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:>::::::::::::::::::::::::::::::::::::::::::::::::::::::xqyaG:3:\"\{\}LSUlUk9PVEc2Jy0lKUJPVU5EU19YRzYjJCIiISEiIi0lKUJPVU5EU19ZR0YnLSUtQk9VTkRTX1dJRFRIRzYjJCImUy0iRiotJS5CT1VORFNfSEVJR0hURzYjJCIlNUtGKi0lKUNISUxEUkVORzYiCap\303\255tulo 27C\303\241lculo de \303\201reas
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">Introdu\303\247\303\243o</Font></Text-field>A \303\241rea \303\251 usada no Cap\303\255tulo 23 para iniciar o desenvolvimento de integral definida. Naquele contexto todas as \303\241reas s\303\243o computadas como limitesexpl\303\255citos. Os Teoremas Fundamentais de C\303\241lculo produzem ferramentas eficientes para avaliar uma integral definida. A id\303\251ia essencial desenvolvida neste cap\303\255tulo \303\251 resumida como fatiar, aproximar, calcular limites, avaliar. O processo geral usado para expressar a \303\241rea de uma regi\303\243o plana como uma integral definida consiste nos passos: dividir em fatias, aproximar e calcular limites. Uma vez formulada a integral definida apropriada, o passo final de avaliar pode ser implementado. Este mesmo processo \303\251 usado em outras aplica\303\247\303\265es consideradas nesta unidade, assim como muitas outras aplica\303\247\303\265es de integral definida fora do alcance desta unidade.
<Text-field style="Heading 1" layout="Heading 1" spaceabove="7"><Font encoding="UTF-8">\303\215ndice de Termos</Font></Text-field>Os seguintes termos, neste cap\303\255tulo, t\303\252m conex\303\243o com o Dicion\303\241rio do Maple; para mais informa\303\247\303\265es v\303\241 em Dicion\303\241rio Matem\303\241tico.
\303\241reac\303\255rculocurvaintegral definidaavaliarexpl\303\255citofatorfun\303\247\303\243ogr\303\241ficovari\303\241vel independenteintegralintegradointegra\303\247\303\243ointervalolimiteteorema do valor m\303\251dionegativopositivoraioraizresolvervalortrabalho
<Text-field style="Heading 1" layout="Heading 1" spaceabove="7"><Font encoding="UTF-8">Inicializa\303\247\303\243o</Font></Text-field>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
<Text-field style="Heading 1" layout="Heading 1" spaceabove="7"><Font encoding="UTF-8">Exemplo 27.1: Regi\303\243o Entre Duas Curvas </Font></Text-field>A regi\303\243o limitada pelos pelos gr\303\241ficos de: 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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNictRiw2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GOlEnbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkQvJSlzdHJldGNoeUdGRC8lKnN5bW1ldHJpY0dGRC8lKGxhcmdlb3BHRkQvJS5tb3ZhYmxlbGltaXRzR0ZELyUnYWNjZW50R0ZELyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGUy1GLDYlUSV0b3AxRidGNkY5LyUrZXhlY3V0YWJsZUdGREZARitGWUZARitGWUZAe: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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNictRiw2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GOlEnbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkQvJSlzdHJldGNoeUdGRC8lKnN5bW1ldHJpY0dGRC8lKGxhcmdlb3BHRkQvJS5tb3ZhYmxlbGltaXRzR0ZELyUnYWNjZW50R0ZELyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGUy1GLDYlUSVib3QxRidGNkY5LyUrZXhlY3V0YWJsZUdGREZARitGWUZARitGWUZAno 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 \303\251 mostrada na Figura 27.1.
Figura 27.1 Exemplo 27.1: Gr\303\241ficos de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSZtc3FydEdGJDYjLUYsNiVRInhGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRidGKy9GOVEnbm9ybWFsRic= (em vermelho) e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSVtc3VwR0YkNiUtRiw2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21uR0YkNiRRIjJGJy9GOVEnbm9ybWFsRicvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnRitGPw== (em azul)
A \303\241rea desta regi\303\243o \303\251 dada pela integral definida :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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNictRiw2JVElQXJlYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GOlEnbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkQvJSlzdHJldGNoeUdGRC8lKnN5bW1ldHJpY0dGRC8lKGxhcmdlb3BHRkQvJS5tb3ZhYmxlbGltaXRzR0ZELyUnYWNjZW50R0ZELyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGUy1GLDYlUSNBMUYnRjZGOS8lK2V4ZWN1dGFibGVHRkRGQEYrRllGQEYrRllGQA==Cujo valor \303\251: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
<Text-field style="Heading 1" readonly="true" layout="Heading 1"><Font readonly="true">Maple T.A. Maple-Graded Question</Font></Text-field>Using the Maple-graded question type, you create a question that uses Maple functionality when creating the correct answer and determining if the student's response is correct. The Maple-graded question type has an option to plot the student's response. To include the plot option, insert the corresponding task template. For information on creating questions, making assignments, and exporting Maple T.A. course modules, see Overview of Maple T.A. Integration.
<Text-field style="Heading 2" layout="Heading 2">Algorithmic Variables</Text-field>Algorithmic variables can be used to create a question that contains randomly generated parameters. You can refer to algorithmic variables in the Question, Answer, Hints, and Feedback input regions, as well as in other variable definitions. To reference an algorithmic variable, include "`$variable`" as text or 2-D Math, for example, x := `$myvariable`. Adding algorithmic variables to the question is optional.
In the following execution group, add an algorithmic variable. To include more variables, add more execution groups. If your assignment contains more than one algorithmic variable, ensure the variable names are unique.with(plots):
with(RandomTools):
randomize():
aa1 := Generate(integer(range=1..3)):
cc1 := Generate(integer(range=-5..-1)):
fn1 := aa1*x^2+cc1;
aa2 := Generate(integer(range=-3..3)):
while (aa2 >= aa1) do aa2 := Generate(integer(range=-3..3)) od:
bb2 := Generate(integer(range=-3..3)):
while (4*(aa1-aa2)*cc1 >= bb2^2 ) do bb2 := Generate(integer(range=-3..3)) od:
fn2 := aa2*x^2+bb2*x;
lo := (bb2-sqrt(bb2^2-4*(aa1-aa2)*cc1))/2/(aa1-aa2);
hi := (bb2+sqrt(bb2^2-4*(aa1-aa2)*cc1))/2/(aa1-aa2);
ans1 := Int(sort(fn2-fn1,x),x=lo..hi);
#DocumentTools[SetProperty]( Plot0, value, plot([fn1,fn2],x=lo-1..hi+1) );LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">Quest\303\243o 27.1</Font></Text-field>The question can contain text, 2-D Math, plots, images, and algorithmic variables. To insert a plot in the question, use the Plot Component.
