiwsYSAUYOtY]y>asPOdm=hCWvDQViWC];RDadXitPEwg_vuCfRiI]qha_x`QTIgDgYcd_x_yFFIvmMeNEX`iYk=wGuhjQYgsEYiEByeD?dsUVTMgxoWogY;wUWawXuTREhycsxUCJQcyYgx_SvmU]IBbucJAwWWsg_vmYgkmUS]gB]c:CgfOSteVeUdhQXcOTtQX>gwxKxfcfQ]RbouUETvSScibWOUiGUyeiXArYEwOasVkYGUdLyyVqvcOfCAyemw;iGvCrXAxwmCw=hvIHnaUogVXECBaiS=SSoWx_hqWXUifPOFvGr<YStEy??jFtoFhvc<M;LTAxrMQoqtPcpjmdoeqpIuoraYceOZPyDht[aqWDOQeXUUvgusXqTwUumxp]MwXu_`IxdqaCwsmWewYgt_j\\I\\gWyu_`VihOYoShxEfcTGaOQbKifNyp_`\\EYnqGccHu[iiqxgFiemGlUxeB^ntPaFggL>ZlflIvkei[aa[KxrI@[I`h_ypryuuipWPiWyvWWy]FyDhvRWqfIf`_`uNliocEWiTywMYiwNx^HnfYjUa[dInq`jcfqnAgDhlxfgaFucObqG]lvo@NqxFxOhol^^GHeE^qv`v_@[@>cNxmx^^iyyeiasWqgx_]GpA>bhGx=xan`yrquyiiwqkyWas?v=`yvvpn`lNwpApmkpbfHhSItnWeyig_xpxQuTvoTg`:fcMYZk>ZQ`tUg`cx[TnasyixAxiy[XPkbiZAG\\=oydNctYkxgq?IuPYgxPmQAyeQsmxrOIsMfZ@qkliedxevhyWHveO`D`mEWwWInbXZcAZ^v\\GW^UO;_S_sSKyixEUeyyugFCyWy_Yr]SU]y>Uristeke`esfeuq[DygXU?umqVBwSYAtZKC>Gu?]c`]D]otugxheSnCiWEyGMeWsxqEi>oErUiasUiUxxginAS?QxbIsxwbNYRbACLmUY_r>;d\\[CccUsGswOX]UgcGiXesdmGQaSimuj=eOsU\\mesitUKtlkETKbqQY?wRTgu]AiWqvLucOmEtMr_wtjilAQrnyWtMn;]xMLvJIT=IjQ]Sf@l:mUITy[uTviUAPSMIwq\\UyuY[TWF=W[eSlQT]hjX<JlPjP\\lXLTgQuUPQTLmQtMLusnQydPm;hjDpWpEq]hjnYPhXUm]sDDj_LsthlrtwkPTeakOQxGdJiiNTaTL\\srdqWeljxRJYTwds;QwAhYZ@j\\XsjIO]PWJ<m:<S=xRiDxcINo@TPHRDIt\\qJaTuHtNLDxo<p<=wUMq;HVkPmu=k@YT`@sehJhQj[dawabYXdAokiyiJY\\lP[:B:CeEUx:GUd?yjAfJYUO]c;<JZTk;Ew;<J:<Tt=J:<J:Ew;<Z:opcfqNxgf^ayQvifakIbqne=X\\HI:;BjmFhAyDKib=tGWG\\kvPgyjyGyGGt]XjicekikYg]WCAyFQ=hGWrgUiqivOYhAorYG[:^^;GwwOsXqb_g[oirj?Z:>ZSOnnigK_lkYkIfqu@]]IZ:BSEgnIx]Kwuueb_Equteot^aeauCPuSFmXiGYkyxY;Iqgv\\EdiehlwExgy^ih?]XXyJ:<dCOl[GhYYeUqgbNdpf_x@ymyegFchPs@guyGfUhtdqwtPqdquQxkXN]dfvAvcvgxdIhy>_DogDGZ:BJgIDuWbov:Wi<miyUvQuRxwEMyty]vhwTEqwwEuJGV]Yw>wgyAhfQhiiIlGyTirMSIjMRKwbm?GEWiyiRMKufwwIwHbKsJIuqgssWXPYrIwYwQXuUG:;JbdYnetFdTnAwepwUYqG=kKiN=]YYUKEpRq]y>Ps\\pvXyX_uy?hN_MvKimuajbLvpUJ:<JDuuOlxgqom\\mlIU]XRY]seTuwInR@Qndpuym:iY><ZJpZ_x`wxfkNiGqp?Y\\MW\\avkkxicvxqxp_idQn\\lwo;BBiRLOuUkgOkSYqVrCucKfMUyYyxDYcoMV^iBbcI:<bqG\\?G]yWxwxdOiuo@wkiqLqmmxxChn;HwnowypgQxsEyluwmdP`M@yhxmBYep?:[v^CSxUsh?WpQgqgR_AiEqRYIWyuy@ygHosPMTwwYSqReYsXiYr=rsyHtqfcISQ;J^APDusIuWyTylIJapkVtuyAnaTKhxjxMx;<ZR^[rptgNwYW\\GxbSfpP>:;s`=Tt=B:;bfmrWgVQYVIoi=iY?;B:;rawB:;B:Ew;;B:;B_wB:;JHaNRqSyHVwqRFIJ:<JJhOVeMc`xY]ylaUfPJ:>^E?ekX_LGwIh]xw[m@:;BSQbIMvcufA;B:;s`ZJOi:>:;Tt=B:<jL[N\\:>DBJJs\\onQTM@U;>Z:naw>Z:>ZZD:<J:W:NcI>:;BDuC:;JV@nnQTdYKaUWIxMbqsNuYa\\m=<J:<RtDXa@SJuLWAni@TNtuqYKNxpQDO?hwiMNi\\U`puj<UCdmyHWOvv?PinPdGniWyoTVieNppoqqpbUvxafviV[_YnYW\\gwp?>ZBwkEFtp`reNdN`pYXj^@]>`xcfq?PhYQdYY`aOwkYr\\AsgfmSYs>XsOFp@_wOPTmH@YfvQv@eff]bVAYJEi[=hs_XYqYSmxScXrOghkY<WUC;BWAS^Ecq]hLcr?_SPMywyBHKEo;sJII=qBIkcmoY[yFOOhyCedeEfoYX;ty_UgwtScXXEGhYU`osX[FX?U^etBwwPywNOvSyrOIc;OwjIYDEuhsinwENSu`SGYaDtYcAgbR[GfEvYGif;USgew;STWDQYcusensHgSydOitORcUU]qiikvs;WIiY@iViMhcedqqy[micUxqUiYEC>iDvqRr;rMYBJgHtcWrOD=uBGkS\\EcqwRQqEwQeF[DuSxe_t?yeJ]Y?gToOxVQHwoSbsYrihRuDeeeJOXfyX=]x;Ws]mdcmrPUc@qRPCfM[bFcU[gw[gsomhrqXeMHCOFhSvY[t^MGwGXuiTosWBIy=KDYaVmYxteujctDgVCuumKUgwchoXgoHXkiyWW=SgoYCXsTauGLuX@eCwcCLmVH?tqMULqiiyWL]CMuFFCTxsy`_HX[UM=y??ep;G\\AWlqswQwKyrOUUByHOWEI]isYERqXwWwbebiIUIgXHSdySfVIiYAUdYCX;cCQXi_D@IWiYuisvYmES?tJsyaoC:Ce?Ib=yRGOrggwiQiMiFXAXOihrICk?I>ygRaVD;hOmRgGTXqYViVAwxi_cooSj_EMqrweUTiD:;BB;RLC\\rFapGm`gsVa]X_jDG_]ndbWibWhxQ`MIskptQy\\w^_bNvlNy;gc`Pty?hjAndPqLVibivWpbgQtQWenV]TikAHsq`fE`e[_tbvrTWt]glsqjIpq?_cRV]mPZ]O[jh^gYypYkSX`FIi_Wyg@[;yu^gu^gfoH]Oyl[G`nH]Pge[?lRf_>YyAfjKwpwogQPxGib[YyGphHVk@@[[grXN[GhnMhlqxjSHp>Hu=`cOyqjoZI>]:o`m>yvHZAn[YV`D@q[Xj@f^_`rMfg\\Hkmfk\\AgJhd@guT^g?ykspcj`]Mof@I_Ma_Y?_l@[w>]egjjXbUvZqhmbfbKw\\QOxB^fjYjT`f_x`^fhbAnmQ\\FN`>NegPnjN^J@na`erNbfakuXn<wm:V]DX_`HmGhyDac[X]T^i;qiSo`fFjqwZHVstF>mFlmC@_viSduablwwGUtCwGnkYHuYMShyCGpgcJmWX[r=kBJgx_=wswEV[IJ_gLssP?xB?W\\UeLchwiX\\wdcMcbWyToEr[xvqch?VFQEfoyhOUH[UhwgjoiTIDxme;_Cw=TM_gnIDGgTWwVQGGbgRpefluTuUGUMBvGXEOhgMhl?udgcX=HFmir=UhahTCwUyvvcffKwcuhssB]OVucWlwx?iGL]WN]wdHtEaxGqRwTvmLgaHt<>bq@^_OxD_au>hRou_ih\\_l>Ifsac`ImEqkg@fN>hY@hWfiVQenyhg?vlfiT?ytAlKw[dWanwbIIa`_pVouYW]v?taHy\\qcP?_chgWYtN>fsauTF_@HyXPrCvleV_PAc=itX`mBXogojv`vEXe<vjExhHfj=algWgFAtwHx>YuAiqygkRfa>xvDbHKVtAE`=hw[g^Iw>QIKMcJexxGDxQvEQSSkxqID\\yG<UVh?D\\cDyutx_T]SbaGH\\geQCf[SfkufyAd@ObhKU`kiVegG;YLydqqWO]FOWeiwd]qdeYGTaT?eW;kgUAGhYio[vaIhEugU_eJYEeov[QB;MgCMVx]im=HMoV?yWnIym_t:ed\\YxUcrqsrlae:;RASCtGrdQxeihkmX]iiy_vcaZeVtNV_yqsdnq>hxtqisHe`hjPFngwdbWwkgkXovYGrdVZC`e`WxMAu]QtqQyVG`jatKXvuy]napuphaNdxA:_S[KfBWf>YbF?YJUVk;vTuhbwYG]HXcfYYY:<JSakddJW@r=<J:\\V]lTU`KxdQ:<J:mTuaxR@J:<J:d^:JN>:<Tt?Z:>jLYZ:>Z:O\\jwftiZFgev_ku@[JHnfXero_@?Z:GwUyVer>kW^;R@IHhmy`]c:;d@;cXYB:<B>ZD[:>?BbJ:;O<;^nW_DPnZ_Z:>ZND^mE:;BJMYBaHSwdLMVA;B:[dX<J:\\XRtP`<JALQnILkaYVpY:>?Cu]SxKKtHUGx;B:K[j@uaN^vAZ:>JAds]RrkwBaI:`T:mRX<J:<JD?^Gpyw>Z:>N>Z:t:;BJGbVYxYYsMIyQqeBQVNObEuugYY?IYaocVsuyAfaguowxY;Ij[WjAVAeU:at?yrXqUkCbYkRpsI]_FeiVcSv`yWXuhjaUAdnBPNHIj_lM:MvImv:XWWQVIYW\\HvblQw<ZjOnIwmgxjEwabfa:BHQvyoymOGEwCQoYrueX;B:KbBEy;YltWaeawiwdWyxPQsUNkLiuIgn[afaXdwWqx?qjWnS`sYWpgGx>wnnywCPt=>:KrxgsIiUvYg]wiWsWFmwwMfl]u<wfasIseWKMYucfHATYouKMwXKCKYY:;BBKfNcUqOY[AYuMijMtnOhtguuQtxmCnWt]Yt=;B:MIRayEywCWYYmeRoxKmfl[tawUkSWnQCAMIqqW@GC=;Bj=CasSeUypyERihmutoYhiwtvggGeCAWviwipox?qhmsfQwSeQyS?ekUyuoUoOucyb^wuHCcn[eaCtPeUiufQ]d[wHvqxWYE<kfUgHqQrhAsi=WmMU<=S?seX;j=@YaimqujGTMleuouUJPqPxlYYpcHnWhxMPNdITcLmwPwbaW[tPgdMrEulXKHlTI]XXUQwMLgelVAL<EvoypFyqeqrWXyFTNtdvsPnWpM:<rc\\YrIv;Pn\\PR]MreiWkUqELqyajDTSDarHxxMquJumBUrsMLgeruax:<JJXRRlYvQrGmqXEOqiqlQVWEunHs?HwxtjFXWaxluumtQt\\yPvmRuis=YO>amcmSdYqO@ww>ZBVx]ypWo`t?jiYsVxfInnui\\uFl;xwMYk<QnKyqrHh:y_<nbepcyO]]NcIB^EF[GU`EsdUhqsulWIneUqqUQMG^mIHggtoYrcRSsirAtuWcWOyV?fnAB:CeDMwlKxtwdN=ynIXfed`AD<My[geX;B:[e?cyXYfnAB:;dGAtAmEDuC:<xcIxcYL?pXt=ZSPcdN`la]\\YtafewWvRQ_eYucIdt?Z:`c_VemNxLGnuHgeY^IIjJfqA>Z:vrsaxS_ir^lX>:_UAoXt]dX<JZYt]YtaLKgax:<JceVEqUIUXeUoNHTPdLXMX?YMiiMlyYElKfTtdIxV@QWAQm]yJ`MkDLxdQDuK:<l;QPy=pZiyqTYQiPciSyTMkYt>tptpwWxOOlPVMYdivkytYeQd\\XxDqqIk=mww<J:\\n=TrUxP^myFpXtYr`yKoeUI=Xexyw@yqXVIaY<AxfirEQNN]wCiqI]mVpswxlvQx:IoblLRIJlHKcdj[isULPyXpkunhXWClY^`tyqPhiwoiYQuWcIyTyWXmuXhxPMnWpQCuSUPNfPLN`kv<XlEmbMjW<NUqMfENoEnuenqXnOtuyhYttT>qmpMy^TynaydAJ:LP<`uKTYvMy^QRudQ:<R`=neQY]UV]Qu;ysymwBEY=UrcXvyXQTMtqaSZEWpdpSyVVAynAOwBL?FmiCGcCAwCYkexQyFySx]TtmUEExgUxa[VkwSIAynIS>?ww;B:mbCayBodI]YymyQKhrQYcufAEw;;Bl;EGMWt_tMsUyst^mUJqSY_WBou=naTgaXhiGWiqomSIoW`tHf]t^mBq^LOsMynIgsvWvmIa\\Vxraxbfa:>b@Vh\\ah]GvCHhiQiYitIGwAn[V>c^W\\?Gdx`yIyoVOivOs?f_]W^^omxNxLvjxNx:>ZZf]Fa]y^vZYpY`]lof>WgeWsmybp`^rhtGNsy_pdgoyIayOi>aitAsE_mVow]v[_xZ:>ceflYx]QVgKYteoetpxTy_^yvaI]x_iiYp@^in_fuogT@_GqcpFqqA:;R@Yynqss[EDuC:;BsoCswxCibbiaSdgGEs]xKwbLYJ:`WMuxBtNUpQlQlBDtuC^uiIuwVWr[_x:;JQInWpM_xJ:>ynAynI[efq<Y`?>Z:>YmD\\cbNObF_I:;bFibVYy^?uD_uu=JZATBiqIMkg@swxZ:>lkqawXH::\\irU\\?tHuC:;dc?HxcYL]W?AynAB:;vJ=EYoIckh\\geX;B:;FWqIwmDYLC;:@?<FjnAtW@ODxoulVceXSA[t^Zw_v_frP_vXYZ^@d`YZ<v]tf;MbJyRXMTfeRYCY:Cg<CWA;bnGynqssBsowVYB:;tHueV=cXpwQHy>tV<<RhHynYUpQYTXUUUntLJ?xlVEx@YYA`yYqx?lvqPYvtNHuPHaMy\\JYpM_xJa@VuUxKlWw=wnLoI<LE`whYNIAlsInsUyh<XgmLtUpqYvEPLVqtoqtyxWPyRyqv_IpQyE?fg?w]sC:;BVKSpuxK@x`iSSxxp<s`Yjtpoa<qgpPhyLQ]WraWemUeyWXmL[PVYXvw]v[OZ:rSmIw?H]UY<Ax`iKitSQYwtplZyRDeq_MtYtof<Y[]XXymyUxlqx>yKQhmb<ynAtwxSZ=SRmmF`Q:<k\\aVEUSjinqXn_Ukq`x?YOq<mH]Y>xVYXmxdQDuKWqJdqK:DpV`whLoiuj>qmpMY:>vJ?w]v_PNqhx`pn`X@]sAeCYwQUTmSw;yuWf_cYIarlgDxcI:;:nlFy`n:kIMuxowHIaUXuwW[xwIyMKXSyfawvV;B:;sXsexgcFyUviysyUBeXBCB_wB:<tktmXyP_dq<MWcdlsERYDY:>ZthraxgoAi^xx=fwngyKYlXpl=wjMFuJOcsOynIo@i[qf^hVx<pht?:;FwqIwGfxwFHuHh]WsAuBobgyrHUYUwCV;S^UR?ETVuYXwxPUrrQYiiRCKsv?FqqE:<QP`wHiqYHQx=sdxViLY_asqLUUUU>qngDKhUobTxTeReyxaySI]uP=ynAZ:ESueuuUsIykEhPIYtesEutXUy?_yvaI=yciiYPAbIocfuwnggBiiA;B:hKxdYppMHdnA<Zsp[]Yt]`x:>Z:xcIxcY@_nXt=>Z^SpucIuepSUKWYI;JVLSpukIumpTUKqSI<ZZfuxfiPv]HfnABZst[gexCsDuGOkEd;B:;rawsx[Y<sSucI:`S?HxcYl\\UOlC:;^v;wcv;ZlnuaxhHIvJOi:BleETIwKMY:<jIukIumb\\pMYJ:\\Vd\\xKxlNTUKyRXJNLyBYSDhobunA<J:<SqxSYhrAXRcI:J_>:kIw>?>vMmCAs=tN]@OFPs:<LILXiYl\\U?LqGDO_LYIn[^qU^pMY:;BcqxcYhrAXbcI:;B^QInWt]_x:<JYnawOnrh\\eH_N>ZtxmQpeLVDoicmYR?d:[cIueNSU_ugIuwekRBAs=;whMRMmCYWYH]sRGVHICFaRlIFp[cIu]?oW;BcuxZYBYeWCygcGD_ivR[CluBTIwKNp?ykqharAaRNlYWeeN_d>xfI^a@cmXlGxcI>ZcGx]Yf[WimqbGAZkxZvOivOiNDBqBykIdwVi]WuaymiEXADlgEtAsENraxZ:`vCaiahyliheasZ?Zhga>XbYFiCkqIw;<nuhVXAvmxm?QkJXQjqQwlQw<R`HWv@SLYsl]JjINq<nWpMYpMZTtVEy^@svQqoMV`aSFPKraxraxrax:lKMHy^Ebx^p;palQl\\W_lwW;X:_s=[R]cRdqGqqIoivEqiQuVHmssmxZex>ahI_EgAxxKx^_Y]EtZWEQ=yxgUouuUUGi=GLMrQ=yZIcioUwuVW=XHayoSuPsSfqh;;iKMY:[VX;FVefP[Yi]xTgWewFdKXMQt;wUwMygyFigGDugRYIwgexuuXiWYAyOIt?WvGGswwSNmcU=xnavbmFdqUouC?oXt=b^IxLYSBaI^]IuqHysTqet?gbPaX[ESSeuhiYcuI?sbqWtecRQdWCaq_EnKPnu\\S>xSI<tGMPydXduVtlr;<XVTNi<OF\\SiAYyumR@UNpt=yVJmwwqqWYQ>EunPrbUkP]sTdq<IMHiQxdQ:Ml:mv[TSvMyWIrpiv<QnKiukMKSPluuOqqQOeXQYomyWE`KWYODAtUlYuqwKYR`yvgYYiPUkTWhYvuUqmlsAxSI<lF\\wYIQltKciNntmv<RQUtnQKEMcWqiOyuuhcBX[MqiWGoHiqI@pOwvHvf`ivWoxwFhiYskiyoQreygSxIR<]DoUumMbLYBneCu]gsCRUaInUBcSYmoGnKVYKECySYWdgAxkIwgaxuiWqqivOYpATayIaKgN]DxeG:ceAAdsQeT[VXKhAOrCSHEqUWIWaAegYuWuTPMdpEfqMYucYNEeQOx=wryOXkAb?yWBSGdwy_SW<aH[yWXkU[kvFUeJieq_DYoEZWh>kbZghAkd?;sD[D_=wfyFyehb=tbIB`yhsssX[SqYGpMrsYvMyWXAW`OuWiXoAbu_YmKshiYsyXQybPqdDoRyQv@IBy?hy_XIue>;Gw;Rl;F?sCloTfyrikInqw\\qwuCBAWynQs>YiI\\XqUei?ygYqq>A;FDuCJ_el?tvYcFYRqOrra@SvMYB:]CSwfgmEtWE@yfIMcg?EEqC:KrsEw_[VX;FOqIwm\\vOiBi`YAuQhn\\V`??a=f][ihQg[=>^A>fvOiNdfIdsAb:dmHAJSxwPpvsqwdHV:\\XAxSiAwVYYNpMZDR^mr?<ruhQSqm><RBtjkIwMBxcI:uVVgXU=s=SDSIXO=Wg;IG_WGAsmmYYCYbcIZagEACkwWqoVJCTU;TVotoUFCqx:CEhYtusvj=Gw[VUWXYIIAoInUghyTwMdgIBlsuawXHIvLyCiEu;mfPqBLybMKT[ASvwBvMYv@_BabCv[fXnrnh^h^A``IYlrw[KAeUWy\\?vMhfxfitfg?YynAZW`^KFmq_p@Y[Ah`IYlF>[g?nI`q^@uDpht?jN@imQrsIasaf[IZnwmIwcufiLF^tSLgHxSSh_rKEUr]HLYRHGRucIDuCSAvJYIWsRoWcMASICiaYtaEx[QtIWU[;ICCs=oSlMT?ccnADGKyB`\\DQeYpekiyIWaw>br^qwv[SXZw_v_bOc_^A]HW[OxtPQhI?^QUawRc\\nFtJ@iweLO>eSGtX@LXDLucITtGoNHiAnrgYsEIqs>jIwKYfnABWUb`IY:[YtaG?_cv;BEsVxGs@YenADQKXiYd\\UGtAs=;s;[EukxvsWLYRV=swwSDggBiQJhwr\\QhusU`xJXYJqCNoFYaPygHQmhhj;NahYtaGx[Adt?jnQfEaq]gy`O`>FZYp]YpqEAtHw[shwJY[<YvJHr^Wg@oedN]HYvRQ?`htSXIfqmF>ow[CBRsexC?^_?Ipsqx;>[WYbhPbufaDw[Jifby^A>^AaitwvVn[_x:Qb=yuMuFnuCraxrXlAdwnAlu=QylWi<kq<R<=tAmElww<RpEvvAqwdQZQR<AtAmULO_QNyBY^H?