?TMkr[?:;JUJNJJH:E<=JFJ:Nv@P:_r<N\\EJ:<:jyyyyyI::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::BmSHmS@::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::vpqxpq<::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::xyyyyy;:bwGyjgYs?hwEij:Bw=igeirogwGijgYs=hwEYjZ<eq]wvuxegYs?XwAIigYs?xvuxeUYncFtAxVGiiIEvihbayqewu_x_SimWVuaX`QimUfu[x]QImMfu_H`Sym[vtQH[WinaFt?hUAYg]dsuWSSYmSvtOh[AygeDtChWAYhsDtCxWSQ@YxZuPkUue\\X\\MqjIU`hWLmLiatV<xRmngUTRhWMMmhaTWdWKeLfmsG`wIykf=TL@XTAOmqUlhX^uQqMwEAygUTuaX^]Yp=wxaYryyywyxYyxiysqywIYsywwyxgiyqIwwixaYyoyvuYx]YymIvuYx::::ruuYxYA:::::::::::::::::::::ZhiysqW:::::BxWYykA:::::::::::::RuuIxUA::::::::::`yqCv>xxQykqytQxxQymqyuaXsYwwyxeyysywyiyoiyqyvoYvuHxOiliis?hvqxcYynaVuUxZMYjKEt?xT?ifEDrSwG=IeiSrTMkqTW<XOAMjatQ<XNmliYtOxWNqLj]TQxwKILkutXLxU=OnAvnpx`URpiV;mx_=RpeVylX_yQpiV;qX`IrpqV>IyhuTuMxYAYfySpevxpX`MrpmV<=Yd]ssuWRQYkautEXWMYjMUqMWEmXa]Rpyv?AYgMttIXWMyjUEkWwAihgisygvuXeWin[Fvcx_cyqeGw=IheiroWw?IieirqgwAIigyrsOluUtywREyhuttMxWQykiutIH:lutIXXku]X]YynYVuUxYQykeutMXXQYlmEuWwCYijkmUuUxZeyqUwx]yp]yoqVtExUQYlqe_qqoivypx_yqp]`IrpAw@AyfItwyxeqyuQxsiwKax]Iqpivy<GijTxZwv>qxaarrYwFaynivwIyjiyriwsawLix_Qrpqv?qxairpyVkitUHw=ih_ypOwv=IhiysIxwIykjniVtIxXAYhiTuUx\\Yym]vu]x^YYnaFOxwMiliItM`CUtOpnivuax_CmiYtS@mIu_HxQiniYtSxwOYmiitWxwOimgYtShxYypsiwQix]iqiitXIvsqYwJyxeAtrawMQylAvxIylaynqvrawMyxdysrYwKAyfQtrawMIyhAuuax`qyuqxxQylAyhqtqYwKAYaHxSYomyukXxYYpqyvAYyoYvwIyiYykiumyuoHxUiomiuiXxYYpmyumhxaIruYxtywMIgiyoyvqIwCIxWyomqgaYrmwv=yhayqiwwQYnyyx]YymYuWYlyuuinYyoyvsyWoYvyhx_yqoiv;ix_IrjsEXx]ypuYxUivMxYI::kiysQx]ypeysIxwMiuax_YyniVJmiYtUHfx`Yyoyvuixa=\\xwQYn[nyvwAyiqywQyxayrMv;:fyrqywIyxiY:::ZtmvqYwIYx]yqmYvuHYaiMrqyvgys=FX@I:_YymYvdYtuyxayyuyxyYymyyuYx;::JyqywuYxYyxiytqywUyxiYuuywgY^yryyyiyyqyw=:ZxiyumvuYxaIfysqyxayyeyyyywyywiyZwyYsApywoyvmxwyxuy:nYtyx;vYxyyyInYtI:ryyA::::::::::::::::::::::::::::::::::::::::::::::::::::::Z_iv_iV::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::xyyyyy;:bwEYjFR:^x[qPAYigYs=hw:rsGXvohc_ypGWwAYh_IqUwtSX\\[ipQGvkXcUymYfu]x^YIpGWu]X_UinkVvmhcUimQfsyGUMykwutSX[Uin\\x\\UQl]UgXXZmPpuV?ax]eqm=vo\\X[MQnMVu\\X[EqnQvvLxWAplmuk@XSiNjuT]<xRmNgEtLXWH]KfqsGXWHekfqsHhwKmLiut[TxZ=Qo]v:uxc]stIxXeYriwwIYkiYtQhoqvvqxbaypQwvyxeiyriwwAyhiysAXoYvuYx]qv;JrGyj=:xxxayq;:::::::::::::::::::::bunW::BxWQv;::::::::::::::::jpSu::::::::::::::::::nWtHUag=joqyuexxYynmYuYXxUYmmytQXxMykmYtIxwIyjmytQXvix`oui`xXyogqsCXw?ag`ip?Wve@`\\aoknu_p^Xqnavubh_YAofvubh_ZYon>vfh`[aooFvg@a^qpI?w:qfeqrpowJikaiq\\WwDyiiItLhwHIkgysExwLilkIu^xwMilhisCdmMfu]x]aiqUWw?YhnpjytX`wGyjgysFHxRInnQvrhx_yqoavvTrigvoHdUymSfu[H^aiqYgwGijeIsugwAIiLXXUylyUsewLyXdYSsqwOUYlyUuIXXWVZwpx]iQfx_]xDsuWwCA:bieyruWwGYjkytShxYioiysGXwCYiPxXQylye_yQnx_yqoYvsHygYtxQykYykAvqyv?yxaYrpyv<qx`Arpqv;es=pl=vtMxWeYreWymYtqYuYXvixaYYn]vu]x\\UymoXChwLF?@oyuoXykiusywMYxUIoiysIpm;KIlFsoYvyxwPymnIvrpxaAsqIwDEtOPnaf^ArnIvqpx`irrQwHyxcYsqEm`X`[dqSOimfsrQwGAYWHxOimJpIwvswQIniqaYyoKbcmmiugHygitqIwEYxWiokyt]poAG_HxSYniitWHygYtwyxcqsMXvmxcgwPAyfatrawNut]XxYipuYxYiyqyvsiwMix[IqtxeowSIygytriwOYylIvwIYwIykYykIvoYv;Yx[IqmIvqXx[yptXfaYrmWxUYouywMYysyuIxsywSYx[IqoYvyXx]iqoYvwhxFyiautYx\\qyvyxxMyoXjuWyoayqawuYx^QylQvtQx\\=rvAixayrJsEXxUYoyyxaYymYvuYx]iwey::::`Yyqyv_ysqYoYyDywQymiytaxwUYomYueXx;VwvqXZfayqEyiARusywUAnWphrywwQyn=uQyqYw;xyxiyyuywyYy;::Jxyiv=nYmYyqYwdysqYwMyxeYt;JyiYuuyxeixayy=RytI:lYymYvWyqqyvAYsAfyt]y=uAnYwQykxeYy[uyYbyxYyyyy;wqy_YlIuax=yAyyytixqYwYyjyuiyyyy=::wAyA:::::::::::::::::::::::::::::::::::::::::::::::::::::fVEYs:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::Zymy;:bw@f_IRJ[Ui=QxVQooQvspx`Qrpqv<yxcIsrQwEQxUAohYtTpwMQmiatV@xQQnlYucHwAiiaArgWwCIjjyt\\@xRan`yqbWvrxdfasAxwMAmbYro_vvHfcyrvGw@YibarnGw?AibQrk_vshebarm?w?yh^IqWWvphd]qpNgubp`WIopFuYH^OilEVtKPZOqlIVu`X`[ipOwv>qhiqtZhx^yqoyv?yxcassywRQyjauuax]iyrqwxaypMv_ypuxVyoqyuaxwQymMsqYwSxjx?Xjqqii=::::::::::::::::::::thsqW:BxWYy:::::::::::::::::::jpSu::::::::::::::::::::^wwAyf=:::jpGyhUxruwYx[iyoIvwix]iyoYvhYsuYxMyxaYqmytUXxQYmeyrmWwyXdayomvuMxWQYgqSsuvxxx\\Mpoeu]`XUqMmIUXLXR]mkuTUDxOEmiYtPtwMulieTS<XPYMkyTZ@xOQMjmd^ipG?wyhfdarj_wEQjcarjWwCaigysGpwKykhAtFhwIikjitT@xOYmgysFlBIYiqtreWMyXd]SrEwC=ycYSsiWNQyluus=XTMYi=UrYwGuxairrUwGUYmEVuQxZoVeyrowvuHe[ioqfu_H_gIsswwIIkgYswgwCIigIsugwCYicIregvsXdcYrewwGijgIsugwtUuMXYsifqqyv=Iyfispqv>ix_qqo=PylKZQyl=f]iqsEooIvkxwOYlgItKhwGyigYsygwGIjgapEjPhtIxUiyqexYYpkytSHxQImgysCPmEfaQroqv;ix_iqqIwBiyqYwwutoYvsHxUIokIu[xwMyl\\X]YymQVuUxZwv?IyiIuxAyhYylIvrawLyxcQSvxbQSnx`armyumXxXQpoUjkitWxwMImiYt\\youVtIxWQYluUvmxb]YoqVvCxOAVwJAY_HxQymkytY`JetYHxSyn<ygiyruWvqXe]YpAgeItrawKEu_XxYYpuIxWixairmyu\\ypYwuiXc]iMyxeItsAxTaypYwwAygYylIvtIxXmg]ypUgeQtsqwPYynivwIykayqYwtYx\\QykAvtIxXAyhAuriwOIyiEygitwAmIvsiwMyxaqwIYkeysExv=yh]YqYgiQU<yxeysKyiYtkwMYlCsHiuYx]MleysMXwEyjaYrmWxYixYypiYcYyqIwfXqYw^xxYY`yriyt]xwQIjmiibayoAwvUtsYwMQuaXxUIdXxOW:iIuwIykyyuyxwyxgiysywwIyiA::ZrqYkA:::pyvyyxiyy[wmxwywyYqYyoIwuYx_YyDitUyoAaam=:JtOynqYRx:wYyqA:yAbyuiysYxlyusw:Zrmw;sAZwyYtyxoyvmxKwky_YvYZyqYwQyuYxuYymyy_YpyyuYycyxIxyyoYwAuaxMywYZyyY:byry:::::::::::::::::::::::::::::::::::::::::::::::::::::::Z_ml;::::::::::::::::::::::::::::::::QxlQXsEYsEA::::::::::::::::::::::::::::::::::::Zymy;:bwEIjgYs;PmIVuQXZMyiAUtuWRUylqUvex^QYkaup=WCex]aQpqV>EyiIUr]WM]x\\iQnUvvxxdasp=wBeX^uQoaV:mXayRpqV@]X\\Yqlmuk`X^mQoav;]X\\QqnUVwTxYiPleuhXXZmPmuUn@xRinimtXxwQUNh]TU\\wHiKe]SCTWFIkeasCpwNemiyt]PXXOwCYjhYtSPxWIppyvAIyhAuweuyyywayyyxiYuYxwIykQxUyxeysGYuawIyjmqqyvyH:::::::::::::::::::::WYymiu\\iw=:::::::::::::::::::::RuuIxUA:::::::::::::::::ZfMp;::::::::::::ZqawwyX\\ypuyv=YyaYrOymqYeyyuixwyxeiyeIsuIvexxQIlkIsewwwHbcIoIFvMhTYijgTuuwLQihGdtmgKKYg?Ts]GIEIfmCsYgH?id[SrQwF?iescrWgI?YfEDrUgH?YfATsowOIijQUtEHWMYjQUt?HUOykmeu[X]YincVuWx\\[yowfu]X^WimMfu]H^]iouVvmHc_YpCWviXa]yowvvqXcaypGWvixa]Ip;WviHbeirkGxKIkcIragvqHd]youFvex_cyq[GxKykiis=hwEyieyrogvqxc[IpyFwyXfkysCxwGYjnQRsPykeusAhpiv;Usyolox_Arp==`;urwWxWIokIuPithx_qqpqv:mZoVeQZYYnYVw=yfayreWwAyg]ynavtMXXQYm=VuYX[UymMvtMxY]yoqvwEyimysAxv=yfeyreWvix`UymIVuUx[oVXhrawIQylquuEsoYvyhx]IqqivyHxSYniYtMhwKikgisAxwMilqIwhysAXvqxcYynifcYSJ`YIcyrqwv;iggis\\yoyVveXaOWhhqAwCM]]IkytYpo=WvehsawLIyhUxUyniyt[HxSYnlhrawKUuchx[IqqIwCIxTwuixa]YpIWvqxc]ypMwwEyjmytYXxQymeYs=XvqXe]YpMgfYTPwwIykqyuqXxQYniYtUXwEYjaYq]WvmxccoqyvAIyiIusavqxcUwKA<Yi]YqYWvmXdiysgyrywwAyhMqmYuehpIWgYtrxLxvyxfaIqIwEIyiYu\\IfYYqv=iqiWiIu^WgAOquiXxYyoCuqYwKix]IrqYwKIykyuFX@I:bvuYx:Nyl=masAXkyu\\yq[syW<isAX:jrSv:ZlexNY:VXoivNX:HIaqwQYyiytswvX:JvCx::pYwSytYxuYxCyiaq=\\IkAvX`ImiyuixwYy:rxyyywyywIyFYJw;rxwYysyywIyyApIuavqywYYwQyuiyEyyqxSyZxMySyfY:yAwAxyyyIZxMy;yyytIwAvyy=::::::::::::::::::::::::::::::::::::::::::::::::::::::jlSs::::::::::::::::::::::::::::::::vjAxj_iv_iV:::::::::::::::::::::::::::::::::::::xIyA:ZpiVTX[gv:axZaplYu`HxSanmiuj`xZypkAu[Hw?qh^Yq[owOimkiugpwJQlcqruGwCyieisDpwKaleYs>PwFyjdIs<pvxxfcyrvOwDaj_yqdOvmpc]ypOovx@gZIpCoud@aXaowNu]P_OqlIvtTh\\RqmZFuZh^WQot>vlxc]Yq\\OwCQjhitYXx[IqsAxTyyxYyyyyyyYnywUytywgysAXmyu>X<I:::Yai=::::::::::::::::::::JqqyvuhrqW::::::::::::::::::::::pxxgW::::::::::::::::::lhraW:::::::::::::rwvX::ZeuwUYymIvwAXIkYyhXxAyceynmUwIxOouV@ySqkqaty_xDIgjYrSww=IegqqK_wvpcdIqEwvo`b`Ipw^viHa^yOAIeacrSWGAYf?trcgLCyfOdr]_opcaiqYGw:yfaiqZGw:AgdyrrgwFijiItHpwIQkeAsuwwJikhysF@xOQmmquiPxWQogqsBhwHyjkqtWXxUIomaufXxXqooAvnHxRInkytVPxTqnmaudXxVQooYvuxxaaRCih_IqIWvmHbaYqOGw=YgTXZUi;qx`ArnYvtXxVaOsXdgYsXYmIVuUXZUylyUuQxZgVJmEf`mlAf_QRbsrjgYs\\ynevwIYiYyn]vtQxYQYm=faYRIyjJmEVvix`eyreWxQYleyriWuQxYsiXx[wv?yxbirqQwFQyjQuuQxXYYAyxDxvqxcQYmEVuYx[CkiItIXxUIoqqhiyrqgoivvqxcMjaypEwu]X^GwByxbUxWYooYvuxwSingItKHxOYmkQaOWvspav<axZAqpyvAAydqSQAXyouvuax_YYouVvmhrawLAY_`KUu`yq]wuiHDggatriwNmcCosYwIyxcIsvtqawKAYeHxUiomIvqxxayrsiwQIy`XwoUSYokYueXxWIpoYvlyt]XxUYomigewOix]iqlhsqWDYjmytYXxQYnwxfiyryWkQxSxYipmiuiXxdWwEyjiYu]XxCygaqmvyH[Yy<irUymqwEYkayqiWwEYjiyt_ypMu;Jp?yhiY[YyDIFylUx]ak=DI_AJwEIaakYYhyt_yqiwwAyiEx:[ajiys=ZkiY]A:NXmAZtQXHit=:wqtgyuyyxqyxaysuxiaqEy:kiy\\I:::iqwYIiQx;JvCxrywIy^yxiYwYyoat=hIbxFyxiYNYjwyivyYuQymIsAbynYqQywYxixyyx]wmx;::wqywYbyyQy;:::yyy::::::::::::::::::::::::::::::::::::::::::::::::::::::::Z_ml;::::::::::::::::::::::::::::sHqsxjAxjEYsEYs:vJfVAxjA@EA::ZEMdMWdQxlgV:HFcHoc@EAZVm_iv_Qh_iV:::::::j_CoZ_=JdMWdMGEa_=::::::::::::xIyA:Zqyv>Us;xvuXe[IomneySqMwFqxbYSoiv?ix_QRqAwAqXcaSreWPaX^ERnAVqlx`aRqUWJix_]RmyUoLxWApnYVx\\X\\UqiutZDXTqnl=VotWPqmf=tIhWKQlfysIdWKULgAtLdWJULgItOhWMEMiiTZHXWApomV?IYjUUwAyhuyx]yyyyyyItywuYxYyxeYsGyiiYFyj=xHYA::::::::::::::::::::JvyHWah=::::::::::::::::::::::jpSu:::::::::::::::::::^WkIu:::::::::::::jumxxYI::::hHQA:::JvSx]iyoYwwyxiYykiusYvmhxIyhkYqsvwgX\\gIoAVw]HXcImWEwOhSaIl?evIHR[Ikydu=hPSiicttqwMKigKTs_GJCYfwcrWWHAYeiSrOgEAieqssqGP=ydgCsaWLIYi=Ut;xStuk\\XZQPpavwtXaURpaVydx]iQpmV<uXbqB[fvmHc[YomVuWX\\WInUNdYSt=XUUylyurYWIqXaaRrUwGIif`x[Ew=YggIsqwvwhe[IogfvohccIr]Ww?yggIswomMVuMxXyxd]ssuWQQykaUuQXYwv;mZUI\\x[MYjIUtAhqyv>Us?xwGijiisrjiis?PnQvuaX_UylIVuUx[oVXx[wv>usEpmQvwEyiaYr]WuYx[Qyl=VuYx\\UymQfbirpyViitdyrmwxYYoGxUyxcyrpejgItExwMIlnrrYwGIygaTairwYxYIygisgItGhwIYkgq]UYn]vuix`aYqQwvuXdiysIxxoWiYtmyukHxMylkitSxwOylmYucHxSyngysGXwIIkkitWpo?Y]xwOYmeisEXwEijkyt[`LEu_@jokc]YpIggYTFygatsqwQmf]iPAygatriwPeugHxWqwIYkmyuixwAYjYYpEwvqXeaYq]wvuXfeyryWxYYpGyiQylQvrqwQAyhytsqwREvVXsywQiyoivwqtiIkYuiXxWYpNUayrqqkiYtQxxYypuinqytaxxUwPymaYrqwvyXheyruWwIYlii^Yynqvuax`aypQwwQym]xYyo=LiuMwMYxYiuYXoQj_x_ayoAwuEtqAgItqiwMyxgYt:sQomidmoqyvyxxiYu_yqqY:::BxwA::::`ivIY:uYxwIy^yrUypYwMyxayrqYwEitQXjsqI:^XoAJymyuyYymYysyuyxyA:wyxyYytyxoYmiyByiiyXIBxjxiyygYlyy_YjxKyOYuYxpYwcxyQxyIfY::lYyuYxCyyqxwYyayeynY:bynywMy[y=:vyy=::::::::::::::::::::::::::::::::::::::::::::::::::::::::jlSs:::::::::VRAxYyuYEYsdUWeuyxqyjl;r[INWeUWQxlQxyxqydUWeEPHRdMWd=Wb=WsEYs=Wb=WbfVPHr[fVEYsVR`tNatlQxl;::PH[F^[VdMWd=_pohpgv_iv_m=C`kF`=Wb=G^[F^EYsEYsVRjlSsFO<SB=SBchoghRs>L@tJADdERsVRxA=Wb=w[Iv[Ea_=XBRsZJl=Yr=klSdVr=Yr_mlC`kF`B^NQjlSd>L<CM__mlsjFO:::jl;::::::ryvY::PYlmUsmwPqxbMsn]v:aX_IRsiWOuXcUsmEvrXXZqPoiV>uxbMsm=vpXXZypnIvt`x]iQnUvwHXVaOkYUeHxViokUUdxWQymgMTPdwJELgITO`WIqKeeSDXWGYkemSHlwMYMkYufXxZAqpAwDYYnaVyayryyxYYyoxxEwuix_qvAisyWmA:::::::::::::::::::>yiiY:WYykiu:::::::::::::::::::::ZgExUA::::::GYp;HbuuHiGaKUykYuuA::::::::::::Jp?Y::::::::::::::XYpwX::::Zeuw:::::::::Bu\\ypcudYswxgYyhItuAw:AyWimpat:hxGAhnYscWxCAgkAs_GxAaflqr[Gx@AfjirZww=yehQrW_wy@edYqLGwspcaap@ovmhb^Qp;OviHaZYonNvj@b`QqPOvixa`IqR?wxPf`YqXwvxXfdyrrowJikcariWwBYijYtKxwKyK]H^UInUfu]h]UInSVvmHcgirqGvgX`YYn[fuYx\\_ypXymIvtMXXWubxwLalkeacYrcgwEyigIsyOmIVrUWGAyeqst=xTUYmAf`=iItChvshd_YqOwwIijgis=PmAvuYX[YymIvuYx[cjPxZYYmIvu_rqqv>usCxwIYkiysGXxQymmIuYxwMYlTX\\UymQVuYx\\ckgysXYoiVwAygiys=xuYx\\wv?EtIxwKykjnYVvaX__x\\iyqQWWyogysCxwMIl`X_YynefdYsqIwCIYihyqivwix[ix[ipiitSxwMilhX`WwGAyeysrYwFYyneysiwuIxYix_iqkyt\\youVvixaaiMyxdisnQvtxXWHxSinkIu]HxSaeewMilkyt[HxSAaHxFygittAXmYueXxUYoZPIyhqtsqWoYv`iSeugXxXGkXxNykiuvyXqIw\\ypGyiAusUpmyuoXx`WxQYnuywQywMylaYriwvyXgwwUIYuhx[Yq@YjuYwMyymyuuYwMYxQYnayqiWwAyhayrqWwEYjeYsAXwEYjiIwIyiQxYIxyxayxaYsiysMXw[[Mkei]uvCyxaanivuaXHYlqYvuxyqYwuYx]IkA:::yYypYwMYxUYoiytYxwQYngxbaYMIy^YOaeaYQAXivyX:fwvyxg=JqmYvuhr=vwvuuRykIvsIxWiyXixmxiyyqIbyqQy;:Jxoyv]xiysiytUyLIRwuyxeYy:nyvAyyqyumxSy:ZvEyJy;jxwYsyytix]wuynyvqywQyxiYVyxuxyArywA:Jyqix=jysynyx=yay]yyY:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::PHEA::::::::FN\\SF]slQxlaDkF`kFqsHqEYsEYs^U\\SF]sNatNQHkF`@DEa_=<cJlNkJC`fVPH::A@:::Z_m=[_YR:PHI^NatNml=CEa_m[;RsvJPHEaA<PH=__mls[Z_mJCocHoB`^UPHEaA<PHr[Z_=:JdC`kF`EaVMB=SBklC^Z_MB;Ea==:::jl;::::::ryvY::PxXQpoaV<EygmTqEwEUxYePmyehYtS`wGQk]AqSgvtpehQtQHwBIj_QqYOvm@d\\ipMWvoPdYqo<Wu]@_VynkNu\\h^PYmOvtW`]NilFNtLpZQamTvuhpBAxW[yoCGxOInqiv=yxcYssiwIYykIu`YrqYw=yxeImIv`yqqyvyH:::::::::::Ji=wSqXlAWaiuDqXlAgthlwAyiquIYpjPlTwrkpjwIyiqvTQrypnqgysqwHYqNhyremoG_uIxpxk=WNYr_Tw\\Itx]iXyslhw]AtHQqN\\H=Tw\\ITREcypnqCxWiqnst`LnSjtuxi=UCe?JmawZ]t=i>pIuIxWA:::bmnuIQpPir]puIQpgumuIxUyk[W[[g^mdsmHjuIxUioExb[oftVWMsxgw`IUKw[OdoExbuqpuwaEEpxkyViyVSqYvqXaeUD;JiCbuuH]VTwRykYuuIxUA:::bqYPNYR_xUMUqx]ypqIW@nUpHWhhaVykIuWhha>GYp;@Zfiw]qsXyskhyrawjPlSwpV@gXysk\\HMiyvRqxkufHIpwyxfqvRArbxJgHk?WyiIuwhm]WuAQaeuCqyumxxYYp?yfiyrmusw::::rtVW::::::::::::::lHSATynqYuYxxQYlmys=XwuxaaylAuuiWFQYcuqsmVpHy^IPsYVjDY^EprYVk<y\\EpqMVjtX\\uOqEvhpxZiopyUglXY]OpquddXWIOn]UaXXVqnlMU^LxSUnkAu[DxQyMk=UZHxSinlIu_PxWiomeUfXXXmooYVutxamrnEVptxaaRrUWGuxbubGijjatOxwLQllQu_@xSQnjatP@xNqliatOhx\\YqnIvp@xQqmiYtPPxTuwGyjgis?Hw=yf[iosFviXaeIsswwIyjgaqEkaIqOWviHagIsXymwXA@\\x\\QYliureWMUi<yxbuwIyjXHPvugRKykiItGxwIYkXx\\ckiysG`Aqx`artAxTQymyupyv@yxbyRXFBliItEHxOImwYxYYx[ipkytUxwMYliYtKxw`FOhwIYkoIvohymyusYwKywOImkytYxwpvueX`YYoevuex_eyqUWy]yquywMYwEyh]youVvqXc]Yp=WviHOYmiIuYxxairwyxcYykqvqhrYwJmb]iKutTYnUvtQxZYyo?ygaTUIomIu_xwOYmiitUHxSynmiueppQwvuXeaYqUWwEYieyqewvuXeaiQmeCpqqleYs=xvyXfSpFUdWw=Yhuyv=Yx]ypayqewv=YhaYrigjaUWYpoyv?iyoyvwatUr@yieiZQYyPrqwv=yhayqiwxayqyYx]yymyuqYwIYwEYkiysExwIykii]QymQvtQx[ev=aZYyoyvwQYyIykiysywwIyiAyYymYymIvqIwhytYxwQymCtqqmss>W\\H:MyxeIt>W:XXx]yquYx]iwey:::vYoyyuix::::VYuixuixaYymqxGX:JsqyvEitQxwQymexaA:byTyyuYxyiv=::ZxayriyuqXqywwyxiQxoYBxwqwoYtI:tixaY`YyqYwcxZu=pIwqyuI:nywMxyIZwuyZxiYJy[yyyy=::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::jlQh_=:::::::j=cf_gfAxjAH`kF`_gf_ghoghEa_MWSdMWdk^=Yr=QplPpJ@lJ\\_Mh[J@mR@m_MFC`^UPHEA:VR`DEA::Z_MBcf_gfA@Z_m=SsPxlSdVRAXsVR`DEa_m=;EA:Z=MB=SBadc\\_m=;Eacl[SsfVXBRsZA<PH::A`cllSs:ZA<PHI>fVHF::::EA::::::Zymy;:RtGhYQYm[Vu[H_Qil?FtCHXIij_utQx[MYkkuriwO?IgaDsqgRAygiDqCgDshcWCr[wKyXe=TqOgHyHe?TqOWIix`sboqf@;ifWds;xUSInevv;IhiYtWXxWipsIwIiymyvwyxeiyqYwdysqyvCxYYykyu::::::::::::::ygcieqYxf=FOXVRQRJqQXpYvuXJqQXTw\\ITJqQXpIygciuk[W[uIxWIb:ZyLeQvK;JiOpZDIBb:nst`lZhivfYxEWhhcVytXJ;IHfEvk[W[kvVUSytXaeUDuG=FOpYvuxx]Yq;Ruuqp;:<txhMREsf<txhmYUTutwaEutuXi]sspLeQvKYUH]px]ypAsntKiyVS=dufyrEf_VPgXkAGbh=xUMUAtwaEuYUTupigAN:jYcoExbkvVUSyfY::::<DUyrWHdIfLwxm]WylXJqqWpifyq`phXUf;WYq;;?vQtVWIs>uoApYvmXiyvRyuLUqxYYp]ssllUmSntWaAuxSZcD:UyrWhqvq_<;WYTXf=VFIQPpyuwq_phXqsk@nwSyiqx;::Zemo;:::::::::::::::OYydH::SQvmxx]YqcuXYo_x\\aylQuuAxNQydQrsQvgxxUAmnatyOxBQflAs[GxBaflIsaOxCyfjir[ww?Qfhar[ww>yeiQrWgw:aefyqSWwwxddaqOOwtPdcAqK?wqxcaqpFgvmPc_ipFgvm@c]Ip>gvmHc_ipJovt@e^ypJGw;Ageyro?w:yfeyrrowHqjiAtJpwIQkhysE@xNIMch__YpCgvmhb[yneVvgXacqTAYfAdRInlYubhxZipoIvqHxTinkytYXxWYopqViysGHw;if_Yp?gvqhciis=pnafbqrpivyXxYqomYubpx`ArrIwCyxaarqyv?yxbaroavvhx^iqpqv=yxbuwPFbkiItGHxOYmkytXymQFK`B=IikkIu[xxaYrmYucHxOImiYtKxwKacQsqIwCqxbyruix`YynYvsAxQIygQtqIwBUtblgItEhxYIpwYxYIycYsoyumhx[YpkIu]xwhvuex_Kw=yfmyuexxYypiysExvyxfeiUAygQTQim`hsqwPiypQwwyxfQyliULWvmXc]ypIWvmXcYyouvtQxZ]YouvvuxegwOIY`YqUwuex`_wMMfaiQeui`RQyjUx[ippxd]ypQwvyhsUpqQliytUXwAYiayqawvWusupkiukHygYtuYx[IycisqyvAYx[YqoIvspqmgjiuuax_qyuYxxYynaypIwuax_YYhYtUXwAyiGxXEvupryWxUYouipqYciyPyxaivyXPynmIsQokwUyniIoiv?yxVYdYsEXx]yqswhytuywQIbwnXjuuYxYiv]riytYxvMxwwwuuuA<yx]YrGyjiY:]YymYv:ZlUxZtQXjsqYwoyvyX`YyGyx=:bxwQw;::^YwyxeaoMucw:ZqMvgYyiysyyhyy_YlIJyqix]vIYsAZwuyvYRyfYrybytIwIywiyxivyYRyfyx=sAfyyyYxI:xyy;:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::RsPxl;::::::BqvjAxjEYsEIocHoRl_iv_AtJAtlSsFNHv[IVF]ccHOQxlQH^[F^sHqsXsEQWOqclNcf_gfMWdMWdNqtPq_ml;:A`cHOEA::Z_=DUSEu=Yr=atNaDPHI^_UsEacHOAp[QHA`cllSsnghogAxjAxJjlSs>lJ@lRD`A`_ml;I>fV`DA@fVXBRsZA<PH::A`cllSs:ZA<PHI>fVHF::::EA::::::Zymy;:RuYX^Sim[VtIxYIIjQurkOmyUo@xSuNjuT\\<xQQnhaTVhwLqLhYtS\\wIykeisFXwGikeeSGhWMIMlmUmdX_URp=wD=yeUTtIXY]ypQwxYYqyYymIxYx]YyeYtqyv=iryWxH:::::::::::::buuIx:jYsiGwWKw[QDdIvL;WYsSynvSIrZhiv>nw_awmYcqfYWIbu=:xE[g^oDf_fPuIxWAw`ZDIBbZPir]@NsCbfYxERy>NjYohXeffwwAYgXkAG`am]=ewUuuAfw]ys;`DknPpIuAZZtHkvVUCdIfLiGaKmaEUiCbhmpwsZhiufyriwRXhgfY<D:y_q`mbgYxEw`XmYUdwMJSy:vQtG;?fYBuuIxSIbhm:M_`Iu:iYSYyZ`Iu:qt?QnRXhfnvSUy>NpifyQRf;oWvxfANjY;:w`ylxYiylB]PItWaAux_w;lxYYpuGy_wMJ;:y_XMJ[eiY:::::::::::::::::btNW::::::jo?yhiysAxxuv\\yp_x\\UvihxSIlmYsiWx;YciYpafwaHZcYmYuvMhS]YlCUvKXShVp@y^aprQvj<y\\APrgfhar\\ww<yehQrYgwy`eeqqSOww@ecYqN?wsXdbAqJwvpPc`YpAwvrXd^Ip=_vnXc`AqOCgUDsiommuiXxX=Pnuuk`X\\yPpevytXaeRpevyfs@@xNylkqtVxwNqljmqIwCEYfETtywRIYhiTrQWGAyfITsmwOEyhitsuwQMyjYutAxUIyi=UsmWO_udhx]YqrIwEyxaQrmquiPxUqnnIvpxxbyrrIwCEtChwGYjaYqUWwCyhkytQxwKikiq\\?w@UtKhwHvuUX[GwAyxcyR:KikmIu]xx_YqiysGxwKykNsrIwDEtOHxOImoYvsxx<xvuXdUynavuGsqQwFyxdaSpVwEyhmytMxwEYieyq]wuex_YiDyXRmmQemyt_YCqsIxwEYjcoiitQ`E]uYxZayqQwvix`YymYVcIsoivwHxWIohXa]iMYylEygQwEYiaYqUWvqXdaypQggaTUyneis?xwQqvKqYGi`RAyfatsqwQUueHxSinmyuvwSYYCqrughAutupoIvq@qIwEIyiytLisEq<isAxWIYshx_IrsawyxhaypYWlXwGvsAxVEvwhx[Yq@YiqYvqhsAxwIyiiyrqwvyxgayriwvAyhewOixayroYvyhx<hlAvuYx]ayqUymiv`Ibx_YyHyxaIkIv>X:@isAX<iryW<IFykaYSyxeqwQymgxbMnStqiwhYuKoiidaYlieewZqYwvyxfaYSAfWiYuJvgY_anuxeYyqAJy[p=::sywwIykQx]ImiysYx:pyvuIZtqYBxFYsAfys=diw=Vyxux:yAyiytyxuyxiIqavqYnyvyYJyqywuIryvYuyywAwQy;yqy;::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::Ea_=::::::dEMWdJF]SFadc\\ysYEYsPHy=FO\\CEANQPH=?VR\\SFWRAxjFn[Hn_ml;:Axj:::`tNgVPH___iv_YR:PHI^NmlC^<SdMWdk[;Rs>MPHs`R<PHI^_mlcfZ_MFslfv_ivJ<jls[Z_=XBRs::^Ujl;=Wb=?Eay;PHy=fVHF=?::FOjl;::::::ryxyy;:rstpmyUoHxU]OjAu^xwP=njIUb@xS?vkPcWQou>uZ`^QQmPvtTP]Uynpvui@c[YpMovx`geasDHxVyosawOyyvyxyyyyyyxiYsQyeys?yjExpii=:::::::::::::::txx]Yq;jYwhZhivnt?Eb>NsSytHxE;?>N<UCe?jUmsn<txlmxsk[oUmsn:xE[_KHgXvq`Ddfyr=I`bxjE[ZlYUtupYvuHpIWhh\\t=enBa`wAygyQgug>nwWAkYuuIxUAUyr@Bk>fY:@CKw[Otk[W[k^XyslhY\\CygcxUMUqx;BbuuHrgsFTiOn\\t=enx]ypyEwPSuwaEuYSy>nwWaqLJSyvrjtiGgW]VTwRyfYBuuIxSIbhm:csJpqIBdIfLKw[OdqYpx_wwMJSylxYohql>uoAXvQMRRAsfpyumxYoH:iIuw`ylxS^KeAKw[nskhw]UZcLiuvRuWaAuY;Kw[xuLUQFIQPpyumxYCdIfL]FTuRyiytXyo;::::::::::::::::btNW::::::::jo?yhiysAxxEwwQvqYuYXxyxceymqUvExO]yhoxQaKaxYcYnouvUXV_YlKUvOXT_Im]EvKxT[ikAEvGHS[ikGuuEXSWyj=eu?xQDVjpxZy_;qeeyqXWwvHedYqRGwsPdaqpGovo`c_apCgvo`CegLEYgWdsigNIihiDtwgRIyhmDtywRQIloutMxXMIkWeuWx\\[ynaFvch_Yin_vu_X^]iowfvqhc_IqOGvgx`[IokNhettEhnyukHxRevmHcciq[Gw=YgcYrggwIyjaiqYwvuHexWSMYk]Uvax^]IeYriGwwheeyrowwKikkYtMxwXvueX^QykeutEhrYwFyxcAsquk`x]OWiYtOHxMQvGsrIwDM_;MpouVxMYlYynmvu]x]sliitQ`FyxcYstAXsywMix[ypgItGxwdfeuwpVvmXbeiSEwAIygysoYvsHxQimiitQpomVvmXbGxVQylquvixaiyruxairkIu_HxQQvix`aYqQWwEYiii]aYpyuiXxUyneYreWvmXcgwNuumxxayrmYvsXxYyomiuiXxWAfwPyxcYsriwMIyhqTSinmas]jYutMwOutAxUmgcpuywhysExv?usIxVUvuXx]Yqoiv;Iy\\Xx]ypiyt]xv=ygaiVQykyusMwEYjiYtUXxSymqxeYsqyv=ywQYneyruWwAYjKwAyiiYtQXxkuqhqMvgY]iyoyvdIZxYyoaypIW_iroQleysWYCyxaIsqYwIIyiIuuIxWIykiusqqmihiyrAXmqxGX:DisQXoivdIjsqI::^XoIw:hYtqywQyxeYtOY::hIqYw:nxwYypqyuUyoIwdYsWypUyRxwqvcxNY:jv_yrqyvAYjv_ys=uYxyiysqywYsqx;wIy:bynywQYdImiyuixVyyUytyxCyyApIwaxuyyyyJycyZyyY::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::PHEA:::::Z[l[SsvJHv[IFJhmWhmGI^_m[s[Iv[:=__myvIfVPplPplQxlky:EA:VRXB=Wb=wYyuYMWdMWbZ=Yr=iVPH[^cTd[F^[vjAxjRsvJ<SB=sJGnRD`Ea_m[SdfVPH_OS]SF]SB=SBeethVPHI^[LB=SBaDRsVSXr=YB\\CEa_m=cUWeU=Wb=WsNPtPqtp=Yb_ml;:B`knJAtJ=Co?fVDE[NB=C___mlsjvJ@Dy]clJ;A`_ml;::::::ryvY::tWOmmiqtZ>oo^udx`[QpFwug`b_iqd_vw@gZIpGouiHcYApF?vjhcbirtGxViotywTyYuqyyyyqYwuywQyxaIkiuuqqqii=::::::::::::tHWA::::::ygc@Rd<jtuxiYUHa@pIeiuyhqYhfUyr[Xykiu[g^otk[oxowZLiyVSUxfAvx]io=pHRuAQiyVSUHwxm_WufYPIZIiYUIf_NaSypXaeEfyriwXySGQZSueiuwhqYpp;uA:::Z;`d:vREfsmHj=FO;bqYpxcsmPiyfomx]ypqxkoU<dufyriwoMiSufYxEwxmJiSynVJmSylxtuxhuwaAUiyvRqYvmxx]Yp;:::<DgHk?GbuMm]WZqifqstXlwyxfiw]eq@upIHZwyxf]oiwWqvRARnUxEua`Au:quHUyfxgiuRXhffWpxkuVi?pwyxeixgauXqsjhw]UyhxpIXauGwhm[WyfyqYW:::::::::::::JoqyueH::::::::::::::>yfiysywxuvwix_YygIsqiuWXxGigkiqyfwkX^gioMVwexZcinsEwYxWaImYuvQXUaIm_m_yPrYvnnr`ckGuuExRYIk?eu?XRUij=Uu<ppAVjpxY=PpyuihxYuOoqug`xW]omaUdXxUAomUu`fpE_vn@c^qpGovqXdaYqU?wy`fbyq__wAqhdYrkOw>Ihgis=xwLIlhqsBxwJykjatPHxQqmkqtX@xNilkitSPxUAooQvrPxVYoiatOHxQUwCYiiysEHwyHg]Ip=Og]ttQxYKvex_MYjMureWMQykeUuMXYYYnYVvex_QYk]usywRYYmEfbyrqIwCyxcISOilXx[QykeUvex^]YoeVveH`FOpoivvmxa]YomVveX_OwEAydYSlvveXamysIxvuXdYYn]feqsrMvihqYwGQyjQuvqxaYylyuqIwDyxeisrawIAyeyssawKQyjauvetuYx]YxYioiitQHxQymkYu]HxUynoyukxxaIruIxUYylXw_urawKAyfUxUynmIvmhx]YqqIwCYymYvwyxeyx_IrkqcaYqUwvuxeeyruWv_tsqwPUueHxSinFUYquixaaYqUWw=ygsp:@YieyrqWw=YheIoYvu@qYwIQuixwIyk?xVQYwPsygkqUaYrqYwpyvyhuaxtermYvuhx]yqoiv=ixDXwOvuEsLYmwxgqYtipqyuMwWyoyvtQx[uvAyxaqwcxayrPYnmYuiXxUYomYuiHQquixx]YquywMiv]qEyiA>Y\\I:::::mQxaI:fysUy::bxpYw;:::jyWyxayruxgYyqYwhyt;:gqwoYZvIyyqyv=wIy^Y::hiwIYsQymYv_yr=Ryoaw]xuxwqw;xYymyyoyyey::::ZyyY::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::jlSs:::::::::::::::::::::^TcHofv_=QxlQXsEql;rj^TPHEA:VRPHEAVR`DEqlQHrl^Tjl;rjVsEYs_ml;BqVSjl;r[fVEYsZA<PH:::Q`N=PH:c`NmlSs:ZNMdSsZEmlSs:::::::Zymy;:rp?GDsxcasqWgK=iggtqYWLyXfWDqGWGuxd?ds=hVYyoAwwOimuYx]apUx_YymIvuIxYQvyH:::::::::::WYykiu:::::::::::wxmXVRQrxcsnst`Ltxx;:Uyr[XwWqx]iHQQRy:jp?yg=::::ZgYVeiuwXykQa[giY::::::::xUMgw]yswUu:Ry:lxx]IZH]raww=:twaAupIhgemwxm]WyfY::ZqUyiA::::Th:yq_phAyo>hyqawwMakugY::::jpIXaoSuqowxe=Z`AuyhyqYwgYV:uA::::::::::::::JowX:::::::::::::::::Fwwyxc=JoctVWpxxYivQxXYyeqrsQvfpxTQlpAuJpxQYkoYt<hxJIinismWxGYhlaslGxFQhkQsh?x@yfiyraww@yfhar`ow?afhYr]gw<QfgQr[Sj=Eu;XRQyi;utwGRQiiFraSiudtwGROii=UtugQKyhmTsgwMEYgSLTiNmaUd\\xYIpnOgdirmOw=yggis@xwJiKUx[Yin_Vveh`YynancUsrQwGEyfITtyWRAiXHxOQmlYuahx^yqpiv:AxPaMlstIxWOwGix]iqlIu^HxRewvxbAsrQwFix]QqkIUgIsywwKikiq^]iFqx_qqmquh@ycAsrQwDM_;QpnaVuQxZYynctSHxhfeYsrYwFIyhitrYwHAydYSOQvix`WWRxWqwEYieyqawu_SQymhHSIniitUxx_IrwYx[YxYyokIu[HxSInFtriwKAyhYttQxUqytIxwUtoyukHxSInmYuappMwvgtsAxSaypIwxYyoayoyvsqwOeucXxYiomyuiXxYiooYvshyoyvwIyhysIXvmhrenmIvoXxhwuiXaaypQWw=YheYriWw=ygCqkYueXxYIpoYvu`VQYu`WYymex<hkiuteqoYvwPsCvsHykYuwyxeabQylyU_YrDyjWx[QymQvtYXVvvutwIygYymYvqyvEyx_yrqyvAyxaIsfvuaXZ`YynqVPxxaYsyyxeYymixaYryuYxuyxcIyiIuqauEtqQnmytaXxCygAOadmomYuswlyumXxYYp;Rusyw:>yhMq;Yai]wuu>X<is=FxwIyk=Jsqilex_QwSxtYxYyyWyy=sA:::fYuyxwIykYyqiwhIXYymyuuIZryyxaYnYoiynYmqxaYyqYwgysyyxaYtIwA::::::ZyyY:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::PHEA::::::::::::::::::::::::::::::VR`DRs:::::::::ZysY_gf_olgV@DEa_=::::::::::::::::::::xIyA:ZRqmYVtM@[NalGvtWH^ZIpJGwCYjnQvwHyiauuYx^ayoyvwyxgUx]akEx[QvgyryW::::::Jqcu::::::::::::::::::::::fWpH:::::::::::::::::::Bu^ww=::::::::::::::::::::::rtuqo;::::::::::::::::::::btuQo;:::::::::::::::::Rtuqn;:ZpIWgAOQueHrtuiwQacUwGYycyrsyv=yxYinoItyGx;YceIpWfweH[einwUw_hYNJ_xYaYmievWHX_immUvQxVYIlOuuGXSWikCeuEHSYYkxX\\QPqMvktX[IppAvkpxZ_w:QffAr\\si=ut;HSQijKut;hSQijQut?xTMIjGUtugQIYhedskGOGIh_tsqwPMyiCUt=HTMyjSEuMHYYInWVuQhZWq@EYfItqAWBEye=tr]wJAi\\PxSanlAu]HxSInoYvuXxVYokAuZXxWiopqv<yXGhvsHd]ipGgwCyikIuYxwGijaYqSgvuxdiYsAXxQimkapqv;QXGGxIykkytWHxdfeuwMIleqVYYoaVvoSlVviX`]InSQQviH:tFhYsqWwyXfWwHMasmkytNwGYymyuuYx\\AygItraWlXb]IvssqwOayoavwyxcQYmXxWIokYucHxUynmQc]YpgYWiyoYvqqjayqYGkXxWYokYucXxTWxUYnuYxUisAxtIxUQyjYusepkqbgwMaYKQwIyx]Yrii[mfeYriWwyXgaiTyXWXxUQwAYieyrmGFXmyu`YriWwEYieyruWwKsuwwMYliYtMhlQvtUrqiv;yx_qwEyjeYsyWxQiyayrqY>yiYyoAwuax^uvAa]]tMw;qYwGYykQymyuyisExWyxeysTyniicaYMadewMyxeYtqYwKqtaHMA>W\\hpQwvAyhqyvAYuYxwqv;jyqyvyI:Nyyiyt=::::jwyyxiI::nyuuxgYyoyvdILIVYfXJucwwAfyuqXsIxyYyqavqyvmwYIiiysA:kiysIxtywyYyqyyuyx;:bytYy[yqY::::::xyy;:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::EqlQH::::::::::::::::::::::::::::::s`NatNiVPH:::::::::Bocp_iFfV::::::::::::::::::::::xIyA:ZTanlNvqXegAtO`x\\iqpqvBIyhAuwAyhyyvyxxYypqytmvkqqYvyH::WYyxHYahMq;:::::::::::::::::::::Uag=::::::::::::::::::rwUqumHSA::::::::::::::::::::::::VWhH:::::::::::::::::::::btNW::::::::::::::::`xxYI:::::bwRtTIdH:::rtXYpSuvwwqxdUwAIy_YqqIvehxSilmysoGx;YciIpSfwaXZgIoAndYRtEW;IYbeqs=WxHYbuQsyvxDyaqqrivrxX^mPraVq<Y^uPrYVqxX]qPqQVnpX\\UppMVmNr__w=Aghqrjgw?yggiri_w?AhfarkWw=YgdIrcOwyPfdyq^Gw:yfbqqZwvt@eaYqUCi;Ut=XTMijWutGhWUylAVuQXZWymQ^O@xNylkitTdpIOgGxTinkea_IqMWw=IhaYqYwvsXdeanIvqXxVYonyumxxaqrpiv:YxXqonAvlxxaExSIngYs=xvuHeeirsGxQYmkyt[HxMilgIsyGw;YgiItIXxSYnkytSHxOImiItExw>yeaSSimkIuYHxtffqstywOIyfITtFYXxSInkqaoWqivwPreWviXaaYpAwvmxb[iAuuerqIwAix[YpkYu_HxUinZMQykYuwAYoyv=ix]YqmyukHxUynkYuJxYYoqYvyxwgvtQxYYylAvsyWpxcayqYwwQYmKxUYniysIxwIYkeyrmwvuxe?xUayoqvxIykiyqawuQX<YheyrOyjex[IqkQbowQYylAvtIxXmieiZIYFxXuvNxZQylIvuUrqAcIssiwKIygYtsiwMyxTxwWVHH^x_aYpYwIYyiixYyoMtqYvyhqawvAYqYwKixaIsoIwCyxcYsqql;GqtYhoyV\\Xx]YquywQivyXsywhyuWyoiysAxwAyjiysAXmA]qv;:JsqyvEitMw;Hyxeys;BwdI:qIwuyxRwuyxeAbyqiwlixiytMw;VYdyssv^XoAZuUyqiwvXsIxFyxuxwiyqiywAxiuyYtyxwYuQycyuawMycyxYyoYtIryvY:::::ZyyY::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::PHEA::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::Zymy;:BvsheiItSXykiuyyyxYymIiYymYv\\Yqqih=::::::::::::::::::::::::phriW::::::::::::::::rwUA:^wwEubxcYtkivIIx_ys:bxcYtsiwQYyfY:::::::::::::::::::rtXyo;::::::::::::::::::::btXYo;:::::::::::::::nxdewRtuqn;::::::::bt:NW`H:bt:::Zemp?yiqyrAxwyxgUwCIy]yolX^?wvHy]AprauXpxRIlpu[iYoIfweX\\eIoCFwcx[cinCvv]HZ_ymuevWHY_YmmUvQXV[YlWuuMxU[IlSuuIHUYikUuuIXUWYkMeuEHUYyk_uuKhW[ylsuuOhXWYlmeuKhXSikaEuChUSyjYet?xTMYjKmZa`wHfaQqSGwypfaiq[Ow;QgdarlWwAyhgYs;xwLQlhysFpwJqklQu]Tp?wuaH__YpGgvmPtyWTIYheTsewLMyiIutExV?vo`xZYP?ygeirkWw?ihgysCXwCIiciroGwyxfHXXaYpEWveX`QYk_xYYpqqv=IygYtrYwHyxcIsoQVgisAHxQymkytY@lhpyv>AYQHxSYnvS<wvmXbaYqQwvuXdaypEwvmxb_WpXcsmqYvwHycIsoyuiHx<WvqhsiWmQdeyrqWxUYniYtMxvuxd]ypEwvqXdaYqUwv=ivqxcaYIyxeYs<ygaypIghaTWIosYwGIygQxQymii`QylqusywQAyhattIxVaypyvwAyfMomyuaXxUyneiYIyjIusAxTQylIvvAyfaypQwtQXoYvdyrSvjv=yg]ypMwvyXfii[QY=yx_amQVaqwEIbv=AqyvAqs;cqx[iiyrywwIYnwvqxcYynuxLhpIwwAyiexaalMs;aam=Rx_qv=I]qvAI>Yjt]xwGwuqxcMoiYueXxUyomYuiHvxeaYBuXYp;UIyiarMvuHrusIxYA:`Yrmyv=yx?X@is=hYtuYxYYywXJvuYx]IfYFY:::vyxYyyqYfY:::::JyoY:xYyyI:::::vyy=::bynYjyyI::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::Ea_=::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::xIyA::RytYwIyx]YqqiiEx[QvuHWAvWtHWA::::::::::::::::::::::ZgExUA::::::::::::::::XypwX:^WlXwStCipqhoUXpaxlmxnQ@LW`UXjYwvIYnqyumxx;::::::::::::::::::Zemo;::::::::::::::::::::btuyw::::::::::::::::nxd=`hpIWdHRtZd=`H:::OAFWdHRtNWdHMANW:::::iYtXyn[pIWiyt\\Yp?yiqytaxwAYqivsxxUImmIt;XxEYgoirOGxsHa`WBUyewxQykpytGhxPiknitF`xNqjmIt;XxKQjmysxOxIqikqsvGxEyhjQsnwwDQhjQso?xDAijYsr?xEuuOXX[YmyEvOHYYil<y`ErruV=yX`IrquV>Osu_w?IhearjWw>qgdIrcSjMUt=xTKIjGetywSOIk]etAXVHvqtx`MRquV>mx_ERrQWG=ydmsqMwEAyeuStqWPMyhqtr]wJEyfMdYUwAihaYqUgvmXceiro_?ax[qpmquihx\\IQ<f`IrrQwFix]iqnIvqpx_YrqIwDIyfQtpqv<ix\\QQGIkkytY`KEu[hwGijgysCpoGyfYtsawJEu]HxQYmmIu[ppEgfItsawLIyfmpAWw=YgeYrewvmXbCopXdsnoIvoxxcIsHYk]iKIYcXxPwvqxcayqaWx?wwAyfQyiytriwLeuvwRQyjYuuuruIxUIyTXw=Yg]YqQwvyxeaYrewwOVgItuqpqYvWymQvsAxRIyiyttIxVYynYvvqxaaypIwwIyiqyuYxuiX<itIxVQYlYuYhqawtQx[QyjYUaYrqA_AdyruWw=YheYsuwwIykWXJtMHCyx^YMyxcqwOvu=AyxcYsqYwGyxcissIxUiyoIwwyxeiyLYyiYtSwfX:fysIxvAyiExWaiiYYYymIvRymatQXDI:FylexNY:Zmex:BwdYt[uaxwQYbynY:gqw;jtqywQIgap=uyxZw=::::::::::JyoY:xYy;:::::::::::ryyA::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::Z_ml;:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::ryvY::pyuuxx]Yqsu\\YqcuvWJqsuZhmq;::Wai=tH::::ruZh=:::xHbuvWJq;RuuA::Jq;UA::sywSIylHUquKpqYvqxx;sav=pIuA^YlIJuqXxUYpqyuqHUA:siwQyxeitqYwOIygIu^WiQx_wvqxeayp=RylXvEymesuTm:MO:@Rd:Zjxlbgxiivvqxf]umwWwvqXuaw=UYylXxCylHrtRyfYSA::sauutqYwOadmomIuawUuZf=jowxeMp;QA::::^WjoCuZeMp;QA^WjoCuZe=::::lHOqueHQadMostZd=hHbtVWJo;::::QANWhHbtVWJo;QANWgytTYooxd=:`hp=NWjnctZcMo;MadMo;MAZcMo;bt:::::Zcmn[qIWiA:Oqu;::hhriwwIyhUx]queXxEygiypiVwUXVayj]TvqwH]YiusumWFUYfAcSilpQuPpxRiloytI`xOakoitEtnIFweX]aynKfv[xZ]In?VvWxY]YmqUvYHZ[ylkUvSxX]ym=Vv[h[]ymEFvQhY[YmCFvWh[[InSVvaX^Dw@=YbeRqmV;ux`QrpeVydxZe`<QgcIrbOw<agbyq[Gw;QgfYs<Pw?ihhAtFpwEIjhqsC@xOyliQT[yosfvohc[iouVvkHb_ypIwvuXeeYrggvoxcaIqSgwIIkgisAhvoXcpwPYymMVvSwCiiayq]WwEiiiItKXxUingisPiuxxaqROImkyt]pouVuQxZUYmIvvmxb_wKMcYYomvuax__wIIygaTRua@lH@ggaTLGrnoqheyrGygQtsUotxd[iuxaYrsiwKYxWIoxXeayqGyiUx`wwMylqYwEYwAirawIAyhYtsAxUQykiuuax]qytIxwAygQylyUYyoNutMwEyimi_iysyWoyvXyoeyrmgjQUVymIvuax]YYCiyoivwIyeiyoIwsqoeiXYylIvuYx[Mlmyt]xwIYkaiUYY?yxVymMtIHCyxFYsxxayrfvuax_=eaoqVcYssQpctqIwEyxRwrsPym;nxbiysIxxayqMvuYx]I:Rxlyv[wIyxmyqYwyYyiyyWYJxyiv=:::::::::jxSyZvMx;::RyfY::::::JyoY::jyuixMyqIbyxIyA:ZxiYpI:bytYywyyyYwqyuI:ryyA::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::ZwuuXI:::::kyu::ZhmqsunWjq;bu:nWjqsu:nWtHYAfwwAyhMq;UagMq;::::UahMq;JxYYpaYtext=ymMyqQXtyXmMyqUxt=ymeyteXxYypaYtaxt=ymMi`aXEiw]ItqiwQixeytgYvIIwYACIwYYseyuGIx_ItsiwSYypxwQyoYyrUxriXkqxmuwpYXiIypIxvIyn]Ys]xtyhnUscAfXjuAymaSuPm:MO:@B:beevSaYuAyw]ys]yt?AUqhIypIxvCygIusqo_xdixiqvn=LIbw[ysoIwOYyiIu^WhxwQiqIx`YxhQvhIwYaw`aufqvViwbqumqw]AylyvuixciyqaWlH::QYyiIu^W::::hHBu::VWJp;:rtZf=jost::NwwutVW::dHrtNWjo;OAVW::::dHrt::TIhHQAZdMoStTYoct::::FWJo;:::::MANWrwOQucw::Mac=rwOquaxx;FWdHOA:::ZeuwOad=:lHOIyeIsqYvcxxMiimYrGwwwXaiYquvwuHagipifwoh_gYpafwox_hwGQyeMstYWDotJXxLyjlIt@XxOqkmYtDPxMYklYtDXxJqjlys>PxLYklAtC@xHIjkQtEPxNIlkAtBHxJQK_H^]in[^IHxNillitStn]Fv_h^WImCFuKxWSikcutEXVOYjQUthPoIVqdx[upoYVvvsDTmKFv_H^[QE=iSPxRAnniudHxPYmlYuc`xZapnyujPxVEwyXfiysEHwyXfaypIgwCQviHAyhtWQUYmAfgQtqAWcYreWwAihkytYXxUqu]X^QYluuuYhsawLIYappQWuUx[UYmEvvuXdgWmYucXxUIokytWHxQimmYueXxUIomqdSotHWiomiue`OMegwNaynYV\\HehxYyooyukhxYYpmyuixx_IruywSYxYIpFusiwNAygattIxXiypIWkiuoivwhx`WwWutIxUMiiysAXyeYsuyv=ywIYkeYriWwgU]YqDYiOxZayqawyayrqyuixuYx[QYw`YYY;yx@hmuxPxxsyuYxwyxcIyiitqyvAa^EwAAfvuYx\\IyhytuYx\\YyoqVcaoqVeisZaYynYV^ypAwvixbayoMu]hp]caYMadiysEyiIusQomiduwOIyiytVWJpwXZgiytYxxayryywQyyiyt=::::jwyiuyywYYby:::By^Y::::::jxyiw=::::::tix=jyuixayxiyuqywYyymy_Y:jxSyxYySytItixqY:yay=:ZyyY:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::pYvyxxYI:iar=Jvsw:vX:\\Irw:::::RuuywWYyiiu:::::::::::fWJq;:jvIYoMW^AU[IUF=vRUSZAUEk[QUGmxmuwuEYnMW^AenHm:IpPHrlxlKAsoPxgYv[Au>arpPm:IpO@rkpl:M[IuE]w`iuvIyneYteXpUxhquNMRKMR`TssDmGiqYTUKuQiaWbuvZiT[IuE=vRUSZ;=`UYt@QxfYvTphoFJ@B:Be_VStWequNMBjIER_TUKuqjmWdQyqQxvIYn]w_IU[IUFS_fLFrkplFyqbxwcyuvqxeaYTYrUxmEXfAVRurPMSmlswxMEIQSTssDMJEr_DuGAQc]vTmXmmWvEymmieiyqawwEuBoYhkYv\\LqrxPfTOeTpkHpAiR>MwaUvxYiw=:QA^W:FvVYtdpn[Pjx_iRodP?ePodnGhiwkExjNys@most::ruOyqGXjmWrshnGXjm_KiyqYww=:::TvZauAir=]OeTOfr]XRVMuPqyuixx;:::NwwqxeewQAjuihpQWgit::::::::ZcewOad=rwOATI:::::rwZpIWiit:ZcMowxc=dH::::::rtXYoctVW:hHbtTYnqYuQXxUYlmYsigfIstyvuTrMwwwXbiiqwvwqX`gYpgvwshagypsvwqx`gipsVwoX`eIpeVwkH_cIpeFwgX^aynOFwch]aynQvvaH]aio_FwcH^_IoWfvah]_YnQfvaX]aioefvax]_inYfveH`ayosfvcx^_Yoifvex_[inaVv_X^]ynevuWX\\Wyl;FuIxWQYkcutAhUQYk_utGXWSIlmEuMhYWimIFvcx_PgkqtTPxRQnlMseWMQYjEusqwPIYiAutAxTQyj]Ut=xSMYjMUv]X]UYl_xZipoYvv@ycYSKIl<XTUyl=Vvixa]yoqvtMXXGvpHyfYttywQAyeyspiv<M\\eYqYwvqXdeYqwxaqrqyv>QyiIUPggiTWiomQc]YpGyhUxWyooyuiXxWajYutAxSuuihx\\Ww?usqwQYynaV`Xw=IdWvqXdaYqUwwEYjqYuahoyvtIxXQyjYUhwv=iuQxYiysqwwuuqIwCix]yq@YiGxXmhWx[iysIxxYyoayqQwtYx[YymQvtQxZQYyhx]YqqIwCiynyuqxxQYsYwKyxcIsqAcIsHiuYx\\QYlIyIymiyqiwhytiytYHCqtUHGALYmiiaQYshx]yqsqnmyt_yo]cayoIWgYtTIdxwQYnmYueXxUyomid=iytsAlXx_Wjpqyv=iuaxwIYuIxYQv=isAXmARv`I:JsGylex_Yy:HyxaInYmyywYy^YlI:::uaw=::::rytyxeYymyuuirqyveysAfYwYybxpI:hYyqI:vYuQyoYqavMx;:uyy::tyyuI:yiyyA::xyy;::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::RyBx[aimq;:::vxi=kAbuuAiqxKv;iarMv;rwvX:\\Ikaq=\\Iiaq=\\Irw:Zr=XIkar=jusw::>Y\\IvxkAwWXipnjS?Z@He::ZSqsvXxgYvKPgUnjS?Z@<@T<aNpYxheuJ=Q=a_@<:@uF]Pu=ymexkMwEEqMTrf<J=;:wVZGT__eEGVP;b[:Z<YpQxwdIvWPionjS?Z@<:HT>EOIuqXTrfnJ:jJIR^LxiQwsuxk=tx\\M=aO:TB:R`ieFKIsmhxeiteIvEIliG_YFTmb[mL=;::beevRGIrixw]isuIxSirsxnuCIucB=CC?SBC;::mtOgDo[xkuIxSYyiqx;ZeQvVQta_f]O^[f^\\F^_ZD?cC?ePod\\F^_N>jXlMY`UTqtxWwwAyeiyqYWiarUruxn?