In the following text region, enter the full contents of the question.Qual \303\251 a \303\241rea da regi\303\243o entre y = `$fn1` (vermelho) e y = `$fn2` (verde)?
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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
<Text-field style="Heading 2" layout="Heading 2">Answer</Text-field>To evaluate a student's response, enter the correct answer. Complete each line of code with a semicolon. The last line must evaluate to an expression that will be stored as the variable `$ANSWER`.
Enter Maple code in 1-D Math that evaluates to the correct answer. Add additional execution groups as needed.LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=evalf(value(ans1));LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
<Text-field style="Heading 2" layout="Heading 2">Evaluate Student's Response</Text-field>To evaluate a student's response, you must evalute to a Boolean value (true or false). The variable `$RESPONSE` is automatically initialized to the student's response. Using `$ANSWER` (the correct answer) and `$RESPONSE` (the student response), one example of evaluating to a Boolean value is, evalb(`$ANSWER`-`$RESPONSE`=0);
Enter Maple code to evaluate a student's response. To add additional Maple functionality, use the Answer input region.evalb( fnormal(evalf(`$ANSWER`-`$RESPONSE`), 5 ) = 0 );
<Text-field style="Heading 2" layout="Heading 2">Hints</Text-field>A question can offer hints to students when requested. Hints can contain text, 2-D Math, and algorithmic variables. Adding hints to the question is optional.
Enter your hints in the following table. You can provide up to three hints.
Find the points of intersection for the interval of the definite integral.Replace this text with hint 2.Replace this text with hint 3.
with(StringTools): with(DocumentTools): response := GetProperty(`TextArea0`, `value`); if response = `` then response := "</mtext><mtext><NO RESPONSE></mtext><mtext>"; fi; hint := SubstituteAll("<math><mrow><mtext>Find the points of intersection for the interval of the definite integral.</mtext><mtext>
</mtext></mrow></math>", "`\134$RESPONSE`", response); with(Maplets[Elements]): maplet := Maplet(Window('title' = "Maple TA Hint", [[MathMLViewer('value' = hint, 'fontsize'='12', 'width'='600', 'height'='200', 'breakwidth'='600')], [Button("OK", Shutdown())]])): Maplets[Display](maplet);
<Text-field style="Heading 2" layout="Heading 2">Feedback</Text-field>A question can display feedback when a student provides an incorrect response. The feedback can contain text, 2-D Math, and algorithmic variables. The feedback can also refer to `$RESPONSE` (the student response) and `$ANSWER` (the correct answer). Adding feedback to the question is optional.
In the following text region, enter feedback to an incorrect response.The definite integral is `$ans1` = `$ANSWER`with(StringTools): with(DocumentTools): feedback:=""; StudentResponse := GetProperty(`TextArea0`, `value`); ANSWER := evalf(value(ans1)); if evalb( fnormal(evalf(ANSWER-eval(parse(StudentResponse))), 5 ) = 0 ) then feedback:=cat("<math><mrow><mtext mathvariant='bold'>Correct!
</mtext><mtext>
</mtext><mtext mathvariant='bold'>Your Answer: </mtext><mtext>", StudentResponse, "</mtext></mrow></math>"); else if StudentResponse = "" then StudentResponse:="<NO RESPONSE>"; fi; feedback:=cat("<math><mrow><mtext mathvariant='bold'>Your answer is incorrect. </mtext><mtext>
</mtext><mtext mathvariant='bold'>Your Answer: </mtext><mtext>", StudentResponse, "</mtext><mtext>
</mtext>"); feedback:=cat(feedback, "<mtext mathvariant='bold'>Correct Answer: </mtext><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mn>16.03901494</mn></mrow></mstyle></math><mtext>
</mtext>"); feedback:=cat(feedback, SubstituteAll("<mrow><mtext>The definite integral is </mtext><mtext></mtext><mrow><mrow><msubsup superscriptshift='2'><mo mathcolor='#909090' lspace='0.0em' rspace='0.0em'>&int;</mo><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>−</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo lspace='0.2222222em' rspace='0.2222222em'>−</mo><mrow><mfrac><mn>1</mn><mn>2</mn></mfrac><mo lspace='0.0em' rspace='0.0em'>⁢</mo><mrow><msqrt><mn>21</mn></msqrt></mrow></mrow></mrow><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>−</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mfrac><mn>1</mn><mn>2</mn></mfrac><mo lspace='0.0em' rspace='0.0em'>⁢</mo><mrow><msqrt><mn>21</mn></msqrt></mrow></mrow></mrow></msubsup><mfenced open='(' close=')' separators=','><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>−</mo><mrow><msup><mi>x</mi><mn>2</mn></msup></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>−</mo><mi>x</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mn>5</mn></mrow></mfenced><mspace height='0.0ex' width='0.3em' depth='0.0ex' linebreak='auto'/><mo mathcolor='#909090' lspace='0.0em' rspace='0.0em'>ⅆ</mo><mi>x</mi></mrow></mrow><mtext></mtext><mtext> = </mtext><mrow><mn>16.03901494</mn></mrow><mtext></mtext><mtext>
</mtext></mrow>", "`$RESPONSE`", StudentResponse)); feedback:=SubstituteAll(feedback, "`$ANSWER`", "<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mn>16.03901494</mn></mrow></mstyle></math>"); feedback:=cat(feedback, "</mrow></math>"); fi; with(Maplets[Elements]): maplet := Maplet(Window('title' = "Maple TA Feedback", [[MathMLViewer('value' = feedback, 'fontsize'='12', 'width'='600', 'height'='200', 'breakwidth'='600')], [Button("OK", Shutdown())]])): if feedback <> "" then Maplets[Display](maplet); fi;
<Text-field style="Heading 1" layout="Heading 1" spaceabove="7"><Font encoding="UTF-8">Exemplo 27.2: \303\201rea Positiva e \303\201rea Negativa </Font><Hyperlink linktarget="Dictionary:Definition,positive" hyperlink="true"><Font style="Heading 1"> </Font></Hyperlink></Text-field>A \303\241rea entre os gr\303\241ficos de: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no 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 consiste de duas partes porque as curvas se cruzam uma com a outra. As curvas e a \303\241rea fechada s\303\243o mostradas na Figura 27.