[s`jmYyQhnA^eBIibwnIOqLYZ^a[SF\\qx\\vPvIFqHfwnA?;tcKH\\suX?tw;BxcYlGfWoElmbF?cDWDtwbH?RYCYC^xKxZJhbHfi@_b?I[WYb<AtAoeL_g?Wawb=dqOIL:`mApXt]<gfHcI[WY:owjMhcufA;wp[d^eXOsd;mCwCfuDWi=QIijqIw;\\MD`pbQYwEJApM:tmXtmXnlLWeewdSN`]agk?w[XjJXiY`<]vX<s^MOd\\RGeS@\\maTRTARa@NqqQcl`hEJGhRiGYiv_IekmhFCW=;D\\aVaEx[ATt=b^IdccGYAInABWQw^UvM<sFMP_DLItjX<ZwOk[hmXNpQ`kJxctWs;p_:AynIC`uuG]eAta_Zv`eAfe:HxcYl\\W_XynA>snN`\\_st@drGqH>^oqawXHDg^QlQ`chn]:_[aVaEx[APTCsj=wmKrEmsr?u=;BxcY`MRucIZAtmMgJGgJyRX@uDpa;>vJyvpIo<Xj[xkv`NOfWoE:sbXsbX;FWqIwB_<lmlUllKw<jm\\mf]Yt=JVLyNaTD=J:tmxdOJqSI<QnaTD=NMEnIZsLnXPAXO_<vf=w]t?xkv<JnXLApMZVynqss^]Dw[:XbI>leAtHwKABr[x:;ynAaDBw;nIuLpuOqAQnAlv<w]:>anIs=pehI^c@tA;q;DYHdQ:\\N`YtaEx[C:uB[=ut;BvMyFOIVKSIXjlImK<lBxJ:xSIPt=\\Vs`YL@kA<ZxXmZV^IN`SInIAnJia:O[ZvxxF?BBeGDOfBqSn;Vm;Rg;BswxCMhOcwnLTeTxWXufTrVLiheHKynIUvBlUCSIwn]xF?s]uH^mEAoE:IExcimm;[F`iFa]Bp_s]At=;vMyXe[hMYbMCcQctIaDiCergI^oE@yfIMcgBbqB<UftITNuI][vM?iw[>bRseX;jVhyFAQI]Mt=JAHynqss\\MDuKJqmvmV>mOXlKw<RQaYtaOxJspv\\XO\\DxqewldRxDMWpL:tmXISJqSIduCujYQpEaLsaVjTMBUKnI<DdvrS[VDYso]cHUCc]bxKxLOVeKucIBVGR@]bhIEWoDZCSxcYPJJTMayjhIS>YJjMoIuwVVbceRqilmRV_FC?Y:;ynqC=oXt=s>KH<yT@IfA_h=uEsE[^MVHj=iY_mufXjhAjxLxLBw>v:^]hY_UQ`IO^X>j=hitwvV:;t[wR`IBLgwMyVkH>?XVweEwrE[x:;qKMiWxfdatF>oB@vJY:hMFDMs=JWUoB@liuKWyJsxxCE`lww;NqIvjAnrCypApw@`uuanRQkVEZWUk]WZ]ergI:mRsaxHIIVp]@@bVq]ZflxfiPb=XJ>XQGqSxtP\\qx:<ynIm:dwnAjMaukEmAI^HA^oG]sOdx?x>ydipqmpsxqhOiiiCi\\lx`qS`SVtmXmwwMGqiaEEfmsmwBewFtCGGAC_wBASvFufSqds]Et=X:CGFAsUyhsIiEwYo]xqWvGGsw:xSXUeWOwOHh]YtUh\\]hZYY]wpfUQwCPkVapn?vQwmxWaGpvdw\\\\xxZAcVV]tx^Yq]lWZ_@wthtEvrUYt?Xl`hlOiwXyl@YnaoeufqKG`dXqdQr<WuXg^co`QNcIFmCX`=Yv^Yu=Okkwv_i]xNhLwxpFqWiZXwgEXbHQgmy_yx^hiqxfm[Aw>_mfa^TQ_CG^>HlQ^\\@nnq_qia^cx^tw[Hgr;pimfsmAl\\oamnylYfAw[Hp]WotLQtZIggOgqgyJqpaAZWX[cYm[Nyupeop^=holqySprVH^cohlXuOwu^NudF[gaxuqhQI[kicuOqj@gnXtd?lvap:InhXpMA^hw[cxfJIiwvZWx`nAu[yxL^eyFkgax?WpQg]Wh]wonSAxvGulX[LAm_olBpw`FtPGcjIwEVcDeUygtYYqGCkEfMoeeKfqAvv[EbQImkGg[vlkfFgfo[EWGeiYtAOeb[HLwcLYB>er;ogmKHICi>GvAyGVavumvqiilQVWEunGsc]dh_suuex?X<aslwTqMuDuiiuXWEUCWd>oebiI:MbHcI:mcsIxUqGUcI:yx_msmwBMQyHAUTWI\\wwtIvNcVbaOxQg;op?Qtgo_Np]lf[ah`LYliw[sHeyh_tpgoIneQqeAwS@uAom\\`kY_ibiu?qkvXm>ww;IfrNoKpmhAXow:oYiI\\UIhHW^wfu[IZZYt]lNInR]X]IvWhTgAJBIPYpQguYmpuaxTt]UtqUYXO@lmtLXvuy=pmputXyYZArjHr=hMoEJMuLYTYuer>lYRDU<hMgtKi]Lq\\rXmnyHmvLuS@RlEMqtYmQq?xvtLwNPND@QAllr=JCxQSXJhXXEPyGMn[AKxdQrLo\\qvFpRkMmaIJZTk:Ew;IVrDNTmSmaQ:<nnAJSUKGYx:<jLYJ^EqFYtvtK:<Ow<Rd`TPDmA<J:Ew[TWcqROhni\\Q:<RcIJlHMLhw;<J_xJBQUBQr=<JNp]PXsvFhu?Z:GW<KGYx:<lgAPdeO^aqqtSmaANt^Ye]is=>Z^V]\\xxZa[LamtqcIqx:>jLEcqFgEgiIBSwFSqE:;\\lh[^o]:Nh?fbB_lXNhJ^fX>:SbF_IBIHimUJYRH;BZ_Pjqv;<JJMY:\\qs=J:\\lXvhMWeenqli\\vHi:>sS?sBYjfwx`Y_d^riwiE`s=>ZDCnuHpuunGsOGYugWx_iVSw<;BDvpL`xXGgGPi=F_r?Z:^pMYbpObYpx:>ZbBSUgkqXTgIwMu=<b=Xvroysq_?Vu=VnJQ\\kxZ:>x=Waw>a@hhearFUQeVXMS^mE:;B_wBAMxSystautqclQtEERSwB:;bj=cXtjshxMunp?fAppDYvDYZ:>N[V@WUi=IbiwdsHTsC:;bLYR@MVr[xpOcYaXM?ykyc?Af;Ede[tPQeWqu[Gx:;BbFrXhy;XZ\\qmu_rZIrxHaYwyt@ifIpZQ[of`nWiA>Z:PtAHn^fqahdBwvgY[OHi=VuaxjFFb`Qg``v=vsiIshY[vhi@Ahfgv>Vw?IygI[_vrvOy^`\\qnbGH^SgrPVq\\Qwl_vpivlg_aGtVHgSWicwkx@kg`m]gqrAxPh]:>Z:o`=PtqWbZ?jmPvN@ae>Z:K:>Z_xry`rJ_mOvpI>ZJOi:>Z:`m?xxcIZ:NdGqjdgfDQhYahsQsWi`OhrkoDorUEFuIgYeTKMHqohwSU?[GdYU_CVESfnAB:;d<CxTIhoOWw_UPMwMIhsUg`oROMF]EecoTsgue[TwQioSVPYsT?ipOH_eUfwdl_h]oD@EwmEb:YgwoscUIn=vccBH]gUySCSvjaWaEC?iLPHyatRHHLoXueikCppXMWCQ]pwoYVdl`ZUGy`vnHQ_YXuPqdoYoP`_q^fw`p=q\\@GwmWb`YZ_nk=OcdwZXPd>G]GHhVDAwVuSfWYYKmIe?ITWIi=Ycgd?YEdGhK=fhYh\\mgREiu_hgWtYUUhmIPUTFyWxuSxgUEsvnCINGdAMUlmDV?E@IvNOHVuvQesUWUUehZKHj_WrWxmurfwUPMc;ObOsE]ObrcVsEyfGggUG?UueebRgxJ_HSuUo_YDex@_Bf[cIuem=v[=BjYXeqDYctJ[X=ISgUfbqfQKGdufbkyFOHKMffuW]Qg`aD?idoKhLQWIwGcoEScrLSV@MuDmUtciD]SSUi[EUcEWvUC]_xswThATTKBlOeEyIqoWMGyRGUoqIWUxioh^]DcWvxSrFOGQSWp]tEOt\\AImSsAeDqWW[]dxsBNcIn_wmwfugf:]coMSHaHN;RQIw@yeUmFBaioQISAeVqXXYfSOgT]GmgS\\ehByst=gr[uPmTXouTgXoidOgr`mWX?EmoiRCeIiT_wsZodEqwgsBKuXVKYBeitegoSBmYXE]dsoiSktUsuRiFtwEygh^;vy]TSGSDGT<=FeyhekhkSswEftAwPkRoYhWEwmkgnmfRoBX[ffgfnEeNWsTqsHCCTybhOeUqGxEXnSg>msgUVJAEPkbVWTtuB@GggYTlmvUUUH=Cp;ImibfuFRsrsyCLcg<=BHKTtausIClqFLmrW?E]?sjMS:;to=E[qB:;B:cN:<J:DmCDMs=J:Do\\Et]xO\\]JfejLYJ:\\VatpIAMHHLjhlM<NtuK:RcIB:;B:c><OwB:;TtDq;PV[<MpiK:<Tt=jf`jHQw;<J_xJBiLwxJ:<b=>Z:>ZDkV\\wrhQGFZ:fNKhPmvkWB:;fnLpM@jFYnqAJ:Pd:JD[J[:`]:G\\PWsZNcI>Z:>jIw[:>Z:>?;J:<Tt?Z:>lx^uS?hGVv`yg`qb<>Z:^faPtiXero_qG\\:>ZZn\\>ww;B:[dx;C]AX:;RPQrBUR:OtUwI=wCIcE@QW:;dw]Er[YFsV@;TtEHn=tZcUQqIv[XNSr;;RpHy]PmPQWNDXRPJlxkHtV^iKU\\Qruy;XjuyKV<rp=JJhORXJBTM?XM@@JNpQZlxNUY;<J:nZ^qU;B:;?<Rc?:;bLJNZnG\\?fnA>:;xcYd?_dtQrSQu]yB^mxSCHEwGG;B:KHW_dFgVa=GYQfU[xOCbh[fi;TXqU^_DpwiC_ijEetUrZAGwGTDYBtydegxtsyHsvQEgEwI;ufO?ZnWlLYebvxgfxCqxXQ]g_u=QvBi_Whoq^yWW]r`eFyopgop`tWaoM^_LXiAQk\\nZ]@Z:BLEfnYyI[En[Bq[XH]yX]FEsIc_dwISfidlKcIoG?iYEatSYb>YDE_gR;rWQyWOTvSyrOIKyg\\QTDyFPAslwgtOBH]i\\?gEwDAEuCGTe?x?kBhwDqmIcmgJmxOexqURnUfP?VIugh?SjebZ]H<qCX[hWQsRTuJirwETFdRYHr:DM;HuUlwJIRnqjE<OwxUw`TotWBIy=LLYaVmYxteujdtlEr_xSZTooItPxkhMyeittiJIXomxLcXQ]pRiyKDyvpEOmNu@ItIppMH[PQluvxexb:>ZOi\\:>ZZ>ZC_b;sAiTe<RU<Qs<PgxWdtWyejCpRoLvCdXk=So]VM]lWQypeVNqSphUiQQdyo:]pw@XtHt@<sNlKVlQd]LhEMqYmOPxGhR=pMx@xghlq\\LcDnMauJAQf\\QyPPZeNsxxcxOYmpuex[XqKMyZtMV\\QbPoh`r^mUXIWr<wpav^dxbend=s[xWCqLsPRbtsHhp`xrdTx?py\\qLkDVf]qweUJq`uI`qOnVy`=QiDyZCHt<GmS^mPvwY^\\MnZoXp<ar;IlXPyFA_UGeuP\\`g\\^YmE@yOAZ^WZ=xsU>hZAxkVnBXfrVqfxfTy`Xgyvy_Yaq[GvrWftwuev_Pii]qlfxq^qkcfqNPfbAnmuPiCpWtAEV>=F;uSs?X>?uSqux_WGkw\\qSLSi:UT`YvuMwxkCEQI[kiCyc@;Fu]rxauIkCLQvPgyF=yfaEkSW]qfiyUxCRv=ikeweWxiUUSgxQ_uKyhfQdnQFSqGswsyWrWWi\\qgs;SSGI<mIqyhhgw^CXf?T;yHEYDRUxvcfFwUF;RpEFseTpsF^oytYyDqEwEXmGvKyWxmSvAx`ICSyY?iuKYXHGEfudqyt@cdoMuRuiZuEhUDS;TNGum_dtwFoibyud;shuEv<eYiiF\\krHMi@gfYywY[CfqHHeD>]cPKx?iGC[gC;B:kc;ET@oSXoYOQcQouVyxDYc\\My>_UrecEiuWkTPuDgSDYmgPqBvCwEUeqOHgidUwgQWNQyT>xvXYmeyY<iX^EoShQq<N^dNx=qd]w>ukRIkfQX?`US\\ohtqXUMauVR\\SlLOMDXiPnTmKnlSrhqoDJ:LT@ApETsXeusxSBPNkxwqtKi@kpQLJ\\p_@XLaplXqXlodTLmtlFDsCPsGEr_xwoiq\\=vcXNAyxy<wcuXgaSFiS?<JB=lBPNhTND]QsHWcArSukTTL_uxxAXniUiLluumZTmPtUvIyquYrqxMxt`MnIumZYls<vTaQkxvOEtj]tGiy@<JBAVqeW\\iuAUJiDkGqqHTj^<s>ijiqMGImEhV>X]:>ZbB:;B:;O:>Z:t:<ZD;uTJ]FDuC:naw>Z:BS_SQuuawYZIyw;EK;Bl[dUyVF>ZDwuxVk`ac=qk:>lpnky_x[wuxWZOg`iXkuFqyy[UG``>nnA:WDk[VxArkewjISKQu\\ghpOw@aEiGyA=WPyUWMwPahSYscgIVkbhWgpaYioGiCGCYEk;IyaV=wDmKBDuK:IqRLPYyqqPuL=npPYfdUQplhXWppoeDJgyKOeYGUL@Qsupxo@MDuY<dnA\\lX<ZMH`vHi=ovogcQa`YPkUOwX^x]iqPa][Wgvh`cosKPbkGmmoatVn[Wb:Gw;>ZV^onqeWAhJi[QouehjbQq?hwSypr_l:x`Y>bK_jdgt=nsnFijH^Z`x:Jedq\\ixDdQJqMiXw[LYh\\RrUQw`LLQmg@S[PuiqLqdpB]WBDQ<twMYJ:<JZwZ:>hRNdQpf`hqnhmpGnbHrbfycpbmOuHirmHtgv`Yg\\;waXqksYZZYt=xkOg\\DgrdPyFQahwhWX`:wpmYxAni<H\\:Nq?ynYAdg`cSogGgli`uWWdS_mUqlIabe_neamGXvfF]_VgdVr`otiPobFmeNnYv`rOf<_dgxlEQcu^hr@iuo[PWm`qt@GumhpcgogGlBY\\H`e]^yNQb`yponfbix>gq`@yAigqaofVZqowHNuap\\GAskwobF_qG^<vk`fqTHunq]THhQavKylyahch_pYxhwqu^`>>fsGyDPg@QZfxhjAcwxZNpa?^lhVllGmoYkXxtChoghsdOnPnncxnlpbPohAh`tPhVAmUqhXQlcIq=X]dxnfgesXiSW]WY_YGqlPgG_[cI`NxbPPyoQbcpcN_w]yws^v>yvDPxd@oTap`olNh`papLgalNmXV]\\i^eOk]@oTAmoQp``txFkLP[KFojGhd^_kykUqwSgh?hdOnngxtEH_MO_<Yo\\G[VGdQvw<OjRQ`iWxJYZEWr?q]Zvb[NiIns\\piOQl_ivmPrnNrf@fR^tNokFhdwA[dGekgfGQsliouNwMvot`rXYpyaj`I]dgyJQjpPZoPrJ^dyPuSxrWQq^^oo`f=gpg@qggxhpiWQ]=wywyvVOqfwxDGp`ge\\qeo_u]qrWOgbOoLgq[^d\\WaLQr]_oh?e<ApoHfphl\\ogbqmt`h?GkVijb?mUFwLwx]?imyaVOvENuQgiuqw:@uAhg\\@cGymAx[:xcYIffQisGyDiuIFksGjbgfAQjrGnkosjhc=HpFgrbNgvYsUQqNnygWodPoPXkcIvX`c:ygbAeRG`@_qTy`UaaJQhewolGrpWi?Wiop_UWnWAas?evwpdgvDioeOZhQhVhg]IelXmiAnYhheOgEyfw^t?Pk<HvywsLhrCS[kdHywh_GhwgH_ILqcgWV<afc]vROuoobdMyIcWNAUdoD>uTNSR:WW<qXogip]snabi?HhIX]yGo[Hoei[owp]hu_RkSBAcH_GdIqboUv>=vPMy=WCUKgg?tCefyKVnourMvegyyOhhcUKMdB;YmqhFYEyews;YpABCUTtUfFCuwKg\\muTGY_KrQCINkXL=U<GRvShVGuT[cmMU;=ugqilkrDKEAYcwQEXYTZKXbuwD]TGuSPiV?UcQUemwfUeF]GEokHWUfckRsAGgOxker@Os_eUooRvAIswILMGEUbpWggsUS?rpGxfCugwXj;YcmdJyrv[UgqxJcGGOUCAcOqUXqEKuxfetUkTDUxlYurmi@?eSWr]_bPuF?GEF=GowXlGVueWOaxTSi;wIxeeCAdJUvkKGG_tgGGD=h`sDTCsIwYVqXHQsvgDeYgPWEywC]ocdktAoT@gsu]HDAIUIHE[gMagV=ToshpUWBGHGivKwsL]sAEFTiDoMyh[r<UtOSiA[UUwwNeGrIsliF@yU[ywKswUuuxWyauIWMygSSrYUviu^AEHciWYShkew;fnie^oTFQCgsVgOcygfvewtmSEmh@gd>obI?hU]TFYU_KSM[GoWsAeDA=GW]TcaceQEE?g_SWVKgfQfl?YNEYsQsA_gMwEskRfuwtgHTIdNiDmUR\\cfkwggSrhAfYmr>Ae?cejAsEgYcECP=RT=s^_vm]tuaysqSiAVgehlgXPwghYDwos^ygngd@YqTttNEpdDUS<\\f>[MqamybO_l>owPA`\\AcMAjevtIHmeOkogccw^FptpQktpxeVw:npFyjlioiWvGYbhVnRiuBg^SGwEyfGgkbNp@gliF[oA_\\g\\ynfjx_\\gm\\W`hAq[NrwFk_IZixee`l>Nv<i]BHaaVd^Vl`gkpI]mNpRIfaau?YaR``fAynghQYwModUYhg@ogh[sooPX_\\>oHobwqoWXy\\OiGQtya]Thh`PkoOnlNnCIgGHdM>giIdgfmyPhCaqogxOpxtGxIXUmT@GbDUrdqRgeCrOh<EhdUBWWdsAGQ]d\\wUSoFGIdeaUh?hSOiIYsqcyoesdufbmxBuUCwVi;t>OGCyS<[Ytqgr]bKGrq?W<;Dg_GEOFacxukhPwcD]hv=CeSSFatYaf`]EaGuTcwmgHccx?sRWIrZ?TgGwtir_crxCvL=Wv[TeUrluITat]]segeY[HBaxdCho]Tk]EYQud]wbAiaoEyAigaeOMBhsioMUugrvcFJqxLIhGUXxiyS=BaIdfQigQxcCVSCi`=SqmY\\cb?ev<GHmuvgOCWWhdmeSQVRCf<UE<gbD=HC?utedbURrOw>UG@_SLYuQ_SaegKqgEwFFSVOybsOTWSin?EP_whWIRKghWhDYWQageArGMhmyr=eSkcVseLKLWMPluxWVyjJ`qpiKOqyPlwbypCAQiDvqpjsuqf@vrxWwUvu=y_\\R^=sQ`sOTp`pLalXVqXHQoWtkVyYTmVgtVw@mL@p?QvYETD@xtesqMvodSbQm\\]YFuLYaWuul;xkwPUXXUklQDPWx]wo]X[XTnYRHEnN\\UtqUYYO@fh^AyxyZUy]SIgyIj=Vr@v[HfmmArmYiPfsSp\\ripIY\\If_RqeL^gMX[Cwkdwpgp_fFhuNe>nangjJinKV]@gupXhsxxkvssOyTAtnqxcXwfX\\jvo??yM>uGImWpp@WygQmg_kOTaAyP_wPWIRCiHQeSEhY]gJcww;BKQeyUVWiypqxfyDceFTuuqcwfKcRyYbqW=mhDOVaqHpoclwvryrguvfOusmt]KXiYDTiRuyTNsiT?d:iUBcvryRYkxysVBQeQQetyeWwwpEeWwvRSH_OEFAhmgVxgrD_vUieXQuS=YXeSDugnEwgsylkyfwrX=yAey;YBqwsRkEa?ceUU\\IBrCb>seFIBQivCOyQaR=Id^YGwCru_soobmkssWCW;i;mWZUGwYHioHpIwW=VbciEQtrAtv[YUexUewT;bhSBDuW?;BnuhqgxYmFZ_xJWRDuS`MCrccLiVeYFUKJnhRQiKOqtvLqnAYGykkirvqW[mJpiq<mpDUv]uSeqUWaybMq\\MOyxW>TUf=KsLRLXYHIPuXvRXmLxxaMPE`Snpj=pss<lYlKJTmEuR^iwVytfdX?UW]HuppleMt_\\yCuxpAOpMkhmXex`jWpVYwMYu?h[;fniAh[amtxtOQ`Ji_Gaae?hAF^=@igim=xdx_iJij=Q[tvpsywqfiROiCwuyxwTyj_FZ_xZ:>h\\v]e^aeIoGXiIvmfoaMA_wNmSXfNQwofqqgrTVlXw[kQxO@pkpw>omUgASgZyuDqbBssA=eK;Tt=B:sbLywfObeqFQcX_uCAIDt=RcIZfNoTxhZAqp?y^@ggGtTWewwwAYiwywCYgPajhfhyydYXeiIxDwohv_cFsUF`rvq_hlqPw;fnAJRTR`YyqqTUMKNqTIxUKiyiLuCUw_LYWyOjIjT<RmUonlTXipihrJMyWyjU=p[<nnCaQXZASEUXMmiSysawUBYBGYxp_vUyWLYe<swYEremx\\wfr_gQWcYYuYAcGCB_wB:;XhkxbghhcQQAY]Xk<UyBDPoqYeqMw\\XMdTdqU<qx:Pt=>s:PrEi^fpojgt:wapQk``quxbhouKFuWyvRQfYGbaqt?P_Fq[jIpX>nnA:XN_HuGlkSIxgpMnIvilOLmOXlmYLqTqtWQYZLYidLmhJYiN^lt=\\lxXp>EM<dnmdYgHU]hV>Euj<QJlb=xf^OvLGtopcXYdMIbv?sW_cv?lL`riqibAh`Fp@iu[qy@f[TIj;XhLoyEfku_uBiiqHUiREmh?aEX?TO]D[?wd=Fa@kiYteLTKeKsxnY\\UBiP_xSlYNYlxmqPA`xhAwH\\kY\\yVETXeLo@lSUPEMc<y`FgwBAcK@snhnWYcfHrf_s;idQYcuX`Tq[YXhuwhYQ_GirDiulpnRXyUqgwwhDQxdhxeirNH_OVnTqkfy``gqfH_ohkVOd[Na\\nxWpy?p^j_urfp@`dROteHmYvlL^gow`VoxKibd_nIwqa>wMYi_@doG_n_it?s[@uQ@clAyninEQrxwmUnthvoTpukPlipiOaa=G[XNeJqtSFeKN`LHgkgfG?wR^uSFqNa]kfaf_[lq[FpmXilgWumxyTFpl>hIVkev\\Ng_YWq[Feqwi=gpWOmAWd_nwi_vWn`xwZ@haGVnh`\\mWbqadypsrhbuhyPp_WopugnRWphf[y@thf]qXcpokCXcOp_?ojPHf@XpxqwXGybYcgHnYx`q?iGAxxhxkGcMInqW`jxlYfcQQmUV]UnsVPamOy^Ooyv^Hh]HGta>hBVv<O]UncUvd^_eQv`q^saxcWqogPf^XfWFoUOayXqldiDUFawRQQ`]VbakKXVdutTdV;EX@qOoLsVixOqyxMQE]LMiMdHOG`k=pRF`LhyXSPLYqpr\\NdLmB=mp@urtR]@lg`oF\\U<EybhVCMquYoP`OiPUJTrQPs_YyUqxXdWbpPWIYcYTxPsThxUilcdtMiYqusJLrT@PMiWihMmdQGtqJqOWtpellFhSNAwwir=ilEXk<aYtyYfqtT]y?qQKYyB\\QGiOdPoxQv?xxQuqlXVayJaTPwQXHYwQYxYuNX=prqjIESGULdTNRdn=Ewu\\OnqTVqY_`pDmqpTspxthePExsj@nVqktETT]mcXSgDPRuUo`YD@odPUx`UfxKODVm]oSHTOLsVIPE\\O?iPvTwsh`@x`XorUqhw@d`@koqiQIqRQdDh^]P\\E^_UnqTqkDVgnVa[yl\\`^WiyGVueWo`xtRIcRFndvlUxxqnwwN`iyi>x^hVftvy`WfEGgtoi[hwXvhsa\\_>tLw]PGpfQn_VfJf`twqgwovgiux`\\gskX^vgZWFtuA[nGowQvsiwIathQewPxuHukgbYGmuyuI^mWYwHx_HHv`qn?GwuNeF`tuaysa]lhqKOeTQywviNgbCgrd@x@wsDQ]sNtF@yh`eynfhHebptNp^vhgcayOhv_VcPg_efofWvFwb^gc?