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\\j:@N<VZ;N>?R>=r:]R:yIk<d:NZ=FZ;>:<::?R:AB;Eb;=R:=R:J:B::=b:AB;EJBN:?B;CR;Ar:?B;Er:ER:<j:F\\=F^kN\\>FbKGfMFhKP^lfZ;HnLGp<_\\KY^jIr\\Oh[Ql\\X`OFx<p\\=Wd^^`@f`KFZ:NZ;VZ<VZ@fZ>NZ=Z:R:]b:=c>ARF=TN=E;]UZ]fBHKrObLgZ[Hp]^\\KIvkY`nvyTE=AR:DjBHjB<jYfxOP[JhbDojb`dTGlJo][dDeR:OY?QCooBZoU[CDooBZ:J]<TP\\TdxTbdP;dv<entUJJm<::hTbdP;dw<enTUJJkQK_Sw:]d@;fg=gNUWJKw<OU?OCooBZg?:::Z^pt?HgJY\\cP]BPeSp[?og^OgGNdTIlbXoKO]<pcEPoON_OAbNqdP^tdfdbh`;fg<gnTWjJo\\NQ?:::::::WEbcxNSWG=fU;odlt@=ph\\tTLkoqjZTOoqj\\do;w\\NO_OK<hOb`TeDtt@jp:gjTPKopJZhOb`dZ`t?fpDfldg;:::R=EdPJOj:p@:::::::::::ZQ?ooFZ_Ob\\`ddVZNQ__Fcbp[b^rjf\\JHufnd>^dG@b>agbhi>Oge^gQ?^h^t@OnWHffX[opZ\\hk[_Oei;??Z^Wg=nb\\h`NVgG>fY?oo^\\eW^Rg_]@ddW`ei[\\OlQYwGnfwGff`pUobZ`taotTNrUqbjptaot@?pPHtfh`Shx@Hp?_peg[`ogZyh?n\\MaooFmu`jqgZP:@RhMkgtNRUwltx=<qbpPgHvfXSVqkZQnTip@TPi<xuRoSGXEYdmVBOsr;hYUYQ]R`cujqRoIWO_U<UDE]rLof[sBXeVH[h]cWnSW]GuWeeBigXkG;uVBUgMAwCADCIEMItOaTWKXokCmYgooBmaxhiDOIDVcWmewTUjlTLsYLBhO]<E_uc]BQKIDgWe=EeQHqWBr?gpeg[awE[uH?v\\OeooBmuGjWi<UsdktT_swABhKcg::ICVWFtoRwIFVIXqAchEDUWY>sXFiILWY[SeuIBVIpM\\uZxtfdM`qS[QQEESgQuCmt_mwM\\uNplO]?`JqUk?aPeunSyLr:GtfiCVqcZb@:Z=ZW`feQ`q=UGSQuFiu:k?==W:eu^S?RgGffcfdOGCEwcGb;UVRSWmsh=;ao;AChKkXAPPevMmOB`mb=wbNa=IeU@qDNv\\A_phOlvlQReLnNLwbpPgRasXNceraRhotLkVEwefeU`AwV?V@sHQuR;griktT_;fo^;Ra=EeU@b[awGh=OMaHUO\\S_En?aPdenBenkTt\\doF]L\\XVZDMFLOSDlH=S]EPRQK>YVkDmJ]k@uR_]W[TuKLPUIllHJkTu@drfAOW\\ReILkTuBTPRUWcPVpLE[OmhtKHODhOaRScxjqD?qdP_e_MTfexd_glYClQxgywDaUMMTketO;XtsE_YUmEXPUtkWf^OdkSwoUCqcWgWDGETQAhQ_x?gclitGUbkMBS]YdSxhyUh_uNOT\\sG>?fPqSZ`VPqslLTUqsjlWShxJhVNMTUuTjiM=qO`XRUdoPhTVqk[IlGALhEp?mPqAShilSYuVqQopRDXOE\\xfpjDaVWYLGtlNLWGulK]u]<qaQqWHOuhwOEnoplLPuuIJVIPd]VeQVE`WhuJjUuU<UUMU_]kYHqNUOkEkSelM\\OXEp\\UKcMSlQULdWmYLthsUqogeLupWT@PN@tplogLspuVGyif?kcpwGH]sV`PNan`vKYnVGfTN_p`c`hmr>xVxvCQnqOl;q[hphPynhIinO`UadWGsfxadwgy>yNnseQho_say[hOusIfoxugGkenrhfxmN_sHq`@ccH`Kv\\gNpy`eJnt_aeFo\\hqpyeNYIsUDSUHKsSXIiVuxtsE@Mu_oRXkV?MxmCrpKyDqvMsR@ogVigKMwSCCEIW?aVdYhuyC>Wi<xpedQjyNupKatQRuxRPNWqKnEy>twalLAyQrPmRQnUYq[dujtXY@JhqLEpwhujnYRVIVV]\\hAwq_cwvr>YaFHdgguJqwRXa>Xaf`lpxuWI^XIaHAxHHxONtqgrqose_q?ywlV__xu]^qmWifpm]Q^tha\\YiahaVWfcP`LYelOql>q\\Od]G_QPghggQoZhA]o@phqa?^nppuZyhFge:qwyN\\LYei?hunnh>vqw]Kfbpxx=Oq\\otAGhDh_uPqWVtIFhAHhD<:::::::::BoiTc_UhCc_SSLuxyPO`hygdsGIRkmRsIs?aPrQLEhwhujn[EibqprhocBPqmodOA`iGoFajV`nLpvUOqshyFIaLVkfwpqWt`VpdnwRXvtGdoWbu>pP@a?iy?p\\bQrk?io`brXklWv`h_MGjGyh^XxoW>Ex@uvDitVsUDMvQcUkwHWIg:qC]cwP=GyIFkwRrwwCyChAHhEh?uXq:::j@]nl@l\\PuuTJeUPcpK^LSUqU^N^?H^NijPfqBGpm^aS_gSo\\QqnRGmFGefS?OUSKVdgrBOCWoS>WbZSgR]GpSg\\GtBuB\\Oh\\qxDSUfeff?ggCHUgeOmXPQcRgwFeBnKgOCXUgBDmCSqfxebhcrD;g]AVGchOOV[;bnKhn?H=?DeOF>_toUu^eFpOgTEHRWUxqtgAcV]cgGY_]ScKuVSiuWCPoUeogFMHYWVs=iewV<mB`qfTGSDwvWEsIquUEX^cTKyDAMDOme`GWUOC[_STGfdosV]Bn?VPcrUEsNUUaUh>SFEGhNIgCQxxqXtqUEKwegyyNeMimUv`^>x>Pmbikl>yUQuoGbaWyXO\\nVaUGy]G_bhyL?_XpuygyWOrWg`ENe[ombhalNov?mh`cdqgTGuRiwGyx_vag?i]VlAP\\@aoHikpwhth_uxd]NoUYx>WenhqUIi]AyqpnY?txvappoaHaKGdaIlqFvphmAYuMxkvV_Y>nhiqNxemWhOqhdxcTP^VIfcNd]ansWnHOxfi\\RHuFXqLxcWAsaQqJApFAwXYnnpjhNdKhcuqpTgnbHsxnnTgjsG`@Wvey`gwtliouP`wAq@aeHXhMPvD^hEy[@Fe<P`c_jaipWx]OaaTP]QIfVQdepjoVtwI]HHpsol@iaoxdC`mnXkiwkSnspWr?WwoXlUhsNXuTWwsFf?vmXgjKocnIoTo_iNlTfw^QtF@hDXstAyVPix`o]?]@?udq_YWhowitI[fhoDijm?qKpd\\xklgxK^eMWldQsMWho_sSA]r^omf`J>xlOxYocAPcDHl;V_F?trOfHhpI_^Gyo?xt>ftmVv>Ymm^l^QnwYcMX`dYw<WyMNct@pg?f?q\\hhgcNaZOjyPd>ao^hyGwq<Nmh^hZgcsoZhPfLqe[neR?iO`_OQy?pi<parX\\IPkNFeUpvTFqBNm[Ajxvq[gbXxq:WokQ\\ipj\\FqibgawO?CAmW_ODY]iDiUH_cDiyVOiOWI_ODrWvYat>UCKYsWCboaDdQCmUVEghM?WgKftySJETaWbh[fbki_EdVeC>SHscfiAWbKEh;iGQCI]dd?UmwDSIGlCTx[SY[UEEcayoOEXQtMNLre=RKuvL]vOxv:xoiLM[xT@PNEdqY=KcLxLXo:ymrPNGmU[yT=o_FX_IIZ?ome@r<H`w?cjiZU@ddg\\x@gc^e;pfLovgwphWuq`ukWyRXfCfcKQ_mpi_i`gOben[^fl@HaVQdCi^ZA\\DGen`qDOgvn_rNadhiEGce_l[GyqnyNAeZ@q;oql`hmfqGyr@qm?ngGov?q\\Sa_b`x?Gim`aTpcChtO^dd>_oPm=HdWOb_`nopxV`lMPkswktXgr@wQogqwfbYkZgo?iqdfcEQn_f_Q@ddW\\\\N_TWcbok\\AdNgkMvvFOcVYoEX_b`dNppm@ddW_b`dnplm@DRNQUGGbboW[Ed?aGN::RDeBoeV\\KSgMh]mVOoBmCUkUceSDSOxrQFbMiF_dpCxlAS\\OTS[VX]VUcUPCUPCTPcuQ?SGQUnSeL?uPaREWS\\?uDMFSSDg]g=CvJ?gDgxDEDp?c^McP]bbGH[KEdMW__gskfeaRcKEtgTPuXM[sfIu;MsceYbAtD_FQOf_uUswFoaf\\cyichdEXg_erSFfSTt]dUSUnGyouHAkghcETIdZYx\\GewSiwOXFeG[wT@eBPqWAAXuwh\\UeyWiCQX^qtdccrehYIWBgt=cF^YftWdaAxUgslYUCGDwQxBQc\\GiWwcJ]tXeUq?hUoFYWdOGVnPPHEtLMPU`NOeVlIltQlpUybuvtyqgEkP\\mgyndPuUpvRuWwAQuiO<yQuqRc`LAtwiiNePwfiv;]n\\exkasRmY=QXyMXXEkS`MapN_qNU]YEElwLT`UqeHohXtS=OadXEuTNDTPmRvEL`Ml_louhKTpYUhOhxWyMtYEsbxiqPgevrxqZbwrMWtOFkhpvLisBhrXWmF`nlPc`pf]VqkW`SicIIlw@arhqCnaN>`bYg]VhSIq]ggcxonyv^qfjgh[PfuX`qfuPvvl_toHbrHpaOiniyQi^`q`S`dToq`FoU`d\\Yu?ytdI[rNqd@fRousN^TfklgZ\\`x_Qitwv@?uGP_\\WkVNfLarnFv=PZ^XlQvc`fe``ed`_ZXoBAoAwZXGfAolbvfVN_dfg<>seirKvj\\vv`>mxxlTHnKoeV^y;YuihpH@vsPlgHhdHn`Nfo^e\\OhWHpNAlqxnOI^^fvlOe]WmT^vUIrHvY]WAySiqihceyIgaGeViFp?yrWFEsulMCDItgSRXyWlyQ\\Xpp<YMLTU\\tH`jNHoShMwxwZXTMpWEPNemLyaxj\\VdIn]qv_yQPLqThSTXvuYKchNhuuK]MWYOTDnyWc[Pu\\vmxNhspBiDmSf?OU[oFhUd>eHHeDWOsD]EOWGTEvAEh]cwoIRJuviGRh;wD[uUes]?TygglEIyuWcqVMsfuYx=Yu>iDlYYOkvy;b@Gx=iYlwu[ssvSVRyx[GVX_upWbW?IoScHOEkQwNGWHauFwdTcVmoVeETTcdUAw]uSnau<YXksRPSI]iWBcubAsneh?kSkGItsI\\]uYWyKITaWRD]IdofPgIfkUSAfteTHwIKcTlaXG?ThYdtQChkiHefleuF_Co;dVCyOMsVIbEKe>STmiWKSHDwC[IX]Igr=dOiFk_GFCYQqrEGV;Ogn?IdOUBmV_Osqss<edgogbeh;_WkSb^=yZiC>ChlkWk[EjUEIex<srYESw;dbixgcbOSE_QEE]d<sFFAUr;YlQe`OgsOV>WwTOYZIsx]UAITvCUREXN;F`keFKEx?YIyb\\=SKwuoKf<ifrKXvcTAyqNEkCAX?MX;@OYMtcHsKyK_`QjfhX_v<vaoA^EolwvZEGxyoBOvrAV:KCimbEQWG]dpQEI[TCkihcER?CQyVn[frkGrQHAiT?;tbuDNORckCewB;ysOyRFeFH;UlQevyDOEbMUcSEt<cfPgirKfbue:OCb[Tf=HekU>;d>=VJKI?KcLEr;;GN?r>evgkdh_SQmhIwF@]BJ=GD_GNKSI?R[MBJ;GwOB:cf<YBJ;W<;DbZQNbMQli_^mPfMGl<>dbVeUilnWtLffcGocGrjH_Z@dw@uOHgBib@Nx:wd;_lWV_:Ypo`cTYbUihIWd:aZ>Pm;Qvsx[bFwn_b@O_vXsnnpea_B>oG?xWNq<HdWobIGlN>_lhr:HqFHlNFxhFkNGdnGdTfjKp_C`eK_gFWsJop_FpeFk^cg]g=CvJAWEWSV?EGmTu]rrMF?wGCqW\\Ee>oR??GbiUs=hBMgQkGx[hWkf]EGceG@=wPEee?wIABMYwpuD]?SwOd[uDkUgloUeAIQMHWCYE?sDqtEOdBgv_kTowC]egUCYiMXLaITIT?SxOwRcKgSGY?udUcIqGYvEIliT;Uh?kWFsrA?cjOTiYBZMe^GyFMF?OS?iGkOFwAToai<[g\\Kya=Bo_TKMfDedborMsc:QgLUVN?YfGsvmgYMTmihMATcgBvQbWcvcMdLMVv?cekXucYlyh_]R]StOYUIExo]editBUWh_gceFhsHNiGMmG_GtHqtLSdcCixmR\\WIoIxSesG_TGQT`SeSCgvAsnQhuceVCCcaHrCd`WGD_WNQVXcg=uhVKe@QGcodrKFNYD;IhOCwd;F_AGDWDoxOjtp^@LgEWreKSxP=@[_OrBxj_pvc@vUomCO`_>]lQgZpdgqnjHiCNuvG`jq_KWcN^y;QuyAZOq\\bYoLOnPy[\\VqmHe\\Vsq`]O_ZmPcsfsOo_VvurasmivPHwliiYwc=a]kwqhfnqhydpcXwxgaetxY?t_ScTwIsWXYGXsSCpkCGOwKOgXmXAObCshakfseSlecrgBRCIvoi_=SsGIsYg_occWho_DXOwbGU`;TnawpsdVWD@[TtWYEUiwYXOmXNeG]yErcEhIxdIIo_YM?erMWgUf;CWSQVMwc[mGyeF\\qYReTr?tisY]IwxodvISqExntnqdwJInr]QC@ThTKIljohu?EOg<TneyJqLYexPIKrmvnaK]poLHVXDM[iPXTpB\\lTtxiLo`\\tdAWWTTg^`j`gUx_V_tT_rf``hw`kHuTgwTQr]islAah^v^hyrfxuVuuXaCOyhGsdoeoF`poxphlgWsMfsRosQ_luym@W`_YrIxgPV\\GhxEyrxImgggLhxvFem?hCqnSH`sX]DhlY?nm`ttXnKi\\IBqIf]UTGchcQTvpnUTRIXL[hmo<K;QsvMLiUNsdVGYv>dVoDllmvDaWP`KdttULWnmWyeMiTsFivWAqV@OO\\khIkbUWvDY]yLPTpK\\WeHWnYN>uWN\\qZlm;eLdaqRPWE]yEhlNLYmhrw`PrQVG\\RmPpFeOCqVjho?hP=mJpqPYul`dpGAq\\HsYMuRYrVMydHKDIpdmTvHya]x>YsN@NPIwh<onantTneEYuTWb<vaTxfusnPvvEsV<Qtxs_pvITtfHsAeLSLpKiyEQwCDqxYTLxSILmUHvqTPdMOQqNOLxqTqTxpYhWaUyp`YXiMxmktQjw]OnhRkISUdngto@XoJuruHtN`P_hTFmRKeQ_Px\\usR`qk@MI`v_XUQhLcTx<qxTmRoDm=]KSfhN`ptxnJYuLxjI_ukp^IhyBIwCiggQihgcs^_MA_sxhfgl[gnmx]mw]QvgmHsQagvi^EPcxwtA_tYF?QxOAeYoDQWD[UWuSexIuIidrQXHCtTSsrIh_atgkRh[yV_RsOFsKhnyfKSUhUSeuc>edxmvRwsrQe;[F]?gXMt_wBXuIPSX?exXeVLQTvyMgpt^hQxPRu`yMYKuMMmqt\\AqZQRGxVD\\OdITI]lGUqteu[XJ^eJCyoT=WHxqLxn;`dI`k]oouIdenlmiga?