Figura 27.2 Exemplo 27.2: Gr\303\241ficos de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSZtc3FydEdGJDYjLUYsNiVRInhGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRidGKy9GOVEnbm9ybWFsRic= (vermelho), 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 (azul), e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjFGJ0Y5Rjk= (verde)
A primeira parte da \303\241rea tem a curva exponencial no contorno superior e a raiz quadrada como contorno inferior; depois que as curvas se interceptam, estes papeis s\303\243o revertidos. Figura 27.3 enfatiza isto:
Figura 27.3A curva por partes amarela permanece em cima; a azul, em baixo
A \303\241rea fechada total \303\251 a soma de duas integrais definidas: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onde LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiVEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= \303\251 a coordenada LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= do ponto onde as duas curvas se interceptam. O valor de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiVEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= \303\251 :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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNictRiw2JVEjYGBGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSI9RicvRjpRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZELyUpc3RyZXRjaHlHRkQvJSpzeW1tZXRyaWNHRkQvJShsYXJnZW9wR0ZELyUubW92YWJsZWxpbWl0c0dGRC8lJ2FjY2VudEdGRC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRlMtRiw2JVEpVF9hcHByb3hGJ0Y2RjkvJStleGVjdXRhYmxlR0ZERkBGK0ZZRkBGK0ZZRkA=assim, a \303\241rea requerida \303\251: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
<Text-field style="Heading 1" readonly="true" layout="Heading 1"><Font readonly="true">Maple T.A. Maple-Graded Question</Font></Text-field>Using the Maple-graded question type, you create a question that uses Maple functionality when creating the correct answer and determining if the student's response is correct. The Maple-graded question type has an option to plot the student's response. To include the plot option, insert the corresponding task template. For information on creating questions, making assignments, and exporting Maple T.A. course modules, see Overview of Maple T.A. Integration.
<Text-field style="Heading 2" layout="Heading 2">Algorithmic Variables</Text-field>Algorithmic variables can be used to create a question that contains randomly generated parameters. You can refer to algorithmic variables in the Question, Answer, Hints, and Feedback input regions, as well as in other variable definitions. To reference an algorithmic variable, include "`$variable`" as text or 2-D Math, for example, x := `$myvariable`. Adding algorithmic variables to the question is optional.
In the following execution group, add an algorithmic variable. To include more variables, add more execution groups. If your assignment contains more than one algorithmic variable, ensure the variable names are unique.with(RandomTools):
randomize():
aa3 := Generate(integer(range=2..5)):
cc2 := Generate(integer(range=-5..-1)):
fn3 := aa3*x^2+cc2;
aa4 := Generate(integer(range=-4..4)):
while (aa4 >= aa3) do aa4 := Generate(integer(range=-4..4)) end do:
bb4 := Generate(integer(range=-3..3)):
while (4*(aa3-aa4)*cc2 >= bb4^2 ) do bb4 := Generate(integer(range=-3..3)) end do:
fn4 := aa4*x^2+bb4*x;
clow := (bb4-sqrt(bb4^2-4*(aa3-aa4)*cc2))/2/(aa3-aa4);
chigh := (bb4+sqrt(bb4^2-4*(aa3-aa4)*cc2))/2/(aa3-aa4);
nn1 := Generate(integer(range=-5..3)):
nn2 := Generate(integer(range=-2..5)):
while (nn2 <= nn1) do nn2 := Generate(integer(range=-2..4)) end do:
if ((evalf(clow)<evalf(nn1) and (evalf(chigh)<evalf(nn1) or evalf(chigh)>evalf(nn2))) or evalf(clow>evalf(nn2))) then
# only nn1 and nn2 matter
temp1 := (nn1+nn2)/2:
if (evalf(eval(fn3,x=temp1)) > evalf(eval(fn4,x=temp1))) then
fn5 := Int(sort(fn3-fn4), x=nn1..nn2);
else
fn5 := Int(sort(fn4-fn3), x=nn1..nn2);
end if;
elif (evalf(clow) < evalf(nn1) and evalf(chigh) > evalf(nn1) and evalf(chigh) < evalf(nn2)) then
# chlow2 < nn1 < chigh < nn2
temp2 := (nn1+chigh)/2:
if (evalf(eval(fn3,x=temp2)) > evalf(eval(fn4,x=temp2))) then
fn5 := Int(sort(fn3-fn4),x=nn1..chigh) + Int(sort(fn4-fn3),x=chigh..nn2);
else
fn5 := Int(sort(fn4-fn3),x=nn1..chigh) + Int(sort(fn3-fn4),x=chigh..nn2);
end if;
elif (evalf(clow) > evalf(nn1) and evalf(clow) < evalf(nn2)) then
if (evalf(chigh) > evalf(nn2)) then
# nn1 < clow < nn2 < chigh
temp3 := (nn1 + clow)/2:
if (evalf(eval(fn3,x=temp3)) > evalf(eval(fn4,x=temp3))) then
fn5 := Int(sort(fn3-fn4),x=nn1..clow) + Int(sort(fn4-fn3),x=clow..nn2);
else
fn5 := Int(sort(fn4-fn3),x=nn1..clow) + Int(sort(fn3-fn4),x=clow..nn2);
end if;
else
# nn1 < cnlow2 < chigh < nn2
temp4 := (nn1 + clow)/2:
if (evalf(eval(fn3,x=temp4)) > evalf(eval(fn4,x=temp4))) then
fn5 := Int(sort(fn3-fn4),x=nn1..clow) + Int(sort(fn4-fn3),x=clow..chigh) + Int(sort(fn3-fn4),x=chigh..nn2);
else
fn5 := Int(sort(fn4-fn3),x=nn1..clow) + Int(sort(fn3-fn4),x=clow..chigh) + Int(sort(fn4-fn3),x=chigh..nn2);
end if;
end if;
end if;
ans2 := fn5;LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">Quest\303\243o 27.2</Font></Text-field>The question can contain text, 2-D Math, plots, images, and algorithmic variables. To insert a plot in the question, use the Plot Component.
In the following text region, enter the full contents of the question.Qual \303\251 a \303\241rea da regi\303\243o entre y = `$fn3` (vermelha) e y = `$fn4` (verde) no intervalo [`$nn1`,`$nn2`]?
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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
<Text-field style="Heading 2" layout="Heading 2">Answer</Text-field>To evaluate a student's response, enter the correct answer. Complete each line of code with a semicolon. The last line must evaluate to an expression that will be stored as the variable `$ANSWER`.
