(* Content-type: application/vnd.wolfram.mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 8.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 157, 7] NotebookDataLength[ 112225, 2432] NotebookOptionsPosition[ 108723, 2310] NotebookOutlinePosition[ 109317, 2332] CellTagsIndexPosition[ 109274, 2329] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"a", "=", "1"}], ";", RowBox[{"L", "=", "6"}], ";", RowBox[{"T", "=", "1"}], ";", RowBox[{"m", "=", "1"}], ";"}], "\[IndentingNewLine]"}]], "Input", CellChangeTimes->{{3.5292382408719997`*^9, 3.52923827971*^9}, { 3.5292383120369997`*^9, 3.529238315822*^9}, {3.5294045250855465`*^9, 3.5294045268927274`*^9}}], Cell[BoxData[ RowBox[{"\[Omega]A", ":=", SqrtBox[ FractionBox[ RowBox[{"2", "T"}], RowBox[{"m", " ", "a"}]]]}]], "Input", CellChangeTimes->{{3.529238286797*^9, 3.529238333086*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"A", "=", RowBox[{ FractionBox[ SuperscriptBox["\[Omega]A", "2"], "2"], RowBox[{"(", "\[NoBreak]", GridBox[{ {"2", RowBox[{"-", "1"}], "0", "0", "0"}, { RowBox[{"-", "1"}], "2", RowBox[{"-", "1"}], "0", "0"}, {"0", RowBox[{"-", "1"}], "2", RowBox[{"-", "1"}], "0"}, {"0", "0", RowBox[{"-", "1"}], "2", RowBox[{"-", "1"}]}, {"0", "0", "0", RowBox[{"-", "1"}], "2"} }], "\[NoBreak]", ")"}]}]}]], "Input", CellChangeTimes->{{3.529238399903*^9, 3.529238467834*^9}, {3.529238512142*^9, 3.52923851881*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"2", ",", RowBox[{"-", "1"}], ",", "0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", "2", ",", RowBox[{"-", "1"}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"-", "1"}], ",", "2", ",", RowBox[{"-", "1"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{"-", "1"}], ",", "2", ",", RowBox[{"-", "1"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0", ",", RowBox[{"-", "1"}], ",", "2"}], "}"}]}], "}"}]], "Output", CellChangeTimes->{3.5292384696610003`*^9, 3.529238520517*^9, 3.5294040668587284`*^9, 3.5294045311531534`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Eigenvectors", "[", "A", "]"}]], "Input", CellChangeTimes->{{3.529238486092*^9, 3.529238491962*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", RowBox[{"-", SqrtBox["3"]}], ",", "2", ",", RowBox[{"-", SqrtBox["3"]}], ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", "1", ",", "0", ",", RowBox[{"-", "1"}], ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "0", ",", RowBox[{"-", "1"}], ",", "0", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", RowBox[{"-", "1"}], ",", "0", ",", "1", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", SqrtBox["3"], ",", "2", ",", SqrtBox["3"], ",", "1"}], "}"}]}], "}"}]], "Output", CellChangeTimes->{3.529238492774*^9, 3.5292385230629997`*^9, 3.529404069288972*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Eigenvalues", "[", "A", "]"}]], "Input", CellChangeTimes->{{3.5292385308459997`*^9, 3.529238534521*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"2", "+", SqrtBox["3"]}], ",", "3", ",", "2", ",", "1", ",", RowBox[{"2", "-", SqrtBox["3"]}]}], "}"}]], "Output", CellChangeTimes->{3.529238535102*^9, 3.52940407067311*^9}] }, Open ]], Cell[BoxData[ RowBox[{ RowBox[{"k", "[", "n_", "]"}], ":=", FractionBox[ RowBox[{"n", " ", "\[Pi]"}], "L"]}]], "Input", CellChangeTimes->{{3.5292386490369997`*^9, 3.5292386721219997`*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"x", "[", "j_", "]"}], ":=", RowBox[{"j", " ", "a"}]}]], "Input", CellChangeTimes->{{3.529238686132*^9, 3.529238691328*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"e", "[", "n_", "]"}], ":=", RowBox[{"Table", "[", RowBox[{ RowBox[{ FractionBox["1", SqrtBox["3"]], RowBox[{"Sin", "[", RowBox[{ RowBox[{"k", "[", "n", "]"}], RowBox[{"x", "[", "j", "]"}]}], "]"}]}], ",", RowBox[{"{", RowBox[{"j", ",", "5"}], "}"}]}], "]"}]}]], "Input", CellChangeTimes->{{3.529238700321*^9, 3.5292387672869997`*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"e", "[", "1", "]"}]], "Input", CellChangeTimes->{{3.529238786785*^9, 3.5292387878310003`*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ FractionBox["1", RowBox[{"2", " ", SqrtBox["3"]}]], ",", FractionBox["1", "2"], ",", FractionBox["1", SqrtBox["3"]], ",", FractionBox["1", "2"], ",", FractionBox["1", RowBox[{"2", " ", SqrtBox["3"]}]]}], "}"}]], "Output", CellChangeTimes->{3.529238789035*^9, 3.529404080004043*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ FractionBox[ RowBox[{"Eigenvectors", "[", "A", "]"}], RowBox[{"2", SqrtBox["3"]}]]], "Input", CellChangeTimes->{{3.5292388205620003`*^9, 3.529238845324*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ FractionBox["1", RowBox[{"2", " ", SqrtBox["3"]}]], ",", RowBox[{"-", FractionBox["1", "2"]}], ",", FractionBox["1", SqrtBox["3"]], ",", RowBox[{"-", FractionBox["1", "2"]}], ",", FractionBox["1", RowBox[{"2", " ", SqrtBox["3"]}]]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", FractionBox["1", RowBox[{"2", " ", SqrtBox["3"]}]]}], ",", FractionBox["1", RowBox[{"2", " ", SqrtBox["3"]}]], ",", "0", ",", RowBox[{"-", FractionBox["1", RowBox[{"2", " ", SqrtBox["3"]}]]}], ",", FractionBox["1", RowBox[{"2", " ", SqrtBox["3"]}]]}], "}"}], ",", RowBox[{"{", RowBox[{ FractionBox["1", RowBox[{"2", " ", SqrtBox["3"]}]], ",", "0", ",", RowBox[{"-", FractionBox["1", RowBox[{"2", " ", SqrtBox["3"]}]]}], ",", "0", ",", FractionBox["1", RowBox[{"2", " ", SqrtBox["3"]}]]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", FractionBox["1", RowBox[{"2", " ", SqrtBox["3"]}]]}], ",", RowBox[{"-", FractionBox["1", RowBox[{"2", " ", SqrtBox["3"]}]]}], ",", "0", ",", FractionBox["1", RowBox[{"2", " ", SqrtBox["3"]}]], ",", FractionBox["1", RowBox[{"2", " ", SqrtBox["3"]}]]}], "}"}], ",", RowBox[{"{", RowBox[{ FractionBox["1", RowBox[{"2", " ", SqrtBox["3"]}]], ",", FractionBox["1", "2"], ",", FractionBox["1", SqrtBox["3"]], ",", FractionBox["1", "2"], ",", FractionBox["1", RowBox[{"2", " ", SqrtBox["3"]}]]}], "}"}]}], "}"}]], "Output", CellChangeTimes->{3.5292388463450003`*^9, 3.529404081424185*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Table", "[", RowBox[{ RowBox[{"e", "[", "n", "]"}], ",", RowBox[{"{", RowBox[{"n", ",", "5"}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.529238858189*^9, 3.529238877031*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ FractionBox["1", RowBox[{"2", " ", SqrtBox["3"]}]], ",", FractionBox["1", "2"], ",", FractionBox["1", SqrtBox["3"]], ",", FractionBox["1", "2"], ",", FractionBox["1", RowBox[{"2", " ", SqrtBox["3"]}]]}], "}"}], ",", RowBox[{"{", RowBox[{ FractionBox["1", "2"], ",", FractionBox["1", "2"], ",", "0", ",", RowBox[{"-", FractionBox["1", "2"]}], ",", RowBox[{"-", FractionBox["1", "2"]}]}], "}"}], ",", RowBox[{"{", RowBox[{ FractionBox["1", SqrtBox["3"]], ",", "0", ",", RowBox[{"-", FractionBox["1", SqrtBox["3"]]}], ",", "0", ",", FractionBox["1", SqrtBox["3"]]}], "}"}], ",", RowBox[{"{", RowBox[{ FractionBox["1", "2"], ",", RowBox[{"-", FractionBox["1", "2"]}], ",", "0", ",", FractionBox["1", "2"], ",", RowBox[{"-", FractionBox["1", "2"]}]}], "}"}], ",", RowBox[{"{", RowBox[{ FractionBox["1", RowBox[{"2", " ", SqrtBox["3"]}]], ",", RowBox[{"-", FractionBox["1", "2"]}], ",", FractionBox["1", SqrtBox["3"]], ",", RowBox[{"-", FractionBox["1", "2"]}], ",", FractionBox["1", RowBox[{"2", " ", SqrtBox["3"]}]]}], "}"}]}], "}"}]], "Output", CellChangeTimes->{3.5292388786549997`*^9, 3.529404083034346*^9}] }, Open ]], Cell[BoxData[ RowBox[{ RowBox[{"\[Omega]", "[", "n_", "]"}], ":=", RowBox[{ SqrtBox["2"], "\[Omega]A", " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"n", " ", "\[Pi]", " ", "a"}], RowBox[{"2", "L"}]], "]"}]}]}]], "Input", CellChangeTimes->{{3.529238970175*^9, 3.5292390062209997`*^9}, 3.5292391043459997`*^9}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Table", "[", RowBox[{ RowBox[{"Simplify", "[", SuperscriptBox[ RowBox[{"\[Omega]", "[", "n", "]"}], "2"], "]"}], ",", RowBox[{"{", RowBox[{"n", ",", "5"}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.529239009972*^9, 3.529239011782*^9}, {3.529239058201*^9, 3.5292390818459997`*^9}, {3.529239141351*^9, 3.529239149699*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"2", "-", SqrtBox["3"]}], ",", "1", ",", "2", ",", "3", ",", RowBox[{"2", "+", SqrtBox["3"]}]}], "}"}]], "Output", CellChangeTimes->{{3.529239082439*^9, 3.52923910796*^9}, 3.529239150275*^9, 3.5294040982948723`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Eigenvalues", "[", "A", "]"}]], "Input", CellChangeTimes->{{3.5292391160179996`*^9, 3.5292391200889997`*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"2", "+", SqrtBox["3"]}], ",", "3", ",", "2", ",", "1", ",", RowBox[{"2", "-", SqrtBox["3"]}]}], "}"}]], "Output", CellChangeTimes->{3.529239120663*^9, 3.529404099344977*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"e", "[", "1", "]"}], ".", RowBox[{"e", "[", "1", "]"}]}]], "Input", CellChangeTimes->{{3.529239170616*^9, 3.529239182148*^9}}], Cell[BoxData["1"], "Output", CellChangeTimes->{3.529239187915*^9, 3.5294041020932517`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"e", "[", "1", "]"}], ".", RowBox[{"e", "[", "3", "]"}]}]], "Input", CellChangeTimes->{{3.529239190467*^9, 3.529239196591*^9}}], Cell[BoxData["0"], "Output", CellChangeTimes->{3.529239197557*^9, 3.529404103356378*^9}] }, Open ]], Cell[BoxData[""], "Input", CellChangeTimes->{{3.529239271225*^9, 3.5292392728050003`*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"y0", "=", RowBox[{"{", RowBox[{"0", ",", "1", ",", "0", ",", RowBox[{"-", "1"}], ",", "0"}], "}"}]}], ";"}]], "Input", CellChangeTimes->{{3.5292392140559998`*^9, 3.5292392497349997`*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"e", "[", "1", "]"}], ".", "y0"}]], "Input", CellChangeTimes->{{3.529239256277*^9, 3.529239259834*^9}}], Cell[BoxData["0"], "Output", CellChangeTimes->{3.5292392605179996`*^9, 3.529404106225665*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"e", "[", "3", "]"}], ".", "y0"}]], "Input", CellChangeTimes->{{3.529239268317*^9, 3.529239274676*^9}}], Cell[BoxData["0"], "Output", CellChangeTimes->{3.529239275067*^9, 3.5294041076228046`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"e", "[", "5", "]"}], ".", "y0"}]], "Input", CellChangeTimes->{{3.529239276166*^9, 3.5292392796689997`*^9}}], Cell[BoxData["0"], "Output", CellChangeTimes->{3.529239280218*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"e", "[", "2", "]"}], ".", "y0"}]], "Input", CellChangeTimes->{{3.529239284892*^9, 3.529239288106*^9}}], Cell[BoxData["1"], "Output", CellChangeTimes->{3.529239288796*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"e", "[", "4", "]"}], ".", "y0"}]], "Input", CellChangeTimes->{{3.5292392914560003`*^9, 3.529239294612*^9}}], Cell[BoxData[ RowBox[{"-", "1"}]], "Output", CellChangeTimes->{3.529239295191*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{ RowBox[{"Plot", " ", "shape", " ", "at", " ", "t"}], "=", "0"}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"Plot", "[", RowBox[{ RowBox[{"{", RowBox[{ FractionBox[ RowBox[{"Sin", "[", RowBox[{ RowBox[{"k", "[", "2", "]"}], " ", "x"}], "]"}], SqrtBox["3"]], ",", FractionBox[ RowBox[{"Sin", "[", RowBox[{ RowBox[{"k", "[", "4", "]"}], " ", "x"}], "]"}], SqrtBox["3"]], ",", RowBox[{ FractionBox[ RowBox[{"Sin", "[", RowBox[{ RowBox[{"k", "[", "2", "]"}], " ", "x"}], "]"}], SqrtBox["3"]], "-", FractionBox[ RowBox[{"Sin", "[", RowBox[{ RowBox[{"k", "[", "4", "]"}], " ", "x"}], "]"}], SqrtBox["3"]]}]}], "}"}], ",", " ", RowBox[{"{", RowBox[{"x", ",", "0", ",", "L"}], "}"}], ",", " ", RowBox[{"PlotStyle", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"Thick", ",", " ", "Red"}], "}"}], ",", RowBox[{"{", RowBox[{"Thick", ",", " ", "Blue"}], "}"}], ",", " ", RowBox[{"{", RowBox[{"Thick", ",", " ", "Black"}], "}"}]}], "}"}]}], ",", RowBox[{"GridLines", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "2", ",", "3", ",", "4", ",", "5"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", RowBox[{"-", "1"}]}], "}"}]}], "}"}]}]}], "]"}], "\[IndentingNewLine]"}]}]], "Input", CellChangeTimes->{{3.529239318619*^9, 3.529239352196*^9}, {3.529239400693*^9, 3.529239424098*^9}, {3.5292394715439997`*^9, 3.5292395160030003`*^9}, { 3.529239560032*^9, 3.529239624773*^9}}], Cell[BoxData[ GraphicsBox[{{}, {}, {RGBColor[1, 0, 0], Thickness[Large], LineBox[CompressedData[" 1:eJwV13c81d8fB3BZScW9H+NmJsmOhvqG8j5mgwrZGUkkZEVokSgJkbQURUik rKac0qBSWprifj5RZrZ7jfI7v7/u4/l43HPH+7ze73M+C7aH2PsKCggI3Jwh IPD/V7518CXbkDgTycNteH/bHpOjOzQ0m9Q9wXBUJPuFkT28/tMekKoeDHai S67mGm2HgUrzlCD1Q9ARt7kj3igc4mWHFd3V00B0EUQ7GsXDq/oNHVvUc0B7 lWBqneEpCLm898Vm9TIon1LyTPovDx6npDzYqF4LR+27hov1KkBENHxmV0AT HI048MTrRR2sj/VOrHb6DJT5eIV18iu4E+P7o+BdKzQZLZoT/e0dfHUL1A+P +glWLV+dz040A3ttqt9j9Bv2PRqsXr3/K7A++lb8t7UHrJO2GOc0twDqM+12 COwB4ZNrk17QLRAqqqwavr8Hck5ove7ta4F3qz5llGb3wCFXw6UKoj/g1CWr sAUtPTDPP1OYs/IHyOzUWDLboxd8bf70Hzv9A+QnOm+0evbBI6EMiVXWrbBQ Jag4cXs/1NkN3VLNbYOU1gVXUsP6QX/FjqnEa20wdvHzuay4fhB/ROfQ5W3Q IGeeVJDTD0ekh9sOP22DICn5nc++9cOLBwel/LraYKvQjlPxWgOwOGdH0Y95 XCgYY9vWXRmAtcM1YxaeXPjW3GttVTwAH8wb+mK2c0Giun7ty1sD8CpioO+6 