(* Content-type: application/mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 6.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 145, 7] NotebookDataLength[ 158829, 3215] NotebookOptionsPosition[ 153075, 3008] NotebookOutlinePosition[ 153450, 3025] CellTagsIndexPosition[ 153407, 3022] WindowFrame->Normal ContainsDynamic->False*) (* Beginning of Notebook Content *) Notebook[{ Cell[BoxData[" "], "Input", CellChangeTimes->{3.4513118353555927`*^9}], Cell[CellGroupData[{ Cell["Mathematica Class 3", "Subtitle", CellChangeTimes->{{3.41979088891156*^9, 3.419790892420446*^9}}], Cell["Numerical capabilities of Mathematica", "Subsubtitle", CellChangeTimes->{{3.419348835600596*^9, 3.419348850909992*^9}, 3.419350237731329*^9, 3.419790931742908*^9}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Sqrt", "[", "4", "]"}]], "Input"], Cell[BoxData["2"], "Output", CellChangeTimes->{3.419291229393813*^9, 3.4193341513920393`*^9, 3.41934906553304*^9, 3.419349173280237*^9, 3.419349360521598*^9, 3.419701580351821*^9, 3.419769040835327*^9, 3.419769088113903*^9, 3.419769220623859*^9, 3.419771052589692*^9, 3.451311863408772*^9, 3.482504931936571*^9, 3.482505726169056*^9, 3.482505824243243*^9, 3.482519028143258*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"u", " ", "=", RowBox[{"Sqrt", "[", "5", "]"}]}]], "Input", CellChangeTimes->{{3.419771037465145*^9, 3.419771039174553*^9}}], Cell[BoxData[ SqrtBox["5"]], "Output", CellChangeTimes->{3.419291229477928*^9, 3.419334151496611*^9, 3.4193490656001883`*^9, 3.419349173332848*^9, 3.4193493605892487`*^9, 3.419701580400393*^9, 3.4197690409027157`*^9, 3.419769088164227*^9, 3.4197692206741343`*^9, 3.419771055544847*^9, 3.4513118634626837`*^9, 3.482504931979653*^9, 3.482505726213554*^9, 3.48250582428788*^9, 3.482519043315816*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"u", "^", "2"}]], "Input", CellChangeTimes->{{3.4197710476057663`*^9, 3.419771049094452*^9}}], Cell[BoxData["5"], "Output", CellChangeTimes->{3.419771058884781*^9, 3.451311863522922*^9, 3.482504932014389*^9, 3.48250572625076*^9, 3.482505824343536*^9, 3.4825190705140467`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Precision", "[", "%", "]"}]], "Input", CellChangeTimes->{{3.419771092807909*^9, 3.4197710973508453`*^9}}], Cell[BoxData["\[Infinity]"], "Output", CellChangeTimes->{3.419771098163157*^9, 3.451311863572157*^9, 3.482504932064143*^9, 3.4825057262979593`*^9, 3.482505824387212*^9, 3.482519098257463*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"u", " ", "=", RowBox[{"Sqrt", "[", "5.", "]"}]}]], "Input", CellChangeTimes->{{3.419771067064747*^9, 3.419771068070547*^9}}], Cell[BoxData["2.23606797749979`"], "Output", CellChangeTimes->{3.419291229579152*^9, 3.419334151598015*^9, 3.419349065667344*^9, 3.4193491733834267`*^9, 3.419349360656905*^9, 3.419701580450308*^9, 3.419769040969556*^9, 3.4197690882831297`*^9, 3.419769220725833*^9, 3.4197710698034697`*^9, 3.451311863639559*^9, 3.482504932113668*^9, 3.482505726352791*^9, 3.482505824420011*^9, 3.48251913627635*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"u", "^", "2"}]], "Input", CellChangeTimes->{{3.419771080356732*^9, 3.419771081742589*^9}}], Cell[BoxData["5.000000000000001`"], "Output", CellChangeTimes->{3.419771082727139*^9, 3.451311863706522*^9, 3.4825049321644583`*^9, 3.482505726397127*^9, 3.482505824474908*^9, 3.482519139861402*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Precision", "[", "%", "]"}]], "Input"], Cell[BoxData["MachinePrecision"], "Output", CellChangeTimes->{3.419291229679399*^9, 3.4193341517929983`*^9, 3.419349065736066*^9, 3.419349173433271*^9, 3.419349360722824*^9, 3.419701580497241*^9, 3.419769041036603*^9, 3.419769088347941*^9, 3.41976922077605*^9, 3.4197710860433407`*^9, 3.451311863755541*^9, 3.482504932215008*^9, 3.482505726435347*^9, 3.482505824521356*^9, 3.482519148228487*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData["$MachinePrecision"], "Input", CellChangeTimes->{{3.4825191758512697`*^9, 3.482519189909363*^9}}], Cell[BoxData["15.954589770191003`"], "Output", CellChangeTimes->{3.4825192030364437`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"Sqrt", "[", "5.", "]"}], " ", "//", " ", "InputForm"}]], "Input"], Cell["2.23606797749979", "Output", CellChangeTimes->{3.419291229883808*^9, 3.419334151985139*^9, 3.419349065880076*^9, 3.419349173534255*^9, 3.419349360858745*^9, 3.4197015806012707`*^9, 3.419769041170641*^9, 3.419769088449069*^9, 3.419769220875668*^9, 3.451311863810544*^9, 3.482504932275672*^9, 3.4825057264809*^9, 3.482505824575531*^9, 3.482519399610866*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"N", "[", RowBox[{ RowBox[{"Sin", "[", "1", "]"}], ",", " ", "50"}], "]"}]], "Input", CellChangeTimes->{{3.482519406473239*^9, 3.482519418355453*^9}}], Cell[BoxData["0.\ 84147098480789650665250232163029899962256306079837106567275170999191040439124`\ 50."], "Output", CellChangeTimes->{ 3.419291230024642*^9, 3.419334152080546*^9, 3.419349065977009*^9, 3.419349173584001*^9, 3.41934936092337*^9, 3.419701580653603*^9, 3.419769041237817*^9, 3.419769088499268*^9, 3.41976922092605*^9, 3.45131186389501*^9, 3.482504932333951*^9, 3.48250572653573*^9, 3.482505824621896*^9, {3.4825194039776697`*^9, 3.4825194208761873`*^9}}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"N", "[", RowBox[{ RowBox[{"Sin", "[", "1.", "]"}], ",", " ", "50"}], "]"}]], "Input"], Cell[BoxData["0.8414709848078965`"], "Output", CellChangeTimes->{3.419291230096054*^9, 3.4193341521761017`*^9, 3.419349066035329*^9, 3.419349173634041*^9, 3.419349360989996*^9, 3.419701580701421*^9, 3.419769041303988*^9, 3.4197690885491753`*^9, 3.419769220976654*^9, 3.451311863957938*^9, 3.482504932381894*^9, 3.482505726581822*^9, 3.482505824675837*^9, 3.482519512834008*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Sin", "[", "1.`50", "]"}]], "Input", CellChangeTimes->{{3.482519519548972*^9, 3.4825195265850773`*^9}}], Cell[BoxData["0.\ 84147098480789650665250232163029899962256306079837106567275170999191040177331`\ 50.192402324441716"], "Output", CellChangeTimes->{3.4192912301952868`*^9, 3.419334152275659*^9, 3.4193490661586447`*^9, 3.419349173685166*^9, 3.419349361057498*^9, 3.4197015807518463`*^9, 3.41976904137142*^9, 3.4197690885953197`*^9, 3.419769221026781*^9, 3.451311864026675*^9, 3.482504932432021*^9, 3.482505726631925*^9, 3.482505824721603*^9, 3.482519528007577*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"x", " ", "=", " ", RowBox[{"N", " ", "[", RowBox[{ RowBox[{"1", " ", "-", " ", RowBox[{"10", "^", RowBox[{"(", RowBox[{"-", "45"}], ")"}]}]}], ",", " ", "50"}], "]"}]}]], "Input", CellChangeTimes->{{3.419768554867469*^9, 3.4197685910065317`*^9}}], Cell[BoxData["0.999999999999999999999999999999999999999999999`50."], "Output", CellChangeTimes->{3.419768596565271*^9, 3.419769041421063*^9, 3.419769088649364*^9, 3.4197692210785503`*^9, 3.419772320609146*^9, 3.4513118640879307`*^9, 3.4825049325049343`*^9, 3.4825057266815577`*^9, 3.482505824776771*^9, 3.4825195742445717`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"1", "-", "x"}]], "Input", CellChangeTimes->{{3.41977239048428*^9, 3.4197723920779676`*^9}}], Cell[BoxData["1.`4.999999999999993*^-45"], "Output", CellChangeTimes->{3.419772393298828*^9, 3.4513118641554403`*^9, 3.482504932565969*^9, 3.482505726731715*^9, 3.48250582482286*^9, 3.482519602071844*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Precision", "[", RowBox[{"1", " ", "-", " ", "x"}], "]"}]], "Input", CellChangeTimes->{{3.419768605833856*^9, 3.419768618316162*^9}}], Cell[BoxData["4.999999999999993`"], "Output", CellChangeTimes->{{3.4197686129203777`*^9, 3.4197686187794*^9}, 3.419769041473751*^9, 3.419769088700289*^9, 3.4197692211258698`*^9, 3.451311864223269*^9, 3.482504932619384*^9, 3.4825057267868233`*^9, 3.482505824877119*^9, 3.482519637136016*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"y", " ", "=", " ", "2.4"}], ";", " ", RowBox[{"Precision", "[", "y", "]"}]}]], "Input", CellChangeTimes->{{3.482505033228683*^9, 3.482505056204357*^9}}], Cell[BoxData["MachinePrecision"], "Output", CellChangeTimes->{3.4825050590682993`*^9, 3.482505726834807*^9, 3.482505824924218*^9, 3.4825196991631107`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData["$MachinePrecision"], "Input", CellChangeTimes->{{3.4825050844117613`*^9, 3.482505089834951*^9}}], Cell[BoxData["15.954589770191003`"], "Output", CellChangeTimes->{3.482505090927003*^9, 3.4825057268824244`*^9, 3.482505824977437*^9, 3.4825197042335997`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"y", " ", "=", " ", RowBox[{"1.", " ", "-", " ", RowBox[{"10", "^", RowBox[{"(", RowBox[{"-", "20"}], ")"}]}]}]}]], "Input", CellChangeTimes->{{3.4825230782133093`*^9, 3.4825231102867947`*^9}}], Cell[BoxData["1.`"], "Output", CellChangeTimes->{{3.48252310454673*^9, 3.4825231109077272`*^9}}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"1", "-", "y"}]], "Input", CellChangeTimes->{{3.482523164838488*^9, 3.482523166365642*^9}}], Cell[BoxData["0.`"], "Output", CellChangeTimes->{3.482523167528707*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Map", "[", RowBox[{"Precision", ",", " ", RowBox[{"{", RowBox[{"y", ",", " ", RowBox[{"1", "-", "y"}]}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.4825231135617037`*^9, 3.4825231516535807`*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{"MachinePrecision", ",", "MachinePrecision"}], "}"}]], "Output", CellChangeTimes->{{3.482523127632882*^9, 3.482523152512127*^9}}] }, Open ]], Cell[BoxData["y"], "Input", CellChangeTimes->{{3.4825230979549923`*^9, 3.482523101069077*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"N", "[", RowBox[{ RowBox[{"BesselJ", "[", RowBox[{"3", ",", " ", RowBox[{"1", " ", "+", " ", RowBox[{"2", "I"}]}]}], "]"}], ",", " ", "200"}], "]"}]], "Input"], Cell[BoxData[ RowBox[{ RowBox[{ "-", "0.28103966684576790767179865444025092304035621980956282410110023340304\ 501788320344931842181453291938042413558961504246638273476877435711661752487873\ 164520423729853714165984626563189675919164487529252711650195561712311059881576\ 5045599`200.14970551812146"}], "+", RowBox[{ "0.0171750620033902321271425488117806130115690519134271577143342065367565060\ 124693077506590436222664319921301231579634787877242195920162656934536638450089\ 697916039147084141507421863773830198879354401374812694183920535105351570278721\ 05`198.93583620973834", " ", "\[ImaginaryI]"}]}]], "Output", CellChangeTimes->{3.4192914307692757`*^9, 3.419349066302899*^9, 3.419349173736948*^9, 3.419349361213995*^9, 3.419701580801736*^9, 3.4197690415234547`*^9, 3.419769088750535*^9, 3.419769221177725*^9, 3.419772531567635*^9, 3.451311864382469*^9, 3.482504932705295*^9, 3.482505726936865*^9, 3.482505825023285*^9, 3.482519799118328*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"m", " ", "=", " ", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"3", ",", " ", "4"}], "}"}], ",", " ", RowBox[{"{", RowBox[{"4", ",", " ", RowBox[{"-", "3"}]}], "}"}]}], "}"}]}]], "Input", CellChangeTimes->{{3.419699784597843*^9, 3.419699812890225*^9}, 3.419699872724568*^9}], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"3", ",", "4"}], "}"}], ",", RowBox[{"{", RowBox[{"4", ",", RowBox[{"-", "3"}]}], "}"}]}], "}"}]], "Output", CellChangeTimes->{3.41969981562528*^9, 3.419699873974771*^9, 3.4197015808514137`*^9, 3.419769041571754*^9, 3.41976908880079*^9, 3.419769221227007*^9, 3.419772752886607*^9, 3.451311864440645*^9, 3.482504932750424*^9, 3.4825057269839077`*^9, 3.482505825077314*^9, 3.482519975198227*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"m", " ", "//", " ", "MatrixForm"}]], "Input", CellChangeTimes->{{3.419699820764063*^9, 3.419699829467332*^9}}], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"3", "4"}, {"4", RowBox[{"-", "3"}]} }, GridBoxAlignment->{ "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.7]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}], Function[BoxForm`e$, MatrixForm[BoxForm`e$]]]], "Output", CellChangeTimes->{3.419699830787376*^9, 3.4196998766372766`*^9, 3.419701580902985*^9, 3.419769041622167*^9, 3.4197690888510942`*^9, 3.4197692212772007`*^9, 3.419772755323007*^9, 3.451311864526428*^9, 3.482504932854596*^9, 3.482505727037594*^9, 3.4825058251233397`*^9, 3.482519986272306*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Det", "[", "m", "]"}]], "Input", CellChangeTimes->{{3.419699836903488*^9, 3.419699843819276*^9}}], Cell[BoxData[ RowBox[{"-", "25"}]], "Output", CellChangeTimes->{3.419699844329886*^9, 3.41969987894536*^9, 3.419701580954103*^9, 3.419769041760942*^9, 3.419769088901038*^9, 3.4197692213269053`*^9, 3.419772757665386*^9, 3.451311864592321*^9, 3.482504932920382*^9, 3.482505727083926*^9, 3.482505825178594*^9, 3.4825199977084293`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"Inverse", "[", "m", "]"}], " ", "//", "MatrixForm"}]], "Input", CellChangeTimes->{{3.4196998870283937`*^9, 3.419699929955645*^9}}], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ { FractionBox["3", "25"], FractionBox["4", "25"]}, { FractionBox["4", "25"], RowBox[{"-", FractionBox["3", "25"]}]} }, GridBoxAlignment->{ "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.7]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}], Function[BoxForm`e$, MatrixForm[BoxForm`e$]]]], "Output", CellChangeTimes->{{3.4196999009961987`*^9, 3.4196999305086737`*^9}, 3.419701581003231*^9, 3.419769041805093*^9, 3.419769088951316*^9, 3.419769221377604*^9, 3.4197727605812883`*^9, 3.451311864714999*^9, 3.482504933081604*^9, 3.4825057271379642`*^9, 3.4825058252245913`*^9, 3.482520007810378*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Eigenvalues", "[", "m", "]"}]], "Input", CellChangeTimes->{{3.419699934759012*^9, 3.4196999454278812`*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"-", "5"}], ",", "5"}], "}"}]], "Output", CellChangeTimes->{3.419699947041396*^9, 3.419701581053196*^9, 3.4197690419322*^9, 3.4197690890037937`*^9, 3.419769221426744*^9, 3.4197727638078814`*^9, 3.451311864830171*^9, 3.482504933172536*^9, 3.482505727184121*^9, 3.482505825337701*^9, 3.482520011590637*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Eigenvalues", "[", RowBox[{"N", "[", "m", "]"}], "]"}]], "Input", CellChangeTimes->{{3.4197727694304657`*^9, 3.419772784412678*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"-", "5.`"}], ",", "5.`"}], "}"}]], "Output", CellChangeTimes->{3.419772788633807*^9, 3.451311864897793*^9, 3.482504933432296*^9, 3.482505727301371*^9, 3.482505825375893*^9, 3.482520046667018*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Eigensystem", "[", "m", "]"}]], "Input", CellChangeTimes->{{3.4197727694304657`*^9, 3.419772784412678*^9}, { 3.482505286389573*^9, 3.4825053135952253`*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "5"}], ",", "5"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", "2"}], "}"}], ",", RowBox[{"{", RowBox[{"2", ",", "1"}], "}"}]}], "}"}]}], "}"}]], "Output", CellChangeTimes->{{3.482505296994953*^9, 3.482505314635062*^9}, 3.482505727355999*^9, 3.4825058254299583`*^9, 3.4825201095859013`*^9}] }, Open ]], Cell[BoxData[ RowBox[{"Clear", "[", "x", "]"}]], "Input", CellChangeTimes->{{3.4197691688882227`*^9, 3.419769171014485*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"sol", " ", "=", " ", RowBox[{"NSolve", "[", " ", RowBox[{ RowBox[{ RowBox[{"-", "2"}], "-", RowBox[{"9", " ", "x"}], "+", RowBox[{"4", " ", SuperscriptBox["x", "2"]}], "+", RowBox[{"6", " ", SuperscriptBox["x", "3"]}], "+", SuperscriptBox["x", "4"]}], "\[Equal]", "0"}], "]"}]}]], "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"x", "\[Rule]", RowBox[{"-", "4.7912878474779195`"}]}], "}"}], ",", RowBox[{"{", RowBox[{"x", "\[Rule]", RowBox[{"-", "2.0000000000000004`"}]}], "}"}], ",", RowBox[{"{", RowBox[{"x", "\[Rule]", RowBox[{"-", "0.20871215252207997`"}]}], "}"}], ",", RowBox[{"{", RowBox[{"x", "\[Rule]", "1.`"}], "}"}]}], "}"}]], "Output", CellChangeTimes->{ 3.419291430918895*^9, 3.4193490664776163`*^9, 3.419349173785501*^9, 3.419349361292892*^9, 3.4196999899324007`*^9, 3.419701581119903*^9, 3.4197690419737988`*^9, 3.4197690890682383`*^9, 3.419769221573576*^9, { 3.419773094257118*^9, 3.4197731167724943`*^9}, 3.4513118650325108`*^9, 3.4825049335572767`*^9, 3.482505727418985*^9, 3.4825058254895372`*^9, 3.4825202960865173`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"2", " ", "x"}], " ", "-", " ", "45"}], " ", "/.", " ", RowBox[{"x", " ", "\[Rule]", " ", "25"}]}]], "Input"], Cell[BoxData["5"], "Output", CellChangeTimes->{3.4192914309829693`*^9, 3.419349066537293*^9, 3.419349173833002*^9, 3.4193493613589087`*^9, 3.4196999922360497`*^9, 3.41970158117115*^9, 3.419769042024252*^9, 3.41976908911872*^9, 3.419769221627775*^9, 3.419773233151354*^9, 3.4513118650938673`*^9, 3.482504933604649*^9, 3.482505727473165*^9, 3.482505825525552*^9, 3.48252044844907*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"x", " ", "/.", " ", "sol"}]], "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"-", "4.7912878474779195`"}], ",", RowBox[{"-", "2.0000000000000004`"}], ",", RowBox[{"-", "0.20871215252207997`"}], ",", "1.