Enter Maple code in 1-D Math that evaluates to the correct answer. Add additional execution groups as needed.evalf(value(ans2));
<Text-field style="Heading 2" layout="Heading 2">Evaluate Student's Response</Text-field>To evaluate a student's response, you must evalute to a Boolean value (true or false). The variable `$RESPONSE` is automatically initialized to the student's response. Using `$ANSWER` (the correct answer) and `$RESPONSE` (the student response), one example of evaluating to a Boolean value is, evalb(`$ANSWER`-`$RESPONSE`=0);
Enter Maple code to evaluate a student's response. To add additional Maple functionality, use the Answer input region.evalb( fnormal(evalf(`$ANSWER`-`$RESPONSE`), 5 ) = 0 );
<Text-field style="Heading 2" layout="Heading 2">Hints</Text-field>A question can offer hints to students when requested. Hints can contain text, 2-D Math, and algorithmic variables. Adding hints to the question is optional.
Enter your hints in the following table. You can provide up to three hints.
Do y = `$fn3` and y = `$fn4` intersect within the given interval?Replace this text with hint 2.Replace this text with hint 3.
with(StringTools): with(DocumentTools): response := GetProperty(`TextArea1`, `value`); if response = `` then response := "</mtext><mtext><NO RESPONSE></mtext><mtext>"; fi; hint := SubstituteAll("<math><mrow><mtext>Do y = </mtext><mtext></mtext><mrow><mrow><mrow><mn>2</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><msup><mi>x</mi><mn>2</mn></msup></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>−</mo><mn>2</mn></mrow></mrow><mtext></mtext><mtext> and y = </mtext><mtext></mtext><mrow><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>−</mo><mrow><msup><mi>x</mi><mn>2</mn></msup></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>−</mo><mrow><mn>2</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><mi>x</mi></mrow></mrow></mrow><mtext></mtext><mtext> intersect within the given interval?</mtext><mtext>
</mtext></mrow></math>", "`\134$RESPONSE`", response); with(Maplets[Elements]): maplet := Maplet(Window('title' = "Maple TA Hint", [[MathMLViewer('value' = hint, 'fontsize'='12', 'width'='600', 'height'='200', 'breakwidth'='600')], [Button("OK", Shutdown())]])): Maplets[Display](maplet);
<Text-field style="Heading 2" layout="Heading 2">Feedback</Text-field>A question can display feedback when a student provides an incorrect response. The feedback can contain text, 2-D Math, and algorithmic variables. The feedback can also refer to `$RESPONSE` (the student response) and `$ANSWER` (the correct answer). Adding feedback to the question is optional.
In the following text region, enter feedback to an incorrect response.The definite integral is `$ans2` = `$ANSWER`with(StringTools): with(DocumentTools): feedback:=""; StudentResponse := GetProperty(`TextArea1`, `value`); ANSWER := evalf(value(ans2)); if evalb( fnormal(evalf(ANSWER-eval(parse(StudentResponse))), 5 ) = 0 ) then feedback:=cat("<math><mrow><mtext mathvariant='bold'>Correct!
</mtext><mtext>
</mtext><mtext mathvariant='bold'>Your Answer: </mtext><mtext>", StudentResponse, "</mtext></mrow></math>"); else if StudentResponse = "" then StudentResponse:="<NO RESPONSE>"; fi; feedback:=cat("<math><mrow><mtext mathvariant='bold'>Your answer is incorrect. </mtext><mtext>
</mtext><mtext mathvariant='bold'>Your Answer: </mtext><mtext>", StudentResponse, "</mtext><mtext>
</mtext>"); feedback:=cat(feedback, "<mtext mathvariant='bold'>Correct Answer: </mtext><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mn>125.4874841</mn></mrow></mstyle></math><mtext>
</mtext>"); feedback:=cat(feedback, SubstituteAll("<mrow><mtext>The definite integral is </mtext><mtext></mtext><mrow><mrow><mrow><msubsup superscriptshift='2'><mo mathcolor='#909090' lspace='0.0em' rspace='0.0em'>&int;</mo><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>−</mo><mn>5</mn></mrow><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>−</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><mo lspace='0.2222222em' rspace='0.2222222em'>−</mo><mrow><mfrac><mn>1</mn><mn>3</mn></mfrac><mo lspace='0.0em' rspace='0.0em'>⁢</mo><mrow><msqrt><mn>7</mn></msqrt></mrow></mrow></mrow></msubsup><mfenced open='(' close=')' separators=','><mrow><mrow><mn>3</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><msup><mi>x</mi><mn>2</mn></msup></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mn>2</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><mi>x</mi></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>−</mo><mn>2</mn></mrow></mfenced><mspace height='0.0ex' width='0.3em' depth='0.0ex' linebreak='auto'/><mo mathcolor='#909090' lspace='0.0em' rspace='0.0em'>ⅆ</mo><mi>x</mi></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><msubsup superscriptshift='2'><mo mathcolor='#909090' lspace='0.0em' rspace='0.0em'>&int;</mo><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>−</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><mo lspace='0.2222222em' rspace='0.2222222em'>−</mo><mrow><mfrac><mn>1</mn><mn>3</mn></mfrac><mo lspace='0.0em' rspace='0.0em'>⁢</mo><mrow><msqrt><mn>7</mn></msqrt></mrow></mrow></mrow><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>−</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mfrac><mn>1</mn><mn>3</mn></mfrac><mo lspace='0.0em' rspace='0.0em'>⁢</mo><mrow><msqrt><mn>7</mn></msqrt></mrow></mrow></mrow></msubsup><mfenced open='(' close=')' separators=','><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>−</mo><mrow><mn>3</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><msup><mi>x</mi><mn>2</mn></msup></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>−</mo><mrow><mn>2</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><mi>x</mi></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mn>2</mn></mrow></mfenced><mspace height='0.0ex' width='0.3em' depth='0.0ex' linebreak='auto'/><mo mathcolor='#909090' lspace='0.0em' rspace='0.0em'>ⅆ</mo><mi>x</mi></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><msubsup superscriptshift='2'><mo mathcolor='#909090' lspace='0.0em' rspace='0.0em'>&int;</mo><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>−</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mfrac><mn>1</mn><mn>3</mn></mfrac><mo lspace='0.0em' rspace='0.0em'>⁢</mo><mrow><msqrt><mn>7</mn></msqrt></mrow></mrow></mrow><mn>3</mn></msubsup><mfenced open='(' close=')' separators=','><mrow><mrow><mn>3</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><msup><mi>x</mi><mn>2</mn></msup></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mn>2</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><mi>x</mi></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>−</mo><mn>2</mn></mrow></mfenced><mspace height='0.0ex' width='0.3em' depth='0.0ex' linebreak='auto'/><mo mathcolor='#909090' lspace='0.0em' rspace='0.0em'>ⅆ</mo><mi>x</mi></mrow></mrow></mrow><mtext></mtext><mtext> = </mtext><mrow><mn>125.4874841</mn></mrow><mtext></mtext><mtext>