Hxei9xyE93gAGgePi8wI4cKGgU495scAOMbejTwYy4U/XXiuoPwgKM38vf92 LhdW/dj9yvTUIEQapHmr/uBCmVa4jP+FQfDNz/VVp7mgtnevV1reIMSC7cVF HVxgScYOf6sYhPf9Qpdk+rjQhdIVIj4MAjvIoPHBFBcuXK0ILJQegth6g+75 CjRMBfJmzz47BIEmM8rBgYbwu5OOS3OH4JxhTn+RMw2dwgKXnYuGINxqIcze SsPHS2IGV+8MwdWJ2XOfeNNwo0nOfc2XIWjcWLmeF0yD5/LVpSFyw1C2vTky LImGxxNxNh+zh2GQzvIqvEPWy4WPheQPQ9TCRfVwn4Zfq3wuzy4ZBgu/sBcf a2iYE2U5YnZ/GB6GVGQPPqbBaXjWxfIvw1Coq+c79oqG7p5TPWkyI1Bp7SWo 20Z+v3hClrbSCKyt2vTqEE2DpHYkPFcbAe0RWPT6Jw0G/s6Zf5ePgFd623H3 Thpi2xWMg+xHIJnnKGo1SIP0j6vJ60+OwNSyD3bmggyoT2UZdJwhiy+WdG4S ZsBQ4VhrXM4I9M9rn+kkyoCn665ld2+MgOmJPT+cxBkobl78Tb1xBHbJmXxW pRgweXNbS3jWKHw5XXXhpwoDtn1FH3JZo3C3sOBgkSoDPnPOHzSeNwplp0Jp PzUGkjbsfxeuMQpHPL5qfdFg4MNziKEtR0FoUr4iQY8Bf9zQUBs/Cihd21LE mIFxQ5aqQfIouE3RZ2JWM5Bc5by/OGMUdt5TS+9aw0BJ8a/Fpy+PgkX4n6ga xMCfTOHMXbXk/fzVUnpWDMRK2PS2PhsFm+eDZ2PXMsA6nmnp8HoUWkMyHjeu Y2DpIVW+ScsoFLx1EHSzZiDCH3lIT4yCk82hpciWAZGfx24fnzEGDv/JNAfb MXDGo0lyWmwMpkdXKZy3Z+COvWddF2cMvl6fncZ1YGBi9QENvGIMZnm7ihq7 MhDHvju4K2wMCs1axJS9GWCnTG9oix4DH/eVt0W3M5AnuvaqQ9wYHJLQEuwh fjLZ7AQnxyCwdDqicAcDor+GH0jfGIPlHo8ede5k4Ow2Y5nkqjF4FqPuUebP gOb3+ODpB2Nw/b+TZ0J2MbD+LXtB98sx8N1b3tYewEDKff2juJO8vzDs+YXd DCitiGozGBgDOTVlqzXBDJTdrF11nUfWL93n/Z246erGntOiPHjjWBIgHsrA tvlZFuISPNi9cpVLNvHA+ZZLsTI8iDBu52qEMUCdDLQNUOOB6ivpJ8vDGcif VVncpsODlXGuipXEBgkTgo7LeZBTtoalt4cBp5jj1WDGg1670HrZCAZ+D7+V qF7Pg9P2x5ITiKOD5/lr2/FArf3N7z7i8z5F8jLbeGDnkhJaGclAkPW8Ol1/ HmQb5K7h7CX5W358l0UocW5nSyQxS2GC5R7NA2mJTZuaiBnBwLt74njwwP92 xsIoBqq6v3udSOLBmjniReHEx97bzMxP58G6F8vSaoh18/Sc3l/mQbNsxTsU zcC/47l/u67x4HfKz8X7id+GsQpmlPOg9Hfu1lvEea6HbeTu8UBj9Rc3LnGk 6dDwksc8iJKK1Zkdw8A6LZ/sdS94QAckvV5CLM/+aLbtHQ9eV3YhO+JevkV3 1FfiD+cTg4hrudUZJ2keXFbLyI4nTm9QNyzq4sGyiBfxmcTbb53l1g7y4JKw iXEuscE5saRP4zzQT+l5WkA8My5G/88MPviseDu/iPjbzu5PIuJ86Mnpsc4n Lt289ZASxYfi7ybrLxAf+q9x0Qp5PlSEN3JSiG3nr3lto8qHDV7n7kQTq84s i9ihzYdu1jXNbcSjf5QVDyzjg0GgYKAZccOnk08yjfgw9ezmofnEF2oFAkvM +LC6754Pj9QjqDCMerKBD/ILdOVfEpukMfe+2fOhRUYq7ywxa+8W7yE3PvQO H5j0Iv7p8VRM3IcP75xj1BcS37ZccWtBIB+07eUW0mR/khYXOhvu4cO1nSGD 54ndZDjTtvv5IJFxMmPj//fv77FC/yN8UDc+KTRF9v9fO39j3Ak+PLRKXFtA /K5x1+jZTD5cEkv2WE+896K1RX0+HzStNAXiSb7WJdT0tJbwgXNzPEWWWD5o ceZYJR+eX1vfW0DyiI0lmUVP+bBtYYdqNcmz2Pf3sQntfNDd+m1PFumHb3Xm Ghd7+ZBn4XdOgLj0etWbyhE+HNU6k+5H+sdu3xmln8LjEKufPqUaQuol5/bA dNE4cMIEGzyCSL1mvNruungc3tvdS8sNZAC6jMXDVozDopgz2i2kn9vvKrle thyHZZsuM5ak3xe70GP/fMehVt7G7bsvAxcp+Hdi9zicMJKJFiIWf31RRC5y HJaswBwNMk86TV2klyeMw/j8tB/byLy5qtO0dGfeOGhPwvEcTwakfukajhSP w7nwJTV5HgzEX05Gh8vHYZLdFJ7nzoCXjNXm7Efj4GRGBZ12I/WZrglqah2H JNabLDMnBo7fk49w/zUO1BPLPlVHBvh7ovd39Y2DsFjsy39bGGjuXJ4s9Jf8 /gYHTjGZp+nvrxf9pzAB2u9yBRtsyLwrPMfkOk9A1e9WH30z0k/bxrp0vSag 4aylcQOZ7+3yDoP3/CaAfdjvkjsw8PikpMDHyAnYb28sFE3OhwMxR5XETk+A roauV8xKBoZsIlxC307AnOCskkItBlqHN79B6yfhfsHbgLI5DKQpfF4YajcJ LqkT0ifJ+WZi7hmT6zoJivEPMgLEGMg9FaT2b9ck7KyIEaHI+bht6fF9D5In IUzrwG/VSRp+Btepr2ycBEtLZY2N5Lzt7DKI1dk8BcISJ4Mbamk4x6756OY8 BbSj6T1hct6vMzTXTvaagqib0n3G92goTrJr7gyZgipLe6nsShoCNIJ1CtOn 4FdIe6jiNRr6dhR9Vnk/BWvnz9TRTadhqE1uiazjX2jUiapJdKdBxYdnMN/j L8j0P6xb4krD5l8fDTV9/wI/vXzqkyMNpb0nzY0iie86SspspsFvXMTZM+sv FDR8fuFsSsM3auhgYfNf+FywIYCvRu4vli9frXT6B8nrVtrf6ORCesm+nc7O 0zBXrPb1AnK/2zrDsrHZcxq+mtgV9ntwQd1ZcqmD3zSYHphKu+fKhRrBqxO2 kdOw16X4tKkdFzpdX6duyJyGmPzRVFXEBRBTqVrTNA0f1q1S0VLiQlTFdoFT CwXQ3QrJnZfJ/VRdUmxjdLYAqlcVWn08uBVKBw4XJuUKoOXBRs2ePq2w7P3k 9Ll8AbT4yaxmHZdWgKz+inslAqhfT0Wm1LQVXBQ+z5t8IIAqwg8PWEq3QrJG YfvBFgF0LvrGL/rOD/gDFgeOKM1Aw5liP9/xW+B2aFxJWu4MNBUrtt1++3f4 uChzpt0pQST8vL+dkv8Cakc+aHqcF0LRDx6e+KHyEQxt2wxys4WR44mrX4Vw E/wITTRJTRFBh6Qa4mU31UOFoevcZxmi6OWdlsVLEh6ArFP912uJM1GBQKHo 6315AIxARl2EGNKX/a5hlX8Fn5f1n6sePQtZdO6My0M1OD5n17EVAeJoteKG Vwbjz/GlN+eep4XORkrzv228LP0WHwzOHFAKn4PKdEZWuGz+iHu8Nee5bp+L 5s9+fWLXwGd84m+3cKufBMIl0ZcXRX3H68JON1wPkEDLFN+X7z7yHQt3rEmJ CpZAW1UzR8pOfseHGtOl2HslkM0vXUGla99xaPZKVYtEsr7Uoqvwy3fsZBgP 1/MlkOmZJ+tCVrVg1Ui5fXu5EqhmPaf64VALvt+7tl/CTRKFR/mYV9i14pVp F5MbPCTRBhMn2cmtrbhCf3BRvLckMooNLl/t14qLwy+4j/pLIhUl25XX97Xi c/zeF9+jJNG6X1Mr9fJb8V7hU1evZUkijuC7ic9DrXi5Your2TtJ9OF6hHJe Shsue7hkdPKjJHq0fqnndFYb1vZKTK/+Iom++wYoOOa2YdU8vXpNriTarr5H pLu8DVOahw0k+yWR+V5tt3uf2jBfLnNmsCgLZZkaSu6V5OJPi1YxRmosJJN8 +/wLBy5ufxdkjtRZyKLK29/VlYuHDl65aqnJQsb3vfLbPbhY8pP4TltdFoqW BNc+Py5ed/RHj68BCwk9XnOlPpqL7/+KH023YKGk83NScrK5OLfotdjvHSyE 7E96vf7BxWVbBAN6/VhourHcrYHm4prpla8G/VloXthodm0HF39xvpw6FcRC CxvCei/2cTEltoeiIllItP9IocpfLk7wn6e4JpGFCvJOp5or0Nhfy0c/s4CF 1IWf0/1baKwsntkZWcRC7EeZtRxnGn/orrviUsxCo+OZ3sZuNDYpVZVWvsFC N1OVeJHbaCylz/CvVZH/G6ttfTeIxrUG3nW1T1jIUsJoMDSBxtLIy7GbZiGd epXVN27R+KXKSYnXP1lo6c3vUTaVNI6dgetvdrDQijxbn9/VNO6uUzaK7GIh qQttVqwHNMaWrcoCgyz00Gmuvt4zGgdYe3TKCLDR89fjE+e/0Pix09b9psps tNVcb8/iKRo/PyXTYKPCRsvVU0WC/9G48U2TtIsqG71PvBlaLMDgL1YWZcHq bKR3qfwNS4TBAysX09l6bPSSUj13ZS6DlTnTVmMmbHSMZfX1pRKD1bbcy5xh ykb5s33K7s5nsPbJPdw55mykUn3f/soCBq+Y2RmzcC0bSb/qEfVZxGAb3ttS 281slO26Q+KaLoP3fc6jSrzY6NnkHI1VRgyOk/Lwuu3NRtOFB8vfGzP46GZO 6WMfNtKvVhTyX8PgjPoTll92stFiTc5EPGLwtTsR0SKhbNSyt1h7nxWDy4b1 nrHC2aj9rR7TvZbBVfpdbMUINvrTHOjhtJ7BuMijZFk0G6n/3X1JyYbBn85a tXrFsdHc42mrdtsxuOWDgE5gPBt1JdYJVtkzmJF8ELU3gY2sAs+mjm5hcN8x fXZqEhvd4FT/9HdisHD0PIv76Wx032JOEmsrg5e7dBdLX2Gj+uAD/j4+DOY2 5G76m8dG8efX6lrtYHCKoeNwx1U2cpXZ6qLmy+Bf8o9W37nGRobGhzrf+zH4 wo+sJtdbbNQk38vwdzF47SbrCLMKNrqdp/nzdgCDR2oF5HSq2Ei5nr0hNJDB my4Hbp+6w0Zzvi+1bg5isKCP6WgOZqNVxrSMfwiDb34YO3/sMRvZFldYzQhl sLtFqUnoEzY6cqi1JYv49iJOkmk9G82Tr1hVHsZgnzONutov2MhJWerff+EM Zs2Mf0e9YqMYEVPN+8S7Onvl29+w0b+c+Ou39jBY1jUPN75lo546F8FFEQyu e+G8o/o9qX9pXO1pYsWSuhtHP7GRqaezj18kg18oRNuHfGGj5lfvrBuI96Ys 5jl/Y6Of1ivOLdrL4Le7zyGtVjbSjNnq/p74YOvGDjaXjUQFhz8siCL52iyU PEGz0R0HpZtBxJ/xXb2fP9loENf3VRAnLAn+8KqDjZbd454cIV56ZWF01W+S rxbnrKXRDG5lf1W81MVGL/qU/u0iTo5Pe5zYw0ZLP6m9vET837C5X3AfGzUU eo03Erf7jIs795P9OVt3gty3cfrHspswyEbiouaHlWIYvMZyh4PmMBsVRH/+ akLcXS03zhol+5sdlbWV+Kx606XxMWJTxao9xBZnE8wYPhvV7cArjhEPzjT6 /XKCjS6ou8ufIc6J7j9ROUX68c0f78vE1l1Xl1z8R/LXGDGnkJjv6tacIECh R1W9cuT5Axe8lNy3W5BCYxZOyeT5A9sbP1N2EqbQ8W0VHtnE0yX7npiIUkic EjqdRlyquMRfQ4xCw8nWiw8Su6R2zGGJU6h0YbrWTmKRfxfK+bMplLj1U5IN cUWwrRM9l0J3vqhZLyb2bBOZfCFJIV//I6GziGfbPsitYFMo898Enzyf4buP Qi2ypSikczurvZLYd6l61xEZCvHeei6PJ6byvqcGcSh06c72DmvioCNWn9co UMh1o/2ed2S/+MnvfisqUejPUNGtNOLEU+78SWUK7b+yPnYtcc6VcLn7qhRK PXL7bQnJh3bxX63zahTqkS7a4kx851aSUbQ6cYCe/z+Sr7c4Z+tKbQrVfHC2 AmL3eq0gGV0KXXmuwfpK8tn1purAyGIKrTPpDgwmFmx9ealiKYUc9Mq+niD5 Xj411qZnSKHq+6YZGaQ/HgnFD8w1plDI7LK+mcQ2s+fO6FtNoVf+vJYY0k87 5BeqliAKsWuvR9iS/juzavMOjXXk8w9lpDSQ/lRF3yJEN1BoT0jLEQXim2t9 EzusKaQ6vEwygPRzg9P+wvzNFLqmUsaMk/6fiCjqnO9MoYsJDYfbyXw4emDZ +D8XCknMcVCWJpZKeDir1Y1CT8962AKZJ7qZH7QvelLIWP5uZBKZP57l00Hz /CjUVuXzqsOL5PNu8kHeTgotabklN+TJ4KhHMmmfdpHv37xsetyD5LtJ5+bp 3SQ/ro/Tp8g8e9znPMiKpJD9rE8fG53JvBllZgzsJflbnPCzmsy/b1O7qaZo Ch27vO3EBUcGD81OWJ56gEJlx6qLnMi8VNO+FTkrgdRfMV7+wiYGJ/mJTczI pNCTygqtTRYkHy+UcmZlUSgoOGLRBzMGm+kuN2OfpdAN5dnj9qYMnhz0SFbJ ptCHlwFa5iYMDj5YKQ/5FHr5UPdBx38MdjztaXygkkJUrvUsA20GL+PtaTtS Tdb3+d7102SwhNvxIyfuUEg56pXVaXVS3/lVry48IPXISBLiqjJ4dcks93tP KDRllzbbSIHsT13VgbEPFOrSvvKWL076R+2lyr9mCqXHOVd/FSPnw7G2pyJf KHRP0Cy+WpTs70bxuTItFLIxVvnsIcjgWV+9Li1vp5B1zYZDYeM0HugXrw0d oZCBnLNdwS8aP1Tynu6WlkKuK9xfmz+kMaoOm2ySlUK9WglaFfdp/NQmnlc1 TwpJXF+hpXiXnM/78/sPKUqhRvxY5mcFjVu+drRRalKoxi+jevU1Gk9lBTwy Wi6F5ploX51/isbGEhGHk+2k0LUhSdni7eS+UZBwMGSLFApUyF6e6kVjszVZ MQ6OUqhnt8Ls3e403hB0O0zZVQoN9Un2zHeisdtLvnfFNikkVZWRYL+exvuO HjT7FiKFSgcqmnr0aHzv31Eh7TQpdL9nKnlkjIvTBhdk/pcuhYLu7N4uNMzF 29trVC1PSaHMmxEOc/u5WPzlkOm2M1KIXvsthfrNxe5ZnnFncqQQX25nCPOJ i//prPwreFMKtVxbI3S+mostXDvGvjdJIfFO0b5dIVz8ptK8O5UtjXr3t8rU F7fh+DVVHRlS0mjTpE9DNbmPrqxXo7NkpFFB/dPSbHJfzfkm8uWSnDRSmnaT 3Xi4De+e0fDsxgJpNNm+osbKpQ3P2Wxz5fVSabTE80jzWeE2vKHbwWWuvTRK 1bT4+MypFT9T8XueckoaFWbqHvhLt+CEO45XaHEZ1Dgp4NHR/BW7q7Z4bk2V QWt78xQCOZ/w5G19BZ2ZskihWV8lZs17fECoqzHrkCya9cvLcL53I5ZVM/Re JMBBoxd0Gp8qPcFRwU4j4jEcdP/pbc5RxyqsuHJHg/p+Djr4R3xzuXAVfvQ3 7KLZQQ7SQElBnyorsXhqqsW+wxw0LyOjRoKqxDklT093HeegdqMNPkZvyvHz zmUrGi5wkMvNkw3qJ8qwtI/k3sQaDtJNNDo35H0V39NW2nClloOaLpfYqOJ8 7DmkrfzwEQed+Rk9Za2Yj68dtno+8pSDtDVLpdM+XcHGlw/K7njNQan5v7UL snLw9h89t81aOagsaewCy/c0nlkwnuzJ5SC9Y/TUD+VMXBo002sfw0GRTwRO FHzJwGOTqjMrfnFQ20r5PevPpeFkeTfnBf0cxP0tG9fim4D1mZ06awY5yDM3 vF7/62H8sThy2mWYg5zzk1ZPnjuElQ0zitJ5HMTAsM48vwj8RCB3f+k4B8kq MpTh+WDs31C6uWGSgzI4aftW+e3Ac9LvL2z/y0Hxug6OPn4OuNy5gTc9zUEm Ts/q9rftqf0f65ZWTg== "]]}, {RGBColor[0, 0, 1], Thickness[Large], LineBox[CompressedData[" 1:eJwVmHc81d8fx7nIvNe618hIskpSGkblfaIkIiPKyArJCmWWb1qikJKolIyS aCkl5JQKlew9rvv5JDukNMzf5/eP6/n4rPd5vV/vc877LPc4YuNF4+Liek39 +f/vX/PAW1ZHYgyJmD58vO+MYaynuka9mgvIaDEPVht4wJfxft9EtUBwupT7 /ppBCEw+M07wV/sPRrMfH3I1OA2npX7KO6slwYC3ydlq/Svwudrsm63abTjP 19FxQTcbjtwJ+7hH7RHsqg7TLlhTBG8TEsos1CrAuE1FYY9wJfAtCeEf9q2H Wi1BfzfNJhjadVL0Z149qIQceBNp3gSfEhOk5/vrQbB1uCXGrwmqLzSnxGk3 gFTvVMW+gia4KDGek5HfADmpVfKqq5qBqbzi/ftbjXBom3WAskoLqG1L5GXF NgN9dqG1TqANpL+mCNzIbQYrr1v4oFobCJy7IbLsXTOsq+e6TBq3wUhNHnMl Vwuwx0+E3vqvDR5bVapsjWqBdSenJfh+toGe25/tXoGtUCB2Zt/p9nbYddL9 XLF9Oxxf65BwJKkTdC69Nck61g6vNh9tOHu/E+QzlwskXmkH7cN/ok5VdsJk BXHBs64d7GsLM9f+7oRrC+7JkiYd0G/Fd+ygcxf0R3vcDN7YCS+S1/3jU+mG mBMHn2oxuyHrrqfA9cwe8E14FyKr0w3TCYEF/i96YG/Gig18Vt2QJLe5WuVL D6iXf33Rc7EbfjawJIxmeqBu9mD5RZ4eINWOXV9j2wvyxz2rh6d6QPUjOVq+ 2AsvI7167zayISWSa7mScR/cM/RrXzrFhsUVHxJm9vXBNZ7gxksSfSD3e03G U/8+CEs88SHStg/+W59pWpzaB5uyUh5atPbBnsijtmIDfeDUz6mI8ufAi02f a7gQB5qqvm4uPsEBe72KLxa7OGCWP1AykcABiVbBo3E2HDAIHCvyfMiBFV2y oVWeHFj69889y3EOKDQ90/OM40CXsOgl5SACvtRaiCrWcsBmXFzkQAwB9bHL vFELBz41MOPTkglQPxL3Zk8PB0pTl54ReUpAK6PNaeMYB24sUwv//YOAHjux 9XLCBDiu3+r66SgJRGQIZ9cOAppYqIf3LAkV6tXOersJMPtr5ABXSVg+6mgn aUuAwWtT2+fPSchd7Z2R5EbA0p17d96eJsE24/uj61EEdDr6aYeEf4UdzNup sw8IuEDu9E+L/QoWZhkPLJ5Qz/uq5JenfoVd3UIuScUEZET2KvM//wqvidyL 3ZgAt/Q9UhmTX6FzIDo0t5kAcaXVtm8XvwIa1/vh20FAZZ5A8gCjH6wy/n1d 1kuAysu3guu0+iFyrYK83QABg63r5z8c7oftk4UOY38ISD8gZjAa0Q+9nj2i anMEmH4bCxOL64eQoGlZSy4SHvy6O+l4rx804zJlDwuQECgp0z9B9gPEvtn/ SZqEZTd/KbGm+iFW6AmEyZHQoNx4wID7G5xzfO8ktowEHZ0L7WeXfYN3l7ar iqqRMG0190nW+RskGHTc3rSehHsdHfzg9w0qyu7X224iwd6teLtn1De4IqYn 56pPQsmRwIpH6dT15oe/AUg4kcR5atz6DeiSF46sMiNBS+r1uE//N2j9z1et ZDcJ7FvXNZN+fgMHliC5fg8J6KHN3Q7xASh/VX9g2pYEntr36QGWA3BP/oL6 HWcSnttmtV45MAD/RQ2+u+VCgmd3tESJ/wCMiQXYxruRUDWyKYF2cQDy08O2 r/IkITxE8qP6jQHQfHM4u8+LBI2ZCT6L/AHQTj44dvoQCRcE80+mVQ9Ax6SI YYovCZsvnysvbxuAnc2vjLj8SRiT8fhHfKPi4fXRcgog4dYdw0380wPQnV05 lxNIgqWG3NHVvINAuxb7uOsICYuP/zy2lhyEM1dOb18MIuGJbstYmPIgtMmm lYqHkCC+M9H7LRoE3vb+HVzHSNieXw6a1oMQkxv68zvFEcJjMqnug+BxZM/e qlASCgPkphaCB+H66YhD8WEkcOrNPvucHoS6CtHVuuEkMHWicpuuDMLhm7uz 6ik2vZofvSVnECLUT1bZRFD6/+6wv/dsECKFxG6+ofjJfoG1Yu8Hgf9cjKJs JAn9pbqCUS2DEBLsa+VMsYzCIfJr/yCs2R6z9gLFu09eK7OYHoT1IokV2RTH EB+uvuQbgg1Hj83cpfi58XTAcqkheP9apz+F4qG7Kjsvqg2Bw+ee4/4Uywvs VZreNATrpe681abYyvfMP5edQ6DxrLK4l4rnbG1RU82+IbC3ztkfRnHJGrJA x2cInui/evCPGs9Ysvi5jIghiLK8WniIYqWfyGVJ/BDcEup1eUPpsdcuSDfo +hB8j9lbyUNx3MtMsa78ITByamlfR+lXLls/bFw6BCc7Le+YUfpOHl+ofPiJ 4oY6eUtqnlBha2VIdw9B1/1wyy1UfvajA6GnRocg48C5TaxgEhKyEyxHZ4eg IWp3WweV3ze85ep2IsOwKGegfZ7K/y/vUS4sPwyxI81GSpQ/ND4u7dLQGoZ2 uRKJXD8SkhMjE+YshiFPy3bcz4eE9xP3vbxdhkFU5e38Y28S/lp3GDYEDkNV 7mADm/Krm5Tuj5xLw/BWouvTHOXnqxHen+h3hsFeefnvUcrvNV2pOeFPhuHJ rNT4B6oe1mb+sjNvHIboMxKWBvupeuBW0S4mhuE7fV9Zix0J6QdtBZZNDYM4 s2bRgaonLo2i0imJEfhv7pWsqiVV/0+OLLuxdwTCmHODr41I4JXM/MvjNQKC u2Q8H1P1qxda1xgQOgJXLk80XNxCwh19rbPbro3AE4bXRT6q/oMqR4aG2kfg REHT+Jw6NY+qLK20GRqB8LVnnUxUSOiI3XWz/O8IKORf6YhSourb/L5Fsuwo pOseZN2VIUGsxatI12kU6ro9li7yU9e/bxvZ6zcKoRMaci94qPcvUVQOOT4K D27pSzgsEtCo13a58OYojIiV/fb4TcCVWybBy3tGQVrottr5rwSwDqmvFT4w RsWR28oqJcAkhsdHI2AM9C3oRUnPCQi73pe5I3oMZmJqe34+IqDtc5pozK0x OD5os+lMDjW/rhWY+NU7Bm5+QQ9fXKTWg5mhh2yX77C0vutK2H5q/ZD88G02 8DtUk/5BL60JiFqdpSB78jt0uJkIfTMjoNvFIdE28zuIbIXLS7ZS68G7j/41 fd/h3zJa1UElAhQTH2gWuY0DT6EdO/ErtS4q+eef85gA5dYjL3qdOJDAXp6V GDwBuuFrvA/acuB3Rnt6aswEeLfPmnaacaBG1jju7u0J2L2VqEnV54C/5NJD H7om4L431y0bKQ448XheOb1yEsYGuI2rrvfB3d/iVpVZk6Bs8oXX8AAbulrH zE3yJ2G1b+uxCFM2MIqrd356MgmbbGtSU9ezIeJoNDThSVil5705QpANZpND a8jeSVhx+ZgN8awXxocxnbb0B4w/WvNzL08v6PUGfN525Qf0rXpU5pDYDY9W hrB8bvwAm9w/ckuOdoNKWJhrUvYPmFUOgpT93SAmevJnV9EPiKsLM7Va0Q3D KFnuWPMPCO63fLH/ZRfcyC3yu8ecgv2dy0QrOjthzu+PsHDaFFyLmZUvFeiA tzMxu1tu/oQBvez/eqRawAfX1FScnoaLYokbBO9Xw/WDeUtZbn8g3nFnGa/q fdDaT/xe8PoHBunP31wfLMXsn3vq0K5ZOHjgl7pZYx1OkmtfEWQ9C1+L0yy1 ZeuxobFLZKbDLHD9d6Ny0q0eZ17xV1k4TN3/OHAX/2Q9dlsXH1V2YRYuTCz/ viW2AX8NrFTbVDsLaChsRCqzEQ8NbzipuWcO1k4oH7Z624zTxctbHPfNgZAw PH1FNmNTfeNVF1znQEr5laoIbwvOj7NuHToyB4bbiRk/kxbsqx6oeS95DmrG z2lJfmrB3z3z2pWa5mBLg/pHdm0rnuqTXStlNw8/edJNDuN2rHTwz4ZlB+YB LbxJV+5tx3sGWvQ1vOaBEHI9+3amHReOXTI2CJ2HtDKeu483dmDvf3z7XFLn wep8bvSuBx24S2Iq+l7rPMQJqp/Yl9SJ3+749HmT/QLUvEyJpm3rxpM1eQ3g sgDJT3DtOqdurLj7XKup9wKcCdjZYRTajaNsUJ9j2AKU6uk8FczvxhtcX0z9 d20BTklamquL9uD7Edmy1W0LcEntQFp8aw9OLog6tG/fIsA7UT8tMzZ24t5R 2+qyCPbbb6wmXNhYbZ/our3ei3BtVqA4/Cgbl9NyZ6xCF+HXk+DPuzPYeMjh S6JZyiL0FBaPXB1jYxBQer61fhF4mCU6Cef7sJDLiEx52yIE3I/Zd/BGH255 9jzagL0IO9XTJOUf9mFf1107db8vwue75YI6TX3Y3Ek/IJ2PCzWcc10Io3Nw eJEH15UVXOjBfImvuS0HO/dW61irc6ERBi0TO3GwkYCWl5gmF9otXM1S8eRg EZc/H5N0uFBuXeyD18c4OFswIeXiNi6kYHryik4qB9e5Faudc+VC2+5duynf zMFqogIWETe5EO/+qZIKIwIXTp66F5fJhcqCbLa93EVgnabZxfQcLqR3XVUv w4rAkDpR9KqAC5XK8tpouhB4v1y7zGwZF2pnpbkfiCDwBfV7/dE91PccFpOF 8gksJqhkmMThQlkFPXFVjwh8beR62u1+LhTLrjkR+JzAOQ8TzfAYF7pcYgqn MYHL14c+4ZrnQhIc/VMlLQQeh+0nzihwIyF9izbHWQIfW17RmrKcG2X/y33T vEjgGZqedq4qN5LSsjDX4yUxf5Um+V6LG7FDKrXei5BYabek6RJDbtTA+zJr QJ7E97QSs6SMuJFqxiGBciUSrxbln1Uz4Ua3RFaOnFAhsX7TzMOdltxopcYf +ltNEtvsJyXjXbiRbMMZLxt9EnfoOwdc9+BGAtCjc2YLiV3k2qryvbmR0vYW p0wgsR/7Y+SnQG5k/fRu0fUdJJ7Cxs1dIdxInyjtDDclcUTW69WjYdzosuGg 5TZzEp/1fNonfJIb0XIXpK5ZkVjIRFNf/gw3etnJObjclsTJ6nevrD7PjcZu 10yl2ZH41kj6DotL3IjP9fpnE0cSvwiKKUjK5EZLLv5RKvAg8YWyyecOOdwo a7NLfJAniV2XuFeo5HGjEP5ndSu8SSyQsa2x9BE3qhw9M2x7mMQ9A0+7zhVR zxt2lzX4kvjpOuV+qxfcaLlyu+dmfxI7VtP+DLzmRr8E9TZ2BZJ4jcRRrqK3 3Cg6kd+REURingNfBaM/UPm5a2W1NpjSJ89W0vQjNxpym5ZCISQunHonL/mF G7m/GS7cepTEMVs3qLEbuNGXovXiK4+R2C4uVzu/hRvFyIwa0UJJvKqZqX+s gxu9eKe/7SPFCwrnjKCHG3lEOgn/F0biJp9pcyEON5r6ceuOUjiJ85552bV+ 5UbznW5cTyk+sdDqcmeQG3GaWKu0I0hstcvEx2+UysdRpHCTYpWrL4I3TXCj +p1hnb8o/sdWO879kxuxml1ctkSSuG5l2tna39zIL+lZQTDF2cf4k9JmuNE4 tQW6SnEYDk/zWOBGH3YTt6n9JjYXGrqjRaMhYJ3fnkuxkt3+B3/5aGgwXaco meJfmTXP3gnS0BmVP4O+FNeM6L1OotPQ/Oy/bzoUZ2zMr3IQp6EdjiGFQ1Q8 QTGyDSosGhIPzt+cQPGOz/GdEzI0dNtnJkWB4qVSM2SpPA3ZuDYVZ1DjHXfz HTunREN7Dj/JEqS4sqBr2kqFhv5dUt3vSel17bfZopwGDXk1tnQWUnr6bisT GNSkoVfLjqp/pfSHBE2JIm0aCner3sZP8dByEVVTXRoKFubnyFD5K/c/sUZy M/X+mU6vJVR+L78c02Ub0tBfcl05cYTEBhZfzI6Z0JDDNG+fewCJGelb94IZ DdGX/nm4hPLPV/LhASFLGpJa7WxznfJXQkRS0B07GlpQ0Vked4jEbu8WIv0c aMjaPt+y34vEGxlHzmw6QEP9S+7sW0P5l52z51qtJw0R1r20BDcSF43jzDQf Goq2f3U/04XE5/XX5nv409CmAliX5UzitfVi5X+P0tDrXIOpgP0k5l166sO7 cBr6eaN5jb49iTs9f9QlHaehuZOu9lNUfZ2eaSRUztDQxzHnI2v2kLhFNYXf +goNCZZpidRtJ/EudRm9gGs0dDBUuq52G4krNG75xN+gobDgC/4vDEmcr5n3 8W02DX1RDbYw0yPxf+vKLuo8o6HDC86CoatI/FMHlVu+pCHjRi7Zz2ok9tnw Ycy3jPLHpxAVkRUkttWtt8h5R0OM1zpojxyJNbZ+FWW20JBwW6JQlxBV74Y+ aG0HDRndPBget4TEEuh70O4eGiq45c6nTCPxvNGfxrP9NJTot+e61D8CN5kK X53+RUONW+M2Lhkg8Im962XaWTxIXIJrPW85gX/YlZj+lOVBFjL7zQ69ILD3 vq2Rooo86IliZl/xEwJbO+7s2qnGg0bvHrnNuktgNTenjJJNPCjE7KQmJ4HA DX5nlG7s40Ft8sS7vP0E3hEgYP3CiQcFXP7CW2VN4NLAxFNNrjzojvZqvQYz At8NTiOFfHhQuWbKtftbCBwVXpB7PIIH9Yi4yvouI7DKmWaNA9d5ULHIute6 BAfvL+JZ532LB11omlsBnRycQKzXP5LFg5o8Z8rXN3LwNFzddSqfB01Exuf3 v+Hgqrm9vndf8aAVvDEB3pkcfDisreB7Jw9y/4eGf+zn4EeHO9f8t5QXJen7 W7NP9GEyXVD3vCIvsj9cl+rq04ela/QhWZkX9QmW1L627cMxajf2ZK/iRXy3 DgaKr+rD1l8dg6oMeJFPdICoTCsb/3Luecpw4kUfFcJfvVRhY32rvg2ZN3nR gqf0wsSDHlw+xPfdI5MXiVRmrxtK6cGGp1bfVcvhRdXWq3Len+jB24siWY8e 8KJiR+0bqyx7sCWT+bv8FS+qT/5t+3CiG3t0mL7saudFP3bkrs7W6sYX3Yr0 pZh8aJlte9hkaifuDTpnmJjAh+S3XJi9r9CGud68UchO5kOWZbZys/OtWEV0 bu7FVT4kHDakuIHdin0fhpRxMviQfuZTD6fbrfjvsKvehod8iK52v/u0QiuW OGig0/2FD/39e/ObnXQLNrWbUF0pugSZSvX7MWcacZG+A/3D5SXoZen8FUHB z1jKvrrz/jl+5Fy7dmVCcBEGkuty5TEB1H1ja7HBzadwXcqHrhYhiCQ3Soxt L/sMJfJW5uPHBdGDtjRZ4cXP0KGsF//ipCCal9vQUmxUCzLaAnw7zwuiuQy/ wZcfa+Hazvtzh64JopqdP80OtX2h+s2h0fzngmg3jF7UH6mHpC6fT1o/qPuJ RMWfc41w+vbh8xt9hag2jketvrWV6rO9xywDhZDx9+ARPN0KPDIHrX1ChJAp 08MzjdUGZy87y92MEkKrEzYO/NvbBrFn9zzmuiiEuCxk1eKb2iDed2P75wIh FKD+TP5pTTskb+JW9/guhH7Xagauu9MJVj/nLx7/IYSqP4yseF7eCeJPZiav TguhnpELG2Wp/uDKyl+l1fNCSNOocjhevAtS5ActtRjCiLHQK0Q71QXXaF/C /q4RRi1p9abrHLvhVl16VVKQMDql2Nz47FcPyL9CPKnHhBF77YO6JpFeyMgZ gpsRwqj5TVRCo0ov9b/eq7wYYXRlLosTsLcXrit3FLxJFkY7nioILSvqhdQw 6ctTT4TRLUZr4+5DbEhUvOZk/0MYvZortFxZ0gcigobpztPCKHjnsjTR2j5I +PmtxeOfMMoNmUhp6uuDizUbLY9wi6Bi7fiV4TwciA9pRXHiIujbROCO1ys5 cK6KqVa6TgR1cpng4RAORAemTCqEiKAt/c02//3hgFnlul52qAgamQi+eHeB AzJSDR8zI0VQ/+oXjuV8BDx/LZKz/JQIev2XnVUiScCISKydarIIWuY3JjW6 hoD9BRGlqx+JIJ4VBlPrPAhQW5TK+/5UBKkezD69x4eAXzbFKY+KRRCvXJ6x cyABl2Z++K99LYJOfdBFxlEEVO3yW7ahVgTVWpFnTC4TsGHowNnNIyLIboVb oEI5AbQtc0Fz30WQbNqGI5pvCWi4dOPA6x8i6LtOm5lGFQF+uu2b4J8ICjK3 ODleT0B2rNWwkQAddYgZOxaSBAR1jbfyiNDRAH3Ho7WDBBiuSax8L0pH07+c S3JGCehs/XjTRJqOGD6Pe+1+ESCmamxppkZHUpMP/w7zksCOIAyEV9HR3vOv 4r4KkFBYe1K9VouO7utaPfosQsLOY+VclhvpiO0rU3CIScJ/7zY+s95OR2M6 1/jqlEnYLd2SKWFKR5NL+Hs2q5Eg6xeS0GxOvc+vUDN9JQnPJR572dnSkfvD Byvl15Iw6q4h4+BBR7deVu6y3kKCo3+3pp83HfFd1BIIAhJqwpIg2peO9K3t 6FFGJNy9+Ms7K4SOzoyrsPeYksC8lhf1LIyOtE1W58iZk3D6jmPShyjqe9cf ZzVZkOBa/KZ4+DQdqeaMGdJsSajDRz/OxtJR143K9ig7ErZ8UuulX6SjOimL 2+x9VLx9Cbw6KXQUv6I8/5AzCc0CDrZROdTzde1HT3qSYCQpcighj442PTm1 3tqbhCcKOOp2AR2lfHtDZ/iQkKijml35jI601uoI7fIjYW5LR3HLSzpaz3yl Ue1Pgu/Oix8HyujI5Pt/jmsDKT2df0wKvaej5NCwH++CSHjhncurUENHR0TL bMeDSVAJ3iejXUtHXOGe73iOknDluNDqbQ10JJKuC7zHSOCOfQ22LXS0sFK8 aoLioOQgW68OOlJ4+s3+/+eh7BsrDoX30NGXk28nz4dR+bnbFhXPoaOMlzVX NoSTUPY4PulmPx0ZmOluqaV4VemW7IdDdOQ04zZmGUFC+vuJYjxGR1HOT7PL KV5Sn/2xcZKOYtoLXFiRJIR22vV+/UXpfXd0mcP/z0e/CvyY/ktH5s0rBs5T bDNexiswT0enjZY9zaL4zd9AmaXcDCR1/03MPYq1eZRXr+ZjoN2JNLtrFN+m t4KhIANd2vNHi9rfgohMnK0VnYE8lD4K61Icpbz5kIc4A63hKx0fpOIZXj0e dYzFQNNtK9rPULxfNyspVpaBxrdFfBCiuGrb3ux0BQaifUClJ6jxbdjN/+LB cgba+FTxRSelR4596cdyVQYa1Pj8ajnFEu4BvXUrGUhwmXTVXkq/GD+lHxwt BlppP9odQuk7HtrM+3MdAwW5ms4dp/JxICZWhm8TA0VdN9EICiGh9oL+amkD BpLTlnLfQ+XPIHUMVhoyEI/UYp4slV/pBzaHLEwYqP/mM68jASTEPuc77mrG QN8ZsX0zlF9+VZQkBVsy0I/wkwHBviQ0Niu+SLVnoFdbZmqXHSIBsRs/5jky 0LoYlL3Pi4RHQ2d7X7kw0PuzuilRB0m4OD/Cy/ZmIOlHVQ2nXEkwDb5a88CX gVanaDy8cIAE3m9bE8IDGahl7zvnU05U/dYmS4qHMdB6wQ9b9Sj/B93cpLz9 HAOFfGkyrqXqR0uU800snoG6N+77bUzV18jp+PzeBAZ6/WBVUj5Vfwd9e9aG X2WggQzFCENjEuz1T8ODHAZS4X9/6pIuCZIPNXnC8xgooaT2QdgGEhqUWquM CxioelNxvfk6EnYJaFj2FjGQ+fq3sm9WUfXY/sVZrJKByMBRoUZ5EpRDZaPC OAxkVsATnTZPQN9Q5Vbjfmo8cWI8bv8IyHD25xYbovwzHYalpglgbcdx+RMM xMp0GLMcI0BA0iutZ4GBuH4lXh7pJGD8yZPnRgqiSLhnSK75KQEFKo4RostF UTd7eNWpQgJ80nm29KiIouo1+8oV8gggTtq/C10tigJP9hxXziCgxXKu8f5m UaTrvpzf6RwBpWM7JxiOooj1+T/bxL0EbErKuFBzQBSdPKGeZWJJQJH2D9XT 7qLoGDsycmInAfkhN5ynfUQRH78ZKbqZgPS/Yx+7w0URudZkW4ISAWG8V3Lv p4oilyrpLxFDHFgv3+Ng1CiKqgx/L7H258Cj12unZ1tEUeHv1WcFPDmwyvVc cnGHKOpa2uz7xIkDytlrqjU4oij7qMHVRjMOSGic2iA6IYom23bpO2pw4K9s Cn/gEjFUt8ldSuZtH7Sp6pEGKmKoO9k+4sBFNvQ3+hsjNTEUYrzc1zyUDVPR Wbk7NMSQ89kMJO3KBtE2oUNWq8XQqVnDRVMdNpjG9o56bRBDeE/pWen2Xigd OD2dvF0M1Zqt0Qtf2guZeV8EBj3FUNjBVtH5uG7wWXlQO+WuGBrmu6QWKtwB ikIpQ6F5YuieSDbXi4l2aB6pzNqfL4YWA4PP9TW3g2GhMlPxIcVOg7NjN9tB Upv8e/+5GJJOSrj+a1U7VGxwr6x4J4Y4pSc+121vAyZytRshxJB7n6BkqE8L vLV3Or5NURzJLJ4qng1tgPX7R/KZWeIIMuR8ss6Ug/8Zk/atchKIf2NX6vqw OzjOW2CGO0UCtbwsLBL5+gG/VnBfHGFKol8p7lXPmpsxKg6erZeSRB3fDw6k TTXj97tP/3kuI4kemHzw8hFvwbXHcyb+k5dEFd1BgnWWLbin81ufhIokkvXb kX6/pgXPpfq+MVgviRb5hZ/HlLTizYxjpy5YS6I0xYZlk+fbccXds9FHbCWR 0Mqr02q57dhoa2rkXjtJ9MzPLs7kTTs2838RrOggiZ7EbQqDv+3Y8dNf9yI3 SXTL0jqEdagDR8VGG3UdkUSeh95qG6BO/GohlmdVkiTSmrate9jXhZN+LE/R Tabi6789zpnpwh795co7rkii2bWq5C9WNxb6NLXN7ZokusMkPlSYd2PnVJeY a7cl0VTkT/n24m68oLlpnvZYErWE0Q4vnqH6BYdvv7vrJdHQjaWr3PnZWGZ3 TOxwoyS65tBBHlNk4zFDOak/zZLIP2F3nddGNk5Vsd4o0UGNJySime3BxgMT 5UdNOZLIOSa9dFU5G8fHXp18PimJAlXfZkpS/U/dM+ORRHEmUt4m+hxsOPj0 1uffLksy0UTngTgHJw7eVK1CpLKYaOQpv6q7Jwff7uLruCXLRLbGOy/ph3Fw AHfNh4fLmUhkjpBgXOdgkT27s76sYyLDkg2hW7s5+E1HeUbjeiZyT9Haof2V g495aKW3bmQigyt6JoxRDu4JZVzq1Wei5RrxJSkzHFyQ0XDi+zYmioDPAWUy BDYb2bufbkPFt2ygN4zqLxeOfrAV38tEuzU3NOpS/WfR/MY9LHsmujK6+eg3 FwIvFZc2UXBkIp+nX+4u8SfwsG7nei0PJsroXTLjeo7AcecOiFqEMFFZmZ2l z3MCbxGtE7I+xkT2IQzO5CsCT6YbLrELYyKs++CZFybwvsJl885RTNQjZyPA /ET1w83EiP9pJvpdk1d5mk3gD0reVQlXmIjUVLmdw0Nipb5G2cCrTHQ+VSc2 l5/EUbe2Buy5xkStv6d/pQiTeO1SFlPiBhPJKfntM5QkcYbke/e0LCZyjg7+ +GY5if80ahdH5DDR5TuSMRtVSWyTfFPA8S4TbV/77k66BokF6Ecfy+czkZOs geQqbRIfW6I8n/WEiYxO1HtGbiZx/ftEqzNFlD7rH0m6G5J41Zl/OZ7Pmajg xEam7jYScxYbzNRLKH0irRYfmpB4c8WW2wKlTBTind5vuYvE107c/zFcxkTI 5YcY25zEu/+dTC/EVLx4dkO1FYnzXo6OJr5lorMfR9T/fz5JC9sHR94xEY+a 9/7DdiQumVozsK6aib47Gxx+70BilbHe9S/rmKgT8sXuupP45INd59MbmGhm qKk46CCJu3yKuyKbmEhboTRulReJk78lnNrSxkTpOcuf+viQeDTnb4tCBxPl H4rm+X6YxCYenhqLndT1WxbRrn4knmNvrn/by0TvI94QjEAS77uVp5zTx0QP xmo+mh8hcZGTZNhZgolMQ8RbwoJITF968qPXVyay0otYvBRMYp+OEfmd35ho Gx4zSwsh8btr9kEag0zk13WkOOEoiRXtKt8JDjPR4BNJw6BjJI6UXCM9OsJE pypmv24LJXFL43Xf2jEq3y3O97jDSKydzFfxcJzy49Los48pvmAZLH5pkom2 iD6PNg8n8TeRXs+gKSZ6E+d7uZVi9Nm0xPoXEyUUL8UWESS+Gf9ceP1vJqqW t1rynOLfO5VcmX+ZqPx2nrdAJImtlyQUTf+j4g2t7zOjuPD9H772WSZaXH8+ +DjF/GcOOpTMM1FxTabcDYo9ttUXXl9kIq/js73UfhC/XjTgOs7NQkHjiSXU fhHLVNyzdeZhoSxF54ILFB89IZG3lY+FVh888cL9/+ehBv/NKPKzUGqAVJca xSv/DVtwCbJQ3K6DUl1UfGdf2mURQiyU5/zQ7zjFaxvN40ZFWKj/yMWLXBR3 j2w7Ms1gIStNmTtB1HhjefXsF8VYSDXhT/5nSh8dxTVbBSVZKDL+W744xb26 KiqSLBZyl3xxx4jSN856qbCCNAvxS9hdcqH03+AnNqUmy0IpnlVhXlR++s4u 6Vwrx0J0jur+fVT+LtyewwYKLCRpmbdhA5XfTSVT97YvY6ETftfoc5QfEkbZ x/avYCFeV8/S3QEk1uNrdfJQZSFFd5vLrZSfvip+NvJXZyG5Q7W+u3xJbGDz UixGk4W2zMSvnvIm8YDfwz/xWiw0IZAho0759fK5HHaKNgtZLm1n7KT8PFRy qTBvPXW/qL+yqSuJU5rOpTzdSOl11nb7ygMkNhw7HlWmy0JVS09GTjuSOHWZ j2n9ZhYKVX2vvsee8oO+i3bnVhaqH1p5r4eqrzGbvVJfgYW6Pf2N7KxJbBSL +n8bs9CfGVUO/24ST47JxCjuZiEL9s8lRxE1nywRPaRhyUKH/yl9cthK4p1K fJY6VizkvavxvaYBiW/b/pAz2ctC++ytj1xeT2Lz0o8vA5xZSEKWyetJzTe/ m/HtcBfqe8P/vudS81H29+Jzp9xYKPjrrzWNCiT+q5Rtm+rJQnY2z6pHWSS+ dz5qotyfhRo3b2xZyUfNV1lBbVWBLJR7kvb7AxeJ50u9XzcEsdCUg8NVizkC 7x23udh/jIUS+eWclv0kMLedprpINAvtVDS/+6WPwM7KPS5OiSz05fElOcdi Aj8K+nLL6BILLXoVnhB/Qt2PK3pWXqb88OjN7pcPCHzPKcvx71UWyr6ksqcu k5q/r3rbp2aw0OUzf0NXxRP4LP8Pi/oCFuIzemBxh1ov2uzIhBcPWai3RMpo mw2BV+Y2f771mIWeuN2jNZoTuA692OX/jIU2KbVwvzYksEzU8R2CZSzU4XD3 cfUKAheO8W01/sRCflG3Sx+OcPCCwZ/jq2qp8XKKUg2p9c06fqhUvI6F1JxX FVRQ699v1c96nEYWYm1WzEmo5WDkmrwhupOF5kvKb7o95FDzx9LVL4dYSP8y 8+KEHwfPvtCW0+SXQu/kpzSqX/XhNRm/PwgISqHdnwwCN+X1YbdTr4MGhKRQ zl/V6PNX+/B7c/OqLIYUaoi1g/rAPpzA8Q6WkZJCcjdP7PmzvA/LC92u5lOV QgHWJ+pfnWbjLQdEjnGMpNDChbCUS2t6caBRs2LFdikU0frttbNML76jfuPj TRMp9CCatoJB68W8U+rL9plJoZcLcVMKrT24Ntb40xdrKUTvCub+FdmDnZ9E KZW5SaEe81jBxIpufIJnuDb1PymkGCa8X3xDF14wNhDOiJFCUkZ6+71kuvCp sxd3ZZ+WQn/yq5ZkzHXiWL41VY9ipRCPtuDY0/ed+BL/UVydJIWET1ntOmPb ibOF55/+uy2F/hnM7+rw68AfJcXTDmAppDfYlr8urg1Lqei7q3JJo58X2MMb wptweKD9L6FIadS/Z/TQEpX3WH6TZ43acWk08/jYtYjWd/jNfHCGUbQ0sjy3 Ma0p9h0WSkzcHnVKGhUEzSfBcCW+XfD+6nC8NPIY3N7N//AtrhrS2VhzQxpl 71J4tdu9AjMPioadK5dGzsfv25y3e45frVIwy6qQRivP5Oe1P3uGXaZWKb5+ I40wh/NHVOIZvn/KpOrXe2mkrfzj9ua6p3jznWgpzy/SaG2V9LaVFx9hj97R F0ZsaSRx9p7EtHsu5r/774ILRxrpf5IMt5TPwYX+/K5RpDSymwy5lNyWhX/P KvMXDUij6jSJ5Q9Sb+MLSx33LZ+QRtcLJa+wvK5ibfKQ5tYf0qjMxvz0g47L uCU/dHH/T2kEjAV32/QkrKh/OS/5jzTi6zt6ZMDrLH7HlXm88J80cnFJkxO9 /h/2qSncUzMrjS7FGwqv9j6GRZJLV/TPU/EfCtB38/bET/fV/FlclEZi9h8q j/edqfgfmLBKUA== "]]}, {GrayLevel[0], Thickness[Large], LineBox[CompressedData[" 1:eJwVl3k8lN8Xx8cuy4xtxhJCQkhRIdG52YpUEtEiu3yFpFIpkijKFpEiSkUK FUrZrn2ZKUuISnayzyCSLL/n98/M6/167uvezznnc859HnnnM1Zu7CQSqYT4 +f//wj6fR5ZngnflB/fgKz3nym66Kqs0KZ2EP64KajV6Vvjz1KBnlJIPuElI DkXpOWNWvlGkl1IQTFdTxnbq+eEQ2qz0CaVoqH2xP3bHjhDMqDMfOqyUCoNf chQPb4/DZx77NxxUyoW+u02kxg3puCIysni/UhmQjjma/v71FpeNffvEn1UG e797dJdp5eGSvcrdDWoYAlkDta6Befg4uxPpqUQ5KK1LVkIi+dim7J/COtkK +JR55rKiXgE219b0EN9YBQG9hu2yIe/xVqWUGR6og8hy4fnyqSKs1W74zz24 Do7ljVS0bC3GW0JHOWor6sCEtE7r1aVirNGvTQ01rofv/90vesdWglVSW3RI 5g1gEvTrvqRwKZam8QQuWDOgMsepM1URYy5uP55RzyYQ+ZUg5hRVgUfMrlFm M5tA7xrP/GBWBaZHRYovDzYBLCgJmdVW4LrbrfHhm5vB48xdkbcrFfiOyNTT lKxmkHRrsV70rsRiCuurqx+1AOnTXS9D0yqstDuKk3qzFYLVKY+2d1Vj8YF4 3ofPWuF9DrPV7nc15g17KLCuqhX8ZIqzbQRq8Fh9pthGUht8sau/8mNnDX5t WaloENAG9kuy60Qe1GBdxz/Gbj7tkHXbJ4xkUYvNrjmFvTvSAYMyH93i4+qw VkyF6ZPzHSClE4c0ntdh6TR53qi4DpjMVb2dWliHWWV9t10bO4DrSErlyo86 nLjiFCtq2gnhZk92f1Sox4OBzslnt3+Dp5fLvs1k1uPGqMoT9oe/gbD8d5+W wnr84ZGCrNnZb3DAoXs8pK4e3yntfyyX8w0Ov/NkPzlcj7WWnTOaFL/DHqdy b5Z8Aw6+6vJ2k9gPWMo6hNxiG7BnZJWfpNYP2Mq7L8LxUQO2Tlm/jcvyB8jw vHZRf9mAlUsG3nfd+QGNPL8Ntlc14MZ/LiV3OLpAl9Mmm2e2AX/grw68KN8F X98qPL2x0oDT1yqCC3TBSidZtGkNHV/YOVihd6ULQqvm2lvX0bH0Fde60Zku UNzrsOOuGR1z36kObxf6CZ4lVLOww3TMeqhoXqHxE9z/ZNXusafjqqLBT0me P6EWiiN0fOnYc9H1y57+n7AS99/rsng6tuarid9K6oYX6iHZCil0bCC1wWad bDeoBkZLWj+jYyG9oY75o92QmxtXL1tAx4WX3X4+b+mG8MD3Gy1b6Dhj1+kO qZlu4F7KOJ/TSceJHGdbYkR6YMvMa4XGHjr2j7pac/lwDygkUMWOTtKxu1UI njrXA6Y+uuSqWTo+Ih7+0eVeD3wNIH1j/qVj7SfxOfvbewj9TofucjGwkvuD zMq5Hriqt/kDFz8D30loal7L3wvmhWuc9YUY+MqxdnqsWi/crHj1mynJwLP6 nXsYO3thjC71wEuWgU+v+1HNZdEL2i7Df14qMPDxwd6yAK9eQJx7HbxUGfhL 7cDOd1d74Tz36gbmJgY2zxr+wIzsBb4h6/VbNRm48s7odtVHvaB7TV5HdxsD 6/lM5Lnm9IJ7TeTuFW0GzrNkbk4r7YWVQfL6sB0MrLp1Jvvb516gnfct+bST gdOpcxvFunshJYU+1WbAwFILfzIOTPWC8Z5byY+AgeO+L66PWOmFXhOnZ0q7 GZivdPlxFbkPMgJdx88YMnBIGkl2RbYPOoWmrC4bMfDidY5k3c19oB6eXWpo zMB+rtwS56APGv+lkT8RPGa6JiHnYB/Q9KU2Uk0Y2HmjgMiIQx+8+FvGkiH4 Oz8lRsG3DxInb5gNE+utpoQF7IP74DHprbgPwfRmsYj7sX2Q6tcL74jzDPPF ub887gNpttWMYkJPUYLUDYG3fTAsaKF1ndCrdUmGtKeiD1jVR+u4EAO/PCYX eL2FON9Q0MJsFwMrGKxfLO7rgxPvUzP26TPww3VKF+en+6A78kGpgB4Di7Bv /L2FvR8sYrouRuow8O1BtbOnRfpBmu9hCZ3IN3udxtRzhX4wZ9meqyPqEZCl ebpXqx/KV5g3QjQYeObOthEpo36w64n5+o+op6ePjpvN4X7w3/fx8FZlBj62 1cCBfq4fROqsz3YRfvhCRV2cof3wsOHM4H4pot4LhkfhXj94BbsrB1KJ+pbu PVxQ0A/Dv37UiBF+y0vb1zxV3Q/uu7PmrxJ+VA05sH9jez8c6WU+SV+lY6k9 1ntS5/pBv1CDpkT4OW6jbXUn1wDwmq4rvDFBx3wCx3aL0gbAkTMgJHWIjheb HXaGaw9AuK+ABX8HHX87dnqz30WCk6oz8Hs6vt2/x+v+zQFgx1Zfk3PpWM9T MaskYQDILgaHDTLoOOXyTwWeggF4bJm/2nSPjh2TDtJSWAOw96N1sdYZOhaW Uz9csToA255qTOi40XFlJm/sMHkQ5nepc7Mfp2PFwoo1mpsGodHKvn7QhI5/ tW9drvlvEEKXntkOSNBxkr2Q3vilQRAK/PGELEjHe4cm/IXCB+HYx4jrKyQ6 fvn7OetYxiC0yXt0qY00YB9RiUFm/yAY5ocKlOQ34DnLJbrkiSEglX+89woa cEZnJw+cHoJaGRkf6S0N+IjjO2PXgCEIeVR26pAcMf/O+JTlJg2B78G0TB5S A74a3fvWqH0I8orbfjwrqcccn6qTvA8Mg575HEeaaj0uOPykPc5+GBY1uoUt xeux649AkQ9ew9DJrk+u4ajHtWPakex3hoF8WLVpkbgPbq/Juna/bhjy+AM9 EyLqsPCeKPcK9Aukf7x+detbLTbOKgG1Q7/A2Yny+WZ5Lb7EPyGR4PQLLFR7 LkJmLe5tMmd4hPwCdf3nV36eq8Vv7Hi3CFX/giJF3c+f1tRiS88bf0/uGYGx yGS7IJUaHPop70u97Qi8FGwfk+CvwR80+l9peYzAM9eLl7wnq7HcLDrJHTEC ftGWr43fVmPWlZXKHPoIlGnaVWRvr8axUZcjl/aPgi/uPuajWYWrmS/c3E+O QmpT/K5cShVeONS5q9lnFFRNHk++mKzEjjSd6acxo3AiNmKq8UUl3pL222Zf yyhc+hRn07O2Eje/ObPuofUYxNXwFcnPlWOhNrc8nePjYFxaP3RttASjyd1j 1qfHIQk2fridWIJ9uWUV/K6MQ2eZkj3VqAS36H69m508Dnbys6yXD4tx3CPT s/JdBL9JV/hpVISpp5S38NtPQOTsqcnooEIstTiS031yEpr/izvRlvgWr5fz ygpzZoJceHvZnYi7OLJb/knUWSb0KouvStbH4PmUjqSEYCagzlJn2YBIXC9p FP48lQmPKyd2aLeHYS9RqVM135lQ7lT9uKHJFx/ncI0L2ciC8pyxS09WQuD5 