diff --git a/.gitattributes b/.gitattributes new file mode 100644 index 0000000..774bc8b --- /dev/null +++ b/.gitattributes @@ -0,0 +1,2 @@ +# Mark Notebook files as binary +*.nb binary diff --git a/README.md b/README.md index 55dbf1e..57e3965 100644 --- a/README.md +++ b/README.md @@ -1,6 +1,6 @@ # Mathematica Class Demonstrations - + A large collection of Mathematica demonstrations written by Adam Rumpf, sorted according to the class that they are most likely to be useful for. See the author's page [here](https://adam-rumpf.github.io/demos/mathematica.html). diff --git a/calc-diffeq-analysis/bifurcation-analysis.nb b/calc-diffeq-analysis/bifurcation-analysis.nb index 0b4cea8..f454402 100644 --- a/calc-diffeq-analysis/bifurcation-analysis.nb +++ b/calc-diffeq-analysis/bifurcation-analysis.nb @@ -1,1960 +1,1960 @@ -(* Content-type: application/vnd.wolfram.mathematica *) - -(*** Wolfram Notebook File ***) -(* http://www.wolfram.com/nb *) - -(* CreatedBy='Mathematica 10.4' *) - -(*CacheID: 234*) -(* Internal cache information: -NotebookFileLineBreakTest -NotebookFileLineBreakTest -NotebookDataPosition[ 158, 7] -NotebookDataLength[ 69409, 1952] -NotebookOptionsPosition[ 66965, 1870] -NotebookOutlinePosition[ 67308, 1885] -CellTagsIndexPosition[ 67265, 1882] -WindowFrame->Normal*) - -(* Beginning of Notebook Content *) -Notebook[{ - -Cell[CellGroupData[{ -Cell["Bifurcation Analysis", "Title", - CellChangeTimes->{{3.776600831050974*^9, 3.7766008318453026`*^9}, { - 3.7771302217782173`*^9, 3.7771302252764606`*^9}}], - -Cell["Adam Rumpf, 2/20/2017", "Text", - CellChangeTimes->{{3.7766008347881403`*^9, 3.776600838290375*^9}, { - 3.7771302419672003`*^9, 3.7771302444085283`*^9}}], - -Cell[CellGroupData[{ - -Cell["Introduction", "Section", - CellChangeTimes->{{3.7766008459498987`*^9, 3.776600848547045*^9}}], - -Cell[TextData[{ - "Below is a sequence of examples of four common types of bifurcation: \ -saddle-node, transcritical, pitchfork, and Hopf. For each example we provide \ -a specific autonomous ODE system which displays that type of bifurcation. In \ -all examples, ", - Cell[BoxData[ - FormBox["x", TraditionalForm]], - FormatType->"TraditionalForm"], - " and ", - Cell[BoxData[ - FormBox["y", TraditionalForm]], - FormatType->"TraditionalForm"], - " represent functions of time ", - Cell[BoxData[ - FormBox["t", TraditionalForm]], - FormatType->"TraditionalForm"], - " while ", - Cell[BoxData[ - FormBox["r", TraditionalForm]], - FormatType->"TraditionalForm"], - " represents the single parameter which will be varied to create the \ -bifurcation." -}], "Text", - CellChangeTimes->{{3.776600856235587*^9, 3.776600860481224*^9}, { - 3.777136540361297*^9, 3.777136541839939*^9}, {3.7771392486350613`*^9, - 3.777139425884313*^9}}], - -Cell[TextData[{ - "As a review, a bifurcation occurs when changing the value of the parameter ", - Cell[BoxData[ - FormBox["r", TraditionalForm]], - FormatType->"TraditionalForm"], - " causes a qualitative change to the equilibria of the system. The specific \ -type of qualitative change determiens the type of bifurcation, but in general \ -it describes a change in the number or the stability of the equilibria. We \ -can attempt to look for bifurcations by solving for the equilibria ", - Cell[BoxData[ - FormBox[ - RowBox[{"(", - RowBox[{ - SuperscriptBox["x", "*"], ",", - SuperscriptBox["y", "*"]}], ")"}], TraditionalForm]], - FormatType->"TraditionalForm"], - " by setting ", - Cell[BoxData[ - FormBox[ - FractionBox[ - RowBox[{"\[DifferentialD]", "x"}], - RowBox[{"\[DifferentialD]", "t"}]], TraditionalForm]], - FormatType->"TraditionalForm"], - " and ", - Cell[BoxData[ - FormBox[ - FractionBox[ - RowBox[{"\[DifferentialD]", "y"}], - RowBox[{"\[DifferentialD]", "t"}]], TraditionalForm]], - FormatType->"TraditionalForm"], - " equal to 0. In general these equilibria will be functions of ", - Cell[BoxData[ - FormBox["r", TraditionalForm]], - FormatType->"TraditionalForm"], - ", and we can look at how the equilibria change as ", - Cell[BoxData[ - FormBox["r", TraditionalForm]], - FormatType->"TraditionalForm"], - " changes. For example, some values of ", - Cell[BoxData[ - FormBox["r", TraditionalForm]], - FormatType->"TraditionalForm"], - " will cause several equilibria to merge into one, or to become imaginary, \ -in which case the number of equilibria depends on ", - Cell[BoxData[ - FormBox["r", TraditionalForm]], - FormatType->"TraditionalForm"], - "." -}], "Text", - CellChangeTimes->{{3.777136538540001*^9, 3.7771366108791237`*^9}, { - 3.7771394295820074`*^9, 3.7771394393980103`*^9}, {3.7771396211951604`*^9, - 3.7771399003029437`*^9}}], - -Cell[TextData[{ - "A bifurcation also occurs when the stability of an equilibrium changes. In \ -order to evaluate the stability of an equilibrium, we examine the eigenvalues \ -of the Jacobian matrix. Given an ODE system ", - Cell[BoxData[ - FormBox[ - RowBox[{ - RowBox[{ - FractionBox[ - RowBox[{"\[DifferentialD]", "x"}], - RowBox[{"\[DifferentialD]", "t"}]], "=", - RowBox[{"f", "(", - RowBox[{"x", ",", "y"}], ")"}]}], ",", - RowBox[{ - FractionBox[ - RowBox[{"\[DifferentialD]", "y"}], - RowBox[{"\[DifferentialD]", "t"}]], "=", - RowBox[{"g", "(", - RowBox[{"x", ",", "y"}], ")"}]}]}], TraditionalForm]], - FormatType->"TraditionalForm"], - ", the Jacobian evaluated at the equilibrium ", - Cell[BoxData[ - FormBox[ - RowBox[{"(", - RowBox[{ - SuperscriptBox["x", "*"], ",", - SuperscriptBox["y", "*"]}], ")"}], TraditionalForm]], - FormatType->"TraditionalForm"], - " is" -}], "Text", - CellChangeTimes->{{3.7771399068080826`*^9, 3.7771399540139265`*^9}, { - 3.7771399910351863`*^9, 3.7771400245503855`*^9}, {3.777140131720338*^9, - 3.777140144319103*^9}}], - -Cell[TextData[Cell[BoxData[ - FormBox[ - RowBox[{ - SuperscriptBox["J", "*"], "=", - SubscriptBox[ - RowBox[{"(", GridBox[{ - { - FractionBox[ - RowBox[{"\[PartialD]", "f"}], - RowBox[{"\[PartialD]", "x"}]], - FractionBox[ - RowBox[{"\[PartialD]", "f"}], - RowBox[{"\[PartialD]", "y"}]]}, - { - FractionBox[ - RowBox[{"\[PartialD]", "g"}], - RowBox[{"\[PartialD]", "x"}]], - FractionBox[ - RowBox[{"\[PartialD]", "g"}], - RowBox[{"\[PartialD]", "y"}]]} - }], ")"}], - RowBox[{ - RowBox[{"(", - RowBox[{"x", ",", "y"}], ")"}], "=", - RowBox[{"(", - RowBox[{ - SuperscriptBox["x", "*"], ",", - SuperscriptBox["y", "*"]}], ")"}]}]]}], TraditionalForm]], - FormatType->"TraditionalForm"]], "Text", - CellChangeTimes->{{3.7771399729132023`*^9, 3.7771399843240213`*^9}, { - 3.77714002741781*^9, 3.777140100754119*^9}, {3.7771401471975985`*^9, - 3.7771401633902807`*^9}, {3.7771427843909597`*^9, 3.7771427935276084`*^9}}], - -Cell[TextData[{ - "If all eigenvalues have negative real parts, then ", - Cell[BoxData[ - FormBox[ - RowBox[{"(", - RowBox[{ - SuperscriptBox["x", "*"], ",", - SuperscriptBox["y", "*"]}], ")"}], TraditionalForm]], - FormatType->"TraditionalForm"], - " is stable. Otherwise it is unstable. Further classifications (like being a \ -saddle point, or orbiting in a particular direction) can also be made. As \ -with the equilibria, themselves, the eigenvalues of the Jacobian are \ -functions of ", - Cell[BoxData[ - FormBox["r", TraditionalForm]], - FormatType->"TraditionalForm"], - ", and the signs of their real parts may depend on ", - Cell[BoxData[ - FormBox["r", TraditionalForm]], - FormatType->"TraditionalForm"], - ", which leads to other types of bifurcation" -}], "Text", - CellChangeTimes->{{3.777140172105179*^9, 3.777140290076988*^9}, { - 3.777140339810768*^9, 3.777140349130089*^9}}], - -Cell[TextData[{ - "Note that, in the case of a one-dimensional ODE system ", - Cell[BoxData[ - FormBox[ - RowBox[{ - FractionBox[ - RowBox[{"\[DifferentialD]", "x"}], - RowBox[{"\[DifferentialD]", "t"}]], "=", - RowBox[{"f", "(", "x", ")"}]}], TraditionalForm]], - FormatType->"TraditionalForm"], - ", the Jacobian ", - Cell[BoxData[ - FormBox[ - SuperscriptBox["J", "*"], TraditionalForm]], - FormatType->"TraditionalForm"], - " reduces to simply the scalar ", - Cell[BoxData[ - FormBox[ - RowBox[{ - FractionBox[ - RowBox[{"\[PartialD]", "f"}], - RowBox[{"\[PartialD]", "x"}]], - SubscriptBox["|", - RowBox[{"x", "=", - SuperscriptBox["x", "*"]}]]}], TraditionalForm]], - FormatType->"TraditionalForm"], - ", in which case we can look directly at the value of ", - Cell[BoxData[ - FormBox[ - FractionBox[ - RowBox[{"\[PartialD]", "f"}], - RowBox[{"\[PartialD]", "x"}]], TraditionalForm]], - FormatType->"TraditionalForm"], - " rather than having to look at eigenvalues." -}], "Text", - CellChangeTimes->{{3.7771402937021027`*^9, 3.777140434198078*^9}}], - -Cell[TextData[{ - "Each section below describes a different type of bifurcation. First an ODE \ -system will be presented, then a bifurcation analysis will be conducted by \ -hand, and finally a Manipulate environment will be defined to show a \ -visualization of the bifurcation in action. In all cases there is a slider to \ -control the value of ", - Cell[BoxData[ - FormBox["r", TraditionalForm]]], - ". Equilibria will be shown in red on the stream plot, either as a line (for \ -the 1D case) or a point (in the 2D case). For the 1D cases, to the right of \ -the stream plot will be a plot of the equilibrium values as a function of ", - Cell[BoxData[ - FormBox["r", TraditionalForm]]], - ". In all cases, solid lines and filled dots correspond to stable \ -equilibria, while dotted lines and hollow dots correspond to unstable \ -equilibria." -}], "Text", - CellChangeTimes->{{3.777140451556507*^9, 3.7771406396788273`*^9}, { - 3.777143704620434*^9, 3.7771437074667997`*^9}}] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["Saddle-Node Bifurcation", "Section", - CellChangeTimes->{{3.7766008885632277`*^9, 3.7766008904796133`*^9}, { - 3.777136401274056*^9, 3.777136416298379*^9}}], - -Cell["\<\ -A saddle-node bifurcation occurs when two equilibria collide and annihilate \ -each other (or, if moving in the other direction, when two equilibria are \ -spontaneously generated out of nothing). Specifically this can occur when \ -changing the parameters causes a pair of equilibria to simultaneously become \ -real or imaginary. The example below concerns the 1D system:\ -\>", "Text", - CellChangeTimes->{{3.777136412348218*^9, 3.777136502673601*^9}, { - 3.777140654593788*^9, 3.77714069874934*^9}}], - -Cell[BoxData[Cell[TextData[Cell[BoxData[ - FormBox[ - RowBox[{ - FractionBox[ - RowBox[{"\[DifferentialD]", "x"}], - RowBox[{"\[DifferentialD]", "t"}]], "=", - RowBox[{ - SuperscriptBox["x", "2"], "-", "r"}]}], TraditionalForm]], - FormatType->"TraditionalForm"]], "DisplayFormula"]], "Text", - CellChangeTimes->{{3.77713651537531*^9, 3.7771365309974613`*^9}, - 3.7771366535696325`*^9, {3.7771370336200256`*^9, 3.7771370357424736`*^9}}], - -Cell[TextData[{ - "Setting ", - Cell[BoxData[ - FormBox[ - RowBox[{ - FractionBox[ - RowBox[{"\[DifferentialD]", "x"}], - RowBox[{"\[DifferentialD]", "t"}]], "=", "0"}], TraditionalForm]], - FormatType->"TraditionalForm"], - " and solving, we find that the equilibria are ", - Cell[BoxData[ - FormBox[ - RowBox[{ - SuperscriptBox["x", "*"], "=", - RowBox[{"\[PlusMinus]", - SqrtBox["r"]}]}], TraditionalForm]], - FormatType->"TraditionalForm"], - ". We can consider different cases depending on the value of ", - Cell[BoxData[ - FormBox["r", TraditionalForm]], - FormatType->"TraditionalForm"], - ":" -}], "Text", - CellChangeTimes->{{3.7771366384229493`*^9, 3.777136834022626*^9}, { - 3.777136865290258*^9, 3.77713686612399*^9}, {3.77713704004583*^9, - 3.77713704004583*^9}}], - -Cell[CellGroupData[{ - -Cell[TextData[{ - "If ", - Cell[BoxData[ - FormBox[ - RowBox[{"r", ">", "0"}], TraditionalForm]], - FormatType->"TraditionalForm"], - ", then ", - Cell[BoxData[ - FormBox[ - SqrtBox["r"], TraditionalForm]], - FormatType->"TraditionalForm"], - " is real, and thus we have two real equilibria." -}], "Item", - CellChangeTimes->{{3.7771368388776255`*^9, 3.777136876907528*^9}, { - 3.777137050530507*^9, 3.77713706427261*^9}}], - -Cell[TextData[{ - "If ", - Cell[BoxData[ - FormBox[ - RowBox[{"r", "<", "0"}], TraditionalForm]], - FormatType->"TraditionalForm"], - ", then ", - Cell[BoxData[ - FormBox[ - SqrtBox["r"], TraditionalForm]], - FormatType->"TraditionalForm"], - " is imaginary, and thus we have no real equilibria." -}], "Item", - CellChangeTimes->{{3.7771368388776255`*^9, 3.7771369074951057`*^9}, { - 3.777137071701436*^9, 3.77713707583746*^9}, {3.7771407238414207`*^9, - 3.7771407246057043`*^9}}], - -Cell[TextData[{ - "If ", - Cell[BoxData[ - FormBox[ - RowBox[{"r", "=", "0"}], TraditionalForm]], - FormatType->"TraditionalForm"], - ", then we have exactly one unique equilibrium of ", - Cell[BoxData[ - FormBox[ - RowBox[{ - SuperscriptBox["x", "*"], "=", "0"}], TraditionalForm]], - FormatType->"TraditionalForm"], - "." -}], "Item", - CellChangeTimes->{{3.7771368388776255`*^9, 3.777136930784681*^9}, { - 3.777140737329257*^9, 3.7771407382486253`*^9}}] -}, Open ]], - -Cell[TextData[{ - "We can conduct stability analysis by evaluating ", - Cell[BoxData[ - FormBox[ - RowBox[{ - RowBox[{ - FractionBox["\[PartialD]", - RowBox[{"\[PartialD]", "x"}]], - RowBox[{"(", - RowBox[{ - SuperscriptBox["x", "2"], "-", "r"}], ")"}]}], "=", - RowBox[{"2", "x"}]}], TraditionalForm]], - FormatType->"TraditionalForm"], - " at ", - Cell[BoxData[ - FormBox[ - RowBox[{"x", "=", - RowBox[{"\[PlusMinus]", - SqrtBox["r"]}]}], TraditionalForm]], - FormatType->"TraditionalForm"], - ". In the case of ", - Cell[BoxData[ - FormBox[ - RowBox[{"r", ">", "0"}], TraditionalForm]], - FormatType->"TraditionalForm"], - ", clearly ", - Cell[BoxData[ - FormBox[ - RowBox[{ - SuperscriptBox["x", "*"], "=", - SqrtBox["r"]}], TraditionalForm]], - FormatType->"TraditionalForm"], - " yields a positive Jacobian while ", - Cell[BoxData[ - FormBox[ - RowBox[{ - SuperscriptBox["x", "*"], "=", - RowBox[{"-", - SqrtBox["r"]}]}], TraditionalForm]], - FormatType->"TraditionalForm"], - " yields a negative one, and so ", - Cell[BoxData[ - FormBox[ - RowBox[{ - SuperscriptBox["x", "*"], "=", - SqrtBox["r"]}], TraditionalForm]], - FormatType->"TraditionalForm"], - " should be unstable while ", - Cell[BoxData[ - FormBox[ - RowBox[{ - SuperscriptBox["x", "*"], "=", - RowBox[{"-", - SqrtBox["r"]}]}], TraditionalForm]], - FormatType->"TraditionalForm"], - " is stable." -}], "Text", - CellChangeTimes->{{3.7771369512069955`*^9, 3.777136989791237*^9}, { - 3.777137243411868*^9, 3.7771372995028796`*^9}, {3.7771373330059586`*^9, - 3.777137413841439*^9}, {3.7771374519786773`*^9, 3.777137512637171*^9}}], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"Manipulate", "[", - RowBox[{ - RowBox[{"TableForm", "[", - RowBox[{"{", - RowBox[{"{", - RowBox[{ - RowBox[{"Show", "[", - RowBox[{ - RowBox[{"StreamPlot", "[", - RowBox[{ - RowBox[{"{", - RowBox[{"1", ",", - RowBox[{ - SuperscriptBox["x", "2"], "-", "r"}]}], "}"}], ",", - RowBox[{"{", - RowBox[{"t", ",", - RowBox[{"-", "2"}], ",", "2"}], "}"}], ",", - RowBox[{"{", - RowBox[{"x", ",", - RowBox[{"-", "2"}], ",", "2"}], "}"}], ",", - RowBox[{ - "PlotLabel", "\[Rule]", "\"\\""}]}], - "]"}], ",", - RowBox[{"If", "[", - RowBox[{ - RowBox[{"r", "\[GreaterEqual]", "0"}], ",", - RowBox[{"Graphics", "[", - RowBox[{"{", - RowBox[{"Red", ",", "Thick", ",", - RowBox[{"Line", "[", - RowBox[{"{", - RowBox[{ - RowBox[{"{", - RowBox[{ - RowBox[{"-", "2"}], ",", - RowBox[{"-", - SqrtBox["r"]}]}], "}"}], ",", - RowBox[{"{", - RowBox[{"2", ",", - RowBox[{"-", - SqrtBox["r"]}]}], "}"}]}], "}"}], "]"}], ",", "Dashed", - ",", - RowBox[{"Line", "[", - RowBox[{"{", - RowBox[{ - RowBox[{"{", - RowBox[{ - RowBox[{"-", "2"}], ",", - SqrtBox["r"]}], "}"}], ",", - RowBox[{"{", - RowBox[{"2", ",", - SqrtBox["r"]}], "}"}]}], "}"}], "]"}]}], "}"}], "]"}], ",", - RowBox[{"Graphics", "[", - RowBox[{"{", "}"}], "]"}]}], "]"}]}], "]"}], ",", - RowBox[{"Show", "[", - RowBox[{ - RowBox[{"Plot", "[", - RowBox[{ - RowBox[{"{", - RowBox[{ - RowBox[{"Piecewise", "[", - RowBox[{ - RowBox[{"{", - RowBox[{"{", - RowBox[{ - RowBox[{"-", - SqrtBox["rr"]}], ",", - RowBox[{"rr", "\[GreaterEqual]", "0"}]}], "}"}], "}"}], ",", - "Nothing"}], "]"}], ",", - RowBox[{"Piecewise", "[", - RowBox[{ - RowBox[{"{", - RowBox[{"{", - RowBox[{ - SqrtBox["rr"], ",", - RowBox[{"rr", "\[GreaterEqual]", "0"}]}], "}"}], "}"}], ",", - "Nothing"}], "]"}]}], "}"}], ",", - RowBox[{"{", - RowBox[{"rr", ",", - RowBox[{"-", "2.001"}], ",", "r"}], "}"}], ",", - RowBox[{"PlotStyle", "\[Rule]", - RowBox[{"{", - RowBox[{ - RowBox[{"Directive", "[", - RowBox[{"Red", ",", "Thick"}], "]"}], ",", - RowBox[{"Directive", "[", - RowBox[{"Red", ",", "Thick", ",", "Dashed"}], "]"}]}], "}"}]}], - ",", - RowBox[{"PlotRange", "\[Rule]", - RowBox[{"{", - RowBox[{ - RowBox[{"{", - RowBox[{ - RowBox[{"-", "2"}], ",", "2"}], "}"}], ",", - RowBox[{"{", - RowBox[{ - RowBox[{"-", "2"}], ",", "2"}], "}"}]}], "}"}]}], ",", - RowBox[{"AspectRatio", "\[Rule]", "1"}], ",", - RowBox[{"Frame", "\[Rule]", "True"}], ",", - RowBox[{"Axes", "\[Rule]", "False"}], ",", - RowBox[{ - "PlotLabel", "\[Rule]", - "\"\\ -\""}]}], "]"}], ",", - RowBox[{"If", "[", - RowBox[{ - RowBox[{"r", "\[GreaterEqual]", "0"}], ",", - RowBox[{"Graphics", "[", - RowBox[{"{", - RowBox[{"Red", ",", - RowBox[{"PointSize", "[", "Large", "]"}], ",", - RowBox[{"Point", "[", - RowBox[{"{", - RowBox[{ - RowBox[{"{", - RowBox[{"r", ",", - SqrtBox["r"]}], "}"}], ",", - RowBox[{"{", - RowBox[{"r", ",", - RowBox[{"-", - SqrtBox["r"]}]}], "}"}]}], "}"}], "]"}], ",", "White", - ",", - RowBox[{"PointSize", "[", "Medium", "]"}], ",", - RowBox[{"Point", "[", - RowBox[{"{", - RowBox[{"r", ",", - SqrtBox["r"]}], "}"}], "]"}]}], "}"}], "]"}], ",", - RowBox[{"Graphics", "[", - RowBox[{"{", "}"}], "]"}]}], "]"}]}], "]"}]}], "}"}], "}"}], - "]"}], ",", - RowBox[{"{", - RowBox[{ - RowBox[{"{", - RowBox[{"r", ",", "1"}], "}"}], ",", - RowBox[{"-", "2"}], ",", "2"}], "}"}]}], "]"}]], "Input", - CellChangeTimes->{{3.77713657768003*^9, 3.7771365828765388`*^9}, { - 3.7771370214122696`*^9, 3.7771370243627615`*^9}, {3.7771371027777557`*^9, - 3.777137152180356*^9}, {3.777137522168996*^9, 3.7771379841682105`*^9}, { - 3.7771380242901864`*^9, 3.7771384015864058`*^9}, {3.7771385034820766`*^9, - 3.7771385543943424`*^9}}], - -Cell[BoxData[ - TagBox[ - StyleBox[ - DynamicModuleBox[{$CellContext`r$$ = 1, Typeset`show$$ = True, - Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", - Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = - "\"untitled\"", Typeset`specs$$ = {{{ - Hold[$CellContext`r$$], 1}, -2, 2}}, Typeset`size$$ = { - 387., {96.5, 102.5}}, Typeset`update$$ = 0, Typeset`initDone$$, - Typeset`skipInitDone$$ = True, $CellContext`r$359$$ = 0}, - DynamicBox[Manipulate`ManipulateBoxes[ - 1, StandardForm, "Variables" :> {$CellContext`r$$ = 1}, - "ControllerVariables" :> { - Hold[$CellContext`r$$, $CellContext`r$359$$, 0]}, - "OtherVariables" :> { - Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, - Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, - Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, - Typeset`skipInitDone$$}, "Body" :> TableForm[{{ - Show[ - - StreamPlot[{ - 1, $CellContext`x^2 - $CellContext`r$$}, {$CellContext`t, -2, - 2}, {$CellContext`x, -2, 2}, PlotLabel -> - "stream plot (x versus t)"], - If[$CellContext`r$$ >= 0, - Graphics[{Red, Thick, - - Line[{{-2, -Sqrt[$CellContext`r$$]}, { - 2, -Sqrt[$CellContext`r$$]}}], Dashed, - Line[{{-2, - Sqrt[$CellContext`r$$]}, {2, - Sqrt[$CellContext`r$$]}}]}], - Graphics[{}]]], - Show[ - Plot[{ - - Piecewise[{{-Sqrt[$CellContext`rr], $CellContext`rr >= 0}}, - Nothing], - Piecewise[{{ - Sqrt[$CellContext`rr], $CellContext`rr >= 0}}, - Nothing]}, {$CellContext`rr, -2.001, $CellContext`r$$}, - PlotStyle -> { - Directive[Red, Thick], - Directive[Red, Thick, Dashed]}, PlotRange -> {{-2, 2}, {-2, 2}}, - AspectRatio -> 1, Frame -> True, Axes -> False, PlotLabel -> - "equilibria (\!\(\*SuperscriptBox[\(x\), \(*\)]\) versus r)"], - If[$CellContext`r$$ >= 0, - Graphics[{Red, - PointSize[Large], - Point[{{$CellContext`r$$, - Sqrt[$CellContext`r$$]}, {$CellContext`r$$, - - Sqrt[$CellContext`r$$]}}], White, - PointSize[Medium], - Point[{$CellContext`r$$, - Sqrt[$CellContext`r$$]}]}], - Graphics[{}]]]}}], - "Specifications" :> {{{$CellContext`r$$, 1}, -2, 2}}, "Options" :> {}, - "DefaultOptions" :> {}], - ImageSizeCache->{438., {144., 150.}}, - SingleEvaluation->True], - Deinitialization:>None, - DynamicModuleValues:>{}, - SynchronousInitialization->True, - UndoTrackedVariables:>{Typeset`show$$, Typeset`bookmarkMode$$}, - UnsavedVariables:>{Typeset`initDone$$}, - UntrackedVariables:>{Typeset`size$$}], "Manipulate", - Deployed->True, - StripOnInput->False], - Manipulate`InterpretManipulate[1]]], "Output", - CellChangeTimes->{{3.7771379244304895`*^9, 3.777137972818993*^9}, { - 3.777138035688207*^9, 3.7771380603054132`*^9}, {3.7771381204860187`*^9, - 3.777138178429568*^9}, {3.777138214210326*^9, 3.7771382557136283`*^9}, { - 3.777138298547415*^9, 3.777138305909398*^9}, 3.777138364876514*^9, - 3.777138402049615*^9, 3.7771385562984977`*^9, 3.7771428359485655`*^9}] -}, Open ]] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["Transcritical Bifurcation", "Section", - CellChangeTimes->{{3.7766008885632277`*^9, 3.7766008904796133`*^9}, { - 3.777136401274056*^9, 3.777136416298379*^9}, {3.7771407765357695`*^9, - 3.7771407784342155`*^9}}], - -Cell["\<\ -A transcritical bifurcation occurs when two equilibria \ -\[OpenCurlyDoubleQuote]slide past\[CloseCurlyDoubleQuote] each other and swap \ -stabilities when they collide. The example below concerns the 1D system:\ -\>", "Text", - CellChangeTimes->{{3.777136412348218*^9, 3.777136502673601*^9}, { - 3.777140654593788*^9, 3.77714069874934*^9}, {3.7771407816953983`*^9, - 3.7771408255748434`*^9}, {3.7771416017729793`*^9, 3.7771416437784433`*^9}}], - -Cell[BoxData[Cell[TextData[Cell[BoxData[ - FormBox[ - RowBox[{ - FractionBox[ - RowBox[{"\[DifferentialD]", "x"}], - RowBox[{"\[DifferentialD]", "t"}]], "=", - RowBox[{ - SuperscriptBox["x", "2"], "-", - RowBox[{"r", " ", "x"}]}]}], TraditionalForm]], - FormatType->"TraditionalForm"]], "DisplayFormula"]], "Text", - CellChangeTimes->{{3.77713651537531*^9, 3.7771365309974613`*^9}, - 3.7771366535696325`*^9, {3.7771370336200256`*^9, 3.7771370357424736`*^9}, { - 3.777140833863779*^9, 3.7771408342711344`*^9}}], - -Cell[TextData[{ - "Setting ", - Cell[BoxData[ - FormBox[ - RowBox[{ - FractionBox[ - RowBox[{"\[DifferentialD]", "x"}], - RowBox[{"\[DifferentialD]", "t"}]], "=", "0"}], TraditionalForm]], - FormatType->"TraditionalForm"], - " and solving, we find that the equilibria are ", - Cell[BoxData[ - FormBox[ - RowBox[{ - SuperscriptBox["x", "*"], "=", "0"}], TraditionalForm]], - FormatType->"TraditionalForm"], - " and ", - Cell[BoxData[ - FormBox[ - RowBox[{ - SuperscriptBox["x", "*"], "=", "r"}], TraditionalForm]], - FormatType->"TraditionalForm"], - ". For ", - Cell[BoxData[ - FormBox[ - RowBox[{"r", "\[NotEqual]", "0"}], TraditionalForm]], - FormatType->"TraditionalForm"], - " this is two separate equilibria while for ", - Cell[BoxData[ - FormBox[ - RowBox[{"r", "=", "0"}], TraditionalForm]], - FormatType->"TraditionalForm"], - " the two coincide." -}], "Text", - CellChangeTimes->{{3.7771366384229493`*^9, 3.777136834022626*^9}, { - 3.777136865290258*^9, 3.77713686612399*^9}, {3.77713704004583*^9, - 3.77713704004583*^9}, {3.777140854183094*^9, 3.7771408949826183`*^9}}], - -Cell[TextData[{ - "We can conduct stability analysis by evaluating ", - Cell[BoxData[ - FormBox[ - RowBox[{ - RowBox[{ - FractionBox["\[PartialD]", - RowBox[{"\[PartialD]", "x"}]], - RowBox[{"(", - RowBox[{ - SuperscriptBox["x", "2"], "-", - RowBox[{"r", " ", "x"}]}], ")"}]}], "=", - RowBox[{ - RowBox[{"2", "x"}], "-", "r"}]}], TraditionalForm]], - FormatType->"TraditionalForm"], - " at ", - Cell[BoxData[ - FormBox[ - RowBox[{"x", "=", "0"}], TraditionalForm]], - FormatType->"TraditionalForm"], - " and ", - Cell[BoxData[ - FormBox[ - RowBox[{"x", "=", "r"}], TraditionalForm]], - FormatType->"TraditionalForm"], - ". We will consider the two cases separately:" -}], "Text", - CellChangeTimes->{{3.7771369512069955`*^9, 3.777136989791237*^9}, { - 3.777137243411868*^9, 3.7771372995028796`*^9}, {3.7771373330059586`*^9, - 3.777137413841439*^9}, {3.7771374519786773`*^9, 3.777137512637171*^9}, { - 3.777140903749477*^9, 3.7771409616009216`*^9}}], - -Cell[CellGroupData[{ - -Cell[TextData[{ - "For ", - Cell[BoxData[ - FormBox[ - RowBox[{"x", "=", "0"}], TraditionalForm]], - FormatType->"TraditionalForm"], - " the Jacobian is ", - Cell[BoxData[ - FormBox[ - RowBox[{"-", "r"}], TraditionalForm]], - FormatType->"TraditionalForm"], - ", which is obviously negative (and thus stable) for ", - Cell[BoxData[ - FormBox[ - RowBox[{"r", ">", "0"}], TraditionalForm]], - FormatType->"TraditionalForm"], - " and positive (and thus unstable) for ", - Cell[BoxData[ - FormBox[ - RowBox[{"r", "<", "0"}], TraditionalForm]], - FormatType->"TraditionalForm"], - "." -}], "Item", - CellChangeTimes->{{3.777140974403208*^9, 3.7771410170516787`*^9}}], - -Cell[TextData[{ - "For ", - Cell[BoxData[ - FormBox[ - RowBox[{"x", "=", "r"}], TraditionalForm]], - FormatType->"TraditionalForm"], - " the Jacobian is ", - Cell[BoxData[ - FormBox["r", TraditionalForm]], - FormatType->"TraditionalForm"], - ", which is positive (and thus unstable) for ", - Cell[BoxData[ - FormBox[ - RowBox[{"r", ">", "0"}], TraditionalForm]], - FormatType->"TraditionalForm"], - " and negative (and thus stable) for ", - Cell[BoxData[ - FormBox[ - RowBox[{"r", "<", "0"}], TraditionalForm]], - FormatType->"TraditionalForm"], - "." -}], "Item", - CellChangeTimes->{{3.777140974403208*^9, 3.7771410546510034`*^9}}] -}, Open ]], - -Cell[TextData[{ - "The two equilibria always have opposite stabilities whether ", - Cell[BoxData[ - FormBox[ - RowBox[{"r", "<", "0"}], TraditionalForm]], - FormatType->"TraditionalForm"], - " or ", - Cell[BoxData[ - FormBox[ - RowBox[{"r", ">", "0"}], TraditionalForm]], - FormatType->"TraditionalForm"], - "." -}], "Text", - CellChangeTimes->{{3.7771410673018804`*^9, 3.77714109176895*^9}}], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"Manipulate", "[", - RowBox[{ - RowBox[{"TableForm", "[", - RowBox[{"{", - RowBox[{"{", - RowBox[{ - RowBox[{"Show", "[", - RowBox[{ - RowBox[{"StreamPlot", "[", - RowBox[{ - RowBox[{"{", - RowBox[{"1", ",", - RowBox[{ - SuperscriptBox["x", "2"], "-", - RowBox[{"r", " ", "x"}]}]}], "}"}], ",", - RowBox[{"{", - RowBox[{"t", ",", - RowBox[{"-", "2"}], ",", "2"}], "}"}], ",", - RowBox[{"{", - RowBox[{"x", ",", - RowBox[{"-", "2"}], ",", "2"}], "}"}], ",", - RowBox[{ - "PlotLabel", "\[Rule]", "\"\\""}]}], - "]"}], ",", - RowBox[{"If", "[", - RowBox[{ - RowBox[{"r", "\[GreaterEqual]", "0"}], ",", - RowBox[{"Graphics", "[", - RowBox[{"{", - RowBox[{"Red", ",", "Thick", ",", - RowBox[{"Line", "[", - RowBox[{"{", - RowBox[{ - RowBox[{"{", - RowBox[{ - RowBox[{"-", "2"}], ",", "0"}], "}"}], ",", - RowBox[{"{", - RowBox[{"2", ",", "0"}], "}"}]}], "}"}], "]"}], ",", - "Dashed", ",", - RowBox[{"Line", "[", - RowBox[{"{", - RowBox[{ - RowBox[{"{", - RowBox[{ - RowBox[{"-", "2"}], ",", "r"}], "}"}], ",", - RowBox[{"{", - RowBox[{"2", ",", "r"}], "}"}]}], "}"}], "]"}]}], "}"}], - "]"}], ",", - RowBox[{"Graphics", "[", - RowBox[{"{", - RowBox[{"Red", ",", "Thick", ",", - RowBox[{"Line", "[", - RowBox[{"{", - RowBox[{ - RowBox[{"{", - RowBox[{ - RowBox[{"-", "2"}], ",", "r"}], "}"}], ",", - RowBox[{"{", - RowBox[{"2", ",", "r"}], "}"}]}], "}"}], "]"}], ",", - "Dashed", ",", - RowBox[{"Line", "[", - RowBox[{"{", - RowBox[{ - RowBox[{"{", - RowBox[{ - RowBox[{"-", "2"}], ",", "0"}], "}"}], ",", - RowBox[{"{", - RowBox[{"2", ",", "0"}], "}"}]}], "}"}], "]"}]}], "}"}], - "]"}]}], "]"}]}], "]"}], ",", - RowBox[{"Show", "[", - RowBox[{ - RowBox[{"Plot", "[", - RowBox[{ - RowBox[{"{", - RowBox[{ - RowBox[{"Piecewise", "[", - RowBox[{ - RowBox[{"{", - RowBox[{"{", - RowBox[{"rr", ",", - RowBox[{"rr", "\[GreaterEqual]", "0"}]}], "}"}], "}"}], ",", - "0"}], "]"}], ",", - RowBox[{"Piecewise", "[", - RowBox[{ - RowBox[{"{", - RowBox[{"{", - RowBox[{"0", ",", - RowBox[{"rr", "\[GreaterEqual]", "0"}]}], "}"}], "}"}], ",", - "rr"}], "]"}]}], "}"}], ",", - RowBox[{"{", - RowBox[{"rr", ",", - RowBox[{"-", "2.001"}], ",", "r"}], "}"}], ",", - RowBox[{"PlotStyle", "\[Rule]", - RowBox[{"{", - RowBox[{ - RowBox[{"Directive", "[", - RowBox[{"Red", ",", "Thick", ",", "Dashed"}], "]"}], ",", - RowBox[{"Directive", "[", - RowBox[{"Red", ",", "Thick"}], "]"}]}], "}"}]}], ",", - RowBox[{"PlotRange", "\[Rule]", - RowBox[{"{", - RowBox[{ - RowBox[{"{", - RowBox[{ - RowBox[{"-", "2"}], ",", "2"}], "}"}], ",", - RowBox[{"{", - RowBox[{ - RowBox[{"-", "2"}], ",", "2"}], "}"}]}], "}"}]}], ",", - RowBox[{"AspectRatio", "\[Rule]", "1"}], ",", - RowBox[{"Frame", "\[Rule]", "True"}], ",", - RowBox[{"Axes", "\[Rule]", "False"}], ",", - RowBox[{ - "PlotLabel", "\[Rule]", - "\"\\ -\""}]}], "]"}], ",", - RowBox[{"If", "[", - RowBox[{ - RowBox[{"r", "\[GreaterEqual]", "0"}], ",", - RowBox[{"Graphics", "[", - RowBox[{"{", - RowBox[{"Red", ",", - RowBox[{"PointSize", "[", "Large", "]"}], ",", - RowBox[{"Point", "[", - RowBox[{"{", - RowBox[{ - RowBox[{"{", - RowBox[{"r", ",", "0"}], "}"}], ",", - RowBox[{"{", - RowBox[{"r", ",", "r"}], "}"}]}], "}"}], "]"}], ",", - "White", ",", - RowBox[{"PointSize", "[", "Medium", "]"}], ",", - RowBox[{"Point", "[", - RowBox[{"{", - RowBox[{"r", ",", "r"}], "}"}], "]"}]}], "}"}], "]"}], ",", - RowBox[{"Graphics", "[", - RowBox[{"{", - RowBox[{"Red", ",", - RowBox[{"PointSize", "[", "Large", "]"}], ",", - RowBox[{"Point", "[", - RowBox[{"{", - RowBox[{ - RowBox[{"{", - RowBox[{"r", ",", "0"}], "}"}], ",", - RowBox[{"{", - RowBox[{"r", ",", "r"}], "}"}]}], "}"}], "]"}], ",", - "White", ",", - RowBox[{"PointSize", "[", "Medium", "]"}], ",", - RowBox[{"Point", "[", - RowBox[{"{", - RowBox[{"r", ",", "0"}], "}"}], "]"}]}], "}"}], "]"}]}], - "]"}]}], "]"}]}], "}"}], "}"}], "]"}], ",", - RowBox[{"{", - RowBox[{ - RowBox[{"{", - RowBox[{"r", ",", "1"}], "}"}], ",", - RowBox[{"-", "2"}], ",", "2"}], "}"}]}], "]"}]], "Input", - CellChangeTimes->{{3.77713657768003*^9, 3.7771365828765388`*^9}, { - 3.7771370214122696`*^9, 3.7771370243627615`*^9}, {3.7771371027777557`*^9, - 3.777137152180356*^9}, {3.777137522168996*^9, 3.7771379841682105`*^9}, { - 3.7771380242901864`*^9, 3.7771384015864058`*^9}, {3.7771385034820766`*^9, - 3.7771385543943424`*^9}, {3.7771411102948675`*^9, 3.777141110664283*^9}, { - 3.777141140776102*^9, 3.7771412353779545`*^9}, {3.777141270010955*^9, - 3.777141270194441*^9}, {3.7771413011098766`*^9, 3.7771413385613546`*^9}, { - 3.7771413736412973`*^9, 3.7771414370261106`*^9}}], - -Cell[BoxData[ - TagBox[ - StyleBox[ - DynamicModuleBox[{$CellContext`r$$ = 1, Typeset`show$$ = True, - Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", - Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = - "\"untitled\"", Typeset`specs$$ = {{{ - Hold[$CellContext`r$$], 1}, -2, 2}}, Typeset`size$$ = { - 387., {96.5, 102.5}}, Typeset`update$$ = 0, Typeset`initDone$$, - Typeset`skipInitDone$$ = True, $CellContext`r$1744$$ = 0}, - DynamicBox[Manipulate`ManipulateBoxes[ - 1, StandardForm, "Variables" :> {$CellContext`r$$ = 1}, - "ControllerVariables" :> { - Hold[$CellContext`r$$, $CellContext`r$1744$$, 0]}, - "OtherVariables" :> { - Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, - Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, - Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, - Typeset`skipInitDone$$}, "Body" :> TableForm[{{ - Show[ - - StreamPlot[{ - 1, $CellContext`x^2 - $CellContext`r$$ $CellContext`x}, \ -{$CellContext`t, -2, 2}, {$CellContext`x, -2, 2}, PlotLabel -> - "stream plot (x versus t)"], - If[$CellContext`r$$ >= 0, - Graphics[{Red, Thick, - Line[{{-2, 0}, {2, 0}}], Dashed, - Line[{{-2, $CellContext`r$$}, {2, $CellContext`r$$}}]}], - Graphics[{Red, Thick, - Line[{{-2, $CellContext`r$$}, {2, $CellContext`r$$}}], Dashed, - Line[{{-2, 0}, {2, 0}}]}]]], - Show[ - Plot[{ - Piecewise[{{$CellContext`rr, $CellContext`rr >= 0}}, 0], - - Piecewise[{{ - 0, $CellContext`rr >= - 0}}, $CellContext`rr]}, {$CellContext`rr, -2.001, \ -$CellContext`r$$}, PlotStyle -> { - Directive[Red, Thick, Dashed], - Directive[Red, Thick]}, PlotRange -> {{-2, 2}, {-2, 2}}, - AspectRatio -> 1, Frame -> True, Axes -> False, PlotLabel -> - "equilibria (\!\(\*SuperscriptBox[\(x\), \(*\)]\) versus r)"], - If[$CellContext`r$$ >= 0, - Graphics[{Red, - PointSize[Large], - - Point[{{$CellContext`r$$, - 0}, {$CellContext`r$$, $CellContext`r$$}}], White, - PointSize[Medium], - Point[{$CellContext`r$$, $CellContext`r$$}]}], - Graphics[{Red, - PointSize[Large], - - Point[{{$CellContext`r$$, - 0}, {$CellContext`r$$, $CellContext`r$$}}], White, - PointSize[Medium], - Point[{$CellContext`r$$, 0}]}]]]}}], - "Specifications" :> {{{$CellContext`r$$, 1}, -2, 2}}, "Options" :> {}, - "DefaultOptions" :> {}], - ImageSizeCache->{438., {144., 150.}}, - SingleEvaluation->True], - Deinitialization:>None, - DynamicModuleValues:>{}, - SynchronousInitialization->True, - UndoTrackedVariables:>{Typeset`show$$, Typeset`bookmarkMode$$}, - UnsavedVariables:>{Typeset`initDone$$}, - UntrackedVariables:>{Typeset`size$$}], "Manipulate", - Deployed->True, - StripOnInput->False], - Manipulate`InterpretManipulate[1]]], "Output", - CellChangeTimes->{{3.7771379244304895`*^9, 3.777137972818993*^9}, { - 3.777138035688207*^9, 3.7771380603054132`*^9}, {3.7771381204860187`*^9, - 3.777138178429568*^9}, {3.777138214210326*^9, 3.7771382557136283`*^9}, { - 3.777138298547415*^9, 3.777138305909398*^9}, 3.777138364876514*^9, - 3.777138402049615*^9, 3.7771385562984977`*^9, 3.7771411143651175`*^9, { - 3.777141152356468*^9, 3.7771412366219435`*^9}, {3.7771412827529573`*^9, - 3.777141338939087*^9}, 3.7771413788874207`*^9, {3.777141419528529*^9, - 3.7771414375930433`*^9}, 3.7771428381608877`*^9}] -}, Open ]] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["Pitchfork Bifurcation", "Section", - CellChangeTimes->{{3.7766008885632277`*^9, 3.7766008904796133`*^9}, { - 3.777136401274056*^9, 3.777136416298379*^9}, {3.7771415021019964`*^9, - 3.777141503857136*^9}}], - -Cell["\<\ -A pitchfork bifurcation occurs when a single equilibrium splits into three \ -(or, if moving in the other direction, when three equilibria merge to result \ -in a single equilibrium). This is similar to a saddle-node bifurcation, \ -except that one equilibrium remains real regardless of the other two. The \ -example below concerns the 1D system:\ -\>", "Text", - CellChangeTimes->{{3.777136412348218*^9, 3.777136502673601*^9}, { - 3.777140654593788*^9, 3.77714069874934*^9}, {3.77714150735085*^9, - 3.7771415679562902`*^9}, {3.777141646656042*^9, 3.777141646985199*^9}}], - -Cell[BoxData[Cell[TextData[Cell[BoxData[ - FormBox[ - RowBox[{ - FractionBox[ - RowBox[{"\[DifferentialD]", "x"}], - RowBox[{"\[DifferentialD]", "t"}]], "=", - RowBox[{ - SuperscriptBox["x", "3"], "-", - RowBox[{"r", " ", "x"}]}]}], TraditionalForm]], - FormatType->"TraditionalForm"]], "DisplayFormula"]], "Text", - CellChangeTimes->{{3.77713651537531*^9, 3.7771365309974613`*^9}, - 3.7771366535696325`*^9, {3.7771370336200256`*^9, 3.7771370357424736`*^9}, { - 3.7771415732464447`*^9, 3.7771415756351213`*^9}}], - -Cell[TextData[{ - "Setting ", - Cell[BoxData[ - FormBox[ - RowBox[{ - FractionBox[ - RowBox[{"\[DifferentialD]", "x"}], - RowBox[{"\[DifferentialD]", "t"}]], "=", "0"}], TraditionalForm]], - FormatType->"TraditionalForm"], - " and solving, we find that the equilibria are ", - Cell[BoxData[ - FormBox[ - RowBox[{ - SuperscriptBox["x", "*"], "\[Element]", - RowBox[{"{", - RowBox[{ - RowBox[{"-", - SqrtBox["r"]}], ",", "0", ",", - SqrtBox["r"]}], "}"}]}], TraditionalForm]], - FormatType->"TraditionalForm"], - ". ", - Cell[BoxData[ - FormBox[ - RowBox[{ - SuperscriptBox["x", "*"], "=", "0"}], TraditionalForm]], - FormatType->"TraditionalForm"], - " is constant and does not change as ", - Cell[BoxData[ - FormBox["r", TraditionalForm]], - FormatType->"TraditionalForm"], - " changes, while ", - Cell[BoxData[ - FormBox[ - RowBox[{ - SuperscriptBox["x", "*"], "=", - RowBox[{"\[PlusMinus]", - SqrtBox["r"]}]}], TraditionalForm]], - FormatType->"TraditionalForm"], - " depend on the sign of ", - Cell[BoxData[ - FormBox["r", TraditionalForm]], - FormatType->"TraditionalForm"], - ". Going through the same process as for the saddle-node bifurcation above, \ -we find that ", - Cell[BoxData[ - FormBox[ - RowBox[{"r", ">", "0"}], TraditionalForm]], - FormatType->"TraditionalForm"], - " results in both being real, ", - Cell[BoxData[ - FormBox[ - RowBox[{"r", "<", "0"}], TraditionalForm]], - FormatType->"TraditionalForm"], - " results in both being imaginary, and ", - Cell[BoxData[ - FormBox[ - RowBox[{"r", "=", "0"}], TraditionalForm]], - FormatType->"TraditionalForm"], - " results in both merging and coinciding with ", - Cell[BoxData[ - FormBox[ - RowBox[{ - SuperscriptBox["x", "*"], "=", "0"}], TraditionalForm]], - FormatType->"TraditionalForm"], - "." -}], "Text", - CellChangeTimes->{{3.7771366384229493`*^9, 3.777136834022626*^9}, { - 3.777136865290258*^9, 3.77713686612399*^9}, {3.77713704004583*^9, - 3.77713704004583*^9}, {3.7771416556914363`*^9, 3.777141821658723*^9}}], - -Cell[TextData[{ - "We can conduct stability analysis by evaluating ", - Cell[BoxData[ - FormBox[ - RowBox[{ - RowBox[{ - FractionBox["\[PartialD]", - RowBox[{"\[PartialD]", "x"}]], - RowBox[{"(", - RowBox[{ - SuperscriptBox["x", "3"], "-", - RowBox[{"r", " ", "x"}]}], ")"}]}], "=", - RowBox[{ - RowBox[{"3", - SuperscriptBox["x", "2"]}], "-", "r"}]}], TraditionalForm]], - FormatType->"TraditionalForm"], - " at ", - Cell[BoxData[ - FormBox[ - RowBox[{"x", "=", "0"}], TraditionalForm]], - FormatType->"TraditionalForm"], - " and ", - Cell[BoxData[ - FormBox[ - RowBox[{"x", "=", - RowBox[{"\[PlusMinus]", - SqrtBox["r"]}]}], TraditionalForm]], - FormatType->"TraditionalForm"], - ". If ", - Cell[BoxData[ - FormBox[ - RowBox[{"x", "=", "0"}], TraditionalForm]], - FormatType->"TraditionalForm"], - " then the Jacobian is ", - Cell[BoxData[ - FormBox[ - RowBox[{"-", "r"}], TraditionalForm]], - FormatType->"TraditionalForm"], - ", which always has a sign opposite ", - Cell[BoxData[ - FormBox["r", TraditionalForm]], - FormatType->"TraditionalForm"], - ". If ", - Cell[BoxData[ - FormBox[ - RowBox[{"x", "=", - RowBox[{"\[PlusMinus]", - SqrtBox["r"]}]}], TraditionalForm]], - FormatType->"TraditionalForm"], - " then the Jacobian is ", - Cell[BoxData[ - FormBox[ - RowBox[{"2", "r"}], TraditionalForm]], - FormatType->"TraditionalForm"], - ", which always has a sign the same as ", - Cell[BoxData[ - FormBox["r", TraditionalForm]], - FormatType->"TraditionalForm"], - ". The overall conclusion is that for ", - Cell[BoxData[ - FormBox[ - RowBox[{"r", "<", "0"}], TraditionalForm]], - FormatType->"TraditionalForm"], - " we have a single unstable equilibrium at ", - Cell[BoxData[ - FormBox[ - RowBox[{ - SuperscriptBox["x", "*"], "=", "0"}], TraditionalForm]], - FormatType->"TraditionalForm"], - ", while for ", - Cell[BoxData[ - FormBox[ - RowBox[{"r", ">", "0"}], TraditionalForm]], - FormatType->"TraditionalForm"], - " we have three equilibria: a stable equilibrium at ", - Cell[BoxData[ - FormBox[ - RowBox[{ - SuperscriptBox["x", "*"], "=", "0"}], TraditionalForm]], - FormatType->"TraditionalForm"], - " and two unstable equilibria at ", - Cell[BoxData[ - FormBox[ - RowBox[{ - SuperscriptBox["x", "*"], "=", - RowBox[{"\[PlusMinus]", - SqrtBox["r"]}]}], TraditionalForm]], - FormatType->"TraditionalForm"], - "." -}], "Text", - CellChangeTimes->{{3.7771369512069955`*^9, 3.777136989791237*^9}, { - 3.777137243411868*^9, 3.7771372995028796`*^9}, {3.7771373330059586`*^9, - 3.777137413841439*^9}, {3.7771374519786773`*^9, 3.777137512637171*^9}, { - 3.7771418289521384`*^9, 3.777142054907627*^9}}], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"Manipulate", "[", - RowBox[{ - RowBox[{"TableForm", "[", - RowBox[{"{", - RowBox[{"{", - RowBox[{ - RowBox[{"Show", "[", - RowBox[{ - RowBox[{"StreamPlot", "[", - RowBox[{ - RowBox[{"{", - RowBox[{"1", ",", - RowBox[{ - SuperscriptBox["x", "3"], "-", - RowBox[{"r", " ", "x"}]}]}], "}"}], ",", - RowBox[{"{", - RowBox[{"t", ",", - RowBox[{"-", "2"}], ",", "2"}], "}"}], ",", - RowBox[{"{", - RowBox[{"x", ",", - RowBox[{"-", "2"}], ",", "2"}], "}"}], ",", - RowBox[{ - "PlotLabel", "\[Rule]", "\"\\""}]}], - "]"}], ",", - RowBox[{"If", "[", - RowBox[{ - RowBox[{"r", "\[GreaterEqual]", "0"}], ",", - RowBox[{"Graphics", "[", - RowBox[{"{", - RowBox[{"Red", ",", "Thick", ",", - RowBox[{"Line", "[", - RowBox[{"{", - RowBox[{ - RowBox[{"{", - RowBox[{ - RowBox[{"-", "2"}], ",", "0"}], "}"}], ",", - RowBox[{"{", - RowBox[{"2", ",", "0"}], "}"}]}], "}"}], "]"}], ",", - "Dashed", ",", - RowBox[{"Line", "[", - RowBox[{"{", - RowBox[{ - RowBox[{"{", - RowBox[{ - RowBox[{"-", "2"}], ",", - SqrtBox["r"]}], "}"}], ",", - RowBox[{"{", - RowBox[{"2", ",", - SqrtBox["r"]}], "}"}]}], "}"}], "]"}], ",", - RowBox[{"Line", "[", - RowBox[{"{", - RowBox[{ - RowBox[{"{", - RowBox[{ - RowBox[{"-", "2"}], ",", - RowBox[{"-", - SqrtBox["r"]}]}], "}"}], ",", - RowBox[{"{", - RowBox[{"2", ",", - RowBox[{"-", - SqrtBox["r"]}]}], "}"}]}], "}"}], "]"}]}], "}"}], "]"}], - ",", - RowBox[{"Graphics", "[", - RowBox[{"{", - RowBox[{"Red", ",", "Thick", ",", "Dashed", ",", - RowBox[{"Line", "[", - RowBox[{"{", - RowBox[{ - RowBox[{"{", - RowBox[{ - RowBox[{"-", "2"}], ",", "0"}], "}"}], ",", - RowBox[{"{", - RowBox[{"2", ",", "0"}], "}"}]}], "}"}], "]"}]}], "}"}], - "]"}]}], "]"}]}], "]"}], ",", - RowBox[{"Show", "[", - RowBox[{ - RowBox[{"Plot", "[", - RowBox[{ - RowBox[{"{", - RowBox[{ - RowBox[{"Piecewise", "[", - RowBox[{ - RowBox[{"{", - RowBox[{"{", - RowBox[{ - RowBox[{"-", - SqrtBox["rr"]}], ",", - RowBox[{"rr", "\[GreaterEqual]", "0"}]}], "}"}], "}"}], ",", - "Nothing"}], "]"}], ",", - RowBox[{"Piecewise", "[", - RowBox[{ - RowBox[{"{", - RowBox[{"{", - RowBox[{ - SqrtBox["rr"], ",", - RowBox[{"rr", "\[GreaterEqual]", "0"}]}], "}"}], "}"}], ",", - "Nothing"}], "]"}], ",", - RowBox[{"Piecewise", "[", - RowBox[{ - RowBox[{"{", - RowBox[{"{", - RowBox[{"0", ",", - RowBox[{"rr", "\[GreaterEqual]", "0"}]}], "}"}], "}"}], ",", - "Nothing"}], "]"}], ",", - RowBox[{"Piecewise", "[", - RowBox[{ - RowBox[{"{", - RowBox[{"{", - RowBox[{"0", ",", - RowBox[{"rr", "<", "0"}]}], "}"}], "}"}], ",", "Nothing"}], - "]"}]}], "}"}], ",", - RowBox[{"{", - RowBox[{"rr", ",", - RowBox[{"-", "2.001"}], ",", "r"}], "}"}], ",", - RowBox[{"PlotStyle", "\[Rule]", - RowBox[{"{", - RowBox[{ - RowBox[{"Directive", "[", - RowBox[{"Red", ",", "Thick", ",", "Dashed"}], "]"}], ",", - RowBox[{"Directive", "[", - RowBox[{"Red", ",", "Thick", ",", "Dashed"}], "]"}], ",", - RowBox[{"Directive", "[", - RowBox[{"Red", ",", "Thick"}], "]"}], ",", - RowBox[{"Directive", "[", - RowBox[{"Red", ",", "Thick", ",", "Dashed"}], "]"}]}], "}"}]}], - ",", - RowBox[{"PlotRange", "\[Rule]", - RowBox[{"{", - RowBox[{ - RowBox[{"{", - RowBox[{ - RowBox[{"-", "2"}], ",", "2"}], "}"}], ",", - RowBox[{"{", - RowBox[{ - RowBox[{"-", "2"}], ",", "2"}], "}"}]}], "}"}]}], ",", - RowBox[{"AspectRatio", "\[Rule]", "1"}], ",", - RowBox[{"Frame", "\[Rule]", "True"}], ",", - RowBox[{"Axes", "\[Rule]", "False"}], ",", - RowBox[{ - "PlotLabel", "\[Rule]", - "\"\\ -\""}]}], "]"}], ",", - RowBox[{"If", "[", - RowBox[{ - RowBox[{"r", "\[GreaterEqual]", "0"}], ",", - RowBox[{"Graphics", "[", - RowBox[{"{", - RowBox[{"Red", ",", - RowBox[{"PointSize", "[", "Large", "]"}], ",", - RowBox[{"Point", "[", - RowBox[{"{", - RowBox[{ - RowBox[{"{", - RowBox[{"r", ",", - SqrtBox["r"]}], "}"}], ",", - RowBox[{"{", - RowBox[{"r", ",", - RowBox[{"-", - SqrtBox["r"]}]}], "}"}], ",", - RowBox[{"{", - RowBox[{"r", ",", "0"}], "}"}]}], "}"}], "]"}], ",", - "White", ",", - RowBox[{"PointSize", "[", "Medium", "]"}], ",", - RowBox[{"Point", "[", - RowBox[{"{", - RowBox[{ - RowBox[{"{", - RowBox[{"r", ",", - SqrtBox["r"]}], "}"}], ",", - RowBox[{"{", - RowBox[{"r", ",", - RowBox[{"-", - SqrtBox["r"]}]}], "}"}]}], "}"}], "]"}]}], "}"}], "]"}], - ",", - RowBox[{"Graphics", "[", - RowBox[{"{", - RowBox[{"Red", ",", - RowBox[{"PointSize", "[", "Large", "]"}], ",", - RowBox[{"Point", "[", - RowBox[{"{", - RowBox[{"r", ",", "0"}], "}"}], "]"}], ",", "White", ",", - RowBox[{"PointSize", "[", "Medium", "]"}], ",", - RowBox[{"Point", "[", - RowBox[{"{", - RowBox[{"r", ",", "0"}], "}"}], "]"}]}], "}"}], "]"}]}], - "]"}]}], "]"}]}], "}"}], "}"}], "]"}], ",", - RowBox[{"{", - RowBox[{ - RowBox[{"{", - RowBox[{"r", ",", "1"}], "}"}], ",", - RowBox[{"-", "2"}], ",", "2"}], "}"}]}], "]"}]], "Input", - CellChangeTimes->{{3.77713657768003*^9, 3.7771365828765388`*^9}, { - 3.7771370214122696`*^9, 3.7771370243627615`*^9}, {3.7771371027777557`*^9, - 3.777137152180356*^9}, {3.777137522168996*^9, 3.7771379841682105`*^9}, { - 3.7771380242901864`*^9, 3.7771384015864058`*^9}, {3.7771385034820766`*^9, - 3.7771385543943424`*^9}, {3.7771420666214676`*^9, 3.777142122868834*^9}, { - 3.7771421668529077`*^9, 3.777142311824276*^9}}], - -Cell[BoxData[ - TagBox[ - StyleBox[ - DynamicModuleBox[{$CellContext`r$$ = 1, Typeset`show$$ = True, - Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", - Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = - "\"untitled\"", Typeset`specs$$ = {{{ - Hold[$CellContext`r$$], 1}, -2, 2}}, Typeset`size$$ = { - 387., {96.5, 102.5}}, Typeset`update$$ = 0, Typeset`initDone$$, - Typeset`skipInitDone$$ = True, $CellContext`r$2240$$ = 0}, - DynamicBox[Manipulate`ManipulateBoxes[ - 1, StandardForm, "Variables" :> {$CellContext`r$$ = 1}, - "ControllerVariables" :> { - Hold[$CellContext`r$$, $CellContext`r$2240$$, 0]}, - "OtherVariables" :> { - Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, - Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, - Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, - Typeset`skipInitDone$$}, "Body" :> TableForm[{{ - Show[ - - StreamPlot[{ - 1, $CellContext`x^3 - $CellContext`r$$ $CellContext`x}, \ -{$CellContext`t, -2, 2}, {$CellContext`x, -2, 2}, PlotLabel -> - "stream plot (x versus t)"], - If[$CellContext`r$$ >= 0, - Graphics[{Red, Thick, - Line[{{-2, 0}, {2, 0}}], Dashed, - Line[{{-2, - Sqrt[$CellContext`r$$]}, {2, - Sqrt[$CellContext`r$$]}}], - - Line[{{-2, -Sqrt[$CellContext`r$$]}, { - 2, -Sqrt[$CellContext`r$$]}}]}], - Graphics[{Red, Thick, Dashed, - Line[{{-2, 0}, {2, 0}}]}]]], - Show[ - Plot[{ - - Piecewise[{{-Sqrt[$CellContext`rr], $CellContext`rr >= 0}}, - Nothing], - Piecewise[{{ - Sqrt[$CellContext`rr], $CellContext`rr >= 0}}, Nothing], - Piecewise[{{0, $CellContext`rr >= 0}}, Nothing], - - Piecewise[{{0, $CellContext`rr < 0}}, - Nothing]}, {$CellContext`rr, -2.001, $CellContext`r$$}, - PlotStyle -> { - Directive[Red, Thick, Dashed], - Directive[Red, Thick, Dashed], - Directive[Red, Thick], - Directive[Red, Thick, Dashed]}, PlotRange -> {{-2, 2}, {-2, 2}}, - AspectRatio -> 1, Frame -> True, Axes -> False, PlotLabel -> - "equilibria (\!\(\*SuperscriptBox[\(x\), \(*\)]\) versus r)"], - If[$CellContext`r$$ >= 0, - Graphics[{Red, - PointSize[Large], - Point[{{$CellContext`r$$, - Sqrt[$CellContext`r$$]}, {$CellContext`r$$, - - Sqrt[$CellContext`r$$]}, {$CellContext`r$$, 0}}], White, - PointSize[Medium], - Point[{{$CellContext`r$$, - Sqrt[$CellContext`r$$]}, {$CellContext`r$$, - - Sqrt[$CellContext`r$$]}}]}], - Graphics[{Red, - PointSize[Large], - Point[{$CellContext`r$$, 0}], White, - PointSize[Medium], - Point[{$CellContext`r$$, 0}]}]]]}}], - "Specifications" :> {{{$CellContext`r$$, 1}, -2, 2}}, "Options" :> {}, - "DefaultOptions" :> {}], - ImageSizeCache->{438., {144., 150.}}, - SingleEvaluation->True], - Deinitialization:>None, - DynamicModuleValues:>{}, - SynchronousInitialization->True, - UndoTrackedVariables:>{Typeset`show$$, Typeset`bookmarkMode$$}, - UnsavedVariables:>{Typeset`initDone$$}, - UntrackedVariables:>{Typeset`size$$}], "Manipulate", - Deployed->True, - StripOnInput->False], - Manipulate`InterpretManipulate[1]]], "Output", - CellChangeTimes->{{3.7771379244304895`*^9, 3.777137972818993*^9}, { - 3.777138035688207*^9, 3.7771380603054132`*^9}, {3.7771381204860187`*^9, - 3.777138178429568*^9}, {3.777138214210326*^9, 3.7771382557136283`*^9}, { - 3.777138298547415*^9, 3.777138305909398*^9}, 3.777138364876514*^9, - 3.777138402049615*^9, 3.7771385562984977`*^9, 3.777142069213477*^9, { - 3.777142100334644*^9, 3.777142123718077*^9}, {3.7771422250715675`*^9, - 3.7771422683455553`*^9}, 3.7771423125655565`*^9, 3.7771428387314763`*^9}] -}, Open ]] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["Hopf Bifurcation", "Section", - CellChangeTimes->{{3.7766008885632277`*^9, 3.7766008904796133`*^9}, { - 3.777136401274056*^9, 3.777136416298379*^9}, {3.7771423512766824`*^9, - 3.7771423523483405`*^9}}], - -Cell["\<\ -A Hopf bifurcation occurs when an equilibrium changes stability in a way that \ -leads to a periodic orbit. This can only occur if we increase our system to \ -at least two dimensions. The example below concerns the 2D system:\ -\>", "Text", - CellChangeTimes->{{3.777136412348218*^9, 3.777136502673601*^9}, { - 3.777140654593788*^9, 3.77714069874934*^9}, {3.777142354913436*^9, - 3.7771423557214785`*^9}, {3.7771424049490695`*^9, 3.7771425240888643`*^9}}], - -Cell[BoxData[Cell[TextData[Cell[BoxData[{ - FormBox[ - RowBox[{ - FractionBox[ - RowBox[{"\[DifferentialD]", "x"}], - RowBox[{"\[DifferentialD]", "t"}]], "=", - RowBox[{ - RowBox[{ - RowBox[{"r", "(", - RowBox[{"1", "-", - SuperscriptBox["y", "2"]}], ")"}], "x"}], "-", "y"}]}], - TraditionalForm], "\[IndentingNewLine]", - FormBox[ - RowBox[{ - FractionBox[ - RowBox[{"\[DifferentialD]", "y"}], - RowBox[{"\[DifferentialD]", "t"}]], "=", "x"}], TraditionalForm]}], - FormatType->"TraditionalForm"]], "DisplayFormula"]], "Text", - CellChangeTimes->{{3.77713651537531*^9, 3.7771365309974613`*^9}, - 3.7771366535696325`*^9, {3.7771370336200256`*^9, 3.7771370357424736`*^9}, { - 3.7771425287026825`*^9, 3.777142543615819*^9}}], - -Cell[TextData[{ - "Finding the equilibria now requires us to solve the simultaneous system ", - Cell[BoxData[ - FormBox[ - RowBox[{ - RowBox[{ - FractionBox[ - RowBox[{"\[DifferentialD]", "x"}], - RowBox[{"\[DifferentialD]", "t"}]], "=", "0"}], ",", - RowBox[{ - FractionBox[ - RowBox[{"\[DifferentialD]", "y"}], - RowBox[{"\[DifferentialD]", "t"}]], "=", "0"}]}], TraditionalForm]], - FormatType->"TraditionalForm"], - ", which has exactly one solution: ", - Cell[BoxData[ - FormBox[ - RowBox[{ - RowBox[{"(", - RowBox[{ - SuperscriptBox["x", "*"], ",", - SuperscriptBox["y", "*"]}], ")"}], "=", - RowBox[{"(", - RowBox[{"0", ",", "0"}], ")"}]}], TraditionalForm]], - FormatType->"TraditionalForm"], - ". This is independent of the value of ", - Cell[BoxData[ - FormBox["r", TraditionalForm]], - FormatType->"TraditionalForm"], - ". We next conduct stability analysis by examining the Jacobian" -}], "Text", - CellChangeTimes->{{3.7771366384229493`*^9, 3.777136834022626*^9}, { - 3.777136865290258*^9, 3.77713686612399*^9}, {3.77713704004583*^9, - 3.77713704004583*^9}, {3.7771425567700644`*^9, 3.7771426590387325`*^9}, { - 3.777142720782019*^9, 3.7771427214294863`*^9}}], - -Cell[BoxData[Cell[TextData[{ - Cell[BoxData[ - FormBox[ - RowBox[{ - SuperscriptBox["J", "*"], "=", - SubscriptBox[ - RowBox[{"(", GridBox[{ - { - RowBox[{ - FractionBox["\[DifferentialD]", - RowBox[{"\[DifferentialD]", "x"}]], - RowBox[{"(", - RowBox[{ - RowBox[{ - RowBox[{"r", "(", - RowBox[{"1", "-", - SuperscriptBox["y", "2"]}], ")"}], "x"}], "-", "y"}], ")"}]}], - RowBox[{ - FractionBox["\[DifferentialD]", - RowBox[{"\[DifferentialD]", "y"}]], - RowBox[{"(", - RowBox[{ - RowBox[{"r", - RowBox[{"(", - RowBox[{"1", "-", - SuperscriptBox["y", "2"]}], ")"}], "x"}], "-", "y"}], ")"}]}]}, - { - RowBox[{ - FractionBox["\[DifferentialD]", - RowBox[{"\[DifferentialD]", "x"}]], - RowBox[{"(", "x", ")"}]}], - RowBox[{ - FractionBox["\[DifferentialD]", - RowBox[{"\[DifferentialD]", "y"}]], - RowBox[{"(", "x", ")"}]}]} - }], ")"}], - RowBox[{ - RowBox[{"(", - RowBox[{"x", ",", "y"}], ")"}], "=", - RowBox[{"(", - RowBox[{"0", ",", "0"}], ")"}]}]]}], TraditionalForm]]], - "=", - Cell[BoxData[ - FormBox[ - RowBox[{ - SubscriptBox[ - RowBox[{"(", GridBox[{ - { - RowBox[{"r", "(", - RowBox[{"1", "-", - SuperscriptBox["y", "2"]}], ")"}], - RowBox[{ - RowBox[{ - RowBox[{"-", "2"}], "r", " ", "x", " ", "y"}], "-", "1"}]}, - {"1", "0"} - }], ")"}], - RowBox[{ - RowBox[{"(", - RowBox[{"x", ",", "y"}], ")"}], "=", - RowBox[{"(", - RowBox[{"0", ",", "0"}], ")"}]}]], "=", - RowBox[{"(", GridBox[{ - {"r", - RowBox[{"-", "1"}]}, - {"1", "0"} - }], ")"}]}], TraditionalForm]]] - }], "DisplayFormula"]], "DisplayFormula", - CellChangeTimes->{{3.7771426694122353`*^9, 3.777142776009329*^9}, { - 3.7771428654505424`*^9, 3.7771429550053325`*^9}}], - -Cell[TextData[{ - "which has eigenvalues of ", - Cell[BoxData[ - FormBox[ - FractionBox[ - RowBox[{"r", " ", "\[PlusMinus]", - SqrtBox[ - RowBox[{ - SuperscriptBox["r", "2"], " ", "-", " ", "4"}]]}], "2"], - TraditionalForm]], - FormatType->"TraditionalForm"], - ". These always have a negative real part for ", - Cell[BoxData[ - FormBox[ - RowBox[{"r", "<", "0"}], TraditionalForm]], - FormatType->"TraditionalForm"], - " and a positive real part for ", - Cell[BoxData[ - FormBox[ - RowBox[{"r", ">", "0"}], TraditionalForm]], - FormatType->"TraditionalForm"], - ". For ", - Cell[BoxData[ - FormBox[ - RowBox[{"r", "\[LessEqual]", - RowBox[{"-", "2"}]}], TraditionalForm]], - FormatType->"TraditionalForm"], - " and ", - Cell[BoxData[ - FormBox[ - RowBox[{"r", "\[GreaterEqual]", "2"}], TraditionalForm]], - FormatType->"TraditionalForm"], - " they are purely real, while for ", - Cell[BoxData[ - FormBox[ - RowBox[{ - RowBox[{"-", "2"}], "<", "r", "<", "2"}], TraditionalForm]], - FormatType->"TraditionalForm"], - " they include an imaginary part. At ", - Cell[BoxData[ - FormBox[ - RowBox[{"r", "=", "0"}], TraditionalForm]], - FormatType->"TraditionalForm"], - " the eigenvalues are purely imaginary and we have periodic orbits." -}], "Text", - CellChangeTimes->{{3.7771429637246385`*^9, 3.777142966166086*^9}, { - 3.7771429962203674`*^9, 3.7771430481636953`*^9}, {3.777143415022867*^9, - 3.7771435095056553`*^9}}], - -Cell[TextData[{ - "The equilibrium displays used above do not apply to this 2D system, and so \ -instead we display only the stream plot of ", - Cell[BoxData[ - FormBox["y", TraditionalForm]], - FormatType->"TraditionalForm"], - " versus ", - Cell[BoxData[ - FormBox["x", TraditionalForm]], - FormatType->"TraditionalForm"], - ". Notice that as ", - Cell[BoxData[ - FormBox["r", TraditionalForm]], - FormatType->"TraditionalForm"], - " goes from negative to zero to positive, the system goes from spiraling \ -inward (stable) to circular orbits (periodic) to spiraling outward (unstable)." -}], "Text", - CellChangeTimes->{{3.7771435211260934`*^9, 3.7771436703194323`*^9}}], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"Manipulate", "[", - RowBox[{ - RowBox[{"Show", "[", - RowBox[{ - RowBox[{"StreamPlot", "[", - RowBox[{ - RowBox[{"{", - RowBox[{ - RowBox[{ - RowBox[{"r", - RowBox[{"(", - RowBox[{"1", "-", - SuperscriptBox["y", "2"]}], ")"}], "x"}], "-", "y"}], ",", "x"}], - "}"}], ",", - RowBox[{"{", - RowBox[{"x", ",", - RowBox[{"-", "2"}], ",", "2"}], "}"}], ",", - RowBox[{"{", - RowBox[{"y", ",", - RowBox[{"-", "2"}], ",", "2"}], "}"}], ",", - RowBox[{"PlotLabel", "\[Rule]", "\"\\""}]}], - "]"}], ",", - RowBox[{"Graphics", "[", - RowBox[{"{", - RowBox[{"Red", ",", - RowBox[{"PointSize", "[", "Large", "]"}], ",", - RowBox[{"Point", "[", - RowBox[{"{", - RowBox[{"0", ",", "0"}], "}"}], "]"}]}], "}"}], "]"}]}], "]"}], ",", - RowBox[{"{", - RowBox[{ - RowBox[{"{", - RowBox[{"r", ",", "1"}], "}"}], ",", - RowBox[{"-", "3"}], ",", "3"}], "}"}]}], "]"}]], "Input", - CellChangeTimes->{{3.77713657768003*^9, 3.7771365828765388`*^9}, { - 3.7771370214122696`*^9, 3.7771370243627615`*^9}, {3.7771371027777557`*^9, - 3.777137152180356*^9}, {3.777137522168996*^9, 3.7771379841682105`*^9}, { - 3.7771380242901864`*^9, 3.7771384015864058`*^9}, {3.7771385034820766`*^9, - 3.7771385543943424`*^9}, {3.777143113760271*^9, 3.777143167703524*^9}, { - 3.77714324489684*^9, 3.7771432725478344`*^9}, {3.77714335304587*^9, - 3.7771433539295716`*^9}}], - -Cell[BoxData[ - TagBox[ - StyleBox[ - DynamicModuleBox[{$CellContext`r$$ = 1.63, Typeset`show$$ = True, - Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", - Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = - "\"untitled\"", Typeset`specs$$ = {{{ - Hold[$CellContext`r$$], 1}, -3, 3}}, Typeset`size$$ = { - 360., {185., 190.}}, Typeset`update$$ = 0, Typeset`initDone$$, - Typeset`skipInitDone$$ = True, $CellContext`r$18043$$ = 0}, - DynamicBox[Manipulate`ManipulateBoxes[ - 1, StandardForm, "Variables" :> {$CellContext`r$$ = 1}, - "ControllerVariables" :> { - Hold[$CellContext`r$$, $CellContext`r$18043$$, 0]}, - "OtherVariables" :> { - Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, - Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, - Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, - Typeset`skipInitDone$$}, "Body" :> Show[ - StreamPlot[{$CellContext`r$$ ( - 1 - $CellContext`y^2) $CellContext`x - $CellContext`y, \ -$CellContext`x}, {$CellContext`x, -2, 2}, {$CellContext`y, -2, 2}, PlotLabel -> - "stream plot (y versus x)"], - Graphics[{Red, - PointSize[Large], - Point[{0, 0}]}]], - "Specifications" :> {{{$CellContext`r$$, 1}, -3, 3}}, "Options" :> {}, - "DefaultOptions" :> {}], - ImageSizeCache->{411., {245., 251.}}, - SingleEvaluation->True], - Deinitialization:>None, - DynamicModuleValues:>{}, - SynchronousInitialization->True, - UndoTrackedVariables:>{Typeset`show$$, Typeset`bookmarkMode$$}, - UnsavedVariables:>{Typeset`initDone$$}, - UntrackedVariables:>{Typeset`size$$}], "Manipulate", - Deployed->True, - StripOnInput->False], - Manipulate`InterpretManipulate[1]]], "Output", - CellChangeTimes->{{3.7771379244304895`*^9, 3.777137972818993*^9}, { - 3.777138035688207*^9, 3.7771380603054132`*^9}, {3.7771381204860187`*^9, - 3.777138178429568*^9}, {3.777138214210326*^9, 3.7771382557136283`*^9}, { - 3.777138298547415*^9, 3.777138305909398*^9}, 3.777138364876514*^9, - 3.777138402049615*^9, 3.7771385562984977`*^9, 3.7771428399820857`*^9, - 3.7771431348484387`*^9, 3.77714316857364*^9, {3.777143263336276*^9, - 3.7771432733456025`*^9}, 3.777143355066966*^9}] -}, {2}]] -}, Open ]] -}, Open ]] -}, -WindowSize->{767, 833}, -WindowMargins->{{57, Automatic}, {Automatic, 51}}, -FrontEndVersion->"10.4 for Microsoft Windows (64-bit) (April 11, 2016)", -StyleDefinitions->"Default.nb" -] -(* End of Notebook Content *) - -(* Internal cache information *) -(*CellTagsOutline -CellTagsIndex->{} -*) -(*CellTagsIndex -CellTagsIndex->{} -*) -(*NotebookFileOutline -Notebook[{ -Cell[CellGroupData[{ -Cell[580, 22, 158, 2, 90, "Title"], -Cell[741, 26, 158, 2, 30, "Text"], -Cell[CellGroupData[{ -Cell[924, 32, 99, 1, 63, "Section"], -Cell[1026, 35, 915, 25, 87, "Text"], -Cell[1944, 62, 1866, 51, 158, "Text"], -Cell[3813, 115, 1116, 32, 82, "Text"], -Cell[4932, 149, 1048, 31, 82, "Text"], -Cell[5983, 182, 894, 23, 89, "Text"], -Cell[6880, 207, 1085, 35, 96, "Text"], -Cell[7968, 244, 966, 18, 144, "Text"] -}, Open ]], -Cell[CellGroupData[{ -Cell[8971, 267, 161, 2, 63, "Section"], -Cell[9135, 271, 507, 8, 87, "Text"], -Cell[9645, 281, 453, 10, 46, "Text"], -Cell[10101, 293, 788, 25, 63, "Text"], -Cell[CellGroupData[{ -Cell[10914, 322, 417, 14, 34, "Item"], -Cell[11334, 338, 476, 15, 34, "Item"], -Cell[11813, 355, 453, 15, 29, "Item"] -}, Open ]], -Cell[12281, 373, 1650, 59, 94, "Text"], -Cell[CellGroupData[{ -Cell[13956, 436, 5322, 140, 413, "Input"], -Cell[19281, 578, 3451, 74, 311, "Output"] -}, Open ]] -}, Open ]], -Cell[CellGroupData[{ -Cell[22781, 658, 216, 3, 63, "Section"], -Cell[23000, 663, 450, 7, 49, "Text"], -Cell[23453, 672, 531, 12, 46, "Text"], -Cell[23987, 686, 1085, 35, 63, "Text"], -Cell[25075, 723, 979, 30, 63, "Text"], -Cell[CellGroupData[{ -Cell[26079, 757, 654, 23, 45, "Item"], -Cell[26736, 782, 625, 22, 45, "Item"] -}, Open ]], -Cell[27376, 807, 387, 13, 30, "Text"], -Cell[CellGroupData[{ -Cell[27788, 824, 6514, 164, 371, "Input"], -Cell[34305, 990, 3800, 79, 311, "Output"] -}, Open ]] -}, Open ]], -Cell[CellGroupData[{ -Cell[38154, 1075, 210, 3, 63, "Section"], -Cell[38367, 1080, 577, 9, 87, "Text"], -Cell[38947, 1091, 533, 12, 46, "Text"], -Cell[39483, 1105, 2018, 68, 107, "Text"], -Cell[41504, 1175, 2655, 93, 132, "Text"], -Cell[CellGroupData[{ -Cell[44184, 1272, 7694, 197, 539, "Input"], -Cell[51881, 1471, 4191, 88, 311, "Output"] -}, Open ]] -}, Open ]], -Cell[CellGroupData[{ -Cell[56121, 1565, 207, 3, 63, "Section"], -Cell[56331, 1570, 463, 7, 68, "Text"], -Cell[56797, 1579, 771, 20, 81, "Text"], -Cell[57571, 1601, 1217, 34, 84, "Text"], -Cell[58791, 1637, 2131, 68, 78, "DisplayFormula"], -Cell[60925, 1707, 1432, 47, 93, "Text"], -Cell[62360, 1756, 662, 17, 68, "Text"], -Cell[CellGroupData[{ -Cell[63047, 1777, 1575, 41, 103, "Input"], -Cell[64625, 1820, 2303, 45, 513, "Output"] -}, {2}]] -}, Open ]] -}, Open ]] -} -] -*) - +(* Content-type: application/vnd.wolfram.mathematica *) + +(*** Wolfram Notebook File ***) +(* http://www.wolfram.com/nb *) + +(* CreatedBy='Mathematica 10.4' *) + +(*CacheID: 234*) +(* Internal cache information: +NotebookFileLineBreakTest +NotebookFileLineBreakTest +NotebookDataPosition[ 158, 7] +NotebookDataLength[ 69409, 1952] +NotebookOptionsPosition[ 66965, 1870] +NotebookOutlinePosition[ 67308, 1885] +CellTagsIndexPosition[ 67265, 1882] +WindowFrame->Normal*) + +(* Beginning of Notebook Content *) +Notebook[{ + +Cell[CellGroupData[{ +Cell["Bifurcation Analysis", "Title", + CellChangeTimes->{{3.776600831050974*^9, 3.7766008318453026`*^9}, { + 3.7771302217782173`*^9, 3.7771302252764606`*^9}}], + +Cell["Adam Rumpf, 2/20/2017", "Text", + CellChangeTimes->{{3.7766008347881403`*^9, 3.776600838290375*^9}, { + 3.7771302419672003`*^9, 3.7771302444085283`*^9}}], + +Cell[CellGroupData[{ + +Cell["Introduction", "Section", + CellChangeTimes->{{3.7766008459498987`*^9, 3.776600848547045*^9}}], + +Cell[TextData[{ + "Below is a sequence of examples of four common types of bifurcation: \ +saddle-node, transcritical, pitchfork, and Hopf. For each example we provide \ +a specific autonomous ODE system which displays that type of bifurcation. In \ +all examples, ", + Cell[BoxData[ + FormBox["x", TraditionalForm]], + FormatType->"TraditionalForm"], + " and ", + Cell[BoxData[ + FormBox["y", TraditionalForm]], + FormatType->"TraditionalForm"], + " represent functions of time ", + Cell[BoxData[ + FormBox["t", TraditionalForm]], + FormatType->"TraditionalForm"], + " while ", + Cell[BoxData[ + FormBox["r", TraditionalForm]], + FormatType->"TraditionalForm"], + " represents the single parameter which will be varied to create the \ +bifurcation." +}], "Text", + CellChangeTimes->{{3.776600856235587*^9, 3.776600860481224*^9}, { + 3.777136540361297*^9, 3.777136541839939*^9}, {3.7771392486350613`*^9, + 3.777139425884313*^9}}], + +Cell[TextData[{ + "As a review, a bifurcation occurs when changing the value of the parameter ", + Cell[BoxData[ + FormBox["r", TraditionalForm]], + FormatType->"TraditionalForm"], + " causes a qualitative change to the equilibria of the system. The specific \ +type of qualitative change determiens the type of bifurcation, but in general \ +it describes a change in the number or the stability of the equilibria. We \ +can attempt to look for bifurcations by solving for the equilibria ", + Cell[BoxData[ + FormBox[ + RowBox[{"(", + RowBox[{ + SuperscriptBox["x", "*"], ",", + SuperscriptBox["y", "*"]}], ")"}], TraditionalForm]], + FormatType->"TraditionalForm"], + " by setting ", + Cell[BoxData[ + FormBox[ + FractionBox[ + RowBox[{"\[DifferentialD]", "x"}], + RowBox[{"\[DifferentialD]", "t"}]], TraditionalForm]], + FormatType->"TraditionalForm"], + " and ", + Cell[BoxData[ + FormBox[ + FractionBox[ + RowBox[{"\[DifferentialD]", "y"}], + RowBox[{"\[DifferentialD]", "t"}]], TraditionalForm]], + FormatType->"TraditionalForm"], + " equal to 0. In general these equilibria will be functions of ", + Cell[BoxData[ + FormBox["r", TraditionalForm]], + FormatType->"TraditionalForm"], + ", and we can look at how the equilibria change as ", + Cell[BoxData[ + FormBox["r", TraditionalForm]], + FormatType->"TraditionalForm"], + " changes. For example, some values of ", + Cell[BoxData[ + FormBox["r", TraditionalForm]], + FormatType->"TraditionalForm"], + " will cause several equilibria to merge into one, or to become imaginary, \ +in which case the number of equilibria depends on ", + Cell[BoxData[ + FormBox["r", TraditionalForm]], + FormatType->"TraditionalForm"], + "." +}], "Text", + CellChangeTimes->{{3.777136538540001*^9, 3.7771366108791237`*^9}, { + 3.7771394295820074`*^9, 3.7771394393980103`*^9}, {3.7771396211951604`*^9, + 3.7771399003029437`*^9}}], + +Cell[TextData[{ + "A bifurcation also occurs when the stability of an equilibrium changes. In \ +order to evaluate the stability of an equilibrium, we examine the eigenvalues \ +of the Jacobian matrix. Given an ODE system ", + Cell[BoxData[ + FormBox[ + RowBox[{ + RowBox[{ + FractionBox[ + RowBox[{"\[DifferentialD]", "x"}], + RowBox[{"\[DifferentialD]", "t"}]], "=", + RowBox[{"f", "(", + RowBox[{"x", ",", "y"}], ")"}]}], ",", + RowBox[{ + FractionBox[ + RowBox[{"\[DifferentialD]", "y"}], + RowBox[{"\[DifferentialD]", "t"}]], "=", + RowBox[{"g", "(", + RowBox[{"x", ",", "y"}], ")"}]}]}], TraditionalForm]], + FormatType->"TraditionalForm"], + ", the Jacobian evaluated at the equilibrium ", + Cell[BoxData[ + FormBox[ + RowBox[{"(", + RowBox[{ + SuperscriptBox["x", "*"], ",", + SuperscriptBox["y", "*"]}], ")"}], TraditionalForm]], + FormatType->"TraditionalForm"], + " is" +}], "Text", + CellChangeTimes->{{3.7771399068080826`*^9, 3.7771399540139265`*^9}, { + 3.7771399910351863`*^9, 3.7771400245503855`*^9}, {3.777140131720338*^9, + 3.777140144319103*^9}}], + +Cell[TextData[Cell[BoxData[ + FormBox[ + RowBox[{ + SuperscriptBox["J", "*"], "=", + SubscriptBox[ + RowBox[{"(", GridBox[{ + { + FractionBox[ + RowBox[{"\[PartialD]", "f"}], + RowBox[{"\[PartialD]", "x"}]], + FractionBox[ + RowBox[{"\[PartialD]", "f"}], + RowBox[{"\[PartialD]", "y"}]]}, + { + FractionBox[ + RowBox[{"\[PartialD]", "g"}], + RowBox[{"\[PartialD]", "x"}]], + FractionBox[ + RowBox[{"\[PartialD]", "g"}], + RowBox[{"\[PartialD]", "y"}]]} + }], ")"}], + RowBox[{ + RowBox[{"(", + RowBox[{"x", ",", "y"}], ")"}], "=", + RowBox[{"(", + RowBox[{ + SuperscriptBox["x", "*"], ",", + SuperscriptBox["y", "*"]}], ")"}]}]]}], TraditionalForm]], + FormatType->"TraditionalForm"]], "Text", + CellChangeTimes->{{3.7771399729132023`*^9, 3.7771399843240213`*^9}, { + 3.77714002741781*^9, 3.777140100754119*^9}, {3.7771401471975985`*^9, + 3.7771401633902807`*^9}, {3.7771427843909597`*^9, 3.7771427935276084`*^9}}], + +Cell[TextData[{ + "If all eigenvalues have negative real parts, then ", + Cell[BoxData[ + FormBox[ + RowBox[{"(", + RowBox[{ + SuperscriptBox["x", "*"], ",", + SuperscriptBox["y", "*"]}], ")"}], TraditionalForm]], + FormatType->"TraditionalForm"], + " is stable. Otherwise it is unstable. Further classifications (like being a \ +saddle point, or orbiting in a particular direction) can also be made. As \ +with the equilibria, themselves, the eigenvalues of the Jacobian are \ +functions of ", + Cell[BoxData[ + FormBox["r", TraditionalForm]], + FormatType->"TraditionalForm"], + ", and the signs of their real parts may depend on ", + Cell[BoxData[ + FormBox["r", TraditionalForm]], + FormatType->"TraditionalForm"], + ", which leads to other types of bifurcation" +}], "Text", + CellChangeTimes->{{3.777140172105179*^9, 3.777140290076988*^9}, { + 3.777140339810768*^9, 3.777140349130089*^9}}], + +Cell[TextData[{ + "Note that, in the case of a one-dimensional ODE system ", + Cell[BoxData[ + FormBox[ + RowBox[{ + FractionBox[ + RowBox[{"\[DifferentialD]", "x"}], + RowBox[{"\[DifferentialD]", "t"}]], "=", + RowBox[{"f", "(", "x", ")"}]}], TraditionalForm]], + FormatType->"TraditionalForm"], + ", the Jacobian ", + Cell[BoxData[ + FormBox[ + SuperscriptBox["J", "*"], TraditionalForm]], + FormatType->"TraditionalForm"], + " reduces to simply the scalar ", + Cell[BoxData[ + FormBox[ + RowBox[{ + FractionBox[ + RowBox[{"\[PartialD]", "f"}], + RowBox[{"\[PartialD]", "x"}]], + SubscriptBox["|", + RowBox[{"x", "=", + SuperscriptBox["x", "*"]}]]}], TraditionalForm]], + FormatType->"TraditionalForm"], + ", in which case we can look directly at the value of ", + Cell[BoxData[ + FormBox[ + FractionBox[ + RowBox[{"\[PartialD]", "f"}], + RowBox[{"\[PartialD]", "x"}]], TraditionalForm]], + FormatType->"TraditionalForm"], + " rather than having to look at eigenvalues." +}], "Text", + CellChangeTimes->{{3.7771402937021027`*^9, 3.777140434198078*^9}}], + +Cell[TextData[{ + "Each section below describes a different type of bifurcation. First an ODE \ +system will be presented, then a bifurcation analysis will be conducted by \ +hand, and finally a Manipulate environment will be defined to show a \ +visualization of the bifurcation in action. In all cases there is a slider to \ +control the value of ", + Cell[BoxData[ + FormBox["r", TraditionalForm]]], + ". Equilibria will be shown in red on the stream plot, either as a line (for \ +the 1D case) or a point (in the 2D case). For the 1D cases, to the right of \ +the stream plot will be a plot of the equilibrium values as a function of ", + Cell[BoxData[ + FormBox["r", TraditionalForm]]], + ". In all cases, solid lines and filled dots correspond to stable \ +equilibria, while dotted lines and hollow dots correspond to unstable \ +equilibria." +}], "Text", + CellChangeTimes->{{3.777140451556507*^9, 3.7771406396788273`*^9}, { + 3.777143704620434*^9, 3.7771437074667997`*^9}}] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Saddle-Node Bifurcation", "Section", + CellChangeTimes->{{3.7766008885632277`*^9, 3.7766008904796133`*^9}, { + 3.777136401274056*^9, 3.777136416298379*^9}}], + +Cell["\<\ +A saddle-node bifurcation occurs when two equilibria collide and annihilate \ +each other (or, if moving in the other direction, when two equilibria are \ +spontaneously generated out of nothing). Specifically this can occur when \ +changing the parameters causes a pair of equilibria to simultaneously become \ +real or imaginary. The example below concerns the 1D system:\ +\>", "Text", + CellChangeTimes->{{3.777136412348218*^9, 3.777136502673601*^9}, { + 3.777140654593788*^9, 3.77714069874934*^9}}], + +Cell[BoxData[Cell[TextData[Cell[BoxData[ + FormBox[ + RowBox[{ + FractionBox[ + RowBox[{"\[DifferentialD]", "x"}], + RowBox[{"\[DifferentialD]", "t"}]], "=", + RowBox[{ + SuperscriptBox["x", "2"], "-", "r"}]}], TraditionalForm]], + FormatType->"TraditionalForm"]], "DisplayFormula"]], "Text", + CellChangeTimes->{{3.77713651537531*^9, 3.7771365309974613`*^9}, + 3.7771366535696325`*^9, {3.7771370336200256`*^9, 3.7771370357424736`*^9}}], + +Cell[TextData[{ + "Setting ", + Cell[BoxData[ + FormBox[ + RowBox[{ + FractionBox[ + RowBox[{"\[DifferentialD]", "x"}], + RowBox[{"\[DifferentialD]", "t"}]], "=", "0"}], TraditionalForm]], + FormatType->"TraditionalForm"], + " and solving, we find that the equilibria are ", + Cell[BoxData[ + FormBox[ + RowBox[{ + SuperscriptBox["x", "*"], "=", + RowBox[{"\[PlusMinus]", + SqrtBox["r"]}]}], TraditionalForm]], + FormatType->"TraditionalForm"], + ". We can consider different cases depending on the value of ", + Cell[BoxData[ + FormBox["r", TraditionalForm]], + FormatType->"TraditionalForm"], + ":" +}], "Text", + CellChangeTimes->{{3.7771366384229493`*^9, 3.777136834022626*^9}, { + 3.777136865290258*^9, 3.77713686612399*^9}, {3.77713704004583*^9, + 3.77713704004583*^9}}], + +Cell[CellGroupData[{ + +Cell[TextData[{ + "If ", + Cell[BoxData[ + FormBox[ + RowBox[{"r", ">", "0"}], TraditionalForm]], + FormatType->"TraditionalForm"], + ", then ", + Cell[BoxData[ + FormBox[ + SqrtBox["r"], TraditionalForm]], + FormatType->"TraditionalForm"], + " is real, and thus we have two real equilibria." +}], "Item", + CellChangeTimes->{{3.7771368388776255`*^9, 3.777136876907528*^9}, { + 3.777137050530507*^9, 3.77713706427261*^9}}], + +Cell[TextData[{ + "If ", + Cell[BoxData[ + FormBox[ + RowBox[{"r", "<", "0"}], TraditionalForm]], + FormatType->"TraditionalForm"], + ", then ", + Cell[BoxData[ + FormBox[ + SqrtBox["r"], TraditionalForm]], + FormatType->"TraditionalForm"], + " is imaginary, and thus we have no real equilibria." +}], "Item", + CellChangeTimes->{{3.7771368388776255`*^9, 3.7771369074951057`*^9}, { + 3.777137071701436*^9, 3.77713707583746*^9}, {3.7771407238414207`*^9, + 3.7771407246057043`*^9}}], + +Cell[TextData[{ + "If ", + Cell[BoxData[ + FormBox[ + RowBox[{"r", "=", "0"}], TraditionalForm]], + FormatType->"TraditionalForm"], + ", then we have exactly one unique equilibrium of ", + Cell[BoxData[ + FormBox[ + RowBox[{ + SuperscriptBox["x", "*"], "=", "0"}], TraditionalForm]], + FormatType->"TraditionalForm"], + "." +}], "Item", + CellChangeTimes->{{3.7771368388776255`*^9, 3.777136930784681*^9}, { + 3.777140737329257*^9, 3.7771407382486253`*^9}}] +}, Open ]], + +Cell[TextData[{ + "We can conduct stability analysis by evaluating ", + Cell[BoxData[ + FormBox[ + RowBox[{ + RowBox[{ + FractionBox["\[PartialD]", + RowBox[{"\[PartialD]", "x"}]], + RowBox[{"(", + RowBox[{ + SuperscriptBox["x", "2"], "-", "r"}], ")"}]}], "=", + RowBox[{"2", "x"}]}], TraditionalForm]], + FormatType->"TraditionalForm"], + " at ", + Cell[BoxData[ + FormBox[ + RowBox[{"x", "=", + RowBox[{"\[PlusMinus]", + SqrtBox["r"]}]}], TraditionalForm]], + FormatType->"TraditionalForm"], + ". In the case of ", + Cell[BoxData[ + FormBox[ + RowBox[{"r", ">", "0"}], TraditionalForm]], + FormatType->"TraditionalForm"], + ", clearly ", + Cell[BoxData[ + FormBox[ + RowBox[{ + SuperscriptBox["x", "*"], "=", + SqrtBox["r"]}], TraditionalForm]], + FormatType->"TraditionalForm"], + " yields a positive Jacobian while ", + Cell[BoxData[ + FormBox[ + RowBox[{ + SuperscriptBox["x", "*"], "=", + RowBox[{"-", + SqrtBox["r"]}]}], TraditionalForm]], + FormatType->"TraditionalForm"], + " yields a negative one, and so ", + Cell[BoxData[ + FormBox[ + RowBox[{ + SuperscriptBox["x", "*"], "=", + SqrtBox["r"]}], TraditionalForm]], + FormatType->"TraditionalForm"], + " should be unstable while ", + Cell[BoxData[ + FormBox[ + RowBox[{ + SuperscriptBox["x", "*"], "=", + RowBox[{"-", + SqrtBox["r"]}]}], TraditionalForm]], + FormatType->"TraditionalForm"], + " is stable." +}], "Text", + CellChangeTimes->{{3.7771369512069955`*^9, 3.777136989791237*^9}, { + 3.777137243411868*^9, 3.7771372995028796`*^9}, {3.7771373330059586`*^9, + 3.777137413841439*^9}, {3.7771374519786773`*^9, 3.777137512637171*^9}}], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Manipulate", "[", + RowBox[{ + RowBox[{"TableForm", "[", + RowBox[{"{", + RowBox[{"{", + RowBox[{ + RowBox[{"Show", "[", + RowBox[{ + RowBox[{"StreamPlot", "[", + RowBox[{ + RowBox[{"{", + RowBox[{"1", ",", + RowBox[{ + SuperscriptBox["x", "2"], "-", "r"}]}], "}"}], ",", + RowBox[{"{", + RowBox[{"t", ",", + RowBox[{"-", "2"}], ",", "2"}], "}"}], ",", + RowBox[{"{", + RowBox[{"x", ",", + RowBox[{"-", "2"}], ",", "2"}], "}"}], ",", + RowBox[{ + "PlotLabel", "\[Rule]", "\"\\""}]}], + "]"}], ",", + RowBox[{"If", "[", + RowBox[{ + RowBox[{"r", "\[GreaterEqual]", "0"}], ",", + RowBox[{"Graphics", "[", + RowBox[{"{", + RowBox[{"Red", ",", "Thick", ",", + RowBox[{"Line", "[", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{"-", "2"}], ",", + RowBox[{"-", + SqrtBox["r"]}]}], "}"}], ",", + RowBox[{"{", + RowBox[{"2", ",", + RowBox[{"-", + SqrtBox["r"]}]}], "}"}]}], "}"}], "]"}], ",", "Dashed", + ",", + RowBox[{"Line", "[", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{"-", "2"}], ",", + SqrtBox["r"]}], "}"}], ",", + RowBox[{"{", + RowBox[{"2", ",", + SqrtBox["r"]}], "}"}]}], "}"}], "]"}]}], "}"}], "]"}], ",", + RowBox[{"Graphics", "[", + RowBox[{"{", "}"}], "]"}]}], "]"}]}], "]"}], ",", + RowBox[{"Show", "[", + RowBox[{ + RowBox[{"Plot", "[", + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{"Piecewise", "[", + RowBox[{ + RowBox[{"{", + RowBox[{"{", + RowBox[{ + RowBox[{"-", + SqrtBox["rr"]}], ",", + RowBox[{"rr", "\[GreaterEqual]", "0"}]}], "}"}], "}"}], ",", + "Nothing"}], "]"}], ",", + RowBox[{"Piecewise", "[", + RowBox[{ + RowBox[{"{", + RowBox[{"{", + RowBox[{ + SqrtBox["rr"], ",", + RowBox[{"rr", "\[GreaterEqual]", "0"}]}], "}"}], "}"}], ",", + "Nothing"}], "]"}]}], "}"}], ",", + RowBox[{"{", + RowBox[{"rr", ",", + RowBox[{"-", "2.001"}], ",", "r"}], "}"}], ",", + RowBox[{"PlotStyle", "\[Rule]", + RowBox[{"{", + RowBox[{ + RowBox[{"Directive", "[", + RowBox[{"Red", ",", "Thick"}], "]"}], ",", + RowBox[{"Directive", "[", + RowBox[{"Red", ",", "Thick", ",", "Dashed"}], "]"}]}], "}"}]}], + ",", + RowBox[{"PlotRange", "\[Rule]", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{"-", "2"}], ",", "2"}], "}"}], ",", + RowBox[{"{", + RowBox[{ + RowBox[{"-", "2"}], ",", "2"}], "}"}]}], "}"}]}], ",", + RowBox[{"AspectRatio", "\[Rule]", "1"}], ",", + RowBox[{"Frame", "\[Rule]", "True"}], ",", + RowBox[{"Axes", "\[Rule]", "False"}], ",", + RowBox[{ + "PlotLabel", "\[Rule]", + "\"\\ +\""}]}], "]"}], ",", + RowBox[{"If", "[", + RowBox[{ + RowBox[{"r", "\[GreaterEqual]", "0"}], ",", + RowBox[{"Graphics", "[", + RowBox[{"{", + RowBox[{"Red", ",", + RowBox[{"PointSize", "[", "Large", "]"}], ",", + RowBox[{"Point", "[", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{"r", ",", + SqrtBox["r"]}], "}"}], ",", + RowBox[{"{", + RowBox[{"r", ",", + RowBox[{"-", + SqrtBox["r"]}]}], "}"}]}], "}"}], "]"}], ",", "White", + ",", + RowBox[{"PointSize", "[", "Medium", "]"}], ",", + RowBox[{"Point", "[", + RowBox[{"{", + RowBox[{"r", ",", + SqrtBox["r"]}], "}"}], "]"}]}], "}"}], "]"}], ",", + RowBox[{"Graphics", "[", + RowBox[{"{", "}"}], "]"}]}], "]"}]}], "]"}]}], "}"}], "}"}], + "]"}], ",", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{"r", ",", "1"}], "}"}], ",", + RowBox[{"-", "2"}], ",", "2"}], "}"}]}], "]"}]], "Input", + CellChangeTimes->{{3.77713657768003*^9, 3.7771365828765388`*^9}, { + 3.7771370214122696`*^9, 3.7771370243627615`*^9}, {3.7771371027777557`*^9, + 3.777137152180356*^9}, {3.777137522168996*^9, 3.7771379841682105`*^9}, { + 3.7771380242901864`*^9, 3.7771384015864058`*^9}, {3.7771385034820766`*^9, + 3.7771385543943424`*^9}}], + +Cell[BoxData[ + TagBox[ + StyleBox[ + DynamicModuleBox[{$CellContext`r$$ = 1, Typeset`show$$ = True, + Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", + Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = + "\"untitled\"", Typeset`specs$$ = {{{ + Hold[$CellContext`r$$], 1}, -2, 2}}, Typeset`size$$ = { + 387., {96.5, 102.5}}, Typeset`update$$ = 0, Typeset`initDone$$, + Typeset`skipInitDone$$ = True, $CellContext`r$359$$ = 0}, + DynamicBox[Manipulate`ManipulateBoxes[ + 1, StandardForm, "Variables" :> {$CellContext`r$$ = 1}, + "ControllerVariables" :> { + Hold[$CellContext`r$$, $CellContext`r$359$$, 0]}, + "OtherVariables" :> { + Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, + Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, + Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, + Typeset`skipInitDone$$}, "Body" :> TableForm[{{ + Show[ + + StreamPlot[{ + 1, $CellContext`x^2 - $CellContext`r$$}, {$CellContext`t, -2, + 2}, {$CellContext`x, -2, 2}, PlotLabel -> + "stream plot (x versus t)"], + If[$CellContext`r$$ >= 0, + Graphics[{Red, Thick, + + Line[{{-2, -Sqrt[$CellContext`r$$]}, { + 2, -Sqrt[$CellContext`r$$]}}], Dashed, + Line[{{-2, + Sqrt[$CellContext`r$$]}, {2, + Sqrt[$CellContext`r$$]}}]}], + Graphics[{}]]], + Show[ + Plot[{ + + Piecewise[{{-Sqrt[$CellContext`rr], $CellContext`rr >= 0}}, + Nothing], + Piecewise[{{ + Sqrt[$CellContext`rr], $CellContext`rr >= 0}}, + Nothing]}, {$CellContext`rr, -2.001, $CellContext`r$$}, + PlotStyle -> { + Directive[Red, Thick], + Directive[Red, Thick, Dashed]}, PlotRange -> {{-2, 2}, {-2, 2}}, + AspectRatio -> 1, Frame -> True, Axes -> False, PlotLabel -> + "equilibria (\!