</mtext></mrow>", "`$RESPONSE`", StudentResponse)); feedback:=SubstituteAll(feedback, "`$ANSWER`", "<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mn>125.4874841</mn></mrow></mstyle></math>"); feedback:=cat(feedback, "</mrow></math>"); fi; with(Maplets[Elements]): maplet := Maplet(Window('title' = "Maple TA Feedback", [[MathMLViewer('value' = feedback, 'fontsize'='12', 'width'='600', 'height'='200', 'breakwidth'='600')], [Button("OK", Shutdown())]])): if feedback <> "" then Maplets[Display](maplet); fi;
<Text-field style="Heading 1" layout="Heading 1" spaceabove="7">Exemplo 27.3: Cortes Horizontais </Text-field>A regi\303\243o limitada pela reta horizontal LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJ5RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUkjbW5HRiQ2JFEiMUYnRj5GPkYrRj4=, a curva:LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNictRiw2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GOlEnbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkQvJSlzdHJldGNoeUdGRC8lKnN5bW1ldHJpY0dGRC8lKGxhcmdlb3BHRkQvJS5tb3ZhYmxlbGltaXRzR0ZELyUnYWNjZW50R0ZELyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGUy1GLDYlUSNmMkYnRjZGOS8lK2V4ZWN1dGFibGVHRkRGQEYrRllGQEYrRllGQA==e a curva:LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNictRiw2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GOlEnbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkQvJSlzdHJldGNoeUdGRC8lKnN5bW1ldHJpY0dGRC8lKGxhcmdlb3BHRkQvJS5tb3ZhYmxlbGltaXRzR0ZELyUnYWNjZW50R0ZELyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGUy1GLDYlUSNnMkYnRjZGOS8lK2V4ZWN1dGFibGVHRkRGQEYrRllGQEYrRllGQA==esquematizada na Figura 27.4:
Figura 27.4 Exemplo 27.3: Gr\303\241ficos de 1 (preto), LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSZtc3FydEdGJDYjLUYsNiVRInhGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRidGKy9GOVEnbm9ybWFsRic= (vermelho), e 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 (azul)
Acima fica o gr\303\241fico de 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 (em azul, na Figura 27.4) para x em 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 e abaixo o gr\303\241fico de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Jy1GLDYlUSJ5RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUkmbXNxcnRHRiQ2Iy1GLDYlUSJ4RidGNEY3RitGPkYrRj4= (em vermelho, na Figura 27.4) para x em 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. Usando divis\303\265es verticais, esta \303\241rea pode ser representada como a soma de duas integrais: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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNictRiw2JVElQXJlYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GOlEnbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkQvJSlzdHJldGNoeUdGRC8lKnN5bW1ldHJpY0dGRC8lKGxhcmdlb3BHRkQvJS5tb3ZhYmxlbGltaXRzR0ZELyUnYWNjZW50R0ZELyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGUy1GLDYlUSRBX3ZGJ0Y2RjkvJStleGVjdXRhYmxlR0ZERkBGK0ZZRkBGK0ZZRkA=O valor desta integrais \303\251 ent\303\243o: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 \303\241rea pode ser representada como uma \303\272nica integral definida se divis\303\265es horizontais forem usadas. Para trabalhar com divis\303\265es horizontais, requer escrever os contornos \303\240 esquerda e \303\240 direita como fun\303\247\303\265es de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=. O contorno esquerdo \303\251 formado pelo gr\303\241fico de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Jy1GLDYlUSJ5RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUkmbXNxcnRHRiQ2Iy1GLDYlUSJ4RidGNEY3RitGPkYrRj4= , ou: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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNictRiw2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GOlEnbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkQvJSlzdHJldGNoeUdGRC8lKnN5bW1ldHJpY0dGRC8lKGxhcmdlb3BHRkQvJS5tb3ZhYmxlbGltaXRzR0ZELyUnYWNjZW50R0ZELyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGUy1GLDYlUSZsZWZ0M0YnRjZGOS8lK2V4ZWN1dGFibGVHRkRGQEYrRllGQEYrRllGQA==O contorno direito \303\251 formado pelo gr\303\241fico de 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, ou: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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNictRiw2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GOlEnbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkQvJSlzdHJldGNoeUdGRC8lKnN5bW1ldHJpY0dGRC8lKGxhcmdlb3BHRkQvJS5tb3ZhYmxlbGltaXRzR0ZELyUnYWNjZW50R0ZELyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGUy1GLDYlUSdyaWdodDNGJ0Y2RjkvJStleGVjdXRhYmxlR0ZERkBGK0ZZRkBGK0ZZRkA=Designando por LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiU0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= a coordenada y do ponto de interse\303\247\303\243o dos dois gr\303\241ficos: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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNictRiw2JVEjYGBGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSI9RicvRjpRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZELyUpc3RyZXRjaHlHRkQvJSpzeW1tZXRyaWNHRkQvJShsYXJnZW9wR0ZELyUubW92YWJsZWxpbWl0c0dGRC8lJ2FjY2VudEdGRC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRlMtRiw2JVEpU19hcHByb3hGJ0Y2RjkvJStleGVjdXRhYmxlR0ZERkBGK0ZZRkBGK0ZZRkA=Note que este valor pode tamb\303\251m ser obtido resolvendo a equa\303\247\303\243o: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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JS1GLDYlUSNxMUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0Y4USdub3JtYWxGJ0YrRjpGPQ==para LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=, e obtendo: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A Figura 27.5 contendo uma esquema da desejada regi\303\243o com os contornos \303\240 sua esquerda, direita e acima destacados em azul, amarelo, e vermelho, respectivamente.
Figura 27.5 Exemplo 27.3: A integra\303\247\303\243o sobre a regi\303\243o contornada pelas curvas em azul (esquerda), amarelo (direito) e coral (acima)
A \303\241rea desta regi\303\243o pode agora ser escrita como uma \303\272nica integral definida: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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNictRiw2JVElQXJlYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GOlEnbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkQvJSlzdHJldGNoeUdGRC8lKnN5bW1ldHJpY0dGRC8lKGxhcmdlb3BHRkQvJS5tb3ZhYmxlbGltaXRzR0ZELyUnYWNjZW50R0ZELyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGUy1GLDYlUSRBX2hGJ0Y2RjkvJStleGVjdXRhYmxlR0ZERkBGK0ZZRkBGK0ZZRkA=cujo valor \303\251: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, as duas abordagens para encontrar a \303\241rea desta regi\303\243o est\303\243o em concord\303\242ncia.
