From b124a5c1333e91a7348a1e0f5f6ba6e5ff917641 Mon Sep 17 00:00:00 2001 From: Jaron Kent-Dobias Date: Fri, 16 Apr 2021 17:52:37 +0200 Subject: Added knowledge about Yang-Lee, dispersion relation. --- figs/F_higher_singularities.pdf | Bin 0 -> 8104 bytes figs/F_lower_singularities.pdf | Bin 0 -> 6544 bytes figs/F_theta_singularities.pdf | Bin 0 -> 8380 bytes figs/contour_path.pdf | Bin 0 -> 9290 bytes figs/figures.nb | 10149 ++++++++++++++++++++++++++++++++++++++ ising_scaling.bib | 154 +- ising_scaling.tex | 255 +- 7 files changed, 10516 insertions(+), 42 deletions(-) create mode 100644 figs/F_higher_singularities.pdf create mode 100644 figs/F_lower_singularities.pdf create mode 100644 figs/F_theta_singularities.pdf create mode 100644 figs/contour_path.pdf create mode 100644 figs/figures.nb diff --git a/figs/F_higher_singularities.pdf b/figs/F_higher_singularities.pdf new file mode 100644 index 0000000..136c212 Binary files /dev/null and b/figs/F_higher_singularities.pdf differ diff --git a/figs/F_lower_singularities.pdf b/figs/F_lower_singularities.pdf new file mode 100644 index 0000000..effbd82 Binary files /dev/null and b/figs/F_lower_singularities.pdf differ diff --git a/figs/F_theta_singularities.pdf b/figs/F_theta_singularities.pdf new file mode 100644 index 0000000..ec21fc1 Binary files /dev/null and b/figs/F_theta_singularities.pdf differ diff --git a/figs/contour_path.pdf b/figs/contour_path.pdf new file mode 100644 index 0000000..e2338c8 Binary files /dev/null and b/figs/contour_path.pdf differ diff --git a/figs/figures.nb b/figs/figures.nb new file mode 100644 index 0000000..2216101 --- /dev/null +++ b/figs/figures.nb @@ -0,0 +1,10149 @@ +(* Content-type: application/vnd.wolfram.mathematica *) + +(*** Wolfram Notebook File ***) +(* http://www.wolfram.com/nb *) + +(* CreatedBy='Mathematica 12.2' *) + +(*CacheID: 234*) +(* Internal cache information: +NotebookFileLineBreakTest +NotebookFileLineBreakTest +NotebookDataPosition[ 158, 7] +NotebookDataLength[ 527303, 10141] +NotebookOptionsPosition[ 516698, 9954] +NotebookOutlinePosition[ 517098, 9970] +CellTagsIndexPosition[ 517055, 9967] +WindowFrame->Normal*) + +(* Beginning of Notebook Content *) +Notebook[{ + +Cell[CellGroupData[{ +Cell[BoxData[ + RowBox[{"p1", "=", + RowBox[{"Plot", "[", + RowBox[{"\[ImaginaryI]", ",", + RowBox[{"{", + RowBox[{"x", ",", + RowBox[{"-", "1"}], ",", "1"}], "}"}], ",", + RowBox[{"AxesStyle", "\[Rule]", "Dashed"}], ",", + RowBox[{"Ticks", "\[Rule]", "False"}], ",", + RowBox[{"PlotStyle", "\[Rule]", + RowBox[{"{", + RowBox[{"Black", ",", "Thick"}], "}"}]}], ",", + RowBox[{"AxesLabel", "\[Rule]", + RowBox[{"{", + RowBox[{ + RowBox[{"Re", "[", "\[Xi]", "]"}], ",", + RowBox[{"Im", "[", "\[Xi]", "]"}]}], "}"}]}], ",", + RowBox[{"Epilog", "\[Rule]", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{"Thick", ",", + RowBox[{"Line", "[", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{"-", "1"}], ",", "0"}], "}"}], ",", + RowBox[{"{", + RowBox[{"0", ",", "0"}], "}"}]}], "}"}], "]"}]}], "}"}], ",", + RowBox[{"Disk", "[", + RowBox[{ + RowBox[{"{", + RowBox[{"0", ",", "0"}], "}"}], ",", "0.025"}], "]"}]}], "}"}]}], + ",", + RowBox[{"AspectRatio", "\[Rule]", + RowBox[{"1", "/", "GoldenRatio"}]}], ",", + RowBox[{"PlotRange", "\[Rule]", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{"-", "1"}], ",", "1"}], "}"}], ",", + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{"-", "1"}], ",", "1"}], "}"}], "/", "GoldenRatio"}]}], + "}"}]}], ",", + RowBox[{"LabelStyle", "\[Rule]", + RowBox[{"{", + RowBox[{ + RowBox[{"FontFamily", "\[Rule]", "\"\\""}], ",", + RowBox[{"FontSize", "\[Rule]", "12"}], ",", "Black"}], "}"}]}], ",", + RowBox[{"ImageSize", "\[Rule]", "340"}]}], "]"}]}]], "Input", + CellChangeTimes->{{3.827382480044902*^9, 3.8273826908509808`*^9}, { + 3.827382820190197*^9, 3.827382840645884*^9}, {3.82738300603374*^9, + 3.827383160348928*^9}, {3.827385962751856*^9, 3.82738598922388*^9}, { + 3.827386034376981*^9, 3.827386035376443*^9}, {3.8273869985697823`*^9, + 3.8273869997536163`*^9}}, + CellLabel->"In[85]:=",ExpressionUUID->"c0a33ae3-38dd-4996-a6db-1046c247f003"], + +Cell[BoxData[ + GraphicsBox[{GraphicsComplexBox[CompressedData[" +1:eJxTTMoPSmViYGAwAmIQrWcv9ur///f7GaCg/HxLbvq+d3D+lSvcrw4mvoXz +ZQ/ki5jLvIHzt2YfYeW/+wrOT+gx/HCz6SWc/2NSdcd++xdw/mK+e5IzHj6D +8+d4GRZd7nwK5zflJFZoej6B86uZV5UXvX0E5yc2nFe5tuIhnD9179MZc7Ie +wPm77mvwrFG6B+crCzg4hcy7Dedv0urIevT4Bpx//+hGBTOza3D+U52pRvu3 +XYbzBetWmukxXoTzdcze6yz9fAbOb3Z5e2FnxXE4XzRk3YRI8UMI+74d5T+h +sgvOX3r7ae/LlnVwfmygzJbbyVPg/J1c1VcPlU62h/FNHzHKNUash/OVP+z+ +aXVoJ5zvufjmWb+IQ3C+q68Q89etx+H8/vjrDQbbz8D5x/1keQOELsL5bxVF +6y7Nugznl5ZoJ/aLXYPzr98RCEo7cQPOT6i0ec7ucxvOP6xt3nWY9R6cr8a5 +58USjwdwvuyebFfWjodwPsMvppVFjx7B+d8D98YdVX0C5982iZdWbXkK5xeE +Cwgq3XkG50tOeRLBIvsCzl8XvWD554qXcH64bb3Hib2v4PyNcblKVn9ew/k/ +uJyZd4a+hfODLlqbyc54B+dD8wOcDwD7wNOr + "], {}], {}}, + AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], + Axes->{True, True}, + AxesLabel->{ + FormBox[ + RowBox[{"Re", "(", "\[Xi]", ")"}], TraditionalForm], + FormBox[ + RowBox[{"Im", "(", "\[Xi]", ")"}], TraditionalForm]}, + AxesOrigin->{0, 0}, + AxesStyle->Dashing[{Small, Small}], + DisplayFunction->Identity, + Epilog->{{ + Thickness[Large], + LineBox[{{-1, 0}, {0, 0}}]}, + DiskBox[{0, 0}, 0.025]}, + Frame->{{False, False}, {False, False}}, + FrameLabel->{{None, None}, {None, None}}, + FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}}, + GridLines->{None, None}, + GridLinesStyle->Directive[ + GrayLevel[0.5, 0.4]], + ImagePadding->All, + ImageSize->340, + LabelStyle->{FontFamily -> "Times", FontSize -> 12, + GrayLevel[0]}, + Method->{ + "DefaultBoundaryStyle" -> Automatic, + "DefaultGraphicsInteraction" -> { + "Version" -> 1.2, "TrackMousePosition" -> {True, False}, + "Effects" -> { + "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, + "Droplines" -> { + "freeformCursorMode" -> True, + "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultMeshStyle" -> + AbsolutePointSize[6], "ScalingFunctions" -> None, + "CoordinatesToolOptions" -> {"DisplayFunction" -> ({ + (Identity[#]& )[ + Part[#, 1]], + (Identity[#]& )[ + Part[#, 2]]}& ), "CopiedValueFunction" -> ({ + (Identity[#]& )[ + Part[#, 1]], + (Identity[#]& )[ + Part[#, 2]]}& )}}, + PlotRange-> + NCache[{{-1, 1}, {(-1)/GoldenRatio, GoldenRatio^(-1)}}, {{-1, + 1}, {-0.6180339887498948, 0.6180339887498948}}], + PlotRangeClipping->True, + PlotRangePadding->{{0, 0}, {0, 0}}, + Ticks->{{}, {}}]], "Output", + CellChangeTimes->{{3.827382624611155*^9, 3.8273826915148993`*^9}, { + 3.827382821172866*^9, 3.827382840956325*^9}, {3.827383007560814*^9, + 3.827383129164433*^9}, 3.827383160604924*^9, {3.827385963050185*^9, + 3.8273859898238077`*^9}, {3.82738602858241*^9, 3.827386035704603*^9}, + 3.827387000123047*^9}, + CellLabel->"Out[85]=",ExpressionUUID->"fa3177c1-247d-40dc-9f56-c55f92b9bc73"] +}, Open ]], + +Cell[BoxData[ + RowBox[{ + RowBox[{"Export", "[", + RowBox[{ + "\"\<~/doc/research/first_order_singularities/paper/figs/F_lower_\ +singularities.pdf\>\"", ",", "p1"}], "]"}], ";"}]], "Input", + CellChangeTimes->{{3.827382842246332*^9, 3.827382891238717*^9}}, + CellLabel->"In[86]:=",ExpressionUUID->"92b6b8b4-4b9d-4606-b12e-d1503be8044a"], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"p2", "=", + RowBox[{"Plot", "[", + RowBox[{"\[ImaginaryI]", ",", + RowBox[{"{", + RowBox[{"x", ",", + RowBox[{"-", "1"}], ",", "1"}], "}"}], ",", + RowBox[{"AxesStyle", "\[Rule]", "Dashed"}], ",", + RowBox[{"Ticks", "\[Rule]", "False"}], ",", + RowBox[{"PlotStyle", "\[Rule]", + RowBox[{"{", + RowBox[{"Black", ",", "Thick"}], "}"}]}], ",", + RowBox[{"AxesLabel", "\[Rule]", + RowBox[{"{", + RowBox[{ + RowBox[{"Re", "[", "\[Xi]", "]"}], ",", + RowBox[{"Im", "[", "\[Xi]", "]"}]}], "}"}]}], ",", + RowBox[{"Epilog", "\[Rule]", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{"Thick", ",", + RowBox[{"Line", "[", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{"0", ",", + RowBox[{ + RowBox[{"1", "/", "GoldenRatio"}], "/", "2"}]}], "}"}], ",", + RowBox[{"{", + RowBox[{"0", ",", "1"}], "}"}]}], "}"}], "]"}], ",", + RowBox[{"Line", "[", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{"0", ",", + RowBox[{ + RowBox[{ + RowBox[{"-", "1"}], "/", "GoldenRatio"}], "/", "2"}]}], "}"}], + ",", + RowBox[{"{", + RowBox[{"0", ",", + RowBox[{"-", "1"}]}], "}"}]}], "}"}], "]"}]}], "}"}], ",", + RowBox[{"RegularPolygon", "[", + RowBox[{ + RowBox[{"{", + RowBox[{"0", ",", + RowBox[{ + RowBox[{"1", "/", "GoldenRatio"}], "/", "2"}]}], "}"}], ",", + "0.025", ",", "4"}], "]"}], ",", + RowBox[{"RegularPolygon", "[", + RowBox[{ + RowBox[{"{", + RowBox[{"0", ",", + RowBox[{ + RowBox[{ + RowBox[{"-", "1"}], "/", "GoldenRatio"}], "/", "2"}]}], "}"}], + ",", "0.025", ",", "4"}], "]"}], ",", "\[IndentingNewLine]", + RowBox[{"Line", "[", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{"0", ",", + RowBox[{ + RowBox[{"1", "/", "GoldenRatio"}], "/", "2"}]}], "}"}], ",", + RowBox[{"{", + RowBox[{"0.05", ",", + RowBox[{ + RowBox[{"1", "/", "GoldenRatio"}], "/", "2"}]}], "}"}]}], "}"}], + "]"}], ",", "\[IndentingNewLine]", + RowBox[{"{", + RowBox[{"Black", ",", + RowBox[{"Text", "[", + RowBox[{ + RowBox[{"Style", "[", + RowBox[{ + "\"\<\!\(\*StyleBox[\"i\",FontSlant->\"Italic\"]\)\!\(\*\ +SubscriptBox[\(\[Xi]\), \(YL\)]\)\>\"", ",", + RowBox[{"FontSize", "\[Rule]", "12"}], ",", "Black", ",", + RowBox[{"FontFamily", "\[Rule]", "\"\\""}]}], "]"}], ",", + " ", + RowBox[{"{", + RowBox[{"0.125", ",", + RowBox[{ + RowBox[{"1", "/", "GoldenRatio"}], "/", "2"}]}], "}"}]}], + "]"}]}], "}"}]}], "\[IndentingNewLine]", "}"}]}], ",", + RowBox[{"AspectRatio", "\[Rule]", + RowBox[{"1", "/", "GoldenRatio"}]}], ",", + RowBox[{"PlotRange", "\[Rule]", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{"-", "1"}], ",", "1"}], "}"}], ",", + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{"-", "1"}], ",", "1"}], "}"}], "/", "GoldenRatio"}]}], + "}"}]}], ",", + RowBox[{"LabelStyle", "\[Rule]", + RowBox[{"{", + RowBox[{ + RowBox[{"FontFamily", "\[Rule]", "\"\\""}], ",", + RowBox[{"FontSize", "\[Rule]", "12"}], ",", "Black"}], "}"}]}], ",", + RowBox[{"ImageSize", "\[Rule]", "340"}]}], "]"}]}]], "Input", + CellChangeTimes->{{3.827382480044902*^9, 3.8273826908509808`*^9}, { + 3.827382820190197*^9, 3.827382840645884*^9}, {3.82738300603374*^9, + 3.8273831764043293`*^9}, {3.8273860050562143`*^9, 3.827386063937243*^9}, { + 3.827386126458579*^9, 3.82738620035579*^9}, {3.82738626700533*^9, + 3.827386268132721*^9}, {3.827386902576284*^9, 3.82738699484161*^9}, { + 3.827387056043375*^9, 3.827387113115541*^9}, {3.827387242150291*^9, + 3.827387318344166*^9}, {3.827387529243909*^9, 3.827387531995368*^9}}, + CellLabel-> + "In[132]:=",ExpressionUUID->"4b23646d-66a7-4f99-9cd1-77b8bfb048e6"], + +Cell[BoxData[ + GraphicsBox[{GraphicsComplexBox[CompressedData[" +1:eJxTTMoPSmViYGAwAmIQrWcv9ur///f7GaCg/HxLbvq+d3D+lSvcrw4mvoXz +ZQ/ki5jLvIHzt2YfYeW/+wrOT+gx/HCz6SWc/2NSdcd++xdw/mK+e5IzHj6D +8+d4GRZd7nwK5zflJFZoej6B86uZV5UXvX0E5yc2nFe5tuIhnD9179MZc7Ie +wPm77mvwrFG6B+crCzg4hcy7Dedv0urIevT4Bpx//+hGBTOza3D+U52pRvu3 +XYbzBetWmukxXoTzdcze6yz9fAbOb3Z5e2FnxXE4XzRk3YRI8UMI+74d5T+h +sgvOX3r7ae/LlnVwfmygzJbbyVPg/J1c1VcPlU62h/FNHzHKNUash/OVP+z+ +aXVoJ5zvufjmWb+IQ3C+q68Q89etx+H8/vjrDQbbz8D5x/1keQOELsL5bxVF +6y7Nugznl5ZoJ/aLXYPzr98RCEo7cQPOT6i0ec7ucxvOP6xt3nWY9R6cr8a5 +58USjwdwvuyebFfWjodwPsMvppVFjx7B+d8D98YdVX0C5982iZdWbXkK5xeE +Cwgq3XkG50tOeRLBIvsCzl8XvWD554qXcH64bb3Hib2v4PyNcblKVn9ew/k/ +uJyZd4a+hfODLlqbyc54B+dD8wOcDwD7wNOr + "], {}], {}}, + AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], + Axes->{True, True}, + AxesLabel->{ + FormBox[ + RowBox[{"Re", "(", "\[Xi]", ")"}], TraditionalForm], + FormBox[ + RowBox[{"Im", "(", "\[Xi]", ")"}], TraditionalForm]}, + AxesOrigin->{0, 0}, + AxesStyle->Dashing[{Small, Small}], + DisplayFunction->Identity, + Epilog->{{ + Thickness[Large], + LineBox[ + NCache[{{0, Rational[1, 2]/GoldenRatio}, {0, 1}}, {{ + 0, 0.3090169943749474}, {0, 1}}]], + LineBox[ + NCache[{{0, Rational[-1, 2]/GoldenRatio}, {0, -1}}, {{ + 0, -0.3090169943749474}, {0, -1}}]]}, + InterpretationBox[ + PolygonBox[{{0.01767766952966369, 0.2913393248452837}, { + 0.01767766952966369, 0.3266946639046111}, {-0.017677669529663688`, + 0.3266946639046111}, {-0.01767766952966369, 0.2913393248452837}}], + RegularPolygon[{0, Rational[1, 2]/GoldenRatio}, 0.025, 4]], + InterpretationBox[ + PolygonBox[{{0.01767766952966369, -0.3266946639046111}, { + 0.01767766952966369, -0.2913393248452837}, {-0.017677669529663688`, \ +-0.2913393248452837}, {-0.01767766952966369, -0.3266946639046111}}], + RegularPolygon[{0, Rational[-1, 2]/GoldenRatio}, 0.025, 4]], + LineBox[ + NCache[{{0, Rational[1, 2]/GoldenRatio}, { + 0.05, Rational[1, 2]/GoldenRatio}}, {{0, 0.3090169943749474}, {0.05, + 0.3090169943749474}}]], { + GrayLevel[0], + InsetBox[ + FormBox[ + StyleBox[ + "\"\\!\\(\\*StyleBox[\\\"i\\\",FontSlant->\\\"Italic\\\"]\\)\\!\\(\\*\ +SubscriptBox[\\(\[Xi]\\), \\(YL\\)]\\)\"", FontSize -> 12, + GrayLevel[0], FontFamily -> "Times", StripOnInput -> False], + TraditionalForm], + NCache[{0.125, Rational[1, 2]/GoldenRatio}, {0.125, + 0.3090169943749474}]]}}, + Frame->{{False, False}, {False, False}}, + FrameLabel->{{None, None}, {None, None}}, + FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}}, + GridLines->{None, None}, + GridLinesStyle->Directive[ + GrayLevel[0.5, 0.4]], + ImagePadding->All, + ImageSize->340, + LabelStyle->{FontFamily -> "Times", FontSize -> 12, + GrayLevel[0]}, + Method->{ + "DefaultBoundaryStyle" -> Automatic, + "DefaultGraphicsInteraction" -> { + "Version" -> 1.2, "TrackMousePosition" -> {True, False}, + "Effects" -> { + "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, + "Droplines" -> { + "freeformCursorMode" -> True, + "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultMeshStyle" -> + AbsolutePointSize[6], "ScalingFunctions" -> None, + "CoordinatesToolOptions" -> {"DisplayFunction" -> ({ + (Identity[#]& )[ + Part[#, 1]], + (Identity[#]& )[ + Part[#, 2]]}& ), "CopiedValueFunction" -> ({ + (Identity[#]& )[ + Part[#, 1]], + (Identity[#]& )[ + Part[#, 2]]}& )}}, + PlotRange-> + NCache[{{-1, 1}, {(-1)/GoldenRatio, GoldenRatio^(-1)}}, {{-1, + 1}, {-0.6180339887498948, 0.6180339887498948}}], + PlotRangeClipping->True, + PlotRangePadding->{{0, 0}, {0, 0}}, + Ticks->{{}, {}}]], "Output", + CellChangeTimes->{{3.82738699503043*^9, 3.827387001000444*^9}, { + 3.827387056404755*^9, 3.8273871135979233`*^9}, {3.827387261706016*^9, + 3.827387318714815*^9}, 3.827387532223402*^9}, + CellLabel-> + "Out[132]=",ExpressionUUID->"e864482d-d84f-4248-97a9-69e174917c6a"] +}, Open ]], + +Cell[BoxData[ + RowBox[{ + RowBox[{"Export", "[", + RowBox[{ + "\"\<~/doc/research/first_order_singularities/paper/figs/F_higher_\ +singularities.pdf\>\"", ",", "p2"}], "]"}], ";"}]], "Input", + CellChangeTimes->{{3.827382842246332*^9, 3.827382891238717*^9}, { + 3.8273862326284933`*^9, 3.827386237604206*^9}}, + CellLabel-> + "In[133]:=",ExpressionUUID->"2a30392f-4cec-4410-b883-5f9d8fbb9b77"], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"p3", "=", + RowBox[{"Plot", "[", + RowBox[{"\[ImaginaryI]", ",", + RowBox[{"{", + RowBox[{"x", ",", + RowBox[{"-", "1"}], ",", "1"}], "}"}], ",", + RowBox[{"AxesStyle", "\[Rule]", "Dashed"}], ",", + RowBox[{"Ticks", "\[Rule]", "False"}], ",", + RowBox[{"PlotStyle", "\[Rule]", + RowBox[{"{", + RowBox[{"Black", ",", "Thick"}], "}"}]}], ",", + RowBox[{"AxesLabel", "\[Rule]", + RowBox[{"{", + RowBox[{ + RowBox[{"Re", "[", "\[Theta]", "]"}], ",", + RowBox[{"Im", "[", "\[Theta]", "]"}]}], "}"}]}], ",", + RowBox[{"Epilog", "\[Rule]", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{"Thick", ",", + RowBox[{"Line", "[", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{"0", ",", + RowBox[{ + RowBox[{"1", "/", "GoldenRatio"}], "/", "2"}]}], "}"}], ",", + RowBox[{"{", + RowBox[{"0", ",", "1"}], "}"}]}], "}"}], "]"}], ",", + RowBox[{"Line", "[", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{"0", ",", + RowBox[{ + RowBox[{ + RowBox[{"-", "1"}], "/", "GoldenRatio"}], "/", "2"}]}], "}"}], + ",", + RowBox[{"{", + RowBox[{"0", ",", + RowBox[{"-", "1"}]}], "}"}]}], "}"}], "]"}]}], "}"}], ",", + RowBox[{"RegularPolygon", "[", + RowBox[{ + RowBox[{"{", + RowBox[{"0", ",", + RowBox[{ + RowBox[{"1", "/", "GoldenRatio"}], "/", "2"}]}], "}"}], ",", + "0.025", ",", "4"}], "]"}], ",", + RowBox[{"RegularPolygon", "[", + RowBox[{ + RowBox[{"{", + RowBox[{"0", ",", + RowBox[{ + RowBox[{ + RowBox[{"-", "1"}], "/", "GoldenRatio"}], "/", "2"}]}], "}"}], + ",", "0.025", ",", "4"}], "]"}], ",", + RowBox[{"{", + RowBox[{"Thick", ",", + RowBox[{"Line", "[", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{"-", "1"}], ",", "0"}], "}"}], ",", + RowBox[{"{", + RowBox[{ + RowBox[{"-", "0.75"}], ",", "0"}], "}"}]}], "}"}], "]"}]}], + "}"}], ",", + RowBox[{"Disk", "[", + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{"-", "0.75"}], ",", "0"}], "}"}], ",", "0.025"}], "]"}], + ",", + RowBox[{"{", + RowBox[{"Thick", ",", + RowBox[{"Line", "[", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{"1", ",", "0"}], "}"}], ",", + RowBox[{"{", + RowBox[{"0.75", ",", "0"}], "}"}]}], "}"}], "]"}]}], "}"}], ",", + + RowBox[{"Disk", "[", + RowBox[{ + RowBox[{"{", + RowBox[{"0.75", ",", "0"}], "}"}], ",", "0.025"}], "]"}], ",", + "\[IndentingNewLine]", + RowBox[{"Line", "[", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{"0.75", ",", "0"}], "}"}], ",", + RowBox[{"{", + RowBox[{"0.75", ",", "0.05"}], "}"}]}], "}"}], "]"}], ",", + "\[IndentingNewLine]", + RowBox[{"Line", "[", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{"0", ",", + RowBox[{ + RowBox[{"1", "/", "GoldenRatio"}], "/", "2"}]}], "}"}], ",", + RowBox[{"{", + RowBox[{"0.05", ",", + RowBox[{ + RowBox[{"1", "/", "GoldenRatio"}], "/", "2"}]}], "}"}]}], "}"}], + "]"}], ",", "\[IndentingNewLine]", + RowBox[{"{", + RowBox[{"Black", ",", + RowBox[{"Text", "[", + RowBox[{ + RowBox[{"Style", "[", + RowBox[{ + "\"\<\!\(\*StyleBox[\"i\",FontSlant->\"Italic\"]\)\!\(\*\ +SubscriptBox[\(\[Theta]\), \(YL\)]\)\>\"", ",", + RowBox[{"FontSize", "\[Rule]", "12"}], ",", "Black", ",", + RowBox[{"FontFamily", "\[Rule]", "\"\\""}]}], "]"}], ",", + " ", + RowBox[{"{", + RowBox[{"0.125", ",", + RowBox[{ + RowBox[{"1", "/", "GoldenRatio"}], "/", "2"}]}], "}"}]}], + "]"}]}], "}"}], ",", "\[IndentingNewLine]", + RowBox[{"{", + RowBox[{"Black", ",", + RowBox[{"Text", "[", + RowBox[{ + RowBox[{"Style", "[", + RowBox[{ + "\"\<\!\(\*SubscriptBox[\(\[Theta]\), \(c\)]\)\>\"", ",", + RowBox[{"FontSize", "\[Rule]", "12"}], ",", "Black", ",", + RowBox[{"FontFamily", "\[Rule]", "\"\\""}]}], "]"}], ",", + " ", + RowBox[{"{", + RowBox[{"0.75", ",", "0.1"}], "}"}]}], "]"}]}], "}"}]}], + "\[IndentingNewLine]", "}"}]}], ",", + RowBox[{"AspectRatio", "\[Rule]", + RowBox[{"1", "/", "GoldenRatio"}]}], ",", + RowBox[{"PlotRange", "\[Rule]", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{"-", "1"}], ",", "1"}], "}"}], ",", + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{"-", "1"}], ",", "1"}], "}"}], "/", "GoldenRatio"}]}], + "}"}]}], ",", + RowBox[{"LabelStyle", "\[Rule]", + RowBox[{"{", + RowBox[{ + RowBox[{"FontFamily", "\[Rule]", "\"\\""}], ",", + RowBox[{"FontSize", "\[Rule]", "12"}], ",", "Black"}], "}"}]}], ",", + RowBox[{"ImageSize", "\[Rule]", "340"}]}], "]"}]}]], "Input", + CellChangeTimes->{{3.827382480044902*^9, 3.8273826908509808`*^9}, { + 3.827382820190197*^9, 3.827382840645884*^9}, {3.82738300603374*^9, + 3.8273831764043293`*^9}, {3.8273860050562143`*^9, 3.827386063937243*^9}, { + 3.827386126458579*^9, 3.82738620035579*^9}, {3.82738626700533*^9, + 3.8273863320539207`*^9}, {3.8273863645590267`*^9, 3.8273863742232637`*^9}, { + 3.827386476137185*^9, 3.827386479416823*^9}, {3.8273870103864107`*^9, + 3.8273870114740887`*^9}, {3.827387151108595*^9, 3.827387206893936*^9}, { + 3.8273873335042467`*^9, 3.827387391017824*^9}, {3.82738742603411*^9, + 3.827387500451023*^9}}, + CellLabel-> + "In[130]:=",ExpressionUUID->"3cdeb246-19f3-4cd6-9c3a-ace23d2eb4e6"], + +Cell[BoxData[ + GraphicsBox[{GraphicsComplexBox[CompressedData[" +1:eJxTTMoPSmViYGAwAmIQrWcv9ur///f7GaCg/HxLbvq+d3D+lSvcrw4mvoXz +ZQ/ki5jLvIHzt2YfYeW/+wrOT+gx/HCz6SWc/2NSdcd++xdw/mK+e5IzHj6D +8+d4GRZd7nwK5zflJFZoej6B86uZV5UXvX0E5yc2nFe5tuIhnD9179MZc7Ie +wPm77mvwrFG6B+crCzg4hcy7Dedv0urIevT4Bpx//+hGBTOza3D+U52pRvu3 +XYbzBetWmukxXoTzdcze6yz9fAbOb3Z5e2FnxXE4XzRk3YRI8UMI+74d5T+h +sgvOX3r7ae/LlnVwfmygzJbbyVPg/J1c1VcPlU62h/FNHzHKNUash/OVP+z+ +aXVoJ5zvufjmWb+IQ3C+q68Q89etx+H8/vjrDQbbz8D5x/1keQOELsL5bxVF +6y7Nugznl5ZoJ/aLXYPzr98RCEo7cQPOT6i0ec7ucxvOP6xt3nWY9R6cr8a5 +58USjwdwvuyebFfWjodwPsMvppVFjx7B+d8D98YdVX0C5982iZdWbXkK5xeE +Cwgq3XkG50tOeRLBIvsCzl8XvWD554qXcH64bb3Hib2v4PyNcblKVn9ew/k/ +uJyZd4a+hfODLlqbyc54B+dD8wOcDwD7wNOr + "], {}], {}}, + AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], + Axes->{True, True}, + AxesLabel->{ + FormBox[ + RowBox[{"Re", "(", "\[Theta]", ")"}], TraditionalForm], + FormBox[ + RowBox[{"Im", "(", "\[Theta]", ")"}], TraditionalForm]}, + AxesOrigin->{0, 0}, + AxesStyle->Dashing[{Small, Small}], + DisplayFunction->Identity, + Epilog->{{ + Thickness[Large], + LineBox[ + NCache[{{0, Rational[1, 2]/GoldenRatio}, {0, 1}}, {{ + 0, 0.3090169943749474}, {0, 1}}]], + LineBox[ + NCache[{{0, Rational[-1, 2]/GoldenRatio}, {0, -1}}, {{ + 0, -0.3090169943749474}, {0, -1}}]]}, + InterpretationBox[ + PolygonBox[{{0.01767766952966369, 0.2913393248452837}, { + 0.01767766952966369, 0.3266946639046111}, {-0.017677669529663688`, + 0.3266946639046111}, {-0.01767766952966369, 0.2913393248452837}}], + RegularPolygon[{0, Rational[1, 2]/GoldenRatio}, 0.025, 4]], + InterpretationBox[ + PolygonBox[{{0.01767766952966369, -0.3266946639046111}, { + 0.01767766952966369, -0.2913393248452837}, {-0.017677669529663688`, \ +-0.2913393248452837}, {-0.01767766952966369, -0.3266946639046111}}], + RegularPolygon[{0, Rational[-1, 2]/GoldenRatio}, 0.025, 4]], { + Thickness[Large], + LineBox[{{-1, 0}, {-0.75, 0}}]}, + DiskBox[{-0.75, 0}, 0.025], { + Thickness[Large], + LineBox[{{1, 0}, {0.75, 0}}]}, + DiskBox[{0.75, 0}, 0.025], + LineBox[{{0.75, 0}, {0.75, 0.05}}], + LineBox[ + NCache[{{0, Rational[1, 2]/GoldenRatio}, { + 0.05, Rational[1, 2]/GoldenRatio}}, {{0, 0.3090169943749474}, {0.05, + 0.3090169943749474}}]], { + GrayLevel[0], + InsetBox[ + FormBox[ + StyleBox[ + "\"\\!\\(\\*StyleBox[\\\"i\\\",FontSlant->\\\"Italic\\\"]\\)\\!\\(\\*\ +SubscriptBox[\\(\[Theta]\\), \\(YL\\)]\\)\"", FontSize -> 12, + GrayLevel[0], FontFamily -> "Times", StripOnInput -> False], + TraditionalForm], + NCache[{0.125, Rational[1, 2]/GoldenRatio}, {0.125, + 0.3090169943749474}]]}, { + GrayLevel[0], + InsetBox[ + FormBox[ + StyleBox[ + "\"\\!\\(\\*SubscriptBox[\\(\[Theta]\\), \\(c\\)]\\)\"", FontSize -> + 12, + GrayLevel[0], FontFamily -> "Times", StripOnInput -> False], + TraditionalForm], {0.75, 0.1}]}}, + Frame->{{False, False}, {False, False}}, + FrameLabel->{{None, None}, {None, None}}, + FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}}, + GridLines->{None, None}, + GridLinesStyle->Directive[ + GrayLevel[0.5, 0.4]], + ImagePadding->All, + ImageSize->340, + LabelStyle->{FontFamily -> "Times", FontSize -> 12, + GrayLevel[0]}, + Method->{ + "DefaultBoundaryStyle" -> Automatic, + "DefaultGraphicsInteraction" -> { + "Version" -> 1.2, "TrackMousePosition" -> {True, False}, + "Effects" -> { + "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, + "Droplines" -> { + "freeformCursorMode" -> True, + "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultMeshStyle" -> + AbsolutePointSize[6], "ScalingFunctions" -> None, + "CoordinatesToolOptions" -> {"DisplayFunction" -> ({ + (Identity[#]& )[ + Part[#, 1]], + (Identity[#]& )[ + Part[#, 2]]}& ), "CopiedValueFunction" -> ({ + (Identity[#]& )[ + Part[#, 1]], + (Identity[#]& )[ + Part[#, 2]]}& )}}, + PlotRange-> + NCache[{{-1, 1}, {(-1)/GoldenRatio, GoldenRatio^(-1)}}, {{-1, + 1}, {-0.6180339887498948, 0.6180339887498948}}], + PlotRangeClipping->True, + PlotRangePadding->{{0, 0}, {0, 0}}, + Ticks->{{}, {}}]], "Output", + CellChangeTimes->{{3.827382624611155*^9, 3.8273826915148993`*^9}, { + 3.827382821172866*^9, 3.827382840956325*^9}, {3.827383007560814*^9, + 3.827383129164433*^9}, 3.827383160604924*^9, {3.8273860069463987`*^9, + 3.8273860642094803`*^9}, {3.8273861334648447`*^9, 3.827386200584742*^9}, + 3.827386268408902*^9, {3.8273863170992117`*^9, 3.8273863329839163`*^9}, { + 3.82738637105767*^9, 3.827386374474081*^9}, 3.8273864799189863`*^9, + 3.827387012286086*^9, {3.8273871575708647`*^9, 3.827387207139093*^9}, { + 3.8273873631427307`*^9, 3.827387392526597*^9}, {3.8273874262628717`*^9, + 3.827387438548918*^9}, {3.827387470865808*^9, 3.827387500818487*^9}}, + CellLabel-> + "Out[130]=",ExpressionUUID->"a7d6bf32-3297-4ed9-9cc5-d1836ef7d9ac"] +}, Open ]], + +Cell[BoxData[ + RowBox[{ + RowBox[{"Export", "[", + RowBox[{ + "\"\<~/doc/research/first_order_singularities/paper/figs/F_theta_\ +singularities.pdf\>\"", ",", "p3"}], "]"}], ";"}]], "Input", + CellChangeTimes->{{3.827382842246332*^9, 3.827382891238717*^9}, { + 3.8273862326284933`*^9, 3.827386237604206*^9}, {3.827386389102764*^9, + 3.8273863926784687`*^9}}, + CellLabel-> + "In[131]:=",ExpressionUUID->"080e0724-5e26-45b1-a939-86c8b13b3107"], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"p4", "=", + RowBox[{"Plot", "[", + RowBox[{ + RowBox[{ + SqrtBox[ + RowBox[{ + SuperscriptBox["0.95", "2"], "-", + SuperscriptBox["x", "2"]}]], "/", "GoldenRatio"}], ",", + RowBox[{"{", + RowBox[{"x", ",", + RowBox[{"-", "1"}], ",", "1"}], "}"}], ",", + RowBox[{"AxesStyle", "\[Rule]", "Dashed"}], ",", + RowBox[{"Ticks", "\[Rule]", "False"}], ",", + RowBox[{"PlotStyle", "\[Rule]", + RowBox[{"{", "Red", "}"}]}], ",", + RowBox[{"AxesLabel", "\[Rule]", + RowBox[{"{", + RowBox[{ + RowBox[{"Re", "[", + RowBox[{"\[Theta]", "'"}], "]"}], ",", + RowBox[{"Im", "[", + RowBox[{"\[Theta]", "'"}], "]"}]}], "}"}]}], ",", + RowBox[{"Prolog", "\[Rule]", + RowBox[{"{", "\[IndentingNewLine]", + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{"Thickness", "[", "0.005", "]"}], ",", "Red", ",", + RowBox[{"Line", "[", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{"-", "0.95"}], ",", "0.0115"}], "}"}], ",", + RowBox[{"{", + RowBox[{ + RowBox[{"-", "0.8"}], ",", "0.0115"}], "}"}]}], "}"}], "]"}]}], + "}"}], ",", "\[IndentingNewLine]", + RowBox[{"{", + RowBox[{ + RowBox[{"Thickness", "[", "0.005", "]"}], ",", "Red", ",", + RowBox[{"Circle", "[", + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{"-", "0.75"}], ",", "0"}], "}"}], ",", "0.05", ",", + RowBox[{"{", + RowBox[{"0", ",", "\[Pi]"}], "}"}]}], "]"}]}], "}"}], ",", + "\[IndentingNewLine]", + RowBox[{"{", + RowBox[{ + RowBox[{"Thickness", "[", "0.005", "]"}], ",", "Red", ",", + RowBox[{"Line", "[", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{"0.8", ",", "0.0115"}], "}"}], ",", + RowBox[{"{", + RowBox[{"0.95", ",", "0.0115"}], "}"}]}], "}"}], "]"}]}], "}"}], + ",", "\[IndentingNewLine]", + RowBox[{"{", + RowBox[{ + RowBox[{"Thickness", "[", "0.005", "]"}], ",", "Red", ",", + RowBox[{"Circle", "[", + RowBox[{ + RowBox[{"{", + RowBox[{"0.75", ",", "0"}], "}"}], ",", "0.05", ",", + RowBox[{"{", + RowBox[{"0", ",", "\[Pi]"}], "}"}]}], "]"}]}], "}"}], ",", + "\[IndentingNewLine]", + RowBox[{"{", + RowBox[{ + RowBox[{"Thickness", "[", "0.005", "]"}], ",", "Red", ",", + RowBox[{"Line", "[", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{"-", "0.7"}], ",", "0"}], "}"}], ",", + RowBox[{"{", + RowBox[{ + RowBox[{"0.", "-", "0.05"}], ",", "0"}], "}"}]}], "}"}], + "]"}]}], "}"}], ",", "\[IndentingNewLine]", + RowBox[{"{", + RowBox[{ + RowBox[{"Thickness", "[", "0.005", "]"}], ",", "Red", ",", + RowBox[{"Circle", "[", + RowBox[{ + RowBox[{"{", + RowBox[{"0", ",", "0"}], "}"}], ",", "0.05", ",", + RowBox[{"{", + RowBox[{"0", ",", "\[Pi]"}], "}"}]}], "]"}]}], "}"}], ",", + "\[IndentingNewLine]", + RowBox[{"{", + RowBox[{ + RowBox[{"Thickness", "[", "0.005", "]"}], ",", "Red", ",", + RowBox[{"Line", "[", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{"0.05", ",", "0"}], "}"}], ",", + RowBox[{"{", + RowBox[{"0.25", ",", "0"}], "}"}]}], "}"}], "]"}]}], "}"}], ",", + "\[IndentingNewLine]", + RowBox[{"{", + RowBox[{ + RowBox[{"Thickness", "[", "0.005", "]"}], ",", "Red", ",", + RowBox[{"Circle", "[", + RowBox[{ + RowBox[{"{", + RowBox[{"0.3", ",", "0"}], "}"}], ",", "0.05", ",", + RowBox[{"{", + RowBox[{"0", ",", "\[Pi]"}], "}"}]}], "]"}]}], "}"}], ",", + "\[IndentingNewLine]", + RowBox[{"{", + RowBox[{ + RowBox[{"Thickness", "[", "0.005", "]"}], ",", "Red", ",", + RowBox[{"Line", "[", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{"0.35", ",", "0"}], "}"}], ",", + RowBox[{"{", + RowBox[{"0.7", ",", "0"}], "}"}]}], "}"}], "]"}]}], "}"}], ",", + "\[IndentingNewLine]", + RowBox[{"{", + RowBox[{ + RowBox[{"Thickness", "[", "0.005", "]"}], ",", "Red", ",", + RowBox[{"Line", "[", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{"0.0115", ",", + RowBox[{ + RowBox[{"1", "/", "GoldenRatio"}], " ", "0.95"}]}], "}"}], ",", + RowBox[{"{", + RowBox[{"0.0115", ",", + RowBox[{ + RowBox[{ + RowBox[{"1", "/", "GoldenRatio"}], "/", "2"}], "+", + "0.05"}]}], "}"}]}], "}"}], "]"}]}], "}"}], ",", + "\[IndentingNewLine]", + RowBox[{"{", + RowBox[{ + RowBox[{"Thickness", "[", "0.005", "]"}], ",", "Red", ",", + RowBox[{"Line", "[", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{"-", "0.0115"}], ",", + RowBox[{ + RowBox[{"1", "/", "GoldenRatio"}], " ", "0.95"}]}], "}"}], ",", + RowBox[{"{", + RowBox[{ + RowBox[{"-", "0.0115"}], ",", + RowBox[{ + RowBox[{ + RowBox[{"1", "/", "GoldenRatio"}], "/", "2"}], "+", + "0.05"}]}], "}"}]}], "}"}], "]"}]}], "}"}], ",", + "\[IndentingNewLine]", + RowBox[{"{", + RowBox[{ + RowBox[{"Thickness", "[", "0.005", "]"}], ",", "Red", ",", + RowBox[{"Circle", "[", + RowBox[{ + RowBox[{"{", + RowBox[{"0", ",", + RowBox[{ + RowBox[{"1", "/", "GoldenRatio"}], "/", "2"}]}], "}"}], ",", + "0.05"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", + RowBox[{"Line", "[", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{"0.3", ",", "0"}], "}"}], ",", + RowBox[{"{", + RowBox[{"0.3", ",", + RowBox[{"-", "0.05"}]}], "}"}]}], "}"}], "]"}], ",", + "\[IndentingNewLine]", + RowBox[{"{", + RowBox[{"Black", ",", + RowBox[{"Text", "[", + RowBox[{ + RowBox[{"Style", "[", + RowBox[{"\"\<\[Theta]\>\"", ",", + RowBox[{"FontSize", "\[Rule]", "12"}], ",", "Black", ",", + RowBox[{"FontFamily", "\[Rule]", "\"\\""}]}], "]"}], ",", + " ", + RowBox[{"{", + RowBox[{"0.3", ",", + RowBox[{"-", "0.1"}]}], "}"}]}], "]"}]}], "}"}]}], "}"}]}], ",", + "\[IndentingNewLine]", + RowBox[{"Epilog", "\[Rule]", + RowBox[{"{", "\[IndentingNewLine]", + RowBox[{ + RowBox[{"{", + RowBox[{"Thick", ",", + RowBox[{"Line", "[", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{"0", ",", + RowBox[{ + RowBox[{"1", "/", "GoldenRatio"}], "/", "2"}]}], "}"}], ",", + RowBox[{"{", + RowBox[{"0", ",", "1"}], "}"}]}], "}"}], "]"}], ",", + RowBox[{"Line", "[", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{"0", ",", + RowBox[{ + RowBox[{ + RowBox[{"-", "1"}], "/", "GoldenRatio"}], "/", "2"}]}], "}"}], + ",", + RowBox[{"{", + RowBox[{"0", ",", + RowBox[{"-", "1"}]}], "}"}]}], "}"}], "]"}]}], "}"}], ",", + RowBox[{"RegularPolygon", "[", + RowBox[{ + RowBox[{"{", + RowBox[{"0", ",", + RowBox[{ + RowBox[{"1", "/", "GoldenRatio"}], "/", "2"}]}], "}"}], ",", + "0.025", ",", "4"}], "]"}], ",", "\[IndentingNewLine]", + RowBox[{"Rotate", "[", + RowBox[{ + RowBox[{"RegularPolygon", "[", + RowBox[{ + RowBox[{"{", + RowBox[{"0", ",", "0"}], "}"}], ",", "0.025", ",", "4"}], "]"}], + ",", + RowBox[{"\[Pi]", "/", "4"}]}], "]"}], ",", + RowBox[{"RegularPolygon", "[", + RowBox[{ + RowBox[{"{", + RowBox[{"0", ",", + RowBox[{ + RowBox[{ + RowBox[{"-", "1"}], "/", "GoldenRatio"}], "/", "2"}]}], "}"}], + ",", "0.025", ",", "4"}], "]"}], ",", + RowBox[{"{", + RowBox[{"Thick", ",", + RowBox[{"Line", "[", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{"-", "1"}], ",", "0"}], "}"}], ",", + RowBox[{"{", + RowBox[{ + RowBox[{"-", "0.75"}], ",", "0"}], "}"}]}], "}"}], "]"}]}], + "}"}], ",", + RowBox[{"Disk", "[", + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{"-", "0.75"}], ",", "0"}], "}"}], ",", "0.025"}], "]"}], + ",", + RowBox[{"{", + RowBox[{"Thick", ",", + RowBox[{"Line", "[", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{"1", ",", "0"}], "}"}], ",", + RowBox[{"{", + RowBox[{"0.75", ",", "0"}], "}"}]}], "}"}], "]"}]}], "}"}], ",", + + RowBox[{"Disk", "[", + RowBox[{ + RowBox[{"{", + RowBox[{"0.75", ",", "0"}], "}"}], ",", "0.025"}], "]"}], ",", + "\[IndentingNewLine]", + RowBox[{"Polygon", "[", + RowBox[{ + RowBox[{ + RowBox[{ + RowBox[{"{", + RowBox[{"0.3", ",", "0"}], "}"}], "+", "#"}], "&"}], "/@", + RowBox[{"SortBy", "[", + RowBox[{ + RowBox[{ + RowBox[{"0.025", "/", "1.5"}], + RowBox[{"Join", "[", + RowBox[{ + RowBox[{"CirclePoints", "[", "5", "]"}], ",", + RowBox[{ + RowBox[{"-", + RowBox[{"CirclePoints", "[", "5", "]"}]}], "/", "2"}]}], + "]"}]}], ",", + RowBox[{ + RowBox[{"ArcTan", "@@", "#"}], "&"}]}], "]"}]}], "]"}]}], + "\[IndentingNewLine]", "}"}]}], ",", + RowBox[{"AspectRatio", "\[Rule]", + RowBox[{"1", "/", "GoldenRatio"}]}], ",", + RowBox[{"PlotRange", "\[Rule]", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{"-", "1"}], ",", "1"}], "}"}], ",", + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{"-", "1"}], ",", "1"}], "}"}], "/", "GoldenRatio"}]}], + "}"}]}], ",", + RowBox[{"LabelStyle", "\[Rule]", + RowBox[{"{", + RowBox[{ + RowBox[{"FontFamily", "\[Rule]", "\"\\""}], ",", + RowBox[{"FontSize", "\[Rule]", "12"}], ",", "Black"}], "}"}]}], ",", + RowBox[{"ImageSize", "\[Rule]", "340"}]}], "]"}]}]], "Input", + CellChangeTimes->CompressedData[" +1:eJwd0FkowwEABvA/ppzLamPkmCPMciRLMmWztpelRaQ0GdFybEkWS2H+eXBG +JFeaBw+OoSWMF1eOltWSrCQSac5cD0b8v//D16+v7+2LrtAVVHkSBBFFBZ7p +PMISyEexKLs0A3KDu6SQM8+Ww2r2dimUvgY0QKPN5EikvP39dULzwsk1nKnw +f4BzgvJ3uL7R4Ya9N4N/8DvugOBTOirJQDhV/ERrUCmUcEugo51suVFD3sSF +Bh7HLDdDxtBVG9SGiEl4qO3vg8EK4RuMyI53Qz/9jlcSpbJuOgh+yTw5UOtu +p5U8xkfSe9YRbavcFQsN9fYUSLKG0yF715ADGz/0Yih0KOWwpHAgH5qM92p4 ++rw3AsucHuPQVTM6S/ci1QK07XMtUOPN3YR2090n7A7o/IIxVv4P/A5dZwgo +w8eufGDe4pIvZL1ImJDXw0yEMo45BZr91ZmwwN4kgsxLRS48X9WsJeNPi2oT +1lo12zAtdWUH/gMYPumJ + "], + CellLabel-> + "In[104]:=",ExpressionUUID->"286de95f-e12b-4640-9016-25c81cee6ada"], + +Cell[BoxData[ + GraphicsBox[{{{}, {}, + TagBox[ + {RGBColor[1, 0, 0], AbsoluteThickness[1.6], Opacity[1.], + LineBox[CompressedData[" +1:eJwV13k4VF8YB3AlibJEKksiOxVKKuFNRVLWSrKrUPZKtuxUsk4KJVuRbFnH +vhy7scVkSwg3ZJmZkhaU+p3fX/N8nufcOe+997nv9z2iV1yNbNczMTE5rGNi ++v/33Z9BUSk7BrLY6PnpquxtmMp76tFpw0DmadXTe/KfwAolfMLEnIEq+vVM +YyJTgHPaV2fGmIEoa3bCuT9fgvg6V/JtQwaSL9/an8meCSq7bITXnWOgL87d +bkRNFugfPR8WrcVANwTpvmGyuXDtouY3QQ0Gil8V8Uq+9gZ8bh42zz7GQGpy +Rt7bPQqAFCXTqqzMQEDy74aSQniVLajQrMBAhq729q+Ti6B38h/zuAQDFTvR +b3QblMDM2qKzkwgD6etymF8TIsNv/qmhFQEGIlEfBe+cIIOkESV3GzcDscX9 +GeM4XwaqLlV8L9kZaGCZpfIpczkYhucFyLMwUIviiXuT+eXg20g6r7NKR9ts +5GJMf1XAuwOXfwdM0VHL3SyT3ybVMKt31pZjnI5uf54+yjxXDWsOaj2Jw3R0 +xqP5006PGpBOF00vfUtHCUN/EvjCasGPd15noYKO2EnXrKVjEMTKj5K9Sugo +lcchrp2lHrLOvhXemE9HbT66kywn6+FdSPE3kXQ6CnqtjWqr6kH6u0+icRQd +KR+5Z7kvrQH6+zfPN9jg/S8ZuDqcaYKga6V1ueZ0BIzTV8O8mmD/d8vHcZfo +yLZO4tK+100QxlusekOXjpi2WrjwMzeDmpFJDPdROtoct/LybWkzZPZkKFlx +09F0pKggbVMreHWoBfypo6HbsXqhXrcpIGH6+fxMJQ3p6VodmEmgwLs5knQv +mYZ4ZF8O7KihwF62KWp6Dg09l47e0sncDpOnw8XPxtPQNZ9fgpGkdtBpGWx/ +5kxD3Mvc9SppHbCr3nXbYSEakkv8xKmb3AVdPIfcVXbQULFGraVcdRf42K72 +qfHQEGvoD9/p910wyH7v8alNNBQcwzTB4O0G0sVEHqPvC0j/6okpm7BuYF5o +5nbuWkAdBWoXdzu+hTk+AY503wUUMXLPQJqjF0odm1m4xuaRNntcBWcCFY6I +uChmDs0jzrz3KlnpVKjq32Gh9m4e9YvfVVUupEK9miPZsW0eFSwr7VZop0IH +F89VStE80jJyW05epcJEiVV90P15pO7ZnnDH7B2w/1n1+S4/j3iuHNB8ydcH +1pGKX4eD5xDF69KhJNd+8CHH3u/2m0Mr1XuYVbz7IW50SajBaw7drS29Tg3u +h469ZWeyXOaQRNY/YXpcPxzsVkn3MJ1Dwc8/7Buu7oeNnKeMeQ/MIVKksWrE +xgHIizGuOTc5i1r7fxpEJwzAcuzdMASzqCNzQ1Ns9iCkc37kfzo5gz5XKVB8 +a99Dko7irb6H0yjZTnkwI/QDBDvZeMmcmULNVeY3Ev6MwF3mHM9bdAIJdhxh +ibMfA5vAHvHBrElEiwxu4oz/CHG100+THCaQbQH3Ocu0cagal96St+cjGiCu +u94wnAAx7uMnLqSMoN1sTvVzNRNQLBvmQHx6j8r/cQloi0/CeEuRiLLyIPrd +VNZ30W8SpvfGHUBlfWgqqgh9aZmErf7ZyvvXUZGvQe7kEBsB98ukKdy/ehF3 +pm5BPTsBq4zXl5dovSj4b+JM1mYCCKtM34r3vShA71GsJwcBxRrpjScKe1Hj +pSsEx1YCjFiS9S5Z9SJPftY7wjsJkOIX7Wa624PqWrf87ZEgYK/yl72vlroQ +aZom4g0E2O0PCKgc60K5kbwmuscJSJXketfd1oX2lJRPiWgQwLND3vPn8y4U +yDzwt+UEAb9+uTScPtWFTpvPHNmkRUBjJePi/JNO9GK7/HuncwSYqDH85ZU7 +kOSn3RblJgTEHvKnnhTpQNFSu109LhPQuY9T3IS9A4nEXhxWMiVAXXh/e+DH +dnTVrLKswIwAsX/OvO/ut6PtmbEJyZYEMOrpr92HKOiyys/1ptcICDlF7630 +akMnnaJZjV3x/to0faWrbegw+eL+NWwm3YW3+bptqHaloDTdjQDfi3Nd6Xva +UNy09QzjJgEedtOUqK5W9JozjOrnTsD1sLF6G5FWRPTrjvl5E3Cuq7uQjdKM +dlzmUmENISC8t0s+tLgZVQ+FxCZiU/o78/8mNaPr30J094USoDnWnrd0sxkZ +29osGNzD98NoyRoTbEb5RpIU0gMCFLjr0opcm1DWx9M8SxEE8F3IJ13e0YiO +7Z7QPvEEvz/JiCpN5kbExcYaWIltsGI/pfilAbmmpMgrxOH9U0SPsLc1IOK8 +9rJgPAF/Z5+MV3k0oB+TKQr0BAJm/O7uFxqsRyMqvzQ9nhPgov/oaa0MQuFP +6zTFXhKQ9V2HFrcOIY1rRckPsYlnG467DNehcRcN1y/YxlOen4Uf1iGXFLOA +ynQCwNtSOXC2FqUY2V04/YoA7nS5/hOva9DD30LDZ7JwvT9buCjiVSibczR0 +/g0B0TkvG9VXKtGi9xP90/kEOFoG3CntrkRu5n5+6djirUdGXnpUoomqDcym +BQTEx+Vm+lEqEGr8VIoKCfBReqR20KkcPX/g1+hcguuZdf6afbwcKauaNtdj +H0zSSRfhK0eDS19leMkE0Jg3sHHWlSHZF04iZdiWfR79s1xl6MtXn+rvpQSc +uGXumFJCRh+DCgovVBAgLHlUmC+MjLYtUBeTsX8P81EjzMkIsUgnzGCTNXqU +vVnIqCwugtOjkgDJrSfWX7hUgq69/FYYVUUAe6HUM7bfRWjmtmhHag0Br0am +o+ZC81H79TFv/XoCPvhuT00+mI/MNIrqg7A5hU8XGhJvkNUvq8ASbA/rrHeV +8AZp1lk68DUQoDXtsCN8NRctBV6Ye4c9y/iSJuuWjQyPPYpXaiJAiCRS/FE4 +G22lLDpZYhsoGjbFdmchDybHmgfYFbeLp1dls1DWhdLW99gPl91lO6czkYTc +pofuzQTIrl8tcTTLQAK/77TFtuDnky7bsps9A9n2zymQsWNPmQ32VaSjMzlZ +vAPYq/drlo9tT0cCBjyafK34+9wcoLaF+gK5i01cisFmelOgVx/wAi31/ozI +w1bSm7By3/8CWZs5H23HTiJpBI9GpKHfKSFM69oIeC+7KfpyVApKi4wDB+zj +zjcKG+aTUaIQTT0EO6ug452MdjISjiWXP8f2Vorasbo+Cd00TefrxBZQ53mR +6PUMXRCWDxGjEBAceLtp/eBTxDt7Vu8I9kJj/7TDwadItGMu9hx2zekE2WOM +eHTrWUHYbWwLQyHyyNUn6MIxkmQ1Nm3px9E7zY+RgkCrYye2b3wP4pR4jMTo +TfIj2EkjwZ0aM4+Qlo+Q0gr2Xn9zwxGtR2g81dudtZ2AahHlIffXJGRNSj/I +h03ufNeiT41GB5Wv7JfH7ue+Tw2OjUL3mFduHMNeunh0rPR8JKrptBY/jX1g +IvW74OBDdIj9NZ8FtqHEeSb9hDDEr/ngnD22m8PGLcEmD5D0BtX1N7ELvjuJ +zX4IRZ4SkvPB2G+PisgLJoUg9hVzoQhshn+fip5FMHI86Ngdi83RfF8rSDgI +qd02XHuGbcLjnnEdBaCKc9x5adgJSR+q32r4oTdnsoYzsQclNfqUmn3Qgzn+ ++3nY24pezydqeaFTL2yLirDPH+Ncv679DgoYiTArw45tcee3P3sbXV+ODK3C +7tUfUejudkMdujf21mELk0NIdmlOiFVK9HwD9nOKATrwyh7xt5CXm7B3ju1i +/M2+guIsxXe1Yst9Gjgab2GGsne71bdhS25xS9hvb4gEZJ8SFOzAful+wSY1 +pBWXFNKOvZdrzIFlnzhIufil/+/BxeBU7mVt0CtXOfG/v+pLfXO9ZQwz1/ut +/r/+7mOtDkclayhy0/nz/35//b2fp8rbAkdx0o6W///fIc+pT9YBGCydRY3Y +zMbjaqySrjCtMtCBsJtEHj5I5r4F/HzVV2qwQ+P3uB2Odoczer7eFdhaW2pM +qJs9oSduJxcZmzX4oobjQ29IJsWIFWBTfjFkWFh9QX14oiwbO9w5jCc11B+o +/za3p2NnLpL8hIICgS+c2zQZ295e1q7sbzA8yEtfjsbW3uNpGqIWCmJCihsf +YEuPNekZ+N4DzZS4WH/seSOLw/MrD8Bl+6SUE3YHR45c+ZGH8IzUqnAFO5fy +c3eoZziQJAIrLmE7qZM2Cf+IhIRDTqc0sHVXRv/MH4wG78kk7UPY+8kyi+W3 +YqCdLaVTGnv5ySRNepkEZXUcepzYlex3BxrvPAbZ3yGn+vD3kbaPr69gzxM4 +KCA+1oB936CgN6nnCWw9XTBWgH0h/lOnh0w8KH4O2B6O/VX0XKPs2FN4Mjlo +dxh76NQM2hH+DH64J6mLYtfZB9ZuOJwIM0Nq/uzYEW/IFR9Jz8HYdPOhEdwP +JI/uKog9lQJLWo8C72BvMS/PC1hMgaqiH/Gm2Ev+hjlOKakwyynGB9jWRKOR +mG8aqAm/1d6IvV/6l+7awAuo6dsZFYX7VXuJ1amihxkQsTx/PwD3P9WWvU1S +ExnQt/feTjPswsEVjRTlV8BXUr5VGTt+5TFEfHoFMjFDKvO4v14Dioqt2mu4 +rJVkfxb7X4eCIv9iNuTnDEktNhJwa3StIOZ0DrxTVFBswp6hd+zfmJIDJm8n +XzzB7uK23bukkwvnPNQrD2EnGj+T6s7Ig+wYC+SG8+AQsU44yKQAno+vl+hA +uP6qS4sK2QWQkP/BLB5bMvZN88RKASQO+HNcwd78Iu9Qmm4hPCMLTP6qI+CP +gcnoP0YhOP4RO7MLe6ywQAYpFsPhhps79XF+fUgy5d1hWgwbihZWeLAHw1jW +XIKLQfH3zMXBatxvrM16hfuKIcZQ188Mu46b1dPfvQQ0HbUfWuE8THWzbFYr +J0PRgu4jPZyfSeZs+XHjZBhpv7aTHfupNjmBzloK2cmZ/C3lBJBE2B2TTUoh +cvVx+FHswN7SrWsrpWDd6yYhVEaAjQKHVY1qOYzt/HyUgvNe7Gv1ikpjJeh6 +MxdV4/nBt/tk6Hd6Jciqi2tZYQ/mdHLm81eByzNBtfXY4bYjYqI3q0CV74aB +Fp5Hvn5Y1WUVqYbkBK/Nbbm4/pajL/v8akBN/19HDp5fTJ+X6zgdReAo/EX6 +9wvcz71gQMIWQW593XQ4Nqdxm9U4CYGO2S5mAewG7iF3o1kEFbtMrZTTcL88 +eVc/6Ww9eMWTkuxTcL+pSPQOXq2HoO/5u/MSCTiTPtytZ9IIjDrupZpYXM+9 +fLsW50YI6pfbfgz76fWQf8dCGuGH+q6Uikc4//ftU5TJbwTVGf3RIhIBYRWB +T5g3NEF+Rjh3cjTuJ91SZhUFTdCg3HvOOJyA08t3ZkVZW+Dw1C/y+SA8f+ry +MP8obQPpG5ycns54HrNhW1xpbwOSaKT5sBPO4ztM43/H2iCFlypyDNshhVG1 +aSMF7jG82Ncc8PovHbeEjCmw4FZu7XMdr38UQpz8SYGYDq8tZlfx+sHvDbHK +HfC9x261BM/zMVZDgQrlXcCHg7wenw/u01RhpqsLAll12r7g84O/98u150QX +jJuWCQljuzx29mHl7Ab+mhyqlzoBem3M7h+vdcNIzn0byWP4ecsr2EfyvMW5 +ObXhihKu52+Y7qxzD5RtsyKbShLQpreLw4CHCpIZJ46d20QAXZTP/11iH7jb +hMQTlEm44y5nE7N9ENikm8/LBE3C0Ci3kR3lPRD6G/bySU+CtbfqZ9ZzI2Cv +vbKnvX0CmuQOhzexfITXqqFaAcYTIMlWM5uhPQHpa9nXparHYVeNoyZL2CTk +NydvGy7+CEyr67NvEQRoPDeUs7k1Br8May1bJKag0cS2LkJsFEaUrAQlQqfB +7svVmoKID+B2iXvrntEZ2HHlsNyBlvfA/2TKZMOuWVjWk8lYmByEfLO010te +c2Bo1hN0E59/lYbEVjf6z8FU9URZl1c/VBu9PicQMgfP1GtuiuLzM+VM/uLx +qDkg9UycLzfrh0+Ha45Fv5iDkATmxsdK/bBz2/se6Y45nCP0ko3TfRDcxbVs +ITgPswvSxeHH++CSWoA2pXYerE6t3tYZp8LojxmuxsZ5GLgXRp3uo8KVfL2h +6rZ5SKP8aPCkUMFpt7BdAXUe0jPO8gQUUSF4XW1I/PQ81NtsucofQoX8ltW6 +axwLcOn+X09HcSps0PM4tM5iAQ4F3dFbsOyF8I0f/6zaLACN9wwoGPUCF9Js +/m63AEJMvJ+va/aCgALf+Vm3BahmZ8yQ5XpBnofs1hO6ANNsHJXXv/SA6eBi +bnLeAlR0/9zjINADRZbOe1T+LIDlkYEpH9NuuFL6dVfaOho4dL7I+abSDdu2 +uPNvZKXBIW9RmROC3eBR6cP9bisNNBFF1W6kC1S2hf29IUWDPRrSkSWXu6Cx +/eWHZ0Y0uDWmJvpRtxP6ld7HrmTRYPJJyKmbXO1wL8Is2iqfBjsjcv/FzVFA +mfj4sKWEBg23m3K8myjwNGY68FEdDbrGbTm9PShgMf/NRaafBq22djFKw20w +k8px9vI/GqwaHu8zJ7XCMvtJ5sqLdDiymDoqWtEEPAzOJ42mdNBxPsQrFN4E +ctQP4l1WdGgtzR5LM2sCy4RbWuM36KBikZSnutYITWIvH7L408Fc0Gbggkoj +jG50EeAKoYPofkUN1U2N8HPuaO7OMDpUFF3QjB5oAOlCapdcLB0EHDfmWrg0 +QLTqOm6jTDp4zbJKsj2th6zd3WlmuXRI2zC/L9O6HhrWP1O0LaTDjfoDbXel +6+E7ReG8VxUdumxJ2paOCEwvWsenvKWDu6qwul54Lbgf2SuV1UeHDImxuOUt +tRAluFxe9J4OoxsqdtlH1UD9ZMxwM0GH1TXuNd4H1SDhgoQWfuLrLWszoy5X +grphxJvvv+ng2s5nrNVaASZKl9T/MjFA6WJ18zX5CghfZVht3cyALSYmu0p/ +lEHGWNVXAW4GXOFk8QKjMqitvx8kzseAvLf2V0azS+HrfeH0w7sZ4HJlLtBK +mwzsDvMHNcQZsG+qI3lHdAmI6ZY168gwQDLyw0mfrmIw5tWbsTjIAPZ7MiXG +8kXg9pPf0/4IA9xHZvOPGxbCw+Fp1ptqDFj8pjPB1p0PNal+MqGnGdDtLjUs +25ADg8FnqqLOMaB31Cui0ScLvtjynU0wZIAaES9F+/UKNp2ZHEkzZgDr5Oml +OZF02LP3jVOOGQNW/2z+KPAoFY5xea+VWDMgRCiZeQdTAlz4diq61pYBPE0q +d/j0AyBlj2SIuh0DOAfYXwe5usB/5zTXsw== + "]]}, + Annotation[#, "Charting`Private`Tag$56431#1"]& ]}, {}}, + AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], + Axes->{True, True}, + AxesLabel->{ + FormBox[ + RowBox[{"Re", "(", + SuperscriptBox["\[Theta]", "\[Prime]", MultilineFunction -> None], + ")"}], TraditionalForm], + FormBox[ + RowBox[{"Im", "(", + SuperscriptBox["\[Theta]", "\[Prime]", MultilineFunction -> None], + ")"}], TraditionalForm]}, + AxesOrigin->{0, 0}, + AxesStyle->Dashing[{Small, Small}], + DisplayFunction->Identity, + Epilog->{{ + Thickness[Large], + LineBox[ + NCache[{{0, Rational[1, 2]/GoldenRatio}, {0, 1}}, {{ + 0, 0.3090169943749474}, {0, 1}}]], + LineBox[ + NCache[{{0, Rational[-1, 2]/GoldenRatio}, {0, -1}}, {{ + 0, -0.3090169943749474}, {0, -1}}]]}, + InterpretationBox[ + PolygonBox[{{0.01767766952966369, 0.2913393248452837}, { + 0.01767766952966369, 0.3266946639046111}, {-0.017677669529663688`, + 0.3266946639046111}, {-0.01767766952966369, 0.2913393248452837}}], + RegularPolygon[{0, Rational[1, 2]/GoldenRatio}, 0.025, 4]], + GeometricTransformationBox[ + InterpretationBox[ + PolygonBox[{{0.01767766952966369, -0.017677669529663688`}, { + 0.01767766952966369, 0.017677669529663688`}, {-0.017677669529663688`, + 0.01767766952966369}, {-0.01767766952966369, -0.017677669529663688`}}], + RegularPolygon[{0, 0}, 0.025, 4]], {{{ + 0.7071067811865475, -0.7071067811865475}, {0.7071067811865475, + 0.7071067811865475}}, Center}], + InterpretationBox[ + PolygonBox[{{0.01767766952966369, -0.3266946639046111}, { + 0.01767766952966369, -0.2913393248452837}, {-0.017677669529663688`, \ +-0.2913393248452837}, {-0.01767766952966369, -0.3266946639046111}}], + RegularPolygon[{0, Rational[-1, 2]/GoldenRatio}, 0.025, 4]], { + Thickness[Large], + LineBox[{{-1, 0}, {-0.75, 0}}]}, + DiskBox[{-0.75, 0}, 0.025], { + Thickness[Large], + LineBox[{{1, 0}, {0.75, 0}}]}, + DiskBox[{0.75, 0}, 0.025], + PolygonBox[{{0.2920745290308737, -0.0025751416197912287`}, { + 0.2902035791284588, -0.01348361657291579}, { + 0.3, -0.008333333333333333}, { + 0.3097964208715412, -0.01348361657291579}, { + 0.30792547096912626`, -0.0025751416197912287`}, {0.3158509419382525, + 0.0051502832395824575`}, {0.3048982104357706, 0.006741808286457895}, { + 0.3, 0.016666666666666666`}, {0.2951017895642294, + 0.006741808286457895}, {0.28414905806174745`, 0.0051502832395824575`}}]}, + + Frame->{{False, False}, {False, False}}, + FrameLabel->{{None, None}, {None, None}}, + FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}}, + GridLines->{None, None}, + GridLinesStyle->Directive[ + GrayLevel[0.5, 0.4]], + ImagePadding->All, + ImageSize->340, + LabelStyle->{FontFamily -> "Times", FontSize -> 12, + GrayLevel[0]}, + Method->{ + "DefaultBoundaryStyle" -> Automatic, + "DefaultGraphicsInteraction" -> { + "Version" -> 1.2, "TrackMousePosition" -> {True, False}, + "Effects" -> { + "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, + "Droplines" -> { + "freeformCursorMode" -> True, + "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultMeshStyle" -> + AbsolutePointSize[6], "ScalingFunctions" -> None, + "CoordinatesToolOptions" -> {"DisplayFunction" -> ({ + (Identity[#]& )[ + Part[#, 1]], + (Identity[#]& )[ + Part[#, 2]]}& ), "CopiedValueFunction" -> ({ + (Identity[#]& )[ + Part[#, 1]], + (Identity[#]& )[ + Part[#, 2]]}& )}}, + PlotRange-> + NCache[{{-1, 1}, {(-1)/GoldenRatio, GoldenRatio^(-1)}}, {{-1, + 1}, {-0.6180339887498948, 0.6180339887498948}}], + PlotRangeClipping->True, + PlotRangePadding->{{0, 0}, {0, 0}}, + Prolog->{{ + Thickness[0.005], + RGBColor[1, 0, 0], + LineBox[{{-0.95, 0.0115}, {-0.8, 0.0115}}]}, { + Thickness[0.005], + RGBColor[1, 0, 0], + CircleBox[{-0.75, 0}, 0.05, + NCache[{0, Pi}, {0, 3.141592653589793}]]}, { + Thickness[0.005], + RGBColor[1, 0, 0], + LineBox[{{0.8, 0.0115}, {0.95, 0.0115}}]}, { + Thickness[0.005], + RGBColor[1, 0, 0], + CircleBox[{0.75, 0}, 0.05, + NCache[{0, Pi}, {0, 3.141592653589793}]]}, { + Thickness[0.005], + RGBColor[1, 0, 0], + LineBox[{{-0.7, 0}, {-0.05, 0}}]}, { + Thickness[0.005], + RGBColor[1, 0, 0], + CircleBox[{0, 0}, 0.05, + NCache[{0, Pi}, {0, 3.141592653589793}]]}, { + Thickness[0.005], + RGBColor[1, 0, 0], + LineBox[{{0.05, 0}, {0.25, 0}}]}, { + Thickness[0.005], + RGBColor[1, 0, 0], + CircleBox[{0.3, 0}, 0.05, + NCache[{0, Pi}, {0, 3.141592653589793}]]}, { + Thickness[0.005], + RGBColor[1, 0, 0], + LineBox[{{0.35, 0}, {0.7, 0}}]}, { + Thickness[0.005], + RGBColor[1, 0, 0], + LineBox[{{0.0115, 0.5871322893124}, {0.0115, 0.3590169943749474}}]}, { + Thickness[0.005], + RGBColor[1, 0, 0], + LineBox[{{-0.0115, 0.5871322893124}, {-0.0115, 0.3590169943749474}}]}, { + Thickness[0.005], + RGBColor[1, 0, 0], + CircleBox[ + NCache[{0, Rational[1, 2]/GoldenRatio}, {0, 0.3090169943749474}], + 0.05]}, + LineBox[{{0.3, 0}, {0.3, -0.05}}], { + GrayLevel[0], + InsetBox[ + FormBox[ + StyleBox["\"\[Theta]\"", FontSize -> 12, + GrayLevel[0], FontFamily -> "Times", StripOnInput -> False], + TraditionalForm], {0.3, -0.1}]}}, + Ticks->{{}, {}}]], "Output", + CellChangeTimes->{{3.8273909699521523`*^9, 3.8273909789452953`*^9}, { + 3.827396042711411*^9, 3.827396059416113*^9}, 3.827396117784916*^9}, + CellLabel-> + "Out[104]=",ExpressionUUID->"753f522e-db04-4909-b8f0-e57c0454a0e0"] +}, Open ]], + +Cell[BoxData[ + RowBox[{ + RowBox[{"Export", "[", + RowBox[{ + "\"\<~/doc/research/first_order_singularities/paper/figs/contour_path.pdf\>\ +\"", ",", "p4"}], "]"}], ";"}]], "Input", + CellChangeTimes->{{3.827382842246332*^9, 3.827382891238717*^9}, { + 3.8273862326284933`*^9, 3.827386237604206*^9}, {3.827386389102764*^9, + 3.8273863926784687`*^9}, {3.8273886033746567`*^9, 3.827388609494101*^9}}, + CellLabel-> + "In[105]:=",ExpressionUUID->"121d3bcb-c71c-4ec8-a01e-74607255b0b3"], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{ + RowBox[{"ComplexExpand", "[", + RowBox[{ + RowBox[{"Re", "[", + FractionBox["1", + RowBox[{ + RowBox[{"(", + RowBox[{"t", "-", "\[Xi]"}], ")"}], "\[ImaginaryI]", " ", "t"}]], + "]"}], ",", + RowBox[{"{", "t", "}"}]}], "]"}], "/.", + RowBox[{ + RowBox[{"Im", "[", "t", "]"}], "\[Rule]", "0"}]}]], "Input", + CellChangeTimes->{{3.827397067296423*^9, 3.827397071104473*^9}}, + CellLabel-> + "In[122]:=",ExpressionUUID->"1fb1f920-f38c-4eb2-9e28-4bcb008fa2d2"], + +Cell[BoxData["0"], "Output", + CellChangeTimes->{3.827397071978077*^9}, + CellLabel-> + "Out[122]=",ExpressionUUID->"d6edca36-a4cf-4c5f-83b3-574289a56af9"] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"ComplexExpand", "[", + RowBox[{"Re", "[", + FractionBox["\[ImaginaryI]", + RowBox[{ + RowBox[{"(", + RowBox[{ + RowBox[{"\[ImaginaryI]", " ", "t"}], "-", "\[Xi]"}], ")"}], + SuperscriptBox[ + RowBox[{"(", + RowBox[{"\[ImaginaryI]", " ", "t"}], ")"}], "2"]}]], "]"}], + "]"}]], "Input", + CellChangeTimes->{{3.827392340498281*^9, 3.827392362569867*^9}, { + 3.8273924560685463`*^9, 3.827392474836338*^9}, {3.827392508669565*^9, + 3.827392517493204*^9}, {3.8273928391881437`*^9, 3.827392839355523*^9}, { + 3.827392914693452*^9, 3.827392918813306*^9}, {3.82739295042251*^9, + 3.827392966942542*^9}, {3.827396544064262*^9, 3.827396544327231*^9}, { + 3.82739666785751*^9, 3.827396678337653*^9}, {3.8273967361390944`*^9, + 3.827396753402955*^9}, {3.827396832461341*^9, 3.8273968573966217`*^9}, { + 3.827396911686181*^9, 3.827396926448296*^9}, {3.827396961350854*^9, + 3.827396964022704*^9}, {3.827397032648273*^9, 3.827397034295686*^9}, { + 3.8273971015378847`*^9, 3.8273971172972393`*^9}, {3.827397325876824*^9, + 3.827397401566285*^9}, {3.827397820590563*^9, 3.827397868142569*^9}, { + 3.827398034378117*^9, 3.8273980344573917`*^9}, {3.8273981362675943`*^9, + 3.82739813831738*^9}}, + CellLabel-> + "In[142]:=",ExpressionUUID->"3411f987-6e0c-43e6-8774-8bab579534d3"], + +Cell[BoxData[ + RowBox[{"-", + FractionBox["1", + RowBox[{"t", " ", + RowBox[{"(", + RowBox[{ + SuperscriptBox["t", "2"], "+", + SuperscriptBox["\[Xi]", "2"]}], ")"}]}]]}]], "Output", + CellChangeTimes->{ + 3.82739236277209*^9, {3.827392458777472*^9, 3.8273924750758343`*^9}, + 3.827392517770557*^9, 3.8273928395865593`*^9, 3.827392921373645*^9, { + 3.8273929523584337`*^9, 3.827392967221002*^9}, 3.8273965446002893`*^9, { + 3.8273966684654284`*^9, 3.82739667888195*^9}, {3.827396736651239*^9, + 3.827396753666822*^9}, {3.827396832987563*^9, 3.827396857586887*^9}, { + 3.827396921612953*^9, 3.8273969268301563`*^9}, 3.82739696425456*^9, + 3.827397034582773*^9, {3.827397108690279*^9, 3.827397119440362*^9}, { + 3.8273973264927893`*^9, 3.827397401861537*^9}, {3.82739782105422*^9, + 3.8273978683764563`*^9}, 3.8273980346259108`*^9, 3.8273981386105013`*^9}, + CellLabel-> + "Out[142]=",ExpressionUUID->"b8cea288-1647-4b56-8f3d-dcdd2b6ae91b"] +}, Open ]], + +Cell[BoxData[ + RowBox[{ + RowBox[{ + RowBox[{"iF1", "[", + RowBox[{"\[Theta]c_", ",", "B_"}], "]"}], "[", "x_", "]"}], ":=", + RowBox[{ + RowBox[{"(", + RowBox[{"x", "-", "\[Theta]c"}], ")"}], " ", + RowBox[{"Exp", "[", + RowBox[{ + RowBox[{"-", "1"}], "/", + RowBox[{"(", + RowBox[{"B", + RowBox[{"(", + RowBox[{"x", "-", "\[Theta]c"}], ")"}]}], ")"}]}], "]"}]}]}]], "Input",\ + + CellChangeTimes->{{3.827549176981242*^9, 3.827549201331346*^9}}, + CellLabel->"In[6]:=",ExpressionUUID->"2cebc6d0-f18e-4865-b6ef-a0d1f3bf0805"], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"iii2", "=", + RowBox[{ + FractionBox[ + SuperscriptBox["\[Theta]", "2"], "\[Pi]"], + RowBox[{"Integrate", "[", + RowBox[{ + RowBox[{ + FractionBox[ + SuperscriptBox[ + RowBox[{"(", + RowBox[{ + SuperscriptBox["x", "2"], "+", + SuperscriptBox["\[Theta]0", "2"]}], ")"}], + RowBox[{"5", "/", "6"}]], + SuperscriptBox["x", "2"]], + RowBox[{"(", + RowBox[{ + FractionBox["1", + RowBox[{"x", "-", "\[Theta]"}]], "+", + FractionBox["1", + RowBox[{"x", "+", "\[Theta]"}]]}], ")"}]}], ",", + RowBox[{"{", + RowBox[{"x", ",", "\[Theta]c", ",", "\[Infinity]"}], "}"}], ",", + RowBox[{"Assumptions", "\[Rule]", + RowBox[{"{", + RowBox[{ + RowBox[{"\[Theta]", "<", "\[Theta]c"}], ",", + RowBox[{"\[Theta]", ">", "0"}], ",", + RowBox[{"\[Theta]c", ">", "0"}], ",", + RowBox[{"B", ">", "0"}], ",", + RowBox[{"\[Theta]0", ">", "0"}], ",", + RowBox[{"\[Theta]0", "<", "\[Theta]c"}]}], "}"}]}]}], + "]"}]}]}]], "Input", + CellChangeTimes->{{3.827550808671958*^9, 3.82755084362461*^9}, { + 3.827551052940673*^9, 3.827551056396649*^9}}, + CellLabel->"In[48]:=",ExpressionUUID->"b3488c4d-f657-46fb-9b11-630b0fd6d206"], + +Cell[BoxData["$Aborted"], "Output", + CellChangeTimes->{3.8275508262823143`*^9, 3.82755104553023*^9, + 3.827551666146019*^9}, + CellLabel->"Out[48]=",ExpressionUUID->"b33dc2d4-cae5-42eb-a0ca-3a6e33f3cb70"] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Series", "[", + RowBox[{ + RowBox[{ + RowBox[{"iF1", "[", + RowBox[{"\[Theta]c", ",", "B"}], "]"}], "[", "x", "]"}], ",", + RowBox[{"{", + RowBox[{"\[Theta]", ",", "\[Theta]c", ",", "1"}], "}"}]}], "]"}]], "Input",\ + + CellChangeTimes->{{3.827554296583604*^9, 3.827554327320253*^9}}, + CellLabel->"In[58]:=",ExpressionUUID->"c7dac445-5908-4fa8-8a0b-bb252cb276f4"], + +Cell[BoxData[ + RowBox[{ + SuperscriptBox["\[ExponentialE]", + RowBox[{"-", + FractionBox["1", + RowBox[{"B", " ", + RowBox[{"(", + RowBox[{"x", "-", "\[Theta]c"}], ")"}]}]]}]], " ", + RowBox[{"(", + RowBox[{"x", "-", "\[Theta]c"}], ")"}]}]], "Output", + CellChangeTimes->{{3.827554317783595*^9, 3.827554327962017*^9}}, + CellLabel->"Out[58]=",ExpressionUUID->"71c3cdc7-d817-4f4d-af37-5b9bfea1f179"] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Series", "[", + RowBox[{ + RowBox[{ + RowBox[{ + SuperscriptBox[ + RowBox[{"t", "[", "\[Theta]", "]"}], "2"], "\[Xi]", " ", + RowBox[{"Exp", "[", + RowBox[{ + RowBox[{"-", "1"}], "/", + RowBox[{"(", + RowBox[{"b", " ", "\[Xi]"}], ")"}]}], "]"}]}], "/.", + RowBox[{"\[Xi]", "\[Rule]", + RowBox[{ + RowBox[{"(", + RowBox[{"\[Theta]", " ", + RowBox[{ + RowBox[{"h", "'"}], "[", "\[Theta]", "]"}]}], ")"}], "/", + SuperscriptBox[ + RowBox[{"t", "[", "\[Theta]", "]"}], + RowBox[{"15", "/", "8"}]]}]}]}], ",", + RowBox[{"{", + RowBox[{"\[Theta]", ",", "0", ",", "1"}], "}"}]}], "]"}]], "Input", + CellChangeTimes->{{3.8275543532807007`*^9, 3.827554388944468*^9}, { + 3.827555347554227*^9, 3.8275553652900763`*^9}}, + CellLabel->"In[62]:=",ExpressionUUID->"6f05087c-413e-4fb2-b2c9-e923fdd92c6b"], + +Cell[BoxData[ + RowBox[{ + SuperscriptBox["\[ExponentialE]", + InterpretationBox[ + RowBox[{ + RowBox[{"-", + FractionBox[ + SuperscriptBox[ + RowBox[{"t", "[", "0", "]"}], + RowBox[{"15", "/", "8"}]], + RowBox[{"b", " ", + RowBox[{ + SuperscriptBox["h", "\[Prime]", + MultilineFunction->None], "[", "0", "]"}], " ", "\[Theta]"}]]}], + "+", + FractionBox[ + RowBox[{ + RowBox[{"-", + FractionBox[ + RowBox[{"15", " ", + SuperscriptBox[ + RowBox[{"t", "[", "0", "]"}], + RowBox[{"7", "/", "8"}]], " ", + RowBox[{ + SuperscriptBox["t", "\[Prime]", + MultilineFunction->None], "[", "0", "]"}]}], + RowBox[{"8", " ", + RowBox[{ + SuperscriptBox["h", "\[Prime]", + MultilineFunction->None], "[", "0", "]"}]}]]}], "+", + FractionBox[ + RowBox[{ + SuperscriptBox[ + RowBox[{"t", "[", "0", "]"}], + RowBox[{"15", "/", "8"}]], " ", + RowBox[{ + SuperscriptBox["h", "\[Prime]\[Prime]", + MultilineFunction->None], "[", "0", "]"}]}], + SuperscriptBox[ + RowBox[{ + SuperscriptBox["h", "\[Prime]", + MultilineFunction->None], "[", "0", "]"}], "2"]]}], "b"], "+", + FractionBox[ + RowBox[{ + RowBox[{"(", + RowBox[{ + RowBox[{ + RowBox[{"-", "105"}], " ", + SuperscriptBox[ + RowBox[{ + SuperscriptBox["h", "\[Prime]", + MultilineFunction->None], "[", "0", "]"}], "2"], " ", + SuperscriptBox[ + RowBox[{ + SuperscriptBox["t", "\[Prime]", + MultilineFunction->None], "[", "0", "]"}], "2"]}], "+", + RowBox[{"240", " ", + RowBox[{"t", "[", "0", "]"}], " ", + RowBox[{ + SuperscriptBox["h", "\[Prime]", + MultilineFunction->None], "[", "0", "]"}], " ", + RowBox[{ + SuperscriptBox["t", "\[Prime]", + MultilineFunction->None], "[", "0", "]"}], " ", + RowBox[{ + SuperscriptBox["h", "\[Prime]\[Prime]", + MultilineFunction->None], "[", "0", "]"}]}], "-", + RowBox[{"128", " ", + SuperscriptBox[ + RowBox[{"t", "[", "0", "]"}], "2"], " ", + SuperscriptBox[ + RowBox[{ + SuperscriptBox["h", "\[Prime]\[Prime]", + MultilineFunction->None], "[", "0", "]"}], "2"]}], "-", + RowBox[{"120", " ", + RowBox[{"t", "[", "0", "]"}], " ", + SuperscriptBox[ + RowBox[{ + SuperscriptBox["h", "\[Prime]", + MultilineFunction->None], "[", "0", "]"}], "2"], " ", + RowBox[{ + SuperscriptBox["t", "\[Prime]\[Prime]", + MultilineFunction->None], "[", "0", "]"}]}], "+", + RowBox[{"64", " ", + SuperscriptBox[ + RowBox[{"t", "[", "0", "]"}], "2"], " ", + RowBox[{ + SuperscriptBox["h", "\[Prime]", + MultilineFunction->None], "[", "0", "]"}], " ", + RowBox[{ + SuperscriptBox["h", + TagBox[ + RowBox[{"(", "3", ")"}], + Derivative], + MultilineFunction->None], "[", "0", "]"}]}]}], ")"}], " ", + "\[Theta]"}], + RowBox[{"128", " ", "b", " ", + SuperscriptBox[ + RowBox[{"t", "[", "0", "]"}], + RowBox[{"1", "/", "8"}]], " ", + SuperscriptBox[ + RowBox[{ + SuperscriptBox["h", "\[Prime]", + MultilineFunction->None], "[", "0", "]"}], "3"]}]], "+", + InterpretationBox[ + SuperscriptBox[ + RowBox[{"O", "[", "\[Theta]", "]"}], "2"], + SeriesData[$CellContext`\[Theta], 0, {}, -1, 2, 1], + Editable->False]}], + SeriesData[$CellContext`\[Theta], + 0, {-$CellContext`b^(-1) $CellContext`t[0]^Rational[15, 8]/Derivative[ + 1][$CellContext`h][ + 0], $CellContext`b^(-1) ( + Rational[-15, 8] $CellContext`t[0]^Rational[7, 8] + Derivative[1][$CellContext`h][0]^(-1) + Derivative[1][$CellContext`t][0] + $CellContext`t[0]^Rational[15, 8] + Derivative[1][$CellContext`h][0]^(-2) + Derivative[2][$CellContext`h][0]), + Rational[1, 128] $CellContext`b^(-1) $CellContext`t[0]^Rational[-1, 8] + Derivative[1][$CellContext`h][0]^(-3) ((-105) + Derivative[1][$CellContext`h][0]^2 Derivative[1][$CellContext`t][0]^2 + + 240 $CellContext`t[0] Derivative[1][$CellContext`h][0] + Derivative[1][$CellContext`t][0] Derivative[2][$CellContext`h][0] - + 128 $CellContext`t[0]^2 Derivative[2][$CellContext`h][0]^2 - + 120 $CellContext`t[0] Derivative[1][$CellContext`h][0]^2 + Derivative[2][$CellContext`t][0] + + 64 $CellContext`t[0]^2 Derivative[1][$CellContext`h][0] + Derivative[3][$CellContext`h][0])}, -1, 2, 1], + Editable->False]], " ", + RowBox[{"(", + InterpretationBox[ + RowBox[{ + RowBox[{ + SuperscriptBox[ + RowBox[{"t", "[", "0", "]"}], + RowBox[{"1", "/", "8"}]], " ", + RowBox[{ + SuperscriptBox["h", "\[Prime]", + MultilineFunction->None], "[", "0", "]"}], " ", "\[Theta]"}], "+", + InterpretationBox[ + SuperscriptBox[ + RowBox[{"O", "[", "\[Theta]", "]"}], "2"], + SeriesData[$CellContext`\[Theta], 0, {}, 1, 2, 1], + Editable->False]}], + SeriesData[$CellContext`\[Theta], + 0, {$CellContext`t[0]^Rational[1, 8] Derivative[1][$CellContext`h][0]}, + 1, 2, 1], + Editable->False], ")"}]}]], "Output", + CellChangeTimes->{ + 3.827554389179389*^9, {3.827555349902762*^9, 3.827555365548625*^9}}, + CellLabel->"Out[62]=",ExpressionUUID->"e72062d6-2b09-4495-8402-b0e6bef938ab"] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"iii", "=", + RowBox[{ + FractionBox[ + SuperscriptBox["\[Theta]", "2"], "\[Pi]"], + RowBox[{"Integrate", "[", + RowBox[{ + RowBox[{ + FractionBox[ + RowBox[{ + RowBox[{"iF1", "[", + RowBox[{"\[Theta]c", ",", "B"}], "]"}], "[", "x", "]"}], + SuperscriptBox["x", "2"]], + RowBox[{"(", + RowBox[{ + FractionBox["1", + RowBox[{"x", "-", "\[Theta]"}]], "+", + FractionBox["1", + RowBox[{"x", "+", "\[Theta]"}]]}], ")"}]}], ",", + RowBox[{"{", + RowBox[{"x", ",", "\[Theta]c", ",", "\[Infinity]"}], "}"}], ",", + RowBox[{"Assumptions", "\[Rule]", + RowBox[{"{", + RowBox[{ + RowBox[{"\[Theta]", "<", "\[Theta]c"}], ",", + RowBox[{"\[Theta]", ">", "0"}], ",", + RowBox[{"\[Theta]c", ">", "0"}], ",", + RowBox[{"B", ">", "0"}], ",", + RowBox[{"\[Theta]0", ">", "0"}]}], "}"}]}]}], "]"}]}]}]], "Input", + CellChangeTimes->{{3.827398353256083*^9, 3.8273983957208767`*^9}, { + 3.827398760367425*^9, 3.827398836928145*^9}, {3.827398896506111*^9, + 3.827398907017392*^9}, 3.8273989826513567`*^9, {3.827399019491435*^9, + 3.827399047403905*^9}, {3.827399266719953*^9, 3.827399276184062*^9}, { + 3.82739933374548*^9, 3.827399335417035*^9}, {3.827399382418434*^9, + 3.827399393305705*^9}, {3.8273994776115007`*^9, 3.827399487643407*^9}, { + 3.8273995869738693`*^9, 3.827399587277536*^9}, {3.827402058892399*^9, + 3.827402085443573*^9}, {3.827402137725361*^9, 3.82740217971719*^9}, { + 3.827402449762793*^9, 3.827402452530192*^9}, {3.8274895683360233`*^9, + 3.827489568495656*^9}, {3.827489688770116*^9, 3.827489715938286*^9}, { + 3.8274897856277246`*^9, 3.82748978623564*^9}, {3.827490092977054*^9, + 3.8274900932009687`*^9}, {3.827491095100894*^9, 3.82749109786831*^9}, { + 3.827491133445551*^9, 3.8274911345971603`*^9}, {3.82754875904348*^9, + 3.827548763579376*^9}, {3.827548968119054*^9, 3.827548973055189*^9}, { + 3.8275490338006268`*^9, 3.827549041834475*^9}, 3.827549174059781*^9, { + 3.827549220027563*^9, 3.827549225027791*^9}, {3.827550187268937*^9, + 3.8275502147414837`*^9}, 3.827550801121107*^9}, + CellLabel->"In[53]:=",ExpressionUUID->"45253125-7b71-4e2c-bc30-668e3b338cbd"], + +Cell[BoxData[ + RowBox[{ + FractionBox["1", "\[Pi]"], + RowBox[{"(", + RowBox[{ + RowBox[{"2", " ", + SuperscriptBox["\[ExponentialE]", + FractionBox["1", + RowBox[{"B", " ", "\[Theta]c"}]]], " ", "\[Theta]c", " ", + RowBox[{"ExpIntegralEi", "[", + RowBox[{"-", + FractionBox["1", + RowBox[{"B", " ", "\[Theta]c"}]]}], "]"}]}], "+", + RowBox[{ + SuperscriptBox["\[ExponentialE]", + FractionBox["1", + RowBox[{"B", " ", + RowBox[{"(", + RowBox[{ + RowBox[{"-", "\[Theta]"}], "+", "\[Theta]c"}], ")"}]}]]], " ", + RowBox[{"(", + RowBox[{"\[Theta]", "-", "\[Theta]c"}], ")"}], " ", + RowBox[{"ExpIntegralEi", "[", + FractionBox["1", + RowBox[{ + RowBox[{"B", " ", "\[Theta]"}], "-", + RowBox[{"B", " ", "\[Theta]c"}]}]], "]"}]}], "-", + RowBox[{ + SuperscriptBox["\[ExponentialE]", + FractionBox["1", + RowBox[{ + RowBox[{"B", " ", "\[Theta]"}], "+", + RowBox[{"B", " ", "\[Theta]c"}]}]]], " ", + RowBox[{"(", + RowBox[{"\[Theta]", "+", "\[Theta]c"}], ")"}], " ", + RowBox[{"ExpIntegralEi", "[", + RowBox[{"-", + FractionBox["1", + RowBox[{ + RowBox[{"B", " ", "\[Theta]"}], "+", + RowBox[{"B", " ", "\[Theta]c"}]}]]}], "]"}]}]}], ")"}]}]], "Output", + CellChangeTimes->{{3.8273983937112637`*^9, 3.8273983995108433`*^9}, { + 3.8273988111915216`*^9, 3.827398852578842*^9}, 3.827398926547677*^9, + 3.827398993620363*^9, {3.827399029117091*^9, 3.827399053448537*^9}, + 3.8273992799360943`*^9, 3.827399341103878*^9, 3.827399422456213*^9, + 3.827399554601347*^9, 3.827399654476961*^9, 3.827402127001665*^9, + 3.827402448064209*^9, 3.8274024949881144`*^9, 3.827489607746436*^9, + 3.827489754705557*^9, 3.827490081610094*^9, 3.827491132020056*^9, + 3.827491245091855*^9, 3.827548905664464*^9, 3.827549083629471*^9, + 3.827550798445965*^9, 3.8275518930000343`*^9}, + CellLabel->"Out[53]=",ExpressionUUID->"b820a378-a24b-40d9-848b-d271118a47ad"] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"itest", "=", + RowBox[{ + SuperscriptBox["x", + RowBox[{"3", "/", "2", " "}]], + RowBox[{ + RowBox[{"Integrate", "[", + RowBox[{ + RowBox[{ + SuperscriptBox[ + RowBox[{"(", "y", ")"}], + RowBox[{"1", "/", "2"}]], " ", "y", " ", + RowBox[{ + RowBox[{ + RowBox[{"Exp", "[", + RowBox[{ + RowBox[{"-", "1"}], "/", "y"}], "]"}], "/", + RowBox[{"(", + RowBox[{"y", "+", "x"}], ")"}]}], "/", + SuperscriptBox["y", "2"]}]}], ",", + RowBox[{"{", + RowBox[{"y", ",", "0", ",", "\[Infinity]"}], "}"}], ",", + RowBox[{"Assumptions", "\[Rule]", + RowBox[{"{", + RowBox[{"x", ">", "0"}], "}"}]}]}], "]"}], "/", + "\[Pi]"}]}]}]], "Input", + CellChangeTimes->{{3.827490241164371*^9, 3.8274902719969053`*^9}, { + 3.827490521401638*^9, 3.827490534121044*^9}, {3.827490678140024*^9, + 3.827490712468458*^9}, {3.827490884984619*^9, 3.827490901968405*^9}, { + 3.827491586461814*^9, 3.82749159659795*^9}, {3.827491746721252*^9, + 3.82749181717035*^9}, {3.827492035774888*^9, 3.827492041462571*^9}, { + 3.827492102391716*^9, 3.827492110375875*^9}, {3.827492176945887*^9, + 3.827492179144786*^9}, {3.827492279235435*^9, 3.827492333115738*^9}, { + 3.827492363276701*^9, 3.827492454085841*^9}, {3.8274925625290003`*^9, + 3.827492562672227*^9}, {3.827492607745925*^9, 3.8274926079140053`*^9}, { + 3.827492690314501*^9, 3.8274927141551533`*^9}, {3.8274930229453583`*^9, + 3.8274930402486687`*^9}, 3.827493076298266*^9, {3.827493432192507*^9, + 3.827493447935803*^9}, {3.827493488161765*^9, 3.8274934949849052`*^9}, { + 3.827493566034436*^9, 3.827493568050148*^9}, {3.827493739070094*^9, + 3.827493748653948*^9}}, + CellLabel->"In[47]:=",ExpressionUUID->"98be6fd6-d0c5-46ca-a3d5-250ea9c619bd"], + +Cell[BoxData[ + RowBox[{ + SuperscriptBox["\[ExponentialE]", + FractionBox["1", "x"]], " ", "x", " ", + RowBox[{"Erfc", "[", + FractionBox["1", + SqrtBox["x"]], "]"}]}]], "Output", + CellChangeTimes->{ + 3.8274927178327208`*^9, {3.827493034238329*^9, 3.827493047437254*^9}, + 3.827493080950856*^9, 3.827493451967753*^9, 3.827493515415063*^9, + 3.827493568497258*^9, {3.82749374361351*^9, 3.827493749101988*^9}}, + CellLabel->"Out[47]=",ExpressionUUID->"02273014-23dc-45c5-a3ff-2366921fabd0"] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"ComplexExpand", "[", + RowBox[{"Im", "[", + SqrtBox[ + RowBox[{"-", "x"}]], "]"}], "]"}]], "Input", + CellChangeTimes->{{3.8274936885252237`*^9, 3.827493710933008*^9}}, + CellLabel->"In[45]:=",ExpressionUUID->"cc5be459-b1a4-4071-bf81-958b4fbe4d9a"], + +Cell[BoxData[ + RowBox[{ + SuperscriptBox[ + RowBox[{"(", + SuperscriptBox["x", "2"], ")"}], + RowBox[{"1", "/", "4"}]], " ", + RowBox[{"Sin", "[", + FractionBox[ + RowBox[{"Arg", "[", + RowBox[{"-", "x"}], "]"}], "2"], "]"}]}]], "Output", + CellChangeTimes->{3.8274937111801863`*^9}, + CellLabel->"Out[45]=",ExpressionUUID->"03b899db-cf29-4fc4-b21a-0c99949276e1"] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Plot", "[", + RowBox[{ + RowBox[{ + RowBox[{"Exp", "[", + RowBox[{ + RowBox[{"-", "1"}], "/", "x"}], "]"}], + SqrtBox["x"]}], ",", + RowBox[{"{", + RowBox[{"x", ",", "0", ",", "1"}], "}"}]}], "]"}]], "Input", + CellChangeTimes->{{3.8274933082944717`*^9, 3.8274933432541*^9}}, + CellLabel->"In[29]:=",ExpressionUUID->"72d5b6dd-c9d9-411c-ae47-018d1493f38e"], + +Cell[BoxData[ + TemplateBox[{ + "General", "munfl", + "\"\\!\\(\\*RowBox[{\\\"Exp\\\", \\\"[\\\", RowBox[{\\\"-\\\", \ +\\\"48951.048951048964`\\\"}], \\\"]\\\"}]\\) is too small to represent as a \ +normalized machine number; precision may be lost.