vLBl5RMWOHK4mTgspoPuT2/G7rhpUF/4IJOd/wEqFoMt2pJnYYEqer33TSN4 4Pr6spA50Esis7jSO+GBS6YU1fEPvOjvUHSZ7YVNdn3zK25/oSbHOa6xcghS RGDljvdfUNhXUDXaOgR8n1O4JC/8BTU5Q+nlwSEY2W0ntjX0Lzg//LrMzzMM z9SaNE+l/4U4O/20evNhkFot8Wrq/gt1Isb7c5uHgTsjqT/NdhHuxPTN5bf/ gguO86PqDosgzjHdnzf0CwalrKc/ui9ChJlMR+bcL6iIoZDaLiyC7Pj+uHPU Ebh6+aYM771FuPZEIDTWegRmLM7b+TYvgt2m3eMtzSPQPXuwEZn9A9HSz79J FaMQvbZjve+hf9AS8Hjke/Mo7DI6eTnt6D9IkXeuzOgdhbQ4L8WV//4BOtne IUoaA0fNiIDi2/9AW17w5O5dYzDgU6mk/ekfuH08mtJZOAYjo9uuqR1cgpQw uae+aYRvhEvajtkugfuP3rtOOeOwd4eR6m2HJQhB06u7i8chK/xQ+8iZJWj9 VSnU8nUcPJV91DJil8D8VCaPkuAETLpmdsh9WQI3nuSYZP8JmOmR3EKzWYba TVUOevqTIOfyZ9s6+2XY7iNLqdwzCQeH23aouC2DB62vTOfwJGRPxBjpXViG 6sSOvon/JsH9L5ftyYRl2C/wMvxq4iR8F5kJzGhfhmTVkyqKE5PAm9gU8vrn MgS9eV8ZOj8JOpI5tz4MLQMfd4P3F9IU3FvncZc+twwpbJdKtlGn4IB697Mp 6gpcfWqWLWowBRUmdIb2kRXwUSTd1YiYAlZ9ZjOcXIGLBq8eHI2bAlmLsPa9 7isQZOLW5ps8BQFWqOeY/wpUcda/dMmZgm0O72eCElfASira82jzFLy4lC5Z 93UFeH8FTVwWYcLXf9dkm7tXwK+yYMVJiglc1+zXfxteAeUIG//tCkxwDpPY ND5PrNc3cEvVZIJ0XDSiiK9CX8/9af+DTIh9FXDK1nYVskdNbujeYsJxNpNP 7SdXgdMpVd8xiglKthRNa/dVEFgM/u9CPBNK2J8tWl5YBdYW58VTaUwYOfo5 yjx+FX5dtuTwfs+E/Nf3Z+ofrsLDvxYuq8VMCOJytt2TvgrNC7bTQRVMEHs7 L2f8dhXeFS1dMPnEBOCVKzBoWoU2q3s7mL1M4Ds5JlHydRUKeHLkx4aY0JZf EKjXvQovFNXmW8aY4OlgtkdnchUO2GYZe/xmwr7jO7yTuEjIOejlAVsOFlzM cybFrSehG6flmj6LsuDEzzqtQ8okpEdy/fGGygJD3k1uQmok5KBJUbgtzgKB k38aorVIyEOh3HLdWhakr4mMv7ObhLKembW1yrMgfNt0jbkJCX13PWjtsZ4F 3g5HFtaYkdD5TV9nZxRZoPtOzj7ckoRUPkSFjimzoNHxnVKYAwkF+Abdc97E goI7UkeNXUio2mTTh0wNFjx4f+0OxykSelh+rb9/MwtcBcxZ131ISGuLAezU YoG5zmuF3X4k9CCh9bTdVhZsdhazIfmT0KFw1/jT21iwWNj9MSiQhJw0VerP abOgt99owuA6CYVW1Dd56LCgRjBLdjmUOC8J6g7rsiDW5dyNK5EkdPnerwB+ PRb4R3e+04sloQiHBs1Ogo9/NBj5G09Co9X9nx/uZIEShXf/pWQSKvh9+RWb AQuyWdczwtNIaKz1j00+wVpf/q0mPSWhUwY2wkd3seBD/oWjWZkkVCLr/32G YEhg5n18ReiXMM8NBhbU+v8nQH9NQn9DPkWwIxZY2A24fc8n4j3L6XmJ4C87 7PFYIQlxvue06CfYbm2HxL9iEkr6Na6OdrOge8nSj7+chHxdBtfEEezaTWes rSYhcyvF3g6Cx7DxBvV6Elp6NZktbMiCs0/KgvQ/kdDOndHeQPBCiG6nRTMJ HXvisM6J4CDXPE37NmL90TrsTzCnqfod704SKirTtggm+LZyxmBgFxE/n1pl IMFCa+R2RfeSkNLJTevOEJw49uB+6iAJdVZ8cbQmWPqT6HTuCAklq5aEbiL4 aU6UOZ4goedXE8MXCX2qMTzPmlhEfqOlPIsJfuN7fbnnNwm5aAgq+xKsbfXv CGuBhCzloVSC4JKtF96QlknIUTVK9R2RD0Mqc40wGxv6zt/rZUJw/byHizwX G8q5rR7SQOT3QGd/ieYaNhR49pzHboLbP54gXqXZUFJ8hUwOUY8TyV/PWAmz obGmzY8FCO6/atngTCX2Ex2YdCDqOQXGV2/IsKGQipGBPqL+5+XL2uPl2VD6 qYpwIYIX2XU3P9vAhu7Fj09rEX7hqVXrr97Ehpwlavn+76/ozOc72zXZ0IZo +0JLwn9iEesShrazodv1YgqGhD/lLET3cu9iQ6VHtNVJhH8zNkU9oRkS+v+M 1H8i/K5O4fmnZMqGJJf2yUZpsmDHl8WcPQfYkHnFjqkRol+s7PpFI04SegOW 2QWJe7xzxwnvB85s6JuOsslFot9Orv1am+XOhiKnT+u0b2DB6e6Gy3QfNhTH M6jipcCCUNe3PfzX2FDBYqQqN9HffKZqO6RvsCFONZ1OQUmiP5Sfx6nfYkPH Uv23rCHmwaOxJJP9MWwouPFH93cRFrz3DX4VnUbkZ2hZZWwN4Y9iVsHRp2yI cWzrm0IeFjhwO5UpZrIhFc84/wAuFvCm7G4pymVDp+TCy3tILDhWx/5nuJQN aV+ajbOaYsKKTJghdLGh0JjBVN8qJnzxmNvH10vocRTNyi9lQma+m037ABuK PTeq01fIBEszU4/T42wol/Hm179XTEg/zxN9f5EN1f789GYzMY9NGBHfmBLs yHFt8+Y4eyZI0Rb7i6TZUeDFHOWgI0yYcvScCJNjR3hlT6k1Me8T581X16qw o1772/QKRMxveYENe3XYkZCA9utk4r6IvBTt+9iGHdGX5KYs+6egbUM8z6E4 dsSf+jyo49AUmClL6HonEuu/d5bs2zMFZSqPPCIesiMO87oTmfpTkKWW2VCR zo6mFhc7xZSnIEiz+I5WPjsambXybFicBBWDAYpYGzvad/19cOqjSbhqvVWi g8qBPBdHVFRbJmDa5sPeWUkO1DxzK+9+1QS42xpcpshyoPLXyrcm303AoWN7 vu9R4kDG76W2Wz2cACXH4ykftDnQ8L01T0nOE9B8+obcQ1sO5FiKhBcnxkHx RquK/QMOdHaMciNjegzs8jg03R9xoIRuTd/AvjGI7Nu648wTDlRZNlO5q2UM 5uCe2fUsDmR79WJt8JsxqF2y9nz+kQNZlB+5yeEzBv/5f301+Y0D7brvrU0e GoXc/75pBElxonvzCdIxVSOww7JnW1oyJ7JuPz+nazIMJSNck85pnOjTjcCz VzSHYdd19edKTznR944N8rkyw2Ccd5ma+5ITNabbWA7ODcEBMbH5ko+cqFhl p2vC8yFw7txb+L2DE8W8PQU09iG445i3gybGhS7TTvv8fj0AP33DdkVFcqEp hYuyx/p7IW/HUcGau9zoAP98W6xbG9CO1H17EcaDcj/dyJ7JLQboJ92tPM+L ZjaoNfz0KsIPaB6CSpfWoIdi62mMyTYckvrfre2efGjb8baabVm92PC4+8QB Hz5E1jzlm1TZizkkXA55+PEh14LXjMkfvTj07om1yQF8SLx3N/Im9+GboQdf k+7woXXhPR0lfn04wnN7B+MVH3qZez4zUrcfx2qzKTtP8iEvn+dGTh8GsOXs 8p0r03yIpb3mTGvTABZ+s8i6N8eHUq/fr9/2a4D4Pv5dVLfMh/5EmRdVUwdx vPSvA5vI/OjD+5hwcb9BnMj+2X9Bgx9JTzNjLikP4UeNSbXRvvyoKfUr5WXo MJb+iDgSzvOjEfXTGVceDOOUpyOQfIkfWfd39ejlDuPkS7ofM4P50ZFxn6Xr HcP4gULnq/JYfnTzKIeK5sZfOMFf/O7MG37k2uY6yNXwC0fJJh4/Mk2sP8Be Kr84ggXW7Eo6McePbGwfPbotMIojZ4fanP/yo5dSdgd6ZEfxnfrtB86wCaDF z6TxfUajOMKvHYULCyDagOOTLXdGcVitmFKRpgCKe/utTlp8DAf6xLNk/ASQ 6OJnb9V149i8UvNn9wUBdDv3GH1o0ziWoDU3pF0WQOW+a/dG64/jglKBp/LX BZC6cVJoxtFxPCZw02ZDLLH/aoHIbNw4tnt1qUg9VwBxX4wzmmObwNtG7EN3 jgkgpVmfU6daJjC7/pLv0qQAGjaxcyj8OYGbYx7al04LINk2qxuzoxP4tE6H NvwVQPaiZtu3sE/i9JuWo4a8guhc56OoIs1JLLTB6IC5kiDKZmt8JRg1iced VCSOOgsidYMsys1tU/iY1w+10+6CCC48b1eAKVzvHw2BnoJoxQEFZJpN4ed3 frs/8RNEa8VlzTxOTmGHd+XvRkME0Ujmf6fqbk7hVt6jhwOeCqK9whdM/3yZ woaiAqciMwWR3NV1MZSuKfxGBgekvhJED7lLPShDUzhKa0N6Zb4gMlWuLauZ n8J7Tkyz+KoF0e0PancEJJm4+HVEdPKgIKql+6Wt2jGxapF+es6IINKu3msW 48jESdXMd3hCECm6yB3k9mDiC99sfg78FkSFh5ddX/oz8WYOBXV1LjIyEVq6 TI9j4lTBdti1howWAVfde8DEAhLhhy0Fyei59Qk708dMPKo+FXCeSkZTfP8d d8hh4qdHihpKNpCRtrdcmkctE4s4ef9s3EhGwZZ2VO9PTBx8Wm66dxMZzQwG MOy+MLF98E0JLm0yMrTrmx36ycTiL61O7Tcloy88++U7Zpn4zvIYZ7c7Gf27 ft3ytiAL7z17r/6lJxmlN/NWPaawMOeQQeRFHzJiO3fzdLYwCwd9ihUV9icj 9TJvh6dUFvZN1lYwDiOj0bt6XRQZFt5E6R0SiiCjyIJgnmZZFh4Licj6GUlG pbjqdJgcC7t4dm25eI+M9ln79zWtZ+EjO0Lg5VMyUhgViR/YyMKiOWocFzPJ SIw39P5+NRZulmuvNXpFRv0Gh75nq7OwGa/KgZ95ZHTWykl232YW5r7aIvzy PRmV6HvJ397CwpXMgHb/IjKSs3JxL9NkYf2OzyeEKskoNU+giHsbC/81vyj3 s4aMYtJb6FLbWfh9mdxgVgMZaXC+kFfUZuHNGedOG7WQ0XsslkHTZeEJSZnN Qu1k1LiB9+sqwS+iame6OskoSqTOsnsHCytckAzw7yX0vqhTu7KThXtGKg2M Bol6Rr2J3qHPwiknvNiERojnZ/N3TxJs10yt6Rono2yhnaaJBixMNcbhWUwy GvcofrRtFwt/KfSw8J8lo543b83qCY5WExEy+kNG1+2e7TsELLwvrbiV8o+M XnGvf95EMK+o2/2uFTLiu19ra4RYuOYm+XgWOwVxSmi6ZRMcslgo689NQffr BZv4drPwLh+nfkM+CtKgCd8/SfC/Pr4MCpmCzjxcKMsk+INNwX9dwhREkryz d5jg8w32m7KoFIQCk7ZLGbKwpgHP9AVJClru+HvLiOCpN28KDGUoSMr+7m5n gl8pHrtEkaegbU7mrsT7MfZI4tDvUqQgPVvJmWsEKwrkrL5QoaClz/8mggju u3ak6oI6BeV5Lxw5R3Dq7OpNwy0UFDQnq2VP8LFTWeaUbRT0XTc8WJ9g8R9W 5C4dChKSOWJMvK/jtgNLLS92UtCDxPxrPwi9dyufJ1wACvLPaNuWTPAB7YNH DY0o6LbtvJslwXwvF6Qpeyior/gk9R+RnzqZ9N4f5hQ0O3rCJJng0Lv7nr04 QEHdf/cubCEYcc2dumBFQUnsoVtKiHwXTexhko9R0CmjJL18oj7a0Sm36+0p 6Mv+jTQFgvM2T28IcaIg3hiJ0ZtEfbP8Hp6Y86AgOt/HIC2i/opizD+5XoTe CCvTy4RfHr8zivfwJfJVKUV5r8fCSQsTDT8uUhCHlXOuMOEvsYe73RKuUFBk Gv/tLYT/Yncmkg5eo6D6KJ2zJjosfCsIdCpvUlDy+hqvQ4Sf/Tnjnr1IoKB3 65HbDNEPM8+HwfkBBRUoHhitIPrFZ8/OH2sfUdD2r4IxtzRY2O32oHDMMwp6 mnN43xzRb9ZCOtcu5FNQbUDC92NKRP+9vSO1uZCCRgru4R+KLGxxuPfdSBFx ns7lbiuif40TIyaOV1LQ0danX9cT/b1VuuuoYQsFSZhL8B+SZOHc0i1z/9qI /T6nS4aKs7CqQ1jsu04KGlQyvppDzA+FdI06lV4K8uQI2DdAzBcRlevbKEwK WhOx+dyPNYT/G9qb6mcoaKX0/Y0KHqJ+p1VPh8wT+TcM5EzlYmG23NYnc8tE /VR93fTYWHhBMp7Hh1sILXX9J8XOYuL3ngbt5rxCKDgihqI9zsTni3+lK/MJ IbbXLvK2w0zMOqG/q09QCGlIWhU5djHxr7Sh89ZUISRK2pYWV8fEXzfo9usp CqGQL302lx4y8WCLlxFSEkLLNn4yq/FMPBP45JmJihD6bynHyDeKiSlf+U5Z qgsh3ajuTuFgJt578+e42zYh1D/y0OWwKxMXDYfMxRoLoamy9SrfVZi4Pq7w SKKpEDqR+HS3gDxx3q6JwuS9hF7VmgsbiftmNtEmIMNCCF1ipjpsWMPE6ntU VouthVBtRtUDxZEpnJb5mfeXqxD6xxHwa1/6FM49zO454S6EtBZyn29/MIVL VrUZ0x5CKI62sJ8/dgp32j6OWvISQqOK2vEBgVNYhPeciMgFIfR4we+sp+0U DvWQkDYIE0I/BNUqknmmsMdGl83xz4WQ1C3BCy+PTmJZvviRC5lCyLV2sGzm wCRuHat8YpclhM6/tVBUM57Eu7IVxGRzhFDuTuELXhqTWHRz/8KLAiFkWcu6 r0Xc/2XbnCrLqoTQu9MLRzozJrAYcrAZ6xNCXe+f1/waHMcVR45f2S0rjH4Z Mver6Yzh2jhqvYWcMJLW4BDMVx7DnxqbxOwUhFFQ/KV96hJjuNPUONdHSRi9 /O2aMLswilnam/qSNYQR3xnWrY6Po1hWfNV0fpcw0nj3zIV7xygO6EgXeeUg jPQnZWSiN43grXZjWWJPhNHB/msJHbND2OuGaYfBWhG05uXvHT6+fTjcnXeR LV4EpfBTFqn3v+FSGafVMTFRdDUn50Xm/ib8ceUmh2q0KJKOuC87qVuCo6fl 43ViRZGHyozd/exi7DxYomASJ4qyPwitvS9XjPnoM7sdE0VR+MT+gw/WFOET CSeDE1NF0cIvT57CnkK8oqa9zP5aFMWeHrhAT8nHxkeH5n80iSLHrAfXEooz sIRF8M3RFlHEcl8Ih6LneGLXWtqfVlHka2K6tuDjM5ygeGi7SCexX6hCEKk4 HQ8zS87t7RVF6DTHcFD0Ixxx8x6rgEXw/PGIM9KRuDHfaCxKWAyRGKS9fLYx EGJQMHRXlOCIK2FtZ+6Cdp1iXwJVDLEqs9r+04qH1O9cnY8kxVDsJd0bjnmJ 4M1WX5MjL4aaNfuSjjx6BAIHLZ581hRDjnFbMiVinoP5mLWdoJUY6joil5q2 5S2snKs5LGwthoJ59i3ox7+FvOXtB6lHiOe1wjed5t6ClLC4qcwxMaRSbCID H/JgVOfb1k3OYui8ZdkNY90CCA+zp+z3E0MCXLL39eULoUbOvTYyTgxdEjpD Uk4oAbmeFkmfe2JoIZHkk9JfAgGPDLwPJhLMocGZvrkUtkhRxUQeiqHI7a85 7etLIUW02un+EzGkOFM5FvW7DM5zKyw/eSOGHgpkMbqSy6GpOsryRp4Yqvw+ fZ+Cy0H1xt+nrgWEHtlr5mv6y6F3tdlc+YMYEvOoW3dIuQIs/l5LyiZcXXlu qXbL6wpQnPi5tbBRDLUF7yhTKKiEay/NbiU1i6HHn2IyS1or4bvHu++Xv4ih Y/eO3paerYTYocjr+l+J/E6T+TQ0q2Cpe2dTxU8xFPSy93Hiyypoa3ng+WlC DDWGll85H1cNoYU2T/r4qIjzSv5vBe1a2NKyL3xcgIpOKusVnrWshR9ju8/M kamo3+rOUoBnLWjJahisEaWi32xTf0se1UJPKPe3LWupKNLotP4KqQ70rAqF gtWo6ETu9xm/ojoYPp3zJ2ITFd2+pS/u0VwHd8OedsdvpiLu2xfvig/XwciH mOzMrVQUkFYZ/lyoHhLWeext2klFAt5v0gKd64E1IREsa0FFpLnsELm/9ZDC TTmlcoCKXrA7jBTzNcAeOa4DWpaEvls+X4SlGyD18PRaU2sqUnQt2jdp0AD7 ihoKvU9QkfGQV4xLUAPMt+LUiyepyLFvrqU1qgHSJ9+FXXekIiFdvS8rKQ2w IJd+OMGVitS3Ht8cVtQAGbcCmCVeVFTPdfOU9UwDWD3x/VrrQ0W0gIXHyasN sFzkXtrsS0VLClIjjwToYD1ldWfwPBWNpQs3tm6gA5uNmrJAIBX5NS1YcdvQ IdtHnky7RkXI9f4hZUc62IWLz627Tui1MKvmOE2H3GKOqq1hxH7KH4F5jQ4n FLpOHo+ioozhBe24DOK57+dHhjFUlGjBU/g3l9gfl3VtvEtF81KzAxsK6ZBx /MmxhXtUZPXs0NVPtXRYyIp70JNIRR/kXDj3NNJh38KNztokKppyjPG72U4H 1j33IwkpVKSRZG1gPUAHwwHbhKupVDThkv6hf5QOCZpmbS6Pqcju3HlbbRYd 9BrVrLSeUZG22xhsWqJDpLTMXckMKjK9f+RlMxsDejzJzaQXVPQyuOPyDh4G hPJM7296Rfih7FrkcWEGfLXpj3yfQ0UjCsEzYjQGbHzWynj0morOa+7huCfF gKsz1Xxhb6nIc2GouVOWAY3ovZlXPhV5qb32HlBggFxMZvjhd1QUwq8zka/E gHM/k+r0Col6HDzsYK7KAImAKyZriqloMG74TMMWBnjWe4WySqjI1+fgtryt DCilnazqKKOivVpbdjppM0DI7SA7Lif85/0s6asuA5zz0e6MSioqiOZ1EtnJ gAI2reCoaipSof99IWbAAB7L9fh8LRWlr9qE/dzFgGOpYivH64l40nbyeyMG ZE9wGRjRiXzErbGs2s2AFb0/V1Q/EftLOvzXa8iAQxEjRcKNVJTyYa13tRED nnV8+7vQRNRH3OHsGWMGzG9g6Pa2EP0xEh7ZR/De8yUX61qpSKRet13KhAHJ lTnvc9up6JLyAee1BE8Jpc0ldFCJ+37EfIBYjxxitwV+I/o3yi3Dj+C4nOvn XH9Qkf4t18gG4ryhf355+35SEW9OpdgIoUfX3HVaq4fot7YU20ZC7+0kmy1S fVQk/fuA91Uinq5h0zNsA1T0bM15nxki3s3bdXNHBqko9M/QuS1EPkJubJxs Gibi8yhN1Cby1dYipV44QkVBbw6xOHcwQElO4HTqGBU15+g+TCbyfdlnOSts gooeZpnmLhL1+FQyNeI1RUWputGmCpoMkOXvVbZmEf2y1jFQRIMBvkdb3HfO UNFV2X3eDKK+VZmVzxV+UxH971rN/coM8DB+vn76D5FP1tfHr9YxoCgu0bnz LxHPdPSN8LUMEOy79QT/oyLXQ/WZGuIMyAv0XBe9SkWPWcuKHYIM+Pd+81o1 HhqyjAkVTlmgg0bKfA3vGhp6UbydbXCGDo7XS32H+WgodGm95sIEHar37at9 QqYhbteEyrBewv+97mclaDR0hP/PZ90aOpTVbJKeF6ehXX+29w6VEv318ndt qyQNfY3ilXJ8T8yHCyHSMTI0JGCkdLWE6GdpvtQ6rg00pJp32EIijA4HmK5+ A0o0xOouH9e8SofgNjWZChUa8ssvyZQ8R4fB1I9+V9Vp6EDZj9nDxPzI3tou M7uVhn6Ti+0v6tJB317gfK8hDX2/prMpsacBfAxbZcuMaajo3sX2x60N8Fj5 YUOyKQ1JTQhlX6lrAM4Z5XW25jTkwPP9THpuA3y6aUT/fIiG5ubfbPoQ0AAn 3gTIFTvSUGyvCI8iMW+jE3YzkpxpqJU/19bwXz2UB/D6+7vS0Keke2u3TtSD okkiQ9ODhi47GyZEfq6HiW9v/V+coaGNnS9C1kfXw1WO0U8JQTS0lbvQn4On HlaM9PhTgol8bjmm/W22Dq6H3jFLD6GhtCD93Vd76+Aml0Zt7k0aUrOi8Kl9 rIMYnnO4LpqG7tvOaGh61EE6//Lbv6k01L5TiU4urYUGUeH79piGwpbCv8Yb 1YCFtXO7SwURz+XSkauqNdB4L1/Us4qGnkWaGesJ18AX6pFY/zoa0lu/u1ar uxq6xJMjYppoiC3ubIS8fzWw1m64WtFDQy63nI6qpVYBTXGH0waSOJoOuMvz vLkC0IOwP7zs4mg/o3E1rqAC/iN/iZrgEEfcbGofnZIqoGTBsyifRxzVvXc1 SXeoAOfPKaKGFHGUbKqV8W6iHHL9SbUnZcVRA7cHjw1bOZg21Kkm6YujdEqZ xbRaCVz0OfKb77I4Iv9Y9+HmTD5Ia7vWK10RRxfPdv+EjHwoXz6bYhgoji7Q +ysaj+YDX1SUccB1cbTL8j8n3/I8SH1VfW80Qhz1xsPh9jtvoXZEa3v9Q3E0 MfAyy08nF8RcKP5hJeIo8ixNUNrsGXxUlTF/UiaObrhlske9eAonZ1RlS8vF 0cjPvbOtPE/hxXXT2t/V4mibtPbG0ZonsPNxIM31szhqHdljmxOcCs4/x98b dosj/2tHbn87eQ94nv+9fbJXHBkLmk6XScZDthePQ0C/ONouMxR/pe0uzP9T 4MkbFkevF/ia+OKj4bbUMVt5pjiyOiv07IBrKGzuP6VmMC2OJLgVDTZ0Xoe2 rAurdrPiSPnyuVuv7geB7I67mbF/xJFK0O+8ArfzUEVKu5L9VxxlPLZQHEry AY/67IP1/8RR1L+p5HXuriAQW7R+cFkcdT25KWPvbg1vbev/rK6Ko36bmsor Ped2/Q9AIDLU "]]}}, AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], Axes->True, AxesOrigin->{0, 0}, GridLines->{{1, 2, 3, 4, 5}, {1, -1}}, PlotRange->{{0, 6}, {-1.016235299777192, 1.0162356354812077`}}, PlotRangeClipping->True, PlotRangePadding->{ Scaled[0.02], Scaled[0.02]}]], "Output", CellChangeTimes->{{3.529239460491*^9, 3.529239516986*^9}, 3.529239590651*^9, 3.529239636676*^9, 3.529404117014744*^9, 3.529404555894627*^9}] }, Open ]], Cell[BoxData[""], "Input", CellChangeTimes->{{3.529238993116*^9, 3.529238994483*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"Animate", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"Plot", "[", RowBox[{ RowBox[{"{", RowBox[{ FractionBox[ RowBox[{ RowBox[{"Sin", "[", RowBox[{ RowBox[{"k", "[", "2", "]"}], " ", "x"}], "]"}], RowBox[{"Cos", "[", RowBox[{ RowBox[{"\[Omega]", "[", "2", "]"}], " ", "t"}], "]"}]}], SqrtBox["3"]], ",", FractionBox[ RowBox[{ RowBox[{"Sin", "[", RowBox[{ RowBox[{"k", "[", "4", "]"}], " ", "x"}], "]"}], RowBox[{"Cos", "[", RowBox[{ RowBox[{"\[Omega]", "[", "4", "]"}], " ", "t"}], "]"}]}], SqrtBox["3"]], ",", RowBox[{ FractionBox[ RowBox[{ RowBox[{"Sin", "[", RowBox[{ RowBox[{"k", "[", "2", "]"}], " ", "x"}], "]"}], RowBox[{"Cos", "[", RowBox[{ RowBox[{"\[Omega]", "[", "2", "]"}], " ", "t"}], "]"}]}], SqrtBox["3"]], "-", FractionBox[ RowBox[{ RowBox[{"Sin", "[", RowBox[{ RowBox[{"k", "[", "4", "]"}], " ", "x"}], "]"}], RowBox[{"Cos", "[", RowBox[{ RowBox[{"\[Omega]", "[", "4", "]"}], " ", "t"}], "]"}]}], SqrtBox["3"]]}]}], "}"}], ",", " ", RowBox[{"{", RowBox[{"x", ",", "0", ",", "L"}], "}"}], ",", " ", RowBox[{"PlotStyle", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"Thick", ",", " ", "Red"}], "}"}], ",", RowBox[{"{", RowBox[{"Thick", ",", " ", "Blue"}], "}"}], ",", " ", RowBox[{"{", RowBox[{"Thick", ",", " ", "Black"}], "}"}]}], "}"}]}], ",", RowBox[{"GridLines", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "2", ",", "3", ",", "4", ",", "5"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", RowBox[{"-", "1"}]}], "}"}]}], "}"}]}], ",", RowBox[{"PlotRange", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", "1"}], "}"}]}]}], "]"}], "\[IndentingNewLine]", ",", RowBox[{"{", RowBox[{"t", ",", "0", ",", " ", FractionBox[ RowBox[{"2", "\[Pi]"}], RowBox[{"\[Omega]", "[", "1", "]"}]]}], "}"}]}], "]"}], "\[IndentingNewLine]"}]], "Input", CellChangeTimes->{{3.529239673718*^9, 3.529239789487*^9}, {3.529239848528*^9, 3.5292398562799997`*^9}, {3.529239965576*^9, 3.5292399678*^9}, { 3.529240209843*^9, 3.529240236251*^9}, {3.529271447063386*^9, 3.529271447631443*^9}, {3.5294041256616087`*^9, 3.5294041494779897`*^9}}], Cell[BoxData[ TagBox[ StyleBox[ DynamicModuleBox[{$CellContext`t$$ = 4.5599097544421365`, Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{ Hold[$CellContext`t$$], 0, ((2 2^Rational[1, 2])/(-1 + 3^Rational[1, 2])) Pi}}, Typeset`size$$ = {540., {164., 173.}}, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = True, $CellContext`t$2384$$ = 0}, DynamicBox[Manipulate`ManipulateBoxes[ 1, StandardForm, "Variables" :> {$CellContext`t$$ = 0}, "ControllerVariables" :> { Hold[$CellContext`t$$, $CellContext`t$2384$$, 0]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> Plot[{Sin[$CellContext`k[2] $CellContext`x] ( Cos[$CellContext`\[Omega][2] $CellContext`t$$]/3^Rational[1, 2]), Sin[$CellContext`k[4] $CellContext`x] ( Cos[$CellContext`\[Omega][4] $CellContext`t$$]/3^Rational[1, 2]), Sin[$CellContext`k[2] $CellContext`x] ( Cos[$CellContext`\[Omega][2] $CellContext`t$$]/3^Rational[1, 2]) - Sin[$CellContext`k[4] $CellContext`x] ( Cos[$CellContext`\[Omega][4] $CellContext`t$$]/3^ Rational[1, 2])}, {$CellContext`x, 0, $CellContext`L}, PlotStyle -> {{Thick, Red}, {Thick, Blue}, {Thick, Black}}, GridLines -> {{1, 2, 3, 4, 5}, {1, -1}}, PlotRange -> {-1, 1}], "Specifications" :> {{$CellContext`t$$, 0, ((2 2^Rational[1, 2])/(-1 + 3^Rational[1, 2])) Pi, AppearanceElements -> { "ProgressSlider", "PlayPauseButton", "FasterSlowerButtons", "DirectionButton"}}}, "Options" :> { ControlType -> Animator, AppearanceElements -> None, DefaultBaseStyle -> "Animate", DefaultLabelStyle -> "AnimateLabel", SynchronousUpdating -> True, ShrinkingDelay -> 10.}, "DefaultOptions" :> {}], ImageSizeCache->{610., {221., 228.}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, SynchronousInitialization->True, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Animate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]], "Output", CellChangeTimes->{ 3.529404151348177*^9, {3.529404575573595*^9, 3.5294045960706444`*^9}}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"ListPlot", "[", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{ FractionBox[ RowBox[{"Sin", "[", RowBox[{ RowBox[{"k", "[", "2", "]"}], " ", "x"}], "]"}], SqrtBox["3"]], "-", FractionBox[ RowBox[{"Sin", "[", RowBox[{ RowBox[{"k", "[", "4", "]"}], " ", "x"}], "]"}], SqrtBox["3"]]}], ",", RowBox[{"{", RowBox[{"x", ",", "5"}], "}"}]}], "]"}], ",", RowBox[{"PlotMarkers", "\[Rule]", RowBox[{"{", RowBox[{"Automatic", ",", "Medium"}], "}"}]}], ",", " ", RowBox[{"PlotStyle", "\[Rule]", "Black"}]}], "]"}]], "Input", CellChangeTimes->{{3.5292400939110003`*^9, 3.5292401636070004`*^9}}], Cell[BoxData[ GraphicsBox[ GraphicsComplexBox[{{1., 0.}, {2., 1.}, {3., 0.}, {4., -1.}, {5., 0.}, {1., 0.}, {2., 1.}, {3., 0.}, {4., -1.}, {5., 0.}}, { {GrayLevel[0], InsetBox[ StyleBox["\<\"\[FilledCircle]\"\>", StripOnInput->False, FontSize->Medium], 6], InsetBox[ StyleBox["\<\"\[FilledCircle]\"\>", StripOnInput->False, FontSize->Medium], 7], InsetBox[ StyleBox["\<\"\[FilledCircle]\"\>", StripOnInput->False, FontSize->Medium], 8], InsetBox[ StyleBox["\<\"\[FilledCircle]\"\>", StripOnInput->False, FontSize->Medium], 9], InsetBox[ StyleBox["\<\"\[FilledCircle]\"\>", StripOnInput->False, FontSize->Medium], 10]}, {}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], Axes->True, AxesOrigin->{0, 0}, PlotRange->{{0, 5.}, {-1., 1.}}, PlotRangeClipping->True, PlotRangePadding->{ Scaled[0.02], Scaled[0.02]}]], "Output", CellChangeTimes->{3.52924016429*^9, 3.529404160871129*^9}] }, Open ]], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"ContPlot", "[", "t_", "]"}], ":=", RowBox[{"Plot", "[", RowBox[{ RowBox[{"{", RowBox[{ FractionBox[ RowBox[{ RowBox[{"Sin", "[", RowBox[{ RowBox[{"k", "[", "2", "]"}], " ", "x"}], "]"}], RowBox[{"Cos", "[", RowBox[{ RowBox[{"\[Omega]", "[", "2", "]"}], " ", "t"}], "]"}]}], SqrtBox["3"]], ",", FractionBox[ RowBox[{ RowBox[{"Sin", "[", RowBox[{ RowBox[{"k", "[", "4", "]"}], " ", "x"}], "]"}], RowBox[{"Cos", "[", RowBox[{ RowBox[{"\[Omega]", "[", "4", "]"}], " ", "t"}], "]"}]}], SqrtBox["3"]], ",", RowBox[{ FractionBox[ RowBox[{ RowBox[{"Sin", "[", RowBox[{ RowBox[{"k", "[", "2", "]"}], " ", "x"}], "]"}], RowBox[{"Cos", "[", RowBox[{ RowBox[{"\[Omega]", "[", "2", "]"}], " ", "t"}], "]"}]}], SqrtBox["3"]], "-", FractionBox[ RowBox[{ RowBox[{"Sin", "[", RowBox[{ RowBox[{"k", "[", "4", "]"}], " ", "x"}], "]"}], RowBox[{"Cos", "[", RowBox[{ RowBox[{"\[Omega]", "[", "4", "]"}], " ", "t"}], "]"}]}], SqrtBox["3"]]}]}], "}"}], ",", " ", RowBox[{"{", RowBox[{"x", ",", "0", ",", "L"}], "}"}], ",", " ", RowBox[{"PlotStyle", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"Thick", ",", " ", "Red"}], "}"}], ",", RowBox[{"{", RowBox[{"Thick", ",", " ", "Blue"}], "}"}], ",", " ", RowBox[{"{", RowBox[{"Thick", ",", " ", "Black"}], "}"}]}], "}"}]}], ",", RowBox[{"GridLines", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "2", ",", "3", ",", "4", ",", "5"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", RowBox[{"-", "1"}]}], "}"}]}], "}"}]}], ",", RowBox[{"PlotRange", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", "1"}], "}"}]}]}], "]"}]}], ";"}]], "Input", CellChangeTimes->{{3.529410137987*^9, 3.529410151303*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"ContPlot", "[", "0", "]"}]], "Input", CellChangeTimes->{{3.5294101573859997`*^9, 3.529410160683*^9}}], Cell[BoxData[ GraphicsBox[{{}, {}, {RGBColor[1, 0, 0], Thickness[Large], LineBox[CompressedData[" 1:eJwV13c81d8fB3BZScW9H+NmJsmOhvqG8j5mgwrZGUkkZEVokSgJkbQURUik rKac0qBSWprifj5RZrZ7jfI7v7/u4/l43HPH+7ze73M+C7aH2PsKCggI3Jwh IPD/V7518CXbkDgTycNteH/bHpOjOzQ0m9Q9wXBUJPuFkT28/tMekKoeDHai S67mGm2HgUrzlCD1Q9ARt7kj3igc4mWHFd3V00B0EUQ7GsXDq/oNHVvUc0B7 lWBqneEpCLm898Vm9TIon1LyTPovDx6npDzYqF4LR+27hov1KkBENHxmV0AT HI048MTrRR2sj/VOrHb6DJT5eIV18iu4E+P7o+BdKzQZLZoT/e0dfHUL1A+P +glWLV+dz040A3ttqt9j9Bv2PRqsXr3/K7A++lb8t7UHrJO2GOc0twDqM+12 COwB4ZNrk17QLRAqqqwavr8Hck5ove7ta4F3qz5llGb3wCFXw6UKoj/g1CWr sAUtPTDPP1OYs/IHyOzUWDLboxd8bf70Hzv9A+QnOm+0evbBI6EMiVXWrbBQ Jag4cXs/1NkN3VLNbYOU1gVXUsP6QX/FjqnEa20wdvHzuay4fhB/ROfQ5W3Q IGeeVJDTD0ekh9sOP22DICn5nc++9cOLBwel/LraYKvQjlPxWgOwOGdH0Y95 XCgYY9vWXRmAtcM1YxaeXPjW3GttVTwAH8wb+mK2c0Giun7ty1sD8CpioO+6 Hxei9xyE93gAGgePi8wI4cKGgU495scAOMbejTwYy4U/XXiuoPwgKM38vf92 LhdW/dj9yvTUIEQapHmr/uBCmVa4jP+FQfDNz/VVp7mgtnevV1reIMSC7cVF HVxgScYOf6sYhPf9Qpdk+rjQhdIVIj4MAjvIoPHBFBcuXK0ILJQegth6g+75 CjRMBfJmzz47BIEmM8rBgYbwu5OOS3OH4JxhTn+RMw2dwgKXnYuGINxqIcze SsPHS2IGV+8MwdWJ2XOfeNNwo0nOfc2XIWjcWLmeF0yD5/LVpSFyw1C2vTky LImGxxNxNh+zh2GQzvIqvEPWy4WPheQPQ9TCRfVwn4Zfq3wuzy4ZBgu/sBcf a2iYE2U5YnZ/GB6GVGQPPqbBaXjWxfIvw1Coq+c79oqG7p5TPWkyI1Bp7SWo 20Z+v3hClrbSCKyt2vTqEE2DpHYkPFcbAe0RWPT6Jw0G/s6Zf5ePgFd623H3 Thpi2xWMg+xHIJnnKGo1SIP0j6vJ60+OwNSyD3bmggyoT2UZdJwhiy+WdG4S ZsBQ4VhrXM4I9M9rn+kkyoCn665ld2+MgOmJPT+cxBkobl78Tb1xBHbJmXxW pRgweXNbS3jWKHw5XXXhpwoDtn1FH3JZo3C3sOBgkSoDPnPOHzSeNwplp0Jp PzUGkjbsfxeuMQpHPL5qfdFg4MNziKEtR0FoUr4iQY8Bf9zQUBs/Cihd21LE mIFxQ5aqQfIouE3RZ2JWM5Bc5by/OGMUdt5TS+9aw0BJ8a/Fpy+PgkX4n6ga xMCfTOHMXbXk/fzVUnpWDMRK2PS2PhsFm+eDZ2PXMsA6nmnp8HoUWkMyHjeu Y2DpIVW+ScsoFLx1EHSzZiDCH3lIT4yCk82hpciWAZGfx24fnzEGDv/JNAfb MXDGo0lyWmwMpkdXKZy3Z+COvWddF2cMvl6fncZ1YGBi9QENvGIMZnm7ihq7 MhDHvju4K2wMCs1axJS9GWCnTG9oix4DH/eVt0W3M5AnuvaqQ9wYHJLQEuwh fjLZ7AQnxyCwdDqicAcDor+GH0jfGIPlHo8ede5k4Ow2Y5nkqjF4FqPuUebP gOb3+ODpB2Nw/b+TZ0J2MbD+LXtB98sx8N1b3tYewEDKff2juJO8vzDs+YXd DCitiGozGBgDOTVlqzXBDJTdrF11nUfWL93n/Z246erGntOiPHjjWBIgHsrA tvlZFuISPNi9cpVLNvHA+ZZLsTI8iDBu52qEMUCdDLQNUOOB6ivpJ8vDGcif VVncpsODlXGuipXEBgkTgo7LeZBTtoalt4cBp5jj1WDGg1670HrZCAZ+D7+V qF7Pg9P2x5ITiKOD5/lr2/FArf3N7z7i8z5F8jLbeGDnkhJaGclAkPW8Ol1/ HmQb5K7h7CX5W358l0UocW5nSyQxS2GC5R7NA2mJTZuaiBnBwLt74njwwP92 xsIoBqq6v3udSOLBmjniReHEx97bzMxP58G6F8vSaoh18/Sc3l/mQbNsxTsU zcC/47l/u67x4HfKz8X7id+GsQpmlPOg9Hfu1lvEea6HbeTu8UBj9Rc3LnGk 6dDwksc8iJKK1Zkdw8A6LZ/sdS94QAckvV5CLM/+aLbtHQ9eV3YhO+JevkV3 1FfiD+cTg4hrudUZJ2keXFbLyI4nTm9QNyzq4sGyiBfxmcTbb53l1g7y4JKw iXEuscE5saRP4zzQT+l5WkA8My5G/88MPviseDu/iPjbzu5PIuJ86Mnpsc4n Lt289ZASxYfi7ybrLxAf+q9x0Qp5PlSEN3JSiG3nr3lto8qHDV7n7kQTq84s i9ihzYdu1jXNbcSjf5QVDyzjg0GgYKAZccOnk08yjfgw9ezmofnEF2oFAkvM +LC6754Pj9QjqDCMerKBD/ILdOVfEpukMfe+2fOhRUYq7ywxa+8W7yE3PvQO H5j0Iv7p8VRM3IcP75xj1BcS37ZccWtBIB+07eUW0mR/khYXOhvu4cO1nSGD 54ndZDjTtvv5IJFxMmPj//fv77FC/yN8UDc+KTRF9v9fO39j3Ak+PLRKXFtA /K5x1+jZTD5cEkv2WE+896K1RX0+HzStNAXiSb7WJdT0tJbwgXNzPEWWWD5o ceZYJR+eX1vfW0DyiI0lmUVP+bBtYYdqNcmz2Pf3sQntfNDd+m1PFumHb3Xm Ghd7+ZBn4XdOgLj0etWbyhE+HNU6k+5H+sdu3xmln8LjEKufPqUaQuol5/bA dNE4cMIEGzyCSL1mvNruungc3tvdS8sNZAC6jMXDVozDopgz2i2kn9vvKrle thyHZZsuM5ak3xe70GP/fMehVt7G7bsvAxcp+Hdi9zicMJKJFiIWf31RRC5y HJaswBwNMk86TV2klyeMw/j8tB/byLy5qtO0dGfeOGhPwvEcTwakfukajhSP w7nwJTV5HgzEX05Gh8vHYZLdFJ7nzoCXjNXm7Efj4GRGBZ12I/WZrglqah2H JNabLDMnBo7fk49w/zUO1BPLPlVHBvh7ovd39Y2DsFjsy39bGGjuXJ4s9Jf8 /gYHTjGZp+nvrxf9pzAB2u9yBRtsyLwrPMfkOk9A1e9WH30z0k/bxrp0vSag 4aylcQOZ7+3yDoP3/CaAfdjvkjsw8PikpMDHyAnYb28sFE3OhwMxR5XETk+A roauV8xKBoZsIlxC307AnOCskkItBlqHN79B6yfhfsHbgLI5DKQpfF4YajcJ LqkT0ifJ+WZi7hmT6zoJivEPMgLEGMg9FaT2b9ck7KyIEaHI+bht6fF9D5In IUzrwG/VSRp+Btepr2ycBEtLZY2N5Lzt7DKI1dk8BcISJ4Mbamk4x6756OY8 BbSj6T1hct6vMzTXTvaagqib0n3G92goTrJr7gyZgipLe6nsShoCNIJ1CtOn 4FdIe6jiNRr6dhR9Vnk/BWvnz9TRTadhqE1uiazjX2jUiapJdKdBxYdnMN/j L8j0P6xb4krD5l8fDTV9/wI/vXzqkyMNpb0nzY0iie86SspspsFvXMTZM+sv FDR8fuFsSsM3auhgYfNf+FywIYCvRu4vli9frXT6B8nrVtrf6ORCesm+nc7O 0zBXrPb1AnK/2zrDsrHZcxq+mtgV9ntwQd1ZcqmD3zSYHphKu+fKhRrBqxO2 kdOw16X4tKkdFzpdX6duyJyGmPzRVFXEBRBTqVrTNA0f1q1S0VLiQlTFdoFT CwXQ3QrJnZfJ/VRdUmxjdLYAqlcVWn08uBVKBw4XJuUKoOXBRs2ePq2w7P3k 9Ll8AbT4yaxmHZdWgKz+inslAqhfT0Wm1LQVXBQ+z5t8IIAqwg8PWEq3QrJG YfvBFgF0LvrGL/rOD/gDFgeOKM1Aw5liP9/xW+B2aFxJWu4MNBUrtt1++3f4 uChzpt0pQST8vL+dkv8Cakc+aHqcF0LRDx6e+KHyEQxt2wxys4WR44mrX4Vw E/wITTRJTRFBh6Qa4mU31UOFoevcZxmi6OWdlsVLEh6ArFP912uJM1GBQKHo 6315AIxARl2EGNKX/a5hlX8Fn5f1n6sePQtZdO6My0M1OD5n17EVAeJoteKG Vwbjz/GlN+eep4XORkrzv228LP0WHwzOHFAKn4PKdEZWuGz+iHu8Nee5bp+L 5s9+fWLXwGd84m+3cKufBMIl0ZcXRX3H68JON1wPkEDLFN+X7z7yHQt3rEmJ CpZAW1UzR8pOfseHGtOl2HslkM0vXUGla99xaPZKVYtEsr7Uoqvwy3fsZBgP 1/MlkOmZJ+tCVrVg1Ui5fXu5EqhmPaf64VALvt+7tl/CTRKFR/mYV9i14pVp F5MbPCTRBhMn2cmtrbhCf3BRvLckMooNLl/t14qLwy+4j/pLIhUl25XX97Xi c/zeF9+jJNG6X1Mr9fJb8V7hU1evZUkijuC7ic9DrXi5Your2TtJ9OF6hHJe Shsue7hkdPKjJHq0fqnndFYb1vZKTK/+Iom++wYoOOa2YdU8vXpNriTarr5H pLu8DVOahw0k+yWR+V5tt3uf2jBfLnNmsCgLZZkaSu6V5OJPi1YxRmosJJN8 +/wLBy5ufxdkjtRZyKLK29/VlYuHDl65aqnJQsb3vfLbPbhY8pP4TltdFoqW BNc+Py5ed/RHj68BCwk9XnOlPpqL7/+KH023YKGk83NScrK5OLfotdjvHSyE 7E96vf7BxWVbBAN6/VhourHcrYHm4prpla8G/VloXthodm0HF39xvpw6FcRC CxvCei/2cTEltoeiIllItP9IocpfLk7wn6e4JpGFCvJOp5or0Nhfy0c/s4CF 1IWf0/1baKwsntkZWcRC7EeZtRxnGn/orrviUsxCo+OZ3sZuNDYpVZVWvsFC N1OVeJHbaCylz/CvVZH/G6ttfTeIxrUG3nW1T1jIUsJoMDSBxtLIy7GbZiGd epXVN27R+KXKSYnXP1lo6c3vUTaVNI6dgetvdrDQijxbn9/VNO6uUzaK7GIh qQttVqwHNMaWrcoCgyz00Gmuvt4zGgdYe3TKCLDR89fjE+e/0Pix09b9psps tNVcb8/iKRo/PyXTYKPCRsvVU0WC/9G48U2TtIsqG71PvBlaLMDgL1YWZcHq bKR3qfwNS4TBAysX09l6bPSSUj13ZS6DlTnTVmMmbHSMZfX1pRKD1bbcy5xh ykb5s33K7s5nsPbJPdw55mykUn3f/soCBq+Y2RmzcC0bSb/qEfVZxGAb3ttS 281slO26Q+KaLoP3fc6jSrzY6NnkHI1VRgyOk/Lwuu3NRtOFB8vfGzP46GZO 6WMfNtKvVhTyX8PgjPoTll92stFiTc5EPGLwtTsR0SKhbNSyt1h7nxWDy4b1 nrHC2aj9rR7TvZbBVfpdbMUINvrTHOjhtJ7BuMijZFk0G6n/3X1JyYbBn85a tXrFsdHc42mrdtsxuOWDgE5gPBt1JdYJVtkzmJF8ELU3gY2sAs+mjm5hcN8x fXZqEhvd4FT/9HdisHD0PIv76Wx032JOEmsrg5e7dBdLX2Gj+uAD/j4+DOY2 5G76m8dG8efX6lrtYHCKoeNwx1U2cpXZ6qLmy+Bf8o9W37nGRobGhzrf+zH4 wo+sJtdbbNQk38vwdzF47SbrCLMKNrqdp/nzdgCDR2oF5HSq2Ei5nr0hNJDB my4Hbp+6w0Zzvi+1bg5isKCP6WgOZqNVxrSMfwiDb34YO3/sMRvZFldYzQhl sLtFqUnoEzY6cqi1JYv49iJOkmk9G82Tr1hVHsZgnzONutov2MhJWerff+EM Zs2Mf0e9YqMYEVPN+8S7Onvl29+w0b+c+Ou39jBY1jUPN75lo546F8FFEQyu e+G8o/o9qX9pXO1pYsWSuhtHP7GRqaezj18kg18oRNuHfGGj5lfvrBuI96Ys 5jl/Y6Of1ivOLdrL4Le7zyGtVjbSjNnq/p74YOvGDjaXjUQFhz8siCL52iyU PEGz0R0HpZtBxJ/xXb2fP9loENf3VRAnLAn+8KqDjZbd454cIV56ZWF01W+S rxbnrKXRDG5lf1W81MVGL/qU/u0iTo5Pe5zYw0ZLP6m9vET837C5X3AfGzUU eo03Erf7jIs795P9OVt3gty3cfrHspswyEbiouaHlWIYvMZyh4PmMBsVRH/+ akLcXS03zhol+5sdlbWV+Kx606XxMWJTxao9xBZnE8wYPhvV7cArjhEPzjT6 /XKCjS6ou8ufIc6J7j9ROUX68c0f78vE1l1Xl1z8R/LXGDGnkJjv6tacIECh R1W9cuT5Axe8lNy3W5BCYxZOyeT5A9sbP1N2EqbQ8W0VHtnE0yX7npiIUkic EjqdRlyquMRfQ4xCw8nWiw8Su6R2zGGJU6h0YbrWTmKRfxfK+bMplLj1U5IN cUWwrRM9l0J3vqhZLyb2bBOZfCFJIV//I6GziGfbPsitYFMo898Enzyf4buP Qi2ypSikczurvZLYd6l61xEZCvHeei6PJ6byvqcGcSh06c72DmvioCNWn9co UMh1o/2ed2S/+MnvfisqUejPUNGtNOLEU+78SWUK7b+yPnYtcc6VcLn7qhRK PXL7bQnJh3bxX63zahTqkS7a4kx851aSUbQ6cYCe/z+Sr7c4Z+tKbQrVfHC2 AmL3eq0gGV0KXXmuwfpK8tn1purAyGIKrTPpDgwmFmx9ealiKYUc9Mq+niD5 Xj411qZnSKHq+6YZGaQ/HgnFD8w1plDI7LK+mcQ2s+fO6FtNoVf+vJYY0k87 5BeqliAKsWuvR9iS/juzavMOjXXk8w9lpDSQ/lRF3yJEN1BoT0jLEQXim2t9 