^^w>efVm;`t:WatgydPwogx\\X\\SafknwxQudgfexiiqj^yhfHjsVohygVXiNIldHpOAhXO]p_spF_qGp<IaWp\\tAgAi\\KXf[N]aN\\sAcavqjQkpqlWHxqOrBaaYwgrpysIZYpmq`wTQfrWxyYx]YqxNaPalWvlmPvAyhXQy=Yiyhy_Xc_`nUajNY_wwj?piWQmTGdUW]nq^?Qh?_ZEyn\\Id_igpF]mNtYOk^OvLG\\lN[uHvLIsDeyeGQmTbkdT]d@EUPSYUUhweYhaddiCOofsqHNubNOs;QtrKY@mUwQg_SUaeBMivDwRDGie[wWaF]qwUoig_xYCtnUVektCOsDauvwikwwKMvlUWPIs\\kWZMv=uCqMTbYVVshgYrusY_QdsUwviw:eUn_VFkRFKTqmwe=TVMSf?Wv_xygSaIdx?RhogeIbkIwIywUwTy=HQiB:MSsWx=WdtGEnKTDqRaYcFsYyAhhyegoR?msrOFOidaGYciwrcvDum?ASrEVbmn>tSIdX=]spYVmdPf<PAaW:m]Mxl`NvLNmdvquwpRxnbVuu>ylPfJifn^nugv=g]sX\\[g_`hn]PsQq^cqwQpciP\\Uwb?A_xXhkqypGvXFyXfkh@iFimLNyHw]qfZP`eoQrhPseobnOivOyapewAVyruaikqUhWC:geDMfcMTK]fXGxS]WPuxAqTMaS>AT?AdT_FNUfRCGYcTTSgj?HcAWh?iK]G@_v]Qex;t<?xR=W@iGguk^@UkTyDQVmpKnpUFEwZhrFulkpXheXouRHLWQHqEYrL<saQkptxkhuu<M]qwUlvJTXaiJpPPYuvU=TSXnqypEtxb\\vKAxyuoRel@xUb]y]QmEUrYiPbDmelVGeOHem_tqrevsYOxApwyRyHutiyAqusqu]UUM\\yf\\yoyQyYyqtyVExfYy_umvtlLyQ:HnnqrAATtakxAMrePmMkULm`tmXaO@mVgqwVqp;`kg@pbiq_axIQPDTlZUqlEW>=SZTvPproamFqpPQucdL]`wVYYeYwVQlHDqpqlEAQQAx:QQ^Aq?]V^iJm<rM@XqiKm]wPDjWXmSDY_HmwuJuDYyUqpukFqVhTvKAT<MU]YsQmn[yLTtyrhrx`qL@j]dTODlTMlnUS`YkPXmDaOopTOUyrpTdlqSdnqPxkiUpQL[yKfYUMIVhpuCXvNxyxenQiw[xyL=wMYSsQwyexxxW^qpamqx\\UCEeRH]qaqQG\\w>iMYvLyxtaE[Io]vr^xnXqpqy=vZ@h[X^]tvv;xvqa_TX`GVat><ETWqi:IIwex:sxbCUVsybYrvsX;=T=YIc_xAwwyYrPYua]CIWT>ihgCxl_c@qjEpqpYqamlyuTBen\\YLgYk^hNRyQUDqgIWU=p]lq`lq[ujPpNh`xoXUFak=XWexYnMvyqWmQYTXprqr_<y^mKrpOI]wxeTnlM_XKC`W_UrDHq\\evv]N>XY><tHlUGMY^MjRHQuEpypNxHFLkQulTtoJmR=HLhMpHeQ<uumPOcAXhtMjukZtvNpuJ=S?ALTqxuPmkdPS=wppPApYOixQqqumxwuLx<xkXuiuY:Amydx;hOyxytEloPjktY@iyxhoipY:yp`=VH@y`YKAyYnetxxr`eSqtvv]oYiW\\qxQlSyAvdDpc<pHHp<iQMPLl]xgena]x\\\\lxtNB]ywTOZqM;\\NIxliuusuvSXPy\\li`YiawemwviVSYtqdLSLLxTvYxKfEQmix\\TSlywMlV=LsOxxVHQkukghsumYwTw]yuyexnyKhMUmayHUn\\@xHHMwxlluWjUOeejQmSy_^lGwKOi:>Zba`Xfcti]nqxwqfS^ya^xeH`kgx=flM^sCX_ahu[n]RIpAAmTwyyWwhWqmIm[oyBfqiWZMgxuasvIqYItyylwNxDQnJhnuObpP_V`xiVdiAowghkidQg^`Ytu_n:IoAGW;sHKYWgtAeTmAh=MTjQWtgde?eBoRDAdyGfYURayDH_edkXRStuuXfWD\\qsjgRLQdsyYSqx:yuHuu^EItiYhycVauVQw;iXwmEF[ElqcuSDNsWcifOoE_wB:_g;AdsYBAih=yF?UWEotTQWxORgihXYfpix=WWoabd=wQ=rOetoetXwwOiv_cFsUF@svY_WjQV@qSkQxHgi<=ui_GfiYyUeJSF]sTjIGv?Gt?Xd?uSCijihQsYhkWuEv@Qrrwbrgw?WTEwg\\KVY_rYYC`;B:_S>AdsqywgtxeYlQyoiHycyuivUsemUy`IeYoIw[cIIIwMCFwSyqIsqrAaUgwSXuumOCHqwSwieuUeGhsICNoIbYtEscQuSbCbX]SvauWKVUqgwoxQiIetphMwFQt<AtbmqNxoTPUxIqCPTPllFpLIltxPMRHWg@Tb=syqpWUY<yVTXmy`q=qmsDx`yJ`pQruui`YA@oy]wuykOYwCpvXYW`XUIiK?ynA<jfDrjqvUMKNeUMiPGqwLitLdoJtQXYWqaJ]esKayLpN^@TVmvVxkHAP>HqYEwwPqs<S:MV;xwCxQrYwhXwhdwmUqIIyXUY\\mXK@Tfxt^qUxhyLHJPawexYxhvquTThQS\\UsYjoxpoYmx<rNXxUyWuhURujRlY=iqytYh]owpVZmnrPxPxmYeQPaUMAu[QnUlmtmXuuQyIN`pyfUsGDKWXmkpkQYkFyrJMYXMS:<jF`TtuoXQwKiPc@Yo@LWupEdYemSExrLAYw\\OB\\obLRo`X]aSMxJULubMmFDWftWAdRc\\qkIw]xP@Xkfhxq`sJ<yUTjWuuReyIyUs@w^Is?mqStQlisYlY]ywHmJpxktTTF]yKIs]xQDPXBpXnpueHlKxt`Py]eP<@vMYJ:mjddq\\ixTXJMQyTYv=UQvtp^qNnhmXqXc]L=YyNLoWqVSat<`NrilXaYGdUDEusUjrypgQsxLqhLWtpnE]YQAwxdQ`<J:<sgenQYLpYmUITUqwoyUGYKKelZeUILTa`x`uTXqxRdP_YO_eS_XRPPKeXVlhN]PqnLtaMmgelo]jpeKQevRpY[amsmTSUyVEU==U_trHQtfQyn<yhup\\pJEtxMek`apWHjiUnUeRyPM\\dRp]sY\\O]Amr]QPUWAuNoLxlijAmmjLwFluhMWLDPVEYWUxdQr_YMopL_xScPtUhRFQmSMTPAuMQSoAsJyUnuXgdXhEXVHWaau?eQoLKrUYNPPmQuOPwhylOuVXhTpqQQmrsasOdvO]lupk;AT>YxtixnxnYdY?mXyxUXiNveqsQMQ]nt`u<`PF@TMAqAtuPYnjxXEUVmypiHWyTWkatSXPwmsxTQnmsUXuImlXMQ\\<TjmumiumyPsiYBpYYPmw\\xxHYiuUsTyMeythXcHTTxlfXOW]PG]oU]qcauiesxdYIPTluuJYm<TupUmBarwPnfXnrMu\\hREpnsYvclvoqqkuuAeuxeqHaQe`WwmodyTwevmXuhqUq@vRiyulR?doXIMTXmHuxfIYpqxI\\Q?DYhDOGIneawIykP`Os`YvaRMYpmES]Yt\\XkY]Qr`xMUvaLSu]SuTYnTaPHg]nj^yyoWy[Y\\aocIx]Oy_HG\\Q]pvgXwtHfmfGy=Yhih`BXpoYf=qcVFsEaxIQmQn]XH`c`vmWviNxtOml@y@i^rafhfegPkMXy>xnkFoxfiwqkgXf<QaK?]snnpggwHdXpheQtLiflgiZ_vfQ\\_^g^aw:_vPa]gfuFXwANvXhw@y\\=qbcF[]FnJafvYhhQnQP]rP^K>[]q^jOdW_q\\p[uqhm`fkXpx_aCYae`wuooL@rdHimgrDiuOhroitcHuyy[Q`y>Ayu`yaXcepqwwpwvv[xZPPuywvWqiqneW_dVIiswywvvDxmoyulyqeyesow=xvlfyl_[ioytHsQfy^qtcPodQv`qjWAw^plNXuewpTPtTNaiWwHPiKOeVimEg_kxeYgpvOkbPoToqV_oIf_gfsT?jJonBdyGyx?iloVwqX_EsboxEathkcLMthIIqMDmah@eTbSXAaGjogbOX;etVQugGcokt`GVVid:?vsKgwAIsyVOgYIiTLMWKUG_gTeISPqIGqBtAdVUW==vyyYuuXY[E?eYAIXvuYqECrAR\\KU>aBmAVrMwjAFDAyAWB^CDDaRCKVd;gmcfm;FbArnOdjAt;GrDcX>Oc]SBHsCCeh=MIH;xYKT[OTFGGSsB^;yAuylgcbcG>QD<=v<[Bsmrv[uhyguAdEmwlAiUWShIxwQeU;SpSYQgiYqYlYyhyWquWQuGmiW?qutQUayU`ifjkIyuv`axfqh<;dj;s_qSVUIysvggBmcbkmf=ABX;vpEiAcCNqeCchsgwQ?C]qfvMxaWiQEUsWBPEw]ktkgHm[gduhf]WxmTxEW:IWsUtQgwTgdoGinUsnqthkinUxPiteUfuWFRMx?_EmoRB_yWuRakGOYgGUyh[c;gW]qg@QfWkr[OY;YdE]gSgRxODccrx=RPOG@SXO[SWwh@Yx=cyu]yEgYaQHIogpodnctUafy;WDKGwgyXSXfagHUt`kcs]GFyIoorCUt=KynArxmUYsxHAUm]WCGTLocgGUtCxb_hMEE=_uEQueQHAcIb_uOwGFiwUSu_mIrwX^AWfKWWCTceWmAcKyiEeDMGidYV[wgr;Th_dQwVCgfxGGUebL[yKCFOUDd_WYCb`;eYSdyUXoQuqyhhmh`_gviUuEeiMxWwe_cDceUBecIkU=OSYyhxgsrkFr]siut[IeMWh@qGEsxIeeFsiDuHY_uoIdwOYO[vXmTUSsVQuayx_udlGxNYduosXgTxUG>IWugUd=siQeXCCuedueUd?FPQR>ovd[YucSTQUnYxaYI_MHBoXhAsdkxemTigW[qr`=bcwYiAX]wXguFqsdPahwiwtqcPsbqyfpqbYevEutfGXvar;SWeSgIoTFoeiYFAgEYGxCQGmuewQdAacXkxbOH=]vqgyX?XksXFwdtyG]acgWgWghoGxLKRnuxXMYxIWJSSOyro?D;IiDcYuSuKybpmT_GYaQIK;xJaD[wInQHi]sZ[bxAi]iTnybQ=yXKe\\GShaw?Hw=XurumQxOvUQcqTq=uYEMhxmTiMxeOOyj;InU\\tpQpFiP_xJDixCqsuHWmuuiEyF`ykptsxx`ypEUpfyKgyJ`pyfElaUSUyug]jVUn`xx_PwUQeCIqDV_mQpsnrQf]qquAVuHAZtO^@vcxys=Vd@xuvPhgpo^xxEf[NIivFgcHoxYdDx[YXiaipaWfZH^FXxixcihkbXgF`fSv^kfi;wuQfteG^LQhOV]gaigyrEx[x^`\\ArCxmX^cT^lZqgwveVOqTyxOYeAAvU`s]@yPinjao]WxXgdDwonWgGgZIw[SiepigGgqa@gHofIfeVwvXv[B`ZpVls^w_aZ_auQQsWX_firdg]EvyCwwbol??dq_emOqVH^H_xihjBXsO_kpX`:pm>YyWng<nsno[qq_hwi@IkS_rmNG?DkGiDgfpmdtAyVaiMegUiVF;uOuWuIYrqt;?YeqHpOtvsGigxL;yTGYqgHh]SIKGw]uoEHU=c;;sO]xKaHGeHhuSiQtnoxEkhUUygiHGitPUvwoiSgsyeD[]S_qFb;fLYB:]rU_IdChtaY]_t>OucoVUehVduDxwPaWPiUfaj`]UPuWVmnKyw_tuIiJMELqdlXhKU=JKuv>yXoIuMLT@unGlwUYtIlYwEXtYvI\\yuyjmap^LVW`VFuKZLOGxSYLpyYoTYsqLMiuuOhOdHxsHn`Uxr<njLQf=J:`jt`N\\@NddqjtKBYWxUJRtuWioTeN`<qXLMl<yQuqRDnn`yBUP\\lU@ax;yq>YQYtM[hM;\\jQxyaAkt=uitodPsOpN_@YyePglJddqWeMxdkD<J:LNpUQR<J:\\ruenaaxw<JkTSBLYv\\R]=TuipLYwipYkQt_MUS<RfIxVmqTInnXt]INdLjTysOpyKalNdSMuOXMWZho;\\rPuwSAndhstuLAukA@oELWi`MYHlQplTPUaIoiXxr=Wk=JkPRBDNu`q_=KwlM\\PNbhyVEwGAwa@tXAJ\\aJwlM\\hMaqu=<J:e>;BdcI:;BZO<::LvQMjn=YsauttSwhXaUY:<JJLU@irmmMGEpqExVdqxXmoluSilmMwvlMQXOk]r]Trb]W:<J<usmEq;uo?qkh`laAViiy?PytulEiSSxJ:<NVMTAxKmUqADwODY:MOw`lDAkAmjMQs:<J>hpRyyFIt[]XAuV^IXrmM:<jjYlHMKltvXYZZnlKGw;>ZZPt=>:OSI;B:KFGMBG=vIetNqd@qFOUxDEIjwfYKYUWe@[VomCT[WwEFFmG[qSvwVjWu_PmGxvjhj_Lk>dlZpjfTY>IkDuwFpMbulEix[EuyqQslY`Py<ikbiY]TrApuutXTAsGTKXPldF^kU];gBWbZODaKGwgGT_Ty[IvMyFeYmyUXayoYHImcFouqKxwes_wXx\\nryWaply`PKhtD=uBLO\\INb`rcXQVtniASYqWwUVhatVyNl`VnTMQHyjYMmunfYovdmZqS^emLlP<Pkr=KdDX\\]SiUkXhldYKqLXY@YFMSGaQ`dN]xxG`QwlxKdyw@qVIkdxpChPE=uBL_v?dCX\\OpuPF^FXuxAodp\\_iuh`gcoghGgh_guwbZ^g>f\\kp]NOv>gnqObMatbpwvgxGVeGgxdpeiVoL@pK^DMDNMv>tuA`SeDLOTWcTOQiuyhWFIoIuLaMKUEkQPo`HlrMr@cQ?fL\\dHX`]A_MQxVqmsXvDpkrqqWGexWvw`eKnt?OlxxZBVe^vqWNjTVj;g`qpxXxuXnjBP\\apwefqZHetput^pUYeCQsoYb`g\\i@_ypijvbRxsvFphouXPmfijShyt?nBweXFghnlWXgQ_pWHkDQKSUByuFCRGwxZOeS;seCyxuy\\aS[wWRxPxIjQTSdpKhlsFDrlILapOp>monmkfiqIkPphlfeuXy=PvvPvdhcSigmycUahZOmXiZyh`^osHvufW_DqogOsONy>ixCWu@w\\Ix_dN_Py^dyst>qrVrdyoQy^sqfXGhrqx``gyI_xxvDWvmgoHQaJot^_e>hcyyceHumvg<QxDVfDas\\ywxQgnApWPrp?fNGgLawpAvSYm[xcSntQHjZpro?dwQae`k?xmPhmCOmWOyOYoUVh?peryxpQ]NqsCPplxbVPjTVtMaZ;GownhbPf`GrpaxHVl?@sXahuQy`V_yobrxuxnieWfHHxWyl?gtepgYqy]Hak`xrQ^wOvsiumqvfAgg>xoXqQy]eHtLqkx``aYy\\QoUQiiW]jaeJnphNr`_xCX\\PxkiVqp?di`rAyyJ``[iwKge>hgLOlXHp:@voQ`=oo=a[qp^PawrHeQ?gQXxVQ[_osyN_qnv^AuCNga`bsQpQXscaxNOyjpgwpkUflXirvpbQxlvQrHwubvnZamFqtuHbwWcpGsNWfuX`wVgVPxSy[tab_AoXiiQvgUPgx`btQnqw\\bIsx^dK?qdYtnVhp`u<`q_ivOX]lXpwWs>qcKOrP>ai`ofvu[`\\PhfUVt_oxmXsOx\\vGjky[Uas<p[;Ysbif@`mFwbSnx_ndL^d<P]JHjpyyggZoXd\\`iw?fHo[kOnLyxqOowqygihHYdy^tTfu\\wnlvejOoryeqp\\SXnV`vWniaPk>nyUWi`PbSvpdVriyhSVdDO_LXcTq^fve_FaKIkjhhQn`=oubakPydBw]MxnVHwh^g;vypQ`=XrFV_ePqrI\\;gkUAntyscyxghsZphWyZLv^dfir`fFw_BYes?wbIy?WklNZ`xmrNpMwutgiofu@Y_FpSOwHUTESshmWBIxUYU?qXdKiGSehOftoTKMHwUuCOYOiwACr`=EjYCLmhxib]?fp]w=CDFkguuuOqd[gWtqdcQrOgbOcRImgukWWGb\\cHgOXWaiwgHcUflax[ytsSXLevKgeDwucAsxYiR_cwUTIaD^idFqUyMrvmwsgueqxPaSwegrsg^UuXOUemhTguiuwhGtt[IQqx\\IFHKrpcHiEi\\YCFGDpOraqfoUDp?riWYSGFw]hgaCaecMMSDYGuksC=T]YHboy[Ctdmxx_Hu_Fi?yoeiJYscmh=OIgixhSy:Mv>AexwYmcw^=EWgi[QYOAwQmFGSSpiSbKyvGFmSTv=hmAx^wrAgDSsuQkDSuevCWwABL=rQQy:?W;qyIqSIcy_Mho=In?wmWE\\StVOHsCiBaeLwhwOW;=rmewfsiGIQPLr`\\r@QogGm^gZ`ovHQowGuD@wl^gWvqhIh@f^mGrAVayqgiVrSY]yv_VNyvApWHjmO\\NAyFNoS^kiVkf`vRH\\ww`U_p`arX?dwgQIhI[FHeY`kwS_yYaNXlqsevTeUCUSIYpPIYvDWcHokhuVtXiauDAUrxw`EuiiLuuvX`Rfqtqxp_HosHpk]rvyQYuQN=wgEW^<w>hkZPNpXjTtWkMpMElAhqV@nVXQ[`uc=VFuuoMV\\`qLYWfir\\\\W>dLkeLNMvNYJddYqEmPHtwqJndSdLmsiKa`pJlP<Pkr<KdDX\\Bkqhn?eA[cf?h>EU\\]x_stNuWEUXMoyh[s_wFkabG?f\\kr=OSV?gnqCbIyRkInquiUgeqR__CKaf`[kslkpPSi]WQQwKxWsTXkQqxqUVmw>dn?hLE=EDQb`rCPSiAjEiwxEXTAsgtmvYXxmSPYT]tMFPt[PlXPydQyUuMwEXtivVIPhtX\\ToO@pK\\T>qhLv^dfqMpvB_cvwwoH_Uy[PggRyxGgx?X]KYYcYeoxOwVxmyxyWlaUhsHegdjGDN]r==TCWDOouXUX^[CLyH@stHyssUW;aS[[U\\=rHsxr_u=oB\\iVochsgwq;C[]wKQycqwOmTe]eAgGfCT^;g>cH^Eu]kSNMYa]fkmTAUdxAfc;RRAB<OEU;iTkG:;BNMY:;BJcX^cdX;B:krnAB:;FHMGwsTWKB:;FvaEWmiBivbiXikUt_SuQB:;D@meEyTWccwgENMyAUTL]HGeirEg;oT@;BZ[S_mi;eTUgxD_WyIGHqIIuePOeTuvcwgmAYbUW:;B<mSBCFueimcYJedXaGpIGn_H:;BKQbmu_:PcI>:>:;fL::JbJ:PSI<J:<?<NL=K_dxUXYLmwuxOe=S<MswxPi`UMhsCmSYMncHWjdwB<J:]JsXX?EqXUWvlwp\\NbLwSqrexPUtoThTYEl[Xu<AXf\\NEqN]=wWYKKynP<l[Dy?msyUknmyU]jFDstHkRAm?pnKXRMYV>QtYmVfdOR=o>QtYxqLLpyDMqPnbMkPQnRtXrHth@OqmWkhx=<J:]Styq_XKPiv``UhDO:<J:<j^PNaLNQENjDB::1:\"\{\}LSUlUk9PVEc2Jy0lKUJPVU5EU19YRzYjJCIiISEiIi0lKUJPVU5EU19ZR0YnLSUtQk9VTkRTX1dJRFRIRzYjJCIlXW5GKi0lLkJPVU5EU19IRUlHSFRHNiMkIiVnZkYqLSUpQ0hJTERSRU5HNiI= Figura 3 Gr\303\241fico interativo da elipse no teorema de Marden JSFH Esta mesma ferramenta pode ser iniciada a partir do Construtor Gr\303\241fico selecionando "Interactive Plot with 2 parameters" como o tipo do gr\303\241fico. JSFH