[gneENyRpmFGfUq[VVxtIhph[lVcFFdCn_RV`UGyevgbf`^Y^WQuYHqMgoFvrhV`WQtww_nfbfilGniEOwBHdeOudaeLqsHVoZpmQHtnQavXp^`toq^IVn_vn?idmWbnxY_edGI\\[trGb:KSvQF=yRh]t]AvwOcIAVNahv;dNUYvkt\\?TsCRyYG>secOf\\KE?WSuixpKF_?rBUbMKvikid_SNaVekeBKgxoDYHqCusYmW>\\sLhXgLLciv:qo?pwVqvdaYRqx\\YpLLY\\eJNLKTPN[uJTyP\\UspiNTHXjUJoPj?dKK@rATp[MsCiPcuMkyNDLtN]yJUURmtoaVDhvFXMdqSgmxEeKgMOjAyOTuLitc]SrIs;eTPHwQ]lbMYOXLgHWKIx]as\\HlNIOQPpHetwdS\\dQE`nYEkPtSlIXMXwMPOaPL_HkMMLUXU[iRZYoe`snpLGDlSuQZdsfxLR@TTPjMIOlPVdDkHDlNHxpToDMvNln=XU?dqFulOtSLDOLEMZ<snAkcLkhLkeLkgLKmdo<As\\@wOdrP`rFuPEL^CN\\>ifbPaW>[ApbTWe<CC?FGgT[KeWEFTKWe=W@QEdUff_WegwBSUgwgZocVOsDYUbWBaQFDEVVsdlOfpYfNsrO_skWBdid;cdO=YoQbbst<sbP]bb_wQ_dsEtQoR=gT\\chlQsj]fD]BX?YPsrVKTTeS^EbXiTFcDHgHe]Wkosr=DOeRAoRRMdccDlkTK?YQGgLkSYKv\\eVAOD]OioCUkcsvUcMegd?Teecl=f<QGQKuDOFysu\\cckmWx]vDWEhcBCAGA]CTWVqgT=aCWUckUhaUYoQg^OsgQs?EwKiR;AYZUcW_GDOdEkg^GynAGkihvWbH?YbCTtovFMXlEcNChpSdOCFW_VeCrncBx?GoaXjSWxUr<WEPEtIOWdaddMfPIh;QfwqwWgeQeWtkt^aMNPtdDNuDuDis>mMK<Yl`scENKXTcxoXeQpuoDinvhQ`DkVQn\\<VnmYAUX_LO@qUTXV\\YxgYRyLuZmtg\\mlTsDyjyXK@tWxMSgyrr`u`Dw?Tm\\hXRUs><PSqO=xurdM[\\k\\PpxenkPn@ellLYWPynaW?@o`AlMDQd\\tceusQT@tvsHsT@KqlMXisKlVrYuNXmOmvomQq`v`YTCUnxpTE]XXeyHqPyIXvUqdhtqXwQDuUHMUYm_XxkmRsYxSuKLqWxLspXumxP_ltlqYAllXEOs\\usEX\\qpLTo`pRWmWWevNuKpVsLpgtoaX`iVpiMh]rhrayaGhdshrtv^J_tH`jpolPicwobxQ^r?a`PqXvkkXk=qyyUEgyVqTj[xhMuAEDXcdfqUAYR\\uecUWecSMqrrAIpAitusKwxp]uNEbNQeCSUpMHqofdWT`mfs;yfwDMuXf[TgMbQmUCChqaD?aYRarF[tssIecxecGhCS`YHWmU[QihEwD_frOiCUgLswmufHwhYYun]Em=ugaxmuDcawGmBHeDGmtGsdOGuPQIMcV^ostmvtAxDQFYwcUysgMh_IrWCufosGGcuUytoFPsFmgDPuvTOthIDrSTwMfQmbeStTGHAaXGegeUtfuD<mhP_dUwvKwB@gxQAtoUhK]Rusy^QRGgyi_CxUy`=iKKeO;Cx]XwWS]MvKoSG?yX?sAoRSwfGICAobdosxuUiUWcwWyshHGrjOEqegR_FrWxYMxUwbsEy?_GHIdxsVhasper=Ydc;yxmwTcyk_tUiswikAIWA@kiXX`MvmMtMTLRenTQmpTYEIyHMOYYVH\\mmymGYlYisdIpZuYQ\\k?UrTdqKhp?mvnev\\mSLaTeQRs\\W[dnR]pomMFluBixvEpt`tsLXOQwFdwWQksRliDlIxU;u^OGXkYaMcJQTUusLAFkqgW=igsdyYIqIi]kd\\gxIIc<CVuUemiDAAGQKrc=cwUcTeFVOi]sT>SWiyHlUtRSvXqtXYVDYGf]y`UdHMcBeUmSSYQD`McGQi@yS?MFusuPYclETGMRcWvK_SMCctgeY]dochD]wemIAMunQdrkuVYfvwsy;b;adycwmCFSeXv[hbch`kEsUxYMSUkcksuTAdGOH>eVgGtniCYofyChTkye[Hw_UYYR`MiSAu`yrTQfDCWQ_WgUcEQTleVL;UtMvfEeUWtqGWdsFxqSiyClSduGHISfryfxmTGsvFKxgeDl=ECohtOt^wepkEGouqCc_eYM_x=iRjuv<iVEsYYeWDCgusS^qCL?Hqurt]vnCWrWuW_BqstWIskESlwbUwdL_xAAdnouYmwH_gx;eUisOic>eXVixcCRSWyk;VliUS?gEIfJqrL[DOgf>IyJkRVWuoiscyfoSuy;rAEBKItYkyVsVxEx^mrCafHOgmeFOaXK_Up?hsOS\\cySMTrEXsIho_IkQyGCijuVFWtZiePiiRmw_whpWTFchosTNeVksfR_erOxhwc[kTVoiiuCxExSkinqTbWUMOe[CCtYghUcIME@gy^OdPEs[GCWqb^iiRmwbqx>]uUEf_qcSEwPQfcQcNGiDEVVAFkmWHIU<icxUV<ODXeSw=WPIeUkWM?UGuBFeyBcTeUxKcD_sTN_dn]i\\eTs[ffQVASgcQGAssLwRpdqr=Y`urp=mnxT=`oGpvwhOCMx^PU?EopQlpirytXOXQL<Uf\\qKLpqXT]yROakiUrePKyDR_yrE`mdUx\\tJ=qrXmVRQkpmXXMKneYEIWp<Ub]lptyHPok\\mYataTphlm_=qDeLNLkQlxaAsH`SsEPcMT_uNIMSKySCpUR`OUmy>px_HSsqjAHS;PmLqx^pq\\EQspv@QtB=NC@BcbD_RZ=\\;>_DWbJ_l:`jA@cLF]\\^`JFsL>lCI]J?lCQZ=_^?_`K_fJGoPfbLVe=hrP^rBOnBAmPHn\\__<G^KqlZAwnO_SF]cGgN^^DH\\\\`pen]>PaOh\\kXe_gkDHuKWe\\wpJIpJqdKHeQwj\\>_AXtNikF>oAg<ut=;fuScO?f?_FQEhVsuKAsNOc>Qg\\;D_wD?GUhGd?;ScgeHqFW;XMgtcAv\\EFX?wPqTOCSdCdjgRQIXtEh_whfSgdiWtKhhsxI_wxweswVIETeQudESmsGrugLwG@cFr[fwqG^eiCeYV?YUqg=eYe[dQYwviRLiTn?FgUFNGdNAGkEUGKcC_hAaHgQWeySbGwXMwNWUg=cLswA[xomrpyewUwgAiykRlWyagW>OVCWwqgSDEcPiTm]rDeukyc;mTheGHQTQGx`ifBGgdaVGSbmQVEsXhMUGir[McBqe_EI]AYcai]KSYcf^qfNmeeCCqmwgixcWSUCeSoUgubHKWiggOghdgtESfL?Y_KsamfgGisuxhoUEuWM;yREfdOsc_Dkkyf]SAivDWyD]H<IWm?UOiUVyUaiBKCTecCvEHWKblQtnoi_=gEoED_E_wVdgCy?TsIXU_DhgbMCYTOVOmsoWuTcUFwVOCWIwta?vVuvvcYbWxWEcckso;vwGYbWBmyswewxyFwEsnYe@ISyIhusu_YcAGeOsVfmCKwscutBCwY_DrSci;hlIcH=Ij[wkGSVCFQgVM<wgMuRaTeaoDqXUuXqxukhtADncIrrYNhDpiYlCESmPqoqlW\\l]toRPTAxO^uoqyOD]uQdNwqkPMtcuNOYRHUsP\\YHaqmMtXxw]IxETSixkIuyDtVGds_`rcURi=O?anvlkwAQymxrxocxtODMfXVQXRiplRXrCUW`Px_YSDetrDqy=jrpo?ps^Yv?eyBimNetbummhQvdx_ik@eQoXoOpvjLlI=wfpw=eLvDm>mW@]UkmR`QuBhlw@uGIW``yGtM]dP]eWUTOsxVZQvrUyWYuCqTcLvaLsXuWYEW_umCyv`Qs[\\XwtmPlwBIMwQQsXYCptJlVcqTVdw?IMgiWaqYi]NqqT@QK=mwR]N`IPsqpqtlqHyxuwbymbIvXYKNtmoDkWEMsLOvdsbpoDETmuS@XV@tyEypiXrciVI`vghKo`oKpT>PLTQso@SGMwD@q_HkM]lLMUCIt^uS@It^lQqaLXAYuYvu=QDiNUikxPqLeLKdRjaPv]yeDOtxQgHmAYjfpqALXw@pqmYGiqstrCprbdLTTyYpYPqug`uAxpNEQKDuvTmIaLIhVxdphTqyXVganQmnLYrF=vOYnoPXMiYRhrmuy]hKZ=YspVliYyerKtkHhVUhNhlwD=Mjuv=ETTmSnF]xnap^vWXgQVdxglVV]=Qow>qNYb[yfmV`m^^^PfrXtGI\\`h[PQ`LQyPX_vggCydOHbSygovbJYt_nhepwaPkinh_i[nHwDXnBqs[Yas_oxnrFxaGPa[WjkvmLIw?ix]iwjGph>uDQlP`nTpvMOvY?pNPv^Ytd`aVi]_gxyGlcyjyPxh_dHI_y^[SN]gHs\\QmwwZQ_\\mHcyNZ^wtiykOq]AqrYN_QpfVfdy?s\\Qso>emvplIop?f]ysvqk^>wKIvIyy:vf;yxrwasQppafWYp@Xod_pmarUQxjOg>AidxoJislhjgo^TAgMQxjgnBHwogrxwj]XlbaiYicyAZux]eGkrfttN]pqgPHw_fyFOpH_kbawuGlohdFpcvg]_Fwxqbx^iwwmV`oEPlpQah`bcHatv^AGsIpdlinsGcMng_qfNPvmhaIolYplthwSikiHs]axrfkKidWvcRPlqO^PPcaN_cg`BAx_oongyAv\\CIwqxbTGmd?uUijVnnbHuqXtFVtaPmeNubXoKOdihtQnrDnqChiSnwHxk;haO?o;yqF_mYOd_ogYFqKAyFfw?GxCgkUv\\cOjHoarn\\LaqMpfMIg^XtAO^gyphogVFmWYugam__dcuFifv[TNyWCloYHn_yVcQltyqAaS@Eu]Mu]IxwAuM\\l`inI@TeuYoQOfxt;xrrLUReMeQTfdtUXka@TYaKXuoyhoBxRQtoolxL@QeAO_pS;DoDYVoercqV<XqCXU<mU^QsgyTDdXAyvHPvPlskLnKqXhtSMXoODQvPVQ]TSImeAvMtV<qVVyiVQkeOmKFntNlKxnS^BWe>gYliX^?ec[ULkyG]TWqt^eiKuvNOSBKGiGcykH[UUrMi^_FsQhAofRsv_oc\\UWjAi?QIlCbW?Uy_WOEYNeV`igcctY]Do=EIECQkCnGubIGMutROhZOxOqCHMugOvrSxc]gIETiKWLoYSGiGoVRgsaOYEMsKGEYmVAmgeSRikdVyup_vY]tcWENodTeWVei?UHech`Gi@GGh_WuirIYcxMvniuasXPwToossUx[gEY`tw\\Tc<yTHycpwE=MqivMESQPTiyOjPTiyOtIriPmXXv^aq=@Qsuo\\xWhmyy`xKhyIyrx=ldlWnmu;yOwYoBypQAyy_nwviDxy:^l>VdYOkWFcx?__wokyelakopyenyLG_Nwl\\qjLweDH]e_yyGwSF_xya\\G_N;sD^MxM]yxSB_yI:yRfcbdQd^ScNsT^MsMiFpcucKxl[D_oiBChx?c>[vt]d_;YlWV`OBiGXOGYSKgFKglCwE_RNoBP;DoSB<CGBoeI?BfCVdOcECDrUDlmwK_hlQC_oRrCYAefLsG<MTj;ItoY[mhL]UVGWRcCOMWCctjMdDUBB[dVceKmfEmVBqTSui[aWT]rP]emee?_d\\aILXtBqp_Uun]n\\YUlmlndnTENgmnJHVc`nUQnZISF`M_eRDaKL]yEUyLiJtTUeuTldUfhRmxwaPJmxmi<tgaNnLyUIRMtweIndEQf@Y\\utx]WoeNFtTLxr<xShqodYTqdqEUui`tKw^Awd<P_QgnTVdh^bXWqe>tMajM_stht`vld_e]y^af\\cAoPQuLOo;IyMX]NgjO>]@g[vFd`XiSpwh^qNVn^Yd_Fiuina>vyAZZh`@_cj@iDVcO`h\\xcoI]nVtGG^NYmG_av?cLgd?IiOf\\oxZGYZnpmcFnVYfTgdZpddQmG?