Beispiel 3.12 (Mathematisches Pendel)Erstellt: 21.2.2020
Ersteller: W. Kemmetm\303\274ller
\303\204nderungen:restart;
with(LinearAlgebra):
with(VectorCalculus,Jacobian):
with(VectorCalculus,SpaceCurve):
with(plots):
with(ColorTools):MFNWtKUb<ob<R=MDLCdNVZxj:\\U>D:;r<yXcA]ZRLCTJcDXoHuux;ktNitAGBVabcSU@WB;cDV[C;]Tj=bB;sLcBq?IdQr\\?cO=X]qUOUgP]Djuww;X[SUKgffcBO[T:eRSAgfcdwSHxWBcEGYMDg[dZ?biygxCYHmss_VvYXU_isGiqaUDSdCaw:>Z:^p?^dN\\:RnU:;B>u@;B>J:FTB:[:<JBZ:RnJ:<;>ZJ:;jb[:><B:[:<ZK=;B>J:<;>:]@<JBZ:><B:@G>ZJ:;B>J:FTB:[:<JBZ:RnJ:<;>ZJ:;jb[:FTB:[:<ZK=;RnJ:<;>:]@<jb[:><B:@G>ZK=;B>J:FTB:]@<JB>jMYo^xdbNZ:B:;cheW:EUSEuHyuyuRWB:CtggCB?CIsYvAwKmYxmIDE:;[pwx=VZS`c`?cJ?`DG:>khgoTfmHw[Gn[[gZr^d=ZrFx]`Zgxbf_cFGdKG\\c_b?obPhlOHkDPkxypUInKAg;Ir;y[X^arwyxiaYv]YwuxhiOgdOgof`orIykQh=JJFZI`ti_gepohpirAv;hvRH`yIv@_iwgiQp_WOmXpmXyqywyCV\\`>sDQs@pj@poUwpHgeWgyBIl]nj@pjbX@;BJqXkiWWQiOcTbeFpsWVAUL]U<QWEKCBKUFoEWatU=IoMwNacSSHDSCEsFH]eRKDLKV\\MVl[WRAhcYtaWcEWcYmgmkXfAuheutGfNAZnHdRytghpBOcDOiYhyxpyd?eb?gGgcGWlhGvoYwQq[Hn[fppEXkEv]YvewAtlivEYipawCogJIsCI[_p:<NtHRmeJYyKd=Yo@ob@wC]WfUlhEv:Ij=\\PTdkn\\PodPuexdixyuOmdldMWdMSTDLKDLsDQs<opJ\\XMnTKaIT_hSwlsnlxiAoa@nZ@rsLo[Hn;QW^tNaTnTA:oHDsbc[hDsEXtmN@mBILWqwimWnqmB`XtdQcDOChtHpkHpMv<YjTu<dJ?dJfpRSEUSLKHjboyuNlLAauvax?yJ@mJ@nKyqyWfhGjCafPgdOGpTQqtPqhqwhaeQV\\N^\\fIumx^Dn;<RnUjyqObqywyooyPlLqkYxmYOcDO_mV`MlpTj;ATOeTg]vWUl:yLXlMhtNatPZ=r:lTIYoQuoNatNAx\\@J:>g?@piXuIxdN_dNV]MVt^@cAitrIx]IeG@uRAetfmHihSXeqpgOn\\PntYgynIwMpohpoSHmSppppx`isUHmFonAxjAinEwljQN^pHgoboeqx`ixeAaax_ypiwUGdKGdkG[Cxmai`rX]J>\\V^\\^Gap_kwXr\\PmTPmnapnhvepdTHmSxdOgd?yr?ycTP`?OnkgtJQtLQax_yrFq?NxAPytQydN_d^gE^uuxhi_urHhMx^IowXiquVoaWsPh_wQyoY^eArbHd]PpmXpqwwXimJ@ljOv>I[df\\Sp=<jbqxGuVIumXIpgUiywiGIZTgyTfyuweu>xtixeiheytUacYpodpnPN]VNlvqvGhsnHgMqnICIEelKr:AvMyfIMcDMSGGiWKdjahoghimuvGSaWt]KF\\[gggg_gf_WwAUB=SBamsVGIumxfUYuUytqS?cB?GEmkVbSGeSdy[wNIgMYfAuchwUyoGf[GFwykBTuFfYwpXmjDX\\yt@pJk]MbLygUV@aks]yrIx\\irEXn]XnOatNaof`otqxgYULMT<moxPYoQWMqnGUoQuoh=qvPqtPQeHviywiIv[IRlUUAqkWDxD@J:>BxX\\hoghMOdLOtMYtMV\\MvqxgYuF`kFpSWPQSIuSikYtQxpyqMTptnHemDeSGeQqmwVdj<ER;D:;kZyJ><Q\\yUQTVlDmeuthhNKpWQqoW]oX`qv`QxlQxDMSDMNAL:<Ze^jwHtyOgHn[HNatNaHpkH`oe`[@VjnatIouEZgh[pPqwaqPqoWWyZIr=`qv`qUx`iOgeWgQodPOisGicIwcixeytIfr;ZncOCxqyxi?gb?SF]S^WtcqxpqxeytiwDN[DV=hZEbUWeUKc=<Z\\X]np_tOitWf@ak[f[dfltovFImGYmqVsCIsCPkDPnlJ:\\bGPdTOdDE\\MV\\=Y[MUT_dN_T=YgrChc;B:;RU?tDoCM=VlCefoB`?g:BbewKiC:>Z:s:>:Z:^B;Z:>B:J:ysPdudTodDUGDV[EVv@`:>Z:Neo_heHohHfo^Z>^ZjQR>ZnPwbq:;J:\\b:J:\\B>Z:@W;Z:>KB:K><JrqOrYUIYR[Htc]o@tMytQX=]JAiSF]SnixS<MR<EV[Efv_ivuuxgYG_cF?s_KG=<LWQUJeRseJeHNLIp]lURB@EXkExLtlXMqnEkIxkiMynIw=yjItsCIsSQp_USxmYxXn]XviyqyqOdLODPO;^bqBZyreKGdKtQytI]SF]DLKDDcCGcFsgcOyifEulGf=ubX;Ij=F]SF]qtgWUb[LbuSjxoU>geplfFe<OhUFgRAuRataq`<ocHogmqvGankWypiwJ@lJ^\\DB>uH:tQRyjItMhtUx`sduSV@QKhWNauVamOAxjAx:eo:NnU>Z:y[paxcYd`VlCQge>_b>pGPsEYsE?cB?l@OhlO`dg:UY<gYWABZgStEx\\iRwUYXaisMr<QrfUCNwdQWdEQhlOHNQKZLAkYjOcDOctqxhiuuWynIw=IiFcb<EwLiNNQ[ZNq;>ZvAfwXiqqoiWcEWcePodpyeym^iv_ir?irSN]Tn`VabQgeWgeXoehf^_fjLPZ:WmJQkpihef_gffo^r>arjQR;xgmdPodvyYIuuwAwKYFhWs^gf_gBAsBmOuQqgWUuywYy]Yv]ilOhlETKETwQHmwVIqhpoh@eI;;BKigCQwqAI`?Tb;Y[=BZYut_XcQpLhNfpPQIsUAMFlrfHUm`UV]UBUqZ@nZqywYyuxXiqNshw]yrIxoXeq\\eOMeUWew]YvMAX=l]:^Bn\\kxfIq]MV\\MNtBpkHpulhfEgyQya\\`n^`j^qpQx_YOqtPqLXoQv_X_hn_h^fkuxhiQ[EV[I>]j>jo@u]xbIP_dN_FhkGHdF?ZbW_ThpiXumxfIQtMYtof`oFqhA^FBn?G;ER;MD?qXhaucQv\\QhwUypuCIsCLKr^_f^OTMUTwiywiHn[H\\KF\\;UaMHW=ijEfb?gbeTOetgWUqoFF=eJIxiYhgib?gbKWS]SF][DM\\pmAwP<MR<qvEyleQwdQlilQ`qcMli@pdQwdqWhmWAukXdrkaeZYywhjkYxiGulhjvh]Kx`_xrIx]aqv`qlOhlcV_eVlBpf`ofPwqqiZeac`pixoi?gb?WpawshxymAT[hausXOSDMSb_NbusKiWYqqwUoQuo`DOgEt\\hR^QwnIwMyYuiwqxQxAy]TOeTW]qrG@kh=JjimC=SB]ScXxgirRUuRqRF@M;QqTeTOeLWdMwTX`?_ZBg=SMwxoUisUx`CsgUxaysaevpkDUUUUMdUar?ireyxZCJJQu^`n^@ob@ojpsl@t[pWIDQLpujXnU<JnxvbqTLMT\\AwbAS[@Txuywyx@hy?ir?aoiQpv]Yv=oc<JnpSwUypiyvIymTj;AwJuXhhjOUoPeX:qkh?ngHgTy[`XeqpgwAykYn[Hn[`qv`i=qyJAtJOhSasivo^YwiVo[^^^^jQn:keUuixey=ybIcwfawtixeHymyvsHqshqtexL]TN]R_?bUNt>hohg`of`avcX`^GnsWWbrOhNpdoghoVo[>_b>kQnZ:bMWdMWYtaxcCCjUtawSy[YrAHsQFDgEWABZgIAuhasSX_dNDNGTTMUt@hyOdLODPkDP\\Qv\\Yj@dKdUto@VlDmsIysyWYqq?IydHJTymWTQp=wbAwJxoBhquuxhIt]xrXhQu=sq`r_XSQPnl<JJqpnDvATtfawfMXSIp]urXeqtePfykHpk`tw@pN`lNguXAup^av^Mxxlw]Yv=MnUunHemDXkEHsqXXL@TCuNUyS=AJJqRWtQx]UKETK=R:=jnXj=XjIdMt\\XmqvG]MKt[TYhnW\\Qv\\avldOgd_gaNoDF[CFwJawWfux?nMynIWar>aNatNacR@`[wyxiy^>mPodPOqr@qf_urHxHimuvthheUVap__P_\\:pphGt\\hbYpawOxnaxv?yjIv]yrIxwWYqaxoixklDJqe]WetOitubtggheCuSSEUSI]erCt[gsXcf_iwgiWauVAMETKMh]urHrtTmo@pj@x@hKULtMYtIemtdPumxfav^aVSEUSqlx]NFmNmTNwdQitOI`pMUTLMxmYx_af[gZ?>vONxyfxUypiWdLOdVf]WflOhlK?\\:>gyItGGcCGgvAykavePgGgcGVwAwjlQxlIgMqnK@lKqbq_h]vc^piIwlsWx`IplWewVeUWeLfux`isQhxUxevDidgsxjKf]OfvkgXUcF?cZsx?Qws[vx=dvYTN]TncHmSesSwQoUrAe;;v?oIo=TA<xm`RqLvjIv=aNwhOV=qJIr;INkDPkqrGXM`mV`myxqyg]X@upr@qr`sFaSPUUQuTQhWN`xJ@PAUnKQN]TNU=Othn_pnhEunHQdLPLXwbmTPmtSYPamsWhQudW@aXaipeeryqmA]<;BBoWGOtwWYqDTKER;ER[Iv[iYuqxoqxpquvHiH^aTItGHbaXpT^tiil<vev@iKwuxGyli^eAySqj>_b>OkEXkMQtLQe\\qu=PZiyoRopf`qv`mogl<GnbHoexxgytQ?cB?ob@pbFv_YcPIh[^c`VxTileHl[I\\aw_VxwsyyA>k:J:DtgyUBLKDlkcXrtPsMHMWAUDqyHDPfXL?uYAtwXiqexWuWxM@vRaooNinAgL@onaxnAixwtXwhhAaiPeGWnKAcU_e<_i[hqwapSV`^hn_X]hVlTPltovnIoUn]QIwnOiPodPapcp`QygXAwKYpantT?:;BKiwy?GcLLUTMUIqmuvpLQ]XUapcOypqgwTi`j?v:ywmwqCGcCWwVhmSGqGWg:Aj]x^HXhWHn:Ge?GiAqoWWd`PufnpqxsEYsuadJ?xehwvYaxnu\\Of\\?ekG:tQaprHEsuhYuqxhhUuPYr=Yn\\wv<XZAJCyMetTh`W]XPthPVamPAsYeReXoexyrYvIhnEulHemtdPZ<^WpcYiquwxiwqwqpZGr<`xnax@au<FoRqvGV]dXodwcWF`n?uJYcQwovWi`G_gIjTytiwu\\frafwnapnvhQw`fhP;J>upyESUTuphWEisGiYyqyweYaxoixwHhMulnGUm@QQ?XXU]nixoIQmkajBLKDLvt`kUXmUhkGhSweM`qsWXQ`]sRXjAtKhXUqpWVAqkUlatSXDP\\]rtixeISFXNOAWFimtQyrarAirMpjf`mfXy[Yr\\LN\\tytyNDLKDtjHpM_eSaxXxawSaof`Of@q:DXkEXiPlXEnH<ZKikEnixoiEV[Ef\\Oflhiuuxr>arJ`lm@ikQfuWiuwdQwtEwlhFdc`tpPy^IoNY\\ancjpcSPikQv?akF`[phZXhauoppgwTI^=ojNyrrHymyvI>]j>n=guKV]fxevFcnWylivE@lJ@lsHQAeucijmwvSgkOuSIU@mJ]tMdpx:ewCUlaTl@dmHuqvEx\\lTVgeu`hS`akOjkHrBimUyiIHivAmxyxkoc:RuqrqgXeqt@aGqSV@aCwcIw_wfawqwo_tTCMlUIqmuvjIv=IYRXuHqmxTTTuXFxn]Qp_uugIyeDOcDwdQwXiquupb@obqtgPuYiNu`XcQNZ<N:mm`Ir=xJgawfaWf]WpqwWYsTQvOPmTPQkMv>mtYlj?hjWeqteX]qrGPUTMUWXQqmXlMXLAtJAyQYquAykYvhimu@S=MUTMyIuLQpNOuSSeR_Qt?XK^HxcwsmwvGYrtX[yFakGhkauV`uBAKkIhkwPisU_vecSdMSDuBDcRxWivSuVcc:;BgIS]uuZASBAtgWrUYiIOcF_wSYha_YqqwVWR_eV_EXIqeG?Hj;WcQDFoEwKyGYeqsbHcEtoYwQyFIemSwYwwJGF==SRWhn_hfwUlmtfGUyaIlAgboCGuInodvSFPUr:AtJWxMif\\Of<iuWiIhkGhMr>GCMyfIuVUcTKET[CRmSHmSH]cIwYxaysfub]OBvab@AUGgilEylSgwivEydUwHh=dyMr<Qr@SFAMeU=URcclkWr=GL;B:ysOcuT=cZ?fZGiCGw^IGM]sAUUjCeFmTaYwQugvaYwqgu=Yf=unGxuaIFCESCegcXBmU^eeDOgeuth_Wa_y\\UxZIJ^\\Xd<Ob\\Pcqkx\\ywXpZuuxhYstRQxOYmYvAykMtjAxjAVj<MoIQlpmdPmTTWHDVquTqpWWQq[ex?x]hxaLpdPodXy[F^^yAyrAyn_hoGc@X`oV`gqu>yyOGZ:>\\WAqU>ab?