JSFH Por rota\303\247\303\243o e transla\303\247\303\243o, mas n\303\243o por escala, os tr\303\252s v\303\251rtices 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 de um tri\303\242ngulo podem ser movidos para os pontos 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 no plano. Estamos pr\303\263ximos de estabelecer que os focos de uma elipse que \303\251 tangente aos lados do tri\303\242ngulo no seu ponto m\303\251dio s\303\243o os zeros da derivada do polin\303\264mio de interpola\303\247\303\243o dos v\303\251rtices. JSFH N\303\263s come\303\247amos com a equa\303\247\303\243o quadr\303\241tica geral LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzZFLUkjbWlHRiQ2JVEocmVzdGFydEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIjpGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JJ21zcGFjZUdGJDYmLyUnaGVpZ2h0R1EmMC4wZXhGJy8lJndpZHRoR1EmMC4wZW1GJy8lJmRlcHRoR0ZULyUqbGluZWJyZWFrR1EobmV3bGluZUYnLUYsNiVRIndGJ0YvRjItRjY2LVEqJmNvbG9uZXE7RidGOUY7Rj5GQEZCRkRGRkZIRkpGTS1GLDYlUSJhRidGL0YyLUY2Ni1RIn5GJ0Y5RjtGPkZARkJGREZGRkgvRktGVy9GTkZXLUklbXN1cEdGJDYlLUYsNiVRInhGJ0YvRjItSSNtbkdGJDYkUSIyRidGOS8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRictRjY2LVEiK0YnRjlGO0Y+RkBGQkZERkZGSC9GS1EsMC4yMjIyMjIyZW1GJy9GTkZmcC1GLDYlUSJiRidGL0YyLUY2Ni1RMSZJbnZpc2libGVUaW1lcztGJ0Y5RjtGPkZARkJGREZGRkhGY29GZG9GaG9GW3EtRiw2JVEieUYnRi9GMkZicC1GLDYlUSJjRidGL0YyRltxLUZmbzYlRl5xRltwRl9wRmJwLUYsNiVRImRGJ0YvRjJGW3FGaG9GYnAtRiw2JVEiZUYnRi9GMkZbcUZecUZicC1GLDYlUSJmRidGL0YyRjVGT0Zgb0Znbi1GNjYtUSI9RidGOUY7Rj5GQEZCRkRGRkZIRkpGTS1GXHA2JEZhcEY5RmBv