<Text-field style="Heading 1" readonly="true" layout="Heading 1"><Font readonly="true">Maple T.A. Maple-Graded Question</Font></Text-field>Using the Maple-graded question type, you create a question that uses Maple functionality when creating the correct answer and determining if the student's response is correct. The Maple-graded question type has an option to plot the student's response. To include the plot option, insert the corresponding task template. For information on creating questions, making assignments, and exporting Maple T.A. course modules, see Overview of Maple T.A. Integration.
<Text-field style="Heading 2" layout="Heading 2">Algorithmic Variables</Text-field>Algorithmic variables can be used to create a question that contains randomly generated parameters. You can refer to algorithmic variables in the Question, Answer, Hints, and Feedback input regions, as well as in other variable definitions. To reference an algorithmic variable, include "`$variable`" as text or 2-D Math, for example, x := `$myvariable`. Adding algorithmic variables to the question is optional.
In the following execution group, add an algorithmic variable. To include more variables, add more execution groups. If your assignment contains more than one algorithmic variable, ensure the variable names are unique.randomize():
with(plots):
with(RandomTools):
a1 := Generate(integer(range=1..3)):
c1 := Generate(integer(range=1..3)):
fn6 := a1*x+c1;
a2 := Generate(integer(range=-5..-1)):
c2 := Generate(integer(range=10..20)):
while (c2 <= c1) do c2 := Generate(integer(range=2..6)) end do:
fn7 := a2*x^2+10*x+c2;
ss2 := solve(fn6-fn7=0,x):
if (evalf(ss2[1]>ss2[2])) then
thigh3 := ss2[1];
tlow3 := ss2[2];
else
thigh3 := ss2[2];
tlow3 := ss2[1];
end if:
low3 := solve(diff(fn7,x)=0,x);
fn8 := eval(fn7,x=low3);
high3 := (solve(fn8-fn6,x));
ylow3 := simplify(eval(fn6,x=thigh3));
ry3 := solve(y=fn6,x);
ly3 := (-10-sqrt(100-4*a2*(c2-y)))/2/a2;
A3 := Int(ry3-ly3,y=ylow3..fn8);
ans3 := simplify(value(A3));
evalf(ans3);
#plot([fn6,fn7,fn8],x=low3..high3,y=0..fn8+1);
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">Quest\303\243o 27.3</Font></Text-field>The question can contain text, 2-D Math, plots, images, and algorithmic variables. To insert a plot in the question, use the Plot Component.
In the following text region, enter the full contents of the question.Usando divis\303\265es horizontais, encontre a \303\241rea da regi\303\243o limitada por:
y = `$fn6`,
y = `$fn7`, e
y = `$fn8`
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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
<Text-field style="Heading 2" layout="Heading 2">Answer</Text-field>To evaluate a student's response, enter the correct answer. Complete each line of code with a semicolon. The last line must evaluate to an expression that will be stored as the variable `$ANSWER`.
Enter Maple code in 1-D Math that evaluates to the correct answer. Add additional execution groups as needed.LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=evalf(ans3);
<Text-field style="Heading 2" layout="Heading 2">Evaluate Student's Response</Text-field>To evaluate a student's response, you must evalute to a Boolean value (true or false). The variable `$RESPONSE` is automatically initialized to the student's response. Using `$ANSWER` (the correct answer) and `$RESPONSE` (the student response), one example of evaluating to a Boolean value is, evalb(`$ANSWER`-`$RESPONSE`=0);
Enter Maple code to evaluate a student's response. To add additional Maple functionality, use the Answer input region.evalb(evalf(`$ANSWER`-`$RESPONSE`,5)=0);
<Text-field style="Heading 2" layout="Heading 2">Hints</Text-field>A question can offer hints to students when requested. Hints can contain text, 2-D Math, and algorithmic variables. Adding hints to the question is optional.
Enter your hints in the following table. You can provide up to three hints.
Replace this text with hint 1.Replace this text with hint 2.Replace this text with hint 3.
<Text-field style="Heading 2" layout="Heading 2">Feedback</Text-field>A question can display feedback when a student provides an incorrect response. The feedback can contain text, 2-D Math, and algorithmic variables. The feedback can also refer to `$RESPONSE` (the student response) and `$ANSWER` (the correct answer). Adding feedback to the question is optional.
In the following text region, enter feedback to an incorrect response.The definite integral is `$A3` = `$ANSWER`with(StringTools): with(DocumentTools): feedback:=""; StudentResponse := GetProperty(`TextArea2`, `value`); ANSWER := evalf(ans3); if evalb(evalf(ANSWER-eval(parse(StudentResponse)),5)=0) then feedback:=cat("<math><mrow><mtext mathvariant='bold'>Correct!
</mtext><mtext>
</mtext><mtext mathvariant='bold'>Your Answer: </mtext><mtext>", StudentResponse, "</mtext></mrow></math>"); else if StudentResponse = "" then StudentResponse:="<NO RESPONSE>"; fi; feedback:=cat("<math><mrow><mtext mathvariant='bold'>Your answer is incorrect. </mtext><mtext>
</mtext><mtext mathvariant='bold'>Your Answer: </mtext><mtext>", StudentResponse, "</mtext><mtext>
</mtext>"); feedback:=cat(feedback, "<mtext mathvariant='bold'>Correct Answer: </mtext><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mn>125.2134360</mn></mrow></mstyle></math><mtext>
</mtext>"); feedback:=cat(feedback, SubstituteAll("<mrow><mtext>The definite integral is </mtext><mtext></mtext><mrow><mrow><msubsup superscriptshift='2'><mo mathcolor='#909090' lspace='0.0em' rspace='0.0em'>&int;</mo><mrow><mfrac><mn>29</mn><mn>10</mn></mfrac><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mfrac><mn>1</mn><mn>10</mn></mfrac><mo lspace='0.0em' rspace='0.0em'>⁢</mo><mrow><msqrt><mn>341</mn></msqrt></mrow></mrow></mrow><mn>20</mn></msubsup><mfenced open='(' close=')' separators=','><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>−</mo><mn>3</mn><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi>y</mi><mo lspace='0.2222222em' rspace='0.2222222em'>−</mo><mrow><mfrac><mn>1</mn><mn>5</mn></mfrac><mo lspace='0.0em' rspace='0.0em'>⁢</mo><mrow><msqrt><mrow><mn>100</mn><mo lspace='0.2222222em' rspace='0.2222222em'>−</mo><mrow><mn>5</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><mi>y</mi></mrow></mrow></msqrt></mrow></mrow></mrow></mfenced><mspace height='0.0ex' width='0.3em' depth='0.0ex' linebreak='auto'/><mo mathcolor='#909090' lspace='0.0em' rspace='0.0em'>ⅆ</mo><mi>y</mi></mrow></mrow><mtext></mtext><mtext> = </mtext><mrow><mn>125.2134360</mn></mrow><mtext></mtext><mtext>
</mtext></mrow>", "`$RESPONSE`", StudentResponse)); feedback:=SubstituteAll(feedback, "`$ANSWER`", "<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mn>125.2134360</mn></mrow></mstyle></math>"); feedback:=cat(feedback, "</mrow></math>"); fi; with(Maplets[Elements]): maplet := Maplet(Window('title' = "Maple TA Feedback", [[MathMLViewer('value' = feedback, 'fontsize'='12', 'width'='600', 'height'='200', 'breakwidth'='600')], [Button("OK", Shutdown())]])): if feedback <> "" then Maplets[Display](maplet); fi;