EzusKaQ6vEwygPRzg9P+wvzNFLqmUsaMk/6fiCjqnO9MoYsJDYfbyXw4emDZ +D8XCknMcVCWJpZKeDir1Y1CT8962AKZJ7qZH7QvelLIWP5uZBKZP57l00Hz /CjUVuXzqsOL5PNu8kHeTgotabklN+TJ4KhHMmmfdpHv37xsetyD5LtJ5+bp 3SQ/ro/Tp8g8e9znPMiKpJD9rE8fG53JvBllZgzsJflbnPCzmsy/b1O7qaZo Ch27vO3EBUcGD81OWJ56gEJlx6qLnMi8VNO+FTkrgdRfMV7+wiYGJ/mJTczI pNCTygqtTRYkHy+UcmZlUSgoOGLRBzMGm+kuN2OfpdAN5dnj9qYMnhz0SFbJ ptCHlwFa5iYMDj5YKQ/5FHr5UPdBx38MdjztaXygkkJUrvUsA20GL+PtaTtS Tdb3+d7102SwhNvxIyfuUEg56pXVaXVS3/lVry48IPXISBLiqjJ4dcks93tP KDRllzbbSIHsT13VgbEPFOrSvvKWL076R+2lyr9mCqXHOVd/FSPnw7G2pyJf KHRP0Cy+WpTs70bxuTItFLIxVvnsIcjgWV+9Li1vp5B1zYZDYeM0HugXrw0d oZCBnLNdwS8aP1Tynu6WlkKuK9xfmz+kMaoOm2ySlUK9WglaFfdp/NQmnlc1 TwpJXF+hpXiXnM/78/sPKUqhRvxY5mcFjVu+drRRalKoxi+jevU1Gk9lBTwy Wi6F5ploX51/isbGEhGHk+2k0LUhSdni7eS+UZBwMGSLFApUyF6e6kVjszVZ MQ6OUqhnt8Ls3e403hB0O0zZVQoN9Un2zHeisdtLvnfFNikkVZWRYL+exvuO HjT7FiKFSgcqmnr0aHzv31Eh7TQpdL9nKnlkjIvTBhdk/pcuhYLu7N4uNMzF 29trVC1PSaHMmxEOc/u5WPzlkOm2M1KIXvsthfrNxe5ZnnFncqQQX25nCPOJ i//prPwreFMKtVxbI3S+mostXDvGvjdJIfFO0b5dIVz8ptK8O5UtjXr3t8rU F7fh+DVVHRlS0mjTpE9DNbmPrqxXo7NkpFFB/dPSbHJfzfkm8uWSnDRSmnaT 3Xi4De+e0fDsxgJpNNm+osbKpQ3P2Wxz5fVSabTE80jzWeE2vKHbwWWuvTRK 1bT4+MypFT9T8XueckoaFWbqHvhLt+CEO45XaHEZ1Dgp4NHR/BW7q7Z4bk2V QWt78xQCOZ/w5G19BZ2ZskihWV8lZs17fECoqzHrkCya9cvLcL53I5ZVM/Re JMBBoxd0Gp8qPcFRwU4j4jEcdP/pbc5RxyqsuHJHg/p+Djr4R3xzuXAVfvQ3 7KLZQQ7SQElBnyorsXhqqsW+wxw0LyOjRoKqxDklT093HeegdqMNPkZvyvHz zmUrGi5wkMvNkw3qJ8qwtI/k3sQaDtJNNDo35H0V39NW2nClloOaLpfYqOJ8 7DmkrfzwEQed+Rk9Za2Yj68dtno+8pSDtDVLpdM+XcHGlw/K7njNQan5v7UL snLw9h89t81aOagsaewCy/c0nlkwnuzJ5SC9Y/TUD+VMXBo002sfw0GRTwRO FHzJwGOTqjMrfnFQ20r5PevPpeFkeTfnBf0cxP0tG9fim4D1mZ06awY5yDM3 vF7/62H8sThy2mWYg5zzk1ZPnjuElQ0zitJ5HMTAsM48vwj8RCB3f+k4B8kq MpTh+WDs31C6uWGSgzI4aftW+e3Ac9LvL2z/y0Hxug6OPn4OuNy5gTc9zUEm Ts/q9rftqf0f65ZWTg== "]]}, {RGBColor[0, 0, 1], Thickness[Large], LineBox[CompressedData[" 1:eJwVmHc81d8fx7nIvNe618hIskpSGkblfaIkIiPKyArJCmWWb1qikJKolIyS aCkl5JQKlew9rvv5JDukNMzf5/eP6/n4rPd5vV/vc877LPc4YuNF4+Liek39 +f/vX/PAW1ZHYgyJmD58vO+MYaynuka9mgvIaDEPVht4wJfxft9EtUBwupT7 /ppBCEw+M07wV/sPRrMfH3I1OA2npX7KO6slwYC3ydlq/Svwudrsm63abTjP 19FxQTcbjtwJ+7hH7RHsqg7TLlhTBG8TEsos1CrAuE1FYY9wJfAtCeEf9q2H Wi1BfzfNJhjadVL0Z149qIQceBNp3gSfEhOk5/vrQbB1uCXGrwmqLzSnxGk3 gFTvVMW+gia4KDGek5HfADmpVfKqq5qBqbzi/ftbjXBom3WAskoLqG1L5GXF NgN9dqG1TqANpL+mCNzIbQYrr1v4oFobCJy7IbLsXTOsq+e6TBq3wUhNHnMl Vwuwx0+E3vqvDR5bVapsjWqBdSenJfh+toGe25/tXoGtUCB2Zt/p9nbYddL9 XLF9Oxxf65BwJKkTdC69Nck61g6vNh9tOHu/E+QzlwskXmkH7cN/ok5VdsJk BXHBs64d7GsLM9f+7oRrC+7JkiYd0G/Fd+ygcxf0R3vcDN7YCS+S1/3jU+mG mBMHn2oxuyHrrqfA9cwe8E14FyKr0w3TCYEF/i96YG/Gig18Vt2QJLe5WuVL D6iXf33Rc7EbfjawJIxmeqBu9mD5RZ4eINWOXV9j2wvyxz2rh6d6QPUjOVq+ 2AsvI7167zayISWSa7mScR/cM/RrXzrFhsUVHxJm9vXBNZ7gxksSfSD3e03G U/8+CEs88SHStg/+W59pWpzaB5uyUh5atPbBnsijtmIDfeDUz6mI8ufAi02f a7gQB5qqvm4uPsEBe72KLxa7OGCWP1AykcABiVbBo3E2HDAIHCvyfMiBFV2y oVWeHFj69889y3EOKDQ90/OM40CXsOgl5SACvtRaiCrWcsBmXFzkQAwB9bHL vFELBz41MOPTkglQPxL3Zk8PB0pTl54ReUpAK6PNaeMYB24sUwv//YOAHjux 9XLCBDiu3+r66SgJRGQIZ9cOAppYqIf3LAkV6tXOersJMPtr5ABXSVg+6mgn aUuAwWtT2+fPSchd7Z2R5EbA0p17d96eJsE24/uj61EEdDr6aYeEf4UdzNup sw8IuEDu9E+L/QoWZhkPLJ5Qz/uq5JenfoVd3UIuScUEZET2KvM//wqvidyL 3ZgAt/Q9UhmTX6FzIDo0t5kAcaXVtm8XvwIa1/vh20FAZZ5A8gCjH6wy/n1d 1kuAysu3guu0+iFyrYK83QABg63r5z8c7oftk4UOY38ISD8gZjAa0Q+9nj2i anMEmH4bCxOL64eQoGlZSy4SHvy6O+l4rx804zJlDwuQECgp0z9B9gPEvtn/ SZqEZTd/KbGm+iFW6AmEyZHQoNx4wID7G5xzfO8ktowEHZ0L7WeXfYN3l7ar iqqRMG0190nW+RskGHTc3rSehHsdHfzg9w0qyu7X224iwd6teLtn1De4IqYn 56pPQsmRwIpH6dT15oe/AUg4kcR5atz6DeiSF46sMiNBS+r1uE//N2j9z1et ZDcJ7FvXNZN+fgMHliC5fg8J6KHN3Q7xASh/VX9g2pYEntr36QGWA3BP/oL6 HWcSnttmtV45MAD/RQ2+u+VCgmd3tESJ/wCMiQXYxruRUDWyKYF2cQDy08O2 r/IkITxE8qP6jQHQfHM4u8+LBI2ZCT6L/AHQTj44dvoQCRcE80+mVQ9Ax6SI YYovCZsvnysvbxuAnc2vjLj8SRiT8fhHfKPi4fXRcgog4dYdw0380wPQnV05 lxNIgqWG3NHVvINAuxb7uOsICYuP/zy2lhyEM1dOb18MIuGJbstYmPIgtMmm lYqHkCC+M9H7LRoE3vb+HVzHSNieXw6a1oMQkxv68zvFEcJjMqnug+BxZM/e qlASCgPkphaCB+H66YhD8WEkcOrNPvucHoS6CtHVuuEkMHWicpuuDMLhm7uz 6ik2vZofvSVnECLUT1bZRFD6/+6wv/dsECKFxG6+ofjJfoG1Yu8Hgf9cjKJs JAn9pbqCUS2DEBLsa+VMsYzCIfJr/yCs2R6z9gLFu09eK7OYHoT1IokV2RTH EB+uvuQbgg1Hj83cpfi58XTAcqkheP9apz+F4qG7Kjsvqg2Bw+ee4/4Uywvs VZreNATrpe681abYyvfMP5edQ6DxrLK4l4rnbG1RU82+IbC3ztkfRnHJGrJA x2cInui/evCPGs9Ysvi5jIghiLK8WniIYqWfyGVJ/BDcEup1eUPpsdcuSDfo +hB8j9lbyUNx3MtMsa78ITByamlfR+lXLls/bFw6BCc7Le+YUfpOHl+ofPiJ 4oY6eUtqnlBha2VIdw9B1/1wyy1UfvajA6GnRocg48C5TaxgEhKyEyxHZ4eg IWp3WweV3ze85ep2IsOwKGegfZ7K/y/vUS4sPwyxI81GSpQ/ND4u7dLQGoZ2 uRKJXD8SkhMjE+YshiFPy3bcz4eE9xP3vbxdhkFU5e38Y28S/lp3GDYEDkNV 7mADm/Krm5Tuj5xLw/BWouvTHOXnqxHen+h3hsFeefnvUcrvNV2pOeFPhuHJ rNT4B6oe1mb+sjNvHIboMxKWBvupeuBW0S4mhuE7fV9Zix0J6QdtBZZNDYM4 s2bRgaonLo2i0imJEfhv7pWsqiVV/0+OLLuxdwTCmHODr41I4JXM/MvjNQKC u2Q8H1P1qxda1xgQOgJXLk80XNxCwh19rbPbro3AE4bXRT6q/oMqR4aG2kfg REHT+Jw6NY+qLK20GRqB8LVnnUxUSOiI3XWz/O8IKORf6YhSourb/L5Fsuwo pOseZN2VIUGsxatI12kU6ro9li7yU9e/bxvZ6zcKoRMaci94qPcvUVQOOT4K D27pSzgsEtCo13a58OYojIiV/fb4TcCVWybBy3tGQVrottr5rwSwDqmvFT4w RsWR28oqJcAkhsdHI2AM9C3oRUnPCQi73pe5I3oMZmJqe34+IqDtc5pozK0x OD5os+lMDjW/rhWY+NU7Bm5+QQ9fXKTWg5mhh2yX77C0vutK2H5q/ZD88G02 8DtUk/5BL60JiFqdpSB78jt0uJkIfTMjoNvFIdE28zuIbIXLS7ZS68G7j/41 fd/h3zJa1UElAhQTH2gWuY0DT6EdO/ErtS4q+eef85gA5dYjL3qdOJDAXp6V GDwBuuFrvA/acuB3Rnt6aswEeLfPmnaacaBG1jju7u0J2L2VqEnV54C/5NJD H7om4L431y0bKQ448XheOb1yEsYGuI2rrvfB3d/iVpVZk6Bs8oXX8AAbulrH zE3yJ2G1b+uxCFM2MIqrd356MgmbbGtSU9ezIeJoNDThSVil5705QpANZpND a8jeSVhx+ZgN8awXxocxnbb0B4w/WvNzL08v6PUGfN525Qf0rXpU5pDYDY9W hrB8bvwAm9w/ckuOdoNKWJhrUvYPmFUOgpT93SAmevJnV9EPiKsLM7Va0Q3D KFnuWPMPCO63fLH/ZRfcyC3yu8ecgv2dy0QrOjthzu+PsHDaFFyLmZUvFeiA tzMxu1tu/oQBvez/eqRawAfX1FScnoaLYokbBO9Xw/WDeUtZbn8g3nFnGa/q fdDaT/xe8PoHBunP31wfLMXsn3vq0K5ZOHjgl7pZYx1OkmtfEWQ9C1+L0yy1 ZeuxobFLZKbDLHD9d6Ny0q0eZ17xV1k4TN3/OHAX/2Q9dlsXH1V2YRYuTCz/ viW2AX8NrFTbVDsLaChsRCqzEQ8NbzipuWcO1k4oH7Z624zTxctbHPfNgZAw PH1FNmNTfeNVF1znQEr5laoIbwvOj7NuHToyB4bbiRk/kxbsqx6oeS95DmrG z2lJfmrB3z3z2pWa5mBLg/pHdm0rnuqTXStlNw8/edJNDuN2rHTwz4ZlB+YB LbxJV+5tx3sGWvQ1vOaBEHI9+3amHReOXTI2CJ2HtDKeu483dmDvf3z7XFLn wep8bvSuBx24S2Iq+l7rPMQJqp/Yl9SJ3+749HmT/QLUvEyJpm3rxpM1eQ3g sgDJT3DtOqdurLj7XKup9wKcCdjZYRTajaNsUJ9j2AKU6uk8FczvxhtcX0z9 d20BTklamquL9uD7Edmy1W0LcEntQFp8aw9OLog6tG/fIsA7UT8tMzZ24t5R 2+qyCPbbb6wmXNhYbZ/our3ei3BtVqA4/Cgbl9NyZ6xCF+HXk+DPuzPYeMjh S6JZyiL0FBaPXB1jYxBQer61fhF4mCU6Cef7sJDLiEx52yIE3I/Zd/BGH255 9jzagL0IO9XTJOUf9mFf1107db8vwue75YI6TX3Y3Ek/IJ2PCzWcc10Io3Nw eJEH15UVXOjBfImvuS0HO/dW61irc6ERBi0TO3GwkYCWl5gmF9otXM1S8eRg EZc/H5N0uFBuXeyD18c4OFswIeXiNi6kYHryik4qB9e5Faudc+VC2+5duynf zMFqogIWETe5EO/+qZIKIwIXTp66F5fJhcqCbLa93EVgnabZxfQcLqR3XVUv w4rAkDpR9KqAC5XK8tpouhB4v1y7zGwZF2pnpbkfiCDwBfV7/dE91PccFpOF 8gksJqhkmMThQlkFPXFVjwh8beR62u1+LhTLrjkR+JzAOQ8TzfAYF7pcYgqn MYHL14c+4ZrnQhIc/VMlLQQeh+0nzihwIyF9izbHWQIfW17RmrKcG2X/y33T vEjgGZqedq4qN5LSsjDX4yUxf5Um+V6LG7FDKrXei5BYabek6RJDbtTA+zJr QJ7E97QSs6SMuJFqxiGBciUSrxbln1Uz4Ua3RFaOnFAhsX7TzMOdltxopcYf +ltNEtvsJyXjXbiRbMMZLxt9EnfoOwdc9+BGAtCjc2YLiV3k2qryvbmR0vYW p0wgsR/7Y+SnQG5k/fRu0fUdJJ7Cxs1dIdxInyjtDDclcUTW69WjYdzosuGg 5TZzEp/1fNonfJIb0XIXpK5ZkVjIRFNf/gw3etnJObjclsTJ6nevrD7PjcZu 10yl2ZH41kj6DotL3IjP9fpnE0cSvwiKKUjK5EZLLv5RKvAg8YWyyecOOdwo a7NLfJAniV2XuFeo5HGjEP5ndSu8SSyQsa2x9BE3qhw9M2x7mMQ9A0+7zhVR zxt2lzX4kvjpOuV+qxfcaLlyu+dmfxI7VtP+DLzmRr8E9TZ2BZJ4jcRRrqK3 3Cg6kd+REURingNfBaM/UPm5a2W1NpjSJ89W0vQjNxpym5ZCISQunHonL/mF G7m/GS7cepTEMVs3qLEbuNGXovXiK4+R2C4uVzu/hRvFyIwa0UJJvKqZqX+s gxu9eKe/7SPFCwrnjKCHG3lEOgn/F0biJp9pcyEON5r6ceuOUjiJ85552bV+ 5UbznW5cTyk+sdDqcmeQG3GaWKu0I0hstcvEx2+UysdRpHCTYpWrL4I3TXCj +p1hnb8o/sdWO879kxuxml1ctkSSuG5l2tna39zIL+lZQTDF2cf4k9JmuNE4 tQW6SnEYDk/zWOBGH3YTt6n9JjYXGrqjRaMhYJ3fnkuxkt3+B3/5aGgwXaco meJfmTXP3gnS0BmVP4O+FNeM6L1OotPQ/Oy/bzoUZ2zMr3IQp6EdjiGFQ1Q8 QTGyDSosGhIPzt+cQPGOz/GdEzI0dNtnJkWB4qVSM2SpPA3ZuDYVZ1DjHXfz HTunREN7Dj/JEqS4sqBr2kqFhv5dUt3vSel17bfZopwGDXk1tnQWUnr6bisT GNSkoVfLjqp/pfSHBE2JIm0aCner3sZP8dByEVVTXRoKFubnyFD5K/c/sUZy M/X+mU6vJVR+L78c02Ub0tBfcl05cYTEBhZfzI6Z0JDDNG+fewCJGelb94IZ DdGX/nm4hPLPV/LhASFLGpJa7WxznfJXQkRS0B07GlpQ0Vked4jEbu8WIv0c aMjaPt+y34vEGxlHzmw6QEP9S+7sW0P5l52z51qtJw0R1r20BDcSF43jzDQf Goq2f3U/04XE5/XX5nv409CmAliX5UzitfVi5X+P0tDrXIOpgP0k5l166sO7 cBr6eaN5jb49iTs9f9QlHaehuZOu9lNUfZ2eaSRUztDQxzHnI2v2kLhFNYXf +goNCZZpidRtJ/EudRm9gGs0dDBUuq52G4krNG75xN+gobDgC/4vDEmcr5n3 8W02DX1RDbYw0yPxf+vKLuo8o6HDC86CoatI/FMHlVu+pCHjRi7Zz2ok9tnw Ycy3jPLHpxAVkRUkttWtt8h5R0OM1zpojxyJNbZ+FWW20JBwW6JQlxBV74Y+ aG0HDRndPBget4TEEuh70O4eGiq45c6nTCPxvNGfxrP9NJTot+e61D8CN5kK X53+RUONW+M2Lhkg8Im962XaWTxIXIJrPW85gX/YlZj+lOVBFjL7zQ69ILD3 vq2Rooo86IliZl/xEwJbO+7s2qnGg0bvHrnNuktgNTenjJJNPCjE7KQmJ4HA DX5nlG7s40Ft8sS7vP0E3hEgYP3CiQcFXP7CW2VN4NLAxFNNrjzojvZqvQYz At8NTiOFfHhQuWbKtftbCBwVXpB7PIIH9Yi4yvouI7DKmWaNA9d5ULHIute6 BAfvL+JZ532LB11omlsBnRycQKzXP5LFg5o8Z8rXN3LwNFzddSqfB01Exuf3 v+Hgqrm9vndf8aAVvDEB3pkcfDisreB7Jw9y/4eGf+zn4EeHO9f8t5QXJen7 W7NP9GEyXVD3vCIvsj9cl+rq04ela/QhWZkX9QmW1L627cMxajf2ZK/iRXy3 DgaKr+rD1l8dg6oMeJFPdICoTCsb/3Luecpw4kUfFcJfvVRhY32rvg2ZN3nR gqf0wsSDHlw+xPfdI5MXiVRmrxtK6cGGp1bfVcvhRdXWq3Len+jB24siWY8e 8KJiR+0bqyx7sCWT+bv8FS+qT/5t+3CiG3t0mL7saudFP3bkrs7W6sYX3Yr0 pZh8aJlte9hkaifuDTpnmJjAh+S3XJi9r9CGud68UchO5kOWZbZys/OtWEV0 bu7FVT4kHDakuIHdin0fhpRxMviQfuZTD6fbrfjvsKvehod8iK52v/u0QiuW OGig0/2FD/39e/ObnXQLNrWbUF0pugSZSvX7MWcacZG+A/3D5SXoZen8FUHB z1jKvrrz/jl+5Fy7dmVCcBEGkuty5TEB1H1ja7HBzadwXcqHrhYhiCQ3Soxt L/sMJfJW5uPHBdGDtjRZ4cXP0KGsF//ipCCal9vQUmxUCzLaAnw7zwuiuQy/ wZcfa+Hazvtzh64JopqdP80OtX2h+s2h0fzngmg3jF7UH6mHpC6fT1o/qPuJ RMWfc41w+vbh8xt9hag2jketvrWV6rO9xywDhZDx9+ARPN0KPDIHrX1ChJAp 08MzjdUGZy87y92MEkKrEzYO/NvbBrFn9zzmuiiEuCxk1eKb2iDed2P75wIh FKD+TP5pTTskb+JW9/guhH7Xagauu9MJVj/nLx7/IYSqP4yseF7eCeJPZiav TguhnpELG2Wp/uDKyl+l1fNCSNOocjhevAtS5ActtRjCiLHQK0Q71QXXaF/C /q4RRi1p9abrHLvhVl16VVKQMDql2Nz47FcPyL9CPKnHhBF77YO6JpFeyMgZ gpsRwqj5TVRCo0ov9b/eq7wYYXRlLosTsLcXrit3FLxJFkY7nioILSvqhdQw 6ctTT4TRLUZr4+5DbEhUvOZk/0MYvZortFxZ0gcigobpztPCKHjnsjTR2j5I +PmtxeOfMMoNmUhp6uuDizUbLY9wi6Bi7fiV4TwciA9pRXHiIujbROCO1ys5 cK6KqVa6TgR1cpng4RAORAemTCqEiKAt/c02//3hgFnlul52qAgamQi+eHeB AzJSDR8zI0VQ/+oXjuV8BDx/LZKz/JQIev2XnVUiScCISKydarIIWuY3JjW6 hoD9BRGlqx+JIJ4VBlPrPAhQW5TK+/5UBKkezD69x4eAXzbFKY+KRRCvXJ6x cyABl2Z++K99LYJOfdBFxlEEVO3yW7ahVgTVWpFnTC4TsGHowNnNIyLIboVb oEI5AbQtc0Fz30WQbNqGI5pvCWi4dOPA6x8i6LtOm5lGFQF+uu2b4J8ICjK3 ODleT0B2rNWwkQAddYgZOxaSBAR1jbfyiNDRAH3Ho7WDBBiuSax8L0pH07+c S3JGCehs/XjTRJqOGD6Pe+1+ESCmamxppkZHUpMP/w7zksCOIAyEV9HR3vOv 4r4KkFBYe1K9VouO7utaPfosQsLOY+VclhvpiO0rU3CIScJ/7zY+s95OR2M6 1/jqlEnYLd2SKWFKR5NL+Hs2q5Eg6xeS0GxOvc+vUDN9JQnPJR572dnSkfvD Byvl15Iw6q4h4+BBR7deVu6y3kKCo3+3pp83HfFd1BIIAhJqwpIg2peO9K3t 6FFGJNy9+Ms7K4SOzoyrsPeYksC8lhf1LIyOtE1W58iZk3D6jmPShyjqe9cf ZzVZkOBa/KZ4+DQdqeaMGdJsSajDRz/OxtJR143K9ig7ErZ8UuulX6SjOimL 2+x9VLx9Cbw6KXQUv6I8/5AzCc0CDrZROdTzde1HT3qSYCQpcighj442PTm1 3tqbhCcKOOp2AR2lfHtDZ/iQkKijml35jI601uoI7fIjYW5LR3HLSzpaz3yl Ue1Pgu/Oix8HyujI5Pt/jmsDKT2df0wKvaej5NCwH++CSHjhncurUENHR0TL bMeDSVAJ3iejXUtHXOGe73iOknDluNDqbQ10JJKuC7zHSOCOfQ22LXS0sFK8 aoLioOQgW68OOlJ4+s3+/+eh7BsrDoX30NGXk28nz4dR+bnbFhXPoaOMlzVX NoSTUPY4PulmPx0ZmOluqaV4VemW7IdDdOQ04zZmGUFC+vuJYjxGR1HOT7PL KV5Sn/2xcZKOYtoLXFiRJIR22vV+/UXpfXd0mcP/z0e/CvyY/ktH5s0rBs5T bDNexiswT0enjZY9zaL4zd9AmaXcDCR1/03MPYq1eZRXr+ZjoN2JNLtrFN+m t4KhIANd2vNHi9rfgohMnK0VnYE8lD4K61Icpbz5kIc4A63hKx0fpOIZXj0e dYzFQNNtK9rPULxfNyspVpaBxrdFfBCiuGrb3ux0BQaifUClJ6jxbdjN/+LB cgba+FTxRSelR4596cdyVQYa1Pj8ajnFEu4BvXUrGUhwmXTVXkq/GD+lHxwt BlppP9odQuk7HtrM+3MdAwW5ms4dp/JxICZWhm8TA0VdN9EICiGh9oL+amkD BpLTlnLfQ+XPIHUMVhoyEI/UYp4slV/pBzaHLEwYqP/mM68jASTEPuc77mrG QN8ZsX0zlF9+VZQkBVsy0I/wkwHBviQ0Niu+SLVnoFdbZmqXHSIBsRs/5jky 0LoYlL3Pi4RHQ2d7X7kw0PuzuilRB0m4OD/Cy/ZmIOlHVQ2nXEkwDb5a88CX gVanaDy8cIAE3m9bE8IDGahl7zvnU05U/dYmS4qHMdB6wQ9b9Sj/B93cpLz9 HAOFfGkyrqXqR0uU800snoG6N+77bUzV18jp+PzeBAZ6/WBVUj5Vfwd9e9aG X2WggQzFCENjEuz1T8ODHAZS4X9/6pIuCZIPNXnC8xgooaT2QdgGEhqUWquM CxioelNxvfk6EnYJaFj2FjGQ+fq3sm9WUfXY/sVZrJKByMBRoUZ5EpRDZaPC OAxkVsATnTZPQN9Q5Vbjfmo8cWI8bv8IyHD25xYbovwzHYalpglgbcdx+RMM xMp0GLMcI0BA0iutZ4GBuH4lXh7pJGD8yZPnRgqiSLhnSK75KQEFKo4RostF UTd7eNWpQgJ80nm29KiIouo1+8oV8gggTtq/C10tigJP9hxXziCgxXKu8f5m UaTrvpzf6RwBpWM7JxiOooj1+T/bxL0EbErKuFBzQBSdPKGeZWJJQJH2D9XT 7qLoGDsycmInAfkhN5ynfUQRH78ZKbqZgPS/Yx+7w0URudZkW4ISAWG8V3Lv p4oilyrpLxFDHFgv3+Ng1CiKqgx/L7H258Cj12unZ1tEUeHv1WcFPDmwyvVc cnGHKOpa2uz7xIkDytlrqjU4oij7qMHVRjMOSGic2iA6IYom23bpO2pw4K9s Cn/gEjFUt8ldSuZtH7Sp6pEGKmKoO9k+4sBFNvQ3+hsjNTEUYrzc1zyUDVPR Wbk7NMSQ89kMJO3KBtE2oUNWq8XQqVnDRVMdNpjG9o56bRBDeE/pWen2Xigd OD2dvF0M1Zqt0Qtf2guZeV8EBj3FUNjBVtH5uG7wWXlQO+WuGBrmu6QWKtwB ikIpQ6F5YuieSDbXi4l2aB6pzNqfL4YWA4PP9TW3g2GhMlPxIcVOg7NjN9tB Upv8e/+5GJJOSrj+a1U7VGxwr6x4J4Y4pSc+121vAyZytRshxJB7n6BkqE8L vLV3Or5NURzJLJ4qng1tgPX7R/KZWeIIMuR8ss6Ug/8Zk/atchKIf2NX6vqw OzjOW2CGO0UCtbwsLBL5+gG/VnBfHGFKol8p7lXPmpsxKg6erZeSRB3fDw6k TTXj97tP/3kuI4kemHzw8hFvwbXHcyb+k5dEFd1BgnWWLbin81ufhIokkvXb kX6/pgXPpfq+MVgviRb5hZ/HlLTizYxjpy5YS6I0xYZlk+fbccXds9FHbCWR 0Mqr02q57dhoa2rkXjtJ9MzPLs7kTTs2838RrOggiZ7EbQqDv+3Y8dNf9yI3 SXTL0jqEdagDR8VGG3UdkUSeh95qG6BO/GohlmdVkiTSmrate9jXhZN+LE/R Tabi6789zpnpwh795co7rkii2bWq5C9WNxb6NLXN7ZokusMkPlSYd2PnVJeY a7cl0VTkT/n24m68oLlpnvZYErWE0Q4vnqH6BYdvv7vrJdHQjaWr3PnZWGZ3 TOxwoyS65tBBHlNk4zFDOak/zZLIP2F3nddGNk5Vsd4o0UGNJySime3BxgMT 5UdNOZLIOSa9dFU5G8fHXp18PimJAlXfZkpS/U/dM+ORRHEmUt4m+hxsOPj0 1uffLksy0UTngTgHJw7eVK1CpLKYaOQpv6q7Jwff7uLruCXLRLbGOy/ph3Fw AHfNh4fLmUhkjpBgXOdgkT27s76sYyLDkg2hW7s5+E1HeUbjeiZyT9Haof2V