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LywuKiZJImFHNiIiIiJJInhHRiYiIiNGJyooSSJiR0YmRidGKEYnSSJ5R0YmRidGJyomSSJjR0YmRidGLEYpRicqJkkiZEdGJkYnRihGJ0YnKiZJImVHRiZGJ0YsRidGJ0kiZkdGJkYnIiIh

e a derivada QyU+ST0jbXJvdyhtaSgieSIpLG1vKCImcHJpbWU7IikpRzYiLUktaW1wbGljaXRkaWZmR0YlNiVJIndHRiVJInlHRiVJInhHRiUhIiIvKiZJI2R5R0YlIiIiSSNkeEdGJUYsRiQ=

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LyomSSNkeUc2IiIiIkkjZHhHRiUhIiIsJComLCgqJkkiYUdGJUYmSSJ4R0YlRiYiIiMqJkkiYkdGJUYmSSJ5R0YlRiZGJkkiZEdGJUYmRiYsKComRjFGJkYuRiZGJiomSSJjR0YlRiZGMkYmRi9JImVHRiVGJkYoRig=

JSFH Os valores m\303\251dios dos lados do tri\303\242ngulo formado pelos v\303\251rtices 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 est\303\243o listados na Tabela 6. JSFH QyQtSSV3aXRoRzYiNiMmSShTdHVkZW50R0koX3N5c2xpYkdGJTYjSSxQcmVjYWxjdWx1c0dGJSEiIg== Qy0+JkkjbXVHNiI2I0kjYWJHRiYtSSlNaWRwb2ludEdGJjYkNyRJInJHRiYiIiE3JCwkRi0hIiJGLkYxPiZGJTYjSSNiY0dGJi1GKjYkRi83JEkidUdGJkkidkdGJkYxPiZGJTYjSSNhY0dGJi1GKjYkRixGOEYxLyZJIk1HRiZGJ0YkIiIiLyZGQ0Y0RjNGRC8mRkNGPUY8

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LyZJIk1HNiI2I0kjYWJHRiU3JCIiIUYp

LyZJIk1HNiI2I0kjYmNHRiU3JCwmSSJ1R0YlIyIiIiIiI0kickdGJSMhIiJGLSwkSSJ2R0YlRis=

LyZJIk1HNiI2I0kjYWNHRiU3JCwmSSJ1R0YlIyIiIiIiI0kickdGJUYrLCRJInZHRiVGKw==

JSFH Qy0+Jkkmc2lnbWFHNiI2I0kjYWJHRiYtSSZTbG9wZUdGJjYkNyRJInJHRiYiIiE3JCwkRi0hIiJGLkYxPiZGJTYjSSNiY0dGJi1GKjYkNyRJInVHRiZJInZHRiZGL0YxPiZGJTYjSSNhY0dGJi1GKjYkRjhGLEYxLyZJIm1HRiZGJ0YkIiIiLyZGQ0Y0RjNGRC8mRkNGPUY8

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LyZJIm1HNiI2I0kjYWJHRiUiIiE=

LyZJIm1HNiI2I0kjYmNHRiUqJkkidkdGJSIiIiwmSSJ1R0YlRipJInJHRiVGKiEiIg==

LyZJIm1HNiI2I0kjYWNHRiUqJkkidkdGJSIiIiwmSSJ1R0YlRipJInJHRiUhIiJGLg==

JSFH Tabela 6 Pontos m\303\251dios (coluna esquerda) e inclina\303\247\303\265es (coluna da direita) dos lados do tri\303\242ngulo cujos v\303\251rtices s\303\243o LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkobWZlbmNlZEdGJDYmLUYjNigtSSNtaUdGJDYlUSJBRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiLEYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GMTYlUSJCRidGNEY3RjotRjE2JVEiQ0YnRjRGN0Y+Rj4vJSVvcGVuR1EifGZyRicvJSZjbG9zZUdRInxockYnRj4= JSFH Os seis coeficientes em s\303\243o determinados pelas equa\303\247\303\265es Qy0+JkkicUc2IjYjIiIiLy1JJWV2YWxHJSpwcm90ZWN0ZWRHNiRJIndHRiYtSSdFcXVhdGVHRiY2JDckSSJ4R0YmSSJ5R0YmJkkjbXVHRiY2I0kjYWJHRiYiIiFGKD4mRiU2IyIiIy8tRis2JEYuLUYwNiRGMiZGNjYjSSNiY0dGJkY5Rig+JkYlNiMiIiQvLUYrNiRGLi1GMDYkRjImRjY2I0kjYWNHRiZGOUYoPiZGJTYjIiIlLy1GKzYkST0jbXJvdyhtaSgieSIpLG1vKCImcHJpbWU7IikpR0YmRi8mSSZzaWdtYUdGJkY3Rig+JkYlNiMiIiYvLUYrNiRGWUZBJkZlbkZERig+JkYlNiMiIicvLUYrNiRGWUZNJkZlbkZQ

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

L0kiZkc2IiIiIQ==

LywuKiZJImFHNiIiIiIsJkkidUdGJiNGJyIiI0kickdGJiMhIiJGK0YrRicqKEkiYkdGJkYnRihGJ0kidkdGJkYnRioqJkkiY0dGJkYnRjFGKyNGJyIiJSomSSJkR0YmRidGKEYnRicqJkkiZUdGJkYnRjFGJ0YqSSJmR0YmRiciIiE=