`"}], "}"}]], "Output", CellChangeTimes->{3.4192914310330677`*^9, 3.4193490666049833`*^9, 3.4193491738861847`*^9, 3.41934936142689*^9, 3.419699994514268*^9, 3.4197015812202187`*^9, 3.4197690420534163`*^9, 3.4197690891858063`*^9, 3.41976922167871*^9, 3.4197733648879623`*^9, 3.451311865163916*^9, 3.4825049336557837`*^9, 3.4825057275225782`*^9, 3.48250582557968*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"x", " ", "/.", " ", RowBox[{"sol", "[", RowBox[{"[", "1", "]"}], "]"}]}]], "Input", CellChangeTimes->{{3.419699982034329*^9, 3.4196999854649*^9}}], Cell[BoxData[ RowBox[{"-", "4.7912878474779195`"}]], "Output", CellChangeTimes->{{3.419699986848332*^9, 3.419699997796693*^9}, 3.4197015812708187`*^9, 3.419769042317878*^9, 3.419769089386471*^9, 3.419769221760956*^9, 3.4197733678881683`*^9, 3.45131186522843*^9, 3.482504933704506*^9, 3.482505727569152*^9, 3.482505825612866*^9}] }, Open ]], Cell[BoxData[" "], "Input", CellChangeTimes->{3.419700240775591*^9}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Plot", "[", RowBox[{ RowBox[{"{", RowBox[{"x", ",", RowBox[{"Tanh", "[", RowBox[{"2", " ", "x"}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"x", ",", "0", ",", "2"}], "}"}]}], "]"}]], "Input"], Cell[BoxData[ GraphicsBox[{{}, {}, {Hue[0.67, 0.6, 0.6], PointSize[Large], Thickness[Large], LineBox[CompressedData[" 1:eJxNxW0s1HEcAPBzEWU7jsn+Z8eOUyuaJiNKp9iUx3losV2nyUMYyW5Dm3FG D7jWmunWkcetxLm4oxcScWlJHqL0cOfqul2XM045Og931Qvf3+/FZx9G6pX4 dDKJRIr55/8R6drpoZ/pJ3e2DKXlK4kw1s5HGwX1EiIRjnw719NApMHn09YH 7hJcWOFzI5RPVMBNTrHXq4hamGcjOXCLaIOTkpvF+hUpbGvmscNdB2HPuCXt SLUMLpwIZAlWX8POUuq8hcUk3KcKHZ888Q4ezm5wSV6chQ37g+1EuXMw2dhh 7+L5GfY3X+xL6JLD4xV+E6OHlLDbHZ2xfekrrFtXzr8/ooLbFvrHKLe/wxT6 w2W1Wg3XZPVmNDE18FpIh/py6Q+Y6yuT7hvRwsouWfU0YwHezJ4VHrymg71O WZsy+hfh8BZGZrfzElxIT3H/xl6GvRfP2c5F62FHO72NbANtOSgUe9SvwDl+ /Z/2RP6CO86mNj1fQxt0NHtN3W+4NyF8V23YKlx6prJRqkEzFBEfWysNcFBA RS3huwazXSeNFjNowxhflc9bhwWWHG488w/sON/bQpahrUp4iYFXjTCpnSNW OWzABffFfIdh9IDXTRtq3iZMjSjwLqdswfLDUzPFz9BPHrCYas42fEHsT6Wb 0GWVzTz5YxMs0tKFlCgzHEelHHu1ga6yIrvIsWVGw7Ye21+lGKFtomkSUWwe tioxOtNpC80V1NRd2kaLasqKi7A1ZVw2Hzspi+3+FDs4yLtrrwm9W/7mZTc2 a2rw0Sh2kUxS/QV7oVMYZ2VGT5TkKJKwrQtShnKxQzISWsuxe2KOZ3Vi6077 RL3AZgZ4+HzA5ng5O+iw77nZGszYfwEIhpSQ "]]}, {Hue[0.9060679774997897, 0.6, 0.6], PointSize[Large], Thickness[Large], LineBox[CompressedData[" 1:eJwdzGs01HkAxnEpsVkjWmnGDolSsauVw1J6lMollxU2FeokRKebtCFiNFlr 2HVqTimJSjc1SUZ7kVVMipXUVMpltIMJM+YvNTQTZn//ffGc7/m8eax37NsY o6ujoxNIRtcvZuDZ/cGYVSv/76FVM7xY+3uYayHP7m+UMEOxvKTwXBXpY9/2 8dvMndjwpP1OMelPDI3VSWYSNu0crz1BGldudnAXk4tux5+98ul28Nh98/go NQvKzmXycdflKGRzy8AxqLL7hVmGcYH5l5MMIcI3X6gYeS/Eb6NlVqfrRTDU ciK8LeuQu26Lv4rbioXByoEGngitvG0JbhIxDre6ofBjEzJyeV89Ov8a5kIT ybRpTyGOdAzY0tSFu1Kvlqcrn2OE1XkuIv0t6hOKLTYrXiB+49n6oO1SqBZ5 GAv2tENfGJjQoemFrvrGbIuFHThU9+cdWV4/XLTb74bc6kLrgjX9Bt0ytHCd WxuX9iCyWG1eNn0AVgVy9XXlW8zu77H4w3IQ8vEeyctlUuya71Rorz+EsqGa ZsavvSiNOfKquncIDPZVqq+vD4MC1WJ+iRx58dWxpbYylIwmH1W5KjDmeaNv V8Y7REezPRY/UiDJSSSc2zCA7LbSfq77MHpuiXjPrIfg7z+YY3ZlGJ8TXhQt SZXD4a9U81AdJexX60/F1ijQ2OQ2WuyjhPdF67hKcyVqQ257PuQpcZi9bcG/ ERSSw9YVbH2ghIMizLA9YASKyDhkK5WYYzxiINKM4AHnSGfCPAoz6ooqbM69 h1F25/xGNwq7nWvefLFhFC3pNYH8cAo3fHeU/j02Cl3Tg2eWJ1JQyVmzZac+ gHv65SZ+NoXqEO/p/LUfMTNIf1ncGQoZPsdLhLKPWGL3Y0H4NQrW3X6vLx1X QfDDh/peIQV3Vy6f6TQG+VLuibT7FCIsn6qnicfg7n3duLKJ/DfnS/dzxuG1 +mWOw3MKhTOikjbafsLAAZuS/tcU5kiqL+qKPuHKiZlf50go6KVzQt0OqJEk 3WBX00tB53pUhdRUg7RgQUrHOwqJZyvyTes1yDd85ndZTqHWPsfAZO9niFes ZzYrKZj4JTpkMSZwwMApzec9ha5v2sQp9yZg6ORRwf9A4fZ52PZFTSKjAZWx KgqRFS4m7KlJbBouch4eo5B5/AKnq3wKYqHofNgnCoIBdhHDX4tj3xmEHVRT CDZhfP9IQ8xZ75mqoZCrp2vRRVzwhBlJW6RWTY4QLz+mSKHtIu1uYH3WItC+ oIo2q0oQtJfYZl/boiPE0tCAOLMJLXQeOxulEScV5p2KntSCEue9SScW5GWm JBN3hAeM0ZZlJkXkE9d5G805ShweH7Hgd2JONM+ftoe7w61ZU1qsPJlZR3tm 1z8PK4k9XgVeziBGW921RuJvJ/TqaSeLqnidxL559yS0h24WBetptZglt5uX Sdyavrs7nNj40ngubf3Ebff3EF9llV+l7RkbcimLOGtiq4j2ncAV8TeJjbS1 k7Tlaxz9HxA3WO1lcYhtXW0cXxE/Lme70o6yNzeVE1uWtoTQPm1lqNISN2tT 99P+D4Anm1Q= "]]}}, AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], Axes->True, AxesOrigin->{0, 0}, AxesStyle->Thickness[Large], BaseStyle->{15, FontFamily -> "Times", Bold}, FrameStyle->Thickness[Large], PlotRange->{{0, 2}, {0., 1.9999999591836735`}}, PlotRangeClipping->True, PlotRangePadding->{ Scaled[0.02], Scaled[0.02]}]], "Output", CellChangeTimes->{3.419291431537507*^9, 3.419349067109894*^9, 3.41934917393349*^9, 3.419349361501734*^9, 3.419701581855447*^9, 3.419769042433016*^9, 3.419769089515831*^9, 3.4197692218344383`*^9, 3.419773522413451*^9, 3.451311865422126*^9, 3.482504934117733*^9, 3.482505727635681*^9, 3.48250582565777*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"FindRoot", "[", RowBox[{ RowBox[{"x", " ", "\[Equal]", " ", RowBox[{"Tanh", "[", RowBox[{"2", "x"}], "]"}]}], ",", " ", RowBox[{"{", RowBox[{"x", ",", " ", "1"}], "}"}]}], "]"}]], "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{"x", "\[Rule]", "0.9575040240772688`"}], "}"}]], "Output", CellChangeTimes->{3.4192914321862707`*^9, 3.419349067590561*^9, 3.419349173983028*^9, 3.419349361560973*^9, 3.419701581941361*^9, 3.419769042502881*^9, 3.419769089589106*^9, 3.419769221859541*^9, 3.41977358421544*^9, 3.451311865527153*^9, 3.482504934300887*^9, 3.4825057276884747`*^9, 3.482505825709865*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"NIntegrate", "[", RowBox[{ RowBox[{ RowBox[{"x", "^", "2"}], " ", RowBox[{"Exp", "[", RowBox[{ RowBox[{"-", RowBox[{"x", "^", "2"}]}], " ", "-", " ", RowBox[{"x", "^", "4"}]}], "]"}]}], ",", " ", RowBox[{"{", RowBox[{"x", ",", " ", "0", ",", " ", "Infinity"}], "}"}]}], "]"}]], "Input"], Cell[BoxData["0.1600785451795007`"], "Output", CellChangeTimes->{3.41929143242934*^9, 3.419349067872167*^9, 3.419349174035882*^9, 3.419349361626938*^9, 3.419701582142179*^9, 3.419769042731226*^9, 3.4197690896544733`*^9, 3.419769221913941*^9, 3.4197737221196747`*^9, 3.451311865770472*^9, 3.48250493443946*^9, 3.482505727738736*^9, 3.482505825743574*^9}] }, Open ]], Cell[BoxData[ RowBox[{"Clear", "[", "x", "]"}]], "Input", CellChangeTimes->{{3.419769074863393*^9, 3.419769077398799*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"sol", " ", "=", RowBox[{"NDSolve", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"x", "''"}], "[", "t", "]"}], " ", "+", " ", RowBox[{"0.5", RowBox[{ RowBox[{"x", "'"}], "[", "t", "]"}]}], " ", "+", " ", RowBox[{"9", RowBox[{"x", "[", "t", "]"}]}]}], " ", "\[Equal]", " ", "0"}], ",", " ", RowBox[{ RowBox[{ RowBox[{"x", "'"}], "[", "0", "]"}], "\[Equal]", "0"}], ",", " ", RowBox[{ RowBox[{"x", "[", "0", "]"}], "\[Equal]", "1"}]}], "}"}], ",", " ", "x", ",", " ", RowBox[{"{", RowBox[{"t", ",", " ", "0", ",", " ", "12"}], "}"}]}], "]"}]}]], "Input",\ CellChangeTimes->{{3.451316900544478*^9, 3.451316909373633*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{"{", RowBox[{"x", "\[Rule]", TagBox[ RowBox[{"InterpolatingFunction", "[", RowBox[{ RowBox[{"{", RowBox[{"{", RowBox[{"0.`", ",", "12.`"}], "}"}], "}"}], ",", "\<\"<>\"\>"}], "]"}], False, Editable->False]}], "}"}], "}"}]], "Output", CellChangeTimes->{3.4192914325988503`*^9, 3.419296659425045*^9, 3.4193490680905333`*^9, 3.419349174065712*^9, 3.419349361711316*^9, 3.41970158231045*^9, 3.419769042850235*^9, 3.41976908976602*^9, 3.419769221978984*^9, 3.419774105916781*^9, 3.451311865994104*^9, 3.4513169808002872`*^9, 3.482504934561982*^9, 3.482505727817338*^9, 3.482505825828574*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"x", "[", "2", "]"}], " ", "/.", " ", "sol"}]], "Input"], Cell[BoxData[ RowBox[{"{", "0.5635239311232755`", "}"}]], "Output", CellChangeTimes->{3.4192914326522017`*^9, 3.419296662167322*^9, 3.419349068145342*^9, 3.4193491741196957`*^9, 3.4193493617781563`*^9, 3.419701582425046*^9, 3.419769042965424*^9, 3.41976908983881*^9, 3.419769222046462*^9, 3.419774227600605*^9, 3.4513118660485067`*^9, 3.4513170671600027`*^9, 3.4825049346088943`*^9, 3.482505727872037*^9, 3.482505825895233*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"x", "[", "2", "]"}], " ", "/.", " ", RowBox[{"sol", "[", RowBox[{"[", "1", "]"}], "]"}]}]], "Input"], Cell[BoxData["0.5635239311232755`"], "Output", CellChangeTimes->{3.419291432846587*^9, 3.4192966651062737`*^9, 3.419349068268091*^9, 3.4193491741698627`*^9, 3.419349361843997*^9, 3.419701582476267*^9, 3.419769043078842*^9, 3.419769089921216*^9, 3.4197692220970573`*^9, 3.419774314865509*^9, 3.451311866115386*^9, 3.451317133099769*^9, 3.4825049346568727`*^9, 3.482505727922161*^9, 3.4825058259464407`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Plot", "[", RowBox[{ RowBox[{ RowBox[{"x", "[", "t", "]"}], "/.", "\[InvisibleSpace]", "sol"}], ",", RowBox[{"{", RowBox[{"t", ",", "0", ",", "12"}], "}"}]}], "]"}]], "Input"], Cell[BoxData[ GraphicsBox[{{}, {}, {Hue[0.67, 0.6, 0.6], PointSize[Large], Thickness[Large], LineBox[CompressedData[" 1:eJwUV3c8Fd4bRjZl79F1iQYNq5Kct0mTlqJEdokipJIiyc5KvjaJSPZex957 Z7vWJXsl83d/95/7eT7ve57znOd933PvEdN/dtOIhoqKio2Oiur/32tXLMI0 nvmouC7vUD5zyMVQan+TpAVK82Nmek/BDbOjT7wkHVB/m6Eg9fYc+snTG/k7 1AWdUt5x/rAxh+bTz3k+lfRGWi862hnW5pDggc78nS4/pJofH+q9NIdO27kf qwkNRAeULr/kn51DelUqcX6PglGoRQxD7MQccuJdEn4gGY7KGhPXjg/Noda0 WzV+K5HIod9/o7FrDhn2yDj/7YpGDa/Daswa59AKNSN6kBeDbORtxdnKKXoP kP4Vh8Yi2dlDLbk5c4jvRkHGvnc/0Dd57einiXPoh13gM/dHCUjAvch8f8Qc qqu6PHZLMgnpRsm+KHKcQ0kvOTUe0KYgkRCWd8GWc+ilx7tf3ispKKF5cv8H vTnEmK5lutSVhu7hmssOp+ZQc2Vlxb6adPQ6SanRT2oO/dcjJ34vLwMtPHhE n8M5hw7S7BkoCM1CWbcIayfGZ9Eiz5tTc17ZaHkfLAc2zqL8A+QgsXc5qFnu 4UHmrFl09UbpLZdHechv3YtHwWkWPYu0rVGXLEJ/am9zFLPNohMZI5JOfBjZ vv3XNTU/g6gM95/Vpi1GooLh+xRaZlDNyy8RnivFiDxl8Ffm8wzSjnimvdBV ivY/VT31m2oGqRyQdHPXKEPkR6Nt+3unETG9L1u8pgy98c7o/JYxjf5UXuLR zCtH0uv/ORCNppH9rHhzXmglUjL7cud5wR+kZ9ezfYunCtWcy+a65PMHnafx lZnxqkJ3NiO+ahv8Qbt5t933vqtGKTFtDEcY/qDw090XnB/VIkWrH7eaL0yh Ek/P/GuSjcghFD8KiSSjoqnf9Szxjcj1+uEJKUMyKlCTGqg51IQ8ZOjtZiXJ 6D7NI6pv/M0os+GjunzCBLpTtEHcK9qCLPgfC8zGjaPLisdM+Q60oabS8rKP TqNITjJ0kQF1IbWjzb9kfAcRHb0Vw+STQTRr3XSTyFOByJfesS3FDSL+SZlb 5S1lqNbLk29rdBDRXp+99NC7FFW5t/m7HhlCopFX7L4xFCMPztlvofFDaGZw 5rXk30zETRQvLw8bRtJ5lycHVRyQ5BkvWh6XEbTQ+qvQPKoU8434MwbHjKBo 35mMa61lmPFjMOveshF0invX9XXqCjxVHcd9gGoUif/DcwE6VThZo1Ti9OtR FM1xZL6Nth6f0Pt73shiDO3+KdY59rEVX3r36GOm5gTauuZD1zfUg2U/l1yM sp5AXisTn57c78XCEWKMXn4T6BetZAG5vRfPFw27GzZOIPHezNtx5X04cPuR D9dFMqow1TjaETiAR9/qh1gqTKJ0nvR7CdTDuNGr9IHOrUmkiGWu5igM45ww ougly0nEvNESI/l4GHsUkiIJvyaRsNuywd7GYSy7pR/bJDGFyBdCjR/6kPB7 e4NUGe4/6Onq6hu2lRH8xLPMSkD2Dzqkyf3ui+govh0qLk+n8QfpKv1dfKw6 iqUKRrL6PP4g7cKe1+uBo7hxw6DAY9c0otWStouSGcM5LOVvX4pNo+Rdhy84 3RjD0UISyABNo8P8Z3ITrMewzanREqU30+gqk/23ppwxLPzGsGpycRodhxJp zRPjmN6j3LWDfQY1W5Zn6GmO4/lgicslh2dQdAdLyK8X47gsb7Q+6MkMynR+ fYM1cRwn1p73dnadQWkij/lFqsZxYE+M+vPYGbTaJH3IYngcP1k3bFUlzSBf 8SnDJq4JfJu5wl+OahaVKbimDxyawKcF993ZKzqLPnlfDJM+N4HZlca6VrUo c/6mqt3p2QTOfmXU/71lFm2Jasiw4wkcq2LWJbg4i96JeKe4tk7gwF2WLZ8p 94TljuuW4NgEtvWyr3h1aw6xZ7sQPBnI2PimE559MYdKlJ2jnvCRsSafa65B wBwqOnn0rL4kGStG+f+61jGHXmTzfAk9Q8aSxv/Fla5Q7kV6T4XBa2Ts8aWp WYhlHllNCrcqaZHxLrvWa5pC8wjiKm2TDcj4jXZHrc+hedT/pvv4aXMyXlLu Vq07NY9iLGeOjdqQsdne3nK6q/PI+/SEW8xbMh6hHjgDD+bRsODkUwdnMr4/ OlT0+uk8Woy9yW7lTsatlSOnMu3n0e+CvNR3n8n4cvx4zpznPJK+MRUY50/G pR6TCgfD5lHSta7dU4FkrGQxnWb4ax4RNEKeqv5Hxmkac0ciCueR74AhR3Ew GR+UW0z83TCPqGrf6N8OIeNonpUD3APzSH3teCMtBQuu/Y29PjuP7qks17ZQ 1vv1rIu7bc+jNH3qrvyvZMxcuBVZtmcB7dWMtisLIGOnCCrRbdEFpHyaUWXS h4zXHXeFnDiygP6aQaGMJxlbGdLzv0ALKDdJJsDXhYynLjJ9+aW+gDRTnUx5 3pOx/gFWTrLuAjJJy5/ItSPjHha2z8TnC6jTd0/Vu+dkfHOWg1Xn/QJ6avqw zMSEjGubud2++iwgeywXZaVDxmfT+ehbIxdQcF2KdNRNMs77IviBNXUBaX/+ eHL5IhnL2olQqZYsID3n0einSmScoE1469iygERe2F1hkSHj4L2SL1cXFlB4 9CITZiNjTpoDy0dpFlGeISdz584Edh89ZGnGuYhypkpF+OYm8Ov4Y2ZDsouo I0Y0RqhuAi96yJMFzy2isyr1SsPZE/iJxXGjO7cWkbXbsnTHtwmsLXdat/bF IjKgP5F79dUEbuWBPlrnRTSa9TS5VX8CX147q4UCFtEV46O5HlcmsFKh2q2M DEq+VRhzqOAEFlS9rRq+sohoJTmPaSePY78Dd8u76ZZQVW3D3jC/cczMqn2G i3cJseTytYvYjOP1Zt1TropL6Pyyq97A8XH8W9vsiNXLJTTo5rjfJWMMu5NU n351WUJ/SzrLFQPGsNITifiCL0to9MxGvdqLMRz6qp/IkLGETowfsQ08Mob1 gtR5Q+eX0OE/BZbbkaN4okNuq+LxMjqWw5kGpiM4SIdd6Y/dMmo98yQmRWUE q41N27K7LiOr1ZKj/3GP4ITl7/PascsoWcLMpKeIhC24+EfnSMvo74bfqcu7 SXhFY7NW4MEKyhxx97vhP4Rju7sZkNkKMrzvcYVNfwhr6mWeN3y9gsy5azX0 jg7hnGcWRUlBKyg0MyTa5esgtvceSj3XsYJaI87cd9jox7vqy4PMr6+iMimB xiuRPZhD1cu4BP4i8otvgeEv2/D5+AJ06MZfpJUeICz+txXbsUzzf3n0F801 7GNQtG3FQ02X60yd/qKXFp27hF604JR7jEfZy/8iXpG3T3ubG7HGkw//Hqqu Ie5bEhyyHpXYx+uV5+a1f2jdurRR3jQOl8/9MDJ++A+VKh6/fBS+4bUb3SrN Fv9Q98KHJBm5cKzHe3zh2+d/qDw5rXbzvAc+GrF850rLPxQUZi8dr+6PmlOe 7Q2+vY7obY9wqe/OROztRmnH728guX/CAhepaxHMnJm6bbaBKnrOz9ZM1qLn 9KJEqzcbSGNNTWukuQ61nOj0TQzZQI0p9DM5wQ3IL+yipVjfBvKf1NJi925G PCZSR1l0NlHTHbY7HRNt6OL7Xab7zTfR0Jmh3dzq7cj2v8GIC283UThDSYRR ZjvqrPvK9j5sE+m7fIuSf9eBgo4yzi33byKr2amIQwxdSHCd/Gvg4Rb6yfxW fHrsN7rMVTG2YbGFjNed6xeUe9Br6SgRgXdbiKf2llGfXw/qfajldStiC9XN 7zHXPNWLQstqnlYPbqEKK/KnYIc+VN/3PWZsbgvlmQhzOdf3oc0Vxz4aqm0k 7PumGgn0I539SldPE7bRl097D+9L7keiXgmH0vS20cscabJF/QC6Huti0PR8 G2nUP7ZJYR9EDlg/ZPr9NpJne66TcWsQDS4IskhFbaPVn7bKmx2DKFLTYypk eBv9uCIzl2Q0hJqfmRBzF7ZRqh2qLXEaQtRu57Q7qXeQ+Ot/lkcihpB+/kYN O3EH6Utxm/N3DiFxwtP4j/o7iJdp3z025WHkOSAW5WW5g5KKZNpu3BxGq6Fd QV/e76Ag31RjKtNhVC1wzvV7+A7Se3rrTKTvMDrWvfbu168ddLL/Y43P92EU HJj0MrNgB32zezj9J2cYPeUSNKno2UE7A1M5Q/3DqKOl6WHD5A6aq2OufTU3 jFR8Pmp2rO0g+uL48/ZUJOTqshZtxUIFwpXkVwUEEio0agtf5aQCqe6zpf+O kNDi+aTg14JUoFT0+XOECgnd32Xo53SACpoNRZgktEnIh6TiTX+MCnSa9R/T mJBQeYmAu/sJKmiQjclSe0FCh983OfqpUoH/z8oMVncS0tdNeMurTgUK//4g 9wAS+qry8VWwJhXk77g/fRZOQlRbSpbRRlRwQJvs9zyFhOT7eMwlzalgZrvZ 0zOHhB7nz5smWFOBw7cP+9mLSSg8uM7wsD0VvBzps9yoJKHWV7F6aR+oQDbM 7NX1BhJi0HJ8oOhBBfrlFreZ2khI+cSDe3l+VPBDvk1YupuEnvMdv60STAVH nI8tZPWR0PdVDo3SKCo431m3HD9EQj0d01cuxlPBn18e6nSjJLQns0q1NoUK 7NN2ZGrGSehcQPS56zlUcKfoTskKmYTsXrxFrZgK3u2+iTymSCjx5r1TmlVU wD56leT2h4SGj8kd72mkgolfhycXKJiXY4/cw04qMO82+1pGwZfnyYdJ/VSg l0ilsENZ79BUdtB4jAq+Spnv+T5JQulJ4ZJT01RQ3plinTlBQmSvV0SLZSpQ Sb5YeHSMhITNb4sublDiZMJZPhIJaVw9Imi7ixrOd8U8ejxAQh8PMfOuM1ND WHmsg1QPCeUxj3E4cFLD01ojqpsdJDQ7iXfTCFJD7c9PNyebSIhYE8zkIkYN SIptbKaGhO7+sKFjPkANq5pXpfXKSMjzkwa191FquL02HQkFJFRsfGiL4wQ1 VA8s4s8ZJLRygf7fF0QNfD+jma8nktDBfcPLAqrUYE5nQ2//jYT8RwKnxTSp 4QX6qnzAh4SqSy3J33WoIWF2NDD+IwltRl0dPWBEDYWm50khr0nIWI+m75g1 NQySSLnd+iQUjPq7Mt9Qg3S27CcJTRJqEs1pO/mBGlq5YqtG1UjoRL953Rk/ ashXddaokCahpANWPKbB1ND/JzQ0QpiEJGxtdb2jqYHbXVz8NwsJsbO9W+pJ o/hlvzfcnDyMJsFHyLqNGjQEP/48HjyM9LwCjIJ7qcHrTRSt1Mdh1Pk7KLl4 hBrc5pnC3z4bRqVWUed2L1PDr8Psq4ZnKfMZk2YWy00DNNwxrMrDQ4h9ISuz XpgGXqnd5v1YNYRcTufvLErQgFfOjTiVX0PIqrPMHynQAN1L/QeML4fQFcaO /O47NMAXv7UuQDuENs3+srB8pYF8AfOJSuYBZJWzcedYBA1gxuuqcZX9iExL FXk3jgauiRe9C3DsR+1hjPIx2TRwb0fTKWq5D/1qEnhwupsGPL1oAnqbetFD OeXEZwK74AG/OHuAzm9Usv7+anvILpiWTix5OtOG2gWsVp992wUtTI0Bd7+2 ofETBpEsP3eBSnjORh20IdaXF5bP5u0Cd+0AEx2/VqS5xBSa2r0LbGoJj2yP tqCpP35/vHloQTqx3kQtqx5x98e4X/pMCx8sK02/7BQjyc0v8mOBtDCdwjro eaYYnRT6NPA+nBauGy23Z9Bj9FDrsWzOL1pIVOR4QdhdgOI7ZHok62lhK3f5 gDh/FlJpzDpAy0QHqhI3ZSb0Y5Aprq4ucqKDF7vPeOXaJuB/J9mJ8u508C3M QpZ88Rd2z7j7Jt6Xgq0vq1syp+Cf8eMyAZF0kDfC8XOpPQ3P+tP6Py6iAzr1 DqG/2jnY2hR0uNfpoPh9IondtwTTjXzKcqOmh9Ion23yyVIcqNPEtsNIDy3u M3Sjw6U4++bD0kk+egj++2btyJFyvK5sL4UV6CFKMFsrrKgSv+fIWXhsSQ/q Pzr4+xPrMIfnzuVBO3q4Gv/Dq+RCPY6mV425/Z4eRCeMuhz763HZRocm+kwP 0Wd5vD4yNWL68aV87l/0cD9VLy3gQDP2zDvigsn0oEH33bfsdisWUXg5KD9P D1msS1kHv7bipOSiEwl/6UGW+WnMcHcrboq59ieAngEU77ESTmi3Yc7PZhpP JCh4X/u81u12/J9BnCCPHgO4JNaE8u/rxE+v8JdKmzJA+U/Hf/f1OrGKnNvj 888ZIImF1zU9uBOTaMxyXrxnAKc/4kVBrF1YOvqwZmskA5jsTznGPtaFt90i tiZ/MABb9v33NfzduNmS/Tt1KgP0Xji76X6lG9ucWVw6WsIARNurh8WSunHR UKbv52EGSHh9681Lk9/Yp1ryZNwkA/ye+zB/3f831k/5OlS0wADFEReXJYp+ Y4b3r47MUjNCSt8J32r2HtxjMtVJx8wItJ0VxwNO9OBE9fsOIpyMoDae8Elb twdr7D3dcJXICEGHXBLa4nswkSHJ2vAgBZ/I++3c0INXZkWF7WUZoXGl/onM fA8OLqIy+3mWEcLkmbofyfbiEZ1yRmYDRuDKX9pzMaEXZ11QSBEzY4Rr6dIn Iit6satM7N2TLxjh95oL28xgL5be+hRr+oERXkktHtTh6MPbo2vX3nswQk/V Qs67/X24pf7xyld/Rgi5P+/qr9KHbUOvnK/6xgjuu+PnvEz6sJpzwZ+Bn4yg JGC81/p1HxZ8KuO/ms4IOSliZZc9+/D0rXClPQWMoMu8iDnC+jA+xUbaV84I 2oP5tDWJfdhP/L3b6XpGyCg67P48vw8bsiwcvdPOCA56JTcZa/qw4tKj7qd9 jEBa+/XEp6MPM/a2vnMeZYRTHrMTjMN9uKf0nFToNCMcPn1yyvJPH05MyGhM X2aEG1KbwXXLfdjBb59t3SYj+J3RkOHd6sM3XgeKjNAyAUPTbP8N2n4soc9Q sc7KBH+MZJYcmPvx6iW7p5w8TGAqvFoQxtaPq49Nch0UYYJeXxyQxNWPgwW0 88/sYwLmNef+VN5+/JS6Tl9L5v/5Rbt+8PdjNHmK2VKBCa5Z3n3rK9CPOVsS U11PM4ECX0KNBQWP5ohoRV5ggu2xF5ZAyc+K9KbKucYEUrZN9AwUPlfXnbim O0yw4HNoXxlnP9Z+/lx9QocJlPYoW9rs6ccy94ZXt42YYMlxOkiUqR+HcqJt D3MmGINdufK7+jFzQyidgA0TPKpZP2W02YdffVpnjbVnAhocXZ5C8YN85h63 nDMTPOiI3eSb7sN3NzOFij2YwD/eJSCE1Icrs7jEr/lT9g/xOqfc3YdjDjUd M4lmgpQLjONdxX2Ya1z65HI8E7TJlT9uT+/DTpHu4JjKBHk3pPYtfO/DujwX 1UOKmcDH+32i96c+3Nj0TXN/NRNsPEk4zfGyDyu7Uz/MbGKCf69++2QbUfpl p+Bp0wAT6HNyq7+APuyWK2j9YJwJ+JVW09yl+/DaC7s3kzNM0NPgVFvD14c7 yHLuu7aY4HNY3pWyP734/DdfXx9aZigh2w+9a+/FaTpzQSKszPBmF9M704Je 7NOaEHdciBnkBa+8KHXrxTuejMnlRGbon/gnofisF1uoGmfdOMgMnRLqQT23 evGVArEKs5PM4H1DpTBPsBfTxwaRIu4yQ2x3Fe9meA+20VudlNZlhuAul1IB hx48Knh7IdeYGT4p8eVYPejBJZ/ZqNptmMHtscmRPt4ebP/KRYQxgBlMMsPP ZTn9xotXre89b2YGr9R9ePB4N37E0Kq71cUMiyd19UxYKPdPyRET90FmCFve 0Tk30IV/Kf6xiZllBhIrs86OYxc2Jej7d7OygBrtMjmnpBMPLKk3wiUWsLnT w1Ev3oG9hbrEn99gAU32Uc9ecjtWOffwVYQWC9DNPdM5/6sdR/g9ldh+zAKy A8VC0vLtWO+Y2+t8dxYorvvRE6LUhkcsSiUV61ngi83XGTXpFkyelH93SJ0V qtlp59fNavDioMBR3ju7IaL/tBC/8A9MMPgrv1dnN9wei4wMTv2O1cfbT+43 2g2rfGd/eat+w4nTn88p2eyGVrGAnXNTodj4H93dh192w8Nx/ZkzRh9wD+fi 29iO3cC/TsyQVQ9FJRdq6xQ194AxU6eNkm4umq+Oa0YP94Ca8Pexg6/ykOjV jx1qxnuA0eNEaZhvPnp9Ewa1bffA/UnMMV5YiOR1sxYdAvfAtrirtBN1Cfph Fy1Q1bkHYhNDzk0KVSCfn69N7t5lA79CkLB2q0f3qS/Udzxkg/J7nm7ic/VI 8i7bsdvGbPCky54T32pABTQx6xo2bBBjsaGQItCIyFoNXpf92SCjy9NePqgJ pSd/XawOZoPavL8vtpebkAOd/l3VaDZY3Yh7prG/GXGnrhLOp7KBxHTBpqxT M0KMhIzTTWxgd2M/+ffhFsT8cIq/oJMNApzDehzvtaD29Iy3SgNsEMctbOPl 2IKe6F5SPT7DBmeEJgrqWlrQlfsnzYPo2GF6E9vXPmlFL9P0qfzE2WGPepk7 h0MbetBfJXtDih3kL5opuYe1obOMMkbsh9hhrwWHhVYB5f/Qw7813rLsMBjY 1LX2tw1FM3n6e5xhh87t3v2HTNqRq/xCxeUL7CAskX5B1bEdmetqrjFdYofb u7cNMoPb0YlMgo6rBjs0iac2fKxrR416mZIfddnhFs+hxD8SHSjDQ1DrvAE7 HD0iRut5sgP9l/XOY5cJO9ycDYI31zqQIevleUcLdlgT3HPuwosOdPl4MvGM FTvYG+35uPdjBzqiz32HypYdWOb8v6kGdqD17IFch7fskMFV+vN9VgcaIp2b Pu3IDgMK0iq+FR2oYne86JYzOzB/DN2ebetAPgYvPrzxZIfkz5ZBvrMdyNa7 O1PJhx1s1eVVO9c70P3c0+R//uxg8iSz0YS+E0myMV6zC2GH/7pL1C2FOlHi vGOsawRFv6GWVNK+TiTburET9I0dHk8onec/0oly0m204uPYoeLUam7y8U6E vsyl5f5kh1WW9G/WqBNV2j5mrU1mhwd+0hImFzvR1XsjRj3p7PD17i+jT1c7 UetJHTyVzQ58C8zBHTc60T2hLv6NfHYIx1HrNzQ70cCmhhVLMTt4BWhUb2p1 IsOB2jqhcnZQ47K80vmgE03h8/ukq9mBy7e+beBhJ7KMKnJQrmeHtvCAHF69 TrTmdKL7ajOlvlwP7jlQsINh2jGddnYw52IX+H+c9qK0h3k3O+ziXDD5/3p3 qdjRt33sMNXjkdtF4WdnIqh4D7FD8Jc0NxrtThQ49d/X8FF2OFhnc1+Xok+4 nmshicwOJWYiubMU/d9+eV3G0+zA2C4mn0o538HPDDFN8+zQWithFEc5f8pz x63BZXYo/DH2p4Xij+LNDc35NYofOUeeHTvRiQrkbFKotij1SW4LraT4e5Zn jomDmgNeK4Qf8JPsRNWrpgZidBxwP/FaS4BwJ7reTSo4xsQBGyufNJs4OlFH 7gPes7s5YE6p2ekspZ4PQjqf3eTgAMFUe8m5fx2IZK9Ro8/DAfL6ifyd0x1o Fp23/yDCAR7GxcaazR3IWqyow1+MA8z+WPktFFP6jebEkZh9HBBgdCSxNqUD MVQeIpXLcMDbD6O+St4dyDvu+6mOYxzwU2qvftubDsTttvfLmAIHlDA17U8y 7UCEq1xq9CocoLNxiSwDHShWxiuK9ywH5IxL8ncc7EDSbAwbkhc54NfBD4ml 3B3oZOv6L9XrHJR+HM6wGW9HN++RuNwecgBX9ZaNDmX+uk8+MP9Pn3I+Sdpm LeN29FCoszLemAMYbqh6x15uR2YDNa9qLTggb8/gd0WOduRsmDrI8o4DqJw9 3t4LbENZz9//9I7ggFd3szRmHVuRe/58htY3DjBszJIk6LYiXfpHRRJxHKD7 RW224VQrYgw905KXxAGslZKV0UstSLuK5u94IQf0EV0/3tNpQdsiH8+iPg5Q jOI0VhRsRhfq3H7P8XMCuhK03uhaiwR510l5wpzwWONn5LRULZrVezL9kcAJ iSg+2bCyBgWuXt4R2s8Jasq8QZbUNYgsxrpP7Tgn/ClvV3n4vAp52nk/j7zD CU8WOU+5y5ej9n3+DDf8OEFvs8m/rD8PXZLiP2EeyAn+NjbnAmdyUdH+MFO3 YE6I/lDHN7uZg+IPxdWURHPCGftDfTcEs5HDsXwP2XROuL7aZzilkY72nx5h 427nhJwTmfb5T+KQ/W05/i4eLrhqFbPxTtoDL9zJUVsS4IJ9Wwotstd9sfHd 06/YRLkg42pkVdCuL/iGtmqPqiQXkLx30hSNQ7Gk3v3QHEUuIHwyIbh++I6b zT4Qgu9ygVnJJiFqPBVLfGjbr/MfhT+0/dSbKxjfS9t1zDiMC0p39nH9YyzG nsNyJ59FcUG1lUHDM7NivIICLjnGc0Gd9VU/msMluHLz9pPvuVywR/ZXu0l8 KX5s2/lz5jcXvLh+pzHatgKHf6fPWO3ngvzHphaH6ytwa7tiwc4wFyS5vHGo IlRiJbmv9RxTXFAULlrDV1WJWefvziisU/TSZR2fZqjGSY9/H3YQ5IZnLE59 uvdqMSmI6fgnUW4Qrrn8IC6sFvNVn0Q+RG4wi0k06R6uxe8lg9WjD3LDvTnj sDnjOnxjRPt5pRI31Job3yo2qMcunB52TSrcYBvjmCYWWY/zzuS/7z7LDcFR QZkPe+sxMVLId+oyN9D6SLsaXW/Ayw/6Uvfcp8QXstbfSjbi/Z6seXy6FL5c 1ip/rUb8IF+5lGDADY/cZ0RfezTiCoGwVlkzbiDK0RSl/2nE62oNPaeeccPR Vd1qWsEmfNhui3T+BTeQaIJHxVSbcGCnzpLmG25wkvS9WxDWhGvpvDd033HD g/t5DcermvCOfNGuxx+4Idr7a8CbuSZs6i/K/caDG35cVX8sLdqMT2oMykeE cMMf5eKxBINmXECmm9GP4Iabuz9GW1s1YxVH6e+S37ghTTzHIuN9Mz6f9oon KYHC56Pw8ktIM668HNlgmcQNVGn6uoo/mvGlkcqPCmnc4NhVlnQ1oxlf5+Ze Lcjlhrt/+Vl+1zbj5kSlpPeF3KD7c3n8ekczvnXhkfH5Em74cKy16uRgM+7s /yTKWMENw8mskf+Rm/E926TOumpuUM65Z2yx0Ix79nR4f67nhrXPpTw5/5qx TtzGxVvN3FD8JvGXLXUL1u9Wy+7pomDikYSbbC149PmzZ+G93NARd0D8OU8L NmEKlNIf5IbAqUe/aIRa8FRUweC+EW5oHK7UYSa04KdKI18nx7mB4/rna58k WvBsK5PGryluYH50PPjV/hZsaXaU0XKWG7IMHYyGD7Xg5V13i+UXucFG0bCj 6HAL5f341m5thRtgUoKb81gLXpOPOVrwj1IPB3mNXtkW/Kahlvxuixtkgk8V CMq34G2jhchz1DwgwMr9uZmC32/zaTHQ8cDEnYpdWxS866sKRx0jD3DIOWpF UrDLEaMab1YekCREtuXJtWDGag/Hm+yUOCks9yqF30Mv7SQvNw88z+O5q3m0 Be/5173wm48HRuIKNrpkWrCP7058mBAPXCDd32g52IK5DkrqP9rLA1tv6n+d l2rBgaVXBfeJ88Aq15LFUfEWzH//RStZkgccP+WHfxFtwSFL/7knHuSBczHc UdYCLVjUs/js88M8INHzp7+BqwVHSkysy8nyQGf//pKo3S2YWLg7/a8CDzjE x+XN07fg73fkzfJP8sCPv0dV8neacYKLY+/ZMzwg/YO2snyuGUvv/eFPf4EH dlurV9BONOPk7MYrtWo8oE0IOV/a34wzyEIFNzR4gMnQYCS7phkrOp615rnN A35SVsILRc04V+Cx9O+7PDBnFcSYkN6Miy5nherp8gCNyRPNMEq/wkjfbQkD Hji978lct3czLnuzazfZmAd4PUQSAh2bcXWixttnFjww1n9RKMSoGV++8FJB zooHqJmYJEc0m3FDf9jMqg0PkNeYNpJVm3Hrnj86Dm8puEi+rUeqGfc//6ji 5ckDVZ1uN7kqmjBVcbFItA8P3LWVaZkPbcISbJubWQE8wPaQoSPvRRN+8ssq fyiUBz4NyyQJizbhtUndE/K/eIA9dvLRLeNGLHQyhO9SKsXfCmmXZoVGrOLa uaqTyQODR60Dr9A24o+S1zI/FfLAvtKZpvPhDZjTQEm2t4GCBZnyXCrrsWKa Dcd8Cw/kx2XxKXrXYy3q1HnaTh7wOTHTvXq7HkdGSCUfHuABvQi1tqzBOizT xy3tNMsDv+9/0H49VYvV7sztO8DGC6PNVsUvuqqxWcxBOhUuXmASmqqy963G 3ktGozf5eME6+NibssvVuMO3L9p+Ly+4GTA28eRXYf3Gmr3NR3jBb7CxkOhf id+qxgi81OCF6yr/Av3Ey3HaSa3dFb68IDt13jUkpxBLLLqHBnzhBSvl9+oM 3IX4S0LBIcP/eKG6XUao3aIA2wkRLu+K4gVCvgd1HDEfq2yNu5xJ4QUtCYNL jR9ycF2xNVVRIy9oyz4LZjqWjkdVfZayWPigViWIZr0gEmtSlTq5sPHB+ebx z65l4bgqZ4lDk4sPNPPbnZ/uDsUJB+4eXRHkA6qIDffX0YH4OYuoudxBPngu 9WBi349PeKvx53iyGh/wslMdLjvyAfFqVv3+8ZEPBtS7Hn73jEcXlWPAyI0P 