`Kg\\aPkeO`t@dq`b]`sShcaIrmQ_LgpdAe`ijNhvgodohbTPt?anZ_uXgc[QjmnlNgw=irvVl_iuPOvpynJgjfvbsh^dqiOYsi`x`^sQfySQvrxbUpy@XglhlCIaBWvIvoKFdmTa]XcuXWkdfgG`]YKitIaX\\gdS?ws=wSIc^SHEoxVOudYBoQfWEYHaDmYIPeGyouCcBvEhIGbryrEif^_u`yVVgCvEVgGDdmibmxPSfaWr]eV=_sfMrJstO]hFCFrgXU_eHCDxssfwrCqhjeVLGGVWuP]u^QVPgcXksD]ukmsFafvWbOWiTCFTEW\\Iysmw\\IfncY@Uel[Uy]XysVsGrcgBvITRqH_ebOMcvmsGWCQkGdwXCqxXWXNCWdcdQScyodVeIaaDAqvigUeirEOT@isJssgYS]mr@UfjYuLaYFWxLmfpwXMQgEut]?s[ESj[G]sDvkd_AtS_uN]dcGUUOWWgULUeg_hiaYXsbOkyf]gv_Vuqd[uHXyWb?pE`MNIl`MsqhvodXrxVf=XIuovunIyR?uVkmO]XoCDxhhPkdSMQmQtR_ULyIVDyY:@lEqX=qPLdNOdThtbwao[GfrfnRoyFHr>_sQWuGQwWqyIaZIQwjYxApbOAqDG_cHi]hhbyirQpcwncIaUy\\CvbEggo>tciu<py^Ntc?vtWxYhlkAi]_yRXy]WyvpxP@gryxGOcD?oaXbZIgrqw\\itDomxcfoyQKHwAxqmiGKsOkrIIW>eVpEeDyqFqm^AqMQw@lweMRKys:mXxxpjtq``ufDo`ULAUM@LyElP]qxMMKIYN=@s^QwSHv`QkDuuy=jJuVSHXHYLPynuyORauDdtCXN]@m@qmPxY:PuKAsqhysDo`dNXtNTqpodNedwxdLw<U_Em=YvlIXHIMHYPSqKVingeLYlNImwkIrKuoKhms\\Qapltg]shb[_ks_`gorvPjqHh]oZvY[hPcIggw>etN`?XgYWpAFsQHsGigaI]lofm>weiroYVmetcWTkyoubN?wb]ID_DYmrYIXlQe^MuCcxv[UWiVowyJGgAyI:MHngf[MIDkgi\\TNDPLaxjMoStSHQlDxNC<PJyWMaTsaTpmqlxQODtpENAusQEYVHUA]kHyVFAOe<xHIoQul=EkbDT`=ymyMl]YYxx=xY:TMilvGUYUTpPYT@lq@xoNXKfqrdpke\\xc@UUqSLIXLxs>itlILQLvopSeXnKESyXN`MybuYppQQMJsQqUlXdhutHRyUt^TNlIOoLUWhm>tMc=xoiv;lkCLtXyM^qQvhyYPXolUiEkqPVEDnspnU`N\\lKgyY:`UDdYCYSqMrc<yNaXxxvwxk_AOaEMh\\tsLlc]oKYuYmRqhwOMoolKAPnKTVTmMXxSQTqwuWGIpEIWpyXQuL=UvbTQCiNclOOloJupfTmIUlsTUa<MIeSWImO]n_pwQptAV`kWn[yvF`rPabdW_Mq`xAoRXr>x^Ap^tnpcQmNhbuOiuQ]jIo`hiEqhPQfaaDQUZOXxgbq?YY[cvqC^YTUOuOWesiFoai]as^_UcOetYxCwSQyvP[XRalM`uclrGenVpSfioWQTMlsyHnCUuUileqMOLSWdsMmKMhsrimrHPflUyhTCImliVQTVwptwAuhHL:ilOUy\\QntMn\\hVV`NvEmwprrAqyHpOiVnPSgAXsLMrUKO]KNQWtHpWXsJtx\\QqFloqhW\\`YTPj^hwCav\\Mykxn]xxapy[ipfdnNxM:DQrpYOyR^ALDDlXAoq\\XSXUqTxPPUaLmPHU>xvHdMylTSMXj<YV]TWEmgLOKeQgHttXR:AsgeX]mWOyOOqWPAPEXWWhrimrvYVZiPfIWWyMAysxavLLwD]j\\TPMQRIYsqqny=JNQRo`LoHrC=y:Hw]AwMEvLEO<isLevUHX>AyHMUoiXiLQQxU>@xNPo]qs=HNPEmXHuxqtY\\tXaRtHyPTOJAY@uUfIRbXsVIXa]SEaWNQOfysQ\\UuXL^IuRekddnO=VilwyxlRqPNpuFEYApVamNqlwyVpavpYFssG`_W\\oXhMp[OqsFoiVyi_vxH^uyw?gRNquWmCFUIqOiGKfyydSorBmYYkvD]YRqThcXSWusydFcrBmYYGFNIVsgiBihr?xgyCvGXuYHy[CNIvGCiLSVHygBKSuQHy]S_iWmmeZSVH]g^IfNKCNsuomfRIFOOSnMh]cgvwESOE=?Wh?WkeBmcto=snsD]ig;MtVuBNEFroseASE?TOGBKOS]Mf@wcJSV@]FN[vfeFVCdlsD>KCZCWGSTVAtNor>mScGVRMRewEu=dpOGeAtnqVMMbVEiOkVRchA_hdsGNeDbSFWOgBOUm_SeEHIoDdMu]?clciBMF[OcZseJ]tdKYI[bhwRCeRlosRCXPGSoOCyQXA?U=EYO_dbiVUGSGKU^CEgcx[cRtGd:OHa]d@?eoYBmmUJ;YE[SR?rZAwL]b?KgiKCXSSKUDemVJmcHAiKAdn_XUme?WTPgs^eRTMed[TZ?sbsDyKhWyF=Gtnir^aiCgtpEhRcTcauZ?WUKBfeuEWVcGFD_GksTqCu^KTPgtmdS]aLbILU<Yv\\YEeNpuxe]m\\EQZQVVauGhP`tOX`nVLOotWVtnfpp\\UOoei^NlbafohgXggEA[fFukvpeNxLqqfx_GQ_<ouKFeoOwlOwtAy]_]kWpXNoiisHadRWd>FqN^pvVnO_tdhcAo`UNopq\\MGh?CeuFHUVdYhxurUSFpiYI_UOOVkeIYUFkwsYicEMIdKYaWWoETKOxdSfMUGlQGfat\\CwbmV>gguocmccQmS;Ey@_eL_STawMCCqOyPYsLcIgaXmcbUSshaUj;UvuBqMdootPytJesl_GasfawR;uWPQg\\?TiqHXOgeEtHQYvmw=Oty;RZUTqCxrAfSMtqYU^_SdOioaBHSTSWv^OBQmh<UeH?w`_VVeUP]r@]XYyrNMHHEI[wxEew]Ys?KwkIeEmfYosGqxgQRpIYnoVR]iwaEa[gt_eomS=CwouxaIrIcyRWWyuc]aGqUeWOh_gVdye]EsYmRHWyGUdiQr>oFtQfwiVqKVMYGW[yeCCQIUDmycAw_YsAgR>Yv?sBkEI_QI_YHLsy]ughYiQcFxCEi[r`qbMUUmSWhMFO_wSItrECDIglGGh?gUGuRgTYWUNkRrGV@Ctrwr<;i^IhLUCViWlOg_MXtcUVwDKIW<Gd]msRAVIYD_qfW=iVWS?ceTkvbAvDotPQfTMGnciWAG<EtmarZkG_WCqaEogvcoDGmUX?itUWwuc=]e]Kil?EBgw>iWV_U^qXiWUNohmQgwsV<=TGCv^MuvoshUFsEwgSvBsdOYCjcXSaskGyssCXAymaB]GXpqvh]M=IvTQPUYxI=w]qWCqvvASimOcxq[trFXp=mNitYx\\mVituLl\\\\Q`hmoIqlXpr`q>gvpnxQIndgiOn[YNhI>asA`Oygdh`vFmIIwkwrMAhAgtCqirigAHsHgvDAadpaGGlu`kVfpKYvRxqYNflnggWtPpZUYu_g`cQlcpujguGhfQirZyrT@isyfxvaaXrCQsKOk@y_fahpwpffsc_lNxeKpsWHqTqlx>gLvtTxrT`aKIakycFpaXHd=Qw\\p^`OpxyqpaxKGpcPfMaeMY]?WqrFqwY_IHl`auavgONeK>Ecyfatmacnsrb[xrobmoeHqxeifd]Uggr_Cyomi;IXW_EuoBhcfb_US_eNciRoYauFgIeSQrLOgH]iukFiwvQaDHAUFIv?WufoRhiCBAwCcbfOiImXKsXOYWxovGaVMgXNetsAtC]eYKicmgc]E`Qx\\QsdIfg_sjeXVUY`SWqKYUahQmfGmGGmTAewdyEqsFdivFEv@_yLqiVefHQd>qw_AyWwIuCwqsSmuUxyfcEsjuIDIhQSdb]cTmYEYhvWeNcSnsR?yuNSReosGgraOT]mrPAWMexVCuH[u_gwTOiVuVneVsuiaKxmOFXIy]Sbb?cc?SqUR[ufWev>YDuKUxkdlgbBofrywJySkExrmRNOwvSSxqtveH@IdpYvMCcmIxlcYn]rlabHaT_kbcMiPuRMevlgSb?wNCGiWdWmGIqVQmRAmIEEcKowbYh[mtrax?_hsAirGI`QhEKd\\ay[qUxgSRQf`QekEwGwgQcXOScdQx`ctK=SQQtpYd;EvWUSgUYLuYMuEmIIwaH][EV=uvEeaOYu[uqiwqOHwsfUExNofKuTkEgTed\\otQcRmqF<QCNeykwsbyxfmbdqhdse]mYrqwAis\\IfakUhICDoySWgECUSUehcwocdmEhauHlOWoyI:MGAiupWW`gh>[IjKenqHeGuo[XrWVX]Ut]CGiiV]UVouayv]OsmqwhubbWhFwUK_V[Qv<uTtEcymCAecYYupeuceyDoFoyI:mWCQWaUtMuCwMvVIXnGdH_YS]rAYf?ufy]iuufDqwToH]_rZYEMoRUaF@UdhqDkMYUwsHYddcdN]Ij=ukasHawTqFoAe[ysSAvrkiyGYpUYakgxaGYcTfeCduh]YdN]y;OuMMbkuGNWGk=I]adxwrcMxoUhEibQ]sU=H^EwVMckygJcUHqebahs]VEWDHMdGmG_kYbQicMRGQHLegNOXDwSMabcmUjigx_veMTrGCy[D<WYGMI_[TncvY?eQer@mGHAYQ]tBcTcSyYID`IbW_SjUwEIh:=U?Ui^AX_OeJsgvovMMY\\uUdcCaef@[ICKYfOW_OUGWU<IgrOS[mghMDH_guciC[wLidCcduogn]eQcb@CWnMgU_xrITwASQmGSsXPOsQ?fQ?Rd?DPMULei:ESbySOats;dTwVeUte?BQsXIWcDCfk]dmMrCMH_gToMWVMExUBDAxwgWxos>OW=_XNMTyAtOYewOgIkG:OFoidd_sYCt=iGEwHI_hA_sZMXCYc?QD_QutEvA[c`OcW?U_eeGmGcWC\\wuMKhhoWF]DOGy`EBDQDHCgy?HsKwNGwqCIyAVMwwUKhfwDa;I\\gxicBOGs`suq[VTpvAqTy@m<XMvyTJ\\P<qttQLudY@YtQPvydVWHqlyY:`NDhr]XLmEMrLXxYvhtvi@pNYqNeKxMQKXTkEmnyKdePhXxuqJSHxQ`uD`lYXVpeMcLX<AomMLWdRmQn;qthXjdTXeLsv@UeuSMeOW@yFHoFaJt`KQLrpdl;ElBxMc`L[MTBQpbhtJeKFMVb@TT@yjLTm\\R>dOSdlRPklDnxEJ>ypJMKZtLIAtLqRMAt]`SbDsDlt?hKldMs@jG`P<ySTdM=Yt:EMSIYfhROPo^UNL]mdeLSPWm\\UXejgPv\\=QtTKDYs=LN[xPK\\qC`KWPs?`kkdR\\`N]lUb`xUhiWfmR_vgNgNIwH?avfjJGgP@abPiow^KWalObLIfUgkj^Zd@obgc_FepX^VIby^cdVs_O_H_ed>gmPa[asAoivO\\BonModMgmUwi`IcWh`VWfTwrNwwqpgEYtV>wkofWIWwdsesxWHs]Wk]wayI:Mv;Ytx_wy;BcAYoeIh[g]kci_ieCY_cFu=xoaIYoY@CGsQSCagMuv<QgMGUXMxG[xXaVU]x?UegWYU;eT=srGYsuY>YiIQPhQSgXtvqkwePRLOUaXcasDEnhiUR`nQTKLXXIpjKypIImSXLVQTPPqd\\qFMTh]Mjpl_iv;QoRpoGao?`lthwTAMa\\XCqUQPPqdQXano`nuhsZEuVaNvUrA@Rl<pIemBQT_xRTxjo`jsPM[EvEIkppTDesj=wNitDyJAEO_uol@YvarelWAMTuDSAaPGAppDw@QP`MUaaxslTxuo=UoGMmaTPSEsT\\t]IrKu\\`amU>rOY`mo_no`pnmHF_xpZeP_Win>HgZYsU`mkGgsG\\q^]nQojvl\\f_VOvjAw\\^jN?pP`]Rpx_aZlQgrP\\N`fbqux>ZdYephn<PomQ`VAYeSdEdsWe`Udo]GU=S@]TsWD]OfsIxrUWkgsn;yM[YuMhGghKuyGAs?OdsaBaAyZIXa]DcauIAvUYW`ycjgwUihmKsDIBasE`KGvQtagrA=iPAI?OTpkTPAhuUUciWmGB\\wuMOY[=tV?id[SgeBKov@CtIYCGyST[e^Wrl;ynoY_QSlSdw[XhAVVGUPsiLgFFQEtUXyMfv=sp_Vm_SWuTRWxy;RkuTPMt]yB]YWicGy[cG]TbcFc_GUqVRieLqfWgrqUrDOY]]B_yRgCCy=dQovreDoueX_YcmEG_TosT[QG`sT]mb]IikqDPEXlYCGcUAGXi_c\\obEmSjueDET\\_u?EXjswCIDrytAOVgiRyMxOMghgFs_YVCen[SjgHaoV?ErlACxKYGMybuD@QgrUylesKUxFOE[qDeEsKMH[UWkGin[VK]tpqsTQT]iDG]tWAybiceUfyGWkOEVEXGIDoWEqwVFcuYWIjcbsUW]IguUTWICx[b]wCtkYaYcuEICahsEVYkXWwt:EtoUxmyI:IxpkUjiwnMfGgio;Yy]TdugMmGcyvxKD_]iyCyNOYIMxV?IKohQcVcyB:cyMqX?wtJ;Yi]d\\Qe`SU]gdsuYNIGOOxFuxgWusGGswCxmVc]i_whGqHvocV_x_MgGkgHQvpAfkUsy;R`csPiVDsEQEuxoFEIfkqxZEwkIcnIVKqgViyGwDWmRJEcuexA=BNsDdaggew=qiMuf@wbOUiiccYAbWAuECeiSf`IC[CwaOIOISUqxj_tb_i=ohm_RL_YdCUUeSu_VVCYkgEOuWeiT_ED_sr@?XMISm_C?WskcBvyI:[UqmwESDdihC=XP_fwccxcT[UrFif@yCAMbyWiNYg\\=CpehjYvk?R?QW^=hdWGJiHmkcqWvDcbLiHEexAoc:aGE=IOmy;OeNUHHyGfuDYAhuYCYQeoCVG]uReROwIngdu=HsGXuUhrQg?abrETDyCWwehMdXgXV_t];fpGEv_VTaIKgeu=XocD<]uUkRkkuN_RGiwuEfYAVtsviKsiUW<EGmGwaOV:wBc[g\\]EvAcMYGUeTXcsFiWW?u`AeN_uwedIKe<eyLMSJcchURLECtOvTef;aXW=eDegm?whisFQvUQI\\ecJWFe;w^OI\\UWkAf[sBdwS`QX<mIowVqEx[ogI=CNAGI=i@cETEV@QdwKwiSR:kxUohyeV=YSDcgykWZcRisBDMGrMVVqVk]dIkd>UWgcv^YVBqEFifgQDj?c@owfMUX]RyYXlmu]KtkaxGeDr?TgIB]qTYMS\\YtkcdXyWGGI?IyIcXDEBmevbaF:_HhKHGAx`_Y@EcjSSWibjyRdgR__XAGDw_eYEe`EExCwMQg`wDKodBIG<gFCkIKOCxKHF?yp?SaMcVKTSwdREcAEW\\cuB[T_?iL;gDcyJYs>UC;oG=?DCOfVMb:ccZKSLEBJETLIBNcb\\=cnKG`eDbAVLUR=CG]]DNsG:GujOBZUGfceeCTnaU=WCbecg_WPmVQiVeiXa]tVQv;MsKErw;RokSwEdOaXOYeGQx^Wt\\ICnMvgIrKUFJetKsT<SF_Pox`NdlQ>HVT\\XdDkqiVOLlAtPlqUslpMttfdN;ilPHXODUOPlGTMSGnOOeFgit>hW^pjynLWptVoFpmOW^Q_`A`xoAb\\qmcflD^pEQ[RvxXAuUikUWlwi[tH_Ch]otNkDs_umWcmsiPWTx]eouXuuyWuCqSrWCCsOYWwgOcdgifG]uPsd;asbKYRaC_YE^]dVIY;kfnowr[VfeiIYU\\kw[WcQoTx]etQeGeIGWVmqFNaGAytdMv`YE<ohPCWfQrg?IxoFYmYoseuahCmf]Uyk;hbEimEg>cV\\MeKufktxe<mp<u^<uLQQM`lSQnWQodTT=hsw\\PRImgQuQARMUmKdob@X^IwolpCyv`ekkUu]EoolVTUs`qJPMpTYlkArOAUneOGXtClnp\\uZTuRmQ>YunHV=pUPDlphOtXVpIl@iwqhRZ<TjexRQnEiK@IoOatbhOVIx@IkQAnkaLXEwZhJSUSCLVHLwVqQ_XSmYlGhPiYOMmwDIKolSbeYKXwUuL`\\RNYl\\EJ^lTQEkalxfhMspTjTsXLNrtRglUbuvhEPNUw<DnWHKKAVdQKMISQQJ?MWtAxa]saaU>@Xe`WPPTCTsImNv@qJlOGEx_mklYVq]Re]u\\Qk>lwEekY<tolOkXRPymITLDXRdxjvhLA@MsAp_pQbdyjpvvYJqlML<r`<Kmmy;UUVanAdWxdksuJ`au?HyO\\vXYtZyTSLOQllOMYjpx^<Ql`po<r@pydmve`mrhN^eleEkwDSmAvlTWVQV=\\TyymrhYSUxHXv\\yLJPJVPM]hSi<lPAvkUk[eOx=OoxrkYY:Ly_`jYptRPlgDT[an]aTQ<oEauYDKtTNYLthaMKalHPsQHPiPk@DK_MooXvBdsUuLTtq;\\MPTtcmo\\MSalvkqx\\EqK<ulEsnDyGHU]Em`ljKiTUht`Aml`LgHx;uNHUR_hNFXMjiVdtp]lje]RVlOaqlRQpwPooDQkEXyMvutl[TJxiVDutlLlieo;XqEPJN\\y:dOVuwR^iRXghP\\Cwa;fyXatvP]QFq<IdNGZo?axgt@O[J_iLffC`nwH[o>Sqh_Ot]eFJMFHiwtUfH?WDkbX_FWGI`oxbyrLYfnAWKADHgDiOW;eugIc\\KU`MelMExavL_UXkcfuEF=ho<RalwEdtPpy:Tymqsotv<=S<MloUjciLhywTYU[eSQuqYLwPlLu@X>TWlqUXhKO@wm\\MhyrFqvWqqhQQVexv=QiTjv\\MsYN^DVx`oFyr=Xq``uj`lMYw>eLciNieSXLXLaUKhsEMsVXOxEpiXUYPl]IrcimRtpBESrUl?al^xMWlsi\\Rc\\UhqURUxsyqkmxuPPFlTMhXeYrOdp>]kchWLXWKhmrXSUaNYHNuDstalx`RoDk`IXaAR?TsImNLeSlexBTRY`rxYjcMkXunO=ViLWi@mCEY\\Mk=]j_YYLtYTqJQ\\kVdLsLvqHnuUMw=wD]k\\UplyK:@K[pLeEkKaJ]xjUXNjaVepx_ewi=RoTRcht:LqOxqWYjc=jcqPXQL]`oDLkOekTQV?HTq`oMtodDjL\\kldmeqS>@WFDpGYTTTMLqUQxLoYV?aO[yMZdLyMwIMk^USHUtGeXfDtLMSNtYTeJhN]O^a<Ntdpbx>o`xttnjrHctYnoq_Ma_\\Qlv?pIndG?oy@nlhlsPdOPkb_`EAa?Gi\\wah@asPnwN`rocIPw:^mYQqyNe=fk?yr:Nl@XdgHiJQm@?]^xuT?lgf^@yel_`hP`gFcEoxKqjSx_TAllhlLa]UI]b>xGwkdaeLO^v`v<ijQ>ysqkdHq[NdIWj]?oyAZa`sEPZyPwS^^sApXW_bi`efsK@nQPbJGdF>kJa^bFcO>^:fb:O\\:Gbfn\\S>kM@iNQhv>bdntbOocFqsna_^p^Ybn_s\\H[CGjHNar@pC`hXov>xhZNp?QjoH\\N@g?NhMXmTgdANtdaZvNsAPjrglD_v_f_gNahX^D_n@O_e>^ph]EIhAQ`bxrshalOy\\Nwa>rbNjQvcZ^lTWfrVjGg\\C>r]>mDyc`fbt?Zs>`OijbocX^f^Npb@\\nQx>VnOHcKoo<^pKq^d__BHqgnZ]`bx^iDXmiw\\KpvuhmX?kIpZg_uOGy_`_]^]QVdofso`nW@hVGehpgkVklCAuek=YqouOew@Qf^_E`_XpqUFYe?QHuqX]sGYEVMITFEcXmVAsfSUUWQicmTL]GQeGeETNYEkmTLeTX[vrQG?qt@UeBuYiMVV;slKbGQUgMulABMgcpwDPqREmh\\;YnGwSEdGgUmGU_UBN]gUQRocIEUFd]yUOyQKSJGX_Eh:cXcGRtGT^SUUEDroVbucgeHXQvp_FrMU\\gi@UicoXOMTB]WN_hdyXFoBougLcWBEsxuD<gW?mxe]eEOtTorI_RSMCEOElitAIDwOcP[CPMivCULADIedKaen_IKOI]gvD;c>]R][e_uu:QTPMt>uiiKW`?T=ihOue:MbKeejYFlOVMIdEsc[gerMitoBFMURoy\\oDO?IteGSAs^WUhgrgiEIKtVyvAogDOTg_uLQvCmgEcsY=TgaILesK]yxCvwivQkCbexAIhuisbavvOrJqV:uEAkVTIvGCiGKfyDpWhP<=sBDtYXSfiMxdsGLUvIO`uRdaU;lU;YUQxJqunGitFqkV_fc?g@fo?imv?kQq_cFiKndrPpuOL;X]QE][dTYvriy@mgE=Eqsu_[v<kdVwURKTWqrQoINOu]?IZuDFGIyMVLSScgiC]Wsiy=IdC;RrMBS_xY;ENcFFOGvOrJMWDEXRgtoGcZWvokBgyfDAFgEiucDYAxgmrXydnCFc_w^ST[iRg_u=CrMUEiav\\qI=;wogWL?GGitpEcQed?_d@gvNUdIKeOIG=aDWGIPcvrAVWwDCMi`GxEMYNQEKWYHGep=EqsFVgFQQXDmCWyeRabhaGkCbVoVkoCbitTWycUv<uSXIx;OH[oeaURNyI:cW;iECuWleCrEtTSfNyEMGTeKXrYTfMsg_VLkY:yTWyCWatA_dLYgMWVRotxAw]oS<_eFEGGSGX[H=qreev]uYiew?msy;rJufemfRwHUixW?yc]uoutAGf:oHxIe@qGw]uL;XtWFPLPFaSkPS[aThTmh]yoyoTaVv\\n\\YQlHtDUVX]PwDlj`v\\hVdAVmporiy>tPqQok]JXyqduYVHLDLy[DwGISy`XbLyYhkWYUodJODsAQxxynYXMMd]h?u[ollPwUgjbhod^`aHdo@_ZWvqI]GwcQ^\\tInXhnuYdC`s^^emOk]hvJgt@fyKWnWfrvXfO^vCFsuYnY?nCVoAgwX?f_x\\LHcPPde_^T@xAF]vNfLHw>O[PoveHc?y^Fi`rNfLHx=wnk?fLYyMFcxqtv@`<fpon_Cva<fhD_pNpinH]PIeDwkO@cfXn=PljQZYFh]g\\A`bDWhPHgaps>hnQ?eIAwe>dPpG;h;wit?HPWWWebjsUCIF\\]tJkVEUboesMCx:ssCEsr[TN?gkMDkyFMuFAKUlaHDEE>QSu=xxqDv;gTEFDOyl_tUCcbsi:_glUeE?glOSLYcL_EJ=WOktjSh@_vkwTAKbXEs`eesArCEsZ]TbOsigwL;XD=XkwGcKyTkBcEtDaxEshtODO?X]ky^Qw`MDwIc[ec^;RnMXC?YKMUkYC;YLrtOpPSQxQlPk?tKpdscDRwAUHyoAiR<`t^Akn`lYpyBLMZDsriKQLRbXSKPnd]V>TTOeJB]N@<J<\\P:<j<PjKyTZPsnLN[pR:dpcDKOaUY]rmdJmEm^LPd<JDdj:LK?<M<@[ZGuonZ>NaKfb<?h>Fl>?_JXtT^jK?nBHf:QmtPZw?ZW_cPPy@VZbnn<>fJIdvNg@OaVAijo^GHZLfkkf\\QI`aGhegwkYcMG[VIcPwnXFcfIw>P^LghaPZExx]hgPGe\\v_hYf`g\\s_mEwtaIidIijobkorUIm_xliYsjGx<Y_^nfVPvjxcKnfUY_gatgQ]sfh>Wm\\_nSYfqhb?Wmgvpphf?G\\pXth^wxWv_gqnHqTVv_gn<Ho@WcPGedp\\a^rMQgOY`BWtNnlGn\\ShpDF_@wkPfe?v\\hadfFtQfl=Oc`Y\\L?q?YhGF`aqxSnbS``HOkO@_cXd`FmhVuwanufgjG^h>ZIwx]^sCHcaxY;RMSG`OYUGi:GHYKC\\ex?sfKehlyFO_ry;bT=RTMbEOSZkrKCV\\WFaMW`cr][tB_Wx?WQGgnQHmEC@ixI]WIoWcGt\\EUBqhTeVMkY<ccvGG<eWkYwUOYEWcE;E`ed\\ICQmgfOXmIex]Rd]yLKhFwDsAvQcCiGFomGBSWXuejqylMgYKsDwrQ]UiusJSTXyGBgB^Oi@AUmmY=GGIwYj=wV;dbKy]CYAwWMUrpsuokfWCg<_iKMFVyeVMuVYW`uRhpj@<Q;xqVMw@EOkuU\\AOQMPoESk=v@mOcEy@hnrMnoYSSPQ^QJPyqI\\Uw`mY@mTuUIAnOEt:pqHDNBUX]MwVK:dukxVpekK`yxTRPaqxHvcaV:euELx=EtEauQEkNtjJ]nt<jpQM?iP]MTnQwHIkmEOEPsCuQ\\`X<EUtPj@D[RoooG^SQl?QfG_\\jwoLajbhbyXcZPe@wjiNhtqjC`oTNo_nrifkSN]nGh[>cpgnTHocvccn^H_llIgl^eMOrI?\\K_hHIaO?njWl@i`ji[H>adabnxmN>mD^mPq[gh[C_o]odCHg_y^oY^=?ec@Z_F___dHyfCyuqg^vihFXfhae_Ysbiho>_?qsIOuU`a?IwD?dhoqshqoVwvnyAq_CGwFxhpWvI`tUSLsE[sXUoEUIXqyslwY;YYfYbMoh<MtYeiECEygrUIxBgds]spod]_hqcTeYXteYHUFQsXqwYIifcwVx_EtGusKYjOg\\ux^uu\\gvnEGtEtksVOSrgUgkiTGUEr?wtOdtUXWcDGuHxkGuUwDOVMMHgsgLASPuT[ewxyVpMBa?gWeYgKf\\sxo_GqkWiUBgywJWwbaUGoIauCoctEOtD_vYCiUWVrIhSGgacsYAucubqIhIKE]wuS=tpavkIcrAD[yviWRgss\\myXMxnctd?ylUGyWgswSeUteGHXAWngysCWSgbvuIlQGaGuBEXteVdSsNwtRqSOUHcSxhUEuYCPWyjIr^st]scyYTVQSakgLetUSBMGxFisFeSMWTNaR>]bWeiUMRRiSwebPmtcCi]GrpCyGgsuGt?qB_CEtAyBYgvyTCUB]cdNSgp?xDsIk=YFqCLQX@UVmWT>gVWYgHAb\\kDGoHISgiqtViSOQguUExUgw?yWISegGgEYBXWoaRs]O_YPtmvvhuXQUGqn<iLHyjP`uviPUux^`L_PStPYRXr^uXLQuN`nKxoqdohUk]mWcUy`qmdLLREWGqJCtQgqQAyQ\\yXipxTlmMlknMvMQXyDpG`qWToXiVhUw>\\kgYmUIvOIQDMNq@YnmxM\\MMMXsYnFyUYiu@DxKMqPMmd=wQyPsiuFiVdhLOHQv`kjama`qFxNhodn_ke_]`PvVwveVsRFoIXgQqbTQlhh`^QcEhnnnpt`mINlsi]GYqhH`Gg^<PtXq^B_y@PxhWkYWmm>]Ye[IYDYvnYSPEweOuLCXlwWxYbr_T\\oCrlkHYS_qw@]V[YYOEmZYMGApsYuX@qrQP@iLOpvFuvrmUXpoXxR^YVtpscDOQAM`iwVTNdmknYNdEyGipAipvhn;AVvmmAQNXESpePhHoxaJEAMWELWxN]HtNhwStWWHslDyOXqMdJN`nllNoppWEqW\\QoissYpA<XKQUaIxjARidxsxWiaPWPnwhP^isthVuEVqIwIpwPxxl=xIUtRHykdwvQqVTVS`nMhsNuseIvfindAqeLVUymFDPSdol`TvasFyRgMW\\XVoioQPS?Isb`NQQqFlQCyV_HYExmGpJw@wAQQDXTMQl@IUwLq^pwDxteHny=jKPO;uOmhssXOELTkXURqrCppGqTg=Od`r>uTbmwi`qSmjZLlnLLBaNDLXC@ND<J:<J:@J:<JdLK:<JJ`J:<L?EKDDJNPN=@TFLr\\`J_<TfmMb@kr\\UOuT<`ldLOnlTNPoDTTatkZPpk<TadphIKkMmbloPamapOrDJqXTNpmVTX?mStYvg`VODUuEwZmkPqy\\aLuDyAeuq<tLpSqlKlxxaaLWPLbapqAPM`t]mXsXyw`sits?uqBlOBUYPimoXKe`N]Ml>QsEUTqiVdDyfHLXTt?qsPaqEioguL[hrj@Os`vEhwgiVULqJPU]\\spDSOhoFqJLmSOAWQiKqTPvqxnASkHr\\TN^\\oJmQk@Wsdxa<WNQO>]QLUMHHR:XKALNwuotXL_`QSLm:ekETJ]tRNqPP\\Lv=TcLKlDuMLOVMw@mm;MkBxLH<QwiRgTP=EovTJUMkPYNBAPadl;UoOMk:aPxDjEtjy<potK<DwX`No<l[hRQMk=`kc\\TdYVXLjrxTDDJVtM\\@OEapEyJdesa`tp`lhdOkekLmVwhvA]xD\\X:qO`PMtHndDqZ`XlEjdEqAxnQ\\UiusJ]ntAjntkJUTX\\WgIP`qrO\\SNdukxFiBGgc]KGGku<Mc@oCbahEyUVcgFqsU[ffEfCwbi=Wb_Y=SCDeivqY>iTlmu>YFNQgs?hBuG>edVCdtifFeeI;UEiDBcqwqrNUrMIW^QJtEyj\\^Uvd>g\\bAjTwbbPdwnbd`v<XoLHZnwrUPxGF`ae@QG^edV?b?sv`OGvWbpUhF[EsMRcAhuebAiv`EcKQfH?wTib`;WRwrA_U;UycaF;gVMeH=cgicBRohYCI;KsnISZobB_yR=EAMuwORkGId?BcgV=;iLOfmSc_ghN;Dt]GLOrWOSIqF_YxLkcg;scksOUsTcyHYIMaXMGEd[UEgHmshQ]uYIGyWRPMIHQheoBk=xWiSGsThwcf_Y\\aWrgSnUV_msOsTvSuk]UC_ULAi?qhxKtnyr`igROBmUSluHPCsrIV]mu>MRdOhpOxGeDEmyTMflgsOUYwasGGhPaDqODwuiggXYkE_ehmodc]YXMFymhQYfTCHQUcO_G_aGUSXSSGsMIHChouCbqydowcqseYCvQhsqwXKroic@mI`WeKiSSqb<MdGKYo]uy;B=OIYCxXgD?mCCWfywfIQeaYyGMgl]i_YBZqhjSisIi@_YdcXxuCeAsRgD_cWosVaYflIXTuR<WseoR^_yaqCykvD[DOsTXaWngwRUsn_hqmel_sjCUWEwaibCSWqsuDwYKyR=UrXOgiKbhUhGqgDshjaTe]rAyI:yS;qcnSUSiC[YH]kVkIeQkRgyerIwS[uwUbo]BegvCisXmgeGyOwTW;Xw_g\\]EVAwbcDIuEpuWeOIQeTVyuhGs\\IxGoWwQXgIGCgdpahAcYisEo_fbIGyKWq]yhIYhUVmMEVAgLGVK_iOMsy;bTwBMwgkoyk]ysUcDWBgCgY?hRcEi?UGSIKGXggvNIwWysSUeQuHceXOqTbKywgWRWujCgNYHwksIMRAqediHCgeyQUVQbOcFS]Y__tFocvqipMYkWiVweBiiSisCIHCAepUuYmFhOTXgDeqwrSsl]u<]w]OVY]dQqXXuS_IHCeFXMw@UWnsvKeHUuuFGvNcynaxy;bAex\\YeJEIj;IYudigYvMHsOWmyFy?vG=CDuh\\WeauFIWxYEhmuTlgyvaXZuvfWv>mRTaU=WE]aW\\IhPMVWwsMEYriw`igUeVP;I]gbiWEwCI_gdeoVNWv?