g495aKW3bmQigyt6JoxRDu4JZVzq1Wei5RrxJSkzHFyQ0XDi+zYmioDPAWUy BDYb2bufbkPFt2ygN4zqLxeOfrAV38tEuzU3NOpS/WfR/MY9LHsmujK6+eg3 FwIvFZc2UXBkIp+nX+4u8SfwsG7nei0PJsroXTLjeo7AcecOiFqEMFFZmZ2l z3MCbxGtE7I+xkT2IQzO5CsCT6YbLrELYyKs++CZFybwvsJl885RTNQjZyPA /ET1w83EiP9pJvpdk1d5mk3gD0reVQlXmIjUVLmdw0Nipb5G2cCrTHQ+VSc2 l5/EUbe2Buy5xkStv6d/pQiTeO1SFlPiBhPJKfntM5QkcYbke/e0LCZyjg7+ +GY5if80ahdH5DDR5TuSMRtVSWyTfFPA8S4TbV/77k66BokF6Ecfy+czkZOs geQqbRIfW6I8n/WEiYxO1HtGbiZx/ftEqzNFlD7rH0m6G5J41Zl/OZ7Pmajg xEam7jYScxYbzNRLKH0irRYfmpB4c8WW2wKlTBTind5vuYvE107c/zFcxkTI 5YcY25zEu/+dTC/EVLx4dkO1FYnzXo6OJr5lorMfR9T/fz5JC9sHR94xEY+a 9/7DdiQumVozsK6aib47Gxx+70BilbHe9S/rmKgT8sXuupP45INd59MbmGhm qKk46CCJu3yKuyKbmEhboTRulReJk78lnNrSxkTpOcuf+viQeDTnb4tCBxPl H4rm+X6YxCYenhqLndT1WxbRrn4knmNvrn/by0TvI94QjEAS77uVp5zTx0QP xmo+mh8hcZGTZNhZgolMQ8RbwoJITF968qPXVyay0otYvBRMYp+OEfmd35ho Gx4zSwsh8btr9kEag0zk13WkOOEoiRXtKt8JDjPR4BNJw6BjJI6UXCM9OsJE pypmv24LJXFL43Xf2jEq3y3O97jDSKydzFfxcJzy49Los48pvmAZLH5pkom2 iD6PNg8n8TeRXs+gKSZ6E+d7uZVi9Nm0xPoXEyUUL8UWESS+Gf9ceP1vJqqW t1rynOLfO5VcmX+ZqPx2nrdAJImtlyQUTf+j4g2t7zOjuPD9H772WSZaXH8+ +DjF/GcOOpTMM1FxTabcDYo9ttUXXl9kIq/js73UfhC/XjTgOs7NQkHjiSXU fhHLVNyzdeZhoSxF54ILFB89IZG3lY+FVh888cL9/+ehBv/NKPKzUGqAVJca xSv/DVtwCbJQ3K6DUl1UfGdf2mURQiyU5/zQ7zjFaxvN40ZFWKj/yMWLXBR3 j2w7Ms1gIStNmTtB1HhjefXsF8VYSDXhT/5nSh8dxTVbBSVZKDL+W744xb26 KiqSLBZyl3xxx4jSN856qbCCNAvxS9hdcqH03+AnNqUmy0IpnlVhXlR++s4u 6Vwrx0J0jur+fVT+LtyewwYKLCRpmbdhA5XfTSVT97YvY6ETftfoc5QfEkbZ x/avYCFeV8/S3QEk1uNrdfJQZSFFd5vLrZSfvip+NvJXZyG5Q7W+u3xJbGDz UixGk4W2zMSvnvIm8YDfwz/xWiw0IZAho0759fK5HHaKNgtZLm1n7KT8PFRy qTBvPXW/qL+yqSuJU5rOpTzdSOl11nb7ygMkNhw7HlWmy0JVS09GTjuSOHWZ j2n9ZhYKVX2vvsee8oO+i3bnVhaqH1p5r4eqrzGbvVJfgYW6Pf2N7KxJbBSL +n8bs9CfGVUO/24ST47JxCjuZiEL9s8lRxE1nywRPaRhyUKH/yl9cthK4p1K fJY6VizkvavxvaYBiW/b/pAz2ctC++ytj1xeT2Lz0o8vA5xZSEKWyetJzTe/ m/HtcBfqe8P/vudS81H29+Jzp9xYKPjrrzWNCiT+q5Rtm+rJQnY2z6pHWSS+ dz5qotyfhRo3b2xZyUfNV1lBbVWBLJR7kvb7AxeJ50u9XzcEsdCUg8NVizkC 7x23udh/jIUS+eWclv0kMLedprpINAvtVDS/+6WPwM7KPS5OiSz05fElOcdi Aj8K+nLL6BILLXoVnhB/Qt2PK3pWXqb88OjN7pcPCHzPKcvx71UWyr6ksqcu k5q/r3rbp2aw0OUzf0NXxRP4LP8Pi/oCFuIzemBxh1ov2uzIhBcPWai3RMpo mw2BV+Y2f771mIWeuN2jNZoTuA692OX/jIU2KbVwvzYksEzU8R2CZSzU4XD3 cfUKAheO8W01/sRCflG3Sx+OcPCCwZ/jq2qp8XKKUg2p9c06fqhUvI6F1JxX FVRQ699v1c96nEYWYm1WzEmo5WDkmrwhupOF5kvKb7o95FDzx9LVL4dYSP8y 8+KEHwfPvtCW0+SXQu/kpzSqX/XhNRm/PwgISqHdnwwCN+X1YbdTr4MGhKRQ zl/V6PNX+/B7c/OqLIYUaoi1g/rAPpzA8Q6WkZJCcjdP7PmzvA/LC92u5lOV QgHWJ+pfnWbjLQdEjnGMpNDChbCUS2t6caBRs2LFdikU0frttbNML76jfuPj TRMp9CCatoJB68W8U+rL9plJoZcLcVMKrT24Ntb40xdrKUTvCub+FdmDnZ9E KZW5SaEe81jBxIpufIJnuDb1PymkGCa8X3xDF14wNhDOiJFCUkZ6+71kuvCp sxd3ZZ+WQn/yq5ZkzHXiWL41VY9ipRCPtuDY0/ed+BL/UVydJIWET1ntOmPb ibOF55/+uy2F/hnM7+rw68AfJcXTDmAppDfYlr8urg1Lqei7q3JJo58X2MMb wptweKD9L6FIadS/Z/TQEpX3WH6TZ43acWk08/jYtYjWd/jNfHCGUbQ0sjy3 Ma0p9h0WSkzcHnVKGhUEzSfBcCW+XfD+6nC8NPIY3N7N//AtrhrS2VhzQxpl 71J4tdu9AjMPioadK5dGzsfv25y3e45frVIwy6qQRivP5Oe1P3uGXaZWKb5+ I40wh/NHVOIZvn/KpOrXe2mkrfzj9ua6p3jznWgpzy/SaG2V9LaVFx9hj97R F0ZsaSRx9p7EtHsu5r/774ILRxrpf5IMt5TPwYX+/K5RpDSymwy5lNyWhX/P KvMXDUij6jSJ5Q9Sb+MLSx33LZ+QRtcLJa+wvK5ibfKQ5tYf0qjMxvz0g47L uCU/dHH/T2kEjAV32/QkrKh/OS/5jzTi6zt6ZMDrLH7HlXm88J80cnFJkxO9 /h/2qSncUzMrjS7FGwqv9j6GRZJLV/TPU/EfCtB38/bET/fV/FlclEZi9h8q j/edqfgfmLBKUA== "]]}, {GrayLevel[0], Thickness[Large], LineBox[CompressedData[" 1:eJwdlQk01O37xuclSxGSJV57XmVJoZDotiZSCUXKviQJ6W2hRKLXGqaUkK0i RWWplOUxYxvfkaWs2WbG2JcRUQYzv/n/n3Pu85zrnPuc+zrP9TnPregZZOfD hcPhKJz6v/vPscBntkGRh8sjR9Ctkau197137W5XcYXf3krqjQZ26Os83T9J JRB8dkiNJRl4ooVys8QAlTvws0F4+pBBCIqSWJI5r/IAml4dTzl4MAqRm63H 7FWygf6tRNn+AB4F5V5vOanyFqip7bi2f/IRITGx6rhKLeCc3Y/8mihFtdP9 rQJFtXD0h99wrXYZqj66a7hFHUH4wmiTd3gZOsflgXu+ow5U5DNVjEXL0ena NSV5OQK0FgaFKhtUIGtdLT9J1XoIo5h2y0V9RDoqWYt80AyJddtW6ua/IO1u 0zXfyGZwLpskdOpUoX3RU9xNhGawwMlrv7lZhTRpuuLR5iT4cfHJlw9/VaPd 2Z16OOsWsLgz8URqWw2SkeAL/+NABmKJR1+2MkI8vCF8U/7tIDqRJuaRRECT VhHCS4XtYBDBt0IvIiAsKVFyg94O8EdFxKqJgJrjvz+M3dsBfkGpoqUsAkoQ nX+eVdQBUj6dDszLRCSmtLOh4Vkn4FpTA0yP1CMVk6RN4ve/Q6SG8LMDgw1I cvQhf8aL7/CxhPHd6VcD4o/JEJSv/w4hslXFpwUb0TSpUEwV1wXfnEi3Bg41 one2RGWjsC5wWZeTF33aiPTdf5v7BHZDUXxgDM6mCVlFeMR8ONMLdNnPPg/x zUg7mXAk799ekNbDG2u+bEYyOYr8SfhemHurFp/9qRkt1FLjvdt6gedMFpE1 0IweszxSth/pg1irPJPPSiRED/fMvHKgH56H1vYvFpJQWxLxvIt9P2xT/BHY +YmEKp8pyVld6YcTbsMzUc0klFBDy1Uo6Qf7D/5cruMkpL3hWdCu/AMsPeou Lyi2oMjbXqV7xAZgveiUsU9KC/JPrA+R0h4AHf5jce7PWpBD1s79PLYDIMv3 zkvjdQvaVT36cTBhANr4fhkdqG9BbWte1Qncg6C/6XQx31ILqhRoCL+hOAg9 pUrP77FaUP7fyuAFg8DqE9revhlD1w7RCQa3BiG6frn7uzyGZG55N08tDoLy UbeDqVYY4k1oiO0WGQL/anGrGHsMLWQoWxM0h8D3d1GTpQuG6r/QW9P9h6AJ quL0gjHkz/T+ZkkbAhb+4rvahxhy2NL4UAc3DK80ooqVsjBkJP3PaXm5YVAL fyDl8AJDIgZjvStnh+HtWzxJrgJDn0J9hl52DkNs+EdV204MFRy+1Cu9OAy8 6wX/lvRh6DH3lc5k0RHYt/hOqW0EQ9eTbjeG2o+AUpq42Nk5DPnaRaH5qyNw JFBfqH4JQ2ckYz97PRqBnjBcP2MVQ7p5D0uOd49w/HucSuUhIxXfp4XE5RG4 bbC3kkeAjBLS2jv+FqCA9afNnoYiZHTLuRtLUafAfcKbXwwpMloy7LMkH6LA NCb9NECOjC7JDzTw2FBA12v892slMjpHp9SGBVDAeNNRtwA1MvrWNHrow20K /MvL/oexh4ysi8YrGYkU2DLmsFNHi4yICVMH1J5RQD9CUU9/PxkZBM6WeZdQ wLcx0YSlS0Zltoy9OTUUYNGFdsYcJCM1ncXi/q8UkPg3uLr1EBnliy+rig1T ICsLm+8yIiPpP78LTsxTwNzyv8xnQEb4H8ydcSwKUCw8XqiYkNGWmo3ceiEq FIR7zwSZklFUDk6OJUeFPpF5u1AzMmLe5c7U30sFjdjiGlNzMgrx5t1xFajQ tpYj1MrR00c2p5WcpIKEobSquAUZeaoKik66UeHVau2CLEf/EBBOVgqmwuO5 e1bjnH67+W2CLpFUyMWVSgZyNNYhFvckhQrZIRT4wJlnWi7J+y2XCjJ/sQuq OH6+pEnfEyylwvhWG+27HL/aN2VxlgQqLDScbeYxJqPXzgrhdzs580232lgd JiMlo53MKioVzn/MLjhmSEYZ8io3Vn5SYTjxaY2gARmJcqn+2sdFA5vkwRuJ emQUT1e/ckmUBjJbMqoxzntzNWvOv1SigfWC49VmTh5hRVqXKNo0qGMx7kVp ktFiwv5JaTMaOI0k96xx8vQP1PM5bU+D68c+2+vsIiNnHSM37CoNRJsdrgxy ePgmbjy4KZoGGS1B9OPSnLz/mJ6FRzQIiPTdFS7OybfmqH1FBQ3GJwYaxTi8 leUc65hvoIGvSdHKbQ6PalEnjqt20+AMhZGXz8aQtKWDZfYyDQw/aUqocHjG qzo29PGMAv8R+U/3ZjG0RdDZZLvEKLhvCovKHsMQs8PtUKzuKMQGC9oI9GKo 3/nS3pAbHJ3eUIA+YiieZhnw5P4ocCG7nsy3GDLwVy6qThsFIS8je6MCDGWF DinxVYxCrm05u/0RhtzTT0pkLYzC0c8OVdpBGNqmoGFPYI/C/ueas3o+GCIW 8qeMC9Fh5bAGL9c5DCl/ImzW2kOHNjsXEt0CQxPdOhuNF+kQvf7CcXQHhtJd RAxmbtJBJHwgT2grho6OzV4XiaWD8+e4uywchl7/erngXECHLkW/QfXJFhS4 fQedQaODaXm0YHV5C1q2Xcekzo8Bru7zozfQggr6+vjg0hg0ycoGyuxrQWfc P5h7h41B1LPaC6cUOP9fUGDt2/QxCD6ZU8iHa0G3H1BKzbrHoKyqa+BFNQlx tzakXz4xDgbWy9w5aiRUYZ/XjXcZB6bm8DZbSRLyHggXrQwYhz4uQ6FGbhJq mtZN5EoYByF7tXYmZx/Eby6KeNI8DmUC4f5pcc1om2WSL8F4AmQG3r35r78J mRdVg/qpCfD0EP56v64J3RSY3ZHmMQE2aiM3oLAJUdqtyX5RE6Bh+PLW0NUm 9N6Jf59IwwR8Udb/2rq5Cdn631t1tZyE6cRMpzu7G1F0a9k3kuMkvN7aPb1D oBFVatLeaPtNwgvvGzcvzzUghSVjV964SQh5YPvOvLQBLdxiEUuwSajVciIU H2hAKUmhievHpyAYDTsHatWjBsYrH1/XKchuf3j4rXA9+nOq73BH4BSoWeTO vZojIncJvZ/Pk6fgfErcfNsrItqX8+v0sc4puNmKPz3yNxF1vA+Sz3CYBnzj li+Ky3VIpMunTO/cDJjXkMYipqqR8ZzJtMOlGUgH1cr4x9UomFdOKeTWDPTV qriIm1WjTv2e1OLMGXBSXFp4nVGF8M+OXFEc5Oj3+UpDZl+Q+IVd+wRcZiFx 6cLcgzufkDRzsmTYdQ46LuLPdz0uRTsVAopiPBmgENtdmxCXihKHFfOSrjCA skuSLUVKRitZvelpkQww7qvxlAtLRCQps9iX2QzIJc4e1O2OQQHbpS80/mBA nUdDbkt7MDrH7Y2PUl2AupLpm3msKHi5ss2WmLcA7tw+Fm7MfNAfukw2wf8E jT+VssXllUBgRtp0ZS7BH/Htdynv28APkUi1UctgkC60wJPfB0+9CqXF3X/D K1qvstcSBfY4UVdYPqvQWOKJbyOOQZYosBIur4LSsYr6qe9jsOVrFo/UtVVQ VzCV2aCPwaSJk5hO9Cp4ZvRsCPCNwwv1dq0L+auAdzLMIVmPgzS7OqB9eBWa Rc2Pv+0YB96CdFqOIxMSkqnL5d0TcM19ZUrDjQmS3D9pZWMTQJd2+PnZlwlx VrK9hcsTQEgWxnVdY4LczHH8VfFJuB16X5b/ERMi8gSjUxwmYdHmX6fgDiY4 7TGZ6eyYhOGlk23GVmuwvebrLxxhCh783bsz+NQadIblTv7omILDZq6hOWfX IEvRk1hAmYIcfIAy6+IaGLt2927HTYO7VlxYVfwa6CpudTU5PA2jgUQV3dY1 8Pl8Nqvv0zRMTu2PUD+5DlkxCs+DczjcbKvucnZcB98BSqpHyQwcPWimFu+2 DlHGP9kmVTNQFHuqezJoHb5PEEU6e2bAf1egekHKOlhfKORT2ToLc96FvQrf 1sGHLzM58/osLI5I7ZM4vQFNe+rdDAznQMHr9355lw04ECgnTLScg5PjXQd3 +2yAnwS1Vs9+Dopnk80Mrm1Aw+Ne6uzFOfBd5XF0TduA44KvY28/noMfoovh Bd0bkKnmult5dg74H7dHvRvagDvvPxKjV+ZAT6rkv8qxDdjC23L5G24eHsn7 pWLLG5D1183q/eLzcEJj+MW8OAtuP7cq3m40DwQLjKx7hgWByrhUzbh5WCAV doArC24YvXl6Fj8PcjYx3Ud9WXDHwqcrOHMewuyMR5yvs6B+E+m1V8k87Hf7 uHjnMQvspB/4n+2Yh1c386Wae1jAP3FnNlSUAT1rEXIdwywIIVawPKQZwBPh srN/nAW74k5fP6DEAM+YHXtmVjj9hkY+2VoMkME/MBaWZAN15MnP6ycZkPIm 7IKjIxuKpyzu6f/HgHN/WbR2u7Jhk0e2oXsSA1QchbUcfNkgyIy8eO0hA6q5 XjBtr7FhYZ8n80IOAybPfk2yfsiGiVBb7ssfGVD+7skiKYMNGas2XuwqBtzh 8XS0zGdDxx/Hn3cIDBArXVEwL2XDhy/r1yxaGQD8ChVG7Wzosnt0kEFhwBbX 6R3VPWyo4CtRnB5jQFd5RbjBMBteKauvdE4zwN/NylJvjg0nHIvM/X4xoOz+ P/dlcThj3P+fBfgf2Epa/g== "]], LineBox[CompressedData[" 1:eJw1lXs41Pkex80MlZnfb9TmtpFw1qXStnaZ6mz5fo7KrbOSXMZtkxWDyFoJ pYd1KbkmymWx8chiG1Y3TfS1KkK1KhZtNrcZM2bm98NEZ+eoTuc8z3k/z+t5 //N63v++zUKOeR5hamhoCD7w3+7gGvENWxig8b/MIf8e5htJBwN4iaoiT4pG 79ZnOqKXDMgomK6KvUejZ4LFfexxBmgGr2241kGj+mtHvIemGFD4nWzbxC0a ebg6CaLkDBD2t8z8u4lGNfEr8y+pGdA99qhl6wUa7e3PHqUNmRBsNLC1KIhG 6/TVkyJjJqScuGp12odGVHCkItOUCfidc4fXfhpdXHJ7b2TNhPGgc32/Ao2k ZoSFyzYmrCZ4zRXmNMpNzI/90ZsJfcumlMckhQYtLqw8UMQETlXd6eEDFHK1 MtweffGD/2KkfZ8zhe5aVwqyy5nAcusJrN9JoYbN9b2/1jCBUqtHdK0odNr2 Ts7n15ggVXlG9qqVyHrXlI7uIBP2pd1MrapUolNeXxgO67EgUi213vRUgea9 21xUH7NgYOFM66V7ChTmuytJx4QFnc1WZ5Q3FOiAv/MLZ0sW7Lm5zt6zXIEs gwN+aOOxQFKsXasRokADUemm5b4sCO6ANWqFHH2S/tw6qIwF387qpF+Zn0X8 VpZtWCULSv60jU2ZmEW5E1/sOHaZBV13F7ocns6iRVTsmtbAAt9TJ7pTW2ZR 97JXZN1tFvyz0yeLFTOLIhJ+b1KOssDhUjSPK5YhYcTop6fXaULxUolxwT0p 2uHxyq66QhO8huIXt++VoHapljKkWhMepad8e9JWghzSbOosazXhxbCFmXC9 BO1pTdITNmrCkxpvj+lFMXLX1V1qv60Jd6y/DC2pE6OQEZdbL4Y1oeCXcKTP FKOc4NYd+rpakKQfFfO6eQqNxWY65OVqAWV+wsR/chy17vAjH5xfAe6cpcHC I4NI36dn9KfMlSB8lP7zgvAOQpMa57viV8GCxebesaMiXKYvIC0TtaFc92/6 /cpB/H1VxBn7SDbYBQw+sGsYx44BYQr3GDZwbcNjS7vGMcvwmwOCODaEXm/u V/4xjjPOBxpVJLPBYPwfEM2dwFkZ+5s1ctiw4eyr4fa4CZwdaT/c38SGRmF8 fe72SVzIY1iFKNlwNKZu9+G2Keyheptzcp4NczztY89/m8JrWtRzxYtsqEq7 9NBuZgoXbXwt6nnLhjd5bqL7etP4gvGM+xYuB9puFpw1iJvGF5mPE/71KQeM 5+mCRCsxrnxS2p0fy4Hfqn7XacyQYOPbwCqJ54DUJurKyTIJ/qFWiioSOeA1 +fLV34USXJG4/XZ9Kgd85DHLacMSXGY+0tRZyIEsP5a17cYZXJJgcH6hhQOh g6HTWr0zOM/kYoDP/AffndlhppZiQtuhNHCRA96+lZXnCBnOVYkHQ/7iQOM6 vvsrExnOeWjvfoxBgPqxhnzfbhnOjhuCs2sI0J8KvvxZjgxndutaimwJKPpl tMfYYBanxFyYWx9HwFr14+hNG+TYrct27M/jBJwT+veJt8ixof5Ab3USAZ2x Ri75O+X4egdRa5ZGgM2e0owrfnI8S2R5WxR+2H9//SNVkRzzmxJFNkICVpwo 2r3IUGA7aVDGl7MEWKpiwsOfKjBz53LsspIAyV7+oVtjCjxQUB7UMU+AyaBn ukqmwFHbhnnoLwKC1rraf8ZU4posD5njKhK+G6nME9kq8WqL3e5uliT8zHjS ROYpsfywtaFfCAk2uxp0suwo7H/0j81RYSSg43VD5ojCDxPyUUokCe8OQXK9 K4Xrcl6HXY4jwcjAxFXwNYUP3ei8IfueBGl9RHhPFoWfr/I7mFxLgsua405v nlHYcS0RnltPgumpDQU6Lyncsh4nVzWRUL6iQ6AjpnDe5xY1XddIcLLqvvtg icLOgfNz7PsknGvbnEN8TOM7zdn5FdMkdPfFVb/n03iTaGfNVSkJvPsurgXB NC69T9/AChI++cZ0/woBjY+Peo9NvSbh1sG3oY0JNN7KMrex0eLC3tXLSX1F NK4ih5CDNhfUCN8rLqMxYXj2oAfJhTqvQL7TjzSW2VDJ8XpcoNgRAYeu0rjW R9TbbsEFXrRptaCbxh8djh57spELqR58vehHNE6NMp0f38KFhenkfv4zGgel Zhlq8bjgyJ9QicdobNDoGf6VExeerfzKbFhF437fp6JQD+7//wb/B6HDHcQ= "]], LineBox[CompressedData[" 1:eJwdVQk0Vd37JoWk3Ms952ZMUkTJUJJovyENVDI2G/NJptCEUBn7TJmLTJlD hVKmY7zuUCgqlQohZCauL/I7//9Z66yznrXPevfzPO/77L3Rzt30wgoeHp5e 8v2/7+i5ef+pZRHg+f9nkuCKxwm48VNgsfuixIrJCeKFs+77I4IUCAyPFtH8 NUF4V/3MUhCiAO8T+41WgxPE5Fmdfb1rKaAiblpp0z1B/Ewf8DbHKCDGszM9 tmWC+LBZq09bngK33/VaXH8wQfS/ddGHLRRYsvCUXo6bIKZvZmYfUKTAxcVi fY/ICULkg9A/JtsooBX5rYsaOEEcCvn668JOCvQNPbA3c5ggKgdv/44xoMB4 7SbFz4oTBDO2wjLRkAJnEx/tF95I7rdvtCLlEMlXqfnKVvEJYibRwifXmALX J9KsN6+eILYdVFyuMqcAI7fxvvzQOJGe90bwpwMF/vD5/DTKGidKzFY4jzpS QJ1bkrPr/jhRvazJmXKiQCzOPbomZpzossqIXHShwLC8ZpzPzXFCVNBLVPQK BTK4npedrcaJIKf1UrrBFPiyVrk+RWCccNpqvyMuhwISoWuvFJ4aI2SE4oau 5FHAgdFfO31sjOgYacg8WUAB72fG8soGY8S+IjmaTDEFSvZSr7iojBFiO/q4 +eUUMGFMJqmvGCNqd9o21DZS4PklrmVX7ihBA2uLkV4KdL/Iaf7Z/4uotzzj u1+GCj/1Jo4q7x4hGLEY01iWClIqfGvLFEaI161ttJNyVPCPu260bf0I0WVo UOK2hQqFsw4JM9xhYlJze2+KChWE3CdDP74aJmToy4Zz+6ig8jzbnn/PMOHz MUv0sTUVdMakpaO2DxEaJ0cKaJlUON4XkPBxZoBwuWP4UVdSFFYXzu5x8+gl whwF/+ONE4XUNSL/YUmfiBpp2+URmhj4FRfn5x1tI179DeFTihIDqfAkmTGt aiJqamPc7hgxcFKcPplUVEXY9VfLHYgVg6KXFMkk2SpCiD293yZRDMJGjx6/ v7qSOJtwPjAxTQy4P50FKr5XEH+VNZdWPBGDmEs/rrBTywiDUwNzX9rEwKbg fkBCVS6x3jgwZPitGEw6csNQZQ4xuk8Sn+8QA48DhpLlr7KJBPkTu0S7yHpB cv48VVnE4ES116EeMYBLfIP+UQ+J8JD4yfJJEs+dCXeXiiBay/RHIqk04OHw HBKyika3dcsH7omRONw3uNP9HtJske9NwGgw2VDQeVE9DqV9XtX1UJwGMde1 7tiUJiJXXmZz8UYatKv1Jls+fIiEjxtnvlGjgU2sat766Bx0ZMT85FpTGnRb yqalqz5Df72azajmNAgUMOLqxD1DpUu7jmOW5DqDGmL7+xmSoNINpU/TQLHq gDR6WYqGd3/S2G5HA2+T2jsGWuUoLPicyFFPGgivkknS2ViBmmUdGRGxNLhO cedRSKhGst/firvF04CbyOOW2leNfB7quh5PJDGfysqsHTVIVQKjiT6gQcSu JyvPMWtQqliTbVImDeSnG0YiZ2uRN7/cUuZTGjwQLuB0p9ShtqZIkzulNGj4 PJUkQtQhpTsLjxzKST4yAUdW99WhnuX2IwovaUBzatlwQqEeGS8EJBeRU93g tchQfVKP5Ee/alS00qAzcE+tXHkDCig8HJrcToOM19F51R0N6LPT88833tHg dPypu1IzDShmIOKWzgfS36l1QipqjWjx2962+q808C/syUgsbESdb+87vx6l QWtQna93bBMKqrDI7BXCYKVv2aycJgOpvjUK+yWMwXkF7YrLJgz0ZWS/++91 GPSZ/rvo48xA6jIquqvFMJjlHV+ofshA34P4P6lKYhChf0nnL08L0jatoAQq Y3C25PO0Z2ULGrxUPB++HYO7oTp0p/YWdC/40be4HRjw3712jz7YgoZeRhfl aWDgk94QlkNhooQNTofa9mIg7Po0/aYdE02Org+UMcaA53fRbdkFJkrlF/lH 8RgG+Sush6qEWOig7Kpj6iYkv1C3d1QpFkozm5I0NMdA3qHSaEyXhYwqWRWu ZzEwGHCJtvdnobkOIu3aeQxsen+/7Yhkoayx58G3bDCgaGm/+5vKQlzZLLME Bwy2aZzZEVzJQrmhPhPVLhgwV4X8Yz7NQqaZHh8YbhjgPtyMlGUWWqp0rGn3 wGBRTmLooTAbmY+b/tvvjcFIFrW1YzMb8VooKwjfxMCzjWvKb8FGRW4b1+EB GIBD0gkFGzY6GUb/veEWydf4cBPfJTYqqeJr1Agm6ym8QhMBbHRWrvv8mUgM cge5mrG55LrHm4d60RgkGgtULJSQ9Yna7q33MJiTmPmxuYKNcs9knubGY2Ca fcLvNYONuAWx978nYvBS1n7lwVY2MuLe6WIkYzBuE+0Z8p6NJuMdLRNSMVBJ Ntc1/8FGej+sEvzSMBi1z3rZN8xGCWqHO+0zMDjp5W2lOclG2q3KpurZGGhe GEHbF9koQkr6nnguBoZJloXtvBz03XldO08+BoWBH2/sEeCgIIGpo22PyXmo DYg4Q+WgDxZ9ES+KMRiSC5ym4Ry0NbuD8/AJBt5qB/niJTjIb7pJKPgZBs7c gfYuGQ5qhReHXcowcFF+4vpDjoNko/PCzJ5jcHvN7tGyLRzk9TW5RbuC7Mdx M+sjShy03sf3wOoqDPpjB91ZqhzkzHQJmqzGwMPt+M5SDQ6qwc83fqzF4JC6 