LywuKiZJImFHNiIiIiIsJkkidUdGJiNGJyIiI0kickdGJkYqRitGJyooSSJiR0YmRidGKEYnSSJ2R0YmRidGKiomSSJjR0YmRidGL0YrI0YnIiIlKiZJImRHRiZGJ0YoRidGJyomSSJlR0YmRidGL0YnRipJImZHRiZGJyIiIQ==

LywkKiZJImRHNiIiIiJJImVHRiYhIiJGKSIiIQ==

LywkKiYsKComSSJhRzYiIiIiLCZJInVHRigjRikiIiNJInJHRigjISIiRi1GKUYtKiZJImJHRihGKUkidkdGKEYpRixJImRHRihGKUYpLCgqJkYyRilGKkYpRikqJkkiY0dGKEYpRjNGKUYpSSJlR0YoRilGMEYwKiZGM0YpLCZGK0YpRi5GKUYw

LywkKiYsKComSSJhRzYiIiIiLCZJInVHRigjRikiIiNJInJHRihGLEYpRi0qJkkiYkdGKEYpSSJ2R0YoRilGLEkiZEdGKEYpRiksKComRjBGKUYqRilGKSomSSJjR0YoRilGMUYpRilJImVHRihGKSEiIkY4KiZGMUYpLCZGK0YpRi5GOEY4

JSFH cuja solu\303\247\303\243o \303\251 PkkiU0c2Ii1JJnNvbHZlRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiQ8Iy1JJHNlcUdGKDYkJkkicUdGJDYjSSJrR0YkL0YyOyIiIiIiJzwoSSJhR0YkSSJiR0YkSSJjR0YkSSJkR0YkSSJlR0YkSSJmR0Yk

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

PCgvSSJhRzYiLCQqKEkiYkdGJSIiIkkidkdGJUYpSSJ1R0YlISIiI0YsIiIjL0YoRigvSSJjR0YlLCQqKkYoRilGKkYsLCYqJEYrRi5GKSokSSJyR0YlRi4iIiRGKUYrRixGLS9JImRHRiUiIiEvSSJlR0YlKihGKEYpRjdGLkYrRiwvSSJmR0YlRjs=

levando \303\240 quadr\303\241tica JSFH Qyk+SSV0ZW1wRzYiLUklZXZhbEclKnByb3RlY3RlZEc2JEkid0dGJUkiU0dGJSEiIj5JJnRlbXAxR0YlLUkmY29lZmZHRig2JUYkSSJ4R0YlIiIjRiw+SSJXR0YlLUkoY29sbGVjdEc2JEYoSShfc3lzbGliR0YlNiUqJkkidkdGJUYzLUknZXhwYW5kR0YoNiMqJkYkIiIiRi5GLEZBNyRGMkkieUdGJUkpc2ltcGxpZnlHRiVGLC9GNSIiIQ==

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LywqKiZJInZHNiIiIiNJInhHRiZGJyIiIioqRiVGKUkidUdGJkYpSSJ5R0YmRilGKEYpISIjKiYsJiokRitGJ0YpKiRJInJHRiZGJyIiJEYpRixGJ0YpKihGJUYpRjJGJ0YsRilGLSIiIQ==

JSFH JSFH Usando , obt\303\251m-se as coordenadas do centro como Qy8+SSNjQUc2Ii1JKWNvZWZ0YXlsR0YlNiVJIldHRiUvNyRJInhHRiVJInlHRiU3JCIiIUYvNyQiIiNGLyEiIj5JI2NDR0YlLUYnNiVGKUYqNyRGL0YxRjI+SSNjQkdGJS1GJzYlRilGKjckIiIiRj1GMj5JI2NFR0YlLUYnNiVGKUYqNyRGL0Y9RjI+SSNjREdGJUYvRjI+SSV0ZW1wR0YlNyQqJiwmKiZJImNHRiVGPUkiZEdGJUY9RjEqJkkiYkdGJUY9SSJlR0YlRj1GMkY9LCYqJEZORjFGPSomSSJhR0YlRj1GS0Y9ISIlRjIqJiwmKiZGU0Y9Rk9GPUYxKiZGTkY9RkxGPUYyRj1GUEYyRjItSSlzaW1wbGlmeUc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYjLUklZXZhbEdGZm42JEZGNycvRlNGJC9GTkY5L0ZLRjQvRkxGRC9GT0Y/

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

NyQsJEkidUc2IiMiIiIiIiQsJEkidkdGJUYm

JSFH de acordo com a observa\303\247\303\243o anterior sobre o centro da elipse estar no centr\303\263ide do tri\303\242ngulo. Se transladarmos as coordenadas com 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 JSFH JSFH a quadr\303\241tica (4) torna-se QyU+SSNXVEc2Ii1JKGNvbGxlY3RHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiU2JS1JJWV2YWxHRik2JEkiV0dGJTckL0kieEdGJSwmSSJYR0YlIiIiSSJ1R0YlI0Y1IiIkL0kieUdGJSwmSSJZR0YlRjVJInZHRiVGNzckRjRGPEkpc2ltcGxpZnlHRighIiIvRiQiIiE=

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LywqKiZJInZHNiIiIiNJIlhHRiZGJyIiIioqRiVGKUkidUdGJkYpSSJZR0YmRilGKEYpISIjKiYsJiokRitGJ0YpKiRJInJHRiZGJyIiJEYpRixGJ0YpKiZGJUYnRjJGJyMhIiJGMyIiIQ==

JSFH o modelo para o qual \303\251 QyU+SSJaRzYiLCoqJkkiQUdGJSIiIkkiWEdGJSIiI0YpKihJIkJHRiVGKUYqRilJIllHRiVGKUYpKiZJIkNHRiVGKUYuRitGKUkiRkdGJUYpISIiL0YkIiIh

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LywqKiZJIkFHNiIiIiJJIlhHRiYiIiNGJyooSSJCR0YmRidGKEYnSSJZR0YmRidGJyomSSJDR0YmRidGLEYpRidJIkZHRiZGJyIiIQ==

JSFH JSFH Se as coordenadas s\303\243o rotacionadas por meio de 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 JSFH onde a quadr\303\241tica LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEkdGFuRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JKG1mZW5jZWRHRiQ2JC1GIzYmLUkjbW5HRiQ2JFEiMkYnRjItSSNtb0dGJDYtUSJ+RidGMi8lJmZlbmNlR0YxLyUqc2VwYXJhdG9yR0YxLyUpc3RyZXRjaHlHRjEvJSpzeW1tZXRyaWNHRjEvJShsYXJnZW9wR0YxLyUubW92YWJsZWxpbWl0c0dGMS8lJ2FjY2VudEdGMS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRlItRiw2JVEnJiM5NTI7RidGL0YyRjJGMi1GPzYtUSI9RidGMkZCRkRGRkZIRkpGTEZOL0ZRUSwwLjI3Nzc3NzhlbUYnL0ZURmZuLUkmbWZyYWNHRiQ2KC1GLDYlUSJCRicvRjBRJXRydWVGJy9GM1EnaXRhbGljRictRiM2Jy1GLDYlUSJBRidGXm9GYG8tRj82LVEoJm1pbnVzO0YnRjJGQkZERkZGSEZKRkxGTi9GUVEsMC4yMjIyMjIyZW1GJy9GVEZbcC1GLDYlUSJDRidGXm9GYG9GXm9GYG8vJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRmVwLyUpYmV2ZWxsZWRHRjFGMg==, assume a forma QyY+SSJURzYiLCQtSSdhcmN0YW5HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiU2JEkiQkdGJSwmSSJBR0YlIiIiSSJDR0YlISIiI0YwIiIjRjI+JkkiekdGJTYjRjAtSShjb2xsZWN0R0YpNiUtSSVldmFsR0YqNiRJIlpHRiU3JC9JIlhHRiUsJiomSShlcHNpbG9uR0YlRjAtSSRjb3NHRik2I0YkRjBGMComSSRldGFHRiVGMC1JJHNpbkdGKUZIRjBGMi9JIllHRiUsJiomRkVGMEZLRjBGMComRkpGMEZGRjBGMDckRkVGSkkoY29tYmluZUdGJUYw

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LCgqKCwuKiRJIkFHNiIiIiMiIiIqJkYmRilJIkNHRidGKSEiIyomRiZGKSwqKiRJIkJHRidGKEYpRiVGKUYqRiwqJEYrRihGKSNGKUYoRikqJkYrRilGLkYyRilGMUYpRi9GKUYpRi4jISIiRihJKGVwc2lsb25HRidGKEYyKigsLkYtRilGJUY1RipGKEYxRjVGM0YpRi9GNUYpRi5GNEkkZXRhR0YnRihGMkkiRkdGJ0Yp

JSFH Fazendo 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 igual a LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=, obtemos JSFH Qyc+SSRyaG9HNiItSSVzcXJ0RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlNiMsKiokSSJCR0YlIiIjIiIiKiRJIkFHRiVGL0YwKiZGMkYwSSJDR0YlRjAhIiMqJEY0Ri9GMCEiIj4mSSJ6R0YlNiNGLy1JKGNvbGxlY3RHRig2JS1JJWV2YWxHRik2JCwkJkY6NiNGMEYvNyQvRiRJIlJHRiUvKiRGJEY3KiRGR0Y3NyRJKGVwc2lsb25HRiVJJGV0YUdGJUkoY29tYmluZUdGKEY3L0Y5IiIh

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LywoKigsLiokSSJBRzYiIiIjIiIiKiZGJ0YqSSJDR0YoRiohIiMqJkYnRipJIlJHRihGKkYqKiZGLEYqRi9GKkYqKiRGLEYpRioqJEkiQkdGKEYpRipGKkYvISIiSShlcHNpbG9uR0YoRilGKiooLC5GLkYqRiZGNEYrRilGMUY0RjBGKkYyRjRGKkYvRjRJJGV0YUdGKEYpRipJIkZHRihGKSIiIQ==

JSFH Infelizmente, o Maple \303\251 incapaz de reconhecer que os coeficientes de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1cEdGJDYlLUkjbWlHRiQ2JVEnJiM5NDk7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GIzYlLUkjbW5HRiQ2JFEiMkYnRjUvRjNRJXRydWVGJy9GNlEnaXRhbGljRicvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnRjU= e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1cEdGJDYlLUkjbWlHRiQ2JVEnJiM5NTE7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GIzYlLUkjbW5HRiQ2JFEiMkYnRjUvRjNRJXRydWVGJy9GNlEnaXRhbGljRicvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnRjU= podem ser ainda mais simplificados, para que torne-se 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 ou 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 ou 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 JSFH Uma vez que LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIixGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRiw2JVEiQ0YnRi9GMkY5, e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= s\303\243o positivos, os coeficientes de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1cEdGJDYlLUkjbWlHRiQ2JVEnJiM5NTE7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GIzYlLUkjbW5HRiQ2JFEiMkYnRjUvRjNRJXRydWVGJy9GNlEnaXRhbGljRicvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnRjU= s\303\243o menores do que os coeficientes de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1cEdGJDYlLUkjbWlHRiQ2JVEnJiM5NDk7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GIzYlLUkjbW5HRiQ2JFEiMkYnRjUvRjNRJXRydWVGJy9GNlEnaXRhbGljRicvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnRjU=. Assim, a f\303\263rmula padr\303\243o para esta elipse \303\251 LywmKiZJKGVwc2lsb25HNiIiIiNJImJHRiYhIiMiIiIqJkkkZXRhR0YmRidJImFHRiZGKUYqRio=

LywmKiZJKGVwc2lsb25HNiIiIiNJImJHRiYhIiMiIiIqJkkkZXRhR0YmRidJImFHRiZGKUYqRio=

onde 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 and 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 JSFH Portanto, temos 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 JSFH 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 JSFH 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 Uma vez que 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, e desde que 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 de uma elipse, o denominador LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1cEdGJDYlLUkjbWlHRiQ2JVEiY0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiMkYnL0Y2USdub3JtYWxGJ0YyRjUvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnRj4= \303\251 positivo, para que 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 JSFH A fim de mostrar que os focos da elipse (4) s\303\243o os mesmos que 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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

NyQsJkkidUc2IiMiIiIiIiQqJCwqKiQsLiokRiQiIiVGJyomRiQiIiNJInZHRiVGMEYwKiZGJEYwSSJyR0YlRjAiIicqJEYxRi5GJyomRjFGMEYzRjAhIicqJEYzRi4iIiojRidGMEYwKiRGJEYwRjAqJEYxRjAhIiMqJEYzRjBGNEY6I0YnRjQsJkYxRiYqJCwqRitGMEY7Rj1GPEYwRj5GN0Y6Rj8=

JSFH e JkkiZkc2IjYjIiIj

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

NyQsJkkidUc2IiMiIiIiIiQqJCwqKiQsLiokRiQiIiVGJyomRiQiIiNJInZHRiVGMEYwKiZGJEYwSSJyR0YlRjAiIicqJEYxRi5GJyomRjFGMEYzRjAhIicqJEYzRi4iIiojRidGMEYwKiRGJEYwRjAqJEYxRjAhIiMqJEYzRjBGNEY6IyEiIkY0LCZGMUYmKiQsKkYrRjBGO0Y9RjxGMEY+RjdGOkY/

JSFH (ou seja, os zeros da derivada da interpola\303\247\303\243o polinomial c\303\272bica), rotacionamos e transladamos os pontos 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 de volta para o sistema de coordenadas xy onde o foco deve ser 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. A parte mais dif\303\255cil da rota\303\247\303\243o \303\251 expressar os senos e cossenos de 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 em termos de radicais. Para o seno podemos escrever PkkldGVtcEc2Ii1JKWFzc3VtaW5nR0koX3N5c2xpYkdGJDYkNyMtSSlzaW1wbGlmeUc2JCUqcHJvdGVjdGVkR0YnNiMtSSZldmFsY0dGLDYjLUkoY29tYmluZUdGLDYjLUkoY29udmVydEdGLTYkLUkkc2luR0YsNiMsJC1JJ2FyY3RhbkdGLDYkSSJWR0YkSSJVR0YkIyIiIiIiI0kkZXhwR0YsNyQtSSI+R0YtNiRGQCIiITJGP0ZJ

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LCQqKCIiIyMiIiJGJCwmKiRJIlVHNiJGJEYmKiRJIlZHRipGJEYmIyEiIiIiJSwmKiRGJ0YlRiZGKUYuRiUjRi5GJA==

JSFH e fazer as substitui\303\247\303\265es Pkkqc2luZWhhbGZURzYiLUklZXZhbEclKnByb3RlY3RlZEc2JEkldGVtcEdGJDckL0kiVUdGJCwoKiRJInZHRiQiIiMiIiIqJEkidUdGJEYwISIiKiRJInJHRiRGMCEiJC9JIlZHRiQsJComRi9GMUYzRjEhIiM=

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LCQqKCIiIyMiIiJGJCwmKiQsKCokSSJ2RzYiRiRGJiokSSJ1R0YsRiQhIiIqJEkickdGLEYkISIkRiRGJiomRi5GJEYrRiQiIiUjRi9GNCwqKiRGJ0YlRiZGKkYvRi1GJkYwIiIkRiUjRi9GJA==

JSFH Expressando LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiY0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= em termos de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEidUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIixGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRiw2JVEidkYnRi9GMkY5, e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEickYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=, n\303\263s temos PkknbGFtYmRhRzYiLUkpYXNzdW1pbmdHSShfc3lzbGliR0YkNiQ3Iy1JKXNpbXBsaWZ5RzYkJSpwcm90ZWN0ZWRHRic2Iy1JJWV2YWxHRi02JCwkLUklc3FydEdGLDYjLCQqKC1GNDYjLCYqJEkiQkdGJCIiIyIiIiokLCZJIkFHRiRGPkkiQ0dGJCEiIkY9Rj5GPkkiRkdGJEY+LCYqJkZBRj5GQkY+IiIlRjtGQ0ZDRkNGPTcmL0ZBKiRJInZHRiRGPS9GPCwkKiZGS0Y+SSJ1R0YkRj4hIiMvRkIsJiokRk9GPUY+KiRJInJHRiRGPSIiJC9GRCwkKiZGS0Y9RlVGPSNGQ0ZWNyMtSSI+R0YtNiRGVSIiIQ==

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LCQqJCwuKiRJInVHNiIiIiUiIiIqJkYmIiIjSSJ2R0YnRitGKyomRiZGK0kickdGJ0YrIiInKiRGLEYoRikqJkYsRitGLkYrISInKiRGLkYoIiIqI0YpRigjRikiIiQ=

JSFH A rota\303\247\303\243o e transla\303\247\303\243o da primeira coordenada do primeiro foco \303\251, ent\303\243o, PkklbmV3Y0c2Ii1JKWFzc3VtaW5nR0koX3N5c2xpYkdGJDYkNyMtSSlzaW1wbGlmeUc2JCUqcHJvdGVjdGVkR0YnNiMsJiomSSpzaW5laGFsZlRHRiQiIiJJJ2xhbWJkYUdGJEYyISIiSSJ1R0YkI0YyIiIkNyMtSSI+R0YtNiRJInJHRiQiIiE=

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LCYqJiIiIyMiIiJGJCwqKiQsLiokSSJ1RzYiIiIlRiYqJkYrRiRJInZHRixGJEYkKiZGK0YkSSJyR0YsRiQiIicqJEYvRi1GJiomRi9GJEYxRiQhIicqJEYxRi0iIipGJUYmKiRGL0YkISIiKiRGK0YkRiYqJEYxRiQiIiRGJSNGJkYyRisjRiZGPA==

JSFH A equival\303\252ncia para a primeira coordenada LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiMUYnL0Y2USdub3JtYWxGJ0YyRjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0Y+ \303\251 demonstrada pelo desaparecimento da diferen\303\247a: JSFH LUkpc2ltcGxpZnlHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywmSSVuZXdjR0YnIiIiJiZJImZHRic2I0YrRi8hIiI=

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

IiIh

JSFH Deixamos tr\303\252s c\303\241lculos semelhantes para o leitor.

JSFH As c\303\251lulas coloridas em amarelo cont\303\251m entradas no Maple ocultas. Estas entradas podem ser vistas atrav\303\251s da verifica\303\247\303\243o da caixa "Show input" perto da parte inferior da caixa de di\303\241logo nas propriedades da tabela, acessado atrav\303\251s do menu Tabela, ou Menu de Contexto. Figura 1 e Tabela 6 tamb\303\251m cont\303\251m entradas escondidas do Maple, mas n\303\243o s\303\243o coloridos.