\\C?cQx_WO^yQwufofVgafkM>\\J>yxynnx\\Of\\gixoIgiWoeXoCYn\\@dbfv_ivkHpkXleqhxVfs>ijAnghogyqHWuKwidXohfes`]OO]J>\\JApGI]Waj>`jRg[Py_aDvUIRiIx]xB_yuiYUqHGeGggtHYWnAXxGY:;RnUW`Kxo?ub]dkwvgWuVWR=ax@whdWTycYxayswMwqNGMmn]yrIXItKIPmTfxmHuO^\\N^b>_bNymHfxUNwmhe[yl<osKgGUixarV]UaCe]Gtc]g@GcSGgf_gfkTY=WG[Yv_iCydSSCEItLMTLuusqgS_S`ixemEYAU:=TB=X>AC=STmUHMSTMqrYcD>NnUypRvkTfroNqS?eFpgOglDgcGg_hn_pPplPsDQslixoipn`pFpkHpnKAg^^ggOunHgIqmwfksdxyTHadNwXVWfAmcVCDN[DFwcIwEykq_TSP@Xh<lxyx^YXUupgUw`tOIhtQLU=xjIlML@w`Aw^atIeToYQYiXLMTLttbqN[DN[]W\\MV`mWpLtJWf`yu;>Z:_heOZ=W^]NlQOoeXoUnhL?_NVdmVtPgdcf]Wfmewthhj@pjx^irAxrIx]Qn\\PnancV@ev@ikwqxgyVauVQ]sh[FWbMWlOAkD`k\\a]gquwXyGX]qnqpypYpawOiwQwoFgBWsBA^qHZn?ouF\\jyywg`LxlavwUnf`qv=ojHfr;oN;FtghNKd;obFcELCDXCtjWXJAv;QhlMXgggRUDeatYeXlMpNYUbYtaxkLukXDmSDMSDwcIL[IvGMQxmxLijE\\o]DQF]SGEp\\QJN`lN`UvtUuTS\\uuxeyFasGAS\\UwyyxQU>KnPhVdmV@qLWaO@UUnxtDXuFUpSypqySLAusYyHtOYuMPaj:yydiYpmxCYva<UgIopTTkPv<\\QDpkX]pRIrFQr<ESCEKOAZyvkPGh\\^jKo^`^gw^vgAqwpdvotVHafXlPpqGocXQpcWhwalbvuJWq]FtLh^OhlO`nWie]?xZHr=Hp\\QZRHmUxyt@f;NhU>ZZNqwAZliuux`VIrSgcWgcKGdkhqP_eF_cfWuYyfufq[IvkpigQqdPodxgfvmYxmyYwvVuaIxIIcUpsi^\\_fa^WmIY\\f@q:>Z:>KycNAxZ_BmqTp]WcUSvCUuuBAOynqH_Mv>AxAGvVWcOuTQUYVei`eI`]Sf]SFCiDafJUXA[S\\gXN_udYxnufyYHfWi:;JxMRghvZ\\O]IT`tjIlMtYQtHmqXytxoTUpTHrZXppuUuelnQspmsVpUDiq@xKQYwWynI@nZ@VkEXkYmqtWXlj?htIEvEAvM<seyWOENMYjoeX]imRmYddts]ppltZ=Z:Z:pt:PuM@qaiv_I_oAwkiyawjtqyb^\\DXxthh=hhnwpgGulIx=yZLYlPPm@oykgerpbDoy]Pq_gkRyyWNhupxpYfxO__gnsAZf`R<:yx@efLeCGgci=Yr]yFSeVQwSOeSoCUkIfQuOWGq[Ihwf^_fjmruGF=ubFay_md^OwZIthqyocTnkh?kTWaY>yR__Gmct<QYF;Z\\Xuqqf\\OgDOnUhrbItyftE>^`n^`wpjG^sylKpmXv\\Qvh`avc`n^`nCVl`nkp`]m>hZppFyumfy@>aHHpjWxi@o`wciWsixbMG_NvbM^cag:<yc<TUus=EM[=P<ESCEW:pxIMqyqTIpmwtNF]mbPtuxPcukn\\PndPmdlc=X@pJ=pQWQJVdOuLKlEkTqSXDTAMrLDpdTZ:>BqieCV[EvGUUq?Tc_TvOGVEEpidqIyg]HQaxpYuO?cMsCM?T\\B>tuOHxbHTrESxHr>eouiMATX[EJxls[TyEEvaMNYUn>=J:JJQkRXWbLYt<UBLxmEY[awh\\QrtLoqJ_LJ:<J:oZg@sbqyoHwG?jIhyoXflVavQixIr?ybCA_K>Z:bbqBg?sRcS_WUE_ssStUSbCaeqmHfQWFYIN?C:<J\\XMnPNPYJt=Yf\\P_QmXqVWpKspy^dJ_LJ::Lv:qUQuLR@xKEOVHwgmvc@vUxSMET\\<J:<J>?tD`cX^nvgtHajDGfIwgnobgOiuhyff[_NZ:>Z:_h=pd^OoHPs_WqK_mcio@psRpil>saIi@Nc>>:;>Lqhuwmqp@]UMYu^YV;pyiTPKM>;:lVGTwuMYhHNQaxpDxbiquHKS=OK<Jn`puDXc]S`TLo=J:]hGP`IwoYIssV^sVyeHgoHwg>`KFwG>ZT?t@YakV\\IpZh>qrA\\ci[:FtGN]eoqxPwCIuVOtUgfGfi<It:AvQwwKO>KU<qBIAeWoyk]fkMI\\ih=ivj]fq<khGpfa[NqkxQf:IuYGdGWpx^iqIblyZN@[:>iegqa_sh@jrPyexrYnqTOioN\\ci[::]VboYjmbxstnqVcqEJkypYFD]B:[ilWIZkwIoBsgc_AXRMvlscb[DA;BKiKPQL]qyhXtnqqLpuvYNYivZ`R:<rMTvoXYDIkETXpYaC?ekg]ci[:ZGIs>Wt_OwjosxQpdPunq\\WPlEP\\;>bmIooWwNNqLQeP_kEOiu>\\nQhGisA?_KbbLMeejSptXHs=EQuYSdTW@Uquyr`xv[`R:<tvMMlQt;YOf@q`xpyTJYxoqak;Ek:<LWAnkptR=WiamZXsSyUVETgMY:ywcmRxLS><JGyn_@NmuYsAUcET[ls[xQ<LvpTY?Qn>=JBpGgx]mBgUEaWxO_x`YEQGU:OD;;RmIWeKsXyUpkTlWfZsnYiyXhWqiYDPL;<NtHR]eWpPMFmykmxQllQqnqxvSumJM^Jai=PiBiZgvpL@vPpup@iyFu_yyFf^<>BbGWtSuWs;dmxvlPOLpuXmV]dq;<JI<wnalE\\XTTrodqg=qMTqqqUvLS><jbqZewv>I^e__@>hpy\\NpdHPuiYmrIvmNc>>:iCOmwL;vbEGh[G:II^aYeIxxYyi;T\\;B>bwSdAggjSt\\qeXaUvuUw]y<OD;vnaPtOyichnB@^yvvJQsUFthGriFd\\BK^_QHo=imF_`sVymQcdnbgyxGosg^bC@ZZdKcYtgBrkccAsgcigSxBOINKe:OD;;FtGjt<Vm\\YcAoxamwIQ?ev@qOxtwlQkJMN:rBqiWayP_c`QeXqdXecvkxZCC_K:PR[@TVqncIQRLommKw=OftPTyvMPjnqZrGrRgpuxt\\W[hHwGIVkYd[yOKS>DDgSiubamcR=VZors[xx?hFAYywWTERkKg>;BGyV`ogZIwZmGBys_Yv`Er?ybaUFYUf>=BBrnqXvmd;aYwqYVWRSueEecW]YlkIO?fD=BJaYPKEDwXPSUB;xkEy>Ihu?xjaYNYEN?K\\BUouHmsp[eawr_ci_]YdgSi]F=IfD=BJnxQOqgAfHImXA]FovvYxIn_yniEP\\;>>HXe=JOPXdmsBIu=QyjmK_hLN@lnqlwiJciK:<Y:QSexroij``UMYuVXP[pMkxwJMN:\\Rq>_v_ddIusobmnjnqvVNcCy_`FwgYb[G]d`Z:rG=ERYwdQBMkIdcbmciGaIOKXmIWdKS>:uDaYEIeEf_ss[xhsgpci_aDOWfD=BJpNILTxZ[QlXqfVP[xhyff;<>TtUDyp\\Qs=Tils[`vVQnKUywMxDXOJeN:<WxHotLOQhw@EX`xPTdmkdy^=lQ]YtLS>JGpSimX`TLAlx^aMtexk@l^xpvQL^xP:<v;HwthqIYuTDX`f`norNYvqiyX_fZ`b:>KNZvaiQq\\RpkU>t=XhbFx=y\\MhYEBLY]EVp@hxwfaQAl]^qOqnqHkAWZiq^^Gn>?:bZsIYiCuUhkKeD]e=uGYyYpcIZyxs_gLcT<;b`YeawtiatVSRHqYLou`[EswDR?cnqB:?w@dmXaQW\\sAUWbLXHdQIqy>MtUEVseLd`:tUYex>awK`=KEwMrKArZwTSAGK;B\\>wnqpRauVge;Xhbn_m@rnAjiG\\LY]:>x<QZ=fp]V`A?hpydNWt@i]xx\\pqv=Nc>>JN^f>riIwZogdptWXhbIg@GjsXmyNtUJ<IrBUrggahHwg_s;AjjypYFd\\:cR>=S:YWkgbKuIsms[?en_IEux:OdDQWNEC:KeIIt>Ux:gsjmgcisLiuyKxWmCD]:T]si_SfgJynevvJ_hdo_Cwg_gdo>oLjiEmcptxHO=AQuYsdPWMYUnMShLS>ZUpu<^]AAwqqvLpuByd[OxPPeH`x@Bi[gnsEjWYLATHqyLOsTGthqykCWs=GKBnKcb?d:wyLUs[QsW=IAOrYqvFgInuDciC:;Y<IYnoxiYvoEIuYceKgGaUwqe`]v]_R:?w@;tbKDWcB=[EgsbnQwvysTYTmyt>sW[uWx[cyKXICwGFkGXfAfgop]Fi`wHmX>xGXsf>bC@ZKi[ZHd^fb>PZWprFnw[VcTQvSIx\\HiCix=GbipuI_aT>eSWb=gL;WxgGPQI^;rkmxQkdQqfqwvSueJMF:]`kHwgqylHpdGqkfmMpwP_htyqsVi=Vllx^XF[fpnKId_>:wwqIxtWWAUWmmxymGeOFciw_mHLYEZKi;[H<eTOetpgheMgYwbJ]R^CW\\ceRpuG]sT@YNDwG<Z@y]Mpjh``MQvfy_bfoVfpYy`cYrQxgyIiXoeXipevdY_ayokDOZ\\X]vanDV[EvvGqm]Yw]YbTqv@qZThu_HaQHxyGmsfxrii^x@fiMwjiV`KavTpuFhevoey_yPOimWaj?f]QyoIdKGdbV^ZNq;ysbV_eVs`Ox^AuR@]Pid=Il]NjQ?ec?sqOvVOtuIi@akMHro>cik?hypTrWtRoyvfyseDojluiYmVXUripy\\v]Px[PY:@w@tQcxvkIxMxNF]SGESgxwKYtQylMtwRLp<QUgXmNtvlyp]Qt`mmHDnm<Mbd]bo^Dfj\\QaGwgkHl@vvJocKGqkXkIYqvP^hxiRodXochfb?