9pQZxW5XJaCXRMc4MS8+MPiUlb9InYi6Z5VsggP4YNnO5t0nyyQU8imJ3fMb H1iUbHIqRqQiQu4X1WclfMDap1ffeC4LaURYJR2q4IMTVfy2l9qzkONHdR5y NR8IPWOMbTDIRqQbTCN6zXzw3luui/QuB32fsne4OcgHR0VC1Nt/5qGDwoaZ Clt8EBR5rcCvqQhp05wRXqTiB+VT8m7D1zHyIIt8SKLlB+fFHzo79RhNZ3Rp SLHyg1uNom2DfjFKvnZlml+IH6on9/dt3CpB8u9kxTdP8MPrxM7Z63xlyMiI zT1HmR/E+9QeZFwtQ4FXpuetgR9an1g4PHYsQ3/5YotmVPnhfJFyXiG5DOWl CGgPavJDxc+vd/4klSNEovItteaHcKEGOy3+SsT+blG02Y4ftrdgMflCJSIJ jSb22/OD4ZjriJhVJXK+U1W95swPpcc4Qm9VV6Laai+qI1/4gV+u8X7z4yoU avTOW/k/fnD9j/ra6OcqZE5jKXw5jB8WMmJfs2RWIXbl2yeMvvPDml47n89m FdJMFnwekskPiJN08MH7arT/Kuv2j1x+uFLQ6rsUXo3+kbc8sgr5IdRF+mRQ QTUKJQ7HtVTwQ85Pqb/0K9XIHLcqDNbwg9opu40mthqk8qC8bLqBH5axr1DM gRo0/CVukKGTH552Xpg1065BabL/mfP08ANNiGTXQ8sa5NzkvkEcoPDtuq92 /1MNkmSy4FMZp2CHbf9nKTVo7bvu9ytT/NB9VXrGpawG1Zy9Iac1yw/7zSXr Yztq0FN7eXXrVX7K74m6/c4qZX8ByX7HdX5QVXjKfYK+FrFl8Zl93uaHepWD xXbctWjoJtO/UBoBMBy3eVUiVovS5tZdEugFIFns8DnOw7Xog+c0dw6zADTt JhwwO1mLbh8YiK7YIwDKN2mg/lwtkqxsOtrGKUB5Lzz/rnCtFv3VLyka4hWA /o/j7+Lu1KLqnbSrs4ICEFqevy2mU4uCQ2N6NkQF4E2dkPZ3g1pkdjLQlElc AM4VbrUee1yLlDs/rfJKCcApe5H0KvNatOfFK2eJQwJgVLl81cSyFg2ymXHK HhGAMI2MDXbrWpSS+CASyQlA5rCyeIVNLXK6dP3wteMC4GXOf9TZlqJ3HBVo nxKA4ySrr9cpeN+HY5dNkQBwZ7N1SVDyV/eKd9ucE4AlbxUbhhcUvQXcxh9U KfuLtlL9fUbRq0W/7HNFAO5d5ONYNqPoXf3rGK4uAMRj9Rd2jCl6/SfZEm8J wKWnfKoCjyh6j/aG5d4VgBDadxVntSn+1tcfqrovACPlA6/sb9ai1MdFue26 AnBrUmtf1SWKXvoUVZKBAIgNXvMVB4reb1EdcyYC8E1d9bOfAkUv+BtsmQlA 3Om/a9wHKXr7nBeYnwvAT+L+lJ8iteg/XtPdknYC8DjDOkuAphblCGtcmX0j AC5Bsle3lmpQN/GEW9Y7Afjb+pvMO1aD+I8w0ql+EoC69U//zZXXoBMK82fZ PARgwzvSPCW9Bt091f2+y1sAdt6mVydEUd4vqj82TQIFoKaGpV39TQ3Kuuaj dDRYAD7TdFptGtegzlt2dmthFH2CnjbjN2oQj57asut3AUiU2V1qu68GBdiR /8RnUPgfWZnHllWjDIfmA1Y5AnDXbe3f/fhq1OacY6JUQKl/iFjKXe9qxOnr OlJbJgB9Jtb6kprVyDd+f++fVgHIqhJzPNdfhVKS2QUyOgXAWdet62phFWrO XNO07xGA07Hyz2JDKfNcWt3KShKAM0+FGtS1qpB3j2mtzIIAdKq/UYqurURJ QxqMq8sCsKrR/Oz290rUMH7iYtGaAAy39Sjqv6tErEuMpdepBOHKk9uvAo9V Ig+W+NxnbILw2tGyyNO7ArkqT/5IlRGElsNzljzS5ejH2ZbxV8cE4d6/Gyan t8pQlVquxFkFQTjqdK6up6EM0d9xi2xVFoSAroZee/My9NH8QNDSFUEYz79W 8zm2FDmFP/6k8EQQWidl012pS9DZ+8bT1y0Egabg8ZGLlcVoF7/BDVMrQTh4 mjHsg3sxcvZ9IBTyWhDi6N5LuXIUIxdn9WQqD0GwD1TU3pArQm5PFLrqfgpC 5/VXNt9k8pCPIrWU/owgjLwqFoyNSUVhjUGV3s+FYFlG6PE16stYOBd2fbEW gtaIczVDvSY49BsZhdgJgUbZo+2ZQGscYnciN+69EKSUrZ5JmnbC/xG7fxb7 CIHEhbwj83R++Istn+9iihAcf4l+KJhEYe5HuGEtQwiG9o3bblhE44ArJsw7 OULQ5xi6FGDzDfsTsj+wlAjBitlxZsK779i3VtNWooUSrxeJ+O4Uj71EA+9r LgiB4uvB/XuiUzArk0rQgxUhOKkT5eIvmIo9l8ba9f8JQd7njXjwS8Ue1QrX n1ELw0jduX8079Kwm1UHuHIIA+lW3kTRtQz8sZJbMu+YMIBZC/VcQTamTS3Q L1YQBs/SLKVTkjnYOcQwovKkMLQcKSm29c7BH55n8LedEYbuC04cyfdzsaPg bZbpG8Lw2fpXeyM5D7+18J8XsRIG2tCC2TN1hfhy6bH+ARthEA34MHpDuAjz 8zbXRLwSBlbdu8+uPS3CGYWs38QchYHacd5ihxHjKVaXO/t8hMF3okvaS7AY 5+hJnB33F4aX8t82f6gUY5eM0sNxX4XhrFiGipx+MRZ7sMNwIEIYaIKKaj7H FeN7P+3ypJOEYbtLYfjmoRIsucMbN5MqDAcNXOjrL5fg5ZuZ/kmZwiBzRfXd r8cl+PP6wtOjhcLws/dNXux3yvv6ktle+XphSF46FabHW4oDwphYV5qEwWz9 x3vmY6VYfyFuLbNNGNRV/H7zXSnFW0GjLcd7Kec5aNyv/bYUy5N1nE9NCYNm YtOYdU8pplHefL45IwyDIrLMMvOluPlzsE7hgjDYNtGwXqArw2bHuxTRP2Fw yVU67S9Thk942IhTbQnDGVlCeTWUYfpBLvYSKhFIvvOs68GtMhztojF5llEE bgwUu0fYluHnPbMdu1hF4OLYjZ/XPpVhlcNepeVsIsA1a6ql9bUM/+6oCbnI JwIBeT+/umaW4dgDpq4MQiKwv8Ck5WdZGbZ+S29TLSoCygdq/hxqKcPs+85d vywpAp3Bo9fOTpXhAbthJZaDIpAfxGXavVKGE+vfSdXLiADVSgNDHVU5fk0Q 5fY6JgKEHTpxQZZyrGpdQHVdQQRyKoozKrjLMXe19syekyJAJ8Bd2CBSjklC /343KYvAHS+JM7KS5Tjl2ddKHxCBl2/FryzJlGOHMoX0G+dF4MTua1PsCuX4 Kl97BKeaCPyTGZf1OFWOBcysPNuuiMD5vUoq+mfK8XgR+6sAdRFwjgk4GHix HGdwJhvduSUCTuvKQlJXyrGT8bWbvHdFoM/c6gSPejnWyPuj0qUtAld2TJP1 bpZj0T3uh4IeisAaw8U0pjvl+M+j/fxa+iJQ1i9sx363HGs/7T1kZiwC+moC Kx73ynG1rTd6+0QEBB9qoUta5ZT31Jlbny1E4Jp5XIoaBX/3WDaOshIBg2aP eHdKPndg3Ot0WxGQs1T1ZaPwOUVqe1e8FgEHv+qOrtvleD5hd3SXA6W+pWF/ Rm6UY93M4sxJJxH4JjV7Tf56OW7EL2o2XESg7YWVQ82lcqxcK9m/20MEbHrN 6WLOl+OE9t/zez+LQBRTnGW5CsWfQU9aWX+KnzyP7h06UY5dJxH/+a+U/nh5 +87vo+V4dWnxkGaICKRtxTE37S/HbYxat15/EwFGQwbVAN5yfJaL1cQzTgRC L6vIGrFS6iOCX4f/FIFZOpbw99Tl2Et2X3RpOqX+J+7RBk+W4U3l7sz2bBGw sswM+K+vDD9R9agZzxcBWhH1lvHGMqz6YGGeuVwE9nr0FpqnluEs4xhakWoR mLu0Tz4+qgxLWN7lP1IvAiYeF0cUfMswtUshutUuAvbVDHkXLcpwfrKbd8jo /+t1/qg+oQwfzFOO/kWm9Nf24YPnWMpwUPlcJp4WgSldXu+3K6XY5ved/pFl EXC9Osq7q7oUH9lFlJamEwVTiaI5S6NSHL67A6kwiYLAAapOFcr8svK73tLY LQodvdtZFkdL8aT07GtrHlHYc1cgYHOtBH/TzKsp2CcKRPXgzRWnEsz5yLy/ 8YAojO+N7dwxKMHvzQgLQzKi0Cd46f3L8yVY570LP52iKOxv+0iftasE8yXc NLl2URRO5aYq/vemGHtsTdEOGIuCi96BpqiYIqxmGVCd8EQUti8pnibcL8K0 Y6c9X1qIQnZG3ak69iLsUO/DxWErChf5STOprwrx8xBF4vmPolBzsEGP/WwB 1jzphBK+Ufi3E0z8k3Mx0Ubgte2QKDhUMj+L4szAedOqc3u098LK1aKZwB/h WNE71L1aZy+Y1jJ8uMEXhtOOLOxzerQXDNJCpkY+huB4q+AHK6Z7YbGRpFui H4SD1qZrel/uBSbXSMYsYT9sS+sX8+PLXjh6/sK/+Oe2WE64T+tsCyXu5vH8 0YgfSio8urLRvhfCLZymTPQD0EHdjz6Z3XvBr0UYRIa+IGL04ar9Q3tB+nuF g2lXEOLc7yjPNkfJ7+9r0sgIR2sC/gwW9ASYxm6Ge9i+o859J0hKEgR4o5Aq 75WZjEZbnp4DSUr8RuFw3bEUtPg2KubCfgI8lpP3ZndNQWydzCYa0gQg/FU/ d002Fam59P8xkifAeT1quctv01DeuNOKz3kCpPN5GO79k4Gq/bI1Ay8S4C3L oQNk+UzUqTKdHaJGgOSCtc3qt5loKfDO69irBGhp0D5Vy5qFpFX37+TfJoDh 3h8svnuzUURcA+OEIQEmNxui3vHmoqRbNE+mjQlQpMCW26uRiwp2FOsWTAlw 4k347DH3XNR9N9Jr8ykBfLKWv1T+y0WcjC84OW0IwPd4RsW0Pg8RMuJe8L0k gGvLpSdPt/PQYb2+duFXBOgx93TSPZKPruRc+Cr1lgD2h7q/7/bOR86m/MKn PxIg6WidwhOVAuTHfe3t2U8E2P1hbqvCpABFFjsOqLpR9J/+LcToU4AK+f9E 3vQigFoifeep/gJUX76X5t5nAognoLpDNIWo5/ltAx1fAmQKCVdv7ytEq9WF +0y/EIBtv/zO5SeFiNZm0cX8KwHUy05PlLoXIk4xKbLVfwTojn0nK5RQiI68 8kl4G0aA5Zip0idjhUhlXwXLhwgCuM8nMD+iLkJXW/49dY0iwHPhmTwF4SJk esDgiP93AqwvrTXaXS9Cosz+ZJs4AqTVRg3qGBahtqnSqHvxBEjcYcu68KoI qSQSuUV/EUC1q3JTOLIILXnebKBKJsCTXQb7WNOK0A9zJ5eRFAIMXX3ivFVa hLiOkNZ+ZBBA+fj+pPHhIlTNxpnmkUXpn9755wNzRchh/oyZRQ4BNBUvaHdv FiG5FkuJG3kEuGC79aqdESNyalS/XAEBHFQ6J1q5MAr3awnkLSLAxyNPy9pE MLr1glrjHyaAkdVx+S5JjBhvH2PqKyFAiMmnx/2HMSqSf1RaVEaA7V3vg8cV MLLm8X0TVUGAAmFO+qVTGB1YLZZ3riJASvniIs0ZjAY652eMawjgUvAlmfcC RgHZhLhLdQRo3ZDyO6yG0aUgDT3pBgIgJfe1y5cx2rZ7L8DWROGzu6L29ApG GVoprQvNBIh2/zbrR8GPlYY82lsJUBNmrocp+aJC7Bey2wkQ85cguEjha99A 2/91Uvo5ujzi0EWM3PqeZdt3U9ZvjNs/PYuRSmHEc90eAowcDTyfeRqj5bCm A2f7CKDvds+X/gRG8Q47JIkBAswmS9A9OobRQ90joQxDBAjd1LpUcQAjbtC9 MzVMgMiinD3yYhjVEj7vaRghgJiL9u4kPozeUeOq5DECvLuTQCu/GyN50ux7 vwkC9Hlr5VdSYzRVKqpkM/n//r2xY7xShCK+XV+6+4cAdfVx33nIRei2s0Oi 0gwByN1f3dt+FyF8YUCUaoEAeR2JMe/zipC15J5u0iIBqm3jMy3ji9BBBhXf imUC2IX3Fdh8LUIB1WG7PNYIIPLaNC3veRG6HN9QYL5OgBXRkxlb94vQjtuW jcYmAZ5ZcLTdvViEnlzRIfNQiQGV9YPfd/iLEEHaK2qNWgw+21xh3twpRB2s hdq9u8RgnSzxp3C8EEGjcEMkgxiEf0FB/6UWIt4bfamH2MQgZTyDtV25ENUf YzXbwyEG0VuT669FCpEjp7LEAqcYVDLz/lXdKkDTbSGBWbxiwHRbF2vlFaAS zftvzoiKwYHPMuYfDxagSj+e6qsEMbh6S1XvMjVlnhubuO8RxWAxaf2eSFc+ 6r54PslCUgzSa60dV97lo3lFmeGQw2Ig8lDgcXxlHhLl27m4qiIGpZy3w3cf zEUSt3L9qc+IAaHybUfWYg46+PnFEOs5MVixMdn0zctBCgzkV+KqYiA6nUZN Vs1BV/82J2qoi8FIUNlXLa1s9LormvOnrhgELe2/GaKVid5z6ehmPRIDBvvY tiDeTOSizpdYYiAGhXOOrxdbM5BvlceFbhMxYNy9bFdxKQP9yLa2o3suBoY5 sHDyaDrq/HpxQPe9GCge5k+aIKUguXtT8dxRYjCzKfIrnRyHhqojrm9Fi4EN 7wc3Ko045HnyztJYjBjQeJ690JUVi8YFi5Wzf4gBp39Rp+KH7yi4/0uTVooY MH/037rG9w3RGJxZCcdiEMjgGJSpH4qazYPgwIAY4Df1O7znHNHbgWtjHENi ECZq+a/+v7fooPou9/VhMZBQNjFpTbJDzkct2urGxGDtc+qQTr45Or50zthi RgzMm+4xc2TcxOF2cx7pm2LQfr1whCfqI3764WLXaSEiDGeh6dNaYXjNvWVC WIQIamS+owTLcPzR78HahigRiKplW58/ReDwKCuBPCIRhkzf6Gx2ReJmHH5f 8SARjGkah5j/RmO5zdXBwyeJ8LAsINaGNQ4X73Ka332KCKaCW5YsHnH4Kstu 6hllIghPcxQmMv7AhoLixJ9ABDnNraO01PE48IS6oZQaEWZeaR6NH0vA69Zx 5L13iSD0smhi500SdrGX/bd9jwjST/ZZVU8mYS7nQqYBbSLo5D2++UQzGUv7 tx0MfUiEHI5Maz7eFPwwdecpvzElv4W3Kns0BU/luL/9a0KEA3/uXe/lTcUv i3m8Ox8TIUyld0BPLRX7NB1KDjAnQsZnuWNe8am4ZObuArsNEVi75YwvGabh 6ysk6nlbItxbNe6775uGezbNOZvsiJB1K4S3qjANL7I4y3nZE6GY5UP4N+50 LHEwxYbJmQgR3v+l3MtLx67GjOvU/kQgabkaj4xmYKMakXCmL0T4YWxIM82U ic9Ky53l+EoEDxLPjujhTLyxoONOCKH4N235lco6E1u8TRdE34iwpl34MmQl E18Zqi66+J0IGgqh3ENcWXj/uQH963FEWLa5Mqx2LAuTGJl+6vwkQlO/r7fz 4yx8J+DhKft0IiQ+jI4PaMrCsn9fDH7IJMLfkpiNqfEsvEfb7YNHNhE2/r57 +GgrC1fvzagLzieCqAHTWKJUNv7uVPMsupAITNOBho6nsrHT2ABXAiYCrUZe ovX1bKz8k+lBbhkRGGh/xWdZZmOBPXupSiqIYGBesEnrlI1Xn8vHVFcRoUe/ 5balbzZubbuk1lxDhHWan182IrJxsqLudFcdEd6WK//89isbe/5n7TPYQNEj m+j2OC8bm266yU80EaH353WZa5XZ+IJuRPdsCxGUhOKCr7dkY2Jphv1qGxG+ 5xgMmPdm4x2JWsJ2BxGYy+/v/jmajfs+DZbTdRPh81mv8/Qz2Th3atl0dw8R TPIF498tZ+PAa8y7efqIkLasZsq3kY1fpOxNFR4gwp0U++wGqhyswaVwR2KI CHczFdqj6XKwtO3lf4dIRMjPXt71lSkHM/3WDZMbJcJTpyMBCaw5ePyUzZlT 40RIenm9p39PDi4Ndx87S6bMV/93uWPsOTiCOtLt8hSlPsRndN8p2N4wU+bm NBGmpEoLTlKwVlVti9YsEaKdvBvnKOsVDw7ZPJonQmxFQHYVhZ/La0Xg8SIR Qit1N0so+8/PMRc9XyaC4ejpA4MUfQ03Cfp2q0QwuqbUupc6BydkKtC/XyPC 7wu8/s6U87nwX0n4tE4EbouzbHtWsrHBG73rnzcp8xLYtVBA8QcGbBYDt4lw Ss15xncsGwuf8QgMpxIHxVGbAq++bPzvW6RSLI04oPPqhNTWbNxJnzXwi1Yc 0qNESZtV2Tj9cZ1TJr04JNy71WpZkI196ockCxnFwfNnejV7Sja+7MfyrJ5V HL6e+3ilOSAbS60QuNr3iMNB898/Fz9mY9p7itm97OLwnxNz3lnbbFwo8mhn ilscztf+1/nsNkVfpuVGE6848PRljLify8blV53+ZvCLw+5eA7R4LBvXv/k2 5yAsDpOnpl7Es2ZT6pfxx0BUHN7SGxE31rJwe0L5hBpBHJIZkmtDR7Nw3++x QU4JcZh9pjTdlpuF9SxXe//uEwdt6DIw+5aFRxkZuvukxOFm41iLpmcWnj6+ vzn2kDikTQSWyzzIwptfnhQryYkDPVPZ6/WlTPxe5k3BXgVxyFMP/qfenYlp KzxyaI+Lg7j6g5s0BZmYdTkxpVFJHN5XODxwcszEwjfnIvXPisPIfxLanHSZ +NQea0f3G+IwHhBqGjCXjou+O799dkscTjd6a2rUpuOzp7+8un1HHLrPzCk7 xKTj/1Vc5uFUbl8cDxkza1CZ4h3ITYNIwl5RKKEkM8lVohQlZGgw3VzEUaYM madz5JyDdIt2Khka0KBSRC5lqKQS3fB7f39+nme/a33Xd639PmvvPHo9UMVZ AxSvKLXqOdZgl/bpA3xPDVh30D7M+Dofh8VFmvYc14CmIxVDom48/M9cnNDq ixqQm3tY8WMRB1/8uurSphQNsIYlk5a6HOz1b4P69lQNuDdU6fWqiY0l2ie3 eqZrgPOgYlza20rsluZxLj1PA0pQqMci8Qo8p60/K1itAf+15K0SMy3B25yH pt50aMCJLboBCpwrWHHXubiRLg3wCOFX/yjPwuMmK5f+fKYBzVYva3xLMnEa sUdP/hXjb4qQg05uOh7+0nDSsl8D7mj71BnFp+L4uMsTtRMaENC+KuV7fQx+ UmM2miRHwDLFtiK2aQiKMq4dYikQ4HK4/GqLZjjSbyEG0pYQ8OPuNq0fi86i vB7hV7nLCVD760vkGe9o5C/Q2ly1ioDz3H1rxaUSkKTtroLH6wnY+XBy2+Dc ZXTnVUNOly4B272WBz75mIaCvNZkvtAjmPfSwMPwrnT09pR0cu9mAqpifvvO 5WUidk5nxKetBBg+DTHt1MpBO0ftnaTsCAic/nuZekQBmjvZvFfOnoCMhvYj x4YKEH9Wz3aJAwFzGpZ731sXohVyy8yVXQhQVxbj6yoVoZFNr3XXeBEgE/m1 UP1aMboQ6y5jfYKAGcGOw+eLy5CRzBOJPUEE7K/ocOucK0MTmSYi+4IJGGmW ur3UqRw5clRn3cIIZt+cWn1WtAJRzwZGj0YRUINLW4KdK1Gz2qEHiakEaEb0 Hx9u4SC1d13Lj10mIP+zdGbVoioUlmvsb5tOgFy6pNIxmyq0bsWSxfJXCPiU Mzn4vLMK5SjcP5BRQMCuk/tWybRdQz+71taFFhEgrP4pI3hhNbJLyRZzKSHg eW9d1UOTaiQmdbJaqYIAv432sZu51ShIRH22gEvAjpZNDxaYcVHH/aTd0XyG /fT4zm5ctDp6psi7loCwhSK1xCku6p/v3EnfYOrV2v1duoSLds2czeRgAgQv KlvRc1xUVj82ltREgG7trXIhBR4SDHZEx+8RcB0LJtrQPHRjUmd4fQsB/rvP BOnY8BAx3qtb/4SAqQzJh1JpPHS2csdfmZ0EZKaMbdhXwkM9h+t6Tj8l4JAZ q0GsjodShhLPG3UT4OWW4lbzlIfGiqafK78ioGPeSb6yn4fMvbw1518T8N+n +5qSn3nod9+WjqZeRp/O/IicKB855papF70j4GZjo3OdPB/xXRWCYwYIuJA+ W3NPmY+kVpxtOzhIgNPmoWEjTT46/GpUyWKI6Yfs9iG1DXx0L90hQPMDARXr 00uPb+EjlX1374mPEHB/cprS2sZHz7uy/B6NE/BitvTo2718tDZF+HbVZwKe rnTb2u3CR3/bBMolTxAwGvH1m+EBPhqS7PUOmCTgRGt+hoQPH8FDyxt7vjP1 VBpu236Uj7LjaxfpTjHnnYilYwF8NGWhtn/xNAHpCvt0fgfx0R6RRP6PGWZ+ K/fyQ0P5iHP/p/DL/wjw1dv4yDOcj0Sj/3S+MUuAQW96ZW0kH3lt7eBkzRMg cDH/XNBZPmqcN1wQLkCCz7bvsfnn+EjxduleNyESDklVTxmc56OTEfJlxsIk WMh5K5gw/MTwzC8VURIK8xRXcZnzWjMj1gvESbDVA99kJl5M/b6CAQkS/mTd 2PyWybeuy+rCmCQJt3uaN+1n9LwZ3Xr8hzQJyqPWXfqM3riFBg7zsiS0dUmG /8nUs0FFx1hcgQR3+m710HE+6t1EEApLSAheoj3R6MdHF/asWKS8jMnn//vu uDcfbTwiO0ktJ6Gp5G3tCQ8+ehcj8nrdShKyFjg77XZk/M77jQ2VSZgKe749 zpaP9G9Mlm5TJWF335mVSyz4aKDrY5LNKhIMduyKnDXmo8SxviAnDRLeJ4wv ho18ZCD8wtWLJOFFzF1WrxYfDao8ND1Kk1Ac+aa8W4WPDO3qZc9pM3681E7v E+Gj4SNVP+PXkJBJxEx+nuEhVmxR36W1JJgK7v7hPs5DH28kc8p0SfhhYrDJ tYOHLj2NvcTTI+Gs63HNMcxDJuPhYbc2kfC3jRHRW81DaaqHLTu2kGAuXNAz msRDsNlj7WtjEhZavwwUi+ChcTv7pYOIBAepJ48SfHnINA7+nTIj4fJHwTst pjw0Ma54TmUXCSGhgvbrP3NRjoiMj6YNCd2GQblZL7nIQk3YZsNuEjTn/5QN uMNFeXu/rjS3JyE+T0LwaAoXWd1sq/d3IwHyQhY2aXHR1DOcF+JBgl/TL59b 0lxU+Kku9rwnCQKTw0tch6vRtFrh3jRvEvbeNnP/HVSNSv8K+9JwlARHSSvf sdhryK4goPvBMRJ+WT84XWJxDc3ePNTYGUCCini9h7fYNWT/2S7h3yASpFnq I//FVSGBfdq0ZCQJbpFbwt6HcpCb+lsP1yQS1ktQ1zU3VKJrAY9zTZOZ/qRf 0KsarUAC+PZbLRbTP/ktJecKK1Cpa4HL9GUSbhDZr1VkK9DE5UMOaTkkcMUC laMHy1CM6FfrDjYJMg5Plu/yL0GccWFjs3YShEYaPqar5aP/rq9dqS1Kge37 nV4a7CikkzPVLCZOgfWPvw/4GZ9HnucbA4YlKOi1GnpYcfUsum9l9aBAmoKz bfeenR89jRL7DwUqLqXA8xd/XYW0P1KSyGsRJim4TG7HXBVPbOQuGdRvSsFr o3nxiO/x+JjpM5Xb2yiwa3S+OmKZgPPpK23Z5hQ441ihwexEvHCSVnXcSUFV 97YEO+Nk/CjOrP3xHgoOaOvcTNRPxW7cMLVbnhQk8G/IKBhl4AihkUdpZyho +KZsfx/l4zkzw0U55ygIkDMzaPg7H5+PSdhRGEWBwdY/nv94no/jhHUeXIuj IPDHGinSpwAni57ELRcpiNusYKYXVYgLF83yZvIoUNhYqmrOKsbELpuJ+XwK GiOFTZw6inFZ4lUdkSKm/uRvlgmSJZgjZcqWL6PAoShqlXVMCb4u81exdjUF 17wt7sr6luI2BbkMd8zkn7KfMRIpx7vsvV782USB/uMl/nl65fjJ5RoFv3sU lJfojIp5l+OnSxxSglso+GQrb/u9sRy/XZYdn9xBgZUrb4HIoQrs4TTektZF Qcrq3/+kJFXggUxjkZxnFAy3P5VXqq3Aw8v7o8pfUqA6JkWun6vAEyvJiKZ3 FAickg4xiavEJ9yCb7YMUDBTVny5vqQS/8hpmX48SMHcnbQ92veZ97Cy36me DxRMtHUfWDBXiSM8btX0j1DQue1ShedyNp7Lk5wcHqNg6H306X902VhIrfrY ty8UnEssE957kI3jPBdUzXylYLb7m9ClCDYWK9gzNv+Ngo8jpdLtqWwsqf7d R3Kagv3HzQyUGtj4otf2UvlfjJ/vBof1O9hYrij9X8XfFAyEWDRZDLDxUmLz AXIBDTn1k1FWghwMWbE/xQRpeH4tn2Muy8G+0k+TxoVoEB2TV3dR5uDUaBWi U5iGj7KNH2K1OLhh2u9mjSgN7a17xNs3cvCwf/3uDHEaWhNvZ1GIg2UGhT6E LaJhUQhdk23JwQZOuyM9pGgQlh0M1trD7KePcxRMZWi4ohQs1enEwYmmIxWk HA22R5NLk/dzcF29Hogr0BBXJnT68EEO7vsjqnt8MQ03ldvuuvhxsFjhk6Od S2lgX/rWeugYB29YtlKoVpGGi3Lcl4mBHOya6JOVsYIGKx6YPj7JwTECtWvD lZh6aqe8NE9x8LXgBQ88VJh4/yhl5zH8amyXm6kaDfnuP+3WMSxwIGuSVGf0 x7fO9DLfr+4euiBO0PB6fYtwORPf3mqD6ieShvGxpd8vMvnP3DlT10nTUBqG LS8x+sr0HlrVatHg7lV8sY7R31m57H2GNg2PTkc4TjH1/VL1Dg1fQ0NSeNsW B2dmE0rjSu9fS0NGRkfPC8Yfa4nZYtP1NFQvTOo5tYODg8/u2ELp0vCKxfug Dxyc/z2tS1yPhseb0uuW63Nwu+97n0/6NMRUbpxT0ebgb306c50GNOSOqkRZ qHKweVvL6kwjGuwbhzyEhTk4wGRxU7gJDVmfLjnnTLFxVo2n435g9E+qPnP+ wMbjuTPR1DYadmmZPrZ6wMyLgvkKCXMaIsa/q0fVsjG6kMr9ZMH0T7+64H0B G6ee0O6ttaKhTDpTnApj44YPISczrWngNkzMSDDzO+R2XzzCloYvt5JWqdiy sYGFu77ZXhoMFkgcfqbGxn0rk5O7XGgIvmbkmnWzEoux3pB1bjQIEAreMlcr 8XoRzYZMDxp0X6GBhqhKHDNx5+N+LxqMXIK237OoxKubJ7d+9qVBp/enZWFr BbY3RK+6jtDASWvcP11agSOrE47V+dMgoZp+OSWmAndmEdkRgTSsKly8OMm4 Aoccc/gucZoGyUr3qnel5XjCZI3KsnAaDqp+zlSMKMd+MgstNSJpgGRb9rnd 5diDy8vecp6GeIETB4anyrD5pKTZ0Xim3yvvWJoaluGlwfdYj7NoEFQMW6Se W4JTzK/cep1Nw1decZP1oRIssSxwaCiX8XcmsuehTgmeq1fZPFdAg/q+ktbW xmI8NHO6X6eSuS8LTjeIPy/CtZHr1qbcpGFs873oV4MFWMdG1DmngYbjAT5Z e4sKcLlKX1T5bRq6zbNCd3gV4Byc0H3nLpP/+VdDbl8+jhb4EPm1nYZOl5tG fkVXsV1s7iO7NzQELDPwETDPxl8TJfyW/KbhevXyZ6GSqVgpZutikuG/UuQU JkVTsUV46O2NDA8o9xsfEUrFub7D8vYMa6dr2bv/YuEd5ndvpTIceuhCDHxk 4YL501KyszSs+2A5K3ifhfecGOFKzNFw4W5gWmg4C0f4qrmuYFjZpt3sSzAL l3k6Cq9m2MrOqO/gCRaetWl23sFwmGraSztfFq7QLhC8wPBJq4292o4sLDDk ZC88T4PH+G+jng0s/Mfb5LnFDOddL+PZ6rCw47MH5QTD7T5SCs1aLFzVtHHW jOEVb9bnVKuxsHOebGkUw78SZlqjpVk4Js1idyrDrxXSi6fFWbg68cyvAoZD t5j4+wuzsHD4uE0TwzUPXjc7/E7B605ozHT+n50G9j38mYJdfV2K+hk2/qD0 DH1LYf7XLOsJhpPi041rP6dgnmPrz3mGBx2c0jRHU/D/APMdCKE= "]]}}, AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], Axes->True, AxesOrigin->{0, 0}, AxesStyle->Thickness[Large], BaseStyle->{15, FontFamily -> "Times", Bold}, FrameStyle->Thickness[Large], PlotRange->{{0, 12}, {-0.7689611361986977, 0.999999999999674}}, PlotRangeClipping->True, PlotRangePadding->{ Scaled[0.02], Scaled[0.02]}]], "Output", CellChangeTimes->{3.419291432999072*^9, 3.419296667996415*^9, 3.419349068389863*^9, 3.419349174312969*^9, 3.419349361945697*^9, 3.419701582577569*^9, 3.4197690434871197`*^9, 3.419769090037722*^9, 3.4197692221468973`*^9, 3.419774392639564*^9, 3.451311866234964*^9, 3.451317162900134*^9, 3.482504934792706*^9, 3.482505728006693*^9, 3.482505826033824*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Plot", "[", RowBox[{ RowBox[{ RowBox[{ SuperscriptBox["x", "\[Prime]", MultilineFunction->None], "[", "t", "]"}], "/.", "\[InvisibleSpace]", "sol"}], ",", RowBox[{"{", RowBox[{"t", ",", "0", ",", "12"}], "}"}]}], "]"}]], "Input"], Cell[BoxData[ GraphicsBox[{{}, {}, {Hue[0.67, 0.6, 0.6], PointSize[Large], Thickness[Large], LineBox[CompressedData[" 1:eJwUV3c81e8Xv7j23uNa9xrJbFApPCcRKZEWSoOMIi2JUiIpkoyMskoqUoqv leS5RLbsvVdmNtf+3d9f93Vezxnv9/uc87nPQ7a9ZmHPSCAQeJgJhP//0g67 xplfC9HrzbmpTNheVuB/aYvSH0VXJM0gKINn3uDqf4NXnis+QNcfm1taTX7D 0/8dCHJRDEaq3Bya+oNU7CsyJ3lWMR6NPqGaqtbW4spSk6HjimloW4FAKteb XnztjXu5mWIBYtuQ9WAhT+M9mQOKvqIY9Zkz3POLnsaES0r61kQq6sr9U2LI O4PL70QkBC1QETef4G+/lRlsnXDNeqalCGmf2PInunQOe/2Tq82L/Y30dOzL jmkv4Qse7RvHhUtRV02G0KN3S9iAMVRt8nkpenYp7mcJFw1zi2wEyniXoT8l +9/c6qTheN1WQ7+LFag8/cwW+esruDAo6IepYg06NpXW/dxhHReMtVVxptSg Ir5dnOJl6zjfeEt3ucofJCo4v2qttIHPMF4kvBOrRXvjt88uDW7gkwWrFBnp OqTfUb4sv4VAPXE1UeXB+TpkUJZ5OsGCQLWQPKTZ9aYO/Ssstr1yn0A1vxtp GCNXj2ruNmVM1hKoJru2O4lubUBHzqlJBlxjoBoPtVx3v9KAUqX3BTpFMFCN Xj7wbEptQOd7UtNf5DFQDWYrA8PVG9GRhqJ96YyMVL00hy+8mk3oRKfOhS2B jFQdG+5s19tNqKAtwl35EyN1H1dmQXV2Eyrf/5jsWs5I3XOFofaZdjMKC1ne msnMRN2pGDvLilqQLL9b4pbbTNQdTfqrDg9bEEf05Q+kF0zUbX6jTL8LW9CE I3nOJJmJqt6/S9jPoBXFia0YW7UyUVVDu6QGHrciSD55dvcUE1UF/BT1S1vR /drIsqPMRKpSfN1ugkkbUtCp5VbSIFIVTT3g/LM29Mz4mdKoPpGqsCZ9qKCq Dfl4p8v0nyRSKdYu1l5m7ahQ+9i1u55Eqiy7oF1HSDtSZ6wyEg8kUmVyvzvv rW9H/odl1/69IlIlRVjv0050oJAHL831cohUiZIvj09HdqBEcdPPOcVEqrjb ieDslg50MZrvjGMdkSomtxopLN6JBNzlTUy7iFSR+rcJbtadSDNxw+XyCJEq 5GOc3BDTiUwTuAp+zBKpgtumvu3o6kTJfymGBmtEqkBPxPdQ6S6UErouyMTM TOUL1imaPt+FfMND9GlczFQe3YEKs7ddaGAPcUpOiJnKPRHQkNbfheYoWbr+ EsxUrphtndzy3cjCWNNKRpaZymHSMuhi340kFw7enJJnprIv35+s/NCNBiqG 8aISM5UtWX5ReaQbZVH3e2upMlNZTlduBGztQbUxVvOp6sxUZpabrKNXehDp GfG69TZm6sghb965jz1ojfZAZc92ZmrF8yDR9cEe5PlNWMWJbjePVL1g4u9F BzuTC8fo/qWBDeFPNXqRW/KLg1QNZmquansU99FedE0/WnhUjZmaUtMbE+bS izZbWV/YqzBTX1//myD6rBcZxL4W3UXH90zg37vYlF5E/flI7Awdv1fm/Edy WS9K0vTfbJRhprqeWk39MNyLetXi9ZPo/M/TGL6pMPchw4zNC+V0fcxfs2V+ k6Pbdp7dBjzM1P06vLla+n2IcoxyQJSVmbqjWzg/70If+rdiRdq/Se8PRa64 OK4PRSTbXI2bJFKZi7eWHcrvQ5GNFsJ1A0Tqov22qpr2PlTHtfX5uTYitTVF t7FVtB+Z/Qj3CCgiUssPG7Ta7OpH50oVDihlE6l5kyad/Sf6kdR3uedyKURq 3HbLwYnQfpTxxjl4x3MiNbjh3MiNb/1o+zuNUqMHROrD2/YTizX96FPScd98 VyLV9vvNeQLXACrVe5RWakqf7/3PicL+A+h3hpGQF5FIFR0IZ3udNIBu/op6 mjTNRGV7/JpL5tcA4ugbO7uzk4k6VvZRaCthEHVkjP57ks5E/WpeJK97dxCt 8rKwKp1kor6ZLVMqih5Efktd3+J1mKhhL/+oGuUMomT5/PRHckxUt9ZOzWPz g4jNVV8gboq+3xeWDOxdh9DDW2X3VH0YqVsZN4zHgobQ2pe6Oc1LjFSJJKLp tdQh5MKsVpV5kJG69pf/pOfIEIoskbWT4WCkUq+p2j+3HUZy0aaZRYEM1EPe Fx9nnfqLygk/7C+6Eag7XhQefOv2F13mlf+33ZxAlUwgsz0P+4u0E6Vlw1UI 1OmCvsBLNX/RkXetseJFmzhy42KI4MERBL8H9rAEb+DB+7YxN7RGUcR3330O hDX80MsuXU1oHP1XvY301m4RXwn6dVN8xzhCheYz/4iL+ESsnCaz+TiKvFQz 8uP9At6SP5Dd+WwcOV4LHusZmsc1q3b5z5gmECN/qlrKhTksee9S6ejsBEq/ o5jFc2Aa53jad72v+4fm9H3aC94N4A96zi0Ss//Q6aUONEjtx5FMN+peCEyh 2GUxyT9dfdj9uVeJ5/Ep1JnLe09EtBfvehv+xbRpCmleVr6azNeGzwz2Ftx1 mUbNutcNOP8rwe2cvC8o12fQAxla1aJgHbL4x89l83AGKRp+UCsoq0cVtUIB USEzCEnmPFq514jyIiQecaXPoL86NLvIrhb0WkbxzuLMDGLnCFMreNaNrHfq nq+4NYsolp6/Yn4NoTZrZ42bd+ZQ/StJ2cnhaRTYb+QS5T+HVC5qRbHvm0F7 r8in5EfMIUMN8u1bwTMo1rOLwpo5h2SlyaC4cxZdiDYTiZ2eQ1Xa573Kb82h v00710suz6MFr0vlSrULKNqGb++4xzzSsYm5Lyq2iIyHJtz5ns6jske56jvO L6JP8++nrT/Mo9h7b9QHxxaRq6DY4FT/PGL5J4jZaEtowXytQvzsAkrcHlrW /XcZfWhtZUXOC2hhNv05lbyCTl3IMrh0dwHdaNS9kmm9gnKvuRakRS8g59fp bNXlK8gruDf9QNMCmtd8SoyPXUVqIj//OQ0uoI3w4KsTNauoO+6VSvDcArog +2xTn7CG4IvF+1b+RdSpc8yIeGENMVUVR189uojGFywH8wTXUebxt01hNnQe au9r1fTW0aWO+wK5LosoJOob71vHdfR7bFcQ47NFpBu2V/txzjq6c1OwfMvr RVQ+0xU237WOlFammE1TFlE8JVDqItMGCmRP8Y4qXUSpJ7mYNA5voH2hj/Pz mxfRdt55/hdXN9CEmO1y39AiepaV8H00eAMdVSLdUiUuIaefeyOCajYQv9Fz h0JYQl/Jutl3928ig5R8pHJsCW3u6dsssdlEHpwTYhEXl9Brxe9M7R6bqPeP SaWT7xKKLpopsk7dREI77ibVhy0h7VDx3t9Fm8j4Zcp9nXdLqOww7e5K6yb6 Zsm2ja94Cf3qGM7uIBBgMG83+93GJfRuyFZfloMAYlKO/QODSyjn94/DZQIE OOId+cN0YQntytOqa5AgwMO+kpc5zDS0fHKgWZ9CgMwDC1fJIjR0L/C9g/BW Aoy8lzd6pkhDzYkqIYc1CCDJdkJ2YRcNKSuOOg1pEsD8yqPlc0Y0xO8/zzmg TQC/qoz6stM0xDQp89pAjwC56v2pO5xoKGZwRJtDnwATIfyPYz1oSKTKXVTT kACyc3COJYCGLFtfXyoyIsCJk9d3X39FQ4OCtZZZhwjwNCeBrz2FhobO7dvO fZgA+eJ/Rg/k0dCWa6nbKuj29L2Noi8VNCRTG50wQbflu9ViRTto6HKqZJUb 3bYEm9s+4zTkeCWW3c6EAEGJQUfHV2loeFI4PceYAFRi/paTXMtITZ+JfOsg AeYdxglYchkp7zryM+IAAZTKJdqV1JaRy5mDUzJAgLMqJv+F6dL9WbIUBHQI EPLcM2jNdBkdMi1vdNlNgOKpZHuHc8voAAfFfdsOAtCOterVui4jaKt8aqNK ANVMVrG93suIUoxC5xUIcEFk98y7F8sIV3CIL0oT4KWHQwX3m2VUfmE4zVaU AGXtEe/ufFtGii5Vw3t5CbAtYf7k4bpl5Jv55MjFlU10iUFeI6tvGe2pa++O