JSFH [1] Dan Kalman, "An Elementary Proof of Marden's Theorem," American Mathematical Monthly, Volume 115, Number 4, April 2008, pp 330-338. JSFH

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= yIpyIr<K_Tn^T^;N:L`^C:yIu@K\\PqkhpvF:CZ:N;xYqo[;_fiOf_CS;P:FZyYUCND<KB`KC`kMXkEXLSTlITLStLMTLMTLQtmTPmTP]x^b;Gb;GBLN\\LN\\::::FZOF]S>^V>^`>]Rn^pn^Zn^p^bpV_en`>_b>OboNb>_b>_B:::::ry;pB\\ZKa:AR:?K;@k:HjB@jyMfOL;Hj:@J:B::FZ<^Z?VZ@FZ;FZ;J:B::F:AB;[j:LZ>VZ?nZ=nZ@NZ<V:@J:@K;HjJ@MCLjZ@o<@prDlCLk:AsJAuZEmbENc<yjEPsHlD@Y;EsSLM=HNLDTSEv;QmB@J:DJ;Dj:LJ;Dj;V:<J:FZKNZLF^=F`;Gd\\N`[Gh;PbKPdMFnk`ZyQUSr:=J;@k;@K:x]pIgd?[PPcgplcGba?d@?nm`yniq=WoBGtNI\\b`_iAdY@oDg_[@o]>dSoyuwnainPvqbX^JKwlMtETgeK;Qm<xsmITdil^pp@HNGQm<xSoAKoEk?]Po\\JdUky\\t]\\T_p<aeK=WmIexCFicibdm=MMolKeYQNYNNo`bOwVFtbXhSoq[p]_@_SinfXh@GpGqftajHhvon`cWwVFtfXhSoq_x_LOmU``oqkbots^oIQdIPdT<jYEoAkTPMA]@^dI`dTpnGic]Omonkew_Oi^dYlMofhHpGQ]Ai`QPwLhxCGomxdRovGXfTXsoA_oIcd`wNqtsVnRovlhyDgaDOgf_tP=NdwNdd_gN=bLAEVMTjecGM]MatPffU@oLq]aW\\NpbeOawirpXsPWpIFvCPeAI[Pxfrvj^`tK>oiV_aaeyNxEouLgxqw[vijeoylvmnyjd`tK>OUSy?XvmiyObFOyp=F[CE=WFJYV\\SyMkIsyGwIvdgXHA_jpxWYbFAk>Nw]V`LxwdylwNeSYofXh@kldYLqUcd`OqtsVNDuXIoKQWuhtNIue:OxHcg]UYGUSeSwVG\\^OynPi^`tppprXx@?qmIe=vhDXfqOkdopPytX>gPmIUoAUOGUSeUwVHDNdwJEQWea=fYucLov`e;rect]ttLQuttRnXWIhpMPwLexcEOgeykqVGHx`MPwLUwLUdUUY]usU>tkPyMedCgXHjxDoXBUghom;pUcb`qnttbP=NmUh@:beGWmutRoVGV_OY^Oq^`hsW;ZcFom<VSKTwMTdHOfTx@cleYLoIccXpMGeaeKfFdQL;:LSdaG:cfXC?:LtXs`e;:dC:JDmpdUGNP_L_@oSYOf:\\ntobGiEP=v^dQlQpf`HpGQ=eS_Oy^eYDGTmU<v?ASoEs@eSGW>xUcB_SEog@fYDobHuc\\_Gl_G_t_nNudS?P`N<M_@;C?qtOkdsbl`n@iVMQtTQQ<PWGtTdut[PLMLk_PlI]uOTnfllpEV[`THMkZlvMUPv<qZ`v=QUcDr>\\M<XnIMLf=U\\XMl=Rf@tHIM;EM\\TTnIJ?QKTYl[LsfmJOEkfTTfUt:EKBaLSQrCQK\\evfPjb`kg]kI@k;pu]Lwe=SBYYPiqPYM^tV_XY_`wGTXp^gxWg^XvKv\\fnbMW`JwqTIl_vhpHn?^rZIqppcL_hSQ^Bh]aVbp>_GIZDxchic`nvbpcrWnKObl^bHFsL>dBiaBHjDycGa[Fht;FlBo]bWZDOZ@vcnFaB>c?>b^qvX`nYPjU^\\N_m^`fA`h_OmcFq=_lNXv^Pfk?dDg\\DQgpng]xd<xoN>yXHZN_uiy^y^Z;_jrFvChd?AtB@fRo_RHvxGeVhqPh`kN`_^vmO_@fr:iuMFlDn^?Qu[vjMg`Fisl_lQY]hVt:prA?^o@ceifTAhR>s^yahO[oNbQg]ZVqwQtaYyNHgb@uZYf\\^iLOyqg_T@_GHb<Xxpifmwo]pokFdagcx_dRG_tP\\JX[GvZ_n[M`nOn[L_aL^tm?cZHv<H_Ch^b`lVNZKO[cHmZ>s_Hm;_r\\@mK@b_^_<@aZf`cNg?ab`_mm?boQf_@obH_bnj^OsH_dD?ab>slFdNadDPjdh`NNa?o^OwcLg`NVp<GnCp]B^tLWb\\h^b@xIGdJowF?_CPwGOsI`ZSAboY^Q_`LpfKg[KIo?O[@`^RHl\\AnR`bBWc<PiDXjc`fZHlbNhL`g\\xjb^hm>nZ?\\;V`^nqcOnMnl?Q]Lxsw`@Csb]TlmrbCs:cV@cbR]d_KTZ_hFMTascf[D<_cJWR@;CASVnKWvMt^[EbsRbMxJ=CoGBc?BNsHn=fLkHj?IJwUTmEvEC[?vsmwcSh[mB]gfRQi]]C_CSs]SEiGsaV_YxR;eiGrCYy]ChECW?WHXofUms\\AsB=h=KXlmJIDTb`XltRlQU;LNJEkSDnFho;LsWLLAMy@dVghSLtk^XMT<olqMxLsidSj@JieRbewDitidWSUQQQuOiYePLVenfllwEVbUS_PrvmLTEt[Ls_XL?LnSLtK`r\\xKnlKvITNTyDTlvdmphRH@SCup:ljlMW>mN=Tnb@JJTT;lnPAtJLsFQjgLnfPLK<RCLvfLptpJ]auv@qwIpIeqYmuY]vPYVh=q?`juhxAmxlmSwQLhPLlLrK`rLDrtMycpkPENV=YFtslLPtplOISV=SZ]qkxw\\iPqXlZYpSilHeooer@QsPuSKauDDlBmjVeTN@j^DSN\\RHEOOLNS<NOLr^mK_TSnTpZDkFTLc@j=DSKYlRmJLmVK]WO]rSItLLL:QoBLPILVlURkQO\\ho>avFLxLas_hR<<OfAXGIKpaJx@SZTNLLtRPVS`odlMCAL[gcVQpDHowFnKPr?wbKIePPnO_wQ@cK`dGWpBa_Ia]o`]jivwqqgXZVGZQh`LouWxbBFlVIdZvf]ff>HkaO^rIZCAhdx`hwvwY^[n[H^d=QqrIolNwhhgHqsY@eDQdXftPgd=qgCVhcv]tWtlPqdwlQH_DWurnrRvpy?ZVX_^hyoAmpqvqhaoQrA_dd`hcAbrWniF]HiZfob<Gr@xZBhdqVeW^p\\f^]vmTYfYHrjWuWw^LavJPemF^YHpsOxEA_Wxoiwhror`N_cPnNGe[fa[_tlp[uXvkF`jWvk^e\\ViL>a>^rk_wBWvTPt;xs<dH]V=?FM=XxOGc]UDCyH[h;KCH?i\\AD=_T:cHckCBCEtACE[iMst^Ar?]DH?GnmBB;U<Sd]sR^[V:OR:KdscFVIh^]E@Kg^IEGWXLGsKER@uC;CIb?eKOUoaV?atBKFE;Y[]fguhmmX>_SseH\\ovp]XaAWUucOmH=mF<SU?UE?mVLcftGVh]SJMXAQYi_icMF@UXjur\\CVSMRZKs?MVlgdR?EXMnsDO?LQeULfHtsPPThn_Is>YqJHmBPXDDvKHKXPsJYUcuk_`LO`vDHmt@MZexu]laHqU]RsLpG@UgxSmXm]qyJEKCEujlOoXkE<Wv<rVaqwuQsxiDgbIAkSWsRVxjvvShrEvnWxpay_nAoUpxZYaY`xeXdga_gykuQb[^he^lffjfHfLPwRI_gBcshnkBRkVkCE<CUS?v\\wCDmBx;c=KulCrS_VCIFY[Vl;I>?B\\[ra_M?QncupnLX==o\\lJLaxS<t]LkSTPI]Nqdp<dsfTlrpNDENFHTLlqCAMbTlLpkfATrqNVET=aoGeUXaUVWcGWhxHl^_[rovP>xDanR@q`WdfGoR`mmW[lobp>bUw[pXcIiohvlrHgTf^NpqYqvwYwipfqv\\fqsMfsfNpNvv@^_MP`mQq\\@snGuFNn\\@u\\om_?`WvZZAoFGsF^d:@hP`gKFdC_mcHZ@@_PpcO^dl_b;Gsj>]\\GjDP_xYukPgQqxfhobhfgxeTIpevZfflEnrD^yl`dh`Zb`td>\\SNk:w`BHoFGaF_vCoxb>oH`e<VljNhYPg\\>`@WcDwfL@f]N`baj<_cdafZNn\\^s:`\\B@cHP[\\`_<`\\ShdYie^atB_srQbkx\\nVl=y]wwiWHgioprfZXG`mN^k^sPH[gn_ExbU@qPQh:htgAvwXlkyrnYxAOsywg;gc=ggNWgY^lvgdeW[OPgcAfdpfvphnysl`_PPg?_[PPsfVl`ns<h]NGbJ`dBaf:hDCE\\_DDGUJ_j@Pv^Ds`MO\\LrS`lSLLaQoBLpAQLK<KheNNUX`mKJqRf`LFduFHUgLNs\\Kl<SmtQ?XnM@NHxnVQKI\\MLYnTTL^mS_HNYDWOmrRaMNIuuatBHVk=R<HNyQV:DNYdnMlsXeRZTP_Pm=<klYnwlmk<O_IlbxXjeUelm`PVeHUwYs^\\y^qu_yvhQMApwbpvOiw;lpkYuAMpMMY?tWkuO\\TNgISLYUAIN:MxWdNAQV<mThiNJ`nuuLQhN_aqEMsEmmMmok\\ksuLFIySLsyo[L_mpFxZ?]j?k]YymOcsxuy>\\=`r`?aahp^xum^gwim;`g>Q[e`lshZbXwBXkCY^c^m]@]_oQIR:KVQOu]wVCARxwuTCfMkf:qUowW`?bDev[ac\\IyowrSmhnmikuSo=GEyrqwh?eV>SvrKwxgBQYD[wVpQGogvpmGsidUwfYys_WruSFUGyWeYsAgrcrM[DdwuJSYB?UTgsLKdO=EfqVfwTh_hCOgQStYQI_Uu>UbHWidyI:gimyCcGYeeD<[VL=i^aiw?DW]BEEg>gwTcwMYue[gckDoEHXgVfUY`GhSwEpmwy;RVOwIifrcrMXtSDk=lMeMMJlPI=SPuxjqoA@ju=pTutCLskmnq`WFTvuXxbytdtqr<YkejRMqJXu?qVr`XUqJMivaUsLluKPuk\\shxuFEulhvriLDYNHEUwIVUaoa]kkUynpsxIn@xMBHTetxOqtD\\rBQVcpKMlQ[qxTaXsetbEL]lKCYPGDXMlvkDUyao\\xLquPQarn@mutJq]uHPyiHTkQKAdtydthARehtnhMFV_m?]]qdaqkWGqVYvvf`HPy=`j;xkigZXA`volOWy=_cCGa[GxTgeFVwIXkbFoV`b>gfIXoWGi_Y`PHasijKypJnks`fdxcw_dIOuyesQrHOWwmbuSWFMfTAiwIhtOwnagfSxPErDsbYwYMawmsFHEXgugqahSuhbyUdSCG_y<iSc;hLsHOiyH=sgYwOsb:YFM=F_QfVodlAG<Yw>SSWshwWdq?e@ieuMidoDJ_BA=HQuWYysb?qodMT`Rr<VNtjAyLdUKk<QuUSmimYdWEtRwIBtpj`OLAMLLp_YmrHwmXu=aSHaMuutXUL[Epj`vo\\L?mrRAyNtrvtOfXPmqmdXYsUlvOwUVcnVc;?sryjOybmwawQluOdxpZc@a[QvDHwv^yy^]rVvkqoYYcchgK_rpa_Hhn\\vgIq^TWqcFk:As^ObBiurypafqmwr@QdeIuHAeqNygGhhxol^s>VbOhKOioWISCDI[Sr[BgoS[ogG?WfmI\\QrFQeHQyx?Y<iUm]ckeepwcqMfa]UHQE_sYRoTGuDE]EM]XT=h\\iXAGTbGVZwYcQbHeFXkuFsCCeFpydNUV^oGNHs=YjZinpHUSmw^@LnLv>MPPMW[uLD`RFeTEEy]ekFuTiTQsIpK<Ka`J?tTBEx>]qPUyP]Rj=JjYUHuvdEkmYWAeMhEVQEvNYouiLhaONXVAPvJXl^Iqt<MTTX;YX<LukuR^XJ;ArSUpBYv:DSwhNk@r;]rKEm[lJl\\s]ML<InEpNs=X@mV@qkC=nAMmW<PJmpfAd[OkwSEabCADbCRn]TFsRNov^aUNOS;;vJos^]UD_btCBmGFWcigMU?[rFEc`afGKum<T`\\vmLvJisXUmL<Nu@LVUTZDX=MqpPsXyt\\tRSTSO<ULXkFPrPuuQQoaLVkDuext>\\urdVOtOAUk@pvRLum`yWYWUPOWpm`amclLMmkuPRw\\vRtOxDTMqSKupPpV@Nd_ojBPZ@`gNAk^IlDNo>Fanw`HNcgWj?F\\XFe\\Nns^kJau<>i:FrGFkvGtKwfhycsP^of\\bnjvi\\OgubPejHs_gwkY_LG]fNsVPpOg_PosDgo[`tR_dRhrBwJ?sReBDIVkED_ysDMsF=CiOCQ]RCgBUar:EbCMt`oH]?wmoFYcD^KhBABbMG;mVn]rDYrdqdd=HPOxB?iO]YRMfQWttsSpOxSMVCgetQv`giVSia[bQiVbaXs[HUmCmsi;QRmYsSEdYUTFIVtKv<IGU]iQSYWIhGEYV_Uh;vc;sseb>sge_GZsB>]eNGE<YX?mTKmFBqR?SCn?dbUb\\YRCsc^]RWCt@OV@ch]MsfOc]EeG?iawFTkcb;gm?fhCe>EeN[fSUhCeeFAf[Orbmvj;r^OUWucDmSe?CCgW<aSRCXdaw;MT\\;uHeX>Si<?cEYRmSDguEd]Sr[YO[tWxST\\rrama=RcpqMLuL=k]mjdEov=TYHNShSmXJU]N>qJ=Gh?OaE`]O^ihxaHaop_vxVg@@vnfxx?nxAtvhykIxqpgc`vpfkvXvHickidhq]Cv`PvkwPeYpkLngZ^cuw\\JVbQn[HV_HXdlqrwg]]_r<qtTiqkF\\DVesIw:@oa__OIdPqpopjf@cSql<x\\wNdSxta_uPWymNv[PakyoNxy:>[T_[@@kxYfa@unhoJXuNW_\\qsxomoim`Oyw`o>@bOYgrf]cyd`AeoWuqa]USy[GQYIQQUqaH@SwgyvM[R]wf<qh]wdncwC;ypyU__dvUdg@X;qUdmMD@KfYkMITG\\Svxity^]a_W?m`vsd_xNnd^odXVtno`yAZax`?Ig=ooQAdpgthBRirbScFmw_srH]E]?U?oGqEtV[brWXYQWcwU=yVxgTQiWPqwgsTf_sDYtWCeDAglyU>AR;WevIxAYEEeTRgvQUYryVfYrRUwDgiZ?YA]Tt=gsQITGBQ_wxQtnIfocrW_Xnid^_C;SSbCubSfJcht[TCSw]SRCsXdUugwdMSB<EYCyX@ufIwbQsdbASHyI:EwoAw_yfI=tPMyViV`?CXEvnqI]yCMuslgwliEQAYHKH<iWCSvgYw_GFvyqHmvjYQ`tYLuOsMUu@QntjdISV]SUExk\\rLpppIV>PRIyvYHvQyY:xMeyQqpOfPUjTQQik?lUO]jxuNCdxg]ra@VCLXChXIUwYEm>YNQHlXePvlrPdVKDQIevdTtYEM]uxgPy[]nBhJ=TK_aSo]K^HQg<ooYj@doxdvmMR`qxAaRWhyklktdVko_kp^:h]_hhbih@A`mnlDwkPwuQWq]NsF>ZqaleQqjWuvNhY>hfQ___][_kjIfvvvX`aPXydX]^hbkOZw>qO@cUGf[AxMOnbitaFfZ>iO^io?aIVs?FqFPvew[H>iIae?yvuW_Wia;Ao@WrZqk=ojevqA?]Box]HoiGwVydRfdRpr?o_Y`hc^nDifVHoO`s]W\\`ytTFkHYf?A_FOwrpmOYnsXoOOb=?a]_w\\YpdGxTwp:WrO^m`Xpyxfh_qpWwPiiOOqcN\\VHoK@fTQnmxfgVe<XiNowCPn`?^qp__qrv`gUOs\\F`EA_xqsr^cHAi]yloAgoY[o>isG`qijYpdTyhAN[xQym@^fnkZG`OopUIsgws>pjsFk_fgFpbm^si>]aW`V`eCwihGpYVufxZJvoyohyVrhYcuIOChPSCXEfm[elssypXcIM[UPKamximbAO<=JCIuKTTKiQ?XxI\\KtXuEEVOmr^@YB\\oNlrspJuxN]]odpJeplIMujxxfhkZdThUKa=SR\\mDmTYEWFAQ<EjTDpC<qRdJMLnUQLRHjkXRkpRK@jJLWYUWkIOAdW[tN:lKdHNBAQh]R^UpX\\XFulvuR^vZIHrIobwG\\BXvHP_:W`VPs^nwN^jROvFXnFHpF?`?Q`Voh`b;OeBSSL_D:CrvMhGARGgFbkF_qI^yfXUfBWH]cf^=SJsRn_V^GdaOE<]SD;I?KvC;r^<t`LVLyN:LT\\MsfAn@`LAAN^DX:AThDtaerqDRp\\SHPOo@kRLW>XX;=VHMQ^LVrmlXIKPpOxMMhhQfttxIo`AMHAQqPKfdPFmss`rt`XqiPKlLAEOApmOivQPNcmxsUQW]QZ]SyeJuYVEPqaMM\\TMndL]PlbmWViMKHJLHnN=J;=t>mKchjJqJGAr]uJ?ltB<VjEt:\\m<Iw_lKdhOhMKo@KZEP>QV_USHUJLmjdXKU\\YEhJa`KPpWRmPeMSSDOdtV_PuJaoVtlCxJ;iR?DYApK:Tkt<\\=VqbhnVImH>mGG\\MNjS>cAhrSbBsHN_SMaVS]b?MD_mXC]tNuuIWS\\QXfuwtQxeAdoEgc;vIcdZaylexnyr@muxsshUuDaiUCVHKxEAUT;EiywKGVesxHsByircHPWaQ=eYxenWAq^LsgUj^XS=<SV<tNEmF@KD`S^LRUdJ>EMl<Qc@JKPkB@J@dxl<LRLOLiO;=NS\\S>INWdt;=lDUM^NoLg[?q^MG^kAc@HrKfsCXbpN_fOwa^]PImmOt_Q\\PPl;ahPH[RFjC`dmG`?Qs@Oc^OwkaZU@bgad?GmDAk?>rBI_K`o<HknVbFflcWZI@fsanRIa:QhLG\\pw^N^]k^sdHnUX\\Yh^HAwUV^@XfJNqBpqcnm?ImB@mcPgr>d>@sIv]a?v[H]<NykWZA@]pI\\oiei@oQYvB@r`i\\UO_GpybVlSvkFY`pyoNVvixrivou`qGWxI`l_`g@_auGpDoZcim<wZIo_evjWxqaTBKesauNwYrcHcoBF]rwQS>IFuswiQdPcExIIrsRsofeUu?uSVwr>=vC_VrMyekgtsXPSI@eFoWHFwROASqeIPQg`ExnKekmcvGvqYUOir=CSAsDQww<atdMTdgIZAWfoXXwUDuUkidtqtXISI;d^YRsCYiuWOYVp?YuMfmQS?ubechu_cOIXLGyOwU`CtduuLIthEcSWePKF\\KvNAWROr\\]iKYISYcUsUosxh[hmctTOh]YxRCiReDmcHlsE>SHbEIHMV=EsSmxnACE=dPoUQIb^USFyUg_BVQSeqt=Uck;UegCR[v\\?Go_skUTTOePeSjAfVaDHGGmmb<GgUIYRIILKHROimyXUCyKOTgPV;tlc`vbtKDxTfUnaUk\\POyMwvpTCmkJAsF]RkxY:dPXPWoUQ[=KbQOUInJ<k^IUMEJhlkExmpQpsio@PVMPotxRmxMuIu`YQ=AVJ=prdoLdJGYvSEMIusoTsLqQRIo`mZLqleAghv[>q_N^xwQ\\Lf^d?[sXbH>aOPd[`s=AefadhHwkIlrgl]Hk:Wk`Gkj>sxqtsGoAgnRxl_Vgy^_JV^IiZS>om?k\\N^enkeagh>]`i\\\\HibFw_Nd[wmq@uT`vhqoBFhrfZMIZPH_cWv_FfVfujxkOf_\\V^?ImIWqXam\\weOFe]^_Aa^@?]snxa>\\@FecX`]irNH\\A>^L>tC_amhhwN^f^m;`_]X`Bvl;>q`pZZHwJHZ`adA@kp?_GQ^:a[JVZ\\ad=@hFgZDfbrq^<nlPXbtVsNGe^NsfOZ>O^]@jCU?gsJoClOFG]iDkDVMTaCbLcsvadS=d=;wZ[I<EeGCU`cX>scZcSdagW=Ga?wbsH`MBZkF<KGeWxdGBFiFXotb]WNOY^oUZCyOStCEY<iV\\AUEWvZIe]eea;sLsXfehyYVIqCdgIiwu<]HawdFEI[gHNmHf?ebQXi=i\\?IqiX]MyKccFifRSdZSRQ?VSKD[acB;gRYdXwSn?V^QH;CVQeR>iBJAXC=Sl;rRsHdagJ]h[OL?N`L_dDYvkNkfydcfZO>sFPd;^cHH_l>j^?jL?[^_bJOsFokbN^<G]C?lBXk[^lS`[=X\\hplGXfnhl@pptyy:nyyVxwo\\\\nxogy[gvfYyoNiBfiCaa\\piE@tSQk;yYYwy;riYCsoY[yGIih=yxfYwQeHlCF\\aDLIFQoFcqD;qf\\qFBSV?sRp_C?mHCMc?Mt`ecGAdD?Sl_c`SDdQfF=TM_fDOGCCcJqvBOtBqVCIg`KiJST\\WTY=VBgRAQG[Eyh_uTWgCWBj_rkuWPSFC?C;QXl]gUtOFHQN@m]=uNDs[MJ<yoDLnAHRg=TJlNHMXWumKdSlDPZxV?etmyMAHjL@kgTuLMW:@MXDkRLLWeTmu^q?>QR_;sj=ruKtKeROsBoCHJYiKmdCABdKW^MgOqwRmrrsRCUXQSI<]RWmfO=dpyH==bYcY[qtZ;XEWGkKrvsDwIXpUWcYfAyVUIfk[EsebpgCNIWBOvhoV@eF\\KvLcW@_wLKTHMgfKBV=XT[rB;Vl[C?mV@?GbCHbWV:SdwCs:?iZSc[eeBaT:cF>Se>]brcDjcE>OFsMH^khESfloSQeR>wBDIeNkccABB=FAmSD_cRMcwKG\\GclKTSCTPEt_CT`eRm_VSgsLOdn;GqaXS[C>;hSKwZ_R]Uc]OUSUSEovBmvEgfLoDV_EcKDrgf^eT>wEL]x[ECIGV<]SC[Bf;IZsrv_dn?BUYDR]D>;uFCxbMTHCyc;VLLoshVLLr^hLQ=sShnRqlL<J:HVT\\S^EunYtIaU^@xEMKTIN^PjsMpx`wN]RVlP;ISUdNgHOFIr]LV@=vB`vtHJGIN@DkbAJB`JmisEDoBlPdiUDDUHMvgDJImLLIl`mMDalBtKnlX`XjaPL?HnaLmwMSTIYhtXS=o@lO`LTsxkAEp><mFLtrdNGmP<ymPAlNHs[ALfYTEAj^\\j\\PLUXNsDRW`QLMTaeSO<jsxNRaL:\\YDYQN@lL=SaUtKPvFLP;Ml:dsFLW@qOYLXd<nddMBeqLlxYPKtDPOQY=LysUYxTwRuskTyCEXi`qf\\w_tNmIUxANepOUysqYWxAwvyTh\\yEuSXpul@Xe\\kOYq<qOvtO\\]K<`s``UJ=T=ANK@M?DNNTQN\\tSiQc]MWASZUyLPvDpKNDo^AMCEt\\ALitR_PsJPSfMX;iNHYs\\DJJUX[\\JcHNJhRJ`TS<k\\lJGeP>DuCLPSLj^EmCAlDUnEpY:ApftyqDT[uo?yt\\eX<au_TxEpSituYmTXpuIUpYqYxxY:lX^Hq:ay<]xLessqMApNWIJF=SitsZ@qpiYWPyxmObeV^Pp^AW;TkYXoiaO`PvTpKV`mO`pDujJIW]pxLIKMIp=<Xe<YNysCaK\\XWAhoxtSkUjCHytMvR=SpmxY<xLMwutYB]JZmmlYSj`OKpvamNIasltSHEx]DpEQoCux<XrpMsj@LheuoaqslvVpxbXVCpu@tRs]w?YlrlRAElYhRQhOq@tpXmvhKPAqcitEEXEHx>qr[<k[PRmeYZQWWIWHLP\\XnTmnm`PeeO_Qm?QRYytVYuq\\M?MXk\\JQhMEuRdasc`J^Dsl@KKxNo`voAvM]oV`xOhomxiXvo^ykCIctQfkpxPxaKguWqcZQrMN^rFfAh\\]`t_P_bN`h`bJ>ufpkixy:>_qibegxI@ylywYf`c@krY`MvxkGwuGkUadfQq^Gwv>i@fd[IqVihE^[bnaVoZ^nxp?ofQf_GpvxbqNyc^hcvkdYbCPtO?mBXuiNf`fx?PqpvhOAfNhomvj`iZyAZtwjKwut?f[^[`oiE>c?xvtVm=yhdHerwckXfY^llIqvWf?HtkhuHQ^m?q@ybWV_HxuwgfPGyu^mkggVwkZqpCQ\\tnjA?\\QgmdYnXgv]xxnvboXgSVuCxfbvtRhhdYeE@gu`c^>bZGeVWni?qFHjtHrb>m^IajAvbhhkpnjy[by]OGonPuHynma_m^Z?wm<Xp@A`AOuSWqgiuXxhMXZZPZ=vxe`pgo_dpiefh;qkZXnxHwxPnT?vT_iYO^mPwVyel@pOWfcYvM^xQ_svWd>QxUi[L`sdyhSGdC`jBxhTOqUNZlPiIavyAZqFtaw]gvv\\ie_?ofgrtpklh`tvolxuDOdliwhvy:Fggqdax]wAZyWjdAoYWpdW_x`]]Wvvqd\\ynIYqm^iFWihngFHvoGhF`k>WsYNiH`xhW_L^pF?[<FtAp\\OWoVYmfAnEowF@janm[>go?d?N`hWf`ynC@kYG`lFoopkeYh=^ff?fEF`Iav_`tiQpE@Zh`b>gjYYn;`vCwy:veKadeyahybsqic`]_IcyVcWOuMAqL^jfApDO\\Hfu]q[DvnJ_uUictHf\\VZ<vofqhMAoCns=A_DI\\bomEv_fxiypyJonv^vs`e\\oug?^F>xR^o]?qrpwvimaockx]\\_ukVsrx_xvixyjyEfSSrQixQeIQcwuGoieqsVxeu]]BxKsk=UhcFKSGhGxKdLIyY:@vXUlvdp>UYjTuUXYadslMpFXvTlQ]PMousmhLtIQTunXauv\\qkmKl`m<isSusoUQlHLqpsJ@yy=j<DqOQXVewfLPfUKBIvVYPtqXXyxSPKfiPJHj=QKkdLMDWmXXG`PqQnDqpt`kT@s;@OHPWaxsYMslQXhoyMYuCyedI^pXxhy]?WlsHubOnw`rlF`TVysIoG`cmOws`eIo]JhqthlK`uO?