=y@WwW?ScstrAScIUsgWv_VekWcEHeUhMac@AE]SDXaW@Ctt`O\\\\yRtpQpM]UXSDwJYOGPNElYdiTVxtrasclW[TYsIMAAkdERnyL^uo@iy_INOAVEdqaUSPXV`lQsMqUhwUlywXqNEscyL;\\XiXQupJXAxnASeUoKqMWYUPHo@yjP@Q_ivDUsnurO`SAyMGElMttPDYxHuSpKSdxhAyS=oSYmdILCTwl]NOHuuPvftXfauEXvKpmOEWgmWQeKEQq^mRmHXNTVyhPhDtMaK_yLGdJeYxrUp@qtOeXoEq`HQTxlFmqKYYTpPYhnYYm>PLcURSxwiXM]@yfyQPdPnQlLYoJQvYexXuNNmXhES<QlMPSAlLltTipnrTpkTt`xndirVQK\\HSG<RR=VDaUFppJ<NLdr><J?<P:DL;aJJ<J:<Z?^mnpnJQ\\CY_DXl?IpUqnZO_LhghXbOVeoIcBapZFn:NuBwblwcUy]lvj[h[bpvbq^UPlGYt:il`W_v>bRxcLOoRfcDO`Lyj:V_wx\\=He`He;wfc^_\\>jL>oL`p_YmfglSvpSo[:Yo<ojAW]sofoIsrfrKw`Tgm@Qk_O[>Hhfiw]ffKOfXagtp`d^huVb@Qt:Of@HuTV^q@cLAnJPuJg\\@?tWQqI^nT@`KN_M>vp^^NOndNr^xtRHd;>]x^ZKg[>_\\BNeZVrRPuBOt:ikv>mcOlaVc]^\\;NwG^cJxrRH\\O?sT^b\\i\\=A^[fbJNnCXrK``OGZVOaMxnGHckgc=Xn\\QZrpp@ojpnm[`nc`bLQr=Ht?`^fNnOWxaVd`y`bP_:ieFW_KY\\XGjA@^\\VoL`[sV\\A@^:A[=AlLgaCOnD>^P>knno]Gdmg[e>MowO[sncXUusJKTDobXGv_YhuWD^_Xj?d^GQB]pjPT:eq;MWG\\on<PIttiDpRPXuUL@]LwARFDywYJbmPwXrO]t?LyAnuZhx:vq:WrJpuZLVEQ@`m@dxA<o?XRJxT?pJoeXItTJQnELjDTx>MTWIs?mV?mRS]o<hLCej^HK]<Vh`qCXnZIk]Lv@MMkAJ]\\YbLXxtshEvhPxEuXyYTi`Rm]vH]u`aPIaLCEPkUSMTTieopqVVhvLXVW\\QtiXZ]sOXsEUYhPleaoSYqrYWPdQPeyj]Ys]mUmtpLtoEQADknQOwmKOuUNyuUhOYEsnqLHUurYWwLyRpvYDYShvthKCAWkDUxPPyEmRhtW\\MkQu^DytImdhsgpr]ItqxP\\`MbIsEDWGlrKyKS\\xexL]qWVYTs`T_Mq\\qkApsX]kLepTEsLYObaXxyp\\IVmdtdUpsmppxY:Pv[\\qcUSDLXw\\mmUpXuOq\\owurIPVxpmHQWQQX_QwSytk@XUTwlpoDTphUtdqpphTr\\QKdysMPepOaevW\\RuLXEEsXYs]iofYW]PkU@om\\snxNLLjkPvFYqWhjWPsxQViTTXaqC<XZExy@ypIUjivpmqThsR<q_`jHlMvQrNHV`uJyxVkqTpLxlmpYQqTURqeKQPoKQoV@o<hLF]KUyqHxPldSU=UxLVhmYexWsdXcyt[pQNPmVPJrxY:\\YqywCQMpuYMTWauNe\\yHeks@Lc=lsXmI`JUmw^pVPao]xY:lkgmLriMWhTbYRduj`xU;iwgESHIm[xnjmTh`UhuqkYT_TjvLRPTo<INIhXkmXqQTQaoGmY[<RmdwpALUuR>=P]HxktpuqUkdpaEMs<y;Xsy=j<=UsylgmythUCLwSUmc=Sv<RQQMdTpwhq?<QEQuFuTDej<tKL<w><L:`J?<j>DJZ<J?]JL<R:<J:@Ld=s:POELn<IoZUrD]s:PlcPSlDtSQNJ=NS]uK=RjQJWXXPPSXHnUYLqmPV=J^hW@Eq[Dk<Ln<<J:<J:\\jJLTR<JO]LN<m:LK?DKDBJkHZOBL;B>CR[;B]?B[[HD]B?Or>;Db]BJAg<;R>KV=[DdORMMD:ib:ke[CBZcwBKDo=DK?RtUBEOU;Or?Qd<UBJAW;iB>Qw@[BkErdORf]G:gRbcI@;BQmc;sb[;HF=BVORB[g<;c?KFDGfbOBBb]gsvCiEuwm]IUMxPetLsThqVuATVWEqeXtGgnciLQSbMgk=G`qfT?g<eUHyt<owhogoYiLcWc[CQOdwqrhixW_Ugmco]RoEv?YRbgemwWLoGGaiWMEoMCoEIyGhuGyqCDUOd^ou`?Hh?sy;b\\uXIeX[MchUxGmr>SeoEIhuWecgtcbtes=ysfmyHYWWoXhOspUUk;eiCF]GeUqw>]S?GyuaDd]tvksYMcviDUyXumT__rLgt<icrKUxuVouHe=uD_ScQEQ]ReavcofUUFYufLwSRIDmIXfiGh?xWWWDGXNUTEcsbGuEUVqwXimWaqw^SgREW[ir;;YMuGYivWYtGGu]kVNaYHyXFkWhgWgmbpev@efAubH_vustPWbyYguMUoOG\\Ue`MVvYSPYv;?Ta?TaWtQIxUCgwaHqWUCutE_f>EXqWYyqcgEy@[TeAS[qt@IErqvb?ytaHdaTdMxpsU]qxWyI:QvhQtN=XLuEiOxEWug_cquSgQg`eDVSwOOcvWSlsYm[hu]xVOrBaVvquxigeOXkoyGcRyQTbcxh]ePCfceHWGGySFmSTMSCMSTP[i<AS[cGqYyGWiNigV[sncVDwyAcHtYuWyhjaW@UtC]UrWT?AIwSsr]SGuxBKC`wWmkg;QrBcVesY]KxWeUkgcdUWtSCxYh^qehqHhcGqWFW?yCurEOgugXaobEKrD[xrseO_iy?Iy=iVeE]adb?ws;yIUhUYYUcuH_TceuOCbGUXuUTnqTaOeVEtVqhjIihQClAhvicukhpGHuCCouYGkuR[TgyWuSubkGisHcwY_eElqfSYGqqgbMieqsH]dYcXQkRCUIjCIpqUysX?EIHqx\\gykUdMUW_eC<iYTWgaOWS]TFQt>Su\\CYUWTYcWcMghItnEdEQWbgG_sCswcOcyUOwiSYHpuOhWgDQjUQYXNyTUeHwueNiPWyUpMak>]RAmX]AoRHMjYWa\\NGIq]XlUEYSXrulOd`TitWCyW@ayITxMhJ?YsKxcHOaYgdFhphpk@X_BpfQOqNHn`OhEXnKggmvkkyxqWqNqvh`n\\Ptcgr]ox^Vfk_fGicu^p`Ak_HaVvsThuVWu<o[Nappxu`fcyHliOfqi[tQtLyy:fuxI`hFubxmM^hVwr=xnRXdSPsrieWiuLympOeVHgFw\\si]uNpMI[tNtCPpF_dLarVIeb`\\FGvvyaCiuyhhUUEeTOWv<;v_wcMSywOGoEuLoDoMSKeYG_gUmvqerU=dPOrqAcIgyw?EkWiOUFEsCXsrmOVxQroYuHiSqqDP;e_KCmAuFqb__UdIgTeGmMsMAr]_yWiuXoTqid>QV_AS;er[cXn]ytaeVOSwqh`=GDexKOTM_Su_XuisTcDtaD^wrYEEhwxuECD?dtQf\\WWFyDnuhvqx\\qwT[C_ESLehCKYfAh>WxFquXqfbigHcdc=dLCyVgua;ssaW_mihWX<Iwr;xd=ygivW_d`qgD]hD;U^gcmaGrWU]ASkaxhoeGAedmdV?IyArUmCqGVdIxJsyT;xj_ypQg_ccKQHcwVdss>=h?SuWirGqdSaXQeHPexvGyDQtEotUEwJAs[_eyWYqeygHOq\\snmo`huNyogqptentdsEauL<sgIw`YqyTNwEqMHmIyPvpxpQooyRdtsZhpvYQkutolrCPV]LRgioJASKDVOiLiLQ\\UxftWhXQEXTnyPp]n?aOGQQZ<sK<N:<S:<JKLT:<J:<Z<@b:FenVpRnjMPZoPa]Aboqq?@j<nbNfhrGpCAZZF[ZB:;:Z<L:<J?AJJLj:<lB<J^PJZDk:<KDTl:=NK@R[Dn<AK>QJ:<ZJ@^b^Z;`ZL>Z?OZ>@jK>b[``DFZN:<NL<J:MLBMk><JJ`J::`mGpYAywvTMdMWQlTIxMOEMxPooQwVYuCYw<`kbXxlAwHisgijEtwO=Salo_mppqXfeopPn\\LQWxPceuVqXemwIxY:xsVijxPVUHSwt_?>yPhnx`mPH_eYgFiwEWvpPtPxpgwdy>xlp^UV]PnvhQbnVlhH_xh^VPvigs]F[MIsCymyWhtHqp_r]>a?qhwpgEHoYOrDYew_rpyxjvgA@eyAZ:ywRWuUWuaX]dGktpvSYeRAeqWahpatxtOoex_fYi\\rnxWWlkgaQicbhrEQlfOxqphGiggng]owLolaPvjiaV?vhhb@Iev>]JXuUgjxPsIXnkAiM`]ppoRowsgiWIoIwgW^swyxaF_yNxwi[Y``oiwfIckgduY^oXh_offY^hGhfXfgid\\ws[Of^YfCnbkxjohd[yxonqnNxa_feqvIIxPaogGnWN\\oaeKGrDAqnIaYP\\Ny`Q`]TXcOymCPumHxUYilVdqP[CGheH\\vqcOQv[yxy_tUXnXOqhHuMqnFxew>_HarVOexoqXnZc_i_gllxwtipbithQrxxZ__ywGk;Oej_x?gtdNpIQvUiwpG_bQsOPfm>oBxkL>hsHmYxZ=Vg\\wdxPa^IfF`loYd<uuEVqqdWeRdcScoBrmYAUciohqmHHoHOYDAOhesiWwxveHHOSxweZaU\\kgauFLGhRGGAuenwiWwiDWhDoSWMTSAVdWdsirC_y>gdamvrEwy;RuuSCuViqw<UDhKgeEvY=xfsxuMUwghhOwlmBksUDIS<yV]mwI=bVQRQgWdieH]yTwy;WUUKsgySU]se?se;IpWyWcgneUeeTN=GcehASdkat>gcq]SFcrvqsqYvgiwQKhpuhLmvKgtIGdCiYimwpoDqYTAocbyxoGrWyUvqePOYuYWhYGKMecQfMcDrYeuceuIxpQYpgfmgYmQhLWIgeVFQGlEIYEtgiUWaeVeVBmtNOimAGxuwdouhOuiaDQ;EbcWkCs_CrScEKWdqUYUmF`wwmmCvUxJeUVMHcMGEyI:sXPyI:cY=sT]iw;eTPOse=wnyu>eWXAhuyI:MwW[IugyxocOEFjgHxuXhuv^iwTefviVuYXSKbkMtgAW;]H?wtpOxuGxp]ukAtduTFqs<AiGOhEOcpAwmyCo]hSCHEIXKeGLWG;yX>oBXoHumVasUDIfrii_WIPCFQ_F_gd_qFsWty;RXKRUIyD_dNwEmmcfUfugxk]EHqhMetbWV`Ocokfc[GjshyycU?YbGW^WTdGcosSlqsU_UkgxouVqSyw[sp=HQCvRQrYmGIuEQGxqmgugcwiu<urDCdheSyYTMgEmYSK?hT]WX=GEUYEkt\\SvBKtlec`qi`qyagbYyXjuTeeY`qxOeEcMW]wtKISrUgLWirGYsOSJOyceXaITvqeOeiWehYGGhEXJKSkCs_:FMuXpGTvyeRIyxEexsrEEvpmX_YEQgV`?tLYddIvbmWUst\\CVvQVjkvy;RvqrMwyquxy;RNWVN]RF?YSSFmCHxasucrWqtd[bmWrFiVnAw_aWfauisYHqE?eyLyI:YUwusA]YEQU]OhX?GgEXo;y\\qCFadu]xTEWGcEEIUNMDHstpAFveT[qigoiYSvtsE[cWUWgIosQsxXqt@gsSsxgoRL]yd?YPoEmYskETkkdiCBa?gVsXfSfkcsvqs`_SpgyGgrvaxAmy_eiJWIUusfqXmqi`ixEuROyI:asnQXUWeOeXdGDfmdCESyeVaAhMSyTETKQVGsbaSsmyrZIBmmgqgewgXoEuCUgeKfsWuhqYUSxGicR?wpYdn[yjIbwucBohPiT?ohX_XcOevASVcWgmwcgeHMg_SC`IY>IWSsfCeeuIIYaYoiw\\sDSyVpqfIisy;Roigy_XlSIUsH[UeleC]uedSgguH`ohZiW;KDe_rFmcKuxdkbmUymYSvquTiduYhhMyckrrSdTeuW_i]?iwwX<MWKOXMuY=yBxUve=ywyMUimG@mrLskXnAtpQHjslS`tWPUvC@kahmmxPshk=EuxESHQQvXnI<wdAyOXuXiuqXrOqxKlUpAv`qOKUwDQMt`LAEV`ULqUVThSQQMxLnmAQqIL?XSOtNyYxsDqp]S]AQ?qXwpSXPNvap_yPyhqv<xiujRiMuTMeUynUVgETq`UUUOuUkHtVqyshhPOytYDmqdRFmxWULkiqVioYyY:<wAmr@xwQxY:hxYMKntS]mVqYqlxKiPqO=xfdQ\\yl]qn\\QoFYm]hVliumTxsAQqdODUYUPXHLqUIoLEUhiwVePVLTcaNMapTUPEHPKejBMxcxlAiw`QwZYOMEJs`RoUnSpk>hUhul_=WoiwbYrcPkwYmj\\joeR_\\mdHmMmy_Lo_pND@QdllVupUTkFEp>aKctvSPlRIqVuPSTx?MnUePUPSJ\\t=ImP<J:DL:ML:ML:<Z::::::;FC;BZ::::ZDHZZZ>::::::::::::::::::N\\:>Z:>::::::::::::::::::::::::::::::::::::::::::::::::::::::xqya5G\"\{\}-%%ROOTG6'-%)BOUNDS_XG6#$""!!""-%)BOUNDS_YGF'-%-BOUNDS_WIDTHG6#$"&S-"F*-%.BOUNDS_HEIGHTG6#$"%5KF*-%)CHILDRENG6" C\303\241lculo I T\303\263pico 9: O Teorema do Valor M\303\251dio Recorde o Teorema de Rolle: Deixe f ser a fun\303\247\303\243o tal que 1) f \303\251 cont\303\255nua em [a,b] 2) f \303\251 diferente em (a,b) 3) f(a) = f(b). Depois, existe algum c em (a,b) tal que f '(c) = 0. 1) Use o Teorema de Rolle para mostrar que 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 tem exatamente uma raiz real. f1:= x -> 3*x - 2 + cos( Pi * x / 2);