H95E0XbH2WRmlxH7k3c/cus2EUEpI29WYAVFpJZX+idtIs3AvvCzcito/rp9 o27QJnKa4Lv6e+cKenLerq755iaq/XZN5vWJFXTLcio/U2cTEQUTaEz2K8ja d3/Nmswm2nO7pu7q7RW0QFkWU2PcRG+01fz2R66g7wmYzfTXBrpeNDYy0rKC HvfMKv3Ys4GS5CWKLEZW0F6vhajbghuo1f9QTD5tBWWthL1QnFxHcDjZNER8 FcWEeI7diltHfI32GbvPrKJDGTZT8zP0fZ/cP3bCeRWpBNiu3ChZQ9dZpCk3 762i4sOvWDej1lDdnubQzzGr6MyHweBje9dQWNzBG+TOVfRCcneckNsqEnbc so3TZg3J5BuacBUso4MPmZyUrq6hkNT9Q+GPlpH7q54Ew/trSH3cStfceBk1 V0bxPoxbQ4LksB03/tBQ9Da2qfmuNWS35tIUQ98riZWRL93n1pFzQ8vAQP4C MhEsGVp1XUfZOdqfpt0X0F3Vt1Li3uuIsetrz9ltC6jjnNXz4wnrKOjoibFz b+nf0V/lLmU96+hTq3GOldcckn7+SSXjwgaijH4S+i42g+RkXVIe226iQ4++ edgQRlBQN/nt8xv0PedtSFOw+4sWY1uiIx5uIlPnU/wPSoZRmfiBp+/jN5G4 Y0PJ3FP6/7qghGNJ+yYKvWi+4sM5gM4wXQrzpe/xNoviN3qsnej9Ir950VsC 6GUoqNwjYdTeNHH4YAoBnJLa+rP58hBPVqlRxTcC7Co6UerDmoU8bt1H9Zi+ t8dHdX/Nv0cm0yPq/V0EuJvc83KcKxH/G8XcjBIMcCQ79rE7lOE9XVcr94cx AI3noPd+4R6ctvWmsNNrBuCbbFUbVurF8u7u54MTGcA54PERg9+9mI/Xe649 gwGu+H18obXRh0chhOTWwACpDULaZ2wH8eukDOcPQoxwbP/Zg8eXRjDfTHZW lSQjjPLEBRf7jWJ/3R+bs/KMQLuwWLLJN4ZvNv8KR1qMwPZSQahIYRwfZmv6 0XqSEZiFzuWtokm85rzEyRnFCGGFUVZ/Xk3jm7mrJ7cnMALnBNfBtqZpPEIk vDn9kRF+T4eFbOGfwY1xbJpJOYww0zwpF/h4Bn/5I35Wt5UR9qpFyuy2n8Xy ktIf7HoZQfK1ZPLOmFn82okyHTDCCIdkk6Uda2exP4OKXzONEdzsi7Jd9szh czt1Pl8TZ4InLJ7XyzfmcKM3LEaQmeCrwSOxE+rz2KTKAPK3MsHYn72GHDbz eLe9aSPbXibYx9crOJ8zj/mizq29tWaC+1aqP2PsFrD/gO3BMlsmOCkQ++RC 0AJe03AM+XeFCeTe0R4bZS7gkbJr8vvuMUFn6B4RD4ZFXLjy8EhjDBN4unGe PhS6iBvFby5ee8cEx6/mBdZ8W8TDe+zecKYyQXkmYV/Qn0XMdcdwXj+PCUwa x9LTOJawdOSu+O7C/+NZtBbYsoS3Z20xvlvOBN723Ac+6y/hU3PssemtTFD3 6FTTwztL2Elg1dC0lwneLUaF5IUs4XvbJ6ZG/jLBkWbiF6WUJfzmWs0B2SUm oL055fKmZQmPjYeNBwsTwfz6+5h5ZRpe4/CLUJYigpJAemqpLg3zKt9Gv+WJ IL9D7XOVGQ1rOp0OX99JhA30K9/5Bg0bPTHWfbWPCJe79e8y+9Cw9Qftv5oH iHDn38FHtS9o2HuQtM/FgghjC9EqK59oOIyJe4jVmgiX7vt/t8yh4STKRvC7 i0TolP7uPFJEwzn7p/agy0TgTLpplFJNwxUXevvbrxPheK3P6ZgWGu70rgty 9yBC4QX9zwW9NDwVX7RL4CER+LnizgiO0jBjwX+9X54QIdmX1efVNA0LdSUF HnpBhCKfSN1jSzSsuBahORRJ9xcu+rF3nYa1SU+6H8YTwU9yz/ZTjMv4yF6P p5IfiMDxKqDtHcsyPmd1eUfuFyJMqGcsyHEs4xse1p3Hs4jwW0GsqplrGftF HfafyifCC6eg5HyeZRyZrbPtWTERQh6bdDbxLuOUJrV2xSoiuKTRflL4lnH+ vLRfUQMRSLkfU97Rz2sE+dTPdRBBTrSBYEWP79vB0LrcT4TRRnnVA/T888dm fSLGiCB2S+yNLfsyZrkxoLJ9lggnT7S05DAvY/GQxqaqZSJ0P8g9foBhGat+ LfF2YmCGqFh4xbxGw3o12VuJ7MywsULeublAw+aTHxsS+Jhh5zOd9G1TNGzH 9er+PjFmmOqLS379l4bdVQK3tMgwQ/hun/90e2j4qcm9uptbmEHMyeyGRDMN x1x2ucejwQxSJmZPtlfRcNpTG4VPu5gh82fK+0eFNNzwG3n2GTLD/iP6vR0p NDw8tE3uvikzSPdsuzcQS8M0IqVa7CQz/PBtIm2lz4f0ASLZ/BIz3Nx4+PYG fZ622S5UjDszwzE1B1X3izR8wGfY7cktZnCXKGDLN6dhJ1xWVuDLDFRM28er RsPL2nwUzUBm0EyYjPOWoOHAzNP3UkKZoVDuioEOKw2npgyrvXzDDCztywLx 3Uv4Xzgx/HIBM4S8qnwu/XgJe/McmeguYYYm/rFqzqtLmC8g3PBENTPcOU3e anqCvm8PKDS9TmbYccDoca3sEnZzAhuhFWYIMJkRWk5fxMwDT7IDGFjgh2GU yYeXizjS5g/vJhsLjI8fSvvmvohzLM4VjYqyAK/ZRn3fnkW8ouO1BWuxgIVq Ykhr1gJ+yJ87c/kGC9R8qBnXDZ/H/EGbJj0eLNDNwHDP0mUeJ7IYJZ14yAIR RI1nQwbz+Ndq0yn0ggXkzlZx28zPYZbhuR9CX1jgVT3TufEjczgoT8Mfj7DA VI+UWvfQDH5l91FC+AIrPHlP+U/g8SR2OSxWpOrEChKuhPUJvkmstzPgssF1 Vtgq5xi1GDOB+xmdc289pPsrHdf59HUcqyaqn6p/wwpWgf8ZCteM4oLerNAX fayQ7LjMQRofwgM2xWwcdmwQYsY3rPGiA2cban0jO7OBkHBxh9LjdvxU7cNp 7VtscG+yc1/m3Tasuv7kg9MjNrD1kLuccqkFu8ceNih9xwZPdzKHyWg1YLaO em+/QTaQSYi2ePC2BKtZ9i1u2LODNT+7DyjloFgBtPHsKjtMYZvapMU8xFEd yyx+mx3EwrK+2xcVoJH9lkI7/dgBCvruFCv9Qkkqf7Y7JrKDT4LL78j3FUhi M9/lTzc7SGp5clclNaKA7xJuZ4fZ4aIe+ZNPYBOi3fK4NzrJDldIGY7S15pR 08jOQKZ1dnCuP989q9mKQuo/fdxN4oCaq/ml5hkdiOVDdH/CaQ5I6E9iUt7d h25fWBxVPc8B/mJJX38m9KFBiRMz3x04wNrheG8Yaz8qfMFLaLzNARs9GjqL jf3Iy9Nfiu0lBzgqB7065jCIZo+4WV6v5YCLmsvVyxf+oous9efXWzigxDww 2zr/L6ot1HAM7OGAe2e/OtaLjKAvu8ZvJ/3jgLM79oatlY0gJ1nb8FYuTthQ 0WhbIY+h7jmzGjjECR3//V3MSJpAwaQWuevHOKGo5ZbVr8UJpHfgnGeCFSe0 vubc/cpoEiWEuchvXOaEiWHgChqaRBe2B9z9EcgJ0xXBYWb0dzufFV/tWBgn aOW8nj1iPYUKH0YpSMRwQunH2jsbb6YQpfZ9rUcqJxjmsknuE55GA65Firuq OMFldbOuKHIavYw85GXfyAmuESeueGRNI4OC2rqXnZxw2/Eon0/DNEri7vGa m+CEpHZ176fcM8jh82r9N24uiL/T53jWcwaJNPoq9QpzwYNL7Z8iw2bQ71X2 B7zSXHDpo90H6dQZtOWw2FZXdS4w7LJ5I9w+g0ZGNb1VzLjAi2woHqYxi6L5 8xutT3PBxWzBi6oHZpGx9gHlwPNc8M/C8RffqVmU8vRY08g1LgjFPS+yPWeR 9bdWZTEPLuiZkXS4EziLOFrPPzR6yAX7zs6p+7yeRVe2uKp8COGCjD+1Wa65 s0jCbOFhUzQX+La281n8nkWV7l7NxLdcUK7Em3C/YRZ5xTOpaqZwwf5D5oYz PbNI9Xegj106F/h5Hvv3eXwWdU7yt4R95wLub5GB3xZnUZDwK9WiQi7QfO3G t0aYQ5OXPrbI1nMBf92FP1cE51B8kLqaeTsX1HCoCgST5tDRzCxf734u2IIS LJYpc2ijQ6c1bYwL9B6affq8dQ6lMRWrdc9yQYTDx33JGnPonMrhR9yrXMBU XKI+oTmHeI/Xt+owccNCn1u6h/Ycot61Unfh5IZrPspLprpz6Hpi76MYQW7g 7mDVdoE5JFvh2FZB4obN+LasBv05VDvzT31Fjn6+IJrhZzCHHoq7+21V5YYm 4vAdb8M5tH3/epulJjew1eVaFtPtfic/jac63JAlP5d+nG6HhXA+zjHgBqXO xr9q9Hj93LD24SPcsLN53e44Pf9sj/g2kZPcoDh/NaIY0evbLWnK2HCDhody bZjOHDIbbtRWsueGBKVNlcw9c+jB5Qy97Ve5QcCWl7yVzu/zxIsDe29zw4lo L9VZ9TnUfu2q8YH73LCqd7+Wl64P+5yJ6ZHH3PByYjDKl67fHncli5PPuUFC VUP0MF1fh2Xm0+ciuME6ffrvZbr+L70GzjjGcUPfa9/kHo459GuTeuH6e25Y v8G49pmBjo/F64pvFjewyosRjk3OoqMBVtee/eSG81swz9b+WXSfa7fbyxJu ULjs7nKmeRa1C8ze/9BE18vsMUd9/ixii/zj+7WLG2TCNTpEv86i3eJfnuQO ccN/9kdFf7yZRS9lnEIrFrhBXOKnipTvLCpKNIxsWOeGkLMc+V03ZtGMglxM JzMPRE393rJ5gV5ftTvpnzAPNNUY7nDSpc/j1x8pS1I8EK+59jldeRal7niV RlDkger/PuHzovT62idyBXbxgJRKYvrkvxlUaFhRuesUD5QuW1dPRs6g6bKP tegcD3y++mTaw3sGSR953GTswANqbzlkbjjOoLsW0GPtzgOjX0XUvmjNIM3z 2bMPInlgf2XBoduV08i2P3zpSTwdT/ZOasDXaRRqf2Mt5AMPpLBw9gmFT6N/ zqos77J5QIL5z96XltMo2SNRvLSZB4o7Sgi5eVOoedVburabB/Yw2la8vDuF mL1t5NqGecD/1Ly+m/YUsn0spja+yAOB4n73Dmb+Q5JhwcArygv2hVFzT+In 6e/Su46nT/PC0z3nc8SMx9EZBsOqpnO8IKrffLV+YwwpnubdfsKBF6yy3jm3 ZY6hfMakFfPbvCAcgdLapMfQiFX1c5NwXrhip5oyOTaCEJtspu4fXmCR8+Gg 2g+jOxm2hDA5PigeOqIVt9yLFHnZTD1i+MDhy0H5X4vF6PO0z4enCXxAU3Ln 7Dn9C+2oX92MfscHcLCfJv69EKGIqYzvqXzQ93H6xjFaPrIktYit/uADI80z tyO4vqHALR8G73fywcrLu9unyO/wP2Tg9UiKHwItiRGKwdXYjVzQFE7mh/Yy BTUy9x+8wrhHI0mBH8auu0RLGtZi1t8q/cVq/BDGoyhthOuw7BFBYxY9fojX j3bR+tiILSz7BQPO8cPaBVFfCWjH2dcfpgYn8INi9HAf8+5+HPhjOtPqHT8o 3K3XYrzfj8+zXCyQ/8gPe+Js/xoV9WO22P11eWn0fK6FjMkmA9i6lHFp+Cc/ 1Dxd6HtqMYg3pB7ro05+mKW01VjoDuN6p4XDHL38ECXl2S98Zxh//M/+ZNMA P4hZiSywfhvG5ocOOjmP88Oy/o/bt2T+4kQ31uCoFX5I2GGoqj//FxtWBrRN iQlAvWC3forbKJYQWenPkxSAiWY7jl9vRvG/C1cmHssKgOVW1yxa5SiOXDTZ JCkJwGfSp5X/ZMbwCJlLwXi3AFwJU6g6lj+G81281AX3CYDc0dPMO/rGcGjO xO5uPQG4xRl2YwvzON5rWm3idlAAjOdIkmYm4zjII/j6m5MCsHTYecG7fBxf +LXh6WwlAI9aWGqXhsexFs+1R7tsBIArykPiIdME7n5nFll1SQCeMNvtoGpP 4Ix/OCHKSQDM2Qlqd45P4Cfa21JsXQSgeOzHjI7LBN72hy+fdksA7t2lBMy9 nsBECZ+SX3cE4PdV2u+BbxO47dJMTfA9un/Zgfd9JRPYd6WuT/6RAPBWtLsy T07gU4b641P+AvDivSWTyuYEVgnJmM8LFADqtvxAG/p9sFEhnPVYmAD4uYiQ RjUm8aEtYnuuRtL1qS9Zv0x/zxcoxTkFvBYAg5RZo2rTSaypTHn1Pl4Azr98 xSR4ZhKnqHwsL0wUAAtFbcN9jpNYWk11peuDANT11KkcvDmJX6qnK698EoAW jeHenV6TmH3brjMiXwXg06270UT6/fTB9h/PdvwnAAOLQqG5QZN4bgfkH80R gMtzPwXNwyexk2bJxJUfAnAjdPNWZfQk7tYykXqCBeBk6TCvStwkPr77j+m7 XwJw6NyQ2bU3k7hsz4kHuFQAtKzvfIhOpN9397aldVQKwKLXzpCP7ybxf/vO 9Sz9EYChl7XhsXRbSXeAV6hRAGq8FPQ96P5xek6wrZXuT9q6ax89nwBMXj/S KQBiDrNCw7GT+On+m2+degXA/kzuc086nnX9pTq/QQF4xlZvtRg2iW8aeDG+ HRGAZP9sHRs6nxFDhp0/JwTg+Ooa01e/SWxj5G/XNi0AcdFnn0zcm8T1xpwv F+YFYPv5N8kidL2MTEKK+ZcF4LnGDQt1up75h4UX1NYF4EvKsocmXe8dpq8V TBgEQUlVWkL56CT+eFTmlAOzIExPa+vywSSWNE/y92UXhH3cMnN/t03isGNb c+K5BSHshsipDNlJ7HVip1iLsCBoS2X8kFufwDMnc43nxAVBI3gvpXp0Ajuc 1vXklRYE/9dx61ebJvAxa6N2I0VBkDJs0Y9JmcC/z1RxXFIWBLFCw7PKYRNY x+bYvofqgjCSZWmc7TmBFS+cic3dJQj8sV3HKwwncMzF3qrGvYLAuy7leFJ5 AvPZ2a9P6wnC4vgBzQHuCbxqf+3cViM6/rBUfe76cVzr/Ej29WlBOPH4/mbZ 0XFseJXtWPYZQWiT3Xo7SmUc57k+96k/LwiiER/43VnH8fsbUf0cToJgp7yN z5m+v3fvpCbd8xCEy5Oti06kMSz/qEHJ5pUgfM2JY3b7OoItM5i2O8QJgrsg 2UXUewQH9e3UvvZWEEwHtnPNmY7gBfTykE+KIBTGnog4M/oX/147ceX9d0HI Pf/rrIboX3zZvTl1sk0Qgk083frMh3D8e5bMxS5BePCUVCYiPITrG3flb/YJ wuoD8eMprYN4786oKv4xQRj+eGttymYQc02fntRaoePhipU2uTiA0y63qT+Q EAJlDlR3y7QP90ez734iLQSiuqznvrL1YdEybRRCEYLErVHpN3714oeKr80S lYUgRf1lYMTuXnxswPr6771CYFUt8cpUqxvPn+1M5zkjBBP+gVvzYtuwtnmP ZkKMEMTrlCc/2PyD80eYJ20ThKBlfSUnrL0G6/movld8JwQVa1V5e7OqsUGG p3DaJyEIcGaecb5ciY8KCS3mfxeCmdm4/ZY1v7Ftq3FOe4sQCB7VODsm/wM/ u5ChLSIkDK7H3u1rmk5EPMutM22iwuC0t73Q6NZHFBK6mRJHEoa8ohulvbOp KLLoiISCnDCUVE+YP3DLQG/k/67s3CEMSf2f/7449QNljpDyj5kLQ27JjZQZ m9+o6/pjvedBwvBhRCy2xqEBEahUqcQQYShLWBQ5/K8ByfOurWW/FAZ9/GK8 1K0RXfly80dvLD3e2kYo/QH9fTd6fo/mF2Hgn45mL3/cggTs9u7oqBYGYwOr xZs2HWhXxm3+6Tph8A2sX9qo70BWDOnTxGZhuNWTGmdi1IneJGz5qt4tDLZZ QdYCql1IrVNI1fefMEwigxiG4W5kfHJKYSuvCOTUHOtHXH3IOUmZWU9QBM73 6Rlq6/Sh4Dn7QQtREXjzhLPHw7kPNYV2JnrJiIDF5zsmJaV9yLamXKZWQwS6 zyaVuN7pR/5SzJuDO0XAyavc5fbbfpTiAt3Lu0XAPy0Kciv60TRHTqwciMDs DR/CP4kBdN8oSfyOuQjUeyvcWksfQG8ie2jPTohAsbr74O+mAVQ8JNH6xlIE Tt7iuFxCG0AcfqGRFRdEQFokQ+uMziCKpj4QlL4hAosXCu0avg+iH7x5sztu i0BK4q0fW1oGUfe5hTojTxF40vCH7dPcIFJYdw654SMCryQ+cO9SHkIZ2lbc JaEi8FQyAp19PoTkZwNjX0aIwC6Vu7ERiUMo4lO+yqVXImBWfcJMKGcIeZBk TZjeisD+fIFHvV1DaKzhWFt9kgio3/vuqTY9hM4EPXJKTBaBs9zO6QUMw0hv fdh//zcREPHu4P9CGUbfssRE+DNF4GVySS/7jmFEdjV535sjAru1+XU/wTAK U/TS/PZDBFSz2diDjw4jYs+XX95YBPgrOdWyzgwj96geC7NfIrB66EWUjNMw GjHj75cuFQFPFSnd6lvDqJLqRiioEYGrHU1bZ58OIx3PDy+e14vAFpGtHpfD hlHa9lZpm2YRMBUc55WPGUayY+xpqu0ikF6eykR5R6+fuE93rUsEDhImne0+ 0eufuVpV2UfHf5TiOPJtGN0WTDgTMyQC+hLp4unZw2i4snbsyqgIsMVOf/n5 YxhZ+jHe3TspArh96wke6jCq0NFk55gRgeYvUfrvfg2jfQv20W3zIlCX75Dl 9XsYff4StSWFRu+vd9a/12XDSNqhPNtjTQT6OQJ3bZQPoxDpVUNjgiiwJt9u /1AxjBhaVJtEiaKgxD+uFkG3b744d+kvqyjcuE4OLKf7DxqFzGVzisLhCuJR A3q+U4QiX39eUbBf1+pmptcrzZ3jPyUoCp+LON7z0PHsuaHwVkFUFI58eS5w Hg+jT1tPb1uQEIVM5QexS3nDSLL/KS6WFoVQX/OC1qxh9Px13tGXFFFoalZb ZqTrsWEx0WWnKAppcvMN7inD6Dqn9NWdyqKg06vVoZk4jPp/ma0xqotCxPui N7qvh9FxL59n9dtFofLP9x+hocOoWPM/iUQtUWgxaCrbTu/XrsnBlBvaolCd on5F+sEwSn4vor1fVxT+2iIjS3p/Jc4Zl/HtF4V74b1cvY7DaL0mdfirsSis vBOV7aTPi+uTrtveR0Rhi79e/7H9w6gX8TKbmYvC0UFRd7Gd9Hrfbsr9Oy0K Qqbk3TFC9HqXkzJ+nhEFr83TTFbEYfSR3Lz/+XlRwIS07itzQygwTPuCqqMo JHy5vjv4zxBaM3GeWr0iCpZxCffe5g+hq0xxDypdRUH50s2zXClDyNyNEHfF XRSGKMK5E95DSORUaVvyY1EwsPI9NKcwhA7qJIF9gCjYKgufteIZQncoPh/J z0Uh+GnQIYXFQdT6b+/t1y9FwV9TuHb21yCKeZLGF/ROFKQze9R9LQdR1dVn d4w/ikJsFGeCJn3/1447dRNTRYFzG+XZSZlBdE6W8vl+higQVAdv/x0YQLLf I4yuFYqCU2se1cVhAJkn3ExTKREF/Wln6UzDAeTz2Ex4pEwUuiq8I27JD6D+ Y+wDF2pFQarHbuB8bz96P+b1wKJHFJ5nx5sLWPQjZclLWVrroqAlzkrmku5D 1oz7JWcJYsBz18LDbaEXPRuRepRGFAOSGCnvSlUvmshsMd/CJQbTM+ldLJ69 6Kvp4QkxkhhwdAf9Pvq6B2l675Bb2yMGYuwHbxYUdyLUTwgtchODmk9/xOOj mhGf96x0rYcYsG/2HKFsaUb9pMHPXV5i8Oyj8qxAdhPyO1laRvMTg21zF7gO 1zeiirLnBI0IMdALlPMIJTagU18lrsdkicHyLxXOtOQa5OKlaea2KAarhhyD rASM9MQVu3xWxOC01KcTWSI/EW+2qPOLDTHI8Tn7z1TtB8qYWvH/xCIOUr68 pk+sc9CSbWFBr4g4fImX4+d1/Yp8Dx1VN90tDu9HyjP5py+gVyJO3Ioe4rDv Ikvlf4w/ca6k+eF/98Qh8lDu9bK0AtxK2ROQ7S0OjjEWksGqVCymwcZs9EQc /v7UD9jSWIgjjZLXHCPFwSXD5dsv0RL80mNkPCVTHNbwoyBr50qc+aB2681c cTjzdnHt0bYq3OCX67g3XxxCvvCnXZ2vwgKhTwcqfolD2Dx8dPaowaEpSh3j 9eKw4hWfoZNbi4PbnSrUZsTh+ND+PHJwA07rNWdbnBcHvaBTFp5DDbh6eM/B Apo4/AiXy2bVacRcc2xFRwkSEOIcEICHG/EzzpTv13glQNhA7OGZHc34qc5o crqaBCRGlXCff9OKk/Xrhj23S8Dhid0REmOtuNT4u7y+lgTwWbNtju1owywn A97U60jAAy8TqV+Fbfjx1a3Rc4clIHlh5YN0Yzv2jb/8ROuKBHh4NNF4Kzqx /hmHiaOuEnA3dj5Tjr0LM4nZHXO6KQGkq21LRKMu7Bd6lhRzVwKq/nw8vRV3 YX8/s6+EZxLQPHfErOZNNz64/4iQxAsJaBR1NqM0d2PWDWPPneESoOC7vXc3 Rw9+ekf/gEOMBKiNX3+W6NqDA65otVSm0s8/bz+kLNSLTbbs0Bn6KgEnOQIK y7f2Yo5B9bcb/0lA9ifT4BK9Xhxoo+S8PV8CepmdL9U60P0lFGpNqBKwfmbL 627PXszZQta6VCwBNGWx+0ZBvTjInLQZWUXXY+Jrx5avvfgIt9ilb7USEFdE +C8e92LuCqHy8kYJ2OUTMO/6pxcHH+AJX+uUgIXY2xUSk734KIGTJtwnAY9H MhcWVnox709WG40h+jltIHcr/b4Zsothi+2kBHwon3R5LduHzefWn92bkYAM LU+pFpU+zP9tZfrlggTsLjg55LyrD9e7LJ1MW5aArYSqDEvow2Fb5/NK1yVA w+i8T9yhPmwxPC3Tx0AC7wr2E3st+rDAu0m/FWYSfEsq3KFhTY8/PzYqyEGC whwPZa+LfThc8u9RNR4SSH6RNCU79eETbQP/HRQgQfhCZLq0ax8WiuwVuyBC Apvyqltut/pwo0XXfU8JEpCVEjIpHn34JW97f5g0CcZax15t9aLHVzUbfaaQ 4NnRb0cDvPuwcEDD5xJFErStUdj0fftws2Etf48yCYYGvrKc8OvDkYzV7jR1 EuzpW3yBH/fhU7i8g38nCWZUnf75+dPv416/QWU3CX5aGdxIotute369N9hH gs4TsS7SdDt6AXOcQySQcTimPUfPZ5mRf+3OARKMaAhryT3qw+LXvjeGGJFA 9evlorSHfbhdJVv702ESuO57axx5vw+/HsmI/2VGAmfyHq12zz5s/f4rU9dx EtS3sTDeu92HSbafnRZPk2CZqLTN83of7pROqeY9SwKmFwcNm6704diO9zu2 XiDB3vnYyheX+vDZ6MQo/Usk4Ny/cCzFpg9LnkxYO+NEAjaBFGfKqT4cVxP9 O/g6CZ4/Ov1Ty5B+/h2YItxIQLA78GhjHz3fuxEU40GC5CB2Lo0dfTjGY8/3 jw9JIMSsJFAh2Ycl7HoXvvjR9W75NKbFT8dv+nRH5lMSfP9JAS7mPvyK0ppK DSGBnm2S6epYLxbjfjjy+yUJzrXhp8JdvTh6aYtCdTQJDjXOHYyr6cVRVXfi 296QwH6Xgg+NPt8R7qKhs99IoKAm9G7BuRcLXcTVtEwS3Mt57R5u1YtfHnbk 2MwlgTJ/UN77g704XDbnEWchnb/5TisVmV4cWnHKXb6OBFaHz534Et6D+bI2 MpSbSPDpvvOUg0MPDkn4MLWtjd5/2wl/8T09+IXbopNuHwnuL/Udv9najZ9L R545NUOC65NJM9u4uzEXu1702QUS2Ck550+3dOGguaFG22US/C7/mP7jbRd+ VqZ19BqDJGwubM/32tGFA242wVN+SThen+05bdyJH/8WUszbLgmqQ+hLz+F2 TEzPt6VqSUJx3C9bX7Z27BdzKeG3tiTEXRhhtS5uw4+uZ4o17JcEi3zRq/9p t2EfiROcE8ck4UaU9N9zpFZ83zV8WuqmJDy2NJZQ+9mETYq2d3XflgRKf6RA 9a0mLCZSW57gKQkSa1sih7Y24cyfXO/IPpLg+zPQKfBlIx7j8j+pECIJ6ddn GsfsGrBlqkeeapokVN4PSj88WYs1R2z89o1JQoC8ym/Tu6V4/KKSmJWtFPic aIty2vIcW7t0qDg7SIGxcWmck7sPLnMPRvevSAGHaTNzl7Ijfv9s3uHtTSn4 k81gLHrPB53PomaN+kqB4mSh7M32BNTAZnX87jspMCcKcvaZ/4f0Bbkcgz5K wcXn7PJHszPRNyl8Nz5VCoQ63JINJLLR8x0KiUX/ScHytp3n47pykdHZmWmO Yikg27o9/mJegH58DQiOGZQCC0PnG8RrxUg5Tyfxy4gUfB4JFNIXLEHRxVNZ eEIK7rPXbTpml6DbbSe7BubpfARY951e/o00mCiqqszSIOqsMaJxoxy9O5VX nq8gDe72Y9vOytcggYtXu2q2SkPnMtOn7Mwa9NBZdqZXTRqefN3annLgD7J5 6C/GvEsarnWIoiT1WiT6ycLR9KA0SOjEPXJHdejZ+hix20EaHC2n2iR1GpDx jZdln65Ig/fK0UAptwZEHNINuuMqDY99P1TZpzagB1Uhgvzu0sD45pFjqWgj uh6zi2LwWBpeZjyTTfnbiNR4e4f4AqRBPnTxJFW8CY35BqR0BUnD4cGUF0KH m5Ddlc5td15KQ3AOm/G11CZ0StsXfXonDTEbdyqqbZuR4BcVpjsfpUHBEM98 Dm5GtbJNvw+kSsPDswq61O/N6BCb0tGuDGlIrgk46c3dgnRaqs/yFUkDQ0/g e8PUFrRscke2q0Qa/h2zbk6tbUHZBbKDKeXSwFF6gAMttCCND7ecD9RJg87u VdfRfa2Iclv8rnuvNBQ4/bPZi1tRz0iR7oFBOr/SpNT5rlYUe9aFgW9EGlDA /rjm1VYkbICfpkxJg1B4uAGvVhuqz3E64j5H5zu4j3bJvA0FqwjwHVii4/n8 7XDvlTbEJmgf1bkhDc8HCZIH49pQiT/PmRRGGWA/EfdHI6sN+a7kSLuzyABh z9MQ3ao2tNrH8YGXRwYyS4YXfi21odyTmZc7+WVg/ZgUhw5XO3Irt1FLEZaB t95enC0y7ejft2+Z+lIycOhiH/G2QTtKlbf24CXLwNmfEh/unGxHTtFMOp3y MjDHMegfa9+O5Lm+bCYryQDbbbfnA27tqM/71K/bqvT6AzwfjzxqR/Fzm/76 22TgFY2hrCWkHVk7ppjwasrAjHDyuF9cO2o8ulaXvE8GzkSmHzbMbEehRe8j biMZiHAkJloWtKOju8ys9A/IwK2JEfXg0nbE8YkmyWskA915BP7hP+2oVCqx t8NEBmxOM7leaGlHfqGHk5KPysDzUb+b613tCJgXHG9byEDYlaljPwfa0bpH vIr+KRmQf+978M1IO8qbMJrisZYBX60ToR8m2tGu4NjAMhsZeCer8LFoqh1l aMwo+F6UgRqRJ7qcs+1Ivc6wcJ+9DPzVG096ONeOUm6+PrvgJAMnCgQ05ebp eghNLaW5yMBaLo/xHP38TdaBcKfrMmB6DAxm6PGSp6PVKW4ysCfZMkxqph1F 0ybKO+7IwLYuy0SPf+1I6PV++4h7MqDCEzbGON6OQvZFEsy8ZeCLRdzf/OF2 xNU1FsP2SAY4GMdJH/va0ZMHaHeRvwxIuH/hLepoR4yyL+vvBcrAqhfPMZ6m dvSgcOSqVrAMzD7f5hZU3Y5WbHXZp0JlwLZcXVC3pB25E8OSkiNkoJYmWSOb 345m3w8j21cy0B/MenhPRjtyNdrXQYqTgXMf57T8PrajsZEX7k1v6PhYe4A5 th3ZBw7yv0ii85ekyuW/aEe9KtpfjJNlYHP9cWyKbzs6W/3cmPGzDNxwEbtW Q5+PE3y7vW//JwOP9KTMCk+1o9r0ZxIaOTJgeX0vY+jBdnTkeG/WSJ4M/HJP sIrRakcGkQETZ4ro+CpnPez429FOyU4r/ToZaMaMZh24DaX93Law2igDgmf7 /rxKaUPK5x+HZLXKgIHj8aDXYW2IkqheqtRLr5/DP+5g24YElHw0eadkQIqJ rfnQcisKLm/6UzZL72+V/7s99P3kcFZ29l2k9yfySvxNaitiSGt4u7AuA+6C wdNVfq2IJh7O6soiC6N5uUO6zK0o+4pukwmbLEySNNqTB1qQ24+/iVs4ZOF6 8V7K5cIWNH1WR6+PWxZeJsmRpu62oL8JQ24nhGWBk8W+YPdwM2pW2NO/V14W 9Ka4nRkTmtBgncsBUJSFvqve3hnXmtDs/bdJhkqy0FhllZSFmhBvM4ejuaos DOXN2/3sakTG/l3j9pqyoIT9arkFGlHesO9CiAE9X6sJ+2ubepTwsZrt7yVZ 2J79WOivbDVKO854ZcJBFoxLOgnZCVUof3NX5YyTLLB3+h7HUlWo9fSb52su snAsgOgWIVqJBNhuCQjclgXXdsFr3YzlyM9JTFL3sSxsJOckXsgvRk5b7TTC 38tCb+LoGW2cg6Q5wkduf5SFCTPRHJyRjRrGit5apshC7KU5Tt4PWUjvM0VI +ossfA8kJSsH/YcENfppyZmycC7OLtI/LQ0VaF4sKvglC0jr1cdThTFICM6f HOuThf/eHHU8v+0drpB9wVM9IAt7Xt00atr1Hnsz4NKvQ7KQeGnp7Jd9H/FY kfTe26OyIMN6p+IgpGJs2C1NmJEF4Qi19bxX6fjKYZsRYQIZdpAsfl+0/o4L T525t1+aDFn2nLzc07/w7zDhsiOyZGg/x3pw3KEYV9X8EbKkkKHL8cOO6s5i 3HrQIM1VkQxDn1qngkpK8PQutb4YdTJ8b9oXFB5YiqVFNw8u6pHh5sM8nNhT geWPfw9n2E8GrbgRFk7DSqz84lYv1wEydJPUHVBKJdZiHfGUMyLDP7PbFgTX KnxkqfazuRkZJPUV34aMVOO7LYkCqefJ4CO0qU81q8UPBW3OZ18kQ40pG5eq Ry32NxP9XGhHhtq6eN+RhFocWvrMsNWRDF7SCvxm9PtNco6bB/N1MrhoSVzP 8q7DaXPqJXw3yVB9LXpHQGIdztQY5Zd0I8OB6NPB74vrMP5ok7rDgwzeX+Sf ZLLU4+aog93nH5Jht8j4RSHfetzZQFBx9iXD3gMFscIJ9bif98cddz8yyCcr yFn9qMeTTzT4nz8lg+Xlm/eTZurx7K9Rm+hAMmx95S2WytmAaZvvPr0LIsN/ Hs2BM/INmOghZpAXQoavWb6V+042YI7M+pCSMDq/yo4oPZcGzDcd1FX7kgyV uY93e/s2YEknhjt/o8lA5NwBuZ8b8E7LsRSht2RY36Qc3lxqwL1lCUfXE8ng wBraVM3aiIO0T84NJdH17hismBZpxMMSVJ2cZDJI9X612LmzEYc/u92X8IkM M+Yf31pAI4Y1Zf+nn8kwyri7seRII37dFfHH6hsZLH5Mvfpo14iNjh52088g wz6dBmER10Y8X0AQV8mk93fu18HWO434rUb2T8FsMjiazaj/e9iIj75xtl3L IYMqq0Dz6YBGvMpHZh36TgYGsUuHhEMbcbJPc2r1DzJ8OZQWoxjdiE/OPjPP /kmGvNCLQ8/iGzGj3f6FeEyGQRN1A8OkRvy1YfHVk0IybIng67BIacRnDT7r Xf9FhlRv5/rML42YPevigGUJGQrZ2C2d0xtxtoLo0/2ldD5SEgnumY3YLrJK VbmcDOUxu3qbsxsxH6tvnUAlGfYctbEKym3E+Xd2u69W0fdjes406nsjvjwy ITFYQ6+vUspCo9siVom4qpYMia856tPodlH56UtZ9fT5LbZkyqfHX9vLzR7f SIZblP/mZHIasWRq0Rf/ZjLoMlAYOuj1y0keFtdayWDH6Rk8ScfnHqS2dLqd DH/7GYiWaY1Ybr0/BjrJcFVf/o/Ep0ZcezUatnbT9dm4ZLvrfSO+3206xN9L Bg8WB63UhEasbMYUuNJHnx/b4WLPV424BeeqDwyQwWxXUVhiWCP22+baUDlE hksFswqKzxrx9rdyHpl/ySBoEczB/KgRd/O3ScaNkiHCtqwO3W3Eu+cOOLhO 0vHtv+NQ6dCIB+2WOU5PkeHi0R/XpM424pDGtK9ohgxz9qfqq83p74ss8WW+ BTJ01P85emRPI45S/BO3vEgGDWa9CpJKIzaI8tPvp5FBIUrI9ohUI473mHr2 3xoZ9P0Muxs2G/Dh0aRtsRtkUHGWNVGdpu+HlXWTH4ECe8sv9Y30NGCLfSXS p4gU+Dx7sin0ZwNm3nidTuOkADeH05e8Gw04w9X8VB83Bb7cu6h8xKYBn+th Xi3npYC9/9FqY+MGnEu9bhAjSIESPfcTTyQbsMujgy26JAp08l5l0Sqox7TA ur+SUhQIc3gz+P19PX4cdpa2Kk2B5oH8yzlB9Tj+7U3xPAoFtvYGesha1eNa HH9mlzIFnv7j5y4br8M71xZ71LUpYKl5TstuuRZTmXynufdRQOvUX/H51lp8 hJObYVKHAqc/yQTw5tbiSxJylFSgAMvbjvkxt1ocucfs0hZjCmjq1/Om1f/B K24fR2ROU4Dy8/IpE69q7O+1Y3nDkgKJUiPc02rVWNDvJ3u3Nf3t3aya1dhd hVXDG5Rjz1FgTP7rjL1eFT6Xvuki5kCBJ17jI4vzFbhw8vQM320KlFp0m1jr l+GnDmwrDOF0ftWf7wvcKsL25VLx7BEUyK6c38PDUYT1VXfq80dR4CHJjBL9 phCvztgEysbQ9Tx48bNDFRW73v9PAr2jgMIrDj2qXgE++fLcPq//KPDJQ+9v iksOphRlei02UGBnENvyU8F3eFO+QnajiQIBBxMcZE69xZ1PeoqZWynQPaq0 PLk9AUeacnALd9L5XFP2P46iMXvb+bidgxR4vdGrcr3SD09PcRRcn6dAZOC3 xFymUPRT6uLmmJAc+Bzf+1+mezqCrBurf0TkQNu0KqxbMwMVH/FdyhSTA3/T BW/SbAaquvdu6oGkHDgyGj7PvZyJOtuGegTk5aDU/XXW3yM5aC3iCnXvTjkQ eqDSfL87Hz1Uu5cvoyUH/xlyyFk/+4mIJc9yibvlwDXptM7irgLENf/5W81e OVD49v2TdSBGkhZTb2z15SCeoSwwma8Q7eNx8wk8JgeH/w0yMfj/QgXv/e5f Oy4Hly2jRM7U/UL6uhGeJ07KwVKRZuwMqRiZuGTfkLaSg/TQTJGqtGJkXUG7 mHFBDjx92qYJlSXorv99/fZrcmB2qXhbQ0cp2pAK1sM35MDJqGpUWKIM+WbF 7026JQdSDuk5HqfLUOAg3uF6Rw5ie2ICov+Uodf6jHKM3nKQbAd3xbLK0fcN fyblYDkI4zP0/Xe8EgXPkMN3h8iBbJCq54Mnlch2MJ9iGCYHleuSO6e+VyKO itn9FyLl4KRQRNlVUhU6G3HuYWS8HOytPqtVUFuFtj1d5k16Q+fHLBu2Y7UK Ee+9TPhfw3UeT9XzxgGcUJGiSElUzlZZv/lqQc0jkqUkUWmRSiWpbBVFIWkT EkqWvpSlhRKlbOPe3EW4J9Fi7SZKEvIrtNDv/Pl+zZl5Zj7n+WOmIJMAmc+j qSfJOpTn8byiNpuAnSMdGtcD6tCY3uLRcfcJCOwyMBTJSdBLnfpo1QICstc8 3/See3/nTPWZrVNIQEfWvaFaawlyGs4wX1ZMgGp84kaNcAkieyxqbJ4SUGFp oB6QJkEjrW+2uJQS0DDbAG48kaAM/uTjhzEB8kyLi+cXCTr6KFcxlEeAj1Jn 3J9xLLLPtUq+8IyAa6P13bs0WaST0j7/moDrHxQ2/6ohiwYvBT/JEhGwcZ6A Sl7JImGYum1hNQFuiv6VXq4sSgm4/6ayhgBd3w0dCvtYZO3WNdTCEiD1f5mQ G8WimWvCoj7Xc/VHzxrmJ7Cod4WWxnADl4+Nuld4Bosq/3mcJf+agN3cLUU3 j0WJ5HrTaW8JsNaxd79czCLvGb1Vc5oJsCV+nJFUsmiF0lkXg1bu/zUGE81i Fk0bnddp1k5AsvTSmSKWRR/7ywJspQTYEH/k3V+xqKRjk9zGDgL+mkYovGli UeyrwfjdnQQoXdT4PaeNRZ7iS7p+Hwlwtuzcs+wdi5aWzn94spsANKGMJaQs Us5/ZhndQ8Cdw2q177hx6X/u9cm9BLDf5EcOtrOo6MpPj5w+AjZ9XvdL0sKi 81EJA0UDXH8mbT4t95ZF7sFGYfxBAqb8bl6r3MCiRT7PVV58J+B7/Dyyp5ZF 43fsudE2RMA0l47WNAGLmtfLGH0ZIeDDOtPN88tZlG+dUjHyixufFHvqQiGL Ti9Z7Dh+lIAjoZWrBLks2rywvk3tLwEzpw1nN6WySF/b5+A8WRKW5JTlimNZ JKM6YdRQjgTD/1y2XAlnUeO4zGgLBRLK7k5tMvNnUe4Pi9n2E0i4sMzFsXIn i0K739zdpEiCw6LkXtKJRc4t/uZ7JpFwbVxI//7lLKIlk2v8J5PQff1xStwC FkkKrXouTSXBNajQ+NyYBEUsL+q6rEZCYJF34PNPErRYRL5PnE4CUpQdHGUl KL1Z4W2aJgm5nY0mK7h+dfY82pChRcLO2A1v10ZI0Pi+j5IsbRL63mgec9kr QQdlxYK8eSRsJfVK1uhJ0NyLS3kFBAmma2pCLZUlqFH9dtkjioS5VmtPmvTW IYv5FwrLF5BQND2pY/rtOqS8bk1G3T8kuB0/ECM/ow5Vvi1LrTchuf4v2Ko2 UIsCdxlce2VKQrZMY4SBuBa1HpkS27aMBPeTjtEXj9Siu6kvQr5akrB6sEtI CWqQfY/L5snOJHhvX2Fwa9lzNBYg2DDVhYSBSJ2j2+Wfo4ejpuumbyTh61rz P1aSajRr6gwb7S0k7HVaZ5C5oxp9XtJkYrCLhKt/jZw+BonRuTPbVdb6k1CT sq7y6VkhEszdK4yOJ6E/4TWMW8BHc9/Vax5KIIEg3332+MBDx9OWH1yXRMJm 5/Y5zmk8ZDxruvq06yTsJmsKfqjwUKpa1c6rGSTE7rv4deJ7jALH645mPCDh b+n4lArLUkT2tpkUS0jQWbfI7dKNAnTqjt3Zay9ICFa52bhzXAFq9nrUHPyS hKA+9+8jng9QXFd0uMVrEkpmB1mO35CP/rSbs7w2Ekz4UT+onbdRY32yd20v