\"", 2, 29, 3, + 31546217051116231707, "Local"}, + "MessageTemplate"]], "Message", "MSG", + CellChangeTimes->{3.827493343468099*^9, 3.8274935170070543`*^9}, + CellLabel-> + "During evaluation of \ +In[29]:=",ExpressionUUID->"c89d0736-26b9-4e13-a981-096b6f1d6e1a"], + +Cell[BoxData[ + GraphicsBox[{{{}, {}, + TagBox[ + {RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6], Opacity[ + 1.], LineBox[CompressedData[" +1:eJw9lnc41X/4/1EklL0pREMlZGS8X7edrIwkinyECkWIZOQo2VFG9t6bg2Me +JzMrZBxJlJDZUUhG+vW7ru/3e/9zX4/r+byv+5/nH09hG2djOxoqKqrn1FRU +/3/r2M0PkhZMEdX/zH51PpcpXhn4Xz6fFp+M59X4P9btI1em8F75Pzaz3Wx6 +xWsLYd6iPRyBC3yfzgWpR/C6Q3PUpb/6W0Zn0zkvPw/lfQap36SnPG1C5HD0 ++BMhvDEQUshFJ3TzlJL4xZfBlS4xsEus8kn8iim9D3Re+NgZA+/2HDK7jhgp +ie47UyThEQuRziWpzu3uSh1/siWG38cBww3Z1iR2ghLTWpzs0fAE6Li1egLr +Pa5cLfUwTvtrAujzuis8cjmvbOVisvlAMRH4+WVLDM1VlMtWmOva5hOhQNIu +Y075qrLxfLCyg2YynHLxvX9zEKe8c/x2SnRyMrTV2esaxoYpZ9tp7jWuJYO+ +0cimhEis8sY0NYk5MwXqHUXyx3nylVOFPwspbKVASO34lOmPCmUtayLOxjAV +skIfrS961ytTUpOnw/JSwTsyw2fBulU5/tNj9eq9VAiR7C8cOtqrrCpgnj1p +mgYd3mHyXWhYedFCnpa+JA1cTGXIY0sTyt29DHgemnR4Z3WBqsp/RvnIstet +krPpIBzmKlHzcVnZlXGBXc08HdwTxRZTxNeVO8SvtY0+S4fn7nYzJ/d2lPl0 +Ot0dy9Nhc21js1ZvH+Z8V06MaiIdPMWtolkfMGBtwTkjMQcyYChRyuAYFRvG +k8/x/NT5DLjHZh8rc4MHc+p8Kke0ygBJhxKHPzZCGGnu55xxaAYU5r8zyV8S +wzjobF5/q86APo3+DPlTZ7G7YoMXfb5kQLdDUPR7nfMYUUPlN8uhTEAVrYx4 +WwWMzbYsP+dCJvCKBbkHp6tg9k+PmCvaZoKZZl1zUaEm1pAZcbA/MhP4jhdl +i/DqYSwtu3W3GjIBvj+9Yi1ijNl+cXT4PZcJhGCZRgZ9M6yW6iNfBFsWTNpb +7Wa8s8SYhHR6hFEW6D2IOZm2Y4NZQ513zd0sCOOzNu5lv4NVW508oxubBYRw +UTydw32Mwe/1xBQpC65ysrjQirhhVil0Ee7LWbBsofro5bYnVtn4EDvIkw1c +PnXcF1Z9MbqJmZUU9WwY9qCnnU4NwCx2TFKlnbNBXnvL5zpHEFbG12rQmZgN +1maOCz64cGy/ovTf6x3ZIMLI81Qq7CV2zTyjbPVHNixxIQ98YCxG+XiFIZMv +B6ovHMDSfydgz63o7UzUc+BToGxnpUoaJvCloXm/Uw58PcES3U3KxPC3nPlq +YnKgK/LST27XXExnTuTh7aYc+KNiFVPQU4h9vjPazzOXAzIU8dIL82WY51KI +ePfhXFDNP3KOf60SO3wfC/SWzwUJ75+GR9xrsJzV1akz1rlg+iVLoD20HlN2 +y1acDM4F/1hnEU39Zmxowyw2siIXiujf8Vs4tGAOjxhXVcZzIdsiNK04tR2j +3iHq/KTJg6zcesYAky4s3tc1J+t0HpRIC72qSezDJKiOU5leyYOb7luKJzQG +sfaADxZ0vv/0Nho2M95h7AZtRDUhJw8SRfQcHM3J2M8gFZa77/Lgp2jMrgnb +RyyEYd2BbzMP7Dn5P70ymcKEIvLae47mQ7FEtrQU9zRGYL4u5KudD/p73Rvf +x2cwg1eHvSUe5INO0HZN3N9v2CxHy8hUQj4YPW4+NR61hPm8fij5siUfzD84 +VmckUTB2vlNhakv5cKy46xU790+sMHlido29APwy/ZgPFq9jKkejVHKUC0Az +SlpON3YTI2eoJ121KwBuEw1+nYlt7L7o5saBFwWQRhUpaBm2h+3PKzSsqymA +572vAxevUqOkU1ZFDlMFIPWTUHwgfx+SLmalE6AvhOF9Y8rtQIe6JNqt+yQL +gZ31ZaGv2EFkXfGowc+8EGYnI3el/mNCv86f4ZIMKAR++nli7A4ziqiZcvlS +WAiq6+d6D/1lRaIK0T2vhgrBfktJHafAgeobtI5r7BaCYp/zdEUlFzJC2/4b +okXg4+hdme7Ci+ZJJR9z9Yuglfizt9tLAD1R/0/umkcRaGdMWEmNHEVcHRwv +D6YVwRLD7/1S7cKoWPvtUn1nETAt6Q81DxxD6j3eWk6rRfBexLUqh/U4Gtc/ +lyHIWwwzlw7Kvg4/iVwGpnfeqRZDY/mL3gyt0+iASdxVf4diEOjvPyilKYFS +Ry5VSEUXA4PNxe2DnZJI9tofxq8NxfDCJ8r4TbQ06h0vt4+ZKYYw0t2DbOEy +yMbS9o3moRI49WCBKRQvh7amuAU2ZUuguiNrYv2QAoqy6fHItyoBI7xYu1Wa +Ejo+6zdoHvTP33ziAo8TQlcWZ583jpVAno11BJudGlpySvhyj7oUfl43Xe6Q +1kABFD3lo+Kl4P4yWFD5pBbidaV6PWBcChxK7j03tbVR+Tr+B867FGxtyBS9 +OB100fO23vnsUqA20P2mz6mPJrf48mZ6S6H69JfoybeXEeNf3I2LR8rgpX14 +ldF3YxR/18zqjFYZrK5Uz4cnXEGiw2esWe+XwaZrN6Ha7iqqQDQ2v2LLIHqP +X2r9yjWECsi3PjaVgWQgsSrirgXqYS+xI82WwV04zzeXcwOdgTf493TlMKya ++smf6SaqK4irJkiUA9MtqwfxUjaI6iZOrlCtHExfl4h4F99CWhxOhOSr5fCu +J/K2pJodCu+6eiHSoRxY9Cwtjdft0ZCfah3OrxyA6Ed80XYH8cmcUXR/VQ4k +Z/bIvCoHZL3A1WCfWw6Hf8f0unU4oRWT5Ubdd+UgP13Z7VnkgmQOkjE0XQ73 +X9OcnFx+gB4T3xAlf5WD/bu3osrqbojkVgzHGCqAxfIHHaHMHR049ZrEeaQC +RA7NN/mf90AGkzhVeukKSNbm1xjr90Qx0U4t25oV4JNAomZ47oWE91Tbpu5V +AK+3gpqbpi+6gz+j+R5XAZrPRDVCjZ6g0jvcHW2xFaDdRchOIfojpaHlzoKm +CniogEucF3iKAoLJ2smD//6V7Dyjv/0MvcVaul7MVkAQqafbsC0Qmea/7nE7 +VAlLfUlzrI3BKNkyQM9euBKsQuwSfa6Fomm2e33XZCuhd9JjaI0xHDn7qvVj +lpXwtHUxyqgxEtVInzWUfFAJD4tU0uo/RaHdb9yDIoGVUDtjx8ey9BKFGK+8 +P1BSCYWEkD+PpWLQwIExk21SJVTQeJ8Yc4xFXE0tw8vDlZCSyY8ProlDWSfi +Rwd3K+G4k7Vc+ZMEtDgRYNbGggeNgj580t9EJPnq3liNKB68qVzHWl8lo6Zd +tfEkPTwU69hOrW+kof2VZ6+/sMaDYQC76eDXdKRzm2fC3x0Ph4ciopfIGYg8 +uPLJLhkPMhOc/1V+zUJHgsasrpXjod9hx053NxvZKrdO6bThYeNXaC+VSC76 +kRv/5dwyHmaNhZ42x+WjCzee2ohQVUFKrjPP4FwB8mO9/5WDowos8nE1zFpF +iNFHfXZLqQrmjnPM6smUIjGj7/OtYVVQypAuxOlSifieXFS8nVEFBpoHDJ48 +wCOWkvQwBkIVUKTSrGv9qtA2vYmE0XQVVHzvyb1CrEGrcsVP1jeroL98+VPK +DwKataUdfH2oGgyqaDkDpOvQAIngNnmhGmoEq9zopxpQ+3eWdpxBNQSo6zXn +6zahegEHLjHbajCKz7P73ElEOY8E6hwjq+GTzDmdxN8k9FgSt/d7thpYvSvS +/MLakLPV+OXknWrQYMZSvwW1I9vwf2WItQY4Np9m273oQJfnZ9WfK9fAoP99 +m9n6t0iDC2JPGdeAFkQSI750IUWN+Lne2zWg822/Wzx7DxJN1wlhj64BLybP +BNmkPsT7Lmu8Jr8GWo0PTvv8eIcO7+6etiDWgPTIM35t8QG0ZVb2Ln2hBgzl +N27oZQyid8wcHBIqBNj+HOD0bGYYtWL37AZNCbBOc5KEvR1BtY4dNe6OBMAi +CWxr+FGU1fnIvCGOAIYf06slssdQ/MZgoVUxAUpC6H6IFXxAL46d3qVuIcDj +X8R9OzXj6NGTT6naKwRIvCkJp79PoHslcqtLNLUQXmco9pd7Etl8jFSN5KmF +ptHHNzN1p5C+vNrMiHot8CYfiC+Y/4xEKLmnbiXWglFx/V1i6VfELUjlTVde +CxTymO+D+zOISde8t6C9FrROv87klJlFm7mMzqurtXAM7tk1D86hXiuXKt+L +dVCwv182wWIRtYR30Qpb1oEJFUvBoP4SItSLmLW51oGztsq6qPYyyuQa2WJI +rYPXd8Wy642/I893ChC/XgeXlKq9GGx+oMMS1bNd9PUQp3Xd+C/lB8qOkAzf +EaiHE/jhz4m4n2hQ78QHK816qJy25D5UvoZO93C4icXVw8aHgQcflH6hFvEo +XrPCenhf5Xp8b/4XuhbKSAom1oMWi6b3jcRNFHiJ5tDyXD2kOobwsDNsoalO +Sm6lfAOU3OE4/+LoLvI44ag/o9sA1h+4c7NXdxFT0Nwap3UDqBO9SNEdf5CC +1icVr+AGOKflsWmA+4ui27rH4UMDyMZ44jQSqUFcVAv3YKUB7PpTfcy5aYD0 +9M2JLOpG8PeNkpV8TQMrarXudOKNIP9VRvdy2j64+CbncN/jRniRs/Mx8j0t +TAoJV++9aISD06E7K/Z04O6ffF0yqxGUFrPX7uzRQQZE50f3NMKBabuUGTl6 +2GnyV7MQaIKHkEpW7WeAV4K782GSTfCspVVkxJcRTvp6RjZp/NNp7/XPnmMC +U+X7E0L3miD/0PEjFamHoKz+use3piYwH+I0P3mFBbT4yAK875sgSPdNL3c9 +C0x4GbfqzDWBnNHhjt/CrHBQ4RJL6WEi4G1T7xVsssItglyh+00itORHJfk1 +sAN3FeskNXUzvH+dVjhZyA03wneuzHA1AxPnRlQY4oFM29mejjPNYC5ygYd6 +hAfOcNbVhV1rhlqjrCMODHyg5mEdy1neDPeF1ral4wUg2ECH6Xd7M1T5fQg5 +pi4Ifcdlno5/bIYE2+ZNsR+CULz0tLZ/HwlaJ2UHA68eBblks9yYcyTwI3Ym +ThwTBvPg3i+BiiS4oxTOI/RcGHzcVQU9NUmguclizbYoDG/0TseYXycBo63S +Cy6CCOj92cMdCSJB3StJfjF7UfjPKtcyf5IEFUzKWjkCJ+GZDn9CwgIJWhTl +FY4mn4Rcuajh0HUS5GVUEuIET8Hy4ce69xjeQHgAyffVcXHwaNZXkJZ7A15/ +BMZ1jM5AuNAGR2PEGyhfjNLlC5KEUiYHw5L4NyD+SzBxnSwJg78nw1Kz3kD8 +MaqIX6ekgGvwLQ2u7g2wBTY3eA9KQQYueVVz9g3kGv1aGpI4DzXT6r39yi1w +1Czz5D4xORjVxv2IuNgCUpd53AlBcvCrlMilZ9wC004Wk+VLciDvrfDf29st +0BnssONDkIda9nO/SK9aQOKc2EizlQLUafAJVc63ACFrkkvguzKMF5ppuqy1 +ABdJRUjPHoNtllgHib0WuBnXtzM/hYHiJ+bqQvZWWL7MwepGRlD/kFYnC7XC +utLaNp2TCjTmrrrFxLQCm+z9pNYoNZhgkkgwTmsFd09u49ExNdh1dSSyFLZC +oX2HGF5YHTCYo49oboWzARjdQLU6EMkfUwIXW+H1kz8ttd80oJm+s9NDpQ0C +Dc7cN3W7CC0OKfzmy23AWXKVjk9aH/ALjo5Wv9rAR9DrMkOkPmTfUWy4RdUO +ou9tnvYs60OgPdniPkc7PE5KsWsrNABtG9bEp/+a/KbH2/2mPIbQbx7IUxre +DuJOC6ohlUZAGjO5g49rh51FNVrSNyMoNxOprU1vh6MHfrywFzSGV6bNZq1V +7RA6d4W4P9QYrhptxY1NtMM1Dq+tl3dMYEL7Hue+sx2QcCTuiLGSKfR1KtnR +y3eA17HZI/WepkDUYqg+pNoBk3jBL/FVppCmkXeFx7QDTqR6Wzaeuwo2Kl+i +z/p2wIfYfVR5p81gXt6U7VpfB8TrHN+6rWgOG8cx5pJ7nTDm6qTpVGMJaFqt +M/RRJ8SQsgu/0VvB8xTtJ3eedsKUR2ffn+tWwMVxhXIsoRO+U43L7O67CXLU +jv2JbZ0w+pPjet5Za3j0MT4ymP8tnJx5S/sh+j/YjVxntu16C/dnTNgvptiC +hu52p+rwW0iTjficPmAL4XRU/ken3sJAigbH5f12IOjLuDq+/u/+h7F3gZMd +IAeRASOhLshwM+q5rmoPTzQMo8CzC8RpOQO/bN8Gmq0iFn6xbvi7qGBZV+YI +/H1qa3CuG65t6v4ZXXAEmYwPI7YK3eAZXyGtLuoEdpcOJJXqd4MZRp4+kOgE +bxNsxNQ8uuHu2siqZsg9iFTkVbzb2Q1u3AnEcg9nEPB5fotwtwdMZY/oMXQ+ +AFlDQa0Jtx7469UdILTwAAxEq05S+/WA41/+zzcZXeFJ75cVnVc9YH/WVs3C +0BWmBbBHk/U9kM/DfxAmXKGgaS2clqkXDP2cbgztuIHcX+sak9JeYByjOeZp +4QF6+qQAzdpeoHWeKKTBecCtpKOX5Vt6YeRGOzchzwOi5Ce/8Y32Asu4WFvi +hgcsOF/nnf7TC4LVGuYG0Z6Q/NnUx0W/DyzEpavujT4C6hYdtYjlPuCUIQm2 +eHtD7zOZdx3i/RDx8HjLoUx/UGTuoXkp2w935+QMMxr9IT/hP/nrKv3w+47V +gD7ZH56WvkinmPZDRXBP6Q8mHCiOzbvy4PrhhMQKt50XDvJPp3A7kPuhwDSE +cfdqAKgtBJTTqQ3Aym/iyTXRZ3A0ammr4PsAvBDH7woxBQPxvycFlWsDcM+r +r7ZNPBiszrObN/wegEbnORW/S8GQPKpY20szCN4ROhXSQcHAIxjqQeEaBLbY +l7/S94UAW+HJNRkYhFieVK5XVKFA22a33Bw5CDiigXQTQzgsbU5Njki+h5s+ +ZZEL56Ige7Gh+/CLIXD/quJZ4BYLhwXzKDMzw9DgxUnnZ54E4Xer7dNFR2Hv +gdxGQEM6/FIpmrnzhAx29j3dGTeywV26rYqrdQw+ReoOutHmw1RpW9ig8Djo ++AexUqsVw47DcNKpxx+ho/VCqJlpOZxWPbBn3zABU54/ShN8K+FipvDtCu5J +CGaSs8lZqQJPwZsiX25MwYlP7yVjLxHgzLIpI1n/M9zdN0d6VFQH7Myr9G3b +n0FC/f39UeNG2N+cVHYs+QuoOlIiwz4SwVGm4cNB3Wkw6N7dMh8mQdElm3Ti +r2mgklD8E6/YAhtLfCxzcV+hU3OYOSKiFapNLu6L0ZiBUiSvl0PdDk+0A9Oq +5mZAv98jJtW6A4Q/6YxlBc7C6Q+tq5ENnaAo/yyGV3oOtjNbORvkuuDGkf4t +6qE56A6/0BiX2A0b3RHTLrhvMBy4fUviSC/E77dyNxadhzuVKrQuIX3APlmd +SdM2D+IdHUX+398BrS/uisKDBUh//qFCXWEAqAqsyqbZFmHjcuGfkH+5cE0s +i2BrWYRLyh8imPGD0HQ6mJ71/hKk7mgd3nB7D6w6rmcCDi/DRI2lZMuJIZg4 +OzDk1bgMXo09BM/FIShPBdEZqxXYwoe//J42DJZlcqyCeyugsMPH5mk0Av6B +GbiJwu/ArfIkPZF1FErmBZMO61Fgjw04bNtGITgl0HrSgAJBu4/kcZ2jYGu8 +IlZqRIFz36kMU7tHQaCxsVzfjAIsxEXrsYFRCI283hFuQwERg2pqvU+jcEcu +4QeDFwXky3KVpH6NgsgzDu0DuRQYMbN/uHaCDHsXfA6R8ymwll6hyHyaDB9W +vr7PLaIAs0XfurgEGaLM8JZaFRRIWbK/aCNDhr/ixm6BjRQQz6y1G1Ahw8Rg +ZOq+IQp4XIx4WmhOhtrnm7eGRiig3MMf036DDDFKN09ljf3zj6GEzzfJoJsj +UaU2SYEXI+dxXPZkqH/U14VboEAj0bUT50qGuLOykUbLFGCaQj7JD8nwYDr5 +ijCFAj3aAWKER2Q4qec0RVqnwJS3temyHxn2Uw9nR21SwIZx/SNdABk+Vys5 +WG9ToMll9apwIBkaHbLOSf6hQBK7cYdSMBleH2Xc+PuXAo8tOcWvhpHh/wEG +4KgU + "]]}, + Annotation[#, "Charting`Private`Tag$61338#1"]& ]}, {}}, + AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], + Axes->{True, True}, + AxesLabel->{None, None}, + AxesOrigin->{0, 0}, + DisplayFunction->Identity, + Frame->{{False, False}, {False, False}}, + FrameLabel->{{None, None}, {None, None}}, + FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}}, + GridLines->{None, None}, + GridLinesStyle->Directive[ + GrayLevel[0.5, 0.4]], + ImagePadding->All, + Method->{ + "DefaultBoundaryStyle" -> Automatic, + "DefaultGraphicsInteraction" -> { + "Version" -> 1.2, "TrackMousePosition" -> {True, False}, + "Effects" -> { + "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, + "Droplines" -> { + "freeformCursorMode" -> True, + "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultMeshStyle" -> + AbsolutePointSize[6], "ScalingFunctions" -> None, + "CoordinatesToolOptions" -> {"DisplayFunction" -> ({ + (Identity[#]& )[ + Part[#, 1]], + (Identity[#]& )[ + Part[#, 2]]}& ), "CopiedValueFunction" -> ({ + (Identity[#]& )[ + Part[#, 1]], + (Identity[#]& )[ + Part[#, 2]]}& )}}, + PlotRange->{{0, 1}, {0., 0.3678794299098268}}, + PlotRangeClipping->True, + PlotRangePadding->{{ + Scaled[0.02], + Scaled[0.02]}, { + Scaled[0.05], + Scaled[0.05]}}, + Ticks->{Automatic, Automatic}]], "Output", + CellChangeTimes->{3.827493343502778*^9, 3.827493517019392*^9}, + CellLabel->"Out[29]=",ExpressionUUID->"61e95316-b804-420e-87f2-f52b4b5bade1"] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"ComplexExpand", "[", + RowBox[{"Im", "[", + RowBox[{"\[ImaginaryI]", " ", + RowBox[{"Exp", "[", + RowBox[{"1", "/", "x"}], "]"}], + SqrtBox[ + RowBox[{"\[ImaginaryI]", " ", "x"}]]}], "]"}], "]"}]], "Input", + CellChangeTimes->{{3.8274934035758667`*^9, 3.8274934072473*^9}}, + CellLabel->"In[22]:=",ExpressionUUID->"9437fa66-ad8a-43e9-8a53-854194067640"], + +Cell[BoxData[ + RowBox[{ + SuperscriptBox["\[ExponentialE]", + FractionBox["1", "x"]], " ", + SuperscriptBox[ + RowBox[{"(", + SuperscriptBox["x", "2"], ")"}], + RowBox[{"1", "/", "4"}]], " ", + RowBox[{"Cos", "[", + RowBox[{ + FractionBox["1", "2"], " ", + RowBox[{"Arg", "[", + RowBox[{"\[ImaginaryI]", " ", "x"}], "]"}]}], "]"}]}]], "Output", + CellChangeTimes->{3.827493407449224*^9}, + CellLabel->"Out[22]=",ExpressionUUID->"3f0d8dc4-237c-43ce-9a29-58fc7f4aeb47"] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Plot3D", "[", + RowBox[{ + RowBox[{"Evaluate", "[", + RowBox[{ + RowBox[{"Im", "[", + RowBox[{"\[ImaginaryI]", " ", + RowBox[{"Exp", "[", + RowBox[{"1", "/", "x"}], "]"}], + SqrtBox[ + SuperscriptBox["x", "2"]]}], "]"}], "/.", + RowBox[{"x", "\[Rule]", + RowBox[{"x", "+", + RowBox[{"\[ImaginaryI]", " ", "y"}]}]}]}], "]"}], ",", + RowBox[{"{", + RowBox[{"x", ",", + RowBox[{"-", "5"}], ",", "5"}], "}"}], ",", + RowBox[{"{", + RowBox[{"y", ",", + RowBox[{"-", "5"}], ",", "5"}], "}"}]}], "]"}]], "Input", + CellChangeTimes->{{3.827491605150834*^9, 3.8274916869278393`*^9}, { + 3.82749188159623*^9, 3.827491882043644*^9}, {3.827491931997025*^9, + 3.827491935380501*^9}, {3.827492233754734*^9, 3.827492239225812*^9}, { + 3.8274926452819767`*^9, 3.827492659626058*^9}, {3.827492731964241*^9, + 3.827492842389308*^9}, {3.8274930360895853`*^9, 3.827493036232737*^9}, { + 3.827493177867917*^9, 3.827493190499373*^9}, {3.8274932291086597`*^9, + 3.827493328390142*^9}, {3.827493360918788*^9, 3.8274933697827673`*^9}, { + 3.827493421656028*^9, 3.827493422967626*^9}}, + CellLabel->"In[23]:=",ExpressionUUID->"534a99d1-416f-43e4-94c2-fadc4c9725c0"], + +Cell[BoxData[ + Graphics3DBox[{GraphicsComplex3DBox[CompressedData[" +1:eJyNnXlcjU34/6vTRqVCSUi27Hu2LOdGtuzhiWQPSQjZ9yVLRXZZyr5TtpKt +c5AtiZRQVJQU7ZEk9Xu+zvWZqXm+vb6/55/z6v2Mmbk/9zXXXDP3LA2mzrOf +rqGmplZLV01N9u9vp/NGL8vKaijxe3X8MB2LjkaScmA1y12NjRmvuyHAb3BQ +VWlfVK3kgbv0GR+qdDK7+0NTuqhXY+2cBG3GPZo1MU5yL5Xf/5uPOuO9lhj0 +mZCZLw/6m75QAf61v9tpX/cP8ut/eRrjq4fOtZ1Y9lJxVMXlLJ+StqEffH7L +T6nyYdzZfO67M34y6a6qXAl88j6njv1mVJHOqurJ+KxrybZFrQ2lXarnYvz3 +nZbrspZUl8JUOjD+2vnD7Hn/mOBvxpVvMwbU7WjG/yb9NrzSXuVow/XE7yPP +CRvHKbme4M8nmcaPr6LF9AT3GHJ3cr3DXE/wZS3v9zxiVsD0BHf+IV+hbZTI +9AQ3q3rq0f7tXE/w7oVTWpv6cT3BD9Y4V9r3DNcTfOfaj+8XLud6gg9LdXS1 +tOV6gq/oazIraD3XE7ygxRjP5pO5nuA6I67N8+nO9YROgbk1p9v14XqChxee +CM+P4Xri1zcoJbhjA64nuOnqgQ6dY7me4J4asZ8d/+F6gqdv9s5zLuN6gvu1 +CG3/7voLpid4ZvMlwWfPcz3BxzSXu3qGcT3BTy/74eDnx/UE/35bs1vSVK4n ++OKMno137+B6guuqay7Jmc31BFdPyPTr3I/rCT0Ca67ou8+O6wletembYesy +uJ7gEV2+JbbqyfXEr9v4Ptk+dcqYnuDf51qNe3+R6wmeOOKy3QqbZKYneHq1 +VQnmA54zPcF1Z/neCY3keoKPNYpfNC2N6wmudtl4l+1jrid4ZhvdoFPbuJ7g +T8fZTWh4nOsJvsP2sH7QMq4n+IdeyXpRw7meeO6G45r+OmLP9QQPGLkldUMZ +1xPc5vv1bdHjuZ7gFjcaz1g6n+uJ36yI3NOGjb4zPcEnjC6Kujv9I9MT/OTS +T85PzjxheoIXxVafH2hSwvRk+bSZWnNYe02mJ7jhhIldLY2rMj3BO9zpZuP9 +mOsJnmNaYtXoBtcTPFFXu+2FLVxP8CWTFnTc48j1xPOtXDnxwfpxXE/wsAVV +a4ysocf0BO/5x65g4jKuJ/iQ/jkmrZ5zPcHf1PGVIoO5nvhddvtzuF6XFKYn +eOj8CPPgW3eZnuDXbRuFjE/meoI3b9V8Qcgzrif4kewVD3PWcT3Bz2yfZD1S +x4jpCW6ecU9r+nOuJ6v/9HvR+vu5nqydbT5q1tOZ64nnOG/Wq2vXiVxP8BlV +i8c4N+B6go8Z5Zt2xJfrCd57kTxksr4ae3/g5x6cKxnZ5wfXhXht90s3lCs/ +Mz3xa+Z8PFI3/ZQceoJLZVFX4jurSdAT/Hj/u/49SrWYnuBnRzt226mvx/Rk +zxWyoGrV5lxPcNPnRwuOJXE9wW12fF4Td4zrCW4526Gr6WyuZ6I0suXnwEk9 +OgQF70ubxPUEz/X69XKTFddT63jeq6FTLe/0eKPjounH9QSvc+OT89w6XE/k +Y/pY75j+Wq4neHIV22ZLrnG9DusVuB86PrSHr9mlwEfej+Rqf/+LvVPHv3OJ +jle3Hldi5h7qNvBpD+jsekTFB05reaN1Kx2mc+kBVX1Oepq1Py/TYTrLXFX8 +yz/3Rtv/w3Vu3UtVH8vLtVo+7WIk7SSdkd7s9KqopDSuM9JXO9Q46vMprjP4 +EbnZmz1zuM6or2i34DMFuwUX7RZctFuWv2C34OaC3YJ7CHaL3z6C3YKfFOwW +/Ixgt+DTBbsFF+0WXLRbcNFuUS/Rr4KLfhW8l+BXwUcIfhVc9KusXMGvsv5c +8KvgIYJfxW8Lwa+Ci34VXPSr4LUFvwr+VvCr4JcEv4ryGwj9Pri/0O+Ddxf6 +fXCx3wfPFvp9cLHfBxf7fXCx32f5CP0+fo2Efh9c7PfBxX4fPEno98GXCv0+ +yhHjUnA9IS4FfybEpeBzhbgUvFCIS8GThbgUXIxLwcW4FNxBiEvBNYS4FL9i +XAouxqXgYlwK/l6IS1kcIYybwMVxE7g4bgIXx03gm4RxE3iaMG4C3yOMm8DF +cRO4OG4CF8dN4OK4Cb9LhHETuDhuAtcQxk34d+K4HvyxMK4HF8f14IuEcT34 +cmFcDz5VGNeDi+N6cHFcDy6O65kewrgefLgwrgcXx/X4zRfG9eDiuB7/v5J5 +J6mSeSepknknqZJ5J6mSeSepknknqZJ5J6mSeSepknknqZJ5J6mSeSepknkn +qZJ5JwnzTmF/849T4Ncm0Sz8ydSrilt/88mTg+/9aRxeNUOTpd+n+pWnfaiY +HvwApV++zLBo4K7qSvwuafhn18ldBuw9gg8d3vjS8c5GLH9w67a1p60zTmXl +gdvZOes3v/mDlcfmFU/d840L/SFHfZB+8DfHtwHX1SRwpC88FJf9K0gN9WT1 +LVl/K2f4U1OmF/ivoAOeLbtw3fTame8ImWOoLJwVmH0rKYXVE9yy458Ys1u8 +PuAvB2lovr2nxvJpMMekXUJIFeWBzJkZaV48H/Bmn4eevneb5wM+YJPB8uFv +eT5d/tZXpizJM/y6POMTywfcq3ahm5WC5wM+smaeLFJDneVz8K99lShKDI7F +7F77keUDfi9z/AXdJzwf8LmyX5ajJ/N8wlX/X+HRYpn3DsMElg+4fkJi2dOc +H8zO0J5KH58ar3wZzewK6efu0vk2cryGhL/x7wav+epd/+Y77t+I959ye1dV +x3vMTsA3LF/v3OhRMftb87Rq3BG3etLcTj33sfgb/z/y/sqVzqtkEvLBbwDl +g3pifNSuXeQh9UgtFk8j/WvKZ4dKL8Z31e9Qc957XWaf+J1Hz4t6sHIEPcEN +SE+UC97Dw9o97esf9jwo/7fwfsHF9wvuLrzfDir7kYoFewP3FuwN3F6wt3oq +e5b8BPsHby7YP7ho/zqq9iWJ7RFcbI/gaI+Cv5Iq8VdSJf5KqsRfSfBXSA+/ +4uSTZFfYMFUh+CsJ/krwb5Lo38Ar8WMS/Bj+Rvpr9SOLCsMZZ99ZpjfQO6zj +bSAJ9VSinrAr/LulLzsavd75Wy7kr0T+SA+/t+nD4SP1jv5m9gk/9ma+2/hP +oZzDL715NfKhdwbn8DMLvFdeMp5Ywjj8QVeyc+iG9qi50qyz3upabDyG/18r +3nhNjyvarN0hvzdfZ27q6Cpj9Yf9ewjlwp7fCvWEfYrPBXuDDoL+EvQXdJag +s9AfSeiP8DyIg/wCwnfvLNc/Ig5qMLVd78hbnCMOWjMveKDFXc7ZfOzUgy+m +3ucccVC19zZzx8ZwDr9bZ5PHWsOJhczO8Rzp5M+RHrwupQfH+xHzR3yUK9QH +8dEqof6IjxoKz4v4CPqE/P37o7zex2o+cxKMlavUdBTNzxQxPqLMLLSszECZ +oDP47Lcgzmf0qDm28SBd5eCdZWeOKThf+fe9aChzC9Juy5M5b/zXHn4pxkeG +zCzr/IvxgL/1zFQ4Kme+dL1ZzPirv/V9pJjfdtDW7G06Ev7G/zc/e61WQutY +9ne7v3ZRIHeefeyi/mmev9ZfeyuTbzr4pMH1Ml6frHjjsyFztKT1caM3no3k +/K2/qe6uxnqS3tRzNzaHcD7lssH1kDlGUp94pazofJE8QsUV+D1sM0gzfMVp +BeoJ3pvq6aV6TvZcIbqvb82boiWBr1dx+W2Bo/yerfsFnf+hISEd3teR5g8N +Nz7LZ/9+mqqeykSHAUOOPsln/x7cluqP9Hi/00YO00wK5/m8V+mg7L67g26i +gucDXpX0QXrYQ49aqdqloTyffJXOylX7P7m3CeL5gEN/pIf9TB21SnvVUZ6P +oeo9Kjb+bO1fZSvPh3F6v0gPe9sbfXBFy8k8HxuVnSjCuup5mxjyfMCnkv0g +Pezz2Oj+TesMzGMc7/eoSXjz6mH8/eH95ugk9k/aXMLaP/jGWKO5Q75psfeI +315VVOlRH/CtZP/4G/9/K5ULO4GfvxXhazgsleeP/x9A9ce/B59I7Q7p0Y6g +D7i5Sk859GTtkLgTtWukR7vzpPcFvlT1fqUp9H6RD3ge+Q2kRztdTfYDPlVl +b1JPsjfkAw6/hPRo17Bn8CEq+5dg/8gHHH4P6eEH0L7A66rao4T2iHzA4VeR +vnSvKt4+79HB82XVJqz/gp3ofTuiXPpQh3H8u7HE3xobOTceVEOJ3+qB1uMG +l1RjfhLcSvPLtss5GQqmA/FPK2auefqc1x9xi7G8xYGwqHykY+XopDc90+jf ++AH5M/98VuOS20wf9jfyk59RceiA9qImFVy1XFXK9IHdJhv6j0sL0ZNgf8in +y94LS8bW4/P74N7UjlAu7LmhWau6Uu1PCkEfqRJ9JOjD/D/xg4fMHrU6WSTq +IEEHxEvo919TvIR64HltyG9DX9RLM+TOzXfWRpJQrhLl4r2DN2r+c/Gff+Ne +5IvnmOjc9uGgBldYvAGuZpRu4pPWm8XV0O2Db7HLVm+uGxtndN3TqvsoJdMB +v3r0vqA/ePfdSU5PV6lLgl1JsCuh/hLqj3LZ9+pd2699/ZHB3ge4w2K3iJor +ub3BDzen9wuO555D9YdeiBMXZuxUu1JUjcX9KOdkZr0rtTuZSUJ6ZSXplUiP +8hBnSgP2XDn2O4XVB/3syB0BjXtHZbD6If585tj9pfNtnh796ebWAxNl+3h6 +xKX/rJhuN2AgT49+8+4/KbcOteLpEa/W1F91LtSJ64P+0Wlgy/5f+qaz9Ihj +U74Zlw6qnszSox+MjIxtNOf4Z8bxPbTGQuudtif6MXuAPXYme0D+iGOThfzR +XyTpDuwf+s8XVh/Et9WF+qNfmNu3T9yxaF5/xL2iPvD/uVbaycNduT6Ih0X9 +4ectDs4zNA7JUAjtVEI7ZfOEFD+L7x1+fo2sVkh+coZCsHMJdo72A346S3fD +1+Pcz4DD/jHuQvk7aZ6EzUsTxzgO/hPvpW/diLgjvbTYfBHa5Qhhvgh8HM0X +4d+zfoziW6H+StQf6VkcR34JvM4xlf1MuznRwbJTMKs30k/+/eWvv0L9oZ81 ++X/4MfB35MeE/ktC/4V0iJPF94K415LeOzji2HyyH3DEpbBDcMSZn8iewfEc +T4R2hLjIkdojOOIctGvWT1HcAv8AjjhkBPkZFjfQPEPUEE3vovucY55h/sz3 +stx1nGOeIeVpwoqnMs4xz7Ax/uWi4x/4c8GOkjs6/MzqlMqeE/344RfVF0/t +rc38Nux3vZAP5g0+CuVi3sBdqCfmDcTnwjzAnss3Gt9Nz2DlZeqo1nV0Do1a +v0ijCmtHqL/Xxr0LH1XXZRzt4F1sZh/7NboS/BTs9+HP3ud3rddh7Qg6J48x +OGl+9g779+BOUw4Pvy1/ycaB6Bcu/rk+oGeD90xHvJfcIbF1SlcqWT7go/d5 +DLK9EMXyQX8Ru+7t/trzElg+eI/h6aPlC5uGs3zAYzWvnjGe8Izlg34kPatU +3bp1PMsH7113b8TTjSERLB/wdNNpffveCGf5oH/xnaRW7f2BNywf/H55u7ee +U7UYlg94kUtZp0bpZ1k+6Hc6bvscY+0ezfoJvGdvg8h6YZ+5/nhvmkI9wVOF +eiK/+Kmnbmt0f83qATtUCrqBi7qhP3L/0Dj9n0bvWD6w2+/CewQfIbxH9FMr +zA8ZPf7C9Yedpwt2BS7aFfqv4jpBzkax3B7QLszO7oqcU3CT5QPedWbDejWf +83zQf7mvW/J66YT3iov6Q5bLPp5icc6BNK1Oc4ZlM454pqfcJ+VLc87ZeuH6 +1/11vmQxjvikbtyjOPOxnF+mOORjr+xTA559Yxz1ndjwTrvjK1IVVwqD3rXq +du3OzP5DLZtNuie/3mdqjQc3w1h6xCPDKD04i0OE/BFv1BHqg7hiv1B/xA+9 +hOdFPAB9mmh3Hh9vf1rRrJdjHceYGlJq58cLWzllK06q0rP5yYkDrla5tD1X +Dg49I8/k11q6lnPoWVr76XenGZyz9bGWX8NbtuEcem5qMdhhukUO49Cz7E7n +c/Kb6YxDtzyBQzdPIR/oJpYL3cR6QjfxuaAbdNAg3UZFLnv25NQ7ed1mv5Ou +xD9T6BN3uDApXr74syLoRfu7U4elKJB+iSq94gqlr6Xi8sjr4bFdRhoro5bN +2f9rV668M/E5BuP6npheXdkycdr+Xfty5Y2IN9bd/Ev9saHS86nnWL1tufIG +xK+c3jhozzd95cw3O2b398yVmxIvcLhkNbumobKxwdknDt65ckviNv3WH7Ay +qqo8vuaD7avlufL6xMNT1mSEWusopeBdJYPccuV1iWvtPfvId0IV5dCPZ/uG +LuF85PpV3QaP01R+a+5lJ3fIlZsRf2e5YuuHVerKr6N3n27SJVduQdzi1YkZ +10/LlCWl7fIvjsiVW0GH1XlXk2z/KGYPedz8rEauvCHxT7cz7TW3/1S4/Qxs +YT0wh+U/06KXwdWk3wr7rDXanh9z5HWIFxZ9yW/2Jk/R+trYUefCsuSNiZu7 +PWpySEpX7OzYd9DAyxks/11+1kN/z89VbHBq1HVdvSyWz0Z6X5Lpselz679i ++hTaXbSubhyraPtg8ij1MUEK6P9cxeVTnqo4dO6usgf5OeWKD7MDvzAdJpH9 +vDRR5d+S+CZVfeSrqT7Ix2N8t0txzQrlNtUORqZp5LD6ZKmeV96Cnhf6TFTp +Ix9J+sAeTrkfC+n/TE3Sv1L1+t1WufIaxO+p9Je7kv4tiJup3pf0h95XNeI7 +Op42bbheWwr2SU5OnsnTD1XZgwR7gJ2oq+xHGkb2g+ddVnh+8Z+u+pK3YmB1 +2YZcObUjubXKPqVjZJ8mxHNV9izBnmcSv/zeYXbmTyPpz6YHWed25sqtiTdQ +tRdpE7WXP1oV2pfUnNpXB2qnzVX+UPmJ/OFnVXrFps8PL2aHVVfe3LNgwaPR +2YoelH9TSr/zT9f0RQdZPvItlP6Fdtq1g/tz5VqUv8Zglf14rbTqkrP1iEJG +/B3Zz4IlKq5DvHT2X7uVe12eFzJizmfmT7aRnTwbU1+nwdAMsZ4S6tm5Yj2l +SuopoZ6uNWutMck7xcaXDW4m2qyals3qs5faSxSVu6HhJHWv+tfuhKr6O0WN +3qr+juxWEax6L8pJE3VHzOiXrahHHH4sYlLBOI9u2QpqF4o1KntQBhp4v/Su +n62oQrwb+atd0VE75lTNZjrsU9mhMnb6g27X32Up8kiHYeSXJlyy22UYlKUo +I35BZf/KTyVXEk/2yWL5PCb/c2HXvj5132ay9OtV7U6RfrHdD8193xjPJz8T +W+efR3P0vyo0KZ9XKn8lbzDcIeXct28KvPfJ1B7ti/e10r+QyZ7rtcpPSp3P +WTevOyFLUUL516V21yutdlyvgCyFNqUPU/lnaUNptVDdz1kKao8KGbWv6yXj +Z7prZCuo3SkuqfoFKTcsMn9qk2xFIepP7eh1+u7L1Tpls3IjVP2RtFnX4k7E +QJ4e7SW/Wu4Oc/tsBdmJ3BrrE9/qTXjwr/20066QXplN6andKb5TfxRL5aL+ +OtS/3KD6/6D0ltRfSKTDb+Ku5P9Hk566lM9X8ocv6b2UUvow8m8XhfdrR/4K +dgI7h//ZTfYGe7YkfwK7xXvsTX7+EPX7iB/w3Xj0/JOxHrtz5TbU7q5Ruygh +f4X0GJd1/WM9aOuWXLk5pUe78CI/ifQYf/nErJPvXsT93m5qFyHkn5Ee46zx +toudO4/gfvgstQv0C0iP8dS4oY7+qd94/7uG2kVP6o+QHnH9D79BdjVnZbF+ +1p7iojDqB1l8RfMr7uZPS6v6KXmcSfM8nWqrOPwS5nUaFG4ZOrrKB2aH4Oet +/KzWnvzEytVW9ftyT+r3kT/mafKonoiv3lD7nU3xBtJjvOZIOqBfjqP2izgH +6TEug87oL+5T++1N8RXSY/yF94j0QdR+XSiuQ3pdGmfBThBPov0inkT8Dzv8 +c+vc8DuOvP2yddnUfqEzxlvjBJ3Bn5LOSI/5rTOusyOiXpwFZ/P5Yy42nZx6 +lI/XoL/HtJHF7rczkD/7PqK7ZbhJn0dfWLngRV5OLT7f/sbKhZ20OL/249Yw +hdjuJLQ7xOc1KQ7cT/0p8sG8vZFQLnipUC7G+45uFZ+XzYddUj0v0sPOfS6o +6gmO+dQZ/c6sSJzI3wu4hf6XR0V7+XvBPH8l6ZVieszndHg7Ok+9P08P/jy0 +0WF7H54e8za5HcYEFdfh6cFbrx4y5dcKnh7zM99/hA1YGZnF0rP5f7fAoEwn +nr4azcOc2Fti6V2bpwff/Sul7ixTnr47zbc033EhbGXhV5Ye8zDmBl27rFiQ +zdKzeXuNbeG6EzNZevCQ4jlnmuzPYekxTzLWP8PAfDOvD/i+SLdTQb15fTAf +4tTwc0DD3zw9+Lq+7Re1mMfTY94jwNTgTWFHrid4zOu9A4d78vQ0DyzFzBg7 +8Nsonh7zHhdOFdjf3PmfOE1CnNaJ7DyKxpUbqR9HeguaZ34l5A9+kfKvTvmQ +/1HmUfyAfDAvfUR4ruHE8VyIW8jvKTdS3IJ8MI89XtATHHo2pXwSaFzZieIl +5LOC5r3F94j5cLxH1CeRxpUNKU5DPmyeXLAf8FCyH0PKZxGNyz5RfIh8MN9s +JdgteC2yW8Qhp2lchrgU+WjTPPxxob2Ao70gjt1J4zLEw8gH8/YFQjtl8/nU +ThGfL6dxGeJw5n9onl/0D++Iwz/gfV2hcdlEiv+RD74LtBf8ErjolxAXHV0i +v+LXk+fTkOKfn4mR5hn6nLP11Vm2tvMvcR0OUTyTm2XvNfYpe79sPvKtxuV5 +Frd4f4R+P0dIj/79t5A/+vEfQn2qUH8t1h/91IzQAyOCx2UrrBbHmrw++Fp+ +MeJGUeSbTj2w7qLXt19R7t9OyK/Gn597oV0HxtG/tr1Q4rK/5z2FyDPP/+Vy +8Mryryyf/6tcMf/sPdXiytbwczAuba1RkLpYT4JfQLxR1m5OqKWzNuNIb9f8 +rG2dJdrS/dia4WVluiy9wnl1gNskdcaR/oW37OhgD+zHkLH0r4cfaB4QWCQH +R/r82/LhE+OLaD3ZHzbOHdnw4TrfVlmMI7399WG2T9ZlyTtTf4P0944Ft9wT +G8040i8OfvR1ossrirNT+LrctfffqkfHKTqqOJtf/edosfYiy2IaRxUwvsrg +QviidhrSMFV9WJyW2vRE+xbddBhH+hAHn4zeg3Uka7JLpE87aXHHwk6fcaSf +3yGgkd0kfemeSk+WPjeg8NQ/F4wYR/ozk0+mDw4xonL5Out8q7e/t7WtwTjS +O/ZskmtgUwP2wNJvr1F7uPFVE8aRfn/O0U97bzPOz/G4PlpLx4vbD/j4e7uX +pWzjdgLevcrKSeHbuT2A20nbAwaa/GLvF/xgq90+sb/5+wX3OZq3PXdgjBzv +C7x0yXS/K234+wKXbCdadbPl7wvcq050r+gZ/L2AR5mvenJ7FdcffNBVl5y6 +D7nO7Hnn5XR1HcD1BB9Yt/d4s8dcN8zDj9JJCC4M4LqB+3VMK+59lusGvjJP +P9EniOsG3mr69RPWzlw38JJmCy6oB2Yz3cAnv/Hb8zowlukGfv6rX/1XA7lu +4NOX/QiaMoPrBt4odmXT3F1cN/ClOT6Wi85z3dj6E/fAc0bvuG7suWIttmqN +5bqBJzzYmLkgluuG7xRX6/We0f06143tg3w2q1FYONcN/Plow06pr7lu4Br3 +vLRtI7hu4H3r2YUVX8lhuoG7tH177oTsDdMNfHno9S0Ja7lu4DP/zJ5w+QzX +DXz7syTX9h+4buDH9YfcHJPJdQN33f3ysm4B1w3cbXdpM8/ZXDemz+7dw9M/ +cd2wPmfjg7XHBjzmuoEfjrdZkZDEdQPPSjWdeuwP142tV28vb7mydzHTDXzr +RtsPed65TDdwvfwLY9IK45lu4DtaNE81r/eb6cbO9xg0bUistYzpBh78uUf/ +gxN0mW7gRZ71ag0aaMB0A9/tnnrcz9iY6QZu9+ReUdQarht4DTv/+Ku5XDd8 +5+oz3O7dw1iuGzs3Q91Vw/g71w18s8sEF796Gkw38OoOe65vvcR1A7c74jj5 +zYg8phs7T8L/+8V2i5KZbuBzj8Z8fZbxh+nG9mn5Va/e9bom0w08ynqL2vGG +VZhu4LeT65+xD+K6gWeUpqhvaM11A0/+c8W07Q6uG7jfs4LFpcVcN5yPMeHh +5sNB77huJSdU6zqa2dpqnPrNdcP5G1YnjE5bteC6Beur1l0cP+gS7JHAdUP+ +thbWPQKvcN1q2h8atmbJ+B6Zb+s9HTPvE9MN60m2d3PW9ZoPHQrk3Yn70zoT +6Naj7eYbLzr265E6afANt/1ctz9GqvrsHb90TP4nrlv8orZ7r+mO6jExc8LZ ++d24bkdDVPk7TJs57Ng+rhvO2Thm2DcooZTrhu+ntoK9gYv2Bi7aG7hob+CD +BXsDPyLYG/h8wd7YuWWCvYG7zCtb3b4p143tnxPsje1nEewNXLQ3cNHe8H1Z +9G/gon8Dzxb8G7iR4N/AvQT/xtIL/g18p+DfwG8K/g1c9G/gon9j+/IF/wYu ++jfwmoJ/w/f3y0J/yvb3C/0peJTQn4KL/Sm4rdCfgov9KbjYn4KL/Sm4r9Cf +gov9KbjYn4KL/Sn4NaE/xfqE0UL8Bn5QiN/YviohfgNvI8Rv4GVC/AbuLMRv +4GL8xtIL8Rt4YyF+AxfjN7Y+VojfwMX4DVyM39j5FcJ4AVwcL4CL4wVwcbwA +Lo4XwL2E8QK4OF4AF8cLLB9hvAAujhdYPYXxAriTMF4AF8cLWN8SKIzTwcXx +OPhLYdwN/l0YX4OL42hwDxovQzdwcVwMLo6LwW8I41/wBcI4F1wcz4KL41Z2 +/qIwPsW866Xzyw7YzPjP/IaE+Q1hHkPCPIYwXyFhvkKYl5AwLyHMP0iYf4Bu +bH+xx+F6qbW4buBtxzdMHdH4P/MJEuYThHkDCfMGwvyAhPkBYR5AwjwA9MFv +npvWwEwPrk9d7Ad0CX36ZgHXZ3Brwz4Jnasry3Im1Mp14/rgu1X+uYVNFeFc +n7MPDQNDsqordWMuPl1kx/V5g/0p+U2fPczl+qA+k1dYFx6pz/VBfRaVrZud +15rrg/r0sdk3/nE/rg/qM/ZuQlSHMeX8GNVncvtsp0lBXB/UZ7lZ5/Ul7bk+ ++TPMhjQeZKD0bjVST28L1we/dZqsb/5nS7lx+v7ajRNCqint9QznxHhyfWhe +UbnszMBGPX5xfTo6G5QOrG6kjEhaWXwuMIvpkEflppt9bGPXmutA9VXuvWl5 +o41UbjxO5TrHLA0xm8h1qErl2loUeJ2by3WwpnI/B8QMW3eb6zCVvjcl5e9w +K+vB29eOEgPXxk+NlIWWT5o+u8Pbl+7JGpkDd+koR63uHZZymOsznb4LbJ45 +bmzi8XLjcfqdYXF+ruEprk99mh9et7jL2K0S9+crtUwPh8ypqlzQYHBCUu9s +po8Oldtm1YAOrftzfZypXPtnBUvGTSo37qZy199tmFKygetjSeXaxa6W1d/N +9VlF5bo4PT959RnXJ56+r/VcO8Yi3o7r06VzLY85CXrK8C1HBs1+wvVRfa9R +V+7RjyvqepXrg+8gmWv/rOqp4Pqovg/KlI0CNyycESH6H5my+e4DdsOOlOvv ++hj3SAjRVA5pYeBvY5HD9KlH5S5NXWn6cznXZzmV63isub7BQa4Pyh2idJtX ++x7XpzOVax7SJG3mY67PbirXttbIH7nJXJ9c+p7o2+/mzvDxXJ+hC6vX3NVY +W5mts+TKs9dcn5l/31eRIrA4P3v7Q65PQ/qOM9r+YNv0eK5Pwl/9fyt8jpWO +98kX5w9LFEsyxo06XoPH7fj9ubP3n+7tcpk+M6jcbbpZ2y/p8fjcksqNqrVz +kJYpj89R7pb+1Rtda8Tj8/1Ubru720d8NOTxuT2Va3Pf0XnKb66PPn0/Pe96 +aWe9eVwfVbtTU94c282tXirXR/U9K0PRxaX6Sr8Yrs8B+t7dpk5ge59cro8q +/xxFryeNDCQTPh5U0neTnxuHVFFs5vqo7DBf4VL4NEL2i+vTgMpdlKRhvmM3 +H/ftpXK93abaPm7Fx30od3eodpNu0brCvFae4saldlnqrlyfVVSusbbZynlm +fPzShfqHlFd2zuvWc31UdvVDsc5qT+m2PK7Pjr9xZojidlKGpm25eYbD9H1f +y3njNKdirs/Nv/WJVgTN3/BDrSnX5yR9938y9qH2zEiuj+oczfcKy/eL99b2 +zuNxI5XrNMjGstoEHTafcJXK7UT7jCrO/0crXLLGpH5ZzsfF56jcRfHhj43D +uD57qFy7l4Udbdpxfe7Ruo69yt5fO+wU5+1TFM3SntkN+831aU/1TbNOd2// +WowbP8ptPjY/Nu6HOD//Xv7nwFezMEuuz2Vav5Hp12Xa/jtcnyeq55LP+1hL +x20J1we/dkcG6s1eVCbEhx/l9Y98uXxioRbTZzuV+67VSv8lLlyfC1Ru/JQY +646xBsK8aLT8j/ngxbc6c33C6XvX8aNvlvvv5fp8Ub0vufEP1wTvcvMtqu+q +P+Q7zoeWejzh+nSg+m5WFg6enML1WaayW3kXzxF3f2lpCHF1nryZbHNc/5lc +H9X6nxz5nNavFzxMyRXGI5nykrVv7i2alMjjH6pP9bFT21v35X6J9f+T/Nps +3M39EupzfN6efT4vdYXxb568JFQ/+sA2rpsm1WfWrMvNLlpx3XZQfQYUNLuw +chvXzULlB+TNc0rsG5Wbb1F9/1WTNqdFmX0P5rrp0vfu+FFV5115ynVDfdv6 +Ne3+K5n77T303faQrntivSLer6m+U//7/OrN5NesuV8iPyk9uDFn0BUv3q9V +pXIz/C6ZRz/h/Rp+77hW3W5WS1cYr5XIXV/Hr7nbmOvzhsp90NsxR16F61OP +1qXo5VXf0Xkl10cVbxTJDTx/3l2Vw/UZourvJHez/o1+HeX65NB3/F6r7Y/e +v1RunKvqT6Wmfn5Hqt7m+qC+2rtPTWrhy/VRxasy6UedoMh7vXm/j3Kf1l9w +9PIQrg/Kddj1+c5+j3LjWSp3RlJOQ90g3u/jt6zftYKpL3i/H0flrsxsPb3Z +N96vLcP6nIbOlo9mcn0oDpGODj/m5fuR69NZFS9Jpj2zS2r7cH2wPsFtm2Xd +Abu5PhQHSiPfJ0b1PvCfuFEqbKP3taBrue84VF8r61tOhTN53EhxmqTWf0dn +v3ZcH4rrpJcOVgtcB3N9UG6LDi03hC/i+lhQuSWdvD8b7+X64LfLo0Hfl7/i ++lBcKh18EHpi72iuD8Wx0iQHq9L6MeX6NVW8LXU1rpWVvJTrQ/G5tPXhzT3q +K7k+NI6QQre67+qx6j/jDil8tGeEayEfd9B4QWqoPj0uP4qPO1BuX5edZpsb +cH1Q7o3AMerbrbk+KPfDkdT5xaO4Plj3WNKm2RSncuOOC1Sunke3rV8UXB/8 +xt3ccGepLdeHxkFSxtfapikPuT46E43Md538dzzbovObBi5cH6zHO5/n1NHZ +hetzTjXuk3zVGjd9MuM/41Ypbsr0kT3LjVuHqMaV0mHZzJKP07g+ulRu7uDG +ck8zrs87Kjd+ferYE1ZcH5Q7tt8Bxcle/xmfSmW1Pxp1Hs31ofGs1CXqYvu+ +V7k+WFf2avDjWUe61BB1UEIHrGfQIv5kZJLzgCc4xzBFkUP/rsekLZuuLoxT +CPVXov7CvIQS8xJ4L8h/8sVYn6bX+DqBXMq/cG12/YW3TFh9ftB4VrNfSUZg +zGtWrjONN2FXSK9H47vvCRqb6yljWfpEGn+hnSJ9AxrvDE17f/DstVcs/Xca +j8DvIf1civ8fFV28u/90JEtfk+LzdOpHkL49xcPd+93pte3tVaYnvn+NfRhd +b3nHEyyfXtTPD6X+uuJ35I+KeIfoXmdbfWTxQALFjXdO1l0ie/KRrUth51DG +V78wYW4wn38jPvdj1tMXheoSW/9A8dJS4rDD4xQvzaoQfxbI11G/70PxPMqt +R/1+NeF50yg+yV3zpG3kpSdsnQzWCRca1B9dP/M3q/9E6q/tPE4ZdiqLZvqY +Un/6ksZZSD+I+q+Tif9snjmPv/dF1L9g3Ir0Hcmfj9Ie98X2HLeryeRvR9I8 +ANJvJ/92uMR+yAtHbv921M4wr4L2lUl2nU/zY0L7ksT2xc4hpHVEyL8OtV/M +X6G94PcHtRehfUli+0L+wvoctp4K85x4L5gHy8uWG56vU8zsB+v08vKvux22 +KhbGfVWUl6MatznYjXOs09uSajMvfyLn2HcQMe27m28o51inV0D2wNbhkH2+ +S995rNFzLVZPrN+LFPLB+r2tQrlYvyfWE/uaxeeCv4UOeF/4npgWrmq/LI6i +ecU1Lv4z19Tl+Vymebbg/IITms04f0T9zF71EPU+PTh/T/MqLtMOKz87c55C +8wnfLhzw2hLBeR0aRw8zH3a0mX0J46k0fqz969P6c55ct/kU/8fluG5f9uQ3 +S9+f2r3G7uNfPgXy/LdTvHdldExj8/GcL6U450eGV5XgLpy3p/49PSEw2qsJ +1w2/asnx32cs6cP+vknj1juN7Rt1XHyGj5dp/tCW4go2TqR5yAzKH7w7zaeV +9VPFaeCYDxTrOZLmlxD3snJpnkp83pk033KfxhHg6P/VBN2KaP7BiMZl4Jg/ +iSH9Vfd9XL6TkapeYlPw4o6f74/lHZw17iI99h0UqV9a4X9HW0J6H4OydVO1 +X/ZYv6Ni+j40bnWheQbwO+TPmwv2YEB+exnN21RsFzlye8GunGj8sp3mwcAx +/soU7NOM4vllNK8IjvHILMHOZRTfYp6WrZuieEdsL1kU72Hem61Po7hRbHfw +z/heILRfSWy/A8hO+9K8BPgBslu39r9diyeos/5xKs0ndKX5HPDjAkc+WG+r +q6F6v+z7LMWBBp2tvqmV88MUTyoRTwrplUiP9lVdXzXvtC/CdufsugrGw8k/ +ONUYtSjo602Wz3yaV1lIzwWOfVgnDrRKaDVRjfVrWOfZ59vDS/ddeL+GdYxz +796P33DvNeNYp2d/Yt2N5wGxjGMd2tiFu5cPmPOKcayzOhdXL31o12fM32K/ +UoBQH6xbOE7pwfFd3kHIH9+dxfrgu+ocof74bojnRbwUQvbwtsJ8VAGLu95Q +/wX+iupvS+cjVVwH+FHRjzjivWtkJ2EU74EH0nt5T/Eh05/6TReKA8EbkX5r +wyv6YZq3lDdsUtEPs3Pa6fsje1/kZ04LdnWY/Mxqsivw0taq9VE7bNrMablb +yfr3/ErmP9djvre+4ZMdgbpMB3xvmnyqwS5t/1dMB3sazx2bO+B5cM0YVi7i +FqPV+gXn6nP7xPepfFnrzV8dysVj1L/sDTo7eGW7OAXyx3echm9uleUFxLBy +Xej7kZ7zqehb42JZuYiL7gTKjS714/aD7z5HBzuaPTjJ+Vrqp3bMGJQ4Yepr +Vi6+j6h7e5qPtX3Nyl1N32VWb38ecHBenNDPypSJt77WOHkjhuWP7ylhtxJv +THbhdr6P+jubom+uiVkxrFw9Gtfs+uWqPqnGW1ZuM/recXHy2J8XU9+xchHX +nQ4yaSTzfMnyn0b9plpUV8vkwmjGx1K/uefH2zdhxS9ZufhNPnM5plvYe75u +ir4jrHZa+ihbliT4sTyF7rL3ScM63mf5Y/7/bnM/80+JTxjfQHa1fPkpm27b +wll5FjS+CKTnAlenecIdpAOzH4o/TwrPi/k9tzIHjcvnIhmPpv7RNfufCSf3 +vWDlYh4M7xH8G82/adB7Rz6Ibz8I77cu9bMF+oO3+d/m/i2G+tk/OaUfclz4 ++8X8UjWyW/A4mteCnVcc31WRbgn2jPmoKtGt5OcfcrsKo/7609XzB69bcHvG +/ATaKfhkmi9Cu2b5U3wutl/M81zze7i61xten7PU798OaxL/uQpvv9h/d3p4 +h5/u/V+J6wok16VPfIILo1m5iP9rTp/x2Pc4Lxfjqth+1YbpLubcjuIH5+9D +lvXfG6dAnDaLzgt6TucFgd+icxVa9q7IMw+r1n/O6SPfsaRgRE/0rxi3zT/1 ++VGXsKps3wV4SPtqW926GbH9A+AfWiapp2vz+2vAvw+I2Be8j9+3wtYv7Blc +alqDr6sG37vm1NFaJfy+FXDPDhP3XT78kvW74Auvqy93P8XX1YEPTrmsk72E +36vCvjsFXJg+vje/VwX8QnWzVg7r+L0q4G07WPXJn2jC9plgPs/TcZeH/guu +D3ijWcazh0lcH/Aj43PDetbh+oAHXjlVu90jrg/bN+Dz4ve3/lwf8AEnikZt +e5DI1mWCp50YZxgcynUAn7KiXTfDnVwHcL3+jp5tx3MdwH8qFnYy38Z1AN8w +2K/4jwu/Xwa879KAapF9zPh9pjTezP0uS5j9kesD3uZxzZfLBnB92Pp05y3z +gjqUu+eUuNvZk4si1crdc0rcbtOX57N9uD7gBqG5P5PSk/i9pcRv/FrT3v0N +1wc8oM6AkgfBXB/wFymP+hxaVe7eUuLngz6f8TlU7t5S4j1bbrDe7FHu3lLi +s3+FS68Hmwn3FsmUo+8EHVj/nesDnt55pMWhYUbCfUYypYbpiM5rhmgJ9xnJ +lP22djy/vn+ZcJ+RTJl3WE+t8EuBcJ+RTBlgH+tT92WycD+RTDm+vsXDt3qa +wv1EMuUW7a7TO2SK9xPJlL4/jnr4nRfvJ5Ipnbo2un/8ong/kUx5wyq6Xut1 +4v1EMmWL4efqtx/D9cE4t6rFr9e52npMH3Bn7RLNTmO4PuCHujzfnTaD6wP+ +4qLRk4TdXB/wfs19Jps68vvy2HfR8e31utf8xPwP+Oic+97O1x6yeRnw2HpT +E4sG8/vywL2e+3TpNJvrydZrLxxkMLc7vy8P3F954VvHT1xPcEW/TfErFFxP +8NuD9SMNt3M9wb0Dp23tOJHrydbnjn2U8tqU6wm+Zdo+y8uOXE/wB9XrtstZ +zfUEd2y7e7ZxMtcTPPLh3qCst1xP8ONn96sve8L3h4Ab1vjsOK1WMNMTfMn7 +ljWOTefrzsGfdKj2x8GM348J3mDLwoZ+J7me4PvHps5SGPL7HMFrH+/W+3s0 +1xPc3d2up+IA1xN8q7R9csF0rif64SXF407pNtRjHP0q7nWFzki/Qs9Ac+5E +I8aRHvfDQn+kfzUtbPHFHVqMI714PyzSr/xQw61PNTV+vzWlF++NRfpamp1H +VrH7wd4j0ov3ySK9fV+l5/4TnxlHevGeWaTvsc98n27qZeGelxRFz0EOOvbx +/P5TNi6ZXX1fSQt+fySLr60fOz010WMc5Yr3zCK9/5jN2R9bGDGO9Lh/FvaA +9J1dSgK3Jldn99IivXgvLdLvnX9p1tjjJowjvXhfLdJf9myrP4Pfr8rS4x5b +2A+b7yS7gp2w+TyyH9gDm7cjO8F7Z/ORZA94v+B473iP4Hi/0Bk8h/SHnuCH +SWfoCQ49oQ/4HtINOrB5a9IHOrD9AYK/At8s+CvwcMFfgTsJ/gpc9FfgJwR/ +xeZLtmy4pe17jcWf4KJfAhf9EvvOIPglcDPBL4GLfgncS/BLmM+oIvSb4NOE +fhP8sNBvgkcL/Sa42G+Co9+EPuBiP8j2FQn9IKuP0A+Ci/0gWz8j9IPgPkI/ +iO/bYtwF/kWIu8BlQtwF3l+Iu8DzhbgLXIy7wB2FuAt8qxB3gYtxF7gYd4GL +cRe4GHfhO78Yt4OLcTvblynE7eBzhLgdfIgQt4NXo7gd7Q58yfXCrG72USxO +AD/RNrjgzV1+zyZ4iBDngx8R4nxwMc4HF+N8cDHOB3cV4nzMP4jjRPDGwjgR +PEAYJ4KL40TwB8I4EbwfjROhJ/io7j2+1zDg95aC35R5tZh26rfQfg0kcVwJ +Lo4rwcVxJXiRMK4EXy+MK8HFcSXmQxbQvIQw/yBVMv8g/fjf5x+kSuYfpN3/ ++/yDNHmK7fvOAVw38Ag30zTPfVw38ErmJaQh//u8hNThf5+XkCqZl5Da0LwE +dAOXpbfq5GFjJmF/CFvX5vwlunaYloR9EeArZk1cpSlTk7AfANzEu03XMxu+ +y7EOHtxq3Dwr80+45yyDcU2l1tXp/g8VmbQOA3zLVpPgg181JKzLBH9eY6GT +Tdi//oDWVbB9eOYrZNO3VJOwDg+872lJrVuT6tjvwdcX/Hmh2VBmImHdFfjD +usHD/yTWkrDfA/MVNo8lh2/RahL2OYCXjt6+8VnTQlpn8IvNtwS6LFpm0uqz +3I/mhdl6rjVXkp5NvqLAulLwJpOP9+5bV1fCukbwelm/p4SnG0hYRwh+4tky +l/xYrLM3Yvz0yC0Lj1ypye5xYfXM1h5d4F1Lwr4IzDP4Wy80C0j4Sees/Wbz +IS7WBt1Hnkpn6+DBl74pW5LU9iRbZwn+vcWUQOVIAwnrC8GdxpeNTtr8bzxH +393BZ35autd2ak0J68nAA88Y7HG0qSVh/wPG+3UOHJduT8qUY90/299M59LT +32x+oA7t78B6Srb+tJZUVtzLWMI6Qjav0r7ZoxkmNen9Vmdcy17naIOvpqgf +Gy93p30Q+I4Lvrmm9mPzZzUkfK8Fdys6kqZ+yJT5KYwTsS8A87/gLb7MaGk4 +xLTSceL/Nb4DryuM48Br0XgN56GDf6JxWQj5MfA9ZpcCH3k/ovUAb++Aq36e +9Agg/wY+cFrLG61b6Ugnyb+Bn/Q0a39epiPd+T/GZeL4a8f/Mc6qbDwljpvQ +zjGOwD4C+D32Xf3g+wcr+2gzvwe+et3SVq/vcr/H1lN0HfpPytFCtg8HPO5a +8ZOWrdPZ/hO2TuHqKDfjIiVbHw/+aYF909xQLeyfYeMd5wFGl7esrcr8Hrjh +1+T3h64aMr/HxoPnfONPe3G/B/5zV+i5JXbc74HXNzZu6V7dDPbJxjubaL8A +9qGBt/f9sO7tCHUJ+6/AVxl6e2/d/pPtOwKf1Ub91fyqGXQ+USbjJ6v2PbTs +0nV5FfKHbD2Crc9vjSlVsP+KjV+svn2uaxFVDfvWGJ9TN7v/sMbVmT9k40F5 +N/MOGdwfgkc/nb/gxDXuD9l6/m47RsSvL2L7o8D3bH0UnTPzK/OH4D+O9yr5 +dPc284fg9XwXZLs/5/4Q/PU0dTfrYO4PwQtX+iS5r+f+EPyD+su5vUdyf4g4 +3KFg4JChEveH4P7kD+H32PjiUMc/BX2432PncrWOrD3LrCZbvwue2Gihf49M +U7a+GfHq+qKc/i8u1WDresF/r7T5qL7JlPkx+LmnsW2D4+qbwt5YnDBt46Dk +dncMJWNa3wM+Irtztcn6fJ8wixMoPnlB6w/Qr+3wqNs9LzJBsZHWfYI/SLw7 +sdX+UrbuAf2L4/2H7wNWJiuO0DoA8LalfnGTbL7Li9qq1hWBxxrXvfbqX/8Z +Resk0C8U0H3Wm2gdA/gmus86hNaPgg+n+6z3U33QL7zueSx+3dAPis+03gW8 +Qcs0n56fUmldSDSbH26Wb9t4a7Pv8nm0HgI8oO+uGYnTfsqxPwfcut6HtO9e +apI7ratj+QyL8d9VU0PCeg70OxLdL4N1D+D36J4mrBNi8710DybWeYBPoHtC +K947n6K4+vj3sWVaz2k9RyZLP+OgfopiuprUitonuB2tN8Z6ZeSzlfzndaGf +2k79FMoFj6J727GuFxz3sGPdGPxh4krH7k+DtSWsJ2brp6ieMaQbuGOKSYaF +PJrF+eBLaV4adoh2rZZqEBE35oMigN4veH16v7BD8Pb0HmGHrF0Ldgi+WbBD +8BFkh/5UH7TfvDvxXaevSVYkkx2ycwuq3HA+tDxNEUr1BO9M7WUR2SHbJ3Lb +6syVnj/l2JcF/pba0QKyQ/CnZ9WWxR5SZ3bIxoN1Vff1wA7BTek+Mtgh+Ey6 +nxR2yPbB0/2k2A/G/BL5B9gb+E5aL61V0V9Jk8lfYT8AeCGtoxa+d0vB9L27 +XkX/Jv1D/k2r4rhDekDjDmGcqMQ4ERz+DeNucPgrzG+Aw//gnnSsu2Lxm3Dv +Oewf8+poL+Dac1+NyXjKzz9i/Rp9z6po//zec5TLvstvzZy/pNz943iuYxH7 +vBaUu4+bnf/x+EuU2R3O8VxeZOfs3j7yb0O9ZlsfecQ5/Mm2BP0uOz9yDn/S +VbZ0Wc2lP5nfYOs0yV8hPXg3Sr+vQrsrkIv5Qx+xPtDHW6g/a3fC87J1KYI+ +sJ+NpOcyao9sHP1i+rkJ7X7Kr1K7YPvSqF1so/TsezS1X6zDA99G61pPC/pv +p/ofrMSusM4bupXeuHhzaNkrti4Quk2i/sKX6gPdzlC/hvqA/9qlWs98WtDT +l+qDddt4v81y2rzvejRcYUbrTdk6rzBn/3ttk9l6U7YOMVRVz+PCuGYAjWtu +VtKPYL0ynreHqdflPvvUJaxXZvsVfOLMc9rKJA9ap4j3tVau39J1VJ78Gvlb +du5Cani0V5/v8gXk99g6DfJ7uwQ+nfhiyh/vsV3MpPn1uufJexFn68PPVD86 +/0MuWx+M9hJK/XuY0L+70Pt6QflAtwnOcw1/OWfIsc4S3HXgBTufiagnt5Nf +K1R2clTQGeNHOeXP9k9Q/lgvzr5bUf44rx/54L5vPBfs7SY913GBI57B+lHY +W1XSx4Q42mlL0rMt1YOdJ0HtBeWi/U6i9xIm9FNJ1B4TK9qDtJns4XBFe5Bq +kT2gXYCPpXXjOyv6AcmX/ADWc0MfnJ98S4iXIiheQv54j71onTnyB6+dcq22 +35xitg4b+STSvdXoR5Ae/Qj6R/De1F5+UvzD1tlRe7kv1DON6ol14WwdOtUH +dgWO78jw82hfPdf98K+tnsr2p6EdTf7kkeT7nO9bQzsaOOKMunw55/CHJRSP +gaN9rTMwq+J/46NCdY5DCOP3/byXOwz+xtKjfZmvi+pb/eAHBc5fAI8V7kuF +Du4LVPcOIx/Yc23KBxz2jPpUTC+TioX6w57xvAuo/uCPByzMc/DIFPI3kKaQ +bqg/uBXFb4L+EvTXI/8MfjVRZlj1WSbzz+Aup153tMtOY99Vxfkldq4B2Y+v +7EDgrNGa7HxPNs9D6w2wXwL8H+ov2L3slP9Uup/3diX+P6FiPZVOVM9PpAM7 +j4p0eEzpYVeRFG9Hk87gd0jnQMHeNPNV7wtxMt67kuzkEeXP9jfTuNKIdAa/ +RnYYKNiDjPKHvaE+7Qfk5dVfLN7j/N97cmHn84xLP4Qb8ft8Yc8RVE/cTwA9 +xXtyUc+5Qj6op3hPLuyznVBP2CHus8Y6aZSL+3Cx3hr1dBqbtKDXPG12Hy7s +anPTXksO7NNl5yaw9SFHyk7MVGpLWFcNPmzG/sX5avxcWtjDaPq+hn0FbD7c +yzepm18kG+eyeXj6vvlEmA//ItzTCv6K7mldTvnjvWg0bHZtxI1X8ro0rwXu +c0I1r4V17dDBetmjSxPkN9j+EPD6NG9wupL26FuJzljvjvdrQfWp+P3xz7/t +UbWODs+L954kPC/4a3relZQ/7GEt6WlGz8v821vVd42T9LywE3f6XvNKGJ9+ +pftk21f8niWp2UzPXbT/Ids3CP5d1qxaW5OPiol6Ffyb8gn5t/uCf2hM9ulD +6eGXZlG8elVo7zHUjn6V/c9/MRXn59fe7+FW4d4Wfj8FOHTDvRKh2Vb77rc/ +zeLG9t2LqsV45MrPqDizk+wOo8z6ZGcqZlM+sIemdP/IFcqHrffw+h3nUCVX +fpnygf4W50s2/izLYvmw79p0z8tFSg8dutq6f10b9FFxhu5dYutR6d6r21Qu +21cRPrzmi1+fGUc+a4gjH+iAfK5TerzHtJeFbbf9z/1WVB/k353qo6D0bF0o +PS89F/MntekelpuUHjpAZ6SHDrjX5jiVi/q87DMqY/uQbEVERa6MIh5csf7K +L1R/3APC1pmTzoGUD967pfBeYG94v6gnW49Ez3WC8sF7zyE7mUz3eojxZwO6 +H+T/l1eWD85VxHONmlo6slEPfYo/+fj3A8XbOBcJfA/N/+AcRujwpZWp/1mZ +Ab738XP/1hiZ3BijIy2leAP8Oc1rLaP96rDPFT0VncZGGGAenvGjBv3nnmuo +i++VjJ9/Wrrl+3INCecxgY+ieTycNwQe0rnum3u/tdm5kLBDd/O9Ezdtr4bv +DowXjTSu2jlLF98pGI/+calHwnCZhP3G4MmH9d/Wmv2b7acFXxr3LMTLV1vC +vlnw5qfWV20/Qp+dR8n2w/X0sfEfZsjOZwT/dP7bY+erVdi5hOA96ug617fQ +ZOfxsXO+P/v7LmrxR479YCwfjSkD8rrk43xA9l211bB/3hX90GPn14DbJrZ1 +nn7XSNKmeT+0677Z/QLeaRpJO2k/HnjZg+5ju7pXZeckgkcqxoXU/qjJzgcE +N95kFHP+Yakc+83AXzzzayvX+i7H/ii2X6rwu1NeqB47T4eNr2t+vx++1oid +IwMe1z9vrmvXcuc3Yt6Dzk9Du2Dz2J9mfPVbpS+FCfMws2hcD/tH+51g5LQu +tiG3f/DzsuBJx9Zy+wdvTd8XcF4D/OqpzF1HJz82YOd4gl8LvzllrIUuO78S +vMhotkakB7d/th6P7B/nXoG3z+k2alAJt3/41an/1EoMcavGzgkF7x6/opNz +GD8fk33nOni5u3Y1GTsXErxmsVnLg1eK5TgPEbwFncv0ltoFO1/K4aRdlyq8 +XYCvjr24I+CjHmsX8PNLIkKKPGvwdgGutVOt6tApvF2Ad52z3sP1ooy1C3C3 +jLQdIz7/luN8RpZevcae8Cm5cpz/xcZlii/a61pr4Xsu+35nH7vdabmMtxfw +8bXO+CqmG7FzVGF3JnM+FGrpVMX3aMbHpn0e3mu4Jr5fM/505BenJlZ/WLsA +7zWwZ4zhsTw54mq2LmuDvEnjSZrsHC7wnBkfZ6W2q4rv9YxrL3G8u/+XIb7v +8/O8B8yd1fRDdUlO7QT9Y0s6Rwj78Nl+NDrPJI/2baJ9FU6Tr7g+OkUeKKyj +SKR1FGkV1zVJG2ldk58wPx9D8+TgsOdY4go6fwH5SyPjWhhvS7hzVfj+5UXf +v3BODeo5hdYPoD7g86/0tZkboCXhPAjERZrOqufC+QLgc06p9mVr0Pd6+M/d +N7fUHW9XRepBf6M/vUX7KJEPGw/Svtq+xNEuImg/JnSGbisbdrvZveVb1k+z +9zKw3eZfHnz/FXiSQ+TjN/P5fiTwBTeGeBbG8nOx2DqxzVMe3ljMz3MGPyNv +ZeQ+mu/3BBfPmwJftsnUr2Nbfl4WuG9RqvPcQfy8LGZve+cMC3fi60fBD9wd +MiPjOj8vC9xLv9m14HJ+HhznU0EH6GQXvMUlagvXAfzTwm+T++jw8+XAa/b2 +Ci18z3Vg32XoPeK52HnR+76lqE3hzwW+tW7ouQ6L+XOxce6S3Sb97vHnAn/f +r4ldXl/+XOw7/ozXiVbhJqz+eL5WV01begz6z/l4ynMO3/dYzslm7QfcdPx9 +r+9+5e4hIv44YttCvehy9xARn9DiVsy8keXuISK+5fzsmoNfmLD4BvWyu7fG +/XH3HFYuuHjOMLhZO81hvqnieeYy5bvrTcI1p4jnoMqU3lcm9nJNMGH5oHzx +PF7wnMabnn+ez/Nh5wa3TY8N/mJS6To0pAd/fmGs9Zd8fi4T/Ix4Dw64eA8O +uHgPDrh4Dw64eA8OOO7Bgc7g4v014OL9NeDi/TXg4v014joxPC9487ynI4PL +3V/D/Ocyn6KTFvx5wbc07Wk59Ap/XvCbSWnXt4/lz8vOxSn+tCjzZTJrd+y8 +JVnzrQU9+PoecI17PhFeoVwHtr4roOizY1uuA7jaAYNXpuXO3QXPv3h78tp/ +40Y8L9tHI5wfC+5R/CWgvYw/L3hd85S1U0bz5wVf3WbwkBpB/PxY8AmRhi+U +tfn3P/BRmQ2iu5/n552CL69v4pFX7hxm8PU2s95qm/PnBR+0rpv1xI38ecEv +jrbqP72A+xmUHxyy2OVMJvcz4MVuSjNNo1xmh+BdG3XZfsKU1wf8yN6tVSao +8fqAd7+/5f2Hhbw+4DviDmQOSed+BuX83Njjl3Vjvq4C/GzMcn2vL0bC88ok +w2s/szynis8rkzRO3/yTm8D9APLb0Wn/nWn2PD0737q/0uzyCxOhnv/GjUap +Dq7hvL3AXmZPHJiy35Ovw4a99Ll6vc7a/eXuuSO+dnHXjpOO8PXceA/+h6+p +FZ0T77mQKV8aD7bfc0O850KmdNmidUfnId8vxMbRLU4Uf7jB4kI2nrX4esXh +7G2eP3hBtfXNY17w/MFPD9dKM/nC+1Nwx/pWSjv1Yma34I0/RcjX6PD3BG5g +HOZaqs37dbSDued6LIiM4PUBb5irFzr7M68PuMe7dP2aOrzdgcsS+h30d+bt +jp0jssJ/xdnYXFZP8IFTLPJ37+b1BH9bu+n6JuO4fbDznps7JTY15fEH4qNR +8vPNXMv5Sbb/0fjArnrlzuVm5/S8bG+xvD6vP9vXud+ySu9gXn/wL7rOj/s4 +cz8JLvpJtr918zvrjG7cT4K3qD9onsY1/lzgVQ7K77q2Ec9vT1F0T1qmdmVH +5eNr6AB/4ulvOrNLBLd/1OvF3HnOX25xfZg/qXm3zrTn2kI+MmnmFpc6NuXs +n+3/ytKMnB0s+mGZ9OmuqcMsJbd/dn7topv7+4Zy+8dzd3ut0+fjPp4/+IbJ +G7zD/Xn+4CW1wo61Os7tH3zjykVm4X25nwTHecWoDztXWH5157x1PG4EH39y +8HXXg/qCbgbSm1p9gy09Rd0MJNc5R9dnbRbP5TaQdE6cl+5tVhf8uYG0OWLr +9Xdaoj83kOxuPb2b/iGL1ZPth6qnbzlwEq8n+OeTr2rql4tvwZ9tCVA7eY/v +x4C9OP5wdzvz33GKtKNK1dv7/ztOkdyaPDWM++84RZq9TP3NyyX/GadI29aX +5M50eMX6S/BKxiPS/Fvja94Z+J/xiDQmM9vC87/jEelN2zMXCv47HpH22RZe +jOvK11XjuXHuKNsHS8+9YO7akAmOGizOYOdF0HmYSM/i4QObne038/NO2T0G +NH5EevDjS2dYWbzn5bJzfWgdKfLB/7/3MGR/ckP+HQU6naB8UE+2v1KoJ1vn +JtQT+qXQeJaVR3w+6VCx3P+e18r2ndE6Q7Zfmp4r/0RaUpwnP4+U7b+us+pj +Vg1+jiLKFc8nRLlRnq6zzrTgnK17FM4hxPt9IaTH+xXzR70KqJ4Vy+XneVb4 +XvXv75b3xc9PmQzqyeJU4tvovkt2XidxXzq3reL5rikK8b4G8PWOc7/P/sXP +B8a/K05UzW8gPfIX79MEx32ayIfdGzD24n6NLH6uFPSJVrbw123Jz2EDj7q7 +9lPT2jw9u+fE55zTr3f8fC1wnK+F9LD/caPSVl/dzM8Bw/83fRVw3iCEf3dn +31WF9GzfwaF+j2vIohUV43OZpBDqw/YLCPWBvcUIzwt7u3FhUatdua8V/w9m +f4A2 + "], {{ + {RGBColor[0.880722, 0.611041, 0.142051], EdgeForm[None], Specularity[ + GrayLevel[1], 3], + StyleBox[GraphicsGroup3DBox[ + TagBox[{Polygon3DBox[CompressedData[" +1:eJw1mwf8T9X/xz93nHu+lJGUloiUFhqioT1pkd2gKJUkpZKKSkRDU3tLe2gb +TQ2tX3tLS0TSQHv9n69e5/94eHu97vncce6557zXeX83OHJ4jxPyWq12eVmr +FWAt1GqNges5OLiq1UbDf6Ptd3D9rFY7HtyJc98Ar+KcY+Gvw48BT+f3/khz +ZJ/C1x5C+55cfwB8C+53A3wqfFd4jfNaIudDt6mM24KDaOuA5MhS5HYkQwYi +7ZF/OW9YZT4Q/IPjv5HTkSMq/34C2JBnXwU/kr6sA78dPhx+V+X7PQ0eWfk5 +J4IXg2ORxkiBbIBM4ZoDonlvzulE/3ehbSP4EnAd2rcCV3DfIWBn8FHaHkGO +5fjENCa/wJfz29FgJ/An5Ci9L/gjMhjeUX0rPc6ngD9wPEhjA17D8W/wfuAC +cC3OWRNcDN6G/AO/RNchzZD9o/vWnX4O5ZoX+H0y9zmbttWRJsgw2t+h/Xiw +EcerIf/j+EnwojQOJ/Cb5sfu4HxwTdrqNCaVn38r95xM20nIGsgi2tYGNwTv +rNyvJ8G7kZL2LuCL4F2Zj4cjfZAVnDdOfQWXMsa709YX+ZnjzWj/HjwUbEtb +N2QhxxeX5heBbZCHaDuD/mwJfwY+ET4Rfgj8YM0F5Dj4v+DI9Cw98+7S3+hq +sHnle/cD1y49V0/gPj0Zz+c5ruPlexaeq9fruZy3VPMcvIzj7tznUrAlx4tp +7w9uRluPzOddwm8HwCeDm2TmOm9zsFfm9/yV+w8Du4CzM4/F+xxvrHWFfKX7 +cN+t4UeBXZH68H3BfZB68L3BMWBDZFXkS47vBe8HuyEzaj5/EBJo3xncij49 +S/skntsZPlfPge+sOZ75vEORPTKP3S6Z+1CHbMT5D9N2JuefWnkt3gA+Efwt +9oNfWLr/F6S5rPt8KN0DnqU5g9wT/B3V/3uRqPcHX8rcfx0PrvzMPcHdkCqz +PvmLZ5/MtbuBfyAnqo/g78hw+M7gLKQN/E8m9VR4PfgS+DT4KvBl8NnwjeB/ +wZ+Ebyz9kvv7rsuzTgbfo3132puBbyJd4KuB79KPnbWueY87OF4V/gPXfgDf +U2uj8Br9Av45cjvH9TXnOefm4j/1W/sKfgtcKvJr+N3w1XQ+/CY4j699Ab+x +sM7+DH5D4XX6Kf9FbtIM/jx4D+1N4F/Sfl/p9TscvKuwnp9P+73w1eEL4O/D +95B+AZ9C2sL/oX137rWf+sC1H9LeW/Mxvbva1wfnIf21XsFPkH7wTcGPkb7w +TcA3kG7w5uCX3GsZvAf4Ecd94G3BTzn+Fn4Q+DTHm2jN5h7772q2Je/S3h1s +Dc6n/VNkS70zx+3BEpyDtIMXhded9OFJ4Kscd6J9VfAVZFv4KuBcZBt4PfBl +pCO8PngF16zHtSOlLzk+iPZW4BGF7cONtD8GbwH/mX4+Ad9A6xjehN8ulD6h +bS345fABGm/4RdIP8G+59xLkSo5b0H4dOIT29eHXwo+G31TaBp2mviBX0z6Y +9ubwa+BHwZvBL4MfrvkCvwDeVxMEfhqwF/wfzT+tPfBvZKR0OziU73sG/Hfw +N45PgO8EfiU/QPZO3wvpAW+jsUcfHi69x/ntK+vYvprzpXV2X+lg6WT6/BT4 +r/QC7XuCjyMt4b8wPo35bRK8j+Y+/Ex4N/gDhefwt5zzoMYO/h18Onxt+Pe5 +9Yns4Il6jmw87T/S/iFtH8gecfwJ+DHSOtkL2aYR0lWcvy5tyzn/Pfq/v8aE +/jfit4nw3lq78PM0P6Ub4OPg3eGnBZ+Ty2cq7efsq3VZegy7wq8r7ZMcDlbI +WdKBtEf4GPj+8G9kL5EJHPeKnld7c+8bSvtFp4L1kXO1Fjj/dWRf+LqFbZJs +082l7Zx07FTNF66/Bd6R+w3lvbbnPlfJJ+L4Pj0f/B55Ed4IHJJsal/pauQa ++E3g3pntjWzN2hyvB77MvT/S/WRP9D24fqbGBlyK3A+vA1dE+16bgZtw7c2c +Pwd8AOnLeP8BXoRsA/8dPAtpDv8FbI3cyPnPgSchjWn/Gfw52odrD17B8amc +Mw18DJkFf77y86Xb/5Au5fhr+AzwM36/Dvmm5v5uDUbw6Mrv2Ad8HDxPekT6 +tGZfR37OeOn71P545Xe/ERyneaS5Rfut4LnJV+mf7P5xmlOZbbyO96DvdL22 +iL6N4beW4K+V/Wzp4Xm579cU+UjHmb+F3qFr5m/0/36J8BjwlsrvNEt2n/s3 +gP/EfSYmG/1rzeMj3AqcSdsTyEqOj+d4C/jh+tal7eBe4B7yh2ifC+6E3Al/ +CbwA2ZJ7/wZ+yYtsx7m7gF8h28N3BRcgO8B3Axciv8H7gV8gHeE7g4uRXRQT +gN8gO+uZ4BJkV/he4LfIbvC9wa+RHeG7g58j28B3At9E1oBvAT4RbQ/WBB9F +/if9Cj4SvWaagA8jr0kvgo9F26Gm4Kxo+7S25nK0HVoLfDxa168Bzoi2ec10 +P6ROvpueg9SDbwpOKb3WzgU/43hrsIv6pdgBvhV4NWN3Duc8VNkPkz/zYGUf +Tn7UZeBhlX3BKULkB77LyeB5yEaM//LKvqt8wgmVfa09ZRcU0zBhM57Vlmd9 +gmwB3w58D2kF31rvh7SFdwLnIe3Ub/AtZE14O/BtZF14B40B0hK+Jfg+0hq+ +DfgBsmFpPfMhsjF8W40r0hS+Ofgp0h6+Azgf6QDfUeONbA7vDN6ivqc5+Sjv +MEFrtbLuUhzZA2yV2ceTX6jnPAKeVfg9HoWPgf9YOp4YpG8je0z72MLPmQk/ +Fz4ijafG9S502YPwFbJXpf3Ko8DWmf1n6VP19ylwQuHv+Rz8Avhjwe390tx8 +DX5F4Tn+PPyiwuvgVfjl8D9K++CKkTWvFXNdV3i+vw2/Vnorcwym+Etr4k3w +6sJr5S34NYXn/hz4hfJZSsd0Fxf+hrPh5xUe7yelt+C/547DFB9VheNUxR2r +F45hFad8kzuOk09+Reb4cCOkZWE/S3mBvQv789dqvcEPhU8rHfvpWt2jQWlf +SD6R5t0s+Dj5cul8Xae5qbhJ8dNhPKMd8hfHsyvHsHeAh3LOKNrO0Pulfqq/ +M1L/9R7Hct62mXXgcKRL5nhf9k3vq/d+K/Vf7zGJ33eQT1BzfKh5dGvpmGOV +zLGTdNgrtF9W2DbuCm8K3lrZF20FPifbmPl448q+qPIAb3PegfANZJMr+7Rt +wWvTete6n693pr0deGnmeajzDknx44ZgO+THmvMknTPHjUuTXyX/SrHs9ZXH +bYDunXSFdIbyDP0yr5nXkdFJ/7fInB/R93sncx5HOZwJSYecAk6XryhdJP8l +2Q7FZx0q5zCWBOv7lzVn6P92mZ+rWFVxtfomH75R8ksHFdaLl8IPLawvL9G7 +6trK86QX2AkZoPlYZz9HvuthhfWK1ubphfXNA/BRhXXY/fDTCuvU++CnFs4L +qC+bgjtW9ouUq5Heuhd+Cuc8GbxelAuR/yB9s2VlH06+XK/kP8t3GlpYF94s +O17YztwEP7awXpwGPxG+PdcfwfEaddZ5N8ouF/bP74CPgN8vmwTWj45HFCc2 +Bp+VjoA3LJyvUUyoeFC+xsjkb8ieKD+i3IhyK8qxfAK/svL6q+rsA8kX+jbY +vp+W5vmUdM+GmtOZz3mvZn2qOXJu5fmieaPcVP/E9dtB8uW4f6izvzAz3VPr +RbH6SzW3z0h6e6r0VuZcz26Zn6dnXZl8JP795yeNSL6N+nVJ6pvs3tDM8bzy +eUdkzt/JBxZXjkXz/fCkK87PbCN0f73T+Ylvmb6pbMcDpc/RO2gdTExrQf7d ++DS2ym8p36cc18qk36TnNH6T0vvuka5VjuK0NA56xsS0vtS+feFciHJHl1b2 +wf9h/DpXfg/lIxULqP/Sn4rjBmeOGXeonHtUDnKvlNNQbkO5T52j33apnHdR +nkY5mGMyH9+V3u1O8KXS6/Rl8MXSfuu90p+yg5nzVuq/bK3yX/2CdfI1lb/p +PUkPyre9OrNvvw/vsCfXDYj+XppPX9D+cOlYqmtpWyGb8W76tvre8l+Vd7o/ +c+5JPuy1mf1Y5VYfSGP+Os9+D3y1cn53Wuac7Ezue1vN60r+p2y6coczSsfH +0heyFVPTfJvF8fSa7f5s5Oma7bj8WNl05ZCeKB1jHZb6/GDmHOjYNAcaZI4P +rs/sTz9WOh5U/uEH+WfYk68rv8fL6V3eypyTium6V9K1Gr+5aQy3Sr63dOyz +3OsY+HbMl4cr27hfg2MX5fiU39N1T6drN0l2RPbkzcw5U43Fs7pXZp//kdI5 +j/3kB5XOOx1QOoaSjZLtml5Z33/Hs/oH26DXKsfmD+t58lMy2zZd8wK/PZ85 +Z/si8kLmPPkzkszxlMbsojRu8j0vzGwvlO/TOtJ6eqNy3P2eYsbUT/X3E31X +eBPO+axwDqE9uGPhnGd/6XWuezuzz6Q8w5Oa4/JRwVac8xvf493M80fv87nm +ZuZvpnzD+8h0pE90u3Jxb1bug/pzC9d3zz2HJoI7I2fqncFNkQHwP9Nc0pxa +zvGKzPscb1XONX3Cfd6uPObi76Z1ofXxPtIBHpTrCL6P7vedYi7uPwl8o3R+ +4iH5j0hT+EJ++yrNPc3BD9K30zf8Ls1/rYP3Of46s4/xceX2+uBHlfMJ4p9U +zik1BudVXlPiS2T/4APp29fw8bLh8P9V7v/r9PeXtKa0tn7gHj9mfof5aY5p +rikPqLxfi8JrWWOuefUVuCCzT/BTWsta0335Fsu0VoJ9btn30Vz7vfxI+DD4 +d5nP0bM/514/Zc79Ktd9PHyy3oMxOji3vrhU/m3u/QOt6bOTLpIPJb9LOk4+ +mGJz6boe0fM91vn6N5LO2aHwOEuXjud+XXLry1PAjZFD4E+ldaH18VpmH07r +U3Hx0Znz54r/z01reaPUH+2zKO8q2yOdLPsjPi/Z+vGJK/ctXVw/6WNx2VnF +6Jqbf8K7lI4PphReH2PSGpGdkt82NOlh5Sb4V5tD3zsgR0k3g9vl9iHuB1dH +9tKap9/7w28DZ4Itcu9VLOO4F/we8HFwPeRA6UmwW26dt4Tf1tbaAceBq+W2 +/5PBVrn3M5by24Hw26VPwK1z2zDlf47NnMP/Humj/HTlvIR8delb5YUOyuwb +K2dycGYfb2bSRdJJV3Hd3rn17nTFMsi++t7CPOlscNvcfsZdYL/cOuYK9Te3 +LpMv3VvfTH6+9BHj16hwDkrvpBhcOku66wO+Q/vc46uxfQF8PreOHpT7WPwQ +PQd5Cn4k+FxufbpV7rHQOKjt2dQ+F3wpt13ZHHwGOVLfnmffK90A7qdcf+4c +2QHaD8idX+ukfYLc66Q3eEfuPI5ybnpX5Rk2o+3W3Puo6+gb5s5Rdc39XfVN +FYvNARdq7HPrSunJZhrL3LmojrnHVOOpvJ6er++rnJ36pbk0OE/vw3FTfZ/c +OcUB4Izc9mbd3HNL86oRODL3t1euQ2tuPDiJtlNzx4vyqTQe0p9TaRude69Y +7zQqvZfu/US6f0/Nu9w5rPVzz2/N7X+5flbud5ye5sto+MPwh3LPraf13XKv ++UPBB3Pb5r/lX8IXgGuBjyD70T4QnJ177A4HH8ttp4WPJr5P7nmpOdkjty6T +HmqX+30GpbWsPTb5Db2D91O6yo4x9wbKzwX/RM6RrS8cw0nvSOfI710O9gEX +ZraFsoNfVNbfskXKGyg3cjbXdoI/Ll2p/EblPLb2/PeL3gecwfkHR+8dHBds +62Xn5fe2qOxrNKpzvq0rbespD624CN4AfAnZDb5G4dzbPvB1FLtVjuu1N/05 +xwPgHcC9guPoVyrvt0iPS4fLj9We+hzlDyrb54nyG0vnTUYrbiudJxpV2neV +ba24X+9on2E1+DqV/dZV6PNalXMX2sduhjSCZ8H7YtrHWZnbPslO/cA1d8LX +h6/QfIneO1gleN9He0w5eFvp/NHp4HqV/bIGdd5z1L5SHbip7iXdXzhPdQf8 +JPj8ZKNlHzej/S74SPlIle3h3bTvLx0Kfyo4ptxCfVZMWjnvcaB8QuW84NoY +XL9yzuQgcJr0dG5b9RPHI3LrOq3pY9O63jX4O66j/GvwPt268HFpv0Px/S7B +exDKl+q5C2rO+Wtsv6x572Ct4LFSzLtO8HhqnPQtXlesEh37y39XjcDanNMc +Xi86PyDjpb0D+SjyVRZyzZTg+Pq/PGpwPK585jXBcbpykldp76TmXOWk4JyD +8sMXwCfXnJMcG7yfonzDGPjZNedyzwpeU8rlbl543X2hmC44p6GYftVUG6M5 +ojmwL21HgW30zWhfFb5+8B6Evnnn4DyScsgbBn+XBvCNgr9dQ+VNg+fPnLQu +VFOifRnNH8UZ2sfYNHjPorHy5fC9a85FNwietxV8p+D1pdz1lsrX1Jzrlg8q +X/Rt+nogx1eCRZ3nvGLx69M8WVTzPo78Ofl18zhvm+B8hfZ4OwSva+XStwrO +XSjHvnWwrVQufbvg9a48vPSD4iHtUVwYnAtSbvmi4DyPci07MO+m5PaDtLci +Oykbt1duuy6b3jm37yK/ZRfw8tx+jzBPXPfYPt1nJdefndtXbJvbfsh27Jrb +3svWtwbPy23vL1Zbbn9ug9y+i/yWUZX9o9Mr264hyX7JTshenFG5VkS6X/7P +zfw+PLePciM4LLfvsiN4Se5cxZ3qb26/R7Z3aLK/e+Tuh/pwSXDNknLvO+WO +T+T/LaocuyvP043fesunjN5/VQzVGn5YsC7dEN4zeP+9Ffyg4L31ltF1VsoH +Ku8ln/tW3bN0Lku+sGqjlENT/ZP22gYE25020fuDsoGyfT2C9/Q3oP0AeC/4 ++tH7RvI75Mtp30i2Vz5kG95jQu6ck2zKczxzMjiCa0/i2o3hHSv7ucoDax9U ++6Hr0b5P8F5/c/gR8CPkX8P3C65DaAF/INr2aA1+k+J9xf3To/05rTXt+2r/ +d4ziksJ7fNrz0t6Zcm9az6qbGgsui87xdof/GF3zofqDs0vXLSjGWVA6xvxM +cZL2g0rvPb8JvlN67/k98LJgPS8dckWwbm9Sed9a+9dngZcH24XVaH8w5Spl +q7Vvof2LIYr/aL9b665yTdt/tW16ZukaiI9L7zMqR6jczejoOpXPue706LqH +z7TPH13n8QV8VHQNxHz4adF1D5/Cx0Tv/S+AnxW99/9VcO2IakjOBM+Mrmv5 +MtkmxTrKr0qnSLeoZky+xHHgomi/RP7JJPDnwn6E6tymB9u1NSvXCshveaW0 +vZfdn6u8Ddd/zTULOffitMctHSK7qbjx08rzRzme5dF1evpeqtlZVHqvfXHp +vQN9fyXJtL/QKfP31n5B5/R9ta+xTXrHxYXzsNrf03689uXPK72vr/39caVr +8uQXKX+u+odR0mfg0tK1HctK10P8Fx+CvxTOwyvXoXWo9ag6SeVdlcdT3n1y +8NpsVLmeTbVW55euSdtJvrHmMOc8IfvCObcG+3JNK9epyH86R35RsL8nX0O1 +WarROrq0X6HYXrG4aiJvp31w6To61XtNKL1ftmvmfQfVCXTMXD+gPReNQV7n +/Z3t0rO0f9ET/Cm6PnPHzHuR2mfXeGpce+n3mvWX9jK076B8keoblYNWLd54 +rlmq3IBsNXwR/Bv4lOialX+1DqL9JL37FdH1Xn/TfnR0vdQrwTq8CTrnr8p6 +e43c/v7g6NqsucFx/RG0ZbKN0TVk/9A+JLp26lX5ETF9M9mx6Pq8P6Sno+tp +VKh1WXTdzJ+0XwNXzU0u2xFd+5LBL4+uRfuLcy6IrvtcEezTbkIfVCDQP7qW +62na16xzfkRz+55of11rRHkh+fcfKi6M9k3lA/wRXas0Vno0eo2pdve+aL9Q +/pVi58N41j9g4zrn496BD4zWiaoZOyS6tuwZ5Ymja86eVe4wukbtOdmc6Bq1 +OfAjo+vYXpRujq6rewE+KLqu7iX4OOll+GL4hdH1ryu1lqNrZ3+BnxBdl/M2 +/MToOqp34cOi63vego+Mrgn7SHYjuj7vA/iI6Lq99+EnR9eufSh9FV1v9A78 +mOhat9fgQ6Prit6Q3wdfCF8EHwtfoNwY/LjoOqT/wSfAv4P/AD8lus7sY/jx +0TVJb8JPja4hmwe/KLre92d9X/gy+I/wSdF1vctlE6JrvGQLpkXXckn/3xld +ByY9PzW6Vqwh/LroGqNSfnt07VEBvz66dirAJ8K/5/4/yc5ExxvSCbdF16I1 +gN8SXXe1ivyW6DqneoqnomvUpHNuiq55qpNuia4nWxV+Q3Q9U6VYP7qeKVau +kZZOWhmd61suPRddK659bdmA7sE1z9Lh+wfXPGucDw6ui9b4d032XbamPbJX +zTarXXD9pOxUF6RnzXZni+B6RdmsXsE12NIV3TQva7ZfqnFRHu0R8OXK+6Ba +O32Cc/Kak9Jx0nWyTdrHVRwqXabaMOU0le9Ujdar4FPR+6/tUo5CNZ/KQWsd +7RBcIyebe3bydRVrnBccRyiGOjXYP5F+0L6jYquBtJ8TXB+oMT8lODcrvXFu +cBykb7RjcD2ebPeZWj81j//pwfV+mhvat1bcId+lY7A/Lx9+VHCtnebM4cE1 +ftKxZwTXIuqbjg6uV9RcGhhcN6s5PzK4Fk66TjX37VMMrrrilVnKb5eu15e9 +U/5ZfmXTOuelFcM1qbNvtjjZYuXSlUtrWOf6s7bJr1Z+W77VanXOq89LfpS+ +gb6F4jLlor/M7Hvp2erDX6VrjpSv/730vsNnyS9SPvlXsFmd6702Tr69ctTf +Z56vsoWyiSvBnpX3zlVXo70MxU+r1nk/bgjtF1bO26vOUDGt9jK0J6H5odz+ +R8kPVM5ZexTae1H8JR9evrxsnmyf9t6/LZyn0T6H9gGPU1wCLim8PyRfSPXn +2jPS3pH2GYdlrhdSTlj7WPeU3mPS3x3It9YesfwQ1RGpfr5nZrugvcInkk+l +2vXuyUc6Obi+Ubb1mOAaUennIcE1orJTynco7yG7WT+43lK6vRmyac16u15w +faZsQcPg2F/xcqPgmk/Z5brgek7ZiMbBtbKys62C63KltzcJzrVKxzYPjmFl +C9YLru+VPm8bHJ8qdm4ZXK8r/b9BcE2v7EJrpHPN9mLd4FhbuQjVCLaB7186 +N6QckezCGsE1z9LnqgvS3ofmjerM5R/9Gp3faZ38MdX2rEhzT3moNulbyA+W +P6y/rVBOqlXyqdYMrmeWLVOtvnyx37jnRI6vr1nPqzZR8f6BWj/B9eeyUw9G +1w0oh7A4d31sN86ZEFwnLP18fnD9sPT86sF17LJfLYJzUMpLKC+m/Jhsdwje +e5JNPyG4NlX+yfjgumLZiOOD63Ll81xZuN5J6+uR4Loj1fs9HFzzozrAR4Nr +kFSz91Bw/KJawWHBdbDykTYPrp+XrTwquG5fNnEwMqJm+zUcGVuzX3dkcD2/ +bKhykcpJymc4KTifI5/t2OAaY9lc5S6frbm2cFZw3ZRqC4vgenj5NlOD60NU +I3dHcG2JatXuD64rU73ivcE+s2r57gyuRVEN27Tg+hPVzp1fuB5MeuN22u+p +ubbtxmC/WnVxNwXXjajuLg+u55ePNzu4Zky1jjODa8xUG1kG1+TL73og2IdX +PPh3dJ5R+uHm4LhSvv19wXVxqo38KzofKh2lvw1R7Pg7bfXrrGuWaWySn6OY +/ZXknyjGL+sc8+hvcOYkv0h5g+eTH654/5nofLTi8ZeTX6Scw3PRMZri8bnJ +h1de4tDgvV09t16d9Zr2o19Nvopi+dnRfzOg3KPyG7LLss8PReeRlft6MTp+ +UD78yei/N1B+8unoPLJyBS8kP1N5j9eic+XKLfwfVX75AQ== + "]], + Polygon3DBox[CompressedData[" +1:eJwtm3ccV/P3x+943/etkNKQSskqqWQklYwUlVUkolKR7FUUIQkh82ePhFRo ++BKypRAyCtmhrKyQkWT8Xk+v+8d5fM55v9/3fu59jzNe59wWw0475NQsSZKn +8yQJ+q0r4TooTZJukPhJoo3EXyn6R4OulXy4+BvE5zWS5F/9nqhrDy6T5Arx +PdXXUvS1xl0m+XLRGvUfUSRJZ7VdJBql/pGi32KSTMj8X2eKv010qfiJoh3F +X6l7dteznaXrj9f1f6l9D40/T79tRZepfy/1n67+Yeq/SnIPyWdLPkHybxqz +r8bfrN+bRLuKHyeqIf4k0SSN30fjR2n8CI0/Un17Z37Xp0VXqL+b+keqf7j6 +a6uvQ+ZrdxZ1FX+F6HLxo0X7iN9NdKb4q0WdxI8XfZi47XLdb2/d70zJx+l+ +80X1xK/QmIH0ST5C8gca8yTPxjNJ/kjy07yr5MMlvy/5Cck7Se4l+TXJcyXv +oDn7WfJhmvMXJW+s3/7qu1xtF2vslvqf00WrGaPnaSj+eNFKyb0kbyC+jWiY ++PaiX3S/sZIz8V3E19L9+uh+EzT+Qt2vvain+MVqe1j/tzXvLvol8R7ZUPwO +ouGsp6i1+NGiv9R/tORC++dl3fMEyX10fQ3JCyU/qr65+r8aGtsi87O2EW0k +fieeWfxOrIH480VF6rY9xU8UrU+8R7rp+QaI/1DP95Tu31Py0ZI/lfxs6f32 +q+THNfYR8b3UP0TyZ+p/Tv2/6vd/ep5J6r9D/YXu3Uh0gOTtRFF8E9HBvJvo +J405WfIq3WML8c3Fc8C+k3yI+kvxzTLz24vWiy7JvHc4Q1Hv/5j+bwznS9cf +qr43RW9Inia6Xs93m8Y115gZer439XzNRPurbRf1XSe6Rfzm6p+m/omSr5Rc +T/JUyeeyRhrfV22d1XeG2r8Uv7/ufZX4i9XfSf3H0yb+/zTmVvHN1Ddd8lWS +/09yI8n3Sr5OtL/Gn6e2k+mTfIDk8yWfIvl6yQdKvkDyqZIvit4Xp4kOYW+p +fxv1H6L+Luq/VnJvyWMlnyR5bOFrS/3fZPWdU/i/Csm3I4s20/geamunvjGS +G0nuLrmt5DrV+ZrJO6lvE8mbSp4j+UTOh+RNJD8geYTk0aJNxe+jtjbqO1ty +Q8ndJG9f+Axxluro/+9S33mibdV/qNp2L3wmOBsbqP9O9Y3nGskbSp4i+VLJ +kyRvIvkeyZdIvgK9K/lu1qfw3EXJd7B+oj11/9PUNkR910juJflcyTtr/kYX +5nONv5X7ibqq/xS1DSy8Bly7LvfanCV5tGSU/S2SRxbWrf+o/ybJowrrzn8l +31xaJw6X/HNuXckanyr5j9xrj04+TvKa3Lr6LD3TPlrbpzif0WvIs6zNvbY8 +8zrJv+d+l7+DzwB7/6ZgnT1C/C+5dfmZhXXz35JvlDym8N4IGnub5NML6+a/ +1H9DaR19rOSfcuvuTOMOEz+R8xH9zodKviTxXPDOfSt9xlyUOn/tJA/ivJa+ +58GSxyf+L+bkkNxrylzxTOjDixI/Kzr9GPE/5tb1l4r2yD1ng9XXu/BeWcmZ +KK1v2PsrODOSrxbtm3uNDuW/9Pw/cD/k4DOErfsz99lqKd0wUvS72o7SPL6h +tqOYW8mXa+wavfNZmfsuFv+m2loxn2o7WWOXSN6O9Zd8iuQ3JLdkPrFx2B/9 +5/uS6+v6U8W/rv5tJa/PfH4+Z89hm9T2iPqWilqzf9B77Bdds4murSc6RXwn +tc1U/9m65kPxz2p8XcnLNf5IybuJHmBt1P8B64c/kHjNWLvOolmSR0v+SHwX +0WzJYyR/LP4L5lz8M2p7VPf+kjOErken614L1NZA/Jf6v8HqW4xNZH9m1g/P +S64v+XPJgyT/omc+Fxugtk90/XOVvviUOVX/W5J34PxxRiWvFF2MrVHbXPUd +r+s31LvXFp0Ar/21VL/t0dHq30Dy65JXSG6s+z+otsfEd1TbA7rX24XHBnyc +0tfwvEuqe+2ntoWSr1L/t+J3F82RfI7k5eJXiCbgS6jtYV27h+S54i9Q26f4 +G6X7eGaevVvpZ2dNWdt9RQskXyn5G55HdIL4O9V2s+7XgzkTP0ltq9BVokck +j5P8mfiHNGaR5N30vOskvye5I/oRn4r5Q4eIn6y2G9X3rmhX8bXwkfB3RE8k +fgfeZZn6O0iuKfkMyd1F8yVfIflr8e+IThQ/RW23aOwyySdJvkvyrfy35Gni +z1Db++I7lO47WfK7pfcUe4s9Nb3wHDKXD0q+r/AeY68xxzMKX8O1d0u+TfLd +ovuwFXrf+9U3WfLDkreVvJbzVPqssEfZq11L958v+RPORuH32Unj/+DZJM+Q +3FryfZJ3Fd2LLtL498S/oP5Gkr/VfhyKfkXHSH5d/Y9IflHyZpK/x6eT/Krk +FujfzPbuKN33T8nNtT976pr91P6KaFFqnznljEpeKP6ZiCHW82f23SZKfk3y +QZV+PF/3bqr7HZvbB8EX6aWxr4pe1vhbU49BN9UIvjZT3wOi2eq7QLS/+MU8 +g/jbRePwCVhvdE+lu9EHX6nvC7UtLu1Pj6z08zxdu059d4qeF72p/oG57zGJ ++EHPPFtj9lXfmGifCd/pDY15tPR/HFzpc/67L76X6HWNn0rsobb+6ntPYx7X +2N+Zt8zvdotoidoGYRs5M8QLlX67X23Hqa+T5D6S35L8mOR/9AwP6/rndO0T +0T4Zvtnb6p+n/k31joNz+1z4XkvVdgy2WfK1kl/VNe/o2h3U9lLpdz9I95tS +zcFa9U+RfCjzK/530WTJfViL6D3H3kMnzNL9Lom2FdiTo8X/K76fxs/Q7/TU +OgPdwRmfzV7NPIa+F1Kfec7+o+qfgy2O9tNPJA4Tv0htTbDPuu5YjX1F8haS +f8s8PzM15j6NvV/UXfyuev8Lc+tEdCM+GL7YS2p7SOML/e4o+WONX6ax/+BX +ZvaV72XPZm6DZw//oXtO47+I7cSv1W/vzHvtNtHfoj6Z1/oe0UOZx9DHGv0h +OkBtk4kHiBkyt8HPT+07E8vMRdbzHBns77wleXf1LSTYzvyOL6bm+2d+X9r+ +5P0lzxI/J3pPc7bW597rL6kvFc1U/0uidRozQ/IJ4q8U/5LGN9b41Wo7RuPr +Vfrhwdz2/G21b66xA0QfErtU8/9YZb9OVNumot6p4wJimcaiA1PHNGdpTF2N +7Sq+la49KXNMRCzEGHwCfINtEvvaJ4gPolap7/kauiPz2XxV9LWeeXDmuZvP +8+OjiA+cNfGvq6+76FrJi1PHqvVF+6WOWc8NxiZOYY2DY8+tmNPUMSix+cai +Lqlj9BHi88z4BPc4JXMMR+zGmcAHwhfCR2qALyy+pqid+gZhw9X/R2Yb3L+0 +DkWXMofEEvgQ+BLoWGIP5hxfCp+JtRgjvhYxse41RHRe5hiZ2Jg9+Qw6Wu/x +tvhX9P7nZo7JicWPIW7KHEMSO/53prMqJk69B/Dp8O3w4eoXPmOcNfZErcJY +xFGiZ1JjEuj6gaJn00rn679PUvtYziAxJv4P6ybqonX/ij2ito05B3q+m9BZ +7A31hcp3Hi/5J3w68YvUv0RyWZ3ns3Tte4nveZ/40cHYwrHoq+D/5L//wH6L +P030Ef6J2mbhE4nGpV5z1v5s0b/qH8oZBJsS9U29nvXQuax9ZqyJ+5zD3GWe +e64Di2iVeW3BJJZwbjKfTfbhUvRU5rPGe9wdrMuY77HEPOr7M7V/zh7FF98m +8/lChx4RvA+J56eLf0t9e2W2dUtFU9Q2IvX6n5obuxgiWpAawwB764ivXr3z +5OC5Yj8MzY3NtMu8N5jHVZrjYZl18Yvir9b4g9IKq9D44Vq/NZl1cK/SOhfd +2zyxreoaffZ+0nW/l/bJ8c3rqD9R/2dqX6n+oyS2ye0j4ysTY4fCGBZYFj5y +Lnkd2B/7R/INGv+j5O9T+9P41R9Hy7Q31P55TddslfiMcdaGiFaJb6i2Rhq7 +VLRc499jD2p8H/0eqL7P1PYx86v+T1lr8XXU/yb7LbXP/4b4AaVjA2ICYoOj +RT2Cz8JkXdu98P1Wqq2urr+dOAMdorZN1T88OJb4Sff8Ldi/591+QXeLXyX6 +OrWP8nVwjEGsQUxRFI4ZiB3wCTLJP2jMtxp/Az4a+7/w3PwuflP9/3v6zy+Z +L9HLYFVq/zH1M/AO6yX/Ffz/j1X3+058KvoOn1FjftX/NdP4DYlNg+//Q7XG +H0X/P2Mb6P8e1fhM1FZjGhf2sfG1d8FHlPyk+BqinSU3K2wziH3aJbYl73BP +3e8LbF6w/GHqNX07GFveXXR2aox5ga6tI9pd/S0Lx4zEjsSkDQvHCMQKxAQt +CscExAbEAFsUfvdfU8dYzP8o9W+YO8bYsnD8zF79XP0rgmMoYilitqbq/0Bt +n2CHEu8pdO7BXJtbF38QvZ5fqa9eDftY+FqDNaZvaYwDrONJ0aPR64WtP1n9 +70bfn/2Kj/J+8H58P3W8R9yHz47vDiZV6nkGRJ9V8MXNxW/J+iTe2z+WtunY +dnz6moV9enx7bHyNwvue/c8ebk4MFWy30QHXiL8yGOvDHq/LvL+J8bPqfBNz +Xq22Fyp/C/+L2HJh5c+BSQ3IjWGBVbWq4t+FuX0D/DP2yqLc2Bkx0PjKfyM2 +al7hB09V8VuLCo94pooH21Xx4au5sb0tKjzi6SoebFvFh6/kxvq2rPCLZ3Ov +fZsqPnw5N5aHP72P5HdyY5/1MtsEbAExAOdjeXUe0X9gesdW/jVYH/g5/vZN +kicUxuiGV/EN2B2Y6ojcmCxYK5jecbkxU7C+maX1R53q/A2N1t3g67ux1sH+ +Mv70FPU/GO37sZ9n46uK7kqNUV8v/ofCeBq+ZK0KK74bXZTYvhAjXlj538SO +YI5HV/EDWCQYa3fxy3Jjr2CoR+TGIMFWB2S2UdgmnuP+aN9+RuWPobNydGVu +XYbOL3j2yhag8/UYyZ25bQE6j7Dxrty6cIJot9wY32Hqu0hyx9wY4qGSLyQm +z43hHVh4T7I378hti8YTA+fGJPsW9nE4C//L7fs0rOKLh3PrEjDZHpzF3Fgt +PtCGzFVu36hpFQ/Py60bwOR2Fj80MVaHfeH8EUs9Kr6F+g5CV4uW5sYgD8+N +CYNNgsGSb7ksMTbLGd1A/LTcZxeMb6fcOQawv0s1OQNT+1yjos9wLfH35j7b +40S75MYUDy5sA5eLvye3bURn1JQ8NbcuwYaR53oo2LaBmR+ZOwcAlk7+ZlAV +DxPfglEPruJVsOtJ0f4IfslfxMPR9hNdBVaFDcIWfVvtv4ei/T38PrDT73TN +/sH6DP+f3A65lXmil9Al0f4TftTfGrswWnd+o+tr6vqHg+NobAj2Al1LfIs/ +/AnzGo094KsNEf+MxixjvdX2XHD+aKx+x6itX+l5YD7Qudj/BaJ3E+eXXgjO ++fB8PCe5qAf1e0Xluw0Qfys2PLX/vx+4QPBZO0LyjeJvD/Y98ef7cc4k90vt +n2+RO4dFnnJs9WyDg5+de94W/B/815Gp/d3DsZmJc6Bzgv1x+s4Rddb9Zgb7 +wo/h3wVj5vial2bG0jO98zuZc7LkZq+Ljo3wHYdX/jr3IgY8Kfp98bXJb5Hn +Iqc0KjeGRa6J9WVumeObo9+HuWMOB0fjE+Br4G3gHeSczpQ8PTH+80rw+nI9 +a7W28NqAcYN1f1/YVnap1p/9QKyxNrE9XcQapY6p2T8LouNAMPHtonNSI3Nj +ZOSqno+OKzmzW0XjUWB90xLjJeSswOvuSoynDIv2vclPkt+8MdpXx2cfJH5A +Yf2KniU3hw5AF3yR2kecG4wN4ENg3x8JxgJWiJaLv1H/NSd1zNIV+x/tD+Eb +baT7PRkc9/+c2ufjfedV88tePTI6liG/SD7xiWB9vJprGBuMU6xK7W8+Hox1 +4APiTzao8ICHcse2x1TvyxnfS/yfpfcsOq2Hxq4unKsgh0QuiTVn7S7S+FvJ +n0TzzAlzgzwwsQ6gP9M7Xaz7bSH5sOgcH7m+ztV+Oz06TiHu+7X0mZsdvN85 +i2BOnAfO4O3iz1dfh9Sx/uniT1Rbx9Rzwtycp7ZdUttzYkVqBqgdwL/EXpKz +ZW/3oE388WBKqX0sfK1Ldc2eqfPHY/CdgmMccu7k3mvr+d6VvAf7rXDMgZ+I +v9hc14+NzpvzfEdExwyfB/ubxBLUPuyd+kxztomROcecQc4i5wGsiD3+MLpV +9FBqnx//kRjoNXRW6tgIHfts8JnkbI6L1jesIWtJzIMPeID+r0Ph+OCpYLxo +RXR+t39wjcA32FeNfzz3nJwQ/Q68C3M+QvzPpeN44vl2scK4xa8OjtfqR/t2 ++Bz4Hm2jxzZNvZ8aSJ6X2AfEFyQfB+Z8bmUfqQ8hr0X8fIbGvqy2T8V/JtpM +8rPRsQz5b+LZNbrHoOD46uzCOY+rKn/1ackpPn3inBXx2knB/uyL+BOSvyts +aztXeAV7kL3YQvc/qDRGD1YfJXeL1vedK31ALD9e1Cl1/cQo8anuMQFbJnnX +aH73yj6h63negcGxfIfomJq4i/jriNI1MdTGsB7UbnAP7gUmT76Sd+bdqQEg +tmf/48/j1/9Qeg25lnu0V9+Fat8tdb3ByGAd+3zwHmOvTRS/V+r6l3PwbQrn +XvEx8TVHRtfisF/biB8dnRs4J/H5Ib+LbsZnwXdhPlhrdMDHmtPW0bgU9m9g +9JllP1ETNCn4/7fCVqttx+B6AGwRuGTQs9YAT0jsQ+BLXBf8HrzPNhrbIxrn +An8BW95AY75ibTXme/F7RuNo6Dh0HTod3d4+cy3LMOwitlvXDMt9/rfkLHH/ +YJ1F30bBuowcKrmp+sG51SG5Y/VvdM03wTkFcmENgnMNE6J9A3Lg+HPYRGxj +w+DcADku8p9bBOe+LozGKi/W8/0cbXPYa7SNj465iL06BGPr2DBsWZPgXADr +3SS1/l6SO+dF7mrL4FwYOTrypS2Cc3fYEGxJ08y1Krwj79pVbadJHiI+SZ0v +J28O3raN5NcT2y/2A7oUDK+f+Pq6/ttgnXB14TP4lvhuwWcTDGNtMF4CtoH+ +36NaH2wve4y9ho7k/J8THZehzw+PtrnTgvcX9gYfBl8GPOyaaBuKLf0CnSP5 +6ui++/V+v4rfRP1fqv96bJiuf0q0lP8LzmeSQzu98g/uVN8TojfF7xmcT+Q8 +MhdpddbxebDN4MknR+eHwWTAlMgP4pNy9tEBp4jfmDOK764xq8V/EX3tKD3f +j+JPjZ77//C86Bw1eNkfwfjU1tG4NPbuqOgc7su6X6fgfCg55lfQZ8H5W3Lw +r/J8wflbcuCLeZ7gfOPTusc/ifNZL0T7XPhe+Fz4Xvj0xJZgGPj6i6NrIfDB +X4vOSR4XnLMkV4m+PDY4J0mukxzviOCcLbnfB6Jjx3v1vj9U+piagLcqfX13 +7jpB8PjjuH9h20Aucn1p+3SBxm+m/j7Re4K9sUs1fmHhWAOMkHjon9J5AHze +a9X/b2kfohE+VPT/4TM05MxE6w30x9bo3MwxD7HPVMl3FN4/5BnJN75f2Xf8 +Pvy/ZdExDLEM+uMBsIzoPnzEqdHPMzVY382r/IeD8DkSY5l1onUJGBxYXK3o +/wJzAnsCkxuKj5e4Hwzq6GAdRP+s6NzRdD376uh9xn7bSVRWeG+vYJuKbeW8 +orf4zw8re7Qm2J8E+8UeXhJ8RjmrP0nuiw+j63er1pdcfi3198b3ieY3EO2P +PxaNXc3V83wjvq+ocepnahG9hqwlc95M/D2xyqVp/LfROQVyC+gc5os1Y+2w +CU2i6/GIw9pV/iFryFoSExMb94+25ej43cVfHo21PKf7fx+t3/FN0XGdovcY +ew0bhz47VNQsdc5u52q/k4uvqbae0WeYOQb/bF3YBo8L9kmxzWB0nwT7/2B3 +zHnTxJj78Co25l0aVnsWm8Ue3CYxnvpbaRsF3nSN5PNy7y38EfwS/LF+wRjl +vsQzscr16l7fRdtLciB7qb9jYTya2IAzD4YJ/gu+T8xB7LGucD0VNWXUY1Ej +QW3DVsG1E7sWxtbBFN+O9mnxbckBvCM5RGNHh1dYSBGNDYIpgS3l0dgImAjY +yIbR2BgYGljayuhc1Cw9//po/AIsnrbH0P/R2AWYI9jjBtHYGxgdWN3j0XlZ +YrAp4kvRVYkxj8lVP7aB+oPnsBfRWB0YHVgdOUdqDag5IBdZNzqWJIYllq0R +jZ2BkYCV3BmN3ZIvmxftk+Ob/4eRVPpyWWof/kj1NYz2PfFBwVbfwT9NHQMS +C4Kp9A7Gx7n+8+h7P0g8H53fB29ZVulfan6o/eEeb0TbtEsS6yh0Ffg1WMmg +an/UjLZ9YIBggU9Gxy68M++Of02uiJjyPuxldOxPTE1sXQ/9khgTmFFdT66W +GPcu7F9pnwG8C3yUGiBqgRZIfrLweQC7Zg8dLr536diK3BH1yftEx77sx5mV +vgFXA19rKXm/6LOHz4h+fUa0beqaMvz52wv70uSQlkdjXmA+5Ht6ltZpq6v3 +A8vEXwZLIE9PLIRPgm9CToX6LvwV4nCe6dPonAq5FWwythlMFmyWnAPxFD4P +84tORbdOj/b1yd89Jb42z5gYIwYrRl/gu6MTD6zsMXUJxOwzxH8Zq2vBcMRv +Gz0X+Hic542jfS0wDLAMfOZlmWtq8aX3jtYV+LR3VPErdRHURyzhbBXmyUlg +f/CfDgjOT7Af0VkrqvW9u9LH2K7Lc+d+WdMlkvcKXmv0M7ZzVm5b+6AozZ0/ +2lZjbxJfN7VO34N1KW1LGuSuf/lf6XwT+SPyP9gYdBt7gL1Afoj8EjkGcg18 +X/BfLjB1PAEeViOxDSA/TH6D58HGUM/8M7mV1Pavp+Q5+BS6Xxtsvu4XS+f2 +wOjB6r/Sb4PUOqh78Dvz7vMlHyC+Yen6E2qCqc8hH7a+yu+T26hd+t15J96t +rqiT5I1y18dvVPq/mSPmapbolyo/1whsWvL2iZ+RZ61fOjdGjoz6pE1EnSXX +zl3vv6loP8mNc9cjNSldz0RNON8L1BN1kbxx7nqwxqXrwzbPXQ/fqHT9fpPc +3xNsVvp7gqa5vz+YXTp/SH6YfCD/wX9xDbVQ+CPYFexLR+2FHdV/R+KaPuKb +sjSWgA/G/kAnoZvAFLBlYATEj9cH4xevlMbHh2rM0ML5a3wZzgv5q8tyf3dB +DEv8SM6cWAJ/ZTPJC3V969w1//0K5+iJFcF4iO+2I2ZKXLNG/Rk6C1tbO1iX +tS5db0MNGLVgzAFzwZzxbQaYNrZ6du74FHyY2JiYHTwXG45v8ERu215TtHni +NWat0XnoPnKSO1T+HblXMI7O0ZgKuXDqDcFaXi2djxgm+RjJO5T2bfAR8BVe +YL/k1qn9iQ0k71jlF44unK98OtiGYEtqld5rrClriz/G/IIBcZC2L+0bDanm +g9w1uhQbtzg4P/xbVe9CvpcaLPLB5PzI/f1buJaammhqo0n+XJy4xppa638K +19Yxv9RW/y15XOJvBKhnpiaY2mBi1mngV4Xr4fnGgHrzvwp/D8A3BtSz/1q4 +fp1veKhPJ592ZoUHk//6s/D3AnxTQP3574Vrq/lGiPpyaoypNSYmn4r/Vbj+ +nW+OqGffN9i3/ES0H3NSuB6db4KoL/9Z8hmJv0G6rNIV6EtsFn7jqsLfUpDz +Ivf1U+H6bWr6qe1/H52XOGdN/vLHwvX61IxTO76mcG0jNY7Uk39dOHdGzozc +GfUI1NaA74HzfVk4N0YOjVzaV4Vza+TMyJ19UTi3Rk6J3NLKwmeNM0du6vPC +e409Ry6MGlnw8+mJ85PUZeCr4H/gh3xUOL+KPiTfC+YIVvphMBaJjqSPMeRi +Py1c7843KORjPytcD883IOQjsTnYHmIC8Hu+b6HejHtyb2wGtgMdTC3lzqXx +F2p+wTvqlD5/7En25i6l8RdyFPiz+OzYnxdz+/I7lcZ3qGkGHyHGJtamhgi8 +iZwt52VGbvuAjkZ/z819ntGJ6PtHcp8ndCy6Fp1NLS6YMfXb2GBs8SeS9038 +zQr57Y8L52P55oR89fLC+Uq+YSG/jY5H16PD+dbrPxuS2wbw7dUH1XwzR+Tf +sRHYCurzqG1dIeqX+BsV8p/YPK59rrIv2GjuPb+yR9hgnv35yn6B4YHl/ZfT +io5piW2JOci/LNKY9rm/qRrE3Ei+OvE3COBlW5fuQyehm6jJYn6Jl17IXc8E +3kbMRv0Xe4xceKvgvdey9Ldy7H/qH6l5AisBMwG3wsZh68C7wevBcKhlbRmM +7WxVulaDZ+RZycnxPmCk4GXEfGBZv+WOBamRIjcAHo5ORCeAZbQJ1hXblj4v +nA9085albQ06GF18jX63Th0TEyc/r7ZWub/Z61PY5mJ7sdF8mzafd8xdU3wA +tqW07uY8YguJAcFWGlf6vnnpsdyTe2Ozsd3YbL4NbF/anlGzAD5IDQu1LNQc +H8b7l36W7dS2oHSMTawNZgJWgY+Nr31PMLZB/R/5OWJi6vXalq7fpqYavBMM +nnweGDdYdxodj/CNDN/KNBMdlvgdeVdq6vm+oF1wrT2YGdhZ++Ba+1alsbMJ +Fd6GD4sve1cwNkN+hroW6luIP7GR2Mqtg2vxycdOTBzjUw/YrnSum5w3+CuY +H98yLEyMBW5eut4afcT3fk1Lz9VWub8PpI0+dBb5emwS30u0DbZVLUp/r4nP +ge/RNvd3iuQIPq7uwb34D7495JsB6v93CP6WgLww+eH11RyCOfItw/OJsUjW +iLXiPw4pXKNN387BtdvUYBNr7RJcm/3/AC2lOg== + "]], + Polygon3DBox[CompressedData[" +1:eJwt13mgjdUexvHtnL33MZMpMweZiZDMQ0gTlSJNyk2qm6IQmUOJhlsaKLrd +0ihu4SapEFFEGjRIhDQJ4aLBcD+/+/rjOXs93/X81n73+653rXXy+992ya05 +qVRqE2XowWwqNR4oTs0KpFIP8dt0fJ6bSp1KXWTa8N/RJr48dcXa8hfTRVQ9 +L5XahU/wmaUXtQ8ar4pcMf2r6DnsZ6wwVpD/lN7ADmP5WGW+F11C+cb4Qd/d +Pj/jF2sfkashV4Uv5RqrplOpG/AnselYfWyv9mC56jSW/wRfIHOAr6zvVL4n +9aCqxt6pb5zPE/wx7bNpmNwd/Cnqq/iOAdhM7BHsDmyf9p/uU0lj3s5XVL9Z +pj5drq+T3NP4DJkF6s+jinxpqqY9UO4puUflvqaVfJqaYPX4rnIF1Y4zfnO6 +n78Qv4Cq+a7vZcf7vIa/mmpp/4rd43MHv137NOplvPOiX/1u7XjoVWgM/ylt +di2l5Dro+4y/VrYfnWacPfi9PgvSPO0/1dWSqyT3jcwarBC1wBryheQW8ilq +4KMCdp9sI3Uj6QR2Fr8rk1z/irxk3sT8uYqupJrYbn2T4zdmkmezPC/53fH7 +66rfY5ztrnsnbeLL6N8gV4XO09dMbjLe2P0r5Htr0yT+EH5ApiUNlLuJ300/ +8Y8Z63L5iXI7sR1YbbpU7ny+DF5f5g7sJexfWGnfu56vTOdiZ2Bl5RrIDcVe +xp6NeSr3EV+JumNNsHFy0yOXTuZrA76s3KcyNahn3Cu53ILmiEwf17bJ78iR +GS87RLsgNcQn8HXwv9T1iHmhdojaE+o+l9lMfeUe5y/DL6Ua8j/KTvS5Jd4Z +fYP4Z9V+y79Az6pZjF9NLfi+sr9r/0Hr5P5jnHLxbqqrSRdhrbBOss9p34Zd +L9s55gD1wPLjnmKN+drUESuDXYzV4U8x3jq+Ip2jr6nxSmKr+bLUCauPPZVJ +rnW/ugPx7GQKqD8R6xLdqW+YTHn8K74u9cbaYw/Eb1MzMp28Y934b/EPZYrE +/JBrzG+hD/jCdCbWiC9mvOV8cWqN1Yp7oL6lsSZgi7HXsApyX/P1qA/WESuK +LeOLUSvsNKw4toIvQW2w2tg/jfek61pozAuoMr8VXytTlM6SO50/Ve2XfB26 +DOsQ79LJe7oq1jS1F8r8F98fv4Fu0HcjP0XudN9R2NyoR/fy39MA7aN4I7qF +Pyj7W7zjNEDtQD7PmK/yf8jWlRsodzblaR/ynUdoGz+NntEeQRl9HfnCahep +LUANjVfeeEWwJXwenYFVlTuA7+ObxxzCBvBv0oZ4hsa7Oe6Nukr0Taw31Fdf +Z5nR6iu4tptpV+wV/Ln0pvbd8e7Hesx3U9tJeya2Ud9bsd7g89UdLpCs3Yvj +mulR/dfK7ZL/ii9CJeO9xKbqm6x2NT3P71FfFCsc+47cIuOskl1Jl/rOz/Gm +se/KfoJtkGmG19C+E3tV3xOxBuFzjXUo3l16g28uVzPuqdw8uRlyLbBaMZ+x ++djMuHeZZD/4IC9Zz2Ndfynea+Mskb2OWvNd9XfUniH7sdolcj8E973H08na +01OmNTXWniT3ltzzMS8yyR7xob7rtPtTK+1GchPxJXLPYWdhDdPJvY9nMAc7 +h67R3oqtjXVJ5gzK1x6OzdX3WOwprqUodknsCfH8sGewWX7HIrwHVYu5rLZi +OllzYu1pi7XBTscmY0uxF9Q2iTmDDcbmYA9hXbAO2BO5yfyKeVYCez83WZvi +fco3XlOsutww7BXscblfaHicl3KSexb3bm8m2cPW5CV7c+zRP2SSs9F7ecnZ +Js44LbXrGm8svtB4T2NX0OvGW4a/G79bZg32gsw+4xeTK8L/mEnORivzkvU8 +1vV1NBfbKVdG7hT+fZqD7caKYIX49+IeYt9jylNZ/l2ahW3J+f/2ncrh/x3z +z7UUwC6n+fwyfLbAVj4dWz2/ItYsbAeWjXnNL4/zD/ZdTnK+TPuTE52KuuEj +NIfHmkav8NvlSmMl+Rfl5vjeN2X7UcvYy11ouXjvZZ+WmybXECuD3YjNwqZi +Z2J1sDHYAmw29lg22ScbYc/HnOY/xF/mt/neUnIl+AZqi+vvH+eB2Mvkep/c +yyrEPIr5JlOfCmlfJfeQvjFqG2FlsZuw2dh92OZMcq6K89UX+jYa68yT7Ft+ +a6wf6urFGUv7SrkH9Y3NJM8unuE6/CPqLbMf2xvvi/bftK+ngrEW6b8YnyQ/ +AWunvxk2Nc5O2FzsGP0Zc5mGxN7MZ9VmYx3FxmKjYn2N587/6r5UiL2Z/4t+ +x9rTbdgg/ij9wXegwXGujPHpCN+ObsVu4bfTF3wF6oa1yyTzLeZdF9/dlbrH +fuJa+vjOT2ijZ7WG/1juNXV7sYryZWPPj3Mw/xGtlVvBfxXzV+4EVl+uJr8x +3iPsN6wSVi7eA9me/Hpap/Y9/jB+MPZUulHu5ri22Mti74w9FBuNbaKl/FG1 +dbDqfFouHXsJPhobieViudi52ChsBFbZ79vGN8lN1rxY+6pg3/FNqR/WHRsZ +5zjXlRtzkkbw58h1Nt6TsVfILZXL4BnsfGwMdhd2PJ4J35mGYrfzo7LJ/pw2 +Vlm6i781m5zDh8daHusl/4Xs2+qOxX4ea128sPhxrAsNZ4dibV1LEzX3YG9j +L55c82Ptr52XzM0pPl9Re1k8R/rY96/mV9F67Q3YdfQO31m2jfEeiT3EeAtj +X8Bfj3seZ5WYG9nkmcSzWc6voF7qfsok59dV2r21+8R7lU3OGWOM35SmxrlE +f1s10+O9McYiufZYc2watgJ7FSuZTc6TcQb+Rd9mvoNcC+37Y93WNy/2jzib +aM/H59FFMkXj3BpnULlp+u6J680mZ48hsb7HuhDnMtlW2v+IvUHf63J149wa +54Lc5Dw2SK4YlcL6YvfL3Su3nubHtfld5bHS/MPZ5H/1KbHnxbj8l/g7/PE4 +18nV4JfhH8itxa6mJXzx+F9UzRWyD8hNifMC/RzPIp3sQa/J/I4dwoZhVbFe +8bvoLeMcK5D8j7CUL0HlY72WnW68BzPJPhX7Vfd4H0J+68p4h2Mt4Avpy+M7 +xfmCfzjOK9iCWFvoMH9F/F+C/Z3/H4tD/JA= + "]], + Polygon3DBox[{{1517, 1002, 1212, 1873, 1371, 1372}, {1367, 1366, + 1866, 1109, 1110, 1867}}]}, + Annotation[#, "Charting`Private`Tag$39642#1"]& ]], + Lighting->{{"Ambient", + RGBColor[0.30100577, 0.22414668499999998`, 0.090484535]}, { + "Directional", + RGBColor[0.2642166, 0.18331229999999998`, 0.04261530000000001], + ImageScaled[{0, 2, 2}]}, {"Directional", + RGBColor[0.2642166, 0.18331229999999998`, 0.04261530000000001], + ImageScaled[{2, 2, 2}]}, {"Directional", + RGBColor[0.2642166, 0.18331229999999998`, 0.04261530000000001], + ImageScaled[{2, 0, 2}]}}]}, {}, + {GrayLevel[1], EdgeForm[None], + StyleBox[ + GraphicsGroup3DBox[{ + Polygon3DBox[{{1682, 728, 1795}, {729, 366, 726}, {726, 366, 727}, { + 1797, 728, 1682}}], + Polygon3DBox[{{1795, 727, 366, 1682}, {1682, 366, 729, 1797}}]}], + Lighting->{{"Ambient", + GrayLevel[0.8]}}]}, {}, {}}, { + {GrayLevel[0], + Line3DBox[{404, 1, 387, 217, 1281, 15, 1293, 29, 1305, 43, 1317, 57, + 1329, 71, 1343, 85, 1358, 1359, 99, 1382, 114, 1393, 128, 1406, 142, + 1418, 156, 1430, 170, 1444, 184, 1611, 267, 426, 198, 402, 292, 911, + 199, 912, 200, 913, 201, 914, 202, 915, 203, 916, 204, 1129, 270, 429, + 682}], Line3DBox[{732, 2, 1134, 276, 404}], Line3DBox[{734, 3, 732}], + Line3DBox[{736, 4, 734}], Line3DBox[{738, 5, 736}], + Line3DBox[{740, 6, 738}], Line3DBox[{742, 7, 740}], + Line3DBox[{222, 8, 1221, 438, 220, 372, 642}], + Line3DBox[{745, 9, 1095, 222}], Line3DBox[{747, 10, 745}], + Line3DBox[{749, 11, 747}], Line3DBox[{751, 12, 749}], + Line3DBox[{753, 13, 751}], Line3DBox[{405, 14, 399, 279, 753}], + Line3DBox[{1303, 28, 1561, 224, 405}], Line3DBox[{1315, 42, 1303}], + Line3DBox[{1327, 56, 1315}], Line3DBox[{1341, 70, 1327}], + Line3DBox[{1355, 84, 1341}], Line3DBox[{1379, 98, 1355}], + Line3DBox[{1391, 113, 1380, 1379}], Line3DBox[{1404, 127, 1391}], + Line3DBox[{1416, 141, 1404}], Line3DBox[{1428, 155, 1416}], + Line3DBox[{1442, 169, 1428}], Line3DBox[{1456, 183, 1442}], + Line3DBox[{917, 205, 273, 918, 206, 919, 207, 920, 208, 921, 209, 922, + 210, 1133, 275, 431, 211, 403, 294, 1469, 197, 1456}], + Line3DBox[{444, 272, 430, 917}], Line3DBox[{398, 277, 742}], + Line3DBox[{398, 579}], Line3DBox[{444, 602}], + Line3DBox[{730, 723, 1796, 725, 1794, 724, 730}], + Line3DBox[{1795, 728, 1797, 729, 726, 727, 1795}]}, {}, + {GrayLevel[0.2], + Line3DBox[{1281, 1559, 923, 1280, 1882, 1470, 1282, 1883, 1471, 1283, + 1884, 1472, 1284, 1885, 1473, 1285, 1886, 1474, 1286, 1864, 1887, + 1693, 1718, 1762, 1787}], + Line3DBox[{1293, 1798, 1963, 1292, 936, 1294, 1894, 1481, 1295, 1895, + 1482, 1296, 1896, 1483, 1297, 1878, 1897, 1484, 1741, 2059, 1562, + 1694, 1719, 1763, 1789}], + Line3DBox[{1303, 1489, 1902, 1302, 1488, 1901, 1301, 1487, 1900, 1300, + 1486, 1899, 1299, 1485, 1898, 1298, 2027, 1800, 1563, 1615, 2047, + 1799, 1639, 1624, 1659, 1658, 688}], + Line3DBox[{1305, 1801, 1964, 1304, 1802, 1965, 1306, 949, 1307, 1903, + 1490, 1308, 1904, 1491, 1309, 2060, 1742, 1492, 1743, 2061, 1564, + 1695, 1720, 1727, 1721, 1790}], + Line3DBox[{1315, 1496, 1908, 1314, 1495, 1907, 1313, 1494, 1906, 1312, + 1493, 1905, 1311, 954, 1310, 2028, 1803, 1566, 1616, 2048, 1641, 1640, + 1625, 1565, 1660, 1769}], + Line3DBox[{1317, 1804, 1966, 1316, 1805, 1967, 1318, 1806, 1968, 1319, + 962, 1320, 1909, 1497, 1321, 2062, 1744, 1498, 1745, 2063, 1567, 1696, + 1722, 1728, 1767}], + Line3DBox[{1327, 1502, 1913, 1326, 1501, 1912, 1325, 1500, 1911, 1324, + 1499, 1910, 1323, 1969, 1808, 1322, 2030, 1807, 1569, 1617, 1869, + 2029, 1642, 1626, 1568, 1776}], + Line3DBox[{1329, 1809, 1970, 1328, 1810, 1971, 1330, 1811, 1972, 1331, + 1812, 1973, 1332, 975, 1333, 2064, 1746, 1747, 1334, 1879, 2031, 1570, + 1697, 1571, 1729, 1698, 1770}], + Line3DBox[{1341, 1505, 1916, 1340, 1504, 1915, 1339, 1503, 1914, 1338, + 1975, 1814, 1337, 1974, 1813, 1336, 2032, 1575, 1574, 1335, 1169, + 1573, 1627, 1572, 1661, 1782}], + Line3DBox[{1343, 1815, 1976, 1342, 1816, 1977, 1344, 1817, 1978, 1345, + 1818, 1979, 1346, 1819, 1980, 1347, 1247, 1748, 1348, 2065, 1749, + 1576, 1699, 1577, 1730, 1700, 1771}], + Line3DBox[{1355, 1507, 1918, 1354, 1506, 1917, 1353, 1983, 1821, 1352, + 1982, 1820, 1351, 1877, 1981, 1737, 1350, 2033, 1582, 1581, 1349, + 2042, 1663, 1579, 1628, 1578, 1662, 1783}], + Line3DBox[{1359, 1919, 1508, 1357, 1920, 1509, 1361, 1921, 1510, 1363, + 1922, 1511, 1365, 1923, 1512, 1367, 1867, 1924, 1513, 1584, 1872, + 2053, 1716, 1690, 1585, 1683, 1701, 1514, 1766, 1871, 2051, 1794}], + Line3DBox[{1379, 1994, 1830, 1377, 1993, 1829, 1375, 1992, 1828, 1373, + 1991, 1827, 1371, 1873, 1990, 1738, 1740, 1739, 1370, 1874, 2055, + 1713, 1687, 1689, 1688, 1369, 2054, 1684, 1685, 1629, 1665, 1664, + 1777}], + Line3DBox[{1382, 1929, 1522, 1381, 1930, 1523, 1383, 1931, 1524, 1384, + 1932, 1525, 1385, 1933, 1526, 1386, 1875, 1934, 1527, 1714, 1876, + 2056, 1715, 1630, 1644, 1764, 1775}], + Line3DBox[{1391, 1533, 1939, 1390, 1532, 1938, 1389, 1531, 1937, 1388, + 1530, 1936, 1387, 1529, 1935, 1587, 1619, 1528, 2043, 1620, 1655, + 1654, 1692, 1012, 1691, 1631, 1669, 1668, 1778}], + Line3DBox[{1393, 1831, 1995, 1392, 1940, 1534, 1394, 1941, 1535, 1395, + 1942, 1536, 1396, 1943, 1537, 1397, 1944, 1538, 1398, 2034, 1589, + 1702, 1723, 1765, 1791}], + Line3DBox[{1404, 1543, 1949, 1403, 1542, 1948, 1402, 1541, 1947, 1401, + 1540, 1946, 1400, 1539, 1945, 1399, 1026, 1588, 1590, 2049, 1832, + 1645, 1632, 1672, 1671, 1792}], + Line3DBox[{1406, 1833, 1996, 1405, 1834, 1997, 1407, 1034, 1408, 1950, + 1544, 1409, 1951, 1545, 1410, 2066, 1752, 1546, 1753, 2067, 1591, + 1703, 1724, 1732, 1725, 1793}], + Line3DBox[{1416, 1550, 1955, 1415, 1549, 1954, 1414, 1548, 1953, 1413, + 1547, 1952, 1412, 1039, 1411, 2035, 1835, 1593, 1621, 2050, 1647, + 1646, 1633, 1592, 1673, 1772}], + Line3DBox[{1418, 1836, 1998, 1417, 1837, 1999, 1419, 1838, 2000, 1420, + 1047, 1421, 1956, 1551, 1422, 2068, 1754, 1552, 1755, 2069, 1594, + 1704, 1726, 1733, 1768}], + Line3DBox[{1428, 1555, 1959, 1427, 1554, 1958, 1426, 1553, 1957, 1425, + 1052, 1424, 2001, 1840, 1423, 2037, 1839, 1596, 1622, 1870, 2036, + 1648, 1634, 1595, 1779}], + Line3DBox[{1430, 1841, 2002, 1429, 1842, 2003, 1431, 1843, 2004, 1432, + 1844, 2005, 1433, 1845, 2006, 1434, 2070, 1756, 1757, 1435, 1880, + 2038, 1597, 1705, 1598, 1734, 1706, 1773}], + Line3DBox[{1442, 1557, 1961, 1441, 1556, 1960, 1440, 1065, 1439, 2008, + 1847, 1438, 2007, 1846, 1437, 2039, 1602, 1601, 1436, 2044, 1675, + 1600, 1635, 1599, 1674, 1784}], + Line3DBox[{1444, 1848, 2009, 1443, 1849, 2010, 1445, 1850, 2011, 1446, + 1851, 2012, 1447, 1852, 2013, 1448, 1267, 1758, 1449, 2071, 1759, + 1603, 1707, 1604, 1735, 1708, 1774}], + Line3DBox[{1456, 1558, 1962, 1455, 1078, 1454, 2016, 1855, 1453, 2015, + 1854, 1452, 2014, 1853, 1451, 2040, 1608, 1607, 1450, 2045, 1677, + 1606, 1636, 1605, 1676, 1785}], + Line3DBox[{1469, 1613, 1131, 1468, 2026, 1863, 1467, 2025, 1862, 1466, + 2024, 1861, 1465, 2023, 1860, 1464, 1868, 2022, 1612, 1463, 2046, + 