[\\:xR@]rxYyowX:Jvgyrmu_hl?h\\F^_N>jXhmX\\OeT?pyuixx;Tyo[qaWjo;OaduwOA:ju;gapmuswZp=:Juswvxe=:dhp=:XI:bwnXXIiYtuqnoxcuw:OAXynctNW::::::::::hHQAZdMo;::QQvqxxayqqYvqhpqvvax[aylauvywMYyeirtivn@yYinqauSDqovwwXbkYrIGxyHciypq^RpxWymoauXhxUimoIuThxRilnAuOhXkVwkh_cyocvviX_ayoe^PXxQqLeH_aYoavviX`cyoovvgx_cyouFwmhbayosNeassaWKIYfETsUwGEyeqSsQwFGtJxwIIkiAtH`wCaifqrp_wAIieqrp_wBYigYs=DmEfuWh\\[IoiNfySs]wJEYfATtuWRIyhutsmwOGvolUQYkYutAHEyigq[UYliUuQxYYymIVuwqpyv<AyeisrQwEix^ewIYkmYucHxUyngysPYlquvuxdeYrewvqxcYYn]vu]htywSeugXxYQvix`OwGQyjQutywRQYkPrawvuxdaypOyiexYYp:@YiiYsyWwyXfaiPeukXx\\wwWvvqxcYykqutAXoYvsPriwwIYjmytYXxQYnii^QYdIoYvrqsYwKYykyusiwfx`uv?qruWwAYiSqsqnqYwEisAxvqxdaYMIyeItqyvdYs=XwAyiii]iYYiyHYyiytqyv=iqQwvyxfMpiytUhnavuax^mlmYueXyeYtuipexcIyiIusYwIQu]HMQuaHKqtYHhytYHwxxeyssywSquiHBu:ZgayqiWlhrqWiiusIxWYyfY:ruuIxYAjv=yx?XjrCvJwMYymyvuyxaYymyuuywoyuiXTiuqX:XYymIXI^Y:ZrqYkA:FYsYxjxeyyuYxgyuqyvIYsIx>Y`ImApyvgYNyxex:VyxiYyAwAsav=jxSy:::ZxMy;ryyAJyky;::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::RyBxBvZi=Jqcu:Zi=tHYAnWjq;:WA::XIBxvXJv;jq[q=:nWkA::::vxgExUQvuHRu:iivIIbwUGQvQ;r\\yD::RmygbWit;y\\yl?;r`mEFEIrixhAwUQvQ;r\\:ZmXmaWxiav;YovWkY?ZE<::trlhj?yO:hB:bjcW_YityHbwUGr\\:::::Z;yoFpwdAv^HjrVkYs\\:ZWXilbrkhw]isCXfIv\\yl?;::::Yw_Ces=yooqn=yoAXO`lPdlNplUTMV@s@]RkmWcqYvgtJyrfGgaO_cf_rv`sntLAswAyeExSAreQWcksGmsDOSEOSDQc^Yf\\[yt;YykIuuIxQquiXWQuQMn[LnOdlPhLOplw\\QupyugyqaWjokOdlPh<r^Yf\\uiwQYylHSaeiYQaf]vxpkX_df_e:ptNItx_WfYBuNWJoctVWhHOAVWgitjuKoctVW:hHnXjuKo;Qad=JostVWdHrtTIdHRtFWdH:OATynwXXI`HbtFWJo;:::::QqueHOae=dHQaeMo;bt:::Ze=BxQAZfmpqihUx]iykYusYwpysmWxyXciYoMvv]XX_vl@yZYnryu\\HyYAoryu^@yXQnqiu[xxXanqyubxxXinpiu\\pxVympauZpxVqmoeaeypZSYMohacipuvvih_cIpqFwkh`cIpqNgATtewJ?uVXxSymnYu`XxTYnmIu]`xUynnauc`xUinlytWHxPYmkatR@xKAliqsCTmEN`IRp]Vwlx^mqpiV:qX`IRquV?yxb=SrMWF=ydesrYwIIygaTsmwNIYheTtyWTMyjUUtywRQYkUUuQxYUylAvtAxUQYkaUvax^YYn]VuMxXUymIvu]x]YyneVvmXbYYn]fairqIwCQyjIUPWuUX\\YymYvvyxeeYreghitrYwGm`eYrsumhxYqvmXc]YpAWwcx[YpoIvoPrkfspxhsiwNQyjYuuQxYYymIvuQXoIvdyrSvuxx_iqsQmmidQykqutAxVQykquuIxXYylAvviXuywUIygQwEYjcqoivyPs=xwMYlqYvqH>yiaYOyxaYroqjeYsAhlyuvqxciysIxwIyiUxYA>xvqxcYymQvuYXjtgYWQwEisIX@IZtYxwAyhYyoyvuixa=^YUiyoivwQtqYwIYxYYqwxfewQae=lhqaWhHBuJuWynavvutuIxYYyfyr]i=Rxpij=@is=:ZlqyuqXsIxhiwevuQsOYVxwQym=LyxeYt;ZuixxUwhytKyoXqiw:vXXYyiyuSxyYytIwIytYx]iv]s=Rytit=:hiw=ZvqyxayyEy:fYpI:vYnY:byZy]yyY:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::pijMr;:YQvyH:::::::::::::buZiMqcuvWxHWAvWtHrunWjq;bu:nW:jpkuEi_Xjo>l_?ZJhf::ZGyq]xtCIoJhf:>L:HsolJjmWdquLyPBQ`J<:TUI]`fYv_`jp>l_C^:Z\\HjnFoDXbJhF[>:Z=ipPxwdAv_XjoZJ<:LSplJRUsgPSppJBQP:<C:bgXpp]XiYt<]MBQP:<C:Rb;fFGirkXt?ineFUU:[>:>pPXeTXhU>l_?ZJ<:tV\\=UtyxlqYvqXnTplpn_dNlyWeqYvqxxgW:lXt@qqTmTXmapNapYvmxx_W>rv`pqn`rv`p>AFs?aqwmx;:XYp=yo=XbtNaXMU\\mUr]Qv[uQpqI:icGksGZxHqkhyqaww=:rtXYpQqs<qUTMVX=IES?UyiIuuQp;:Qae=::::::::::::::::dHOA:::::VWJo;:rtZdmostZd=hHOAVW:::lHOadmost:::JvixxkuCxSaemo?YZfUxWYy<itIxwAyhiypivvAxMYydQrtAwvPyaqqtqvr@y[YosIvaHy[QorIve@y[aorQvhxx[YoqyuaxxXinqyubtqIoieTuqWKQyg=ttmWKQyhITumWKQyg_xSYmnau\\hxWqnpau_`xTymnQu[hxVynnYu_`xUYnoiudhxYqomQu]hxXaooAvlhxXqooiueXxTinlyTLwE=YcEsqyV@osApwHIkiysEhwFijgaSYYnYvu]X^[iooFvgx`_YpCgvVxUAooIvo`x[ipnAvnhx[Aqoavwpx]YqoQViysCxwKykeyrqgwEIjlhsYwIqx^qqqyVkitUHxDWv?tpAw?AyeaSSinoIvqXxWYo\\X]]yoyVwyXgeyrqwvuxd]iJIyhex[ypoIvq@xxfaYqYWwyxfeiRQYqxx]iqoYvw`VmheiW]uYx\\ayoyvuaXqYvwxxxglyU<XxovwyxgayoyvtQxYQYdYs=xwEYjiYt_yqYwwQylaypIwtMwGvuurqyvfXsqnqijqyuixwIykYyoyvuYx]uv?yxayrPymmifuwUYythtQxxUwwixcYykIvqYwIyxcYsqIwEqt_YQqvyhryWmyudYs[u]pEypihaypQwvyxeaYQafMpqyv=yxOxwevVXDYxYYpmYvuxx]yq?Y:jv=isAX:@yx?Xjr;BvsywUIyiYuuYx]QwMit=::hIPI:gqw;:XIiQx;\\Yy?YjuWypEyBxFYsAfysqYbxwQw;rxVYZy=sawey:::vYnY::::jyyI:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::RyBx::::::::::[Yyjq;:::::::::::WYytH:::ruZh=vX\\t=YmDep;PSoH::xvZIt_]U@QSoHjD;:sHp[hiIgUefTAR_:ZrTT[yt?IdIvGR_:ZUit@AxeIvOPg=fL::LvUUsqexj]t=Y=PC:bfkvPUItwXgmFOdp;PC:RgwfSMIsqxdMVHefTAR_:Z_DGGYrkXn=X`efTPC:bcGVGMIsshoKhcefTAR_:Znhm_?xeIvvyxeqn\\PmSitEiyrUykA:JaeV[EnZDN[@^qXpfhyrevUirYTMWtJ?tJAdJAtasf_uywSqumHRuuywSAZfqsCIr=Ob=WBjaev[qyumxx[gYb<Wb=;tV_EvxYypqIZeuwSaemoEqqpp[rJVoaHnwyxeiY:SAVW:JpCu::VW:hH:Bu:Ze=lHrt^WdHrt::Zd=:hH:bt::Ze=:::::::Jo;::QA:\\yowXXIkar=ZfiYrt:Zf=:::phsqwwEvuixciymYuuYvixxSyloit?hxMiioismWxAIfkirQGxAIfkqQ]ykyTv=XO]YkqTvIxQGvhxx[iOyxcgyqKww?IfgyqQgwyxdtWMQyhUdXAopqudpxXYOqhbeiqOgw=ifgyqQGwsHcgiqUgw;ifcypEoheTuEXUQyiuTtmWOUyjQUuAxTOvrpx\\IqmiueXxSQnkiT[in]vuYh\\YymSvu[X]lV<yxcQSrIWD=YdUsrYWJEyfITsiwMEygaDLYkYUt=xSUYlqutIXWQykeUuMXZUYmIvtQxYQYlmUvex^OWgYs;hwEYjkiucpqYWuUxZUYnUvvqhsywRIygItpyv>IygatsAxTQykUxWioiYtOhxYIpoYvuhx]iqmiueHxtvvyxeGxWmhwwREvmPsqWwAYieiXYykmsWymIV_yqqA_A^x]aYlyt]hlAVaYrHIBwCYyiyt`iuYXDyjii]uvAQtMxwQiwAYwyxgYykQwIyjiyskliYtSwGyxeItsywUiyqYwlIPYxsxcYsvvuiXsYwlidaYlIuix_iysIxwQvgYuix_IygitTIgYtNWiIusqpqYvuxxwWxHtywYyyqYwuisqYmatyywUyoarqwwmx]ImIv`Yr;Rvdysqim=JtqYwIItywMisAxvEu`yqCwuQt;:VYhytuIZpqyuqX:juuywYivyXsABxlIjuWypEyfYbydI:qiy:Jw;qQyoYxiw=tI:nywey::byjykyyInYtI:ryyA::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::Zw]rAX<I::ruvWJr;:Bv:vWxH::Bv>XxH:Yaj=xH::Wah=xHbuZi=tH::ruZh=:vXMIeSFIoVVMb`]U<:RnAxb=xd_e`]U<o>:Fsv`my@ojOmkG[T<:hULmPriXkmT@m=dC:brwHocyudsr`JG;:bkkW`Yit;IeSFIb`:ZutT_YuCikWgWoVVMb`:ZjxlTgvZytipkxNmkG[T<:`t>]ml=xeIvOEQGc`:ZlplMwwdyuaquAQmkG[T<:Xt=UmoUXhiYuixxgwwUu:^WiYuXypKhYwaqn_hn`hn_LR;uqxYij`o`pcF_cH_cF[^quOiyqaWiIufww=SAfWlHtPpdPalN`t>oEXeUyiASAWDMt>RnSHkuywSYy::hhqawtwhnocF_cHkb;uQp;:QA^W:::::jo;SA::VWhH:::::::::::::::::BuZd=Jo;Qae=kytXIiarMv;iA>Y:ZfExSA::::Ze=:pHUA^Wjp[sUyeyrqyuaxxTvw]xXeymauvQxSaylQuvYXWaYmYUvIXQ]yjitvQxTovs@y]QpqIvg@y]QP?IfiyrcwwyXdiiqIww?Yfiir_gw;YeeYqEgwyxdiiragw<utmWMUYj=UuEXTQYiiTtmwMUyjMUu=XSgudhx[YppQvqhxZIpoAvlpx\\AqoAvlxx^aqpYvt`xVAomQu^HxOyljYtOxwJakiAtHxwLQliItKxwLEvgx``wKOu`PxUynnyul`xZYpnIvqhx[AQ?Iheyrool=vugrpqv<qx`YrqAWiItGhwEYjmIu_XxSYniysExwKikmyuiPrewuYx\\GwCIYFxVIyhitqQwEQyiQuuYxZIygYtqQwFQyiAU]iqoqhGX<ygeYragkux_qwwutAxUmgiys=xwEYjOXJtMhnMsAH?qsEHNx[aypIwwuuNVayrVvu=lytYXyeiwIyiUwIyxcIsJt;^yqYwxYyomtmYuehoyvvusTYnmibewKQuSwtywwyweysIxuix]IygQxKuehqYwvyxe=lhqYWkiuwqtkyGyyiysmwGyjmpqYvuxx[imq;ZsAxwEv:FxxYypyYsqxwyw=:Jyiyy[vqyvAYHiuaxwQynuxcqwQyxiInYtI:nxxYyp=sywlyu;:BxwIykaqUyoyywIyyiyRy::ZxeyBywYyoiyuyxwYynYyayEy::fYyAwAvyyqyx=vYwA:ZyyY:wIqsHrghoqxvaIwyyyyyy:::ZbAwdqtPYubAwdyyyyyy=:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::pijMr;::::::::::::ru\\yq;::bu\\IxH::::::WAvW:::vxlIwk@lD?nqO]ZxH:RnAxccG`eDbie@;?:froXl:Qor?nqO]Z<:tuMMqrmxkAUBaNJYQG<D:BrsHoayuEIb>N::XVWqsqexjAUBa><D:biGosqXlaVS=RJYQG<D:RcCvIAiqehf_fL;wW<D:ReUfKAiqexjSgX;wW<D:biFxeQvnyw_AN<D:bdOvJGYrkxxeytuywUYyiYu:::Mgc;WOctNeDOatYueXuqpUqsDqePodXodPo:uqwpyugY::Bu^WZn@pcxdOgdQ;\\xkawxYYpqIiTOetOZMqs@iyqUy::Z;piuwdOgdQkc[g]w=::::::::rtVWlHSae=:lHQae=:lHrt^Wjo;Bu:ZeMpCu:VW:hHSAZf=kIuXyo?ye=iytXIBx:>YZfExrt:Zf=:::rwSqu;jowxfMp;rtZf=ZxAyfqyr=:fwxAygUxYiykYu\\YouyuaXyQyliyrYwwuXaeynAVwYxVeYmQuvMxSeymmuvUXUaylQe_yptqvtPyaaQAIgkIsaWxIyhkYsmGx=ieiqQ]ylae^ypqAvfpxZaoqYvp@y_QqqIvjpx[Ipravsxx\\appIvjxx\\ipqavupx[YpoAvjpx]yppQvplR]YmAVuExUUYjMuuIXWQyjQUuIxVUykaUtuwQMyhuttqwPAydesrQwF=ycESrAWB=YcEsrQwFotUdpIgvqxcaiqWGw;yf<hpiv;axZaP<VuUx[Uyl=vu]x\\YymIVviXaYYn]vuaX_]Yp?ydYsqIwCUucXxUquaX_WwHQylyusmuax^KwAYhCokytWXxUIovUFyhqtrawLYymQV_IrDYjeyrmWw=itQXqyvRrNVxgkyUVymQVaAAIyeissQn_x_YYAQtMHCAsYwGaciyqEygyssYwEIyeisPYm;pyvAitEykYusiwlytYXxKu]hoyvuix`ayqawyiysqyvAywAyhayqYWiIusywSQueHOaeewOAuYx]qxayyGYXyxeYsqYvuxxSymyuuYx[QvuHWAsIxWIy:pXyiiyuxpYwgyt=ZxYypiytQXoatYXLit=:waxYyoqYcYyoqx[m=LiuaXqYwuAnYeAZpqyu=lYuuYxYYywX:JvuYx]ImqxaYyqIJwgyt=jwgYrywYyrywiyjyuiyMyqYyuYxCy:fyyqyw=:yayyyy=wax=:jyyIriygkKGd]GtKitry:::ZPqtUAobHpPqtUyyyyyy=:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::pijUx[qvAyx]Yr?yjUx[A\\IkAZsIXBx:YQvyH[AvWRxZrmvSx[Qv=IYQv;::::::::mA>Y::::::ianplRonxw_`pii:ZJYrc@pIpc`piinN:JWMtv<VOyQMua`<:<VOyqsuXlYuEeOMuqQTD:RnMHhUIt;icwuEG?:ZCYq\\xwdIvnplR[`<:<FBmgg\\GgYTD:BdKVLAiqexgifPbc:ZkPlOWvXit@Ap>pnxw_`<:<F[yt?YwYisGgYYcc:Zj@lMGw^auuixemp?Yuyw:jsuxlytOQtipOhxohl?<s@arsyxl=PipOjtohJQitLqyugyriWiA>yguwZrmuqhqeo]Hl;eQuDRZxPqlhyqiwwAY;eQ<@bo]Xluywvxg]wEu:fwA`j;@fXgeZKe[giYZqaWjp?Yjumhr]gEx>YjumhqaWkIujuCxZqMv;:BxvX::XIkAZrmuswZr=XI:Bxrt\\IkAZqaWhHQafExvxe=Bx:QAZfMpstZf=:::::rwvXfWiASAVWiIu^W::nyraWjp?ygMp;:UA:jvuXyayqGyjqysMvexxYYnqYuMxxEYhmYrEWxqx^eYoAVwUXVeYmUuvUxVeymmUwUxVeYmeuvUXWaymiuvUXW]YmauvYxY]YmiUvMxTayleUvUxWsgHXT]yliuuMXVYykQUvMXUYylauuIXUYykQuuIXVYYleuuIXVUiq@y`yqqavsxx]Aqqivxxx^iqqYvs@yaarqivy@y`Irrivyxx^YQAyheYrcWwyhfcyqYwvsPsawK?uY@xMiljatP@xOImkytXPxRQNsHdciqYWw=YgLxXOvthx\\IqqAWeyrqOmIvuax^YYnYFKxwKikmIu_HxOimkytYXxWQvixa]YoqvvqXd]yoyfeIttAxTQyjYusiwNUuahx]Yqqyv`YqYWvmxbeyrugmQvueroyukXxYyoqIwhysExwMykOxXQykqUrvAyxayrLIcyrHYk_x^Ml;JxUynqYvuXxQymmyt[viXvVgqx]iwIyiuwSIy\\XxwVbwMIygYtRymIvwyxcQvuHlYuehpIwv=Oqu_YOYykiuwQtuYxYyxeYtGykUx]A\\YqmyumhrEykYu:XYpqyvAYymyv_yrMvSxhYuqim=qIwhixYYfxwQymUx]YymA::NylMs;aqwCykqxeIoAVyx=xyxiyy;:Jyiyy[vMx;:tiuqYmiysavAY:uYxFYuYxpYwcxVyyux^yy=:RytYycy:tIpI:vYxI:xyy[xMy;:yyi>O\\hd]y=:::TGK_Pmysy:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::ZwIykUx:::BvuYx]ak=:JrCv:::::::::::JvgysAXmAZr=`IBx[ai=mA:ZrAXmas=iyvOYdMFMgFUwbaeuD;GXYCbkuEMgZscm?xdQW[;tdEFJ::iga]EjSg[QW[;td:Z=qoBhxkAwHIqKXo?@be<:TUGaPfIw`it<=nO;:bluwcYit?YhqfSQW[hD:rjXrsuXlyvVIsOQRZhD:J@EokuWeiuHYpOQRZfJ:RgkfRAiq\\vSmrOQRZhD:RjSg[SyswxvWIsMxfQVk[G\\EHfK>bmuWa_YuCIyiYu\\YqqYv;vsEYrZhmS@hhggagf^wf__FZ>Art@uMasbof_?g`gFNpiHowAygExUAnwwUufW:ZdqvVAg`CTZl<pICVZyETGUSK]RYtEiyriww=::PPjXOSplLdLLhK]AVU?YuA::::::Jp?yg=lHUAZg=JpCu:::Zg=lH::UA^WpH:UafMp;UA^Whxx_WlHrtZf=::pHBu:fWpHSaf=pHUA::Xypqyu[xAyfiyqeylXy;fWkARu:::::::nwxIygqyseytHrudixQylqysMvmxxUYmmYseWx=Yemyq=wwiX]eynyUw]XWeynAfdYrsyVXxWeYoMVwaxZaymmuvYXYaynIvveX[aymqUvUxXaymuUvUxWgvt@yaArrqvw@y_QQGYiXxY]ix@y`iqsAw<Ay`yQ\\UvYxZ]YmyUvQXX]ymAF=xwEiikItEHxGYjvQOylTX[]yn]VvYX\\KuMXXUIeIr_GwttsiwMEyfETsaWLAyemSsawKGu[XxUynmuecyq]OkaUt=xTUykiuuUx[UYmIVuOrrQwFqXGxwMIlkytYPoqVuUX\\]iJIyhqtrYwHAyfITYIpmasuooyuiXxUIooQhOxZIyhUxPWw=iuaXqyv=YxYqvGuuax^UwEyxayroYvsPreWxMYmiYtCwVx]YylIvuYx[ayoqvuax_Uwli_aYIacUwGaaUwIAJugyrywvyxdUwBtsqnmYuaHOIygItuYxYiyqIwuYx[IygItsAiitXivyXsywQaeiytYxxEwwixciyLyxkumHSA\\yp?YXypmYvuXyiytuywUYyiyt;gAJxgytYxwAyiiYpI:ZkmrcvwixcQxYYymYv_Y::Zsmv;:oat=:::jwuiu=::vYqyyJxCy::bynYoat=hIqQymYyuywyiwey:wQyuiyqYbynywmx;byxIyyyyQyky[xMy;xuYUF\\Xn[y=:::TGK_Pmysy:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::ZwUvFX:ZxIykiY[aj=@yxcymYvwawUv>xwEv::FX::Jr;::]A>Xjr;[A::::::ZiiysyW::<yuGwSxhoFjNSZ<::TuKyq:MO:dRitj@APCprjDKC]PH\\sqTlLQR`LUIUqLuQWPTyd=ht<MnRmraTVSyruEiniw[Ir]Xhk`kIGpFxC:fpQ`fk`K]?:ZFyqdxwdQvxHnkGpFxck<:TFaiuDWYesRmra@E:beYVPAiqixi?wV]G]@E:bhuVUAiqixliG_]G]@E:rh?WXQxiQwmAxeWhjWWm=heUXjJaEVQIw^YUqexjiYuqxx]yqMyqUXUIuP]qtHqqlpoxPph@:J<ArxpYvuXgQWaAQqpprtppJ`YVZqYvuxxoW::::FhhSVVgcwff@o[hyrUyfhkOgB_bxFanf_EqruhyriWkqx[g=tH\\Oc\\nJhkB@lG@K]AvUqYvuxx[giYbu:fWpH::::::buZg=Jp?YfW::::::JqCu^W::::::jpSu^W:lHUiypxx;uqpuI:wawyXbyfYJy;::ZfqYRu::nWkYufWJq;buZg=tH:::ruwIxWahmqGyiExYajUxtYwIitQXiitsyvwHy[ioqIvaxxWimqYuMxxOijqit=xxQikmItygxOijqytIhxQikoitAhxOIkhX_]YnuuvYXYeYoYVweX]]Ymmuv]xZaYoYvv]xZwvxHycirsIw@Ay^YqsAw=AycarrivwHyaIrsIw@eswWxKikmItExw@Vv]x\\aynYVv]x\\OwDAyaYrrAw?utUHxMykmIu[HxMiliis?xwEiigirkOjMusqWPIYhcpGwvqXdaYqQgvohcciqYGwwHfeYrgWwAyheirqgwGyjFrqAwAM]UYmAF`ypIWveXakvotsiwLAyeexYIpoIvsPpIwvqxceiWevyXxNyiIutAXVvuax]IYdyrqgmEyXxwIyjeYriWwwuuax_YyoqV\\xwIyjGxWaynivvMxQIgqwMylWx[aypAwvixbayoMu]hp]cmomYuahpIWdhpQWrwOIyiIuwix_YykyusiwMqusw:SIyiytuIxpYwEYymyuOymiYUIydhriwvAYsQqqiiiyrqWmyudysOymqyvAyxayrUytywQYx]Yqsu\\yqGYuQrSvuYx]AjwsxgiyqYwwqtcwlInyw]t=:jwgytEygYyqIwuyxRwfX:JuWypEygiyXivqXju;kQx;:uqyuIJxyIfYpI:By^Y:nyxayymy;:ZwMyky;Jyuix=jysyryyAJycyri>O\\HyamYxnAwbQwmYxnyYxI:bo>OTGyasIytAwbQwgiwiyyyyY::::::::fwgywbAwd]yuy:::KIt\\XnWXjy;::RxZbmvaYwyyywY:::`IKabmvsyvY::::::::::::::::::::JnCtfWry:::::::::::::mabMnSxvYxI:::::::::aabMnSxZy=:js;Kaymy;:::Rx>W\\Hmaymy;::rvZbmysy:::ZsMnCtFYxIyA:::::::::::::::::ZwAykiyrIX:mas=wYx:::::::::pIby:::Zw=tI:uAnY:jx?xxEvRy<yx;bynY:pIuAvXOY`iUGRZ:ZcHl^GjN?Z;<::Lt@=p:M_;<:ttD]puEyniYuqXvEynuwbiUUesnPso@lGIqPhssp<JMyQY`t;MnNIR\\:dvX]TrexkEvMmqUMshXUDq?:`VUUStuxlQwZAtUMshXE:RfaVRCiqiHkKWYiG_XE:biAGXAiqixmqw`iG_utg:::::ZvHnpwv\\Quuqxfyv\\IuBhj<phnOhp_H::yEYoUheweuIxWQvuXhYwa]QuLQvTQtHQrtP^MvWqihiY:JySykqx;:=s@]RB@;xr>yqx]ixMfDO^jJrk=xgwIxYiykyuuaw=tIBPZ[J]cykiuuaxeuRy:pxx]YqKy;:uqpuIwAfYWagiYWiyJqqIwaxmxSypHbuwax=pIuax=pif=pHJygWfYpIwax=jxSy:nY:tIuAnYpIuax]q=wA:JquIfWJqSufW::::tHRu:nWtH:UAnW:::jquI::`yq[rmvSx:::BvwA@YyeYsuYwEyxgwwix]aykytvywKayhqsuEmqYuShxQYkqIuKxxSIloitCpoUFIpoYVwqX`iYpeVwax[ai?QyfYssIw>IybIRQIloytMHxKIjmitKXxMikmIt?XxOykoQ_aYnEVvax\\ayoivv]X\\aYo]feasryv<IydAsrIwAAycyrsQwEIydQsrAw?m`SlmytWXxSimmytQXxUYnmytUPomvuQXYQYjMUt=XTMyhqTtyWRIyhmTseWMIyhmttAxUMYi=e\\Qqoavwpx^iqqyv?AYXymMVveX`]Yp=geqsrYwHEu_XxYyokIu[XxWyoRxUinmYu_HyciroYvuXxUQw=yfiytQHAYxUIo@yhiInvuurmqdiYtWyoivvqxaYynex_yqHiuiX:qYwGyxaYrPym;KacaypMuaHKadMowxeaYQaduwpyvgyriwvyxeaYSaf=pXxYypCuuayaysayriwwyxfiyrUykiunWjq;tywMyyuywyyxayxayq;pyv=yxGxwIyk=:bxpYwgYtisyyxaYuyxyYyqAwIykYyqIwdysqI^XoIw:hYtWyomt;gqw;:Byrw::>yxaY:ZsqYmiysavmxSy:oqxeI:xYyqyyKy;Jxoyv=:pIuAUYuWIdIWfKwc]WuUiuyyyyyytyyuYywyxuy::yio>OptPUuyyyyyEbr?YsEXkQHdKON]tRkYyU]qxpyHyAboZPMeUwg]DK?