CUs7n8788iUdRRa7ZrxXoiDB0C38dlcYNq53OPdFmYJzri06kfOjcEuP5eEf UyhwmnnaomPfRbxIx3C5ohoFdd9lZB5/jcfvIsc3GWtRcCkms8TeNg2bORer hulRcCbEfHkdPxd/PJA3fN6AgqI1DpYLZe7gy2dutl8xosCTjWwcNL+Lu5/E 3ssx4eqlqxen5OfhxDletqw5BYs/t66ORwV4oHdmmM4aCu6lmSxS63iEU8er 7JvvSEH1dLetD/0e49VzFRwXOVHwK+p08WKZYpy+4ZuWjQsF+84xQa2aT7BD SXXxwW0UpMmp7dZGJTj77PH+Mh8K9utLJuStrcDOGb6vhYcoUMw0bImtrsCj JXvLX/hyTjIdUrPG2KXP+WJnIAWqAmlQ0KxKLOuqxyiHcuvbVc+vHcfD23Rb 3bde4uq79U94cZ+P833r0lbGUmB11efC3XY+lsUVrQsuU/C8ZFDzjfIznL01 Y8tIAgXxmyY1a+57hgcS9m5MTKXgx/GpkUZqVXjlh02JIekU/L7U+MXHogon /mPXuPs/Cl69lB385lmFzSR6zotuUUCku2uwhVU4csK3texdCvripuAyWwF+ 7doR/TiP899D/do+ArzgVkNN2n0Klir7NeMYAZbAYzufQgoEtH4fv16AZx4/ sUqxlAJeEhI9dBRib7FP5EAZBZYm1I7xPkJcruH+7E0FBV75hn6J54R4VyFY ZvMp+BS0vm03FuJ7vQrLrZ5TYPgw/p8iQoTHzIZPLKylgI3xq35lJsLrz3eX TJVQIDGzX2K0XoSHqJql0noKQGXrynMnRNg2sOyYqIGCtefdbc7GinAKP+9x /isK9If+97UsU4RhR9y/oU0UWKvrW9QIRTg+LzzAs4WbP14l9OYbEe767f/Q oY2Cyz7ySQWfRPjCNVfjWe8pOCjdV3NIQYxbP9oclv1AwQfti4+01cTYyHRp fncnBZFGemrj5opxY/0s/eJuCk7wJk86sESM6bnKB9J7KIjr8c/ptxTj4EOj t8/0UjDsKyq97SDGtWV93T59FGxsMnRLdhFjnUlSxmWAgrIXulcrtomxr1v9 XvNBCm7rB1zR9BTjZzn8LN3vFMh9WeV/x1uMNYYKOxWHKJi6aIa7n68Ye1ln Ed+GKTjt9PTsoSNiXBKftOvtT24/5S50ZrAYT35/NgP/piB0ptcx5VAx9jAK lmaPUuC3QFyRd0qMH4Z6z4n5S0Ge9IZNVLgYy9dudT8iS0PvRt8dSRFivHHW 2rRtcjS41ql6tHPO9VrRaqVAQ2BefpY759+PjbT0JtDwev/TKzO4+YapQ4KJ ijQ86wlqnM6t7xFe7vtRiYYMcraja4gYx++N1KpSpuF/1uqHXweJcZWDgzBj Cg3yTm53kwPFeMh4mt8pVRoG5nqH3DgsxvM1mrS2T6Mhdf+and37xXjL7xtC M3UaSh5GtwfuFuNo6V6/mRo0PN+64uQqLr8KgcHsoRk0TE/5zW7h8h24813Y oEnD/dAur0dc/rpxpX4FWjSc/HTzgyv3HnA5EjE7VpsG/St7pBZLxThqi53I Zw4NS6ZJ5Q8YiPETpOpvP4+Gztp1f6TzxHi2UrpIgaLhgcMV/ZyJYuzY7+n/ gabBkjjzeuSXCIc16mnz5tOwPbDn38ReEe5Mf+ofok/DwkFFpqBOhDUiw7S3 GNLwpiZ8w6Jyrn/3rxYvMaZhcnD3Htl7InzP5JX2/0y489loZkefFeH2mani F6Y0qLgdTrQPFGHVsV0B+UtouKVb+9XNQ4QDxQPi/eY0/Nhel+C7WIQttisH SlfS0LH26fC1ZiE+tLJBp8Ka28+sPutRnhD/x1yvTrGhQVZ9cKAkV4jlB5k5 m+xpaD1y7pFNoBDXRlk9r1tPw8yXeppYTojHDigdubuBhsvq+nsnfxRg4/X1 c8670mC7VI2qEAlwgtaOI9ZuNNRNnfza4bwAb3twfG6pBw1ZOjZK5goCHJNo WXNtFw0tdxbU4Y4qXHl84tGjnjSMNhcbFeAqTK5KqvnHiwbn3W+XvjtWhXub Co7mHqbhu8OBuzHvn+EQuc+1iSdp+GsZs+t4Ch+PWZlNSg2jQVfv58oqHz4O j7xolxlBQ0OQxviQ5XwcpWAozI+iQbE3ctHyNh6OnRCARTE0VE/MkkEaPJw5 abTgZzoNPrq/bClpBa5Wm3p1O6Yh5/Ku5iO3irEGuWwnJcNAUWD1tmVx6RiS zwxPHMeATk65ztWsVLx/ystLvXIM2Br0pw+VXMdlI94lhRMY2GL2Y+VIVxLe VZeqtlKFgYUqRpM9Q2Nw/lEZobsOAzL0iEdxhAy2qRYtvGbBwJMQ08JbqWnI d4U678QKBjrNP5XO8b6Bkgs9Nu0ABv48cI3suP4f6k37eZq2ZiB3IrPy3u5M FO+v11bkwEBTXbKnxucs1K4VG1u/hQGTxX7xCeX30LFDG78rBTNg8dnzMV1Q hAZWGOjMOMFAYcIvm1szHiFvFXlbIpQB+96J9+jQR8j9QUGKeTgDmuaXphms eoxsBpWtfM4zcCw94Hy3uBhpHH12uS6ZAccXrefDUktQnM310qYUBto0bTWl 30qQ0gy/rq40BsTfHFQ1bErRWLHOsrEMBma0Ou373VOKun4GSw3vMHCq32Kx F12OikKNjeJKGMiPlL5v3omRoeMEt9QyBnxFGmTcTYxyddojcisY6Jd7mvfz A0ap+OLrSj5n94N7/Ywr0WnZT6HfnjPgI3U39c2qRH/qy3NGaxkYdJ3go8Cr REczE+oVWQYSR+xz+loqkbfVSkq3gQGVyMzkEu6+5Hwmrda5hQE28Ogwc5iH al0Dh9zbGBjnE3Z3zRkesqEd5h54x4CT4FN/5XUeMhONBJz+wIByi11o0jMe KrrKpsV2MeDl92Rs6DUPGXpli1I+MXBoMz806zMP6Sq6aBV9YcDd5cqcL8p8 lNq0cFXlVwYu1D/ID9fmI407sodr+xkI4h9S2mPAR0oO9/md/2NA+tPSfqoD H0VqRfUO/GBAEBPd2LSZj8a+bNMYHWbAob7wYN8ePvoWreQ9/Q+X19f7Hr9D +Wh2pKU6xfnLcqJn/Uk+Wn0iqOJfzjVPd9rnck7b/3GaC2c3Hop1OcVHdjb8 0njO336HLLwbxkcZf4Mnq44ykGndme10mo/W+39+oDTGfR9R+DjkHB+F7J+7 dRbn92ZumhLOOR6bFBZyVh0VOs85z0ejjgI3O85Vdr/seJxv62WMO8e5u7Lc Tu4iH8l2bXZR+MtAcW12zKlLfKTfGjumztnx/rPtEs6bGoS5JOcPu3PktGP4 KI/376gV5+Wj/IannN3SVbMjOBtPtzvzLZbLJ3G1UzznpDvXlVAcH92PPvkr g7Nv9MO90ZwVTvQ68jgvGP73Jn2Zj4z9iZ8vOB/eeeN0AOet+7fclHL+2cya VXKO8ri8doCziqtQrBzPRwWbxMN/OZvyIgzcOP8fsGDimQ== "]]}}, AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], Axes->True, AxesOrigin->{0, 0}, AxesStyle->Thickness[Large], BaseStyle->{15, FontFamily -> "Times", Bold}, FrameStyle->Thickness[Large], PlotRange->{{0, 12}, {-2.6491244665140212`, 2.0370724171171015`}}, PlotRangeClipping->True, PlotRangePadding->{ Scaled[0.02], Scaled[0.02]}]], "Output", CellChangeTimes->{3.419291433163088*^9, 3.4192966709192038`*^9, 3.419349068534965*^9, 3.419349174401248*^9, 3.419349362084941*^9, 3.419701582668653*^9, 3.419769043868689*^9, 3.4197690904909678`*^9, 3.419769222236161*^9, 3.419774426479185*^9, 3.4513118663680573`*^9, 3.451317205378495*^9, 3.482504934937727*^9, 3.4825057281499023`*^9, 3.4825058261761093`*^9}] }, Open ]], Cell["\<\ The preferred way, in my opinion, is to convert the replacement rule by a \ function as follows:\ \>", "Text"], Cell[BoxData[ RowBox[{ RowBox[{"ans", "[", "t_", "]"}], " ", ":=", " ", RowBox[{ RowBox[{"x", "[", "t", "]"}], " ", "/.", " ", RowBox[{"sol", "[", RowBox[{"[", "1", "]"}], "]"}]}]}]], "Input", CellChangeTimes->{{3.4197753552321987`*^9, 3.419775387369096*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"ans", "[", "2", "]"}]], "Input", CellChangeTimes->{{3.4192966437671432`*^9, 3.4192966468863497`*^9}, { 3.4192966897493668`*^9, 3.4192967021701517`*^9}}], Cell[BoxData["0.5635239311232755`"], "Output", CellChangeTimes->{{3.419296676789568*^9, 3.419296703010871*^9}, 3.419349068655528*^9, 3.41934917453279*^9, 3.419349362255458*^9, 3.419701582717401*^9, 3.419769044118333*^9, 3.4197690906873198`*^9, 3.419769222268836*^9, 3.4197746146564693`*^9, {3.419775361242696*^9, 3.419775390784547*^9}, 3.451311866579207*^9, {3.451317323467135*^9, 3.451317331603176*^9}, 3.4825049350401382`*^9, 3.48250572827008*^9, 3.48250582632934*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"ans", "'"}], "[", "3", "]"}]], "Input"], Cell[BoxData[ RowBox[{"-", "0.6263180347831008`"}]], "Output", CellChangeTimes->{3.4192914333115396`*^9, 3.419349068749035*^9, 3.419349174622263*^9, 3.419349362347032*^9, 3.4197015827606373`*^9, 3.419769044317284*^9, 3.419769090775528*^9, 3.419769222314582*^9, 3.419774622591238*^9, 3.45131186665049*^9, 3.4513173351816597`*^9, 3.482504935112276*^9, 3.4825057283243847`*^9, 3.482505826399234*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Plot", "[", RowBox[{ RowBox[{"ans", "[", "t", "]"}], ",", " ", RowBox[{"{", RowBox[{"t", ",", " ", "0", ",", " ", "12"}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.419775156364932*^9, 3.419775188764215*^9}, { 3.419775229514915*^9, 3.419775230380636*^9}, {3.419775377088327*^9, 3.419775377669587*^9}, {3.451317390357278*^9, 3.451317404665827*^9}, { 3.4513174366020947`*^9, 3.451317451083885*^9}}], Cell[BoxData[ GraphicsBox[{{}, {}, {Hue[0.67, 0.6, 0.6], PointSize[Large], Thickness[Large], LineBox[CompressedData[" 1:eJwUV3c8Fd4bRjZl79F1iQYNq5Kct0mTlqJEdokipJIiyc5KvjaJSPZex957 Z7vWJXsl83d/95/7eT7ve57znOd933PvEdN/dtOIhoqKio2Oiur/32tXLMI0 nvmouC7vUD5zyMVQan+TpAVK82Nmek/BDbOjT7wkHVB/m6Eg9fYc+snTG/k7 1AWdUt5x/rAxh+bTz3k+lfRGWi862hnW5pDggc78nS4/pJofH+q9NIdO27kf qwkNRAeULr/kn51DelUqcX6PglGoRQxD7MQccuJdEn4gGY7KGhPXjg/Noda0 WzV+K5HIod9/o7FrDhn2yDj/7YpGDa/Daswa59AKNSN6kBeDbORtxdnKKXoP kP4Vh8Yi2dlDLbk5c4jvRkHGvnc/0Dd57einiXPoh13gM/dHCUjAvch8f8Qc qqu6PHZLMgnpRsm+KHKcQ0kvOTUe0KYgkRCWd8GWc+ilx7tf3ispKKF5cv8H vTnEmK5lutSVhu7hmssOp+ZQc2Vlxb6adPQ6SanRT2oO/dcjJ34vLwMtPHhE n8M5hw7S7BkoCM1CWbcIayfGZ9Eiz5tTc17ZaHkfLAc2zqL8A+QgsXc5qFnu 4UHmrFl09UbpLZdHechv3YtHwWkWPYu0rVGXLEJ/am9zFLPNohMZI5JOfBjZ vv3XNTU/g6gM95/Vpi1GooLh+xRaZlDNyy8RnivFiDxl8Ffm8wzSjnimvdBV ivY/VT31m2oGqRyQdHPXKEPkR6Nt+3unETG9L1u8pgy98c7o/JYxjf5UXuLR zCtH0uv/ORCNppH9rHhzXmglUjL7cud5wR+kZ9ezfYunCtWcy+a65PMHnafx lZnxqkJ3NiO+ahv8Qbt5t933vqtGKTFtDEcY/qDw090XnB/VIkWrH7eaL0yh Ek/P/GuSjcghFD8KiSSjoqnf9Szxjcj1+uEJKUMyKlCTGqg51IQ8ZOjtZiXJ 6D7NI6pv/M0os+GjunzCBLpTtEHcK9qCLPgfC8zGjaPLisdM+Q60oabS8rKP TqNITjJ0kQF1IbWjzb9kfAcRHb0Vw+STQTRr3XSTyFOByJfesS3FDSL+SZlb 5S1lqNbLk29rdBDRXp+99NC7FFW5t/m7HhlCopFX7L4xFCMPztlvofFDaGZw 5rXk30zETRQvLw8bRtJ5lycHVRyQ5BkvWh6XEbTQ+qvQPKoU8434MwbHjKBo 35mMa61lmPFjMOveshF0invX9XXqCjxVHcd9gGoUif/DcwE6VThZo1Ti9OtR FM1xZL6Nth6f0Pt73shiDO3+KdY59rEVX3r36GOm5gTauuZD1zfUg2U/l1yM sp5AXisTn57c78XCEWKMXn4T6BetZAG5vRfPFw27GzZOIPHezNtx5X04cPuR D9dFMqow1TjaETiAR9/qh1gqTKJ0nvR7CdTDuNGr9IHOrUmkiGWu5igM45ww ougly0nEvNESI/l4GHsUkiIJvyaRsNuywd7GYSy7pR/bJDGFyBdCjR/6kPB7 e4NUGe4/6Onq6hu2lRH8xLPMSkD2Dzqkyf3ui+govh0qLk+n8QfpKv1dfKw6 iqUKRrL6PP4g7cKe1+uBo7hxw6DAY9c0otWStouSGcM5LOVvX4pNo+Rdhy84 3RjD0UISyABNo8P8Z3ITrMewzanREqU30+gqk/23ppwxLPzGsGpycRodhxJp zRPjmN6j3LWDfQY1W5Zn6GmO4/lgicslh2dQdAdLyK8X47gsb7Q+6MkMynR+ fYM1cRwn1p73dnadQWkij/lFqsZxYE+M+vPYGbTaJH3IYngcP1k3bFUlzSBf 8SnDJq4JfJu5wl+OahaVKbimDxyawKcF993ZKzqLPnlfDJM+N4HZlca6VrUo c/6mqt3p2QTOfmXU/71lFm2Jasiw4wkcq2LWJbg4i96JeKe4tk7gwF2WLZ8p 94TljuuW4NgEtvWyr3h1aw6xZ7sQPBnI2PimE559MYdKlJ2jnvCRsSafa65B wBwqOnn0rL4kGStG+f+61jGHXmTzfAk9Q8aSxv/Fla5Q7kV6T4XBa2Ts8aWp WYhlHllNCrcqaZHxLrvWa5pC8wjiKm2TDcj4jXZHrc+hedT/pvv4aXMyXlLu Vq07NY9iLGeOjdqQsdne3nK6q/PI+/SEW8xbMh6hHjgDD+bRsODkUwdnMr4/ OlT0+uk8Woy9yW7lTsatlSOnMu3n0e+CvNR3n8n4cvx4zpznPJK+MRUY50/G pR6TCgfD5lHSta7dU4FkrGQxnWb4ax4RNEKeqv5Hxmkac0ciCueR74AhR3Ew GR+UW0z83TCPqGrf6N8OIeNonpUD3APzSH3teCMtBQuu/Y29PjuP7qks17ZQ 1vv1rIu7bc+jNH3qrvyvZMxcuBVZtmcB7dWMtisLIGOnCCrRbdEFpHyaUWXS h4zXHXeFnDiygP6aQaGMJxlbGdLzv0ALKDdJJsDXhYynLjJ9+aW+gDRTnUx5 3pOx/gFWTrLuAjJJy5/ItSPjHha2z8TnC6jTd0/Vu+dkfHOWg1Xn/QJ6avqw zMSEjGubud2++iwgeywXZaVDxmfT+ehbIxdQcF2KdNRNMs77IviBNXUBaX/+ eHL5IhnL2olQqZYsID3n0einSmScoE1469iygERe2F1hkSHj4L2SL1cXFlB4 9CITZiNjTpoDy0dpFlGeISdz584Edh89ZGnGuYhypkpF+OYm8Ov4Y2ZDsouo I0Y0RqhuAi96yJMFzy2isyr1SsPZE/iJxXGjO7cWkbXbsnTHtwmsLXdat/bF IjKgP5F79dUEbuWBPlrnRTSa9TS5VX8CX147q4UCFtEV46O5HlcmsFKh2q2M DEq+VRhzqOAEFlS9rRq+sohoJTmPaSePY78Dd8u76ZZQVW3D3jC/cczMqn2G i3cJseTytYvYjOP1Zt1TropL6Pyyq97A8XH8W9vsiNXLJTTo5rjfJWMMu5NU n351WUJ/SzrLFQPGsNITifiCL0to9MxGvdqLMRz6qp/IkLGETowfsQ08Mob1 gtR5Q+eX0OE/BZbbkaN4okNuq+LxMjqWw5kGpiM4SIdd6Y/dMmo98yQmRWUE q41N27K7LiOr1ZKj/3GP4ITl7/PascsoWcLMpKeIhC24+EfnSMvo74bfqcu7 SXhFY7NW4MEKyhxx97vhP4Rju7sZkNkKMrzvcYVNfwhr6mWeN3y9gsy5azX0 jg7hnGcWRUlBKyg0MyTa5esgtvceSj3XsYJaI87cd9jox7vqy4PMr6+iMimB xiuRPZhD1cu4BP4i8otvgeEv2/D5+AJ06MZfpJUeICz+txXbsUzzf3n0F801 7GNQtG3FQ02X60yd/qKXFp27hF604JR7jEfZy/8iXpG3T3ubG7HGkw//Hqqu Ie5bEhyyHpXYx+uV5+a1f2jdurRR3jQOl8/9MDJ++A+VKh6/fBS+4bUb3SrN Fv9Q98KHJBm5cKzHe3zh2+d/qDw5rXbzvAc+GrF850rLPxQUZi8dr+6PmlOe 7Q2+vY7obY9wqe/OROztRmnH728guX/CAhepaxHMnJm6bbaBKnrOz9ZM1qLn 9KJEqzcbSGNNTWukuQ61nOj0TQzZQI0p9DM5wQ3IL+yipVjfBvKf1NJi925G PCZSR1l0NlHTHbY7HRNt6OL7Xab7zTfR0Jmh3dzq7cj2v8GIC283UThDSYRR ZjvqrPvK9j5sE+m7fIuSf9eBgo4yzi33byKr2amIQwxdSHCd/Gvg4Rb6yfxW fHrsN7rMVTG2YbGFjNed6xeUe9Br6SgRgXdbiKf2llGfXw/qfajldStiC9XN 7zHXPNWLQstqnlYPbqEKK/KnYIc+VN/3PWZsbgvlmQhzOdf3oc0Vxz4aqm0k 7PumGgn0I539SldPE7bRl097D+9L7keiXgmH0vS20cscabJF/QC6Huti0PR8 G2nUP7ZJYR9EDlg/ZPr9NpJne66TcWsQDS4IskhFbaPVn7bKmx2DKFLTYypk eBv9uCIzl2Q0hJqfmRBzF7ZRqh2qLXEaQtRu57Q7qXeQ+Ot/lkcihpB+/kYN O3EH6Utxm/N3DiFxwtP4j/o7iJdp3z025WHkOSAW5WW5g5KKZNpu3BxGq6Fd QV/e76Ag31RjKtNhVC1wzvV7+A7Se3rrTKTvMDrWvfbu168ddLL/Y43P92EU HJj0MrNgB32zezj9J2cYPeUSNKno2UE7A1M5Q/3DqKOl6WHD5A6aq2OufTU3 jFR8Pmp2rO0g+uL48/ZUJOTqshZtxUIFwpXkVwUEEio0agtf5aQCqe6zpf+O kNDi+aTg14JUoFT0+XOECgnd32Xo53SACpoNRZgktEnIh6TiTX+MCnSa9R/T mJBQeYmAu/sJKmiQjclSe0FCh983OfqpUoH/z8oMVncS0tdNeMurTgUK//4g 9wAS+qry8VWwJhXk77g/fRZOQlRbSpbRRlRwQJvs9zyFhOT7eMwlzalgZrvZ 0zOHhB7nz5smWFOBw7cP+9mLSSg8uM7wsD0VvBzps9yoJKHWV7F6aR+oQDbM 7NX1BhJi0HJ8oOhBBfrlFreZ2khI+cSDe3l+VPBDvk1YupuEnvMdv60STAVH nI8tZPWR0PdVDo3SKCo431m3HD9EQj0d01cuxlPBn18e6nSjJLQns0q1NoUK 7NN2ZGrGSehcQPS56zlUcKfoTskKmYTsXrxFrZgK3u2+iTymSCjx5r1TmlVU wD56leT2h4SGj8kd72mkgolfhycXKJiXY4/cw04qMO82+1pGwZfnyYdJ/VSg l0ilsENZ79BUdtB4jAq+Spnv+T5JQulJ4ZJT01RQ3plinTlBQmSvV0SLZSpQ Sb5YeHSMhITNb4sublDiZMJZPhIJaVw9Imi7ixrOd8U8ejxAQh8PMfOuM1ND WHmsg1QPCeUxj3E4cFLD01ojqpsdJDQ7iXfTCFJD7c9PNyebSIhYE8zkIkYN SIptbKaGhO7+sKFjPkANq5pXpfXKSMjzkwa191FquL02HQkFJFRsfGiL4wQ1 VA8s4s8ZJLRygf7fF0QNfD+jma8nktDBfcPLAqrUYE5nQ2//jYT8RwKnxTSp 4QX6qnzAh4SqSy3J33WoIWF2NDD+IwltRl0dPWBEDYWm50khr0nIWI+m75g1 NQySSLnd+iQUjPq7Mt9Qg3S27CcJTRJqEs1pO/mBGlq5YqtG1UjoRL953Rk/ ashXddaokCahpANWPKbB1ND/JzQ0QpiEJGxtdb2jqYHbXVz8NwsJsbO9W+pJ o/hlvzfcnDyMJsFHyLqNGjQEP/48HjyM9LwCjIJ7qcHrTRSt1Mdh1Pk7KLl4 hBrc5pnC3z4bRqVWUed2L1PDr8Psq4ZnKfMZk2YWy00DNNwxrMrDQ4h9ISuz XpgGXqnd5v1YNYRcTufvLErQgFfOjTiVX0PIqrPMHynQAN1L/QeML4fQFcaO /O47NMAXv7UuQDuENs3+srB8pYF8AfOJSuYBZJWzcedYBA1gxuuqcZX9iExL FXk3jgauiRe9C3DsR+1hjPIx2TRwb0fTKWq5D/1qEnhwupsGPL1oAnqbetFD OeXEZwK74AG/OHuAzm9Usv7+anvILpiWTix5OtOG2gWsVp992wUtTI0Bd7+2 ofETBpEsP3eBSnjORh20IdaXF5bP5u0Cd+0AEx2/VqS5xBSa2r0LbGoJj2yP tqCpP35/vHloQTqx3kQtqx5x98e4X/pMCx8sK02/7BQjyc0v8mOBtDCdwjro eaYYnRT6NPA+nBauGy23Z9Bj9FDrsWzOL1pIVOR4QdhdgOI7ZHok62lhK3f5 gDh/FlJpzDpAy0QHqhI3ZSb0Y5Aprq4ucqKDF7vPeOXaJuB/J9mJ8u508C3M QpZ88Rd2z7j7Jt6Xgq0vq1syp+Cf8eMyAZF0kDfC8XOpPQ3P+tP6Py6iAzr1 DqG/2jnY2hR0uNfpoPh9IondtwTTjXzKcqOmh9Ion23yyVIcqNPEtsNIDy3u M3Sjw6U4++bD0kk+egj++2btyJFyvK5sL4UV6CFKMFsrrKgSv+fIWXhsSQ/q Pzr4+xPrMIfnzuVBO3q4Gv/Dq+RCPY6mV425/Z4eRCeMuhz763HZRocm+kwP 0Wd5vD4yNWL68aV87l/0cD9VLy3gQDP2zDvigsn0oEH33bfsdisWUXg5KD9P D1msS1kHv7bipOSiEwl/6UGW+WnMcHcrboq59ieAngEU77ESTmi3Yc7PZhpP JCh4X/u81u12/J9BnCCPHgO4JNaE8u/rxE+v8JdKmzJA+U/Hf/f1OrGKnNvj 888ZIImF1zU9uBOTaMxyXrxnAKc/4kVBrF1YOvqwZmskA5jsTznGPtaFt90i tiZ/MABb9v33NfzduNmS/Tt1KgP0Xji76X6lG9ucWVw6WsIARNurh8WSunHR UKbv52EGSHh9681Lk9/Yp1ryZNwkA/ye+zB/3f831k/5OlS0wADFEReXJYp+ Y4b3r47MUjNCSt8J32r2HtxjMtVJx8wItJ0VxwNO9OBE9fsOIpyMoDae8Elb twdr7D3dcJXICEGHXBLa4nswkSHJ2vAgBZ/I++3c0INXZkWF7WUZoXGl/onM fA8OLqIy+3mWEcLkmbofyfbiEZ1yRmYDRuDKX9pzMaEXZ11QSBEzY4Rr6dIn Iit6satM7N2TLxjh95oL28xgL5be+hRr+oERXkktHtTh6MPbo2vX3nswQk/V Qs67/X24pf7xyld/Rgi5P+/qr9KHbUOvnK/6xgjuu+PnvEz6sJpzwZ+Bn4yg JGC81/p1HxZ8KuO/ms4IOSliZZc9+/D0rXClPQWMoMu8iDnC+jA+xUbaV84I 2oP5tDWJfdhP/L3b6XpGyCg67P48vw8bsiwcvdPOCA56JTcZa/qw4tKj7qd9 jEBa+/XEp6MPM/a2vnMeZYRTHrMTjMN9uKf0nFToNCMcPn1yyvJPH05MyGhM X2aEG1KbwXXLfdjBb59t3SYj+J3RkOHd6sM3XgeKjNAyAUPTbP8N2n4soc9Q sc7KBH+MZJYcmPvx6iW7p5w8TGAqvFoQxtaPq49Nch0UYYJeXxyQxNWPgwW0 88/sYwLmNef+VN5+/JS6Tl9L5v/5Rbt+8PdjNHmK2VKBCa5Z3n3rK9CPOVsS U11PM4ECX0KNBQWP5ohoRV5ggu2xF5ZAyc+K9KbKucYEUrZN9AwUPlfXnbim O0yw4HNoXxlnP9Z+/lx9QocJlPYoW9rs6ccy94ZXt42YYMlxOkiUqR+HcqJt D3MmGINdufK7+jFzQyidgA0TPKpZP2W02YdffVpnjbVnAhocXZ5C8YN85h63 nDMTPOiI3eSb7sN3NzOFij2YwD/eJSCE1Icrs7jEr/lT9g/xOqfc3YdjDjUd M4lmgpQLjONdxX2Ya1z65HI8E7TJlT9uT+/DTpHu4JjKBHk3pPYtfO/DujwX 1UOKmcDH+32i96c+3Nj0TXN/NRNsPEk4zfGyDyu7Uz/MbGKCf69++2QbUfpl p+Bp0wAT6HNyq7+APuyWK2j9YJwJ+JVW09yl+/DaC7s3kzNM0NPgVFvD14c7 yHLuu7aY4HNY3pWyP734/DdfXx9aZigh2w+9a+/FaTpzQSKszPBmF9M704Je 7NOaEHdciBnkBa+8KHXrxTuejMnlRGbon/gnofisF1uoGmfdOMgMnRLqQT23 evGVArEKs5PM4H1DpTBPsBfTxwaRIu4yQ2x3Fe9meA+20VudlNZlhuAul1IB hx48Knh7IdeYGT4p8eVYPejBJZ/ZqNptmMHtscmRPt4ebP/KRYQxgBlMMsPP ZTn9xotXre89b2YGr9R9ePB4N37E0Kq71cUMiyd19UxYKPdPyRET90FmCFve 0Tk30IV/Kf6xiZllBhIrs86OYxc2Jej7d7OygBrtMjmnpBMPLKk3wiUWsLnT w1Ev3oG9hbrEn99gAU32Uc9ecjtWOffwVYQWC9DNPdM5/6sdR/g9ldh+zAKy A8VC0vLtWO+Y2+t8dxYorvvRE6LUhkcsSiUV61ngi83XGTXpFkyelH93SJ0V qtlp59fNavDioMBR3ju7IaL/tBC/8A9MMPgrv1dnN9wei4wMTv2O1cfbT+43 2g2rfGd/eat+w4nTn88p2eyGVrGAnXNTodj4H93dh192w8Nx/ZkzRh9wD+fi 29iO3cC/TsyQVQ9FJRdq6xQ194AxU6eNkm4umq+Oa0YP94Ca8Pexg6/ykOjV jx1qxnuA0eNEaZhvPnp9Ewa1bffA/UnMMV5YiOR1sxYdAvfAtrirtBN1Cfph Fy1Q1bkHYhNDzk0KVSCfn69N7t5lA79CkLB2q0f3qS/Udzxkg/J7nm7ic/VI 8i7bsdvGbPCky54T32pABTQx6xo2bBBjsaGQItCIyFoNXpf92SCjy9NePqgJ pSd/XawOZoPavL8vtpebkAOd/l3VaDZY3Yh7prG/GXGnrhLOp7KBxHTBpqxT M0KMhIzTTWxgd2M/+ffhFsT8cIq/oJMNApzDehzvtaD29Iy3SgNsEMctbOPl 2IKe6F5SPT7DBmeEJgrqWlrQlfsnzYPo2GF6E9vXPmlFL9P0qfzE2WGPepk7 h0MbetBfJXtDih3kL5opuYe1obOMMkbsh9hhrwWHhVYB5f/Qw7813rLsMBjY 1LX2tw1FM3n6e5xhh87t3v2HTNqRq/xCxeUL7CAskX5B1bEdmetqrjFdYofb u7cNMoPb0YlMgo6rBjs0iac2fKxrR416mZIfddnhFs+hxD8SHSjDQ1DrvAE7 HD0iRut5sgP9l/XOY5cJO9ycDYI31zqQIevleUcLdlgT3HPuwosOdPl4MvGM FTvYG+35uPdjBzqiz32HypYdWOb8v6kGdqD17IFch7fskMFV+vN9VgcaIp2b Pu3IDgMK0iq+FR2oYne86JYzOzB/DN2ebetAPgYvPrzxZIfkz5ZBvrMdyNa7 O1PJhx1s1eVVO9c70P3c0+R//uxg8iSz0YS+E0myMV6zC2GH/7pL1C2FOlHi vGOsawRFv6GWVNK+TiTburET9I0dHk8onec/0oly0m204uPYoeLUam7y8U6E vsyl5f5kh1WW9G/WqBNV2j5mrU1mhwd+0hImFzvR1XsjRj3p7PD17i+jT1c7 UetJHTyVzQ58C8zBHTc60T2hLv6NfHYIx1HrNzQ70cCmhhVLMTt4BWhUb2p1 IsOB2jqhcnZQ47K80vmgE03h8/ukq9mBy7e+beBhJ7KMKnJQrmeHtvCAHF69 TrTmdKL7ajOlvlwP7jlQsINh2jGddnYw52IX+H+c9qK0h3k3O+ziXDD5/3p3 qdjRt33sMNXjkdtF4WdnIqh4D7FD8Jc0NxrtThQ49d/X8FF2OFhnc1+Xok+4 nmshicwOJWYiubMU/d9+eV3G0+zA2C4mn0o538HPDDFN8+zQWithFEc5f8pz x63BZXYo/DH2p4Xij+LNDc35NYofOUeeHTvRiQrkbFKotij1SW4LraT4e5Zn jomDmgNeK4Qf8JPsRNWrpgZidBxwP/FaS4BwJ7reTSo4xsQBGyufNJs4OlFH 7gPes7s5YE6p2ekspZ4PQjqf3eTgAMFUe8m5fx2IZK9Ro8/DAfL6ifyd0x1o Fp23/yDCAR7GxcaazR3IWqyow1+MA8z+WPktFFP6jebEkZh9HBBgdCSxNqUD MVQeIpXLcMDbD6O+St4dyDvu+6mOYxzwU2qvftubDsTttvfLmAIHlDA17U8y 7UCEq1xq9CocoLNxiSwDHShWxiuK9ywH5IxL8ncc7EDSbAwbkhc54NfBD4ml 3B3oZOv6L9XrHJR+HM6wGW9HN++RuNwecgBX9ZaNDmX+uk8+MP9Pn3I+Sdpm LeN29FCoszLemAMYbqh6x15uR2YDNa9qLTggb8/gd0WOduRsmDrI8o4DqJw9 3t4LbENZz9//9I7ggFd3szRmHVuRe/58htY3DjBszJIk6LYiXfpHRRJxHKD7 RW224VQrYgw905KXxAGslZKV0UstSLuK5u94IQf0EV0/3tNpQdsiH8+iPg5Q jOI0VhRsRhfq3H7P8XMCuhK03uhaiwR510l5wpzwWONn5LRULZrVezL9kcAJ iSg+2bCyBgWuXt4R2s8Jasq8QZbUNYgsxrpP7Tgn/ClvV3n4vAp52nk/j7zD CU8WOU+5y5ej9n3+DDf8OEFvs8m/rD8PXZLiP2EeyAn+NjbnAmdyUdH+MFO3 YE6I/lDHN7uZg+IPxdWURHPCGftDfTcEs5HDsXwP2XROuL7aZzilkY72nx5h 427nhJwTmfb5T+KQ/W05/i4eLrhqFbPxTtoDL9zJUVsS4IJ9Wwotstd9sfHd 06/YRLkg42pkVdCuL/iGtmqPqiQXkLx30hSNQ7Gk3v3QHEUuIHwyIbh++I6b zT4Qgu9ygVnJJiFqPBVLfGjbr/MfhT+0/dSbKxjfS9t1zDiMC0p39nH9YyzG nsNyJ59FcUG1lUHDM7NivIICLjnGc0Gd9VU/msMluHLz9pPvuVywR/ZXu0l8 KX5s2/lz5jcXvLh+pzHatgKHf6fPWO3ngvzHphaH6ytwa7tiwc4wFyS5vHGo IlRiJbmv9RxTXFAULlrDV1WJWefvziisU/TSZR2fZqjGSY9/H3YQ5IZnLE59 uvdqMSmI6fgnUW4Qrrn8IC6sFvNVn0Q+RG4wi0k06R6uxe8lg9WjD3LDvTnj sDnjOnxjRPt5pRI31Job3yo2qMcunB52TSrcYBvjmCYWWY/zzuS/7z7LDcFR QZkPe+sxMVLId+oyN9D6SLsaXW/Ayw/6Uvfcp8QXstbfSjbi/Z6seXy6FL5c 1ip/rUb8IF+5lGDADY/cZ0RfezTiCoGwVlkzbiDK0RSl/2nE62oNPaeeccPR Vd1qWsEmfNhui3T+BTeQaIJHxVSbcGCnzpLmG25wkvS9WxDWhGvpvDd033HD g/t5DcermvCOfNGuxx+4Idr7a8CbuSZs6i/K/caDG35cVX8sLdqMT2oMykeE cMMf5eKxBINmXECmm9GP4Iabuz9GW1s1YxVH6e+S37ghTTzHIuN9Mz6f9oon KYHC56Pw8ktIM668HNlgmcQNVGn6uoo/mvGlkcqPCmnc4NhVlnQ1oxlf5+Ze Lcjlhrt/+Vl+1zbj5kSlpPeF3KD7c3n8ekczvnXhkfH5Em74cKy16uRgM+7s /yTKWMENw8mskf+Rm/E926TOumpuUM65Z2yx0Ix79nR4f67nhrXPpTw5/5qx TtzGxVvN3FD8JvGXLXUL1u9Wy+7pomDikYSbbC149PmzZ+G93NARd0D8OU8L NmEKlNIf5IbAqUe/aIRa8FRUweC+EW5oHK7UYSa04KdKI18nx7mB4/rna58k WvBsK5PGryluYH50PPjV/hZsaXaU0XKWG7IMHYyGD7Xg5V13i+UXucFG0bCj 6HAL5f341m5thRtgUoKb81gLXpOPOVrwj1IPB3mNXtkW/Kahlvxuixtkgk8V CMq34G2jhchz1DwgwMr9uZmC32/zaTHQ8cDEnYpdWxS866sKRx0jD3DIOWpF UrDLEaMab1YekCREtuXJtWDGag/Hm+yUOCks9yqF30Mv7SQvNw88z+O5q3m0 Be/5173wm48HRuIKNrpkWrCP7058mBAPXCDd32g52IK5DkrqP9rLA1tv6n+d l2rBgaVXBfeJ88Aq15LFUfEWzH//RStZkgccP+WHfxFtwSFL/7knHuSBczHc UdYCLVjUs/js88M8INHzp7+BqwVHSkysy8nyQGf//pKo3S2YWLg7/a8CDzjE x+XN07fg73fkzfJP8sCPv0dV8neacYKLY+/ZMzwg/YO2snyuGUvv/eFPf4EH dlurV9BONOPk7MYrtWo8oE0IOV/a34wzyEIFNzR4gMnQYCS7phkrOp615rnN A35SVsILRc04V+Cx9O+7PDBnFcSYkN6Miy5nherp8gCNyRPNMEq/wkjfbQkD Hji978lct3czLnuzazfZmAd4PUQSAh2bcXWixttnFjww1n9RKMSoGV++8FJB zooHqJmYJEc0m3FDf9jMqg0PkNeYNpJVm3Hrnj86Dm8puEi+rUeqGfc//6ji 5ckDVZ1uN7kqmjBVcbFItA8P3LWVaZkPbcISbJubWQE8wPaQoSPvRRN+8ssq fyiUBz4NyyQJizbhtUndE/K/eIA9dvLRLeNGLHQyhO9SKsXfCmmXZoVGrOLa uaqTyQODR60Dr9A24o+S1zI/FfLAvtKZpvPhDZjTQEm2t4GCBZnyXCrrsWKa Dcd8Cw/kx2XxKXrXYy3q1HnaTh7wOTHTvXq7HkdGSCUfHuABvQi1tqzBOizT xy3tNMsDv+9/0H49VYvV7sztO8DGC6PNVsUvuqqxWcxBOhUuXmASmqqy963G 3ktGozf5eME6+NibssvVuMO3L9p+Ly+4GTA28eRXYf3Gmr3NR3jBb7CxkOhf id+qxgi81OCF6yr/Av3Ey3HaSa3dFb68IDt13jUkpxBLLLqHBnzhBSvl9+oM 3IX4S0LBIcP/eKG6XUao3aIA2wkRLu+K4gVCvgd1HDEfq2yNu5xJ4QUtCYNL jR9ycF2xNVVRIy9oyz4LZjqWjkdVfZayWPigViWIZr0gEmtSlTq5sPHB+ebx z65l4bgqZ4lDk4sPNPPbnZ/uDsUJB+4eXRHkA6qIDffX0YH4OYuoudxBPngu 9WBi349PeKvx53iyGh/wslMdLjvyAfFqVv3+8ZEPBtS7Hn73jEcXlWPAyI0P 9pQZxW5XJaCXRMc4MS8+MPiUlb9InYi6Z5VsggP4YNnO5t0nyyQU8imJ3fMb H1iUbHIqRqQiQu4X1WclfMDap1ffeC4LaURYJR2q4IMTVfy2l9qzkONHdR5y