1680, 1681, 1637, 1679, 1678, 1780}], + Line3DBox[{1561, 1480, 1893, 1865, 1291, 1479, 1892, 1290, 1478, 1891, + 1289, 1477, 1890, 1288, 1476, 1889, 1287, 1475, 1888, 1560, 1614, 929, + 1638, 1623, 1657, 1656, 1788}], + Line3DBox[{1611, 1609, 1610, 2041, 1457, 1856, 2017, 1458, 1857, 2018, + 1459, 1858, 2019, 1460, 1859, 2020, 1461, 1881, 2021, 1760, 1462, + 1275, 1761, 1709, 1711, 1710, 1786}], + Line3DBox[{1781, 1650, 1651, 1580, 1649, 1160, 1368, 1583, 1989, 1866, + 1366, 1988, 1826, 1364, 1987, 1825, 1362, 1986, 1824, 1360, 1985, + 1823, 1356, 1984, 1822, 1358}], + Line3DBox[{1796, 1666, 1618, 1643, 1686, 2052, 1515, 1667, 1652, 1670, + 1653, 1586, 1717, 1731, 2057, 1516, 1712, 1750, 1751, 1736, 2058, + 1517, 1372, 1925, 1518, 1374, 1926, 1519, 1376, 1927, 1520, 1378, + 1928, 1521, 1380}]}, + {GrayLevel[0.2], + Line3DBox[{732, 924, 1882, 733, 936, 756, 1965, 948, 769, 1967, 960, + 782, 1971, 972, 795, 1977, 984, 808, 1985, 996, 1920, 821, 1008, 1930, + 834, 1020, 1940, 847, 1997, 1033, 860, 1999, 1045, 873, 2003, 1057, + 886, 2010, 1069, 899, 2017, 1081, 912}], + Line3DBox[{734, 925, 1883, 735, 937, 1894, 757, 949, 770, 1968, 961, + 783, 1972, 973, 796, 1978, 985, 809, 1986, 997, 1921, 822, 1009, 1931, + 835, 1021, 1941, 848, 1034, 861, 2000, 1046, 874, 2004, 1058, 887, + 2011, 1070, 900, 2018, 1082, 913}], + Line3DBox[{736, 926, 1884, 737, 938, 1895, 758, 950, 1903, 771, 962, + 784, 1973, 974, 797, 1979, 986, 810, 1987, 998, 1922, 823, 1010, 1932, + 836, 1022, 1942, 849, 1035, 1950, 862, 1047, 875, 2005, 1059, 888, + 2012, 1071, 901, 2019, 1083, 914}], + Line3DBox[{738, 927, 1885, 739, 939, 1896, 759, 951, 1904, 772, 963, + 1909, 785, 975, 798, 1980, 987, 811, 1988, 999, 1923, 824, 1011, 1933, + 837, 1023, 1943, 850, 1036, 1951, 863, 1048, 1956, 876, 2006, 1060, + 889, 2013, 1072, 902, 2020, 1084, 915}], + Line3DBox[{740, 928, 1886, 741, 1227, 1228, 1897, 760, 1232, 2060, + 1233, 773, 1237, 2062, 1238, 786, 1242, 2064, 1243, 799, 1247, 1248, + 812, 1989, 1109, 1110, 1924, 825, 1216, 1217, 1934, 838, 1024, 1944, + 851, 1252, 2066, 1253, 864, 1257, 2068, 1258, 877, 1262, 2070, 1263, + 890, 1267, 1268, 903, 2021, 1272, 1273, 916}], + Line3DBox[CompressedData[" +1:eJwVzV0rg2EYwPFri6wkScvxvgsnkvQ4cEKLpeaED+AL8GEob3k7Q+aE1aZM +oVCjNnmpUdsO/Hbw6999Pdd9P7mltWQ1FREJ9XTEeF/EBPmBiB29ocw1g5mI +Sd2lyi0VhsyndI8a99wxbD6t+zzyxKd3H3SGA14YsfeqzyTMssEmc2yzRb+9 +K72kxBkXnJPxbV3n+fGPBT3kjXfqjNrJ6xFNPmiQNV/UY7579/n1xpcWOOmd +GbP3py2WOaVDlzZFVvgHxKA3Tw== + "]], + Line3DBox[{745, 931, 1889, 746, 942, 1898, 763, 954, 776, 1969, 966, + 789, 1974, 978, 802, 1981, 1226, 990, 815, 1990, 1212, 1002, 2058, + 828, 1114, 1014, 1935, 841, 1027, 1945, 854, 1039, 867, 2001, 1051, + 880, 2007, 1063, 893, 2014, 1075, 906, 2023, 1087, 919}], + Line3DBox[{747, 932, 1890, 748, 943, 1899, 764, 955, 1905, 777, 967, + 1910, 790, 1975, 979, 803, 1982, 991, 816, 1991, 1003, 1925, 829, + 1015, 1936, 842, 1028, 1946, 855, 1040, 1952, 868, 1052, 881, 2008, + 1064, 894, 2015, 1076, 907, 2024, 1088, 920}], + Line3DBox[{749, 933, 1891, 750, 944, 1900, 765, 956, 1906, 778, 968, + 1911, 791, 980, 1914, 804, 1983, 992, 817, 1992, 1004, 1926, 830, + 1016, 1937, 843, 1029, 1947, 856, 1041, 1953, 869, 1053, 1957, 882, + 1065, 895, 2016, 1077, 908, 2025, 1089, 921}], + Line3DBox[{751, 934, 1892, 752, 945, 1901, 766, 957, 1907, 779, 969, + 1912, 792, 981, 1915, 805, 993, 1917, 818, 1993, 1005, 1927, 831, + 1017, 1938, 844, 1030, 1948, 857, 1042, 1954, 870, 1054, 1958, 883, + 1066, 1960, 896, 1078, 909, 2026, 1090, 922}], + Line3DBox[{753, 1096, 1097, 1893, 754, 946, 1902, 767, 958, 1908, 780, + 970, 1913, 793, 982, 1916, 806, 994, 1918, 819, 1994, 1006, 1928, 832, + 1018, 1939, 845, 1031, 1949, 858, 1043, 1955, 871, 1055, 1959, 884, + 1067, 1961, 897, 1079, 1962, 910, 1131, 1132, 1133}], + Line3DBox[{911, 1080, 2041, 1127, 898, 1068, 2009, 885, 1056, 2002, + 872, 1044, 1998, 859, 1032, 1996, 846, 1019, 1995, 833, 1929, 1007, + 820, 1919, 995, 1984, 807, 983, 1976, 794, 971, 1970, 781, 959, 1966, + 768, 947, 1964, 755, 935, 1963, 731, 923, 1091, 1134}], + Line3DBox[CompressedData[" +1:eJwVzjkvhFEUBuAzY4JGpdJRKBVaiVovChoJiXbGFvu+x75kYl/GlmASKvED +6P0APY1uGmJ7FE/ec8/73Zuvqj3TmE5ERAfZooj6VMQ1Q5zzUxJxJhd0tXKe +QU751uXksK5azjHACV+6Y5nWVchZCnb98ohD2nRlMlkaMSP7OGCfJl1CJnTT +spU9dmnQFbgz39LCDldsU6dLufcms85TNHPJPcW6C1mjf2HS3MsWn/5xU1ba +PzNh7mGDdcrtHhk3v/u2W66x+v+u/QPh/THnLlZY5iMZkdf9ujPq3MkSi7zq +croRc4Y8NzzxByJ2ON0= + "]], + Line3DBox[{918, 1086, 1130, 2022, 905, 1074, 2040, 1126, 892, 1062, + 2039, 1124, 879, 1050, 2037, 1122, 866, 1038, 2035, 1120, 853, 1026, + 1115, 840, 2043, 1013, 1141, 1192, 1191, 827, 2057, 1001, 1225, 1213, + 1215, 1214, 2055, 814, 989, 2033, 1108, 801, 977, 2032, 1105, 788, + 965, 2030, 1103, 775, 953, 2028, 1101, 762, 941, 2027, 1099, 744, + 1888, 930, 1094, 1095}], + Line3DBox[{1277, 1174, 1279, 2051, 1172, 1278}]}, {}, {}}}, + VertexNormals->CompressedData[" +1:eJysvHk41dHXNi5NKlPmaKBoEEUoCqvSoJEopcxTxgwJmceQmQwhY5EykxBt +U4lCGUKZOZ9D5iYV8tufQ8/3eZ/3ef/79c+5rGvbe+217nWvde/ORUDPUsWQ +no6OjpuBjm45/vT8w5xekEBAjMxh773rnJD82ycaiikEcMgLSXfjz7KS+NQD +O9yQWpPs3TV43WOrz0/WZhBwtUP/VqCNBzL+UC5ZHU3A7RtGmyLzCKhWPVzt +luaJ/DWSI7eEEOC27r7glTIC7rYM6VQ6eKKHSm/PnvImwIm3gyL1hoAzdYpd +hze5o+0GfIUGDgSUMttOfWgmgP2aXOobCTtUNbc9qNEC709IBPR2EChkf8zh +16a66LT018N11wk4PGijKN5MIMejm0rPrbNHB9qyEm7cIEDduGe7cS2BWH5M +SNWou6P86C0B+24ToCihsjz0BYF+fGATfervibxmJh3ZfAgwKfC8NZlLIO33 +jx6dvO+JNBh1h15j/98xDRmHPCbQ1suBrvsveSDW4ZhDh2MIeMW+TNUvhUBj +0q+dK/pckaxkBb0Ojk+X9jQqu0+ARA3SHpB2RfeuG6mIphMgCBtXRj4ggPGt +L1eqmCeSGXpisy+VALbASyvFHhLgcfm4Xre1DxKQW+NtEk+AytwHx8hsAtJs +RNmVFP2Q03XDvIYwAqixu7ZolxPwNvLUwHyoP5I8VZ3z3pOAAnl+q9gmAhrj +87bHp/siVr7ROw5WBOxslqT37CfgvNaZBw1cOF8MCdujtAhwzRb4pD1GoJqK +su5IHzN0SbXrd70qAckT2S2GfQTy7A26lpLrgS52fz+bp02ATVt1/7lGAt0S +dxUyG/ZFLYco0q+tCfjC/EBEvoxA57Mi+y8E+qMX3UId370IKO/sXKjMIlCC +6O3+qk1+aCSbg/FROI6D5ZWSR6kEovY+sZ2Q8UEKex8pzuD7GoQm7T76AOdR +6/iq9b89UK1CyJwvjo+kYJnAN/x7x4V8q0UV3NHmr2xCQ1kEuIQeXOsZScDM +x89s3mHeSHn73xX8TwkQ5npobBBHwP1maRXnan/EZ0YpGMPx1TvZ61iXRoC2 +ts6ri5ohaE3zWnNOnKf83SbEnlICTEvOH6scD0OPrzDs34nxYMy2dcHgIwF+ +p14tS2QJRy5559b5GBPwTDfll/ZPAq4kdh7/yxGIOpPtG+0VCTj9rWO8dh0V +SQVbLQRH2qMMn8vRchIE2Oq/FIfvBEoxXWvGMB2IHGN0DaJP43wbzHbIthIo +9ho3+2WhcNT7gU+kwJSAc0dYIbaYQBE7p0KONIUhOXuKz+s7BMwKEIrNj3A8 +BVUPZc0Fo3HTm66csQQom3Nl9cYSyNvuOt2Qvj9yz5n/Zv+IgEO10juORRLI +X1Z+35nD3mjX4GV5PRyfiMS57+p3CehefeKXiLM7Yt6w4axFEQHBPoFhQtge +zr2VbmzOB42cVH6uhu1Nn4S+0wcR8Gtr0AU7zyD0dsx9zc98ArYdUJN3isL4 +bdxrJ5IcgeT8O77GPyYAim4zPswkIDUqnyOE+T5iyKCo8GDchl1JsM3E8ayw +7kzckhyP+js0rjoZEjCZIDH/hY0KRnOPzQu57yPbKLUc+50ErIeXKfePUtGD +pytVU7LvoHPSdjflf1PAu67slxUzFS2TCnCOS7+Pio4U/fwpQkDetr5B/hYC +ld86uG3aNR5JsGXt2GZCwHCetf6TJwQ6o8lhT5cbg7j45Y7ticA89cqkLArH +J1ftg37isQh0Ped86D3Ma/ZmlVn5gQSSmDLtXjUViFpE20IvFBDQtkIvm+8u +gcLn7+ayhPmgNtmpeSMcnwIGI70gd3xOzs5kFR1XtEeSe6N4BQFWn0ZqPzsR +sCrpxOwxDR90/GSZhk8NAT+Kx/5KYp4z3rrsW2BHMFKn9tHb1GK+VQ0XP4f5 +6YqaPv++F1GoIjW2tA2vD9Bu2jLuR4Dh0HGe7JIkZJbQws+M439BVja4GfOq +Y9BHpufr0pGwMJHugPd9KFLZcHkvFeyylboFKY+RfyWLjTQdAXYKk57HM6mI +KX2e+dXf+yiYoqjB4k3BOJfpkRSios/Ls863rstAt8X8zxStJaCwmPqj6TmB +vB5bsZfFpiFVzvoVcy7Y/9pDZxV9CaTDumPHrvNJaPssHftfHJ/Sm22/Vt8m +kH1LM9vq7VGIO1O4Qf4VASk7G74bORCoILcn8gR3MDrNVTmgjO+rIuRyX8SZ +QD13fO1Me73R1/09b2TxfZmfrbVYZk/A5+AfrUn19uiM8+mi8joC6Fvo1maZ +YxxypL3R8/VAaw//pWS1YH4LnRLbjPkpUV/ztCVfAKqSurRbr4+A9Ol1fyLO +47r58Cb5omgUKjmcrN02QUBHm9yejMOYJwq4OsIhFdE7mtz/hut52GGTsyPJ +f8yWe1mP5qFJnq+rC3EfonaPH786i/uUUI6Z7aUXSOl0lc4kjue3mKT6Rq9h +9MNIVvHaQAGK6o+QyjEdAv0qurEbwwRi6tM8xxdaivRb1+wz4CHgjahQwYIy +gTKahD44ROciC9ZUW952zMuXynh9jhAo6JBN0rKgFKTAZWeZh/0x/8ml9VaJ +QJ8Gv2zUso1Esk6xps3juB9MCwRv0yHQcjmz+KILd5FiP9MR614C6lxOpNta +EMikSjexhM0Dleemn5vE/g9ZD4h0WxKwW33odKquKYrau33f8Hucx69rme7q +YHwqa1MyOWzRsrtvFj7jfV41F2/6jvksyHWDWJOqO5rsMJZ4gP05lHPl/vmt +uA/Ysym0rAxC9UxNOjx8VKBrmHFn7aFA1P4FE7YDD5DDpRT7k1eoYHbiYoOE +JgWeFl62PBaah67GyK38UUyFv+HHV3MFDUHtXdUjdCfrETiF/hlNpsK9+Jhl +z75SkaenW4kaZwdSFlduMnPsB0nn8G/c+UPI07ypKcP4DXqsc6k8B68/6yLZ +a2RCQeefWd9XeJiLMoKfmMTnUiF0TZpM9yAFGbvpaVmNxaGilffuy6pSYX3B +ankHIQIZO6zj/jQRgB4nJPcK8VBhLYuP3sfTBJLsLYguuu+GikbPTDR+x3hI +q/Uq1yVQd/7y7mGvm8jt58CmvB7c746fDhLH8wjd4j/3wgFho2iMQ/qyrQpt +1/5jT48a7Y0ZwjwY44K64D/2OrVy5roFAqLC7BV1mf9jbyy00DuC6zaiUVoh +LIMCyd2PLgcHnXy5+EkFC9mQXuOHQ/Dkjyu14Ka0/OLnMDy5Nvfp0tk+CGmU +vPrZf7f84ucoTD5QFDv7ph0IXuWRXab5smV72CcNno2DBk/ej0tyo3B7i6Si +p5iJ/CyHg8+yt30wJ/5Eii6wDwUxCgTW6V97ufg5CoM+ucuVXwyhf35ab6lr +P6MzDAHmrT2QT/kv+6nprXtDfKhgv1M3y52N+C+7SNbDxxd3U0H1FF8O/9H/ +2APojzRFzxPQOnx6q5Tmf+yhmTJbjwwSsKXw/F4St5UlIWm3dE3BddnvvSRu +6wWcmUncxvtftk3msIWDIb5/SdzuPymwkcStp6ydyjtVd/D4ziFF4vZw4WYa +btf5B67pXBkEfL7hNNyyhft5krhlpeZmrT/wAMzaDe1I3G77cJ+GW42fmw9j +3MKV93dpuJVoDmcgcathsfMwxi2svO31m8RtTsTWhUKM2wtq7m8wbiFWy7vh +f8Et/MNtVOrbIRK3XB++f8O4BfHCBH0Styylkgokbj/aT7mbjsXBYRnN8P8F +t/APt5G5qdokbtmHH3BW3XeDppyOqf8Ft/APt/94lVjkVfjHqz6qtutIXuXL +Za7T8vUAUfOqIZJXOfLT9pG8urZpi6IFXwDQtzXuInnVcegM3T3Mqz/9Y/kw +r0KXaZY6yauMHx+JkLyqti9ZPQJS4QT4xZK8upM45ELy6pRe7WbMq3BXkZHG +qxKGCjRevb3Z1xzzKkwJWemSvKpCb/Ka5NUd1jznMK/CX9mwgySvXiq0GCV5 +1edI2F3Mq/Bx3kmc5FXen7FFJK96yn9SwrwKzKdLbEhefb9akI/kVe0z0Yl0 +QSnwhaOfxqv59CE0Xv2jsJ33qm0kvO7kNCN5lcciy4/kVb8XwSmYV0EiRv8E +yatqq7oekrx6nsUvsZzNAyr92pVIXt2y66Um2ffLOLf9vKzjCi0Rkfxk34+O +8n1N9v04NSflExo+kLh5lRbZ95u799NL4f7M9C4mNqAjGIbV0YI17oMRMRZ7 +yb5vv1xBQOJFFAgLOZSRfb9v4v5Wsu+PiOZUZpUkQcL4uc1k32/h5gki+36I +Z6ge7vsgPFD0mOz7IWdc35F9/6SkTj3u+3DJ6vZNsu9v/eTmTvb99j0ybLjv +w2zrDy2y75ddCPhE9v1h1nWquO+DPb+u0n/v+3cX+z786/t0VXLKZN8XVz8n +iPs+ZE8zsJB9n51n52+y75dsYTVbsT0Knhu70vr+c3O+r2TfH+PXvY/7Pvju +M6GQff9vxPcosu/LZ5+ysun1hqSakXqy7/cGUGhz6W3vF9Nizu4g07GMNpfK +Lf8STs6lFrnudKNzPkAdWVFEzqVig1dmyLmUqdLsHJ5LISlCdRU5l/bEyh0h +51Jb1CsumhwBe5rrJ8m5lErlYSHnUvrs1+vxXAr57MeUybm0Ks7djpxLx34t +68JzKeR91LxCzqUlv6P/kHOpPXrDhudSKD++I5+cS2+GXnhEzqV88Qff4rkU +DgcUWpFzaWCZAJ01nktRbfYknkvhYfPQBDmXGtzS6yfn0i0PhTKmXOOB/7Km +MDmXvrhyxZCcS9GZY9/wXAoHA/YdJefSIsZCRM6lZy4Y6Ccci4C093JB5Fy6 +IJxFm0tPeTR2MkwFwtP6CtpcGpzjmkvOpdY+bg85w3zgGrjMknNp7XgGTTf9 +FD83JabgDj8e0dF0k/DfPgZSNxWXCPVi3QSnO0+vInVTHJO9IambNq9rvYR1 +E1R+Zn1O6qbmqc7bpG569Uo07JJmCMhuWKDppvAWLgqpm+I13thj3QTPglUP +kLop86nsHKmb7F4e3IR1E2ysPsRM6qYMub+/Sd2kOy/GhnUTZMtyNpC6KS2t +jaabbLsPB4VG2sOqKxdpusmib06U1E35qiaPV08HgoOzkjGpm5xcBlpI3ZRv +PZ6vJhQOh/foiJO6qced/RCpm55Zt2ocbQoDybtV/v9dN6Uu6ib4p5sswjpy +SN00PjT6oU/fH3Spt6ZJ3eR1IGkrqZuiHFzenT3sDQdZ2o6SuonB4hdN1xty +HnjRK+0K0w4WNF1Pb2K6itT1QhFOL7Guh28PLlqTuv6e7JdVpK5f4H6lg3U9 +yPHYepK6/pbOeydS19dw9ZSfV/QDdyezXFLXe5jb8ZO6/nbv2z6s6+GH2M1s +Utcb14vfIHU9r1r1TqzroSC+3++/63rlRV0P/3T9Qel7vaSuL7MUSw71MYOv +y898J3X9L+YCmq6/esqzMDnXA2yJXzRdz+8n3Evq+oq/7U1Y10PssMshUtfz +PXggTOr6LXcXJFQD/WHXebZPpK5nvDZF0/VvDxpAxSY/uMC5m6brX9Q+eEnq ++k08zy2xrgeNcC0FUtfrqeXRdP0aR1E95t8eYM6cRNP1/+PdCf4f707w791J +xK6V9u5072FwVJCNB0BX0f/27gT/3p161CNp704XFeanKh08YUt6Le3d6brq +Z9q7k8BLp7OHN7nDm7DNtHend/GL707WGx2uvZGwA22/HbR3J4WHUrR3J3uw +flVpqgt249/+t3cn+PfuZHpgmPbuZBbtcKdK3R24ju+ivTsdqTtNe3cyf3bu +XKa/JxxJHKa9O3EqONHenZZnmrxWvO8J1DR12rvTui3dtHen2FvliQcuecC5 +v2G0d6c9QRMq5LvT+g91x2v7XIExL4v27hQwm7Ss9Xg7uKsU707I+4z2dN/W +pxp+gVUeeq10tp9RCFfsJp1nn9CsijrfytQR2LqBno5cr/bw8QG8HsyKC3TI +9WFbuirI9bKJAwJ4PTR/vrWFXF9i8ULgID5HbOOAzE9xN6Sz39QyE+cp5vAO +Jkuc5zbDx3kP8pzRY+7+w94Y9+bj55hS8dxhMZpWl7f2JroweNu7QZeAvS3T +ToMDuE4Tzzqui96OSge/jN3TxHmP02Hv6STQaoGnPPtXb0V8Z1OM3hlhHj+1 +en5VD4HObeesFTxqi5L1ZfKM9bDOfeg8d/Aj5gHeIY2balbIKDj2jQnmgT/+ +4lrLMA6b1VQlYd4DvXu58vkbXJ/TLMccxZMItI1btWbnM3d09btS0uMkApzD +fDR88dyU9N3lT2WnK/rG5q0oeIYARXann5lzWOeOe2VxfdiHbB/R87ArEJAz +MdOg8Y1Aj9KF6rx03JHSr4jas2dxHUqLsEhxU+HxjqMnOBQDUN4fPWX37Zjv +7POTPu6kooqgfIZQmyNoeIg3bxMnzqMxb3s+BxUJjKxz4fkciDR3M8bM4/7C +4du1RVSZCiu3MKuqKMahKMo6ZVUqBfbUpdy970JFz27LORlyqSI5M+Gcz6UU +oGPYK/b5FBX5JQ4w/UmKRyHSQpEPxilw6QMRXfWICoK8P2NSzueiZo2zHCZ2 +FHi/raxJSn4YMVcnarB3m6GjH5OFWQaH4FicBrtnOBXV0w8JitfkosSXjBe3 +3aXAL2HJI3+NqJBhva7Lt+UNGmpcpeEzNgQSsbdMHpp+QQO8duucX4YjrR7n +e5OMAxDS+exj3JshEC5nm7sd+hHJlhj97g+mgKjbmlO/JanokOLT60VfalHo +YeusPEkKqBt9LbHrG4SMOh2hucRCVPFjm8Dc9DCk+Nv/lqntB7ujpvQqW1+j +Q51W8g6rvkDGW5kGVvMxtM541+xRw8/or4JsSK32KwgVLL8V8uEdCGj9iMn5 +ekzeQu8SU6boJGw7/Xawkb4FeR28x7NW4AviVPuadjK7F9aXs3eS+1y/ll6L +9wFZk11x5D7Pl6PH6wxfoRPcZ/0qAy3lFz8nwcbccZTc53PlWXa8D4jZVRSQ ++/RcftA8vHIIiR5jTs4PLQCtybxHhu3DcObVeiXyvsxXeGXxfaHBfCSDvK+w +iw4tntfjrrTjeMJtyz20eK6c4DQm48l8auSO08tw6JlOjiLjeeuFncLnFSPI +Uo/rZcndGjAtzrthcnIQcuOqaPm17yVycX4hw233/5HfDYv5hX/5XXPw1loy +vylP4+bEanJBLl1Ri8wv63kxARJvgkzK6zDegC6m+Px/x1vpIt7gH97mLi+j +4S0GXdk+mxQPJRJ/7pF487z6kYnEv9E3DjeMfyibrbpA4p950/oEEv+WOVpv +HtgcgTHjrgIS/+2nBZtJ/G9/98oL4x/kPPc/IPHf7OtLq8cYlZFjuB6h6Y8P +rR53aNZ9I+txKjDkquiHfcDvU89L1iN9zTdaPdboVbt667jDz9EQWj1mClXR ++GpjRl/dN3E3SJu0ovHVXTYBGl9t4OwRSMpzBkPqJxpfRfWdofEV81WRv/lr +b0Jmv/3/xlfwj68k5qxf5eA5Z3S7MiN33g0QUVK9/wPPdVx8K2l8daooZVbo +qC0wHzlA4yu3jEV+czKcP8y2eivIX13kt9v0TjQeS0tpdLJVs4Kv32JoPHax +fheNxyK2sZgfnveAKbq/RSSP1Qyo8BzH84w2mgz4Y+EOC08/HorGc1u9usyD +EMxnBwfkKdt5XVCiiKOqHv45usKG5ufgabNxzrwbaITlIs1P0Qbd8qB+AmXv +lPxbX2iIYt+yswzj+cFZ+Sxt/x/bz2bNWrijOxvf0/bn4/xSwPmHQFU1gqe0 +GqyRF2XsfOpxAu4I3ejm20ZFV+uihWvZ3NFp4QTNSl4COn1i7Q7doCJCtXHv +iWeh6GVH50RrHQWsdjxhmlk5jJq6B+xHCx6hr/uEz0fwUCBSS+oYiXPnhNIe +jHN0vyPIjMS55+30YxdnJ+HkcePqvE4H+e3tz+vvnEoGhS2nCAbBAXSaIXWD +tcIrCGSiK2j9MAJjrJyxOr+G0Oih0nNZuq2wxTP6Kd0oBeJKWdaQ5x4qPeKC +zwWNBD1V8txv4kE0Pxu/7X+B/YQ/NxtofhIPrWj3euYSVvaazR34g5Jo92q/ +MkaLA+ejCz0aDdZgxz1Ji8NzjqO0+K/xu+G+jdcFnKietPi/1NOjxfmpW1td +XaEhtGly0OIc0y1L60ecGgfmdj1zh8+VirR+FH0m2UdqAvfBg0IHXD+KILdX ++z1/XyBgd67vlRAWKnqQmOr7fL8M8mkPCvXcS8AJ34rYZ2eoSDc9m35E8BRa +LnksXXmKAhKurA/k3mD+uUOZP7BeG609fLyIyYQCHMu+h0mvHEG7GIsfW35y +Rl/eSAWVfh0Ee7+KZyPNY2hS+imj55M8VCeR5zRh/Rn2NKa0k3xubvr3O+Zz +MPDU+EPyuWBTfBG5vmJV2qTHkzwQL5K/Ta7/t7/U4v7wb//XIk9iSX+Ksp/Q +ya3Xhv6G8WLSH/bnw4mk/7dK8s/3C56CR8P1yaT/g9zdl8j7Dpsqz1Tvl4Fi +QdUI8r6C8ovx2awpxhjxUQSuFy/G56SaldxrKoFUQuZLH8lcRRe/cuwIvUKA +mcddw4gVuK/ZaRlYshuhZ339zN0HCUjO0LUv309Fn0usa6RKbFFXyg039VV4 +Djz77OpEDBWJMQe/OjxzB+1PvHvZJJ4Cq+0evN7oOIw6j+baLu9IQuUrAxtH +I4egiZ/egPXuF/QxqddRb8srdG87G10/Rz+scuwoeN7YAlOWsl0L+eMo2Yoz +Ocq1HiS25p9vSO2Dtzva1/UcGgRVuS3Pa8wGwW53p6zAlRGkcipAkVcqD3ac +aWckTAchYf1eQ90pKnqntyHDpzYc2udKf3McxP6sN2CgalERi9jwrw2srhDe +Sx8d8JmC561jjSMbcJyXrRynVloAe1BZeZog1t3zfL6aWE9J9Z1rGmjWAamX +j/UTMK9aHepIuHdiADY7xC1bta8Ffbh0OT/h5jD8hJxzpJ+nTdVYsJ8o2vRO +IeknUWR0SVQ4H9KlosLl8/oRnaFwjnzYF9Af09i4B9sFi/dnYTtwdJyPI+0a +YYEDKw4NoE6Vpmemln3wRkU5c953CO7McWTM4HzFntJoMhxTxfPty83aOF/P +j1Z9T8F+nonJG7LxUwe+59Mx6thPFt9NNP/l9jGW9zTroPlDT2j+/8r7yfIL +59dT9G3ngVIdUOBXdL6N8xud8CXAg5eK5n2ywoQ9jGBzm+sfVhwHSdWR92R8 +FnZnioxWWqBMr5+lZHyqRQauZx2gogw+F6EkBUvwfPRa22Il5r3SoZbbOlTU +dXaOKTvGDm6qvXtN94kCh2JOLyfjX9J4nY6X1RW5BNvFk/HvzRW7VRdHRT4N +5sP5Ih7wO1imJOk+BdIopWZbf1LRiYwMtZy+AKh6tnfeG88De1VtrpP5jdv+ +QPVObThaR88wQ+a3SuOWprfvMFpZNzTW/DwGpM94Bgj4D8FGod21ya4jSORu +643Od49hYR1H/aqT/8HPqUX8oH/4CfRedkaFfxStp6ypsnlUDvpcZbbU0D5o +fXRBEAzG0MjAxy0pxW3QL86pu2GhBe6bv7koe2EEiQf+6VoIGYRoVpE7koXh +4FG41Xu3WTs4+PXeyVw+gh56PU7au6vv3/v1//g3Bbpm03kk/m/9yiPxD13f +/BNI/Nu4l+wkz5WVqVqFz0Ut+8/rk+c2WD+pNOT+CBuSI8XdGG7IL35OAOEY +fJ70f+yGgzr2H5Uf7LAm/VfTFDUk6+4ww0N1XHdQipppdbfW7OgrMj6dGuo5 +OD5IxODkOzI+u/lvaZPxvFElWtTyPAapWg74kfF0LWt9Q9b15SpLwHUNw5yc +78i6jqmzNSHzFfbhBV12XwA6eK97gcxX3spsezK/f34Hl+WJeCCFnpAiMr/H +NXdokrxxXzPp8pGZO2Ck1HaR5I3Hce8bSfwQjb5rMmPskG6QwjsSP+phmXok +3tKertVMULBE7odOGpJ4e3lz/jbJSwMenysxL4FhW7YzyUv/8LzsDg3P6B+e +6Vf9oOFf/tzAGdlSHUTvdYKG/0EGfxrvEdJC12zYjWD9rT4a73HY2M2Q9fVD +USnmlp86eiOzM4qsr+qMa2lkPU6ldn7A9YgyP/gLkPWo2TV4lOTVa64MBUky +V8H2p5sAyav/r7zHeb9jOzfwAY1JdbwyfDyBPv3O+DF/IhckmqtFSHtL4/tK +bIeui5/Y/mJ7dvy5a054Tltd5rKwm94FCU6+HbTDc5qQwINeri4CGp5IRpyo +MEGuGz/vvW1AwDHpLWVfuwn0JMAnbyRbCc5eZU5LwvNVV7zB1Wd4vpLk7nvs +Y3EWDmvtav+O56vk1Q/NKrBeNo+O/7H9oTuq2T99kBefF9TGxcX3qhp1ZXJl +rFRoQBeTTjQzVU1AziP39aQ9rINx3SqFBmhIT3lH2i/kW880UobRby1Gh85H +vWjs4ZhV2dsOYDX+I5fsPgmCFjmSA11W8mKycKLD6TU8i08qm97QhTwmd+TL +h76C8KyzWr5yY8ByUNCYrCPKF9cAXEcQzPwolayjP3yt4cq9VOB3l09U8v0A +a1fL3IwxH4SxFDVafK60iDjupHeB3z9bafFp44+nxUfLgeWCYoUJmAt8osXn +596phEYcn737PA0xBKGC67h3DY7Pu7JiWhwY18xbbXvoDtnUlYfIOKyIeBtN +zktH9pjr4nkJcQZLZJDzUo/Pg88kb3888b4Y8zY6+4U1l+TtUfbrVgl4Ds1n +1Ilm7HdCmoOuZ9VTCYjVmaSdy3nRREOt7SKqOHOMdu6RmIlKATwP9z99ckZ2 +myASKHf/Y43tehabdRhOfYbWsxcDVu+uQQlHYg6Ou4/BL4adDbd/N4Jj0m2P +N5xNyP+DSp4vywREWTn9YvZ+j8SNBHdcLm2BFkm5UwNnx+HSbxAMXVYKuyM/ +pvXYEXDIWnzeOJgAVp8Tc2S+njuMmOB8gdhMiCWZr1cuY2nvdw2hGxJBl3bG +DQBrLIVy1KHvf+IK/cPV45JF/9mM2Zd/3SoILd2L/rc4JLNt6CBAuiPtzx+B +68hYUssq2BjXrzlTVxue2y+sL7y2c8ANOdRq3GPE8WKqGqHlN+CMbDrOL6oY +ULYm86vkwCtE+m+5aXcy9h95MbfQm2D/w7sSLe8lYr2y570udb0zeOxUztFL +JmCfkZPvjWSM5xvaE3vwXPqwT2fEBq/Lvf2Itp7rlvtmynpntP71Jdr6rBe2 +i+tb03jF8Hz+bP9V2nr+mXBOo2ECdu71+CS+3AG9+zHnU3aZgN8SjmuFpvFc +f2+47meCLbqcFPS38TwB3xdehNYtp0JmQWtf12Fv9FROU0voEAGhHMpNguxU ++O4nkzE864FuLItvVt1NwHXbolxBMSr07lKJ2Todjjgrq8NN1hHQSPeoaud5 +KjSWV+eWPwtDGVYjgeMYb08ieW9cc6BC3RvvCjX/hyjp6LZLLUUUSDAvz7j6 +ggqGUV4Hds48RBtFL2XxWVDgSJ32o/oqKnxi0PASDX+B5rMGFUt3UIDNrEeX +QXMYgqvdXJYVV6BYnlZ7UBmC2dQ1h7/NxkBtc5uo2UtJ+cB9qfkh85PQe3Y4 +hsTDrvZRY4wHFJUh0k/i4dnZz2nk/iHdBgZ4f2jv+HSS3N+P/5JML9MwrPsz +uXr2cx5s0lZpNp0bAmeP1TT/x0PnhrH/0BO3nub/vZPT1UecqbAiuqKiyikW +qoV7rikWU+C6pnUOGZ833l9lcXyg5ZLoPTI+jE1a0+oiVPD/K3pQ5o0fvN7g +XhDCSoCqvHkEGf+mLZ6ZOP5gWBR9jYx/UEzk0OwCAeldL5VUKY5g+OLS7uuA +89tlTqtTJZ3r8mv7nWBtljetTidUu9nIvNcG28qKLXeAtTxv/ci8s/bGa9yk +ECBwR8v+g5AVmEZ6ifdc/b9wDv9wLrtymXgU5ttdZy3jXHJUQKKlq4H9OgHG +jKtp+NerCU8QHnADRhM1Gv7pKw5/JN9JzBj3LCsILUCfrt5LJt9J/oeOQ/90 +3MKqQY+apgFUN74+npL3AWk0xC+fVh2Gc2LtpeR7UV7aW8G5xEKwiLTkJ9+L +1Ews/5DvRazMvAwqW19D5jZHOfK9iFi1IZGcb4V8+Ffg+RaElR7nkfNtZhAd +zf8NozZcnjkqaFZz0f+puFZtkpdERV4+xrwEBhMaMiQv0TeyrGqa7ISw62eb +BI7IyS9+jsMzu4k3JF8Z587kYL4CZvnobJKv6N7tnCT5X+DWACeEvkLJO36d +JfnfXKl3OwvmMZcfzZcxjyHTLx4HSR7TtVzsXwtZ3dvuWpxFGeKL/euyvro2 +mZe95ZVDTUJW6PWj0j1kXhbOUfrJvNcv51PFeUfPD23aQ+ZdZtuLCRI/O9sD +8zB+0Es1uSISP+yH+mg4LKn4JlbtFIs0jBppODyunbifxLOp4sYzGM9oYciv +lcSzxcoyPbKOHFwdvXEdgczdG3ZkHf2rR7PFeoR/9dh/PYFW1ydyD3zFdQ3L +ZQdpdZ174xyNH7q2VK8fmfWAnXb3afwwuXzzGpJnzKgLDjMJtlC9Z3qB5Jni +lOXpfL8ImD7amZruZI8YLr3bFnOSgPnffOOfNlPBAI7bKa7yQSGdVkPTm3Ec +PE+cNNCnwibmjB2KPpFoYfjFe5NWCkQT7eUWA1Sgjogv7Od8ip5m2K+/j+dq +O5vY0N3qw+DevHG+pKsWHVjgYro3OAid9V6i9qs+oQ4NnugNspovFz/HQe0t +OyL3iWdtouB9oDRVkpXcp7LhNO3c4rtoBT4X/L4g2rmsp6smST+DDsXIYj/h +mlJOP+nnv3t9X7wX/LuXStC7au8+3E91ZxkEas2hOe0E06Q2AW9zyny4fQfR +Mf0hpzZ1E/nFzxG4wnX8x8WvFBTQd3mPeGop0jdNrQ5hpMJq3uKYDkYKmj3K +z6xGfYF+9N7SYuukQkZnSYkb6xBqZ+hjVHapRCyi9TUFd4fhbWOmnHcvAabp +z6zaT9xFRZt7pll1CDggXZPGMIp5KNozLbnQB2WFfbOMuIh1t7jnB/0vBPSG +culsDXFHj0UtBbwuYZ53/Hnl0TgBnSlH1A+4RaI3I2fZZpTwPHeE7UDxcvJ7 +Kyk/XwSGowC1rrjPMnjdp/etl1ZSobTy6fT43kDUviUnkw7bgwMj2Zx+YJ7Y +U/BnqCgF2dt8k0w5innnrojcu61UWFfaEFltnowG7B22R3BgPXh5+8liUdwv +OFj83INjUTpllncB86dgEj/fw/cEZL8ocH33NxeZFx04YaCG540yK9V2XBeb +JhhWXD6Zj4zkTG4EfaXA13bROndtKowupy+Szs5E6+fETHTeUGBzyHel5GmM +o9yefRkcZajuzl2kvYoK63claFrgednEPe7+Tv4aNO1TciDbkICHsUbs/duo +kCdXs3CXtwoxFYtKmqVQYGh958xs2gCyVunym12bi9SVR4eSxkZA1aKOh/Rz +xlT5GvYTzMxWnyL91Lh1RoX0k1JTNKZ2Mh/PtWOWpJ8fB3tFfI2owPZo7Gy5 +YRE4VBQoBj7Cc9pfhfVk3EJeX9tCKUoB+9di+8m4ud3TkyHjVnNOYi+OG1jW +VAqTcXsd/zmQ+yQVymO4nudvSwW7tCPPesawns1zukbmcUDSwwbnEa435rCQ +edzmZC5N5pH1YksnziPkfHSKJfNoQOWai+OmwsVxfXMN1giYSSwt5xAi4OKf +aXkSV2OjL+IxrqDWKXjqv+OKZRFX8A9XzPOsA/Y/cf75HZbNa/mAk3O30kdF +PK+OFRqzthCQ0MFyemKZBxTPGVWpWmB+vqKqe6eTgMjS2WofdSeQ14/ZMIh5 +0vH7+XV+uI4a0pvOrtnuCKPU41yVuI7Y9z3a3oJxW5qjOTv/3hqVsB7OVcO4 +lTMZuPeEgQpDa3vz6Qxckd1Fu7rL+/E8vCFoyPgQFUz+/o3OnA9Ee+Tjv+rS +ETDqz6NIH0MFdefWKKdrSch5r8DW+WgKiFIeEnX7h8Hre8yNbMlitOB5L9e8 +YAgidhmwX5UioFl8or3/9CcUKBpZ5jo6AA2aMR8uFX6BVmH9uaeHM9COtRWu +YSH9cHdp/Z/F9XB3af2//RMW94d/+08u+RO26A/YL/mzesn/qTma/7Bryf8T +S/eNZaDdFyyW7su5FJ8fi/GB50vxabMKYVv4hOtJWC9eqNAAOGXSlsVjnNvx +F8Z+HCeQ0oJyzk+LK2CV+PvlZRU8/3/26HrHTEUs3Gvp3ZcbQj48mzkqhuuk +jXEt5RQVpcazppVctYWdv/ZO8WA8ux1fr1VVRUWrpqTXriv0hYljWpVqNyjw +5fDobs+xYbS6asX2w6tTIf/eEH8PwxDsu/h7ak/5KIp1drm+Vb8BzuaGx/Cr +dv2XvXPRjuSW7GNL+3As7oNyl/bxWjr38ATtXDS6dK72kp+Ri34iySU//92L +m4d2L/TvXqZLcTi17AIZB+SyFAeP2Sw5//ctYKYU+YBVaAS6b+Xb6G/th9J9 +4xxWNwYhVMJ4U6boAJp4EKrg9bof/i6tv7C4Hg0srRfjqgu/9YVAUrk2Aj9D +tWDv8QaiAedFJyzAQZeC7SfY2Zn3aUCv9xWj5dewvgjqX9s0Q6A6t2zJyIf6 +ULeR+wcLrqMFwaRJrjVUNBS4Zw+l2QTo6QrDduO8O/GE9z+ioyJjifLxSfvr +ULR1bP2YPAFUMR+tuS1UdNWihDfIyho845TzTuL+dbKdlWs3UNFZhknJ/Zcd +QAIF7TKcp8C+/FXNWXupyPlmB+Sk3QLrzMe1NUwE7HpsGsdkRkWK+3O88nI9 +IGmqydOokQJagbHZp59SUdHvRJY/6wPAz+CE14IvBayVBteF3aWiklYLOqYz +vjBozpjMkIn7qYSmdwPTMJqLOVp3TzAKdhvwclG5KcDrrRTxPnMYHb0iskKn +IRXedZcgbbUhqJpabe14ZRip5fdybdiUBCFcYCv7cgi+nvw8uez5CEo+QIlm +mCuAe9GuNon9A+C7otw98OQoim4IdRC2rYUy/vp200u98K5D6O+G619QEFOg +nEFGJRyfXdhg5NcPM+si9YM9R9Gli7ImbL8/g/98dHLl6HvgTRJ6kjXaA8NH +hxM+V4/Cl5SDqwtXvIQHyYt2t0U7WrFkV5GSXqj7+AXB1wDhOekOhHhFpuhY +OuHr0v43F/dH1kv7f1jyJ3vRHyS75I9JUu3aMYwb1SgW0xTpHKT9QUufI28Q +Zpfu+3zxvshv6b4VS/FJXowPCluKzxOtAP7iT1SUr9F5Ne5+OJL/w/v+pgoF +uJbiv/k+Lf5o21L8VZbydfcjLV9opcVivqwOiDPRX6Kinwwpe6KXuyFN7fxm +ToICO5bwULOIB5SyhAeFJfzctqXhB+ks4efX4XCV5xxUZBTVo3jfwBLJ7Ht9 +lEX4/8In+odPzSU8n13EM/q4hOcda/dKXJwm0CEv89Y/f3URX2H5tXI8Z/It +1UueC61eUOlSvRgs1Ze+Eq2+0Oel+nq3xIcvd9L4EG1Z4kPGgzLGJ3qwjg4R +9nxdaoTiXCQYjuhhHbWuyXpZF4F+iMmxpX9Wg5+OHd9iDfD8kxDzaKqXQLzn +Aun2yV+B/freBZG4P1bw/Vxx6lAbWiPFONDBMoAIrZPV+8SGgbpkN5Ck2eGK +9qLdRuLZkfuICt5a250emLVADB3n5pItg7BDygq+2eD5bvp+Hr9pA7BlmizL +PD0Id8y+3rAhv788HHHfecEI6hB9LTv2U3TJT39xmp9oZMnP3iU/HRb9RGJL +flLbt7Rex/1XZM0vO9U111HcPNM+GaybPJbzN55/g+fqZ45dXyTeIq/Wap+r +6wfBdqnfWS32O8hc6nfNjHf0yiYI8EwTTpDZYY1u3HyQdvECAT4/voevwfPM +BdGIl+sTbVB0v+nt1tMEZDG6Ltdgwf3L7fDNK/UuqO3Jz23GewnwF0LMe3mp +sNBN+Rvj7o5ClYGbfBfl95swZVOkQu8Yo3akaBASq9O3mMF87nPKlT1KA+tr +bqbdvhmhSHP1dFZlFwUYIldFcxZQIXhZJV/17mQUU8/bmHibAkrvq9PVeqiw +f1NTWXbsQ1R0qO6Q3QkK3JpKl8ywGgbjch/JaasXqJ746RitNQS2dBL81aXD +EGp6r+HpXCXyCr1dvLJxEFamVtRelxgGt4NKg8dX5YHyanUYbBmCQb1j4ld4 +h8FAu0T1uOZTEM22fZzxZwh4fMPuzAfi+R0tk75xOgZMYtd9eZ1GgXTnQRZD +RyqI73qy8X7MPQjSUH07+IICTy+dHI+SpAI34bNqVOUOPMyLDGNhwPrqfZ3V +xC48t/AfV1jw8YK7xW+dbrBj/neyOeK7ggosH9XWVP2yh00qK4cqDmKef+6j +IvyXgCc8qmYFhrfAq0NAXOcIgX9/zxexYQJsi1ccFY80B49SL02OK3ju5bCV +2jmE57Eu1xe5AyYgu6Y+SUaDgK6c7W4nPxEooNN89bOrF1BZg46kNp7TMp8z +SrgNEnD0fGRdwYgpOlO/xoyC1xstnXuPk3Yu0l8613DJ/9Vbaf6jsCX/ny3F +YXQxDsh1KQ49S/H8q0WLJxJbiqdp3BHhkyHDYKcwXceSUQHTrzem7OUagtNL ++V2zmF8oW8pvwBJO3i7iBC4v4cR3CW/ve2h4g/AlvAUt4VZ4Nw23ELKEW7UO +0Y07Lahw5Hv4zbrSLnBul30dZdgHncN9M5sHCERpHchiitKBY8GRA5e1CPiU +V8CUP0Gg5ZvcNVkTDUFZYc8uS1wXx+rXV4nNEqj82Zmw0wfNoGfKgjngGJ4X +vx6vXGChoggOH6HUxzZw0FIxcGIP9uccvVy4EBUZcDksLEt0gJJdGuOqPFgn +XNQ9Y3CGiqQfeoRPCXrCKV779r1TFDh2oGbfF1squv+jm2l7jj/MqYeuOVNN +gTD75v1jeF46lPooXPJAJIgZpo6qm1OginKLMrR5GKEvbvObu5OA4Vz6Wzc6 +vI9fyNPkj8Ooa+gnl/fqPBj5+OnIZtYhWJtNt5shdQSpHWsb2tJRATaaV4/F +ZQ/A6+tKFnuNR5D5lvia5P2dwDT2Vs8vpRv8Td++9cqvRClByu+CCieg0qet +KsGwCQaqEjtJu99xhzpsR0bVQVTS/iay2DVsaADu6R7J2E9Pge4NFx8NruuB +COaRxpXHCWR+bdZDVXkQ5fCkCxygdoDWkZT26V8jKHRoI5OUdgu6FbFTtO13 +LwSGCguTfsbrfKBgP9GtWevjpJ9ZENP+Lm0YzYyLPvX8kIkOxUs9GVQZAgp1 +5QAZB5kfW3i2dCehZdHeTWQcBj7whXVmU9GsnF2AXm840ncWOMzhheec1afF +yDivYw/8I5jjj8oklRnJOOdRGl9OHqEix8TzD+qj3dFdnXaVU38ocDg2Bcg8 +Hvx2tYM+0QF1c8Z8IfOoP6DnPLIW9997QQknNayRIneMxSFJPIcT1TUkTl53 +DwVhnKC9ZY/WkTi53pAnlDlKoKo0E5OyqwaIVypgWwDWX3yvQqRi+wloORX8 +QEHTEDW/P5/yGePwoX1C2plOApW1xkQ43L8KTNt1WjUxz3t6K9mTcdatYi3A +cUYqKb7xZJwdB+JekXEWfuIWguMME8Q8DxnnzIyXhZYz3eg8dyEPVzGBxrTT +BaXa+kCidubcq4BR+Ng3uyN4Xx9cvx+bWcDyFHRWNQ077xyBkafcJfv0a2Bi +duUpB75BYBnW1j0hOgJemz5krbFpAv8PN4XSNw/AfTd7Ty+GL8j69IaQL171 +qEM1ZkFavx+4vVgDRHJz0MYDodfKWcfBRiW4MMjxE4TYLdbdvR8yA8xROiho +82LdvdZuuFsVPAxRju7DL7w/oj551uz47f1QFT2mQ55b3hP7Cp+LWO+4bSPP +/SCu5UGeWxLP8hifC1Trrr/kubuvaIaS92Xh3SuB7wvU97zryfuq3VccqsH3 +vX9VrwvfF9V0jx4n79ttf+QR6WfpEw/ST/SlWZnm51qdmh8ruwl4r6TGMcqn +D4OsXSUB+gTEuUs+dOgmENfwl4XQVE2Ut+L3pw3YbpW4uJ6d4aXbFz599Ov8 +/7oe/q0/e8eydegrAZcHDP0+F91AaZPvL7CfI0D7nUF82TcCfTtcueHe5+uQ +VTKXJHeWAHrjDpv3XFSoaqp+ceurI+ovzL9euIOAmW1DoTE8mE92UI3fztnC +quuPC78KETCtfG+X1GUqmKnSKXi13kXn3ysYMw9S4HX6M/eMa1Qk2uLKNbjg +Das8zmoX9FCAyt155207FQTPrz9qcDQJnZdbpRh0gQJS64wc5QgqmgpIjKgq +vg9Jne9lsxUoEM1bv5mpbxjYvsok/Xn4Au1VtRVtax0E0eHJ3Zd3jSC5MIcT +Xm5F0O7/QPtH2CDwDBcEWp4chkcq30XE1TOhg7tiF8+rITAPflv60HAYXTk4 +LfgzPQ1tLj8hHv94CIrO8Os8C6BChHjb7ky4B1v/GlZIZVDgzlFbc+MIKvKZ +v/hNuTUEKU/Wc5YlU4DlQ/Xcb3EqBL16oP81zROiZCRvrFqHddANXd4SSSo6 +fZ8rW2CTC4rb+SlSFfflGvZ9PbfpqfBh9AnvLw5bKF97bMuULAFabeePZS/H +8dHTvNF2yBJtHWM6gw4RUP/qwYMiAuu/3qAHPXTGYFd22+mBOgG+yzwZVKgE ++hwx49KRpId6Xt27vBzbX6i5nx/uIEB+WDsudIcusE0c8anA9Su9/enz31jv +J9q1/hJWM0WtkZH0slhXxgyqJZH7X9L9+amXzhg18mQ7kPt3j9auJPfn9Xta +0ZmkBx27ta+S+5eXvj3ltoYKW2zv8B8zsUP6ORe3JEsRwJK14xN5r9NFrb9+ +c9iioiizbeS9gloeHCHv5VC9w6TjkCUc+dp8jrwX45Oe6Fh5KiQ3GCTCJR/k +G9UsE4x1ZQzj+r9kPC0D/eNxPNHd0GZzMp5SobMbyXhKT+WGb93kAgyt3BFk +PG/2KRuvfESFv3NF4/tZY1C+Mod9VCCe98Lb9Mk86vFonMN5ROqKamVkHk/G +GtHyyM5ns0mlNQQ0r7+k5THZ82hCgfMw3CkYlL25kIeMpxPNxByHgFvU3p/E +j9GMGQ/GD7LtfihK4ufr3h9lJH7WBe7YivEDJX9e7CHxw6UfbmSQMgy6mysb +Dog+g5pvQc/cDw+BYPTvTSRuhZbtD8e4hfEVb/aQuEVv1guTuL06I3IK4xYV +t8zokrgNau38bfccz4Es4pm76ePw/eL4jO0p4PWXx4+sl6HsXE5cLzByrurE +f6+XmcV6Qf/qpanKSePhSSqUpi9ciFfyBS7jv3pd3yiQqy4gQtZp0/HlHrhO +wTv9jiFZp0KPwYus07JKtyhcp+hWdLAGWad+6JyCNTMVVhrFqtBxOMB6jvUd +9mIEHLzRRuOHj+vEfth9dYTRzpz/gx8OLvID+scPO5WSKqbGCfhgIFos+8sM +dL8dK9yjQkA63bs2kpfGQxyaOopuAAvXDWWSl/6AEY2X7EQ69MI+X0d5W//S +eIk9v3mT2B8CjJ2dvzl5WqNC6pU5v+MEHBqXbtPeRgUYmZfsDHND+3wLAlx4 +CSh+dmT/ZksqtOcV2tVphaLzL0Icpt9QIDb2qPi1tcPg1dKyU/HAI5QV7rtq +PQcFMjWUMs7hfmSrEMKoZFCDegOmfVNxP1LqN6StpxfhHzh54BHkuafR1ovJ ++R0g919R+FEF7w/D0gfsyf3Zvn5uJ/3pfcsojv2B8IUpP9KfU2OtNP+JP0/8 +HD2t4TrrNZr//R3v6Mi+rBE2R6HTNoRztfEfyb6stkb2zs75STC0TjJlNHCS +f/Ek78XuX7Hgue/vwsLCJKya7Hrg6NQmP9MY/JU7UlXu+6eCHVe/jyO/7Gs3 +LDw/wp6tDad96d3+n9/f+P/LvqHs1Vby3ESjWD98LlKzDj9Oniu5t0WS9wH5 +fVL2VZsaPZAUC8vq/FSs4wY5It3S8Zw7keLx/o87UjrYwXrpPgGyN2sa/VMw +X8mnnw1J9kaMc+ynNiYQ8MOdkqqbjfnwHWf/CglP1MAloacZjueWqla13CcE +sIUGaVEO+KIvCgmr6yIJ2F4/eWKmCOue1CcbkkM8UXbVZ85n/gTmhSuxs88I +YPKMGE4f80PPMi2clMm/gyDsfOxdBdaRuqYT1lEeyFt9n1+rG9Yp9llHD9QQ +4NLjdM6p0w8J2EW6TTsRwNBz9kBPPQF7nVt3tBW7oMpXp2wrbuH+++riRu5W +rJ8YEvaZLb+DFN0+ZdCbE9CZL/OprgWf8zw36bezLTpR8aSqA9u1x5dnfhwj +kPsl+4wAbkN04W7Y78uqBByo5+s0HiSQ9LbyPZm/XRDBe0OgDOsm5/gnO269 +JVCsX7e5LYcLOquUkySMz92YNrOXt41Ad14a/fWM8EE+QjYPl5nhOcc/mN2l +Euv6D2G2xdYeiJUtxnUbvpfLdbHfJ18R6NIy9SSdUj/UICps2+tIwLdr8Yb3 +nhOIT3qd2h0ctwsaZcVcOG57DDvfvS8iUM4pk7Buen9kuuIYrwO210/cfNue +jet0f06qgqIn2i/1MZwSRsDVWIGHh54S6EPHX49GA18UdslK+SDOS9bVK9Sy +dALVnFDsuM7ngXxGJJm5cN7DFJdHdaYQyPb1D+aWD96oEtlk1WHcBCkIBYnh +3/vtyJZQstobaXxXH3F4SsCco1vXGP69a9+H9BfssP8TUvcc0whY0/Ajwgfj +53w8k1iaQhAyeuyw3Q/vk7JnSsYtl4B30jLs0o2hqPZOT5tACAERflpGtTi/ +qv4bkP2fMFR0cGqPJY4DW0/mPtMeAurCVn++xhyG7g0VMfnpEJCmeGOinJGK +tJMqtNZw2qBN/IdbVfYRcJz3Q5ToHwJ5d1qc9kn3Q8eLX79+h+dw+ev7tY/3 +EUj9iklsUE0oosv4dDAX1/XnfaX9lq8JxODiUK6Ez63/M7ql0oGAr116a8Lz +CMS+NdJ3dCoUbec0oKwKxv5FSolxk//PriD0wzkqCP3mzMqYjMf3fHWrRSSW +QKtucQZaIz9kfruwVQrH4eexcwUiGNdrvx/NbD3rg9rrdPiv4nroCJf1PhdI +gIMNGwdXcgC6eGCtwPsCrK9V7cK/4npS9vrmINUQhtTPK7/3zCRA8jd7eXQy +ASs3VVdRLkehkQNdxQP43JR1N3ttygjo3dXbFm4Yi5i2ztPXuRPAq7huTwOF +AJHtj/06X8YhXeNXfGfUCBh4ckF46hgVDby6vuz+dQ9kxsf8dP0MBewbN55J +4aOiI78MlbPZoxCPZZ7qHn4CmJN0/9qMEGjHY4Lx1I04NFvfvy0N94sf9XlP +p18S6JDqbPed6FjknIPiJF0JqPXMU6vH+NmUq65fnR6F7iy7OBUXR8AClPLr +RhDIgs6c32l9OAoe3yq7Gt+Lz+9Dj04ggQaT50/vWhGINlUoX3iG4yAhvqPa +xhnPy3ULslVR3sjcZX3ibDUBj2q/5QvcJgA1mdW43g5E6w08KCWvMY/Vak2M +4bw9jnSJSZ6PQBxCGQqdrwiIfn2MTsID85DOFnM97niUqT887/uCALNZJBKE +4+exI2fyHk8qMvcQ4k7CP3sJXtbP6SRgeM/ul0qe6ajzVmlrylUCUr8d2R1d +gHXiiwnRxNkIxG1vVxvrQoHOctuayJNU5Fb17eDZNWlI0iGQJ2mEAtIh6WN8 +/QQ6Oko9bOGTjtbbOJxZhfnkDyfjy6JEAtF9czoabZuKeAR94nfg+qnfaeu5 +3JNApsI3y5hz49Fe6e4e/1J8H5vl2oQDgXqSxnbaat9D5h1erPX4XhRJA5V+ +bM/5cljq3FQgur3mNPMUjgMDPaf1LwsCig6N8wu0uKPAa8EvrZoJ0C28meCj +h+O2m/eYVZEf4n4WT5HGukVL+I9EG9ajO4IE+H2mw1F8yp0v9iMEbFj562HD +SQIaZFnBRS0BiVnsnOH4RkAf2wfei4oEKKklKMz8foxGNu5KnsPrzw13y3fj +/Ce/MDq9800BKqJ/j3ISCRjJvnZJP30Yfa7lD9N7mY3UNfyjrioNwQ11uxPx +KlTUdjzx8cHhYuRn+seTNZcCB64+EDIJIJA+p8crEbVCNL25XmE/5rEa06bh +T6cIVJJ48+GTngxkVJbxxJNKgKke3xaGkwRa2Jd6ZbNsIlIdTC/wxX5OFgXr +jaoSyGBlM+sd3Qjkl9V07Riev5VGfpc06RIozWzfic5d/mjzqjiuQRyHgYgb +B27h+LxwLduxT/om2jJSrfwX27tu13J2nyfg6NsPDwhPF/TmIJPz1BQBg/1l ++p/I/2e7FlvGr+CHqlZ9t3JgooKUVO0JMzoCbmzr1JbpjkTB94hfEzJUWGOS ++3hNDgVUzfQCX55PQy4jgUJTLlQoCDi4aaUEBWZCjCunr5Wi/JmL8zIvqRC1 +K7AwxWkEPeGbPX7EuAXdO+moKIX64MJC/G7+gSFUbOY5ynnpPXo0czrbEvc5 +hj2zmuuEKOgXb5diC3cJkmkzOr/9PRWmkraZdadT0D3j3trnSenoyAOn0aNe +VBDKfHP5yRwFEXTW5dW5UShMomPmlBwVjn5ZmOjcQ6CNEz71hoQfKn03lneV +hQrF/GOiz84RKFukyHqByxVVNHntYsLzInfKMo9lWv/5Xmoes5PJ7QH8c2jr +n+4T/7Fr8p/cT/ebgJABXZdZ/v/Y5fMkC9w3UWHT98gtIl0U+Jq3YuuroAMv +A2+UyCRoUUHA7cmZOkUKbKUvfJx+QvLlQGrs+x0UKsxHlcrfihuEyRQz9tCP +UvKhLkxKPKdH4JXM5EwVZRye/orSVZ6zkB/3Gdzd/P4jUJa+Z9K+9D2T9qXv +mWyMrpZTaBtEewecf1qv0JcXeG6e37VxBKxZHD/2H/ivv7NBp33jWsXu71S4 +f9Em0+vjf+w3Q2xbqfpUePttq6f15v/6exp0n15cz5rYQgWLN6unvI//x87b +N15yHs+dDT8XpEm88WaEnhaSvgn08kZKJN7udn7jIPH2UHDjrV5PFzj/aYGG +N3U+BhrepFnvHd+m4Ad1V+2tSbx1nNc+SeLNR+7wzYPdkTCaw0nD25bw1xkk +3sQv8e3BeIOaHIogiTftlZ9oeLsid+sBxhvcljGi4U0jz7mAxJve8JwSxhtI +i4ifJPHWxOMvQuLtrZtdP8YbtM3K55B4kw7v+bJ6LwWt5nsgJV9dBlEU3ROJ +RVQwU99wk8TbRQHdp0VJ6WD9/BiFxJujXIomibf6oD62itwoKLCS/EbirVX2 +KA1v7Z/kDl4n/CDC5m4+ibcTAca7Sbz1zFPc1nC7QufDit0k3hoE1W1Ifls5 +eTJ5U4s7yLHeLif5LdqIN4nkN+v1vlUWRX6gu194iOS3m1y+0iS/zUl0mnlP +h4O8myxB8tvEo0vpJL9JHwxzwfwG8u9qv5P8tstMnMZvHN7r/DC/gemb2zR+ +G7p1F0h+c3PYLI/5DZIMlGj8JqsmrULy20kZ2xjMb9BseS6W5Lf++sljJL+9 +e1bcjvkNpJhee5H8dig/fwfJb3CqIgDzGxS7+Bwl+e1O6csvJL9dO1eYkvH/ +0fXl4Vh13/sqVCIpUqQQDYoklalWkSGpSBIlVCihDJVknoXM8zwkYyGZom2q +SIhQKTI956Fo0hz12/vp6X0/r+v3/eu9Otd5j7XXXmvd973Ofs7qywH5l69z +SH0rso9g1LdswbBoQaUU0AlfWULq2w9ZT1NS37Y4XeL2Mo2A798vGpH6Vm9D +KyH1DT5GNuP6BqX1VwRJfaO6j9QSPJVU7q2qj/aGMo/aVIKnT9l5bhM8HT92 +ih/jKUT1Og4RPJ0Tqs7AU/2Ll75hPIXcqVwGnqYohTPw9MzzD1EYT+FJ41UG +nh6P4ZUieDrX3+A5xlOQrh/iI3jaICZxnOBpzYYf3zCegsOewi6CpzsedKwh +eLqOz2wXxlMY8BV+SPDUedaSWoKnezUytmM8hVXSgssInrrOUn5D8PRKqa8y +xlM4sZ6mRfCU/S1HDcFTc3munRhPwW3CN57gqYjIch+Cp3ZBbJVchYkQfybw +JcHT+fNCjxE8/fLEZ52dcST4ZFvwEDzlbC3ZT/A07Z7f1n3vg0C58sUCgqe+ +opdLCH+7a1G/B/M3sHilsILwN7a6H76Ev1UX8bTzpQXCCKW3nPA3ZeXLUYS/ +3VR0Hsf8DW7Tt7YQ/rahpgsR/lZQt3IFpR8N2pyzSgl/o0ybBwh/E/0Y/xrz +N/B3i2Uh/C1e+RGDv808qpWC+RusuvpNgPA3n8ZAScLftryqUcL8DaxZUq8T +/sbNpaVD+Nvb7Pu3MX+Di0miewl/m2ub/JvwN+pCyxsNmwRoaswSJfztxOBx +Bn+79pr1FeZvkLeeO5HwtxXjKwwIfzss1q6N+RsIXBgdJ/wtPkFiJeFvsvcz +U5x4wuF3f6s84W+RSjNfEf7m9Vvn/jrWIJAwfqdN+NvWTZ8CiV7guXKmtHK2 +N4QbOb0memHNxP3nRC9EnM+Lw3oBduiORhO90LdJNJzoBVHOpkKsF8ARlNcQ +vSAg1CBH9IKayqgx1gvwYt6vbqIXmkMcThK9wKkcNor1AshwPJMmemHG6ufS +RC+YpawbxXoBfkqHcxO90HK0dpzoBfUvLyo5+Oxgq8o7hl7gWPErguiF+geS +r72v+4OYUVkT0QsV5cmGRC+wrG6Xx3oBmualANELLt1SvUQvtO/pmsB6AYwk +ncWIXjC8M8xO9EJnTcbssfeh4LeklU70wtH5dIZe0L3itxbrBTiyiJOhF6gn +e7qIXigwKPxig/zBMoTzCdELIuXfNhOdXjO/xgbrdIguHWYjOn27qfpjosfZ +hr3OYz0OY9ZX1YkeX2Q87zDR3WZleWuw7gaNX6fZie4+/9AlgejrF9yS1Vhf +g2uthhPR105n6xk6evkuXaKjYZuCG0NHF8sPChC9vDdxnSzWy9CZq5tH9LLi +7KWFRBdXHDDl9uc3A9n7Jz4TXcwf5NxDdPGtbQlBud9dwL2VS5jo4varhlJE +/17OUZTwivCBp0q8WUT/nvw99IXoXJ6hymTTSn8wLrG6QHTud8P0ZqJnLz5Y +eQrrWdAychckeja2z/Ma0a3rVm30e3TSD5YGSO0nujU7OD2e6NOLb4VKO9q9 +wfTq02yiT1dxLe7fjf0zNyz3xscMV+AL2dycgv0T2czN6G+wiHsZtv9wB+VV +Txj9DdH7g4w+BlXvs5dtkycIHZNm9DE4340z+hWhL0pN00I8YfXYc0a/wn73 +ZUZfYv77oIV20R6gcGkjoy+xTGM/o/+gbLxhe2e5C2is1mL0H8r7TLgUn1Oo +5YfPQ/c6Q1jkVHfbxoKCvOEvFVs6KcRVnZ40UGgPuqF2jVbYz5PchYx+gm6o +v44drwscKCxh9BPkNUIZfQMf50/ry2094Ov9OEbfIPRdJKM/sNr90gU/bOey +3yWM/kB7shWjD7DV4mrDLg1PuPa2ldEHaF2U5nMX+4lDN3VXxRUP9HOn6joe +HFfycpWOL/F/eX5Jz9z3wwsF7HqT14Hj8yrnkQAvnN9d4veF1pT7IItHwy/n +ReL4k7s3z6WMAglh6fxaQV/UvnQjx09/ClJ/tiyLxHjSMNUte8jSG/Fsb+ft +w3gj/1n0ZmArjisa1+ysI+7oRHLVgwlbrB/VRtCi1xTyLT0wJatzEnUd4toh +heub+fyTv+VeYT7/OJBW1n4ZCTd0+3GbUrBrQDG9qY1Cp0dOzrRQ8UKC1yar +A89hfq65M+Yp9s+ppYoruCe8UWAF6axgfm5fxm6G40rSf53wljRvFGRzrWgd +jv8ZYq4/kwoo1JRot9Zupxe6YGDwYVEEjp93Vr/mRlPwtUZs5+CgF4rVKtVK +x3mlMrnJ6SOuf2fOLZ3b2OeHdknVzXfPpGCJrwZ35zUKgsVa5nJdC0SeEWcX +GcRTcHA4+OOpEgroi9hrP/BcRYPpTjkegRTcv/TFognjCaec/ykT32DUK6y1 +ZxLXDU++BXc3zKGjhsMfRzL32yI7pbiD3FsxTmcoLe6aoNArvX1LW7J9UZu7 +8TfHPRRs3NB38sUzCuXHGctOaQejsy2nDNPMKXj+SrnYuZ5CavMWW3nWByNN +tR3UPuz/85qcvs9vUYh9Y1e9Y3QgSt96q28Xxq0DggEfOXJwfvkotGmd9UcS +Udu0jsRQoH5RgLMnjUKHLE/5Vwr4oA3m+9ffI7/nTxVatAOvI7n35GSJqg96 +WrN4y25cX94MJ2aK43psvOijxja1QNRvfevirCIKLv2U0TaMpcDKakb/qaVh +yHahmqcyzkMVhfDY+zkUFEac/5J7LBLlx3++tgrn9b6qWW2fcV2q4lVKFPwQ +hSyNuunHMC85tTJI95YSHWUq00QyfdzRTSm63pPfNBgQeH4/m4eO9EyEqq5z +RCKJ/UU7F6zDumtWk08xjp8PJUYSN5Vi0FXL/rWdRhREb8oK90YUUjD3vXPH +MgoFfPZ1noHzyL9fJcEN15lrX4+v1jwSjt7DnHM9OB567HlWBWNeUarrbuR3 +6SpaziaobpFKwTfDD2KNsTje+l39roz6o0fNIS3ReF3vNq9xz3ehIIhW3aNc +440+rpbUrq/D19/xTZXgfVB4zpOUkxaElt28yrcB5wl/ZlVONcb593N697tX +R6DD6LeG1F0K7vGtT+jG/vR18mi3uhKP+J3FVjoW4PofdmrfDIyrYoWHTNdc +SkVmB8ZKVuO8Q8/fJdan05HA0LUG3epwlLqv2uR4KA3e99m0DGylo1sukg0O +NzLQHvPlE66TNICOfsEiHD/7F99UuvA+HSmen/140hjnv0zgbH2cF6l6Wssf +Bycj1WatvmKMX6lxZ80F8XojjB1Cdapi0Mk5K87MxDglQAu5o32VQt+W1qw1 +2xKOTOctT5mL953Pdd+zjCsUyp10u/V5PBCtkogcOYfj5MeRWCGJsxTs8Rg6 +6azkgW50PzaAdoxPs/d/1sHxqyQdWp6TF4CGhuutzj4n33k4v20Hxlvj3i2q +U5kRSLgi01C4H8etxFOFLXg/93LV33FOSkbGpZpzRTDe1xn8dqvC9fJd228H +Z/Pr6GzNR9e1iILR8w8Er7qPoBuvHz+T1c5HPSXnt2d4DMOHI57vBYCO7r1a +ppWfdxuJz9gX/aiDBrlm+idTcfwfzRj3Xb/yBtKTDEhxx3E/eCDXldWFQjdZ +m9dvjMxEr3Zsul6E+aTUlvjTyXYUMm3XCfSxTkTtH1coPGnCfG/zYqmX+PoV +idG3D6gIVLGj++2zZqwjolYrcF6k0I7vxpcqLgSh3Z2CWo2NeL0XVioYnqAg +SehHgFWgA9Jy8HJdink7i0KfK10H15X768bKUt1R70OhXGocr7PXokFKnoI2 +CRdBtn1BKEhkxezVbHToNlGnxy/GOF+wkNu/OA6N64oF9qykQzB3l/WrMRp8 +quJXzNucg7oL1Z7s3UkHw6fhiqqnRlEz26HOnWfbUf/2ffIHTg5A7RX+wbGf +NFT5Qr51TKYR2XAZl9XZU+B6KoRjZzsNrZZcM1IlVo4q4084tGyhA8eJZS5l +ghQyuNzYOhFxHcV0a4h6LaaDeGWB3NGtFEoI2xXujv1jMOGhn0jOtd8R2521 +j0Kz9iwI+7wgHG15N3Qi9x3WXUKmnEdNKOR8PIe9AfxR7+/JuGOvKDCqdWQ/ +jOMhf6/T8WumCuhxSUO82CDm5SGCKeT84NhkffEt3oOoLuteeNdXrNPmwA97 +MVyfEs4e7nI5hSSUpa8JC2Bd+S71sxFFg7bFPiHm7C7oFatXZONBOjQseHWt +wJIG+3ySt+vuCkeZnht/ctyjw8bL9Wd4MD7b//jtkjs+gK4NiA/5qr6Euczf +GbEyf2eUzvyd0cWebRZntwyjjhpu/RyjAjScpsvqWT0CKXUlU49Daeij+u7K +8KxUVMnfpXU0mQ43h+NPDXymITMFmXMbHcLQzKG1QZ276MAZP958dz32W8eD +c9sxrl1JqPmYwkMHA3X52tVYF/PFtCT7Zl1GXdW+w+lYF7/QmdQUwfr3hsrA +Iu5wWxB/PNygh/NCRyLIrXQv5jny38KrXRyB13nMaxW+/+JBL7krkhTUhn2a +vL/SE4pzBy/PxM+/Ucy+svsLDYwtyp4Pbg2Gfayzf1lie54NnPjKievKw9By +0y1H4+HxnJPrd6TR4VjhyoRHgSOIdf/2d5EzXsIHnVXhr9j7gCdH3OvO2QGk +d9755ILSJ3Byn/3L159GYJbZSJy5yTA6Y3Boku9pMVT4l+ZmhYyAd5vIQIUO +DQX1pwZtfRcIpi3puWte0mEctG2e9NKQ1axNc10nHMDmhEHE2FE67KlZei1X +mEIN2sesXsUZg97854WNQnSY+6TUaoka1n0ag3ilKhBEd9yGvuN6cfaFMZ81 ++T1Xmbr7WnewWpLqr/8E16vhhFJPXP+WQ8Xwhqe+EKnz5bgmrjMRkYUGsVqY +X+wzMVs5FgrbWo9fGfiAeXL5yhu0jRRsftI94ecRj/Wp6iP7uXTYcr2G+9Q8 +rG8WBL7n4c2C156ew6Gr6XBmXUT34UYahP+0nuhnLQEBD+3Ctn10mExUunvs +3QiyfVOSey+oGOgaJjD6ZggEEpuKz/HSkcnW6tSZyXXQ/L6UPp5HA5/95hxP +a2nonMbKjdHVVcCxPJHrgDQdfiaqPhvspiGTCWn982M5MDPAtWS9Hh006ryy +Izkp9IP2dH2+WxwoZhhzXpDE8byK9aa0LIVu67ktS/cLBHH/Rz3sHHTYLVHy +c/1+Ci3ue6y67Y0bHH4bMRz1HuN4kpuKMtYHvHdFJU9LesOSjQu3SmG9bCo+ +YGOA6+1yLidlDe9AcBYtvOyHebCIn7VQMK7zd/pEAjZpRoAZ57JtSm0Yx/PD +lV9jHdD1o9Mv8HECfNYxXJP4mIKVRbM7w/H9MfxNb+zzM4G1uptt4AEFIeFZ +3k6tdLTNyEZQ80Q0NA7ths3GNNhxO36b6VE6crUyGa3TLADanvSs0Yc0OCCX +xJHwiEJbNEIe7JtTBJZyVZVmhpivDogLfrWikItKadd5lA2jOdrpxzEPU+A6 +Oex/iEJi6y6+a3JNAeMv45aGwxQY7NnE9cuAQokXVrza0hMBDi56y7bj69b8 +g/Ovn6BQIGf483MZASBrt20N10vMg2kXcycwDhtv11h/cKUPHHDuWRmB+fHK +02HxVfj6irN6rm8dA0HrfuMBI3xdnf1h1hqMJ5zRqclHucKBq5YzTRbzRcc9 ++lvnYN5Bz2ZL+DAcA8KabDfZsV7ekPo1fivG2xc2utdvZ6YAa7L2rUuYLw2O +uDc/0KajGEe3N0YvPEHv1yib1WuM70ud5mxbT0ehPIdOm4slgMoD48UmXBQU +Jdr1GX+kUM43nhVOWunQ2bNKX0oN8wehz6EBWLemJ/9eEncpDQKNvk71Y7sL +l7G+r8e6XqLtYFtEQgIcWN4xJIt1+J0t5gM/MQ7O5O0qD1KIhKaup51EF60b +dbye4kSh6HKuLV7swZBTWftoM46TgsSoLCGsG/atfPiuZ743DC0c2n8F6wob +x0SLxZhvzpeJHnze7g+HZ357q4F54SCndJoo1ikdb3vK1PKuQs5AHrRgXddm +2Rt9NBvri9xtIS4PwqGI+xLPa8zXv3mqmhhVUbBtV0wn29lo0AwTH/7gQYHF +3uWDPQvpKPvmrPcqivaguMxa4BPmh5Y3akTcWOmoX7inkZ8Kgu0rzts8xjja +sWrsznqsR0LeDEZrfomEpKaKzdlY52q2n1L9gnXrlEJxhszqGNC+dVOJi3zv +XVgvjJ6NdcTGTjObbVFwpshp5RO8L4Y9ls1voylUE+Fu/TUlDF6YeClEYLvd +WJOc7gfj5xs16S/qCYRDxz6p6xXjONzjJroT662EaoG8zx894NKVGJYArC+k +HVjsfTDfvOl/TKhR3gcqXk7NX4L/nfSqm8cM883syxfZPbv9QbOWU/sn5tn0 +JcKRS/DzbrTrLt5wMQimPgzs/RqMdUG5ThVgHkolrVy6RCME3tr+QDaYp3rm +c50wfk+hMo3FxxXWm8PnB/2Hbu/H+5tnbj80SiGbkY83I+d4gBPfghUzsC6z +fvpQNuwlhWZsL1YsbA6ANvbjekKYr2zTXT5TrRHHVSlvT+Cbq9C11sjy6EWs +6/1FdEJKKNSvmXBVZV8IHBzPEST6oUNk3yHNaxR62j8neEZQEHiPSC1vx7pp +Yc3ehZIJOE81vQv8LviDQch+dkWsr+x5jwaUpGG7OqIfUWvdIGnskKFMCgWC +ib7tkuT7qPUuoYvSPYAl1jQiBT+nOtTBIRTH1/u6/on6Yi/YHhgZtAzH3/7J +RP1LmIcu4+4vv2LiA7sOa86Yj+0pubb5h30tBayT+z/Hs/lC3ESR/RjWjwX6 +Dkf0X1Do+DDVcrrrCJwxC1+tTuYmcPGyCmH+3JlkX1iZdR7O9kx6W53CPNNi +7c2HjymkVWp753CPO/iUtlhdw3WNfche6WMDha4u8BPmxvvIJvEw4Syup3q9 +/EdmlVOoTk6IXeaDL7gvzNEyx3nnL3+R5WI+hR5cnV+RcsYXDj8OcObC9tPM +DRl+KJWOOUVf64Yqt+sx/LDMmj58vwv7e93uEK/T55HqUq7PrZZYp/04rPAI +49gaTxvHoZOuaGiF8YgZxjktOT6G/TyD6xdj+5HfrymG/df7vzL6EkfiJecP +FNqjIj97Rl/C0suLY/11Cl2Und0o5+aBbLxyXdPjcN5FL550zqDQ2Ru6n+uw +3j8tnz+1DuetiHWUwrvPOK7dqjomX/sjbRGQXLObglfP/8TVnYmcbBxXaA78 +ias076zd3Lx08L86+KNHIRo1JZeOcqyhQP/zslUkT10sWlctoYKQqN3oaZKn +tCh6TtdWzNdOTb2R4MtCAWfE2lV+0KB43hArqXvQFZxhJpaAek4cFyB1j69B ++epxjMPjtgX3dkWVo+gY/rrrr2hQ4PhBheDI6dsB3PWaBcj7QkYKwREXaU09 +wz00SH75Iix1ogltLbCW/TlJeFT2w2fZw/D9xfGjLxa0oW1XWrwS1tHBbHhf +IcHriQCb6xivUejor1GC1ydC31vopA1DZdlBA2uBW0iLs1LN4vAIrncJKyTV +hyG4W1W5LTMTtc3z35hSPgIG0Xt/OFn0Q+Lr5DH2mlY0NKl16KHJa6ju8NvZ +ur0PaTiOZy05P4IeVA84t/O+BPkZpdrkeqOFUDK+DuE1ioHkuu7OMycJ/5Rd +dv1+tlEB8JvvnU34p+MRoBE+f29BSDnm83Cxovo24fPXTu0+RNb7IPB+CF4v +GA5nbSLr5X1ZNSkrSIcnDTue2TvWwPcNjy2ca2hwSVsosMxqFAU7r9Pjm10D +bD23g8JnDcH29opLBnvp8KtyiWvGk1x47b4HxPtoUJb28A3RWeNXYw9hnQVt +zyQSiM7aMLVBYK8oHfokE+e/y4iDlbd+nYQlOG63OzUT3Xph/3nO8zcy4JXx +209Etx5Plvsa9wvnO83VvGkgEK5bmLn9Alznw3gaSR+gpOHY1+sckdBRe2wH +6QO83JI7tYvCurmBPUw33x1sqgd23zGgwJnvMC/pq+z5/HBhS7YvBNQf+EH6 +KrOKk3xJf2xQPsah4gquw0FqEqQ/ZrDjT365+UZn4fyCznFORn6lP/lzjihu +b8XV784OENL/5xyRjtSf/tWx7/eelbVfBtahP/2rKus5LC44X35EB0K9pTfY +L7n9neTLGVNnRn4JzXjxVt7NA1LMMhj51ff2ION8juny7lOnBD0g130j43xO +f80iRp9zpXuf30SGK3qmvInR58wJaJk3PEChZA23+Z/TTNCMlweEI4+R798q +vKr+QaHXK6m3sZpnUOelHQEzVDEeaPrvDRejo4WLeDweXHdEPLsPPjNeSsHp +pbEcm+3oSMvRr6I2OwC9Dtm4Y8t9Gkw94/z4iXcE7esaV+IoS0UGdYscZnLS +YLuMQBCJh1m9I7Y4HlA7f38AiYfevhKVsKX9SM7pcq5Fbwckt37RFfk9Cnx3 +E96S5xgv+7oDPwdySlkcyXM6rUIZf9daNPtKXXYAaFlJMP7u+hP9WsTOIotZ +mthOiOFle07s3CQb0kfWNSNngXeM5hm4rzLBWFfSqz9+mCElt/pTmgnMk9Zl ++EFsfnMzyV+278/0cf7CS/91jPxdtrXMMneYQpvbvu1oO2WKVld3+lQdwXjD +3VSs9xvzPcMlVvxPrdAPynLPzh1YL10QPP0e1xnxPUcOmJ91Qu4H1X6HLsB6 +QUiX95oXHQWKZH3+Lh2EdDMduKVu0cCqvEXjwo4RJLBNP2avWgZauSivMPHp +MIxuNE9SahlFKyUcpCueNyDFBUVL5GQGQZTrmJee4GUQPtd4Ku/mOHo+0LC8 +d+gpzH/lTEvcPIqsZ9fbektWg1S4yrrUY0PwceiZW/pPOur1+FqgviQFFrx4 +5Vu1lgYiAcEq6eZ0dOVKXfcxeX/YsWafSA3Ou5NmZ8p8l9NRWZtW7i6vi9AQ +79hQtgLzhGOPmhW+Umjb/pkpbVsswYYt/lca1tXKAtknv9kNge9mhaljMo/R +/U1vly5ejPXa5Wb2Rp5BOB+FOmz1WlHTgUWb1LRGwVPhkAnhFUsylb5iXoGu +bc4zILyi4M6f52uevM2Cn48mjf88/+A32yHC0/rXsX3HPA3dcJ+3lPC08ro7 +5cTOTA+lEVWvi6jzyaJ6Yqf9/pwHhPfO6FUpwrwXTQTN4iC892Ic+06y3o2B +cnvxepG7BZcYWW8sxy9foiPGgecs1hFoi0KsEtER/lzKXsRvtcmdU9hvqGkm +zZP4Le6nZg3RZaKFStlYlyHDa91KRJd9nD+LIv4POJIUjv2P4HvrWuL/Yua8 +jzmZ390dC8eVmpjzPr67yiwSGu8CqdLE9raaN+jlifeiBkJPoZ15fytzPkg9 +8/7qV1eMSZ9B19gkInd8AHTbip6QPoO4teT2gzge0iRMLXA8wJHCLnESDy/a +rzH6NuEObKRvA7Klaoy+zciNHEZc/XL248ZxBc9YCgRIXEVFtAiQPlhU4sJ6 +We18CNh7F0gfzMsuW53Ep3LzWTccnyBts7iYxOcCy7eMvuLhvfdf61aHg2hc +KaOveFLTj4/E+cNMgYc/pINgnT3ffBLnl+TFDpE+7dI0Q6NMH3eofr9Kl/Rp +x35ZWpJ8KVTmGDI76wRWU/Qpki8ryrkYfe9R/SDrrP220PEpmtH3jmT9k3cG +3NnOOO+Ao/dP3tUvPnKPvC849X2+0EadkyD145ICeV+gWW5rTfJX2efRyZZT +pjD8jcOL5K/cZrV40pe4MyVJ+hLoae3cKNKXmCzLXvvw9wBin6e2+/tHGgp5 +fixZJqgXqpjfDTvB/G5YGPO7YTXTvicWwry+XX1yFtlfawuRTry/YCSsJk72 +9+X4p6QbuP6f0W/mrOA2AXMrzrJuEwr4Be0ZfHJZmEeDbdcRtGJDGINPZiz+ +cz+HecnJO9wmqCNuHuN+PZP0Jq0FffDZrerylh0l6I41Z1eH6BhY8/a50D1f +wdUPVsK7ttxDbl8ulzfrvwGloUtSZF3jzqtV8Lrg1YvHmWRd16QvbmLJoZCl +9duT5toDsDvNU+P6nF7oT7DhVxrC/PTrwiMzM9xQImdcY/9RCjozxDZUf6dA +uKJ7xfcVV1B/U8uYOK6rwduyhJUF6PDZo+v5kqsxSODKM3clEazLHL8MVuyk +g4Zmyx7d1uvI87W2/a9xGjh+ezj7nSQdGsOFPjmb3UES75Lu7G+mwb0ELQli +j9nYBTtsD5o4+GwXsUdCpYBx/zsLtnF8P7zfNMC4X2/X7wHy/J+6Zer4+SDk +fcSBPH9WpMlyYk9eRpQbtgdGGvd7EXu4arqkif2bameNfVtxBeTqFr4h9n/W +rl1M1ntpImRiRoYbWBdrNZH1ck5KJpB+1LzN9ZKLnxajl/ULckg/KknbXIPg +l8yjudkYv1DrDncdgl8zZ//5PlIt8/tIR5jfR/rF/G4SYl4/xrzeJPqNwffq +LwTbYb4Hu1wXMfheEs3nFOGH9yctd2J+CNohvgx+WHb9B4MHLk1W/Ip5IGyz +EtQjPPCYu6MZqcOxr+V/4ToMs98LMOrwwgDz2aQOl/1e9gzXYViWtU2G1OGB +XmPG+0e/cSkvvzpDtMW1lvH+MVg8jRFXPM3S13FcAf/1kE4SV7H5t1xJXB1a +NEcGxxWsHj5RRuIqmXOrlKBOL9g02T1yDtq83W0Ju+MP2zHgYvY/RZn9z1Rm +/3OtYhj3CAfWF3LzvXeKlCNOe49PYix0WJugJhD2FOu8CY4Kxa/+aJ6r5EU1 +rDu+cYWZfO+h4PITVnmeTSFo4C1H9v6TFPwyiZltOU6BjFLoj2JRbyTs8nWv +/AEKetzsTCZoFPhUduh963BHRtxN/FyGFFjZBluVkfMvp21nDIl4IRUPfVtO +PQqiahc7cQxifWZyuP7sgwhkatm5TQXv+1sJ33pZfH3b7UAnuQVx6FfGi0cN ++DkHzv7clTiHDqe2yK2KOBCGljw54TB3M9bnwR6bXk5RMCHzs/iiaBBqm8px +q8Z1ye2RU/wVVjoc6syccfRAKKoY3hpni3WK28hkzmrMP6e6TVGjVypa5Sq+ +QfQg1iNsZ0D1Oca9+DWdpwcy0bsPj+TyjHDdG+H9JCtFB+s1h0uynVKRhnRp +34G5FKj5qh86JEwHD/3PlSuexKHNnZ+HQADznMIFsH8NHV6Xr1/IV5KMnvEm +uOvhujolNvKG9wEFn2RbZZb45CNkcSbmPt73uV4RSmbhFEg0Xgm+KVyEbu/3 +FBnEujLc8NoNwz108OHJ0jJtKkJr2Wy0G5/QQLRo83pfdToEsX8MfdSUi6JE +4+pPDtOgqrbez0yNDrunuL+Y7i9ECXM9Xuf30iDQO0hmYiUFpvy/kh7mlyLN +2dfHfuL9M51jXySWQ4ONEx9aNDpL0Yog7XQ/Uzo8vWIt8Rz/faTY5H9i/z2k +b9E38yVe74Fzu1ySF9Ah6aYx6/X7CAW9N1NLxTger/zoZG051rPSnPLqy+uR +84TpuuVsFOzQ+qhI1lW33cMerwts7e1EybriHIVfEz+4ON+Rx34Aha6NccQP +SiI1BWS9HofFduL1gtYafx2yXqiTuXJ2Ix12cQ93CfeVw1jWW8nb+LrtnrcT +P3bT4Vm+rsKjQyVwdMvcct1HNLgltnE72cd7i18ssBzIBKO3nfJkH/W378ol ++156DfXjfQfe7Hopxr4fi/hA9ncfp/UxvL+QvTtugOzvvLTXxw8o0uFoVSKP +D2sWnPLS7Mr8QoNVPH5bJ2XpELvgxGIVjXS417f1Th0LBbMtK++RuN1stuMa +jluY5Ln6kMRtvtDIJRLnQutLenGcg7DOL0ac36Zlq5J4Rm2l/DieYVtVsT2J +5+X9p0Q0+ejAeyI0YT5vNIx91457tArr8UAbp3wuOlRz7Vx0tTUczuocP+9E +vnd9otaY5On8ha6WOE9hZUwPI0+noj4uJXn9MI3/Mc5rSA3wYOT1IGssI3/p +D3qHcP6C6bJvjPydurB1wvoLBXcFUOnvCn+QOWXMmoN54Pberey17ymI3fVx +7uMAH1jdeTTx9j4KsrtX2uu3U3CSdnHOg4PekPQyXGzEhgLbyegXGS1kbpJc +a0yIOzzqqR97aUfB9eecSq3Yzq6Rns521UvAGe5rkoxxVl+6pYZtgIJemx9y +T9a6go6p0cH1ZA5LXq/H7F4KJuWb+h8gJ0h3GzU9cALjGvP7CZ7M7wWtZH4/ +4SLzuijzuwo5zOsHUpg8cHbUogNWxUoXmLxu+3Gx7duxPjO78UFvZq8HSmne +6x+M9Zv8vEfGp+MpeEVv3sXz1AV9+hUr4JVFQfHdNWXNmRSc42uLn/jgjTot +hPi7EihYNBXM8+UGxq+GGR18kX4oQ8YrxDEM45zLVkWopmDBrPfHvxb4o2vG +O6pYvHD8FwmvuNlKQXun/qROqS/S9a9Wv2hLgSjrPih4heNuw4T+Rn13RP/6 ++Iwr5hsNPcleqX0UKkt2fK7yxh1Rbdc2XsG6da2wpoVdC4VYufJ8Y774Ildn +0Z8l2M/eMmZH11ZR6E17J++vPH+0N4XXbak3Bc9K1fasuYH1VHKfoKy1H7pt +yTe0G+fn+/xyDZVMCv0O6nigX+2NNPbo1pgkYr4Rn6/kF0OByA5+Ba3vXuju +Rhde8RwKnhyqabiG8zjK3Chs6qMbMq1blr8lH9cHfsttsVg337cKjeO76Y8i +bt3teoT9WdrpZHo3mwLZ9aadfLHBiCYQcFw1hsR5vtevSqw/MsI17TND0ZJ+ +thdR2E6O3OuNZZ0UzFQ6WnzDPRQZWmzb7od1/XdOib597yg0qBFS+1n4CqKN +Xysfwvolcb/B6fsdFJriLru6MC4UIdFb4i6Yr0/NW5TlW0GhgPQB2lRQKIIZ ++q58vjg+c/zZH2P9PqW8YfLTrmAUv9tTWjEW76vHnoULkyjEZfot1MLAHxlR +V/IOZ1DAeqR+8a4YClVmX5ztcsMLRa+4ucwK+6FJy2OSfFc1Ni7uzjUHHyR+ +XmdCtJiClkH1BxHBFJz9cSqwxdwdSbIngcItCo4XG6w4jf296/76mB6BIKQS +OCBRUkDBBQ+fS4nY34/jS1q3rwpHlQrP2Fqx3/RUf5yqLaIg4MnDBXuOR6O2 +kGyv60FYD4akG2V243hMm4zNyI1FUe8WHyoyx7z9pKJXGSsdBaWdVea4EIVu +J3xyWCeH6+DPZXuSnmA/RA/ctEyKRcvqomsfnsb1/47n0vGbmO9d77OsFYxG +Jmo3FoXi9ShpplQWJlAoZUbXlFpPGJL8ZBfZiP3AstBoMVs4hTbd5sm7nBCI +3p9rchfBcf97tVvonqsUelWxJPf+Qh+kuoR1TBX7oWq+RusMHO+fLl+OjMv3 +QYNZnlJncT54Wh5QdfDB/9+lUWH9fDfUmLqmbT85p7pDzSzZE8eJq9CAt+RV +lMSl6LgF3y9woc72tR8FrT2h4pulopBttmMSKqVgVsFw4Aucp09nLF0/f2cS +EubbvzkrDd8nrZv9rQnH3dZjGgdupKMcHZNdMmcp8Dvjd1lFgI4EDBS1JN+n +o/2u0UeUl1Hwrp3TouAehdYFNEqrWqej1q7O9np7CqQvXHjOEUehIysvRUJW +ItrncfH2deyHvMcOa/X8KCR0hC388O1IND/kW8DZMgq+iu0XDPGkUPE99soc +r2BkMPEoQBfbv6cyXk7ci0LNZTpLtsv5oIvHen8cwNcLD0pwrL+A+ZErz13b +MS/E6nHUZMtDCrTVHjz+7kzB4Th7/o0jlxHtxYb6+/X437f5FB/j+jqUI/Yo +yzYYOX749abtMQXr3ZR/aeP9/LlQ49gc32hU+kibPQXnj/zLYcsP1hT8OLNR +72deGspSjjw38xHG9Ue1Oj1ROM+0Azd6G+ShbUvPdz7Ffnx8Xf9uLeb5OsNO +D490FCK/zGVR2zHeTSQqifa/o6PXh3M+zffLQEvXrGW7u4kGcpUtdQEL6Gjx +m9kJxs1F6Oukv+wrHgrKBpNu3AmjUJD+7NhX4bno8KunQQMp2O7O2AMK1hTi +Dl0j3iaehkIuTM0UwjgxR/TWSNxpCoFj5vpzQ1HofcuZn67Y/pRPNqo6ZykU +aSy5YXNBELI53JhvgtdrkWChm3OBQtr3vqTk2HmhL+rl52vxftsFHK/Own7Q +2PWwXVnbDV2+//31HZwnU/VObvLncR5Y+AlIiZ1HhWP8zgHN5L2XhmucAd5n +LbuU4NP+KF12/vAXzF/L1+nuDlfB+Lw6VbhRORItjkxW/4J1S4tom8jmNTjv +5fcaVixORxcb2O44c2MeUHecal1MgbOiULfOoSLks7PhhCzGaT/piDcF13D8 +n3n8bBW9Bv0e3xEajPH9rbkN7fvDETTakPib1/suSvTaZ2TcNwTj96T0yo9T +qFymvfglXw2aF3PXIQ3nw5fkwmIaP4WMl82coZpQiKwOs3Bqz6dD3PK1O3dL +UEhuea2TvUUaKi/yl2HF109r6G1WVaXQdiOuEqmoCPRo5b2jF75h3F9UiboM +KSQclxbrU+iHugQrNFuHsc5S/S0dYEmhpPJ5bYtcXFHcGZsVg10Y321e2HzG +OKwjMNi9JNwW7bmskH6+f/pc1x1Vf+e6Oj17HO5PzhEdK6k9y2eBjgpt+7K9 +ffp8WOmqv/Nha+I4HLvVcT18FaJfFO6Msj+GLW/8SkEmcz7sDMb9GlUPmfNh +9+wZbx1YgXFy1We59WYBKI5DVfSmEB1imHNj/9yvXdXGnBvrRDvw/P5TrFNZ +fKw8Q+OQm0Cxq6Lxv/NkWVj6/zNP1qio72ObOg2i7jU8f3f3BlrDEpW6pePf +ObP44dT/zpm1DbcKNRkcAgTrVp5Ra0ILw2fZ71UZAZGizJRvWyh09fecALO+ +PuR0O+B93pIBOJw/87oM7zCqTE18/P3aA7TRWH+em+wISDnxv1ivR0MtLGvQ +VZECtHjnqKZGI33anFnHqr9zZpcdCc0d7aWhyKr2z2vPxqLqC1rHmw2wHmDO +n/3jB5MqTeb8WZ3T6a/XrKSQ/SbeRQts/dGdYA72RIHpc2m1q/7Opa3LG0po +2I3r21TMsE/WZfRl82Hh8c/UtHm1GlV/59U6RB49JGVKoePqRVLWi2yRa/Wd +2aqvCM/7M8d2BjNOwphzbFX3LjtH4up86bcn88NtoefUijQSVyfLxiJJ/LT1 +0drV+SzAvODAJxI/88QzL5A4yU+4oZsf7gyK6ezCJE7WUDWMeKhZnKe20SwA +3txazIiHfeK3e8i+D/RlxXqExoHz11QXsu/fNnBOkP3d7wAReH+B0/QBY381 +L8zvJ/53eFdkFCJSADJTxarE/wsfdBcTP7PcpT0ROxsLP48PHyF+/utPnz/+ +hEqmP4cem8YRvzmLN38MyboMWzujRYnf/vrH6o9/wIXpH6N93XdJvXK2E/8i +r+0GgT7Vo6ReXc9f6k7qlesaFvM1Yudhyi/0MqlXKzjXu5F6pct+1DzwtD9o +5+sNkXpVyf5+L6lXXysaHXC9Av2mRSqkXo0emsWoV+cSxjNwvYLcJyGMeiX0 +WItO6tW9ivZqXK8gY4Eko14tGrku7oXteT/ztLvg8xr4opsZNIb55By3nIOk +Lt1eWdWE6xLECmxj1KVOm5xSUpdUrDNKdyUUwsIdc+aSuhRxrleF1CXlNutf +thZpsE5m/kZSl/KdrjPqUgf7h6J1URGQH7nUiNSl229plaQuSaz5zOlX6Acs +iw7vJ3UpePnGDaQuyQpqtC11cQWZubwipC5luDyfS3DzyR2nRRg3QcD9NgM3 +LVL7WghuBoeHWsmOXIaY5b/vEdy0/NK4jeDmRhqn7DXbYBje5DhKcHOd+o7f +BDfTbNweYdwED1clNoKbxlILrAhuUul5+zFugu88u7MEN49EWTNwc2HrVwOM +m3BML5aBmxITBjUEB2ftt7iFcRCUzz/cQnAwVuH5TYKDbg++bcE4CGpa3Awc +jOvcoUdw8EU7V32reBrMsMxlIThILeMdJTh4VrhmpvVQFGiXtzJwcP7zkp0E +B3/wFGzCOAiG2+0KCQ6KhL/RJjiYxim8rNDOCzpKOi4SHPT5rMrgXR+sVBHm +XbBe6g/vmhU1oUx4V8O23gajfDeY6jraTngX9w3vU4R3fdV/JoN5FyifW3Se +8K4dOeJ2hHfJ5/TM2iIVBffODiYS3hUQEXOV8C7ry3M7uXYmwXz7ChnCu1Zn +3mbwrtrcRg/Mu+C6+yMVwrsESo+4EN5l0C15BvMuWHsj3IDwLi2hx2aEd+k+ +3LUQ8y7gW7rhCeFdb+JPvSS8q6elpA3zLmhmcSgmvIs9Snkd4V0Xj49VH7od +CSc04/wJ71ocOLaU8C7+kz8qcr2CwW0zfyDhXR8NzBi8K+CdJLeqnA+wKOYy +eNfBlOcM3t44dvYU5u3gG/PrI+HtT6/JMHj7LbRMrt3cHQYz/Ri8/XfdamHC +2z0+vI/CvB0EAnkZvN1tZMKJ8HabWfKWsCoc4ubtYSW8PbRXyJLw9mezdoli +3g5lta6ehLd3OFcyeHt+9WAj5u3gfuSDHuHtGS0FbYGz6XDrRfwntw2RMFdK +SiMA84S5lRLqM9bRkYqxoE5dhQfYhbzSMV9IwTcbR1/C86tejZthng9PpcJs +Cc/Xqs5UJzzfTcwbMM+H5Urb7xGefyZShsHzr3zRZqsTjIaOec8ZPP/G+7wq +wvPjjUKMMM+HpjTfcMLz84SO8BOeHzh2ogzzfJAubHYjPL8nmJ/B8zctPz35 +cKEPTPRIMHj+EokpRaITOx7tmcI6EUQNRPiITvzRWMLQifc7T+bNmHCDdHEe +hk7M6rJWJDpReg0tAetEKNavfEp0og7vVxOiE3vVR/QXxwbDMeeZJ4hO3Jcz +k6ETv1v9Ood1IjyNzWXoxBXLWO4TnZidueUB1onwtmh8B9GJUVvmjZS+p6Dv +vV9+x7A/nLHpWem/D/Ouh6lsH2bS0eVFmUWORQ6gtqAn0k4JX99k8ILoSnX/ +DjasK2EyPfYO0ZWRU30nia6seT5wBOtKaN69R4LoSr6XUelEV0ob9+T8CgqF +92vKPYiuVHQJYehKNt88XawroZsvgKErDRoK+Iiu1B/vXW9m4A9+FQeyia4s +WXBoEdGV1u9FwrGuhNViC4WJrtRt0wDSl7Bio4/M7PWA0EOifqQvEVkfUE76 +D4gts3rigzcUdVTwkf5DiqvVQtJ/YFE86scX6QdiNtlXSf/h0BJDJdJ/eD6S +af+1wB+iby69Q/oP4oHnhEj/ofOR5JhOqS/YlZ3fTfoP+a4L73lhXOrfOmKx +R8kdVj+v5sg1Ib+/M3+dN0ohr5pZEcY8lrBid+7D8EMUNO9LZ/Ql3PX2qau8 +cQcn6RxGX0L7MZsZ6UvIn2+mxXzxBeGB01OkL7GkJdOQ9CV+jX4z+Z3nD/zp +de6kL8Gaf5jRl/AdWPlxo7UfFGquZvQl3kkf3Ev6EouFMuj61d7AZVByh/Ql +uI884/uF/XnxmYohX7YHNEssUnqM/TOzKVqfHfuHvqe4ka/UG00s95BOxvcP +vOATouF85fb2LI2x9kNlbd+PBuPne2pNrKLj+tdwOdz65i1/VDeW034E29NQ +YBe/CddjCSn5TXUz/JB8gsz8T9h+kbJTgoZ9OO93u8kmfXVHNskjQe14vUqs +2tyPX2F+bnRok1ucG7JqDuU0xX47aah+sKUV4+ZwqzrfUV8UtBRtP4b9vDbx ++pFr1RTaVfmCd6a5PzrT1uNI6i9rFX+bM85TuV+8n3ac8UO1CZwPJkIxjrhn +ue2/RqGd9CuCPTRvpHrT/6EO3vef7pqCxckUYtVILlj2wwNxPtu6bwn2g1DA +TctVWThvXv786TQYhDp4gqrHyXzqRqmkvbhecpod1Tp2ORRZiH9JPORPwaM8 +n99rMZ6oFipeeFEdipI2Teoux3V7Vb+f6ufXFIz0H058KxmIvorcOa9+kIKI +ia1Kuk8p9CR645RCZgiaJ2ad+MsC/73fCalcdyn0Lq/onefhULRxTONZkAcF +ICG891wehWazxSnGpwaj90k/j4TiunCxvLIxLgXXeY3Z5kYLA5C6e3JNQyoF +wj5uZ3tjKXT5tklHias3ClkhatZ4nQKe+yHj7rlYT105+DjrShRyLFFnX4Wf +M3dz6GY+jM/yfg90PiXFoqXjyQX22M/HLjcX//qC193ue/SYWTSaXbF+fLka +5ovrP23SqaRQkXA/2wKlaDQS9uMJN973vKjwirvpOD69Da+nlYejCPWcCfK7 +Wa13syZFoink2pbT3VQSjDzaBtz6cJ42NnLtsAilUOpwhb0Iix+K6fhsw11I +waYyZynO2xQs/5a35k5TGqrVPlC7BONuCPN7/rOZ3/N3ZH7P/+/vO9Km/b6D +XyiVbQTzh4joZdqLzsQglt/Hzqji+ikmaV7PjnFQ3fl88Oo1YcilXeCWUzkF +9Rca5jp4U2iP0syCaro/OrlmY1LznX9/B2E87XcQtl++TdRhXrFcNVJU/EE4 +eieskyLahuvzdcMyXQcKrYs4mxW/OQAVgMvsEsw/eab9LmAr83cBzU9aOCJM +KPTR2di8TdIX7Srxs9R8NV0nyvyjE/+r75T+0Xf/1XG7/tFx/+q1x//Ra/+j +y+j/q8vyj0z26Gn1k+cceBGwbntIq6zhi4A3QDHf789kPN+9CjH7wEeXFH3W +2/aGXFfylD69/Sevo8+M5n74uTF3M0tQP9Y77iFNJ47cDeYUCWo68WaaLvP/ +R5f9V385/qO//quzTP7RWf/VU4f/0VP/1U0a/+imv78jKJz2O4JgNTnxQ3tw +Hi+e3ED0kam1SuXxT7gON5dvW7gK7/NPVVkprI8ERTsW1PLTwUHJea/xMA1u +Sq1+ewbrIx/d59fP6tIhOeRrlcwpGjyyV7k/B+ujHKGWyyK36eC6+KtCvOUw +XOHauuDOgftAexpbJ8Iygu+bUqsTHkIdNy1fnZ/5GL7yxW9wNR6BcNfbghsW +0tCra2oDD02KoN/ioZbCJB1KqbIl1YiGQjedOpuP9RRH+WmvkfN02PYuyHsb +1hGrtLTZxLCeuiSe1jdjFR3qfTqKn6pQ6NbJNXejsJ7a/TJ0Rf5PzGtHfnG3 +Yv8MKL4MsMF6ysG+TjZ88N/fC4hM+71AbqdYv+pezCvSPocH5YdD2/X8kQHM +D1adlB41laeg/PfR2bAjFWZWwrL9LHSQ41IpltyKcVY58ZNsYAEIs02+2ojz +dldG41YvzEfMZvtcmDVSDgPbOp8SXGNr/8qjOEFDtp8T3tYVl0Pj8Se5h3jp +oCFeuiCUE+OX9+Je/m1Z4Hjzfe1+vC6pU8klMzbjOqlmOB65MAZev9jLaor5 +3/mTBia+OjgezrRyLai4Ao5OcZ754xQMpya8az9JIW9vo8Wate7weLb9BqsX +FAz267XKYL788Ax32W75JAj/4hnDgvPaqHPHsSRcP5zK2xxcU67BIuFHi5Ux +r6qILn+SMoJ5tEPG05Gym6BcGDAgvhPXW8XhObfsKWT//UmSZkYWGJkvyP5Q +i/l/flj2afx3rcLd9B7UJsADE6myqacUyNyeaaSIdcrY5tbJCbswiOyWDHiM +ddnkmPvBG7YUenZc4bjOa1+QPZdafB7zDJcN83o+3KSg1F99gy1HChSfC702 +Gkj9M6cjcNqcDsPvm+pCMM80mbDYmPI+DiRiRitGMb+xz4/OGMU8/1as8tf5 ++8PhjcHutINVuE7O375GzYNCuYq7n2/qDIB3hvpd/XcpmHCwNorD/GqHbVdF +ekso2OdyLOPBfpDhiiwaC6FQcYbsyVU3AsBm4r72EVy3j3htXuWE+bDtBWsJ +qQA/uCpn/2gK84llch0bXmK9Y+f18vzqi66oYbfIRi6Mr85VtX0PRyiUvVbc +btc9GyQtdD/BXp+CKVoLg5/QPx2dzZ/tgfSL5zD4yToV8QEnvN54vqNfvtT4 +oKrqT/O6dlPQusoVRf+m0MaFKVna65yRZo6HVROuj0fe1OnKLqaDItdW2kyP +UMR1vFaeezUF7TUfxtWk6cg15UT3DLohFG+3k9XkwriTIrN8qzC+PshmO1s7 +EJ0RCB7jF/p3fjrftPnpG5jzrF84/pmfvn3a/HTfafPTf13h8Wz1xM95FWXy +/doNZL2R+2twCg1u87sWfSqkw821j4RzH+Yi/++z7i23o8FRo2A+f4ERxG/y +ULNy1AHsLAyPC3DSILgupCqFfwR922fsckHFF9k2msa9mE+D3V5FFb1xdHQH +ukeVLPLRFnEU4xBAw7rqkmrERTqqc+G5jk7fRNyXi9yu5dL+mS9TyZwvw8mc +L8PDnHcWx5x3lsCcd7acOSd0KuDPnNBfzDmhl5hzQuWYc0JXMeeE1q1+6g9F +gxB9Y5Br39JniFvg3W/lmbheJbe3KNPpyKKfzzL7cw36MBQetO758D/njWde ++XPeOIR53rgkql6e1M+T0RI8uH6i6l2h9aR+5jJxChd5rf/FqXDm3HZc/6+S +ue02zLntVcw57Pi6z//OYb9P7x20vDqM2tp7uOc2NsAO6sPs21/pkPTFuJXY +qUcp6GE7oU7kN8POlx8CzzVupQOdU8pVYVc91DsGvqI54/316xwkfenFp+UH +eL3vwj0BDVPSl64Mi78a4k+HsLLJtejmDfBddfSeUhwNnq85xUv2Nyy661P5 +qAOiXG+eIPureNG0mOzjtvUPCvA+wqx2nlSyj3/nqotOm6v+Nw5FmXPV/8bh +FHOuejBzrnolc656ZXdzpzXGMZuw90u2GoYC1+nfKW3iFFxYwGLxUATX3Wo5 +EYk5V+CjgGDTFUEKksTYX5N8yaSxJk9ShihXMkKO5EtlZ6RA2wY6Eh8rvnSV +bg7DraEWNeR6tYggyaMlLKKROI+AbxN6R/JIXUjeZ9MiOkp32HB8uVIYSEqv +sOaUwLqCOa/Hjzmvx5k5r+cqcw7dDeYcOnPmHLpZzPmkYsz5pLOmzSd9OG0+ +KdtJJ0Z9qJIVX3lgnTOYs7ky6sPf89Ly085Ld0g/Z9Sr2enn+8QuusKE6hpG +vWJlnqN+xTxH7cQ8R12Q3cZ43300047G/dQFxpITGe+77aSeDZL65jc5a8XO +ezYwfj0uhtS39FV6DN0hsu8yi+APD8jwUGbojpzD2hTRiQ17vFtO8Fii7ZXd +rUQnBo390d0SIuKpWHejRKk/unv/oKca6W/s4Aj3qavwQK8Egg+Q/sbfOenj +0+ak/517Po+F5S6Ze76JOff8KLOvfvdPXx2kmH31l9pN4af3DCGr0+/PaS3v +hr3WeVZ7cf6y/JBYTt5nOZ1b/H2+XwZs5q2eS95n/Z17/nDa3PPWC+6hpm8o +JHucTzpdbR0SZw+h+rEOij73SVGYnY5uGd3iH521Bd33VujWwnzCYZttd8RG +OmoQefFUwlgFTaYUpL6bR/0T53cv/bfeihXrePwSHkElZW2S2xtPIb8556wf +sdLg3Jzq4+5Voyi8obu85HsA2s8vpbN51hAcUIwoMVAdR3EyNZOVtxuQZkOs +yHDxU+jcZBlA6tWzzvR5uF7BCav5LCp4vYseJZWS+zdvUu7G98NY95sV5P5z +7DMYz29TXCWLnw+8b7YeIM+Xe1TpTuwp/7y+FdsD1j7LbIg9f+0vnZanTbkN +XWS9WfJpCpuMVUCt7HgaWe8tDTV54p+ba3iyfszaAhyCM54T/6hY//HneaG+ +tiK1ddAzeZXhT6Q2fOnXawrJsGzUuNC5F0l8EzqtqvfvvPLqafPKtS7GMPL3 +rqBuQxDdHI22hTDyt455DpydeQ7cg3kO/K/9iU7/9f/fuGJncWfElQYzriYC +tRcUjAwC79wuc8vuPhiskDoTUzL8z1xpJeZc8jVMvLhXbHWH4FrIyNOO8yq+ +sI2rMp7g2t9z4LHTzoH/tWe303/9+XOeztL94UNwZuCEW8lYJ3KSP7n7FRcd +qKrolDDPQbj1Wk5JImQQtVmwfOM5MggJOw25iZ0Dht+ssZ2oa5fFaWLnYaau +YWNhUSa6ZgbfH11zk4kjs1hYPAmOqDNxZMa1B+J3gIYM9v+WUy16CUMqGc1z +Vg2B6s+nF1LKhpDt8IJZI409UHnP/jZlQAOTkza1STjfFV6EHav5Ygg9q/nO +5+N8t0q/sYkf7++GmQ8uRuvsgMstbSPr8T5+Z84lD2TOJd/FnEv+9/r5add/ +1o/FnJChI9sh2bciSfZwe29m9kcOCjRnD4c9ZxtBHy5VqVQbRUB4gjctQ4QG +Qkx83z1tDvhF5n5ZMfH97349CEY/vnq/RpkNh9m7VjyD9FkVeZcu9YBqylWh +LLVxZHWkYIfz7Vp4+XHm5aNqz/6JE24WlgckTiSZcWLI9DMrCwsQP/9i6sdc +3w/vNczeoO+HnBs5LJ6iQ6nWC9YaP4WW9zHLyfOjUmwk8fNRSqjPJfL8Jua8 +b4zv6/933vff+d0Uc363FHN+99/rxdOu+/uIMPxTItY/F/sHWU/aUMQ/w7PX +RhN/Pn/yKRX7E52od88l/vx7Djx72jnwvzi15//Aqe/TcIr/GrvtGZy/hRwv +78p0m6DkURapp2SunMIBGRIPCwQyXkXo7EBNFza/JvHw99z4jmnnxo8dS3Im +deCE9cse+869wPnkgDmpA//fzyqzvAePf/lSCOFLZ5l8SYl5zrydec68innO +PNFSoupL0BukwTWV1uzageSk+BrCHvb8M7ealcV9A5lbvZU5t3oial4EwRFp +IRlXjCPogOqu0wRHxj34xEi+fOrYuhnnC5ph966V5Et9GqsdyZejktXcOF9Q +suA7Rr7E/2tnOLHTmmnnadWMu8SelCdl0dge4O0oqiX2cA4uyyTvkY/fkr1s +1tcHB+Z8Z7xHfua+8ONnGgUKeV/tF967gFxDzEx2GlLwsSFgQGKSAs6Uk239 +3R6ot31IYrUKzi/fI5kXhTAOcCSL57wNRmZTXqy1K/7VBdzTdMHc43Pf3o+n +Q1/OigQUW4DKtD9cfu5LA3UtGTPfDjo8E7r7bUZlJjqxyc00TJcG7+aLbszC +96t3H+lm061HgU/2FStz02ARk4eHMnl4HJOHVzDnDmM/CJC5w8HMucMDF2bI +kOeIWux5hJ8DhRtGishztj4bHSf23Pq2ugnbAy8TOhn2/OWTy6fxydUb5maQ +9QbaBori9cJ9RGMj6z03a+fuWgk68Efs58zf6wOr1+zpv4D5RrXl0CDx2/qw +bj/sN3jr77mW+O0vf0uext92aM19T/zPsjDkCs+9C1Ap63ac+H/Nu2RfFToF +7oWeklS3NdyOuMLFbkDBiybOC+MUBY/n33f34HWAxPV9i/fh65P/9JdYrv5v +fykv0Pxu2Zsh5ML3uEmA5wk6vHIp19E1dNinmRlGzhv0apSS8wbwkeunLTlv +0Helh4EXb/Q5XTBewHjARQZe/J3Pi59f97/zee/9oyPcff9XR+yzvu9I7Cxx +dPXFdqI7GxbxEjv/ztXtnDZXN5ztsDnh2+DmsgPzbbQ8vZHBt1XPHdUgfj6h +UiaL/YxY0uUGiJ//xhvrtHizYs7VdWDO1VVgztXVlT/L0JWKv2vksK6EPscv +DURXKjPjsOpPHII5Mw7/xgP/tHhYdeeORKI4Hcbmz3ukTPdFd0Jp5+v4/52T +KzZtTq5BKQc1rw3rp+xHOfrs2eiS/ZO3U7r/xnPctDnaL5jfL8X+jCffL33O +/H4pnM5mPCeHJpCEnwN5tzcynvN3Tu6taXNyH2SYSBI7K1l97LGdcGrJKnti +5984zJgWh3/n4bKwmPxnHm5e44sleTYU4rt3LXN9QiXa4HhJ5V4EBSdCJZdl +PBpGOjr1QuFPKpDvwYLsMwIjMFfETmPyxDA6ejorruZzAxoSf33KeOkIUHbX +xwVDh5E2x6wQSXuEqn0Pj0ZsGoE3W43o5P1anczR+x3D/mg8NFCMvF/ri1vH +/h7Hv/ynbW8r1WPQkI5Xpwmu23XsBxjvN4dm3hR23xCJag96Md5v/u2Hs0/r +h/+db7tg2nzb2/NXv/3YTIF2t/jBiztvosd8LjbrjCk4/aC5i/S1vLwv8IyW +3UTURd5XpK8FHIpXJi9SEDaz9DVVege5iFVuWO2D/cjsG5Qw+wbzmX2DqX/y +sSaY5GMQMx//9bPwf/zMv5xvjNjTkbRZFtsDSqX3zhF74qPWVpNzdAcWJ5ce +6SiEzftio8k5ur/9rqD/Yy5t7bS5tKfP+88h/jRXkFtwRz0G9AXmdxB/Juuz +l5D3GlsOTx4+ZhYNJpMjb8h7jSmDZ2rkfU3hNb/Yt5KBMLrouAN5X/NXn4ZM +06dvXVa5U73kPOGoXTSPB3wO4rZWO06B087TFy4OU9B+tmtzEu8l2ORvJ4uO +YD3oI6AkOErBZz05aw9DKzRvPpiJ6f9bH+5Pqw+G14dkTbRxvm55bSWyuh96 +ZW6xJYUPgA0z362nzdFmSf7Tn5/FaM+XK1Uy+/N/51O8mzaf4u9cCfZpcyVw +AYg/gfXIzlQb+UOSjuD0JqF/HOuRn91+xetf0mHOy2/SSqIZKPn16U5lzX/n +5ohPm5tTHGma68Aygm74hTvfMYxBLXlKNnWraLDlKdfb6+vpsCT2+wJ3BS+g +FUWfjl7w7/yaJ9Pm1+ys4N0ehnXJwcGiyBNV/VD/JeddJGc/qDLniwVNmy9W +wHst5rXHCOKhXtJbJnrBj/ur1Wm5lxAyK3XzD8z30M1tsWv1elG3zbvrizY/ +/2d+Vu/C/87PKvt/dV15PJXb9z6SRImKkhKVpERCZMgWCUWGCJVCSsilUIbI +fMzzVKlMGTPPHHZE6YpG4RoynX1ImVIk8tvH77juPZ/7/et8ej9vrz2s/az1 +7L32eozidkvgOIoi8EVrX8MluDZphrgOx1cZ8aRmQ7UBkKPWm2EnjO16bFuN +/6dekEvrr///9xe8o/VXlKYfdJimH/SRph+0xUD4LnWcdfPYvuiLOMH5qsA+ +6jgv6fXw0en1uByNGc3H9vyk39fbbLU1sP1g6XbXENunLLe3P7arjdekuBaC +LOGRkeniMtxOle+3sy5jfpHrPKNvaGUC2sfJTINnlvV0NOj0dEiV7ovzYjN2 +RADPC7zIybc4L0v6Mlto+jKjdPoymnT6MnUrvi/ayRnxqR3YToAjx/x7qp14 +0/REuAhDi3oiG7GZ6sWcPvK/4tIlXRIegocNVZekiaZL8r/el6lPaYiIxX5y +L0lZUdIbCj1XthDIWua/XXT8d6kOYSddHULf/lvmDiEIFPLLyR5v84bMegYe +IkUIPKrYpyQVjsD5jY7v+YQCoYX75xss+Rg3czcTqftahzh6lbbLR8AxVglr +6r7WH1ymLLzeCGg9vtcm+8ULptTJ+LpWI1DTWGsl7omA3P7PtXVWgVCOUBw6 +XIOAhIqH5CH8fpDRDKNSTSS80tsp+K0K/b2fHEe3n/z9/SQheADBAcvuqISy +JOj462NpP8Y32dRhp63OCEiOuTj3cnhAr4m4PV4vEOj6KLSH5zoCDTJ5f856 +E6HGOpaq+Rb8/aRUz4yrCBySvqRYMRUBK8OzPFQ/Ynz7zLlO1RyB4fg2pZnU +BFh+8ZJPRxv1fGh3Tu5HBC0fhAWe43kCMxjdU69gO5TNe6bSGISgmO/JsgGu +x7DIoBrEZGP/2/2AdBn/3ZPjxQyC3TfhNLHIWfU1tsPx2ulnl/Bzhi1vPGU9 +ocq5CoJtFwLTWqTZGS0EtuZ3lPLEBsFPmbt6t48h4NZ0qDBTHIGhv+RXrxiP +gx3mIRQrFuyHDp/gYWBB4OZkwC9RmXRo79rkUoXjveJXlQq5OP7vqGvT7TJ9 +Ahe0hBQEphFIdKu/0SSLoHB6m2W1ziMoXZdXeRbj7yxHyw9jGwSO1TbetuOy +gPqNtptN3uP4P8y42ek8Vf9QYC1P5HXYvq9YqGcAgWSRzwW52E+2RL8WKIu8 +DdMyWQTgPJ7vVUryFhsR2HM9T0z5cgBsNk8D9/ZSAO8txRBKGRmknnatFIm4 +C2cEM1S6blPAUzXTQ2/sydDBkmmuiT8H9lS++pX5hAIcYyfDx4fJsOBL5noe +23jIp8NzxusUfr/LdIB3L4JRrVW96677ww6xVyZkzuX6adx09dOebBRZ44b7 +tXB5zzmlODegrqHnQcD9WtqHMaDtw+yl8fqzYVqlbC7YT1HGlXJee4LC+5rG +7s8R+HrEgfWzPcbpmKRrAn8FgHtVwnc5XmGcoXw8Qj1fiOTLt4aWeeAFj4Y/ +9Xzh9VHxVedxvND4fCA7JNYLPEzceOc4tud7uzd8s/fBccpRl7xLtgHgXGuW +dh1+Dn+mmpkQsZ+xucP+1C8CtN+3amQvR3/vY8fR7WPnvg+8lDWHYPvlUx1s +aSkgy1fD4ipe11tXWZ8ODMV+fD/yOrjSC4wY9WYdLERgTfIvlUd4/RZ6335+ +yYII1p2Y3/Y2D4EVc4KEAowb86wXPoVKhgLSFasrKpkI7GbpzSSnIEC0l0/7 +PB8JXo6MiRneX67LpEBXl+mau2RLxQyCfpUd77s+xgLjbDdemWMIlJZcC1N5 +iWCM2gv+PW7xwFymXd3AAYETpHLxhBj8/342cIXWeICRnJvah/F60UGN9qJ3 +sZ+R8em4/9IHrNDdpmOfjvlXFZ+yeCICY9P+xYXmAQCETgcL4n/Lf7rJfeMJ +nl/9SJLy5xAg2V5tQ4yi6sJwxYVDPI9cfAbqFuHgvdgWZkYPBF4aVY+9xH7N +brJ2Zig3COzh9VhtheOcAk3VYOUWBOtekPrCmsNBf4wdYsHr9mGY37bhEgT3 +hJDkRC6Gg2xBr/XPAnC80vB83cpHCMR4r5Lv4/YCbOxB3fVJCNSmlyt0P0ag +QrNT4ga3L9gxb9nx9B4CAW/XfDmF8XLlYIDshVAiULECR7bj+ZjJ3jVXhfGv +Wp0g5m/mDx5UW+73xePZvEG1RLUbwbnZGYYXvp5AJ2LPygEcXymcb4yebkKw +TNZYJUaeCCJ/uhw4iMczs3VXXGslgp9uZEh8y/EH2Wwvz9lh+2Otu5yyLQfB +6w/P8OcfIwL1P8wtjKKW6whJ0NURWqr/40BX/6f5pNSdwYVBMJIrDpB+ITTU +zXSwYBn6Zx7F4D/zKDaP6izmNTkGUXzd794BhlmRi3lNS/vzn+j255f2z2vp +9s/7aHkXLxxGahZM38k/pcV1Wct5GgrU869w2vnX20PG3NT8gZB245I/TQrg +R4qMNjV/YFzAJ2tT4wBUvjKwjWOiGeo0ZbZ7MA4B64aUxX5FXE7civsFXKVL +F/t1mXYv2592L5uJdi871aVusHcngi7Hr96LfVgC/+A9zc/9bfm+sy/dfecq +2r1aPbp7tcl09zHtaPcxcwmRN5zfIODs3sYl/tsXvDJ0+Zhvi0C70fw+Cbwe ++daN5Ixq+sCelirPW3heopNn92vgdUN4MV/+q8wPXvgaXSOJ15Xoqsvy50sR +SJ9/lfLHYX8YQVAz/4XtNiFD++Dmeow3vX7ODj+IUJ+UdWHHbQT+queyFca4 +eJS5zJ1/gy8UymlkZ7BZthNhOjtRNHfcqNOHoFBKplwh+TaUtpyZJV/Afk1n +FbP+ewQNNsVlCLT4QME76QV/XcN8ZE7z6rV6BK8IlzcHNxKhY3bwjhZXjI8/ +M/6sKkWwuxM6Buz0h7YbucMTcDutZRWbk7IRvBjwIwQU+8HDRSZMn6KX7fM6 +nX1Ws79nq0xFYPAoRVXxQDB8emX1l6sYr4hFFeUOhdR7ftltB9vC4IAVr6ku +9X6d4mxjbAPGYbKb/N6CcJi98XRsl/PyPHrSzeNeYMum34ngnXb94NUVoTCt +7c9Hc9h/s5Slsc3gfsUdy4Qsf4TD/P6fTwOw/1jPSdrlVojgr+samprGYZA/ +XyJGD//dzXoN2pyP8Tgwnqh81hMEORi2Q07czqbil2wXExBMZO3vnyomwk8j +KqabcH/YD5pmVmH841l7zXS2KxoOb2i6Tq2vd/7q1h8RtQhoKscc0KqIgwoL +OR+M8DzGWUpZX4LY71/9zjlZEgt7pe+8euuOcbbE8wpzBsYTyxnotjEaDrDP +8c9g3Lc5X6TvfBdBnQ9fmXakh0O+qr2OMmnYHtIWvhZGIOg1eDHsQV4gDP49 +g3xyESjjKbP1x7+Op3k7HRYSYd1pJm9q3emlPLQUujw0Li25+OIoap00i9j+ +inj405oB7cBxqaZRo6gYEcHD38LHakcjYY/kcePpMjx/U3psLN7Ue0kH0vPO +B8NTfQTVSdJyHpoZXR7aqUnCeKkNgkfSvNui30TBHP+p51/x+vnhRtaft0Nw +4uSuRgPfIPhaNtHsXcv/zkMT4ZLMLjZGUPb7QtO+MT8YcngoaW0/vQ6OOOm/ +dXDkSf+tg3OMRK+DQyBo/0sHZydNB4eBoJhJ1cEZoNPBwR/h+KcOzr/1a5xI +/61fY0L6b/0aQ9J/69eokZb0a5byxPLo8sQc1t3ccOIU9s+h9p2nCK7AqYr0 +Z9AEAka8p/bVYtzy8d+Um3/YD4zc5F+ZsY4C/nR5LMr2mwzknnjD0bXRILeE +LTJGngIusB749juDDLS1edaEu6YC3hrLy8K+FMBUeqhrz8ggMCcXzhwllYLt +PK2r7NcOAa7dc8rtI4PwSF5nb/TNCnB6Q+NDCmEIqD3aNvw7kgzDub0lNzml +gFa3yWKpexTw484jkdQfZBjw8PiohkQUkOpLTq9XpgApV9NB4n4Ed/bn3oq5 +6gs0dt2cb15PAWYmH1ekaGAcEzyDWne5AK5XNtP7vi3ng/HR5YMJPwk+bojj +88zgqta78RGgMa0jnRPbz7c7LH09mEceE1tvxnItAWSnCdWr/8Z+f+OFl+uo +elKJske036aDG7bfjcsx/8yVebMjSQmPm5Zi21hXEUhl6AzMxbhDlD57WHcV +9u/sjKozExWArf1oUdIcAgz6zH3JHAh6rzbW+ETOBFIKNaMPt1PvHwm8qz6A +oK3V5rGO8QRwXJ30pomVAtiDFyJM1TEO9BRe0vKKABbElKjBKQTE5jWkPc8j ++D2ZaTTD3w+on1qwAziez6lI0VDA8U6x3O945f774ORk5oJhEwKfJWd9EnA8 +UjJ5c+ckayrg5wkYeoT9CkMCoxp0RhDJJ7m0XUsHnA2pVvup8a1VE9OMBYJy +KswSZy8+BElhjTnZ2K9sUrx39ZYl7leD74GObdFA5UCgGUsrAiObe6SbbBHk +QNyM8n44HmNVc1ig1pX13fYgF+OED6OP79b4h+DFnx83n4tAoM0wYP4AxiUR +weru1Q/vAdW3Rvk8OP5TquML4PdF8LJld4+EVxSwSa6XGahAwPyrhO4RLwRZ +k0WTm+OCAd+hytNlmIceaT8Hf8QjGND8pkl0TwQI23uhMwXj3mzyB0dd/P3i +Ly3CrNOB4OX12/c/Ybw7UbJ973GMz6VrYLn6BBHw2serCGN83h4mHrAW43H6 +1lPHn8d6w+pnkw2pOH4+090Tthnj33XlijOdn31gm0v4kCv2Q7VHqtgmcdxn +cFBJ9UJLIHx9PY2olEfFw6mu1Zj/nj8Yustrzgeyazf43KDed3ZKZh3G4z+1 +4f4jAY1gmPClMZ0Dx4ts292vXMI8YpUOvys4GwV1Mg7vTa/E/bUrNOXuwu3n +56SwkJNgUOvr/gvG2D6ZUhvqbiKgV12WNSroDXlumZs9eUm9h9OzhYTjCw5h +u7nYDUFQgyV5ZhPGT5M6EesxzIvHCHO3HBujoPr18yeS8HydjfG/IHcFAY+O +fN7fvx5AD6LuRw/8PPFY+yapKgQLHjuKDrllQ247cuMWRxxneOr4leJ5EfNq +fKSlkQpFg4XT9fA4SD670jFhhUBP4frnNRQ3qH2f95Y7/s5WjW+OC5hvEgcc +fwat9IOdnBf5X2G8nYvmyWpWR4DJ6pHr+KoI6BxS+yES23MxWxFBBeMP0bLs +RdzKBOhi9W5HwBoKeB76YdRzDR5vAo/0+I5MKJcRMXFWgAIg6V6lIObFTcOW +DHPdpRC8uf00thOBopXMd9vF8brYLGxiUpEBS24d+msD5sXXuq2m4uQR7DJK +LmEzfgCrdjM+VsLrWt7ltmOvKQJCRZykByV2MDLKuiUO42TAdEFCjSZe70/U +k3/YOMNnmelBPJiHujxM3G8piv2Vt3eHTbIPrJ329WfloICBvJEjq2bJgLnk +e5CVVCRkLk+zaVCkgE+9JAUYTwaTfHcO/ficBD/tPGsiGksBbxUedFJxsncm +dZMSqRRauw4t4qSDo3ORz+Ag/DZXzXaRsQymBvNu3rt+CNx3MfQ4lEyG2zdE +M53ofwzNBlI7BAMpIDsis8l6lgwNhbSIXyaiYRefm+g7QAFKOtvXN4sgmPTM +qO3dFz94zWcfmzvHMr/eTMevww7aMURa43n80H26xt4dWJ6n6PR8QCDVYczz +1i0E3lrvYhU77A2uzhSp/2xEIEme87L0DQQuJDkYP14bBCS4o/TTmrGdSLIU +xmP7d5zVZt9M8QGt5RpGZOz3ww3SRQPx86TYnWKOLUEgwy3ziht+PlHwOdMH +8+Ugh+IfD+0igXu9v181jh9Stn2R/jmKIMw5ITFskAK+fp4afKWGea+PwLwt +Xo+cyh5BofU+oGfWXVYQ2+GJ1shxHOeA7B6XX04ygWC2e79nCF7vlF/p0xyY +hwYyZHqp6IaDr7rRzAUYHyovfJfLwb+/eKK17mZHgQTbE5xW8cu8GNDx4gzR +mOThYQRtnoeWlQXHgbHGqHnV0ziuEzjcJ4XjxrfIPUSdMR74OHK+jcfxp6ph +XuYhjCdrtFdUe9l6g2NdbwfcMJ4MSPbp8ydgO9I7bxlvhnmflJ/xWYw/1QKC +vs74tzxCbfayexAQ6RnfV4bjSRGZZC7NAmq98/qAtyxhwLv7NQzB/V+j2efL +/Qz7r8Rnc77W4aBUL+2lLY4bJWufP33Vg6CM8z6eELtQcDBUj8sJ87W9hYc5 +z79AULd1/4s15eFglfrKIXYnjPODnb7hRQj6b0neyMEVDjb4nTYQwXEgQfn0 +1d2YpwxF7Sl5vMMHxO3UrCXi+Fw83qmSA/OUVD2bnGxvP5Cd0Z5vj3lK2y/e +m51UvZGJX18TWfyB4a4Pxz0C8Xq8r9B5Erfz6S0FstgQEexQ4Rcex+3cMv3k +Rtk7zIeE3h/fst8XuLh0RjpinnLp3W5OKh9JgofMC8i3Qa2W2iIfkZW5L6bw +AfuFXWU+uUk+YJ23KhrD9vooxnpCvAFB5n4tG7a/iEBLMILCiPmIYpqGkHQZ +gn3Ju3dq6fqD4yZrGHkxHwEzLy52YD6y7+NaEakhP2BEuDeZEr28j9pNt4+6 +Y9LK+tI6Cpw1UqXUp+I4c5Xfnga8/q1odTj1aHU4R2h1OM/6+mcJi1Mge1v9 +mquJiVBJV9uIlQn9XZdJh44/rnYPi3fTp8CPz+ZvH7XIhz/VDNjVm8nAnJZH +OkerWxtJyyMdSCnYtBqPm5jRti+KHHWAIWOngPRPMjBOT4mkfifshNZ1/B1Q +8eoNF/U7rbS6nVa0up2atLqdvGSDbGo7mclGprid4A44ZEht5xKfLafjs6V+ +YHEcpCZmmRtSI4GB2pPFcVjKP1Smyz9cyjPso8szXOlke2A/5zA86/Shqqan +DDo9bB2OSRsA2kPW0h6SA3DqllqQI8c70Jv23m3rN8rfeSnFdHkpWVcTVZ4x +UqCzXfioeJUtMJWyas+QW84nMaHLJ5HxSVp839w61/RglS1UV7VefH8pT0yG +Lk9M0YNXlNpO3333n+B2gsHhlhFqO5fyuBpoeVzraXlcw7Rzq1P+dewWZu/k +g2j7G/U0vcuVBMIZqt7lFE3vcqluGw7aa/5Zt+0ALV9lgJav8oGWr9J/VOz4 +ye4BeEeksEma+S0UIvD4nr1L+Xt/I5q2v7GCtr+BaOfRBNp5NL2eJoHA/y89 +TbPWEMctOF5e2VfhR9YlQka5c7sPaCBwQ7B3XAT77SprZzHWmjgY9y1/g9A5 +zPdtDfqur6WAludswUbfI6FFiAVrBY6Pf7nufVX/CQF94tCKx4XJ8KHGUOmU +IQIxtPpp9rT6aeq0+mnD73n9V+J4Z+SnmdSpqRyYuHb3EyF7vN639PEcIyMg +dXMmVcGzFt45aMNt84UM3kw88KO+z0kKEcXvg1He4hzq+9wqZiQpDQqo6Tqq +o6eXDyx2FZ6ybiODefaCJmp7ZG9PHMTtAeGS8mXU9izV+zpJV+8rvtF1ktpf +cyZuA9xfYHGWYT21v73MZTvj8fisY0onDu0ggrebH03kYTv/P0sdn+4= + "]], {}}, + Axes->True, + AxesLabel->{None, None, None}, + AxesOrigin->{Automatic, Automatic, Automatic}, + BoxRatios->{1, 1, 0.4}, + DisplayFunction->Identity, + FaceGrids->None, + FaceGridsStyle->Automatic, + ImageSize->{333.1684660200303, 232.66417503602338`}, + ImageSizeRaw->Automatic, + Method->{"DefaultBoundaryStyle" -> Directive[ + GrayLevel[0.3]], + "DefaultGraphicsInteraction" -> { + "Version" -> 1.2, "TrackMousePosition" -> {True, False}, + "Effects" -> { + "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, + "Droplines" -> { + "freeformCursorMode" -> True, + "placement" -> {"x" -> "All", "y" -> "None"}}}}, "RotationControl" -> + "Globe"}, + PlotRange->{{-5, 5}, {-5, 5}, {-1.78317191774893, 10.521122133645196`}}, + PlotRangePadding->{ + Scaled[0.02], + Scaled[0.02], + Scaled[0.02]}, + Ticks->{Automatic, Automatic, Automatic}, + ViewPoint->{-3.0805265197629583`, 0.3495271567675202, -1.3557975983601265`}, + + ViewVertical->{ + 0.3981203849070422, -0.045172111096923005`, -0.9162203007467778}]], \ +"Output", + CellChangeTimes->{3.8274933701200447`*^9, 3.827493423229261*^9}, + CellLabel->"Out[23]=",ExpressionUUID->"841b2917-c78b-4172-8955-8980d32fc3ec"] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{ + RowBox[{"itest", "/.", + RowBox[{"x", "\[Rule]", + RowBox[{"x", "+", + RowBox[{"\[ImaginaryI]", " ", "0.0000001"}]}]}]}], "/.", + RowBox[{"x", "\[Rule]", + RowBox[{"-", "4"}]}]}]], "Input", + CellChangeTimes->{{3.827490361437801*^9, 3.827490363781784*^9}, { + 3.827490571145834*^9, 3.8274905761138678`*^9}, {3.827492149105356*^9, + 3.827492149464531*^9}}, + CellLabel->"In[91]:=",ExpressionUUID->"9c8e9828-9a2f-4f15-b149-d240b7e77eeb"], + +Cell[BoxData[ + RowBox[{ + RowBox[{"-", "0.1440638531600313`"}], "+", + RowBox[{"5.8680622917611165`*^-9", " ", "\[ImaginaryI]"}]}]], "Output", + CellChangeTimes->{ + 3.82749036399016*^9, {3.82749057132627*^9, 3.8274905762640743`*^9}, + 3.827492149631466*^9}, + CellLabel->"Out[91]=",ExpressionUUID->"4629de9f-997d-434a-b579-502d66aa00a1"] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Plot", "[", + RowBox[{ + RowBox[{"Evaluate", "@", + RowBox[{"{", + RowBox[{ + RowBox[{"Im", "[", + RowBox[{ + RowBox[{"-", "itest"}], "/.", + RowBox[{"x", "\[Rule]", + RowBox[{"y", "+", + RowBox[{"\[ImaginaryI]", " ", "0.000001"}]}]}]}], "]"}], ",", + RowBox[{ + RowBox[{"-", + SuperscriptBox[ + RowBox[{"(", + RowBox[{"-", "y"}], ")"}], + RowBox[{"3", "/", "2"}]]}], " ", + RowBox[{"Exp", "[", + RowBox[{"1", "/", "y"}], "]"}], + RowBox[{"HeavisideTheta", "[", + RowBox[{"-", "y"}], "]"}]}]}], "}"}]}], ",", + RowBox[{"{", + RowBox[{"y", ",", + RowBox[{"-", "5"}], ",", "5"}], "}"}]}], "]"}]], "Input", + CellChangeTimes->{{3.827490171099155*^9, 3.827490179042816*^9}, { + 3.8274902806768513`*^9, 3.827490282900653*^9}, {3.827490316733444*^9, + 3.8274903427976217`*^9}, {3.827490375462688*^9, 3.827490428967375*^9}, { + 3.827490562601927*^9, 3.8274905680577393`*^9}, {3.827490625163025*^9, + 3.827490625802943*^9}, {3.827491008171384*^9, 3.827491019978979*^9}, + 3.827491719728731*^9, {3.827492207866467*^9, 3.827492216009801*^9}, { + 3.8274934584087477`*^9, 3.8274934808888817`*^9}, {3.827493584603359*^9, + 3.8274936145714483`*^9}, {3.827493646668025*^9, 3.827493667980644*^9}, { + 3.827493770966469*^9, 3.827493828662982*^9}}, + CellLabel->"In[52]:=",ExpressionUUID->"e9b86a63-3e78-4de0-8cfe-6232fd09eb3b"], + +Cell[BoxData[ + GraphicsBox[{{{}, {}, + TagBox[ + {RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6], Opacity[ + 1.], LineBox[CompressedData[" +1:eJwVxXk01AkcAPCZylHbuqaQCr0oKtXLw4r6/lCNWynank7X6jIxOuTYrESX +jGtJVmPkNq7IiL4/xjREOWJcxbQ5GqmtkbOJ3f3j8z7rPBmuPosoFIr7f/4/ +bNRJurBAIy2Si4PCy6jESIj6ZL+MRrYI6V7PSqiEs8rg9JNZGjmhW2E4z6US +uuYXfjAmaKQgfWRXWAGVqL8VrygeoZEiveg/grOohOLWbm3yJY2UfeYzzyRT +icSgkw7X0mjkF6/QIqOrVKKAysyimNFIg9t7NplZUQk5H/qOVcfUSJ7NYr1T +fApB6xGcy2SpkvGrK5y67CmEK/++l+ELFXINJvQZcBYg5J9d5+LeK5PGlAh6 +ceI8VF2+f6bYRYm86dc9+jTuBzjHu+nOpy4nPcOHyzT8ZUBPr3W2HV9G9usJ +B9/t+w7ZwmAR02Mpae59N7LbcA6OX09c2ZqrQDpYldrqSmYg/ORi7k80eXKt +cYWMUzoNFCMdtIlaQmZ3Un8rZU5B3+3U6IKuRSS7/mOHdNkkrFnml/fNmkoG +DKscKcmbgLMmm+T61yygIEO4VVtdCl5mA7l8/nfcLS5lUAO/wKYrOxf8s2Yw +gzIlAc4nYL892BBsNYmFOdUvVw9IYDRipSVdU4p/SW1i49RHoDrJYO8H90/Y +6VEgtCh8B9slvd+2pY9gn1xdbhWlD/ZU9y/94S5G3mH0lojagJv/yFxoIUY1 +tn/NOLcNNNMYp1m6YhxJO50zcaMNRNPy8Q6dg5jz56O6n83aQD/EXSV9bgBl +00SibGsr1EdMLifob/EX5p0y7/IWkMUay98Q96JjzFHnqZdCaGMIfbTye3HH +jbKommtC4Oz3EHCZvcgIt3ArNBaCvVrk9W75XhwpcXmodP85pCZ1LDI06sFW +4k224mkBmD4IWGgOFmHQDFeeUOXDhbziGVXaa7QyCT7osq0Wtiv5R1qLO/Bv +S9tGreIa+Bq4RYlZ1IHmm5MOpGyrgUDLvPWd9A48oSWprNrxFC62Zjonh7Zj +1JhL5awVDybGNtuZtLRizZnoMXF0BQQ9zj2e7NuKpTlV+9NWVMBUmH7QNKUV +h44rc/ZmPoYZFZ0MnskrXCy1PhBMloPMVG1yV0YLvo2kVQgUy0A+cubhvsAm +pFvYBWqkFEG048XKnOVNKKqavfmhoxAU1aXNijmNGM4MGZFTKYRleR+nXvQL +cWeY/VdzVj4otw44uux9jv3eou0KJTkQl+LhWTIoQIamnmLNj2xQ8+y5rHpV +gCtYG6MHnLJhxWR75mtuA44lzKldnswCzdWCmcOafNSlcRSMPDMhdchKiVdW +j+nxL41j+GzQ4j5br+VUj+fpm0yPbWTDWqsq5zcRdfgukVCVjGeAzSt3uzoR +ova1RQ/veaeBu+96dkcoD2ebnlsO706AWwHMmPiKKnTtHq0rOBQPtaF8huvn +J8jNusTTYLBAL8Frd8eJSrR4k6Yk8LoHUuT0t1uXI7Vh83mdwRjY0DxRzwop +w/yaxO8st2g4IrLJP/C4FK915dxO7ooCcvz9lXb9Eqyq1nAqlf4B2sa2WzJV +85GvrG+x1i4Eouw+zK2LzMVwpaNjNV1XYPxETBP7WzY66o1Ndl++BNV3Gn3Z +3Rx8JH6yKm4+ANZx/EzW2WXieOCDpMZGBsTwFJewqx/ihE4s37XhLBS1sKyt +LNLQSTu/0trVG0Jm2wcJ7RQUGTX4qUtOgt0GtTCCmoSS4f2nKgM8QOOgqxYx +xEIe1cDH/pYbNC/oMX6PvYu1w0+/zuvtB78jj/LCD0WjQo/MtCBtHywp1x8K +04rAliW3fG+6WwKxynHXHHkRO+/mhbaXbYGY53Ntv+qcwfSNBxwKCrXgXzLN +yZQ= + "]], LineBox[CompressedData[" +1:eJwVznk01AsbB3AmZC35uZVQiVerIreF6jy/ct1UyE0o5HbH8laIJEuWsjSU +bTIZe2YLP2sRIT1GUdfSXEWEkqIhW5YsdSuv94/nfM/nnO/5nkeL7nXMlSYh +IRG2cP/P6KffWk6sOQcSm/N7qtln0drwdTVjfyRclWYVLTrrh+WdduFRQTdA +eDXOvCEhEJWEw9p19kwQDj4I+GwbjMDKZ9T5s0ConbjN/3UoXnBz/1R3iw3M +zRqLdROvIs9os3n9vVQQhv57LoIXhm2Kw0X1ogzwJjscl3HDMePkDmPnSC60 +BJjt1roYiTtMktz7VPgwHiIt63r4Goq2TGc4cwUgVLhadHcFAyUkyuadMQf0 +HQvbI1KiMPWTqkG/OQXKWh6GJRbRuL3Vl+7SnQf6rd5eZt+j0SX713qXuUJY +22EfLjp4A1107eu3q5XA1c7/aFfzY1FfXb7Hp7cEvE8l3DbVj8MfS6tmSnJK +YfBejYpOZRyyv6ptMNxZBr1dJ/mlwnh81tx5w9C6ApiPs2XnbJh4JqDrmcPm +SlDWllk9douJsjrdUpGLquC+KfRffsnEw0FvQttKH8LrE88cMw7dxOaN73wu +qdZA/7WjzskbE9Hj1bvizJEaeH2R/ovYKREZpPcMnS6E/iilK7tYibh+xNsw +xrgWMg7Yjcp+TcQzJj6F3UOPYTCp597xKhbuTp1s+mz7BDTWVdoVDLJQ9rPP +0KInT+BvC07y78tvIZV2cf2W9DpQjVHQdfC6hUMTvtzgI09Bscl1IFMtCT04 +/kmaBQ2wcnuHZMIxNu6dmS01WNkIiS1pdXR/NiqaB7w0jWwEc6aqRU06Gwtn +A5aed2yCHpc599V9bByzvHwdFZ+DStPyb0KPZKwIRSze2QKrrNKr8zxT0Fiv +tsQquRWK7pb+LmeYhjva2tnY0AriS/bnnY6koX7QyOUt31uhJXXUOtQ5DXUb +VpjI/tUGKW1fn2ix0pBwPd9as+kV8By+SywZT8ORDPUvW7Ed5Kslnq7jpmOW +ot8OpY+d0CF7KDWnPwPTSmPUglZ0QZYs0ZA3m4Fse+6PwUNdYPZQxjNWPhNj +c5vr64q64ORur7qRbZkY8Ju2bXBAN9z9kaSjF5iJx4Jb/IYV3sKqbTaraTK3 +keb3yxsXtV4wLu4VWStkof3pvJcVv/ZCpkm1tLZGFpYchgZFq15Q5W/T6diS +hfQ1Z8vvM3phKpZ2/LNFFj7+u5op9aUX+nhxXQPxWRih7mIqEL0Hryq9zRoy +HJSqLSnqi+iDnvHo2/JBHHTMP3hnV1Yf2N2qcaaFc/B+0pv0mKo+8J01iRiP +5qDLOZnrhhN9kPeiVf8um4P1hL1zhFM/tNlGttTc4yDDTXKlttFHGFvv4W4o +5uBiRasw+pgYUsw/BMyacfHEenvhTrkBeLmqifnMkot5B1zm5XUGoCrqWjnz +OBctAwNCSk8OAEvayW3JaS6yxZxAqfoBcPPcM1Thx0Xd2okL2emDMKVldaOd +x0VTPxZ9yGwIOmv+cY6d4WJEb7uJD38UhnvljI3iedhTecQzoHoUtJM5DqcS +eWjMErJDX42Cus2FRyFsHo6b5n26sXgM3Aj2ydLbPHTKD0ngu4/B8oEnyZNF +C30/ne42w8/wYva3NU9FPPwqbVSpTh8Hx6PDvmIFPt5NZ1iFTk4AeBcoqoTw +sYlgDCyVmIR/TJKty6/yURxzLZSrNAkOa83i7CL5qBEcWVC3YRIGpZ8PMWP4 +GO0YLqvw5yR8+UO54V0qH09rhgqTmybBJ9qicaKMj8pZl/TvCabAcMvzD7QR +PnrxXJT7baeh1XrrSq6VAOMDUzPinachZLxojae1AIusRBuMvKdhOPnygV22 +Ahz7uWt//PVp2Epv+1DvIEAPBwWf3dXTsC93qKnZTYDnVEtaY7Vm4NCp8NUR +wQJ0Y8yzd4zMQJhb3WJOtgCdzqVpRoXNgb8urZk2I8Drf/gZGWb8C/xUzf9G +h91BKdUk8ZVvP2Fu+Y+4/dLZ2NF0bTxyqSRZ4JP71vtCNtoE0XemPaGRvr4N +4prObPRQGF4nspcirxg8MFhhkINr8p+yZYakSR6rbOOL0BwMqjCxXpq+mPw5 +WpCa2ZSD3tke5Tu3yZHNvGjLfUq5qEjbRd/6UZ5k1vUXU5a5aOp5PGkTS5H0 +iEXO++u5uLJS08tUZwmZvthdZvujXEz0ib6p37GUPCwellCayMVjjKN6meXK +ZJVswvCR1RRucoi0EYQsI/U0fZk/D1LYLpbjsWxUSLey2kdxPhSK6B/3q6wh +SHvaFe6PZArfS+XMJa0jyFzxqbWcFAq/ZJ8pVtMlyJnym/4HUilUGx7W0NIj +yFA/o2JGGoUuFydnt+0hyC1dVqZKmRR+i5gvtLAjyPPch6sIHoW6d9RWXU8g +yPC3VzolCyg0OtjdosgiyH6bL2FZCzb/lBHFZBNk11S51L5CCi/orZ1OzlzY +93JO9S+isLpMtyU7nyCLNklKDt+l8NhTQ0bdM4IUVF9obyyj0PXM9F6zJoL0 +ke/Y5FZOYYD8g6kmEUF+6wy0l3xAYaal8V+trwgysKjkyK4KCgfbyb0f+ghS +2eCGP7dq4d8A2pTrAEHmNPrm7HlIoZJ6HfVpiCAzvJeVvlrw9j8PrpiYIMjy +mLRTco8oNJWUE/lOE+TDWv533oJP8Bsj5+YI8s21FP+9SOE509g9wd8J0lsn +SvRqwSEDFpPz8wRZ/z5E0quGwv8BoJIl9A== + "]]}, + Annotation[#, "Charting`Private`Tag$67634#1"]& ], + TagBox[ + {RGBColor[0.880722, 0.611041, 0.142051], AbsoluteThickness[1.6], Opacity[ + 1.], LineBox[CompressedData[" +1:eJwVlnc41Y/jxY1IRhmRj7KbihQaRrkk3VIJSUTcUlEpMkLKHqFIxI/MzMoo +2fd9rh2XcO3syEhG9sdHfP3+OM95znP+Pq/nSFIe6FmyMDExfVrX/zuzyfOs +WRZO2r+zBRwm6ny0lGrntkcmm2g8OlZlm5x4aWberwUb0jbSFJnLeNJZeWhP +zVkzuQTYaft8WicMfTbRmGTFoemzgWbDc1GBTGKnfQ+M8nvfykKrPGZX8Pcn +C20H5530OQ1m2hT1cbHQyBruKsmwde1YQ+rOjirFP//ixtHetPLy/yBaqh67 +GDwHmcfKazbvltB/a9Z2YnYKCT36Fc6kefAXV1PYBEdweOjwcoviPApHrLPF +F4ZR8YtPXn7veq7SGj/bPozhxYbo4c3zuJasrdkSNQwZfp1H+t1zYIhrH/ss +PoxPp09JyTrNITOeZW+a3E9UZCm693+YhXvCtfHYq4MY8RBU1RaewVoF6W5e +bR843bKmwjhnsD2X3fpOaB/kHpOT+lf+IEjfzve0UR8cbdw4XQb+oNgo9Z7f +cC/YTX52fMj4gyNphSQxtl7sVPziwK/2B+azU6OfznaDMmyQ1WMxDdai10IC +Sx3wHZikyBhMQyLKc+ejig5kdPsLOZ2eRqKM8T8soR2YYZS48e6fxpm/skIf +ZTrA8owc6Ts6hcH7/zd/3LwdJw+NNV3imcJzb2HDUy2tKArfqzVqOIE1e4eJ +6n4GOExGbjCrTqBY8CArRy4DhhIpniKSE/jwKpX82I+BmQxpms74b9Bp3PQx +OQb20cRUcp79RuM3dz0B9yZE/tp6yCVtHHdPOChH7G+Ew0lmUe7lMbz4ofJc +WJeOsg00lV19Y1C/E8bNzkoHb+1T4xMVY4gQdDtlnFeLDwYrbx6+GIPhd813 +R8VqMWS1yN8qNYao2KoG+sxX6L2e4Ig9Nwqmgwx1v6wqyI91zh18O4yl07c8 +cx+XwX5adt8272H47KsXllIrQ8Gih+mq9TB0wv6mTDKXgcQuU1V3bBi+Or/O +JQeVQk/a5Y1Vy090cM4KBafQ4GAqopzE9RP2s7I8jA4qim7a2DyfGQLF+7hC +zn0qVu+WJdp2DmHr4xxpfVYqfF2sudRTh0Cqb/Dvly9B5Jui7m6NIVSMcZL2 +hRehqMn4mZDLIDYNnurL9MzHakfm57/mgygO1nPrks6HRj/L6JD2IJpzdCUa +KvNAn8zQ/Sw4iAh71Rvc3Hno5vpPUjfnByJK34v9TMjFmlZ0RcDoAM5YL6mr +zebg1PmppYcNA6hRDXaZjc+Bv4GmrFHeAMyfpXY8upgD3hvj4bu9B+Cu3RTW +nJkNKXeV2+XiA5D1eCuzazITp4q6Nv017EcU27eaMyYZyMxIPl6t0g9xQpXz +fkU6hKMfWIVK9MP1W03Ug4PpaFtkf3WupQ9GZRJRW7jSsMvVkPftci+mCgPG +CzqSsWTy68Ghil6QPkR/qNdNRp3q04bK4PU+frAMte9gv5r8YlKiF+f9dUuV +K5JQ5jHPra7dA1v7FReP+gREUALutfD2YFGNI9bRIAFWmqJ1d753Y5OoZYJW +Tzx42bQCQ+93w02k3aJnNA7X/V9vGgzrAt35ZE+WbQxWXiiw+/Z3Yv+xt2zm +hyPQ+KDaUiSjEzLWoc3ZLuFI0jWpzHzUibsfCeewqtc4y+/l3c7eiafO+VrM +VmGICmew7JPtQLVnPsv2jhDcc7xFoS60gxgwL3ijGgL1K8ull2jt2LabcpiX +/BKjwlIeLvrr+WL23ht/g3AkxnaN7tyGbHKJnnK+/zoP2K6ba7YhSknp3LU8 +P/SYRhFz3G04662cwV/iC2/xUjfR+FZMFA+HcHV5w4jpck+OVSuOkFY8FOe8 +cGBgVPW0Qiv09APSCAEvNCfyrthUtYDJQTqYsPRAitc7E9aQFmxusZDaFukO +l5vHit9cbUEIJeWgbMIzSO02d6H9boZrPxM5PPUJHqZnLfEJNOPJA4lVMw0n +yG+28dJY3/2xtRvXXEUc8cfuwOZHHxmg2n77fX3FHnaq6dIt2gxo6EgGMPXY +QSHhduYGQQb6tMDj0mWLObbdx5V+NOHQiHvukcGHcGhIvBDxpAkHlXKPtm+3 +wRFFi84qchMcx+VmlCzuYSFS/OaiUBPUs+0sF/Ot4USJcTbKaUR+yxbf+5G3 +cazaeEPA00bo/DrT6iV5C0v7/3lZeK4R1E1m+2hFNzH7az9Zqa4BAUFmFqY7 +KLDPTTOLuNWAA29N2wWGzLHgtst+kakBf2K2bD7qcB1LvOJxhUrfUD3zPtB+ +lwmcv0fnijTWY3Ct/+vRPVexnCRc62pdjy0uQRPVmlewcoR/Xi2uDlc/6Kaa +1erDjeklZ9zxOpTHSNJGDuthtYZLgqmFDnfBsG2an3XhHuavZGFDx6cjPnHG +4RfAbMp2royDjmFJRa7y6XPw3O1pLp1UC0vGKqeCExkbplcdvNVq8ay2c+OO +Pdpg91qKP21Xg6TzLkFCfzXgp+OQl8pdg2TTLZQNEiRwCM3QOVK/Ikz5Rxu5 +7gQC+mwGrEhfEd4YT62LVgFn+vhCbVc1NK0S9zx8fwyBdne4DzhWw2w22Vho +SQncqj8lg3mr0RmSEp7yVAEv2ChHJzOqUDHP57lZ9RC2NPTqXNSqwu2pwZt+ +xnIIiTShZPdVrvPhtfHzWBnwUzqc+FwqUXRZm035xB6E7b8cbLe1EmwSP1rK +FXZi63xTYnNmBQLmzjbbOksinLhQoEiugGnM6ISJgBiE/On14YPlyJXhm+Yk +/sGbS2cGF9zKsaBtrmk0Kgjh7ZVLV4TL0euiJb/mx4+oIdLmwk9lkPwvVVZm +9xaIZBLSIufLIB/z9ag4EydinFSOu46UwjdQTDA8kA2ipIIL3R6lSKqvyBDJ +Z0Ysp9JNtR2lkCdt9FUfWiHEW3KcY/NoiPu1fSuz8SIR/1bu5ZouDX1jgT68 +n2YIzW+G5NI2QFanRmAmYYI4baFr78UFnKSombopjxBn5shxWuoE3j4XHatZ +HSDO+mnWbnSgQiyR0V/q10XoiKjN16SXwCfdIC20soW48PGIRFBvMdTpb8R7 +Br4Rl9Tlz10QKMakmHPPWEQVYdC8z5H3TBEKZ+tv31SlEYa3pBMYTwqxnHJ5 +WednHvHc9pH/qy8FKLz+lD74PYugPil/oDeZD8pL+SmZj8nEtJ/AFf49+ZhM +OiFzlB5D7Ay7cYJxPQ91992ffI59RRjFft71KvILQkdlfttb+BGB6ydMrykX +OtWtIvesnhBErv4cH2cu2v3d28rfPSRmkNTVpPEZl9LkWtkKKMRu+mxZqOsn +8Ak/1YzYbkBcbdPMuJSbg/DQkUgWz1NE0EBYKN9ENrwXLfUOFSgQtN+Dj5t2 +ZaM8KVpJv0iSGJ26TZOiZsLAUpajyJ2HuMjO8TJR7uP63pr2RNstUPN2pJlK +xb/HTnrKw7bKXqqYwpkDiXwZ6CblM0JTy6g+5NFlSa80xLEHOTICk6i/r/vX +JMylwDH7QOUFeQ+qvuPeSMlbyfD1e2Xz0saIWhT09VZCexIi4lOHXb/IUCWT +7ihJkhPBVldEXWGdL/Ev5NiQUBSPO2bhITYlX0p64y4lk4xisShLDXFisi75 +WBeqQVKJRp6xvJNcD0+J679NfepikRBd4Fj0bI8sJu/md1NnDseS8ZITsxhr +MX1t54NnL4LhfTYo7I2waKF/1XKjkbg1bGzvylv6DST+D5pIDd8= + "]], + LineBox[CompressedData[" +1:eJxTTMoPSmViYGCwAGIQ3XHs14UI+Sx7BigINr6xp82xBc4vTMt+eWTKNDif +gWHr/+R9y+H842dudhkH74DzMypuHY/W3gnnc6jcZmlh3gXne1XfqbuyeTec +f0bzflGpyH6EfueitbdfHYLzcxaUT5VdcxLOt9I9uClg+mU4n6lM9E6K5AM4 +n50noDHp3TM4v/nBNeeixW/h/A2z2wLqPn2E8/MXpQg8CfsK58dlzZJtb/wB +53cGllkaz/kN57OITH1W/+sfnH/9dOuHFn5GBxg/tDrJbNZhJjg/h/u10rko +FjhffvWxaWyvWOH86h3Owfyz2eH8gmU528z0OeF8HibzJL2nXHC+a27IVK3J +PHC+xE7ZfFcVPjh/UlHHRIPr/HB+UJu/7txtAnC+VnRL6JJaQTj/2jPORZND +heD8c0lPHYXkheH8hyzLf0xVQvC/LMtYL6mG4Eu+fi2jqIvgpxR/+q5vjeD/ +av6/1jccwVdbKinV2Y/gW7rfvsAzGcH3eTmnfcI0BL9QV+Hr9LkI/p6taheW +rUbwg44Ztx05juCnZny18TiN4Fdwbf98+hyCP9fPKvHyVQT/xTUHm0ePkdxb +wfQ59TmCzyt9ZOXLVwi+Uby7+MePCL4rI+e5kq8IfsTiUy0/fiD4Wa491jV/ +EPza576f/v9H8AFRFcl0 + "]]}, + Annotation[#, "Charting`Private`Tag$67634#2"]& ], {}}, {}}, + AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], + Axes->{True, True}, + AxesLabel->{None, None}, + AxesOrigin->{0, 0}, + DisplayFunction->Identity, + Frame->{{False, False}, {False, False}}, + FrameLabel->{{None, None}, {None, None}}, + FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}}, + GridLines->{None, None}, + GridLinesStyle->Directive[ + GrayLevel[0.5, 0.4]], + ImagePadding->All, + Method->{ + "DefaultBoundaryStyle" -> Automatic, + "DefaultGraphicsInteraction" -> { + "Version" -> 1.2, "TrackMousePosition" -> {True, False}, + "Effects" -> { + "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, + "Droplines" -> { + "freeformCursorMode" -> True, + "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultMeshStyle" -> + AbsolutePointSize[6], "ScalingFunctions" -> None, + "CoordinatesToolOptions" -> {"DisplayFunction" -> ({ + (Identity[#]& )[ + Part[#, 1]], + (Identity[#]& )[ + Part[#, 2]]}& ), "CopiedValueFunction" -> ({ + (Identity[#]& )[ + Part[#, 1]], + (Identity[#]& )[ + Part[#, 2]]}& )}}, + PlotRange->{{-5, 5}, {-4.312847267426144, 2.212155257805333}}, + PlotRangeClipping->True, + PlotRangePadding->{{ + Scaled[0.02], + Scaled[0.02]}, { + Scaled[0.05], + Scaled[0.05]}}, + Ticks->{Automatic, Automatic}]], "Output", + CellChangeTimes->{{3.827493655651678*^9, 3.827493668239517*^9}, { + 3.827493771473319*^9, 3.827493828967701*^9}}, + CellLabel->"Out[52]=",ExpressionUUID->"5cd5b531-c23a-42bb-bea0-db89ec6f1525"] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"ComplexPlot", "[", + RowBox[{"itest", ",", + RowBox[{"{", + RowBox[{"x", ",", + RowBox[{ + RowBox[{"-", "1"}], "-", "\[ImaginaryI]"}], ",", + RowBox[{"1", "+", "\[ImaginaryI]"}]}], "}"}]}], "]"}]], "Input", + CellChangeTimes->{{3.827490076041252*^9, 3.827490130315631*^9}, { + 3.8274901830512238`*^9, 3.8274901845467873`*^9}, {3.827490769653777*^9, + 3.827490849440147*^9}, {3.827490905273271*^9, 3.827490940233993*^9}, + 3.827493554442696*^9}, + CellLabel->"In[34]:=",ExpressionUUID->"110a6801-f97d-466b-81da-59937fec81c7"], + +Cell[BoxData[ + GraphicsBox[{GraphicsComplexBox[CompressedData[" +1:eJx12z/IUFUYgPGPaqihwClwiWh1dGkQmxorbAlqsWhoKqTNpaFGhxoaBWlw +CZK2QrAcJBAicIlykCii/0JBa9/nPb83ei65HB4U73d87jn3/efjL79+5tX7 +Dg4OPr7/4OBo3X7dvWa9cOX2rQdv/jZ8/Ownl4+9/8vwIZw/fvan4ZPXzz37 +xIkfhz8/wr+/H37mkE5e/27428O//dSFO8NfHeGV28M/v/b2Dxef/nr4gXu/ +fWv41Au/H/6JL4fP3fsBb/z7vKMf9/ynw2+cP/oDl4avbnwav7n9+eF3tr9v ++LntecOPbD/P8F/bzzv8zbaf4Tvbfoef3/49hm9s/17DT27/nsMfbv/ew49t +Pobf23wNr7U8Xrvyi/nF/GJ+Mb+YX8wv5hfzi/nF/M7zll/ML+YX84v5xfxi +fjG/mF/ML+YX84v5xfxifjG/OZflnUfclV/ML+YX84v5xfxifjG/mF/M7zxv ++cX8Yn4xv5hfzC/mF/OL+cX8Yn4xv5hfzC/mF/Obe7a8O5f1iLvyi/nF/GJ+ +Mb+YX8wv5hfzO89bfjG/mF/ML+YX84v5xfxifjG/mF/ML+YX84v5xfzmu1ne +3bM9l/WIu/KL+cX8Yn4xv5hfzC/md563/GJ+Mb+YX8wv5hfzi/nF/GJ+Mb+Y +X8wv5hfzi/lNHFTefTd7z/Zc1iPuyi/mF/OL+cX8Yn4xv/O85Rfzi/nF/GJ+ +Mb+YX8wv5hfzi/nF/GJ+Mb+YX8xv4tryLg7qd7P3bM9lPeKu/GJ+Mb+YX8wv +5nees/xifjG/mF/ML+YX84v5xfxifjG/mF/ML+YX84v5TZ5S3sW1jYP63ew9 +23NZj7grv5hfzC/mF/M7z1t+Mb+YX8wv5hfzi/nF/GJ+Mb+YX8wv5hfzi/nF +/CbvLO/ylMa1jYP63ew923NZj7grv5hfzC/md563/GJ+Mb+YX8wv5hfzi/nF +/GJ+Mb+YX8wv5hfzi/lNHaG8yzubpzSubRzU72bv2Z7LesRd+cX8Yn7necsv +5hfzi/nF/GJ+Mb+YX8wv5hfzi/nF/GJ+Mb+Y39SFyrs6QvPO5imNaxsH9bvZ +e7bnsh5xV34xv/O85Rfzi/nF/GJ+Mb+YX8wv5hfzi/nF/GJ+Mb+YX8xv6nzl +XV2odYTmnc1TGtc2Dup3s/dsz2U94q78zvOWX8wv5hfzi/nF/GJ+Mb+YX8wv +5hfzi/nF/GJ+Mb+p25Z3db7WhVpHaN7ZPKVxbeOgfjd7z/Zc1iPuyi/mF/OL ++cX8Yn4xv5hfzC/mF/OL+cX8Yn4xv5jf1OHLu7pt63ytC7WO0LyzeUrj2sZB +/W72nu25rMd5XtbJjxZPfrR48qPFkx8tnvxo8eRHiyc/Wjz50eLJjxZPfrR4 +8qPFkx8tnvxo8eRHiyc/Wjz50X95V4dv3bZ1vtaFWkdo3tk8pXFt46B+N3vP +9lzWI+7KL+YX84v5xfxifjG/mF/ML+YX84v5xfxiftMnK+/6Kq3Dt27bOl/r +Qq0jNO9sntK4tnFQv5u9Z3su6xF35Rfzi/nF/GJ+Mb+YX8wv5hfzi/nF/GJ+ +0/cs7/pk7au0Dt+6bet8rQu1jtC8s3lK49rGQf1u9p7tuaxH3JVfzC/mF/OL ++cX8Yn4xv5hfzC/mF/ObPnZ51/dsn6x9ldbhW7dtna91odYRmnc2T2lc2zio +383esz2X9Yi78ov5xfxifjG/mF/ML+YX84v5xfxmLqG862O379k+WfsqrcO3 +bts6X+tCrSM072ye0ri2cVC/m71ney7rEXflF/OL+cX8Yn4xv5hfzC/mF/Ob +OZPybi6hfez2Pdsna1+ldfjWbVvna12odYTmnc1TGtc2Dup3s/dsz2U94q78 +Yn4xv5hfzC/mF/OL+cX8Zm6ovJsz6VxC+9jte7ZP1r5K6/Ct27bO17pQ6wjN +O5unNK5tHNTvZu/Znst6xF35xfxifjG/mF/ML+YX85s5sPJubqhzJp1LaB+7 +fc/2ydpXaR2+ddvW+VoXah2heWfzlMa1jYP63ew923NZj7grv5hfzC/mF/OL ++cX8Zq6vvJsD69xQ50w6l9A+dvue7ZO1r9I6fOu2rfO1LtQ6QvPO5imNaxsH +9bvZe7bnsh5xV34xv5hfzC/mF/ObOc3ybq6vc2CdG+qcSecS2sdu37N9svZV +Wodv3bZ1vtaFWkdo3tk8pXFt46B+N3vP9lzWI+7KL+YX84v5xfxm7ra8m9Ps +XF/nwDo31DmTziW0j92+Z/tk7au0Dt+6bet8rQu1jtC8s3lK49rGQf1u9p7t +uaxH3JVfzC/mF/ObOerybu62c5qd6+scWOeGOmfSuYT2sdv3bJ+sfZXW4Vu3 +bZ2vdaHWEZp3Nk9pXNs4qN/N3rM9l/WIu/KL+cX8Zi6+vJuj7txt5zQ719c5 +sM4Ndc6kcwntY7fv2T5Z+yqtw7du2zpf60KtIzTvbJ7SuLZxUL+bvWd7LusR +d+UX85v/51DezcV3jrpzt53T7Fxf58A6N9Q5k84ltI/dvmf7ZO2rtA7fum3r +fK0LtY7QvLN5SuPaxkH9bvae7bmsR9yV3/y/lfLu/zl0Lr5z1J277Zxm5/o6 +B9a5oc6ZdC6hfez2Pdsna1+ldfjWbVvna12odYTmnc1TGtc2Dup3s/dsz2U9 +4q78/t//S+IX84v5xZ2r7hxu5zY759e5sM4Rde6kcwrta7cP2r5Z+yyty7eO +27pf60StKzQPbd7SOLdxUb+jvXd7Tuu1q/0+9cqlt/54+PhV+8X2i+0X2y/+ +c+0X2y+2X3xm7RfbL7ZfbL/YfvG7a7/YPsPXHrp85YMXHz037zP2PmPvM/Y+ +48/W+4y9z9j7jL3P2PuMvc/Y+4y9z/O89T5j7zN+6cTpj3794uJ6v/26e+3Y +9vvT78f2j+0f2z++vvaP7R/bP7Z/bP/Y/rH9Y/uf5639Y/vH/wDqNunt + "], {{ + {Opacity[1.], Texture[ + GraphicsBox[ + TagBox[ + RasterBox[CompressedData[" +1:eJx83EeTJOmZ4Pc18sIjvwK/Ba975HVpnCWGi1kAAwxmIBtooBst0KK6qrq0 +1lmptYzM0FprmTp0hIdr+Qr30BlhRnfPzO4GwKXZ/3Vz9+vPnuP7/G8/+/1/ ++bf/6T/9p//04f+iP/7LTz/+z3/8408/+T//V/3j//rdh//xy9/94uf/x+/+ +9Itf/uKP//vP/mf955OrY7y3et1WV09rXtfoqpfVu9gM1S7TYPUqUDFSykay +3rkm6Z1pot6pJpjxJyqnd6yyekcqc6TSh0ZUSSX1imqnoBIFtZ03auXUZlZt +ZNW6WS2nVnNqxaycU89z6lne6DSvnuTxsdlRAR8WcKmAiwVcMMsXca6Is0Wc +KeJ0CadKOFnCiRKOl3DsEEcPceQQhw/V0JEaOFL9x6rvVPWdqb5z1VdRfVXV +X1P9ddXfUP1N1d/S/G3NT2j+juYntQClBWgtwGgBVgtwWpDXgkLXSOyGpG5I +7oYUozDohqFRBHUjWK8XVXtRzSjWNev14r1eQq/fTfa7KbP0wCgz6Gb1ht3c +UNPLmxVGRkWzktmhidVtGl1iaddYV141PU3HQtdY0MQC5Wuvc9PrzPQ61VMF +vRNV9+KPTa8j08vEokuml4lleF1jtbKmV0atZ9SaXlatZtVKVi0b4fMcPsvh +0xw+MTvO4aM8Pszjklkxjwt5nC/gXAFnCzhTwOkCThWNkkWcKJpeJRwp4XAJ +hw5x8BD7D7H3WPWeqN4z1Xuuesuqt6J6a6qvrvoaqq+p+lqqr636CM3X0Xyk +5qc0P635Gc3Pan5OC/BaQDATu0GpG5S7QdMrBLoh2A2hblgPd8NqN6L2IqZX +tGtkenX1Lr2uyK68NL3s0Oh7stE/kF1j/dBLu/ZSaxo207Eu07GgiXXldW4k +n6l60qkqmulYgolleJlY7KHpVTK9iippYnXyptc1VjOjNtJqPa3W0mo1g/Uq +GVzO4PMMPssanWbxSRYfZ/FRFh/mjEo5XMzhQg7n8ziXx9k8zpgZXgWcLOBE +AceLOFbE0SIOF3GohIMl7C9h3yH2HGHPCfacYs+Z6imrnorqqaqemuqpq96m +6m2p3rbqJVRvR/OSmpfSfLTmYzQfq/k4zc9rfsFM1AJSNyB3A4pBFgTdoOll +ZHoZad1ItxcxvLrRXjdmesX7PyAbaHpp0ysz/Fuy0SWZqlfUG6ul5vde3Wss +zcDSdKwrr6qR4WViwbKRQWZgqYqJJZ8aXgaZiSWYWPyR6XVoeplYdFGlCroX +7uSNiBxuZ3Eri5sZ3Egb1VO4lsLVFK6kcdnsPI3P0vg0g08y+NjsKIMPs7iU +xcUsLmRxPotzOaNsDmdyOJ3DqTxO5nEij+N5HCvgaAFHCjhUxMEiDhSxr4i9 +Jew+wu5j7D7B7jPsPsfusuququ6a6q6r7obqaaqetuohVE9H9ZCqh9K8tOZl +NC+reTnNx2s+wUzU/JLmlzW/0g0AM9gNIjPcDalGule4axQxva7I+npaoq8l +9a690qbXNZmaG6l5s7/z6l1jda+xtLqm1a69qtdeFbPytde5CkwsxcS68jox +vMRj0+vI9DKwMFvCTAnTRUwXMFXA5DUWkTW9Mrj5HVYSV80qKVxO4fMUPjM7 +TeOTND5O46M0PkzjUgYVzQoZlM+gXBZlsyiTReksSuVQMocSORTPoVgeRfMo +kkfhPA4WcKCA/QXsLWJ3EbsOsesIu06w6xS7zrGrjF0V7Kqprrrqaqiupupu +qe626u6oblJ1U6qHVj2M5mE1D6d5ec0rmImaT9J8suZTND/oGsFuAHUD2PAK +qt2g1g3pmV7hXjdy5aXF+tqlV2Jw5XVFNlQzZpdef082VoumV69x5dXVpS67 +9KoaGV4VIx0LlVWoZ2KBs7/1OjG9jk2vI8zrHWLOxDK8TCzDK296mViGV+ba +K4XrSdMrgSsJXNZL4vMkPkvi0yQ6SaHjFDoyO0yhUhoV06iQRvk0yqVRNoMy +GZTOoFQGJbMokUXxLIplUTSHIjkUzqFgHgXyyJ9H3jzyFJCriJ0l7DzCzmPs +PMXOM+w8x84Kdlaxs4adDdXZVJ0t1dVWXYTq6qguUnXRqptR3azq5jQ3r3n0 +BM0jal5J88qaV9F8QPNBTffyo64fG2QB0yvYNQpdeWl6UdPrimxwSaam9IZq +2uzSKzv6W7KxUdHE6l1jXaZjGVWvvUwsXFaRmY5ldGZ4GWSnRrKJJR1jUe8I +CyaW4VUyYouYMbHovOmVwx0Ti8iYXmncTOFG0vRK4GocV+K4HMfncXSWMDpN +oJMEOk6ioyQ6TKJSEhVTqJBC+RTKpVA2hTJplE6jVBol0yiRQfEMimVQNIMi +WRTOolAWBXLIn0O+HPLkkTuPnAVkLyH7IbIfY/sJtp9hxzl2lLGjih017Khj +RxM7WqqjrToJ1dlRnaTqpAwyF6u6ONXFq25BMxI1j6R5ZM2jaF6geaFB5kOa +D3f9qlFA6wa6l2RaqKeFL736RqaXGh+oiYGaNNO9UtdemZHhlR3hnFleb4wL +Y1xsXHppvWus7jXWlVfFSMe68jo30rGuvEws5UT3wvIxlkwsw+vQiDexuCJm +C6ZX3vTKYTKLOllEZFBbL41aKdRMokYS1ROoFkfVGKrEUDmGzmPoLI5O4+gk +jo7j6CiODhOoZFZMoEIS5ZMol0TZJMqkUDqFkimUSKF4GsXSKJpGkTQKZ1Ao +g4IZ5M8iXxZ5s8idQ84csueRrYhsJWQ7QrYTZDvFtnNsK2NbBdtr2F7H9ga2 +t7C9je2E6uioDlJ1UKqDVp2M6uRUJ6+6BD3NJWpuSXPLmlvRPEDzQM2LzLDm +U7s+revX6+pk2qXXFZnhperFTK/vya68sF5mZJQ1y5lYl16Fa6zLdCyj6pWX +ZmCpqollZGKhs2uvUz2snBjpWIbXkZFoYgkl06uIuYLuhZg8ovVyiMoiwytj +eqVRO4VaSdMrgerxa68oKkfReRSdRdFpDJ3E0HEMHcXQYRyV4qgYh4U4zCdg +LgGzCZhJwHQSppIwmYSJJIylYDQFIykYTsFQGgbT0J+Gvgz0ZpA7g1xZ5Mgi +Ww5ZC8haQtZDZD1G1lNkPUPWMrZWsLWKrXVsa2BbE9va2EZgWwfbSdVOqXZa +tTOqg1UdvOoQVKdo5JI0l6y5FM0NNDfUPEjzYCOvqnk1nUzzd40MsisvNdxX +I9desWuvxBAnzVKmV3r0PZkxYuNrsobWv8bqXWNdplVUzcS6TMfCJtZl8BTr +gRMj5dhINrGkQ8NLLOleiC8irmDE5g0vJoforOmVMb2usQyvBGrETa9LrAg6 +D6OzCDqNoJMIOo7Coyg8jMJSFBZjsBCD+RjMxWA2DjNxmI7DVBwmEzCRgPEE +jCVhJAnDSRhKwmAKBlLQl4LeNPSkoSsNHRloz8CDHNzPo/0i2j9E+0fo4AQd +nKGDc3RQQQdVfFDDBw180MTWFrYS2NrBVhLbKNVGqzZGtbOqnVftguoQVYek +OmTVKWtORXMBzQU1N9Lcupdqpulkmu/aK9BTgz01dO1lkA10L6wXH2DdK3Ht +lRoZXunvRmyMcmZ5PdOrb2IZXWN1TSytbGR4nRvhMyN0ipGJBU0sYGIpR4aX +fKh7IbFkJBQRXzDi8qZXDjFZ0ytjeqURkUJtAws2E7ARh/U4rMVgNQorEVgO +w/MQPAvB0zA8CcPjMDwKw8MILEVgMQILUZiPwlwUZqMwHYOpGEzGYCIO43EY +i8NoHIYTMJSAwQQMJKEvCb1J6ElBVwo609CehtY03M9CSx5aCtBSQpYjZDlB +llNkOUeWMtqvov0a2q/j/Sbeb+GDNj7o4AMSH1DYSmMro1o51carNkG1i6pd +Uu2y6lBUB1CdQHNCzYU0F9bcqubWDC+DrKuTqf6ueullkPV1MhzRG+DotVf8 +2ssgGyG99AhlzHSv7N95XWNdpmMZla+8NBNLNbAwNrGMTgwveGx6HZleh0hP +0rGKRoKJxedNLxPL8MpAKg3JNOykIJGE7SRsJWAzbnrFYC0KqxFYCcNyyPQK +wpMgPA7CoxA8DMFSCBbDsBCG+TDMRWA2AjMRkI6AVBQkoiAeBbEYiMZAJAZC +cRCMg0Ac+BPAm4CeBHQnoTMJ7SloS8GDFNzLwL0c3CvAvRLcO4R7x2jvFO2d +ob0y2qugvRqy1JGliSwtbGnj/Q7eJ/E+hfdpfMDgAw5bedUqqFZRtUmqTVbt +imoHqgPqaU6kObHmUjWXdkmmertGBllPJ8PBHg71jcLXXgbZUPdCeokhSupd +exlkY6PvR+yH81VVjSpGOtZlOpZmYqlnWD01vLCJhUwsw+tIDymHRnIJSUUj +sWB4CXnTKwfZrBGTgXTa9ErBTtL0SsBW3PSKwXoU1iKwGr72CsLTADwJwOMA +PArAwyAsBUExCAohkAuBbAhkwiAdBqkwSEZAIgJiERCNgkgUhKMgGAOBGPDH +gC8OPHHgjgNnAjgSwJYAB0lgScLdNNzJwp083CnCnUO4cwR3TuDOGdo9R7sV +tFtFu3W020B7LbTXxnsEtpDYQmELjfcZvM/hfR4fCOqBqFol1SqrVkW1AdUG +VTtS7Vh1YM2hak5NdWmqW1M9l1497DcL9HHw2is8QJEBig5QbGh06ZUYXXld +kV17Zccwp9dQ+3Wzmvq91zVW18TSzrBmYl15mVjo2AgeIR0LmFhKCclFI6lg +eIl5KOQhn4Nc1ojNQCZteqUgmTS9ErAdN71ioBEF9QiohUE1DCohUA6CswA4 +9YMTHzj2g0M/KPlBMQAKAZAPgFwQZIMgEwSpEEiGQCIE4mEQDYNIGIQjIBQB +gQjwR4EvCjxR4I4BZww44sAWB9Y42E+A3QTYToHtDNzOwe0C3C7B7SO4fQK3 +T+H2OdyuoO0q2qmjnQbaaaHdNtol0C6Jdym8R+M9Bls4bOGxRcD7It6X1ANZ +PVBUK1CtULUh1YZVu2rk0NQrsi72dLG3h33XXoE+CvZRaIAuvQyy4Q/IRlAv +OYIpvTFMj2HGLGv2P/LqmVhGJpZ2amSQnRhe2MBC6AjpXvDQ8AIlpJhYcgFK +BahjGV45yGeNuAxk06ZXClJJQCZBJwGIOGjHQCsGmlHQiIB6GNRCoBoClSA4 +D4AzPzj1gRMvOPKCQy8o+UDRBwp+kPODrB9kAiAdAKkASASVeFCJBZVoSAmH +lFBICYYVf1jxhRVvBLgjwBUFjiiwx4A1BvZjYC8OduJgMwk2M2AzBzYLcLME +Nw/h5jHcPIVb53CrDLeqaKuGthpou4m222ibQDsk2qHQDo13GbzL4T0e7wnY +ImKLhPdldV9RD4B6AFUrUq1YtX3vhV1d7Dbz9HQy5Oshfx9degUH12RDqBcd +wtgQxkdGl17Ja6/vyS7+xsskw70K7pWNuudYxzIysbQTA8vwOkZGR4YXOkSw +ZGCBou4FlQI0vPJQykExBwUTi89ALg3YNGBSgE4CwysByDjoxEyvKGhGQCMM +6iHTKwjKAXDuB2c+cOoFxx5w5AaHHlD0gIIX5L1KzqtkfUrap6R8StKvJPxK +LKBEA0okoISCSjCoBIKKL6R4Q4o7rLjCiiOs2COKNaLsRxVLVNmNga0YWE+C +9TRYz4L1PFgvgo1DuHEMN07hxhncKMONKtyswc0G2myirTbaItAWibYptE2j +bRbvcHiHx7sC3hXxnoT3FGwB2ALVfaQe6GHVqupk2K5hh4ad3Usy5Okhr5mv +f002gCGz8LWXQTb6AdnY8LomA5kxyF6AbAP362Y1oyuvS7LzK6yuiWV0jNVj +pB4ZWPjQwEIlwwsWIdArmF55KOdMr6zuBYQM4NPA8EoBJml40QlAxQEZM7yI +KGhFlGZYaYSUekipBZVqQCn7lXOfcuZVTjzKsVs5cikll1J0KwW3knMrWY+S +8Shpr5L0KgmvEvcpUZ8S8SthvxL0K4GA4gso3qDiCSquoOIMKfaQYg0rB2HF +ElF2I8p2VNmIKmsJZS0F1jJgLQfWCmCtBNaOwNoJXDuD62W4XoHrNbjegBtN +uNFGGwTaJNEmhbZotMWibQ5t83hHwDsS3pXxroL3AN6D2IJUC1b3sXqgYquK +bZpJ1kXOLnJ1kbtnkvV1L+jXG8DAAAavva7IRiBmFh+BhN4YJMcgZWZ4XRj9 +nVf/H70uyQwsZHRkeKmHhhcu6V4QFSE0sQyvPFRyplcWiHoZIKRNrxRgk0ZM +AtBxhYopZEzpRBUiorTDSjNkegWVWkCp+pWyTzn3Kmce5cStHLuUQ6dScigF +p5J3KjmXknUpabeScitJtxL3yDGPHPXKYa8c8skBn+z3yV6/7PHLroDsDMj2 +oGILKgdBxRJSdkPKdljZDCtrEWUlrqwklZWMspIDKwWwUgIrR2D1BKyegdVz +uFqBazW4VodrTbjehusEWifRBoU2aLTJok0ObfFoS8TbEt6W8Y6CdwDehXgP +4T2MLRjvq9gg05BNQ/YuMsh6yNWD7h709KG3D33XXoEBCA5BaAjCQxDRG4Ho +tVd8fOV1SZa+MPoHL9Svol7FrIx656h3hrp6p6h7coWlmViqiYVNLMOrYATy +EOR0LyBngZQxEtOmVwrwScAlFDahMHGFjpleUaUTUYiw0g4pzaDSCCr1gFLz +K1WfUvYq5x7l1K2cuJRjp3LoUEp2pWBX8g4565AzTjntlJNOOeGSYy456pYj +bjnkkYMe2e+VfV7Z45XdPtnpkx1+2eaXDwLyfkDeC8o7QXkrJK+HlNWwshRT +lhLKUlpZyipLeWW5CJYPwfIxWD4Fy+dgpQJWanClDlebcLUNVwm4RsI1Cq3T +aJ1FGxza4NGmiDYltCXjLQVvA7wD8Q7Cuxjvqdiion0NXXtBRxc6e/A7L08f +ePvANwD+AfjO64rM9LoiGysJs+RYSeldKOkLJaPXQIMG6teRgWV69X/odf69 +V/fS69BILUE9XDRCBYjyEBpYQE/JAjljJKWBmAJCShGSCp9QDK+4wsQUOqpQ +UYWMKJ2wTITkdlBuBeVGQK775ZpPrnjlskc+d8unLvnEKR855EO7XLTJBauc +s8lZm5y2yym7nHTIcYccc8oRpxx2yUGXHHDLPrfsdctuj+z0yA6vbPPKVp+8 +75P3/PKOX94KyBtBeTUoL4fkhai8kFAWUspiRlnMK4tFZfEQLB6DxVOwdA6W +KmCpCpbrcLkJl9twhYArJFyl4CqD1li0xqF1Aa2LaENCmzLaBHgL4i2EtzHe +wWhXRXum14EGrV1o60KDrKeTAVcfuPvA8BoYXgbZEASGOpkSGirhkVFkpERH +Smxs9D3ZheF1Rfb/5wWNzmD3FHZPYPcYakdQO4RayUgtGuECxHndC8CcEcgC +kAGK7pVWpJSRmFSEhOkVV9iYwkRlOipTEZkMy52QTATldkBuBeSGX6775JpX +rnjksls+d8mnTvnEIR/Z5UObXDyQ8/ty7kDOHMhpq5y0yQmbFLNLUbsUdkgh +hxRwSn6n5HVKbpfkckkOt2R3S1aPtO+V9rzSjk/a8skbfnnNL68E5MWgPB+R +5+PyfFKZzyjzOWW+oMyXlPljZeEULJyDhTJYrILFOlhsgqU2XCLgMgmXKbjC +wBUWrvJoVUBrIlqT0bqCNgDagGgT4S2MtjHaMbygRYP7GjzoXpIBew84esDZ +vyYbKN6B4hso/qESMDPIrr0Msmsvg+zC8Epee6VNr4HhBY2qsF8x6pXhP3r9 +kMzwMrCAHsoBlAVQL6N7KUpakVNGUlIRE4oQV/i4zMdkLiqzEZmJyHRYJkNy +JygTAd1Lavmlpk+qe6WaR6q4pbJLOndKpw7pxC4d2aTSgVTcl/IWKWuRMhYp +tS8lD6T4gRSzShGrFLJJQZvkt0s+u+RxSC6H5HRKdqdkdUn7bsnilnY90rZH +2vRK615pxSct+aW5oDwblmdj8mxSnk3Ls1lltqDMlpS5I2XuRJk7U+bKYL4K +5utgoQkW2mCBgIskXKTgEgOXWbjMwxUBrUhoVUZrCloDaB2iDYQ2MdrCcEeF +uyrc03QysN8FB11g7QFbTydTHH3F2VdcA8U9UK7IhldkwZGsFxrJ4ZEcGctR +s9hYjo/lxIVR8kJOmaUbcKBXh4PvvKp/5wV6p6B7ArrHRtoR0A6BVgJqEagF +oOpeOYCzhhfKAJhWgF5KUZKKnFSkhCLFZTEuCzGZj8pcxPQKy3RIooISGZAI +v9T2Sy2f1PRKdY9Uc0tVl1R2SucO6dQuHdukowOptC8VLFJ+T8ruSuldKbkn +JSxSzCJF96XwgRQ6EANW0WcVvTbRbROddtFuF20O8cAhWpzSrkvadkmbbmnd +La16pCWvtOCV3vulmZA0E5VnEvJMSp7JyjN5eaakvD9S3p8o78+U2bIyWwWz +dTDXBHNtME+AeRIs0HCBgYscXOLhkgiXJbgioxUFrUK0htA6ghsYbmK4repk +YFcDexqwGF6KtafYeoq9/0Mv2TOQvUMj31D2D+XAd15jo8i1V+xCjl97Jf+H +XqBfAf0y6J2bfed1SXbtpV17qVnDC2cUlFZ0L5hSQNL0SshyXDa8YrIQlfmI +zIUlNiwxIYkOSlRAIv1Sxye1fVLLKzU9Yt0t1lxi1SmWHeK5XTy1iccH4tG+ +WLKIhT0xtytmtqX0tpjcEeO7YmxXjOyJIYsYtIj+fdG7L7oPRJdVdFhFm008 +sIkWu7jrEHcc4pZTXHeKqy5x2S0uuKVZj/TOJ70NSW8j0tu49DYlv83Ib/Py +26L87kh+d6K8O1NmyspMVXlfV943wfs2mCXAHAnmaDDPwHkOLvBwUYSLElxS +4DJAKxCtILiG4LrhBbZUsK2BHQ3sdhVLV9nvKgc9k6wv2/uyoy87B7JrIBtk +33mNDK/ASAqOpNBYCo+liFn0QopdSPELKWGWvJBSEyl15QUGNSMD69qr/72X +0jtRunrHSvdI0Q4VraRoRUUtKGpeUbOKjoXThhdKKTCpe8kgIStxWY7JUkwW +o5IYkYSwxIclLiSxQYkOSJRfJH1ixysSHrHlEZtuseESa06x6hDLdvHcKp4e +iMf74qFFLO2JhV0xty1mtsTUppjYEuPbYnRbDO+IwV0xsCv69kSPRXRZROe+ +aN8XrQfivlXcs4o7NnHLLm7YxTWHuOwUF53inEuccYuvveLroPQ6Ir2OSa+T +0uuM/Donvy7Kbw7lNyfymzPlbVl5W1Xe1ZV3TWWmDWY64D0J3tNglgVzHJgT +4LwIF2S4qMBFAJcgXEZwFYE1DDZUsKmCLU3Z1hTda08n68n7PfmgJ1v7skE2 +kB0DnUxyDSX3UPIMJe9I8o0k/0gyvMaG13dkl17fkSUnRqkGGOhdew2uvJR+ +WemfKz29M+XvvLrXXtqlV+7KC6cUlJRRQoYJGcRlJSYrUUmOSlJEEsOSEJL4 +kMQFRTYgMn6R9omUV+x4RMIttl1i0yk0nELNLlRtQtkqnB8Ip/vCsUU43BNK +u0JhW8htCZlNIbUuJjbE2IYQ2RRCW0JwW/BvC94dwb0rOHcF+55gtQj7FmFv +X9g5ELYOhA2rsGYTVmzCkl2cd4jvHeJbp/jSI74IiC/C0suY9DIpvUxLL3PS +y6L86lB+dSy/OpNfl+XXVeVNXXnTVN62lbcd5R0FZmgww4L3PJgVwKwE52Q4 +D+AChIsQLCGwgsEqVtZVZUNVNg0veacr73blvZ5skPUla1+y9SX7QHIMpH/0 +8o1E/0gMjMXgWAyNxfBYjFwYRS/E2IWoe8UnUuL/w0sZVJW+3qXXJdmVl6zX +PZa7R3L3UNZKslaUtYKs5mU1J6sZGadlnJINr7gM9WISiEqGV0SSwpIYkoSg +yAdFLiCyfpHxibRXpDwC6RYIl9B2Ci2H0LALdZtQtQrlA+F8Xzi1CMd7wuGu +UNwWCltCblNIrwvJNSG+KkTXhPC6ENoQApuCb1PwbAmubcGxLdh2hINdwbIn +7O4J2xZhc19Y3xdWDoQlq7BgFWZtwju78MohPHOLz/zis5D4LCo+T0jP09Lz +nPS8IL04lF4cyy/O5Jdl+WVVflVXXjWV123ldUd5QylvGfCWBe94MCOC9xKY +VcAsgHMQLECwiJRlrKxgZU3VyeQNTd7S5O2uTibt9iRLT9K9DnSygWQbiPaB +6BiKzqHoGorukegZid6RaHiNr7wMsgsx/AOv2ESMT8TEREzqNcCwoQzqioFl +eg2uvGSjc7l/JvdO5b/z6pYkrShpBUnLS2pOUrMSTks4JeGkhOISikkwKoGI +kRKW5JAoBUUxIAoBkfeLnE9gvQLjESi3QLqEjlNoO4SWnW/Y+LqVrx7wlX3+ +3MKf7vHHO/zhNl/c4vObfHadT6/xyRU+vixEV/jwKh9c4/1rvHedd2/wzk3e +vslbt/j9bX5vh9/Z4Td3+fU9ftXCL1v4hX1h7kCYsQpvrMILu/DEJTzxiU+C +4pOI+CQuPk2JT7PS04L09FB6diw9O5Wfl+XnVflFXX7RlF+2lVcd5RWlvGaU +N5zyhgdvRfBOBjMKeA/ALATzSFlAyhLWyeRVVV7TdC9psyttdaXtnuG11xct +fXG/Lx4MROtANMiG12QjnUzwjATvWPCNBf9YCIyF4IUQuhDCZgbZ5Mrriqyh +6F7D771ko4r8t15S78TsWOoeSd1D6R+91L/zikgwLIGwqIREOShKAVH0i4JP +4H0C5xVYj8C4BdrFk06+4+AJO9+y8U0rXz/gq/t8xcKf7/KnO/zxNn+4xRc3 ++fw6n13j0yt8cpmPLfKRRT60xAeWed8K71nlXWu8Y523rfMHG/zeJr+zxW9t +8xvb/OoOv7zLL+7xcxZ+xsK/3edfHvBPbcIjp/DIKzwKCo8i4qO4+CglPs6K +jwvS45L05Fh6cio9LUtPq/KzuvysJT8n5Bek8oJWXjLKK055LSivJfBGBm8V +8A4o76Eyh5R5JC9ieUmVV1RpVZPWNWmjK252xa2euNMTd/uiQTYQ9geCdSDY +hoJ9KDiGgnMkuEaC4TX+G6/AxfdkkYkQNYtNhPhESEyEay95WJMHNfk7r4Hh +JfXPpf6Z1P+BV+9I7B6K3ZLYLYpaQdTyopYT1ayopkWcEnFSRAkRxUQUFWFY +BCERBEUlIMh+QfIJolcQPALv4Tk3z7h42slTDp6084SNa1u55gFX3+dqe1xl +lzvf4U63ueMt7nCDK65z+TUuu8Kll7nEIhdb4CJzXHCB8y9y3iXOvcw5Vzj7 +Cmdd5Sxr3O46t73BbW5ya1vcyha3uM3N73Dvd/m3e/wrC//cwj8+4O87+Pse +4X5AuB8WHsSEBynxQVZ8mBcflsSHx9KjU+lRWXpclZ405Cct+SkhPyPlZ7Ty +nFVe8MpLUXklKa8V5Q1Q3gJlBsqzSJ7D0gKWFlVpWZVWNHGtK653xY2e7iVs +94SdvrDbFy69DoaCdaiT8fYR7xjxzhHvGvHuMe8Z894x7xvz/gs+cMEHL/jQ +BR/Wm1yRXXoZZA15qPc3XtKgIg3K0uD8Oy+xfyL29I7Fv/UStLyg5QQ1K6hp +QU0JOCnghIBiAooKMCzAoAACAvALik+QvYLk4UU3z7t4zsmzDp6xc5SNI61c +54Br73NNC9fY42q7bGWHPd9mz7bYkw32cJ0trrH5FTa7zKYXucQCF5vjwu+5 +4Cznm+M885xrgXMscrYlbn+Z21vhdla5zTVufZ1b2eCWNrj5TW52i3u3zb3e +4V7sck/2uAf7/F07f9fN3/ULd8PC3ZhwLyncy4j38uL9knj/WHxwJj0oSw9r +0sOG9KglPybkJ6T8hJGfsvIzXnkuKi9k5aWivALyGyi/g9J7JM1iaR6LC6q4 +pInLmrjaFda6wnpP2OwJW31hu8/vDvi9AW8Z8PtD/mDIW3/oNf6B18WV1xXZ +RPfiIxM+OuFjZvEp/wMvSc/A+t5L7OudiT/wEnpHQu9Q6JaEblHoXntpWV5N +82qKx0keJ3gU41GUh2EehngQ4IGPV7y87OElNy+6eMHJ8Q6Os3OMjaOtHHXA +dvZZwsK29tjGLlvbYatbbHmTPdtgT9bZo1W2uMLml9nsIptaYBNzbHSWDc+w +gXesb4Z1z7LOOdY+z1oXWMsiu7vEbi2zGyvs6iq7vMYurLNz6+zMBvtmk3u5 +xT3d5h7tcHct3G0bf9vN3/bx34b4b2PCt0nh24xwJy/cKYl3j8W7Z+K9snSv +Jt1vSA/a0sOO9JCSHzHyY05+IshPJeWZrDxX5JdAfg2lt1CaQeJ7LM6p4rwq +LGrCkiasdIXVLr/e4zd6/Gaf1712BjoZtzfkLEPuYMhZR5xtxNlHnGPMOcec +a8y5x5zngvNecL4Lzn/BBS644IQLTbjwd2RTPjY1vOKGlzSsS5deQ8NLHFTE +QVnUvQZXXkL/xOjai++V+G6R7xb4bp7Xcvx3XmqSwwkOxzgU5VCYgyEOBjjD +y8Mrbl52cZKTEx2cYOc4G8taWeaApfZZ0sISe2xrl2luM/UtprrJlDeYs3Xm +ZJU5WmFKy0x+kckuMKk5JjHLRGeY8Fs28Jr1vmXd71jHDGt7z+zPMnvzzPYC +s7nIrC0xK8vs4go7t8q+X2PfrrOvNthnG+zjTfb+Fnd7j7tp4266uJs+/maI +vxnlbyWFWxnhVl64XRJuH4vfnol3KuKdmni3Kd1rS/c60n1aesDKD3n5kSg/ +luQnsvxMkV4A6RUU3yDxLRJnsDCrCnOqsKDxi11+ucuv9Pi1Hrfe5zb63NaA +2x5wO9de+yPuYKSTsbYRax+zzjFreF38rdfE6JqMi0y56JSLmcV1rO+9xGHV +6NpLMDoTrr34/jHfO+KvvbhugevmOS3HaVlOS3Nqirv2YlGURWEWhlgYYIGP +Ax5OcXGyg5PtnGhjBSvLH7DcPstYWHqPIXeZzg7T3maaW0x9k6lt0JU1+myV +Plmhj5bo0iKdX6Czc3Rqlk7MMNG3TOg143/FeF4xrteM/Q1jfcdYZpjd98zW +LLM+x6zOM0sLzPwS836ZebfCvFplnq+xT9bZBxvsnU32xi77tZX72sl97eW+ +DvI3ovyNBH8jw3+TF74pCTePhVtn4q2KeLsuftsUvyWkO6R0l5busdJ9Xn4g +yg9l6bEiPVXE50B8CYXXSHiDhXeYf6/ysxo/r3ELXW6pyy33uNU+t9ZnN/rs +5oDdGrA7Q3Z3yO4NWcuI3R+xhtfY8HLoZBes64J1X7CeC9Z7wfomrH/CBiZs +cMKGJmx4anh9R6Z7jfTqooF16VXREwZl4dqLH5zyBpbp1T/ieodcr8T1rrzY +bo7VsqyWZrUUqyZZNcHqXtjwYlCIgQEG+FjgZRU3qzhZ2cZKVlY8YIV9hrMw +7B7D7DLUDt3ZpolNurVBN9bp2hpdWaXPl+nTJfpokS7N04U5OvueTs3Qibd0 +9A0dekX7X9CeZ4zzBW17RR+8pvfe0Nvv6M0Zeu09vTxLL8zRs/P0zALzeol5 +scw8XWEerjJ315hb68yXO+wXB+wXDvZLL/dlkPsywn2Z4L/K8F/l+a9LwtfH +wo0z4ZuK8E1dvNkSbxHibUr6lpHucNJdQbonSQ9k6ZEiPgHiMyi8gMJLxL/G +/FuVm1G59xo31+Xmu+xij13qsSt9drXPrg/YjQGzOWS2h8zOkNkdMZYRsz9i +DsaMdczYxoz9gnFcMK4Lxn3BeC4Y74T5zssgm7KhqU7GRqZsdMrG9BriSK8u +jq68BB3LyPDijUyvwQnXPzY74vqHbK/E9opsr8CaXkw3y2hpRksxapJREwyO +MTjKmF40DNDQRwMvA9yM4mRkOyMdMJKFEfcYfpfhdmhmm6a3aHKTJjao9jrV +XKPqK1R1mTpfok4XqON5qjRHFd5T2Rkq/ZZKvKair6jQC8r/jPY8oR1Paetz +ev8FvfuK3npNr7+hV9/RSzP0/Hv6/Sz9do5+uUA/W6QfL9H3l5lvV5gba8zn +28zn++znDvZzD/t5gPs8wv01wf01w3+R57845L88Eb46F76qCl83hBst8ZuO +eJMSb7HibV76VpTuSOI9WXygCI+B8BTyzxD/AnGvMPdG5d5p7IzGznbZuS67 +0GOW+sxyn1kdMGsDZt302hrS2yN6d0TvjWjLmN4f09Yxbbug7Re07uW8JJsw +nsklGeOfMIEpE5wyoSnznVf0b7wEvWsvfljmh1de3OCU070GhhfbP2J1r77h +xfQKTC/PmF60lqa1FK0laTVBqzEaR2kcplCIQgEK+ijgpYCbUpy0bKflA1qy +0OIuLezQ/DbNblHMJkWtU501qr1KNVfI+jJZXSTLC+TZPHk8Sx6+JwvvyNxb +Mv2aTLwioy/I0DPK94RyP6IcjyjrE8rylNp5Tm2+oNZeUcuvqYU31Ow76t0M +9fo99XyWfjJPP1ig7yzSN5foL1boT7aYTyzMJ3b2Ew/7SYD9NMJ9muA+zXCf +5fnPD/nPT/i/nvNfVIUvG8KXbeErUvyaFm9w4k1BvCWK30rCXVm4r/APAf8Y +ck8R9xyzL1X2tcq+1Zh3XeZ9l5nrMfM9erFPL/XplQG9OqDXh/TGkN4cGV47 +OtmY3jO9DnSyiysy54R2TWj3hPZMaO+E9k1p//R7L5OMiUyZ6JQxvYRRXbj0 +GlV5A+vKizMyvNjBCTs4NuofMf1Dpl9iTC+6l6d7ObqbobtpSktRWpLS4pQa +o9QohcMkDpEoQEIfCb0kcJOKk1TspGylJAsl7lLiFiVsUtwGxa6T9BpJrpDE +MtlaIhuLndpCpzLXOZvtnLzvHL7rFN92cq876VedxItO9BkZekL6HpHuB6T9 +HnXwgNp7RG4/ITeekavPyaWX5NwrcuY19eYt9eId9XSGejhL3Zujbs1TXy/Q +ny3TH23SH+0xH9mYj9zMRwH24wj7cYL9S4b7S4H75JD79JT/tMx/VuM/bwp/ +JYQvSOFLRviKF78WxG8k4ZbM31H4e4B7ALlHkH2C2GeYeaEyrzTmtUa/7dIz +PXq2R8/1qYU+tTiglgfUypBaG1LrQ2pzRG2NqO0xtTum9saUZUztX1DWC8p2 +QdknlGNCOSeUa0IZZFPaO70kowNTOjilQ1M6PKUjUzo6pWM61pUXb1TlR4YX +NyybWOfs8IwdXnkxgyOj/iHdL9H9Im16Ub0c1c1Qulc3RWpJUouTaoxUoyQO +d3CogwId5OtAbwe6O8DZUewd2dqRLR1plxS3SGGD5NdIbpVkVjrUcqez2Gkv +dJrznfpcp/qeOJ8hTt8RR2+I4msi95JIvyASzzrRJ53Qo47vQcd9r2O/Q+7f +JXfvk1sPyfXH5PITcuEZOfucfPuSfPWKfPaGfPyWvD9DfvueujFLfTFPfbxE +fbhBf7hHf2hjPnQzfwowf4qwf0qwf86wfy5wHx1xH59yf6nwn9T5T1r8Zx3h +c0r4Kyt8wQtfisINib8pc7cV7i5g70P2IWIeY+Yppp+r9EuNftWl3nSpdz3q +fY+a7VPzA3JhQC4NyeUhuTok10bkxojcHJPbY3JnTO6Oyb0Lcv+CPLggrRPS +NiHt33lNKc+U8k4p35TyT6nAlApOqb/zGhte/LUXN6qYlVkD68qLGZ4wphc9 +ODTql6h+keoXqF6e7GXJXobspsluqtNNdrR4R4t11CihhgkcInCAQD4CeQno +JoCTAHZCsRKyhZB2CXGbEDY6/GqHW+6wSx16kSAXCGKOaM0SjfdE9R1Rfts+ +fdM+ftUuvWznn7czz4jkEyL6iAg9IHz3CPedjv12Z/9WZ+dOZ/NeZ/VBZ+lh +Z/5xZ+Zp582zzosXnScvyQevyTtvyJvvyK9myE9nqT8tUh+sUx/s0h/Y6A/c +9B8CzB8izB+S7B+z7IdF9sMj7k9n3J8r3EcN/uM2/xeS/4QRPuWEzwX+C5H/ +SuK+kdlbCvstYO5B+gGiH2H6iUo906gXGvWyS77ukW975EyffN8n5wadhUFn +cdhZHnZWRp21UWd91Nkcd7bGne1xZ/eis3fRsVx09ieday/SMSGdU9I1Jd1T +0jMlfVPyB15UeEpFplR0SsUa/LhuZnhx116s7jUysBgjw4seHtOmFzUoGfWL +ZL9A9nO6V6eX6fTSnW6K6CaJbpzQYoQWaavhthps40Ab+9rI04LuFnS2gL2l +WFuypSXvtqXttrjRFlbb/BLBLRDMPEHNtjvv2+2ZdvNdu/amXXndPnvVPn7R +PnzeLjxtZ560k4/asQft0L22707bdZuw3yQsXxPbN4mN28TKXWLxHjH7gHj3 +qPPqSefZs86j5517Lzu3X3W+ftP5/C358Qz5wQL523Xqt7vUb630b9307wL0 +7yLM75PM77PsB0X2D8fsH865P1a5D5vcnwj+zxT/Mcv/hec/FbjPRfZLmb2h +MDcBfRvSdxB1H1MPMflYJZ9q5LNu50W386rXedPvvOt3ZgbE7ICYHxILQ2Jp +RCyPiNURsTYmNsbE5pjYviB2LojdC8IyMbwODLKOfdpxTDvOacc17fzAiwxM +yeCUDE3J8JSMTMnolLz24sY1o1GVNbAML2Z0zowML3p4Spte1PCIMr3IQZEc +FDr9fKef6/SzRC9D9NJEL9XuJtrdeLsba2mRlhZuqcGWGmhiXxN5msjdhM4m +sDeBtalYmvJuU9puihtNYbXFL7e4+Tb7vs3MtKl3LeJtq/Wm1XjVqr5snb9o +nTxrHT5tFR63so9aqQet2L1W6E7Lf7vtvtm23WhbviS2vyLWvyGWbxEL3xLv +7xJv7hMvHhJPHhMPnhJ3nhHfvOh8+arzyevOh287v54nf7VG/mqH+pWV+pWb +/nWA/nWU/k2S+U2O+W2J/d0J+7sy+/sa90GL+2OH+5Dm/sTxH/HcX0T2M4n5 +Qqa/UuhvAHULUt8i8i4m76udh1rnsdZ52iWe94iXPeJ1n3g7IN4N2u+H7blh +e2HUXhy1l0ftlXF7bdxev2hvXrS3Lto62e6E2JvoZMTBhLBOCduUsE8Jx5Qw +vTqeacc77finncC0E5x2QtNOeNqJTDvXXty1FzuusmPDizG96NGZ2Sk1PKFM +L3J4SA5LnUGxo3sN8kQ/R/Sz7X6m3Uu3e6lWL9HqxlvdWFOLNLVwUws21EAD ++xrY00CuBnLWob0OrHXFUld26/J2Q9poiGsNYbnBLzTZ903mbYt+0yRfN9sv +m80XzdrzZvlZ8+xJ8+hxs/iwmXvQTN1rxu80w7eb/pst942W7auW5a/trc/b +a1+2l2605262333bfnW3/ex++9GD9r1HxK0nxNfPiM9fEB+9JH7/uvPL+c6/ +rZG/3CF/aaV+6aZ+GaD/PUr/e4r+jzzzq0Pm16fMbyrsbxvs79rs70nuA4b7 +A8f+SWA+FplPJfpzhfoSkF9D8ibq3MadOypxTyUeaMSjbvtJr/2s137Rb78a +tN8MWu+GrZlha3bUmh+1FkatpXFredxavWitX7Q2Llo62fakvTNp707alkl7 +f9o+mLZt07Z92ja9CPeU8EwJ75TwT4nAlAhOidCUuPbqxBomVp01sAwvZlwx +GpXpay9K9xqdkMNjcnjUGR52dK9hkRgUiEG+Pci1Ta9WP93qJ5u9RLMXb3aj +jW6koYUbWrBurPjx1bGnhl015KhBWw0e1IClpuzW5O2atFET12rCco1fqHOz +dfZtg37ZoF40Os8brWeNxtNG9XHj/FHj5EGjdL+Rv9tI32nEbzfCNxv+G033 +V037F03LZ62tv7RWP28tftGa/br19pvWy9utp3faD+617zxof/Oo/cWT9idP +iQ+fE795RfzrXOdfVzv/ukP+3Er+3E39PEj9Ikb/Ik3/W4H+5RHz72fMf1SZ +XzXZXxPsb2j2dyz7Ac98KNAfSdQnMvWZQn4BOl/Bzg1E3MLEt2r7rta+3209 +7LYe91pP+63n/ebLQfP1sPl22Hw3ar4fNedGzYVxc3HcXL5orlw01y6a65Pm +5qS1NWntTFq709betLU/bR1MW9Zpyz5tOaZt17TtnrY907Z32vZN24FpOzht +m15EZEpEp4TudaFjXXkxV15l2uicMrFIoxNydNwZGV7EsEQMi+1hoW16tQbZ +1iDT7Keb/WSjn2j04vVetN6N1Luhmhasaf6asZvJU8WuKnZUkK0CDyrAUgG7 +FWW7Im9UpLWKuFwVFqr8bJV9V2Ne1ehndfJpnXhcbz6q1x7Wy/drp/dqR3dr +hW/rmdv1xM165EY98FXd/UXD/nnD8klz66Pm6l+aC58133/RevNV6/k3rce3 +Wve+bd262/rqfuuzh+0/P27//mn7ly+Jn8wSP1nt/GSn8xMr+VMP+dMg9bM4 +9bMM9a9F+ufH9C/KzL/VmV+2mH8n2f9g2F9zzO94+o8i9SeJ/FjufAqIzyHx +JWp/jdvfqK3bWuuO1rzXbT7oNR/1m0/6jWeDxotB49Ww8WbUeDdqzIwas+PG +/LixcNFYumisXDRWJ431SWNj0tyaNLenzZ1pc2/atEybB9Omddq0T5uOacs5 +bbmnLc+05Z22fNNWYNIKTtqhSTs8aUcm7eikHWuwupeRjmV40eOKiVWmdK/x +GTk2vDqjk47pRYwMr7bp1RrmW8Ncc5BtDjKNQarRT9b7iXo/XutFa71ItRuq +doNVzV/RvBVj44+rjB1lZCujg3NoOQe758r2ubxxLq2di8vnwkKZny1z7yrs +qwr9rEo9qnUe1tr3a4171erd6tmd6vHtavFWNftNLXmjFv2qFvyi5vm8bv+k +bvm4sfWnxuqHzfmPmzOfNl/9tfnsq+bDG807t5rffNv64m7rL/dbf3zY+vXj +9r++aP94lvjxKvHjnc6PbZ0fe8h/CZH/kqD+e5b6SYn66Sn9swr9rw3m5wTz +C5r5JUv/iqN+K5AfiJ0PZeIjhfgEtD+DrS9Q6yvcvKE2b2mNb7uNu73G/X79 +Yb/+eFB/Oqg/H9ZfDuuvR/W3o/rMuP5+XJ+7qC9c1Bcv6suT+uqkvjapb0wb +m9PG9rSxM23sTRuWaeNg2rBOG/ZJwzFpOCdN96TpmTS9k6Zv0vRPmsFJKzRp +hSetyKQVnbSuvRjd66JKXxhelIFleJGmV8fohBgdE6Oj9uiwPSq1RsXWsNAc +5pvDXGOYbQzS9UGqPkjW+olaP1btR6u9SKUXqnQD5a6/rHnPNc+56jpTHWfY +dmZc7bacwt1TsHWqbJzKa6fS8qm4cCbMnvHvztjX58zzMv24TN6rEHcrrTuV +2u1K+Vbl9Gbl8EYl/3Ul/WU19tdq6POq99Oa4+Pa/p/rW3+sr/y+Mf9h493H +jZefNp78tXH/y8btG82vbzY/+7b557vN399v/fvD1r+8aP9otv2jVeJHu8Q/ +2zv/7O38c5j8f5Lkf8tRPz6k/uWM+u81+ict+qck8zOG/gVL/QdP/kbs/F4i +/ii3/wxaH8Pmp6j5OW58qTa+1urfdOu3e7U7vdq9fu3BoPZoUHsyrD0bVV+M +qq9G1Tfj6rtx7f1FbfaiNn9RW5zUlia1lUltbVpbn9Y2p7XtSX1nUt+b1C2T ++sGkbp3U7ZO6Y1J3ThruScMzaXgnDd+koXsFJs3QpBmeNCOTpunFGFiGF216 +URcV6qKsR5peV1hGx+2x4dUyvZqjQmOUbwxz9WG2PkzXhqnaIFkdJCqDWKUf +LffD5V7ovBc47/nPut6zrvtUc56qjhPVdoIPTpDlGO0cw61jsHGsrB7Ly8fS +wrE4e8K/O+Fen7LPT+nHZ9T9887tcvtWufFNuXqjfPZ1+eircuGLcuav5cRn +lfAnFd/HFeefq/sf1rY+qK3+pj73+/rbD+svPqo//rR+7/PGzS8bX95ofHKz +8cdvm7++2/z5/eaPXrT+abb9T6vtf9ol/slO/Fdf579GOv93ivxRgfzRMfXP +Zeq/NagfE/S/UPRPGPLnXOeXAvFrsf07ufWB0vwQND5CjU9w/TO19oVW+6pb +u9Gt3upVv+1X7w6q9weVh8PK41Hl6ajyfFx5Oa68HlfeXlRmLiqzk+rcpLow +qS5Nq8uT6uqkuj6pbk6q25PqzqS6N6laJrWDSc06qdknNcek5pzU3ZO6Z1L3 +Tuq+Sd0/aQQmjeCkEZ40TK9m9MqLNr0o04vUsS7KnYvzzoXhpWO1jY5b46PW ++LA5Lv2/ZN3lc1xpnuD7v+Du3RszsTMLM9M7M93TTNXdBd3l7iKXXS6XmZlZ +JtmSQZYtS7IkS7KYmTOVSmZmZmYxpzLzMOWLm6ly7W7cG/F7rczIz8nnOSci +9XwThDO+7RUjbFHcEsXNEdwUwY1hTB/CdCFMG0TVAVQVQBV+ROZHpD5Y7IOF +XojvBbkekO0BmO4sw52luzNT7vS4e2vUnRpyb/a713vca52e1TbvcpN3qd63 +8MY/VxFMvgzGyoOhF0FfWdD1PGh7GjQ+CWpKQvJHIdHDMOdeeLooMn4zOnAz +2nU32vow1vg4VvM0VlEWe14ee1wRv1sZv/4mfq42cagtcbA/eXBi9hBz9pBg +7pB87rBu/rBl/ohr4ah/4Vhk8Xhy8eTC4qmlhXMr85fWZq9uJG9sJm5vxe+m +Yw8ysUfZaAkQeQpFnkPhcjj8CglXoqFqLFSDherwUD0RekeEmslQKxlqp0Kd +VKiLCvXkQn250EAuNJQLDedCo7nweC48mQvTcuHpXJiRCzNzYVYuzMlFuLkI +PxcR5CLCXESUi0pyUWkuKstF5bmYIhdT5mKqXGybLJ73ysWWcgWvbazIwrbX +/LbXHBWYo/yz1PdYBa/EtlecdMZIR4ywRwlrhLBECHMYN4VwQwjXB3FdANME +MLUfU/pQhQ+VeRGJFxF7YKEb5rshrgtiu0CmE2A4s3RnZtKZGXekRxxbQ47N +fudGj3O907nW5lppci/XuxdrPPOvfbMv/Inn/ugzf/Cp3/Mk4CgNmB8HdMVB +5cOg+H6IWxRi3AqPX48MXI123Yq23I3WP4xWl0RfPo0+LYs9fBm7XRG7XBU/ +VRPf15bYN5DcN5ncx5rdJ5rdr5zbb5g7YJs/6Jk/FFw4HFs4Mrd4bHH+5PLc +2dXZi+uJKxvx66nYra1oUSZyPxt5CIQfg6EnUOgZHHqBBF+iwddYsAoLvMED +tUSgngg0koEmMtBCBdqoQEcu2JUL9uSCvblgfy44lAuO5IKjueB4LjiZC9Jy +QXouxMiFmLkQKxfi5ELcXJiXCwtyYWEuLMpFJLmINBeR5SLyXFSRiypz0W2v +mCYX08aXtr0Wc9HFXGQhV/D6AavgNbvtlaS8ScqToDxx0h0nXTHSGSXtUdIW +Ia1hwhImzCHCFCQMQVwfwHV+XOPD1T5M6cUUHlTmQSVuVORChC6Y74S5Dojt +gJh2kGEHaLbspC0zbsuM2LaGbKl+22aPbaPTtt5mX21yrDQ4lmqdC5XuuXJP +8qkvXuoLl/j8j32uRz7rQ7/hgV91LyApCvBuB2duhCauhgcvRjqvRppvRd7e +i1QVR16UREufRu+XRW+8jJ1/HTtaE/+2Lb5nILFnKvktJ/mtePZb9dxe09x3 +jvl9vvn9kfkDyYWDC/NHluZOrCTPrCXOb8Qub0avbUVupsN3sqF7QOgBGHwE +BUvhwFMkUIb6yzF/BeavxP3VhL+W8L8l/Q2k/x3lb6b8rTl/e87fmfN35/y9 +Of9Azj+U84/k/KM5/3guMJkL0HIBei7AyAWYuSArF+TkgtxckJcLCXIhYS4k +yoUlubA0F5blwvJcRJGLKHMRVS6qzkU1uWjBK7743iua95rPhedzoTkqP8HZ +ba8k5UtQ3gIW5Y5TrhiVx3LkvSKkLUxaQ6QlRJqDhDFAGPyE3k9ofbjGi6s8 +uNKDyd2YzIVJnKjIgQocCM+OcGwwywbNWKFpK0izAJOW7Jg5O2LODJq3+s2p +HvNmp3mjzbLWZFltsC7X2har7PMvnbPPXIlHnlixN/TQ633gddz3mu76NEU+ +2W2/4GaAeS04eTk4eD7UdTHcdC1cdzv8+l6krDjyqDRS9Cx69UX09KvYgdrY +rvb4rqHELlpiFze5Szq7Wzu72zL3jXtuT3D+2/j8d3Pz+xdnDy8njq/GT6/H +zm1GLm6Fr6ZDNzLB20CgCAzch/zFsL8E8T1Bfc8x3wvM+wr3via8VYS3hvTW +Ud56yttIeZty3pactz3n7cx5u3Pe3px3IOcdyvlGcr7RnG8855vM+Wg5Pz3n +Z+T8zJyflQtwcgFuLsDLBQW5oDAXFOWCklxImgvJciF5LqzIhZW5sCoXUeci +mlxEm/jBK7bw3qtAlvea3fZKFsafoHxxyhunPDHKHaVcUcoZoexhyhYirUHS +EiRNAdLoJw0+Qu8ltF5C4yFUblzpwuVOXOrAJHZMZMcENpRnRTkWhGWBZ8zw +tAmimcAJIzBmBEYM2UFDps+w1WNIdRo224wbTca1BtNKrXm5yrL4yjr/3J4s +ccbvuSN33YEij6vIY73t0d/yKm74RNd87Cv+qYuBobPBrjOhpkuh2hvhijvh +Z/fDDx9Fbj2JXHweOV4e3VMb+6oj9uVw/MvpxFf85FeK5FeG2Z322a99c7si +c7tn5/cszO5bShxaiR1bi57aCJ9NhS6kg5czgWtZ/03Qdwfy3YO9DxHvY9RT +inme4Z4y3P2ScFeQ7irS/YZy11Lutzl3Y87dlHO35NztOXdnzt2dc/flPAM5 +zxDlGaE8o5RnnPJOUl4a5aVTXgblY1I+FuXjUH4u5edRfgEVEFIBERUQU0Ep +FZRRQTkVUlAhJRVWUWE1FdZQea/Fgld8YdtrvjCRuYJXeJYKJalg3ivxg1eM +8kS3vSKUM0w5QqQ9RNryXgHS7CeNPtLgJXUeUusm1S5C5SQUTkLuwKV2XGzD +hVZMYMF4ZpRjQllGZMaI0A3wlB6a0ENjOnBYBwxqs33aTLc23aFNtWo3m3Tr +Dbq1Ov1KtWGpwrRQZp4rtSYe2GO3XOFbLt9Nl+OG23Tdrb7mkVzxci/56Of9 +w6cD3ceDTedCNVdCr26GntwN338Yvv44fO5p5HBZ5Mu66Gedsc9G45/NJD4T +JT5TJz83J79wzX4RnP0qPrdzLvnNYvy75ejBtcjRjdDJVPDMVuB8xncp67sK +em9Antuw+y7ifoC6HmGuEtz1FHc9J5zlpPMV6ayknNWUsybnfJtzNuScTTln +a87ZTjk7KWc35eqjXAOUa4hyjVCuUco9TrknKTeN8tApD4PyMCkvi/KyKS+X +8vEon4DyCSm/iPKLqYCUCsiogJwKKqigkgqpqJCaCmmocMErse1VIMt7zRUm +MvuDV6IwgTjlj1G+GOWNUp4I5Q5TrjDlDJGOIGkLkFY/afGRJi9p9JB6N6lz +kRonoXIQCjshtxFSKyG2EEIzzjfhXCPGNmBMPcrQoXQtMqWFxzXwqBoaVoMD +KqBXle1WZTpU6VZVqkm12aBar1OvVmtWKnRLL/TzT4yzxeb4HVv0miN4zem+ +6rRecekuu+WX3PzzHsZZ3+hJf8/RQNOpYM2F4MtrwZLbobv3QleKw6dKw/ue +R3bUR3d0xz4dj33Kjn8qTezQJXbYkn/1Jf8Wnf1sNvnlQnz3UnTvavjAevDI +ZuDElu90xnsu67kIuq9Aruuw6xbiLEId9zFHMe54TDieEPbnpP0FZX9F2V/n +7FU5ew1lf0vZGyl7E2VvpeztlL2TsndTjj7KMUA5hijHCOUcpZzjlHOSctEo +F51yMSj3DOVmUR425eFSHh7lFVBeIeUTUT4x5ZdSfhnll1MBBRVQUkEVFVRT +QQ0V0ibzXguFic8XvGI/eEWSVDhJhfJe8fde/ijli1DeCOUJU+4Q5QySjgBp +95M2H2nxkmYPaXKTBhepd5JaB6G2EyobobASMgshMRNCI8E34Fw9ztbhTC3G +0GA0NTqpQseVyIgCHpJDA3KwVwZ0ybIdskyrLN0kSzXIN2vl69WK1Qrl8gv1 +4lPt/CN98q4xdsMSvmT3X7I7LzpMF5yq8y7RWTfztGf8hK/3sL/5aODN2UD5 +5eDjG8HbRaGLD0LHHod3vwh/0hj5pC/6yVTsE178E0X8E1Piz67kX0LJTxPJ +v87HvlyM7FoJ7V0L7N/0Hd7yHk97TmVdZwHnBchxGXZcQ+w3UdsdzHYPtz0k +rI9IaylpfUZZy3LWl5T1NWWtpqy1lPUtZW2krE2UtZWytlPWTsraQ9n6KNsA +ZRuibCOUfZSyj1OOScpBoxx0ysmgnDOUi0W52JSbS7l5lEdAeYSUR0R5xZRX +SvlklE9O+RWUX0kFVFRg2ytY8Er+4BWf2/aazc+2V6LgFYpTwRgViP7gFaY8 +IcodpFwB0hkgHX7S7iOtXtKy7WV0kgYHqbMTGhuhthJKCyE3EVIjITbgQj3O +0+IcDc5U4wwlTlNgk3JsTIaOSJFBCdIvgXvEUJcIbBcBLaLsO1G6XrRVK96s +lqy/lq6Wy5afKRYfq+buaxO3DNHL5tBZm/eczXbWrjvjkJ52ck66J495+g/5 +Wg7435wMvLgQKL4WuHk7eO5e8FBx6Mvy8IdNkT8NRv80HfuTKPYnTfxDW+JD +X+KjWPLj2diOhcgXy8Fda/5vN7z7U+5DadexrPMkYD8D2c7DtkuI9SpmuYFb +buPmu4T5AWl+RJlLKPNTylxGmV5SpteUqZoy1VKmesrUSJmaKVMrZW6nzJ2U +uYc095GWAdIyRFpHSOsoaR0nbZOkjUba6aSdQTpmSAeLdLJJJ5dy8SiXgHIL +KbeI8ogpj5TyyiivnPIpKJ+S8qsov5oKaKiANo9V8JovTN4rPpuL5b2SBa9I +ggrH33sFo1QgQvnDlC9MeUOUJ0i5A6TLTzp8pN1L2jyk1U2aXaQp72Un9DZC +ayU0FkJlIhRGQmYgJDpcpMUFGpyrwtlKfEaB02XYlBQbF2PDImxQiPYJkB4+ +3MmH23hgCw94x8vW8zK1vK1q/maFYL1cuPpMvFwiXXigmL2jjl/VRc6aAict +rlNW00mb8oSDf9xJP+IePOBp2+N7c9Rfdsb/8HLg+s3A6bvBfQ9Dn1aE/9Aa ++WAk+gEr+oEs9oEx/oE7/odw4o/J2Mfz4R1LgS9WfV9vePakXPvSjoNZ+1HQ +egKynIbN51HzJcx0FTfeIIy3SWMRabxPGYspQwlleEbpX1D6V5S+ktJXk/pa +Ul9P6htJQzNpaCUN7aSxizT2kMY+0jRAmoZI8whpHiUt46RlkrTSSCudtDFI +2wxpZ5F2Nungkg4e6RSQLiHpEpFuMemWkh4Z6ZFTXgXlVVI+FeVTU34N5dfO +bnsl815zhfneK5akoon3XuEYFYr+H14hyhukPAHK7SddPtLpJR0e0u4mrS7S +4iTNDtJoIwxWQmchtGZCbSSUBkKuI6RaXKzBhSqcr8Q5cpwlwxgSjCbGJoTY +qAAb4qH9XLSbg3awkTYW3MyCGpngWyZQw8xUsbYq2KlyzsYz3mqpYPmhaKFI +OntDGbuoDZ8w+o+Z7cesumM2yRE785BzZJ+74xtvzQFf2Unfg4v+q9cDJ+4E +vnkQ/ENV6Led4d9MRn7Dj/5GHfuNLfbbQPy38dgf5sIfLwV2rHq/WHd9nXLs +Sdu+y1oPguYjkOk4YjyNGs5hhou4/gqhv07qblG6Ikp7n9I+orSllOYZqXlB +al6RmkpS84bU1JLaelLbSGqbSW0rqWsndV2kvofU95GGAdIwRBpHSOMoaRon +TZOkmUZa6KSFQVpnSCuLtLFJO5e080iHgHQISaeIdIpJl5R0yUi3nPQoSI+S +9KpIr5ryaShfwWt2vuCVzHvNFrziyfde0TgVib33CkWoYJgKhCh/iPIFKW+A +8vhJt490eUmnm3S4SJuTtDpIi5002QijhdCbCZ2R0BgIlZ5QaHGZBpeocJEC +F8hxnhRnSzCmCJsWYFN8bJyLjXDQQRbay0S7GGjbNNJERxrocB0NqqEBVfRs +BT1dPp16NrNRylot5izf4y/cEievyKNnNMFDRu8hs/mwRXnIxj1gn/jO1bXb +U7fXW3bMd/+c7/JV/5FbgS8fBn9dG/pVX/iXjMgvpNFfGGO/8MZ+GYv9ejb0 +h0X/JyueHevOz1P2nWnrN1nzd6DxAGw4jOiPY7pTuPYsoblAai5T6muU+hal +ukuqHpDKR6TyCal8TirLSWUFqawklW9IZR2pqidV70hVM6FuJdQdhKaL0PQQ +2j5CN0Dohgj9CKkfIw3jpHGSNNJIE500M0jzDGlhkRY2aeWSNh5pE5B2IekQ +kQ4x6ZSSThnpkpNuBelWkh4V6VGTXg3p1c5te83OvfdKbHvFE1TsB69IlApH +3nsFQ1QgSPkDlM9Pen2kx0u6Pe+97A7SZictNtJsJUxmwmAi9AZCqyfUWkKp +weUqXKrAxXJcKMX5YpwrwlgCbIaH0TnYJBsdY6LDDHRgGu2hoZ1TSOsk8m4c +qRtD3ozBlWPgq3HgxXjm2eRW6dRG8fTafebybc78NUHyvDRyXB34zuDab9Lv +t4j22ejfOvq+dtXv8pQd9t4747tw2X/wpn9HSeDnjaGfjYR/yo38VBP9qSP6 +00jsZ8nQbxZ8f1xxf7Lu2JGyfp4278wavgH1e2HtAVRzGFMfw1UnCeVZUnmB +Ulwm5ddJ2W1Sdo+UPSSlj0npE0L6nJCWE9IKQlZFyN4QsjpCXk/I3xGKZkLR +Sig7CFUXoeoh1H2EeoDQDBHaEUI7RujGCf0kYaARBjphZBAmJmFikWY2aeGS +Fh5pFZA2IWkTkXYx6ZCSDhnplJNOBelSkm4V6VaTHg3p0c7N/2+vZN4rWZiC +V5yKxajotlckQoXDVChEBYNUIPCDl5f0eEi3m3S5SKeTdDhIu420WkmLhTCb +CKORMOgJnY7QaAiVClcqcbkcl0pxsRgXiDCeAOPwMCYHY7Aw2gw6MY2O0tGh +KbR/AukeRzpGkZYRpHEYrh2CqwbhlwNw2SD4bChbOpJ+NLZ5f3LtDn35BnP+ +Ei9xWhI+qPbtMdj2mpR7Lew9tqGdznefe17s99w95T13ybf3hv/DssB/tId+ +MhX+sSTy7+bIvwei/x4P/Xze+9tl5x/XbZ+kzDvShs8B3U5IsxtR7UWV+3HF +YUJ+jJSdJKVnSclFUnyVFN0kRXcI0T1CWEwISwjhU0JURoheEqIKQlRFiGsI +cR0haSAk7whpMyFrI2QdhLyLUPQQyj5COUCohgj1CKEeIzTjhHaS0NEIPZ3Q +MwgDkzCyCCOHMHEJM4+wCAiLkLSKSJuYtElJu4x0yEmHgnQqSZeKdKlJt4Z0 +F7zmtr1mZwteybxXouAV3/aKRanoD17hEBUKUsEAFfBTfh/p85JeD+lxk24n +6XKQTnvBy2YhrWbCbCRMBsKoI/QaQqsmNEpcJccVUlwmwSUiXCTABDyMy8HY +LGxmBpueRqdo6PgkOjKODo4ifcNI1yDSPoA098ENvXBtD1zZA5d3Q0+7oZIe +oLgvc38wVTSyfnNi+cr0/DlO/Lg49K3as1tv+MYk3G2Z+MreusNdvtdz97j3 +zAXf7hv+X70O/Ftf6F854f+pjfzIE/lRLPTjOe8vlx2/W7f8KWX8JKPbAag/ +h5U7EfluTLaXkO4nJYdI0TFSeJoUnCf4lwneNYJ3i+AWEdz7BLcY55bg3Kc4 +rwznvcR5r3F+FS6owQV1uLABF73DRS24uA2XdODSLlzag8v6cPkArhjClSOE +coxQTRDqSUJDI7TThI5B6JiEnkUYOISRSxh5hElAmIWERURYJIRVSthkpF1O +2hWkQ0k6VaRTTbo0pEs7n/eaK0zeazZZ8Eomcol4wSv+vVeEioapSIgKB997 +Bf1UwEv6PaTPTXpdpMdJuu2ky0Y6rKTdTNpMhMVAmPWESUsY1IROSWgVuFqG +KyW4XIRLBbiYhwk5GJ+JcRkYi47OTKH0CXRyDB0fRkYGkYF+pLcX6eqB27rg +5k64oR2uaYcq26DyNuhJG/SwDbrfkS3q3rrVv3FtZOXi1PxpVuyQKPCVxvm1 +Xvm1ifGVrWuHs2K3++4xz6kL3i9u+f61PvCj8dA/S8P/ZA//UyT0o1nPfyzZ +f7Vu+n1K/2FG/WdQ8VdY9jkq2YmLdpPCb0n+AZJ7hOCcJNhnCdYFgnkFZ17H +mbfxmbv4zAOc+QhnluLMZzjrBc56ibNf45xqnFODc9/ivAac34TzW3BBGy7s +wEVduLgHl/Th0gFcNoTLR3D5GK6YwJWTuIqGq6dxDYPQMgkdi9BxCD2XMPAI +o4AwCQmTiDBLCIuUsMoIq5ywKQi7krSrSIeadGpIZ8FrPu81W5i812zivVci +RsWjhYn94BUJUuEAFfJTQd97L7+b9DlJr2Pby0o6LaTDRNiNhFVPWHSEWUMY +VYRBQehkuEaCq0W4UoDLebiUg4lZmJCB8egYZwpljaOMUZQ2hE4OIGN9yHAP +MtCJ9LbDnW1wWwvc1ATXv4NqGqHKRqi8EXrSCD58B95pAm+1pa93bV4eWDk3 +Pn+cGftO7PtcY/nKIPjSMvipo/or190jnuPnvZ8W+/65I/A/OKH/Zgz/11Do +vyXd/7Zk/dm64Tdbmg+yig8h6Z9R0V9xwecEbyfJ+YZg7SNmDhOM4zj9NE4/ +h9Mu4bSr2NQNbOoONnUPoz3EaI8x2hOM/gybfoFNv8IYldhMNcasxVhvMXYD +xmnCOC0Ytw3jdWD8LkzQiwn7cdEALh7CJSO4dAyXTeDySVxBw5XTuIqBq5m4 +hoVrOYSOS+j5hF5AGISEUUSYJIRZSphlhEVOWBWETUnYVIRdTTg0pEO7MFfw +mt/2mvveK56fglci7xWhYuHCRH/wCvupkI8KesiAm/S7tr3spMdGuq2ky0w6 +TYTDQNh0hFVLWNSESUkY5YReimvFuEaIq/i4goPJWJiEgYnomGAK442j7BGU +OYQy+lFaLzLRhYx2IMOt8EAz3PMO7myA295CTXVQQw1U+waqfAOWvwGfvgGL +a8A7deC1huyV1tSFntXTI/NHZiJfSzyfadWfG6d22Oo/c9077D5y3vuHl/7/ +Phr8R2XoHwLh/5J0/8uS5Scbul+klb8FpX9AhB9hvL8QnL8SzC+J6d0E7Tt8 +8iA+fhQbO4mNnsFGL2Cjl7HRa9joLXS0CB29j44Vo2OP0fEn6MRzdKIcnXyF +TlWitGqUXotOv8UYjdhME8ZswdhtGKcT43ZjvF6M348JBjHhMCYawcRjuGQC +l07hMhoun8YVDFzJxFUsXM3BNVxcy8d1AlwvJAxiwighjFLCJCPMcsKiIKxK +wqoibGrCriHs/4dX8r3XbN4rRiW3vRIRKp73ClGxIBUNUBE/FfZRYS8V8pBB +Nxlwkn4H6bOTXivpsZBuE+kyEk59/q8SNk3hRcyK/MviBkn+jRTekZqbf4OY +YgaT0THJFCYaxwQjKHcIZfejzB5kuhOhtSETzcjoO3ioHh6og3vfQJ1VUNtr +qLkCangF1r4Eq8rBVy/B5y/BxxXg3Urg2hvgYkP6XPvayaH5AzPhHQrH33S8 +HZa2vzjvH3IfvOD5yTv/P/CCf+8K/V3C9d+XTf+2qf5ZVvorSPB7jPMngvkx +Qf8rMfklPrYLH9mLDR3ABg6j/cfR/tNo3zm07yLadwXtu47230b67yID95HB +YmSwBBl6igyXISPl6GgFOlaJjr9BJ2vRqXqU1ojSm9DpVnSmHWV2oqxujN2L +cfox3iDGH8YEo5hwDBNNYOIpTELDpNO4fAZXMHElG1dxCp+Lho9rBbhWiOvE +uF5CGKSEUUaY5IVP0KwsXPpWDWHLf6y6vNfCbMFrPu+VKEzeazbvFS3M917x +H7yifiryvZebDLnIoJMMOEi/jfRZSa+Z9JhIt4Fw6giHtvD1zX+P819osxQ3 +iXCDANfxcC07vwZgymlMPoVJxzHxKCocQvn9KLcHZXcgM63IdBMy1YBM1MGj +b+DhSnigAuoth7rKoPZnUMsTsLEUfFsCvikBK0qAF6VA6VPgQRlw4yVwrho4 +07RxrH/+W2bwz2rdDuPgnxzFh1x7b3n/cSTwd+bgf467/nHZ8KOU/Ceg4Bco ++7cE4wNi4mN85K/YwJdY3y60+1u0az/acQjpOIa0n0TazyDt55H2y0j7Nbjj +Jtx5B+68C3c9gLsfIT2lSO8zpL8MGXiJDFYgQ1XIyBtktA4Zq0cmGpHJZnSq +FaW3o9OdKKMbZfairH6UPYhyhjHeKMbPX50TmHCqsLJIpjFp/qplYnJ2fsXB +lbzC0qMWFNag/Eqky1/fUtwgw/Nrk1FJmPLXvZqwaAprllW3uO21sO01v+01 +t+01m/eKUMkwldj2igepWN7LR0W9VMRDhd1UwctBBuxkwEb6LaTPTHqNpEdP +uLSEU0M48iuuorBnWsS4WYgb+biBg+tY+W0WU9Mw5QQmH8WkQ6i4HxX2oPwO +lNuKsJuQmXpkuhamVcETFfBYOTz8HBp4AvU9hrofgh33wda7YFMR2HAHqL0D +VN0BXt0Fnt8HHhUDRaXApXLgVF3qSO/8V1zvX7SsD+xPD7t2Vvr+XhH4TzHX +369q/jkj+jHC+jlB+zU+8kes789Y19/Qti+R5l3Iu2/hxn1ww0G4/ihcfwKq +Pw3Vn4MaLkINV6DG69C7W1DTHaj5HtTyEGp7DLeXwh3P4K4XcPdLuPc13FcF +D9TAg3XIcD0y8g4Za0bGW5HJdmQqv1J0o9O9hVWeOYiyhlH2KModR3kTGH8K +E9Ax0TQmnsEkTEzKxmQcLL+pK/i4SlDY4zViXCvBtVI8v+vrFbhBiedvAkzq +wt2AJb/HFLwW817JwuS95uMFr7ltr9nvvUJUIkjFA1TcT8V+8Iq4qbCTDDnI +YN7Luu1lIr2GvFf+EYFwqQmnknDICXv+zlSEWwS4iYsb2bh+BtfRMc0kphrD +lMOYfACV9qDiTlTYivCbEG49zK6FmVUw4xVEfwFNPQUnHoOjD8Hhu8DAbaD3 +BtB1FWi/DLRcBN5dAOovALUXgKpL2ZdXss9uZIuLsjceZ0+8yh7unv+T3Pon +S/Ux18eT/v8Udf0/G/J/hlg/JiZ+jvf9Hm37CHn3KVz3GfzmK6hqF1T5Lfh6 +H1hxEKw4AlYcBytOga/PgpXnwcpLYPVV8M0NsOY2WFsEvr0P1heDjSVQ0xOo ++TnU+gJqewV1vIa6quGeGrj3LdzfAA/mF/FmeKStsAGPdyGTPchUH0IfQKaH +0JlhlDlauK/iTKLcKZRHRwUMTDiDiViYmI3lb79kPEzOxxQCTCnCVWJcLcE1 ++S1fjusUuF6JG1S4UY2bNIUbbvN7r8Vtr4Vtr/lYwWtu22s2TCW3vRLbXnEf +FfNSUTcVcVERJxm2kyEbGbSSATPpN5I+A+nV5Z/CCbeKcCkIp4xwiAmbELfy +cQsHNzFx4zSun8J045h2BFUPoqo+RNmNyDtgWQssaYREb0HhG5D/GuCWZznP +sqySzExxevpemnZ7a/L61viV1OjF1NDZ1MDpVO+JVNexVNuRrabD6beHsm+O +ZCtOZMvOZouvZy89zh7snP9YP3TJ83dR1/+d5f0LMfxTtOX3cM1H0Ku/gM// +Bjz5AijZCTzanX30bbZ4X7b4QPbR4eyjY9nHJ7Mlp7NPzmWfXsw+v5Itu5Yt +vwm8ugNU3AUqHwDVj4CaErDuKVj/HGwsB5sqwOZKqLUaaq+FOt9C3Q1QbxPc +3wIPtMFDHfBIFzzWg4z3Iflb3qkhhD6CMEaRmXGUOYmyaSiHjvIYKH8GFbAw +ERsTczEJD5PyMZkQU4gwpRhTSQrPPxo5nn8Q0ilxvQo3qHGDBjdqcZNuafa9 +12Ki4LWw7TUfpeYihcl7zYao5LZXIu/lpWIeKuamonkvBxmxk2EbGbKQQRMZ +MJJ+PenTkl414VESbjnhkhJOEeEQEHYubmPjlhnMPI2ZplDjOGoYQfSDsK4P +1nRB6nZQ1QwqGgB5bVZWlZG8SovLtkRPUoJHm/z7m7zbG5zr6+zLa8zzqzNn +VqZPrNCPLk8dWp7YvzS2d2lkz9LQ7uWBXcs9X6907Fxt+nqjenf66cnMgY6F +iOv/Qpt+BZZ8mL39l/TVHelLn21d+GLr/M6t87u2zn+zdWHv1sV9W5cObF05 +vHX16Nb1E+mbp9K3z6aLLqTvXUo/uJopvp55fCvzpCjz7F627GG2/HH2VWm2 +8hlQXQbUvATqKsCGKvDdG7C5FmytB9sboc4mqLsF6m2D+jvgwS54qAce6YPH +BuCJIWRyBKGNIdPjCGMSYdLQ/DMnh4FyZ1AeCxWwUSEXE/EwiQCTCjGZCJOL +MYUUU8owlRxXK3CNEteqcJ0a12twgxY36hJINI5E4kg4hoSihQlG4EAY9odh +Xwj2BGF3EHIFIKcfsvsgmxe0ekCzBzS6C11jnRPQ2AGVLauwZmWWjNhcaMoU +GiX6NFO7RVdvTapSo4rUoHyzT7bZLd3okGy0iNffidbrhWs1gtVK/upL3spz +7nIpZ+khe+kua/Emc+HKzPyF6bnT9LljtNmDU8m9k4ldE/EvxuM7RmOfjET/ +OBT53WD4V/3hn/WGftwV/Nf24L+0BP5Ho/+/1vr/ocL3X0q8f3/R8/dHXZ98 +ZGw3/JNm/hd3lz46u7Lj2Ornh9e+Ori26+D6noPrew9t7D+8cfDIxpFjm8eO +b548uXn6dOrc2dSF86nLl7auXtm6cW3r1o100e30/aL0w/vpxw8zpY8zz0oz +ZU+zL8uyFeXZqgrgTSVQWw3U1wKNb8GmBrDlHdjWDHa0Qd0dUG8X1NcDDfTB +Q/3wyCA8NgxPjCKT4whtApmeQhh0hDmNsGZQDhPlslE+BxVwUSEfFQkwiRCT +ijGZBJNLMUXBC3vvpcZ1GlyvLXgZdPGCVzSGRGJIOO8Vgd97hQpe3iDkCUBu +P+T0QQ4faN/2srjBQoraCegdgNa+XYe0ZOXmjNSUERsyhVKJLs3WFM57pytT +k/LUmHRzSLzZJ9zo4q+3ctcLJzixV2tYq5UzKy8Zy8/py6W0pYeTi3cnFm6O +zV8dmb8wPHd6cPZYf/Jgb+K77vjuzviXbbG/tUT//C7y4dvwBzWh37wO/uJF +8KelgR/f9//rNd+PLnl/fs7zhxPuv+137d/huP6xsXPfQKJ6V9r4z+rQj1qT +Py6b/+2DxQ9vLX96beWzK6tfXVrddXHt24tr+y6uH7y0fuTyxvErG6eubZ69 +vnn+ZurS7dTVO6kbd7du398qKk7ff5wuLk0/fpp58jzz/EXmxavsq9fZ11XZ +6jfZmlqg7i3Q0Ai8awKbW8DWNrC9A+zqgnp6oL4+aKAfGhqEh4fh0VF4fBye +nECmphA6DWFMIzMMhMVE2CyUy0F5XJTPR4UCVCRExSJMKsFkUkwuwxRyTKnA +VEpMrcI1alyrwXVaXK/DDfo4Eotte0WRcGTbKwwHQ3AgBPuDsDfw3svlg5xe +0O4BbW7Q6gLNzkLg2GAHdLbtRqQ5qzRl5MaMxJAW6dICbSGpwFamZhQpumxz +UrI5JtoYEmz089a7OWvtrLVmxmo9faVmauX1+PKLkaXSocWHA4t3+xZu9sxf +7Zy70D57piV5/F3iUH18X238m+rYzoroZy8inz4Jf/wo9OH94EdFgU9u+v9y +zffXS74vznp3H/fsP+A+sdN19QNHyZ9N3X9UWI6+XX9+IkP/KGb6kdr3P0ei +//4u+R8V8799tvDh46W/PFj+7N7KV3dXdxet7r2ztr9o/XDR+rG7GyfvbZy5 +v3n+weal4tTVR6kbJanbT7buPt168Dxd/CJd8jL9tCJTVpkpr85U1GQr67Jv +6rO1jUB9E9DYAjS1gS0dYHsX2NkDdvdBvQNQ/yA0OAwNj8KjY/DYBDwxBU/R +ENo0Ms1AZpgIk4WwOSiHi/J4KF+ACoSoSISKxZhEgkllmFyOKRSYUompVJha +jWk0uFaL63S4Xo8bDLFtr2jBKxKBw2E49L1XMO8F+QKQ1w95fJDbCzk9oMMN +2gtehYZ4oXFs286wWrIacyFmpzBkCv0mbVqo2a5gKFIseYoh3T7uWLgxyt8o +HBrJXuueWeuYXm2ZWmmcWK4bXa4eXno1sFjWu/Cka764fe5ey9ytd7PX6pOX +ahLnquKnKmLHX0SPPIscKg0fKA7tvxfcfyew/0bgwGX/ofO+oye9pw57Luxx +39jhevix/fUOU++fNbI99NDxinTphWznlyvC3/nN/6b2/Ds99JOe+M8aZ39R +Pf/By4WPyxZ3PF3+4sny1yUre0pW95WsHSpZO1qyfrJ048yTjfNPNy8/27z2 +PHXzRepO+da9V1sPX289qkyXVqef1WRe1GVe1mdeN2Sr32VrmrN1rUBDO/Cu +E2juAtt6wI4+sGsA7BmC+oahgVFoaAwamYDHpuAJGjw5DdMYyDQTYbAQJhth +cREOD+XyUb4QFYhQoRgVS1CJFJPKMZkCkysxpQpTqTG1BtNoca0O1+n/l1e0 +MNHID16h916BAOT3Q17f916gywM63aDDBdqchey72Q6YbNsxVnNWayr0B5X6 +QnKrUAVSbwmVW3x5iiNLsSSbDNEmTbAxwVsfZa8PMdf6Gas9tNWOyZXWseV3 +I0v1g0s1fYuV3QsvO+aft849aZp91JB8UJsoqk7cqohfL49dfRa9VBq5WBw+ +fy90/nbw/LXAhUv+i2d8V455r+/33PnaXfyJ6/kO+9vPzAN/1Qn+JnYeHpg9 +XZ59fDX7ds/W1I6k/Ncey0/U7v9gBX82Ev1FZ+LX7+Z+Vzv/YdXip6+XPn+1 +/PXLlT3lK/terB56sXbsxfrJ8vWzLzcuvNq4XLF5/fXmrcpUUVXq/put4pqt +krr00/r084ZM+btMRXOmsiX7pi1b25Gt7wQau4HmXqC1H2wfADuHwO5hsHcU +6h+HBieg4Sl4lAaPT8OTDHiKCdNZCIONzHARFg9h8xGuEOWJUIEYFUpQkRQV +y9CClxKTqzCFGlNqMJUWU2sxjQ7X6nGdAdcbY0g87xXZ9grDkRAcDsGhIBwM +vPfy+SCvF/J4QLcbdLlAhxOwOwrx90JJ3Jo1WrIG03Yy0pBR69JKbVqu3m4D +KVICWYon2eSIN5nCDQZ/g8ZZn2Ctj86sDU2v9k+t9IyvdI4utw0tNfcvNvQs +1nUuvGmbf90897Jxtqwu+fRNouR1vPhl7MHz6L3SSFFx+M690J1bodvXgncu +BopO++8d8T3c6y35wlP2mav6C3vLl+bhz/W8v6gt382EjncsXyjLPr6RrT6Y +Hdi5xPkkov6l2/ozjfvn3MAvJyO/GYj/rjP5h+a5DxsW/lK3+FnN0s43y3uq +V/ZVrR6qWjtWtXaqav1c9cbFNxtXazZv1G7erkvdfZt6UL/1qHGr9F36WXP6 +RUv6VVvmdXumujNb25V925Nt6AOa+oGWQaBtCOwcAbtHwd5xqH8CGpyChmnQ +6DQ8xoAnmPAUC6az4WkuMsNDmHyELUA4IoQnRvkSVChFRTJULEclCvT/66XD +NHpMa8B1Rlxvir73ioXh6Pdewe+9oKAfCvggvxfyecD/5eV0Ag7HdvzdWkhU +F5LHpkLlU6vPaLTbrTTVlky5VSjOSFMC8SZPuMnmb59WzV6nMdcmGGtjtNXh +yZWBsZXe4eWugaX23sXCQRnt8/Ut87Xv5qrfzlbWJF9VJspfxsvKYs+eRJ8U +R0rvhUtuhUquBksuBEpP+Z8e9pXt8b78ylO109X4tb3ra8vYTiP3M61ut8h7 +ZDxxqmn9Shnw+Ha28kS2Y8867YtZ8UdB3S9dtl9q3L8WBH7LCP9+LPbH/uSH +XXOftM1/2rT4eePS1w3L39av7H+7evjt6vG3a6ffrp+vX79cv3GtYfNm42bR +u9T9plRx81ZJ69bTtnRZe/plZ7qiK1PVk6npzdb1ZxsGsu+GgOZhoG0U6BgD +u8bBnkmwbwoaoEND09AIAxpjwhMseIoN07jwNA9h8BGmAGGLEI4Y4UpQvhQV +yFCRHBUrUIkSlaowuRpTaDClFlPpMLUe0xgwrRHXmb73ihSm4BUqeEWCcDgA +h/xQ0Pe/vbxu0OMC3U7Q5QCcdsBuAwoJeHOhemwybrc+dYUcoVqdVim3o06y +lESSKqQxBJs83gabs85krTNm1mj0tcmp1bHxleGR5cGh5cIpTz2LnZ0Lba3z +zU1z7xrm6mtn66qSNRWJ6hfxyiex14+ir+5HXt0Ov7waenUh+Opk4PUhf9Ue +X823noZvXW3f2vv3WCd3m3g79ZqvlK6DrPDJwYWzDanrZUBJUfb12Wzz/q2R +3Yucz2Lyj/zG3zjsv9V6ficOfMAK/2kq9tFI4s8Dszt65j/rWPiibWlXy/Le +lpWDzStHm1dPNq+dbV6/2Lx+pWXjRsvm7dbNu22ph+2pxx1bTzq3nneny3vS +r3ozlX2ZNwOZ2sFs/XC2cSTbPAq0jgPtE0DnJNhDA/vo4MA0NDQDjTChMRY0 +zoEnuTCNB9P5MEOIMEUIS4xwJAhXivBlqECOChWoWIlKVKhUjco0mFyLKXWY +So+pDZjGmPfCCl7mCJLIe4WRWAjOTzQIRwLvvUI+KOiFAh7I7wZ9LtDrBD0O +0G0HnDbAYQXslkII3mLMmg0Zoz5j0G4XJFVptbLQ4SqkgsQpiXBTxN8UcDe4 +7HU2c505vcagbZ//ObYyPrw8MrA81LvU37XY277Q3Tzf0TjXVjfb8ma26XWy +sTxR/yz+9nGs7n609nak9lq49kKo9mSw7mCg/qCv6YCn/YCrZ79jeJ+NvtfM +/8ag+lLr2C8MnKAlzvYsn6/L3C4DntwDXl/MNhzO9H+3Ov31nOhvEfVHPvPv +7Y4PtJ4/SgMfcsOfMGJ/mUz8dXT288G5L/sWvu5Z/KZr6bvO5UMdK8c7Vk93 +rJ3vWL/UsX6tc+NW52ZR1+b97tSjnlRp79azvq0X/emXA+nXg5nqoUztSObt +aLZxLNs0AbRMAu1TQCcN7J4Gexlg/ww4yISG2dAoBxrnwpM8eEoA04UwQwTP +iBGWBGFLEa4M4ckRgQIVKlGRCpWoUakGlWlRuQ5T6DGlAVMbt71MmM6M6S15 +r3B+4HjeK1jwigbgiB8K+6CQ9//vBeS9XDbAaQEc5kIO3mosFJALRV1N2qBO +65SFzp1atlWoO4k2pYJNCW9DxNkQsNZ5M+sc+hpzqnBkK31kZWpwuXD2XffS +cMfiYOtC/7v53vq57prZzsrZ9pfJtueJlpJ484NY851o07VI04Vw08lQ84lA +23F/5zFv71H30BHnxCH7zAGL8DuTarfeuk/uO86JnB2bv9C5drEGuFsGPH0A +vL4KvD2R7Tm4Mbl3kft1QvZZSPexz/onu/NDnfdjWeDPgvAOVuxv04kvJmd3 +js3tGl7YM7j4Xf/Sgd7lI70rJ3tWz/asXexZv9q7fqN3407f5r2+zYf9qZKB +1NPBrbKhrZfD6YqRdNVopmYsUzeeaZjMvpvKttCANjrQMQ10z4C9TLCfBQ6y +oWEONMqDxvnQhACeEsJ0ETwthmckCEuKsGUIV47wFAhfiQpVqEiNijWoVIvK +dKhcjykMBS+VEVObMI0Z01owXd4rmfcKFbziQTgWgKP+glfEB4W9UMgDBd1g +wAX6naDPAXrtgMcGuK2Ay5J1mrdz8IbtaLU2Y9IU0p96xZZOvqWRptTilFJY +yNBIuRsS9oaIuX0+PG2NM7HKGludGV6ZHlim9W6fgNe2ONq8MNwwP1g3N1A9 +2/cq2VuW7C5NdD2MdxbFOq9HOy9FOi+Eus8Fe8/6B077hk95xk+46Mcc7CNW +8UGz+jujZZ/ae0wUOsNIXBxauty2ebUGePACeF4MVN4A3p4FOo9ujR5YYX47 +J/o6pvosZPyz1/aJzfVnve9TRfBvosjnvNiXzMTX07PfTM19O76wb3Tx4MjS +kaGV44MrpwdXzw+uXR5cvz64fmtw4+7Q5oPhzcfDqScjqeejW+VjWxXj6aqJ +9JvJTN1Upp6WfUfPNk9n2xhAxwzQxQR62GAfBxzggkM8aIQPjQmgCSE0JYJp +YnhaAs9IYaYMYcsRjgLhKRG+ChGqUZEGFWtRiQ6V6VG5AS14GTGVCVObMY1l +28saRpKhglciCMcDBa+YH476oIgXCnugkDs/YNAFBpyg3wH67IDXCngsgNuc +dZmyDkPWrt/ujGsyhbSuMm1UFAKFOklKI0qpBdvlIM6GjLUhYayL6Nunjo+v +ckdW2IMrzL5lRvcSvWOJ1rI4+W5h/O382Ju5kdezwy9mh54mBx8lBu7G+2/F ++m9EBq6FB68Ehy8Hxi76Js976WfdrNNO/gm79KhVc9Bk2a/3HJcFz3JjF6fm +rwysXm3ZulkDPCoHyh4DVbeB+otA28nM0JH16QOL/L1J2a6o9oug5VOvY4fN +8zeD/3NV6EtpZKcgtpub2MOc/Y4xd4C2cGhy8ejE0onxldNjq+dGVy+Orl0d +Xb85ulE0unF/bPPR2GbpeOrZxNaLya1Xk+nKqfQbWrqWnqmfzjQyss0z2VZm +toMFdLGBHg7YxwUH+OCQABwRQmMiaEIMTUpgmhSelsEzcpipgNlKhKNCeCqE +r0YEGkSkRcU6VKJHpYZtLyOmNGEqM6a2bHtZMZ1t2ysZfO8V98MxX8Er6oUi +Hiic93KBQScYcIABO+i3AT4r4LUAHlPWZcw6DdlCGl6bsakLQeRCsFVeyErq +xdslNf6mmrupZG8omBuy6XUJbU08sSYcXeUPr/AGVji9y6zOJWbbEqNpkd6w +QKudn6qcm3g5O/5sduxxcqw4MXY/NnY3On4nMnErNHkjSLvmZ1zxsi55eIV/ +cHDIT9m0xyyWgybPCVXgnCh6iTV7dXzpen7pas4U1YAlL4HyUqD6LlB/FWg9 +kx04sTl1dIVzcF78XUL1TcTwVdD2mdf5uc37pSGwUx3aJY9+I47vFST3cWcP +suaPzCwcm148SV8+Q1s5P7V6cXLtyuTajcn1O5Mb9yY3iqc2S6ZST2mpMtrW +S/rW6+l0NSNdO5N5O5NpZGaaWNlWdradA3RygR4e0McHBwTgkBAcEUFjYmhc +Ak1KIZoMnpbDDAXMVMIsFcJRI1wNwtcgAi0i1KFiPSoxoFIjKjOiChOqNGMq +y7aXFdPa8l4hZDYE572SATjhL3jFfVDMC0U9UMQNRVxQ2AmGHGDQDgZsgN8K ++CyA11zwchuyLn3Wqcs4NBm7utBEtsjThWyrZMso2o7f8TY1nE01a0PJ2FDQ +12WTa9LxNfHIqmhwRdC3wu9e5rYvcVqWWI2LzLqFmep5xqu56Rez9OdJ+pME +vSROfxSjP4xM3wvPFIWYtwPsmz7eNa/wilt60ak6Z9eftlqPmT2ndIHz8shl +fuIaY+Hm6Mqtns1bTcCDWvDpK/DVU7DmAdBwA2i9APSf2Zo4ucY8uiQ8NKfY +F9ftiZi/Dtq/8rh32n27jMFvtOG9yug+afyAKHlYMHeUO3+CvXCatXR2ZvkC +Y+UyY/Xq9NqN6fXb9PW79I2H05uPpzefMlJljNTLma3XM1vVzHQNK/2WnWnk +ZJo42RZutp2X7eQD3QKgVwgMiMAhMTgsAUel0LgMmpRBNDlMV8AMJcxUwSw1 +zNEgXC3C1yICHSLUI2IDKjFue5lQuRlVWra9rJjGtu1lz3sF4dnAe6+ED457 +C14xDxT9wSvsAEN2MGgDAlbAbwZ8JsBrzHoMWbcu69JuN+JV2xlrWdoq3Y6B +ClNGfkrP3dSxN7UzG+rpDRVtvZDPGF2TDa1K+gvnWos6lwWtS/x3S7y3i5ya +BU71PLtw2NosqzzJep5gPY2xS6PsRxHuwxDvflBQ5Bfd9klveBTX3JrLTuN5 +u+201XPGGLioilyVxG9w5m7Rl+4Mrxd1bxU1gY9rwbLX4OvnYG0x2HgHaL0C +9J1Pj5/ZmDm5wj+2ID2cVB+IGb8LW78JOnd7PHvs/r2m0D5d5IA6dkiROCpN +HhfNnRLMn+EvnucuXeQsX2GvXGet3mSt3WGu32NuPGBuPGZuPmGmnrNS5YUf +929VcdI1nPRbbqaBl2niZ1r42XZBtlMIdIuAXjHQLwEHJeCwFByVQeNyaFIB +0ZQQXQUzVPCMGmZpYI4W4eoQnh4R6BGhAREZUYkJlZpQmRmVW1CFFVVZMbUN +09gxrR3TOYLI3PdefjjpK3glvFDcA8XcUMwFRZ1gxAGG7WDIBoasQNACBMyA +3wj4DFmvPuvRZtyajEuVKWTi5Wm7LG2TbPdbBSkTL2XkbBqYm3rGhpa+oZlc +V4+tKUfWFIOr8t5VadeKpH1Z3LIkaloUNiwK3y4IaucFhfPxkvyKBL88LiiL +CZ5GhaVh0eOQ5GFQdt+vLPKqb3n0113mKw77BbvnvDl4RRe5rojfEs7eYS3e +nVq9N7R5ryvzoAl8UgeWV4JVLwo/9mi6B7bdAHsvZ0cvbE6fXeOeXpKcmFce +TeoOxcz7w45vg+69Ht8+R+CAJXzIED2ijR9XJU7KZ09L58+JFy6IFi8Llq7y +l2/wVm5zV4u4a/e56w85G485m6WczWfcVDk3VcHdquJtveGn6/jpBkHmnTDT +Isy2ibKd4my3BOiVAP1SYFAGDsvBUQU4roAmldCUCqKrIYYGntHALC3M1sFc +PcIzIAIDIjQiIhMiMaNSMyqzoHJrwUtpw9T2bS8HpnPmvQIFr9ltr6QXTnig +uLsw33tFHWDEDobzXhYgZAaCJiBgzPr1WZ8u69VmPOqMW5VxKbbj49K0Xbxl +E25Z+SkLN2VmbRpnNg3TG/qpDd3EunZ0TT20pupfVfauKLpX5J3L8rYlWcui +tGlB2jAveTsnqZ2VVCcllQlJRVxaHpOVReRPw4rSkOpRQPPQr7vnNd7xWG+4 +nFcd3su24HVD5JY6dkeavMtfuD+z/GBi/eHg1sMu4HEz9PwtWFEFvikH65+A +zQ/B9ttg7zVg9PIW/eI65/yK6Myi4tSc9njCeDRmOxR27Q96D3r8hxyhI9bI +MWPspC5+WpM8q5q7oJi/JFu4Ilm6Ll6+KVq5I1y9K1x7IFgvFqyX8Dee8Def +81Mv+KlXgq1KwdYbYbpOmG4QZd6JMy3iTJsk2yHNdkuBXhnQLwcGFeCwAhxV +guMqaEINTakhugZiaOEZHczSwWw9zDUgPCMiMCJCEyIyI+K8lwWVWbe9bKjS +jqrsmNqBaZyY1hkoeM354VkfPOsteCU9UCLv5YLiTijmAKN2MGoDI1YwvO0V +MgJBQzagz/q1WZ8m41VlPMqMW552SbcT5KItu2CrEHJlpyzMTTNj00TbME5u +GMbX9dupGu3gqqYQaFhWdy+rOpaUbYvKlgVl07yiYU7xdlZRm1RUJ5SVMdWr +qLo8onke1j4N6ksCxmKf5b7XXvT/8nWfXXJc6bmm/+TMLM05skcttbqptmx6 +EgRJeIDwKKBQKO9tVqX33nvvXWRkeO8jk18m9i6ApEZzZq3rH9xfalXueJ9q +5feVxm9LnY+yvT8mhn8Oj//qRT62zz85Iz7ZZz7Z4D95LX/5XPn2kXL7rvzg +O/nx1/KLT+XXf5bXfi/v/Ad//O/M5b+S7n/BAv80i/7DJPU/R7m/G5T+z171 +/2g3/q966+/K3f9R6P99dviPqdE/Jyb/Gpv+W2T22xD6++D8PwPYH/34X3zE +xz7yUy/1uZf+0kN/42G+9bDfedhbXu6ul3vg4x/5+Cd+4ZlfeAk+ExXfBMW1 +kLQekjbD0nZE3o3K+1H5IKYcxZWTuHKaUM+Tqi2lXqZUe1p1ZDRnRnNnNU9O +8+Y0f14PFPRgQQ8V9XBJj5SMaBn2qrQ0pAl6TWGvSU0dV5VxRRmVlWFJGRbl +QUHu5+V+Tu5lpW4G9OokxXZCbMXEZlRohIV6SKgF+JqPr3r4iosrO7mSHc65 +wsXJ3CmdBTtrVHqfTMPBmuQmnljHEm/n8TfgOHns5Sz2DIk9mcZ+nMQejuP3 +hvE7g8QP/eR3vfSNTuardu6LVuHTRvnjeu1P1eZHle4f8/2/pIcfx8afBJFP +3ehnV/jnp5T1J/bnG+Lnb5RvXig/PFbu3lce3VKe3pBffiG/+Vhe+4O885Fw +/DvW9lvK9W+4/1/nkX9Bkv80yf7DqPg/B5W/69X/73brf9Q7f1/p/WNx8M+5 +4f/KjH+Tmv42gfwuNvsoiv4xjP05hP81RHwSJD4LkF8EqK8D9A0/c9PPfO9n +b/u5u37ufoB/FOCfBIVnQeFlSFgJiW/C4tuwtB6RNqPSdlTejcl7cfkgrhwl +lJOkcppUzlOqLa1eplV7RnVkNWdWc+c0T17z5jV/QQ8U9WBRD5Vgr7IerRix +ihGvtlSrF9JQp3V1WgO9Jh96jWCvYUEeWL2ycj8j9dJSNyV1EmInLrajYisi +NENCIyg0Anzdx9e811vkYC65fMWULpniBV04o/MnVP6IzIFBKCK7A2ZQ0htY ++t089RZNvZmlVpDUi2nq2ST1ZJx6NEo/GGbuDjK3+7nve/mbneI37fKXrepn +jcbf6u0/V3t/LQ7+lh1+mhx/HkG+8KNfurAvL8mvTpiv9vivNqSv3yjfvVTu +PFEePFAe31Gef6esfK2sfqqs/0Xe+aN4/J+c7fe083ek77dY+N/Q+G+QzP+a +5P95VP7HQe3ve81/aLf/qdH952r/f5WGvymMfpud/C49/Sg1+0MC/VN8/tcY +9rco/mmE+DxMfhWmvgnR34bo70LMrRB7J8TeC3EPQtyjEP84xD8LCy/CwkpE +fBMR30aldzFpIyZtxeWduLyXkA+S8lFSOUkpp2nlPK1eZNTLjHqVVR05zZnT +3HnNU9C8Bc1XhL1Keqish8t6pAJ7Va1eTXXWUJE6YPWaVtVJRZmUlXFJGRWV +UUEe5uVhTh7AXv201EtK3YTYjYudmJVMaIWFVkhoBviG30oG5uNrbrBwXbHD +HV4bmJ4snVLFY7JwRBbALBSe38FyW1huY54FEwCz7Gsk+2qafTHJPR3nHo/y +j4b5+4PC3X7pVq/8Xad6o13/qtX8vNH5pN7/tDz8vDD6IjP5Ko58HUa/9mHf +OIkbNvrGCXtjT/hmQ765qtx6pdx7pvz4SHl6DzwMfn1DWftC2fhE2f2LdPwn +3vZH1vmflO8jIvS7efw/Zul/n+Z+My7966j6L4PGP/Vb/9Lu/Guj92+1wW/L +o98Vxx/lp3/IIn/KzP6SQj9OYp8k8M/jxJcx4usYeSNK3YzSP0SZ2xHmboS9 +H+EeRrgfo/yTKP8sKryICisx8U1MfAuuVEgbCWkrIe0k5b2kfJCSj9LKSVo5 +zSjnGeUiq17m1Kuc6sirzrzmLmieouYtar6SFijpwTLsVYG9qnqsZsRrsNfM +6lUDplVlCntNSsq4qIwL8gj2GmalQUYapKV+ykom9q6TRYVORGiH+VaQbwX4 +po9reLmGm6272JqDqdmZ6iVduaAqZ1T5lCwfE6VDorSPF+F+TXFzXlhHC2uz +wipSWJkWX06Kz8elp6PSj8Pyw0HlXr92u1v/odO82W5/0+p+0Rh8WR19XRp/ +k5vcSCHfxtBvQ9hNL3HTQX13wdw85m/uSTc3lR/eqndX1IfPlSePlRcPlJXb +yup3yruvlc3Pld2/yccfC7a/cM4/094/kqE/4LGP5qnfz7K/mxZ/O6n8+6j+ +m2HrN/3Ov3V6v232f1cbflQZ/6E0+VMB+Ut+9nEW/SQz/yyNfZHCv0oSN5Lk +zQT1fYK+FafvxJl7cfZBnH0U5x7Huadx/nlceBkXVuLCm4T4NiG+S0obSWkr +Je2k5L20fJCWjzLKSUY5zSrnOeUip17m1au86iiozoLmLsJeJc1X1gJlPVjR +QxU9XNUjVT1ag73qTRVt/CoZ7DUtXyeTx0X5OtkoJ1nJhiCZ2E+K/YTYiwu9 +mNC1koX5TohvB7mWn2v5wI580w2mruvXg7w2qnZBVc/I6glROSIqB3hlDyvv +zMtb8/IGWn43K79FKm+mlZVJ5cW4+mxUezKsPxo07vebd7vtW53ud+3+jdbw +Rn38bWVyszD9Lot8n0S/j2I/BIkfPNQPDuaHC+6HY+GHPfmHTfXumvrwjfr4 +pfr8qfrqkfLmnrJ2S9n4Vtn+Stn7TDn+VLT9jXd+zHr/SgX/TET/hCX/iGb/ +MCt8NC3/flL73aj522H7P/rd33f6H7WGf6iP/lSd/KUy/biEfFJAP8vPv8hh +X2XxbzLEt2nyuzT5Q4q6naLvJpn7SeZhkv0xyT1Jcs+S/Isk/yopvE4Kb1Li +25T4LiVupKWttLSTkfcy8kFWPsrKxznlNAeuMl3k1cuCelVQHUXVWVTdJc1T +0rxl2KuigV5V2KsGe9Wve10nq6uzmjKrKlYyBCabluRJUZ4U5HFeHuekUVYa +ZaRhWhykxAFIJvStZFGhF+G7VrIg1wlwbT/b9rItD9MCg9d00043LqmGjaqf +k/VTon5M1A7x2gFWA8NDaG0LrW3MamtIbXVafz2pvxo3no+aT4etHwfth/3u +vV7vdmfwfXv0fXPyQ216q4Tczs9uZ9A7CexOhLgTIO946Dt29s4Ff+dYur2n +3NlSH6yrj1fVZ6/Ah0ivH6tvH6jrd9St75WdG8r+l8rJF5LtM8H5Kef9hA7+ +jYx+TCT/imX+jOb/NCv/cVr9w6Txn+P270fd/+z3/tgd/Kk1+ktj/HFt+kkV ++aw8+6KEflWcf1PAvs3j3+WIH7Lk7Sx1N0Pfy9APMsyjNPs4zT5Nc8/T3Ms0 +v5IWXqeF1bSwlhHXM+JGRtrKSjtZaS8rH+Tko5x8DO5nKecF5aKgXBbVq6Lq +KKnOkuoua56y5q1ovooWqGrBqh6q6eGaHqnr0boea+jxRkudN9V5Q0XrFuV9 +soqClGWr14dk0jgvfUgmWsmGSXGQEAZxoR/j+1G+F+Z7Ia4b5Lp+tuNjrwfl +20665aBbV1TrEoyHNs+I5gnePMYbYNhr3thFG9toc3PWXEeaa9PWm0lrZdx+ +Oeo8G3afDPqP+oP7vdGd7uROa3q3Pr1XQe4V0fu5+f00dj9O3A+T9/30fTd7 +387fvxDvHcv39tUH2+qPG+rTt+rL1+rKC3X1qfrukbp5X92+re59px58o55+ +Ldu+FJ1f8N7P2eBndPRTMvEJnvkblv8YLf11Vv3LtP7nSetP484fR70/9wd/ +7Q4/bo8/aU4+ayBf1GZfVdGvy/MbJexmEf++SNwqkHfy1L08mOZ7lGMe55gn +WfZZlnuR5V5l+ddZ/k1WeJsV3mXF9Zy4mZO2c9JOTtrLywd5+aggHxeU04Jy +XlQuisplSb0qqY4yuF7nrmieiuatar6qFqhpwZoequvhOuzVgL2aLRWDvWAy +BYW9gIpsJUOsZEV5WpAmeWmSk8ZZcZwRR2lxlBJGSWGYEIZxfhDlBxGuH+b6 +Qa4XYHt+tutluh6mC5evO2CfF+y9ts+J9inePsHbR1j7YN7eAwtE7a1ZZwPp +vJt2Vyfd1+Peq1H/+XDwdDD6sT9+0Js+6CAPm8jD2uxRGX1UmD/KYo9SxKMY ++ShMP/Izj9zcI7vw8EJ6eKI8ONB+3NGebqov3qkrq+rqK3XtubrxWN16qO7e +U/dvqUc31dMb8uU3ovNr3vsVF/ySiX5BJT4nMp/h+c/mpU/Ryiez+t+Q5sfT +zl8nvb+O+n8bDD/tjT7rTL5oTb9qIl/X0Ru1+c0q9n0Fv1Um7pSIeyXyfpF6 +WKB/LDBPCsyzPPs8z77Mcyt5/k2eX80La3lhPS9u5MWtvLhdkHYL0l5BPijI +R0X5uCiflpTzknJRUi7L6lVZdVRUZwXciPRUNW9N89Vgr7oGejX0SEOPNvVY +80MvmEyZ15V5DSRDYa9ZWZ6VZKRokaxkU5BMnMBk47QwTgqjhDCK88MYP4xy +gzA3CHGDINv3s30f0/cyPTBWDvavu3Cit3tBdM/w7inePca6h/PuPtrdRXvb +s94m0l+f9tcmA7ARMBq9GI6fDSaP+8jj7uxJa/akgT6pzp+UsCcF/EmGeJIk +n8ToJyHmiZ974uYf28XHF/KPJ+rjQ+3ZnvZiW1tZ11bfamuv4Uv2Z+rOj+r+ +A/Xwrnp8C3xGcXVTcn0r+G5wwW/Y6Nd04msq/RWR+xIvfjGvfIHWPp81P0Pa +n067n0z6n46Gnw9GX/QmX3Wn37SRG63ZzQb6fX1+q4bdruJ3K8T9CvmwTP1Y +ph+X6Kcl5nmRfVlkXxW510Vutci/LfLvisJGUdgsittFcaco7RWl/ZJ0WJKP +SvJxST4tK+dl5QKc71SuKqoDXPNU3TXVU4O96lqgrgUbWqihh5t6pAl7tfR4 +q6Xi18kaClb/kKwqoxUAJpOsXkhBQvLSNCdOs+IkI07SwiQFko0T/CjGj6Lc +KMINw+wwyA4DzMDPDLz0wEMPXGCyvG8n+1dk3wa2RPtneP8ELOj14c7XYGc2 +2EKGG9PRu8l4dTx+PZq+HCLPB7PnPfR5B33emr+oYy8q2IsS/iJPPM9Qz5P0 +8xjzPMQ+9/PP3MIzh/TUpjw91Z4daS/3tZUdbXVTW3unra9qWyvazgt176l6 +8KN69EA9uaOe31KvfpBd34u+7/jQTS76LZP4lk7fIHPfEMVv8MrX89pXaOOr +WftLpPsF0v9iOvhyPPp6OP6mP/22i9zszL5vo7da89sN7G4Dv18nHtbIR1Xq +cZV6WqGfVZgXZbiRXubelLm3ZX6tzK+XhI2ysFUWt8viblncK0sHZemwLB+X +5ZOKfFpRzivKRVW5rCpXVdVRU5011V1XPXXNW9d8DS3QgL2asFcLHNgFvdpt +0AtvqrjV6zpZzSLPr5OVZbQkzYrSrCDN8iJigcmmaWGaEiZJfpLgJ3F+HOPG +UW4cZkchdhRkRn5m5KOHXnropoYuauggh3ZyeEkM4aLo8BQbHs+Hh+hoHx3t +zsbbyHhzOlmfTN+OkTej2ashutKfr3TnK21spYmt1PCVCrFSJFdy1Ks0DSbk +o+yrEP/SL7x0Sy8c8gub+vxMe3msvT7QVne1tS1tY0PbWtN23mh7r7SD59rR +E+3kkXZ2X7u4q9rvyO7bkv+WEPqBj37PJr5n0t9RuZtk8SZR/havfYs1bsxb +36Cdb2a9r5HB19PRjfH42+HkuwHyfW92q4ve6czvtrH7LfxBk3jUIB/XySd1 +6lmNflED6+grVfZNlV2tcmsV/l2F36gImxVhuyLsVMS9irhfkQ4r0lFVOq7K +p1X5rCqfVxVbTbmsKVc11VFXnXXYq6F5G5oPHj4ONrVQSw/DU8jRth5r6/FO +WyVALwWAvQDYa16R51avsmQlQ0Ey0Uo2y4lIVkAyAgKS8dMkP7WSxbhJlJtE +2EmYHQeZcYAZ++mxlx57wND82EmO7eT4ihjb8PE5Pj7Dxifz8RE6OUAne7Pp +DoJsTZGNyWxtjK6O5qtDbLWPrXbx1Ra+2iBWa+RqmVwtUm9y9Js08ybBvo7y +r0PCa7+44pFXHMqrS+3Vuf76RHt7qL3b1zZ2tK1NbWdd23urHbzWjl5qJ8+1 +syfgS0Dbfc1xT/Hck/x3xdAdPnabS95m0rfo3C2q+ANZ/p6ofY83vsNa3807 +N9Hezdng29nw5nT83Xjyw2h6azC700fv9ub3u9iDDv6oTTxuEU+a5LMm9bxB +v2zQK3XmdZ1drbFva9y7Grde4zdr/FZN2KkJuzVxvyYe1KTDmnRck05q8mlN +Pq/JF3XFVlcu64q9rjoaqrOhuhuqp6l6m7BXSwu2rF5auK1H2rBX50MvoqUQ +sBdQl61eWBWqSPOyNC9J86KEFkQ0L6I5cZYVZhlhlhaQFI8keSTBI3FuGuOm +UXYaZqchZhpkJn564qMnXmoC5ubJiYOc2InJJdiBnZ5hU7BWiSKHKLI/m+0i +6PZ0vjGdr4+x9RG+PsDXe/h6h3jXIt7VyXdV6l2ZXivQazlmLc2+TXBvo8Jq +CPzz+41HfuNUX19qby70t6f6u2N940Db2tN2trW9De3gnXa0qp281k5faufP +NNsT7eqR5nyoeh/IgftS+L4Qu8cn77GZu0zuDl28Q5Vvk7XbROM23rqFdW7N +ez+ggx/Q4fez8Q/Tye3J9M4IuTec3R/MH/axRz3scRd/0iGetcnnbepli3rV +pF83mTdN5m2DXWtw6w1uo85v1fnturBbF/bq4kFdPKyLR3XppC6d1uWzhnze +kG0N5bKhXDUUe0NxNFVnU3U3Ya+W5m/BXvAiPOgFDsTrsa4e77ZV0gJ7AbAX +XoNgL6wsYaXrZOK8IM5BMgHNCihIxs9S/CzJzRLcLMYhURaJsEiYQYIMEqAR +P414KcRDIS4ScZII2MXGERs+O8dmZ/PZyRw9QtGD2XwPwXYQfGuCb43xrSGx +1Se2uuRmm9xsUpt1arNKb5SYjQK7keXW0/x6QngXFd+FpDW/vOZR3jq11St9 +zaavn+mbJ/r2kb67r+/t6gdb2tGGdrKmna5q5yua7aV2+UyzP9Fcj1Xvj0rw +kRR5KMYe8skHXOYBm7/PFO/T5XtU7R7ZuEe07uKdu1jvDta/Mx/eRsd3ZpO7 +yPTeBHkwnj0coY+G88cD7Ekff9YjnnfJlx3qVYd63abftJm3LWatxa63uI0m +t9Xkt5v8TlPYawr7TeGgKR41xOOmdNKUzprSeVO+aMq2pnzZVOxNK5bibKmu +lupuqZ6W6m1r/rYWaGvBjhbqaOGOHunq0e4vvRSrFwB7EXUZgL3wioR/SIYV +RQz2mueEeVaYZwQ0zaMpHk1yaIJD4xwaY2dRdhZmZiFmFqRnfnrmo2ZeauYm +Zy5y5gDT2Ogljl5g8zOwMYodo9jhDN9HiL0psTshdkfk7oDc7ZM7XWqnTe00 +6Z06s11htkvsVoHbyvKbaWEzIW5GpY2wvB5Q1r3qO5f2zq5vXOpbF/rOqb4L +7+Qc7ulHO/oJvBFxvqbZVrXLFc3+UnM819xPNd8TJfhEjjwW44+F1I985kcu +/4gtPmLKD+naQ6rxgGw9IDoP8O59vH8fG96fj+7NJ/dn0wcI8nA6+3GCPh7N +nw6xZwP8+YB42Sdf9cjXXepNl37bYdY6zLs2u9FmN9vcdpvbafG7LX6/JRy0 +hMOWeNwST1rSaUs6a0kXLdnWki9b8lVLsbcUR1txtlVXW3W3rViqz+rV0QId +2KurhbuwV0+PgeWMjkq1FepDL7Jhed+LqFpAL7ws4SURt3rBZFhewHICBpLx +8zQ/T3HzJDePc/MYO4+y8wiDhhk0SKMBGvVTcy8195BzFzl3EnM4kI3ZMOx8 +jp/O8WOUOJyRhwh5OCUPxuTBiDoYUPs9ar9D77fovQazV2P3Kuxuidst8DtZ +YSctbiek7Zi8FVa2AuqmV9tw65sOfftK37Hpe/AO1eGRfnygn+zpZzv6+Sb8 +QH9Nt6/qjhXd9VL3vND8z9XQMzn6TEo8FVNPhewTPv+ELT5mKo+Z2mO68SPV ++pHs/Eh0HxH9R/jwETZ6iE0ezqePUORHZPZkij6dzJ+NsRcj/OWQeDUgXw/I +N33qbY9e69HvusxGl93sslsdbqfD7Xb4vQ5/0BYO28JRWzxui6dt8awtnbel +i7Zsa8tXbdnehrE6iqujuDuqp6N6O6qvo/q7WqCrBbuwV0+L9D706l/3gsmo +JmD1IusQSCYRFYkoW0QCJsMLIp4X8JyAZwUsw2NpHktxWJLDEhwWZ7EYi0UY +LMxgIRoL0pifwnwU5iExN4k5CdyB41c4fokRF2DJlzxBqZMZdYJQxxPqeEwd +D+mjPn3UY446zGGLPWywBzXuoMLtl/j9grCXFffS4m5C2o3JO2FlJ6hu+/Qt +t7HjNHbt+v6lfnChH53pxyf66ZF+dgC/8N7WrzZ1+7ruXNNdq7r7te59pQVe +quGXSuyFnHghpp8L2ed8/hlXesZWnjG1p3TjKd16SrWfkN0nRP8JMXyCjx7j +k8fY9PEceYLOns7Q58j8xRR7OcFXxsTrEfFmSL4dUmsD+l2f3ugzmz12q8du +97jdLrfX5fe7/GFXOOoKxx3xpCOedcTzjnTRkWwd6bIjX3Vke0d2dBVXV3F3 +FU9X9XZVX9eKpQZ6miXY00I92KuvR/t6rA970W0FaF0nk6kGBHuRVQmovO9F +FEWiIBB5AM/xeJbHMzye5vAkhyc4PM7iMRaPMniEwUM0HqTxAIX7KNxLEh6S +cBGEgyDtOHmJkRcYdT6nzlH6DKHPpvTZhD4d0adD5rTPnHTZkw573OKOG9xR +jT+q8Ecl4bAgHmTFg7S0n5T3Y8peRN0Lart+fddj7LuMA4dxeGUc2/STc/3s +VD8/hh927+tXu7p9W3du6q513b2me1d132s9+FqNrCixFTn5Skq/EnMvhcJL +vvSCq7xgay+Yxgu69ZzuPKe6z8n+c3LwjBg9I8bP8OlTHHmGzZ6j6IvZ/BWC +rUzx1xPizYR4OybXRtS7Ib0xpDcHzNaA2e6zu31ur8/t9/mDHn/UE457wklP +OO2JZz3xoivZutJlV7rqyvauFUt29hRXT3H3FE9P9fZUX0/190CvYF8L9bVw +34oFew30ONBRmM77XkBTpj/0omoSAHuRZZEsQUWBvE6W44ksT2R4Is0RKY5I +ckSCJeIsEWWICEOEaSJEEwGK8FOkjyQ9JOkmKCdBOXDqCqMvMdqG0rYZbUOY +iylzMWYuRsz5gD3vs2dd7qzNnTa50wZ/WhNOKsJJSTwuSEdZ6SgtHyaVw7h6 +ENEOQvq+3zjwGoce48hlnDiMU3id7+LcsJ3Cr/APdce+7tzVXdu6ZxMc+vCt +gfMRoVUt+kaNv1FSr+XMayn3WiysCKUVvrLC1V6xjVdM6xXTeUV3X1L9l9Tg +JTl6SYxfEtMXBPICn73E0Ffz+QqKvZnhqwjxdkqsTch3E2pjTG2O6K0Rsz1k +dofs3oDbH3AHA/5wwB/3hZO+cNoXzvrieV+86Eu2vnTVl+x92dGXnX3Z1Vfc +fcXTV7x9xddX/X010FeDgBYaaOGBFhloVqwY7JUYwl5MG3jfCyaj65b3vaiK +RaTKIlUSKdiLzAtkjiezPJnhyTRHpjgyyZEJloyzZIwhowwZockQTQUpKkBR +PpLykrSboF0EDfboMcY+Z+woczVjrhD2asJejtnLIWsbcLYed9HlLtr8eZM/ +bwjnNeGsIp6WpNOCdJKTTzLKcVI9jmtHUe0wpB8GjCOfceI1Tt3GmdM4txsX +l8blhXF1bthPDcex4TzU3fu6Z1f3buu+Ld2/oQff6eE1LbamJt4qqbdyZlXK +r4rFVaH8hq++4etvuMZrtvWa6bxmuq/p/mtq8JoarZDjFXK6QiArxGwFR19j +8zdzbBXF387wNYRYR8iNKbU5obYm9PaY2R0zeyN2f8QeDLnDIXc05E+G/OlA +OBsI5wPxYiDaBtLlQLoaSPaB7BjIzoHsGijugeIZKN6B4huo/oEaGKjBgfo+ +1hCIDrXYUI8PrV5dhf05WcsiM02ZaVwnk+iaRFehikh/6AUUBCrPUzmeyvJU +hqPSHJXiqCRLJVgqxlBRhorQVJimgzQdoGg/RXtJxkMwLoJ14awLAyvnTpR1 +IKxjyjomnH3E2Yfc1YC76vGXXf6yLdiagq0uXtTEi4p0XpLOC/JZTjnLqKcp +9SShnUT147BxEjRO/eAO8LnHuHAZNodxaTeuLg3HheE8M1ynhvvY8Bwa3n3D +v2sEdozglhHaMCLremxdS75T0++U7Ds5vyYV18TymlB9y9ffcs23XOst21ll +uqtMf5UerNKjVWq8Sk3ekMgbcvaGQFeJ+VsMW8Pwd3N8HSU2ZuQmQm0h1M6U +3p0wexNmf8wejNnDMXc04o5H/OmIPxsK50PhYijahuLlULwaSvah5BhKzqHs +GsruoewZKt6h4hsq/qEaGKrBoRoCtPDPsUZafKRbEiPYC2gr7M+9YDKmLjE1 +6EMvoCTQRYEuCHSep3M8neXpDEenOTrF0UmWTrB0nKFjDB1hmDDNhGgmSDF+ +ivWRrJdgPRac9cw5Nwq2zl0I55pyrgnnHPHOIe/o846eYO8I9rZ41RSv6uJl +TbqsyLaSbCuAX2LPM+p5SjtL6Gcx4zRinoXM84Bx4TdsXuPSbVy5DLvDcFwZ +zkvDfWF4zgzvCbytdWgE9o3gnhHaMcJbRnRTj29qqU01s6HkNuTCulRaFyvr +YnVdqL/jm++41juu847tvWP6a8xgjR6t0eM1arJGIWvUbI1E35LzNQJ7h+Pr +GL45J7ZQchuldmbULkLvIcz+lDmYsocT9mjCHY+5kzF/NubPx8LFSLCNxMuR +eDUS7SPJMZKcI8k1uo4lv481sqiBkRocqaGRGh6pkZEWha57JcaWrsJ1P/QC +yWS2CV33qr/vxVREoCwyJYEpCkxBYPI8kOOZLMdkOCbNMSmWSbBMnGFiDBNl +2AjNhmg2SLEBivOTnJ/gfDjnwzjfnPOinHfGexDeM+XdY9494l1DwdUXnD3B +2REdbdHRlOx1yV6TryryVUm5LIBnDrasZkvrF0n9PG6cR82LsGkLmpcB88pn +2L2Gw204neByqfsKXvq5AFf7/KdG4NgIHhqhAyO8Z0R2jNiOntjWUttqZkvN +bSmFLbm0KVU2xdqmUN8Umht8e4PrbHC9Dba/wQ43mNE6M16nJ+s0sk7N1il0 +nZqvk9gGgW/i+BZGbGPkzpzaRam9Gb0/Yw4Q5hBhj6bs8ZQ7mXJnE/58wl9M +BNtYuByLV2PRPhYdY8k5llxjyT2SPZB3pPhALCUwUkCssRqGImMtOtZiYy0O +Wb2S1724DtRWOKtX630vtiGxdYmtQVWRrYhsWWRLAlAU2ALP5nk2x7NZjs1w +bJpjUyybZNkEy8YZNspwEZoL01yI4oIkbwkQfADnAxjvn/N+lPfNeN+U903A +jrZ3JHgGgqcvunuiuyO52pKrKTkbsrMmOyqKo6Tai+pVXrvK6pdp/TJp2OKm +LWZeRsyrkGmHB7edPnAW2O02PE7D6zB8V4bfBu+fnRmhUyN8bESOjOiBEds3 +4ntGcldP72rZHTW/oxR35PK2VN2WattiY1tobgntLb6zxfW2uP4WO9xiR1vM +eIuZbNLIJj3bpNFNar5JYVskvkXg2zixg5O7GLU3p/bn9AHKHKLM0Yw9mbGn +CHeGcOdT/mLK26bC5VS4mgj2iegAJOdEck0k91j2jGXvWPaNFf9YCYyVIPC+ +V2SsglgTID7REhMtOdGTk67C/7pXW7aScU2oIXF14L/0Kv/cS/h1Ly7NcSmW +S7JcguXiDBdj+CjNR2g+TPFhkg8TfAjnQxgftMyFwEwIIEJgKvgngn8M1rR9 +A9Hbl7w9ydORPG3Z3ZTdDcVVU1xwNcxZ1Bx5zZ7V7RnjKmVcJUx7zLRHTUfY +dMIb6W6/6fGaXo/pc5l+p+G3w7NnNiN0YYTPjMipET0xYkdG/BBcr0rt65l9 +LbenFvbU0p5S3pWru1J9V2rsiq0dob0jdHf43g432OGGO+xohx3vMNMdBtlh +Zts0uk3Pt2lsm8J3SHyXJPYIch+nDjDqEKOP5vTxnDlB2VOUPZtx5zPuAuFt +CH+JCJarqWCfio6p6JxKrqnknkieieydyL6J7J/IgYliCU6U0EQNT9QIFP1V +rMRUS0711LQHegEdhW/LwH/rxdUkrioCFZErC1xJ4IoCV7DwXJ7ncjyX5bgM +x6dZPsXySZaPM3yMEWK0EKUgUogQQgQXwpgQngshVAjNhBAiBqdicCIGxmJg +KPkHkr8v+XpgSdbblr1NxdNQPHCVz13WXEXNVdCdOcORMRwp05E0nXAtwhUx +3WFw1t4bMH1+0+c1/R4z4DKDTjNkN8NXZuTSiFwY0XMjdmrET4zEsZE8NNKH +evZQyx9oxQO1dKBU9uXavlzfl5r7YmtP7OwJ3T2ht8cP9vjhHjfa48Z77HSP +RfaY2R6D7jLzXRrbpfFdCt+jiH2SPCCoQ5w6wuljjD7BmNM5ezZnz1HuAuVs +M/4SEK5mgh0RHIjoREQXIroRyTOVvFPZB/mncmCqBKdKaKqEp6olMlWjUzU2 +VeNTzQJj/fdenfe9gKbMNySgLvE1i8hXRb4i8mWBL0FFgS/wfJ7nczyf5XjY +S0ixQpIVEgwQp4U4JcRIiBCiuBDFxMhcjKBieCaGETE8FUMTKTSWgkMpOJAC +cKnZf70n21R8DdVbU71V8ALFU9LdBd2VM1xZ05k2XSnTnTDdcdMTNb0R0xc2 +fUHTHzADfjPoNUMeM+Qyw04z4oDHVi/N+IUZPzcTZ2byxEwdG5ljI3ekF460 +4pFaPlSrh0rtUG4cys1DqX0gdg7E7oHQPxAGB/zwgB8dcJMDbnrAIgfs7IBF +95n5PoPtM/g+TRzQxCFFHpLUEUkdE/QJTp/izBnGnmPsxZyzzblLlL+C7Kjg +mAnOmeiaie6Z6EEkL+RDZD8iBxA5iCghKIwoEUSNImoMiiNaAkoiWgrR0khP +EbpQxyILbei6V/NDr/qvelWE98mKglDghTwv5HghywkZTkhzVi/RkmTEJA0k +KDFBinFCjONADBNjczGKitGZFEGkyFSKTKTwSAaz9QM51JeDPSXYUQJtNdBS +/Q3VXwcPT3wV3VvSPQXDkzfdWdOdWXhSpjdpehOmL2b6o6Y/YgZC4L59KGCG +fGbYa0Y84Fpn1GnGHGb8ykxcmkmbmbowU2fgpl/21Mif6IUTrXSiVY7V6rFS +P1Yax3LrSGofSZ0jsXck9o+EwZEwPOLHR/zkiJseccgRNztk0UN2fshihwx+ +yBCWI5o8pqgTijol6VOCPiOYc5y9wFkbxl1i3NWct0MOVHCiggsV3ajomYne +mWTxzST/TA7M5CDwcywl+qFXHFF/iTUD0jOr1y/JfukFNCWhAdUloSYKVagi +CmVBKAmC1avIXycTc5yY5cQMJ6ZZMc0AKVpMUUCSFJOEmMClBAbE51IclWIz +KYZI0akcnciRkRwZyuEBGEMP9ZRQRw211WBLDTbAEwZ/VfdXdB8c6fPmTW9u +4c0sfOmFL7XwJ80AXPoIRs1QxAyFzHDQjATAuceo14x54DVcJ7hDm7SD66Zp +m5m+MDPnZu7MKJzpxTO9fKpVTtXaqVo/VZoncutEbp9I3ROpdyL2T8TBiTA6 +EcYn/OSYnx5zyDE3O+bQY3Z+zGLHLH7MEseMhTyhqVOKOqPoc9LCXBCsjWAv +ce4K5+wYb3FgvHMuuOaCey565qIXtUg+VPKjUgCVgyjoFZop4ZkSgaIzNTZT +41BipiUhGAv2Ei1dqCMDbVlsQU1JbEB1SayJQFUUK6JYFsQSVOTFAi/CXlLW +wgIZBqKlNCWlSSllIaQULiUxKTmXEqhFjs/kOCLHp3JsLMdGSnSoRAdKpA8n +0TtquA1+Vg01tWBdD9b0QMUIlA1/0fQXTF9u4c8uAplFIL0IwiWdUNwMx8xw +1IyEwb3AaNCMBeBFVa+Z8IA7zymXmXKYabuZuTKzl2bWZuYvjMKFUTrXy+da +9VyrnauNM6V5prTO5M6Z3D2TemfS4EwcnoqjU2F8KkxO+ekpj5zys1MOPeXm +pxx2yuKnLAGRpwx1RlPnNH1BMTYLyV6S7BXB2QnOgfMWJ867MMGNCR5M9M4B +31zyz6XA/H2vECqHUSUCRVElhqqWOKomUDWJapYUqqWhDNr//+rV/tCr+aFX +/Ve9KoKVTCoJUpGXCryUt3BAjoUYKUsDGUrKkFKGkNIWXE5hcmoup1A5OZOT +iJyYyomJEh8r8ZESGyqxgRrrq9GeGu2Coe1ISws3wcu7UM0IVY1g2QyWzEBh +EcgvgrlFMLsIZRah1CKcXEQSi0h8EY0twOW5MDjJCQ6pBsDF4qTXTHnMtNtM +u8yM08w6wJnT3CU4nlm0GWWbXrHpNZtWv1AbF2rrQmlfKJ0LuXsu98+lwbk0 +PBdH5+L4XJicC9NzATnnZ+c8es7PzznsnMPPOeKctZDnLHXOUBcMbaOZS8rC +XpGsneQcJOckeIsL59244MEFr9ULE32Y6MekAAZ6BedyaC6HASUyV6JzJQa8 +jwV7qakPvTLXvaQe1LXIUkeW2lDLIklNSWpAdVGqiVIVqgjSz72ukxU4qcBK +eQsjW3K0nKOALClnCTljweUMJqfnchqVUzMlhSjJqZKcKMmxkhipiaEaH6jx +vhaDQ/bRDpzbbuqRhhGuGeGqGaqYodIiWFyE4GZfOLcIZxaR9CKaWkSTi1hi +EYsv4rFFPALmJJIhMxmE56X9ZtoHrnNn3WbWZeacZt5h5u1m8cosXRnlK6N6 +qdcutcal1rxUW5dq26Z0bUrPJvdt8sAmDW3SyCaObeLEJkxtAmITZjYetfFz +G4/ZOPyCIyDygqNsLGVj6EuGuaIZO83aKdZBcU6Sc5G8xU3wHkLwWnDRh4t+ +XAzgoFcQk0KYHIYimBz90Cs+VxNQcq6mAC0NZeZadv7fe3X+971gMrkiyGVB +Lll4oMhBrFywMECelvMUkCPlHCFncYuSxZTMXMmgSnqmpBElPVVSEzU1VpMj +NTlUEwMt0dfiPS3eBe9KYm091jSiDSNaNyNVM1JZhMuLcGkRLi4i+UUkt4hm +F9HMIpZexOEKUiKxSMTBXEsyskiFF+kQ2CnIBBYZv5n1mTmvmfOYebdZcJkF +p1l0mGWHUbEbNbtet+sNu9a8UttXaudK6V4pvSu5fyUPruTRpTS+lCaX4vRS +RC7F2aVgQS+F+SWPXfL4JU9cchbykqMsVyx9xTJ2hnEwrINmnTTnojg3xbtJ +3kPyXlLwERbRT4gBAvQK4lIIl8K4bAGxACWGKXFATWBqEkphahrTLBlMywJ9 +Re5BXYssd6A21JLkJtSQ5LoI1ET5utd1sjIPlDiIBcmKjFyk5YKFkgukkrcQ +Sg5XchiQnStZVMnM1AyiZqZqeqKmx2pqpKWGWnKgJftasqcnunqio8fbRrxl +xOCUc7RmRqtgcDYKZzFjhUUMjvfFs4t4BqyMJVKLZHKRSixS8UUajoBkwotM +CM4jBOAUiW+R9y4KnkXRvSi6zJLTrDjNqtOoOfWGQ286tJZDazvUjkPt2ZW+ +XRnY5aFdHtmlsV2a2KWpXUTs4swuonbBMrcLmJ3H7TwBkXaesnM0wDIOlnEy +rMVFc26a89C8h+K9FO+zepGCnxQDpBgkLFKIkMIE6BXB5SgUw5U4lMCUX8VS +r2Nd98qBXr8k+//pJV33UqoWAajwEKeULSxQYiBaKVoopUgqVrICoeRxJY9Z +1NxczaFqdqZmETU7VTMTLTPW0paRlh7oqb6e6unJrp7sGIm2kWiZ8aYZr5ux +2iJWXcQqi1h5ES8t4sVFvLBIwAm/ZHaRzCxS6UUqtUgnwSJSJr7IxMB9/Wxk +kQuD+REwGhNYFPzguHrJuyh5FmW3WXGbNZdRdxkNl9506W2n1nFqXafac6p9 +pzJwKkOnPHLKY4c0cUhTh4Q4xJlDRB3i3CFYMIeAOwTCwVtIB085eBrgGCfH +uFjW4mY4DwN6eWneR/F+SrAEKDFIAiESxiKkCCFHoRghv4+FK0lATUFpXM3g +miUL5fD/0uu/JFNaEtCUlAZUF5XaNQGo8hAHklVYoMxAtFKiIFIpEha1gKsF +DMjP1Tyq5mZqDtFyUy07AaxkmZGeGepWsnTfSHWNVMdIfpi2TzTAAHe8uoxX +wFJworxIlBZJOJGZyi9SuUU6u0hnFhm4YJVNLrIJeFY/tshH4epIGC78BBfF +wKLkX5R9i7J3UfEsqh6z5jEaHqPp1ltuve3WOm6t61Z7LrXvUgcuZehSRi55 +7JInLnnqkhCXNHOJqEucu0QMEHCXQLgEEuApF09DjItj3BzrZlkPy3kZC+9j +eD9tEQK0ELR6UWKIEsNWL1KKkFKUlC0gFqAkCCUJpQjVAmOpv4oFeymWHtS1 +yEoH+nWv98lEkKwuACAZD3EgWZUFKoxSoS1qmQJKpFoigCKuFjG1OFcLFlTL +z7Q8ouWnWm5i0bNjPTvSs0M9MzAyfSPdM9JdM9UxUy0z2Vwk4WZ6Ai47J+FY +cKoEJk3ThUU6D4YXMzkw55fNgNGxXGqRSy7ycG2nEIMTMZFFMbwohcB4QTmw +KPsXFd+i6lvUvGbdaza8RtNrtD16x6N3PVrPo/U96sCjDj3KyKOM3crELU/d +MgJIM7eEuqW5W8Qg3C0SboGEKLdAu3kLY/HwrIdjvRznYy28n+EDgBCkhRAt +WsJWL0qKUFKUAr1ipByHEqRigbFArzSUIdQsoVlyUJ4YwF6/JPtVr7astiS1 +eU1UG9cEoM5DnFqzsECVgWjV6lWhgDKplgmghKslTCvOIVQrzLQCohWmet4y +0XNjPQd6GdmBke0bmZ6Z6ZrpjpluL1KtRaq5SMHl9FRtmaou0xUwGZwuLTNw +KDObX2Rzi1x2kcsA+fQin1oUkmAgqRgHez6lKFgGKYcX5RCYMKgEF9XAoupf +1P1mw282fUbLZ7R9esend31az6v1vdrAqw696sirjL3KxKtMvTLilWeAhHql +uVfCvCIOEV6R9AoWyivQEOMRGC/PWnwc57ewfIDlgxZGCAFimBYjAIxFSTFK +jkMJ2CtJKikoTaqWDKlmSfVXsWAvtQ/1oK4MdGS1DVm93hNBsqYAgGQ8YPUC +WKDGQDRIVrV6kRatQmhlHMK00hxCteJMLyK61QuY6PmxkR8ZuaGRGxi5vpnt +mdmumeksMu1FurVIw6X7NBxPz1ShyjILh2izcC4zl1/kc4t8dlHIQOlFMbUo +JhclOLtTji3KUbAPUoksquFFNbSoBRe1wKIeWDQDZitgtv1Gx290/XrPr/f9 +2sCvDX3qyKeOAWXiU6Y+BfHJM5+MAtLcJ2E+CQdEwieSEOUTaIiBWB/P+nku +wFn4oIUVQqwQtjBiBIrSUgyK0zAWJScBJQWlKeWXWKSaA7Q8VCD/d71AMukD +EfQCYK8m/16Dg2CvOgPUaA2gtCoJEVoFhzCtPLfoJVQvzfQSApIVp0ZxYhTG +RmFk5IdGfmDm+2auZ+a6i2xnkW0vMq1lpgk1llk4oZ6tLnNwODgH52jzxWW+ +sCzkwQ5jMbsAMotSGmyQlZNgKakSB6qxRTW6qEXA8EQ9BDSCi2bQbAXNdtDo +BIxuQO8F9H5AHwS0YUAbBdRxQJ341alfsSB+ZeaXUb88ByTML+F+iYBIv0hB +NMT4BfZagOeCAB/iLDAWK0RYMWphxBgjWeKwV4KWk9AvsSglQ6mWLKXmoA+x +rnv9OllX1q51LNJ7bfG9lgDxQJN7r8FCjFa30FqdAr1qJGD1quIWvYLplTlQ +RvXyTC8jVjKjBHsVx0ZxZBaGAEy2yPcWVrJcZ5ltL7OtZba5zMHJ+xxcUc/D +red8eVkoAUW4m1nML0u5ZSkLlDOLcnpRSS0qyUU1AcUXtdiiFl3UI0AjvGiG +F62Q2Q6ZnZDZDRm9kNEP6oOgPgxqI2gcVCdBdRpUkaAyg9CgPA/KWADAAxIB +kQGJCooWGmICIgsIXBAKWb14PswJESgKe8UAKc5ICUBOMjAWoKShDK38l1iA +VoCK1EDRLH2oZ/nQC/jQqyMCbeED2KvFAU0WYkCvBg1YvQDQS68Reg3XrV5V +TK/CXhVUr8yMMgJNjdLEKI1NqxdgJRssCrBXvrvId5a59jLXWuYtzWUert4X +alB1Wawsi2UwIlyyFJelwrIMBxktleyykllW08tqCqglF7XEoh5f1GOLhiW6 +aEYWrciiHVl0wqalGzZ6YaMf1gdhfRjSRyFtHNImgDoNqUhInYUUFJqHZAzC +QzIRkixkSKIgOiRamJDIQhwgcGGBD/N8hBcsUasXJ8Y4Mc5apASUhL1SUJr5 +EItWsrSag/LQh1j/r1592Os9CfQCRAAkE4DrXgDs1WIBqxcAezUoHSD1uoXQ +6zhIVsP02txKZlRRw+oFwF7liVkem1ay0sgsDRfFwaLYXxR6i0J3WegsrWT5 +9rLQWhaaUGNZrC+LcE69BEefS+VluQTBwdNKflnJLasWOB5XSwP11LKeXDYS +UHzZjC2b0WUrumhHF52o2Y2YvYjZjxiDiDGM6JZRWB+HtUlYm4Y1JKxaZmEV +DStzCAsreFi2EGGZBCQKosMSA4gsxF2LCLwlKghRXogBYpwDEhyMBcgpKA17 +ZRglC+WYX8UCtOJ7173eJ5Pfu+517boXAHt1+PesXgDopbcYoElDFGD1AmAv +ADNqcwg1qjOggpiVqVmxesFk5dHC6lUaLEp9K9my2FteJyu2oday2FyWGlB9 +WYIj3UBlWYFrwhW4eVqFM5o1OM5Yyy7rGaABh64aSTCf1EwsW/FlK7Zsxxad +2KIbM3tRsw8Yg6gxjBqjqD6O6hNLRJtGNCSizSKqBY2o84hiwSIKDshERCYh +CpDoiMRALMRFrFgiH7XAXjEB9IpbvXgrlpjkJEvKYpWCMsDPsUCvPFSAPsTS +SvRQ0Qc/k/X+Nem9nviBoHev8XrHwr3XZiHYq0VDsFeTBBqE0cABq1d9Dli9 +ajPTUkXM6hSwklXGC6tXeQiUBstSf1nqLYvdn4qdZcnSXpZaQLm5LDeW5TpQ +qS0rVaBaAQPQ1dKyZoHLp/U8BCf/gAzYJmumli1LctlKLNuJZSe+sHTji17c +7MfMQcwcxowRoI9j+iSmT2PaNKohUW0W1dCoaplHVSyqWPCoQgAyCVFRmQYk +BmIhDgK9YoAQF4CEICZ4MQnAWJyU5mRLhgO9slYvVslBefaXWKAXo1lKgNXr +mhXrFx969UXgutc1qxfwoVeHBaxewIdeAGk0LYTRhL0amNGAveqoaQHJELMG +ei2qk0V1vKiMgPJwWR4sy7BXqfdTuftTuWNZltvLcmtZaUKNZaW+rFrgunqt +ApVBr3oJjNXWC8sGnNRs5JbNLNCC82SWdmrZTgKdxLKbWPQSi37CHFji5jBu +jOLGOG5M4rplGteRuGaZxTQ0ps4hLKbiMcVCQGRMoWKyhYYYQGIhDuItcYso +JCywVxJKWb14Kc1L72Nxchb4ORboVYCKFtgLxtLKzOhDr6H8nhXrZ9e9gOte +/HtWL4B936vDAG3aACijZSGNFgFYvQCrF2Y25mYD9qrPzLrVC1nUposa7AWM +lpXhsjJYVvpWsp/KvZ8qXajzU6VtWVZby2oTaixrdQgOrNcrUHnZKEFFMIEK +5JetHJQFi3JAetlJAd3kspdcWPrJxSBpDhPmCDDGCWOSMKYJ3YIk9FlCs6Bx +bR5XLVhcxSEirpAQBcg0xEAsxMUlLn4dS+ITEuiVFEVLSgDSAozFSxletmR5 +0Ctn9eKUPPRLLKjEapYyYPV670OvoQSAXuJ7Vqz3PvTqcYDVq8saXQboWGjA +6gWQH5LhFrOJQbAXAHotANgLGC+tXtUhUBn8VOn/VOn9VLV0f6p2oPZPNUtr +WWsC9cayXofgzDoAx6CbcGK4WXw/hNrKg7nGdm7Zzi47lsyyk152LallL7Xo +pxaD1GKYModJc5Q0x0ljAk2TOgLNkjqa1CzzhIYlVAueUAmITCgWCqIBmYFY +iIOsUiBW8poVCwKxBCkDZa9j8XIO+BALUIvXQCz1Qyytwo4/xPrZdS/gQ6+B +AMBexrUeB7HAdS8A9upQgNULIEwrFoABVq8malk0ZosGAli96hPL0upVGwHV +4U/VwU/VPtT7qWbp/lTrQO2f6i0I9mpY6hBcWm/C/e5WGYLDtW0LnNfs5MFo +o6WbXXYzQC+97KeXg/TCMkz/P03dZ5KqUBRF4fnPq1VA226VJKCYs0gQCffP +O3tf6HpV3wzWAFazGtRrigfVhraDz472g89hUB6+yuNXeYL3mS5QXOn2Vdw7 ++YOelNBLDDKRDoX0SrNRyliQmy8dK7ekV1KME/TSsb5702cpfnSvCvJqpWWd +SKSd8NXTvZ4d3Wt5B90L0Kv2LiC93BPoXs5BNNLL3gGSbVohveZrmK3ULFKz +kAKYL9XcJw8Wrlo4ZCvpZYs58bcOvELDN3g8ogrfIrNdGhCMIBw10ahZiWG9 +HtYxVJthtaXd8LMn6XWkE50Hb3EZvK90GxTiTg96DnItoZc2ZK+RSDOjZ7KX +pelYSTGB93fyFwu9fjoxY/356wV9r+gFuhf0vYIH6F7LG/i32r+C7uWda4+9 +3KNoJBbsG4e97G1rs9cibhfopeYrNY8oJPZaCJ/YyxYO2cpZ0LwVLpfr8IOX +t8fdsPAnNG6XFpltIIw2NNrIaMTKaNYjUcejegPVdlTt4LMffQ5i+DkOS3Ea +lme6DN/iSjco7vSgZydP6KWNcsbKUiPLhJlquZUi1hgKMXmh17fulbyn1Mcq +f9ErzqFLloGO1Xl1vaIEdC9N9wrutVjeeuzlXwC9kKzxjo30cg+AXkjWOtKL +yWzpFavFWi1WFFGoFgHYS/LJQy9HOGQrd0Fz8GYtxut8r/tiSvzYwrgNhAWh +CZHZrsxmbUBs1BvaGpXYGdVesNeRTqNSnOkC7yvd6A7Fg56UdFBKSw1NYpGl +Y6X5GFiKvqErhVhQ/nb+ekHW9YL/emm6F3S96vABuldwA90L2Ms/NwK9mMxj +L3cvWt0LpNdG2bGy110yW0TKDikAZ0m+cjxylSscspW3oDnNlM/9uvRaiil9 +t4GYQDhuQwsiq11Z7GU2MW3Meks7sxLS6wCfI52gPBvlha7wvvXu9DAK8aSk +96IulgmMBfk407HyifQixiqm0ot+XujVxypnySavNv/10nQv7a/XKqlFJJ4d +3Su8g+4FXa8G2Ms/AXohWevtW+nl7oC9FMRdMpu9nIhCCmipXOEr1yNXecIh +JvPFnGbdgX3Jr3cgpugVigmN24hW43ZtiSa2mg3UW6ve0V56mdWBjubnRGco +L3SlG7zv9Og9zUIkvRelnTy18gyybMxeE01K9aZp0ZWiXyjFDL3+Ack3k/s= + + "], {{0, 144.