NiM+JSNmMUdmKjYjJSJ4RzYiNiQlKW9wZXJhdG9yRyUmYXJyb3dHNiIsKComIiIkIiIiJSJ4RyIiIiIiIiIiIyEiIi0lJGNvc0c2IywkKiYjIiIiIiIjIiIiKiYlI1BpRyIiIiUieEciIiIiIiIiIiIiIiI2IjYiNiI=

Vamos tra\303\247ar f1 para ver onde as ra\303\255zes est\303\243o localizadas. plot(f1(x), x = -4 * Pi.. 4 * Pi, color = red);

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

Isto aparece ser precisamente uma raiz real. Vamos pegar numericamente o Maple para resolver isto. fsolve(f1(x) = 0, x = 0..5);

NiMkIitaMm5jUiEjNQ==

Assim, parece que a raiz real de f1 \303\251 aproximadamente LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbW5HRiQ2JFEtMC4zOTU2NjcwNzQ3RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnRi8=. Como verificar nosso c\303\241lculo num\303\251rico com o Teorema de Rolle ? Suponha o contr\303\241rio que f1 tem 2 ou mais ra\303\255zes reais; dissemos a,b s\303\243o ra\303\255zes reais de f1, ex., f1(a) = f1(b) = 0. Depois, pelo Teorema de Rolle l, existe algum c entre a e b, com f1 '(c) = 0. Mas f1 '(x) = 3 - LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVElJnBpO0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRidGMg== /2 sin( LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVElJnBpO0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRidGMg== x/2 ). Desde |sin( LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEoJnRoZXRhO0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRidGMg== )| < = 1 para todo LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEoJnRoZXRhO0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRidGMg== , n\303\263s temos que |LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVElJnBpO0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRidGMg== /2 sin( LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVElJnBpO0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRidGMg== x/2 )| < = LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVElJnBpO0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRidGMg== /2 < 3. Assim, f1 '(x) > 0 para todo x e assim n\303\263s temos uma contradi\303\247\303\243o. Logo, f1 tem precisamente uma raiz real. Vamos tra\303\247ar f1 '(x) para ver que realmente isto \303\251 > 0. plot(D(f1)(x), x = -4*Pi..4*Pi, color = red);

-%%PLOTG6)-%'CURVESG6#7c[l7$$!-#*eqjc7!#5$"1mAuW"y-A%!#:7$$!1(enI]THC"!#9$"2(pu:;?+")R!#;7$$!1u^@ZfCH7!#9$"1"flbM*\'p$!#:7$$!2x'*)Gp")RA7!#:$"2DMASV@8a$!#;7$$!27wi8R]b@"!#:$"2(*)yL(Q'))zL!#;7$$!2[bOMh-(37!#:$"1W7UL-19K!#:7$$!2%[.^N[&=?"!#:$"1ra*pvfd/$!#:7$$!1.Hf0%Q**="!#9$"2k%e7iBx_F!#;7$$!2yXvc(>-y6!#:$"2%zfxA>UoC!#;7$$!2E,eda0h;"!#:$"2M%GC)GUE?#!#;7$$!2scSe6*=a6!#:$"2$)4,C`=Z'>!#;7$$!23!z4WyyS6!#:$"2(=/*[@A2u"!#;7$$!2WBbBd'QF6!#:$"2W0RRfABd"!#;7$$!1oDh+`)R6"!#9$"2OUgpXapY"!#;7$$!2=!*p)GSe+6!#:$"1RcDs(p#H9!#:7$$!2m=_G]6s4"!#:$"28tzBG52V"!#;7$$!2<ZMo(*QQ4"!#:$"1&**4a#QbO9!#:7$$!2nv;3Xm/4"!#:$"2X(>$e+%yY9!#;7$$!2</*zCR4(3"!#:$"1d"G.7s8Y"!#:7$$!2=hjF()[.3"!#:$"1a-x;jW.:!#:7$$!2>=G2#Qgt5!#:$"2EfJua/Bc"!#;7$$!1Atl;P6g5!#9$"2PL[-(=bF<!#;7$$!2AY'e7OiY5!#:$"2PCepz@(\>!#;7$$!2EWDYi(>L5!#:$"2k*G/'[.v@#!#;7$$!1BWmO;x>5!#9$"2V9TB@f*>D!#;7$$!2K"RoU'eI,"!#:$"1&*)3+rX+o#!#:7$$!2NS.([cM15!#:$"1:3tPloVG!#:7$$!1O*GsaEj***!#:$"2:566$Q14I!#;7$$!1QQU2m>H**!#:$"16deN/MuJ!#:7$$!14Vc70s/)*!#:$"2.8`M=7VZ$!#;7$$!1"y/xTW-o*!#:$"1%)='fO3iv$!#:7$$!1`_%GKodb*!#:$"1m/4+iG4S!#:7$$!1Cd)zA#HJ%*!#:$"0:*RT6!RA%!#97$$!0[&pTWS-$*!#9$"1MM!)*R')oR%!#:7$$!1P_Sbm^t"*!#:$"1310>0"G^%!#:7$$!1;,EiF24"*!#:$"1(=K0#yzZX!#:7$$!1&*\6p)GY/*!#:$"1u8[P"Qpc%!#:7$$!1t)pf(\=!)*)!#:$"1\q`.b.qX!#:7$$!1_Z#G3Td"*)!#:$"0#Rg1#eqb%!#97$$!1*\n)\^W#y)!#:$"1-n^6['*zW!#:7$$!1[-"p@\"\')!#:$"0<$\,gAQV!#97$$!1'*H&RG`e^)!#:$"2:@=1)H.QT!#;7$$!1Vd*4NdDQ)!#:$"2`%yqa-8))Q!#;7$$!0(3RDJ7;$)!#9$"2/YhIMS$[P!#;7$$!1'*fy**))o\#)!#:$"1,X))z%3/g$!#:7$$!1@6=uYD$=)!#:$"1**zalT%fW$!#:7$$!1\id[/#o6)!#:$"1emctzi'G$!#:7$$!1w8(HA'Q]!)!#:$"/(RfE$>CJ!#87$$!1-lO(*>&R)z!#:$"2CR_TL2/'H!#;7$$!1H;wrx^<z!#:$"0TC5<_qz#!#97$$!1bn:YN3^y!#:$"1`ug#30fj#!#:7$$!0#yJzxu#y(!#9$"2300%3dHuC!#;7$$!1$))yC,7Wr(!#:$"1Wd9(zP(=B!#:7$$!1Z*RcCwgk(!#:$"1dw')**>-r@!#:7$$!175!)y/uxv!#:$"1B*Gep[G.#!#:7$$!09B^%*o5W(!#9$"2"GK3]NO"z"!#;7$$!1p_W6uR/t!#:$"2`"36_%p`g"!#;7$$!1L**=]q,%=(!#:$"2<Nhe[pV\"!#;7$$!1(fM*)oOO1(!#:$"2a[CS)[/P9!#;7$$!1HpI3lW.q!#:$"1(\YApE#H9!#:7$$!1h#zwKcK%p!#:$"2,<>[DRaV"!#;7$$!2Nf^q9mI)o!#;$"10Atyqib9!#:7$$!2l#RUmf(G#o!#;$"1@!R&Q)4'*["!#:7$$!2bVh;>cto'!#;$"2ywJ)>'[[h"!#;7$$!2X%*)*oTO=b'!#;$"2yQ))=J>E!=!#;7$$!2NXO@k;jT'!#;$"21Ya#3^WW?!#;7$$!2D'RPnoz!G'!#;$"2xX$*R"*3%HB!#;7$$!1$*[Q^(eF@'!#:$"2M=*oalv%[#!#;7$$!1CeRN1sWh!#:$"2$ydnNP)fk#!#;7$$!1cnS>Dowg!#:$"2Z-LJm]7"G!#;7$$!1(o<MSW'3g!#:$"2XbI\Wr'yH!#;7$$!2&='GuG11%f!#;$"1L#**3hNj9$!#:7$$!0bR9<oD(e!#9$"28<nN"*HBJ$!#;7$$!1"[]a0IX!e!#:$"2F1)eg,wuM!#;7$$!189YR>\Od!#:$"1*)ysHGxJO!#:7$$!1YyjvsN0c!#:$"1e7B?Vc7R!#:7$$!2&yU"=hAUZ&!#;$"1@\AnAxaT!#:7$$!162*z%z3V`!#:$"1uAqKg:[V!#:7$$!1Wr;%G`>@&!#:$"0j)Q#GRX[%!#97$$!0fG`'=T_^!#9$"1-&[')*[*f_%!#:7$$!2l.!\Y/(G4&!#;$"1(*=["y6Tb%!#:7$$!1f22P(*4j]!#:$"14f^un3jX!#:7$$!1$[^w-HL.&!#:$"1YX*4;W'oX!#:7$$!11AB=$eN+&!#:$"1@i)**yr2d%!#:7$$!1HH")3wyt\!#:$"1$oU&4]YpX!#:7$$!0#e8rZqa[!#9$"2N=)))GL1IX!#;7$$!17(eM$>iNZ!#:$"1[ziq8GPW!#:7$$!1u>_@4-%f%!#:$"2&Gp=MN2iU!#;7$$!1O_e4*>CX%!#:$"1CYGENoCS!#:7$$!1ooh.%>;Q%!#:$"2vROhU?i)Q!#;7$$!1*\[w*)=3J%!#:$"2nLxl^2ot$!#;7$$!08!o"R=+C%!#9$"2`'>&y)3HyN!#;7$$!1h<r&)y@pT!#:$"2m5nB6HET$!#;7$$!0.mZDj#\S!#9$"16*f]$4V@J!#:7$$!/.#Qi3$HR!#8$"1h.()[U$f#G!#:7$$!2%pX(G*RN4Q!#;$"2Y"Gn!G*fOD!#;7$$!2)Q)G>O*R*o$!#;$"2NBW*R"oOE#!#;7$$!28\O%4O')\N!#;$"2Z?h]^$fz>!#;7$$!2Q9Wp&yK5M!#;$"1CY5bTMW<!#:7$$!2iz^W5#zqK!#;$"2_wl'ok<p:!#;7$$!2([%f>Nc78$!#;$"1$H`g-sCY"!#:7$$!2Ynke:y.5$!#;$"2ONi$>!*o[9!#;7$$!2/!*p(f**\pI!#;$"2:cfO([bQ9!#;7$$!2j7vOw@'QI!#;$"2bb:cU$4K9!#;7$$!1_.enNu2I!#:$"2iq&Ht)>$H9!#;7$$!1yb[r`'o(H!#:$"2'GDTS2CI9!#;7$$!1/3Rvr)f%H!#:$"2B;")4'Q&[V"!#;7$$!2'HgHz*3^"H!#;$"2e,9WQ[JW"!#;7$$!2bD,KyIU)G!#;$"2=fU5![5b9!#;7$$!1f@#))*zrgF!#:$"21"41u#f)Q:!#;7$$!1iIW9_?PE!#:$"01e#\0Wx;!#97$$!0&fD9@p,D!#9$"1)zON$4L')=!#:7$$!2v$)oS,zhO#!#;$"2%p6nsB\X@!#;7$$!28GvRYA%)H#!#;$"2n6()GuV.H#!#;7$$!1D<)Q"fmIA!#:$"2Dut:JEKW#!#;7$$!1p")yj$4H;#!#:$"2DE#p-*4Cg#!#;7$$!2Fh%p8G:&4#!#;$"10yOJI4mF!#:7$$!2/Ax\bK1.#!#;$"21VRGOYW#H!#;7$$!2w#)fiH7h'>!#;$"1%zQg2vN3$!#:7$$!1NCaP?f,>!#:$"2C-kh3Y=C$!#;7$$!2E/D)y<2P=!#;$"1YKt5^j(R$!#:7$$!2vD!Rh7.3<!#;$"0Nx-%QT&p$!#97$$!2DZbRu!**y:!#;$"2(ok38'=Z'R!#;7$$!2B\^7]]VW"!#;$"1"o5'z([M?%!#:7$$!2A^Z&e-r48!#;$"1ewk)=]&)Q%!#:7$$!1KN%e,q]<"!#:$"0$*)pZUx6X!#97$$!1_&RJxH//"!#:$"0*zLx(Hwc%!#97$$!1%Q^EFi9$z!#;$"11#>-#Qg)[%!#:7$$!1[s!R"oiea!#;$"1$G&3zyy(=%!#:7$$!16haeK)\7%!#;$"2v*)pI;g![R!#;7$$!1u\=.(R8z#!#;$"1n)))fXyom$!#:7$$!2bS/b#z^C@!#<$"2Dmu"**y_9N!#;7$$!1PQ#y9'pd9!#;$"1H'3fWPlN$!#:7$$!1'oK9qV(3z!#<$"1uf\x)QY>$!#:7$$!21+FY#f_S7!#=$"211yK"ogII!#;7$$"1$f4qFyeo&!#<$"2WKL0-$*)fG!#;7$$"2'=Y'yCG7E"!#<$"0r784O3p#!#97$$"1y#G!o'oQ&>!#;$"1<tkU_VDD!#:7$$"2t$>>)34lk#!#<$"2&Rb%eXYcO#!#;7$$"1c#>&G**yJS!#;$"1H/;9[Pq?!#:7$$"1vl%)o22<a!#;$"2#\zD_q%*==!#;7$$"1$HAk&G&)Gy!#;$"2:jLHgr'>:!#;7$$"1,)*R%\jS-"!#:$"2YOa&zcKI9!#;7$$"1e`xIIIa6!#:$"2[R4EL=^Z"!#;7$$"2Z"4:nDa%G"!#;$"2k?8%3%4Ne"!#;7$$"2;ZEN5#y99!#;$"2i(fNF#y4v"!#;7$$"2&G?!*R;-X:!#;$"1(3.t9S0(>!#:7$$"2DyD\#=dz;!#;$"2&4]NpuLUA!#;7$$"2l`\*4?79=!#;$"1eB.*=`ya#!#:7$$"2OThC5(R")=!#;$"2A-[z(*[!4F!#;7$$"21Ht\>s'[>!#;$"1%H$*H)3\tG!#:7$$"1o^[(GZf,#!#:$"1*RP'RUMRI!#:7$$"2Y/(**zBA$3#!#;$"2/c-fjeZ?$!#;7$$"1#)32Lz.\@!#:$"2LwIc['QkL!#;7$$"2)>Z9'[`[@#!#;$"2BrEnBB,_$!#;7$$"2tb=#R!p1G#!#;$"2;*GMbeIqO!#;7$$"1&R#H#f%[YB!#:$"2j0)R<1L8Q!#;7$$"02S%)p:"yC!#9$"1w0Eg,*=2%!#:7$$"1Xxe/ou4E!#:$"1U$oNC(y%G%!#:7$$"1&*48om5PF!#:$"0&>HtavQW!#97$$"2WCu;`mW'G!#;$"13>O7GLNX!#:7$$"2o0gv\1j*G!#;$"11J)>Z0+b%!#:7$$"1peWjk9GH!#:$"1[0-S<!3c%!#:7$$"2:oJ$Hk)*fH!#;$"19m?;YpnX!#:7$$"1%\<_RE=*H!#:$"/LAiomqX!#87$$"2jI.6OmO-$!#;$"1NL"[/6(pX!#:7$$"2(="*)pK1b0$!#;$"1M*pVbH[c%!#:7$$"1J\(GHYt3$!#:$"0pe*)fMgb%!#97$$"2Nug(ei=>J!#;$"1dlyt"[La%!#:7$$"2FAjHn(fgK!#;$"1)fMhG>5W%!#:7$$"1-d;(34?S$!#:$"1,Ac;3)yE%!#:7$$"1"=o8]?Ma$!#:$"1aAXO0WKS!#:7$$"0mqb">$[o$!#9$"2E:9rjniu$!#;7$$"2uJe2O'*="Q!#;$"1/Bw&=.uX$!#:7$$"2Y(f%f!3'*QR!#;$"1M![P_x.:$!#:7$$"1KO8^_-mS!#:$"2%3z];6QPG!#;7$$"1*G@jp*3$>%!#:$"2s$=9)\T3`#!#;7$$"1%*=#H6e(GV!#:$"1*o)\7&)RCA!#:7$$"1)\A&HlUkW!#:$"2s.bp>YI&>!#;7$$"1.J7Y\4+Y!#:$"1vZ]!Rh!H<!#:7$$"2vqBFOjdt%!#;$"2QNme(ydi:!#;7$$"1<`X7"*pe[!#:$"21%\yLptn9!#;7$$"1Ep=i[j")\!#:$"1P6(oBd)H9!#:7$$"2&G)>'*zoB,&!#;$"2=r-m8+&H9!#;7$$"1JF0PF5V]!#:$"2K'QT.E!GV"!#;7$$"1Mc[um$Q2&!#:$"2c.@>%pvR9!#;7$$"1N&=>hqX5&!#:$"2sXwr%pM]9!#;7$$"1RVy'[Qg;&!#:$"2HrCm$oK#["!#;7$$"2X9];O1vA&!#;$"1MD?oVWG:!#:7$$"1$[$p2w!>O&!#:$"2R5%y$zgin"!#;7$$"1@ot`)3j\&!#:$"1oV0pz&G)=!#:7$$"1f,y*452j&!#:$"2arS#H>1R@!#;7$$"1(\BeM6^w&!#:$"2.Cbh"f\LC!#;7$$"1\i@WCd"*e!#:$"1z%RxHdPt#!#:7$$".4EaL!=g!#7$"1j!oB.!\WI!#:7$$"1_<+TY\Wh!#:$"10vTpHZ`L!#:7$$"1/XRRd&4F'!#:$"2nD%)zx`&[O!#;7$$"1NTKDS9.k!#:$"0/Pujb&HR!#97$$"1mPD6BLNl!#:$"07(yTPiqT!#97$$"2vR$=(f?vm'!#;$"18Ei$z,9O%!#:7$$"1HI6$))3(*z'!#:$"1/yheRp$\%!#:7$$"1w0x))zKko!#:$"2&Rp8[0ENX!#;7$$"1C"GW4Z*Gp!#:$"1`wM**H-hX!#:7$$"1sc3+ic$*p!#:$"1Fyy5hrqX!#:7$$"1>Ku0`=eq!#:$"1,)=05SUc%!#:7$$"19$eq^Bu=(!#:$"1a?HMJ@.X!#:7$$"2%4MPG<m;t!#;$"1(o7l][/Q%!#:7$$"1iiWe@'>X(!#:$"1%)prqHH">%!#:7$$"1:">&)eise(!#:$"2u%ok_/`[R!#;7$$"1Ubb.G"\l(!#:$"2`#eT3*y."Q!#;7$$"1o>f=IcAx!#:$"11<z?]3jO!#:7$$"2XRGOB8-z(!#;$"2_1Nb\5$3N!#;7$$"1@[m[M'y&y!#:$"1()frJ9!yM$!#:7$$"0ojhk=I#z!#9$"1&41zJ"[*=$!#:7$$"1QDmVQ<))z!#:$"1Q&GH>y"HI!#:7$$"1'Rh6/HL0)!#:$"1@)HWqp&oG!#:7$$"1b-mQU[=")!#:$"2jTHepO$4F!#;7$$"1szlLYz[#)!#:$"1ADhw5j,C!#:7$$"1*ob'G]5z$)!#:$"17E(*p(3*=@!#:7$$"1J#)oGiO7&)!#:$"2oyQ(3Y"z'=!#;7$$"1u2sGuiX')!#:$"2Ne-ooWjm"!#;7$$"1;LvG')))y()!#:$"2K"*QC3**H_"!#;7$$"1feyG)\@"*)!#:$"2#*4&RMf8W9!#;7$$"1'R*Gh#*=X*)!#:$"2(>n&p#>-N9!#;7$$"1KHz$pG#y*)!#:$"1Zq"[7A,V"!#:7$$"1okHE"o7,*!#:$"2xakAs\%H9!#;7$$"1.+!)evIW!*!#:$"26re*Hl+L9!#;7$$"1xq!QU'Q5"*!#:$"1=E*>5eFX"!#:7$$"0:9))Glk<*!#9$"2X[xVBk"*["!#;7$$"1'HG)=Ii3$*!#:$"2N(p:@w>5;!#;7$$"0WU)[2yS%*!#9$"27ee][44z"!#;7$$"1kXNx*>Ac*!#:$"2us+7OjH+#!#;7$$"1)ome?fOo*!#:$"1&Q(R!\(=^A!#:7$$"16)yVV)40)*!#:$"2k;qz&odED!#;7$$"1N4*GmPl#**!#:$"2B))>`&49>G!#;7$$"1PL.$>Hh***!#:$"29bzaA\/*H!#;7$$"2Pd<B2sl+"!#:$"1*3](4:(=;$!#:7$$"2P"=LD7`85!#:$"2$\>QB9OJL!#;7$$"2P0Y$y.\?5!#:$"2&R@l\c*o\$!#;7$$"2P`uVo3W."!#:$"2$*>->Zj#3Q!#;7$$"19IS!*pK[5!#9$"1ELc38:"3%!#:7$$"2s@O#*ov21"!#:$"1[^S\h&>G%!#:7$$"21Up!)QCK2"!#:$"1&owHR)*QV%!#:7$$"1CE!p3tc3"!#9$"1kfEhm=JX!#:7$$"2s#et&y@")4"!#:$"1rEG[F6qX!#:7$$"2***z38+W,6!#:$"0-y_\%RqX!#97$$"2B<S/CeZ5"!#:$"1aPp:3TmX!#:7$$"1XBznk236!#9$"1)3+)HD<eX!#:7$$"2v^W^p%R66!#:$"1/],9?qXX!#:7$$"2G')[)\6.=6!#:$"1v>H$=6#3X!#:7$$"2y?`XgnY7"!#:$"1Vdxp`MaW!#:7$$"2")*='R^Sz8"!#:$"1%4xPc****H%!#:7$$"2&)eqLU87:"!#:$"1daAo%\$*3%!#:7$$"2Yyf7H<R;"!#:$"2y2J"=rRVQ!#;7$$"1")*["f6iw6!#9$"1D3X)=rRc$!#:7$$"2u<Qq-D$*="!#:$"2&>n/7=;iK!#;7$$"2OPF\*)G??"!#:$"2Ago")\Z*\H!#;7$$"1_kU:\&)37!#9$"1oY**Qv@#y#!#:7$$"2-`Df$4o:7!#:$"0$fbr*))ph#!#97$$"2%3YUcp]A7!#:$"18'oucfhX#!#:7$$"2ooBp(HLH7!#:$"1PCsqld,B!#:7$$"2M%=#z,&)HC"!#:$"2`T%Qf'f"=?!#;7$$"-#*eqjc7!#5$"2Vtd_&=sz<!#;-%%VIEWG6$;$!+iqjc7!")$"+iqjc7!")%(DEFAULTG-&%&_AXISG6#"""6'-%+_GRIDLINESG6&-%&COLORG6&%$RGBG$""!!""$""!!""$""!!""-%*LINESTYLEG6#""!-%*THICKNESSG6#""!-%-TRANSPARENCYG6#$""!!""-%&COLORG6&%$RGBG$""!!""$""!!""$""!!""-%*LINESTYLEG6#""!-%*THICKNESSG6#""!-%-TRANSPARENCYG6#$""!!""-&%&_AXISG6#""#6'-%+_GRIDLINESG6&-%&COLORG6&%$RGBG$""!!""$""!!""$""!!""-%*LINESTYLEG6#""!-%*THICKNESSG6#""!-%-TRANSPARENCYG6#$""!!""-%&COLORG6&%$RGBG$""!!""$""!!""$""!!""-%*LINESTYLEG6#""!-%*THICKNESSG6#""!-%-TRANSPARENCYG6#$""!!""-%+AXESLABELSG6$Q"x6"Q!6"-%&COLORG6&%$RGBG$"#5!""$""!!""$""!!""-%%ROOTG6'-%)BOUNDS_XG6#$"#!)!""-%)BOUNDS_YG6#$"#g!""-%-BOUNDS_WIDTHG6#$"%]Q!""-%.BOUNDS_HEIGHTG6#$"%]D!""-%)CHILDRENG6"