NR8IPWOMbTDIRqQbTCN6zXzw3luui/QuB32fsne4OcgHR0VC1Nt/5qGDwoaZ Clt8EBR5rcCvqQhp05wRXqTiB+VT8m7D1zHyIIt8SKLlB+fFHzo79RhNZ3Rp SLHyg1uNom2DfjFKvnZlml+IH6on9/dt3CpB8u9kxTdP8MPrxM7Z63xlyMiI zT1HmR/E+9QeZFwtQ4FXpuetgR9an1g4PHYsQ3/5YotmVPnhfJFyXiG5DOWl CGgPavJDxc+vd/4klSNEovItteaHcKEGOy3+SsT+blG02Y4ftrdgMflCJSIJ jSb22/OD4ZjriJhVJXK+U1W95swPpcc4Qm9VV6Laai+qI1/4gV+u8X7z4yoU avTOW/k/fnD9j/ra6OcqZE5jKXw5jB8WMmJfs2RWIXbl2yeMvvPDml47n89m FdJMFnwekskPiJN08MH7arT/Kuv2j1x+uFLQ6rsUXo3+kbc8sgr5IdRF+mRQ QTUKJQ7HtVTwQ85Pqb/0K9XIHLcqDNbwg9opu40mthqk8qC8bLqBH5axr1DM gRo0/CVukKGTH552Xpg1065BabL/mfP08ANNiGTXQ8sa5NzkvkEcoPDtuq92 /1MNkmSy4FMZp2CHbf9nKTVo7bvu9ytT/NB9VXrGpawG1Zy9Iac1yw/7zSXr Yztq0FN7eXXrVX7K74m6/c4qZX8ByX7HdX5QVXjKfYK+FrFl8Zl93uaHepWD xXbctWjoJtO/UBoBMBy3eVUiVovS5tZdEugFIFns8DnOw7Xog+c0dw6zADTt JhwwO1mLbh8YiK7YIwDKN2mg/lwtkqxsOtrGKUB5Lzz/rnCtFv3VLyka4hWA /o/j7+Lu1KLqnbSrs4ICEFqevy2mU4uCQ2N6NkQF4E2dkPZ3g1pkdjLQlElc AM4VbrUee1yLlDs/rfJKCcApe5H0KvNatOfFK2eJQwJgVLl81cSyFg2ymXHK HhGAMI2MDXbrWpSS+CASyQlA5rCyeIVNLXK6dP3wteMC4GXOf9TZlqJ3HBVo nxKA4ySrr9cpeN+HY5dNkQBwZ7N1SVDyV/eKd9ucE4AlbxUbhhcUvQXcxh9U KfuLtlL9fUbRq0W/7HNFAO5d5ONYNqPoXf3rGK4uAMRj9Rd2jCl6/SfZEm8J wKWnfKoCjyh6j/aG5d4VgBDadxVntSn+1tcfqrovACPlA6/sb9ai1MdFue26 AnBrUmtf1SWKXvoUVZKBAIgNXvMVB4reb1EdcyYC8E1d9bOfAkUv+BtsmQlA 3Om/a9wHKXr7nBeYnwvAT+L+lJ8iteg/XtPdknYC8DjDOkuAphblCGtcmX0j AC5Bsle3lmpQN/GEW9Y7Afjb+pvMO1aD+I8w0ql+EoC69U//zZXXoBMK82fZ PARgwzvSPCW9Bt091f2+y1sAdt6mVydEUd4vqj82TQIFoKaGpV39TQ3Kuuaj dDRYAD7TdFptGtegzlt2dmthFH2CnjbjN2oQj57asut3AUiU2V1qu68GBdiR /8RnUPgfWZnHllWjDIfmA1Y5AnDXbe3f/fhq1OacY6JUQKl/iFjKXe9qxOnr OlJbJgB9Jtb6kprVyDd+f++fVgHIqhJzPNdfhVKS2QUyOgXAWdet62phFWrO XNO07xGA07Hyz2JDKfNcWt3KShKAM0+FGtS1qpB3j2mtzIIAdKq/UYqurURJ QxqMq8sCsKrR/Oz290rUMH7iYtGaAAy39Sjqv6tErEuMpdepBOHKk9uvAo9V Ig+W+NxnbILw2tGyyNO7ArkqT/5IlRGElsNzljzS5ejH2ZbxV8cE4d6/Gyan t8pQlVquxFkFQTjqdK6up6EM0d9xi2xVFoSAroZee/My9NH8QNDSFUEYz79W 8zm2FDmFP/6k8EQQWidl012pS9DZ+8bT1y0Egabg8ZGLlcVoF7/BDVMrQTh4 mjHsg3sxcvZ9IBTyWhDi6N5LuXIUIxdn9WQqD0GwD1TU3pArQm5PFLrqfgpC 5/VXNt9k8pCPIrWU/owgjLwqFoyNSUVhjUGV3s+FYFlG6PE16stYOBd2fbEW gtaIczVDvSY49BsZhdgJgUbZo+2ZQGscYnciN+69EKSUrZ5JmnbC/xG7fxb7 CIHEhbwj83R++Istn+9iihAcf4l+KJhEYe5HuGEtQwiG9o3bblhE44ArJsw7 OULQ5xi6FGDzDfsTsj+wlAjBitlxZsK779i3VtNWooUSrxeJ+O4Uj71EA+9r LgiB4uvB/XuiUzArk0rQgxUhOKkT5eIvmIo9l8ba9f8JQd7njXjwS8Ue1QrX n1ELw0jduX8079Kwm1UHuHIIA+lW3kTRtQz8sZJbMu+YMIBZC/VcQTamTS3Q L1YQBs/SLKVTkjnYOcQwovKkMLQcKSm29c7BH55n8LedEYbuC04cyfdzsaPg bZbpG8Lw2fpXeyM5D7+18J8XsRIG2tCC2TN1hfhy6bH+ARthEA34MHpDuAjz 8zbXRLwSBlbdu8+uPS3CGYWs38QchYHacd5ihxHjKVaXO/t8hMF3okvaS7AY 5+hJnB33F4aX8t82f6gUY5eM0sNxX4XhrFiGipx+MRZ7sMNwIEIYaIKKaj7H FeN7P+3ypJOEYbtLYfjmoRIsucMbN5MqDAcNXOjrL5fg5ZuZ/kmZwiBzRfXd r8cl+PP6wtOjhcLws/dNXux3yvv6ktle+XphSF46FabHW4oDwphYV5qEwWz9 x3vmY6VYfyFuLbNNGNRV/H7zXSnFW0GjLcd7Kec5aNyv/bYUy5N1nE9NCYNm YtOYdU8pplHefL45IwyDIrLMMvOluPlzsE7hgjDYNtGwXqArw2bHuxTRP2Fw yVU67S9Thk942IhTbQnDGVlCeTWUYfpBLvYSKhFIvvOs68GtMhztojF5llEE bgwUu0fYluHnPbMdu1hF4OLYjZ/XPpVhlcNepeVsIsA1a6ql9bUM/+6oCbnI JwIBeT+/umaW4dgDpq4MQiKwv8Ck5WdZGbZ+S29TLSoCygdq/hxqKcPs+85d vywpAp3Bo9fOTpXhAbthJZaDIpAfxGXavVKGE+vfSdXLiADVSgNDHVU5fk0Q 5fY6JgKEHTpxQZZyrGpdQHVdQQRyKoozKrjLMXe19syekyJAJ8Bd2CBSjklC /343KYvAHS+JM7KS5Tjl2ddKHxCBl2/FryzJlGOHMoX0G+dF4MTua1PsCuX4 Kl97BKeaCPyTGZf1OFWOBcysPNuuiMD5vUoq+mfK8XgR+6sAdRFwjgk4GHix HGdwJhvduSUCTuvKQlJXyrGT8bWbvHdFoM/c6gSPejnWyPuj0qUtAld2TJP1 bpZj0T3uh4IeisAaw8U0pjvl+M+j/fxa+iJQ1i9sx363HGs/7T1kZiwC+moC Kx73ynG1rTd6+0QEBB9qoUta5ZT31Jlbny1E4Jp5XIoaBX/3WDaOshIBg2aP eHdKPndg3Ot0WxGQs1T1ZaPwOUVqe1e8FgEHv+qOrtvleD5hd3SXA6W+pWF/ Rm6UY93M4sxJJxH4JjV7Tf56OW7EL2o2XESg7YWVQ82lcqxcK9m/20MEbHrN 6WLOl+OE9t/zez+LQBRTnGW5CsWfQU9aWX+KnzyP7h06UY5dJxH/+a+U/nh5 +87vo+V4dWnxkGaICKRtxTE37S/HbYxat15/EwFGQwbVAN5yfJaL1cQzTgRC L6vIGrFS6iOCX4f/FIFZOpbw99Tl2Et2X3RpOqX+J+7RBk+W4U3l7sz2bBGw sswM+K+vDD9R9agZzxcBWhH1lvHGMqz6YGGeuVwE9nr0FpqnluEs4xhakWoR mLu0Tz4+qgxLWN7lP1IvAiYeF0cUfMswtUshutUuAvbVDHkXLcpwfrKbd8jo /+t1/qg+oQwfzFOO/kWm9Nf24YPnWMpwUPlcJp4WgSldXu+3K6XY5ved/pFl EXC9Osq7q7oUH9lFlJamEwVTiaI5S6NSHL67A6kwiYLAAapOFcr8svK73tLY LQodvdtZFkdL8aT07GtrHlHYc1cgYHOtBH/TzKsp2CcKRPXgzRWnEsz5yLy/ 8YAojO+N7dwxKMHvzQgLQzKi0Cd46f3L8yVY570LP52iKOxv+0iftasE8yXc NLl2URRO5aYq/vemGHtsTdEOGIuCi96BpqiYIqxmGVCd8EQUti8pnibcL8K0 Y6c9X1qIQnZG3ak69iLsUO/DxWErChf5STOprwrx8xBF4vmPolBzsEGP/WwB 1jzphBK+Ufi3E0z8k3Mx0Ubgte2QKDhUMj+L4szAedOqc3u098LK1aKZwB/h WNE71L1aZy+Y1jJ8uMEXhtOOLOxzerQXDNJCpkY+huB4q+AHK6Z7YbGRpFui H4SD1qZrel/uBSbXSMYsYT9sS+sX8+PLXjh6/sK/+Oe2WE64T+tsCyXu5vH8 0YgfSio8urLRvhfCLZymTPQD0EHdjz6Z3XvBr0UYRIa+IGL04ar9Q3tB+nuF g2lXEOLc7yjPNkfJ7+9r0sgIR2sC/gwW9ASYxm6Ge9i+o859J0hKEgR4o5Aq 75WZjEZbnp4DSUr8RuFw3bEUtPg2KubCfgI8lpP3ZndNQWydzCYa0gQg/FU/ d002Fam59P8xkifAeT1quctv01DeuNOKz3kCpPN5GO79k4Gq/bI1Ay8S4C3L oQNk+UzUqTKdHaJGgOSCtc3qt5loKfDO69irBGhp0D5Vy5qFpFX37+TfJoDh 3h8svnuzUURcA+OEIQEmNxui3vHmoqRbNE+mjQlQpMCW26uRiwp2FOsWTAlw 4k347DH3XNR9N9Jr8ykBfLKWv1T+y0WcjC84OW0IwPd4RsW0Pg8RMuJe8L0k gGvLpSdPt/PQYb2+duFXBOgx93TSPZKPruRc+Cr1lgD2h7q/7/bOR86m/MKn PxIg6WidwhOVAuTHfe3t2U8E2P1hbqvCpABFFjsOqLpR9J/+LcToU4AK+f9E 3vQigFoifeep/gJUX76X5t5nAognoLpDNIWo5/ltAx1fAmQKCVdv7ytEq9WF +0y/EIBtv/zO5SeFiNZm0cX8KwHUy05PlLoXIk4xKbLVfwTojn0nK5RQiI68 8kl4G0aA5Zip0idjhUhlXwXLhwgCuM8nMD+iLkJXW/49dY0iwHPhmTwF4SJk esDgiP93AqwvrTXaXS9Cosz+ZJs4AqTVRg3qGBahtqnSqHvxBEjcYcu68KoI qSQSuUV/EUC1q3JTOLIILXnebKBKJsCTXQb7WNOK0A9zJ5eRFAIMXX3ivFVa hLiOkNZ+ZBBA+fj+pPHhIlTNxpnmkUXpn9755wNzRchh/oyZRQ4BNBUvaHdv FiG5FkuJG3kEuGC79aqdESNyalS/XAEBHFQ6J1q5MAr3awnkLSLAxyNPy9pE MLr1glrjHyaAkdVx+S5JjBhvH2PqKyFAiMmnx/2HMSqSf1RaVEaA7V3vg8cV MLLm8X0TVUGAAmFO+qVTGB1YLZZ3riJASvniIs0ZjAY652eMawjgUvAlmfcC RgHZhLhLdQRo3ZDyO6yG0aUgDT3pBgIgJfe1y5cx2rZ7L8DWROGzu6L29ApG GVoprQvNBIh2/zbrR8GPlYY82lsJUBNmrocp+aJC7Bey2wkQ85cguEjha99A 2/91Uvo5ujzi0EWM3PqeZdt3U9ZvjNs/PYuRSmHEc90eAowcDTyfeRqj5bCm A2f7CKDvds+X/gRG8Q47JIkBAswmS9A9OobRQ90joQxDBAjd1LpUcQAjbtC9 MzVMgMiinD3yYhjVEj7vaRghgJiL9u4kPozeUeOq5DECvLuTQCu/GyN50ux7 vwkC9Hlr5VdSYzRVKqpkM/n//r2xY7xShCK+XV+6+4cAdfVx33nIRei2s0Oi 0gwByN1f3dt+FyF8YUCUaoEAeR2JMe/zipC15J5u0iIBqm3jMy3ji9BBBhXf imUC2IX3Fdh8LUIB1WG7PNYIIPLaNC3veRG6HN9QYL5OgBXRkxlb94vQjtuW jcYmAZ5ZcLTdvViEnlzRIfNQiQGV9YPfd/iLEEHaK2qNWgw+21xh3twpRB2s hdq9u8RgnSzxp3C8EEGjcEMkgxiEf0FB/6UWIt4bfamH2MQgZTyDtV25ENUf YzXbwyEG0VuT669FCpEjp7LEAqcYVDLz/lXdKkDTbSGBWbxiwHRbF2vlFaAS zftvzoiKwYHPMuYfDxagSj+e6qsEMbh6S1XvMjVlnhubuO8RxWAxaf2eSFc+ 6r54PslCUgzSa60dV97lo3lFmeGQw2Ig8lDgcXxlHhLl27m4qiIGpZy3w3cf zEUSt3L9qc+IAaHybUfWYg46+PnFEOs5MVixMdn0zctBCgzkV+KqYiA6nUZN Vs1BV/82J2qoi8FIUNlXLa1s9LormvOnrhgELe2/GaKVid5z6ehmPRIDBvvY tiDeTOSizpdYYiAGhXOOrxdbM5BvlceFbhMxYNy9bFdxKQP9yLa2o3suBoY5 sHDyaDrq/HpxQPe9GCge5k+aIKUguXtT8dxRYjCzKfIrnRyHhqojrm9Fi4EN 7wc3Ko045HnyztJYjBjQeJ690JUVi8YFi5Wzf4gBp39Rp+KH7yi4/0uTVooY MH/037rG9w3RGJxZCcdiEMjgGJSpH4qazYPgwIAY4Df1O7znHNHbgWtjHENi ECZq+a/+v7fooPou9/VhMZBQNjFpTbJDzkct2urGxGDtc+qQTr45Or50zthi RgzMm+4xc2TcxOF2cx7pm2LQfr1whCfqI3764WLXaSEiDGeh6dNaYXjNvWVC WIQIamS+owTLcPzR78HahigRiKplW58/ReDwKCuBPCIRhkzf6Gx2ReJmHH5f 8SARjGkah5j/RmO5zdXBwyeJ8LAsINaGNQ4X73Ka332KCKaCW5YsHnH4Kstu 6hllIghPcxQmMv7AhoLixJ9ABDnNraO01PE48IS6oZQaEWZeaR6NH0vA69Zx 5L13iSD0smhi500SdrGX/bd9jwjST/ZZVU8mYS7nQqYBbSLo5D2++UQzGUv7 tx0MfUiEHI5Maz7eFPwwdecpvzElv4W3Kns0BU/luL/9a0KEA3/uXe/lTcUv i3m8Ox8TIUyld0BPLRX7NB1KDjAnQsZnuWNe8am4ZObuArsNEVi75YwvGabh 6ysk6nlbItxbNe6775uGezbNOZvsiJB1K4S3qjANL7I4y3nZE6GY5UP4N+50 LHEwxYbJmQgR3v+l3MtLx67GjOvU/kQgabkaj4xmYKMakXCmL0T4YWxIM82U ic9Ky53l+EoEDxLPjujhTLyxoONOCKH4N235lco6E1u8TRdE34iwpl34MmQl E18Zqi66+J0IGgqh3ENcWXj/uQH963FEWLa5Mqx2LAuTGJl+6vwkQlO/r7fz 4yx8J+DhKft0IiQ+jI4PaMrCsn9fDH7IJMLfkpiNqfEsvEfb7YNHNhE2/r57 +GgrC1fvzagLzieCqAHTWKJUNv7uVPMsupAITNOBho6nsrHT2ABXAiYCrUZe ovX1bKz8k+lBbhkRGGh/xWdZZmOBPXupSiqIYGBesEnrlI1Xn8vHVFcRoUe/ 5balbzZubbuk1lxDhHWan182IrJxsqLudFcdEd6WK//89isbe/5n7TPYQNEj m+j2OC8bm266yU80EaH353WZa5XZ+IJuRPdsCxGUhOKCr7dkY2Jphv1qGxG+ 5xgMmPdm4x2JWsJ2BxGYy+/v/jmajfs+DZbTdRPh81mv8/Qz2Th3atl0dw8R TPIF498tZ+PAa8y7efqIkLasZsq3kY1fpOxNFR4gwp0U++wGqhyswaVwR2KI CHczFdqj6XKwtO3lf4dIRMjPXt71lSkHM/3WDZMbJcJTpyMBCaw5ePyUzZlT 40RIenm9p39PDi4Ndx87S6bMV/93uWPsOTiCOtLt8hSlPsRndN8p2N4wU+bm NBGmpEoLTlKwVlVti9YsEaKdvBvnKOsVDw7ZPJonQmxFQHYVhZ/La0Xg8SIR Qit1N0so+8/PMRc9XyaC4ejpA4MUfQ03Cfp2q0QwuqbUupc6BydkKtC/XyPC 7wu8/s6U87nwX0n4tE4EbouzbHtWsrHBG73rnzcp8xLYtVBA8QcGbBYDt4lw Ss15xncsGwuf8QgMpxIHxVGbAq++bPzvW6RSLI04oPPqhNTWbNxJnzXwi1Yc 0qNESZtV2Tj9cZ1TJr04JNy71WpZkI196ockCxnFwfNnejV7Sja+7MfyrJ5V HL6e+3ilOSAbS60QuNr3iMNB898/Fz9mY9p7itm97OLwnxNz3lnbbFwo8mhn ilscztf+1/nsNkVfpuVGE6848PRljLify8blV53+ZvCLw+5eA7R4LBvXv/k2 5yAsDpOnpl7Es2ZT6pfxx0BUHN7SGxE31rJwe0L5hBpBHJIZkmtDR7Nw3++x QU4JcZh9pjTdlpuF9SxXe//uEwdt6DIw+5aFRxkZuvukxOFm41iLpmcWnj6+ vzn2kDikTQSWyzzIwptfnhQryYkDPVPZ6/WlTPxe5k3BXgVxyFMP/qfenYlp KzxyaI+Lg7j6g5s0BZmYdTkxpVFJHN5XODxwcszEwjfnIvXPisPIfxLanHSZ +NQea0f3G+IwHhBqGjCXjou+O799dkscTjd6a2rUpuOzp7+8un1HHLrPzCk7 xKTj/1Vc5uFUbl8cDxkza1CZ4h3ITYNIwl5RKKEkM8lVohQlZGgw3VzEUaYM madz5JyDdIt2Khka0KBSRC5lqKQS3fB7f39+nme/a33Xd639PmvvPHo9UMVZ AxSvKLXqOdZgl/bpA3xPDVh30D7M+Dofh8VFmvYc14CmIxVDom48/M9cnNDq ixqQm3tY8WMRB1/8uurSphQNsIYlk5a6HOz1b4P69lQNuDdU6fWqiY0l2ie3 eqZrgPOgYlza20rsluZxLj1PA0pQqMci8Qo8p60/K1itAf+15K0SMy3B25yH pt50aMCJLboBCpwrWHHXubiRLg3wCOFX/yjPwuMmK5f+fKYBzVYva3xLMnEa sUdP/hXjb4qQg05uOh7+0nDSsl8D7mj71BnFp+L4uMsTtRMaENC+KuV7fQx+ UmM2miRHwDLFtiK2aQiKMq4dYikQ4HK4/GqLZjjSbyEG0pYQ8OPuNq0fi86i vB7hV7nLCVD760vkGe9o5C/Q2ly1ioDz3H1rxaUSkKTtroLH6wnY+XBy2+Dc ZXTnVUNOly4B272WBz75mIaCvNZkvtAjmPfSwMPwrnT09pR0cu9mAqpifvvO 5WUidk5nxKetBBg+DTHt1MpBO0ftnaTsCAic/nuZekQBmjvZvFfOnoCMhvYj x4YKEH9Wz3aJAwFzGpZ731sXohVyy8yVXQhQVxbj6yoVoZFNr3XXeBEgE/m1 UP1aMboQ6y5jfYKAGcGOw+eLy5CRzBOJPUEE7K/ocOucK0MTmSYi+4IJGGmW ur3UqRw5clRn3cIIZt+cWn1WtAJRzwZGj0YRUINLW4KdK1Gz2qEHiakEaEb0 Hx9u4SC1d13Lj10mIP+zdGbVoioUlmvsb5tOgFy6pNIxmyq0bsWSxfJXCPiU Mzn4vLMK5SjcP5BRQMCuk/tWybRdQz+71taFFhEgrP4pI3hhNbJLyRZzKSHg eW9d1UOTaiQmdbJaqYIAv432sZu51ShIRH22gEvAjpZNDxaYcVHH/aTd0XyG /fT4zm5ctDp6psi7loCwhSK1xCku6p/v3EnfYOrV2v1duoSLds2czeRgAgQv KlvRc1xUVj82ltREgG7trXIhBR4SDHZEx+8RcB0LJtrQPHRjUmd4fQsB/rvP BOnY8BAx3qtb/4SAqQzJh1JpPHS2csdfmZ0EZKaMbdhXwkM9h+t6Tj8l4JAZ q0GsjodShhLPG3UT4OWW4lbzlIfGiqafK78ioGPeSb6yn4fMvbw1518T8N+n +5qSn3nod9+WjqZeRp/O/IicKB855papF70j4GZjo3OdPB/xXRWCYwYIuJA+ W3NPmY+kVpxtOzhIgNPmoWEjTT46/GpUyWKI6Yfs9iG1DXx0L90hQPMDARXr 00uPb+EjlX1374mPEHB/cprS2sZHz7uy/B6NE/BitvTo2718tDZF+HbVZwKe rnTb2u3CR3/bBMolTxAwGvH1m+EBPhqS7PUOmCTgRGt+hoQPH8FDyxt7vjP1 VBpu236Uj7LjaxfpTjHnnYilYwF8NGWhtn/xNAHpCvt0fgfx0R6RRP6PGWZ+ K/fyQ0P5iHP/p/DL/wjw1dv4yDOcj0Sj/3S+MUuAQW96ZW0kH3lt7eBkzRMg cDH/XNBZPmqcN1wQLkCCz7bvsfnn+EjxduleNyESDklVTxmc56OTEfJlxsIk WMh5K5gw/MTwzC8VURIK8xRXcZnzWjMj1gvESbDVA99kJl5M/b6CAQkS/mTd 2PyWybeuy+rCmCQJt3uaN+1n9LwZ3Xr8hzQJyqPWXfqM3riFBg7zsiS0dUmG /8nUs0FFx1hcgQR3+m710HE+6t1EEApLSAheoj3R6MdHF/asWKS8jMnn//vu uDcfbTwiO0ktJ6Gp5G3tCQ8+ehcj8nrdShKyFjg77XZk/M77jQ2VSZgKe749 zpaP9G9Mlm5TJWF335mVSyz4aKDrY5LNKhIMduyKnDXmo8SxviAnDRLeJ4wv ho18ZCD8wtWLJOFFzF1WrxYfDao8ND1Kk1Ac+aa8W4WPDO3qZc9pM3681E7v E+Gj4SNVP+PXkJBJxEx+nuEhVmxR36W1JJgK7v7hPs5DH28kc8p0SfhhYrDJ tYOHLj2NvcTTI+Gs63HNMcxDJuPhYbc2kfC3jRHRW81DaaqHLTu2kGAuXNAz msRDsNlj7WtjEhZavwwUi+ChcTv7pYOIBAepJ48SfHnINA7+nTIj4fJHwTst pjw0Ma54TmUXCSGhgvbrP3NRjoiMj6YNCd2GQblZL7nIQk3YZsNuEjTn/5QN uMNFeXu/rjS3JyE+T0LwaAoXWd1sq/d3IwHyQhY2aXHR1DOcF+JBgl/TL59b 0lxU+Kku9rwnCQKTw0tch6vRtFrh3jRvEvbeNnP/HVSNSv8K+9JwlARHSSvf sdhryK4goPvBMRJ+WT84XWJxDc3ePNTYGUCCini9h7fYNWT/2S7h3yASpFnq I//FVSGBfdq0ZCQJbpFbwt6HcpCb+lsP1yQS1ktQ1zU3VKJrAY9zTZOZ/qRf 0KsarUAC+PZbLRbTP/ktJecKK1Cpa4HL9GUSbhDZr1VkK9DE5UMOaTkkcMUC laMHy1CM6FfrDjYJMg5Plu/yL0GccWFjs3YShEYaPqar5aP/rq9dqS1Kge37 nV4a7CikkzPVLCZOgfWPvw/4GZ9HnucbA4YlKOi1GnpYcfUsum9l9aBAmoKz bfeenR89jRL7DwUqLqXA8xd/XYW0P1KSyGsRJim4TG7HXBVPbOQuGdRvSsFr o3nxiO/x+JjpM5Xb2yiwa3S+OmKZgPPpK23Z5hQ441ihwexEvHCSVnXcSUFV 97YEO+Nk/CjOrP3xHgoOaOvcTNRPxW7cMLVbnhQk8G/IKBhl4AihkUdpZyho +KZsfx/l4zkzw0U55ygIkDMzaPg7H5+PSdhRGEWBwdY/nv94no/jhHUeXIuj IPDHGinSpwAni57ELRcpiNusYKYXVYgLF83yZvIoUNhYqmrOKsbELpuJ+XwK GiOFTZw6inFZ4lUdkSKm/uRvlgmSJZgjZcqWL6PAoShqlXVMCb4u81exdjUF 17wt7sr6luI2BbkMd8zkn7KfMRIpx7vsvV782USB/uMl/nl65fjJ5RoFv3sU lJfojIp5l+OnSxxSglso+GQrb/u9sRy/XZYdn9xBgZUrb4HIoQrs4TTektZF Qcrq3/+kJFXggUxjkZxnFAy3P5VXqq3Aw8v7o8pfUqA6JkWun6vAEyvJiKZ3 FAickg4xiavEJ9yCb7YMUDBTVny5vqQS/8hpmX48SMHcnbQ92veZ97Cy36me DxRMtHUfWDBXiSM8btX0j1DQue1ShedyNp7Lk5wcHqNg6H306X902VhIrfrY ty8UnEssE957kI3jPBdUzXylYLb7m9ClCDYWK9gzNv+Ngo8jpdLtqWwsqf7d R3Kagv3HzQyUGtj4otf2UvlfjJ/vBof1O9hYrij9X8XfFAyEWDRZDLDxUmLz AXIBDTn1k1FWghwMWbE/xQRpeH4tn2Muy8G+0k+TxoVoEB2TV3dR5uDUaBWi U5iGj7KNH2K1OLhh2u9mjSgN7a17xNs3cvCwf/3uDHEaWhNvZ1GIg2UGhT6E LaJhUQhdk23JwQZOuyM9pGgQlh0M1trD7KePcxRMZWi4ohQs1enEwYmmIxWk HA22R5NLk/dzcF29Hogr0BBXJnT68EEO7vsjqnt8MQ03ldvuuvhxsFjhk6Od S2lgX/rWeugYB29YtlKoVpGGi3Lcl4mBHOya6JOVsYIGKx6YPj7JwTECtWvD lZh6aqe8NE9x8LXgBQ88VJh4/yhl5zH8amyXm6kaDfnuP+3WMSxwIGuSVGf0 x7fO9DLfr+4euiBO0PB6fYtwORPf3mqD6ieShvGxpd8vMvnP3DlT10nTUBqG LS8x+sr0HlrVatHg7lV8sY7R31m57H2GNg2PTkc4TjH1/VL1Dg1fQ0NSeNsW B2dmE0rjSu9fS0NGRkfPC8Yfa4nZYtP1NFQvTOo5tYODg8/u2ELp0vCKxfug Dxyc/z2tS1yPhseb0uuW63Nwu+97n0/6NMRUbpxT0ebgb306c50GNOSOqkRZ qHKweVvL6kwjGuwbhzyEhTk4wGRxU7gJDVmfLjnnTLFxVo2n435g9E+qPnP+ wMbjuTPR1DYadmmZPrZ6wMyLgvkKCXMaIsa/q0fVsjG6kMr9ZMH0T7+64H0B G6ee0O6ttaKhTDpTnApj44YPISczrWngNkzMSDDzO+R2XzzCloYvt5JWqdiy sYGFu77ZXhoMFkgcfqbGxn0rk5O7XGgIvmbkmnWzEoux3pB1bjQIEAreMlcr 8XoRzYZMDxp0X6GBhqhKHDNx5+N+LxqMXIK237OoxKubJ7d+9qVBp/enZWFr BbY3RK+6jtDASWvcP11agSOrE47V+dMgoZp+OSWmAndmEdkRgTSsKly8OMm4 Aoccc/gucZoGyUr3qnel5XjCZI3KsnAaDqp+zlSMKMd+MgstNSJpgGRb9rnd 5diDy8vecp6GeIETB4anyrD5pKTZ0Xim3yvvWJoaluGlwfdYj7NoEFQMW6Se W4JTzK/cep1Nw1decZP1oRIssSxwaCiX8XcmsuehTgmeq1fZPFdAg/q+ktbW xmI8NHO6X6eSuS8LTjeIPy/CtZHr1qbcpGFs873oV4MFWMdG1DmngYbjAT5Z e4sKcLlKX1T5bRq6zbNCd3gV4Byc0H3nLpP/+VdDbl8+jhb4EPm1nYZOl5tG fkVXsV1s7iO7NzQELDPwETDPxl8TJfyW/KbhevXyZ6GSqVgpZutikuG/UuQU JkVTsUV46O2NDA8o9xsfEUrFub7D8vYMa6dr2bv/YuEd5ndvpTIceuhCDHxk 4YL501KyszSs+2A5K3ifhfecGOFKzNFw4W5gWmg4C0f4qrmuYFjZpt3sSzAL l3k6Cq9m2MrOqO/gCRaetWl23sFwmGraSztfFq7QLhC8wPBJq4292o4sLDDk ZC88T4PH+G+jng0s/Mfb5LnFDOddL+PZ6rCw47MH5QTD7T5SCs1aLFzVtHHW jOEVb9bnVKuxsHOebGkUw78SZlqjpVk4Js1idyrDrxXSi6fFWbg68cyvAoZD t5j4+wuzsHD4uE0TwzUPXjc7/E7B605ozHT+n50G9j38mYJdfV2K+hk2/qD0 DH1LYf7XLOsJhpPi041rP6dgnmPrz3mGBx2c0jRHU/D/APMdCKE= "]]}}, AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], Axes->True, AxesOrigin->{0, 0}, AxesStyle->Thickness[Large], BaseStyle->{15, FontFamily -> "Times", Bold}, FrameStyle->Thickness[Large], PlotRange->{{0, 12}, {-0.7689611361986977, 0.999999999999674}}, PlotRangeClipping->True, PlotRangePadding->{ Scaled[0.02], Scaled[0.02]}]], "Output", CellChangeTimes->{{3.41977517613492*^9, 3.419775195761546*^9}, 3.419775232110504*^9, {3.419775372333411*^9, 3.419775378558496*^9}, 3.4513118667567663`*^9, 3.45131733932185*^9, {3.451317392679284*^9, 3.451317405594623*^9}, {3.451317438697255*^9, 3.451317453690647*^9}, 3.482504935207793*^9, 3.482505728417259*^9, 3.4825058264945517`*^9}] }, Open ]], Cell[BoxData[ RowBox[{"Clear", "[", RowBox[{"x", ",", " ", "y"}], "]"}]], "Input", CellChangeTimes->{{3.419768967108124*^9, 3.4197689690897207`*^9}, { 3.482505778707512*^9, 3.482505779041802*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"orbit", " ", "=", " ", RowBox[{"NDSolve", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"x", "''"}], "[", "t", "]"}], " ", "+", " ", RowBox[{ RowBox[{"(", RowBox[{"4", RowBox[{"Pi", "^", "2"}]}], ")"}], " ", RowBox[{ RowBox[{"x", "[", "t", "]"}], "/", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"x", "[", "t", "]"}], "^", "2"}], " ", "+", " ", RowBox[{ RowBox[{"y", "[", "t", "]"}], "^", "2"}]}], ")"}], "^", RowBox[{"(", RowBox[{"3", "/", "2"}], ")"}]}]}]}]}], "\[Equal]", " ", "0"}], ",", " ", RowBox[{ RowBox[{ RowBox[{ RowBox[{"y", "''"}], "[", "t", "]"}], " ", "+", " ", RowBox[{ RowBox[{"(", RowBox[{"4", " ", RowBox[{"Pi", "^", "2"}]}], ")"}], " ", RowBox[{ RowBox[{"y", "[", "t", "]"}], " ", "/", " ", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"x", "[", "t", "]"}], "^", "2"}], " ", "+", " ", RowBox[{ RowBox[{"y", "[", "t", "]"}], "^", "2"}]}], ")"}], "^", RowBox[{"(", RowBox[{"3", "/", "2"}], ")"}]}]}]}]}], " ", "\[Equal]", " ", "0"}], ",", " ", RowBox[{ RowBox[{"x", "[", "0", "]"}], "\[Equal]", "1"}], ",", " ", RowBox[{ RowBox[{"y", "[", "0", "]"}], "\[Equal]", "0"}], ",", " ", RowBox[{ RowBox[{ RowBox[{"x", "'"}], "[", "0", "]"}], " ", "\[Equal]", " ", RowBox[{"-", "Pi"}]}], ",", " ", RowBox[{ RowBox[{ RowBox[{"y", "'"}], "[", "0", "]"}], " ", "\[Equal]", " ", RowBox[{"2", " ", "Pi"}]}]}], "}"}], ",", " ", RowBox[{"{", RowBox[{"x", ",", " ", "y"}], "}"}], ",", " ", RowBox[{"{", RowBox[{"t", ",", " ", "0", ",", " ", "1.6"}], "}"}]}], "]"}]}]], "Input",\ CellChangeTimes->{{3.482505705817089*^9, 3.482505706935061*^9}, { 3.482505817420747*^9, 3.482505818620996*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{"{", RowBox[{ RowBox[{"x", "\[Rule]", TagBox[ RowBox[{"InterpolatingFunction", "[", RowBox[{ RowBox[{"{", RowBox[{"{", RowBox[{"0.`", ",", "1.6`"}], "}"}], "}"}], ",", "\<\"<>\"\>"}], "]"}], False, Editable->False]}], ",", RowBox[{"y", "\[Rule]", TagBox[ RowBox[{"InterpolatingFunction", "[", RowBox[{ RowBox[{"{", RowBox[{"{", RowBox[{"0.