^pn`q\\Qv_yyyyyy=\\Xn?obHpylyyiymYCd>WxIyANv\\ivn`pv@obHpb<LE?aymy;g`ghop@obDdZyLn]Xo]hdAO`uVAvyyyyyIUqqqtPUE\\Dg`betrivYxIRxVsEAtb@ok@O:xEUayuy:g`bLesyvY:jYCd>WOyyvY::JnCd>O::JTSkExlsHq;yyyqy;:Rx>tJitghop\\b<pDghoq@yA>WjYsyvY:\\H:ry:>W:jy;maE=\\D:y_g=yAbo>OTGyay=:xEK_bmysyfW`uVAVN]db<jYSuvYyABqsHrKGd\\DRuUyugho\\Dg`ymy;Rx:>O:hv_=wsIYtUWeiWNCn[XoyyyxIs@>OjpCt>OxEyay=`IBd>O:xEUayuy:g@nTxIyA:vQ\\DKaymy;:::::::::RymivuYx_A:::bymivwA:::@isQXDI:::]akMscv:FXJsSvFX:::::::::::>ymYwSxhpFjN?Z;<:HSr<m:SZ::ZY`jLGjN?Z;<:tTEaptyxmAYpMxmIxgUxjaWlyWf]wbQvUItyHspXl:MO:@B::Bj]w_[ytAY`iUG>Z;<<sl`KBQpFTUIQQtyXmEVO=RBQ`JlIYqSxsuH=Pt<mNlyWfEuCuoIYqSxCbbseHWW\\WDhqVUCyqihlgG_WW\\WdeMfM:::::BgkfTGirmxxeYucF^OfSAuQYdLCtMODKRPeTMkF_SvmQxjwqqsuJvyx]Af[V]KF^UF<vkD@jxAyiqyrmvSx:[Qvkq;DXhIwJhkB@<r]RxYiykiuktNMTBqR>=[AMyayqGYnWmareymiuvwRWdC[[j];wYxYA\\ItHYqvCx:ZsqW:jqcuJv;myu::ZhMq;:::>yh=:mAZr=`I:Bx>Y:::::::ZiExRufWtHWA:::::::vWJqsu`yq[ryWkasmv;:::<is=>X:::::::@Yy[jMrSvJwCxQQsiWxAydmYqyvwuXa_wDYyfQSUYmqiuWPqufgqsuiwEYyfQSWymqYuSxxWymoiuYhxSImmytMXxOykoYuWhxSyloytOhxQylmytOXxQyloYu[XxOYlmitMhxQyloytQXxlVwqxaayomffyssawFIydAstiwKIYSXxQImlxaaiIutUhxUYnnSUYnpXcaiMIY]PomvvmXbUykeUuExUUYkaUtuWRMih`xXAP;IgeyrqgwCYigQYYi@qx_IrrQwFAycQSMqvqXdYYoivvmXcaYqQwvqXdaYqUWw=yfaypQwvqhtQXoivwXxWYoxhvix`QykUxWio@ivqxdUwGYxYYpoYvuxxeissywOyxeisoatQxZaypyvvqxcayqQwvixaQylyuvEtsywQQuehq=qIwCIydXx_wvEu:JuaHQquqHUYykYu:jvAIaQvyhrUytHYqvyHYA`Yr?yiqyvyXXyx]yqqI`YrSv`I:oivuix_AZmqYkyywyxtYxuywUyxWxwQYdI:qIwhytqywMYygXPI:giyqA::^YwA:\\Yy?Y:::`ivmxaI:bxwYy::rxpyw;nYwYyxYywYxyywYwQyqixaYjx;`uV=VNYtR=WbwyxqYryZxqYry:`uVAF<GxiydkK_nLN]Dvqyprghop@obDd>WOyyvYTGK_nLN]dglYyU]MUTmE\\Dg`ymyCtKQNsiTvysyvQ\\DKQoyIyaVauZ]bLTsi^P\\TN?OlWh=xycr>obHpbLTsiFqsHR>O`ErlvYxIQxl[HdfOjpCt>OxEyaymvShmWjBdFQxuY?O\\DU_giWyqyKeCdnTxIyA:vQJnOwymy;::KabLN;:::RhFysQyyyYyAFY`EK_bLT;c_b@OK_Emysy>WjYsyvY:\\H:ry:>W:jySx:>O`Ey_bLNSe:xITGK_Pmysy:Zy<\\hdyYpxpgOgGd>OxEywipDReVxmaxymyCgcGi\\dnlYsynT\\Dg`ymy;Bn[XoKGd\\Dm?^P\\DU_n`PBqZyMT;c_ylyCt>OxEryFYJNCdFQxEK_blPSuvYyAg`bLesyvY:jY;KQoyIyA:::::::::ZwuvuYxaaliY:aANX:ZxIylmsuyvEI_A:VXJs;:aANX@I_al=:jrSvNXDI]AZk=::DI:RvJwAYyeImANYjv?ymmuZ;<:dRk\\k:MO:@B::R^WeE=FO;RZ:ZhlsuXmuTC=pEMQTTssHMEIqSPssDmDIQSDXiYwbIvNARd<j:;:Rj_W`[ytCY`ieGRZ:ZhLtyXmiUKMq:M_;<:TssHMlyWfisvXm:M_;<:TCBgqVU=FO;RZ:ZF`fSVmqo`HpfUFjNSZ:ZMTFKIssHyiiu=s@@<RIiSEIXjkgymIv`Yr;::@lG@kJ:?VYaeymIvwA:jqGyi=ZAIrqH>@lGZehnUpysywxMfFCF>XFwYxtI::BPZ[j];wA::::<Iru::::nwx]ryW:Jq;YahMq;Yai=:tHWaimqcuZi=tHru::nW:jq;:bunW::jq;WAvWxH:ZsyWkiu`yqGYJvyHFY::>X:<IYai=:Jr;YajMr;::::RvwYx::::NylqysQXoatIXkyufwwIygiynIvvQxTaYexxUYmnSWymqiuY`JYyhATYYnqiu]xxUYmvSNyhAtuqWqqbeYpqvwuXbcnqYuYhxUimqiu]@oYu[hxWinoIuShxUQwmXaeypuVwuXcgwJIyfistqwMQyfqS@WwqXceypAG`YpuVwWttqwNQyhittywPQyhqttqwOIyfAtsYwIIygITSInfssawIyx`Yrpivyhx]QqnAvnDraGwnx^iQpuuUx[YynwxcQsqul>TSYnmIu_@tXeayq]wvuxeeYriWwyXfcpqQjSqmyukxxHxwMYleYrigkauviXsIwCix]YqoQimYuaXxUyniysIXwEyigx`iyrEyhxwoV_yq>wwAygMpwxemmiYtIXxUYoqYvqHRuJu_ypUyiIunwweu:jvyxx?XkarmvyH[qvyHBvvwxYynqYcYyoYvuYx[akUx]QwgY_A:ZmqYxyxeYymyuWyomtqIuqsWynqY:eiy::JuWY:::lyvyYyqyy_YlI:::uaw=ZxiytUymiyuYxZtMw;rxwYy::xYyiyyqiyEy^Ypyy[x]yqywmx;lwguWNYdghOyiywAxI::fwgqwb@ok@OHysMIxEBdnTjy;Q`blPkywYTGK_bl_ifsIytyyyuy^U\\DK_g=yItKQNsiTvysyvQ\\DKItxImaghop@obdovYxIbo>OpDmYxoYkExlK_JmysyZgiWmoZ]DK_PmysyvQJksyvY\\HK_ylysynT\\DU_giWyqykvShm?`uVwYxIg@nTxIyA:vQ\\DKaymy;::KabLNsyyqy;:UaPmPqdblV;yAnT\\DU_bAWyay=\\HUWe\\DKay=\\Dy_ymy;Bt:Zy=Jn;:yaP=pDUayuyRxZblVsyvYTGbovYxI:ri>O\\HyaEMNSkExlmYxoyyvYj_;[@vY\\TNAUNSxmAxIg`bLesyvY:ptP?ODHryZ\\mPqD>O\\Hry>O\\DmAvY\\HK_ylysynT\\DU_g=yAmasLNShvYxIg@nTxIyA:vQ\\DKaymy;:::::::::RyHyxWX:::::oasYXmAtimexaiymiv`ysGYNX::js;_AZm=:DI:::::::::::JvIYpasuT=@B:::B[ot<=FO@BB\\;e?=FO@B:beFxfivSxhpZ;<:HXiaWtyxmARdFJ::LvTmSsqXmasuT=@B:be^XGih=wV=FO;RZ:ZP<mx`mEH=FO;RZ:ZP<kHgsfU=FO@B:ReeFTUIt=IhyfV=FO@B:R_aeFUYt?YykIv=s@]RBZ\\iuOqysIXmA:[ajmrSvrLEtH=s@]RBVc?cymIv>X:::ZIPk:H^URBZ\\EowYx[iy>eMGc[jJrk\\EYqv=Yy;:bZuuV=s@@<I@<Yy;:::::::vWkyuvWmIv\\I::xH[qvCxru`Yr?Y\\ImAru>XBxZs=\\ImasAXxH>Y\\I::masMvkq;:FY::::Zj=xHBv>X:xHBv:::vWJrsuZj=:::::::@YyeyrOY`ImANYdIJscv::::VXoAciyqA[YykYuuywQiygysuIw;Iy_ipqyu[HyYinsIvcHyYYn<ycmYrMgjaTYynsQdmyqMww=YdiYrUwwoTPwwyXdiyqIgiaTPwwyxd;chxWinqiuchx@wwuxciYqQWwyxdiiPQyiiTbuc`MuudyqUww=yeeYqQwwyxeeIoqdeYqQwvmhtywQEv>xSQyiAUdWwuXdaypMwvmXbayoyVvax_wv>yx`YrpeigIsugwtUuMXYov=yxbASMilkitUHxSYnmYuaHxSYnoqfaYqUghqttIX<YheiVQYqxx_IrqqjeyrmwwIYkWx\\QylyuuUrqIwAyxcyrHykmiaUwhYtMxwGVeissIxlicYynMtQXxYiwAYsywUIygItqIwAIy`xxaYrsu\\YqqYv_yoMukqqyvyhryWRx[IykYuXiwIyiUxpyv=I:]YymANymiY_qvAI_QwEI:aAZm]xayqqyvAyxYypuxcqwMyxiYtuIwqtWyo=:JuSwZp=PivmxeyyqywgYtywoYwaxexwQw;::rxVY:ZyEyry:Zx=oauqYjyWyy=By^Y:jxyIjywyxqYwYytIfogppbxnkPv[avyqyxuyvY::[HneHdfRxyywYxEriTvysy:ZyLNCqvYTGK_glvaiymy;boZEmyCtKQNsivYxIy_bLnsynTjYsyvY:jVaebLhsiygkK_\\mysy:FY\\TN?OTGyyyxIy?>WjyCt>OxEyaymPCdKOnsyvY:`IUWejp[yqT\\Dg`ymy;:y_bLn;yA::>W\\DK_ymy;::UYupDboZymP;Kaymy;:?a?MkExlyIKablYsyvY:\\H:ry:>W:jySeZbmysy:FY:pHyqyUGK_Pmysy:ZyLNCtZ?irEAOHIry:NV\\Dy_ymyCd>OxIyAnT\\Dg`ymy;Bd>O`Iyay=Jk;K_b=xIK_blysyZbMNsiZymP;Kaymy;RxfOjp[yqT\\Dg`ymy;:y_bLn;yA:::::::::ZwQynexcA::::::VXoyv:^XoyvVXRxaQwcxZs=dI:mANY`Ibx::FYJwSx:FYNxxuvdIHINY`ImANYjv?ymiwSxhpZ;<:::Dsqxl:M_;<:::tDaiuIy`kuG=FO@B:brwHpayuIYZFJ::`VWATt=YnasuT=@B:be\\prmxl]uIEA@B:r`qEJEIroHaoUH=^;<:TCGirqxgwVV=FO;RZ:Z^pjJowdYvs@nlGjNSZ:ZZXjFOxgyvwIykI^UF\\[JfHo^tilUx]AdYsGY`I:bxpSFyrJhkB@<brPWyayrSv`ImA:NYrLF>]RB>eM[k]xIYktN@<=[AQrspysIxx=BvwA@itu]OVZ=s@@<Y^xQYwixFY`IoAFY:::JwKr[s]j=:@IBvZk=:<I]A>X::@I]aj=Jr;]A:>Xjr;[A::vWJr;:::::Rv::FX<I[ak=jrCv>X@IBv:JwAI]AdIoas=dI:Rxbvwix]QwAI::_al=:::HitQXjs;::ZuaXrxeapUxYQvmxxUYmqYtAxxMYjSpsIvcprYgkqtvAxPaykIuvIxRayjytvQxSUvmxx[Yo<yeiyr]ww=YemYrYww=YfiYrYgk]R=TwwKrKfsooyuePr]GhINuuIxTYyjIutuoqIvmxx[ipoyuipq]WwyxeeYqMww=yfspqIvoPrewwWuueqqivw`YYylexYIpmYucXxUinkQaGwCyXOxwIIk\\x]YymMVuUx[skkQ`YynaVvmhriWmYuchxYYpmyuiXxWionutupoQgOXHYksqoYvuxxcYsPYmOxYuv=IyTXxQYmiYtKlmytYHKIygitsYwIqtYHKIygItXyosusQo[pIwvyxf=^YUIygYtNwwAyhiysIxwIYJvyhqawvut`YrqIdImasQxwQylexFyimrOYdysqI:::^xxYypuxpYwoytaXPYygX::TIgA::lYvgYwAdIqiyZyiYwqv_yqEy^yr=::Ryfys=ZyiYyiysav=jxyiv=nYtiuyYqavyYsA:Zwmx;Zyuywax]xAtJ=Qxl[`xMyyIxI:^pnXqb@O?aymysijRmGyyyyyy:ZVMNGpE=TGKGd:xI:rv>obHpnlyyibAWK_ydkyaymYCd>WxyygRJhsyvY:JnCqsHrayvTGBg^uVAvbAwdyYxIriZPmysyvQJn;yabMNsivYpxp?obDgvYxI::E@nTJeCdZymy;:y_bLnsyvY::JnCd>OxIyA::ZPMNCgZg=:xI::::KAvQxIyAZb=:xI:KA:fWJT;yA:Z?=TGyaPMN;yay=:xEK_bmysy::fWTWe_pn`qb@OQ@vY\\DK_ymy;g`bLesyvY:PFriNv\\ivgiwiyYyABd>O\\hd]yMNCdvYxIBt>OxEyagMNCgvYxI::E@nTJeCdZymy;:y_bLnsyvY::::::::::pioiytaxwEwfXJt;:::::tYwMI::rvZnms;cA:Zm=LI:::aA^XHIBwVX:HI:::JvMypasuZ;<:::TTAEp:M_;<:::tddgxkYwdhkOGjNSZ:ZRatHaVqXZcl:;:rpehleYvOY`ieGRZ:Zb@l]GvXyt_@kKGjNSZ:Zf`laGw_yuVPisFJ@B:b_vv^quGaqWHjNSZ:ZPLjmWeAuFmp:MO:@B:BgwfWcYvMiyoivusGUSBqR>QTKtYwEYyOX:jriTMqSyeInY]IvSIsusGU;=[nwg`oytIxxevNX::vr<Qq[V]KF>j]cyoQy[kAeMSBqjJrkdUyeYscv:ZkqYxR?ArJRBvKtIwQs;:RvjvEisIXmA:::::::::::::::::::Bv`yr;[akmrCvZkMr;:]QwAismv;::::bxNYjvSxNylex_akex]A::Zl=@I:bv:NX::::::HYyOXDIaamMscvVXHI:::cAjwMINYhYtCwfX:oariWiituIw=IyaiqLYimysiWxEygmysmWxEyfOxTaylQU:hgkIuvepqivoxx_ypsivhyriWxEYhiyregkQuvIxUYykuxdwwGuuIxUMhiYsmwwWURvs`UmgOxWYyliUJi?xSQyjAuuQxW=]IqDyhWxYevhiXuv;yxxgmAVaQxIyjiYsyglUxWiomiucXxQymdX`]YoiVveX_]YomvuOsrYwGAyeqsrQwHIygatsawLQyiIutywRQYkpruGsxx_iqqqjeYs=xw?VDxwMykiYtMxwIiuax^ayqQwvqxbYymQVeYsXivutPIeisTIkqx]yqoX:ByiYuuYx]qvyXxkugyriWmIvdYskxayrmyumXx]iwAYuawQymex_almsGyjEx:NyniY:tinux:eYymAtipuxeiyPI:bwnXjuWyq=sywjwkvCywQw_Ylyu;:kQxkvuYxaIZwey::diwQY:::hYysywYyyAwYywiyqauMxyiv=::pyygY:Jy;byaivcIdKONsiPvYyu\\;:`uV=fbDghuyyiy=xEBtvYxI:Bt>Oxe@yYTGK_Pmysy::>O]GdvY\\HriZymYCd>WxI::yA:::vQJN;Refr?Ysn`PKGdTGryvQJnOWvY\\HK_yly;:ry::nT\\Dg`y=\\DryvY:jYCd>WxIyA::>W\\DK_ymy;::rv>O\\DUab=LevptPYuPup:::sHqxyy?WjYsyvY:\\H:ry:>W:::jy;:bo>OTGyA>Ojysy:ZyLNCtvYxIbrVsEAtghop@O\\DRefwguyxI\\DK_ymy;g`bLesyvY:HIcGgsGdKON;BgVsEAtbLNCtdHxIK_blysyZbMNsivY::xI::g`bLesyZb<xIyA:vQ\\DKaymy;:::::::::byqYwuixeYy:nyuiXfY::cYyPIeA:::byoIwdIPYygXLIcAZo=:LI:eA^X:::jsOY^Xjs;cam=LI:aAkIwWY`ieGRZ:::Z:QpTHjN?Z;<:::tDgivSilgw^=FO@B:r_iEImVXuSZcl:;:GFQSRtEyqiyvUY`Z;<:PrgljLqrjTrghj:M_;<:<uEeppeXlmSw`m:SZ:ZPLnQxiqxmmw=uOA@RdFJ:PBCG];e[qt<RZ:ZSAt:YyqyWoivYN;AlG@kJhkBLWb]VyeyscvwixrvuF`[VBqJrmxluYwIYy[latJAs[V]KF>jOUDHIaA:BvQIsusGU;=[<DWwixtilqYrvktNOTBqjJrknysQXoQyOX:jsyR?ArJRBvKtINX:::::miv:Jw;mANY:jv;oA:::::ZsIXbx]akMs;]qv;oas]lMs;]QwKsSv:Zl=::::::::HYyOXDI::::::::rvZl=HIaA:::::hysuYw;bx:VYhILIcA:ZoqyuaXjt;:::gapEyiiyoivuYxWYyeIsuIwwXycYrRycIrsyvwHyaiqPyjmYt=XxEYhmYt=hmyuvYxXuv;IyaiqLYj_xYaymiuvQxWaymyUtG?IyaiqHYiOxXaymmsyGyPsuGVX>VxwwII_iq@IpWx?V<H=Qs=hlyuuYx[aynQvuYx[Mlii\\aY?yxcamIVeQxMYlmYtMHEyx@XwyxewwQIygYtsYwIutUHxxfgaTWYokIu_XxUAgPqYWwAyhaYqYwwII]QwAiuYx]YyluxDxw_vuax]EwAa^ayo]dYyoyVLhpIwwAyiaYbsPymqYvuH]quqXxQivUtnWoiv>xveusiwOYykasMwEitQXHYx]ypmifiysAxwQymiYaanMtuywgysMv=yxeYsKy;wqt;:gYymivZomtcwwyx:Zv]q=::\\IiaqMvCx:ZsEy:ZwIyx=bxwqv;oA:Vyx=:::xYyKx;:::uaw=::JyyIxiyTkKGd\\TN;::ZPepyyyxIriZb=xI:Bt>Oxe@yYTGK_Pupyay=:JNCdvY\\HriZymYCd>WxI::yA:::Z\\=xuYgogppbLN;boZymYCd>WjyCt>OxEyA:Zy=:JeCdnTxIBdZymy;:y_bLnsyvY::JnCd>OxIyA:::^pnDdKOh?vb=\\D::::y_yMn;:yAZb=:xI:KA:::vY::TGK_Pmy;K?vYxI:ri>O\\hdyY`IywiG@K?Zgl_iVbIIyay=\\DK_ymy;g`bLesyvY:jvCqsp\\Qv_yuYUF\\D:BtZyMNCdvYxIBt>OxEyA:Zy=:JeCdnTxIBdZymy;:y_bLnsyvY::::::::::tyw;qA:::::eAZo=:TIgaomt;:gAfX:::::oIwwixcqwsxNYjw;oAZtmwsxNYjw;bxNYkYwYY`ieGRZ:::vlnsnQXi=FO@B:::be>ynqwtyxjqljW_;`D=>::::>q\\XipYxgIypywSxHRZ:::::Zy`oDPxhIwWPitFjNSZ:ZP<hYvAYWATt@Rd<j:;::::yWeOFw]ituixaQwIYrqXmin\\lmJhkBxlNxkOYtI=YpUXkuWfyR?EB@lG@kOomxQynqYaiyZAQRYSDyRBqjJr]DRkuWfuYwMI<YpUxOUTIylNx;@<?>nYcydGwaktNODPadLYSDjJrLEDIktNODPZNAtBQvXyt[V]KF>:::jAcyoQd=W^ErxLQ;qQttIwqs;:::::::_iyjs;:bvNXHIbvVXJssvZl=:HIaalMs;::aam=DIrv::::::NXjscvZmMs;aA:NXjs;:ZuYXoat=hIqANYjwMIcam=LI:::::::::RwhYt;eA:::nXjtcwnX:jt;cqvuXyYYogx\\iyoaVeirLYjqYuQxxMyiqYuUhoQV@xxQYlKxMYjqIPYkcruQmmYt=XxQykmYtAXxMyk_x]MkmytMXxMyjCsLIDHbrLYlsrHYj_x\\UwEIycyrPyl[nMtIHAa^UwGQtMhnivvUs^VeaoiVeisnVcyrfVgYtsYwGa_EwAyx_iqoIvmhx]IqmiueXxSInlXbgwLIyhex[ipmyukhx]Yqqivyhx]amQvtIxXYymYVcqwIiuax`ayoAwuix`UwIabaypIwvyxeaypQwvqXuIxWqucwKIydxxaYrGYsavqX^wxEwuqsqYvyhqYWiYuFxwYYuixcYyHIWIyiIuuaxYyoMtWYfxwQymUxYYykqxiytuipMu;:^YuixaajiyuaxxaYwA:::Jv_yr=rxVyoqyvmxaivMxSymqx;:Jwcx:::Vyx=::xYyKx;tiuqYxIyA:pIsAfY:::JykyCqsxqKGdLeu@wbIwbAwc=Nv\\avb@OK_m=xIri>OTGry:ZVMNslQHnyaPqTK_?mysy:ZmMNCgluyCt>Oxe@yYxIy_bLnsyVsEEd^UxyywY::::::`I?irEIgcGiKGdTGyaymY;KQokyCt>OxEyagiWK_nlysy::VSJe;g`bLbsyvY:jYCd>WxIyA::>W\\DK_ymy;:::y?nTHysMILEg`PqT::Qxl[@E@>WjVaeyyYyAZb=xEyay=Jn;:UA^PxIyA:ZE=TGyaPMNCnZy=:xEK_bmycoZblVCn[PkExlyIyA:ZbLNsyvYJe;[`ymy;:::rv^uVAvbLNCtZyMNCdvYxIBt>OxEyag=LEry::VSJesynT\\D[@vY:jYCd>WxIyA:::::::::ZxYyquxgapmu;rwnXTI::::rwZp=:::jtWYnX:PI:bwZomtcwnX:PIeAnXjt;:::JvQyqsG=FO@B:::Ag[[tsEIr=^;<:::ttEiPvQyqqYwMyrixjmTA]o:SZ:::Zn`miOxhIwvAymQyqIxU@irFjNSZ:ZbhkVWmr?AFJ:JDyPO<YpYxuIypqSwdm:SZ:ZP<;IykyvTYr=VOEr=uOA@B=>::vjWg[<yoF`xjQwvIymqytaxxEwBvSisGURmTBqjJF<:ZijAeR;CwwArxtYwQYrmXmMqqTpJhkB@<:u[[jJ:kL_Xv[iUyeYtCwdiIPk<H>@<:::rkhUkuWf]ocdNfrEF>@<u[RWdD?EjOUtIuYwIyVMuPUpj\\oH]SBuYwMYy;dI::::jsuYwIIcAVXJtWY:dYt;aAZmMt;aqwMIcamex:cAVXLIrvZn=HIBw:hI:oIwZmmsWYZmqytMw;rxcqwIiuMwksCwhYt;rvZn=:::::::::jtWY:Zn=PI:::::gAfX:TIgA::::JxUYymIju_yp=XIVypuxeanex]QvqxxYYnqytIxxUymqytMhpiVgYsju]H?YygysTylgx]=bwGYyPxxUylcs^vvix^iyoivvEsnvwix_]vqx`ayoavw=GIycyrsqkgx`iypyvvix`UwnxamloxbUwGIyeisuiwKIygItPI`XxUymoxcUwKIyeQxUynoxcMnoxcmngXTIThniVeysqqkeyrOykYutIxUuu`yqYghytsywSQykex_iqqiv;qsAxwIykSsqIwEIyTxwMyloxcewhytYXxYyost:ZfExYIykYusqoqYvgysIXkiuuIxlifUx]QwII[QvuxxKwEYyiYtWyniY_YykyuvWoyvwQucwfxwEwuYx]qv=itYXPYymixaY:hyuSwuAoataxxaYlYv_Y:::ZsEykaruxJyiYucwpyvKyOY:::hYyOYjwyyxwY:nyuyYsau=nYoat=hIBy:fyyUy::::Zx]y=jPqTU]tMWxlaxyyyxyYJh[khRjy;riZsHq;yYxI:riZPupyaPupKoR]DmayyYyAZP=PFBt>Oxe@yYxIy_bLnsynTjYsyvY:j_Cn[XoayvcItVsEeogxpyay=:xEK_P=xIy?>WxIyabMNsivYxIUOU?OKaymy;RxfogpPfWxiyqT\\Dm?vY:JTCdKOnOWvY::JnCd>OxIyA:::vQ\\Dg`yMTSeUggmYxxIyA:nT\\Dry>WJNSxZy=DHK_blv;yANVjYsyvYpDK_bmysy:FYpDRujyUGK_s<xI:Bg>obDtdHxEK_Pmysy:^UDXkQxvaYwyIyabLNsyvYJeCdFQjy;Bqfr?EtKitry:ZbLNCtZyMNCdvYxIBt>OxEyaymP;Kaymy;RxfOjp[yqTjV;yA:^P>OKQoky;:::::::::bysywvX::rxiQxCyZumw;:::sAVY:Jx;qA:bwhyuswnXTIiaq=TI:gA::::vX:Ju;JvQYrasuX=@B:::[ootxoYxD=qO@RdFJ:::tDkQruywUYysxkIwIyq]hh?gWCG[MTaquHuvXq;OW]itiOwZCIqSXxgIvuixcqwQYxaysivVQsWMtuhuKUqWITu:\\w_EuuMYqevUMsLQR_pswdmKIR^PVS=ss=yoiYvIyvUYrqswhm:M_;<:TStLMnQXjGymqyu=Yit;Ylgw^Qg]iTaquHu>dmRUslTVTASpUXheyuAyxeYtKygX:Z\\yuSimSHlIXk=xkEXJFqohoxYypqYRwwATIRw:[YuIYheWeYv\\Av]:Voaxm\\yuRqyuixx=::JfHO_@\\KF>Xv[mUyiytuI::BPZ[jAibxYyoqY::::::::ciyjt;cAfXLIRw^XLIRwfXLI:cAfXPI:BwZo=:::Jt;eanMtSwZn=PIBwfXJtSwfXJtCwfX:Jt;eao=::::Ju;eAZn=PI::::bw:nX:BygA::::::ZqEygapmu;rw:::::ZrEyRxvXqYw^XoatAxxAyeiyqIWXxxUIiYt>WiIt:TymqYvixxUYmqyuexxYyn[qQWgis\\yp;MadmmwxeaypyvwetFwwqxbiyqEyeYsuqmoxbMowxeiypIWiytZciYOQucwMquiXxGwwmxYYowxdmomITYoqyumhqYwwEu\\Yqwxfuw>ygMpmIsQomyt]hoyvvix`mkiyskjKwgU]Yqqiv;Qs=hmYVayrLiuiXTIeysTIiytsQooxcExUYykiusywQYytxx]yqCv`yq?yhMqGykex_qvAiryWbx_QwIyxeyscv`IoyvwQtqimiYaA^XTiuiXPIBw:fXsIxZrmuuipMuSwhyt[vyXsYxpyvuI::ZtEymQxKvSxZr=::`ImqxaI::oqxeI::rxwqwkyuiyEyfYlIRy:::^Yjx[yuy::>T\\D[`yeyyAFQ;`kPVxiyyY:xEK_bl_ifsmysynTjPSx:ZblVGrmYXyqyyI?agdgK_b=\\HK_ydkyaymYCd>WxImagdgbovYxIbo>OpDyyypxp?Ojpqhyuy:KabLNCqsHryaymY;KaymyCt>OxEyayMe;U?jykvShmONsiZyMe;K_EmysyZVMN]dbls;yA::>WJNsyvY:::jYCdnTxIg`blVsvZy=lGUWeptPGysuy>WJNSkFYjySkhVNCdVS`IryfR:xIyaP=pDUAxI`ImWh\\Dy_ymycoZbl_;yA^U\\DK_m=PFbovYxIBtZblvsyvY\\DK_ymy;g`bLNcrvYxIboZslvaIvYJe;K_m=xIK_blysyZb=xErynTjP;vYFY`EK_y<xIg@>OhFryZV=\\DaAvY::::::::::tYx]IkA::::::::vXXI:BxZqMv;:iar=XI::::::::::::JvUyrasuX=@B:::AxfgFw_YuuvXqSZFJ:::tDkqruywYIiapiytqxuAyoQyqYxsqxlIypQXNyqYxuAyoiytiXqiwwQuswRyPYxaYtmyvMI:eYyoqxCyPyw]ysSvoyw_QvMyxeytuImiw]YaquHRZ:ZP<=IymYwwyxtipiYlinYyrYXFypIXNY:tIwA:::::ju;gA:::::::::::ktNO<=kBtywUYy;::BPZ[jA[pqY:::::::RwhITIeao=JucwfXPIbwnXPIbw:Zo=TI:eAnXPIeA:nX:jt;bw:nXPIeA::nXTIeAZoMucwfXJu;RwZp=siwhyt;^YhYu;ZvmwQivqXsA:::::rwwA::TI:rwZp=XI:::::BxZqMv;iar=JvswZr=::uYxFYByiqwQitQxxQykUxYafiyrawwyxcExQQvihqQWkyt\\ixAyfqYQiyhHSYykytuqpCuZfMpSuXYoCuXyostfW`HvxcuwbuXYocuVWphriWiitfWkIu\\YpSuZfUxWYyiIuuIxUag=:RxYaguwUYyRx]QvuhsIXmYv\\ypCuXYpmidUwGIyeysPiu]naVcYsLILHCqtUxwgvvEtNWiytsywQQvqXxkuqhryWkiusqpqYvSxFY>XmARvwyxcamUx]YybxtiouxeYyHyx[lqyuixx=gapuxRwnXqArwnXTivyXsYxbyrxVYlIsyw:>yxaYpyvgytMw;qiy:jv_yrEymQxaiwIY:uAbxNY:::hIqA:yiyxIyiy::::sAfY:Jyky;:JyWX\\DcoWyixuyHysMYN[vxYxI:ri>OPFRevqyprnLN]dbLhsyvYTGRkZblYorsTjBdVsE=yabAWrivYxIy_bLnOwymyCq>O\\Dc_ydkc_b@OK_Pmywyym_?tbLNShmoYSh>O\\DU_sIYKItOId>O:JnOwbMNsivYxImasHQBdFQxEK_blPSuUAyAg`blVCdfOxEm?