<Text-field style="Heading 1" layout="Heading 1" spaceabove="7"><Font encoding="UTF-8">Exemplo 27.4: \303\201</Font><Hyperlink linktarget="Wks:../Dicion\303\241rio/A/area.mw" hyperlink="true" encoding="UTF-8"><Font style="Heading 1">rea</Font></Hyperlink> de uma Elipse </Text-field>A \303\241rea de uma elipse com eixos de comprimento LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1JI21uR0YkNiRRIjJGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYtUTEmSW52aXNpYmxlVGltZXM7RidGNS8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPi8lKXN0cmV0Y2h5R0Y+LyUqc3ltbWV0cmljR0Y+LyUobGFyZ2VvcEdGPi8lLm1vdmFibGVsaW1pdHNHRj4vJSdhY2NlbnRHRj4vJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZNLUYsNiVRImFGJy8lJ2l0YWxpY0dRJXRydWVGJy9GNlEnaXRhbGljRidGNUYrRjU= e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1JI21uR0YkNiRRIjJGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYtUTEmSW52aXNpYmxlVGltZXM7RidGNS8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPi8lKXN0cmV0Y2h5R0Y+LyUqc3ltbWV0cmljR0Y+LyUobGFyZ2VvcEdGPi8lLm1vdmFibGVsaW1pdHNHRj4vJSdhY2NlbnRHRj4vJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZNLUYsNiVRImJGJy8lJ2l0YWxpY0dRJXRydWVGJy9GNlEnaXRhbGljRidGNUYrRjU= \303\251 a \303\241rea limitada pelo gr\303\241fico de: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A parte superior desta elipse \303\251 dada pela fun\303\247\303\243o:LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNictRiw2JVEldG9wNEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIzo9RicvRjpRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZELyUpc3RyZXRjaHlHRkQvJSpzeW1tZXRyaWNHRkQvJShsYXJnZW9wR0ZELyUubW92YWJsZWxpbWl0c0dGRC8lJ2FjY2VudEdGRC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRlMtSSVtc3ViR0YkNiUtRiM2Jy1GLDYlUSZzb2x2ZUYnRjZGOS1GPTYtUTAmQXBwbHlGdW5jdGlvbjtGJ0ZARkJGRUZHRklGS0ZNRk8vRlJRJjAuMGVtRicvRlVGXG8tSShtZmVuY2VkR0YkNiQtRiM2Jy1GLDYlUSNxM0YnRjZGOS1GPTYtUSIsRidGQEZCL0ZGRjhGR0ZJRktGTUZPRltvL0ZVUSwwLjMzMzMzMzNlbUYnLUYsNiVRInlGJ0Y2RjkvJStleGVjdXRhYmxlR0ZERkBGQEZfcEZALUYjNiUtSSNtbkdGJDYkUSIxRidGQEZfcEZALyUvc3Vic2NyaXB0c2hpZnRHUSIwRidGX3BGQEYrRl9wRkBGK0ZfcEZAEnquanto que a metade direita desta elipse \303\251 dada pela fun\303\247\303\243o: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Usando simetria, a \303\241rea total dentro da elipse \303\251 ent\303\243o: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onde faixas verticais foram usadas para formular esta integral definida.Esta integral pode ser avaliada, por\303\251m, n\303\243o usando as t\303\251cnicas de integra\303\247\303\243o discutidas neste curso. A chave \303\251 o fator 4 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSZtZnJhY0dGJDYoLUYjNiQtRiw2JVEiYkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GO1Enbm9ybWFsRictRiM2JC1GLDYlUSJhRidGN0Y6Rj0vJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRkkvJSliZXZlbGxlZEdRJmZhbHNlRidGK0Y9 fora da integral e observar que a integral definida restante: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\303\251 um quarto da \303\241rea de um c\303\255rculo com raio a. Este valor \303\251: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Como resultado, a \303\241rea de uma elipse com eixos de comprimentos LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1JI21uR0YkNiRRIjJGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYtUTEmSW52aXNpYmxlVGltZXM7RidGNS8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPi8lKXN0cmV0Y2h5R0Y+LyUqc3ltbWV0cmljR0Y+LyUobGFyZ2VvcEdGPi8lLm1vdmFibGVsaW1pdHNHRj4vJSdhY2NlbnRHRj4vJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZNLUYsNiVRImFGJy8lJ2l0YWxpY0dRJXRydWVGJy9GNlEnaXRhbGljRidGNUYrRjU= e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1JI21uR0YkNiRRIjJGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYtUTEmSW52aXNpYmxlVGltZXM7RidGNS8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPi8lKXN0cmV0Y2h5R0Y+LyUqc3ltbWV0cmljR0Y+LyUobGFyZ2VvcEdGPi8lLm1vdmFibGVsaW1pdHNHRj4vJSdhY2NlbnRHRj4vJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZNLUYsNiVRImJGJy8lJ2l0YWxpY0dRJXRydWVGJy9GNlEnaXRhbGljRidGNUYrRjU= \303\251 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSVtc3ViR0YkNiUtRiw2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYkLUYsNiVRJ2VsaXBzZUYnRjVGOC9GOVEnbm9ybWFsRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0YrRkA= = 4 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSZtZnJhY0dGJDYoLUYjNiQtRiw2JVEiYkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GO1Enbm9ybWFsRictRiM2JC1GLDYlUSJhRidGN0Y6Rj0vJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRkkvJSliZXZlbGxlZEdRJmZhbHNlRidGK0Y9 (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 ) = LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2KC1GLDYlUScmIzk2MDtGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2LVExJkludmlzaWJsZVRpbWVzO0YnRjcvJSZmZW5jZUdGNi8lKnNlcGFyYXRvckdGNi8lKXN0cmV0Y2h5R0Y2LyUqc3ltbWV0cmljR0Y2LyUobGFyZ2VvcEdGNi8lLm1vdmFibGVsaW1pdHNHRjYvJSdhY2NlbnRHRjYvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZOLUYsNiVRImFGJy9GNVEldHJ1ZUYnL0Y4USdpdGFsaWNGJ0Y6LUYsNiVRImJGJ0ZURlZGN0YrRjc=.Note que esta f\303\263rmula se reduz \303\240 \303\241rea de um c\303\255rculo com raio LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= quando LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUYsNiVRImJGJ0Y0RjdGPkYrRj4=. Note tamb\303\251m que este resultado poderia ter sido obtido com divis\303\265es horizontais. A integral definida para esta abordagem \303\251: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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNictRiw2JVEqQV9lbGxpcHNlRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y6USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGRC8lKXN0cmV0Y2h5R0ZELyUqc3ltbWV0cmljR0ZELyUobGFyZ2VvcEdGRC8lLm1vdmFibGVsaW1pdHNHRkQvJSdhY2NlbnRHRkQvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZTLUYsNiVRKEFfZWxsX2hGJ0Y2RjkvJStleGVjdXRhYmxlR0ZERkBGK0ZZRkBGK0ZZRkA=A avalia\303\247\303\243o desta integral \303\251 quase id\303\252ntica \303\240quela encontrada com divis\303\265es verticais. O fator 4 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSZtZnJhY0dGJDYoLUYjNiQtRiw2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GO1Enbm9ybWFsRictRiM2JC1GLDYlUSJiRidGN0Y6Rj0vJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRkkvJSliZXZlbGxlZEdRJmZhbHNlRidGK0Y9 externo, reconhecer a integral restante como um quarto da \303\241rea de um c\303\255culo com raio LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiYkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= e simplificar para obter: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Como o esperado, os dois m\303\251todos de divis\303\243o levam ao mesmo resultado.