6l5bTQ6iXDi+gqgj5881O/mDFgfZlcH+3AYMyqMEbUX3clA5r3pgZBMGiuyF fJouBwmYbCK8GRhkLVsEf93HQafTaH/PMEk96XvXuAIHFY2u0tVnk37ErjZp 3M9Bf7XnfZVek/XFrS/26HHQifChSmorBqkvJV2b9Dko++OnBW4b2R+69WV3 Aw6a28zR6nlL5mMoLKKXxIe8q6+1dGAgytR6L3GAg1Iail+UvMfgusIxO0kS j1PSfyd8xMj7fujID/J/sI7ZefMTmd/IC7meJI4tvuXl8AUDnVCHCBa538Af z1KjrxgIFjfQhkg+WkccptS/k3nrTLVqJfneTbZQlejFQGr2mKsfqad70NCd 9wcG2au93aZJvTt2aZUM9WMQND/gpUr6cfvO1rG2QVKfU02iJulX51uJbRVD GPg/PTG5cg8HbZEVvpQ2gkF7sdaDFNLvG25LBcGjGDwoMCz5j+zH6+rxIZdx DNK0ogzl1DhIZk2PgvkkmRdJm5uiKhzkceqt495pDPxkjFw5ZH8b8xpy5GYx YC9Iqh1V4CAng5xNU/Okn5MfMh5v4KDK2ES7rgVSz1TUnTBJDlrbG5pJ/MHA 4QQzT4XOQaU3nTdELWOQMbkk/3EtB/15sUNSWQAHk+ggaiqXjVRS55oFV+OQ X7WLt3+ajWxu1XgMCuEQtLhJjTvKRk1GRozMdTjwOyQ0BPeQ89/jeHk9joPl mvk3Ws1sVNu8XWqOjsO++V09AzVkvgpnGR3iOHyIFJSweUGeD1duS0VL4yCs v8WvmsyzlFBay6rNOCiVmhmvD2ajYxMOnj+24DD5re6Xmh8bBXYqS9cr4uBZ Vp0n7sVG/WmvPP224XCs9suMGXl+FGm8l57RwGF2XdW5a1pspHNO2LtHD4fP Abu3J35nITe9DplaAxwq46+9z+hgoQyFB6wUQxwkRilFvi0stHJaYYPVERys BT67Z5Ww0OsQffabEzj8nnu6/aUPC5196iNbZYNDTI+ogDx53kYl7Ock2+HQ sabESu8PE9X5CF696oDD6+R4SY1RJpI/kMhRc8Lhhp1eQsQbJhr99OxqvjsO W7vyb2+KYiI/vuHXCf44aPBXXOUTYKK/+tprUgNJP1VPa36aaUG3gv49nHUb h3R/nf1+PS0oZJUKoyQEB2VTESHlVy0oWsCLaInCIclqWkXNqQVlrVl6tpCG w/u9W9jrahiIJUZNOkfgELwY9iFOvxkZm9u9t68n9dyoGfJTakat8WVizo04 ZEccNtCmNqN3mGXM1RYctDftZ6h/a0Ld9JTw6DYceGMvh2+82oQmJTf71X/H wT7U9pRyWiPC5ffYbuahw5TPPYGc9noE94PnBVfQ4SindTm2vB5dXPcucpSP Dvy8yq9sk+tRNde5skyADi0vHA5kWdcjuzepYnoidEgxVM99PlqHSq7yMM7L 0IHF7yRgwVuHDFktSsk6dMgSqTWeUq5G19wsZ4Vu0GHdlw0vQ6bLkJSmA3OL Lx2uXf72FeWWobqly6l6N+lwhd1X33qqDAlFRhr43KLDPpOLth51pSjtcVP8 cDgdeuKQ2ft/nyHGkPou5gM6jP4oLPDcXYJo9iJXg6vpEHEZXyt1OBu9UpI+ kllLhzsX8lZE5j9C56eVZGrq6DD09dBMh8AjlH/LkDHbRIedUppbh5sz0d6M m7jDGzp0DB20Kg5MQ3Zff73Q+0aHqwGWdz+dj0cCOQt3z/fQwWCt4VSteBwq chGw9umjwy7pgTjfznto7o+cQOkgHZ5whdqE4qLQXYnTVhsn6GB6mZJ9zCEI 7ej7R1l3ig7r+eV1N3fdQp0FV5ZPztBB4YZX6OMkfySz515ezDwdFP1nS8sv eKNGnnTfogU65GYYyw8kuyEnZtFx5h86RP4ZT9ng6ICEYyo39S/RoTszRPqc ozl6ZsWcX16mQ59Fc4Pvd699/wMUXYXf "]]}}, AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], Axes->True, AxesOrigin->{0, 0}, GridLines->{{1, 2, 3, 4, 5}, {1, -1}}, PlotRange->{{0, 6}, {-1, 1}}, PlotRangeClipping->True, PlotRangePadding->{ Scaled[0.02], Automatic}]], "Output", CellChangeTimes->{3.529410161972*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Animate", "[", RowBox[{ RowBox[{"ContPlot", "[", "t", "]"}], ",", RowBox[{"{", RowBox[{"t", ",", "0", ",", FractionBox[ RowBox[{"2", "\[Pi]"}], RowBox[{"\[Omega]", "[", "1", "]"}]]}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.529410165847*^9, 3.529410192697*^9}}], Cell[BoxData[ TagBox[ StyleBox[ DynamicModuleBox[{$CellContext`t$$ = 8.90942571385505, Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{ Hold[$CellContext`t$$], 0, 2 2^Rational[1, 2] (-1 + 3^Rational[1, 2])^(-1) Pi}}, Typeset`size$$ = { 540., {164., 173.}}, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = True, $CellContext`t$1169$$ = 0}, DynamicBox[Manipulate`ManipulateBoxes[ 1, StandardForm, "Variables" :> {$CellContext`t$$ = 0}, "ControllerVariables" :> { Hold[$CellContext`t$$, $CellContext`t$1169$$, 0]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> $CellContext`ContPlot[$CellContext`t$$], "Specifications" :> {{$CellContext`t$$, 0, 2 2^Rational[1, 2] (-1 + 3^Rational[1, 2])^(-1) Pi, AppearanceElements -> { "ProgressSlider", "PlayPauseButton", "FasterSlowerButtons", "DirectionButton"}}}, "Options" :> { ControlType -> Animator, AppearanceElements -> None, DefaultBaseStyle -> "Animate", DefaultLabelStyle -> "AnimateLabel", SynchronousUpdating -> True, ShrinkingDelay -> 10.}, "DefaultOptions" :> {}], ImageSizeCache->{610., {221., 228.}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, SynchronousInitialization->True, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Animate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]], "Output", CellChangeTimes->{3.529410194205*^9}] }, Open ]], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"DotPlot", "[", "t_", "]"}], ":=", RowBox[{"ListPlot", "[", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{ FractionBox[ RowBox[{ RowBox[{"Sin", "[", RowBox[{ RowBox[{"k", "[", "2", "]"}], " ", "x"}], "]"}], RowBox[{"Cos", "[", RowBox[{ RowBox[{"\[Omega]", "[", "2", "]"}], " ", "t"}], "]"}]}], SqrtBox["3"]], "-", FractionBox[ RowBox[{ RowBox[{"Sin", "[", RowBox[{ RowBox[{"k", "[", "4", "]"}], " ", "x"}], "]"}], RowBox[{"Cos", "[", RowBox[{ RowBox[{"\[Omega]", "[", "4", "]"}], " ", "t"}], "]"}]}], SqrtBox["3"]]}], ",", RowBox[{"{", RowBox[{"x", ",", "6"}], "}"}]}], "]"}], ",", RowBox[{"PlotMarkers", "\[Rule]", RowBox[{"{", RowBox[{"Automatic", ",", "Medium"}], "}"}]}], ",", " ", RowBox[{"PlotStyle", "\[Rule]", "Black"}], ",", " ", RowBox[{"PlotRange", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", "1"}], "}"}]}]}], "]"}]}], ";"}]], "Input", CellChangeTimes->{{3.529410210051*^9, 3.529410240633*^9}, {3.529410301665*^9, 3.529410310692*^9}, 3.529410390836*^9}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"DotPlot", "[", "0", "]"}]], "Input", CellChangeTimes->{{3.529410242223*^9, 3.5294102456280003`*^9}}], Cell[BoxData[ GraphicsBox[ GraphicsComplexBox[{{1., 0.}, {2., 1.}, {3., 0.}, {4., -1.}, {5., 0.}, {1., 0.}, {2., 1.}, {3., 0.}, {4., -1.}, {5., 0.}}, { {GrayLevel[0], InsetBox[ StyleBox["\<\"\[FilledCircle]\"\>", StripOnInput->False, FontSize->Medium], 6], InsetBox[ StyleBox["\<\"\[FilledCircle]\"\>", StripOnInput->False, FontSize->Medium], 7], InsetBox[ StyleBox["\<\"\[FilledCircle]\"\>", StripOnInput->False, FontSize->Medium], 8], InsetBox[ StyleBox["\<\"\[FilledCircle]\"\>", StripOnInput->False, FontSize->Medium], 9], InsetBox[ StyleBox["\<\"\[FilledCircle]\"\>", StripOnInput->False, FontSize->Medium], 10]}, {}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], Axes->True, AxesOrigin->{0, 0}, PlotRange->{{0, 5.}, {-1., 1.}}, PlotRangeClipping->True, PlotRangePadding->{ Scaled[0.02], Scaled[0.02]}]], "Output", CellChangeTimes->{3.529410247262*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Animate", "[", RowBox[{ RowBox[{"DotPlot", "[", "t", "]"}], ",", RowBox[{"{", RowBox[{"t", ",", "0", ",", FractionBox[ RowBox[{"2", "\[Pi]"}], RowBox[{"\[Omega]", "[", "1", "]"}]]}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.5294102651730003`*^9, 3.5294102948459997`*^9}}], Cell[BoxData[ TagBox[ StyleBox[ DynamicModuleBox[{$CellContext`t$$ = 1.3521938547403427`, Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{ Hold[$CellContext`t$$], 0, 2 2^Rational[1, 2] (-1 + 3^Rational[1, 2])^(-1) Pi}}, Typeset`size$$ = { 540., {164., 173.}}, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = True, $CellContext`t$2748$$ = 0}, DynamicBox[Manipulate`ManipulateBoxes[ 1, StandardForm, "Variables" :> {$CellContext`t$$ = 0}, "ControllerVariables" :> { Hold[$CellContext`t$$, $CellContext`t$2748$$, 0]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> $CellContext`DotPlot[$CellContext`t$$], "Specifications" :> {{$CellContext`t$$, 0, 2 2^Rational[1, 2] (-1 + 3^Rational[1, 2])^(-1) Pi, AppearanceElements -> { "ProgressSlider", "PlayPauseButton", "FasterSlowerButtons", "DirectionButton"}}}, "Options" :> { ControlType -> Animator, AppearanceElements -> None, DefaultBaseStyle -> "Animate", DefaultLabelStyle -> "AnimateLabel", SynchronousUpdating -> True, ShrinkingDelay -> 10.}, "DefaultOptions" :> {}], ImageSizeCache->{610., {221., 228.}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, SynchronousInitialization->True, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Animate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]], "Output", CellChangeTimes->{3.529410266488*^9, 3.5294103248929996`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Animate", "[", RowBox[{ RowBox[{"Show", "[", RowBox[{ RowBox[{"DotPlot", "[", "t", "]"}], ",", " ", RowBox[{"ContPlot", "[", "t", "]"}]}], "]"}], ",", RowBox[{"{", RowBox[{"t", ",", "0", ",", FractionBox[ RowBox[{"2", "\[Pi]"}], RowBox[{"\[Omega]", "[", "1", "]"}]]}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.529410341257*^9, 3.529410368947*^9}}], Cell[BoxData[ TagBox[ StyleBox[ DynamicModuleBox[{$CellContext`t$$ = 7.851471960785112, Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{ Hold[$CellContext`t$$], 0, 2 2^Rational[1, 2] (-1 + 3^Rational[1, 2])^(-1) Pi}}, Typeset`size$$ = { 540., {164., 173.}}, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = True, $CellContext`t$3979$$ = 0}, DynamicBox[Manipulate`ManipulateBoxes[ 1, StandardForm, "Variables" :> {$CellContext`t$$ = 0}, "ControllerVariables" :> { Hold[$CellContext`t$$, $CellContext`t$3979$$, 0]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> Show[ $CellContext`DotPlot[$CellContext`t$$], $CellContext`ContPlot[$CellContext`t$$]], "Specifications" :> {{$CellContext`t$$, 0, 2 2^Rational[1, 2] (-1 + 3^Rational[1, 2])^(-1) Pi, AppearanceElements -> { "ProgressSlider", "PlayPauseButton", "FasterSlowerButtons", "DirectionButton"}}}, "Options" :> { ControlType -> Animator, AppearanceElements -> None, DefaultBaseStyle -> "Animate", DefaultLabelStyle -> "AnimateLabel", SynchronousUpdating -> True, ShrinkingDelay -> 10.}, "DefaultOptions" :> {}], ImageSizeCache->{610., {221., 228.}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, SynchronousInitialization->True, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Animate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]], "Output", CellChangeTimes->{{3.52941035438*^9, 3.529410370881*^9}, 3.529410403032*^9}] }, Open ]] }, WindowSize->{1006, 700}, WindowMargins->{{1, Automatic}, {1, Automatic}}, PrintingCopies->1, PrintingPageRange->{32000, 32000}, PrintingOptions->{"Magnification"->1., "PaperOrientation"->"Portrait", "PaperSize"->{600, 780}}, Magnification:>FEPrivate`If[ FEPrivate`Equal[FEPrivate`$VersionNumber, 6.], 1.5, 1.5 Inherited], FrontEndVersion->"8.0 for Microsoft Windows (32-bit) (February 23, 2011)", StyleDefinitions->"Default.nb" ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[557, 20, 371, 9, 71, "Input"], Cell[931, 31, 197, 6, 79, "Input"], Cell[CellGroupData[{ Cell[1153, 41, 639, 21, 127, "Input"], Cell[1795, 64, 780, 22, 68, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[2612, 91, 125, 2, 43, "Input"], Cell[2740, 95, 795, 25, 81, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[3572, 125, 129, 2, 43, "Input"], Cell[3704, 129, 239, 7, 50, "Output"] }, Open ]], Cell[3958, 139, 198, 5, 66, "Input"], Cell[4159, 146, 162, 4, 43, "Input"], Cell[4324, 152, 432, 14, 78, "Input"], Cell[CellGroupData[{ Cell[4781, 170, 119, 2, 43, "Input"], Cell[4903, 174, 368, 13, 68, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[5308, 192, 182, 5, 77, "Input"], Cell[5493, 199, 1924, 73, 178, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[7454, 277, 219, 6, 43, "Input"], Cell[7676, 285, 1479, 54, 123, "Output"] }, Open ]], Cell[9170, 342, 343, 10, 67, "Input"], Cell[CellGroupData[{ Cell[9538, 356, 378, 9, 48, "Input"], Cell[9919, 367, 285, 8, 50, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[10241, 380, 134, 2, 43, "Input"], Cell[10378, 384, 240, 7, 50, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[10655, 396, 165, 4, 43, "Input"], Cell[10823, 402, 91, 1, 42, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[10951, 408, 165, 4, 43, "Input"], Cell[11119, 414, 89, 1, 42, "Output"] }, Open ]], Cell[11223, 418, 91, 1, 43, "Input"], Cell[11317, 421, 238, 6, 43, "Input"], Cell[CellGroupData[{ Cell[11580, 431, 138, 3, 43, "Input"], Cell[11721, 436, 94, 1, 42, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[11852, 442, 138, 3, 43, "Input"], Cell[11993, 447, 91, 1, 42, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[12121, 453, 143, 3, 43, "Input"], Cell[12267, 458, 67, 1, 42, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[12371, 464, 138, 3, 43, "Input"], Cell[12512, 469, 67, 1, 42, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[12616, 475, 143, 3, 43, "Input"], Cell[12762, 480, 84, 2, 42, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[12883, 487, 1841, 54, 203, "Input"], Cell[14727, 543, 38652, 642, 342, "Output"] }, Open ]], Cell[53394, 1188, 86, 1, 43, "Input"], Cell[CellGroupData[{ Cell[53505, 1193, 2804, 78, 340, "Input"], Cell[56312, 1273, 2672, 52, 473, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[59021, 1330, 734, 22, 119, "Input"], Cell[59758, 1354, 1026, 28, 346, "Output"] }, Open ]], Cell[60799, 1385, 2285, 68, 242, "Input"], Cell[CellGroupData[{ Cell[63109, 1457, 126, 2, 43, "Input"], Cell[63238, 1461, 35756, 597, 359, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[99031, 2063, 327, 9, 73, "Input"], Cell[99361, 2074, 1960, 40, 473, "Output"] }, Open ]], Cell[101336, 2117, 1326, 38, 148, "Input"], Cell[CellGroupData[{ Cell[102687, 2159, 125, 2, 43, "Input"], Cell[102815, 2163, 1005, 28, 346, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[103857, 2196, 336, 9, 73, "Input"], Cell[104196, 2207, 1986, 40, 473, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[106219, 2252, 428, 12, 73, "Input"], Cell[106650, 2266, 2057, 41, 473, "Output"] }, Open ]] } ] *) (* End of internal cache information *)