>OxEyay=::Jn;K_ymy;:::U_bLk;yas<\\Dm_yLTKN?OlGyayMn;m_ghOUWexE:K_VmPSevQ:\\D?AvY`IBd>O`Ey_bLNSefWYay]P=`EK_glYShZblYsyvY\\HBd^PxEm?>OhFyaP=\\D:ry:FQjYCg>tJitsIY:K_ylYyenLNCdvQxI:K?:vY\\HriZymv;BdFQxEK_blPSujyKe;m_blPsiFQJNsivYxI::::::::::bysYxlI:\\Ikas=\\I::::::::RxZr=::::::::::::XIBxZqmuKvOxSxhqZ;<::jaQvSYyt=YVATt@B=>::ZhLvUyruYxYYy;:hyu_YlI:::::::::::FyqQxWXiuZ;<:TCTXkmYwQYymyuuI::::::::hIBylyvIYymixMxcxgiuqywYYxeYumIwSYyoiwwIytI:::jwoY^Y::::Yv\\CVBqR>=kBtYxoY:::\\ochnJhkB@<ktNQdysywwA:rxgAlIJu_ypmuswZp=:Ju;rwZp=:ju;:gAvXJuswZpmuswZpMuswvX:qAgA:::::::::vXsiw:ZqMucwvX:XI:bwnXjusw::::::::::::>Y\\I:iA>Y:::::::::ZyMymix=jysy`I:Jy;yAdyyOYBykiyqIwwAoasAxxIyiUxUiykYuwYxYYypXyaYqGyhiyriwxEvuIxQiymiuwAJrSuvWkYuuYxWqvyHtI`YrGyhExpYvqhsmv=I:YahqytIxwAyhqYBvnwwuu>XkiuuQrGyimqOykiysAXnY]YymApyvAIZtQxw=bvZkqytYXoivuQrwxguwpYv_ypQWgIt>WeapAWgYtTIdHMAXYpmyuKpqihExWA`yrqYvyH[qvAitMwEisIX@itYXoqxeYtsvVXLItywUIpywMyx_XrxeAFYnyvyxxYyomtcwhIsIx>Y`iwIyxiYlIXivyX\\IkAFYdIoA::VYuqyuywyivyYsA::::::fYpI:::sAfY:JxCyfYpiyuybyxYysyvYtIwaymy[y<\\hcyyyqyJMNcovYxI:ri>O\\hdAtJ=K?fogDqsHryay=TGK_PMhSe>O\\DBnvYxIBt>Oxe@yYxIy_bLnsyvYJkCgBd\\DRe^UxIyAZPmPqTU]DK?ZsHQUYuryKabLN;:KQo]HK_ylysyZsm_Cd>O:xEUYury:g`bLeCqfOJN;y_sIYyay=::Jn;K_ymy;::RuUQNCdVXxIyAnTpDBdZnLn]XoyIyA>W\\Dy_gmVCd>OJhsyfWLUT?obDdZJ=xI:maE=\\D:y?vYyAbo>OTGs`g<\\DriFYxIyANV:\\D:[`s=TGK_b<:xI:?asHq;]blVsyyqvslZb<:PFmayMe;K?:vY\\HrivYxIRxVSJN;rifWry:g@nTlG:K?vQ`Iyay=::::::::::tYxaivIY::uAmqxaI:::ZvMxSy:Zvmx;::sA:::::::kAZrmv;Rx:>Y\\ImasMvCxmywcy`kEHRZ:::fv]AvtAynQrgpj;`D=>::ZkPmhGyqYxxayrqY::::::::::::::Jw]Ytqswh=@B:r_eUGSitGixiYvmYwWYxeiu:::JuuhrIxxayrqYJvMyoMYqIXsiXiUyrUxsqxiEyoiwoEX`iXkmVnuW]yWcIugmVOMXfmUl]WYeW_]TjIWUAXdauoAXaMYqEXvIyoQYrMxt=YlMYqEXu=ylMYqAXtuxjaYtmxtuxkAYoiwraxgMypEXu=YmYYsaxuEynaytuXwQYqeYuuxUIuOAlGfaqn_xayrqY:::\\ochnJRB>EQdyjuCxwAXIBxvXXI:karmu;kaq=\\Iiaq=JvCxZq=juCx>YXI:Bx:Zq=\\Iiaq=:::::\\I:rw>Y:ju;::karmu;kA::vXXI::Bx>YXIBx:vXJv;::::::jy?yxaYry:nYtIyAjvyis=:::::::::::::dyyqyv;:oA:bydivyXqIwNxxQyjex]iymIvwix[A`YrSvdYrOYFX<I:_qv=INykiysywxYymiysyWoatIxxIyiqY_YyxHtIFxxevRy<YyiYtSvwix]amiys=VxxmxeyruIuqruilMsqikmsuimiytIxwuvuqscvwqsuiniytIXmYvhIHyx[nqyuqXoyvwqsWyoexcYymIvuQrsuuywSIyjo;SIypXxYypqYvuhryWkyujv=I[AFxwEwFXmivVXqAaQwIiueyqauiXqYw:nXBykiyrxgap=sywlIuawQYju;:katUy:qiydImQxCyfysUymA:NYhyyuywyIZvyYsA:::::fyyqY::^YlI::uawMyoYjywYnYtyx;wAxIyA:lGrlQpyCgZm=xI:::Rx>WpxpyHyA::::Kabmysy:ZbMN]dydkyay=:::jpqhbAWUayuy:::Ru>W\\HaQtky;:y_bLnOwymy;::::Kabms;yA:::ZbMnsvZy=:::JnCd>OxIyA::Zy<xEyay=:JnCtVXjy;:::RuZsexyay=JnCtFYjy;::Bt>WHIry::::>W\\HaAvY::jp;Kaymy;:Bd>OxIyA::>WpHyqy;:\\HKAFYjy;:K_blysy:::::>W\\HaAvY::::\\HKam=xI:::::::::::byuixNY::::::::::::::::jvSx::::::::::::qixgIlgW_gwacegyvVgwaa=:biOwZcyv[IyqywMyreHh=WWgwaaeg::wvVgwacUoKXfqYxgiysYxFY::::::::::::::^ytyxDAqPxpY`hppmmca:LVSAsrqXnMyqUxtyXmUyr]xvQyqaytyH:Tyr]xtyXm=ynqWpIXdUXhaVg_pNaraht?AoOirbpt@AoSQsh@uDaoQAsbptAqnBYpFxrmPkEAqJpsv`lGQqKxrlpjBYpA@snxjCipC@txxlNYrXHtyHmFAqHXsphkGIqKHuCAoXAtmPuDQoTedmXlKwpSXeyXnegrchhGipCXuCyn]ituhxgIvuyxkiysYxWytIYBq:BxlYvSxwQvCxZs]\\AvUQjxohiF_Y>eMWC`Itir=`ImarMv;mA>Y`IBxFYJv;RxZr=:`I:Bx::::::::::::yqvuYxoY:::::jy;wA:::vYkyy`ItIry\\ItIFYJvyis=\\Imyy`I:^ysyyvmxSy:::::::::::::::bxyA::::::::::::::hiwQYdItYx]YygxxYynex_iyqivwyxaiyoiv^X@YyOXHI]qw;PiuYXJt;VymMs[uYXoYvdysOYhysWynexRwdyscv^XqIwdYs_ypexVYhyt[tmwUit]muxBwdysSwhYt;RwdYtuiouxNYJxYiu=lyucwhYtWYZoexZvMwMyxeYsqYwEIFyjExUYykyu\\YqGyjUx[akex_AdIoyvdYsKyiYtkx[oqYVYuQtuipEyiQxYiuqXqiwlYvswlI\\IkA::jxwYqiy`YyGYuAZwQYuixFYhix]v=nYqiydIoA:Zumw;:nyuqyxmxSyxIyA::jxyiw=JyoY:fYpI:vYyA::::fOptPOv\\ivbl\\syyqy;:::::::::::::Bt>Oxe@]y=:::::::::::::jYCd>WxIyA:::::::::::::::::>W\\DK_ymy;::Q`bTfK_bmysy:::::::::::::::::::::::::::::::::ZbTfK_ymy;::::::::::K_blysy:::::::::::::::::::::::::ZxiyuqY::::::::::::bxNY:::::::::Zymy;:::::bysYxuyxkIyoywsixiA:RyqIxwqvyit]wMxCy:ZuQyqayuAyvYyrqywQyxiY::::::::::::Zsmv;oat]waysayuAyuQyqYY:liqiyvIyymy;:FYJwaytqXu=ym]YtmXx]ysyyxeYsmXj]XimVlaw\\qWbUuh=WUkgqVSew_yTeYVOuVXiS^QuBAVPQR[qt<EvPwrmpkDypLPsqPlIiqSPt;ymNYr[HuDQoSQsexuKapZYtq@vMyp[atqHvN=MyqKxuGYogIvEYyqYwyqvSx:ZtyYXPkd?xyxeyyGY`I::bxRvYitehnUxyuYxyqv;:::bxZsMw;mA:::NYjv;:::::::::::::::::::::::::::::::::::bx:NY`IbxFY:Jw;:::::::::::::rxyYyqA:::::::::tywgYpIby:nYpYwcxFyxayrEygqwMI_aoqyuaXLivqXDivyXqIwhIPI^Y^XqavqXsiwhIsywVXLiuaXPIRwhIsiw:vXPIbwnXqIwvXjt_yqEygao=:juWYhYu_yq=:siwnXJvWYhIsYxwIy:iAlYvWY:lyuWYZruxVynexcamiYaaliysIxwQymms;cYyLYy[o=TIgQxYIgAlIsIxhI:uYxJxYIiqxSymA:ZtqY:RxZtyYqiywAqyyuyxpix=:::::jyuYxCy::::fyyqY::::nYyqyKyuix=:xIyA::ry[`bLTKNOVxIyA:::::::::::::ZbMNsiTvysy^U;iogpsIYtyIyA:::::::::::vQ\\DKQoyIyamMeUgVmywyy=::::::::::::::JnCd>OTGg@:VSLUTmebDd^Ujy;:::::::::::::::::::::::::::::::::Bd>OxIyA::::::::::>O\\Dyay=HIBqZy=::::::::::::::::::::::tyxiiwayxiYryuIywax=:::::::::::::::::::::jyWyy=::::bx:ZuMwcxZu=dIqA:NYhIqiydYy;:ZuqYbx:Zu=dI:::::::::::::::::xit=::::::::fytqxqQXiaiyvTqw`AuhqvR=::FxdiuqQxcIYUyyuixyA::::ZAar:I^UF\\e@o\\xywQyy=:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::rxyAdIrxZt=hI:::::nyu=uA:nY:tIuAnY::::^YhIqA^YjwCyZuMxCy:::jxiiwQYdImyy`Yymyu_yoEyeaqMu_YvXTI:gAZqmu;:gAvXTIrwZr=TIrwnXjucw>Yju;kAvX\\IbwFYjuCx>YXIfY>YsawmxaivyXsAmarmugYpIsYx>YuawQyxUxlIsYxZrmu_yqMv;iqwsx:Rwdix]u]pEyiA>Y\\IiQx]Imas=RymAlIuixVYByRxpYwgYVY::dIrxtIwaw=tiy]x=::ZwyYuA::Zxeyuaw=::::tiyqyy=:::::ryyAVX\\DK_nlysy::::::::::::::Zb=xe@yYxIy_bLnOwymy;:::::::::::aayxq@Awb=yabMNsivYxI:::::::::::::::KA>O:::JTcr?AxI::::::::::::::::::::::::::::::::::Bt^pn`qymy;::::::::::KAZy=\\HK_y<xI::::::::::::::::::::::JymIsA::::::::::jxmyyuIwaw=:tIRyfY::VYuIy^Y:hIByVYwAfY^YhI:qQycyqau=lIsaumw;::::fYJySyZxeyuawuyuQycyZymy;:::::wAvY:Jy;yaxMysyvYtI:ry::Zx=:xI:::::::::::::::::::::::::mDOStEMCBmgg_wyuyxyae@o]Xv[quyiyuyY::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::nYyA:::JxCy:::Zu=lI::::::::::::::::RyfY:hiwmxeIxIwIyiAyQvuir=XItyx]Yy?Ysaw=FYuYxJx]iv=:pYvgysUykAFY:ByZw=>Y:jv[v=pI::JwSxFYdIoQxkvcxpI`IbxFY`IoyyhYyOyx=bxyQwuIwayuxyiytitqY::mQxaivmxaIkQx;:::`IfYNYBymAVyx=oAVYhI:xIVyxmyqywuYyoYnyueysyylI::::uaw=::::::Jyoyx=:::yiyyyy:::yyytIxI:bonTDXk[y=::::::::::::::HIg`V=xIsHqTGaaymy;:::::::::::::rvnTlGyay=::::::::::::::js;g@::Zbmysy::::::::::::::::::::::::::::::::::::::::::::::::::Zm=lGry:::::::::::::::::::::::wYyfYJxCy:::fYJx;:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::Xw^qTVysq@tyxmJyAZj`lX?rcpiQIsgxwcauyqYyA:::::hIBy:::VYhIsavitMAtiF_ZF^URB:vr?AryqyvyY:rxZv=:::hIByZu=jwCy^Yjwsx^YuqyqIbynyv=Ry::fYtIwaw=jx;wAZx=::::pIuaxYYuawMymix=ZueyqavMxgYJy;jwsx^Y:lI::qA^Y::jw;:sau=lI::::::::::::::::::::::::::::RyfYlIsawmx;:sAfY:::::hIqqxayyOyyex>yyUxFY:dYyGyymyGYJwuIryjv;oiyZyMy;yA:nYtyxwYbxwqvyiuUyoatyYqiyuQyOYdyyWYnYxit]x=xiu]xmysyhYy;yAnYtiuyyxaYuAxIyAwyxwA:lYyOyx=qyywIyyaxuxVYlyygYlYy;jxoYqiydIoA:::VY::hI::xYywYsAVyx=ByZwmx;:::By:Zw=::tix=:::xYyyI::::vyy=::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::nywmx;::::::::::::::::::::sAZv=pIuA^YlIRyZvmxSy^YlI::::Ry:Zv=::::::::::::::::pIBy:::::::::fYJx;:::XG]VT;SZcl:;:::R^MEBkwaYuuMIqry::::::::::ZO=jJ:QWdCwywIyyA::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::pIuAZv=JxSyfY:::::::::::::::::::::::::::tixaYhyyWYuixtywsxyYyoqxkwcxtIRyoQykw[xaYuixpIwIyZueyqqxeiwYYlix=tYx;qaueysqxSyrxjxKxoYwQwyIjxiiwMycyxIVYwIy^YuAnYVYhIsavmwgYZvmwoyuMxSy^Yhiw]w=lI:uawMxCyZwmx;savmxSyZvMx;qQymIsA:jxSynYtI:::jxSy^Yjx;:::wawmxcynY:::::rywyy::::jyyI::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::JyqIuA::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::;Iowg\\;E>=FO@B::::::[G_ytuMYqyiyxI::::::::::]IvWyZyUXusGYSBqJBmr=yYyqyy;::::::::::::::::::::::::^Yjx;:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::wQyqIby:::::fYpI:ByVYhIsavmw;rx^YjwCy^YhI:qavMxsxZvmw;sAVYpIBy:VYlIuA^Yjx;sAfYJxSyfYlIsaw=lIRyfYlIsawmxCy^YpIuA^Yjx;sAfY:::tIRy:ZxMySyfY:JycyZwmx;::::::waxmxSy:::nYtIvyxyY::::::ryyAJycyvyy=::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::nyxey:::::::::::::RyfYtI:wAfYJySyfY:tIRy::::::::::::::::::::::::::::::::::::::::::::::]ituxgqvQOfQ;B\\sD:=FO@B::::bZeD:AfO;B[iD:EFP;R[mD:?Hewuywqy;:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::ZxMy;::::::::::::::ZyqyyqYtIryvY::::::JycyRyfYJx;uavMxSy:fYlIsaw=lIuawMx;uav=pIByZwMxCyfYpIsAfY::::::lIRy::::::nYjx;byZw=JycyZwmx[ymycywaweywaxuyvYJycyuAnYyay=:tIwAvYxI:::waxmysy:::::::::yyy::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::tIwA::::::::::::tIrynYjycynYxIby:Zy=tI:::::::::::::::::::::::::::::::::::::::::::::NxfyuCYp:HlaGZYHiZ>rb@h:AO=FO@B:::?>fjRc[oD:IvP;B\\sl>qO:drh<J?uO:@tx<mreXiyYywY:::::RyZx=:::jx;wAfYJy;RyZxmx;waw=tI::uAnY::::::pIby::::::fYJy;:::::uAnY:jx;RynYjx;wax=::::::jx;wA:::::::xIyaxMy;::::yAZy=::Jy;yA::::::::::::::::::::::::::::ZxMyqIuA:::::::::nYjx;:byZw=::tIRynYtIuaw=tIRynYtIuAZw=:ryby:xIyaxMy;::::ryvY::::::::::::ZyyYwax=:::::jyyI:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::ZxMy;::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::JmmW[AvMUpF=Q>xuLIpleWZyyyuyy;=^>@e;>l__ZQhg?fk\\WZ;`D?VOvd:fjSs[ql>q?VkZ?ZFHf:fk\\?ZHXf:nk]s]AE:gVU[bt?imyay=:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::yyytIwA:JyqixqYJyoyw=yAwQysyRy:xIwaymycynywuyvYtIryZx=xI::::bywAxI::byZy=tIry:::::::::::::::::::yyytIwA::ZyyYwAyA:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::tIwA::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::BwYYsaximfqYhfMyqShuIIpMyqQhnwg_=XcUUd?vFWg\\wsmqW]miw[yyyqy;:yHowgpQhcyfWkragu?yVWgr[oD;EVP;:r\\yD:UVR;b]A]^S^GE:_vS;b^KU:aFT=r^:MU:gxkyvyvY::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::ryyQyky[xMy;:::ryyQycy:vyy=::bynY::::::::::::::::::::::::::jyyixMy;:::::::::ryyQycy:ZyyYbynYjyyI:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::Zx]yeynYxyyoYvYwax=:::xyyoYtI::::::::::::::ryyAtIwayyYwax=:::::::jyyixMy;:yyytIxixMykt=YnIuAEoPYr\\pt=MnPUr[lT=ENPUR[<vKu`sHlcyuGyyyuy::::VraXha@jnvnyW`QhgTFkW?:bRxRl:KMDaP;PsoHJEmP<TSpPjEqp<Xsp:ZRAsZxyyuytI:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::ryyQycy::::::ZyyYwax=::::::::::xyy;::::::::::::::::::::::::::::nYtI::::::::::::yyytIwAvyyeynYjyyInYtIryyQycyZyyYwax=xyy[xMy;yyyJykyoYvY:byrytIwAvyy=:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::Jw]Ytaw]etmmw^mxkIWpIxceYvMyyyiy=:::::JwYys=U?in[YtutWbQu@AP:xRlZM@g;nmpg]fpj;Wmko[SxgANmkG[UPhENnt?^WD>sfVUr`_E=qfVQb`]U<chjgvyvYwAyA::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::tIwayyYbynYxyy[xMysyyQycyvyy=wax=xyy[xMysyyQycyZyyYbyry::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::ZQYr^HxdAvyyyyqoIhbL@g;fldWZ]Xi`npLPepPlSWqV@fXhhMvmpw\\phlJWw\\QtJYqMHnro]Z@iW>nqW]YphRnmo_\\<Aoewyyuy::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::Fsn@jP`g>vn;p_ypmhwqXhgXisnxyyUhqfPEgYUCioVSqYxgyyfuHAp_pihfnw__^`icVntg^[HiZ^rdHhyyYyA:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::NxgAvLArLPtt@mCYo;PtsxlyyYyasyxlyvVyrDio>@vIypyyYyaYAtoPo=`acPjsvn:h``pij^nvO_nXlGGyqIxyyYyA:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::nxkQwWIsipXxyywY:lYw]ynqW`yyywYJeIvKuT>UNPUR[hT<umP]r[NlMgpOPdhqvPyyyuy:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::ZHAqLHpFpcn@lOWttPmOiqYPtsxl=qnmwwaQuyyYyA:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::ft;AnaauCIxaau\\yst@vFapYYsmxuEYp_qt<Ax`YupAxcIxcquuIyp]y=::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::pYxiYtuXmyxkUwrYxg=YmiwpEXdqxjIwtyxmyyywY::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::J:<5:\"\{\}-%%ROOTG6'-%)BOUNDS_XG6#$""!!""-%)BOUNDS_YGF'-%-BOUNDS_WIDTHG6#$"%+!)F*-%.BOUNDS_HEIGHTG6#$"$!pF*-%)CHILDRENG6" # The following was implemented in Maple by Marcus Davidsson (2008) davidsson_marcus@hotmail.com # and is based upon the work by # Shone,R (2003) Economic Dynamics- Phase Diagrams and their Economic Application # Stability of Differential Equations # 1) Basic Concepts of Stability # In the discussion below the equlibrium E is represented by the black line and # x(t) is represented by the red line. # We define x(t) as stable if 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when 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 which leads to that x(t)=x(t-1) # We define x(t) as unstable if 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when 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 which leads to that x(t)LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2MVErJk5vdEVxdWFsO0YnLyUnZmFtaWx5R1ErTW9ub3NwYWNlZEYnLyUlc2l6ZUdRIzE0RicvJStmb3JlZ3JvdW5kR1EqWzI1NSwwLDBdRicvJTBmb250X3N0eWxlX25hbWVHUSxNYXBsZX5JbnB1dEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQC8lKXN0cmV0Y2h5R0ZALyUqc3ltbWV0cmljR0ZALyUobGFyZ2VvcEdGQC8lLm1vdmFibGVsaW1pdHNHRkAvJSdhY2NlbnRHRkAvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZPLyUrZXhlY3V0YWJsZUdGQEY7x(t-1) # Our General Equation is given by x(t)=7+(B)^t where 7 is our equilibrium E # From this equation we can derive 9 different cases # special cases # 1) if B=0 then x(t) will be located at the equlibrium # 2) if B=1 then x(t) will be located a constant distance from the equlibrium # 3) if b=-1 then x(t) will oscillate around its equilibrium # stable equlibriums # 4) if B is bigger then 0 and smaller than +1 then x(t) will have a stable equlibrium # 5) the mirror image of the previous one is given by x(t)=7-(B)^t where again +1<B>0 # 6) if B is smaller then 0 and and bigger than -1 then x(t) will converge towards its equilibrium with oscillation. # unstable equlibriums # 7) if b is bigger then +1 then x(t) will have a unstable equlibrium # 8) the mirror image of the previous one is given by x(t)=7-(B)^t where again B>+1 # 9) if b is smaller than -1 then x(t) will divergence away from its equilibrium with oscillation Case-1 (located at equilibrium) restart; n:=15: B:=0: with(plots): x:=[seq(7+(B)^t,t=1..n)];