_bJWb:_h=xmEiy:ArYonIAyvIwYhm<Xqe^hQ?dbhamfiaGkTaxPyoevlnqhmIgdasM?ci?:qFwgETGfy?r:ecm=w=EVsGtxseNay\\ms[_sF_ctwxecBN;DJc]BIymxvxWe^AdSGeSApm?wjxiHodMidL_^^gjOwmHQlVxiugyCOsVX`[@ci?:aFwgEYgVjsUywEaAtuQrlSFQsenQbLobWgBsIyfWBN[hn_hJeI:]`D^htfyqigUAsynZAoxTnaVwo[idsG_KAlOpddNhL^mqNh_nvWaymy[JpU;vCMYuCIUAXXoEQ_xPgXU;uFgC:;BB;RLCTJXXcHlExX`ynyMtUioUxpBYmRAt[UR_ev^ATt<RngwYgf_gvLvj?yvIqm]QaDouGFut_\\tFk?holpw_V_HIqjiJCuhQr=mFMGcdOB:UXy[hb_dMUX@msXktAWXbSvMCSimISyUDESu[Gn[xZWeUCWFeepcC?UbpmbYcF:kSYOCDkDTIuwscaqISKd\\Of\\_YqqwVgyoGwgefoAswmu^iCNgWbaUNYEdcf=Igskb^YSmKsELm=xkDeQutsbpjHAqPTm<qPNpTJMPXiui]Tk]kaioUavdajCULAySR@jDHJ\\XMnxY\\Mv\\qWApK_yv_iNyHSxLY^ASpmTPUrKIvtQYYUy=eNSDxjhl]AStUstasXpuHaRxHLZYnXdy?AJci[nvawhetihNfm;aqka`oHfy@`gPXUuOYhbsbYweyyt?kXesTiorUkCnwIrIrN;iJKDLKTJ=TR;Ib=dJ?hJSGqGGn;I>UWRAx[yurYuXOh^ciSuXQOD_aEtkyjitLYgK?y_aD:;YLouh?uS_SX[teyeIYhdQXswrQ?yEOXf[Gf[YiqBfoXpmfLExSsBBoWjYHCocDOUqorS_HPEIiGiQ[ENueRQEXkUDidl_e>=udkwciwj=U\\lMRHuV<Jr=ndPp\\=YsMnNyvTiKi]YOeVwTVh@mxEOVaUTId:`oDPplNw=>kh?xmGkIXkq?pY_dMWdmYsfHeE`]V^j>`jHp]yntmxdipeDiqt`hcQxixiXYqm`fBQcepgL`e`Ornw[C?eH`x@Rmaiseyt]g?Aw]owhQtIuWpeGDeu_wGaiwZAHwOTbWC=Oy[QsW_f_UUjGbYKue[weqBV]F`kFTqsWWTTMT\\mW[EhsUuPmTa?i>_rHyIpEyrUYqKx@MypEdDCU[eV^QvMWUVErp[vT[yLweIOyaad[=Go<yIlQx]yrtWpamvayvMxwMX_QwOmL]xRmpYUdLM<LvUpxuPc]qy`vSIjDynx=VElxoUJ>uPbuyXpQsMvj@tx`nr`rJAsBixZXQYtuytN;\\Mt\\WRtt]USypRoXUa@lOlt@mOXIy_dlfURuQJYXxMEOy]STLk<XJ:UTgeuvHm^qp;UjAtmu@Y;]n;IYhPYfLmOIj;AYmHXieWtUqjUl<ysapxaqR^xPbuVjYZrya;Ib;WhxGmoIymyf]Vf]Y^AykCN[DNpg>nb@oRanU^dQxoGwglPf<am=WqiqriOxDhbGIZZHcLnex`[xx]^^^^^pYisO_j]ay^haPvscYqwg^ehmwor]istiurivN>\\WAnWQamOynQfuibOgdOWv@yky^ifA_swf^IsGqxiq_W^q<Qc@XetWu[yxfWmIY\\No]:N]i>wxiilGgsnhFPrQocHOumGkgwmGYsRgwFYvQHeUFV[RqpoN]TN]_vgrhxuq?tcax?nxEfeVw[jQ_qHpbG_BaZgv]UIc>XsgogoIiDOZVne<BTCGdKhpAIaSHmUxi]GMYWSgeDQi_sY_wh]wDYaWTybtGB\\WMyLLMLL`LUIXxlaxN\\LL\\uuxWYXxthXgDpe=kpPnfDSiMlWdJstjpDY?qwsXMIxL<<JTTNcDPK`UdXWb]YuEPOhtE`lQAQjPuStjIiNiUQ:Pt;Uy:XrNlYd]PTdwbIv]tRI`MhpodpTdIt]AskXndPWdeOquX=PYBiJgtplDQZYUVETGqPnpxpYVxMO_ensAJv@O:<xGdTOeTpqKHdJ?dJlQxlyyt@XiipyHPcaxntlM\\nWpwpMm<ysQyV=^tJ>\\WUeOb<swiQusWHmSF=_haOuRaWRaiC]SF]g_wwNufa_UZWtRSXqsYHaxpOw`YFxKG_EecoDXME:;yTCF[Cf_oSG=cY]FeGHc]XLWuBUe^=IDsEYCsm=G];FtGRUSDqawSWwxYBKGDKchYQSuuxXahoUcxAcKsugquAOGqECj]hVcw`yULEU=qHn_yt]HOORk]HKare]B:[iLyXEQXLoulkCYWFgatwwRc_yvQse_wKmD:]X=oH:GrZ]b>sbVgIwMwkYfAavd?eR?uiUSQOuxQIYweyYYioBtMGWeyQOUHoXqyGeOfkgCsCY>ExmITQSEc=voQB:kUcyxuQG`SbXGYnQFcuiUiXJOrIyteEeWKs<;ch=tteiIqsxGY]qrWWuXGUouvLwDPkDxiVpaw?YSxUdN_dvITICW>uehmyEurJ_xPETGqeXqYuOD;yS__GVCgHwDH;BrmdXqXfGw:uV^mer_STyWqWiL_xPYXCgGDQ:QcJAWn?iausXcRyKCHKCD=YsQdOIuoWUqGEmsVFuekSR@mTpybyKrKgYuGygCEwkxJiUHax`uYc[eIOSwiX>OGXuR:;vCKC?Otiyco_CTcGuacACiT_iSib<eveIhrmCdSBBoW:YBywWWqvaYweOf\\Of`ogh?gb_tWEfu_b>_ryoSnoTV]UVGdXUGkCF[CH[Cx_YcQcf_gffGF;EF;UDMStkYD`;ETSEC;CB[hXwVd]gTiueEh?Ay]sxrStUQbEwCb_dHkhtASi=B:Yhnqfpyv@mFGoyxQrGMXooXdoUdchpauS=BBoWJaSYmivECxwE>myo[w^CwGMTLMTVMR<=iHSgm?gb?gdOhl?hboxyOeTkxwoyCmvMyEkKrBAur]b;GBaIw\\MUCSHoeBIlv]yKYYo\\HtUlxmDmW\\wh\\Q^yv]psXltqyRwlPitOixTipU_itsivQxUfdOgDplMJnhxnqnx=VEuJ@dqpaynaNwhoYiS[yvMM`=fl;^bq>gPh<iTWQipUSGeSGmSxUxxSIuYruyC?yYuqrYECDCCdCGdcxbIu=UfyofdOedot:GBWUipeWMssQpj\\xfoHwgpJKEpYHR_ssuV=Ayc_tSSRtuyJwBP?eR?eN_d^Iv[IR]GtB]X=QeC;tHMtUWwpkF=Gy[QsWKXoixTgeNEBxebsWTKEE:]Pyim<Pj<AqkYvUlxJIwnaqv`qLPv\\QwdQw\\Pn\\xY\\QmZ@VAqkWdr_\\NttXhaSTdWqIOUmxQMxn=PY@Yn<lmdqGQQWLrAenRAwb`YyyRopYwQYlEMV\\MVxmYxQ\\YQHym<<JgTmXAoNeKqhWFMQwYnAxKsPmn`YUuJdtm<awC=oF<NtHJIAh]YwPwnWvaAIpTgah?uUhcwniYX`whsvf\\FgnJonFndxqyIP_of`ov^avbQwdQ_eV_]eI^:WyCwgv_iwy[gAfPAtlogA^t`xp_Web^dDwxYo^\\P`JQy[a]`@tD`kQqwsgg;H_yv]uQgCwfNqNqxm_hiyyJOr<QrBifKGdKkUW;bpydXaHIwwhQHXQfpQCMGebah_YrosWNgBJcu:Ke`MtZoUQewF=gNKCUuYGcekcy^=dqYxnywvAY<MR<=DWABTYXtUIswfmAImOue[C@MrLgcYsWtIff;bbqBJaHMmBesUW=rwciGEIpuuyiV`yxv=H[EV[]Tdct:Ar:sgE;RuayN[vayttChqWhOGCeciw_UnoGaqsW]d?;<or@uR_QvvUVhGo>XNqqw`\\VwumAHxhiuuxxiyuILMn<KuLq;\\payK<ER;doMUy^qRUdyOpuP<QaQY?Lnf<jbqJJaPmtjpIQutsBXWtUmr]xX=V\\yxBuW[Hn[hMjYWc<rIIlXqJVXQZTWTUqwemCuny@UrpNQyNBdV;\\Rq<j`Hmm\\qiIosTNsLrUujDQMtaj]VjYgqyqaKisRAuRvo?>rIAlXapiNqCakLyoGwgo^pQnhePx<NbKo\\:[TVewgtMXpGFauY_dHgPyjiqaBoyJQtKikDgn\\obqp\\L@lJ@\\Xn]HAfvY`Q^[GpbEocHob_?vAhIOR<ghcisr=Ieciwseq_Iyqy=]d?;<ovQIDdwraEEjeSimdhIB[yWykhJiyxGYmqFasFa=v:IbLKDL;YO;Ye_f^_rNatNUTMUX^AsK_fKETKErdyUv?YkyrIwEKuErIbrQIDSWY]XQoEs[dOou\\yVskD>sRZ_G:??SCAMgYkesKveCwGyIl`mP@qM]sbqtlmVGQmO`mV`QwMynMLWQn\\FeSGe?fZ?FasFaoOwNIsJAtJfx;x]Vpu>OaH^ql?oMpmHyaci_^N[_GjPYZaWd:pp[GpKpZGpsjOxZwi=f_ePoGswsfkWrOMijqxXCUmKi[uRqkeEgcGgfKAWcCGcKB<KB^QWOeTOCSCyvIyeaMHSwDikU>eYZgd^wh;utIoIWOVY=ybIE]OgtkYpWFCSXlkb=ATS;WG;hOiCTaCAUDGYBpSrsSyEMGemRuWyAaf_IxpqwRUHtG>WTKETs_YsQHeshKKR<MRlOhl_F:iewSYPOrs]SD;rI_Siur^obbUdpSf\\OHhmvLwsKGhbSCZKQbMm_mnTUy`@XsQvU]UKeW`QwqaNwtmQuXnQwOYov`qvdWgeWCESC]lWxp^hn_hn^`ndyo@qr@qwTipeaxcYtoIVH<nO@vQTLS<YwAo^ps:lTt_s@IvE_xM_l?>\\WAn_@`S`ciwghyv]YkCHkSH`]oZCi^Mn^F?fgItOqjf``Y>puOtJyo^x`YAqFQZX`uEVuFpgpohp?e]Pe<xmYxu;YjAvoVGq<HcIHnoO\\J@\\Y^hmAm>AbGxqMYu\\x_IXvJo\\:_h=p\\khheqtIwmxFhpYqtPqHf]t^t=Yr=`ktGisGmTd[Iv[iWeIgsscPqukCRQWhy?hvOunAbiYxfwSGyiEwrIwEMWSPyg_wEx[YZWtcAU]?YhasSWHxkIxsvHieMKDLKRo;fosfqGrXwf>yBbWdpcifOb^wh<Aur]d?;l;tk_mV`mqvEyLqtPqlgxy`isUXwPioulXfAU;ER;mTPmTHmSHpmXpuHimuTuVYLVAP`=tPUw;amwymEQoBMYuEmWaunqTMUT=mOOhlOHs_ikUtP@ikUtjOPkq`UV]UBQODmT?MOOtw<=t@LtUpkaISkeSOQunqTLmxfMs\\PnaxOKmL:CiCisGiggUuodgWhj?hjUv@tMx\\YbuWiuOgdOGMYt`XcQXcQt_xLilUnhraAq?QUaUtRIRVhy?dnOXnpYy`lYrauVXMYpPgMMs`yNuNj<PJQtLQLedLIdWTapC`Ys=Qj=v:UrHaj>`jWTQp=nr<tDUtU`l^AVIYT\\MMwESUpTLMynMt<PvraRNhJJFZi?tb_`lI_r^fBA\\ppyMv^H?lI`cWsyqYd]TLMTLgdOgW]wsnUyreuomd=CiawHQsuQuEy_yaYUXsIx]yOWGQmCWKIngXeqTquXqEn<AUi@Yriq<=SB=wIxQxAWRIUKETk@WKQnKXNAMnx<tdEKDUScAlnqnPyjOpuX`SV=TvQvOLs<tuYlvoUWApMylYfpn`prSxvXqqwUq`esTls_IUU=vTAoWULA@tbakyTJYXpoyvO`TFPuiYMpPttxUQEoyqXEYPdAVoMvgXuqxWixUypuFasFauVaUMUTMuSIuSOeToIymyvuxXiqwQyoYLnU\\ppax`TOgXvoMQPQYXEuU`TTETkYtCpXtlUa]ruyx]ekPxn_eTyMy\\dn]hj<EJ\\XMndSLMTLAp[]wm<WrMYtmST`PCXX[aj>`JlIKTqnYxwXIO=AWFlr;@NpiUIMXDPsAewqIKUEQhxSQ\\SjIdrWx`ishheuPtLQttvhhamLPl\\?gb?qywyxotJHkCHssXhaAd\\>g]FwgacfhpgGyUapTx_?wcdWtUIgkgxTy]LWx<NbxfZA_[xhhLfd<p\\?x]FWu[`of`oHgmtFpoouthhEasFakmGvynyrYfhaushgwI_iypKYhlFvL>by^\\PX]u@y^`vOFfg@gGNZ=VZCydBNlUQaNicFY]KF\\kVf@a[]V^]hquwxtIysIkDPk\\`bJq^BfhPhtoQa]NnLYjnXgxfisO`xytLytiAmFovuYkqpa?pbyGktOjLFbEPrPwpp?oIwmxFv[IvPn\\PfxwfZ?fZ\\cRsIySyEiYcQt_KIWog]WfMqCXgx;Se[aHtSvj=Euqc=ywESsFwxuqIReVWYSPsVKwy;qdhcUTAxduKumUsPX?dV;pLoAv;YjgTUp@sCIsOxlQXQuTQmQwAEY[poleXUqu`iT^hVkPtUus_pp_uWLEsJYuWxJA@yWxR_In_AVeXUu\\VZ=VZqwhqyvIyyTqyEYsEYG\\MBqqutySYpaupgUup=xZIrpIxfHONLs;IMtqx]dtrtjlpQQP]kIsreZeu:;yc_RAuRMwGkWgQugpUXmUgdOglGhkGVlCevOikEVsqGtouaUIpaTZcwdayIEsU]URey?GtIEXtOY:]X=ofcIumwvLgFE]xoixCYiOeR?eRAOicaunghoWwQ;SDMST_HcMt@gCU;S^WFYmRUisMsFciwbyG@siH?T_aEDAyNUeXAS@WrdIBjYxRUh`ecJ?dJgf_gv[YJAtJAtTQuTmqxpijuxXOIxxTONinhiUnHRb\\SsYvZLkIdOAtQRppIUuqxWiTOe^gSQpoWwPImTPmLxxfV\\MVlaysYxf`ofLpxMx^IobH`]Co__iv_YuSY\\aFwgavfIlFnZmagNY]pHnnPjLNlXQrPGee^hLVrTNZJqw_^^^^b>_bRXmUXdc`tkYvAyn`pnhnev@mvhbjAxhNcYwn^x]tVeOxRwYi?wcYsvWi[eeAUE[iT:[Rq;WnYwDysiqv`qHp]wRYFAmcrIysItb]hOYgQUhLgsBGD][Iv[If]WfMueYXigSiUX@MHR_smItCaW=EGsir^ciw;UokSXMCu]r=[hmEdKGdWkyxceWAd[SRhoUwOs=YEioyniv_gyTyS[CdYUUZcVQIRsSC=mu`cR:[RqoxIaiHCScEIsCIHqsHQhlOhwWYqqdKGdcuxI]eIOSwcIQAd@AVXmYvqdg=wWmuYEwgWg^?CPAD:oXfkF`kbVmCT[HbgFh]UJmfMAreuby[UpaSSYX^lcHiZDO\\XavtgZpgmZGjQNZro[uQqoXhOgdOGZ;FZ`n^`VfAqkWNan?wIAlUQwMYusWe]HgtN_VXbCIq?_^whvOvdZgXKuw]XU;HZ=REeYvMxmYGFietKvc=RYgge;y_CiV;rxqWAWEMGr:YC;[IAgghewV=Xj=XcEWcsv[ifyCStUifuHDos^muvMeDqHnQIa?dowuU_eruRf_F:cwCSb;Aghogh?OK`lN`N_dN_TOeTUSEUc<NZ<rAyrQQNiYPWdjuEQHyTRXQ_dsoaX`IkEakDPstInlatFykqdy^iWfxYZyTqosHIhkGhWXwrPqtPlt>fGFbnWjPqwpiwUavlyvFpgf`xpgtHaj;AfXqkEWfUNctAy?afyxgBQ[eFe^x`:ph^_vBIlSGeS_^tHlFvblXcypioxfcPwTipeYnAwkTogIY`;FcCpqUolqApYhllxxbox?YmW>wyggfWcSYh^Xw^VcdvyIHybhpkTlUXmUF]SFIwEykicUt`cSGes?UcPCVGCRnUbPqygYtUYuUMUTMUKETkyvWersAgQuDR_SuCDnuFxceg=w_YyIqfA[y<mTTESEOvfQx:cw>]R>]Bs_F[eVKeetYdggYGcc@USCESKwdQwDQsDaexN_dNxWqDkJuTsdxwYmumOSxxhunumkaiULYTKploIvdxl<awCyuypK[DN[\\vwyYYqqw]NyPQsDQKxnCYxsHT:DtG<YiTQuTQytQyMsNHOyDYW\\JsIyvlLTpSxlLbYy\\Tlg=wsmxaPunqp<QSD]RBTOF<RuHLQtLQIvYqkK=SDMSTAp[UJeAyg`uVauqxWYqwWYqQYsEYkCaVhXUqpwytuo@klPlPIwweQWpYwUqwAra@lb`tytkCySUtRO\\yXyqNmMsLX>`UdYweYkB@kfdUt`lVmOR=p:TO@LnU\\ppMSDMS[Hn[vrsooTxmXqggN`Y@h^qe:ObPVyU_i`GjcIZYAv_qdL@ci?Zgibv_ivFqf?aOFaUXoQwoX^ar?xTipe_vwOlOYdN_d^of`o\\UV]Uf\\?YjmG^B?gch[xHi\\Yh>__C>hSy\\hO_SisrqsO>kB@kJN\\LN]v>ijFgyYw`xbbWej_jcWaa_f^_^`njS>gyQciomHn\\PN]D^m=wcmN[FiuvYkDYoJg^:ph:HrZ_qrGx<`ZQfdOgdhX[^f^_FasRXkEXcxsgcJ_dN_hmWhMcDOctOit_it]CdXCfu[vXiVCcWGwwVEbfaosHqshyuyxAIXC<kh=JgUmJ@RgMYmTTaQlXQVLQxfdu=Lke<pi<K:UmQ`mV`UKET[HocHsyil]YJHdMt\\Pj=v:msW@jo\\Pn\\KF\\KrIYt]T;dj<ElLIt\\dkiIQK=SEuSFPJBpW:tuIuR;myulK`YnNEqVHJfLQotXFIr:PtDQMNEKZhS]ewbqxGxUEUn]XnEUSs`mKAmHunUPmTppJYnDIqmuO]As?lROUsxuQfpohpof`o^tSJ`pOitOISuPoDtqa\\pq<uQ_yn_b>`ZvoiUfgcq]jAxgybpHnByhsVfHNyYihVVbPHb[@ZTahnWy@I`DNkDPkxnaxVoQwoXWp`gkV`mVgiyHj;HZearSg_[XsRWlBfmkF]Aw_b`oUO^yfsTPt<VxFiuvHimgtdhdFo^mYvAQuqv`Qv\\QvhqwhdfltXhaqsSX`aOf?AbnWZbWuci_:ItLQrGya\\ieHVuJ?yUamkxjhQygF]G`x@>t@gyeI`DV[P^_jixoiuqxgYF[qNmTPm]pbGPmrFh\\AsKX^cfhT?wKGd?`ZOxdiNcTopoFhCqrnYjaOyf_hdaaPajqxhkfnHwjtHifQhmWhYwqxg_[F^;TbuYjYbc[yFIwg]cXOSQks[?hqsE@yEswTXebYmS;Kud]X]CCFUSEUweUCRUUUub@obTGeSGCB;Cv?YkQrOitOAtJAxu[SQUGySX<urXghuQuPgiCecYgwnAs^MyaAcRmeYYSheE_eV_yWaqhbAwbMD[eWgeWaysYwIqmwVAdJ?dTOeTGgMufLAWn[g<egVkhtGrIYSF=ipcqjUxu]lTxrp\\LnQwwar]HjXuqS=KE<vyIL:pp^YrAxKsIysQWdMW\\Pn\\xuR]sjpSsEYs]TN]laxnaIymyvIxMylQp]wRMldQUhIpKEysiTVxLa<QfxVWeOHXSrMPHqT`]lxumGYs^\\pNAYR`Uu\\i@wb\\grDh\\YvAsCX<TPmTP`U_dXriwqxupxWYqST\\yvAYMYWgApOiKxMWLdM?twtlkKiwctrs\\LR`lwDxB=VodkHPO;\\p[\\oWdu@hKUlro]lKunxQoB@kBHocHw[YrAXJ<LJBitJAtJqlx=YWqnFhLKEwKApaYTB]v]TncxOxeUOmmTHs=QKvUVQuQQuTQaj>`jEyliTplUMepKApKWLNy=Wf]WFhTBDtG<noXlNDLtxqf]wZqMl`m=uXMTp`lM?MY=<WEmmwTY@mOAekTdro]l>\\lBAsBmsxUJ=TJkDPkpjA`On@LDtMYuwGTSsTym]QiqRHTMQ`p\\UYOmSxtS\\XuQqSWeUXmUhawfaqlevDMOoyy<<jb@obpn`pnCHkClT[\\Rq<jpPlXao@LOkESimyiTPapMyxknqJJqT>xjAXKDLKHXMqlkeAWJ=TJttSMsmUXmUSEUSGdKGtq=YNfQPXQRFUnitVyTl@UsxtXw\\YjhvUiwhhP?erGakhuUuIrnLQtLqtPqTMUTMmm=SV]UVuUYuMe@L\\XM:UuJISnpXUYu:dJSls[twaonY`[dHbtWZbgox`I_itexdWRWarf]FT?UTMUleu=ue;AVv[YrAdosvSSEQsDQGgMufdIwciYAwREEfJMYiwUtidIaVd_hxogjOVqKUCEuyUikQhlOhquwXIsCIsCYsEYXW=bioWLMdWSIp=d\\GhGCitOixUYACR:]X=;WW]V>abiyGYSgSieEydKusr_xSsf<GwYIXl[X:;W^_r>arhiuuwxiyuyYvAyckIxkif_gfmmvFIvt_FScGdKGtCX\\xLilUNyXlDmFYJAlKv<YjGx]yryXu]olUfg^F`bxaUw^y`nrApJvk;wtIP_TqceAoJiwyhulFid_vSfi]A]?Hn=wjpowVIuUYuUGdKGh<ajC^^hHpLw_KyoYwafpcgOZH^^;>gjqidnuk>i?hlKqaY`nI`wYybigaEWmsO_^QkWA_xN_x@x:^p\\FdKGdOf\\ON[DN[lN`lVypiwm`pn`mnFgLvt_V^\\N^powVIgiwgiAwbAy_YsQfdOc^aif_gfGv=ybAmR@mYIYFeSWq[igWUtaWdgY=qSTETCMwxWVTufqITUGX\\ItiuwbqRn]wRIHn[HNqtPqH`kF@YgHCwncHocitexdeyKUC:?w@;t@QtU=wDUW=iYXygmMCSqbhwICEvaOTh[sqkRtUBbeIf[Gf[TN@lFmXpawSAnZ@NPIp\\`UGymytmoXnUivEWlnxb<Wm^`n^wlhfex?s=qloFtQP]p>ojIdgIbONbliedpa`ihZO`mai=xef>em>vnqqyaihhZP_hMItKIy@Q`dQwdykYvaHasFa[F^[^f\\uXhaq[s`er@h[iwUypkPaoH[raZ<>fQIe\\p`whxgQ^CIang^`iuvYxI>xEI_:Ww[`n^`b<@ccGgc`lN`dN_dNytpIx\\N]X>nJIp]wrxhiuqyb`u@Qdy?ocAjmp_wy[gAwJwxW@`IYyxY[uh`FOyy_uspxUYh]@pOisHqshQuoXg^NrLPdrWiuWvfwnBpg:BP`nB=sDTwXims`wcaY[LQSqw<YR`TlCPO;\\pLLPlLPypytYwnHWMQuPqUpQttQqLqj=aNomJBEwdUsIAMiHvphkOymeiXiiv\\hXyINwhTQuTa\\N^<OeTOeLOdLXW=VmqvGamWPXlMXmmvFINiIWrtk<LnU<RUqtwXlb=wDUW_EQhDwgaUNYMuXKI<lXAJZHmtuoYMOaEWnytumsiTLOiupXpTIQq`yMllf]WdMYuMynIWOeTOhkGhKQItn`pnxlitUleMdDOcDtPqt@Iv_@kh=Jgmm<uNk@pOptwdV>IQAps>mqS]Xc\\MciK:Lm=MSq=j\\hwyDSEEVpaNohyyeWRTybIvM@wnhjSAkWYP\\Yv]YsEYsu\\tGIWAmOaxSYpsoEpj@pj`r>aRHqyDQsDYuqxWuTQuTv_ARnUJbuKNdn?QrPEUeDSmEm=Yx>=yehNQUNKpu:<ns\\J^pyiupTersmPdXYqfpy^esXln`gEypYaf`qsWXaj?v:ilevdLpx=yjIVyqywy>f:AZhXc@`j>`qwWypqrGX]GVaeXoehwgiwG^[FnqphoHNe[^][O[jy_t?sBXlnq`lyciawi^wM`fXF[E_vaPdVqn]oyk?ZZI]_VqS^cTfyGQyWanwqyLxfAN_YPy;h_NN[?Xw<yxiyuavl^no_av^AlbqhiquwxoWagF_cF?gb?woYwQygWQq_gf_g^]V^M@lJ@bTqpppp^fq[`wBpGUiLYSPMFfoX@ADYwx?