2) Suponha que um objeto ande numa reta com fun\303\247\303\243o de posi\303\247\303\243o dada por: 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. Encontre onde a velocidade instant\303\242nea \303\251 igual a velocidade m\303\251dia no intervalo [0,LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVElJnBpO0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRidGMg== ]. Tra\303\247e o gr\303\241fico. Primeiro vamos tra\303\247ar a fun\303\247\303\243o posi\303\247\303\243o. s:= t -> t/2 - sin(t);

NiM+JSJzR2YqNiMlInRHNiI2JCUpb3BlcmF0b3JHJSZhcnJvd0c2IiwmKiYjIiIiIiIjIiIiJSJ0RyIiIiIiIi0lJHNpbkc2IyUidEchIiI2IjYiNiI=

plot(s(t), t = 0..Pi, color = red);

LSUlUExPVEc2KS0lJ0NVUlZFU0c2IzdTNyQkIiIhISIiJCIiISEiIjckJCIxZkQyTHp4Wm8hIzwkITFOUkpaJVEmPU0hIzw3JCQiMU5weCpHKmYhRyIhIzskITFBdnUoW0Ihb2ohIzw3JCQiMDYjZXhHbV0+ISM6JCEwKXAjM0BVKUgnKiEjOzckJCIyWFQsPTNvXmkjISM8JCEyM283QVxOREciISM8NyQkIjBcRDBbbmtIJCEjOiQhMkdgciZHVyYpKWUiISM8NyQkIjEiPVphJnolKT1SISM7JCExPDwkXDAnKSlmPSEjOzckJCIyd2JXdilvR2pYISM8JCEyOCl6KFshNCJcNyMhIzw3JCQiMSUzKipIYm0oSF8hIzskITJAcVBrLkcoekIhIzw3JCQiMVBScjQpM1QqZSEjOyQhMVQuV0gnZjtoIyEjOzckJCIxI1speXlrWXhsISM7JCExSyMzSFU9WSNHISM7NyQkIjFzJ29jR28kenIhIzskITJDZjxIXlAnKSlIISM8NyQkIjFRMDtncidwJnkhIzskITE8LlYtXXBXSiEjOzckJCIxR010PyRbdGApISM7JCEyYWFoISlwRShvSyEjPDckJCIxI3AzMGtAST4qISM7JCEydSQ9VTdlRmJMISM8NyQkIjBDIlxIZVYpeSohIzokITFvK3lNKDNWUyQhIzs3JCQiMkdbKSkqKTNXJ1w1ISM7JCEyYGYiXF4uQ0NNISM8NyQkIjEnW0BYU0AnNDYhIzokITJhVDhScyY+Mk0hIzw3JCQiMlZoUDNHKlF6NiEjOyQhMlozX1toJnlZTCEjPDckJCIyVTMqM3RjOVQ3ISM7JCExZiNRW19FZUQkISM7NyQkIjIkeTBEQkEhKjM4ISM7JCEyeCpSIzQnPl05SiEjPDckJCIyUG1LP1tBTVAiISM7JCExd1hBSnB0UUghIzs3JCQiMWFAWC5FdVM5ISM6JCExd0p5aGkkPXIjISM7NyQkIjJRdSMpKipbakRdIiEjOyQhMUI4OSEpSCJSWSMhIzs3JCQiMjdtPHltWCNwOiEjOyQhMmB5KD5RJ2ZQOiMhIzw3JCQiMm5aLio0KDQmUTshIzskITI9KlxgKHBNWHkiISM8NyQkIjJgS2BARS8pKXAiISM7JCEyQUM7a01nVFUiISM8NyQkIjJ4UjEvLkNSdyIhIzskITE2KkghKkhzWSUqKiEjPDckJCIwdCYpSDcqPko9ISM5JCEyKEdcOj0oeSdvXSEjPTckJCIyJGZiN3dZLCgqPSEjOyQiMiQ0SXNKWE1ZNyEjPjckJCIyWS5oemclcGc+ISM7JCIxd0NmZXcmKlJiISM8NyQkIjFwSjg6LlNKPyEjOiQiMjIqKVwlSCdmIio+IiEjPDckJCIvMnpQRCRcNCMhIzgkIjJkSW4neXE0PD0hIzw3JCQiMngsZmh1bUY7IyEjOyQiMUEjeSkzZFM6RCEjOzckJCIyW1gnM0BZQkNBISM7JCIxVV5fQy0+Ij0kISM7NyQkIjEvYjxXX1YiSCMhIzokIjBqXHBRTEwlUiEjOjckJCIwR05NemxZTiMhIzkkIjIob1ZLLipmOXAlISM8NyQkIjJtT21rJCpmMlUjISM7JCIxJFJXVyRbcC5iISM7NyQkIjExKCk9VSF6YFsjISM6JCIxaSlbZnUjb0RqISM7NyQkIjFrSEhkI0hJYiMhIzokIjEtLygqPSJ6TUAoISM7NyQkIjFfciZbWCU9PUUhIzokIjFfXDk0R2QjNCkhIzs3JCQiMUstJVwwOltvIyEjOiQiMW9QTDc7XDghKiEjOzckJCIyMGM4KyNSKjN2IyEjOyQiMSJcMHRzQmglKiohIzs3JCQiMS8wTE1OaDZHISM6JCIyOSFmIUhcJHkiMyIhIzs3JCQiMkdvVVgxMDcpRyEjOyQiMiYqekZ2VlpKPSIhIzs3JCQiMiU0NnhlJltNJUghIzskIjE2R0wrVShbRiIhIzo3JCQiMkw1IillNTgpNEkhIzskIjI4Pj1bMzNOUCIhIzs3JCQiMkx4IVJYQ0x0SSEjOyQiMU14UTYhZiVvOSEjOjckJCItWF1FZlRKISM2JCIyaz8mM0FqenE6ISM7LSUlVklFV0c2JDskIiIhISIiJCIrYUVmVEohIiolKERFRkFVTFRHLSYlJl9BWElTRzYjIiIiNictJStfR1JJRExJTkVTRzYmLSUmQ09MT1JHNiYlJFJHQkckIiIhISIiJCIiISEiIiQiIiEhIiItJSpMSU5FU1RZTEVHNiMiIiEtJSpUSElDS05FU1NHNiMiIiEtJS1UUkFOU1BBUkVOQ1lHNiMkIiIhISIiLSUmQ09MT1JHNiYlJFJHQkckIiIhISIiJCIiISEiIiQiIiEhIiItJSpMSU5FU1RZTEVHNiMiIiEtJSpUSElDS05FU1NHNiMiIiEtJS1UUkFOU1BBUkVOQ1lHNiMkIiIhISIiLSYlJl9BWElTRzYjIiIjNictJStfR1JJRExJTkVTRzYmLSUmQ09MT1JHNiYlJFJHQkckIiIhISIiJCIiISEiIiQiIiEhIiItJSpMSU5FU1RZTEVHNiMiIiEtJSpUSElDS05FU1NHNiMiIiEtJS1UUkFOU1BBUkVOQ1lHNiMkIiIhISIiLSUmQ09MT1JHNiYlJFJHQkckIiIhISIiJCIiISEiIiQiIiEhIiItJSpMSU5FU1RZTEVHNiMiIiEtJSpUSElDS05FU1NHNiMiIiEtJS1UUkFOU1BBUkVOQ1lHNiMkIiIhISIiLSUrQVhFU0xBQkVMU0c2JFEidDYiUSE2Ii0lJkNPTE9SRzYmJSRSR0JHJCIjNSEiIiQiIiEhIiIkIiIhISIiLSUlUk9PVEc2Jy0lKUJPVU5EU19YRzYjJCIkZyUhIiItJSlCT1VORFNfWUc2IyQiI10hIiItJS1CT1VORFNfV0lEVEhHNiMkIiUhXCQhIiItJS5CT1VORFNfSEVJR0hURzYjJCIlISlHISIiLSUpQ0hJTERSRU5HNiI=

A partir do gr\303\241fico, vemos que o objeto primeiramente se move para a esquerda e para a origem e depois continuamente se move para a direita. A Velocidade m\303\251dia do objeto no intervalo [0, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVElJnBpO0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRidGMg==] \303\251 dada por: ( s(LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVElJnBpO0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRidGMg==) - s(0) ) / ( LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVElJnBpO0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRidGMg== - 0 ) . A Velocidade instant\303\242nea no tempo c \303\251 dada por '(c). Assim, somos perguntados para resolver: ( s(LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVElJnBpO0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRidGMg==) - s(0) ) / ( LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVElJnBpO0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRidGMg== - 0 ) = s '(c); Precisamente o MVT. s(Pi);

NiMsJComIiIjISIiJSNQaUciIiIiIiI=

s(0);

NiMiIiE=

D(s);

NiNmKjYjJSJ0RzYiNiQlKW9wZXJhdG9yRyUmYXJyb3dHNiIsJiMiIiIiIiMiIiItJSRjb3NHNiMlInRHISIiNiI2IjYi

Precisamos solucionar: 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 para t em [0, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVElJnBpO0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRidGMg== ], ex., queremos cos(t) = 0 para t em [0, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVElJnBpO0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRidGMg==]. A Solu\303\247\303\243o \303\251 t = LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVElJnBpO0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRidGMg== /2. Vamos tra\303\247ar o gr\303\241fico a reta secante entre os pontos (0, 0) e ( LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVElJnBpO0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRidGMg==, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVElJnBpO0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRidGMg== /2 ), e com a reta tangente para t = LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVElJnBpO0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRidGMg== /2 . As retas podem ser paralelas. D(s)(Pi/2);

NiMjIiIiIiIj

s(Pi/2);

NiMsJiomIiIlISIiJSNQaUciIiIiIiIiIiIhIiI=

with(plots):

Warning, the name changecoords has been redefined

data:= ([0,0], [Pi, Pi/2]): a1:= plot( [data], color=magenta, thickness=2 ): a2:= plot(s(t), t = 0..5, color = green, thickness=2): a3:= plot((Pi/4 - 1) + 1/2 * ( x - Pi/2), x = 0..Pi, color = magenta, thickness=2): a4:= textplot([1/5,1,`Secant Line`], align={RIGHT}, color = blue, thickness=2): a5:= textplot([1.5,-.8, `Tangent Line`], color = blue): display({a1,a2,a3,a4,a5});