NzEiIihGI0YjRiNGI0YjRiNGI0YjRiNGI0YjRiNGI0Yj

tt:=[seq(i,i=1..n)]: A:=pointplot(tt,x, thickness=2, style=line, color=red): B:=plot(7,t=0..n, color=black, thickness=2): C:=textplot([12,7.08,"Equilibrium E"],align={above,right}, font = [TIMES, ROMAN, 15]): display({A,B,C}, labels=[time, X(t)],view=[1..n,6.8..8]);

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

# Case-2 (located a constant distance from equilibrium) JSFH restart; n:=15: B:=1: with(plots): x:=[seq(7+(B)^t,t=1..n)];

NzEiIilGI0YjRiNGI0YjRiNGI0YjRiNGI0YjRiNGI0Yj

tt:=[seq(i,i=1..n)]: A:=pointplot(tt,x, thickness=2, style=line, color=red): B:=plot(7,t=0..n, color=black, thickness=2): C:=textplot([12,7.08,"Equilibrium E"],align={above,right}, font = [TIMES, ROMAN, 15]): display({A,B,C}, labels=[time, X(t)],view=[1..n,6.8..10]);

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

# Case-3 (oscilated around equilibrium) restart; n:=15: B:=-1: with(plots): x:=[seq(7+(B)^t,t=1..n)];

NzEiIiciIilGI0YkRiNGJEYjRiRGI0YkRiNGJEYjRiRGIw==

tt:=[seq(i,i=1..n)]: A:=pointplot(tt,x, thickness=2, style=line, color=red): B:=plot(7,t=0..n, color=black, thickness=2): C:=textplot([12,7.08,"Equilibrium E"],align={above,right}, font = [TIMES, ROMAN, 15]): display({A,B,C}, labels=[time, X(t)],view=[1..n,5..9]);