}, {144., 0}}, {0, 255}, ColorFunction -> RGBColor], + BoxForm`ImageTag["Byte", ColorSpace -> "RGB", Interleaving -> True], + Selectable -> False], DefaultBaseStyle -> "ImageGraphics", + ImageSizeRaw -> {144., 144.}, PlotRange -> {{0, 144.}, {0, 144.}}]], + EdgeForm[None], GraphicsGroupBox[ + TagBox[{PolygonBox[CompressedData[" +1:eJxNmnWYV9UWhuf8Dh3SDcLQjUM3QzPAEEM3Awzd3Tl0gyDd3SEhUooiKSqC +dDcCSkrJXd/d732e+8f33OV31l5rnfUexpF9g9v0iOgeCAoKaucHBcWw//VM ++udMpowms//rZzYFE8c0ZcGLb0pgym3KxVmf3EzkxjJl5Yzi2KZseHFN8Uw5 +TTmI41MrJ7lxTNk5o14JTXnoqfgzU148xYlM+fBSmlKZipgKmxKbkpgKmPIT +JzV9gZfMlNxU0BRCrcTk5mOWuMyanbPJyFWNtKZ0phKm4vRObSrKDIrTmIrh +pWBGzVaI3imIC5Kj3Aam+pxNS+1i1CzKs3ow097LmsoQi0U5vBzstYqpsimD +6XNTaVMpcsU1lDOZ4VYeLxvvXclUkTgHtSqRK64VOJMTllXpmQtu1fBywy0M +ryDvXtdUB4baew1TdWKxqIlXgL3XMoVTKy+5YbBIbyoJk/ycCadGenZQipxC +sIhghsLsuB5eCDNqttr0DiGuxbtnYzcVYCRWDWHYwtTSNNQ0hJnUt7GpEbFm +aYJXCjZN8crAsbmpGYxCqdkCBmLR1tSGGTRLpKk1cSWeRXJWnFpRoyw1W9Cj +h6mnaZppKrXFsR09qsKtvSmKWHvvgBcGi4541eHWCa8GHDrjlWfm1swUzl67 +mroQa9fd8GrDojteHbj1wKsLt554VZg5incoDoNGMIqAdS/O1IdbH1Nv8sSl +v6kfsbgMwGvNXkeYhlOzEbl9yRXLgZxpxp4HmwbBQO89LMh9I62oORyvOWyG +cCYSliPp2QYuo/Da8p6j8bqwt0mmiexBnKJNY4jFaSxeR7iMN42jVhS5o9lV +fXbTi7MdyR3L7hry7n3oLU6TmaEbnKbgdWZGzTaB3p2Jx5MrjlM505O+04Pc +N3rddMP0r+kjPdV7lmkmsVjMxhvKXheaFvAefcidQa64fsmZ/nCbgzcYFvNN +84iHUms+uWI9lzPDYLmInsPhthhvBNyW4I3n3deYVsNQe19mWkosFsvxotn7 +StMKao0iVzUHMbNm/Yqz0eQuh4H2usG0nt5isZYZJsJtHd44ZtRsq+g9jngl +Oco9avqRs5OpvY6aa3n2Axy19y2mzcRisRVvHnvdY9od5JhPJ3cTueK6jTOz +4LYdbw4svjbtZAfzqLWLXHHdwZn5sNxLzwVw+wZvIdz24a3k3b83fQdD7X2/ +6VtisTiAt4y9HzIdpNZicvfBQt/6Rpgs5cxBakxlB5vIWQWLI8ywmh3/gLeC +GTXbYXqvID4EE7H5CWbr6XsM77TpZ9Ofpsf0VO8TpuPEYnESbwscdO4UtTaS +e4zcLTw7Se42epyGkVj9ZvqVZ+JyhpxdsPvddDbI/SzQn2F9N9N5Jm7nyNkL +pz9M53lv7UI/N66xc+3+oukCsThdwjvA7q+YLlNrH7mquYOZNesvnD1A7iVm +2Uvvc/QWpxvM8D2cbuIdYkbNdpXeh4ivsIsd9DrDWbG+RQ3F+rN1G+84XB6Y +7nNOsz4zPSXWrv/CO8YZ5d5jx9rjc9PfQe6bOMazuzAUy0emhzDSXE+C3Ddz +hp5P8U7B+TFnTlDjITPqdwP9DqB/J3Smt/b2ghmuspsPpvcwEIvXplcw097/ +Mb1hF/qu77CT85xR7kt2epVa7+h1nmcvqCWWb6l5DW4fmeEyNd6Rc5Qd3aXn +BWZ6w4w77D+Wtpt22H947fQcc3H7FOT+HXaLOT39h5nnYtUJeM67Q23fc95d +WMTwnHcPdjE9591nr7E85z1g17E95z2EQxzPeY9gE9dz3mM4xvOc9ycc43vO +ewLbBJ7znvIdJfSc94xv6zPPeX/DMbHFiTwXa89JPOe9YPdJPee9hFUyz3nv +2Xtai9N4bqfabQqLk3suFqeUnvP+gUsqz3lvYZXac9472KuWvA+wTee5Hq/g +ptqa4SOc0nsuJwlzfWEq4DmO4va5KQMMxS0jnge3THgBuAXj+XDLjBcDblnw +YsItK14suGXDiw237Hhx4JYDLy7ccuLFg1suvPhwy42XAG558BSLZV68RHDL +b8pHnIRd5GfH2mtRUxF2pT2GsLNkcCuIlxxuhfBSwK0wXkpqFsH7lz872nV6 +eollMXqmgWNxvLRwK4GXjnMl8dLDrRReBriVxvscbmXwMsGpnKksO9eeK5kq +wkhcKpjKE2fjWQXOimsoNTJSsyw96poiTD1NPagtbpXpkRNOVU1ViMWpGl5u +OIXh5YFddbx8cKppqsEsWZg1FI7iVMsUTixOtfFC4FQHryCc6uIVglMEXg5m +rsI7FIZlPXKKwK0+XlG4NcArAZfGpkbE4tIErzx7bW1qBeMS5DbkmXYfSU4p +ODalRhl239zUjFhcWuCVYy8t8ULp2QqvNDWaUbMO7y123ektbm2YIZw9djV1 +YS/iFmVqRyxu7fHCYNfR1IEdViG3LbUrE7fhbBi57dllcXbRgN7i1o0ZajNz +d7yazKjZOnvuG6lJ3Mlzvzvrd2z9DqTfSyLg1stz3+wS01LTAdN+GKpvH1Nv +Ys3SF68hrPrhNYJrf7zGcBqA14Q9D8Rryu4H4TWD22C85nAbgtcCbkPxWsJy +GJ5ifSfD8VrDbQReJHseideG3Y/Cawub0Xjt4DgGryt7nmyaBCOxGmuKJhbr +cXid2P0E03hisZmI14Wak/C6wXIKPaLoEc0MeqZvcyo5o5hrGdx6wnK6aRqx +uM3A6w23mXh94DYLry/cZuP1g9uXeP3hNgdvANzm4g2E21d4g+A2D28w3Obj +DYHbAryhcFuINwxui/CGw20x3gi4LcEbyU6W4k1gr2tNa9iV9ricnY1htyvw +ouG2Em8sLFfhjaemaq2GRU92PZVeYrmOnpPguB5vMtw24E3h3Ea8qdTahDcN +bpvxpsNtC95MOG0zbWXn2vMu09cwEhf97rqDeC7PdnJWXLdTYwY1t9JDPxv0 +M0DfTS9qi9tuesyH017THmJx+gZvIZz24S2C07d4i+G0H282M+9gpqVwOui5 +n0nL4HQIbzmcDuOtgNN3eCth9z3ePGbewzuMs9/tx/puH3qf8b7zdvF8gu+8 +3ZyZbPEk372L5p/iO2/f/+a3eJbveqmncif6bhc6c8T0g+mW6aZ4+67Gt+xg +usXTfPeuer8ZvvMO8n4zfecd4v3US95h3k9nVXM/+7rJf6Po91r93qXeP5pu +M8Np08+mP02PTT+Zjpnume4SHzfdxzthOml6aHpgOsoZ5d6h9lHi25w9Qa5q +aBfa6R6+D/U+Y3rCDIp/MT3FO8WMmu0RvU8RPyT3V9Mzzij+zfQXnuKzpr/x +zpnOm16aXhD/YXqFd9V0zfTB9N70O2eU+5zcC6bXnFF80fQG77Lpiumd6S3x +VWq9I/eS6R/OqNd100d6Kr5h+hfvJpx0cfeJd9a7x7F/jh1wO9auAxZ7AReL +hR9w3j32HtPiGAFXS2eUq5qXmPktM92Fs3JV4wl7TWBx/IDrLRZxA26Gx3CL +F3DeA2bUbLECrrc8xTHJUW5OU46AO6se8fHjkKNn2QOOm/ae2OJEAReLRZKA +896y19QWpwo4xjqj3M8CLldckwbcmZdwSxZw3hveO6XFKQIuVk3VkvcKrskD +7sw7WKYJuJ7v4ZY24LwPcEsXcF5M9pDVlAWG2vvnpgwwEIuMeAH2HmzKFHC1 +9C2kD7iaT/muEwYcE48zmajxjO9c756Q3mKRjRlis+PseDGYUbNlpncM4mCY +iE0umMWnb268AqYvTLVM4fRU77ymPMRikQ8vMRx0Lj+1EpKbm9zEPMtHblJ6 +FICRuBQ2FeKZuISQk5LvoAg520zbTWdMP/NM3IqSkwZOxU3FeG/torwplJ1r +9yVNJWAmTqVNpdi5dl/WVIZa6chVzeTMrFkLcjYjuaWZJQ29i9JbnCowQ1Y4 +VcQLZkbNVo7ewcRl2UVyeoVwVqwrUUOx/mxVxssDl+qmMM5p1rqmOsTaYwRe +bs4otxrPtMd65OQiR8+qwlAsa5pqwEhz1Q64byaEnnXw8sM5nDN5qVGDGV/z +czMF71mEvdVnhnLspqWpBQzEopGpIcy096amJuxC33UVdlKMM8ptwE7LUas5 +vYrxrD61xLIZNUPh1ooZylCjOTk52VFVemo2fVuNmVHf6g7TLwH3zZaHe2tq +VoRbG1MkM6tOO1NbYtWOwqsKi/Z41WDXAS+MvXbEq86uO+HVgENnvJqw6YIX +DseueLXg2A2vNmy74ynWd9QDT7G+m554EXDshVePPffGq8/u++A1gFVfvBbs +fahpCDvVbvub+sFcnAaaBhCLyyC8ZrAajNecmkPwWsJhGD0a0qMfM7SC1XBy +ejPXTNMMmIndSNMIYnEbhdcWbqPx2sFtDF4U3KLx2sNtLF4HuI3D6wi38Xid +4DYBrzPcJuJ1gdskvK5wm4zXDW5T8LrDbSpeD7hNw+sJt+l4vdjJDLxB7HWe +6St2pT3OYmd92e1svH6w/BJvANzmmuYQD6LWXFhEsmsx0Z+dyuy5Db3Fdj4z +DIXbQtMCzujsYtMiYnFagjeOPa42reLscHIXkiuOSzkzCo7L8KLhtNK0gngc +tVaSK87LOTMeTmvoOQFOa/Emwmkd3kz2pn8PboWZOG0wrScWp4140+Cy2bSJ +WpPJXccs0cy6nLPTyN3IzrX7Xaav6S1O25lhNux24M1gRs22hd4ziDfDdC61 +dlJbnHbTYwjMFsBwAXv/xrSXWCz24a1gr9+ZDv/fGeXu4Zl2/z05i+D8LTWW +wO2AaT+xuBzEW8ZeDuEtp+dhvMXU2E9N/WzXz3R9o63pLa5HmGEzuzhlOglT +cThq+pFYbH7C2wCH46ZjAfdNrCX3B2qvIT7C2Q3k/sRu57OL3fQWm9PMsBWO +P+NtYkbNdoLem4g1g/6uWn8nrb+T1N9D7oTlb6ZfTVXtvwWrmdqbonzXU73P +mX4nFpvzeAfZ41XTFb6B3eSeJVec/+DMN3C7gLcfTpdNl4gPUusyueJykTOH +YHeNnof5Lq7jfQenG3jHefcHpvvsWLu+ZbpJLBa38Y6y97umO9Q6Qu4NZtnP +rBc5e5Tc2zAQiz9Nj+ktFg+Z4STcHuEdY0bNdo/ex4jvkqPcOMYitu/Onqb2 +I2oqR89i+Y6j9v636S9isXiOd4m9vjX9A/PfyH1Grri+4Mw5uL3Eu8B7vzG9 +Jr5ErTfkiusrzlyG5Tt6XoHbe7yrcPuAd5d3j2Hv4vuOofb+r+kjsVh8wrvF +3j39n2h9V+s6uR9god/bnsDkJmeU+4ln+t3uKTn3YBHTdzPcZ8farbw7zKjZ +Ar7rLU+xZngEm7i+Y/aYvvF85yU2JTEVMOX3XU/1TmBxfN8xEIvPLE7oO2bi +oHOJfFdLZ5Srmn/BVc905jmcktDrNVxSWJzcd8/EJSlzvIFdSt/lZDZlMZU3 +hfrumbil8l3OOzilsTg1O9Augk2ZfLdz7T6dxWl9F4tTet95n9j956YMvqul +M8pVzVd8V5o1me/O6oxyVeMt3416p6J3DOYOJo7JO2SGSYDZMvKNeMSa4SXf +qnol5axYZ6VGLP7cZcPT3sUqtykXM2rWgqYQYu2xEF48zig3J8+0x8LkxCVH +z3LAUCzzmfLCSHN9wTeTlJ4heIngnJ8zCamhs3l892fxAjt9BWftrQgzZGQ3 +ZU1lYCAWxU3FYKa9lzSVYBf6rrOzk9ScUW5RdpqRWqXplZpnRagllqWomQlu +5ZghAzVKkxOHHeWgZ1pmKsGM+nfXLn7O6edYMNxDqXmWvzN8zt9DZadWZVMl +Yu2+Cl4B9lrLFM47Zie3IrliWZUzufgWquHlg0VNUw3iAtSqCROxqW4Ko5dY +1qanYn03dfAK8p3UxSvJXpqYGsNQe61niiDWruvjFWNPDU0NqFWY3LrMko9Z +q3O2GLn1YaI9tjA1p7fYNGWG0rBuhleCGTVbI3qXIG5IjnIHmQZytiy1m1Gz +Kc8GmCqw90hTa2KxaINXg712NnXy3c+tCuS2Ildc23KmMtza4YXx3h1NHYhr +UKsjueIaxZmasOxCz3C4dcWrBbdueA15936mvjDU3nuYuhOLRU+8euy9t6kX +teqQ2w0W+rZbwiSCM72oEcoOWpHTCBb9maExOx6A14AZNVsfejcg7g0TsRkM +s+b0HYK31LTMd/cEujtoSe9hpqHEYjEcLxIOI00jqNWS3CHkRvJsOLniNIoz +uhvSfdBZ7hLawmU0OXqm+6HfuWfQz2z9Ga7Id6Fnuu84x88F3X/oTugP7h50 +d6M7nOvcBeguSfdBF7lbUKz7nEvcHeh+R/dBV/h7e9XSmQvcTei70e/S0aYx +nNWZy9w7aBbNcJ57DfXWndUN7h6+tHiO7+6JdFeluybNeI17DPWWd5W7De0i +il6jOTvXd/dAqqH4K9/dCclbYPFC390J6W5I8SLf3evIW23xKt/dreqOdb7v +zihXd1HKXey7OyCdUbzEd3dE8vRtLPfdvZC+EcUrfHcvJG8J35C+HZ1Z47ue +6qX7Wv07OCvs9F2v9V2Onun+dpvFW313V6r7yQ0Wr/fd3a3uazdZvNF3d7W6 +n9W7z/PdHZl2oNx1vrv71Zl19FBteTqrmv+tpRq+q6lauo/V/xdRM6i37kg1 +yxbf3ddqJsU6o1x56q0danea4T99a3/S + "]], + PolygonBox[{{930, 931, 901, 466, 465}, {931, 946, 435, 436, 901}}]}, + + Annotation[#, + "Charting`Private`Tag$63431#1"]& ]]}, {}, {}, {}, {}}, {{ + LineBox[{2, 1, 31, 61, 91, 121, 151, 181, 211, 241, 271, 301, 331, 361, + 391, 421, 932}], LineBox[CompressedData[" +1:eJwVz8kxwwEUwOG/fUsssZNkJldJBYkCIkcncXSQ2BJbFrHFMhoQKlABKqAB +VEADqACfwzfv8ubN7yVWyoultiAICrTTQSdddNNDL330M0CIMIMMMcwIEUYZ +Y5wJJplimhlmiRIjzjzL1LnlkTe+/+8LS5GjyBV3PHEt9N38ISo8zRJVWtzz +wichu3NkWeWSC845o8kpJxxzxCENDqhTo0qFffbYZYdtypTYYpMN1lmjSIEF +koT50vXKAzfUyJMhxq+/PnimZf8PWakoqA== + "]]}, {}, {}, {}}}, + VertexTextureCoordinates->CompressedData[" +1:eJx1mz2oHUUUgB8KErWKjRBsxNZS7OR1Em1EK8EqRgsrwTYqFmInWEURDIjF +Q6tMqiTdBLHYgDAEFlklWf//1uVZ2fru5X1nOd+9azN8uffue8fvzsyZM+c9 +/uqbL71+38HBwbX7Dw42o//75NK5CzeOPj/MXIJfu3F09vKlm3q9Br+7wbPf +6P1d8PMvz2+8/+u3+nwLfvj2Mx9e/eGOntcH/3vy6SvPfqfnD8H9me0Dgp/b +/ry7wXfvbN4wBn+8/fk/Br/4xJP/PXXrp+CHto/7Ofjrt144eccvwe9sf7/f +gp++tXnD78HH29/3j+CvTn7bcxf+DL64/f3/Cn5s87jLfyueKfijk/85Z27/ +o/jm4NOfKl687h9LMH7z6zUYv/n9XTB+8+dbMH7z8/pg/ObnD8H4hfEL4xfG +L4xfGL8wfmH8wviF8QvjF8YvjN8czxSM3xzfHIzftXm63+syZr/8ew3Ofov8 +Fvnl8y04+y3yW+S3yG+R3yK/RX6L/Bb5LfJb5LfIb5HfIr9Ffov8Fvkt8lvk +t8hvkd/ddXf/PF28esQvjN/8vi4Yv/nzLRi/+Xl9MH7z84dg/ML4hfEL4xfG +L4xfGL8wfmH8wviF8QvjF8ZvjmcKxm+Obw7G79o+un/dLTse8+vLmOdvDb9w +nr81/MJ5/lbN36r5W8MvnOdv1fytmr9V87dq/lbN36r5WzV/q+Zv1fytmr9V +87dq/lbN36r5WzV/q+bvbl60fx8tO/PSHmGP+IXxmz/fgvGbn9MH4zc/fwjG +L4xfGL8wfmH8wviF8QvjF8YvjF8YvzB+YfzmeKZg/Ob45mD8ruW5+/OiZR/1 +uut5aq8e8/rchV84r89d+IXz+tyFXzivz53W507rc6f1udP63Gl97rQ+d1qf +O63PndbnTutzp/W50/rcaX3utD53Wp87rc+755b9eW7Z2Te9znpe2iPsEb8w +fvPz+mD85ucPwfiF8QvjF8YvjF8YvzB+YfzC+IXxC+MXxi+M3xzPFIzfHN8c +jN+1c+j+c0vRPLup1+vOOut5aY/588uY998WfuG8/7bwC+f9t2n/bdp/m/bf +pv23af9t2n+b9t+m/bdp/23af5v236b9t2n/bdp/m/bfpv13t66AX59TnNc6 +D/K+6XXW89IeYY/4hfGbnz8E4xfGL4xfGL8wfmH8wviF8QvjF8YvjF8YvzB+ +czxTMH5zfHMwftfqRDm/Ws6dPqc4r3Ue5H3T66znpT3m5y1jzq/68Avn/KpX +ftUrv+qVX/XKr3rlV73yq175Va/8qld+1Su/6pVf9cqveuVXvfKrXvlVr/xq +t+6HX9cRfO70OcV5rfMg75teZz0v7RH2iF8YvzB+YfzC+IXxC+MXxi+MXxi/ +MH5h/ML4hfGb45mC8Zvjm4Pxu1bHzfnzUhdyHcHnTp9TnNc6D/K+6XXW89Ie +8/OXMefPg/LnQfnzoPx5UP48KH8elD8Pyp8H5c+D8udB+fOg/HlQ/jwofx6U +Pw/Knwflz7t1efy6zue6kOsIPnf6nOK81nmQ902vs56X9gh7xC+MXxi/MH5h +/ML4hfEL4xfGL4xfGL8wfnMcUzB+c3xzMH7X7lnw67qt63yuC7mO4HOnzynO +a50Hed/0Out5aY+wR/zC+IXxC+MXxi+MXxi/MH5h/ML4hfGb45mC8ZvjmoPx +u3Zvhl/X4V23dZ3PdSHXEXzu9DnFea3zIO+bXmc9L+0R9ohfGL8wfmH8wviF +8QvjF8YvjF8YvzmeKRi/Ob45GL9r96D49b2K6/Cu27rO57qQ6wg+d/qc4rzW +eZD3Ta+znpf2CHvEL4xfGL8wfmH8wviF8QvjF8ZvjmcKxm+Obw7G79q9Nn59 +T+Z7FdfhXbd1nc91IdcRfO70OcV5rfMg75teZz0v7RH2iF8YvzB+YfzC+IXx +C+MXxm+OZwrGb45vDsbvWp8Cfn3v6Xsy36u4Du+6ret8rgu5juBzp88pzmud +B3nf9DrreWmPsEf8wviF8QvjF8YvjF8YvzmeKRi/Ob45GL9rfSf49T227z19 +T+Z7FdfhXbd1nc91IdcRfO70OcV5rfMg75teZz0v7RH2iF8YvzB+YfzC+IXx +m+OZgvGb45uD8bvWR4Rf9yX4Htv3nr4n872K6/Cu27rO57qQ6wg+d/qc4rzW +eZD3Ta+znpf2CHvEL4xfGL8wfmH85nimYPzm+OZg/K71heHXfSbuS/A9tu89 +fU/mexXX4V23dZ3PdSHXEXzu9DnFea3zIO+bXmc9L+0R9ohfGL8wfmH85nim +YPzm+OZg/K71+eHXfUPuM3Ffgu+xfe/pezLfq7gO77qt63yuC7mO4HOnzynO +a50Hed/0Out5aY+wR/zC+IXxm+OZgvGb45uD8bvWt4lf94G5b8h9Ju5L8D22 +7z19T+Z7FdfhXbd1nc91IdcRfO70OcV5rfMg75teZz0v7RH2iF8YvzmeKRi/ +Ob45GL9rfbj4dV+f+8DcN+Q+E/cl+B7b956+J/O9iuvwrtu6zue6kOsIPnf6 +nOK81nmQ902vs56X9gh7xG+OZwrGb45vDsbvWl81ft2n6b4+94G5b8h9Ju5L +8D227z19T+Z7FdfhXbd1nc91IdcRfO70OcV5rfMg75teZz0v7RH2iF8Yvzm+ +ORi/a33y+X5h6bt1n6b7+twH5r4h95m4L8H32L739D2Z71Vch3fd1nU+14Vc +R/C50+cU57XOg7xvep31vLTHHM8y5vuFKfzmv3M4Fi9/94Bf91G779Z9mu7r +cx+Y+4bcZ+K+BN9j+97T92S+V3Ed3nVb1/lcF3IdwedOn1Oc1zoP8r7pddbz +0h5hj/jNf7dyLF7+jiXfHy198e6jdt+t+zTd1+c+MPcNuc/EfQm+x/a9p+/J +fK/iOrzrtq7zuS7kOoLPnT6nOK91HuR90+us56U95viWEb9rf5eE38zL3z3g +N7++9FW7D9d9m+7zc1+Y+4jcd+I+Bd9r+x7U92a+Z3Fd3nVc1/1cJ3JdwedQ +n1uc5zov8j7qddfz1F495nhHxTsq3lHxjop3VLyj4h0V73j4ZYp3VLyj4h0V +76h4x8PzKd5R8S73ZUdXv3jl0UeW+9DMJZjvc369Br93+n3O7++C+T7nz7dg +vs8w32eY73N+/hDM9xnm+wx/9sAHn15/8N5O/NeuXD/fvr8X8WcuwcSfX6/B +b5/Gn9/fBRN//nwLJn6Y+GHiz88fgokfJn74fyOOH6w= + "]], {}}, + Axes->{False, False}, + AxesLabel->{None, None}, + AxesOrigin->{Automatic, Automatic}, + DisplayFunction->Identity, + Frame->True, + FrameLabel->{{None, None}, {None, None}}, + FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}}, + ImagePadding->All, + Method->{ + "GridLinesInFront" -> True, "ScalingFunctions" -> None, + "TransparentPolygonMesh" -> True, "AxesInFront" -> True}, + PlotRange->{All, All}, + PlotRangeClipping->True, + PlotRangePadding->{{ + Scaled[0.02], + Scaled[0.02]}, { + Scaled[0.02], + Scaled[0.02]}}, + Ticks->{Automatic, Automatic}]], "Output", + CellChangeTimes->{{3.827490846107746*^9, 3.827490850472845*^9}, { + 3.8274909084807987`*^9, 3.827490943504459*^9}, {3.8274935528686123`*^9, + 3.827493574483676*^9}}, + CellLabel->"Out[34]=",ExpressionUUID->"df9e29c5-0d24-4bbb-91d1-382b57cb444b"] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Plot", "[", + RowBox[{ + RowBox[{ + FractionBox[ + RowBox[{ + RowBox[{"(", + RowBox[{"x", "-", "\[Theta]c"}], ")"}], " ", + RowBox[{"Exp", "[", + RowBox[{ + RowBox[{"-", "1"}], "/", + RowBox[{"(", + RowBox[{"B", + RowBox[{"(", + RowBox[{"x", "-", "\[Theta]c"}], ")"}]}], ")"}]}], "]"}]}], + SuperscriptBox["x", "2"]], "/.", + RowBox[{"{", + RowBox[{ + RowBox[{"\[Theta]c", "\[Rule]", "1.27"}], ",", + RowBox[{"B", "\[Rule]", "3.12"}]}], "}"}]}], ",", + RowBox[{"{", + RowBox[{"x", ",", "1.27", ",", "10"}], "}"}]}], "]"}]], "Input", + CellChangeTimes->{{3.8274898100367002`*^9, 3.8274898789332952`*^9}}, + CellLabel->"In[19]:=",ExpressionUUID->"5707a3d0-1ca0-4632-af53-b2e5ab76b965"], + +Cell[BoxData[ + TemplateBox[{ + "General", "munfl", + "\"\\!\\(\\*RowBox[{\\\"Exp\\\", \\\"[\\\", RowBox[{\\\"-\\\", \ +\\\"1797.1865711754858`\\\"}], \\\"]\\\"}]\\) is too small to represent as a \ +normalized machine number; precision may be lost.\"", 2, 19, 8, + 31546055972801521149, "Local"}, + "MessageTemplate"]], "Message", "MSG", + CellChangeTimes->{{3.8274898759897757`*^9, 3.827489879213965*^9}}, + CellLabel-> + "During evaluation of \ +In[19]:=",ExpressionUUID->"1a833013-cc34-42af-abf5-a8dfaa80161d"], + +Cell[BoxData[ + GraphicsBox[{{{}, {}, + TagBox[ + {RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6], Opacity[ + 1.], LineBox[CompressedData[" +1:eJwt1nk8lN/3AHDLMIslSRERJrK0WSKFc5JUIkoqa1mzpbIrEllDVIhSCSWJ +hElZYsxTxEdEKUoqUp+oPjSDrL/n+3r95p95vV9n5t773HvPOY+S6/F9HgJ8 +fHw7+Pn4/vd9i3+8amQvF/j+/4OK+YaDjlxwkS2yamxN1/1ovI/oO8qF179l +fz/QEtoc6SRg0RXAhRHVyw6x+u+3rIio6H4RyQXDmAM//SqaDWuuujqwE7nw +RyD4Ut7wASO7J5KDjy9zQZAYFZFRqDaaetvkU36DC/vr9JeJCs8ZZU0EjBcV +c0HvJ5y3jtYy1l3KPHWziguM4/N7LPrsjLt1uvmvNHDhob99xSDjtHHAvnNJ +F1q5wF46oaM6l2kscVJncfwbLpwv+Ob9LqPUuCxtMDvyExcOVdNzWtazjS3L +LisGj3Dh5G23qRutr4xH/9l212+CC5s7bvDoLz4Znx/5s96dnwcLD6Kovxx/ +GqsxCqsdRHmg/Fal7MfKKeNmtf1gI80DpdMS2ns6BMBzB6XZXJkHbw8GPmxd +JAoUz6o9Jmt5MO5kDkJqUlAQ695jsIkHjYN1HTXUFWBSIOWstY0Hpdc7NLrH +leETm/iqtocHiRMK3qILahD1KeiYoh0PottfzcYpbwCFhVU8aXceGHwM+1J0 +XBfq5N9ELDrOg5bf2h3CgQbgYBhHoZ7igSa7wjlWH2DafmPKfCwPrtg6CBwe +NIHs8K9LJtJ4UBtQ6hSXYQb62ZnXfl7lgQttrK6hwhx6Hm1nfr3Ng1xVqYBZ +tIKgN7x7H8p5ILTbUK9VcR9Icm9rv67lwd2QT2Xq7/fDQ8kDNW3PyfW2Cbli +50Gw1hI24bziQdONLXVBfA7wy+rRi5oPPEjdc7aG6+sMqf6eeyu+8aASYz2c +6C6wJnVZb/E4D+b7Cs13TbuCd2vI92zaBHiayrWN6BwF2r+qJ9KXTEBs3xVn +sQhvuEN9O5mgMAHSA4ptFz/5wpCpPjVUdwIO6weEnzlzApwbJlVsj0zAr6DB +Oo/NITDbX1Rq4TsB0XG56j9aQuHa7MGNpiEToDGFyv5u4fDO4LGpTsoEODE8 +pDVrI8CmKsxt8eMJ+J1YKbR6Ihp2Fv/Na180CeYSLCMN4fOQIq5q/VBuEqpi +5r7aayXDq8B9CxmrJ+H+cepszpEUsDcucXKESWh3/JuT3HoBfLsdZUf8J0H9 +xqddjwcvwoW5hsu0l5NQMb8tQEvpCrzeGx+/LWUK7pQkb6hfdguOTEv6PaFN +w591DoUJqveBsWW5V/eSaZCP9Lq/NuQ+sE6vdP+pMA3h7OMjmc/I+Jymo9LG +aXC/HTRx160UqhZMLZJcpkFcKuzj09wyoAuFrrGrmQZ038mbPlsOFYvej075 +zsDpQCOnHa0V4Gj9+btk6AzcWq/FuPSzAqgXvw2tiZmBHQ5KyiyJSnCU5H44 +kj0DZt6rtsYeqATqUrH2FmIGzsg/8jP9RMZloTRbfhbe7zzXs220CoRUCo5t +6piFl23fJXYMPwKNGvF7sn2zIKvg7zIvWA3WVqeGZ4dmIca9ajxNqRpyw/ce +Zk+Tvz/lscrEsRp0Xy5Ym6vOgeF3BYGvHdXgHuqo6xg5BxLSSoGbyh8D8WLp +TJTmPCyI1lz4x7YGfjhH67vqzcOuqwE/pv1rQII7Gmi6dR7+K5/tEk6sAUcF +YpR2cB6GTVtaqp/UADcg4OPFmHngKJwkouVqYdWKDnZB7zw88LRz6HpXC7H+ +iYnNCQswrhLMs9xSD9bmJ0YzLy/ALRE+fb199bBC9ZC1+80FcH061THtVQ+V +/atl+KsXoOs+pWp5Vj18sWgu2jy8AL257ryKX/WQt/Tc4AFlPqwPE6wNy3kK +83/YAq1n+fDFLVOrsJ4GGPrM0n0Yz4dfQwtSjf5tgNaOYs/sFD502vLTeWim +AbJKLrZ6ZvPh6g9bS30lGmGtm8slwXI+LAmbSCjRbQTHLj5lowE+DC0I+Hb8 +VCPUlMPWciN+fPAs6136TCPYpOTlaG/jx21W6arlAmwYPUoW9J38mM1JNiHo +bFBYycl/YsOPh9W75Nuk2RCTakbhePPj9S693/t12GDuY9n8JpMfF9sO6Hl4 +saGP6WA585MfXddkjPW0siFwofZ25B9+rN91LvteJxtE36+YX5jix2N59Jqg +HjYYX/pYRqEI4KYA9xujn9mQz+cqIS4rgNKDDdv8ptjg0+/VrWgmgMOuFsks +ZhP8zQqxM7shgN/yn9uzA5tgKDPzmXGhAHrL2K/+FNYEnRlVWvr3BPCESUsI +L7IJ7l4ap6s9EkDjUf7XgolNcOiCfw39pQBufu03W36tCarjPOXa5wRQxiTa +7xC7CfJj4xKeCQrihoQjF74+a4IL5wr/1NMFMfXpH36f1ibwjP7SVrZUEJeJ +hyyy626CZZHOEelrBXGhpFfm1VATBAcd6LdxEsQTKkb7dYQ5cCQweJeFG+l6 +TZ0tDA5YBGSwTL0F8YiyqNIWcQ6sOtGVujFYENOW3DvAXMaB1757jKVTBVHv +McMlS4UDOm5mN/vqBHH/4S+nJbZxYGyvnovLCgryWA3/XQ/jgOxMwk8jZQpa +hIq9LT3NAdPC3nBZNQoOPcndX32GA9kTEZe6dShYFLvIoDqWA8bXOJztuyl4 +VSDwum86B84PWatqnKLgOttpx7I7HKhKza8QPktBvz0RLQ7FHOjX4xoPxpFx +9jcbwfsc2JB05WDuRQou/8Q/gg850LP2Y6J4MQVdVY7NhNRygBnqOzL+loyr +705685J8XsX60I5+ChIH75SoveJAyAtxyv1BCoYE/esT0s2BVrmKFR6/KRgw +9q2f/x0HTjROWb4VFkKNhlq33k8cqKPHl9duFMJNptGGF8c4YJubFxx7WQhD +V1fF7l9EgLbOYbXZbCF0c9pXPyJBgHir/PvAG0LoU8+kREkS0DJ5Fd2KhTCJ +c7UzZykBm20yRUwahDCqhn8sT44ARcb5Wws/hFCx4fy1v6oEzObt3B/6Hzne +4Qe0/WoE9OpTqb95QiihwNd1T52ASx6xfh/5hPG9cnOy5RoChNhn9OuXCePa +J/MrvLQI+BEa2H7KRBj33l9UwttMQLO49tnxHcIYtdZnTtqQgMLb/2n7WArj +5nn2Hz0jApy6j2XbHRLGdM3L/T5AQOc6L7dN/sIokXVnRck2AlhfHf/ycoRR +492Pn+m7yfkj5O4fuymMZ30yQqMsCPBf0uf8tVAYDf85+s3HkgC1rQeJ1w+E +scrCKWmTFQFXc/emVT4TxoxZedMH+wg4a2OmcnKMnH+n5ZiYHQHlYpwR50ly +/Fmtgg+kB5qhwmJOGB1q2JNF9gQYGxqAGp2Kk9tDr+k6kvuzao3dgCIV8dIX +S9XDBKwZuLuyXZWMl/Ey+0g75KgM16yhovoZvdvJRwioEVsZmLWJim+MGJpD +LgSETyxOtbSmokbqSqvj7gTcLb9gs+UAFV2SxnYzPAh45yMiq+5IxRf1g9r5 +pDcNUIooXlTsM1/f2eJJwETzZGNtFBVP65o9HfMiQDUmKKE4jopha1fHBHkT +YGs4ZnklmYqRS6/v5ZKuKv/RF3CFir3xGcwRHwICcvq56g+o+LAsnfLIj4B8 +G/taaRYVJcdWZikdI+CV2NtooVoqNp2xsDlPekNMp/jn51TsVl5+xMafgCOG +lm9e/kNFzYzw6krSaRMvrtV1UbF22dSuxccJ+OXDUcv+SP7fL3M9QVpBBX/H +DVGxVcX8/PITBFgO1LECf1Cxs3Xnej/S920emVhNkOt3X3aUfpIAX8NiR2Fx +Gu4uDOYxA8jzm1BhcpfQ8BtDieFOurU8/9/Py2m4sDQ0/hZpDZXckHoVGoYZ +BBFSgQTYD8gYlWjSMOGafqo56aScTMEcLRrOb/vYFkn6u1haepARDSWz3j3+ +QFqmReSg6zYaHn+n5E8LImBHTKK89S4a9uUZFGmRDjEUGjKyouH2/gtHD5G+ +MxF9T9OWhm9akisiSPeUz59Y7kDD3vHM5BukhXxP61NdaFiyXXyinrSuytQc +15Ncj9heXh9p94Eg4osfDR0XWCk80mYJzg99A2joGT+gJxpMgPr6nTe4oTSM +6f3crkha9K1WcmQkDU3DffbrkP51Ri5M+BwNN0cy27eRfqUq5JGWSMNb2ZWb +95Guevlrr8wFGlJXPr3pTDor5J3xrcs0HKcNznuRDldo0tTIoWHQ1FP7k6Qd +n5fIVN6gYYvRCCuUtLF/ppBhIQ3fvZ+TjCCttCxqnCimISclKegMacpTrwHL +BzQ8+ly+/38e9tj3T08VDVufmllFkn4hZvjkcA0Nb5xIbQ8nfZ+lcud7A7m+ +m6H2QaQvOC26fPIZDYX6E6b8SJ8U+hs13UrOl2x0z430/tIvfuc6abj3q1TA +IdJ6tv/YifbQUH0uft9u0svnWGaZ78n78Iy+x5D0bOFNHYXPNFy9VOKoJumP +FkmKRcPk+RTR82RIs7kBYhtGaeij6jYjSLow13H68RgNldTjT/8k9z/e1Ozb +1kkarjTsVX5D2nt0/evWWRrmDzb8qSG9zlCw7AOVjibjz+WiSS8eGr3qIUbH +nYdvhrqQ5ib3JPySpGNT0GlhJP3kfbELnwIdeYsvPJ8k71fuuct7kph0dBL0 +mO0kfUYzcoukOh1Tw8763yVtetp66SpdOrp/vC2xj7Qqc7NAqQEdO+UMtq8i +TW9j/t4IdDx4htnAJe/7S9nJlh3mdHwqNZacTvph0ydWpxUd/+WaDTqQzvBp +zbezpaOzfW+iCmm7musRvkfouPzMqeZKMr+G7Ew3pIXQsdYg1qqOzL/n/Ovk +ZSLoGNdZZHuKdHGxNONWNB0lH+6p1SPt//fHYEUKHRc9yCq9R+bz3+yLV3ry +6bhePc0risx/8Xcf5+U76DjIvC340ZfcL40ZkeTXdLyaON0cS9oqQnr5VC8d +tSxs5TRIpyta63QN0VG2MTjkBFmPFnuzj8ZP05HCdNEaJeuZ1HRB5y8VBkoN +F5rfIuufrkVjv4MmA9n8Hm+1SNve+PCjZQMDb85dWcQm62eWyVKhgi0MtAld +nfTejQDp5HiDg3sZ+CNhfSefKwGyK7zzGyIY+OykvZK4M9n//OMerIlhYIR6 +2trzTmS9brxVl5PAwPjQ9AUK6Vz3vp7ASwzcnGs+M+FAgHzpbhG1uwy0sz8e ++Q/ZHxSN1wWldzNwLPw3BWwJUDnyZ7uLhggqvc6IsyD7U/abdk/TDSJI0Y7s +zzQn83f33YTVeiK4SWv5TP8uAsY3Or34uVUED/k7XfDZSUCDSLPFKTsRdHTR +2R68nTyv6qs2lxNFcN7r+bF9ZD9MFTdxeTYsgj1z92n62gTw6tIj1AtEMTTm +2as5KQJWKL7jFN0VRRkdwYKlpE3OrRRRLRPFjsp01polZL7tKstRfiKKA1pV ++YcWk/2xp+2RXIco7l6S9KRIjKyXv4XHxGZE0eHt8GOmMAGNSpEe4/vEUPzz +TH3OBAeS47331AqII++XinX5Gw70rWpb1BW1CBlJ5X8zEziwu3jEf+qUBH4e +8xs/o8uBlJC0Aj/1xbjhVcdK18Em0CibtCoYXowHhav1Vyc1gWbu3AvjK5K4 +WiDUY0anCRK5zbW5B5Ygw+dlTt5bNuRmfKs8IymFf1+EmeRGsmHJSGH4M7YU +llvPajzUYMNwiWr1y6il2LarRGZvVyPIM82aDLWWoaxSKftUdCMwvtR0rxtY +hr82v3Tk6ZDv9yJcx8Fr0vhC4c29Lk4D8I20Vs7ulsHSz+c3lq5rAPpGz5h3 +jOXIok1bBF58Ci3PDxzc9Hw50tepKWbN1MOI+Ne/s0Gy+JtKjWsLrAcftr5U +rLYcqoi83/1mqA4sNNRmjw/KIUNaU+KQWx187Tv2YyB9BZY4ao/Sv9dCHy/U +WtJSHl1G3XCjZy1oN6+MLZ6Vx7+FQXwV/9XAN4GU9YK1CngiJU5OObgGFriZ +d9l+K1Fsu0m4oVANHL0yvSRGTBE57HuZ5VefQIR3ShrFTxGpH30vJGo8Ac6y +nycNCEXMPOdQ/Id4DJv+rk/vYCrh1mzhnSvtH0Ni1PWHRdFKOLvVNdaLWw2M +z70G2r1KaM735zBmV0NN6NSc/CZlDAk0XbZBvxqu/ftVrS5dGeVuyxerDTyC +QwtzB3K/KeNG4mWzdvIj2GY+1di/nYnWwcn1edqP4PAJ9sVX15mYXBQ/YvKF +BVNnXXfb32TiASwd+/SJBZcuCgoN5jGxQkVGOWqABc8rtodxC5hY7XaTv+4D +C9bxXjhL32PiiY7KGv23LJgN79J0esTEBc+/4vr/sODqucFn318yMe2ws4Tt +IxboZsRGnexkYm5t796pKha8LFQxmH7FRAeZxrprlSwQeH70vsgbJupOV4gP +lrPAmzZ6ad17JpaXBucHlrBgUyr3cNA3JkqpZ57LzWNB1/XM5XPfmWhx9voh +k5ss8CvT6477wcSb07cPfL/OgryOMLMrP5mY0prbrnuNBVTJuTU1f5hI0fe6 +05FJxpVvDJvwmOg5X90UksGCzTqQ1zbBROeRLqrCZRb4749e0v+XiQ/arUSP +pbOA5qHc7jHDRM7FwjapNBbkB3Pif80ycVDmXmVdKgsM490xdJ6Jju12hHsK +C3qyhKYXFph4R7Z0TjSZBf8HDoyFNg== + "]]}, + Annotation[#, "Charting`Private`Tag$163013#1"]& ]}, {}}, + AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], + Axes->{True, True}, + AxesLabel->{None, None}, + AxesOrigin->{1.27, 0}, + DisplayFunction->Identity, + Frame->{{False, False}, {False, False}}, + FrameLabel->{{None, None}, {None, None}}, + FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}}, + GridLines->{None, None}, + GridLinesStyle->Directive[ + GrayLevel[0.5, 0.4]], + ImagePadding->All, + Method->{ + "DefaultBoundaryStyle" -> Automatic, + "DefaultGraphicsInteraction" -> { + "Version" -> 1.2, "TrackMousePosition" -> {True, False}, + "Effects" -> { + "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, + "Droplines" -> { + "freeformCursorMode" -> True, + "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultMeshStyle" -> + AbsolutePointSize[6], "ScalingFunctions" -> None, + "CoordinatesToolOptions" -> {"DisplayFunction" -> ({ + (Identity[#]& )[ + Part[#, 1]], + (Identity[#]& )[ + Part[#, 2]]}& ), "CopiedValueFunction" -> ({ + (Identity[#]& )[ + Part[#, 1]], + (Identity[#]& )[ + Part[#, 2]]}& )}}, + PlotRange->{{1.27, 10}, {0., 0.15983567997641332`}}, + PlotRangeClipping->True, + PlotRangePadding->{{ + Scaled[0.02], + Scaled[0.02]}, { + Scaled[0.05], + Scaled[0.05]}}, + Ticks->{Automatic, Automatic}]], "Output", + CellChangeTimes->{{3.827489829580755*^9, 3.827489879228238*^9}}, + CellLabel->"Out[19]=",ExpressionUUID->"c3a406bf-e1bf-4a93-9a41-58b5a6908c17"] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Plot", "[", + RowBox[{ + RowBox[{ + RowBox[{"Evaluate", "@", + RowBox[{"Im", "[", + RowBox[{ + RowBox[{"\[ImaginaryI]", " ", + RowBox[{"Sign", "[", + RowBox[{"Im", "[", + RowBox[{"\[Theta]", "+", " ", + RowBox[{"\[ImaginaryI]", " ", + SuperscriptBox["10", + RowBox[{"-", "5"}]]}]}], "]"}], "]"}], + RowBox[{ + RowBox[{"iF1", "[", + RowBox[{"\[Theta]c", ",", "B"}], "]"}], "[", + RowBox[{"\[Theta]", "+", + RowBox[{"\[ImaginaryI]", " ", + SuperscriptBox["10", + RowBox[{"-", "5"}]]}]}], "]"}]}], "-", + RowBox[{"\[ImaginaryI]", " ", + RowBox[{"Sign", "[", + RowBox[{"Im", "[", + RowBox[{"\[Theta]", "+", " ", + RowBox[{"\[ImaginaryI]", " ", + SuperscriptBox["10", + RowBox[{"-", "5"}]]}]}], "]"}], "]"}], + RowBox[{ + RowBox[{"iF1", "[", + RowBox[{"\[Theta]c", ",", "B"}], "]"}], "[", + RowBox[{"-", + RowBox[{"(", + RowBox[{"\[Theta]", "+", + RowBox[{"\[ImaginaryI]", " ", + SuperscriptBox["10", + RowBox[{"-", "5"}]]}]}], ")"}]}], "]"}]}]}], "]"}]}], "/.", + RowBox[{"{", + RowBox[{ + RowBox[{"\[Theta]c", "\[Rule]", "1.27"}], ",", + RowBox[{"B", "\[Rule]", "3.12"}]}], "}"}]}], ",", + RowBox[{"{", + RowBox[{"\[Theta]", ",", + RowBox[{"-", "2"}], ",", "2"}], "}"}]}], "]"}]], "Input", + CellChangeTimes->{{3.8275494800734243`*^9, 3.827549502632869*^9}}, + CellLabel->"In[19]:=",ExpressionUUID->"1c60fc4d-168d-40ec-9dc9-800241fe6f2d"], + +Cell[BoxData[ + GraphicsBox[{{{}, {}, + TagBox[ + {RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6], Opacity[ + 1.], LineBox[CompressedData[" +1:eJxFjn001Xccx+9UvvfSritkyuOdhzt1cIVSwvG0Q7Kh0ZFWrsdkNCqruyNx +GWe2kBziyMmGRWslJcPnY6vm4eZhXYQrrFC0Yn6/n0txd/fX/nif93n/83q/ +zERJQdFqLBbLTZX/2sZt86xSqYQfuPRW4Sc8TFr+MGd5RQkGdibyh/48/KVB +aLlIK6GpafJ6uB8P7QX7RdNzShiZ+zo7x5uHO7UlI9IhJWSnbedO7uGh+7OF +rtIbSqBDZDmXBDwM+uZR3Y4jSqhYLG3ZqMbD1F7JF7FtazDoU2ydHK+FMpnm +bHvEKoTVK1toEy4aYZLuTsN38CmsueGbjdh4/P4GrbEVWLXVa0/o1sSjecL5 +4YxlSBxNyAgr0UBFoTgH3BQgyWz//UkOB2cM22d9divAS6pbnyDh4GC1+v4e +BwV0TnuGq6VzsKG5QHvsIwXkDptZ7EjlYOJfNZdXdBSQ7Njffy2ag8+EsnrH +F0twvGxBwnhwsKdve39d/hJYjQe6minZWMV9alAyycBwt8Hw2zQ2Fh5yI85y +BsT3KsJdxGzMqK2khgcZWFeeSJ1LZaPII7J3q5SBx55JZ3kn2Mg//UJy5Q4D +DnOdBaERbLw69s+b6m8ZkO0VxmR6sbGynjxsdGRAKklaO/M+G/OX4xpC7BjY +sHf1K4EGG9N9uiqXrBnwnHlyc0SdjUcn8sTOpgywSgrj/FhsNNHdJGzVYGD9 +fLRx6CLBCrFh+f1xGjr6XInlCMFyP2Hy41waxFEmrPPXCJpr+nX1SWgoEay/ +LKshWNct4veco+He3zVj1j8SbPYv+rPjFA3yLk+r8SsEhwOW7NsiaPCum1ZG +XSK4Obh1sdaZhtr0UvFAuupPZ3BftQMN8T6v4valEbSQva6qsqVBzzel+zcx +QYfPTA9UWNDQ/bFlUeNpgkGhmbcvatMQFj55qzaB4IVDvqfSXlJw0mcq5tZB +Fd9Q9Ej8nILcKe9sxxAVX37W4sw4BdlOZpNNwQR/Plw/kDJAwehVF2MMICg9 +ouV0rJ2CtbIxWa8XwQOmgu9jWii4Y2LyPNiD4OiE+3TkXQr05etWhtwIzkYk +F39+nYKnewrsJ3YTZEcNMMGlFPgTC5i3I5hv/jogsIiCX4fspk/aENSfUq8J +uEDBu5vV3OVtBC1jdoX6ZlEQ87Yz8j0rlY9l4A2fdApcL6bmZ5kTdJo5RrzE +FFQ/+K6NwyfoHVd21/VLCvh8xniTkcpXcFvLJYGC+QjfwOItKt+X0ljnWApM +Y0nWlg8Iyn+aAicRBV6tds0VegSj4tf0HQ5T4D7/YJ6vQ/CVtf4J4UEKduX9 +IajhEUyZs+2wCaag1MhJtI37/3Zu7T2/0G+F/wKbVhlJ + "]], + LineBox[CompressedData[" +1:eJwVVnk4Ve0XJWkOhTJGhaRIlKFkX0UhCZ+QJJX6ikJCQqZkqqT6SCXzTClD +ItmK0qCUVESGkiHce865pnsP+Z3fX+dZz9nPefdae+31npVHPG2OzRIQEHAX +FBD4/7PXML+w35WLuVvjFpg2rmERG/suxh7iokpXwO/r00osC9tfubKOXEz9 +d5fwudhVrDy/7ndFtlwUq38csMZdkTX79g/Otr1czAs1tvm0Wp7l8vS7eJMZ +Fx3FwUW/X5pV/eObrosxF6e6cguPiyxnSQl8OUAactGpa++e87ESLJ9VzSHh ++lwc2uXguHbvUtZH46ZM8U1cDDk1NsvYRoy1/t/GhiwNLopuuOURu2wxKzrm +zdDmtVycV7xbTqRvPqu38JVow2qm//bXr4TmzmWxPtRpO6zg4oolKe+0PGez +kola+0EpLmZ3bvXql5zFmlxaExggzkXzfe87D/fPgO3mp6kLRbj4VtZ/3H72 +FDy0f1KXPI+LAiJXWA/OTcKigPJ+dSEuPpAG8U7dMTiRXLIQpyls3FS1PsOA +gvqa4g1WkxRW+86TvjLNhkChgnPeIxQ6XbXeF2nyGzxuO89xGWDqZTVtLLb2 +wJEN4gl7flE4mdC/cIzzHexeNqze2kmhlFV6Wd6fz2B+IKhEtY1CzYtu++Qq +3oIhqWm0rIVCFykfg9yf1bAx6neTUBOFAh9fn3WKvwVSpZYjnfVM/YiP0O+J +57jITCioESkUE74mox38Dmc6KxZUVVFo6ns46dOWZuxbsFI14SGFeRZPI/he +3/F72pfH4YUUqsa8YOGmTnyvE2vilcOc9+r0iqGebiw7wj2yO5lCC/0ZBb21 +vZg3mUvq3aLQQT3x8Oai33g3zilU5QaFivcTJh1l+zG86uU9wWgKV2WUDerW +DaKfVcB6TjiFkfeFhLf+/YNufRpPOy5QuGA46c0stWG0XprUWnGWwqQR3v0r +9mw0zrP4N9uDQi8LT1meIwf1DAXHb5yk8Ku3DcVaS6Cim5u4xyEKC3NaOvaI +kSghoJBxwJHCIe/dlHYQiXMTP2ua7aPQZLTDwfUXieznBpZKuym8W3cmNSeL +wp/2ZMeSnRT+t9dhQmOGwi8j2e4zLApXsuYDZx8Xq6VFY77rUGjjPy3VMcnF +h8V1y19vpHB44oTCUZNRzDLxzylfT6GIx4Tvt7hRvHympy5+FYWX9udfU5Ae +w+C5iTbB8hRqcbod9R3H0PueeY+7FIV+Wbu/NyaNoeOb0r87RSgcDeWafhMZ +R9WVkfrTPBL75NtrHHvGUa5iy+s/oySqme0v11wygaJ7OHatHBLlTliVm8AE +jvs7+JT+JtHom2HcucQJ/COyWCi9m8RpnUTrCpzAH1nPr8e1k/i3pnhpUP8E +1n9UKz75icSgxJmuj1qT+OR41zb7RhKjFiZvuGA3iYVTNxuNG0hUCV8v2+8/ +iTdUpwcVnjHn/fxnQKlqEg+HNil9zSOxbGhIJ3QDD+3aUg1/ZJI4T+W0wicz +HppreTn0ppA4cvmb2LajPNzUK3aF+o9Ei/SwW5du8nDttp5s3jUSuwxcJc4U +8HBF4iMUuExiNKfOO6GWh/NMbbgiYSQ69VzXy/zDw+m0VYuXMXNsOiehePsv +DykepSJ/jsR610Ciewkf2wtvOq47TeIW7a9RQTp8fCD65fmu/SRK5pzu9fbn +Y+aJ7HZLWxLDJGTXxkTxMem579i+vSQa24kdl0rkY9jZZWtdTUh8e9eg7dEj +Pvo19m13ZzHvqZ7yuho+uilXOHlvJTGDu6P94Ds+2n6zjw/dSOJYbGa93i8+ +mmmqFkStJ1GX+0Q6lM1Hw5jJurg1TP3GlA4nHh9Vt96eSJYn8c7J6Kifi2mk +U747V85n+p1j98Bdi0ZiosC/djaJ2juPBRdtobHXKvBGwwyBfjFufbe20/hh +ltyrL2MEhngtcztnTWPdgeGuDoJAn0/l7zwdaHxSVs37NURgQs87G9lDNGYc +P6hO9RAod2r8zk13Gm+h+i5eB4FsEwMp1zM0XpH66yLQSqD/uaxNHD8afd+m +/CfygcAldXIrDMJodFvt+UDyDYEWlTpagpE0OgfBa7l6As/r3/KJiqXRVKOb +VqsisH7U7NKPGzRui3ooqVVO4O/8mzoPE2nU6g7doP+QQEMc6zC7Q6OKvrUZ +q5DAuSrmHwrv0Sh7Y+XRXTkESgVI2X1Lo1FsiAyyTCeQEpoof59J42zjF4n7 +kgmMi+tXjs+hkT125O3RGwRqNWoOXCik8Zeldq/bVQJHsPRC4X0aW3OF/p6J +JnD8nUFBfjGN7wValp+/SKB8yOeA849ofLE/a2NoMIF5c96NypbSWFHiszvq +PIGi43OW3SijsWihybE4HwI3GW770lFOY5qrZEiCJ5MrfptXTT+mMeHZ76Rk +NwJ3JAj3cSsYPfzvBOseI3Bs+lvxpyc0qmrvdW0+ROAHm9qK0EoayREh89OO +BD6+Eicyq4rGqrwnG+btY/gMzH1mx+CLR09LZu4lMKJdsz6EwRYrVtHbzAk0 +HrwpH8xgybav3a3GBNqGX3pqw+DOm5dfnQUC9USPxfxlvp9rySoS2ULgR/N2 +93AGe80fu56/icCdi5YZdTH96NfnnzPeQODLVMEeSQbPCnE+2MXk5Lx3IfJr +mP7f6YvvCFAiMPZ28gtxht9/ow2qkgqMHxY8T+xg9HAuDhJ5KE2gd+Uvx3BG +rzVuG0fNJRj9ble8FS5h/KrU1/ZbhEBsa03+9yGNlV13MHQ+gQ+EJ8PzHjB+ +K5i37PQ0Bz2N9m55W0CjmqJ3TwbFwRcHn9oX5dFYndBe1NrPwQ/5rSu9mPl2 +hz7YYdzMwdIXj5RT02n0Hl8uGtDAQcu2rbELUxk/nAr7XlzNwdkrbckDyTSu +tbc9I5vLQTHle9wCxm/e6vwUKpCDSlaPDMUYf87OPOqmeoaD5y/KmBYy/k2U +er/Z+TgHrw742WlcpPGpUFrjGysOdkqKmLEDmfrvJvw0ZQ76fZzlcvgUUx95 +fd/eJjZW2nfLuJsx853iK16qZ6OUwofrj42ZeZ5xHa6qZOODFyZLCKCxy0n3 +okoWG73blY5o6PzfDz8eTvuzUVi50q97JVPfpbqoaBVzj8ltyrEb52OQgeD9 +O1JsNGWCVZjk47bbbXtiRNjYe6vIKn+Ij7U2sdeO80cwrcQ+vbGbjw0vh5au +bB7BQeJ8duxbPrYUPpBODBvBRWqhkXOT+cg+t2lNaPcwBi0x0aB1+bhajLXd +NmUIDbhWQXX7eRin2RPgdnMISxKGfn605uGkVXhpaPQQdgacUmll8rrxer3S +fe8hTGIrXW/R56GPuNncObuG0Gb5+ZlIaR6+WmbTWMH5g4TtudSeb5PoJu9q +J2v0B5M/f77WbjWJJWrRbj9/DaBbdLpdls4Edr18pKij04eRXyOelQ2N4u/1 +CVr4+BcKH3XcEVhM4ZLgfB0NwR4M+GFYaqpF4HodzvpsbgcmVTSd/1gwhBeN +Rz5W+n/DeI+t6wwv9KGk7YP4/cub0TSDpVJ+sAdLxl+KvlZ6i64Bs6/oKrZh +dvvvq4MRNVhbIGg+4PgeD1rLlbUfzUJC4NH1pJRSrFwQ+OWFbyYQL7NXRlSW +wOafgivCHBAeekXnsFQ+wGriKW/LizfQWixOVj9vBbPMtveWDs2QcszF8+nd +HjDZs1RorPwbJF8+q+5Q0QfXDn0L1azogIGxZf9OnBmCBkv5xVZLe2ASE0+o +bydgZKVkcPOdX+Cbrickl0iBr8+6w9eW9QHuyZzX2jQK3zrEbI6/HoCMHef0 +2xUmwPzysVaf5gFw9Gh+o606AdX6Vc4XOwZg+umb9zGaE5CWeNQ9jRiAqgQv +KQ2jCThh9Tjiu9Qg7K+oWmh/ZAL4dQcqLE8OwoNszRdKWRMgV5gjp7vgDwyn +csovKE+Cy3mD/rkWQ7A7e6chS54Haq6vv7DthkBf3DXWXpkHXEvb+i+Hh2DL +YLn8SXUeRCqdSs88NwRT5nOaA7bxoKjp7gHIHIKRCrOTdgd5wFOmm/z4Q1Bm +Mj7/x10e3GiufPI7bxiEphTnXhbng9Mzk9zG0mGoaeNPP5fhg3Lep4TSmmH4 +6ae4h1jJhycXBr3DWoZBj2vkr6XJh05VaXV5gRH4GDDngpkFH9RC/NNt7Ucg +co3c4qxwPtSt042tE2aD7h3dJG4fH5w32GaSomwYWJFCnBzmw6TWmWoFGTaU +HD6r2kLyYf2WQnagBoMrZgdcnOLDf6YK/2yyZ0O+bYip6RIajh+bK5edxwaJ +8JDdBno0CJxU2vy5hA2bfSVPtRrQcOeUkaXgMza4O+gKHDOi4cPZwNCDn9gQ +NNV7wdKcBt1wTq8knw1lw0scDxygofnSor87ZnNgz+YThWcP0XAqZu1ybxEO +fF1/DAKO0pAWf9TswyoOtEk8mLRyp2Fe6rf7kbs5YO0T8EE2gIaMjNFXZfs4 +0CF33PneBRoMcpZ0/zzEgQz3sZsLwmjwur97KfhwYK9hb2BOFA0LHp1YdzqY +Az51tR4tsTRklV0yvhvNgWofmejhqzS0PUW/iWQOLMpoSWi7SYMPdlxTzuXA +w+yOivuJNIjU8fL+ecSBI9mXD7jdpmH7W+324pccULNIO343hYaO91ajP5o4 +UCJ8sU8knQa/T6cXL/rOgWsLO6ROZtJQ0JoLJ9gcSNaty27KpcGko94hcZID +P3zGBNrzaSA4hN4RQQIevywTfVdIw7MzISbn5xBQ5iFvnnqfhljuYpv4hQRc +2flZyb6YBnvfZOdcMQLk8n6LUQ9pUJpQc6+RJCDNriTQs4QG0r/y3BcZAjxM +Gz58KKWhhr8rYliBgMDddZ6i5TRcDvoaL6RMwM5zm2s1H9Pg8Nf1nowaAULO +gfJaFTQoh3LzN24gQIdzr3vpExoowfDHppsIsJpa79zMYLwoVndInwD2Xuk+ +z0oarginNvkZEtC182rdHwbvj1LvuLqDgOi2OoPtVTSozK8eyDIlIECo84Yv +g6kGDbeMPQSY3tsnGcHgmsj0oVQbAjofuh72YHCsicTpe/YE2B0eLNVmsN3s +KPYdJwLK1Q8Zf2a+v6qO55l0mIB148XGFgxmh50iE44ToCYj1HOP6a+K1eV9 +052AU0mx0MDwuTRjPRrvRcCwlGVoA8PXqqbeN86X4dPArb7H6CF3QXficgAB +639FzjMro2Fga4F/TAgBjYNbPV8zepbx5fiREczNtVVrXOYRDaGV1wIjYghQ +UdS+C8w8LPxnTYfFETBLwMN2MzMvKV3f4JCbDP+ajWJ0AQ29Y/0zQUkE5Ahm +ll3Lo+FhmWNYwD0CTph6KlDZNASdfT/LP4OA+Kwg5ZWMX0y1WBG+uQTMGU64 +IZtGgwRZIny2iABKW3xtdzIN3cXKUV6PmPOPBaefZvxY5JE0z+MxAS3l2gUv +EmjYMXxh4claAsQD7xPPGH+LFBJXjr8kwMyxyPZwDA3fTx4VcX1LAO9j7H+v +Imjw7jddcqiF0fvvMq+PzH4Z5jy94dTG9G9k33TGl9mfYxoSjp0EOMyNj//g +yezfT/Hl+wYIGAt3Vi5l9tUjPTLJZoSAoFciZroHadjiwpO2ohj9Zuef9rRj +9v1Hp9zuKQJeq4hncXfRkJJsnWIqSEJBwJbgrSwa3A7UK+ycQ4LS1JkBDSZf +BNvyVxmJkTAZrbdGdA0NjbfksgwlSZhn83T1hDwNSXbXlA1kSKhPsvsbKkGD +ZouPqq4SCXnvt6R6CtDg0gQa6nokyGUUy5z4zORbXEmx2jYS7r+x3CDawOSf +hfJG1e0k3FTSmoIqPlx7u2DTagsSnCx5zpqpfHCMuVCuaE3C1qqFbgPxfFAx +JXRW2JGw/4auhCyTrzUvv+hLu5AwsrPXv+sIH2IjTJ8uO0ZC/p4O5xM2fLDb +8dRAwo2EgIueOo5GfGDXpoGoDwk1f77SrvJ8kK92NxGOJsHqs1Nc6HseSEjz ++R5XSRBoDJ/bXs6DRX7RD1tvkKB/JeHOnns8mNqQLVt0j4Qc4ZCj9id5MHpF ++5NkJgl2+xVz2/fwYGjweWRIHgnxa/YttdnIg++ZnaRNKQmDVzX4g6OT0Cxw +Orf6CQk/pk86jrZMwpuDtJNKDQlJXcOJL0on4clyqde81ySk/Vfr6nt6EhIv +W6ekdZLAvSVnktA0AXEDXf8s6CVBi1LNX83cl5dMPOb7DJLQuTZAedxvAnxm +Yn12jZJwwFi9T2L5BJxyklZ7xCNBKNu6eVPvOBytzO2SmSEhavzdBBSPg83Z +enP2fAoGX4YnFBuOg/lHGwEHUQpMX2rUtc8aByP1nvLnEhQoRojYhtePgWb/ +tGKCAgXW+TsWV8IYiBzQndi6mYIrsYRU5pJRmPPkZVH2Fgq0jpc0RDzjwrSE +7RFRFgVvVO3e3jjGheEPXu9/mlPAvyb5cW8+Bb3rZsItrCiQUR3SCjemoD36 +qt7jfRT4mEn96vtOwtvtBZkxLhTwdAd2L5sk4EWq3n7uMQqanLp99IMJqJx6 +JXLQnYI5o6FGF6Y4kPf413lNPwpqDT3+pLaMQJq494Y7gRSk/dsNIwXDkOQl +8FsojAK56kLhY8z/T5SavNW3yxSU7N0z95+3AxAcVShsdJ2ClqmNwbsc+8Gv +V/9pAfMf1LE+Webgl9/gYfTaSyKZAjHljPmzt/TC8RQ7leB0Crx8P9pERv4E +Z7q3vT+HAuMWn9NCld2wz+HsdesiCuIXvDn3NeUHGC+Nn1KqoCBPVZdns+0L +GHiuKImrpmDyx4ujPlkfQbux6N/J5xR078v1PRHUAGprt8ofaaAg9Gc/KS1a +Basi3zS/a6RAQFpFM7v0Ksj8so/e3Mzw1SvIadAqwyWsvm2p3xi+Q2e/Lht8 +hQL8WfnePylw0biyV+NJG7r8auOG9DPzvbvxhXp8N9Y2PjS8OkzB64ktTsEx +vaj4OCrmDkmBf16AUtOHAQxNdW7JHaeg9Z2bUfW/I9gdvVmhnKZAZ/9As7sG +iSzvRW4vBLgQ4PpOr7+dizPGVTMdC7jgNZDgtaePh84a183/iHJhnjXHNcJq +GmuWn0iYkODCP1JXg7ZHCNSuEITu2TJcsOuum/3m8qza4D+S65YqcGGxoZ+u +av3s2s7Pw74KSlwI8yFNLmrPrTV8Vle7fi0XHqn33hntnl+bknNn4RYNLvzq +Ur9d3bKo9u+1M3a7tLkQLXxo/7ZFYrXO503TbfW4IL3hUHVl+5LamiMKw4e3 +ccEvRyHibJd47QqLcR3P7VzokcuRNVRYVhu8+X1Y0C4uyLnIrDiaJVXbuSKr +McaCCzsrq9eOn5etNZwXuPyWNRdaKMMCw/sralNI6yNZdlxwPK0vp7BmZe30 +d9X7jw5w4fxmZT0NvdW1TvUzEzUuXNC89UYhI0G51ici7ftvVy7oP2sKIz+t +qf0fkAxpyg== + "]], LineBox[CompressedData[" +1:eJwBsQNO/CFib1JlAgAAADoAAAACAAAASAKdfB1S9D+nO44KSMwnQEgCnXwd +UvQ/NHl266MNB0DgFUTVClf0P4qRtSEVEAdAa502VIRc9D/U1mDRyxIHQIKs +G1J3Z/Q/ECHQNTkYB0CwyuVNXX30P+rB/RIUIwdAPFLYzNaC9D/MKYDOyiUH +QMfZyktQiPQ/6cSwi4EoB0De6K9JQ5P0P5G3GgvvLQdADAd6RSmp9D8dR8we +yjgHQGlDDj311PQ/VA2bUoFOB0D0ygC8btr0PzfOPJM4UQdAgFLzOujf9D8k +4/oB8FMHQJhh2Djb6vQ/2aPFnl9ZB0DGf6I0wQD1P2sk+LVDZAdAIrw2LI0s +9T8SUM/BM3oHQNs0XxslhPU/IsDAMnmnB0Bm+TUPhYn1Px9q+RhXqgdA8L0M +A+WO9T96l7AeOK0HQARHuuqkmfU/FtqXyAOzB0AuWRW6JK/1PwWKuSLDvgdA +gH3LWCTa9T+m6OJ769YHQCbGN5YjMPY/eZlm9wgKCEBwVxARItz2P2+Hql0s +ewhAYqgvmiXh9j/lCFLWq34IQFX5TiMp5vY/7Wa2+C2CCEA6m401MPD2P4Rx +8yU6iQhABd8KWj4E9z+oJCiRcZcIQJpmBaNaLPc/blZqKli0CEDEdfo0k3z3 +P/LnDmzh7whAGZTkWAQd+D+ME0LR5GwJQK5boKfzePk/shbNr8ePCkBXPX9I +yL36P19JgzkwrwtAsV5tIjr8+z/Sl2GbJtIMQPgKQwO5Vf0/kjKWDqEUDkBS +0Ts2HZj+PzLDqfL1RQ9ACjsLwbyd/j95wgT3UEsPQMGk2ktco/4/V9qGN6xQ +D0AweHlhm67+P9DnvGtjWw9ADh+3jBnF/j9I9DeY1HAPQMlsMuMV8v4/g19w +vcGbD0BACCmQDkz/P51XUjTF8Q9A+HH4Gq5R/z8H0vMqJ/cPQK/bx6VNV/8/ +3L2eVIn8D0Aer2a7jGL/P8KEBiCnAxBA/FWk5gp5/z8IJSQ4bQ4QQLejHz0H +pv8/CFa///0jEEBuDe/Hpqv/P+e+kISwJhBAJne+Ukax/z+RNPcgYykQQJRK +XWiFvP8/FVAOoMguEEBy8ZqTA9P/P2UTPbSUORBAKltqHqPY/z8rVY3yRzwQ +QOHEOalC3v8/Ao+NR/s+EEBQmNi+gen/PyvXLjViRBBACAKoSSHv/z/5zJjN +FUcQQL9rd9TA9P8/IolEfMlJEEB21UZfYPr/PynvFkF9TBBALj8W6v///z+k +DvUbMU8QQLt2pCk= + "]], + LineBox[{{1.267240853696378, -11.91004567776564}, {1.267240853696378, + 11.898987130987576`}}], + LineBox[{{-1.2678618147245122`, -11.91004567776564}, \ +{-1.2678618147245122`, 11.898987130987576`}}]}, + Annotation[#, "Charting`Private`Tag$383226#1"]& ]}, {}}, + AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], + Axes->{True, True}, + AxesLabel->{None, None}, + AxesOrigin->{0, 0}, + DisplayFunction->Identity, + Frame->{{False, False}, {False, False}}, + FrameLabel->{{None, None}, {None, None}}, + FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}}, + GridLines->{None, None}, + GridLinesStyle->Directive[ + GrayLevel[0.5, 0.4]], + ImagePadding->All, + Method->{ + "DefaultBoundaryStyle" -> Automatic, + "DefaultGraphicsInteraction" -> { + "Version" -> 1.2, "TrackMousePosition" -> {True, False}, + "Effects" -> { + "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, + "Droplines" -> { + "freeformCursorMode" -> True, + "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultMeshStyle" -> + AbsolutePointSize[6], "ScalingFunctions" -> None, + "CoordinatesToolOptions" -> {"DisplayFunction" -> ({ + (Identity[#]& )[ + Part[#, 1]], + (Identity[#]& )[ + Part[#, 2]]}& ), "CopiedValueFunction" -> ({ + (Identity[#]& )[ + Part[#, 1]], + (Identity[#]& )[ + Part[#, 2]]}& )}}, + PlotRange->{{-2, 2}, {-11.91004567776564, 11.898987130987576`}}, + PlotRangeClipping->True, + PlotRangePadding->{{ + Scaled[0.02], + Scaled[0.02]}, { + Scaled[0.05], + Scaled[0.05]}}, + Ticks->{Automatic, Automatic}]], "Output", + CellChangeTimes->{ + 3.827549412502462*^9, {3.827549481280747*^9, 3.827549503000692*^9}}, + CellLabel->"Out[19]=",ExpressionUUID->"8056aa05-0321-45e5-8da2-df8f351d8564"] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Plot", "[", + RowBox[{ + RowBox[{ + RowBox[{"Evaluate", "@", + RowBox[{"Re", "[", + RowBox[{ + RowBox[{"(", + RowBox[{"iii", "+", + RowBox[{"\[ImaginaryI]", " ", + RowBox[{"Sign", "[", + RowBox[{"Im", "[", "\[Theta]", "]"}], "]"}], + RowBox[{ + RowBox[{"iF1", "[", + RowBox[{"\[Theta]c", ",", "B"}], "]"}], "[", "\[Theta]", "]"}]}], + "-", + RowBox[{"\[ImaginaryI]", " ", + RowBox[{"Sign", "[", + RowBox[{"Im", "[", "\[Theta]", "]"}], "]"}], + RowBox[{ + RowBox[{"iF1", "[", + RowBox[{"\[Theta]c", ",", "B"}], "]"}], "[", + RowBox[{"-", "\[Theta]"}], "]"}]}]}], ")"}], "/.", + RowBox[{"\[Theta]", "\[Rule]", + RowBox[{"x", "+", + RowBox[{ + SuperscriptBox["10", + RowBox[{"-", "7"}]], " ", "\[ImaginaryI]"}]}]}]}], "]"}]}], "/.", + RowBox[{"{", + RowBox[{ + RowBox[{"\[Theta]c", "\[Rule]", "1.27"}], ",", + RowBox[{"B", "\[Rule]", "3.12"}]}], "}"}]}], ",", + RowBox[{"{", + RowBox[{"x", ",", + RowBox[{"-", "2"}], ",", "2"}], "}"}], ",", + RowBox[{"PlotRange", "\[Rule]", + RowBox[{"{", + RowBox[{ + RowBox[{"-", "0.5"}], ",", "0.5"}], "}"}]}]}], "]"}]], "Input", + CellChangeTimes->{{3.827549509625074*^9, 3.827549599242432*^9}, { + 3.827549631563613*^9, 3.827549698476205*^9}, {3.827549772830533*^9, + 3.82754977298168*^9}}, + CellLabel->"In[37]:=",ExpressionUUID->"bbfb8326-a554-4830-88ec-6a7a9e5c9f47"], + +Cell[BoxData[ + GraphicsBox[{{{}, {}, + TagBox[ + {RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6], Opacity[ + 1.], LineBox[CompressedData[" +1:eJwBMQLO/SFib1JlAgAAACIAAAACAAAA5wWM78Dp9b8AAAAAAADgP557HJzE +3/W/Dh3dNE/S3z+cSjFy04n1vwmwdEE8Vd4/JAtKytCE9b9bfcPyqz/eP6vL +YiLOf/W/53TyDDEq3j+6TJTSyHX1v565oDN9/90/2U73Mr5h9b88f/CAKKvd +PxZTvfOoOfW/FHstMxQH3T+eE9ZLpjT1v77irCUE89w/JdTuo6Mv9b8a/RLy +Dd/cPzRVIFSeJfW/ASBLKG+33D9SV4O0kxH1v/k6OURmadw/j1tJdX7p9L8y +3F4V+NHbPxYcYs175PS/6vwa9XK/2z+e3Holed/0v/qM6Z8Drds/rl2s1XPV +9L9D25doZIjbP8xfDzZpwfS/BTd3URZA2z9UICiOZrz0v/bm0CwyLts/2+BA +5mO39L893K4gYBzbP+phcpZerfS/kQ7ByPD42j8IZNX2U5n0v38Hmajbsto/ +kCTuTlGU9L/WpommfqHaPxflBqdOj/S/EZMPPDGQ2j8mZjhXSYX0v2zfyEHE +bdo/riZRr0aA9L/J5gtDpFzaPzbnaQdEe/S/UNxo/ZJL2j9FaJu3PnH0vwBL +4NibKdo/zCi0Dzxs9L+WonWctRjaP1TpzGc5Z/S/wHHQXd0H2j/cqeW/NmL0 +vy5sUvIS99k/ZGr+FzRd9L/rmNEwVubZP+wqF3AxWPS/D3CA8abV2T9z6y/I +LlP0v7VhZqgExdk/c+svyC5T9L8AAAAAAADgPyy2I5I= + "]], + LineBox[CompressedData[" +1:eJxN1/c/Ffz7B/BjJXJLhLrtsslICDkXpahsJWRnlJVk3EZIC9l7E9myV8I7 +Kzsch2OdiHASJ5yKKD7dn8/3h+/1y/V4/gOv13UJ2N41tKfGYDBMVBjMvzs2 +wdYrXeobwvx35pDuMSPJ/VP/M0vYJJQo6+vHiP7XOV5Kk3DAQsdT4OS/Dg5g +FJ0Em6ArKdU8/zpUMJFjEppfaDZfOPavV09L0E3CsU6NOTzrH/MzMgxRJmD4 +IIhu0f+xB38jjEyAWpxco8omBbm95i1qi5iAjFqZmYFVCmo3bV5q95+A7fFT +GMtlCrLPOXBgxGkCKrlEtYJnKCjo67AP2+UJ4Mvnnuh8R0FPjxqrSx2YgL0G +um2ddAoKo/NfzQ8hgNkUNfdsIgUV0RjfuONBgPpf++AeQ0H43tsnz9oSwE19 +51ncEwrKzvWK2lInALGPzEm4S0FZAkZRu1QEaCYSFK01KOjJI0+Zg4/HwZ+m +xMdjbRM9vWpG0x49Bm6plgesSZtIP77t2+DDMbCVZkvUWdhEfAcEj87fH4Mr +NwOqRSc3kYuISe0JkzE4VqO79qFzE6HeSntagTGotaXYXs3YRNteyhfVa/FA +bjunK3h1E2029HDYzY2CTfCQ4HjRBjIUNU8t08FBYstiSobTOnLntDz/cv89 +NM2KMpWdIKOFX//4TeT2wkkWtfPXsr4gfFm5gOHZLqgWD3WaXyChYKq4V6OY +NpjtquJXUFhCcQ8q/ES6m2BRMvE0ql9AgTtce9PLtXAksFhBiuojOr7QrDUy +VQ5P60V7WLbm0IkMN9CuK4cdcqEpZXUODSTerJ+NLod5q4KAxok5xPkslU3/ +YjlUq+e1n6+cQ63BbmzGVa/AkC5T94bVHHpDq+NJiSwDkeMCgxj/WVR9WmXN +2LQEJBW+SuZTZhAXczL1smIBOEgFBb0mziAsx7R8G3sBZAsfxg12z6ArX8mH +Gij5wMop7fMjfQYN4fWiv1fkw9aWW5umxgy6XBnk3yKWD+2vyddXEqaR0y8a +Va8TL8FElRworTCFbKPd1hxFcyFOPnDkAv8UYodCv3KGXOg/xSxowjiFDnNl +i7F8eQFYXqne4A+TiFI6RBQsfwEn913ZcE8nkVSHomK8/Asgv10r9CRMoBq/ +Lf/gyznwSGNt+PU/BISLeSfMcCgT2rVW9c7cIqAd50hzvbEMwOh8eV+uQ0CD +JwoP9mZnQMD1zwN5JwhIqEGr1Fg+A7wdFnsiB8aR4BST+5RtOtwOJb614R9H +SZHSLYHdqaA9MFjJ0INHLjvbVKwNSRA+PCD9uBqPymQ0Xr55lgQ9+P7yvQw8 +Kh4g0aWYJMFFYm8Z5R4eqbGJbpJ2EgFL7ioicuFRSrfxzIp6IsiwtOZU3R1F +v4e6/Z0m44H9WnmMKScOqUpQWypIxUK18POmizQ4FO998M4afSzo/3T8JPt1 +BGl5d3AMf4yB8CyBs4zdI0i9ZPjqsaQY2CMlzDZ5j6Cl/syGGkwMLD3wl+Ie +H0ZmdeR94eZIcNOLTWkRG0IpGq/FWj3CoOjbldVEqiHEdZ41jF42DOZTadXc +Jt8j/E+KceHXUDD+5LPMG/YeHf6IE1pxDQXwtVQIJg0iI1GfJX+3Z8CSJ4E/ +XziAjnJTdfYFPYHqH12HewT7UIkmHZDnH0JUSW479mcvMtMzDLQofAjOlkFe +dYO9SFxK7rGsy0MQfHd2Ote7F231UPXRbwVDUmJpwYOeHtSqlBLhciQY/M7E +qsq5dKM3XJ1sJ6sDwJjkul6s1o0S8NvRCZoBIJdxJY+fvRvd1LEaf0/0h1Ua +Wgbm1ncoKUs0IZPJHyxHvfGkw++Qjp5fau59XzjvYe6cVdOJrFS/XlB39AZe +YSVe9tBOtOxtrKzM4A27k+wjz807kULjsO5uqRfUqg8p+NJ1oh0XxpIxiicI +HzlPfe1GB5Jj6uVYibgPjJUiqQy7bWh8nicg7JM75E8vRn5+3IpWyxaEeg1v +w1QAR3amXCs6V2xwomXEEZh5NSsN5ltQgbWcAJOhI3hbF+FeQwsKaD6+1WTs +AJcWnTjDd96gDRPOt2budkAif80Rd3+NyJ89OVM/WQN3DH/1B97XKJzb+oei +rzXoyxp0xA02oiM+NWKyh62h8X714o54I9poZhi0C7SEsG1P8f7FeqTcwmHx +wfImiFPv1DjfrEUjUTf4E15cB8s88S4+xlp04QZPH9uPaxCncXN8tLEG0bxM +o9LUuQY7T5u3VThqkHJ293Q3jRH0HwpSZRqpQpMfdFNlY/UB86pC921QFRoO +nOdI+aEHZ3TnrDylqtCb6zgJuWFdyIhRD5l5XonWhsf90+O1YUL8YJRpZDk6 +Ru9KlL2pBWqudyrbVl4hFuVHLolmmlBU0YcT03qF6lzCbSytLoHvmUjOHeoy +xG31XIDfVwP+xrK+SPunGOVVcMVZr6lBSPD9DurxIpQciFla5VSDL+34RSe5 +IhTw9MjKm2gsNGsmi6uQCxA7VnBj+q4KWBhw107feonCxP1UnlXJwyrlu5JX +Zx5qsfVwe3DrDAQkDSFmoTwUe5JUNMwnBxnTIf3qSy9Q1KX99sgGGZAMNDeY +vvQCmeqGTpCFpOENvwLBszAHXSxOt/bfkITaflyX3kgWOlZ9RBu9EwU8y9OR +kLhMtBloY+A9LAyU60rEOqMM9E2dfXiRLAin57K/cY2nopHx3Ni1OwJgIGSE +0UtOQfI2xxkPRfKBu9MBphCTZHRC/nt+yV1uqPjmcpI0lYBGfc8tK1ZxwHsl +fmmujHg0IMVwSIjlKJADR5V1LeKQcEXmXHDKEfir8+mlh7yxiOpzunVSAjOY +sHq+vI2iEVlRLIL+KiMkZ0y9ea8eidwiRBauXTsA48Lqo2c6w5EdQZgpsJIa +jlYVrqRdCkWHX//lRIf2sEYqzNRUvU/QFP1Xoa72bWxcl+dxx6uPkMvHpU5l +Fwp2WG9aZnAwGPUipsx+7zUsb+2jGIecAKS6sFv13HoRm96jj07n+yB6WiNB +Jwki9hiRh7xX7IHGvUq0oiRxWImFMaUkC2cU6bJTRRfWgRVmck+WcrRBpCDx +lrNpFdhgvCieq0MHsawfldTneoaVPEx0ojt1BjDSjc6D565jxzdCslm2TWD+ +0ymnuxdysOt6Ipt3PRyg8RvnmcbLTVj/+Et9zmfcgTaCIuTv0I/dC/RNz5b2 +gstsGH6iEwEb7FTmMiruB9KUzO6CmY9YGuNZVXrhILC8LrOrqfcZ28Ef9iyT +JQTYP1vcKT6wgX2cdMJdMeoxkOvqGewO/cBeYmo2GTn0DLQZ5/TwdbtY+pDr +6s5hYRBKj7f4TU0FPVtkMTr6CIgqe7v25QEthLuGsmY/joLAICXh+qsHoWAj +5gH3wz85HnHEwtyFCRwdxR3q9+KApX+Cn2+UFbRO+Jg9Uk2AXnm8VYsVO4gS +O3T1AxIhbkPCrY/9GKwYWiiu/EwGnmLDDdk9Huj7q0Si4Wwq8Is0eV1K4YfS +nh98j33SgOXtwKzEpRPggo05yPs9A7LFHI7yzQmBzs+ZXytyWcDErShzakAE +pGrFNho8sqGzOXOaMiAG2wkfV0W3c8CddS65lEkKXjP6j7V75YH4No7Ovl0O +ck6xj1b86XliZMFujYg8PNWvGM4Yegl8EvK28qkKcC1pod9brADcys5zD+co +wbqAdrs4sQgy8mDhjIAaEDSWEGd4MXRcwVsU0apDq2NwC61iCSRcPdQsT1aH +569qGz/ElMLfEceeZI1eAGElnoo4jXKg0rM7XrqsCUzmDWVBG+XgZqAdsL6r +BZRAgxKXrArYLZ1I0ue4Atbz7YYnAyrh7djebRsLbZAS3dL5PVYFr3Q43e3S +9KG3xkqjKqwW7nSWHHWgNYZzXZIdInO1kA/omAMyhsrxn+pZCnWgTcUU7vng +BiT9jIfnC3XQY7pI00JtCnbQo2yv2gARDN3xe7LmsN8nI3t84zUQ6ZOTSmNt +wGPmd0W0ZhP48OGoXtLbwtJan9SBrCb4IpF8XTDIFgZY7CUpV97A7GkSqdnj +FqQZp4oMvmwGSbplYT0Xe5Cfp+J9aILAPKy6n6b4Dkg13diQKUagwHiS9PWU +EwjHveqc+4kgizaW+XStExx6USafo/MWZk1zSho7neGXvsnMPvktmCRIBQ1/ +dwViZYUYkm2H27WmGC7tezCVYcbGadYOJDtVW43UezAeSvfbLaQdfiV+PH18 ++R68t745zDvaDjyGrKpdjz2glYXeJ9CzA6puyreJ9NyHbHfLTtWGTvjsIMjH +c9cbMswZyhNnO0FVzXUF0+0NKVq1yWv0XeAM/lkxfD4Qw8/onGnSBUM5hR9r +cD4QPFx35PfPLjC1E21hVPcFG5m/rJrPdQP3hcRLVNgAOLn+5qdyey9ECbQG +F5k/hIDBC4+/rfXCkohi4m7yQxgv6WcuP94HW063dGtHH0K4/fRJgXt94Ld8 +tNdYOwTWp3Z06Pn7QfCHbJr1+UfQ2qWUO/pgAAKYjPIj1Z+AWXrDFRelIeA8 +rFESFBEGtf/AmJD9EGgLwdcEfBgwG3dbzcYMgT33jzYWnnBoYyF4GpKG4FXv +hsy5inA4esFfL+PqMJTZ3fj71sRz8G9M8w3ZGYb4Si63bdUouJw3OahrgoP1 +22QxKI2F9SflDl2uOKiLDaBQ8LGQcvvRvsojHLRqOlZN7cUC6dQpWbFyHLh9 +r+DGGsVBaGNwAg3tKPjp7Jy2+JMLPYMiNxsrRsFXxT4EY5kAmtteJAH6MZiY +7Du+dz4ZLuqw0nyvI8BvDvaDey8zIcqGYeNnLwFUPoTblBMyYcILM7tHJMD0 +8UPmzxmzwCmL3HTwz9+m0hGg1e+eBVFf+zy4jSeg+2Bi1C3IhonYR/MXfkzA +uEKu1AOPHHAa/9YWpzAFbQyZ2pQ/93y0FSFYpmEG7vG5vPg1mQ9PV8/B0sAM +mDwwO5W1mw+Bvrm/0+dnIM3t0YgZz58ciHf1o2cmAn3plftCNgWg203j+cGO +CDypbPGYlQJglpZxjGD9AN/3WuhwmCKI2gvVIbnOwq13Rq2YCyXQrcvzlz7r +R8D9aqtL/LsC1gTYA3FpC4DZ8vn1qaQWvDwlbKI5lkAN3b464tMEhBkWQ4ce +EmylLAeqTb4F6z89Sq/9BfzSlTKfVHVCh4RieAcdGbI19pdFXHtBmKGZ9FJr +HUyxCpLh7u+Bp9n5Il3oBqzewp2+uz8CmB3qYo/5TSCyof2we2NgvTBJCVre +BP3Zd2YOQWPwdqASG7m6CVkXvUeuRI5BcLYlvvDHJiyq+itLFo/BvkbT/gwj +BfIOcfIZfhyDveh7xppyFKhIsu+SMxqHX0JzNNyPKbAjDWZ5qgQwP9ygKxZG +gW/v1UtTtf/8w9uRqQpRFAjRji1JvUmAgH4VaYMUCuRs/KbU+xJg1z3Z7GkZ +BRTiwoNv1xNg541u1TqeAmekV9fqZSdgy6DFskvoG2AwmNBomUkImawgYiX+ +awycnwRmm1zzRpn/GXNtEtJICdOyCv9nzBxETD9b+n9G/wG0NE1p + "]], + LineBox[CompressedData[" +1:eJxTTMoPSmViYGAQAWIQvb+C4YqK4xd7BjB4sH/T98qbCD4Dg219TsQ8NwT/ +BFv8dXEfBD+kLzBsYiCC/0DU5SpX+Bf7rVNenbl88aZ99lyzkJaYL/ap8zUk +eZ7ctP+monn5b+IX+22qO+pDvt20b1ojHVSe/sX+gHecyVqOW/Z8JnwXP+R8 +sf/Vcz5HTPqW/czdDAFZRV/sWX5cSZige8t+w6mnvrG1X+xvT9BK2x50yz7T +mc/265Uv9meOaD+e3nbb/rZJvLRqy1f7UKFzq0/Z3LNP+2nK39r51T7A44rn +q+B79h/28jA/7ftqH63jLaCUfc+exX3XqyUzv9r/rme9dn3mPXu9SNFdKuu/ +2p+a/v+r94979g21pyNUbn21v1/2gefCjvv2Vc6Xohe8/AoLL3sA2w2PqA== + + "]], + LineBox[{{-1.2638825342134823`, 0.5}, {-1.2638825342134778`, -0.5}}], + LineBox[{{-1.2652089609137678`, -0.5}, {-1.2652089609137678`, 0.5}}], + LineBox[{{-1.2678618147245122`, 0.5}, {-1.2678618147245122`, -0.5}}]}, + Annotation[#, "Charting`Private`Tag$384194#1"]& ]}, {}}, + AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], + Axes->{True, True}, + AxesLabel->{None, None}, + AxesOrigin->{0, 0}, + DisplayFunction->Identity, + Frame->{{False, False}, {False, False}}, + FrameLabel->{{None, None}, {None, None}}, + FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}}, + GridLines->{None, None}, + GridLinesStyle->Directive[ + GrayLevel[0.5, 0.4]], + ImagePadding->All, + ImageSize->{375.9999999999988, Automatic}, + Method->{ + "DefaultBoundaryStyle" -> Automatic, + "DefaultGraphicsInteraction" -> { + "Version" -> 1.2, "TrackMousePosition" -> {True, False}, + "Effects" -> { + "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, + "Droplines" -> { + "freeformCursorMode" -> True, + "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultMeshStyle" -> + AbsolutePointSize[6], "ScalingFunctions" -> None, + "CoordinatesToolOptions" -> {"DisplayFunction" -> ({ + (Identity[#]& )[ + Part[#, 1]], + (Identity[#]& )[ + Part[#, 2]]}& ), "CopiedValueFunction" -> ({ + (Identity[#]& )[ + Part[#, 1]], + (Identity[#]& )[ + Part[#, 2]]}& )}}, + PlotRange->{{-1.999999918367347, 1.999999918367347}, {-0.5, 0.5}}, + PlotRangeClipping->True, + PlotRangePadding->{{ + Scaled[0.02], + Scaled[0.02]}, {0, 0}}, + Ticks->{Automatic, Automatic}]], "Output", + CellChangeTimes->{ + 3.827549412502462*^9, {3.827549510156433*^9, 3.827549518064516*^9}, { + 3.827549591055779*^9, 3.827549601051997*^9}, {3.827549634351198*^9, + 3.827549698804183*^9}, 3.827549773209572*^9}, + CellLabel->"Out[37]=",ExpressionUUID->"8c65a08e-3559-435a-a819-b2b78b9896c9"] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Plot", "[", + RowBox[{ + RowBox[{ + RowBox[{"Evaluate", "@", + RowBox[{"Im", "[", + RowBox[{"(", + RowBox[{"iii", "/.", + RowBox[{"\[Theta]", "\[Rule]", + RowBox[{"\[Theta]", "+", + RowBox[{"\[ImaginaryI]", " ", + SuperscriptBox["10", + RowBox[{"-", "5"}]]}]}]}]}], ")"}], "]"}]}], "/.", + RowBox[{"{", + RowBox[{ + RowBox[{"\[Theta]c", "\[Rule]", "1.27"}], ",", + RowBox[{"B", "\[Rule]", "3.12"}]}], "}"}]}], ",", + RowBox[{"{", + RowBox[{"\[Theta]", ",", + RowBox[{"-", "2"}], ",", "2"}], "}"}]}], "]"}]], "Input", + CellChangeTimes->{{3.827549272684514*^9, 3.827549406087624*^9}}, + CellLabel->"In[14]:=",ExpressionUUID->"5b7a21c5-3f4a-4014-ac1d-c9e8a64be69d"], + +Cell[BoxData[ + GraphicsBox[{{{}, {}, + TagBox[ + {RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6], Opacity[ + 1.], LineBox[CompressedData[" +1:eJxFkH9Q03UYx0nUz4TlxDmWhgELJtG1MSN0HsWjB8pId7EB0unUDRFBkpQw +cVGE44Sy/AFS/JCW5ELFmCl6EPNxHUe2+HUIFooCFxKwWqmf71fgJt/WX/3x +vueeP57X87p3sCFHkz7Hy8tL6cl/UxbjP8lxHPquLQmuusOHnOkXS6ZnOHxY +UB697Dc+WC8rpI8ZDrvnxKdW9fNhZdgmw5iTQ8f5syeqeviwys90p+NXDmEU ++NXtfIDfHzoqGznst0uCa77ng+ZI54VXt3MYvZV11H7Ch/e7Te9kXJ/FuFhF +uGUNH/r6fCft+qd44we7OeEzX1h+I2fJqgA3Hteu9s53+kDTnrZ5gnszOKFr +lI9s9IEdRxX/DBRNY7VAFDduXgBTJ40lGDOFwoNru/K9FkDdwvtLvxxhMS3Y +WWfV8ODklhiiHGSxrFL49vy3eFBUb6YDt1kMLftGsHUTDwzr0rqf72CRs3h/ +TOJ5IDkwbvrqKovJwT3vbXudB2fuPfrb8imL/tzBr/lhPDA3kPam11j0zYvx +z3pK4Pj07sspESwutqbP4AyBwvUO85NwFs120bBoisCO4aNGZRCLQ7Niq/0R +gcAlixU2HxbvD7YZlo4TqDUG1LQNMThvT7Pw514CNQmK/bdKGVS5T51/qZ5A +iG+Co8fEYIMwteLiWQIXfjFIuj5i0Ly3+LCijkDLxvLem3kMZpUGGZS1BAbU +T1Ze1zPY1RwfoSon4K+1Pa5XMmgKLRZkFnr+CW+/aYlk0Cb7wu+vAgKhfa66 +OjmDle5nRPuMBCKTg5JqQxl0mgcC8w8Q0Gw+fKXMj8H200lxpdkEjm1R5X04 +QdGS3Nh5LtXDDzB0Gkcpjul1o6+kePiDh0LzhyhW7FW5L2kJfKdr6M/tp7hB +PihvURPo2C6IyrRTTGjxtjhiCSQFhX2+q5WiJONqu3odgbvDMJZ2jeJPOut4 +bwyBSf3+im0XPfc1RRF31xDg7exntZUUb7kGup0Rnv5DXOrEcoqtPdxMjoyA ++MH8b9XHKJ4WfbCCvkxAumv1ZlUxRTakwOSWenykiY3rCykK0+c2FYYQiPoj +k8QaKQa6x8bmSgjE7a6+9sY+iq7cH9XPLvf4hl0RRGdT1OhsphPLPL4THRnK +DIptl8StoucIDJ57gFEGijX6XlopIrAza1YcqaM4kuKSvSAk8Ge4+F1FKkV3 +XnbWmUUEcp3ymzItRVtiUL104f/7oVPNQhxZAf8ClwPGTw== + "]], + LineBox[CompressedData[" +1:eJwVl3k4VV8XxwnNERENoqKQDA2ksK6iKISQhFT4FUmJSIgGU6VSVBLKGIok +krKIUlIkkiFDZAj3nnOu6d4T3vP+dZ7P8+y99hq+a+2zVx7xsnKdISAgcEJQ +QOD/XxsTxxlzXbmYmzPnxquOtWV3xAYO8Vy42DkzYtf1xrVlhGbvpahDXPQ5 +u5WKmVQoM7Xuzlhmz8UkOVdx/6hVZZlnOz/nWHOxMWVjmJKHfJnw/V8cvb1c +7L8z9d/31bJlziUti2pNmP3nSny29S0pe/OrSdvZkItj1/pLj4lKl8kINB4k +9bl4tNz20PkoyTKfVfUXLupw0cporce6vRJldYa1KYs2cXGGS7TETquFZar/ +1VSlqnGx553z1ejFC8oiIj8Nblbm4s/IPC2J3jllPdkfxKpWc/H+rZr2WbNm +lbG+Vmy0W8FFZRXDLi0v4bIEomz/gAwXDzeGXxqUmlE2IVF6PmARFxObiwTc ++6bRenNJ0jxRLhL8kkXOwv8wb/+rioTZXLzOVT9Q6DeB8wNe9q0X4uKC+yZr +e7VH8VhC/jycpDD0s6Zuli6FlaW56hYTFFYltqslTLLxvFCWn/cwhUGuyw7E +Gf3Bk/edZjr3U6itlWjmsK0Lj6gvijXrplAscCUlSbSg7fuq1dvaKdT7Zhb1 +8e933H0wMF+pmcJm8fqOg0XVqE9qGCxuoDCTei62pvsNaob/qRWqpdBl6G2J +bcxdlHlhPtxeSaHIS6DTxsthvolQYA1SKPfr0oaRoM8w3V409/VrCo8/cdyU +v7UeeueuVIrNo/DVxous1lMt0JLcWHgxm8Kcj1bzkze1wxetKKNT6RTWOItf +a+3qhIIj3CN7Eijc90D/oZJyD2ROZJBb7lL4VyyuVzHnDzyIdghZE0PhMUOz +K3uW9cHF1+8fCkYw/j4qv6JUMQBnLQJUORcpNLj5LHPd1F9w71UraQuiMMmo +2YerPASWEvd+Fp2hcPke02NB+9lgmGn6X9pJCouP6v8asOfAFn3BsZjjFMZZ +jtjqKBMg7+6+6OQhCvN0Oox3LiRBUkDu8UF7Ct+fFz6iGkjCrLjvGiY2FArd +ZtU4dJPALtc1V9hDoediuaVJqRT83k+2ie+kcOJ7qu/aaQoah9M8plkU2uuR +ZX02XHizRCyyRYtCwSPijxsmuJCXWyH9UZPCZ/8tyDloNAKpRv7pL1Up/FSr +NLMuegSunu6quLmKwk6Rv2tkloxC8Kw4q2BZCsNEUkc17UfB++HuLg8ZCte+ +uO7//t4o2H96MbVTlMIsU2V2regYKK0M05nkkVjsW3d6X9cYLC/a+vHvCIn0 +oUIPZfFxEDPj2P7kkHhpnoSXPozDmL+dz4s/JHYvKTM/FTcOf0UXCD3qJPF9 +vLdUHo7Dr9TyW9GtJHqr9TT79I1DZZ1K7vFvJD6faHn6acMEvHLr0NtfQ2LI +kQ8CZ20nIPvf7RrDKhK/fn/M6fCfgBilyQG5tyTK2xyokH09AYdDahV+ZJJo +LjK84pw6D2ybk/R/pZD4aSB2brUJD3ZvOGXXk8jsN1Oc3nyUB5t6Fl6j7pD4 +/bT4teDbPFDW60rj3SCxS0l8vnsWD1bEPUeBqyQKHr7qGV3Gg9nGVlzRUIaf +h+kk/OXBZPKqBYsDSbypslwhZooHFI9aI+tHYuy52+PN4nxozb5tv86TROGH +s2J9tfjwTKyxfNcBEt3CCyY9/PmQciyt1dyaxHj7w0YXw/lwr9x31GYviZ3p ++66Ix/Eh9MxiZRcjEqVEzkxlPefD2Zre7R4sEt96i7a/KeWDu2KRg/c2EmV2 +uMzc/5kP1k37b4Zokuj8nKlnNx9MNJSywlVJ3KaSYXaOzQf9yImK6LUkmm33 +W2TL44PStvvjCbIk3r6vUdm6gAY6scWpeA6JP+MujrlsoIEYz/IvEybx9WPP +T2lbaeixOB9TNU3g+gemm25tp+HrjOUfGkcJrCpKe3vKkoaKg0MdbQSBWcky +q47b0fCq4A2ve5BAIU2BHMlDNDx2c1xPdRH4/UUV75oHDXdx/S5eG4H185vP +OZ6m4ZrMlLPATwLtK+fe7z9Lg2914h3RrwSa6i+M2BxKg/tqr2dSnwj80j2c +yL9Cg1MgfFxeSWDT2oU9IVE0GKt10iqvCVQoZPF/xNCgF54nteElc37ozmdP +4mjY0BmirpNH4PiXI/t3xNOwRsfShJVNoNctrz1pD2lYFrPy6K50An3cRxrr +kmlYOEgGmj8iMC81fEtVCg3Chu/ibBIIBNF12ZHpNLBHj1QfjSGw7VGDt182 +Dd3mG3vcrxP4XEJkXtpTGn5mCE2djiAw8YfO1pRcGr4INEifu0Sg04WABWee +0/DuQKpmSDCBmnpLo6Re0FCU77Mn/ByBF9P/Pb1aQEPOPCPXaB8ChXObvH68 +pCHZRepCrBeBmYQ3jhXSEPv2z70Ed+Y8154rw0VMPvzjg7VdCdzld8Pq8ysa +lDbudak/RGBDgLljQDEN5LDQbk97AnNPkIU0w68zX6nPtiFwy3W9Yxavabh0 +1FMqZS+BYjba3ucYNl2xitbbzcS75/hXP4almn90/jQk8EX3Wi9ThttvX/1w +BgjUiaqHCcZehjkrR3QrgTMmxRUDGT41Z/TWk00Eei+WnPzJ+KNT+cTPUJ1A +WvF9khjDMy44OXYoExgyMrNDnvH/s86iHQEKBKbf/BO2gInvzkiVkpQcgRX/ +Pjn+YPLhlBsomreEwLCmLIVAJl9r3TVHdksSuFl6291pJp+EQm/zH1HG3vDi +E4fzaCjuiMeQOQRaD7CtHz9j9JY1e7HnJAe5QfnilVk0qMh7dz2mOLhEuV4z +PZOGN7GtOT/7OOhp8mjqOFPfzpBnOwzrOZjW+3PW/Uc0eI9JiwVUcZDKF/MS +SWL0cCK0JfcNB2UEv/+0SaBBeb/16WUZHFwv5tmZyujNez0/kTrPQa9oMa25 +jD6FU466K53m4KCxzPa0MBriZL5sdnLj4IYHEvuULtFQIpRc88mC2d/Rubv/ +PLO+xYifrMjB1VMaJw6eYNaH3bLZW8tGemfgNlcTpr7/+PJXKtnovIwsyDNk +6nnaZeh1MRsV7Nhaf4GGDgftS2tS2XjVouGaktb/9fArb9KfjdJ7XLNbVjLr +O5Tm56xiI8JdtsUYHwJ1BZ/Gy7BxFtbvEiD5oHe/2SxSlI3d6QkPUwb5UGYV +dcONP4xrpOuoD518qHo/KLGyfhjrvUanL1fzoSH72ZK40GEc6K+hBBP4wPbb +tDakcwjN7N3fjmrzYfVC1nbrxEGc2rXTvPQAD6I1ugLcbw9ig6tk0WdLHkxY +XHwREjGIuZ+q/tUz87rmVqXCU+9BLDT57VGrwwOfRSazZu4axKMD7N+hS3jw +YbFVTRHnL9IPNO60NU2Au6yL7TKDv/h2pVv6D4sJyFeJcP/d3Y8yNseeJWmN +Q8f75/JaWr0o37Hset7gCPxRjd2Ahd34r6A8wC+XAvHgJ1pqgl14Y52ftdEG +AlS1OKpp3Db85pHiV501CJcMh+uK/Ztw0sZicEtQL0hZP7t5QLoeP1H/HuY5 +dkH+2HuxjwrVWPdE/6O6fDOktf65PnC5FHU8vS+12n8BR8vlBa1HU9E4e4nE +5cQXUDz3fOM73xRgDd8puV2cj5t/C64ItUOYDv1Ta7TmK64mSnhb332C7fMH +dpeW/0STlOYv5nb1ENM3fKrkQRcamUkIjb5sgicxAlf2F/XijUNNIRpFbTDa +eVl27PQgVpnLLrCQ6AIp9dPuqtsJHF4pFVwf3w2e/Stzl8ZR6Ouz7vCNxb3w +QGqj44/aEWxqW2jl9rEfHge+UWmWG8fdV11/+tT3Q2d4fLGm0ji+0XntdKmt +HyqcJd+Ea4xjctxRj2SiH4r3opCqwTgesyi83CIzAO3XFpDWR8aRX3GwyPz4 +AGQpnn+wKnUcl2enL9ee+xf6H/ecPa84gc7ndPtmmQ6CV7bbFz1ZHqq4fGxk +2w7CL/8aaRtFHnLNrSsbDw9Cr4rbE7f1PAxTOPEoxW8Q3hcZ2vvr8TCn9sFB +SBkEvc2Jf/c58pCnSNee5TP2tjoGtTzgYUx98as/mUNg6mLgFLGIjw5vjTJq +XgxBabflPlzKR8XMb7EvSofgWcTT5OGVfHwVNOAd2jAEb3bofFTX4GO70pL1 +sgLDUMeufr/TlI8qF/wfWe8fhpJ3DrseXeRjxTrtqAoRNvAGyAKil49O6tYp +pBgb4jruz/tviI8TG06/kVvKhsMjuQbfSD6qbs1mn1djg4Zo+Y2Qf3y8Yyy3 +bxPzH3k3fuN+I3Ea3VxnLU/LZIP9JWFTnS00ChxX2Pw9nw0Lbn1zb9SlMf6E +gbngWza861KePGxA49cz50Mcv7Gh02a7357dNGpf5PRI8dkglqRraneQxvor +86d2CHMgM7jywalDNJ6IVJb2FuWAkR213u8ojck3j5p8XcWBu13x3WYeNM5O +anoatocD9S2y+TIBND5+PPKhwIYDb202s+KDaNRNF+/8fYgDp4s5Z2aF0njq +6R4J8OHA9nMb7FLCaZz7/Ng6z2AO2DVom3yLojG14IrhgwgOJNwvdh64TmNz +CZ4dT+CAa2q5+4/bNPpg2w3FDA6s8uJEZcXRKFrBy9z3nAOGXhWq/92ncXv1 +xtbc9xwg3sptupdIY9sXi5FftRzwW66YP+8RjWe/eS6Y38KBZ3TSb9cUGrN+ +ZsAxNgcOe3/0qMmg0ait0i5uggMWK5a+b3pCI8EhthwRJEBwwcS3qmwa356+ +YHRuJgGpocFzE57SGMVdYHVzHgE3LC279+XSuN83wSljIQHw48IXdh6NCuMq +HqVSBNz69p/WiXwaSf9iv8alBJzccjf88wsaS/m7Lg/JEbC/KWfN/Jc0Xg38 +cVNIkeFKbd/1hTTaTbk8XKpCgPrN2Dq1IhoVQ7hPNNUJaFaqvcXch0gJXiw0 +3kTAdiefBbUM46WFFYd0CLjE8719opjGayJJtWf1CWiwmTrZx/CB8PVt13cQ +IOxu3Kv/msY1c970pxoTMFvDd6s3w1SVmvtjM8ZfzdklIQyXhj0aTLIiQO2L +pogHw1FGkp4P9xPgpFBno8GwrXA4O96BgPACp55axv6qCp7XvcME6DlU/TZm +mB16gox1I2DLOc2geMa/16wO79seBFyeXdtcwcRzZdpy5OYpxl5ehkwlE69F +aaVvtC8BWfGH98Uz+VgepD1+NYAAJZHZD40KaOzfluUfeYEAR49awfdMPgv4 +y/lhlwlYr9oUJv2cxpDiG+cvRxKw6lq/si5TD1P/GZOh0QRMURu6NJl6yWj7 +Bl+4TUClgciD8Swae0b7pgPvEWC3/LLetUwa8wrsQwMeElAy7ZDOTqMx8MyX +Gf6PCXhM+2bJMnox3sC67JtBwKvu+1IyyTRKkvkiZ3IIEP0sn9WWQGNnrmL4 +qecEKNy7I+/O6DHn5L3ZJwsJoIIt12IsjTuGguYdLyMg26bp+GtG36LZxDW3 +9wS4Zbd8doykseX4UVGXagJWR76ZU3GZRu8+Y/FDDQTU7THtqmH6Sz+9JMah +mQBO0TX9k75M/7iqSdq3ExByrXKy2ovpv9+LpG36mfx9vh6dy/TryUdh96yG +CZhTqpO30ZHGrc68JRYUc09d+VrvYcv0+6/25Xv+EVCjoyJC7KIxMcEy0ViQ +hO6bxr+0WTS6H6yU2zmTBLXfvkbrmPki2PxklQHzLl3mphAyby2NNXeXp+pL +kdBvfj+AK0vjPdsbirpLSSC9FfcFSdKo0eCjpK1AQmZUH8dDgEbnWlBbv4WE +ApPZR12+M/MtOj9XRY+EmzNu+M6rYuafqaKm0nYS1ofbsXRf8/FG9dxNq01J +uFTUl6iaxEf7yKCX8pYkJI60ZvTc5OMaY0JrhS3zTpbr3yvNzNfS9406S5xJ +yOmyyGs9wseoy8Yli11J2BuncMfFio+2O0p0Jd1JZt7eOm5rwEd2WTKI+ZBw +4EKmymFZPsq+8TASiSAhSN2/IPALDyWX8Pknr5MQe1R3XdNLHs4/G5H3M4aE +OYqDJSYPefhPPW1ZzkMSZhSJhOw7zsORaxu/SaWQIDFDt7zJjIeDA+VhFzJJ +OGkmpGKuycOWlHbS6gWzfoQ3v3dkAusFPDPevCKBNYXuRMMEfnKkHdaUkmD5 +rDq19MUEvpKW+cj7SEL51jTP054TGHfVMjG5nYSqT/07btWOY3R/x765PSQ8 +PeCWJsfcl1eMTs7xGSDBX1hRjjo7jj7TUT67RkgwkshoWSg9jicclqg855Hw +645qpUbPGB4tzuhYOk1CRoRQ37bcMbQ6U7mbPYeC3I2uF7L1x3B3nZWAnRgF +03+dsppmjKHB+q6X5ZIUmLSHbQmuHEWNvkn5WDkK5BK2DhXAKIoe1B7ftpmC +/uqYoUTxEZz56n1O2lYK4is87oW85eKkpPURMRYFCU9k70W7cnHo66kvv3dT +IFPdenfPEwp71k1fNLWgYEZg8niQIYWtEde3FNpQoFSel/q7hcTq7Vkpkc4U +zFOVmyUxQeC7pC0HuK4UHPaqU93MvIuK/30QdfSgIOZMfpbPPw5mFnaf0zhL +QVfzd6O7DcOYvMhbPf48Bcb9K+/0ZA3hvVMCf4RCKejzirdyYP5/wlVkLZqu +UuAcM264u7ofg8OzRQxuUTD6tuOFvn0fnu3RKcmKo8C3fraxdeMfPGnw8ZRk +AgWn34aq0To96JZouyb4EQU73349GRT2G53onta+dArkF28K4b/qRBu7M7cs +cyhoiJuIrEz8hYYSN/8pFFHg4UZ0sfQaUddrRX70GwqW3ZXROpJahxtrcv6b +KKdgZvrY3x2BVaiivE32SBUFZr08vzrR17gq7FP95xoKSg5GzbJ9fh2Xdu+P +2FxPweOcQ1PiGwtAnNWrl9TE+Cv1G3QHPoAAf8YT798UeNufNzF41QzO3c3c +C30UWNx3tdS+2QllNXn614coEAszmA6P7AH5wvDIeJLxx0Ph18+v/RCS5NSQ +MUbBp+Ya8Q//DUNnxGa5lzQFP0Dp4yk1Rsfe893fCXBh3tZA3aFWLkwbvp5u +m8sFn8ktcVa9PHBSu7X7rxgXihelJUZaTEKp9LHYcUkuCG0uVDC6LMBaIQid +wku5YFD2qvjz1Rms4L9S6yTkuBCWNsFXqRRmtX8f8pVT4IJ+kdTSsI2zWPpv +K8pUlblQMbbq4njnHFZievy8rWpcOHQoIA4b5rOmbpy23bWRC0u663r05y9k +OZ0zfmS9hQui8qW2Ja3irNIjckOH9bjwQFRAw7djEWuF6ZiW13YuLMha1wZy +i1nBm7+EBu7iwrpTy8ddUmVY7StSayJNudDoPCo3cW4ZS3/2eem7llwIVYqo +YD1dwUokLY+k2nKh12yevvzalazJFqWnzw9ywWZH4Rn1LatZDpXT46XOXHAQ +7ghIiVVkDTnoaQq5ciEgtngRdq1l/Q/uPoj4 + "]], LineBox[CompressedData[" +1:eJwBUQOu/CFib1JlAgAAADQAAAACAAAASAKdfB1S9D96lbkTv+EnQEgCnXwd +UvQ/IN4wlJ8NB8DgFUTVClf0Pyf5hIIREAfAa502VIRc9D8ZhTcRyRIHwIKs +G1J3Z/Q/n6/ggDYYB8CwyuVNXX30P3ybpVYRIwfAPFLYzNaC9D9Q1g0QyCUH +wMfZyktQiPQ/lOccy34oB8De6K9JQ5P0P8YcMEbsLQfADAd6RSmp9D+WJxpQ +xzgHwGlDDj311PQ/bPQosn1OB8D0ygC8btr0PxlLq4U0UQfAgFLzOujf9D8X +lcZa61MHwJhh2Djb6vQ/ayDECVlZB8DGf6I0wQD1P+6Iw3o0ZAfAIrw2LI0s +9T+pWlOo63kHwNs0XxslhPU/7dxYMFulB8Bm+TUPhYn1P48nTYsFqAfA8L0M +A+WO9T9CacPnr6oHwARHuuqkmfU/AUk1pQSwB8AuWRW6JK/1P1e3KTKuugfA +gH3LWCTa9T9YBiCUAdAHwCbGN5YjMPY/ghrBdan6B8BwVxARItz2PyL3TZP9 +TwjAGZTkWAQd+D/yXLgVPu8IwK5boKfzePk/zBB8L/+bCcBXPX9IyL36P4vU +JG9YPQrAsV5tIjr8+z9m2hQelNsKwPgKQwO5Vf0/t5CAqk+HC8BS0Ts2HZj+ +P7tIUhucJwzACjsLwbyd/j/zDe35ZyoMwMGk2ktco/4/uLlr2TMtDMAweHlh +m67+P2GME5vLMgzADh+3jBnF/j8rmgQp+z0MwMlsMuMV8v4/160ob1pUDMBA +CCmQDkz/PyusYqIZgQzA+HH4Gq5R/z9XgOWc5YMMwK/bx6VNV/8/OLpCmLGG +DMAer2a7jGL/P/83i5FJjAzA/FWk5gp5/z+eUUyOeZcMwLejHz0Hpv8/wRlP +sNmtDMBuDe/Hpqv/P2X6VbilsAzAJne+Ukax/z+RszLBcbMMwJRKXWiFvP8/ +tZBs1Qm5DMBy8ZqTA9P/P6ol2gc6xAzAKltqHqPY/z8k+YcWBscMwOHEOalC +3v8/12oJJtLJDMBQmNi+gen/PxkOhkdqzwzACAKoSSHv/z+QsoBZNtIMwL9r +d9TA9P8/EttNbALVDMB21UZfYPr/P2hB7X/O1wzALj8W6v///z9xn16UmtoM +wJdlkx0= + "]], + LineBox[{{-1.2678618147245122`, + 11.940910927204403`}, {-1.2678618147245122`, -11.936954946452117`}}]}, + Annotation[#, "Charting`Private`Tag$382923#1"]& ]}, {}}, + AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], + Axes->{True, True}, + AxesLabel->{None, None}, + AxesOrigin->{0, 0}, + DisplayFunction->Identity, + Frame->{{False, False}, {False, False}}, + FrameLabel->{{None, None}, {None, None}}, + FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}}, + GridLines->{None, None}, + GridLinesStyle->Directive[ + GrayLevel[0.5, 0.4]], + ImagePadding->All, + Method->{ + "DefaultBoundaryStyle" -> Automatic, + "DefaultGraphicsInteraction" -> { + "Version" -> 1.2, "TrackMousePosition" -> {True, False}, + "Effects" -> { + "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, + "Droplines" -> { + "freeformCursorMode" -> True, + "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultMeshStyle" -> + AbsolutePointSize[6], "ScalingFunctions" -> None, + "CoordinatesToolOptions" -> {"DisplayFunction" -> ({ + (Identity[#]& )[ + Part[#, 1]], + (Identity[#]& )[ + Part[#, 2]]}& ), "CopiedValueFunction" -> ({ + (Identity[#]& )[ + Part[#, 1]], + (Identity[#]& )[ + Part[#, 2]]}& )}}, + PlotRange->{{-2, 2}, {-11.936954946452117`, 11.940910927204403`}}, + PlotRangeClipping->True, + PlotRangePadding->{{ + Scaled[0.02], + Scaled[0.02]}, { + Scaled[0.05], + Scaled[0.05]}}, + Ticks->{Automatic, Automatic}]], "Output", + CellChangeTimes->{{3.827549290811028*^9, 3.827549407027862*^9}}, + CellLabel->"Out[14]=",ExpressionUUID->"4b349b45-a209-4f2c-95d2-cc1f086f08a1"] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{ + RowBox[{ + RowBox[{ + RowBox[{ + RowBox[{ + RowBox[{ + RowBox[{"Evaluate", "[", + RowBox[{"Im", "[", + RowBox[{ + SuperscriptBox[ + RowBox[{"(", + RowBox[{ + SuperscriptBox["\[Theta]", "2"], "+", + SuperscriptBox["0.2", "2"]}], ")"}], + RowBox[{"5", "/", "6"}]], + RowBox[{"(", + RowBox[{"iii", "+", + RowBox[{"\[ImaginaryI]", " ", + RowBox[{"\[Theta]", "/", + RowBox[{"Abs", "[", + RowBox[{ + RowBox[{ + RowBox[{"1", "[", + RowBox[{"\[Theta]c", ",", "B"}], "]"}], "[", "\[Theta]", + "]"}], "-", + RowBox[{"\[ImaginaryI]", " ", + RowBox[{"Sign", "[", + RowBox[{"Im", "[", "\[Theta]", "]"}], "]"}], + RowBox[{ + RowBox[{"iF1", "[", + RowBox[{"\[Theta]c", ",", "B"}], "]"}], "[", + RowBox[{"-", "\[Theta]"}], "]"}]}]}]}]}]}]}]}]}]}]}], ")"}], + "/.", + RowBox[{"{", + RowBox[{ + RowBox[{"\[Theta]c", "\[Rule]", "1.27"}], ",", + RowBox[{"B", "\[Rule]", "3.12"}]}], "}"}]}], "/.", + RowBox[{"\[Theta]", "\[Rule]", + RowBox[{"x", "+", + RowBox[{"\[ImaginaryI]", " ", "y"}]}]}]}], "]"}], "]"}], "/.", + RowBox[{"{", + RowBox[{ + RowBox[{"x", "\[Rule]", "1.1"}], ",", + RowBox[{"y", "\[Rule]", "0.3"}]}], "}"}]}]], "Input", + CellChangeTimes->{{3.827551824274338*^9, 3.827551835538342*^9}, { + 3.827552093255658*^9, + 3.827552097839314*^9}},ExpressionUUID->"a965ddd5-a893-4434-9238-\ +c098b3e4986c"], + +Cell[BoxData["0.3257787412683152`"], "Output", + CellChangeTimes->{3.827551845675845*^9, 3.82755190814505*^9}, + CellLabel->"Out[54]=",ExpressionUUID->"b149c712-91a6-4ee7-8d16-92cad228d46d"] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Series", "[", + RowBox[{ + RowBox[{"x", " ", + RowBox[{"Exp", "[", + RowBox[{"1", "/", "x"}], "]"}]}], ",", + RowBox[{"{", + RowBox[{"x", ",", "\[Infinity]", ",", "0"}], "}"}]}], "]"}]], "Input", + CellChangeTimes->{{3.827468489747037*^9, 3.827468497122335*^9}, { + 3.827468550029158*^9, 3.827468569747735*^9}}, + CellLabel->"In[4]:=",ExpressionUUID->"87d802ec-af41-45fc-bdcb-d506ef1418cf"], + +Cell[BoxData[ + InterpretationBox[ + RowBox[{"x", "+", "1", "+", + InterpretationBox[ + SuperscriptBox[ + RowBox[{"O", "[", + FractionBox["1", "x"], "]"}], "1"], + SeriesData[$CellContext`x, + DirectedInfinity[1], {}, -1, 1, 1], + Editable->False]}], + SeriesData[$CellContext`x, + DirectedInfinity[1], {1, 1}, -1, 1, 1], + Editable->False]], "Output", + CellChangeTimes->{ + 3.82746849735259*^9, {3.827468560630088*^9, 3.8274685699875803`*^9}, + 3.827481962269148*^9}, + CellLabel->"Out[4]=",ExpressionUUID->"3e6bf624-2d34-47d3-a821-004cfbb725e6"] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"iii2", "=", + RowBox[{"Integrate", "[", + RowBox[{ + RowBox[{ + FractionBox[ + RowBox[{"x", " ", + RowBox[{"Exp", "[", + RowBox[{"1", "/", "x"}], "]"}]}], + SuperscriptBox["x", "2"]], + FractionBox["1", + RowBox[{"x", "+", "y"}]]}], ",", + RowBox[{"{", + RowBox[{"x", ",", "x0", ",", "\[Infinity]"}], "}"}], ",", + RowBox[{"Assumptions", "\[Rule]", + RowBox[{"{", + RowBox[{ + RowBox[{"y", "<", "x0"}], ",", + RowBox[{"y", ">", "0"}], ",", + RowBox[{"x0", ">", "0"}]}], "}"}]}]}], "]"}]}]], "Input", + CellChangeTimes->{ + 3.827399065803953*^9, {3.827399110076665*^9, 3.827399110380816*^9}}, + CellLabel-> + "In[158]:=",ExpressionUUID->"b6e097f9-9f11-4738-9df9-1bb1c5732eff"], + +Cell[BoxData[ + FractionBox[ + RowBox[{ + SuperscriptBox["\[ExponentialE]", + RowBox[{ + RowBox[{"-", "1"}], "/", "y"}]], " ", + RowBox[{"(", + RowBox[{ + RowBox[{"ExpIntegralEi", "[", + RowBox[{ + FractionBox["1", "x0"], "+", + FractionBox["1", "y"]}], "]"}], "-", + RowBox[{"ExpIntegralEi", "[", + FractionBox["1", "y"], "]"}]}], ")"}]}], "y"]], "Output", + CellChangeTimes->{3.8273991150292797`*^9}, + CellLabel-> + "Out[158]=",ExpressionUUID->"a5d9b280-e936-4513-a7bf-6c1d1444f0ed"] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"FullSimplify", "[", + RowBox[{"iii", ",", + RowBox[{"Assumptions", "\[Rule]", + RowBox[{"{", + RowBox[{ + RowBox[{"x0", ">", "0"}], ",", + RowBox[{"y", ">", "0"}], ",", + RowBox[{"y", "<", "x0"}]}], "}"}]}]}], "]"}]], "Input", + CellChangeTimes->{{3.827398872425025*^9, 3.8273988827608223`*^9}}, + CellLabel-> + "In[189]:=",ExpressionUUID->"41965605-2b79-48db-a227-2111a1e5bd93"], + +Cell[BoxData[ + RowBox[{ + FractionBox["1", + RowBox[{"x0", " ", + SuperscriptBox["y", "2"]}]], + RowBox[{"(", + RowBox[{ + RowBox[{ + RowBox[{"-", "2"}], " ", + SuperscriptBox["\[ExponentialE]", + FractionBox["1", "x0"]], " ", + RowBox[{"(", + RowBox[{ + RowBox[{"-", "1"}], "+", "x0"}], ")"}], " ", "y", " ", + RowBox[{"ExpIntegralEi", "[", + RowBox[{"-", + FractionBox["1", "x0"]}], "]"}]}], "+", + RowBox[{"x0", " ", + RowBox[{"(", + RowBox[{ + RowBox[{"2", " ", "y"}], "-", + RowBox[{ + SuperscriptBox["\[ExponentialE]", + FractionBox["1", + RowBox[{"x0", "-", "y"}]]], " ", + RowBox[{"(", + RowBox[{"x0", "-", "y"}], ")"}], " ", + RowBox[{"ExpIntegralEi", "[", + FractionBox["1", + RowBox[{ + RowBox[{"-", "x0"}], "+", "y"}]], "]"}]}], "+", + RowBox[{ + SuperscriptBox["\[ExponentialE]", + FractionBox["1", + RowBox[{"x0", "+", "y"}]]], " ", + RowBox[{"(", + RowBox[{"x0", "+", "y"}], ")"}], " ", + RowBox[{"ExpIntegralEi", "[", + RowBox[{"-", + FractionBox["1", + RowBox[{"x0", "+", "y"}]]}], "]"}]}]}], ")"}]}]}], + ")"}]}]], "Output", + CellChangeTimes->{3.827398883332217*^9, 3.827398934722471*^9, + 3.827399284708077*^9, 3.827399346864921*^9, 3.827399566084638*^9}, + CellLabel-> + "Out[189]=",ExpressionUUID->"42c191f3-52e7-443a-b3d1-6dd6c714a8cb"] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Plot", "[", + RowBox[{ + RowBox[{ + RowBox[{ + RowBox[{ + RowBox[{ + SuperscriptBox["y", "2"], + RowBox[{"Re", "@", + RowBox[{"(", "iii", ")"}]}]}], "-", + RowBox[{"0.2", + SuperscriptBox["y", "2"], "ii"}]}], "/.", + RowBox[{"x0", "\[Rule]", "2"}]}], "/.", + RowBox[{"\[Theta]0", "\[Rule]", "0.5"}]}], ",", + RowBox[{"{", + RowBox[{"y", ",", + RowBox[{"-", "5"}], ",", "5"}], "}"}]}], "]"}]], "Input", + CellChangeTimes->{{3.827398837880198*^9, 3.827398847831921*^9}, { + 3.827399118949429*^9, 3.8273992107183113`*^9}, {3.827399290472872*^9, + 3.8273992992959223`*^9}, {3.827399354665359*^9, 3.827399355017283*^9}, { + 3.827399450730795*^9, 3.827399465762721*^9}, {3.8274000991186028`*^9, + 3.8274001518795977`*^9}, {3.827400621736384*^9, 3.827400622783819*^9}}, + CellLabel-> + "In[206]:=",ExpressionUUID->"92c22ee6-96dc-4a23-9b99-2945672a4526"], + +Cell[BoxData[ + GraphicsBox[{{{}, {}, + TagBox[ + {RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6], Opacity[ + 1.], LineBox[CompressedData[" +1:eJw1m3k81N/3+Mc+Yw8VJclSSJIkie6rKJSQLaQIRVIkW/GWypYosiaVkIRs +SVI5r+y7GVtk3ybZQpaxf1+fx+P3+2sez8c599yz3ft6nXnM7LJ1MbrCTCKR +TFlIpP99/vf77OzGhiCeFMmSd6FiEug+W+a7VgVxxVLqrErCJOjz9y1+XhLE +qa7f3oi7TIL4Edc1l3+CuKHLa6OdIpNQGvqM3E8n1mPfjWpvTABZ4acY3iCI +49ldtp0i4xDtbnPG/4UgTprrqpv2HYVMptuppMPE+g+UiHyXIWC7oq0kclEA +J+mq3Xr0shkEOyqckyM34aSGnK2mD18CvvdNSMATgsVsXk9mPgfne76pVx8T +XNZzPK09Bip3H+yWCyQYJ8nP2YfBXY+kMx+9CbbROREcYoAGBXzkyq0JBtLh +ztlXKP+s4ujIvk04zvrSbLNhITIqS7CTreXHbZ7ZpV74XY2kWod7qyr5cf9p +F7mXFjVoYVjB8moZPy5+snkqpK4GPWcvM0z5RsjJ/ZWXsmtRv+64xo4cfpz0 +qes7ybUe3aAeFd4UzY/3R2u3sQ01oZCe7nrGRYInrB6ka7Ygy6ndOnGW/Hju ++UkLI68WJL/hWnboPD/u+oH6pCmjBTWJsxW7GfLj/ENv2jQ3taIt9vveTZwg +7C9EqAp0t6KUsf/u9+/hx5NucB85cq0d+fzVcI4Y4sNJXhKUk5c7UeLlw6NY +Dx+eFP1Ad19YJ/rWomg/086HR5wxX5so7ETrnyWtjGoJudJY6CzXL/TAn6In +lEfI+4zrhQp+odBNbXvj/fhwm8UolLHahRIOOo+/FuHDDRVLir7c7EVf315x +MBTkw6e1xs56Rvei7q3WQyQePrzffy6JXNyLxFbPdV0m8eG5rM7a2ax9KLn8 +cJ3kb1486dEhltW4PvTelCXzXQEvHpLfhk5f6EdFXglOOQa8uKLVq770awNI +wv7W2w4dXrzIVs9BwWcAhRvq9DOd4MWFo3XZEsIGkK3sgqmJMi8ef8bLSjJn +AHF1nTu+JEzw2oj12uwAunSMIqw5yIP3n/YfrvAYRNVy/UbOXTy4q0OxSHrg +IFLa+jk8ppUHjy+cKnWJGUQc0/Yso5U8eMenVO2cgkGU+wafCsvkwWX6ZOcn +ZwYRC5t3Rbs7D65DXX1p4zCEbs7ok0g3eXCbuR+7YjyGUEeP9FFZB2J9xw2X +7IdDKKuwJdfHggfHRfvUn74eQmaO+xPFj/Hg2EXZG+T2IZReR3dz4uDByQK/ +XJs0hpH+M1Px9efcONlYrcyGMYzuKvHpakdx4+JvYph+M4+gtObqWxFh3HjI +pei0czwjaF1AvUziHjfO2G662LJrBH2Ikriqbc+NKzqJeT7WHUHcMX8zIxS4 +cVKo0MDXqBGkeuh9a+cewn7urMLDxBFk32a7JrGLG59WNtyr8HYEfdvcrv9J +kBuPeORC2l84gq7HfpvpZHDh5qvt1F/tI6g27tFhyTIuHJt+GkMVoKOFw5o2 +zt+4cMWm0yoNInQk0bEa8ukTFy4emFCRJU5Hd4Vdf2mnc+E2J6f9hBToSPa5 +2X/O4Vw4+UEkS6A2HZkc4U/7FESw3Ek87iwd+XfWNK7f48INxz6Tw43pqENE +QzzSjQsPie3n3GlNRyEJkmWfznPhOlDp3udORwVqPePrhoR8cb8i21066v8V +K6RzmvBHKUWA5x4dqW7nvPpLndBP/CFSFkJHoy+myRu7uPDctI3aygQ6ElLP +OKCznQuXieaxWH1FR1i3nWWkEBfu2PTqnWAKHcWL/syU5ODC/e3vG/3OoCPt +l9/1dSY48XQc3d71hY6mw7tXWemceP/cw3vy3+gowW8l40cfJ95BPdwvCnQ0 +YX2E42gLJ65YrOr+oZyOYg3NPy3WE3J/sWdnq+gIHfeyK6jkxBkebzuba+jo +mcQn2FfMibsWPSsOa6QjdcHWG2MfOfGIWadjP6h0NMLyb/u7D5y48Jlq/Fcz +HT2Z21Rr944Tt5n9qdLZSsQ7ougt/oaQe5fGfGuno8E2g909CZw4f2dmc0AH +HT2uvNn6PJoTF3/8cfDALzrqfZelKBhCyB0CDdV6iPzG1/U23SfWG3vHx/TS +0YFHY2FhPkS8il3BbX109OsO5aiuB+Ff0mfB5X46CnCS+cPmQsj5BQ+wDNKR +wgXtuFJHTly1fqp1muCfZ66evGfLictw6cyVDhH1VQ/8d9SKE09iEg64M0xH +cvtS3zBMOfH4GeM7QiN01LqjzOCTASdOVZusjiL4P97BtVu6nHiIM81hkeDd +G6QsBU1O3PH82GlEpyPq352W4+qcuOFOMYfrBN/tP0ZOVyHyrW+Q50OwJO1i +ob0iJ07+bSXmSnD9D1/7XXKEvTsSKToEe+a/EOiVJPxV8VZmI1g8pRhP2EHs +z3Sw6i2xX01U583zW4n6PpYylCPYLYAhKrSJqJft9vJnhP+iHlvrqJxEPrmG +tvYR8VVeUbkTzkrkU0gL4yPYxcx0z+l1Cj66n1VJksiHsLZ7GzuDgueeoQ9s +G6Cj0sNRD8tmKHj/2wytBSK/zjL5B/zHKbjqKK/BJyL/m0VofeojhBw1zp8n +6lNCmQ5f6qUQ9X2zr7eLjhyXedULOyi4tyAa1ybqKTC+b8ytmYKnO1yQjCHq +/bVLL35/PQWXKUqvrSD6gfd76Fw6UPCOrJgjNKJ/ij68T77yhYKH+EWMZRL9 +dflVtaHERwquM+TWc43ov4J77B9epFFwhmfUhadEf15ylb5gnkTBDXvFqQuV +dMRxWYuyOYFYH6pscZzob8sTD648CSfkxvd97pXQEevBN4Jngon4S5jW3b7S +0QdJ/AfHfQpOMo5z0C2iIxLb+o777hS86Hto6as8OkqrutN++wIFxya0LcaS +6ei5kqfmexMKbqO2dzSROJ9hL91ye88S8o1zrfLE+XW7fT1UF6PgVHa/0OEI +OtLYefHYTmkKjnOodeb50pFiqEWmiRgFrxbe8f2sF3E/zZsKh24l8nf1dWjl +LToi1+nPzlEIefVQuv5Vov88sbTaKTI+em3Z+jNxH1UNqAuSRsm445jhuipx +XxXrHfE/NEDGDct9BeMwOkqSULJMaiHjmLzJtVElOrreKMnrWURwo8+h3s10 +xLybw3PXAzJO/ctYo7SNoPkIliEzHzKeG//xul79CBpd2TAIcyf0o7hdncpG +UCONIbt4lYyv8rCwH8kbQc//G+upP0PGbRIZ42KPR5BiW8NJ781kfCKweoVJ +dQRJYrX5H3jJeLVWWfii/Ajaklm5c4iDjMfL2A1VEc+DVX9YOrvMgccfffCO +wTmCquTzPkj2ceDfEneoPe8aRpcCojc3pXPg4iE/t9Z7DKNGtMDhncyBh8jo +KJy9NozQyvll8UQOfOLQ8r4PVsNI3G17n9tTDrw7/lYlRXMYDVonp2/x5MD7 +36m5KPMOo6tHc49e0uTA5yyyU3VeDaH2hU0KHBocuP/XSb+Cp0NIO/+2eK4K +B95x8Uzluv8QkpE9zMYsx4GLetk+ULAbQmNbShrf8nPgRdf9WJaliefrbN3l +yR52PORWxCX1t4Oo98M+k9if7HhW+8+LYdGDyODa01OIxo4PfyjzKn44iBT7 +jfZGlrPjhr4npnIvD6LZhs455Ux2XErgZSy76CDyfP872NebHa8WOnzYOHQA ++dmwZHMJsuOkbVMp7mf7UW6T9pNWboLle19Pq/ajwWNhN1+ys+OOVQcV9aT6 +0akdm/fvX2bDiyaGTbXm+xDvr925RgNseEcx1hF9pg+9Mj6d/zyHDedPm4+T +nehBcCqycI8eoR+CWdLXfiHSvp2gGciKk2++EPO+2Yp8txy/FOjHinvHJXtm +H2hFixu2a5VerDjD4Fn2+7kWNNWcdvS0EytueHOf/sydFtTlrVBkaMCKm0/f +Ueq434wKyzXyLoqw4vzmL3dmBlPRDSurFK8PLLj4ubdgPVSNfj1+HpzZxoz7 +3ys/pbcjF7VUiGfZNDHjpFJrqyTtbFS/8Y66uYZgDuaTwaZZqOR2oYj/N2Yc +yzaoOuiejpIvtGSapDDjuMWR0Z6SJOS0l4e65kro46KPusOvIbsr0XP5TgQn +vbXbxHIcrF5vF3G0J1io0qh20RX0BeVsm88THDnXdUQtGJRWTs2lHSP8aRVa +XZVKgJVaf2FDboI13ZqYRTNhjpWswcZO6J+mjLQ2ZcHUsaeXizeYcJJz2jVn +/2zoz3+ZIfWPCe+PcuRrGs+F8oRi9aVOJhw7urlydV8BhDnN2SS/I+T+seZh +ZsUQmOoTeP4Nsb5dst1B4Cv49TJncL8g+Lexgnj9V3A12vTP8wnBp0CT/8h3 +MFFTCDzjQfCfBOYrDABRTsf3cyeYcPHZ9Pt7AkvhUkl9mIQ6E06tED1892cp +vHE74Gp4iNBnSTl/R6YMdnctq2TtIfQLWumBlWWwPyu83I6bCc8VXA9W/FcO +bjaz7yLZmHDcq+Lu0aMVUCB0/jGsk3BFdTVB/gcVoPqfuNH2GRI+uvnh8F7u +Sjih/7GvuY2E97NU8rQIVEEAs3AZqYmE89dOxjScq4KqQt80hWoSnkvX6P/x +tAr0dp66EVpMwl17HpXnkqvBbLpj+fhrEp4k8fi3/t9quPZsfXOeIwnXIc1m +sETXQtYpu6XeyyRcvPYaiFXUwtRyVTf3BRLuzT/Bd2++FtzsIlMczxL29f5s +325SB77KUgfElUg4wyb9BTelHkpGQ4T095Jww+vbTr5Srgeml5OLPlIk3LE4 +cfqRdT0EsX0u+bmF0H+7sd37Yz2IfYiKF1vcAPIWg+E/xg2Qsvmi9d0/G2Bz +5zUWdLcBZPx2727v2gCZlwn5YUkNcMDgy8dwfAP8ySyjvWMNoDXT27j6iODb +coVV3o1w/ZAcW5foBqTr6x1k82kCN7Yv7zz5NoDf8XSYV3wT3G3TPi3AvAHx +h+Neun5qglCPK091f6+D6iHxtJXJJsj4lCRSlLcO9vK2abXyVMgP3P/NOHUd +5tTjq7KPUKHYtOTS39h1UB+5W2J5igq1810pu33XIcI9SZ3bmgp/Dm1ViDm1 +DlKb212GwqkwzZZGVTyyDgG8bZpCz6nAaFO+Xb93HVjzRX/yp1KB7GlUxLJp +HYpE9bhdvlBBpjD8hFvXGsxtKuSoH6CCgwrreQPXNWAo3m67IkuDm+xRS2O2 +ayBDnawMPEADz/ZdiUGma2Dj8YzD+wgNgjzRwHe1NWgVLx9r1aFBWuHd6/Js +ayBqP7P77hUaZAdReKsXV2FC/X6IijMNCs3ic+3GVqFj81fWajcaVC58mk9o +WoW5zpxX1+/RYERl5h4lYRWmH0dalcTSYILdX+Jt2Co4Mye/kk+kwVw7bwV2 +bxW+LcYHur2hAauXPKe3/SpoxezzDMqkAbf21yzB86ugJ5yx1TSXBkJbTxvk +6K5CGFNL+GoBDaQ+O0TTFVah6MGq2M/vNJAPXlB5sGsVrDbfruMspYHy+cDO +HUKr4G/7yEW4kgZai8lipksrYPVX7UtpAw3sDveml5WtQIjplhHLLhpcTT9s +durzChSEK4Uo9dLASSSSpSZjBbTK/02N9dPAdUXzUmPkClD3KHStj9DgtvNL +rnOBKyAVY1ljOUrks2ehqMWbsG8Xqxc/RgNfeC/Yab0COFd4b9EUDe4psvy4 +YEzwv3NGidM0ePDG6mbvqRVI+q0hbTtLg0CBwu2X1VaA9Q6EcM7RIOQhX83Q +vhXoGOv4EDNPg8dzjp5XdxH+duyqYFmkwZMrpZJ/hFZgtaV63YRBg8j27bTr +5BVQXY0OfbREg2htD7+plWUwD/0d92aZBnFFjXtv/V0GYfPvpi9XaJAgK9P5 +b3AZyq1yZ31XafAy4X6QZ/syuEotJWJrNEji6jq4VLMMExquD0YJTvFVHvD5 +TnDyU6r7OtEfk+FP1nOXwUbYvWCE4IxLv4/eT10G1pBey6MbNPjQhP1hiV8G +eZND0x4E52IJsUGPCU4JTIohuCDvnybl3jKYpAXEJRD8WeLszGO3ZRD/FUEK +JLg4Ku0V79Vl0EEf2U0J/s5K0ou0WIb6p0mtnATjHhZLgmeXIcC5ODqN2L+M +np8WixHyIP5bMgRXnuc2EVFeBu6yy1ERhP811VeYEvcsg/v5HdJ9RLz1RyBb +bDvh77CdgRDBTRnCVm94l0E5mHxUkchP83Y3ihTzMoSNR/IfJPLXFlZXmDa/ +BBHGRxmiRH471qTsZf8sgWPivMgUUY++vp8lCtQlmDaZfX+KqNeg4QHnvLIl +sPfNvNr4jwb0H6Eiyp+XIKDPflmDqPdEiob7kVdL4CxTirUR/fFXKG7Xt8gl +4NbNRWsTNJgNnG48FrgE5XTlbJ5xGjAcUmS1nJdAVKfYZZROg5WO1fZK6yUY +9pzn/jhMg3VdswBd4yUQfquRfXWQOE/ylD59tSUo0Pv45FEPDTZN34y2IC+B +KuIt/NFMnKfL1ce7VxiQqq1t39FEA+HmXX8v/WWAjfTUwc56GogVtOratzPA +9uLIj+fE+ZHzVtu4mcoA0XSK6bYvRP579OWGYhmgRRvTO/yJBmaadqbnHzFA +fn5vw9E8or95wzLRTQYI0wp4V9Np0Jnac55flQG5JaJil+KI+4hz9kGAHAOs +OhWGvj4j/HVlz2aIMmA09NEd5ic0UDy6n3WAiQH+UrlfTgcQ54Hmn5tXtwj+ +ViY/61wI/w7HdEmXLEKHFsnb3Ynop8T37Am5ixDgMiXBQdxX/Q7NVg9iFoH1 +cdb+cQsaHF6XpBhbL0L64f3H808Q9ZCrujw3uwAyFfNeVvzEeY3oCnMcWYBW +2pOdnyk0EFj4+7n75wKoRrwXWWemwbEfwrwV3xbAMDA54tw8FWLOOxXHBC2A +vft5fYFOKmgF8Age3rYAtgLmr4RfUuFNj3H5nePz4HRHYERUmApKw0rLrcrz +wLzRlNfJR4XysU2KijLzYPXnU28IBxXoi00v6Lzz0B3n5PEf8TyRE9C7bdw9 +B0lBPCe3vG+C/FNaEvu85kBqLg7z2t4E5TnK/v1Z/yBMemaLxlQD/L6/WV1b +eBa835RpxpnWAed/OX+jOGeBMd+l3qJRBwreuin9qzOwGi2luSpdB543/+O8 +OzADUqMW2lsWaoH9wkhHVsYMyAtc6nSJqQUp5U8eAhozwK1qup9OrQFbuklO +z+VpyDox362pXg3FMTInR80mwV3N2//z33JQ/NM5t/8lHeIpd61C/b+B+/Q+ +2a0BdLBSpIjwGnyDosX7F9ed6JB6/5xJ4o5vcJxdrrJelQ7V5Q+fdxZ/BSPJ +u3HXWkeg2OBjZv98MXhc3KaWwjUCd/nWhZxvfoFimuW9LXeHICPkxZee64Ww +3pH9cc1mCPpfxb6yUC+EE/3Mo8PaQ/CEyZpznLsQ6qYyDD9uHoIOFZE/Btmf +oJtrZZdh3iD0Rg8v7J0tgI2TL8ofjQ6Ao8u3iXt+H0GruIuyZtYPr1weG6pn +5UJ2xtsjVUf7YdjR+egN31wQfuFyLVK8H9xe7G+s0MuF9kX2Z2da+0Ds9Y2/ +fV05IO1jxv9yuRfMVctibthnQ+n9eW5Muwcc87mG2IMyYfXJQfag/k6In3E/ +kyuQBlSXqivbMjrBrHw7hQJvIcXwQkX27U5g/y/sccv1t3Ba4GHAT/ZOUA9+ +bFdamQrPY5qZZfd1AKc66+49D1JAJfHWRt2ddvAskN3Cw/8GXN/nMDYJtsBV +8N1bIf4cFHlvPjzR3wyXVBTq1FPiYcZNnvf2h2YwrLMU+Lo7HtzU30u2ajeD +kaGmdItiHHg0JevH+tLApl1fNO1cDPwb26t7qL4JejZcbe5WRYJ7Qfql2KtN +YHguw1HjQiQs/CftvkhqgpXcxiGp6Qhg8O98/eVQI1w4etDDcUcErKoIzGu8 +Jt7T/urUjHKFA/tDRtIptxporajLNt0VDMF6HoXvuGvAjOeOhZBLEPEeN1tH +flcNU73PaMYQCJzvxxdqu6pgG8u6ia1DAPA19eoZnKyE+5Y9h4Tb70NE/AXb +3L4K6N1xmKyqeh8EbDu8Nt2tgMZoEZXZRH8Qmqclt2SXQ9ZjjxcPu/1AeHsF +47xwGYQereA6cfkuPB8+zvslvxROiE8KNhrcgW3ZJZLbzpZC8uX+4O+a3rDj +eJF+9/0f4HpsLrT7qCdoNprp/mgHeJs+xJpzww1OXTZ0f8gFoC3ZyDoefAt0 +5nRfn8RKYPDP0aaP71xBb5vGfM37byDz8ZLp2t8bYHZV8k2z7xewVODVm/7s +AKG3boc8+1QEbQsmFy3PXoXvvmUuRlOfISPrwFD+pD1IRdkda7YuhKB3Q3F6 +BrZg/uqj9LP4T8B6UfX3C/7L8Pg9C48RrQDUxJ+1jX+xhllI6aKd+AgmhmJ/ +q/ZdgN11/0ojffLhRLp6C5liARbtmhnnCvJALLkOj1g2A3xiyJsmnQt6UdIe +yeLGMPrXAZf4TsxFssFex03PgQE7+WmywgdIetYwnYIZgNhBHfnkTRnAEbic +1flPBwJ1R5d3PUwHzMPt5qZNp2DCOqTmzVwa9O92POx2QROMPWXid119C/3b +PshytWBQHFZ99c3PFPAOj+lv/asOu1IcD+3STQbe6G2+atGqEPKFzPqmOAl2 +yujEW0cpQ+/rc2+Pm7+CA6g4z3JSET7UR544fvQFFNcMP/fX2gs+S7Q+TCwe +ZC7YjJ60lwbd3QL/YUwxsKea7fpuNXHYamy0DRuOhOVWuQC/sK1QtyHlcu9J +OBzbVrrDeBM/OFq8fe9nEgyO3W/K/7CxAutH6eH/thF9tPX3buGg+RJMRE9j +GfcAz6eGbOzXBkqm45/bzzy3BbW7zbdrPL6U+DJHV5xS1UWlU3J9T68Glygk +2FUJqbgglpyEs27jtJJekbwpLj5fpM72SHdkYaLE+GDHt6DjAUgJ319uprhe +Uth5/kGwTyhKs5sWiK+nAA8+LlluGYHs77a4Xf4gCCgqM6jcKwqVH15K2T+w +HW5dvf6nPDoWXeeR3VOOS0Dykb16FXnPEXnNMnKbtgy0co9nVzQmom7XJ+M+ +DxWAvT9jU+X4azRZoPd4sFgJEi0OqdkFvEHLPs5+v5+owCHNmOtDAiko20ry +zOfvatAoP59o9yYVFZz/z1NNGwGJ9GnDruQdCjtVmLhUoAXP/wgdGNZ7j/R1 +PvB539cGpRZ3W/uuDLT7ivrDrT6nwT5NucKe8QGdao/Z+vWuIaw9jV4YDspB +Ly15CslHjaBOfTkqPzQXsfMpd5VuMgH73ZYVSiL5iBzq/tqY2RwUt3P2uvXn +I8yjMkxI1BLW+IoX8t99RKWHbF9v0bOC2CURmYMqn5CcmNW0mZcNVNV3hh40 +LkKDyu6c1q+ugKP3r6oLe78gueCrTDYSDkCW6mINYClGw3aG6kc+OsJpn26/ +1o9fEXdXyS+9letQL9vn5iEEqNf5BctY5C1wbuvLeTkBaL+3+KHiIDcIwlwX +bG1xJPVC4Ebd/duwZ8L14GO1H8iMa3IhPtQDHDXdPnSNlSK38VpOJfodUH0+ +W/fXrAwZ2Xf+tuL2AfJftzGWsjLE+9CoO0aVmAYSbu+Rf1GOQnLtA7ek+MHY +jPsb3zOVaJ+xsnll331wTvKK2ZFVg2KL7St/BweD+sLixwPCtWjdRuBzkW4I +cOt5N58MqEVZMQqBJryP4MOiN99NqzqEsVpYdb8OhSn9u49KuBuQaLLNj6Kh +cCjyKynJUaGim9HO3p4ez0Bt3498w7gWFL/K3I85J8Ch1vbYkpoWZK8e1uk2 +kQCKPhN35Vdb0Nh38sqrGy9gd81WTfLlVlTtUXW61y0RBK/cbAG5NuRsOre3 +IuQVTCRun1MoaUevjohcPu36Bl5zex7iGelEhl+TUaZIGjB7bu62F+lH5r/a +N6ljuWBpk9FcpNyPjCYy6nlccyH/NKrhNuxH/XoZ7zmScsF257XCgqB+FDKj +8+UWKQ9Kq79FsM71o8ofA838ZXnwcLv9ydTGAfQuAp5RDD4C64/87KGHQ4hh +3yTt5lcIHNyG922n6Mhx8V/5qPh3eNjfrumWMonmvNS/dqgRz4kvZ254f5tE +yf4RAheNK0AtCo/1a5tEagF1hl3XK2D6ZMafUI4p9MpdYLw8sQIuZf73NOX6 +FMp+zOels07oe0p1tR78ixxL56b/QiUssR35st12GllNSZkVEe9DuS+CDP1m +Z5CYtaZAr2Ad1AkG/eYjzaKQB78jQ/bWAf1xoN8bnlmks6coWVyzDkR9A7LK +ZWbR6pfbH4Td6iDE6gGZy3oWyZdCh0RTHdjs8MPj6maR+3HaZ7fAeuB/7aGY +l/oP1XfnNUQNNMDerR5VJ/L/oYLNu4+FLTTAqaful1rhH5K/Up53nasRfO/d +Dlv89Q8ZHtxR1avcCKPWt0Y1Ns2hAspE0tOgRsDFbyTV/jeHvEXGFMalmsAl +2Z5/2Gwe8Q9l71mVpsKTO88Tn9jNI0su6+4dClTINmyUOeI6j9KDdB4dUKHC +1Prh408eEXKpxw4Kp6jgfIHLTfXbPMolhbv5XKGCk1B+S9iuBZSwzn1O7w0V +Qsfp1ocVFpD3bFzU/XQqZJRunxhQW0D1vtiBdzlU+OMayHrYZAHFOxQLlH2n +gmOD+aGBoAVUGax+R414v74atBF7aGIBTXSblvLx0CDoorJkP2MBMYIkRjQE +iXlU+VpOKNsimjZ69c5ShAYjg81VfWKLqFyIP95amgb2KI3x6NwiEpbOmI9S +p0HAlq4A5UuLaLT9y8hBYh5IneTb1Oe0iFyL7oT+0KbB0Is7ssoBi2isK+XO +WyMa2DL0LHsLF1HR0a6EMAdivmm6Tw8pW0RJzF97Yp1pkJxW6HaQuogi1LT6 +w2/RYMBE/HHIn0WUX/Yq7bgP8V6V9++rkigDMXxTS76F0+CSU8KO4PsMFH9Y +/+NwNjHPdVIaZ8IZKNr451p8Pg3ide/4WSUwkIwiH021kAY0GfO+Ax8ZqIgR +9VTtOw20fm9+0z1M2Bvb3Hqilph3zALPac8wUO7Wp/UGDTT4r3KOKX+Ngbh1 +nmhpU2lQ+LbFNnjLEuqWjJObb6OBrH2klJLOEuJO6mLX7Sfm5RZSW6LJEtJi +5jiURsyPtpqugRyXl9DE28G6CWK+TJQwoHffWUJC2QMph/7QQPVZSax20BKa +TgtKPEzMp21MCtr5z5aQu0uPs8QkDXgHuNODM5dQ/+gEKX+aBpmGvuazn5eQ +/BfZu2bE/KuDj5Mvli+hbwNiKkPEfDy8/8KXKuoSyro9ymtOzM/3X9deU+oh +9n9wqbdggZj3+NS2vfyzhAw1hPyWiHm72O99LcfCEsLXzKqkiXn8/JSwjxvz +Mkq6sC/qCDGvz10M2dvDu4wmDpkVKxPzfETDYpf29mU0V6S9eSsx7+/TcAjL +37OMUi8r+PYTXJvVrr5DeRm5Lo9X/u/7gquipyaDsWUUH72lYc86DVjCPr2c +1VtGoz6LV94SnLQipX/RYhn57g51pGzQQP169HrVlWXkLuaTaUxw5y+WHCW3 +ZdT6ezdbAMGep29bv/RbRul98Wf+932HQPEgH/kx4c+WUJNYgnNkjXC3uGWk +t8dm3otgvec/XHtSCHvM8iyI4FHygV06ucvI/mu60Tixf6B3Ei3/2zIyP61W +5EuwxCjfgx01hL7uBMc/wv+S8/eUQtqWUXmW62Z9gi9UTQ3ODiwjHTexgnAi +XobKpaiLU8uIW2+6MI/IT3Rag2b1MhGv5sPpL0T+DmzRmFPiWEFaZpsPphH5 +bQzMSn0puIKiOQMMPRk0cJrfbkoWX0GOa6e3yRH1SG1d/tSjuoLkU3sWjs7R +ANNyuqpzcgWpxr7PeE7Uu+dj55aP51ZQq0yd3i+iH7ZEFXmFOK0g/GDkcxai +Xz4yy8j881xB7pOjA+NjNDB0i+u4+HAF5TotGReO0uDROc8jBxNXkPmNofHp +IRo8q5dzznq/ghRr0q/tGSD6U7vvlfTnFcS/m0o90kuDXA0dVuHmFaQndcxw +5ifRL0WrKpF9K0gq8fxATCsNyg/mXeOcXEFz2W5nN9No0CG7rWmVYxWtXoak +lBoaDKY2MnluXkWJKYoreRU0mNj5UPmvxCpK4hHdmvCDBqQtE88HNFZRxKWv +txaKaCDDXGJfeXsV2fhyvPj5lgZK/7nFofuryL/O7G9mEtEfjN21RU9WEdlX +9sP5F0R8U0/3Z75fRVZ7vGSVI2jg9evy8tO+VYQdKtFneNHA33TLPsrkKvL9 +IrPzHnGfhFJrrR8sryLzE/trfjnR4FXlwQr3zWvI6vJdA76LxPnNZ4uwOLOG +RsVFXOwQDaj7ikubzdeQovKti8GHafAr/eb8matrKLH9q/F/+2kw9eqn5bH7 +a6j/OersESPq8fi9tOTnNeRL1g65ukIFcfZL5onla0iKuWydb5YKcvcFHm9u +XkNFziYXQ0apcMzLZ5pjcg0xWLRlhlupcMXu7NcJiXVkv8i+cDSTCjd7maau +KK6jEFb4bJhEBW+LQvE+jXVULms3pBhDhTCDnUE083WkqsX+/JwfFQqOzhgW +PllHwlPPFtn1qcAqFEO/t0wwjXMtsaIJBKb8eAU4NpBiVyp7dkYT7Kp2VEkV +3EAROFe3ydMmOOarHlQtv4Fyv7r+tT7fBHeGh6Q3WW8gzOR6h/5gI0wVKF1J +LttAVB6WnLjBBlh7IhquTN1AIe2lzx7iDcB9jf1TZfcGSs/5Mz77sgFkd/xi +HZ/fQKOKGYFm5xsgvxRrFhEiYYb7SQco5fUwITd6y/YUCfO+vDFU/LAO5rb2 +BGbqkbCi2c+yuy3qYIW1+fmcEQkL2b/33PK+OuDs+/ojyJqEdVB8PrW21cKe +qKebMr0J/UM7uTaJ1YKCf4D0nB8JiwigrD+YqgGVG3eOaASSsOmH2VKnS2pA +S9vuclMkCVON219Sd6EGbFdU8v5lkDDFn6PNR59Uw7XRvRXqeSRsVD5TlWFe +Da5t4p2Bn0lY7pqF1YRENdzL4WQSLidhNnvtc64VVEGiXa+heg8h70h+qNRQ +CT/rAqcD+Jiw3Beneb/QyiH62MuTpluYsOmCpI5/weVglFeQIL2DCcPtLitN +qpdDY+yQVqUcE8ZfcSOIK6UMKi8ff85xiglTDOjb8sq6FAoXV4+H+jJhSWF3 +PiYeAHB3EoqzfEis93lUMHO7BJR69k7IhRJcYTGc/vE7ZJdaxtbFEfr23yuN +936DtPCiMe6PhDwlhcNitQhiJd2jnv5hwvpx01OV8vlgEvt41HqaCfNXTVqd +18kDAUqKhuIioa8VdGmbXS48maL9prIyY5gvXj0o8QGCvuxXFxBnxvBK8932 +OW/B02B8ONqMGSOdfLr9TFYImPrYqiSUMWP+f5TwU6kZKPalEPtiDSHfseIi ++iILtUNlmzGVsCfJGjr8LBuZse714OlhxmzOCPoHnMhD5uH/PvovEOsTRKon +VT8hy9cBBxxkWTBxFWMkqvgd2ZSlySs/ZcHwE0UjamGVyJlrXKLRkhWrZsI/ +zI43o/E7xaxcl1kxx8Rs0JVuQU6jj+jaDqxY0XfGZ9dLLcihQibjx21WDGMP +3ytPbUG2964e+BTGiuFk9YDTea3I4t8ASiwh9GX/qBRfa0enujqsnCTYMGru +zJbXuZ2oQjf92DsZgpttb24b6kRaRV7iwwps2HSnt4vF5l/oeMyW4YtH2TDF +HXJ+u+78QuoGJtfPmbBhozTrly0aXUiprOmOahAbhk29aYz62o12ZlbGso+x +YYb8h41cg/uQyeuiL7XTbJhOCEdc8qc+FBqV0f1kkQ2Tef3IPGSoD835PJHY +ysaO6e3JWVXZ2Y9q9cyy94izY9xPmqsMvPuR59RIhY4ZO5bqZ3VTW3IAZQ3+ +HOW+yI4lRa0+YhweQAPtNVw0O3Zs4rX+4gO9AaQHH85Z3CLkkeQSSY8BJBHh +0XMtjB0zWYxriy4fQA0H2OZDS9mx+qxIk0NWg4h59+JWgxp2LPeS1gWfm4NI +ddsfNUEqO5Y4V1KS4D+Ikpkb/F/0sGO41MXMK6mDyLslmjuLwY6RVLzi5McG +kZSHlFSDAgc2LLX/0cObQ8inSNOY7wUHpv7n4VqI5TBSsqJOW7/hwEg9EvW7 +HIbR2IbVk9x3HJiqfXTF89vDyFLbs+ZcAQdm6Fd9YU/YMFJrT0fRDRyY8C9h +vuKvw4jxj0dehETG0rW2f6gQGkG5cQk119jJmOhN8i3TnSPI8egeh2JuMsb9 +q3++XHYEdTzAki+IkLH6+FQnzWMj6POm28KvlMhYPH5eDK6MIM/9HaySV8iY +o75uU3H2CFJosU++fZ2MJfG99znzeQTRPWdQ+S0ylktdi/gGI8i0hNPnih8Z +MzQ4IYFRR5DyWY2Zd3FkDD8eJNj4dwRNTNc8YbwkeH/EUbvFEZQabSavm0rs +r7ku1bk+goS6XRzGcskYI3rA0YGHjv45JffI1xL7mZpO88rSUQbvfp//qGTM +/PfPS5n76cg2/6twYzsZ4zfa80dGhY6al1qNXYaI9TJtflUn6Cg/hKM2b5WM +qe4T+xtlSUdO8tEOzCwUbDonwlfNho4kqOJsxhQKJuOScL/0Ch1FblXD5jZT +sIjJVHEvVzpyTXMuVNlPwcy/xi/cDqCj3qbtMbwqFKzI27sj9BEdnV2qvU1X +p2Cq5zXP+j2hIzk92QOxp4n1Q1VyK3F0FO/RwXfzHAVLMt6RF5BIRxyvg6dO +mlMw8q9otvEkOhqeGcmcv0LBOsYOmOi/pyOj7TGhDc4UjJS5dv3MBzr6oaV1 +7e1tgp0Oh0vn0dGruOTdpvcpmOOOU3tuFdER949zbPtCKBg1pOz74Fc6ujtG +GmZ9Svh7bSP+ANDReQ3rNwWJhD/ta+YOFXRUeZXXPyyFiD/J7oJ+NR0pR3y/ +ZJ9B+P+3oUegjk7MbdtFhYooGOPm75fKVDry465bHi+hYIat+5Yim+lo8tDd +zrIKCpb7I42voZWOakM6Ym+3ULDRplPvuzvoSDU/2OPMLwpWPTKrm/eLjt51 +qZhIDhDxCXb123XT0RY2utLKbwqm87HYd66HjgIUYja1TBH25nXl7froaPa8 +1nTG/P/yrbGe009Hl+//a3ywSuTrujZT1wAdUTOSP1iycGLxtUJaw4N0dKz1 +XJgSJyeW+9OgrW6IjrLWSNc5N3Fi3imvyiKH6Wj7nlzdwa2cWLp8yg6VEToK +NbSWKRbjxBzVV2aKCGbc4eV4Js2JKWpiBtvodHQ15fvINXlOjP8wh5YlwW31 +zuXHDxLs1t/rTbDWwvYUETVOrCPyvIInwfk76+7PYJxYiPk/zOh/v9fTvWtT +o03sF35Imofgp26y6I0+J2bTn/Anjdhv/UXHjjumnFh1TULiToKdK4JXDa04 +MZlb7/S8CH9/Tal0ydgR9p/uI2cT8egI07+QnDixftPonjIi3sLjMfEdrpxY +kaFGVxGRD+nrWl65XpyYq2EAXziRr+jof6YhfsT+BhCCEflkLklWtgnkxEYt +j5m2EPl2/X1OUDWMEyPfOfPwJFGPXn6mWb4ogqPldsUR9dJTy6X+fs6JYXYi +GtX/+72enXUOJHFiqqYGIx3tRD8Xfnd2yebExF31BZ8T/cDe73xG+xMnxtC/ ++kmH6BcPiqjczm//s2cr2tFA9LPV3d+NNUS8bVa3Yol+wwNlK9OoRHxS7j4V +RD/uz+lI9fvJiflbJT9oLSX6mfmwrcIIoa8ohz/7RkdfvFiM6eOEP+4cLee+ +EPWZbNJ8NUvEV+eDzX4i7HU4SvOSuDDx/W+tf2bT0e2chNHJbVyYo0WfqPJr +oh7SDp1vd3ER92GI20YCHdUnHKy9KMOFKfrxPM6KpaPdQfWZDYcINjijmhVO +5N9q/eYHQy6s+p7l+Im7dBTcXGt95TwXhgv0wA4P4rzoxBnuuMSFqfqXfP/l +QkdPDioqhV8n9j9p6rhiT0fHOW3nnYO4MP6Tqr86ztJR+ucKH/lvhD9L/pJ8 +2+jIdN8z5+FSLozqz+wqIEjUJ+XSxcQaLiw3y+oDg4uOrJ4sHuP+yYUl5bjs +vbk2gviuyDJPzHBhhhJKj9Z7iftYIDwkcw83Fo/RjCBxBEmGWNyxUyD4UK3p +YtQIoq5JO20/xI0pxjhTBB+PILk/JWcenyDk5yLz5r1HUC9M816/yI3lqvad +uWY8gk7eMImRi+LG+sMoZYIsI8j92VeSy3NuTMbcQubE0jBK/Szh/PE1N+Zf +mxpq/ncYMTPPnFDP4sbMMzKdNLqGER4bPn224n/rE2JH84jnEV555tYiN0a9 ++t2nnnieKQgeYS66wIMJe7qokF8MoYuqSTdWL/MQ99GOO9pPhlDYRY5OzJEH +owY9obncH0Lj79pyatx5sI43Z0d8HIZQurrbxa5wHszwrfSDB0pDSPJqZtE6 +8GDVOQMNhuWDSPjLDpeTUrxYv+1WF7mfA2jd7t32TXt5MXP5r5FnKgfQMO+B +6u4DvFg18+t/Rp8GUK691i53xIvFt7gnCkUNIG3+6y3JlrwY+cBglP3ZAeTp +UHSYFEmsrzv7BH3vR22bjUlf13gx8UIM1xbqQ8V4d1YQKx/G/4j/17GJXpR0 +/aqFERcfZmOwvZ61vBc5/7iT/0eYkN/28V9z60WsN5LshZX5MFf2XNHUxh6k +XD5Z7eHEh+UKTT1q8+1Gz9xCIhV/8mGYukn18U+daLk+qyikh+D5jp6ToZ3I +dg+tr3+ID5v+LMYQt+5EB7tFFCKnCXkch6sVuRONJZuOMFj5sQg+9r4/5h0o +jPv3fQsxfszwXaGs02w7auyjfN12jh+jZlrutORoRUZBBvteFvJj2GbLlnNe +dSjNYlr3yxd+jMTbLvSZrw4tyUdebftGsLesa8u7WpTU0vyap4zQV/xWfeBn +DZoUNxPwayLkS8Zng5WqUchXq8VLo/wYXhff9q6rHJVMX/shvm0Thi84WL2Y +/orkLgSYpv63CSO1yhmN87tDO52SHGUqgOUqc73YO0+DRtuR4wI7BbGQihsx +qVqDMMD6jhEjIYiNzh/TN3cdhLk0xxyR3YKYqsd32Z2JgyAyPi66a58glq5b +e4j+bxDsb88u7j8qiE2LsYhZpA7B8sOND2fPC2KOZz9ubSSPwO63ItsePRXE +ihx4n7b2/YYj2l1U7ihBTDx9MXWIZxT0/iQGR8QKYuQMqzNs6qNwa5/4fNxL +QQw7yK/qHz8K3z7tpqZlCmL+J6e3mBj9AaPKg0HlVYKYocfULteaMbjiOK+u +UyeIUQ8sq6QxxsCb8/O/ukbCfu3TuKk94/BSX+1ySxvhX46XXGHQOIy2Y+qD +Q4R+SMou8ZMTsOzN/O/Kb8KepumOUfcJ4Nle/v7PmCBmY7tJszR1ApSstbfO +zAhiuZtEVrNYJ+EkE6XRfV4QU2SSDP6uPAnmKbUBDAZhn69gb7/9JDidDDvq +u0r4+yZvRChmEv7f/6ew////qf8D5DOaVQ== + "]]}, + Annotation[#, "Charting`Private`Tag$972971#1"]& ]}, {}}, + AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], + Axes->{True, True}, + AxesLabel->{None, None}, + AxesOrigin->{0, 0}, + DisplayFunction->Identity, + Frame->{{False, False}, {False, False}}, + FrameLabel->{{None, None}, {None, None}}, + FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}}, + GridLines->{None, None}, + GridLinesStyle->Directive[ + GrayLevel[0.5, 0.4]], + ImagePadding->All, + Method->{ + "DefaultBoundaryStyle" -> Automatic, + "DefaultGraphicsInteraction" -> { + "Version" -> 1.2, "TrackMousePosition" -> {True, False}, + "Effects" -> { + "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, + "Droplines" -> { + "freeformCursorMode" -> True, + "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultMeshStyle" -> + AbsolutePointSize[6], "ScalingFunctions" -> None, + "CoordinatesToolOptions" -> {"DisplayFunction" -> ({ + (Identity[#]& )[ + Part[#, 1]], + (Identity[#]& )[ + Part[#, 2]]}& ), "CopiedValueFunction" -> ({ + (Identity[#]& )[ + Part[#, 1]], + (Identity[#]& )[ + Part[#, 2]]}& )}}, + PlotRange->{{-5, 5}, {-0.9303415734580547, 0.7156351531106733}}, + PlotRangeClipping->True, + PlotRangePadding->{{ + Scaled[0.02], + Scaled[0.02]}, { + Scaled[0.05], + Scaled[0.05]}}, + Ticks->{Automatic, Automatic}]], "Output", + CellChangeTimes->{ + 3.827398852732707*^9, 3.8273989378862534`*^9, 3.827399058504977*^9, { + 3.827399120292354*^9, 3.827399210951322*^9}, {3.82739928762567*^9, + 3.8273993001692142`*^9}, {3.827399348722337*^9, 3.8273993557907543`*^9}, { + 3.827399429923098*^9, 3.827399465958661*^9}, 3.827399568428409*^9, + 3.827399687181246*^9, {3.827400101329447*^9, 3.8274001522375298`*^9}, + 3.827400623136322*^9}, + CellLabel-> + "Out[206]=",ExpressionUUID->"8c4b66cb-8732-4825-b27e-681a4d43fbfb"] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"ComplexExpand", "[", + RowBox[{ + RowBox[{ + RowBox[{"(", + RowBox[{"1", "-", + FractionBox[ + SuperscriptBox["\[Theta]", "2"], + SuperscriptBox["\[Theta]c", "2"]]}], ")"}], + RowBox[{"(", + RowBox[{"\[Theta]", "-", + RowBox[{"0.1", " ", + SuperscriptBox["\[Theta]", "3"]}]}], ")"}], + SuperscriptBox[ + RowBox[{"(", + RowBox[{"1", "-", + SuperscriptBox["\[Theta]", "2"]}], ")"}], + RowBox[{ + RowBox[{"-", "15"}], "/", "8"}]]}], "/.", + RowBox[{"\[Theta]", "\[Rule]", + RowBox[{"\[ImaginaryI]", " ", "\[Theta]"}]}]}], "]"}]], "Input", + CellChangeTimes->{{3.827401001552004*^9, 3.827401034215644*^9}, { + 3.82740134999053*^9, 3.827401377741975*^9}}, + CellLabel-> + "In[220]:=",ExpressionUUID->"5073e95c-759c-4f6b-bccc-e97ba8930d41"], + +Cell[BoxData[ + RowBox[{"0.`", "\[VeryThinSpace]", "+", + RowBox[{"\[ImaginaryI]", " ", + RowBox[{"(", + RowBox[{ + FractionBox["\[Theta]", + SuperscriptBox[ + RowBox[{"(", + RowBox[{"1", "+", + SuperscriptBox["\[Theta]", "2"]}], ")"}], + RowBox[{"15", "/", "8"}]]], "+", + FractionBox[ + RowBox[{"0.1`", " ", + SuperscriptBox["\[Theta]", "3"]}], + SuperscriptBox[ + RowBox[{"(", + RowBox[{"1", "+", + SuperscriptBox["\[Theta]", "2"]}], ")"}], + RowBox[{"15", "/", "8"}]]], "+", + FractionBox[ + SuperscriptBox["\[Theta]", "3"], + RowBox[{ + SuperscriptBox[ + RowBox[{"(", + RowBox[{"1", "+", + SuperscriptBox["\[Theta]", "2"]}], ")"}], + RowBox[{"15", "/", "8"}]], " ", + SuperscriptBox["\[Theta]c", "2"]}]], "+", + FractionBox[ + RowBox[{"0.1`", " ", + SuperscriptBox["\[Theta]", "5"]}], + RowBox[{ + SuperscriptBox[ + RowBox[{"(", + RowBox[{"1", "+", + SuperscriptBox["\[Theta]", "2"]}], ")"}], + RowBox[{"15", "/", "8"}]], " ", + SuperscriptBox["\[Theta]c", "2"]}]]}], ")"}]}]}]], "Output", + CellChangeTimes->{{3.827401024319312*^9, 3.827401034406571*^9}, { + 3.827401359748621*^9, 3.827401377935137*^9}}, + CellLabel-> + "Out[220]=",ExpressionUUID->"9f4fcd66-9d81-45fd-8f5c-1c2cd6ec6392"] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Plot", "[", + RowBox[{ + RowBox[{"Evaluate", "@", + RowBox[{"ReIm", "[", + RowBox[{ + RowBox[{ + RowBox[{ + RowBox[{"(", + RowBox[{"1", "-", + FractionBox[ + SuperscriptBox["\[Theta]", "2"], + SuperscriptBox["\[Theta]c", "2"]]}], ")"}], + RowBox[{"(", + RowBox[{"\[Theta]", "-", + RowBox[{"0.1", " ", + SuperscriptBox["\[Theta]", "3"]}]}], ")"}], + SuperscriptBox[ + RowBox[{"(", + RowBox[{"1", "-", + SuperscriptBox["\[Theta]", "2"]}], ")"}], + RowBox[{ + RowBox[{"-", "15"}], "/", "8"}]]}], "/.", + RowBox[{"\[Theta]", "\[Rule]", + RowBox[{"\[ImaginaryI]", " ", "\[Theta]"}]}]}], "/.", + RowBox[{"\[Theta]c", "\[Rule]", "1.2"}]}], "]"}]}], ",", + RowBox[{"{", + RowBox[{"\[Theta]", ",", "0", ",", " ", "1.5"}], "}"}]}], "]"}]], "Input",\ + + CellChangeTimes->{{3.8274008254366617`*^9, 3.827400873612925*^9}, { + 3.827400910685648*^9, 3.82740098397512*^9}}, + CellLabel-> + "In[215]:=",ExpressionUUID->"b6d6ce4a-b418-42c4-a061-c998db199010"], + +Cell[BoxData[ + GraphicsBox[{{{}, {}, + TagBox[ + {RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6], Opacity[ + 1.], LineBox[CompressedData[" +1:eJxF0X0s1AEYB/Ar1Zkl2XQrb/P6S6xdq5SreW+MEtXceetyxx3pOrLyGnnp +VLq7OVdbkrc/DGNrsRhFhHNNmLkyq/NyIXfk7UQYV231PM/27Nnnv+d5vtbs ++MucnSQSKeBP/52/zvNLguIj3Uj/Ki/6sMMA4eb+333zk3Ei4iJ4scFbyCOY +4ByK1jyC4IN7e/ynrhCZ4PjypA+BhBjcIRS+CSBKwbv3JJLVcS/BfvdYgtf0 +JnBTKkdZOdgGHgm7QU1M7gQb+4q4HR494P0KTv3p8F6wrRWvRsAeALsob/Z6 +Fg7iPhtZFxTFQ+DYd3J5W84ncFFUlemByGHw0ZCJ1W3OCHhUG9jv4fcFvDx2 +6BglWAkuqE2LYTDGwISRfkBK8Ti4MSGrVlw2AVbYS8mXClVgu9whh6tF38C0 +oLGTZcWTYGWCwE0knALX00INuyXTYAq9Z6Ra8B3sriJJ3t+ewfsosYZEihrz +LL3+wDlOAy7pfyYTJ8yCM/jSRYvEOfAsy+FgKPsH+PGWZtcodx7cMue7sC9s +AfzZ3kV1xm4R/30kiiqtRHfQw9M9LZfAJ0I0NSYVaF6uz7Cr2TL4IVd/Y4cU +3WrB0mlMtODm7Tw9RzG6v8FbIzJeAXdbcWXCQvT9puCKCYOf4Aibr8xwEXqz +kWrmRF4F39VTf3yaiabY0Vj2pDVwMp++YpCKNj8VLSfS0e1bt154ZaANRKJz +adno0tquJ+pHaNnMcWf5c7RJlFGS4C262dHCv6INzVx2tGxtR1dn+8hWutBn +yzMo0X1otnK20WsUTa5cz2eOo+t45GtpKvTqpg25fhqdbxrGsF5AU1UxTq5L +aEXNHV2IFm1Jk1QVrKE7SWXpdevoWHldoHwTvbegxXZyC/2KIV/T6dC/AThl +OnM= + "]]}, + Annotation[#, "Charting`Private`Tag$973377#1"]& ], + TagBox[ + {RGBColor[0.880722, 0.611041, 0.142051], AbsoluteThickness[1.6], Opacity[ + 1.], LineBox[CompressedData[" +1:eJwt1nk4Vd33AHA0KCnJkCGS0ECRoYG0hEQUlVkoyZSQsUyZNSBjL5FSSb1o +QFSmREhKZioclQZ5c6dzLhV+63yf31/r+Tz73nvW2Wvtte8aF99DJ/h4eHgU +eXl46Dhl6nPNwvfoLvb/xwTXdes7lHbB6ZGAircY3/z64pWsdAC0muTzLmFk +lBskeSs5wYSU5cETGGPE2auOKPnAhcrQLYDxdcu+scNKkfDwuMYOQjESfG8E +vzJXSoFWlWS1aIUUaEhKqt6vlA8rys40ia7OhwUL/fl/eD2ApBcbai33PQCT +c8fiH1tXgXfhOp/0NVVQdfbEUGFnHZzYXTOqbFsHg/YnVf1DGkGp9FKG1uwL +EN6b7Nag1wJT9/mCTwc2w/KeE2XbHF7DsH16hIFIG6yV874X79IBjbrzH2iE +vYHtQ6de707vBIbYf0rvd7+Dht9RZj253UB+sxg/39kJHvWtrXUxvWCk+bq2 +c0s35BwvkhI72g9at4balUJ6YJPtKDV7YhBYB1drn2nohWG2+Vs9kw/wY3S2 +xJvoA9aIpJq41RCYq+jrpvEMQGpxqLuNzQhMlm7Z3jR/EJSEFu0/k0uAWuFz +gTefB6HSL6o45foo1Anf6ZdueA89ihn8B9M/Aa/sXzH1iA+gENu93jHnM8g9 +MQz6qfURdliMaF7P/QKJ0kLZkoMfYcgvfldy0hgkVsxYybkMQdkOu6Uv076C +qqdlIHwbAnHrlsG78d9AptHAXdR6GOATT9qLwO8gtfyWqGjVMOSIeyxVOvMD +GtzznMxERyAm3zNRy2scXP028JFHR+Da2+zmFL+fIC1t/Lz13ghE+GQwZPwn +wOPJwOrhbyPw89h6CTuX/2BacPCG+FICLs2Mzx92+wVJ1aYPbyoQ8Gxi7+Qy ++0mwtXnvELKNgD7F7Z+0FRgQriw/z3gvAV86vQ30lBjQd6Z6XyKaFVFwe896 +BqjV7nFrRgv1CbhbqDCg6WyMpKExAcYJQz9PaDKgwZrhr2uCv/81hkw1ZEDv +Dfn5600JuF70ZtE3VwZ4LEpTHzpAgMeG46oZhQxoO1av225FgKxAxvegIgbw +R4rmzqC7x18U2N5jAHUnum+zNQG7SuRFZUsZ4Prg87dUtIjqp6m7FQwI84wJ +PmxDQJ3msRd1jQzY+p1r0WVLgKies9X4KAO2HZH1qHIgMC+HsN2yTEjIcj4r +f4yA5nSxVjM5JtTV2Zmbo9vfdojayjMh6NMUbzh6wMjwvo8SE+5l+M30oBlb +N43mbmaCf/B+83gXzHflnBG1iwmid8d8Ro4TENp/c0WxMxPsVHxlQt0I0LAd +vydawAQ5q29y+08SQLRePzBzkwkftj038EUn7bBij91mwrLLhaZp6K9Sz3dW +3WVC70C7QC/66lBWh91DJhSGChk7eBPAd3w3mV/PBL55Lm0upwh4dypbb8Mw +EyTClPY7+RLgHWvUryvNAuOT79QFAgiYutj5bZUMC3IqlEMU0fHpR6b+yLJA +6m77bT10foG/5DN5FvxVFKoJRr+rz3fYupEFps8+fRhFa/ylRjbvYMEjG4mf +5YEE/A4s+r7ahgXzeGJy9gYTkBCuPj1rywKRXxYyR9EicbWLh+1Z4Gr6/tIZ +tEpG98Y8JxaU9ZlsuId2ejTnLeHGgkMjg26LQ7Ae/9kwlwexYEvnNeol+rzb +ot+8GSxYbDhaqXqWgBOvZPIXZ2F+P1Jj9qL1VTT0hf9hgXLf0FZn9B+m40W5 +XBY48ibapaB9Isql4BYLnJk553+irTKddMLLWSDZ0pZTEEqA/IuKcKqbBY03 +o779DSNgTqFNbraXBcsSLEeFwwn4mDjStGCABTVOIS+V0Ff2CywV+8gCnufD +ZhboxYPO1zS+sKD71W27m2jGpECdHwfz4YkO1o8goFbm2Ny4KBskW3kkAiIJ +0Ht8+k+HOBvW2fHujEM3mcVwKyTY4BkTeyAL3R52azJyFRssArWgCv1xcGxk +hQIbRIe9LX6j/2Z5PdfWYEN0+AKdiHME6CwLjL54kA1TDHZwcBT2e2FchO9h +NsxLKIqMR+vrZp21tGLDro2rgjPR+7wrT8vaseFKhq9mGdq+bepY2VE2VDe8 +nZxAhyZE6L/3ZUOg+qinczQBT2cT5m1MYYP0WeX722MISGGuydiWyoZfjmP9 +RmiXLzXye9LZoDvJnLREC7Sxdh+9woZsK/WffugjWU5RV/LZUNKVI3QXPau8 +dYbvARsOpOhJicQSYGg3Rn3oYENISF/iR7SEWVTCj042OCp6p39HT+ySFud2 +s0Fd42USB52lcFBrxQAbKgx/WQjG4fmYrAkwJthwU9hKQgd9ISGTUcFgw6Xz +KqVZ6LflBuPJwhzgK2nVgXgCYnQrxtJEOODeuEXRBL21RWE0S4wD7U57eA6j +898vGLgmyQHdY5mX3NCneFtflq7hQLb7ODcJLWhuVvBmCwcCXVXV+tH7xi1t +lx7iQL3vEtdjCfh+AS8PC1tyYMCfzPJEl81omYtZc0BerOnZabSU8EojGXsO +5HlqDUWjf2wb1NjkwoGlXf4JBejz8Y5C+/05UJF43X8Y/VLOrTkpnQPxf9ex +DyQSIDfSKemTyYGn5nvkrdCh13RPmV/hgM29GSMHtJqUmOiKqxyIen/ktDs6 +T6Tp2D8FHHgdfnPfOXTgQvmZgoccsIsvFitFdzQlW8SW4fs0jBWUoTfGTt9y +reDAGWdVhSdoYu7dvnVPOHAzYOmSRrTZ9LnsknoOMHVrXQbQChNDGlVvOdAj +qaDHe56Ac/+aJGa/44ByRLHaQvR7j8fvz3Zx4J/G8pVL0KljSdE7+ziQwnV5 +JYr+O6zT0TDEgbUH56rXoXs6c7zaJzgQYLf7iyk6rsqqYFSAhLUVX/2S0Wqd +pud/CpKgNJ6bmob+ML7bl1xGQvS19Xey0Oqym3UXi5AQenK87Bp6JG7hoJo0 +rh/9e7gUrX2oanmUMgmbo8ur29BfT5ZyL2wioXSqa+dbdFr8reEMVRIe81hU +dKK/P7lcUqRBwt2W2IQBdNZqD+MOHRKMkp48GUMzJiSiZM1I0OCLdJhF5y0U +cl9/gIS4h/uNeC8QsFduwQF1C7TrzLr56PzDTGkjSxIOza56txht+uxV1akj +JHRJ6FaIou8khk7WeJNgcoLqWo8+VODX1+xDgttcjKoyeuaZW+07PxJuXPKJ +3YS2/HXo0pdAErqro4XV0bxWyusEI0gwj/Nv0UYfkf/o5JBMwpIG/YJ96Pt+ +b67pXyZBUMjL1oz+fH3dxw1puC4XsugA/XyHAvupTBJqTRwOH0QzMt2ss/JI +YByfyrRB63+2yQrPJ6E39reIHTpri0nP8RskDBaIJNmjtd8qH1K/TULknlvu +jug4fub+jmISqq9+andB91l9SqosJaFeZa+YK3rD7e7X1x7g963Y1ifQb/Uq +TbzLSfh7QbvZHS0RGrZncTUJWlUqVt5or1bvOEYNCQkWwR6n0LXiTo39dVjf +s9uCfNAu5Xq777zA+u/dHuaHLplYoGvQRkLGl8EdgehZbW7YxnYSLsokSAah +D174/kz4LQlr9AZZtCnF19uJThICn19KD0EbB9aEtHSTsKOfsj2Dzn1RWnm/ +l4RiEznJs2g951TNiEES2rNfJoSi00ujA1w/kLBAer9mGHrsj3+Z6RAJ0wb/ +fqB9MdtKTWqUhJBnf1dGoD9+NfLl/UyCwtWZEtqqWtvvf/+C9TT8qRN5gT4P +UipV30mYmX977zm0kpzgyfxx7J+c0CbaZ31m7sVPkOBCWepEoWWXEOssGSTw +/1JeGY32s+t002FhP3E0wmk3Fr0olOeQUHTV+gNtD8PCtUwu5h/Hdz4G/Sz9 +isvANPbzmn96aS8dTSyo/0PC5DJHmVj0UbyE78yQcJRj50y7LMJrdcocCeeD +MnJpz293cAripWCpplAXbWup/deOzKNgR0cXXxz6rseujwYLKOB+/ryJ9p9K +VWllfgo+Chofpr05j3q5aDEFccIB/rSPRtf6fRWgINZJM4l2ulucdJMgBWOa +aTdoN5maNhcsoyC9O+UBbUptxelzyykwCFF/Snu9+KC04woKkuyja2nb/7ne +rC1KQf/jqBraSYTbaQlxCrzqtSpp173ctIpaSYF7ceG/tBn/cpq7JSl4Xdyb +Q1s+tfr0I2kKPBhtsbQtg2JWXZahgH3nogftBHuTFu/VFPD9kTSm/QSW++9b +QwGPeKQ87XGF/lXr11Kwc3UNl96fVQL5LQsUKfiqM9hC+8Ckq/9nJQqWXH6f +TjuqR1mmYT0FV3e8tP3ffj9lteRvxPzs8yVpf8l/6h+uQoH8spP/q5d4XJSM +/WZc91VLom3subd1mxoFj66wdWmXaPTKsDUoqE1JTKfrPyyR1/pOiwJmvIsW +7eWzLgH3t1EgkmreTfdTYCuj1VOHgt8rAnlo3ymtCtirS4FPwePLdP8NpEfK +KgIF231kpGjvdBQMJPQp0O8PkKP710e/W7bOkIJLZ7zz6P6+se7qq1wjCna5 +XBehPZ+1brXNPgo28LWy6fPRnmDQ9uYgBZZFD8Lo8zV7UiCo+DAFVW8WdNHn +T+1g5+oLVhQE/1e7lnamtHOQoR26zf1pMD3vHobKVR/FfnNRvh+ATsna/Trb +hYILr6QIf/Tz0EXBwa4UiNlmLKWtsOfK6y0eFKg4aDjQ82Ji8FHwXV8K7lyt +bKDnTfi8H+1ZkRQM+fI8p+fVrIH2krwoXH+nnnUcHR13yeRmDAVFQ5En6PmW +sGBz8/0ECjI3hnOd0Zf5A+pbUnD/tStG6fl4c8nMo+l8Cs+7dY85/XyzA4y5 +GxQUx7Md6flblHR988JbFHCuLv5Mz+eSpfrFK4ooaGt8MmKCrhRKvK38gILB +ueZbBuhXIsL/ONZT4Ml56rAVbWbp0nu8gYKylYXXNel5mlku4tVIQZOm2wh9 +P3SJWacGt1Agpxl9SJWePytzL1zuwPrnPeWn7xuGtGJ4wwgF20CpXILuJ4Ud +xxR5uFCvPa3JxftNLyeeu4iPC9p3oxRItOeyruSJeVx44sknzEbXTHk9K+fn +wia/haO/0C5v8kT0hbjA7L3o+BV9P5in2UmWC4rbD7b3oI1etWzM3smFbxd7 +8h+gQ3ysOQJnuXh/1PA6oVdtdW1VCuPCbNYsjwP6+czpPP0ILrwUfTVjgxZI +TjYMjeZCdbgg4yA6v7gp88cFLryOHKvag27+rq7VepULz4ncQRW06HGh4Pga +Lhw3OnVxGv+/PN0os6+gjgvF09J7KLQTa6Ns7XMu5Az+nWGh70YbNXOauPCg +zNNrAq1zI0Lc9Q0Xzhqc2zyCdhn6Wak/zAVLv6UeTWj+wumLTgQXTv7VX9SA +LvHmdw79xIUTI3/u1KKpP/L8ZV+5kHFtCVGJvihlb7NmkgsrpDbvvodW/eSu +rMvkQnvy4r5CdM+9oDlbNu7/3GXPm2jZHWlFqVwuJMQ+SspFN/JcDyuZ5sL3 +Y9arstEerSXmrX+4UND/9N9MtGDqs7VfZnC9idiWhn5k08qdm+NCCv+7xmT0 +/wFEcWjd + "]]}, + Annotation[#, "Charting`Private`Tag$973377#2"]& ]}, {}}, + AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], + Axes->{True, True}, + AxesLabel->{None, None}, + AxesOrigin->{0, 0}, + DisplayFunction->Identity, + Frame->{{False, False}, {False, False}}, + FrameLabel->{{None, None}, {None, None}}, + FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}}, + GridLines->{None, None}, + GridLinesStyle->Directive[ + GrayLevel[0.5, 0.4]], + ImagePadding->All, + Method->{ + "DefaultBoundaryStyle" -> Automatic, + "DefaultGraphicsInteraction" -> { + "Version" -> 1.2, "TrackMousePosition" -> {True, False}, + "Effects" -> { + "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, + "Droplines" -> { + "freeformCursorMode" -> True, + "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultMeshStyle" -> + AbsolutePointSize[6], "ScalingFunctions" -> None, + "CoordinatesToolOptions" -> {"DisplayFunction" -> ({ + (Identity[#]& )[ + Part[#, 1]], + (Identity[#]& )[ + Part[#, 2]]}& ), "CopiedValueFunction" -> ({ + (Identity[#]& )[ + Part[#, 1]], + (Identity[#]& )[ + Part[#, 2]]}& )}}, + PlotRange->{{0, 1.5}, {0., 0.516786928298488}}, + PlotRangeClipping->True, + PlotRangePadding->{{ + Scaled[0.02], + Scaled[0.02]}, { + Scaled[0.05], + Scaled[0.05]}}, + Ticks->{Automatic, Automatic}]], "Output", + CellChangeTimes->{{3.8274008521440563`*^9, 3.8274008740375223`*^9}, { + 3.82740092116224*^9, 3.827400984185636*^9}}, + CellLabel-> + "Out[215]=",ExpressionUUID->"347ea2ac-e790-455e-97dd-2b0a927b9cd9"] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Plot", "[", + RowBox[{ + RowBox[{ + RowBox[{ + FractionBox["1", + RowBox[{"(", + RowBox[{"x", "-", "y"}], ")"}]], "-", + FractionBox["1", + RowBox[{"x", "+", "y"}]]}], "/.", + RowBox[{"y", "\[Rule]", "4"}]}], ",", + RowBox[{"{", + RowBox[{"x", ",", + RowBox[{"-", "10"}], ",", "10"}], "}"}]}], "]"}]], "Input", + CellChangeTimes->{{3.827398577188295*^9, 3.827398615524055*^9}}, + CellLabel-> + "In[145]:=",ExpressionUUID->"0f797cd1-c8f0-4dac-9564-88a85f1a227a"], + +Cell[BoxData[ + GraphicsBox[{{{}, {}, + TagBox[ + {RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6], Opacity[ + 1.], LineBox[CompressedData[" +1:eJwVymc8FQwbgPETlYp6c7Z5VhQSIZRxW0VLHiUlhETJqoQipEI7xPNQ4kFl +NKSMzDvH3jlGOTaZGZlF5X3fD9fv/+ViOXiYnxYgEAjv/tf/vTp0cHp5mYP/ +TLP0QuxzYdCPOsf/xUFYZt187pILphu7F3J+ctDkKHV77cVcYO70/O0xw8Ff +gx8aNofkQsntiDU9gxyUnxN+zkzPhTXb2qSxjoOz/N4cyflceORltz/oMQeH +xjKunXz4AdJXXEwmaHDwsFT0uFxbHmgeTlsdo8rBxQ/hwW/68qA8uffMdmUO +pkm8nNaeyIMeYzNFBzkOqpwxCvZYlQ/U+4rZXAkO9jAMVNXU8iFYfLgihMDB +kB8FcQaR+XBM1WZMpJqNbiuvv0i3LIBVp41VxGzY6DTaZByxVAhNttstx46z +seq9PNdpTRE8PSbhX3iUjYp5QQJGlCJQPzBZZm/Gxk87vkzQlYrASfXv42mG +bHQ2OuuqeKoIKlcMBWnJs9HMp/vBmroiuPs0pMFmgYXV/JFz5S+KgfS5zDUx +nIUhQxZTxYUIqPBv2I37LJzc8WRZrwzBNdA/2ekOC7cEnL5UUYtQLqvaIX+T +hXaaXmkDfIQrlxL2v/Nl4VxISYvdIkIf0U++9CQLm2OTOKc1P0LmQeXhr4os +fM9KqSzP/Qjm3NhTctVMpCxKHzpcWwKbmge6KsqZuEbmQT27tQTmB7ZZOXGZ +uFL1Y+RidwnErOaaJRUw8fDK31TuTAn07B3TkXrDxGifnWIfJLjg1qhFF33E +xGqX/SsN3LgQ1tlR+8OGieaJgfFEWin4Teq4Puxn4Mw9nRajsDJ4Yq8xrNfJ +QNrwC/dXkWVQwFN2/N7KwDmHyG5GfBn8yeFYm1czcD7Q3JedXQbBQWsPkN8y +UPz61Y74gTK4Ldqi8E8AAyXdJs6GGJZDrKrrWLwYA/21rpTYrq2A/Gennc1I +DPTo2mkoQa2ADtrJfsJ6BtpOD+/pZ1eA9K+/+PYEBoa43SJGa1dAYqlGDWdI +Gs2z7tiFeVZAqoVg+ov30hjnWG71qr0Ccn1iXd4cksYLNQ3XXHIrge14/tln +E2kckEreMlJRCffMTHpWGPzvf3SwxKetEhzk5i2OqEnj6GvVrWXzlSDM/0v/ +J10ab3P7vDnqVWCru5Zu2CeFXW9bnQVzq0BwlW9Zq5cUljZrCglVVYP7d1MC +wV0KrzrS1LPaq+Fzp4yWnLMUvuzenuL9rRpeZvMy/I5LYeWfgnrVjTVw9IzS +E6auFMpZmQXGHquBlJrBCy5CUmhi3UbaMV4DphEWzD8xkljq0XL8tmwdXFH5 +z17jSEkMapzacm1XHTxvqjz/8K4kBqRopd43rYM/RG0uO1ASf96gm09418Gr +SLaTsaMkkuPeOpdW1oFI1GT6w22SmFaoWzPuWQ/Vf9/S4HAlcN/kZdrx5gaY +1zC0cy2QQL58SoDXWAOwP/8Ky8qSwOyE/BmLFY1whe7ZbpwigSK35D/m0BtB +LuboVdd7EmhAskjbbNIIYbEcbpalBCaOb7dsSG0E47hCU5Nv4vhYJUmbcPkT +TN3r+LVyUBytr3iqxdz8BLEBS2kfu8Ux4i3XXT/iE3w7uVNIiyeOEvFAxfRP +EMHOKlbME8cBTRnFy92foOvFS2VSmDjOq2/fMbO3CbwzHxO7OOJYmG7f3a7A +A2ZSHsZKieNBLxGpqF08qIr84m5JE8dk6PZ32MsDyUu0msZ14jjrka2q4cyD +Eo3I69zvYjjooBVam8SDDYW3Z1OKxbCvSmBPJbMZnldcbr14QgwfaXtoyii0 +QIyKt2HqETGMFz4XtE63Be7GXcjoOiiGybS7N0T+aoELF8/d3qsnhi1HUtHZ +pwV0GDa6DBkxtB3iKQaXtUCzt97z6gk6hj4+FBXs3AoCskLerGA6fvO4pFBQ +2gZzDwX7j/rRsSlUTLaU3wbDS8uH7nrRsVtpwXd6ug3qP/2QW3Cio1ffqqdc +1meIuTraWbufjqeLlJ0Nrn0G5Za63b4UOurY3dmyzuQL2N54RGlIoaFIZtbZ +uoV2qId5Id9EGtb1qPqFEPkAS5aLzCc0dKuK8nFT5APzgkT3hQc03GBduaLi +FB/6TiamUL1pKFRc6JzVxAcnrQwtW0MaOiomK49/6IDWedFtQjo0HKVzCora +OsA48yIzQ52Gh+UK1MrnOmCLnMYqAXkaRr/s3npZpRNGqUX1zzbS8MS4n3Pg +605wn66xH++kovdWoatRb7ug65Xikeg2Kr7nar1az+uCQ2cf7IFPVLz8QLC0 +bLYLlHvMFcJLqShZ/dX7h2Y3TNd9mVVLp2Jf12FD/9Ju8E4dCvX3peI6mQMv +j3j1QICd4GthEhXDRezONmb1QkaD8f1mESq6OfAejVT3Qp/uXfe41VSclrDa +pdTTC3ukKEpKixQ8vzOQaSDcBxvaZTPMeynYJ7OOHH2qD54e3pcZ84aCgfPx +gf5S/dBYcj/CIZWClq/fhift6AcBFd4FhSQK7tvxfppg2g9OG61VC6MpOBvi +7Gsf2A/b6tze91ylYPr5cNn6gX4o3hOevfkABd+n5xFW5w/AdFZL9NRuCiqf +b9OYaB2ATTLiPh+Agv9mymaIzQxAmGCSxn5VCrZV7VXQ3foVzPB9rrs4BZ3U +Gws///sVenZ+zssaJmO6ZoKy3uNBIKZKPg7oI6NITeJgW/4gGNHt/Yw7yBja +1mlY2jEIKfMjWl8ayJizqYSawBgCz3dLBb+yyah8qO/urdQhICgyig1vktFf +ZcjMuWEY/Kn6tjcDyLhpXFRf9+cwLCw7/C73IeOV3107ojgjMNH0XGufCxll +ouJO1F4eAb7vtlyzQ2QMFpxfTtw6CtmlOm9txMg4MeLzTe/1GKi8PmkWTySj +0aRXxv7eMXj197XJHmEy2lD23RWgfINklzJFxz8knEoQUQoO+AYRGw+mufST +MCczu1zRahzcrK2TfF6RUDu1YvqtxiQM7w4w+PCchG5OG3MO+EyCo1JC72I8 +CSutnjm35kyClcAAIyCChPr33vG/Sk2BScq5Jzd8SNjkZfl4/MUUlIbf0yr3 +JGF0Fe9jac0UgN+bdiEXEtpMnM+Rn5oCddMZ+h1rEqrze4Mydn2HTbNXosL1 +SbjumMIHobbvkND5RI23i4SR0Xvbc5e/g0RFEY+sRkLB0DeJVLlpIMYKEP+R +JeH6hx0BI1enYRlu338qTEKw2MpyV56B9jsxoektRIyPSE4IL5wFXhnzpV0D +EZ90rFaumZyF2uUXjZQqIo5yZIVH2HNQdDFbLKiAiOXNVwxH78xB4gle+pEk +IobUe4znn52Hx1FWjWvjiGjuGp7WkDQPjxp6Z4uiici36Nde7pqHEMMpHbnb +RHQJ1eU3HVsAF4X1jb89iSgdwXXbfeIHnDr9aDbThYhIYu1Xiv8B1vESYmcc +iRhWV0sPGvgBpiR5hyZLIkr9Usu9fvEnqCztmX2uS0TDie5N55IXQWFHPd1a +k4hG2xOKemcXYZOHhY6oChGDNV1ObzZeAmr/qRA/GSK2GiwFnvy+BEvVQXQz +ESJuSfylec72N8yuXKOzajURWdohCrrFv2FC94F93rIo+sYufPRi/4GezLi0 +TTOiqC+s6XR26g+UxuZp//wiikJW+VFPjxL0Cpv17V/zRLF5e2Tgz3CCXvaG +qpun6kTRZM07odl6gl5KcFt9HYrimxTXvvWmK/TOxKrvMXolinvPThYTZAT0 +/guRtpIO + "]], LineBox[CompressedData[" +1:eJw12Hk0Vd/7B/DrXq7ruhkbDKmEjE3G0nCOzKVBRCiE1EdlCimkIlRKMkUq +Q2QoQySpPCdTGSIzmc695nmep+/5/fH766zXOnudvdbez/vZex1xG6ezl8kk +EsmZjUT6v2fqOfUft1IZ2I8wWwP3o+xYr+qkL1cMAzuxrz8hupuCjVDv7UwK +ZmBjufYNP2Io2EwTTynqy8Aij/ix8RtTMPZbCnRPOwbmYvWEp7uKjEl+uRLe +t4eBzVWfb2luYMMUAudUH4gzsNKSwy/or9gwZdOHrWIbGZhja05tuQ0bpjWf +sO3cIjfWY7pfIGuOhNmqdaYUF3NjOWyKWRF7SJh9ipqJzhdu7L2Sl+pPMglz +EA6llKdxY27+8q8aM9fBeVnTsjqUG3tnI3h0N30dvCFVsNWKG0v2nL0xXb8K +vvsoPy2MuDGbIa/YW49X4UH8BcdOHW5sz4AMxe/YKgT58ZZ37+bGnCnhK+t5 +KxCu6353bJmOuUHWZuusZYjKr5Z3GadjERu2VfS7LEOMrEzrNIuOXdE6L5So +vAxx3G1Ki+V0LIb/1ErojyX4WIMOUl7SsWMCW186ty9CmSnDWFiZjg14Pzfn +11uA8t+X2WKl6ViiwhtbC+EFqDoIGdtE6ViFNSXqxvA81Im6ckmS6VjZ0/vT +TaHz0NXVXLjnLxf27CjT5kj/HCxcSZTVus6F5RnvkanImoXllpWmMisuLLKq +QSkqeBbW9E389Y24MOaR4cLRq7PArsDVdUqdC4sxynOXl5gF/gnHcDMaF1Ze +fHo15vUMyHmqrzu+o2GnqmejNqVMA9ZxSq47koYJXxqRqg+aBhNN23Omj2jY +Vbnsy+wO0/CAJzgdcaRhQT5WBvm7p6H1XYcp3wEaZvjwYYJUwRQE1d7Lyq7k +xEJqZJ11eydhm1pEm1QhJ0bNqu07UjUJubGp1JgsTixZy3BjUM4k4FfqLjyI +4MTuk8b1+P0mQW1NgsvIihMb1maq/JGahD65X5dmpqhY4GvM6avnBHg/bwu+ +2kvFqCqzERp2EyAwN/6lvZmKrT0L0KWdmYCjP4V4Sr9TMab6NO2kzAREmDoU +RARQsXdvT5P2fhkHLf8NgmoiVCwYa6v//nIM/g2KH01nUDHO9uen8zzGwPm0 +6n/b1zmwTxlJGO+5MXglYgWcPRyYSMDJwHaBMZjKyrrW8pEDS3Z94vP5xSjE +dxiV3NbgwMxvuT8+lDACij2KSw3KHJj0SEytR+AIlAzx79snw4E5GVh8m74+ +An3zNa/6eDgwXDRhMuPACMgJGNw0amfHfI127xKsH4ZPOlo7d99ix9JTx+tw +gWHQPClxPsiBHePWPfSoYXkIGozIz7ovsmOOE89vr/YMwZw1thitxY7ZR61b +j3wZgkNeh2upAuyY+far5xSsh6AkU/ke/oGC4ak76j5+HYRzeYJ5h+IoGCkh +RDQ9aRD6vk8NR4ZRMMnwx/saQgeBVpFlevIO4SmPnPcOg3CyR2FvgS4FSzA3 +PqGzbRCahKQ6w1hkbNcP7TuLwQPQf3/TYV0hMmYee4h56mE/0H0yx8PoZCwu +683+RLd+2OOpn4ivELlvUogVtesHD0cf+h0mG9YS0LXrlmY/UC16Wz6ksWHJ +dpfUqyn9IKn82V3gCBvG/q3ZLO1xH+jtPS1rtZcNO1EZfEPQuw+uyw22p4uz +YRznNDtjbvRB7g4xLW0qG/YPnQqnGPaB5oaHAp41JOxso3KlknAf2PQZZ3Zc +ImF3WmyDqjN6IYA5ZiNnTMJONXatLsb3Qlp70OZbOiSs9XutNhLRC1N13334 +5EkYyzrLYLN3L5B99V8GDKzDlgwpu/HjvYDsH6w13LAOcTENbcKjPVAQIaM9 +YLIKdpyrW1o0eoBm0W/LdngVMgZPbFhX6wGTHckPRMRXIW1jXsiBPT0wlSaB +GQyvQOXRH7EskR6QxbYdyvZdgY6Elpc8s93wcmjj/jspy5C9oPs+6UM3uCNs +YoylReBbLy5kSXdDETt2SKprEUg3m95s3tENfBV3zY+WLAJP9DjrvFA3fDBe +iXJ+tgi8o2/kaFzd0PPfvEDjzkXIuMdTyzPMgrPho7Q3JxYgf4HtUHI2C/YN +ts7sfT0HcQoCzWZ6LHCb2C27xX8O+CQd6sKPsSB//v7FNYc5SJ4NbGw9zAIN +qlxZ1YE5IL9z+nx/P/E9iTtR/zXMwlvyVhVdURa4XxRRT+SehU0pR7xiJ5hQ +UGvuu/nONDybNM3nT2DCWktGzqr1NJSeVXnq+poJx3DyQI/uNDS9vvKz7SUT +KsfSzuRsmgY3/l2iv0KY0M69LH4mewr21ny6RLrLhHXtVyWPBiYhUbyDbcaC +CVoFbVyrJhOwTWs/1ysxJmSkJR38dWgC4g755yUJM0HoldN/oTsmYGTLg7/5 +m5jQNE99caJhHC62ouILG5gg5WXC93ppDMjFZqL/1nAouj/LQHVHQTFSd3En +C4dIm0fXG/hGoQSpaczsxOE/TbGqq/+IHKf5B2i14cDHof0k9MYIvHAZ1XjY +gINVUDhXd9gw/BbSUbb9hcPKMyVqAD4Io5ONk48ycPjr9OuySNogzFxKVH2e +jkPiGYvSjJuDoP5G8e/rFByOC/j5N1MHQci+oac6AYfoiDqy7O4B0CH71QRG +4aAa67JeebsP3Lp/lZ96gBN547Cy1uwDEruR9C9fHDouRhfOMPpAeduyk44P +Dv7bf/qIxfVCmdpEmpknDvUJfCuOZT0w2JIhVeeIg3Nq5gK/YDdcyRi6QL2I +wz4eR79jOAvubnSz4bHAYdJVgefmRxa8UKmV3GqGg+vhVIkGXRaUl1n+1TuH +g3tNwqlIbyZMKayZ9p3EYXpIXl+lqgvKKYYre1Ac3HJTLCPtu+B8aKRg6FEc +5nyk3OZJXRCPQsbCYRwW+La//arSCV5fpO1aDhLrpSowe+RtO1iY97q3KuFA +9VuI03FtBRM7p8wuGRwCDdzz3jNaYWDgW+JLaRxom6cqae9bYEtuy5jJLmI9 +UofnKtqaway7zLdbAgfemk6D09pNRH6yjh/ejsPzlxY2WV2N4EB2zNm+DQcB +m5Zb/Hca4cLhWGuaGA4bZ2sT6jMaIOTAgO+gCA5CoqULpkL1oPGyJnpoM7Ef +PRo8Xz/VQQ/t4uj8JhxEMgolRE7WQafuO3c6YTGN/FPt92vh8KK+GCKIg2a1 +if7PphooyAqP7uPFQefSGTc/7hrQzjxuK0ZYb0b/rTZaDVnxUcZmPDgYiByZ +LU+tgnPeUik4AwcTe4n4Ou9yKEl8MqJAx+Gxy82gF59/Q9y1kJ4QLhx+eBc7 +nR37BUOTqWXzNBwkw2yP1lmVQR6pXquJE4fzb3KkXrwsBW3pv50GhJ+kUjac +rS2BvqM/LX9TcZiCxLbaY8WAiWCMag4cdlVOF4V6FcG+VvaD5wmbNWmmGeb+ +hGm3dN1+dhywkW7PWikMhsXGaRsJD4xfwXb+KIT6NXpBNgWH01RaSMKeHxB5 +MeC4MeFtSnoKCfwF4PNwmZpCxuGh/sCSuF8+9D/9tt+M8IhVUHn8TB6IP71y +kJewkYfMS3H7z2DT4SlWwYZDQfBv+/jmHIjPd+l4RFg88aqKuP4nMFft8DxF +OOgrjT2+IAvu6Z8e30K4861hksb5DHhQaIf2kXD4WBV6TONQOsQeLL72lbDX +Ym0Xui0FZFWEXUIJ6+8S8EHZkgAhbTvjSHiL0VkRtCceLH6E0s4QrlyXdPJ9 +9ho0Lx2JUSV81Swp9a5xFHB/mmLfSZg9R6rHRyQUNHSC9QQIo8IGR5awh6Dr +P2rHSXjiZbTdZLQrVMeTzdkIe5PDS3UOmCE+iZg0ifCeGNtfG1V9kcILUtUU +wp3C2WPcvMFInpPaSQZhI6WW7wEa4YjNSWqSMOG8VtMHgV4xSLtKWqM84Q3Y +sESJeRxSfUCr6xhhJCw9oORWIkJWXftpSdjF/tpgSXgyItFJv+tLOOGgvEFp +diqSnJMkmES4gTGcUVr9AanlFvSrIUzF0/jLhjORVd64qjXCsWYq6rb+2chQ +YcKEIrG+KpoR17oFcpATY7fHrxGuVpiNtY3PRTwMnpanEiaRPq/bFn5B+sOV ++JWJ/Ywe3Li/x+ArYi1T5HuPsGK9m41dWwESqOFfWUvYLlm51G7hB7KTsbLy +gKiX1ZDwuZ4AQBT8ZrpZhCsPL4V9eowh5XzJabpEvdntMi9VFC5CSmS3/ttO +1Oc+UXqnK16E8Ew7aIURXuUtmPv0vhipORcYyk3Ud+SisIySainyWiaumU7U +/6+q1sdKRr+Ryt6nu7WI/Fz1/PfLQr4cuVARsGOEME2yjd2fUoFEd460RxN5 +O+7VfrchpxLxa+n7QiXyWCXb5eq+sQZJeJe0cxeR3+uNXZmvR2oQm3PFwSuE +A1DnORubv4iAiv2fFj4cpEeclZ6o1yIhwd9aEwSI+TRdP7YN1SFPdq+e8yH6 +yYHoqcpxk3pkqOhY+oMtxPzjrkOU4nrkA8el/qdCOKTG3JRWeNWARLw+IZZH +9KOhSbd47xNNSOquoqKTRD+7HncrQuxDK2J2elgtVhaHw3PzOfuF/iFzFQMy +bPI4MAw867T9/yG1lz3krysQeZj35HW80IYUCDe5GO/FYezUnUeFjA7kmUiz +paMKDvl3CwszVXHkByZXXHEMh7jUtT9fr+NIcdcLuxdaRN4ajnYUJ+BIQrXX +GWsdor/IwXIzDxPRWxIR4j2Ow2IjHCD1M5HYW9T2fEMc1Hf//HQmqhv5ev79 +Zg0bon4amiILy7uRD0fZBvXtiP3zGrmjsNKNyJUmu523J/pP+RZN2qUepOvb +hd8BDjgIXnasB7lepJWP0SJzk+gXsaIzewr7kIgs9dsBD3Ho19zfEjvRh+Dx +rOGRQBxYQzrf6RL9iP0jfmuzxzi0HnD17wvsRzoUV6y1QnAoa/i98Y3hAHLQ +l83YNhqHtwwPlQ29g4ja/Oj7cuJ8jsl5Iuy1ZQiJdFpKeZFN1I95/OqA/hBi +b6xJtsnFITilqrQkYwhxvnKxUbAAB08tCRNvz2HE+uPmlJJSHM56//UY5h5F +fCI8H1sT9wWyx6Z2O+EJJKwC18reyARz67S6fOUJRB/PPB0nxIRPx5FyxpkJ +RN1NpjlqKxNstv+XlxswgZitOwXESTKh6Pf35+wzE8hhfvsIYRUm+Inaab+r +nkTOTQYa5ZoS9yOOxUMLg5MIycXdat8FJihPPFU04JhCZkpT3362ZkJPyZft +M4emkCY5k/G2/4j7kiP3kmbqFDLZ+Vw5mji32X9+yuj2m0aKjNg3sxKZcCFd +N0nt7TSy9RXvq/kUJuRGtL96UjCNzOWP79mSwQQ7B+ojpUnifboSuOUzoVTQ +3NbPcgYpG1Xbm/6HCQH2bEISB2cRQ20JfcElJnAyzty3GZtD4ppfrehbsOC8 +tDmmyjWPnD9qcifxEgvSjtmt0yXnEdYF/RraVRacuu3pk2M2j4S3vz8978aC +yL642+yl88im0hcjl0NYsOvnpEvyqwUkWdbYKbaMBdoeYTZDekuImOx7EEC6 +ITL0dXyh7RISqOw+JqDbDQMf3uMv7i4hZ5wC58VPd0Nw9zfLQ7lLSM7eAMYN +q25oONNjHrx9GcFJz+8X3OsGO3kVoz1zywg5VLD4ZFk3+OFNmq6Jq4hFi36C +pmUPdH49ccPz+yoiXUT6m3mlB9TDsMi7jatIgn//ZwWXHpjQTht8zLmGtOdm +K5v594Bluk9I4rU1JFzubOe9dGK8h2Rbg9I6wuuScVJ+tQciT0eztxmsIy8S +WMK5nL0wKcOzh3l5HdEMTVg6LdALKW3z90aj1hHH7TbxP6V7YbNG5S7qyjoi +m2SqGmrUC4scB7+K2pDQfZdvd9AyeyHZdfrPG0cSugsJ+dxc0AvGXR9Z4l4k +VPZh+b3vZb2Qlb+TIRNOQg2ijH787uwF+2sMK+UyEip5Iyl4krcPGv52sZ+U +Y0OPejlguR59kPUq4MzdKTbU5Wrcjg+m/VApGNDPSyKj72v1uCau9EPfk4d3 +4zeQUQb/4AZTz37Y6u3/oUSGjNYxfq2ERPdD0IUHNG4rMuo9vbU0v6MfrMXu +YlGVZNRY7/EOnRsD4BXhYyrbSkYxhVjdMd8BiNzgM1bQR0bX3z+PxF4MQNWq +19ZONgpqy5DO7s0fgAOdtz0lD1DQx69H3VDOQeB7674v+x0F9fFWSMr9MAjy +W9x/HftEQfVWRcPRokHQCXGzbAAKulPesHq9eRC8fW8Gz/+joMc95n6LsA/B +gJXLwBF+dlQ8aGmt0XIIsB034ip82NH7/t4GHNuHwSnBjq/HhANds9sQJvd3 +BJ7djo59ZsuB0vpjlbKHRyDjTLXMQWcONHWjwHYfzlEYW1PTePaIA30lMPFt +ABmF6xbcrge+c6AOM0tW8rmj4LDxU32wOBWdv4TPGaaPwePhPiu1PVTUzIRS +8KFyDNKKREeY6lR0y7BjseXIGAw6P2RXM6aiTV9Ulv/sGYerf86rMAOoqLPu +SuX6l3GwD1iPVBmhopddX9rec5yAgIvKEvgCFV2RD0+C+xOQrPxf5mMOTpT0 +dH5BNWICell1v7q2caJH+yuf1X6fADskeeGRISfadS2wuJZnEmwWDMw78zjR +3YvCBiOFk/Cg5n5fUDEnarQFT5JpmoSE5DxXpb+cKI97HWSMTgLTeMeToEFO +9PIFqejXYlNgnT39TXErDZ0MEn60+/4UWDrEiAXep6Fiz3K4bp6fhuVWrurJ +pzT0rsNAvpPbNLzUv333QgwNtc/uQ6ueT0OtzPmu/Tk09BDfszsfKqZBq39T +fHsPDX3/83erhuYM4CYPDXUnaSjDrRt1t5kBn7IZtk+rNFSls0ha+MEM5CXV +2wRu5kLrzMsGvhXNgKxdqKSiHhdq0qivmqM/C2X1pMZYYy5UrHJOIev6LNho +Oj/kvMSFyrWJXVZ8PguxO0/3td/mQpPuzdyqa5kFHiYjJTCdC32oe+lsq/Mc +zFwMku/goaMjs6shwjAPz//Mt+mK0tEM6boiysg87D5yJfiTNB0V6T62liG8 +APZbdUYDUTqqvmP3pgu3FqD1HyVT0ZWOLtupLCccXgSP4zetXt+lo5JqlfG7 +nBdBoIDFS3tCRx/4nOOMercIBtE/nTsS6ai3RlKhKd8SFJr6KgY10lExAwN5 +kZklsPg1xppi0lFXBjOxeO8yLKhahl0co6MlJ9Vbw64vw/7NR2YUObnReyfa +ZyoGl+Fdw9LnjgPcaFG9c8/L6RVAtRzs9bS50US/OUmvg6vQkdO6OceQG602 +SS6su7cKm8PybwU5cKNJF6ss+TeuwSNDj4NKsdxo77CxgcqpdXhRJXf9Qyo3 +apmwy/FkyjrE6na9kfrCjfL/fVJwmkzCso7osQvVcaO+e7e9k7AhYS2yIjUr +nAxUfWuw9o79bBjrXTWbxyYG2pjEsXbxKhs2st1PeXwnA/037Vm2LZ4NI20e +iWYeYaDeos1PHbaQMRlyoV3ZTQZqeDVNVkaYgin6uEYh9xmo44tpcw9LCnZ4 +YVdF/jMGuqndmtSbRMHOjIXsTU9loDIlf9MfH2LH9ibWucinMdD//9/9P0Z/ +J/c= + "]], LineBox[CompressedData[" +1:eJwV0Gk8FIoaBvAxkRMis5oxGDOKUyIpleR9KyVakCWEIktZ2kg5TsqpG4lK +IYVIWY64LcKMLdmXbMmeNWtUGPvW7X54fs/v+fD/8ig6nDvqRCQQCOm/8//e +7ek1rZAmjQZnfr4nrCViYgjvm0S6NM4aV3041SOEjoQ66OBLY6Vh/Q54JIQc +z8GwtAJpXKmb+tjGSAifWtLgSI00hsn80zxdQsAIrtfDe8PS6DGvVWMd9gvM +Iu4MnRiTRnqUpgdb4ReQVj3ftWlGGteTUJ+atgx3f9QP1gmT8Ea0a6r4pyW4 +xVfXIbFJWLRlS/qyziLoqeqH9q4joeT0Y23hzgUgxtoNvN1IwhndI1Q7/wXw +uxly33QnCTP94l34NfPgbTTSF2ZBwjLP+BM//edgSyFR28mWhDpGnz3Oa87B +xBbmva2OJNyfdbLg7cAsnGUa7Gi6QEJLmVhfPDoLzv2JIfQQEpYes48U1ZkB +c18HrSdFJEzdXsbdbDwFETGUlTMVJBQZffE4Q3YKmt6XNprWkfD+/JUG5aFJ +sBDecGl1BwltDF+9eX9jEixDBOnXp0l47Ak1llkigMhXCTc6FklY/ZRPO/9I +AC31x0y1V5DR3dIvJ8BVAFa03AmBFBnb17nEfSMJwDr2pobLn2QMV5PhEd0n +4MkHLaFidTJeLXQyGt07Ae1fh+rYWmQUOaH84xJrAmxUDp9v20PGOZPOaOva +cbB9Q3112IaM26NaDq7SGYeTRYmqW+6RkShzQMVAbQzi+i0X74f/3qzrfq8l +x6BHVPzj9ygyqg+x/lnT9RMcDp1zS0omY1aYeP4vx59wqnFbCrOQjPYT32wT +/voBzoPlykJTZLyk9VkQVTEKiat8Z2wXyNhm4n84JGIUBjdsLMsWouCzCvVw +juMonD4f6uwlScGzGSc6VIVG4cycVcKgMgWtma5fz+0ZAXfxEU6NNQXB0uf8 +qa5hGPHJFha3p6DcLdMjCpnD4Dp0e0DfhYJ5iT8iTEKGwaVEJeWDJwVv1rs9 +ld41DA7XnDUygikoc7HIourZEFgJeiA6n4IH+J2MF36D0GL/RrG1mILBFqL8 +8eODYFF3fQWtioLCkcJLT3YMglmaQtm9ZgpyzkoNzU8NgLGL7ZEbYxQkrooh +Vl0cgP3tLTauHOrvP/n6j3z7ocQgWTdJhYpBzquDVtr1gx7vMrtPjYrJpZ9U +8rEfdofT+mx3UlFEd+VZomg/6BiZuZmYUZHVyf5QFNEHm4tqfbbfomJd4BdT +28KvoPCyNGLlNyruNdp0xUyvF8xiefzKMSoua1JWHlDthaCHKV/uzlDR55yP +nielFyZ973LoIjRct7yjx6O/ByoPWfxXmU1Dj4iOjK7bPeD9o7/kgAUNn1M2 +RbO/dENqb/OQhC0NOTa6BrvKuqGnqUK8/hQNy0bLdALedsOh92kmVhd++9PB +2XG3u4Fz/1LHmWAa+gezh9t2dEO1hshUUCENn6To9An2dgFx3QzdqIKGLK9D +45YKXbCdOaxNrqPhVbrQoz8WOiGeWH09qoOGIlWopZfeCVcawiRSZ2lYK5y1 +j6rcCUqXlJSq1eh4kr+N7iHbAb68vaZSUXTsDgvVWNBoh802dWMnntFxmhKV +pkxvh2+/bO6+TqJjeaV6lf9iG1jre1eYvKNjftA95byyNtBuSoawajpy3LVt +9U62waxgtSqDIIPMgOTx7Y9bwVu9RZjrJINikrXb5VRaQK3BMd7TTQYzby7x +d5JaYMB7HIovyODWqEn234vNYJ4v5uvkJ4Oj2c/O2dc3w5bDu8aTHslgcWTp +aMbfzSBwje9QrZTBsUoj8QOtTXA+0T1TS52BKy3j9u5PboTOWtlwSS0GJjnc +NXgc1giH5yo9B3QYeLa4NUHMvxHWH/pTI8KQgdlKUqb61o3QN97/csqJgbk5 +H/cpSjbCsV0nnr2LZuBMwNJatu9n0P1sErxZjIltSlHUt6cbIHWJ4CYmzURq +Xs8Oa8sGkFV+bdBLZ2LQZHcw40ADzPpIij5Yy0SG5nmhDuUGeKtQ5T+OTFxj +5SB9cegTrHXTu/z6MhOJUiYFaR6fQIK4zUGtn4l3cmNEDAPqgX95henACBPj +JHZ/LfapB+fvtXufTjAx4Fa2pol7PRS0nF4rSZBFv8KMlzEm9eD56snQd6Ys +Kh1M9CPK1UObzfLZNGNZ/Bjp09WdWQfJWSW+qrmyWNx0e8R4tBbMNz5w7yuU +xXLD2fRNjbVAfG5nG10hi9Pv7CxV82vB5u6MrkTzb7/8zMv7fi1IOf1JHB2X +xWvKabXGWrXgTQoJfKnMwv+Y2q2evlUD+zzMwtc/ZOHn0pE3TdrV4PUgh3Du +MQtfStmu1lSphhdZHPf0WBaewuE1z6nVQCSO79FJZaFSTt7jvLGPUBARMna4 +hIXMyDX+rUkfQbug9OCFGRaWbd3U9JDxEdTIO4i843JI2z4vdUysCmy3x3ks +2sshNzJTUjBXCcG2oq14Wg4fOKBL7HAljCQ1vqrwkkPJzcnlKhWVkKxz0bY9 +5LdPT69cCKwErvNL3vJ7OZTf90vvnnglyPDlzu1TksfRe6XCLbIVsHwqSVZ6 +gzxqqx2KZ0lUQJ+kRvkXDXmkjOk7XVgsh9eOeopeII8jk8ZLhh3loL/GrSHe +Wh5n4/eP5MSWg7cLbxshVB75GlXz15XLoZFqSshZksf1Wld0iHvK4MHFwNBN +zQoYvOsNLe1pCcx/TOUFdijg64QVThseloCDcn1X91cFDB0xSkgPKAHNLwy1 +0DEF3EzmVvWcL4Fv8eb9s8JsZF2SPJ6+twSCJQb9reTZ+CR6Vk9xpBhqulbl +ME3YKDYdn9eKxXD0ltHGmEw2Lmx8p3FNpAgSrcYM+Hw2BrZEk80WC2FONdS5 +MZeNs8Qa6iZBIcQ1fIpdXcTGqoMVx5e6C+E724LkV8tGqd5a6mhuIQTm2MzY +DbExRX3Pc7J3IeSPnfnAZipiyOQxE8vvH2D98ZvmL64qoppzoAB/FIDVhUyS +sL8i9n7ZkiI0UACBAUO1p24q4oMkqfryjgLoTz9kyL2jiFr9a0xdqwsgToIK +8ZGKyMrnO86lFgA1P0ElLl0RJ4uSCnd7FABBsWwhalgRq4Kmfj7pew9NA6vi +H5pz8L015dICIx9KzW5H8y05GF2d1K69Oh8yC/941HWcg63K9M5/CPkQ8VQ0 +eIMDB/81XwpXHcwDcwsR76KzHIxh4Fj/uzz4XEIwFARwUP/ZX/bDJnnw6cXM ++NFsDhoO8XKXQnOhxqF/N0mBi336TubVKjnQI5w0G87hIsX9g2cWKwcmE0+/ +Yqzj4kGXg4yUNTnAGBlhKW7k4us7R1uSZ7PB0XNiRn0nF3ltLrvEK7Jh/sav +tMPHuBirNXDNxi0b1iUwmLfvcbEgpb11LoMPO/Tb6yQecnGl4Ynj/Sl8ODQc +HXA/gotXshJdW2L5cGEje+pRDBdFZ2uojbf5kJuxri7xJRcdGx82K9vx4Wip +5q3iMi5ymnO+q/7BB6fTUzoHqrhoaxlBuLvEgytiWYKqGi4KfTm6eXqCBzFH +tO0bGrlIN+5obu/gwVAT6vR+5aLh2qGLC+k8mL9CFDgNcpE5YlAc9i8PVssW +/zv8jYumRpqErbE82HxCnz4+zsW9QcLyQUE82Ce0qsZriou6VpoC3es8sHxe +eXN2lot34i4/nr/EA9d9wTv/XuSiRFOAWJ4bD64OHp749YuLkROKeMueB/8D +KKwn4g== + "]], + LineBox[{{3.996278092705496, -2.5304971664322395`}, {3.996306801500057, + 2.268067836278679}}], + LineBox[{{-3.998012662994029, + 2.268067836278679}, {-3.997964291724142, -2.5304971664322395`}}]}, + Annotation[#, "Charting`Private`Tag$85436#1"]& ]}, {}}, + AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], + Axes->{True, True}, + AxesLabel->{None, None}, + AxesOrigin->{0, 0}, + DisplayFunction->Identity, + Frame->{{False, False}, {False, False}}, + FrameLabel->{{None, None}, {None, None}}, + FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}}, + GridLines->{None, None}, + GridLinesStyle->Directive[ + GrayLevel[0.5, 0.4]], + ImagePadding->All, + Method->{ + "DefaultBoundaryStyle" -> Automatic, + "DefaultGraphicsInteraction" -> { + "Version" -> 1.2, "TrackMousePosition" -> {True, False}, + "Effects" -> { + "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, + "Droplines" -> { + "freeformCursorMode" -> True, + "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultMeshStyle" -> + AbsolutePointSize[6], "ScalingFunctions" -> None, + "CoordinatesToolOptions" -> {"DisplayFunction" -> ({ + (Identity[#]& )[ + Part[#, 1]], + (Identity[#]& )[ + Part[#, 2]]}& ), "CopiedValueFunction" -> ({ + (Identity[#]& )[ + Part[#, 1]], + (Identity[#]& )[ + Part[#, 2]]}& )}}, + PlotRange->{{-10, 10}, {-2.5304971664322395`, 2.268067836278679}}, + PlotRangeClipping->True, + PlotRangePadding->{{ + Scaled[0.02], + Scaled[0.02]}, { + Scaled[0.05], + Scaled[0.05]}}, + Ticks->{Automatic, Automatic}]], "Output", + CellChangeTimes->{3.8273986156860313`*^9}, + CellLabel-> + "Out[145]=",ExpressionUUID->"e550adac-e0a6-4efd-b952-1d1016d97b7f"] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"iiii", "=", + RowBox[{"Integrate", "[", + RowBox[{ + RowBox[{"D", "[", + RowBox[{ + FractionBox[ + SuperscriptBox[ + RowBox[{"(", + RowBox[{ + RowBox[{"-", + SuperscriptBox["\[Theta]0", "2"]}], "-", + SuperscriptBox[ + RowBox[{"(", + RowBox[{"\[ImaginaryI]", " ", "\[Theta]"}], ")"}], "2"]}], ")"}], + + RowBox[{"5", "/", "6"}]], + RowBox[{"(", + RowBox[{ + SuperscriptBox["\[Theta]", "2"], "+", + SuperscriptBox["\[Theta]p", "2"]}], ")"}]], ",", "\[Theta]p"}], + "]"}], ",", "\[Theta]p"}], "]"}]}]], "Input", + CellChangeTimes->{{3.827393611251314*^9, 3.827393616586507*^9}, { + 3.827393782574443*^9, 3.827393786454549*^9}, 3.827393833679454*^9, { + 3.827394143980788*^9, 3.827394148860531*^9}, {3.827400047949716*^9, + 3.827400049789692*^9}},ExpressionUUID->"d9105b21-3e64-4aac-abae-\ +2d82f616b07a"], + +Cell[BoxData[ + FractionBox[ + SuperscriptBox[ + RowBox[{"(", + RowBox[{ + SuperscriptBox["\[Theta]", "2"], "-", + SuperscriptBox["\[Theta]0", "2"]}], ")"}], + RowBox[{"5", "/", "6"}]], + RowBox[{ + SuperscriptBox["\[Theta]", "2"], "+", + SuperscriptBox["\[Theta]p", "2"]}]]], "Output", + CellChangeTimes->{ + 3.82739361678843*^9, {3.827393783418345*^9, 3.827393786628747*^9}, + 3.827393834081977*^9, 3.8273941490919952`*^9}, + CellLabel->"Out[69]=",ExpressionUUID->"574c6df6-7af8-4004-ad57-60b1a3aeebc3"] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Simplify", "[", + RowBox[{ + RowBox[{"ComplexExpand", "[", + RowBox[{ + RowBox[{"Im", "[", + RowBox[{ + RowBox[{"(", + RowBox[{"iii", "+", + RowBox[{"\[ImaginaryI]", " ", + RowBox[{"Sign", "[", + RowBox[{"Im", "[", "\[Theta]", "]"}], "]"}], " ", + RowBox[{ + RowBox[{"iF1", "[", + RowBox[{"\[Theta]c", ",", "B"}], "]"}], "[", "\[Theta]", "]"}]}], + "-", + RowBox[{"\[ImaginaryI]", " ", + RowBox[{"Sign", "[", + RowBox[{"Im", "[", "\[Theta]", "]"}], "]"}], + RowBox[{ + RowBox[{"iF1", "[", + RowBox[{"\[Theta]c", ",", "B"}], "]"}], "[", + RowBox[{"-", "\[Theta]"}], "]"}]}]}], ")"}], "/.", + RowBox[{"\[Theta]", "\[Rule]", + RowBox[{"\[ImaginaryI]", " ", "\[Theta]"}]}]}], "]"}], ",", + RowBox[{"TargetFunctions", "->", "Conjugate"}]}], "]"}], ",", + RowBox[{"Assumptions", "\[Rule]", + RowBox[{"{", + RowBox[{ + RowBox[{"\[Theta]", ">", "0"}], ",", + RowBox[{"\[Theta]c", ">", "0"}], ",", + RowBox[{"B", ">", "0"}]}], "}"}]}]}], "]"}]], "Input", + CellChangeTimes->{{3.827556158248519*^9, 3.82755628029881*^9}}, + CellLabel->"In[69]:=",ExpressionUUID->"f94b376c-aafb-420f-a0ba-4122dfe2f2a4"], + +Cell[BoxData["0"], "Output", + CellChangeTimes->{{3.827556184988991*^9, 3.827556280519479*^9}}, + CellLabel->"Out[69]=",ExpressionUUID->"452e7106-44ad-423b-b013-47704d5fa045"] +}, Open ]], + +Cell[BoxData[ + RowBox[{"ii", "=", + RowBox[{"Integrate", "[", + RowBox[{ + FractionBox[ + RowBox[{ + RowBox[{"iF1", "[", + RowBox[{"\[Theta]c", ",", "B"}], "]"}], "[", + RowBox[{"\[ImaginaryI]", " ", "\[Theta]"}], "]"}], + RowBox[{ + RowBox[{"(", + RowBox[{"\[Theta]", "+", "y"}], ")"}], + SuperscriptBox["\[Theta]", "2"]}]], ",", + RowBox[{"{", + RowBox[{"\[Theta]", ",", "\[Theta]0", ",", "\[Infinity]"}], "}"}], ",", + RowBox[{"Assumptions", "\[Rule]", + RowBox[{"{", + RowBox[{ + RowBox[{"y", ">", "0"}], ",", + RowBox[{"\[Theta]0", ">", "0"}], ",", + RowBox[{"B", ">", "0"}], ",", + RowBox[{"\[Theta]c", ">", "0"}]}], "}"}]}]}], "]"}]}]], "Input", + CellChangeTimes->{{3.8275560742812*^9, + 3.827556117207822*^9}},ExpressionUUID->"69c24b28-334f-4371-a917-\ +fb68280ac4c6"], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"ii", "=", + RowBox[{"Integrate", "[", + RowBox[{ + FractionBox[ + SuperscriptBox[ + RowBox[{"(", + RowBox[{ + SuperscriptBox["\[Theta]", "2"], "-", + SuperscriptBox["\[Theta]0", "2"]}], ")"}], + RowBox[{"5", "/", "6"}]], + RowBox[{ + RowBox[{"(", + RowBox[{"\[Theta]", "+", "y"}], ")"}], + SuperscriptBox["\[Theta]", "2"]}]], ",", + RowBox[{"{", + RowBox[{"\[Theta]", ",", "\[Theta]0", ",", "\[Infinity]"}], "}"}], ",", + RowBox[{"Assumptions", "\[Rule]", + RowBox[{"{", + RowBox[{ + RowBox[{"y", ">", "0"}], ",", + RowBox[{"\[Theta]p", "\[Element]", "Reals"}]}], "}"}]}]}], + "]"}]}]], "Input", + CellChangeTimes->{{3.827393253300413*^9, 3.8273933386213913`*^9}, { + 3.827393483240753*^9, 3.82739348581619*^9}, {3.827393562674301*^9, + 3.8273935722975693`*^9}, {3.82739420638988*^9, 3.8273942641107283`*^9}, { + 3.827400077854945*^9, 3.827400090615223*^9}, {3.827548879309278*^9, + 3.8275488839093943`*^9}},ExpressionUUID->"47275aa3-a518-40c0-8636-\ +2a1702e8b8a8"], + +Cell[BoxData[ + TemplateBox[{ + FractionBox[ + RowBox[{"\[Pi]", " ", + RowBox[{"(", + RowBox[{ + RowBox[{"-", + SuperscriptBox["\[Theta]0", + RowBox[{"5", "/", "3"}]]}], "+", + SuperscriptBox[ + RowBox[{"(", + RowBox[{ + SuperscriptBox["y", "2"], "+", + SuperscriptBox["\[Theta]0", "2"]}], ")"}], + RowBox[{"5", "/", "6"}]]}], ")"}]}], + SuperscriptBox["y", "2"]], + RowBox[{ + RowBox[{ + RowBox[{"Re", "[", "\[Theta]0", "]"}], ">", "0"}], "&&", + RowBox[{ + RowBox[{"Im", "[", "\[Theta]0", "]"}], "\[Equal]", "0"}]}]}, + "ConditionalExpression"]], "Output", + CellChangeTimes->{{3.827393260285619*^9, 3.827393274875136*^9}, { + 3.8273933250956783`*^9, 3.827393342172038*^9}, 3.8273934877599573`*^9, { + 3.8273935657796707`*^9, 3.827393574361773*^9}, {3.827394211507577*^9, + 3.827394232690776*^9}, 3.827394268062793*^9, {3.8274000870282173`*^9, + 3.827400091639617*^9}}, + CellLabel-> + "Out[194]=",ExpressionUUID->"4d62362a-0bd4-4ef2-b97a-6130a8ecb486"] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Plot", "[", + RowBox[{ + RowBox[{ + SuperscriptBox[ + RowBox[{"(", + RowBox[{"1", "+", + SuperscriptBox["x", "2"]}], ")"}], + RowBox[{"5", "/", "6"}]], "-", "1"}], ",", + RowBox[{"{", + RowBox[{"x", ",", "0", ",", "10"}], "}"}]}], "]"}]], "Input", + CellChangeTimes->{{3.827402664798593*^9, 3.827402705254951*^9}}, + CellLabel-> + "In[225]:=",ExpressionUUID->"d1af5436-7da6-4fe1-ade5-4cbb449a5163"], + +Cell[BoxData[ + GraphicsBox[{{{}, {}, + TagBox[ + {RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6], Opacity[ + 1.], LineBox[CompressedData[" +1:eJwV0Hk81AkUAPCfRnJVjKVoMPwUUcpu7UZ4r+gnVrJJSiqNKyWhHCG5NiZH +iNBWjlLJnWPLllyV+xqFiGFCOZbJEbFr7ft83ud9vv+8S4l14ZDDCoIg4pbz +/3o3gCWkZR+hT/wfqaReNYdpasV0BoJQc+h34+ovvSkLYTIvLztTI9GNgDVx +JfmincHLHnC9HkCHu+VRiiuZbCBS92s5uzFhy4R99JLTDSBsS4yj8jbDxzX3 +/l3siANCQmDYMuBHUHko8vP3hQQg8pt5vRra4KLnef6bYjIQ3HWvNN0QCtu5 +D6YN7gCxPctvqNEQvp8z7eE7pQDx+OI3qTxjSBXoYX/bl7bsKK0iqYNg2Bi7 +cbYjHYgGnbH+K4fgc5JRxbTzAyAm12akFFpCpP0/NlMLGUAcFTGR1DgGnIUz +8ZOKmUDI2LwLuWALXm8Vtk8UPAHiwdN3VVEskLvZXj9ukA3ENCnZ1WAPLHWk +jTrlATGbln4lxxlWLPg2T/vnA3EpaUHkoAu0cy3lp/cVABEdl+AgeQF8ssWe +f+14CkSyfs8efw8wiRsS+ppaCESjuEXamkvA8Kk4zHcuAsJHutm+wBPKDbwn +JxaKgbiW0iyldhlWdQ+ojis+X/6vb/O8SyB0lr/0HPu87EibpCfeQfDkYVLV +aEEpBLpH9YZfDwYzD7NTIwYvgHjRY1hfEwq3REpvDTu9AiJlrcLhR2wo8jbx +uLi+HAKbmxJPTF2HOyO/yE75lwPhfqgz2igSXFvoTl/3VQBR2XbZQfgG0O/U +rOB3VAIR2Pdl0DMOFtaUZLrpVgGhd5MRoHsTPgXdN59MXfajwqpNq+KhxCng +3oRzNQR6MqMePU4A65926Py98BrKTUm7Y4xkSKtLcR9VrAVbBTpX0C4VppOK +1fsia4ErOu3az08Fyqme1zZfC/j6ix0jJA3GaN8sSzl1YOvhMZuVnQ679Mx0 +2GENQKyNyd3EyICWvMUVqhPNwDzjn7zV5QnQQeTkas0W4DrzH71iZsHuTfE6 +YfYtwOyLP5HZkQXR05lTvq3LthobCDLNgR2x7xxYWa0QGCMnKr85H67WbTHR +OsWB7XLmmdmOhfC44M9NWQkcMCdo/QmcQmhL2kvb2MABN+nI6Yd7ikDF6eiL +9drtMJnTeQ+UiqGOFqpJSL0DojbsosHfJSCj101vfvMemIUeO61elUJuHrvb +RfMDhO9Xnm2/WwEj9JFIk9MfQDjJZTyrvwJUvUz01eI/AOFPtS5trIRUXbE0 +3vwHsB0e6pbPr4S42khH69fd8Cwg325bXRV48W7wjWw+QouSkHKE9BtIEasP +kdzHhTnpI2K7hOtBX8/PJvAkF7D74LVzx+uhx1Vj54Q3d/l+eu66vHpY3xYx +1PCEC1zvLO8uqwaITTI1DpfoBwnWlNxSbiOEbGxas9TdD0fZfG6Xdgs4QWvy +mAcPHtfoMAbVOUCkz5Z2R/CAMWr/bNKaA0mCjJ66Bzw4DNVaOyI4UFPrqJD5 +ngfZK+d9WGMcUDu8mO6g8wkes6kQ64J2+HxGNbtXYBCyDy12Z+57D2fjrpS1 +xAyBvXtJvnliF7gObuYV5X4BR5fU+Njzy3ue7BKuqP0CQ867Nf6O5oJFZ7hm +46cvkL/y5U7nfC7sqh++PCg3AuntRwJKp7hAK8iQkAkbAX9DtTc1fv2Q5K+k +731qFNRKngVHxA5AhZRssrbEOHgJt1o4cD6BqFKoat+uSTgr3s4+tjw3WqJe +Pc12Cp5Z/Lv1p2k+sLoPv6I1zIKPCl/E9cAcuL8OZV1Q/Q5eDbp7lQ4sQYGb +uMV6439AlyaoN69LwzS/cyPbrQhkDdsLVnutwuCUxd+mxwTQNrFfbKJYDAkO +F1/40lC294hQAV0CN11y9DmsvhIbNwytPZ5Kx08ziUfEXgrhWQfKJ0pFGk0G +z16JcxdGhs+4pwJtPZp9itFQUBDFE6eG1i1+k8ORKlZgTY4Y5hpR0zOd8qgp ++V7e4NRq7HXs1fsrkomiMHO6Z2oNRiQfP3GVqYxG49bflC0lcIeZm4nJEImd +lfYC1lskUcvidM1C4UYsDq8+yZyRxCAXhnS/myo6rvTkNjXR8Y6i0zF31ma0 +8/ArFr8thZ2dwb2r92jgNieNJtPTP2BQmW6EPrkVm+lbxDy1pVFNMk4uW3cb +/pUb/McWmgwaBxp9Lk3Zjn4C6uYNH2Wwu1bxQPtLLRTt8d3vWrQOWyT2mLR/ +/BEHHyrFp/ivx3UB3RdeTP6E8Wqygs8tZbFD6GhnmtJOjLnt+PY0Uw7t7COt +2IY/o3X8iSbxYTn8kK0Te93pF5wzzJhPKduALytpka8zdyFvcK9PZRgDz0ts +vX2uRxvT9bQ2NJ6Wx0LNz3SLbbsx53dPSaetCjgT0lfX7K6LYZZ2v9JmFNCR +T1rcLNTDnT1pmWGNivgkQ9+vUQYwafMfOY2/MnF+95YNa3cgXi2PSvr1OROR +lF83NY54YINlRp2KErYcZd9KeLQH97i+PS7JVsLroXpe16z2YgqDpdIwo4Sj +9QGvTWUNUKXq0S2z48qoODvzg0CrAcZsrVRvK1NGdjBj6WmYITpOCbbWqpPI +XPnSvMl8H7IKvjLZN0j8OXzVB7W1FLoEWyyaxJJYfTG2MJBOoadFUYf4TRLd +hO6Vd0pTGD7jGR1zi8Sh97s82QwKc7XnFxLvkmioarx/fDOF8xVL7x9mkRiC +nvFlhhTGtIlHVb8lcdZErDTMl8Lb98+fuVZL4tTbfmLoCoX3LzUZ7K8nUWhO +2M8wiMISmZjv9U0kvgADkRXhFPZYS53hvCNxA0M36moChao8WYMBHonFjEGt +0HwKtxf5KjwYJFHdZnXOYCGFOr93zzsMk9hw9/xxoz8pNFW9m/9lhMQBgZbf +xMoo9DjHVODzSfzFnP8goZ5Cf92g+adTJIam5z6fa6Lw99UD7ZdmSAzMTxSw +aaMwKe9+xNwciV19Q+pkF4XpgYJOpd9J5PCNxcN6KMz6zWGv/yKJJaltzNE+ +CouU38jr/0vifoerZw7yKCyb2jS/tLTc75kZr3CIwv8AMzI39w== + "]]}, + Annotation[#, "Charting`Private`Tag$2197828#1"]& ]}, {}}, + AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], + Axes->{True, True}, + AxesLabel->{None, None}, + AxesOrigin->{0, 0}, + DisplayFunction->Identity, + Frame->{{False, False}, {False, False}}, + FrameLabel->{{None, None}, {None, None}}, + FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}}, + GridLines->{None, None}, + GridLinesStyle->Directive[ + GrayLevel[0.5, 0.4]], + ImagePadding->All, + Method->{ + "DefaultBoundaryStyle" -> Automatic, + "DefaultGraphicsInteraction" -> { + "Version" -> 1.2, "TrackMousePosition" -> {True, False}, + "Effects" -> { + "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, + "Droplines" -> { + "freeformCursorMode" -> True, + "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultMeshStyle" -> + AbsolutePointSize[6], "ScalingFunctions" -> None, + "CoordinatesToolOptions" -> {"DisplayFunction" -> ({ + (Identity[#]& )[ + Part[#, 1]], + (Identity[#]& )[ + Part[#, 2]]}& ), "CopiedValueFunction" -> ({ + (Identity[#]& )[ + Part[#, 1]], + (Identity[#]& )[ + Part[#, 2]]}& )}}, + PlotRange->{{0, 10}, {0., 45.80236474365029}}, + PlotRangeClipping->True, + PlotRangePadding->{{ + Scaled[0.02], + Scaled[0.02]}, { + Scaled[0.05], + Scaled[0.05]}}, + Ticks->{Automatic, Automatic}]], "Output", + CellChangeTimes->{{3.8274026843923197`*^9, 3.827402705454937*^9}}, + CellLabel-> + "Out[225]=",ExpressionUUID->"f14d8dda-8aef-46f4-9268-1e49eb0a6ab8"] +}, Open ]], + +Cell[BoxData[""], "Input", + CellChangeTimes->{{3.82740275528027*^9, + 3.827402756743431*^9}},ExpressionUUID->"2a89c62c-d8e8-4906-9a9f-\ +eb121a3679d1"], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Plot", "[", + RowBox[{ + RowBox[{ + RowBox[{ + SuperscriptBox["y", "2"], "ii"}], "/.", + RowBox[{"{", + RowBox[{"\[Theta]0", "\[Rule]", "0.18"}], "}"}]}], ",", + RowBox[{"{", + RowBox[{"\[Theta]p", ",", "0", ",", "1"}], "}"}]}], "]"}]], "Input", + CellChangeTimes->{{3.827393492808857*^9, 3.827393548633919*^9}, { + 3.827394219734305*^9, 3.827394219861763*^9}, {3.8274027269674063`*^9, + 3.827402727655208*^9}}, + CellLabel-> + "In[226]:=",ExpressionUUID->"46cab2db-f51c-4f1d-9971-16ff4eabde9a"], + +Cell[BoxData[ + GraphicsBox[{{}, {}}, + AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], + Axes->{True, True}, + AxesLabel->{None, None}, + AxesOrigin->{0, 0}, + DisplayFunction->Identity, + Frame->{{False, False}, {False, False}}, + FrameLabel->{{None, None}, {None, None}}, + FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}}, + GridLines->{None, None}, + GridLinesStyle->Directive[ + GrayLevel[0.5, 0.4]], + ImagePadding->All, + Method->{ + "DefaultBoundaryStyle" -> Automatic, + "DefaultGraphicsInteraction" -> { + "Version" -> 1.2, "TrackMousePosition" -> {True, False}, + "Effects" -> { + "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, + "Droplines" -> { + "freeformCursorMode" -> True, + "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultMeshStyle" -> + AbsolutePointSize[6], "ScalingFunctions" -> None, + "CoordinatesToolOptions" -> {"DisplayFunction" -> ({ + (Identity[#]& )[ + Part[#, 1]], + (Identity[#]& )[ + Part[#, 2]]}& ), "CopiedValueFunction" -> ({ + (Identity[#]& )[ + Part[#, 1]], + (Identity[#]& )[ + Part[#, 2]]}& )}}, + PlotRange->{{0, 1}, {0., 0.