\(\*SuperscriptBox[\(x\), \(*\)]\) versus r)"], + If[$CellContext`r$$ >= 0, + Graphics[{Red, + PointSize[Large], + Point[{{$CellContext`r$$, + Sqrt[$CellContext`r$$]}, {$CellContext`r$$, - + Sqrt[$CellContext`r$$]}}], White, + PointSize[Medium], + Point[{$CellContext`r$$, + Sqrt[$CellContext`r$$]}]}], + Graphics[{}]]]}}], + "Specifications" :> {{{$CellContext`r$$, 1}, -2, 2}}, "Options" :> {}, + "DefaultOptions" :> {}], + ImageSizeCache->{438., {144., 150.}}, + SingleEvaluation->True], + Deinitialization:>None, + DynamicModuleValues:>{}, + SynchronousInitialization->True, + UndoTrackedVariables:>{Typeset`show$$, Typeset`bookmarkMode$$}, + UnsavedVariables:>{Typeset`initDone$$}, + UntrackedVariables:>{Typeset`size$$}], "Manipulate", + Deployed->True, + StripOnInput->False], + Manipulate`InterpretManipulate[1]]], "Output", + CellChangeTimes->{{3.7771379244304895`*^9, 3.777137972818993*^9}, { + 3.777138035688207*^9, 3.7771380603054132`*^9}, {3.7771381204860187`*^9, + 3.777138178429568*^9}, {3.777138214210326*^9, 3.7771382557136283`*^9}, { + 3.777138298547415*^9, 3.777138305909398*^9}, 3.777138364876514*^9, + 3.777138402049615*^9, 3.7771385562984977`*^9, 3.7771428359485655`*^9}] +}, Open ]] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Transcritical Bifurcation", "Section", + CellChangeTimes->{{3.7766008885632277`*^9, 3.7766008904796133`*^9}, { + 3.777136401274056*^9, 3.777136416298379*^9}, {3.7771407765357695`*^9, + 3.7771407784342155`*^9}}], + +Cell["\<\ +A transcritical bifurcation occurs when two equilibria \ +\[OpenCurlyDoubleQuote]slide past\[CloseCurlyDoubleQuote] each other and swap \ +stabilities when they collide. The example below concerns the 1D system:\ +\>", "Text", + CellChangeTimes->{{3.777136412348218*^9, 3.777136502673601*^9}, { + 3.777140654593788*^9, 3.77714069874934*^9}, {3.7771407816953983`*^9, + 3.7771408255748434`*^9}, {3.7771416017729793`*^9, 3.7771416437784433`*^9}}], + +Cell[BoxData[Cell[TextData[Cell[BoxData[ + FormBox[ + RowBox[{ + FractionBox[ + RowBox[{"\[DifferentialD]", "x"}], + RowBox[{"\[DifferentialD]", "t"}]], "=", + RowBox[{ + SuperscriptBox["x", "2"], "-", + RowBox[{"r", " ", "x"}]}]}], TraditionalForm]], + FormatType->"TraditionalForm"]], "DisplayFormula"]], "Text", + CellChangeTimes->{{3.77713651537531*^9, 3.7771365309974613`*^9}, + 3.7771366535696325`*^9, {3.7771370336200256`*^9, 3.7771370357424736`*^9}, { + 3.777140833863779*^9, 3.7771408342711344`*^9}}], + +Cell[TextData[{ + "Setting ", + Cell[BoxData[ + FormBox[ + RowBox[{ + FractionBox[ + RowBox[{"\[DifferentialD]", "x"}], + RowBox[{"\[DifferentialD]", "t"}]], "=", "0"}], TraditionalForm]], + FormatType->"TraditionalForm"], + " and solving, we find that the equilibria are ", + Cell[BoxData[ + FormBox[ + RowBox[{ + SuperscriptBox["x", "*"], "=", "0"}], TraditionalForm]], + FormatType->"TraditionalForm"], + " and ", + Cell[BoxData[ + FormBox[ + RowBox[{ + SuperscriptBox["x", "*"], "=", "r"}], TraditionalForm]], + FormatType->"TraditionalForm"], + ". For ", + Cell[BoxData[ + FormBox[ + RowBox[{"r", "\[NotEqual]", "0"}], TraditionalForm]], + FormatType->"TraditionalForm"], + " this is two separate equilibria while for ", + Cell[BoxData[ + FormBox[ + RowBox[{"r", "=", "0"}], TraditionalForm]], + FormatType->"TraditionalForm"], + " the two coincide." +}], "Text", + CellChangeTimes->{{3.7771366384229493`*^9, 3.777136834022626*^9}, { + 3.777136865290258*^9, 3.77713686612399*^9}, {3.77713704004583*^9, + 3.77713704004583*^9}, {3.777140854183094*^9, 3.7771408949826183`*^9}}], + +Cell[TextData[{ + "We can conduct stability analysis by evaluating ", + Cell[BoxData[ + FormBox[ + RowBox[{ + RowBox[{ + FractionBox["\[PartialD]", + RowBox[{"\[PartialD]", "x"}]], + RowBox[{"(", + RowBox[{ + SuperscriptBox["x", "2"], "-", + RowBox[{"r", " ", "x"}]}], ")"}]}], "=", + RowBox[{ + RowBox[{"2", "x"}], "-", "r"}]}], TraditionalForm]], + FormatType->"TraditionalForm"], + " at ", + Cell[BoxData[ + FormBox[ + RowBox[{"x", "=", "0"}], TraditionalForm]], + FormatType->"TraditionalForm"], + " and ", + Cell[BoxData[ + FormBox[ + RowBox[{"x", "=", "r"}], TraditionalForm]], + FormatType->"TraditionalForm"], + ". We will consider the two cases separately:" +}], "Text", + CellChangeTimes->{{3.7771369512069955`*^9, 3.777136989791237*^9}, { + 3.777137243411868*^9, 3.7771372995028796`*^9}, {3.7771373330059586`*^9, + 3.777137413841439*^9}, {3.7771374519786773`*^9, 3.777137512637171*^9}, { + 3.777140903749477*^9, 3.7771409616009216`*^9}}], + +Cell[CellGroupData[{ + +Cell[TextData[{ + "For ", + Cell[BoxData[ + FormBox[ + RowBox[{"x", "=", "0"}], TraditionalForm]], + FormatType->"TraditionalForm"], + " the Jacobian is ", + Cell[BoxData[ + FormBox[ + RowBox[{"-", "r"}], TraditionalForm]], + FormatType->"TraditionalForm"], + ", which is obviously negative (and thus stable) for ", + Cell[BoxData[ + FormBox[ + RowBox[{"r", ">", "0"}], TraditionalForm]], + FormatType->"TraditionalForm"], + " and positive (and thus unstable) for ", + Cell[BoxData[ + FormBox[ + RowBox[{"r", "<", "0"}], TraditionalForm]], + FormatType->"TraditionalForm"], + "." +}], "Item", + CellChangeTimes->{{3.777140974403208*^9, 3.7771410170516787`*^9}}], + +Cell[TextData[{ + "For ", + Cell[BoxData[ + FormBox[ + RowBox[{"x", "=", "r"}], TraditionalForm]], + FormatType->"TraditionalForm"], + " the Jacobian is ", + Cell[BoxData[ + FormBox["r", TraditionalForm]], + FormatType->"TraditionalForm"], + ", which is positive (and thus unstable) for ", + Cell[BoxData[ + FormBox[ + RowBox[{"r", ">", "0"}], TraditionalForm]], + FormatType->"TraditionalForm"], + " and negative (and thus stable) for ", + Cell[BoxData[ + FormBox[ + RowBox[{"r", "<", "0"}], TraditionalForm]], + FormatType->"TraditionalForm"], + "." +}], "Item", + CellChangeTimes->{{3.777140974403208*^9, 3.7771410546510034`*^9}}] +}, Open ]], + +Cell[TextData[{ + "The two equilibria always have opposite stabilities whether ", + Cell[BoxData[ + FormBox[ + RowBox[{"r", "<", "0"}], TraditionalForm]], + FormatType->"TraditionalForm"], + " or ", + Cell[BoxData[ + FormBox[ + RowBox[{"r", ">", "0"}], TraditionalForm]], + FormatType->"TraditionalForm"], + "." +}], "Text", + CellChangeTimes->{{3.7771410673018804`*^9, 3.77714109176895*^9}}], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Manipulate", "[", + RowBox[{ + RowBox[{"TableForm", "[", + RowBox[{"{", + RowBox[{"{", + RowBox[{ + RowBox[{"Show", "[", + RowBox[{ + RowBox[{"StreamPlot", "[", + RowBox[{ + RowBox[{"{", + RowBox[{"1", ",", + RowBox[{ + SuperscriptBox["x", "2"], "-", + RowBox[{"r", " ", "x"}]}]}], "}"}], ",", + RowBox[{"{", + RowBox[{"t", ",", + RowBox[{"-", "2"}], ",", "2"}], "}"}], ",", + RowBox[{"{", + RowBox[{"x", ",", + RowBox[{"-", "2"}], ",", "2"}], "}"}], ",", + RowBox[{ + "PlotLabel", "\[Rule]", "\"\\""}]}], + "]"}], ",", + RowBox[{"If", "[", + RowBox[{ + RowBox[{"r", "\[GreaterEqual]", "0"}], ",", + RowBox[{"Graphics", "[", + RowBox[{"{", + RowBox[{"Red", ",", "Thick", ",", + RowBox[{"Line", "[", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{"-", "2"}], ",", "0"}], "}"}], ",", + RowBox[{"{", + RowBox[{"2", ",", "0"}], "}"}]}], "}"}], "]"}], ",", + "Dashed", ",", + RowBox[{"Line", "[", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{"-", "2"}], ",", "r"}], "}"}], ",", + RowBox[{"{", + RowBox[{"2", ",", "r"}], "}"}]}], "}"}], "]"}]}], "}"}], + "]"}], ",", + RowBox[{"Graphics", "[", + RowBox[{"{", + RowBox[{"Red", ",", "Thick", ",", + RowBox[{"Line", "[", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{"-", "2"}], ",", "r"}], "}"}], ",", + RowBox[{"{", + RowBox[{"2", ",", "r"}], "}"}]}], "}"}], "]"}], ",", + "Dashed", ",", + RowBox[{"Line", "[", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{"-", "2"}], ",", "0"}], "}"}], ",", + RowBox[{"{", + RowBox[{"2", ",", "0"}], "}"}]}], "}"}], "]"}]}], "}"}], + "]"}]}], "]"}]}], "]"}], ",", + RowBox[{"Show", "[", + RowBox[{ + RowBox[{"Plot", "[", + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{"Piecewise", "[", + RowBox[{ + RowBox[{"{", + RowBox[{"{", + RowBox[{"rr", ",", + RowBox[{"rr", "\[GreaterEqual]", "0"}]}], "}"}], "}"}], ",", + "0"}], "]"}], ",", + RowBox[{"Piecewise", "[", + RowBox[{ + RowBox[{"{", + RowBox[{"{", + RowBox[{"0", ",", + RowBox[{"rr", "\[GreaterEqual]", "0"}]}], "}"}], "}"}], ",", + "rr"}], "]"}]}], "}"}], ",", + RowBox[{"{", + RowBox[{"rr", ",", + RowBox[{"-", "2.001"}], ",", "r"}], "}"}], ",", + RowBox[{"PlotStyle", "\[Rule]", + RowBox[{"{", + RowBox[{ + RowBox[{"Directive", "[", + RowBox[{"Red", ",", "Thick", ",", "Dashed"}], "]"}], ",", + RowBox[{"Directive", "[", + RowBox[{"Red", ",", "Thick"}], "]"}]}], "}"}]}], ",", + RowBox[{"PlotRange", "\[Rule]", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{"-", "2"}], ",", "2"}], "}"}], ",", + RowBox[{"{", + RowBox[{ + RowBox[{"-", "2"}], ",", "2"}], "}"}]}], "}"}]}], ",", + RowBox[{"AspectRatio", "\[Rule]", "1"}], ",", + RowBox[{"Frame", "\[Rule]", "True"}], ",", + RowBox[{"Axes", "\[Rule]", "False"}], ",", + RowBox[{ + "PlotLabel", "\[Rule]", + "\"\\ +\""}]}], "]"}], ",", + RowBox[{"If", "[", + RowBox[{ + RowBox[{"r", "\[GreaterEqual]", "0"}], ",", + RowBox[{"Graphics", "[", + RowBox[{"{", + RowBox[{"Red", ",", + RowBox[{"PointSize", "[", "Large", "]"}], ",", + RowBox[{"Point", "[", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{"r", ",", "0"}], "}"}], ",", + RowBox[{"{", + RowBox[{"r", ",", "r"}], "}"}]}], "}"}], "]"}], ",", + "White", ",", + RowBox[{"PointSize", "[", "Medium", "]"}], ",", + RowBox[{"Point", "[", + RowBox[{"{", + RowBox[{"r", ",", "r"}], "}"}], "]"}]}], "}"}], "]"}], ",", + RowBox[{"Graphics", "[", + RowBox[{"{", + RowBox[{"Red", ",", + RowBox[{"PointSize", "[", "Large", "]"}], ",", + RowBox[{"Point", "[", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{"r", ",", "0"}], "}"}], ",", + RowBox[{"{", + RowBox[{"r", ",", "r"}], "}"}]}], "}"}], "]"}], ",", + "White", ",", + RowBox[{"PointSize", "[", "Medium", "]"}], ",", + RowBox[{"Point", "[", + RowBox[{"{", + RowBox[{"r", ",", "0"}], "}"}], "]"}]}], "}"}], "]"}]}], + "]"}]}], "]"}]}], "}"}], "}"}], "]"}], ",", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{"r", ",", "1"}], "}"}], ",", + RowBox[{"-", "2"}], ",", "2"}], "}"}]}], "]"}]], "Input", + CellChangeTimes->{{3.77713657768003*^9, 3.7771365828765388`*^9}, { + 3.7771370214122696`*^9, 3.7771370243627615`*^9}, {3.7771371027777557`*^9, + 3.777137152180356*^9}, {3.777137522168996*^9, 3.7771379841682105`*^9}, { + 3.7771380242901864`*^9, 3.7771384015864058`*^9}, {3.7771385034820766`*^9, + 3.7771385543943424`*^9}, {3.7771411102948675`*^9, 3.777141110664283*^9}, { + 3.777141140776102*^9, 3.7771412353779545`*^9}, {3.777141270010955*^9, + 3.777141270194441*^9}, {3.7771413011098766`*^9, 3.7771413385613546`*^9}, { + 3.7771413736412973`*^9, 3.7771414370261106`*^9}}], + +Cell[BoxData[ + TagBox[ + StyleBox[ + DynamicModuleBox[{$CellContext`r$$ = 1, Typeset`show$$ = True, + Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", + Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = + "\"untitled\"", Typeset`specs$$ = {{{ + Hold[$CellContext`r$$], 1}, -2, 2}}, Typeset`size$$ = { + 387., {96.5, 102.5}}, Typeset`update$$ = 0, Typeset`initDone$$, + Typeset`skipInitDone$$ = True, $CellContext`r$1744$$ = 0}, + DynamicBox[Manipulate`ManipulateBoxes[ + 1, StandardForm, "Variables" :> {$CellContext`r$$ = 1}, + "ControllerVariables" :> { + Hold[$CellContext`r$$, $CellContext`r$1744$$, 0]}, + "OtherVariables" :> { + Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, + Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, + Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, + Typeset`skipInitDone$$}, "Body" :> TableForm[{{ + Show[ + + StreamPlot[{ + 1, $CellContext`x^2 - $CellContext`r$$ $CellContext`x}, \ +{$CellContext`t, -2, 2}, {$CellContext`x, -2, 2}, PlotLabel -> + "stream plot (x versus t)"], + If[$CellContext`r$$ >= 0, + Graphics[{Red, Thick, + Line[{{-2, 0}, {2, 0}}], Dashed, + Line[{{-2, $CellContext`r$$}, {2, $CellContext`r$$}}]}], + Graphics[{Red, Thick, + Line[{{-2, $CellContext`r$$}, {2, $CellContext`r$$}}], Dashed, + Line[{{-2, 0}, {2, 0}}]}]]], + Show[ + Plot[{ + Piecewise[{{$CellContext`rr, $CellContext`rr >= 0}}, 0], + + Piecewise[{{ + 0, $CellContext`rr >= + 0}}, $CellContext`rr]}, {$CellContext`rr, -2.001, \ +$CellContext`r$$}, PlotStyle -> { + Directive[Red, Thick, Dashed], + Directive[Red, Thick]}, PlotRange -> {{-2, 2}, {-2, 2}}, + AspectRatio -> 1, Frame -> True, Axes -> False, PlotLabel -> + "equilibria (\!\(\*SuperscriptBox[\(x\), \(*\)]\) versus r)"], + If[$CellContext`r$$ >= 0, + Graphics[{Red, + PointSize[Large], + + Point[{{$CellContext`r$$, + 0}, {$CellContext`r$$, $CellContext`r$$}}], White, + PointSize[Medium], + Point[{$CellContext`r$$, $CellContext`r$$}]}], + Graphics[{Red, + PointSize[Large], + + Point[{{$CellContext`r$$, + 0}, {$CellContext`r$$, $CellContext`r$$}}], White, + PointSize[Medium], + Point[{$CellContext`r$$, 0}]}]]]}}], + "Specifications" :> {{{$CellContext`r$$, 1}, -2, 2}}, "Options" :> {}, + "DefaultOptions" :> {}], + ImageSizeCache->{438., {144., 150.}}, + SingleEvaluation->True], + Deinitialization:>None, + DynamicModuleValues:>{}, + SynchronousInitialization->True, + UndoTrackedVariables:>{Typeset`show$$, Typeset`bookmarkMode$$}, + UnsavedVariables:>{Typeset`initDone$$}, + UntrackedVariables:>{Typeset`size$$}], "Manipulate", + Deployed->True, + StripOnInput->False], + Manipulate`InterpretManipulate[1]]], "Output", + CellChangeTimes->{{3.7771379244304895`*^9, 3.777137972818993*^9}, { + 3.777138035688207*^9, 3.7771380603054132`*^9}, {3.7771381204860187`*^9, + 3.777138178429568*^9}, {3.777138214210326*^9, 3.7771382557136283`*^9}, { + 3.777138298547415*^9, 3.777138305909398*^9}, 3.777138364876514*^9, + 3.777138402049615*^9, 3.7771385562984977`*^9, 3.7771411143651175`*^9, { + 3.777141152356468*^9, 3.7771412366219435`*^9}, {3.7771412827529573`*^9, + 3.777141338939087*^9}, 3.7771413788874207`*^9, {3.777141419528529*^9, + 3.7771414375930433`*^9}, 3.7771428381608877`*^9}] +}, Open ]] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Pitchfork Bifurcation", "Section", + CellChangeTimes->{{3.7766008885632277`*^9, 3.7766008904796133`*^9}, { + 3.777136401274056*^9, 3.777136416298379*^9}, {3.7771415021019964`*^9, + 3.777141503857136*^9}}], + +Cell["\<\ +A pitchfork bifurcation occurs when a single equilibrium splits into three \ +(or, if moving in the other direction, when three equilibria merge to result \ +in a single equilibrium). This is similar to a saddle-node bifurcation, \ +except that one equilibrium remains real regardless of the other two. The \ +example below concerns the 1D system:\ +\>", "Text", + CellChangeTimes->{{3.777136412348218*^9, 3.777136502673601*^9}, { + 3.777140654593788*^9, 3.77714069874934*^9}, {3.77714150735085*^9, + 3.7771415679562902`*^9}, {3.777141646656042*^9, 3.777141646985199*^9}}], + +Cell[BoxData[Cell[TextData[Cell[BoxData[ + FormBox[ + RowBox[{ + FractionBox[ + RowBox[{"\[DifferentialD]", "x"}], + RowBox[{"\[DifferentialD]", "t"}]], "=", + RowBox[{ + SuperscriptBox["x", "3"], "-", + RowBox[{"r", " ", "x"}]}]}], TraditionalForm]], + FormatType->"TraditionalForm"]], "DisplayFormula"]], "Text", + CellChangeTimes->{{3.77713651537531*^9, 3.7771365309974613`*^9}, + 3.7771366535696325`*^9, {3.7771370336200256`*^9, 3.7771370357424736`*^9}, { + 3.7771415732464447`*^9, 3.7771415756351213`*^9}}], + +Cell[TextData[{ + "Setting ", + Cell[BoxData[ + FormBox[ + RowBox[{ + FractionBox[ + RowBox[{"\[DifferentialD]", "x"}], + RowBox[{"\[DifferentialD]", "t"}]], "=", "0"}], TraditionalForm]], + FormatType->"TraditionalForm"], + " and solving, we find that the equilibria are ", + Cell[BoxData[ + FormBox[ + RowBox[{ + SuperscriptBox["x", "*"], "\[Element]", + RowBox[{"{", + RowBox[{ + RowBox[{"-", + SqrtBox["r"]}], ",", "0", ",", + SqrtBox["r"]}], "}"}]}], TraditionalForm]], + FormatType->"TraditionalForm"], + ". ", + Cell[BoxData[ + FormBox[ + RowBox[{ + SuperscriptBox["x", "*"], "=", "0"}], TraditionalForm]], + FormatType->"TraditionalForm"], + " is constant and does not change as ", + Cell[BoxData[ + FormBox["r", TraditionalForm]], + FormatType->"TraditionalForm"], + " changes, while ", + Cell[BoxData[ + FormBox[ + RowBox[{ + SuperscriptBox["x", "*"], "=", + RowBox[{"\[PlusMinus]", + SqrtBox["r"]}]}], TraditionalForm]], + FormatType->"TraditionalForm"], + " depend on the sign of ", + Cell[BoxData[ + FormBox["r", TraditionalForm]], + FormatType->"TraditionalForm"], + ". Going through the same process as for the saddle-node bifurcation above, \ +we find that ", + Cell[BoxData[ + FormBox[ + RowBox[{"r", ">", "0"}], TraditionalForm]], + FormatType->"TraditionalForm"], + " results in both being real, ", + Cell[BoxData[ + FormBox[ + RowBox[{"r", "<", "0"}], TraditionalForm]], + FormatType->"TraditionalForm"], + " results in both being imaginary, and ", + Cell[BoxData[ + FormBox[ + RowBox[{"r", "=", "0"}], TraditionalForm]], + FormatType->"TraditionalForm"], + " results in both merging and coinciding with ", + Cell[BoxData[ + FormBox[ + RowBox[{ + SuperscriptBox["x", "*"], "=", "0"}], TraditionalForm]], + FormatType->"TraditionalForm"], + "." +}], "Text", + CellChangeTimes->{{3.7771366384229493`*^9, 3.777136834022626*^9}, { + 3.777136865290258*^9, 3.77713686612399*^9}, {3.77713704004583*^9, + 3.77713704004583*^9}, {3.7771416556914363`*^9, 3.777141821658723*^9}}], + +Cell[TextData[{ + "We can conduct stability analysis by evaluating ", + Cell[BoxData[ + FormBox[ + RowBox[{ + RowBox[{ + FractionBox["\[PartialD]", + RowBox[{"\[PartialD]", "x"}]], + RowBox[{"(", + RowBox[{ + SuperscriptBox["x", "3"], "-", + RowBox[{"r", " ", "x"}]}], ")"}]}], "=", + RowBox[{ + RowBox[{"3", + SuperscriptBox["x", "2"]}], "-", "r"}]}], TraditionalForm]], + FormatType->"TraditionalForm"], + " at ", + Cell[BoxData[ + FormBox[ + RowBox[{"x", "=", "0"}], TraditionalForm]], + FormatType->"TraditionalForm"], + " and ", + Cell[BoxData[ + FormBox[ + RowBox[{"x", "=", + RowBox[{"\[PlusMinus]", + SqrtBox["r"]}]}], TraditionalForm]], + FormatType->"TraditionalForm"], + ". If ", + Cell[BoxData[ + FormBox[ + RowBox[{"x", "=", "0"}], TraditionalForm]], + FormatType->"TraditionalForm"], + " then the Jacobian is ", + Cell[BoxData[ + FormBox[ + RowBox[{"-", "r"}], TraditionalForm]], + FormatType->"TraditionalForm"], + ", which always has a sign opposite ", + Cell[BoxData[ + FormBox["r", TraditionalForm]], + FormatType->"TraditionalForm"], + ". If ", + Cell[BoxData[ + FormBox[ + RowBox[{"x", "=", + RowBox[{"\[PlusMinus]", + SqrtBox["r"]}]}], TraditionalForm]], + FormatType->"TraditionalForm"], + " then the Jacobian is ", + Cell[BoxData[ + FormBox[ + RowBox[{"2", "r"}], TraditionalForm]], + FormatType->"TraditionalForm"], + ", which always has a sign the same as ", + Cell[BoxData[ + FormBox["r", TraditionalForm]], + FormatType->"TraditionalForm"], + ". The overall conclusion is that for ", + Cell[BoxData[ + FormBox[ + RowBox[{"r", "<", "0"}], TraditionalForm]], + FormatType->"TraditionalForm"], + " we have a single unstable equilibrium at ", + Cell[BoxData[ + FormBox[ + RowBox[{ + SuperscriptBox["x", "*"], "=", "0"}], TraditionalForm]], + FormatType->"TraditionalForm"], + ", while for ", + Cell[BoxData[ + FormBox[ + RowBox[{"r", ">", "0"}], TraditionalForm]], + FormatType->"TraditionalForm"], + " we have three equilibria: a stable equilibrium at ", + Cell[BoxData[ + FormBox[ + RowBox[{ + SuperscriptBox["x", "*"], "=", "0"}], TraditionalForm]], + FormatType->"TraditionalForm"], + " and two unstable equilibria at ", + Cell[BoxData[ + FormBox[ + RowBox[{ + SuperscriptBox["x", "*"], "=", + RowBox[{"\[PlusMinus]", + SqrtBox["r"]}]}], TraditionalForm]], + FormatType->"TraditionalForm"], + "." +}], "Text", + CellChangeTimes->{{3.7771369512069955`*^9, 3.777136989791237*^9}, { + 3.777137243411868*^9, 3.7771372995028796`*^9}, {3.7771373330059586`*^9, + 3.777137413841439*^9}, {3.7771374519786773`*^9, 3.777137512637171*^9}, { + 3.7771418289521384`*^9, 3.777142054907627*^9}}], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Manipulate", "[", + RowBox[{ + RowBox[{"TableForm", "[", + RowBox[{"{", + RowBox[{"{", + RowBox[{ + RowBox[{"Show", "[", + RowBox[{ + RowBox[{"StreamPlot", "[", + RowBox[{ + RowBox[{"{", + RowBox[{"1", ",", + RowBox[{ + SuperscriptBox["x", "3"], "-", + RowBox[{"r", " ", "x"}]}]}], "}"}], ",", + RowBox[{"{", + RowBox[{"t", ",", + RowBox[{"-", "2"}], ",", "2"}], "}"}], ",", + RowBox[{"{", + RowBox[{"x", ",", + RowBox[{"-", "2"}], ",", "2"}], "}"}], ",", + RowBox[{ + "PlotLabel", "\[Rule]", "\"\\""}]}], + "]"}], ",", + RowBox[{"If", "[", + RowBox[{ + RowBox[{"r", "\[GreaterEqual]", "0"}], ",", + RowBox[{"Graphics", "[", + RowBox[{"{", + RowBox[{"Red", ",", "Thick", ",", + RowBox[{"Line", "[", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{"-", "2"}], ",", "0"}], "}"}], ",", + RowBox[{"{", + RowBox[{"2", ",", "0"}], "}"}]}], "}"}], "]"}], ",", + "Dashed", ",", + RowBox[{"Line", "[", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{"-", "2"}], ",", + SqrtBox["r"]}], "}"}], ",", + RowBox[{"{", + RowBox[{"2", ",", + SqrtBox["r"]}], "}"}]}], "}"}], "]"}], ",", + RowBox[{"Line", "[", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{"-", "2"}], ",", + RowBox[{"-", + SqrtBox["r"]}]}], "}"}], ",", + RowBox[{"{", + RowBox[{"2", ",", + RowBox[{"-", + SqrtBox["r"]}]}], "}"}]}], "}"}], "]"}]}], "}"}], "]"}], + ",", + RowBox[{"Graphics", "[", + RowBox[{"{", + RowBox[{"Red", ",", "Thick", ",", "Dashed", ",", + RowBox[{"Line", "[", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{"-", "2"}], ",", "0"}], "}"}], ",", + RowBox[{"{", + RowBox[{"2", ",", "0"}], "}"}]}], "}"}], "]"}]}], "}"}], + "]"}]}], "]"}]}], "]"}], ",", + RowBox[{"Show", "[", + RowBox[{ + RowBox[{"Plot", "[", + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{"Piecewise", "[", + RowBox[{ + RowBox[{"{", + RowBox[{"{", + RowBox[{ + RowBox[{"-", + SqrtBox["rr"]}], ",", + RowBox[{"rr", "\[GreaterEqual]", "0"}]}], "}"}], "}"}], ",", + "Nothing"}], "]"}], ",", + RowBox[{"Piecewise", "[", + RowBox[{ + RowBox[{"{", + RowBox[{"{", + RowBox[{ + SqrtBox["rr"], ",", + RowBox[{"rr", "\[GreaterEqual]", "0"}]}], "}"}], "}"}], ",", + "Nothing"}], "]"}], ",", + RowBox[{"Piecewise", "[", + RowBox[{ + RowBox[{"{", + RowBox[{"{", + RowBox[{"0", ",", + RowBox[{"rr", "\[GreaterEqual]", "0"}]}], "}"}], "}"}], ",", + "Nothing"}], "]"}], ",", + RowBox[{"Piecewise", "[", + RowBox[{ + RowBox[{"{", + RowBox[{"{", + RowBox[{"0", ",", + RowBox[{"rr", "<", "0"}]}], "}"}], "}"}], ",", "Nothing"}], + "]"}]}], "}"}], ",", + RowBox[{"{", + RowBox[{"rr", ",", + RowBox[{"-", "2.001"}], ",", "r"}], "}"}], ",", + RowBox[{"PlotStyle", "\[Rule]", + RowBox[{"{", + RowBox[{ + RowBox[{"Directive", "[", + RowBox[{"Red", ",", "Thick", ",", "Dashed"}], "]"}], ",", + RowBox[{"Directive", "[", + RowBox[{"Red", ",", "Thick", ",", "Dashed"}], "]"}], ",", + RowBox[{"Directive", "[", + RowBox[{"Red", ",", "Thick"}], "]"}], ",", + RowBox[{"Directive", "[", + RowBox[{"Red", ",", "Thick", ",", "Dashed"}], "]"}]}], "}"}]}], + ",", + RowBox[{"PlotRange", "\[Rule]", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{"-", "2"}], ",", "2"}], "}"}], ",", + RowBox[{"{", + RowBox[{ + RowBox[{"-", "2"}], ",", "2"}], "}"}]}], "}"}]}], ",", + RowBox[{"AspectRatio", "\[Rule]", "1"}], ",", + RowBox[{"Frame", "\[Rule]", "True"}], ",", + RowBox[{"Axes", "\[Rule]", "False"}], ",", + RowBox[{ + "PlotLabel", "\[Rule]", + "\"\\ +\""}]}], "]"}], ",", + RowBox[{"If", "[", + RowBox[{ + RowBox[{"r", "\[GreaterEqual]", "0"}], ",", + RowBox[{"Graphics", "[", + RowBox[{"{", + RowBox[{"Red", ",", + RowBox[{"PointSize", "[", "Large", "]"}], ",", + RowBox[{"Point", "[", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{"r", ",", + SqrtBox["r"]}], "}"}], ",", + RowBox[{"{", + RowBox[{"r", ",", + RowBox[{"-", + SqrtBox["r"]}]}], "}"}], ",", + RowBox[{"{", + RowBox[{"r", ",", "0"}], "}"}]}], "}"}], "]"}], ",", + "White", ",", + RowBox[{"PointSize", "[", "Medium", "]"}], ",", + RowBox[{"Point", "[", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{"r", ",", + SqrtBox["r"]}], "}"}], ",", + RowBox[{"{", + RowBox[{"r", ",", + RowBox[{"-", + SqrtBox["r"]}]}], "}"}]}], "}"}], "]"}]}], "}"}], "]"}], + ",", + RowBox[{"Graphics", "[", + RowBox[{"{", + RowBox[{"Red", ",", + RowBox[{"PointSize", "[", "Large", "]"}], ",", + RowBox[{"Point", "[", + RowBox[{"{", + RowBox[{"r", ",", "0"}], "}"}], "]"}], ",", "White", ",", + RowBox[{"PointSize", "[", "Medium", "]"}], ",", + RowBox[{"Point", "[", + RowBox[{"{", + RowBox[{"r", ",", "0"}], "}"}], "]"}]}], "}"}], "]"}]}], + "]"}]}], "]"}]}], "}"}], "}"}], "]"}], ",", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{"r", ",", "1"}], "}"}], ",", + RowBox[{"-", "2"}], ",", "2"}], "}"}]}], "]"}]], "Input", + CellChangeTimes->{{3.77713657768003*^9, 3.7771365828765388`*^9}, { + 3.7771370214122696`*^9, 3.7771370243627615`*^9}, {3.7771371027777557`*^9, + 3.777137152180356*^9}, {3.777137522168996*^9, 3.7771379841682105`*^9}, { + 3.7771380242901864`*^9, 3.7771384015864058`*^9}, {3.7771385034820766`*^9, + 3.7771385543943424`*^9}, {3.7771420666214676`*^9, 3.777142122868834*^9}, { + 3.7771421668529077`*^9, 3.777142311824276*^9}}], + +Cell[BoxData[ + TagBox[ + StyleBox[ + DynamicModuleBox[{$CellContext`r$$ = 1, Typeset`show$$ = True, + Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", + Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = + "\"untitled\"", Typeset`specs$$ = {{{ + Hold[$CellContext`r$$], 1}, -2, 2}}, Typeset`size$$ = { + 387., {96.5, 102.5}}, Typeset`update$$ = 0, Typeset`initDone$$, + Typeset`skipInitDone$$ = True, $CellContext`r$2240$$ = 0}, + DynamicBox[Manipulate`ManipulateBoxes[ + 1, StandardForm, "Variables" :> {$CellContext`r$$ = 1}, + "ControllerVariables" :> { + Hold[$CellContext`r$$, $CellContext`r$2240$$, 0]}, + "OtherVariables" :> { + Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, + Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, + Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, + Typeset`skipInitDone$$}, "Body" :> TableForm[{{ + Show[ + + StreamPlot[{ + 1, $CellContext`x^3 - $CellContext`r$$ $CellContext`x}, \ +{$CellContext`t, -2, 2}, {$CellContext`x, -2, 2}, PlotLabel -> + "stream plot (x versus t)"], + If[$CellContext`r$$ >= 0, + Graphics[{Red, Thick, + Line[{{-2, 0}, {2, 0}}], Dashed, + Line[{{-2, + Sqrt[$CellContext`r$$]}, {2, + Sqrt[$CellContext`r$$]}}], + + Line[{{-2, -Sqrt[$CellContext`r$$]}, { + 2, -Sqrt[$CellContext`r$$]}}]}], + Graphics[{Red, Thick, Dashed, + Line[{{-2, 0}, {2, 0}}]}]]], + Show[ + Plot[{ + + Piecewise[{{-Sqrt[$CellContext`rr], $CellContext`rr >= 0}}, + Nothing], + Piecewise[{{ + Sqrt[$CellContext`rr], $CellContext`rr >= 0}}, Nothing], + Piecewise[{{0, $CellContext`rr >= 0}}, Nothing], + + Piecewise[{{0, $CellContext`rr < 0}}, + Nothing]}, {$CellContext`rr, -2.001, $CellContext`r$$}, + PlotStyle -> { + Directive[Red, Thick, Dashed], + Directive[Red, Thick, Dashed], + Directive[Red, Thick], + Directive[Red, Thick, Dashed]}, PlotRange -> {{-2, 2}, {-2, 2}}, + AspectRatio -> 1, Frame -> True, Axes -> False, PlotLabel -> + "equilibria (\!\(\*SuperscriptBox[\(x\), \(*\)]\) versus r)"], + If[$CellContext`r$$ >= 0, + Graphics[{Red, + PointSize[Large], + Point[{{$CellContext`r$$, + Sqrt[$CellContext`r$$]}, {$CellContext`r$$, - + Sqrt[$CellContext`r$$]}, {$CellContext`r$$, 0}}], White, + PointSize[Medium], + Point[{{$CellContext`r$$, + Sqrt[$CellContext`r$$]}, {$CellContext`r$$, - + Sqrt[$CellContext`r$$]}}]}], + Graphics[{Red, + PointSize[Large], + Point[{$CellContext`r$$, 0}], White, + PointSize[Medium], + Point[{$CellContext`r$$, 0}]}]]]}}], + "Specifications" :> {{{$CellContext`r$$, 1}, -2, 2}}, "Options" :> {}, + "DefaultOptions" :> {}], + ImageSizeCache->{438., {144., 150.}}, + SingleEvaluation->True], + Deinitialization:>None, + DynamicModuleValues:>{}, + SynchronousInitialization->True, + UndoTrackedVariables:>{Typeset`show$$, Typeset`bookmarkMode$$}, + UnsavedVariables:>{Typeset`initDone$$}, + UntrackedVariables:>{Typeset`size$$}], "Manipulate", + Deployed->True, + StripOnInput->False], + Manipulate`InterpretManipulate[1]]], "Output", + CellChangeTimes->{{3.7771379244304895`*^9, 3.777137972818993*^9}, { + 3.777138035688207*^9, 3.7771380603054132`*^9}, {3.7771381204860187`*^9, + 3.777138178429568*^9}, {3.777138214210326*^9, 3.7771382557136283`*^9}, { + 3.777138298547415*^9, 3.777138305909398*^9}, 3.777138364876514*^9, + 3.777138402049615*^9, 3.7771385562984977`*^9, 3.777142069213477*^9, { + 3.777142100334644*^9, 3.777142123718077*^9}, {3.7771422250715675`*^9, + 3.7771422683455553`*^9}, 3.7771423125655565`*^9, 3.7771428387314763`*^9}] +}, Open ]] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Hopf Bifurcation", "Section", + CellChangeTimes->{{3.7766008885632277`*^9, 3.7766008904796133`*^9}, { + 3.777136401274056*^9, 3.777136416298379*^9}, {3.7771423512766824`*^9, + 3.7771423523483405`*^9}}], + +Cell["\<\ +A Hopf bifurcation occurs when an equilibrium changes stability in a way that \ +leads to a periodic orbit. This can only occur if we increase our system to \ +at least two dimensions. The example below concerns the 2D system:\ +\>", "Text", + CellChangeTimes->{{3.777136412348218*^9, 3.777136502673601*^9}, { + 3.777140654593788*^9, 3.77714069874934*^9}, {3.777142354913436*^9, + 3.7771423557214785`*^9}, {3.7771424049490695`*^9, 3.7771425240888643`*^9}}], + +Cell[BoxData[Cell[TextData[Cell[BoxData[{ + FormBox[ + RowBox[{ + FractionBox[ + RowBox[{"\[DifferentialD]", "x"}], + RowBox[{"\[DifferentialD]", "t"}]], "=", + RowBox[{ + RowBox[{ + RowBox[{"r", "(", + RowBox[{"1", "-", + SuperscriptBox["y", "2"]}], ")"}], "x"}], "-", "y"}]}], + TraditionalForm], "\[IndentingNewLine]", + FormBox[ + RowBox[{ + FractionBox[ + RowBox[{"\[DifferentialD]", "y"}], + RowBox[{"\[DifferentialD]", "t"}]], "=", "x"}], TraditionalForm]}], + FormatType->"TraditionalForm"]], "DisplayFormula"]], "Text", + CellChangeTimes->{{3.77713651537531*^9, 3.7771365309974613`*^9}, + 3.7771366535696325`*^9, {3.7771370336200256`*^9, 3.7771370357424736`*^9}, { + 3.7771425287026825`*^9, 3.777142543615819*^9}}], + +Cell[TextData[{ + "Finding the equilibria now requires us to solve the simultaneous system ", + Cell[BoxData[ + FormBox[ + RowBox[{ + RowBox[{ + FractionBox[ + RowBox[{"\[DifferentialD]", "x"}], + RowBox[{"\[DifferentialD]", "t"}]], "=", "0"}], ",", + RowBox[{ + FractionBox[ + RowBox[{"\[DifferentialD]", "y"}], + RowBox[{"\[DifferentialD]", "t"}]], "=", "0"}]}], TraditionalForm]], + FormatType->"TraditionalForm"], + ", which has exactly one solution: ", + Cell[BoxData[ + FormBox[ + RowBox[{ + RowBox[{"(", + RowBox[{ + SuperscriptBox["x", "*"], ",", + SuperscriptBox["y", "*"]}], ")"}], "=", + RowBox[{"(", + RowBox[{"0", ",", "0"}], ")"}]}], TraditionalForm]], + FormatType->"TraditionalForm"], + ". This is independent of the value of ", + Cell[BoxData[ + FormBox["r", TraditionalForm]], + FormatType->"TraditionalForm"], + ". We next conduct stability analysis by examining the Jacobian" +}], "Text", + CellChangeTimes->{{3.7771366384229493`*^9, 3.777136834022626*^9}, { + 3.777136865290258*^9, 3.77713686612399*^9}, {3.77713704004583*^9, + 3.77713704004583*^9}, {3.7771425567700644`*^9, 3.7771426590387325`*^9}, { + 3.777142720782019*^9, 3.7771427214294863`*^9}}], + +Cell[BoxData[Cell[TextData[{ + Cell[BoxData[ + FormBox[ + RowBox[{ + SuperscriptBox["J", "*"], "=", + SubscriptBox[ + RowBox[{"(", GridBox[{ + { + RowBox[{ + FractionBox["\[DifferentialD]", + RowBox[{"\[DifferentialD]", "x"}]], + RowBox[{"(", + RowBox[{ + RowBox[{ + RowBox[{"r", "(", + RowBox[{"1", "-", + SuperscriptBox["y", "2"]}], ")"}], "x"}], "-", "y"}], ")"}]}], + RowBox[{ + FractionBox["\[DifferentialD]", + RowBox[{"\[DifferentialD]", "y"}]], + RowBox[{"(", + RowBox[{ + RowBox[{"r", + RowBox[{"(", + RowBox[{"1", "-", + SuperscriptBox["y", "2"]}], ")"}], "x"}], "-", "y"}], ")"}]}]}, + { + RowBox[{ + FractionBox["\[DifferentialD]", + RowBox[{"\[DifferentialD]", "x"}]], + RowBox[{"(", "x", ")"}]}], + RowBox[{ + FractionBox["\[DifferentialD]", + RowBox[{"\[DifferentialD]", "y"}]], + RowBox[{"(", "x", ")"}]}]} + }], ")"}], + RowBox[{ + RowBox[{"(", + RowBox[{"x", ",", "y"}], ")"}], "=", + RowBox[{"(", + RowBox[{"0", ",", "0"}], ")"}]}]]}], TraditionalForm]]], + "=", + Cell[BoxData[ + FormBox[ + RowBox[{ + SubscriptBox[ + RowBox[{"(", GridBox[{ + { + RowBox[{"r", "(", + RowBox[{"1", "-", + SuperscriptBox["y", "2"]}], ")"}], + RowBox[{ + RowBox[{ + RowBox[{"-", "2"}], "r", " ", "x", " ", "y"}], "-", "1"}]}, + {"1", "0"} + }], ")"}], + RowBox[{ + RowBox[{"(", + RowBox[{"x", ",", "y"}], ")"}], "=", + RowBox[{"(", + RowBox[{"0", ",", "0"}], ")"}]}]], "=", + RowBox[{"(", GridBox[{ + {"r", + RowBox[{"-", "1"}]}, + {"1", "0"} + }], ")"}]}], TraditionalForm]]] + }], "DisplayFormula"]], "DisplayFormula", + CellChangeTimes->{{3.7771426694122353`*^9, 3.777142776009329*^9}, { + 3.7771428654505424`*^9, 3.7771429550053325`*^9}}], + +Cell[TextData[{ + "which has eigenvalues of ", + Cell[BoxData[ + FormBox[ + FractionBox[ + RowBox[{"r", " ", "\[PlusMinus]", + SqrtBox[ + RowBox[{ + SuperscriptBox["r", "2"], " ", "-", " ", "4"}]]}], "2"], + TraditionalForm]], + FormatType->"TraditionalForm"], + ". These always have a negative real part for ", + Cell[BoxData[ + FormBox[ + RowBox[{"r", "<", "0"}], TraditionalForm]], + FormatType->"TraditionalForm"], + " and a positive real part for ", + Cell[BoxData[ + FormBox[ + RowBox[{"r", ">", "0"}], TraditionalForm]], + FormatType->"TraditionalForm"], + ". For ", + Cell[BoxData[ + FormBox[ + RowBox[{"r", "\[LessEqual]", + RowBox[{"-", "2"}]}], TraditionalForm]], + FormatType->"TraditionalForm"], + " and ", + Cell[BoxData[ + FormBox[ + RowBox[{"r", "\[GreaterEqual]", "2"}], TraditionalForm]], + FormatType->"TraditionalForm"], + " they are purely real, while for ", + Cell[BoxData[ + FormBox[ + RowBox[{ + RowBox[{"-", "2"}], "<", "r", "<", "2"}], TraditionalForm]], + FormatType->"TraditionalForm"], + " they include an imaginary part. At ", + Cell[BoxData[ + FormBox[ + RowBox[{"r", "=", "0"}], TraditionalForm]], + FormatType->"TraditionalForm"], + " the eigenvalues are purely imaginary and we have periodic orbits." +}], "Text", + CellChangeTimes->{{3.7771429637246385`*^9, 3.777142966166086*^9}, { + 3.7771429962203674`*^9, 3.7771430481636953`*^9}, {3.777143415022867*^9, + 3.7771435095056553`*^9}}], + +Cell[TextData[{ + "The equilibrium displays used above do not apply to this 2D system, and so \ +instead we display only the stream plot of ", + Cell[BoxData[ + FormBox["y", TraditionalForm]], + FormatType->"TraditionalForm"], + " versus ", + Cell[BoxData[ + FormBox["x", TraditionalForm]], + FormatType->"TraditionalForm"], + ". Notice that as ", + Cell[BoxData[ + FormBox["r", TraditionalForm]], + FormatType->"TraditionalForm"], + " goes from negative to zero to positive, the system goes from spiraling \ +inward (stable) to circular orbits (periodic) to spiraling outward (unstable)." +}], "Text", + CellChangeTimes->{{3.7771435211260934`*^9, 3.7771436703194323`*^9}}], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Manipulate", "[", + RowBox[{ + RowBox[{"Show", "[", + RowBox[{ + RowBox[{"StreamPlot", "[", + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{ + RowBox[{"r", + RowBox[{"(", + RowBox[{"1", "-", + SuperscriptBox["y", "2"]}], ")"}], "x"}], "-", "y"}], ",", "x"}], + "}"}], ",", + RowBox[{"{", + RowBox[{"x", ",", + RowBox[{"-", "2"}], ",", "2"}], "}"}], ",", + RowBox[{"{", + RowBox[{"y", ",", + RowBox[{"-", "2"}], ",", "2"}], "}"}], ",", + RowBox[{"PlotLabel", "\[Rule]", "\"\\""}]}], + "]"}], ",", + RowBox[{"Graphics", "[", + RowBox[{"{", + RowBox[{"Red", ",", + RowBox[{"PointSize", "[", "Large", "]"}], ",", + RowBox[{"Point", "[", + RowBox[{"{", + RowBox[{"0", ",", "0"}], "}"}], "]"}]}], "}"}], "]"}]}], "]"}], ",", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{"r", ",", "1"}], "}"}], ",", + RowBox[{"-", "3"}], ",", "3"}], "}"}]}], "]"}]], "Input", + CellChangeTimes->{{3.77713657768003*^9, 3.7771365828765388`*^9}, { + 3.7771370214122696`*^9, 3.7771370243627615`*^9}, {3.7771371027777557`*^9, + 3.777137152180356*^9}, {3.777137522168996*^9, 3.7771379841682105`*^9}, { + 3.7771380242901864`*^9, 3.7771384015864058`*^9}, {3.7771385034820766`*^9, + 3.7771385543943424`*^9}, {3.777143113760271*^9, 3.777143167703524*^9}, { + 3.77714324489684*^9, 3.7771432725478344`*^9}, {3.77714335304587*^9, + 3.7771433539295716`*^9}}], + +Cell[BoxData[ + TagBox[ + StyleBox[ + DynamicModuleBox[{$CellContext`r$$ = 1.63, Typeset`show$$ = True, + Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", + Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = + "\"untitled\"", Typeset`specs$$ = {{{ + Hold[$CellContext`r$$], 1}, -3, 3}}, Typeset`size$$ = { + 360., {185., 190.}}, Typeset`update$$ = 0, Typeset`initDone$$, + Typeset`skipInitDone$$ = True, $CellContext`r$18043$$ = 0}, + DynamicBox[Manipulate`ManipulateBoxes[ + 1, StandardForm, "Variables" :> {$CellContext`r$$ = 1}, + "ControllerVariables" :> { + Hold[$CellContext`r$$, $CellContext`r$18043$$, 0]}, + "OtherVariables" :> { + Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, + Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, + Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, + Typeset`skipInitDone$$}, "Body" :> Show[ + StreamPlot[{$CellContext`r$$ ( + 1 - $CellContext`y^2) $CellContext`x - $CellContext`y, \ +$CellContext`x}, {$CellContext`x, -2, 2}, {$CellContext`y, -2, 2}, PlotLabel -> + "stream plot (y versus x)"], + Graphics[{Red, + PointSize[Large], + Point[{0, 0}]}]], + "Specifications" :> {{{$CellContext`r$$, 1}, -3, 3}}, "Options" :> {}, + "DefaultOptions" :> {}], + ImageSizeCache->{411., {245., 251.}}, + SingleEvaluation->True], + Deinitialization:>None, + DynamicModuleValues:>{}, + SynchronousInitialization->True, + UndoTrackedVariables:>{Typeset`show$$, Typeset`bookmarkMode$$}, + UnsavedVariables:>{Typeset`initDone$$}, + UntrackedVariables:>{Typeset`size$$}], "Manipulate", + Deployed->True, + StripOnInput->False], + Manipulate`InterpretManipulate[1]]], "Output", + CellChangeTimes->{{3.7771379244304895`*^9, 3.777137972818993*^9}, { + 3.777138035688207*^9, 3.7771380603054132`*^9}, {3.7771381204860187`*^9, + 3.777138178429568*^9}, {3.777138214210326*^9, 3.7771382557136283`*^9}, { + 3.777138298547415*^9, 3.777138305909398*^9}, 3.777138364876514*^9, + 3.777138402049615*^9, 3.7771385562984977`*^9, 3.7771428399820857`*^9, + 3.7771431348484387`*^9, 3.77714316857364*^9, {3.777143263336276*^9, + 3.7771432733456025`*^9}, 3.777143355066966*^9}] +}, {2}]] +}, Open ]] +}, Open ]] +}, +WindowSize->{767, 833}, +WindowMargins->{{57, Automatic}, {Automatic, 51}}, +FrontEndVersion->"10.4 for Microsoft Windows (64-bit) (April 11, 2016)", +StyleDefinitions->"Default.nb" +] +(* End of Notebook Content *) + +(* Internal cache information *) +(*CellTagsOutline +CellTagsIndex->{} +*) +(*CellTagsIndex +CellTagsIndex->{} +*) +(*NotebookFileOutline +Notebook[{ +Cell[CellGroupData[{ +Cell[580, 22, 158, 2, 90, "Title"], +Cell[741, 26, 158, 2, 30, "Text"], +Cell[CellGroupData[{ +Cell[924, 32, 99, 1, 63, "Section"], +Cell[1026, 35, 915, 25, 87, "Text"], +Cell[1944, 62, 1866, 51, 158, "Text"], +Cell[3813, 115, 1116, 32, 82, "Text"], +Cell[4932, 149, 1048, 31, 82, "Text"], +Cell[5983, 182, 894, 23, 89, "Text"], +Cell[6880, 207, 1085, 35, 96, "Text"], +Cell[7968, 244, 966, 18, 144, "Text"] +}, Open ]], +Cell[CellGroupData[{ +Cell[8971, 267, 161, 2, 63, "Section"], +Cell[9135, 271, 507, 8, 87, "Text"], +Cell[9645, 281, 453, 10, 46, "Text"], +Cell[10101, 293, 788, 25, 63, "Text"], +Cell[CellGroupData[{ +Cell[10914, 322, 417, 14, 34, "Item"], +Cell[11334, 338, 476, 15, 34, "Item"], +Cell[11813, 355, 453, 15, 29, "Item"] +}, Open ]], +Cell[12281, 373, 1650, 59, 94, "Text"], +Cell[CellGroupData[{ +Cell[13956, 436, 5322, 140, 413, "Input"], +Cell[19281, 578, 3451, 74, 311, "Output"] +}, Open ]] +}, Open ]], +Cell[CellGroupData[{ +Cell[22781, 658, 216, 3, 63, "Section"], +Cell[23000, 663, 450, 7, 49, "Text"], +Cell[23453, 672, 531, 12, 46, "Text"], +Cell[23987, 686, 1085, 35, 63, "Text"], +Cell[25075, 723, 979, 30, 63, "Text"], +Cell[CellGroupData[{ +Cell[26079, 757, 654, 23, 45, "Item"], +Cell[26736, 782, 625, 22, 45, "Item"] +}, Open ]], +Cell[27376, 807, 387, 13, 30, "Text"], +Cell[CellGroupData[{ +Cell[27788, 824, 6514, 164, 371, "Input"], +Cell[34305, 990, 3800, 79, 311, "Output"] +}, Open ]] +}, Open ]], +Cell[CellGroupData[{ +Cell[38154, 1075, 210, 3, 63, "Section"], +Cell[38367, 1080, 577, 9, 87, "Text"], +Cell[38947, 1091, 533, 12, 46, "Text"], +Cell[39483, 1105, 2018, 68, 107, "Text"], +Cell[41504, 1175, 2655, 93, 132, "Text"], +Cell[CellGroupData[{ +Cell[44184, 1272, 7694, 197, 539, "Input"], +Cell[51881, 1471, 4191, 88, 311, "Output"] +}, Open ]] +}, Open ]], +Cell[CellGroupData[{ +Cell[56121, 1565, 207, 3, 63, "Section"], +Cell[56331, 1570, 463, 7, 68, "Text"], +Cell[56797, 1579, 771, 20, 81, "Text"], +Cell[57571, 1601, 1217, 34, 84, "Text"], +Cell[58791, 1637, 2131, 68, 78, "DisplayFormula"], +Cell[60925, 1707, 1432, 47, 93, "Text"], +Cell[62360, 1756, 662, 17, 68, "Text"], +Cell[CellGroupData[{ +Cell[63047, 1777, 1575, 41, 103, "Input"], +Cell[64625, 1820, 2303, 45, 513, "Output"] +}, {2}]] +}, Open ]] +}, Open ]] +} +] +*) + diff --git a/calc-diffeq-analysis/cobwebbing.nb b/calc-diffeq-analysis/cobwebbing.nb index d9f1f02..d010b0f 100644 --- a/calc-diffeq-analysis/cobwebbing.nb +++ b/calc-diffeq-analysis/cobwebbing.nb @@ -1,578 +1,578 @@ -(* Content-type: application/vnd.wolfram.mathematica *) - -(*** Wolfram Notebook File ***) -(* http://www.wolfram.com/nb *) - -(* CreatedBy='Mathematica 10.4' *) - -(*CacheID: 234*) -(* Internal cache information: -NotebookFileLineBreakTest -NotebookFileLineBreakTest -NotebookDataPosition[ 158, 7] -NotebookDataLength[ 21974, 570] -NotebookOptionsPosition[ 20953, 529] -NotebookOutlinePosition[ 21296, 544] -CellTagsIndexPosition[ 21253, 541] -WindowFrame->Normal*) - -(* Beginning of Notebook Content *) -Notebook[{ - -Cell[CellGroupData[{ -Cell["Cobwebbing", "Title", - CellChangeTimes->{{3.776600831050974*^9, 3.7766008318453026`*^9}, { - 3.7771303814556313`*^9, 3.7771303897679653`*^9}, {3.777130431756935*^9, - 3.7771304426145535`*^9}, {3.7771538104310255`*^9, 3.7771538107522936`*^9}}], - -Cell["Adam Rumpf, 11/4/2014", "Text", - CellChangeTimes->{{3.7766008347881403`*^9, 3.776600838290375*^9}, { - 3.7771303785432096`*^9, 3.7771303802837615`*^9}}], - -Cell[CellGroupData[{ - -Cell["Introduction", "Section", - CellChangeTimes->{{3.7766008459498987`*^9, 3.776600848547045*^9}}], - -Cell[TextData[{ - "The initialization code below defines a function called ", - StyleBox["cobweb[]", "Code"], - ", which accepts a pure function, a parameter ", - Cell[BoxData[ - FormBox["r", TraditionalForm]], - FormatType->"TraditionalForm"], - ", an initial value, and a number of iterations. It then produces a cobweb \ -plot for the given function. This is used for the main Manipulate environment \ -at the end of the Notebook, which has a number of simple built-in discrete \ -dynamical systems, each of which depends on a single parameter ", - Cell[BoxData[ - FormBox["r", TraditionalForm]], - FormatType->"TraditionalForm"], - ". Note that the meaning of the parameter is different in each system." -}], "Text", - CellChangeTimes->{{3.776600856235587*^9, 3.776600860481224*^9}, { - 3.7771601060172977`*^9, 3.777160276365533*^9}, {3.7771607213398085`*^9, - 3.7771607394812503`*^9}}], - -Cell["\<\ -Some of thesefunctions are arbitrary and only meant for showing off how \ -different shapes of function can behave, but a few have some significance:\ -\>", "Text", - CellChangeTimes->{{3.776600856235587*^9, 3.776600860481224*^9}, { - 3.7771601060172977`*^9, 3.777160276365533*^9}, {3.7771607213398085`*^9, - 3.77716072716536*^9}}], - -Cell[CellGroupData[{ - -Cell[TextData[{ - "The discrete logistic map, of the general form ", - Cell[BoxData[ - FormBox[ - RowBox[{ - SubscriptBox["x", - RowBox[{"n", "+", "1"}]], "=", - RowBox[{"r", " ", - RowBox[{ - SubscriptBox["x", "n"], "(", - RowBox[{"1", "-", - SubscriptBox["x", "n"]}], ")"}]}]}], TraditionalForm]], - FormatType->"TraditionalForm"], - ", is usually thought of as describing a population whose size is limited by \ -finite resources. ", - Cell[BoxData[ - FormBox[ - SubscriptBox["x", "n"], TraditionalForm]], - FormatType->"TraditionalForm"], - " is the population at time step ", - Cell[BoxData[ - FormBox["n", TraditionalForm]], - FormatType->"TraditionalForm"], - ", scaled so that ", - Cell[BoxData[ - FormBox["1", TraditionalForm]], - FormatType->"TraditionalForm"], - " is the holding capacity. ", - Cell[BoxData[ - FormBox[ - RowBox[{"r", ">", "0"}], TraditionalForm]], - FormatType->"TraditionalForm"], - " is the intrinsic growth rate. This system is famous for exhibiting chaotic \ -behavior when ", - Cell[BoxData[ - FormBox["r", TraditionalForm]], - FormatType->"TraditionalForm"], - " is sufficiently large. Try increasing the value of ", - Cell[BoxData[ - FormBox["r", TraditionalForm]], - FormatType->"TraditionalForm"], - " slowly to watch as the nonzero fixed point goes from being stable, to \ -being surrounded by periodic orbits, to complete chaos." -}], "Item", - CellChangeTimes->{{3.777160287433982*^9, 3.7771604336737385`*^9}, { - 3.777160482102011*^9, 3.7771605580480304`*^9}}], - -Cell[TextData[{ - "The discrete logistic map with proportional harvesting has the general form \ -", - Cell[BoxData[ - FormBox[ - RowBox[{ - SubscriptBox["x", - RowBox[{"n", "+", "1"}]], "=", - RowBox[{ - RowBox[{"r", " ", - RowBox[{ - SubscriptBox["x", "n"], "(", - RowBox[{"1", "-", - SubscriptBox["x", "n"]}], ")"}]}], "-", - RowBox[{"p", " ", - SubscriptBox["x", "n"]}]}]}], TraditionalForm]], - FormatType->"TraditionalForm"], - ". This is exactly the logistic growth model, but now a proportion ", - Cell[BoxData[ - FormBox[ - RowBox[{"0", "<", "p", "<", "1"}], TraditionalForm]], - FormatType->"TraditionalForm"], - " of the current population is removed each iteration." -}], "Item", - CellChangeTimes->{{3.777160287433982*^9, 3.7771604336737385`*^9}, { - 3.777160482102011*^9, 3.7771606279540477`*^9}, {3.777160744824355*^9, - 3.7771607448283534`*^9}}], - -Cell[TextData[{ - "The discrete logistic map with constant harvesting has the general form ", - Cell[BoxData[ - FormBox[ - RowBox[{ - SubscriptBox["x", - RowBox[{"n", "+", "1"}]], "=", - RowBox[{ - RowBox[{"r", " ", - RowBox[{ - SubscriptBox["x", "n"], "(", - RowBox[{"1", "-", - SubscriptBox["x", "n"]}], ")"}]}], "-", "h"}]}], TraditionalForm]], - FormatType->"TraditionalForm"], - ". This is similar to the proportional harvesting model, except that now a \ -constant amount of population ", - Cell[BoxData[ - FormBox[ - RowBox[{"h", ">", "0"}], TraditionalForm]], - FormatType->"TraditionalForm"], - " is removed each iteration." -}], "Item", - CellChangeTimes->{{3.777160287433982*^9, 3.7771604336737385`*^9}, { - 3.777160482102011*^9, 3.7771606279540477`*^9}, {3.777160744824355*^9, - 3.7771607963231335`*^9}}], - -Cell[TextData[{ - "The linear map simply consists of a line passing through the point ", - Cell[BoxData[ - FormBox[ - RowBox[{"(", - RowBox[{ - FractionBox["1", "2"], ",", - FractionBox["1", "2"]}], ")"}], TraditionalForm]], - FormatType->"TraditionalForm"], - " with a slope variable between ", - Cell[BoxData[ - FormBox[ - RowBox[{"-", "1"}], TraditionalForm]], - FormatType->"TraditionalForm"], - " and ", - Cell[BoxData[ - FormBox["1", TraditionalForm]], - FormatType->"TraditionalForm"], - ". It is meant to act as a clear demonstration of how the stability of a \ -fixed point depends on the slope of the function curve where it intersects \ -the ", - Cell[BoxData[ - FormBox[ - RowBox[{"y", "=", "x"}], TraditionalForm]], - FormatType->"TraditionalForm"], - " line." -}], "Item", - CellChangeTimes->{{3.777160287433982*^9, 3.7771604336737385`*^9}, { - 3.777160482102011*^9, 3.7771606279540477`*^9}, {3.777160744824355*^9, - 3.7771608420031204`*^9}, {3.777160895152163*^9, 3.7771609378928003`*^9}}] -}, Open ]] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["Code", "Section", - CellChangeTimes->{{3.776600864408964*^9, 3.7766008650447807`*^9}}], - -Cell[CellGroupData[{ - -Cell["Initialization", "Subsection", - CellChangeTimes->{{3.776600871130811*^9, 3.776600873087188*^9}}], - -Cell[BoxData[ - RowBox[{ - RowBox[{"(*", " ", - RowBox[{ - RowBox[{ - "generates", " ", "the", " ", "cobweb", " ", "plot", " ", "for", " ", "a", - " ", "given", " ", "pure", " ", "function", " ", "f"}], ",", " ", - RowBox[{"parameter", " ", "r"}], ",", " ", - RowBox[{"initial", " ", "value", " ", "x0"}], ",", " ", - RowBox[{"and", " ", "number", " ", "of", " ", "iterations", " ", "n"}]}], - " ", "*)"}], "\[IndentingNewLine]", - RowBox[{ - RowBox[{"cobweb", "[", - RowBox[{"f_", ",", "r_", ",", "x0_", ",", "n_"}], "]"}], ":=", - RowBox[{"Module", "[", - RowBox[{ - RowBox[{"{", - RowBox[{ - RowBox[{"pts", "=", - RowBox[{"{", - RowBox[{"{", - RowBox[{"x0", ",", "0"}], "}"}], "}"}]}], ",", "y"}], "}"}], ",", - "\[IndentingNewLine]", - RowBox[{"(*", " ", - RowBox[{"generate", " ", "sequence", " ", "of", " ", "points"}], " ", - "*)"}], "\[IndentingNewLine]", - RowBox[{ - RowBox[{"Do", "[", "\[IndentingNewLine]", - RowBox[{"(*", " ", - RowBox[{"vertical", " ", "to", " ", "f"}], " ", "*)"}], - "\[IndentingNewLine]", - RowBox[{ - RowBox[{ - RowBox[{"y", "=", - RowBox[{"f", "[", - RowBox[{ - RowBox[{"pts", "[", - RowBox[{"[", - RowBox[{ - RowBox[{"-", "1"}], ",", "1"}], "]"}], "]"}], ",", "r"}], - "]"}]}], ";", "\[IndentingNewLine]", - RowBox[{"pts", "=", - RowBox[{"Append", "[", - RowBox[{"pts", ",", - RowBox[{"{", - RowBox[{ - RowBox[{"pts", "[", - RowBox[{"[", - RowBox[{ - RowBox[{"-", "1"}], ",", "1"}], "]"}], "]"}], ",", "y"}], - "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", - RowBox[{"If", "[", - RowBox[{ - RowBox[{ - RowBox[{"y", "<", "0"}], "||", - RowBox[{"y", ">", - SuperscriptBox["10", "30"]}]}], ",", "\[IndentingNewLine]", - RowBox[{"(*", " ", - RowBox[{ - "break", " ", "if", " ", "we", " ", "reach", " ", "a", " ", - "negative", " ", "value", " ", "or", " ", "too", " ", "large", - " ", "of", " ", "a", " ", "value"}], " ", "*)"}], - "\[IndentingNewLine]", - RowBox[{ - RowBox[{"Break", "[", "]"}], ";"}]}], "\[IndentingNewLine]", - "]"}], ";", "\[IndentingNewLine]", - RowBox[{"(*", " ", - RowBox[{ - RowBox[{"horizontal", " ", "to", " ", "y"}], "=", "x"}], " ", - "*)"}], "\[IndentingNewLine]", - RowBox[{"pts", "=", - RowBox[{"Append", "[", - RowBox[{"pts", ",", - RowBox[{"{", - RowBox[{"y", ",", "y"}], "}"}]}], "]"}]}]}], ",", - "\[IndentingNewLine]", - RowBox[{"{", - RowBox[{"i", ",", "1", ",", "n"}], "}"}]}], "]"}], ";", - "\[IndentingNewLine]", - RowBox[{"(*", " ", - RowBox[{"draw", " ", "diagram"}], " ", "*)"}], "\[IndentingNewLine]", - RowBox[{"Show", "[", - RowBox[{ - RowBox[{"Plot", "[", - RowBox[{ - RowBox[{"{", - RowBox[{"x", ",", - RowBox[{"f", "[", - RowBox[{"x", ",", "r"}], "]"}]}], "}"}], ",", - RowBox[{"{", - RowBox[{"x", ",", "0", ",", "1"}], "}"}], ",", - RowBox[{"PlotStyle", "\[Rule]", - RowBox[{"{", - RowBox[{ - RowBox[{"Directive", "[", - RowBox[{"Thick", ",", "Black"}], "]"}], ",", "Blue"}], - "}"}]}]}], "]"}], ",", - RowBox[{"Graphics", "[", - RowBox[{"{", - RowBox[{"Red", ",", " ", - RowBox[{"Line", "[", "pts", "]"}]}], "}"}], "]"}], ",", - RowBox[{"PlotRange", "\[Rule]", - RowBox[{"{", - RowBox[{ - RowBox[{"{", - RowBox[{"0", ",", "1"}], "}"}], ",", - RowBox[{"{", - RowBox[{"0", ",", "1"}], "}"}]}], "}"}]}], ",", - RowBox[{"AspectRatio", "\[Rule]", "1"}], ",", - RowBox[{"Axes", "\[Rule]", "True"}], ",", - RowBox[{"AxesLabel", "\[Rule]", - RowBox[{"{", - RowBox[{ - "\"\<\!\(\*SubscriptBox[\(x\), \(n\)]\)\>\"", ",", - "\"\<\!\(\*SubscriptBox[\(x\), \(n + 1\)]\)\>\""}], "}"}]}]}], - "]"}]}]}], "\[IndentingNewLine]", "]"}]}]}]], "Input", - CellChangeTimes->{{3.7766008761831923`*^9, 3.776600882799075*^9}, { - 3.7771555265254726`*^9, 3.7771555956462235`*^9}, {3.777155660625909*^9, - 3.777155740927166*^9}, {3.77715578405746*^9, 3.7771559343330507`*^9}, { - 3.777155999295798*^9, 3.7771561977500076`*^9}, {3.77715672559943*^9, - 3.77715676271062*^9}, {3.777157939775195*^9, 3.7771579539182663`*^9}, { - 3.7771586587903957`*^9, 3.7771586589976068`*^9}}] -}, Closed]], - -Cell[CellGroupData[{ - -Cell["Demonstration", "Subsection", - CellChangeTimes->{{3.7766008885632277`*^9, 3.7766008904796133`*^9}}], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"Manipulate", "[", - RowBox[{ - RowBox[{"Module", "[", - RowBox[{ - RowBox[{"{", "}"}], ",", "\[IndentingNewLine]", - RowBox[{"cobweb", "[", - RowBox[{"f", ",", "r", ",", "x0", ",", "30"}], "]"}]}], - "\[IndentingNewLine]", "]"}], ",", - RowBox[{"{", - RowBox[{ - RowBox[{"{", - RowBox[{"f", ",", - RowBox[{ - RowBox[{"4", "#2", "#1", - RowBox[{"(", - RowBox[{"1", "-", "#1"}], ")"}]}], "&"}], ",", - "\"\<\!\(\*SubscriptBox[\(x\), \(n + 1\)]\)\>\""}], "}"}], ",", - RowBox[{"{", - RowBox[{ - RowBox[{ - RowBox[{ - RowBox[{"4", "#2", "#1", - RowBox[{"(", - RowBox[{"1", "-", "#1"}], ")"}]}], "&"}], "\[Rule]", - "\"\<4\!\(\*SubscriptBox[\(rx\), \(n\)]\)(1-\!\(\*SubscriptBox[\(x\), \ -\(n\)]\)) - logistic map\>\""}], ",", - RowBox[{ - RowBox[{ - RowBox[{ - RowBox[{"3", "#1", - RowBox[{"(", - RowBox[{"1", "-", "#1"}], ")"}]}], "-", - RowBox[{"#2", "#1"}]}], "&"}], "\[Rule]", - "\"\<3\!\(\*SubscriptBox[\(x\), \(n\)]\)(1-\!\(\*SubscriptBox[\(x\), \ -\(n\)]\))-\!\(\*SubscriptBox[\(rx\), \(n\)]\) - logistic w/ prop. \ -harvesting\>\""}], ",", - RowBox[{ - RowBox[{ - RowBox[{ - RowBox[{"2", "#1", - RowBox[{"(", - RowBox[{"1", "-", "#1"}], ")"}]}], "+", - RowBox[{"0.5", "#2"}], "-", "0.25"}], "&"}], "\[Rule]", - "\"\<2\!\(\*SubscriptBox[\(x\), \(n\)]\)(1-\!\(\*SubscriptBox[\(x\), \ -\(n\)]\))+0.5r-0.25 - logistic w/ const. harvesting\>\""}], ",", - RowBox[{ - RowBox[{ - RowBox[{ - RowBox[{"4", - RowBox[{"(", - RowBox[{"#2", "-", "0.5"}], ")"}], - RowBox[{"(", - RowBox[{"#1", "-", "0.5"}], ")"}]}], "+", "0.5"}], "&"}], - "\[Rule]", - "\"\<2(r-0.5)(\!\(\*SubscriptBox[\(x\), \(n\)]\)-0.5)+0.5 - \ -linear\>\""}], ",", - RowBox[{ - RowBox[{ - RowBox[{ - RowBox[{"5.6", - SuperscriptBox["#1", "3"]}], "-", - RowBox[{"7", - SuperscriptBox["#1", "2"]}], "+", - RowBox[{"2.5", "#1"}], "+", - RowBox[{"0.4", "#2"}]}], "&"}], "\[Rule]", - "\"\<5.6\!\(\*SuperscriptBox[SubscriptBox[\(x\), \(n\)], \(3\)]\)-7\!\ -\(\*SuperscriptBox[SubscriptBox[\(x\), \(n\)], \ -\(2\)]\)+2.5\!\(\*SubscriptBox[\(x\), \(n\)]\)+0.4r - cubic\>\""}]}], "}"}], - ",", "PopupMenu"}], "}"}], ",", - RowBox[{"{", - RowBox[{ - RowBox[{"{", - RowBox[{"r", ",", "0.65", ",", "\"\\""}], "}"}], ",", "0", ",", - "1"}], "}"}], ",", - RowBox[{"{", - RowBox[{ - RowBox[{"{", - RowBox[{ - "x0", ",", "0.25", ",", "\"\<\!\(\*SubscriptBox[\(x\), \(0\)]\)\>\""}], - "}"}], ",", "0.01", ",", "0.99"}], "}"}]}], "]"}]], "Input", - CellChangeTimes->{{3.7766008920271177`*^9, 3.7766008970415297`*^9}, { - 3.7771562414820786`*^9, 3.7771563442494297`*^9}, {3.7771563995143404`*^9, - 3.777156516567629*^9}, {3.7771565579644203`*^9, 3.7771566308395443`*^9}, { - 3.7771566638834124`*^9, 3.7771567107130213`*^9}, {3.777156784185316*^9, - 3.777156786028338*^9}, {3.777156832919155*^9, 3.777156870190647*^9}, { - 3.7771569076381054`*^9, 3.777156910114409*^9}, {3.7771569530182934`*^9, - 3.77715697366871*^9}, {3.77715700935042*^9, 3.7771570454786167`*^9}, { - 3.7771571178308992`*^9, 3.7771571287366505`*^9}, {3.7771571818975186`*^9, - 3.7771571866982684`*^9}, {3.7771572231348476`*^9, - 3.7771572812355137`*^9}, {3.7771573628429117`*^9, - 3.7771574205793257`*^9}, {3.7771574629188404`*^9, - 3.7771574683729973`*^9}, {3.7771577370959873`*^9, 3.777157812798995*^9}, { - 3.777157872216112*^9, 3.7771579054766293`*^9}, {3.7771580044952917`*^9, - 3.777158057902335*^9}, {3.777158151432196*^9, 3.7771581525935416`*^9}, { - 3.7771581963046274`*^9, 3.777158237238636*^9}, {3.7771582732210417`*^9, - 3.777158299544817*^9}, {3.777158353884241*^9, 3.7771583694134836`*^9}, { - 3.7771585371169043`*^9, 3.777158628695525*^9}, {3.77715873093116*^9, - 3.777158760363877*^9}, {3.777158804844178*^9, 3.7771589222902794`*^9}, { - 3.7771589589736195`*^9, 3.777158994414666*^9}, {3.7771590629657545`*^9, - 3.777159081959144*^9}, {3.777159113553509*^9, 3.7771591154797077`*^9}, { - 3.7771591503647776`*^9, 3.777159194511875*^9}, {3.7771592775912194`*^9, - 3.777159279203702*^9}, {3.777159347378621*^9, 3.7771593806264257`*^9}, { - 3.7771600726679134`*^9, 3.7771600741784315`*^9}, {3.7771606474508095`*^9, - 3.777160692919137*^9}, 3.77716086758996*^9}], - -Cell[BoxData[ - TagBox[ - StyleBox[ - DynamicModuleBox[{$CellContext`f$$ = 4 (#2 - 0.5) (# - 0.5) + - 0.5& , $CellContext`r$$ = 0.29, $CellContext`x0$$ = 0.25, Typeset`show$$ = - True, Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", - Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = - "\"untitled\"", Typeset`specs$$ = {{{ - Hold[$CellContext`f$$], 4 #2 # (1 - #)& , - "\!\(\*SubscriptBox[\(x\), \(n + 1\)]\)"}, {(4 #2 # (1 - #)& ) -> - "4\!\(\*SubscriptBox[\(rx\), \(n\)]\)(1-\!\(\*SubscriptBox[\(x\), \ -\(n\)]\)) - logistic map", (3 # (1 - #) - #2 #& ) -> - "3\!\(\*SubscriptBox[\(x\), \(n\)]\)(1-\!\(\*SubscriptBox[\(x\), \ -\(n\)]\))-\!\(\*SubscriptBox[\(rx\), \(n\)]\) - logistic w/ prop. \ -harvesting", (2 # (1 - #) + 0.5 #2 - 0.25& ) -> - "2\!\(\*SubscriptBox[\(x\), \(n\)]\)(1-\!\(\*SubscriptBox[\(x\), \ -\(n\)]\))+0.5r-0.25 - logistic w/ const. harvesting", (4 (#2 - 0.5) (# - 0.5) + - 0.5& ) -> - "2(r-0.5)(\!\(\*SubscriptBox[\(x\), \(n\)]\)-0.5)+0.5 - linear", ( - 5.6 #^3 - 7 #^2 + 2.5 # + 0.4 #2& ) -> - "5.6\!\(\*SuperscriptBox[SubscriptBox[\(x\), \(n\)], \ -\(3\)]\)-7\!\(\*SuperscriptBox[SubscriptBox[\(x\), \(n\)], \ -\(2\)]\)+2.5\!\(\*SubscriptBox[\(x\), \(n\)]\)+0.4r - cubic"}}, {{ - Hold[$CellContext`r$$], 0.65, "r"}, 0, 1}, {{ - Hold[$CellContext`x0$$], 0.25, "\!\(\*SubscriptBox[\(x\), \(0\)]\)"}, - 0.01, 0.99}}, Typeset`size$$ = {360., {172., 176.}}, Typeset`update$$ = - 0, Typeset`initDone$$, Typeset`skipInitDone$$ = - True, $CellContext`f$290522$$ = False, $CellContext`r$290523$$ = - 0, $CellContext`x0$290524$$ = 0}, - DynamicBox[Manipulate`ManipulateBoxes[ - 1, StandardForm, - "Variables" :> {$CellContext`f$$ = 4 #2 # (1 - #)& , $CellContext`r$$ = - 0.65, $CellContext`x0$$ = 0.25}, "ControllerVariables" :> { - Hold[$CellContext`f$$, $CellContext`f$290522$$, False], - Hold[$CellContext`r$$, $CellContext`r$290523$$, 0], - Hold[$CellContext`x0$$, $CellContext`x0$290524$$, 0]}, - "OtherVariables" :> { - Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, - Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, - Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, - Typeset`skipInitDone$$}, "Body" :> Module[{}, - $CellContext`cobweb[$CellContext`f$$, $CellContext`r$$, \ -$CellContext`x0$$, 30]], - "Specifications" :> {{{$CellContext`f$$, 4 #2 # (1 - #)& , - "\!\(\*SubscriptBox[\(x\), \(n + 1\)]\)"}, {(4 #2 # (1 - #)& ) -> - "4\!\(\*SubscriptBox[\(rx\), \(n\)]\)(1-\!\(\*SubscriptBox[\(x\), \ -\(n\)]\)) - logistic map", (3 # (1 - #) - #2 #& ) -> - "3\!\(\*SubscriptBox[\(x\), \(n\)]\)(1-\!\(\*SubscriptBox[\(x\), \ -\(n\)]\))-\!\(\*SubscriptBox[\(rx\), \(n\)]\) - logistic w/ prop. \ -harvesting", (2 # (1 - #) + 0.5 #2 - 0.25& ) -> - "2\!\(\*SubscriptBox[\(x\), \(n\)]\)(1-\!\(\*SubscriptBox[\(x\), \ -\(n\)]\))+0.5r-0.25 - logistic w/ const. harvesting", (4 (#2 - 0.5) (# - 0.5) + - 0.5& ) -> - "2(r-0.5)(\!\(\*SubscriptBox[\(x\), \(n\)]\)-0.5)+0.5 - linear", ( - 5.6 #^3 - 7 #^2 + 2.5 # + 0.4 #2& ) -> - "5.6\!\(\*SuperscriptBox[SubscriptBox[\(x\), \(n\)], \(3\)]\)-7\!\(\ -\*SuperscriptBox[SubscriptBox[\(x\), \(n\)], \ -\(2\)]\)+2.5\!\(\*SubscriptBox[\(x\), \(n\)]\)+0.4r - cubic"}, ControlType -> - PopupMenu}, {{$CellContext`r$$, 0.65, "r"}, 0, - 1}, {{$CellContext`x0$$, 0.25, "\!\(\*SubscriptBox[\(x\), \(0\)]\)"}, - 0.01, 0.99}}, "Options" :> {}, "DefaultOptions" :> {}], - ImageSizeCache->{411., {247., 253.