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

# Case-4 (stable equlibrium-1) restart; n:=15: B:=0.7: with(plots): x:=[seq(7+(B)^t,t=1..n)];

NzEkIiN4ISIiJCIkXCghIiMkIiVWdCEiJCQiJixDKCEiJSQiJzJvciEiJiQiKFx3NighIickIilWTiMzKCEiKCQiKixbdzAoISIpJCIrMk9OU3EhIiokIitEdkNHcUY9JCIrbkt4PnFGPSQiKyhHVFEsKEY9JCIrLCopbzRxRj0kIitKQXkxcUY9JCIraXZ1L3FGPQ==

tt:=[seq(i,i=1..n)]: A:=pointplot(tt,x, thickness=2, style=line, color=red): B:=plot(7,t=0..n, color=black, thickness=2): C:=textplot([12,7.08,"Equilibrium E"],align={above,right}, font = [TIMES, ROMAN, 15]): display({A,B,C}, labels=[time, X(t)],view=[1..n,6.8..8]);

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

# Case-5 (stable equlibrium-2) restart; n:=15: B:=0.7: with(plots): x:=[seq(7-(B)^t,t=1..n)];

NzEkIiNqISIiJCIkXichIiMkIiVkbSEiJCQiJipmbiEiJSQiJyQ+JG8hIiYkIiheQilvISInJCIpZGs8cCEiKCQiKio+TlVwISIpJCIrJFJZJ2ZwISIqJCIrdkN2cnBGPSQiK0xuQSEpcEY9JCIrOChlaClwRj0kIisqNDYuKnBGPSQiK3B4QCQqcEY9JCIrUUNEJipwRj0=

tt:=[seq(i,i=1..n)]: A:=pointplot(tt,x, thickness=2, style=line, color=red): B:=plot(7,t=0..n, color=black, thickness=2): C:=textplot([12,7.08,"Equilibrium E"],align={above,right}, font = [TIMES, ROMAN, 15]): display({A,B,C}, labels=[time, X(t)],view=[1..n,6.0..7.2]);

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

# Case-6 (stable equlibrium-3) restart; n:=15: B:=-0.7: with(plots): x:=[seq(7-(B)^t,t=1..n)];

NzEkIiN4ISIiJCIkXichIiMkIiVWdCEiJCQiJipmbiEiJSQiJzJvciEiJiQiKF5CKW8hIickIilWTiMzKCEiKCQiKio+TlVwISIpJCIrMk9OU3EhIiokIit2Q3ZycEY9JCIrbkt4PnFGPSQiKzgoZWgpcEY9JCIrLCopbzRxRj0kIitweEAkKnBGPSQiK2l2dS9xRj0=

tt:=[seq(i,i=1..n)]: A:=pointplot(tt,x, thickness=2, style=line, color=red): B:=plot(7,t=0..n, color=black, thickness=2): C:=textplot([12,7.08,"Equilibrium E"],align={above,right}, font = [TIMES, ROMAN, 15]): display({A,B,C}, labels=[time, X(t)],view=[1..n,6.2..7.8]);

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

# Case-7 (unstable equlibrium-1) restart; n:=40: B:=1.1: with(plots): x:=[seq(7+(B)^t,t=1..n)]: tt:=[seq(i,i=1..n)]: A:=pointplot(tt,x, thickness=2, style=line, color=red): B:=plot(7,t=0..n, color=black, thickness=2): C:=textplot([25,7.08,"Equilibrium E"],align={above,right}, font = [TIMES, ROMAN, 15]): display({A,B,C}, labels=[time, X(t)]);

NigtJSVURVhURzYnNyQkIiRdIyEiIiQiJDMoISIjLSUpX1RZUEVTRVRHNiNRLkVxdWlsaWJyaXVtfkU2Ii0lJUZPTlRHNiUlMFRpbWVzfk5ld35Sb21hbkclJlJPTUFORyIjOiUrQUxJR05SSUdIVEclK0FMSUdOQUJPVkVHLSUnQ1VSVkVTRzYmN0o3JCQiIzUhIiIkIiMiKSEiIjckJCIjPyEiIiQiJEApISIjNyQkIiNJISIiJCIlSiQpISIkNyQkIiNTISIiJCImVFkpISIlNyQkIiNdISIiJCInXjUnKSEiJjckJCIjZyEiIiQiKGg6eCkhIic3JCQiI3EhIiIkIilyclsqKSEiKDckJCIjISkhIiIkIioiKSllViIqISIpNyQkIiMhKiEiIiQiKyJwWnpOKiEiKjckJCIkKyIhIiIkIipZVVBmKiEiKTckJCIkNSIhIiIkIisxbjZgKSohIio3JCQiJD8iISIiJCIrUUclUSwiISIpNyQkIiRJIiEiIiQiK0ByQVg1ISIpNyQkIiRTIiEiIiQiK00pXCh6NSEiKTckJCIkXSIhIiIkIis8W3M8NiEiKTckJCIkZyIhIiIkIisqSChcZjYhIik3JCQiJHEiISIiJCIrR3FXMDchIik3JCQiJCE9ISIiJCIrSjwqZkQiISIpNyQkIiQhPiEiIiQiKy80ZjY4ISIpNyQkIiQrIyEiIiQiKyYqKlxGUCIhIik3JCQiJDUjISIiJCIrJSpcLVM5ISIpNyQkIiQ/IyEiIiQiKyVcRlNeIiEiKTckJCIkSSMhIiIkIitWLVYmZiIhIik3JCQiJFMjISIiJCIrb0soXG8iISIpNyQkIiRdIyEiIiQiKyVmcU15IiEiKTckJCIkZyMhIiIkIithdyI9Kj0hIik3JCQiJHEjISIiJCIrPiUqKjQsIyEiKTckJCIkIUchIiIkIitoJCo0VUAhIik3JCQiJCFIISIiJCIrKEg0akcjISIpNyQkIiQrJCEiIiQiK0YtJVxXIyEiKTckJCIkNSQhIiIkIipETSU+RSEiKDckJCIkPyQhIiIkIit2d1A2RyEiKTckJCIkSSQhIiIkIitVYV5BSSEiKTckJCIkUyQhIiIkIisnKXB3YUshIik3JCQiJF0kISIiJCIrJm9WLV4kISIpNyQkIiRnJCEiIiQiK2Ahbzd6JCEiKTckJCIkcSQhIiIkIitmW1IrVCEiKTckJCIkIVEhIiIkIitXVlZTVyEiKTckJCIkIVIhIiIkIit6eFo5WyEiKTckJCIkKyUhIiIkIitkYiNmQSYhIiktJSZDT0xPUkc2JiUkUkdCRyQiIzUhIiIkIiIhISIiJCIiISEiIi0lKlRISUNLTkVTU0c2IyIiIy0lJlNUWUxFRzYjJSVMSU5FRy0lJ0NVUlZFU0c2JTdTNyQkIiIhISIiJCIjcSEiIjckJCIxbW1tbTsnKT0oKSEjOyQiI3EhIiI3JCQiMk1MTCRlJzQwaiIhIzskIiNxISIiNyQkIjJubW1tNmhPWyMhIzskIiNxISIiNyQkIjJ0bW1tInlZVUwhIzskIiNxISIiNyQkIjFMTExlRj4oPiUhIzokIiNxISIiNyQkIjFubW0iPksnKilcISM6JCIjcSEiIjckJCIrRHQ6NWUhIiokIiNxISIiNyQkIjFubW0iZlgoZW0hIzokIiNxISIiNyQkIitEQ2gvdiEiKiQiI3EhIiI3JCQiMU5MTEwvcHUkKSEjOiQiI3EhIiI3JCQiMW9tbTtjMFQiKiEjOiQiI3EhIiI3JCQiMiwrKys4IVErNSEjOiQiI3EhIiI3JCQiKiYqM3EzIiEiKCQiI3EhIiI3JCQiKig9XHE2ISIoJCIjcSEiIjckJCIybm1tImZCSVk3ISM6JCIjcSEiIjckJCIyTUxMTE9ba0wiISM6JCIjcSEiIjckJCIyTkxMTCZRIkdUIiEjOiQiI3EhIiI3JCQiLEQyWDtdIiEiKiQiI3EhIiI3JCQiMkxMTEx2di1lIiEjOiQiI3EhIiI3JCQiMi4rK0QyWWxtIiEjOiQiI3EhIiI3JCQiLHYiZXBbPCEiKiQiI3EhIiI3JCQiMlBMTCRlL1RNPSEjOiQiI3EhIiI3JCQiMk1MTGVEQkoiPiEjOiQiI3EhIiI3JCQiMm1tbTtrRCEpKj4hIzokIiNxISIiNyQkIjFubTtmYEAnMyMhIzkkIiNxISIiNyQkIix2dyUpSDsjISIqJCIjcSEiIjckJCIxbm1tSnkqZUMjISM5JCIjcSEiIjckJCIqOWI6TCMhIigkIiNxISIiNyQkIiswVE46QyEiKSQiI3EhIiI3JCQiMi0rK0QiUlYnXCMhIzokIiNxISIiNyQkIis6I2ZrZSMhIikkIiNxISIiNyQkIjFMTExgNE5uRSEjOSQiI3EhIiI3JCQiMi0rKys6P1B2IyEjOiQiI3EhIiI3JCQiMmxtbSJ6TSk+JEchIzokIiNxISIiNyQkIjIwKysrKGZhPEghIzokIiNxISIiNyQkIjJLTExlZ2AhKSpIISM6JCIjcSEiIjckJCIyLisrREcyQTMkISM6JCIjcSEiIjckJCIxTExMJClHW2tKISM5JCIjcSEiIjckJCIsRCJ5aF1LISIqJCIjcSEiIjckJCIxbm1tJylmZExMISM5JCIjcSEiIjckJCIxbm1tLEZUPU0hIzkkIiNxISIiNyQkIjFNTCRlI3BhLU4hIzkkIiNxISIiNyQkIjIvKysrYWQpek4hIzokIiNxISIiNyQkIjFNTExHVVlvTyEjOSQiI3EhIiI3JCQiMW5tbTFeclpQISM5JCIjcSEiIjckJCIsRDI4QSRRISIqJCIjcSEiIjckJCIyLysrdlMpMzhSISM6JCIjcSEiIjckJCIkKyUhIiIkIiNxISIiLSUmQ09MT1JHNiYlJFJHQkckIiIhISIiJCIiISEiIiQiIiEhIiItJSpUSElDS05FU1NHNiMiIiMtJSVWSUVXRzYkOyQiIiEhIiIkIiQrJSEiIiUoREVGQVVMVEctJStBWEVTTEFCRUxTRzYnLUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHNiI2NVEldGltZTYiLyUnZmFtaWx5R1EoREVGQVVMVDYiLyUlc2l6ZUdRIzEwNiIvJSVib2xkR1EmZmFsc2U2Ii8lJ2l0YWxpY0dRJXRydWU2Ii8lKnVuZGVybGluZUdRJmZhbHNlNiIvJSpzdWJzY3JpcHRHUSZmYWxzZTYiLyUsc3VwZXJzY3JpcHRHUSZmYWxzZTYiLyUrZm9yZWdyb3VuZEdRKFswLDAsMF02Ii8lK2JhY2tncm91bmRHUS5bMjU1LDI1NSwyNTVdNiIvJSdvcGFxdWVHUSZmYWxzZTYiLyUrZXhlY3V0YWJsZUdRJmZhbHNlNiIvJSlyZWFkb25seUdRJmZhbHNlNiIvJSljb21wb3NlZEdRJmZhbHNlNiIvJSpjb252ZXJ0ZWRHUSZmYWxzZTYiLyUraW1zZWxlY3RlZEdRJmZhbHNlNiIvJSxwbGFjZWhvbGRlckdRJmZhbHNlNiIvJTZzZWxlY3Rpb24tcGxhY2Vob2xkZXJHUSZmYWxzZTYiLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWM2Ii1JJW1yb3dHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHNiI2Ny1JI21pRzYjL0krbW9kdWxlbmFtZUc2IkksVHlwZXNldHRpbmdHSShfc3lzbGliRzYiNjVRIlg2Ii8lJ2ZhbWlseUdRKERFRkFVTFQ2Ii8lJXNpemVHUSMxMDYiLyUlYm9sZEdRJmZhbHNlNiIvJSdpdGFsaWNHUSV0cnVlNiIvJSp1bmRlcmxpbmVHUSZmYWxzZTYiLyUqc3Vic2NyaXB0R1EmZmFsc2U2Ii8lLHN1cGVyc2NyaXB0R1EmZmFsc2U2Ii8lK2ZvcmVncm91bmRHUShbMCwwLDBdNiIvJStiYWNrZ3JvdW5kR1EuWzI1NSwyNTUsMjU1XTYiLyUnb3BhcXVlR1EmZmFsc2U2Ii8lK2V4ZWN1dGFibGVHUSZmYWxzZTYiLyUpcmVhZG9ubHlHUSZmYWxzZTYiLyUpY29tcG9zZWRHUSZmYWxzZTYiLyUqY29udmVydGVkR1EmZmFsc2U2Ii8lK2ltc2VsZWN0ZWRHUSZmYWxzZTYiLyUscGxhY2Vob2xkZXJHUSZmYWxzZTYiLyU2c2VsZWN0aW9uLXBsYWNlaG9sZGVyR1EmZmFsc2U2Ii8lLG1hdGh2YXJpYW50R1EnaXRhbGljNiItSSNtb0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkc2IjY+UTAmQXBwbHlGdW5jdGlvbjs2Ii8lJ2ZhbWlseUdRKERFRkFVTFQ2Ii8lJXNpemVHUSMxMDYiLyUlYm9sZEdRJmZhbHNlNiIvJSdpdGFsaWNHUSZmYWxzZTYiLyUqdW5kZXJsaW5lR1EmZmFsc2U2Ii8lKnN1YnNjcmlwdEdRJmZhbHNlNiIvJSxzdXBlcnNjcmlwdEdRJmZhbHNlNiIvJStmb3JlZ3JvdW5kR1EoWzAsMCwwXTYiLyUrYmFja2dyb3VuZEdRLlsyNTUsMjU1LDI1NV02Ii8lJ29wYXF1ZUdRJmZhbHNlNiIvJStleGVjdXRhYmxlR1EmZmFsc2U2Ii8lKXJlYWRvbmx5R1EmZmFsc2U2Ii8lKWNvbXBvc2VkR1EmZmFsc2U2Ii8lKmNvbnZlcnRlZEdRJmZhbHNlNiIvJStpbXNlbGVjdGVkR1EmZmFsc2U2Ii8lLHBsYWNlaG9sZGVyR1EmZmFsc2U2Ii8lNnNlbGVjdGlvbi1wbGFjZWhvbGRlckdRJmZhbHNlNiIvJSxtYXRodmFyaWFudEdRJ25vcm1hbDYiLyUmZmVuY2VHUSZmYWxzZTYiLyUqc2VwYXJhdG9yR1EmZmFsc2U2Ii8lKXN0cmV0Y2h5R1EmZmFsc2U2Ii8lKnN5bW1ldHJpY0dRJmZhbHNlNiIvJShsYXJnZW9wR1EmZmFsc2U2Ii8lLm1vdmFibGVsaW1pdHNHUSZmYWxzZTYiLyUnYWNjZW50R1EmZmFsc2U2Ii8lJ2xzcGFjZUdRJjAuMGVtNiIvJSdyc3BhY2VHUSYwLjBlbTYiLUkobWZlbmNlZEc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkc2IjY1LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkc2IjY1LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHNiI2NVEidDYiLyUnZmFtaWx5R1EoREVGQVVMVDYiLyUlc2l6ZUdRIzEwNiIvJSVib2xkR1EmZmFsc2U2Ii8lJ2l0YWxpY0dRJXRydWU2Ii8lKnVuZGVybGluZUdRJmZhbHNlNiIvJSpzdWJzY3JpcHRHUSZmYWxzZTYiLyUsc3VwZXJzY3JpcHRHUSZmYWxzZTYiLyUrZm9yZWdyb3VuZEdRKFswLDAsMF02Ii8lK2JhY2tncm91bmRHUS5bMjU1LDI1NSwyNTVdNiIvJSdvcGFxdWVHUSZmYWxzZTYiLyUrZXhlY3V0YWJsZUdRJmZhbHNlNiIvJSlyZWFkb25seUdRJmZhbHNlNiIvJSljb21wb3NlZEdRJmZhbHNlNiIvJSpjb252ZXJ0ZWRHUSZmYWxzZTYiLyUraW1zZWxlY3RlZEdRJmZhbHNlNiIvJSxwbGFjZWhvbGRlckdRJmZhbHNlNiIvJTZzZWxlY3Rpb24tcGxhY2Vob2xkZXJHUSZmYWxzZTYiLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWM2Ii8lJ2ZhbWlseUdRMFRpbWVzfk5ld35Sb21hbjYiLyUlc2l6ZUdRIzEyNiIvJSVib2xkR1EmZmFsc2U2Ii8lJ2l0YWxpY0dRJmZhbHNlNiIvJSp1bmRlcmxpbmVHUSZmYWxzZTYiLyUqc3Vic2NyaXB0R1EmZmFsc2U2Ii8lLHN1cGVyc2NyaXB0R1EmZmFsc2U2Ii8lK2ZvcmVncm91bmRHUShbMCwwLDBdNiIvJStiYWNrZ3JvdW5kR1EuWzI1NSwyNTUsMjU1XTYiLyUnb3BhcXVlR1EmZmFsc2U2Ii8lK2V4ZWN1dGFibGVHUSZmYWxzZTYiLyUpcmVhZG9ubHlHUSZmYWxzZTYiLyUpY29tcG9zZWRHUSZmYWxzZTYiLyUqY29udmVydGVkR1EmZmFsc2U2Ii8lK2ltc2VsZWN0ZWRHUSZmYWxzZTYiLyUscGxhY2Vob2xkZXJHUSZmYWxzZTYiLyU2c2VsZWN0aW9uLXBsYWNlaG9sZGVyR1EmZmFsc2U2Ii8lLG1hdGh2YXJpYW50R1Enbm9ybWFsNiIvJSdmYW1pbHlHUShERUZBVUxUNiIvJSVzaXplR1EjMTA2Ii8lJWJvbGRHUSZmYWxzZTYiLyUnaXRhbGljR1EmZmFsc2U2Ii8lKnVuZGVybGluZUdRJmZhbHNlNiIvJSpzdWJzY3JpcHRHUSZmYWxzZTYiLyUsc3VwZXJzY3JpcHRHUSZmYWxzZTYiLyUrZm9yZWdyb3VuZEdRKFswLDAsMF02Ii8lK2JhY2tncm91bmRHUS5bMjU1LDI1NSwyNTVdNiIvJSdvcGFxdWVHUSZmYWxzZTYiLyUrZXhlY3V0YWJsZUdRJmZhbHNlNiIvJSlyZWFkb25seUdRJmZhbHNlNiIvJSljb21wb3NlZEdRJmZhbHNlNiIvJSpjb252ZXJ0ZWRHUSZmYWxzZTYiLyUraW1zZWxlY3RlZEdRJmZhbHNlNiIvJSxwbGFjZWhvbGRlckdRJmZhbHNlNiIvJTZzZWxlY3Rpb24tcGxhY2Vob2xkZXJHUSZmYWxzZTYiLyUsbWF0aHZhcmlhbnRHUSdub3JtYWw2Ii8lJ2ZhbWlseUdRMFRpbWVzfk5ld35Sb21hbjYiLyUlc2l6ZUdRIzEyNiIvJSVib2xkR1EmZmFsc2U2Ii8lJ2l0YWxpY0dRJmZhbHNlNiIvJSp1bmRlcmxpbmVHUSZmYWxzZTYiLyUqc3Vic2NyaXB0R1EmZmFsc2U2Ii8lLHN1cGVyc2NyaXB0R1EmZmFsc2U2Ii8lK2ZvcmVncm91bmRHUShbMCwwLDBdNiIvJStiYWNrZ3JvdW5kR1EuWzI1NSwyNTUsMjU1XTYiLyUnb3BhcXVlR1EmZmFsc2U2Ii8lK2V4ZWN1dGFibGVHUSZmYWxzZTYiLyUpcmVhZG9ubHlHUSZmYWxzZTYiLyUpY29tcG9zZWRHUSZmYWxzZTYiLyUqY29udmVydGVkR1EmZmFsc2U2Ii8lK2ltc2VsZWN0ZWRHUSZmYWxzZTYiLyUscGxhY2Vob2xkZXJHUSZmYWxzZTYiLyU2c2VsZWN0aW9uLXBsYWNlaG9sZGVyR1EmZmFsc2U2Ii8lLG1hdGh2YXJpYW50R1Enbm9ybWFsNiItJSVGT05URzYlJShERUZBVUxURyUoREVGQVVMVEciIzUlK0hPUklaT05UQUxHJStIT1JJWk9OVEFMRy0lJVJPT1RHNictJSlCT1VORFNfWEc2IyQiJCsoISIiLSUpQk9VTkRTX1lHNiMkIiNxISIiLSUtQk9VTkRTX1dJRFRIRzYjJCIlXWchIiItJS5CT1VORFNfSEVJR0hURzYjJCIlIVskISIiLSUpQ0hJTERSRU5HNiI=

# Case-8 (unstable equlibrium-2) restart; n:=40: B:=1.1: with(plots): x:=[seq(7-(B)^t,t=1..n)]: tt:=[seq(i,i=1..n)]: A:=pointplot(tt,x, thickness=2, style=line, color=red): B:=plot(7,t=0..n, color=black, thickness=2): C:=textplot([25,7.08,"Equilibrium E"],align={above,right}, font = [TIMES, ROMAN, 15]): display({A,B,C}, labels=[time, X(t)]);

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

# Case-9 (unstable equlibrium-3) restart; n:=40: B:=-1.2: with(plots): x:=[seq(7-(B)^t,t=1..n)]: tt:=[seq(i,i=1..n)]: A:=pointplot(tt,x, thickness=2, style=line, color=red): B:=plot(7,t=0..n, color=black, thickness=2): C:=textplot([10,30,"Equilibrium E"],align={above,right}, font = [TIMES, ROMAN, 15]): display({A,B,C}, labels=[time, X(t)]);

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

# 2) Stability of Differential Equations restart; # Our general equation is given by x(t+1)=a+b*x(t);

Ly1JInhHNiI2IywmSSJ0R0YlIiIiRilGKSwmSSJhR0YlRikqJkkiYkdGJUYpLUYkNiNGKEYpRik=

# Since previously we know that in the equilibrium x(t+1)=x(t) this means that # the equlibrium for the above equation is given x(t+1)=x(t)=x_eq is given by x_eq=a+b*x_eq;

L0kleF9lcUc2IiwmSSJhR0YkIiIiKiZJImJHRiRGJ0YjRidGJw==

# we solve for x_eq isolate(%, x_eq);

L0kleF9lcUc2IiomSSJhR0YkIiIiLCZGJ0YnSSJiR0YkISIiRio=

# note that a determine the equilibrium value and b determind the stability # different value of b will lead to different outcomes # From this equation we can derive 4 different cases # stable equilibrium # 1) if 0<b<1 then x(t+1) will converge to the equlibrium # 2) if -1<b<0 then x(t+1) will converge to the equlibrium with oscillation # unstable equilibrium # 3) if b>1 then x(t+1) will diverge away from the equlibrium # 4) if b<-1 then x(t+1) will diverge away from the equlibrium with oscillation # Case-1 (stable equilibrium-1) restart; # Our general equation is given by x(t+1)=a+b*x(t);

Ly1JInhHNiI2IywmSSJ0R0YlIiIiRilGKSwmSSJhR0YlRikqJkkiYkdGJUYpLUYkNiNGKEYpRik=

# we assume that a=3 and b=0.5 subs({a=3, b=0.5},%);

Ly1JInhHNiI2IywmSSJ0R0YlIiIiRilGKSwmIiIkRikqJiQiIiYhIiJGKS1GJDYjRihGKUYp

########### Stability and Fixed point # Since the slope is +0.5 we will have a stable equilibrium %-x(t);

LywmLUkieEc2IjYjLCZJInRHRiYiIiJGKkYqRiotRiU2I0YpISIiLCYiIiRGKiomJCIiJkYtRipGK0YqRi0=

# fixed point x(t+1)-x(t)=0 subs(x(t+1)-x(t)=0,%);

LyIiISwmIiIkIiIiKiYkIiImISIiRiYtSSJ4RzYiNiNJInRHRi1GJkYq

solve(%,x(t));

JCIiJyIiIQ==

# This means that our fixed point is 6 ########################################## # Our recursive equation is given by n:=10: x[1]:=10: for i from 2 to n do x[i] := 3+0.5*x[i-1] end do: xx:=[seq(x[i],i=1..n)];