<Text-field style="Heading 1" layout="Heading 1" spaceabove="7">Resumo</Text-field>A computa\303\247\303\243o de \303\241reas \303\251 uma das aplica\303\247\303\265es fundamentais da integral definida. Uma integral definida para a \303\241rea de uma regi\303\243o plana pode ser encontrada pela adi\303\247\303\243o de uma cole\303\247\303\243o apropriada de fatias finas horizontais ou verticais. O integrando \303\251 o comprimento de cada fatia e os limites de integra\303\247\303\243o correspondem aos menores e maiores valores da vari\303\241vel independente que descreve a regi\303\243o.A \303\241rea de uma regi\303\243o verticalmente simples descrita por:LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2J0YrLUklbXN1YkdGJDYlLUYsNiVRInlGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2JC1GLDYlUSlpbmZlcmlvckYnRjdGOi9GO1Enbm9ybWFsRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi1RJSZsZTtGJ0ZCLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZNLyUpc3RyZXRjaHlHRk0vJSpzeW1tZXRyaWNHRk0vJShsYXJnZW9wR0ZNLyUubW92YWJsZWxpbWl0c0dGTS8lJ2FjY2VudEdGTS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRmZuRjRGQkYrRkI=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 para todo LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVElJmxlO0YnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUYsNiVRInhGJ0Y0RjdGPkYrRj4=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2JkYrLUkjbW9HRiQ2LVElJmxlO0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGOi8lKXN0cmV0Y2h5R0Y6LyUqc3ltbWV0cmljR0Y6LyUobGFyZ2VvcEdGOi8lLm1vdmFibGVsaW1pdHNHRjovJSdhY2NlbnRHRjovJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZJLUYsNiVRImJGJy8lJ2l0YWxpY0dRJXRydWVGJy9GNlEnaXRhbGljRidGNUYrRjU=\303\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 \303\241rea de uma regi\303\243o horizontalmente simples descrita por:LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2J0YrLUklbXN1YkdGJDYlLUYsNiVRInhGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2JC1GLDYlUSllc3F1ZXJkYUYnRjdGOi9GO1Enbm9ybWFsRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi1RJSZsZTtGJ0ZCLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZNLyUpc3RyZXRjaHlHRk0vJSpzeW1tZXRyaWNHRk0vJShsYXJnZW9wR0ZNLyUubW92YWJsZWxpbWl0c0dGTS8lJ2FjY2VudEdGTS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRmZuRjRGQkYrRkI=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2J0YrLUkjbW9HRiQ2LVElJmxlO0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGOi8lKXN0cmV0Y2h5R0Y6LyUqc3ltbWV0cmljR0Y6LyUobGFyZ2VvcEdGOi8lLm1vdmFibGVsaW1pdHNHRjovJSdhY2NlbnRHRjovJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZJLUklbXN1YkdGJDYlLUYsNiVRInhGJy8lJ2l0YWxpY0dRJXRydWVGJy9GNlEnaXRhbGljRictRiM2JC1GLDYlUShkaXJlaXRhRidGUkZVRjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0YrRjVGK0Y1 para todo LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJjRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVElJmxlO0YnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUYsNiVRInlGJ0Y0RjdGPkYrRj4=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2JkYrLUkjbW9HRiQ2LVElJmxlO0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGOi8lKXN0cmV0Y2h5R0Y6LyUqc3ltbWV0cmljR0Y6LyUobGFyZ2VvcEdGOi8lLm1vdmFibGVsaW1pdHNHRjovJSdhY2NlbnRHRjovJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZJLUYsNiVRImRGJy8lJ2l0YWxpY0dRJXRydWVGJy9GNlEnaXRhbGljRidGNUYrRjU=\303\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Embora seja importante ser capaz de avaliar uma integral definida por uma \303\241rea, o passo que requer mais habilidade e compreens\303\243o \303\251 construir a integral.
<Text-field style="Heading 1" layout="Heading 1" spaceabove="7"><Font encoding="UTF-8">Pr\303\263ximo Cap\303\255tulo</Font></Text-field>O pr\303\263ximo cap\303\255tulo nesta unidade considera uma \303\241rea na interpreta\303\247\303\243o gr\303\241fica do Teorema do Valor M\303\251dio para Integrais. Neste cap\303\255tulo o valor m\303\251dio de uma fun\303\247\303\243o ser\303\241 desenvolvido usando o processo dividir em fatias, aproximar, calcular o limite e avaliar. Os cap\303\255tulos restantes, nesta unidade, usam o mesmo processo geral para desenvolver propriedades adicionais geom\303\251tricas e f\303\255sicas de integrais definidas.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>:::::::::::::::::::::::::::::::rYyYp:4:\"\{\}-%%ROOTG6'-%)BOUNDS_XG6#$""!!""-%)BOUNDS_YGF'-%-BOUNDS_WIDTHG6#$"&S-"F*-%.BOUNDS_HEIGHTG6#$"%!4#F*-%)CHILDRENG6"