`", ",", "1.6`"}], "}"}], "}"}], ",", "\<\"<>\"\>"}], "]"}], False, Editable->False]}]}], "}"}], "}"}]], "Output", CellChangeTimes->{ 3.41929143348479*^9, 3.419349068898696*^9, 3.419349174711491*^9, 3.419349362434376*^9, 3.4197015828173437`*^9, {3.419768952847188*^9, 3.41976897693123*^9}, 3.4197690444480753`*^9, 3.419769090921709*^9, 3.419769222379484*^9, 3.419774748703429*^9, 3.4513118668812637`*^9, 3.451311910990094*^9, 3.451317766234529*^9, 3.482504935341465*^9, { 3.482505707934689*^9, 3.482505728539995*^9}, 3.482505782830326*^9, { 3.482505819521058*^9, 3.482505826577318*^9}}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"ParametricPlot", "[", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"x", "[", "t", "]"}], ",", RowBox[{"y", "[", "t", "]"}]}], "}"}], "/.", "\[InvisibleSpace]", "orbit"}], ",", RowBox[{"{", RowBox[{"t", ",", "0", ",", "1.6"}], "}"}], ",", RowBox[{"AxesLabel", "\[Rule]", RowBox[{"{", RowBox[{"\"\\"", ",", "\"\\""}], "}"}]}]}], "]"}]], "Input", CellChangeTimes->{ 3.419768986383165*^9, 3.419769023455125*^9, {3.419774966762343*^9, 3.419774977983849*^9}, {3.482505672951344*^9, 3.482505684860819*^9}, { 3.4825057940522623`*^9, 3.4825058099341917`*^9}}], Cell[BoxData[ GraphicsBox[{{}, {}, {Hue[0.67, 0.6, 0.6], PointSize[Large], Thickness[Large], LineBox[CompressedData[" 1:eJw113c8le//OHCllF2hRVa0jIZIGa9S3iQSRRKJSEsasstMJQqprGhYkSJF Ea/smb234xzHds5tz/O9P4/f4+cfno/7dp/rPtdrXRJW9oY2K9nY2C6zs7H9 7/f/+2HA//+rq3bl/LmJcSh1O7jIo3Edkhxbpl/3j0OC642VqzVc4OR+hYz2 ynFoGXKapR17BoeTX3o5hI2DTNWuRzbHwiFhyu/qP5lxGKKZ+ZyHz6D/NMPk i8YYaP8LPZWn9Bs42T8/slIYA43BQ/Cd9Rs+Bf+KXSk1Bq68qhpBpVnAuJmW yrZ6DJSUFsrXmf6BqHHT1UTRKCh2BHatc0fQG9V5HXl8FCKY83WZnflgv95w MUJuBHbu+HhWYX0ZSCn5bBvaMgIdXmdr1ruXgWv0b/5tHCMgHZqV09RfBoH7 +rfIdw2DU5rwl/V/yoFfUiRlPmAY3mXbtKjYVIKW3W4LOdoQJDw7tq0zrRrU jBSS3DwG4aztpO7kpnrIcG18JnFtEN7uLEw+cKoeLqubcX0+MwgOuHP+wqN6 kH7Jl24mMQgifiojltR62LZGeYNR3gAMbdX9rPutAUo5Sv57tEAHbwflnYeO NoFcrR/TyqQfdGVvMXxPtYKKf6b+pHo/eEXL/ptyaoWjGv/x3JDuh7WSLmu0 YltBSDAgaCVBgysCezc8W2yFHdy7r9Gf0WBNq3i1Z3IbHFMZ8330gwrulJLn 9JUdMPI1KepcOBXC+ulVe+U6oCOpYZ7vERWed7pJG57vgAW6T/A+LSqY5JbZ bk/ugLqQ4Ts7W/og3V3h/ciZTkj4byKWPkmBTYHrtbJDu+DbY+lW9hYKqPWv uXLvTxcU3jn/cVU2BTQddhcv9nVBq1rUph+eFPBiOMU8O9ANycYDsRVcFNCN /XbI6V83DClr59C39IKM6bkq0Yc9MOL11uaZdhdEZJXESL7pBaUqPwUrzi5w fP7nvH18L6S6irlzlXeC7sbXATEZvaB2/65euU4nyO/ZFvC5qRf89bjpPDod 4OPVlWMuRAHbUcfyWmiDWfWwcaFACri3zKrnLLWC7UNOBc9ICsiafmBzz24F /S1nHcs/U+CgHyXAQakVnhIovlxEgQ0byxcv7GkBaVFbno5FCrya/r1blasJ Ho94iR+37oN1X2KEvIoaIf+k75rQO33wQ17RLtqzEeaOGr7Nc++D+znQeGW6 AcYyUqhpoX1g5RvOJdVTDyI376b25vdBsL1fpVJEPSjF5RttqOqDKt83a6TP 1cPQmI+AaGsfxLS4Pn1dUgeX03Q3FY/1wZLC5Pm6L7XwtHn/urObqXDkkrd7 pU0tvCp7+N95SSoUF6S6xInWwsfbF0QVZakQ+/1s0dTLGlj6sY3tIVAhaUHt uzKlCpjmY0XK1lT4cCGfomBYBQH61rDajgoeXvvEJ/P+QefmDyuTHlBhE3Mw suR9JSSJzha6+VHB2zWWq+liOXQJajBU4qlknAUI/8opAzeFO7uvfaXCOc1h 1UtiZbDn6PQR6wwqeEpsmVroLQEUzT1QUUSFts72g9MaJaCfsD9P8R8VBD16 mn5/KoYoD2tn+wYqXHkxmPrRugiSRqjZ+hQqRIcy48sLC+HYBZ7ZqQEqlPbu dsuTKoR7D1P+3Binwl39XUYS1HxY2yCmgwtUqMwat6+9/Bf2Wv+OXLeBBhrH m/7t9UC4a3vryM5NNDCk62ndVc2F5bW+htwiNNC7IxyyLSMb+iO73VSkaRCq yaH14l4WjMQ4Gj/ZTYO9zpdPo/xv2LuwRe29HA1GXJWP3o7PgPi8lH/KiuT9 apd3EZY/4egCr84vZRrotHFc0tj2AyQ4LZxWqdLgovJyv2XLd1AbLTy2DWgQ F+ZTcfZVGkx7v36zUoMGtzslNgqfToXOrybWP06Qn7ewM+HB+q/wX2BpxAEt GrwbPy19yy8Zut/X7nl4kgZbAtRKxRYS4dSKVxyhp2jQICHx8419PIwLWkg4 6dHAq1ZdsLnvE3wYz7PfoU+Dg/oR6+jnP4D6P0/6hzM0GBB+9i387TuYFQnz GDSgwfwjLoVtHmHQEay2b8mQXI/oGn6bq6+gXpNCdJylQdu63LMLEQFQVHEw /+k5GnRwSbf2X/MGqydiEWxGNJDy5117yu4ObHxQ4nSCdE1ap8ZSlj6a6wZd OEf63pWvX9nMnDHFVxj2kd497y2ncNkPxbv/291CPu8/pQHcdDIIdzD2bNUl LTKQqzpm+RrfVW4VCiA//92ZNXFBrhE4AgmiYeT6Avb7vyJCYjB0wzvVO+T6 i+t0632MPuKFTnZHQfL9onm1/1r2xqJhyLZ639M0OJC4k8pjl4Azq6+a5+mS 71fbI+gx+xkfWoeIlevQ4K+Bvsx3ny949e9L6RhtGiz4ZbK/5/uGX5q93I/+ RwMVg+1Ytv47Fv/pPD9wlAZ+M0qOxcbpuNbw9eKYGg3u8z42DY38gVcuth3I P0KDz2d6Xr6VykTNkLwPVQo0cLTe1VZ87RemdMivWruPBk68N05kf/mNdYnZ p/hkye/neNhzusIfVE5/OeS1nQaelarb/C1zMHp/lTSI0SDlZLPa+ItcZA2Y K9ZsJePX2aHOzeEvio8Jyt9eT+4n++NNFVx5mJeaoOXGQ4OHZZX06fd5KBxu 8cZsDQ1eh6s+6q7Mxx0qB9SiFsl6ke9LhFsV4KGm05Xz01SQuXX1tOxsAXYY v1iWY1LhUfY62QbJIqxI2V+wgUbWg4Ka0XWOJciV73aotZwKBrYTK25ylWLC /icnegqowL5OlCc0uhT/arFN//lDBSuz7d9OF5fhycMdDTMpVOCWeH9JW6AS repTXjq9oIJAavsGBYMaTGlsCc4j+8w6C4d94eGke3axKapTQVpFMbartwb7 TVzDPQ9SobOu4+vqe7U4Wf2F/YM4FRxl7j7MDKrDHb4Harln+uARh+A3rZIG PKHlnpMe1Qc3Nsb8tONtRN7vKSf+BvXB/nSQu3W2ERU37Vub6NsHMisTaIyu RqzRY27kutUH8ePvVvBPNiF34Jvdoof7YEvZhrjTG1sx12m06mclBeIfblR/ YNGKMiuuJVzKoUCJ/nLb1cRWPKDz07wnhQIhWq+jPh9uw5ymw4/tX1Dg+xNz 3k8X2lF1UiCjUI8CxMXaI1tfdqKW448O/6Je2Hbt78OShk50bXzY0ZfeC6vF WAFHtnbhPeVThls/9kJ7/66Vd2O7kCFLKRV/1AvnGFs0N2d0Y8GmvWxRB3uh Rza8jY/egy99blgHRPaA5J/V1avX9mJZsuyj7ic9kGDkON65qxfNUxuTBR16 QPHtUav9N3rx2Vr/qzt0e0A8XGzBargXFaiPQrqmusEurvMvhU5BPi6Pvcnx XWCyyTafo4yKISbeRDalHZiZal+8aFSM3l19sPpnO/gvf0vsXEFDUQabw++n 7fD6pnCr8hEa7uSwqBKUb4f66Jm97p9pWFExsWHSsQ2uhL3rV/bux2NhH2Oy V7TCSCD+SxUZQOPPnzg8lxsheJ9XuZHiANZwvBw9868RzJ/rRXToDWAu/XQC R1QjXO0R7X35aAADYqu3SR5uBK3iCLMXXQN4sLcmc/u9Bpi21DCdDhtEi32+ J2O76yBsvr+oeWYIjy+opQsZV8OsHCXuOvcw1qyo6T45VQUv8okOiugwrglp q7UMrYLaMnz6XHMYXS5YTavX/YM/3zKuZgYP48tu64hs3Upo/Rgz91h6BJVS XYal1cqAWZWZbqsyihtfXr1VzlcAo9JTW1fojmLqmeVQo+R82K1emu1jNooP 00SO1GnlA9+88eCJh6OYoN724INnHpQ9N//2K2cUxS/L1h3vQ/g1c7H6/pEx PFIW9m7i42846WkllLh9HCMuFN82kUmC+o3Bu74fGMcuxcNVk46J8Im189+n Y+P481fKqkf58aDyLFBY3WIci3VOJZhd+AQ6WdzsBuHjqLFnbWwfTzhM28dW eK5i4PvS8X93ea1Q/+/qZwE3Gbgz39rb+dYXZG02Xh19l4EZy/PcKP4Vo522 PYl1YuDRB1bOzIZvuMBvkRfkw8A7B3VG/KPT8JubuzA9grx+RP2AOMdPDM89 n/iqhIHrtKd1PtRloxv9JkV2CxNzbWa+Dn0txHzvXebvtzFxaeZgYZZAEZ64 fvI/bkkmqnfL6Ho6F6HzHznPkj1MtKv8sGX4WDHGuT02aVNhYtw96ccqDSWo s/btb3sz0lflPyVMl2Nx1Sob88tM3MQX75djWoG/CPkxDWsmngvfG1WcW4EZ ryt+TN1kYo29eWuaXyXO2ztUz7syUdTn8fpBoSoUYiZyPXvLRI6BntfdYTUY 2f3y+0wEEyeybn51L69BDZHZD5eimTibNXB9w2INchfO3RGKYyI7Xg/eaVGL fZJa3ju/M7GUkBefkarDUWLVJKWciZGKU5Fi3+oxqHN+BWWaicoNlHzIaUIV 2nnOC3NMdBU2L+8bacKKkzcvly0wcdy356SHSDOm5p4VeMNGDpudmf5Rbs1o 4nFHsoeTQDsBNl77wy3YHyn2VEWYwKdr1eVupbfi6bpbnDrbCPwaceuGD6UV 5y/+ljcUI1AjQSM4eH0b1kK2i/52Avdw27qF2LchjUs7ZnkPgbdMSinSMu1o e8PlqcJhAgMlo08FvO/AoJiY2K4jBLJ0Uzz4qjuwl2r8w0eVwCHVPKknSx24 wSYnLxsItE58GH/RtBPF2Ay2UjUJDJleqggS6EKr1RwXLLQIjBq+UlF0rAs/ v7FMa9AmUGZTBgfTvgv9a/LzUk4ReNWdtmlPZRdm6yj1bTEgUGp19Iy0bzfa +GrdvWpIoMmvTbt5vnejrf2CWspZAi9/LrAZ6O7GgBGnuN3GBOpMlTjkbevB nMN8Ml2mBI59O54r5tKDJ9+9k126SKB/r/GPoZc9uH9VdtBGcwLfqn8NT43v wdftmiHKFgTOewTvlGvowdYEtanDVwhsy/iwZlC+F0fpNX1HrQn0GXRxc9Lq xbbiJItjNgQarL3fw7LoxRYNAaG9tgQ6ctvdXQ7qRV//BL7cGwTmq225+J3o RWLvE1bwTQLzTuqxr+OmYC+lO9HiFoFuQb2+ttsp2FMpd2TAjsBj++fWrjpH wTBp26Gvdwi0anUqJX5Q8ObE5QMGdwm037ViXPQfBVslks1GSfecu9F6gkZB RWrmLYH7BC7a5Yw/FOrDQME0s3ekbe982Rgs14f7Bm2PSzgQyDj7eOadZh9e oWhwbnpA4HGn852xD/rQ7LoD8ZS0SdXrzujAPtS3ftQ/SdqCV/tFSFwfFv0z HTJ1JPCKhNSoR04fyocur8wmvT+UPnO1sQ8NYy4oCjmR8eh8/ovWaB/mNRr7 XSeda3R0reRqKkq5lL9lcyZwZLg+peAgFfk7lyyPk75sqDrhr0tFqrXeJU/S dRNhzaesqWh2/HlwJum9oW0mHO5U1K30ZRskfXB51iHrFRULXVamCroQWEYQ u68lU1GeWRJ7hPSVzVUP+AuoeGNtaJ8p6YdDb4xT26g4Ui5+9wHp2cTL5ToE FbsfbTf0J+2ppVndxUlD1STd5+GkJ81srtySoOHYJm2JT6TbNwz4TijTcKTj z+YE0oWCC/sdztDwormeYxzpOI+6a2O2NEwweKseTdqwNnGnlQcN4ysUHINJ 9zbn3qp+Q8OfKpkSHqQFP1xUUvpKw84HaZq2pBuuV3q/KSL75K+U/pOkLwRZ n2F00JCWeoBzJ+lrjx++Oz5JwzKf/LRl8v2Tsh2vBXH3o3NVG7WGtEz4z29N kv34PWUy/h1p/utxdzce6Udyflu0Jq2ol/lF36AfaxUXBneQrt9rZeF9rR9l /xbc7yP3Z89PyadfPfpxOFkzOoL0Ljk36YY3/fiivc9OlzTH4wnFiZR+vFm1 2D9L7veS8pZf3EX9mBw3xPuedJ+mR9K2jn5U3s1OP0b639Zc7t0T/fj8x9Tf B2T8WOVqCMlK0NHqONsZftL5kboeEUp0XLE9UD+WjMf1Wuxy7Lp0zHy1mPKX jFebdHX9Akc6hnnnCmiTFluZlrc1gI77H+fNlN8j31cq+f6tD3S8GbJDu4CM /zv9KiHLFXRs/HQ6W5n0zytdi+q9dBTpPJ71+X/5Yy7+yWWajvxOrGuP7Amk MvOjO8UH8Mtaop8g80+5lufw5QcDKMxWI6RJuihI2Pae/wD+e7o8FELmq5dj fNmjmAHsUDF6LUHms/+/nl1+ZQO45prLCW4y3wNa7x3W3zaIbLwPmjdcJvDi dfb5soJBvP9ZZkScrCd4RknAo2UQxfKXWvdcItezsNVIfnQQ30Rp6B0wI9D5 wL0zbhuHcPvuJjq/CYEbB08IVl8bQlqHcdBafQI7qzkMzHmG8dl55Y+NemS8 GGp9+yE+jKcoe3OidQmsfGEux6E4jNWLK7ZK65D5HrPvyVvzYdRU4fi7kqy/ i/kr4u5/HcYr6/+qrCLrt39Rutx6/RF8d8aQz0GZrOcar6wzrUdQXnXCrluJ wMP/or4Yu46gtftlSqICGf+hQbc940aQVb1rxRo5AlOkDL55LoyglfU7oQlR An/4HmlRiB/FzR6yxtvIfhPCqThzI3sUr6zSMT1O9qP/NGQkI2tGcXWrRZb3 JgKNX4lE9s+PorPua8VqfvJ9vm8V2KM/huaHNwx/YDHxPveXCavpMdz7K2fw 2RITZ4IfZe/hHsfIpLPddmQ/fPP1c8Cw2DiWJKVk755hopZYqo7JyXFU++Xx 8u4YOU989FToiiTnnEMP9E50MJEq6dz8T4yBIcTDHq6fZH+mvUsf+8tAY6cN sT5kf/b5LBr2o5yBPdLZXbPfmLg4yybp1MDAatnigpYkJgbukttB0BlIrUp5 ffs9EymHyCbKx8SGlx/DJv2ZWD/vnJR1kYlVRFecmzkTbz8wOy03wUQ4r6T0 1JSJEm6/uJ8uMvHjPYPA4PNMTPn59273agInDqiERxgwkYiwVvbd/L++qXXd T5N8ztql9Dg1AgfLt48XyzJR8ge/n/YTAoUfnTi3MMtAxoqw33ybJ3BHxPrq rikGbviWlmctPoHLV09kIcFA1j7H/sxdE+jalDXgMsJAo+V3fkaHJzB2FBur uxkYUV8ufdt0Ao9vCLnBXsxAkzIHdqGoCXSQP7budRADw/7FXj2ybRIDf7E1 7A5kYGfFLqOD0pN4hStb9c8zBk59z7SRkZsk39+Svc2bgcK3v42uU5tE3jts wXMODLx9Xjz6t9kkqhlu4yg3YSBNyizJK3ISc6IsKVmiDGzIe5o/unEKLRIP MTO2MtAsW/HgfrEp7L6veD91IwP/jn3Su7tzCr1TmM2RfAx88bXYmX5oCmvY jn5NXBzHGcWjmckmU8h7tto1Mmscn7Vr8YWGT+EaT7fmDnL+1cliTtI2T6OI 63Vrf6ExtFQ1d3jHO4N7/6uRneQZw7Yd2vIvBGfQXWeXmumqMbxzYY7HXXgG r0f6gfDEKLqHBx3W3z2D8Xui+O+ScZt7Is+o/sQMvls1smjnP4olqokVhm4z yH7k0q8cMg9OPH9yeF//DDI/8CkqNgzjR5nbjnfTZ7FgKFNxrmwY1fTzTA5k zaKUv6jvbxxG9ZINzPG/s8izpUVwb/Iw2hpUnLCsmsWG/56dGfMaRqnNOp4i g7P44lSSB8oP400RzsdT2+bQtvpae+7jIXx+K/yrwuM5bL2XoZWzexDrJxYC x0/Oo0LmO/sO0UE8q9l0vVB/HqkHrd7PCgziicyXe94YzaNT2z7pXcsDOJQf dnGf5TxqXbCcvVI3gFYdFd7gPI9hfuOxZ1wH8Iz5F+GyuHncEiDczFNKR9oe Icnny/N4ZCZvwPtiPx6y0fFtjl/A/JWnFbLP9OOU3MSboOQFbBWXMGVq9mOX m8NKrdQF3NNSqHF+Xz/qvfpJTf69gPuvTSRxru7HEnuxdqPKBbx2VESWi+yD hwp/ZexhLiC/jq6j7zLZ5+d/m7cqL2Kvj4BoangfHulSKDn7dxEZvNQdzuRc Uh+QOJBduIj+JRFb1L360ChPc1a8bBGluP4WFFwjD0r2BZTe2kW0+UK5mHGo Dx9Eag+p9y3iIeNi8SONFCzYMjlms3oJa1lWrBI+ClYd79l+XWsJr0QVlJq6 92CGiIrz6fwltLteLON9pwe7XUL+/SxawqfMLVsTrck5cXrWY2vZEmZebHs3 rtuDiTfdF9url5DH4LeNHTl3Kt3fZAKdS8hp7LZHx70brUWEM5/MLCFmtr0T Xuok+/LMvNieZWzXMpDeQOtE28yMAwpyy6jDfkCQ418n7vePqji+bxldtQQO 9Ed1ovyUiYS50jJuWjZIf6LaiVcvT1rc0VjGrL9bmAZuHRi8x+zEFtNl1NyZ ayY404bio3UuD54so/6ps4RSdxu+zVzW3Om/jPuKv589X0Je/0kENQUso1lC sXfw2zY8xBX1SS5kGY8sNNcMH2pDYeHK3JyoZXz+5YTYEedWfPhmQ59N2jL+ Tv04rzvTjHZryoObWpaRkcZhJNdNnkPOMW2V25fR3ftPHndJMz4mY/lt5zKG tpe05b9pRpHZVdOnKcvYO9evtVWpGbnfvnaPGV7GiKO1DHuHJuz2tF5TtrSM XFk2jkXjDfju3K4UdXEWjmVFnLzY2IA1J8QqHkqycAXj1q7xrAbcUKS19FuK hUP68QLr/RowXCs0evduFt7PcxxWE2lAiay+Ztp+Fnk+rZpW0ybPWfn7Veo0 WPjfpkS+oehaVGkxveVmxULRq+8f/udbi/oXW8HcmoXfy+Z0P1yvxdFDnntU r7LwhK3GJsODtUgXeqfJvM7C98TeT+/LajAm++pr5bssXG86nkOnV+NcyNUU FQ8WNmTQ2bheVmKM+KeTguEsvNBS5T1vVokpt4T/84hgoU2B89+BPZUYmMjz hx7JQr/nXz1yiytwr0WIYFo0C3d2p3npL5fjXp1UF+lYFjYWvj7AbVeG2Rv5 xV9/ZaHdhJVl65Ey/LPKI6v5GwtjPm94Ebe2DF/uVK/elMbCjwqBzEOxpdiz o8M2KJ2FnWGzZzXbS1DvGMP4yi8W9qDiNo6TxajjOa4UlMfC475vN2ZsLMYB 3yW3pHwW3pO6pW9NLUK59E2q+QUsnDzy92W2RxE6nYuSGypioXe5co5RRiGy RQg0C5ez8OAi70XV7QV4sLpKl6OOhYIhJw/WMfIxOCBAa5b0pZfcL67m5uNP 8fkcej0LE4xM6v0v5OOrE1yi2MhC1ysPNua/zMM1h1jJ+q0szNIaXdc1gxhV PsYx283CG+wq5lf9EVeMEs/reljIUWKUMyyCaCydL5LUy8Ikvfne0WO5WGU3 aHmmj4U/JNg7ap7/wR8t19xc+lm4P6aApiH6BxW2NFio0snv5+ZJo++p2Zi0 3vjMIunM4KAXzxqz8J5NntH9QRZO95x5ulXsN+5/IzWhNsLCoODHXc5pv9Dh qeLhQdL3lo6NNBz/hUZi758Hj7Iw5YPUeb9rmbhX5INR6xgLIwxknlan/US9 LkkPTSYZPyZqv0RO/MQ9D+p2tZJ+KnqDadv0A+8OCXVfJ8j9KK9JmJ1PR77Z e3e9J8h4eNt2bNWJ71j/+5B80BQLZ4WrmzWa0rDL4LAazzQLo+K0Sz2upeFF fbYLj0l3HX/QOxmQipKfJzNuz7BQSs9dVE4sFb8Vyc51kR59czmnxOobKpSC tu4sC9ku+0hGJKfgtCcXr+gcC01tuvayqr/gzt4Kb2/S8/X1oZaTybjfzW01 lXREfmGGqFoSch7I3B89z8LYz+tfuVfF47Y+oR3jC+T3NRT2uoqIw1k1ZFdd ZGHgVsEQ0U1x+G7ScewxaaMPq8t/WXzCU0zR4XVLZP6Kccmz+37ES9FCSwak b9BEO08lfkDDBztFgkh/aBZtT+2NwdOMBC/2ZRb+GhkcU94TjVtpwqXKpN0p i0dy70XhobifwjdJN1zqph/NjsAsLyf3CNKL8ptF89jDcSzxylAx6Wu6chyg +xav73C3YZDeNfSpNCv0NXL2keMHi4VHvdleHOx8hZOxh32OkP5DKX70RToE 3/BTpC+SvlM7MLHLMQiHLhUYOJNWzgqhaQUG4vamnfEhpHtWuB5XkffH++/X bU8iXRq697RstR+Wlj4qzSW9rtzUUPiOD/47fP9NDekW3Y9Ra9d7Ii1nLKD7 f8+3M5kYuOKCCixm8jBpttOqt3Lj7mHQk4cTk6TFbR64SlXbYvDf4CsLpP8u Plh+FXcOfSbkF5f/d/8DEcXnuofB/qRRDov0mchXviNxl2F9xaqEJdJBT1fu +k/yNlAuq/2eJX05Wf7l6eoHwFe/PMH43/pFn251DnQHtzLt8/2kb4VavqiO 84KCiq19LaQLT+o86l31GBSPObwtJV2z1SSIeeUpNN855/CT9OIlqhMr/zlY eWW5xJDeXKA1wCX5EjRd4hL8/rf+LXblz44GQ4y64PIN0knmLmE8jBA48Xb1 Q93/re/PRGZgTCj82eUsJUP6Wo7fSl79N6DmfGOS43/Xz3UY+C+/hbShtpFu cv9ym995rP4aDt8LS3gzSCuFc3RO8ryDA+L8ZRdI+y0u4rU/0XDumc2VnaTF cHliRPE9aO3et4Mg42tkVWvGBdoHsHbZLO1B2kHuPPLmfIQPfPstj5He+f7j tr+hn6A+Nr2IjfQwP/WF2Ik4SDgyvMaJjOeDyy5ulcLxkCUSQZMjncSz7a7T RDwkFMYP95L58KioYE/Jx0SAkoo7x0ir3rQqven6GZJXdI6PkPnjK3xCks8w Ce7kqb19TZqjeznn1IovkCXbdamLzLe7a2+6JVp8gzLxHbV6ZL5mzMbciRJO hcYmCKGQ+TwwWn3wypNU8Pb0c3MgHQr+OiOX0iCP5Vf8kqwHtYMC0cO86dDR UqAWO0nW39IWvQSXdPA59BMkSeuFDh2zpKXDLlri9XdkvRFit6+p/vMD7B54 KD4n69Gv8wdc3tzMAMszql9OMMh6I5ZRvqomAwT49p3KGGehxaqf5+8ezITN rz7dkSatFlu3SnMpE5RdJk4vkvXQcc2hmsYXv8GVI9QkYJiMT2lV/Tdpf0Dy 0r0IRbIeizjXJ1OFckA6JjDag8ZCvkyr4n2uObDzc8GuEioLrYUnhfI1cqHS 40r1abKe9/MGapTWI6SmxVofJeu/irjldIprHsRF3En8QvYLdsV+lbwvebC2 I5mruoWFK2eMJeq78uD7TV9irJmFW1bI/CE08iE+Z8hwZxO5f5sb8sW5C4Cz +JWRK9mfrDleRR2MLITe0uOmn8l+NpH9+6tYVgnIRzgJy/xm4eqEF7cUGSVg NXvmDTWThVzbDkxr7yiFy72R0pEZZH5w3jG5HlIKAud1vFhkvxWau1324kYZ rHO/JBNH9utLe6DHdmsFuEaHq1p/Ivu5CPFP3rkKkv8JdKX6k/Us/S3fZEoV 6Ka/KOF5xsKSsv4HGX1VsNrLtMDmCQt37/v06YB+NRxtf8vk8yXzaUP8JLtA DZhrPdmh/pCMP/bpgqDBGuiwzOzht2dhmPTcZsfXdSC9xZjd8wwLk3W2frP4 WgcRrj1G70+T8Z3GlatVUgdRzxo35+qS9x+IVxOYq4NO7fRxpja5vqQyv7dm 9eBVI9595BiZz8GG589ub4Azes/TDch5qmpWPfDpt0awSfL/FMLPwq0mtUuq pY1QJOPZcZmXhWsu/Xw/3tMICg2nfGS5WXjgpJeD/oYm6DrBs/UPBwulJ+4J zTk0wZHkrOt/yHmvVltXkzjcDPZ//z48Rs6DfPeEfW/lt0Dv6T91ZoXLWNh5 Osi2rQWin73Tp+Ut4+E5kcjLRAtYnpY0uInLGI7Nn3QlW6FfPKPXPoucf3Mr T/B4t4LgJQuli6nLeFKXaNt5rA3Wh8iFZUUuo4ih09DfnHZga/IIiLyzjELr Kp86NbaDR9BVuwa7ZVz5k7NbZrQdJn/9rea6ST5vMyQFinSAidCVzXdslnGy 75q7olsHnOa3yRAh521BEWVBQeVOWHVTmXeZnMcfqlisX/rWBYcz+C73bFjG WOMGGeuyLtgs9K3kMf8yKkTOQCmlC47YHlXZxbOMZ+zPnnwi1A0mplGa1quX MefWnYAe127I8mVRfpHnhdT6yLBHkj0wXnFItKF9Cek/tGuth3vgvTv1Ye2H JeR322LO5kyBGMVt6V1SS2jsOB3g4EOBH9175XkkljCuPEmQ/oICZol9vIe2 LeHOZthREkcBqw9v532FltBE1l/2fj0FtpzgfryCYwkzbAzeusj3QcnOT6oP +xcxPVPHWKmvD24+R+lHcYuoruq6RUKLBmVSltzvhBfx87nrgzxnaXCI3j+d t3ERF7Q7zaYv0eD1xL7ivvWLuNSSuyPfkQZv/yjwi65dxD0+EuvV4mnQzd12 wm5yAddL8L7KXdUPXz0ceB3J82DfC6cUCvaDrPaiz17XBTQr2DCmLj8AllZO 0oqV8xhllSFUpDwA9eXsE4ziedzb+y1H+/gAuJ68sfQ5bx7PrI14om0yAFu2 zJUIZM7j19l/tbu9B+DXa2/54g/k+bYsI/Vu4wAs5+0WjHecx5UvZMY4XQdh qnSp4YzoPKaLpZRMZA2B8FEZ//9s5tAkiSUbUTgEcXNNfXYWcxgnk52pVjUE c3vZnoVcmMPM71WK7r1DMH9o/ke93hyGUBujm9YMw2uehkBFpTm8FSvnwDo7 DNmFCkJOHHPoVcJlLzA0DOp2rWsZsbNYU2TVWsczCrde5TWktM5g+jrOXfc3 jsJE25mssLoZLCqP8OQXHwX5HxcsPStmcGDTwROqCqNwcHMBoZkzgxYdv4ps LozCrwhL4aT3M+Sc+HDvdOwoOLjt0mq6OoOcps7is8pjsLTZbPsfxjRm/13D J6gxBhVd1Wnqg9M43X4qQebUGKw2FZjL6Z1GtdToGj3zMZifm0z9XjeNxZeS Esy9xkD+9utchx/TmFre+jmxdAw2abIELzpN41RdTnjj2XHQ2PGp6uv8FA6s shSvvjgO1olXp05PTGGJ1danhVfGYZiOh0eGp1Bdumn84/1xkO022SraOYXv XQ7Wy70aB55aWUULnELPW1ouLrXjML+56YOxzxTe1eSXvSHNgGi3Hd2bOaew v65UU3I3A0ourDtjtmIKDc9pSLbIMqDiRU9z1NwkfhZw3KZ2kAHetdYyQkOT mGD7mRjWYEBn4IUOSvkkBs315bdbMEDS7uRh4vkksjgPC869ZcB1RS+vbu5J 3DT5oulbJAN8hxULN7FPIu3Mlz9XYhgwaRUTqjs/gW8GO4fz4xnAr/mxM3lg AstnxCIv/WTAYjfBeaxoAg95elpw1jEgVmVNeNHDCaQv+R7cxsmEtbYe3Eoj BNof3HjUgYcJSxeW37AoBL7XXru7lJ8J01rGn4taCXxiX/js6kYmlOz+Z6lV QmBzuaTmw+1MuNf9SkTiI4FL9BXB69SYsPp3f5DceQKPnZV6mGPHhGT1q1qf c5mYEqM09O4OE4z0hq7s+8nE4Tx1Drf7TOB6ckHyRzITv1+zPibjwoRzB9x9 08KY2PN99tEVXyb0Kz1u87lH/n9iAX1fBBNeaMn89JNmIrhVbWmPIq8vD1Ca hZl40OljnVcME6L9e1OlNzDRj0uvqjCWCZlxsnKZywz8IZkbK/6NCTaPidi0 ZgZ+L5l4JFfAhAGnIq9VzxgoWH2eEl3EhIIG1yQxDwZuPbjhI08pExxvWN07 9ICB8k7hMp2VTPBTft9tZkleF6nfYtjEhIW5IXmPwwy83VnAfDrABOlAeeXj deN4Pmrx0UYuAgJ4T9/Pfj6GEdmKR0e4CfAcOe3r7jyGP9id/XJ5CfAXmPtx yGYM51Skw0zWE5DIX/YgSn0MI51X+1ttJmDu9EEXMeYoSrQX2FdIE7DxbEUy t9EoOhwNNby2kwBvw6Gy28dG8YPxp+AVuwn4peDOVSk3irLii1t2yxIQ5zQ8 4cAxiuYcAZy6Bwig7eWy98wcwdRMHp5uNQKKPntoPto8gpxS+feOAgH8jnbJ PqtG8Bcrmiv6KAGHH/kp+zCGcXTgR77ecQK2GqSX3SkdRu5Efg4PbQJYxoV1 q52HMbK9OiHvJAFCWmXuHVeGce0lDWu2UwRYm+4wSNEfxnasl7inR4BuUrKr 2s5hNFuWs9hhSIBSc27npqYh/PFgs9/JswRoHj1Dx7wh/NMflXrtHAEvnrJE rVKGsLXj56pIYwIud5Rvfe07hHy7rIyrTQkYYcmf/XlgCP3LItkcrAj4ITqn 3R04iNXXbzVfu0KuZ8f+8zedBvFlWGiRiTUBYufWhjMuDyJYbWjZfZUAmf2S 2f0Kg5j7c9om6DoBk5frQ7xaB/DH99on5jcIiDmacb45fwC9Y4feS98kQDYt //yOLwNYcuZhYvwtAtYU3+FNfTSAcX9qw2/aE/DSqvbWve0DqHDfeuW6OwT4 1gftCuEZwMuam499I/1hUGpX8hQdW+pW7+u6S8DiottMaQkdw/4rbra7R0BN z6eyf6l0fKL688QsaRW9G9SKcDoW7lkyW7pPgJR4w2z6TTq+ishiOTkQ0L5u 9dS7c3RUuWtvPEp6xc9xdS81OtpdN+ErfUCA6Of/8hT46cguUnVVzpEAr+c3 FlfO9uN+vVzLQNJnzTL9K3r6UTb4spyaEwEGRo7x2t/7kefzvqkA0rfdK5SW IvrxLGTqNZMWi+cXT/bpR7f1zgdEnAnoUMu/YnirH11MiOiLpCn519gnzvWj fdn7F69Jcyi9ZAtU60dL37nFMtJ8N0rMxHf043Xe27RZ0rnLiVtS+Mj7tW4e l3Qh48OhVllhhobU2xc2/Ee6V52a/b2bhg8Eo/SsSW9s84+VKaVh5aYQhjvp mx0Ok+9SaQgfX0+/JF3BZZLCGU7DVxKLpu9Ir7zFqLntRcNkjY1b4kirmLFZ /rtOw/9G9somkH72/oyFtCENfx0OevmJtKJr6j/HIzSMeeCiHkHaM2sqJU+S tODug89JzzYuruDgpuHm1OabjqRbZxIrjk9QsY/td89F0uVCVB63diqyty0E qpCWYY8pSS6g4tXt5beFSMf41i41JlMxrEH70SD5/n5XXNPmXlHx0fjbzEzS 7l4x1I3uVORzqxPyJF0/rBcuZ01Fjkd8oRqk+cfDa9V0qZg0ZybHIvfj6p6Y l1oHqfiAWtbxk7TyJ89GHREqtkiZvbtKOrDlWpzWKiqOPRe6sZ50cNOzFeoj fcir2ihgRO7/oz+6tpv+9GGn0BvGJBkv6d8qgkLj+jBVpfP5S9KlhZcleV72 YX267egPMr7i/9x7PGTZh5V5RslA2tWq1tTgVB9GeYttKiLjs7Gb8/33g334 lteejmT8ahqu97Ze04fXjTyOK5IWmJ2Q/Mmg4CZDT9U4Mv67sppV2Noo2K2t NulA5kfXJ96ux18oyC2wdWW9HQF6XCHi+gYUvLzh+D8R0uHX0nLuH6GgsHf+ Bksy/xKjjakh2ykoIbJroYXMV7f1js1/p3rRkTAuemxLAFfxrbft4b14YctW +kcy3/VtxvIbvHvR2Oe5RZYNAZWCSs9Lb/ZiSdxZjRayXkyPayzGqPUi50F3 /WoLAszmd37m6+1BQfX6+NxLBHRauLF3lvVg5tDWfYnmBGRIpfHHf+9BMYGy ousXCQh6Rtfe5duDRqLoEk/WqxsvT70Y3dGDigUtHVeNyP0+qVESzN+DAsZr dCXI+taecT/EktGNnimXVHwNCNBqSb+WG9KNbX4bmlboEpDF2re00NSFIyLr NoTokPndtzOFmdCFvI/FFUTIehuq+02i07kLP/vFrBP9j4BlBb77r7d2oUOZ QEozWc8bS30eBJh3YlXy3MI2sv77/GuVi+htx8faDXZn9xFQvT7nRvf3dhQY 0U73lifj13/kqLBvO9op7Iyr2kPAPK5tdtzRjnf/FoUJbyfg7YcIj9wbbbiV FXHm8Qay/u/nTn3DbMHvBsvRRuvI/uMQInMyvwV1HZztxfjI+t95JI8IaUEf lySvGE4CpJ9KX5I52IJmP4qbzrARsMdslamCYzNaKvQH3x9hApt3iV/8bCMO +DZ5tg4ygRoWOV1V2ohsFwIilelMKG24s3k8rBGJp2vUKb1MKHQOjtx4uBFV bS9GUMh+XMr+t4TdpQGPvB36FYJMuPhoxbnLM3V4L+1R8ZPnTFD3/GEw1FGN J6devsl+wgQvvSZdzvvVeKZhn0e/DxOcK76c3sxJ+oadq4Q7E2oMZGY5FKuw g+fsYZlbTJgLPT65J6ASdRyti/x0mFCZmHf/26EydLvhZbLrP3I+sRLI76ks xd6vot5/jzGhR1I8cJVVKT44fdGpQZkJd2fpmlIBJahR2Lr0bAcTPK//J1DW XYR1X1vYpdiYIDvadqDGNx+DvwexyywwoFxCyF19Sz568sas2zXNgAChLTIf U/Iw9KjX3lUjDFifruan0/QX0/iVnx5vJue7i1r5J0/nomD9laqmZAYcXhM8 fulFJv7xUv3Er0fOk1fPZzasjUXH9gepB7QY0PhWyXj+/kdc9zRdUPcYA15+ 7Foh1P0eeyUkCywVGbCihmeX6Y1IDExW7ty0jQH5N9d+5/ANRKOEe6fONI5D i17gcK7YY8jicM7TWByDmJ8bB6Ref4UnYLnIGh2Dfem3VbMFUyFnIZue0D0G O3WPM1q6UmHHpeEXmflj8OtS0XfGve8gJfDPpOEJaTZOT8+In2DhJRo3xTsG W21uX3/Vnw0/i5ZjbThHge/X/HmqUiFkKIxoD02PwJ6k86YrPxXCDtVr3mep I1CcI9DAw18EusKaNvW5I2DYul2a1l8E721EfvndGwHlayM5oa9L4C/lxYGk hmF4e0Hqt9NYOXxc3R1l7jMEasfqOKWKauBT6r49+nZD4Gs9ZXdnrgYKwhpG Jc8PgYU789tnuVoIvMbTcGfPEHT0pt7vfV0LecpyJ2OrB8FTNcbMzKYOXhbR 6i8KDkLzulUG+9gaYJ+p8PNEPzo4m+vyfZVsht5XYr2Ux3SYPyA3skOqGZRN mXu3kfZ3n8uPkW6GQO2lzGAfOly2M7gYvKsZPlX9uOvqSYejVYNKDvLNIBz3 6rmOKx1WpwiGKx9pBsbDCBOaHR3iE9ev+mPQDEpP9paKkt4wMbKkcLYZSlYG 7TO5RYdjnyMZyeea4Q1f+nD5DTqsMLrzN/J8M1xK8uBOtaXDuYBeTjfzZgh7 LsV0tqRDje2R48rXm6GGdW007TIdblKYZd9uNINttxNlyIIOnD/unNx5qxlM YyYzzC7Roc0o78BG+2boNr3GefQiHW5YhX+dcGiG7VbLFc6mdAi3dly44dgM aHjpSdoFOpz5JniM4tQMht/cBiRN6KC4MSSjxrUZ5ueVX1w8T/qrfb+WO7m+ cZQNNaaDlR83Pz5shsvu6worjejwrMN6n5JHM9CD95xbTfrmmKtOimcz/B9W yOp0 "]]}}, Axes->True, AxesLabel->{ FormBox["\"x (AU)\"", TraditionalForm], FormBox["\"y (AU)\"", TraditionalForm]}, AxesOrigin->{0, 0}, AxesStyle->Thickness[Large], BaseStyle->{15, FontFamily -> "Times", Bold}, FrameStyle->Thickness[Large], PlotRange->{{-1.154700371391125, 1.1547004438459836`}, {-1.999999751646637, 0.6666661977091156}}, PlotRangeClipping->True, PlotRangePadding->{ Scaled[0.02], Scaled[0.02]}]], "Output", CellChangeTimes->{ 3.419774981147234*^9, 3.4513118671191463`*^9, 3.451311914767214*^9, 3.451317913630878*^9, 3.482504935454123*^9, {3.4825056757834787`*^9, 3.482505685630451*^9}, 3.482505729011374*^9, {3.4825057862835693`*^9, 3.4825058266912518`*^9}}, ImageCache->GraphicsData["CompressedBitmap", "\<\ eJzlfXl8lsW1/1PyBtx6u957e1t766/r9V4btbW1dY9a12pUcH8VUYkiqBFR iRsa1wiicalR1LhFxbgFl4AQl1A0igGN4AsaNaJRDBj0RX3F2M4935nznWd7 A+HaT/3jZz8Bmplz5syZM2fOOXPmPPuNmnDi6JNHTRhz3KjN9hw/qurEMced vtkep46XX5V8Iwi+caL8TNwsyMi/TRDE/sB/Y/BHENyIv4bg1x2D/cUU+9cw k+/tMX0FE/mvYHp7ekxvvhAMTQLV2L9K5I+8aahwdGTsn5uYoLLJAE93S7Vx NFaaTvlFf0+ryeL/l1fY32fr2ky/MZkk7osUd39Pm6nQOZYQd1BlugSoo65c cZeb9r4uU2X/nTU5Ac3VO/xVTV0p3Bfbv75naSkDDQ3tplcm3pVrszgau4TQ fLdpbqg3d8xaZJ6/c5wbZ+fLzaNzusy9U8/XcY8xF9TNM1dOaQuGmEsvearU ErihuWrqXHPtNfPMrbfMN/fe87KZ0fyqebK1yyxYIIN0rTSffLImeMbRUq3z LOQaDddyqP3z+6a+I++X4bNX77LtZ9yywDz22BJzc91j5szqWeaEygfNiIPu MrvsdIP59Y9/5HB861Cz/Y43mh1/c6Ti3Mpsvd2NJWbnHW+0JG6IfwUbmD/t drMZMfwuc/K4ZlNzYau5reFF0/L4UtPZ+b75+OPCrASJ3S0mW1FhstmsLDP+ 3NAcfvgRZtffjzBnXvuCnTUw7b3nrWb7rQ6yQ2+6+YXSF6MNNbvucr357aaB I+mnY81Z5z5hLj3t9CEqN8fXPmfub3rFPC6zkx/ysum+TnN340LLy+uuedZc fulT5txzZtmRskfca/b80y0yEzfCgQfcac44/TFTf0O7ZRJ4/be//f0RN49z 7V+lZuWKT82cOa+bybXPmFEjm4Sum+S3wPBNwXCN2fZ7jsZjhSMg5uWX3zfv v583/f0fUcxFfOsNFqfQWR9wAg2d4XJR4jaxY25gPv+837zzzkdmQUeP5TAo rLlgjqk8/gGz1x63uOFLLevGVz1qbrl5vnm+fZlZvXpN8JCjfqL9K2Opnz37 dXOFUH/E4fc45m6ESZhjjr7PXHLxk+b2+jnmKYFeufJTgek3TZWO6PLa9ozS 015bnpyHikqFac+bEj+B71mAoebvf/+7ea/nY9PW9pZpuPVFc+GkOebQgxsz SvguO91ojhFeYoXan3vbfPbZF0GTI3yCEi4LYV4Rwbqx/nlzVHY6Iffa41Zz xoTHZY1fss3CKeGo00adsonLa9usIil0q+KQn4q6joAz6W2tcZRX1Nt+va21 7v+X1ZpeE5nJf3D5hSttz7xp/nL9c+akMQ+b3XedFtitISh3K59mqk59xNxz 90vmzTc/vNfN4DSdwaefrjFPPfUGdrrZ/8+3l0QWDTMAUC7Xa7788m9OV0I1 FjpJtaqvEpNtzFFG/ExFUZoa5X8nVJuuT01rTxDqrx/rFCBNL7/0npl20wtm zAkPmfKdb/JTOOyQu82UyW3mxRffBSV3uSmcolP44osvzV/nvmWXTyZOoMMP vccuHcRTgDbWRQfPK8sCKiZTUd1k+owpVTJMX4epss1lTtc2dgSlntj/p0Pm 859b5XfZpRGuZUzFfrebqVfONS8tfA+icbujc5zybdEry+0s/rzPbcIjBwEZ Gze22UpK91t93/anT7/p6+01fXJEbZD6XX/k2Pp5RBKXLllhd9mRh9/rKCqx nMOvli1bFTQ4csYovr6+z6wSOjo7PWD3Y49psr8T1RD8yo/xXwrx2msrrKQf MqLRQ4wVaZvZstSK+M1ugBO0OyQfGlgEUOdbYrXZDX9phyAG/+0H+G+dhCyT XWPoQ9lDBNp37wZz3bXP2knc5MY4XseA1MyY8SoI9zwVyTHnyDEy76/dot/+ toUf5tcKJBvZPPZoDmLm53F29UyrFNHjBjfGsdpdFJZpvGshVtfPAyt9043P mw+Wrw629ANspRC5Vz8wk694BmeRh8Ch1ioHrVAUXO8GOEa7Y/di58qUfffR