NywiIzUkIiMhKSEiIiQiJCsoISIjJCIlK2whIiQkIiYrRCchIiUkIicrRGghIiYkIigrRDEnISInJCIpK0RKZyEiKCQiKitEYywnISIpJCIrK0QieSsnISIq

t_:=[seq(i,i=1..n)]: A:=plot(6,t=1..n, color=black, thickness=2): with(plots): B:=pointplot(t_,xx, color = red, thickness = 2,style=line,labels=[time,"x(t+1)"]): C:=textplot([2,6.1,"Equilibrium E"],align={above,right}, font = [TIMES, ROMAN, 15]): display({A,B, C},view=[1..n,5.9..11]);

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

# Case-2 (stable equilibrium-2) restart; # Our general equation is given by x(t+1)=a+b*x(t);

Ly1JInhHNiI2IywmSSJ0R0YlIiIiRilGKSwmSSJhR0YlRikqJkkiYkdGJUYpLUYkNiNGKEYpRik=

# we assume that a=3 and b=0.5 subs({a=3, b=-0.5},%);

Ly1JInhHNiI2IywmSSJ0R0YlIiIiRilGKSwmIiIkRikqJiQiIiYhIiJGKS1GJDYjRihGKUYv

########### Stability and Fixed point # Since the slope is -0.5 we will have a stable equilibrium with osilation %-x(t);

LywmLUkieEc2IjYjLCZJInRHRiYiIiJGKkYqRiotRiU2I0YpISIiLCYiIiRGKiomJCIjOkYtRipGK0YqRi0=

# fixed point x(t+1)-x(t)=0 subs(x(t+1)-x(t)=0,%);

LyIiISwmIiIkIiIiKiYkIiM6ISIiRiYtSSJ4RzYiNiNJInRHRi1GJkYq

solve(%,x(t));

JCIiIyIiIQ==

# This means that our fixed point is 2 ########################################## # Our recursive equation is given by n:=10: x[1]:=10: for i from 2 to n do x[i] := 3-0.5*x[i-1] end do: xx:=[seq(x[i],i=1..n)];

NywiIzUkISM/ISIiJCIkKyUhIiMkIiUrNSEiJCQiJitdIyEiJSQiJytdPCEiJiQiKCtdNyMhIickIikrXVA+ISIoJCIqK103LiMhIikkIisrXVAlKT4hIio=

t_:=[seq(i,i=1..n)]: A:=plot(2,t=1..n, color=black, thickness=2): with(plots): B:=pointplot(t_,xx, color = red, thickness = 2,style=line,labels=[time,"x(t+1)"]): C:=textplot([8,2.4,"Equilibrium E"],align={above,right}, font = [TIMES, ROMAN, 15]): display({A,B,C});

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

Case-3 (unstable equilibrium-1) restart; # Our general equation is given by x(t+1)=a+b*x(t);

Ly1JInhHNiI2IywmSSJ0R0YlIiIiRilGKSwmSSJhR0YlRikqJkkiYkdGJUYpLUYkNiNGKEYpRik=

# we assume that a=3 and b=0.5 subs({a=3, b=1.5},%);

Ly1JInhHNiI2IywmSSJ0R0YlIiIiRilGKSwmIiIkRikqJiQiIzohIiJGKS1GJDYjRihGKUYp

########### Stability and Fixed point # Since the slope is +1.5 we will have a unstable equilibrium %-x(t);

LywmLUkieEc2IjYjLCZJInRHRiYiIiJGKkYqRiotRiU2I0YpISIiLCYiIiRGKiomJCIiJkYtRipGK0YqRio=

# fixed point x(t+1)-x(t)=0 subs(x(t+1)-x(t)=0,%);

LyIiISwmIiIkIiIiKiYkIiImISIiRiYtSSJ4RzYiNiNJInRHRi1GJkYm

solve(%,x(t));

JCEiJyIiIQ==

# This means that our fixed point is -6 ########################################## # Our recursive equation is given by n:=10: x[1]:=10: for i from 2 to n do x[i] := 3+1.5*x[i-1] end do: xx:=[seq(x[i],i=1..n)];

NywiIzUkIiQhPSEiIiQiJStJISIjJCImKyFbISIkJCInKyt2ISIlJCIpKytiNiEiJiQiKisrRHciISInJCIrKyt2dEUhIigkIisrXWlTU0Y4JCIrK3YkNDQnRjg=

t_:=[seq(i,i=1..n)]: A:=plot(-6,t=1..n, color=black, thickness=2): with(plots): B:=pointplot(t_,xx, color = red, thickness = 2,style=line,labels=[time,"x(t+1)"]): C:=textplot([8,0,"Equilibrium E"],align={above,right}, font = [TIMES, ROMAN, 15]): display({A,B,C},view=[1..n,-20..500]);

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

# Case-4 (unstable equilibrium-2) restart; # Our general equation is given by x(t+1)=a+b*x(t);

Ly1JInhHNiI2IywmSSJ0R0YlIiIiRilGKSwmSSJhR0YlRikqJkkiYkdGJUYpLUYkNiNGKEYpRik=

# we assume that a=3 and b=0.5 subs({a=3, b=-1.5},%);

Ly1JInhHNiI2IywmSSJ0R0YlIiIiRilGKSwmIiIkRikqJiQiIzohIiJGKS1GJDYjRihGKUYv

########### Stability and Fixed point # Since the slope is +1.5 we will have a unstable equilibrium %-x(t);

LywmLUkieEc2IjYjLCZJInRHRiYiIiJGKkYqRiotRiU2I0YpISIiLCYiIiRGKiomJCIjREYtRipGK0YqRi0=

# fixed point x(t+1)-x(t)=0 subs(x(t+1)-x(t)=0,%);

LyIiISwmIiIkIiIiKiYkIiNEISIiRiYtSSJ4RzYiNiNJInRHRi1GJkYq

solve(%,x(t));

JCIrKysrKzchIio=

# This means that our fixed point is 1.2 ########################################## # Our recursive equation is given by n:=10: x[1]:=10: for i from 2 to n do x[i] := 3-1.5*x[i-1] end do: xx:=[seq(x[i],i=1..n)];

NywiIzUkISQ/IiEiIiQiJStAISIjJCEmKyZHISIkJCInK3ZYISIlJCEoK0RjJyEiJiQiKit2ViwiISInJCErK0RjIlwiISIoJCIrXVBNbkFGOCQhK0RjLHJMRjg=

t_:=[seq(i,i=1..n)]: A:=plot(1.2,t=1..n, color=black, thickness=2): with(plots): B:=pointplot(t_,xx, color = red, thickness = 2,style=line,labels=[time,"x(t+1)"]): C:=textplot([1.3,10,"Equilibrium E"],align={above,right}, font = [TIMES, ROMAN, 15]): display({A,B,C});

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

# 3) Further Discussion restart; # Note that our general equation given by x(t+1)=a+b*x(t);

Ly1JInhHNiI2IywmSSJ0R0YlIiIiRilGKSwmSSJhR0YlRikqJkkiYkdGJUYpLUYkNiNGKEYpRik=

# can be expressed as a difference equation if we subtract x(t) on both sides lhs(%)-x(t)=rhs(%)-x(t);

LywmLUkieEc2IjYjLCZJInRHRiYiIiJGKkYqRiotRiU2I0YpISIiLChJImFHRiZGKiomSSJiR0YmRipGK0YqRipGK0Yt

# which can be written as collect(%,x(t));

LywmLUkieEc2IjYjLCZJInRHRiYiIiJGKkYqRiotRiU2I0YpISIiLCYqJiwmSSJiR0YmRipGKkYtRipGK0YqRipJImFHRiZGKg==

# Note that at the equlibrium x(t+1)=x(t) which means that x(t+1)-x(t)=0 # Not also that the above equation can also be expressed as an differential equation since 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 # This means that the above equation as a differential equation can be written as diff(x(t),t)=(b-1)*x(t)+a;

Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSJ4RzYiNiNJInRHRilGKywmKiYsJkkiYkdGKSIiIkYwISIiRjBGJ0YwRjBJImFHRilGMA==

# where the fixed point (equilibrium) is given by diff(x(t),t)=0 # Now note that we can have to different cases : # stable equilibrium # We have a stable equilibrium if the slope of the differential equation is negative # In such a situation we are moving towards the equilibrium # unstable equilibrium # We have a unstable equilibrium if the slope of the differential equation is positive # In such a situation we are moving away from the equilibrium # Basic intuition # If x(t+1)>x(t) then x(t+1)-x(t)>0 which means that diff(x(t),t)>0 which means # that x(t) is increasing over time # If x(t+1)<x(t) then x(t+1)-x(t)<0 which means that diff(x(t),t)<0 which means # that x(t) is decreasing over time # Case-1 (stable equilibrium) restart; # As previously our general equation is given by x(t+1)=a+b*x(t): # We assume that a:=3: b:=0.5: # so we get x(t+1)=a+b*x(t);

Ly1JInhHNiI2IywmSSJ0R0YlIiIiRilGKSwmIiIkRikqJiQiIiYhIiJGKS1GJDYjRihGKUYp

# We can express this equation as a difference equation if we subtract x(t) on both sides lhs(%)-x(t)=rhs(%)-x(t);

LywmLUkieEc2IjYjLCZJInRHRiYiIiJGKkYqRiotRiU2I0YpISIiLCYiIiRGKiomJCIiJkYtRipGK0YqRi0=

# Since the slope is equal to -0.5 we have a stable equilibrium # we know that our fixed point is given by x(t+1)-x(t)=diff(x(t),t)=0 so we get subs(x(t+1)-x(t)=0,%);

LyIiISwmIiIkIiIiKiYkIiImISIiRiYtSSJ4RzYiNiNJInRHRi1GJkYq

# so our fixed point is given by isolate(%,x(t));

Ly1JInhHNiI2I0kidEdGJSQiKysrKytnISIq

# we can now plot our equation x(t+1)=3+0.5*x(t) and the fixed point as follows n:=10: with(plots): A:=plot(6,t=0..n, color=black, thickness=2): x[0]:=10: for i from 1 to n do x[i]:=3+0.5*x[i-1] end do: xx:=[seq(x[i],i=0..n)]: tt:=[seq(i,i=0..n)]: B:=plot(tt,xx, x=0..n,labels=[time,"x(t+1)"],thickness=2 ): C:=textplot([8,6.4,"Equilibrium E"],align={above,right}, font = [TIMES, ROMAN, 15]): display({A,B,C}, view=[0..n,5..12]);

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

# we can also plot our equation x(t+1)=3+0.5*x(t) against x(t) # Note that in the plot below we have also included the equlibrium x(t+1)=x(t) # In a x(t+1), x(t) plot the equlibrium will be 45 degree line where x(t+1)=x(t) # In the plot below we can see that we indeed have an equlibrium point at 6 with(plots): A:=plot(3+0.5*x,x=1..10, labels=["x(t)","x(t+1)"],thickness=2, color=red): B:=plot(x,x=1..10, color=black,thickness=2): C:=textplot([6,5,"Fixed Point 6"],align={above,right}, font = [TIMES, ROMAN, 15]): display({A,B,C},labels=["x(t)","x(t+1)"]);

NigtJSVURVhURzYnNyQkIiNnISIiJCIjXSEiIi0lKV9UWVBFU0VURzYjUS5GaXhlZH5Qb2ludH42NiItJSVGT05URzYlJTBUaW1lc35OZXd+Um9tYW5HJSZST01BTkciIzolK0FMSUdOUklHSFRHJStBTElHTkFCT1ZFRy0lJ0NVUlZFU0c2JTdTNyQkIiM1ISIiJCIjNSEiIjckJCIsdlF1aD4iISM1JCIsdlF1aD4iISM1NyQkIi5ESm5rb08iISM3JCIuREpua29PIiEjNzckJCItRF5QIyllOiEjNiQiLUReUCMpZTohIzY3JCQiLXZlXzBfPCEjNiQiLXZlXzBfPCEjNjckJCIuRDFQb1YlPiEjNyQiLkQxUG9WJT4hIzc3JCQiLkRKQ25FNyMhIzckIi5ESkNuRTcjISM3NyQkIi5EIilSJkcyQiEjNyQiLkQiKVImRzJCISM3NyQkIi5EImV4QClcIyEjNyQiLkQiZXhAKVwjISM3NyQkIi5EY3pQJilvIyEjNyQiLkRjelAmKW8jISM3NyQkIjItKyt2TTBWKUchIzskIjItKyt2TTBWKUchIzs3JCQiLXY4dnRjSSEjNiQiLXY4dnRjSSEjNjckJCIyLisrREhiM0QkISM7JCIyLisrREhiM0QkISM7NyQkIix2OHFkVyQhIzUkIix2OHFkVyQhIzU3JCQiMi4rK3ZxMU9qJCEjOyQiMi4rK3ZxMU9qJCEjOzckJCIuRCIzLj0vUSEjNyQiLkQiMy49L1EhIzc3JCQiLHYiKTNxKyUhIzUkIix2IikzcSslISM1NyQkIjIwKysrPEopeVQhIzskIjIwKysrPEopeVQhIzs3JCQiLkRKVCwoeVYhIzckIi5ESlQsKHlWISM3NyQkIitYL2liWCEiKiQiK1gvaWJYISIqNyQkIi5ESm1HKFxaISM3JCIuREptRyhcWiEjNzckJCIyLyt2JCplbFgkXCEjOyQiMi8rdiQqZWxYJFwhIzs3JCQiMSwrREpOVUZeISM6JCIxLCtESk5VRl4hIzo3JCQiLkRjS0ZYSSYhIzckIi5EY0tGWEkmISM3NyQkIjImKioqXFBwZGJcJiEjOyQiMiYqKipcUHBkYlwmISM7NyQkIi5EImVYKVJwJiEjNyQiLkQiZVgpUnAmISM3NyQkIi52b3M6bidlISM3JCIudm9zOm4nZSEjNzckJCItREAsRmBnISM2JCItREAsRmBnISM2NyQkIjImKioqKipcMSoqZkMnISM7JCIyJioqKioqXDEqKmZDJyEjOzckJCItRE9uYU1rISM2JCItRE9uYU1rISM2NyQkIi5ESkl3cGgnISM3JCIuREpJd3BoJyEjNzckJCItdkxLYD5vISM2JCItdkxLYD5vISM2NyQkIjEqKioqKlxrUjorKCEjOiQiMSoqKioqXGtSOisoISM6NyQkIjEsK11QLihlPighIzokIjEsK11QLihlPighIzo3JCQiLkQiR0cnPlAoISM3JCIuRCJHRyc+UCghIzc3JCQiMjArK0RWeVdjKCEjOyQiMjArK0RWeVdjKCEjOzckJCIxKipcNzgxaVh4ISM6JCIxKipcNzgxaVh4ISM6NyQkIi5EY1FtXCR6ISM3JCIuRGNRbVwkeiEjNzckJCIsdlsnMz8iKSEjNSQiLHZbJzM/IikhIzU3JCQiMSoqXDd5KypRSikhIzokIjEqKlw3eSsqUUopISM6NyQkIjEsKytxZmErJikhIzokIjEsKytxZmErJikhIzo3JCQiLXZ5Jkc5cCkhIzYkIi12eSZHOXApISM2NyQkIi5ESmVJMikpKSEjNyQiLkRKZUkyKSkpISM3NyQkIitsJXpZMCohIiokIitsJXpZMCohIio3JCQiLXY4WC9hIyohIzYkIi12OFgvYSMqISM2NyQkIioqKmVCViohIikkIioqKmVCViohIik3JCQiLkRKVHpDaSohIzckIi5ESlR6Q2kqISM3NyQkIi52byIqW1chKSohIzckIi52byIqW1chKSohIzc3JCQiJCsiISIiJCIkKyIhIiItJSZDT0xPUkc2JiUkUkdCRyQiIiEhIiIkIiIhISIiJCIiISEiIi0lKlRISUNLTkVTU0c2IyIiIy0lJ0NVUlZFU0c2JTdTNyQkIiM1ISIiJCIjTiEiIjckJCIsdlF1aD4iISM1JCItdiQ+KDMpZiQhIzY3JCQiLkRKbmtvTyIhIzckIi9EY09CViRvJCEjODckJCItRF5QIyllOiEjNiQiLkRjKD1UelAhIzc3JCQiLXZlXzBfPCEjNiQiLnYkSHctd1EhIzc3JCQiLkQxUG9WJT4hIzckIi9ESiY9JT1zUiEjODckJCIuREpDbkU3IyEjNyQiL0RjQE9MaFMhIzg3JCQiLkQiKVImRzJCISM3JCIvRDEqcFVPOiUhIzg3JCQiLkQiZXhAKVwjISM3JCIvRDF6KTMiXFUhIzg3JCQiLkRjelAmKW8jISM3JCIyJipcN3kqKW9VTSUhIzs3JCQiMi0rK3ZNMFYpRyEjOyQiLXZ0RTpVVyEjNjckJCItdjh2dGNJISM2JCIudm92byRHWCEjNzckJCIyLisrREhiM0QkISM7JCItRFl3VURZISM2NyQkIix2OHFkVyQhIzUkIi12b10pR3MlISM2NyQkIjIuKyt2cTFPaiQhIzskIi12YEwhbyJbISM2NyQkIi5EIjMuPS9RISM3JCIvRDFhLDQtXCEjODckJCIsdiIpM3ErJSEjNSQiMjArXSgzV10uXSEjOzckJCIyMCsrKzxKKXlUISM7JCIrJmU6JSozJiEiKjckJCIuREpULCh5ViEjNyQiL0RjMTJOKj0mISM4NyQkIitYL2liWCEiKiQiMSoqKipcQS0ieUYmISM6NyQkIi5ESm1HKFxaISM3JCIxLERjSlYnW1AmISM6NyQkIjIvK3YkKmVsWCRcISM7JCIxLHZvJXojR25hISM6NyQkIjEsK0RKTlVGXiEjOiQiLkRjdzZQYyYhIzc3JCQiLkRjS0ZYSSYhIzckIi9EIkdtakFsJiEjODckJCIyJioqKlxQcGRiXCYhIzskIi52byUpeXh1JiEjNzckJCIuRCJlWClScCYhIzckIjImKlxpIXpBKnAlZSEjOzckJCIudm9zOm4nZSEjNyQiL3ZWanlOTGYhIzg3JCQiLURALEZgZyEjNiQiLkQxMU5tLSchIzc3JCQiMiYqKioqKlwxKipmQychIzskIixEYCoqSDcnISM1NyQkIi1ET25hTWshIzYkIjEqKlw3b0xGPGkhIzo3JCQiLkRKSXdwaCchIzckIi9EY14iKVszaiEjODckJCItdkxLYD5vISM2JCIudm9obSg0ayEjNzckJCIxKioqKipca1I6KyghIzokIixEIylwMl0nISM1NyQkIjEsK11QLihlPighIzokIi12b14kemYnISM2NyQkIi5EIkdHJz5QKCEjNyQiL0QxOTkpZm8nISM4NyQkIjIwKytEVnlXYyghIzskIi1EOyNSQXknISM2NyQkIjEqKlw3ODFpWHghIzokIjEqXGlsSTVHKG8hIzo3JCQiLkRjUW1cJHohIzckIi9EIkc+JFtucCEjODckJCIsdlsnMz8iKSEjNSQiLXZWSy9ncSEjNjckJCIxKipcN3krKlFKKSEjOiQiMSpcaSFSXSVwOighIzo3JCQiMSwrK3FmYSsmKSEjOiQiMjArK10pSEZdcyEjOzckJCItdnkmRzlwKSEjNiQiLnYkKkc5ZE0oISM3NyQkIi5ESmVJMikpKSEjNyQiL0RjIkhsLlcoISM4NyQkIitsJXpZMCohIiokIixEdFJ0XyghIzU3JCQiLXY4WC9hIyohIzYkIi52b0RBcWkoISM3NyQkIioqKmVCViohIikkIismXHpocighIio3JCQiLkRKVHpDaSohIzckIi9EYzEoUjcieSEjODckJCIudm8iKltXISkqISM3JCIvdlZlV0EteiEjODckJCIkKyIhIiIkIiMhKSEiIi0lJkNPTE9SRzYmJSRSR0JHJCIjNSEiIiQiIiEhIiIkIiIhISIiLSUqVEhJQ0tORVNTRzYjIiIjLSUlVklFV0c2JDskIiM1ISIiJCIkKyIhIiIlKERFRkFVTFRHLSUrQVhFU0xBQkVMU0c2J1EleCh0KTYiUSd4KHQrMSk2Ii0lJUZPTlRHNiUlKERFRkFVTFRHJShERUZBVUxURyIjNSUrSE9SSVpPTlRBTEclK0hPUklaT05UQUxHLSUlUk9PVEc2Jy0lKUJPVU5EU19YRzYjJCIkSSghIiItJSlCT1VORFNfWUc2IyQiJD8iISIiLSUtQk9VTkRTX1dJRFRIRzYjJCIlU2shIiItJS5CT1VORFNfSEVJR0hURzYjJCIlU00hIiItJSlDSElMRFJFTkc2Ig==

# we can also plot our difference equation x(t+1)-x(t) = 3-.5*x(t) against x(t) plot(3-0.5*x,x=1..10, labels=["x(t)","x(t+1)-x(t) or diff(x(t),t)"],thickness=2, color=red);

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

# We first note that the slope of our difference equation or differential equation is # negative which means that we have a stable equlibrium # we can see that above our fixed point 6 diff(x(t),t) is positive # which means that x(t) is increasing over time # we can also see that below our fixed point 6 diff(x(t),t) is negative # which means that x(t) is decresing over time # Case-2 (unstable equilibrium) restart; # As previously our general equation is given by x(t+1)=a+b*x(t): # We assume that a:=3: b:=1.5: # so we get x(t+1)=a+b*x(t);

Ly1JInhHNiI2IywmSSJ0R0YlIiIiRilGKSwmIiIkRikqJiQiIzohIiJGKS1GJDYjRihGKUYp

# We can express this equation as a difference equation if we subtract x(t) on both sides lhs(%)-x(t)=rhs(%)-x(t);

LywmLUkieEc2IjYjLCZJInRHRiYiIiJGKkYqRiotRiU2I0YpISIiLCYiIiRGKiomJCIiJkYtRipGK0YqRio=

# Since the slope is equal to +0.5 we have a unstable equilibrium # we know that our fixed point is given by x(t+1)-x(t)=diff(x(t),t)=0 so we get subs(x(t+1)-x(t)=0,%);

LyIiISwmIiIkIiIiKiYkIiImISIiRiYtSSJ4RzYiNiNJInRHRi1GJkYm

# so our fixed point is given by isolate(%,x(t));

Ly1JInhHNiI2I0kidEdGJSQhKysrKytnISIq

# we can now plot our equation x(t+1)=3+1.5*x(t) and the fixed point as follows n:=10: with(plots): A:=plot(-6,t=0..n, color=black, thickness=2): x[0]:=10: for i from 1 to n do x[i]:=3+1.5*x[i-1] end do: xx:=[seq(x[i],i=0..n)]: tt:=[seq(i,i=0..n)]: B:=plot(tt,xx, x=0..n,labels=[time,"x(t+1)"],thickness=2 ): C:=textplot([6,5,"Equilibrium E"],align={above,right}, font = [TIMES, ROMAN, 15]): display({A,B,C}, view=[0..n,-10..800]);

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

# we can also plot our equation x(t+1)=3+1.5*x(t) against x(t) # Note that in the plot below we have also included the equlibrium x(t+1)=x(t) # In a x(t+1), x(t) plot the equlibrium will be 45 degree line where x(t+1)=x(t) # In the plot below we can see that we indeed have an equlibrium point at -6 with(plots): A:=plot(3+1.5*x,x=-15..0, labels=["x(t)","x(t+1)"],thickness=2, color=red): B:=plot(x,x=-15..0, color=black,thickness=2): C:=textplot([-6,-8,"Fixed Point -6"],align={above,right}, font = [TIMES, ROMAN, 15]): display({A,B,C},labels=["x(t)","x(t+1)"]);

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

# we can also plot our difference equation x(t+1)-x(t)=3+0.5*x(t) against x(t) plot(3+0.5*x,x=-12..0, labels=["x(t)","x(t+1)-x(t) or diff(x(t),t)"],thickness=2, color=red);

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

# We first note that the slope of our difference equation or differential equation is # positive which means that we have a unstable equlibrium # we can see that above our fixed point -6 diff(x(t),t) is positive # which means that x(t) is increasing over time # we can also see that below our fixed point 6 diff(x(t),t) is negative # which means that x(t) is decresing over time # The End !!! Legal Notice: The copyright for this application is owned by the authors. Neither Maplesoft nor the authors are responsible for any errors contained within and are not liable for any damages resulting from the use of this material.. This application is intended for non-commercial, non-profit use only. Contact the authors for permission if you wish to use this application in for-profit activities.