[Bqrm^_AgpAOiq>`Qah`W^:>hIx]LhoP?whqgUQwuYn`v^XX_EGo@XuIIumycM^kQFhNXppynqOqFhnEV]Cofy>v_tuawU;U]aUEEwowd\\wrdyC`sU_WufwIuyu_OiOyWiIcHUEYYWUKGqMbKgEpEs:ibU]y[ErMiuh_wOmE>gF\\ww_siL[XpUycKToqC=Cxbgr;?vesWtwFYUV_[FCau;?Sfar@_EoCxtAhgyXTHmvhWQmJrpXe`KkpxuYmppLDdWwmo;HkZayPpXWLO_UlLlTMTLVTpthNP=TZXWKpkhQoHiWOit<Uvq`Ky]WQqYn<m=aqcxtnpLieWFexB<RA\\QHeVhMokHKQHqsLS\\em_=qwyoYpXL<qmEsLAUieWq<KUMn>ApAum?xTdLSOprw\\PY@r>UxiIUOim_Ixptwp@QRhVY@PhDPMlmvDM_EPx\\yptX@ATdPXCLv=PqDQnGitkaM]yQjDqAxK;IWh]vgPuDItN@NeqKUfep?guqcKxaD@mAW\\iYgVXxXrnMyhMguStbsCMAdhYiiaWlCglESc;F=AgnEfRiFekemaRymgDuiK=ys?Th?rRyB?;fNYgCWwRQR`EiAyvh_wlsudCuL?vmSXEUdIEXZwErou]wCfAe]GwD]h;kFo_SB?xSermmwoeFqqUDYycOct_SZ?SJ]OUAwhupJaL]=VTTsryQ;qUd=rG`qUXp`EonQohxMDLldar@@OmmtxpPShY\\EqUuuIAscLVT=U:TYOis@PWEeooLUCIx=TXDdy@AuEDVCTjb@rd=lDhlUIJdaQrUJYpL`tqO@OHHMEQoDyW=QWrUS;ilwuvhhrULquhKbLjPMJIAky=j<tTt@rOArAlXf<U@eUAQxYyL_AlmxkaUrWyMIPpyXpGpJ=hVllnLUYuuJotRcqWauXylOpDpayRvqlWUj=<r:<RihqMIwOltcaJFqKLdX?XvRDMaYOGHVjDV_UymmvC]W<hrAER`iwfdUhaJ>xnpeKFAYvqlwhPRhWBinBEjmasl@rUEU_IxStO\\@jK\\W_HP`anIIk@tkHeUEEX]Nf=YdehyDynBgkxGdjv]NQs^_ywNkuAZmxlPHpkYsUviwglSonL>^j^_nX^rxZho_xy\\wFvMopIhdrPqvVfFVajidbNqM?ogqbm_lUOwoxdK>y\\ov`vijYpMyppvergjL`^nVkgVc^V_;pl:OZPgbK^\\i_r@Nb@O_aqdmhbX?eHyfZa<YCDYWOGxTmriET=wgx]HSsUlab:]eYEtTWiToGKGT\\KrGuhB]wGgfjuh@?sRGgBwbEExhcGgyDMSCHgvRwx>wsDOCMmEiUu]etpqfe_YKkVhWbVAHpcGEUFoUucMSmSY;Cx[EsJEuy\\myLMYite\\tApywhMYatE]s;ykCllpAthuX\\mrPppPXYuhYETRpevPauCMU\\UnXhtSTtpmTV]neAP=IsElKeyReDlW`q:LV:asx\\tAqTOMy`Mxp=uempHIv\\iYDdQEEY_mTBdT`HvIdpj]UPmxqLrkIS]xO?uRkuklDohykaIPATXeDTuMYEuPopughoupSb@SLHSB`nOxMNuXPet`QM^TrATleTqCpQTaJ^EjA<UPetu=OM`xf`K^\\WTLVAIJuQP@IpFmyTHM\\MMUYM_eytlKmlkIDtKiUEiXoDlm<PMloKHVjYs]hu`TrKMs=MVQpWl<m=aQehTWLYDiU]qWUPQqqPsqxHyrfLv]yr^UOhuPQtrmevCDLW<ruEUc]wyoriXqdqdHWwxygsInnacsOsy_ZkA\\JQwuvsE?vA`uloi;Vh@Xsm_f>_wrpR]R?itdkGq_fV;ugsTMCg=IB>awIsbRAUosEmyxbeFFcFBASReXFmVPuvKeUSgUtOGK[c@mvT_fBMBH;Bf=chCFiAIHKx`[E;[Uy[wNKRhsfdixEcRokHQiE?MFLsWZaXCEeZGHtgXt_WOyBmsrWEfgQXHEHSkWm=hSGfsyfVoeOqRKuNo]opXXpayOet=YOrAWiENeyMnpYMuoLXxeqQBiqoyk\\QkZmon=odeuQ=uYauwDmryLT`q=adOFrqWq_vrIg`ZYi_nZGGmBWf<`bN^dSG^;xrDPmBH]lGdJogvVtfWd;>xSnnlgdJ?]ZfZj>]ZojNwhc`eHPc_HbO@q^Akdg^C_bZPkMNb>^jJIjlV\\<_ZMH_^FjlF]pNbFnwkpew`oyAZ?`nvPnqy\\Ng_hhdYD<wDA?v<sbjcIwYx>YrGSuV_rgaxSEiuQw_]yGyW;SISiB[SF]KB^Sx?wdt_c?CDMCEJwSwwFtGYCWWd?IRmfC_DSiv;?USATWgGqqFIUXg?FHAU@CEg_bOGc^?EpIWcWyGad>uHmMEA?seYeWebu;GBseCySTsR?GxJUsUySruvRsYfQUpYewAylOGlKIrsYI=IPmHw]GKsytEgsqta;ePMdFWtVGSftdjXqq?aT`xnxbMfs<gqi@dFXfX?qBpZRnfAFqfG^Wovch`EppQOdcyfmw_lNn>FmBxlOnsHymvPqgp\\SQ\\GqnvVyEi_NHm]FayAZ@FpyVsynnf_wTQbJgpkp_RNqixhB_lanvgyfZpvAAwPOr?@pNXj<OeEovHYmGwutXwOneFiky`oWakh>jVVehy]?vhs?pihhKN\\TGduif?ih]Pgd_mhamopcfW[@^[QnhPOhaQvKxkVFpeIuiIoXfepwbIwZ[AxWoxw_`gwvaYegnhvwZiQe?n^^Ou^otSf]=wnWWqq`enFwZG`e^nbvuS^bS?abaZx^mRYiPVmkWb`VtNOmAqloWyg?sjpsE@ZANxCIhA`clXs?VqsPjYqlvVebipUPklfc_hh>`^Yf\\W`tpndh_kvop;yuKovn`x[Hm\\VgRHeEPkJolPyuD?_=YecwsFvtWgq`Nq]geF`c=o\\>Y_tfiBAfP`blvjDGtnggfHjK>^FwcKIeYIdeVwontHqc^OpppsGh_TXqIWlRGxhynMqxphge`lf^gEojh>qioxPnw``[n>pGFkTGiahnMHguh`DxtKYmGnpuYr=>aBpZR^]RWiNv`wq`gis@AhMin:p[POpZo^mY\\`Glk^cdAoYI]>Yer>wAfrap`qq_AnnXyhx>iLQuoq`hp]_QpBifqVlBGdYaxrqwkiZ`P`yNkahappyOGi>nbKGsVQaTafq^`FpnCnr_VmqHuUodPahPxta^gsOoupiW`qUQ\\e_l=>vkwi\\XuagcSx`YPxc_]xG]MQuhy^qdW]rDGSX;y;mGPqhn=EMOUfsV=IC\\gT@aXSgCPGX`]StwSO]igMW=?cJGtCIfViWi?wWehD;imme_gT`EbGmF`yfR]C\\MF\\eyScYuuv`kdmgsGKfZcS_IHdcutigOMrJQD:kX_SWlasdcgqwhc]fPoyF=egyx>kbm]E>Sr<GujkXcgup_uCMSN;unAcwQhZ]HSiCGqHwQUxgVQucF_EgydhkV^kRtYvS]HTyV>eeB[rlasFwcO]C\\[imOyHqsGoTKUUrieVOPcasclnohSotRFXKkmtnUN?pX]UtRiQN@oTMUqtRkUVmDLVLxLMWUIwh=N]pJNYkvPktpS@hs`xwRmtdhqSelfyw@LUUEYcanwmQhpY?iMY`SWHTltlcUTjxj>lQEeTThTXyY:LSc]MxEMuho?TYEak;Hk;@r]Uy\\YQgqppdtoylTus[Dv]QlxDsm`N_MP@ElYTryDOgynuXt[lmi`KEpOuLsfQO[hufHX:EPviLw<o^YUDdu\\mxMqUKYOdh`s^gNQaxOtGao_F]p`^JfrX?Z[fmpNvGHiUitAwfpppe`gxpts_v?IuA?oga_WIwJysQnr??gq^`qW_nhu`HpTWp_^pVQy[wbA@d;ixxwelgvq@uio`IivDWZP?ixivixnDhgCie_``IPsO`\\hW^dxdBQ\\GA[=XjuilWvqGSuEiemGJMt`yCqgGjcEFaTTIC<yVrGt@uUjWwmocJaD^aH>Wr<WvkGWpMD`qWLSvrIg:eW@MBgovjIsTaxeqxPOgCGs;?RssVEGt:EcCcEFOBMyh^]seOrHUTgewpEufGuaAc]OUGcUrWtsWH;MEkKfweFb;VHQGgovjGcqyFYigIsEGgWb;C=mwD_cpmXIshUaVX[ElOukygqWwwGcBqfLQe<qhxIWhKwogBC[fmidAuFgqgTEs<cC`svJQd\\[hSADEUikww\\sDuIhpcytOIqQbmgfVqtOycRyGiGgOehD;ipEWmmtJQSHSTmGWf]jhtu[iQUAQh<tTXp?QXpqoUikHpVdUVC@MDQyF\\nCYRj\\kPTNlDmqXmnlTvHoimxxmO:<V`LPyhRIYxk`mp@tUqTImLlySw<w^mLdmRMyM;EpFPupylQipP\\uc]TCYveHJGaUTetgdqkTO\\Tp]eRp]VllSP]RMmMwQQy=tiUoBEXduki`uudxWhmudO\\LM=EQilOeeR``XXAYYlvouKHTmTeNGIPhhWd<QZmtweupTYitPAUSduJSPXpiO@`vS`tFlN`dvditqTMBqW=TS<PPQdnHioPpxKpNeLn]YuuQRPmv<IlN\\rQEnKiVWhohNok_l>ynvV`[G\\AqjdouLIqK_cd>s>QfAQkhAsaOdlGmDPg\\>mAqnXy`@NynykP>nFvqlwthGgl`gdivNxsLP^KHsF^n=QkBfh@HlSgahgcBvbSx^VqpSGihip`Wo>xiFoiewnVoeFwf@a_?YoJYgOAqlfykvaO^lwx\\wqigh`HWtsYkINfnqxGWfhfakGi=Od?IsQHe`An<Gxw>g:PjNFmLQ_B>lranknwMogC>ZbAom^jp>acxp>FmCidK?_;FcVHnKheeO[NQhOWwPoZDOpc_\\LIbNn^>H[nF^:^j[NZ<?g:?lT@c?^vtfpXnb`Yb>`q]Wuuytj@ewxigoob`umFj]_uyOicytovlgYslx_YVtGyoWOthVxpGpay];nxxgv^qdaiytgymfmaVxGVbvp_wIproyVPi`Qpwiq<Nc?g^]QiCH[[@dLDC]V<[Vl=G^ED^Mhfmb:?DTcTKERL]tqOi;Mwk]SIwRlwew=DVGvJ_CmiGVWefac[]dgcdASiI=gKQfMIYXkuYCRZCwYcfYWCdcH@CgmaGTsgmoFtyVq[efubpGtYOYOiw@MVpggbawwmTE_duIvuCTUsFF=DsMW@QDoeTROHV]yWAHyiTIwGruXWiUsQBRGuX=yxmf;=FAObXkrHScaeFSWgFcwyLXDYtqiVjqtBPng\\vCUMWyODam[YU:]jP@RNEl[`nkHRPaSqmL=Yws<TBGf>xcZffuAtlyn[GoEQrKG`l?yLFZsQno@caIr<n_VNfPvcO_liau=og^ydZPc:o\\NIcf_dqYhdhoZalhI\\lar>WgkIfIa_k^dc_[l_b]xnhIr`gk[a`hyvF?pH@`Q@ivydbNgaxnFQjVOcln[Y?k;Gp^XpFhlEwoJpusW^gA`F@jV^udhm<odEghWGhKPZJN\\:n\\kY\\YHrn_uQY_tojRxv_irrqi^P]>?gGAc>glLx^GWiEorTqf<_[Yo\\A>pVPxZYnNagWhpgAv^qb\\OdJhZWHmNP]hirlH_Rppaf^IGdoah>IxbXlXi\\Wnp\\Qk_`ffaqFGueXdCVir>h;Wp[GtKn^_>sHHZwiqCYZb@aRopWaftai_No<Odlp_VWjLXtcaxsih@aaKndRWppH[>WgI^]Pp_\\Q\\Xywf^kCYt=Nnk^i:^gwOwwob>VeHou^>k<O]Rp\\?AuuGlTVvVNZBNtV^veXkFvhjxkeyoKwwDvkB_m^igt`bSH\\\\^elAauGlT_rKFkBnwRWm=V`npqCQ\\F?n`GcyFmmPeuV[Gfl=p_>A^CVugfsjXf\\p^fVeI^peF^HXcdFwUqa^Pe?WoLaZY_[@oaoAfYO_aWqKvrEQ]]iwE`yJipLArkhsFFyfnmO`d^yxSW^cFsoPc?otAQicN`OVbNqxv`_>^mRVZrY_:pqBW\\kWbpV_@@yM^bBqsG>fyAZhvi?ndmWxqWedweB^rUq_lA`tQnn>cZFaR>^?OxS_\\h?_eHh_olXa^`_f^N]S?hXfrHYwfYpa`tVfkmWth^ZFpif_lPXurn\\rF_@?a<pbHVp_OoXNlv^v\\WiQP_affwPbmO`gF]bIZjQtunabnpkppxphWigag]m>lWNscArkHr\\wtN_gmXhen[T`j_qoHWr<VqW?q?`hKgf^Ns<fsr>qkokRNnU?dGH^BIrj_uhW^>g`EQ\\H?m>yfcniSQoufkVxglXeKX^r>cAp[@om@avuPctvpoWZBhkl_lAGaMVyK@bP@wrynbVbGNe:F]u_iX_uQ>chqZr`rx?idy]\\VpvXk]fppXs;fxP>j_NyvPd]_wSn_jHku>mO_[dao>oxDgbUAuOnbkpkV`fR>^A>s`Wpba\\<w`OacoAc<obG?o:xbka]WvdVqwfVp[WcL^aCa`UplrN^UaeF@e`Qj>VbOpbCqsrhg^pc`niSgwY>pV_yUoo^Hfl^it@sMyZ;uWWUC[XT[FJaEZ;t=gvDyRUkgbQGU_wpCH]eY<;RCSY@[UNsxQEu`OrJ]feUeC=HjcuLSEaQBAcH[WB;CytgSpOdA_vEiIIYbWOb@SyfKglot\\?TN;v\\;Imyb=iXJ?udIgSGipaW>gF=_C=ebbqR<;efICMSuiauDWZ@HqLVrZVqY_h]ocXihB?meA`l?[=q]r?x;Go^`m<`kvGeffu>ynx^nHQeT^`A@rxnioAtRQfqomwN]xGuYVsbpf<HyTVhDOrZOfBv^Mwl=>ZVqtb^uMypUIiOWehPfK_lUvdvVhMOwTwvG^q>^n>^joa`HHa`Wj^?\\lGb@F^HIZ=ggIN_=VkINl?IwUYhv@ltPv_O^>GsanxCIbvhrW@pK?]\\I`SghDqhoG[GySwDPYBZQfVadfmyoWdv[CEQUE_BHyCx?GGSvP?rFMXDkeYSi?AdmwVaucF;S`Cd:kIxKFYcDe_sbIuN[Ef=Bq=TJ]GQsUJeXAUf_mHPuFbIFYmT_UXfchBODlKisQHesFe]F^aGNava_V=;uAeg=uBhEv^uRsAvcOTVUSI?d:uDuurWMI_oRrKg^sThCShES>uE^CGl]T>WET_DS_cZoCNCGlETKaVMaVSeRADOl<l?Al^HSlLoFXWBqwgYxh`MrYLAPXoem<uw\\HkIUkjtwe@SitSFIyCYRp\\Y:qUMevAynUQRx<n]muQAMcUUiItr<Ky\\WvQTpuOYQNa`xrirh@oxmS_`k^<s_uVpIRJPRM@N>\\tRhNJdULDN;qJ?mNWmKcIJ?eL@@VbUJOlN:Qke\\NQHh@IZpO[lHg`^jC>[<GZBNb>^J=VBcCBKTMKb>EVgGDpoRscvZeRnKBIECwOx\\ECQaW\\EUEUwsYEUUuAcvruXkSuy;BpgSXWuRsyfoyA?GjwDqIEUwDIAWPqEnCDZ[Fl?Y[mFniiQeeAmtxQwjmXjOuEwRNatMcTMEh^ODLmDO[d`[BCGS[?dJKEKEd<KTKET_uEqsIdmRtaSBSfRyCNMhPKTkaIO;EuASIWgq_DaSRsiIfuyTYGLqhloWjyVqmvuqdAkT:[fBGRLMEMMS<qTiaB]SRRkDTygFwtKoX\\?tOYIA;dkkW=]cY_HsUwmWcEUi\\cs;geOOhSeiF=UJCfBEUHAB@]VxeERwe<UgZcDusGdCT`[VR_rIKc_QeW]d>UxBkdSQTD]VOAwSeDVSVCMCl]wj;rHcxSuUGWe]=Ie_S^YF[AD^IUoaVEAFOYT;aBKYB;kRokVAggsiU<Gt>agOwDBCYFstWqSZmgeqSQkW^QV\\WdVWFa_w:oXgiuxMTqiT_mT>MFBQx;gUQgupkto]b[MSSasSOWuGYfmB<KfKWCX[VxMsuEb:yhGuXVaF:cEjKh?WiPwIPiUSmrOMbs?WfUigacpkdDCfqwE>qbA_i_;ILSU]?DCOhKmCV?uFqd:KGkgeC=S@SbFgdlCUQeUV[ch]XFCuRCG\\IhOGWxqeNWFtqThufc_B>ufJ_rsIxEoEpeVFgF;;SN]B^[tcwfGihQgXmeWN_GKCHKKtjKDxefouhOOD\\GtCoYVgVd[UkgVp?Gf]e<wDQmuDEeFYefAuWsTr_Ro=X\\ms?CIhOxPUEiCGJ[g^MD>]xmiWCqGbeR<]T<sB_Ms`qgvEGKAUI]d:?DRGhH]guMrkKG<iDQ=U@mrLisAKUusi?]feIcj_dv;CH;sl_gxMCgwHKCXcsFKSRZuC[uuNsXQcDmYsfsDMADXAUd=XrGVKMe`=eIKBGAhB[rR]ThevhAwhcFC=C@KI[ysFwEwcUycTNaCDMHliF[Ie\\oX]]c]=TFKBvgdl=UuAiDguF=V\\_C_cCFGiJUiKGyHOetSgKGdVwCI[S:QUXAeC]TG;DrEfFWbukvqUCmAGSMtIGu_cXpsbFgieebMAhO`WZaSiiJ]lMVxJrhOM]RI`J]]T:AVPPTYhs;dJZamOMTWDPK`mMTSOhl:iW\\XsONf\\>]c>ZU@^_Yf:FcH>]<xZ_fkmp\\SOqX@v>irIqja^xAAZqHmLi\\B`vJFfRqhNIecf`IP^HGjA^rlIacvg_ovQgcoOrYoim@sZWhgireOsR`c\\I`FgdJNoMW^sG_dAn<g^eq^@_eMVaTphqYm>of_O``QZrVZ>QwCagRVZ;qbNObR?l[`cbncpvtvg_FXnE^_mQ^nGqGIxCfevw_?`d<Y`bGubPsK_gRVvYPgXQx\\_sCi[vxZ?^g`p`eyhBftt>gFhv^orAH`kVZqx]\\`weNi]pv<^clG`Ia]jQvnhkJ^i@W_`@jFAnmQvu>idg\\Eh`Eax@IdyNwgVxTWaw^ppVnNwb\\qosG\\GacA?jPOsZgdoWaRGeOGhlpfK?luI]Y`q]qu^hbo_wcgkiq\\P`ZAVfIhZk`v:_mk`dqYysfuZPZ?FhtFmrxx[Pcm^utYqdh\\@qeOw^M?skFlhieporLguS?iC@kl>h_^u<VtaxgR>Z;ahJ>kw>oMo\\agg>_vTwr^fm<v[ChwCalqxnFijoNraF[ew^:@rvqdnHw>Hp[F`NOh<GmuVtcNcBPr_VwsG]jOdqHhGw\\U`xFqsF?xKFrsQwCYgTNvr?_H?mBAyJPfDQuiikjQpm^ka>flx^E_mU>`u^lioqqnrTXw>PuM^tFWj[wwUOnBX`:>kKAZj?]\\XddFqUvhmXqCG\\tVeQ?fKoo@whXwfCFiP?vA_]SptIylRnmNax>fp`h^pfgZibkW\\Sx^F`;YyY?wtcXS[T?OhPCvd_bnAs:;sQCIgsI\\qSv_T_]d_=U;aBoCrSORrMR>EGsKtjmgOIWVWDomYWMb^WT>[cIybUQDP]T>=h;Kf>SIbQxf]eMoXtwtn_c_osBibVyxdEcMwsSGwisTL_gvUiAyBhYSJOsBScj?Ed;FmUoRXUKHNn`lBTLcLSalKFlrbmUd]POATCtnRELv<JEXWE]Jm@NQmmBakbexBdTm<K<mvkXKutVhDrLqJhUmD]vb`kGUPA\\SF@XC`q_mLEXxCIk?MLu<YX<Kj`YchTlTMkULcLSKmOl`kSioW\\onmT;huvApFMS<ao_@KlDmGALDAKlTL=o\\G_lS`[ZpjcOpMH^KHdGa[^pj;_\\lVlbns<?qSXs:VZOhd=xtqx[b>tr>i_`xRWkhPv]AqlpdEIaQfepVaMWqth`josWWsUakeWkCY`phcxijoPxcXx_wxSwksAigFac>Z\\>]ZOZEwrN`uUitKFdB_n`Hslfk\\njLWbb>^RInC?lBAolhc<Xm[>l:_ZlVl[bMQCd[d\\kVOafJ[RZ=KJ\\>Hk^<J<EWZ@L><nJFbENgG@tovsR>skneafhqplTIuO__Aarmoe_ifoimAHoi`s:pYwsBiFroWwEyNadrsth]ChkwvSbAmvhcygMvAcGxEUqqy_]gQEr_QGtqwmwsaWsQsEFYIAyS;wGqyufuRPyeO?WL=WXwhZ?DT;D^oV>MB=oF>GcJKEJmF=oNLTL<aJMDO[\\JSak^Ll><SGQk>LSpTRN]SlAXRIO[dr[exrDUGaTOIKFaQ^IKNaUZAYeTmsiTk@l`DSWTTmIlFtKsATeIqKaylyY:LWQiowMQqHLMATS@PE@SHURA<qZaPEURmAWWtp=]K[=pwYSQHsKdMklY;it:LqxqNeMv]PO`<jQ<SedqYhyK\\UNhtSeuDdVR@sraN^qK^eU=dV`EP`lox@W`ulc\\ge^i`Q]lqid>tGNjen^rysagppPdNXkkFjKPheapqNqv?mqnkMAjxI\\SPydVaWArYyuTF^Gh`CqvAovJ@vunqegnlnouGr[gj\\hf]h=ocRIRggTQoSQ_HaSG]MVEEU`yI:]sOiGWqRb?gFcVViUZ?efgs`=FQSi]oh;ktlqb=[fxQvfosiGts]UHyI:gT>CF:CS^?cY;ECSGHWusuSceS\\KT`me`At_Cs?utT?wjKEiWTSYhpEUrWEMaWm_ftqU^;uy;bTkrOqhmydZ]htqrmEDNEFXuHI=sAyI:ACpaBvyv_ORUqs\\WCbKD\\MfL;Ck]gweRAEy[EEMQEoUd[AEJECssxVEx_Wt^aGG=hmsUxwVTYUTeRNQCE]iL_GGWxQau>avcOgxos<YCaUE_KV?miV]H@SVQaWCQTcoTUGgCkd_QBcCWCeW`wY<sU_UR]gXoCDIOwrSSF_S`YFnKGGiu`AEh;R<ODEyTjAs?YYSOTu]h]Oih?SWKtKoYakyGiWG?UdyHhCV[AvlYc[MVYqDtQguAg@ScdCT:qSGMBfIeUOC\\Wi[WyXMVtcVr[DB=T`_GkqYoOxBMYD_cgCdk;r^MCA]tgmhkMV@AD<KTA=DvmtKiU=ghpebpUC^ueN[hB_xR;fEuEdkUyWwKauHiw@MuAKbfmGlIHq?TsaxsUuhMVpmc>_IaSTL;HK_B:EU=UY_?HOWdBYxFIDZ=EZ]uwguwQSGWhtGiUwF\\cX:cFsAcryc?CDWkhQGUSst\\kfL]twebb]gXSSSucOKXFmvFiy_itGqReUhV?S?GXN;IMKhIUiDYcbMy<iBdGtpicR]B_CHWITu]V:shvothtVrTJZMjGUk^QpqPXxXYIQOudnR@KAAkPhSLEkRAnQIPMaT_UNcHQDQtIEmQUNneVsxtsYN;eVYaVpPvw\\qADMsTJ]TO^<xIDXdTTLdQ@MrylnApvbtq`qxdPwm]NvaN:HQL<yhHxJ<ljEpqLjuHKMewAMY<XT:qyq`rvEugeTK<m:`nJHKtPJIIOv]w^hU?TRoIStLM]Do?Ay:EpJqk@=QRiWBLjLYYIdpf=PHLX?]vhenwpMXQQ^`sv@S@moV=LrUO]HYwAugyRVEVehNR=qumtfuP=xY:DqPDPn`TtAjvyvY<thTUm`uiLP`qpC\\sBMSMEl`]vR@xZUohdmPDUU]rFYSP@MOTwsqpO<vBLSKyWKmnxixQXTqmrOHwTmT_ALFiwPLL=uYBTo<imW=jHiSFUVWExHLv>eY<Xo@PwsETtLnEaSCDKqmj\\YqgqpMijT`S_AoCeXCHs<qSUIkiuXATxj@R[AklyK\\UxdtuOiuTXVcEoyhtR`rxAkmyw^ym>`yrdWahOgmnT\\n=lLk\\OBuJFPrPtWkiospnBHSgQxrIqMYUjmTpTMyPOWDpkUj@dskqUPIOFh_GNm>a[r@spwx\\fnVgg[xxPVum^e;Fl>^kxO[Wn]pGuMVaCo>QhAYRjWseWEhiTgYfyAddyulyBkWgjiUU?Y;edK=tfaCBygW_F\\UIoYi_yXUmsoCFvSvMSu\\OSNuV_SUwOhKGThCDiQf^MbRIWigSQaW^cW:Kcl_cBkc[_rACdUIG@SuLwQ>xY:DY>tKuqv`EsGpQVAM:`jgLP]\\MyAotEogmXmelDEPsTj\\lvT]qXeXUUxWwuQHlb?[TVrZA`IqugprcQiSitVNmlfa>xvnIbIQhaWpTYlcN\\>Wv]HdmGkCY]SqgaO]vhkKGkL^l_y]<Xos@qoi_:iky_wPAhyNoVWyAhZ]hyvpb<?u[?`RQqr_a]Hp\\@sMFaHYdlvgrhoPFeopwI^olHnFHbI`qFpd\\PkEH^CO[d^_@hcB^jBafJQjfVm`^jC>lCInJhbF^n@@bSp^L;\\jC@lCMPNHkJbDaBEwTioWn=BKae__cuuyt?upACOSrsCfRsreibhwwPqVSSuf]vwEroQw@qfwaEuOhbuGqirdKqQxne`sRHXIqm[Er]]xxyMdaWQIPw=qaMUsmyeltgpx_ey]Ey]UoYdW^LT_anQhMbmN=q^MF>?dZSc[_DS_cDSc[_TL[fCMD_mfG;DZaTLeCN=C<;L>:::@n@iUnuupTrt<m=DkALMUqUOpxTER^]sj]ss\\ruqLLqlqQM``pE@P>Dn[AP>Dn:NB:Z>NmJFj[^`Z:abJOrHUHciw>=vYSr<aoqQNd]gJY^`VSguO[vZqSlwglEW<KT<MtjKFr=BrcfWiyJQH[KD>;FlSbL_hJgWDOx?qBKeGX;RUActqGQGCReH^ECmIVQ[FbMHwqi_]c;]byotk?ye?dcYRxIV?=E<KCUgiIAdtCh^MTIQigGyhEc?KWZShLoSamdJSBhaXh=Xs[R:yBUqbEMRpWds_Do[YIGGiwuTUd<ohNEFNsHJKT`AbB[Ev;iIOSiqyPiISQBccc:oiRkrIOuo?TPOd_UU\\CWo?BkGfWcewqVRSDG_iO[fbQgqUsAUYTyI:[CyeB@SUuufiuEcODRcsJkuK]wT=sPmrXOvWiCkcHSAs:=Fn]sBoHeUeg[dcoSPsdJAfIuX^uVn[wrkR]]s\\WsHUV_qx^GWpYBEiRn[rjqXmQUBqdL]eb=FOkdEGFBMWBEdCcd;WxK[eU]vW;EFKX;;G[crWctp?S=oEQCUSirBmwOqsHEYDYHNaBaCTGMElUCSQSTSTbaXsudIUDSKRrkFYiVVQRm?FKUF:gS^aiD_I?eDH?xukcm_Dv[g:As[YYQiCF_WNOElsRwItNQG<=D_KCqEid;SRgYjwgdCIdGs;Wd>=SauVP?d<qTEkvp;tKgKIuxOYp<UPW\\Q]AOdutJTjlPQqLn:Em?ujBHRWTnHUwM]qVHxluyt]t<qpNTNBlW[lJkEOslqblY?ptXpsgisKhMl]jAiWFTR>eOninNdSUDkDUxoiJC=Vjlv=PjJMTlLt<QK_ew^Yj_hmr`Vm`OSYur\\lvmtJljk\\J=xj`mpJTjxLsgUjT`XLTJ=@N^mon`wh=ODITJXPSHYDETqQUBqtLEm<iKEEwL\\kAAxPuuOQuMMQr@R>qXcyOmeVwEK_YPpTQI@NSPLliNCIqL\\pJejN@LT<<K:CB[[pJ:::\\ltqkPiSNeRj=NAEQyhLRLqG\\MFyd?@qHQfd>]VP^`gvEyg>ohji\\:A`ENnb?ef?lT@\\^n>MR<=g:?DT;D^oF>DMn<nCENB\\J[<K>:::::::::::::::::::::::::::::::rYyYp2:\"\{\}LSUlUk9PVEc2Jy0lKUJPVU5EU19YRzYjJCIiISEiIi0lKUJPVU5EU19ZR0YnLSUtQk9VTkRTX1dJRFRIRzYjJCImUy0iRiotJS5CT1VORFNfSEVJR0hURzYjJCIlITQjRiotJSlDSElMRFJFTkc2Ig== JSFH