_wcisw[F;OS[_ERofAOG;;BIqikkGTgt;GrrUhkuWgMYu?XMOrIyfpyv@mgciwQwUxESGeSOuTQuewSYpqvGYeAwCYkyoWuv_XcQdhoghGdKGT@mR@]TN]TtMYtoeXouLifEeb?gbK=X>uH:@lDuVCAtOpt@mOXyMDTsSqjVUjYMxmITyaml\\KOMJ:VciWkaA`S^x^ish^nWhi@YjDysYywIhpVHwgysyvyFV[EVcB?cjGhkcn_hxGX=_FqgyoUso=T[qhESytGBnkTYoGLGFe[guOSD?XHcwE[YxowpYVN<JjATIiNphYptO]epmtSVmYmHVItt?akF`kPtOX]ygau@<kh=JyDoxeU_PRP=UomLiAss\\puqWvqNi@UN@K:<YbxtlTqtYXOyVXTqnqV]ymbHKZLq;N]opgWPbPOeCQkkGuu^fAxumhgxvcJO^:>v[fvOoxdnsEHegak]vvMxphybG?\\WEbMEGCYcAdO[uMYuPuea_F:If>=B:YR^KiK?BAQWaWiYGYuWrGcH;]X=;b`GtN=dCKUheFgKG>IInGsekXq=RVKS>rueyLqUEawRewngyasugqIFOeZKi;;RMaCJ]gGuWLMF<_e=UwvSVpiBxsRC?B:wbtaWXmt]EsvkTucXiItNgiAETM[:TJO`VCMYM@wBiNwfimIle?tE^lBBXKwqgYOOd=aWPUI_ux[atwyFJUD>u@XYBiJgtMEiPwhOypMgqMvQL_LJ:^ntXtSGsxy\\PWyWq[qa`qXtbH[\\X]JgpNX^:>ZZJ\\^d:^`GpgIqsqg]AAhGwgHo]Kwb<Q\\KO>@TyhUeeLgqVjPuiupW<Sy\\YHdP;]H^e_XkyQdEG`[FZHInYqo>_mr?m>P\\;>Zi@db^\\Oiaei\\fwytFfvOx`hiSvbiNnf>khCnccxuwhoyHod\\KbVmShsVyEGvaX>YWN?[[OiMWuqHouawCaoexgp^wCAaxG[_GbnWZ:pnk>wMik^xpH`uLYu<XkIns@O>=B:YsnqfhQiOmyQGcyefqgXuWhHuU=EUJc=lxOxxWMPTXPwHPShMfqOv\\atF]_NZ:bciS=iWU_yFGxfWgioTiAsxsY=cV;]X=;JmLSoXqQo\\<QZv_gwa[`VtpaeRilAygKO>`OwHTcPMhYuuHuRUphpNgtuPhYkqPDQ:nrFge[qs\\W[;oidvftWmwo^nQyM`\\N@;TSi]YveyItwbQQCQxi`xp`WEYyEqmbTK\\XM:\\PGhj@PNCuW<\\YVMtUasMErqtm`Pn>=J:Yrnqns]YqulkqLoxTR`s>ungtMhHY]`OBpW:BEqyDuhW[ssStUceKUeXqWyS[<>ZXonqXluOaIX`eXyH@sB?elHx]icy^l?FTbLQwkeY[GGaMYeGfmkNS\\vwaQWdN<<ZuabayvQQakxpmhlCV_whqV_phvvHieNh:bS?HjwtOiB`[yVQtUad]uxwyU`Dk:<jauMdQj<LUapxCikpLV_xpQlXeMXwPJKmL>[MxZcvesihNfl<GvFwgMnkVYqU@l?P\\;>ZIVtUAjmwZ^gcGnyDwgEnt^Qy>Fnf>kh[MghNooRiiofq?n^\\fq;:gYCiU`]dxCWmCWnwDpUglay==TP[RqbcMiwwsUQEkmfqOGTcY<It:AfQE]:>r]ax`_avp`whtJqmUqoBy[v?jl@^tHZ:WtFQ]Pyxnae=osnqdKgcUvhrqu=`vI>_K>:Ora[G^gYKiUTAXRSGwgrIqXd;CDsyQyiD=YsQXYquyShmGx_MDKiC:KwFYteyXlmsBmsxMdXaGWYB<yux]RC?B:wVciS^Wv:YsASIcYwxYdXQb]siwyFUqhfeIp]vBYu^]eowCKiC:kypsUYex^awigfqsyByXs;GK;BjAHwgClAI\\cHv=HcUHdOg]yvrcYDcctqTf;f\\;EZKi;;BASI=ch]wiR;XpydOet`whbadV]dbYyEuSE<lYxkt<RudSiuR_pjH\\oGuWOdlkUpVtQAxrveW[Qn<QRlEO\\LNDPq[Lq;<ryIU^=ox=X@pQauYCeVGAWquyR`pv\\lbYqCeSCeUs`Y?QwOXo^]V_ETG<WQ@y?aRBMYM`tOqV_xpaUtQtYCPY<IqRdk@UsBAsZdK_pMD=OTLnU<JjXU\\]uYiXTpMauYkeRoHmexuM`XfEJdEXiquwXUhAw^EVdMw_IwcaqheO?XvBLL:pxMpu^\\r@durLOs<UmyonqV]Ax_Itmlp_MN<YreMWd]LN\\LthXeqjDHNt>Zh^mF_`qYuFvyDOimiiPHjnqtLOlYaqk?ebwgcofhYvgis^O`Gi_f^hnghKo\\bwu>^^>yZWQa[FngHbTaxlQkao`EP[]OvTn_jgxDi\\lGat_k_Ng?@w@>ZYgpVadeww^InVhy?hvoXuXQvmP[JO^XQiwQwOygE`]@qkp`qY>]BObUgwPA[xoyOqse?dS>yCOtUAFafrodTeWtLUxaWdXR[]wmMthPohpymusXAvuIRv]YvUlapS?EnTUPx]l:<vAXUgEnGUVjttuMpiAQvIqfPsfAjY=sDTOGeJS\\TcHyLTLMtKsHqM`r@qtyTXPyOw`lOXueYp`HtbeJ?dJ_iv_QsgyxsLRMQtU`n>pkaIoaTvayl^\\q[hlNpQUPVYMq[EttXTaMolQWIUwlhwqyuuaxcYjdDNtHJ:yqRuVs<l@uVfmx`uuk=qZ`pl]txuujhTPQMlQtbPdfFv_Ys=pghGr;GrVXb\\N^\\VcVf]UivmpxpqxphpohyvIymFgqGwLi^avnKWxHa\\Qv\\E?cB?fWHgaIwgXl^AfIYdIxrGyirqxOiiDynfieUAcafeZXnOQZaHwmvfZpaBpg:BDqFeGrnkBmUiiYThCwGifpTTeqtCdTdMoaIxkyJWau=QR=uqp@rLuNaDWcqxSTkAikUtlV`mv=yjIvgTUp`kVDQlHPyMvZAvj]wRIpsTX`amytYXTOIUQPxmYxYxawsXMODmY`Rd@sOmJY@VKPlHEVIINApuo=TGdSrisrxQD]jbqJ:dklhWVpKWHrRIwYtrPymQMTKUqgiW_hXypoL=oLUvOeTOequuxHxkIPSj<MFls?\\vuxXYXPimWulo:`kF`KGpR]dK]UV]qrftYwQyoMXsUv@ikmtVHAxkIx[eLduYLYtLaUqyMrXMJ<rTEPrin^QXt@WOtXQQVlYKkpLRMXoLlYxkduQLeMoPRnS]_wR?H>orZmwslmgxQa@ov]txumjhl]QynEl>elTDSB=SbMxNHO^yU@MYtQt?yq_dN_Dpg<pTIYGDU`hYQDNnpWEXnKHlKUnx`QfUupXXaqssYxaYNqhpEmuXmUeimQqTPmTL=ONHl@pj=yrHMXFTsg`nkxYeHUnE_yfltYwBfdN_[Ki[:juMtJMMWHvluy?TUyyj<QX]uLYxJe`oOMQ]dqodS`mVPMSDMKUun`plPhlohXuqY\\iLOdLIxMylwVwfof`oprfvq^p[P?mpG_tN_dgjMQ`LA]_OflPigX`eAe>f^G`okwjiqdm_nqVqEv[b`lHnptAcigoKn^AFZbgkpicWnqFabMXpyii[GmKXkIOe;G`D_trGb;xxQnytYgOgdgqawNn\\xyVpuagu@hxgqiHnub@obPmTPm@owbqZgYa>yoSgpT```wSaercYdoyRKTEcC?YIEgG>;yr_b;SiEsCIyRwGRcADW<R]ewqHMhAQDXsHQrSyUDakpIy^]YdN\\onjIxpqQl?YkC_i[fggIj=voXAqHQyc>tNauf?sJIngqycyj>`jn?gnqkh?tHHiYIxtAy[YjlPklqjGWmRqjfVyeZaM@TlstyvYjEykYQnteoGlYjdJbenb\\LDXwndQTTjs]NfDlg=OmYXceuitn]aL_hrJ=oi=qkeytqjoXwRuJb\\KWlPnarcYt\\Pn\\pTPqtxmqxXWVxtpTx@Yn\\PnH`MsLTR=UbmV`mv^avNuuyIv=yj?UkPDMSDMg@UkPvAxTZYMuLq_dN_DKB<KjmsZiTKET[QwdQMR<MRmTPmRltuphWUaj?hjkpOohXxpQx\\vlmoghOytQQxswUOgpMQyLTPuV@KdHnm<uLYuVXP[`NOIubAoZpjgxJpPq;\\pdaxp=W@py<UJhTYcdnO\\lJ`xPhy_`LOMyTXkaysiXU]asDiW]d[XPauoloYgchj_AwcY`aO_e``eoiTy\\ineV`asOxNIoM_^nh_UopFysIyox?knYyrAyfpewPqtPqtyrP?j^woRAuRGasFaoghpYn?V[DN[fawfa\\Of\\SQymOhloZH^]rpiwQyaysYxqxgytwwXiq]yrIxrt`tPIlyY[\\qmOqmh`tjYwAWoF?]RYwTQZMoihWuXqfV`[xHynf\\__gw>pOi[ZtciwRaG=KE=GX`KdwufM_dvQVPqhqCYcCTNKcGIx]wrxaumTogmVhmwp=wZ@nZ@NeQw:IR=pJeAwnTx=@X_QsOpmXpm<Qr<a_Vqat_xb_wRIpfHtSWp`GqrD_cF_cDOcDoyXDitxgYuAsYKhHmrOabqeWxmYauVaIR=oBwYwLGdKGdnKEGWwHoWUuhheFIKdgUXTeSGec_gf__iv_yOYgQehoghCus_YsQgWgeWYsIx]InyFrIXsgEEASIugf_gNgdMgTJ=Trqr\\Ud@cxtOWaMHgaRJSvyytCQunqXd;eDEfJgBJ]S>uH:;WNMYucHAAd;awjmc]ud[yXsuY_whhOd\\;GNeiwYyVmcVKI>QWUucUsxaqYQobyKDCIsCiHmqxweYwuRF?E[kFPUyeeHeyDCeGgcgtITOcDOktNSELOdyQXZ;hTOeTeTOeTMUfUDJ;psWXQqlVCmt]UvVItgYxaysSIeAx[YnsPyyaymyOl>qhlavCQylGlRN]Pn\\Pv\\Qvjbqt`HkDHkgphpoflF]yQq^al;QsQw\\R`srF]FqlXAgnornYl;w`fis@YgqabwF\\WA:]VtUECmuFuG>uFmgC_svPChLYUaEcH?GNCc;Uip]wvSYtaHeQgGaxcuiiauCYxcKsX_IsMVauVQIfhaxZoIxkI<Ob<oV`mVGsDZCrHeToyuaeTRSUagvdGxogmWEqleVXaqs]WWhLOdL;DJ;Dr;IrfUy<EMTLM`qv`QVOQWMASPypq=UNAs?hWn]TB=TUhY`\\lgdqOAtSTTIxuqaXjtMeht=dNwIpjxoU<RUArAenXHme=Qm=Sims[xtsdj^dq_ylN]y^iN\\=PRTmp\\WbxsgUX`isWIyAyMgDPo`wpiwUilN`lBUj>dm<Pj<TSEOdLwyqolExsYxaU?eR_yRQgNplPPlBH_eV_eHn[Hrp^v_iv?Imaq_WOqnxhiqeHyerGsgApX`_vaa`o[gYhpomKfl]OwVNlXq^Xf[F>cBabC@\\WmRaxpEVxHPQYRwPlxlYkDuiYymtnqLQWpqtevdXWQmolpoTYQfLuvhXeUSIUupevDilTyssHmmDutYV]UVU]XmMU]]R>]RJPmvyowXy:TW\\aYvAJHmJ>@J[uwGLJDLP^EO=IkUdRnhX[qpTepgXnomtPQoydptyoPPUgUwhetTuRW@qJ]uBhLKELKDTSYYiiM<\\jyYKkHSF=t\\AJL@xwaQvtxVmuEtl]qKHxgqiqqigkHnUF_QFsT`br?ir@iON_kWwPioPok>efCe`IWmYynqY\\yY:eSciWAidJ?uF[w\\[Rq;jTaxp]VpxsRutPlmH`kCQOX\\qoQVKeNuXLhqLHtjm@xEHyausVHvw`Ul`WcQpOTOTQy=EqVmWJ=TJdk@UxMTMLHj>iMauVaqtf`npppPhyP@Yw]twynQixbqRlUMixX\\EV[EV[mSHmS\\YOChkGhNuqpOhSeAR@asjQwtxWTuavQtPy`FHusgvdYpF_w\\pk<pph?ZL?mXqfsAhshkaXnL_bPfbao\\GnysQvGhr]ftO@]WxfA@lnV`yYpIygovpeQ^xHyhgtaVp`gp=yv``n^`lQxLmXp]S`YGg_C]SF]CS[UWh=yG?EkKFr;IriExKyvIymYFAmcvUxu=Sv]duyh[WUkEXkmR@mBi[eK_gSmTPmTKET;QVk?yimIkMv>Qt_WS?mt:mumSV@ac=sBH;vIogMQy>YiUUBqGXHIfUQF_iHVOYyiE[CrEkbqywd=cw_bbqB:syGmeHUItIw:IXuwgXWcHUDS]DOoUr;WeibeyUG_TeaEcigtOitmsfGuqQr=ivTwE`AUqGV==r^ISgYxKIcCGclugxSUDYh]urHgHemtnoVGsrIwEi[Gf[YAos;]CGsy]yy_eV_eFC=dTMUT]i@oWAwCYkhkGh[yuQUxnaxVWIqmGc[v_YSlGBqmwVIuxgQ[iP^qv`qYvIxAYvAykQtWdtJWPsahYfUwU<qYxMsXNXpuvuYs`XsEniuUUTJfinpmjDTT:Do^@RahmRXQRyt[hjpYvKHW?XRphJQhTQQsvqSb@OitmxdVdtOqHTc`tgtQ?lpUmW]\\sFQmXXp]DxB=qj\\Qv\\U=UR]hlgQyOhlOHsD]sYQlkHpkDy[uuvpvN`lNlOQXwZAv:YKaEr;Ir<iPaxuyuywinEultyxiyynIwMEq`qlsMmTPmvGaVnshheu@sqQqutEqdgSrYQEvmtyWypIcXQv_isciGrqS<mCpETuSrWuH:CGHuWamIUKvyYUBiVkoF=yxMMxAwWy_XsEdiOGMERPuYvQv\\QvSSTagIEgWTcFFmUXmYeqxgUr@wCiusG;wTiheCCXEV[EV<IbchkUtSX`QSIvutjf=MWpSaiJl`r>aRLxO?xMWdtOitwpXgQuRHP]=SxTpkHpKuTQunKAWuyxiysIysyMx^Is_YsQXWeUW=TJ=tvHimExql<vS=v]usg]WvQxiYq\\dvOepGyxXqLsQYoEtAqUduPnhpeut\\uOBmkJXSQXv]Qv@pKYltohLWPR;<tb`tkpoPtKLUKLPKDiRPdVP`T?hN`qkqew<MLXUmhUrxyuyAof@oR`Q_MkppppUqwAv?dJ?TT<lN?iqrER`IMFlriUqpmKXLP^hmqmQ?PRkixoiQl]vBiletTr\\MHDSfEr;IruuxhiTLMwrqwKHsxDNshwbIt]`OPTWeqtgXQqmw^iK<lra=Wb=QgMunLTRDMSDMUTMUHmSHYpawSMlaQXmUX=LJ<lSV@Q;xnDER>xj_pmTTT[\\NP]xcaJHeQqav]`LYpo@prT<MLEqW@vhXM:`XM]laxPWYYUILlewsmlBQnyMLmeYyEKx`qJyTCHNiTSyLXpmTPatCYTLQTMEsvTlCaumYyxtSitoHDuLTMUTmausXhr>arJ`r=MVVYyIXtjIJGymytuYyuydPodX`asSPxliOvQJbEWceoXeqt]urHXpmXpUqquwp@pj@PkDPkppppWEpmjARp\\Yo<skpq;XqvaT>@SsEiHAlgGrQyqTFw`oo=hqNq[JqtG>bdIl^ohpYx[h_xNwOnl:OtUindQutFmsIfMQtLq^Hxm:YsgO_fnt;XbyohNog]Yhj?hR^ar?p>gvpn]LfrtaxcYt\\og]Y[DN[\\vgZFxH`yBfuthh=og=x`Uo`nxr@I`wfrEIctW]nhx<YnnPZfQ^>w`:>ggOiu@ay?eYVwPNmU`j@yvFPyg^bpNtUOf\\Ov>Ip]QpmPmhy_dXoexyo_vjYiH^^IvnIwmhquwXyUXvW>jjhl=imQikdGviqofH_whev_mK?kW_jbqZ:foGwgQp\\tQiUgpJpuhxqBQ]mXxDVqhpedxi:AUkXLAyCcB?cSQgxTQITyRxqI`uwZAb]qyxKHmSHYkIv=uDqu=GBrqiUCwtotIiTv_i^OiP_fqwFSgRRiRBoW:;tdKsGEwg=iagfX?y\\WGIQHAawrOrcwWJOtYcGdKGdMS:=RkEXkCeQyHj;Il]wiUMuPvBxqa@nZ@NldXkEX;qo:xpoprIiWOAkPlYmMkdDu=tYt@LUhUFhU>@w@<JgPrL]TZDwgxl?UK]tLWmkGAMmXTdTtU]rwXYmlnFeobtoJXWhuqo]w>IXEqOP@QPywiLPlLl@Uno@QHIO:yYTuwiqyoApXLv_ijO`w;DjaymaalZuL[Lq;<Re@ocDP<mLsQqShpJQWx<Q`dYVqwePtOpuhuj@psTHPmPodPkFYl>?uCY\\@qr@AaDy]>qrGX]]N^\\^rA^j:>g_hcYfxTOa^hjKygEN_TPtU_ehG_pG\\\\X]:^ppfqWgyd_jEHgEf]ghmEpcU@qqQeW`l^xpeF^[VhawiDqfmHsvw`UqgAwyxYeIwcIvrqYbk>`j>hogh?qi:xxkhffxrQWjT?goOmQoe=OtUObXG]pG<b\\ouVout=ebEciKIMcdT;hiQY=sdeCvyKrsWhauDvmy?eUWUtmGhHoSHubIgEMQWAqUyEBZgdxMEiihb=VECwgsffOe^wh>aY^wH>uH:;WWcS_erewUH?XnktNsUnMwKMS:qUCoSiuYYcIp_xegrGcCGuXAcuViuIkyo=SGeSGsrN;RlcWWswssY:uXkQxfOtdKdXQd?qbuEB>uH:PPgmLmQuQUNuXMd=kiLQKDmvdxIXmLHmXqKhyQjiwDilVqvgUxhiuuuyYxJS]OPlk`<j>QnJ=OUyNtuseyValqbTp^HOwhnPlTZuO[LA@wj@mqtlrIuT<oExOtLYyDxMXj[PlPpupewRIpxyYyYvGyKV\\PjusiYyR`S`lk]<j^ynqhMMPYIqwWQr:\\ucirO`NwhVNtT\\uOw=LRTrN<nm`nqpYylpjArQym[IxNMK_ykciyBIWqhleUscdoDPsbLYThUFmS>Iu_htsivo\\njYk]tXFiolakNilgaKNiMF`ptHweXTc`lq=uNyMqtW[DtGxPiYQl]RZqtg@wbyM:MkLYuXHowEqGhky]yMtNl@Oo@o\\xYZIyJinxeoVdnx`otpP\\dNyIVTERnmVkmTceThEUoETOUt]QSD\\PTpodTt>URS`oaxnspkuHqhXjKpvuhmg=LWAJ:MncIodduV]QL`nq`JkpN=yJhqrKXxXqqcuWDuWVmW]yQCEqAyM`dUHhsB]sye^OVttqZsqn;QdmooaQ[XPeOeRSbfec@AIU]cn]H_EGd[h`UCUSEUsHfWUq=XyIBXYsIorx]icybY;H^oF:_t_whwWTuIXUSeH]G\\ScLWCDyB>keygh^]dKoblYwxgibOdwMxKMxcyRcsH\\QheYETmgJ;si?gsMeOat_ywXAhaaVdwg`_HtwbsAUQSsxiUG;WNqSKudB?OZXpj<TQmWxxxpmOC]oCAPs`R`XTcXq``xKtSienOipuPRYhwwXx\\ioTLMQ`TQqmB`S`tUDMKnISwdoPdKn=pqLtvUruYMTLMPuoTexqIt]]qQXla`SSUqxeUeyW>LJ:`vZPTcTy`hxg=vluKWYSJDU>mOvaYxMNcisI`mH`RPdN^ilgEqLdya=YvewUmXW]lUmTGmsK]vEQTAeXkANAHmXeUO@MllYepmppXgQUvqmCmkJXSQXFZqpgRY]jIrcP`OnalGprV]Wpb\\hlBQnBax<QjDopihqCvajFhdY]pvj>wkWiio>a`feviyvOgcw[bgxohv`nsG^kPno^XwT>qIPtEvh@pauGlMOw`on]po>AgkvpgVev`vnIsM_qQXpaaitPgoQg^q`:F_HwgNNsbv^m`jvQhXiwkFf?gdox\\]OtAIqTOovY]j@cpQmy_xHynAPb]VtDV]rhkiay[`vnf\\va`]wyWAalOnmo`Kql[YhBnwtHZno_@Q]d^qTXtNQ^KyZxphVQk_XdcvaI?x\\vnvXgIY`aqyOnxtXagobdPkpNuDqvTd[Og\\IyuaxdkhVaIISxteTW_cLmXVER_MVKedrIwqywAGSaqe^ggoYXW]IBIdHUDNMWj=IVgRmyDVeilebqQX[ydYmGvQXKkCM;bnWfKEgAoIS;TYArwCDS_Gl?w?mWcwSZibUUSwahO]DCMttQwr=YseCA]YG[G@cu?ATGqUYgV`osnKTM]FiCEnMW_eW=EROeWpEIuChbOIlSgnkiZOS^aVMWTPeIaAtgiYqmUVcew;tLuROCtG;B^EbcoDEwTmMehkx:ytpYEIUEUwgRwhYAcc]YoacBmGZeuFgt@]XMYwaEg?MDUsivQivcgDmSh]RqcUmUCEkUCeVgeY>mRCifrObeEC?cHoQbPQGo[etiDaOFHwIFMIxsVjswNOUMUTmirvwshub@OxXAh\\evDySaqs;IB<;dS_xp]xMIb^aRlMTfciwSscCFQ;dW]XRuDX_fE_GLETZGySQwGOhMyXl;T_ghvay;tT;eNodXqLlDts@qvXysbdLxTVWySCypyyuChYMUyHMw_ekbqJ:Lp:aUuiVtUsfDoLDUnYsGxn\\dNlaTDAMueySmw`pvTLSgHUsPK=pQJQSA`YK`Kq]yCmx;yRSHqOLjtqtBap<uxGxnIesULvh]optVPaoBXYK\\qlipeytGEmtdLApJ:mrLYuKHUx\\UhUvcAoNDl?usmMS>mjbxt^MsIIw_mPXIt:EU[hp[aR=HOyIpwHJsQSb\\oTIYidPriRxUnJip\\avYyWvlsbLy[YvXMPPEYDpphMl?dWWAnWAWbTP@EQShmx]lLErhXY=Yu@LUcuwRdwjlrXARWHulUsYAnMyneXoexRrikNutJdwryT;pSomPLUmbaVbtS]`RaalmYUk`tNiPviYqlPnuvqysY`REiPoLW`pyYqlGYL=LJj=T:\\VldqGHXptkC_y@HtbIcjPm`QfvYubwjXonTN[nxhsOcNWcCGfbhkhxcQfwRaqD`ydFboYwWanv@yvQpKok`OpnAxcNq^iZbaqf`hOqghFxm>deGyXOmDPZgyfypw^vpShphqfUYwjfvcWxw`_h^sbIwZxylPm=PscptxxhbV`kiZSxnMIwUwpgWyr_wR_]H>ZSgn:wnWrFKE[AVTQvLUFOer]CBhsutAUe?HXyh`;tHucoMVDWwaqe`MrOcgAuwaksv;ETAuRAGmSyMCtG;fMUhPYWDuWt_GKIvD[so;eakfrgCiQguIfx;sNees]V\\WsruR=KUgefKYb=acD_YL=uBefg[UuGW>wuB]EB;BSwSiufySEl;hUGdBEiEGdTIgckg^My;QVGcbl?sUQXqAEAeFsERi?dAWFLkTXGiI?w@;BlKfeoitWteWRNYueYhxqe^QWcGyTYeguBqywikGhkDisWb=WrsDnmHocF_iHaqWdaYacCu?eygDdOcBYShcdXWvvkXg]TOmVCkbAIBJgYlaHd_yegd[oU`MEy]coMtJMTrAvYgtQQTeyckmSdQc<WuruIVmYV[DOObbqB:DrpXwktTYxVkyUTQwd`MRtt]iXgTurMWdXW`usRHy=qrGutipUeXoeMWdtx^LyCqqwTYBEvKYrAhSFUUhpLCQsDQUx@YCeXkERMmW]HO^AqH=oKQpb<oZuYvXwd`nGXnD<JY\\uPYWktl]UPryOuEmbxwXTvBaliUoKTTVhKOqXy]vBAnELXHak=tpl`rX\\s<]X=<JcTlV=TxiWJ@nXDRYhrZtL;aoyQWkMvciwGqVmXRieuD\\ulhnn`pcHwkqoWTQHumvdlQxlQYt]xTEXnQen_pnhtUl`pZ@nctpc@ob@uFxy<ho[MrU]XydNyUqRYVg@ZP`nNnqlOokfdaoydygi@biWuJrj[Tuyi[MbamyDQWrSXxQiG?w@;BLiW[IhyMgdUwsUxlaTDqxKmxTggb_ij@VIQVkPUHeXXmU\\ijCHKCTOPpOeDWhXVOUTMUyyh_vAag?kGppZ_x?xwHqaBi_epr[AZJhdEnkxYrhXgZymdopsihQgdfwk[QovWqcii\\qf<yiS^]MpixNaGFtG>Z^htGy\\Sw\\]_ZwIfHYxjVhl>gOwv]a`TfoaxbiFxloZ=HvfQv\\Ndra_pIuDiVOxlqf;GEncHosHAkBTmXk_TZGTqocfqGIUYsAERCcIWgIiI>ID;;dCuXMOX?wSoseuMeUIwkOuiQBOYu<=i_qwqGRqifwIWM]Rq;bHYWWirA]ysUTomvVoU`egyqUisGiEx<uVQuDLou>WS\\wEAugTEilOgdGgwEchoeXqdgwIS?ex_i<khLqTPkiTkIjuHhcUf]Wh;JEtnTXKK`ysULodrIUYTp`IwfDYtxX]b>]MG^`VoramNxurWbnWZban\\O`Epg?ifmyeh@wQivgPi<ahkWhOFccOvsow;iyuYgPgo\\WpSafXAsRAiE?fZHj;HjjY]`qxlVtvyxs?ktpZhqsJyfrn_:N``IepGcB_g`vy_ylwh__Iggimw^qFa`wfc?fi@xyngxCNnU>:yViieQ[ysUSGeFYSGgyhtqXLWuV]UWuUsSeJEg<ihbwyVIimoYgyyr[e`oWGisFasx=ykUcHogH?sD]dO;wM[eFCyisxWIYKUyiUWR;BJgCuyw@IxaiSNaLeQoMINUHPqxlZqTYiw>`m>ayl\\Rq<JJpNG\\UhIvB`JxYscpO@atqxM]yS^Ik>pwpqxdPoiTmDiurpYwUt@xweYwUpM:@plpptINjyRGeSGqLQMPSIuBxu\\iojPlwUOxTMAuJ:mlVtYR`rYxmNYrBpu;UJLEYRPWRHoELyXtQSDmF@w@<ZC?iLoekgtEI^[IclO]KiwWobG?w_ItEP_no\\pAxnavGaet@]V>qsW[qHqep`UWauhcUx`mY^W@aWff@wgmFbdX[t_mDXn=>^mnmaal^x\\y`wmWmVOnG`pOYwbh_[@dbnq<w^tXtLauwv_\\X]:CWADdevPYtReUgieXOtaEgdOuu;IBKfUwTM]XuSXdaxiSupGxX;vl]XlMyxyypCGeSGyGYwSr>obUQih[ts;H:;SuWgIaBg_utGwd?wd?Ht;X]mBUUCdQW]StDSWrcxBoW:;FokE^ovEKfUGc@?x\\_eV_e>ab>oThwrEYy_YXCkvPkD@kB@srH_EWYiuuHi_rwwVIyyg=Ui?gb?yHkGwYB:;r?]VLCTJctYWGkUHP[CY=eJwUPwUXUb=[BZSE\\OHD?ymiiF]tukX]]WoeTNuygyWVWuRAYiCIICtG;JK]Xe<vIyxj\\Y_pPMUSEUwyqqYAQwMxNhMypyPdxbILihqTYwjqwnHsottPpwyiyqyQI\\MZiqnqwgiqdesdExA=TU]VfprNqLdyJrISPELH<L:`WBpsN\\ystplXuBqPF]QNLKCuWvylkDU?QTtxTcAy?QJbaWdDuoEY<uXp`ooxUc@tN=TJ=mjDOZUwIHjQlsWXNYMSDMShmwhqmXqU^MOXexcXoeXW_eWO@mJ@mOhlOlLTLse\\MZYvm@YSQtPtj=QYWpWtPOqMTYmm@UtD@PTdQ:`kBxsedvIYUdM_jiwkPtLokBAisHcSQduNjENnU>baXlUo_rFfk>wNg_kHli`qvhqqhyntwsVJeUWeYu[HN_YKIwnuxXgIw[ivSYpQw_of`;g\\axnQxHAsBAvaqh[qixwUf[U:eYEybBaxN]DT]uv;BJoUo[etmyrSY>GdTpKYaNwmlZPOZtSdUu`=NtHS\\xrKukCyqC]wA<W]DKseVDIqiTQoUtZMt=qWq@tg<kHpohmUhmojESweYw=yWYq^Yk>QPupwpmMXfaw`qF^[GfsFasdGuiv]Pg]wItRxcaqs_`qwwa]Nr=vnP?peAhF@Z^?b[g^U?y_VkKIxyytN_jpHnbitGYbnWjqQxaIj=^ypVb:fglGwc^`yH_\\iwxxlEivxfksOcxpxgIueOg`ov[Iw[@s^sTOeCCBMsfIaesqyUqTXUr;IB<TJ>xjDdTK=nwxsdPMDPSDqkXxNmLKPlrdTNvmQBqvo<SgAS`@khMlBIoAXl[HnKlx=\\pSinjesGyYutJ[MsMQyS=WCxqalvCYllPpqdxplW^]V^Iv_ivcivSisPqXBAt[`NwhqhXtWyp?aT:IYC<RP<KYAji`vvxt:EOGdN_ivyeJodmY\\qVmQN]X]hqwey:LnU\\qPaxSXPAEyuYVy<RUDYThTv]wyuNrUxT`SsyWx@wgLx@lOQXQk]urqLI]rWUqoUxnQxlAxnavIPNI=MTdqiil@eWwtlyto>@w@<NM\\pOmUc]uPETUuu[iX`hl<eWiapN]L_`XAQvNDKJIwbQp>Tn;aLQatkXwT\\L_yUcXsrExviR_eR?ty_dlDepq=paDkgxWyqyTLMTdWkHSshLo`yseMchQYPJ:@P`PJWEm;uvyDoJhT@qw`\\tqtRA@LxdtbYolDLWAJ:MWhdj?xsaHW_hPWeXXEQYpUrtYhHwnXs^MqtHqs=YsMquXqm`TUqp=mnnPT;YT_pnTPOrlR:VjGpmt_dtG^ioas@qdXr]Xe\\GdOviXAbGG[Ki[:r:efLMicYgAmfw_IYor^qdEsRq_xn_H`STceuqYEV_eV_vO[DTIVuMgrcxCcb<WxcgfHOGHGD:_WjMHPQvAupsdvxhunQQjUVrhkGxsmiJWqRt<McMScqU?AWD<JWHlUHmJAUxEmi`QH@VdmVp@VKQRqtXqqxCiW>YlVPXhyqIMYcHPO\\MGhpj=j:\\V=XpC@vIImYyLhuR[Dqg`yYQu@LO?Pv[EoadnueLKiKZXPdiW_<wX\\vHMUktp=uMLxqK`NRLOAYuDuMAuJ:mVFlpmlvIyqByoFyofhw:iksPmZ<M:<tOaSUMYYlVA]X=<wF`YW\\Scxyx<MYxUCIYRHUPITUMRLUVB]qZaYtLt;aLAuJ:?po>tZypXg^Q>kQnmyXwBxwvYsEO_oieQ?tR^y\\vmyQx]w\\EGwWYoBpg:fmKpnlPfYVg;iygXvIOpuNgEooan\\`iyuG^HWnL_yV`sj_h:^fCAiqp_vIy]vkmPws`uqGq@YoxGabg\\OGwWv]EfqQpeLpdTW^Nfuf>\\WAZ:OsvOuAqlyvicn_yVpfXf@Xxu>\\SHrYxxox`ont:Yv_@Zlff`xdQoyvobSVyl_e;wjforhAknoyvweeWZefeo^bq>:_sAmsP[yXCGeIiGwIYIScuyg=iW_U^[UQUIiweWkcE;J]uVbHPfXqZxJiymiaNQiPjUusUMhqnOtjaxljyUhDM\\AOOYqNDtGMpF\\Mv<WHaqspTPqtRiLJqtRPKniN=hJayoEtsmqM`mpeYxY]m@lw@YmC\\yQpO`Pu<yvq=JJHMYiknEvIyVNHpqquIuWIySauto\\oypOrdtr<McMysLSqUrF\\RqDslLtIyWsytYUuSIvXYJnxjitJt<MdxqfallHTHmWO=sEPmtpjpUyniWqMTLMS>dpnXMAax^PTc<Qb<JlxreXkxAK[xNJpX>xn@iLNmpUynyQXqdNs@UJIwqqnkdQc\\LcqQOANtHJnmUFeJtqlIhQryOC=lLlqpdWMuPMPKyuYZ<qlqNQDr=EXEiK:mXwQLZisiak]pkUAQyawMQXpeUu\\Yhinr`ywuK>PMNQQRpkj]ltyV[@LWAJtdpCeqfhY?po@xSwdss\\xbTpgxQN`UjuOw@yFxuO`mdTT[yt:tWVTK:DM`EngPqk]puty_MYces<XXk`mtqpg]xPdmMmyoinaayQPWFejwTTtQs:qs>]X=<wfqKFAwihOnLvuqjUDKAdjXPyvAvLMkexVVtYVEsK\\tFqylDtUaTEhj=DJZTuPdKn=LhpPwxlXMPqasMppe]nKdlWmPaaTnTUbdMX\\ms<rBURSDtG<nw\\LN\\LVXQqmO`lN@Tq\\hObApRxVxTM\\tSM\\mGlPXaSVYYydokhK@@UBhse@mtyXNEXG@n\\`veHRHTtvdWj]L:\\VXdj<EQvTsaXoxPQy`vhMUCawMEt_dtVxyvqu@QWpYsO@POTUmIUqXlEpVW@khdVQYxEmTHtXpyw[mOUTYLpppegrii<FcpWx`isoWwPIeUWeA^Z>^`n^`nqwWYerGgZ?fZAt[XbafcT`nhpoHhioqsFgpRo\\TaomFdcPra`t^Pvdqu`QmD^xInh;xh\\IcpQnmIpvI`>fvTXydauwfnIfxgYmFvesPh_GylivuUuahoghgWeY?sHUSEUFaUh=cs<Qr<aeV_eNatTOygMsFasVAh[Ur[YrAGSs=SB=CcstJAt:IDA;wJKclaxKkC`wF]STdkyg=wPgUXUYckg:IRYet:exGEefoGwSidQSRCe[]XqoTlqXuUruCiGgcy_uGeUmeGHWtZ;iraeVYstyt:sWcuYtCbIsXWAR\\gfawfiAukWvRIp`\\SR@toXWQixeytmuUgIkuuthhUOhlO`K@TJuQwwdSkApSixdMkt`LQxQtysADvceriyqlayDQuIqs>aotPLa\\UsEPfXqCInImJJqux=UU`wfawWXQqmmrDX\\=ujHV]pRGPYvAykIumxVQhOUmpZEr<LxePXhaus@uRAUYtMYPmTPmEtLh\\sYxQyYpIqQ]DqgasSXPsDQslMXlM_dN_<QVAJWdr<UUoQuQUNF\\tN@y_DU_awCuRYdWvHmJEOneUqqWXhvO]ku\\MsYUrMOQ=oHAVLuSehyMYyCaShUl=iUq<ljUOP]oRMqnEoxpqxtj=INyAmS`S`Qx_YssyY;HUSEUepTgPplPptqvUxWjxoXymUHmHuLWlt?AmnqjyuSuevohx;uslqU^yTTUWeTWcDOvXrtTOdUwqiuIuUvEvS]Y[eljEy>tphtraqKL=nMqu[emUxPimMmlVFhpohX\\MV\\IwMyn]Qv\\ASZxumxVIpn`pnVUX_`KCqXatSX`NSpQtLQtAt[XRTMUT]qlQr<QRlqYuTQutNatNVlW:pk\\hs\\mkmepv`LUHTNEs`yL@uvNxmFHs[XTclPtLO<iwq<YdQPlmUXiXmhpdExhXU\\EVOyxqLLp\\uB=si`Y_PyoExZuRlETDUnCatGPOtlYA@R\\etPqt@qr@QQtlPoUMUlLPlr`UpwiywIo<uPcmWWQq?mnwYyqyrxPyJmnr=uRMwbpSVYYwTnR=teQto`r<YwChjwaOopNuTMoaPPuTNxWOmu\\tlyHRIQXCIqrPkmQSm\\VddjlHVnXyDHnwlusxLqXsQxOiHUmpjFaR?eRodmMYwdqPgMunQSX]ob@NMYSQpOwlYvAmHuLVhvruxUAXQiKZXrSPWkpMxUxKak=tPIeQL\\k]QTVUTqHwPMvitXM]yfexvYqeYQS<oxyVeMkllXWDQudJ?qvXysbNtrvlc@bYy`oxw^pel>u?ia\\X]Bo_hvLeutgdqsYnAwKMHoYxmYDxUBiKiG;Ej;BuQw=KxdQfYCygyRmwyFcIQce@yG^sv>YUCiR^YSSmePYsNUr?ASGIRYgV:QVR;hNCYGGvrgcGgBO]efOHpMXket]awlYIcgrscDoOvesFs?xIIe=[ig_xYIYmASjQwUyhisGJGx\\Wu@gCU;giottoRAuRMGwditeDmi`kNeyZIr=LPoEh<XnF>t[adNfvIosUNxAyain\\Yv[iVoK^udVo^a`VfkHq^YOoFNasftrV]dH]dP`FPxe^pTxlP^dPqr^v\\`alQq^Qvdy>sffiKxeSQv]adw`_nwkxOaJQbUgd`vhWNNNxywtGiocqrrvj=IaoOwNVj;A]oNgN@xUngXaqcvjupgg?bAhrvVy?ApmxkMwqtniqfnjPbrGdOge=ik^PblixPybMGjx@iJXrqVrWhlRNxiYpgO]TN];Hj;`qYQkB@kBf^_f^iwgKqa[q]wNi>on=qjGV\\cv^Kik>`a>w@MXvMnUxowHwqtVhyMBtkMDYbhqvppXxX?AS`YY`anhxWh\\qP@UrYscyPoqPZ=n``pXyuwmnQuTSlMWNnU>c;@lJ@lLQtLwiywiPVcJYyQodPodLOdLhlOhl[Hn[nhKWejyw[oaVqu^ArWAqiYj]PtExuw_tTfbsOuVqqpWcA@aTVgb`i:is]FqGhs`w[SN`>oexilf>]Yv]YxmYxgiwgIYg\\qrqaxcYt<Qr<q]wNibV_eVvZQZBo[wg`_xa`_xyqrQIim?cnym[IxohxiAuMYeQf]Oi^=h]a?iogvIVu:@w@>t[?iqwt@wkXf_V?k@pggAb;pcUXtQqgpwgUYskH]Apw?ymGpceHVExB;eQuDwGsw_gacxnOTQMyjyc:SxxEBv]Yv]RDyWYqiWQvikrKlkJHwrHX]AXREJ^<lOpoTqmchYqdkcIY\\LPsAu=`ruHSseXGLjALt_IqiTxVeMO]pghoXPOm]j=HwNpUPiYg]KXIvChX>uP:pPkawSYPldpqxpQtsm=WbqtH<oNMkiXjcDy\\utOyuC]sGtSDYqYPmYTmWMlWMUg\\Yw]S_@TBIQNQTAetOaTUYrLuWJhoKpKEHupUUoUv@ikPTNT=Wb=WExqRtrHhM]TtCXLaLlcUR=UrWXQqMyoYwAXjE<NK]pN]LaixmXNYevo\\Mlmms=lT=x^TpbTp^Ps^`w_ALi\\SOdNAUVGUVGdLMdK_uXmeUqUXWTY=eSSloUdRnUJcelUXmEmnplP<pQqIqVmweqymURUITNxnILpolNY]yL^xDywC_bOH_YqgQ`qohpoxxhiuMOdLOhoghgG`LIk>QpbAWcF_crWiuWQtLQdv_Iymyv]UV]E\\WE:_rLeVd;CYgWlmSLYVhoBKGELOwxMUWIuiie]WSX=d<kXpmX^MeQwdAyGsIxAyECyY\\]HnUd>WteoblSbqitXgTO[i@oWXmUXMrwuYJ[FJgVauVEwHnUvOQfHmevCeqQxqwuxUekSV@kCY;BZKa`nlgVe@AfjnytYwiFq`yvDvpgWupYyiyqEIvPXean\\PntNIaa@i=wpQilmQqkovoarugvDilXiquWwcIw[w`<>jnNb?H_BGZawfaYyqywiguthhvAykQwdQw]xbIphn_hFxkIdHcEDgeMIIKWfIUfKaRtSc[kUv?Y;mf^yx>]fvMunGOhauCMtyixeydayviQuoX[uA\\:>\\WAZTA\\CQguyxiyvGYhr^m:@j:fawfaywiy_wSpscWsPh_EwlhfwXiqu@csypYqiEOhUwsXha?OsOgdOWn\\Pn\\N^\\^`n^`>omqGZ:>bnWZrAflOhlonHgmT?dJ?\\Xn]h`nnQhrPvYwiwipv`qvGsLh^\\f]tGbaInUacv`m^V`kau@YnZ@nJynIw]fQa:>bnCTAt;YbAsgYuiHmycqtQyifqSf_f^_VwQyoqUXmUekTf?rxIB:;wFKEswGuAY]?TKqRYCtG[FUSc?QxnaxVAikUfdOWMATnev_iv]oRGOtMYtEKCDKVj;ERyI:;BWGR=eVoYsNQr<AWb;ch=FSqfIuexmyvIyrAyrmFMGeJ?dJ;ER;Iv=yjiLipTN]dWXZ:>ZBpg:Nl?gb?gv\\irEH^[F^In]v>pohpGf[GfvWqi=>Z:>bnC^CDGoRmixoirx=B:;BJWRQ_i:;B:;BBoW:;B:;B:?w@;B:;B:??<JJ:sw_GfdiVyoWncF`kx@KfU<J:<lbekGdKvHMDdMwTVZLq;<J:<JZLq;J:LnU<J:<J:L>>Z:;<J\\Z:^BB:MdjUWs[iSKcv_IpqB\\JJBpeGimb@aVZuWZKi;;B:;BZKQ:B:K><jHUK]Ej;<J:FePWdMWpnGwLapn``MWdMicUp`cHocHhstBId]sDikU^SH_iv_Yt`gSE;CB;FiaWf]WvcYtaxsYxaYwdQwDQsDaywiyaesTgR_oipqIQMWdMwpiwUYdLOdByHHgEukdfwF]SF=ETKETAuRagwx]ETQuoWWk=T;;B:;R\\eD?oueccBOFmKYxUbSmXpsWuiwYaYmisbIt]wTf?UkcVDadawSYOysIyG]erCtHqshYwiwi`CcGuUYuefcHkCHkGhkGFi=FmsuwuxWAikUvf[Gf;SsCs[eYtaxcEXoWiquw`CuhMr>GC;Gb;_V?GF[CFKCDK[vUMf]WfasSX_upUY=cD`?B:;BZCXdWTmKTyeuIywP[RReY_eXlySuMEs_uPagaOf\\OFlKHlwYyqynKEGUTMUxfIumWtawSYaisUHCuTFmFM_i;_G\\=HRSUp_WSwHimulivEyIsavMKIwGgHMt=Yr=eSGeWIqewcGhoxayeymFiyUv?YkyDY]Y;EfJ=gNMGCobukXfAggggosHqsWMiI=OCM=B:;BJ?IDmv`CEuqc__WuYRy]sjkXpmGi?hvIsEOtB?gVWvQ[X@gxa?TUeXuIwFIemkYxmY^mff_gfcHocdFasXgIUQsDQcyqBHUhr?irtpsXquXxEYwdQwdXoeXUVuvmxVIqlgTU`qv`qpheutDvluLQtl^av^IJ=lJZLq;BZWt[CyfcYIIvFgYAEy_CWyowaisbqcV[tDid^[F^[sUwHI_svkYvAeFUypiwu[VBAD[yHvcYtahkGhK_bsGemsVDsdAuRAUdnqRLAerQIysyvYxtQytIEm@nJ=O<ivKDLKLXGypkQunupZPrN<J:<J^DlhAk;hOauL?g_YvoPoo^gytix@ob@_f`qxgYu^Oan?wJGlq^b@obLHwjHf=abl?u=xZI>sN?yx^]I?hj?hb?gbflDg]qngV@hsOhlOh@ob@hoghgUpa]@jbq:N\\Dgu=Imhpndnehhajx`WGecigQqhmqvGO`oIxkI\\cvv?OakQeHYwQu^MwgiwgKTxMwNIGlcwMyfIoghogjEygWUq_vTqyPWE\\WE:>^[@olQxTYjtWkQXwH`]rqpePvj?a[Iv[Q_dN_hoghO^EPr<QrBapYwqxOr?hv_ivQv_X_fk@e\\fpe`bF_cFFmtPqtppRf[UQq[X]\\D:>chFxtVdDfmhX`nxuUqoaquwXifo`UYuUYmqaxbvelOhlodPolwhqwplPpljGiJ?dJggggoyxqyPn\\PnVWh]npdPodnu\\PkDP[lfwXiQKxKCf[Gfl=ieqB:;JtTPgtMiLk<`qjEk@uWqEYoepqhUItopTT^qtTDX]qrGnvgXtaxcMHw^HcM@iivlgVe`v_yQhm^_gf_Cat@qvOpw_q]x^iRqaGfuJfu:>Z:>blGsePpnfqYGo\\atmY]nq[eIvOqfDxbqXgQqoCipNWsSn\\Pnn_hn?Yogf^YYwfawf@nZ@rU_reg_Q`mV`syWhGgcGQr?X[_Qu_qlUNnUZB_`Wwe[PaMSKiEhYxpWWbWgeWiquwXOhlOhrYv\\_F\\GTb[DkASastVeFDUfKAsqqwXiiuevDidvQxsYxaYuRAuV_IsMdqQHgcGgMunGW_cF_KXgQtJiCKiC:;B:[FTosjCRhOTgItWGfyqtoKdSEUS]WpSY^AsK_yDuSXOcDOcfawfIb=sBD_HnUFpcWTaDYsEyWWQqgCWDakGT]hBuUYtYKTj;AN;=lvUkixoiajCTLplWVAyMySydlOhlCipQiUq\\XCYK:<Z^vl\\Hl;VsKqp\\IsmO`ixyKApq?e=HqsHir?irXj=XjBGaEhrtxiyqaihwT@ksVh`a[WNanF_cF_Z>^:gcG_pcgm@pj@qywYysy_MN\\LNhlOhTyn[X]\\<KdHutQybQcuXutCuwyMxjAxbEhVdLdtmSUpPaoVxxF\\RuatPPs[PrN<:\\mHApxaVDQpiQo^mWLIjUHtRAurmyvIyZAvZEllmUadqmlVFARnU:<lMeXnhTnLtyuvUmWYLs;YZHP]oNsIysIhs`W[aqpJ@lJNlUqujWZiYr<gjc>:\\NWpkixkhYQoUKlIJ_qv`QlcaqsUxreynqPplPhYuqxW;Qj?Tp`esTiquuXuhW@djv=PxEN:<J:<RLhT?yNeTuRmXfqPNuTQuoSUp`IsMxNFmNMeR?enhpoHeTOeXxaysqSHmSgIqS<qeqJ:<Z^feAxvpNbCGccWsPh_WnqS>geqZ:>:;SG[Rq;Z:><B:@w@<J:>ZK=;B>J:FTB:]@<JBZ:RnJ:@G>ZJ:;jb[:FTB:Ccjyy:Wfl;roiIqMtv;B:;B:MTKWDKWgJ;eZ4:\"\{\}LSUrQU5OT1RBVElPTkc2Jy0lKUJPVU5EU19YRzYjJCIjNSEiIi0lKUJPVU5EU19ZRzYjJCIiIUYqLSUtQk9VTkRTX1dJRFRIRzYjJCIlIVElRiotJS5CT1VORFNfSEVJR0hURzYjJCIlP0FGKi0lKUNISUxEUkVORzYiImpulserhaltungBerechnung der Bewegungsgleichungen mittels Impulserhaltungode_ey:=m*diff(y(t),t$2)=-fS*sin(phi(t));
ode_ez:=m*diff(z(t),t$2)=-m*g+fS*cos(phi(t));Zwangsbedingungen zufolge der festenL\303\244nge des Pendelstabsset_zb:={y(t)=l*sin(phi(t)),z(t)=-l*cos(phi(t))};Einsetzen der Zwangsbedingungenode_ey1:=eval(ode_ey,set_zb);
ode_ez1:=eval(ode_ez,set_zb);sol1:=solve({ode_ey1,ode_ez1},{diff(phi(t),t$2),fS}):
simplify(sol1);DrehimpulserhaltungVektor zum Schwerpunktrr:=<0,l*sin(phi(t)),-l*cos(phi(t))>;vv:=diff(rr,t);Drehimpulsll0:=simplify(rr &x vv *m);Drehmoment um Punkt 0ff:=<0,0,-m*g>;ttau:=rr &x ff;Damit folgt die Drehimpulserhaltung zuode_phi:=(diff(ll0,t))[1]=ttau[1];Parameter des Systemsset_param:={g=9.81,m=10,l=1};L\303\266sen der Differentialgleichungsol:=dsolve({eval(ode_phi,set_param),phi(0)=175*Pi/180,D[1](phi)(0)=0},phi(t),numeric);Darstellung des Ergebnissesodeplot(sol,[t,phi(t)*180/Pi],t=0..10);