LSUlUExPVEc2LC0lJ0NVUlZFU0c2JTckNyQkIiIhISIiJCIiISEiIjckJCIxJHoqZWBFZlRKISM6JCIybSpbekVqenE6ISM7LSUmQ09MT1JHNiYlJFJHQkckIiM1ISIiJCIiISEiIiQiIzUhIiItJSpUSElDS05FU1NHNiMiIiMtJSdDVVJWRVNHNiU3UzckJCIiISEiIiQiIiEhIiI3JCQiMkxMTCQzeCYpKjMiISM8JCExaCQ0bSlmc0ZhISM8NyQkIjJubTtIMlAiUT8hIzwkITJIdmBRNSgpXCsiISM8NyQkIjJMTExlUndYNSQhIzwkITIvZSlILWhsLTohIzw3JCQiMU1MJDN4JTN5VCEjOyQhMicpSD9mIj1hbz4hIzw3JCQiMW5tInolNFxZXyEjOyQhMnMoKXl1elplUSMhIzw3JCQiMU1MZVItL1BpISM7JCExYSEzOCJ5JD5zIyEjOzckJCItRGNtcGlzISM3JCExLil6Mj4vJjRJISM7NyQkIjFNTGUqKT5WQiQpISM7JCExbl1FRDZSTEshIzs3JCQiLURKYnchUSohIzckITInW2dvWiFSUVAkISM8NyQkIjJvbW1USU9vLyIhIzskITImUjsjb3JsVVUkISM8NyQkIjJOTCQzXz5qVTYhIzskITFbaiwvWTglUSQhIzs3JCQiMiwrK0Q7di9EIiEjOyQhMjojUUoudycqUUshIzw3JCQiLHY9aChlOCEjNSQhMTkkUSQ0MEMjKUghIzs3JCQiLHYkWzZqOSEjNSQhMndxU2tIMGxpIyEjPDckJCIyTUxlKlt6KHliIiEjOyQhMXVIUVdleDRBISM7NyQkIjJvbW1UWGcwbiIhIzskITJOcGVbZXV1ZiIhIzw3JCQiMm9tbW1KPGd3IiEjOyQhMS8qUj5vOycqeiohIzw3JCQiLkQxTWNxKD0hIzckITIjKVxFQDtsUlwiISM9NyQkIjJtbW07cFdgKD4hIzskIjAwKG9wKjMjUm8hIzs3JCQiMi4rRDFmIz0kMyMhIzskIjJZWD0zIj45KzwhIzw3JCQiLnY9eHBlPSMhIzckIjFpVi9nIlE/dyMhIzs3JCQiMW5tIkgyOElIIyEjOiQiMUcjb3FUVjsnUiEjOzckJCIyb20ienBTUyJSIyEjOyQiMXBBR0JJRFJeISM7NyQkIjJMTCQzXz9gKFwjISM7JCIxVzUvZV89JFsnISM7NyQkIjJPTGUqKT5weGcjISM7JCIwPFd3ZGcwJnohIzo3JCQiLnYkZjR0LkYhIzckIjFtJ1xqQTsneSMqISM7NyQkIjJQTCRlKkdzdCFHISM7JCIyZFtKNVBgYzIiISM7NyQkIitEUlc5SCEiKiQiMigzeDBcOi1LNyEjOzckJCItREpFPj5JISM2JCIyaHomXCNwLHZRIiEjOzckJCIyLitEMVJVMDckISM7JCIxJ3pBcFtBI1I6ISM6NyQkIi12PVMyTEshIzYkIjInZW00SDMqeXEiISM7NyQkIjJqbW07cCk9TUwhIzskIjEzTyQ+Iz5dZT0hIzo3JCQiMi0rK3Y9XUBXJCEjOyQiMjx1VHApeTc8PyEjOzckJCIxTCRlKlskeipSTiEjOiQiMmtRJm9lOiN6OiMhIzs3JCQiMjErK0RZS3BrJCEjOyQiMngpKj5kLnJ2SSMhIzs3JCQiMmxtIkgycWNaUCEjOyQiMk84Z3hyWUxXIyEjOzckJCIyLytESjVmRiZRISM7JCIyPEYoenB1NHpEISM7NyQkIjJsbW1UZy5jJlIhIzskIjJQPzxyb1tbcSMhIzs3JCQiLkRjRXNLMSUhIzckIjIoZkMnSDxhI0dHISM7NyQkIjFNTEwkKSpwcDslISM6JCIxPilSPCpcUlFIISM6NyQkIjFNTDN4ZSx0VSEjOiQiMms6MFNXRTovJCEjOzckJCIxbjtIZE89eVYhIzokIjJsMzpgNWpQOCQhIzs3JCQiMjArK10jPiNbWiUhIzskIjJuZUUkelZLNEshIzs3JCQiMW5tVCZHIWUmZSUhIzokIjJYZXImKW9nWkckISM7NyQkIjFNTEwkKVFrJW8lISM6JCIyJ2U6OnJxJD5NJCEjOzckJCIuRDFNbS16JSEjNyQiMlhzKzVFLUBSJCEjOzckJCIyMSt2JDQwTyIqWyEjOyQiMUt4JFFiMihITSEjOjckJCIjXSEiIiQiMidRSm11VSMqZU0hIzstJSZDT0xPUkc2JiUkUkdCRyQiIiEhIiIkIiM1ISIiJCIiISEiIi0lKlRISUNLTkVTU0c2IyIiIy0lJ0NVUlZFU0c2JTdTNyQkIiIhISIiJCEjNSEiIjckJCIxZkQyTHp4Wm8hIzwkITFzak0uNmhkJyohIzs3JCQiMU5weCpHKmYhRyIhIzskITFLOjZiLnFmJCohIzs3JCQiMDYjZXhHbV0+ISM6JCExWCozN2NvWS0qISM7NyQkIjJYVCw9M29eaSMhIzwkITEkSCo0ZmZUKG8pISM7NyQkIjBcRDBbbmtIJCEjOiQhMWFzdGZpd14kKSEjOzckJCIxIj1aYSZ6JSk9UiEjOyQhMTRrRkFnZFMhKSEjOzckJCIyd2JXdilvR2pYISM8JCExQHhBY2xOPXghIzs3JCQiMSUzKipIYm0oSF8hIzskITFlL11CbjYmUSghIzs3JCQiMVBScjQpM1QqZSEjOyQhMUtJOSZmWEgwKCEjOzckJCIxI1speXlrWXhsISM7JCExZmRnZ25FNm4hIzs3JCQiMXMnb2NHbyR6ciEjOyQhMWtjO2RlSjVrISM7NyQkIjFRMDtncidwJnkhIzskITFKKD4qPmtecmchIzs3JCQiMUdNdD8kW3RgKSEjOyQhMSdHTCdSZUtKZCEjOzckJCIxI3AzMGtAST4qISM7JCExYWN1eiIqWy5hISM7NyQkIjBDIlxIZVYpeSohIzokITBRYV8zI3kwXiEjOjckJCIyR1spKSopM1cnXDUhIzskITEnZWRdYno8diUhIzs3JCQiMSdbQFhTQCc0NiEjOiQhMGQjUnhIKj1YJSEjOjckJCIyVmhQM0cqUXo2ISM7JCEyJkc+ImVmYEk1JSEjPDckJCIyVTMqM3RjOVQ3ISM7JCExelhiTTtGJXokISM7NyQkIjIkeTBEQkEhKjM4ISM7JCEyKDNydSQpKSlbYk0hIzw3JCQiMlBtSz9bQU1QIiEjOyQhMjpvTykqZSgpRzgkISM8NyQkIjFhQFguRXVTOSEjOiQhMEJSRilwRyd6IyEjOjckJCIyUXUjKSoqW2pEXSIhIzskITEiRyczXUQ9KFsjISM7NyQkIjI3bTx5bVgjcDohIzskITJUcDY0bXJQOiMhIzw3JCQiMm5aLio0KDQmUTshIzskITJuaCNbXTlYMj0hIzw3JCQiMmBLYEBFLykpcCIhIzskITJQUEwjKm95Zl0iISM8NyQkIjJ4UjEvLkNSdyIhIzskITI8LG96JSl6Lj0iISM8NyQkIjB0JilINyo+Sj0hIzkkITEoXDgyJlEvUyUpISM8NyQkIjIkZmI3d1ksKCo9ISM7JCExTj9zJD5tI1xeISM8NyQkIjJZLmh6ZyVwZz4hIzskITFzI1s+Z3BfJz4hIzw3JCQiMXBKODouU0o/ISM6JCIyJVwlZW12OitkIiEjPTckJCIvMnpQRCRcNCMhIzgkIjIlKipcYCopb2lZWiEjPTckJCIyeCxmaHVtRjsjISM7JCIxJCkzJnpJUCRRIikhIzw3JCQiMltYJzNAWUJDQSEjOyQiMlFGS2E1dDY3IiEjPDckJCIxL2I8V19WIkgjISM6JCIyMl94M0F3clgiISM8NyQkIjBHTk16bFlOIyEjOSQiMigqUndyJypHTHgiISM8NyQkIjJtT21rJCpmMlUjISM7JCIyRyQ9TCNvKnouQCEjPDckJCIxMSgpPVUhemBbIyEjOiQiMiRITiU0QCYqb1UjISM8NyQkIjFrSEhkI0hJYiMhIzokIjE+W1knR1ledyMhIzs3JCQiMV9yJltYJT09RSEjOiQiMWZkR3VBIzQ0JCEjOzckJCIxSy0lXDA6W28jISM6JCIyJWY2cXVfMkNNISM8NyQkIjIwYzgrI1IqM3YjISM7JCIyQyF5MSsncFd2JCEjPDckJCIxLzBMTU5oNkchIzokIjFARGxydzFlUyEjOzckJCIyR29VWDEwNylHISM7JCIxOU1yQWAtMVchIzs3JCQiMiU0NnhlJltNJUghIzskIjFaYiZRelVzciUhIzs3JCQiMkw1IillNTgpNEkhIzskIjE7YlNIYjFcXSEjOzckJCIyTHghUlhDTHRJISM7JCIxblEmcEFpbU8mISM7NyQkIi1YXUVmVEohIzYkIjEqKipcQURqenEmISM7LSUmQ09MT1JHNiYlJFJHQkckIiM1ISIiJCIiISEiIiQiIzUhIiItJSpUSElDS05FU1NHNiMiIiMtJSVURVhURzYnNyQkIiIjISIiJCIjNSEiIi0lKV9UWVBFU0VURzYjLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkc2IjY2LUkjbXNHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHNiI2I1EsU2VjYW50fkxpbmU2Ii8lJ2ZhbWlseUdRMFRpbWVzfk5ld35Sb21hbjYiLyUlc2l6ZUdRIzEyNiIvJSVib2xkR1EmZmFsc2U2Ii8lJ2l0YWxpY0dRJmZhbHNlNiIvJSp1bmRlcmxpbmVHUSZmYWxzZTYiLyUqc3Vic2NyaXB0R1EmZmFsc2U2Ii8lLHN1cGVyc2NyaXB0R1EmZmFsc2U2Ii8lK2ZvcmVncm91bmRHUShbMCwwLDBdNiIvJStiYWNrZ3JvdW5kR1EuWzI1NSwyNTUsMjU1XTYiLyUnb3BhcXVlR1EmZmFsc2U2Ii8lK2V4ZWN1dGFibGVHUSZmYWxzZTYiLyUpcmVhZG9ubHlHUSZmYWxzZTYiLyUpY29tcG9zZWRHUSZmYWxzZTYiLyUqY29udmVydGVkR1EmZmFsc2U2Ii8lK2ltc2VsZWN0ZWRHUSZmYWxzZTYiLyUscGxhY2Vob2xkZXJHUSZmYWxzZTYiLyU2c2VsZWN0aW9uLXBsYWNlaG9sZGVyR1EmZmFsc2U2Ii8lMGZvbnRfc3R5bGVfbmFtZUdRK01hcGxlflBsb3Q2Ii8lLG1hdGh2YXJpYW50R1Enbm9ybWFsNiItJSZDT0xPUkc2JiUkUkdCRyQiIiEhIiIkIiIhISIiJCIjNSEiIi0lKlRISUNLTkVTU0c2IyIiIyUrQUxJR05SSUdIVEctJSVURVhURzYlNyQkIiM6ISIiJCEiKSEiIi0lKV9UWVBFU0VURzYjLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkc2IjY2LUkjbXNHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHNiI2I1EtVGFuZ2VudH5MaW5lNiIvJSdmYW1pbHlHUTBUaW1lc35OZXd+Um9tYW42Ii8lJXNpemVHUSMxMjYiLyUlYm9sZEdRJmZhbHNlNiIvJSdpdGFsaWNHUSZmYWxzZTYiLyUqdW5kZXJsaW5lR1EmZmFsc2U2Ii8lKnN1YnNjcmlwdEdRJmZhbHNlNiIvJSxzdXBlcnNjcmlwdEdRJmZhbHNlNiIvJStmb3JlZ3JvdW5kR1EoWzAsMCwwXTYiLyUrYmFja2dyb3VuZEdRLlsyNTUsMjU1LDI1NV02Ii8lJ29wYXF1ZUdRJmZhbHNlNiIvJStleGVjdXRhYmxlR1EmZmFsc2U2Ii8lKXJlYWRvbmx5R1EmZmFsc2U2Ii8lKWNvbXBvc2VkR1EmZmFsc2U2Ii8lKmNvbnZlcnRlZEdRJmZhbHNlNiIvJStpbXNlbGVjdGVkR1EmZmFsc2U2Ii8lLHBsYWNlaG9sZGVyR1EmZmFsc2U2Ii8lNnNlbGVjdGlvbi1wbGFjZWhvbGRlckdRJmZhbHNlNiIvJTBmb250X3N0eWxlX25hbWVHUStNYXBsZX5QbG90NiIvJSxtYXRodmFyaWFudEdRJ25vcm1hbDYiLSUmQ09MT1JHNiYlJFJHQkckIiIhISIiJCIiISEiIiQiIzUhIiItJSVWSUVXRzYkOyQiIiEhIiIkIiNdISIiJShERUZBVUxURy0mJSZfQVhJU0c2IyIiIjYnLSUrX0dSSURMSU5FU0c2Ji0lJkNPTE9SRzYmJSRSR0JHJCIiISEiIiQiIiEhIiIkIiIhISIiLSUqTElORVNUWUxFRzYjIiIhLSUqVEhJQ0tORVNTRzYjIiIhLSUtVFJBTlNQQVJFTkNZRzYjJCIiISEiIi0lJkNPTE9SRzYmJSRSR0JHJCIiISEiIiQiIiEhIiIkIiIhISIiLSUqTElORVNUWUxFRzYjIiIhLSUqVEhJQ0tORVNTRzYjIiIhLSUtVFJBTlNQQVJFTkNZRzYjJCIiISEiIi0mJSZfQVhJU0c2IyIiIzYnLSUrX0dSSURMSU5FU0c2Ji0lJkNPTE9SRzYmJSRSR0JHJCIiISEiIiQiIiEhIiIkIiIhISIiLSUqTElORVNUWUxFRzYjIiIhLSUqVEhJQ0tORVNTRzYjIiIhLSUtVFJBTlNQQVJFTkNZRzYjJCIiISEiIi0lJkNPTE9SRzYmJSRSR0JHJCIiISEiIiQiIiEhIiIkIiIhISIiLSUqTElORVNUWUxFRzYjIiIhLSUqVEhJQ0tORVNTRzYjIiIhLSUtVFJBTlNQQVJFTkNZRzYjJCIiISEiIi0lK0FYRVNMQUJFTFNHNiVRITYiUSE2Ii0lJUZPTlRHNiUlKERFRkFVTFRHJShERUZBVUxURyIjNS0lJVJPT1RHNictJSlCT1VORFNfWEc2IyQiJHEkISIiLSUpQk9VTkRTX1lHNiMkIiNxISIiLSUtQk9VTkRTX1dJRFRIRzYjJCIlXU4hIiItJS5CT1VORFNfSEVJR0hURzYjJCIlK0chIiItJSlDSElMRFJFTkc2Ig==

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>:::::::::::::::::::::::::::::::rYyYp1:\"\{\}LSUlUk9PVEc2Jy0lKUJPVU5EU19YRzYjJCIiISEiIi0lKUJPVU5EU19ZR0YnLSUtQk9VTkRTX1dJRFRIRzYjJCImUy0iRiotJS5CT1VORFNfSEVJR0hURzYjJCIlITQjRiotJSlDSElMRFJFTkc2Ig==