xz1gZj/xOoQ72Br9MtEBVq36zC6ryJ6HOOKwe8yDDyyyENe6AY7W7h9++Knd ClF6ThOV8MLz79gev/UD/CbKVznhRRt7iIOHN5pHZuTsDOrcAFntjv0AyYgO cM7Zs6xEosfv/ADbKASWGhpLDisPAWHF4YQBrnIDHBGhB2sgouC7Y8lef32l 7bGtX4M/KAQ2BPh91JHTPYRsDKvs0ONKN8Bh2h1nAQ4xsTtiLILyQ48/+gG2 iwwwc+bSGIuwG7D46DHZDXCo6p3Xlq4wlaMfREf7c7ws8Pz57+zg8e6geGX2 pvnhxeaA/e/weLEh3MlnglqH92D71zCrwGGXQeqBF7bPrFmvYULBjh75TpHe OKdFT9reOKmmT3/Z6vfLHeIRSjAYNfzAO203IMcO/PTTL3b2OHfRju+++7Fd i+jMhG2XOXQHaa8eOWhxorAXdLysXrlHt6t2fO7Zt3EK+3GvEWtUyL7EoTtA JwL5weEEcw89oSPANUx7V49zN8VZKPSL2nnOWhSWSWJdyqnvjGY5nlyvt97q MydWPuRJvOSiJ6Eld/fo/qQdIXXYz+x4waTZsC2d7xDsp70gUiCRvMbKtLcv 28Oj20M7QpKwc8Vosh2hXORAu9Ch+7P2grl26imP+EGhYMTo3tOj2yuyHqee PCPsKFaVqLxJDt2+9q9Sq1xwyqOHiBrYHuztt+mekTnAWiWbsYOWLOk93+Ha W3utWfMlHAY/4nliBa9aVdjHo9tbBxW1b81TdNp1l2lAHZzncO2lXSAnkCB0 waii3R0LLKJ9IiNC6jki7E6Z4zkO156KC4YdBAM9YA7IAeZWx/Jrf+31zNNv 2n2AXjA3xaYNznaIuOCQNmhoDgdjXY6F/T2uCsX19turYAjaTvvs1YAzSH2N YHftAl05/rRHPQ9k+zmptogO0BFlp5nzhY0cEWaRyMlZDtduiktMBqv3uYji 5AQHelwHaS8IIdUDLHGhIDjTIdpVu4gmsvRy/+JcO8gjGq69YEphGPTCLN97 Lx+c4RCVa5eHHlrsdxnoh10w3CMaob0EvTWtSbeoC7WpVauU2uONk8dJi409 wiM6WHvJBvDMFK/JzJvXHZzuEO2kXbC7KJzggmj54BCP6BDtBa0La469Hn5o cTDeIdpRu8DO5JJAMmWLOu1uEbmDJGP9TdItJ5azs1W5l1r9C2OcKktMDgdp pftQxQGLBpahzr3K4dheccBw4w6BPfVG14fB4R7HYdoL3iAX4uqr/mr55yxm PcFkFT5YjdPLdsHfWM4jPKLDtRfMKG5/eAk4Kk52iP4YWU7sL3SB4SLmSXCk 50xWe3WIZUcVBw0BQ8XZxnpoxxHhsISvmPWIjtJeixYt99saCwJ7YaxDtK12 WbHikxSiozyio7UXDFrqQFiMmNpJDtHvtYuoMb+h4dgC0dEe0UhdMFgJ++17 m+11+WVPK47fKQ4YkIBFK7SfHBUO0uI4RnEsXvyBFWH0El2jca9tIvJ5+vjH 3FrJjheTzkFaHKMUB/xr6BT0uvOOBSdGcWTs6vF8kbUe5cGP1Q5PPfmGlzux /pwh76xDaYUK4j6TCR/rwY+LiC33jxwnlQ78N9qK09npvJvgTh/nwY/XDtzx kBGxlkY78K21FWJIJSbG+/EefLR2QJSAW0LkyGFVi9lxd4/dHXdli472Yn5c hMHcmTgFsNCuzRn4gkN4Bovbdrmi9plKj+N4xQHVfrQKCxQtBNPxVrxJKoAv vOaDOQSRCxFxLjjrD6xwilZsP8Xxa8WBQ5kGF2QTobcTPD9OjMgk962cAKOi OMLFFGcUB96JHnyMdoBHzeVasKDHSWmwBSVFjEO2isc2xoOfpB2gsilrvb2f uI0S/I+2ImxEVSA2wEkJcKe0Ke4IaICTbtd6ZxEuwXGj7ufxP9bjGKsdsHVh c6GDGJEJ8DrRiWg5VJwOYWAIPi4iMYidoJOYCE75BJtrKwJCaEEP8XLc/IbG Y839BZPvy5t8oX+Yx36ywt9//yv+EBA97HSketoZq+LBOfS4u/Eldy4g8tJl arM2iqIRumFWtCprW1KB6cfur/HRmaC8yrR05RU5SWH8ZOJZLXYgRB+F70fG SaHNDmdIBO9w/XVPS40PoTR2FVzMZ6NI+Honc+6+jLJUmMa2LtPb1WrD3vUd fWkisFjYuW5/digRvyK3mhy3oGNFtR+hvw4jfFnTUTBDdBEY525szZlVvV2m oyNn+vq1ucR01guNZXWIEQZhKO1UxYn4A5XYK53vu6GCX2qrnLXenhfrskJR piPdw2KR7nwkFCm/DjZUdL2dTaZcQ5Z9GtgrjYoJfDUrpeIQiUZy3A9+oa2w gqGr0GPK5LYDSE0kqF1q/9zAVJRnTVNuQIpKFWN/X5dpbWk2TQ11pqqibAgF qKLBKKwL78WIhOqka3txTWuCSE4BroP4YVn9dVEChPaukJN+dBFxpT0IWUTJ gbtDPSeHhLN/fFwMtgKWEj/y76PWNjqiaj02ZFlWkTWVVTWmoanV9GizpWa8 wt83vdMfNqL13QYNfqatUE2YLnrcWP981mMvGNEHpq+jLjr4UG1uqy43VU0d pru723R1dZlcZ6fJ9eQzqcGh/xE0BPray59ODE7NC8EQE8sP3t9lasrDuGds 8BKT9zRF+C6bpC+66rbhdB0Hrg63ghwQzpAOfsqN8saH1hKBOSF8H6m/7uvu MPXVWeswtIejR0PK4arbsH1idEbe77i9w46M6xLZBgdHR3dxGLReNXWuD+P1 5/NGNXPwrRQ+yDCP7ltvma/4GO+FMW2XW85kOSwmePAztANCh+gAhghjnJ8T bKatCDgi5KC2yxke/EylDS46GsUACRKwPKixwWThk7AZ89FHBW+VtM7pcr5a 8BNthTvNVZIT7UwPfpZ2QEQPjQj1iHFyUBS8xFRPdGaGuEYOIgYLQWTA5Ia/ tCvsf2orjFG0wMIWc9UCZaKUL1nS65kmFs+BDvzHkRXB6qLHvfe8PNGDn6W0 ITyDxotqWoME7PR7X3bW0ZHTgScJmzHLxdGg0pDj22nOYFNthcEOwwit7e3L qv3Ez9ahEUvSQzGIwZb47XfqKY+47hFAd3FA12X+C++48yP4kbYixEcXQBYr BD9HOyA2TxddmL9/FLzEXlZaV+bsWQ4iBgulxHieyInC/lBb4XnBlsF+7X6r LwQ/NyEncBTFaN0vCl5ipk6ZS0PMQcRgET6hozmzZanC/oe2wtj1Q3evCsHP 0w64X4gM/ecouIuNolXEwUHEYBNDK+wPtBWBcYqB2KQh+PlFhhaG7xsFD9ca DD/fy1h01oeMcIFMcYcU9t+1FZELRlxeXfxBCH6eIqcMi6YPYrAl9rbIytjJ M4JJCcCMdTEoY2LBuJBZ8G+RbUUxENme5Kd8gSK/edoLdIiDGGyJDXfr0eK6 RwCd0YqtjHWUQ3nvOCxN9cceWxKBvZCLeNnTtlWscg0WBv+qaHEpyDiRaPok rDtq6DfK/torCl5iJp0/27bKtByEhWWaB2NHD9z/ikYgg+8rWoQQ4N7gR/6d hsUFIGBHHnVfHLbEu7KTzpvtukcA3RLQ1n1p4XsuWqm30tqqvp+0huAXJZGf PzuIwZZYJxlNuNO7KAGYgR+mM5oGyd8jDov7GvU3IrAXs7V6FjWxxq2D76YY NQ0a7CIvkGTU3La3vNjEYEu8Qjvv3CfcUJkko3i0yWHxpzis8J1GXwSWXGJ0 +GqRKAX8jqLFVQyagFqGuNhP9hLtgPg+3Q0xoXaPgpfYixBivsTDXqqtuEK1 3sEzb2rIN/i2ooVC4LrLlk/Dkhs40WKwJTZ4porIdY8AZmwWA7eA2Ni7xWFx JY1WMSUisJdp65gTH+KZoHFlZx7ppTIJFqalYXE1QFGMwZb4bXvYIXe77hFA d/6SYNnUu8Zhr7/uOYbBIrCXaytjn8/OeztIAFLTIw6eBrz9tg7azAT8F6Vn 2bJVfsVl1knYUMnAK5d1LI+Cl9grNPV+HEQmyiXca6JVWBIkAE/TiJMYmEUA cWeLVtnxBPym0oNAMjYc/BpRemlYBijEbozDltgLD54stX6mtYoZdgLPRFHp u8RhhXe25a47F0Zgr9BWJCrZk3bm0iAByJMQdzBpQPpTl17yFAE3KbI0cgSn YRHFVR85DlvijZYLJs123SOATrxp5skO2jkOK2tpWx58YFEEdrK24gZIzfkg AcjTFTkO7kwebA4ikeMSBRjOF62oyDdWmuHtUncJNyYoRDoy9E0zUGRoLSmL kegQaYGbp/5BnJYS8+gjOU8mDet1xoUGmdY4RcfgdRNyP3aKD0/7H2c3hy8a Edo4FhFa2lzlulQk08SqTbeJRhhqdSBe+sB0SdBAhSPaUeOO6x8McllfCAn1 m5Zql3YUlDvXO5HDVoQ4qp4rap8hcRspM+AZoglxbznnPH3rHx5yJLoIRmM2 SPKP2YL18WzBGJ0IxFgjYGRTnM4SmKFeHzElcEAC8sXyFdeWrjhFMSJYRo0p DvmOcRruvGOBpUHMhoFocEGi9cgzvFJxj9YDS6y5IDEsRUv8DHWLBwwTcfhB JwdyeF5+3nP3S8nheTLJ6RYOXzxQ5IYfbFYfx0bGKg0EHZuxT7jCaMJZIycq mV40QrSuvDwOh/Csxhrjw5XYu2s0nVj5kLrE8ZCQD0UVTbO7UqlDJAf+DQRJ BGqH+Bjci0ievtLDTtVWRmrF9AsSgLy7an54cRFAJNGh9XHRPwlA2kKLXlle BJB30eKnEnADnQhCN7wPW716TRqWRoIc6XHYEnsPZqNhB9zpumeiGtu3VtyR BJz/wju26ZRxM1KAjiQaHmLebB+HpYUwdcrcCCwXnqG7rq6VQQKQ5nrjXQsd oJ3mVdp61pnu8kN8lCTgRG0SThQBpG0GQygByKgVdlUa8KEHF9nWyaKwE4CM /cjsiwAynoagkwIO0yYkUKuN5LrHAJHXxF2RABRZtE2ioooAIg7mrPRbk4DI 3UNT9cSZEcCrtZXhB3EHNdvAA3L62CNpwOOOdVECJIQkABmXEKEuAsh1hDOY AGSACJlEacArNPQ6o/nVJCCvvuBoXOVFjhuEbnjDrS8mAbkrMYs0ICUZR00C kM6WeOpFAJGzilYEYxOA3DdIt0nPcd48FxY484zHCUh1h1MRTUjSvToFyEMb TkQC8AP14KAE0oBUAkgVTgDSk0LYJA2Ie0BKcgKQHuW4k5qLAHIiePmQAKR9 MUFUWQhYp61MeMAV8x/jgE/rLTeiE2lACrmYWUlAZJLSnUkD0hVCvk0CEDm3 dFHTgEz1Eps8CUihuqZuXhFABiXgfK0LMBPVAGsB5OGCqEIakDcwsHkSgHj1 gib5uwignA22dcGCnnUCxub4/zkglwNxzjSg7JmBliOqjr6a5MQAmeSCEzkB SL9RFHMRQOb+ikeeBEReM5oQH0tLDm/Yli9fnQRs0wgkYtppQIbhkReZAERe JM/cNCDzkYqoDl4Iyj4ooqwQeUCr6J6ksurudv62GBFFABFjV/c/CYg3AWxK A9IGANoEIO4L3Cl/SxFApBHZI+D4B5KHDrNjRPUWOXQYgIIBmQBkhAQrlQak 8kQwbYCDdcmS3iKADJ8ibJgAZC6RHAXe+o/GYOhfrjN/h2MxGxjR8sRYNOYR LnD3fhsPFG+x/61f1g4JYPQDTkGCAGZciE+rycfftV7dAEEXS8R6J+6Qjihn E3Q8rGEsWLqOjn8x3WuPvqx37k5p1AughwVllaCF9urZ1TM11adYoGZDzHGd QZhhuiQDZu+Qnog3k6SHhrcYvCE9qcDMMA3M9BaLumigb4Nk2GX9knjotn38 sTO89t4zZetTs+DxzUTdKGsNxJQmAzFI6wkypCOZzhPzOXj3gsuiGB1xB/GT T9Y4UgYXjxlMbg8p4GEh5n/SQePbhaVLVgQcfh3xGGqWdWb3cHhk6/M8TgzP bAzcLbnh1x6PYVLV4JN7SATv8+9veiVJxNWaOImbQLeri0dn1j+3h4PzFgG+ XGJweo+IdjIZIxqx+U4KGVJA6IwnkDHVD3HH0N2eqtKG2zpmznz22RcJWOTO owWPApOwJf7OAu5PImLDfHPkyA8cdYGnlgDkPR1sv4FDPaL7k4D0cHGRYQFj 4ZpJ57n7cVzZJACjIZc0IEMuCH0nABnnAWNDwMnKWLyjwH0xHC/xV2OwGR/K gHclG36KnymVKi0rBJIT4cyD1H3GZUEakMcRzM4EIDfW7NmvFwFkdpbwIwnI sDHugtOANJ5f6Xw/CbhwYY8PvISADIXhvRqMS7BJWBSDda3MTBDJnJwAL7E1 GXi4JC4s+A4BUpQGpO6ZeuXcJGDd1fO8UZEGZKzsiVmvJQGZO3fWmS0RQAoD dDod6Q+Wr47BhtfEKgzpaziatSOG35W8hqOXDQfkCi+EvI7gW4ULJ81JAkbv ldKAeGWOVtFESUD6NeeeM6vIbSNmymSGd5Z9FIN1SVBogS8imid9y4mntFQp iatVxhsXLVpe5GoVz2ZphSUAmRhwx+0dRQD5GuKpJ99IAjL9HwlIxW+QmQgk ZkUM1sX9nWxPg+txeQK8xD4AtR5HeHPN63JGFRCtTQPicT1aEZFLAHKfInQW AvJyH0tD3SG2Yww2429AcVUsnl46r2Cx2nIHD29MJiTQIoV1nAbES3h60AlA 6nOs2mVeCJkowkAQ3PkYYMZfgSBRQdzMSz0sk1vwBjPSQcGZK8ILTWBOwoZs RHgqkWQSnUs6UYSvZcW2igNmPPfgvgs9yayY8MobbzRFtBSc2ThkhRzmRbJx mPKB5MBEGg/jt4jRpQH55gsLFwMM6UG0XgQ4nT7EhATNL1Jwpi3hmYV1Dx/N BUnYMIczkrZEwMf1Lg3xzxDwYh0UpyrVixAQg3X3VnxwI8onnd9FLX3cqPuZ o8XEMObm4RYpDciXxri6igGGSdFw90Wn0Z1wfncvjOVgSOx3zhdnDYJ8X6/p 6e3zPWDt9uf75Hf0LfpFmYh/ni/Y3IVtPG3bFsGaUQzxTIw4hj8MSKGYuIU+ kbEus8MOXPk1nC8zBqmH7796kvhtZc6P/6ZY2hWm2frxBV+2Jqhqts7CQHkY 7rkYDgdx/apgVJebChjY5TUmR+r72llGylz24APAE9rXZaZWnA2gsuyM1F7Y ZNDBiIVvtg6EtEw51d1ah6lGjPtN1jrfXLNzlrba8ucGz3sOGzdjzygTv+/v UOEExJ1M769g6qaONVzgxwwc3HCEbmDaapxbVNshZPQ0q8fmHOL+7ia60jtM GEtPyVTVi4PY2y38F6exphXzDitx/JYLNOi4SrlpmVlD/7gIbuXpdwY962Ud zs/d5bJnzYEH1Jufboy2zU1rr4lL5gbWuYfnjBMZuYKd9VkTiSYwTaY312Ya 6htMe3d+XYEafQkoZ2RfmwuCIEBkU4u8u+eKjsm6d7Y0mvqGFtOzus90dogP 3FvwGz9XbwULcZUkd9cvWlToXytyPuIsOvWNIlN/zzN/u7FIDr7ObP9j1ppq U77S4ss1VFJcglIVIeycUy50V46oieIHdOGJ9cn24XMWKxHZeKAqW98hfn0s QUUQdHjeZxs6feDE5HOmLluma5Tf2ivKbdaDmAGQpfiamGaEpB9uc7nl50nb xoSb5xyZ2iU6oqIiG89PytaYRzqWe8NlwfVHpkdbR35SSTRQpu9rHG+bqrMy AkfbyGQryk11Y26t/K2o6yghR0Ty2ltbTHNTo6mtzob6stwHObZKsHwdpKZj eoMYo2zwK/H9n51v9tt3mrluvxgBXIl/UxqZs3/DuP2Lc3stMcCSaAxQX91u kEypKs5R/NljqnVfMRxe2dDOU6ooO9dCy9BUPFIHyBTBvV5sPEesojZTX7FW NvIRScV2O0YxDjKfbAuyLpIO1p7c7I05R1+pHDgVVudlK6tMbX2jae/qc+rU suJ3gxtzbcj4IL+zYUD+DFey/vXn55kVK1aG/HGB8iR/CqtWmgOHN5gtfvSj YvxZR4CV/DH50Byq64gfRM09/d7+EzaWVTaaLo3DduU6TWeu257AW6f4NKjg 7tqR/lpnCdO1IP9rripL8w1hxX4zZgdH7ub73Gz1AwVadDlrsBX68l5S+dqk kA9/l4mztkfss5/4RD4voYNJ5ivTPk4G5HdtAtjbYquLaiVUHU32a3/OVCb2 a0uv32uREmm/G8TIpYPE+j+RSZalJ0nOwvfZe+cTbNOvTplhVUVduTPZRAfx aTcWoB0yXW6tQr4fyjXI9LMNpqffM/ffdXd8/vlqs9t248ymKK75iwutaK8t X3FLpRcENNdUhPRm6013v38CHTmM/bSrW7qLMPP3axls6CCxbUEcsqBdbU2m qiLg3YD3mfgUbWTFaJV+t3Bi5QdR9rXWYBxbyJbBk0Jft8l15kwulzNdPe7+ UHs3VwFLDabu9L5/V8cww9gxDxQtf0gPsSAeYq/zBl3UMeH9hRA76+/g6XHm rFMJz5k30s/Oe1sYkRes4v3Jiv8wsmQ8rcuqm02uzYpcMcOCxnSPqo66joQr VFZmapqdd9DVXGvKy8p0YTLea8BwLbVZpjUH5eVOwCtqjZjU3u7IdziNV92C /T8kykT3iJWZDYsXf5B82xjmGqF24k/8tsxbQsvqxLrsbvbbSkzfINRUPbp1 q23JYvef802q2/ocdd8KVacFb9duETtThLWhk85NwbTWyu8rGiNON8WkzPZt 6enXGfLlJ59fIgcx/fITUUiW/3jqyTc28yvZFxoKdjlqZD6GglnINUS18xCd TL6j1ur8XE+PvcHr6emMJEn7yywDf72Ovxf3Mh7j6BWbo9y0MY9f/uQhCmtd Z+faSF9g/7W1CXhDUqpMjLiVPf0B6zfQviqLikRpuGRlWVNdXQ2HzRcQQTFa /x8lypljQWiPQWVWFCUd/ZR04zR8wGuy0kg4QT3Ejr7wVlJpLa9p85qmqzFr ymptTevwoHSLHwrFQDZjX4pG+mdFaRymY+La3R8fcrD19TqPtqGjN6BYeOMr ctUPBEJKuRwjbR1NMRT9URkePLk0OctDcq1msBc/JV4GqMY1n8FvXTNg543W +q9B9BvyD8EyYD8qeaQiIYgZUD6LdXYn24aI25jaLNIlKk1lpfiLVXWmpbne VGazolSzcjoVAq8qe1s1VSNit5WGZjDFszMfggx+3doUTW1bbxDVUVwoRl7x AHA73xBW59zR/257xYhy1IDwjGDlpPAkEUXS5yfS3xPqarrV4THR7iM0FfWd yT0N3z7Ut32qvipNjlk38bnc1uAi6ieNeXgdc2GhVKSPaH1FJ85baEOhq8kS VdnUFWQi8+NBW9Pay/mZfBhlgjWWj+lVp9wacgX/u/7uELUaFyzuAHMwUi8j XdyBN51IXGPB3W77rE30UHfBG7197bWWUf7RGKYkZ6bS6WuoB2VVYKbQZNsY AmxECky/s4LLauwzPZLKMha8UETlXTnOJnpSq7UD8gxYZeX111duTco6G015 RX1ECtQacoFvf8nUUZc1lY2dnvWRoZGhyGT822/rSA4d3vjiRk2rb7DwB++2 ESZfseKTsG4I3/jwJQM6rFzxqYL/RDGfp2+icDGTrjkSLdRyd+PCWL2SeLmT XK43Xe6ElaRQ9mvNmi8VnMEgXmLhisXC2gABa8TgoTvTN+a2vTU8Cute5LJm 18yZS89IgIeZFuNPe5RFXlhfxkcIBD6f/3yCh2WxHdil6IAg7rvvfqzgjA/y DgaXhWFtmgkRwmgIiWUdK5XjbjeZyCkLd3oKnPk+eG4vzFdwVhviPSVeksnO Gu/BSTmqnkM8ceUrZughcXCsJsVsyuS2EJy1jmCc86H/X65/TmsdsboT7jK5 3O3ty05LgUeLT8kOUnCWpmLCKMotrFpVqPLgrI6PJwd8H/DSwvcOi4NjjzAj +5zqWSF4lXZAjQ+mMwsbtTAWPSYkN9BAl51+agqc9UhxF1ko9Cs4a6KhgK+7 Fr0FtUtO8eCsZMaURzDojTc+1EpmrOvGR2Wo3yOrcLIHZ10tZDixpuV90zsT ZeHgXUAtoXXaTS+c7CXWvTIttelTvOrEXQ7qjyoO1tBDmXymUItKGJfAkfFP fvAsZuXKT7VIHiv40UuEMu/t/WSsB2cNQiQSYPXws6Cj56gouKuiyEwzpMcj iTssREgSUKmQ+Ski61pEkKcxXqvQdRRRS9cxhEFD8cVbfxEZ1jFkKUXckrJQ 65w5r4elFMdECOVzc+xjZI6NdDhYzZHVBKEeZJOlqzmSV5AF0YtazZGhTr4Q xWPr99/Pp2tJkpMqqqOi4PHapJgs6lFWehwnKA4ktpOT1137rNa03FJxYKuQ UcCF1RjtcVRqL5gSfLMKyxfsVEQs9ImXR1TDMq8Qx2jFAb+QRauQTw5qtdAn Q5tISWCi6fR7Xw5rjbLQJ5aExxTWX04GbfPlTlFLFc1gW1vbW+lypyxygUMw LHfKYqtcMJAhavlYL9ws9cpULRz/7c+x2CpLvTKzB8eVIB/lwVltlg9z8dPy +NITouCu/CYTncDMd5Z95CAtjpGK44lZr3mpEA2h1WZZ9RZSMUH3F8QW35QY 6blAOpB3QB0gRq9WvWVgC5lufLqCdUdZ6nT1XRTiIQ7uwrAUMCSL6ScoCYzK uclSwK6gKXfhddc8q+WEWZc4WsEXRwkeLiTrEmds8mak5LLWNmaRZMgujzrw A4+4kkWS3VxYwXfqlLlaaHm7CB3kB9Qe8pCP8DiOVBx4VM51kTNTqz6zfDTk ny8bIR7I9Dnc42BpTR6NVjuObXZnii9jjbWlfEBC8ULyMI+DlaNx+8ktACsC nFdErKkdLc4N1iF/MKypfWikF5O7wBykaWph7Z2VXsaC1MhJF/iGIUELDCSj 3r0W+GbJcVSzId9QXR86aISXehZBR5G2kzQPDcc3nDotOc4i6Dh5qT9wxKCW 8HCPiGXZkelOuwx/I1FRi6CzLDsUEX0VZGYhiTldlh3PFPl0GNIhpxLLsrNQ PLQihQ8GA1Krw0LxzgB31f6jdddRMFr4prXid9deEKCLtDgKfgAhp32FR3eA DopMP2bWYn+i0r1zATQ/odSKGVkOa0GMjiBdVR+cYjonsvDmz3+HVfVZ6h8p r0zhg9WCCaZL/aMGNV+94wzAGzMt9c+vJ+BI52Ni/MAbFEdhX4+L32NATkX0 sxeojCPM0k8Q7KMjIp2F5jUWAKnJ+3hc/BgD7EyKAs5I0QL8LgK7oFgic92w gqgY4dTker1kCksa8OMN2Muw4qlBIduiq/UTD5wtnAiajGrvYie44+qrv28K 34FwHVCki9mTkBDUwRRSJzmyuKB4K0aXDJIxS/SHO8X/YU+eQtL4vQ5sAOgb 6mksi9iX+r0Ofk0E9nP0gydwmMVOcAbPP/QhVPiYh99QwW5gJieYByEWqvUD JdzuYB4tMmgyhBtEBTjDdP2SQhJPoUKK+JEYnFzMo8cPlnbRouX6BRZ+JAbJ /9QY+MG5LfYxL/rWM2ei6DuoTPQdlCdzZx0BXwyiGoGtjGiXSJ1+fGZEkV74 wVEoW2ZzT+Y/5G1U+DCGTIQvje/mcFykQ4tZrV/a4ReBEOBC/JAnEP6GuIov ou7bV30zFT5a4neFkFTGSov02FSc+F2hQ7UrCgdEjw8436jTBVv+l0reV3tT Fe7YHXRMSB9ebDJWgDMAxxY+6efS3dVoGWqPXD61sYI6sgm2wi8U0//tuVUm +tzKU8cAKTTwA+LBRb/mhaMX9RrRQ78kdaSSAOk7VJ0g/EAiUGIRvHZxlfV9 kJUx8TssR94fIuTBXcDLA5KHiBM/7qVf0uK3wFCIAadedDZgIsjGGodJbeH1 7Lf9oDzSoGPxTSQUdSMW+If4LAF66PfB+IUzOApwgqOf70I6LnKm8Z2RMAOG HyBDcSwce1Ey8VYMYRVwUr9wxm+0wXzEmxGUM/QfsxPJRR1qFIAIU0d4OY0t gY8MiKx5CNgcMA4xgH6jzZenFi6jvmr4JTv3fhR2L77wEt76b6kQsIoRF0Sc mp+xg+WCsAp66FfmRmt3VJBUwyZGD6qKYB+kv5OHNylQgNE1wM7BA2dYovVu AH7vD5FEmPnhN9oy9mzG+zNUXxJ6rYa0uo75LAiQ4BxCuWROAl4a3Fu8x9fv /fGjhRALBEvxrJ5fXYSuwbjQjsLYX/oxGKfD2qEEChLZhX7SBu5CEeGNv8Dp 1wv5tUaEKxB/EmL8SHD1saQIcIvF+zM/EoOpIA/PR1FyRtjACcGyhTZEqKHB DcM3vzDroJnCbypmrMUPHmPHiJW5mV8YhosROUSNQJgUMiEOg3Q9xA2E9OAO N8x4HQav+OGOoXwov/EJwwAnCCwr8ABCsKkfixcBqDgABwMclh2ViUgOxoIX 2+jGYi10vMnCF4IR7/Lf4yy11hIUK0KyQAjb+wd+uB+o4sI2gOkHduERKmoW ZZQvsFUQCMOmFttTv2Q6USEhSah/C26iWDo+IMrP9MIjgC0GnQ+u4pGM6Knv +uH5SViYuQjI4UBCDAUGiMwh/LDrLfbDLtj1+Lwlvt6in4Q915OxxhacAVcx JD7j5z6Fu6HlOOLB+OIG6tOCSwiAYMLwO6AWwutW9wjOfWcXygQDIuQCrQUB w8fgDh7eOFRpg7rDZ9Cwc1C3B7Tpd3Yv1NlBbhBggDWAcr8AETYNsxg2tn4K QoBQg1DwsMRwDuFNClYNtUlgWMCPsxQOsU8iN7RKAqxFTSzsD9hDkE1wD3c1 0Aj8njGOYIRSIOAgFZpBePaoo/RSnTOix/i4GQQFXAJmBNxgNoqdvzGQKZMc a0E74tE4DOHmg/3Q13iKihguuKHffnZPZje2BxWcecgrqMDRAt2CY+euOxfa qeoXmv3bBnyMECuH2WIdcNDh3MHXi6FiYD3gUkJXUz+IPciPl1tVMn+9fhHF gT/5ufSv8m8+RSoUCj6tsNs1XaRC7pK96D5VmLbefv/ec10ZirOjqFw+jnvV UG7q6qtMWdamT7BO3SCy8hThxUpbb2ebaWrGM5W8IC5HxmCYu/5VktSeiIqo S+epxZW6T7T/GnK+ZkVpykQS1q0TyQzary9ja1ZUpFySoXfgLJ+YDvS1Zl7F qBwaS6aorM6KSNo5+lygryfHKkFkm99+1TJwn4hiGUSdyQn/5OSqWdE9OMz0 R1Kq8FAF/3XWyYiemq8jpUqJdJpnQxO+/ND8oco605FrNdVZ+Z2gET/8a8gf UiKv8vvpn5jvo2OztM8/KT9H9Srrf/2TUm101Gs4wv8hZUYPnuAb/wvaEMZh \ \>"]] }, Open ]] }, Open ]] }, WindowSize->{806, 703}, WindowMargins->{{49, Automatic}, {Automatic, 0}}, ShowSelection->True, Magnification->1.5, FrontEndVersion->"6.0 for Mac OS X x86 (32-bit) (May 21, 2008)", StyleDefinitions->"Default.nb" ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[568, 21, 71, 1, 40, "Input"], Cell[CellGroupData[{ Cell[664, 26, 104, 1, 69, "Subtitle"], Cell[771, 29, 174, 2, 39, "Subsubtitle"], Cell[CellGroupData[{ Cell[970, 35, 57, 1, 40, "Input"], Cell[1030, 38, 394, 6, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[1461, 49, 151, 3, 40, "Input"], Cell[1615, 54, 413, 7, 45, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[2065, 66, 117, 2, 40, "Input"], Cell[2185, 70, 187, 3, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[2409, 78, 130, 2, 40, "Input"], Cell[2542, 82, 198, 3, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[2777, 90, 152, 3, 40, "Input"], Cell[2932, 95, 414, 6, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[3383, 106, 115, 2, 40, "Input"], Cell[3501, 110, 205, 3, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[3743, 118, 62, 1, 40, "Input"], Cell[3808, 121, 411, 6, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[4256, 132, 111, 1, 40, "Input"], Cell[4370, 135, 90, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[4497, 141, 100, 2, 40, "Input"], Cell[4600, 145, 374, 5, 56, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[5011, 155, 180, 4, 40, "Input"], Cell[5194, 161, 485, 8, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[5716, 174, 115, 3, 40, "Input"], Cell[5834, 179, 390, 5, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[6261, 189, 128, 2, 40, "Input"], Cell[6392, 193, 476, 7, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[6905, 205, 303, 8, 40, "Input"], Cell[7211, 215, 337, 4, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[7585, 224, 116, 2, 40, "Input"], Cell[7704, 228, 211, 3, 44, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[7952, 236, 161, 3, 40, "Input"], Cell[8116, 241, 303, 4, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[8456, 250, 191, 4, 40, "Input"], Cell[8650, 256, 158, 2, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[8845, 263, 111, 1, 40, "Input"], Cell[8959, 266, 161, 2, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[9157, 273, 235, 6, 40, "Input"], Cell[9395, 281, 97, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[9529, 287, 115, 2, 40, "Input"], Cell[9647, 291, 72, 1, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[9756, 297, 242, 6, 40, "Input"], Cell[10001, 305, 169, 3, 40, "Output"] }, Open ]], Cell[10185, 311, 95, 1, 40, "Input"], Cell[CellGroupData[{ Cell[10305, 316, 207, 6, 40, "Input"], Cell[10515, 324, 967, 16, 202, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[11519, 345, 337, 10, 40, "Input"], Cell[11859, 357, 490, 12, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[12386, 374, 135, 2, 40, "Input"], Cell[12524, 378, 911, 23, 78, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[13472, 406, 122, 2, 40, "Input"], Cell[13597, 410, 345, 6, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[13979, 421, 166, 3, 40, "Input"], Cell[14148, 426, 1024, 27, 100, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[15209, 458, 132, 2, 40, "Input"], Cell[15344, 462, 365, 7, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[15746, 474, 160, 3, 40, "Input"], Cell[15909, 479, 254, 6, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[16200, 490, 183, 3, 40, "Input"], Cell[16386, 495, 461, 14, 40, "Output"] }, Open ]], Cell[16862, 512, 126, 2, 40, "Input"], Cell[CellGroupData[{ Cell[17013, 518, 367, 11, 49, "Input"], Cell[17383, 531, 848, 20, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[18268, 556, 159, 4, 40, "Input"], Cell[18430, 562, 398, 6, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[18865, 573, 62, 1, 40, "Input"], Cell[18930, 576, 562, 10, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[19529, 591, 178, 4, 40, "Input"], Cell[19710, 597, 342, 5, 40, "Output"] }, Open ]], Cell[20067, 605, 69, 1, 40, "Input"], Cell[CellGroupData[{ Cell[20161, 610, 249, 8, 40, "Input"], Cell[20413, 620, 3425, 65, 364, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[23875, 690, 238, 7, 40, "Input"], Cell[24116, 699, 418, 7, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[24571, 711, 364, 12, 40, "Input"], Cell[24938, 725, 366, 5, 40, "Output"] }, Open ]], Cell[25319, 733, 124, 2, 40, "Input"], Cell[CellGroupData[{ Cell[25468, 739, 824, 25, 64, "Input"], Cell[26295, 766, 705, 18, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[27037, 789, 90, 2, 40, "Input"], Cell[27130, 793, 444, 7, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[27611, 805, 142, 4, 40, "Input"], Cell[27756, 811, 421, 6, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[28214, 822, 218, 6, 40, "Input"], Cell[28435, 830, 27898, 464, 337, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[56370, 1299, 288, 9, 40, "Input"], Cell[56661, 1310, 27903, 464, 345, "Output"] }, Open ]], Cell[84579, 1777, 120, 3, 62, "Text"], Cell[84702, 1782, 278, 7, 42, "Input"], Cell[CellGroupData[{ Cell[85005, 1793, 179, 3, 40, "Input"], Cell[85187, 1798, 495, 7, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[85719, 1810, 74, 2, 40, "Input"], Cell[85796, 1814, 410, 6, 40, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[86243, 1825, 447, 9, 40, "Input"], Cell[86693, 1836, 27883, 463, 337, "Output"] }, Open ]], Cell[114591, 2302, 203, 4, 40, "Input"], Cell[CellGroupData[{ Cell[114819, 2310, 2207, 64, 156, "Input"], Cell[117029, 2376, 1140, 31, 64, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[118206, 2412, 666, 18, 64, "Input"], Cell[118875, 2432, 34172, 572, 586, 18291, 309, "CachedBoxData", "BoxData", \ "Output"] }, Open ]] }, Open ]] } ] *) (* End of internal cache information *)