}}, + PlotRangeClipping->True, + PlotRangePadding->{{ + Scaled[0.02], + Scaled[0.02]}, { + Scaled[0.05], + Scaled[0.05]}}, + Ticks->{Automatic, Automatic}]], "Output", + CellChangeTimes->{{3.827393502087903*^9, 3.82739357508897*^9}, { + 3.82739422025972*^9, 3.8273942356371307`*^9}, 3.827394268803383*^9, + 3.827402728111472*^9}, + CellLabel-> + "Out[226]=",ExpressionUUID->"745b57d7-b217-49b8-8db2-7ef71fa6ac32"] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"i0", "=", + RowBox[{"Limit", "[", + RowBox[{ + RowBox[{ + RowBox[{ + SuperscriptBox["\[Theta]p", "2"], "+", + RowBox[{"3", + SuperscriptBox["\[Theta]p", "4"]}], "+", + RowBox[{"0.8", " ", + SuperscriptBox["\[Theta]p", "6"]}], "+", + RowBox[{"x", " ", + RowBox[{"Exp", "[", + RowBox[{"1", "/", "x"}], "]"}], + RowBox[{"ExpIntegralEi", "[", + RowBox[{ + RowBox[{"-", "1"}], "/", "x"}], "]"}]}], "+", + RowBox[{"y", " ", + RowBox[{"Exp", "[", + RowBox[{"1", "/", "y"}], "]"}], + RowBox[{"ExpIntegralEi", "[", + RowBox[{ + RowBox[{"-", "1"}], "/", "y"}], "]"}]}], "+", "ii"}], "/.", + RowBox[{"{", + RowBox[{ + RowBox[{"\[Theta]0", "\[Rule]", "0.18"}], ",", + RowBox[{"x", "\[Rule]", + RowBox[{"\[Theta]p", "-", "0.5"}]}], ",", + RowBox[{"y", "\[Rule]", + RowBox[{ + RowBox[{"-", "0.5"}], "-", "\[Theta]p"}]}]}], "}"}]}], ",", + RowBox[{"\[Theta]p", "\[Rule]", "0"}]}], "]"}]}]], "Input", + CellChangeTimes->{{3.8273957950347958`*^9, 3.8273958036902657`*^9}}, + CellLabel->"In[97]:=",ExpressionUUID->"d97b0acd-9ab2-4bfa-a926-8144e113e7af"], + +Cell[BoxData["3.9662400044020547`"], "Output", + CellChangeTimes->{{3.827395798643058*^9, 3.82739580404287*^9}}, + CellLabel->"Out[97]=",ExpressionUUID->"b9b7a5df-f22f-4613-aa7a-d1a79e12ed16"] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"ComplexPlot", "[", + RowBox[{ + RowBox[{ + RowBox[{"(", + RowBox[{ + RowBox[{ + SuperscriptBox["\[Theta]p", "2"], "+", + RowBox[{"3", + SuperscriptBox["\[Theta]p", "4"]}], "+", + RowBox[{"0.8", " ", + SuperscriptBox["\[Theta]p", "6"]}], "+", + RowBox[{"x", " ", + RowBox[{"Exp", "[", + RowBox[{"1", "/", "x"}], "]"}], + RowBox[{"ExpIntegralEi", "[", + RowBox[{ + RowBox[{"-", "1"}], "/", "x"}], "]"}]}], "+", + RowBox[{"y", " ", + RowBox[{"Exp", "[", + RowBox[{"1", "/", "y"}], "]"}], + RowBox[{"ExpIntegralEi", "[", + RowBox[{ + RowBox[{"-", "1"}], "/", "y"}], "]"}]}], "+", "ii"}], "/.", + RowBox[{"{", + RowBox[{ + RowBox[{"\[Theta]0", "\[Rule]", "0.18"}], ",", + RowBox[{"x", "\[Rule]", + RowBox[{"\[Theta]p", "-", "0.5"}]}], ",", + RowBox[{"y", "\[Rule]", + RowBox[{ + RowBox[{"-", "0.5"}], "-", "\[Theta]p"}]}]}], "}"}]}], ")"}], "-", + "i0"}], ",", + RowBox[{"{", + RowBox[{"\[Theta]p", ",", + RowBox[{ + RowBox[{"-", "1.5"}], "-", + RowBox[{"1.5", "\[ImaginaryI]"}]}], ",", + RowBox[{"1.5", "+", + RowBox[{"1.5", "\[ImaginaryI]"}]}]}], "}"}]}], "]"}]], "Input", + CellChangeTimes->{{3.827395215904148*^9, 3.8273953048571787`*^9}, { + 3.82739538369901*^9, 3.827395449756003*^9}, {3.8273954875413218`*^9, + 3.8273954989164762`*^9}, {3.827395540918079*^9, 3.827395594198576*^9}, { + 3.8273958067545147`*^9, 3.827395846170776*^9}}, + CellLabel-> + "In[100]:=",ExpressionUUID->"b322468a-712f-49de-b702-6be478a69ce7"], + +Cell[BoxData[ + GraphicsBox[{GraphicsComplexBox[CompressedData[" +1:eJx9202I1lUUgPEX2xhtplXUSrGlLYIgJ8aGIIJWQitXYUGQbSIpWkhCIGEL +h4poV9hKCQKXuRKKKLFFZBCBQl9CiyhKs6FF5PSf34X3+WNuLo8MM/Pe536c +e86Z3U8//8QzOxaLxR+3LRZb4/Rv87zxueNX33vs4I3BX++8uP/k2euDHz55 +9vKlndcGn7nznaP3PPX74Hv3/vXAx0d+G7x5kw7s+WXwF/u3vsHPg089dvDX +w8evDn7xwJ6b3+GHwW9s/biLVwbv2/p2e78Z/N2lrV/wy8ErW7/u5U8GHzt3 ++uZv+MHgRydexzumrx/87fT9Bt8//bzBr0+/z+AXpt938LvT5xl8Yfq8g/+c +5mPw7mm+Bp+e5nPw/mm+B1+afAw+PPkavD2Wh9eO/GJ+Mb+YX8wv5hfzi/nF +/GJ+Mb+YX8wv5hfzi/nF/GJ+Mb+YX8wv5hfzi/nF/GJ+Mb/Zl+WZR9yRX8wv +5hfzi/nF/GJ+Mb+YX8wv5hfzi/nF/GJ+Mb+YX8wv5hfzi/nF/GJ+Mb+YX8xv +ztnybF/WI+7IL+YX84v5xfxifjG/mF/ML+YX84v5xfxifjG/mF/ML+YX84v5 +xfxifjG/mF/Mb+7N8uyc7b6sR9yRX8wv5hfzi/nF/GJ+Mb+YX8wv5hfzi/nF +/GJ+Mb+YX8wv5hfzi/nF/GJ+Mb+Jg8qze7PnbPdlPeKO/GJ+Mb+YX8wv5hfz +i/nF/GJ+Mb+YX8wv5hfzi/nF/GJ+Mb+YX8wv5hfzm7i2PIuDem/2nO2+rEfc +kV/ML+YX84v5xfxifjG/mF/ML+YX84v5xfxifjG/mF/ML+YX84v5xfzmnVKe +xbWNg3pv9pztvqxH3JFfzC/mF/OL+cX8Yn4xv5hfzC/mF/OL+cX8Yn4xv5hf +zC/mF/OL+c27szx7pzSubRzUe7PnbPdlPeKO/GJ+Mb+YX8wv5hfzi/nF/GJ+ +Mb+YX8wv5hfzi/nF/GJ+Mb+Y3+QRyrN3Z98pjWsbB/Xe7DnbfVmPuCO/mF/M +L+YX84v5xfxifjG/mF/ML+YX84v5xfxifjG/mF/Mb/JC5Vkeoe/OvlMa1zYO +6r3Zc7b7sh5xR34xv5hfzC/mF/OL+cX8Yn4xv5hfzC/mF/OL+cX8Yn4xv8nz +lWd5oeYR+u7sO6VxbeOg3ps9Z7sv6xF35Bfzi/nF/GJ+Mb+YX8wv5hfzi/nF +/GJ+Mb+YX8wv5jd52/Isz9e8UPMIfXf2ndK4tnFQ782es92X9Yg78ov5xfxi +fjG/mF/ML+YX84v5xfxifjG/mF/ML+Y3efjyLG/bPF/zQs0j9N3Zd0rj2sZB +vTd7znZf1iPuyC/mF/OL+cX8Yn4xv5hfzC/mF/OL+cX8Yn4xv6mrlGd5+OZt +m+drXqh5hL47+05pXNs4qPdmz9nuy3rEHfnF/GJ+Mb+YX8wv5hfzi/nF/GJ+ +Mb+YX8xv6mTlWV2lefjmbZvna16oeYS+O/tOaVzbOKj3Zs/Z7st6xB35xfxi +fjG/mF/ML+YX84v5xfxifjG/mN/UPcuzOlnrKs3DN2/bPF/zQs0j9N3Zd0rj +2sZBvTd7znZf1iPuyC/mF/OL+cX8Yn4xv5hfzC/mF/OL+U0duzyre7ZO1rpK +8/DN2zbP17xQ8wh9d/ad0ri2cVDvzZ6z3Zf1iDvyi/nF/GJ+Mb+YX8wv5hfz +i/nF/KYvoTyrY7fu2TpZ6yrNwzdv2zxf80LNI/Td2XdK49rGQb03e852X9Yj +7sgv5hfzi/nF/GJ+Mb+YX8wv5jd9JuVZX0Lr2K17tk7Wukrz8M3bNs/XvFDz +CH139p3SuLZxUO/NnrPdl/WIO/KL+cX8Yn4xv5hfzC/mF/ObvqHyrM+kfQmt +Y7fu2TpZ6yrNwzdv2zxf80LNI/Td2XdK49rGQb03e852X9Yj7sgv5hfzi/nF +/GJ+Mb+Y3/SBlWd9Q+0zaV9C69ite7ZO1rpK8/DN2zbP17xQ8wh9d/ad0ri2 +cVDvzZ6z3Zf1iDvyi/nF/GJ+Mb+YX8xv+vrKsz6w9g21z6R9Ca1jt+7ZOlnr +Ks3DN2/bPF/zQs0j9N3Zd0rj2sZBvTd7znZf1iPuyC/mF/OL+cX8Yn7Tp1me +9fW1D6x9Q+0zaV9C69ite7ZO1rpK8/DN2zbP17xQ8wh9d/ad0ri2cVDvzZ6z +3Zf1iDvyi/nF/GJ+Mb/puy3P+jTb19c+sPYNtc+kfQmtY7fu2TpZ6yrNwzdv +2zxf80LNI/Td2XdK49rGQb03e852X9Yj7sgv5hfzi/lNH3V51nfbPs329bUP +rH1D7TNpX0Lr2K17tk7Wukrz8M3bNs/XvFDzCH139p3SuLZxUO/NnrPdl/WI +O/KL+cX8Yn7Dsz5q3D7c9m22z699Ye0jat9J+xRa124dtHWz1lmal28et3m/ +5omaV+g7tO+WxrmNi3qP9tztPq3XjvxifjG/4VlfPG5fdftw27fZPr/2hbWP +qH0n7VNoXbt10NbNWmdpXr553Ob9midqXqHv0L5bGuc2Luo92nO3+7ReO/KL ++Q3P/s4Bt0++fdXtw23fZvv82hfWPqL2nbRPoXXt1kFbN2udpXn55nGb92ue +qHmFvkP7bmmc27io92jP3e7Teu3Ib/hWf7cy+7uH9sm3r7p9uO3bbJ9f+8La +R9S+k/YptK7dOmjrZq2zNC/fPG7zfs0TNa/Qd2jfLY1zGxf1Hu25231arx3f +XJq/xery/K2cW56/ldXl+Vs5tzx/K6vL87dYXZ6/XeeW52+xMH9vPX73Q3cd +e2XtxPb83ffkZ69ubr685uf8/89d3PLnvvb3iZdu33N01EGNJ6f/H/Owsf11 +b+f/rXdfb71j6x1b79h6x9Y7tt6x9Y6td3xkez1h6wlbT/jG9nrC1hO2nrD1 +hL/aXk/Yehrf/8L6j2f++f78vlPPrt9x7dOPzLd5w+YNmzds3rB5w+YNmzds +3rB5w84JbJ1j6xxbp9g6xfY5ts8xL5gXbJ9jXjAvmBdsn+PlfX5o7afPH1l9 +f5d9e2jtysRjXfNnvfu82OfFPi/2ebHPi31e7PNinxf7vNjnxT4v7v1k/1p3 +2LrD1h227rB1h607bN1h6w5bd/j6tD/WH/xvf3y4z/7dyDrZyDrB9u9G1slG +1slG1gm2fzeyTm5x3g02j9g8YvOIzSM2j9g8YvOIzSM2j9j+xfYv7v61zv8F +q1Nf1Q== + "], {{ + {Opacity[1.], Texture[ + GraphicsBox[ + TagBox[ + RasterBox[CompressedData[" +1:eJx03FVwZOt2J3jHzMs8zmP3hLvdtnvstu+43dfuue7rC+cUqiQVq7hKVWLm +EjMzMzMzs1IpJeOGZGbGvZMzdSImU3XO8Wl7OuJfFVl6qYz85fr2+vZen/48 +Lvtl0v/2J3/yJ1//j+BfL2OL7uTlxZZE/Z/Bf7zO+pqanJWYEJ6Vn5icmPc/ +4v734A+7f/wTeq3xmtReg8qrV3q0Co9G7lHJ3AqpWyZxS8QuodDFFzg5fCfM +dQBsB42FkiAUByAYBnJCt+/RbVt02xrdukS3ztEtk3TzKN00wDB1M4xtTEMj +U18D6MtAXSGkzYE1aWx1Ikf9haf6wFe+EiqeieXhEtl9qfR7qfgPMuFvZfzf +SHn/IOX+vZTzKzHnr0Xcv+Dz/gPM//ck3r874v27Gc6/r2X/X3Hw376HIp6B +X+4DWb8FSn7PqPuO3nqH3nmP3nOf3hfMA3rvA0bPA0bXfWZHfK85rt8YN2CM +HTTEDOqD+TKg/9Jn+Nxl+txq+VKHJJcjuXn28kR742v7cKR++Z58//eC89+w +cf8AkX7NoPwjlfYbCv23FMYfqMw7NOZ9BvAIBJ7AwAsO8IYPfBIC8WIgVQpk +y4FCJVCuBmu0YJMe7DBAvSZoyAKNW+EZO7yIsFYd7E0ne8/FOXRzTz1cjJd3 +5ePj/QKyX0jzi5gBCRSQsgMyXkAuCChEN0rJjUp2o1bcaFQ3Ws2NVnuj0/+g +N/xgMP5gMP1gtPyg9ppUXqPSq1d4dHKPRuZRSd0KiVsmckmELpHAyec5uVwn +i+0AWSgdQikAQmAgWJr9jGI7JNm2idZVonWRaJkhmieIpmGiqY9o7CIZWkiG +epK+iqwrpWjzqZpsqiaVpk5gqD4zle8BxStQ8RSWh7Nk99nS7zjS33Elv+GK +/4Er/q8c0d+yhX8NCf+SIfhzkuA/XvL/wx7vT+e5f9rF+dMC1n+Mg//xIxQR +BX6MAFPvAl//GSj9A7P2O0bTHUbrXUb7PUbHPUbnfUbHfWb7PWZrfLclrscc +12uKvU1Mjymm2xTTYfnSYoupR5KqkMxipCDHXpFob3hv73lmnorQrD6Q7d4R +nfyRf/EHztXv2fjfs4h/ZJHusMn3OZRHXMoTHuUFn/pWSP0kpsZJqMkyaqaC +mqeiFatpFVpanZ7WbKR3mOi9FsaQlTFuZ84gwIIDWHWCmy5o1w0deuBTL+vC +x77ycwl+HtnPp/mFQEAEBcTsgIQXkAoCctGNQnqjlN+oFDcq1Y1ac6PR3mj1 +P+gMP+iNP+jNPxgsPyi9JqXXqPDo5R6dzKORuFVit1LkkgtdUr5LxHMKuE4u +28GCHSCEMgCUykCINPs1xX5Bsp0QrHs46wbWsnRpnr40jV2ahi6NvZeGjktD +86W+DqurxGqLrzRfrzRZ1+oUnCoer/xMUL4jKqKI8qckWThZdp8i/Z4i+R1F +8k8U8T+SRX9PEv0/BOHfXAn+6kLwl4f8P9/g/adZ3p/1cf+smv1nKaz/FAf/ +80fo8Wvow1Mw8RGYfQco/B1Q9geg5jtmwx1m011my11mazD3gi+A5vhOS1yX +Ja7bHExslzm20xLbbo1pscU2IIk1SFoFkluEFGXbK5PtDdH2tij70DPjzGPN +SrhiO0x68FB88kB4/lCACRNgIwRXjwXXz4W4KBHunRj/SYqPleGTFIR0JSFH +TSjQEEt1xCoDsd5IajGTOi3kPht52E4ZR6kzDuqCk7bqom+6Gbse5oEXOPFB +GB985WMT/ByKn0v38wG/AA4I2QExLyARBKTigEx6I5ffKBQ3StWNSnOj1t5o +9Ddaww9a4w868w96yw8Kr0nuMco8BqlHJ3FrxW61yK0UuOR8l5TnFHOcAraD +BzvYIAoBKJOB0Gh2EsWOI9kuCbZTnPUQa9nGmNfOzfMnpokj48CRofvI0H6k +bzrS1Rxry4+1RceavBN15okq5VQZd6qMPlO8O5dHncufXsjCL6QPLiTfX0h+ +fyH+H+ei/34m+vWJ8L8eCn+1K/gvG/y/WuT/5wneX/Zy/6Ke8xd57L9IYv23 +WPjOJ/jZG+jDCzAhEsx4CH69Axb/Hiz/I1D9HVD3PRBUa7wDNN0NpTG+wxrX +eZvgi3ZrbJsttsUe24gk1iGpweIqQ74WIsU5SGWqvT7W3hIssSjr6AvjzDPt +8hPVxhPFzmPZ/hPp4VPp8XPpaZT07I3s/L3sIlqOiVFgElWXqerLLA02T4ct +0mPLjVfVpqsGy3WrFddlw/Uh+GGUMO4gzLiIC27Sioe84aXsemmHXsapj4nx +gdc+iOhnUfxsup8L+HlwQMAJCHkBkSAgFgck0hup/EauvFGobpSaG6X2RqW/ +URt+0Bh/0Jp/0AW9PGaZxyT1GMRuncitFbrVApeS55JznVKOU8xyCGEHD0Q5 +TBRmIAANoVHsZJINT7Bhr63nWMsRxrJ3bt44MS0fGWf3DWO7hv4tfduWrmFL +W72lLdvSFG6pc7dVGdvK5G1l3I4iekf+blcetSt7uiuN2JU+2JXc2RX/YUf8 +223RbzaF/7gu/G/Lgr+b5/9qkv83Q7y/7uL+VT3n/y5k/+dU1t8msn4XC4d9 +gl++hT69hBKegOnhYO59sPB7sPQPYMUtWe33QP2doNpt4ttt8e0hqbg2W1yr +La7FHteIJNQjKbVIeiWSXYrkFyIluUhlOlKXaG/6bG9/Z+97bR2NMk6/1C+8 +1K68VK9HqbZeqXbeKPfeKfc/qA6jVUex6uMEzXGK9iRDd5KjP803npWYzirM +57XW80bbRZsd04Vg+h2Xw07suOtqxn294MGtegibXtKel3LkpZ756Jc+Js4H +EP0QxQ/T/WzAz4H9PE6AzwsIhAGhOCCWBiTyG6nyRqa6kWtuFNobpf5GZbhR +m2405hut5UbhsQS9JG6j2K0XurV8l4bnUnFcCrZTxnJKIIcQcPCZKIeOwFQE +INvpRDsFbyNcW6+w1guM5eTMvH9i2j4yre4bF3YMU1v6kXVd76q2bUlbu6Ap +XVAXLKhyFpXpi8qkRUXsovzTkvzdkixqSfpsSRqxJHm4KL67KP7jvOh3c8J/ +mhH+90nBr8cEfz/I/7tu3q9auH9Tzf0vBZy/Tmf/Kpn12wTWvRj4ySf4zVso +OgpKeAalR4I5YWD+PbD4e7DsD2DlH8FvZHW3avUhr7ZQ4lrtIawmJKEBSQ4W +Vw2SWYnkliIFQa88pCITqU1BGuPtrZ/tHe/tfW+tI2/Nk2+Ms28NC2/1y+91 +qx9065+0m591W7G67QT9TrJ+N92wl23czzPtF5oPSq2HVbbDOvtRE3Lchh53 +O0/6XafD7rMJ98Ws53LJc7XmwW178fte4rGXfO6jYn00nI9B8gFUP8jww6Cf +Bfs5nACXF+AJAwJxQCgNiOQ3YuWNRHUj1dzIdDcK/Y3ScKMy3ahvveRBL7c5 +6CVyGwQuHc+l4bhULKcCdspAhwRwiBiogIZyqQiLbAeJdgbeRr22ErFW3IXl +8sx8dmI+PDTt7hs3dgzLW/rZdd34im5wSds9r2mZVddOqcrGlXljyrQxRdKY +PHZM9mlM9m5cGjUmeTYmiRwTh42K742IvhsW/n5Q+Nt+wW96+P/Ywf91M+/v +a3l/V8b9VR7nbzPYv05l/y6JdS+OFfkFfvkRfv8WjomCkp5D6Y+hnEdg/gOw +6C5Y+l2wxMCq78Ca738i+4YV32qPD2I1IwmNSFIDklKHpNcgWUGvMqSgCCnJ +RypykOoMpD4ZaY5H2mKQzk9I7wf74Afr6EfL5EfzzCfT3GfTQoxxKc64nGBa +TTatpZnXMy0buZaNfOtmsW2r3L5djWzXO3aanbvtrr0e18Gg+2jUfTLlPp33 +nC97MBse7I73+sCLP/ESLnwkrI+C99FIPjrVz2T4AdAPsfwwJ8DmBzjCAE8c +4EsDAvmNUHkjUt9INDdS3Y1cf6MwBpSmgNoc0FgDcrdVGvIyiVxBLz3PpeU4 +1bBTCTrkTIeUjoqpqICC8EgIm2CHcDbmlY12aSVfWPBnFuyx+fzQdLxn3N8x +bG0aVtf1Cyu66SXt6Lymf0bdOaVuHlfVjijLhhT5/fLMXllilyy6S/quSxLV +JXnWJY7sFIV1iO63C79vE/6hRfDPjfx/quP/v1W8fyjh/for9++zOf+Qwflt +Gvu7ZPaDBFZkLOvFZ/jtBzj6LRwXBSU/hzKeQDnhUP5DsOgeWHoneBUDK78L +lliILOhVd+tlv/VC4puQxEYkuR5JrUMyapDsSiSvHCkoQYoLkPI8pCobqU1H +GlOQlkSkLQ7pjEG6vyB9n+1DX2yjMbbxWOtkvHU60TqbbJ1Ls81n2hZy7Itf +kaVCZLkUXalwrNY41xqdG62urS7Xdr9rd9i9P+E+nHEfL3pOVj1nm56LXe/l +offq1IvDeAlXPiLBRyb7qDQ/jelngH6A5Qe5fpgfYAkDbHGAKw3w5AGBMiBU +B8TagFQXkBkC8qCXOaCyBNTWgCzkZRG7zEKXke80cJ06tlMDO1SgQ8FAZVRU +TEKFRISHt3Ou7TDWBmCs9HMr5dRCODZfH5gwe6bTbePBpmFnTb++olte1M7N +aSdmNMOT6r5xVceIsmlQUdMvL+uRF3TJsjukqa2SuGbJp0bxm3rR81pRRJXw +QaXgTrngj6X83xXxf1vA++1X3j/ncn+fzf0uk3M3jfMghR2eyH4az3oZw3ob +DX/6AMe8gROjoNTnUOYTKDcCyg+Diu6DpXfB8u9CXrclBtbe+VZft8UVHyyu +n7zSvnlV3XqVIsVFSFk+UpmH1GQj9RlIYxrSkoK0JSGdiUh3AtKbgPQnIAOJ +yFASOpKCjqWh4xnoRDY6leeYLnTMljjmKhwLNc6lBudyi3O107Xe69oYdG2N +uXem3Htz7oMlz+G653jbc7rnOT/yYs68WIz3+tqHJ/gIZB+J5qMw/VTIT2f5 +mVw/wA9AwgAsCbBlAa4iwFcFBBq/SOuX6P1Sg19m8ivMfqXFr7L6ZS6bxGUV +uSxCp4nvNHKderZDCzvUAKpkoHIqIiUhIrxdcGXnXtpYFzbwzMo4sVAPzcR9 +M27XdLllPNswHK3q95b1Wwu61TntwrRmZlI9PqYaHFb2DCrb+xRNPfKaTll5 +u7SwVZrbJMloECfViWNrRNFVwncVwldlghcl/KdF/MgCXsRXXnguNzybG57J +iUznPE5hP0tiv4xnv45lvfvM+vQRjnkPJ7yBU6Kg9OdQ9hMoLwIqCHo9gEJe +3996ff9Lr7Z/8UpqRFIafvKqRnIrkfwypKgEKS1CyguQqjykNgepz0KaMpGW +dKQtDelIQ7rSkJ40pC8d7c9AB7PQoRx0JA8dzUfHixwTZY6pSsd0jWO2wTnX +4lzocC71uJYHXKsjrvUJ9+aMe3vBvbPi3tvwHOx4jg48J8fes3PvxaX3Eue7 +IvquKT483UcE/GTIT2H7aVw/Q+AHRH5I4mfJ/ByFn6fy8zV+oc4v1vslxpCX +3OxXWP1Km1/qsotdNpHTInCaeQ4jx2FgOXQQqgFQFR1RUBAZyS7G24VXNt6F +jX1qhY4szAMLbc9M3jHhN41X68aLFcPJkv5gXrczq92Y0ixPqOdG1VNDqtEB +5UCvortb3tYha2yT1bRIyxslxfXir7XirGpRWqUwqVwYVyr4XCz4WMh/l89/ +k8d7ncN9lcWNyuBGpXFepXBeJ7HfJrDfx7E+fmF9jmbFfoAT3sLJr+G0l1Dm +MyjnMfQ1AioMg4r/jVfdT/3G7Xr4S696JKMWyapBcquQrxVIYRlSXIKUFSEV +BUh1PlKbh9TnIo05SHM20pqNtGcjnTlodw7ak4v2fUX7C9DBInSoxDFS7hit +cozXOiYanFMtzul252y3c67ftTDsWhp3rUy5V+fc60vuzTX39pZnd9ezf+g5 +PPEeX3hPsd5znA9D8l1SfVd0Hw7wE2A/ie2n8Px0oY8p9oFSHyz3sZU+rtrH +0/oEOp/I4BMbfRKzT2bxya0+hc0ncSFip03otPIdFq7DxHEYYVQPolomoqYh +SopdTrRLcTYR1iq4sHJPLaxDC7hrZmyZKOsm4qrxetlwuaA/m9MdTWv3JrVb +Y5q1EfXioGq2XznRoxjpUvS3y7tbZW3N0sYGSW2dpKJGXFIlKqgQ5ZYJM0sE +aUWCpAJ+wld+bC7vSw4vOov7KYP7KY3zMYXzKYn9KYH9OY79JYYVG82K/8hK +fAenvIHTo+DMF3DOUyjvMVQQDhWFQSX3obK7UMWtV3WouEJeDT97JbQgCc1I +UhOS0njrVYdk1SI51UhesMQqkKIypKQUKStGKouQ6kKktgCpz0ca85HmfKQl +H23LRzsK0M5CtLsY7SlF+8rR/krHQLVjqM4x3OgYbXGOtTsnup2Tfc7pIdfs +qGtu0rUw61pacK+suNc23Bvbnq19z/aRZ/fMu4/xHl55j/HeU5LvnOrDMHxX +oA/H8hE5PjLfSxV6GRIvIPNCCi9L5WVrvFytl6/3CoxekckrNnulVq/M5pXb +vRInInLaBQ4b32HlomY2aoJRA4DoGHYtza4m25REmwxnlWCtwgsL/8TMOTTD +uyZg00RbNZIXDfg5w9WM/mJSdzKuPRjV7AypNwZUK72qhW7lTIdivE0+3Czr +b5R21UvbaiVN1eK6CnFVmaisRFhULMwvFOTk8zPz+Ok5vJQsXlImNzGdm5DK +iU/mxCVy4uLZ8bHshC/sxGhW0kdWyntW2ls44xWc9RLOeQ7nPYHyI6HCcKj4 +IVR6Hyq/9QoV152QV/3doFeHLaHdlvALr+RGJLUBSa9HMuuQ7GCJVSNfq5CC +IFk5UlKGlJcilSVIVQlSU4zUFaMNxWhjMdpcgraWom1laHs52lmJdlU7emod +vfWOvibHQKtjsMM53O0c6XOODTrHR1yTE67padfMvGtuyb2w5l7adK/setYO +PBsnnq1z786ld+/ae0DwHpG9pzTvBdN7CXmv2V48z0MSeCgiD03qYcg9gNID +qT0sjYej8/AMHr7RIzR7RBaP2OqR2rwyu1fsRIUOhO+w81AbB7WwEDOEGAG7 +gW7XUW0akk1FsCqurdJLi/jcLDgx8w5M7F0jtGlkrhqoi3rSrB43qbsc0Z4N +aY4HNPu96u1u1XqncrlNMd8in26Sj9fLhmulfdWSrkpxW7m4uVRUXyysLhRW +5AtK8wRFOfz8bH5uJi87nZeZxk1P4aYlcVITOKnx7JRYduoXdmo0K+0jK/09 +K+MtnPUazo6Cc5/DX5/C+Y+hwgio+BFU+hAquwdV3IEqvw8VV9Cr7m7IqzHh +m1ebPaEVCZIlNiPJTUhqsMQakIx6JKsOyalF8mqQ/GqksAopqkRKKpCycqSi +HKkqR6vL0dpytK4cbahAGyvR5iq0pRptq0Xb6x0djY7OZkd3m6Onw9HX7ezv +cw4MOodGnCPjrtEp1/ica3LRNbXintlwz227F/Y8S0eelVPP2oVnA+vdxnn2 +SJ5DqueY4TkDPRiWG8tx4/hugtBNFrupMjdd4Waq3KDGDWvdLL2bY3DzTG6+ +2SO0eEQ2j9jukSIekcMhcKA8FOGidjZihRELaDcz7UaaTU+xaYlWNd6ivLLI +MWbpmVl0bBIcGLk7BtamAVzVMxZ1lFkdcVJ7ParBDGhOe9SHHardNuVWs2Kt +UbFUL5+rlU1VS8cqJENlkv4ScXeRqL1Q1JIvbMgT1OYIqrL45Zn8knReUSqv +IIX7NYmbm8jJiedkx3KyYthZn9lZn9hZH1jZ71nZb1k5r+HcKDjvBZz/DC54 +AhdFQsXhUGkYVPYAKr8HVd6BfiyuW6yGe0BTQqf1lsz+rcSCXknNSMotWXoD +kvkzWS2SX4MUVCNF1UhJFVJahZZXoZVVaFUVWl2N1lajdTVofR3aWI82NaLN +TY7WFkdbu6O909HR7ejqc3YPOntHnH3jzoEp1+Csa3jBNbLsGltzT2y6p3bd +MweeuWPPwpln+dK9du3eJLh3KO59uuuI6TqFXOds1yXPdSVw4UUuotRFlruo +Shdd7WJqXKDOBRtcbKOLY3bzLG6+1S20uUV2txhxCx1OPurgoigHQViIHbJb +AbuFYTNRbUayVU+waHEWNdasvDDJT02SI6No38DfNnA29PCKDljU0me1lEkN +YVR9PajC9KhOO5SHLYrdesVmtXy1UrZYLpsrlU4VS8YKxcMF4v6vop5cYUe2 +sDVL0JTBr0/j16TyqpJ55Unc0gRuSTy3KJZTGMPJ/8zOj2Z//cj++p719R3r +6xvW11es/JdwwQu48Blc9AQujoRKfsKquA9V3g1iQdW3K2GouO4Bjb/w+rHE +EltCXsm3ZGnfyBqQ7Hokpw7Jq0O+1iIFtWhhLVpci5bUomW1aHkdWlGHVtWj +1Q1oTSNa24zWtTga2hyNHY6mLkdzj6Olz9E26GwfcXaMObsmnd0zrt55V9+S +a2DVNbThHt52j+27J49cM6eueYxr6cq5indukJzbVOcew3kAOo9ZzjOO44Lv +wAod1xInXuYkKpwUlZOmcTK0TqbeCRqdsMnJMrs4VhfX5uLbXQLEJUTdAtTF +Q50cxMFCUNiOgHYb02al2SwUq4lkMeAt+muz9tKkPjcpToyyQ4NkTy/c1vPW +dZwVLbygAWY0tAk1eVRFGFRe9SoxHYrTFvlhg3y3RrZZIV0tli7lS+byJFO5 +4vFs0XCmcCBD2Jsm6EoVtCfzW5L4jQm8+nhebSy3OoZb+YVTHs0p+8Qu+cAu +ec8ufscqesMqes0qimIVvYCLn8PFT+GSJ3BJJFwaDpWFQeUPf8K6E8KqufsN +CwwV1z2gOaHL+nOJJbbZE39Blhoka0LSG5HMRiSrAclpQHMb0LwGNL8eLWhA +CxvQ4ga0pBEtbUTLmtDyZrSiBa1sQ6vaHTWdjtpuR12vo77f0TDoaBxxNo85 +WyadrTPO9jlXx6Kra8XVs+7q33YO7TlHD50Tp47pC8cc1rGIQ5eJ6BoF3aSj +OwC6B6OHbPSEh54JUIwYxUrRazmKV6IktYOiddB0DrrBwTQ6QLMDsjhZVifb +7uQiTh7qEjhCajzExUGcsN0B2lGmDaHbbFSrlWyxECwmnNmANekwJs2ZUXVs +UBzoZbt68ZZOuKblLWvY82poRs2cUNFGlOQBBaFHcdUhx7TIThulh7XSvUrJ +VqlkrVC8nCeazxJNp4kmkoUjSYLBBEFfPL87jt8Zw2v7wmv5zG2M5tZ/4tR9 +4NS851S9Y1e+ZVe8Zpe/YpVHscpesMqes8qewmVP4LLHcHkEXB4OV4RBFQ+h +yvtQ1d2gVCi/wAJDxXUfaPnZKzGYX5K13JI1I2nNSHoTktGEZjah2U1oThOa +24TmNaFfm9D8ZrSgGS1sQYta0eI2tKQDLe10lHU5ynscFX2OygFH1ZCjesRR +O+6sm3TWTzsb55wti462FUfnhqN7G+3bQwcP0ZETZOwcmcQiMzhknogsUewr +NPs6074F2XfY9n2u/UhgPxHZzyQIRoZgFci1CsFrEKIOJetRqhGlm1CmBQWs +DsjmCNKwkeAa6OA7HEK7O1hrHJuTZXOCNgfDitKsCMViJ1qseLPlymS6NBrO +jboTg+ZIr9rXKbZ1sg2teFUjXFLz5lTsaRU0rmQOK2gDcnKPjNAhu2qRYhol +Z7WSo0rxfqlou0i0/lW4ki1cyBDMpgimEvljcfzhL/yBT7zeD7zu99yOd9y2 +t5yWN5ym15yGV+z6KHbdS3bNC1bNc1b1M1bVU1bVY7gyEq6MgCvD4cowuOoh +VPUAqroPVd8NpeYuVPtvsJpDXt3WW7Jbr5/J2pCk1lCSW5CUFjS1BU1rQdNb +0IwWNLMFzWpBs1vQnFY0txXNa0O/tqP5HWhBJ1rQhRb2OIp6HcX9jpJBR+mw +o2zUUTHuqJpy1MyidfNowxLStIq0biDt2/auPXvPob3/xDZ0bhu5tI1f26YI +tlmybZ5mXWJaV0HrOsu6xbHt8m37QtuR2HYis50pbBiVHau2X2vteL2daEDI +JoRiRoIQDFtwxUOC6x4bQYPXLL4DDV7IgpczrtUVrDvI4mBaHDQLSjYjBLP9 +2mTFGi0XRtOZwXCs1x3oNLs61ZZWsa6RrajFCyrhrJI3qWSPKeAhOdAvo3dL +yR1SQovkukF8WSs6qxQdlwkPioQ7+YLNHMFaJn8pjT+fzJuJ503Gcsc+c4c/ +cgfecfrecLpfcTpfcNqfs1ufsZufspuesBofs+qDiWTVRcC14XDtI7gmDK55 +CNc8gGvuQzX3Qqm9Td29kNSPWPfBH7HuA60J3ZagV2JnML8ga7cnBcm+JajW +iqa0oqmtaFpbKOltaEY7mtmOZnWgWZ1odhea043m9KC5vWheP5o/iBYMoUUj +SPE4UjqJlE/bK+fs1Qv22mVb/ZqtcdPavG1t27N2HFq7Tyy955aBS8vQtWWU +YJkgW6ao5lmGeQE0L8GWVY5lnWfZElp2xJZ9qeVQbj1RWs/U1gut9VJnuzLY +cCZb8MMnW+xUq51hswP2YFMRbAXtwYYw2MYHe0W+xc21uNhmF2R2AiZHsBIp +RoRotOOMtkuD9cxgOdGbDnXGPa1+W6vd0KhX1YollWxeKZlWCCfk/FE5Z1AG +90mBLgm9XUxpFhMbRLgaIbZSeFEmOCniH+bz93J521m8jXTuSgp3MZE7F8eZ +/sKZjOaMfWAPv2MPvmH3v2L3vGR1PWd1PGW1P2G1RrJaIuDmcLjpEdwYBjc8 +hBseQPXB3P9lQkah3A9J3WL95PXg1iux25r4M9mPavakYNp/THI7EkxKRyip +wXQiaZ1IeheS3o1k9CCZvUhWH5I9YM8dtOcN27+O2vPHbIWTtqJpW8mstWze +WrFkqVyxVK9barfMDTvmpn1zy5Gp7dTUeW7qvjT1XpsGCMZhknGUapxgGKcA +4yxsnGeblnimFYFpXWTalJp25OY9pflAbT7SWE51lnODBWO0XJsswZWNZLFQ +rRa6Ldj+WYNNIAuxclArz2ELbseCHT7X5GabXLDRBRidwYsd1YCS9AhOb8fq +bBc664nOcqA172iNmxr9mlq7rFIvKJWzCvmUXDImEw1L+QNSbo+E1SkG20SM +JiG1XkiqEeAr+FelfEwR7yyfd5zLPcji7qZztlI464nslXj2Ygx77jNr+hNr +8j1r7C1r5DU8FAUPvIT7nsM9T+GuJ3DnY7g9EmoLh1rDoZZHUEsY1PwQagrm +AfgtvzD6Mc0/YYW8En/2+pZvZJ22pF8kudMeTEpXKKndoaT12NJ6bel9tox+ +W+aALWvImj1szRm15o5b8yYs+VOWghlz4by5eNFcsmwqWzNVbBirto01u8a6 +A0PDkaHp1NByYWjD6juu9d0EfS9ZP0DVDzH0o4B+HNZPsfUzPMO8wLAoMixL +DGsy44bCuKUy7mhM+zrTsT64jpkwRlPwGoQ3B5s9U7Dlo9uCeytzcIcFI2Y2 +auE6LEKTN7iJ5ho9bIM72PMDeidD56TqHCQtitciVxo7RmM7VVsP1ZZdlWlT +ZVxVGRaVujmFZlqumpDJR6TSQYm4TyLoFnPbRewWIdQoYNbxadV8SjmPWMLF +FXKxXzkXuZzTLPZROns/hbWTxNqMZ63Fwitf4MVoeO4DPPMOnnwLjb+GRqOg +4RfQ4HOo/xnU+wTqeQx1R4KdEWBHONj+CGwLJgxsfQi2fMsDsPl/yo9SIayQ +V4/lX5PdJunH2JK6rcnB9ISS0htKap81td+aNmBJH7RkDFsyRiyZo+ascXP2 +pDlnypQ7Y8qbM+YvGAuWDYWrhuJ1Q8mmvmxHX7GnqzzUVR/ras909RhtI1bb +jNO2ErQdZG0XVdvD0PYD2kFYO8zWjvG0EwLdtEg3K9HNy3SLCv2KSr+h1u9o +9fs6/ZFef2bQY4z6K5M+2OYRLQaK1UCzGRh2I4gYYcTERk1ch0lo8PINXq7e +w9Z7YJ0b0LqC/T9V4wz2lgQ1eqVCgpfCM6XtSGndV5i35aZ1uXFJrp+T6SZl +2lGpekii6BfLekSSTqGwVchvEnDq+XAND6zkMcq41GIOqYCD/8q+zmFdZrLO +01knKfBhErwXD+/EQptfoLVoaOUjtPgenH8LzrwBp16BE1Hg2Atw5Dk49BQc +eAL2PwZ7I8GeCLA7HOwMBzsegR1hYHsY2PYwGKD14S3NL6R+xPqfvP5Nknp+ +Sq8lOZg+S0q/JWXAkjJoTh0ypw2b00ZM6WOm9HFTxqQxc8qYNWPInjPkLOhz +l/R5K7qva7r8TW3htrZoV1tyoCk90pSfqCvO1VUYdc2Vug6nbiCqmsiqFpqq +jaHqAFXdsLqXo+7nqQcF6hGRekyimZRpZhWaBaVmRaXZUGu2tZp9XbCd05wa +NBdGLdakxZm1BIuObNVRbTqGXQ8geggxsFADx2EU6n18nZer87K1HkjjBjRu +htpFVTnJSgdB6bhWoJdy5ExuP5bZDqSWHal5Q2JakRgXxPppsW5cpBkSqXtF +yk6hvE0gbeaLG/iCWh6vissu50AlHKCITc9nUXJZpGwYnwFfpUGYFOgsETqJ +Bw9jwb0v4HY0uPkRWPsArLwDFt8A86+B2Shg6iUw8QIYewaMPAWGnwCDj4H+ +SKAvAugNB7rDga5HQGcY0BHMQ6D9IRBUa/vZ6Jf5yetnMkvoJ9/SawlKJfVZ +kvrNwSQPmJMHTclDppRhU8qoMXXMmDpuSJs0pE3p02f0GXO6zAVd5pI2a0Wb +vabJ2dDkbqnzdtRf91UFh6rCY2XRmbLkQlmKVZZfKyrwiiqSooaiqKMrGpiK +JlDRwlK0cRQdPEWXQBn8oAYlilGpYlKmmFEoFpSKFVWweVNsa5V7OuWhXnli +UJ4bVZcm1bVZjbeoSVYNxaah27VMRAsiOhjVsR16gTZ0656j8bLUXkjtAVQe +htJNVbjIcidB7riWOS6l6LkEOZHYD8S2XZFlU2ReFZoWBcZZgX6Srxvlawf4 +6m6eqp2naOLJ6riSaq6ogiMoZXOLWKwCFpQHM3MgWiZESQeJqSAuGbxKBDDx +wFkscPwFOIxm7n1kbn9gbr5jrr1lrrxmLr5izr9kzr5gTj1nTjxjjj1ljj5h +Dj9mDkYyByKYfeG3ao+ArrBbtYc/qT34N2o/YVn+lVQofebEW6mkAVPSoClp +yJQ8bEweNSaPGVLGDSmT+pQpfeqMLnVOmzavTVvUpC9rMlbVGeuqzE1V1o4y +e0+ZfaDIOVLknsq/nsvzMbKCK1khTlZMlJWQpWVUaTlDWglIqyFpDUtax5U2 +8qWtAmmnUNorlgxKJKNSyYRcMqOQLCgly2rpuka6pZXu6mTBve2xQX5mkmPM +iiuzAmdREq1Ksk1Fs6sYiBpANBCqYTm0Ao2fp/ZxVD6WygspvYDCQ5d7qDI3 +SeoiSJzXEuel2HEuQk+EyKHAviuwbfEtazzzEtc0xzVOcQxjHN0QW9vHVney +VK0sRQNLHnyT5SxJEUtUAPPzIG4OxMoCwXSQmQrQkgFyIpMYz8TFMrExzIvP +jLNPjOOPjIP3jL13jO03jI3XjLVXjOUoxuILxvxzxswzxtRTxsQT5thj5kgk +cyiSORjB7A9n9j1i9jxidofdqv2vyP4XWOZvWIkDpsRBU+KQMWnYmDRiSBo1 +JI3rkyb0yVO65Glt8qw2eV6TsqhOWVanrKpS15Wpm8q0bUXarjx9X55xJMs4 +kWaeSbMuJNlYSc61JBcvziOJv1LE+TRxAVNcBIqKYXEZW1TFEdbxhI18YatA +0CkS9IoFgxLBiEwwIRdMKwTzquAeVrimEW1qRTs60b5BfGSUnJokF2Yp1iK9 +tsoIVjnJJqfaFXREyURVIKqCHWq+KsBT+TlKP0vhg+Q+psxLl3qoEg9J7CaI +XNdC56XAec53nPDRQx6yx7UH93rrbOsyyzLPMs3AxgnIMALpBkBtD6jpAFTN +gLIekFcBsjJAUgiIcwFhJsBPB7ipTFYyE0xkMOMZtDgGOYZO+EzHRdOxH+kX +H+in7+nHb+kHb+i7r+lbr+gbUfTVl/Tl5/SFZ4y5p4zpp4zJJ4zxx4zRSMZw +BHMwnDlwS9YbImN2PfyJ7MH/RNbyr5fB/z+sxGFD4oghcUyfOK5PnNQlTmkT +ZzRJc5qkBXXSkippRZm0pkjaUCRvyZN3ZMl70uRDacqxJOVUnHohTr0UpV2J +0vDCdKIwnSzIoAoyGYIsQJAD8fNhXjGLV8bmVnE5dTxOI5/TKuR0ijg9Es6A +lDMi44zLOdNK7pyKu6jmrmp4Gzr+tp6/ZxAcGgUnJuG5WYSxiK+sYrxNQrRJ +yXYZFZEzUDmAKiCHkq8MDQyw5X5Y5gelPqbERxd7KSIvSejBC9zX/NA95HOu +84TjOGSjeyxkC7avQ7YV0LoAWGYA8yTTOMowDDL0vXRdJ13TSlM30pS1NEUl +TVZKkxbSxLk0USZdkELnJ9C58XRWLB2MoTE+02jRNPJHGuED7fo97fId7fwt +7fQ17egVbT+KtvOStvmCtvacvvKMvviMPv+UPvOEPvWYMRHJGIsIkjGGgmSP +bqss7Eeyf+UVajxC3eAvvBJ6zQl95oR+c8KAKWHQmDBkTBg2JIwYEsb0CRO6 +hEltwrQmYVaTMK9OWFAlLCsTVhUJ6/KETVnCtjRhV5pwIEk4EieciBLOhQkY +YQJWkIDjJxD4CSReIpWXSOclM7hpADsLZOVCrAIYLmZDwSt4FRes44ONArBV +CHaIwR4J2C8Fh+XQmAKaVEKzKnhBw1rWstZ17C09Z9fAPTByj028UzP/wiLA +WoXXNhHBLiLZxRREQkOlDFQGOOR8eYArC7CloWEPUOxniPw0oY8i8BL5oUdp +V1w3hu0+Z7lOYOch5NgD0S0AWWfaVxi2Bbp1lmaZpJrHqKYhirGfrO8m69pJ +2maSuoGkqiEpK0jyEpKsgCTJJYkzycIUMj+BwouhcqKprE9U8COV8Z5KfUcl +vaXg31CvXlMxr6lnr6jHUdSDl9TdF9St57T1Z7TVZ7Slp7T5J/TZx/SpSHqQ +bDRIFs4YfMToD5ZYWIis6yGz8yevENbt/Y3mHxv4bmvoRse/eJl+9Aph6UNY +4yGs+GlN/Kw6fl4Vv6iMX1bErcrj1mVxW9K4HUnsnjj2UBR7LIw5FcRc8GMu ++V+ueV/w3M9EzmcK5wuNHUeHExlQChNMB4AsiJkHMwpY9GI2vYxLq+LRavm0 +BiGtRURrF9O6JbQ+GX1QTh9VMCaUjBk1c14DLGnBVR24oYe2DfCekXVoYp+Y +OWcWLsbKu7LxcXYBwS4kIyIqKqaHxgulfFlohootCcCiACAMMAR+Gt9P5oWe +U+PY3iuWBwN7ziD3MeA6YLp2Gc4tumOdhq5QkUWKfZZsmyJZx4iWYYK5n2Ds +wRs6cPpWnK4Rpwm2tVXXyrJrRTFOno+T5uDEGXhRCkEQ/E7GELmfSOx3ZPgt +GXhDpr8mU16Tia/IuCgKNopy8ZJy8oJy+Jyy95y6/Yy68ZS6+pS29IQ2/5g2 +GxkiG4+gj4Yzhh8xBh4x+m69um+9Or55fcMKbp9DtzVuyf61V6i4QpUVP6qP +H9fF32LFzarj5lVxi8rYZUXsqixmQxqzJfmyK/6yL/p8KIw+EUSf8z9heB+v +uB9wnPfE4JtnfaBA0VQwhh5c4RlJTFoKQE0HKVkQOdgM57NJxRxiGZdYySfW +CIj1QmKziNgmIXZKSb0y0oCcPKwkj6soU2rqrIa2oKUv6xjreuamEdgxgfsm +6MgMn1pY51b2pY1zZefiQ8OEAioqZKAiwCEWSENjihxRABYGQEGAwQuN65DZ +fgLLj4N9WNB3AXjPmKFHogc09y7VtUVxrpMdK0R0kYDM4pEpnH382jp8ZRm4 +MvdiTZ2XxrZLQzMmtHOswWgqMKpSjLIII/96Kcu5lGRgxSlXwoRrQQyO9wnP +eUdkRZHgKBIzikR7SSK/JOFfkK9ekDHPyafPKUfPKPvPKNtPqRtPqKtPqEuP +afORtJlI+mQEfSycPvKIMRQssTBG78NbrwfMUH3dD3k13wea7oGNt3czbm/5 +/otXqLjiB43xw4b4EX38mC5uQhs3pYmbUcfOqWIXFTHL8phV2ZcN6ect8edd +UfS+8NOR4OMp7/05990l5+01+zWe9YoEvyGD7ynMj1T6Zxo1hk6OZxCTAEIK +iE+HcFnwdS7rKp9zVcTFlvKwFXxstRBbJ8I2iq9aJVcd0utu+XWfAjekxI+q +CBNq4rSWNKcjL+kpqwbqhpG2ZaLvmhkHFuDYCp5ZIYwNvrazCXYOGeHSUD4T +FYAOoUAc4IlCw6UsfgDiBZhcP43tp7D8RMiPA/1Ypu+C7juleY+o3n2yZ4fk +3iS61/CuZZxz4doxe4VOYZFxjH0EYxu4sPaeW7rOzO1npuZTY8OpvvZUV3Wi +LT9VF5+qCk6VeWfy7DNp+rkk5UIUvATEYPnRV9x3OPYrPPycCD4nMp4TKc9J +hGek62ckzDPy2VPy0VPy/hPK9hPKxmPqymPqYiRtLoI2HUGfCKePPqIHvQZ+ +6XWL1XLvFuse2JDYYQs9/PqZ7NYrfsD4o9eoLm5cGzepiZ1Wx86qYhYUMUvy +L6uyz+uS6C3xp13Rx33B+yP+u1PumwvOayw76hp+QYBekoDXZPpbCvU9lfyJ +FmyZ8LGM63gmNhG4TIEw6fBFJus8h332lXNWwDsr5p+VCc4qhWc1orMGyXmz +9LxNdtEpx/QoMAOqy2E1dkxzNanFzejw83rCkoG4aiRtmCg7ZuqBhX5iYZxb +gUsbiLNDRDuLgrBpKJeJ8iAHXygK8IUBLj/A5gUgTgBg++lwaI6RBPjxTP8V +3Yeh+s4oviOSb5/g3cF7N689a1fuZax7AeOavXBOnTvGz9DhU2TgxN57bOs6 +srYfWloOzY0HproDQ/WBvuJAV3qgLTpQ5x+qco8UWUfytGNp8qk44UwYcyEI +LjLvsJxX16xneOgJgfmUQH1KJD4lXj8hYZ6QTp+Qj56Q9x5Tth5T1iOpy5HU +hQjaTARtMpw+9og+HBby6gt6PfjJ6x7QfA9ovAs23AXrE9vtt162n0rMHP+j +lyFuWB83Giqu2Cl1zIwqZl75ZVH+eUUWvS75tCn+uCN8vy94d8R7c8p9dcF+ +iWU9w0FPCcALIj2KFFq631LxH2hXn+iXnxkXMcyzOOA0ETxJho5SWYcZ7MNs +zkEu9yCfd1DEPygVHlSIDqrFh3WSw0bpUYv8uF1x0qU87VWdDajPRzQX41rM +lO5yVn+1aLheM+K3TMQ9M+nQQjm1UC+sdKyNibcDRDtEQWA6ygJQDuTgCgUB +Pj80b8/mBGC2H4T9DMhPBfxkhp9A911TfZdk3znRd0LwHuC8u1fezUvvGsa7 +dO6ZP3PPnLgnj11jR87hA8fAPtq7h3Tt2dt3bS071sYdS922uWbbVLltKNvW +F2/rCnY0ebvq7F1l5r4i9UCWdCiJPxYFL+KfznnvMJxXwY/lGorEMx8TqI8J +xMfE68dEzGPS6WPS4WPybiRlM5KyGkFdjKDOhdOmwmnjj+gjYfTBh0EvRsjr +PrPtW3F9w7oD1obGAH4kC5aYJf6bV78xLug1oo8b08VOaGKm1TGzyi8Lis/L +suhV6ccN8Ydt4bs9wZsj3qtTzssL1jMs/BgHPiEwnhGpL0jEKDLuNQX7lop5 +Tz/7yDiJZh59AQ5iwb14aDcJ3klhbadxtjK5W9m8rTz+VoFgq0i4VSreqpBs +V0t36mQ7jfLdFsVeu/KgW33Ypzka0p6Ma0+ndefzesyy4XLdeLVtwu2b8Udm +4pmFjLFSrmw0vI1BsjOpCEhHIABlQQ62iB8QcAM8ToDDCsCwHwT9TMBPY/gp +ND+R6sORfVii7wLvO732Hl159y+92xfejTPPyoln8dgze+iZ3HeP7bmHd1wD +287eLUfXJtq+gbasI43rtvo1a82apXLNXLZmKlkzFK7r89e1uRuarE1V+rYy +ZUeeuCeNOxB/ORJ+POG/PedGYVhPr6BwPBCBp0YQiJGEq0jiRSTpOJK0H0ne +jqCsR1CWI6jz4dTpR7SJn70ehLw67jNDxXU3VFwhrO/B6tAYW6s9NL/RYYvv +ssZ3W+J7TXE/ecWOaWMmg16qL3PKz4vy6BXpx3Xxhy3Ru13Bm0Ne1Ann+Tnr +CRYKxwGRBPpTIvk5Cf+SfBVsh15TT9/Sjt7TDz4wdz8B25/BzRhoIw5eS2Ct +JrFXUrgr6bzlTP5ytmA5T7hcIFopFq+USlYrZGvV8vU6xUaTcrNdtd2j3hnQ +7I1qDya1R7O640X96arhfNOI2TFhD8xXx2bcuYVwaSVd28gEG5Vsp1MRBgMB +ABSEHbCIGzovxmMFOLCfBfohZujcBJ3mp1B8JJIPT/Rd4X2Ya98Z1nuM8R6c +e3dPvVsnnrUjz/KBZ37PM7Pjnth2j2y6B9bdvWuuzhVX+4qzZdnRuITWLSI1 +i/bKRVv5oqVk0Vy0aMpfMuQt67NXtJlr6rR1VfKmImFbFrsr/nwg/HDED64/ +wa908FN6hGM+wlPC8YQIAjaCeBZBOoog7UaQNyMoK+GUhXDqTNArjPazV9e3 +A7B3gaY7wI9Yd6CqxGbkG1locLTzm5f5m1fsiO7WS/1lRvV5XhG9JPu4Kvmw +IXq3I3i9z4s65jw/Yz2+DL6N4DeHFiz24Pr8nIR5STmLoh69pu2/oe+8Y2y+ +B9Y+giufoKXP8GIMaz6OPZfAmU3izqbwZ9IEMxnC2WzRbJ54Nl8yVyydr5At +1MiXGhXLbcrVLtV6n3pjWLM1rtmZ1u7N6w6W9UdrhpMt4+mu6fzQjDkxY88t +15dW/LWNSLCRyHYKDaExEDqAMmEUFHECQlaADwW4oJ/N9EN0P0DzMyh+KslH +JvgION/1lQ+L9V5gvKfn3qNT796xZ/vQs7HvWd31LG675zbdU+vu8TX38Ipr +YMnVs+jqWHC1zrkaZ511M46aGbRyJvQotmTGVjRjLZg1582ZcuYNWQu69CVN +6ooqaU0RvyGL2ZZE7wnfH/JfB7/YF6xILPgQxwjDkR/hceEETDjxJJy0H07a +CievhlMWH1FnH9Emw2ijD+mDDxi99xld95htd5nNd4DGO2Dd7RRi5V2oIqkp +NCYaOpzSZo/vsMZ33R5n7gsdP48d1sWMab9Mqj/PKKPn5Z+WpR/WxO+2hG92 ++VGH3OenrMcYKOwaeISjRYRW5qunpIvn5OAuY/8lbecVfeM1Y/UNc+ktMP8e +mv0AT39kTUazJ75wxmO4Y3G8sQT+aLJwNFU0liUa/yqeKJZMlkunamQzDfLZ +FsV8h3KxV7U0qF4ZVa9NajZmtFsLup0V/d664WDbeLRnOjkynZ2aLy4sl1jr +Fc6KI9rwZDuRhpAZCBVEaTDKELMCQijAB/1cZuiEJkz1gxQ/g+SjEXxknI94 +5cNd+q4uQscrzk68x0fegwPP7p5na8ezvuVZ3ggNss6uuKeW3WOLruF5V/+s +q2fG1THtbJ10Nk44a8edlWPOsjFHyRhaNIYUjNvyJqw5k+asKWPGjD5tTpu8 +qE5cVsatyb5sSj7uCt8e8INr0dNz+BEWeICjheGIj/DYR4SzcOJhOGknnLz+ +iLL0iDIbRp18SBt5SB94wOi5z+j8ubi+A2u+C2KBFfehsuRGJLEJiQ+R2UOn +9jqtobPMvabYAUPMT17RM8pPC/IPy9J366I324Kofd7zY/bj2//9IY72CE+M +IFw9Jp0HO9VnlN3n1M0X9NWXjMUo5uwrYOo1NPEGHn3LCj0f/8AZ+Mjtj+b1 +xfD7EgX9acL+LNHAV/FgkXi4TDJSLR2tl403yyfbFVPdypl+1dywemFMvTSl +WZnTri3qNlb1WxuGnR3j3r7p8Mh0fGo+vbCcY60YnBVLtF1R7DiancBASCBK +gVGqGAoIgQCf6efR/WyqHyb7QZKfSfDRcT7KlY906cNfeK/PvJcn3vMj78m+ +53DXs7ft2d70bKy7V1fdS8vu+UX3zLxrctY1NuMamnL1Tzh7xp0do87WEWfj +sLNuyFE16CgbdBQNOvIH0bwhJGfYljVqyRgzpU0aUqZ1SXOa+EVlzKo8ekPy +YUf4+oD34oQdeQE9uGI+wFEe4nFhhItHhKNHxN1HpI1H5KWwn7we0AfuM3ru +MTruMlvuAA3fAbV/DI1kV9wDyx5CJan1SHJD6BhRkCx0xLLdGtdlCf2ugH5D +zJDuy5j2c9BrVvFxQfZ+RfJ2Q/hqh//igPPklBWOAe9fB6ubFE64iiCeBxue +J5Sdp9T1Z7Sl54y558ypF8DYC3DoJTwQxeqNYoeGT95xO6J5HbH8jiR+R5qg +M0vY9VXUXSTuKRP3Vkn666QDjbKhVvlIp2KsVzkxqJoaUc9MqOdmNAvz2qVl +3cqafm3TsLlr3D4w7h6b9s/MhxjL8ZX1FG89J9owFDuWZr9mIngQJcIoSQwE +RIyAgO7nUf0csp9F9EN4P3Dto2N9VIyPdO4jnHqvj73YQ+/Fvvd0N3Sg6WDD +s7vm2VoJncJYWXAvzrnnZlzTU66JCdfomGto1Nk/7OwZdHYMOFv7nU19oYG9 +6t7QMFhxjyO/B83pRbP67BkD1rRhc8qoMWlCnzCjiVtQflmWBTu0tzuCqAPu +01NWGAa8d017gCM8xF+GEU7CiHthpI0w8nLQ6yF14gFt5D69/x6j6y6j7Q6z +6XugLnQeFqy4C5Y9AEseQUVpdUhKfehMZXwTEtdsj2uzhX5FQI8ppt8YM6T/ +Mhr0Un2aVXxYkL1bEb/ZFEbt8p4dsSPOoAdY5v1rSlhoKb6IIB5FknceU9ae +0Bae0KefMMeeAkNPwb6ncNdTVvtTdssrTvN7TtNnblMcrzGJ35jGb8oSNOcJ +mwtFraXitkpJe42ks0Ha3SLrbZf3dysG+5XDQ6rRMfX4pHpyVjOzoJ1b0S2s +65e2DKu7xvUD4+aJafvMvIux7F9ZjvDWE6LtjGK/oNkvmQgWRK9hFC9hBEQ0 +v4Aa+o0QHKKfhfdD1z4A62NgfLRzH/nURzz24g68V3tezI73fMtzsuE5XPXs +LXt2Ft2b8+61WffytGthwjU75poecU0MuUYHnUP9zv5eZ0+Ps7Pb0drpaOp0 +1Hc4qtsdFe1oSTta0IHmdKIZXWhajz2l35I8ZEoc08dNaYL7oOhl2fsN0etd +/vPgR3cO3cMy712THuCuHuJPHxL3w0ibD8nLDymzD0Jew/fpfXcZnXcYrd8z +G/4I1PwBrLgDlt0Hi8PAwggoP6MGSasNndFLbEDigmQt9th2a2yXOabP+GVQ +/3lUGz2h+jQT9JK+XRW/3hS82OM+OWaFXYB3r+gPcMQw/OUj4nEEaSeCshZJ +nY+kT0YyRkKPTcHOCKg1nNX4jFX/ml37gVPzmVsdz61K5lWl86uzBNV5gppC +YW2JqK5C3FAtaaqXNDdJW9tk7Z3y/4+s9w5v4zyzxf/93b2bTW6cxCkb23E2 +cbzrrJNYlsQmUY3qEiWzi0UUSbH33nvvFCn2XsUiSpQoiiLFXkESvffBzGDQ +MQOABIvs/L6h7M3evfI8j+nHEvBhznfec877vQNV1UG1DYpHzXBDG9LYhbT0 +om0Dyo5hrHtM1ftM3f9CM/RKMzytHZ3VPZ3XP1vUv1gxTK4bpzbx6W38DZWY +pRNzTNOCdPtQTDkUrh/yVw+5K4fspUPmwgH97cHOzMHW9MHm1P765P7Ki/2l +Z/vzT61vR61vhq2vB62T/XsTvXvPuvfGOvaG23YHW8inn3oe73bWW9rqLC01 +lsYqS32FubbcXFVmLi81l5SYC4tNucWmzGJT2vE0ZmyZKaLcFFJFBNcaghq0 +AS0qf2AAeiGvJxKw2+++4N6YZl6ao51f3Ly4vHRpZcZpddJp7anT+tAlEq+2 +i1uNF7Zrz+9UOFJLztLyHWjZZ+npF+ipTvSkq+SjK3FR2eSjyqF5xMMCIqCQ +8C/B/cuN96v092u1fg0q32YSr3vdkCeJl+ibcb7zS871aebF43e8tLzktDpz +Ze0FUEzSkYKEvtNIHgfQy50YhVeZuc6sbFd2hhc7zY+TGsBNCeamhPNSovgp +cYLURGFaqjA9Q5SZI87Kl+QUSfPKpAWVsqIaeWk9VN6oqGyBazqQum60oQ9t +HFQ2D2NtY6qO5+rul5reKU3/tHZwVjc8rx9d0j9dMTxbN05sGl9u45NUYopB +vGGb3sooB5KNA9HagWDlgLd0wJk/YL49oM8cUKcPtl8dUF7ur0/srz7bXx7b +Xxixzj2xzgxap/usr3r2XnbtPW/fG2/dG23effJ4d7B+t69ut6fG0llpaSu3 +tJRZGkvM9UXm2kJzdYG5It9cmmcqzDPl5Zmy8kxp+aakAlNskSmixPSwjAgC ++aheC2y2Xyfs3Sf3GBZ/84x/8xX78izdcXHr/NLyxeXZS6uTl9aeXiLx6r5I +ab2w1XB+uwaQ6yy10IGWa0/POEdPvURPukKPv86IvcmIjs4kIgFkOeQXOAQV +EP5FhH+p8X6F/n6N1q9e7duk9G5D7nVBHv1St2HR3XH+rZfsq28Y5+Z3zi+t +XVyec1p9Beh8eWMAaOXl7UYnavVFkO8YeVeZmc7MNDdW8j12gh87LoATG8yN +CefFRPFi4vgxiYLYFGFchjAhW5SUJ04ulKSWSDMqZFnVspw6eX4DVNikKGmD +yzqRyh60uh+tG1LWj2CPn6qan6tbX6o7pjRdb7Q9b3V98/qBJf3QimF4wzi2 +ZXxGxV8wiFdsYppnmpVv7kvX98Wr+8Llff7CPndunz2zz5zep73a33m5T3m+ +vzG+vza2vzxsXRyyzg9YZ3utb7r3XnfuTbbtvWjZe9a4+7Rhd6Ru90nN7kCV +pa/c0l1q6Sy2tBWaW/LNjbnmhmxzXZa5OpN8hKo0w1R0/JxOdqYpPcuUlEPE +5pGPHoCsBCy3P6hULUrvLoXngNRlTHD7BefKG8bZhZ1zS6sXlt9eXHmP1+DF +ja4LlJbzW/XntqvO7pScoebb07LO0tMu0JMu0+Ov0WNuMqKcGeGx6QSALCKL +CMshgvOIgALifjF+v8zgV6XzrVP7PMa8WxEvgFef1HVYdGecd3OSffkN/ezC +9vmllYsrM5dWJ5zWnzhtdpGFF6gkrdiRkX2VkebMTHRjxd5jRfmxwwM5ocGc +4HBucBTvYRw/OJEfnCIITReGZYkicsVRBeKYYklcmTShUpZcK0+tl2c0Qtkt +itx2uKALKepFSwfQ8ifKqlGsZlz1aELdMKlunNI0v9G2zuk6FvXdq/r+DcPQ +tnGEZhxn4hNsYpJHvBaaZqANq2zNKl22ihetwnkrf9bKfWNlTVkZk1bahHX7 +mZUyZl0ftq4OWZf6rQs91rdd1pmOvenWvVfNey8f703U747X7o5V745U7A6V +WgaKLX2Flu48S2eOuT3L3JJhbkozN6SYHiWbapLIZxXLEk3Fiab8JCInhUhP +I5IyyEdTgTcArsC/Ug92vk8r4tkrA/fQ+Tn36mum49yO4+Lq+eW3F1YmL66N +XVwfuLDReYHSdG6rznG74sxOkT01x56Wfo6efIkef5Uec4MeeZsRdpcREp9K +fslGVAYJWUgOEZRH+BcSfiVGvwq9b43GpwHzbkG9Oo/xekLidWOSdWmGdnaB +cn5p8eLKa3JvbPRdpLSAqutILT5Dz7zMSL7NiHVlRtxjBfuxAgPZ/iEc33Au ++UxoHM87ke+dIvBJF/hlCe/nih4UiIOKJMGlkrAKaUS1LLpOHtcAJTRBya2K +tA44oxvJ7kNzB9GCYWXRKFbyTFX2Ql01pamb0TTMa5uXdO1r+q5Nfd+2YZBm +HGbiYxz8OY94KSSmxKY3irU9aGVPtrQnWdgTvd0TzOzxXu9xXu2xXuwxnu9R +n+5tj+xRnuytD+yt9u4tde0tdOy9bd2badp93bD7qm73Rc3u88rd8bLdsRLL +cKFlKM8ykGPpyzT3pJs7U8ztSebWBPIx7ccxpvpoU22UqSqKKI8iHxAuiCFy +4oj0RCIplSQCqFpg//tV63waleA2ug2Kncd5V18xz73dObu4dm6JxOvC2tiF +9f4LGx3nKY8dt2rObpc6UPNtaZlnaCkX6AlX6DHX6ZG3GKF3GA9dGIGJSUR8 +ChGTSkSlE2FZRHAOEZBP+BXhfmUG32qtzyOVdxPq1a5w75W5DImcn/KuT7Iu +ztDOLGyeW5o/3hvDFzc6AYsdd0oBf0GlvcWIcmUGezH9/VjegWyPELZLOOdu +NNc5jnc7kXc7hX87XeCcKbybI3TJF7kViT1LJd7lUr8qqX+tLLBeHtwIhTUr +ItsU0Z1wXC+SNIimDSuznirzJrDCSVXptLpyVlOzoKlf1jat6Vo39Z3b+h6a +YYBpfMLBR3n4uJCYEBOvpKbX8OqeYnlXvrArndsVz+6KpncFU7u8l7ucCQtz +3EIftVCHLduDFkqfZb3bstppWW6zLDRb5h5bZust07WWqSrzZLn5RYn5WaH5 +aZ55NNs0nGEaSjUNJJn6Ekw9sabOKKI9nGgJNTUGmxoeEnVBRE0QUfGQ/OaE +wjAiJ4pIjyO/aiYyg/waLr9Sg0+d2qsVduuT3BnjX5tknZulnlkAeM2eX3l5 +YW3k/Hrv+c22c5T6s1uVDjtFdtQcO1raOVqiEz32GgCLDsAKcmE8cGP4pcQT +iYlEfDIJWUQ6EZpFvv79fMK3xOhbofOpVXs/Vnq1we7dMpdBEq9rL1kXSLw2 +wN44vzJxYX3w/Gar41aVPTX3HC0J7IRvGIFeTG8/lmsg63YI+2o451I091wc +90wizz6Fb5chcMgROOYLLxaLLpeJr1eKb1dLvqmTujfIvJrkvq3yBx3Qw25F +WB8cNQjHDiOJY2jqc2XmSyxnCit4oyqZU1csaqpXtI/WtY8pupYdfTtd3800 +9HGMQ3x8RIg/FRPPZcRLyDSFLO/CixZo3iKftUjfWMRTFuGkhT9h5j4zs8fM +zGEzfchM7Tdv95gpXeb1dtNqi2m50bTYYJqvM72tNs1UENOlxFQRMZlPvMjB +n2fi42n402TjaIJxONYwFGUYCDf0hxh6gvRdAfp2f0OLn+Gxj7HWm6jyJcr8 +icJAIieUSIsm4hOJsAzCL5/wqdR6NaFuPbI7I4KrL1mOsztnFlYdl2bAPTy/ +Nnx+vfvcZrMjpe7Mdpn9Tr4NNeMMLekCLe4KPfIGPdSZHvQNw9+N4ePB8EqL +IVLATkgg4pKI6FQiPJ0IziIe5BK+hbhPmd6nWnOvAfNqgd275C4DYudR/rUX +rPNvaA4L647k3nh2fr3PcfOxw3aJLS31Mj3KmR7gwfD0Zd4OYDmFsB0i2Cdi +OF+kcr/M5v21kH+iVHC6UmBXIzxbJzpfL3ZqFF9rltxqld5tl7l1yry65T59 +kP+AImhIEToCRz5FYp6jCS/RlFfKjGkse1aVP68qXlKXrWqqNrR1W9oGqq6Z +rm9jGbq4hl6+cUCID0vwMRnxDCJewKZX6JIFmTcr3pqhN2bZa7PklVn8wiR8 +ZuI/NXFHTOwnJuaAid5LULuJ7Q6C0kpsNBFrj4mVR/hSDb5Qic+V4bPFxpkC +43SuYSrL8Crd8DJF/yJRNxGnexalHQ/XjoVoRoM0ww/UT/zUA97qPi91t4em +zV3b6KardTOWe+JFfnj2QzwlCo9OwgOzCO9SvVeD0q1L5jxM4nVmdsdhYcVx +6c25lWfn1obOrXc6bjae2aq23y62pWbb0lIcafFOtKjr9NDb9MC79PuuDG8P +hocXwyUjgkiLIpJjiIR4IhbwN5UIzSACs4+3RLHBu1J7r07l1YS4d0AufRLn +Ef71CfaFaZr9/MbZpdlzK+Pn1rvPUupsd3LP0uJu0IPcGO4+zGsBTIcQ1n/G +sf+YxfmsmPt5Fe+LR/wvGwV/axGebBPadogcusTnusWXeiRX+6Q3+6V3BmSu +Q3LPYchnFPIfUwQ+g0Mm4IiXSMwUGj+tTJ5Vps9hWYuqvBVV4bq6dFNTua2t +oWnrGbpGtr6Va+gQGHpExn4JPiTDRyFiHCYmUNOkcsGMvjUhMybFtEn+yiR7 +SUieE6JxQjBK8J8Q3EGc3Yczu3F6J05tw7ebjZRG40a9ca3WuFplWC43LJYa +For0c/n6tzm6mUzdm1TtdJLmdbxmKlr9KkI1GYK9DFK+8EcnfNHnXsi4OzLm +Co/cRYbuIL3Oyg5n1eM72opvjIX3yO+NTIjGQ1Jx7wKjVx3m1im/Pcy//JJp +/3bbYWHp7NLrcytPz631O260nd2sd9iqsNvJP03NcKAlXqBFX6WF3aQH3aH7 +uTK8PBhuXoy7Psxb2SF4ZhieFoknx+Dx8XhMEhGeSgRnEv45hE8B7l2mv1ej +9nqMerQpXHukd54Irj/jXHhNt5vfPLP41nFl3HG9y4FSfWon/SIt/A7dy4tx +9QHzZBjrkyz27yq4nz7m/Vs777Me/r/3C/48JPzLsPDEiOj0qNh+VOw4Jrk4 +Jr3yVHrjqcx5XO7yTO4xAXm/UNx/qQh8BQe/RsLfINGzaNycMmlRmbaMZa6p +cjfUBVvqkh1NOV1bzdQ+4uge8/TNAn272NAlNfbJjYMKfBghniqJ55jpJTZn +Us4Q6DQBTxGKl7h8ApeO45JRXDRsFAwaef1Gbo+R3WlkthvoLQZqo2GnwbBV +p9+s1q9X6NfKdCvFuuUC7VKudjFLM5+umUtWzyWo3sZgs5HK2VB0JgiZ8Yff ++EBvPOXTrrLXd6RTtyST1yUvrkqeXZGOXJH3XYVbr2NVt/X5nnhqMB6RgHvn +4p61KpdO2a0R3qVXDJs5isPi/NnlScfVEce1nrMbzWcotfZbJTY7OaepgFxx +TrTw6/QgZ/p9F7qXO8PFi3EbEMGP6ZQXSNI2MxRPjcCTovG4eDwqCQ9NIwCF +ffMI72LDvUqN1yPMowV27ZLdGRTeeMoFb2c7t3X8ds/PrnXZUyq/piZfoQW4 +0W/5Mb6OZv1rCftfm7m/7ed9PMb/3QT/314JPnst/I9p4ZfToq+mxaemxXav +JWdfSy++ll6Zkt2Ykjm/lru8hjymIe83Cr8ZOGAWDp5DwhbQqEU0blmZuIal +bmAZFFXOtjqfpi5maMpY2iqutpavaxDqm8T6NqmhEzL2wMYBBH+iJEZVxLjG +9EI9S2DTuHIKR17i8IQRGjfKx4zSYYN4yCDqNwh6DLwuPbddz27VM5v09AYd +7ZFup0a3XamllGs3S7TrhZq1PM1qtnolQ7WcqlpKxJbilItR6GIYvPhQsfgA +WvSRLXpIFl3Ei7eFi9cEi5d4C+e482e4s/bcaXveizOCkXPSDiek4qY+yweP +jsa9s3GPWuybbsn1pxzH11Tb+TWHxRlwAx1Xh86ud54BmkKptN0uOEXNsKMm +nKdFXaEF36L736V7uZFg3fJhXPFjnn/AdCj0xfP88exAPCMYTw3HE6PxmHg8 +PBl/mE7czyYAi++V67xqVR6NiFuH/G6fGGyPyy+YZ2Z27BaWzyy9PLPaa7dZ +dZKacIPm7UU/E8H8dQ37lwPcX07yfjXP/80q/7cbgt9RhP9GEX6+Kfrzhviv +6+KTqxLbFenZJemFRdmVBdmNBbnzAuSyAHksKO4tKPwW4YAl5OEyEraKRq6h +sRvKBAqWso2lU1VZdHUeU13I0ZTytBUCbY1I90iib5TpWyBDB2zsRo19GD6k +JkY0xFOd6blm2qiaMmIvjeiEARk3wGMGaFgvG9JL+/XiXr2oSyfo0PFaddwm +LfuxlvlIy6jV0qo01HLNdqlmq0hNyVdv5qg2MrH1NGw9WbmWgK7FwGsRirUQ +aC1AtuYrWfcUr38j3LjJ23TiUM6yKHY0yqntza8oG3/ZXPszZfk/qLN/YT63 +EXRcgAvuGGPDca9s3K0Bud0vdJpg2r7dsltYPLP06uzK2Nm1vjPrrQ6bdXZb +pae3c05SU85QYy/Rwq7TApzp91zpLp6Mm94MJz/mmQfMU4HMv5R44KDM5gFx +DMDTg/HkcDw+Bo9KwENT8YBMwGLiXoneq0rt0YC6tUJge9weElwb55yfop2e +27RfnHFYGbbbeHRiJ/EWzdWP8Yca9s9fcD/Y4H3A4f2Mz/m1kPOxiPt7Ee+P +QsHnQtEXPPFf2ZKTDIktTXp2R3ZhS3ZlU35jQ+68DrmsKTzWFPfWYL91+MEG +8nATCaWgkVvKmB1lPBVLpqvSmKpMtjqXqy7ga0qE2nKxtkqqq5PrGxT6ZsTQ +pjR2qYy9GnxAiw/riTGD6Zl2yqB+aVBNGLBxPTqmR4Z1iiEd1K+T9WqlXVpx +h1bYqhU0a3iPNdx6DbtWzapWMyrU9FIVrVhFLVDt5GLb2cqtDCUlFaUkIpQ4 +mBIFUcLklCDp1n3Jlpdo24VPvcmlXmXQLm7THdcY9ouMUzPMr6aYX75gfPGc +/qeJ7T+8Xv396uTfOHVO6rgQ3KNQf7cDCADbYXrHZn7FfvHNmeXnZ1aHzqx1 +OWw02lOqbbeKTu5k2lATzlEjr9Ae3qT5fkN3c6ffuse45Mewf8D8WyDzT6Gs +jyvuGktcye9SzvPBsx7gacF4YgQeE4uHJ+FB6bhvNn6v0OhVrvWsw9ybYJcO +2Z1+0U1AsQnmGfJ9V+0XJ+1XO09sZd2i3Uln/myG8y985k/llN8g679Trv1B +ufE5SvkC2fkSpv8NYp+Q805JRTYSqZ1AdpYru8iSX2HIb9AgZyrksqPw2Ibv +bcN+28iDHeThDhpKRSNoymiGMp6JJbFVqVxVBl+dI1TnizRFEm2ZTFsJ6Wpg +fT2qb8QMrWpjh8bYo8P7DfiQkRjFiXHtpE4zoVOP61SjOuWwDh3UIv1aRY8G +6tLI2jXSVo24SS18rBbUq3m1Km61ilOhYpVhzGKMUYjR85S0HCU1E6WmITvJ +8E6CYicG2omQU4Ol1AdimreQ7sZn3GUxb+2wrq2znRa5597wHCb4NiOCE73C +v7SJ/vxY9Hmd8I+1vE+bqJ+MjX0tCI/C7zZDTuMs25ltm/llAJbD0sSZlRFQ +nQC57Dce2VHKT2/nndhJtafGXqCGXqP5O9M8XenOngwnX4adP/PLQOYnMazf +prF/W39LW31bX3IHL3THc33wzAd4SggeH4VHxuPBKbh/Ju6Vh3uV6jyrVe4N +qGsrdBdQbEB4fZQLeH3mNfXU3Jrd4ivbtebL1Htj7B8hy78yvvrU/PyP5ol/ +N7/8MzH9F+Pbr/RLJzUbNqptOyXjDMJxVAjOy8UXZbJLIvlVPnSTC91hK1xZ +Cg8m7M2A/RjIAwYSxERDWGgEWxnNUcZxsUS+KkWgShepsyTqPJmmENKWwNoK +RFet1Nep9I81hmatoV1v7DLifTg+SOAjJnxc91Kjfa7RPNWoRzTYkEbZr0F7 +NHCnWtGulreoZE0qyWOV+JFKVIsJqjF+BcYtU3JKlOxCJSsfZeagjCyEkQ7T +U2B6ooIeB9GjZPQwKSNIzPQTsrx5bA8mx2Wb67zGvzEvuDIluvhUfLZPatci +P1UNnSxUnMqATyfApyOQ0w+RkwHyP8U5TtBPzS3YLMzYLb62X3rpsPzMgQSr +32GtA5DLbrPGZqvk5Hb219SkM9QoJ9rDGzSfu3QXd/pVb4bDfcZfApn/msD6 +TS77NxWc37RfUzZeV9fc1JU44wXueLYPnhaIJ4bh0TF4aBIekI575+BeRXrP +So3HI6UboFi77E6PGEB2Y5h3dYzj9Ix1foLh8Ip6an7GWv8f5qyT5tzTlhKb +vVoba5vNwaDN/jOb3df2pvmzhtXzuq2LarqTknMFEVxTiG9Aspsy6LZYcVeo +cOPDnjzYm4v4cZEHXDSIi4bwlOF8ZZQAixViCSJVskSVJlNnytU5Ck0Boi1W +asswXZVaV6vV1+sNTQZDm9HQhRv6CMOQyThiNo7rX6h0zzDtGKYexlSDGNaL +KbswpB2DWzBFIyZvwGR1SkmNUlylFFUoBWUovxjlFaLcfISTi7CzYFYGzEpV +MJMhZgLEjJGxIqWsEAk7UMjx53F9mTyvHb77uvCbebHzlAQ43Mu90IUm+HwF +cjFH6RSPXXmouu6uuXXZEHTWUnxCufBLV5r9ia1su7Vm+9Veh5UB8gI/rHU6 +rLfYb9Tbblae3ir8eifjFDXekRp+mRZwi+bpQr/lST/vyzjxgPlxAuvXhexf +PeL8qoPzq4GLUJcT3HwVq7mhK3bG8zzwzPt4cjAeG4mHJ+CBqbhPFu5VYPAs +03rUYEAxXVugb0BV7JY494qde0V3uiTfNENuRbq0e0b6R0/gr0KxC99objsZ +gp1M6Zd3Ky9b250ORi7tv7pkmbtCrF7Tb93QMm6pOM5KwR1EfBeWfQMpXGSw +uwT2EsE+QuS+EAkQokFCNESoDBcpI8VYjASLl6mS5KpUhToDUWejmjxMU6jW +lmp0FTpdjV5Xb9A1GXVtuK6L0PeZ9ENm/YhFP66fQHXjqHYU1TxB1P2IqgfB +OhG0DUGaEbgBgeoQeTUqq0Ql5Yi4FBEVI8JChJ8P83JhbjbMzVBw0hScFIid +KGfHyTjRUk64hBsi4j7k8QJYgvtUoc+myGtJ4v5G5vIcch6Eb7SiN6uVznmq +u/Fqlwdad2dj1GVLocNBzxea2Y8WOf/sQ/+3C9SAr7dybTce2a+1krQCF6iE +6412G7W2lLJTW6AYptlQY89RQ6/S7t+mubrSr96j291nfBbN/FUh68NGzi/6 +Ob94zv3FMwfhsKOk54Ki6QpWeUNXcBfPvoenBuLx4XhEHB6Ugvtm4p55Rs9S +rUeVyv0R6gooBoxHuwxcLq1y13rEvUQbnIDnORun/sxifdoj+zwLcQhXXfcG +y8bj75hL7+y13jkYuX3w+tbugjOxcddAddGyXNU8N0zojko8ELknrPCC4Hsy +xFeK3JcgARI0SIKGSJVhUmWkDIuBsDiFKhFWpaDqdEydpdLkajQFWk2JTlOh +19QYNPVGTROubSO0XSZtn1k7ZNGN7OrGDc9h/VOFbkShHVRo+iB1N4R1QMoW +CG2EkHpIUauAqhTycoWsRCEpgsX5sChPIcxRCLIU/AwFLw3ipUDcJDk3QcaN +lfGiJLwIET+Mzw/hCB4yRAHbYv81qe+83HtK4TmGuHYr3R6rPEvV3mla3xB9 +sLsp6+Zew1nr2H+qFz5lc/+lif3BPfqJy1S/v+2k2GyW22002K832wNmrTfZ +bzTYbVbbUEpPbuV+tZNiS405Tw2+RvNxpt11p1/0ZnwVwPhlFuvDevbPn3B+ +9ob7wTrvg5m/Ml+e4o04iLsuKOqvqItvGnPd8TR/PCEUj4zBHybhfhm4J8h6 +JTqPSrV7HVga7NqscGmBXJoh18ewe7XKI9cYHovnuOM9jtDSH3ZYnw1JvihH +zqSobodpfXzwJC9L1T1rt9fBc4+Dt+67q57ElpeBcU/H8VYLvDGxj1Lmg0C+ +MOwLI34KxB9CA+ToQzkaAinDIGWEAotGsFgUS1CqklWqNLUqU6PK1aoKdapS +varSoKoxqupxdROhbjOpu8zqPotmcFczsqsZNz6TG8bk+mGZbkCm6ZWpu6Sq +NinWLFU+lqKPpHCNTFEpg8pk8mKZtFAuyZOLc+SiTEiYDgnS5IIUOT9Jzk+Q +8eNk/BgJP1rMjxQKInjCMJYolCYJpkiDVuQBbxX+k6jfMObbqXrwSBNUqAtJ +MEQ/MBd5WNuv7r04pVr9dy7vF4PcD8OZv3alX79ADT6xnW5L4lVPIkVC1mRH +FsPv8QJo2u5En6c+vEbzvkNz9qA7+jK+iGJ+WMb6eR/npzPcn9C5PxYyfrH+ +x5WFz2mTJzhPHCStF9GKa7o8FzzdF08IxiOj/4GXxz/wQlybFCRYzQrwM8DL +s8AQnISnBuHlNw0jjpKV/6CyvnwqPVmPXslVe8brQx4S+UG7zYH7IwGHb+5b +l+9bKPdxur+B7a/l+6tF/pjUXyn3RxX+CPwAQQJgNBBGH8JoCKIMQ5QRKBal +xGIxLEGFJauVaRplllaZq1MW6pWlBmWFUVmDY/UE1mTC2sxYp0XVu6sa3FON +7KmfGselhlGJfkis6xdre8SaDpG6VaRqEmH1IrRWhFSJ4XKxolQsL5LI8iXS +XIkkWyrOlIrSpcJUmTBZJkiUChKkgniJIFYsiBEKo/nCKK4okiWJoEnDKfLQ +FUXIWyT4JRY0rA7p0kbW62IKDQnxppJga6fX/isnzfppgeDTUd4nCexP7jGu +XKMFAC9hs1Vst1F3DFbr8dUMuGa7UWNDKTu5lffVTqrNzjG/qACvWx70M76M +PyQzf97A/mCC8xMq90fS7Q+xpY8Zfxim/H52/jPqs5P8bkeo9oom/44xwwdP +/AEv3wzcI8/oUaJ1r1K51aGAUy7v+dVCQuZej3pWaIAniUzAswLx2jv68cvS +jZM0nv1zxcUmlWexLiwVT4+2NERbn0Qevg47WA7epQSb6MFG9kM9P0gjClJL +AjFZoBIKRBWBKByEIkEoGoyiISgapkQjlGg0hsaq0AQ1mqxB07Rolg7N1aOF +BqTEiFbgaA2B1pvQRjPaakE7d5W9e8oBKzZsxZ7iT0XGEaFhUKjvE+i6BNp2 +vqaFr3rMxx7xlTV8tFKAlAkUxQKoUCjPE8pyRNIskSRDLE4Ti1IkwmSJMFEi +TBAL4sXCOJEwViiM5YtiOOJopjSaJo+iQFGrSNScMuqVOnJUG9erT2k0ZJYS +ham77dGHL/2I9Vtyvs0r4Zdp3C/8mC5X6ZE2OzkOlGqHjSaHtXbSZoDMtdYB +hOxYv+psNitObRV8tZ1+cifWkRpyhQrq4W13uoMv49MM5s862P9nnvMjIf2n +6rmP9kY+E/+hhPlp/9rvFqe+ZPU7SB85qfJvGzO8SX5FROOBybh3Ju6Rb/Ao +07hXY271x+RqlZP61UFeLm1yt2YFSGfexYaIdCInknh8zzB1V0a/vCO9/Qzz +adHFlBuzMi2P06zDKYfTCYer0datKDMjEueEG/hhWlGoWhqikgVj0EOl4qES +fojCwSgSokRClUg4hkRiSLQKiVMjCRo4WQun6eAsPZxrgAtwuISAK0xwtRl+ +ZIEbLXDrLtyxh/RYkYF9dHgfHcPH+MYnPMMAT9/D1XVyta0cTRNH3cBR1XKw +Ko6ynIOUcOEiriKfB+Xy5Vl8aYZAki6UpArFySJRkkiYKBImiITx4BIK4wSi +OL44jiuJY8ni6PL4bUX8OpqwiCVOa5Ke6zKGDPkdeGmtubFw/2nGwWq4lutN +lV+pE50P4wZdZmZf2mq+sDbkuDJ2hrxGHFaevPeH9mudADK7dUCx6tOU4q+3 +sr7aSXDYCXei+oEw60Y760v/fSbzg172jzc4/1u+8QvTs0/NuaeQUw8Fv6ve +/mRy5nP6oK2k/hKJV5oPDiJ5WCz+IAX3zMI9ivTuFWq3OiVJrhb53f/yh/3C +24PC20MC5ycC136JbysaVmoqTTMNhBk2AqRAlLGwMX1GG15SZWkrsj7NP3yb +dbSRbKUmWljxBDfGIIzSiSM00jC1PBSDQjBFsBJccMjxFYbB4So4UgVHqxWx +GkWCVpGsg9L0UKYBysGhAgIqNkHlZqjaAtXtQo/3oJY9qMOq6N5X9B/ATw7g +MWKUgw+xjf0sQzdL38HUtTC1jUzNI6a6holVMpVlTLSYhRSw4Fw2lM2RZ3Jl +6VxpKk+SwhcnCUSJQnAJE4QkWPFCUbxAFM8XJ/AkiRxZIhNKpsIpFGXaqipj +Tps9pS96hlcPmR637w40HMxV7TNz1Yq4efhhiSTZh1fvSpm+Nke/Nsk6O0O1 +I5PyNEjKDstjDitDDqt99quddmstwDQCip2k5P9tO/U0KWGB16luLrSL3vTP +U5kf9LB/vM35J2T5l9bB3+Mxtkp7T/Hv8qkfj739IxXgVXdJnXvHmHIfjw7H +HybgvulkMXQv1bpVY64NCJCtux3SO93i233Cm0N8kJovP2c5vgYrIY+2nZY3 +Al5K0tvMPRWWlXytNE2gzl0wVo6ZGsFnqd+fqjpcLjnazrEyMiycVEKQaBDF +6STRGlmkWh6ugkIxRahSQYKFweDnMEwRrlJEqqFoDRSrhRJ08iS9PNUgy8Bl +OYQs3yQtNkvLLNKqXWndnqzBKmu2ytr35d0H8v5DaOgQGiVGmPggw9hLN3bR +DW00fTNV20DV1FHVVVRVORUroSkLaUgeHc5hKDKZUDpLlsqWpnAkSVxxIk+c +wBclAIx+wCsBwCcQJ/ElyTzw26B0JpxJVeZQ1AWrupJ5Y/U00fLC3De692Lg +kNJ3IGnX6Wrn1VVNyHAWdydxDIsqJA87XDpl56ZoNvPLdotv7Jde2C8/tV95 +Yr9yDNl6s+1G3enN0q+3cv5KUizsMtXbmXbDk/5VFOODVpJf/wtZ/vCg//d4 +hI3S3l3ySTb1o9GZz2i9drKKy9osN2NCIB4ejfsn4x5ZuHuRzq1S5froGKx2 +mXO3+Fa/8MYT/rVRjtNzssVhu7B4Zq3bnpZ4g5n6gDlWvAGPvrBuDYAShRna +aabet5Yno9bJnoOllqOt2kNm6R433yzIwkWpekmiVhankUeroIhjgI7xUgCi +kdipoHA1FKGRR2nlMTpZvF6aZJCmGCXphCTbJMkzi4ss4tJdceWeuNYqrt+X +NB1I2g4kXYfSviPZ4JFsxPSERgxQ8Z4dY8e2oXVL37ile7SlraFoKijq0i2s +aEuZv43m7CBZVEUGDUqly1OYsiSWNJEjSeCK43mAU8Lv8SILoyhRJE4G1VIg +S+dDWVw4j6UsoqvLt3W1G8bGZVPfwu6zt9bZ10fsmSPlG5N5ik68mdVzX3Dw +0brdpYvcia954O6dn6SfmtuwXZg/7nIcQ7b8A2RrTTYbtac2S77ayjwBVGwn +6BpJsXM+9N9UsH7ylvNP0NrPrIO/wyNtUDt38cd52x9NTP6Z1eoI598wpvji +UeF4YCLulYG7F+rdKgBY6DdNACzpD2Dxro4edzYm6TazW+QC1ptecX6yLfxT +PZQ2rOSu8/dFm4f6t7h5Wrw3Q7HOTB+sjR9R+99xmvf5tbuiMpMk3yjL1MtT +NFC8WhED6h4GhynhULISkniFYBDAC9TJcMA+rTRaL4kzSBKM4mRclGYSZZqF +uRZhwa6wZE9YYRVW7wsfHQgbD4Wth6LOI3HvO/HgO8mw6ck20U8hujfx9g1j +84ahYV1ft66rWteUr6uL11UFG1juBpq1iWRswanboMTJk2iyBIY0niWJ4wCp +AoIFZIs0G8ByJIiFSRLgQ8TpYmmWWJ4rVBQJ0HKuqpata2YYu2nm0Z29me39 +je0jIe07HfPAylXti2ErjijfGaaw3aaYIc7P7RanTs9uAbxs5pdsF2YBZHYA +sqVx++Vh+5V+u9Uuu7Vmm426HyCLObcTcIN6x512Kpbx0yH2Pwto/2Ie+5iI +PYXaeAo+Kl/77cLwSWGlkzbDwxgTggfF4/feg1WpcnmEfNMM3emQ3u4R3RwQ +XP8BrAsvGGenqDYz5Bouj7NGzoh1sSW7+peSPUSJH+mRd7sCyz4TOaBzDhnr +R9yZd8KxQ0mPVdpkllfjULFekQP8AzASKiQGQyKUSJgS2Aw4mLwUwH6EqOSh +almYVhqhk0TpxTFGUTwuTCIEqWZ+hoWfvcvL3+MVW3ll+7yqA17dIe/xEb/l +Hb/jnaDnW+HAO+GwaXjT1L9OdK/hbavGphVD/bK+ZllXsawtXdYULqvyVrDs +VWXGGpK6DidvKhK35Ak7sjiaNJYhjmGJYrjCGD6whYJYEWnpgbFPkglT5aIM +MqZJC2RQqQypkWCNYm2XyDgsNE0K9paEBwzxkVT6rQH99kCz/w7fe3d4sP/d +d2YL18ICsn5pgvker9PzKzbzC99Dtjhpt/TcbnnMbnnIbqXXbrXdZr3h1EbF +CQoojHGOO4E3qM6etC8LmD9Z4fx/2te/NqV8jZz0Zf+27fWf6I3n0CwXY2ww +HhiPe2TibsVa12rlN48Vd9pkt7vEt/qEN4b410a4V8bY78FyfEUjjwbINWza +LcxcZubIhEff7Zn3v7VaD787MH97pNk7QrVHcsk7BeNbZPkImdxHnljQdgJ9 +ZFCWghgF8hSmTFAqo1FlODDwCLDxwMzDQUpFELCLwDSqpaFaSZhOFGEQRhsF +sQQ/wcRLtnDTdjlZe5xcK7vwgF16yK48ZNcecRoAed9x2t9xe95xB97xRszD +a6aBFaJ7GW9bxJsWjI/mDVVz+rI5bdGcJn9enTOvylhUpi2hyStw4poifkMe +S5HF7AC7Lo5iiqI4wiieIFrIjxHzY6W8RBkPJOgMSJCtEObD4hJEVoEqHqFo +G9np0j9DiLfILkV5wFUdIdpvjcbvDna/++7g2+++/e67v//9u++++/bvXcoX +dm+2AV4n5zZPz62dnl8+huyt7cKM7X+htgRQewJQs11ts1l/dHKz9K9baTY7 +YVeprh60v9Sy/kW89WNL0V8UX4Zs/HamwwHKdDFGhuF+ybhbnt61UvVNA3yn +lUTqZp/w+hDv6gj38hj70jPWxQnG+Zd0EixgM47XQO6ZubWJN/vf/v1bcnl/ +/+5b8G+w3l3rt7jxOyP6nYF3pN/c183sascIbZdBU6/VlKo0OagqDcYSFFg0 +pAyH0BAFGgSjAQgcgCoClPJAlQxEs2CtOEQvDDMIInFetIkbZ+Yk7rJS91gZ +VmbOAbPgkFF8xCh/x6h+x6h/x2h+x+h4x+x5xxx8xwJ4LZsGFk3d80T7HN40 +a3w0Y6h6oy99oyt4o819o8mcUaXNYslzaMICErekiFmFotZlkRRJBFUcwRBG +sAURPH6kkBcl4cbJOElysp2YBXPzEF4xKqjERI9U0ha1okejHNFpJw3GJYOF +hu+LTUcqy7cm63cHh38Ht+DvAK1//LKZ2T4F8Hq7eWpu/RSAbG7l9PzS6flF +m/l5m/m3NgC4hde2i5O2ixO2S09tl4dsV3ps1ppPbVT+dSvDfifoLu1cC+tH ++/2fiD/K6bGVJvsY/RNw13y9S43yTpP8dqf4Rp/g2hDvygjH6Snr4jPmhQnG +OQDTJO3sKypAyn56B4BFFsO3lPdr+O9rI1cKFnx08PcD07dW1dGuaN+ys2ua +I4inOmO3St+AaMshTb5UlS7BEsXKGLEyXIIGS9FACHkAI/cRxX2l3B+TPlCL +A7XCh3pBiJEXTnAiTawYCzN+j5Fspacd0LIOqXlH1KJ31LJ3O9VHO/VHO81H +Ox1H1J4j6uARbcQ8Mm8eeGvqmSXa3+BNr42PpgxVx0/4509qsyY16a/Uya+x +hGll7CwSPaeIXITCV2RhG5LQbVEoXRjK4ofxeOEiTpSUHSdnJUHMdJiZgzIL +lawyFbtWzW3UCjp1kiEDNIEr50zaTQvO3duFDg60R+8s7747BDv3/wIL/DoG +i3J8bZLX3MbJufWTx9gdX6un5lZOzS2fmls6Nbdwan7u1Pzs6fnp0wuTNovj +NssDp9ce/+d2XAfrn/tOS9wy8TuPoRs9witPuJfGWOefMRwn6Gdf0hxeUe2n +duxf79hN79hOb9sCgI4xOg0uQKvZ92B9v4b/sby/k9Xg8NtvzYdH6r0DsclK +1VkWMOK5wtgn1TcJtZV8dQFXlcHBErnKaC4axkcfCpEACXJfjvjACh9U7otJ +/dRif60gQM97aOSEEKxwMyNqlxZrpSYcbKccbmccbeUcUQqPNsuONqqPNuqP +NpoPN9sPN3sOKQOHWyPkBX4A/7nZDv7X8W+oJn8z+CNbOeCPgxcBLwVeELws +eHHwFuCNwNuBNwVvDRYAlgEWIzk+MgDLA4sESyUXTJ6cFoCPAD4I+DjgQ4GP +Bj4g+Jjgw4KPDD44+Pj/434cw0TeK3DTwK0DNxDcRnAzwS0FNxbcXnCTwa0G +NxzcdnDzAQQACAAHAAVAAwACMAGwAGQAOAAfABFACQAFsAJwSYgB0CTcy8fQ +r77fCe93Bbk93u+T92uY3fqfeB3DBTYb2HJg44HtBzYh2IpgQ4JtCTYn2KLk +KXyZCmxacuumw2Abg80MtjTY2GB7g00OtjrY8GDbg80PKACIAOgASAGoAQgC +aALIAigDiAPoA0gEqAQIBWgFyAUoRhIN0A2QjqRePaAhICOgJCAmoCcgKaAq +ICygLSAvoDAgMqAzIDWgNiA4oDkgO6A8ID6gPygCoBSAggDKAigOoESAQgHK +BSgaoHSAAgLKCCgmoKSQhYWUhP+bX+CmgUL0lgIwAqUJFChQpkCxAiULFC5Q +vkARA6UMFDRQ1kBxAyUOFDpQ7kDRA6UPFEBQBkExBCURFEZQHkGRBKUSFExQ +NkHxJEsoKKSgnIKiuvAaFFiyzM7Pg5JLFl4SwbXv1zAL9sn2/2AXWDAo46CY +g5IOCjso76DIg1IPCj4o+6D4AwkAQgDkAIgCkAZSIJLkQCyAZHzfDI9gAykB +ggJkBYgLkBggNEBugOgA6QECBGQIiBGQJCBMQJ6ASAGpAoIFZAuIF5AwUsiA +nAFRI6UNCFw1EDsgeUD4gPwBEQRSCAQRyCIQRyCRQCiBXALRBNIJBBTIKBBT +IKlAWCHyvCAcSC0QXCC7QHyBBAMhBnIMRBlIMxBoINNArEnJ3gUS9u0xYuAf +wLRvgbifJm/XBqAVAAsgBQwAsAHADABLAIwBsAfAJACrAAwDsA3APAALAYwE +sBPAVABrAQwGsBnAbADLAYwHsB/AhAArAgwJsCXAnACLAowKaTKBaQHWBRgY +Ug1fk5ZmAQC3AEzOaZJum+/XACwQWQO+Iw3HsTU6ADYJmCVgmYBxAvYJmChg +pYChArYKmCtgsYDRAnYLmC5gvYABAzYMmDFgyYAxA/YMmDRg1YBhA7YNmDdg +4YCRA3YOmDpg7YDBAzYPmD1g+YDxA/YPmEBgBYEhBLYQmENgEUmjCOwiMI2c +ZmAggY0EZhJYSmAsgb0EJhNYTWA4ge0E5hNYUGBEgR0FpvSHfmbQ+/4z8r7/ +rAwHVhYYWmBrgbkFFhcYXWB3gekF1hcYYGCDgRkmLbFmD9hjYJKBVQaGGdhm +YJ6BhQZGGthpYKoBWMBgA5sNzDaw3MB433qPVJsMGHJgy4E5BxYdGHVg14Fp +B9YdGHhg44GZB5YeGHtg74HJB1YfGH5g+4H5BxEABAEQB0AoOEZtiIwJx6jZ +kajNHkO28n7PgHABIgYIGiBugNABogcIICCGgDACIgkIJiCegJACogoILCC2 +gPACIgwIMuSpU4YcRBsQcH44vzjuh8fwQQgCUQgEIhCLQDgCEQkEJRCXQGgC +0QkEKBCjQJgCkQoEKxCvQMgCUQsELhC7QPgCEYwMYoIeEMpANAMBDcQ0ENZA +ZAPBDcQ3EOJAlAOBDsQ6EO5AxANBD8Q9EPpUx/3M42bm8UX2n8NASARREQRG +EBtBeAQREgRJECdBqATREgRMEDNB2ASREwRPED9BCAVRFARSEEtBOAURlQzL +M1sgtL4HC8RYEGZBpAXBFsRbEHJB1AWBF8ReEH5BBAZBGMRhEIpBNAYBGcRk +EJZBZAbBGcRnEKJBlAaBGsRqEK5BxAZBG8RtELpB9AYBHMRwMowvjYNg/gNk +S99zfHEKRHgQ5EGcB6EeRHsQ8EHMB2EfRH4Q/EH8N4/uGLtpumaGqpaNlnMV +RQJ5rlCaJRanHx9hJJHnF8L35xf/6IdzpPEsWQJDnkQju6yp20jGFpq1ieVu +qAo21MVks0JXRTYuDA3rxuYNvH2D6N4k+immJ9vvJMPvxINH4t5DUeehsPVA +2LgvfGQVVu8JK3aFJRZhgVmYaxJl4qI0ozjZIEnQS+K00v9qZoZhZD8z5H0/ +UwmHYnCYCo5UK2I0ULxenmKUZZok+buisn1+LUleav/B2rh1ZnpvhmKeFuvf +4qLNw3X+/rCSWw+lbQv/9IrzE7v1JtuFecCv85P092DdeMK71S907hbfbZd+ +0wS5PkLdKkiwvDLI5lJUOJ7ii+ffMLY6wpN/Zm1/NCH+OA+1c8cjbayDv4PW +fvaW808VrJ/40H/jQjt3jermuBN0Yif2B8hq7daa7Fc7yWbX8hOy8fU9ZPMA +L7AAl2Zo4mve0kXuaN3uCw4+q+fSCbKNdqR8c8Sesc6+3n321tS3YGxc1tVu +qMu3lUV0OI8FZXFl6XxJqkCcLBT99/OL45a4OJ4nSeBKEzmyJJY8hQml0hUZ +NCSLiubsKPO3saItdemWpoKiraHoHpHtQUPrlrFjG+/ZIQaopie0I9nIkWzw +UNp3IOk6kLTtS5qs4vo9ce2uuNIiLjWLi0ySPEKSbZSkG6QpemmSThavlcdo +5FFqKEIFhb/vYf63fmaYimxmRmtlcXpJIi5KNQuy9rj5h8zSo63ag6UW62SP +5cmoqfetoZ0Gt2JbA5bRF9biDfgBc+wGM9WelnhmrZtstL6mOj1nXiPB4v8A +low8/H3PrCKdRxbZtg2PxhMC8Sw3Y8Vlba+dbOYzGvWjUckn2Up7dzzC5qD/ +98jyhxuc/9XK/nEU4wNP+lfOtBuXqd4OQMt2Er7eyjm9WWoLWLbe/D1kK/8F +2Rub+eVzUzSXTpl/Dvl3GCWOYVncnSZkeF5dpdPVHkjaDyl9ey8GzH2jRMsL +Y/W0rmReXbCqzKHAmVQonSlLZUuSeeIkvihRIPrH+YVQlCAQJ/DFiTxJElea +wjnuirMUmUw4h4Hk0ZWFNKyEpionm+2aOrLxrm+mGtpoxi66sZeODzKIEeYh +NHoIDR3I+/fl3VZZu1XWvCdr2JXWWaRVZmmZSVpMyPJxWY5BlqGXp+rkSVoo +QQPFqqFolSISU4ST/ed/9DNDVVDo+2amThJtEMURgkQLJ9XKyDjazjlcLtmf +qtodqDc1thsrx9S5C9I0wUq+tqfCkt5mDngpcVomn72ym19zfE29/Jx1fZR7 +c4h/u094B4DVISXBakDcqjH3Uq1HntE3nTwWiQbkuo/n3jHWXVIP2kre/pFK +/XhM/Lt8pb0nHmNrHQR4/XKb80897B+nMj/wpn/uQrt4nep2nhp4eif6b9up +Jyn5NpsVthuP7NZaAGQOq33k8c3ymMPShP3itN388tkZ6rVJ1rU5uitl2odX +XyJJnocfqhVx+8zcgznwWRpMj9vx6iF90TNt9pQqY06ZtgqnUECJkyUyJYkc +cQJPFM//R0ucPL8gL3GSQJLCl6byZOlceSYXyubAuWykgIUWs5Rl5DGWuoY8 +0tI2ksdb+g6moZtl7GfhQ2xilHMAjx3AT/YV/VZF9x7UsQe17EKPLVCdGao2 +QeUEVIxDBQYoRw9l6qA0rSJZo0hQK2JVcPRx8zlcSfafj4uhIhg77meq5aEa +aZhOHGEQRhHcGAsr3kpNPNpIPnybZX2ab2krwkuq9BltWNiY2H9tI0A6EGYo +TSP/niDfVtS1X+L8RHB7SHB7UOgMaNUrvtMtudshc2mRuz6G3eqU7hVqjyK9 +ZxZ54BgWSx4+pvng+beN9ZdUAK+Zz+nbn0wKfleNnHpozj1levapfOMXG5z/ +3cv+cSbzA1/6791oZ2/R7jhR/Rx2wr8iKZZ1mlJsu1Ftt95AnmKvdTp8P0f3 +hBxSXRlzXBm7sDZ0aav5MjM7jBtUJzpPlV/Rcr0PVsP3n2aYGwvx0lpDfocu +Y0iT9BxLnEYTFhXx6/L4bVkcXRLH+kc//IfzC2EiecgrThZJUoWSdKE0QyDP +4kO5fEU+Dy7iIiVcZTl5TKyqJY+MNU0cbStH18nV93ANAzzjEx4+xt9Hx/bR +YSsysIf07MIdFrjVAjea4UcmuJqAK3C4xAAX6OFcHZwF/IMGTj7uPMdhSDSG +RCqRcCUSiiIhKOk3yIPvH/qZIVpRqIEfhnNAeI+0bkUdrkYfTidYh1Msj9OM +WZm6mHLMp0V6+xn98s7UXdnje4acSPIpSO9ig2cd5tascGmTvz+X/366rEnh +Vo+4V2MeZRqPfIN3JnmgHxFNHu5neJN4PXJS9TtIp75krf1ukflpv/gPJXsj +n6nnPhLSfzrP+VEH+/9kMH/my/jUne7gTLt9herjSA05CVRsO/3UVgGg2PG4 +SOMPE3Rdx6MI7eRYAqXaZifnKj3Sj+mSxv3ilfBLOd+GWL91+NJvtz2aKEw1 +ZJbqUxq1cb3qyFFl1Cskag6KWpVHUcj+ajRTFMMRxpL9cGA2BO/PLxLJIQry +CCNNLMkQS7NEshyRPE8IFQoVxeToBVopUNaQwxiqx+Rghradr+sS6PsEhkGh +kXzOUmTFnlqx4T3lwK6y14J2mtFWE9pIoPU4WmNEKwxIiR4t1KG5WjRLg6ap +0WQVmoChsUo0WolGoGjY8QDJ9/1nVEGOl2CyQLUkUCMK0vODjOyHJjo5iHKw +HHz4Osz6JNLSEI2nR+vCUlWexYqLTTz75xsnaeOXpbV39FmB5HCLdw7uWaFx +r0ddf5h+cWlWHJMLda9SeZQcF8MMcmAmMpocnskA/LpjrL2i6XaEnp3kz39G +pfx+lvGHYWzpY+n2h1TujyY4P2lgf5DM/Lkv4w8e9DN3aLeuUb3PU4NtgFHc +ST25lWdDKbPdqPlhfO79hE8TOS6yVfw1NekaLeAe40oC+5NR3icCwaea9dP7 +r5ysnV6mkmBDQrwuplAbWU9+rVLQMBL8UhHyVh66Ig2nSCJookiWMIorjOYL +YoTkMNL784tEqTBZJkyVidLJsSVJtlSaSw4yyYskilJytAmpEqO15LCTqokc +fNJ0iLQ95CiUfkhsGJUYx6V76qd7qpFd1aBF1WvGOk1YG4E14Vi9UVljUFbo +laU6ZSGIURplFshTKiwZwxKU5OBcFKKMQJRhMBpyPKYViCAgNT9AFf7HLU1y +oEvLJ4e7cLq/hUKOex2+ub8/ErDbHEjkB+lDHqo949ErudKT9awvn678B3XE +UVJ+05AahAcn4Z4FBvdqFTlg1nw8YNZ0PGBWp/SoVHuU6DxzyVG093gBfqX7 +4nkueMU1XetF9ImDZPIEZ+Fz2vofV4SMX9C5P57h/qSP89My1s+jmB/6Mr7w +oDveoTlfowG8HtoCCdtJObmVa0Mptd2s/n/G58pPbKdfoAa70q+HM389yP2Q +y/uFavXf916csrZfNRd5GKIf6EISNEGFqgePMN9O1G9Y4T8pD3grDVqRBFNE +oTRhGOt9M5wc84uRkCN/CTJ+EjkEKEiTC9MhUSYEYpokTy4tlMuLyaFBRaUM +rpGhj8hhQqyZHCxUd0k1veSooX5YZhiTG5/JdzXju5oRi2bQrO4zqbsIdRuu +bjKq6g2qGr2qUqcq1aoKNapctSpTpUpTqpJRLAHBYo8PCyIgZZgcDZGjDyE0 +QIH4w4gfDPsikK9S5oOJfdQCbx3H28C4R2x57a56Hrx1P3juYe0mxyzxJC+t +j4/qdhhyJkXyRTnrs6GlP+z0OEI57nh4LO6RawR4HQ+YfT9d5vYYfo+X53/H +K4Yc/kzzx3Pd8eKbxvor6q4LihEH8ctTvJm/Mtd5H7zhfvCE87N69s+zWB8G +MH7pzfjKnX7RmXb3Gs0H8MuWCvj1PV52m9X2JL+ajsdTyfE5m81ygOZlqt89 ++okm9gds7r+oFz61jv3nXsNZU9ZNfbC71jdE7Z2m8iw9nlzsVniOyb2npL7z +QJRFAduChwx+CIcfxudFiMjDi1gZOVKbJOelQLw0iJ9BDtwKcxSiPIU4H5YU +wbIScigXqlIoahVIPTmsq2whB3fV3ZCmD9IOkgO9+qcKw3N4Vzdu0Y2YtUMm +bR+h7cK1bUZNk0FTr9fU6DQVWk2JRlOg0uRi6ixUnQ6rUhSqRAiLk2ExUmWk +VBkmQUPIMWMkQIrclyG+EHwPVnghck9U4oEJ3dU8Ny3L1UB1ITbu7i44H7y+ +dTBye6+VHGbG4+9o3Z1V170Rh3DZ51msT3um/szKczYGJ+DuJVrXeuT76TJS +vwDFYPdHqEcVuD1aT1APM8mB6og4crg6NZActC64i1fe0DVdwXouKIYdJc8c +hM+55GB2I+cXhawPo5m/us/47B7dzpV+9TbN9Srt/jlqqA019sRO2qmtPFtK +md1GLdAvh/XvJ8CBkAHT+PVW7gVqgA/93xY5/6yZ/eig5wtLoYMx6jJYttrl +gepuvNI5D71ZDd9ohZwHZS7PJe5vRF5LQp9NwX0qL4DFfcjjhog44RJOtJQd +J2MnyjkpECdNwc1QcLPJgXZ+PiwsJEfcxaWIpByRVaLyahSqI8fgkWayu4V1 +kuPx6n5E8wTRjpJj8/oJ1KIfN+tHTPohQt+H67qMujaDrkmvq9fpajS6CrW2 +FNMUopo8RJ2tUGfIVakyVZIEixdjMSJlpFAZTg7wo0HkMD9yXwT7SGAvGewO +KVxg2TeI+K5ScEfFcdYybum3bhCr1yxzV/ZfXToYuWRtd9qtvGxKv2wIdtLc +dsIufAN/FUr/6EnaPaNbkY48pu+SOPeK3vtD4DpcWyC3BsSjBvMs03oVGHyy +yAcWwhPIhxeSg8kHGfI88GJnvOaGrvkq1uUED1yEOjjkgw+F7F8lsH79gPmx +L+OEJ/28C/3WLZrnZVqAIzX8FDX+652M01uFtpuV9hv1DustDv/whwP2q712 +a80ntrJdafbKhV9aik8Ygs5qbl1WXXfHrjxUOsUjF3Pg8xXQhSbZ5V7Jjadi +5ynhN/N893We1w7Xl8nx57EDhawQCStSyoyRkQ+D/P98vddzHFmWp/kX7D7s +zJrNTHdbi2m53b1V012TWZVJLQEQJEESIEEQWgsSBEForbXWWmutVQABILQO +dw+ttZbuAUXyZf0iM6uqa8bW7BiNTwxafH6u3+vh5/vl6gT5ekGRQVhiEJUb +xZVGSTUYHpE1mBRNYJxE1WbWdJi13WDMxDAARk7MY2D8xDoLRlEcyxbnmsW1 +afV5VjHPIuqe87qnPO4xt3vI5e5zuLpsznaLs8XsaDA6avX2Kq2tTGMrVlkL +FNZcuSVLZvkkNadLzGliUzIYkzHGio1REkO41PBWrn+t1L/U6J7rNE/1ykCj +LMAs8rNBj5zsB27qPez49vnejas1MJJzOQTGc87qfucr/62v5LvLrn/+/phw +c4d3b+P6MdSyKHBB8nxG/mJCGTysed1nCO00v222h9W48D1JXCEYC/qYAUaE +CuLBuFDVG28djuyps/eJbTjA3CQCg0VZgj+LR/48Gv51OHzzDeT/EgoO5Ec8 +4ife4qXje4nvOKW/Y9f9yGy7yejF2woMLlEWb5LXbpC2fjwFj+6/J57c2YC0 +/5hp/C7O+NtEw2/fG36bpf++SPddtfb7VvWPA8rbU4oHKzK/XWngsTiIJgrm +CEMRQbgEiZLDCUooVQ0GrDJ1YNgqzwAXGuASI1JmElSahNVgLEvcYJY2gUEt +RbtF2QlGtzR9Vu2AVT9sM4zaTBNgvMsyB0a97Ctg7Mu5Zce8q6h30eud9Xin +XJ4xh3vY7u63unrMrg6js9XgaNI56jT2apWtQmErkVkLpdY8sSVbZM4Umj8K +TO8RUzJsTADDaIYoxBAu0IcK9SFi3Qup7qlC66/RPNQqH+hl94yiO2b4lpXz +o53xOxfpO8/Rv6P7v/Zt/SsYf1v/e8/O3xjJ/3VZ+H885r37gdb/4+nO90Qa +eMSxgeCnZhzZy3FVyKDuTbfpbas1rN4ZVgEG7pLywPDd53QwiFccC4byqnFk +L7ytz11dzxwFwr/IEPxFPPJXMcivIuEf38KPQqCgIP7bAH7MfV7KDbAY5v+W +U/Ejq/EGo/MWfRCMBOKwwEkZPNz4gcB5tCp42a9LS/cu/08Z76+WJX/TJ//7 +dsU/dSj+tUf+6yHZbyalv1uU3NwQ3z0QPjoVBNCRZ1z4pQB6LeWHy3mxSl6S +mvteCwYYs/TcXAOvwMgrNvHLzFCFGa4GA4+CBouoCYxAStqtsi4wFKnss6kH +wZikbsyun7Abpx2mWYd5AYxS2lbBWKVj2+lFVz3okts75/RO2z0TNs+IxT1o +cvUaXF06Z5vG0axyNCjsNXJbpdRWJrYWCa35iCUHNn/mmz/yTO+5phSuMZFj +jAUjn4Z3XH0oTxfM1wXB2kCB1k+seSDT3Fapf1QrfqeVfK8T/sYA/ZuR+ysT +61/MjH8y0/7OSP9rLevPpMj/RRD9n4XIf8YPs79hl4CnQ6fbvzum3trnPt5A +ni5KXkwrgkc0b/oM+OksrNHxrtoTWQrGWtNywIhr9nsw7loSC0Zfq99660K8 +TS89KYK/jEf+MRb5tyj4xjv44Rvo2Svo9VN+pB8/8S7vw+94Wd9xi39g19wA +r3/33qKNgZFb8vo1LMrNfa7fivDliDq02oUfyTse2bb/TUT971TO3+1B/7gB +/8s68qtN5N934e8J8I1T6A6N/4DD84d5T8WcYCk7TMGOVrES1GAoOF0HBoSz +jax8E7vIzCk1c8stvCowSgzVW+EmMFwMfoXvAuPGsn67fBAMIKvHHJpJh24a +DCYbF5ymZZdl1WXdAGPLjl23G1tzocsO74LdO2P1TJo9Y0b3kN7Vr3V1q50d +SkeL3NEotdeJbVVCWzliLYasBTxLLtf8mW3OYJk+MI0pDGMi3RBLM0SBwWp9 +KF0XzNAGMbWBbI0fV3Ofr74Nq34Qqr6TKP+HXPEvctk/KSR/rxD/d7noL6Wi +/yaS/GeG5D9tiv9Tm/D/joL/7hk/5Dfc7B8ZnTcpCzdOCb8lMu/t8gNWRc/n +ZK/GVa8HdaHdprAW27s6V3g5GlcMhsfTs8AgeW4aGCovjQMD5tXvvHWh3njk +17HI91HIrXD40Vv4aQgUHAS9e8KPe8hPvcX79B0v77ecsh/Z9TeZHXhz3aZN +3aYs3yLt/Hhy+sMRG+/r59Ny/I4ZVur9lOateuEZuW9Y/53s8NcI+Z95tH8F +w/LMf2exvueA8fnbAuYjEeOphP5KTn+rpEWqwKB9sg4M3WcYaFkmeq6ZXmBh +FFuYZVZWpY1dY+PUg4F9fosdbgcj/MIeh7jPIRkEo/2KMadyEgz7a+ZcugWX +YRlIAEwbbssW0ALY9z1AEYCu2NBFi3fO5JkyeMZ17hGNa0Dl6lU4O2WONomj +SWSvR2zVkK2CZy3hWApZljyGOYtm+kQ1fSAbU0nGxFND3Ik+CogLdKFAYqAN +OtEEnmr8SOr7FPVtquoHuvI7hvJ/MBX/ypL/E0v+twzZX1Olf3Es/bNtyX+d +Ef+XNuF/eY/8tzDoViA//Dte1o/MFrA64TeRE/ItAvfxJvJsUfJySvl6RBva +awxrt75rdIZXeaJL0cRCNC0XiBqyPwJpQ1ESEDhUxHirI72xyM0o5F4E7BcG +P3sNB7+Ewp5BMX78pHv89B95Wd/zin7gVN1kNd9i9tymjwJZBHn95inhh+un +l09WRPjlEdpuCS8FiomSCG/TU9fII+PiXfXmLdn+DcnhDaCkOLkrPn0oAZKK +53IgrAhVAXlFrA6ILFINp+kmUqaZlG0h51spRVZqqY1WYadX25l1QIXBaXZw +24AcA+p2In1AlyEedknGXLIJoNFQzrnVC27tMtBrGDY8xi0g3LDse22HqB3b +tKKrZnTJ6J03eGZ0ngm1e1TpGpK7+qTObrGjXeBoge0NfFstx1bJspYxLEU0 +Sz7ZnH1qyjwxpRONqYeGJIIh7kAfta8L39OF7mmDdzVBu5rAPbUfkIeobu8r +fwQ6EcW/78t/tSf/5x3ZP2xI/3ZZ+tfTkr/sF/9FnfDPPwr+PAr+n6+hZ35g +nij3Bqv5Nm3s+gs8/oHIfrgDB66IX8zKQ8Y0oQOGsE7Lu2Z7eK07sgLIT1IK +0PQcoEPJ+QjUKMUpQJNSEe+NQh5FIAFh8PM3cHAwFBYERT+BEh7x0+7wM3/L +y/sdt+wGu+4Wq/02o/8ObeIOdfE2eRv/uN8RWfjH4ZdH8Kjmbbs1vBwoXPKT +vJVvvS3PXYNPLFP+hkU/7ZqfetMfiF92n6n2Xqj3QzQHb7UHETpCjIGQYDxM +MR1+MB9lWIhZVmKu7bjQflpiJ5U7yFUOSq2T1uCkNwHhDLvDxe0GChpowI0M +u4WjQE0jmQaaGsWCR7UExDXaDa9+y2vYBUIbMwG1EDELtmVG143oit67oPXM +qj1TSveYzDUscfWLnD2IoxNytHLtjWxbHcNWRbOWky3Fp+YCojnn0JR5YPy4 +Z0zbMSRt6eM39dEbuvA1beiqNnhFE7SiDlxW+y2rHiwp7ywpbywqfrsg/82c +/NfTsn+dkP4/w5J/6JH8bZP4b0qEf50q+KtY5Lsw2P8FFPaAn/Y9t/Amq/UO +fewOZfXW6dGPx8z7e9CTNdGLeVnIhDp0SB/WY3rXZgtvcEVUeWPKgGIoLR/N +yEE/fwbqoYIPQENUmuyNQJ6FwS9D4dchcNgLKOoplODPT73P/3iTn/1bXtGP +3Mqb7KbbzK47jKG7tOm7lJXbpL2bJ6QbR5zHW8jzBenrUW1YhwXv4uR8IEoq +TgDLbNMrT88Lx0iQdTLIPPfCuPgS6JVW3xjXw4wbkabNGNNWgnk72bLz3rr7 +0bb32b6fYz/IdxCKnUdlTmKl66TGdVoPJE7UFjetHWidWL0eTr+HNwR0T8g4 +UD+JZ73SeSCDUqwCMZRmC9XuAFWUkYCZjjAgj8K2DeiGDl3VeJdU3jmFZ1rm +nhC7R4SuQdjZy3d0cRxtTHsz3VZPsVafWiuIlpJDc+G+OXfX9HnLmLFheL9m +SF7Wxy/pYhZ0EXPatzOakGn1iyn10wmV/7jy4Zjy7oji5pD8hwH5d72yf+uU +/qpF8i+14n8qEf1DpvDvkwX/bxxyE2+E1/CbQCjhNj8TKLZYHXfp43cpq7dJ +hzeOGff3+U82hEGL0uAp1ZsRXVif8V2HNbzZEVHrjqoECq+UIqDz+pQD1F65 +GUDzVfQeDYODQ+HQEDj8JRT9HIp/AqU84qff4X/+gZ/3A6/0Bqf2Frv1DrP3 +Ln0UaMQoa3dIBzdPKLcOuf5bgqAF2esxTVi3ObzehbfwxxygI8PbtibK2/jW +2/7a0/vaOfTGMR5qnwoDErP5KNtCrG0pwb6cbF9Nc6ylOzYynZvZzq08104h +0KDtl7sJVZ7DWg+xAUjSSG1eSqeX1gPkaaxBIFLjjaPQJIrMAMGaeBHI1uRr +mHITU+0ACZvuAAjZjMc+E+nMgO3o0E0NuqbyLsu9C1LPjNg9KXCPQa4hnrOf +7ehmODqo9haSreHYWntordy3lO6Yi7ZMeeumrBVjxqLhw5w+ZUafMKWLGddG +jGrC8KPSoPplv+pZrzKgS/moQ3GvTX67WfZjvey31dLflEr+R774Vxmif3kv +/E2y8Gac4FEk8jwUfhsExT2G0n/g59/k1N1h9tyjT90D3+HhzRP6vQN+wKYg +aEkaPKN8M6YNGzC867ZEtNojGlyR1d7YciDKSysE0rzMHCDQy8tECzLQUDjs +NRzxCo4JghICoRQ/6MN9fuYtfs7veEU3uJW3OA138KuC2X+PPg40fZSNOyQC +EPdd83qxKHs9oQnrM0U0O/BLIrUI6P4KPgL1X3U80AC2RKLt4WhPhGcgyj0c +4x6Lc00kuKaTgTxwLt298Mm9lOVZyfWsFgDB4GaZd7sSKAf361FCE3rUClSE +p91AS0gdwOjDGGsM6Ap500BdiCwAjaF4zSfd8Mm3gd5QfQBUh7rjM8PpmZF8 +rsN2NeiWEl2Xe1ek3kWRZw5xT0Guca5rmOUcoDt6KI7OU3sr0dZ0YK3btVRt +WcrWzcXLpvwFY/as4dOUIX1cnzqiSxzUxvZpI7s1YR3qN62qV83K5w3KJ7WK +x5XyB2WyO0Wym3nSH7MlNzLFtz6K76aJHiYL/eMFz6MEIWFI+CsYv/4/3OXn +3OCV32G33GMOAl0kZeMu6ejWCeM+gR+AX/MrkuBZxZtxTdiQIbzHHNFui2xy +RtZ5oiuBiDKlBPwck5EPBJXZ2WjeZ/Q1HBUMx76AE55BKQHQh0fQp7v87B/5 +BT/yym5ya26zm++yuu4xh+7RJ4EGk7J1l3QIxJiH4AfKF8vS11OqsEFDRIct +qt6N//sfioBUszATCDarU4FssykRiDc7EtDuRLQ3CRtIwYbT0NF0dOITEHXO +5ABp50IRtlSKrVQAmedmHRB77rb49tuB6pPYA7Sf5CGgAKWPAx0oZxaoQaEl +oAkVbZxJtoA4VLEPJKJqIhCK6snnBuqFGttTojtydEPiXRV5lxDPPN89w3FN +MF2jNOcg2dF3Yu86tLft25q3rfUbluoVc8WCuWTWVDBpzBk1ZA7pP/brP/Tq +Uru0Se2a+BZ1TKM6ql4VXqN8W6l4XSYPLpa/LJQF5UmBNDVT8vyjOChN9DJZ +GBwvDI0ShIchMSFI0jM4/SGUc4Nfcodbf4/d9YAx+oC2cJ+yfZd0fOuE+YDA +f7J9zWtO8WYSb2B9OH7ld1ojWx1RDe6oGm9cJdC9ppYA9StAlge+22A4/gWc ++AxOwa8EPyjjPpR1C18J+cU3eZW3OfV32G33WD33GSNAMEtbvv6sIyCePeL6 +7yBBq5LXs8qwUV1Erzmq1Rld602uANLanHwgsC3LBDLbuo9AbNuSjranA9Vt +TwbQ3g5mYcM5QIQ7UeibKvbNlAFB7kL12XLd2WoDEOdutgGJ7l73OaHv/GgQ +yHVJY0C0S58B0l3OIhDwwutAxivaAWJeGQFIelUnQNiro1zoaRdK7ECO7krQ +LZF3HfEu8z0LHPcs0zVFc42RnMPHjn6CvXvX3rFpa1mzNixZ6hbMNbOmqilT ++bixdMRQNKgv6NPlduuyOrSZrZqPTer39arUGlVSlTKhXBFbIo8ulEXlySKy +pUBKnC4OTxNHJIsi44UxUYL4d4KkEOT9c/jTYzj3FlR8h1d7n9P+gDXwkDH1 +kLbygLJ3j3R6+4T1kMAPxK/5VUnIvCJ0So1/jeEDpohuS2SbParJFVXniakG +OuXkMqBWTi8CmuXP+ehLOPk5nBoIffCHMh5Cn+9CuTf4hTd4Zbe4NXc4TXfZ +HfdZfffxC4M+8+Ca1z3y0Z1T6h0i138PCVoXhywo3k5qIgaNUV22mGZXXC2Q +Qn8qBYLowgIgi67MQWuv9dHN2UAl3ZmLdedhfQVAMT1c4hst841XAPX0TO3Z +XP3ZYhNQUq+2n290nW/1AFX1/uAFYeTiaAworEnTQGdNXwBqa84a0FzD20B5 +LT4A+mv5MVBhq8lAi61jXMoxggTdE6LbiHeD71nleBYZ7jmqa/rUNU50jhw4 +Bnft/du23g1b96q1c8nSNm9umTE1Tprqx4w1w4aqAX15r660S1vUrs1v1uQ2 +qLNqVZlVyoxyZXqJ4n2hPDVPlpItTcqUAul3mjgpSZQUL0qJEqa9E6S/FnwK +QrL94YI7cOk9fu0DbutDdt8j5tgj+vxD6sYDCuEeiXL7hPP4AHq6LQS8Fq55 +jenCB40RPZZIfLFqcUY3uPHrP64KSMtTr5HhjfCpEA2C057C6QFQxmPo830o +5zZUgPfvLby5uHV3OS14F99nDTxgjD2kz15fG9v3yUd3SdTbJ1y/A/j5pih4 +WfZ2Rh0+po8aMMd02uOa3Ql1QL3+qQLNKUMLS4CSvfJaz15fBFTtrcVYRwmQ +t/eWA5H7ULVvtBao3acaz2ZazubbgPJ9pft8rfd8cwCo4PdGLw7GLw4ngSL+ +dO6SvHBJWwbqeNY60Mjzd4BSXkgAennpCVDNK6lAO69lXkmwQyG6D6M7PO8m +27PG8CxT3Ask19yxa+bIOXXgmNi1j23ZRtZtgyvW/kVLz5y5a9rUMWFqHTU2 +Dxka+vR13brqDm1lq6asSVNSpy6qVuVXKHNLFTlF8qw8eWa27FOmFOj00yQZ +SeKMONGnKGHmO2HWa0FuEFLgjxTfgyse8Ose8Vofc3qBnJ8xA3I3qDsPyMR7 +JNrdY67/AfxsS/hyVfoa5zWtfofzGjJG9pnxKz+6zRHd5Iqp98TUgFAAfNVK +KwMxATiyp/DHJ/AnP+gzvtLehfJvQEU3+eW3edV3uQ33OG332d0PWIMPmeMg +gIC28pC6/YB8eI9EvnPKfnwIPd0RvlqThi4ow6e0UaOGmH5LXJcjodWd2IC+ +rwMxBzlVIPKg5Dr+oLoCq6/AmipBLEJ7NYhI6K3zDTSA0ITR5rOJtrOpDhCm +MN9zvtR/vjoIQha2xi52Ji72p0D4AnH+8mTxkrwMQhnoG1esrSvODghrgAgg +uEF0DEIcZBQQ6KBifNGwvgixIxg94KG7HO8207NF92xQ3Gsk18qxa+nQubDv +mN21T2/ZJ9dt48vWkQXL0Ky5f8rUO27qHjF2DBjaevXNXbrGNm19s6amQV1V +o66oVJWVKUuKFMX58sJseUGmLD9dCuIqksR5ceK8KFF+mLAgRFgUJCj1R8of +wdWPoUY/Xrs/txfEXjCnQWgUbfMRlfCQTAJhHET+k30kaEv0alX6Bl+jcF7j +uohhQ2S/OarbGt3uiG5xxTR6Yuq8cdUgeiOlAsRwpJeiT+BMfzjrEZRzH8q/ +DRWCwA5+5R1e3T1uE1h12b0PWUMPmROP6HMg5oO6/ZBCeHD9iQ+J/MB95OWm ++PWKPGxeFTmpixkxxg1YE7odSe3u5Bb0fSMIE8muA8EixdchI9W1WF0diB1p +aQARJF1Nvt4WEEoy1HE22nU20QPCSmYHzheGzpdHQIjJxuTF9vTF3iwINzla +ujxeuSStgdAT+vYVc/eKvQ/CUKCjL8jJFyEJhKRIqSAwRcn6quZ8RbATCCXy +0EOO94Dp3ad7dinu7VPX5rFr7dC5su9Y2rEvbNrn1mzTy9bJBcv4jHlk0jQ0 +ZhwYMvb2G7q79Z0duvYWbUujpqlW3VClqitT1RYrq/MVlTnyikxZebqsLE1a +liQpjROXRorLwkTlIcKK54Iqf0FNANwQALU84XeCKBnOyBPWVABzMYC+7kfb +e0w5fkim3TvlPD6Cnu4JXmyKQ1ZkbxaUYdPq8J94DZijeqzRnfaYVmdMkzu2 +3htbC6JtkqpAzM37cjQAznoM5TyA8u7isKDiW/zyOz81F7flAacTX3gfsoYf +4bwYc6CdaVuPKAcPyaf3SfT7J7yAQzhoVxiyIX27rIiY00RP6WNHTQmD1qRe +R3KXK7Xd+74VRPZkN4P4nuImrKwJBPrUtoBwn5Y2X3s7iPvp7Tob6Dkb7gUx +QBODIBJobux8cQKEBK3PXGzOgdig/eXLw9VL4jqIEyJvX9H2rhgHIGaISwSR +QzDpi4ACQogkDBBIpGB/VXG/IRgFwkg89ITtPWZ6j2geAsW9f+raJbq2CM6N +fcfatn1lw760altYss7OW6anzZMTpvER48igcajXMNCl72vT9TRpu+o1HdXq +tnJVS4mqqUDZmKNoyJTXpcvqUqW1idKaWElNpLj2rag2WFT3TFgPwpiQVhDM +xO99yhsEUU3s6UDm4hPGegBt15969JhCfkBiPsS/OgL8fFf4akOCX+2h8zgv +TfiELnLEgN9Wonut0V32mHZHTIsrttETi7dYLQiQSq4CewM/OPchlH8PKryN +w4LK7vAr7/Jq73Eb73NbH3C6HrL7H7GGQZQY4LUMwqqo+4/ARUK9T2I/JkLP +DgSvtsVv1mXvlpVRc5rYaX38uClx2Jo8YE/tc77vdqd3ejM6sKx2LK8dRGWV +dYDYrNpOX0MXCNJq7wGhWr0DZwODIGZrbPR8cvx8ZhLEby3NXqzOX2wsgliu +vbXLg43Loy0Q10Xau6IeXNEPQYwX5+QLn/QFpoB4LxEDRH3JOF8V3G9KPs6L +DmE0Hkphe0lM7wnNQ6S4D0/dB0TXHsG5s+fY2rZvbNjXVmwri9bFOcv8lHl2 +3DQ9bJzsN473GEY79MMtusEGbX+NprdS3V2q6ipUduQq2z8r2tLlramylkQp +CDKLkDSHipuDRS2vhG2vBB0vke4XUO8L/mAQbzSIOwlC51lLT5nrgfSdANqh +P/X0MZn+gMT1J0JPDwQvtkXB69I3y/K386p305oIwMsYNYjzssTgm7cOR2yr +C8SxNXjj6kBAW1I1mlKFPoLz70OFdwAsfCWsuMuvvserv89tfsBtf8jpfsTu +B/dK5oQfYxbEwNE2/Ki7j6lHjyjkh2Tmw1PekyP4xb4wZFsSti6PWFZFL2jj +ZvSJk6bkMUvqiO39oCN9wJXR58nsRbN6sNzrQLrSHl9lr6+mDwTVNQ+A0Lqu +4bPeURBjNzJxPj51PjUD4u0WFi6Wly7WVkDs3c7G5f7W5eEuiMMjEa4oR1f0 +YxCTxyF/4VG/QHQQnydkgSg9Ke+rnP9NCeO8WBDG5KJ0tpfK9JJpnlOy++TE +TTxyHR44D3Yde1uOnXX75rJtfcG6OmNZnjQvjprmB42zfcbpLsNkm368STda +px2p0gyVqQcKVf25yr7Pyp50RXeqvCtB1hUt7YyQdL4Td4WJukOFPW8Efa+R +gRB4OJg/+oo38ZI784KzEMRaec7ceMbYDaQfBlBP/Sg0EEd4wg88RIL2hK+2 +JK/XZKFLirA5dfi0NmJcHzVijMZ59Vlium2xOK82Z2yLO67RA6IP60AMYlIN ++gAuvAcV34ZKbkPld/lV+P7zPq/hAbflIbf90S+8/HBezFkQGkVf96ft+FEJ +fpSTx2Taw+tPf3aIvNoXvdmWvtuQR62oYhc1CXP6pBlj6qT5/bg1fdSeMeLM +HHZnD3lyB9H8Qaxw0FcyCCIga4ZBHGTz2Fn7OAiI7Js6H5w5H50DwZHTixdz +yxdLqyBQcmPzcnv7cm8XBE0SCVenR1fkYxBAySCDMEou/QvEBPGUQg6IqpRC +X+XwN6UA58WFMDYXZbFRBsNLo3koZDf5xH165Do+cB7tOgibjv01++6SbXve +ujltWR83r46YlgeMiz3G+Q7DbLN+pl43Va2dKNeMF6lH81Qjn5XD6YqhFMVg +knwgXjoQKxmMFg9GiYYihMPvBCNhyNhbeOINf+o1bzaEuxDMWX7JXn/B3Api +7D+jHwXSTgOoND8y+zGJH0iEg/BFaUf8ekMauioPW1SGz6kjprSRv/CKwXn1 +2GI77bHtzrhWFwgVbfTG1YOY0cRa9B5cfAcqAVmxUOVdfs09Xt19XiM4MnA7 +HnF6HrMH/NgjfqwJf+YMiDGlr4JIU9q+P5XoRyE/JjMekblPTqCgI0HIvujt +jjRiUx69popb1iQu6lLmDWmzpvRpS8aULXPSkT3hzB135497isa8JeNo+ThW +Oe6rmThrmATRq+0zIIa1b/58aBEEs06uXMysXSxsgMDWtZ3Lzb3L3QMQ5HpE +vDo5uSKdgoBXBvULi/6FywTBrzAHhMCKoa9SGMTCKkQ4L4iP8bgoh42yGV4m +1UMneWjHbsqhi7TvPNlxEjcch6v2g0Xb/px1d8qyPWbeHDKt95lWO43LrYal +Rv1CjW6uXDtbrJnOU09lqSYzlSDK9r18IlU2niwdTxRPxIsmYoWT0YKpSGQm +HJ59B82/5S+Gcldec9ZD2FuvWLsvmYQgOvEZjRRIpQVQ2H5kfuAxHEQQvNoT +hWxJQtdlYcuKdwuqiFlN5JQuatwQPWKMwXn1W0CYcpc9rsMJ4nrxFmvygMzl +ehBQdRcuvYZV8Yfm4jU95LY+4nY+Brz6/djD/qxxfEcawJwHYcH0DRAcTCME +UE/8KVQ/CtOPzHt6Ar88Erw+EIftSiO35TEbyvg1TdKKLnXJ8GHR+HHenDln +zZq15c448mecRTOukhlP+Yy3cgatmcXq53xN82ct8+cdi+fdSyDyeHjtYnz9 +YmoTRCEv7l6u7l9uHICI5D3iFeHkikgC0ckUGohRZjK/cNggWBnmgZBlEfJV +IgCxywrxN8SH8DGIi/JZKJfh5VA9LJKHceymH7qoe07ytvN03XGyYicu2A5n +rAcTlr0R8+6AebvbtNluXG8yrNXqVyp1y2XapWLNYoFqIU85n62Yz5SDwOgP +0rk0yVyyeD5ROB8vWIhFFqPh5UhoJZy/FsbbeMvZfsPeDWEdvGIevWScBtEp +z2iMJ1SOP5mPf0tBhwJ8LXq9IwndkIWtKt4tKSPm1ZEz2qhJffQYzsuE8wIx +5T/zcgBerW6QZv4Lsp9g3YNwWDX3+XUPeA0Pec0PuW0/8fLj/MRrLABsSucC +mEtPGGsgmJu+B0K6qaDNAygsfwr/2Sn8iih4cyh+ty+N2pXHbisTNtXJ69q0 +NX36iuHTsilryZyzZM1ftBUuOkoWneWLrqpFd82Sp34JbVrGWlewjlVf99pZ +3/r54ObFyNbFxA6IGp/fv1wmXK4dgQjy3dOrA9LVEQVEk5MZX2isL0w2iCzn +8UF8OYJ8FQlAoLlM/E0h/Qb7hHxMwEFhFgrRvTyKh3vqYRPdTIKLseukbTkp +aw7ykv10znY8ZSWOWQ6HzAe95v1O026bcadJv12v26zRblRq1svU68WqtQIl +CGHPloFA9o8SEM6eKlpNFqwlIutx8EYMtBnF347g7b7j7r/lEN6wiCHMk1cM +8gs67TmN9ZTKDSRDz08Q/JIOPhC93pWEbsrC1uT4Di1iQR05p4ma1kVP4LyM +McOm2EHLT7zicF6djrh2Z3yrC0TPA2Te+Ebvz7Cg6vv82gf8+ge8xoe8lkd/ +xMufPeTPHg1gTQawZp4wF54wVwIZG/iGJ5B+EEgjBl43eyCV9YTCe06Cg08E +oURR+KEk+kAWt6dI3FGlbGs+bOk+bugzN4zZ66a8NUvhmrVkzVa+5qhcc9as +u+rX3U0bntZNb8cm2r2F9W37BnfPRvbOx/cvpggXs4eXi8SrleOrjdOrbfLV +PvXqkPblmPGFxPpC5XxhcL+y+F+58FcI+YoIvwpF38SSb1LpN7kM5yXmYyIO +JmCiCM0LU7z8Ew/vyM05cLF2XMxNJ33VQVu0U2ZspAnr6ajleMhM7DcddRsP +OwyEVv1Bk26/XrtXo96tVO2UKXeKFdsF8u1c6XaWZPuTePujaPu9cCdFsJME +7yZA+7H8g2geIZJ7FM45DmOfvmFRQhi0V3TmCxrnGZX/nAy/PBEEHwnx9Sd0 +V/J2S/ZuXR6+ooxYUkXOa6JmtPg5KHrcEDNqjB02xw5YYvuscTivbsArHufV +5orHW6wFBNAnNHl/gXXdXHy8uZoAL17bY5wXt9uP0+fPGQxgjwSwx5+wpp+w +5gKZS4HM1aeMzaeM3af0g6fX6/MzGu0ZFb+QeM8pcDBJEHoiCidKoo9k8QR5 +0oEydU+dvqv9tKvL2jHkbhsLts3F25aybWvltq1m21G/42zacbXuujv2PN37 +3r4DdIiAjR76Jo7OponncycXi6cXK6TLdcrVFvVql/6FwPxCZH055Xyh8L7S ++V9Z8FcO8pUv/AqLvgkl38TSb1L5N7kC5yXlYRI2JmaiQppXQPbCxx7o0M3f +d3G3XZx1J2vZwVyw02dttCkrddxCGTGTB02nfcaTbsNxu47YoiU2ao7q1IfV +qsNyBaFETiiUEfKkhGwJ4bOIkCEkfBAcpiFHyTAxgX8cxzuJ4ZIiOZRwNvUt +i/GGyQphcF7S+S+o8CsSEnIifH0kCj0Qv92VvtuShW8oIlaVkUuqqAVN9Kw2 +eloXM2GIGTPGjphih8xxA5a4Pltcjx3nFY/z6vg9L9BiCc2e+zgsqObn5rrm +9ehnXh1+gFevP2cggDMcwB57wp4MZM0EsuafMpefMteeMbZAQDaD8JxOfE4n +BdGpQTRmEI0bRIOCKUgoWRhxKo4+kcYT5clHirRD1UeCOpOgzT7Q5x0Yig6M +pfvmigNL9YG17sDeRHC0Epwdh67uI3c/0TNE9I6eoBOn2DTJN0c+W6Scr9Au +1ukXW4zLXdbVAfvqiPPlhPeFDH2lwV+Zgq9s4Vee+Css+SaQfhPJv0kU32TK +b5BPzsNkbEzKQMVUr4jkFRI9CMEN77mhbRd/w8lddXCW7ewFG2vWypy0MMbM +9GEjbcBA7dVTOnXkNi2pWU1qUJ3WKE8rFSdl8pNi6UmB5CRXfJIlOv0kOE1H +SGkwORmiJPKpcVxaNIcRyWa9Y3HeMnmvGVAwHQmhCN6QhKHHorf4PeJAEr4r +i9iSR24oIleVUcvqaBzWnDZmRhczaYgdN8aOmvDmihu0xPVbf+IV3+34mVe7 +6ydkCS144bxqHgBY183Fb/yPvLr8uDiv/gDOIHiuwh4PZE89Zc0+ZS08Yy0/ +Z649x/erzN0gxsELBvEF4/QlnfKSznhFZ7+i817RkVCaIJwiiiZL4kmy5FP5 ++xNlxrHq87Eml6gtIOqLiYZyoqmKaK4jWhqPbS3H9o4TR/eps+/UNURyj5K9 +ExR0horO07Alhm+VebbBOt9mX+xxLwm8yyP+1Qn0hYx8oQq+MoRf2eKvXMlX +SPYNkX8TKb5JlN9k6m98n5KLKViYnI7KKKjk1Cs+9ogO3cIDl2DXiWw54HUH +tGLnL1l5cxbutJkzYWKPGllDBmafntGtZXRo6C1qeqOKVqegVclp5TJaiZRW +KKbliWhZQvonAT0dZqRBzGQ+K5HHjuNyozm8CBYUxoRDGYK3NGEYWfTuVIwv +MhGH0oh9WeSOPGpLEbWhjF5VRS+rYxY0MXO62Bl97JQhdsIYN2aKGzHHDVni +Bqzx/bb4Xls8zqsL5+X8Pa8EnNc1sgfQT7DqH17zesRvxnk9xnnx2v24nXiL ++XP7AjgDTzhDTzijgeyJp+ypZ+DYvvCctRzEWgtibr5g7rxk7uPboVfMk2AG +GV+6QxjM1wzOGwY/lIGE04XRNHE8VZpMlb2nKDLIyiyyOo+sLSTpSkn6SrKx +hmxqIFuaydZ2iq2Lau+jOgdprlG6e4LhmWF651noEhtb5fg2uGfbvPM9/jkB +viAil6eCS7Lwiib6wpB8YUu/cmVf+fJviOKbUPVNrP4m1eC81ByfioUpGaiC +6pWTvbJTj5TolhBc4n2naMch3LQL1mzIshVesECzZmjKxB838ob13AEdt0fL +6dRw2lTsJiW7XsGulrMrpOxSCbtQzM4TcrIFnEyEmw7z0vj8ZB6UwIVjOUgU +WxjJFEXSRFEUcRRJEn0sjT6S4jfxmD15zI4iZlMZu66KXVXHLmliF7Rxc7q4 +GX3clCHuGlb8iDl+yBI/iMOyxvddw8Kb6094tbl/QvYLrN/zarrm1Qp48UCL ++XN7Arh9T7g4suFAzuhTzsQz9tRz9uxz9kIQe+kFa/Ula+MVazuYtRfCIoSw +iK9Zp2+YlFAW/S0LXx+44SwogiWIZonimZJkhvQDQ/6Jrsymq/LpmmK6tpyu +r6Yb6ujGJrq5jWHpYlh7mfZBlmOE5Zxgu6Y57nmuZ4nnXeWjmxC2A/v2kbND +wTlReHEqvqBILmnSK6bsii3/wlV8hZRfEdU3ofqbWPNNqsV5abmYho2pmaiK +7lVSvQqSR3Hilh+5ZAdO6Z5Dsm0Xb9jEq1bRkkU4ZxZMmwQTBmREDw/q4D4t +3KWG2lVQsxJqkEM1MqhSCpWKoSIRnCeEsxHkEyxIhwSpfGESV5zAkSSwJPF0 +CX5NxpOl8Scy/BYQfyiP31fE7yrjt1XxG+r4NXX8iiZ+SRu/oIuf08dPG+Kn +jPETpvifYA3/BMsGYPXaf+Hl/IlXQrsL1C/IHv4RrJ958ZuvebX5AWSd/rzu +AG7vNbLBQO7wU87oM874c87Uc85MEGf+BXvxJXvlFXs9mL0Vwt59wz4IZR++ +ZePbJNI7NjWCja/q7Gg2N4YDxXEE8RxxMkf6gSP7xFbksJUFbHUJW1PB1tWw +9Q1sYwvH1MGx9HCtA1zbCM8+zndO813zkHsJBkm9mwJ0R4jti3yH4rNjyTlJ +ek6RXdDll0zFFUd5xVN9gdRfEM1XofarWPdNqsf3G3o+puNiWhaqZXg1NI+a +4lGdupVEl/LQqdh3yHfssk2bbM0qXbZIF0ySGaN40iAe04uHtKJ+jahbLWpX +iVoUoga5qEYqqpSISsWiQqE4TyDJQiQZsDSdL/vAlb1nydIYsjSaPJUiTz1V +pBwrUo6UyQfK5D1V0o46aVOdtK5JWtUmLusSF3WJ8/rEWUPitDFx0pQwbkoY +NSeMWBKGrAmD1oR+W0KfLaHXntDjSOh2JHQ5EzqdCTisDtd/4NXm/gXWf+D1 +iA9azA8g6/D/CRmv5wm3L5A78JQ79Iw78ow79pw7GcSZfsmZe8UBj19COKuv +ORtvONtvOXthnIN3nKMIzkkkhxzNocZyGXFcdgKXl8SDUniCNL74A1/6iS/P +4SsL+apSvqaKr63j65v5hnbI1A2Z+2HLMGwbR+xTAsecwLUkdK+KPJti744E +3Zdih1LfseyMJD+jKs7pyguW6pKjvuRprmDtF4Hui0j/VWL4KjXg52UjhBl4 +mIGD6lleHd2jpbq1JLfmxKU+cqoPHKpdu2rLply3KFbMikWTYtYonzLIx3Sy +Ya2sXyPrUck6lLIWhaxBJquRyisl8lKRvFCoyEOUuZAim6fMYis/M5WZdOUn +ijKDpPp4oko/Un0gqN/vq9/vatK2tKkb2tQ1XcqKPmVJn7xgSJ4zJs8Yk6ZM +SRPmpDFz0qglcdiaOGRNHLAl9tsS++z/f7B+5gXqF1gNv6yHv7QYjoz/E7J2 +HFkAr+sJjozXG8jrf8obfMYdfs4dDeKOv+BOveLOBHPnQriLr7nLody1t9zN +d9ztcO5eJJcQzTuK4Z3E8cgJPFoSn5HCZ6dBvHQIyoAFmbA4G5HmChRFAlW5 +QF0t0DYIdC0CQ6fQ2Cs0D4osoyLbpNg+K3YsSpyrUteGzLMj8+7L0UMFdqz0 +kVRnVNUZXX3O0lxwtJd83SWsvxIYrkSGLxLjF5npq8BnhjETHzVxUSPba2B4 +DDS3nuzSnzp1RKeO4NDu2bTbVs2GRbNqVi+Z1HNG9bReNa5TDWtVA2pVj0rV +oVS1yNUNMnWNVF0pVuP/yTJYXcJXF3HVhSx1PkOdR9PkkDXZp5osoubzofbT +gTZjV/dxW/dxU5++rv+wYni/ZHi/YEybM6XOmFKnzCmT5pRxS/KoNXnEmjxk +Sxq0JQ3Yk/rsib2OxB5HYrcjESf1MyzX/xbW/8LrT5ABan78Vn9+mz+/I4DX ++YTXHcjrecrre8YbeM4bDOINv+CNvuRNBPOmQngzb3jzobzFMN7KO95aBA8/ +8u/E8Pfi+IQEPjEJOk2ByGkQ7QPMzIDZmQgvWwDnCgQFQnGxSFYmVlSKVbUS +TZNE1yYxdEuNA1LziNQyIbPOyOwLcseKwrmhcG0rPfsq76EKPVZjJI2PqvUx +tGcs3TlXf8E3XMLGS4HxSmS6kpi/yMxfhD4rglkg1MJDzRyvmekx0d0mistI +chqPHYZDu2Hfpt+x6jct+jWzfsmkmzfopvW6cZ1uRKMbUOt6VLoOhb5Vpm+W +6BpFunqBrhbSVfN0lRxdOVNXStcVU3RFJF3BiT7/SJ9L0Ofs6bN3DJ+3DJnr +xk+rxoxl08dFU/q8+cOs+cO05f2kJW3cmjpqTR2xpQzZUgbtyQP25D5HUq8j +qceR1O3ESYHqdCX+b0i5r+v67+3/Ky9Qj36hdo2s2Y/f4n9NLYDf8YTfGcjv +esrvecbve87vf8EffMkffsUfDeFPvOZPhfJnwvjz7/iLEdBKFLQWA23GQTsJ +8H4yTEiFie+R048IBd8MZwmYuUJOvoiP38FLxcIKiaRaKquTKhtl6ha5Fv+i +ehXGIYVpTGmZVlrnVfZllWNd7dxWu/Y0HoLWe6xFSTqMqvcx9D6W4YxrPOeb +LmDThdB8KbZcSS1XcusXkc8uwGwwauOjVq7XyvJYGG4L1WUhO80nDvOR3Xxg +M+1aTVsW05rZtGw0zRtM03rThM40ojENqkz9CmOPzNglMXaIjG2IsRkyNHIN +9WxDLcNQTTPg29ryU2Mp0Vh8aCzaNxbsmvK3Tbkb5pw1c9aK+fOiJXPe8mnW +mjFt/ThpSx+3fRi1vx+xpw050gYdqf2O1D5nSq8zuceZ3O1K7nIldbqSOgCp +xHb3T/ULoz+pP+FV/0eFI7suqPExqCY/qNkfVEsA1PYEag+EOp5CXc+g7iCo +9wXU/woaDIaGX0Ojb6Dxt9DUO3gmAp6Pghdj4JU4ZD0R2UxGdtIE+x8EhxmC +489CUraIkieiF4pZJRJuuQSqkiK1MvzOLm2Ry9sVqi6lpleFX+TGEY15UmOZ +1VqXtPY1rWNL59zVuwl6D9HgPTWgVCNGN/pYpjOu+YxvPkcsF0Lrpdh6KbVd +yW1XYp9DiDkQ1AGhdq7XzvbYmG4bzWUjO22nDivRbiXYrLtW65bFum62Lhut +8wbrjM46pbFMqCxjCsuwzDIoMfcJzT2IuYtvbueaW1nmZoa5gWquI5trTsz4 +ybGCYCnbs5TsWIo3LYXr1vwVa96SLWfBlj1ny5q2Z07aP407MkYdH0ec6UPO +DwPO9/2u932utB5Xarcrpcud0ulO7gCV1H5dbe5EvFo9ia34nz/v3v9Qf8rr +F1JQ3R/XI6j+p3oMNfhBjXj5Q00BUPMTqCUQbnsKtz+HO4Lgrhdwzyu4LwQe +eAMPhSIjYch4BDIZhczEIPNxgsVEwUqyYD1NuJUu3P0kOvgsOsoRn+SLyUUS +WpmUWSll18h49XK4SSFsU4o7Vfi9XtmvVg9rtGNaw6TONKO3LBhsKwb7hsGx +Y3QdGN1Ek+fU5KWYUboZY1l8XMsZ33qG2M6Ftgux/VJqv5Q7cF4uIeZCUCfk +dfK8To7HyXQ76C4Hxek4dTiIdgfB5tizOrYsjnWTY9VgX9bZFzX2OZVtRmGb +ktnGJbZRoXUIsQ7wrb1cazfL2sGwtlGtzSRr44m1/shWe2Cr3rVVbtvKN+yl +a/biZXvhoiN/zpE348yZcmaPO7NGXZnDrk9D7owB98c+d3qv+0O3532XJ63T +k9rhSW33pLR58UpuBZXUAiqxxfP7Svh9/UdkP8G6fhhV9wCqA8fnP1TNQ1C1 +eD2CQT2G6/zgen9QDU/gxkCk6SnS8gxpDULaXyKdr5DuEKT3jaD/rWAwXDAS +KRiLFk7GCWcShPPJoqU00Wq6eOOTeDtLspcrIRRIicXS03IZpUpOr5WzGhXc +FiV+5BF0q8V9aumgRjGqVU3otNN6/ZzBuGg0r5jwRrBvm537FteRxX1i8ZCt +XroVZdkwjs3Ht58h9nOh41zsuJA6L+XOS4nPI8LcAtQNe918r5vjcbPcLrrL +RXG6SA4X0e46tLkOLK5dk2vb6NzUO9e1zhW1Y0nhmJc5ZiWOKaFjArGP8u3D +XPsAy95Ht3dT7R0kR9uxo+XQ0XjgqN911G45q9edFavOsiVXybyreNZVOOXO +n3DnjnlyRjxZg57PA97MPu+nHu/Hbm96J/qhA33fjqa1oWmtaGoLmoJXM5p8 +XUlNoBKbvD9XszcB1O+p/cwr/prXL7B+ZoTX9UPF6gd4wVW/r4fX9QipfoxU ++yE1/khtAFL3RFD/VNDwTNAUJGh+KWgNFra/FnaFCnvChH0RosEo0UisaCxB +PJksnkkTz6dLlj9J1rKkm7nSnULZfon8qFx+Uq0g1ylpTUpmq4rTqeb3aJAB +rWhYKx3Tyaf0qlmDZsGoWzYZ18zmTbN1x2Lft+Kt4Tq2ucl2D83uZdpRjgPj +O3yw80zoPBe7zqWuC7nrUurzijGvEPXCXi/f6+V6vCy3l+HyUp1essNzavMc +WzxHZjfB6N7Xu3e07i21a13pWpW7liSuBZFrFnFNQ84JrnOU5RxmuAaorl6S +q/vY1XHoatt3Ne+4GzfddWvumhV31aKnYs5TNu0tmfQWjXkLRtC8ITS3H83u +xbJ6sMwu7FMHltGOZbRhH1ux9BYsvRn70IS9b8LSGrHU60ppwJIbsKQGLLEB +TWz8uRKavKCun/H+hAw89W1zPfgjXvd/JlUFCq68D1dcV/kDuPwhUv4IKX+M +lPsh5f5IRQBS8URQGSiowuupoOaZsPa5sC5I2PBC1BQsanktagsVdb4Td0eK ++2LEg3GSkSTJeKp06oN0NkO2mCVbyZWvF8q3SxR7FQpCtfK4XkVqVlPb1Iwu +DadXyx/UISN64YReMm2QzxuVSyZ8y63bsBi2LaY9q4Vgsx3ZHSd2vE3c+JfP +cKJsF8Zz+WCXT+A+E7vPpe4LuedC6sPEGCZEMcSLQl6U60HZbpTpRBkOlGZD +KVYvyew9MXrxWyFB59nXeHaVni25Z0Pqwc96SwL3AuSe5bmn2OCx2CjVM0Ty +9B97eg89Xfue9h1v66a3ac3bsIzWLqDVs2jlFFY+gZWO+oqHfIUDvoI+X36P +L6/Ll9vhy2n3Zbdi2S1YVjP2uQnLvH7HL6MB+1iPpddjH+qx9/VYWj3QgqXU +Y8n1WFI9Cqg1oAk4ssY/IAO/pwBe7p9g3ef/DOv655XKe3DFPbj8Hlz2AC57 +CJc+gksfI6X+SEkAUvIEKQlESp4JSp8LSoMEZS8E5S+F5a+ElcHCqhBR9WtR +7RtRfai48a24OUzSFi7piJJ2x0r7EqSDybLR97KJj/Lpz/L5XMVSgWKtRLlV +odqtURHq1cRmzWm7htqtZfTp2EN63pgBnjQIZ42SBZN82axcs2i2LLpdK74J +Nx3aLcd2fM+A34lcNJeb6fLiILhuDPL4BJ4zkedM6j2Xe3FePjHmE6I+xOuD +PT6+28dzYXgnsuwYw4rRLBjFhJIM6IkOJWpQggrdV3h3Zd4tsXdd6F2FvUs8 +7zzbO8v0TtHQcTI6coIOHqL9+2jPDta5ibWtYS3LvsZ5X/2Mr2byrGrsrHIE +vJFS1u8r7fWVdPuKO8HLYIWtvoIWX34zlteI5TZgOfXgbcysOuxzLZZZi32q +xTJqsY+12Ida7H0tllaLptahKXVoUh2aWI8m4NXwB2Tg98rrFsN5/Qmsu3D5 +XbjsGhZOquQxXOyPFAcgRYFI0VOk8BlSGCQofCEofCUoDBYUhQiL3giLQ4Ul +b0WlYaLycFFlhLgqUlwTJamPljTGSlvipG3xss5EWU+SvD9VMZyuGMtUTOUo +5wpUiyWq1Qr1Zo16p15z0KwltutOu3XUfj1j2MAeN/KmjPCcSbholqxa5BtW +JX623bPpCHYD0WE6ceDbchvV5WC4XCw3fm/y8Dx4E+Gt5BOhZxL0XIaX71yC +nYvRM6H3DO872HUGOX08uw+/2bEtPqbZh+8tKXqMpMVO1BhRiRFk2L4E2xFi +mwi2zsdWONgiE5ujYTNkbPLEN3bkGz7wDeyc9W6eda2dtS+dt86fN8+cN02e +N4yf1Y+c1Q2e1fSfVff4qrrAC3sVbb7yFl9pk6+kESuux4rqsMJarKAGy6/B +8qqxnGosuxrLqsIyq7FP1VhGNZZejX6oQdNq0NRaNKX2GlndH5CBX5Z/4XX/ +5+b6BRb0E6zSB3DJI7j4MVzkDxc+QQqeIvnPkPwgJO8FkvdKkBsiyH0tyA0V +5L4V5oUJ88OF+RGiwihRUbS4JEZcFiepiJdUJUprkqT1KbKmVFnre3nHB3n3 +R0XfJ+VQpmo0SzWZp54tVi+Ua1aqtRv12p1m3UGHntijPx0wUIeNjHETe9rE +nzcjSxbRmlWyaZXv2FT7ds2hQ3fswM+8ZorLSnfhW3QH2+PiedyQ14OvewIU +E6E+CXYmw87l2AVODe81sedc5D4XOM8RxxlkP+NZwf6fbTpjGs5oujOK5oyk +OjuR+46kPoLItyc424bONrlna6yzZfrZAuVs9vRsing+fnA+sns+uHXRt3bR +u3zRvXDeOXveMXXeNn7eOnLWPHjW1H/W2HNW3+mra/fVtvpqmn3Vjb7Kel9F +HVZeg5VVY6VVWHElVlSJFVZg+RVYXgWWU4FlV2CfK9DMSjSjEv1YhX6oBqMH +qTVo8h8hi29A4wGyn1sMwOLX4LDA+1FQxZ1fYD0EsAr94YIncP5TJO85kvsC +yXmJZAcLsl4LPocKPr8VfH4n/Bwh/BwpzIoWZcWIcuLEufHi/ERxQZKkKEVS +miotfy+tSpfVfpQ3fJI3f1a0Zyu7cpR9earBAvVokWayRDNTpl2o0q3U6zaa +9TvthoMeA3HASBoxUSfMzBkzZ97CX7YiazbRlk26a1ccOFRHDu2JU092Gaku +M8ONn4LtXI+D73Xhm0AB6hWhKH7PkmI+ue9MiV4ovNc3MveFxHUhcl4I7ef4 +nh+ynPNM5xzjOUt/ztCe09TnFMX5qez8WHJ+KDw/gM93eedbnPN15sUK9WKR +dDF3fDFNuJzcuxzfvhzduBheuRhcvOifO++bPu+ZOO8ePe8cOuvoP2vrOWvt +PGtu8zW1+BqbfA31vrpaX20NVlOFVVVileVYRRlWVoaVlmIlpVhRKVZQiuWX +orllaHYZmlWOZlagGRVoeiX6oQogS7lGBnjVofEA2R9aDOd1j199zaviDmiu +0vsAVtEvsPKeIrnPkewXSNYrJDME+fRGkPFW8DFM8DFcmB4pTI8WpseI0uNE +HxNEGYniT8nizymS7DRJ7gdpfrq0KENWmimryJJX5yjqcxVN+cq2QlVXsaq3 +TD1YoRmt0k7W6GbrdIuN+tVmw0a7cafbdDBgIo6YSRMW2oyFuWDlrtigdZtg +2y7ec8gITgXRqT51aSkuPc1tZHrMbI+V57XjJywEdQlRN74hlGCozIcpfD41 +eqn0Xio8l2CviG/vHRci24XAeoGYLyDTBc9wwdFdsDQXDOUFVX5Bll6ciC6I +ggsCdLnHvdxhXW7SL9fIl8snV4tHl/MHl7O7l9Obl5NrF+PLF6PzFyMz50OT +5wOj5/1D5739Z909Z12dZ51tZ+3NvrZGX0udr7nG11Tla6zA6suwulKspgSr +vp7TqSjCyoqw0iKsuAgtLELzi9HcEjSnFM0qQzPLf0b2vgpNvUaWVPt7Xn9o +sXu/NBcOC7wrBZfch4sfwYV+cEEAnBcI5zxDsoKQz6+QTyHIxzdI+lvB+3eC +tAhBapQwJUaYEidMjhelJIpSksWpqeK0NMmHD5KPH6WfMqRZmbLcLFlBjrw4 +T15WoKgqUtaVKBvLVK0V6s4qTV+tdqheO9aom2rRz7UZljqMa92mrV7TXr+Z +MGI5nrCSZ6z0BRtrxc7bsMPbDuG+U3LolB27lCS3murW0T0GlsfE8Vr4XhuM +2gWoU4S5JJgH38bLfajyDNN4r9SeK6X7UuECxzH8EC2xXYoslwITeNLI119y +tZds9SVTcUmXXVIklyTh1TF8dcQD7xvsMq62qVebpKv146vVw6vl/cvF7cv5 +jcvZFfAi6+TsxfjU+djY+cjw+VD/+WDP/1fWeTC3cd5p/GskN05z7uLEvsSx +nXNOlmSJKpbVLVFWJSX2TrH33sVeRUkkVUiKRZTYKfZeAIIAuAV9ASx6r+8u +OsCZ09LxJTc383yD3/x339n3/3vW8azd8bTF0dnoeFxHtteQbZVkaznZXEo2 +FVMKVX0BUZdPPMojqnOJqlyiIpcoywUleaA4DxTmg7wCkFMIsopARglIKwUp +ZSC5AiRWgvgqaps3poZaE/15xGyRFK+qoJ+H6yRccgopOoMUfofkn0dyLyLZ +l5EPsNKvo6k30Ie30KQ7nIR7nLhQTswDbnQ4NyqSGxnNi4jlRcTzIhP5Ucn8 +6IeCmFRBXLowMVOYnC1KzcUy87CcAnFBkaSkVFJRLq2pxOur8eZHso56+dNG +RU+LsrdNNfBY9eaJerRLM9mjff9Ct9CrX+k3bAwatkeMu2Mm5pQJmjWjC2be +ikW4bsW2rFKaTbZrUzLtarZdCwEdShi4hIlPmIWkVUTaxA671AHkdo/M5sGt +HonZIzZ5REaPUO/haz1cDfUZH1F4IJmHLfXsYZ5dIXVPvcXxbsDeVbZ3ec+7 +SPfOb3tmNzwzq56pJc/EnHt8xj064X476nrzxjU04Broc/a/cPZ1OV89cb5o +dzxvcXQ3OLpqHU+ryScV5ONSsqOYbC8kWvOJllyiKZtyFeszidpM4lEmqM4E +lZmgPAuUZoPiHFCQC/LyQU4ByCwC6cUgtRQ8LAdJFSChEsT9C6/IOju15dtg +C6J4fRiu8hNw6Um4+JBXwTkk7zyScwnJuoKkX0NTg9Hkm2jibTTuHic6lBMZ +xgmP4D6I4t6P4YbE8UISePeS+JQTmioITRM8yBCGZwmjckQxeaKEAiy5SJxW +Is4qk+RVSIuqpOWP8Oo6WX2DvKVZ0dGqeNahfN6p6numHuzWvH2hHX+lne7X +zQ3ol4YNayPGzXcm2riJMWVmz1rgRQtnxcpft4q2bGKaHWfY5Uyg3AdqmNCi +hJ5HGvmkSUhaMIdV4rBJnUBh88qtXpnFKzV7JUav2OAV6bwCrZev9nKVXlRO +3W/uS7wszMsQ+Ohc3w7q24J8Gyzv2p53le5d3vIurnvmVzyzC56ZWffUlHti +3D32lrIwRvpdb166hnoo+6m/w9nX4njV4HhZ63he5egpJ7tKyGeF5JM8sjOH +6Mgi2jOI1jSiJZVoSiUaUkBdCiUIV6eCyjRQng5KM0FRFijIAbl5ILsAZBRR +aurDMpBUfsirCsRUg6gaEPnoX3lVnjx8GJ6ASyhecOFZJP8cknsByb6EZFxF +Uq8jyT+iCbfQ2LtoVCgn/AHnfgTnXhT3Tgz3VhzvxwTejSR+8EN+cCr/Rrrg +x0zhzWzh7VzRvXzR/UIsohiLKRUnlEseVkoyqqW5tXhhvaysUVbdIq9vU7Q8 +Vj5+ourqUr98ru5/qRnu046+1k0O6d+/MSy8M66MGTcmTdvT5t33FuacZX/R +iqzYuBs2wbYdo9slDCBjAQVEqBBCwyF1PNIgII0ih1nssEicNtxpV9p8CqtP +bvbJTD6p0SfR+zCdT6ihbjN5Ch9H5kOkPkhMLX4w+T4G17eL+GiQb5vl3WR4 +N2jetS3vyppnadmzMO+Ze+9+P+meHnVPvnFNDLjGel3vnrtGnjmHHzuHWp0D +jY7+WkdfleNVGfmymHxeQPbkkF2ZlKb9JJXofEh0JBHtiURrAmhOAI0JoD4B +1CaCmmRQ+RCUp4KSdFCYBfJzQE4eyCwAacUgpZTyvBIq/i+v2kNe9T/xKv9/ +vHIuIFmXkfQfkJRgJPEmGncHjbqHht3nhIRzbkdyf4zhXo/jXk3kXUrmXUzh +n0/jn88QnM8SXMgRXswTXikQXSvCbpRgt8vEoRWS8CpJTI00qQ5Pa8Czm2SF +rfKydkVNp7LhqbK1W9X5Qt3zStPbrx0Y0I0M68dH9NOjhrlx49KUaW3GvDVr +pi1Y9pas7BUbvGbjbNj523YRHYj3AM4m5BChREk1l9TyHXqhw4g5TGKnReq0 +ypw2ldWntPgUh7xwg0+q94m1PpGGunrmK/xcmR+V+hHMDwn9+3wfi0PtMTL2 +fXSmd2fXu73j3dz0rq9SesXynGdxmhKaZt+53w+5p/tdky9d492u0U7nuzbn +SJNzuNYxVOUYKHP0F5F9eeSrbPJlOvk8hehJIroTiGdxxJMY4nE06IgCbVGg +JQo0RYP6GKo5oToBVCaBshRQnA4KMkFuDsjKB+mFIKXkH7xiKymN6J+86v7J +68QhrxOHvM7AP/HKvIyk/YAkByPxN9Hou2hYKBoSxrkVybkezb0Sxz2fwDub +zDuVwj+Rxj+WIfgmS3AkR3gkX3i0UPRtsSioBDtbLr5QKf6hWnLzkTSkThrR +iMc3y1Ja5Vkd8oJORdkzZU2PqvGFur1X87Rf+3xQ2/9GN/xW/27MMDlhfD9t +WnxvWp03by5adpatjFUra90GbdrRbTuPBgR0AtsjJGxCBpMKlFRxHRq+Qyd0 +GDCnUeI04y6LzGVVW/0qi19p9suNfpnBj+v8Eq0fU/tFSr9ATu1QcSV+DuZH +hX6Y74M4PjbsY+779pi+3V0vbce7s+HdWvVsLHrWZj0rU56lMffCiHt+0D3b +65p57pp66procI43O0frnG+rHSNljjdF5HA+MZQNBjPAQKr9dbKtP8HWF2t9 +FW19EWntCbd2hdmePLC137e3PABNYaA+AtRGg+o4UJ4ISlJAYTrIzQJZeYe8 +iile8T/zivzA63/fX/W2k1DFhxzyKv0WLg6CC0/D+d/BOecpXqk/IEnBSOwt +NOIuGnofvRXOuRbFuRjLPZvAPZHEO5LC+zKD/3me4IsSwZcVwv+qFv69VvRN +PXa8ATvZKD7TJD7XLLnYLL3aLA1uxm83y0LbZNEd8uQnisxnyoIeVflL9aNe +ddNrTceQtuuN7tU7/cCYYWTSMD5tnJk1zc+bl5cs6yuW7TXr7oaNuWXb37Ej +dMBlAMEeIWIRkn0Sh0k56lDyHGqBUyty6sVOg9Rlwl1mucuqsfrVZr/S5FcY +/XJ9ANcFpJqAWB3AlAGRPCDEqTVFHubnCv0oz49wfBBMeROsPR+T7mVse+nr +3p0V7/aCZ/O9Z33SszrqXh52L752L7x0zXW53ne6pludUw3OyUeOiUpyohSM +F9rHcm2jmdbRNMu7ZMvbBPNIrGk4yjQUYRwIM/bfN/WGmF7cM3fds3Tetbbd +tTeFgPow8CgSVMaC0iRQlAryMkFWDtUA8LCYUpXjKiinMqoaRPzLcB3yqjxE +Ro0YpezBRafg/LNwzvdw5iWKV2IwEnMLDbuH3nmAXo/gXIzhnI7nHk3ifpHO ++7SA/1m54M+PBJ83Cr9oFX7VIfq6EzvyFDv2THyiS3K6W3KuW3qxW3q1Bw/u +lt3uloV0y8O7FTHdyoQeZfpLVUGfuvy1pnZI2/JG1/lO1zOu75s0DM8YR2dN +Uwvm2SXz0oplbd26tWmlbdv2aHb2rh3eAxwmwWcTIogUw6QUdcg4DgXPqRI4 +NSKnTuz6wMso+8DLbdFaAmpzQGUKKA0BhT4g0wVwTUCqCkiUAbE8gOHUDrAA +o/bteTw/B/WhsA9m+6A9H5vuZW5599a9u8te2rxne8azNeHZeOteG3Kv9LmX +nrsWn7oWOpzzLY75emKuBsxW2GdLbO/zrTPZ5pl003SKcSrRMBmrn4jSj4fr +xu7r3oVoR+7qhu/oBm7p+24ZXtw0Prtlbr9lbbxjr7tvr460l8eBomSQl07V +oaTlg+RiEF8GYitAVBWIqAGUwvwzrH+cNw6RnYDKv4VLj1MuWMFpOPccnHkR +Tr1K8Yq6hYSGoDfD0MtRnNOxnCOJ3M+yeJ+U8v9Yy/9Ti+CzTuGfu0WfvxB9 +0Yv9rR/7+2vx0UHJt4OSU0PS74bwC0P41SFZ8JD89qA8ZFARPqiMGVQmDqhS +B9RZA5r8IapVpv6drm1c/2zS8HLGODBnGlkwTSyZZ1YtC+vWlU3rxrZth2Zn +7NpZewBiAXSf4EGkECExjkPKdch4ToXAqRI6NZhLK3HpKV5uk+KQl8YcUJsC +KkNAqQ8otAG5JiBTBXBlQCoPSHA/JvGLML9QQCktPNTHhXwoy4cwfBDNt7/l +Za1595a8jDkPfdqzM+bZGqHaPzZ6Xes9zrWnjtUOcrUZrNTbl6tty+XWpSLz +Up5pMdO4kKpfSNLNx2nnozRz4erZUNXMXdX0beXkTeX4DdW7YNWb6+qB69pX +1/Vdwcb2H60Nt+019+0V0fbiRJCXBjKzQUo+SCymChyiKkFE9U+wbJTF3GCN +pHJ4nj/MB2oUMugDsqKTcP4ZOPs8nHYZTrxO8QoJQa+Ho+eiOUfjOZ9mc/+9 +kvcfzfw/PBF88kL4p9fCz4ZFf36H/XUM+2pC/PWk5MiU5PiUNGgKPzuFX5iS +XZmSB0/Kb08qQieUERPK2AlV0rg6bVyTPa4tGNeWjuuqxvX1U4aOGUP3nLFv +wTS8bB5dtUyvW+Y2rcs7tnW6bZth32UCJhtA+wQKEzyUFHBIjOeQ8B24wCkX +OZWYSy2meOlwt+GQl1lnOdCaDzTGA7XhQKUPKLUBpSagUAXkygAuD0jxgETi +F4v8mIDyxQSonw9RhiaH4UNoPnjTu7/qZS96mbMexpRnd9RDf+OmDbh2ep07 +PeT2U2KrHWw12zbrrBtVlo1S03qhcT1Hv56uW3uoWYtXr0arVsMUK6Hy5Tuy +pZuyxWB8/gd89go+cxmfvCQbvawYvqzqvartumZsDbbW3rFXhtuL4+25qSAj +GyQXgPgSEF0BwqtBeK09/JBURKM1oolKZKOV+r4B1QR9yH71SajqBFTxAdkx +uDAIzv0OzrgIJ12Do24id0PQq+FoUAznr+ncjyt5H7fxP34u+P0gVc/4hynR +H2exzxawvyyJv1gW/21F8t8r0mMr0pMr+NkV2fll+ZVlefCS4vaiMnRRGbGg +iltQJ89r0ue1OfPawjld2Zy+Zs7QMGdomTM+XjA9Xza/XjW/XbdMbFlnd2yL +dNsaw77FtNPZgAkR+zCBoCSXSwp4DpHAIRE6cZFTLnYpJS611KXF3TqZ2yB3 +GxUek95yoDMfaI0HWsOBRh+g/kqmCShVAYUiIJcHZHgAl/ilIr9E4Me4fhHq +F0I+PsvHY/i4Oz50w4useqEF7/57D3vKzRpzMUecewOOvV6S0UPsPrXvttvo +TRZ6rZlWaaSVGGj5up0szU6qeidRuR2j2A6XbYfgW7clW8HizR+wjUui9Qui +1XOi5e9EC2ex999JJs7hb84rei9pnlw11gfbq0LtxbH2nBR7Wg5IKKJqvsKr +QFitLbzBGt5kCW82UyLzhzRbIpssp6BHp/drT+3XHaY2aL/mxH7VcajsKFQQ +BGV/D6dcgaN/RO7eQy5FoN/EcX5byv1NO/83fYLfjAp+Oyv83Yro9xuiP+xg +f6KL/3NX/DlD8hVD+neG9CgDP7krO0OXnafJr9AUwTvK29vK+1uqyE113Ibm +4YYmY12bu64rXtNXrBkerRka14xta6Yna6buNfOrdcvQlnV0xzpNty0w7CtM ++yYb0CBiDyHYKAlzSQ7fwRc4REKnGHPiYqdc4lJKXSqZWyN36xRuvdJjVHpM +BsuB3nygNx7oDAda/YFGG1BrAipVQKUIKOUBBR6QiwO4yC8V+CVcvxjxY5Bf +yKQaIfg7Pu6Gj7PiRRc9yKwbmXLBY05oxAENkPu9gN1jZz+xstosrEYT85GR +WaFnFmmZuWqqfzhZsRcr24uQ7oVI9m5hjGtCxmUB43v+7hkePYhL+5azfYyz +cYy7cpy38K1wKkg8clb28oKm9aq56g7VG5mVak/OBTElIKwSPKi1hTVaqJab +VlN4GxVKP2+l9NifBNgz7MbT7KbT7MZT7IYgdt0Jds3x/fJvoPxTUMYFOD4Y +vncPuRCBfpXF+XUz76PX/I+mBR+tCX9FF/2aLfodgv2ei33CE3/Kl/yFL/mS +L/2ahx/l4ic4sjOo/DysuAIpbuwr77BV95nqqD1N/J4mhaHN3NXl0/UldEMl +3VBLMzbTTO0001Oa+TnN0kuzDtKsI3TbBMM2y7QvscE6BHYQgsEhWFwS5js4 +Agdf5BBiTrHYKZW6ZLhLIXOr5G6Nwq1TevQqj1HtMRktBwbTgcF4oDcc6PQH +Wm1AqwloVAG1IqCSBZTSgEIckIv8MoEf5/qliF+878eYPtGuT7jtE2x4+ase +/qKbN+viTju5Yw7OCIkOArTXjvRYkScWpM0ENxrgGj1cpoUK1VC2EkqRQ/E4 +FCmBQjDophC6xoMuo9D38P4Z9n4Qk318j3WEwfyaajOmf8He+hJZ/po7c0w0 +fFr+9KK++kd7YbQ9Ld0eWwgeVID7dRaqoq3dQBXddFKh9PPHxp+M5jOU/dp8 +lmpvaDvDav+Q06zWIFbTCVbdMXbFESjvDPTwKvzgDsXr03Luv/Xyfjkn+AVd +8AtU+Euh4Fdi/scS3ic47zOc/zku+FIm/FqGHcElx3H8pFR2RiI/jymuCpU3 +BKq7PPUDrjoa1SQg2lRYlw3pC/b1ZfuGaraxnm1qYZkes8xdLMsLlrWfZR1i +2d6ybOMs+zQbLEBgFSG2OASdSzL5JCR0oCIHD3MKJU5M6pLiLpnMpZC7VQq3 +RunWqjx6tceg8Zj+B2Hs0kk= + "], {{0, 144.}, {144., 0}}, {0, 255}, + ColorFunction -> RGBColor], + BoxForm`ImageTag["Byte", ColorSpace -> "RGB", Interleaving -> True], + Selectable -> False], DefaultBaseStyle -> "ImageGraphics", + ImageSizeRaw -> {144., 144.}, PlotRange -> {{0, 144.}, {0, 144.}}]], + EdgeForm[None], GraphicsGroupBox[ + TagBox[{PolygonBox[{{906, 912, 436}, {905, 913, 465}}], + PolygonBox[CompressedData[" +1:eJw1m3fcz9X/xu/P52Q2jMyo7J2ZHcpK9pbsmb3JJlIIWWXviiKjIWnQoOzK +KEmRVUmhoZT6XtfvPH9/XA+vx+u81rmu87nvz/0+b3m7Dmw+IJmSkjI6pKTc +lBKRSsgv5BMSgtfzCHcLgRiv5WUtYOchN7VQgBpphLRCIaGgcLNwi1BMKMpa +OqEwMV67VShOTGpqFKRmbuFOoapQhdjbhBLkZBQyCaWEkkJm4XahjFAaO4tQ +Fl9WIZtwr1CO3MzEliI2K2tlic0ulCfHvTMI9zBDDiGnUFGoIKRnz95rEdbu +ECoRk52cCtT0Wi6hMjHpqFEEjnLBQRVizMVdwn1wkg/eHxDuhzNzV0uoiYbW +qbpQDd3yEVsDDr2P+sJDxOZlrTq1rFNtahZFp3rCg6x5zjrEFKPmQ8TkZ6aa +zFiFudsKD6OZeW8kNIQj89BaaIVm1qGp0ARdrENzoRmcVKFWG3QsQ2xjeK5I +rZb0Ks1aI2pZhxbUrETNNsxQnhotiTFX1r4BnJVlpmbMWBVtHmGP1eCxvdBO +6C70ECYLk+DZWnQUOmCbp074asJ7F6EztWoQ2x6ePUcv4VFyaxLbCQ0eYq2n +UBfdejDLg8T0xFcbLbsJXeldG7sLa3XJ7UZvc9GbGVrB2zBhqPCz8Itwq36w +3JKIvFub/kI/ODN3A4UBaNKYtb4p8Uw0wu5DrHUaRE4LtBkiDKa3tRvODLZ9 +Nkbga8mMQ8lpTo3B1PTnrii81CXXOj5GjXbwPloYhUbmeZwwFtvcj8fXBe4m +ChPQrSOxY6jVAXs0uV2IHY9u5vVJYQoaWasnUuIZ6knMFHzd0MZn63F6d8Oe +yF58Nkeyp15o9xQ9hsLbXGEOOlmXGcLT2OZ9Jr5BcPeMMAvd+hM7Hd36YU8j +dxCxM9G0L2tT6W2d5jHDcHifj28IM3q22fQegu0ZfLaaMqfnKIym1rIOe/be +nxOeRQfrtERYjG3el+KbAG/LhWXoNJbYRdRwrdeF18idQOxSdDGvzwtr0Mw6 +rRZWYU9hbTU6WbuVwgp6P469nLXJ5K6ktrV7gR5z4G2zsAkdrNPLwkvY5n09 +vlnw9oqwAZ2eJnYdukzHXkvuLGLXo9k01l6kt3Xawgzz0O5VfLOZ0bNtpPds +bM8wGo7N7UJyn4XbV4Htz4RP0cE6vSVswzbv2/Etg7d3hLepu5jYN+mxCHsr +ucuI3Y4u5vUD4X14t047hR3Ya1jbiU7W5T3hXXqvwPYMC+jpXm9Q29p9SI9N +8HZQOIAO1ukT4WNs874H3wZ42yfsRaeXiN2NLuuwd5G7gdg9aLaWtY/obZ0O +McMWOP8U30Zm9Gz76b0Rex/a+LPwORpthdujwhHha+Gk8LdwHY3M85fCF/Bu +nr4SjlPDtS6nxN8j28hx7DE4M3enhVP02sbaUWqZ+xPU3IlW3wrfsPYec51g +7QNqfctsbzOLZ9xBjW/Yxy64PSucgTPzdEn4CY3M8wXhPLybpx+E71Pi7xCf +eZ+JBej2CbHn4PkgtS7S62PWzlLL3P9IzUNo9TMz7KfGRWI+YmbP+h2z7WWW +C3Cxg719Ta3P4N41D6PjVeEKPFuL34XfsM3TH/iOw/ufwjU0OUbsr9Q6in2V +3OPE/oEG1uJf4QZzmft/UuIZ+oaYG/hOMLfP1l/0PoH9J7V8Vv6j5hl4TOq7 +SSIReTLX6WWnS0QdzEsq2TclIk/mOY3s1In4Gd7KPg6ji3McGxKxtn223eMC +XDvXNX9Al7SJWPMndLs5EWfw7z7/zvLPwPmsWQd/l3LMd+zBs/uPtx/R2rO7 +pnXzZ+e2RPwOdgWeM8rOkIi2uc+UiL7f0O122ZkT0bYOWRLRdw0es8nOmoi5 +znFsJnq4VwmheCLmOsexrnED3nPLzpWIGlq3O2TnTETbMV6z7y+0zCE7eyL2 +ts+2Z7jOOXCuY/5F2zsTsUc6eCwiFEYTa5NPyIttHfLjS40OBYUCaBaIzcMZ +SWLfTW5qYvOjQYK1u+htnYoyw818Dy6GLy0zerZC9E6LXRAOzWV94SFyb8Vf +DBRnrR6aWacyQmls814WX1Z4u1coh2aZiS3FGciEXZLcrMSWRTPzWkWojGbW +qZJQETsXa5XQzLpUEMrTOzu2Z8hAT/e6h9rWrio9CsNbXaEOOlin+4Ua2Ob9 +AXwF4K2WUBOd8hJbHV3yYFcjtwCxD6DZ3azdR2/r9CAzFIXzevgKMaNnq03v +Qti12HtOuKnAHr3XhkIDoZXQWhgmDEUH69REaIxt3pviKwdvzYVm6FSa2EZw +Zu7aCg+TW47YpuhShbU2zFWJGVphV2atNTp57pZCC3qXx27OWkVyW8KZuWsn +PAJn5qmH0F3oLfQRpgpPoYt16yh0QANr0VnohE41WGtP7erY7Yg1z13IqY0W +3YSu9LZWPZnBtj8rj+Krw4zdyalFja7ULAnHjdDMuf4s9qJGQ9b6sq8m8DxA +6I9t7gfiaw53g4VB6NaE2H7Uaozdl9zmxA5EN2v7mDACjazV8EQ8Q22IGYGv +Jdr4bA2hd0tsz9CAPfRBm0fgdZQwEl7M22RhEjpZl3HCWGzzPh5fF7ibKExA +t47EjkG3Dtijye1C7Hh6t2dtFL2t0xPM0BPep+Drxoye7XF6d8OeSKy1epKc +PvA6LRHP4M6g73xCG6FyiLxbi6eF6djWbQa+AegwE99AtJmFbxC8PoNvMFzP +xjcELebgG4puc/ENQ7d5+Iaj5Xx8I9D+WXxT2NvzwppE/Ex5Xy8KL8CjuV4k +LMS2FovxjUW3JfjGocNSfOPRZhm+keiyQHgOjs31CmE5trVYiW8Suq3CNxnd +VuN7gj2swTeKmRfSYwI9ljPDVLRbyx6X4n9b2I5m1uklYR22dXoZ3wx0Wo9v +JjptwDcLnV7B9ww6bcQ3G5024ZuDTpvxzUWnLfjmodOr+Oaj3Wv4VrP394Wd +7G06s6+FA3OxVXgD27q9iW8Rum3Dtxjd3sK3BI6245utM/5MiNq9Dnfm9h04 +XI5u7+JbgW7v4VuJbjvwrWIPO/E9x8xvUN9789n8gD0+qd5TQuTK/DwVom8z +/EyTPTVEbszRDNlPh1jP+/1Y+EQ4L5xLxFjX2AKfXtsjXCDGudNDnMU1dlPD +uWeFj4RdwhnhO+zdrNk3S7kzQ+TWfNr2TFvh+0NqOPc0vfcK3zPDYeGIcFW4 +IuwT9gs/Cj8IB4SDwk/CRdYOYDvGP6v6cSZ8Nj6npmtdptc+arnnIeFT4Wfh +Er2PCr8ywxzNPlf4RfZnxPrfX8g5SI1LzOTcY8Jv1LD9hfA7PttfCn/gOy58 +JfwpXMM+IfyFz/bXwnV8tk8Kf+Oz/Y3wDz7b3wo38Nk+JfyL7zTc+2LqP2zr +lkhG3xm0TCaj7yzah2T0fcnM19jDOc7NTckYcwFeU8tOlYw8W5e0stMko22t +0iWj7ye4u1l2+mTMdY5jXeMivHrNOZfg/ZZkzDnPuXEvz3AZrTPIvi0Zny2t +Sol/o/tv9SvomjEZY35Gy1uTseZVdMuUjDG/olvmZPT9hm63J6Pvd3jIkoy+ +P9Epu+xsyWhbpxzJ6PsbXe6QnTMZeXSOY7NS03XKCKWTMdc5js2BBuY5r5AH +zazT3cJd2EnW7LuB9rll50rG3vbZvoMzkELundQ2j/nocRs83SOUQEPrVkgo +iG1dCuNLjy5FhSJomIbYApyJ1Nj5yU1PbGF6p2ItH72tQ0lmyIgOpfBZM2tX +XChG71uwi8KhuWwiNCY3M/5SoDRrjdDMOpUX7sU27xXw5YS3SkJFNMtGbLlk +PAdZscuSm5PYCuhiXmsI1eHdOlUT7sPOw1o1NLN2VYTK9M6F7Rlup2dZ9pkX +3u6nRwl4ayDURwfrVFuohW3e6+ArAm8PCnXRqSCxNdGlAPYD5BYhtg6987N2 +P72tU0NmKAnnjfAVQ7uHhHr0LobtGe6EI3NTlT16r03R9BGhnTBKGIkO1qmF +0BzbvLfEVxHeWgut0OleYpvBmefuKHQgtyKxLdGlBmvtmasaMzyCXZ21duhk +7R4W2tC7MnZr9nQfuW3pbe46MUMDeOoj9BbOCueEoN9JyRB1sW5dhS5oYC26 +C93QqRZrnaldE7sTsea5Bzn10OJRoSe9rVVfZrDtz0o/fPWZ0bP1olY9cnug +VTm4bUqudetPjaasDRQGoJF5HiIMxjb3Q/G1hrvhwjB0a0HsIGo1xx5Ibmti +h6KbeR0rjEEjazU6Gc9Qe2LG4GuLNj5bj9HbWo5ghibsYQB76giv4+jRG96m +Ck+hk3V5XJiIbd4n4esBd08Ik9GtK7ET0K0L9nhyexA7id6dWRtHb+s0jRn6 +wvt0fL2Y0bM9SW9rP4UZ+rGvp8npz15n4BsAzzPxDUKLZ4RZ2NZtNr4h6DAH +31C0mYtvGLzOwzccrufjewwtnhOexbZuC/CNQreF+Eaj5SJ8Y9BlMb7p7OMl +YR229/EyvvFwvUxYim0tluObiG4r8D2ODivxTUKbVfjGossSZngCrtcIq9HA +WrwgPI9t3V7ENxXd1uKbxh7W4RvHzEvpMZkeq5lhBlqtZ4+rWNsp7EAz6/SK +sAHbOm3ENxudNuGbg06b8c1Fpy345qHdq/ieRafXhdewrdMb+Bag01Z8C9Hp +TXyL4G0bvnXo9LGwm73NYvb18GCd3ha2Y1und/AtR6d38a1Ap/fwrYSjHfgW +w+tbzLAa7d6Hw+fR6UPhA2zr9BG+F9FpF7617GE3viXMvJ0e/mwNYk8z2at1 ++4Q9r2eve4U9aGRd9gv7sK3LAXyb0eGQcJDcV4jdS03XPp+Mv2c2kXOQGm+y +72PCUTSyLkeEw9hvsnYEja3r58Jn9PZZ+JQZXqfGYWK2se8v6PEhPH0nnEYj +63JC+ArbunyNbwc6fCOcRON3iD0Or29jf0nuDmK/pvd21r6gt3U5wwy70Oos +vg+Y0bOdorfPwrfMsBtOz5HzCTpdgOOX0XAPa3vR4gfhe2zr9iO+/ehwEd8B +tPkJ30F4vYTvEFz/jO8zeL4s/IJt7q/gO4xuV/EdQctf8R1Fl9/w7WHm79nT +MXj7nZgv4fqa8Ac6WKe/hD+xzft1fCfh7R/hb3K/IvYasSdZu06sub5Bzhf0 +/IMZTqObX8L8Lxm/K/k7kn/vdmXNOiZCjDlFjmP/Zc26+buWY/zs3c/c/Ry3 +I3/7+W84f+fPAgfmIrViU4WokXVJJzttiJpYh5tlpw/xe9xNQj4hb4gaO8ex +aULk0Pu4XXbmEGs7xmvucQltbwmx5lV0ySQ7Y4gaW9fbZN8a4pprupZjLnJO +PItnvILOzs0QIo/mPavsLHBkHu4W7gpRM+uQQ3b2EHWxDnfIzsmevLf7hRoh +6ugcx2ZDkxRq3RliL8d4zT3/QdtcIdZM8L03DzP8i1bOzR0iV57Zs5qz65wV +z5KDWfILDzDTZc6593obWqQiJh+amZfCQiE0M89FhSLEWocC5KQhx7EF0cxz +lBFKE5uGtQLUsnbFqJkRXUoJJdHMc5UQirOWmVqlmC09sxSGmwDvedDMPJYT +ysKzeasm3Idm5qWCUB7NzHMloSI18qJddTTLTuy9aHYXtarSKxtr5ahl7SpT +825qVmeG3NRwbhW4ysKsZZgtJ7N4xgxwZG7ugXPzWBNNGwqNhL5CH3QwL3WE +2vBknh8U6sKj+zQRGqNLIWJrseZZmhJTgJha9CyKdvWoWRJdGjFLcbSrLzzE +Wml6NWK2IsxShz2VJLcBvc1jM2aoBnfthXbwbC1aCM3hyFy1ElqyVgHbMef5 +GeVzexO6VaPWI/S6l1rN0Mza+b6nNb19FjowQ1VqOLctGlbFfphZKpHbij01 +RJvecHMPfnN0Pzp2EjrCibnpLnSDY3PdU+iBBtaii9AZ3eoQ2xXNzNsAoT+x +tVnrgibu20t4FE2sTb8Qz1B9ZutNTGNq9iemLjP1YMYa7KEjHDWDy0HCQHg2 +b/7/BKPQxbwMFYbAk7keLgyDi5rsrRMatiR2MLy3o9ZIerVgbRAaWIvHhBH0 +9lxjmKEtNUYS05SZB8JZK2Yaxoz+WZQBzUpQy3sdS82OzDkOXw+0ekKYLGwW +toT4zsnplHjf4PsBP3f3c/pu8DhJeBydumFPRLOu2BNCvKtwDef6Wb/vSnw/ +4ufyvhfozgyTqen7CN9RHONZ/QbZr4T4Tqjf67W9McR3DO2zvSnEd+bsmyf7 +5RDfaff/a+jMTJ5lvPCxsDvE525+NuK7A98heDY/m/Zsvn85xN2B16axD8fM +xrbP9znrQ5zRs/m98RnswbObM8/iGK95Jt9VzSbX92b+3unPvD/r/r0wldr/ +f5exCU2shfc4X/aCEO9ofFfzmuzXQ7xD93sStt8I8U7VvoWyF4V4B+S7oGWy +l4d4x+K7Fq8tDvEOyTG2l4R472Sf7aUh3gPZZ9s1nGufZ3EP1/ZMr4Y4k2fx +ey/utSLEeyD3XCt7XYj3Hr4Led5ahnhv4rsUa7MrxOfa1shn0TVdy2dytew1 +Id7D+J7jKTgzV9ZsVYgxXvNdiGPdw7Wd494fhXjn4hleDHEmz+K7Gs9in23P +tDLEmq7lu6FLsn8K8T01vxu1x1yF+JzGzwZ+kf1ziO/d+N2RfeYqxL87/bfI +/hB9tv1d9qDsAyF+T8pNrGu6lnO85pxTfN89FGKOY6vQyzN5Fvf8NMQYr/ln +yxF/9kK8e/Ud7BnPHuLdpu84P/dZC/Fu3ffPR8lxrO+XvzU3Id6l+v70uLkI +8S7Z98dfheiz7ftj/2zpzGdtHLFfhHgX7ZyT1jrEu1vf4R4Lsad7+f76VIg9 +3cv3s6dD9Nn2/axncQ3neibXdg3nusdzIXLgvY9g796j92YOzobIgffu+9sf +Zf8Q4nvffnf42RBjvOY73iuyL4f4HonfFfhe9oUQ/x+H3/U3l57Rs5lTr50P +8f8BOca1neNY9/DZuRjie6s+Q67tM+Oz4h5e80yexTGudS7E/xfmmu+6V4jf +uf13ld/1uBri76M2rO0I8TudY97Uv9tCfGbs5/hbQ/TZ9r2M194K8ZmiY3yW +/TPSPxt9prdb+xCfofg5mO13Qvwb2j7nOsZrruHefgelMjM41jP/36zC/wCW +KM8U + "]], + PolygonBox[{{988, 987, 910, 440, 441}, {927, 937, 901, 461, 460}, { + 987, 928, 471, 470, 910}, {965, 963, 914, 496, 526}, {937, 986, + 430, 431, 901}, {962, 1009, 376, 406, 911}, {949, 962, 911, 405, + 375}, {963, 950, 525, 495, 914}}]}, + Annotation[#, + "Charting`Private`Tag$56188#1"]& ]]}, {}, {}, {}, {}}, {{ + LineBox[{2, 1, 31, 61, 91, 121, 151, 181, 211, 241, 271, 301, 331, 361, + 391, 421, 977}], + LineBox[{2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 915}], + LineBox[{17, 16, 997}], + LineBox[{17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 60, + 90, 120, 150, 180, 210, 240, 270, 300, 330, 360, 390, 420, 450, 917}], + LineBox[{916, 451, 481, 511, 541, 571, 601, 631, 661, 691, 721, 751, + 781, 811, 841, 871, 872, 873, 874, 875, 876, 877, 878, 879, 880, 881, + 882, 883, 884, 885, 1010}], LineBox[{510, 480, 964}], + LineBox[{510, 540, 570, 600, 630, 660, 690, 720, 750, 780, 810, 840, + 870, 900, 899, 898, 897, 896, 895, 894, 893, 892, 891, 890, 889, 888, + 887, 886, 918}]}, {}, {}, {}}}, + VertexTextureCoordinates->CompressedData[" +1:eJzNmzGoJtUZhi+msd1ACGwXJF1KW1kwuKQQJKkCWkRBQiohXTRlSrddrBSx +2HZPSKEXLNYixQgLwyaXZbKYfxydTMZxWGwslXv93/fwPjN/ZbM2w7P+/8yZ +8/znnO/7zrm/eO2N373+1NnZ2Tc/OTu7vPK/d966/upHd96/kVzMf/jozrXb +b52bb1/9/3vmv17itX/i84355u/XP/3ty/v4fmt++tPnbt199MB89b+vXZgv +v/3uzYe4f2d+8MMNzC9cPe8z86OrDxzw/N780jO/+vbZTz5HewbzJ3++/MQX +aN9ofvbqA/9DeyfzZWuvv/p/tH82X93u9ld4n8X89t3LN/ga/bmaf/jvMbh6 +3b8Ws/yK5Vcsv/n5xiy/+f3WLL9i+RXLb96/M8uvWH7F8pvP783ym+0ZzPKb +7RvN8pvtnczym+2fzfKb77OY5Tf7c72R4/IxuI7Tfa/1mn4L/Bb4LfBb4LfA +b4HfAr8Ffgv8Fvgt8Fvgt8Bvgd8CvwV+C/wW+C3wW+C3wG+B3wK/BX4L/Bb4 +3c67++O0euVVfsXym59rzPKb32/N8iuWX7H85v07s/yK5Vcsv/n83iy/2Z7B +LL/ZvtEsv9neySy/2f7ZLL/5PotZfrM/V7P8nlpH9+fdsvEo5lV+8/ONWX7z +e61ZfsXyK5bfvH9nll+x/IrlN5/fm+U32zOY5TfbN5rlN9s7meU32z+b5Tff +ZzHLb/bnapbfU3HR/jpaNuOSHsW8yq9YfvP7rVl+xfIrlt+8f2eWX7H8iuU3 +n9+b5TfbM5jlN9s3muU32zuZ5TfbP5vlN99nMctv9udqlt9Tce5+XFTXUc67 +HKf0ymvOz439inN+bjA/N5ifG/sV5/zcYH5uMD839ivO+bnB/Nxgfm4wPzeY +nxvMzw3m58Z+xTk/N5ifG8zPDebnBvPzNm/Zj3PLZt3kPMtxSY9iXuVXLL9i ++RXLb96/M8uvWH7F8pvP783ym+0ZzPKb7RvN8pvtnczym+2fzfKb77OY5Tf7 +cTXL76k8dD9vKRhnNS7iOsp5l+OUXnnN9bfF+tti/W3tV5zrb4v1t8X629qv +ONffFutvi/W3xfrbYv1tsf62WH9b+xXn+tti/W2x/rb2m3WEx+BaV9jPQ8sm +rmUcxHWT8yzHJT2KeZVfsfzm/Tuz/IrlVyy/+fzeLL/ZjsEsv9m+0Sy/2d7J +LL/Z/tksv/k+i1l+sz9Xs/yeqhPt1xXKJk9hXMs4iOsm51mOS3oU8yq/ef/O +LL9i+RXLbz6/N8tvtmcwy2+2azTLb7Z3Mstvtn82y2++z2KW3+zP1Sy/ybXu +t18nKpu8k3kK41rGQVw3Oc9yXNKjmFf5FcuvWH7F8pvP783ym+0ZzPKb7RvN +8pvtnMzym+2fzfKb77OY5Tf7czXL76k67n7dr9aJWFdgHsq8hXEu4yKuo5x3 +OU7pldeMnzvEzx3i585+xRk/d/Yrzvi5s19xxs+d/Yozfu7sV5zxc4f4uUP8 +3NmvOOPnbV1+v45bNnUh1hGYdzJPYVzLOIjrJudZjkt6FPMqv2L5zef3ZvnN +9gxm+c32jWb5zfZOZvnN9s9m+c33WMzym/25muX31D7Lfl2+bOp8rAuxjsC8 +k3kK41rGQVw3Oc9yXNKjmFf5zef3ZvnN9gxm+c32jWb5zfZOZvnN9s9m+c33 +Wczym/25muX31L7Z/j5L2dRtWedjXYh1BOadzFMY1zIO4rrJeZbjkh7FvMqv +WH6zPYNZfrN9o1l+s72TWX6z/bNZfvN9FrP8Zn+uZvk9tQ+6v29WsE7Vujzr +uKz7sU7EugLzUOYtjHMZF3Ed5bzLcUqvvGb+29uvOPPf3n7Fmf/29ivO/Le3 +X7H85vss5sx/e+S/PfLf7b72/j5o2eyrsA7Pui3rfKwLsY7AvJN5CuNaxkFc +NznPclzSo5hX+RXLb7ZvNMtvtncyy2+2fzbLb77PYpbf7M/VLL+nzins72sX +xJHn+F3XfRbW5VnHZd2PdSLWFZiHMm9hnMu4iOso512OU3rlNesbg/2Ks74x +2K846xuD/YrlN99nMWd9Y0B9Y0B9Y3vuZP+cQtnse3KfjPsqrMOzbss6H+tC +rCMw72SewriWcRDXTc6zHJf0KOZVfsXym+2dzPKb7Z/N8pvvs5jlN/tzNcvv +qXNE++dOCvK8c6w7dR+U+2bcZ2FdnnVc+WVdiHUE5p3MUxjXMg7iusl5luOS +HrN99Zr1q9F+xVm/Gu1XLL/5Pos561cj6lcj6lfbc2H754jK5lwC97G578l9 +Mu6rsA7Pui3rfKwLsY7AvJN5CuNaxkFcNznPclzSo5hX+RXLb7Z/Nstvvs9i +lt/sz9Usv6fO+e2fCyuow5wjLqznFLivzX1Q7ptxn0V+WbdlnY91IdYRmHcy +T2FcyziI6ybnWY5Lesz21mvWJyf7Fctvvs9izvrkhPrkhPrk9tzm/jm/sjk3 +lHH+vc25hPx8s9n35D4Z91VYh2fdlnU+1oVYR2DeyTyFcS3jIK6bnGc5LulR +zKv8iuU332cxy2/252qW3+R6Dnf/3GY955f153puSMxzJzynwH1t7oPKL/dV +WIdn3ZZ1PtaFWEdg3sk8hXEt4yCum5xnOS7pMdtfr/Kb77OYs/48o/48o/68 +PVe9fw63bM71ZR5+b3NuKD/fbM4l5Pfbzb5nxhkXm32VvH+3qduKWfdjnYh1 +BeahzFsY5zIu4jrKeZfjlF55lV+x/GZ/rmb5Ta7n5PfPVRf8js5RV6nn/Hgu +LPcXFuwv1HMJmec9QNx4gXXoIe5f91lYl2cdl3U/1olYV2AeyryFcS7jIq6j +nHc5TumV19xfWLC/sGB/Yft3D/vn5Mvm3C3PafJcH8+B8dwQz5nwXAL3sbnv +yX0y7quwDs+6Let8rAuxjsC8k3kK41rGQVw3Oc9yXNKjmFf5zb9beQyuf8ey +/3cPBfP8Oeqe9Rwuz23KL8+B8dwQz5nwXAL3sbnvyX0y7quwDs+6Let8rAux +jsC8k3kK41rGQVw3Oc9yXNJj9me9yu+pv0va/zuWgnX7HHXseq6a53DlN597 +H99vUVd7gDz9AnH/Q9y/w7xU90G5b8Z9FtblWcdl3Y91ItYVmIcyb2Gcy7iI +6yjnXY5TeuX1zei/A/rvgP47oP8O6L8D+u+A/jug/w7ov8ONe9F/hx/93L+/ +++Fv2v/8d/P3dHfufvDyz39aPetz/Hfni8d/d754ZOeLR3a+eGTni/H5xux8 +Mb7fmp0vHtn52JGdjx3Z+diRnY/F82ez474jO044steVaO9qfuUv//74i7N/ +ud/Vj+q35GJWv4nVb2L1W36+Mavf8vutWf0m1jwh1u8879+Z9TvN+w1mjfO8 +/2iWl3zeVH9nRy/5/NksL2J5EctL9sdqD//4443nm/fquP3li4fPrt+t85Z/ +H8er6wLxuxvMrgs8Yb9Djecn9Xf321//7P1b331pD0/K72R/vqvz4pM5713g +9/UQ96/jV7/z7wGYXRBW + "]], {}}, + Axes->{False, False}, + AxesLabel->{None, None}, + AxesOrigin->{Automatic, Automatic}, + DisplayFunction->Identity, + Frame->True, + FrameLabel->{{None, None}, {None, None}}, + FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}}, + ImagePadding->All, + Method->{ + "GridLinesInFront" -> True, "ScalingFunctions" -> None, + "TransparentPolygonMesh" -> True, "AxesInFront" -> True}, + PlotRange->{All, All}, + PlotRangeClipping->True, + PlotRangePadding->{{ + Scaled[0.02], + Scaled[0.02]}, { + Scaled[0.02], + Scaled[0.02]}}, + Ticks->{Automatic, Automatic}]], "Output", + CellChangeTimes->{{3.8273952271817093`*^9, 3.827395238989222*^9}, { + 3.827395270301259*^9, 3.827395305430221*^9}, {3.827395394648394*^9, + 3.8273954510449343`*^9}, 3.827395499869747*^9, {3.82739554866005*^9, + 3.827395595065257*^9}, {3.827395808656426*^9, 3.8273958166193438`*^9}, + 3.827395847104451*^9}, + CellLabel-> + "Out[100]=",ExpressionUUID->"7b2363ca-8275-4a47-8245-046941182984"] +}, Open ]], + +Cell[BoxData[ + RowBox[{"Integrate", "[", + RowBox[{"(", "\[Theta]0"}]}]], "Input", + CellChangeTimes->{{3.827393172522952*^9, + 3.8273931892343903`*^9}},ExpressionUUID->"b3967aa8-d9f4-4400-85cf-\ +8bcd1f2ab4e3"], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Integrate", "[", + RowBox[{ + FractionBox["1", + RowBox[{ + SuperscriptBox["\[Theta]", "2"], "+", + SuperscriptBox["\[Theta]p", "2"]}]], ",", "\[Theta]"}], "]"}]], "Input", + CellChangeTimes->{{3.82739288657297*^9, 3.82739290885294*^9}, + 3.827392957254546*^9}, + CellLabel->"In[45]:=",ExpressionUUID->"ac9985f6-5e53-4c73-baf4-717d4796770f"], + +Cell[BoxData[ + FractionBox[ + RowBox[{"ArcTan", "[", + FractionBox["\[Theta]", "\[Theta]p"], "]"}], "\[Theta]p"]], "Output", + CellChangeTimes->{3.827392909052237*^9, 3.827392957670755*^9}, + CellLabel->"Out[45]=",ExpressionUUID->"960cd19f-1194-4599-8d56-09ed0f031dff"] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"2", "/", + RowBox[{"(", + RowBox[{"15", "/", "8"}], ")"}]}]], "Input", + CellChangeTimes->{{3.827394739791679*^9, 3.827394744807044*^9}}, + CellLabel->"In[77]:=",ExpressionUUID->"c1a5584c-2fbd-41f7-a170-624f78802f89"], + +Cell[BoxData[ + FractionBox["16", "15"]], "Output", + CellChangeTimes->{3.827394745198503*^9}, + CellLabel->"Out[77]=",ExpressionUUID->"57731670-f6f1-4925-9ad5-f29c3ddcba40"] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"2", "/", + RowBox[{"(", + RowBox[{"0.326419", " ", "4.78984"}], ")"}]}]], "Input", + CellChangeTimes->{{3.827394759072097*^9, 3.8273947713194017`*^9}}, + CellLabel->"In[78]:=",ExpressionUUID->"42ede6f3-4fa5-430e-b5f0-314429a92794"], + +Cell[BoxData["1.279185592300865`"], "Output", + CellChangeTimes->{3.827394771908967*^9}, + CellLabel->"Out[78]=",ExpressionUUID->"2b9fc3f0-2481-4b4e-8ffd-a6f477d0d541"] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Series", "[", + RowBox[{ + RowBox[{"1", "/", + RowBox[{"(", + RowBox[{ + RowBox[{"(", + RowBox[{"\[Theta]", "-", "\[Theta]c"}], ")"}], " ", + RowBox[{ + RowBox[{"h", "'"}], "[", "\[Theta]", "]"}], + SuperscriptBox[ + RowBox[{"(", + RowBox[{"1", "-", "\[Theta]"}], ")"}], + RowBox[{ + RowBox[{"-", "15"}], "/", "8"}]]}], ")"}]}], ",", + RowBox[{"{", + RowBox[{"\[Theta]", ",", "\[Theta]c", ",", "0"}], "}"}]}], "]"}]], "Input",\ + + CellChangeTimes->{{3.8274831460759163`*^9, 3.8274831854284153`*^9}, { + 3.827483258989862*^9, 3.827483317542597*^9}}, + CellLabel->"In[10]:=",ExpressionUUID->"7e931f21-b59c-42d4-9a08-0efc3abce952"], + +Cell[BoxData[ + InterpretationBox[ + RowBox[{ + FractionBox[ + SuperscriptBox[ + RowBox[{"(", + RowBox[{"1", "-", "\[Theta]c"}], ")"}], + RowBox[{"15", "/", "8"}]], + RowBox[{ + RowBox[{ + SuperscriptBox["h", "\[Prime]", + MultilineFunction->None], "[", "\[Theta]c", "]"}], " ", + RowBox[{"(", + RowBox[{"\[Theta]", "-", "\[Theta]c"}], ")"}]}]], "+", + RowBox[{"(", + RowBox[{ + RowBox[{"-", + FractionBox[ + RowBox[{"15", " ", + SuperscriptBox[ + RowBox[{"(", + RowBox[{"1", "-", "\[Theta]c"}], ")"}], + RowBox[{"7", "/", "8"}]]}], + RowBox[{"8", " ", + RowBox[{ + SuperscriptBox["h", "\[Prime]", + MultilineFunction->None], "[", "\[Theta]c", "]"}]}]]}], "-", + FractionBox[ + RowBox[{ + SuperscriptBox[ + RowBox[{"(", + RowBox[{"1", "-", "\[Theta]c"}], ")"}], + RowBox[{"15", "/", "8"}]], " ", + RowBox[{ + SuperscriptBox["h", "\[Prime]\[Prime]", + MultilineFunction->None], "[", "\[Theta]c", "]"}]}], + SuperscriptBox[ + RowBox[{ + SuperscriptBox["h", "\[Prime]", + MultilineFunction->None], "[", "\[Theta]c", "]"}], "2"]]}], ")"}], + "+", + InterpretationBox[ + SuperscriptBox[ + RowBox[{"O", "[", + RowBox[{"\[Theta]", "-", "\[Theta]c"}], "]"}], "1"], + SeriesData[$CellContext`\[Theta], $CellContext`\[Theta]c, {}, -1, 1, 1], + Editable->False]}], + SeriesData[$CellContext`\[Theta], $CellContext`\[Theta]c, {( + 1 - $CellContext`\[Theta]c)^Rational[15, 8]/Derivative[ + 1][$CellContext`h][$CellContext`\[Theta]c], + Rational[-15, 8] (1 - $CellContext`\[Theta]c)^Rational[7, 8]/Derivative[ + 1][$CellContext`h][$CellContext`\[Theta]c] - ( + 1 - $CellContext`\[Theta]c)^Rational[15, 8] + Derivative[1][$CellContext`h][$CellContext`\[Theta]c]^(-2) + Derivative[2][$CellContext`h][$CellContext`\[Theta]c]}, -1, 1, 1], + Editable->False]], "Output", + CellChangeTimes->{{3.827483172946851*^9, 3.8274831857145033`*^9}, { + 3.827483266203372*^9, 3.8274833178135366`*^9}}, + CellLabel->"Out[10]=",ExpressionUUID->"f42be88b-bc68-4685-9bf0-cd79b3d47ff7"] +}, Open ]] +}, +WindowSize->{957., 529.5}, +WindowMargins->{{Automatic, 1.5}, {Automatic, 16.5}}, +FrontEndVersion->"12.2 for Linux x86 (64-bit) (December 12, 2020)", +StyleDefinitions->"Default.nb", +ExpressionUUID->"c08a3e4e-4726-4b51-96f5-38c9f0dc1f4a" +] +(* End of Notebook Content *) + +(* Internal cache information *) +(*CellTagsOutline +CellTagsIndex->{} +*) +(*CellTagsIndex +CellTagsIndex->{} +*) +(*NotebookFileOutline +Notebook[{ +Cell[CellGroupData[{ +Cell[580, 22, 2208, 59, 59, "Input",ExpressionUUID->"c0a33ae3-38dd-4996-a6db-1046c247f003"], +Cell[2791, 83, 2867, 68, 168, "Output",ExpressionUUID->"fa3177c1-247d-40dc-9f56-c55f92b9bc73"] +}, Open ]], +Cell[5673, 154, 337, 7, 24, "Input",ExpressionUUID->"92b6b8b4-4b9d-4606-b12e-d1503be8044a"], +Cell[CellGroupData[{ +Cell[6035, 165, 4321, 113, 128, "Input",ExpressionUUID->"4b23646d-66a7-4f99-9cd1-77b8bfb048e6"], +Cell[10359, 280, 4083, 95, 168, "Output",ExpressionUUID->"e864482d-d84f-4248-97a9-69e174917c6a"] +}, Open ]], +Cell[14457, 378, 393, 9, 24, "Input",ExpressionUUID->"2a30392f-4cec-4410-b883-5f9d8fbb9b77"], +Cell[CellGroupData[{ +Cell[14875, 391, 6260, 169, 178, "Input",ExpressionUUID->"3cdeb246-19f3-4cd6-9c3a-ace23d2eb4e6"], +Cell[21138, 562, 5069, 116, 168, "Output",ExpressionUUID->"a7d6bf32-3297-4ed9-9cc5-d1836ef7d9ac"] +}, Open ]], +Cell[26222, 681, 443, 10, 24, "Input",ExpressionUUID->"080e0724-5e26-45b1-a939-86c8b13b3107"], +Cell[CellGroupData[{ +Cell[26690, 695, 11753, 327, 394, "Input",ExpressionUUID->"286de95f-e12b-4640-9016-25c81cee6ada"], +Cell[38446, 1024, 13251, 271, 167, "Output",ExpressionUUID->"753f522e-db04-4909-b8f0-e57c0454a0e0"] +}, Open ]], +Cell[51712, 1298, 482, 10, 24, "Input",ExpressionUUID->"121d3bcb-c71c-4ec8-a01e-74607255b0b3"], +Cell[CellGroupData[{ +Cell[52219, 1312, 513, 15, 38, "Input",ExpressionUUID->"1fb1f920-f38c-4eb2-9e28-4bcb008fa2d2"], +Cell[52735, 1329, 153, 3, 25, "Output",ExpressionUUID->"d6edca36-a4cf-4c5f-83b3-574289a56af9"] +}, Open ]], +Cell[CellGroupData[{ +Cell[52925, 1337, 1323, 26, 39, "Input",ExpressionUUID->"3411f987-6e0c-43e6-8774-8bab579534d3"], +Cell[54251, 1365, 967, 19, 44, "Output",ExpressionUUID->"b8cea288-1647-4b56-8f3d-dcdd2b6ae91b"] +}, Open ]], +Cell[55233, 1387, 561, 17, 22, "Input",ExpressionUUID->"2cebc6d0-f18e-4865-b6ef-a0d1f3bf0805"], +Cell[CellGroupData[{ +Cell[55819, 1408, 1292, 36, 41, "Input",ExpressionUUID->"b3488c4d-f657-46fb-9b11-630b0fd6d206"], +Cell[57114, 1446, 204, 3, 25, "Output",ExpressionUUID->"b33dc2d4-cae5-42eb-a0ca-3a6e33f3cb70"] +}, Open ]], +Cell[CellGroupData[{ +Cell[57355, 1454, 398, 10, 24, "Input",ExpressionUUID->"c7dac445-5908-4fa8-8a0b-bb252cb276f4"], +Cell[57756, 1466, 419, 11, 33, "Output",ExpressionUUID->"71c3cdc7-d817-4f4d-af37-5b9bfea1f179"] +}, Open ]], +Cell[CellGroupData[{ +Cell[58212, 1482, 901, 25, 24, "Input",ExpressionUUID->"6f05087c-413e-4fb2-b2c9-e923fdd92c6b"], +Cell[59116, 1509, 5736, 150, 52, "Output",ExpressionUUID->"e72062d6-2b09-4495-8402-b0e6bef938ab"] +}, Open ]], +Cell[CellGroupData[{ +Cell[64889, 1664, 2258, 46, 40, "Input",ExpressionUUID->"45253125-7b71-4e2c-bc30-668e3b338cbd"], +Cell[67150, 1712, 2040, 50, 41, "Output",ExpressionUUID->"b820a378-a24b-40d9-848b-d271118a47ad"] +}, Open ]], +Cell[CellGroupData[{ +Cell[69227, 1767, 1834, 40, 24, "Input",ExpressionUUID->"98be6fd6-d0c5-46ca-a3d5-250ea9c619bd"], +Cell[71064, 1809, 500, 11, 43, "Output",ExpressionUUID->"02273014-23dc-45c5-a3ff-2366921fabd0"] +}, Open ]], +Cell[CellGroupData[{ +Cell[71601, 1825, 275, 6, 25, "Input",ExpressionUUID->"cc5be459-b1a4-4071-bf81-958b4fbe4d9a"], +Cell[71879, 1833, 376, 11, 39, "Output",ExpressionUUID->"03b899db-cf29-4fc4-b21a-0c99949276e1"] +}, Open ]], +Cell[CellGroupData[{ +Cell[72292, 1849, 397, 11, 25, "Input",ExpressionUUID->"72d5b6dd-c9d9-411c-ae47-018d1493f38e"], +Cell[72692, 1862, 510, 11, 18, "Message",ExpressionUUID->"c89d0736-26b9-4e13-a981-096b6f1d6e1a"], +Cell[73205, 1875, 9941, 182, 177, "Output",ExpressionUUID->"61e95316-b804-420e-87f2-f52b4b5bade1"] +}, Open ]], +Cell[CellGroupData[{ +Cell[83183, 2062, 391, 9, 25, "Input",ExpressionUUID->"9437fa66-ad8a-43e9-8a53-854194067640"], +Cell[83577, 2073, 486, 14, 39, "Output",ExpressionUUID->"3f0d8dc4-237c-43ce-9a29-58fc7f4aeb47"] +}, Open ]], +Cell[CellGroupData[{ +Cell[84100, 2092, 1235, 28, 29, "Input",ExpressionUUID->"534a99d1-416f-43e4-94c2-fadc4c9725c0"], +Cell[85338, 2122, 120863, 1990, 187, "Output",ExpressionUUID->"841b2917-c78b-4172-8955-8980d32fc3ec"] +}, Open ]], +Cell[CellGroupData[{ +Cell[206238, 4117, 472, 11, 22, "Input",ExpressionUUID->"9c8e9828-9a2f-4f15-b149-d240b7e77eeb"], +Cell[206713, 4130, 339, 7, 25, "Output",ExpressionUUID->"4629de9f-997d-434a-b579-502d66aa00a1"] +}, Open ]], +Cell[CellGroupData[{ +Cell[207089, 4142, 1469, 34, 24, "Input",ExpressionUUID->"e9b86a63-3e78-4de0-8cfe-6232fd09eb3b"], +Cell[208561, 4178, 11260, 208, 179, "Output",ExpressionUUID->"5cd5b531-c23a-42bb-bea0-db89ec6f1525"] +}, Open ]], +Cell[CellGroupData[{ +Cell[219858, 4391, 569, 12, 24, "Input",ExpressionUUID->"110a6801-f97d-466b-81da-59937fec81c7"], +Cell[220430, 4405, 78633, 1306, 275, "Output",ExpressionUUID->"df9e29c5-0d24-4bbb-91d1-382b57cb444b"] +}, Open ]], +Cell[CellGroupData[{ +Cell[299100, 5716, 798, 23, 37, "Input",ExpressionUUID->"5707a3d0-1ca0-4632-af53-b2e5ab76b965"], +Cell[299901, 5741, 512, 11, 18, "Message",ExpressionUUID->"1a833013-cc34-42af-abf5-a8dfaa80161d"], +Cell[300416, 5754, 8517, 158, 175, "Output",ExpressionUUID->"c3a406bf-e1bf-4a93-9a41-58b5a6908c17"] +}, Open ]], +Cell[CellGroupData[{ +Cell[308970, 5917, 1667, 45, 41, "Input",ExpressionUUID->"1c60fc4d-168d-40ec-9dc9-800241fe6f2d"], +Cell[310640, 5964, 12312, 224, 179, "Output",ExpressionUUID->"8056aa05-0321-45e5-8da2-df8f351d8564"] +}, Open ]], +Cell[CellGroupData[{ +Cell[322989, 6193, 1561, 42, 41, "Input",ExpressionUUID->"bbfb8326-a554-4830-88ec-6a7a9e5c9f47"], +Cell[324553, 6237, 9075, 169, 187, "Output",ExpressionUUID->"8c65a08e-3559-435a-a819-b2b78b9896c9"] +}, Open ]], +Cell[CellGroupData[{ +Cell[333665, 6411, 774, 21, 24, "Input",ExpressionUUID->"5b7a21c5-3f4a-4014-ac1d-c9e8a64be69d"], +Cell[334442, 6434, 11964, 217, 179, "Output",ExpressionUUID->"4b349b45-a209-4f2c-95d2-cc1f086f08a1"] +}, Open ]], +Cell[CellGroupData[{ +Cell[346443, 6656, 1706, 48, 24, "Input",ExpressionUUID->"a965ddd5-a893-4434-9238-c098b3e4986c"], +Cell[348152, 6706, 188, 2, 25, "Output",ExpressionUUID->"b149c712-91a6-4ee7-8d16-92cad228d46d"] +}, Open ]], +Cell[CellGroupData[{ +Cell[348377, 6713, 426, 10, 22, "Input",ExpressionUUID->"87d802ec-af41-45fc-bdcb-d506ef1418cf"], +Cell[348806, 6725, 569, 16, 39, "Output",ExpressionUUID->"3e6bf624-2d34-47d3-a821-004cfbb725e6"] +}, Open ]], +Cell[CellGroupData[{ +Cell[349412, 6746, 772, 23, 38, "Input",ExpressionUUID->"b6e097f9-9f11-4738-9df9-1bb1c5732eff"], +Cell[350187, 6771, 523, 16, 51, "Output",ExpressionUUID->"a5d9b280-e936-4513-a7bf-6c1d1444f0ed"] +}, Open ]], +Cell[CellGroupData[{ +Cell[350747, 6792, 425, 11, 24, "Input",ExpressionUUID->"41965605-2b79-48db-a227-2111a1e5bd93"], +Cell[351175, 6805, 1483, 45, 44, "Output",ExpressionUUID->"42c191f3-52e7-443a-b3d1-6dd6c714a8cb"] +}, Open ]], +Cell[CellGroupData[{ +Cell[352695, 6855, 926, 23, 24, "Input",ExpressionUUID->"92c22ee6-96dc-4a23-9b99-2945672a4526"], +Cell[353624, 6880, 19799, 344, 182, "Output",ExpressionUUID->"8c4b66cb-8732-4825-b27e-681a4d43fbfb"] +}, Open ]], +Cell[CellGroupData[{ +Cell[373460, 7229, 828, 24, 40, "Input",ExpressionUUID->"5073e95c-759c-4f6b-bccc-e97ba8930d41"], +Cell[374291, 7255, 1390, 41, 46, "Output",ExpressionUUID->"9f4fcd66-9d81-45fd-8f5c-1c2cd6ec6392"] +}, Open ]], +Cell[CellGroupData[{ +Cell[375718, 7301, 1129, 32, 40, "Input",ExpressionUUID->"b6d6ce4a-b418-42c4-a061-c998db199010"], +Cell[376850, 7335, 8562, 163, 178, "Output",ExpressionUUID->"347ea2ac-e790-455e-97dd-2b0a927b9cd9"] +}, Open ]], +Cell[CellGroupData[{ +Cell[385449, 7503, 522, 16, 38, "Input",ExpressionUUID->"0f797cd1-c8f0-4dac-9564-88a85f1a227a"], +Cell[385974, 7521, 17337, 307, 179, "Output",ExpressionUUID->"e550adac-e0a6-4efd-b952-1d1016d97b7f"] +}, Open ]], +Cell[CellGroupData[{ +Cell[403348, 7833, 953, 26, 44, "Input",ExpressionUUID->"d9105b21-3e64-4aac-abae-2d82f616b07a"], +Cell[404304, 7861, 521, 14, 45, "Output",ExpressionUUID->"574c6df6-7af8-4004-ad57-60b1a3aeebc3"] +}, Open ]], +Cell[CellGroupData[{ +Cell[404862, 7880, 1308, 33, 41, "Input",ExpressionUUID->"f94b376c-aafb-420f-a0ba-4122dfe2f2a4"], +Cell[406173, 7915, 173, 2, 25, "Output",ExpressionUUID->"452e7106-44ad-423b-b013-47704d5fa045"] +}, Open ]], +Cell[406361, 7920, 860, 24, 40, "Input",ExpressionUUID->"69c24b28-334f-4371-a917-fb68280ac4c6"], +Cell[CellGroupData[{ +Cell[407246, 7948, 1077, 28, 42, "Input",ExpressionUUID->"47275aa3-a518-40c0-8636-2a1702e8b8a8"], +Cell[408326, 7978, 1093, 28, 54, "Output",ExpressionUUID->"4d62362a-0bd4-4ef2-b97a-6130a8ecb486"] +}, Open ]], +Cell[CellGroupData[{ +Cell[409456, 8011, 447, 13, 24, "Input",ExpressionUUID->"d1af5436-7da6-4fe1-ade5-4cbb449a5163"], +Cell[409906, 8026, 4875, 99, 179, "Output",ExpressionUUID->"f14d8dda-8aef-46f4-9268-1e49eb0a6ab8"] +}, Open ]], +Cell[414796, 8128, 151, 3, 22, "Input",ExpressionUUID->"2a89c62c-d8e8-4906-9a9f-eb121a3679d1"], +Cell[CellGroupData[{ +Cell[414972, 8135, 537, 14, 24, "Input",ExpressionUUID->"46cab2db-f51c-4f1d-9971-16ff4eabde9a"], +Cell[415512, 8151, 1646, 45, 171, "Output",ExpressionUUID->"745b57d7-b217-49b8-8db2-7ef71fa6ac32"] +}, Open ]], +Cell[CellGroupData[{ +Cell[417195, 8201, 1217, 33, 24, "Input",ExpressionUUID->"d97b0acd-9ab2-4bfa-a926-8144e113e7af"], +Cell[418415, 8236, 190, 2, 25, "Output",ExpressionUUID->"b9b7a5df-f22f-4613-aa7a-d1a79e12ed16"] +}, Open ]], +Cell[CellGroupData[{ +Cell[418642, 8243, 1658, 45, 41, "Input",ExpressionUUID->"b322468a-712f-49de-b702-6be478a69ce7"], +Cell[420303, 8290, 91631, 1519, 275, "Output",ExpressionUUID->"7b2363ca-8275-4a47-8245-046941182984"] +}, Open ]], +Cell[511949, 9812, 211, 5, 22, "Input",ExpressionUUID->"b3967aa8-d9f4-4400-85cf-8bcd1f2ab4e3"], +Cell[CellGroupData[{ +Cell[512185, 9821, 377, 9, 39, "Input",ExpressionUUID->"ac9985f6-5e53-4c73-baf4-717d4796770f"], +Cell[512565, 9832, 269, 5, 50, "Output",ExpressionUUID->"960cd19f-1194-4599-8d56-09ed0f031dff"] +}, Open ]], +Cell[CellGroupData[{ +Cell[512871, 9842, 242, 5, 22, "Input",ExpressionUUID->"c1a5584c-2fbd-41f7-a170-624f78802f89"], +Cell[513116, 9849, 171, 3, 39, "Output",ExpressionUUID->"57731670-f6f1-4925-9ad5-f29c3ddcba40"] +}, Open ]], +Cell[CellGroupData[{ +Cell[513324, 9857, 256, 5, 22, "Input",ExpressionUUID->"42ede6f3-4fa5-430e-b5f0-314429a92794"], +Cell[513583, 9864, 166, 2, 25, "Output",ExpressionUUID->"2b9fc3f0-2481-4b4e-8ffd-a6f477d0d541"] +}, Open ]], +Cell[CellGroupData[{ +Cell[513786, 9871, 713, 20, 24, "Input",ExpressionUUID->"7e931f21-b59c-42d4-9a08-0efc3abce952"], +Cell[514502, 9893, 2180, 58, 43, "Output",ExpressionUUID->"f42be88b-bc68-4685-9bf0-cd79b3d47ff7"] +}, Open ]] +} +] +*) + diff --git a/ising_scaling.bib b/ising_scaling.bib index 9f4f14d..3ba248f 100644 --- a/ising_scaling.bib +++ b/ising_scaling.bib @@ -1,7 +1,21 @@ +@article{An_2016_Functional, + author = {An, X. and Mesterházy, D. and Stephanov, M. A.}, + title = {Functional renormalization group approach to the {Yang}-{Lee} edge singularity}, + journal = {Journal of High Energy Physics}, + publisher = {Springer Science and Business Media LLC}, + year = {2016}, + month = {7}, + number = {7}, + volume = {2016}, + pages = {041}, + url = {https://doi.org/10.1007%2Fjhep07%282016%29041}, + doi = {10.1007/jhep07(2016)041} +} + @article{Butera_2011_Free, author = {Butera, P. and Pernici, M.}, - title = {Free energy in a magnetic field and the universal scaling equation of state for the three-dimensional Ising model}, - journal = {Phys. Rev. B}, + title = {Free energy in a magnetic field and the universal scaling equation of state for the three-dimensional {Ising} model}, + journal = {Physical Review B}, publisher = {American Physical Society}, year = {2011}, month = {2}, @@ -15,9 +29,9 @@ @article{Campostrini_2000_Critical, author = {Campostrini, Massimo and Pelissetto, Andrea and Rossi, Paolo and Vicari, Ettore}, - title = {Critical equation of state of three-dimensional {$XY$} systems}, + title = {Critical equation of state of three-dimensional $XY$ systems}, journal = {Physical Review B}, - publisher = {American Physical Society ({APS})}, + publisher = {American Physical Society (APS)}, year = {2000}, month = {9}, number = {9}, @@ -27,6 +41,20 @@ doi = {10.1103/physrevb.62.5843} } +@article{Cardy_1985_Conformal, + author = {Cardy, John L.}, + title = {Conformal Invariance and the {Yang}-{Lee} Edge Singularity in Two Dimensions}, + journal = {Physical Review Letters}, + publisher = {American Physical Society (APS)}, + year = {1985}, + month = {4}, + number = {13}, + volume = {54}, + pages = {1354--1356}, + url = {https://doi.org/10.1103%2Fphysrevlett.54.1354}, + doi = {10.1103/physrevlett.54.1354} +} + @article{Caselle_2001_The, author = {Caselle, Michele and Hasenbusch, Martin and Pelissetto, Andrea and Vicari, Ettore}, title = {The critical equation of state of the two-dimensional {Ising} model}, @@ -52,6 +80,48 @@ school = {Cornell University} } +@article{Connelly_2020_Universal, + author = {Connelly, Andrew and Johnson, Gregory and Rennecke, Fabian and Skokov, Vladimir V.}, + title = {Universal Location of the {Yang}-{Lee} Edge Singularity in {$\mathrm O(N)$} Theories}, + journal = {Physical Review Letters}, + publisher = {American Physical Society (APS)}, + year = {2020}, + month = {11}, + number = {19}, + volume = {125}, + pages = {191602}, + url = {https://doi.org/10.1103%2Fphysrevlett.125.191602}, + doi = {10.1103/physrevlett.125.191602} +} + +@article{Enting_1980_An, + author = {Enting, I G and Baxter, R J}, + title = {An investigation of the high-field series expansions for the square lattice {Ising} model}, + journal = {Journal of Physics A: Mathematical and General}, + publisher = {IOP Publishing}, + year = {1980}, + month = {12}, + number = {12}, + volume = {13}, + pages = {3723--3734}, + url = {https://doi.org/10.1088%2F0305-4470%2F13%2F12%2F022}, + doi = {10.1088/0305-4470/13/12/022} +} + +@article{Fisher_1978_Yang-Lee, + author = {Fisher, Michael E.}, + title = {{Yang}-{Lee} Edge Singularity and {$\phi^3$} Field Theory}, + journal = {Physical Review Letters}, + publisher = {American Physical Society (APS)}, + year = {1978}, + month = {6}, + number = {25}, + volume = {40}, + pages = {1610--1613}, + url = {https://doi.org/10.1103%2Fphysrevlett.40.1610}, + doi = {10.1103/physrevlett.40.1610} +} + @article{Fonseca_2003_Ising, author = {Fonseca, P. and Zamolodchikov, A.}, title = {Ising Field Theory in a Magnetic Field: Analytic Properties of the Free Energy}, @@ -65,9 +135,23 @@ doi = {10.1023/a:1022147532606} } +@article{Gliozzi_2014_Critical, + author = {Gliozzi, Ferdinando and Rago, Antonio}, + title = {Critical exponents of the 3d {Ising} and related models from conformal bootstrap}, + journal = {Journal of High Energy Physics}, + publisher = {Springer Science and Business Media LLC}, + year = {2014}, + month = {10}, + number = {10}, + volume = {2014}, + pages = {042}, + url = {https://doi.org/10.1007%2Fjhep10%282014%29042}, + doi = {10.1007/jhep10(2014)042} +} + @article{Guida_1997_3D, author = {Guida, R. and Zinn-Justin, J.}, - title = {{3D} {Ising} model: the scaling equation of state}, + title = {3D {Ising} model: the scaling equation of state}, journal = {Nuclear Physics B}, publisher = {Elsevier BV}, year = {1997}, @@ -81,7 +165,7 @@ @article{Gunther_1980_Goldstone, author = {Günther, N J and Wallace, D J and Nicole, D A}, - title = {{Goldstone} modes in vacuum decay and first-order phase transitions}, + title = {Goldstone modes in vacuum decay and first-order phase transitions}, journal = {Journal of Physics A: Mathematical and General}, publisher = {IOP Publishing}, year = {1980}, @@ -119,9 +203,37 @@ school = {Cornell University} } +@article{Langer_1967_Theory, + author = {Langer, J. S}, + title = {Theory of the condensation point}, + journal = {Annals of Physics}, + publisher = {Elsevier BV}, + year = {1967}, + month = {1}, + number = {1}, + volume = {41}, + pages = {108--157}, + url = {https://doi.org/10.1016%2F0003-4916%2867%2990200-x}, + doi = {10.1016/0003-4916(67)90200-x} +} + +@article{Lee_1952_Statistical, + author = {Lee, T. D. and Yang, C. N.}, + title = {Statistical Theory of Equations of State and Phase Transitions. {II}: Lattice Gas and {Ising} Model}, + journal = {Physical Review}, + publisher = {American Physical Society (APS)}, + year = {1952}, + month = {8}, + number = {3}, + volume = {87}, + pages = {410--419}, + url = {https://doi.org/10.1103%2Fphysrev.87.410}, + doi = {10.1103/physrev.87.410} +} + @article{Mangazeev_2008_Variational, author = {Mangazeev, Vladimir V and Batchelor, Murray T and Bazhanov, Vladimir V and Dudalev, Michael Yu}, - title = {Variational approach to the scaling function of the {2D} {Ising} model in a magnetic field}, + title = {Variational approach to the scaling function of the 2D {Ising} model in a magnetic field}, journal = {Journal of Physics A: Mathematical and Theoretical}, publisher = {IOP Publishing}, year = {2008}, @@ -147,4 +259,32 @@ doi = {10.1103/physreve.81.060103} } +@article{Yang_1952_Statistical, + author = {Yang, C. N. and Lee, T. D.}, + title = {Statistical Theory of Equations of State and Phase Transitions. {I}: Theory of Condensation}, + journal = {Physical Review}, + publisher = {American Physical Society (APS)}, + year = {1952}, + month = {8}, + number = {3}, + volume = {87}, + pages = {404--409}, + url = {https://doi.org/10.1103%2Fphysrev.87.404}, + doi = {10.1103/physrev.87.404} +} + +@article{Zambelli_2017_Lee-Yang, + author = {Zambelli, Luca and Zanusso, Omar}, + title = {{Lee}-{Yang} model from the functional renormalization group}, + journal = {Physical Review D}, + publisher = {American Physical Society (APS)}, + year = {2017}, + month = {4}, + number = {8}, + volume = {95}, + pages = {085001}, + url = {https://doi.org/10.1103%2Fphysrevd.95.085001}, + doi = {10.1103/physrevd.95.085001} +} + diff --git a/ising_scaling.tex b/ising_scaling.tex index 7e94f43..5066ea5 100644 --- a/ising_scaling.tex +++ b/ising_scaling.tex @@ -1,6 +1,6 @@ \documentclass[ aps, - prb, + pre, reprint, longbibliography, floatfix @@ -19,6 +19,7 @@ \usepackage{amsmath} \usepackage{graphicx} \usepackage{xcolor} +\usepackage{tikz-cd} \begin{document} @@ -78,46 +79,71 @@ described above will be applied to the two- and three-dimensional Ising models. \subsection{Universal scaling functions} -Renormalization group analysis of the Ising critical point indicates that the free energy per site $f$ may be written, as a function of the reduced temperature $t=(T-T_c)/T_c$ and external field $h=H/T$, -\begin{equation} -\label{eq:AnalyticSingular} - f(t,h)=g(t,h)+f_s(t,h) -\end{equation} -with $g$ a nonuniversal analytic function that depends entirely on the system -in question and $f_s$ a singular function. The singular part $f_s$ can be said -to be universal in the following sense: for any system that shares the -universality with the Ising model, if the near-identity smooth change of coordinates -$u_t(t, h)$ and $u_h(t,h)$ is made such that the flow equations for the new -coordinates are exactly linearized, e.g., +A renormalization group analysis predicts that certain thermodynamic functions +will be universal in the vicinity of any critical point in the Ising +universality class. Here we will explain precisely what is meant by universal. + +Suppose one controls a temperature-like parameter $T$ and a magnetic field-like +parameter $H$, which in the proximity of a critical point at $T=T_c$ and $H=0$ +have normalized reduced forms $t=(T-T_c)/T_c$ and $h=H/T$. Thermodynamic +functions are derived from the free energy per site $f$, which depends on $t$ +and $h$. Renormalization group analysis can be used calculated the flow of +these parameters under continuous changes of scale, yielding flow equations of +the form +\begin{align} \label{eq:raw.flow} + \frac{dt}{d\ell}=\frac1\nu t+\cdots + && + \frac{dh}{d\ell}=\frac{\beta\delta}\nu h+\cdots + && + \frac{df}{d\ell}=Df+\cdots +\end{align} +where $D$ is the dimension of space and $\nu$, $\beta$, and $\delta$ are +dimensionless constants. The flow equations are truncated here, but in general +all terms allowed by symmetry are present on their righthand side. By making a +near-identity transformation to the coordinates and the free energy of the form +$u_t(t, h)=t+\cdots$, $u_h(t, h)=h+\cdots$, and $u_f(f,t,h)=f+\cdots$, one can +bring the flow equations into an agreed upon simplest normal form \begin{align} \label{eq:flow} \frac{du_t}{d\ell}=\frac1\nu u_t && - \frac{du_h}{d\ell}=\frac{\beta\delta}\nu u_h, + \frac{du_h}{d\ell}=\frac{\beta\delta}\nu u_h + && + \frac{du_f}{d\ell}=Du_f+g(u_t), \end{align} -{\bf [I've been wondering for some time about eqn (1) and the flow equation for $df/d\ell$. If $df/d\ell = D f +$ [arbitrary stuff involving f, t, and s], what arbitrary stuff is allowed in order for eqn~\ref{eq:AnalyticSingular} to hold?] } -then $f_s(u_t, u_h)$ will be the same function, up to constant rescalings of -the free energy and the nonlinear scaling fields $u_t$ and $u_h$. In order to -fix this last degree of freedom {\bf [the two rescalings?]}, we adopt the same convention as used by -\cite{Fonseca_2003_Ising}. The dependence of the nonlinear scaling variables on -the parameters $t$ and $h$ is also system-dependent, and their form can be +which are exact as written. The flow of the parameters is made exactly linear, +while that of the free energy is linearized as nearly as possible. Solving these equations for $u_f$ yields +\begin{equation} + \begin{aligned} + u_f(u_t, u_h) + &=|u_t|^{D\nu}\mathcal F_\pm(u_h|u_t|^{-\beta\delta})+|u_t|^{D\nu}\int_1^{u_t}dx\,\frac{g(x)}{x^{1+D\nu}} \\ + &=|u_h|^{D\nu/\beta\delta}\mathcal F_0(u_t|u_h|^{-1/\beta\delta})+|u_t|^{D\nu}\int_1^{u_t}dx\,\frac{g(x)}{x^{1+D\nu}} \\ + \end{aligned} +\end{equation} +where $\mathcal F_\pm$ and $\mathcal F_0$ are undetermined scaling functions. The scaling functions are universal in the sense that if +another system whose critical point belongs to the same universality class has +its parameters brought to the form \eqref{eq:flow}, one will see the same +functional form (up to constant rescaling of $u_t$ and $u_h$ and choice of +$g$). + +The analyticity of the free energy at finite size implies that the functions +$\mathcal F_\pm$ have power-law expansions of their arguments about zero. This +is not the case at infinity, and in fact $\mathcal +F_0(\eta)=\eta^{2/\beta\delta}\mathcal F_\pm(\eta^{-1/\beta\delta})$ itself has a power-law +expansion about zero, implying that $\mathcal F_\pm(\xi)\sim \xi^{2\beta\delta}$ for large $x$. + +The free energy flow equation of the 3D Ising model can be completely linearised, giving $g(x)=0$. This is not the case for the 2D Ising model, where a term proportional to $u_t^2$ cannot be removed by a smooth change of coordinates. The scale of this term sets the relative size of $u_f$ and $u_t$. +For the constant scale of $u_t$ and $u_h$, we adopt the same convention as used by +\cite{Fonseca_2003_Ising}. This gives $g(u_t)=-\frac1{4\pi}u_t^2$. The dependence of the nonlinear scaling variables on +the parameters $t$ and $h$ is system-dependent, and their form can be found for common model systems (the square- and triangular-lattice Ising models) in the literature \cite{Clement_2019_Respect}. -With the flow equations \eqref{eq:flow} along with that for the free energy, -the form of $f_s$ is highly constrained, further reduced to a universal -\emph{scaling function} of a single variable $u_h|u_t|^{-\beta\delta}$ (or equivalently -$u_tu_h^{-1/\beta\delta}$) with multiplicative power laws in $u_t$ or $u_h$ and -(sometimes) simple additive singular functions of $u_t$ and $u_h$. The special -variables are known as scaling invariants, as they are invariant under the flow -\eqref{eq:flow}. Reasonable assumptions about the analyticity of the scaling -function of a single variable then fixes the principal singularity at the -critical point. + \subsection{Essential singularities and droplets} -Another, more subtle, singularity exists which cannot be captured by the -multiplicative factors or additive terms, residing instead inside the scaling -function itself. The origin can be schematically understood to arise from a + +In the low temperature phase, the free energy as a function of field has an essential singularity at zero field, which becomes a branch cut along the negative-$h$ axis when analytically continued to negative $h$ \cite{Langer_1967_Theory}. The origin can be schematically understood to arise from a singularity that exists in the complex free energy of the metastable phase of the model, suitably continued into the equilibrium phase. When the equilibrium Ising model with positive magnetization is subjected to a small negative @@ -150,6 +176,16 @@ In the context of statistical mechanics, Langer demonstrated that the decay rate \operatorname{Im}f\propto\Gamma\sim e^{-\beta\Delta F_c}=e^{-1/(B|h||t|^{-\beta\delta})^{d-1}} \end{equation} which can be more rigorously related in the context of quantum field theory [ref?]. + +\begin{figure} + \includegraphics{figs/F_lower_singularities.pdf} + \caption{ + Analytic structure of the low-temperature scaling function $\mathcal F_-$ + in the complex $\xi=u_h|u_t|^{-\beta\delta}\propto H$ plane. The circle + depicts the essential singularity at the first order transition, while the + solid line depicts Langer's branch cut. + } \label{fig:lower.singularities} +\end{figure} This is a singular contribution that depends principally on the scaling invariant $ht^{-\beta\delta}\simeq u_h|u_t|^{-\beta\delta}$. It is therefore @@ -162,8 +198,41 @@ $f_s$, and moreover part of the scaling function that composes it. We will there The exponent $b$ depends on dimension and can be found through a more careful accounting of the entropy of long-wavelength fluctuations in the droplet surface \cite{Gunther_1980_Goldstone}. -Kramers--Kronig type dispersion relations can then be used to recover the -singular part of the real scaling function from this asymptotic form. + +\subsection{Yang--Lee edge singularities} + +At finite size, the Ising model free energy is an analytic function of +temperature and field because it is the logarithm of a sum of positive analytic +functions. However, it can and does have singularities in the complex plane due +to zeros of the partition function at complex argument, and in particular at +imaginary values of field, $h$. Yang and Lee showed that in the thermodynamic +limit of the high temperature phase of the model, these zeros form a branch cut +along the imaginary $h$ axis that extends to $\pm i\infty$ starting at the +point $\pm ih_{\mathrm{YL}}$ \cite{Yang_1952_Statistical, Lee_1952_Statistical}. +The singularity of the phase transition occurs because these branch cuts +descend and touch the real axis as $T$ approaches $T_c$, with +$h_{\mathrm{YL}}\propto t^{\beta\delta}$. This implies that the +high-temperature scaling function for the Ising model should have complex +branch cuts beginning at $\pm i\xi_{\mathrm{YL}}$ for a universal constant +$\xi_{\mathrm{YL}}$. + +\begin{figure} + \includegraphics{figs/F_higher_singularities.pdf} + \caption{ + Analytic structure of the high-temperature scaling function $\mathcal F_+$ + in the complex $\xi=u_h|u_t|^{-\beta\delta}\propto H$ plane. The squares + depict the Yang--Lee edge singularities, while the solid lines depict + branch cuts. + } \label{fig:higher.singularities} +\end{figure} + +The Yang--Lee singularities are critical points in their own right, with their own universality class different from that of the Ising model \cite{Fisher_1978_Yang-Lee}. + +\cite{Cardy_1985_Conformal} +\cite{Connelly_2020_Universal} +\cite{An_2016_Functional} +\cite{Zambelli_2017_Lee-Yang} +\cite{Gliozzi_2014_Critical} \subsection{Schofield coordinates} @@ -199,6 +268,120 @@ truncation an upper bound of $n$ by $h^{(n)}$. The convergence of the coefficients as $n$ is increased will be part of our assessment of the success of the convergence of the scaling form. +One can now see the convenience of these coordinates. Both scaling variables depend only on $\theta$, as +\begin{align} + \xi&=u_h|u_t|^{-\beta\delta}=h(\theta)|t(\theta)|^{-\beta\delta} \\ + \eta&=u_t|u_h|^{-1/\beta\delta}=t(\theta)|h(\theta)|^{-1/\beta\delta}. +\end{align} +Moreover, both scaling variables have polynomial expansions in $\theta$ near zero, with +\begin{align} + &\xi= h'(0)|t(0)|^{-\beta\delta}\theta+\cdots && \text{for $\theta\simeq0$}\\ + &\xi=h'(\theta_c)|t(\theta_c)|^{-\beta\delta}(\theta-\theta_c)+\cdots && \text{for $\theta\simeq\theta_c$} + \\ + &\eta=-2(\theta-1)h(1)^{-1/\beta\delta}+\cdots && \text{for $\theta\simeq1$}. +\end{align} +Since the scaling functions $\mathcal F_\pm(\xi)$ and $\mathcal F_0(\eta)$ have +polynomial expansions about small $\xi$ and $\eta$, respectively, this implies +both will have polynomial expansions in $\theta$ at all three places above. + +Therefore, in Schofield coordinates one expects to be able to define a global +scaling function $\mathcal F(\theta)$ which has a polynomial expansion in its +argument for all real $\theta$. For small $\theta$ $\mathcal F(\theta)$ will +resemble $\mathcal F_+$, for $\theta$ near one it will resemble $\mathcal F_0$, +and for $\theta$ near $\theta_c$ it will resemble $\mathcal F_-$. This leads us +to expect that the singularities present in these functions will likewise be +present in $\mathcal F(\theta)$. This is shown in Figure +\ref{fig:schofield.singularities}. Two copies of the Langer branch cut stretch +out from $\pm\theta_c$, where the equilibrium phase ends, and the Yang--Lee +edge singularities are present on the imaginary-$\theta$ line, where they must be since $\mathcal F$ has the same symmetry in $\theta$ as $\mathcal F_+$ has in $\xi$. + +The location of the Yang--Lee edge singularities can be calculated directly from the coordinate transformation \eqref{eq:schofield}. Since $h(\theta)$ is an odd real polynomial for real $\theta$, it is imaginary for imaginary $\theta$. Therefore, one requires that +\begin{equation} + i\xi_{\mathrm{YL}}=\frac{h(i\theta_{\mathrm{YL}})}{(1+\theta_{\mathrm{YL}}^2)^{-\beta\delta}} +\end{equation} +The location $\theta_c$ is not fixed by any principle and will be left a floating parameter. + +\begin{figure} + \includegraphics{figs/F_theta_singularities.pdf} + \caption{ + Analytic structure of the global scaling function $\mathcal F$ in the + complex $\theta$ plane. The circles depict essential singularities of the + first order transitions, the squares the Yang--Lee singularities, and the + solid lines depict branch cuts. + } \label{fig:schofield.singularities} +\end{figure} + +\subsection{Singular free energy} + +As we have seen in the previous sections, the unavoidable singularities in the +scaling functions are readily expressed as singular functions in the imaginary +part of the free energy. + +Our strategy follows. First, we take the known singular expansions of the imaginary parts of the scaling functions $\mathcal F_{\pm}(\xi)$ and produce simplest form accessible under polynomial coordinate changes of $\xi$. Second, we assert that the imaginary part of $\mathcal F(\theta)$ must have this simplest form. Third, we perform a Kramers--Kronig type transformation to establish an explicit form for the real part of $\mathcal F(\theta)$. Finally, we make good on the assertion posited in the second step by fixing the Schofield coordinate transformation to produce the correct coefficients known for the real part of $\mathcal F_{\pm}$. + +This success of this stems from the commutative diagram below. So long as the +application of Schofield coordinates and the dispersion relation can be said to +commute, we may assume we have found correct coordinates for the simplest form +of the imaginary part to be fixed in reality by the real part. +\[ + \begin{tikzcd}[row sep=large, column sep = 9em] + \operatorname{Im}\mathcal F_\pm(\xi) \arrow{r}{\text{Kramers--Kronig in $\xi$}} \arrow[]{d}{\text{Schofield}} & \operatorname{Re}\mathcal F_{\pm}(\xi) \arrow{d}{\text{Schofield}} \\% + \operatorname{Im}\mathcal F(\theta) \arrow{r}{\text{Kramers--Kronig in $\theta$}}& \operatorname{Re}\mathcal F(\theta) +\end{tikzcd} +\] + +\begin{figure} + \includegraphics{figs/contour_path.pdf} + \caption{ + Integration contour over the global scaling function $\mathcal F$ in the + complex $\theta$ plane used to produce the dispersion relation. The + circular arc is taken to infinity, while the circles around the + singularities are taken to zero. + } \label{fig:contour} +\end{figure} + +As $\theta\to\infty$, $\mathcal F(\theta)\sim\theta^{2/\beta\delta}$. In order that the contribution from the arc of the contour vanish, we must have the integrand vanish sufficiently fast at infinity. Since $2/\beta\delta<2$ in all dimensions, we will simply use 2. +\begin{equation} + 0=\oint_{\mathcal C}d\vartheta\,\frac{\mathcal F(\vartheta)}{\vartheta^2(\vartheta-\theta)} +\end{equation} +where $\mathcal C$ is the contour in Figure \ref{fig:contour}. The only +nonvanishing contributions from this contour are along the real line and along +the branch cut in the upper half plane. For the latter contributions, the real +parts of the integration up and down cancel out, while the imaginary part +doubles. This gives +\begin{equation} + \begin{aligned} + 0&=\left[\int_{-\infty}^\infty+\lim_{\epsilon\to0}\left(\int_{i\infty-\epsilon}^{i\theta_{\mathrm{YL}}-\epsilon}+\int^{i\infty+\epsilon}_{i\theta_{\mathrm{YL}}+\epsilon}\right)\right] + d\vartheta\,\frac{\mathcal F(\vartheta)}{\vartheta^2(\vartheta-\theta)} \\ + &=\int_{-\infty}^\infty d\vartheta\,\frac{\mathcal F(\vartheta)}{\vartheta^2(\vartheta-\theta)} + +2i\int_{i\theta_{\mathrm{YL}}}^{i\infty}d\theta'\,\frac{\operatorname{Im}\mathcal F(\vartheta)}{\vartheta^2(\vartheta-\theta)} \\ + &=-i\pi\frac{\mathcal F(\theta)}{\theta^2}+\mathcal P\int_{-\infty}^\infty d\vartheta\,\frac{\mathcal F(\vartheta)}{\vartheta^2(\vartheta-\theta)} + +2i\int_{i\theta_{\mathrm{YL}}}^{i\infty}d\vartheta\,\frac{\operatorname{Im}\mathcal F(\vartheta)}{\vartheta^2(\vartheta-\theta)} + \end{aligned} +\end{equation} +In principle one would need to account for the residue of the pole at zero, but since its order is less than two and $\mathcal F(0)=\mathcal F'(0)=0$, this evaluates to zero. +\begin{equation} + \mathcal F(\theta) + =\frac{\theta^2}{i\pi}\mathcal P\int_{-\infty}^\infty d\vartheta\,\frac{\mathcal F(\vartheta)}{\vartheta^2(\vartheta-\theta)} + +\frac{2\theta^2}\pi\int_{i\theta_{\mathrm{YL}}}^{i\infty}d\vartheta\,\frac{\operatorname{Im}\mathcal F(\theta')}{\vartheta^2(\vartheta-\theta)} +\end{equation} +\begin{equation} + \operatorname{Re}\mathcal F(\theta) + =\frac{\theta^2}{\pi}\mathcal P\int_{-\infty}^\infty d\vartheta\,\frac{\operatorname{Im}\mathcal F(\vartheta)}{\vartheta^2(\vartheta-\theta)} + -\frac{2\theta^2}\pi\int_{\theta_{\mathrm{YL}}}^{\infty}d\vartheta\,\frac{\operatorname{Im}\mathcal F(i\vartheta)}{\vartheta(\vartheta^2+\theta^2)} +\end{equation} +Because the real part of $\mathcal F$ is even, the imaginary part must be odd. Therefore +\begin{equation} + \operatorname{Re}\mathcal F(\theta) + =\frac{\theta^2}{\pi} + \int_{\theta_c}^\infty d\vartheta\,\frac{\operatorname{Im}\mathcal F(\vartheta)}{\vartheta^2}\left(\frac1{\vartheta-\theta}+\frac1{\vartheta+\theta}\right) + -\frac{2\theta^2}\pi\int_{\theta_{\mathrm{YL}}}^{\infty}d\vartheta\,\frac{\operatorname{Im}\mathcal F(i\vartheta)}{\vartheta(\vartheta^2+\theta^2)} +\end{equation} + +Now we must make our assertion of the form of the imaginary part of $\operatorname{Im}\mathcal F(\theta)$. Since both of the limits we are interested in---\eqref{eq:langer.sing} along the real axis and \eqref{eq:yang.lee.sing} along the imaginary axis---have symmetries which make their imaginary contribution vanish in the domain of the other limit, we do not need to construct a sophisticated combination to have the correct asymptotics: a simple sum will do! + + + \section{The 2D Ising model} \subsection{Definition of functions} @@ -269,15 +452,17 @@ the Kramers--Kronig transformation of \eqref{eq:im.f.func.2d}, where $\operatorn \section{The three-dimensional Ising model} +\cite{Butera_2011_Free} + The three-dimensional Ising model is easier in some ways, since its hyperbolic critical point lacks stray logarithms. \begin{equation} \label{eq:free.energy.3d.low} f_s(u_t, u_h) - = |u_t|^{2-\alpha}\mathcal F_{\pm}(u_h|u_t|^{-\beta\delta}) + = |u_t|^{D\nu}\mathcal F_{\pm}(u_h|u_t|^{-\beta\delta}) \end{equation} \begin{equation} \label{eq:free.energy.3d.mid} f_s(u_t, u_h) - = |u_h|^{(2-\alpha)/\beta\delta}\mathcal F_0(u_t|u_h|^{-1/\beta\delta}) + = |u_h|^{D\nu/\beta\delta}\mathcal F_0(u_t|u_h|^{-1/\beta\delta}) \end{equation} \begin{equation} \label{eq:schofield.3d.free.energy} f_s(R, \theta) = R^2\mathcal F(\theta) -- cgit v1.2.3-70-g09d2