}}, - SingleEvaluation->True], - Deinitialization:>None, - DynamicModuleValues:>{}, - SynchronousInitialization->True, - UndoTrackedVariables:>{Typeset`show$$, Typeset`bookmarkMode$$}, - UnsavedVariables:>{Typeset`initDone$$}, - UntrackedVariables:>{Typeset`size$$}], "Manipulate", - Deployed->True, - StripOnInput->False], - Manipulate`InterpretManipulate[1]]], "Output", - CellChangeTimes->{{3.777159073259899*^9, 3.7771590827182055`*^9}, - 3.7771591166822023`*^9, {3.7771591663559117`*^9, 3.7771591948043566`*^9}, - 3.7771592797965126`*^9, {3.77715934801046*^9, 3.777159380865356*^9}, - 3.77716007487621*^9, {3.7771606504230127`*^9, 3.7771606937288465`*^9}, - 3.777160868560651*^9}] -}, {2}]] -}, Open ]] -}, Open ]] -}, Open ]] -}, -WindowSize->{759, 833}, -WindowMargins->{{91, Automatic}, {Automatic, 84}}, -FrontEndVersion->"10.4 for Microsoft Windows (64-bit) (April 11, 2016)", -StyleDefinitions->"Default.nb" -] -(* End of Notebook Content *) - -(* Internal cache information *) -(*CellTagsOutline -CellTagsIndex->{} -*) -(*CellTagsIndex -CellTagsIndex->{} -*) -(*NotebookFileOutline -Notebook[{ -Cell[CellGroupData[{ -Cell[580, 22, 249, 3, 90, "Title"], -Cell[832, 27, 158, 2, 30, "Text"], -Cell[CellGroupData[{ -Cell[1015, 33, 99, 1, 63, "Section"], -Cell[1117, 36, 879, 18, 106, "Text"], -Cell[1999, 56, 339, 6, 49, "Text"], -Cell[CellGroupData[{ -Cell[2363, 66, 1513, 45, 115, "Item"], -Cell[3879, 113, 900, 26, 66, "Item"], -Cell[4782, 141, 846, 24, 64, "Item"], -Cell[5631, 167, 1005, 29, 75, "Item"] -}, Open ]] -}, Open ]], -Cell[CellGroupData[{ -Cell[6685, 202, 91, 1, 63, "Section"], -Cell[CellGroupData[{ -Cell[6801, 207, 102, 1, 43, "Subsection"], -Cell[6906, 210, 4846, 121, 455, "Input"] -}, Closed]], -Cell[CellGroupData[{ -Cell[11789, 336, 105, 1, 35, "Subsection"], -Cell[CellGroupData[{ -Cell[11919, 341, 4593, 104, 228, "Input"], -Cell[16515, 447, 4389, 76, 517, "Output"] -}, {2}]] -}, Open ]] -}, Open ]] -}, Open ]] -} -] -*) - +(* Content-type: application/vnd.wolfram.mathematica *) + +(*** Wolfram Notebook File ***) +(* http://www.wolfram.com/nb *) + +(* CreatedBy='Mathematica 10.4' *) + +(*CacheID: 234*) +(* Internal cache information: +NotebookFileLineBreakTest +NotebookFileLineBreakTest +NotebookDataPosition[ 158, 7] +NotebookDataLength[ 21974, 570] +NotebookOptionsPosition[ 20953, 529] +NotebookOutlinePosition[ 21296, 544] +CellTagsIndexPosition[ 21253, 541] +WindowFrame->Normal*) + +(* Beginning of Notebook Content *) +Notebook[{ + +Cell[CellGroupData[{ +Cell["Cobwebbing", "Title", + CellChangeTimes->{{3.776600831050974*^9, 3.7766008318453026`*^9}, { + 3.7771303814556313`*^9, 3.7771303897679653`*^9}, {3.777130431756935*^9, + 3.7771304426145535`*^9}, {3.7771538104310255`*^9, 3.7771538107522936`*^9}}], + +Cell["Adam Rumpf, 11/4/2014", "Text", + CellChangeTimes->{{3.7766008347881403`*^9, 3.776600838290375*^9}, { + 3.7771303785432096`*^9, 3.7771303802837615`*^9}}], + +Cell[CellGroupData[{ + +Cell["Introduction", "Section", + CellChangeTimes->{{3.7766008459498987`*^9, 3.776600848547045*^9}}], + +Cell[TextData[{ + "The initialization code below defines a function called ", + StyleBox["cobweb[]", "Code"], + ", which accepts a pure function, a parameter ", + Cell[BoxData[ + FormBox["r", TraditionalForm]], + FormatType->"TraditionalForm"], + ", an initial value, and a number of iterations. It then produces a cobweb \ +plot for the given function. This is used for the main Manipulate environment \ +at the end of the Notebook, which has a number of simple built-in discrete \ +dynamical systems, each of which depends on a single parameter ", + Cell[BoxData[ + FormBox["r", TraditionalForm]], + FormatType->"TraditionalForm"], + ". Note that the meaning of the parameter is different in each system." +}], "Text", + CellChangeTimes->{{3.776600856235587*^9, 3.776600860481224*^9}, { + 3.7771601060172977`*^9, 3.777160276365533*^9}, {3.7771607213398085`*^9, + 3.7771607394812503`*^9}}], + +Cell["\<\ +Some of thesefunctions are arbitrary and only meant for showing off how \ +different shapes of function can behave, but a few have some significance:\ +\>", "Text", + CellChangeTimes->{{3.776600856235587*^9, 3.776600860481224*^9}, { + 3.7771601060172977`*^9, 3.777160276365533*^9}, {3.7771607213398085`*^9, + 3.77716072716536*^9}}], + +Cell[CellGroupData[{ + +Cell[TextData[{ + "The discrete logistic map, of the general form ", + Cell[BoxData[ + FormBox[ + RowBox[{ + SubscriptBox["x", + RowBox[{"n", "+", "1"}]], "=", + RowBox[{"r", " ", + RowBox[{ + SubscriptBox["x", "n"], "(", + RowBox[{"1", "-", + SubscriptBox["x", "n"]}], ")"}]}]}], TraditionalForm]], + FormatType->"TraditionalForm"], + ", is usually thought of as describing a population whose size is limited by \ +finite resources. ", + Cell[BoxData[ + FormBox[ + SubscriptBox["x", "n"], TraditionalForm]], + FormatType->"TraditionalForm"], + " is the population at time step ", + Cell[BoxData[ + FormBox["n", TraditionalForm]], + FormatType->"TraditionalForm"], + ", scaled so that ", + Cell[BoxData[ + FormBox["1", TraditionalForm]], + FormatType->"TraditionalForm"], + " is the holding capacity. ", + Cell[BoxData[ + FormBox[ + RowBox[{"r", ">", "0"}], TraditionalForm]], + FormatType->"TraditionalForm"], + " is the intrinsic growth rate. This system is famous for exhibiting chaotic \ +behavior when ", + Cell[BoxData[ + FormBox["r", TraditionalForm]], + FormatType->"TraditionalForm"], + " is sufficiently large. Try increasing the value of ", + Cell[BoxData[ + FormBox["r", TraditionalForm]], + FormatType->"TraditionalForm"], + " slowly to watch as the nonzero fixed point goes from being stable, to \ +being surrounded by periodic orbits, to complete chaos." +}], "Item", + CellChangeTimes->{{3.777160287433982*^9, 3.7771604336737385`*^9}, { + 3.777160482102011*^9, 3.7771605580480304`*^9}}], + +Cell[TextData[{ + "The discrete logistic map with proportional harvesting has the general form \ +", + Cell[BoxData[ + FormBox[ + RowBox[{ + SubscriptBox["x", + RowBox[{"n", "+", "1"}]], "=", + RowBox[{ + RowBox[{"r", " ", + RowBox[{ + SubscriptBox["x", "n"], "(", + RowBox[{"1", "-", + SubscriptBox["x", "n"]}], ")"}]}], "-", + RowBox[{"p", " ", + SubscriptBox["x", "n"]}]}]}], TraditionalForm]], + FormatType->"TraditionalForm"], + ". This is exactly the logistic growth model, but now a proportion ", + Cell[BoxData[ + FormBox[ + RowBox[{"0", "<", "p", "<", "1"}], TraditionalForm]], + FormatType->"TraditionalForm"], + " of the current population is removed each iteration." +}], "Item", + CellChangeTimes->{{3.777160287433982*^9, 3.7771604336737385`*^9}, { + 3.777160482102011*^9, 3.7771606279540477`*^9}, {3.777160744824355*^9, + 3.7771607448283534`*^9}}], + +Cell[TextData[{ + "The discrete logistic map with constant harvesting has the general form ", + Cell[BoxData[ + FormBox[ + RowBox[{ + SubscriptBox["x", + RowBox[{"n", "+", "1"}]], "=", + RowBox[{ + RowBox[{"r", " ", + RowBox[{ + SubscriptBox["x", "n"], "(", + RowBox[{"1", "-", + SubscriptBox["x", "n"]}], ")"}]}], "-", "h"}]}], TraditionalForm]], + FormatType->"TraditionalForm"], + ". This is similar to the proportional harvesting model, except that now a \ +constant amount of population ", + Cell[BoxData[ + FormBox[ + RowBox[{"h", ">", "0"}], TraditionalForm]], + FormatType->"TraditionalForm"], + " is removed each iteration." +}], "Item", + CellChangeTimes->{{3.777160287433982*^9, 3.7771604336737385`*^9}, { + 3.777160482102011*^9, 3.7771606279540477`*^9}, {3.777160744824355*^9, + 3.7771607963231335`*^9}}], + +Cell[TextData[{ + "The linear map simply consists of a line passing through the point ", + Cell[BoxData[ + FormBox[ + RowBox[{"(", + RowBox[{ + FractionBox["1", "2"], ",", + FractionBox["1", "2"]}], ")"}], TraditionalForm]], + FormatType->"TraditionalForm"], + " with a slope variable between ", + Cell[BoxData[ + FormBox[ + RowBox[{"-", "1"}], TraditionalForm]], + FormatType->"TraditionalForm"], + " and ", + Cell[BoxData[ + FormBox["1", TraditionalForm]], + FormatType->"TraditionalForm"], + ". It is meant to act as a clear demonstration of how the stability of a \ +fixed point depends on the slope of the function curve where it intersects \ +the ", + Cell[BoxData[ + FormBox[ + RowBox[{"y", "=", "x"}], TraditionalForm]], + FormatType->"TraditionalForm"], + " line." +}], "Item", + CellChangeTimes->{{3.777160287433982*^9, 3.7771604336737385`*^9}, { + 3.777160482102011*^9, 3.7771606279540477`*^9}, {3.777160744824355*^9, + 3.7771608420031204`*^9}, {3.777160895152163*^9, 3.7771609378928003`*^9}}] +}, Open ]] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Code", "Section", + CellChangeTimes->{{3.776600864408964*^9, 3.7766008650447807`*^9}}], + +Cell[CellGroupData[{ + +Cell["Initialization", "Subsection", + CellChangeTimes->{{3.776600871130811*^9, 3.776600873087188*^9}}], + +Cell[BoxData[ + RowBox[{ + RowBox[{"(*", " ", + RowBox[{ + RowBox[{ + "generates", " ", "the", " ", "cobweb", " ", "plot", " ", "for", " ", "a", + " ", "given", " ", "pure", " ", "function", " ", "f"}], ",", " ", + RowBox[{"parameter", " ", "r"}], ",", " ", + RowBox[{"initial", " ", "value", " ", "x0"}], ",", " ", + RowBox[{"and", " ", "number", " ", "of", " ", "iterations", " ", "n"}]}], + " ", "*)"}], "\[IndentingNewLine]", + RowBox[{ + RowBox[{"cobweb", "[", + RowBox[{"f_", ",", "r_", ",", "x0_", ",", "n_"}], "]"}], ":=", + RowBox[{"Module", "[", + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{"pts", "=", + RowBox[{"{", + RowBox[{"{", + RowBox[{"x0", ",", "0"}], "}"}], "}"}]}], ",", "y"}], "}"}], ",", + "\[IndentingNewLine]", + RowBox[{"(*", " ", + RowBox[{"generate", " ", "sequence", " ", "of", " ", "points"}], " ", + "*)"}], "\[IndentingNewLine]", + RowBox[{ + RowBox[{"Do", "[", "\[IndentingNewLine]", + RowBox[{"(*", " ", + RowBox[{"vertical", " ", "to", " ", "f"}], " ", "*)"}], + "\[IndentingNewLine]", + RowBox[{ + RowBox[{ + RowBox[{"y", "=", + RowBox[{"f", "[", + RowBox[{ + RowBox[{"pts", "[", + RowBox[{"[", + RowBox[{ + RowBox[{"-", "1"}], ",", "1"}], "]"}], "]"}], ",", "r"}], + "]"}]}], ";", "\[IndentingNewLine]", + RowBox[{"pts", "=", + RowBox[{"Append", "[", + RowBox[{"pts", ",", + RowBox[{"{", + RowBox[{ + RowBox[{"pts", "[", + RowBox[{"[", + RowBox[{ + RowBox[{"-", "1"}], ",", "1"}], "]"}], "]"}], ",", "y"}], + "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", + RowBox[{"If", "[", + RowBox[{ + RowBox[{ + RowBox[{"y", "<", "0"}], "||", + RowBox[{"y", ">", + SuperscriptBox["10", "30"]}]}], ",", "\[IndentingNewLine]", + RowBox[{"(*", " ", + RowBox[{ + "break", " ", "if", " ", "we", " ", "reach", " ", "a", " ", + "negative", " ", "value", " ", "or", " ", "too", " ", "large", + " ", "of", " ", "a", " ", "value"}], " ", "*)"}], + "\[IndentingNewLine]", + RowBox[{ + RowBox[{"Break", "[", "]"}], ";"}]}], "\[IndentingNewLine]", + "]"}], ";", "\[IndentingNewLine]", + RowBox[{"(*", " ", + RowBox[{ + RowBox[{"horizontal", " ", "to", " ", "y"}], "=", "x"}], " ", + "*)"}], "\[IndentingNewLine]", + RowBox[{"pts", "=", + RowBox[{"Append", "[", + RowBox[{"pts", ",", + RowBox[{"{", + RowBox[{"y", ",", "y"}], "}"}]}], "]"}]}]}], ",", + "\[IndentingNewLine]", + RowBox[{"{", + RowBox[{"i", ",", "1", ",", "n"}], "}"}]}], "]"}], ";", + "\[IndentingNewLine]", + RowBox[{"(*", " ", + RowBox[{"draw", " ", "diagram"}], " ", "*)"}], "\[IndentingNewLine]", + RowBox[{"Show", "[", + RowBox[{ + RowBox[{"Plot", "[", + RowBox[{ + RowBox[{"{", + RowBox[{"x", ",", + RowBox[{"f", "[", + RowBox[{"x", ",", "r"}], "]"}]}], "}"}], ",", + RowBox[{"{", + RowBox[{"x", ",", "0", ",", "1"}], "}"}], ",", + RowBox[{"PlotStyle", "\[Rule]", + RowBox[{"{", + RowBox[{ + RowBox[{"Directive", "[", + RowBox[{"Thick", ",", "Black"}], "]"}], ",", "Blue"}], + "}"}]}]}], "]"}], ",", + RowBox[{"Graphics", "[", + RowBox[{"{", + RowBox[{"Red", ",", " ", + RowBox[{"Line", "[", "pts", "]"}]}], "}"}], "]"}], ",", + RowBox[{"PlotRange", "\[Rule]", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{"0", ",", "1"}], "}"}], ",", + RowBox[{"{", + RowBox[{"0", ",", "1"}], "}"}]}], "}"}]}], ",", + RowBox[{"AspectRatio", "\[Rule]", "1"}], ",", + RowBox[{"Axes", "\[Rule]", "True"}], ",", + RowBox[{"AxesLabel", "\[Rule]", + RowBox[{"{", + RowBox[{ + "\"\<\!\(\*SubscriptBox[\(x\), \(n\)]\)\>\"", ",", + "\"\<\!\(\*SubscriptBox[\(x\), \(n + 1\)]\)\>\""}], "}"}]}]}], + "]"}]}]}], "\[IndentingNewLine]", "]"}]}]}]], "Input", + CellChangeTimes->{{3.7766008761831923`*^9, 3.776600882799075*^9}, { + 3.7771555265254726`*^9, 3.7771555956462235`*^9}, {3.777155660625909*^9, + 3.777155740927166*^9}, {3.77715578405746*^9, 3.7771559343330507`*^9}, { + 3.777155999295798*^9, 3.7771561977500076`*^9}, {3.77715672559943*^9, + 3.77715676271062*^9}, {3.777157939775195*^9, 3.7771579539182663`*^9}, { + 3.7771586587903957`*^9, 3.7771586589976068`*^9}}] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Demonstration", "Subsection", + CellChangeTimes->{{3.7766008885632277`*^9, 3.7766008904796133`*^9}}], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Manipulate", "[", + RowBox[{ + RowBox[{"Module", "[", + RowBox[{ + RowBox[{"{", "}"}], ",", "\[IndentingNewLine]", + RowBox[{"cobweb", "[", + RowBox[{"f", ",", "r", ",", "x0", ",", "30"}], "]"}]}], + "\[IndentingNewLine]", "]"}], ",", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{"f", ",", + RowBox[{ + RowBox[{"4", "#2", "#1", + RowBox[{"(", + RowBox[{"1", "-", "#1"}], ")"}]}], "&"}], ",", + "\"\<\!\(\*SubscriptBox[\(x\), \(n + 1\)]\)\>\""}], "}"}], ",", + RowBox[{"{", + RowBox[{ + RowBox[{ + RowBox[{ + RowBox[{"4", "#2", "#1", + RowBox[{"(", + RowBox[{"1", "-", "#1"}], ")"}]}], "&"}], "\[Rule]", + "\"\<4\!\(\*SubscriptBox[\(rx\), \(n\)]\)(1-\!\(\*SubscriptBox[\(x\), \ +\(n\)]\)) - logistic map\>\""}], ",", + RowBox[{ + RowBox[{ + RowBox[{ + RowBox[{"3", "#1", + RowBox[{"(", + RowBox[{"1", "-", "#1"}], ")"}]}], "-", + RowBox[{"#2", "#1"}]}], "&"}], "\[Rule]", + "\"\<3\!\(\*SubscriptBox[\(x\), \(n\)]\)(1-\!\(\*SubscriptBox[\(x\), \ +\(n\)]\))-\!\(\*SubscriptBox[\(rx\), \(n\)]\) - logistic w/ prop. \ +harvesting\>\""}], ",", + RowBox[{ + RowBox[{ + RowBox[{ + RowBox[{"2", "#1", + RowBox[{"(", + RowBox[{"1", "-", "#1"}], ")"}]}], "+", + RowBox[{"0.5", "#2"}], "-", "0.25"}], "&"}], "\[Rule]", + "\"\<2\!\(\*SubscriptBox[\(x\), \(n\)]\)(1-\!\(\*SubscriptBox[\(x\), \ +\(n\)]\))+0.5r-0.25 - logistic w/ const. harvesting\>\""}], ",", + RowBox[{ + RowBox[{ + RowBox[{ + RowBox[{"4", + RowBox[{"(", + RowBox[{"#2", "-", "0.5"}], ")"}], + RowBox[{"(", + RowBox[{"#1", "-", "0.5"}], ")"}]}], "+", "0.5"}], "&"}], + "\[Rule]", + "\"\<2(r-0.5)(\!\(\*SubscriptBox[\(x\), \(n\)]\)-0.5)+0.5 - \ +linear\>\""}], ",", + RowBox[{ + RowBox[{ + RowBox[{ + RowBox[{"5.6", + SuperscriptBox["#1", "3"]}], "-", + RowBox[{"7", + SuperscriptBox["#1", "2"]}], "+", + RowBox[{"2.5", "#1"}], "+", + RowBox[{"0.4", "#2"}]}], "&"}], "\[Rule]", + "\"\<5.6\!\(\*SuperscriptBox[SubscriptBox[\(x\), \(n\)], \(3\)]\)-7\!\ +\(\*SuperscriptBox[SubscriptBox[\(x\), \(n\)], \ +\(2\)]\)+2.5\!\(\*SubscriptBox[\(x\), \(n\)]\)+0.4r - cubic\>\""}]}], "}"}], + ",", "PopupMenu"}], "}"}], ",", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{"r", ",", "0.65", ",", "\"\\""}], "}"}], ",", "0", ",", + "1"}], "}"}], ",", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{ + "x0", ",", "0.25", ",", "\"\<\!\(\*SubscriptBox[\(x\), \(0\)]\)\>\""}], + "}"}], ",", "0.01", ",", "0.99"}], "}"}]}], "]"}]], "Input", + CellChangeTimes->{{3.7766008920271177`*^9, 3.7766008970415297`*^9}, { + 3.7771562414820786`*^9, 3.7771563442494297`*^9}, {3.7771563995143404`*^9, + 3.777156516567629*^9}, {3.7771565579644203`*^9, 3.7771566308395443`*^9}, { + 3.7771566638834124`*^9, 3.7771567107130213`*^9}, {3.777156784185316*^9, + 3.777156786028338*^9}, {3.777156832919155*^9, 3.777156870190647*^9}, { + 3.7771569076381054`*^9, 3.777156910114409*^9}, {3.7771569530182934`*^9, + 3.77715697366871*^9}, {3.77715700935042*^9, 3.7771570454786167`*^9}, { + 3.7771571178308992`*^9, 3.7771571287366505`*^9}, {3.7771571818975186`*^9, + 3.7771571866982684`*^9}, {3.7771572231348476`*^9, + 3.7771572812355137`*^9}, {3.7771573628429117`*^9, + 3.7771574205793257`*^9}, {3.7771574629188404`*^9, + 3.7771574683729973`*^9}, {3.7771577370959873`*^9, 3.777157812798995*^9}, { + 3.777157872216112*^9, 3.7771579054766293`*^9}, {3.7771580044952917`*^9, + 3.777158057902335*^9}, {3.777158151432196*^9, 3.7771581525935416`*^9}, { + 3.7771581963046274`*^9, 3.777158237238636*^9}, {3.7771582732210417`*^9, + 3.777158299544817*^9}, {3.777158353884241*^9, 3.7771583694134836`*^9}, { + 3.7771585371169043`*^9, 3.777158628695525*^9}, {3.77715873093116*^9, + 3.777158760363877*^9}, {3.777158804844178*^9, 3.7771589222902794`*^9}, { + 3.7771589589736195`*^9, 3.777158994414666*^9}, {3.7771590629657545`*^9, + 3.777159081959144*^9}, {3.777159113553509*^9, 3.7771591154797077`*^9}, { + 3.7771591503647776`*^9, 3.777159194511875*^9}, {3.7771592775912194`*^9, + 3.777159279203702*^9}, {3.777159347378621*^9, 3.7771593806264257`*^9}, { + 3.7771600726679134`*^9, 3.7771600741784315`*^9}, {3.7771606474508095`*^9, + 3.777160692919137*^9}, 3.77716086758996*^9}], + +Cell[BoxData[ + TagBox[ + StyleBox[ + DynamicModuleBox[{$CellContext`f$$ = 4 (#2 - 0.5) (# - 0.5) + + 0.5& , $CellContext`r$$ = 0.29, $CellContext`x0$$ = 0.25, Typeset`show$$ = + True, Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", + Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = + "\"untitled\"", Typeset`specs$$ = {{{ + Hold[$CellContext`f$$], 4 #2 # (1 - #)& , + "\!\(\*SubscriptBox[\(x\), \(n + 1\)]\)"}, {(4 #2 # (1 - #)& ) -> + "4\!\(\*SubscriptBox[\(rx\), \(n\)]\)(1-\!\(\*SubscriptBox[\(x\), \ +\(n\)]\)) - logistic map", (3 # (1 - #) - #2 #& ) -> + "3\!\(\*SubscriptBox[\(x\), \(n\)]\)(1-\!\(\*SubscriptBox[\(x\), \ +\(n\)]\))-\!\(\*SubscriptBox[\(rx\), \(n\)]\) - logistic w/ prop. \ +harvesting", (2 # (1 - #) + 0.5 #2 - 0.25& ) -> + "2\!\(\*SubscriptBox[\(x\), \(n\)]\)(1-\!\(\*SubscriptBox[\(x\), \ +\(n\)]\))+0.5r-0.25 - logistic w/ const. harvesting", (4 (#2 - 0.5) (# - 0.5) + + 0.5& ) -> + "2(r-0.5)(\!\(\*SubscriptBox[\(x\), \(n\)]\)-0.5)+0.5 - linear", ( + 5.6 #^3 - 7 #^2 + 2.5 # + 0.4 #2& ) -> + "5.6\!\(\*SuperscriptBox[SubscriptBox[\(x\), \(n\)], \ +\(3\)]\)-7\!\(\*SuperscriptBox[SubscriptBox[\(x\), \(n\)], \ +\(2\)]\)+2.5\!\(\*SubscriptBox[\(x\), \(n\)]\)+0.4r - cubic"}}, {{ + Hold[$CellContext`r$$], 0.65, "r"}, 0, 1}, {{ + Hold[$CellContext`x0$$], 0.25, "\!\(\*SubscriptBox[\(x\), \(0\)]\)"}, + 0.01, 0.99}}, Typeset`size$$ = {360., {172., 176.}}, Typeset`update$$ = + 0, Typeset`initDone$$, Typeset`skipInitDone$$ = + True, $CellContext`f$290522$$ = False, $CellContext`r$290523$$ = + 0, $CellContext`x0$290524$$ = 0}, + DynamicBox[Manipulate`ManipulateBoxes[ + 1, StandardForm, + "Variables" :> {$CellContext`f$$ = 4 #2 # (1 - #)& , $CellContext`r$$ = + 0.65, $CellContext`x0$$ = 0.25}, "ControllerVariables" :> { + Hold[$CellContext`f$$, $CellContext`f$290522$$, False], + Hold[$CellContext`r$$, $CellContext`r$290523$$, 0], + Hold[$CellContext`x0$$, $CellContext`x0$290524$$, 0]}, + "OtherVariables" :> { + Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, + Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, + Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, + Typeset`skipInitDone$$}, "Body" :> Module[{}, + $CellContext`cobweb[$CellContext`f$$, $CellContext`r$$, \ +$CellContext`x0$$, 30]], + "Specifications" :> {{{$CellContext`f$$, 4 #2 # (1 - #)& , + "\!\(\*SubscriptBox[\(x\), \(n + 1\)]\)"}, {(4 #2 # (1 - #)& ) -> + "4\!\(\*SubscriptBox[\(rx\), \(n\)]\)(1-\!\(\*SubscriptBox[\(x\), \ +\(n\)]\)) - logistic map", (3 # (1 - #) - #2 #& ) -> + "3\!\(\*SubscriptBox[\(x\), \(n\)]\)(1-\!\(\*SubscriptBox[\(x\), \ +\(n\)]\))-\!\(\*SubscriptBox[\(rx\), \(n\)]\) - logistic w/ prop. \ +harvesting", (2 # (1 - #) + 0.5 #2 - 0.25& ) -> + "2\!\(\*SubscriptBox[\(x\), \(n\)]\)(1-\!\(\*SubscriptBox[\(x\), \ +\(n\)]\))+0.5r-0.25 - logistic w/ const. harvesting", (4 (#2 - 0.5) (# - 0.5) + + 0.5& ) -> + "2(r-0.5)(\!\(\*SubscriptBox[\(x\), \(n\)]\)-0.5)+0.5 - linear", ( + 5.6 #^3 - 7 #^2 + 2.5 # + 0.4 #2& ) -> + "5.6\!\(\*SuperscriptBox[SubscriptBox[\(x\), \(n\)], \(3\)]\)-7\!\(\ +\*SuperscriptBox[SubscriptBox[\(x\), \(n\)], \ +\(2\)]\)+2.5\!\(\*SubscriptBox[\(x\), \(n\)]\)+0.4r - cubic"}, ControlType -> + PopupMenu}, {{$CellContext`r$$, 0.65, "r"}, 0, + 1}, {{$CellContext`x0$$, 0.25, "\!\(\*SubscriptBox[\(x\), \(0\)]\)"}, + 0.01, 0.99}}, "Options" :> {}, "DefaultOptions" :> {}], + ImageSizeCache->{411., {247., 253.}}, + SingleEvaluation->True], + Deinitialization:>None, + DynamicModuleValues:>{}, + SynchronousInitialization->True, + UndoTrackedVariables:>{Typeset`show$$, Typeset`bookmarkMode$$}, + UnsavedVariables:>{Typeset`initDone$$}, + UntrackedVariables:>{Typeset`size$$}], "Manipulate", + Deployed->True, + StripOnInput->False], + Manipulate`InterpretManipulate[1]]], "Output", + CellChangeTimes->{{3.777159073259899*^9, 3.7771590827182055`*^9}, + 3.7771591166822023`*^9, {3.7771591663559117`*^9, 3.7771591948043566`*^9}, + 3.7771592797965126`*^9, {3.77715934801046*^9, 3.777159380865356*^9}, + 3.77716007487621*^9, {3.7771606504230127`*^9, 3.7771606937288465`*^9}, + 3.777160868560651*^9}] +}, {2}]] +}, Open ]] +}, Open ]] +}, Open ]] +}, +WindowSize->{759, 833}, +WindowMargins->{{91, Automatic}, {Automatic, 84}}, +FrontEndVersion->"10.4 for Microsoft Windows (64-bit) (April 11, 2016)", +StyleDefinitions->"Default.nb" +] +(* End of Notebook Content *) + +(* Internal cache information *) +(*CellTagsOutline +CellTagsIndex->{} +*) +(*CellTagsIndex +CellTagsIndex->{} +*) +(*NotebookFileOutline +Notebook[{ +Cell[CellGroupData[{ +Cell[580, 22, 249, 3, 90, "Title"], +Cell[832, 27, 158, 2, 30, "Text"], +Cell[CellGroupData[{ +Cell[1015, 33, 99, 1, 63, "Section"], +Cell[1117, 36, 879, 18, 106, "Text"], +Cell[1999, 56, 339, 6, 49, "Text"], +Cell[CellGroupData[{ +Cell[2363, 66, 1513, 45, 115, "Item"], +Cell[3879, 113, 900, 26, 66, "Item"], +Cell[4782, 141, 846, 24, 64, "Item"], +Cell[5631, 167, 1005, 29, 75, "Item"] +}, Open ]] +}, Open ]], +Cell[CellGroupData[{ +Cell[6685, 202, 91, 1, 63, "Section"], +Cell[CellGroupData[{ +Cell[6801, 207, 102, 1, 43, "Subsection"], +Cell[6906, 210, 4846, 121, 455, "Input"] +}, Closed]], +Cell[CellGroupData[{ +Cell[11789, 336, 105, 1, 35, "Subsection"], +Cell[CellGroupData[{ +Cell[11919, 341, 4593, 104, 228, "Input"], +Cell[16515, 447, 4389, 76, 517, "Output"] +}, {2}]] +}, Open ]] +}, Open ]] +}, Open ]] +} +] +*) + diff --git a/calc-diffeq-analysis/complex-newtons-method.nb b/calc-diffeq-analysis/complex-newtons-method.nb index a5fb405..04e6a78 100644 --- a/calc-diffeq-analysis/complex-newtons-method.nb +++ b/calc-diffeq-analysis/complex-newtons-method.nb @@ -1,6883 +1,6883 @@ -(* Content-type: application/vnd.wolfram.mathematica *) - -(*** Wolfram Notebook File ***) -(* http://www.wolfram.com/nb *) - -(* CreatedBy='Mathematica 10.2' *) - -(*CacheID: 234*) -(* Internal cache information: -NotebookFileLineBreakTest -NotebookFileLineBreakTest -NotebookDataPosition[ 158, 7] -NotebookDataLength[ 377475, 6875] -NotebookOptionsPosition[ 375359, 6799] -NotebookOutlinePosition[ 375703, 6814] -CellTagsIndexPosition[ 375660, 6811] -WindowFrame->Normal*) - -(* Beginning of Notebook Content *) -Notebook[{ - -Cell[CellGroupData[{ -Cell["Complex Newton\[CloseCurlyQuote]s Method", "Title", - CellChangeTimes->{{3.776587885602626*^9, 3.7765878892047005`*^9}}], - -Cell["Adam Rumpf, 2/23/2016", "Text", - CellChangeTimes->{{3.7765879645996017`*^9, 3.7765879864409084`*^9}}], - -Cell[CellGroupData[{ - -Cell["Introduction", "Section", - CellChangeTimes->{{3.7765879027790375`*^9, 3.776587905025833*^9}}], - -Cell[TextData[{ - "Newton\[CloseCurlyQuote]s method (a.k.a. the Newton-Raphson method) is an \ -iterative root finding process. Given a function ", - Cell[BoxData[ - FormBox["f", TraditionalForm]], - FormatType->"TraditionalForm"], - " and an initial guess ", - Cell[BoxData[ - FormBox[ - SubscriptBox["x", "0"], TraditionalForm]], - FormatType->"TraditionalForm"], - ", the process is defined by:" -}], "Text", - CellChangeTimes->{{3.7765873898669224`*^9, 3.776587628077781*^9}}], - -Cell[BoxData[ - RowBox[{"\t", - FormBox[ - RowBox[{ - SubscriptBox["x", - RowBox[{"n", "+", "1"}]], "=", - RowBox[{ - SubscriptBox["x", "n"], "-", - FractionBox[ - RowBox[{"f", "(", - SubscriptBox["x", "n"], ")"}], - RowBox[{ - RowBox[{"f", "'"}], - RowBox[{"(", - SubscriptBox["x", "n"], ")"}]}]]}]}], - TraditionalForm]}]], "DisplayFormula", - CellChangeTimes->{{3.7765873898669224`*^9, 3.7765876343990145`*^9}, { - 3.7765880045342627`*^9, 3.776588004542261*^9}}], - -Cell["\<\ -This method is taught in basic Calculus, and it is mostly of interest because \ -it is (a) simple to define and understand, (b) easy to visualize, and (c) \ -good enough to still be used for scientific computing, despite being over 300 \ -years old.\ -\>", "Text", - CellChangeTimes->{{3.7765873898669224`*^9, 3.7765876554799743`*^9}, { - 3.7765880294968214`*^9, 3.776588034544223*^9}}], - -Cell["\<\ -Many students will be surprised to know that this method does not just work \ -for real-valued functions: it works for complex-valued functions, as well. \ -Its behavior in the complex plane can be a bit more complicated to describe, \ -and depending on the initial guess, the method may not necessarily converget \ -to the nearest root.\ -\>", "Text", - CellChangeTimes->{{3.7765876439551272`*^9, 3.7765877526697845`*^9}}], - -Cell[TextData[{ - "This Notebook defines a function called ", - StyleBox["newtonplot[]", "Code"], - ", which accepts (in order) a pure function, a bound ", - Cell[BoxData[ - FormBox["b", TraditionalForm]], - FormatType->"TraditionalForm"], - " for the complex domain ", - Cell[BoxData[ - FormBox[ - RowBox[{ - RowBox[{"[", - RowBox[{ - RowBox[{"-", "b"}], ",", "b"}], "]"}], "\[Times]", - RowBox[{"[", - RowBox[{ - RowBox[{"-", "b"}], ",", "b"}], "]"}]}], TraditionalForm]], - FormatType->"TraditionalForm"], - ", the number of nodes ", - Cell[BoxData[ - FormBox["n", TraditionalForm]], - FormatType->"TraditionalForm"], - " into which each axis will be divided, an iteration cutoff, and an error \ -tolerance. The function will divide the square domain into an ", - Cell[BoxData[ - FormBox[ - RowBox[{"n", "\[Times]", "n"}], TraditionalForm]], - FormatType->"TraditionalForm"], - " grid and conduct Newton\[CloseCurlyQuote]s method using every grid node as \ -an initial guess. If the method comes within the error tolerance of one of \ -the true roots, then the method terminates and we record which root was \ -reached. If no root is reached within the iteration cutoff, then the process \ -is deemed to have diverged." -}], "Text", - CellChangeTimes->{{3.7765877574128275`*^9, 3.77658778055941*^9}, { - 3.776587824735916*^9, 3.776587850473181*^9}, {3.77658806101051*^9, - 3.776588456805036*^9}}], - -Cell[TextData[{ - "The output is a coloring of the complex domain showing which initial \ -guesses converge to which roots. A larger value of ", - Cell[BoxData[ - FormBox["n", TraditionalForm]], - FormatType->"TraditionalForm"], - " will lead to a sharper picture but a longer computation time." -}], "Text", - CellChangeTimes->{{3.776588459669097*^9, 3.7765885063788424`*^9}}] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["Code", "Section", - CellChangeTimes->{{3.7765879208719325`*^9, 3.776587921823886*^9}}], - -Cell[CellGroupData[{ - -Cell["Initialization", "Subsection", - CellChangeTimes->{{3.776588544504778*^9, 3.7765885464741445`*^9}}], - -Cell[BoxData[ - RowBox[{ - RowBox[{"(*", " ", - RowBox[{ - RowBox[{"roots", "[", "f", "]"}], " ", "returns", " ", "a", " ", "list", - " ", "of", " ", "the", " ", "unique", " ", "roots", " ", "of", " ", - "function", " ", - RowBox[{"f", "."}]}], " ", "*)"}], "\[IndentingNewLine]", - RowBox[{ - RowBox[{ - RowBox[{"roots", "[", "f_", "]"}], ":=", - RowBox[{"Module", "[", - RowBox[{ - RowBox[{"{", "r", "}"}], ",", "\[IndentingNewLine]", - RowBox[{ - RowBox[{"r", "=", - RowBox[{"DeleteDuplicates", "[", - RowBox[{"x", "/.", - RowBox[{"Solve", "[", - RowBox[{ - RowBox[{ - RowBox[{"f", "[", "x", "]"}], "\[Equal]", "0"}], ",", "x"}], - "]"}]}], "]"}]}], ";", "\[IndentingNewLine]", - RowBox[{"Table", "[", - RowBox[{ - RowBox[{ - RowBox[{"Re", "[", - RowBox[{"r", "[", - RowBox[{"[", "i", "]"}], "]"}], "]"}], "+", - RowBox[{"I", " ", - RowBox[{"Im", "[", - RowBox[{"r", "[", - RowBox[{"[", "i", "]"}], "]"}], "]"}]}]}], ",", - RowBox[{"{", - RowBox[{"i", ",", "1", ",", - RowBox[{"Length", "[", "r", "]"}]}], "}"}]}], "]"}]}]}], - "\[IndentingNewLine]", "]"}]}], ";"}]}]], "Input", - CellChangeTimes->{{3.65954843910914*^9, 3.65954848479572*^9}, { - 3.6595485169148393`*^9, 3.6595485598267083`*^9}, {3.659555212555744*^9, - 3.6595552904228373`*^9}}], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"roots", "[", - RowBox[{"Function", "[", - RowBox[{"x", ",", - RowBox[{ - SuperscriptBox["x", "3"], "-", "1"}]}], "]"}], "]"}]], "Input", - CellChangeTimes->{{3.6595485653603544`*^9, 3.65954859823431*^9}, { - 3.6595552298253365`*^9, 3.659555232700883*^9}}], - -Cell[BoxData[ - RowBox[{"{", - RowBox[{"1", ",", - RowBox[{ - RowBox[{"-", - FractionBox["1", "2"]}], "-", - FractionBox[ - RowBox[{"\[ImaginaryI]", " ", - SqrtBox["3"]}], "2"]}], ",", - RowBox[{ - RowBox[{"-", - FractionBox["1", "2"]}], "+", - FractionBox[ - RowBox[{"\[ImaginaryI]", " ", - SqrtBox["3"]}], "2"]}]}], "}"}]], "Output", - CellChangeTimes->{{3.6595485756723404`*^9, 3.659548598922804*^9}, - 3.6595552340602794`*^9, 3.6595552931736403`*^9}] -}, Open ]], - -Cell[BoxData[ - RowBox[{ - RowBox[{"(*", " ", - RowBox[{ - RowBox[{ - RowBox[{"newtonplot", "[", - RowBox[{"f", ",", "lim", ",", "n", ",", "cut", ",", "eps"}], "]"}], " ", - "creates", " ", "a", " ", "plot", " ", "of", " ", "the", " ", - RowBox[{"region", " ", "[", - RowBox[{ - RowBox[{"-", "lim"}], ",", "lim"}], "]"}], - RowBox[{"x", "[", - RowBox[{ - RowBox[{"-", "lim"}], ",", "lim"}], "]"}], " ", "of", " ", "the", " ", - "complex", " ", "plane"}], ",", " ", - RowBox[{"divided", " ", "into", " ", "an", " ", "nxn", " ", - RowBox[{"grid", ".", " ", "Each"}], " ", "grid", " ", "point", " ", - "is", " ", "used", " ", "as", " ", "the", " ", "initial", " ", "guess", - " ", "for", " ", "complex", " ", - RowBox[{"Newton", "'"}], "s", " ", "method", " ", "on", " ", "function", - " ", - RowBox[{"f", ".", " ", "Each"}], " ", "root", " ", "is", " ", - "assigned", " ", "a", " ", "color"}], ",", " ", - RowBox[{"and", " ", "after", " ", "cut", " ", "iterations"}], ",", " ", - RowBox[{ - "if", " ", "we", " ", "are", " ", "within", " ", "distance", " ", "eps", - " ", "of", " ", "a", " ", "root"}], ",", " ", - RowBox[{"we", " ", "assign", " ", "that", " ", "point", " ", "that", " ", - RowBox[{"root", "'"}], "s", " ", - RowBox[{"color", ".", " ", "If"}], " ", "if", " ", "is", " ", "not", - " ", "that", " ", "close", " ", "to", " ", "any", " ", "root"}], ",", - " ", - RowBox[{"we", " ", "color", " ", "it", " ", - RowBox[{"black", "."}]}]}], " ", "*)"}], "\[IndentingNewLine]", - RowBox[{ - RowBox[{ - RowBox[{"newtonplot", "[", - RowBox[{"f_", ",", "lim_", ",", "n_", ",", "cut_", ",", "eps_"}], "]"}], - ":=", - RowBox[{"Module", "[", - RowBox[{ - RowBox[{"{", - RowBox[{ - "fp", ",", "newton", ",", "rootlist", ",", "array", ",", "grid", ",", - "dx", ",", "i", ",", "j", ",", "iter", ",", "x", ",", "numroots", ",", - "rootnum"}], "}"}], ",", "\[IndentingNewLine]", - RowBox[{"(*", " ", - RowBox[{ - RowBox[{"fp", " ", "=", " ", - RowBox[{ - RowBox[{ - "derivative", " ", "of", " ", "f", "\[IndentingNewLine]", - "newton"}], " ", "=", " ", - RowBox[{ - RowBox[{ - RowBox[{"Newton", "'"}], "s", " ", "method", " ", "iteration", - " ", "function", "\[IndentingNewLine]", "rootlist"}], " ", "=", - " ", - RowBox[{ - RowBox[{ - "list", " ", "of", " ", "all", " ", "unique", " ", "roots", " ", - "of", " ", "f", "\[IndentingNewLine]", "array"}], " ", "=", " ", - RowBox[{ - RowBox[{ - "array", " ", "of", " ", "values", " ", "corresponding", " ", - "to", " ", "each", " ", "grid", " ", "point", " ", - RowBox[{"(", - RowBox[{ - RowBox[{ - RowBox[{"-", "1"}], " ", "means", " ", "no", " ", "root"}], - ",", " ", - RowBox[{ - "positive", " ", "integer", " ", "corresponds", " ", "to", - " ", "one", " ", "of", " ", "the", " ", "roots", " ", "in", - " ", "the", " ", "list"}]}], ")"}], "\[IndentingNewLine]", - "grid"}], " ", "=", " ", - RowBox[{ - RowBox[{ - "array", " ", "of", " ", "actual", " ", "coordinates", " ", - "of", " ", "grid", " ", "points", "\[IndentingNewLine]", - "dx"}], " ", "=", " ", - RowBox[{ - "space", " ", "between", " ", "grid", " ", "points", - "\[IndentingNewLine]", "i"}]}]}]}]}]}]}], ",", - RowBox[{"j", " ", "=", " ", - RowBox[{ - RowBox[{ - "coordinates", " ", "of", " ", "point", " ", "currently", " ", - "being", " ", "examined", "\[IndentingNewLine]", "iter"}], " ", - "=", " ", - RowBox[{ - RowBox[{"current", " ", "iteration", " ", "of", " ", - RowBox[{"Newton", "'"}], "s", " ", "Method", - "\[IndentingNewLine]", "x"}], " ", "=", " ", - RowBox[{ - RowBox[{"current", " ", "guess", " ", "in", " ", - RowBox[{"Newton", "'"}], "s", " ", "Method", - "\[IndentingNewLine]", "numroots"}], " ", "=", " ", - RowBox[{ - RowBox[{ - "number", " ", "of", " ", "roots", "\[IndentingNewLine]", - "rootnum"}], " ", "=", " ", - RowBox[{ - "index", " ", "of", " ", "root", " ", "under", " ", - "evaluation"}]}]}]}]}]}]}], " ", "*)"}], "\[IndentingNewLine]", - RowBox[{ - RowBox[{"fp", "=", - RowBox[{"Function", "[", - RowBox[{"x", ",", - RowBox[{ - RowBox[{"f", "'"}], "[", "x", "]"}]}], "]"}]}], ";", - "\[IndentingNewLine]", - RowBox[{"newton", "=", - RowBox[{"Function", "[", - RowBox[{"x", ",", - RowBox[{"N", "[", - RowBox[{"x", "-", - FractionBox[ - RowBox[{"f", "[", "x", "]"}], - RowBox[{"fp", "[", "x", "]"}]]}], "]"}]}], "]"}]}], ";", - "\[IndentingNewLine]", - RowBox[{"rootlist", "=", - RowBox[{"roots", "[", "f", "]"}]}], ";", "\[IndentingNewLine]", - RowBox[{"numroots", "=", - RowBox[{"Length", "[", "rootlist", "]"}]}], ";", - "\[IndentingNewLine]", - RowBox[{"dx", "=", - FractionBox[ - RowBox[{"2", "lim"}], - RowBox[{"n", "-", "1"}]]}], ";", "\[IndentingNewLine]", - RowBox[{"array", "=", - RowBox[{"ConstantArray", "[", - RowBox[{ - RowBox[{"-", "1"}], ",", - RowBox[{"{", - RowBox[{"n", ",", "n"}], "}"}]}], "]"}]}], ";", - "\[IndentingNewLine]", - RowBox[{"grid", "=", - RowBox[{"Table", "[", - RowBox[{ - RowBox[{"N", "[", - RowBox[{ - RowBox[{"(", - RowBox[{ - RowBox[{"-", "lim"}], "+", - RowBox[{"l", " ", "dx"}]}], ")"}], "+", - RowBox[{"I", - RowBox[{"(", - RowBox[{ - RowBox[{"-", "lim"}], "+", - RowBox[{"k", " ", "dx"}]}], ")"}]}]}], "]"}], ",", - RowBox[{"{", - RowBox[{"k", ",", - RowBox[{"n", "-", "1"}], ",", "0", ",", - RowBox[{"-", "1"}]}], "}"}], ",", - RowBox[{"{", - RowBox[{"l", ",", "0", ",", - RowBox[{"n", "-", "1"}]}], "}"}]}], "]"}]}], ";", - "\[IndentingNewLine]", - RowBox[{"For", "[", - RowBox[{ - RowBox[{"i", "=", "1"}], ",", - RowBox[{"i", "\[LessEqual]", "n"}], ",", - RowBox[{"i", "++"}], ",", "\[IndentingNewLine]", - RowBox[{ - RowBox[{"For", "[", - RowBox[{ - RowBox[{"j", "=", "1"}], ",", - RowBox[{"j", "\[LessEqual]", "n"}], ",", - RowBox[{"j", "++"}], ",", "\[IndentingNewLine]", - RowBox[{ - RowBox[{"x", "=", - RowBox[{"grid", "[", - RowBox[{"[", - RowBox[{"i", ",", "j"}], "]"}], "]"}]}], ";", - "\[IndentingNewLine]", - RowBox[{"For", "[", - RowBox[{ - RowBox[{"iter", "=", "1"}], ",", - RowBox[{"iter", "\[LessEqual]", "cut"}], ",", - RowBox[{"iter", "++"}], ",", "\[IndentingNewLine]", - RowBox[{ - RowBox[{"If", "[", - RowBox[{ - RowBox[{ - RowBox[{ - RowBox[{"fp", "[", "x", "]"}], "\[NotEqual]", "0"}], "&&", - RowBox[{ - RowBox[{"Abs", "[", "x", "]"}], "\[NotEqual]", - "Infinity"}]}], ",", "\[IndentingNewLine]", - RowBox[{"x", "=", - RowBox[{"newton", "[", "x", "]"}]}], ",", - "\[IndentingNewLine]", - RowBox[{ - RowBox[{"x", "=", "ComplexInfinity"}], ";"}]}], - "\[IndentingNewLine]", "]"}], ";"}]}], "\[IndentingNewLine]", - "]"}], ";", "\[IndentingNewLine]", - RowBox[{"For", "[", - RowBox[{ - RowBox[{"rootnum", "=", "1"}], ",", - RowBox[{"rootnum", "\[LessEqual]", "numroots"}], ",", - RowBox[{"rootnum", "++"}], ",", "\[IndentingNewLine]", - RowBox[{ - RowBox[{"If", "[", - RowBox[{ - RowBox[{ - RowBox[{"Abs", "[", - RowBox[{"x", "-", - RowBox[{"rootlist", "[", - RowBox[{"[", "rootnum", "]"}], "]"}]}], "]"}], "<", - "eps"}], ",", "\[IndentingNewLine]", - RowBox[{ - RowBox[{ - RowBox[{"array", "[", - RowBox[{"[", - RowBox[{"i", ",", "j"}], "]"}], "]"}], "=", "rootnum"}], - ";"}]}], "\[IndentingNewLine]", "]"}], ";"}]}], - "\[IndentingNewLine]", "]"}], ";"}]}], "\[IndentingNewLine]", - "]"}], ";"}]}], "\[IndentingNewLine]", "]"}], ";", - "\[IndentingNewLine]", - RowBox[{"ArrayPlot", "[", - RowBox[{"array", ",", - RowBox[{"ColorRules", "\[Rule]", - RowBox[{"Join", "[", - RowBox[{ - RowBox[{"{", - RowBox[{ - RowBox[{"-", "1"}], "\[Rule]", "Black"}], "}"}], ",", - RowBox[{"Table", "[", - RowBox[{ - RowBox[{"k", "\[Rule]", - RowBox[{"Hue", "[", - FractionBox[ - RowBox[{"k", "-", "1"}], "numroots"], "]"}]}], ",", - RowBox[{"{", - RowBox[{"k", ",", "1", ",", "numroots"}], "}"}]}], "]"}]}], - "]"}]}], ",", - RowBox[{"PlotLegends", "\[Rule]", - RowBox[{"Join", "[", - RowBox[{ - RowBox[{"{", "\"\\"", "}"}], ",", - RowBox[{"Table", "[", - RowBox[{ - RowBox[{"rootlist", "[", - RowBox[{"[", "k", "]"}], "]"}], ",", - RowBox[{"{", - RowBox[{"k", ",", "1", ",", "numroots"}], "}"}]}], "]"}]}], - "]"}]}]}], "]"}]}]}], "\[IndentingNewLine]", "]"}]}], - ";"}]}]], "Input", - CellChangeTimes->CompressedData[" -1:eJwdy1soQwEAh/E1ymWLPKFGKCWXRwvNtOzFRtgoZGK1J2luSZaatszDUHNt -bVkSm2ZIok0bmqUkS2uF5HYyucxtxchy/ufh6/f0ZUrlIhmdRqNlkkF1vnk5 -lv/Eiw0vrsOi/rATVmqm/PDWMXwFudmqa3jCl4bhQMVEUhxp71pqCnR7Fbkw -wShlw4+ekmK4c+7gQnvQJICjx9diyGQPNUHv07QMCoOSdhh95uqC96xDBSSI -DCVcavzTwN8Wtw52Whx6+Py1+RpPak2MhGBhY1UpgzSwusWDVkZqDcyx+EQw -8ZLeADnPb5Q2TXMbZBpj2iGXJuyHvoUsJfQY5tRwOyo0BmuJoymo4mgN1P+j -NcH32W4LHHlxrUBnh5uyYJizAc2D9j047x7zwVLb2wWc1OfdwLqrwB3cnSEe -oMC6GYT+DPYnZCRNhmB9YP8bJpzKY5ikunF1GhQ9/lB6B8xlkFA4KFvTD8ph -xBbhw0pvigCyJHeUyfF91ZDu8YjhP6o68js= - "]] -}, Closed]], - -Cell[CellGroupData[{ - -Cell["Demonstration", "Subsection", - CellChangeTimes->{{3.776588557645573*^9, 3.776588560857557*^9}}], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"newtonplot", "[", - RowBox[{ - RowBox[{"Function", "[", - RowBox[{"x", ",", - RowBox[{ - SuperscriptBox["x", "3"], "-", "1"}]}], "]"}], ",", "2", ",", "101", - ",", "20", ",", "0.05"}], "]"}]], "Input", - CellChangeTimes->{{3.6595549152958674`*^9, 3.659554978383319*^9}, - 3.659555332709116*^9, {3.659555509656427*^9, 3.6595555100001802`*^9}}], - -Cell[BoxData[ - TemplateBox[{GraphicsBox[ - RasterBox[CompressedData[" -1:eJzt1tGN5DYWBdABNhJH4hw2BAP+duoOwVhg+6PLrSIpkXqXqiNggOlDie+S -VSW+3/74679//ufXr19//v/f//7//fr7938R55xzHuOt62ydVr3qnGef45le -XZ9zzvln+Wi/kpK75UdXWk5e69X1Oeecf6a/jqflG+2vWs/39p/82V5dn3PO -+TM9JcdZP/v8p+8bf+/V9TnnnD/bj8bv7jdWzfvlq8/ZtM+Vn/Pq+pxzzp/t -r+PV59rsenf3ea/jaZ83f+/V9TnnnPMrXl3/1Xebl9/r1fU555w/01vnTlWu -1S4Hf+fV9TnnnO/tZ8+d1bmq/On1+DWvrs855/wZ/jqu71rjvXVT9oNn1eec -c/5sr65/l89e/9W6PNOr63POOd/bz54vq3Pd7XftQ+/+80yvrs855/zZXl2/ -2lv70ns/f4ZX1+ecc763j/YVT/HZ9/HP8Or6nHPOn+3V9c/6rPVUr4NneXV9 -zjnnz/bq+qv6o9fxlHXwbK+uzznn/Nl+d/2zOXrn4fyKV9fnnHP+bF9dp/U3 -50leXZ9zzvk9fnW+s/Ouqsv5jl5dn3PO+Tl/HU/Nl5KH8wSvrs855/xnH31v -V58jV3Ol7DvnK726Puec8/feur6eu6ve6Lyr+k/Od/Tq+pxzzs/50dXbt1yt -X903pX0enPd4dX3OOec/e3W/NMt3m5fzlV5dn3PO+c+u76qZl/OVXl2fc875 -Oa+uf3ff9Dqesg7OR7y6Puec85+99d6uytXrZ8+do/GrfRvnCV5dn3PO+Xuv -rj+777rab3G+s1fX55xz/t5bV0re2fdx/kSvrs855/y9t660vF9eXZ/zRK+u -zznn/L1X13/11t+c831+z5xzzu+pk7ZOzj/Bq+tzznmKt96Tvc/1ztOat3dc -H8X5Pl5dn3POU/qrND+60nJyzvu9uj7nnKe8/6pzHN33tH6S80/26vqcc57y -/lvVR7XqtvxqrrR95/yTvbo+55yv8t6+qPXc2XlmeXqfyTnv9+r6nHOe1nel -+W7zcs71XZzz5/vR+K7vv9m5e+fnnK/z6vqcc37VW++3qlxXfXV/Wb0+zj/R -q+tzzvms99anveeurjdlHZx/klfX55zzWX1GVa5VPqvv5Jzn+Oz7OOf8rvdW -Wq67+019F+f7+dG49yDnPM1b75+qXFWu7+J8Px99vneeVfOn7V/K59Z6Li3/ -7v467nt7j+/ed41+T6rzcs7n+9nnV78Pz55jZ+tV+6z5Zu/j1c8r3c9+j+7e -59GcT+0Dd/ndz/r9V6+Dcz7fj+7b5f0wmueuXFV9V69Xn1+fss+9f48+f3ae -o/G0/Try6u/tVa+uzzmv96PxtJyr+8y761efV/Z/rqd9z+/ar6Pxp/ZdKb8j -zjnf3Vv3pZz7KeffbN+tzq77XL2/R+N3911p+8Y55/y9r34ubb1pPvs5fVSW -9463nktbF+ec87l+dKXlfKofXWk5+Tk/utJycs45n+tnn59936f62edb832N -p63303zWfWnr4pxzPmf8rn5q9PxJ2+fZfdSor/q+pO1n6ud49fc16/eZtm+c -88/xo/vScu7WXx15yrpTcoyOp+5/2vd8lz5q1Ku+N6N5OOd89H21S582mmdV -jt3O7bTz6y6v/p6e/X6u7pd2+b2kfZ9GPSUH5zznPDj73Or5e++fVX/X9/Hr -+KxzebTuLn52PaPzHM23qk/epY8a9V2+f7P65JT1cM7r+q7Vfc9Tz4tVPnpf -Wv5d3fe2xnf/fuu7OOdH9606/znn/FP7rtn+Op6Wj3N+fPX2U6tycM55r6fk -uMt7n0vLzTlvX2n5OOe81VfcneMuH31vp+TmnOu7OOfP8dH+KyX3bD8av7qP -nPN1npKDc87P+mhfsouPvrdn3c85X+cpOTjnfHWf0nt/is9+b++2fs6f6Ck5 -OOd8to/2Yam+qk7aOjn/BE/JwTnnKX3XrHnS+q7W35xzfRfnnK/yVX1I67q7 -70rZb855Tg7OOX9K3zW7r+qdN2VfOef6Ls45360/ObrScnLO+z0lB+ecV3vr -Pdk7PtpHter0rqd6/zjnbU/JwTnn/GffbV7Oub6Lc8539ZQcR+Np+ThP9pQc -nHPO33tKjl37Rc4TPCUH55zz956So5Wv9Vxabs7v9JQcnHPOf/aUHKM+6zxK -WQ/nMzwlB+ec8+/eem9X52v52XOnd90p6+R8xFNycM45H/OUHGd99LmnrZ9/ -pqfk4Jxz/t1n9SvVvqpO2jo57/GUHJxzzr+7vuu9p62T8x5PycE55/ycH10p -/duqOmmfA+c9npKDc875e2/dt7qPuzqf/orznBycc86/++h7u/ocudp3Ve83 -53d4Sg7OOedj3vq72o+utJyc3+kpOTjnnK/1Vc9X1eV8R0/JwTnn/Jl+1zn2 -NZ6ybs57rrR8nHPO9/aUeqPPpewff5an5OCcc/5MT8nR8tHndl0nr/WUHJxz -zp/pKTlGfda5mbIenuEpOTjnnO/prfOlOt8q730uLTev9ZQcnHPOn+kpOap8 -tG9Lyc3XeEoOzjnne/rZ86U692y/ax9ex1PWz/s8JQfnnPNnekqO1T77nLW/ -z/SUHJxzzvf20T4kJfdsX12nt27avvCsHJxzzvf0tL6k2u+un7Z+/t5TcnDO -OX+Wp/Qld3t1ff1Ytqfk4Jxzzs94So7VddLWyc95Sg7OOefP9Lv7pNE8q+vP -rpPed/L3npKDc875M711/nyN33XeVa3zap2Uz5Nf85QcnHPOn+XV9a/63c89 -Zd/4e0/JwTnn/LO89Xeqt67efixtXfweT8nBOef8M3y0n6nO2+tHV1pOXusp -OTjnnPMenz3vqjrVz/M0/wd/O/nA - "], {{0, 0}, {101, 101}}, {0, 1}], Frame -> Automatic, - FrameLabel -> {None, None}, FrameTicks -> {{None, None}, {None, None}}, - GridLinesStyle -> Directive[ - GrayLevel[0.5, 0.4]], - Method -> { - "DefaultBoundaryStyle" -> Automatic, "DefaultPlotStyle" -> Automatic}], - FormBox[ - FormBox[ - TemplateBox[{"\"Divergent\"", "1", - RowBox[{ - RowBox[{"-", - RowBox[{ - FractionBox["1", "2"]}]}], "-", - FractionBox[ - RowBox[{"\[ImaginaryI]", " ", - SqrtBox["3"]}], "2"]}], - RowBox[{ - RowBox[{"-", - RowBox[{ - FractionBox["1", "2"]}]}], "+", - FractionBox[ - RowBox[{"\[ImaginaryI]", " ", - SqrtBox["3"]}], "2"]}]}, "SwatchLegend", - DisplayFunction -> (FormBox[ - StyleBox[ - StyleBox[ - PaneBox[ - TagBox[ - GridBox[{{ - TagBox[ - GridBox[{{ - GraphicsBox[{ - Directive[ - EdgeForm[ - Directive[ - Opacity[0.3], - GrayLevel[0]]], - PointSize[0.5], - AbsoluteThickness[1.6], - RGBColor[0., 0., 0.]], - RectangleBox[{0, 0}, {10, 10}, "RoundingRadius" -> 0]}, - AspectRatio -> Full, ImageSize -> {10, 10}, - PlotRangePadding -> None, ImagePadding -> Automatic, - BaselinePosition -> (Scaled[0.1] -> Baseline)], #}, { - GraphicsBox[{ - Directive[ - EdgeForm[ - Directive[ - Opacity[0.3], - GrayLevel[0]]], - PointSize[0.5], - AbsoluteThickness[1.6], - RGBColor[1., 0., 0.]], - RectangleBox[{0, 0}, {10, 10}, "RoundingRadius" -> 0]}, - AspectRatio -> Full, ImageSize -> {10, 10}, - PlotRangePadding -> None, ImagePadding -> Automatic, - BaselinePosition -> (Scaled[0.1] -> Baseline)], #2}, { - GraphicsBox[{ - Directive[ - EdgeForm[ - Directive[ - Opacity[0.3], - GrayLevel[0]]], - PointSize[0.5], - AbsoluteThickness[1.6], - RGBColor[0., 1., 0.]], - RectangleBox[{0, 0}, {10, 10}, "RoundingRadius" -> 0]}, - AspectRatio -> Full, ImageSize -> {10, 10}, - PlotRangePadding -> None, ImagePadding -> Automatic, - BaselinePosition -> (Scaled[0.1] -> Baseline)], #3}, { - GraphicsBox[{ - Directive[ - EdgeForm[ - Directive[ - Opacity[0.3], - GrayLevel[0]]], - PointSize[0.5], - AbsoluteThickness[1.6], - RGBColor[0., 0., 1.]], - RectangleBox[{0, 0}, {10, 10}, "RoundingRadius" -> 0]}, - AspectRatio -> Full, ImageSize -> {10, 10}, - PlotRangePadding -> None, ImagePadding -> Automatic, - BaselinePosition -> (Scaled[0.1] -> Baseline)], #4}}, - GridBoxAlignment -> { - "Columns" -> {Center, Left}, "Rows" -> {{Baseline}}}, - AutoDelete -> False, - GridBoxDividers -> { - "Columns" -> {{False}}, "Rows" -> {{False}}}, - GridBoxItemSize -> {"Columns" -> {{All}}, "Rows" -> {{All}}}, - GridBoxSpacings -> { - "Columns" -> {{0.5}}, "Rows" -> {{0.5}}}], "Grid"]}}, - GridBoxAlignment -> {"Columns" -> {{Left}}, "Rows" -> {{Top}}}, - AutoDelete -> False, - GridBoxItemSize -> { - "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, - GridBoxSpacings -> {"Columns" -> {{1}}, "Rows" -> {{0}}}], - "Grid"], Alignment -> Left, AppearanceElements -> None, - ImageMargins -> {{5, 5}, {5, 5}}, ImageSizeAction -> - "ResizeToFit"], LineIndent -> 0, StripOnInput -> False], { - FontFamily -> "Arial"}, Background -> Automatic, StripOnInput -> - False], TraditionalForm]& ), - InterpretationFunction :> (RowBox[{"SwatchLegend", "[", - RowBox[{ - RowBox[{"{", - RowBox[{ - RowBox[{"Directive", "[", - InterpretationBox[ - ButtonBox[ - TooltipBox[ - GraphicsBox[{{ - GrayLevel[0], - RectangleBox[{0, 0}]}, { - GrayLevel[0], - RectangleBox[{1, -1}]}, { - RGBColor[0., 0., 0.], - RectangleBox[{0, -1}, {2, 1}]}}, AspectRatio -> 1, Frame -> - True, FrameStyle -> RGBColor[0., 0., 0.], FrameTicks -> - None, PlotRangePadding -> None, ImageSize -> - Dynamic[{ - Automatic, 1.35 CurrentValue["FontCapHeight"]/ - AbsoluteCurrentValue[Magnification]}]], - "RGBColor[0., 0., 0.]"], Appearance -> None, - BaseStyle -> {}, BaselinePosition -> Baseline, - DefaultBaseStyle -> {}, ButtonFunction :> - With[{Typeset`box$ = EvaluationBox[]}, - If[ - Not[ - AbsoluteCurrentValue["Deployed"]], - SelectionMove[Typeset`box$, All, Expression]; - FrontEnd`Private`$ColorSelectorInitialAlpha = 1; - FrontEnd`Private`$ColorSelectorInitialColor = - RGBColor[0., 0., 0.]; - FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; - MathLink`CallFrontEnd[ - FrontEnd`AttachCell[Typeset`box$, - FrontEndResource["RGBColorValueSelector"], { - 0, {Left, Bottom}}, {Left, Top}, - "ClosingActions" -> { - "SelectionDeparture", "ParentChanged", - "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> - Automatic, Method -> "Preemptive"], - RGBColor[0., 0., 0.], Editable -> False, Selectable -> - False], "]"}], ",", - RowBox[{"Directive", "[", - InterpretationBox[ - ButtonBox[ - TooltipBox[ - GraphicsBox[{{ - GrayLevel[0], - RectangleBox[{0, 0}]}, { - GrayLevel[0], - RectangleBox[{1, -1}]}, { - RGBColor[1., 0., 0.], - RectangleBox[{0, -1}, {2, 1}]}}, AspectRatio -> 1, Frame -> - True, FrameStyle -> RGBColor[0.6666666666666667, 0., 0.], - FrameTicks -> None, PlotRangePadding -> None, ImageSize -> - Dynamic[{ - Automatic, 1.35 CurrentValue["FontCapHeight"]/ - AbsoluteCurrentValue[Magnification]}]], - "RGBColor[1., 0., 0.]"], Appearance -> None, - BaseStyle -> {}, BaselinePosition -> Baseline, - DefaultBaseStyle -> {}, ButtonFunction :> - With[{Typeset`box$ = EvaluationBox[]}, - If[ - Not[ - AbsoluteCurrentValue["Deployed"]], - SelectionMove[Typeset`box$, All, Expression]; - FrontEnd`Private`$ColorSelectorInitialAlpha = 1; - FrontEnd`Private`$ColorSelectorInitialColor = - RGBColor[1., 0., 0.]; - FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; - MathLink`CallFrontEnd[ - FrontEnd`AttachCell[Typeset`box$, - FrontEndResource["RGBColorValueSelector"], { - 0, {Left, Bottom}}, {Left, Top}, - "ClosingActions" -> { - "SelectionDeparture", "ParentChanged", - "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> - Automatic, Method -> "Preemptive"], - RGBColor[1., 0., 0.], Editable -> False, Selectable -> - False], "]"}], ",", - RowBox[{"Directive", "[", - InterpretationBox[ - ButtonBox[ - TooltipBox[ - GraphicsBox[{{ - GrayLevel[0], - RectangleBox[{0, 0}]}, { - GrayLevel[0], - RectangleBox[{1, -1}]}, { - RGBColor[0., 1., 0.], - RectangleBox[{0, -1}, {2, 1}]}}, AspectRatio -> 1, Frame -> - True, FrameStyle -> RGBColor[0., 0.6666666666666667, 0.], - FrameTicks -> None, PlotRangePadding -> None, ImageSize -> - Dynamic[{ - Automatic, 1.35 CurrentValue["FontCapHeight"]/ - AbsoluteCurrentValue[Magnification]}]], - "RGBColor[0., 1., 0.]"], Appearance -> None, - BaseStyle -> {}, BaselinePosition -> Baseline, - DefaultBaseStyle -> {}, ButtonFunction :> - With[{Typeset`box$ = EvaluationBox[]}, - If[ - Not[ - AbsoluteCurrentValue["Deployed"]], - SelectionMove[Typeset`box$, All, Expression]; - FrontEnd`Private`$ColorSelectorInitialAlpha = 1; - FrontEnd`Private`$ColorSelectorInitialColor = - RGBColor[0., 1., 0.]; - FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; - MathLink`CallFrontEnd[ - FrontEnd`AttachCell[Typeset`box$, - FrontEndResource["RGBColorValueSelector"], { - 0, {Left, Bottom}}, {Left, Top}, - "ClosingActions" -> { - "SelectionDeparture", "ParentChanged", - "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> - Automatic, Method -> "Preemptive"], - RGBColor[0., 1., 0.], Editable -> False, Selectable -> - False], "]"}], ",", - RowBox[{"Directive", "[", - InterpretationBox[ - ButtonBox[ - TooltipBox[ - GraphicsBox[{{ - GrayLevel[0], - RectangleBox[{0, 0}]}, { - GrayLevel[0], - RectangleBox[{1, -1}]}, { - RGBColor[0., 0., 1.], - RectangleBox[{0, -1}, {2, 1}]}}, AspectRatio -> 1, Frame -> - True, FrameStyle -> RGBColor[0., 0., 0.6666666666666667], - FrameTicks -> None, PlotRangePadding -> None, ImageSize -> - Dynamic[{ - Automatic, 1.35 CurrentValue["FontCapHeight"]/ - AbsoluteCurrentValue[Magnification]}]], - "RGBColor[0., 0., 1.]"], Appearance -> None, - BaseStyle -> {}, BaselinePosition -> Baseline, - DefaultBaseStyle -> {}, ButtonFunction :> - With[{Typeset`box$ = EvaluationBox[]}, - If[ - Not[ - AbsoluteCurrentValue["Deployed"]], - SelectionMove[Typeset`box$, All, Expression]; - FrontEnd`Private`$ColorSelectorInitialAlpha = 1; - FrontEnd`Private`$ColorSelectorInitialColor = - RGBColor[0., 0., 1.]; - FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; - MathLink`CallFrontEnd[ - FrontEnd`AttachCell[Typeset`box$, - FrontEndResource["RGBColorValueSelector"], { - 0, {Left, Bottom}}, {Left, Top}, - "ClosingActions" -> { - "SelectionDeparture", "ParentChanged", - "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> - Automatic, Method -> "Preemptive"], - RGBColor[0., 0., 1.], Editable -> False, Selectable -> - False], "]"}]}], "}"}], ",", - RowBox[{"{", - RowBox[{#, ",", #2, ",", #3, ",", #4}], "}"}], ",", - RowBox[{"LegendMarkers", "\[Rule]", "Automatic"}], ",", - RowBox[{"LabelStyle", "\[Rule]", - RowBox[{"{", "}"}]}], ",", - RowBox[{"LegendLayout", "\[Rule]", "\"Column\""}]}], "]"}]& ), - Editable -> True], TraditionalForm], TraditionalForm]}, - "Legended", - DisplayFunction->(GridBox[{{ - TagBox[ - ItemBox[ - PaneBox[ - TagBox[#, "SkipImageSizeLevel"], Alignment -> {Center, Baseline}, - BaselinePosition -> Baseline], DefaultBaseStyle -> "Labeled"], - "SkipImageSizeLevel"], - ItemBox[#2, DefaultBaseStyle -> "LabeledLabel"]}}, - GridBoxAlignment -> {"Columns" -> {{Center}}, "Rows" -> {{Center}}}, - AutoDelete -> False, GridBoxItemSize -> Automatic, - BaselinePosition -> {1, 1}]& ), - Editable->True, - InterpretationFunction->(RowBox[{"Legended", "[", - RowBox[{#, ",", - RowBox[{"Placed", "[", - RowBox[{#2, ",", "After"}], "]"}]}], "]"}]& )]], "Output", - CellChangeTimes->{{3.6595549649674387`*^9, 3.6595549834231453`*^9}, - 3.6595550653028927`*^9, {3.6595553128265676`*^9, 3.6595553387644897`*^9}, { - 3.6595554958307996`*^9, 3.6595555144114237`*^9}}] -}, Open ]], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"newtonplot", "[", - RowBox[{ - RowBox[{"Function", "[", - RowBox[{"x", ",", - RowBox[{ - SuperscriptBox["x", "3"], "-", "1"}]}], "]"}], ",", "2", ",", "501", - ",", "20", ",", "0.05"}], "]"}]], "Input", - CellChangeTimes->{{3.6595549152958674`*^9, 3.659554978383319*^9}, - 3.659555332709116*^9, {3.659555509656427*^9, 3.6595555271955185`*^9}, { - 3.659555597485504*^9, 3.659555640728051*^9}, {3.659558440044022*^9, - 3.6595584402002287`*^9}}], - -Cell[BoxData[ - TemplateBox[{GraphicsBox[ - RasterBox[CompressedData[" -1:eJzs103O5TpyINAyvJJeiffgJRjwuLfek54bhpFwlerx8p8RlA6BBPKeIBlB -SqL0/Z//+L///p//+re//e3//8v//Pvv//9j+3//9k/EOeecc84555xzzjnn -nHPOOeecc36VP+Oj42vz9sZPrXv1/LP9VtczO//o9evtl+25yHZf1lq2deza -j1P7OZqPc8455zybR+fnnHPOOeecc84555xzzjnnnHPOOV/lveNq88zOv8pb -6169X894tuvdev2irvuueW/xWstW76l1t46/7bnjnHPOOT/1nZWtLs4555xz -zjnnnHPOOeecc84555zzqPy136Ne6pdt3/mYt7be8bvuxyz7sSt/9HXNtg7O -Oeec89s9Oj/nnHPOOeecc84555xzzjnnnHPOecl35enNl21f+Lt9VXw0/+p1 -9Lav1sU555xzzn97dH7OOeecc84555xzzjnnnHPOOeecx/vufLPxU/WVWpbr -xHmPt7Zd58GqerLk4ZxzzjnnsR6dn3POOeecc84555xzzjnnnHPOOed5/Bk/ -la+1tc7Tuj7O+Xtatv3knHPOOedrPTo/55xzzjnnnHPOOeecc84555xzzs95 -qV9pXG//VXVl2S/Oeb6WbX8455xzzvkZj87POeecc84555xzzjnnnHPOOeec -8/MelX91P855/DlyumXbB84555xzfsaj83POOeecc84555xzzjnnnHPOOed8 -vZf6Za1rtB/nfL/f0rLtG+ecc845X+vR+TnnnHPOOeecc84555xzzjnnnHO+ -3kv9stWVZb84/5LPtl35Vs3rnOGcc845f6dH5+ecc84555xzzjnnnHPOOeec -c875ei/1i6ory75w/kafbVnqPpXPucQ555xzfqdH5+ecc84555xzzjnnnHPO -Oeecc875Pt+VJ9s6Of+Cz7Ys68lSRymerT7OOeecc54jP+ecc84555xzzjnn -nHPOOeecc87Pe++42m/O+fhz2NtvdR2nPUsdJe+9Xlnq5pxzzjl/u0fn55xz -zjnnnHPOOeecc84555xzzr/opX6lcb39R/Nwztf7aL/VdWTxLHWs9mc8W32c -c84557d7dH7OOeecc84555xzzjnnnHPOOef8C/6Mn8pX6lf7zTmff853j7vF -s9QRvf6vXn/OOeec8+jvbc4555xzzjnnnHPOOeecc84555zH1zEaz74uzjP4 -6XFv8yx1RHutuY8455xzzts8Oj/nnHPOOeecc84555xzzjnnnHP+Jn/Gd83b -G6/VM1rX07NdD85/tdX9Wse93XefM2/x1nHZ6uacc845z/79xDnnnHPOOeec -c84555xzzjnnnPNxL8VXzbPKo8dzvtNL8Vr/1XW83aPOr7d4rdlfzjnnnH/V -o/NzzjnnnHPOOeecc84555xzzjnnb/ZSv+i6nl6rs3VdnO/w0fjofHzO7fuc -19ro/nPOOeec3+7R+TnnnHPOOeecc84555xzzjnnnPM3eO/4U3Wt8tn1cj7j -s+NWzcfbfPV15L/9Ge99HrKth3POOefc9yTnnHPOOeecc84555xzzjnnnHO+ -z3vHn6prle/aB/5uH43P3m+t+fkeH70f+FpvjfeO45xzzjnP+n3DOeecc845 -55xzzjnnnHPOOeec83YvxXv7Z/PW9XA+M642z2gdPNaz1MH7xmWrm3POOec8 -Oj/nnHPOOeecc84555xzzjnnnHP+Zi/1i66r1aPz8zt8dtzuPHyPn7pP+JjP -zpdtPZxzzjnn0fk555xzzjnnnHPOOeecc84555zzN3vv+FN19frsunhOPzXv -qbw81kvN+XGHl9qu9x3nnHPO+ej3Sra6OOecc84555xzzjnnnHPOOeec8zd7 -qV90XSVvrZ/n9Fp7633Lz3jvfZKlbv67X+t8q+rgnHPOOa95dH7OOeecc845 -55xzzjnnnHPOOef8yx6dv+bR+b/uveOj77NTeXgOb71vd9fB53zV+bNqHOec -c8657wvOOeecc84555xzzjnnnHPOOec8v5f6RdWVZV9Oeamtnj9qHafy8294 -9H3O13r2+TjnnHPOo/NzzjnnnHPOOeecc84555xzzjnnvN1P549eZ+/42u/V -ebNdv9X7yXmPZ6mDn/HZOOecc8756u8PzjnnnHPOOeecc84555xzzjnnnN/r -s/OtrqPUL8u+jdbfO9+u67u6fs57fre2LOvhe7zUspybnHPOOb/Xo/Nzzjnn -nHPOOeecc84555xzzjnn/Lyvipf6ZVvvLh/dn9V5suwHf6evPl/43b77vZBl -nZxzzjnP59H5Oeecc84555xzzjnnnHPOOeecc57HSy1bnad9dh+zrIPzGXdu -8F/9VuXJsk7OOeec5/Po/JxzzjnnnHPOOeecc84555xzzjnf5894rV+ttc6T -bR927VvrfmZbH+ct3tvvGc+2Hr7GT597q+fjnHPO+b0enZ9zzjnnnHPOOeec -c84555xzzjnn7f6Mr5631kbzta4ni5fas3/r+Gzr4/yvfPY5aX0++Lu91lbf -h5xzzjn/jkfn55xzzjnnnHPOOeecc84555xzzr/opX6ltru+LHX07tOfeGu/ -1nlr/Th/s7c+L73PHf+2t47LVjfnnHPO83h0fs4555xzzjnnnHPOOeecc845 -5/zNnqWOUc9SB+c8zmvnQ3R9/G7PUgfnnHPO83t0fs4555xzzjnnnHPOOeec -c8455/wL/oxnr683zjn/jmepg+f0Z3z0PmrNm239nHPOOd/n0fk555xzzjnn -nHPOOeecc84555zzG70Ur/3O6lnq4Jyf89l+q+bn7/BT753W93KWfeGcc875 -Oo/OzznnnHPOOeecc84555xzzjnnnN/oz3i2+lavM7oOzvl+X30+RK+Hx3it -Rd+3nHPOOb/Xo/NzzjnnnHPOOeecc84555xzzjnnGbwUb50n23pWrf90HZzz -OD91nvB3eu1+2JUny/o555xzvt+j83POOeecc84555xzzjnnnHPOOeeZvRSv -/b7NS/16+3PO7/fW8213Hfxdvmq+t71/Oeecc97u0fk555xzzjnnnHPOOeec -c84555zzDN46Llvdp9Z/qg7OeR5vbdnq5jl9dr5s6+Gcc875eY/OzznnnHPO -Oeecc84555xzzjnnnGf0LHWc8tk45/w+n+23an7+bZ+Nc8455/w7Hp2fc845 -55xzzjnnnHPOOeecc845P+mr+tV+3+azcc75vX56HOe/Wrb6OOecc57Ho/Nz -zjnnnHPOOeecc84555xzzjnnJ7zUbzZe8yzr7433juOc3+et5+Tqc4bf7avv -k948s3k555xzfq9H5+ecc84555xzzjnnnHPOOeecc84z+Kr5ar9Xe2+81m+0 -Ds75/Z7tPOU5PGr86n6cc845v9+j83POOeecc84555xzzjnnnHPOOecn/XT+ -bOupzTNaB+f8fs9+nvJcvjvPbD3Z9otzzjnn8x6dn3POOeecc84555xzzjnn -nHPOOY/0Ur9VeXrH7apj93yc8+94ljr4Xo+6/qveW1n2kXPOOefrv0Oz1cU5 -55xzzjnnnHPOOeecc84555xHeqnfqvlq80ftQ3R+znm8R50bWdbPf/eLqivL -vnDOOec8zqPzc84555xzzjnnnHPOOeecc84551/wUhud5xnv7c8556v7ldqu -PPyMR+eveXR+zjnnnJ/z6Pycc84555xzzjnnnHPOOeecc875m73UL7ouzvl3 -PHp8zaPz89/+tjycc845v9ej83POOeecc84555xzzjnnnHPOOedv8FXzrq6L -c86fXjt/dp1vvXl5m/eOO319su0X55xzzu/16Pycc84555xzzjnnnHPOOeec -c875jf6M75q3N845561e+x3t0fmjr8cp3x3nnHPOOfd9yDnnnHPOOeecc845 -55xzzjnnnJ/33flm45xzXvPa+dLa/9R5WOoXvY81n11vqa2+Lr39suwv55xz -zr/n0fk555xzzjnnnHPOOeecc84555zzzP6MR9dxKh/n/Lte+33Ka/2y7FeW -/Kfuh1L/LPVyzjnn/L0enZ9zzjnnnHPOOeecc84555xzzjmP9FK/3v67fTbO -Oeerz8us52GW98WpumZ9Vd3R6+Ccc875+z06P+ecc84555xzzjnnnHPOOeec -c57Zs9UxGuec81FvPR9P1bU7T/b3wel13/re5Jxzzvn7PDo/55xzzjnnnHPO -Oeecc84555xzfpPvztfasuwH55w//dQ5eercjd7PU75rP7Osj3POOef3e3R+ -zjnnnHPOOeecc84555xzzjnnPNJL/VrnG62j1m91nZxzns1vGfcWP7UvrXk5 -55xzzn3Pcc4555xzzjnnnHPOOeecc8455+1e6tc7X28drfO2ztM7H+ec3+a9 -LVv92X32fZVlHZxzzjl/r0fn55xzzjnnnHPOOeecc84555xzzjN6qd/pPFn2 -g3POo723Zas/y3ts9j2UZX2cc845/55H5+ecc84555xzzjnnnHPOOeecc86/ -4NH5Oec8m4+O35W/1LLt2x9f9b6JXgfnnHPOeatH5+ecc84555xzzjnnnHPO -Oeecc87f5Kv7cc55tI+eg7vqi96PUjudv/f9km3fOOecc85v+e7inHPOOeec -c84555xzzjnnnHPO3+Sr5l1dF+ect3rtXIquL1sdnHPOOef8rEfn55xzzjnn -nHPOOeecc84555xzzm/y3flaW5b94Jzn9dHzJ7rummepg3POOeecn/Xo/Jxz -zjnnnHPOOeecc84555xzzvkbfNW8s3HO+fu9dj6cqiPKs9TBOeecc87PenR+ -zjnnnHPOOeecc84555xzzjnn/Cbfna+1ZdkPzvk5bz03Tp9bp87F0TjnnHPO -OX+HR+fnnHPOOeecc84555xzzjnnnHPOb/TWcbPjV43jnL/fs9Sx27PUwTnn -nHPOz3p0fs4555xzzjnnnHPOOeecc8455/xGbx3XO77WvzUv5zyPrz4Hotdz -2p/xbPVxzjnnnPMzHp2fc84555xzzjnnnHPOOeecc845/4LXWrZ6Oef7ffX5 -Er2eXZ6lDs4555xzHuvR+TnnnHPOOeecc84555xzzjnnnPM3e+/4U3Vxzs/5 -qvlm68juz3i2+jjnnHPOeaxH5+ecc84555xzzjnnnHPOOeecc87f4KvmnY1z -zvP5qfPhdn/Gs9XHOeecc85jPTo/55xzzjnnnHPOOeecc84555xz/iZ/xmfH -98Y55/l81/mS1Wv1t47Lsh7OOeecc57Do/NzzjnnnHPOOeecc84555xzzjnn -b/BV887GOef3eNbnvDU+O8/o/nDOOeec8296dH7OOeecc84555xzzjnnnHPO -Oef8C/6Mt/brjXPO7/XRfrvqaT2vRutpzc8555xzznmG/JxzzjnnnHPOOeec -c84555xzzvkXvdQvui7Ov+ijz+OqOnrzZvNd+8I555xzznmm/JxzzjnnnHPO -Oeecc84555xzzvkXvdSvtWVZB+cnvPV5ae0fvZ7R8afqKvmudXHOOeecc97i -0fk555xzzjnnnHPOOeecc84555zzL3rv+FN1cR7pq+abreOUR9UxWteuejjn -nHPOOW/x6Pycc84555xzzjnnnHPOOeecc875F73UbzbO+Ru89Xm57Tl5xrPV -xznnnHPOeWaPzs8555xzzjnnnHPOOeecc84555x/2aPzc57J3/r8ZKmDc845 -55zzmz06P+ecc84555xzzjnnnHPOOeecc/5lX92P8y94ljpq9f2JZ6uPc845 -55zzGz06P+ecc84555xzzjnnnHPOOeecc/5F7x1/qi7+LV99H+6ue1ee3vVG -XzfOOeecc86/6NH5Oeecc84555xzzjnnnHPOOeec8y97Kd7bn/MW773PSu1U -fTXfnT/LdeOcc84555zH5+ecc84555xzzjnnnHPOOeecc855vV90XfxdPhs/ -ff+vXp/njHPOOeec8/s8Oj/nnHPOOeecc84555xzzjnnnHPO6/2i6+Kxvvs+ -iV4P55xzzjnnnNc8Oj/nnHPOOeecc84555xzzjnnnHPO+1u2enmbt17vZ7/Z -Okbz7soffR0455xzzjnn93l0fs4555xzzjnnnHPOOeecc84555zX+0XXxdd4 -7fquytead3be0Xk455xzzjnnvNej83POOeecc84555xzzjnnnHPOOee83LLV -9XY/dT1qrbWe1v6cc84555xzfrtH5+ecc84555xzzjnnnHPOOeecc855vV90 -XV/x2v73ztvbb/Y+4ZxzzjnnnPO3enR+zjnnnHPOOeecc84555xzzjnnMV7q -F1UPb/Po/Fn91H7N1sM555xzzjnnfMyj83POOeecc84555xzzjnnnHPO+S1e -iq+a5+mj43vr2lX/6rxf81rLVu8u3/WcZlkf55xzzjnnnPM2j87POeecc845 -55xzzjnnnHPOOeenvdRvtH+trV5Haz2j+7F6/lXzzF7Ht3h0/t3PX6nV7n/O -Oeecc8455+/26Pycc84555xzzjnnnHPOOeecc77ba202T+336jqy7e/q6zS6 -n7P3Rbb96N2nrF5r2erlnHPOOeecc57To/NzzjnnnHPOOeecc84555xzznnJ -S/FV86zy2fp4rI+26HpP53efc84555xzzjmP9Oj8nHPOOeecc84555xzzjnn -nPPv+qp5W9uf8b3zZNkvnttr/U7d76PzZdtPzjnnnHPOOec8U37OOeecc845 -55xzzjnnnHPO+fu91G93nizr5zyiZVsv55xzzjnnnHM+49H5Oeecc84555xz -zjnnnHPOOefv86j8td+c3+CrWrZ1cc4555xzzjnnMx6dn3POOeecc84555xz -zjnnnHP+Hi/1i6ory75wnqll2wfOOeecc84557zFo/NzzjnnnHPOOeecc845 -55xzzt/ntTaaJ9s6OR9ps/lW1+v54pxzzjnnnHN+g0fn55xzzjnnnHPOOeec -c84555x/x5/xbPVxvrLtqu+2eTnnnHPOOeec8xUenZ9zzjnnnHPOOeecc845 -55xzfs5L/UrjevPV5uM8o8/GszzH9olzzjnnnHPO+Zs9Oj/nnHPOOeecc845 -55xzzjnn/JzvztebP8u+8Hd5qd/ofZvNs9TR2mr7zznnnHPOOeect3h0fs45 -55xzzjnnnHPOOeecc875eX/GR8f35l/dj3/bZ+O3eJY6spw/nHPOOeecc86/ -6dH5Oeecc84555xzzjnnnHPOOef5fXa+3nmzrZ+f8dZ477i3eZY6Vnut1c4T -zjnnnHPOOefv9uj8nHPOOeecc84555xzzjnnnPN9/ozX+p2q6+m13/xOL8VX -96/1u8179+d2772+WermnHPOOeecc37Wo/NzzjnnnHPOOeecc84555xzzvd5 -dP5Wr/3md3opXuu/uo7b/PbnOZtnqYNzzjnnnHPO+ZxH5+ecc84555xzzjnn -nHPOOeecn/daO11X7TfP4aP9Vtfxdq/ta3R9Wbx1XLa6Oeecc84555yPeXR+ -zjnnnHPOOeecc84555xzzvk5L/XLVleW/fqq947Lel/d6quuy1f9Gc9WH+ec -c84555zzMY/OzznnnHPOOeecc84555xzzjnP46fzZ1v/W/30OD7nrsceL8Vr -vznnnHPOOeec5/Do/JxzzjnnnHPOOeecc84555zzeC/1250/y/qzeqlfrX/2 -687b+vX2523NucQ555xzzjnnd3p0fs4555xzzjnnnHPOOeecc855Xi/1W5Vn -93p6x0Xte/b5+Fl3Xc/6M56tPs4555xzzjnnOfJzzjnnnHPOOeecc84555xz -zu/1WquNm8337HdqvbVxq9fdus7VefgZ772+Wer+qj/j2erjnHPOOeec87d6 -dH7OOeecc84555xzzjnnnHPO+Xe8t2Wrf3S9f+Kt+zLan9/lo9c3uu63+Ozz -taoOzjnnnHPOOedtHp2fc84555xzzjnnnHPOOeecc/4eL/UbHZfda+sdjfNv -uPsj1kfPq6dnWQ/nnHPOOeecv92j83POOeecc84555xzzjnnnHPO8/szPjp+ -VV3Z9+F0XTy377r/+F5vHZetbs4555xzzjl/q0fn55xzzjnnnHPOOeecc845 -55yf92f8VL7V886uu3fc6nr4t7z2+1QdfM6f8Wz1cc4555xzzvlbPTo/55xz -zjnnnHPOOeecc84553yfP+PRdZzKx/kN3vrc8lxeatnPYc4555xzzjm/3aPz -c84555xzzjnnnHPOOeecc87n/RnPVl+t7ug6OD/hrc/v7jr4b199XrmunHPO -Oeecc77Go/NzzjnnnHPOOeecc84555xzzuuepY7VnqUOznf66HMRXffXfdV8 -XznPOeecc84553y3R+fnnHPOOeecc84555xzzjnnnNf7lcZlqbvmWergPMJH -n5four/qq8+x1vk555xzzjnnnP/26Pycc84555xzzjnnnHPOOeec83Z/xrPV -11p3b5zzN3uWOnibt47LVjfnnHPOOeec3+7R+TnnnHPOOeecc84555xzzjnn -9X69/aM8Sx2cZ/Tbn2/+156lDs4555xzzjl/u0fn55xzzjnnnHPOOeecc845 -5/zL/ozX+rX2z7Ke3jjnb/TR56jUotfzdl91XbKsh3POOeecc87f4tH5Oeec -c84555xzzjnnnHPOOf+il/qtyrOq7tk453z8uSv1i17P2/wZ331dsq2fc845 -55xzzm/x6Pycc84555xzzjnnnHPOOeec83IbnS+qjto8o3Vw/kbf9fzzNj91 -Xq3uxznnnHPOOedf9ej8nHPOOeecc84555xzzjnnnPN2bx1XG1+a53SdnPNy -y1bfW/1teTjnnHPOOef8rR6dn3POOeecc84555xzzjnnnHO+z0ttdJ5s6+P8 -Jm99vlqf59m8/Ewe14NzzjnnnHPO13h0fs4555xzzjnnnHPOOeecc875ei/1 -i66L8y9763Pa6715+dr5sq2Hc84555xzzt/q0fk555xzzjnnnHPOOeecc845 -5+PeO/5UXZzzuu/Os3q+KH/GV+9DKT573nLOOeecc845X+vR+TnnnHPOOeec -c84555xzzjnndd+db9e8nPP236v9VJ5d51ip367zrRbnnHPOOeeccx7r0fk5 -55xzzjnnnHPOOeecc8455+X2J34q3+p5Oedlj36uT59jWX11P84555xzzjnn -ezw6P+ecc84555xzzjnnnHPOOee83P7ET+frjXPOx732e9RXz3db/tH9n+3H -Oeecc84553yPR+fnnHPOOeecc84555xzzjnnnMfXcTof57zds8y3uo6s52uW -ejnnnHPOOeec58rPOeecc84555xzzjnnnHPO+Re91K93XG8dq+vhnJ/zVfOd -Hhftu89JzjnnnHPOOednPDo/55xzzjnnnHPOOeecc84551/22flWzztbD+c8 -r/e2bPXvOg9318U555xzzjnnfI1H5+ecc84555xzzjnnnHPOOeect/sz3tqv -N845f4/Xfve26HX1nmvR9XLOOeecc845X+PR+TnnnHPOOeecc84555xzzjnn -417qF10X53y915732XNjlfeO711X9HXgnHPOOeeccx7j0fk555xzzjnnnHPO -Oeecc8455+3+jLf2641zzs/52/NxzjnnnHPOOecrPDo/55xzzjnnnHPOOeec -c84557zuq+ZdXRfn/H+99txF15etDs4555xzzjnnvMej83POOeecc84555xz -zjnnnHPOy+1PfPW8o+M55+3P7W2epQ7OOeecc8455/xXy1YX55xzzjnnnHPO -Oeecc84551/0Ur/SuNb+o/Nzzv/Za89RdH01z1IH55xzzjnnnHPe49H5Oeec -c84555xzzjnnnHPOOef1fqVxtf6t87WO4/zN3vs8Zqm717PUwTnnnHPOOeec -93h0fs4555xzzjnnnHPOOeecc875vNdatno5j/Ta75qvquOUP+PZ6uOcc845 -55xzzls8Oj/nnHPOOeecc84555xzzjnnfNxL/WbjnL/ZW5+jtzw/z3i2+jjn -nHPOOeec8xaPzs8555xzzjnnnHPOOeecc845b/dnfHT86ro4v9lnn8MsXorX -fnPOOeecc8455zd4dH7OOeecc84555xzzjnnnHPOebs/46PjV9fF+c3e+rys -rmM0b2ue6H3lnHPOOeecc85XenR+zjnnnHPOOeecc84555xzznm7P+Ot/Xpb -tnVznsFL7VQ92faDc84555xzzjk/6dH5Oeecc84555xzzjnnnHPOOef7PDo/ -5zM+G5/1Wt7T+bNdH84555xzzjnn/KRH5+ecc84555xzzjnnnHPOOeecj3vv -+FN1cf4rfrqOVn/GVz9fu55rzjnnnHPOOef8Cx6dn3POOeecc84555xzzjnn -nHM+7r3jT9XF+ci4XXXUPHqfOOecc84555xzXvfo/JxzzjnnnHPOOeecc845 -55zzeW+N78rP+V/56vt41qP3g3POOeecc8455+MenZ9zzjnnnHPOOeecc845 -55xzvt5L/aLr4t/y2n14+v7nnHPOOeecc875vR6dn3POOeecc84555xzzjnn -nHM+76v78Xd67feuOmrt1HOQ5TpwzjnnnHPOOee836Pzc84555xzzjnnnHPO -Oeecc87Xe6lfdF08xmv3w+n7cPf9Gb3fnHPOOeecc845X+/R+TnnnHPOOeec -c84555xzzjnn673UL7ountNXzfuMZ1kf55xzzjnnnHPO7/fo/JxzzjnnnHPO -Oeecc84555zz9V7qF10Xb/Pd89bG9daVbf8455xzzjnnnHP+Po/OzznnnHPO -Oeecc84555xzzjk/79H5v+q7r8fofdA6X/T+cc4555xzzjnn/LsenZ9zzjnn -nHPOOeecc84555xzvs9rLVu92X33dTldB+ecc84555xzzvktHp2fc84555xz -zjnnnHPOOeec5/RSPFudfMyj89/qu8a3xlfVwTnnnHPOOeecc36bR+fnnHPO -Oeecc84555xzzjn/uq+adzZe89q8tdY6T5br8naPzn/KV69/Ni/nnHPOOeec -c845H/Po/JxzzjnnnHPOOeecc84551/xUr9d+XfN35uvddzq/emtO8t9csqj -849673p676vo9XHOOeecc84555zzv/bo/JxzzjnnnHPOOeecc84559n8GZ8d -3xtv9drvUd89f/R17e1X6p9tfavv0yzee51W5+ecc84555xzzjnnOTw6P+ec -c84555xzzjnnnHPO+Wkv9VuVp3dcrd/suvgZX93vVL2n8rfux+m6OOecc845 -55xzzvkdHp2fc84555xzzjnnnHPOOed8t0flr/3m3/bRlvW5WD0f55xzzjnn -nHPOOeeZ8nPOOeecc84555xzzjnnnO/2WjtVV7Z94e/wWpsdl229nHPOOeec -c8455/ybHp2fc84555xzzjnnnHPOOed8t6+ar/ab80ze27LVzznnnHPOOeec -c855pvycc84555xzzjnnnHPOOefP+Oz41njtN+c3+Kp47zjOOeecc84555xz -zk96dH7OOeecc84555xzzjnnnH/Hn/HV85b61X5znslP5butXs4555xzzjnn -nHP+bY/OzznnnHPOOeecc84555zz7/gzPjq+N//qfpyv8Na2q47szzvnnHPO -Oeecc84555nyc84555xzzjnnnHPOOef8/V7qF51/tB/nPS36/i95lny9/Tnn -nHPOOeecc875Nz06P+ecc84555xzzjnnnHPO3+O943fX1Zs3yz7yHH56XPbn -9dR+1/pnq5tzzjnnnHPOOeecn/Ho/JxzzjnnnHPOOeecc845/45H53967Tf/ -ts/Gs3uWOkpe2/dTdXDOOeecc84555zzHB6dn3POOeecc84555xzzjnn7/FS -v+i6ah6dn5/xUvzW+3b2ubzVe69Xlro555xzzjnnnHPO+ZxH5+ecc84555xz -zjnnnHPO+Xf8dP5s6+drvRSv9V9dx62epY5of8az1cc555xzzjnnnHPOc+Tn -nHPOOeecc84555xzzjk/nT/b+nlbv+z3VTa3L23+jGerj3POOeecc84555zn -yM8555xzzjnnnHPOOeecc74rT7Z18rFxtXlG6/i6Z6kj2p/x3vst23o455xz -zjnnnHPO3+rR+TnnnHPOOeecc84555xzzmfny7aer3mtjY7rnY//o+963r7i -reOy1c0555xzzjnnnHP+Vo/OzznnnHPOOeecc84555xzXvLWcdH1lfrVfkd7 -qd/s9RjNy9f6quv4VW8dl61uzjnnnHPOOeec87d6dH7OOeecc84555xzzjnn -nPNef8ZHx5f6nap/tJ7WfRn10X3juXz3fcJ/9yuNy1I355xzzjnnnHPO+W0e -nZ9zzjnnnHPOOeecc84557zXSy1bnavX+4zvytu679n2if/2LHXc6r37mqVu -zjnnnHPOOeec87d4dH7OOeecc84555xzzjnnnL/Pn/HV8/aOz7Y/s3VH18Vz -eu/9k6Xu23x2vmzr4ZxzzjnnnHPOOb/Fo/NzzjnnnHPOOeecc8455zy/P+PR -dczO27rOUx61D/zbnqWO2733Oc1SN+ecc84555xzzvltHp2fc84555xzzjnn -nHPOOefnvRSv/Y72qDpm62ztPxrn/Fe/3v78jGepg3POOeecc8455/wWj87P -Oeecc84555xzzjnnnPN5L8Vrv2/zLHVwnslXnRd8rY+eY287tznnnHPOOeec -c85XeXR+zjnnnHPOOeecc84555zPe+u4bHWPrjO6Ds4z+ey5wGO8dVy2ujnn -nHPOOeecc86jPDo/55xzzjnnnHPOOeecc87n/RnPVt/senrjnH/Re5+XLHV/ -1VvHZaubc84555xzzjnnPMqj83POOeecc84555xzzjnnfHz8qnmyeZY6OL/B -V50b/Ky3jstWN+ecc84555xzznmUR+fnnHPOOeecc84555xzznm936o8WdZZ -89aWrW7OI3z0+Yqum+esg3POOeecc8455zyrR+fnnHPOOeecc84555xzznm5 -zc5X+x3ts3HOed2z1PE1333uZ1kn55xzzjnnnHPO+SmPzs8555xzzjnnnHPO -Oeec83JbnSd6PaV+p/eB8zd663PkeTvjvedh73XJsk7OOeecc84555zzUx6d -n3POOeecc84555xzzjnn9X6r8vSOq/VrrX/3ujj/su9+rvmcz86XbT2cc845 -55xzzjnnUR6dn3POOeecc84555xzzjnndS/1651vdJ4s9XPO/9lXzTdbB/9r -XzXf6nOZc84555xzzjnn/DaPzs8555xzzjnnnHPOOeec831eimerh3O+3j2H -OXxXnmzr5JxzzjnnnHPOOd/t0fk555xzzjnnnHPOOeecc77eS/1K43rztbYs -+8E533eu8N/eOi5b3ZxzzjnnnHPOOefZPDo/55xzzjnnnHPOOeecc87b/Rkf -Hb+6Ls55Xq/9LrXaOdNbx+3eum+lNnpuc84555xzzjnnnPMc+TnnnHPOOeec -c84555xzXvdV866ui3Oex0+fJ7VzJsu+1PwZX32unt5/zjnnnHPOOeec87d6 -dH7OOeecc84555xzzjnn/Mv+jJ/Kt3peznmcR+cvtSx1RZ+Hq/txzjnnnHPO -Oeecf9Wj83POOeecc84555xzzjnnX/BnPEsdvXHO+T0efc6U+u3KP1pPVF2n -xnPOOeecc84555y/xaPzc84555xzzjnnnHPOOedf8Gc8Sx29cc75fV77vdpr -Lfqcy+LZ3xecc84555xzzjnn2Tw6P+ecc84555xzzjnnnHP+Bi/16+2/22fj -nPP7/JbzJ3q+U+vv7Z9tHZxzzjnnnHPOOedRHp2fc84555xzzjnnnHPOOX+D -l/r1jotaz+l8nPO8vutcOj3ulPfWHV0v55xzzjnnnHPO+a0enZ9zzjnnnHPO -Oeecc845f5PPzrc7X22e3vk457z3nNl1fkZ767qy1Ms555xzzjnnnHN+m0fn -55xzzjnnnHPOOeecc87f5LVWm6827+o6s+0f5/w73tuy1Pnsl21fOeecc845 -55xzzt/q0fk555xzzjnnnHPOOeec8y97KT47fy3fqjycc17y1f0455xzzjnn -nHPO+bc9Oj/nnHPOOeecc84555xzzvtbtno559/16PGcc84555xzzjnn/Bse -nZ9zzjnnnHPOOeecc845/4JHj+ec85rXzp/T9UXvB+ecc84555xzzjnP5dH5 -Oeecc84555xzzjnnnPM3+O58rS3LfnDO83rtnImq7xmP3ifOOeecc84555xz -nsuj83POOeecc84555xzzjnnN/ozfjpfb5xz/j2/7bx4xrPVxznnnHPOOeec -c85jfXbcbJ5s+8E555xzzjnnnHPOOeect/gzHl3HqXyc83zeek5l9Sx1cM45 -55xzzjnnnPPcXorX+rfmW1UP55xzzjnnnHPOOeecc57BS/16+/f6bJxzfr+v -Pjeye5Y6OOecc84555xzznlu351vdd5s+8c555xzzjnnnHPOOef83d46btW8 -tf6t9XDO8/vo8x5d96yX4m9bJ+ecc84555xzzjkf81P5WvO39p/NyznnnHPO -Oeecc84555zPeK39GVcb35q3tY5s+8Q5H/dV50CW9dT8Gc9WH+ecc84555xz -zjmP9dXz1n6v9lXx0fycc84555xzzjnnnHPOeYuXWm//0fyc87xe+13z3vmj -vFZ/1ro555xzzjnnnHPOOd/pre05Pts6OOecc84555xzzjnnnN/tpX7RdXHO -83jrudHrq+c7XVe2ujnnnHPOOeecc855rJfi2eo8tQ+llq1ezjnnnHPOOeec -c84557l81byr6+Kc3+ez58aqOmpeq8c5xznnnHPOOeecc85Xeu+4bPVn2x/O -Oeecc84555xzzjnn3/BnfPW8o+M55+/11vOo5qfOn9a8nHPOOeecc84555y3 -+Kr5sq1rdB9K/bLVyznnnHPOOeecc8455zzWn/Fd8/bGOeff9Wznxup+nHPO -Oeecc8455/zbvmpctnVF78/X3X5yzjnnnHPOOeecc87f4rX2Z9zsvNnWzTmP -89q58YxHnTPR+8Q555xzzjnnnHPOv+W7x2db79fW17qu3XW01rN7XJbrwjnn -nHPOOeecc845v99L8drv3vGt4zjn8b7qHOn11edaa57o/eacc84555xzzjnn -3/JV89bmb43ftj+n61pd5666st2fNc9233HOOV/rvf2y1c8555zv8FI8W52c -c875jV6Kt753d9XFOe/30ef0dN3R+8Q555xzzjnnnHPO+QnPUsfTV/db7bvm -i8of7bddL84557/jp79fRufLtp+cc875Di/FW9+LvfHReTjnnPM3eO09WGtZ -1sH5lz1LHb2epQ7OOeecc84555xzznd6ljpOrTN6vlrLtm+nvPf+vO1+4Zzz -W/wZ3/W9sWq+2fpqv2fzZru+nHPO3+2r5pt9P46+T7Pt59s86n7inPOv+eh5 -u7suzvn6795VdYz6M55lXznnnHPOOeecc8453+lZ6rjFe1u2+m/12u9Rr7Us -6+ec89XeOi5rfaX4rvfF6u+rbPcD55zztb5qvt15T7+fRuPZru/pfYre597+ -nHP+dT91bnPOxz3q+361P+PZ6uOcc84555xzzjnnfIdnqeMW723Z6n+b137X -vHd+zjl/iz/jWet79stWp/cO55x/w0tx5/hej84/66e+E1r7u16cc37GV5// -nPP475hTdbTmz7Z/nHPOOeecc84555yf9Cx13Lb+2Tyz+flf++rrEr0ezvl7 -vfe9tPq9t+t9N5p3VV3PeJbrXfPo/Jxzzn/7Mx5dR6lf9vrf8t6Mzr/ao+9P -zjm/3Z/x1e+P0XGc837f/Rz2zh+9H5xzzjnnnHPOOeecZ/Qsdezy2+at+el8 -b/Hafma5H1rjs3k45+e9dVz0e6T1fJut49S5m+0+2P0+ivZSW7Uf2dbLOX+/ -R7+Xez3LuqLfQ7v2cXWebL7rPlk93+46W8e//buOcz7vq/txzue9NV5rt32P -cc4555xzzjnnnHP+Js9SR81r9Z+uL/p6tV7PXXVE++r7Ybae3T56vUvzR6+H -c16Of+39vsp7z/foemstut7d99Wu75/aOm79DuCcl/2283l03Op9uv29uWp/ -fUeN+a73eO+47Ost9YteD+d8v3u/cD7vUd/Tq9/7s3mirwPnnHPOOeecc845 -5xk9Sx1/vFanffpdV2+/1XVkvb5vu9619Y2uK8t6OH+T957HreOyrO8rHv1+ -P3UfRu9zzXe9t1bPxzk/78/46nNgtK63e+/7Jfq9WWvR+/k2L7VsdZ76DllV -B+c8nz/js+dltvVxvtJb36e76+ith3POOeecc84555xznsej6qjVk3WfavXf -4qOtNU+26zt7vXvj0etbvV7OebmNvhd21cVjfPYcXn0+r64jm2efj3N+zlef -A6vn5bFeatnqzO67nqfRerK47w3Oue8Qzts963vzGY/eJ84555xzzjnnnHPO -ed2z1PH0LHWUPEsdp7zUb/X9dut1OZ2v5qP1R9fNeUZ/xt96bvBc3tuy1Z/1 -fec9yPm9Pnperh7Hc/mu76zZeFbfvR7fyb/jpfG796F3/rfd95yf8Gf8a+8X -zlv8lvs+Sx2cc84555xzzjnnnPOy7843mvf0fmS7Lm/1Uqv1z369ZuOnPHt9 -nN/gt58DPLf33m+1lmVdWTz6+cxWD+cZ/BkfHb+6Lp7Lo8fXfFU9pXGr+2e9 -TqO+et5s98tpf9t6OI/0WstWL+c7Pfo90loP55xzzjnnnHPOOec8v+/ON1pP -9H6M1s/5TPzUc1Frb3uuOR/xqPcm/4av7lfz2Tg/463xUr9s6+G8xZ/x0e/X -0fw8p6+eN9v6Vr8fVn3H3rqftX69+3P6fludf9Z335+cf8Fved45/3uP+n6o -jZvNE72vnHPOOeecc84555zz9b47Xy1v9LprdXJ+0nfPF3UOtLZn/2zXh7/T -s703+bs8evyoz8az17G6X/Q+RF8nzme8FG89D3fVxc/4qXzZ1h2931/fn1K/ -bPu2a97o58n3DH+jP+Oj9/Pqujhv+R1Vx6jvnp9zzjnnnHPOOeecc57fs9Yx -O3+2fea8xXvju5+/2XlXP6e76uDf8mf81vcmP+tR51L0ukutN76qf5b9XF1X -q3tv8jd5tueL73F1cL7eR+PRdd32Hc55jz/jq59fzkc8+hzfNS/nnHPOOeec -c84555yPjp/Nv6qebPvJ+Zt8d77RerLtE3+H11q2evkez3b+RO/HrJf6jb53 -suzbbPzt9y3/pt/y/cnPeLZzKXo/OD/htbbreRnN0+qrv9M4P+G+c3gGP3VO -tublnHPOOeecc84555zz3b5rvtXzcs73+erxvfNk2w9+lz/j3k+8xU99FzkH -3+mz8dnrX2tveS54bn/GT39/8hhvPb9211GKZ9knzr/ku/NFnzOc/3LfOXzG -T51vs/NF7xPnnHPOOeecc8455/y7vjtPtvVyzvf56XE1jzr3eA5/xmv9TtXF -c3j0OTVbD3+H944bnX90vPcs73HvWf737n3KOV/dr3X87Hy7vsv4O/3088Lv -9t7v59P356p5OOecc84555xzzjnnfLePjq/95pzz1b5q3tr82dbNx7zWstXL -c3jv+TB6nrTm5XzGZ+Ojz4v37Dd8dT/+Lo/6nuec3+u9/bJ9/8zOy9/ptZat -Xn7Gd8/re4lzzjnnnHPOOeecc8455zyHr5q3Nn+2dfPf/ozvvn94bt81ftV8 -WfaJf9tL8dH3Y+98/JsenZ+v8V3v41XzcM756u/5XnfO8V/9ouvie3zV+NF6 -su0H55xzzjnnnHPOOeecc845/+275zuVl495Ke66vdN3X9fo9XEe6bV+vefs -aB3ev7l993XnOTx6POecn/JaP98/fMR9L93pvddx13dRqV+WfeKcc84555xz -zjnnnHPOOec5fNW8tfmzrftW330deU5f/XytqotzXvfe8d6nOd15+g0ffb5r -zy/nnH/NV8+bbX38r9330rvc88k555xzzjnnnHPOOeecc85v8t7xtXmyre9W -X3W9+Blf9VyMXvfWeTjn+7zWRuebPT94n3v/3um7rm+W9XHO+W1+epzvpbPu -e+mM73q+ai163ZxzzjnnnHPOOeecc84555z/8lq/2u/aPLX+2fYji49eL77G -R5+jXdedc/4db22j51jr+Lf76P7srov/du9Tzjn/lveO9/4+46uuF//tq+7n -6HVwzjnnnHPOOeecc84555xzntGjx3/No/O/xVftb+880evmnN/ntX6t40bz -f82j87/Fd+9v9Po455zHeCk++h3VO9/XffU+f8137XOW9XHOOeecc84555xz -zjnnnHN+s8/Gn55tfav3qdSy1ZvdZ/vNzss559HeG1/1nn6LR+fP7rP7mWUd -nHPOv+Gz41pbtnWf/g6Irivae1tt/mzr45xzzjnnnHPOOeecc84555zX22y/ -7P729a3y2X3Lsg7OOY/2Unz0fZRtfav242s+u29Z1sE555zv9NX9bvday1bv -qfsgW72cc84555xzzjnnnHPOOeec8zxe65et3tb6ouva7bP7kGUdnHP+Va+1 -bPV+7f07e92yrINzzjm/2Vf3y+a1lq3e0f3PVi/nnHPOOeecc84555xzzjnn -/H1e6lfrf7re3vqj/bZ6Oeecn/XW+K78b3ufrfpuiV4H55xzzute65e93tP5 -R7+DstTFOeecc84555xzzjnnnHPOOeejXmvRdX01P+ec83f46Pi3vv9b37vZ -riPnnHPOz3trO/Udtfp777b8nHPOOeecc84555xzzjnnnHN+m++ab1We1fNx -zjnnJ320Rb8va/Nk22fOOeecv89HW9bvqNH5OOecc84555xzzjnnnHPOOeec -//aolm0fOOec85Nea7Pjsq2Xc8455/zUd9Sulm0fOOecc84555xzzjnnnHPO -Oeecr23Z1sU555xn9t6WrX7OOeec81u+o0ot27o455xzzjnnnHPOOeecc845 -55zHtmz7wDnnnJ/01tY6/tkv23o555xzzk9/R61u2faBc84555xzzjnnnHPO -Oeecc87f6lnnbW3Z9pNzzjlf2bK8f5/9s+0z55xzzt/nsy3Ld9TsvJxzzjnn -nHPOOeecc84555xz/lZvbafry7If2a4X55zzu/z0uOzvvVI8y3cA55xzzvN4 -rZ3+jsry3RZdB+ecc84555xzzjnnnHPOOeecr/JSvNZ/dR01760/2mfjnHPO -3+2j/VbX8Zb376rvlizr4Zxzzvn4d8ipOnZ9/0XX57uIc84555xzzjnnnHPO -Oeeccx7ts/Fov7XuWX/Ge/ch23o45/xr3tqy1f2V929rvNQv23o455zzG701 -3jsum2epY/X3bO27kXPOOeecc84555xzzjnnnHPOW+O947L66D58zZ/x3n3L -th7OOY8+T5/9Zt/L2dbZ6lnqiPbecfaRc875F7013jvuds9Sx+l1lsZlq5tz -zjnnnHPOOeecc84555xz3u61fqPzZVvnqf3ibd46rvc6ZFsn55yvev96L+Ws -I6v3jrO/nHPOI331+NXz3+arvg/e4r3N9yjnnHPOOeecc84555xzzjnn8T47 -btV8X/Esddzurfdlbb7eebKsn3N+j6+Kz9bxFc9Sx+2+6j1b8izr5JxzftZL -/Ua/k1aPe7vbrzlvHdc7Pts6Oeecc84555xzzjnnnHPOOd/hvfHeeWr9a/2+ -6qPXi6/x0edoNn+W9XPO49/LpTZ7jo3O9zYf3Z/our/ureOy1c0553zMe8f5 -/jnjq64X/+2r7ucs6+Gcc84555xzzjnnnHPOOed8hfeOq80zWgf/R191vfgZ -X/VcjF731nk45/u8tc2eK94Pe93+3umt43rHZ1sn55zf4qPjs7wv+G+3v2d8 -9fPV2rKsn3POOeecc84555xzzjnnnH/bV81Xm39Vnq/77uvIc/qu52t0HOe8 -3XvHeZ/mdOfoN7x3XOvzyznnX/Ps8/E97vq9y1vHZaubc84555xzzjnnnHPO -Oeec5/TV89Z+78rLx7x2fVr78zt89/OYZZ2cR3hvfHSeLM87H/Pd153n8Nn5 -sq2Hc859//CT7nvpTn/GVz2Pq86lbPvFOeecc84555xzzjnnnHPOf/uq+Wrz -r8rDz3jv9c1SN9/js/Otnrd1fs5Peqnf6PvRuctbPEsdfM5bx+0+lzjnfNf5 -tStPdF38rLve3/BaO/WdnG1fOOecc84555xzzjnnfLevGpdtXZzz9/mq+Wrz -r8rDc3iWOvgd3nsfjd53rXk5n/Fav13Pi/P4Wz4b5+/0qO95zvm93hqf7Xf6 -7wXOM9XBY73WVp9P2dbPOeecc84555xzzjnnq3x3vmzr5Zzv89Hxu+qKOvd4 -Du+9H7LUzc949PfSqXOQ5/be8aPze8/yE+49y1v67c6TZf2c8/Z477gs3x+n -8vDc7n7iPf6M7z7PVp2j2faRc84555xzzjnnnHPOS7573mzr5ZyX2+z5cTo/ -5y2/T9XB7/LT30U1z7IvvM1r/aLew297Lnhuj7rveaw/49Hnxux9yDmf9915 -os8Zzn+57xw+46fOt+jxnHPOOeecc84555xzPuqnx/3xVfNm20/O3+S784zW -s7su/m3PUgeP8Wz3RZZ9GfVSfPS901pH9Dnx9fuWf9Nv+f7kZzzbuZRlXzjf -6a1t9fPSOu+or/5O4/yE+87hGfzUOTl7bnPOOeecc84555xzznmvZ8m/ev5s -+8x5i9f67brPe+tY5av3h/MWX3UfZlkPP+NR51KW9Zda7z7N9p/127+fvTf5 -mzzb88X3eHT+rO9Tzme81i/qeXzbdzjnPb7qvs2yHv4OX/1+mZ03y75wzjnn -nHPOOeecc87v9915anl352+tK9t14d/01fP2Po+n19faP9t14u/ybO9N/i6f -nS+67lK/6Py9/Uavz+i8Wb4LZsdzfsJbn7+szykf81qL/t57q5f6Zasz6vss -276tni9LXb5n+Bt99jxZVQfnv1rrd/WuunzPcM4555xzzjnnnHPOV/nuPKP1 -7K6r5LP1c/6rjd5vs3Wsnve255rzEY96b/JveOu4qPcRP+u9/ZxP/E0++j28 -ug6ew2tt9XfdLd47fvd7JOv+tMZX7XPv/Le8v3ffn5x/wW953jlv6TcbP/1c -tOblnHPOOeecc84555zf67vzjObdXdfTs12Xt3qptfbPer1q/bLUO1o/57x+ -/tTmia6b3+HPeO/7dHU9b/Po92C2ejjP4LPvy1V18Nw+O9+p+mbrKY1f3b/W -L+s+nzoHVs93298Fu+9/zr/oWergPNKjn4/b3secc84555xzzjnnnPOyR+e/ -ra4/Hp3/tJfiq6/r6LzR1+VUnlYfrX93XZzf6LPP1y3nBs/hvS1b/dHP56iv -rotzvt5nz03P/zt9Nj56X2Tbh9n35qo8vpN/9yuN270PvfM7Lznv91XPUZb1 -cL7Db3m/ROfnnHPOOeecc84555zXPSp/rZ6oukreWv8tPttq+bJd39n9yX79 -n/HV6+Wcr38vrKqD5/BnfNf7evY763a/bV7O+X7fdY7zu73UstV5i+8aNzpv -Fve9wTmPPmc5v8mzvjdn6+Scc84555xzzjnnnJ/36PxPr9UZVVeW/KN19fZ/ -2/V9y3VurXf2Psm2Ps5v9t5zuTZ/9Hq+6tHn++y8bzn3n/Fs+8w5j/PZc7t3 -fv67X2//0+f5rvz8d8tW5+nvkF11cc7jfdV3SJb1cL7Tn/Fs781s+8U555xz -zjnnnHPOOS+3bHU9vVb/6bqir9eqfrf66nVnWVfJW9fbOn9vfs75uef7a+/3 -Vd77XshS96r4qe+cVflWf/+01vvV7ybO3+y3nc9Z3jO3vzdXnedZ3ru3+a7r -MlrPbo8+Nzjn97nnn/N979/d+Ve/92fHZbkenHPOOeecc84555xn8uj8t67v -bet5u9f2czbP6uvb2280H+f8nK/uN+q98azvo9ZxWa5/zbPUsWs9vfNkve84 -59/zLO+z1fNF7+suXzXvV99Dz3i261LyqOfxK991nPN5n41zzud9tN+uek5/ -j3HOOeecc84555xz/iaPzh+97lKrzXc6H2/z1ddldF7OOR99j5TG73r/rX7f -jeZd9f2ya99Of5dkq49zzr/uWd4vo/Es9b/lvZltP7KsZzbOOee3euu5ump+ -zvn576JVeXrnz7IvnHPOOeecc84555xn8uj8t3hvy1b/W/0ZX33/j9bFOefZ -vfY72kvxbHV673DO+Te89dzOUu9bPEsdo37qOyHL/blrXs45v81Xn/+c832+ -ut8ub/3+45xzzjnnnHPOOef8Cx6d/xbvbdnqv92f8dPXNdt+cM75rK/ut9pH -63rGo+v3/cU559/0U++T2bzP+C3v97f7quvaO9+q/pxz/nU/dW5zzsd99XMa -5c4LzjnnnHPOOeecc/5Fj85/an3Z5p0d/zbvvT9vvW845zy77zpvW9vse2P2 -O2j199LoOM4553zEs7wfR9+LtTif89nvt+j6Oef8Fp9973LOz/kzftt3bOt3 -OOecc84555xzzjnnb/Lo/LN1Rde3e95S/2zXa9ZvvV6cc/51j/6+WDU+y35y -zjnnO7z1PTj6vu3NV+vHOeec3+yt78HddXDOxz06/+rzh3POOeecc84555zz -N/mq+Wrzt467bX9O1fHHV9e5a5+y3Z9Z8nDOOY/11vipejjnnPNIH31fcs45 -57zure9Z72PO8/voc7q7rqdn2S/OOeecc84555xzznf67LjafNnWu3p/TtUx -6r3XL3qfe8efut8555xzzjnnnHPOOef86aV+z3itX2//LOvnnLefC73nQK+v -Wk9vPMu+c84555xzzjnnnPNv+Oj42u+3eJY6bnP7yTnnnHPOOeecc845f5vX -+o3Ol22dnPN47z2Hos6ZLPvFOeecc84555xzzr/hq+bNtq7RfRiNc84555xz -zjnnnHPOOf+W136Pem9ezjmvxbPV8/Rs+8g555xzzjnnnHPOc3rv+Gz1Z9sf -zjnnnHPOOeecc84559/w2u9RXz0f5/w9Xjs3Wuc7df605uWcc84555xzzjnn -vMVL/bLVeXofSi1b3ZxzzjnnnHPOOeecc85z+Kr5ZuvgnN/vo+dGrZ0691rn -2VUX55xzzjnnnHPOOec3ea3VxmVbD+ecc84555xzzjnnnPM7vRQ/XQfnPK8/ -46vnHR2/y1f345xzzjnnnHPOOeff8N3znaq/1K913GwdnHPOOeecc84555xz -znmL/1f7dZIlOQoFAfD+t+5VbeI1ySAGRzJ2ss/gEBJZVWqt/dP2wzl/7r/1 -p+N767u89547nZdzzjnnnHPOOeecZ3nKOq39U/fHOeecc84555xzzjnn/Jte -6zc67tdr86SdC+f8uf/WR++B2blWeev9yTnnnHPOOeecc875znVmrzsrF+ec -c84555xzzjnnnHPe4rP7ldq/frX+KefCOV93vzytp3vrvlLycs4555xzzjnn -nPO9XupX69+6zqw8nHPOOeecc84555xzznmCl+q9/Xu91u/0uXDO1/vseyPd -T6/POeecc84555xzzrN89vhS/9r4tHPhnHPOOeecc84555xzzv/y2vMuP70+ -5/y81+6HU7la/fT6nHPOOeecc8455/wOT8nBOeecc84555xzzjnnnN/ktefZ -3puHc85H75NT7l7jnHPOOeecc8455395Sg7OOeecc84555xzzjnn/GZfvU6t -nd4/5/web71nTudKOS/OOeecc84555xznuEpOTjnnHPOOeecc84555zzL/ju -cZxz3uq1+2d3rpRz4ZxzzjnnnHPOOecZnpKDc84555xzzjnnnHPOOef1lpaP -c86fzpe2H84555xzzjnnnHOe6Sk5OOecc84555xzzjnnnPMveqnf0/lXzcs5 -563eOi4tN+ecc84555xzzjnP9JQcnHPOOeecc84555xzzvmbfHT87Pl61+Gc -8933Y62l5vw3Lu18Oeecc84555xzzt/qKTk455xzzjnnnHPOOeec8zf47vG9 -69TmSTlHzvk9/lsfva/S9vX0HFqfOeecc84555xzznmbp+TgnHPOOeecc845 -55xzzm/2Ur02vnWe1b5rHc55vv/WZ8/bOz7tfFrzlcal5Oacc84555xzzjm/ -zVNycM4555xzzjnnnHPOOec3e6ne23+11/qdPkfO+Xz/rZ/OMWvetHNu3Xdv -/7T9cM4555xzzjnnnJ/ylBycc84555xzzjnnnHPO+Zu99rzLa/1SzotzPv+7 -/1fffc/U8sz2tPNv/V1anznnnHPOOeecc86/6ik5OOecc84555xzzjnnnPM3 -e+15l9f6pZwX53z+vbPLn9ZHffd6rf50vpT3iXPOOeecc8455/y0p+TgnHPO -Oeecc84555xzzr/otefZvmsdzvk+T8lRaqfznb4PW8edPifOOeecc84555zz -dE/JwTnnnHPOOeecc84555zzss+a72kOznmut47blWP2vKu89lzz3nrKvjnn -nHPOOeecc85v85QcnHPOOeecc84555xzzjmve+255rNycM7v8d967/1Q6z+a -6zZvPYfavKf3wTnnnHPOOeecc36rp+TgnHPOOeecc84555xzzvk8L9VL43vX -qbXT++ecz/fT69/qs/txzjnnnHPOOeecf9VTcnDOOeecc84555xzzjnnfL6X -+qXl4ZzP99r3fyrX1/y2eTnnnHPOOeecc85TPSUH55xzzjnnnHPOOeecc87L -Xqr3zjs6T+86v75qXs75vHln5+Jz5/2tp+yPc84555xzzjnnfJen5OCcc845 -55xzzjnnnHPOebk+a73e8b312fNzzuu++rvmz/z0eM4555xzzjnnnPO3eEoO -zjnnnHPOOeecc84555zfO2/NR+spvwfnN3ip3vpdrcr1VZ913/XOzznnnHPO -Oeecc/5WT8nBOeecc84555xzzjnnnPP58/7WU/ZXaqvOgfMv++n1v+qz78On -83POOeecc84555zf7ik5OOecc84555xzzjnnnHNers9a7/T+Wr3W0vJyftKf -fl8p+/i6n16fc84555xzzjnnPN1TcnDOOeecc84555xzzjnnvH/crHnS/PT6 -nN/ks+4NvtdX/b6cc84555xzzjnnb/WUHJxzzjnnnHPOOeecc845H/fa821e -65eWl/MEL9V7+/M9Prsf55xzzjnnnHPO+ds9JQfnnHPOOeecc84555xzzsd9 -dr9UP70+54le+15O5eJ/+1fubc4555xzzjnnnPNZnpKDc84555xzzjnnnHPO -OefjXur3W0/JO+qn1+c80Ue/o9W5vu6j91jrPJxzzjnnnHPOOedf85QcnHPO -Oeecc84555xzzjnf56V+v/WUvKfXH8052v/p+vybXqqnfU88a33OOeecc845 -55zzWzwlB+ecc84555xzzjnnnHPOc732vMtnzVebf9Y6rX7qHPi3/fT6b/He -8z2dl3POOeecc8455/xWT8nBOeecc84555xzzjnnnPP3eO151HePO+1v2w9f -67/1Wr9dud7mp8dzzjnnnHPOOeecf9VTcnDOOeecc84555xzzjnnnPd6qaXl -fOq1/c9ed/d6fK3XWlreVO/9Lk7n5ZxzzjnnnHPOOX+bp+TgnHPOOeecc845 -55xzzjlv9dpzzZ/WZ/lonqfz1fz0ufA5vvo94X/XS+NP5+Wcc84555xzzjm/ -1VNycM4555xzzjnnnHPOOeec//rsfrO9t55yrrV6rX/reqPnxuf4rN/xq55+ -/3DOOeecc84555x/zVNycM4555xzzjnnnHPOOef8u356PH/mrW3VeP7/3nre -KXnT3P3DOeecc84555xznuUpOTjnnHPOOeecc84555xz/l2/bV7+zHvH1+ZJ -298tfnr9FG+9N3r7c84555xzzjnnnPO5npKDc84555xzzjnnnHPOOeff9bev -x9v8ad3v3NbvdK40995wzjnnnHPOOeec3+EpOTjnnHPOOeecc84555xz/n5/ -+3p8r5f61fqn7eP0+aXlOn1PpOTinHPOOeecc84553+3tHycc84555xzzjnn -nHPOOb/HS/XdOVo9JQff46V+t723o/tOy7Xrnjmdl3POOeecc84555zP8ZQc -nHPOOeecc84555xzzjl/v6fkKNXT8vGzXuuXlvfp+5/mrb/L7lycc84555xz -zjnn/Iyn5OCcc84555xzzjnnnHPO+f3eO25VjtF1T58fz/LR8Wn7OPX9Pc1V -6p+Wl3POOeecc84555zv8ZQcnHPOOeecc84555xzzjl/r5fqu3K0jjt9Tvxu -L7XT73/K+q3n5nvknHPOOeecc8455y0tLR/nnHPOOeecc84555xzzt/jteea -rx6Xck78G15ru9ZP/d4555xzzjnnnHPOOf+rpeXjnHPOOeecc84555xzzvl7 -vPY86r31lPPg/K922zqz5+Occ84555xzzjnn/K+Wlo9zzjnnnHPOOeecc845 -5+/32nPNe+cv9U85D857vNavdVzrfJxzzjnnnHPOOeecn/CUHJxzzjnnnHPO -Oeecc84556t81ry/9ZT9cT6jpeXnnHPOOeecc8455/yvlpaPc84555xzzjnn -nHPOOed8lp/OkXYe/B3e2ka/i7T9cs4555xzzjnnnPNvekoOzjnnnHPOOeec -c84555zzVX4qx2895Tx4hj9tKd/F7Fycc84555xzzjnnnLe0tHycc84555xz -zjnnnHPOOeezvVSftV7v+Kf12r74Hm+t945b5SnrlVra78s555xzzjnnnHPO -z3pKDs4555xzzjnnnHPOOeec8xSvPde8d/6n6/yrz5531fynvLU+a750T8lR -89Z67zjOOeecc84555xzfpen5OCcc84555xzzjnnnHPOOX+7l+qz19s1f+v6 -s/o9zfk0x9s8JUev9/6Ove9Vyj4555xzzjnnnHPO+d8tLR/nnHPOOeecc845 -55xzzvnbfdZ8tX5P12ldd9Y8p3+Xt3tKjtU++31zvpxzzjnnnHPOOednPCUH -55xzzjnnnHPOOeecc845z/JSv1N5+FxPyXGbP52vNu/q9TnnnHPOOeecc85v -9ZQcnHPOOeecc84555xzzjnnnPN1npLjdl81X+88aefCOeecc84555xzvtpT -cnDOOeecc84555xzzjnnnHPO93lKjq95qd+sdXrH9dZTzpFzzjnnnHPOOeff -85QcnHPOOeecc84555xzzjnnnPN5XqrvzsH7vNaervO039N5Oeecc84555xz -zkc9JQfnnHPOOeecc84555xzzjnnfJ6X6rtz8Dt81ny1Z84555xzzjnnnPNR -T8nBOeecc84555xzzjnnnHPOOZ/npfruHDzDa+/DqvV7x83KkXLunHPOOeec -c845n+cpOTjnnHPOOeecc84555xzzjnnz/1pnb/bf+u1fqvWXz1vaVza78E5 -55xzzjnnnPN2T8nBOeecc84555xzzjnnnHPOOZ/npfruHPzbXnsPV62fsn/O -Oeecc84555zP85QcnHPOOeecc84555xzzjnnnPNxL/UrtZTc/N3eO351rpRz -4ZxzzjnnnHPOeb+n5OCcc84555xzzjnnnHPOOeec93vvuFU5OP8/H30/V+f6 -9ZTz4pxzzjnnnHPOedlTcnDOOeecc84555xzzjnnnHPO+7133KocnP+f197D -U7lK3pp/9PtqnTflPDjnnHPOOeec8yRPycE555xzzjnnnHPOOeecc845n+8p -OTjv8dn9Rr227q5zqOXhnHPOOeecc86/4Ck5OOecc84555xzzjnnnHPOOed1 -rz2X2tN+nH/ZS+30988555xzzjnnnH/JU3JwzjnnnHPOOeecc84555xzzute -e675rBycv8lr30utja4/uu7TfXHOOeecc8455zd6Sg7OOeecc84555xzzjnn -nHPOed1rzzWflYPzN/nod7Q6V6+3fvcpeTnnnHPOOeec8x5PycE555xzzjnn -nHPOOeecc8457/dSvTbP6dycn/Tf+uj42blWue+fc84555xzzvkbPCUH55xz -zjnnnHPOOeecc8455/y5p+TgPNl/62//zmrPnHPOOeecc875DZ6Sg3POOeec -c84555xzzjnnnHNerpfG1/rP6sf5F/y3/tbv5vT6nHPOOeecc875iKfk4Jxz -zjnnnHPOOeecc84555yX66Xxtf6t69fqnPN6v9O5Wv30+pxzzjnnnHPO+Yin -5OCcc84555xzzjnnnHPOOeectz+P+uz5OP+i176vU7me+un1Oeecc84555zz -vzwlB+ecc84555xzzjnnnHPOOee87LPme5qDc1722nd3Ktevn16fc84555xz -zjkf8ZQcnHPOOeecc84555xzzjnnnPO6155LrXUc53y/714/bf+cc84555xz -znmLp+TgnHPOOeecc84555xzzjnnnPd7qb47B+d8vde+99b5VufuHde7r5Tf -g3POOeecc875Xk/JwTnnnHPOOeecc84555xzzjmve+251FrHcc7f57/11ntj -VZ7Z92Cp1fbLOeecc8455/wuT8nBOeecc84555xzzjnnnHPO+Rd91fhTeTjn -ed7b0vLvug9n5eCcc84555xzvsZTcnDOOeecc84555xzzjnnnHP+JS/Va+Nb -56mNn5WHc77PZ817ev30cyv1S9kP55xzzjnnnH/VU3JwzjnnnHPOOeecc845 -55xzzs+tv2sdznm7p82bdj6r7rm03JxzzjnnnHPOs3JwzjnnnHPOOeecc845 -55xzztufZ3tvHs75/O/vX33Xd73a08659fxLnpabc84555xzzr/mKTk455xz -zjnnnHPOOeecc8455+3Ps33XOpzzfes9rafvb/f9l5abc84555xzzr/mKTk4 -55xzzjnnnHPOOeecc84552Vfvc7s+Tjn5bb7u5497657rFSffb+19uOcc845 -55xzftZTcnDOOeecc84555xzzjnnnHPO+7133KocnPN+X73eqnlPn9Psc2i9 -L1POg3POOeecc86/6ik5OOecc84555xzzjnnnHPOOefzvFTfnYNzXq6vmre3 -/nU/PZ5zzjnnnHPOeZun5OCcc84555xzzjnnnHPOOeecr/NSa50nbT+c3+il -euv3Nntdvme933rKvjnnnHPOOef8Nk/JwTnnnHPOOeecc84555xzzjmv+9N+ -T+uzc3LO6y0t79t89++bsm/OOeecc845v81TcnDOOeecc84555xzzjnnnHPO -c8aXWm18bZ6U8+U8wWd9d3zMd91XT/NwzjnnnHPOOc/KwTnnnHPOOeecc845 -55xzzvmXvFSftd6svLvW4fzNPvrdrb4neNtz67yt66bsm3POOeecc85v85Qc -nHPOOeecc84555xzzjnnnH/Ra8+94097rV9aXs53+NPvqNRS9vc2n/W7nN4H -55xzzjnnnL/NU3JwzjnnnHPOOeecc84555xzzsv13v6n/PT6nCd7qe57uttP -r88555xzzjnnX/GUHJxzzjnnnHPOOeecc84555zzuteeU73WLy0v5zv99Pq8 -z2f345xzzjnnnHPe5ik5OOecc84555xzzjnnnHPOOeflemn86bytfnp9zk/6 -6PeyOhf/f599j7XOzznnnHPOOef8b0/JwTnnnHPOOeecc84555xzzjkv++n1 -V/np9Tnf4aPfxepc/G9fdc+l7I9zzjnnnHPOb/OUHJxzzjnnnHPOOeecc845 -55zzca89p/rp9Tnf6aW67yPLZ/8erfNzzjnnnHPOOf/bU3JwzjnnnHPOOeec -c84555xzzud77XmXn16f80SvfS+ncvE2L7XUe5hzzjnnnHPOb/eUHJxzzjnn -nHPOOeecc84555zzfV57nu271qmt/3R8yu/H7/Tf+qr3la/13fcn55xzzjnn -nPOsHJxzzjnnnHPOOeecc84555zzXK8913xWjlXzzT6H1Tn4XT77vZ89L/9/ -3/37cs4555xzzjn/21NycM4555xzzjnnnHPOOeecc87v91K9Nn5VntVe209p -ntO5eYaPvj98js+6j07vg3POOeecc86/4ik5OOecc84555xzzjnnnHPOOeff -8d6Wlr/Va8+940dz8Ewf/X1X5/qKPz3/Vbk455xzzjnnnP+/p+TgnHPOOeec -c84555xzzjnnnN/rs/vVxo/Wn/rTfrPynNo/X+O/9dXvD3/mo/cC55xzzjnn -nPNnnpKDc84555xzzjnnnHPOOeecc57npfqs9Vbvo3f8qfOePe/p94Y/813v -CW975pxzzjnnnHOe4Sk5OOecc84555xzzjnnnHPOOefnvFRfneP0vtO9VK/1 -b13v1O/O2+p+n2c+Oj5tH5xzzjnnnHPOs3JwzjnnnHPOOeecc84555xzzs/7 -29f7qo+OT9vHV3z278j/7vdbT8nLOeecc8455/zvlpaPc84555xzzjnnnHPO -Oeeccz7PS/XdOWrrnz6nr3vv+NT36laf9bt81VvPk3POOeecc875XZ6Sg3PO -Oeecc84555xzzjnnnHO+39Ny/KunnRPvq69a/yue/r2m+Ox+nHPOOeecc86z -PSUH55xzzjnnnHPOOeecc84553y+p+So+W89LR8f81K/1vfgq957nvxvP70+ -55xzzjnnnPM5npKDc84555xzzjnnnHPOOeeccz7fa8+7cvSun3J+/JmX+s3u -n7bv2d9tqaXkfeq9v+/pvJxzzjnnnHPOz3hKDs4555xzzjnnnHPOOeecc855 -rq8aXxqXsm++12f3e6ufXv/0e5CWl3POOeecc875Hk/JwTnnnHPOOeecc845 -55xzzjnf57Xnmq8el3JOPNtr/dLyPt3f7vVT7x/OOeecc84559/0lBycc845 -55xzzjnnnHPOOeec8/W+ep3e+unz4O/0Un30vU3z0+vXcpX6peXlnHPOOeec -c36Xp+TgnHPOOeecc84555xzzjnnnK/3Ur00vned1nk5T/Jav9S8u9cfPT/O -Oeecc84553yGp+TgnHPOOeecc84555xzzjnnnL/fa8+cJ/lo25Vr9jpp5885 -55xzzjnnnP/V0vJxzjnnnHPOOeecc84555xzzu/12fOm7Y/znjZ7ndnfU9p5 -cs4555xzzjnnf7W0fJxzzjnnnHPOOeecc84555zze7xU353j1Hqc9/iplnYO -nHPOOeecc855i6fk4JxzzjnnnHPOOeecc84555y/x0/l+K2nnAfnPT6rpe2L -c84555xzzjl/4ik5OOecc84555xzzjnnnHPOOefv9VJ99nqt63Ke4Ktb2n45 -55xzzjnnnPMnnpKDc84555xzzjnnnHPOOeecc/49nzVfrf2O653n9DnxO/xp -/el7v3s855xzzjnnnHO+01NycM4555xzzjnnnHPOOeecc875r5f6zZpnlv/W -U86Pt/nTlvJdeM8555xzzjnnnL/ZU3JwzjnnnHPOOeecc84555xzzvlqXz3v -v3rr+rV5eue/3Uv9Ws99dJ2n8+32lBw1b21puTnnnHPOOeecZ3pKDs4555xz -zjnnnHPOOeecc8453+Wl+tP+vTlGvZand/7f+qr5Z80z+ju+xVNyjHprvdQv -bT+cc84555xzzvd4Sg7OOeecc84555xzzjnnnHPOOU/3Ur9Z8/Su93T+1vrT -+Wet+1VPyXF6/7O/07R9cs4555xzzjn/21NycM4555xzzjnnnHPOOeecc845 -3+ul+qk8vM1TcqT5rvfZ78Q555xzzjnnZzwlB+ecc84555xzzjnnnHPOOeec -c87L9d05vuq18x9dZ/b8KefFOeecc84557s8JQfnnHPOOeecc84555xzzjnn -nHPO83J8zUv9Vq3/NI/3hnPOOeecc/4VT8nBOeecc84555xzzjnnnHPOOeec -83J9dw6+xmu/76p1Zu2n1C/lfDnnnHPOOefv9ZQcnHPOOeecc84555xzzjnn -nHPOOa+3tHy8z2u/82i95qvmbfXWPJxzzjnnnHNe8pQcnHPOOeecc84555xz -zjnnnHPOOS/Xd+fgWf5bn/2ejI6b/Z5zzjnnnHPOeclTcnDOOeecc84555xz -zjnnnHPOOee8XN+dg7/TZ/fb9f6v2qfvjXPOOeec83s8JQfnnHPOOeecc845 -55xzzjnnnHP+RS/16+3PeYv/1mv9am123qf7eepP83DOOeecc87XeUoOzjnn -nHPOOeecc84555xzzjnn/EveO25VDv5tn/0ezspV8t3z7s7BOeecc845r//7 -/HQOzjnnnHPOOeecc84555xzzjnn/Mv+tM75F7zWUvLWnjnnnHPOOefP/z+Q -lo9zzjnnnHPOOeecc84555xzzjl/s6fk4DzBe8fvyvXUT6/POeecc875Gzwl -B+ecc84555xzzjnnnHPOOeecc/4lL9Vr85zOzfkO/62Pjp+d66n7njnnnHPO -OR/3lBycc84555xzzjnnnHPOOeecc875l7x33KocnCf5rHln51rlp9ZfXeec -c84553yFp+TgnHPOOeecc84555xzzjnnnHPOv+Sleq2dzs35Ca99L739Z+V6 -6r3jVuWYvf7pc+Wcc8455+/0lBycc84555xzzjnnnHPOOeecc875l7xU352D -cz7+Pc7OtWre1f5bT8vHOeecc87f4Sk5OOecc84555xzzjnnnHPOOeec8zd7 -7bnUWsdxzu/1Whu9L2b5rbk555xzzvm7PCUH55xzzjnnnHPOOeecc84555xz -frPPmq/W7/Q+OefzfPQeSMk1Os/THJxzzjnn/JuekoNzzjnnnHPOOeecc845 -55xzzjl/g9eea947P+c832fNOzvXKq/lb62f3gfnnHPOOc/ylBycc84555xz -zjnnnHPOOeecc875zT5rvlq/0/vknPf7rvvhdnffcc4555zzvzwlB+ecc845 -55xzzjnnnHPOOeecc/5G7x23Kgfn/JzPmnd2rjRfdW6cc8455/wdnpKDc845 -55xzzjnnnHPOOeecc845/4Kn5OCcn3f3Sp+fXp9zzjnnnJ/1lBycc84555xz -zjnnnHPOOeecc875Tf60X2lcrX/K/jnn5+6BWblu8dH7l3POOeecv8tTcnDO -Oeecc84555xzzjnnnHPOOec3+dN+q9flnH/PT6+/y0+vzznnnHPOz3hKDs45 -55xzzjnnnHPOOeecc8455/wGX71OrZ3eP+f8nNfujdF6urfelyl5Oeecc875 -Gk/JwTnnnHPOOeecc84555xzzjnnnN/ss+ar9Tu9T875eW+tr1r/tJ9en3PO -Oeecn/GUHJxzzjnnnHPOOeecc84555xzzvkNvnqdWju9f875Pf70/knZx6+f -Xp9zzjnnnJ/xlBycc84555xzzjnnnHPOOeecc875zT5rvqc5OOd81Gv30qlc -v356fc4555xzfsZTcnDOOeecc84555xzzjnnnHPOOedv8qd1zjlP8dH7b1Wu -lHMptV05ev++pJ0b55xzzvkt/+7inHPOOeecc84555xzzjnnnHPOv+QpOTjn -/LTXWm2+lBynvXVfu86Tc84553z3vyPT8nHOOeecc84555xzzjnnnHPOOecn -vFSfvV6pfnr/nHOe4r0tLf/pc3v69661P+ecc8757n8XpuXjnHPOOeecc845 -55xzzjnnnHPOV3qp3jtv7/q968zKyTnnt3lvS8t/i5fqq/4Ocs4555w//Xdh -Wj7OOeecc84555xzzjnnnHPOOed8pZfqtfFP1++tj87DOedpfmp82jns9lW/ -R22dlP1zzjnn/H5PycE555xzzjnnnHPOOeecc84555zf4KvXqbXT++ec85rv -vifT573F0+fjnHPOOU/JwTnnnHPOOeecc84555xzzjnnnCd7yvqlfmnnxTl/ -j7feS6tz7Fov9e/AbX/nZs/HOeecc56Sg3POOeecc84555xzzjnnnHPOOT/h -pXpv/9Ve63f6HDnn7/ff+ukcu9Yb/XuxKsdsn3XOKfvhnHPO+Xs9JQfnnHPO -Oeecc84555xzzjnnnHOe6LXnXX56fc75d/y3npKjt37678VbvFT/yv4555xz -nuMpOTjnnHPOOeecc84555xzzjnnnPMbfPU6tX6n9885v99r90/KvfO0ftqf -3v+1cbvPefa6nHPOOedP/72Ulo9zzjnnnHPOOeecc84555xzzjlP9NrzqPeu -yznno/5bT813OscuTz1nvw/nnHPOUzwlB+ecc84555xzzjnnnHPOOeecc36z -z5rvaQ7OOa957f757bc636p5v+Kr/87szsc555xz7t+NnHPOOeecc84555xz -zjnnnHPO+X4v1Xfn4Jx/15/Odzrf7PV4n+/6/XetxznnnPN7PSUH55xzzjnn -nHPOOeecc84555xz/gUvtdZ5avO29uec89Zxq+adNY6v9ZQcJU/JwTnnnPN9 -/349nYNzzjnnnHPOOeecc84555xzzjlP8lJ9dN7e+UfXeeqnz51zft57x51a -l6/1tN/p9Hlwzjnn/Lyn5OCcc84555xzzjnnnHPOOeecc85PeKk+a73e8a1t -dy7OOa+1tLz8ma/++1jy1vdvND/nnHPO7/WUHJxzzjnnnHPOOeecc84555xz -zvkOf9t6veNr86T8Tpzz/PtqVy6e6bv+vo3mSTknzjnnnM//98HpHJxzzjnn -nHPOOeecc84555xzzvlJnzXvb331Pmr9Wvc5Oxfn/D7fdS/xOz11XNo5cc45 -53ydp+TgnHPOOeecc84555xzzjnnnHPOV3qpXpvnaY7T+661p/045/f6b333 -PcPv9FXv3+w655xzzt/nKTk455xzzjnnnHPOOeecc84555zznT67nra/0fMo -9UvLyzl/7qfHc560Puecc87zPSUH55xzzjnnnHPOOeecc84555xznuSn19/t -tX5peTnnz7113Oj40Vz8Wz76d4lzzjnn3/OUHJxzzjnnnHPOOeecc84555xz -zvlJn93vNq/1S8vLOV/noy1tHzzLT4/nnHPO+f2ekoNzzjnnnHPOOeecc845 -55xzzjlP9FK/33pK3lEv1Xv7c87v9996rd+uXPxu3/1+cs455/x9npKDc845 -55xzzjnnnHPOOeecc845P+mlfq3zpOxj1Gv90vJyzuf7rvuEv9Of/h1t9dZ1 -Oeecc/4+T8nBOeecc84555xzzjnnnHPOOeec3+S157f46fU55/t89v0wKxe/ -03etl7ZvzjnnnK/zlBycc84555xzzjnnnHPOOeecc875TV7q91tPyVvz0+tz -zvd767jR8aO5+J2+6+9Oqd76d5pzzjnn93pKDs4555xzzjnnnHPOOeecc845 -5/zNXns+7bV+aXk55/u91tLy8jPe+vfjaf2fp+ybc8455/v/PZqWj3POOeec -c84555xzzjnnnHPOOb/ZT6//1E+vzzk/77X74VQu/i4/vT7nnHPO8z0lB+ec -c84555xzzjnnnHPOOeecc/4lL9VLbXWu0+vXcv3Wa8+1eXrX4/xL/lt/ep+k -7Y+f8dn9OOecc/49T8nBOeecc84555xzzjnnnHPOOeec87rXnke91mbnXrXO -bC+1f/1r49L2w/lfPvp9+A54S1v1HnLOOef8O56Sg3POOeecc84555xzzjnn -nHPOOefzvfbc2kbnSTmHXm/db+0cUvbDeY/XWu99kLY//sx3/d6r5uWcc875 -vZ6Sg3POOeecc84555xzzjnnnHPOOec5XmppOXf56Pmdzs35TG+tr1qfZ/jq -e+/0/jjnnHOe6yk5OOecc84555xzzjnnnHPOOeecc77PS/1a53taf4vv2n+p -fnr//Bs++r6uzsXP+Oq/C6f3xznnnPNcT8nBOeecc84555xzzjnnnHPOOeec -8/l+evys+i6fne9pnpq3/l6rc/Bv+G+91q/W0vbH53qpjd7DnHPOOecpOTjn -nHPOOeecc84555xzzjnnnHNe97evN3vc6nVH5x8dX/PZ58l5i9daWl4+x0/d -c5xzzjn/rqfk4JxzzjnnnHPOOeecc84555xzznm5vjvHqfVOe6mtmn/3ftLO -m9/t3rt3uXuHc8455+mekoNzzjnnnHPOOeecc84555xzzjn/oqfkKHlKjq96 -77jaPKM5vC/8/7z1fSu1lH183WfdP7PGc84555z7dwbnnHPOOeecc84555xz -zjnnnHOe46X67hyt/ltPy8f/9tb2tveW7/Hfeut7mLaPr/rod706F+ecc855 -raXl45xzzjnnnHPOOeecc84555xzzm/23nGrcjz133paPj7mq+ZrbWnnwce8 -1G675/jfbfbfO84555zzp/9OScvHOeecc84555xzzjnnnHPOOeec3+yl+u4c -o56Sg2f77PGl/mn7/rrvfk94n58ezznnnHM+21NycM4555xzzjnnnHPOOeec -c84552/wUr/e/mn+W0/LxzO9d3zv98OzvdbS8n7FZ/fjnHPOOd/lKTk455xz -zjnnnHPOOeecc84555zzm7133Kocq7x1XFpuftZr/Va9b63j+RoffR/4XG/9 -HUotZR+cc84556WWlo9zzjnnnHPOOeecc84555xzzjm/wXvHrcqxyn/rafn4 -u/30eN7nfoe9Pnr+q3NxzjnnnM/2lBycc84555xzzjnnnHPOOeecc875G71U -352j5rWcv/1ScvNveK1f73eWtr+3+ejvyP9uT8+fc8455/x2T8nBOeecc845 -55xzzjnnnHPOOeecv9lL/WbNM8ufzpdy3py3tNp7uyvX27z3/Pn/++x+nHPO -Oee3e0oOzjnnnHPOOeecc84555xzzjnn/A1eex713nV7+7XmqHnK78D5X631 -Oxgdl7bv0/dgqaXkPeWz+3HOOeecv91TcnDOOeecc84555xzzjnnnHPOOec3 -+6n1a/1q41L3xXmCj45P28fp80vLdfo8ZvXjnHPOOf+ap+TgnHPOOeecc845 -55xzzjnnnHPO3+y159neW085J85v9tHxaftYdR6710/x2e8L55xzzvlXPSUH -55xzzjnnnHPOOeecc84555xz/iUv1Uvje/vPqnPOn3trfdX6aX56/VXeem9z -zjnnnPMxT8nBOeecc84555xzzjnnnHPOOeec833eO/63nrIPzm/21vqq9VP3 -fdp7c5/OyznnnHP+FU/JwTnnnHPOOeecc84555xzzjnnnPP5ftu8nPOyj7bU -faTkcr9xzjnnnN/hKTk455xzzjnnnHPOOeecc84555xzPs9L9d05Tq3H+Zd8 -tKXm3XUPpf2OnHPOOef8b0/JwTnnnHPOOeecc84555xzzjnnnPN5XqrvzlFb -//Q5cf5FH223reOe4Zxzzjl/l6fk4JxzzjnnnHPOOeecc84555xzzvk8L9V3 -5xhd//T5cc7va2nnxjnnnHPO53pKDs4555xzzjnnnHPOOeecc84555zv81M5 -WselnBPnvP49725p58A555xzzvd4Sg7OOeecc84555xzzjnnnHPOOeecr/dS -vTS+t/+o/9ZPnxPnPLelnQ/nnHPOOd/jKTk455xzzjnnnHPOOeecc84555xz -ft5rz7O9t9XmaV0n5bw5T/LbW9p5cs4555zzuZ6Sg3POOeecc84555xzzjnn -nHPOOefnfPU6tX6n9t/aTv8+nI94rdXGpX9nT1va78U555xzzv/2lBycc845 -55xzzjnnnHPOOeecc84557++e97SuJTz4N/wWr/WcU9zrNpPqaXkKLW094Rz -zjnn/GuekoNzzjnnnHPOOeecc84555xzzjnn/NdP5fitr5p3dB6e6bXWO673 -PUr11nZr7tJ8afvhnHPOOb/dU3JwzjnnnHPOOeecc84555xzzjnnnD/13vGt -9dH5Z/lvffa8pX5PzzflvEbrT9fvbWnnuOs9e4uPtrd8d5xzzjnn/l3JOeec -c84555xzzjnnnHPOOeecc97mteeat7an68zyUps9f23c0/G9eUbnaZ13dD+t -/b7mrS0t9679rzrPp+twzjnnnOf4f7/KwZE= - "], {{0, 0}, {501, 501}}, {0, 1}], Frame -> Automatic, - FrameLabel -> {None, None}, FrameTicks -> {{None, None}, {None, None}}, - GridLinesStyle -> Directive[ - GrayLevel[0.5, 0.4]], - Method -> { - "DefaultBoundaryStyle" -> Automatic, "DefaultPlotStyle" -> Automatic}], - FormBox[ - FormBox[ - TemplateBox[{"\"Divergent\"", "1", - RowBox[{ - RowBox[{"-", - RowBox[{ - FractionBox["1", "2"]}]}], "-", - FractionBox[ - RowBox[{"\[ImaginaryI]", " ", - SqrtBox["3"]}], "2"]}], - RowBox[{ - RowBox[{"-", - RowBox[{ - FractionBox["1", "2"]}]}], "+", - FractionBox[ - RowBox[{"\[ImaginaryI]", " ", - SqrtBox["3"]}], "2"]}]}, "SwatchLegend", - DisplayFunction -> (FormBox[ - StyleBox[ - StyleBox[ - PaneBox[ - TagBox[ - GridBox[{{ - TagBox[ - GridBox[{{ - GraphicsBox[{ - Directive[ - EdgeForm[ - Directive[ - Opacity[0.3], - GrayLevel[0]]], - PointSize[0.5], - AbsoluteThickness[1.6], - RGBColor[0., 0., 0.]], - RectangleBox[{0, 0}, {10, 10}, "RoundingRadius" -> 0]}, - AspectRatio -> Full, ImageSize -> {10, 10}, - PlotRangePadding -> None, ImagePadding -> Automatic, - BaselinePosition -> (Scaled[0.1] -> Baseline)], #}, { - GraphicsBox[{ - Directive[ - EdgeForm[ - Directive[ - Opacity[0.3], - GrayLevel[0]]], - PointSize[0.5], - AbsoluteThickness[1.6], - RGBColor[1., 0., 0.]], - RectangleBox[{0, 0}, {10, 10}, "RoundingRadius" -> 0]}, - AspectRatio -> Full, ImageSize -> {10, 10}, - PlotRangePadding -> None, ImagePadding -> Automatic, - BaselinePosition -> (Scaled[0.1] -> Baseline)], #2}, { - GraphicsBox[{ - Directive[ - EdgeForm[ - Directive[ - Opacity[0.3], - GrayLevel[0]]], - PointSize[0.5], - AbsoluteThickness[1.6], - RGBColor[0., 1., 0.]], - RectangleBox[{0, 0}, {10, 10}, "RoundingRadius" -> 0]}, - AspectRatio -> Full, ImageSize -> {10, 10}, - PlotRangePadding -> None, ImagePadding -> Automatic, - BaselinePosition -> (Scaled[0.1] -> Baseline)], #3}, { - GraphicsBox[{ - Directive[ - EdgeForm[ - Directive[ - Opacity[0.3], - GrayLevel[0]]], - PointSize[0.5], - AbsoluteThickness[1.6], - RGBColor[0., 0., 1.]], - RectangleBox[{0, 0}, {10, 10}, "RoundingRadius" -> 0]}, - AspectRatio -> Full, ImageSize -> {10, 10}, - PlotRangePadding -> None, ImagePadding -> Automatic, - BaselinePosition -> (Scaled[0.1] -> Baseline)], #4}}, - GridBoxAlignment -> { - "Columns" -> {Center, Left}, "Rows" -> {{Baseline}}}, - AutoDelete -> False, - GridBoxDividers -> { - "Columns" -> {{False}}, "Rows" -> {{False}}}, - GridBoxItemSize -> {"Columns" -> {{All}}, "Rows" -> {{All}}}, - GridBoxSpacings -> { - "Columns" -> {{0.5}}, "Rows" -> {{0.5}}}], "Grid"]}}, - GridBoxAlignment -> {"Columns" -> {{Left}}, "Rows" -> {{Top}}}, - AutoDelete -> False, - GridBoxItemSize -> { - "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, - GridBoxSpacings -> {"Columns" -> {{1}}, "Rows" -> {{0}}}], - "Grid"], Alignment -> Left, AppearanceElements -> None, - ImageMargins -> {{5, 5}, {5, 5}}, ImageSizeAction -> - "ResizeToFit"], LineIndent -> 0, StripOnInput -> False], { - FontFamily -> "Arial"}, Background -> Automatic, StripOnInput -> - False], TraditionalForm]& ), - InterpretationFunction :> (RowBox[{"SwatchLegend", "[", - RowBox[{ - RowBox[{"{", - RowBox[{ - RowBox[{"Directive", "[", - InterpretationBox[ - ButtonBox[ - TooltipBox[ - GraphicsBox[{{ - GrayLevel[0], - RectangleBox[{0, 0}]}, { - GrayLevel[0], - RectangleBox[{1, -1}]}, { - RGBColor[0., 0., 0.], - RectangleBox[{0, -1}, {2, 1}]}}, AspectRatio -> 1, Frame -> - True, FrameStyle -> RGBColor[0., 0., 0.], FrameTicks -> - None, PlotRangePadding -> None, ImageSize -> - Dynamic[{ - Automatic, 1.35 CurrentValue["FontCapHeight"]/ - AbsoluteCurrentValue[Magnification]}]], - "RGBColor[0., 0., 0.]"], Appearance -> None, - BaseStyle -> {}, BaselinePosition -> Baseline, - DefaultBaseStyle -> {}, ButtonFunction :> - With[{Typeset`box$ = EvaluationBox[]}, - If[ - Not[ - AbsoluteCurrentValue["Deployed"]], - SelectionMove[Typeset`box$, All, Expression]; - FrontEnd`Private`$ColorSelectorInitialAlpha = 1; - FrontEnd`Private`$ColorSelectorInitialColor = - RGBColor[0., 0., 0.]; - FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; - MathLink`CallFrontEnd[ - FrontEnd`AttachCell[Typeset`box$, - FrontEndResource["RGBColorValueSelector"], { - 0, {Left, Bottom}}, {Left, Top}, - "ClosingActions" -> { - "SelectionDeparture", "ParentChanged", - "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> - Automatic, Method -> "Preemptive"], - RGBColor[0., 0., 0.], Editable -> False, Selectable -> - False], "]"}], ",", - RowBox[{"Directive", "[", - InterpretationBox[ - ButtonBox[ - TooltipBox[ - GraphicsBox[{{ - GrayLevel[0], - RectangleBox[{0, 0}]}, { - GrayLevel[0], - RectangleBox[{1, -1}]}, { - RGBColor[1., 0., 0.], - RectangleBox[{0, -1}, {2, 1}]}}, AspectRatio -> 1, Frame -> - True, FrameStyle -> RGBColor[0.6666666666666667, 0., 0.], - FrameTicks -> None, PlotRangePadding -> None, ImageSize -> - Dynamic[{ - Automatic, 1.35 CurrentValue["FontCapHeight"]/ - AbsoluteCurrentValue[Magnification]}]], - "RGBColor[1., 0., 0.]"], Appearance -> None, - BaseStyle -> {}, BaselinePosition -> Baseline, - DefaultBaseStyle -> {}, ButtonFunction :> - With[{Typeset`box$ = EvaluationBox[]}, - If[ - Not[ - AbsoluteCurrentValue["Deployed"]], - SelectionMove[Typeset`box$, All, Expression]; - FrontEnd`Private`$ColorSelectorInitialAlpha = 1; - FrontEnd`Private`$ColorSelectorInitialColor = - RGBColor[1., 0., 0.]; - FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; - MathLink`CallFrontEnd[ - FrontEnd`AttachCell[Typeset`box$, - FrontEndResource["RGBColorValueSelector"], { - 0, {Left, Bottom}}, {Left, Top}, - "ClosingActions" -> { - "SelectionDeparture", "ParentChanged", - "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> - Automatic, Method -> "Preemptive"], - RGBColor[1., 0., 0.], Editable -> False, Selectable -> - False], "]"}], ",", - RowBox[{"Directive", "[", - InterpretationBox[ - ButtonBox[ - TooltipBox[ - GraphicsBox[{{ - GrayLevel[0], - RectangleBox[{0, 0}]}, { - GrayLevel[0], - RectangleBox[{1, -1}]}, { - RGBColor[0., 1., 0.], - RectangleBox[{0, -1}, {2, 1}]}}, AspectRatio -> 1, Frame -> - True, FrameStyle -> RGBColor[0., 0.6666666666666667, 0.], - FrameTicks -> None, PlotRangePadding -> None, ImageSize -> - Dynamic[{ - Automatic, 1.35 CurrentValue["FontCapHeight"]/ - AbsoluteCurrentValue[Magnification]}]], - "RGBColor[0., 1., 0.]"], Appearance -> None, - BaseStyle -> {}, BaselinePosition -> Baseline, - DefaultBaseStyle -> {}, ButtonFunction :> - With[{Typeset`box$ = EvaluationBox[]}, - If[ - Not[ - AbsoluteCurrentValue["Deployed"]], - SelectionMove[Typeset`box$, All, Expression]; - FrontEnd`Private`$ColorSelectorInitialAlpha = 1; - FrontEnd`Private`$ColorSelectorInitialColor = - RGBColor[0., 1., 0.]; - FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; - MathLink`CallFrontEnd[ - FrontEnd`AttachCell[Typeset`box$, - FrontEndResource["RGBColorValueSelector"], { - 0, {Left, Bottom}}, {Left, Top}, - "ClosingActions" -> { - "SelectionDeparture", "ParentChanged", - "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> - Automatic, Method -> "Preemptive"], - RGBColor[0., 1., 0.], Editable -> False, Selectable -> - False], "]"}], ",", - RowBox[{"Directive", "[", - InterpretationBox[ - ButtonBox[ - TooltipBox[ - GraphicsBox[{{ - GrayLevel[0], - RectangleBox[{0, 0}]}, { - GrayLevel[0], - RectangleBox[{1, -1}]}, { - RGBColor[0., 0., 1.], - RectangleBox[{0, -1}, {2, 1}]}}, AspectRatio -> 1, Frame -> - True, FrameStyle -> RGBColor[0., 0., 0.6666666666666667], - FrameTicks -> None, PlotRangePadding -> None, ImageSize -> - Dynamic[{ - Automatic, 1.35 CurrentValue["FontCapHeight"]/ - AbsoluteCurrentValue[Magnification]}]], - "RGBColor[0., 0., 1.]"], Appearance -> None, - BaseStyle -> {}, BaselinePosition -> Baseline, - DefaultBaseStyle -> {}, ButtonFunction :> - With[{Typeset`box$ = EvaluationBox[]}, - If[ - Not[ - AbsoluteCurrentValue["Deployed"]], - SelectionMove[Typeset`box$, All, Expression]; - FrontEnd`Private`$ColorSelectorInitialAlpha = 1; - FrontEnd`Private`$ColorSelectorInitialColor = - RGBColor[0., 0., 1.]; - FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; - MathLink`CallFrontEnd[ - FrontEnd`AttachCell[Typeset`box$, - FrontEndResource["RGBColorValueSelector"], { - 0, {Left, Bottom}}, {Left, Top}, - "ClosingActions" -> { - "SelectionDeparture", "ParentChanged", - "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> - Automatic, Method -> "Preemptive"], - RGBColor[0., 0., 1.], Editable -> False, Selectable -> - False], "]"}]}], "}"}], ",", - RowBox[{"{", - RowBox[{#, ",", #2, ",", #3, ",", #4}], "}"}], ",", - RowBox[{"LegendMarkers", "\[Rule]", "Automatic"}], ",", - RowBox[{"LabelStyle", "\[Rule]", - RowBox[{"{", "}"}]}], ",", - RowBox[{"LegendLayout", "\[Rule]", "\"Column\""}]}], "]"}]& ), - Editable -> True], TraditionalForm], TraditionalForm]}, - "Legended", - DisplayFunction->(GridBox[{{ - TagBox[ - ItemBox[ - PaneBox[ - TagBox[#, "SkipImageSizeLevel"], Alignment -> {Center, Baseline}, - BaselinePosition -> Baseline], DefaultBaseStyle -> "Labeled"], - "SkipImageSizeLevel"], - ItemBox[#2, DefaultBaseStyle -> "LabeledLabel"]}}, - GridBoxAlignment -> {"Columns" -> {{Center}}, "Rows" -> {{Center}}}, - AutoDelete -> False, GridBoxItemSize -> Automatic, - BaselinePosition -> {1, 1}]& ), - Editable->True, - InterpretationFunction->(RowBox[{"Legended", "[", - RowBox[{#, ",", - RowBox[{"Placed", "[", - RowBox[{#2, ",", "After"}], "]"}]}], "]"}]& )]], "Output", - CellChangeTimes->{3.6595585246496677`*^9}] -}, Open ]], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"newtonplot", "[", - RowBox[{ - RowBox[{"Function", "[", - RowBox[{"x", ",", - RowBox[{ - SuperscriptBox["x", "4"], "-", "1"}]}], "]"}], ",", "2", ",", "401", - ",", "40", ",", "0.1"}], "]"}]], "Input", - CellChangeTimes->{ - 3.6641612785202837`*^9, {3.6641613500474806`*^9, 3.6641613529304647`*^9}}], - -Cell[BoxData[ - TemplateBox[{GraphicsBox[ - RasterBox[CompressedData[" -1:eJzs+e2N9LiyMFqei7FkLGkfxoQB7u+x5XpYJqQJgxcbAnrHqagglaRISSuA -RjUXKYpJ8Ut6/t//3//f/+f//n/9z//8z//zf/3nv//z/3/Hzz//+fv551o/ -4hPyf/75Pb+3POcjvHecx3qycb9q3nHOOeecc84555xzzjnnnHPOOX+WH/FJ -yp2tP6uH82885lfjNiu/at5V7WuN2e3s7c/Ms3WG8xVerTej90HOOeecc845 -55xzzjnnnHPOOefv8CNi/idcl9UT05yv8JjfOp5j/ux5l0XWnrP90Fp/1c7Y -jqv6n/MrPKYrH7Uurd73Oeecc84555xzzjnnnHPOOeec9/kRn5D/88/v+Zln -9WRetYPzKzzmV+O2d/xn865qT4ze+Ti6H3rb07rOZN77ezmf6d+O5975uNs5 -gXPOOeecc84555xzzjnnnHPO+Rw/4sjPPKYrz+4b05yv8Jg/ejxXkdUf8zO/ -qh++raf3d3G+wqt5c3Z96F03Vp8HOOecc84555xzzjnnnHPOOeecn/Mjjvze -euL1MT96Vk9VL+crPebH8dx6fW89vd77u3rrqdaBb+/L+U7euk/F/GoeZeVH -7cucc84555xzzjnnnHPOOeecc87XekzH+ITrforrW8v3tofzHbwa/1n5bD7G -enrve9Z7141v689i9PrW207Oz3jvPK3K73Ie4JxzzjnnnHPOOeecc84555xz -vocf8UnKnS3P+QwfNf6zyMrPbmfVvjjfsvnY61n9mbf24xGr1jHOv/GYbt0f -d9vfOeecc84555xzzjnnnHPOOeecr/UjYv7nn9//xuD8G589zrPoHf+Zj+qH -rP6snb2e1d/rZ39XjOx5reof/k6P6dHjf/X+zjnnnHPOOeecc84555xzzjnn -/Bo/4sjPPKYrj/lZfZz/FXE8VeO2qu+I2eM/89n9s8pH/67e8r3jhPMWr8bv -2XnRe1/OOeecc84555xzzjnnnHPOOed7ekzH8lm5T1Hf8bf3vpy3eMyP4631 -+qx8r2ft4X97tf60rmNVtI4Tznu8dz+t1rmz9+Wcc84555xzzjnnnHPOOeec -c76nx3SMT7iuqj9e13tfzls85lflzs6XrB3ZfXmfZ8+tWk9aPYtR44HzFq/G -+S7nAc4555xzzjnnnHPOOeecc84553v4EZ+kXMzn/C/vHYdZjG5PVi4b93wv -bx03R/SOw97xw5/tMV2Nw9X7OOecc84555xzzjnnnHPOOeec8z39iJj/+ef3 -vzH4sz0bJ73jLYveccjf6b3jtopYbzXO+bs8pqt1r1o/d9v3Oeecc84555xz -zjnnnHPOOeecj/UjjvysfCwX/2bl+Ls85lflqnGY3S+rn/Pf8o+oxlVWvnf9 -5M/0aly17pur933OOeecc84555xzzjnnnHPOOedz/YhPyK/qya7L6uXP9Gpc -9daTlcvGGed/ee+61zqOj+hdJ/mzvXed5JxzzjnnnHPOOeecc84555xz/m4/ -4pOUi/n8mZ6Nkyyy8RPTx9+q/mz8cX6Ft477GNk4j/n8Xh7TZ/fH1fs755xz -zjnnnHPOOeecc84555zza/yIIz/zmI5/Y/B7ecyvyvWOE86f5NX4j5Gtw9l1 -veszv8ar51Wtu7H+3c4DnHPOOeecc84555xzzjnnnHPOx/gRn5Bf1ZNdl9XL -13j2vKrx0Fp/zI/lOH+jt86rI86uzzGfr/VqHd5l3+ecc84555xzzjnnnHPO -Oeecc76HH/FJysV8vsZj/vE3e75ZZM89q59z3j7vWufhEdl85Ht677q9en/n -Y3zU8431VesJ55xzzjnnnHPOOeecc845X+tHfEL+2fpjfbv9Xv6dHxGfb/Rq -nPG9PIveeR3LxXzOee3ZvKvqiTFqPeffees+G68/Ww8f61lk5bPrR42fWO6q -8XlV/ZxzzjnnnHPOOeecc8455996TFc+u/6Yf/wd3f5YLqs/i92e49v8iNZx -Mmr88HPeO79iffFva3nO+fXeO8+rfZnP9d51m1/jR8TnNPr5xvLV9a3zffb4 -HH3fXZ4755xzzjnnnHPOOeecc87v6zFd+U9yfea99ffet7pf9N76e9uZXb/b -c3+rHzF6fPJznsWo+c45v7/HGLX+8789pmP53fb33T0b11c9r6yeat+uyvf+ -rqz+UT7qPWW38cM555xzzjnnnHPOOeec8/v7EZ+kXMzPIrv+W8/um7U/+71Z -/Vn53t/b22+jfhf/24+Y9bze5mf7P4tZ6wbn/L5+dh2JUe2n/Hcftf4/3Y84 -288xfXZePNVHnefPPq/dxhvnnHPOOeecc84555xzzu/nMV15Vk+87vhbtSde -91SP6cp7n0vv83qrHzG6n9/m1TjvLd86Lzjn7/HefS0L55C/PabP9j//27PY -bX/fzXvnb0zH8d+7DuwyfjjnnHPOOeecc84555xzfl+P6ap8vC7+ba3nJ2kH -/58/Y7fxczc/IpsH1Xh+m1frQGv53v7nnPNeb12nYsTrdzsPrPLefeHpfkTr -+Iyxah9/qsf8s+tGNS+y61vbeXY+7jb+Oeecc84555xzzjnnnPMneExX/pNc -X3nrfWN+dl3lZ9vJf/cqYv9X42eX8X+VH1H1z9s85lflqvH57brBOeejvHc/ -7d1Hnu6j9t/d/IiqH2bvv/xeHvOr9Ser563zjnPOOeecc84555xzzjlf6TEd -y2flPkV9x9+sHv5Oz8ZbNQ53mS+z591TPeuHLKpyresP55zv5q3r4BG77eOr -zgm77eNn/YjYD9m4icHv5aPGQ+972dn3vt3mC+ecc84555xzzjnnnHP+JD/i -yM/Kx3Lxb4ysnt7yVTv5vXzUeLiLH1HNl6d6Fln/xDTnnL/dY6zex1d57Jdd -vbX92XPm9/Le8RDT1bx3Duecc84555xzzjnnnHPO7+NHHPlZ+Zg+69l9Yzr+ -zerp/V38Xt46DlfPo1YfNY/u4lVk85xzzvk5j7F6H//WYzqWj+V29SOq58af -7TH/23Eer3vr/OKcc84555xzzjnnnHPO7+RHfP75/W9WrtV775v5T5LPn+29 -42o3P2LW/FrlVbTOa84553M8xm77e+YxHcvHcrt59hz4Oz3mn53XV83HXeYR -55xzzjnnnHPOOeecc/4kj+nRHvOz+1f+k+Tzd/su8yjz2O5svMdyu3gV385r -zjnn13qM1ft49JiO5WM5+zi/o8f81vEf8992ruacc84555xzzjnnnHPO7+gx -Pdpjfnb/4+9Pks95i8d0LH/1/MraM3venZ2nWbTOX8455/f0GKv399i+qzy2 -J+sn/rf39mfvuW6339vrMb/6vXc/D3POOeecc84555xzzjnn/H/7EZ9/fv+b -lcsiuz76T5J/F4/pqt+yenrL87+96s+r51fvPBrlVbTOU8455+/wGKv399i+ -p+7Xo7z6vfH63veCVfVUv7e1nlXjJOa3tjNet9t84ZxzzjnnnHPOOeecc875 -9x7TlWf1xOuOvz/J/Sq/+vf2tierJ+avrqfqn3j93Xz3+TLKq4jjhPM3e++6 -yjn/33G3fTzWn/2+Vd57fuZ/++jzbet4691fdjvHcs4555xzzjnnnHPOOed8 -f4/pGJ9w3U9y/aj7Zp7Vk7WT/+3V84rXrfLe8TB7HPZ6FbuMB8538N51oLf+ -0fN6l37jvMdjjN7H4/1225czz35XTPNrvfd5jRq3WXt2e4/jnHPOOeecc845 -55xzzvl9/YhPyM/KV9e3+k9Rb2wPv8Z7n9dV/u04HzVuq9jlOXLe4qPm6aj7 -ZuWvWpdG7ZtZfnZ9FruME/4sjzFqvq/el3frZ76X947zUeOzd9zOPg9zzjnn -nHPOOeecc84552/wmI7xCdf9JNeP8qw9ve3k/N9/R4/b1vmVtefsOM9il37m -z/BR63ZV/7f7VK9n7T/bznjdbK/aOeq+revY6vpb68m8d9z2eu9z5P/zZ4we -bzHO7su79Rtf42f3o9b9ZXZ7RnnWnt3efznnnHPOOeecc84555zzb/yIT8j/ -+ef3/NmetSfz7PdU/TCrPfzZfnb8xMjGZzU/e2OXftvNq/6cNU7O1tM6TkbV -s6r+3vuOqr/Xe3/vqP16dv29++ao9ozq/9n9draeeP2q8RCvO7uv9Y6Hqtxs -j9H7XEb1M3+2986LUfvs6PNGdV12n9F+dh2bvQ9yzjnnnHPOOeecc8455/+O -T8iv6onXzfas3VW56Fk9Z/sn5s9uP3+Gn51fWb29ser3VtfF/Fav7vttP/d6 -7zozuj2z65lV/9l+G+WxPbPr7x3no8fh1e256r6t9e9WDx/rWf/HdKuPiln7 -5uj3gixiO3r35d72Z/Xc3UefH2bt47Hc6vPe2XNgzN/tfZxzzjnnnHPOOeec -c875sz2mY3zCdT/J9aO8tz1VO1t/b+Zn+znWm5WP5arfdRfv7Z+qntbyWYye -R7337+3PUdF632r8x+v4WD+7/uxez+j6Z983q+fq9vS2s7c/s+t72zNq3Rt1 -X85neG/str/cxWP67Dlz9rrUW370fjdrPxr1XDKfPU+vOudwzjnnnHPOOeec -c8455y1+xCcpd7aeUV61r9Wz39Xrq55Lb/+M6s+qPVX/XfVc3ua9MXuecv6N -x/S369K39x29b7a2Z7d1hvM3eBbVOSeLaj5X9a86b7/Ve/t5VvmYHr2/7PZe -lvnoeT3q/NA7TznnnHPOOeecc84555zz39KVx/zj709Sb69n9Y/y3t87ynt/ -b1VP63OcXZ6f8955WkU1bs7WP2pec87bfbf1ivOdPebH+TXrnDzqXJfFVe8F -sb2c93g1X6t5kXnvfc+uD9n1s9YTzjnnnHPOOeecc8455+/0Iz7//P43i1ju -55/f87P79tbf67335bzFr5qP2X2z9rXO3955Omo9qe7LOa/nL+dv8Jjfuq/N -Pj/Hdo3al1vPAa3tnPV7z54r+Lu8d173eu+8O/u7Zs8vzjnnnHPOOeecc845 -5/y3dOUxP/5tLd/rP43XxXz+Lu8dJ7PnVxZZOzOP6bPj/6p1JmtH67zm/A2+ -2/rJ+Qyv5sWq83DWnugxfdZ7+y2LVf12hH2cn/FR59Ws3tXrCeecc84555xz -zjnnnHM+0o/4hPyqnnhd5tX9OP8tv3Uczp4XMXrHf0yf9d7+XNVvVXtiOc6f -5Lutq5zP8NXn2Ni+s956Hs589Pknxup+bu2f3dZhPsdnzd+YrubXVe3knHPO -Oeecc84555xzzv/ymI7ls3Kff37/m9Uzq538GR7zj7+7zZcssvnS6zFd+ez5 -srr/Y/s4f5Lvtg5z/lf+2f1otcf2jpqnVbnWc/Lo5xVjdf+3nk92W5/5Wu+d -d6PWt93mC+ecc84555xzzjnnnPN7+RGfkP/zz+/5mffWU7WDv8ur8bbbfInR -O19Gza/MZ8+7XZ/Lt/3D+Q6+2/rMn+0xv1o/774vzJ6nVblv+3n0c4+x23Os -/IjV6za/1nvnezbfsutj3OU9hXPOOeecc84555xzzvlaj+lYPparPKvv809b -+ep6/kzfbV5U4znG2fnS6jF91rP6Rz3H6r67PMdR/Tz7uXP+b99t3ebP9phf -jcPV6/m36//seVqV+9avGg8xVj/H6nesXrf5NT5q3vXOi93GP+ecc84555xz -zjnnnPN7+hFHfuYxXXlWT7wuuw+/p8f8OB52Gf9Z9M6L2fOo11fNu92eb++6 -F9OjnzvnLb7bes6f4TF/132516v9KJYbvY9nMWofb/29V42fGLuNh1HvO3xv -r8bv2XNdb/nV45lzzjnnnHPOOeecc875Xh7TMT7//P63tXzmve3h9/Ldxnnm -WfyEcnHczvaqv6v5VXlW7yzv/b138SOy9S3mc/6N77bO8z095lfj56nr827z -N6ZH+27rRhb2az7DY7pax3rXz975tXrd45xzzjnnnHPOOeecc76nH/FJysWI -5bJ6svtm9VTl+D085lfjYbZnUY3bWd7bb6N8t3Gyet371qvflZXrXT85//ff -GJz/ld+678TYbb0ddb69ylvPvbN91/EZY9V7zepxwvf03dYxzjnnnHPOOeec -c8455/y3NH+3/yTjoyr/7TjMImvPKo/pq3y3+bvbOjZ7vMX06nHI7+W7rfN8 -rVfrUjVuqnru4r3nkLfu+9V1WXuv8ixGjYeY33oujdfxZ/hV42SXdZJzzjnn -nHPOOeecc875Wo/pWD4r9wn1ZeWz+vkzfNQ46R23WVT1X+1Vu7Nys/wu42e3 -dXLU+DwimxdZ/fE6/k7fbf7ytR7zR++zd/Ejevthtre2c5X3vhesHucxetsf -83cZJ3yNx3TlZ8+3u6yTnHPOOeecc84555xzzvfwI478zGO68pif1cef5TG/ -GlfZ+Myid9xe5VU/nZ1Hozxr567jZLd18lsfPV/4u3y3dZ6v9Zh/dp+6u2f9 -s9s8HXWunu27jfPWc2F23ep1m9/LY/rsvNhtneScc84555xzzjnnnHO+hx9x -5Gce0/FvDM7/yq/K9Y7PVR7Tqz3r16z9q8ZD1c+7rZPfeu+82G2c87W+23rO -r/HefWe3dW+3c+xuHtO7+qh1qar/2+eehfHGf/PZz323dZJzzjnnnHPOOeec -c875Go/pymfXz/f0UeMti1H3jfUdf3/++T0/86rdWbldfLfxs2q83cWPaH2O -veOZP8N3m6d8rFfRu6/tsr6tWj/vMn+rcrv72X0qe75Z+ei97cni7DhsbSe/ -l8d06zjfZT3knHPOOeecc84555xzfk8/IuZ//vn9bwz+DO8dP1nMHldZe6ry -re25i2e/a7dxFfNj+3dbD2d5b/9kkT13/gzfbf7yazzmt67/u6xvo/yI1nPC -bvO393e9zUf1z9n5FaO3PavHFR/jMX12XO22fnLOOeecc84555xzzjnfw484 -8jOP6fg3Br+Xx/w4Hqrrjhg1rs62p7Wep3rWP7uNt97xsHqdnOVH9D7fmM+f -7bvNXz7We9eNUfU8xY9YPU9HzeuqHP/dR83HLHYbP3yOW4c555xzzjnnnHPO -Oeecz/AjjvzeemKaP8uzqMZPq8c0b/OsP3cbP72+ej286zo8aj7yPX23ecrP -eTZ/43Vn1//V69gsP2JU/+ziWfv5NX72ucTofT/abRzyv713Peecc84555xz -zjnnnHPOe/yIT1Iu5vO9PHuO2XOvIo6D6vqsHJ/ru43DUeNk9Xo4y6/qn3gd -v5fvNn/5WI/5Z8fDbuvbqnPpbvN39vrPr/HqecWoztut851f4zH99vWWc845 -55xzzjnnnHPO+TV+RMz//PP73xj8Go/5x9/s+WbR+9z5Ws+eV/bcdxu3Wfur -8rutk7PW27PzPebzZ/hu85df473rPP9vP2L1/HW+eob3nq+y2G0c8jbvXWd2 -Ww8555xzzjnnnHPOOeecr/GYPlue7+lZ/CTPNXvusVw2Lvgevts47F1n+O/p -WD6W48/23eYvP+dnx0PrvrzbOjbbj8j6Ieav9tZ1PuavPlfwvz177lU9MZwH -9vSq/3dZDznnnHPOOeecc84555zf04/4JOViPh/jWf9nz6uK+Pyq67NyfC/v -HSe7jfOYX7X/qX5Eaz+MXk/4PXy3+cvHeswfvf4/1e+2Hrau//zZXq0DWfSu -A/yct64zu62HnHPOOeecc84555xzzu/pRxz5WfmY5t95zK/KZc+rqoc/03eb -p9V6kvlu6+EsP7sOZM895vNn+G77FB/rMf/b+b7L+rbb+nn23JvdL9Y/an/M -6ufP8N5xmEVWT3XfmM//21vXmWpe77JOcs4555xzzjnnnHPOOd/DjzjyK4/1 -xDT/O7/qz+r6GFU98b78GV6Nh3hd5r31jxqHvevMU7133cj87HrO7+G77Wv8 -Go/5o8fJbuvh3dbPb9vp/MZbvBrnWTgnjPGnrp9v9SPOruecc84555xzzjnn -nO/gMb26Pfw7P+KTlIv5/HeP+VW5rP+revi7vHf+jlrPz47zrP3ftnNXP6L6 -vb392Vs/f4bvtq/xa3zUOhPTT1mHR+1Td9k3+Tv97HyPMWo9eaqfXTd2WQ93 -9SOqcV7tg/G6s+O/tZ7e3xuvN04455xzzjnnnHPO3+1HfEJ+bz1Vva3RW89P -0Y74u6p6dnkuu/kR2TjJ8rPr3+JVf35bf8yvxj9/p2fztPJv1/9V7Vnlvf0w -aj0525/83r7bfsfHesyv1sOsfLWexOtm7wt3WZ/P9kNWX3a/1vZw/o1X4y3G -bvvdbr7b+rab965vs9fJ3n2zqidrX+t9Oeecc84555xzzjn/LT7//P43i6xc -9N77VvXE/MzP1rPLc1ntR1Tjgf8dveOT82+8d53MxnO2PvTuC7uut9+2p3d9 -OLtPte6bvc+d38t32+/4WI/5o/eF3nXpqvW/9b6jvLf9uz1Hzmd6jLPnqLt6 -73xffY6d5Ue0roe95Uedq0c9r9HlY7ld34M455xzzjnnnHPO+RiP6cp/kuur -+44qP8pb7xvTVf1V+V2e+2g/ouqf3vF2F8/6p4qsXzjf0Xvn+9l6dtnvYv7Z -9vfup9l9R/lV+yxf47vtj/waj/nVupSV7/Xe+nebL6P2Nc7f4NX6E2O3+btq -/139nj7Ld9sHd9t/e33V+xHnnHPOOeecc845v8ZjOsanuK7ynyT/rb7Lcx/t -R2TjIuY/zbPI+iemOX+T7zZ/z873bL+r6vt2P22tf/V+x9f4bvOFP9t73y/O -lo/lRs2LrFxv+2e3h/M7e4xR82g3P7tu7O5HtK6T/G/v/T4w6r5Z/buNN845 -55xzzjnnnPNVfsQn5P/883t+r2f1Z+0Ydd+3eUzH8ruMt7N+RDV+7uLVfMwi -+/2c38lHzevedWN2e87ua63tP1ue85G+237Kn+Gj1vPdfHY/rJrvVTnOr/Bq -fGYRr99tnz3r2bqxi8d2O1fM8VH7SExXz+vu45NzzjnnnHPOOed8tsd0LJ+V -+/zz+98YVf1ZO+P1/JzHdCy/yzjsHZ938Zhflet9jpxf6dn4XDW/Ru0jMb2r -20/5Dr7bPsuf4U9dz0f3Q1Xf1etDa3s4v9Kr9SHGbvts7/672/t71u7d9p23 -ecyv1vPZ+wXnnHPOOeecc8752zymz3pWf7zu+PuTtINf4zEdy+8yPrP2jxq3 -sz2Lqnz2Ozm/wmfvF73jf9S60bservJR++9u+w5/hu+2z/JneMw/ux9l9Yzy -2fNi1Pk5a9+q94tVz4vzHo+x2/4b09U6effvS/ycnx0/Mf+p45NzzjnnnHPO -Oed8lR/x+ef3v1m5Vu+t/yf4UY5f628Zn6PHeRZZuzm/wrP5npW/ar5k7Ry1 -nsT79Hpv+0d57/p8th7Oz/hu+y9/hsf81nUyKxejdx/MfHY/rD6fZ/ft9dbn -EvNXn5c4/81j7Lb/eh/nf+WfHf93GZ+cc84555xzzjnnd/MjPkm5mJ9Fdn2r -Z+3haz2mY/ndx+cor+Lb8c/5DK/me3Z9jF6fvT5U943lZq+HmZ9tZ9Xf9lO+ -wlftv5y3+Ox9bbbH/GpfmO1Ve2J+b/9n9XN+B4+xer+etQ7stk7u5jG/Gi93 -aedu45BzzjnnnHPOOef8qR7Tlf8U13/CfbLyq/wu7dzVdxmHo7yKOE4439l7 -5281L7L6r96nqvbE/F09+727tZPzf/+NwTmf57u9D8b8an3Iyvfe92z5rNwu -5zT+LI+x+jz57XzfzWefn2P6bP+Pqmf2ur3b9x/OOeecc84555xz/nu68ph/ -/P1J6p3dzqo939bT2z+ZV783Xr+rXz3ezo7PLLLnyvkZr+Z7vO7sOlDNg2r+ -9pZfvU9l7eGcj/fZ+zLn/H+H/fecZ/1ZleN8hsdY9d69eh2rrtvleV3tZ9f/ -zFv7edf9hXPOOeecc84555z/7jEd4xOu660n85/i+njft3n1HON1V/m346rX -q9jlefFnezYvRo3z2b7b/rJ6HeP8jb7busQ5/9/RO39714Gs3lHnh9H7ftV/ -VflR/ZCV5+/2GHd5v+6dX3wPjzFqPGT3HbUvcM4555xzzjnnnN/Nj4j5n3Bd -Vr7Xq4j35Wu9d/yc9dZxm42j1vGVXbe6n/la710Ps/GWjdvqvt+O81Hza1Q/ -9Lbz7O/inK/33nWAcz7Pe/fx2Z61Mys/6j23qj/LjzF7nRxVT1Zu1HjoHYdV -e3qfV2v5p3uMs99zsnIxep8vX+uz94vd9rXV31E555xzzjnnnHP+Xo/pWD6W -m+0xHf9+286sfr7Wz46fbFy0jp8qdumf2d7bn2fLx/xR87R6vq3tqX5PjFH1 -jKo/Kzdqv6jqj/lVu2f5bvsa5/x/+6h1knN+vY86J8w+L509/2T36z1vzD53 -tdYzqp2zf2/vc5l933i/1vu2tjOr/yqPcfa9I4tVv+vtPnudH/V+mvmq9u/2 -nZZzzjnnnHPOOef39ZhurSde3+sxXXlWz13az+d4jN5xUsXVv2vUPO2tf/V6 -MspjO1bVE6+f1f/xPtl9Rz2Xqp5Yrteredrbn9+2h3N+vVfrKeecf+sxf/Q5 -ZPR5pvWcOfu8N6o/e9u52/i5u5/9vtEbveM8XrfaZ82L2d7bz6PWjau+B85a -H3b9vsE555xzzjnnnPP7+hFH/tnyvR7rj+VifvTq+hij+qe3/ur6WT7qufT2 -82w/28+90TreRs8L/t/pI3rrielZ7WltZ9We1vqrelrb31vP2ftyzvm3vts5 -hHPOOX+DV+8RrXHV96WnetZvvf3ZWr53PIz6vVU7Wr13nGf1zH6v55xzzjnn -nHPO+Xv8iM8/v//NIpb7+ef3/Myzenq9+j2tXvVb1a6qnrP3ba2H/yeqcd4a -veOBc8455/N8t/MG55xzvrOP/l6U1R/b0Xr92fZUvzeW4/fymD7r1X2r+XT2 -XLrb917OOeecc84555zv50d8knIxYrms/t56ej2rn9/Ls3HYO56zODvOs3pm -zTvOOeec/2/f7dzCOeec7+B3+V5UlY8xqv1Vv8VyfE8fNV+yekd9j+Kcc845 -55xzzjkf5TEd4xOu+0mu7/XsvnxPr57vt+Mwi+y+MX12vF0172J7OOec8zf7 -bucczjnnfIbPfo8e9R4a05X39kMWq7+PHbH6XPQ2j+lv50VWX4zV85Fzzjnn -nHPOOefP95iO5WO5qnzrfbN6q3J8rq8ah1lk4zDzmK58t/7pnY+cc875k3y3 -cxHnnHM+w+/yXhnTlfe2J/MsVn9PO2L1eYn/7TFd+W7zl3POOeecc8455/f3 -I478zGO68pif1cf38FXjMIve8VnVP2vc9rZn1fzlnHPO7+i7nZc455zzFl/9 -nph51p5Wj+mzPqqfs7h7P/OxHtOjx+eu851zzjnnnHPOOefXeUzH8rFc5jFd -eXZfvtZXjcMsesfhqPGZ+d37edR855xzznfw3c5RnHPO+b+j2tfidXd/H4zp -s97b/l7P4qrnEtvH13o1TlrH59n2XL0OcM4555xzzjnn/HqP6cqzeuJ1x9+f -5H699+XX+OzxlkU2Ts566/js9dH9HMvttg6Mfi6cc875SN/tHMU55/ydvtv7 -XeVZO7/1mB7ts59jFld9J4m/c7dz11M9pqvxlpXvPa+uXgc455xzzjnnnHN+ -vR/xScrFiOWyerLyWf18rMf8+LxmjasssnEyymN6tM9+XqvXgez3Z+2M5Tjn -nPMrfbdzF+ec82d4tR/F6+7mR4zel2N6tK8aD1mM/n4Sf+du5y7+e7oan6vn -O+ecc84555xzzvf3I2L+55/f/8bgaz3mH39HjZMssvEz22N6tM9+Xqvn+7de -/a5YjnPOOf/Gdzt3cc45f4bv9p51l/ey7L5VuW991TjJYvZ3tt3OY2/zmG59 -XrusD5xzzjnnnHPOOd/Pj4j5n39+/xuDX+Ojnlc2HrLI7jvbY3q0Z/dd9RxX -rwOz1hPOOef8G9/tPMY55/xefvb9JSu/i8d2X71ft7Zntq8aV1lU5Vc9L97n -Md26PmT177JucM4555xzzjnnfJ7HdFU+Xhf/ZuX4Go/5x9+fxnFwRFZ+tsf0 -Vd47X656XrusG6PWk1XjinPO+TN8t3MX55zzPT3mt+47sb67+BG9v3eUt7Zn -Nx89rqrrjtjtfMXbfNTz3WXd4JxzzjnnnHPO+TyP6Sp66+F7ehbZ8431HX9/ -knGQeVbPbr5qnPe25y5+9vfGfM455/zfvtv5inPO+Z5e7S/xuqqemL+bHxH3 -y1X7ddae3Xx1P8Q4Oz6/bSc/5zFdPefd1g3OOeecc84555zP9yNi/uef3//G -4Nd49ryy51vF1c83u+9uvur5Zu1ZvT58u55k5c+Oc8455/zff2Nwzjnn/47V -70er/IjV+3VMP8Wr7zCt9WTXZ3F2nMfr+TmP6bPPd/X6wDnnnHPOOeec8+v9 -iJj/Sa6LHvOz+nibn31eWT1Z+dbnm7Wnt567+N3Gw1P9iDgOOeec83//jcE5 -55z/ld+678T67uJH9P7eWd77XN7mZ59vDO/X13r2XGM8dZ3hnHPOOeecc855 -u8d0LB/L9dbDz3nWz1n0Pvd4/+x5Pt2zcb7quWft2G3dGLXOxPzquXDOOef/ -9t3Ob5xzzvf0mN+678T6dvXY/qwfdtuvq3Jv97PjPMbo74H8d4/pylevG5xz -zjnnnHPOOb/Oj/gk+dGr6/nv/pP0a/VceuvJ2tH6fN/mWb/tNk6q8rusJ5lX -47v1uXDOOef/9t3Oe5xzzvf0LLLyu71PnfUjVu/XMc3neO/4322c3N1juvLV -6wPnnHPOOeecc86v8yM+SX706nre51n8JM8hpvkc322c7LZunPUjqvmQleec -c87/7bvt15xzztd6zI/lovfuL6vfp1r9iNbfu2pfrq7nfX72u18WV4+fp/su -6wPnnHPOOeecc8738ZjmbR7zq3JZ+ey5VPXzPv9J8jNfNX52Wx8qP6J1Hsx6 -Xpxzzp/tu50DOeec7+kxv3XfifXdxbN+6H2P6+2fWC5rF9/Ds+ebxW7nwN08 -prPncMRu6wbnnHPOOeecc87n+xEx//PP739j8L+jKp/1L9/Ls3nUO0565+Pq -9eFb7x3/VT9wzjnn//4bg3POOW/xmF/tL3d5X+v9vWf35W/bmbWH7+1ZjBpX -d/dd1oG7+RFn+zmWq8bz277Lcc4555xzzp/nMV2Vj9dl9R1/e+/b2x7+t/f2 -89095lflqvJ8L181L6r2xPy7rANZ+2O69fdyzjnnf/mq8yHnnPNn+Nn3r97y -V3v2e2N+6/777X1728P39Op9P8bZeXRXH73O3NVH9UPvujHqvln9me/W/5xz -zjnnnPPn+RGfJD96Vk9W709RLqs/5o+67279P8p7+6EaB3f1apy31hPzq3HL -13o13zP/dn6dbc9d1o1R6y3nnHP+l+92nuScc76n9+4jWbne71RVe6rf0bo/ -xnpmfwfr7f+YX/Ubv5dXzz3GbufJUR7TZ9eBu/kRo8fPVfvCt+vk058v55xz -zjnn/Ho/4pOUq8r31j/bY7ry6vfu9ry+fb4xXfXD3T2LUeOH38vPrjNZvTHO -rpOt9cf8s+twVs/Z+2b5MVbtC5xzzu/lvec9zjnnvMVjfiwXvfd9arf9tIrW -fuC8x7PYfb6M+l70VN9tPR+1zmc+6j1lt+fIOeecc845H+dHHPmZx+tjZOVa -vbc9q3235zjLs+d+F4/5VbmqPOffeIy7zJdR6//qdZtzzvkzfbf9lHPO+Ts9 -+64Sr6v2r6x873eqrJ6q/lhu9n35Oz0bV1lU8y6WW+3Z74+x23fg2N5qveJ/ -e8z/dh3mnHPOOeec38+P+CT50X+SfP63x3Qsv8t4qH5X9ntirPKq/1vrifnV -c+Tv9N55MXodbr1vVU92fe96Fa/jnHPOr/Rqf+Wcc86v8N73ppi+ys+2v/V3 -zf6exp/t1feTLLJ6Yv6qc2nVzt55961n7dltXd3Ne/tz1PhZ/e8FnHPOOeec -83Y/ojrnZ55d33tf/nu6tT9nedWeLD+7fpa3tuOI3t/Ln+2zx+eo9TmmV/eP -dZ5zzvnOPnt/55xzzlt81HeYUT67/Vft+633jWn+LK+ee4y7nFdnf+/dbZ18 -qsf8q9dDzjnnnHPO+XqP6bMe84+/o98v+N8+e/zE+44aP6PHYW/57Pfwe3v2 -3Gevh7337Z13mcf0aJ/dfs4553yGz97fOeec8xYf9R7X+11odvtHfYcc9R0s -qz/mn+1//iyPsfoc2zqPnvpd96ke88+Ok6qe2eOHc84555xzft6PiOf5qlwW -8fre9wt+zrPnMnv89I6TUV5F1i/8XV7No2/Hc2/9vfcdvW603jfmV/18Vfs5 -55zzM967v3POOef8f8du3y1nv+fyd3uM1efbb+fRbuvJXTzmV+Olt55V44Fz -zjnnnHO+j8d05TH/+Fu9R2T1flsP/2+/ejyM8iriOOH8339750VVz6r1OWs/ -55xzzmuv9nvOOeecn/dV3yev+q6YtbP1vvxZHmP2eXXUd6RV60PWjt55N3q9 -yu7b663PJV4/un7OOeecc8758zymY3zCdaPq7/WfpN6zPqofRrWn1av+6R0P -rfX3ehXZ/fi9vXd8nh1XvfeN11213mb35Zxzzvl57z0/cM4557zdY361/456 -L87ue9V7d9VPVTv5szzGVeM5uz7G7Pn+VB+9XsXorf9sOznnnHPOOefr/Yh4 -ns/KVfVk9bZ6bzuf6tn712ifNU5ax0dVP3+2Z+Otd1yNWk9G1Z/Nu+y+V813 -zjnn/I0+6lzBOeec83aP+dW+nJUfVU/vd7Cs/lXnlqzcqHr4HI8x6vvtqHnq -O/xYH9XPq9bnzHf79yzOOeecc85n+BG95+SYP8qr+2a/q7Ue/rf39vNZz9oR -I/MqdunPp3r2fKvn9W09o7x3fPaun6PWpbPrZMznnHPO+TyffW7hnHPOebuf -/a4Vy4++b1Vfdv+qnb3tz2LU973R34Gz/Bijvhv31l+1b5XHGDX+q9itH+7q -s9e33vuO8uy+u/17Geecc8455zP8iOw8HPNHeXXfrFyM3veR7L78O4/R+z5Y -1ZfFLv0wahyOGudVf7bet7c9vfVk0Tt+ete3zM+uq1k7W9s/6rlzzjnn/Hrv -Pf9wzjnn/D0e82O56KO/t3x739nfk7N6z34//LY/z36HmdXO0d+3Y4z6ntbr -vf3ZW8/s9o/ys+Owd3xG723nqPegs/ft7QfOOeecc85X+hHfnrd7z+G9963a -HWPUe0pvO1d5bz9n/TDqefV6NT6/bU/vOKnaGfN7+7N3HM5uZ+/8HTXeVq1L -q+/LOeec8+d77zmKc84555zzHTyL3c7bozymq/P8qH93OPu9d9R9Wz1rT69X -/dnbzt5+4JxzzjnnfKVn5+Hec3JMjz6fn21naz9k7entt1HvR1l7RvXPbp7F -qPdHzjnnnHPOr/Tdztucc8455/zZPvu7dBaj7sv39JhuHRet5UePZ84555xz -zu/oR5w9n486z/M9vXdcVdE6HmaPZ84555xzzr/x3c7tnHPOOef8Xh7z4/kz -Xtf7PXbUd/uq/tZ2Vu3P+iHm82v92+eYlRt1X84555xzznfw3nNvTJ89D1fn -cj7XY/7Z51i9Z8XoHVet9Vbt6X0frN77OOecc845/8tXnfM555xzzvmeHvPj -eTJeN9rj/Ud9p61+b4yrfu+3/cDHekxX5bNxtXr8cM4555xz/o0fUZ17s3JZ -eX6Nrxo/WYx6L9utH7J29v5ezjnnnHP+bB91zuecc8455/fyVd9pq/bEcr3f -aTPv7Z8sfNd9tsf02XF1dvxfPR8555xzzvk7/Ih4Hm4tH9Nnz8l8rMf81uf7 -rWex6v0r87Pjf9V85Jxzzjnnz/TecyznnHPOOb+X3/07ZEyf9VH9mcVV373j -79nt/eIp3tv/reV76+Gcc8455/wbP+Lbc2lv+ep63ucxv+r/0eMnxqj3r5g+ -6739uWo+Vu2J5TjnnHPO+TO897zKOeecc8739OocGK+7yrP2tHr2e6ty0Wef -h7O4e//z//befl713DnnnHPOOT/jMX22PD/nq557FqPep6r7ZeWi99Z/l/6v -2hPLcc4555zze/mo8yrnnHPOOV/ru33Pn32OjemzPvu5ZHGXfuZ/e0yfHVer -5ynnnHPOOX+2H3HV+ZaP9VHjIYtV7029fpd+XjV/Oeecc875nj77HMs555xz -zs95zK/Ob0/9ThjTo331842R9XPvONntveOpHtO7z1POOeecc87/7UecPd/y -sR7zj7/Ve0pV3xG7vTeN8tnP5S7zdNXz5Zxzzjnnf/vs8yrnnHPOOf/be7+/ -rf4eWP2+q86x2X1H+arzcxZnx1Usx+f4qHmxy7zmnHPOOefP8OycGvOrc2l1 -3uVjvPd9JIvZ70G942qUz+7/7L53mddVPfF6zjnnnHN+jc8+x3LOOeec8789 -5ree62J9u34PjOVme0yP9lHn6t5+zsJ31z09pqtxstu85pxzzjnnz/Ijzp5X -+TWePccsRo2HzKt2ZOW+9dX9H8utnr9Zf2UR+3H2+y/nnHPOOf/bV51vOeec -c87f5jG/Oo/t9t1v9vfes149h5g/y3ufe+/vquqPsevzeovH9FvmO+ecc845 -39OPOHte5ee893llUb2PZM81i/i8e8fJbO/9Xaue165+RGs/x3zOOeeccz7W -Z59jOeecc8757/nxnBave4ofcdU5tir3NK/6IYtsHMZ8/p33zovd5i/nnHPO -Ob+3x/TZ8vycx/yqXPa+UNXzNM/6Yfbz2m3+jvIjWvuZc84555yP9dnnWM45 -55xz/rdX57d43d38iKvOsVW5p3nvuMpi1XN8m1fPa7f5yznnnHPOn+FHVOdS -fs6z/s+iqicrlz2/p/mqcbt6nn7rveOKc84555xf47PPsZxzzjnn/D9RndPi -dXfxI+L5cvY5Nrsv/9uz51fF1c/37l6tA9n8yurfZb5zzjnnnPM9fdT5M6uH -/55flfM+O9ZXPd/d5vvo9SGW45xzzjnnY332OZZzzjnnnP8ner/H7vYdL/Oq -/TF/9jm2Ksd/92p8xuj99x3e5rvM66f6Eb3rVTZ/YnjunHPOd/ZqX4wxan+M -+fbBa733ufP/RHWebK0n5mfPh//3397vAKO8as8u87r3fefsOs8555xzzsf4 -7HMs55xzzjkf673/PjLas/bF8+XZ9mf+bXv4Oc+eYxa7ve/cxav5Mnte7+69 -60lMXzUvRq1vZ++7y/PinHM+x4+o9qne/fQp++xuz2uXcdL73Pnf4T30Gq/W -gavXt972rHoP4pxzzjnne3rveZVzzjnnnJ/zmN96fov17fbvEbN/76h+5td6 -jCx/t/ej2R7Tq+fvKj+itR965/uo8r3jNqs/81W/d7fxwDnnb/MjsvU55veW -771v5qPOb1n9q37vbuNh1XjrPf/c3avxlkXrfOFj/ez7V1ZvFt+uM6u+t1z1 -eznnnHPO+RjPzmmcc8455/wan/3vEdV9Y/6o74Qx/2w7ez27L7/Gq38PirHb -+9Fu71+rvv+P9iPOjp/d1u3R639rv40ab6vHA+ec8/9Onz0nrNpfdvWqn96y -Px4x+lx6d8+id/zwa3zV+tBbz+h5mvVLFr3rW3ZfzjnnnHM+16vzKOecc845 -X+Nnvx/G8qvOmVm05sdy/NkeY7f3ptHzIpu/WT3ZvN7NY/t3W1fvtp7H/FHv -+6vHCeec8/9Oj943s3p3e1/Yze++b/aOh93OS6PHfxbZ7+fP9FHfK2b73b// -cM4555zzv33VOZNzzjnnnJ/z3u9vMX2VV+2v6otxdfv5Hp5FLL/be9ZZz+b1 -bh7bv9s6eReP+dW8eOt445zzp/lT9pG3eNb/u42r2eNt1/NSb3n+TD87f2P5 -2e3M/Ow6E+vjnHPOOed7enbe45xzzjnne3rvd7mYHu1ZO7Pyo74r9raT38ur -5x5jt/ess57Ni1Ue27nbenh3j/ln58VTxhvnnL/Fn7KPvN2z5/LU8bb6vNRb -vnVe8Ht57/jJ5kVW/27fVUZ9P+Gcc84552u99xzLOeecc87v5aO+Q569byx3 -9t8XsnpaPab5Mz3Gbu9fo+fFt57FbuvY2zzmV+N/t3HFOef8nF+1L/C5nsVu -42o3r6J1/PN7+ajxM2pejPr3tazc7O8enHPOOed8Tx917uWcc84557zFe7+X -xvpaz72xnqzerH7+LI+x23vZqn+n85441ketS73r1apxdbY9V7eTc85Hr7dX -t7NqT8wftR+tPhfd1av+3H38z/Yqsn7k9/bZ7++j3oM455xzzjmf4dn5lnPO -Oeec8xk++t8d4v16z71VOf5sj7HqvSxr5+j5kt0vxlN9VP+MKt/r8T7VOMnK -r+r/rD1n59GsecE5399Xrz/fetWeb9f/0efqUeV763mqz5oX8X677PtZZO3j -z/RR/z616nsC55xzzjnn33jvuZdzzjnnnPNvfNW/U8w+P1fl+L08xur3uG/H -/27rQO88yvonK7/KRz33qv6qX6txvZuPWoev2kc459f7EWfXt9X7eKvH9Or1 -P6t/lY86P+zqdz3vVbHL+OHnfPa/K83eR+6+L3DOOeec82f4qPMz55xzzjnn -LT7qHBvTsXwsl3lVT2t7snqrcvxeHuOq97jW8XyX976Yv8vz3cWr9bP1uY+6 -76rxcNV84Zzv66vXk289a0/mq9b/t/ldvs/Pni9n51cWuzxffs5HvUdU9beO -56yeUeN5t3WAc84555w/20edYznnnHPOOZ/hvf/elNWTlR/17x1V/TG/93xe -leNrPcbo97hvx+eq+cj/9tHrVXX/qv5en72+9dbTO1845/fxI65aT1atn73r -W2/9ve3kv+cfcdX3/Nb50jueq3GexS7Phf/n7+z1bdT47K0/K796PnLOOeec -c37Ge8/nnHPOOeecv9lH/Tta5bH+Uef8rFzv93Pe5jHOPt/W8TNqnMf8Xfrz -rn52nZm1bmTtHOW943lUPZzz9/ioc86qffBt+8LbfPT3/G/nRTXOs9ilP+/i -o845vc9x9rpR1R/Lc84555xzzv+3jzrnc84555xz/iQf/b065mfls3p7v6v3 -1tPbnqr+mN/bn733vZvH6O23LKpxmJXbrX+e5mfXmdb5MspjerX3rttZPWfX -Jc75eB89f7N677qO9fqofSSm+RyvnmO8Louz8yuLXfpnlPfOl951KfOz5/ms -ntZ5Pao9o95zd/v3L84555xzznfw6hzPOeecc845f77H/Pg3Ru+/a/T+O8Ls -35u9H2Xtucqzdrb281Xt/PZ3ZeVnv/9W7fx2HI7696necXuX7wa9/ZO1Y/a6 -V7WTc177EbPW+az+2evzbt9XR7VnVP9U7bj6vFe1p7f81V71f+vvmd3OzFed -Z7L2nB3n355bdvv3IM4555xzzvn1/gke8znnnHPOOeecr/EqjuuOv7u9b97d -Y3p1e3bzbNz+JPmj+j/zUfOuamf2uzh/o5+dR60e06PXgd71ardzwurzyax1 -mP+eX5Xb7ZzAOeecc8455/y//8bgnHPOOeeccz7Wszje1+J12Xtcbz3x+uPv -bu+nnP/bY7ryUfO09/tJNX85f5If0TovYvm7rAOcz/CYH8d/6/mxdz/KYrd9 -n3POOeecc86f6p/gMZ9zzjnnnHPO3+4x//j7E9JHnPWsHfG+VTtjzG4n5zO8 -dz5m3ju/qnaOmkecP8F75+nseb3b+YE/20fNoyxGnQ9Ht7N33+Scc84555zz -t/sneMznnHPOOeec87f48d4U80d5vP/xN3tf6y2f3S+L3X4v5795Nt5i+d75 -nsXsecH5GzyLUd8ts/vudq7ge3rMb913rp4Xve3f7feuPj9wzjnnnHPO+S7+ -CR7zOeecc84553x3r+K47vj7E9JHXOWxXZln7c98VL+t6p8jsucV8zn/zVvn -XUyfnUer1xPOr/Qjzu5fvfNot/MG39Nj/urzXha7nQNX90/V7lhPvI5zzjnn -nHPO7+Kf4DGfc84555xzznfxmH/8/QnpI1Z7bG+vx3Tlo/s5xqr+zNq52/s1 -v5fH9Oj5VbVnt/WKv8tHrasxfdU+xd/pu62rWdxln6r6eZf1KrZ39fmBc845 -55xzznv9Ezzmc84555xzzvnVHvOPvz8hfcQqr9oZ83s9q7/XRz+XGKv6P2vn -bu/d/F4e01X5UfNrt/WNP8uPODsvevfr3c4V/F5ejc9V573edrZ6TO9y3sv2 -wV3Wt6qdMZ9zzjnnnHPOV/kneMznnHPOOeec81ke84+/PyF9xK5+RGz/tx7T -Z/2q5xhj1XM5IhtXMZ+/27P5k0Xr/Oq9L+dXeu+4jenR84u/02P+6nUyC+e9 -/8Ru65hzIOecc8455/wu/gke8znnnHPOOef8W4/5x9+fkD7ibn5E/F2tXkXs -t15f9T6YxeznkrVnt/dxvre3jrd4fTW/Vq9XnP/bj2jdR75dhzn/d4xah8+u -273t+dZ7z8lnPav3W1+9Xo167q3nZM4555xzzjkf5Z/gMZ9zzjnnnHPOW/3s -e0qsb1fP2j/LY3q0rxonWVz1vHZ5vvwZHtOj59fqdY/fy4/YdTzzd3o2bmev -e1nstl+M8t2e725+9nfFcpxzzjnnnHPe65/gMZ9zzjnnnHPOZ/nxnhLzV3ts -92yP6at8t/fELHrHT1V/az9w3uIxXXk1nlvrX71O8jV+xKxx1Vs/5y0e81vX -29ZzWha7fW+vys3yVc99t/Vzt/MD55xzzjnn/D3+CR7zOeecc8455zzG8X4R -8+/uR3xC/uz3suy+qzzrn1XjKovedsb8q54vf4f3riffluf8t5g13nY7h/B7 -ecz/dl2NUc2XrP5R3jq/Vvnq57vLOjnaj9jlHMI555xzzjnf1z/BYz7nnHPO -OeecZ3HkH3+r95FY366etX+Wx/SunvXb6nEYY7f3bv5sj+nWdS+rf7f1kN/b -s/UzKx+vy/aHqn7Ov/EsVq//rfNlN1/1HHdbD3vXyZi/+rzBOeecc845v69/ -gsd8zjnnnHPOOY9RvXfE6+7mR8TfNctj+m7eOx6qelqfV9XOGHcZD/zZHtPV -+K3W4d3WT36NH3HVeOO8xc/u41nMOidk5av27XLu6vW7jIfdvPpdsRznnHPO -OeecZ/4JHvM555xzzjnn7/XR7yPxPqv8qt/7rcf0U3xU//fWn8VTxw/f02P6 -2/myy7rKr/UjRo8rzv8do851WYza33vbn9V/d3/q+Fn1XjD693LOOeecc87f -65/gMZ9zzjnnnHP+Xo/5x9/qvSPWt5tnv3e397WY5m1+dpzHyMZPdt/dxg/f -02P67Hi++zrM//be5x7To9dJ/k6P+dU6k4XzzzW+2/i5+z51dl7EfM4555xz -zjn/BI/5nHPOOeeccx6jeu+I193Nj4i/a7a3tiemeZv3jvMsVo8T/mzPxnGM -1eskX+tHnB0/nH/jWfSuezHN27x3X1g1Tlavk9969btiOc4555xzzjnP/BM8 -5nPOOeecc87f68d7RMzPPNZ3/O2tZ7ZXvzeWu8pb+5Of82qcxOuq+mP0jreq -nTGfv9NjuhqPu623/Ds/4ux44O/0mP/tOaS1/t51KauHn/Pec8hs7x1vqzy2 -79t2xvo455xzzjnn/BM85nPOOeecc87f6zE/lotevY/E62d71c7e8jF/9ntZ -VY6v8ep5ZTFqHvF3eUyfXTdWrcP8bz+idR3Iyu92fuBrPea37ncxeschX+ur -vv9X7eld965eh0fNo93OD5xzzjnnnPN9/BM85nPOOeecc87f6zE/lotevY9k -18fIyvf6qN979v2rtZ3ZffmeXj3feF0Wu30f4Ht6tU721v/tusrHeu8+5fse -/8az6D2PxetW78v8b3/q+bn3PNb7e2N+az9n9+Wcc84555y/1z/BYz7nnHPO -Oeecz/LR7zvxPpln7Yn5q+/L9/Te8VnVHyMbP1X51vbwZ3hMV+Ord73i1/oR -Z58vf7Zn0btfxPucHVdZPXxPf+r5udd328c555xzzjnn7/FP8JjPOeecc845 -5zGq946qvpgfffR7UHa/GL31jHrPGtVv/F6ePe8szo5b/kyP6dZxla232frG -x/gRrftdVn638wC/xqtx0lt+l32Qj/Xe82rvOXb2uXrUfIn5Z/vNuYtzzjnn -nHM+yj/BYz7nnHPOOeecxzjeL2J+9t4R06P9Lu9H1f34Oz1GNr/Olp81X/ge -3roOn62Hj/FR++xu5wF+zmN+NR+z6C2f3Ze/0+/y7w5Vvd967zq8et/nnHPO -Oeec388/wWM+55xzzjnnnLf68d5RXRfzr/aq/fG6Ve3k/K/8Knrn427fK/g5 -j+nWdS/m8zl+xNnnxe/lMT/O39Z13fmE7+zV/hKvW9XOzHvXbc4555xzzjnv -9U/wmM8555xzzjnnrV69j8TrMo/Xx/zoV7WztXzWTs6/8d73+ix2+y7Bx3pM -V+Nk1LrNf0/H8lm5b/c1fi/P4uw6v8s+xZ/hZ9e3b9fD3nUy89nrNuecc845 -55z3+id4zOecc84555zzp/nxfhTzK4/19npMcz7Cz463GNn4770vX+tn18Os -/t518u1+tp+j77Zv8t/zq/lSRayn976cf+Oj5sWqczXnnHPOOeec38U/wWM+ -55xzzjnnnD/Nj/ejmH/W4/16PaY5n+nZvMiimkexHN/TYzqWH7Ue8t/9iNb5 -yPf0an71lt9lX+DP9tHjf9Q6Ge/HOeecc84550/1T/CYzznnnHPOOedP8+P9 -KOaf9Xi/s179jpjP+Rk/Ow5jrJ4vvM9jOhsvMbLxM2r9vKsf0Tq/svK77Y9v -87PPvbWe3vnF+TfeOw5nzxfnAc4555xzzjn/778xOOecc8455/zuXr0fxet6 -PdYb68/u+217svtyPsOz8ZfFbt89+H/7t+seH+u77Zv878jmV0xzPtNnrzOj -7tvbntX7I+ecc84555zP8k/wmM8555xzzjnnd/WYf/z9Cekjej2rv7pvzM/q -7/1dnM/ws+Mwxm7fQ/jv6ep5jlo/n+JHnO1PvtaraN3Hs/Kcz/BV58nZ5+fd -9kfOOeecc845H+Wf4DGfc84555xzzu/qMf/4W703xfp6PWtP73tZVY7zO3qM -UfOIn/OYrnzUOnl3P6K133bbH+/uvft4Fbutk5yf8d5z5qrzcNa+3fZHzjnn -nHPOOR/ln+Axn3POOeecc86f5jE/los++72stz2c39Gr+Rhjt+8nb/Psef0k -+W/1I6p+49d4FvZf/ma/at61tme3/Y5zzjnnnHPOZ/sneMznnHPOOeec86d5 -zI/lZvlPUm70e1/Wjiyu7gf+Ts/GZ1VPjKvm0dt8VH9m9dzVe/eXUfXw/0S1 -bmQxav3hfKSPOr+Nnke79QPnnHPOOeecP80/wWM+55xzzjnnnL/Fj/em6rrj -b1a+t/7KY729HtOc38GzeZTFbt9bnuK969Xbfbd97e6ehf2OP8lHzZfR58zq -/q37RVY/55xzzjnnnL/FP8FjPuecc84555zzMV69r8Xrznpr/Vk7Y352Hec7 -eoyz8+XtHtOVj17HdvEjWvtht31nN6/6OYvd1hnO//JR57FR61hVf9ZOzjnn -nHPOOedj/BM85nPOOeecc845H+Mx//j7E9JH9Hpv/Vl5zu/o1byLsdv3mbt4 -1s+j1rFd/YiqH/jfnkXWzzHN+Z191Plt9Pkw5nPOOeecc845H+uf4DGfc845 -55xzzvlcr97j4nWVV/drvW9Wz+ef3/9mkZXjfAePcXaevsVjuvKz69jVnrU/ -8932kd32ryp2Wwc4/z8x6vzTOg+q8r3rmP2Lc84555xzzvf0T/CYzznnnHPO -Oed8jcf8WK7Vs/p/kvyz75tZO7L49ndx/o1n4zaL0fPlrh7T364zu/kRZ3/v -U33UfIn3Wb0O8Hf6qPPM2XUvu3727+Kcc84555xzvsY/wWM+55xzzjnnnPO9 -/Hi/i/mj6sk81nf87X3frMpxvtKrcRtjt+88V3nruvFU321fmO1ZZOMkpjnf -yUedW86uJ7G+s+ttbz2cc84555xzztf4J3jM55xzzjnnnHP+Lj/eH2P+WY/3 -G/XempWvrud8hsfY7fvPVT5q3djFd1ufZ3sVu807/kzPxufs79u7nX8455xz -zjnnnD/DP8FjPuecc84555zzd3nMP/7+hPTZ8pXH+nrfZ6tynF/prbHb96Je -j+lv14GrPWv/buvz2fW8N3abR/xdPuo79qh14Gz5mM8555xzzjnn/J3+CR7z -Oeecc84555zz/xPHe2XMH1VPb/0x//g76n05q5/zHm+N3b4XjfbW+b7Kd1tv -R/nZ2G0e8Xv46HEb6x29zmT19NbfWw/nnHPOOeec83f5J3jM55xzzjnnnHPO -R/rxflpdd/ztfZ/N6h/1vlyV4/wbj7Hbd6Szns3HXXy3dbLXq9htnPN7+6jv -zL37dTX+s3a21s8555xzzjnnnM/wT/CYzznnnHPOOeecX+Gj3lt/kutGe2xH -5dXviPmc/xW7fV/KPIur5mnVjiN2Ww9b251dt8u45Xt5Ni/uvs9W7Wyth3PO -Oeecc845n+Gf4DGfc84555xzzjl/ssf8+DfGT5KfeVb/qPf3qhx/tsfY7btT -5a3zaJTvtv5UzzOL3cYhn+ujvutW9ffOr+x+3+53nHPOOeecc875k/wTPOZz -zjnnnHPOOee89uy9O6aPvz///F4u86qemF95a/38nh5jt+9RveN/lO+2blSx -27jifT5qHPbW37vO9+5rnHPOOeecc845b/dP8JjPOeecc84555zz6zx7f4/p -4+/PP7+XO+vxPr3fE6pyfK3H2O171OzxvGpeV7HbOHm7jxo/o8Zz1o7efYRz -zjnnnHPOOefX+yd4zOecc84555xzzvn9PObHctGzen6K67PysVzmve3JyvPv -PMbs71FZe7Lx1utZ/VfNuyx2e+539VHrydl1LBuHre3JfLfvxpxzzjnnnHPO -Of/eP8FjPuecc84555xzzt/rvd8TfpL86ntF1a7W+8brsnp4m8e46vtVNn5a -ffa8qGK357i7j5rXveOhd73qbSfnnHPOOeecc875J3jM55xzzjnnnHPOOb/a -Y378G6P6HhKvG/X9pCr3VI8x+vtV9rxaffQ4zGK35zLLR31X7H1e2X1728k5 -55xzzjnnnHO+yj/BYz7nnHPOOeecc87507z6fhKvG1V/TD/NY4z6TpU9l1Hf -u6rYrZ+/9bPzIvPW+bLbd1HOOeecc84555zz2f4JHvM555xzzjnnnHPO+Rqv -4rguXr+bxzj7XSu7Xwz9yTnnnHPOOeecc8538E/wmM8555xzzjnnnHPO7+3H -d6GYn30viulZnrUzXpe1v6ovi1m/a1T/c84555xzzjnnnPNn+Cd4zOecc845 -55xzzjnn/C8/vjtV18X8zEdF632z9u/2HY9zzjnnnHPOOeec38s/wWM+55xz -zjnnnHPOOedX+KjY7fsb55xzzjnnnHPOOX+nf4LHfM4555xzzjnnnHPO//KY -f/z9CekjMh8VZ++btT/mc84555xzzjnnnHPe4p/gMZ9zzjnnnHPOOeec39tj -/vG3+o4U6xvlWWTtien4tzVm/67R/c8555xzzjnnnHPO7+2f4DGfc84555xz -zjnnnK/xLI7vPPG63TyL3u9XMR3/xtCfnHPOOeecc84553wH/wSP+Zxzzjnn -nHPOOedP8+w7SUzHv9/W/5PUd3fPYtR3qqzcqO9dWezWz6P87LjNrm+dL7t9 -F+Wcc84555xzzjmf7Z/gMZ9zzjnnnHPOOef8aj++Y8T8qnxW7hPqG/X9JGvn -Uz2LUd+pYvqsjxqHWez2XK7yI872c3Z977zubSfnnHPOOeecc875Kv8Ej/mc -c84555xzzjl/r/d+T8jKZfVU5bNyre3M6uF/exazv1PF9FmfPS+y2O053sVH -zetYbvR6dbadnHPOOeecc845f69/gsd8zjnnnHPOOeec38+P7wAxP/Osnpgf -/2b3jddV3tqe3t/F//YsrvpOVY3rbFxU3juuRnkWuz33p/gRo597Vn9Mnx3n -Z38X55xzzjnnnHPO7+ef4DGfc84555xzzjnn13n1Xl/VF/NbfdT3hKydfK1n -sdv3qKrct+N51bzOYrdxwv/bjzg7fqrre8dzVi7Gbt+fOeecc84555zzN/sn -eMznnHPOOeecc8557dX7eFVfzI+e1dP7HeBs/fwensVu36Ni+irfbd3IYrdx -xc/5Ed+Ow9n7yNl9jXPOOeecc84557V/gsd8zjnnnHPOOef8yX68L8f8rHzM -z647/mb1j3p/r+rnz/QsdvvulHlMX+W7rT+tz/WI3cYhv9aPODueq/Wkd1+L -+aP2O84555xzzjnn/En+CR7zOeecc84555zzK3zUe2t1/bfe+95d1RPLcd4S -u31fqsZ/FrPmaeVZO3b3LHYbt3xPPyLOi7vvs73nCs4555xzzjnn/Er/BI/5 -nHPOOeecc875SI/5x9+fkD6i9322qj/m99ZftZPzM57Fbt+Rej2md/Xd1smz -62qM3cY5f5YfcXYeZdeP2pd76+ecc84555xzzmf4J3jM55xzzjnnnHPOf8uP -f7+tp7f+nyR/9Ht0Vj/nf3lv7Pa9aJTH9K6+23o7et1ujd3mEb+Xjxq3vft7 -TFc+ah3bbb3lnHPOOeecc76nf4LHfM4555xzzjnn7/Lj/bG67vjbW76qJ+b3 -vs9m7eH8Su+N3b4XnfVv14FVnrV/t/W513tjt3nE3+1HVPt+Nf6/XQd6y69e -hznnnHPOOeec7+Wf4DGfc84555xzzvm7PObHcq0++721qidex/kMz2K37z+z -Paaf4rutz1et/zF2m3f82d677z/1/MM555xzzjnn/Bn+CR7zOeecc84555zv -5TE//v22nsx/knK975tVPZyv9Gq+xNjtO89sj+m3+m77wlX7Toxq/Owyrzn/ -zY84e26prs/OUTG/d73dbV/gnHPOOeecc/63f4LHfM4555xzzjnna/x4j4v5 -vZ7VH/OPv73vlVk9s38X59/4EdV4rcrv9p3nKv92ndnNR/3ep3rM/3a+7LIO -8Hf7EWfPM6PPV7N+F+ecc84555zztf4JHvM555xzzjnnnM/17H0tpiuv6mm9 -b+VZO7L6Yz7nO3gWvfP0rd7bz63r2Crv/V277SO77l9Z+V3WAc5/8yPOnn9a -95vW8q3rmP2Lc84555xzzvf0T/CYzznnnHPOOed8jB/vZdV1Mb/Ve+vPynN+ -R8/GfRa7fZ+5i1f9/O06tpv7njbWs6jG4S7rDOff+BHfnt96vWpnvI5zzjnn -nHPO+Vj/BI/5nHPOOeecc87HePZeFtNnvbf+qp0xn/OdvYrW+cL/23v7/9t1 -bDfv7Yfd9p3dPOZX5XZbZzjv8SPOnsey8r1enffidZxzzjnnnHPOx/oneMzn -nHPOOeec87d4zD/+/oR0Vb63/uq+Mf+sx/txvrNX8yjGbt9b7u4xzdt8t33t -7p6F/Y4/yUfPl2/PmVX5ql2r9y/OOeecc845380/wWM+55xzzjnnnD/Nj/ej -mD/bY7uOv6Pe77L6d+sH/k4/Ihv/WfksZs2jt3lMj67n7t67v4yqh/+eX5Ub -tf5wPtOPGL3+9M6j3fqBc84555xzzp/qn+Axn3POOeecc86f5sf7UcyvPNY7 -2nvbw/mdPJuPWez2/eRtXj2vrNxb3He2PT0L+y9/s8+ed7ueqznnnHPOOed8 -F/8Ej/mcc84555xzflc/3oNifvZ+FNNnvWpPVV8sn7Wf8zt5Fd/OI/6d9z7H -b9fJu3tvv+22P97dz+7jWT27rJOcj/Ajzu6n1fWtXt23tf2cc84555xzfnf/ -BI/5nHPOOeecc35XP96Dqutifqtn9VeetTvW3/u7OJ/hZ+dXVj7Wy/fw1uce -88+un3f3Uf3J13oWvfv4bus2f4cfcdV5Mqu/18/OL84555xzzjm/q3+Cx3zO -Oeecc845v6tn70ExfdZ/knK972Wj78v5SM/mVxa7fffgv6f5Hr7bvsn/jmre -7bJu82f7EbPWmVH37W3Pbvsm55xzzjnnnI/yT/CYzznnnHPOOedP85gfy7X6 -qPeyqv5YjvMRfkTr+M/i6vnCv/PsOcXIysfrzq6fd/fe+dXb//waj/mj18Pe -+cX5N35E6zi8ar44D3DOOeecc87f7p/gMZ9zzjnnnHPOn+YxP5Zr9dHva/F+ -nM/wal7EyMrv9n2Dt3m1Xp5dD/nf3jsf+Z6eza8s7Pt8Bx81/mP+t+thzOec -c84555zzp/oneMznnHPOOeec86d5zI/loo9+L4v343yEH1GNtyqy8d97X77G -e9fDrJ6qXv679/az73X38mpdrZ5fVU/vfTn/xkfNi5hfrZO77Zucc84555xz -Pts/wWM+55xzzjnnnLd69t4R05X/JOUyn93Os+Vb2895jx+Rzacqdvsuwed4 -6zo5at3mv+cfMep58Wd4Fr3r/Or9iD/Tj2hd33rLj9rXett/VTs555xzzjnn -PPoneMznnHPOOeec81aP+cffn5A+YpVn7a/ep3ZpP3+nV/Mui975GK/j9/Te -8RPHCR/ro54Xv5dnzzdeV81P5xO+s1fjP5bbrf2xfbvs45xzzjnnnPPn+Cd4 -zOecc84555zzLI7842/1PhLrG+3ZfVt9dr9d1Q/8Hl5FNS6r8rPnC1/rMT26 -Hj7WR+2zu50H+Dmv9oVv1/8sdtsH+R5+xOh9avZ8GeW96/Bu5wHOOeecc875 -/v4JHvM555xzzjnnPEb2fhHTx9+ff34vV3msr9ez9oz+XVl+jMyr+nv7jd/D -q/EQo3fc8nd467jKysfrqnWPn/Oz+13r8+XP9up80lp+t32Qj/UjsvUn5vee -Y7NyZ8dtaz1n58u3/ebcxTnnnHPOOR/ln+Axn3POOeecc85n+aj3mpiuvGpP -zF99X76nH9E6brPnn0U1br5tD3+GZ+tOFq3rFb/GRz1f/myvone/+HZcrd5/ -+Tk/4ux6dXY8zLrv2XEby3HOOeecc875bP8Ej/mcc84555zz9/rxHhHzK8/q -/fzz+98ssnKtPvr3xut7f2/mZ/uZr/EjsucY87PY7fsA39Or9aq1nqpevsbP -7lPVfap6+Ds9i97z2G77Mv/bj5i9LmXtidfP3qdGvY+Meg/inHPOOeec80/w -mM8555xzzjl/rx/vETG/8qzeT3LdLM/a2Vt+1XvZ2f7ncz17XlmMmkf83d46 -DnvXPb7Wz64DreOBv9N7950sesch38OPqM6Zs8db1o7d9qlR82j1OYFzzjnn -nHO+r3+Cx3zOOeecc875ez3mx3LRf5JyvfXM9qx9q97LsnZm/cnP+RFZP8f8 -qp4sesdb1v6sPfydnq0XWeyy3vJzPmo88Hd67/4S09X6Mmpd2u2ccHc/ovUc -ctU4zMrttt629mdVT8znnHPOOeec80/wmM8555xzzjnnMbL3i5i+m696Lzvb -nng9/9t7x3kWu73X82d4TGfrVoxd1k9+jY8aP5x/41mcXQ93OSfcxXv3hdXj -ZJf1s9ez37Xb+YFzzjnnnHO+v3+Cx3zOOeecc875e/14j4j52ftFTO/q1e+N -1632rP/57947zquI46Z3XnD+m387nu++DvO//ew+NWud5O/0bPzE66r91fnn -Gt91/GTldllvM++dF6vPFZxzzjnnnPN9/RM85nPOOeecc87f66PeO2J6tc/+ -vaM9tvfuPrr/W+uv4qnjh+/p386XmL96XeXX+Oxxxfm/Y/S5rrX+UePW+Wqt -3/29YPR445xzzjnnnL/XP8FjPuecc84555zHyN4vYvpuvvp9Lbbvbn5Eaz9X -4+7berK4y3jgz/Zs/MWoxvcu6ye/xleNN85bPOa3jvMYV50TYvms3Orz1bd+ -t/Gwi1fjIV7HOeecc84555l/gsd8zjnnnHPOOY9xvF/E/Oy9I6Z39dXva1l/ -7uKx3Vm/xnKzPIvVz5G/01vny93XSX4vr9bPbHxm9WbXcz7Ss1i1zsd0NV92 -89XPcZf1MPOs/b3vO5xzzjnnnHOe+Sd4zOecc84555zzLI78WO6u/pOUu+p9 -Lbvv1R7bl/VfLPetZ/etorWdq58vf6bHdDWvR5Xn/N9/Z4+3VecN/gzv3X9j -+ux5YLf1f5Wver7xutXr5Cjf7RzCOeecc845398/wWM+55xzzjnnnM/ymB/L -Xe2r39di+67y2J7V46G3fGx3Vr63Hzjv8dZ5V43P1vpjudXrJ7/GZ4+r3vo5 -b/He/Temq3U4i92+t686760+1+22fsZ8zjnnnHPOOZ/tn+Axn3POOeecc85b -vfd9JKZ39dXvcbF9o3zVOKli1vPqLc95j8+aXzF/9XrI9/S7jGf+To/52biu -yp/1GLvtF0851+2yHmbe+7tWjxPOOeecc875c/wTPOZzzjnnnHPO+bd+vI9U -18X83X3Ue1kWWb+d9Xjf2c+9ilnPpRqH8TrO/+0x3boOZOWy2GUd4+/0al58 -u1/P3l/4M3zUOnzWW9sz+zv8qPNeFqOeV8xfvY71eu85mXPOOeecc85H+Sd4 -zOecc84555zzWX68p1TXxfxd/Kr3uNiOXp/9HKtY9Vyy/onX8Xd6TGfj64je -+dV7X86v9N5x27uu9t6Xv9N3PQdm7YzXvfW8t8s6lrlzIOecc84553w3/wSP -+ZxzzjnnnHN+tR/vL9V1Mf9qz9o5+j0uq7/VRz2XKq7u/2r8xOs47/HWeT16 -fu2yvvFn+Ozvh7P3Hf5Oz8ZhTF/tre28+3nPOZxzzjnnnHPOx/oneMznnHPO -Oeec8138eK+prov5V/vo97h4v8xH9XMVV/dnNR7idZz3+Kz5ld03pjlf4aPX -1av3Kf5O33VdbW3nXeZXzF/dz1U/xOs455xzzjnnfDf/BI/5nHPOOeecc767 -Z3G8B1X1xfxZfvY9Ltab+ah+i9dd3T/Z743Xcf5vj+mz8+vsPLp6vnB+pY/a -v3rn0ahzAn+273bey2LXc+Cq9aRq1xG7nTc455xzzjnnvNc/wWM+55xzzjnn -nL/FY34s963/JOWq97jW8tXvymK338v5b+mq/Nn5nsWsecH5mzzGqO+WWblR -5wH+bM/OJ/G61fOit/27/d7dzhWcc84555xzvso/wWM+55xzzjnnnL/dj/ep -6rqY3+rVe1x2fW/MbifnI713Plae3be1fNU+zt/ovfN09rze7fzAn+0x/9v5 -FWP0+fDbdp7dZznnnHPOOef87f4JHvM555xzzjnnnI/xKo7rjr/Ze9zZeuL1 -u72fcv6bZ+M2+qh52vv9pCrH+RO8d17cfR3gfIZn4zZe17rfVPlVudX7O+ec -c84555y/xT/BYz7nnHPOOeec8zWexfF+F6/b7X3zKa6ff/dq3MZyo/s/+qh5 -l7Unpjnn/fNot3Ug5p9d997ms9dh/p/I+jmL3c4JnHPOOeecc87/+28Mzjnn -nHPO+Xv8eF+I+Vn5mB//tpb//7d3t8mWqkoCQOc/yx5CD6Gjo8J4VflOHj42 -SOpe+afCBSJbERG5544ed/Xvjfmy+uz2VvSe51P1H/1drXKuiNdllffWf7Rd -xfTZes62212+6r7Lyh29Xrv7vayenPN+v6uf7+0fWvX8tD6r+qXZfuzT+mT7 -V3vOru7ne/Of9it678cYp+o/2m539w8xX6uc0fynx7ecc84555zzuv6/wWM6 -55xzzjnn3+gxfXZcneXL8v9PIz3bP6tnbzmj9Wl5PE6rnjF99rjVPYvR85ZF -6zrGfNXOz1t9tH/I/K55g+rnbba/yvbvPf+c88991f371n5s1GP6p8+RKuft -rd5q/618MXrvryyqnZ9T467Zfqm3v8qOu/u9b9V72ej5rPb9i3POOeec8wqe -jas555xzzjnn/x2r5qsz3z3OH53/b83z8589i9HrGLdbvrqdVzmfT/fR8x/T -d/Ubu89DPG6r/p+Wwzn/Hh99fq0qx3OBj/gVs9clbs/eF612FeP0eXuqX5Hd -j73tZPQ67u43Wv1kzM8555xzzjn/bx8dz3POOeecc36nt8a3cb9WOa3jZ+W1 -xs+j8+2z895Z+fyMZ7HqfS1uz7bPU/cj/91X9Ven+5N43NX16S2nlY9z/jw/ -1Z+c6j9H+7fZ/rnKc/Ap3moPMd/Tx4FZVLsu/F+/Ylf/lu0/2p9/2l+duh85 -55xzzjn/xEfH55xzzjnnnH/iq8e3rePH9Oiz88Ot48RysvL5MzyL3e9rcbu3 -Pbf2y45zl1e7vtW81f56r/uq455uD3H/VfcL57y+n+pPdo9Xq/X/3+pX3N0e -oo9e98x3P6+zOH0d+Vq/YnU/3Co36996+8nZesZ8nHPOOeec7/BV41jOOeec -c857PBuXxu3Vvnv8fHr+nK/xLE69r8XtWa/WD8zeR3H/au1ndXtonb9W/mrX -d/S5MNoPt/Jxzp/nq+Yzq83HPqX/P/087f1ddz2Xd3ncnvVTz/EsqrUf/plf -sbq9tcrddV9U6wc455xzzvm7fdX4mXPOOeec8x6P6TFfr68a956e3+ZnPIvT -72ut+2n2fsm8Wv9Qrf8ZLeeufq+3nWT5T53/1n0a9888bnPOv89P9T+nnvu7 -xwmj/e2q/vn0+b/b4/Zqr/bcz6LaewG/16+Y7c9b++t/OOecc855RR8d93LO -Oeecc/6Jx/SYL/rovG5WTlaf0/PSfK9nUe29LG7f5d4T1/qqfmm2v+o97iof -rU+19s85/x5f1d+equfu/rZ13N7y+b//ZlG9/e/2LKq9R/A9fsXq/jArJ/Nq -/QbnnHPOOX+3t8avnHPOOef82R7T4/gw7rdq3Dg679qqZ0yf9ez38md7FtXe -v1bdF6s9RrV+7Nt89r7Iyj3VrjjnnI/57ucCv8dbUaVdVfMsqr138LW+uv2s -6m/jfqPzJK331rh/tX6Mc84555yv9VXjXs4555xzfo/H9N5xYCxv9zzqXfOQ -u34Xr+FXtO6Hau9Zox63T7v3x3t81X3x9PbGOeff5k9/jvB//83ibe3tlGex -+r7gz/DZ9hPvh9l+8u7fFdNP93ucc84553zOR8exnHPOOef8rMf03nFgLO/U -vOLouLTaPDC/x7NolXNF731RxeN2VfdeudZn75dY7lvbG+ecv9Wf/hz5Ns/O -fytfFV/V3k756vcF/m6/otX+nzJ/EtNP94ecc84553zOs/Ee55xzzjk/6zE9 -juta5Z0eZ2aRpZ+ev+VnPItq702rPTs/MX/crureN3/3mD7bHla977fycc45 -3+u7n5tPeV+o5tn5auWr4qPtYVV7q+ZZVHsP4vf6Fb33+d0e02N/pT/nnHPO -OX+2nxpncs4555zzP9Eav8X9WvOKcZyXHTfLP+qt39U6H6vHpafne7/dr+ht -f9Xej6q9f7X2r+6j/VtWTrV+e5XH9LvaWysf55zzvb57nnb0uE/3uB3zZ/my -qNJORt13gd+9Fb3th9/rV9zVP4yWM+qr5nNG+7dq/TbnnHPO+bd5Nk7jnHPO -OedrfdW83+55wlHf/XtXn2e+17NoXa+Y7+3eaten7+vdPnoeRu/3Vfln2+3o -/XL3782Oyznn/B4fHSevfo/Iyhl9vmT1zLzK783yv9VXjX+e7q32k+XvvV/4 -Hr+i1c/E7ez+mD1uVv5ub7XTXb+Xc84555yv9WycxjnnnHPOa/qpecLWODPb -P8aq+dXR+vA5z65jFtXed57irfO8675+is/2J3ffF6v7t9H7scr14pxzvtZH -n3dZOa18MZ7ynI3b3+rm/9d6Ft5D7/HWdbm7fxutzyqfrT/nnHPOOa/lo+NV -zjnnnHM+56PzfjFfTK/irfnVuN/ucWy1+eSn+RXZ+Y2RtYeYzn/3uM33+Gz7 -j+XM9vO95XPOOec7PKbHfDFWPx9bxz99ft7qo9ed/5zemy/G6fe7p/sVd7Xn -p/dXWf1H+3nOOeecc77Wd49jOeecc875n3jrd/nRedTVnh2X/+xZ+8zi9PV9 -qrfOc3YfxfRWuZxzzjnnnP+UHiPm871gzrP3oyy8z67109e3yv0+6q3fG/fj -nHPOOedrffc4lnPOOeec/+5vXY9xahxbbd741Lx0q11lcfd1/DZvXYcq9y/n -nHPOOX+H+y5wj8f03nwxWu8Xcb+3+xV3tdvW8ar7bLvinHPOOed7ffc4lnPO -Oeec/4lsvjHuF9Of6qfGsafnje/27DxkMTrvzec8bs/m55xzzjnn/BOP6TF6 -8/M5b80DZPljudXeQ+/yK+5qn63jPdXNA3DOOeecn/Xd41jOOeecc/4nsnmw -LH9Mz/ar6qfXvcR8u330uo/+rlY7yaLK9fpW/5b7nXPOOeec1/RV41U+5zG9 -9zrGWPX+OPp+eur9Otaj9btOX68qPnsds/ycc84553yN7x7Hcs4555zz3310 -fixun/bW74r7nVoPs9rjcUeve2v/Vrmtck6ff/7vdkzPosp9zTnnnHPO3+Gr -xqv8Ho/prXyt/KPtoff4u9+7T53/t8zDZOc5lsc555xzzu/xU+NbzjnnnHP+ -c3pr/JblP+Wn5/2y467yeNy72sOn5VR773irx+3Z+yIrh3POOeec8088pl+R -jVdHy+FrffZ95NNyVn1X2v2eftf5770vTnnr+sd81d6jOeecc86/zXePYznn -nHPO+ZyPzkPG9Gy/1X7XODbW4ynzuq3rlUU8z6PtpNp7x9u9+n3KOeecc875 -3/+uGt/ytT76fhe3s3Jb5Xiv/91jetX79PT15ZxzzjnnP/vu8SrnnHPOOb/H -Y3rMd7c/ZV73ruuSxVPOM//dP21XMf30/cs555xzzt/hp8a3fK3H9E/bSQzv -7z+nP/X+5ZxzzjnntXz3OJZzzjnnnN/j2Xgvbt/lu8ers/O6veWPeiueev75 -z9uz+TnnnHPOOa/sMT1Gb34+5zH97vYQ41vf66vcd9XeiznnnHPO+ZyvGq9y -zjnnnPOaXm3dyOw4NpY76qvOZyt2n7fs98b9+JzH7db5H80/Wg7nnHPOOeef -+Kpx6Wj+Vj4+5qffI7L6xP2e8r4f0++6H1vXN+7HOeecc87f4aPjVc4555xz -/g6P6THfLs/qs3v+dvb8ZLHr/LR+V9yP7/FP21VMb7X/LD/nnHPOOeefeDbu -Hc2/+/2Lz3l2/uN+u9pbVp+436l2Ndr+d/vp91zOOeecc37GR8exnHPOOef8 -3X5qXnfV/O3o723Frt+bebX3hW/1eJ1G36da+TjnnHPOOa/oo+PeVe9lfK3H -9LvbVYzT7/u775eY7/T7LOecc845r+Wj41jOOeecc87/jmweMu4X01vj0Vh+ -3G90nrYVo/WMbj62psft2evYav+fHpdzzjnnnPMKHtOvGH0vW3Vcfo+vfq9v -Xdd43Ljfqfd97/Wcc84553yHrxq3c84555xz3uMxPeaLPjv/v/u4vKZn1zXG -aP5V7ZlzzjnnnPMn+qrx+arxPK/pMb23vcUYbQ+jxz393so555xzzr/Lq43b -Oeecc8457/Esqo23V3s8H63zk437o2fHbeVvXbfZ4646P6Oe/Z7R+sRtzjnn -nHPOn+AxPeaLcWp8PuoxvXUeRt93Vh83pu8+P9U8i9Pv45xzzjnnnM94tfE2 -55xzzuv46HxpLG92vLHquJm3yo/7jY6jsnyjv3e0nCx/Vv/d9RydT26Vn8Xo -9V3l8fiz9Yn73VX/T320HWY++17z6fWq1i9xzjnnnHNewVeNt0fH4aveRzJv -1SM7DzG92nvZ6PlZNf+wu/5ZfbLY/T67an5g9ri95a+ex8jSs3rHuGse79N+ -6dRxOeecc/49PjqO4pxzzvk+j+mt53iWf9VxW/WJ+VbNt7TqGWP1fEtvOaPz -MKuu+13zind7FqvnObPyq5yHp/vu/m30uKt8Vf/GOeecc875E/30OoR43Kye -Wb4s/+z7Ph/zLL7tff+KT9vhqnaelbPqvTs73mw5MUbbT+a75zlXzVuu7t84 -55xzfp+Pjn8455xz/rmPzm+sWhexaj6hVX7cb/e4ZXR+eNV55nOexe55qlHP -yq92Pp/iq87zqf55Vf/JOeecc875E332vSCWt9rjcVv17y2H/+5XjJ7nXs/K -b9WjN6qdz7f7Fa3ruKqcVT7aPjOf7SdX9ben+mfOOeec3zdu4Zxzzr/Zs/ff -LH9M//S536rv6nFFq/yYj7/bs9jdnjM/db+/1a/4tD9pxWj5n7YTzjnnnHPO -+f2+av6kla/Xs/KrvZfd5VfE8/Cpx+3V7aR1fWOcPs/8jF8R29tou1rVn6wu -P6afut8555zzb/ZV4wrOOeec55E9dz/17Li737uz+swelz/bs9g9Xm3l622f -p/qH0fsxbq+u/6rrldUz81XngXPOOeecc/49HtOvGF13MVr+qO9+zxo9D9W+ -Q7XyRd/9Xp9FtXkYvtZH2+dsP9B73FPzIdW+X3POOedv8lXjVc455/ybPabH -fLt8dL4xy1dtPoTX9CxOjWPj9qxX60+e4qPzirP9T9z/1Pwk55xzzjnn/H6P -6TFfjFXvF6vL+XaP23e1h1WeRbV5G17br2i189H53t1erT/hnHPOn+inxrGc -c8753zE7D5Z5drz4/Ntd/+y4o/VZNd/VKn/0PPN3ehanxqtxe7UbJ5/10f58 -9HkR893VrjjnnHPOOef9no3n43bLV79f8DHPrksr36c+2k5WeRbV5nl4Db9i -dXuuNi99ar56d/0555zzT/zUeJVzzjn/LT3mi777ffmu+sf03e+5o+sZ+Lv8 -ilY7fsp4tZXvU6/WT77VR9vtqv6Qc84555xzXsdjeszX67vfL/jvHrdX+1O+ -c2Ux2275s73VTnb1h6PHzXy2f9h1Pu+qP+ecc77Sq41XOeecf6fH9N7nWiyv -2nt05nc99+8+P/ysX9Ea5/WWH8s7NS5dNQ+zykf7B/5zem9/FfcbbT+tfJxz -zjnnnPPzvur7xej7Y7XvNVW993zu9tH3x9H2s8pb5y2L0d/L3+m722dMn+2f -q52fmF6l/+Scc87//jcG55xzfqfH9Pj8ivtl5YzOz4wed9X83qrj8u/2K3rv -qxjVxqVxuzVezfKf8lPzaW/1Vf0w55xzzjnn/Lm+6n2Z93k8nzFflfYQ07P8 -rd9zt6+ezxm9L/h3+RW990WWf/dxZ/vz3uOe7lc555zzv/+NwTnnnH/iq+fN -RvPf7VlUex/n7/AsnnK/zN5f2fj1bV6tP1/dz/e2z9H6tPbnnHPOOeecP89X -fe/Y/f5SzeP22z277k/x1fM/nM94Fk+5X1b3/7Fczjnn/BOv9jzlnHNe01fP -d8VyRt+nsnqMHjcrJ/PR8zNazuz55M/2VjuPUW08udo/7Qee4qPnYfT87PaY -PttPvvX6cs4555xzzu/32fmrmH+0/FPvy96j//Xe8/B0z2JV++HP9Cta90vc -Xt1Pzpbfug9W9wOj53P0/HDOOed/e7XxJOec82f5qvmrLP8pb/3emL77/XS2 -PrymX5Fd1xi999HTfVU/83RfdR5G+43V/XzvfZGVwznnnHPOOeerfNV7SpZv -dJ1AtfUST/HR89C6rk/1mN6bL8bp+TE+51fEfiZ63P70/vq0Hzvlo/fRbD/P -Oeec/+bVxpOcc86f5bu/75/y0d+7+70489PzAHzMs1jVrp7ucZv3+arzPNue -e+uT5eecc84555zzUx7TY8R8q96bWvl668N/99Hz/HRfPR/Fa/kVd98Xo/OW -q+q5ylu/K+5nnpZzzvkOrzZu5JxzXtOf/v416tl5yPKfWhfBa/gVrXZTbRxY -1bP7JIsq/QbnnHPOOeecc873+ar5BP57ZPlPz7/xMb8i3kez7aT3fszyP8Vn -238sj3POOf/bq40DOeecn/VV61Ky8lv5qvip96y7rhf/2a/obQ9ZeE9f63Gb -c84555xzzjnnPEuP+fjPvmq+Kx7n+rfavN9b/Ip4nqOfbj9V+ofMR8/b7uvF -Oef83V5tHMg557ymZ9HKnz1vqnu15/Xp9/1v8dH2f7o9vNV7r1fc/3S/wTnn -nHPOOeec832+ap6Hz3kW5jPPetV2UqXfGPWsPWdxeh6Vc875M7za85pzznlN -b70PZvtnz5sqPvp8rPa8rjYPUM1H23kr4vWo1k7e4r3XN+5/uj/hnHPOOeec -c875Pn/6epWn+Ox8b2851nF95le0rsOpdtJqF1X6k8xbv7f3unDOOed/e7Xx -Huec85r+1nVZmVd7z5q9Lt/iV4xe9yyy9hDT+ZzH7d523lsO55xzzjnnnHPO -3+cx/YpV8w98zmN6K18rf/Rq85Cn/YrT7Xn1PG0VH/291eZdOeec1/Rq4zfO -Oec1PabHfG/zas/r0+/7u/yK7Pz3ltNqt9nxWulVrvtbfdX1rdJvcM4555xz -zjnnfJ/vnmfgcx7TW9cri1XXt1Wf3nKe4k9pD2/10/OrnHPOn+HVntecc85r -eus9Oj5XsnKy/NW89f4b96u2juW0Z/Vf5a32FaO3fZ6+vvzf7ZieRZV+g3PO -Oeecc8455/t81XwCv8dH55OzOHV9T8+v9vrp69va73S/kfmq7x2n51E555w/ -w6uN0zjnnNf00XU4cftpfmrd0Wx9qviqdhX3y9JjOXE/XtPj9uz1bZXDOeec -c84555zz93hM743ecnhNb0W8rqvndbNyqnis913t/OnrsjIf/b3V5l0555zX -9GrjK84558/ymN567mT5q7l1WT9v3+VZZPm9Fz/TW+3iLf0J55xzzjnnnHPO -P/eYHiPmqzbfxX/30fm9LKrNd1mXVdNn+5OYzjnnnPd4tXEX55zzd3hMj/mq -e/a7Tj2Xv239Vdyv93z2/q5q47Fv9d7rFdNP9w+cc84555xzzjmv46vmH/g9 -ftd80ehxd3us32qPxz11HVv1qO6n2wnnnPN3erXxGOec83e497LPPNbj29Zf -jfrovASv4b3tM6af7gc455xzzjnnnHNex63Leodn1yvu92n7yY4b9zMP/LvH -9NP9wKi32mHcj3POOf/Eq427OOecf6c/ZR2X9/HfvRW7r0t2HuJ+fI/3trfR -69Vqb1X6B84555xzzjnnnO/z0XmD2fmirB4x+Fq/a11Wq93E+sT9zAP/nH66 -f2i1q7gf55xzfqdXG3dxzjnnf0e19Vqj9Tz1Ph7LXf3cb8Wu819tHMX//TfG -aPscPW6rHpxzzjnnnHPOOX+Px/SYL4u4/6r/Xoyf9Zi+qx3GWDWflh232rqs -avNyo/XknHPOK3i1cRTnnHPe49XeB6uty1p1nlvx9PPM1/qu9lntfuecc845 -55xzzvn9HtOvqDaPwe/xmH53+4zx9vnhp9/vnHPO+UmvNo7inHPOd3hMj/k+ -9ey4u9+7R+vTOj9Z7DpvmVcbL/E+72231e5fzjnnnHPOOeecP9erzWPwsx7T -726fMUbbZ1b+W/+7yNPzmZxzzvkdXm28xDnnnO/wp71XxnJXr2/JYtd5yLza -uOhbvdWOZq9jtfuRc84555xzzjnn3+Mx/YrReYzR41rfVdNj+t3tM0bVeeMq -9yPnnHP+Jq82LuKcc84reEyP+T712XUsWbmj8Wn9W/WM+/Gavup+ac0LZfvv -ur8455xzzjnnnHPOM4/pV4zOb/ge926/a16r97ij7bN1nF33V7X5T84557yC -VxvncM4555U9psd8ox5j9j06i976ZOVXG7fwzzxe51mP5cft3uNm+2Wx6r7j -nHPOOeecc875e3x0niGbr8j2Hy1n1Fv14M/w1eu4estv7ZfFrvuOc8455//t -1cYtnHPO+Td4TG/la0Usp9p4o5rH7ZbPrkdqHSfG7usYj797nnB0XdbovCjn -nHPOOeecc8756DzG7HxF5lk5vZ7Vc9Rjeqv+o+WM5h8th/+c3srXit72wDnn -nPN9Xm28wTl/n696L477tfqxVd/3R+s/Wv7u8zlaz2rt5+k+u/6kN0bbebVx -SFbPVffFbo/1mh13tfKtuo6f/q5V98Vo+Vl+zjnnnHPOOeec81X/Pd2qea3d -67Ky47bq09qvVf6p+bdT8427Paa3zvNozH6Xifn4nMftT8vfdV/M1rPV3j/t -J3vrP3t+Pj2fnHNuXRbn3+MxfXZcsao+p8Z7o+dntj6fjjNX1XP378181fWd -PW7v+d89T7J6PU+M2XmSrJy7fxf/eXvWY/rsuO4p9c/yc84555xzzjnnnI96 -TI8R863+HhePv2rePst3uv58jWfx9HnjK1bdp73lr/LReq7y3d/dZsvZdf5P -fR/Mytm9HmPV9y/OeX1v3eec8/u82nvQqnHCqK96P71rvLSqnN7fu3t9xew4 -8NP8b/UsRq9vzDf7HK92fvjP2y1f9X566rkWtznnnHPOOeecc87v8ph+xenv -d1m9V9Uzlsdr+BWt6xi3Z9tPFqfPw91+Re/5HM2/+z5t9Q+99Wn9zqz8T8tZ -VX6175XVvi+cfq5xztf3k5zzfT47Don5V733teoRfVU9s/Jnx8nZcVeNb/l3 -eRar2nnmq/qZrPxq55n/HqufO7ueC5xzzjnnnHPOOedP8dnv71n+Xs+i2jwV -/zdG20+vZ+Vn3qpfb1Q7z7yGX9HqD1vtLbtfeu+v0Xa+6v5adR5G6zman3Ne -x0f7Ac75577qub/Kq/VLs+ONauNS/k7P4inv16s8q0+163XKR/v/0fYw+l6c -lcM555xzzjnnnHPOz3pMv+LU+oRq82yn54Hj+T31fSSrT+aj7SHzLKpdL/4d -fsXqdr7bY3qV50vcj3O+z6v1S5x/g8f0Ks/fbP/e/KPHna1n3O/0OJC/07Oo -9n6debV+b7QfWH2es+ue1S+rz6fljPpoP3yqvXHOOeecc84555zz3z2mx3wx -njIftaqc0fOTeVafat9nnz4/nEW1eX7+Dm/1J1m+3n6glb+3Hz7Vb496tX6P -82/w3c9lzj/xmP60djv6nrLbV40HRn8v55U9i6e/d2derZ+s5rvnhU7Vs1o7 -5JxzzjnnnHPOOX+rx/SYL8aq7/un/Sn1rOJx+3Q7XOVZVPsuwPmIXzF73z39 -e3E1j9un68N5j596LvN3++y6iNHnV9xv9Lh3nYcs3+7naUxf9Vxbdd05v9Oz -qPb8beVb1T/c3R/yOd/9/litfXLOOeecc84555w/xVd9dzs1/8Pv9Va7qNo+ -V3kW1b4jcP6TX9G671bfL7v6h9bzKO63uz8c/W41el08T3kFP/X85e/20XHm -aDm7n6fVnpunnwujz8Fq4yX+XZ5FtefvqffxUa/2fPk2n31/yfKPevX2yTnn -nHPOOeecc37KR+fPR33Vd2p+j8ft0767fa7yLKp9d+Df7Vecvr92z9vvXn9y -6npl9Tv9/Z1/l1d7/vJ3eEz/tN1Wef6uOg+Zn+r/Z+vD+Z1+Ret+q/acHX3+ -tvLd7U95f/82H33/euv8Euecc84555xzzvkpj+kxX69n5fteXNtb1/l0+3z6 -d+Essvynv19w/nfsel6Mtv+sPpn7jv9v+TGd80+82nOWv8Nj+tP67bf258ar -vLK37qMYb52XiNtVfVU/yX/3mP5pe+u9Xk9vn5xzzjnnnHPOOee7PaZfsWp+ -JvOsPtXmOd/iretzuh1mPtquqnnr/Gf5Y7nVvoPw7/YrTt+nWT1W9ZPV3POU -V/Bqz1n+bo/prXY4mv/U+qXd/flofTh/orfibeOi0X7jKb5qfon/id3zeKPP -l7jf6fbGOeecc84555xzfspHv7+v+t4dt3cd99s8O69V2tuov/W7cExv5av2 -HYTzFX7F7H2d7T/aT+7uZ7Lys+Otys/5Dq/2POX3+Og4c/W6i9Hy435P82rP -a87v8NZ4L8bp+/RuHx0PP92rPQerPX9XvX/Fbc4555xzzjnnnHP+TI/pV+ye -X/o2j9tvcd+Ffw/f9TjP+5EYT3HrH3hlr3a/8LV+qn8eHd/O1j+Wd2pcPVr/ -ateR8x3eimx8EtOf7qP3e2v/p/rsc6Q3f3bc3c/Z0eOO5q/2vOOcc84555xz -zjnn93hMj/lijM4Xrcq/e33U7PqZ3vzZcZ/uvhf/nN7KV+07C+cjfsXq/jNu -V3nefVr/0edp1evIn+HVno98rY+OM1etv1rVb8+Oo+5+Lqzq/1fdp6ef+/yd -3rofY1R73lXzav1bNR/t33b3k1k9V4+re4/LOeecc84555xzzvnf/6767yJP -z49l3ltOVs9vc9+F5zyL0+s0+Hf6FbP3dZZv9rkQy2vV4+7+bbSc0f5h1fcd -67K+06s97/g9HtM/bVfV++dRn+2Hd52H1fXh/G+/onc8k8Wq/uRtPnqftvb/ -dh99HrXOf1ZOa/9Pyxn9vdoJ55xzzjnnnHPOOf//WDVf1Nq/N0bLWTW/F9NP -X5dqPvpdYPQ6vtVjem++Xj/9PYg/y6+I93X0uD3b/5+qzykfPQ+r+pNq3zH5 -PV7tecfv8d3jsdb+1X31eCkeZ/dzM8t/evzAa3mr/cRY1c75v/9mUaU/5L/7 -0987OOecc84555xzzjn/LT1GlXry39134bXeWg+Z5Y/lVvtOxM/6Fb33b5Y/ -81XtfPT74Gg9q/mq732+q/K/vdpzja91/eecz467Pu23V62/Nd77Tr9idPyW -RVaO8cOYx+3Z529WDuecc84555xzzjnnnPPv9FPz1d/mo99lsuhNj9cx7sff -4a32FvPt/r4c03vbYVZulX5yt4/2G763fqdXe67xtW5d1pzPnueY79R6j2rj -Cn6Pt8ZRMTz37/G43epnsvycc84555xzzjnnnHPOeY9bl3XWW+u4svyx3Grf -ofg9fkWV+3TVd7G3+mg/4Pvsd3q15xSf893rebL8b/Wn9IdZ/Vf3//ysX9F7 -n2Yx2k6y4/I13rp+VfpDzjnnnHPOOeecc845589y34XP+ux6laycbP/e/Ly2 -X9FqJ1XbeWu/0/3hbt+9vq7a900+59XuX36PW78659Xu39F1O7ymX9H7XM7i -dHvjYx63Z/NzzjnnnHPOOeecc845/06P6TF68/OansXsd4eYj9f0au1wtJ/h -P6dfUe17Jb/Hq92/fK2Prr/9tn519DxUu3+zes+2B37GW/ddFll77r3f+b0+ -et2r9JOcc84555xzzjnnnHPOn+Wr5qv5PT763/Vn4e85PNOvaN3XVdttzNdq -p1X6yVU+u96gtz3wd3i1+5fPeUz/9DmbHa9K/7bKV52fql5tXPFtfkXrurSi -d9x1ur3xMR/tzznnnHPOOeecc84555zzHvdd+B0++902Kyfbvzc/v8ertcNV -7SSWd7qfXOW7z0+175t8zqvdv3ytx/TZfmO0nKd7tft01X1dbVzxFF99P8ao -1n74Wo/b+mHOOeecc84555xzzjnnK3z3vDR/h2fh70XU8Cvecj/G9NP95G5f -1Q9X+77J13q1+5Tf49av/vl3dn14zFdtvcfp8UMVv+LT8zM73shitD5xP/5M -X9WuqvSfnHPOOeecc84555xzzs/6qflqXtNnv/Nm5cT9Vq3LyupT7Ttjte+b -VdtbzGe9QZ/H8vi7vdr9y9d6FqP9QNx+uz+lnxwddz3FR5/vcfvT89xbn1aM -trfRevJn+Wi7qtIfcs4555xzzjnnnHPOOX+WW5fFf0vvbVcxTv336Vn+VevE -qvoVrfNwyr9t/VXms+cnyx+Pw9/h1e5ffo9bv/q7V7tPd69LP+2x/qee+611 -X1lob/yn7dXXfbR8zjnnnHPOOeecc8455+/2mB7zZbGrfF7TY/qn7XDXcVf9 -3YysPqe/h/Z6tfZzur1V91V/h4S/26vdp/ysjz7v4vZbvFo/OVsf44cxz2LV -OJB/t396X8T00/0k55xzzjnnnHPOOeec87N+ar6af6e3/k5Clj+WW9Xj76r2 -XbXaeg/rB/6E78i8x6v15/ysW5f1599q/edsPe/2rJ7V2nkrPGf5J957v8y2 -2yr9JOecc84555xzzjnnnPOzXm0em7/DV38vzsqP+/kO+7tn9azWTuJ+p/vJ -Vb7qfuHf6dX6eX7WY3rrudOKKv3kqLf61bjfaT81Hoj1qdqes9j1nH1a++Fr -fHc7aR2Pc84555xzzjnnnHPO+Xd5TL9i9rtS6/gxnT/bV7WTuN3ro/W521vn -LTs/u/wp7SduP9VjjK5Dq9ae+Vmvdv/ymj7a/7eiWr/a69Zp/7x92lux67qP -jkP4d3rc5pxzzjnnnHPOOeecc84reUyP+fh3+eh3sVa+Ue+tz2mP9d7tsR6n -79+sPk/zGKvWK3L+t1fr53lN9/de/vxb7f6967kfj3v6+Z7Fqfbg+ftub7XT -1n2x6v5q5eOcc84555xzzjnnnHP+XT7735XH9FV/NyA7Ln+Wj34fucuzesb9 -Tq2v+Na/m1GlPxz11nWM+/kuzD/xavcvf4dXfV6f6p8/9Szevr46iyrtIfNq -/Tyf87jdO+4aHY/15s/qwznnnHPOOeecc8455/w7PaZfMfv3FmL6U74r8bUe -00+385bHeMt3pdbvzI6/2t/63co6K36nV+vn+bt9dBwY00/3z5lbdz3nrah2 -fT2Xv8tX3Xez90WV9s8555xzzjnnnHPOOef8WT47Tx7LHf0+EvPFdP5sf9rf -5Yhx1/em0fuo+n3XOl4VX/V3Ejjf4dX6c/5uX7WeIaZX6ed39eerzqf1V3Ne -rd/m93jcbt3vWf7ZfrK3PpxzzjnnnHPOOeecc86/02P6FU+ZD+fv8Jh++r5o -eYynrdeK5a+6jk9Zd7d7fSnnO7xav8353zHaf8byqj8Xen3V+blr3JVFlevS -Op9xP/6dPnrfrerfWvXgnHPOOeecc84555xzzn/z1esQesuJ+WI6/y5/2n+H -HqPqeq1Yzqrr1Sq3Wj+2qn/j/A6v1j9zvsNj+t3Pi5i++79T2L0uqxVPeV7H -/fg7PG7vun9776+nvXdwzjnnnHPOOeecc845f6fH9CtWzYfvrid/hz/tv1uP -cWpdVlbPVdclK3+3V/vOyPkOr9YPc77Dq62LuGu9dFaPGK3nbxanzlv2e+N+ -nP/tq8afT3tf4JxzzjnnnHPOOeecc85nfHQ+3HdqvsOrfpfJ6hn3q/r99+7z -1rq+cT/O3+TV+lXO7/RT6/wzX/W8nn3+ZnH37/Vc5j0+el/Pelaf0fzR4zbn -nHPOOeecc84555xzvtNjeswXY/Q71O75+dH683f7aDtp5VvlvfW86/vvrt+7 -+zsa52/yav0n55V993rs0XHF7LqyLE49lzn/zeN277hu1HuPO9o/jN6/2XE5 -55xzzjnnnHPOOeec8x5fvZ4q2z8ed7b8Xh89Luc9HtN33acxVn3/3f33Aayz -4vxzr9bvcf4N3orR5/XocUafszGdz3ncPp1/1bjuLs/Ge5/6qvt61bg0bnPO -Oeecc84555xzzjnnIx7TY74Yd627yMr/1Ed/7ypf/XcVeq/j7vx8zmN67/0b -Y/X336z8uB/nfJ+ver6M9j+nv49XeV5z3uOjUa2feZr39htx/1Z/uKpfWtWP -xfTe8WGvV3tfOzXeXvXc5JxzzjnnnHPOOeecc857fPX33Jj+1vn/mH7XdZk9 -P6P5e8tp1f/u6/JtPhqnv6ty3uOf9kurjhvzzT43d6/Lau0ffbSeu+uz+7i7 -xzm7y+FrffX6n09jVb9313g1xu71S1l9Vr0XVPMrevvtLH/mo8+jVjm72u3q -+723Pq36cc4555xzzjnnnHPOOecrPaZfcdf38VZ9e+uT7df7ezNv1S/6Xd87 -qvsVvedn1XqzVnx6v9zVbj+N1X8XIubja320/3lKObvXFax+vsT8p+ozetzM -d5ef+e7fu/s5fqqc3esHZusz+lzu9VXPzdXjlqw+V9x9nvm7/YrZ/u2ucfiu -+q/yrB6j54dzzjnnnHPOOeecc8453+Gr5/N3eVa/VetPsuOt+i65qv78HX5F -7/2V5W+15xinz8MVrfqP+u7zPOqz/cyn9Tm1vmhV+aPnbZXvbg+j5Z9eN/jp -827293563FXlz5bTO97Y3a+e7uerexar+70Yq55r/Dt9tP3E9E/7/0/rc2q8 -xznnnHPOOeecc84555w/0Xd/t139HTn7PVlkv3dXffh3+BWt9tOK2D6z/XrL -u+L0+anu2fmstr4i7t9qJ6vKOVX+6HFXlT973/U+T1u/K+a7ax1db7tddb04 -/8SzWDWui/la99Hu/o3zn/yKVjvf/RwcrWerfpxzzjnnnHPOOeecc845z9Ov -OLW+K6vPbD05/9uvmG2fcbvlq9afZHH6fPJ3+xWz/XbV9RIx3+z6q97zubr+ -1doJ5795Fqeey5mvuk9390v8Hp+9Xr0et1vXPcvPOeecc84555xzzjnnnHM+ -6qPfI1r5et13sZo+e712edye9VXtNotq15HzEb/i0/v30+O2+p9q543zk57F -U57Lo/3AKY/pxquf+RW97WFVO5x9vnx6XM4555xzzjnnnHPOOeecf4/H9Ct2 -f4/Ijpt5Vk6170pP8Suy8xnTT/loexj10XY4225jVGsPnFfyK/TznNdbf1Vt -Xcru5/hd44Te8Vgrf2+/uruc7Peeaj+j16Xa+jHOOeecc84555xzzjnnnNfx -mB7zZRH3n/1unh3v7t+7+vtR67zeVU6Wv9p6qmrtJPPR+2WVZ1Htuz/nnPOz -nsW3Pa+z+px6jj/dR89nq51k1+/Tep4+P6P3byx39LzFfKfvO84555xzzjnn -nHPOOef8m33Vd5C7vjtU897ztvq7Ff/Zs/PZyrfLR++jVZ5FtXUCnHPO13oW -1Z7X1daTvHVdED/r1d6P4jbnnHPOOeecc84555xzztd5TI/5PvVq3x34d3ir -nd51fz3le24W1dYVcM45/92zOP1cHvUqz/FRr/Z852d99f0ej2ddFuecc845 -55xzzjnnnHNe32N6zPepP+V7BH+Wx+2q/pR1WZlnUW0dAuecf5tnUe15/W3r -srLfVe35zu/x2fu6t1192/3FOeecc84555xzzjnnnD/Rd68bGT2udVn8bx9t -V9X86euyWuc/RrV1C5xz/nTPotrzerfH7ao+Wv9qz3c+5zG9t533jg9330ej -v4tzzjnnnHPOOeecc8455//tp74TrfoekdWz2ndDPudxu9UOs/zVfNV99BTP -oto6B845P+Wz/Wfc/63+9Od+5tZrfafH9Nn2MPo+lZXz1vuLc84555xzzjnn -nHPOOa/ss98FsnxZxHJG81f7bsjnPG7Ptoen+Oh357d6FqPfGTnn/Gl+RW// -+O3jn7j9Fl+1Po1/p69a//lt9x3nnHPOOeecc84555xzXsFj+hWr10tk5fDv -8qy9Zd7a/6k+eh6e7jG9N1+M0+srOOc86997w3jpd/+28UDmo+PwLKqNB57u -d63b/HTcaD0k55xzzjnnnHPOOeecc17HY3rMF2PVPH+r/JhuPdhZz2L2O3WV -9r/b/R2M3330+/Lq9aKcc77q+dWbv9rz/bQbP9zjMaqNB6p5TJ9tz6PlZPk5 -55xzzjnnnHPOOeecc85HPabHiPlWfb87/f2xureiSvt5iq/6Hv1tHtNn26d1 -XJzz1euyYmT5qz3fn+Kzz4Vv8d3r4oxPfk5vnbdW/phuXRbnnHPOOeecc845 -55xzznd7TI/5soj77/4+8haP52f3d7eYfrq9nfLR7878dx9dT2hdFud81Fvx -af/P+7x3XMd/99Hn6epxZsyf1XP0us/+rt39SXbc6K1+p0r74ZxzzjnnnHPO -Oeecc875c33VepVTfzfj9Pem3nrOns8sX5X28xT3dyfWekzvvS4xqq0D4Zzf -/xzP4vR6pG/31f0/X+O71yOtWk81W36vj45bRstvHY9zzjnnnHPOOeecc845 -57zXY3rMF2P3d5PZ48b9Vn0nmq1na7/T1/3bfHf75HOexem/s8E57/crWvdp -K3r7bb7W43bv89Q4p6ZnEfNn+61qP6vWj2Xlt467q3zOOeecc84555xzzjnn -nPNVHtNjvix2lT/6HXC2/Cxfq9xWffg9vup78Wj74XMe01v5ZtdbxnTOeb9f -0dtPZlFtPRL/3XePA3lNX3V9rd/jnHPOOeecc84555xzzjl/lq/6vuO/l3+3 -7/7uzM96Fqv/jgfn/D8xej/G/Xrvu7gfP+ut617luc8555xzzjnnnHPOOeec -c8455/ysW5f1LJ9dh5mVE/ertu6F80p+Rev+ivla92W1dUf833+zyJ6no/0z -55xzzjnnnHPOOeecc84555zzZ/vo92LrtZ7ls3/vbrT8mM75m7x1f8Twd66+ -w3vbSW//eno8wDnnnHPOOeecc84555xzzjnnfK2f+h7Na3prnV6WP5ZbbV0N -/06/Iuv3evuxVqzqV/mzvdV+qjz3Oeecc84555xzzjnnnHPOOeecn3V/F4v/ -lt7KN7peKyu/2jof/izP2lnWPlvR20/yd/toPzna73HOOeecc84555xzzjnn -nHPOOX+Hz66TaR0npvN3ekzvzRfD393in/hsu43ROm4sl3+39z43Z/tPzjnn -nHPOOeecc84555xzzjnnz/bW343J8mf5YvDv9Na6hSx/LNd6Ld7jve0sRm8/ -2WrncT/+HT7aDqs89znnnHPOOeecc84555xzzjnnnJ/1Vd+j+bt9dF1fy3vL -r7YuiP/uo+1n1Fuxqt/j/Ddvtccqz3fOOeecc84555xzzjnnnHPOOednffS7 -M+c9HtN72+eu+lj3dY/vbg+t+sTyOO/xuD3aP/X2J73H5ZxzzjnnnHPOOeec -c84555xzXtNj+hXZ9+KsnFXfrznv8Vb7zKL3vrAua62vuu5ZjLaTaut8+LM8 -bs/2D61223tczjnnnHPOOeecc84555xzzjnnNT2mX7FqXcrocTnv8dm/M5OV -E/PPeu99cZeP1j/zT+szen1bMdqP7T4//Dt9d/uvMk7gnHPOOeecc84555xz -zjnnnHO+1qt9p+b871j9///Kyo/7VVu/tOr8nLrfW1Gtf+O8x0fbf5XnPuec -c84555xzzjnnnHPOOeec87O+6ns05594TN/V/mNUW5e4en3a6P0+Wn4Wu/sl -zld6637szd/KxznnnHPOOeecc84555xzzjnn/Lt893dqznd4TP/0vugtf3c9 -V52f1etJPj0u5xU8bvc+77L9e/OvWlfJOeecc84555xzzjnnnHPOOef8rMf0 -K2b/P2i9+Ufrw3kFb7XnLGL7XrW+cfe6x+y+zmJ1f8L5SY/bvc+71n02+xwc -LYdzzjnnnHPOOeecc84555xzzvlZX/3/O4v5Rr9Tt/JxftJn1x9+Ws7udVmj -6692r2Optj6Hf6fH7dn2PHo/ZsflnHPOOeecc84555xzzjnnnHP+Dp/9rh3L -tS6LP9F3t+csVq1TGv29rfpk+2f9RpYvK7/3PFdbt8O/23vb7ar+J+53epzA -Oeecc84555xzzjnnnHPOOef8d1+9/iErJ6tHDM7v9NXrglrHz+7LVqxal9WK -Xf3MXeef8zs8brf6gdb9WGU8wDnnnHPOOeecc84555xzzjnn/KzvXpfC+Z2+ -al1Q3N7lMUb//4l31TPrN3rPp3VZ/E6P27PPwdb9V+U5zjnnnHPOOeecc845 -55xzzjnn/Fm++zt1Vg7nn/iq/+9e3O/u+/E/8X87kfTI - "], {{0, 0}, {401, 401}}, {0, 1}], Frame -> Automatic, - FrameLabel -> {None, None}, FrameTicks -> {{None, None}, {None, None}}, - GridLinesStyle -> Directive[ - GrayLevel[0.5, 0.4]], - Method -> { - "DefaultBoundaryStyle" -> Automatic, "DefaultPlotStyle" -> Automatic}], - FormBox[ - FormBox[ - TemplateBox[{"\"Divergent\"", - RowBox[{"-", "1"}], - RowBox[{"-", "\[ImaginaryI]"}], "\[ImaginaryI]", "1"}, "SwatchLegend", - DisplayFunction -> (FormBox[ - StyleBox[ - StyleBox[ - PaneBox[ - TagBox[ - GridBox[{{ - TagBox[ - GridBox[{{ - GraphicsBox[{ - Directive[ - EdgeForm[ - Directive[ - Opacity[0.3], - GrayLevel[0]]], - PointSize[0.5], - AbsoluteThickness[1.6], - RGBColor[0., 0., 0.]], - RectangleBox[{0, 0}, {10, 10}, "RoundingRadius" -> 0]}, - AspectRatio -> Full, ImageSize -> {10, 10}, - PlotRangePadding -> None, ImagePadding -> Automatic, - BaselinePosition -> (Scaled[0.1] -> Baseline)], #}, { - GraphicsBox[{ - Directive[ - EdgeForm[ - Directive[ - Opacity[0.3], - GrayLevel[0]]], - PointSize[0.5], - AbsoluteThickness[1.6], - RGBColor[1., 0., 0.]], - RectangleBox[{0, 0}, {10, 10}, "RoundingRadius" -> 0]}, - AspectRatio -> Full, ImageSize -> {10, 10}, - PlotRangePadding -> None, ImagePadding -> Automatic, - BaselinePosition -> (Scaled[0.1] -> Baseline)], #2}, { - GraphicsBox[{ - Directive[ - EdgeForm[ - Directive[ - Opacity[0.3], - GrayLevel[0]]], - PointSize[0.5], - AbsoluteThickness[1.6], - RGBColor[0.5, 1., 0.]], - RectangleBox[{0, 0}, {10, 10}, "RoundingRadius" -> 0]}, - AspectRatio -> Full, ImageSize -> {10, 10}, - PlotRangePadding -> None, ImagePadding -> Automatic, - BaselinePosition -> (Scaled[0.1] -> Baseline)], #3}, { - GraphicsBox[{ - Directive[ - EdgeForm[ - Directive[ - Opacity[0.3], - GrayLevel[0]]], - PointSize[0.5], - AbsoluteThickness[1.6], - RGBColor[0., 1., 1.]], - RectangleBox[{0, 0}, {10, 10}, "RoundingRadius" -> 0]}, - AspectRatio -> Full, ImageSize -> {10, 10}, - PlotRangePadding -> None, ImagePadding -> Automatic, - BaselinePosition -> (Scaled[0.1] -> Baseline)], #4}, { - GraphicsBox[{ - Directive[ - EdgeForm[ - Directive[ - Opacity[0.3], - GrayLevel[0]]], - PointSize[0.5], - AbsoluteThickness[1.6], - RGBColor[0.5, 0., 1.]], - RectangleBox[{0, 0}, {10, 10}, "RoundingRadius" -> 0]}, - AspectRatio -> Full, ImageSize -> {10, 10}, - PlotRangePadding -> None, ImagePadding -> Automatic, - BaselinePosition -> (Scaled[0.1] -> Baseline)], #5}}, - GridBoxAlignment -> { - "Columns" -> {Center, Left}, "Rows" -> {{Baseline}}}, - AutoDelete -> False, - GridBoxDividers -> { - "Columns" -> {{False}}, "Rows" -> {{False}}}, - GridBoxItemSize -> {"Columns" -> {{All}}, "Rows" -> {{All}}}, - GridBoxSpacings -> { - "Columns" -> {{0.5}}, "Rows" -> {{0.5}}}], "Grid"]}}, - GridBoxAlignment -> {"Columns" -> {{Left}}, "Rows" -> {{Top}}}, - AutoDelete -> False, - GridBoxItemSize -> { - "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, - GridBoxSpacings -> {"Columns" -> {{1}}, "Rows" -> {{0}}}], - "Grid"], Alignment -> Left, AppearanceElements -> None, - ImageMargins -> {{5, 5}, {5, 5}}, ImageSizeAction -> - "ResizeToFit"], LineIndent -> 0, StripOnInput -> False], { - FontFamily -> "Arial"}, Background -> Automatic, StripOnInput -> - False], TraditionalForm]& ), - InterpretationFunction :> (RowBox[{"SwatchLegend", "[", - RowBox[{ - RowBox[{"{", - RowBox[{ - RowBox[{"Directive", "[", - InterpretationBox[ - ButtonBox[ - TooltipBox[ - GraphicsBox[{{ - GrayLevel[0], - RectangleBox[{0, 0}]}, { - GrayLevel[0], - RectangleBox[{1, -1}]}, { - RGBColor[0., 0., 0.], - RectangleBox[{0, -1}, {2, 1}]}}, AspectRatio -> 1, Frame -> - True, FrameStyle -> RGBColor[0., 0., 0.], FrameTicks -> - None, PlotRangePadding -> None, ImageSize -> - Dynamic[{ - Automatic, 1.35 CurrentValue["FontCapHeight"]/ - AbsoluteCurrentValue[Magnification]}]], - "RGBColor[0., 0., 0.]"], Appearance -> None, - BaseStyle -> {}, BaselinePosition -> Baseline, - DefaultBaseStyle -> {}, ButtonFunction :> - With[{Typeset`box$ = EvaluationBox[]}, - If[ - Not[ - AbsoluteCurrentValue["Deployed"]], - SelectionMove[Typeset`box$, All, Expression]; - FrontEnd`Private`$ColorSelectorInitialAlpha = 1; - FrontEnd`Private`$ColorSelectorInitialColor = - RGBColor[0., 0., 0.]; - FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; - MathLink`CallFrontEnd[ - FrontEnd`AttachCell[Typeset`box$, - FrontEndResource["RGBColorValueSelector"], { - 0, {Left, Bottom}}, {Left, Top}, - "ClosingActions" -> { - "SelectionDeparture", "ParentChanged", - "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> - Automatic, Method -> "Preemptive"], - RGBColor[0., 0., 0.], Editable -> False, Selectable -> - False], "]"}], ",", - RowBox[{"Directive", "[", - InterpretationBox[ - ButtonBox[ - TooltipBox[ - GraphicsBox[{{ - GrayLevel[0], - RectangleBox[{0, 0}]}, { - GrayLevel[0], - RectangleBox[{1, -1}]}, { - RGBColor[1., 0., 0.], - RectangleBox[{0, -1}, {2, 1}]}}, AspectRatio -> 1, Frame -> - True, FrameStyle -> RGBColor[0.6666666666666667, 0., 0.], - FrameTicks -> None, PlotRangePadding -> None, ImageSize -> - Dynamic[{ - Automatic, 1.35 CurrentValue["FontCapHeight"]/ - AbsoluteCurrentValue[Magnification]}]], - "RGBColor[1., 0., 0.]"], Appearance -> None, - BaseStyle -> {}, BaselinePosition -> Baseline, - DefaultBaseStyle -> {}, ButtonFunction :> - With[{Typeset`box$ = EvaluationBox[]}, - If[ - Not[ - AbsoluteCurrentValue["Deployed"]], - SelectionMove[Typeset`box$, All, Expression]; - FrontEnd`Private`$ColorSelectorInitialAlpha = 1; - FrontEnd`Private`$ColorSelectorInitialColor = - RGBColor[1., 0., 0.]; - FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; - MathLink`CallFrontEnd[ - FrontEnd`AttachCell[Typeset`box$, - FrontEndResource["RGBColorValueSelector"], { - 0, {Left, Bottom}}, {Left, Top}, - "ClosingActions" -> { - "SelectionDeparture", "ParentChanged", - "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> - Automatic, Method -> "Preemptive"], - RGBColor[1., 0., 0.], Editable -> False, Selectable -> - False], "]"}], ",", - RowBox[{"Directive", "[", - InterpretationBox[ - ButtonBox[ - TooltipBox[ - GraphicsBox[{{ - GrayLevel[0], - RectangleBox[{0, 0}]}, { - GrayLevel[0], - RectangleBox[{1, -1}]}, { - RGBColor[0.5, 1., 0.], - RectangleBox[{0, -1}, {2, 1}]}}, AspectRatio -> 1, Frame -> - True, FrameStyle -> - RGBColor[0.33333333333333337`, 0.6666666666666667, 0.], - FrameTicks -> None, PlotRangePadding -> None, ImageSize -> - Dynamic[{ - Automatic, 1.35 CurrentValue["FontCapHeight"]/ - AbsoluteCurrentValue[Magnification]}]], - "RGBColor[0.5, 1., 0.]"], Appearance -> None, - BaseStyle -> {}, BaselinePosition -> Baseline, - DefaultBaseStyle -> {}, ButtonFunction :> - With[{Typeset`box$ = EvaluationBox[]}, - If[ - Not[ - AbsoluteCurrentValue["Deployed"]], - SelectionMove[Typeset`box$, All, Expression]; - FrontEnd`Private`$ColorSelectorInitialAlpha = 1; - FrontEnd`Private`$ColorSelectorInitialColor = - RGBColor[0.5, 1., 0.]; - FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; - MathLink`CallFrontEnd[ - FrontEnd`AttachCell[Typeset`box$, - FrontEndResource["RGBColorValueSelector"], { - 0, {Left, Bottom}}, {Left, Top}, - "ClosingActions" -> { - "SelectionDeparture", "ParentChanged", - "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> - Automatic, Method -> "Preemptive"], - RGBColor[0.5, 1., 0.], Editable -> False, Selectable -> - False], "]"}], ",", - RowBox[{"Directive", "[", - InterpretationBox[ - ButtonBox[ - TooltipBox[ - GraphicsBox[{{ - GrayLevel[0], - RectangleBox[{0, 0}]}, { - GrayLevel[0], - RectangleBox[{1, -1}]}, { - RGBColor[0., 1., 1.], - RectangleBox[{0, -1}, {2, 1}]}}, AspectRatio -> 1, Frame -> - True, FrameStyle -> - RGBColor[0., 0.6666666666666667, 0.6666666666666667], - FrameTicks -> None, PlotRangePadding -> None, ImageSize -> - Dynamic[{ - Automatic, 1.35 CurrentValue["FontCapHeight"]/ - AbsoluteCurrentValue[Magnification]}]], - "RGBColor[0., 1., 1.]"], Appearance -> None, - BaseStyle -> {}, BaselinePosition -> Baseline, - DefaultBaseStyle -> {}, ButtonFunction :> - With[{Typeset`box$ = EvaluationBox[]}, - If[ - Not[ - AbsoluteCurrentValue["Deployed"]], - SelectionMove[Typeset`box$, All, Expression]; - FrontEnd`Private`$ColorSelectorInitialAlpha = 1; - FrontEnd`Private`$ColorSelectorInitialColor = - RGBColor[0., 1., 1.]; - FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; - MathLink`CallFrontEnd[ - FrontEnd`AttachCell[Typeset`box$, - FrontEndResource["RGBColorValueSelector"], { - 0, {Left, Bottom}}, {Left, Top}, - "ClosingActions" -> { - "SelectionDeparture", "ParentChanged", - "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> - Automatic, Method -> "Preemptive"], - RGBColor[0., 1., 1.], Editable -> False, Selectable -> - False], "]"}], ",", - RowBox[{"Directive", "[", - InterpretationBox[ - ButtonBox[ - TooltipBox[ - GraphicsBox[{{ - GrayLevel[0], - RectangleBox[{0, 0}]}, { - GrayLevel[0], - RectangleBox[{1, -1}]}, { - RGBColor[0.5, 0., 1.], - RectangleBox[{0, -1}, {2, 1}]}}, AspectRatio -> 1, Frame -> - True, FrameStyle -> - RGBColor[0.33333333333333337`, 0., 0.6666666666666667], - FrameTicks -> None, PlotRangePadding -> None, ImageSize -> - Dynamic[{ - Automatic, 1.35 CurrentValue["FontCapHeight"]/ - AbsoluteCurrentValue[Magnification]}]], - "RGBColor[0.5, 0., 1.]"], Appearance -> None, - BaseStyle -> {}, BaselinePosition -> Baseline, - DefaultBaseStyle -> {}, ButtonFunction :> - With[{Typeset`box$ = EvaluationBox[]}, - If[ - Not[ - AbsoluteCurrentValue["Deployed"]], - SelectionMove[Typeset`box$, All, Expression]; - FrontEnd`Private`$ColorSelectorInitialAlpha = 1; - FrontEnd`Private`$ColorSelectorInitialColor = - RGBColor[0.5, 0., 1.]; - FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; - MathLink`CallFrontEnd[ - FrontEnd`AttachCell[Typeset`box$, - FrontEndResource["RGBColorValueSelector"], { - 0, {Left, Bottom}}, {Left, Top}, - "ClosingActions" -> { - "SelectionDeparture", "ParentChanged", - "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> - Automatic, Method -> "Preemptive"], - RGBColor[0.5, 0., 1.], Editable -> False, Selectable -> - False], "]"}]}], "}"}], ",", - RowBox[{"{", - RowBox[{#, ",", #2, ",", #3, ",", #4, ",", #5}], "}"}], ",", - RowBox[{"LegendMarkers", "\[Rule]", "Automatic"}], ",", - RowBox[{"LabelStyle", "\[Rule]", - RowBox[{"{", "}"}]}], ",", - RowBox[{"LegendLayout", "\[Rule]", "\"Column\""}]}], "]"}]& ), - Editable -> True], TraditionalForm], TraditionalForm]}, - "Legended", - DisplayFunction->(GridBox[{{ - TagBox[ - ItemBox[ - PaneBox[ - TagBox[#, "SkipImageSizeLevel"], Alignment -> {Center, Baseline}, - BaselinePosition -> Baseline], DefaultBaseStyle -> "Labeled"], - "SkipImageSizeLevel"], - ItemBox[#2, DefaultBaseStyle -> "LabeledLabel"]}}, - GridBoxAlignment -> {"Columns" -> {{Center}}, "Rows" -> {{Center}}}, - AutoDelete -> False, GridBoxItemSize -> Automatic, - BaselinePosition -> {1, 1}]& ), - Editable->True, - InterpretationFunction->(RowBox[{"Legended", "[", - RowBox[{#, ",", - RowBox[{"Placed", "[", - RowBox[{#2, ",", "After"}], "]"}]}], "]"}]& )]], "Output", - CellChangeTimes->{3.6641613068615923`*^9, 3.664161466270402*^9}] -}, Open ]], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"newtonplot", "[", - RowBox[{ - RowBox[{"Function", "[", - RowBox[{"x", ",", - RowBox[{ - SuperscriptBox["x", "5"], "-", "1"}]}], "]"}], ",", "2", ",", "401", - ",", "40", ",", "0.1"}], "]"}]], "Input", - CellChangeTimes->{{3.6595549152958674`*^9, 3.659554978383319*^9}, - 3.659555332709116*^9, {3.659555509656427*^9, 3.6595555271955185`*^9}, { - 3.659555597485504*^9, 3.659555613597739*^9}, {3.6595559120050316`*^9, - 3.659555925976593*^9}, {3.6595559620470605`*^9, 3.659555962328335*^9}, { - 3.6595560196305175`*^9, 3.659556025819849*^9}, 3.6641616469815435`*^9}], - -Cell[BoxData[ - GraphicsBox[RasterBox[CompressedData[" -1:eJzs/UmypcrWKNwdmVryt+T1QU2Qmcpqi2pSLbp1mvDVbhNkT/EjLsnEExyY -sMY0C4vNgOU4jpN4stf+P/7v/8//2//j//rPP//8v/4vf//975//3/+f/x3/ -87/++f/Ff/7P/znnnHPOeVb/s/Ap/vO/Il9+7t//f3qj8hOlH21XF9Px/Bse -F+/z/e3+DetDtP1XPSq34/KJy+tXvLX+9JVzdJ/hnHPOOeecc84555xzznN6 -tnFGzjnnnHOe05exnd+y//4Zf37f4/TX/meRz/V63up9847W6cbn613eWm95 -5K31Ldp+uf75djTnnHPOOeecc84555xzXuPZxvs455xzznlOn6L2PfPPIp0p -/hOmu95umV69R/vlxz79FJ3f48gyn+o675tHFJXfVz2qP1dvzznnnHPOOeec -c84555zn9GzjfZxzzjnn/Fn/s/Ap+t8/92O7vjQfbPLlfuo9Oi5+7MfnpXye -e89XNj++LuL6+k2f1/eW26j5n5xzzjnnnHPOOeecc855Zs82Dsg555xzzp/1 -ZdT+vcJWj/YXp7Ofnzjf++nmme/0Fp9+Wpd7afvldv++3qPj7Zu39jveV255 -2succ84555xzzjnnnHPO+RnPNg7IOeecc86f9T8Ln2Lc+2cp/f2I19e+30b7 -5X0+/RSd9+Xn//2875dDVG/f7vP66bivvm9wzjnnnHPOOeecc84552/0bOOA -nHPOOef8WZ8iep+clqf1x+ls0z32bfxZpL/eP3/K+877Ot1/w3r1Fo/KZ/n/ -Ot7u0f2hdXvOOeecc84555xzzjnn/NuebRyQc84555x/w5dx1d+D26bful8+ -1qPzGG2/n258Hp/1uB7ubxdfD+/wef26fLK0ZznnnHPOOeecc84555zzzJ5t -/I5zzjnnnL/L/yx8iva/f1ea37X/frvdbj8f/wb5i731uPixTz9F7ZTl59vP -19PeVj/f4vP66fj6rlPOOeecc84555xzzjnn/Dc927ge55xzzjn/TZ+i9j32 -zyKdKcrvw+sYNd+MH/v+dv9+zNcR1btsvg3zrzjnnHPOOeecc84555zz855t -PI5zzjnnnPP/9inOvt9G8Wex/RT55jV91f+pimzzr2q/Pyo6vjxeOi9Z2q2c -c84555xzzjnnnHPO+Rs927gb55xzzjnn/+1T1L7HLuPs35uL01n7n0V+1ut5 -5L3z8Zbpxuflan/XvKx5/XG5zpGl3co555xzzjnnnHPOOeecv9Gzjbtxzjnn -nHNe48s4O08men+Ot1/v989iv+v1vNWnn1rbO8t0/73cj/Mf19dcnqd9yjnn -nHPOOeecc84555x/ybONr3HOOeecc36nT7H//rzdrnfe17R+2k+Uzp+Frz/H -l/9H8evzsuLI0g7lnHPOOeecc84555xzzn/Bs42Lcc4555xznsH/LHyK9r+7 -V9p+8uXntm4e1/K4l9tt2z378SvzsuJyyNIO5ZxzzjnnnHPOOeecc85/wbON -f3HOOeecc/5Gn2L9vv1nsf0U8ft5afvldv8WPMrfdfOmnvLl8UXH/7V5WXE+ -s7Q3R3lUzsfXY339H3W9c84555xzzjnnnHPOOX+Xt/5e/Hp5Si/buBXnnHPO -Oec8nu8xee/7fBRRO+Krvr/dvzd5fF7Peum8Z2/Pro9v+lzv+V3vd1T9Oc5/ -/flqzT/nnHPOOeecc84555zzsf53ubX/+T8rX68ve7ZxKM4555xzzvl1vr8c -e9QeidJvbdc85fvb/TvY68v52OP9PtWejWK9fbb63+r3tNPz9EtwzjnnnHPO -Oeecc875V/3v8qh+3XrP1u/NOeecc845z+9TrNs10fZRe+cpXx/Hfnx/Xlbp -/K73m60eZqv/dfWtfB5L6WTpx+Ccc84555xzzjnnnPNnfV6/H+X+7eN0Wn2b -z2z925xzzjnnnPPv+RTr9sifxfZTZJmvlWde1tn2abb6wPeivr7l6vfgnHPO -Oeecc84555zz+721P/bPwqco/f7yenmOKJ/T8rQ+W78055xzzjnnnO8vxxG1 -p1q9bm/j52WV8tPaPl3nJ9v5/TWvq29n5/Xl6Q/hnHPOOeecc84555zzq/2e -ftrtflvTydZfzTnnnHPOOeetPkVt+6jV97f7t+Db/B17ezt0HTnPS3SetuWc -Lf+j6+fk5+pPnn4PzjnnnHPOOeecc845z+at/bd/Fj7FuO/RytZfzTnnnHPO -OedPedT+inx/u39Xvo715+aI2pXrGHW8x/moL4ervfe4srR/o/yU6lXt9q37 -5ZxzzjnnnHPOOeecc17n6/i73XX925xzzjnnnHP+VY8iak+VPtca63Zfa/5b -24O/5tNPZ8v5uP6U6kX5e7Cj7Vvb9aX0Oeecc84555xzzjnnPLvX9eef/3sW -63RG9QNnGwfhnHPOOeec3+9THLdbyt8HNTr9tvZatL//2exndLndHdFx8bE+ -/VTbD9Cb/nK7Ur9Be79Elv4TzjnnnHPOOeecc845j/zvctSP+p+Vr9fX+rx+ -2n+031H9rtnGgzjnnHPOOef1voxyO2L/c1M7Id4+S7vsac8Z0Xy5LL4tv6g+ -R/Xwam89rtb8t6a//7kove36dfrZriPOOeecc84555xzzjlf+9/lqH/1Pytf -r4+i3B8b7ffceM0c2caVOOecc84551tvbY+U2gVZ2ll3+X5E60ufuztG5zPL -fK1Wr6/nrdfL2OurXO/q6mlrOvmuO84555xzzjnnnHPOOW/zef1+1PeLrrf/ -+/+2HzjybONEnHPOOeec83o/jmi7+PO52k1Xt7Nay6e9PNvyc33UHf8Uo8sh -y7yseo/a0dNPtfWwtZ1+nM/68i/dN3Jdv5xzzjnnnHPOOeecc37eo37RPwuf -Ik4n2r7Vs40rcc4555xzzrc+RW27IPp8lM7bfHn80fp5u7NeNy9u/PcYt0Zv -+n3lv47z5dxbn6f1pfLP4fWR7brjnHPOOeecc84555zzr/q0fLx+3m4tfz9X -3z/POeecc845z+PR+/x6u3Vka9e0eXRcV/u8fpmveo/OV2u7bIq6duD4eYBR -vOM8jjq/0fkYfR77/95itH1pv5xzzjnnnHPOOeecc/5Nn9cvY+t/P9/a37tN -J9u4Euecc84553zU/I1s7Z2t980nudrn9evyrPWovTaqHTdFW7uyPp931duz -7eKx3lo/S1F7PeY7X23555xzzjnnnHPOOeec87f4vH4/7uuP5ZxzzjnnnOfx -6P1/uX5uX5TmXeRqB83Hc7x+e9znPNpvvfeer9p0lunVnt/6443yOaq9GeW/ -z6+uD+Pqz5j8b9O/63y1HRfnnHPOOeecc84555y/xef1+1Huj43SyTauxDnn -nHPOOa/31vf/5eeytHeiiNaP8nn9Ml/nPTovkffOk1mX5/H258vhqeOKvK/+ -v93n9aXr6bh86utP6Xzt5yfffYZzzjnnnHPOOeecc/673jfOMi9P6UXbZxs/ -4pxzzjnnnNd7FKXts7R3jj06zlEe52daXq7v9fX+tu2yUe210nG1lXPpuPrn -ZUXpHB9X/Xk83u/V9eopn9eXzldr/Wm9/0TpcM4555xzzjnnnHPO+bt8Xr+O -9fZ/l8/383POOeecc87z+BRn3/+jdKP0R3lfflo9zs+0vFxf71E5j/Kr60P0 -+VL6y3THlUPrfu+pP+/11vO+3q7uurj/vsE555xzzjnnnHPOOedjfV6/H74X -i3POOeeccz571C5YLy/bH9naQa3to8jj4z3rreXfel5az/ty/+fbm1E663y2 -5v9c+bTmcx2t9Se/99WH+nS+fT/hnHPOOeecc84555z/js/rl1Hvf9Pd9pdm -GyfinHPOOeecX+f7y3F7Ybl+bqdE27em05r+/v7+bU6/lE6tR+XcWj5Xt9dK -5TCmHbo+nvbyPPbz9bbvuH7N5/X752UbufpPOOecc84555xzzjnnfJxPy9P6 -1n74bONEnHPOOeec8/t9irPthSjdY6/f7zq9Ujvoz8KjfNTPF6rNZ7TfUd57 -ftfHVSqf9fGOLs+z3lo+x/lvrbdv93n9cX9DXG6t9xPOOeecc84555xzzjl/ -l8/rl9ud77fnnHPOOeecf8+nONu+WC8v02v17X6P81mK2vTr9xuVQzY/Pp7R -6d83/yry43reet5/zef1deW5vS767jOcc84555xzzjnnnHP+Xv+7XN9/nm2c -iHPOOeecc36dR+2Fq32dj978rD8/RXS8y/2U21OldJb5i7+v6SlvPe9RORwf -/zof/wb5e87HHu9XfV6/Ls/oemlNP0s/Ceecc84555xzzjnnnD/l2caJOOec -c8455/f7FPvtiGi7/1n5uHlE+5/ftm9K+e/b73XHm82j4z32dbr/Bvt72luP -69d8Xj+V23E9ydOPwTnnnHPOOeecc875Ge/rJ499Wj5e358+v8Pj8zWtnz73 -Z1F/5vXZxn0455xzzjnnPPIprmof8b++v92/n/Xj+hbVq7f7vP6acsvWf8I5 -55xzzjnnnHPO+V8f1a/V27+9jr504nSzlPPb/anzyznnnHPOOedP+RT77aZo -u/9Z+Xo787XWvvx/G7Xlv7+/f8Pyf8r7yuHXfF4/lVvfdco555xzzjnnnHPO -+T0+ul96HX8W20+x/ty2fzLK/3r7KP3Io/yX8pnlfL3Np+VpfbbxFM4555xz -zjmPfIq2dtD288c+r1+3i9fe2v79qk8/1bZD3+KlerifTmt9y+bz+lI9n37K -1u/BOeecc84555xzzr/t0/JyfX06Ub/fn4XP+2lNZ3+5HPv5L6VT//cQ97ff -xj399u/3/eM/X38455xzzjnn/GrfX55jTDs9Tn9/+236UTvr1/z4PLb3n2Tx -1nZ0dPzv8tb+pXz9IZxzzjnnnHPOOef83f53OeqX+8/K1+u30Zb+vLz8XMlr -8/MWn9evj3ddnvoP/7uc6vvPOeecc8455/wtPkXUPjqO8d+nFLW/fs2nn+7p -97jf9+tbVO/yeGu9Xa5/vn+Dc84555xzzjnnnH/J5/X70f/3C6J0jvfLj31e -vyzPOHLVt/Me1bds4yacc84555xz3urH7ev/rHy9Pgp/r/Aq39+u1O8Rbf8W -b62HeTy67qbI0u/BOeecc84555xzzr/k8/opWvuNo/T/LLafYvu5UjrHn+OR -f7W/sXX8Its4C+ecc84555xHPkVt+7q1HRTt79jX+/M9WiX/pyqyzLNq9db6 -c7W390dl6d/gnHPOOeecc84559/2v8v1/belfuNluvHv2/ZtH++Pt3lr/382 -bx1fyDbOcu76+s5xcc4555xzzu/3KfbbX9vtjrev72f4NV/+v42oPJfp/vuY -H9ef6Lie8nn9+riy9GNwzjnnnHPOOeec81/2ef0Urf26fxY+Rfv3/L+r3+97 -3tdvn6feRvUt2zhI77jJOrLlk3POOeecc57fp2htl+1//n9W6/PNj8rm0Xlp -7T+52o/rT1Qv7vfR9ZxzzjnnnHPOOeec8zu8tV/3z8KnaJ+Xtb8++hwf7aXz -laV+RvnPNt4x6jrKlk/OOeecc875e721nX68/fpz6yi391v7E37N97f793Lv -O+9X+zafpe1z9WNwzjnnnHPOOeecc/7fPq+fIurXjeLPYvsp1p+7qj9tm06U -n9Z+7ON8vt3jcm7d/mqflqf12cY7+sZBrqu3nHPOOeeccx75/nJp+952XDmi -/Ubto1/z/e3+Heat7dZRXjreXP1mnHPOOeecc84555zf4639pevt1lGbfmv/ -cGn7yafP9eW//rj60rnfj8vhuXq4jmzjGq31pzWdbMfLOeecc845/x1vbSdG -6ewvxx7t99d8f7t/h/nY/pDz53e5/vl+MM4555xzzjnnnHP+LV/H3+1a++Xi -9Pa3j+Ns/qNo7e897tedt9s/rrd6fJzPeJ7rIts4RZT/1nreWv8555xzzjnn -/C3e195fL4/b71t8fTz78db+hzif2frr+voxyt/7fZxOXG7ZjpdzzjnnnHPO -Oec8i4/th8nmrVGffqncJl+W33u9tV/6au+rt6O8Pj9Xe5TPq/v/s42ncM45 -55xzznk2j9pT6+VSu3tUO+5qj45rrK/3E+0/9lL+c/XL1ed/1Pk6zk8cY/ob -Oeecc84555xzzt/u8/opWvt/RvmfxX6j7fq/376uH+ns7wnGXpv/t/tT9acU -d19fV/fnHx/n/f3t2cY7OOecc8455/wtvr88x7q92dp/8lQ7Mcp/lM8+j8qt -1e/vf3t7+/o4spU/55xzzjnnnHPOeT6flqf1f/+P+tnWn6vtt+nvf4vyU9rv -/vFG+Yujtjzvzefz87Ii7+t/HuXXXRc5+j+f72/P1j/MOeecc84557/mU5zt -57naW/N57NvjP/Y4/TH9Btv9ZqsnT9XDUf0JUfqcc84555xzzjnn2bzUvzH5 -8nOxR/ttS2ebjz+LfK4/V9+fc5zP6Pi3+WzNz1Me5T+rt52XVh93Ha3jrv7M -/ePJU9+y9QNzzjnnnHPOOT/2bO3K/e3a+5GO/br+NH7s+8vrqD2/efpXOeec -c84555xzzlu9tb+udftov9H2pXTWcdz/01o+0efz9FuO8v3ttuW0H1fN14r2 -O8rr60Nr/e/rn4zyl6eeXF0OnHPOOeecc87f5VGM7ZeIPMpHnL+z/WN8rE9R -2y93vD3nnHPOOeecc855fj/uJ1kv18b475u6uv8n2m90XFH6o443my+Pb1uv -lp//96SvI6qH7fXz7HVxdX17i2fr1+Wcc84555xz/qxPcbb9u79d1A8RfS7O -z+jj3d9f/fGOao9H+ctWH1rLc9R+Oeecc84555xzzsf6vH4ZW6/rDynPRxqV -/2z9Ra35PE73un65bL78P4rx3691nJ/4/K7jLf2xo/wt/bqcc84555xzzr/h -pfZ7a5ztX8rWTr+n32a9XdzvN/r81vZnRulH2x+nzznnnHPOOeecc17vff0S -kc/rp/38WaQ/r2/th4nSz9Yf+BbfX54jqj+1EZ33UV6Xi7N/vyCO9edH1fOr -y62uPMvfP9Z6nUae7brgnHPOOeec87d7a7uvtP0z/Vfr/LaXw9XR1+7e5m/U -+crm6+NcR23/ZF8/RrT/9vLP0n/LOeecc84555zz93pd/1Xt91xtP/9nsf16 -u+322foz+T0eRVR/jutVXP+Xn4/Wl6P2OmrtVxzl+9vVHu+ovyNpXhbnnHPO -Oeec1/oUo9qzWfqdnvZ74r529Ghfl9tT/RKl62KdzvH28ef3PV+95Zxzzjnn -nHPO+fd8Wp7W1/WHzBFt/2fh836y9X/yd3kUUX0rfe5stNb/Vq/LRZ5+3VrP -Vq8455xzzjnn/GqfYr9/Zrvd8fbv8Wn5eP28XZs/FaPz/3w7/djr62ep/h/v -d7tdrZf6VbJdF5xzzjnnnHPOOf91n9cvtzvfv5GtX5Qf+zLO/37ufjrX1ZOn -onS9HEeWftfrPFs955xzzjnnnPOrfX95jiz9Qsft2Sj/5/243ObP7bc3x0cp -P2f72e7xef3T/QBRzsaWM+ecc84555xzzvlTPq9fRuTz+im9v/9v++Wy9XP+ -mk+Rq7495++KbP2i5mVxzjnnnHPOea239pMsP/d8O/o4n9t8j/V5fW/7sbf8 -a/MzOv1r+/GuK//IR/UTRun3pRMfb5brjnPOOeecc84559/zv8vbfpL15/bX -zxGlk61f9Kt+fB7z1LfWfrbSdm3+lhh1vKPLbfz3mLlvcM4555xzzt/uyyi3 -m7L58XHFxznG5/Xrcqv11nZlFDnSOVt/njtfY+pn/X5H9Sfcc1ycc84555xz -zjnn13m2/tKv+v7yHKPO77R8vL6Un1Hems+SZ4+nyvl+z3Z9cc4555xzznnk -fxY+xX82y1M7NEpnmd7d/TnbfIz1eX1bO708Dyfy3nLez0/9cZXqQ22/WSmf -belcfX7vrz+j6kPvdZ2l35VzzjnnnHPOOedv8Xn9fvh7hVk8Kv/1dutoO+/X -+XH+5+Vlfnu9db93R+v5ir0t/fye7brjnHPOOeec81ZfRpbv4YnzN8bn9WPa -9bXznbb5KZ2X4/Z1/7ys1vz31qtc5z1/vTouz3i/ufpvOeecc84555xz/kZv -7T/8s9h+Xp+t//PXfBn9/ZZ9Hte3dX5GeXRcrfXz6hidn7uv99J2V3m264tz -zjnnnHPOI19GfTv3mX6hON+1ftzPMC8/3d4vna+29nJUPvcfVyk/V533Z30b -dfUwinK/R2v94ZxzzjnnnHPOOW/1v8tx/8Z6+2z9om/3KdrO4/bzy6j/Xv31 -9ld7lJ9WH1vOpfKM4r55jMf5H+fRcV7l2a5HzjnnnHPOOY/8uH39n5Wv18/R -2g8TeZTPdbq17b/j7cZ/f1HOfoC4fNbHFXlf/YnTbzsvrcf1Fp/Xl8p5iiz9 -rpxzzjnnnHPOOf81n9evY719tv7Pt/ufhU9Rmhe3PV9j+xvX+fg3yF/Jo3zU -H2/kY/td68vn+Lys833f7/lGcdV94zg/Uf7qPdt1yjnnnHPOOeej/Dii7eLP -t7XX5vTW7fp1Oq3t31Z/e/9A6/H2+Xa/0XG19iO93UfVk2V6WfppOeecc845 -55xz/iX/u3xdf9eveVRuy/Xr8/Kf1fbbz0Xrp/RK+63dvjX/relcXd+i443y -v/+5+fOl9ev01/7U9TXFM/eZuNxqt892XXPOOeecc8555Muo/x6q46ht78fp -H+fj7PdpX7ff3v6KdfrR+eo73vrjutrv6Xd6i8/rS+VTun6z9NNyzjnnnHPO -OefX+bx+GZFny//bfVvOf7er78fgfb6M8f2Tb/Fz5baNq+8/0/pleltvLYdo -T6PrW5b7zDLK/eecc84555xzns33l+PoayeW0m+d5xPlq7/dl62foZT/5eej -9eu4b/5Vaz776s/bvXR+o/B3DznnnHPOOeecZ/R5/TLqfVS/VrT9n4VvP5+r -PPP5tLxcv/Vs/Z/P9ru2lmf0+Tz9llf7XeW/9uP7Q+v9bX2c8fWSs9zi48py -X8p2vXPOOeecc855q09R2z5t9f3tSvNMovxt02893mz9D73lWds+3U837h+4 -16OonYf2Fp/Xl/phpp+y9HtwzjnnnHPOOef/7ef6H6Ko70+I8rneflS/UGm/ -3/T4vK4lWz/n1f2lkbfWK/7Xrz4vx15fz/ePp3y/WvtT5fbUdTHKs90fOOec -c8455/wtPkVbu3iK3/0e73+CKJXzMt32foNR3tfPGR/PO3xeX+ofLqWTq5+W -c84555xzzvm7fF6/jMi36UTt2T8Lj9Lt//7tp7yvX+u93nq82fobn+q3jOo/ -/+v3nJdR9734fjitr7uPbX1UeUY5e/a6uP++xDnnnHPOOee8Ltray1Pc187N -5sflfL7cnvK+43qLz+vr+pnz9MdyzjnnnHPOOX+jz+uniNrdfxY+xfrz75tP -Nda35VxXbuV0svryOL/79wpb63+0Pf/r+9v9uyrv+uuott6O7Vesvy5a/ery -v+u6uPu+lO2+wTnnnHPOOefZfIqz/YeldKblUn9Rtv6K0f0eV/UbXO3HxxXV -h2y+jWz9GJxzzjnnnHPOf8On5Wl9b3/OOp2S7+cnTvdr/mdRntvtstWTq+pP -Nt9fXof5V1f5/nbx/eQ4nauv6/p8tuZ/bHlu85+zn/+8Z7ufcM4555xzzvlb -fIox7bVtutF+s/VLjO7fqO1Py+bH9WR7frN5X/7z9btyzjnnnHPOOf+GT8vT -+tZ+mz8Ln9OL0t9fH32OryNL/YnOe7Z+xd5+yOVxmn/V6/8E0doPXEp/v962 -X1/L/ZXuV9H2rR4d/6jy36Z/z3V0/30s2/2Ec84555xzzrP52H68KLbbZ+uv -yNFP8vz8qz6P6sP93lv+WfpXOeecc84555z/pj/bn8OPyzNK57n6s45s/Y2l -/E7rp+OLyp/3+fRTW706f76O60Mpnv/906vPy9PXXZbnF+ecc84555z/mk+x -bk+N7QfY7m//87/XD9N7vpbpXt9f0Xd+n/J5fV3+8/TDc84555xzzjnn/+1R -/8CfhU/xn81ytJ91HG/3ne/THuvP1ZNpuXRenu1v3JZbVG95n7eWf11/YxRZ -fj/0Oh91XqL0n7ruprj7OcU555xzzjnnfKwvo7X9u411+y5bv8fVvr9dvv6K -/fxGx3G9l8ozS78655xzzjnnnHNe41E/zJ+FT/GfzXbrqE2/lM60fplefFzr -7Y/zH6UT5edqn9fXHu+1vs3ns/2B2/xE55f/9XP9rutorbft9fyt3lr+o87v -P0E8dT0uj+++5xTnnHPOOeec87G+jHI/VZROtn6SbN5b/td6nI9rvTU/efrV -Oeecc84555xn9nn9crttOz3afqxv81nXP7D+fGv+5+2W+8/jx+Vw3Xk5Ls/r -6ufT/X61+YzK59d8VP/n/nal+r/dnv/1q8/78v857rlO658jozzbOAXnnHPO -Oeec/5ovo769XNufE+03Wz/M2HZ93C5efv6u/o34fF/lpfqWqz+fc84555xz -zvlb/O9y1B7/z8rX6/v9eL/z8pTfuu23sV8Opc89P4+i19uOt9Wvrp/b/V7d -jxfVK/7Xp5/W56u1n6o1/f38PX99ZffW+/nYenLd9Rulv5+/0v3wvGcbj+Cc -c84555xzfuxTjOkvnZdL7fGv+v52d/WHbM9rn8f7zdJvzznnnHPOOef8nT4t -L9dHvv7cvN2+t6a/9b//b9v7x/0q2/y0phNtv1x/tjyf8tbz2H7ex9bPOZ7q -l4vqw9t9f7va76Fax3a7unSyXBff81H3vb778DY/o6/TqBzufp5mG1/gnHPO -Oeeccz7Wp6htDy6j/3u6svnxccbHe63H5V7rreedc84555xzzjmv8ai9+Wfh -U/xns13d9vPycv/biNLpaxdvt4vyE+33aj8+nt7yHOXriMqzPf+19bO1PvT2 -py339/7fZ9w/vlI51F8v/F3eej32PRei/NTfN6J0RvWTX+3Zxgs455xzzjnn -nD/rU7S2N6flt/VTlcphfVxjPd7fWkafr2s9Oq75+EaXT+TvKjfOOeecc845 -f4+v4+9223Z3a/pROpHXteuj/M77jdJpzc9bfH+7fzs9Kvf68zFFbT0Z3Q+2 -Pq5s56v3/PZd18/PF+L3+n59KN3v+++fUfp96UTHVZ//qz1b/z/nnHPOOeec -83f5qH6/rP1X63z2+Tq9aD+xR+U/xbX9CVE+8/czHOe//rg455xzzjnn/Dd9 -Xr+Mrf/9fNS+jtKZt1vuf+tXtxOj/I/qD8nm+9vF5R9573k/Wz/7znuUjzzn -pbXe1h1vnvk//E1ef/+fovY6jdKpu1/15+cpz9ZfyjnnnHPOOef8294X288/ -2w+2/ny5f+Ns//ZxOvoHWr2vX/r+88I555xzzjnn9/i8fhmRz+un9P7+396+ -Xufn7e3H4+2vK+erPcrPsbcfb93nx53Hu8qn7bqL0+E8s9dev6V45nk3Rf1x -HR/v+HnFnHPOOeecc875nT5Fbbv42X7IKLbHUwr9AGN8bD8q55xzzjnnnOf3 -Uvt68uXnIt9+/s8i/flz2dqDv+at5yXaPvL97db1Zx1R/auvt6PyX3dc5Xzu -p1u6jjh/s8/Rep+J0m+9Hu/qf17nc5Kz9yvOOeecc8455/xLvozxv2capT/J -fn9dlL/W/vZtOtnK/y2+jLvPI+ecc84555zf73+XS+3cKIxT/7rX1Z/a+Vrb -aN1v5L39AJx/z+dovY76rq/4eovytc7/qHwe36+2+Wk93tbtOeecc84555zz -X/a+9vt6u1J/yPpzc2Tpx362f+a6ctjPd/m8rLcvpZ9lnIVzzjnnnHPO/zmM -7fq/n4/av9vts7Xr3+JT1J6vu9qhtfuta3dfF8f5zzYfhvOxXlv/o/v58X1+ -m87Y+1t0vyg/r0rl03q8ffex+nxme+5wzjnnnHPOOeeZPYrWfozadEv5ae1n -eLv/cxjb9a3ltp+P+nGM2v4xzjnnnHPOOb/b69q55XHtbO30t/j+8hxZ6kmv -fy2i+h/58v8ovajc8szz4W/ybX3r7QerfV6UniNt9434ObTv8/q7yrm13KL8 -Z3secc4555xzzjn/hve1W/P5tDytby2HUdHaHzgqP63n9ylf5683//v7i/u7 -vlLPOeecc84559/343bienn6fH17k+/Fdb+/s59+nI8x/pa4uhyu8+i6W64v -ne/tfqbPtV7XdfvJMk8pj4/tjzq/3/3l/vvbmPvY6PvSffPfpqg9rmzPKc45 -55xzzjnnOb0UWfqZn/Z74vn+pVY/169Y/3cDj/Mzx3F+2s9ntnrIOeecc845 -5/s+r19ut20fZeuXyOZRua23W0fteRnrpeifn3BcDuej1A9QW//7zteveVye -62i9Lkr1ZL3f4/O+zVdff1F9fa6r5+V5mK3pn8vPOtrP+93Po1F+zX2pfx5s -tucX55xzzjnnnPN7fFR/Qlbfj2h9q5f2W54X1BvX9mP0Htfz39Nel842stVb -zjnnnHPOOR/lURxv3/990fzYl3H2+1iidM77n0X+1+u3Xjre/fyX62kp+vZb -78fpx+eV/411eUb1J0qn7jpa76++3rbm/1z/an/6d11f1z6PstXPqBxb60m9 -Z3secc4555xzzjkf66P6H572abmu37LVS3H190HNMbaf86n+kHn9Xf3DpfI5 -m87Y8uecc84555zz53xantZn68fI5lPUluexb9PtS6fe/yyOa72+3seWW305 -3JOf8x7l8/h4+Xp93fUSp1N7vo7ryfn0W+tta/rrdNf3gbbjjdKJ8ld/3yjt -71c823ONc84555xzznmfL+N93xd0fFzxcdZ6b7ld26/Sm8/67fv6c9ZxvvzX -60vlPNrX+322/5lzzjnnnHPOr/dpebm+Pp1s/R539ascl2cUZ3+fqLSf8jy6 -aL+Rt6Y/qt+jLup/D24dWdvv0XHyJ31ef67+n09/irb7+fnj7Ut/VH5+x7M9 -7zjnnHPOOeec9/lxP9V/Vj7HM/3DUX7Oe2t/Y+Sj+i2X+Wrtn8zy+6HXna8+ -r89n63kcW87ZrjvOOeecc84zePt78rR8vL6cDt+PbP0bz/afbMst2v4tvr/d -6PlX7df7Oj+Rtx5v73FFcdX12NefwN/irfeZZ+vDvL7uucFbPdtzkHPOOeec -c875sS/j/Pfhv7t/qbXffuuj+vdK+z3bP3lXP+SY/tVs3l5PasuhtZ+Nc845 -55zzX/BR7d/S+/a0PO0/2j7yse2jPN7abs3W7zG2/yQ6/m05RNu31qunPDqu -nP0D23xGfq4c5hhdf66+rpfHGddPznl+z/Z85JxzzjnnnHPe58f9Uf9Z+RxX -9SP15SfO5zLduL/u2Lfpj+q3L/UHtvVb1h9Xaz4jP87nqH7XPD62fErncRtZ -xms455xzzjk/Px+gvj3Y1246n5/S9uv0x7ab8pzHqPyz9W+M8qh8WuvnW/zq -foDjdKLrq/66i3zU/eSefpLr/Ph4W8ufc36nZ3s+cs4555xzzjnv81J/1LRc -6meOfLmf2n657X6j7frSqfer+/GO810/LtB6HnuPa51OX37i8/Q1b+33Xn7u -+f5bzjnnnHPOW3xaLrU7ou2PPc97fuSj2stPebb+ilEeHW9UP7/qrf1CY+tt -6/VViuf7c66un6O87z6c577K+S97tucp55xzzjnnnPM+n2JMv/o23d78rPd7 -vF20fa/P8VT/53J9uT+zrzxjP9tvX8rHN31eX7pe+sotz3gN55xzzjn/TW99 -v21tBx23j7K9/9d7X7sgz3nP1o/RWm6t9e3XfPn/OrZ+Tz/AvH55Put9VPk8 -3S939/08yh/n/H7P9pzlnHPOOeecc97nU5ztb19vt98/to39/qIof9v8HO93 -m06U/6v7Oceer7jc932dv/b+zMhL56X2/L7dx57HPOMvnHPOOeec13jr+/Co -9t3bva89lf/8ZuvH+DUfVZ5v6Zc4Pp48/Tlvv973lznnV3q25y/nnHPOOeec -8z7fXx7Xf9Xb7xTF2X6kbP2l6/yVom/84jnfP1/R8X7Pj6+7+XN15cY555xz -znlOb22HRu2a1nbrt/258zstT+uf7a+oz2dUr37N97drb6ePvU7j/Jz1q8vz -6Xp+9/V+7Nnuk5x/27ONI3DOOeecc845v8dH9VMt0+vvXz1OP9rfNp1svszv -Vf1p1/lvjrPM60vlcPz5PONrnHPOOeecn/HWduV6u3Ws06973659P9/uty+f -97c7Jhl1HtfpP9X/EOUnOi+/5vvbReezvZzf6XOMKuex9bn+/na199W3p+57 -nP+mZxsX4JxzzjnnnHOe06do6y/afn4Z3++P7S3nZbpZ+kW//z1ax+cluh62 -5325/vlxNM4555xz/g3ve/8c9f68Tb+1vVPK/7R8V7um9f1/rMdxVT25q99g -/3jytNOv9uX/22i9rpfbPd8PcK1vy62v/M/fr3r7bd7xvLj6/sY5/+/I1s/P -Oeecc8455zynT1HbrxV9fr2+1C+XrX/1rn7a5eef6xft6x+OjustPq+vG6/J -0+/KOeecc86/5K3thevehyMf1a5s3e9T3tf+bS//s/Xnrv6Byaf9/1lsv17/ -Xl/+H0X5e5/qtv8Vry/PvvO1TeepfrOr/Z5+PM75Gc/Wz88555xzzjnn/Fkv -9WtdO45Q//t9b/GonKPj3U/36f7S2NvO+1t8Xl83/pJt/I5zzjnnnL/dW9tx -+8vrGPV7GduobdfUpV9+D29N5x4f1x65u/60tnei8n+L72/X286N0+FtXqqH -6+1H3U96r4vouLI8R6Ly6XuOcM7PeLb+f84555xzzjnnz/r+8hyt/ULTcqm/ -OspPtv7bUX5c/q3leb8f939G9Se/l/p1s/Svcs4555zz3/RR7b572i/Re/h6 -f9d/z1Ip/+v8jPX69khvOzFLPXnKo3L4pxDH2z/f7v6615Z/a/1s3W9fOnH9 -uvu5MPa+V3+/4pyff75zzjnnnHPOOef/7Vf3e2fr1322Pzkqr/Xnn+9H3ff4 -fOfy+vGLaHvOOeecc86v8/b32+Mot79a24ml/By3E/K2B1vzf+zXtV8iv7q9 -f0/5R+2x+Hwt0326Xcz7vL7+t/Y7tW7fmp+s3nZcnPMrPFs/P+ecc84555zz -b/hxlLbr/73It3tdeebvL23b/imf16+PN1s/Kuecc845/7LH76u125faEet0 -nmonRu2gKJ+l7feP8/523P52ve2p+vowqvzvKp/W+r9M9+n2L3/Kj+tVqf7U -R5bnwrP3Gc75FZ6t355zzjnnnHPO+Td8itp+p9b0n+pPztmfn8eP68O2fjzl -o+ot55xzzjnnLT4tT+tb2wXR9tnag2/3KO5p38X5WG+XI/9RPN8+5d/w1npb -d13cd18tHW/tc6Rvv3E+OOf3ebb3HM4555xzzjnn3/DWfrPWfuCr95vNo+Pd -//zT/ahx/nL5vL63X5RzzjnnnPPzHr+v1qaTrT3I/0bUvlsv77ez+uN4v3F9 -O84P521+db9NqZ+k9f68zn9rfqJ8HOev9/5w9vvEOOd3erb3E84555xzzjnn -3/Yojrcvfb48r2ZUv99THpXPqH68Ud53Hq/2OHKNx3HOOeec8297e7tm7dna -d9l8iiznvbVdfE08Pz+H/4JH1+H5fo+x1/v5+3Dkddd77e+FxZ/nnL/Ps70v -cc4555xzzjnn/+2t/XXr7Ur9Y639hNm8tRzu8Tgfd3tUbsv1z4/XcM4555zz -b3tre2S9XGrXfNX3l+c4e15ay/84P61+dYzKZ33+z7Vba6P0+SzzlH7Nt+el -dH3V3idL0XYf6K3n/eXTWg59+eScZ/Zs71ecc84555xzzvkZn6Ktvz36/Hb7 -t/j+dtf3xx6fl2053+N5xuP6vL5+Rtuvt6sbV4q2jz1XuXHOOeecZ/PSe9cc -2dpZ2dp3JZ+W69576/1c++u6GFMP3+7n21N97e7z+Smls8xHXJ9L11Ht9mPL -pxTXtSv307+6vtXvN2f/Cef8Cs/2fsU555xzzjnnnJ/xKfrGQb7z/VrRcV3t -x+clKv9Rnm3cbdQ8q3m51F99z/W1zX/peqzNP+ecc875V7wt6t+vfs33l3u9 -FNd9H06Uztn2Qt17+Db66nPe70ke5a39DL39FbX7Pa5XcbrrfJbq56jjqq0/ -vemcbXdzzvlTnu39inPOOeecc845z+BTtPVLbz3q/3zKRx1Xn2/Lt8+zjbtF -9WZb/tnq+T3XxVvOI+ecc8756HlZ/b/X8Gu+v1yalzIvj26/tLazxr5XR+/P -59sdx+nX1/O+9PkUZ9ubo9Lpbfe15nNaX7rvlfbblk628845/2XP9t7FOeec -c84555xn9tK4QG1/dWs//9W+v12+eVmt5T/Wt/nJVj+zXhfT8rqejBnfyTcO -yznnnH/H699/lvG735M5qr3wdo+Od10upXbEcXnWvx+OapeNLYf299tl/uLy -GX2+znrfez6/x+f15667eu9r12crN845r/ds72mcc84555xzzvkv+P7yc/O1 -1vnYj+fnZU2RZfyR93lf/XyqPnDOOeeZvf59sjWduuj/fqEoP335z+Ot7z/Z -3tP62jXn62c2H1sOvdfd+L+feM9xjSoHzjnn/Bue7f2Nc84555xzzjn/ZW8d -F7h3vtZ35mVlO+9v9yj60imlW18Ps4zPcs4551f4qPkYfduPeq+rf98r5T/L -eYnyl+39rfd972vzr6Lj6n1fHTPvaJ3v9nlZo+ebRfm5+vra3+/V9x/OOed8 -rGd7r+Occ84555xzznm9Pz1+sdxu9LysOL42L+st+RxVD/e3668nucZhOeec -8yt8+xxsfa+ItuvbPo+3zre5x+vPVzYvHe+03DsvKJuPLp+vzcsaWw7n22tR -PjjnnPPMnu19j3POOeecc84559f5Ms7+3Zko3W36pXxEKWSZfxUdV7Zxpd75 -UWfLs2/+VeTbci+dl1zj5pxzzvkVXv987Hsut76nZfN5/fp9I/v5erpdcPZ9 -7+2+Ps4p6toF6xhXb/c9On/1xzuq/oxqX/T68ji/ch/jnHP+Vc/2Hsg555xz -zjnnnPP7PYreeT7L7cbNyxp7vNv9Zhsnemoc6thbf599nY/n5ulxzjnnX/Lo -+fub87Lq3+uW6++bN/L0e35t/rO9r47y1vJpbUccp9t6PW699Xq/el7WqPrW -6ve0OzjnnPOxnq0fmHPOOeecc845v9OnuGo8Ikp///Px9y9F6TxVbr3jHevj -Pd7u/PhItvGgt/vo6265v6e/14Jzzjkf663vUaPmER2nU//etZ+/9vfV4/0+ -5fP60e8hT82HaT3v2d4zn3qP3V/u9XU+4nlWrX51+/Tb7/PZ7j+cc85/zbP1 -h3POOeecc8455zU+RW1/8jL65wV9xfeP839W69v750v9/7XRmv6ocZlR4zh9 -46H15TTqfC3TOzuuUR+j7gOjzu9yfZ7rlHPO+Re89bk/yuvfA/ven8976/vV -KL/rfWAdV7eDWo/3LT62fVd6jx1fz0f51eXZVw/ztaOXx99bHzjnnPOxnq1f -nXPOOeecc845/2/fX17H2d/f56P9nnh+fOTtfny9bM9n7/VVu9+r7ye9433Z -ri/OOee5vPV5Wkp/mW77c7z1Odh6vK35HOtReY7y8/XhnvbRfByl+vAWrzve -beSqn9f5U+XfWg8neeZ+G+Xn6vsG55xzfuzZ+ts555xzzjnnnH/bp6gdv1hG -7e/X5xmnu9r7yiEu3zF+dVyX/+PyLB3v8+M1o7x3vKy2vkXptI6zjL0vxec3 -y/XOOec8p1/z/jDH2Ofydr/3zqu57n1mzHtvnnlZUT6vnp8zyqP8L4+jNG9m -Hc+/Jz/lo96fl5/rr7dROk/7/vFe3f7lnHPOjz1b/zznnHPOOeec82/76HGl -d/v2OHP6vL5tHOG66OufX8dXynn8OGbv9RgdT2n9XePCd40ncs45f7cfPwfr -n++tz9NRz7vj4422O//8HZ3/5ed733PGvafVvv+0to+i9J86L33vS63tnXW6 -+eZBPev19bD1vTdK59vvw9nafZxzzn/Ns/XPc84555xzzjn/hu8vl/qHt9sv -P5elX3dUP/ZTPq/vHS8YOz64jdHjd+/uz5/Xl8q/b7zsqfLZHledz3HPeNN7 -70ucc87rfFouvT+0vve2vhc9+x6ef17Q/nbj571EcfZ8ZSvP1vpz7Ov9PT2v -6ate/17a1y47f98Y66P6EzjnnPNnPVu/Peecc84555zzb/gyyv3JpXTeMX4X -H/+1HuWn3dvmsWyj7zzWH1fruNI99eqp836dH5fb+fTHjreW6k85P2+7/3DO -Ob/WR81fyvZ+nu09/5r5WlH0z2+JvLXcnp1ntf780/OL+D1e/5486v7Q+p7f -m86vtMs455x/w7O9z3POOeecc845/4aPnXeRbTxufRzR8fV6Kcb3248d94mP -66p5WTnna23zf3y8vPV+0loPn64PnHPOM3r9e0gp/fX22d7P3+7LOP89rut0 -jrfbRut7S998s/b6yd/to+pVb3ttnZ+x9XkbY/sN8rRrOOec8/+ObO/VnHPO -Oeecc86/7ct4fv7VcX7ifI/x1vyc95zzmuLyOT6u9f62+Y/2e89xjSqH3/FR -5/Hqev5sPeGcc97r+1H/PMr2Xs2P/dx8jzlGvW/U7Zd/07f3mavfY5fp1be/ -xrRP64/3OD+cc875NzzbezLnnHPOOeec83f5FFeNi63X987jOh4fifY7ykvx -/Pyrq+dlHW/fft7PHu/T9d+8rDt8Xt9bf56tD5xzzu/y/diuz/Ye/uz7f1x+ -2c5v23nvjSzzf/jbvLZdMPb987r36sj75pVla19wzjnnfZ7tfZ5zzjnnnHPO -+bt8f3kd5b/LEG1fSr92/s/V87L6juu8tx7vcTmMm091Np1SPpfHE49rPDUP -rdWvrp+/6e2/73/t+co3Hs05H/+8uzr91uc4/2+vf9/I9r79lI+ub9Ny3Xv+ -uPeBayPb+097O2VMe6p1/s/8+azzoKJ0RrW/zrWvt3HtvKzz9erq/HDOOeeZ -Pdt7Puecc84555zzd/kUZ+fD7G9X6lff5qM1P2PTac1/q0flXl/OT81HOk4n -Lv9lvsf9XvbYcZNR83mi44rKhx/71ddve73NNT+B89/2abk0zh5t3/q8qLv/ -zDH2eVR/n+R/Pdv79tPv+ZPXXS/nn+Ojnte919Go+PV5KaPuV+fuq6PmZZXz -M+p477n/c8455/xOz/aezznnnHPOOef82z5qnsz+du3zJVrzebzf63xUuY2d -lxWX85h5cfXnseRj5g1u83NcPr3zgrbHyUf6U+NinPPn5l/N0fe8q09/Gdd9 -f0vtfLNjb0//HX7+PfDXfIqz89aufn8e9X57fLzn3weuLuco3V/zUjlPXqo/ -009n60OUTm97ap3/1uMtbcc555zz+zzb+z/nnHPOOeec82/7FGfnyYz9/fft -dnXp5P3+q1HjBVef3+jzx74+zuvnv0XHO2p8hz/r98xjzDZvgfNf8Prne+99 -flo+N88qz31vuT7LeTzvo+7nX/UpWucfnp0f2HrdPXUe95d752/H5frMfEXe -58qZc8455/We7f2fc84555xzzjmv8Smu+j334/TPe7Tfq+dlXT2e1VoO0eeP -fX084+ZlHXtrfuLtfR9CRp/Xl85j33VRXx84z++l66g16r8P5O7nbyn9df6j -fL/L48hVD1ufp9vI9n479n2s/nmX7b30nvf28++Zo96rSzHqetk/rmz3H845 -55zz73m29gLnnHPOOeecc/7fPsVV4yxjx1OifG/Tz+b72/X/nccx40HR9vm9 -dzyxNp3S53mbt14X++lu99M7T4/zTD4t182beuq6vn5e1rRsPsN+ZKm32d5j -73lPfu/75+h5TW3z9M6/f9bdN+a4px1kvhbnnHPOeTbP1o7gnHPOOeecc/5t -753P0zb/KvJ5fWk8hf/1/e3+LZ6vdbSOu52bJ5PXjftn9vN/D6s1Hc7f4NNy -7f2+bfv7r+u+5875+0Zf/rP5vL72fSBLvc32Pnz1e/VbfH+70d+bN66er/2e -+Waj7j+j5q1xzjnnnPNWz9aO4JxzzjnnnHP+bZ9izLjbNt1llMdTonxmG7fK -Nl42Sds4fZzOr3vf9RKVN7/aW8dbj9PPN5+Bf9NHPZdb63lpv5Pfe1+tf38Y -9Z7z1ft86f3h7no+aj7MPe/D9fUw2/vh2PfM9vf5sfOv+vd7z7ysOO6+jo7z -xznnnHPOI8/WHuGcc84555xz/g0fO89n/bkovTlqvz8hSifbuFU2j877FFfN -o/uK19bPvuur9Xrhxz6vL42P994Ps8zb4bl9Wq67zzx9vbRuf9886tLz66r8 -93n9+8lxPq/zbPe3bO/D63IZPc/n7f5PV1zdLoj97nlZfe/bvkeLc8455zyb -Z2uncM4555xzzjn/tk9x1bhA63ywKP1s41Zv8avP1zd8Ww7H/t7vUfmGn59H -V0qH8yPvm+dw3f121H6ffR7V31dbn2v7+cv6fHnu/jnG68/X0++303LpOvqq -j7qOeucBrtNp9VHthafaU6N9XT5R/jjnnHPO+d/I1j/POeecc8455/wbvoz+ -8dwprhpnifabbTwrm+9v116erfXn17xUPuZr5fK+88V5nx/Xt/h5Oq3vnX81 -6r7U+9xpK4fz39/YOw/k2veWVv/e/TDne6/3yf3teud51qdzl6/r4W/Py1pH -nvcxzjnnnPNsnq39wjnnnHPOOef8G76/PG58Kko/Wz5/zUeV//7+nh+Pu9uP -yy1KJ96Oj/R5/dnx5SzzfPg1vh/X1cNo+6vnQY2axzX2PaR9Htfkpet61PMx -57yU6++fY66v8++BvfVq/3jyvI/dNc+qdp5SKZ3s/lT7ZYqczzXvn5xzzjnn -tZ6t355zzjnnnHPOOf9vP47SduPHU/ixl85j2/gOj7zuejFeNsZHjUvmG1fl -13rv/bC2vo2aZ9Wa/7f4frm0fw9Y1ufp+rhG+fF+2++f0X6vur7G1p/ous3z -3jV6ntV+1JdDXfrv9bP35yid3uv9qefXfn6yvb9xzjnnnOfxbO1lzjnnnHPO -Oee/6cuoHXeIPh+ls90+23jZ231/u955RHyS2vp/fF7icuf7Xqq3tfOxSuuz -zCPi9/q0XLoPjLrf8mOf4qp5cdmey30+6n57/nvnrj7v2c7jqHl9vzqfaozX -1+fW97G+97f75zeu82deFuecc855nWdr/3LOOeecc845/02fom18Yfv5ZfSP -d/Oxfnzez59HvvS264X3+by+dv5htnlBvM/3o77+9I6/T+vNv7rXpzg7P/bp -eVln5wcee/v98+w8xr7zmP989b1HlSLP+8lbve89tvU8nZ9P1XofqKtX3jM5 -55xzzs96tnYu55xzzjnnnPPf9P3lOVrHE8+OF2Qbj3u7Tz+NOY/x9r/iY8dt -66+L3/R5/ZjzuI1s845+3euuo/rvs2p7HuX5O258rE+RZX7Xen/78fy8rFHl -n+29qLf+LNPN937C//qo50Lfdb1NZ2y9yvaexjnnnHOe37O1TznnnHPOOeec -/6bvL7dvP8VV4+x8rE8/tc6jWKabbzzuHo/r/37E9Z7v+7n5b/XnK8t8JH7s -rc+jUfMxOK+53987jyvvvKyn57N5b/mGr8/jqHl3UfpX57+vPcU555xzzkd5 -tnYl55xzzjnnnPPf9Clqx0GO09mm25o+H+vL/6PwfVlnfdT3M/Aan9dP5dp6 -f+MZvP28XzW/i/M7ffQ8k+Xn2+ejXp3/1vlmffPT+Lu8/v4/ap7tMr3+78s6 -Pq7IW59r2d67OOecc87f69nag5xzzjnnnHPOeY1P0TaOMEX//Bbe5/90xfnz -+Gteul6iMB7X4/P6tvmE28g1T+l7fnxd1J/fUePynNd4tvrWNz8kvr5qr9Or -519xXvMe1XtdXDtPuPX9JNt7FOecc87573i29ibnnHPOOeecc17jU7SNv09R -O48i2t//rDzfPKi3eOv5jbbb31++8b6nPCrn4/HE+Prhf+N4vPPs91Twe/z8 -/STb85E/61Pkqufn/15w3ftVf5hnxe98zzmuz+PeB8a8J3DOOeec87d7tnYr -55xzzjnnnHNe4/vLc7SNg9SPp2Sb1/R2X/6/jvj8LtPNNz74rPeWZ+32fL2+ -dt5CtnkX3/RtuUfnpfW+lO05yO/xZfS/P2T1KEalMzai52A56s5vf/TdZ87/ -PcconWi7dT7qnl/t79t3vz8fH+f68+2/l9G2n9L2nHPOOef81zxbO5dzzjnn -nHPOOa/xZfT/nanWdPg9fny+tuev9fzypY8Zl+SlephtPsZbvW5cvlzPW+8/ -/NveN394VL3Ncx879nl97/yosZGtfPI9dyY/O5+wNp3W97en8jlqXu5xfvLU -E84555xz/qxna/9yzjnnnHPOOedX+BRnv08gSifbvKa3e+v57Z2n8Ss+dvwx -ul5+zbfRd//hfX7dfTvb84vf463PkZz3yW0+R/m5ee/l6E3nt+bFcc4555xz -zt/o2dq/nHPOOeecc875FT5F7e/1t6aTbV7TV/34vGzP0366+eZN3eOl8llH -tD3vnZ+Qa15Tfm8tZ/OseMtzobYejnof6M3PMt3r51mNnX9V/1wePe/r7P2n -r15xzjnnnHPO+daztZc555xzzjnnnPMrvHecdB3Z5in9mreeX9+jdexReU7R -9j1FX/XSfIkozv89Jn7k9fftbM8jPtanOFt/rnl/eP5+Puo5O/Z5sc1/3fN6 -jnvqSe/f0dseJ+ecc8455/x3PVs7mnPOOeecc845v9NL44BXjTPyPt/frvfv -SW3T+U3flk9feX7V5/W18wdyzV96i9eXf7bnCB/ro5/Ltd9DdfVzqtfX+b96 -nvPx/f/6vze6v7/z+R97XOPKwfxnzjnnnHPOv+/Z2t2cc84555xzznkGn+Ls -eG6Ufrb5Tm/30nlcfr78PVHr7b/qY+c/fM/76km0XbZ5UPl8Wu6dJ5PtOcL/ -Rut9pvd5PXnb9y99fx51X3m23sda77frfLfPy4rSubp+3uXr49pfv80v55xz -zjnnPJ9na6dzzjnnnHPOOecZ/Hic7j8rn6NtfsY2fd7n+9vV/32hp+dHPe3G -hds8um9MkW2+Uy6vvx6zPRd4ny+j//7c+rz+Ne89L9de1+efv0/Nzyzl/9n7 -5DryPB8555xzzjnnW8/WTuecc84555xzzt/oU5ydh3Cc7v/8r/3P8dbx2f3l -deSZN3W3j63nX/Vs852yeen6muPq+RV8rO8vr2P89/jxv37Pe8uo+bqt6Wy9 -b572Nj9Pl9tZ77seOeecc8455xk8W7uec84555xzzjl/o09xdhwt2/jv231/ -u97vifq6n41tff62Z5sHlc3r729ROtnu81/1ZdTeJ+PrYp1OtufC2/2e83v1 -/Ns4P2sf9dx/9nq5zlvnp3HOOeecc87v92z9AJxzzjnnnHPO+Ze8dR7CervS -/Jls48Vv8eh87S+vI9t8qvHeV2+jcnu7z+tL4/tT5Jofdf/3t7TeD7Pdt3/N -95djb50Hku3+/xb/J4i+85t//lXkT81nu6ecr/dluZS+34xzzjnnnHN+hWfr -B+Ccc84555xzzn/Bpzg7HpptHPktvr+d79Eqjdv+5vdyzOuf/l6UnH6+nmS7 -P7/d95fHzRPOdj//qu9vd/Y5tY5x98mrnptXl+fV190Ud9+fza/mnHPOOec8 -j2frN+Ccc84555xzzn/Bpxjz/Qbb7bONL7/Fe8/jMt2n51Odd+O5f2P0df12 -P45yvcp2H367T3H2+3Oy3Yd5n/8TxNj5tOt8PPc8Mi+rxlvPY57nL+ecc845 -51/ybP0JnHPOOeecc8453/oUxt+f8emnq74PJJv31cPtdm/33vrwTa8vn2z3 -z7f7Mvrn60ae7X77az72fWC7XV+9iv3u5+DY53h9+Zy7TreR5b7dtz3nnHPO -Oef8jGfrZ+Ccc84555xzzvnWW7//IfJs49Fv8avPy1s8Kocp3j3OO2pc+7u+ -H9v12e6f2Xz0/M/19tnun/yvL//fxqj5Nst8lL7/sD6dpzzbvLjSczA6rrvv -2335zPZc5pxzzjnn/BuerV+Cc84555xzzjnn532K2vH69bJ5XHU+/XT394c8 -5X3j+2/xef25eWhv9+g4t+c9230vm5+bDzNHtvse7/NR95NSOst85HuOtHrr -9dX7HK/d7/7yOu6el7XNT1/+Oeecc84551d4tv4KzjnnnHPOOeec3+/LuG88 -9O2+v12+ce1R3lp/Stvl8vPfU/R2HzVvgS+jtl5lu7/xPu+rD9vt+u63X/Wo -HEc9x+Pnwjo/velcdd9urW/H22d7LnPOOeecc/4Nz9ZfwTnnnHPOOeec8+u8 -bt7FHK3p/Jov/5/jq/O4SsdVO98gp8/ra+ehZZlP1ef19TbbfSzb/fPc/da8 -rOzeWk/2l+donf/J27x0325Nv+98baN2flTre9qo+8zxfjjnnHPOOednPFv/ -Buecc8455/x3/Knx3+X++7+/Ilt5cn7F9ThqflG2cfZnvy9lez/aTzffeHfJ -vzYva5Jc86navfa4st2XnvJl9M/TyHZf4n0+/XT2vEfb82Pvm0c0+u9CltO/ -9760jmzPU84555xzzvl/R7Z+D84555xzzvn3fIqz48ut+x097tY6jlM7P6E1 -nWznl3/b95drw/yEtf9TFc+Pg0fed1zR+mweRbx9tvlXx/NGyseV7f6TzZfh -/vZWn3669n1vnY989/O3e997S/m+WJf+dvtR9bN1v2Pf6zjnnHPOOedXeLb+ -Df43Wn+vqrcdt+43eKo9yDnnnHP+az5F3+9r949TPP0ee9W8rKfG766Zp1E+ -j1enz/mI+9vko+vz23153OX7yX66Xx8fv9+vfn5d7dnuA9n8+PzW1wee05f/ -z9H6Hh5tt5+PfPdh3ud9/eHZ6kme5ynnnHPOOed869n6SfjfuLo/sLUf4zh9 -9Ypzzjnn/OrxweXn+t/3WvO5/vzo3wcfNU4a5bPV69KPYtQ4y9n0S/m9bt6X -eQL8f0ff/a3+ev+qt96Hs/mo8/6Ul8o/y/yrY68/rq96VA7Hft28a36PTz+1 -XkfLdP39wa/4Nc/fbdw9r+/tz1nOOeecc85/2bP1n7zdW/sHWttTo/ud2tI/ -37+R7XxxzjnnnPeN902x7T8/O64XpTPKR73f9h7XcrvaeUTrON8OavW+9+T6 -9PvqQ1xube2Oefmu8a/j4zK/66t+Lu6bF5rN/6mK58fBj/P7Fo8j1/yr+ThK -10W2+8Bd95Oz5caf9emns9fF/vp1ZLl/8lE+el5WWz3M9lzjnHPOOeecZ/Bs -/Spv8Sn6+gei6P/9rLHjiaX8lscfI7+n/OP8145PZatvnHPOOc/jyzg7Th2n -M6af//z7z9XzeY7Lub79Eh3vcX6iz183XnPPe++ocquvV6Xtp/W98xhH1ROe -0/eX2yPbvILR48LH8fw4+CRj5ktc7e3zV3POy4ri+78f11oO2a73X/On+y35 -N7z2vj26Ho65Pz/1vOOcc84555xn8Gz9Km/xZYxvJ47yUj7bPDr+/N/PMGq/ -2eohv8enuGpe36jx32zlxjnnb/FlnJ0fFaVT/x5eyk9t+qV81j5Hou3r8lmb -n/ryHD1uwo+8vd5edb1E24+a3+L9/12+jO/Puxj7vLjL5zjOf+tz4byPan89 -5b92v8p2PfK/Pv3U+j65H63vCfw3/Xx7qu95dN17Neecc8455/x3PFt/SzY/ -7n/Ylme2fpJ75nFF9a2+f+bZ43W98GNv7YeMfHQ//zqylRvnI66vabnUj8r5 -E/f5afmu+QCt+Sl57Tjv/n62+Rrto56/PLdPy6X6uf+58d/nVvv+xnP6/vL7 -2+l19TyKLOPp2capW/OZf37sW3wZ5f6lbNfdV335/xz3zrNq3Z7/lsf1qvY9 -s/d+VXvfztae4pxzzjnnnOfxbP0z2Xx/eR33jcfl7O+tr1dR+n39dVvva0ef -z39fu9u4z1v6gY+3L0X5/lBK/2z/T7Z5DtnqA+/zZfSPa4+al5KtfHhO319e -x/ve685dv9vINR7NeZ/f+x5Ybo94L3rW95ffP9+jd77xMt3rx9P7nsvXeet7 -5lP+1fvG/vIcteXA+3x/u/g5+NTzlPN6r7+fXP3+kO15xznnnHPOOc/j2fpn -svn+8nf7b0eN6z3bD1zKX/28l9r99h6veQV3XL/nfy97dP9nW32L63PtcbWW -z9h+XfX87b6Ms/fhVr//+wSi9EeNK2U7v7/mU9TWn7e8v7UeV13c93vlnOf3 -9veryUvthWz3ya/6/nLJ3zs/ZH+758bNj/M56r2x3t/y/Mp2HY26vlrnE/Jj -39+ufJ2O6pdo3S/nR/XqnvbRNj/ZnlOcc84555zzr/p7+3+e8mz9MKX+mbZx -urieLPc3epzu+npem//W9Ov6x8rbZ6vnb/cosl6ny+3G9V89dR9b7sfzJbsv -Y3x/aV/93+537Hyq7X5HX7/qfy6f4mz/fLbnQms6o+YZjh4f4fxLPi3XXXfb -7bUX7vHjuO7952rvO951uuZlrdePvT+s9/fe6z06vmzXxVt8f7vy+97Zdke0 -X87Pe+k5dFU/c7y/2vxke35xzjnnnHPO3+vG0/fKo9yflq1/9ep+ldZ6cvU4 -3bP5icp3TnddnmPGa7b7zXYdZb1+p+VSfX6L7x9f+zzS/f2N62e7ej7YMr3v -P6eempd1z3lsva/G29fWh7vGPc++P4yah8aXkeW9bux1sfXW++eo/R6nzzmv -8VHzqFvT58e+v/ye+SfrfO9HlvH6q/3peZtzZKvnX63/2Xx/u/br4p72Pudn -vL6/aPS82dr8cM4555xzzvnV3tp+z9YvZJxuL677PaZR43et4w5Zxkd6y+Hs -9q3jqtmuL/3D+/ndvx63UXt9HsdTz53e/H//uZPtelmvn8r/bddR6/0zSqfV -x47T9T83PS+OfV0upfN7dX2+el59331gXDsi13sa59/wUb+nkO3+/HbfX87X -HrnrvajN87VTrvLW9wH1+V1e9163jvp2GecZfPRz55n3q6eeO5xzzjnnnHMe -xXb7t/QjvX1eVpSf/c9n7S+N0x81vvA1Hzt++jvj7+/qjz1/HY2aj3Hs9fls -Hd853v7q9H/nuvjK867V9+Ou96ja+TD1113r9dKan1/zKXLV//b3qDa/rv7n -HGfhnJ9/vrTPc/7196vW+RjZ2i91+b66/2G7vzEex93Xnfr5Lt/frv/vQa/T -4fwNXvs+cPXvi43dnnPOOeecc86f8t75P3Nk61/6xjjdervrf79pf/9RvmI3 -z+oKj8rxfP/hWzwqh6fma139PSclr71vf/t6jJ9r63IYdX7f4qPKIdv10vr8 -ah1H/opPy733jf31+eq5970av64d8e3nC+e8/r3re88L30e0n9+r2jX7Mer5 -FcdV14v69i7f36633vamw/lIb28XH6dfm058H77qvaI1Hc4555xzzjl/1u8f -B8zZT7WNe/t/onjfOF3peHONL3zVt+cl23U36nuxnpqXtb/d09fpNp1fGzfv -6yf83vWS7fvl9rdrvy5az2/rfWP5uefr89U+avwuWz3Pdr1cPY/3nnGKPPWW -c57fW9vddfGd3zfJ1i/x7f6K6+v/OtSfe7zvPlP/frufj6fn23C+9LPP31G/ -z9KXn1H3ec4555xzzjl/i9/VT1UeV326/6q2vTm2nzM+L8vPn22/b9Md4/F+ -s4wL8P/27XnMNh6RbT7JXd+LVXu+jr01fV7yabm3//PXfi9+f7v266LvuXn+ -/jZFtnqYxUfdP7P5/vGM+365/f3E++3z97cXOOe89n347c+dt7zXXf2+d+z5 -n1/qwz3e2x5vbd9xfp/Xtg/ar+u6VM/2R23TMf+Kc84555xzzmv8/vG79XKp -HffVeSBRObT6Xd+TEOUnV7897/V1ZBvviPLrOv0bpfxnq2/ZfVT/f455JnOM -vS7anxdtPvr5tY0s9e0rPi1P67M9R556D1ymN2p8cB352wWcc36P178nZ3vu -ZHvfq2sfRZHnPfCq9vJXz+/V3tcuXqf79Lwa/pteXz/r7p/9/QnR9q35MZ+K -c84555xzzu/0/P2oOfo5r/7+hDz9ltF+c9UTfrW3jlO/fdzcdcrPXBfLeH6+ -cRRjr4v2+rn2vvTf8j7DSz4tP3293PMcOX+9LPNbfn+u2+82stUTzjm/+v1t -vX229k6298C3tZuuqj9vP1+j/Nz3S0eRZR4O/6q3tgtK6V/13Im2P/ZR90/O -Oeecc84552M9T39pq7/l7xuu09uPu79vJ8955G/0bb16etwhy3V67O3XaZR+ -rvrASz4tl+7nb5l/Eh1Xn3uf4Uuflp++XkZdR/9Uxfeul3WM+v2Ip4/r7vp/ -vP358976fuXvwPJf8trI9px6dt5+KVrfG7efr9vPHHc/v94+/6qU3754fh4O -f4PPcVw/o/eP8/W8tP36vtG6fWv+j/PLOeecc8455/xdnq//s7b/P2q3ZhuP -q+sHeN943Oj+jWW6pXEons1b+6O+PS+r/XqMIsv55WPd8+sovZLnOY/8Tt/W -h7fM+z33PRLPX0dP3a+e+nuy0f5Gjb+Pmgd19d+dGZX+1e24ZXrlcjvOv3lo -/Aq///n11HyhUnpvjW/PvyrlO9u8HX61t/bzrNMZVQ9HPcdLvs6/v+vHOeec -c8455/w6z9Zvmb//813j2tfNi3tq/sCo4+J3+nXX49jvM4mvo+Xn437LUjp3 -l/Nx/n/tufBeHzvutj3vX31+8d/wabk0HvSb35eV5/4z6n2v9fw+e77O19u6 -fH1tv1H69fkZ216rf4+N8uN7j3n7c22ObPO1xHGMuv88/fzi7/DW52lrvbp6 -fvLY+efb4z3ennPOOeecc845v9Pz9UNe5bnH6c6Pj5wdx3z7uNvY8ZHW7ePz -sk4nOt5f82/My7rufvvs+Et9/n2PxLOe7fl17NfdJ6/+fqRS/l0XGb1U3+bI -eh2drYeRZ/s9hbHP6/b7zNrvmT+TrT34VR9V/vXtqb7to+dEtvljnndZfR3m -ZT0bY593pXh+XtBXfWw/3vn+rtZ0os9H6RxvzznnnHPOOeec8zPe1w8QpZ+v -fzJLf2bfeFzr+b3uuKJ8XtPfOL4/7er5WqXt1tJaDmPnFbzXc46bn78fXj2f -ZNT9fFQ/c7S/aP2ovzMV5fMrPi333jfGPr/GzSdZx9XzD3vrz7S8/zxaf77+ -Oor8ru9Dy1bPr/LW9+FRf7dovVyqP6X9XfXcGfW+1zv+uPx8+7zNUrqcf8HH -jsvPn29rf5XzM+r5FW2//Nzzz5esLjLH8/ORsvpV7+G98xLPttda93e8Peec -c84555xzzt/rUcTbjxkHyddvedV41nr53HyP7fZPzbMaNf+qb7w423V013Xa -X55fnccydtxnXu69TrONg0f5HzsvZdR9vv66GHXf+8bfV60vn2efX9sYNe9l -1HyksfXh/udF77yXY69PP9d1cf98rbrr6Gxcd72Per7sf37cuG1ffjjn+f38 -/LFR9/NSft7u4s7IM9/prLe+J4z+Xr79fGa7j3HOOeecc84555y/3ef1tb9P -l2W+1qh49u+4Xe9ZxrX5/vrSeP0U2a/H3vmEZ+dvPDXvMXLj2mc8jrPzBqN0 -RvnY51d9/kd/r93ZcdvIXRd3+rw+6/Ml8rvma731Oup174Gc83d7e5iX9Qvx -1Hyq+vxxzjnnnHPOOeeccz7etzH692Sfjbv790rH7fcZeY/HkWU84up5U32e -7TzyezyOLM+va77HyXXBe3xef/d8sLPx1HOnb7/ZzjvnnP+ai5yRrZ5wzjnn -nHPOOeecc/5GfyqylQPnmf3qyHa8nJ/xUZHtuDi/06+ObMfLOec8p4t7Itt5 -55xzzjnnnHPOOef8Tt/GNd8/cH888/cO4vX+Hg3v91Lc/fcdtjH6e/bGeLbz -yO/xUjz//Or9e2quCz7ee7/P6nefO337zXbeOef811zkjGz1hHPOOeecc845 -55zzZRyPo93398Ki8eW6+V39EaUfjZcdj6O1l/M98778HZxc/vT49fjrsXdc -u3a/rddj3/V79Th7tnqYzUtR+/e/Suk/f72U8leb/7HPr236k7gu3uT5ny+R -j37uHMf7rqNe389PtnrLOefj2vdTes8818TV8ezztDayXUecc84555xzzjnn -X/UoStufHTeJ0snj98z3OF/Ord9Dkm3eSN+4Ybbr6Prr9Gx5XvO9cM9767yX -q6/TUfeNsddj+31jfVzLz529j0Vef12Muu+dm0fxfP2P8pfz+bWN1vlgo59T -63yOrQ/3Py9ar4uSt6Y/Lee4Luq99f5wzfyr2rjuen/LPH/zJzn/qs/re+eL -jrqfl/LzDRdXx1Pzsu5+/o7qf+h7j812H+Occ84555xzzvkve18/SZT+vF2u -fsX+fsjWftp7xrV7y3+9v/b+56vmcUXpj/LW47q636+1HIwX/PWrr8d755+M -P67W9Fvz3zr/pG8eQlTu9fn/tetiedz9942xz68on/c/v+6qP7XHOWpeX+tx -jf7epK/5NeP1c5y7jtZx/3Pn6nnCfe9d9ce7/7ntfjh/s/fOk5zW9853ilIc -1c8w+ri4yBxZ5lll9Wl59Ht463tdKT9t+azdTylfnHPOOeecc845z+/z+lz9 -hHnH3a6e73FX//NV4/i94/vrfI4eJ6093r7t4/MyZjzxe/5UfRv7/R7X3W+v -Lp/e+lybz9bj5c9eR/fMp73uPjm2/kf7dV28y0vna46s11HfceW9b9zzfVzt -95kx73ut5yVbe/CrPq8/V/5ROqPmD2z3e9f3oLa2j9bH5XmXyee45r1I1MY1 -3+O6jbb3cN7qY/vxpujv72pN5zgf23RK+eacc84555xzzvlZn9fn6lccPx6X -bRxqma+z49rXnd9R5TaqnEcdF//G9Th2fDy+ju4eN+/z1vz/2nPhvT52fG17 -3r/6/OK/4bXjYs8+X+LIfh1le98b9fdn7xoHX+c/2v6e95O37Pf8/N6n/+7z -Oj+tz+Vjn9dnuQ/zK3yOq+/Dpfos2uLZectxtD6/+Dt81PyxUfPEWn1UezY6 -3uPtOeecc84555zzO31en6sfstxOv3rcbdT4zrPj2ted99b+wLHfF8Gzeeu4 -6jXjBeX85B43j+L588vvuV48v2p8Xv/0eeR3elT/7hqP7n++lNLPfh09db/q -Lbd1/keN952rP+V0rs5/q49K/+p23P524/6Oc+t+Oc/w/Bp1vxrdnnprPFWe -z37/ZJ55R/xen5ZL74FROvfMfx7XTlzn/+r3K84555xzzjnnv+zz+hz9lvX+ -lvG4UtT2k4ztH5jXP30e+Rt9W69yjCM8f50ee/t1WttfynN77f38an92Xlae -eSY8t2e5XkZdR6X49vUyR+/zva0c7jqu++r/8fbnz3vr+1Xr9py/38uR7TlV -d53OkfX7mvajfn/rz931/Hqq/O86j60xpr3Av+7raJ3HNaqej/oe12j71vyX -0uWcc84555xz/iaf1+fo/9zm8+l+y3X+vj6u3TYexL/q0XWR7Xsz7uqXdp3y -mvHo9Xl5+vm1jmy/Xz+2/3le/3Q94XWe5Xp52/dRLI+nNK5Vul6iyFNPOOf8 -rNe9L83bZ2vvZHsPfFu7aVo/uv68/XyN8tb2UXS8pe05H+mt7YJS+st0xz13 -ou2PPdu4A+ecc84555zz9frR/Z+t7dls/Zlv6bc8bu+Pqydt44P8nT5HtvGI -dT5K+fy163RsPx4/N75w3zjOU+M7pf3kHI+L4vn69hVfn8dsz5Gn3gP39xeX -W8mjdMd4nE/OOX+H178nZ3vuZHvfe9f3DN/1XJvjq+f32XlcV7cvOD/j9fXz -qfldrfnpux4555xzzjnnnPf5vP5Xx+mi/L/t+xOeGr+r7U/gGXx7HrONL0Se -s9949HVaPl/H7noc7Wf7S599rm3ryVvmMY76Hq1R7wP8r4+6f2bzZX7L9fDb -49fPtRc453zf699nsj1f3v5ed8/3Yr1tXtbz7//R8Wabf/V0e3xarm3fcX6f -17cT7mp3TMul52+UTuv9inPOOeecc85/0+f1Z/upatt3Ofs5t/GN3zO9f/zO -9/Zk8G25Z7vuWr21n/Y3xyNa+8fm5Rz19rw/NZ/nLf728bvW89s7vjMtP12f -r/ZR433Z6nm266V3PLHW7xkHmdc/XW855/m9td1ditr73tt9e+R/4+n3tyhy -tYOefn7Nof7c4333mfb+q2vrOefnfFruff62totb+3vvaadwzjnnnHPO+Vt8 -Xr/uXzpu982RrT/zXP9Vub35lvHryEfNWzjOt/Husb4t57f/ndC+67S+vj3d -D3x3/1u0/bevx9JzqXzf++o8k1HlkO16GTUva/25HPV5nJ+9b+x/7jvXxXK7 -777vRfsb5d9+vnDO69+7vve8eKpdk23eyxT3tGvWMbq/K97P6OtFfXuXTzGm -3uabt8N/0c/3H67X16XTOu4wqt1xXXuHc84555xzzsd6FNvtvz5+vdzu+XG6 -dX4mydKuP/bRv8+VZTziOh/bz1Cf/ts9W7/u6PO4vo5ay2G93ehxt9b+vdHz -atrSn/fz9eviK8+7Pt+me62Pmg/ZWv/P5+fXfH+7p+t/+3vUte9v4+7/kz/9 -fsU5P3/9er/q83+CyNZ+KeX36v6H/bi6v2v+3F3Xnfr5Lp+i7T3/ueuI8+vu -z+X3gb77T+v1Mmp7zjnnnHPOOb/ff+37dt4yTpdz/G7ef21/am27vvW85PRx -5bbe3jjIsS//nyPn9dv++7bTdvv1sDaeeu7M62vz/yvPnWzXyxTr8n/ndVR/ -/7yqv7rXzz43PS+Offqp9vy+5XvkIu+7D4xrRyzz8fR7Guff8N52k/era335 -/xzZ3qOe/l6sfc/aThnvb/k9x3X+pshWb7N53f15HVf373E+1nP/ftbZ/lvO -Oeecc845v86N3+0dd39/2lP9PFeP6436feqry/+e/ET7ax+vrx0fifab7TrK -ev1e1Y+UbX5mVD73jL+cz8+ofrxs9fMtPv1Ue196dr5xvP0y3+3zl64Zf+l/ -f2hNP1u9yub72313Hn7fOMj5/R6nzzmv8b723fnnIz/25f9zZHuO1N3/tzGm -XWBeVp3Pka2ef7X+Z/Mpzl4XOedbcv7ffr4/c3+78v0213OHc84555xzzuf1 -+mnrPFt/zthxt7ierD8/th19fT2vzX9r+q393m/5Pdm3+z9BZL1Oz/Zrtdar -p+4/2eoJ/+vTT2fr29XjEa3Pl9bjvfr7u7Kd91/z/e3yzeON8tOaz2j7vvef -ebspvavn4XP+Zm+77uqv62z31bf7P4dx3ftPzu/tuf/7VY7zdZ3neE7N8fbr -fZ3v0nHxY5+i9X1v8t52R7Rfzq+bf3t1P3MU9fnJ9vzinHPOOeecv9ez9edk -8+X/c2Trt7n6e7da+3Wf/X29OF9ROsvjLP1e1fnx0Gi/2er/231/u/Z5gHd9 -T3trfa49rtbyMS+F/7dPP425D7f6On+lca7z7zlR+q3vCa3p8Ht8f7u4/rzl -/a31uEpxz/gI52/y9ver2vZCtvvkV335/zrqn+PZngtv+Z6cbOPab3l+ZbuO -Rl1fUTrZrqO3+BSt1+m0fLZfIst9hr/Rz7e/eu/n2Z9TnHPOOeec8+95tv6c -bL78fxu17bi3+3HU16vednRtu37UeOWofsIo/Sg/2er/V336aVR/Y+32o+Y1 -RZ5tvC9bfvhYn36qrbdj76v16XP+3778fxtvfa/rvX6P4/nxaM7P+F3vgbXt -Ee9Fz/ry/zmy3c9H3f+zzdfqey5f572/R3O3f/W+sT6e/SiXA+/zKWqfg089 -Tzk/M79rGf39BlH6ff3becaDOOecc8455/d7tv6ZbN463yZbf8s9v2cX1bcp -xo/Ljz1e1ws/9lH99qX+zNp09vevfvJ3euvzKFv++Td81Pcc3jtPvpyfkq/T -yfZ74m8ZN+fnvLZ+7q+//vtDst2v+LEv/58jW7v7nt+fyjZuPkX5ur7Hz/9e -zD3+vX6J5XGU+5eyXXdf9f3l2u8jWkfvdVe/Pf9Fr+9/jtLpvV9F6a89W3uK -c84555xznsez9c+8xaefzo5z5ZxnNa79u/ZR46RXf4/EV38vlff5/nbjfn95 -1PexZys3zjl/i08/1b7X7a+fo/Y9qjc/be9p9e9vveMRteXSm8/a8ZRSPnmP -t9fb2nSW6dW3O9bbn3uPmsP7/7t8+qm2Przdxz4v7pp/Ncdx/u/vBxv997Du -9l+7X2W7HvletL5Pbj8frcl2f+NP+vn2VN/zaN5u9Hs155xzzjnn/Hc8W3/L -W3x/u9p22TZq+5Oj7ceOP0b15/zvk95T/nH+19v/Wn8m55xzzse9h5wdRyil -s8xHb3/+Np1sfw+rdXyk9/289rxcPV5/z3vvqHKrr1el7Wvr+ai/C5PtvsGP -ffl/f2SbtzB6/lUUZ+/Do31a7r0P3+PbfL7zexq3Ufucfbtvj3wZ63LIdr3/ -mo99325/3+Df8Gm5dN8eXQ/X+63zdeQZD+Kcc84555zf79n6Vd7urf14Y78/ -vLU+bGN0O/RX+gM555xz/js+/XTVeEGUzigf9X479ntc699Xj7e/v920Xj6u -F3H6ffWhVG617Y7z42VX1/Ns9wHe5/90xtn69nYvxdnrd6zn6e/q81KMfy73 -eu11ke0+cO/9pL/c+LO+jP7r4jjdbPdPPsqvmRddWw+zPdc455xzzjnnGTxb -vwr/61eP0/X9vfsoffWKc84553zs+17r+9jWr/6+gnvG47bl8NT8olKc3e/Y -9OP01tu31s9Rf8+If9v77m/11/tXvfU+nM1HnfenvFT+03Lp+fus659Z/r+O -+verbPcHfuzLqL+OWt8Ds9xv+bHf9X2V03a17/W//pzlnHPOOef8lz1b/wn/ -6639AKN+32dU/3C28uScc845z+b728XzWKafavvts77Hro+31Vv3e/V439Xf -JzbqeFvT5/yMTz9dVZ/f7uvjL91Ppqi9/z/lx/UhTz9Y5E99j+Uoz3YfyOaj -5oHznL6/PPr7TvPcb/lY7+sPz1ZP8jxPOeecc84551vP1k/COeecc845/57v -b3f9uPNTf1/vOJ36dlnrfjm/wpf/18e63mcbx88xL2sb0f0ii/cdV55+sGOP -orR9/3PtXi8fV7b7TzaffnJ/e7cv46r3vTz37a9633tLfD9vS/+6+0Drfse+ -13HOOeecc86v8Gz9G5xzzjnnnPPf8VF/b7HV97dr/7s22cqT8zM+6nvYIs82 -Lv/s3yWM+m3yjHf3+rR8vH7eLpe3Htd7vPa4st2XnvLpp9b68Ov3va/6MvrP -e7Q9P/a+v983ry/dJ+vaC+X0722/bPPBOeecc845z+vZ+j0455xzzjnnnHN+ -nbd+31FrOr/m+8vj5rNl8755C3n6wY69/ftSlts9P/+qzevrbbb7WLb7Z+/9 -tvb64s96az1Zf34/ttdplvv82710325Nf5lu7XzXKOZ0Rr2njbrPHO+Pc845 -55xzfsaz9W9wzjnnnHPOOef8fp9++ru+PL6Zbdz86e9RWZfbV721/qzXR5/L -4fP65XF893u01t5az7Pdx7L5/na+X+vr3lcf6vvtl+uffy7c49vyuXp+dZSf -q7+/q9Vb69vx9tmey5xzzjnnnH/Ds/VXcM4555xzzjnn/Lzvb9c+7yLbeHc2 -X8ZczpOsy/Pt/u3v2fi178uKfFs+vkerz8/N35gj232P9/mo+0kpnSzPi1He -en2Nml99XM71z5H15++6b/fln3POOeecc36FZ+uv4JxzzjnnnHPO+dZHfV9T -tnHqt/jV5+UtHpXDejlK7/hzT/u8vi7/0fZf93Xobxx9P19+vv1727LdP/l/ -x6j7SZxO7XO/NZ2nPNvfqSw9B2uv06u9L5/Znsucc84555x/w7P1S3DOOeec -c84553zr+9uVx+mWy+Zl9foyyuX8du+rh3n6u0Z5b334pteXT7b759t9+mn/ -fET1Ms+8F37sY98H6vv/l+vrnxf7+80/L2t/efy8rON4/r7dtz3nnHPOOef8 -jGfrZ+Ccc84555xzzn/B97crjW/G42vr7bONO7/Fe8/j/vl6r/fNR8rT3zXK -R1/X3/Bt1NarbPfht/v+dubr/qpH0fd9WfXvG1f7U3+vsO96LJ2Pu+/brecx -z/OXc84555zzL3m2/gTOOeecc8455/wXfH+79vkt2caF3+JTHJf7+rzkmTd1 -j9fXt2j7b3iev0uV08/Xk2z357f78v85Rn0fYLb7+Vd9ilHPqf0Yd59szU+t -m5fV5+ZXc84555xznsez9RtwzjnnnHPOOedf8tF/F28d2caR3+LR+Vpvt47o -vHzNjecuY32cx/VnXl5f11/zUffDbPftX/Pl/+vYeuu8u2z3/7d4FH3nd71d -7/csnb9/tvpT34d5Tzlf7/vlnO05yznnnHPO+bc9Wz8A55xzzjnnnHP+Rt/f -Lp63sP+5fOPCb/cppvOxv34+X6Xtv+pjIk9/1z0+r1/XH/53+Z9VtM73y3af -/6pPP7XdJ+PrYr1dtufC2/2e8xv5uPtn7XMq5/di5fkexd/8HkvOOeecc87f -5dn6ATjnnHPOOeec8zf6/nbt49fR9tnGhd/ix+er9bz8jo+t51/1ef2yHPi0 -/E9l+B6td/ny/22cvf9ke45k83veW2KvfW/pS2fUvKzrxkFKx3WV912PnHPO -Oeec8wyerV3POeecc84555xn8L7vH1inux5fmyPbOO/bfYpluf8n3O54+9/z -aXldb9vK83c8um+sl/fvA7/u9ddjtucC7/Ppp7P359bn9a9573lZbjf6uj7/ -/H123lrv+95198koH5xzzjnnnPO8nq2dzjnnnHPOOeecZ/D97eL5Kq3jg9nG -c9/upfO4Pl+t23/VW/+uXGm7r3lfPYnSnz+/vp/wv1FbP32/1rv86r9fOf3U -en87W9/e4n3l2Xofa73f1v9d3av/XmHfc/B6b3u+cM4555xzzjN7tnY655xz -zjnnnHN+p4+dl/I747zZvhcrOr/R56N0ftPr+4ui7b/to+az8WOvL/9szxE+ -1kc/l/e3v+55HaXf6+v8v+v7tdqfv+vI+vcc27y1fmZ7DnLOOeecc87PeLZ2 -N+ecc84555xzfoWf+7uEc2Sbp/Rr3np+7xo3f6tH5blejtI7/txXfF6/LIc4 -jssrSoe3ef19O9vziI/1/e3a68/o94cs9/Nn52vVl0/dfLz156+uJ72+jmzP -Nc4555xzzvmdnq0dzTnnnHPOOeecX+H72/X/vaR1OtnmL33Vj89L1B+SZx7U -sx6Xz37k6b/K5r1/T3NaXp4fHvmo+ZnZnkf8Hl/+H0W5Ho56H+jNz1XPhdF/ -Lzg6nmhNbX769jtv13v/6atXnHPOOeecc771bO1lzjnnnHPO+f+3vbvLdlTl -FgBaPbtdrW6dXnxNuA8ZDksi8iPo0kxe9s6UICoaxSVyzmf4fr6z79lZy4kW -v/R0b92+xsU69tY4geP9KE6/1r3+nfqOP7zP5x23o/1+8Wv8mvfnzj8uXf07 -UnfcK6dz5ZSPG33xcpxzzjnnnHN+3qNd/3LOOeecc8455zW+/PeZfv6+YW05 -/Bo/3l71/Rvb6ffHR0X15fPx9DUf3/dSO1w+b9czb/XeOMzacqL93vFrfPQ4 -V6m/Iy6otH9dnaKtn3i/O22/+3mvLaf1/O2ueo6NV8/VJ0474Zxzzjnn93q0 -61/OOeecc84557zGt39zafl++/2anEeLX3q6738ueby4pljevj7b8vMlpev/ -+Hi1fi4dZ/gZr+//HHVfnr/bl//Onj/E9lwaVc75VNrP675fOj73p77jzJpv -Wb7e9pmWczy/UeO/5eb77decT+ZT2/7rPIpzzjnnnI/1aNe5nHPOOeecc855 -je/nKz2nf/6+TLS4pqd76/bdn76mXL5f99x6fsf4LXf5On27vlvj5fLl8Cv8 -/PEk2u8jv9f3893dztu9tp3/GZR643Ci/M7ye731POe4PY87H8h523kC55xz -zjl/uke7buWcc84555xzzmt8P9+4++zR4pee7n3p/Hb8Na/bX3Kpdj/iSzpe -X+n6LKVcfn7Wj/eL+u3rvYf8So/W3vrio0q/P+X9dPR5SJTfax7TR+8X2+/3 -xgmPOj+Jdh7FOeecc/47Hu16k3POOeecc875b/p+vvx7T47Lyd+nqC2fj/X9 -z2tatkfue9vpce7fRfO++4Nx+qme5d5j+A5v3+5n5xvt95f/po8e33J/v6rf -j2bXvzVeS3zXL3j98X9UnOR+vvzv0dh22Pq7Fu28i3POOef8uR7tepBzzjnn -nHPO+W/69u+aWvPvz6/9/YbR4pre6tu0bq+Sp9vrN73U/tMUpz/qKX5XfAKP -6a2/R9HGO+Lv8D+ZdNXvddvx7fxxr3X9xBj/03nL0335vEy/5j3d8+rfdz3F -Oeecc85HebTrSs4555xzzjnnv+nbv7m0fL98/2I/f/31crT4paf7Np3djvHu -313t5+4DpilOP1VMH32fNJe+2zm/x0v7Ue3+eDzf9t+72nrymL6fr32cnKvi -i9qOb+3H1WX6Ve082nlRb/uJch7Cj33U78Ko8WnHtqto52mcc8455/E92vUp -55xzzjnnnPPf9P18pfvpuevf8/dN+Fg/3u7ntyPf+vK5bn/hfe49hr/taapv -P6Pe9xrtd/ytvp/vvniqq+Ki27z9+JmrT209+7Zj/O01Nu463vnJU73vPLa8 -fXLfK+0Xufq0HgdK7cp5Juecc875GI92ncs555xzzjnn/Dd9+e8z/Wz/f/19 -w2j33Z7uS0rXf+925/+mcvvvi/fgOS+12+XzdrvkUv54dVwOf6vXHgdGHW/5 -se/ny2+vaL+/fe8fvGucnHV62360ptnbPdp2HBXHdU07eavXt+fW87HeeN10 -vq0+9notzvkb55xzznk0j3b9yznnnHPOOeec/+t/DlN++qe8590/fbrXbcdl -e48er+N3vLSe98uJ0x/1LF+n17Xb9nL4O733eJjzs79ro+r/FF/+q11vuXKi -/p7e8/vSfvzMzXc7v/nxJH3t53u5op13jY7T20/166FU/tN9+dx7fM6V07u/ -5+pz1p1ncs4555yP9WjXy5xzzjnnnHPO3+Hbv2sae1/p/HXu7Hr+mo9a/9vy -4tyPu9qP15v7Yvf6+XGN0vlsp/N3eZrmtcNc/lFxXLnj0qh43bHnIfXlb+s7 -Pq67db3l6nONzz9+LtPP7V/X3+/ILUm087Fr47jW7RKzPZ/3u65f0s9Rftec -f3LOOeect3m0fnvOOeecc8455+/w5b/P9Nq4hfb7d2n5ff4932j3xaL5ks6u -z9b282teWj/bfKVxL/hs79tenPf5cXvL/57WHn/Gjot4/nc2V/7Y4+T5cW9K -fs/vy/uOhzHPe51PLunscaa1nKt8+bxMn/38QuzzijTFOR/jnHPOOY/m0a5f -OOecc84555y/2/fzjbvv3Hp/J1d+tPtcT/HZ2+sd3tqfs07PzaeuHN7n6/T0 -eFV7PCmVw/mRjxqP5Zo4ivr53v0ewOVz6bja+ru2/V7035f7jp9jPM79jlL9 -a/ejt/qo/ag3TvLs/jXqeuGu66nR/ozjD+ecc855HI/WP88555xzzjnn/B0+ -9n1e4+4D7pf7XU60+1nRPLfd08912zFa3NT14y3k8vftX3H6nd7h58cRGj3e -Dv9NbzvO3Le/tOavXa7W/evc79f4+vd5/fnJcT3nebTjW7Tz4eW/2vOBaOd7 -V42v1ZZmXxcYL+t4vtHO0zjnnHPO43u06xTOOeecc8455+/2/XzjxklYUi5f -6rl6Rrtvdff9suP1ntte36l2u/ya9+0vcfqXfs1HjweyTD93POT82Ef9Lre2 -89J87zmu1p8/jDrPeetxPlpc1ux4mLHnw/XtMNr54djzzPbz+eXzuf0ln2rn -Ozsuq6621+1Hx/XinHPOOec5j3Y9wjnnnHPOOef83T72/l37/Zf0+9HuT0Xz -JR2v99z2WtPo8YVy9YnufcsVpx/p3b5OLx1/osUhcD7T245L0Y5j6/SlXn2/ -O+ePG331j+a95wP3t9to58Ozz6uf4kuq3V7762X+9ULOr4nLGnX8+fa++XLO -Oeec81aPdh3BOeecc84555z/6/v5xo2jNfu+SbT7X6Pui/XGpexvp/P3xaJ5 -7/uzasvZ/8x7/Vxc4ndqbefL9LrjG+fXeu3vwvZvmmb7Or20XL2/a2379a/5 -Ov3udhvtPPaa8+Tnnn/OGVeq3B72v7ems+d7x+XOvg5qd8c3zjnnnPO5Hu06 -gnPOOeecc845r/H9fPm4id44mf3yz3tuvk+5/zV2vbX2b9wVf9Van9L9uXJ7 -OC6Hj/X67di3X9S3B87je6k916e03Nm/y62/v6Xy247/T/FSitIOv72u/awp -2vnt2POx+t+7aOel15y3nz/PfNr7Ct95vOKcc845j+/Rrhc455xzzjnnnL/b -9/Pl3ws2535Nmuqvl7fTx8f5XDUu1uJLve7avqX67Xucca767uPH6Rfin3TX -OB6c89l+vj987Ht+4x/30u/F2I7nfXZc+tN9P1+6PnPpO3/teVfrfnfXdkzn -11ufXDn79bgqnpb3+Trdeuacc855yaOd/3POOeecc845f7fPfu9eLl8uf2s9 -j+d7fbzQve+Lqb9PcXdcVm19Wut5vH7q53uc4vQjvcPX6cftJd44e5zzXl9T -3+9dffnb+fT/Tu1PT9N3fdrm217+M/z8eeCv+X6+/Hq+6/z5mvG1zp8PzF7P -uXr+mpfWc237Sb/f2x5y5fReT9Uer3L5S/XjnHPO+XUe7fyfc84555xzzvmz -fD9fb9zLvPuJfXFBreVc/x69e+Oy0nyj7yvFiWcbtR7GxhnyY1+nz9l/29tt -Wh/O+X2e7qel43zt70uunNa43NlxJsf5ebTz7bvP89v2l/O/46N+r8eOr9ub -atthtPOoefcf08+l9dB7XG07H6vf/mOvm+rb/9jjP+ecc86v9Gjn+Zxzzjnn -nHPOn+Xbv9/p871Zz/mm9et9fn/+fYf95Trvrct71fPdZ8sZdZ8lWnxaaz1z -y89rfJ2erv/a9pPzUXGenPM4Pur3bnb5v/b+wbFef74R7Xz7Lh/d3trO80ef -D8xK0c5/2q9Tls/nrqe+yznOd/34w6PqOer669zvQi71Hw9bfez1UZz9hXPO -OZ/h0c7zOeecc84555w/y/fz1d4vS1N7v33tfO+Ne8mn3HKd9WjjaB3nP3+/ -ZvZyzWn/qcfpL3qHzxtP45r2wDnn/FpPk/spvedv2+9H2b612709zTqf57/h -y+fSdcHY889559U5HxufxjnnnD/Lo53Pc84555xzzjl/ty//fab3x1mN9v36 -zI8baavP9fFavds3t1z73t7/n6ZR44CNXa5Wj9NfdJeP2o7viNPjnHM+x9NU -/3sU7byaH/u58VfTfOfPN0rz5W/2+vuz17xvffb1af3yHteHc845f4dHO0/m -nHPOOeecc/4OH30/Yju/+ffvjK/1SXPeu5Gu/9J9sOhxZXnfX844/ULRvPV4 -0toO724PnHPOI3r9eUip/DR/tPPzp/vyX+35YWs56fRSaj1v6Yvjam+f/Nk+ -ql31Xq+dvf6qe85iTWP7DeJc13DOOef/pmjn1ZxzzjnnnHPO3+HLf5/pZ5+f -Ted39/27aP3A896j0dqv3rcdz98X6G2f+/Vp9Tj9PKP8eL2dL/+a+y+59Pzj -D+ec87neOn7jr42vtV2+/vP82fEerfVM61dqJ63rbdTyjo1D4+/21v3k/PGh -9Ty/t5zt9997XcY55/wdHu18nnPOOeecc875O3z7d029z4Nv5/e0+3dx+gGW -tF2e9n7+se/R+E6j7zcdz7fW42yvc/crZ+0X89thmkbdN++tf1o+55zzZ3rt -+UPreW/redG95+Hf9ZkdR3TvewDr41W2qX97RVufre3n2KPFI73V689L+67L -zh83xvqo/gTOOef8Xh91ns8555xzzjnnnNf4nHiep3qc/oFjPx8/Mye1rv/v -78fy++77LJ+X6ef2xzTVL+/s+4yj3x+0TI9xPOGccz7Kj38Hz99/yc139PhI -afm5esaMC5odx9J+nrZML53/tF4f5cqPFsc1dvyiaPFO0by+Hbae9+bKeff5 -cLTrPs4557/md/XDc84555xzzjn/Td/PV44DWfL1lv9W71sPs/sfZqfr+0mO -y4l2HyfaeGj163nUe0/6jktPv9/EOef8Lh99/pCm0c811P7ux4yzah0ftfc8 -dnx7GHV+Ei0ua048z3eKcp58l486f06/39tuc+Xc7fvLG+e+POec89/0UeeH -nHPOOeecc875DN/+/U6f75XvK+3P7/5+43f7vJRud97nrffRevev2vnOPp4Y -r49zzvkMHx2XcvZ3vPV3sHV5W+s51mffR1un97aHa66P5sXXRR0/7ThFaZ/X -n7fPXv+t7XD/+1cdb8Vlcc45j+mzzw8555xzzjnnnPMZvp+vfdyt/fLStJb/ -Ll/TqP75uvt95dRa/uz33B23q9b4pd77g+XyR+1Hx96/XXvrOWp7idvknHN+ -vd91P6hUzzX1nT/PG//neLnO+7XnA2uafR2UW55o8VfXjMPWvr/Mauej/K74 -q779NP3+dcfhMe2Bc845H+ujfn8555xzzjnnnPMn+n6+/HO4fe/v+C5/ke3n -9riRu9bbNfdN6pc3V060+0pP99H73X57SL9/9/10zjnnvM9bz6NGxQvNHr+r -r55x7ostadZ5SLRxQfc/xzvPvDe+a367Ouuzr0/ffT4f7fjDOef81zxafzjn -nHPOOeecc86v9z+Z1NvP/5nP+efWt/UeF4eWm2+0+0ezPbcejn2dXtouy3+z -2gPnnHP+y577/fWer0+6e5zMdD3HOM8v1z/a+eq170msPb8d1w7398f69nPX -cxaj2lurX3PdwTnnnI/1aP3AnHPOOeecc845n+fLf5/p/c9f739eU1r+cf55 -cTjR1ls031/+q+7/1reT0naprT/nnHP+XK//ffzNuKxo4/bEvx+Xq39ru3q6 -73+uPf9M07h2W7uf3hWXFS3usVQPzjnn/E6Pdh7IOeecc84555zzer87nudT -r/77CMdeSst6uS9ea5Q/pZ6j2uGSxraT/vbAOeecx/dRccutv6dx7mfl/O74 -kH1/7v240vKmyxktzmp2nFJp/ez7vHitu99Lvr+85/14vnGOP5xzznmNRzvf -45xzzjnnnHPOf9lb+89jxl/Nfn55nb6dT71H2+5P9z+Z1FfO+ftT+/O7+346 -55xzPtZbz99Kv+Nt+Wffz1qnl87fcvnv9ffdj2td3mjxV63xe73nq2k5pfnl -Sqg9770qDu2u8+39+ca5z84555zXeLTzOs4555xzzjnn/Bd8+3dNMe5HfKfP -crwnLuvY9Z/M9tHvzdzO7+77sJxzzvmVXn8+2VpOKaXfHxUPE3P8q3pvPf+J -dp7Wd12T5nt+vNbY9ZDzeXFZufzXLFerx7lvzjnnnM/waOdvnHPOOeecc855 -ZB/1nHW0+w5LWuqdTh/j5/sx7r1Pp1+ld784Xo/l/SVXbq4czjnnnI/y+vOf -7fTy7/5bfdT1wtM9t7yL1F5HjIrbH3VdNnY9tJ/f1q6f0dvrrPed5/NrfNR+ -N/u6Ptp645xzcVmcc84555xzzvkZ38837j7C3fFXZ5erz8f1G+fqf4/X9zNH -a+fX7BdP2Y6cc8455+O89jw52vneveeZ7fEbs65fYsZrnb/uOC4/V59v7yuf -p9Prjifzyum97mutZ+1xrzTftnKibXfO+S97tPMuzjnnnHPOOef8jO/nG9dP -GC3O6t7xr6L1i67Tt/WK5uPuN6XlX7N/tffn19afc8455/xdXpvcv7vmOiKf -zl4HjTqfz32/L/6qlOrb83794tzvHuV167P/+mu/Hvn5jhovbvY4frlytst3 -Pi6rzeO0K845j3Z+xTnnnHPOOeecn/H9fKV+yPp+76f4kpblT6fP8uPtcld/ -yDp9W9+neGscV338YV9+cVacc845531eHy8U7Tor2vVdydvOe+v9XPzV7HS2 -HT7d1+m911N9193n61Mqp7Y91+1H5fxzxuvOzX/edeWs48Co+R5vr2j7F+f8 -jEc7v+Kcc84555xzzv/13ueCP9PL8ULR4qlGvS8jtx6u8Tj9Hr3vc+Scc845 -53ykt16PLKn2uuatvv2bS/3bpS/OanRcx6x0VRzUmuaM61Vfn/3txa/x89fj -59pJ7XFgVFzcuPH0xtSTcx7Zo51fcc4555xzzjl/t//JpOP87f1j23rk+9uf -4rn1Y7ysGi+ltZ1wzjnnnHM+z8/f9599vfZ0389333avq+e8VNuuOD/v9XFZ -rf0eY/f3efFXpXoe16O2npzzJ3q08yXOOeecc8455+/w2e/jmz3faJ5b3tz6 -udfj9Hscu/fxcc4555zzCF6K0ymXM/v6jvf5Xe89HPvec877vHW/GN1Psq1H -+fic1n/sey3r49Zy9WmtZ2t9OOfisjjnnHPOOeecP8v38427jxAtbmp2HNpT -/Lg9xO8PST+X2i3nnHPOOectnp4/t14XjBpnhh/7n0y65vquPk7v7vrnUtvy -cn7ss59rm31cLS3v9vv535G++cbph+H8lz3aeQ7nnHPOOeec83f4n8OUn/4p -b+2nypUfLZ7KuFjb1Jb/LjdeFuecc845j+D1cTi5/HXXZWs5rdd3o7wU/5PW -sy7/mp71fE379csyvXc73r1+0vqXlrdtffK3eu/4b33p/t+Fe48znPMZftd5 -F+ecc84555zzZ/ldzyf+mu9/XlO63mJ6nH6PY1+nL8tRardpfs4555xzzud5 -7/ntd6q9/mq9Tqyrz/fyRr8ebK3/sc+7fsl563aMuf6/18Nbx53m//q46/e0 -/Nb8rfWJ6nOPS5zzGm/9Xeacc84555xz/m7f/s2l5fvj+n9y9YnWP3zVuFjL -57r1+ZTnVeN7730ZzjnnnHPOr/BR133XXL/krytrry/eMS7x+fu26eeo7SRq -HN1xinvd/XZfPpfWf2v7bJ1vXzlx4rXGHvfi9M9w/iYf9bvMOeecc8455/wd -PjYupb4fPldOtP7eX4u/Kvl+/eP0e/R5+3O123zx7t9xzjnnnPNnee788/i8 -tP36K/XW9waWlqu1/Nrz8JjjJo27HlmmX9V+jtvVd/nRrrtHv3cyXd7c90vl -8DYvtcNZx5Pe/aKt/Vzvff1U0fpnOH+Hjzr+cM4555xzzjl/t+/nK40bP+++ -wNN9//OaatfPbB/73OhTXFwW55xzzjmP4K3XC/POh3OeO0/uPX+Och3Uurz7 -y5db7pKv03vbT+t26d2O6fqJdt199/V7a/7f8vr1OSru7qr9Yptv/u9Fa32u -OY5xzv9Ns48/nHPOOeecc87f4fv5xt1HiNbvOnu8rNJ6zq3HaL5dntJ2j+/H -2+U7v/cecs4555zzK73v/HNevFDr9U60ca5az//HeimNbyet26vVc0sS7Tr9 -7jiuZXrtfn31fnGv1193tx4PR7fz4+Ns9N+LOP0wnP+Cz/795ZxzzjnnnHMe -00fHEW3z/ZeUt/ZTjRpHPVq/6+j4nHS93eW/Oe79/Pe5cM4555xz/iTPnf/f -FZfSOt+Y8Qnz4zrS8nPbcbbn6hPt+v3ufoP99lB/f/+4nOd4mu56bu54Pdcf -32b72LhBzvkMv+v3l3POOeecc875WN/+XVOMuKNcyuVfPbe8MftR6+N1nvY8 -7PL5ePqa721+vN/Ff06Wc84555zzGs+d97Zelx2fP8c5z7/G1+lXb9/0OqV1 -+47y1npGu96PGa+1pPJ1+tj99PrnwqLFZfW289netv6jHSc5f7ff9fvLOeec -c84553ys7+drf3/Bdnq+X28/rfPNfW/286FP6cfLLdexX9//ub88pXbxXB+7 -HdPvx7vvxjnnnHPO+b/eej486vru6f6U95u3bt/ZnqtntPiou3zU+jzOH6df -IjffaP05T9/fS/XmnI/3aL+/nHPOOeecc877fD/f2j+z/dz+3ofe+qTzzZV/ -nD/+uPej4pr61uf58ZqO5xunH+Man/0+xzVfabtwzjnnnHM+w0fFLfza+7N6 -n3taPt+93Vu3712eq3+0uKlovv8578frf971datHi8uKtr+/9XjL+Zs82u8s -55xzzjnnnPM+b31OubX8/XyleJ7z418dlzOvH69veVvjcOr7+UcvV+120b/3 -SU+//8I555xzznmL11535PIfe5zz/JznzvOfcv7fWv+neG55o8VH3TWO1jXX -re1xWblUe9yY3Z8zu32OcuMTcv5cj/Z7yjnnnHPOOee8z/viZ9Jyr+ovau/H -286vN16rPt7mrvGyWpdr9vsO+uof38eun/b+5/1yOOecc845j+G111O5ckbF -UYyqTyl/mm/sddN9ni7XXeMI3eX7+d4bxzVq/eT8uJx5/Tx3xWXlyrnLPTfH -+XM92u8j55xzzjnnnPNjX/77TK/vl97Pn85vXH/Rcf1HXefm65Nb3tRH9XOW -5rtfz/rtFa0/9rj+0XydXttOcvlT772vxDnnnHPO+Zu99Xok57PHE87Nd9R6 -uMtLy5Wut1HbK5qny52mdD3k8keLv7prvPRjjxqXlc5vXPvZfn/8fl3bPjnn -8T3a7yPnnHPOOeec8z6PNl7Wsc+7zh31fo1R/Zzp57r1YFysY1+nl+o56j5O -33qOtt9xzjnnnHMewUc9T+F8+5yv6TM9Tv/GbG99viZa/NU74rWuf56ubrly -afz+eFyfaP0wvNVHjec2u55Lavud5a0e7XeQc84555xzznmfL/99ptf2d6fl -3tc/fLxc865/t9Nz622t59jnrNvr2Ze/dbukaXY/T2896z2db8zxxzjnnHPO -Oed8nG8/t1+nfP7G6feY7fv50vXzndL13NdvUH8dnSsnZrxWbb9Uvj7XjIuV -q/9oT1OcuJHf9FHt/3z5+/MrHc/H9cu1lS+Oq9Wj/d5xzjnnnHPOOR/rzxpH -K+/bz6Ov9/Npf769/YS55V3TNe/XuOs5u/M+6v2S4q8455xzzjnnv+rbz8v0 -OP0Y0Xw/X359Hnuc6+h7n1eqXw9PuX7v63/jS2rbX873Zx63k/PlX/X+3OP9 -qnZ5573XNVfOr3m03zXOOeecc84559d47/v+tuXe35987GkaHcf1Pd/j9TYq -pfO9b7nu8fZ+7Nbl5ZxzzjnnnPN3eC59599+XqbH6cd4ui//pes5nb6fyttr -lI+K1zqu//n+kr751vtx+XHiPWL6On1Zn61xO3Xbd01j44W+65+rT+t4bq3l -X7t/zfo9itY+6+PNRpUf7feIc84555xzznlM/1OVlu9H6X++y+el7fzujo+a -P55YWk6pfebqk6Zz/XK5FK0dcs4555xzznnq9fej/248LY+PHZ/8qjiZ75Sr -x763xjOcT7n1n34utX/j+dT4On1/fa6pdb9o7Rc63u7tcVxn2/Oo51tHjV/X -t9/1bvfrfo9G+ejjUm37yXm03y/OOeecc8455+/wc+/1i+Pbz+3rYX+529Oc -51XLqXX73uW55ettn+l2z+V7SzvnnHPOOeecv98/f3PXieK1Rvny33Z7jBvH -6bj8++K7YqVo8U6j40ly7eQ7pe2krx8p3x5y7fzXPbc+e+O7zs73eH69/Zxn -j2Pjjktzt+/5ONtov1Occ84555xzznlk/5NJo+J8cilXn2jxUdGe+2tdb9vv -1W+v/fzr/LbTOeecc8455/x6//zNX+duv98ev8GPffs3l+5vJ+f8PWn2e/EW -Sfc7zut9XD/Y4qXfi9LvSFrOsUeLvxo1/r+4LM4555xzzjnnvMZHj1u+7/X9 -dU9ZD6Ofu9zWb9x62Narfruk+Uvlp/XnnHPOOeec8xieptZxe9x3HuX7+fLb -61w5/e3k3HLNTt/1336+O36G8zm+fC61/1H9nGOPb/Pisq5578D5/kPOOeec -c8455/xNvvz3md5/nd4bl7WtX6n/IZe/vpxo6/8pvvx3z3bknHPOOeec8+u9 -b7zi+uumv5vy0+n86X6un6ScWufbG3eRqyfnb/I03fs8Zn1c0zXj89fHJ7ce -l6IdtznnnHPOOeec8xrfz9fez3zNuFi51Pv8aHl5c/WJth3v8rHxdZxzzjnn -nHMe3z9/89fX2++3jzPsfnRMHxVXMDb+qv75plHL27tctfVcpG0/4vyZnqZR -8ZCt++Ps42eunvvfF4fMOeecc8455zyG/+lK9f291zznNWpc8fbnxfbLOe/R -2sls7+tPNi4W55xzzjnn/K0+bzyTvxvPlbvWJ5f/Lm+9fmwdj+XYrx83Zuxz -aqP7PdJ6nN+OUcdRb1vPnMfw5XNp/61LV//ejXtOMy0n2u8a55xzzjnnnPNn -+ah+qrv6FUePi7Xvrf2QuXp8r//083b+o3zec6yz/bj+4qw455xzzjnn/Njr -r6f64pHqr6//bspP63v+OnH2uFLRfLt85fWf897tvkzvbZ992/07Rdsure22 -tLxnty//ZT/fnzbqOFyaX2197vJRv1+cc84555xzzt/h+/nK15vbz8/pnyyt -h3S5xvpT4rJafdTznk+PZ+Occ84555zzt/ua6u6nl8sffV1/nNb55sqJ1o8R -LS4rV+6xl1K5neS2V6sv/6XLFW17nXsPY/1+PaY98Kf58vl4epr6j5+58vvK -iT/u/ajjFeecc84555zzmL6fr/S8Uv11erR+p9nP5451cUecc84555xzzmP6 -5+/39Wbrdfe5976Vy8nVM7dcpfmk+aL1Y1wTZ1W/XY6n946HU26fre2h1bfl -3d8e5sRrrel4PUTrT+OjvHV/7PtdGBfPmZbTu1+nyzXbRx2XOOecc84555xf -4/v52vuplrT9/vP7l+59PvT6uKzSfJfPpXbCOeecc84555zv+fbz6OvceXEF -fzee1qM+XihXTm980dnlvcZH9VdcNV7NmnLba5Tn6hOtv2t2v1nd+klT+/OG -sfaL9/ns97e2bt/R+2luPWy/P//3dPZxiXPOOeecc875sS//fabXX0dvy21/ -TjBaP89V47S3rucxPrs/s71fa/mcrh/OOeecc8455/zI+8apPu+jnjurS+l6 -mBdXdre3Le/d8Vflev7dbPf0e+c9Wj9YNN+mdXvl1mcu/7P6/Z7ro8brGzUe -4Kj9NFf+dj61x8PzPvu4xDnnnHPOOef848t/n+nl675cOdH6W6J57/qf69fH -ZfXVZy1v+z3OOeecc8455/xfb42bmn/9m9bz76Y+5e/31T9OfEXOj9fDfXF0 -2/qNa5+55Z3trfWM1p8WrR/vqnG9ouyn0fyu97Res59e3y9613GJc84555xz -zn/Nl/8+0+uvi4/TMr/f689ZUuv6vMfvisuK0y/KOeecc84555zP8M/f736Y -3jir2vJL5WzrXY7bSfP3Xb9Hey4sV8/Zfn28R2s7idbPFs371nMujXueMdfO -nup3vX8hl+7aH/e/P/93inPOOeecc875x/fzjYuD2v+8pmV+S75o/SRR+2HS -9Tbb730u+Hx/qXgtzjnnnHPOOedP9M/f7/6Bvue82u/Xp+Xk6nNc/lt9nX51 -O6ndLnf59u+aovXLPd1b1/9x/nzaP568z2c/b3vXfrf//fm/U5xzzjnnnHPO -Pz6nHy9N+mHeMS7Wc8fLEpfFOeecc8455zyyf/7e1Z/DR40/dq2vqbX9zPbt -31x91/YZrb/u6b5Nte3q/PY6bg/5lKvHLG89rt71fO7o/W77/ft+vzjnnHPO -Oeecf3w/X+/1Wv3zWdH6Ma7qD8mtryh+3E7i9KPmvK/+a75z7Z9zzjnnnHPO -Od/69vMyvb7fRlzWlb5Ov7v93BXvMdu3y7G222j9e0/xXCqt/+Vzqb3l8pfy -Hder9ng17znT2e+PuGY/EpfFOeecc84559F8P1/p+qv9+i79fq4+0foxxGV9 -/FnvMSz3Qy3JOFqcc84555xzzu/w7edlent/TlpOyffrE+36fZ6/pR/gbPuJ -5tu/3yld3mj9fk/3JdUeT+7tJ4zzvsKYcVlpvvnHpWjHE84555xzzjmP5n+q -0vL9Un9dnOvfu/x4Pc9+zst4WX3e+77OdL/gnHPOOeecc85rvP5+/ag4itz3 -3+Hr9GW5W8cRypUT1dPtm2s/T/fW9h+tnzCaL+n4eNS6H5XbbW77lsrd9/x8 -246H17efq/aL7ffnH5eiHTc455xzzjnn/Cm+ny/ff7ikNF+0/oeo44Tn1u/V -fs345NF8VBzamm9bHuecc84555xzXuPn4xM+f7+vZ98a35Vb3vRzjO173luX -N5f/6Z5b3v3p8foPo/k12yXns5+7vD4u67h+d+0X8zza8YFzzjnnnHPOW30/ -X/55pVHPSR3Xp75/o3V5o/VLjHpfYWn7puv/bs+l/fxx+mP7fFR8Guecc845 -55xzfq9//rb3P+RSLv9xOd/1TPPn6jmqH+bdfj5u7em+ny+/3qL1Hz7FZ2+X -Y39uXNZT9otRHu34wDnnnHPOOec53/4tp1HvtV/Sp16t/Wy5tCxn+3VctP6H -Uv3318+8/oGxXh9fd7xcT/d1+n77/E7p+jzer0vlc84555xzzjnnI33eOFQ5 -by1HnNU5z23v1Fu341t9P19pfRp366r1n/rY/snnxmWVlmv7/fuOS9H2d845 -55xzzjnP+fLfZ3q5H6CU0nJ647W29c73V/SNhz9vvrPHDesd/792uWb7b76v -8Px4WaX9d/mcbl/OOeecc8455/w9Pvp5KN7m9fFCfzeelsdbffkv3R7R4qmi -xWv9qUrzjj+575/djsfzG9fetvnuPs6L/+Scc84555z/jv85TOf7x0rzXfLt -l7uW0xu/VOsx+hPW5T32u8bRGvW8arR4qvM+qp2kn+vaA+ecc84555xzznm9 -P+V9ak/xa55bPP9866jx/6PGax2v39x+8b2cuSm58s+u51HtcD/fVceZ1nja -+n5mzjnnnHPOOY/mo+JhRo0Dn6vn8t/2++PGv2r11vV5TVzWvOe2+trPqPG7 -4sRTjXXvJeScc84555xzzvlT/Pxzl7zP++Kj6uNY9utR3u65fG1+/nnGaM/D -zo5/O7dcuTT+uHFcn/P9q9H2U84555xzzjnP+fLfZ3r9dfS23Lv7f8bFj7Wu -h9Tv6h84zh/nua1SfdLlOs7/FP9OreOQL2l/vYzqZ+Occ84555xzzjmv99bn -NP9u8qfTeavv5yttx3nja832mPFa9f16rct1bzvp9TTN63eNtj9yzjnnnHPO -easv/32m564zl+9f1f9z/fhFo/ya59faxxM7W//edpWr/75Hi7O6vl0dr8/2 -8eI455xzzjnnnHPOa/3zt77/0PsNY/ryX+322v/c62n9/svWZ5SPfc50XppT -n+v29+N6icvinHPOOeec89bnnnLl7M/vqv6i+HE1c/oBvtfPfn3GPQeXzndU -ezguJ1qc1fn2M/s5vlHvFeWcc84555xzzjlfPv/JpDSfuKx7vS/OKi23tN3n -+VXjdLXO9540+nnM2vLje7T9jnPOOeecc85zvvz3mZ67Pl2+f3f/z7cfL9dz -47VK2ytNd5czpv3ct73a6tla//njjz11/+Wcc84555xzzjn//I3TX/pW3/7N -pfPbd/v57ucuW+tZH8cVM8WJm5rt0fYvzjnnnHPOOW/10eM4Xe3H9YwTrzVn -/Zfrc+/42HHWf85nx031lTO/34xzzjnnnHPOOec89VHvuTOO1r3+lPHVc/Vf -/tt+f3R/71NSnPioJe1vl/V7pe3b2m6j7V+cc84555xzPtu3f3Np+f7z+5Fa -/Xi9Xf8cVqk+y+e69Rzvev8u36/fqPXMOeecc84555xzfpef77cRXxHT9/Pd -3d7u9vgpt3/+ikfbjzjnnHPOOed8tu/nK/Xb5PI/x/eX8+nPZ703bqpte63L -t3yv1P5b232tP+V5Rs4555xzzjnnnPPl858kjerf+LspJ53Oo/ny3377GPf+ -wTT/6Ppfner2l++UWz9v82jtnHPOOeecc87v8v18pevo98ZxjfV5aX+7PMeX -z8v0XD9Gqx/P9/w4acf5e+P6orVbzjnnnHPOOeecv8m3n5fppX7CNeXyG1+L -z/A/mdQbB3U2tbb/3v7M4/n/9/W96B6tXXHOOeecc8750701Tibm+EL1cTs5 -31+Ocanvur79+cfa7RXN69K63Ue15+N6GF+Lc84555xzzjnn1/vnb77/avv9 -/xXyt/ZvnO9n4+/wP5l0rt/vu/2n7bk0/+NU3o9yflX/Z+vy7ucXl8U555xz -zjnnPKbPeT5rmV+86/1ovqRlfZXWz5ztu26v4/p9l39cbq58zjnnnHPOOeec -83r//G3tl6iP6xg1Xlau/NZy+Me3f3Mp137K6e7nLtN2cuzn47JGtfNo/ai5 -JW/dT3Mebb/gnHPOOeecc36v7+drf7/ekpbvb6eff8/dnOVd0+x+gOP6xHmO -cj9f+TnTs/XPzZdzzjnnnHPOOed8rNf3U32+l+/HSMst5T9b/1z5s31UPffL -i/dc5DXxQrPHdxo9jn1av/j9sb/Wr8s555xzzjnn/F7/k0mjnzPa9/NxWTmP -tp7f6vv5Sv2Zufycc84555xzzjnn8f3zN9dP0j4e0XZ+48YRytWz1ffz5Z/f -zC1Xrvxo8TZzxrn6blfp+un13PzavJT694vZ7e0pPmr9cM4555xzzjm/xqNd -Vy7pU9/afoN5cVk5j7Ydn+Lbv9+pbfum84vXv8o555xzzjnnnHOe88/f+v66 -1vy5+Y56/12uPrn5HvvvjHO1pP3lnz3O1aj+1Xn9sdfGB64pWjsRl8U555xz -zjnnMX0/33qdu/18X1xWaz2Pvb0fIFd+rj5tbnzp/Xzj+lVy5XPOOeecc845 -55xH88/ffP/G9vu14xp9z7etnPNxUKXl2q9nfX9dtHiYsc+Z3ufL57rtcv3z -sLkSc+1tlOfmG629zV4PnHPOOeecc/5W3/7NpeX77eN7390vkdY/V88+j9pv -kHp9f1e09nncbnMp2vrnnHPOOeecc845j+fbz6Xxr+qfB8yV3+pXxWUdp/L6 -vCt+LJofL2+ccbFKXrtcsz1XH3FZnHPOOeeccx7TW+OpWsuJ5rnlGuvn+w16 -48pmeW67t9Z/1PY6rk8p1S7Xd37OOeecc84555zzd3hrPNW8+JlR/Xi9cVBp -OaX823zl9V9b/6f7Xe2nLl23f+XWwyjPLaG4LM4555xzzjnv877+hPp+ldb5 -PsVz62FJn+U+2/8wuz+hvf7L5+3053i6XMftPFeO8a8455xzzjnnnHPOW/3z -d1Q/TDRvTfXll9Zbbn091Y+X9/rt29duR/n5fvhRnqtnLr+4LM4555xzzvnT -vXW8o1w5pe+nEi0+6q3jYvXFg71vHC3OOeecc84555xz/ku+pr5+ud7nEHOp -v/7H9ajv783l307/Xq5ne9S4u/v3i1x7uMtz9W9t5+KyOOecc84557N9+3dN -x/nTcu/rH/g1X9J2/YrL4pxzzjnnnHPOOef8jf75W99fuv85TeXyc95azvLf -djlH90N+16evnOs9dr/omlrbyWxvbT+t5URbXs4555xzznl8b43zGfsePeNf -RYu/yvldcVnH3v4c4jJ9+z3OOeecc84555xzziN473Oyaxo9rtfZ+o+Kbzmu -59N9nb6/nlvzz/N0e7dux7u8tX9bXBbnnHPOOed8lO/nq70uW1O0+KWneG67 -RIvLOm4/cfox5rRzzjnnnHPOOeecc87n+udvfb/u2Oc94/Tv/ZrHHhcr9fr+ -2Ke4+CvOOeecc875bN/Pl7/OOs7/7dHioO4d56p9fea2x9V+3H7i9GMs6bgd -l9st55xzzjnnnHPOOefz/Hx8y6i4rFz5ue/zsX68/tfPUdvtW+Oa0uV8y3Jx -zjnnnHPOS+f/S772eKfj8s/HveTKjxYfdff7B3MpXZ/P8jj9GOn00v6Sy885 -55xzzjnnnHPO+Qwf+16/7/661risvudMeauXtuPy+e72mfPj+r9vHK10ed6y -XJxzzjnnnPNvH3tdXB9vEy2u6Sm+pP31fH67xPQ4/Rutntvv0s/b5eacc845 -55xzzjnn/Iyfj2PJld/73GhtPfmxt26vp3huud46XhbnnHPOOeec7+dLr5u+ -0zZfexxOrj7R4qPujstafFl/fXFc8TxdrtLyR/HWdpvm29+/OOecc84555xz -zjnv8frnN695bpQfe6m/NJeitLfzLv6Kc84555xz/nTf/s2l5fvl66bt5/7x -mtLyo8VB3eXH23H9XLdd4nhfnFK0fpL2fpVl+rJcvduXc84555xzzjnnnPMe -H/3ehLbye5/frK3PU7y+n/zvZn3myr2/Xc128Vqcc84555zzp/t+vtL10bjr -zdSjxUdFGxdrkdr1Gc1L7XC/nGj9J+fbv3G0OOecc84555xzznkk335u7zf+ -/P3u92vtB8uVc/z9Ukrr39qPfX6cq9xyHS9vrv5v9zWNaj+cc84555xzHs33 -8+WvL1ufh4oWB3Vv/FXrOGbn49/u8rHP5b3V2+PZtvmi9J9wzjnnnHPOOeec -81/xz9/R/dJr6h2PK1f/NP+o9x14HnOOp9trVHvjnHPOOeec87t8P1/uunZN -ab5ocVDRfEm59fs2P25v0eKj5o9PPma9rZ+33+Occ84555xzzjnn/F7//D3f -r5Urp678NfWV0/pcLW/1u7Yv55xzzjnn/Hd8P99ynVI/PtWo53q209N61F+H -9s133vJG89zyHnucOKtjjxYfFc2935BzzjnnnHPOOeec/6Z//rb2k+d9+1k8 -1TP9fD9qrl1xzjnnnHPOf8ejxf/0ju+Uptzypp8/+fqvx7ffjzceV+t2z62H -43zR4q9GxRdFi5u6bxyt5fP+/lJf/nE5nHPOOeecc84555xz/n7//I1zn4hz -zjnnnHM+z/fzLdcL9XFTS8p9v8174zq+U1v558fdiua59Nb3Hh6382hxUNH8 -/PsK+44znHPOOeecc84555xz/lxv7T//u8mflsc555xzzjn/Bd/P1/te9fNx -UKV6LvlK9RkdX1Rbz7vGxWpdb63jSkWL1xo7bli0uKm7xsuqj89sPZ5wzjnn -nHPOOeecc875s/x8fynnnHPOOef8d3z7d02j4nP63h9XX/6Stt/vjwPJlVPr -ufV8V/zV8XbPr4d9H/devDF+vt32LdeveWn/yqX6/Y5zzjnnnHPOOeecc86f -4tvPy/T6fvhcfs4555xzzvn7/Kp4p3s8ThxR6/qfPe7xfr7e9Zkv567101rP -XL63eV97qC/n3ccTzjnnnHPOOeecc8757/j5/ljjaHHOOeecc/47vp8vPw7V -cTnt8Tlnva8+59+fuMj287j36939HsN0eVvf61cqf9Z6aJ3vNe3nud73Psfz -45ul8xl93OCcc84555xzzjnnnPOxXt9fKi6Lc84555zz3/E/mVSXv/Z65C6f -/x63XH1y9Wj1NN0Vl3Xs5+NzZo8PVqpnulx98UhP9/PjmKWfl++1Hn9y5XDO -Oeecc84555xzzvmz/Hy/9N+Np9/jnHPOOeecP9F7x8nZlnv39U6+fnN93nsP -74rLOs5/fVzWqOXKubisf/O1jqO1zqfUfkrbK9d+0vI555xzzjnnnHPOOef8 -Lv/8bb3PYhwtzjnnnHPOf9lHxV3k8t/t289XvbfufFxW7/aqLSf9XLd9z4/P -fO94Xzl/StzU+r1z9b9ve7UtF+ecc84555xzzjnnnD/Fz/fH5sr5u8mfzp9z -zjnnnHMe2ffzrdcX6fVCKX8UP17eePE2tT4qfqZUz2X68fbPL9fs532O69la -/+vfg1m3XN+pbX+Mt72eejzhnHPOOeecc84555zzY4/TH8s555xzzjmP7+96 -v2Gti9dKP++vt7Te59tbrvy6+kTZjqO2b/37BHu3Y+18j8t/63GAc84555xz -zjnnnHPOW72+33jUc9a5/JxzzjnnnPP4vp/vvx+N17r+fYil7bJfn/PP3ezX -L5/mxH3lPE3n13Nve65d/3d7X4qz33HOOeecc84555xzzvlbffu5/b6Dcbc4 -55xzzjl/n/85TOff7/Ysb43buep9ebX1uSrl1ud3vjEeLz6q1o/jxNblLm3P -1vHTjus5Lp5wv/6cc84555xzzjnnnHP+XP/8/e4Xbe3vbe3XFZfFOeecc845 -bx2PKFfO/vziXX/N8TSNi9eam+bHlT3D69t56/4ydv+aHWdYig+Mtt9xzjnn -nHPOOeecc855rY/rF03zi8vinHPOOeect/ry32d6+foil/rGF/pVj5PS7R7T -z8dTzfbW5Wqtf2v5ue8fu3gtzjnnnHPOOeecc875c731+dljP//+hb8bT+ub -v1+zX48495U455xzzjnn1/t+vvX6aPu5/friXPnf+ff9+vfCp/O7Kt0Vv/Rr -vk1re8u1h2vee1hfn1x+zjnnnHPOOeecc845j+Zj47Lq47Va7yO0LleuHM45 -55xzzjn/Nf+TSa3jj51LS/3ar9eixTVF823qX8/H7ef6cbbr2vN3+Zxzzjnn -nHPOOeeccx7dP3/z/Z/b7497H8HxfM+XwznnnHPOOee/5qPff7ef6sdByuUY -tby58qPFU51brnV93tWucvVpjR8Tl8U555xzzjnnnHPOOed3+Jpm929zzjnn -nHPOeTTfz5ePYxkdf7Xv7c/jpPWv87R+0bbL9e+XjObb5TvbftL5RemX4Jxz -zjnnnHPOOeec8/v987e+/7bvedj6/tvW+nDOOeecc875bN/+Lac577n7Tp/6 -/vf1vX2vj8tqHTep5Gl9om3fX/O+eL+r4vo455xzzjnnnHPOOef8ef75O7uf -9nu+reW01pNzzjnnnHPOW30/37jxrO4dF2tUXM28eJto7YF/fPmvtb1ty43X -H8I555xzzjnnnHPOOeez/fO3vj929rhY2/L++7/t9Dj90pxzzjnnnPP4vp8v -fx0UNf4ql5blSb/X5uPisnLzXT5vp9d7afum843WDqO1/6uet0rzc84555xz -zjnnnHPO+W96fb/653Ouv3fec9a5+XLOOeecc87f59u/aap/v16u/GjxV9eM -i/XcuKxznktr/mjtv9X72pX3D3LOOeecc84555xzznk0H9uvW+9/N/NN68U5 -55xzzjm/0pf/ttcP/eWkKVp81Dvir2bHZdVfx6Wft/W63lvb+blxz9b5jmo/ -x/U/H9+Yqz/nnHPOOeecc84555zzsX7Nc7jisjjnnHPOOZ/h+/na30c2Nr6o -Pj7k6b5N39dfbeut3u96vqZUz+Vzuh6e6qPiplrLad3fOeecc84555xzzjnn -nD/LP3+/+4Fb79fkyuGcc84555zXn2/n8u+X2z5eUM5b6/lWz62fXL7j/E+P -y/K+PM4555xzzjnnnHPOOec8sn/+xrn/xTnnnHPO+ZW+n285f259f1x9XFCu -nGhxUNF8//OacttvlseMyyql+69DOeecc84555xzzjnnnPNf8M/fOPfFOOec -c845r/Hlv+35bil/6zhC9fE/0eKXnu7bVH+9k9t+szxmXJZxtDjnnHPOOeec -c84555zzCP75G+f+Guecc8455//6fr7+9wOm5exPX1MuX+rR4pqe4q3bffu9 -8naZ7cf1jxd/tb9c4rU455xzzjnnnHPOOeec8xn++RvnvhvnnHPOOef/+n6+ -9vPbP5kULU7p17yUttv7vvirnB+3t2hxWd8+erwyzjnnnHPOOeecc84555yv -/vkb574b55xzzjn/Td/Plz+PPRdPsqZcfaLFLz3dl7TdHvHirHp9P8WJvzr2 -7zRqP+Wcc84555xzzjnnnHPOf9k/f+Pcj+Occ84558/yc+Mjlc9Lc/mPyz0f -bxMtrunpvk3f1ylnt9fdvr9c0eKvzr/3sG8/5ZxzzjnnnHPOOeecc85/0z9/ -49zX45xzzjnn7/Dlv+35aD7e6bic8/FX0eKU3uq57fiOcbTK42PlykvzPcNb -49A455xzzjnnnHPOOeecc/6vf/7GuX/HOeecc87v9f186/nk9nOpnPPvU4sW -d8Q/qW+7R4uzmjeu2vF6eLqv03PrqS4/55xzzjnnnHPOOeecc/5u//yNcx+Q -c84555zf673voav1uvK/51eaXjq/jRbX9HTfpu/tvv0cL55qtO+vh2jxVPPG -0Zp93OCcc84555xzzjnnnHPOn+ifv3HuA3LOOeec83t9+W97Hjn6/WXt4+rs -f78+niRaXNNTfJvW7fKO9xKeHxfreD+KFk91vfett/XzueMM55xzzjnnnHPO -Oeecc36vf/7GuQ/IOeecc87v9Tnj3nx/P5VcfbbT//uqV61Hi3d6ih9vF+8r -PF4Pb/XZ8Wzr57bjDOecc84555xzzjnnnHMeyz9/49wH5JxzzjnnMX0/X/48 -sy+ORfxVtHGx9qev6ez2eorn9gvxWvvTc+t1Tn7OOeecc84555xzzjnnPKZ/ -/sa538c555xzzmP68t/2/LIUr3X9ODy8z4+3+++Mi3W8vLzVW9vbnPH6OOec -c84555xzzjnnnPN7/PM3zv0+zjnnnHN+7KPGQRpVn1z5x/XIp/T70eKXnu5L -StdzafvmtuvbfGzc2u94a/vxfkPOOeecc84555xzzjnnv+D/D7EdQyk= - "], {{0, 0}, {401, 401}}, {0, 1}], - Frame->Automatic, - FrameLabel->{None, None}, - FrameTicks->{{None, None}, {None, None}}, - GridLinesStyle->Directive[ - GrayLevel[0.5, 0.4]], - Method->{ - "DefaultBoundaryStyle" -> Automatic, "DefaultPlotStyle" -> - Automatic}]], "Output", - CellChangeTimes->{{3.6595559215072565`*^9, 3.6595559434163*^9}, - 3.659555989004507*^9, 3.6595560561097507`*^9, 3.6641619814216256`*^9}] -}, Open ]], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"newtonplot", "[", - RowBox[{ - RowBox[{"Function", "[", - RowBox[{"x", ",", - RowBox[{ - SuperscriptBox["x", "6"], "-", "1"}]}], "]"}], ",", "2", ",", "401", - ",", "40", ",", "0.1"}], "]"}]], "Input", - CellChangeTimes->{3.66416194052215*^9}], - -Cell[BoxData[ - GraphicsBox[RasterBox[CompressedData[" -1:eJzs9+vNJLuyAFZeQZbIEvkwJgiY37JFnsoEQRg0BoenoyOCZCZZVSuAjW/X -4iuSZDLZ/9v/8X/+f/6//+v//M///F//y//vv//3//8z/u///b+Ic84555xz -zjnn/CP8z+/Is3pR3PJ8u/1T+u2OE/2N6nXj1nm6zbN5ztYpiluej3POOeec -c84557zrt+TBOeecc84555xz/uf3bD9Rf1Hc8ty3+u5+V+tF7aK/WbtVf6rf -b/WxvLs/rAPnnHPOOeecc84/zW/Jg3POOeecc8455zyqV41bnuNXPFuv1fV8 -Ksb8T88j/7tH9Wb3Heecc84555xzzvnbfksenHPOOeecc8455932b+W16tX8 -s3ZPe7e86rfH7P7cPU+75vV0XrvOge58P50X55xzzjnnnHPOeddvyYNzzjnn -nHPOOee/439+R/WjyOq/9RxR/vyz4pb34Va/ffxq+ez4nHPOOeecc84556t+ -Sx6cc84555xzzjn/He/WG/9GsTvfaNxTnsWteX1anFrvaj6n/elxquOePh84 -55xzzjnnnHPOM78lD84555xzzjnnnP+OR78zj/rPYjbfal6zvru/Vd/V36fF -LfP21j5b9af664576vk555xzzjnnnHPOq35LHpxzzjnnnHPOOf89X42x3+x3 -1D5qlz1Ptf/Z8apenfdd40f9f1rsXv/uelX37y6v/s76644XtauOsytuO/84 -55xzzjnnnHP+/X5LHpxzzjnnnHPOOf8+j36Pf6v1u/1GeWb9d8ur7bq+u7/Z -58litt1tMbtf3l6/7Pdsf1n9bnl1nOx39xyJxrnlXOScc84555xzzvnv+C15 -cM4555xzzjnn/Hd9/BvFWF79XR2nOv5sHtV+nvIon2p5d36q674ruvMQtauW -Z887Ow+n9kF1f0f9dMfptp99/zjnnHPOOeecc85P+S15cM4555xzzjnn/Pf8 -rfH+/I58Nqr9dfOpenfc3e2yvLJ+u+2r7ar9PlWezc/qOs/2t2tesljNZ3Z+ -qnlxzjnnnHPOOeecv+W35ME555xzzjnnnHNe9ah8tv/Zfqt5Vsfr/p71XeM9 -NQ9ZvDXu7D5cXf/Zdct89/zP1lvdl5xzzjnnnHPOOeef4rfkwTnnnHPOOeec -c77L//yO6kcxtsvar5Zn41f763q3vJpXtg5PrVNWXh1397rvGn92X2T5ZeVZ -Pt3+ZvPinHPOOeecc845/1S/JQ/OOeecc84555zzVa+Wz9bL2lfz7Nab9dnx -x/Jd85a1q+Y12/7p9Y3Kq+Ps8iyfqP3b8/b2+8A555xzzjnnnHP+tt+SB+ec -c84555xzznnkUb1uf+Pfbr1q+0/x7ryuzlu1/mw+q+Ou5tPN83aPymfnrfu+ -7+qPc84555xzzjnn/JTfkgfnnHPOOeecc8555Nnvqo9/u/Wq5d28bvPZ56rO -22x+1Xqzeayu7675OOVRdN+LrJ+un34fOOecc84555xzzmf9ljw455xzzjnn -nHPOI99dr5tH1n52/FMelUfP2623y7N4K4/ZffB2frMexa73ottftf/b3ivO -Oeecc84555zz0W/Jg3POOeecc8455zzzsbzavvu729+3+FgezfNbnsXb+a2W -f5qPkT1vVD9rv7pPOeecc84555xzzm/1W/LgnHPOOeecc8457/qf391+qv3t -Gu82H8uz9tV52O1Z3JLfrn10m0fl3fnI+svitveHc84555xzzjnnvOq35ME5 -55xzzjnnnHP+llfbjeWR787v9PNn9brzM+vVvN7Or5vXqfnb9ZzddVp97zjn -nHPOOeecc86/xW/Jg3POOeecc8455/wtj8q79VfzuNWzecnq7fIs3sojKj+V -x27P4q33iHPOOeecc8455/zb/JY8OOecc84555xzzp/2rF5UXu33luec9ahe -9Xl3+6fkdzqPVa+Wj/Weas8555xzzjnnnHP+LX5LHpxzzjnnnHPOOee3elRe -7ee251n1P7+f9izeyiP6eyqPWR9jdf92++Gcc84555xzzjn/Nb8lD84555xz -zjnnnPPbvVtebXerd59rt2dxOr/o7235jVGd9+q6cM4555xzzjnnnPO/+y15 -cM4555xzzjnnnH+qj39vy2/Vx/LoeXd7Fk/lsVr+qR795pxzzjnnnHPOOedz -fksenHPOOeecc84559/qf35367+VX+ZRefU5Zz2L3eNl8/L0eLP5deuN9Tnn -nHPOOeecc875M35LHpxzzjnnnHPOOeff7lmM7bLft3g1765nMdtvVL6r390e -5Rf9rsbpfcM555xzzjnnnHP+7X5LHpxzzjnnnHPOOed8b/lb+WX1//zuenWc -1fGe6nc1jyivbjnnnHPOOeecc845P+O35ME555xzzjnnnHPOax7Fn/rj36fy -qHqUT+ZZzPabzdNbHv3O4pZ15ZxzzjnnnHPOOef/9lvy4JxzzjnnnHPOOefP -+vj3rTyicTPPYrbfbD52e/Sbc84555xzzjnnnH+335IH55xzzjnnnHPOOX/X -x/K384jGzfKtto/+dttnPpZn+XLOOeecc84555zz3/Bb8uCcc84555xzzjnn -d/hY/tR4Uf9ZXtX20d9u+2jcLC/OOeecc84555xz/tt+Sx6cc84555xzzjnn -/G4fy3e1H+tn7bv9VMuj/rPxOeecc84555xzzjn/m9+SB+ecc84555xzzvlt -/ud35LORjd8dN6pfbbfqu/vtjlOdt9l12z1/3fIs713rtboOnHPOOeecc845 -5/zOPDjnnHPOOeecc85PefV3Vm93Xqd9tn11/qrts3yiv1n9LI/ZfD7Vx/Ld -68o555xzzjnnnHP+a35LHpxzzjnnnHPOOedveVT+5/dt+d7uq/V2RbZ+WR6z -z/Vr3v39Vl6cc84555xzzjnnt/kteXDOOeecc84555zv9mpU29/yfN18V+cn -yycab/e4s5HlcXpfVdvftv/e3lecc84555xzzjnnn+a35ME555xzzjnnnHO+ -6qfH73q3/FP8U+L0+u/y0+PPevabc84555xzzjnn/NP9ljw455xzzjnnnHPO -Zz0q79Z/2v/8jv5G9VY9iqfHvz2envfuujy9706Nn5Xf9p5yzjnnnHPOOeec -7/Jb8uCcc84555xzzjnf5Vm9bv+7+o3yrPru/rJxxnrV/j4t3p6f3fug67v6 -6/a7+n5xzjnnnHPOOeecf5rfkgfnnHPOOeecc875rI/l49/ZGNvP/q7mk7Xv -elZv1zifGtlz7Jr/qN/Vcaq/o/FX86tGd99XyznnnHPOOeecc85v91vy4Jxz -zjnnnHPOOe969DurF8XYvtpPt/9s3Myzfrv9ZeN0x++WvxXVPFfnade8j/Wq -/WXtq+NE4+16vzKv5sU555xzzjnnnHN+q9+SB+ecc84555xzznnXo9/dfqP2 -q+PN5lUdZzbP1fnJyqvjVOcvax/l112f6nir61BtN7u/Z+ezmudqeTT+LecK -55xzzjnnnHPO+S6/JQ/OOeecc84555zzp737u9tf1i7LM6qX+ex4Ucy2y/Ko -Ple339lxu+PNjjO7b7P+ds1nltfse3HLe88555xzzjnnnHN+ym/Jg3POOeec -c8455/xWH8vHv1H77Hc2fvX37PNUx4nqV8fP5quaZ7XdrnF3rdfsulXXdTbP -p+aBc84555xzzjnnnN+VB+ecc84555xzzvlpr7Yb/0btonrZeG8/f3X82X6z -+crGi8bZvU5RP1ke2bjV516dp2zcbr2xftVn23HOOeecc84555x/m9+SB+ec -c84555xzzvlbXm03ls969fdpH8tn663OWxZZu+p4s+NW+zvl3bxXPRuvWs45 -55xzzjnnnHP+bX5LHpxzzjnnnHPOOedPe1Sv26473vi3289bHpXPPm/Vd8ds -Htl6ZePsmo+n53X1ebPf3X4455xzzjnnnHPOv9VvyYNzzjnnnHPOOef8LZ8t -z+pX8xn/dtu/5bO/d3kWu8frzku2nqc9+p15VG91/8/mwznnnHPOOeecc/6p -fksenHPOOeecc84555/if35HntV7Or9V3/28q/1GsXu81fV6ej5WPSrvzjfn -nHPOOeecc845r/kteXDOOeecc84555zf5n9+Vz2KrJ/Z/HZ7tV13XmY9i6fy -6K7TW/Oxe/6y+t114JxzzjnnnHPOOed35sE555xzzjnnnHN+m2f1ovLdeZz2 -sTx6/t2exVN5rJbf6lGs7vPb9ivnnHPOOeecc875LX5LHpxzzjnnnHPOOeff -4mP5+DdqH9Xbnd+sz+Y/61nsHq86/08/9+y+yOqN9bvlnHPOOeecc84557zn -t+TBOeecc84555xz/un+53dUvxq3PE/k0XPu9izeyiP6eyqP2ejOK+ecc845 -55xzzjlf81vy4JxzzjnnnHPOOed35TF6lGeW/2r7KGb7jcqz8VfH2+1Rfpxz -zjnnnHPOOef8Dr8lD84555xzzjnnnHP+77g1v7E8+t31LGb7zZ5zV7+788vi -tv3BOeecc84555xz/ut+Sx6cc84555xzzjnnvOZj+S35RfnMeha7x4v+Pj3e -GNV155xzzjnnnHPOOed3+y15cM4555xzzjnnnPO9Hv0+lUfXs5jtN/q7q99q -nmM555xzzjnnnHPOOf8uvyWPKLJ8Z5/zU+eHc84555xzzjnnvOtj+VvjZfWj -fKr9Zu1n52OXj+VZHpxzzjnnnHPOOeef5lm9Xf1H9aP4lPnZ1e/udrP9ZP29 -NT+cc84555xzzjnnpz2Ksf5sv1k/f35Xx4v6r/YblXfbd/PM6nPOOeecc845 -55x/qme/o6j2k/VXHT/r76356darjhvVy+Z1V37ZeFnM7qtd7TjnnHPOOeec -c85P+dP9VseL+sv6rdbLPBqfc84555xzzjnn/Fb/8zv6G0XUT9RvllcW1Tx3 -51HtL2uX9Vftv7pOp311frv9dvvp1uOcc84555xzzjm/zbvtq/1k7cd6WR5R -vax9lg/nnHPOOeecc8757Z7Vi/52x4vKZ9uf9qxeFNV+o3bVcT/do9i1Xlke -t80H55xzzjnnnHPO696t96c8+hv1M1s/y2vVn2oftavOQ3UddnuWX9Q+q786 -TjY+55xzzjnnnHPOP8ezeuPf6jhRRP19ulfLZ+tn+UT1b/eovDuP1XZPvy+c -c84555xzzjk/51m9qPzpvJ726Pl2zVtWL2oX/c3aZf1187vdf3Xfcs4555xz -zjnnv+C720ftquVjvfFvVH67V6Pab9b/t3k2L6vzv/u94JxzzjnnnHPO+XMe -1Tud16d4df7ejmqev+5/fmfreEu+nHPOOeecc845/2+Pfmf1ZvvL+v82j8pv -Wf/bvDpP1fbVPKr1OOecc84555xzvt9313vKs3yi3097FtV6T8fqc+3yW/Oq -7r8ov1N5cc4555xzzjnnPI6x3urvqP/ob1TvV3yMT/Vd+221/7H+7P7lnHPO -Oeecc875ex7Vq8buvKL8quW3+qm4ZZ/N+lhe3b+7x8/yeGp8zjnnnHPOOeec -z/uf35FXY+wn6jfLZ7X/T/MxnvasXne9ZvdPVj8bZ7X/zKv1Zse55f3nnHPO -Oeecc84/yce/u/qrlmftonG7/c36p8fb8/TWPprtb1d+nHPOOeecc845z+tF -f7sxm082XpbXrv5m+8l+n/Is36f97efcvZ/HuG2eV/cn55xzzjnnnHP+S14t -z+r/+R151D76m9XvejW/7nNUy9+ObD677brr1O0v86z/qF51vasxuw8455xz -zjnnnPNv9uz36FH9pzzKoxur8/GWn5rn7j6K4vT8ZZ7luytufd4ov249zjnn -nHPOOef8Fz2qN5bP9he1n21XHX/2ObPo9nsqds1v1O/u9Yr62bUuq+Pc8r5y -zjnnnHPOOec3eVbvz++s32q7Xb47xnFue97qPMz22+1ndbzV/LJ8Z+dpNXbt -n+p7XH3O7jjd8TjnnHPOOeec82/wP78jX+13NrJxsry7z5Pl252PqLw6Xjey -5119vizv7vxW17E6TjWicVf3UTQO55xzzjnnnHP+jZ79jtpn9aL6Ufvod9V3 -Rzbu6jxG/T7t2b6oPsdb+b49XnfddvVTXZ/Z9qsxuy8455xzzjnnnHNe9z+/ -d9XP6nXHy/qvthvHzcavPmfWPsqvO4/V8uo43XmojpflObu+nHPOOeecc845 -X/eoXjX+tM/6zfLJ8oj664672s8uf6rfzLP5firf6jhvzXtUf3V+upGNO/t+ -dMfv9re63pxzzjnnnHPO+Tf5n99R/Wq71fZRvVmfLc/yqpZXI2s3O251XneN -0x2vO+7s72xczjnnnHPOOef8F3wsHz0rX42o/6xet3ysV+2vms/qPK/6W3ns -7q/7XLv96ecYy6uexex7M/t79znS7Z9zzjnnnHPOOf9mH8vHv9161fZPeZRH -Vj/qd/V5q/ll5dG42e9uvW4/q76aR9RPt5xzzjnnnHPOOf9k75ZHv6seRbd9 -1avjd/t/e9268/zU+lX91jyfzvep9ynqb5d339O33u/T5yPnnHPOOeecc/6k -R/Wq7aK/1XbZOG95VN6dx+rzd6M7XrYuUf/Vft/yan5jve7v7r7gnHPOOeec -c84/yZ8qz8aPyqvj7vYsz7Heqbyj8mo+ma+2r/a/a9yov93PU82j+/xZ+a3e -Xf8sTj8P55xzzjnnnHN+0sfysV7m3XFvff4sZuen+vzfNt6qR/llvnt+btuv -nHPOOeecc875m94tH+vd9jyrzx893+n8svrV9cnG7/bTna/Z9tV1qD5vVv7r -Pvu7uv5R3PL8nHPOOeecc875kx6V//k9/n07v9nnGetlz7fqt+Xx1nhP5R39 -HuO2/cc555xzzjnnnD/hY/lYr/q7Ou5tz3+bj+Wr810dL6vf3R+zvto+itvW -mf/dq+v5dB6cc84555xzzvkneFT+53fW363PM9arPt+s35bHW+PN7pvZ31l/ -nHPOOeecc875L3lUnv3md/rT/Vb3SXW/VfPP8uOf4dabc84555xzzjnv+y15 -7H6esTz6vcuz2D1eNi9Pj/fW82Rx2/7jnHPOOeecc87f9KjeWP+2vHnPu+sa -Rbd9NG7Wb3e8W+bzdF6f6tX5zNo/lR/nnHPOOeecc36jj+XVervzWM07+73L -s9g9XjYvT4/X3RfVvLN+OOecc84555zzb/KxPKq/Ws7/7tl8nsor8t3P9VTc -Ml+zfnr8T/PV/Ta7zznnnHPOOeec82/ybr1b8u56lH/mWcz2G/3d1e9u7+Yf -teOcc84555xzzn/Jo3pRu1vy/hY/Pf7u5zgVt83H6nrflvenejSft+THOeec -c84555x/ko9/o/K384vyqOaZeRar462W7/ZuHlE7zjnnnHPOOeec/7eP5dlv -/m/vzl+2Drf4bXHLvGTrWI3qPsr6v+U9OO1j+W353e6z34HuvuWcc84555xz -/hke/a767vyyvLJ8Ms9itt/sOXf12x2v245zzjnnnHPO+Z0elWf9zPbL/9Or -8/90Hp/mu/dtNY+xPOr/bb8t3n7ep/qr9tPN71c8m78oTuf9tFf3U/c9r35/ -d52fv76OnHPOOeecc367R+XZ76f9z++uZzHbb/R3V79ZvtHvrD7nnHPOOeec -82d9/BvFWB79ruaR/c7ad/M4Pc9Pe/e5387vVq/OTza/1f3ffW+iPLv9ze6P -U7Hr+Xb31x1n9dyqlkdxy3u2y2/J4y2PYvX7vVqvms/qfaDbD+ecc84555zz -Mx793T1eFNF41Tyi/qr9rrZfnbfT688555xzzjnn/N/l1XrV8iyfbl7V9tn4 -3XFOr9dbfkseuz2r191/3feoO+4uj8bN/PaYfZ6n5/vt9cza7foOfIrPnvu3 -+Vj+9Pv+9vmbxa57yliPc84555xzzvm7Hv0+lUeWXxRZ++hvt33m3XLOOeec -c8455+/4+DdrH9XrRjTubV5tF8Xp9c28+1y3++r6re6P2z2L3f3tjt3vW7fd -LefSqfMt6ydqd5t/yrkXlc9+v097FLvWI6v3KevOOeecc8455/zv/nS/1fGi -/rJ+q/Uyj8bnnHPOOeecc36nj+XV312vxmz/p7z6e4xPW/fbvLqvuuu6K7+3 -PKs32191/3Tf725k482uY1Y+2y7L61M8iu650m3/tH/Ke39LHqc826fd/fbp -3zvOOeecc8455//2bvtqP1n7sV6WR1Qva5/lwznnnHPOOef8M/zP78hn+4v6 -z8b7Nh/j9Lrfnl+1XvYcu/I47Vmsrufsfq62z/Lqnju7z5Esr+4+u+38eWqe -xvqzccv79u3jfYrP3h+6/XLOOeecc875r3n0O2rfHScbb7bfWX+qfdQu+hvV -y/p7yqN6s/OXPVe1nHPOOeecc85/1bPf3XbR36jet/sYp9f3tEf1uvW/zaPy -bL9F9bLxu+1nx8vGfyrPbv7d9lm+t5w/u32Mb3lv3/6+3vLcUfns963aX7fe -0+vVPZc455xzzjnn/C3/8zuqfyqvp3zXc67Wi9pFf7N21f667T/Nu/PNOeec -c8455097td1T+VR/d/ONIuu/Ou4p75bv9tP7NfPZeX4rv7e8Wz47X2+9P1He -WfnqebLrPOr+7rar5nnLOfb2vjj9PX06j1vOmbf2QVYvqh/FLfN56rvOOeec -c84555mfHv8Wz+bnVFTz/DU/PT7nnHPOOef897xb/rRHeWQR9Z/93u2r5bt9 -jKf2z+l9nPkteTzt2f6I6s3un2o/T+3j1XWO+uvmder93nWO3pL3U88fxW3v -7Wr7p869bNxqHrfug2o8nefu/XLL/uacc84555zf793fT+c1/o3Kd3u3PPNs -3nZFddzqOp/al6fHOf38nHPOOeec8+/xrF70N6qX9TPrq/FWnrufd3b+M8/i -6X31tt+Sx9PP031/btnv1fcgim756jiz+d42v9XzJfqd9XP6eTIfo3te3npO -Pt3v057F0/u5O/7q+756Lxg9itu+Y5xzzjnnnPN7/c/vqj+dVzef2/xU3LKf -Zv3pcWbzeTovzjnnnHPO+ff4+Lfbbrbfqkf9dyMbr5tndbzV56/62/O96rv6 -rfZ/+j2b9W69t/fdqo+x6xx4ah+O5d116Lb/FF/dt6fynvUxTr//T7XP+p19 -329Zz26+0e8xZvvP+s3G45xzzjnnnPNVr7YbyzPP+un2V/Xd/e3O66245bmr -67Tq1Xa79vHs+JxzzjnnnHNe9bE8a5/V647X7T9r97bv6ndXXmOs7pOn9t9t -70E2j1G92fflW32M6vsTtav2V+1ndX9mefyKf/p7UI23zpHIV7/n2e+nv2uZ -R+Wr6zh7vmTl3ffgre/N7Hicc84555zz7/Fu+6yf2Xyy8bL6q767v1uiui63 -zdvs/ovqze6v2XW+5f3mnHPOOeecv+fj3yiy8rfGq7arjrNrvOz3Lp9tH5V3 -20f5ZL7a/u1+d+e3ez1+xXftw9n3bNarUX3eW9bjlM+ec5Gffp4o3jr/Vvd5 -9/2J+nvr+7VrvCx2r293fne9L2/tI84555xzzvn93m2f9VP1br/V/rp5rOY9 -O3+nojpvb81v9/fT65HNw1N5cM4555xzzj/Ps3rR36x+1v9sPlVfHf/pdcjG -z/LJ+q22z9Y3m48sn26emd/y3ow+u4+67X/Nx9i976vjV/Mb62f9VJ/3lvX4 -dj+dxxhPf993j/PUvK62Xx1vjE/zXfP7VH6cc84555zz7/duVPup5vHnd9er -v7P+snaz5d15Wp3Xan/V8XatU/S3G0/vX84555xzzjkf/c/vzKP+ns7vbc+e -d5dn41e92747TpRn5rv25Wz7WY/qzc43n/Pqfh+ju39PPW+UV/e5u+fWLc// -KR6Vv70vMl+tV63/1nenOj9RnPp+3OZRzJ4j1X6yepxzzjnnnPPv92q7sX7U -7un+q+POtquOX52HrH2UX3eeu+XZc3Tz7P5+uv8xOOecc84557/r0e9qvWy8 -KG55/tP+1njddc36zerN5rer3qxXx83mk//dx+jut8hX26+O9+kexez5sDu/ -T/cxnl63aLzMu9/16nuR1V+dR/6O796Hp5+Hc84555xzft7H8vHvbL1o3Oj3 -U88T+a7nrc5D1u/ucbN5Xx2nm//suNX+onbVcs4555xzzvn3e1Sv2t+uPPic -727/5/f4t1reHS/zar3VfqP61Xn4Nt/9O1uf255/9b34VI/q7fqeVMfvtvsW -3/WeVGO23ew4s/m/9d14+zv0bb7rvOCcc84555x/j2e/Rx//Zu2iOPX8Wb3o -OVfnZXZ+nhq3uw+64+zyKGb3YXU+u+0455xzzjnnn++rv/l//o7qz46zms/s -OE/F7uccvbp/v92r+yGLqN/Zc+Nb/PT43+JjedW75d++b8eo1rstPvW+cXr8 -W333e88555xzzjn/PI9+j3+rEbXLfr/tT89bdbwoqnl2x1udl9XnXp2n6v6K -2nX7zdpzzjnnnHPOP9+j8rfz+FQ/PX7Vs/xPRze/6Plu86je7H6q9tf12Xa/ -7qfH53d5Vq8bu9/vT4tbvp9Z+eq5/m2+63vHOeecc845/z6PyqPfWb1v9ez5 -V+crGn93Hk/1e4tn0W13y/7jnHPOOeec7/fxb9Qu+/2tHtWL2mXz+bZ/euya -l13jrubBv8tPj8/5v/zT41PmM/v+Vtt/uv/680cxu5+y39V62bicc84555zf -4GN599572/NkPvtcs57F7vGq6/L0c696VF7dx91yzjnnnHPOT3r33pv181T9 -T/VoXrP5/lYfy6v7rdr+lH963DafnN8wPv8tF/8Zt63H7LmRtY/qfZrvnudT -Xv0ORO2y8brv/6/uJ84555xz/h1evbdm9W95nszH8ux5dnkWT+WxWn6LV6M7 -35xzzjnnnL/p0b13tt+oPBpvd36n5zPybD6ifk7nPeuz89GtV63/tIv/jNPr -wX/DT4/Pz3gWt3xHvy2idcnKb/UxuudN1v4Wr87DLe/N6v56O7/qvtvd/2x/ -nHPOOeec/yuq98+n8nj7OaP7+27P4qk8VstPezW6837bvuScc84555/t0T27 -er/N7rPV/nd7t95t3l2PW/KOvJp/dZ/szu8p77b71HjrvZ59D6J6b+fLz/jp -8fmcr35fTvlqu1uj+7zd8zjyW/Zj5t3yT/Hbn+fW/Mby1X0TjXfbc3POOeec -89/0brvb77VjeXRf3+1ZPJXHavlbPsbqPpptxznnnHPO+U7v3mur7Xfdw3d7 -9Pttj8rfzmO3V9fjVH6Zd9t117Na/1Oius9vOQeyPLv1+F2++t7yv8eudbnt -O5zFar7V/k9/F2bP67E86/+tvG7zsTyK0+/Dqfw+5XzY/Zzd+b7lOTjnnHPO -Oa94dh8+nV8UUZ67/bY83hpvdl/ctm8455xzzjmf8ex31D76G9W73bPYPf9R -Pk+Nt+pj+W35rT5PN2b3f7f90/H0/GR+2zlQXYfd41X3Ca/Vmx0n6mdX/6e/ -Z7P7O4tbvwtvj1Mdv7qfs/qzeT09btZvVD/7/ak+RnX+x/pv+er3cHa8bPyn -8+j66vncfc5bnptzzjnnnPNKvW79Ux6VV+/vs57F7vGyeXl6vNn8qnlG9Tnn -nHPOOb/JZ3/P+mr73d4t3+XdeX/ao3rd+p/iWb3Z/RP57L7M+s/qr74P1d/d -vHb57edJNWbPpWr9W3z3+by7/yi653b3vVrtt1uvWv9T/anvVRaz51W136e/ -I9U8Z8frvse7+rvdo9+nfXe/tzxHVP+p71O1fpZXVm/W3xqHc84555z/tn/6 -fTR6jlnPYvd40d+nx8s8iuq8cc4555xzvsPfvvdm9bL+d/c3m++peVv1p/rd -vf9uya/qUb3d+yvLZ3U/Rf2sniOreXTb7eovm99T58Puc2ZX/Syq+2T29+z+ -m91nq+9HNd4651f3wbd69z6y6tV2q+/7rd+X2fxXfdd7ets5v3ofyerv9qfe -o6fz3eVRzO7LrJ+n7xPdPKr9cc4555xzXvGo/Jb7aFRv17391Hi7+636GN15 -uW3/cs4555zzz/Zd99un7stRzLbflefou58/e67d676739N57PZqebf/p/Zj -NZ9u+ew5kI339vsw2252XZ9e59u8W171t9pH5avfz+r41fdtNa/V/L7NZ8t3 -f49375fue7rr/R/rVb2bV/b7LV99/2//XkS/n/bT7bN+n5rf3d/h7njdcXd/ -D2/7PnDOOeec8+/07n346fyy8Vf91Hi7+50dL4pb9iPnnHPOOf9uz+pl99rV -e3MU1fv17Li72lfnZ/c8Pb3uuzx7nlM+llfXK+v/qX1UHW9232Tl3fXcdW5k -eWXl3TxX+8vqReOf2ke3+2x59/tR9afO693vBZ/zLN7+LnV99/v19rk9+/3d -9d6+7d3vxhinvyPdPFd9tv3u/Tn+7q5zt33m3XyzePq9r9a77fvAOeecc875 -v8p395v1P+unxtvVb9R/tZxzzjnnnPMTnt1vs9h9P67mE7Xr9tv1KI9u+2z+ -Z+ch89X2b/e7a19lMbset3m1XRar+3P3fI7lUby1j54a55Z99K0elVffk9V2 -/G6/ZT13tdv93Xj7PK/Wq67jt/ju8+rp8zaLp/bH7ve5Ov9Pre9sv1nsnpfZ -8yWrV41bviecc8455/y7vXsPP5VHNb9onNnxVttXPYtb9gvnnHPOOf8NH8uz -9t160fjV+3LVu/fw7nx0x6s+b+bdccaYff5T7Z/a15HvXt/bPKsXxer43Xa7 -x+vGU/trt6+eD/wOH4Pf6Vm89Z7Pjv/U+br7PK/2E7Wr5jk7zm3nx26fXZen -8htj1/u0Wq86T9V2p+f5rflf9eo6ReE7zDnnnHPOb/Snx8vuwav37ax9VN5t -n3k1blt/zjnnnHP+W969x3bv67c8z6k8uh7Vy8bN1vGt+Tu93tm8/ZqP8fT8 -VfvdNd6ufdVtVz03n34fxvJb9h2v+Rj8rJ8ef/Y73z23Zs/drPzp70Pks/3P -1u/m962+e3+srkPmb9WL2u3eT1len3rOZb76nX06P84555xz/oxH5bfl+dZ9 -d/d43ft0tX30t9u+Ou5Y/i3efS8455xzzvldnt17s6i2u927z9sdL+tvNY8s -r6z/2XV8e59mefyqd9/z2XMhqz/rT/eX+a79f8t5Nvot+5T/3cfgd/kt38Ms -unnOng9Zebf/bn+nfHZ+o/qnn+e0R+Xd9mO9qmf1Zt/71eetxi3n4y2+ez5P -Pw/nnHPO+bf46j19rF+9f1fvj91xovpv++5+u88d9Zf1213Hapxen+7z7Npn -UazO8+n55Jxzzjn/Fu/ep7vlfK5etk7ZPXr1Xl2tV91Pu5731z2K7nrf8jzV -/bpr3mb38er7PptH17N62XzzO3wMfpc/9T1c7bfb3+x5nOU1u99vew+fep9X -y2fX6bZ5mfXZ738Ws+9Ztd/V96ub1+59+S1uXjjnnHPOz/rqPf6W56h69nxv -zXPVq+uVRff5Z/fFU+v11nhv+ew6PJ0X55xzzvmvePW+fSq/W3ws785Xd9zV -et14+nmycb7Fs3mcfR+zuOX5d/tqf9Xf3fGi+ln7rN0u7+6zW9ab//03/0w/ -Nf7s+TN7/mb1Z8/76vi852NU61Xjluesfu9uiU/9Dpwef9Zn5/t03pxzzjnn -n+Ld+/fpfG/33f0+1T5ql+2L6n65dT6/1bP1OpUX55xzzvmne1bv2+5bp8df -XZe3Y9d9/WnP8q1GNu7s+8Jr3p3nt86z2X321rlxy/rxPT4Gv8tXv0dvnwuZ -Z/2tjtftp9ov/26Pfmcxu/9Px6nzIqpXna/T59wu/5XnjDxb99n36fRzcc45 -5/x5r94HuvfxW57vU7zbfvc4UbvZ9c/yiPyW9fgUj9Ylq1d97znnnHP+fZ7d -B7r1nsrzNu/Ox6d7976Y3Uuf8tui+zxP9ct/w2fbjzH7fmX9z+bxlj89z/wd -H4Pf6Vmcev93t6/GbD6n3zf+3f5pET3PWL57vGz8LK+s30/xT/8+R+Xjc1Wf -c3bdd+XNOeec8/s8Kq/eN6qx+zlm89l9H8ra7fbVeruiOi+7n2vWZ8ffVb9a -/tbzRr7rOTnnnHN+zqN7WnZ/m60/22/0O2t/i88+1+3eXfdqu9VY3Ue3Rnc+ -OZ/x6vu5+h5Vx13N52kfy0+vH+/5GPwzvHpuRPHUe75rnCxmz03+G57VG+Pt -/Xs6nl6HqLxar9p/FG+t99Pn+y15vJ1fFN3v4O68OOecc/6ed+8fs/eEbl5Z -ZON+uo/RXZfTseveeMt7stur5bPjVMddff+7eXHOOef8vM/eE6r1dnsWp+fz -tjwyXy3v7q/qeq+O+6mx633J+s9+89/22fM3iqfOj9n+Zvut9sPv9DH4d/hY -3j1Xqv11v7/V/bh6Hu8+5/le78bt71e33S3x9P3hNo9+3+LV8/Mpj/J5O4+q -V+et2n5XXpxzzjnf952PYvV+ODv+bffb232MrPytcP/r+Wz71XmO6q3uN845 -55w/7917QfW7nt0HTt97376ffOp9aHYeT9+Hd7e7LWbX7fR7143bnuPbvNuu -2s8Y1XPk6XO829/u+eOf5WPwOz2q1z3PovbVfrM8uvl1z7ds/Nnz8Kn5+zaf -jeq+Ov1+PdVfdb/vjtn3rtpfVH56n86eW1n9p/3t/bm737d99rx/Oi/OOeec -7//Or7bv3hOidrP9vn3/vc1vj1vm6TYfy6NYfS+jPFb32S3nGeecc87n7wXj -79l7wun7VBaz8zl7j3t6XWf3wWnfXV5dv6fjqeed3Z+nPfrdjdPPcYvvahdF -9317el92v1fVet15uG0f8JqPwT/Tq9+Pbr1T5/dYr+pR+ez39env/Knf3fN+ -jO537rQ/df51y3e9p933qXtv6OaTjfepHv1+y3f3O7tvdvnuc7g6zuo6r47b -7Ydzzjnnse9qX70Hde8Pt91nT+f7afH0/L81zq59sSv/rP2u/jjnnHO+7tV7 -XfYd7/bfHTerl7VbzWvX/amaX9Wf6nd1H3yKR1Hd51m72ftutb+sXTeq7/Ws -R8/z1Pu4eg7tmo/Z8+Pp+k/NSxS75/ep51ydl9u/U/xdH4P/pnfLV/dfNt5q -u6xeNWbvCbvGy8atto/Kb9uHu/ft2+N0v/tvvae785l9b7vjn/Jquyie2o+n -28+Ot/u+Ut1n3X1Y/Z3lsdof55xzzt/zajx1n9zV7q1711Pzezp2zdNqf0+t -32x/UT+74rbzgHPOOf9F7973snvB7H1kd3+r/vS9bYxd67i736h8133y7bzH -37PjVPdJdbxs3Gz8bJy39uVsu+58R+W3+hi71zHqvxuz5033PF/dP93y3e2e -Xl/+3T4G/03vtj+d56522fm4u/+sn13ft2z8bh6nfSx/+zyrjt/9vs9+z6u/ -u+NH9Xb5rvfh1Hczym/1/Jg9D95un/W76/yrtpt9X6vjVfvJwv2Lc845j/3p -72T3XjFbP8tr13109d7Vvf90Y7bdbTF7z5y9x57eH919kdVbrb/LbznnOOec -85u9en/rfner95Fq7L5X7L4vdb2bb+ZP74Pd4836WF5dl6z/Xeu6ut7d/LL2 -u/Jc3S+rXn0vu+1O+1hejdn+uud1dfxuf7vO79vW65Z9xe/2MTj/RB/LZ78L -3e9fNn61f95rN3ueVdd593d/tf1q3qvjz+b39nfsVB5RPtXy7v493b7ab9Tf -7vnuPudT+y/z3f1xzjnnn+RP30u694bZ+8XsPWF3v7vWabZd975TvS8+HbPz -kJW/df+cbVf13e//7HuR1d+d12p/nHPO+c3e/f5Xv+OzXm3XvQfsep5uPrPz -GY0z60+tz6n9W83nNh/Lo+jO/1vveTe/zLvrG3l3v9+2L27zarssuv13981t -88b5Dh+Dc85PeRa3jLP7npOVd+8tWXm1n9u+V5nfksfo0e+uz7Zf3Xe76+1+ -v7rjZONm9Xbls3t/cM455zf7ru/tU/eJLI9ueTWfrN+n12lXu+p9J/Lu/a3a -rrp/ntoPs/tx1/5dvYdG/c6O282vu3+qv6O45bzknHPOn/Dqd7f73Zz9bs/e -E6J+q+Nmeeyet9X72Ox9qOqz83zr/n3bo3rV9ymr/9T+2v1+Vdvt6q87r5xz -fouPwTnnT3sU2Tn1Vl5Zu+55m5XP9lsdL/s9m+9sfrf5GG+Nt7oPu79n+8vy -q+7n3feW0+dad953rTfnnHP+CT6W7/6u7vZo3F15Vvtf9W677j1ldV5n21fz -2j1ud56r+e/O96n3YPX93dWu6t3xxvIobjtfOeec845n39Hsd/W+c/p5do3X -fe6ov6fuKav3mafXKRs/y+dWn61X7Wd2n1Tf86pH+VbLd7dbfW+jdrftL875 -7/gYnHP+tkf1nh5ntr/ueZuVz/b71PegW2+2n0/1MZ7uN/Pd7091f5563k/3 -6jyeyo9zzjlf8afad9vN3ks+3Xe1W52/3fMfxa15rq5PN69P8V3tsojmsTte -Ni7nnHN+o1e/f6fyO+Vv9Vu9h1Rj9jl2PW83r0/3rN6ufp7y1f7G8ihm99fT -73027un9xTnnY3DO+dOexVPjR+dht7/ueZuVz/Z7i8+uy+m8n/Zd/Y4x+17t -il3v0a969T72dB6cc875TR6VV++b3e/tbc//9P2i+/zV+163fbff2XrdfbPr -fpaVV/OK6nfn9TYfo9vf7O9sXM455/wbfPX7+3R+n+bVe+jb8db63XaP3O1j -dN+f255nV39jeRS736On3++x/PQ6cc5/18fgnPOnfSx/63zK8pntb7X+6NV5 -Of39eMrH2L0fbnnO7rrPztNszI779Pv79n5526P4lntc99zM2t3yXJxzzv/z -d/V7Xf0uVPvN8vtW734fV++f3X6q/UbtqrF7X+2+x8zWm12vT/Eont5X3Tw4 -55yf9dn7Thann2vWu/elW/Lu+ul1XJ332Zi9P2btb/Ms76pn7/3p59ztu9Z9 -1+/u+Fm7Ve/OH+ecv+VjcM750z4bt+RVPWez8u65fNv341s9qjf7Hd2V3y3x -9L0iKv/We8yu8+OUV/fp6jxE9avjVPPgnHO+x3e323Uv+xYfy2fvk7v6f+qe -O1tv9X61+ly7894935/mUezaT7vPMc455zWfvS/Mfi+q/dz+XfjUvHf57n01 -ew+5JXY/5+r8rubB53yMbL2yfqvl3Xj6nKiOf9v6cc5/x8fgnPO3fTynTo0/ -W68aq+Py3/Tb4vS9pHpeZP3c7tlznc4v8mxdu8/VXf/Z+Ts9b5xz/qkela+e -x6vfD/6fv1fvF9X+Z706flR/dpxdeUf9R7+zfHbl9+mexdP3QecO55zv9eo5 -2/1uZuWz/d0yb6PP3qdu9+o6dNfp1D3l7bjtHsfPePfcm43d466eh9l4WZ6c -c/6Wj8E550/7WJ6dW9V+Mj/VX1T/tu8Bn/NqZPtl9j16O3bPU/e9yPqvnh+7 -zoFTLo9/e3d9T+fLOeff4tV7S/W8rtb/Ve9+z7r3qLc9yjuL2ed+y99ax1/x -sfyp+lE7zjnnc/6p37sov9N+Sx6Zj+Xdeqv1q+VRv7fE0/eot8bnZ7y676Py -2femus+q34NqXrPzwTnnT/sYnHN+yrvlq+db1s/seNVzOCvf3Y7//fcYt+7/ -rN3bsfocp9a/mme3/m6vvv9P+dvjrfrqOs5+N7L6nHPO/+3O2T1eve/Mzv9p -z+J0fpl37ylZP6ef51bvlnPOOf+3d7/DmXe/h7d/B6vx9rqc2jfVfE7nt7vd -qajuk9vei9ve40/z7PfqOmXtZ/vvnufV/KrjROWcc/62j8E557f46rkWjVMd -rzpu1m913G5/s+f7p32HonXpts/qPe2reY3l1f24Gt1xnnqu0x79PuWf1u/s -uFG76jq9tZ7dcTnn/Nt9LK/e37rf6dn8vt1Xv5On71uZV+udfp7MPzXv0x6V -d9uP9brlnHP+Ld79Xu06d1fvK6vjPv2divLd5bfsm9N5RLF7XaLyrH433nqu -aB1P3euq9arnQbXf097NM6ofRXe/dt/v7jndzXPWT68r55yvnuOcc/4pHtVb -PTdX88nadfPo1lvNJ2rXzXP2963+dH/V9VjdR6fHjfrP+jvt0e+nfPc+rPb/ -1D5+aj2yPHf3n7XP8sjqcc75p/hT7Xf1/y0+lp++D536vt+S325fLf92zyKa -r9n+b3v/Oed81bu/o3j6XP/U7+xYHkXWbrb/3X5LHllU53v2eWfvDafGrZbv -zuuUj7G73ezvzKvlWf1svqL2T517s/ndtq8453y3j8E559/ms+ffrnxmx63m -0+2nGtV22XNleXyKn+qvOn/de0CWx+z+qeadjdNtd/v9aozZfbT7nFnNayxf -na/d+3X3+9Ud7+nvFOec3+az53AU3fP6V7za7vR9aNWzeOo7/pbvurf8qkf1 -Zt+z295zzjlf9eh8rN4vdn/Hd32vs353f5dPz8db+2NXv7u9Wz67jrvyqI7b -zW91P+1qt/u9OO3R78zfqtd9T6vjnT7fsjxu2yecc777u8M55/xdj6J6jnfH -6X4nsn6/1Xf1N7tuY7vq+syub5TH7nGeutd07zen7l1Zfll59Rzp7s9u+6yf -XfVW53V1/t9+3iyfrD7nnN/mUb3Z83J3ft/ib31vT3sWp/Pb7bPr/uselVf3 -URSn33POOc88O+d23xuq43XLq/lFeVW9237XdzlqX/Vd7avP9ZRX291yn4ii -O8+7nzfKo/s7itn1PrVut3m1XRSr51A3D8455+/4GJxzzvkv+Fj+1Hey2q77 -Hd/dPopd7U7fd7rz+JaP5VFU2+2ul7XP+p1dl9l9PbvOY3nm3XMlq18d57Zz -9FO82271N+e/7N3vQ9b/7vy+xaN6u9bpFs9i9rt/i3/rup3eF2P7qD/nDud9 -nz23quPNtvt1r55ru8tn90F3H3Xzm/3eVOvNjhPlm/mu+Zgdf9V3zfdTHv0e -o/qcs/t9tX0Ub5/D3fsX55xz/ks+Buecc/7NHn0Xnxq/2q77Ha+2j8bv1o+i -O/5t96DMTz1PNF7Vs3rV8ar3yO58Pj1vb73fu86jrN1YXm33bb46P7vWZfZ9 -iOpz/k3+dL+3POdbPpbv+k7ccs/K8uvGbc9TvRdVo9vft3pUvrv/sR7n3+TV -82f1e7zre/Tr7+nu+Tn9PFF099cu795Pnt631Xqn1nXXe32rj3Hq3tLtN4q3 -2lX3f3ceOOec82/yMTjnnPNv9qe+h6v9db/jq+VPexS33YN2PWd1X+ye16f3 -fTeP1f2cxS3nyNNeXa+n8zjt1fKxXrYPu/1U85ld36c9ex+rvznf4VH5rvvQ -t3m3/Jb70W7P4nR+p55/9r35dI/KZ79rWTnnM57tzyhO5bmr/a73bHW+uuPd -7tV9tHt9P81391ud/6jeU+v11Hx1x73tfjB7H+iu7635RbF7vzz1Xt22Xzjn -nPMnfAzOOef8mzyr99b4Wbvq9zr7zt92z6h6FN16tzxPdz13z193H3XbZfsu -65fPeXUdn85jt0fl1X2227vndfW5Vtczq7er/dvzzX/Lq+VR/due5/R3YLWf -2z2L7rl9m+967lue5y0fy6vxLfcmfoefOo+r0R0n+t3trzreLq/+jvK7zWf3 -1+m8v8Vn681+33e9j5lH9W75rlff8yhuPZ9mfXa/RTG7X956z26Zd8455/wN -H4Nzzjn/Js/iqfGj7+9qu9n6t90/Zu8r1fbdcZ7Ke9Wr+d0S3X072z7zt8Y5 -7dX35VR+s376e1E9R6L6Wcyef7O+a9ysn6jfW/YVP+ur59mvehRPnzu3eRan -83vqvleN257ntI+xOu/8u7y6D6r97Dq33j4vq+XZ+Kvlu32M0/tt1mfPuW/z -p8eZzeetmL0PjL9v8SjPyKvvwW3PuXp+v/07irff79vWg3POOX/Cx+Ccc86/ -2aPv4lPjZP1n+XS/36vzwHu/s3Wu1l/Nu5vP7nj7npmN+/T7fZtX9/FpH8tv -y2/3Ouw616P+qx71231/3lrvW9aTv+Pd7/AteZ/y2XvHbfer7r2rGrc9T/c7 -sbq+p5/nLY/Ku/PHf8O735en9mc0/uw41XOgOk5W77ZzYHVdoji9b2e/j5/q -q9+9qHzWo3Gfju587X7Oaj5v5fcrPntedc/nrF0Uu/Kq1ju9HpxzzvkbPgbn -nHP+zT5+F6vfx6fz6kY1/9P3DP6O3xZvPW/3dxa3nFOrfvoc657Hb+cxm9dY -/tT+2v3+zL4Xs/tp93d19zryu3x1n2XtP93H8u58nb6frHoW1fW/5Xm669L9 -Ppx+nqd89ncUt73n/O/ePSdWz9fqOFm7LJ56b7P+Z/OLyrP21fze8izPt333 -fv4Uj6I7H6fvH2/H6e8wf9ef2o9vnWPV8/ep7yHnnHN+s4/BOeec/4Kvlme+ -+v2d7T+qVx3n9L3kWz36HcXsfr4lqvuz2m5132fj73pvb/HZffjU+XrLOT+7 -v2bf4yyPWzzKM/LV9y+qv+u9P73/+TP+q+s6lq9+Pz/Vszid31vPP/v9+lQf -Y/f3jN/hs/s46nf2POmOu+s8O/196UY2z936p8+xsTyKt/b/0+M95avfsazf -rP1qv7fG6rmY9Ts7Dp/z1XZjvazfXd/DWc/yiso555zzb/YxOOec81/wqLz6 -He2O3/1OV/vvjlMd97b7ytuexW37ttrurTj13pzaF9n79rZ33+/dHuWzu99s -vF37IBs/Grfb365zftd5FpVX13VX+ez8ZPX4XT6Wd/fPbc/z1rlX7feW72h1 -/WbvM7c9z+7vTVR+Ou9T8/LUPYK/49117NbbtX9Wz6vd+7Gbx+q5s2uczGfH -WT1nsvGq+XT99nPq9vxW85q9Z7wVb+3/2fcly6ta/m3enYdd34/VcXd9r2/d -t5xzzvlNPgbnnHPO45j9zna/06t5VdtleYxe7S8av3ofme0ny/M2P9VuVzy1 -n7P+bvNu+Wn/tH6z8XZ5t313H6yeh7fsn6d8dn12zevp5+d/97F89lz+Vb/t -e7l6PkdxOr/dfksep73aLopb3sNf8er7mrXvfg/sg1p5dd6q79uuereek2M8 -/Z1+a7xqHtV9cotXY/U9eDp2ve+j3/Z9754fWbssVt/7XedhNb9q+13nende -P3Vfcc455zf4GJxzzjmf96jeav/ddln7rF11nOq9o9t/9fct6x757P2rOo9j -veo+2pXnbP/VfrP+u/fet30sj+KtfflWHrvbR/Vn12m1/ew+jPLI8svilvPu -Ke+eT93v0FvfVz7n3Xbd7+Kn+lg++x7d5rvj9POsfp+idrfl/dbzj/HWveZX -fdc+jGJ1/X71+1ud5+787cqj+56vepTn6v6M+u36rfeRsfy2/Gb3YXd9q+fa -U/nNvs+r52w1z1vuCd3y6HcUT91DovrdPGfnZfd7cct+4Jxzzj/Zx+Ccc875 -5/lb3/9snF+5h4zlTz1fNE51nrvtq3ll/VXzysbp9hP1N7s/n/Junlm7qnfz -6frT/c6eL0+t5+738al1/1V/+vv5rd+3W3z1u/h0fqe9Wh7Vu+27OPv81fa3 -PWf1uaJ2t+T99r7w3XzXV7+Db33H+Vy9XeM9/Z53/alzedd7tKvfrF43n1Pe -rbf6Xaj2082vug92vY+r5bPn/+n7wO7zJvOsv9l+V+89t80n55xzzus+Buec -c845r9XbPU7Wrnqvy+6D1ftiNb/qONl4q97N/6k8Vj2Lp/b92+2jek/NV3ff -z743s+8pP+O71rF73lXz43//vWtdPtWjervm8TbP4nR+q/eWb1233d/dKG57 -P2/1XeWz59Xp5+d//7vab1R+yzk/2z4af9afWt/uvN56b9m9fk+td9TP7HtX -vSd083x7P992r+Ccc845v9XH4Jxzzjnn/+m7+tuVRzffrH3WbzW/an+n77+z -83k67+j3Lq+O/1Re3edfXffZ8m6+UZw+13jN3zrfZvP7Nd/9HfpUr7Y7/d1a -9Sw+5b4ReXd/35L3bo/Kq/vitvfzVn/qffRd+0x/+l4SjbPrHOm2X93vs+9X -tf3seLfvp27909+hMXatw1N5PvW+Rv70d4Zzzjnn/Nt9DM4555xzvre/6D4W -tcvaZ+N226+O91Set/nsvD2VXzV27d9d9bL23XmOfLU8yve2c4rf4bvf59PP -c7tH8dZ5dZvf8p18yrM4nd/b95DTecz6GG+/97/is/eZ7nvIf8u773n1/V/d -j0+dn1G+me+a/9X2T6/3Ld+Vp79P1efOfr+VZzWvrL+u37aenHPOOee3+hic -c84557/mWb3d48z2F93ronrV9qv3yCyvapy+Fz/lY7w13lP7sFqvm9/sftu1 -37P8OJ/x3e/p6ee53cfyXefmbR7F6nf7Vs/idH6zvnt9b/dquyhuew9v8dnz -cHcenK+0H8t3f8+6/UV5detlPpafvj9k+Xyad2PXfot813c0ym/Wd/V32/pz -zjnnnN/mY3DOOeec/5pn9d4aPxs3utdl5aPfeh996nk/zcd4a767Pvs+Vfvr -7udqPrP5Rd7dp91zgH+3r56DT+f3ad4tf/t7//Z9Jqp/23evux5jnM7v9u/+ -res2hnPu7969Z2T9n34e/q5336vu71mfbV89d6L3Z9f59PT7XPUobvsevPX9 -HOufzi9b96eft1p/l5+eX84555zz230MzjnnnPNf9bfH797TVvs7fe/c7W/P -222+u98squ2r/VfbZc+b5beax9PenYe38uJnPFvvKE7nfat3z61b8p71KHbN -1ynP4nR+q9+vMW7Je9aj8u7z87/7ajn/bP+079nqc+1qXz2Hdt8jTt1vbvPs -d/f7f/p5Vu8D1XbZ7+68ZfVmvVvOOeecc/6rPgbnnHPO+a/5WP7Wvak6TjdO -3y9v8131sjj9nLvKu3F6X3fzmfXVdlG9rL/d+fDP8O57Wi3fld+neneePtVn -5+FWz+J0fru/u7fk/ZRHv3/NV8/9bv/8O3z2/M/az+az2m72nOjG7Py8NV+n -z+Xuc+/6Pq/m962+GtV7xi7fdQ/inHPOOf92H4NzzjnnnPdivG9l/VXzmO3v -9P3y130sj35HcTrvbr1Tkc1v9vxZf2/5bKzuL/6Z/tR50+3/033X+f1pvnpu -nvIsTueX+ey63O5jdO8Np9+Ht3x1Prv988/y1f2QxW3nxu77ydvRzeP2+f2V -79Wn+xjV70y3XVY/q3fLfHHOOeec3+pjcM4555z/qmf3pe69qls+22/UfrZe -NS/+GT7GU/2eim5et61L99zZff5k9Vafh5/11ffj2z2r92n7fSyvni/Vdqc8 -i9P5ze6b2fP+Fq+WR3Hb+/P2eRPVvy3vX/fu76ze7P7onutZuyyvt86Pbr3T -sXs+blsXvsdn39coZt+f6n57qt9b1oNzzjnn/BYfg3POOeec/9ur7Xbd22bz -Wh0nGu/0/ZW/498Sp+cx8+o50o3VcaPf1fGqcdv5/ite/U6cyu8tXy3/NK+u -822exen8dp/zn+JZ/Mp7Nf7+9XP1UzyL2fNndv1X71vffs5/SpyeR37Gx5g9 -j6rlu+4X3e/SbfPOOeecc/5pPgbnnHPOOZ/zarvofrar/6xdNb9qefU3/7tX -I5vn3f4p8fb6dN/f2f5u8yjvbruofbWcr/nq+f50fqd91z6+zaN6t5wvs/vv -lvxmn+d0Hk+f41m9T/PuPu3eF/gzPlve/X2rZxHt7+53s5rP7vxvibfP4Wr5 -7L3v1/2pdmN5FKvfo9Xz67b14Jxzzjn/Fh+Dc84555zf6d121XvgbH7VfnfX -7z5P9z4cxW37YXb/RLG7v7dj13sz+ux+5P/22XpjPLXuv+bROmRxOu+3vLpv -T+WXeRS3nQuz3+nT+XX3x+k8ZvP+tH3/1nvlO/SMd9tV9/Vtz/np/nZ/t8Xq -891yzq9+z6r9VNt38+re27r1o3pVn53Hbn+cc8455/xuH4NzzjnnnH+nR/fC -an9Zv6t57fo9m8e3+Gq7bn9vxe79/NS+ifLi//Yssvkd61X74//2bB2rv7/F -b8ljdT2zdrecC911uCXv1fLbvBqn9/dur353TuX36b56HliPZ/xUf6vn6dvx -1Dl52/l/+vsye395+tyKYnY/37YunHPOOef8GR+Dc84555zzf5VH98usv9ue -6zbP4qn1jLy6zrsjGzfLr9o+G393u26+/N++2l+1/6jdr/jq/D6d39tebXdr -3lHcfk5lcTq/1ffhdN5RXlWfbXfau+v2bc+/299+X7v58Xfbra7nbPun49R8 -zvZ3y/flNh+j+12Y3aecc8455/y3fQzOOeecc875umf13hp/tV3WPqqXtZ/N -Y1c+q+sxWx7lUZ0/vuZZvax+Vu/XfPZ9eyu/t727r27x2ffl7fc2itP5db9P -t3v0+1N91z5/Kr9P99n34HTev+rdc7b6Hr3Vb9TP7Di788nyqPpsu9V9wDnn -nHPOOX/Ox+Ccc84555zXPYu3xq+2+/M7+pu1y/qJyqOolmf9VfOo5pn9zjyL -7nPzZ3y1vyhuO6duPR/fyuPtc3h2/73tUb1b3s9vyft0HrPnXhS37WPn0rM+ -lu/ef3yPZ7G73ew+2LV/svyq43fznO23+jvz2Xan33vOOeecc875fwfnnHPO -Oec897fv16v9jX+j8qx9tTxrN9brlmfP1c2vmn/3uWbn4el8+ZpHv8fIyrN6 -3+K73oPb/JY8Zj2KW9+3LN9b8r49v6e+27f4rnP627y6vlE/WXv+jo/ls9/f -bH9U++2O99a5U82rml/2ezW/Vd/dX3V9b/lOcc4555xz/gk+Buecc84557z+ -+7Zxon6i8tl+s/az7TKP+u+O32236t18ZvOu9sf3elQ+u/+z8m/x1fPl6fxW -/ZY8Vs+TyN9637K45Ty/5XuTeTVO78vMu/vllrzf8rF89v7wVH787+Xde0bU -f3cdT59HT9+XZuc1G2dXf7vuOafO4eo5wznnnHPO+S/7GJxzzjnnnP+yZ/Xe -Gn+2v/FvVB71123XHS8aZ1d5lleW361e/Z3F6j7hPa+WR/W75d/m3XPklryj -uC2/7vydPv+iuC2/6Jy97VzK4tZ9Oftd/FafLe+er3zNq+VR/VvP593n0eq8 -zo6/el5X+4naVctP99d9fs4555xzzvl//+acc84555zHvqu/rP/ZccbyaNys -37fbRbHr+bvjdJ/nds/2X3V/3vI83+5ZPH0+3e6r+/cWvyWP1f331ntSzev0 -+/pp58nY/lbv7o9v9dVy/ox312Nsd8t58dS53T3XV/f37Dm5+jyz43Vj9dyc -7S/q97Z9xznnnHPO+c0+Buecc84559/k1fKnxt+db3S/z8p3tav22+0nalct -j/qv5hX1860+u25j3PI83+7VdlH9KG47r2f9054zKl9d1935ZfXfeh+qeZ16 -L2/NI/qd1X/bq+fet3m13ex3gu/13fv4tnvGU+f26vxE9XblVW23+7xe3W9V -n2331n3i9D7lnHPOOef8TR+Dc84555zzX/K3x8/GrfYX9VPtP+t3dbzZ/Lpe -LY/qP/U83+rd8u44tzznp/gYq+dLVn6rnzrPd/tteUT7cPz9tGdx+v07fY5V -47b9vnpefYqP5bPfz6fy+1Yfy6v3j9l1ue1+cKtXY/e5OttuNY8odn2XIz91 -z3hq3jnnnHPOOf8GH4NzzjnnnPNv8izevi/vGifLu9q+67Ptqp7lO/tcUf2s -XrV/Xiuvxu79/2selc+ek2N/n+Zvn/OzXo3TeVS/a099F6J83nqfTucxG6f3 -e3XfnMpv1aN6s+/L7vw+3VfbRfVv+35/qq+u2+w5uKvf2ec89Z3p+i3nfLcd -55xzzjnn3+RjcM4555xz/gs+lkf35t3jZ/VWn6M6fua7+zvtUXTX/Zbn+VTv -thuj+v6cfs5bfSyv/s7itvN9dp/ckl8Wt+Xx9D6+LY/T728Wp/dv9Xv6qR5F -9Vy57Xlu89X+dt9DeM27943VdTzlu74T0e/Ms/6r5bPjr87D6fXjnHPOOef8 -pI/BOeecc875L/p4b+62iyLrp3tfz8bJ+umO2+3vdt9V7+28f9Wz+c9itn/e -+33LOV712X11Ku9b84jqP7X/svGfyuPt8Xafe2/5avkt3j33bsn7U3z1Pa/2 -z5/1KLr3iU/1sTyqvzoP1eiOW22X1e/mc8v6cc4555xzfsLH4Jxzzjnn/Bc9 -ujd3y6PYlXc1uvlUn7s6b9/q3fJqO/6sW6e9HpVn9cd2t/steWTn9eo+r3oU -T++/6vhP7/e3x3trXb/9fYm8W++WvG/32ff7tu/ct/sYu86j255zt6+eI1F0 -v7vV9rPn+O79cMv6cc4555xzftLH4Jxzzjnn/Je92q567476q/ZTzbM7fubZ -OPzfHpVnv/mzPpavRnXdf8W75Z/qt+Xx1nxn42f5zHp1/Kf39dvjVfN422/J -Y9V3rce3erW8Gu5BZzyqd/qc+xZ/u9/VPLq/q9/lap6cc84555z/so/BOeec -c875L3u3/Kn7epZP1m4sfypP/m/PorqO1Xb8rGfx6+9l9fcYt3wnsvU7nV9U -/tZ4Wf3VfZON89R39+nz4pZ9tPv9vWX/j7/fei9u82p5VO/094P/z1+jep51 -251+zm/32e9Stb9deY4+mw/nnHPOOef8v4NzzjnnnHNej9V7eXXc2fIsj9X8 -+ZpHv7vtn8qP17y7zt7Lv8dt5371PVv9buz20+NF9VfPyWycp/bjW/s/y+Mp -Xy2/3W/J4y0fy7vfm6j/274f3+5jzNZ/Kj9e82y9dr3f3e/O7d9HzjnnnHPO -v9HH4JxzzjnnnL/vu9qNf7N61fb8GY/qZes9Rnecajt+xrP41fe1Gree79+a -R7X/1XMyG2f3/vqVfXtLHp+a31vPPzs/t53jv+pRvdXvfzZOtR1f86e+P93y -3XlxzjnnnHPO9/kYnHPOOeec8/d9V7vo3p/1u7t//oxH9arrODtOtR1/xrvn -xi15v+XVuPXc//Txqv2vnnvZOLv30bftz7fH+7b8Tj3/7L2AP+tRvdVzMhun -mh9/x6PfWftu/1G7rL/b5otzzjnnnPNf9jE455xzzjnn7/tqu6y/7N8D2e+s -Hv8OH2OsX63H3/UxZt/nqPyW51ydlyhOfw92fxdm5+HpfqN+dvUbjfPU93N3 -3qv75/Q+rvotebz1Xu1+/287Z3/Nx3Av+i1/6r3txux3gXPOOeecc37Ox+Cc -c84555y/71lk7Vbv/WP7rJz/pq/ur1N58//5a8yWf7pX463vQXUdnvLZer8a -t+2r6v3gbb8lj7ff46zdLefgr3pUr3vPeTtvfrdX99sYq/suKz89L5xzzjnn -nPP//s0555xzzjm/z8fy6F6flWe/V9t1++Xf5d39M0a3/25+/B2/JY9ZX423 -vgdP9yuejdv3w+o+eTqPt/22c4r/PbrnevWeMZsf/2yPyqv1o5gd96l2nHPO -Oeec8/d8DM4555xzzvk9Xi3f1c+f8vFv1H72N/9Nj+pV34tqP9X3JeqHz/m3 -ngersft7IMTf4u19dtt9afaeVD3H+JxH8fR3/1u+P/wdH8uj+rP7era/2X44 -55xzzjnn9/kYnHPOOeec8+/zbrusn2776m/OKx7V2/VeZP112/F/exS35NfN -uxq7z3fxG/H2vrn1PlOtd8t58Wle/R1F9n1eHZ/zGR/Lq/Vn62Xtb5kXzjnn -nHPO+fM+Buecc8455/x3PCr/8zvyLMb2WV7VetX8OK94VK/7vmT1qvuf13yM -2/MT4hPi1vtJVv+29/9TvBvZd7L7neV8xbv7sHqPqOaRRTVPzjnnnHPO+e/4 -GJxzzjnnnPPf8ag8+t3tp1tezauab7Ud50/4GN161ffl9HPe4tW4PT8hnozT -941q3HKunPYo3vrucP6mV9tFv7Oovlez+VX74ZxzzjnnnP+ej8E555xzzjnn -XZ8t//M7Gy+rNzsO55/oT8Vtz3nLPN6+bkJ0Yvd3f3bc286D3b4ruvckzj/Z -x+iWd39H/d02L5xzzjnnnPPP9zE455xzzjnn/Cn/8zuqn7XrjpuNUx1v7G/1 -eTk/4W/F6ed8yoUQ//+45b10TnK+z6vvx+x3Mypf/R5n+Wf1Ts8755xzzjnn -/Pt9DM4555xzzjm/3f/8jupn7bIY+6+2i9pn/WZ5Vvvj/A3fHaefZ9WF+Oa4 -5T1zXnEee7Tfd70v3fLq97L7HFl9zjnnnHPOOb/Vx+Ccc84555zzX/E/v6P6 -1f665d08unlW+6vmyfkT/lY8/TxCfHM4Bzhf9+p7kNXP2lX7ne1nNs/qPHDO -Oeecc875t/oYnHPOOeecc87/7WP5+LdbHtXP6u3KK+un22+WD+dvuBDic+L0 -ecF/08eYvbdV+41i9T4WebXf2f4455xzzjnnnNd8DM4555xzzjnnn+Vj+fg3 -q9/t/+m8sojy7vYf1c/659/pQoh9cfp95u969xzt3hu6MXufycpn71mz943T -68o555xzzjnnfI+PwTnnnHPOOeecr3hUXu2n+7s6/q7+ovbVfqr5ZD7bjvdc -CBHH6ffz2332vNr9nezG6vd/9n6RzV/Uzy3rzTnnnHPOOef8O30MzjnnnHPO -Oeecv+d/fkf1Z8d5O6rP9WkuhIjj9Pv5lJ+O7LzP8o7q3TK/nHPOOeecc875 -L/kYnHPOOeecc8455097FH/qd9sJIb4/dp0nnHPOOeecc84552/5GJxzzjnn -nHPOOee/5kKI9fjzfo3vGeecc84555xzzvmv+hicc84555xzzjnnXAgRxZ/3 -ZXxvOOecc84555xzzvnff3POOeecc84555z/qgsh1uPP+zW+Z5xzzjnnnHPO -Oee/6mNwzjnnnHPOOeecP+1R/KnfbSeE+P7YdZ5wzjnnnHPOOeecv+VjcM45 -55xzzjnn/DmPyqv9/Pldbf923Dbfu9dNCPHfcdv7+qnvfXa+R3+r/XW/J5xz -zjnnnHPOOV/3MTjnnHPOOeec853+53dUP2s320/WPhtvtt9qZO268zvbntdc -CBHHbe/rt/lsve53t9ou66/7vczaZe1X+1nNl3POOeecc845/5ePwTnnnHPO -Oef8szyqV+1nV/2sXjZON7rPEbW/bT35WRdC7Ivb3m/+jHfP0+53uhvd+8z4 -e/U+M1u/mwfnnHPOOeec88/wMTjnnHPOOeec/9uzetHv1fG740TjVvOZzSvr -57b15N/tQojPidvOD/5dPnsfOX3P2/W8UczmwTnnnHPOOee85mNwzjnnnHPO -+bd6VF7tp1uv2r7aT9Y+Gz8bj/MT/lZ8y3MIcSK+5f257fzjv+HZvWz2Hjl7 -z5ztJ3qe7rjd5+Wcc84555zzT/cxOOecc8455/w2j8qr/fz5Xe0/+tuNLL+s -f85v9t1x2/Odng8hborb3rfT7+dtz8d/27v358xn23fvt937dlafc84555xz -zm/1MTjnnHPOOed8l0fl1X7+/J7NJ8ur2l+339vWgfMTcdtzf9r8CfEJcdv7 -+Wnv+W3PzX/bZ+/dq+XRuNV8qvln7Wbz4ZxzzjnnnPPMx+Ccc84555zzVY9+ -d9tHf6txy3xwvuLdfb8atzz3W55FdP50XYgb4q335unxP8VXo3qe3PbcnK94 -t92u39m/OzjnnHPOOed81sfgnHPOOeec/653f3fbRe2j/rLxduXL+Rte3beZ -R3H6+W7xLLJ1eMqFuCFufS+juO18uW3+3vrucP6Gz97vs/em+++U6nd8th/O -Oeecc8757/kYnHPOOeec89/1P7/Hv1k/Wftuu6we5zt9LO++L7P9Zf3wf/tY -np1nb7kQnxi3vt9R3Jbv7b46z9V7ne8df8N33ddO/TuIc84555xz/ns+Buec -c8455/z7/c/vqlcj6q/6m/OOj+W734us3W3z8ekelWfrcspn4/T44jNj1z5e -Hfe0j+XV57rtOW732XMoOq+7/XW/E5xXfNe+694PV98LzjnnnHPO+ef7GJxz -zjnnnPN7Paq32s+f39Hf2f66efHf8LF8dl9H/WT1u+Pwns+eN1H5aZ+N0+OL -34hd+3513Ft9LF+9b/E579bb9d3fdW/m3+3VfbR6D1q9r1b74ZxzzjnnnN/n -Y3DOOeecc87v8dn21d/j325e2Tj8u311/6z2n43D3/VovT7FZ+PtvHaNI96N -2/fDrn1y+hxa9dPj87/76j05q7/7Hs6/w6vnxGq96ri33Jc455xzzjnnfR+D -c84555xz/r5Hkd3jZ+/71fxumyd+xrv7bLWcP+vjenbPi0/3LN7Oq/p+7R4/ -iu58/Vrctq92neOn9tW3ePX9fTsv/ncfy2f39e68+Gf76ns/ew/o9sc555xz -zjl/38fgnHPOOeecn/fuPT7qL2tfHTfqn3+3R3+jOJ3vr3u3fXU9u+fTLZ7F -Lfnu+i7Mfi+ycVf7646zO1bnYdd+2zVO9Xw+va+jPMa47Rzdtf+r87DrPOfP -+O56/LO9+t3ulnfPgdXvAuecc8455/x9H4NzzjnnnHN+3qv3+G69aNxu+S3z -9Ks+lmfrmLWbHZe/47PnRve8+FTP4vZ8nx6/Ou6sZ/Gp43zL/ozGe2v80/vz -U3wsr37f+Vkfy2ff/93l/Bnvnrvdczk7J6t5nD7XOeecc8455//tY3DOOeec -c87Pe/UeP9aL2q3mMdue13wsz+p12+3aD/xdj+pl7/u3eha353sqr2o+s57F -p47z7fs2yuN0Xr5X//bu94Lf5WP5rvOiOy5/xp+uVz1PT5/fnHPOOeec8//2 -MTjnnHPOOef9qPa3mk/3vv9WXnzOu+tg3e707vsWefd9/nQ/Pf6qZ881xtN5 -Vcfd7Vl86jhv7f9bxv+Vc2os/zbvtj99fvCaV8/9X933t3v1d7feW+d+VH7L -uc4555xzzvkn+Bicc84555zz/Pfu+3W3XpTHrnH4nGfrEbWv7rvZvPi7HtXL -3t9v9bG8+/sW75a/nW9U7+39/i3jnFq3t8ef3S+n8+3m0S3/du9+v/idnu3n -KKrtTj/ft3v3veye2918onGi+tV8OOecc8455/8dnHPOOeec8/3tZ/uJyrv1 -u571e8v63Oaz6/B0Xvw/f1ffqyjGfrL35Fd8jFvy+rbni+o9/T5l8Svjn1rn -t8e/df+/Nb9j/Lrvei/N9xkfy6vredtznPbud3j2nF2tn/VT/V313fPAOeec -c875N/oYnHPOOeec/4JH5Vk/Wf1d9/Qs7yi6+XSfv1vv0333fuBnfFc7/vfI -zpXT+e56vtN5nT5vsviV8X99/316vqvPkdX7de/ON7/DZ7/fT+d1q8/O5+x5 -FMVT94rd++G2855zzjnnnPMTPgbnnHPOOee/4FF59f4c1cvqz9aLoppvd9zu -70/zsTxb3+588j1enf+sfbd//vfyKG7Jt/s+V/fVqXyr+bzlWfzK+Kffx9vz -6t53bvPo9xiz5+aveVS+69ybzYv3fPVczNp9mnff/6fmb3bc7r1o9f50+lzn -nHPOOef8Bh+Dc84555zzX/CoXrWfXffyartdeUT9VNtV25/2av7V592VF19r -n+3zXe/lt3v1dxann2PWu/Nzep3GOP3d7Ob91Hf7qXG6+6jbbtazOL1fs7xP -57Xq1dg1P/w/f+8+b255vk/32e/prd+56ndh9/7bPY+z5d1z/lvPe84555xz -zp/wMTjnnHPOOf8mr8bb9+/sObJ+u+NH48z6W+uZPW/Wbtaz/nnNu+/lU/v/ -13yM7j6vtv8UPz1+9btQjVPfzdXv2lN5PT3+29+f1ff17bxW9/1tee16f6vn -UdYf/7vvOletw5o/9d2dzSOrt8tvab86X6fvN6fPb84555xzzt/0MTjnnHPO -Of8lz+7Ju+/fUfls++r41ajO4+o6PLW+3ec+vf8+zav7eLVfXvOofPZ9ue35 -dp2Ht+Ub5TfGbe/96byyuOU8PHUORHF6f89+R07ntepRvdXzKqrP/x2z389b -z8NP9yieOlerec1+FzN/avzV53/7PL/tnOacc8455/xNH4NzzjnnnPNv9qhe -Vv+te3m1ffa81X6j9pl316Gax67xZ8fp5vGp3p2fXfuNz/kYb50zn+LdfXzb -Od/dB097FvL6d/mp86G6r07nG+X5Kfmu+u72Y/BnfPb9fzqv230sX52fp76f -1fGfqjf66vlRrff0d2mM1XXknHPOOef8k30MzjnnnHPOee677uXROKfbZ56N -0+1v1zjR32icW/bT096dv6i/p94D/u+YXb9v9+z3bR7FLedENeT17/Jb9l0W -t+XrO/R3z+qNcdt58u2+Wv5UXqd99v3uth999ZycvXes1stidT6i/t6aZ845 -55xzzvl/B+ecc84557/sY/nb9/LVfrvtozyq5dXn2d3f7DzM5vG2z85rFKv7 -hM/5GN3yW57j9PxV3/fT+X7aeVNtt/tcn/Usbjmfo/q37NMsbsm3+x08ne/b -ntWL4pb3+dd99r0cf3/aes5+56v1Vs/D1fmsjrdrHk6dg6vlnHPOOeec/6KP -wTnnnHPO+S97VP7WvTzLd7Xf1fGzmO1v9jm685Ll8ZR38+nugyiP3fuU/93H -mF2nt/K9xbv7/XS+VY/itu/dpz1HFqfP893f77fOq9vznT0HxvJT+b7tUb3V -7xJ/xqN63fMkGue283x3+133jSyPar3ueFG7qmd5vfU9mT2nOeecc845/yUf -g3POOeeccx5Hdq9+6r6+2m+3/RireVf7q/afPVc2XjWPbr2o3eo8ZP3xd3ws -z6K6L295vqe8Op+35DvrY/ntnoV813wsv2Wfru7rW/KaPTfG8lP5nvLV9+u2 -9+zXPKs3+/2N2lfHzfrbXS9r352H2f6j312ffa9X269+B06fZ5xzzjnnnH+S -j8E555xzzjmvexRv3eO77aPy2eeu5jfbrprn6nizeWX9Rf1Xn+PpffTrPkb1 -fYnq3/Z8t8xrFLfk+/Q5HP0+7WP5p+Qbxel8q9+xbrvdPsavnG/VuCXf096t -l7XP6vE1j6K6HlG77vu1e1/M1ovO3+p5mI0fjTPb7y3n8BinzyHOOeecc86/ -ycfgnHPOOeecr/tYPntf7/ps+yzvrF71d7ddNn+r/XbzXB0nKn96X/y6j+XR -76z+7rw+3cfyyLvr8Sk+xuo8nfLT41c9i9P5fvp5MZZHfku+Vd+1z08/xy0+ -RnWes/6r4/CeR+Xd/b1rv6zm1W03uz+7+XT7O3W+rJZzzjnnnHPO530Mzjnn -nHPO/xXR/TLqp1v/Vz2K7v0+8m77bN2eiuq41efM2mXtn55PPudjZOtaXZ/Z -9t/qq+dN5Lc8X9W77T/l+5K1/7TnuCXfav6n9/Xqfr8l36fOtzG+9Xx7ysfY -9d3I6vE5f+o7uLpfqr/filPzmXmUzy3nwW0elVfrv5Un55xzzjn/Lh+Dc845 -55x/h0fl1X6ye+Xu++jq7yhuW5e3vTr/UUTtT8Xqfu7u867vfj9+xauRta+e -h7c89+3ene/T+T7lUdxyzld913f2lGdxS77d9+e2/d6d/9vy3f3cs+cgr/ns -emRxy3nw6b763ezug9nv7lvRvSeM9Wbn4Vu9GqvnxFPnVFa/up9vWxfOOeec -c/6Mj8E555xzzj/Dq/e/2XFW75VR+a76Wb1sHrI8svE+zaPYtc6norsPur7a -nv/PX2PXez1bj//7bxan833bq79v9Sxuy/dXnuP0vu6e22O903ndOh+R3/Yc -t/ps+6ifXe14zZ9a99ti17lx2/u3uh7Vda62y9rPjrOaV/c5d++L2/YD55xz -zjmv+Ricc84553yPZ/V29Z+NO9abzWt23Kj9r3o2v9X2T+f9KZHtx1WPyqvv -SRZP5//0PETlUXTPK77Xu+u663v0ad59f2/3sfxTv9dZ3Jbv7H67zaNY3W+f -5rPvj+/eGc/qRbHa321eje4+f2sePiXeOoer+7lbj//9d/U9iPrrtt/1PZp9 -/tn+Oeecc855zcfgnHPOOec9v6XeeO/r3g+zuGW++bv+LXHbvGbv4ep7utpv -ddzq+VXNg7/jY3n396d7Vm+M0+fELj89/qpncVu+s+fxp3gUv3KOOFc/07Po -7veo3a79kbWPxu+2u8W/JW6bV/6O7+ovO9eq59TseN1xOeecc855zcfgnHPO -Of9V39Xfar3s3jbWy/LP+o/q8c/01X25ut/fjtm8bluXbvmu8yc7d7rPx+/w -1f13y3M85VlU293mUb3qveKpvN763tyW7+y+PP1+dL8HY70sbnuOt+cpqn9L -vnztd/f7XI3Z7/rq+/vWub46P2/HU9+D3ePwM56tb/V9Xj13snrVqD5vtZxz -zjnn/Fd9DM4555xzXovxnhXdu6L6mXfzu23+fsWz9VndX2/7WD6b/1ORvW/V -8qjft70b3fMjq8c/w1f7G2N3/5/q2fkw+32+1U+Pv+pZ3JZvdd5PvwezHpX7 -Hs2V7+6ff5bPniNZ3PJ8o1fz7bZ/Oj7t+5TF7PnNz3hWb/d3vZrP6fOEc845 -5/xT/P9pt162ZFd1RQGe///q277sqSUJsMFZoU4NBw8JjMkag3POOef8r3nU -763/w6p1ZeH/vv/2sT17X7Pv5ZZ1r57TLLL9Wt3HLN+uerrf6ew6u+Nm2/m3 -ffVeWp3/13yM6nf1dZ89J0/XtepZ3FZv9XclGnfb97Trd/Gvrbt6D1efx/jr -9/xf913tY79qPdV+s9/F7O/BGN39mf0Oq571u+V3K4ruvdQd99e8u0/VOHVP -vZ2Pc8455/wrPgbnnHPO+V/17P+lp/4/q/6fls2bjf+V/wdP79stvvs8RtH9 -PrJx0fzV/N35Vr/Dpz16HuNUffxdr57zcfyper/iv/67mMXsPXybZ3Fbvavf -9envZtbHWO3H/x3de43/hkfPY5yue9e6Zr+Dal1ZfVl7dd3RfFXfPd/bvmvf -dtd1yk/t21vf+9P5OOecc86/6mNwzjnnnP81H9vf/j+sm7e6jsxveQ9vrfdr -PravnrtqHbPnM4qn2rvnJBs/61GdUX2r+89/w6v3YPSc9ftrnvUbo3uffcWz -uK1e6/vv9tu+s9nvMovZ7/qvePdey+Z5ul5+t4/tq8+77oXZ9u59Ons/7Vpv -971knsVtv3OrPvv7+XRdXX9qvad+T/3+cM4555zXfAzOOeec87/mY/tT/2+t -zhv1G6O6/qf2bzVuOx9Pn7OnPHtePYfR/Nl8Ub+qR+2r65wdx/l/+a7v9PQ6 -bvfZfmN8xaOo3m9f9Sxuq3f197E67is+xq7v+q/66u9IdRznO3xsz6L6u521 -z34H1fGzvru+qmdx+nfxKe/G6nnL/Kl+u85h11fbOeecc87/io/BOeecc87/ -7av/h2V5sv/Xsnmicdl82TzdfLvrvM27+7b7HFVj93mdrW/3OeiO273PT71P -/ls+xmo//n//GU/fV7f56fyn1x3FbfXu9tPf3+7vbPZ3+K16v+rVfdz1fvjf -8Opz5lm/p34Pn76vdu9zVMdTPtt++ndx1md/Z3bt69N1Zr46vvq7wznnnHPO -//3MOeecc87/7dn/Ubv6ZR71i+rOfPb/w269q3U+5d06V9/frI/tWX278jxd -d9b+9Pl5+j1Gceoc8Z4/fb+dXt+v+Bizv2tf9939Tnn2fqPxT/9ePO3V++K2 -7+/p7zjrf9s6vuZjdL/HXz+Xf8Wf+p3I+u3O071Ho/ZsfNWz513f66nfsah9 -9T295d37LfLu79quOnefq9n7YjU/55xzzvlf8zE455xzzvm/25/6P6w6PuoX -zZu1z/5/uFpnN1/Vu/Xvfp+7z8UYT+V/aj1jexTd/cjmy/JkXj3Pu/fj9Ln7 -q77rPc6+1269/N/tY7/o+Vd8bM/25a263lp3FLfVW70XuvfD6e9vt4+x2o// -27u/U91+3XuZv+Nj7HqPka/+DmfRXdfs/dmddzXfU3nGOOVje/d+2u2r57la -fzd/lKc6X7f+rt9y3jnnnHPOv+pjcM455/x+77bv/r/hr/8fEvV7ap+jv9l8 -UZ3Rc7W+rJ4sb7d9dp7ZfXvLq3Xuyj9bz6xH82c+O+6t+XZ/j0+/97/mu37X -Mt9VL695FLvvn6/66u/ord6910/Xu+pRv9V77qs+tnf737KOX/EoVt/bXz3f -b/9urt6Xs+PezvPU/bPrPI/9duWJYraet3xs7/4+zo7P5pnN1x3fHdedb/f9 -f9s9t+v3bPe5e+p39vS+cc4553zdx+Ccc8553avtq3mz3/HV3/8ouv9fdPOM -88yus5r/1HmY/b+tei6y/t26qnV256/WlfXrnsvTnj2/5d33tuteWb0nVufb -Xd/qOaz2q9Z9+ly97WPM3ofVeavjb9unr/vs+G77Vz3rt/r7fdp3x23r+8r/ -DW/52J49/9V9Ou2z46OYPQezdfyar+7L7L28+55/ar7V8zk7X7TPt9xbWZ1j -3OZR++z7zeaL+j31+1Yd99R3UD23b3tUZ7fuLFa/02o89Z0+9V3cdh4455zz -L/sYnHPOOc99/H3dNV+3X/f3P4usju580bzV9WfzRO23nJOuV/9v2/3eV2PX -eY76n/o/eXZ/b6kru6fe2pddvnu+1Tyr7d3nX/fZfZt9v9X6qv34Xp/tN8Zf -89P531pfFLfVO+unv79bfAz39d0++91meWb7n96Ptz3rt7u96rPjTt+Tu+e7 -/X6vPt/qWUT7P3tud8fu77263tt8bI/iqd+JXeO79WX5Zt9vta7u+K+dK845 -5/wmH4Nzzjn/i9593t1vdVz0tztf1v9XPduHt+roevf/vLeieg5nz/Mpz2J1 -vbu8ei5258/qGeOp73a2X9Wr7d06uvOuntvZ81HtP7ve1fl23Z/8HY/6zd6n -Uf9f8d37fptX643muWUdVd/9vdz2fT99Xrvn5/Q6+H//Hftl843x1vnpPnfr -7vru380sT7e+rlfX8dQ98/b5H+O2ezaKp97/Lu/uwy2x6/58yrt1R/1+1bv7 -MHsvVs9Dd96n5j99bjnnnPObfAzOOef8L/ru39vu72+13mz+bFyU55b38Ku+ -+xzcHk+fu6fbZ+u41bPnp/J093u3Z/2q6+vmyfLfej6qPnt/Vft330t3nmxe -foeP0Z2nOt/tnvXb/X3f7lncVu+ue/av3mfVcd3+/C4f26vPUcyO647f/fv2 -tq9G9j6zOm45f6freivPU/sV+ey+dtu73j23p2P2PHXnG9v5Mz57D8322/Ud -r66jWg/nnHP+F3wMzjnn/Jc8al/9fXz69ziLaL5sXv7bfls8td7ucxan/x/f -7afusVWP6tztUR3Vc5XVn+Xb3T773VSjOm72O13d5+p75Hd7do5X27/qUb9d -3+Vtvuv3e3ddT/vq7+Qt3/FuH9uz5+7vBb/TZ9urebJ+Uf8ouvdWVk91/u55 -X/2d6e7navtufytPd/2r5/krXo1d3+nu7+mWOLUP/F3ffR5P32PVum67tzjn -nPMnfAzOOef8lzxqr86z63c3q6tbfzR+dR5eez71nrN5q/Xsiu75f/o9VfM/ -9Z2f8tP5M4/63fKdz3rUPrsf1flXvVrXar6sX3Ye+N/y2d/lX/dqe3Xcbeub -vY+ieW5ZR9dX3+8t3/FbPsZqP/6b3r1f3j6fu++T6j1Yrbs67muePd/mX6v3 -6e/nrfzd72Q1qvsw6911zN5r3br+us9+/9V5svm657/7+zv7fe+qg3POOb/R -x+Ccc85/yaN463c3q7e6nl39b3s/s++zuq/dfZyt6+11d8/70zH7PTz1f+1b -+W7z7PmrPrY/5Vm/2Xsjm+/t+3pX3tVzV+3Hf9Or46L+f8WjyPY1G/dVz+K2 -emfXt+s8/FUfY/Ue4r/l1e+rOk/1HM7Os3r+s3FZ/2r76fca1XdLXX91Havn -+K17YPa7ejpm82fn6S3vjn973Gmvnv/dz7O/F7vvt7fycc455zf5GJxzzvkv -+dj+9u9rdXzUL5o3a7/tPVTrG9uzfrvresqr7787LsvXHT/2y9q79fA5nz0H -p+qtetav277L3zr/1edo3qpX66meu+58nFf6RdH93n7Nq+2r89zi1XWO/b+6 -7u730J3n1z16HsPvGX/Cu/dad77Z+6Fa32y+6vf39Puo1nP6nHS9+/5O1/vr -Pka1/an3mNXRrW92vlOe9avu/+66nvLZ95nNd+qe3PU7yDnnnH/Zx+Ccc85/ -yaP23b+jq7/P3fFjnP79r9Z32/nYte7Z9c++9+65mq03es7GrebP5v1Vnz0H -p+p9yrN+WWT72p0nq2f3+33rfI39smfOVzzrl/WPnv+az+77r3gWt9U76933 -fvr7ftvH6N4bt6yD/7ZX20/VuWu+6DmK7vdc7XfLe3/6fVXP2el63/Yosv2q -jpv9jt96X2N71aOY/d5v9+69+HRd3X3etf7Ve/6p38fb7hXOOef8CR+Dc845 -/yWP2qvzrP6+Vsd380R1P7UPWb7Z/Ld7t32Xr44b+3XHZeOr/aO8T+3bru/x -ad/1Xk6v47RHMXu/z56n1fk4/2Uf26sete+a/yve7bf7Pbzt1fcdzXPLOqpe -XV82723f/Vv3StRv9711y7o53+m7f0+q32H0XJ23Wueve9Yvav/KOqrnY9Z3 -j9t1bqt5ZvPt8rfyvOW777nu/bq7zmz87Pnt/r6s7gPnnHP+iz4G55xz/hc8 -6rf797U6vptnjGod2bhs/Ox6d9Wx6t32t/8fWz0/s3VE+avtu8Y9tc/VvLP7 -nPWv3kPZvN16/7p3x89+n6t1cv6LvnrvR9H9HfpVH9urvze3raP7/qPxX133 -7O/Y6e/7tGdRvYe63xfn/H/bo/7dPLvr/Gs+tkfRfZ9R3tX3260n86zfU/u1 -+p7e+o527fOsn86f+a57afY8zNbV9VP38FPzcs4551/0MTjnnL/jWcze27O/ -A7ftzy2++rub5am2Z+do1/utrqe6H1m+Xd7dx9P/d63ON8au+VbPa9Vnx3W/ -t+776H6/Vd9VT3Uezjk/5VF079Vd9++v++n8b3sWt9X71Hu97bu/xceo9uuO -55zzWzxqr84TRdSe3aur9XTXleXPvDqu2/7UuLFfdb6o3659XPXd/d6et7rP -s+81q2e2rmye1e/39P142sdY/U5n77Fqfs455+/4GJxz/nWP2lfvzdl6ZvPO -3tvZPFlUx3Xru+2cvPUeV8fveh9vnZ9ontn+s/tz2qNYzfPU+YzmybxaR3e+ -2XxVX/2+ovkyz+a97RxzznnXo+dofPe+3/X79Wu+u98pr56HsX827pb1Rd79 -Xm777t/2sb06T/Q8Ox/nnN/uUXu13+hR/6f6Zd7tN1vf0+8j8ur7WK3vqffz -lHfXmfXL8nf7Vd9jNu/q9/XWubnlvlv9HiNffW/VfFHe7ncazTM7/1P3Wzbu -lnPCOee7fQzOOf+6j+2z999Tdb61zqx/N2+WZ1f+2Ty3+Orv8div+n6r82bj -385bne/0/0uz52J3/l3ncHX+zKv1reZZPV+754/G3XqOOef8aR/bo5j9Pfmr -nvW7rd6n1v12/rf9lu/4Nq/GOH723rpl3ZxzvupRe/RcjewerfrT81fXv8tX -83Tn31131r867ikf23f3qz5n/U7ljero+i33V+bd9ixmv+tuPd26quOq9eze -/27+rK7Zejjn/FYfg3POT/mu+arPu+abzTtb5+y9/pXfgWr77ve827O6xufZ -85Pl3xWz69y1rlMe1X2qrlvXP+vVc9y9x6rjdn/vs3k55/xXPOrXve+rz/zf -fjr/Ll89L7d7t53/O3bdG7esj3POT/vuebt5u+O6eZ/ex93zvVV39/1U13/a -d73Pav7VeHtdp89XtY6of/X5Fl/9vmbv79n+u9/D7Lno+un7knPOu/c955yf -9uw+695v1Xm746rzduevztsdz/87bqlv9nw/Hd1zH/mp/3+q7dX+T3n1/T/9 -f2HWfvq77X4Pu87f2++Fc85/1avPfK597HfbOmbXHcVt9Wb7Xo1xntu+41t8 -jFvq4pzzr3r1nu3Ok82b5Tm9L9V4+72c2pcouvv4tlfXNfv+n4ruObntuxjH -8//26vnM5p29z6vzVc/B7O9D9zu97feCc85P/55wzv+ud8dX56/eg9183Tqy -cB//pkfRPX+r+Z6OXf9vRPNmz7vug9lxp/10/szH9lNebb9l3zjn/Fd9jOwe -nu3/Vz16D9X+T9W1y6vn4+26uv70e/yrHvVb7f9UvZxz/le9Ou62um+t63T+ -qlfrj2K2f7WOqF/mp+Lp99Otg3/TV9/3rvu0O756P2d++l7knPMxOOf8aY/a -q/fV0/djVmc3duflf9Nvi7f2YbY963e7V/frdL1Rfd17r3rv78pzet845/zr -nvWL+kfx9vhf9ai9+p7e2u/V9z327653to7d+x6NP/193+LV2H1/zN57nHPO -/+3de3/1/s7yZ3XM9n97P7O6b6m369Vz0X1vT/ltcWof+B0+e+/Nxq77dvd9 -0a2Tc87f8jE45/xp78bb9+BqXVG/2f1zf5/xqP2p99yt61S8fS5X9/92z87N -bfVmPlt39fvZ9Z3dtm+cc/4rPjs+itn8v+67xu+ef7Xf2N6tfxw3u/7VdVX3 -ddf8v+5ZrJ6T2X6cc87XfPV3IerX7Z/V0x3/tkfPWb+v+BhPnatq/lujul+R -r+7/U3Xxf3v3fc22Z/NX4+n74pY6OOd89p7mnPOnPOr39j24WsfYPts/Gnfb -e3vKV/f1V37nVs9f9XurRjfvW99vdx++4lGc2uenPftef/U9c875X/HqPZ71 -z/JmkdXxVY/as+fRu++5O89sXVm/ah27ztVs/dX22e8mG/8Vj+LpczV7Pjjn -nN/hY4z9f/Wer+5H1H7LOmZ9jLf3OatnNbp5u+//dl99X7+2H5HvWueu5+73 -1B2/6m/n45zz7D7inPO3PIq37sGs3ur4av4oT+a3vbfZ35db6n3bd53favtb -ses7+ms++75P1cs555y/4Vm/bv/deW71qL37PHr0txuzdUT1dPOsjs+ie06r -/brvJxt/m6+273rmnHPOf9Gjfln/U/V+zU9Ht86uz477Fe++99P1Zr67XzZ+ -9jt6+7u97V7hnP89H4Nzzp/2anvUb/W+y+rN5u3mj/Jkfsv7md3P3XXd5mP7 -6jntjtv1Hrrtp9b7Kz62d58555zzL/nYHkXWHvXLnlf7fd2z9xX1m33P2fzR -c+ZZnlvq7O5z5Ld9x7vvg7Ff5tX5onlW761b9o9zzjmv+Njeff4rPrZXvdue -5Z8d//Z6o9iV5zaP2rN9r87ztO/ul41fzb/rfEex+3vinPNZH4Nzzp/2LLL7 -6ql7sDq+m2eM6n6t9ptt7/5uZO1f8bH97XPXnW923ih2fa+j79q3br63PYru -ek6vg3POOV/xqN/Yns0XzbvLZ8c/Pf9ur77H6rq756JaX/ScxdN5V/c5Gld9 -H29/x9V6d8+/y2frzJ4555zzL3vUb+wfxel1VOupjotidlw2X1ZvlCcbX923 -1XPw1L581cf26v5X59l1Tnf3y8Z3z+Fuj/JG7afvZc753/UxOOf8lEfx1H0X -5cnm7eaP8lTzRs9dn61vNt/bfvr3dLXuyHf9rq+2V707btf31f3us3zderNx -1TpvO8ecc875Th/bs/Hdecb+1efuuCx/NG83b7X/Ls/eY9SvOq6avxrd89Ct -c/Y8dPdn1bt5x/5Z7DoPs/Puqiub5/T9yDnnnD/pY3vkUXvUL6sjG1fNE7Vn -nj1nXh232l4dV9337rpX93m3n86/Wm/3XMx+z1m/3d/D6nmL5tt1v+2el3PO -d/sYnH/Ro37R+Y/mq86f5evOz//tWb/Ze3B13m7+KE/0vLvf0/W/7d33+/bv -6e48T9Ud1VttX70vZ332/5qn9jWrN4rT55Vzzjl/06Pn2Xmj9qjf7Hy76tvt -T8+7+n677+WtmN3f1XOx+1xFda76qfm665w9n7PjOeec81/yXeN3edavuo7V -urKo1lndz6y96k+fi6fee+ZRPW/l33V+u+Oj/a/u02y+1fm65352fPc7vO3+ -vcXH6O73rvmjftW6OP+ij8H/po/t2Tm6pf7q+a7W3c27On+3/mrc+r5mPer3 -1v2465xl46rRPS/ReejWuerd36Oo/dTvZtT+1Pf/9nqqPjtu935m0T3ns78P -1XlvOcecc875TR4978oX9cvq6PaPojrPWz62z47P+nfH3xLZvmT9Vvf19HlZ -Xf9s/933ye55Oeec81/0qD2KqD2aLxqX5cliV75Z3/U+ZsftrmN2P3fva9Wj -fk+d61mf7Te7v1FU81Xnma1/t7+d7+31VOPp/NX7Z/W8V+t86/7bff5uO2/8 -rI/B+X89z56j2Xp2/+5Wo/p7sppnnC967tZVnf+W87bLb/l9zc7D7vf4dD3V -umbznf4dnN2ft+p6ep27fPd8s3m67av79tTvKuecc86f825080TjM+/W/bRn -dVXH3x6z73fXe1/17Lx0z181/2yc/v4555xz/r+xuz3LH80TRdY/q6vrp/d9 -dh93+2y/MW7x6v5V562+39k6s3yz5222ntVzsnrOb7k3d33vu95jdVwW3Xu2 -ep7G9tX7cNd9Go3vzpvVecs55Hf4GPybXr1nZ+/Fp9bR7Td772X5ovy73sfp -56zO1d/p0+c/iu55qXrWL6pj9Tvtnvfq+Nl6sv63/d5139/sd74rf1THrnMb -PT/lq+doV92r5+DUueCcc875//rYHkV3vmo9s/nf9tn6d/nX4qn9qL6P0x61 -7/oeovlmv/tb7iPOOef8F32MsX80fnX+at5sXHfe3Z7V8bU83X2sjrvFo6ju -eza++pzl79Yzu97sede5rX7fb/vYnsXsPRS1d+va1b87PhsXzVPNX31vs/fj -qlfryuLU7xR/18fgd/rYXv2uV++fXfdF9bk7bvb3Osq3q95f99mYPa9v++p9 -Ovv/wFMx+/9Rdfzq9/i0Z3VG8Xa9b53PbP5bfbb91nPJOeec87qP7VF026t1 -zNab1fXX/Pa4bb/e9l3js3mr38vqPXHL/cU555zzvD16HqM63y2exa79rO7r -be852q9bfPY9d/s9HbvXu+t8nvoed+/7Lef1lK/e77vO5+x3t7rO7jxR+2wd -t3xfvOZj8N/wrN/sPTX7vWfzZXVW5+/et9W8/Bmvxm11r96zp2P2O1u9B075 -2B756Xq79+Lu/wOqvwun74vZ9377++ecc8557GN71H92vtU6b9mn27za/las -nre/6mP7U99hNe/seeOcc875Oc+eR49i7P/1da56tG+37kvWvzrutHfPQfV8 -n4ruebvlfK3GLefpV707fmzv/i5k41fr697Ht/xO8Lt8DH6nR+2r73f1/4cs -z9O/n841/y9fbZ/Nd3s8/ftSzbdr/rF/9nyrn87frWuMt76jp37HOOecc36P -R8+z42fnicZl85zev6e8O666f2/F6rmp7suvePb+du1bNG/3Ppitg3POOefn -fWyPIuv3Vt2n83f381bP+o0RtWdeHTc7f9W/ErveczVPt53/LV/9nlbv99V7 -LLqfZ9f51fue/98/g9/pUdxynqJ6uu1ZvP3/Gucz/rWY/a525cvqyOa55R5c -vTdvqav6f0N3XU+999Xv9vR+cs455/x/PesXtUf9onhqPbP1jPPt7v/0emfn -2x3dcxP5W+c8iqfPQeZvrbfbPntvcM455/y8z47P5oui26/7/BXPnr/m3feZ -+Wx09/ur0d1PzjuefdfV774as79HWfvTfksdfM3H4Ge9O+5r52bX/02rdc2O -47/p1fMUxez5OxW33G+r/3d91Vfvy6/5GKv7Ue3HOeec89/3KKr9b1vP7d4d -F8Vqezaue16i8dV5ec+j99L97m9ZD+ecc86f86jfGN1+1fFf9azfbfXu9rE9 -6n+qrtuiun/Vebrz8b/hs99RNl8W1XswG5flP3WvReNuuY/5v5/5b/jb52n1 -+8/GVftXn7PxfM5nf/+6sfp79LR3/x94K776e3xLHU//3p6ui3POOef8Kz5G -1L/aj/87ns7TzV+NMe9sXV/Zz1/z7nm5pW7OOeec89s8ah/jlnpX/ZY6dr2X -tyLLn52bt3z3vlXfXzaO93x2n2fvr24d3frevjdO3198j4/Bz3p13Klzk9VT -9Wqeanu3rur4r/rs+Nn3MJvvdl/9PmbnXY0sT9Qv827e0WfzftVXf39vWQfn -nHPO+Ve9+jzG6bpnvbsfT3mUd3VcFtV5Z9fx1PuK8j2d/2mvfme31c0555xz -/nXP+o1xut63vdsvitV6svlmY/YcZO27x93u2XvLPHsP1bhlP3b5rvspmy+K -Xffr7nmr+brn7un6eM/H4Ge9Ou7U+cjqyTxq3/1/SveevNWr76f7+37L+k55 -tF+r57g6rlpXdVx33mqeaN7bfsdO+679PL0OzjnnnPNf97G9GrP5q/Psyve0 -Z/VWfXXc7Hyz5yXLd+t76p7DU9/L7DjOOeecc/5vj9qjiNpPr+N2j6K7n915 -o7qiftl82bhqvur83XG/6rve9+66nvKnvpvMq/PMfu/V8U/f59Vx/KyPwe/y -28/H6u/07PhqnU//7nf/H1n9XaiO+ys++/6fOseR78o39utGdd7ZeyJb92qe -0z7bPsbpdXDOOeec855H/W6r86n1Rs+zvjpudr5d+5TlPf3+dnv3u+Ccc845 -53d61i+K6viv+hjZesd+3VgdV62reh6646J8u/ytPF/z3ee3O29UV9e799Bs -v+481bpWv7un/ZY6+L99DH6nR/H2dxzlf+seiPJnvnpPr76v2f2p5vs1X/2/ -Yvd52/397K5jbI9i9r2c+p16K8+u388oTu8j55xzzjnn//IoovZZ3zVfFqt1 -rO5rtb7bzgHnnHPOOf8bHrVX45Z1ZD62P+VPz5eN77ZXz8Nt+z/bfupcvO2z -/Z5+z6v1rfabnbe7/tnxt+fjz/gY/E6P2k+fm7fvjWh85k/d52N71q873694 -1i/6G/Xb7VnsPqez8+0+N7PjnrqHsvp27+Nqe/ScxW3/B3DOOeec87/hUfsY -u/yp+Xbnees9RHHL+eCcc84553/Dx9jVr9qePc96Nn/mWb/ufNX9jHz2ve46 -D9X5qvOc8t39vuaz7avnMMv71nuq1lU956fv7dn3wu/wMXb1u+3e+VWP4q1z -szrvqft81+/47Pe1a12nfPY8nv696Na5K8/u39vq/LPjnj6fu7//1XMVPUf5 -Mj/9u84555xzznml39gejcu8W8dqnix/17v7tOs9rM7HOeecc875kx71y6I6 -vurd+bL1dfN3x6/OV11HdR+q46p1Vb06/ymfPddP17XLZ89HFLvOZ5Rv17qq -42fP89P38Bi3/B78uo8x+z09/V6r80Tjnv5d/Gte/R2P2qterataz6339uw9 -3P0Oqu27ffX3N5rvtEd1Pp3/9HqiePo87Zqvu5+76nnq++Gcc8455/xJH9vH -yPrt8izf7jxZ/q5393mXR/Wt7jPnnHPOOec7PGofo+qr/cb2ap2rda+Oy3zX -+5sdt7uO2fOze19XPerXXd/uulbP7ex32D0/u/bjqXto9X566l6t7if/d6ye -z9336lN1ZvM+tX9Zv+j51z1qf+v3dPV+Xr23s367fneeqn/1Plj9Tm+7V6v3 -ZHff3/o93fUdPX0/7PbZftVYrXN13277HjjnnHPO+W951K86TzTfbs/q2J0n -y9/1Xfu9y7t1vFUX55xzzjn/W77aHkXU3vUsqvVk43f57veUPT/13p/Ok80T -9b/NZ7+DU3XNjo/e6+r6q/m7vnr+dnnUfvref8vHOD1fdZ5s/tn8u+eLYvV8 -Rj57vmf7f8Wj9t3nI8u7697O8lSfu+Pe+n2p1lHtd8t9u/r7FPnXfzdO3zNZ -zH43o+/uf2rfbvtOOOecc875N32MyGfHPe1v53kr/+lz0d2H6no455xzzjlf -8afzZXmzfqNX+0f9ql6t5+19W51v7Lc7z+739xUf26vvYTVf1K863+z9MJs/ -G1etazbPW/fZ1zzq1+0fRXe+6vNqntn7J2uf/R5n5z/tUaz+bkf9b1v/27+b -Uf7Z+yrq360jy7cr7+y81f2/7X7e9fvU/R5P1fuUV59P+1vz/cq555xzzjnn -f9PH9tn+pzx73u1ZPL3O6G/U7y3v1nm6Xs4555xzzv/Lo/boeYyoPfNb1h/F -qbpO56++z27/W31sf/q7eWpcFru/89l6nr7Hbvludu9vdZ5q/9O++37ePf6v -evc77nr1ezntY/vq99+dv/ud745dv1Pd8dG42+/5Xb8Lp+vKzt+p/LfdD6v3 -yfi8+/eSc84555zzm7z6fNrH9rfrzWJ3/uw93nKOxrilLs4555xzzme8Oi6K -2flu9Sie3v+snlv2Jas7GvcVXz33s9/TbB274un9iXzX/XTL/TDrs+fkr/uv -3kN/zVd/B5+ur+uz98ht8dT9tfp/0S0+xi11rfrq9/j07+6t90DUb3Udt5wL -zjnnnHPOZ8ZXx0V53vKs39v5n8qz672+5VH70+eWc84555zzJ7w6rtv+dN2z -HtV5qq6v7mPm1eev+K73We3/lejuyy3nNKszi1vOJf9vv6UO/q5n/Vb/P1j1 -X4nZ37/bPYrV35fbvPsdnK43qqPqb33Xb7ff9l4455xzzvlveNQv6z9G1H6b -Z/3ezv9Unu77vtWz6J7b29bHOeecc85/w6P2qF8UWf9s/qfW0/Xb30vUfrre -2fWNUT0n0bjbPKu/+53dGqfP0e57i/+m31IH/xsu/v+45Xd3dp7V9q/42B75 -LfVW61z9naj2n11Ptz7OOeecc85P+NgeRTZf1P8Wz/q9nf+pPNm6bjl3Va9G -1v/0OjjnnHPO+d/2rF91vqxflj+Kbr/q+NMe1Zk9f9W77V2f3efdLv7/OPUe -+N/yW+rg/Bfj9v3s/n9aHfc133WPft2jfrv6d/f7tv3hnHPOOee80i8al43P -+t3ip/Jn8fY6bzuP2b6tnsvb1sc555xzzvm/ImuP+kV5dvX/us+OP1XvUx71 -y85bFtl5ftu/HrftJ+c31cHv8Gp7Nf7q/X/be539f+H0/zdve7f9dL2cc845 -55zz5z3qN9s+xtf97Txv5T997t4612N0z/HpdXDOOeecc86f96jf2D97/is+ -RnU/b6n3q1E9n5nvyjubn/+m31LHV/yteVd/73bX95aP7V/5Xbj1dzTzW+q4 -1e0f55xzzjnnPHsevRrdeqI6nvLZ9WfP3X5RVPe/mz/z2X17yqvjspjtd/r7 -5JxzzjnnnD/vY/vY77Z6b/Fb6ui+3+h9n47Zuqrn97SP7d3vLhq/69xkdfD/ -9lvq2O1j++y5qc7XHf+r3m2vvp9uvt0xW//u+2zXfKd/32/1sT3qf0u9nHPO -Oeec8+c9eo7GV+fLIsv3lI/t3XVn81Wfs3grb3X8qXMaRfccrvbjnHPOOeec -/65H7d1n/t/ts/NG41fny/I8Fdl5yvpXfXbcr3j1++5G95xn8/yK31JH16vv -afXcdev6dR/bd93rq3lW862er9nzdPr3/q/5rnN4eh2cc84555zz8x71i8aN -kfWr5o2ed3nWr7vebp5svqfzdte/er6y/N3zNntObvveOOecc8455+c8ao8i -aj+9Dv5//4zZ9xm1z+afXVe1rlnPYleer/qu5+ycdOu6zd+eNxq3+n6y+XnN -o3P/1n0/+7u/+vuy+x7fXW9Wxy2/36f/bxhj9txl/W5ZN+ecc8455/ycj1Ed -X21/ev7VdWT9quvr7kN13Op7y/JU17ta52x9u+bP8nDOOeecc85/37vtY7/q -c3X8X/Moqvv+1HxRe3Q+svlXz2HmUb27vPr++L89O2fZuOr7eOu72v09Rf1m -943v8afvrdV77qnf/W4dUTw17tR72VXfbb7rd/X0OjjnnHPOOeff825055lt -r3p1vVn76rxZndXo7ldWZ3cfuu1d7+5jtZ7VeTjnnHPOOec88rE98uq429aX -+Rir+1T11fqy+bI8s+cjG3f6nK56tb636/or/tQ9Vc3bzdeN6HtZ/a5/3Xe9 -r1t+f1bHjf121VHNUx23Ol/1e9n9XrI6s3p31bU6f/Q8xu7/GzjnnHPOOee/ -52N75uM83TxRZP2766zOPzu+m//tqL6f6vua3ddsf2bzztY1tq+e59u+Z845 -55xzzvl+j9rHyMZl/aP5q/V0PesXRXc/dvtq/ixm32+2j7PjorpW6zjlu9e/ -q66v+Wq/sX33vZLl2XWeozx/1bv31+nf12o8lefte3XX79fT52f19241f5an -Wmc1/65z0u3POeecc845/zs+tmc+zhO1d+fNYrXuyJ8afyqy9zz2m/Wn3kcW -2Tzd9VfPczUv55xzzjnn/O941C+bJ+oXPVfn664j6letO5qv6931r3p3XHV/ -Zs/D6jmZfe/Z/Lf57n6/6rvO4Wx7Nc+ufmPc8h52efU9rr7P0/50nrfqrvrs -uNvPf3efdv9/0v3dq47nnHPOOeec867vGl/16O9qHVHe1Xqf8rfjlvV/Jd/b -3xHnnHPOOeecjz7Grn5R/u74ah23+Op8u9/r6nynzuNtPrZn68rmvW19q57t -29hv9n5YPZ/ZPNVxY9zuq+u67Xere+/tOm/d+W+7J2fH7c4fxdPnOZo3e59Z -Pat17fo94ZxzzjnnnPPMq+PequP0fsz6qcje09f8rfeUvb/bzhfnnHPOOef8 -Xs/6jRH1j/pV59vVLxq3O381uvPN+q7zMTuue95W51udP5rvtFfHPXWeT/vq -+lbPYda/e76i+U97d9xT3/HbnsUt9b413xirfuv9M/v73Y2n6tz1e3H6XHPO -Oeecc86/56vPu/3UfoyxWn80z65Y3a/q8yl/+pyfqoNzzjnnnHP+ux61j1Ed -F42vzl/12Xi7zlWP9n3XOYjiqXN1yqO45T3P+tievYcsblnf7vGr52bXvdEd -v7uOrP3273jVT+evfp+n9+Upz/q9fV+Oz7vHveVP3X+cc84555xz3vVb6jjt -2f6cimqdf81vqYNzzjnnnHP+93xsP11ftX3sV33Oxu/y0+81qu+p83Pr+qv7 -8lXfNW71e+zOk3lWd1bX7LnN6srmr46vjtu1rl/xMbrn+zZ/a79W9/Ote2z3 -+Op3Hs3/1Pvq1nv6nHLOOeecc8752H5bfbs8W+dsnmy+aux+L1m/7nxf8zFu -q49zzjnnnHP++z62jxG1785bfe6OiyJbVzXv236q3lvW/1S9Y/yaP7Ufq3Xs -6pd9L7Pf0Wy/aFy1jq9/f5lHUe0XjTu9vtP5x/hr3m2v7t9t75dzzjnnnHPO -T3v1eYzVfNm8q3mqXq2vWn80brWup9cfxWqe7r6e/h4455xzzjnn/LRXx41R -bb9lnaf9VP5b1t89L1lk+/srnr3P6rgouvNl81TfX7Weah2r+7K6f7d9Z7Pr -GftHfsv9Fvnqez79Pn7Vu+2r5y175pxzzjnnnHP+bR/bM8+eq5HVt7qOW/aX -c84555xzzvmcr44b+2Xtt63/1v19yrP6bqs3qjM7b2P/r3oU0b6Nz9XzsOu7 -766jGrvObbXfrvZbfYxd98ct6/tqvVm/bvstHkV1P6rzf/W9c84555xzzjnv -+dhe9dVxs/M9te5b3gfnnHPOOeec85pnz6vzZnF6/VUf27vPt/nX6s3O1ex6 -v+Zj+673X/3+u9/30/H0ubndx8jO0+72r3n2fJvP9hvjNu9G93x2f78555xz -zjnnnL/j1efdvjpudr6n9zWr5/T75pxzzjnnnPO/6lm/bL7ZuGX9mXfrPl3v -7Ppuq+ut9Y3tma+OP+1RdPf5tnj6e9/tu+7h2fqjfrd8t7t+126r6ymvRvce -3HW+qvVUz3/2/Cu/z5xzzjnnnHP+Kz7G2L87rupZ3DLf0/tdre+2c8M555xz -zjnnv+5jexSr83TzVPtn9UTzrM7/q346/1OeRXfc7Dmr5ln1XfPeHk/t32q+ -Xeeuer5u+97evq9mz/8t61j1MarnZfa73/X/QHe91fycc84555xzzp/1qF91 -nmi+WX9qvt15nn4/3Xy783POOeecc84573nUL+vfba8+R5H1y+qP/PT+7/Lq -/kd+yzpOexTVc7z7nK6OX813Op5e7+r3kcXq/Znl/2s+Rvd3h//3czS+e25v -Wy/nnHPOOeec8//26Hm13y5/Kn8Wu+qO/kb9Zn1XnZxzzjnnnHPO7/SxfYys -fzT+9Lq+4tn+j3G63lt9jNlzW23P+p3y03HbfnTvp2o/3vPT+TnnnHPOOeec -8y/7GFm/6rjdnvV7Ks/qfNX9fNu7dZ6ul3POOeecc845/7Jnz/y/PXqOxp+u -t+q3xS37suuc8JrPnsuvfW+cc84555xzzvmbPkY0Lut32p+ab3ee295/91xk -/W9bB+ecc84555xz/oZH7VFUx92yvtv9ljpW/anI8q2e89O+ui7+3/2qccs6 -OOecc84555zzNzzqN7ZXx2X9n/bsebdn8fQ6s/f2tM/Wkz1zzjnnnHPOOed/ -wbOI+t22jq/6GLfUt3tdWazuy+w4/i3P4rZ6Oeecc84555zzNz2KqP2rXl3/ -Ls/i6XVGf6N+t3oWt9XLOeecc84555y/6VncVi/f41F7N7JxUXu1nu45vmV/ -ec3H9ihuqZdzzjnnnHPOOT/hWb9q/+q4t3xsz9b/VP6srl3efT+nffcz55xz -zjnnnHP+Fz2KaPzpevmcj+1Vnx23e76xffe5z8bvzv9rXt23KLr3U5aHc845 -55xzzjn/Jc/6ddtv8bE9W/9T+bO6dnn2Pm87d9V1zp5bzjnnnHPOOef8l3yM -rF91fDTfLeu+1Wf7jTH7/qLYfR6ifrvXc/t3ddv5e+scR3HbOjjnnHPOOeec -8ze92y8bP1tPN99uz2J1f3bl73q13uq4t33XuO58s3k555xzzjnnnPNf8jGy -9rfqestn+43xtGdRnW92PbvXsTrf+L5OfSfVumbH78qX9e+eu+75WP3+OOec -c84555zzL/kYWb+xPesXPd/m3f2pzpeNi+aZXc/s+/vqeRz7Zc/d/eGcc845 -55xzzr/oY3s2PurXbe/W9fY+RfVW64rG7/an8u+a7+n9eCrPW99ht18Uq3V3 -n1fvh9n75/R9yTnnnHPOOeecv+FRv2jcGNV5s3G7PepXXU81X3W9u+rqPs+u -522v1hU9d8dxzjnnnHPOOee/6GN7Nn5szzzqN5tndl1ZHavzZ3m6vnu+t/Nk -+/90vrfyVPtX96N6Tqv5unl21VH1an7OOeecc8455/wv+tieje+2V/NW5+l6 -dV92zVuNrI5unm590fvYdb6iqObN6s7qyPJyzjnnnHPOOed/0WfHd6M7b9Wz -uqp5quuszlPtP+tv59m1P0/5U3l2n6/qPN3vdjZvN6r1cc4555xzzjnnfJ9H -7dX+1XzRc+bVOqp1d/NUo7o/0XO1X3UfuuciqmPX+N35OOecc84555xznnvU -3o1ovmzerJ5o/Oq41Xl2+1t5Zt//6f156lzuyrOaf3bfs/HV/tX3e8u9xTnn -nHPOOeecv+lR+xiRV9uzmK2jW2+2/ixPlr87766o1jU+V89Hd/6uV9/XalTX -Va2vOo5zzjnnnHPOOf+yV8dFUe1XzZ/NG9X7dHT3abau1f2oerf9q+vM/PQ5 -u2W9Y3u1XzaOc84555xzzjn/yx5FNr7bHs3bbc/6rY4f27P1no5d76Wap+rd -ftX6uu+l+x3c9n1yzjnnnHPOOec3+BjZuO74t3w1onXeut5qXd3z8VRdt+7j -2F5971l0v7+3vNp+y/3EOeecc84555yf8KxfFFn/at6of1ZHNs/s/F2f7fdW -dN9rNH523tV9Xp2/eu5n8932PXPOOeecc8455ye8Ou503dX2LLJxs+27/fT5 -6Na76lFdWX2r53U172wdq+9jtf2Wc8Y555xzzjnnnH/Rx+j2y/Ktjq+Oq9bb -9ep+3B6r56Drs+818tn53zrnnHPOOeecc875X/aofYxsXBar9VTzra632281 -7+lzMMZXvNoe9aueq93nvFsP55xzzjnnnHPO3/dqvFXf2/lO7+vuiOr4ikf9 -3jp31fxv18c555xzzjnnnPPcq+OqMc7Tzbc6/9d8jL/mUfvq+enO1x3HOeec -c84555zz53yMqP103dnz23WMUd3fp2N2f7J5Zj2qo9p+6r1m+3ZL3Zxzzjnn -nHPO+V/0MaJx3ecsT9T/ln05/T6yff5177Zn+7w6nnPOOeecc8455/f6GLfV -d4tH7aejWif/7/bb6uOcc84555xzzvn/+mx7FNX2W9b/lo/R3ads3Fc9Ow/V -ePu74JxzzjnnnHPO+X2+2v4Vf2q+sV83xvl31509f9VX2znnnHPOOeecc37e -d80XPUeR9YvqPL1fq96N7rhq3q97FN33Us1/+txwzjnnnHPOOed83aPI2qP5 -o3HVurL+2fhdHuXttmfjVut6a/2z5yHrN5snG8c555xzzjnnnPN7PWofI+qf -jYvilvXv9jGe2pdq3u77estn9yWbb/Z9VL8LzjnnnHPOOeec86/62J559lyN -rL7Vddyyv5xzzjnnnHPOOedVj9rH6I7L5omimv+0R/VW17e7jm6/aNzsfNV8 -3XMXjVvdn+yZc84555xzzjnn/HYf26u+Om52vqfWfcv74JxzzjnnnHPOOY88 -ap/tV22fjW6dVc/6ze5Pdfxuj55X61mdZ3c9nHPOOeecc84551/zKKrzZPNl -ebvzZdGtI/ob9YvmrdZ7+n1zzjnnnHPOOeec7/bquDG680TzVeeJxkXz7PLT -72f0LLJx1flX3xfnnHPOOeecc875VzzqN7ZH42Y9i1vmO/Ue3s7POeecc845 -55xzvtuj9jFW82bzR/1u3R/OOeecc84555xz/htefd7tT823O8/T7yGr5/T5 -4JxzzjnnnHPOOefP+On8nHPOOeecc84557znUb+xPRq329/O81b+297z2/k5 -55xzzjnnnHPO+Zqfzs8555xzzjnnnHPO/+1RRO23eHU9Xc9iV93R36jfW57F -bfVyzjnnnHPOOeec/3U/nZ9zzjnnnHPOOeec13xsP+Wn6s1i13pmx91yLm6p -i3POOeecc8455/yv++n8nHPOOeecc84557/qY3s3ovGn/Jb8UbxV1y3nazaq -7/eW9XHOOeecc84555x/1U/n55xzzjnnnHPOOf81j/pF47LxWb+3/VT+LN5e -5y3nrlrf2J49c84555xzzjnnnPM1P52fc84555xzzjnn/GtebY/6f9Wzfm/n -fypPtq7bzuPs+R1j9pzftj7OOeecc84555zzW/x0fs4555xzzjnnnPOveHVc -FNk8Uf/TvrvfrGdxav2z5+Qtr8bs+zi9Ps4555xzzjnnnPNb/XR+zjnnnHPO -Oeec86/72D72i55v9+p+vFVXFk+vf3bcbV6tu9qPc84555xzzjnnnP/bT+fn -nHPOOeecc845f9uzflHM9ovGZflPedTefX6qriieyl99T6fP9ew6u/u969xw -zjnnnHPOOeec/7qfzs8555xzzjnnnHN+2scY+63OU60rG3/KZ9c767tjtq5s -3VG/W851dX9X17s6D+ecc84555xzzvmv+un8nHPOOeecc84552/7rvFdr+bZ -lW/Wu/12raNaTzVvNX83bzTv6XM9u85Zf/u745xzzjnnnHPOOf+an87POeec -c84555xzfot3x0f9snmr/ar9Zz3L361vdT+yOqP53l5fNX92TnZ5lq+6P6vn -87bvmXPOOeecc8455/y0n87POeecc84555xzfrtH/aJx2fju/LPzZb6at7oP -2TzVOqP5nsq76311z121jtn3Fc2/ax8455xzzjnnnHPO+R35Oeecc84555xz -zt/21efq/GNE46J+2byZZ/mqPrve6ryr8+3az26eaJ93nceur65zHNete9d5 -4pxzzjnnnHPOOf8VP52fc84555xzzjnnfNWrz5ln/bJx1fan1zFbR3fe7D1l -ear1zI6b3cfZdc3ua7e+bp3d6Na5+h1X5+ecc84555xzzjn/mp/OzznnnHPO -Oeecc77q0XPmWXTnz/Ks1ltdx+q8u8dX9+fp6NbZPY9ZvlnfNe9T53PX95XN -zznnnHPOOeecc/41P52fc84555xzzjnnfNWjftG42ajmr9YXzZ+1d/2pebN+ -X4nqOVnd/93zZs/V9zJ7Truxez2cc84555xzzjnnt/vp/JxzzjnnnHPOOedv -eXVc9pz5bN7uOqI6d/vu8bfH2/tT9d3zrp73qF83bzUf55xzzjnnnHPO+df8 -dH7OOeecc84555zzVY/6dfu/5d16d+9TFFmdq357PLX+7nvZvd+3fAdRv1vq -45xzzjnnnHPOOd/tp/NzzjnnnHPOOeecr/oYt9WXebaO0/XN+leieo5u9+z7 -uO18dL/n2+rmnHPOOeecc845z/x0fs4555xzzjnnnPOnvBvZuNPrmV1vNG42 -unXuyrsaUR2nz1U27pZzV61rNm5ZD+ecc84555xzzvkuP52fc84555xzzjnn -/G3P+nX7/3VfnW93VN/r0+v6dV995pxzzjnnnHPOOf91P52fc84555xzzjnn -/BaPnsfozvNVH2PXfnbzVGOsZ/d6np7vtHf7jXHbejjnnHPOOeecc85P++n8 -nHPOOeecc84551/xqL0b3XzVvNX+u/cniqzO7rgsqvvWnf+t81QdH/WfHf/0 -OM4555xzzjnnnPO/6qfzc84555xzzjnnnPNveNRvbI/GRZHlq0a37qrvno9z -zjnnnHPOOeec/w0/nZ9zzjnnnHPOOeec3+VRv7E9Gpf56rjZ+Z7ep9X5OOec -c84555xzzvlv+en8nHPOOeecc8455/yMR/3G9mjcrK+Om53v1L4+lYdzzjnn -nHPOOeec3+2n83POOeecc84555zzZ32MqH91XNWfmm93nqffQ7cOzjnnnHPO -Oeecc/4bfjo/55xzzjnnnHPOOe95NaJ5svl2+VPz7c5z6n1m9UVx+vxxzjnn -nHPOOeec85qfzs8555xzzjnnnHPO/+1ZvzGi9qc9i6/mOfX+s3qyZ84555xz -zjnnnHN+h5/OzznnnHPOOeecc/5XPItxfHX+LM9b/nSeLJ6q+5ZzFLXvOm+c -c84555xzzjnnfK+fzs8555xzzjnnnHP+1zxqz+aJ+p/y7Hm3Z/H0Oqvv8W3P -6ozitnVwzjnnnHPOOeec/5qfzs8555xzzjnnnHP+VR8j6l8dd7tn/d7O/1Se -bF2nz91TPrZHfku9nHPOOeecc84557f76fycc84555xzzjnnt/sYs+Or8532 -0/mzuqI4Xe/pc1r1MXad31vWxznnnHPOOeecc36Ln87POeecc84555xzfrtH -/Vbnj/Lc6rfkj+Ktuk6fx93nbvacv1Uv55xzzjnnnHPO+Vf9dH7OOeecc845 -55zz015tjyLKk/W71cf2W9aXxVt1ZefqlnM9+x2M/brts98Z55xzzjnnnHPO -+a/56fycc84555xzzjnnb3vUr9s/iqj9a346fzdu2ZfbzvvsOR77Z8+r3xHn -nHPOOeecc875r/np/JxzzjnnnHPOOedv++7xY3zVo36n66rGLXWN5+f0eV/1 -MU59d5xzzjnnnHPOOedf89P5Oeecc84555xzznd51J49j94dn4271bN+1X19 -y7N4q65d5+wrPsbs+qM81Xy37AfnnHPOOeecc8551U/n55xzzjnnnHPOOa96 -1G9sH6M7X3V8tf/XPOt3S11v5589R1/3qL3bvzrf2J49c84555xzzjnnnN/q -p/NzzjnnnHPOOeecz/oYUftb46vz3OrjOm+pqxpv1VU9R9l+3uZRPPVdVOft -5uecc84555xzzjm/xU/n55xzzjnnnHPOOa969NydN+oXzZc9d+v7ilfX9Vb+ -bPxT+Xefv9s9i9Xvc7aO2/aJc84555xzzjnnPPPT+TnnnHPOOeecc85nfYzq -+O581eeverYP3f7VfZqtozruqfdbnW/0W76bXd9Z9TnrV/1eo/lu2SfOOeec -c84555zz0U/n55xzzjnnnHPOOV/1MbLx0XzVeVbzZ96dP/MoX3V9u/ctmj/r -n8Wuc7JrXPW9P/V9dMed+i6q4267dzjnnHPOOeecc84zP52fc84555xzzjnn -/Gkf26uRjY/yVsdn+ap5d3l1H7P1rOarxmw9s/VV+1X3bbdndVf7d99793xn -7afvC84555xzzjnnnPNdfjo/55xzzjnnnHPOedXHiDxqr+bN5s3mq9bR7Zfl -W/Vund19m82XzfdU3tV+2f50vdterTMbF0V137vrq+Y5fR9xzjnnnHPOOeec -Z346P+ecc84555xzzv+uRxG1d311XBbV9a7WU92/XfNm+cZ+1XVX83fHz+53 -1t7dh8h3fTdZfVXP5p99n1HM1rO6P1k+zjnnnHPOOeec86f9dH7OOeecc845 -55z/XR8j6h+Nq84bzd+db3VcVudTvmt8d3+y95nVsRqz+zB7vrvfQVbH0179 -3mbfexTd9u65ml0P55xzzjnnnHPO+W4/nZ9zzjnnnHPOOee/79nz6FH/zKN5 -s3m6/aI6dq1jdn9n562Oj6I67+2RnYOsX3d8198+f7u/i9l9ydqr80fznL4f -Oeecc84555xz/rt+Oj/nnHPOOeecc87/ru+OLM9sfVG90fhu+y7P9nU1X3f8 -V6J7fqPxXX/7fGTPu87Xrny74/R9xznnnHPOOeec87/np/NzzjnnnHPOOef8 -73r0nPWL+kexWvfT+xHVe9p3zfu1uGXfvlbH6j1Qzft2fZxzzjnnnHPOOeez -fjo/55xzzjnnnHPOeRTdcU/Vd/s+RZHt01P+a3HLPp6qo+qnzn32nb5VH+ec -c84555xzzvnop/NzzjnnnHPOOeecj+1RRPM8XV/kt+zfrf6ViOrm//a3zlPW -L6szar/l++Ccc84555xzzvnv++n8nHPOOeecc84555mP7VHcVvfoWf1jnN7v -sd+u+W6L7vqqz295FN113Oqz98TpujnnnHPOOeecc85P5+ecc84555xzzjnP -vBq31f1XPHpf0bjTEdWf1XvLfv8Vj6J67m5bD+ecc84555xzzv+en87POeec -c84555xzHnnUHj1X53+67l/xMU7lqUZ2fmbrO70/v+LdflH/6nu4bf2cc845 -55xzzjn/e346P+ecc84555xzzvkuH9vHftFz1P/0enb7GLvyVOdfHZdFdh6q -+5LNO+vRvLvz3OKz31m1H+ecc84555xzzvm9/v8ALjYi4Q== - "], {{0, 0}, {401, 401}}, {0, 1}], - Frame->Automatic, - FrameLabel->{None, None}, - FrameTicks->{{None, None}, {None, None}}, - GridLinesStyle->Directive[ - GrayLevel[0.5, 0.4]], - Method->{ - "DefaultBoundaryStyle" -> Automatic, "DefaultPlotStyle" -> - Automatic}]], "Output", - CellChangeTimes->{3.6641621075311346`*^9}] -}, Open ]], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"newtonplot", "[", - RowBox[{ - RowBox[{"Function", "[", - RowBox[{"x", ",", - RowBox[{ - SuperscriptBox["x", "2"], "+", "1"}]}], "]"}], ",", "2", ",", "201", - ",", "20", ",", "0.05"}], "]"}]], "Input", - CellChangeTimes->{{3.6595549152958674`*^9, 3.659554978383319*^9}, - 3.659555332709116*^9, {3.659555509656427*^9, 3.6595555271955185`*^9}, { - 3.659555597485504*^9, 3.659555613597739*^9}, {3.659556133025359*^9, - 3.659556138135767*^9}, {3.659556178511237*^9, 3.6595561786634045`*^9}, { - 3.6595564436249084`*^9, 3.659556460417568*^9}}], - -Cell[BoxData[ - TemplateBox[{GraphicsBox[ - RasterBox[CompressedData[" -1:eJzt2MEJwCAQRcGFVJJK0kNKEHK2znRjCSLRi6QAhXmwsEwJ/0z5fo6IePu1 -/6tc8RvnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc845 -55xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc845 -55xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc845 -55xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc845 -55xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc845 -55xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc845 -55xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc845 -55xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc845 -55xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc845 -55xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc845 -55xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc845 -55xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc845 -55xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc845 -55xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc845 -55xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc845 -55xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc845 -55xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc845 -55xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc845 -55xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc845 -55xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc845 -55xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc845 -55xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc845 -55xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc845 -55xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc845 -55xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc845 -55xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc845 -55zzvVySJEmSJEnaubF7zfsX55xzzjnnnHPOOeecc84555xzzjnnnHPOOeec -c84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeec -c84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeec -c84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeec -c84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeec -c84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeec -c84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeec -c84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeec -c84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeec -c84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeec -c84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeec -c84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeec -c84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeec -c84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeec -c84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeec -c84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeec -c84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeec -c84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeec -c84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeec -c84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeec -c84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeec -c84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeec -c84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeec -c84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeec -c84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeec -c84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeec -c84555xzzjnnnHPOOeec89W9Algh3kA= - "], {{0, 0}, {201, 201}}, {0, 1}], Frame -> Automatic, - FrameLabel -> {None, None}, FrameTicks -> {{None, None}, {None, None}}, - GridLinesStyle -> Directive[ - GrayLevel[0.5, 0.4]], - Method -> { - "DefaultBoundaryStyle" -> Automatic, "DefaultPlotStyle" -> Automatic}], - FormBox[ - FormBox[ - TemplateBox[{"\"Divergent\"", - RowBox[{"-", "\[ImaginaryI]"}], "\[ImaginaryI]"}, "SwatchLegend", - DisplayFunction -> (FormBox[ - StyleBox[ - StyleBox[ - PaneBox[ - TagBox[ - GridBox[{{ - TagBox[ - GridBox[{{ - GraphicsBox[{ - Directive[ - EdgeForm[ - Directive[ - Opacity[0.3], - GrayLevel[0]]], - PointSize[0.5], - AbsoluteThickness[1.6], - RGBColor[0., 0., 0.]], - RectangleBox[{0, 0}, {10, 10}, "RoundingRadius" -> 0]}, - AspectRatio -> Full, ImageSize -> {10, 10}, - PlotRangePadding -> None, ImagePadding -> Automatic, - BaselinePosition -> (Scaled[0.1] -> Baseline)], #}, { - GraphicsBox[{ - Directive[ - EdgeForm[ - Directive[ - Opacity[0.3], - GrayLevel[0]]], - PointSize[0.5], - AbsoluteThickness[1.6], - RGBColor[1., 0., 0.]], - RectangleBox[{0, 0}, {10, 10}, "RoundingRadius" -> 0]}, - AspectRatio -> Full, ImageSize -> {10, 10}, - PlotRangePadding -> None, ImagePadding -> Automatic, - BaselinePosition -> (Scaled[0.1] -> Baseline)], #2}, { - GraphicsBox[{ - Directive[ - EdgeForm[ - Directive[ - Opacity[0.3], - GrayLevel[0]]], - PointSize[0.5], - AbsoluteThickness[1.6], - RGBColor[0., 1., 1.]], - RectangleBox[{0, 0}, {10, 10}, "RoundingRadius" -> 0]}, - AspectRatio -> Full, ImageSize -> {10, 10}, - PlotRangePadding -> None, ImagePadding -> Automatic, - BaselinePosition -> (Scaled[0.1] -> Baseline)], #3}}, - GridBoxAlignment -> { - "Columns" -> {Center, Left}, "Rows" -> {{Baseline}}}, - AutoDelete -> False, - GridBoxDividers -> { - "Columns" -> {{False}}, "Rows" -> {{False}}}, - GridBoxItemSize -> {"Columns" -> {{All}}, "Rows" -> {{All}}}, - GridBoxSpacings -> { - "Columns" -> {{0.5}}, "Rows" -> {{0.5}}}], "Grid"]}}, - GridBoxAlignment -> {"Columns" -> {{Left}}, "Rows" -> {{Top}}}, - AutoDelete -> False, - GridBoxItemSize -> { - "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, - GridBoxSpacings -> {"Columns" -> {{1}}, "Rows" -> {{0}}}], - "Grid"], Alignment -> Left, AppearanceElements -> None, - ImageMargins -> {{5, 5}, {5, 5}}, ImageSizeAction -> - "ResizeToFit"], LineIndent -> 0, StripOnInput -> False], { - FontFamily -> "Arial"}, Background -> Automatic, StripOnInput -> - False], TraditionalForm]& ), - InterpretationFunction :> (RowBox[{"SwatchLegend", "[", - RowBox[{ - RowBox[{"{", - RowBox[{ - RowBox[{"Directive", "[", - InterpretationBox[ - ButtonBox[ - TooltipBox[ - GraphicsBox[{{ - GrayLevel[0], - RectangleBox[{0, 0}]}, { - GrayLevel[0], - RectangleBox[{1, -1}]}, { - RGBColor[0., 0., 0.], - RectangleBox[{0, -1}, {2, 1}]}}, AspectRatio -> 1, Frame -> - True, FrameStyle -> RGBColor[0., 0., 0.], FrameTicks -> - None, PlotRangePadding -> None, ImageSize -> - Dynamic[{ - Automatic, 1.35 CurrentValue["FontCapHeight"]/ - AbsoluteCurrentValue[Magnification]}]], - "RGBColor[0., 0., 0.]"], Appearance -> None, - BaseStyle -> {}, BaselinePosition -> Baseline, - DefaultBaseStyle -> {}, ButtonFunction :> - With[{Typeset`box$ = EvaluationBox[]}, - If[ - Not[ - AbsoluteCurrentValue["Deployed"]], - SelectionMove[Typeset`box$, All, Expression]; - FrontEnd`Private`$ColorSelectorInitialAlpha = 1; - FrontEnd`Private`$ColorSelectorInitialColor = - RGBColor[0., 0., 0.]; - FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; - MathLink`CallFrontEnd[ - FrontEnd`AttachCell[Typeset`box$, - FrontEndResource["RGBColorValueSelector"], { - 0, {Left, Bottom}}, {Left, Top}, - "ClosingActions" -> { - "SelectionDeparture", "ParentChanged", - "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> - Automatic, Method -> "Preemptive"], - RGBColor[0., 0., 0.], Editable -> False, Selectable -> - False], "]"}], ",", - RowBox[{"Directive", "[", - InterpretationBox[ - ButtonBox[ - TooltipBox[ - GraphicsBox[{{ - GrayLevel[0], - RectangleBox[{0, 0}]}, { - GrayLevel[0], - RectangleBox[{1, -1}]}, { - RGBColor[1., 0., 0.], - RectangleBox[{0, -1}, {2, 1}]}}, AspectRatio -> 1, Frame -> - True, FrameStyle -> RGBColor[0.6666666666666667, 0., 0.], - FrameTicks -> None, PlotRangePadding -> None, ImageSize -> - Dynamic[{ - Automatic, 1.35 CurrentValue["FontCapHeight"]/ - AbsoluteCurrentValue[Magnification]}]], - "RGBColor[1., 0., 0.]"], Appearance -> None, - BaseStyle -> {}, BaselinePosition -> Baseline, - DefaultBaseStyle -> {}, ButtonFunction :> - With[{Typeset`box$ = EvaluationBox[]}, - If[ - Not[ - AbsoluteCurrentValue["Deployed"]], - SelectionMove[Typeset`box$, All, Expression]; - FrontEnd`Private`$ColorSelectorInitialAlpha = 1; - FrontEnd`Private`$ColorSelectorInitialColor = - RGBColor[1., 0., 0.]; - FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; - MathLink`CallFrontEnd[ - FrontEnd`AttachCell[Typeset`box$, - FrontEndResource["RGBColorValueSelector"], { - 0, {Left, Bottom}}, {Left, Top}, - "ClosingActions" -> { - "SelectionDeparture", "ParentChanged", - "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> - Automatic, Method -> "Preemptive"], - RGBColor[1., 0., 0.], Editable -> False, Selectable -> - False], "]"}], ",", - RowBox[{"Directive", "[", - InterpretationBox[ - ButtonBox[ - TooltipBox[ - GraphicsBox[{{ - GrayLevel[0], - RectangleBox[{0, 0}]}, { - GrayLevel[0], - RectangleBox[{1, -1}]}, { - RGBColor[0., 1., 1.], - RectangleBox[{0, -1}, {2, 1}]}}, AspectRatio -> 1, Frame -> - True, FrameStyle -> - RGBColor[0., 0.6666666666666667, 0.6666666666666667], - FrameTicks -> None, PlotRangePadding -> None, ImageSize -> - Dynamic[{ - Automatic, 1.35 CurrentValue["FontCapHeight"]/ - AbsoluteCurrentValue[Magnification]}]], - "RGBColor[0., 1., 1.]"], Appearance -> None, - BaseStyle -> {}, BaselinePosition -> Baseline, - DefaultBaseStyle -> {}, ButtonFunction :> - With[{Typeset`box$ = EvaluationBox[]}, - If[ - Not[ - AbsoluteCurrentValue["Deployed"]], - SelectionMove[Typeset`box$, All, Expression]; - FrontEnd`Private`$ColorSelectorInitialAlpha = 1; - FrontEnd`Private`$ColorSelectorInitialColor = - RGBColor[0., 1., 1.]; - FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; - MathLink`CallFrontEnd[ - FrontEnd`AttachCell[Typeset`box$, - FrontEndResource["RGBColorValueSelector"], { - 0, {Left, Bottom}}, {Left, Top}, - "ClosingActions" -> { - "SelectionDeparture", "ParentChanged", - "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> - Automatic, Method -> "Preemptive"], - RGBColor[0., 1., 1.], Editable -> False, Selectable -> - False], "]"}]}], "}"}], ",", - RowBox[{"{", - RowBox[{#, ",", #2, ",", #3}], "}"}], ",", - RowBox[{"LegendMarkers", "\[Rule]", "Automatic"}], ",", - RowBox[{"LabelStyle", "\[Rule]", - RowBox[{"{", "}"}]}], ",", - RowBox[{"LegendLayout", "\[Rule]", "\"Column\""}]}], "]"}]& ), - Editable -> True], TraditionalForm], TraditionalForm]}, - "Legended", - DisplayFunction->(GridBox[{{ - TagBox[ - ItemBox[ - PaneBox[ - TagBox[#, "SkipImageSizeLevel"], Alignment -> {Center, Baseline}, - BaselinePosition -> Baseline], DefaultBaseStyle -> "Labeled"], - "SkipImageSizeLevel"], - ItemBox[#2, DefaultBaseStyle -> "LabeledLabel"]}}, - GridBoxAlignment -> {"Columns" -> {{Center}}, "Rows" -> {{Center}}}, - AutoDelete -> False, GridBoxItemSize -> Automatic, - BaselinePosition -> {1, 1}]& ), - Editable->True, - InterpretationFunction->(RowBox[{"Legended", "[", - RowBox[{#, ",", - RowBox[{"Placed", "[", - RowBox[{#2, ",", "After"}], "]"}]}], "]"}]& )]], "Output", - CellChangeTimes->{ - 3.6595561427769833`*^9, 3.659556184448927*^9, {3.6595564465319443`*^9, - 3.6595564731067934`*^9}}] -}, Open ]], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"newtonplot", "[", - RowBox[{ - RowBox[{"Function", "[", - RowBox[{"x", ",", - RowBox[{ - SuperscriptBox["x", "2"], "-", "1"}]}], "]"}], ",", "2", ",", "201", - ",", "20", ",", "0.05"}], "]"}]], "Input", - CellChangeTimes->{{3.6595549152958674`*^9, 3.659554978383319*^9}, - 3.659555332709116*^9, {3.659555509656427*^9, 3.6595555271955185`*^9}, { - 3.659555597485504*^9, 3.659555613597739*^9}, {3.65955606434665*^9, - 3.659556065221777*^9}, {3.659556100512431*^9, 3.659556120459993*^9}, { - 3.6595564492510743`*^9, 3.659556464637117*^9}}], - -Cell[BoxData[ - TemplateBox[{GraphicsBox[ - RasterBox[CompressedData[" -1:eJzt1sFJZVEQBNAPRmIkk4MhCK6Nc7KZEAZRN4XQlKtuOAUPHqf67uv59f3l -7enxePz9+j7+P/Pvz+PHcM4555zz3/mU73f5nnPOOeecd5593nHOOeec886n -bNmBnHPOOefXPfu845xzzjnnnU/ZsgM555xzzq979nnHOeecc847n7JlB3LO -OeecX/fs845zzjnnnHc+ZcsO5Jxzzjm/7tnnHeecc84573zKlh3IOeecc37d -s887zjnnnHPe+ZQtO5Bzzjnn/Lpnn3ecc84557zzKVt2IOecc875dc8+7zjn -nHPOeedTtuxAzjnnnPPrnn3ecc4555zzzqds2YGcc84559c9+7zjnHPOOeed -T9myAznnnHPOr3v2ecc555xzzjufsmUHcs4555xf9+zzjnPOOeecdz5lyw7k -nHPOOb/u2ecd55xzzjnvfMqWHcg555xzft2zzzvOOeecc975lC07kHPOOef8 -umefd5xzzjnnvPMpW3Yg55xzzvl1zz7vOOecc85551O27EDOOeec8+uefd5x -zjnnnPPOp2zZgZxzzjnn1z37vOOcc845551P2bIDOeecc86ve/Z5xznnnHPO -O5+yZQdyzjnnnF/37POOc84555x3PmXLDuScc845v+7Z5x3nnHPOOe98ypYd -yDnnnHN+3bPPO84555xz3vmULTuQc8455/y6Z593nHPOOee88ylbdiDnnHPO -+XXPPu8455xzznnnU7bsQM4555zz65593nHOOeec886nbNmBnHPOOefXPfu8 -45xzzjnnnU/ZsgM555xzzq979nnHOeecc847n7JlB3LOOeecX/fs845zzjnn -nHc+ZcsO5Jxzzjm/7tnnHeecc84573zKlh3IOeecc37ds887zjnnnHPe+ZQt -O5Bzzjnn/Lpnn3ecc84557zzKVt2IOecc875dc8+7zjnnHPOeedTtuxAzjnn -nPPrnn3ecc4555zzzqds2YGcc84559c9+7zjnHPOOeedT9myAznnnHPOr3v2 -ecc555xzzjufsmUHcs4555xf9+zzjnPOOeecdz5lyw7knHPOOb/u2ecd55xz -zjnvfMqWHcg555xzft2zzzvOOeecc975lC07kHPOOef8umefd5xzzjnnvPMp -W3Yg55xzzvl1zz7vOOecc85551O27EDOOeec8+uefd5xzjnnnPPOp2zZgZxz -zjnn1z37vOOcc845551P2bIDOeecc86ve/Z5xznnnHPOO5+yZQdyzjnnnF/3 -7POOc84555x3PmXLDuScc845v+7Z5x3nnHPOOe98ypYdyDnnnHN+3bPPO845 -55xz3vmULTuQc8455/y6Z593nHPOOee88ylbdiDnnHPO+XXPPu8455xzznnn -U7bsQM4555zz65593nHOOeec886nbNmBnHPOOefXPfu845xzzjnnnU/ZsgM5 -55xzzq979nnHOeecc847n7JlB3LOOeecX/fs845zzjnnnHc+ZcsO5Jxzzjm/ -7tnnHeecc84573zKlh3IOeecc37ds887zjnnnHPe+ZQtO5Bzzjnn/Lpnn3ec -c84557zzKVt2IOecc875dc8+7zjnnHPOeedTtuxAzjnnnPPrnn3ecc4555zz -zqds2YGcc84559c9+7zjnHPOOeedT9myAznnnHPOr3v2ecc555xzzjufsmUH -cs4555xf9+zzjnPOOeecdz5lyw7knHPOOb/u2ecd55xzzjnvfMqWHcg555xz -ft2zzzvOOeecc975lC07kHPOOef8umefd5xzzjnnvPMpW3Yg55xzzvl1zz7v -OOecc85551O27EDOOeec8+uefd5xzjnnnPPOp2zZgZxzzjnn1z37vOOcc845 -551P2bIDOeecc86ve/Z5xznnnHPOO5+yZQdyzjnnnF/37POOc84555x3PmXL -DuScc845v+7Z5x3nnHPOOe98ypYdyDnnnHN+3bPPO84555xz3vmULTuQc845 -5/y6Z593nHPOOee88ylbdiDnnHPO+XXPPu8455xzznnnU7bsQM4555zz6559 -3nHOOeec886nbNmBnHPOOefXPfu845xzzjnnnU/ZsgM555xzzq979nnHOeec -c847n7JlB3LOOeecX/fs845zzjnnnHc+ZcsO5Jxzzjm/7tnnHeecc84573zK -lh3IOeecc37ds887zjnnnHPe+ZQtO5Bzzjnn/Lpnn3ecc84557zzKVt2IOec -c875dc8+7zjnnHPOeedTtuxAzjnnnPPrnn3ecc4555zzzqds2YGcc84559c9 -+7zjnHPOOeedT9myAznnnHPOr3v2ecc555xzzjufsmUHcs4555xf9+zzjnPO -Oeecdz5lyw7knHPOOb/u2ecd55xzzjnvfMqWHcg555xzft2zzzvOOeecc975 -lC07kHPOOef8umefd5xzzjnnvPMpW3Yg55xzzvl1zz7vOOecc85551O27EDO -Oeec8+uefd5xzjnnnPPOp2zZgZxzzjnn1z37vOOcc845551P2bIDOeecc86v -e/Z5xznnnHPOO5+yZQdyzjnnnF/37POOc84555x3PmXLDuScc845v+7Z5x3n -nHPOOe98ypYdyDnnnHN+3bPPO84555xz3vmULTuQc8455/y6Z593nHPOOee8 -8ylbdiDnnHPO+XXPPu8455xzznnnU7bsQM4555zz65593nHOOeec886nbNmB -nHPOOefXPfu845xzzjnnnU/ZsgM555xzzq979nnHOeecc847n7JlB3LOOeec -X/fs845zzjnnnHc+ZcsO5Jxzzjm/7tnnHeecc84573zKlh3IOeecc37ds887 -zjnnnHPe+ZQtO5Bzzjnn/Lpnn3ecc84557zzKVt2IOecc875dc8+7zjnnHPO -eedTtuxAzjnnnPPrnn3ecc4555zzzqds2YGcc84559c9+7zjnHPOOeedT9my -AznnnHPOr3v2ecc555xzzjufsmUHcs4555xf9+zzjnPOOeecdz5lyw7knHPO -Ob/u2ecd55xzzjnvfMqWHcg555xzft2zzzvOOeecc975lC07kHPOOef8umef -d5xzzjnnvPMpW3Yg55xzzvl1zz7vOOecc85551O27EDOOeec8+uefd5xzjnn -nPPOp2zZgZxzzjnn1z37vOOcc845551P2bIDOeecc86ve/Z5xznnnHPOO5+y -ZQdyzjnnnF/37POOc84555x3PmXLDuScc845v+7Z5x3nnHPOOe98ypYdyDnn -nHN+3bPPO84555xz3vmULTuQc8455/y6Z593nHPOOee88ylbdiDnnHPO+XXP -Pu8455xzznnnU7bsQM4555zz65593nHOOeec886nbNmBnHPOOefXPfu845xz -zjnnnU/ZsgM555xzzq979nnHOeecc847n7JlB3LOOeecX/fs845zzjnnnHc+ -ZcsO5Jxzzjm/7tnnHeecc84573zKlh3IOeecc37ds887zjnnnHPe+ZQtO5Bz -zjnn/Lpnn3ecc84557zzKVt2IOecc875dc8+7zjnnHPOeedTtuxAzjnnnPPr -nn3ecc4555zzzqds2YGcc84559c9+7zjnHPOOeedT9myAznnnHPOr3v2ecc5 -55xzzjufsmUHcs4555xf9+zzjnPOOeecdz5lyw7knHPOOb/u2ecd55xzzjnv -fMqWHcg555xzft2zzzvOOeecc975lC07kHPOOef8umefd5xzzjnnvPMpW3Yg -55xzzvl1zz7vOOecc85551O27EDOOeec8+uefd5xzjnnnPPOp2zZgZxzzjnn -1z37vOOcc845551P2bIDOeecc86ve/Z5xznnnHPOO5+yZQdyzjnnnF/37POO -c84555x3PmXLDuScc845v+7Z5x3nnHPOOe98ypYdyDnnnHN+3bPPO84555xz -3vmULTuQc8455/y6Z593nHPOOee88ylbdiDnnHPO+XXPPu8455xzznnnU7bs -QM4555zz65593nHOOeec886nbNmBnHPOOefXPfu845xzzjnnnU/ZsgM555xz -zq979nnHOeecc847n7JlB3LOOeecX/fs845zzjnnnHc+ZcsO5Jxzzjm/7tnn -Heecc84573zKlh3IOeecc37ds887zjnnnHPe+ZQtO5Bzzjnn/Lpnn3ecc845 -57zzKVt2IOecc875dc8+7zjnnHPOeedTtuxAzjnnnPPrnn3ecc4555zzzqds -2YGcc84559c9+7zjnHPOOeedT9myAznnnHPOr3v2ecc555xzzjufsmUHcs45 -55xf9+zzjnPOOeecdz5lyw7knHPOOb/u2ecd55xzzjnvfMqWHcg555xzft2z -zzvOOeecc975lC07kHPOOef8umefd5xzzjnnvPMpW3Yg55xzzvl1zz7vOOec -c85551O27EDOOeec8+uefd5xzjnnnPPOp2zZgZxzzjnn1z37vOOcc845551P -2bIDOeecc86ve/Z5xznnnHPOO5+yZQdyzjnnnF/37POOc84555x3PmXLDuSc -c845v+7Z5x3nnHPOOe98ypYdyDnnnHN+3bPPO84555xz3vmULTuQc8455/y6 -Z593nHPOOee88ylbdiDnnHPO+XXPPu8455xzznnnU7bsQM4555zz65593nHO -Oeec886nbNmBnHPOOefXPfu845xzzjnnnU/ZsgM555xzzq979nnHOeecc847 -n7JlB3LOOeecX/fs845zzjnnnHc+ZcsO5Jxzzjm/7tnnHeecc84573zKlh3I -Oeecc37ds887zjnnnHPe+ZQtO5Bzzjnn/Lpnn3ecc84557zzKVt2IOecc875 -dc8+7zjnnHPOeedTtuxAzjnnnPPrnn3ecc4555zzzqds2YGcc84559c9+7zj -nHPOOeedT9myAznnnHPOr3v2ecc555xzzjufsmUHcs4555xf9+zzjnPOOeec -dz5lyw7knHPOOb/u2ecd55xzzjnvfMqWHcg555xzft2zzzvOOeecc975lC07 -kHPOOef8umefd5xzzjnnvPMpW3Yg55xzzvl1zz7vOOecc85551O27EDOOeec -8+uefd5xzjnnnPPOp2zZgZxzzjnn1z37vOOcc845551P2bIDOeecc86ve/Z5 -xznnnHPOO5+yZQdyzjnnnF/37POOc84555x3PmXLDuScc845v+7Z5x3nnHPO -Oe98ypYdyDnnnHN+3bPPO84555xz3vmULTuQc8455/y6Z593nHPOOee88ylb -diDnnHPO+XXPPu8455xzznnnU7bsQM4555zz65593nHOOeec886nbNmBnHPO -OefXPfu845xzzjnnnU/ZsgM555xzzq979nnHOeecc847n7JlB3LOOeecX/fs -845zzjnnnHc+ZcsO5Jxzzjm/7tnnHeecc84573zKlh3IOeecc37ds887zjnn -nHPe+ZQtO5Bzzjnn/Lpnn3ecc84557zzKVt2IOecc875dc8+7zjnnHPOeedT -tuxAzjnnnPO7/h+Twt5A - "], {{0, 0}, {201, 201}}, {0, 1}], Frame -> Automatic, - FrameLabel -> {None, None}, FrameTicks -> {{None, None}, {None, None}}, - GridLinesStyle -> Directive[ - GrayLevel[0.5, 0.4]], - Method -> { - "DefaultBoundaryStyle" -> Automatic, "DefaultPlotStyle" -> Automatic}], - FormBox[ - FormBox[ - TemplateBox[{"\"Divergent\"", - RowBox[{"-", "1"}], "1"}, "SwatchLegend", DisplayFunction -> (FormBox[ - StyleBox[ - StyleBox[ - PaneBox[ - TagBox[ - GridBox[{{ - TagBox[ - GridBox[{{ - GraphicsBox[{ - Directive[ - EdgeForm[ - Directive[ - Opacity[0.3], - GrayLevel[0]]], - PointSize[0.5], - AbsoluteThickness[1.6], - RGBColor[0., 0., 0.]], - RectangleBox[{0, 0}, {10, 10}, "RoundingRadius" -> 0]}, - AspectRatio -> Full, ImageSize -> {10, 10}, - PlotRangePadding -> None, ImagePadding -> Automatic, - BaselinePosition -> (Scaled[0.1] -> Baseline)], #}, { - GraphicsBox[{ - Directive[ - EdgeForm[ - Directive[ - Opacity[0.3], - GrayLevel[0]]], - PointSize[0.5], - AbsoluteThickness[1.6], - RGBColor[1., 0., 0.]], - RectangleBox[{0, 0}, {10, 10}, "RoundingRadius" -> 0]}, - AspectRatio -> Full, ImageSize -> {10, 10}, - PlotRangePadding -> None, ImagePadding -> Automatic, - BaselinePosition -> (Scaled[0.1] -> Baseline)], #2}, { - GraphicsBox[{ - Directive[ - EdgeForm[ - Directive[ - Opacity[0.3], - GrayLevel[0]]], - PointSize[0.5], - AbsoluteThickness[1.6], - RGBColor[0., 1., 1.]], - RectangleBox[{0, 0}, {10, 10}, "RoundingRadius" -> 0]}, - AspectRatio -> Full, ImageSize -> {10, 10}, - PlotRangePadding -> None, ImagePadding -> Automatic, - BaselinePosition -> (Scaled[0.1] -> Baseline)], #3}}, - GridBoxAlignment -> { - "Columns" -> {Center, Left}, "Rows" -> {{Baseline}}}, - AutoDelete -> False, - GridBoxDividers -> { - "Columns" -> {{False}}, "Rows" -> {{False}}}, - GridBoxItemSize -> {"Columns" -> {{All}}, "Rows" -> {{All}}}, - GridBoxSpacings -> { - "Columns" -> {{0.5}}, "Rows" -> {{0.5}}}], "Grid"]}}, - GridBoxAlignment -> {"Columns" -> {{Left}}, "Rows" -> {{Top}}}, - AutoDelete -> False, - GridBoxItemSize -> { - "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, - GridBoxSpacings -> {"Columns" -> {{1}}, "Rows" -> {{0}}}], - "Grid"], Alignment -> Left, AppearanceElements -> None, - ImageMargins -> {{5, 5}, {5, 5}}, ImageSizeAction -> - "ResizeToFit"], LineIndent -> 0, StripOnInput -> False], { - FontFamily -> "Arial"}, Background -> Automatic, StripOnInput -> - False], TraditionalForm]& ), - InterpretationFunction :> (RowBox[{"SwatchLegend", "[", - RowBox[{ - RowBox[{"{", - RowBox[{ - RowBox[{"Directive", "[", - InterpretationBox[ - ButtonBox[ - TooltipBox[ - GraphicsBox[{{ - GrayLevel[0], - RectangleBox[{0, 0}]}, { - GrayLevel[0], - RectangleBox[{1, -1}]}, { - RGBColor[0., 0., 0.], - RectangleBox[{0, -1}, {2, 1}]}}, AspectRatio -> 1, Frame -> - True, FrameStyle -> RGBColor[0., 0., 0.], FrameTicks -> - None, PlotRangePadding -> None, ImageSize -> - Dynamic[{ - Automatic, 1.35 CurrentValue["FontCapHeight"]/ - AbsoluteCurrentValue[Magnification]}]], - "RGBColor[0., 0., 0.]"], Appearance -> None, - BaseStyle -> {}, BaselinePosition -> Baseline, - DefaultBaseStyle -> {}, ButtonFunction :> - With[{Typeset`box$ = EvaluationBox[]}, - If[ - Not[ - AbsoluteCurrentValue["Deployed"]], - SelectionMove[Typeset`box$, All, Expression]; - FrontEnd`Private`$ColorSelectorInitialAlpha = 1; - FrontEnd`Private`$ColorSelectorInitialColor = - RGBColor[0., 0., 0.]; - FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; - MathLink`CallFrontEnd[ - FrontEnd`AttachCell[Typeset`box$, - FrontEndResource["RGBColorValueSelector"], { - 0, {Left, Bottom}}, {Left, Top}, - "ClosingActions" -> { - "SelectionDeparture", "ParentChanged", - "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> - Automatic, Method -> "Preemptive"], - RGBColor[0., 0., 0.], Editable -> False, Selectable -> - False], "]"}], ",", - RowBox[{"Directive", "[", - InterpretationBox[ - ButtonBox[ - TooltipBox[ - GraphicsBox[{{ - GrayLevel[0], - RectangleBox[{0, 0}]}, { - GrayLevel[0], - RectangleBox[{1, -1}]}, { - RGBColor[1., 0., 0.], - RectangleBox[{0, -1}, {2, 1}]}}, AspectRatio -> 1, Frame -> - True, FrameStyle -> RGBColor[0.6666666666666667, 0., 0.], - FrameTicks -> None, PlotRangePadding -> None, ImageSize -> - Dynamic[{ - Automatic, 1.35 CurrentValue["FontCapHeight"]/ - AbsoluteCurrentValue[Magnification]}]], - "RGBColor[1., 0., 0.]"], Appearance -> None, - BaseStyle -> {}, BaselinePosition -> Baseline, - DefaultBaseStyle -> {}, ButtonFunction :> - With[{Typeset`box$ = EvaluationBox[]}, - If[ - Not[ - AbsoluteCurrentValue["Deployed"]], - SelectionMove[Typeset`box$, All, Expression]; - FrontEnd`Private`$ColorSelectorInitialAlpha = 1; - FrontEnd`Private`$ColorSelectorInitialColor = - RGBColor[1., 0., 0.]; - FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; - MathLink`CallFrontEnd[ - FrontEnd`AttachCell[Typeset`box$, - FrontEndResource["RGBColorValueSelector"], { - 0, {Left, Bottom}}, {Left, Top}, - "ClosingActions" -> { - "SelectionDeparture", "ParentChanged", - "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> - Automatic, Method -> "Preemptive"], - RGBColor[1., 0., 0.], Editable -> False, Selectable -> - False], "]"}], ",", - RowBox[{"Directive", "[", - InterpretationBox[ - ButtonBox[ - TooltipBox[ - GraphicsBox[{{ - GrayLevel[0], - RectangleBox[{0, 0}]}, { - GrayLevel[0], - RectangleBox[{1, -1}]}, { - RGBColor[0., 1., 1.], - RectangleBox[{0, -1}, {2, 1}]}}, AspectRatio -> 1, Frame -> - True, FrameStyle -> - RGBColor[0., 0.6666666666666667, 0.6666666666666667], - FrameTicks -> None, PlotRangePadding -> None, ImageSize -> - Dynamic[{ - Automatic, 1.35 CurrentValue["FontCapHeight"]/ - AbsoluteCurrentValue[Magnification]}]], - "RGBColor[0., 1., 1.]"], Appearance -> None, - BaseStyle -> {}, BaselinePosition -> Baseline, - DefaultBaseStyle -> {}, ButtonFunction :> - With[{Typeset`box$ = EvaluationBox[]}, - If[ - Not[ - AbsoluteCurrentValue["Deployed"]], - SelectionMove[Typeset`box$, All, Expression]; - FrontEnd`Private`$ColorSelectorInitialAlpha = 1; - FrontEnd`Private`$ColorSelectorInitialColor = - RGBColor[0., 1., 1.]; - FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; - MathLink`CallFrontEnd[ - FrontEnd`AttachCell[Typeset`box$, - FrontEndResource["RGBColorValueSelector"], { - 0, {Left, Bottom}}, {Left, Top}, - "ClosingActions" -> { - "SelectionDeparture", "ParentChanged", - "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> - Automatic, Method -> "Preemptive"], - RGBColor[0., 1., 1.], Editable -> False, Selectable -> - False], "]"}]}], "}"}], ",", - RowBox[{"{", - RowBox[{#, ",", #2, ",", #3}], "}"}], ",", - RowBox[{"LegendMarkers", "\[Rule]", "Automatic"}], ",", - RowBox[{"LabelStyle", "\[Rule]", - RowBox[{"{", "}"}]}], ",", - RowBox[{"LegendLayout", "\[Rule]", "\"Column\""}]}], "]"}]& ), - Editable -> True], TraditionalForm], TraditionalForm]}, - "Legended", - DisplayFunction->(GridBox[{{ - TagBox[ - ItemBox[ - PaneBox[ - TagBox[#, "SkipImageSizeLevel"], Alignment -> {Center, Baseline}, - BaselinePosition -> Baseline], DefaultBaseStyle -> "Labeled"], - "SkipImageSizeLevel"], - ItemBox[#2, DefaultBaseStyle -> "LabeledLabel"]}}, - GridBoxAlignment -> {"Columns" -> {{Center}}, "Rows" -> {{Center}}}, - AutoDelete -> False, GridBoxItemSize -> Automatic, - BaselinePosition -> {1, 1}]& ), - Editable->True, - InterpretationFunction->(RowBox[{"Legended", "[", - RowBox[{#, ",", - RowBox[{"Placed", "[", - RowBox[{#2, ",", "After"}], "]"}]}], "]"}]& )]], "Output", - CellChangeTimes->{{3.6595561119560795`*^9, 3.6595561241792593`*^9}, - 3.6595564518143454`*^9, 3.659556485561829*^9}] -}, Open ]], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"newtonplot", "[", - RowBox[{ - RowBox[{"Function", "[", - RowBox[{"x", ",", - RowBox[{ - RowBox[{"(", - RowBox[{"x", "+", "1"}], ")"}], - RowBox[{"(", - RowBox[{"x", "-", - RowBox[{"(", - RowBox[{ - RowBox[{"-", "0.5"}], "+", - RowBox[{"0.5", "I"}]}], ")"}]}], ")"}], - RowBox[{"(", - RowBox[{"x", "-", - RowBox[{"(", - RowBox[{ - RowBox[{"-", "0.5"}], "-", - RowBox[{"0.5", "I"}]}], ")"}]}], ")"}]}]}], "]"}], ",", "2", ",", - "401", ",", "20", ",", "0.05"}], "]"}]], "Input", - CellChangeTimes->{{3.6595549152958674`*^9, 3.659554978383319*^9}, - 3.659555332709116*^9, {3.659555509656427*^9, 3.6595555271955185`*^9}, { - 3.659555597485504*^9, 3.659555613597739*^9}, {3.6595562242242994`*^9, - 3.659556229922743*^9}, {3.6595562733917246`*^9, 3.6595562737355576`*^9}, { - 3.6595563138893795`*^9, 3.6595563587354765`*^9}, {3.659556405332657*^9, - 3.6595564061608486`*^9}, 3.664161638484193*^9}], - -Cell[BoxData[ - TemplateBox[{GraphicsBox[ - RasterBox[CompressedData[" -1:eJzs1uupbbt6JdBrKhJH4hwqhIL6XbE4U4dgCrPh3sXW0nhI+rqG2oADZzc9 -epfmY81//z//73//3//1j3/84z//7X/++////z/Pf/3HP/768G/73fVP9087 -N+ecc84555xzzjnnnHPOOeecc8455ys8pQef47Pzerlp98E555xzzjnnnHPO -Oeecc84555xzzvkKT+nB3/nbce8vzjnnnHPOOeecc84555xzzjnnnHPOx3lK -D77WR+37NDftPjjnnHPOOeecc84555xzzjnnnHPOOR/pKT04/+1J68U555xz -zjnnnHPOOeecc84555xzzvlvntKD8xFenc8555xzzjnnnHPOOeecc84555xz -znlSD85nenU+55xzzjnnnHPOOeecc84555xzzjk/y1N6cF7h1fmcc84555xz -zjnnnHPOOeecc8455/ybntKD8xH+dH3aOTjnnHPOOeecc84555xzzjnnnHPO -+d6e0oPzJK/O55xzzjnnnHPOOeecc84555xzzjnne3tKD86TvDqfc84555xz -zjnnnHPOOeecc84555zv7Sk9ON/Bq/M555xzzjnnnHPOOeecc84555xzzvke -ntKD8xHeGp+9P+ecc84555xzzjnnnHPOOeecc84554k9+Nle1eNpz7T745xz -zjnnnHPOOeecc84555xzzjnnWZ7Sg5/hb8dXeXo/zjnnnHPOOeecc84555xz -zjnnnHOe7Sk9+Nme0uOP93pW9+Occ84555xzzjnnnHPOOeecc84559me0oOf -7Sk9/nivZ3U/zjnnnHPOOeecc84555xzzjnnnHOe7Sk9+Nnemnd3/mhPuyfO -Oeecc84555xzzjnnnHPOOeecc76Hp/TgfAevzuecc84555xzzjnnnHPOOeec -c84553t4Sg/Od/DevLS+nHPOOeecc84555xzzjnnnHPOOee8xlN6cL6z9+al -9eWcc84555xzzjnnnHPOOeecc84553M9pQfnJ3l1Puecc84555xzzjnnnHPO -Oeecc845n+spPTj/ovfmpfXlnHPOOeecc84555xzzjnnnHPOOedjPKUH57w+ -n3POOeecc84555xzzjnnnHPOOeecj/GUHpzztlfnc84555xzzjnnnHPOOeec -c84555zze57Sg/OT/On6tHNwzjnnnHPOOeecc84555xzzjnnnPO/e0oPzvl9 -r87nnHPOOeecc84555xzzjnnnHPOOed/95QenPNxXp3POeecc84555xzzjnn -nHPOOeecc366p/TgnI/z6nzOOeecc84555xzzjnnnHPOOeec89M9pQfn/P76 -3j5p5+Occ84555xzzjnnnHPOOeecc845P8VTenDO76/v7ZN2Ps4555xzzjnn -nHPOOeecc84555zzUzylB+e87b15aX0555xzzjnnnHPOOeecc84555xzzk/3 -lB58jvfmeZ9806vzOeecc84555xzzjnnnHPOOeecc85P95QefK2P2i/tXDwj -n3POOeecc84555xzzjnnnHPOOef8dE/pwTO8Nd6bfzUv7byneXU+55xzzjnn -nHPOOeecc84555xzzvkpntKDZ3hKjz8++lynfC5689L6cs4555xzzjnnnHPO -Oeecc84555x/zVN6nOqj9uvtPypnF797P6d8LqrzOeecc84555xzzjnnnHPO -Oeecc85P8ZQe/Pcnrd/XvTp/llfnc84555xzzjnnnHPOOeecc84555yf4ik9 -TvWUHvyaV+df9d68tL6cc84555xzzjnnnHPOOeecc84551/zlB67+dUnrTef -49X5V706n3POOeecc84555xzzjnnnHPOOef8FE/psZun9OB7eMrnrjqfc845 -55xzzjnnnHPOOeecc8455/wUT+mxm6f04Ht69fu2+vycc84555xzzjnnnHPO -Oeecc84551/3lB6pntKDf8ur81tPWi/OOeecc84555xzzjnnnHPOOeec8109 -pUeqp/TgZ/iq93P1OTnnnHPOOeecc84555xzzjnnnHPOv+4pPao9pQfnf/PR -7/Pq83DOOeecc84555xzzjnnnHPOOeecf91Teoz2u+t6+zztwfkIr/pccM45 -55xzzjnnnHPOOeecc84555zzZ57S46nPzunlzs7n/DdP+7xwzjnnnHPOOeec -c84555xzzjnnnPOsHq2num+v59Nxzkf4089XdW/OOeecc84555xzzjnnnHPO -Oeec8697So+U/Ku9evNW9eJn+1c+X5xzzjnnnHPOOeecc84555xzzjnnX/OU -Hq2nuu+qc3E+0nvvw+p+nHPOOeecc84555xzzjnnnHPOOedf96oeqb1W39vo -Xpz/Nr66B+ecc84555xzzjnnnHPOOeecc875qZ7So+dp+avyRu/Lz/KUHpxz -zjnnnHPOOeecc84555xzzjnnp3lKj6c+e7/qc63K43t66ueIc84555xzzjnn -nHPOOeecc8455/x0T+nx1HvzTjsv39ur8696dT7nnHPOOeecc84555xzzjnn -nHPOebqn9Oj53fVp/avugdd6df4sf7o+7Rycc84555xzzjnnnHPOOeecc845 -57M8pQd/5yk9vuZXPy935/OMfM4555xzzjnnnHPOOeecc84555zzWZ7Sg7/z -u+tW9Zmd9/Zco/bha7w6n3POOeecc84555xzzjnnnHPOOef8qqf04O981H67 -9E+7f17r1fmcc84555xzzjnnnHPOOeecc8455z89pQef43fX6ckT/O54b97d -/TnnnHPOOeecc84555xzzjnnnHPO33pKD77WW/PSenK+0nvz0vpyzjnnnHPO -Oeecc84555xzzjnnPNdTenDO+W5enc8555xzzjnnnHPOOeecc84555zzXE/p -wTnn1f50fdo5OOecc84555xzzjnnnHPOOeecc17vKT0453yVvx3/46NzOeec -c84555xzzjnnnHPOOeecc/4dT+nBOec8K59zzjnnnHPOOeecc84555xzzjnn -zz2lB+ec82tenc8555xzzjnnnHPOOeecc84555zzvqf04Jxz/s6r8znnnHPO -Oeecc84555xzzjnnnHOe14Nzzk/1p+vTzsE555xzzjnnnHPOOeecc84555zz -vB6cc/51fzvue51zzjnnnHPOOeecc84555xzzjnfx1N6cM45//35M2/0/mnn -5pxzzjnnnHPOOeecc84555xzzr/gKT0455xne3U+55xzzjnnnHPOOeecc845 -55xzvpOn9OCcc76nV+dzzjnnnHPOOeecc84555xzzjnniZ7Sg3POebb35qX1 -5ZxzzjnnnHPOOeecc84555xzzis9pQfnnPNveXU+55xzzjnnnHPOOeecc845 -55xzXukpPTjnnH/Lq/M555xzzjnnnHPOOeecc84555zzSk/pwTnnPMNb857u -k3Y+zjnnnHPOOeecc84555xzzjnnfIWn9OCccz7H3477e8I555xzzjnnnHPO -Oeecc84555zf95QenHPO1/qqvLRzc84555xzzjnnnHPOOeecc8455ys8pQfn -nPMMH71v2vk455xzzjnnnHPOOeecc84555zzFZ7Sg3PO+Rlenc8555xzzjnn -nHPOOeecc84555yv8JQenHPOz/DevLS+nHPOOeecc84555xzzjnnnHPO+RNP -6cE55/xs781L68s555xzzjnnnHPOOeecc84555z/5ik9OOec89+etF6cc845 -55xzzjnnnHPOOeecc875b57Sg3POOb/y+DvGOeecc84555xzzjnnnHPOOed8 -B0/pwTnnnN/x6nzOOeecc84555xzzjnnnHPOOef8N0/pwTnnnI/w6nzOOeec -c84555xzzjnnnHPOOec8qQfnnHN+5fkzrzc/7Rycc84555xzzjnnnHPOOeec -c87P8pQenHPO+R3vzUvryznnnHPOOeecc84555xzzjnn/CxP6cE556d6b57v -7Xtenc8555xzzjnnnHPOOeecc84555wn9eCcc/5uXVr/NK/O55xzzjnnnHPO -Oeecc84555xzfpan9OCcc37NR+07uk/K35fUXpxzzjnnnHPOOeecc84555xz -zs/ylB6cc76br16X7ul/X6rzOeecc84555xzzjnnnHPOOeecn+UpPTjn/Cue -0iPVq++/+vycc84555xzzjnnnHPOOeecc87P8JQenHO+m6f02M2rX6/q83PO -Oeecc84555xzzjnnnHPOOT/DU3pwznm1vx3nc3zV68s555xzzjnnnHPOOeec -c84555yP9JQenHNe7Sk9+L/6qte9+pycc84555xzzjnnnHPOOeecc86/5Sk9 -OOe82lN68Gv+9PWt7s0555xzzjnnnHPOOeecc8455/wMT+nBOeejffU6vta9 -rpxzzjnnnHPOOeecc84555xzzpM9pQfnnD/1Ufv19h+Vw+f67PcJ55xzzjnn -nHPOOeecc84555xzfsVTenDOec9n5zztM7sXv+dV7x/OOeecc84555xzzjnn -nHPOOec8sQfnnLeeVd9bo3vyTE/pwTnnnHPOOeecc84555xzzjnn/Nue0oNz -zp/6qP1G547qxcd6Sg/OOeecc84555xzzjnnnHPOOeff9pQenHM+2lvjVbmz -8k710a9Xa171OTnnnHPOOeecc84555xzzjnnnO/pKT0457znd8dT+1f3SPXq -/Ldenc8555xzzjnnnHPOOeecc8455zzLU3pwzjl/5yk9/nh1/ixvzXu6T9r5 -OOecc84555xzzjnnnHPOOeecj/GUHpxzfqrfXbcq9+d42r191avzOeecc845 -55xzzjnnnHPOOeecj/GUHpxzfqrfXbeqz895afd2mvfmpfXlnHPOOeecc845 -55xzzjnnnPPTPaUH55xzzsd5dT7nnHPOOeecc84555xzzjnnnJ/uKT0455xz -3va763v7pJ2Pc84555xzzjnnnHPOOeecc86/5ik9OOecc17nvXlpfTnnnHPO -Oeecc84555xzzjnnPN1TenDOOed8H6/O55xzzjnnnHPOOeecc84555zzdE/p -wTnnnPM6f7o+7Rycc84555xzzjnnnHPOOeecc57iKT0455xzXueteU/3STsf -55xzzjnnnHPOOeecc84555yv9pQenHPOOf+u9+al9eWcc84555xzzjnnnHPO -Oeec87ee0oNzzjnnPCWfc84555xzzjnnnHPOOeecc87fekoPzjnnnPOUfM45 -55xzzjnnnHPOOeecc845f+spPTjnnHP+XW/N681POwfnnHPOOeecc84555xz -zjnnnF/1lB6cc845399H75t2Ps4555xzzjnnnHPOOeecc845v+opPTjnnHO+ -v78d9zuFc84555xzzjnnnHPOOeecc/4VT+nBOeecc97z6nzOOeecc84555xz -zjnnnHPOOb/qKT0455xzzp96dT7nnHPOOeecc84555xzzjnnnP/0lB6cc845 -56O9Op9zzjnnnHPOOeecc84555xzfq6n9OCcc845H+3V+ZxzzjnnnHPOOeec -c84555zzcz2lB+ecc875Kq/O55xzzjnnnHPOOeecc84555x/31N6cM4555yP -9t68tL6cc84555xzzjnnnHPOOeec8+94Sg/OOeec13lv3td+P1Tnc84555xz -zjnnnHPOOeecc86/7yk9OOecc57nd8fv7pN6Ls4555xzzjnnnHPOOeecc845 -f+spPTjnnHM+zlvjvfmje/R8l3vjnHPOOeecc84555xzzjnnnPO7ntKDc845 -5+M8pcdoX3Vv1efknHPOOeecc84555xzzjnnnO/vKT0455xzft9TelT76Pus -Pg/nnHPOOeecc84555xzzjnnfH9P6cE555zz+57SI9Wf3md1b84555xzzjnn -nHPOOeecc875/p7Sg3POOedtT+mxmz+95+renHPOOeecc84555xzzjnnnPP9 -PaUH55xzzu+v6+3ztMfXfdT9c84555xzzjnnnHPOOeecc855y1N6cM455yf5 -qP16+4/K+ZrPfl0455xzzjnnnHPOOeecc8455zylB+ecc36Sj9rvae6o/F19 -9uvCOeecc84555xzzjnnnHPOOecpPTjnnHPenleVu4uvup/qc3LOOeecc845 -55xzzjnnnHPO9/GUHpxzzjnf35+uP+V3S3U+55xzzjnnnHPOOeecc84553yd -p/TgnHPOeZ3fXTdq/7R7SPPqfM4555xzzjnnnHPOOeecc875c0/pwTnnnHPO -f3/8juOcc84555xzzjnnnHPOOec811N6cM4555zzNV6dzznnnHPOOeecc845 -55yf6KP2Hb0f5/y9p/TgnHPOOeeZXp3POeecc84555xzzjnnnCd6a15r3age -d9dX3VdvXsrryPkbT+nBOeecc86zvTWvNz/tHJxzzjnnnHPOOeecc8738FH7 -VuVWeWs8refo8/6cN+r9wL/ts96Ho/fnnHPOOef8ilfnc84555xzzjnnnHPO -Oa/x2Xl316fcC1/rvSetL7/nVd8nLU+5F84555xzfrZX53POOeecc84555xz -zjkf47PzRu2bcl98T6/OP919z3DOOeec85P96fq0c3DOOeecc84555xzzjm/ -57PzRu2bcl/8W16dn+6jPtdV3zMp98g555xzzs/2p+vTzsE555xzzjnnnHPO -OeeneGve3f1SzsOzvTWe1nP2eb/qT+/n57yU83DOOeecc/5Fr87nnHPOOeec -c84555zzr/nd9a0n5Tx8rffmXX2/ve1R7aPvM/X15JxzzjnnnJ/n1fmcc845 -55xzzjnnnHOe4q15rXUpvXmGvx3n73z0vb8d55xzzjnnnPOWV+dzzjnnnHPO -Oeecc875ak/pwff0lB78mlfnc84555xzzr/vvXlpfTnnnHPOOeecc8455/yq -t+bdnc/P9JQefI5X53POOeecc87P9ep8zjnnnHPOOeecc845v+opPfientKD -z/HqfM4555xzzvk6v7tu9/6cc84555xzzjnnnPM6T+nR6/d2Xdq5eK2/Heff -8up8zjnnnHPO+Tqv6jG6f9q9cs4555xzzjnnnHP+BW/Nuzs/zUftm3YuXuur -1/E9vTqfc84555xz/txTejz1p+et7s0555xzzjnnnHPO+c7emnd3v9m9rz6r -7i/l9eN7ekoPnuHV+ZxzzjnnnPO+p/QY7b3zVvfjnHPOOeecc8455zzJW/Na -61J6jxpf5dX5fG9P6cHneHU+55xzzjnn/Lmn9EjxlB6cc84555xzzjnnnCd4 -So+nntKj59X5PMvfjvNveXU+55xzzjnnvO+r1+3qKT0455xzzjnnnHPOOV/p -KT1Ge0qP3n2n9OLZntKDr/HqfM4555xzznn/+Tnv6n5P99/Ve+et7sc555xz -zjnnnHPOz/bWvFH7fNVTevReh5RePMNTevA5Xp3POeecc845389Tevzx6nuo -Pj/nnHPOOeecc845X+utea11d/Oe9nqbu7tX9Ui7B/4NT+nB33l1Puecc845 -53w/b41/NbfqXJxzzjnnnHPO+Ql+d/3sPpyvzJu17x9Puceve2s8rSffy1N6 -8DF+9fsjpS/nnHPOOee8zlvz0nru4q15vflp5+Ccc84555xzfpbPzrs7b1Vu -yv3zsV7VY3Zeyv1We2s8rSfnvz1p/U716nzOOeecc8455zVenc8555xzzjnn -fK6P2vfu+pTz7+a9eWl9d/G7866O73LOUfP57/PSevIzvTU+6u87/92r8znn -nHPOOeec13hr3tN90s7HOeecc8455/zvPmrf1ryUc57qvXlpfVfdx9P35938 -9PNX9+Gcz/NR+83+nvy6r/49xjnnnHPOOef8TK/O55xzzjnnnPOv+d31rXkp -5/m6t8Z36Znm3uecc/67z85Z1X9WXur9/xxPe19xzjnnnHPOOa/11vjd+Zxz -zjnnnHPOf/eUHl/3t+PpfvV9NSuPc875HJ+dU32un/NGzeecc84555xzzhP8 -7fhPTzsf55xzzjnnnK/21rzWk9L7657SI9Wr8znnnP/de/Nm/W6pPq+/85xz -zjnnnHPOed+r8znnnHPOOed8lqf0ONVTenzFq/M555yP8da8tJ5Pz3V1PK0/ -55xzzjnnnHO+0qvzOeecc84557le1SOtz2n+dpy/8+p8zjnnnHPOOeecc845 -5zVenc8555xzzjnve+/3/M95o3q8He95yv2e6ik9vuLV+ZxzzjnnnHPOOeec -c85rvDcvrS/nnHPOOecn+8/x6h6z8tLu/TRP6fEVr87nnHPOOeecc84555xz -nuXV+ZxzzjnnnJ/oKT1az6oeafdwmqf02M2r8znnnHPOOeecc8455/x0b42n -9bzbn3POOeec8xM8pccqX5V3+j1//fU9xavzOeecc84555xzzjnnnP/dn64f -Pa/no/fjnHPOOU/xVb+Lfo773ZXhP8dn/55PO/+oc931tPOe5ik9dvPqfM45 -55xzzjnnnHPOOT/dU3pc9d6/ez6qB+ecc8757N9dKecc7dX5af5zPO33f9p9 -jXq/pfXkzzylR7VX53POOeecc84555xzzvnpntJjtD+9h+renHPOOd/Pf46P -+j2Wds7q+23NS+v7tl9r3ur38ej9OZ/hrfGn3ye7enU+55xzzjnnnHPOOeec -n+4pPar96b1V9+acc855naf02M1782bd86j9Rp037XXh/Et+d92q77erPvse -0l4vzjnnnHPOOeecc84538VXr/u6uy/OOef8HE/pkeopPVb93uOc7+t311V/ -f/p7xDnnnHPOOeecc84553v43XW9fZ72OMVTenDOOec7+qrfRT/npZw/1VN6 -rPLqfM75ud4aT+vJOeecc84555xzzjnn/Nm63j5Pe3zFn95/a171eTjnnPMV -/nN89L5P14/u81VP6VH9u45zzjnnnHPOOeecc84555zz354/82bvv7tX57/1 -u+tG7cM553d99vcbX+PVf+/e7ptyj9We0sPvPc4555xzzjnnnHPOOeecc87b -ntLjj1fnz/LWeNXruMv9jPJdenJ+xWd/b6ScMyU/xXf//r+7PuXeUz2lh9+B -nHPOOeecc84555xzzjnnnLe9NV61D3/mrXlpfVq+y7mqXq9VvXiWp/TYzVPy -q/N2eV3Seu7iKT1Ge3U+55xzzjnnnHPOOeecc8455yO9NS+tJ9/LR+2bdq40 -r87f1VN6fN2reoz+vFzdn/MET+nh88I555xzzjnnnHPOOeecc84553P87vq0 -/qvu5+q62fvv5q3xt/c26v3c8rR7HP2+WtXj1Pvn/Mr4qu+3q7l353POOeec -c84555xzzjnnnHPOOecjx1f76n1b657e89t9RuXe9ZTXf7Sn9Dj1/vmZ3hrf -ZX/OOeecc84555xzzjnnnHPOOef8iqf06Hl1/q7eGk/r6X2ekc8555xzzjnn -nHPOOeecc84555xzzsd4So+eV+fzvT2lh/c555xzzjnnnHPOOeecc84555xz -zvkZntLjj1fn82/66nXez5xzzjnnnHPOOeecc84555xzzjnnZ3hrvDd/dI8/ -nnY//NveGq/ah3POOeecc84555xzzjnnnHPOOeec8yvjaT0555xzzjnnnHPO -Oeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPO -Oeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPO -Oeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPO -Oeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPO -Oeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPO -Oeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPO -Oeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPO -Oeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPO -Oeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPO -Oeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPO -Oeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPO -Oeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPO -Oeecc84555zzZG/NS+vJOeecc84555xzzjnnnHPOOeecc84557O9Na83f1av -tPvh3/bWvKp9OOecc84555xzzjnnnHPOOeecc875t706/6en9ODf8qfrvZ85 -55xzzjnnnHPOOeecc84555xzzvkTr86/6ik9+J5ene99zjnnnHPOOeecc845 -55xzzjnnnHN+llfnX/WUHrt5a15aT+/zrB6cc84555xzzjnnnHPOOeecc845 -5/yd9+al9h2dczdvVO9d7ivtfZB2P7M9pQfnI7w1b5f9Oeecc84555xzzjnn -nHPOOeecP/O769L6r7qfq+tn77+bX33fVb2fW55yf0+9Ny+t7279OL/jrXmr -vt+u5t6dzznnnHPOOeecc84555xzzvmXvDWe1pPv5aP2SztXmqf02M2r80/x -qvzRnxffS3wnr873eeGcc84555xzzjnnnHPOOee8/fyZV7UPf+at8bQ+Ld/l -XFWv16wePNur83f1tB5p3yfV9/FzXlrPXbw6f5an9OCcc84555xzzjnnnHPO -Oed8hFfn//SUHqO9Na/qddzlfkb5Lj05v+Kzvzeqz9d70vpVv+53961+HdN7 -7uLV+X4Hcs4555xzzjnnnHPOOeec8528NT57/909pcdTv7t+1D6cc37XZ3+/ -8TVe/ffu9L/7afe5i6f04JxzzjnnnHPOOeecc84553v63fW9fdLOt9qf3r97 -5ZxzfrK//Xs6++9oyj2lenV+yu86zjnnnHPOOeecc84555xzzn97eut7+6Sd -L82r8znnnPOdvervdPW50706f7Wn9OCcn+eteWk9Oeecc84555xzzjnnnL9b -n3aOFB99z5xzzjnP9er8dK/OX/17j3O+r99dX/39uboP55xzzjnnnHPOOeec -8zVenZ/iT+9tdi/OOeec53p1/q5+d3x07tP1T/u0xtNeF86/5HfXr/p+u+qz -7yHt9eKcc84555xzzjnnnPPTvDp/lj+9h9m9OOecc/49H/U75O0+X/W349W+ -y/uhNa/6/jj/zVvzdv2+eOopPTjnnHPOOeecc84555xf8+r8t32frh/di3PO -Oefn+ezfXdXnm+UpPVJ89et+d13KPT311ry0nvyZV+eneEoPzjnnnHPOOeec -c8455+989rrRPZ+u55xzzjlP9VW/i3r/frs/f+ZXX5dRv+dTzt3z2Tlp5z3N -q/N39ZQenHPOOeecc84555xzzn9//sxL63m3P+ecc8455yd4df5qr8pJu4ev -enX+1zylB+ecc84555xzzjnnnPNsT+nBOeecc875SV6d33pW56fdw2lenb+r -p/TgnHPOOeecc84555xznuFvxznnnHPOOefrvPfvVT47J+W+T/Xq/K95Sg/O -Oeecc84555xzzjnnGZ7Sg3POOeecc9723u/5n+Oj8mfnVN/r6V6d/zVP6cE5 -55xzzjnnnHPOOed8jqf04JxzzjnnnOd5VX5an9O8Ny+t79c8pQfnnHPOOeec -c84555zza57Sg3POOeecc85He3X+6V6d/zVP6cE55/ydt8bTej49V2ve187L -Oeecc8455/wb3pv3dL+0c3LOOeecc875Km+Nt57qvqd4dX66p/TgnHM+dvzp -75bq875dn3YuzjnnnHPOOef8t+fPvLvzOeecc84555z/7tX5p3hvXlrfp+fr -va9G5aedn3POv+qz86rPdfXv8d35nHPOOeecc875jp7Sg3POOeecc86/4nfX -tcarz3GKt+bt0jPNvc855/x3n523qv+snNT79/eLc84555xzzr/prfGn+zxd -zznnnHPOOed8rY/arzVefb7T/e341/zt+/NtXrW35qX15Jy/91H7zv6e/Lpf -XZfWm3POOeecc875Gk/pwTnnnHPOOed8jo/a7+666nPv6m/H+e9+dbw1L/19 -3hofNZ//Pp7Wk5/prXn+rqzxlB6cc84555zz87w1ntZzF2+N9+aP7sE555xz -zjnnnN/x2TlXx6tyq++fj/Wq/Nk51fea4q15aT05T8rnf/eUHpxzzjnnnPPv -emveV3OrzsU555xzzjnnnJ/gd9fN7sP5P/vsnNH7/fTq+zvFW/PSevK9vDqf -j/XWuO9tzjnnnHPOeetJ6VV9D9U9OOecc84555xzzvlab4231t/Nebrube7u -XpWfdg/8G16dz8d4Sg/OOeecc875fX87/sffrt/Ne+et6sU555xzzjnnnHPO -+W/jo/b5qlfnX+2V1o/XenU+n+spPTjnnHPOOefj/On6tHOsuqe0Xpxzzjnn -nHPOOeecz/Tq/FlenX+1V1o/nunV+XyNp/TgnHPOOeecv/fq/DSvzuecc845 -55xzzjnnPMmr8996df5VT+nBM7w3L60vn+spPTjnnHPOOefjvDp/lvfOW9WL -c84555xzzjnnnPNEb4231lf37T2pfVN68D29Op/P9ZQenHPOOeec83Fenf/W -n553di/OOeecc84555xzzr/srfG7+87u23tW32P168b39up8nuUpPTjnnHPO -OefjvCp/dP/R+3LOOeecc84555xzztvjd+en+aj90s7Fa/3p+rRz8Lme0oNz -zjnnnHM+3++u370/55xzzjnnnHPOOee83qvze73uru/9m5/tvXlpfflcT+nB -Oeecc845560nrR/nnHPOOeecc84555z/8ep8vrdX5/O5ntKDc84555xzfp6/ -Heecc84555xzzjnnnPNUb43fnc/P9Op8PtdTenDOOeecc87P85QenHPOOeec -c84555xzvsqr8/neXp3P73lKD84555xzzvl3PaUH55xzzjnnnHPOOeecV3tr -vLW+ui/P8t68tL5f86evy6r9OOecc84559/1lB6cc84555xzzjnnnHP+Fb+7 -rvVUn4PX+N3xp/uk++j7HL3v6NeVc84555xznuOr13HOOeecc84555xzzjl/ -563xu/tWn4Pv4a15aT1nn/er/vR+fJ9wzjnnnHPe99XrOOecc84555xzzjnn -nGf47JxR+1XfE/+mp/RI9VGf66rvmer745xzzjnn/Imn9OCcc84555xzzjnn -nHP+zmfnjNqv+p743p7S41T3PcM555xzznn/SevHOeecc84555xzzjnnfI7P -zrm7rvo+eI1ffdJ682te9X3S8ur74Jxzzjnne3hrvDd/dA/OOeecc84555xz -zjnnZ/io/apyq7w1L63n6PP+HB/1fuDf9lmfu7e9OOecc845T+rBOeecc845 -55xzzjnnnCd5a7y1flT+3XVV9/R2nPMdvDqfc84555zv4Sk9OOecc84555xz -zjnnnPOTfNR+o/pwzsd7dT7nnHPOOX/mb8c555xzzjnnnHPOOeecc8455+u9 -Op9zzjnnOX53/aj90+4hzVN6cM4555xzzjnnnHPOOeecc87ve3U+55xzzr/j -s9elnffpOat7cM4555xzzjnnnHPOOeecc87ne3U+55xzzvvjVbm7+Kr7WZXH -Oeecc84555xzzjnnnHPOOd/fq/M555zzE33Uvk9z0+5jtc9+XTjnnHPOOeec -c84555xzzjnnvDqfc845P9FH7dvbP+3cKT77deGcc84555xzzjnnnHPOOeec -8+p8zjnnnLefp3/HR/f6mo+6f84555xzzjnnnHPOOeecc845b3l1Puecc877 -Xp2/qz+959m9OOecc84555xzzjnnnHPOOeff9+p8zjnnnD/36vx0f3qfs3tx -zjnnnHPOOeecc84555xzzr/v1fmcc845f+7V+Sk++j5H78s555xzzjnnnHPO -Oeecc845P8+r8znnnHM+3qvzZ/mqe1uVxznnnHPOOeecc84555xzzjn/rlfn -c84553y8t+b15q/uu8u9cc4555xzzjnnnHPOOeecc875Xa/O55xzznmu9+b1 -/t3bJ/VcnHPOOeecc84555xzzjnnnHP+1qvzOeecc17vd8fT+j89b3UPzjnn -nHPOOeecc84555xzzvl3vTqfc84553yWvx3nnHPOOeecc84555xzzjnnnPOn -Xp3POeecc77aU3pwzjnnnHPOOeecc84555xzzr/r1fmcc84557M8pQfnnHPO -Oeecc84555xzzjnn/Dyvzuecc845n+UpPTjnnHPOOeecc84555xzzjnn53l1 -Puecc875W0/pwTnnnHPOOeecc84555xzzjnnf7w6n3POOef8qqf04Jxzzjnn -nHPOOeecc84555zznlfnc8455/w73pv3dL+0c3LOOeecc84555xzzjnnnHPO -ec+r8znnnHP+HU/fj3POOeecc84555xzzjnnnHPOV3l1Puecc86/763x3vzR -PTjnnHPOOeecc84555xzzjnnfJVX53POOeec9560fpxzzjnnnHPOOeecc845 -55xz3vPqfM4555zz3pPWj3POOeecc84555xzzjnnnHPOe16dzznnnPPv+9tx -zjnnnHPOOeecc84555xzzjnfzavzOeecc17vrfGn+zxdzznnnHPOOeecc845 -55xzzjnnX/HqfM4555zX++p1nHPOOeecc84555xzzjnnnHP+da/O55xzzvl+ -ntKDc84555xzzjnnnHPOOeecc85TvTqfc8455/X+dpxzzjnnnHPOOeecc845 -55xzzvm/enU+55xzzvt+d11vn6c9OOecc84555xzzjnnnHPOOeecX/PqfM45 -55yP95QenHPOOeecc84555xzzjnnnHN+qlfnc8756X53/ao+P8fT7u00fzvO -Oeecc84555xzzjnnnHPOOed8rVfnc8756X53/arc3r/5HE/pwTnnnHPOOeec -c84555xzzjnn/J1X53POOR/j1fk/PaXHaG+NP93n6XrOOeecc84555xzzjnn -nHPOOefZXp3POedXvTev9+9qr85P95QeTz2lB+ecc84555xzzjnnnHPOOeec -8wyvzuec81nemleVOzrndB/9ej0d55xzzjnnnHPOOeecc84555xzzv/m1fmc -c/7WR+07OjftnnhGPuecc84555xzzjnnnHPOOeec8zO8Op9zzlvP0/FV34ez -evC5Xp3POeecc84555xzzjnnnHPOOef8DK/O55zzqz4772mftHs63aveP5xz -zjnnnHPOOeecc84555xzzvk/e3U+55y/9VH79vZPOzf/u89+n3DOOeecc845 -55xzzjnnnHPOOedXvDqfc85n+dP1aefgf/dV7wfOOeecc84555xzzjnnnHPO -Oef8iVfnc855ilfn83v+9PWd3YtzzjnnnHPOOeecc84555xzzjlPyOec8xSv -zud/91Wv+6o8zjnnnHPOOeecc84555xzzjnnZ3h1Puecp3hvXlrfU3zV68s5 -55xzzjnnnHPOOeecc84555yP9Op8zjnf1avzd/Xq16u6B+ecc84555xzzjnn -nHPOOeec8zO8Op9zzr/m1fnpXn3/q3pwzjnnnHPOOeecc84555xzzjk/26vz -Oed8V3+6Pu0co+8j9e9LSg/OOeecc84555xzzjnnnHPOOedneHU+55zzez5q -v9F9fs5LvZ9VPTjnnHPOOeecc84555xzzjnnnJ/t1fmcc87/7nfXp/VP85Qe -nHPOOeecc84555xzzjnnnHPOz/DqfM45P93vjqf1T/OUHpxzzjnnnHPOOeec -c84555xzzs/26nzOOef8ib8d55xzzjnnnHPOOeecc84555xzzmd6dT7nnHP+ -m7fGe/NH9+Ccc84555xzzjnnnHPOOeecc87veHU+55xzPtJTenDOOeecc845 -55xzzjnnnHPOOT/bq/M555zzJ57Sg3POOeecc84555xzzjnnnHPOOf+bV+dz -zjnnv/nbcc4555xzzjnnnHPOOeecc84557zCq/M555zz3zylB+ecc84555xz -zjnnnHPOOeecc37Hq/M555zzEeOcc84555xzzjnnnHPOOeecc855klfnc845 -P8vfjnPOOeecc84555xzzjnnnHPOOec7eHU+55zzszylB+ecc84555xzzjnn -nHPOOeeccz7Tq/M555xnefp+nHPOOeecc84555xzzjnnnHPO+Q5enc8557zG -v5bDOeecc84555xzzjnnnHPOOeecJ3l1Puec87nemzc6J+38nHPOOeecc845 -55xzzjnnnHPOeYVX53POOc/y1vjTfZ6u55xzzjnnnHPOOeecc84555xzznf2 -6nzOOeff9JQenHPOOeecc84555xzzjnnnHPOeYVX53POOf+mp/TgnHPOOeec -c84555xzzjnnnHPOK7w6n3PO+R7+dpxzzjnnnHPOOeecc84555xzzjk/yavz -Oeec7+0pPTjnnHPOOeecc84555xzzjnnnPMkr87nnHO+h6f04JxzzjnnnHPO -Oeecc84555xzznfw6nzOOed/99b46P1H78s555xzzjnnnHPOOeecc84555zz -+nzOOT/Fe/NG56Sdn3POOeecc84555xzzjnnnHPOOT/Jq/M55/x0X72Oc845 -55xzzjnnnHPOOeecc8455/O9Op9zzvkYT+nBOeecc84555xzzjnnnHPOOeec -8/p8zjnn9zylB+ecc84555xzzjnnnHPOOeecc87bXp3POef8757Sg3POOeec -c84555xzzjnnnHPOOef3vTqfc85Xe2/e1f1G53LOOeecc84555xzzjnnnHPO -Oef8O16dzznnKb56Heecc84555xzzjnnnHPOOeecc86/69X5nHO+q6f04Jxz -zjnnnHPOOeecc84555xzznmeV+fzGm+Np/XkfKW/Heecc84555xzzjnnnHPO -Oeecc845/+PV+Xyu312vJ0/w3rzev+8+aefnnHPOOeecc84555xzzjnnnHPO -+f5enc/H+Kh9d+mfdv+81lN6cM4555xzzjnnnHPOOeecc84555z/8ep8Psbv -rl/VZ3XOqHtLe315Vg/OOeecc84555xzzjnnnHPOOeec855X5/MxXp3/Vf85 -3pt3dT7P6sE555xzzjnnnHPOOeecc84555xzPtqr86/63XVp/avugdd6So/R -vnod55xzzjnnnHPOOeecc84555xzzvluXp3/1u+Op/UffV6+t6f06HlKD845 -55xzzjnnnHPOOeecc84555zzVK/Of+uj9+39e5VX5/M9PPVzxDnnnHPOOeec -c84555xzzjnnnHN+ulfnX/XqHr1/j/ZVOfzbXp3POeecc84555xzzjnnnHPO -Oeecc36qV+W/Ha/2VffA+RPvvd+qenHOOeecc84555xzzjnnnHPOOeecn+LV -+a3n6Xjq/bztwfkd770Pq3pxzjnnnHPOOeecc84555xzzjnnnJ/i1fm9J6Vf -79+renD+Zv2qXpxzzjnnnHPOOeecc84555xzzjnnp3t1fut5Or7qfnr7pN0r -/6Y//XzN7sU555xzzjnnnHPOOeecc84555xzfrpX57/12Xm93LT74Gd52ueF -c84555xzzjnnnHPOOeecc84555xn5M/yu+t7+6Sdj5/lVZ8LzjnnnHPOOeec -c84555xzzjnnnHP+zKvzU7w6n/PffPT7fPS+nHPOOeecc84555xzzjnnnHPO -Oef8X706P92r8/lZvur9vCqPc84555xzzjnnnHPOOeecc8455/xUr85P9+p8 -/k1P6dF60vpxzjnnnHPOOeecc84555xzzjnnnO/m1fm7enU+39ur37fVPTjn -nHPOOeecc84555xzzjnnnHPOv+7V+bt6dT7fy3+OV/dYlcc555xzzjnnnHPO -Oeecc84555xzfqpX5+/qvSetL5/rKT16ntKDc84555xzzjnnnHPOOeecc845 -5/zrXp1/ulfn83ue0qPnb8c555xzzjnnnHPOOeecc84555xzzvk7r87nf/fq -/NM9pcdoT+nBOeecc84555xzzjnnnHPOOeecc/51r84/3Uft29s/7dyr7vXq -/Vydv7un9OCcc84555xzzjnnnHPOOeecc845/7pX5/Msr87/6aPPdXV9yvmf -+ttxzjnnnHPOOeecc84555xzzjnnnHP+zqvzeZa35vXmX81JO+9pntKDc845 -55xzzjnnnHPOOeecc8455/zrXp3Pa3zUvmnn4lk9OOecc84555xzzjnnnHPO -Oeecc85P9ep8Ptffjnuf7OkpPTjnnHPOOeecc84555xzzjnnnHPOT/XqfM55 -39+Oc84555xzzjnnnHPOOeecc84555zztV6dzzl/vq63z9MenHPOOeecc845 -55xzzjnnnHPOOef8nVfnc86fr+vt87QH55xzzjnnnHPOOeecc84555xzzjl/ -59X5nPPxntKDc84555xzzjnnnHPOOeecc8455/xUr87nnI/3lB6cc84555xz -zjnnnHPOOeecc84556d6dT7n/Lmn9OCcc84555xzzjnnnHPOOeecc8455//q -1fmcn+ir13HOOeecc84555xzzjnnnHPOOeec87Venc8573tKD84555xzzjnn -nHPOOeecc84555xzfs2r8znn7SetH+ecc84555xzzjnnnHPOOeecc845v+bV -+Zx/2d+Oc84555xzzjnnnHPOOeecc84555zzPb06n/MTPaUH55xzzjnnnHPO -Oeecc84555xzzjmf49X5nH/B345zzjnnnHPOOeecc84555xzzjnnnPNveXU+ -5zv523HOOeecc84555xzzjnnnHPOOeecc36GV+dzvpOn9OCcc84555xzzjnn -nHPOOeecc84559lenc/5b+N356/qxTnnnHPOOeecc84555xzzjnnnHPO+W9e -nc95Qv5P7/Ws6sU555xzzjnnnHPOOeecc84555xzzvfw6nzOE/J/eq9nVS/O -Oeecc84555xzzjnnnHPOOeecc76HV+fzs7w3L6Xv0/6cc84555xzzjnnnHPO -Oeecc84555wn5HNemf+05+xenHPOOeecc84555xzzjnnnHPOOed8b6/O53yk -t+bN3p9zzjnnnHPOOeecc84555xzzjnnnPN/9up8znfylB6cc84555xzzjnn -nHPOOeecc8455zzbq/M5T/SUHpxzzjnnnHPOOeecc84555xzzjnnfE+vzuc8 -0VN6cM4555xzzjnnnHPOOeecc84555zzPb06n/ORvnod55xzzjnnnHPOOeec -c84555xzzjnnf/Pq/P9uh45uAASBIAr237UdaCB37inzOwHeBs6TPmUH55xz -zjnnnHPOOeecc84555xzzjn/l6f7nL/hU3ZwzjnnnHPOOeecc84555xzzjnn -nPMzPN3nvNKn7OCcc84555xzzjnnnHPOOeecc84552d7us/5nU/ZwTnnnHPO -Oeecc84555xzzjnnnHPO+Yqn+zzjVe/tdqv6nHPOOeecc84555xzzjnnnHPO -OeecT/R0n9f407n0rmn/xTnnnHPOOeecc84555xzzjnnnHPOeaen+7zXuztP -3e4+55xzzjnnnHPOOeecc84555xzzjnnEz3d5xlfvbf7/u59zjnnnHPOOeec -c84555xzzjnnnHPOv+kX/MR5Lg== - "], {{0, 0}, {401, 401}}, {0, 1}], Frame -> Automatic, - FrameLabel -> {None, None}, FrameTicks -> {{None, None}, {None, None}}, - GridLinesStyle -> Directive[ - GrayLevel[0.5, 0.4]], - Method -> { - "DefaultBoundaryStyle" -> Automatic, "DefaultPlotStyle" -> Automatic}], - FormBox[ - FormBox[ - TemplateBox[{"\"Divergent\"", - RowBox[{"-", "1"}], - RowBox[{ - RowBox[{"-", - RowBox[{"0.5`"}]}], "-", - RowBox[{"0.5`", " ", "\[ImaginaryI]"}]}], - RowBox[{ - RowBox[{"-", - RowBox[{"0.5`"}]}], "+", - RowBox[{"0.5`", " ", "\[ImaginaryI]"}]}]}, "SwatchLegend", - DisplayFunction -> (FormBox[ - StyleBox[ - StyleBox[ - PaneBox[ - TagBox[ - GridBox[{{ - TagBox[ - GridBox[{{ - GraphicsBox[{ - Directive[ - EdgeForm[ - Directive[ - Opacity[0.3], - GrayLevel[0]]], - PointSize[0.5], - AbsoluteThickness[1.6], - RGBColor[0., 0., 0.]], - RectangleBox[{0, 0}, {10, 10}, "RoundingRadius" -> 0]}, - AspectRatio -> Full, ImageSize -> {10, 10}, - PlotRangePadding -> None, ImagePadding -> Automatic, - BaselinePosition -> (Scaled[0.1] -> Baseline)], #}, { - GraphicsBox[{ - Directive[ - EdgeForm[ - Directive[ - Opacity[0.3], - GrayLevel[0]]], - PointSize[0.5], - AbsoluteThickness[1.6], - RGBColor[1., 0., 0.]], - RectangleBox[{0, 0}, {10, 10}, "RoundingRadius" -> 0]}, - AspectRatio -> Full, ImageSize -> {10, 10}, - PlotRangePadding -> None, ImagePadding -> Automatic, - BaselinePosition -> (Scaled[0.1] -> Baseline)], #2}, { - GraphicsBox[{ - Directive[ - EdgeForm[ - Directive[ - Opacity[0.3], - GrayLevel[0]]], - PointSize[0.5], - AbsoluteThickness[1.6], - RGBColor[0., 1., 0.]], - RectangleBox[{0, 0}, {10, 10}, "RoundingRadius" -> 0]}, - AspectRatio -> Full, ImageSize -> {10, 10}, - PlotRangePadding -> None, ImagePadding -> Automatic, - BaselinePosition -> (Scaled[0.1] -> Baseline)], #3}, { - GraphicsBox[{ - Directive[ - EdgeForm[ - Directive[ - Opacity[0.3], - GrayLevel[0]]], - PointSize[0.5], - AbsoluteThickness[1.6], - RGBColor[0., 0., 1.]], - RectangleBox[{0, 0}, {10, 10}, "RoundingRadius" -> 0]}, - AspectRatio -> Full, ImageSize -> {10, 10}, - PlotRangePadding -> None, ImagePadding -> Automatic, - BaselinePosition -> (Scaled[0.1] -> Baseline)], #4}}, - GridBoxAlignment -> { - "Columns" -> {Center, Left}, "Rows" -> {{Baseline}}}, - AutoDelete -> False, - GridBoxDividers -> { - "Columns" -> {{False}}, "Rows" -> {{False}}}, - GridBoxItemSize -> {"Columns" -> {{All}}, "Rows" -> {{All}}}, - GridBoxSpacings -> { - "Columns" -> {{0.5}}, "Rows" -> {{0.5}}}], "Grid"]}}, - GridBoxAlignment -> {"Columns" -> {{Left}}, "Rows" -> {{Top}}}, - AutoDelete -> False, - GridBoxItemSize -> { - "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, - GridBoxSpacings -> {"Columns" -> {{1}}, "Rows" -> {{0}}}], - "Grid"], Alignment -> Left, AppearanceElements -> None, - ImageMargins -> {{5, 5}, {5, 5}}, ImageSizeAction -> - "ResizeToFit"], LineIndent -> 0, StripOnInput -> False], { - FontFamily -> "Arial"}, Background -> Automatic, StripOnInput -> - False], TraditionalForm]& ), - InterpretationFunction :> (RowBox[{"SwatchLegend", "[", - RowBox[{ - RowBox[{"{", - RowBox[{ - RowBox[{"Directive", "[", - InterpretationBox[ - ButtonBox[ - TooltipBox[ - GraphicsBox[{{ - GrayLevel[0], - RectangleBox[{0, 0}]}, { - GrayLevel[0], - RectangleBox[{1, -1}]}, { - RGBColor[0., 0., 0.], - RectangleBox[{0, -1}, {2, 1}]}}, AspectRatio -> 1, Frame -> - True, FrameStyle -> RGBColor[0., 0., 0.], FrameTicks -> - None, PlotRangePadding -> None, ImageSize -> - Dynamic[{ - Automatic, 1.35 CurrentValue["FontCapHeight"]/ - AbsoluteCurrentValue[Magnification]}]], - "RGBColor[0., 0., 0.]"], Appearance -> None, - BaseStyle -> {}, BaselinePosition -> Baseline, - DefaultBaseStyle -> {}, ButtonFunction :> - With[{Typeset`box$ = EvaluationBox[]}, - If[ - Not[ - AbsoluteCurrentValue["Deployed"]], - SelectionMove[Typeset`box$, All, Expression]; - FrontEnd`Private`$ColorSelectorInitialAlpha = 1; - FrontEnd`Private`$ColorSelectorInitialColor = - RGBColor[0., 0., 0.]; - FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; - MathLink`CallFrontEnd[ - FrontEnd`AttachCell[Typeset`box$, - FrontEndResource["RGBColorValueSelector"], { - 0, {Left, Bottom}}, {Left, Top}, - "ClosingActions" -> { - "SelectionDeparture", "ParentChanged", - "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> - Automatic, Method -> "Preemptive"], - RGBColor[0., 0., 0.], Editable -> False, Selectable -> - False], "]"}], ",", - RowBox[{"Directive", "[", - InterpretationBox[ - ButtonBox[ - TooltipBox[ - GraphicsBox[{{ - GrayLevel[0], - RectangleBox[{0, 0}]}, { - GrayLevel[0], - RectangleBox[{1, -1}]}, { - RGBColor[1., 0., 0.], - RectangleBox[{0, -1}, {2, 1}]}}, AspectRatio -> 1, Frame -> - True, FrameStyle -> RGBColor[0.6666666666666667, 0., 0.], - FrameTicks -> None, PlotRangePadding -> None, ImageSize -> - Dynamic[{ - Automatic, 1.35 CurrentValue["FontCapHeight"]/ - AbsoluteCurrentValue[Magnification]}]], - "RGBColor[1., 0., 0.]"], Appearance -> None, - BaseStyle -> {}, BaselinePosition -> Baseline, - DefaultBaseStyle -> {}, ButtonFunction :> - With[{Typeset`box$ = EvaluationBox[]}, - If[ - Not[ - AbsoluteCurrentValue["Deployed"]], - SelectionMove[Typeset`box$, All, Expression]; - FrontEnd`Private`$ColorSelectorInitialAlpha = 1; - FrontEnd`Private`$ColorSelectorInitialColor = - RGBColor[1., 0., 0.]; - FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; - MathLink`CallFrontEnd[ - FrontEnd`AttachCell[Typeset`box$, - FrontEndResource["RGBColorValueSelector"], { - 0, {Left, Bottom}}, {Left, Top}, - "ClosingActions" -> { - "SelectionDeparture", "ParentChanged", - "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> - Automatic, Method -> "Preemptive"], - RGBColor[1., 0., 0.], Editable -> False, Selectable -> - False], "]"}], ",", - RowBox[{"Directive", "[", - InterpretationBox[ - ButtonBox[ - TooltipBox[ - GraphicsBox[{{ - GrayLevel[0], - RectangleBox[{0, 0}]}, { - GrayLevel[0], - RectangleBox[{1, -1}]}, { - RGBColor[0., 1., 0.], - RectangleBox[{0, -1}, {2, 1}]}}, AspectRatio -> 1, Frame -> - True, FrameStyle -> RGBColor[0., 0.6666666666666667, 0.], - FrameTicks -> None, PlotRangePadding -> None, ImageSize -> - Dynamic[{ - Automatic, 1.35 CurrentValue["FontCapHeight"]/ - AbsoluteCurrentValue[Magnification]}]], - "RGBColor[0., 1., 0.]"], Appearance -> None, - BaseStyle -> {}, BaselinePosition -> Baseline, - DefaultBaseStyle -> {}, ButtonFunction :> - With[{Typeset`box$ = EvaluationBox[]}, - If[ - Not[ - AbsoluteCurrentValue["Deployed"]], - SelectionMove[Typeset`box$, All, Expression]; - FrontEnd`Private`$ColorSelectorInitialAlpha = 1; - FrontEnd`Private`$ColorSelectorInitialColor = - RGBColor[0., 1., 0.]; - FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; - MathLink`CallFrontEnd[ - FrontEnd`AttachCell[Typeset`box$, - FrontEndResource["RGBColorValueSelector"], { - 0, {Left, Bottom}}, {Left, Top}, - "ClosingActions" -> { - "SelectionDeparture", "ParentChanged", - "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> - Automatic, Method -> "Preemptive"], - RGBColor[0., 1., 0.], Editable -> False, Selectable -> - False], "]"}], ",", - RowBox[{"Directive", "[", - InterpretationBox[ - ButtonBox[ - TooltipBox[ - GraphicsBox[{{ - GrayLevel[0], - RectangleBox[{0, 0}]}, { - GrayLevel[0], - RectangleBox[{1, -1}]}, { - RGBColor[0., 0., 1.], - RectangleBox[{0, -1}, {2, 1}]}}, AspectRatio -> 1, Frame -> - True, FrameStyle -> RGBColor[0., 0., 0.6666666666666667], - FrameTicks -> None, PlotRangePadding -> None, ImageSize -> - Dynamic[{ - Automatic, 1.35 CurrentValue["FontCapHeight"]/ - AbsoluteCurrentValue[Magnification]}]], - "RGBColor[0., 0., 1.]"], Appearance -> None, - BaseStyle -> {}, BaselinePosition -> Baseline, - DefaultBaseStyle -> {}, ButtonFunction :> - With[{Typeset`box$ = EvaluationBox[]}, - If[ - Not[ - AbsoluteCurrentValue["Deployed"]], - SelectionMove[Typeset`box$, All, Expression]; - FrontEnd`Private`$ColorSelectorInitialAlpha = 1; - FrontEnd`Private`$ColorSelectorInitialColor = - RGBColor[0., 0., 1.]; - FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; - MathLink`CallFrontEnd[ - FrontEnd`AttachCell[Typeset`box$, - FrontEndResource["RGBColorValueSelector"], { - 0, {Left, Bottom}}, {Left, Top}, - "ClosingActions" -> { - "SelectionDeparture", "ParentChanged", - "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> - Automatic, Method -> "Preemptive"], - RGBColor[0., 0., 1.], Editable -> False, Selectable -> - False], "]"}]}], "}"}], ",", - RowBox[{"{", - RowBox[{#, ",", #2, ",", #3, ",", #4}], "}"}], ",", - RowBox[{"LegendMarkers", "\[Rule]", "Automatic"}], ",", - RowBox[{"LabelStyle", "\[Rule]", - RowBox[{"{", "}"}]}], ",", - RowBox[{"LegendLayout", "\[Rule]", "\"Column\""}]}], "]"}]& ), - Editable -> True], TraditionalForm], TraditionalForm]}, - "Legended", - DisplayFunction->(GridBox[{{ - TagBox[ - ItemBox[ - PaneBox[ - TagBox[#, "SkipImageSizeLevel"], Alignment -> {Center, Baseline}, - BaselinePosition -> Baseline], DefaultBaseStyle -> "Labeled"], - "SkipImageSizeLevel"], - ItemBox[#2, DefaultBaseStyle -> "LabeledLabel"]}}, - GridBoxAlignment -> {"Columns" -> {{Center}}, "Rows" -> {{Center}}}, - AutoDelete -> False, GridBoxItemSize -> Automatic, - BaselinePosition -> {1, 1}]& ), - Editable->True, - InterpretationFunction->(RowBox[{"Legended", "[", - RowBox[{#, ",", - RowBox[{"Placed", "[", - RowBox[{#2, ",", "After"}], "]"}]}], "]"}]& )]], "Output", - CellChangeTimes->{3.659556259184917*^9, 3.659556302150953*^9, - 3.6595563906887107`*^9, 3.6595564366805267`*^9, 3.6641617768839207`*^9}] -}, Open ]], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"newtonplot", "[", - RowBox[{ - RowBox[{"Function", "[", - RowBox[{"x", ",", - RowBox[{ - RowBox[{"(", - RowBox[{"x", "+", "1.5"}], ")"}], - RowBox[{"(", "x", ")"}], - RowBox[{"(", - RowBox[{"x", "-", "0.75"}], ")"}]}]}], "]"}], ",", "2", ",", "401", - ",", "20", ",", "0.05"}], "]"}]], "Input", - CellChangeTimes->{{3.6595549152958674`*^9, 3.659554978383319*^9}, - 3.659555332709116*^9, {3.659555509656427*^9, 3.6595555271955185`*^9}, { - 3.659555597485504*^9, 3.659555613597739*^9}, {3.6631017052455835`*^9, - 3.663101720860613*^9}, 3.6641616424542694`*^9}], - -Cell[BoxData[ - TemplateBox[{GraphicsBox[ - RasterBox[CompressedData[" -1:eJzs1t2t5MphhdFrKBJHohwUggA/OxZnqhAMQTgPc9DdbP7uXVWLgADNKpLf -ZmsAzX//83//8T9/++uvv/7vv/7zn3//9/9c//r7Xy+vWf3q59q+bzVP9/nY -3rKDc84555xzzjnnnHPOOee81d+db/15VT97zjnnfC5P99s93ecdfT6nt+zg -nHPOOeecc84555xzzjlfzVt2HPWz55xzztfwdL/d033e0edruL+XnHPOOeec -c84555xzzjnnc/m781SXc875Wp7uj+rp/qye7vO1vGUH55xzzjnnnHPOOeec -c845n8vTfc455x2e7q/iR8/bviP9O3F+pbfs4JxzzjnnnHPOOeecc84553N5 -us8557zD033+2tN938dX8JYdnHPOOeecc84555xzzjnnfC5P9znnnHd4us/3 -ebrvO/hM3rKDc84555xzzjnnnHPOOeecz+XpPuec8w5P9/k1nu6Ptouv5S07 -OOecc84555xzzjnnnHPO+Vye7nPOOe/2dJ9nfLYO55+8ZQfnnHPOOeecc845 -55xzzjmfy9N9zjnn3Z7u8y5vfx/nn7xlB+ecc84555xzzjnnnHPOOV/D033O -Oefdnu7zsf3sOedHvGUH55xzzjnnnHPOOeecc845X9vTfc45592e7vOx/enn -+Fq+9eendnDOOeecc84555xzzjnnnPO1Pd3nnHM+pqf7fGzfus+/f/g33rKD -c84555xzzjnnnHPOOeec809X2y7OOefdnu7zsT3dn31vu7fs4JxzzjnnnHPO -Oeecc8455/xOT/c555yP6ek+H9vT/af96t/h7l2cc84555xzzjnnnHPOOeec -8+893eeccz6Xp/t8bE/3Oeecc84555xzzjnnnHPOOef8Kk/3Oeecz+XpPh/b -t+5r28s555xzzjnnnHPOOeecc8455+883eeccz6Xp/t8bE/3Oeecc84555xz -zjnnnHPOOed8r6f7nHPO1/B0n4/t6T7nnHPOOeecc84555xzzjnnnL/zratt -L+ec87k83edje7rPOeecc84555xzzjnnnHPOOZ/f39139pxzzjm/09N9Pran -+5xzzjnnnHPOOeecc84555xznu5zzjnnrzzd52N7us8555xzzjnnnHPOOeec -c8455+k+55xz/srTfT62p/ucc84555xzzjnnnHPOOeecc57uc84556883edz -errPOeecc84555xzzjnnnHPOOZ/P033OOed8j6f7fE4/+nzbd3DOOeecc845 -55xzzjnnnHPOezzd55xzzvd4us/n9HSfc84555xzzjnnnHPOOeeccz6up/uc -c875FZ7u8zk93eecc84555xzzjnnnHPOOeec93u6zznnnN/p6T6f09N9zjnn -nHPOOeecc84555xzznm/p/ucc875nZ7u87U83eecc84555xzzjnnnHPOOeec -P+/pPuecc57wdJ+v5ek+55xzzjnnnHPOOeecc8455/w+T/c555zzJk/3+Vr+ -1PvavptzzjnnnHPOOeecc84555zzpO99/uw555xzzvN9zq84P/vvSs4555xz -zjnnnHPOOeecc875+6ttF+eccz6Cp/ucN/Q555xzzjnnnHPOOeecc8455++v -tl2cc875CJ7uc97Q55xzzjnnnHPOOeecc84555y/v9p2cc455yN4us/5J0/3 -Oeecc84555xzzjnnnHPOOV/B033OOed8Rk/3Of/k6T7nnHPOOeecc84555xz -zjnnK3i6zznnnM/o6T7nnzzd55xzzjnnnHPOOeecc84553wmT/c555zzlTzd -5/yIb93XtpdzzjnnnHPOOeecc84555zzJz3d55xzznm+z/kRT/c555xzzjnn -nHPOOeecc845b/Z0n3POOef5PudXerrPOeecc84555xzzjnnnHPO+ZOe7nPO -Oef8vaf7nD/hbe/z72bOOeecc84555xzzjnnnHO+x9N9zjnnnO/3dJ/zpD/9 -3G9v+z0455xzzjnnnHPOOeecc8551tN9zjnnnF/n6T7njX72/Ftv+27OOeec -c84555xzzjnnnHOe9XSfc84559d5us95o6f7nHPOOeecc84555xzzjnnfG5P -9znnnHN+v6f7nDf61n1teznnnHPOOeecc84555xzznmnp/ucc845z3m6z/lI -nu5zzjnnnHPOOeecc84555zzTk/3Oeecc97n6T7nI3m6zznnnHPOOeecc845 -55xzPqu/O9/681170h3OOeecj+/pPucj+dHztu/gnHPOOeecc84555xzzjlv -96ve+/RznHPOOec/nu5zPoOn+5xzzjnnnHPOOeecc84557P5Ve89e84555xz -ftTTfc5n9nSfc84555xzzjnnnHPOOeecd/Q555xzvp6n+5yv6EfP276Dc845 -55xzzjnnnHPOOed8FE/3Oeecc76ep/uc854+55xzzjnnnHPOOeecc875rJ7u -c84553w9T/c55z19zjnnnHPOOeecc84555zz0T3d55xzzjn/8XSfc77t6f7o -39f2vZxzzjnnnHPOOeecc845v8/Tfc4555zzH0/3OefHPd0fZW/b78A555xz -zjnnnHPOOeec8/Oe7nPOOeecb3m6zzm/3rfue6rf8ru07OCcc84555xzzjnn -nHPO+XWe7nPOOeecb3m6zznPe/v7znrLDs4555xzzjnnnHPOOeec7/d0n3PO -Oef8qKf7nPNef/q5s972+3HOOeecc84555xzzjnn/HtP9znnnHPOr/Z0n3M+ -j6f7nHPOOeecc84555xzzjnv93Sfc8455/wpT/c55/N4us8555xzzjnnnHPO -Oeec835P9znnnHPOn/J0n3M+j6f7nHPOOeecc84555xzzjnv8XSfc8455zzt -6T7nfB7fuq9tL+ecc84555xzzjnnnHPOz3u6zznnnHPe6uk+53x+T/c555xz -zjnnnHPOOeecc75939lzzjnnnHP+p6f7nPP5feu+tr2cc84555xzzjnnnHPO -+cqe7nPOOeecz+LpPud8fk/3Oeecc84555xzzjnnnHP+/mrbxTnnnHM+i6f7 -nPN1Pd3nnHPOOeecc84555xzzlf2dJ9zzjnnfHZP9znn/N2197ztOzjnnHPO -Oeecc84555zzBk/3Oeecc85X9XSfc86/9XSfc84555xzzjnnnHPOOW/2dJ9z -zjnnnP/p6T7nnH/rW/e17eWcc84555xzzjnnnHP++bxt5yie7nPOOeec8+88 -3eec87Oe7nPOOeecc84555xzzjl/7e/uS+0ZzdN9zjnnnHN+ztN9zjm/y1vf -1/Y7cc4555xzzjnnnHPO+bvzb+9P7ZvF033OOeecc36Pp/ucc97iZ89/e9v3 -cc4555xzzjnnnHPO+bfPte2+6zvt4pxzzjnnd3q6zznn7Z7uc84555xzzjnn -nHPOecp/n7ft+3b3an3OOeecc97h6T7nnLd7us/Hdn+vOOecc84555xzzvnI -/vu8bd/Z72l7H+ecc845n8vTfc45H9XTfd7p6f7R/99/egfnnHPOOeecc845 -H9Nbdhz1s+ecc84555zv8XSfc85n86372vbyz57uP+0tOzjnnHPOOeecc875 -WN6yY8tbdnDOOeec8zU83eec81U83ecd/VG9ZQfnnHPOOeecc845H9Pfnbe9 -h3POOeec8ys93eec89X96Hnbd7R5ur+Kt+zgnHPOOeecc84553yPp/ucc845 -53wNT/c555y/9nR/FE/3+Wtv2cE555xzzjnnnHPO+aerbRfnnHPOOZ/L033O -Oef7PN1v83Sfv/aWHZxzzjnnnHPOOeecf7radnHOOeec87k83eecc36NHz1v -+46j38e73f+unHPOOeecc84557zJ033OOeecc76Gp/ucc87v9XR/9r38tbfs -4JxzzjnnnHPOOef809W2i3POOeecz+XpPuec84wfPU/v4mN4yw7OOeecc845 -55xzzj9dbbs455xzzvlcnu5zzjkfw7fuO/q+tu/k13jLDs4555xzzjnnnHO+ -tqf7nHPOOed8bU/3Oeecj+1PP8e7vGUH55xzzjnnnHPOOeefrrZdnHPOOed8 -DU/3Oeecr+UtO/g13rKDc84555xzzjnnnPNPV9suzjnnnHO+hqf7nHPO5/T2 -9/F93rKDc84555xzzjnnnPNPV9suzjnnnHO+tqf7nHPO5/TV++3esoNzzjnn -nHPOOeec8ys83eecc8455/yVp/ucc87n9HT/Wz+6/+5de71lB+ecc84555xz -zjnnd3q6zznnnHPO+R5P9znnnM/pW/e17b36u+/63rvfzznnnHPOOeecc855 -s6f7nHPOOeec7/F0n3PO+Zye7nPOOeecc84555xzzufzdJ9zzjnnnPM9nu5z -zjmf09N9zjnnnHPOOeecc875uJ7uc84555xzfoWn+5xzzuf0dJ9zzjnnnHPO -Oeecc97v6T7nnHPOOed3errPOed8Tk/3Oeecc84555xzzjnn/Z7uc84555xz -fqen+5xzzuf0dJ9zzjnnnHPOOeecc97j6T7nnHPOOecJT/c555zP6ek+55xz -zjnnnHPOOef8uO99/uw555xzzjnnM3q6zznnfE5P9znnnHPOOeecc8455897 -us8555xzznmTp/ucc87n9HSfc84555xzzjnnnHP+vKf7nHPOOeecN3m6zznn -fC1P9znnnHPOOeecc8455+c93eecc84553wET/c555yv5ek+55xzzjnnnHPO -Oef8vKf7nHPOOeecj+DpPuecc/7NfW17Oeecc84555xzzjlfwdN9zjnnnHPO -R/Z0n3POOW/oc84555xzzjnnnHPO319tuzjnnHPOOR/B033OOee8oc8555xz -zjnnnHPO+cqe7nPOOeeccz6jp/ucc855Q59zzjnnnHPOOeec8xU83eecc845 -53wlT/c555zzT57uc84555xzzjnnnHM+k6f7nHPOOeecr+TpPuecc/7J033O -Oeecc84555xzzkf0dJ9zzjnnnHOe73POOeef/Kn3tX0355xzzjnnnHPOOeff -eLrPOeecc845f+/pPuecc37Ez55/623fzTnnnHPOOeecc87H8L3Pnz3nnHPO -Oeec93m6zznnnF/pR8/bvoNzzjnnnHPOOeecj+17n39qF+ecc8455/w5T/c5 -55zzKz3d55xzzjnnnHPOOef8jKf7nHPOOeec8+s83eecc86v9K372vZyzjnn -nHPOOeecc97U55xzzjnnnF/n6T7nnHN+paf7nHPOOeecc84555x/4+k+55xz -zjnn/H5P9znnnPMnPN3nnHPOOeecc84557ypzznnnHPOOb/f033OOef8Cd+6 -r20v55xzzjnnnHPOOZ/D033OOeecc855ztN9zjnnPOlHz9u+g3POOeecc845 -55x3errPOeecc845z3m6zznnnDd6us8555xzzjnnnHPOx/J0n3POOeecc97n -6T7nnHPe6Ok+55xzzjnnnHPOOR/L033OOeecc855n6f7nHPO+Ug+e7/t9+ac -c84555xzzjlv83Sfc84555xzPo6n+5xzzvkM3v6+b73td+Wcc84555xzzjm/ -y9/dl97FOeecc845n8fTfc4553xmf/q5s972+3HOOeecc84555zf7ek+55xz -zjnnfF5P9znnnHN+3flvb/s+zjnnnHPOOeec8zZP9znnnHPOOefzerrPOeec -854+55xzzjnnnHPO+aye7nPOOeecc87X83Sfc8455z19zjnnnHPOOeec81k9 -3eecc84555yv5+k+55xzznv6nHPOOeecc84556N7us8555xzzjnnP57uc845 -53zb033OOeecc84555yP51e99+r3zb6Lc84555xzzn883eecc875tqf7nHPO -Oeecc8457/Hf5y07Ru9wzjnnnHPO+dWe7nPOOed824+et30H55xzzjnnnHPO -r/eWHannOOecc84557zV033OOeecH/d0n3POOeecc845572e2vHt1fI7cc45 -55xzzvldnu5zzjnn/Lin+5xzzjnnnHPOOR/P9z5/9Z6r38c555xzzjnnrZ7u -c8455/x6T/c555xzzjnnnHPO33m6zznnnHPOOedPebrPOeec8+f86ufavo9z -zjnnnHPOOef9nu5zzjnnnHPO+VOe7nPOOec87+k+55xzzjnnnHPO1/F0n3PO -Oeecc86f8nSfc845572e7nPOOeecc84553w+T/c555xzzjnn/ClP9znnnHPe -6+k+55xzzjnnnHPOx/V0n3POOeecc87Tnu5zzjnnfDxP9znnnHPOOeecc97v -6T7nnHPOOeecpz3d55xzzvl4fvVzbd/X5k/3W3ZwzjnnnHPOOR/b033OOeec -c845T3u6zznnnPP5Pd1v83T/Lm/ZwTnnnHPOOef8WU/3Oeecc84557zV033O -Oeecz+/pvu/LessOzjnnnHPOOef3eLrPOeecc845562e7nPOOed8XU/3Z9/b -7i07OOecc84555yf83Sfc84555xzzls93eecc845f3et2l/FW3ZwzjnnnHPO -Of/s7+5L7+Kcc84555zzdk/3Oeecc86/9dk6q3vLDs4555xzzjnn33m6zznn -nHPOOeejebrPOeecc37Wn36OX+MtOzjnnHPOOeecf+fpPuecc84555yP5uk+ -55xzzvldfvac3+stOzjnnHPOOeecd/U555xzzjnnfBZP9znnnHPO7/Kz5/xe -b9nBOeecc84557yrzznnnHPOOeezeLrPOeecc36Xt79vFW/ZwTnnnHPOOef8 -O0/3Oeecc84553wWT/c555xzzu/y1ftPe8sOzjnnnHPOOeffebrPOeecc845 -57N7us8555xzftbT/dG/o+134JxzzjnnnHP+jKf7nHPOOeeccz67p/ucc845 -52c93eecc84555xzzps93eecc84555zzVT3d55xzzjk/6+k+55xzzjnnnHPe -7Ok+55xzzjnnnK/q6T7nnHPO+VlP9znnnHPOOeec8wZP9znnnHPOOeec/+np -Puecc875Wd+6r20v55xzzjnnnHN+h6f7nHPOOeecc87/9HSfc8455/ysp/uc -c84555xzzvkR3/v8U7s455xzzjnnnF/j6T7nnHPO+VlP9znnnHPOOeec8yc9 -3eecc84555xz/p2n+5xzzjnnZz3d55xzzjnnnHPOn/R0n3POOeecc875d57u -c84555yf9aPnbd/BOeecc84555w39TnnnHPOOeecn/N0n3POOef8rKf7nHPO -Oeecc875HZ7uc84555xzzjk/5+k+55xzzvlZT/c555xzzjnnnPM7PN3nnHPO -Oeecc37O033OOeec87Oe7nPOOeecc84552c83eecc84555xzfo+n+5xzzjnn -Zz3d55xzzjnnnHPOz3i6zznnnHPOOef8Hk/3Oeecc87v8nSfc84555xzzjlv -6nPOOeecc845f9bTfc4555zzuzzd55xzzjnnnHPOm/qcc84555xzzp/1dJ9z -zjnn/Gm/+r1t38c555xzzjnnPOvpPuecc84555zzDk/3Oeecc86f9nSfc845 -55xzzvncnu5zzjnnnHPOOe/wdJ9zzjnn/C5P9znnnHPOOeecz+3pPuecc845 -55zzbk/3Oeecc86f9nSfc84555xzzvk+v+q97e/jnHPOOeeccz6Xp/ucc845 -5097us8555xzzjnn/PV5y46955xzzjnnnHPO+StP9znnnHPOn/Z0n3POOeec -c875Pr+7d9d7Oeecc84555yv7ek+55xzznmLb93XtpdzzjnnnHPO+efzu9/P -Oeecc84555x/8nSfc84557zF033OOeecc845552e7nPOOeecc845H9PTfc45 -55zzFk/3Oeecc84555x3errPOeecc84553xMT/c555xzzts93eecc84555xz -nvV0n3POOeecc875mJ7uc84555y3+2idtt+Pc84555xzzkf3dJ9zzjnnnHPO -+Zie7nPOOeecj+pPP/ett/1OnHPOOeeccz66p/ucc84555xzzsf0dJ9zzjnn -fDZP72j7PTjnnHPOOed8dE/3Oeecc84555yP6ek+55xzzvlsnu5zzjnnnHPO -Ob/W033OOeecc84552N6us8555xzPpun+5xzzjnnnHPOj3m6zznnnHPOOed8 -Lk/3Oeecc85n83Sfc84555xzzvkxT/c555xzzjnnnM/l6T7nnHPO+Wy+dV/b -Xs4555xzzjlfxd/dl97FOeecc84553xOT/c555xzzmfzdJ9zzjnnnHPO+TFP -9znnnHPOOeecz+XpPuecc875bJ7uc84555xzzjk/5uk+55xzzjnnnPO5PN3n -nHPOOZ/N033OOeecc84558c83eecc84555xzPpen+5xzzjnnq3i6zznnnHPO -Oee8o88555xzzjnnfA1P9znnnHPOV/Gt+9r2cs4555xzzvmsnu5zzjnnnHPO -OV/D033OOeec81U83eecc84555xz3tHnnHPOOeecc76Gp/ucc84556v72fPf -3vZ9nHPOOeecc57ydJ9zzjnnnHPO+dqe7nPOOeec89d+9Pm27+Ccc84555zz -q/z3+dZ9T+3inHPOOeecc85febrPOeecc85fe7rPOeecc84556N7us8555xz -zjnnfG1P9znnnHPO+WtP9znnnHPOOed8dE/3Oeecc84555yv7ek+55xzzjl/ -7Vv3te3lnHPOOeec8zZP9znnnHPOOeecr+3pPuecc845f+3pPuecc84555yP -7uk+55xzzjnnnPO1Pd3nnHPOOef7/Oh523dwzjnnnHPO+d2e7nPOOeecc845 -X9vTfc4555xzfo2n+5xzzjnnnHPe5uk+55xzzjnnnPO1Pd3nnHPOOefXeLrP -Oeecc84553f5u/vSuzjnnHPOOeec80+e7nPOOeec82s83Z/V0/3f3rKDc845 -55zzJk/3Oeecc84555zzV57uc84555zze33rvra9V393264Wb9nBOeecc875 -FZ7uc84555xzzjnnrzzd55xzzjnn93q67zvG8pYdnHPOOeec7/F0n3POOeec -c845f+XpPuecc845z3i6P9quVbxlB+ecc84555+utl2cc84555xzzvkrT/c5 -55xzznnGV+/zfd6yg3POOeecr+3pPuecc84555xzvsfTfc4555xz3uXt7+Nd -3rKDc84555zf4+/O2/ZwzjnnnHPOOeeNnu5zzjnnnPMx/Ow5n9NbdnDOOeec -82v97t7Zc84555xzzjnnfARP9znnnHPO+RjesoN3+NG/P+ndnHPOOeer++/z -1n3pHZxzzjnnnHPO+RWe7nPOOeec8zH87Dmf01t2cM4555zza/3u3tlzzjnn -nHPOOed8BE/3Oeecc855l7e/j3d5yw7OOeecc36Pvztv28M555xzzjnnnDd6 -us8555xzzjO+ep/v85YdnHPOOed8bU/3Oeecc84555zzPZ7uc84555zzjKf7 -o+1axVt2cM4555xz/ulq28U555xzzjnnnL/ydJ9zzjnnnN/r6b7vGMtbdnDO -Oeecc77H033OOeecc8455/yVp/ucc8455/xe37qvbe/V3922q8VbdnDOOeec -c36Fp/ucc84555xzzvkrT/c555xzzvk1nu7P6un+b2/ZwTnnnHPOeZOn+5xz -zjnnnHPO+StP9znnnHPO+TWe7nPOOeecc875Xf7uvvQuzjnnnHPOOef8k6f7 -nHPOOef8Gk/3Oeecc84557zN033OOeecc84552t7us8555xzzvf50fO27+Cc -c84555zzuz3d55xzzjnnnHO+tqf7nHPOOef8taf7nHPOOeeccz66p/ucc845 -55xzztf2dJ9zzjnnnL/2rfva9nLOOeecc855m6f7nHPOOeecc87X9nSfc845 -55y/9nSfc84555xzzkf3dJ9zzjnnnHPO+dqe7nPOOeec89ee7nPOOeecc875 -6J7uc84555xzzjlf29N9zjnnnHP+2o8+3/YdnHPOOeecc36V/z7fuu+pXZxz -zjnnnHPO+StP9znnnHPOV/ez57+97fs455xzzjnnPOXpPuecc84555zztT3d -55xzzjlfxdN9zjnnnHPOOecdfc4555xzzjnna3i6zznnnHO+im/d17aXc845 -55xzzmf1dJ9zzjnnnHPO+Rqe7nPOOeecr+LpPuecc84555zzjj7nnHPOOeec -8zU83eecc845n83Tfc4555xzzjnnxzzd55xzzjnnnHM+l6f7nHPOOeezebrP -Oeecc8455/yYp/ucc84555xzzufydJ9zzjnnfDZP9znnnHPOOeecH/N0n3PO -Oeecc875XJ7uc84555zP5lv3te3lnHPOOeec81X83X3pXZxzzjnnnHPO5/R0 -n3POOed8Nk/3Oeecc84555wf83Sfc84555xzzvlcnu5zzjnnnM/m6T7nnHPO -Oeec82Oe7nPOOeecc845n8vTfc4555zz2Tzd55xzzjnnnHN+raf7nHPOOeec -c87H9HSfc84553w2T+9o+z0455xzzjnnfHRP9znnnHPOOeecj+npPuecc875 -qP70c9962+/EOeecc84556N7us8555xzzjnnfExP9znnnHPO2320Ttvvxznn -nHPOOeeje7rPOeecc84553xMT/c555xzzts93eecc84555xznvV0n3POOeec -c875mJ7uc84555y3eLrPOeecc84557zT033OOeecc84552N6us8555xz3uLp -Puecc84555zzTk/3Oeecc84555yP6ek+55xzznmLb93XtpdzzjnnnHPO+efz -u9/POeecc84555x/8nSfc8455/xpT/c555xzzjnnnO/zu3t3vZdzzjnnnHPO -+dqe7nPOOeecP+3pPuecc84555zz1+ctO/aec84555xzzjnnrzzd55xzzjl/ -2tN9zjnnnHPOOef7/Kr3tr+Pc84555xzzvlcnu5zzjnnnN/l6T7nnHPOOeec -87k93eecc84555xz3u3pPuecc875057uc84555xzzjmf29N9zjnnnHPOOecd -nu5zzjnnnD/tV7+37fs455xzzjnnnGc93eecc84555xz3uHpPuecc875XZ7u -c84555xzzjnnTX3OOeecc8455896us8555xzfpen+5xzzjnnnHPOeVOfc845 -55xzzvmznu5zzjnnnJ/1dJ9zzjnnnHPOOT/j6T7nnHPOOeec83s83eecc845 -P+vpPuecc84555xzfsbTfc4555xzzjnn93i6zznnnHN+1tN9zjnnnHPOOef8 -Dk/3Oeecc84555yf83Sfc8455/ysp/ucc84555xzzvkdnu5zzjnnnHPOOT/n -6T7nnHPO+Vk/et72HZxzzjnnnHPOeVOfc84555xzzvk5T/c555xzzs96us85 -55xzzjnnnD/p6T7nnHPOOeec8+883eecc845P+vpPuecc84555xz/qSn+5xz -zjnnnHPOv/N0n3POOef8rKf7nHPOOeecc875Ed/7/FO7OOecc84555xf4+k+ -55xzzvlZ37qvbS/nnHPOOeecc36Hp/ucc84555xzzv/0dJ9zzjnn/Kyn+5xz -zjnnnHPOeYOn+5xzzjnnnHPO//R0n3POOef8rKf7nHPOOeecc855s6f7nHPO -Oeecc76qp/ucc84552c93eecc84555xzzps93eecc84555zzVT3d55xzzjk/ -6+n+6N/R9jtwzjnnnHPOOX/G033OOeecc845n93Tfc4555zzu3z1/tPesoNz -zjnnnHPO+Xee7nPOOeecc8757J7uc84555zf5e3vW8VbdnDOOeecc845/87T -fc4555xzzjmfxdN9zjnnnPO7/Ow5v9dbdnDOOeecc8457+pzzjnnnHPO+Sye -7nPOOeec3+Vnz/m93rKDc84555xzznlXn3POOeecc85n8XSfc8455/ysP/0c -v8ZbdnDOOeecc845/87Tfc4555xzzjkfzdN9zjnnnPNvfbbO6t6yg3POOeec -c875d57uc84555xzzvlonu5zzjnnnL+7Vu2v4i07OOecc84555x/9nf3pXdx -zjnnnHPOebun+5xzzjlf19P92fe2e8sOzjnnnHPOOefnPN3nnHPOOeec81ZP -9znnnHM+v6f7vi/rLTs455xzzjnnnN/j6T7nnHPOOeect3q6zznnnPP5Pd1v -83T/Lm/ZwTnnnHPOOef8WU/3Oeecc84557zV033OOeecj+dXP9f2fW3+dL9l -B+ecc84555zzsT3d55xzzjnnnPO0p/ucc845H8/Tfc4555xzzjnnnPd7us85 -55xzzjnnaU/3Oeecc97r6T7nnHPOOeecc87H9XSfc84555xzztOe7nPOOee8 -19N9zjnnnHPOOeecz+fpPuecc84555w/5ek+55xzzvOe7nPOOeecc84553wd -T/c555xzzjnn/ClP9znnnHP+nF/9XNv3cc4555xzzjnnvN/Tfc4555xzzjl/ -ytN9zjnnnF/v6T7nnHPOOeecc875O0/3Oeecc8455/wpT/c555xzftzTfc45 -55xzzjnnnI/ne5+/es/V7+Occ84555zzVk/3Oeecc37c033OOeecc84555z3 -emrHt1fL78Q555xzzjnnd3m6zznnnPNtP3re9h2cc84555xzzjm/3lt2pJ7j -nHPOOeec81ZP9znnnHO+7ek+55xzzjnnnHPOe/z3ecuO0Tucc84555xzfrWn -+5xzzjnf9nSfc84555xzzjnn4/lV7736fbPv4pxzzjnnnPMfT/c555xz3tPn -nHPOOeecc845H93Tfc4555xzzjn/8XSfc8455z19zjnnnHPOOeec81k93eec -c84555yv5+k+55xzznv6nHPOOeecc84557N6us8555xzzjlfz9N9zjnnnF93 -/tvbvo9zzjnnnHPOOee8zdN9zjnnnHPO+bye7nPOOecz+9PPnfW2349zzjnn -nHPOOef8bk/3Oeecc8455/N6us8555zP4O3v+9bbflfOOeecc84555zzu/zd -feldnHPOOeec83k83eecc85H8tn7bb8355xzzjnnnHPOeZun+5xzzjnnnPNx -PN3nnHPOGz3d55xzzjnnnHPOOedjebrPOeecc8457/N0n3POOW/0dJ9zzjnn -nHPOOeecj+XpPuecc84557zP033OOec86UfP276Dc84555xzzjnnnHd6us85 -55xzzjnPebrPOeecP+Fb97Xt5ZxzzjnnnHPOOedzeLrPOeecc845z3m6zznn -nD/h6T7nnHPOOeecc8455019zjnnnHPO+f2e7nPOOedXerrPOeecc84555xz -zvk3nu5zzjnnnHPO7/d0n3POOb/St+5r28s555xzzjnnnHPOeVOfc84555xz -fp2n+5xzzvmVnu5zzjnnnHPOOeecc37G033OOeecc875dZ7uc84551f60fO2 -7+Ccc84555xzzjnnY/ve55/axTnnnHPOOX/O033OOef8iJ89/9bbvptzzjnn -nHPOOeecj+F7nz97zjnnnHPOOe/zdJ9zzjn/5E+9r+27Oeecc84555xzzjn/ -xtN9zjnnnHPO+XtP9znnnPNPnu5zzjnnnHPOOeeccz6ip/ucc84555zzfJ9z -zjn/5Ok+55xzzjnnnHPOOeczebrPOeecc875Sp7uc8455w19zjnnnHPOOeec -c85X8HSfc84555zzlTzd55xzzhv6nHPOOeecc84555yv7Ok+55xzzjnnM3q6 -zznnnDf0Oeecc84555xzzjnn76+2XZxzzjnnnI/g6T7nnHP+zX1teznnnHPO -Oeecc845X8HTfc4555xzzkf2dJ9zzvlanu5zzjnnnHPOOeecc87Pe7rPOeec -c875CJ7uc845X8vTfc4555xzzjnnnHPO+XlP9znnnHPOOR/B033OOedzerrP -Oeecc84555xzzjl/3tN9zjnnnHPOmzzd55xzPqen+5xzzjnnnHPOOeec8+c9 -3eecc84557zJ033OOedzerrPOeecc84555xzzjk/7nufP3vOOeecc875jJ7u -c845n9PTfc4555xzzjnnnHPOeY+n+5xzzjnnnCc83eeccz6np/ucc84555xz -zjnnnPN+T/c555xzzjm/09N9zjnnc3q6zznnnHPOOeecc8457/d0n3POOeec -8zs93eeccz6np/ucc84555xzzjnnnPNxPd3nnHPOOef8Ck/3Oeecz+npPuec -c84555xzzjnnfD5P9znnnHPOOd/j6T7nnPM5feu+tr1Xf/dd33v3+znnnHPO -Oeecc845b/Z0n3POOeec8z2e7nPOOZ/T0/1v/ej+u3ft9ZYdnHPOOeecc845 -55zf6ek+55xzzjnnezzd55xzPqev3m/3lh2cc84555xzzjnnnF/h6T7nnHPO -OeevPN3nnHM+p7e/j+/zlh2cc84555xzzjnnnH+62nZxzjnnnPO1Pd3nnHO+ -lrfs4Nd4yw7OOeecc84555xzzj9dbbs455xzzvkanu5zzjkf259+jnd5yw7O -Oeecc84555xzzj9dbbs455xzzvkanu5zzjkfw7fuO/q+tu/k13jLDs4555xz -zjnnnHO+tqf7nHPOOed8bU/3OeecZ/zoeXoXH8NbdnDOOeecc84555xz/ulq -28U555xzzufydJ9zzvm9nu7Pvpe/9pYdnHPOOeecc84555x/utp2cc4555zz -uTzd55xzfo0fPW/7jqPfx7vd/66cc84555xzzjnnvMnTfc4555xzvoan+5xz -zvd5ut/m6T5/7S07OOecc84555xzzjn/dLXt4pxzzjnnc3m6zznn/LWn+6N4 -us9fe8sOzjnnnHPOOeecc84/XW27OOecc875XJ7uc8756n70vO072jzdX8Vb -dnDOOeecc84555xzvsfTfc4555xzvoan+5xzvoqn+7yjP6q37OCcc84555xz -zjnnY/q787b3cM4555xzfqWn+5xzPptv3de2l3/2dP9pb9nBOeecc84555xz -zsfylh1b3rKDc84555yv4ek+55yP6uk+7/R0/+j/7z+9g3POOeecc84555yP -6S07jvrZc84555xzzvd4us855+2e7vOx3d8rzjnnnHPOOeeccz6y/z5v23f2 -e9rexznnnHPO5/J0n3PO2z3d55xzzjnnnHPOOeec85T/Pm/b9+3u1fqcc845 -57zD033OOW/xs+e/ve37OOecc84555xzzjnn/Nvn2nbf9Z12cc4555zzOz3d -55zzu7z1fW2/E+ecc84555xzzjnnnL87//b+1L5ZPN3nnHPOOef3eLrPOedn -Pd3nnHPOOeecc84555xz/trf3ZfaM5qn+5xzzjnn/Jyn+5xz/q1v3de2l3PO -Oeecc84555xzzvnn87ado3i6zznnnHPOv/N0n3POv/V0n3POOeecc84555xz -zjlv9nSfc84555z/6ek+55y/u/aet30H55xzzjnnnHPOOeecc97g6T7nnHPO -+aqe7nPO1/V0n3POOeecc84555xzzjlf2dN9zjnnnPPZPd3nnM/v6T7nnHPO -Oeecc84555xzzt9fbbs455xzzmfxdJ9zPr9v3de2l3POOeecc84555xzzjlf -2dN9zjnnnPNZPN3nnM/v6T7nnHPOOeecc84555xzzrfvO3vOOeecc87/9HSf -cz6Pb93XtpdzzjnnnHPOOeecc8455+c93eecc845b/V0n3M+j6f7nHPOOeec -c84555xzzjnv8XSfc8455zzt6T7nfB5P9znnnHPOOeecc84555xz3u/pPuec -c875U57uc87n8XSfc84555xzzjnnnHPOOef9nu5zzjnnnD/l6T7nvNeffu6s -t/1+nHPOOeecc84555xzzjn/3tN9zjnnnPOrPd3nnOe9/X1nvWUH55xzzjnn -nHPOOeecc873e7rPOeecc37U033O+fW+dd9T/ZbfpWUH55xzzjnnnHPOOeec -c86v83Sfc84553zL033O+XFP90fZ2/Y7cM4555xzzjnnnHPOOef8vKf7nHPO -Oedbnu5zzrc93R/9+9q+l3POOeecc84555xzzjnn93m6zznnnHP+4+k+57yn -zznnnHPOOeecc84555xzPrqn+5xzzjnnP57uc857+pxzzjnnnHPOOeecc845 -57N6us8555zz9Tzd53xFP3re9h2cc84555xzzjnnnHPOOeejeLrPOeec8/U8 -3ed8Zk/3Oeecc84555xzzjnnnHPOeUefc8455+t5us/5DJ7uc84555xzzjnn -nHPOOeecz+ZXvffsOeecc875UU/3OR/Jj563fQfnnHPOOeecc84555xzznm7 -X/Xep5/jnHPOOf/xdJ/zkTzd55xzzjnnnHPOOeecc845n9XfnW/9+a496Q7n -nHPOx/d0n/ORPN3nnHPOOeecc84555xzzjnnnZ7uc84557zP033OG33rvra9 -nHPOOeecc84555xzzjnnvNPTfc4555znPN3nvNHTfc4555xzzjnnnHPOOeec -cz63p/ucc845v9/Tfc4b/ez5t9723ZxzzjnnnHPOOeecc8455zzr6T7nnHPO -r/N0n/OkP/3cb2/7PTjnnHPOOeecc84555xzznnW033OOeecX+fpPudPeNv7 -/Dubc84555xzzjnnnHPOOeec7/F0n3POOef7Pd3n/EpP9znnnHPOOeecc845 -55xzzjl/0tN9zjnnnL/3dJ/zI57uc84555xzzjnnnHPOOeecc97s6T7nnHPO -833Oj/jWfW17Oeecc84555xzzjnnnHPOOX/S033OOeec5/ucf/J0n3POOeec -c84555xzzjnnnPOZPN3nnHPOV/J0n/NPnu5zzjnnnHPOOeecc84555xzvoKn -+5xzzvmMnu5z/snTfc4555xzzjnnnHPOOeecc85X8HSfc845n9HTfc4b+pxz -zjnnnHPOOeecc84555zz91fbLs4553wET/c5b+hzzjnnnHPOOeecc84555xz -zt9fbbs455zzETzd5/yK89/e9n2cc84555xzzjnnnHPOOeecj+jpPueccz6y -p/t8LX/qfW3fzTnnnHPOOeecc84555xzznnS9z5/9pxzzjnn+T5fy9N9zjnn -nHPOOeecc84555xzzvl9nu5zzjnnTZ7u87U83eecc84555xzzjnnnHPOOeec -P+/pPuecc57wdJ/P6ek+55xzzjnnnHPOOeecc84557zf033OOef8Tk/3+Zye -7nPOOeecc84555xzzjnnnHPO+z3d55xzzu/0dJ/P6ek+55xzzjnnnHPOOeec -c84553xcT/c555zzKzzd53P60efbvoNzzjnnnHPOOeecc84555xz3uPpPuec -c77H030+p6f7nHPOOeecc84555xzzjnnnPP5PN3nnHPO93i6z8f2dJ9zzjnn -nHPOOeecc84555xzztN9zjnn/JWn+3xsT/c555xzzjnnnHPOOeecc8455zzd -55xzzl95us/H9nSfc84555xzzjnnnHPOOeecc87Tfc455/yVp/t8bE/3Oeec -c84555xzzjnnnHPOOefz+7v7zp5zzjnnd3q6z8f2dJ9zzjnnnHPOOeecc845 -55xzzt/51tW2l3PO+Vye7vOxPd3nnHPOOeecc84555xzzjnnnPO9nu5zzjlf -w9N9PrZv3de2l3POOeecc84555xzzjnnnHPO33m6zznnfC5P9/nYnu5zzjnn -nHPOOeecc84555xzzvlVnu5zzjmfy9N9Pran+0/71b/D3bs455xzzjnnnHPO -Oeecc8455997us8553wuT/f52J7uz7633Vt2cM4555xzzjnnnHPOOeecc36n -p/ucc87H9HSfj+1b9/n3D//GW3ZwzjnnnHPOOeecc84555xz/ulq28U557zb -030+tj/9HF/Lt/781A7OOeecc84555xzzjnnnHO+tqf7nHPOx/R0n4/tZ885 -P+ItOzjnnHPOOeecc84555xzzvnanu5zzjnv9nSfd3n7+zj/5C07OOecc845 -55xzzjnnnHPO+Rqe7nPOOe/2dJ9nfLYO55+8ZQfnnHPOOeecc84555xzzjmf -y9N9zjnn3Z7u82s83R9tF1/LW3ZwzjnnnHPOOeecc84555zzuTzd55xz3u3p -Pt/n6b7v4DN5yw7OOeecc84555xzzjnnnHM+l6f7nHPOOzzd56893fd9fAVv -2cE555xzzjnnnHPOOeecc87n8nSfc855h6f7q/jR87bvSP9OnF/pLTs455xz -zjnnnHPOOeecc875XJ7uc8457/B0f1RP92f1dJ+v5S07OOecc84555xzzjnn -nHPO+Vye7nPOOe/wdL/d033e0edruL+XnHPOOeecc84555xzzjnnc/m781SX -c875Wp7ut3u6zzv6fE5v2cE555xzzjnnnHPOOf//9ucgBQAQBALg/3/dCyLI -SMs5Oouscs457+ZV7tj1aM4557yHZ/ff9tN71f7r5tn9/G2vcgfnnHPOOeec -c84555xzznlVn+WruatHc84557/4AEAsnLA= - "], {{0, 0}, {401, 401}}, {0, 1}], Frame -> Automatic, - FrameLabel -> {None, None}, FrameTicks -> {{None, None}, {None, None}}, - GridLinesStyle -> Directive[ - GrayLevel[0.5, 0.4]], - Method -> { - "DefaultBoundaryStyle" -> Automatic, "DefaultPlotStyle" -> Automatic}], - FormBox[ - FormBox[ - TemplateBox[{"\"Divergent\"", - RowBox[{"-", "1.5`"}], "0", "0.75`"}, "SwatchLegend", - DisplayFunction -> (FormBox[ - StyleBox[ - StyleBox[ - PaneBox[ - TagBox[ - GridBox[{{ - TagBox[ - GridBox[{{ - GraphicsBox[{ - Directive[ - EdgeForm[ - Directive[ - Opacity[0.3], - GrayLevel[0]]], - PointSize[0.5], - AbsoluteThickness[1.6], - RGBColor[0., 0., 0.]], - RectangleBox[{0, 0}, {10, 10}, "RoundingRadius" -> 0]}, - AspectRatio -> Full, ImageSize -> {10, 10}, - PlotRangePadding -> None, ImagePadding -> Automatic, - BaselinePosition -> (Scaled[0.1] -> Baseline)], #}, { - GraphicsBox[{ - Directive[ - EdgeForm[ - Directive[ - Opacity[0.3], - GrayLevel[0]]], - PointSize[0.5], - AbsoluteThickness[1.6], - RGBColor[1., 0., 0.]], - RectangleBox[{0, 0}, {10, 10}, "RoundingRadius" -> 0]}, - AspectRatio -> Full, ImageSize -> {10, 10}, - PlotRangePadding -> None, ImagePadding -> Automatic, - BaselinePosition -> (Scaled[0.1] -> Baseline)], #2}, { - GraphicsBox[{ - Directive[ - EdgeForm[ - Directive[ - Opacity[0.3], - GrayLevel[0]]], - PointSize[0.5], - AbsoluteThickness[1.6], - RGBColor[0., 1., 0.]], - RectangleBox[{0, 0}, {10, 10}, "RoundingRadius" -> 0]}, - AspectRatio -> Full, ImageSize -> {10, 10}, - PlotRangePadding -> None, ImagePadding -> Automatic, - BaselinePosition -> (Scaled[0.1] -> Baseline)], #3}, { - GraphicsBox[{ - Directive[ - EdgeForm[ - Directive[ - Opacity[0.3], - GrayLevel[0]]], - PointSize[0.5], - AbsoluteThickness[1.6], - RGBColor[0., 0., 1.]], - RectangleBox[{0, 0}, {10, 10}, "RoundingRadius" -> 0]}, - AspectRatio -> Full, ImageSize -> {10, 10}, - PlotRangePadding -> None, ImagePadding -> Automatic, - BaselinePosition -> (Scaled[0.1] -> Baseline)], #4}}, - GridBoxAlignment -> { - "Columns" -> {Center, Left}, "Rows" -> {{Baseline}}}, - AutoDelete -> False, - GridBoxDividers -> { - "Columns" -> {{False}}, "Rows" -> {{False}}}, - GridBoxItemSize -> {"Columns" -> {{All}}, "Rows" -> {{All}}}, - GridBoxSpacings -> { - "Columns" -> {{0.5}}, "Rows" -> {{0.5}}}], "Grid"]}}, - GridBoxAlignment -> {"Columns" -> {{Left}}, "Rows" -> {{Top}}}, - AutoDelete -> False, - GridBoxItemSize -> { - "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, - GridBoxSpacings -> {"Columns" -> {{1}}, "Rows" -> {{0}}}], - "Grid"], Alignment -> Left, AppearanceElements -> None, - ImageMargins -> {{5, 5}, {5, 5}}, ImageSizeAction -> - "ResizeToFit"], LineIndent -> 0, StripOnInput -> False], { - FontFamily -> "Arial"}, Background -> Automatic, StripOnInput -> - False], TraditionalForm]& ), - InterpretationFunction :> (RowBox[{"SwatchLegend", "[", - RowBox[{ - RowBox[{"{", - RowBox[{ - RowBox[{"Directive", "[", - InterpretationBox[ - ButtonBox[ - TooltipBox[ - GraphicsBox[{{ - GrayLevel[0], - RectangleBox[{0, 0}]}, { - GrayLevel[0], - RectangleBox[{1, -1}]}, { - RGBColor[0., 0., 0.], - RectangleBox[{0, -1}, {2, 1}]}}, AspectRatio -> 1, Frame -> - True, FrameStyle -> RGBColor[0., 0., 0.], FrameTicks -> - None, PlotRangePadding -> None, ImageSize -> - Dynamic[{ - Automatic, 1.35 CurrentValue["FontCapHeight"]/ - AbsoluteCurrentValue[Magnification]}]], - "RGBColor[0., 0., 0.]"], Appearance -> None, - BaseStyle -> {}, BaselinePosition -> Baseline, - DefaultBaseStyle -> {}, ButtonFunction :> - With[{Typeset`box$ = EvaluationBox[]}, - If[ - Not[ - AbsoluteCurrentValue["Deployed"]], - SelectionMove[Typeset`box$, All, Expression]; - FrontEnd`Private`$ColorSelectorInitialAlpha = 1; - FrontEnd`Private`$ColorSelectorInitialColor = - RGBColor[0., 0., 0.]; - FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; - MathLink`CallFrontEnd[ - FrontEnd`AttachCell[Typeset`box$, - FrontEndResource["RGBColorValueSelector"], { - 0, {Left, Bottom}}, {Left, Top}, - "ClosingActions" -> { - "SelectionDeparture", "ParentChanged", - "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> - Automatic, Method -> "Preemptive"], - RGBColor[0., 0., 0.], Editable -> False, Selectable -> - False], "]"}], ",", - RowBox[{"Directive", "[", - InterpretationBox[ - ButtonBox[ - TooltipBox[ - GraphicsBox[{{ - GrayLevel[0], - RectangleBox[{0, 0}]}, { - GrayLevel[0], - RectangleBox[{1, -1}]}, { - RGBColor[1., 0., 0.], - RectangleBox[{0, -1}, {2, 1}]}}, AspectRatio -> 1, Frame -> - True, FrameStyle -> RGBColor[0.6666666666666667, 0., 0.], - FrameTicks -> None, PlotRangePadding -> None, ImageSize -> - Dynamic[{ - Automatic, 1.35 CurrentValue["FontCapHeight"]/ - AbsoluteCurrentValue[Magnification]}]], - "RGBColor[1., 0., 0.]"], Appearance -> None, - BaseStyle -> {}, BaselinePosition -> Baseline, - DefaultBaseStyle -> {}, ButtonFunction :> - With[{Typeset`box$ = EvaluationBox[]}, - If[ - Not[ - AbsoluteCurrentValue["Deployed"]], - SelectionMove[Typeset`box$, All, Expression]; - FrontEnd`Private`$ColorSelectorInitialAlpha = 1; - FrontEnd`Private`$ColorSelectorInitialColor = - RGBColor[1., 0., 0.]; - FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; - MathLink`CallFrontEnd[ - FrontEnd`AttachCell[Typeset`box$, - FrontEndResource["RGBColorValueSelector"], { - 0, {Left, Bottom}}, {Left, Top}, - "ClosingActions" -> { - "SelectionDeparture", "ParentChanged", - "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> - Automatic, Method -> "Preemptive"], - RGBColor[1., 0., 0.], Editable -> False, Selectable -> - False], "]"}], ",", - RowBox[{"Directive", "[", - InterpretationBox[ - ButtonBox[ - TooltipBox[ - GraphicsBox[{{ - GrayLevel[0], - RectangleBox[{0, 0}]}, { - GrayLevel[0], - RectangleBox[{1, -1}]}, { - RGBColor[0., 1., 0.], - RectangleBox[{0, -1}, {2, 1}]}}, AspectRatio -> 1, Frame -> - True, FrameStyle -> RGBColor[0., 0.6666666666666667, 0.], - FrameTicks -> None, PlotRangePadding -> None, ImageSize -> - Dynamic[{ - Automatic, 1.35 CurrentValue["FontCapHeight"]/ - AbsoluteCurrentValue[Magnification]}]], - "RGBColor[0., 1., 0.]"], Appearance -> None, - BaseStyle -> {}, BaselinePosition -> Baseline, - DefaultBaseStyle -> {}, ButtonFunction :> - With[{Typeset`box$ = EvaluationBox[]}, - If[ - Not[ - AbsoluteCurrentValue["Deployed"]], - SelectionMove[Typeset`box$, All, Expression]; - FrontEnd`Private`$ColorSelectorInitialAlpha = 1; - FrontEnd`Private`$ColorSelectorInitialColor = - RGBColor[0., 1., 0.]; - FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; - MathLink`CallFrontEnd[ - FrontEnd`AttachCell[Typeset`box$, - FrontEndResource["RGBColorValueSelector"], { - 0, {Left, Bottom}}, {Left, Top}, - "ClosingActions" -> { - "SelectionDeparture", "ParentChanged", - "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> - Automatic, Method -> "Preemptive"], - RGBColor[0., 1., 0.], Editable -> False, Selectable -> - False], "]"}], ",", - RowBox[{"Directive", "[", - InterpretationBox[ - ButtonBox[ - TooltipBox[ - GraphicsBox[{{ - GrayLevel[0], - RectangleBox[{0, 0}]}, { - GrayLevel[0], - RectangleBox[{1, -1}]}, { - RGBColor[0., 0., 1.], - RectangleBox[{0, -1}, {2, 1}]}}, AspectRatio -> 1, Frame -> - True, FrameStyle -> RGBColor[0., 0., 0.6666666666666667], - FrameTicks -> None, PlotRangePadding -> None, ImageSize -> - Dynamic[{ - Automatic, 1.35 CurrentValue["FontCapHeight"]/ - AbsoluteCurrentValue[Magnification]}]], - "RGBColor[0., 0., 1.]"], Appearance -> None, - BaseStyle -> {}, BaselinePosition -> Baseline, - DefaultBaseStyle -> {}, ButtonFunction :> - With[{Typeset`box$ = EvaluationBox[]}, - If[ - Not[ - AbsoluteCurrentValue["Deployed"]], - SelectionMove[Typeset`box$, All, Expression]; - FrontEnd`Private`$ColorSelectorInitialAlpha = 1; - FrontEnd`Private`$ColorSelectorInitialColor = - RGBColor[0., 0., 1.]; - FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; - MathLink`CallFrontEnd[ - FrontEnd`AttachCell[Typeset`box$, - FrontEndResource["RGBColorValueSelector"], { - 0, {Left, Bottom}}, {Left, Top}, - "ClosingActions" -> { - "SelectionDeparture", "ParentChanged", - "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> - Automatic, Method -> "Preemptive"], - RGBColor[0., 0., 1.], Editable -> False, Selectable -> - False], "]"}]}], "}"}], ",", - RowBox[{"{", - RowBox[{#, ",", #2, ",", #3, ",", #4}], "}"}], ",", - RowBox[{"LegendMarkers", "\[Rule]", "Automatic"}], ",", - RowBox[{"LabelStyle", "\[Rule]", - RowBox[{"{", "}"}]}], ",", - RowBox[{"LegendLayout", "\[Rule]", "\"Column\""}]}], "]"}]& ), - Editable -> True], TraditionalForm], TraditionalForm]}, - "Legended", - DisplayFunction->(GridBox[{{ - TagBox[ - ItemBox[ - PaneBox[ - TagBox[#, "SkipImageSizeLevel"], Alignment -> {Center, Baseline}, - BaselinePosition -> Baseline], DefaultBaseStyle -> "Labeled"], - "SkipImageSizeLevel"], - ItemBox[#2, DefaultBaseStyle -> "LabeledLabel"]}}, - GridBoxAlignment -> {"Columns" -> {{Center}}, "Rows" -> {{Center}}}, - AutoDelete -> False, GridBoxItemSize -> Automatic, - BaselinePosition -> {1, 1}]& ), - Editable->True, - InterpretationFunction->(RowBox[{"Legended", "[", - RowBox[{#, ",", - RowBox[{"Placed", "[", - RowBox[{#2, ",", "After"}], "]"}]}], "]"}]& )]], "Output", - CellChangeTimes->{3.6631017417896557`*^9, 3.6641618531627593`*^9}] -}, Open ]] -}, Open ]] -}, Open ]] -}, Open ]] -}, -WindowSize->{759, 833}, -WindowMargins->{{553, Automatic}, {Automatic, 52}}, -FrontEndVersion->"10.4 for Microsoft Windows (64-bit) (April 11, 2016)", -StyleDefinitions->"Default.nb" -] -(* End of Notebook Content *) - -(* Internal cache information *) -(*CellTagsOutline -CellTagsIndex->{} -*) -(*CellTagsIndex -CellTagsIndex->{} -*) -(*NotebookFileOutline -Notebook[{ -Cell[CellGroupData[{ -Cell[580, 22, 125, 1, 90, "Title"], -Cell[708, 25, 107, 1, 30, "Text"], -Cell[CellGroupData[{ -Cell[840, 30, 99, 1, 63, "Section"], -Cell[942, 33, 473, 13, 49, "Text"], -Cell[1418, 48, 515, 17, 45, "DisplayFormula"], -Cell[1936, 67, 391, 7, 68, "Text"], -Cell[2330, 76, 427, 7, 87, "Text"], -Cell[2760, 85, 1405, 36, 144, "Text"], -Cell[4168, 123, 371, 8, 49, "Text"] -}, Open ]], -Cell[CellGroupData[{ -Cell[4576, 136, 91, 1, 63, "Section"], -Cell[CellGroupData[{ -Cell[4692, 141, 104, 1, 43, "Subsection"], -Cell[4799, 144, 1473, 39, 112, "Input"], -Cell[CellGroupData[{ -Cell[6297, 187, 287, 7, 34, "Input"], -Cell[6587, 196, 493, 16, 61, "Output"] -}, Open ]], -Cell[7095, 215, 11016, 259, 1146, "Input"] -}, Closed]], -Cell[CellGroupData[{ -Cell[18148, 479, 101, 1, 35, "Subsection"], -Cell[CellGroupData[{ -Cell[18274, 484, 383, 9, 34, "Input"], -Cell[18660, 495, 16926, 334, 376, "Output"] -}, Open ]], -Cell[CellGroupData[{ -Cell[35623, 834, 485, 11, 34, "Input"], -Cell[36111, 847, 52522, 918, 376, "Output"] -}, Open ]], -Cell[CellGroupData[{ -Cell[88670, 1770, 337, 9, 34, "Input"], -Cell[89010, 1781, 66648, 1151, 376, "Output"] -}, Open ]], -Cell[CellGroupData[{ -Cell[155695, 2937, 608, 12, 34, "Input"], -Cell[156306, 2951, 60137, 990, 374, "Output"] -}, Open ]], -Cell[CellGroupData[{ -Cell[216480, 3946, 281, 8, 34, "Input"], -Cell[216764, 3956, 58447, 963, 374, "Output"] -}, Open ]], -Cell[CellGroupData[{ -Cell[275248, 4924, 583, 12, 34, "Input"], -Cell[275834, 4938, 14251, 277, 376, "Output"] -}, Open ]], -Cell[CellGroupData[{ -Cell[290122, 5220, 580, 12, 34, "Input"], -Cell[290705, 5234, 16523, 313, 376, "Output"] -}, Open ]], -Cell[CellGroupData[{ -Cell[307265, 5552, 1030, 26, 52, "Input"], -Cell[308298, 5580, 33995, 611, 376, "Output"] -}, Open ]], -Cell[CellGroupData[{ -Cell[342330, 6196, 623, 15, 31, "Input"], -Cell[342956, 6213, 32351, 580, 376, "Output"] -}, Open ]] -}, Open ]] -}, Open ]] -}, Open ]] -} -] -*) - +(* Content-type: application/vnd.wolfram.mathematica *) + +(*** Wolfram Notebook File ***) +(* http://www.wolfram.com/nb *) + +(* CreatedBy='Mathematica 10.2' *) + +(*CacheID: 234*) +(* Internal cache information: +NotebookFileLineBreakTest +NotebookFileLineBreakTest +NotebookDataPosition[ 158, 7] +NotebookDataLength[ 377475, 6875] +NotebookOptionsPosition[ 375359, 6799] +NotebookOutlinePosition[ 375703, 6814] +CellTagsIndexPosition[ 375660, 6811] +WindowFrame->Normal*) + +(* Beginning of Notebook Content *) +Notebook[{ + +Cell[CellGroupData[{ +Cell["Complex Newton\[CloseCurlyQuote]s Method", "Title", + CellChangeTimes->{{3.776587885602626*^9, 3.7765878892047005`*^9}}], + +Cell["Adam Rumpf, 2/23/2016", "Text", + CellChangeTimes->{{3.7765879645996017`*^9, 3.7765879864409084`*^9}}], + +Cell[CellGroupData[{ + +Cell["Introduction", "Section", + CellChangeTimes->{{3.7765879027790375`*^9, 3.776587905025833*^9}}], + +Cell[TextData[{ + "Newton\[CloseCurlyQuote]s method (a.k.a. the Newton-Raphson method) is an \ +iterative root finding process. Given a function ", + Cell[BoxData[ + FormBox["f", TraditionalForm]], + FormatType->"TraditionalForm"], + " and an initial guess ", + Cell[BoxData[ + FormBox[ + SubscriptBox["x", "0"], TraditionalForm]], + FormatType->"TraditionalForm"], + ", the process is defined by:" +}], "Text", + CellChangeTimes->{{3.7765873898669224`*^9, 3.776587628077781*^9}}], + +Cell[BoxData[ + RowBox[{"\t", + FormBox[ + RowBox[{ + SubscriptBox["x", + RowBox[{"n", "+", "1"}]], "=", + RowBox[{ + SubscriptBox["x", "n"], "-", + FractionBox[ + RowBox[{"f", "(", + SubscriptBox["x", "n"], ")"}], + RowBox[{ + RowBox[{"f", "'"}], + RowBox[{"(", + SubscriptBox["x", "n"], ")"}]}]]}]}], + TraditionalForm]}]], "DisplayFormula", + CellChangeTimes->{{3.7765873898669224`*^9, 3.7765876343990145`*^9}, { + 3.7765880045342627`*^9, 3.776588004542261*^9}}], + +Cell["\<\ +This method is taught in basic Calculus, and it is mostly of interest because \ +it is (a) simple to define and understand, (b) easy to visualize, and (c) \ +good enough to still be used for scientific computing, despite being over 300 \ +years old.\ +\>", "Text", + CellChangeTimes->{{3.7765873898669224`*^9, 3.7765876554799743`*^9}, { + 3.7765880294968214`*^9, 3.776588034544223*^9}}], + +Cell["\<\ +Many students will be surprised to know that this method does not just work \ +for real-valued functions: it works for complex-valued functions, as well. \ +Its behavior in the complex plane can be a bit more complicated to describe, \ +and depending on the initial guess, the method may not necessarily converget \ +to the nearest root.\ +\>", "Text", + CellChangeTimes->{{3.7765876439551272`*^9, 3.7765877526697845`*^9}}], + +Cell[TextData[{ + "This Notebook defines a function called ", + StyleBox["newtonplot[]", "Code"], + ", which accepts (in order) a pure function, a bound ", + Cell[BoxData[ + FormBox["b", TraditionalForm]], + FormatType->"TraditionalForm"], + " for the complex domain ", + Cell[BoxData[ + FormBox[ + RowBox[{ + RowBox[{"[", + RowBox[{ + RowBox[{"-", "b"}], ",", "b"}], "]"}], "\[Times]", + RowBox[{"[", + RowBox[{ + RowBox[{"-", "b"}], ",", "b"}], "]"}]}], TraditionalForm]], + FormatType->"TraditionalForm"], + ", the number of nodes ", + Cell[BoxData[ + FormBox["n", TraditionalForm]], + FormatType->"TraditionalForm"], + " into which each axis will be divided, an iteration cutoff, and an error \ +tolerance. The function will divide the square domain into an ", + Cell[BoxData[ + FormBox[ + RowBox[{"n", "\[Times]", "n"}], TraditionalForm]], + FormatType->"TraditionalForm"], + " grid and conduct Newton\[CloseCurlyQuote]s method using every grid node as \ +an initial guess. If the method comes within the error tolerance of one of \ +the true roots, then the method terminates and we record which root was \ +reached. If no root is reached within the iteration cutoff, then the process \ +is deemed to have diverged." +}], "Text", + CellChangeTimes->{{3.7765877574128275`*^9, 3.77658778055941*^9}, { + 3.776587824735916*^9, 3.776587850473181*^9}, {3.77658806101051*^9, + 3.776588456805036*^9}}], + +Cell[TextData[{ + "The output is a coloring of the complex domain showing which initial \ +guesses converge to which roots. A larger value of ", + Cell[BoxData[ + FormBox["n", TraditionalForm]], + FormatType->"TraditionalForm"], + " will lead to a sharper picture but a longer computation time." +}], "Text", + CellChangeTimes->{{3.776588459669097*^9, 3.7765885063788424`*^9}}] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Code", "Section", + CellChangeTimes->{{3.7765879208719325`*^9, 3.776587921823886*^9}}], + +Cell[CellGroupData[{ + +Cell["Initialization", "Subsection", + CellChangeTimes->{{3.776588544504778*^9, 3.7765885464741445`*^9}}], + +Cell[BoxData[ + RowBox[{ + RowBox[{"(*", " ", + RowBox[{ + RowBox[{"roots", "[", "f", "]"}], " ", "returns", " ", "a", " ", "list", + " ", "of", " ", "the", " ", "unique", " ", "roots", " ", "of", " ", + "function", " ", + RowBox[{"f", "."}]}], " ", "*)"}], "\[IndentingNewLine]", + RowBox[{ + RowBox[{ + RowBox[{"roots", "[", "f_", "]"}], ":=", + RowBox[{"Module", "[", + RowBox[{ + RowBox[{"{", "r", "}"}], ",", "\[IndentingNewLine]", + RowBox[{ + RowBox[{"r", "=", + RowBox[{"DeleteDuplicates", "[", + RowBox[{"x", "/.", + RowBox[{"Solve", "[", + RowBox[{ + RowBox[{ + RowBox[{"f", "[", "x", "]"}], "\[Equal]", "0"}], ",", "x"}], + "]"}]}], "]"}]}], ";", "\[IndentingNewLine]", + RowBox[{"Table", "[", + RowBox[{ + RowBox[{ + RowBox[{"Re", "[", + RowBox[{"r", "[", + RowBox[{"[", "i", "]"}], "]"}], "]"}], "+", + RowBox[{"I", " ", + RowBox[{"Im", "[", + RowBox[{"r", "[", + RowBox[{"[", "i", "]"}], "]"}], "]"}]}]}], ",", + RowBox[{"{", + RowBox[{"i", ",", "1", ",", + RowBox[{"Length", "[", "r", "]"}]}], "}"}]}], "]"}]}]}], + "\[IndentingNewLine]", "]"}]}], ";"}]}]], "Input", + CellChangeTimes->{{3.65954843910914*^9, 3.65954848479572*^9}, { + 3.6595485169148393`*^9, 3.6595485598267083`*^9}, {3.659555212555744*^9, + 3.6595552904228373`*^9}}], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"roots", "[", + RowBox[{"Function", "[", + RowBox[{"x", ",", + RowBox[{ + SuperscriptBox["x", "3"], "-", "1"}]}], "]"}], "]"}]], "Input", + CellChangeTimes->{{3.6595485653603544`*^9, 3.65954859823431*^9}, { + 3.6595552298253365`*^9, 3.659555232700883*^9}}], + +Cell[BoxData[ + RowBox[{"{", + RowBox[{"1", ",", + RowBox[{ + RowBox[{"-", + FractionBox["1", "2"]}], "-", + FractionBox[ + RowBox[{"\[ImaginaryI]", " ", + SqrtBox["3"]}], "2"]}], ",", + RowBox[{ + RowBox[{"-", + FractionBox["1", "2"]}], "+", + FractionBox[ + RowBox[{"\[ImaginaryI]", " ", + SqrtBox["3"]}], "2"]}]}], "}"}]], "Output", + CellChangeTimes->{{3.6595485756723404`*^9, 3.659548598922804*^9}, + 3.6595552340602794`*^9, 3.6595552931736403`*^9}] +}, Open ]], + +Cell[BoxData[ + RowBox[{ + RowBox[{"(*", " ", + RowBox[{ + RowBox[{ + RowBox[{"newtonplot", "[", + RowBox[{"f", ",", "lim", ",", "n", ",", "cut", ",", "eps"}], "]"}], " ", + "creates", " ", "a", " ", "plot", " ", "of", " ", "the", " ", + RowBox[{"region", " ", "[", + RowBox[{ + RowBox[{"-", "lim"}], ",", "lim"}], "]"}], + RowBox[{"x", "[", + RowBox[{ + RowBox[{"-", "lim"}], ",", "lim"}], "]"}], " ", "of", " ", "the", " ", + "complex", " ", "plane"}], ",", " ", + RowBox[{"divided", " ", "into", " ", "an", " ", "nxn", " ", + RowBox[{"grid", ".", " ", "Each"}], " ", "grid", " ", "point", " ", + "is", " ", "used", " ", "as", " ", "the", " ", "initial", " ", "guess", + " ", "for", " ", "complex", " ", + RowBox[{"Newton", "'"}], "s", " ", "method", " ", "on", " ", "function", + " ", + RowBox[{"f", ".", " ", "Each"}], " ", "root", " ", "is", " ", + "assigned", " ", "a", " ", "color"}], ",", " ", + RowBox[{"and", " ", "after", " ", "cut", " ", "iterations"}], ",", " ", + RowBox[{ + "if", " ", "we", " ", "are", " ", "within", " ", "distance", " ", "eps", + " ", "of", " ", "a", " ", "root"}], ",", " ", + RowBox[{"we", " ", "assign", " ", "that", " ", "point", " ", "that", " ", + RowBox[{"root", "'"}], "s", " ", + RowBox[{"color", ".", " ", "If"}], " ", "if", " ", "is", " ", "not", + " ", "that", " ", "close", " ", "to", " ", "any", " ", "root"}], ",", + " ", + RowBox[{"we", " ", "color", " ", "it", " ", + RowBox[{"black", "."}]}]}], " ", "*)"}], "\[IndentingNewLine]", + RowBox[{ + RowBox[{ + RowBox[{"newtonplot", "[", + RowBox[{"f_", ",", "lim_", ",", "n_", ",", "cut_", ",", "eps_"}], "]"}], + ":=", + RowBox[{"Module", "[", + RowBox[{ + RowBox[{"{", + RowBox[{ + "fp", ",", "newton", ",", "rootlist", ",", "array", ",", "grid", ",", + "dx", ",", "i", ",", "j", ",", "iter", ",", "x", ",", "numroots", ",", + "rootnum"}], "}"}], ",", "\[IndentingNewLine]", + RowBox[{"(*", " ", + RowBox[{ + RowBox[{"fp", " ", "=", " ", + RowBox[{ + RowBox[{ + "derivative", " ", "of", " ", "f", "\[IndentingNewLine]", + "newton"}], " ", "=", " ", + RowBox[{ + RowBox[{ + RowBox[{"Newton", "'"}], "s", " ", "method", " ", "iteration", + " ", "function", "\[IndentingNewLine]", "rootlist"}], " ", "=", + " ", + RowBox[{ + RowBox[{ + "list", " ", "of", " ", "all", " ", "unique", " ", "roots", " ", + "of", " ", "f", "\[IndentingNewLine]", "array"}], " ", "=", " ", + RowBox[{ + RowBox[{ + "array", " ", "of", " ", "values", " ", "corresponding", " ", + "to", " ", "each", " ", "grid", " ", "point", " ", + RowBox[{"(", + RowBox[{ + RowBox[{ + RowBox[{"-", "1"}], " ", "means", " ", "no", " ", "root"}], + ",", " ", + RowBox[{ + "positive", " ", "integer", " ", "corresponds", " ", "to", + " ", "one", " ", "of", " ", "the", " ", "roots", " ", "in", + " ", "the", " ", "list"}]}], ")"}], "\[IndentingNewLine]", + "grid"}], " ", "=", " ", + RowBox[{ + RowBox[{ + "array", " ", "of", " ", "actual", " ", "coordinates", " ", + "of", " ", "grid", " ", "points", "\[IndentingNewLine]", + "dx"}], " ", "=", " ", + RowBox[{ + "space", " ", "between", " ", "grid", " ", "points", + "\[IndentingNewLine]", "i"}]}]}]}]}]}]}], ",", + RowBox[{"j", " ", "=", " ", + RowBox[{ + RowBox[{ + "coordinates", " ", "of", " ", "point", " ", "currently", " ", + "being", " ", "examined", "\[IndentingNewLine]", "iter"}], " ", + "=", " ", + RowBox[{ + RowBox[{"current", " ", "iteration", " ", "of", " ", + RowBox[{"Newton", "'"}], "s", " ", "Method", + "\[IndentingNewLine]", "x"}], " ", "=", " ", + RowBox[{ + RowBox[{"current", " ", "guess", " ", "in", " ", + RowBox[{"Newton", "'"}], "s", " ", "Method", + "\[IndentingNewLine]", "numroots"}], " ", "=", " ", + RowBox[{ + RowBox[{ + "number", " ", "of", " ", "roots", "\[IndentingNewLine]", + "rootnum"}], " ", "=", " ", + RowBox[{ + "index", " ", "of", " ", "root", " ", "under", " ", + "evaluation"}]}]}]}]}]}]}], " ", "*)"}], "\[IndentingNewLine]", + RowBox[{ + RowBox[{"fp", "=", + RowBox[{"Function", "[", + RowBox[{"x", ",", + RowBox[{ + RowBox[{"f", "'"}], "[", "x", "]"}]}], "]"}]}], ";", + "\[IndentingNewLine]", + RowBox[{"newton", "=", + RowBox[{"Function", "[", + RowBox[{"x", ",", + RowBox[{"N", "[", + RowBox[{"x", "-", + FractionBox[ + RowBox[{"f", "[", "x", "]"}], + RowBox[{"fp", "[", "x", "]"}]]}], "]"}]}], "]"}]}], ";", + "\[IndentingNewLine]", + RowBox[{"rootlist", "=", + RowBox[{"roots", "[", "f", "]"}]}], ";", "\[IndentingNewLine]", + RowBox[{"numroots", "=", + RowBox[{"Length", "[", "rootlist", "]"}]}], ";", + "\[IndentingNewLine]", + RowBox[{"dx", "=", + FractionBox[ + RowBox[{"2", "lim"}], + RowBox[{"n", "-", "1"}]]}], ";", "\[IndentingNewLine]", + RowBox[{"array", "=", + RowBox[{"ConstantArray", "[", + RowBox[{ + RowBox[{"-", "1"}], ",", + RowBox[{"{", + RowBox[{"n", ",", "n"}], "}"}]}], "]"}]}], ";", + "\[IndentingNewLine]", + RowBox[{"grid", "=", + RowBox[{"Table", "[", + RowBox[{ + RowBox[{"N", "[", + RowBox[{ + RowBox[{"(", + RowBox[{ + RowBox[{"-", "lim"}], "+", + RowBox[{"l", " ", "dx"}]}], ")"}], "+", + RowBox[{"I", + RowBox[{"(", + RowBox[{ + RowBox[{"-", "lim"}], "+", + RowBox[{"k", " ", "dx"}]}], ")"}]}]}], "]"}], ",", + RowBox[{"{", + RowBox[{"k", ",", + RowBox[{"n", "-", "1"}], ",", "0", ",", + RowBox[{"-", "1"}]}], "}"}], ",", + RowBox[{"{", + RowBox[{"l", ",", "0", ",", + RowBox[{"n", "-", "1"}]}], "}"}]}], "]"}]}], ";", + "\[IndentingNewLine]", + RowBox[{"For", "[", + RowBox[{ + RowBox[{"i", "=", "1"}], ",", + RowBox[{"i", "\[LessEqual]", "n"}], ",", + RowBox[{"i", "++"}], ",", "\[IndentingNewLine]", + RowBox[{ + RowBox[{"For", "[", + RowBox[{ + RowBox[{"j", "=", "1"}], ",", + RowBox[{"j", "\[LessEqual]", "n"}], ",", + RowBox[{"j", "++"}], ",", "\[IndentingNewLine]", + RowBox[{ + RowBox[{"x", "=", + RowBox[{"grid", "[", + RowBox[{"[", + RowBox[{"i", ",", "j"}], "]"}], "]"}]}], ";", + "\[IndentingNewLine]", + RowBox[{"For", "[", + RowBox[{ + RowBox[{"iter", "=", "1"}], ",", + RowBox[{"iter", "\[LessEqual]", "cut"}], ",", + RowBox[{"iter", "++"}], ",", "\[IndentingNewLine]", + RowBox[{ + RowBox[{"If", "[", + RowBox[{ + RowBox[{ + RowBox[{ + RowBox[{"fp", "[", "x", "]"}], "\[NotEqual]", "0"}], "&&", + RowBox[{ + RowBox[{"Abs", "[", "x", "]"}], "\[NotEqual]", + "Infinity"}]}], ",", "\[IndentingNewLine]", + RowBox[{"x", "=", + RowBox[{"newton", "[", "x", "]"}]}], ",", + "\[IndentingNewLine]", + RowBox[{ + RowBox[{"x", "=", "ComplexInfinity"}], ";"}]}], + "\[IndentingNewLine]", "]"}], ";"}]}], "\[IndentingNewLine]", + "]"}], ";", "\[IndentingNewLine]", + RowBox[{"For", "[", + RowBox[{ + RowBox[{"rootnum", "=", "1"}], ",", + RowBox[{"rootnum", "\[LessEqual]", "numroots"}], ",", + RowBox[{"rootnum", "++"}], ",", "\[IndentingNewLine]", + RowBox[{ + RowBox[{"If", "[", + RowBox[{ + RowBox[{ + RowBox[{"Abs", "[", + RowBox[{"x", "-", + RowBox[{"rootlist", "[", + RowBox[{"[", "rootnum", "]"}], "]"}]}], "]"}], "<", + "eps"}], ",", "\[IndentingNewLine]", + RowBox[{ + RowBox[{ + RowBox[{"array", "[", + RowBox[{"[", + RowBox[{"i", ",", "j"}], "]"}], "]"}], "=", "rootnum"}], + ";"}]}], "\[IndentingNewLine]", "]"}], ";"}]}], + "\[IndentingNewLine]", "]"}], ";"}]}], "\[IndentingNewLine]", + "]"}], ";"}]}], "\[IndentingNewLine]", "]"}], ";", + "\[IndentingNewLine]", + RowBox[{"ArrayPlot", "[", + RowBox[{"array", ",", + RowBox[{"ColorRules", "\[Rule]", + RowBox[{"Join", "[", + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{"-", "1"}], "\[Rule]", "Black"}], "}"}], ",", + RowBox[{"Table", "[", + RowBox[{ + RowBox[{"k", "\[Rule]", + RowBox[{"Hue", "[", + FractionBox[ + RowBox[{"k", "-", "1"}], "numroots"], "]"}]}], ",", + RowBox[{"{", + RowBox[{"k", ",", "1", ",", "numroots"}], "}"}]}], "]"}]}], + "]"}]}], ",", + RowBox[{"PlotLegends", "\[Rule]", + RowBox[{"Join", "[", + RowBox[{ + RowBox[{"{", "\"\\"", "}"}], ",", + RowBox[{"Table", "[", + RowBox[{ + RowBox[{"rootlist", "[", + RowBox[{"[", "k", "]"}], "]"}], ",", + RowBox[{"{", + RowBox[{"k", ",", "1", ",", "numroots"}], "}"}]}], "]"}]}], + "]"}]}]}], "]"}]}]}], "\[IndentingNewLine]", "]"}]}], + ";"}]}]], "Input", + CellChangeTimes->CompressedData[" +1:eJwdy1soQwEAh/E1ymWLPKFGKCWXRwvNtOzFRtgoZGK1J2luSZaatszDUHNt +bVkSm2ZIok0bmqUkS2uF5HYyucxtxchy/ufh6/f0ZUrlIhmdRqNlkkF1vnk5 +lv/Eiw0vrsOi/rATVmqm/PDWMXwFudmqa3jCl4bhQMVEUhxp71pqCnR7Fbkw +wShlw4+ekmK4c+7gQnvQJICjx9diyGQPNUHv07QMCoOSdhh95uqC96xDBSSI +DCVcavzTwN8Wtw52Whx6+Py1+RpPak2MhGBhY1UpgzSwusWDVkZqDcyx+EQw +8ZLeADnPb5Q2TXMbZBpj2iGXJuyHvoUsJfQY5tRwOyo0BmuJoymo4mgN1P+j +NcH32W4LHHlxrUBnh5uyYJizAc2D9j047x7zwVLb2wWc1OfdwLqrwB3cnSEe +oMC6GYT+DPYnZCRNhmB9YP8bJpzKY5ikunF1GhQ9/lB6B8xlkFA4KFvTD8ph +xBbhw0pvigCyJHeUyfF91ZDu8YjhP6o68js= + "]] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Demonstration", "Subsection", + CellChangeTimes->{{3.776588557645573*^9, 3.776588560857557*^9}}], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"newtonplot", "[", + RowBox[{ + RowBox[{"Function", "[", + RowBox[{"x", ",", + RowBox[{ + SuperscriptBox["x", "3"], "-", "1"}]}], "]"}], ",", "2", ",", "101", + ",", "20", ",", "0.05"}], "]"}]], "Input", + CellChangeTimes->{{3.6595549152958674`*^9, 3.659554978383319*^9}, + 3.659555332709116*^9, {3.659555509656427*^9, 3.6595555100001802`*^9}}], + +Cell[BoxData[ + TemplateBox[{GraphicsBox[ + RasterBox[CompressedData[" +1:eJzt1tGN5DYWBdABNhJH4hw2BAP+duoOwVhg+6PLrSIpkXqXqiNggOlDie+S +VSW+3/74679//ufXr19//v/f//7//fr7938R55xzHuOt62ydVr3qnGef45le +XZ9zzvln+Wi/kpK75UdXWk5e69X1Oeecf6a/jqflG+2vWs/39p/82V5dn3PO ++TM9JcdZP/v8p+8bf+/V9TnnnD/bj8bv7jdWzfvlq8/ZtM+Vn/Pq+pxzzp/t +r+PV59rsenf3ea/jaZ83f+/V9TnnnPMrXl3/1Xebl9/r1fU555w/01vnTlWu +1S4Hf+fV9TnnnO/tZ8+d1bmq/On1+DWvrs855/wZ/jqu71rjvXVT9oNn1eec +c/5sr65/l89e/9W6PNOr63POOd/bz54vq3Pd7XftQ+/+80yvrs855/zZXl2/ +2lv70ns/f4ZX1+ecc763j/YVT/HZ9/HP8Or6nHPOn+3V9c/6rPVUr4NneXV9 +zjnnz/bq+qv6o9fxlHXwbK+uzznn/Nl+d/2zOXrn4fyKV9fnnHP+bF9dp/U3 +50leXZ9zzvk9fnW+s/Ouqsv5jl5dn3PO+Tl/HU/Nl5KH8wSvrs855/xnH31v +V58jV3Ol7DvnK726Puec8/feur6eu6ve6Lyr+k/Od/Tq+pxzzs/50dXbt1yt +X903pX0enPd4dX3OOec/e3W/NMt3m5fzlV5dn3PO+c+u76qZl/OVXl2fc875 +Oa+uf3ff9Dqesg7OR7y6Puec85+99d6uytXrZ8+do/GrfRvnCV5dn3PO+Xuv +rj+777rab3G+s1fX55xz/t5bV0re2fdx/kSvrs855/y9t660vF9eXZ/zRK+u +zznn/L1X13/11t+c831+z5xzzu+pk7ZOzj/Bq+tzznmKt96Tvc/1ztOat3dc +H8X5Pl5dn3POU/qrND+60nJyzvu9uj7nnKe8/6pzHN33tH6S80/26vqcc57y +/lvVR7XqtvxqrrR95/yTvbo+55yv8t6+qPXc2XlmeXqfyTnv9+r6nHOe1nel ++W7zcs71XZzz5/vR+K7vv9m5e+fnnK/z6vqcc37VW++3qlxXfXV/Wb0+zj/R +q+tzzvms99anveeurjdlHZx/klfX55zzWX1GVa5VPqvv5Jzn+Oz7OOf8rvdW +Wq67+019F+f7+dG49yDnPM1b75+qXFWu7+J8Px99vneeVfOn7V/K59Z6Li3/ +7v467nt7j+/ed41+T6rzcs7n+9nnV78Pz55jZ+tV+6z5Zu/j1c8r3c9+j+7e +59GcT+0Dd/ndz/r9V6+Dcz7fj+7b5f0wmueuXFV9V69Xn1+fss+9f48+f3ae +o/G0/Try6u/tVa+uzzmv96PxtJyr+8y761efV/Z/rqd9z+/ar6Pxp/ZdKb8j +zjnf3Vv3pZz7KeffbN+tzq77XL2/R+N3911p+8Y55/y9r34ubb1pPvs5fVSW +9463nktbF+ec87l+dKXlfKofXWk5+Tk/utJycs45n+tnn59936f62edb832N +p63303zWfWnr4pxzPmf8rn5q9PxJ2+fZfdSor/q+pO1n6ud49fc16/eZtm+c +88/xo/vScu7WXx15yrpTcoyOp+5/2vd8lz5q1Ku+N6N5OOd89H21S582mmdV +jt3O7bTz6y6v/p6e/X6u7pd2+b2kfZ9GPSUH5zznPDj73Or5e++fVX/X9/Hr ++KxzebTuLn52PaPzHM23qk/epY8a9V2+f7P65JT1cM7r+q7Vfc9Tz4tVPnpf +Wv5d3fe2xnf/fuu7OOdH9606/znn/FP7rtn+Op6Wj3N+fPX2U6tycM55r6fk +uMt7n0vLzTlvX2n5OOe81VfcneMuH31vp+TmnOu7OOfP8dH+KyX3bD8av7qP +nPN1npKDc87P+mhfsouPvrdn3c85X+cpOTjnfHWf0nt/is9+b++2fs6f6Ck5 +OOd8to/2Yam+qk7aOjn/BE/JwTnnKX3XrHnS+q7W35xzfRfnnK/yVX1I67q7 +70rZb855Tg7OOX9K3zW7r+qdN2VfOef6Ls45360/ObrScnLO+z0lB+ecV3vr +Pdk7PtpHter0rqd6/zjnbU/JwTnn/GffbV7Oub6Lc8539ZQcR+Np+ThP9pQc +nHPO33tKjl37Rc4TPCUH55zz956So5Wv9Vxabs7v9JQcnHPOf/aUHKM+6zxK +WQ/nMzwlB+ec8+/eem9X52v52XOnd90p6+R8xFNycM45H/OUHGd99LmnrZ9/ +pqfk4Jxz/t1n9SvVvqpO2jo57/GUHJxzzr+7vuu9p62T8x5PycE55/ycH10p +/duqOmmfA+c9npKDc875e2/dt7qPuzqf/orznBycc86/++h7u/ocudp3Ve83 +53d4Sg7OOedj3vq72o+utJyc3+kpOTjnnK/1Vc9X1eV8R0/JwTnn/Jl+1zn2 +NZ6ybs57rrR8nHPO9/aUeqPPpewff5an5OCcc/5MT8nR8tHndl0nr/WUHJxz +zp/pKTlGfda5mbIenuEpOTjnnO/prfOlOt8q730uLTev9ZQcnHPOn+kpOap8 +tG9Lyc3XeEoOzjnne/rZ86U692y/ax9ex1PWz/s8JQfnnPNnekqO1T77nLW/ +z/SUHJxzzvf20T4kJfdsX12nt27avvCsHJxzzvf0tL6k2u+un7Z+/t5TcnDO +OX+Wp/Qld3t1ff1Ytqfk4Jxzzs94So7VddLWyc95Sg7OOefP9Lv7pNE8q+vP +rpPed/L3npKDc875M711/nyN33XeVa3zap2Uz5Nf85QcnHPOn+XV9a/63c89 +Zd/4e0/JwTnn/LO89Xeqt67efixtXfweT8nBOef8M3y0n6nO2+tHV1pOXusp +OTjnnPMenz3vqjrVz/M0/wd/O/nA + "], {{0, 0}, {101, 101}}, {0, 1}], Frame -> Automatic, + FrameLabel -> {None, None}, FrameTicks -> {{None, None}, {None, None}}, + GridLinesStyle -> Directive[ + GrayLevel[0.5, 0.4]], + Method -> { + "DefaultBoundaryStyle" -> Automatic, "DefaultPlotStyle" -> Automatic}], + FormBox[ + FormBox[ + TemplateBox[{"\"Divergent\"", "1", + RowBox[{ + RowBox[{"-", + RowBox[{ + FractionBox["1", "2"]}]}], "-", + FractionBox[ + RowBox[{"\[ImaginaryI]", " ", + SqrtBox["3"]}], "2"]}], + RowBox[{ + RowBox[{"-", + RowBox[{ + FractionBox["1", "2"]}]}], "+", + FractionBox[ + RowBox[{"\[ImaginaryI]", " ", + SqrtBox["3"]}], "2"]}]}, "SwatchLegend", + DisplayFunction -> (FormBox[ + StyleBox[ + StyleBox[ + PaneBox[ + TagBox[ + GridBox[{{ + TagBox[ + GridBox[{{ + GraphicsBox[{ + Directive[ + EdgeForm[ + Directive[ + Opacity[0.3], + GrayLevel[0]]], + PointSize[0.5], + AbsoluteThickness[1.6], + RGBColor[0., 0., 0.]], + RectangleBox[{0, 0}, {10, 10}, "RoundingRadius" -> 0]}, + AspectRatio -> Full, ImageSize -> {10, 10}, + PlotRangePadding -> None, ImagePadding -> Automatic, + BaselinePosition -> (Scaled[0.1] -> Baseline)], #}, { + GraphicsBox[{ + Directive[ + EdgeForm[ + Directive[ + Opacity[0.3], + GrayLevel[0]]], + PointSize[0.5], + AbsoluteThickness[1.6], + RGBColor[1., 0., 0.]], + RectangleBox[{0, 0}, {10, 10}, "RoundingRadius" -> 0]}, + AspectRatio -> Full, ImageSize -> {10, 10}, + PlotRangePadding -> None, ImagePadding -> Automatic, + BaselinePosition -> (Scaled[0.1] -> Baseline)], #2}, { + GraphicsBox[{ + Directive[ + EdgeForm[ + Directive[ + Opacity[0.3], + GrayLevel[0]]], + PointSize[0.5], + AbsoluteThickness[1.6], + RGBColor[0., 1., 0.]], + RectangleBox[{0, 0}, {10, 10}, "RoundingRadius" -> 0]}, + AspectRatio -> Full, ImageSize -> {10, 10}, + PlotRangePadding -> None, ImagePadding -> Automatic, + BaselinePosition -> (Scaled[0.1] -> Baseline)], #3}, { + GraphicsBox[{ + Directive[ + EdgeForm[ + Directive[ + Opacity[0.3], + GrayLevel[0]]], + PointSize[0.5], + AbsoluteThickness[1.6], + RGBColor[0., 0., 1.]], + RectangleBox[{0, 0}, {10, 10}, "RoundingRadius" -> 0]}, + AspectRatio -> Full, ImageSize -> {10, 10}, + PlotRangePadding -> None, ImagePadding -> Automatic, + BaselinePosition -> (Scaled[0.1] -> Baseline)], #4}}, + GridBoxAlignment -> { + "Columns" -> {Center, Left}, "Rows" -> {{Baseline}}}, + AutoDelete -> False, + GridBoxDividers -> { + "Columns" -> {{False}}, "Rows" -> {{False}}}, + GridBoxItemSize -> {"Columns" -> {{All}}, "Rows" -> {{All}}}, + GridBoxSpacings -> { + "Columns" -> {{0.5}}, "Rows" -> {{0.5}}}], "Grid"]}}, + GridBoxAlignment -> {"Columns" -> {{Left}}, "Rows" -> {{Top}}}, + AutoDelete -> False, + GridBoxItemSize -> { + "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, + GridBoxSpacings -> {"Columns" -> {{1}}, "Rows" -> {{0}}}], + "Grid"], Alignment -> Left, AppearanceElements -> None, + ImageMargins -> {{5, 5}, {5, 5}}, ImageSizeAction -> + "ResizeToFit"], LineIndent -> 0, StripOnInput -> False], { + FontFamily -> "Arial"}, Background -> Automatic, StripOnInput -> + False], TraditionalForm]& ), + InterpretationFunction :> (RowBox[{"SwatchLegend", "[", + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{"Directive", "[", + InterpretationBox[ + ButtonBox[ + TooltipBox[ + GraphicsBox[{{ + GrayLevel[0], + RectangleBox[{0, 0}]}, { + GrayLevel[0], + RectangleBox[{1, -1}]}, { + RGBColor[0., 0., 0.], + RectangleBox[{0, -1}, {2, 1}]}}, AspectRatio -> 1, Frame -> + True, FrameStyle -> RGBColor[0., 0., 0.], FrameTicks -> + None, PlotRangePadding -> None, ImageSize -> + Dynamic[{ + Automatic, 1.35 CurrentValue["FontCapHeight"]/ + AbsoluteCurrentValue[Magnification]}]], + "RGBColor[0., 0., 0.]"], Appearance -> None, + BaseStyle -> {}, BaselinePosition -> Baseline, + DefaultBaseStyle -> {}, ButtonFunction :> + With[{Typeset`box$ = EvaluationBox[]}, + If[ + Not[ + AbsoluteCurrentValue["Deployed"]], + SelectionMove[Typeset`box$, All, Expression]; + FrontEnd`Private`$ColorSelectorInitialAlpha = 1; + FrontEnd`Private`$ColorSelectorInitialColor = + RGBColor[0., 0., 0.]; + FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; + MathLink`CallFrontEnd[ + FrontEnd`AttachCell[Typeset`box$, + FrontEndResource["RGBColorValueSelector"], { + 0, {Left, Bottom}}, {Left, Top}, + "ClosingActions" -> { + "SelectionDeparture", "ParentChanged", + "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> + Automatic, Method -> "Preemptive"], + RGBColor[0., 0., 0.], Editable -> False, Selectable -> + False], "]"}], ",", + RowBox[{"Directive", "[", + InterpretationBox[ + ButtonBox[ + TooltipBox[ + GraphicsBox[{{ + GrayLevel[0], + RectangleBox[{0, 0}]}, { + GrayLevel[0], + RectangleBox[{1, -1}]}, { + RGBColor[1., 0., 0.], + RectangleBox[{0, -1}, {2, 1}]}}, AspectRatio -> 1, Frame -> + True, FrameStyle -> RGBColor[0.6666666666666667, 0., 0.], + FrameTicks -> None, PlotRangePadding -> None, ImageSize -> + Dynamic[{ + Automatic, 1.35 CurrentValue["FontCapHeight"]/ + AbsoluteCurrentValue[Magnification]}]], + "RGBColor[1., 0., 0.]"], Appearance -> None, + BaseStyle -> {}, BaselinePosition -> Baseline, + DefaultBaseStyle -> {}, ButtonFunction :> + With[{Typeset`box$ = EvaluationBox[]}, + If[ + Not[ + AbsoluteCurrentValue["Deployed"]], + SelectionMove[Typeset`box$, All, Expression]; + FrontEnd`Private`$ColorSelectorInitialAlpha = 1; + FrontEnd`Private`$ColorSelectorInitialColor = + RGBColor[1., 0., 0.]; + FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; + MathLink`CallFrontEnd[ + FrontEnd`AttachCell[Typeset`box$, + FrontEndResource["RGBColorValueSelector"], { + 0, {Left, Bottom}}, {Left, Top}, + "ClosingActions" -> { + "SelectionDeparture", "ParentChanged", + "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> + Automatic, Method -> "Preemptive"], + RGBColor[1., 0., 0.], Editable -> False, Selectable -> + False], "]"}], ",", + RowBox[{"Directive", "[", + InterpretationBox[ + ButtonBox[ + TooltipBox[ + GraphicsBox[{{ + GrayLevel[0], + RectangleBox[{0, 0}]}, { + GrayLevel[0], + RectangleBox[{1, -1}]}, { + RGBColor[0., 1., 0.], + RectangleBox[{0, -1}, {2, 1}]}}, AspectRatio -> 1, Frame -> + True, FrameStyle -> RGBColor[0., 0.6666666666666667, 0.], + FrameTicks -> None, PlotRangePadding -> None, ImageSize -> + Dynamic[{ + Automatic, 1.35 CurrentValue["FontCapHeight"]/ + AbsoluteCurrentValue[Magnification]}]], + "RGBColor[0., 1., 0.]"], Appearance -> None, + BaseStyle -> {}, BaselinePosition -> Baseline, + DefaultBaseStyle -> {}, ButtonFunction :> + With[{Typeset`box$ = EvaluationBox[]}, + If[ + Not[ + AbsoluteCurrentValue["Deployed"]], + SelectionMove[Typeset`box$, All, Expression]; + FrontEnd`Private`$ColorSelectorInitialAlpha = 1; + FrontEnd`Private`$ColorSelectorInitialColor = + RGBColor[0., 1., 0.]; + FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; + MathLink`CallFrontEnd[ + FrontEnd`AttachCell[Typeset`box$, + FrontEndResource["RGBColorValueSelector"], { + 0, {Left, Bottom}}, {Left, Top}, + "ClosingActions" -> { + "SelectionDeparture", "ParentChanged", + "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> + Automatic, Method -> "Preemptive"], + RGBColor[0., 1., 0.], Editable -> False, Selectable -> + False], "]"}], ",", + RowBox[{"Directive", "[", + InterpretationBox[ + ButtonBox[ + TooltipBox[ + GraphicsBox[{{ + GrayLevel[0], + RectangleBox[{0, 0}]}, { + GrayLevel[0], + RectangleBox[{1, -1}]}, { + RGBColor[0., 0., 1.], + RectangleBox[{0, -1}, {2, 1}]}}, AspectRatio -> 1, Frame -> + True, FrameStyle -> RGBColor[0., 0., 0.6666666666666667], + FrameTicks -> None, PlotRangePadding -> None, ImageSize -> + Dynamic[{ + Automatic, 1.35 CurrentValue["FontCapHeight"]/ + AbsoluteCurrentValue[Magnification]}]], + "RGBColor[0., 0., 1.]"], Appearance -> None, + BaseStyle -> {}, BaselinePosition -> Baseline, + DefaultBaseStyle -> {}, ButtonFunction :> + With[{Typeset`box$ = EvaluationBox[]}, + If[ + Not[ + AbsoluteCurrentValue["Deployed"]], + SelectionMove[Typeset`box$, All, Expression]; + FrontEnd`Private`$ColorSelectorInitialAlpha = 1; + FrontEnd`Private`$ColorSelectorInitialColor = + RGBColor[0., 0., 1.]; + FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; + MathLink`CallFrontEnd[ + FrontEnd`AttachCell[Typeset`box$, + FrontEndResource["RGBColorValueSelector"], { + 0, {Left, Bottom}}, {Left, Top}, + "ClosingActions" -> { + "SelectionDeparture", "ParentChanged", + "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> + Automatic, Method -> "Preemptive"], + RGBColor[0., 0., 1.], Editable -> False, Selectable -> + False], "]"}]}], "}"}], ",", + RowBox[{"{", + RowBox[{#, ",", #2, ",", #3, ",", #4}], "}"}], ",", + RowBox[{"LegendMarkers", "\[Rule]", "Automatic"}], ",", + RowBox[{"LabelStyle", "\[Rule]", + RowBox[{"{", "}"}]}], ",", + RowBox[{"LegendLayout", "\[Rule]", "\"Column\""}]}], "]"}]& ), + Editable -> True], TraditionalForm], TraditionalForm]}, + "Legended", + DisplayFunction->(GridBox[{{ + TagBox[ + ItemBox[ + PaneBox[ + TagBox[#, "SkipImageSizeLevel"], Alignment -> {Center, Baseline}, + BaselinePosition -> Baseline], DefaultBaseStyle -> "Labeled"], + "SkipImageSizeLevel"], + ItemBox[#2, DefaultBaseStyle -> "LabeledLabel"]}}, + GridBoxAlignment -> {"Columns" -> {{Center}}, "Rows" -> {{Center}}}, + AutoDelete -> False, GridBoxItemSize -> Automatic, + BaselinePosition -> {1, 1}]& ), + Editable->True, + InterpretationFunction->(RowBox[{"Legended", "[", + RowBox[{#, ",", + RowBox[{"Placed", "[", + RowBox[{#2, ",", "After"}], "]"}]}], "]"}]& )]], "Output", + CellChangeTimes->{{3.6595549649674387`*^9, 3.6595549834231453`*^9}, + 3.6595550653028927`*^9, {3.6595553128265676`*^9, 3.6595553387644897`*^9}, { + 3.6595554958307996`*^9, 3.6595555144114237`*^9}}] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"newtonplot", "[", + RowBox[{ + RowBox[{"Function", "[", + RowBox[{"x", ",", + RowBox[{ + SuperscriptBox["x", "3"], "-", "1"}]}], "]"}], ",", "2", ",", "501", + ",", "20", ",", "0.05"}], "]"}]], "Input", + CellChangeTimes->{{3.6595549152958674`*^9, 3.659554978383319*^9}, + 3.659555332709116*^9, {3.659555509656427*^9, 3.6595555271955185`*^9}, { + 3.659555597485504*^9, 3.659555640728051*^9}, {3.659558440044022*^9, + 3.6595584402002287`*^9}}], + +Cell[BoxData[ + TemplateBox[{GraphicsBox[ + RasterBox[CompressedData[" +1:eJzs103O5TpyINAyvJJeiffgJRjwuLfek54bhpFwlerx8p8RlA6BBPKeIBlB +SqL0/Z//+L///p//+re//e3//8v//Pvv//9j+3//9k/EOeecc84555xzzjnn +nHPOOeecc36VP+Oj42vz9sZPrXv1/LP9VtczO//o9evtl+25yHZf1lq2deza +j1P7OZqPc8455zybR+fnnHPOOeecc84555xzzjnnnHPOOV/lveNq88zOv8pb +6169X894tuvdev2irvuueW/xWstW76l1t46/7bnjnHPOOT/1nZWtLs4555xz +zjnnnHPOOeecc84555zzqPy136Ne6pdt3/mYt7be8bvuxyz7sSt/9HXNtg7O +Oeec89s9Oj/nnHPOOeecc84555xzzjnnnHPOecl35enNl21f+Lt9VXw0/+p1 +9Lav1sU555xzzn97dH7OOeecc84555xzzjnnnHPOOeecx/vufLPxU/WVWpbr +xHmPt7Zd58GqerLk4ZxzzjnnsR6dn3POOeecc84555xzzjnnnHPOOed5/Bk/ +la+1tc7Tuj7O+Xtatv3knHPOOedrPTo/55xzzjnnnHPOOeecc84555xzzs95 +qV9pXG//VXVl2S/Oeb6WbX8455xzzvkZj87POeecc84555xzzjnnnHPOOeec +8/MelX91P855/DlyumXbB84555xzfsaj83POOeecc84555xzzjnnnHPOOed8 +vZf6Za1rtB/nfL/f0rLtG+ecc845X+vR+TnnnHPOOeecc84555xzzjnnnHO+ +3kv9stWVZb84/5LPtl35Vs3rnOGcc845f6dH5+ecc84555xzzjnnnHPOOeec +c875ei/1i6ory75w/kafbVnqPpXPucQ555xzfqdH5+ecc84555xzzjnnnHPO +Oeecc875Pt+VJ9s6Of+Cz7Ys68lSRymerT7OOeecc54jP+ecc84555xzzjnn +nHPOOeecc87Pe++42m/O+fhz2NtvdR2nPUsdJe+9Xlnq5pxzzjl/u0fn55xz +zjnnnHPOOeecc84555xzzr/opX6lcb39R/Nwztf7aL/VdWTxLHWs9mc8W32c +c84557d7dH7OOeecc84555xzzjnnnHPOOef8C/6Mn8pX6lf7zTmff853j7vF +s9QRvf6vXn/OOeec8+jvbc4555xzzjnnnHPOOeecc84555zH1zEaz74uzjP4 +6XFv8yx1RHutuY8455xzzts8Oj/nnHPOOeecc84555xzzjnnnHP+Jn/Gd83b +G6/VM1rX07NdD85/tdX9Wse93XefM2/x1nHZ6uacc845z/79xDnnnHPOOeec +c84555xzzjnnnPNxL8VXzbPKo8dzvtNL8Vr/1XW83aPOr7d4rdlfzjnnnH/V +o/NzzjnnnHPOOeecc84555xzzjnnb/ZSv+i6nl6rs3VdnO/w0fjofHzO7fuc +19ro/nPOOeec3+7R+TnnnHPOOeecc84555xzzjnnnPM3eO/4U3Wt8tn1cj7j +s+NWzcfbfPV15L/9Ge99HrKth3POOefc9yTnnHPOOeecc84555xzzjnnnHO+ +z3vHn6prle/aB/5uH43P3m+t+fkeH70f+FpvjfeO45xzzjnP+n3DOeecc845 +55xzzjnnnHPOOeec83YvxXv7Z/PW9XA+M642z2gdPNaz1MH7xmWrm3POOec8 +Oj/nnHPOOeecc84555xzzjnnnHP+Zi/1i66r1aPz8zt8dtzuPHyPn7pP+JjP +zpdtPZxzzjnn0fk555xzzjnnnHPOOeecc84555zzN3vv+FN19frsunhOPzXv +qbw81kvN+XGHl9qu9x3nnHPO+ej3Sra6OOecc84555xzzjnnnHPOOeec8zd7 +qV90XSVvrZ/n9Fp7633Lz3jvfZKlbv67X+t8q+rgnHPOOa95dH7OOeecc845 +55xzzjnnnHPOOef8yx6dv+bR+b/uveOj77NTeXgOb71vd9fB53zV+bNqHOec +c8657wvOOeecc84555xzzjnnnHPOOec8v5f6RdWVZV9Oeamtnj9qHafy8294 +9H3O13r2+TjnnHPOo/NzzjnnnHPOOeecc84555xzzjnnvN1P549eZ+/42u/V +ebNdv9X7yXmPZ6mDn/HZOOecc8756u8PzjnnnHPOOeecc84555xzzjnnnN/r +s/OtrqPUL8u+jdbfO9+u67u6fs57fre2LOvhe7zUspybnHPOOb/Xo/Nzzjnn +nHPOOeecc84555xzzjnn/Lyvipf6ZVvvLh/dn9V5suwHf6evPl/43b77vZBl +nZxzzjnP59H5Oeecc84555xzzjnnnHPOOeecc57HSy1bnad9dh+zrIPzGXdu +8F/9VuXJsk7OOeec5/Po/JxzzjnnnHPOOeecc84555xzzjnf5894rV+ttc6T +bR927VvrfmZbH+ct3tvvGc+2Hr7GT597q+fjnHPO+b0enZ9zzjnnnHPOOeec +c84555xzzjnn7f6Mr5631kbzta4ni5fas3/r+Gzr4/yvfPY5aX0++Lu91lbf +h5xzzjn/jkfn55xzzjnnnHPOOeecc84555xzzr/opX6ltru+LHX07tOfeGu/ +1nlr/Th/s7c+L73PHf+2t47LVjfnnHPO83h0fs4555xzzjnnnHPOOeecc845 +5/zNnqWOUc9SB+c8zmvnQ3R9/G7PUgfnnHPO83t0fs4555xzzjnnnHPOOeec +c8455/wL/oxnr683zjn/jmepg+f0Z3z0PmrNm239nHPOOd/n0fk555xzzjnn +nHPOOeecc84555zzG70Ur/3O6lnq4Jyf89l+q+bn7/BT753W93KWfeGcc875 +Oo/OzznnnHPOOeecc84555xzzjnnnN/oz3i2+lavM7oOzvl+X30+RK+Hx3it +Rd+3nHPOOb/Xo/NzzjnnnHPOOeecc84555xzzjnnGbwUb50n23pWrf90HZzz +OD91nvB3eu1+2JUny/o555xzvt+j83POOeecc84555xzzjnnnHPOOeeZvRSv +/b7NS/16+3PO7/fW8213Hfxdvmq+t71/Oeecc97u0fk555xzzjnnnHPOOeec +c84555zzDN46Llvdp9Z/qg7OeR5vbdnq5jl9dr5s6+Gcc875eY/OzznnnHPO +Oeecc84555xzzjnnnGf0LHWc8tk45/w+n+23an7+bZ+Nc8455/w7Hp2fc845 +55xzzjnnnHPOOeecc845P+mr+tV+3+azcc75vX56HOe/Wrb6OOecc57Ho/Nz +zjnnnHPOOeecc84555xzzjnnJ7zUbzZe8yzr7433juOc3+et5+Tqc4bf7avv +k948s3k555xzfq9H5+ecc84555xzzjnnnHPOOeecc84z+Kr5ar9Xe2+81m+0 +Ds75/Z7tPOU5PGr86n6cc845v9+j83POOeecc84555xzzjnnnHPOOecn/XT+ +bOupzTNaB+f8fs9+nvJcvjvPbD3Z9otzzjnn8x6dn3POOeecc84555xzzjnn +nHPOOY/0Ur9VeXrH7apj93yc8+94ljr4Xo+6/qveW1n2kXPOOefrv0Oz1cU5 +55xzzjnnnHPOOeecc84555xHeqnfqvlq80ftQ3R+znm8R50bWdbPf/eLqivL +vnDOOec8zqPzc84555xzzjnnnHPOOeecc84551/wUhud5xnv7c8556v7ldqu +PPyMR+eveXR+zjnnnJ/z6Pycc84555xzzjnnnHPOOeecc875m73UL7ouzvl3 +PHp8zaPz89/+tjycc845v9ej83POOeecc84555xzzjnnnHPOOedv8FXzrq6L +c86fXjt/dp1vvXl5m/eOO319su0X55xzzu/16Pycc84555xzzjnnnHPOOeec +c875jf6M75q3N845561e+x3t0fmjr8cp3x3nnHPOOfd9yDnnnHPOOeecc845 +55xzzjnnnJ/33flm45xzXvPa+dLa/9R5WOoXvY81n11vqa2+Lr39suwv55xz +zr/n0fk555xzzjnnnHPOOeecc84555zzzP6MR9dxKh/n/Lte+33Ka/2y7FeW +/Kfuh1L/LPVyzjnn/L0enZ9zzjnnnHPOOeecc84555xzzjmP9FK/3v67fTbO +Oeerz8us52GW98WpumZ9Vd3R6+Ccc875+z06P+ecc84555xzzjnnnHPOOeec +c57Zs9UxGuec81FvPR9P1bU7T/b3wel13/re5Jxzzvn7PDo/55xzzjnnnHPO +Oeecc84555xzfpPvztfasuwH55w//dQ5eercjd7PU75rP7Osj3POOef3e3R+ +zjnnnHPOOeecc84555xzzjnnPNJL/VrnG62j1m91nZxzns1vGfcWP7UvrXk5 +55xzzn3Pcc4555xzzjnnnHPOOeecc8455+1e6tc7X28drfO2ztM7H+ec3+a9 +LVv92X32fZVlHZxzzjl/r0fn55xzzjnnnHPOOeecc84555xzzjN6qd/pPFn2 +g3POo723Zas/y3ts9j2UZX2cc845/55H5+ecc84555xzzjnnnHPOOeecc86/ +4NH5Oec8m4+O35W/1LLt2x9f9b6JXgfnnHPOeatH5+ecc84555xzzjnnnHPO +Oeecc87f5Kv7cc55tI+eg7vqi96PUjudv/f9km3fOOecc85v+e7inHPOOeec +c84555xzzjnnnHPO3+Sr5l1dF+ect3rtXIquL1sdnHPOOef8rEfn55xzzjnn +nHPOOeecc84555xzzm/y3flaW5b94Jzn9dHzJ7rummepg3POOeecn/Xo/Jxz +zjnnnHPOOeecc84555xzzvkbfNW8s3HO+fu9dj6cqiPKs9TBOeecc87PenR+ +zjnnnHPOOeecc84555xzzjnn/Cbfna+1ZdkPzvk5bz03Tp9bp87F0TjnnHPO +OX+HR+fnnHPOOeecc84555xzzjnnnHPOb/TWcbPjV43jnL/fs9Sx27PUwTnn +nHPOz3p0fs4555xzzjnnnHPOOeecc8455/xGbx3XO77WvzUv5zyPrz4Hotdz +2p/xbPVxzjnnnPMzHp2fc84555xzzjnnnHPOOeecc845/4LXWrZ6Oef7ffX5 +Er2eXZ6lDs4555xzHuvR+TnnnHPOOeecc84555xzzjnnnPM3e+/4U3Vxzs/5 +qvlm68juz3i2+jjnnHPOeaxH5+ecc84555xzzjnnnHPOOeecc87f4KvmnY1z +zvP5qfPhdn/Gs9XHOeecc85jPTo/55xzzjnnnHPOOeecc84555xz/iZ/xmfH +98Y55/l81/mS1Wv1t47Lsh7OOeecc57Do/NzzjnnnHPOOeecc84555xzzjnn +b/BV887GOef3eNbnvDU+O8/o/nDOOeec8296dH7OOeecc84555xzzjnnnHPO +Oef8C/6Mt/brjXPO7/XRfrvqaT2vRutpzc8555xzznmG/JxzzjnnnHPOOeec +c84555xzzvkXvdQvui7Ov+ijz+OqOnrzZvNd+8I555xzznmm/JxzzjnnnHPO +Oeecc84555xzzvkXvdSvtWVZB+cnvPV5ae0fvZ7R8afqKvmudXHOOeecc97i +0fk555xzzjnnnHPOOeecc84555zzL3rv+FN1cR7pq+abreOUR9UxWteuejjn +nHPOOW/x6Pycc84555xzzjnnnHPOOeecc875F73UbzbO+Ru89Xm57Tl5xrPV +xznnnHPOeWaPzs8555xzzjnnnHPOOeecc84555x/2aPzc57J3/r8ZKmDc845 +55zzmz06P+ecc84555xzzjnnnHPOOeecc/5lX92P8y94ljpq9f2JZ6uPc845 +55zzGz06P+ecc84555xzzjnnnHPOOeecc/5F7x1/qi7+LV99H+6ue1ee3vVG +XzfOOeecc86/6NH5Oeecc84555xzzjnnnHPOOeec8y97Kd7bn/MW773PSu1U +fTXfnT/LdeOcc84555zH5+ecc84555xzzjnnnHPOOeecc855vV90XfxdPhs/ +ff+vXp/njHPOOeec8/s8Oj/nnHPOOeecc84555xzzjnnnHPO6/2i6+Kxvvs+ +iV4P55xzzjnnnNc8Oj/nnHPOOeecc84555xzzjnnnHPO+1u2enmbt17vZ7/Z +Okbz7soffR0455xzzjnn93l0fs4555xzzjnnnHPOOeecc84555zX+0XXxdd4 +7fquytead3be0Xk455xzzjnnvNej83POOeecc84555xzzjnnnHPOOee83LLV +9XY/dT1qrbWe1v6cc84555xzfrtH5+ecc84555xzzjnnnHPOOeecc855vV90 +XV/x2v73ztvbb/Y+4ZxzzjnnnPO3enR+zjnnnHPOOeecc84555xzzjnnMV7q +F1UPb/Po/Fn91H7N1sM555xzzjnnfMyj83POOeecc84555xzzjnnnHPO+S1e +iq+a5+mj43vr2lX/6rxf81rLVu8u3/WcZlkf55xzzjnnnPM2j87POeecc845 +55xzzjnnnHPOOeenvdRvtH+trV5Haz2j+7F6/lXzzF7Ht3h0/t3PX6nV7n/O +Oeecc8455+/26Pycc84555xzzjnnnHPOOeecc77ba202T+336jqy7e/q6zS6 +n7P3Rbb96N2nrF5r2erlnHPOOeecc57To/NzzjnnnHPOOeecc84555xzznnJ +S/FV86zy2fp4rI+26HpP53efc84555xzzjmP9Oj8nHPOOeecc84555xzzjnn +nPPv+qp5W9uf8b3zZNkvnttr/U7d76PzZdtPzjnnnHPOOec8U37OOeecc845 +55xzzjnnnHPO+fu91G93nizr5zyiZVsv55xzzjnnnHM+49H5Oeecc84555xz +zjnnnHPOOefv86j8td+c3+CrWrZ1cc4555xzzjnnMx6dn3POOeecc84555xz +zjnnnHP+Hi/1i6ory75wnqll2wfOOeecc84557zFo/NzzjnnnHPOOeecc845 +55xzzt/ntTaaJ9s6OR9ps/lW1+v54pxzzjnnnHN+g0fn55xzzjnnnHPOOeec +c84555x/x5/xbPVxvrLtqu+2eTnnnHPOOeec8xUenZ9zzjnnnHPOOeecc845 +55xzfs5L/UrjevPV5uM8o8/GszzH9olzzjnnnHPO+Zs9Oj/nnHPOOeecc845 +55xzzjnn/JzvztebP8u+8Hd5qd/ofZvNs9TR2mr7zznnnHPOOeect3h0fs45 +55xzzjnnnHPOOeecc875eX/GR8f35l/dj3/bZ+O3eJY6spw/nHPOOeecc86/ +6dH5Oeecc84555xzzjnnnHPOOef5fXa+3nmzrZ+f8dZ477i3eZY6Vnut1c4T +zjnnnHPOOefv9uj8nHPOOeecc84555xzzjnnnPN9/ozX+p2q6+m13/xOL8VX +96/1u8179+d2772+WermnHPOOeecc37Wo/NzzjnnnHPOOeecc84555xzzvd5 +dP5Wr/3md3opXuu/uo7b/PbnOZtnqYNzzjnnnHPO+ZxH5+ecc84555xzzjnn +nHPOOeecn/daO11X7TfP4aP9Vtfxdq/ta3R9Wbx1XLa6Oeecc84555yPeXR+ +zjnnnHPOOeecc84555xzzvk5L/XLVleW/fqq947Lel/d6quuy1f9Gc9WH+ec +c84555zzMY/OzznnnHPOOeecc84555xzzjnP46fzZ1v/W/30OD7nrsceL8Vr +vznnnHPOOeec5/Do/JxzzjnnnHPOOeecc84555zzeC/1250/y/qzeqlfrX/2 +687b+vX2523NucQ555xzzjnnd3p0fs4555xzzjnnnHPOOeecc855Xi/1W5Vn +93p6x0Xte/b5+Fl3Xc/6M56tPs4555xzzjnnOfJzzjnnnHPOOeecc84555xz +zu/1WquNm8337HdqvbVxq9fdus7VefgZ772+Wer+qj/j2erjnHPOOeec87d6 +dH7OOeecc84555xzzjnnnHPO+Xe8t2Wrf3S9f+Kt+zLan9/lo9c3uu63+Ozz +taoOzjnnnHPOOedtHp2fc84555xzzjnnnHPOOeecc/4eL/UbHZfda+sdjfNv +uPsj1kfPq6dnWQ/nnHPOOeecv92j83POOeecc84555xzzjnnnHPO8/szPjp+ +VV3Z9+F0XTy377r/+F5vHZetbs4555xzzjl/q0fn55xzzjnnnHPOOeecc845 +55yf92f8VL7V886uu3fc6nr4t7z2+1QdfM6f8Wz1cc4555xzzvlbPTo/55xz +zjnnnHPOOeecc84553yfP+PRdZzKx/kN3vrc8lxeatnPYc4555xzzjm/3aPz +c84555xzzjnnnHPOOeecc87n/RnPVl+t7ug6OD/hrc/v7jr4b199XrmunHPO +Oeecc77Go/NzzjnnnHPOOeecc84555xzzuuepY7VnqUOznf66HMRXffXfdV8 +XznPOeecc84553y3R+fnnHPOOeecc84555xzzjnnnNf7lcZlqbvmWergPMJH +n5four/qq8+x1vk555xzzjnnnP/26Pycc84555xzzjnnnHPOOeec83Z/xrPV +11p3b5zzN3uWOnibt47LVjfnnHPOOeec3+7R+TnnnHPOOeecc84555xzzjnn +9X69/aM8Sx2cZ/Tbn2/+156lDs4555xzzjl/u0fn55xzzjnnnHPOOeecc845 +5/zL/ozX+rX2z7Ke3jjnb/TR56jUotfzdl91XbKsh3POOeecc87f4tH5Oeec +c84555xzzjnnnHPOOf+il/qtyrOq7tk453z8uSv1i17P2/wZ331dsq2fc845 +55xzzm/x6Pycc84555xzzjnnnHPOOeec83IbnS+qjto8o3Vw/kbf9fzzNj91 +Xq3uxznnnHPOOedf9ej8nHPOOeecc84555xzzjnnnPN2bx1XG1+a53SdnPNy +y1bfW/1teTjnnHPOOef8rR6dn3POOeecc84555xzzjnnnHO+z0ttdJ5s6+P8 +Jm99vlqf59m8/Ewe14NzzjnnnHPO13h0fs4555xzzjnnnHPOOeecc875ei/1 +i66L8y9763Pa6715+dr5sq2Hc84555xzzt/q0fk555xzzjnnnHPOOeecc845 +5+PeO/5UXZzzuu/Os3q+KH/GV+9DKT573nLOOeecc845X+vR+TnnnHPOOeec +c84555xzzjnndd+db9e8nPP236v9VJ5d51ip367zrRbnnHPOOeeccx7r0fk5 +55xzzjnnnHPOOeecc8455+X2J34q3+p5Oedlj36uT59jWX11P84555xzzjnn +ezw6P+ecc84555xzzjnnnHPOOee83P7ET+frjXPOx732e9RXz3db/tH9n+3H +Oeecc84553yPR+fnnHPOOeecc84555xzzjnnnMfXcTof57zds8y3uo6s52uW +ejnnnHPOOeec58rPOeecc84555xzzjnnnHPO+Re91K93XG8dq+vhnJ/zVfOd +Hhftu89JzjnnnHPOOednPDo/55xzzjnnnHPOOeecc84551/22flWzztbD+c8 +r/e2bPXvOg9318U555xzzjnnfI1H5+ecc84555xzzjnnnHPOOeect/sz3tqv +N845f4/Xfve26HX1nmvR9XLOOeecc845X+PR+TnnnHPOOeecc84555xzzjnn +417qF10X53y915732XNjlfeO711X9HXgnHPOOeeccx7j0fk555xzzjnnnHPO +Oeecc8455+3+jLf2641zzs/52/NxzjnnnHPOOecrPDo/55xzzjnnnHPOOeec +c84557zuq+ZdXRfn/H+99txF15etDs4555xzzjnnvMej83POOeecc84555xz +zjnnnHPOy+1PfPW8o+M55+3P7W2epQ7OOeecc8455/xXy1YX55xzzjnnnHPO +Oeecc84551/0Ur/SuNb+o/Nzzv/Za89RdH01z1IH55xzzjnnnHPe49H5Oeec +c84555xzzjnnnHPOOef1fqVxtf6t87WO4/zN3vs8Zqm717PUwTnnnHPOOeec +93h0fs4555xzzjnnnHPOOeecc875vNdatno5j/Ta75qvquOUP+PZ6uOcc845 +55xzzls8Oj/nnHPOOeecc84555xzzjnnfNxL/WbjnL/ZW5+jtzw/z3i2+jjn +nHPOOeec8xaPzs8555xzzjnnnHPOOeecc845b/dnfHT86ro4v9lnn8MsXorX +fnPOOeecc8455zd4dH7OOeecc84555xzzjnnnHPOebs/46PjV9fF+c3e+rys +rmM0b2ue6H3lnHPOOeecc85XenR+zjnnnHPOOeecc84555xzznm7P+Ot/Xpb +tnVznsFL7VQ92faDc84555xzzjk/6dH5Oeecc84555xzzjnnnHPOOef7PDo/ +5zM+G5/1Wt7T+bNdH84555xzzjnn/KRH5+ecc84555xzzjnnnHPOOeecj3vv ++FN1cf4rfrqOVn/GVz9fu55rzjnnnHPOOef8Cx6dn3POOeecc84555xzzjnn +nHM+7r3jT9XF+ci4XXXUPHqfOOecc84555xzXvfo/JxzzjnnnHPOOeecc845 +55zzeW+N78rP+V/56vt41qP3g3POOeecc8455+MenZ9zzjnnnHPOOeecc845 +55xzvt5L/aLr4t/y2n14+v7nnHPOOeecc875vR6dn3POOeecc84555xzzjnn +nHM+76v78Xd67feuOmrt1HOQ5TpwzjnnnHPOOee836Pzc84555xzzjnnnHPO +Oeecc87Xe6lfdF08xmv3w+n7cPf9Gb3fnHPOOeecc845X+/R+TnnnHPOOeec +c84555xzzjnn673UL7ountNXzfuMZ1kf55xzzjnnnHPO7/fo/JxzzjnnnHPO +Oeecc84555zz9V7qF10Xb/Pd89bG9daVbf8455xzzjnnnHP+Po/OzznnnHPO +Oeecc84555xzzjk/79H5v+q7r8fofdA6X/T+cc4555xzzjnn/LsenZ9zzjnn +nHPOOeecc84555xzvs9rLVu92X33dTldB+ecc84555xzzvktHp2fc84555xz +zjnnnHPOOeec5/RSPFudfMyj89/qu8a3xlfVwTnnnHPOOeecc36bR+fnnHPO +Oeecc84555xzzjn/uq+adzZe89q8tdY6T5br8naPzn/KV69/Ni/nnHPOOeec +c845H/Po/JxzzjnnnHPOOeecc84551/xUr9d+XfN35uvddzq/emtO8t9csqj +849673p676vo9XHOOeecc84555zzv/bo/JxzzjnnnHPOOeecc84559n8GZ8d +3xtv9drvUd89f/R17e1X6p9tfavv0yzee51W5+ecc84555xzzjnnOTw6P+ec +c84555xzzjnnnHPO+Wkv9VuVp3dcrd/suvgZX93vVL2n8rfux+m6OOecc845 +55xzzvkdHp2fc84555xzzjnnnHPOOed8t0flr/3m3/bRlvW5WD0f55xzzjnn +nHPOOeeZ8nPOOeecc84555xzzjnnnO/2WjtVV7Z94e/wWpsdl229nHPOOeec +c8455/ybHp2fc84555xzzjnnnHPOOed8t6+ar/ab80ze27LVzznnnHPOOeec +c855pvycc84555xzzjnnnHPOOefP+Oz41njtN+c3+Kp47zjOOeecc84555xz +zk96dH7OOeecc84555xzzjnnnH/Hn/HV85b61X5znslP5butXs4555xzzjnn +nHP+bY/OzznnnHPOOeecc84555zz7/gzPjq+N//qfpyv8Na2q47szzvnnHPO +Oeecc84555nyc84555xzzjnnnHPOOef8/V7qF51/tB/nPS36/i95lny9/Tnn +nHPOOeecc875Nz06P+ecc84555xzzjnnnHPO3+O943fX1Zs3yz7yHH56XPbn +9dR+1/pnq5tzzjnnnHPOOeecn/Ho/JxzzjnnnHPOOeecc845/45H53967Tf/ +ts/Gs3uWOkpe2/dTdXDOOeecc84555zzHB6dn3POOeecc84555xzzjnn7/FS +v+i6ah6dn5/xUvzW+3b2ubzVe69Xlro555xzzjnnnHPO+ZxH5+ecc84555xz +zjnnnHPO+Xf8dP5s6+drvRSv9V9dx62epY5of8az1cc555xzzjnnnHPOc+Tn +nHPOOeecc84555xzzjk/nT/b+nlbv+z3VTa3L23+jGerj3POOeecc84555zn +yM8555xzzjnnnHPOOeecc74rT7Z18rFxtXlG6/i6Z6kj2p/x3vst23o455xz +zjnnnHPO3+rR+TnnnHPOOeecc84555xzzmfny7aer3mtjY7rnY//o+963r7i +reOy1c0555xzzjnnnHP+Vo/OzznnnHPOOeecc84555xzXvLWcdH1lfrVfkd7 +qd/s9RjNy9f6quv4VW8dl61uzjnnnHPOOeec87d6dH7OOeecc84555xzzjnn +nPNef8ZHx5f6nap/tJ7WfRn10X3juXz3fcJ/9yuNy1I355xzzjnnnHPO+W0e +nZ9zzjnnnHPOOeecc84557zXSy1bnavX+4zvytu679n2if/2LHXc6r37mqVu +zjnnnHPOOeec87d4dH7OOeecc84555xzzjnnnL/Pn/HV8/aOz7Y/s3VH18Vz +eu/9k6Xu23x2vmzr4ZxzzjnnnHPOOb/Fo/NzzjnnnHPOOeecc8455zy/P+PR +dczO27rOUx61D/zbnqWO2733Oc1SN+ecc84555xzzvltHp2fc84555xzzjnn +nHPOOefnvRSv/Y72qDpm62ztPxrn/Fe/3v78jGepg3POOeecc8455/wWj87P +Oeecc84555xzzjnnnPN5L8Vrv2/zLHVwnslXnRd8rY+eY287tznnnHPOOeec +c85XeXR+zjnnnHPOOeecc84555zPe+u4bHWPrjO6Ds4z+ey5wGO8dVy2ujnn +nHPOOeecc86jPDo/55xzzjnnnHPOOeecc87n/RnPVt/senrjnH/Re5+XLHV/ +1VvHZaubc84555xzzjnnPMqj83POOeecc84555xzzjnnfHz8qnmyeZY6OL/B +V50b/Ky3jstWN+ecc84555xzznmUR+fnnHPOOeecc84555xzznm936o8WdZZ +89aWrW7OI3z0+Yqum+esg3POOeecc8455zyrR+fnnHPOOeecc84555xzznm5 +zc5X+x3ts3HOed2z1PE1333uZ1kn55xzzjnnnHPO+SmPzs8555xzzjnnnHPO +Oeec83JbnSd6PaV+p/eB8zd663PkeTvjvedh73XJsk7OOeecc84555zzUx6d +n3POOeecc84555xzzjnn9X6r8vSOq/VrrX/3ujj/su9+rvmcz86XbT2cc845 +55xzzjnnUR6dn3POOeecc84555xzzjnndS/1651vdJ4s9XPO/9lXzTdbB/9r +XzXf6nOZc84555xzzjnn/DaPzs8555xzzjnnnHPOOeec831eimerh3O+3j2H +OXxXnmzr5JxzzjnnnHPOOd/t0fk555xzzjnnnHPOOeecc77eS/1K43rztbYs ++8E533eu8N/eOi5b3ZxzzjnnnHPOOefZPDo/55xzzjnnnHPOOeecc87b/Rkf +Hb+6Ls55Xq/9LrXaOdNbx+3eum+lNnpuc84555xzzjnnnPMc+TnnnHPOOeec +c84555xzXvdV866ui3Oex0+fJ7VzJsu+1PwZX32unt5/zjnnnHPOOeec87d6 +dH7OOeecc84555xzzjnn/Mv+jJ/Kt3peznmcR+cvtSx1RZ+Hq/txzjnnnHPO +Oeecf9Wj83POOeecc84555xzzjnnX/BnPEsdvXHO+T0efc6U+u3KP1pPVF2n +xnPOOeecc84555y/xaPzc84555xzzjnnnHPOOedf8Gc8Sx29cc75fV77vdpr +Lfqcy+LZ3xecc84555xzzjnn2Tw6P+ecc84555xzzjnnnHP+Bi/16+2/22fj +nPP7/JbzJ3q+U+vv7Z9tHZxzzjnnnHPOOedRHp2fc84555xzzjnnnHPOOX+D +l/r1jotaz+l8nPO8vutcOj3ulPfWHV0v55xzzjnnnHPO+a0enZ9zzjnnnHPO +Oeecc845f5PPzrc7X22e3vk457z3nNl1fkZ767qy1Ms555xzzjnnnHN+m0fn +55xzzjnnnHPOOeecc87f5LVWm6827+o6s+0f5/w73tuy1Pnsl21fOeecc845 +55xzzt/q0fk555xzzjnnnHPOOeec8y97KT47fy3fqjycc17y1f0455xzzjnn +nHPO+bc9Oj/nnHPOOeecc84555xzzvtbtno559/16PGcc84555xzzjnn/Bse +nZ9zzjnnnHPOOeecc845/4JHj+ec85rXzp/T9UXvB+ecc84555xzzjnP5dH5 +Oeecc84555xzzjnnnPM3+O58rS3LfnDO83rtnImq7xmP3ifOOeecc84555xz +nsuj83POOeecc84555xzzjnnN/ozfjpfb5xz/j2/7bx4xrPVxznnnHPOOeec +c85jfXbcbJ5s+8E555xzzjnnnHPOOeect/gzHl3HqXyc83zeek5l9Sx1cM45 +55xzzjnnnPPcXorX+rfmW1UP55xzzjnnnHPOOeecc57BS/16+/f6bJxzfr+v +Pjeye5Y6OOecc84555xzznlu351vdd5s+8c555xzzjnnnHPOOef83d46btW8 +tf6t9XDO8/vo8x5d96yX4m9bJ+ecc84555xzzjkf81P5WvO39p/NyznnnHPO +Oeecc84555zPeK39GVcb35q3tY5s+8Q5H/dV50CW9dT8Gc9WH+ecc84555xz +zjmP9dXz1n6v9lXx0fycc84555xzzjnnnHPOeYuXWm//0fyc87xe+13z3vmj +vFZ/1ro555xzzjnnnHPOOd/pre05Pts6OOecc84555xzzjnnnN/tpX7RdXHO +83jrudHrq+c7XVe2ujnnnHPOOeecc855rJfi2eo8tQ+llq1ezjnnnHPOOeec +c84557l81byr6+Kc3+ez58aqOmpeq8c5xznnnHPOOeecc85Xeu+4bPVn2x/O +Oeecc84555xzzjnn3/BnfPW8o+M55+/11vOo5qfOn9a8nHPOOeecc84555y3 ++Kr5sq1rdB9K/bLVyznnnHPOOeecc8455zzWn/Fd8/bGOeff9Wznxup+nHPO +Oeecc8455/zbvmpctnVF78/X3X5yzjnnnHPOOeecc87f4rX2Z9zsvNnWzTmP +89q58YxHnTPR+8Q555xzzjnnnHPOv+W7x2db79fW17qu3XW01rN7XJbrwjnn +nHPOOeecc845v99L8drv3vGt4zjn8b7qHOn11edaa57o/eacc84555xzzjnn +3/JV89bmb43ftj+n61pd5666st2fNc9233HOOV/rvf2y1c8555zv8FI8W52c +c875jV6Kt753d9XFOe/30ef0dN3R+8Q555xzzjnnnHPO+QnPUsfTV/db7bvm +i8of7bddL84557/jp79fRufLtp+cc875Di/FW9+LvfHReTjnnPM3eO09WGtZ +1sH5lz1LHb2epQ7OOeecc84555xzznd6ljpOrTN6vlrLtm+nvPf+vO1+4Zzz +W/wZ3/W9sWq+2fpqv2fzZru+nHPO3+2r5pt9P46+T7Pt59s86n7inPOv+eh5 +u7suzvn6795VdYz6M55lXznnnHPOOeecc8453+lZ6rjFe1u2+m/12u9Rr7Us +6+ec89XeOi5rfaX4rvfF6u+rbPcD55zztb5qvt15T7+fRuPZru/pfYre597+ +nHP+dT91bnPOxz3q+361P+PZ6uOcc84555xzzjnnfIdnqeMW723Z6n+b137X +vHd+zjl/iz/jWet79stWp/cO55x/w0tx5/hej84/66e+E1r7u16cc37GV5// +nPP475hTdbTmz7Z/nHPOOeecc84555yf9Cx13Lb+2Tyz+flf++rrEr0ezvl7 +vfe9tPq9t+t9N5p3VV3PeJbrXfPo/Jxzzn/7Mx5dR6lf9vrf8t6Mzr/ao+9P +zjm/3Z/x1e+P0XGc837f/Rz2zh+9H5xzzjnnnHPOOeecZ/Qsdezy2+at+el8 +b/Hafma5H1rjs3k45+e9dVz0e6T1fJut49S5m+0+2P0+ivZSW7Uf2dbLOX+/ +R7+Xez3LuqLfQ7v2cXWebL7rPlk93+46W8e//buOcz7vq/txzue9NV5rt32P +cc4555xzzjnnnHP+Js9SR81r9Z+uL/p6tV7PXXVE++r7Ybae3T56vUvzR6+H +c16Of+39vsp7z/foemstut7d99Wu75/aOm79DuCcl/2283l03Op9uv29uWp/ +fUeN+a73eO+47Ost9YteD+d8v3u/cD7vUd/Tq9/7s3mirwPnnHPOOeecc845 +5xk9Sx1/vFanffpdV2+/1XVkvb5vu9619Y2uK8t6OH+T957HreOyrO8rHv1+ +P3UfRu9zzXe9t1bPxzk/78/46nNgtK63e+/7Jfq9WWvR+/k2L7VsdZ76DllV +B+c8nz/js+dltvVxvtJb36e76+ith3POOeecc84555xznsej6qjVk3WfavXf +4qOtNU+26zt7vXvj0etbvV7OebmNvhd21cVjfPYcXn0+r64jm2efj3N+zlef +A6vn5bFeatnqzO67nqfRerK47w3Oue8Qzts963vzGY/eJ84555xzzjnnnHPO +ed2z1PH0LHWUPEsdp7zUb/X9dut1OZ2v5qP1R9fNeUZ/xt96bvBc3tuy1Z/1 +fec9yPm9Pnperh7Hc/mu76zZeFbfvR7fyb/jpfG796F3/rfd95yf8Gf8a+8X +zlv8lvs+Sx2cc84555xzzjnnnPOy7843mvf0fmS7Lm/1Uqv1z369ZuOnPHt9 +nN/gt58DPLf33m+1lmVdWTz6+cxWD+cZ/BkfHb+6Lp7Lo8fXfFU9pXGr+2e9 +TqO+et5s98tpf9t6OI/0WstWL+c7Pfo90loP55xzzjnnnHPOOec8v+/ON1pP +9H6M1s/5TPzUc1Frb3uuOR/xqPcm/4av7lfz2Tg/463xUr9s6+G8xZ/x0e/X +0fw8p6+eN9v6Vr8fVn3H3rqftX69+3P6fludf9Z335+cf8Fved45/3uP+n6o +jZvNE72vnHPOOeecc84555zz9b47Xy1v9LprdXJ+0nfPF3UOtLZn/2zXh7/T +s703+bs8evyoz8az17G6X/Q+RF8nzme8FG89D3fVxc/4qXzZ1h2931/fn1K/ +bPu2a97o58n3DH+jP+Oj9/Pqujhv+R1Vx6jvnp9zzjnnnHPOOeecc57fs9Yx +O3+2fea8xXvju5+/2XlXP6e76uDf8mf81vcmP+tR51L0ukutN76qf5b9XF1X +q3tv8jd5tueL73F1cL7eR+PRdd32Hc55jz/jq59fzkc8+hzfNS/nnHPOOeec +c84555yPjp/Nv6qebPvJ+Zt8d77RerLtE3+H11q2evkez3b+RO/HrJf6jb53 +suzbbPzt9y3/pt/y/cnPeLZzKXo/OD/htbbreRnN0+qrv9M4P+G+c3gGP3VO +tublnHPOOeecc84555zz3b5rvtXzcs73+erxvfNk2w9+lz/j3k+8xU99FzkH +3+mz8dnrX2tveS54bn/GT39/8hhvPb9211GKZ9knzr/ku/NFnzOc/3LfOXzG +T51vs/NF7xPnnHPOOeecc8455/y7vjtPtvVyzvf56XE1jzr3eA5/xmv9TtXF +c3j0OTVbD3+H944bnX90vPcs73HvWf737n3KOV/dr3X87Hy7vsv4O/3088Lv +9t7v59P356p5OOecc84555xzzjnnfLePjq/95pzz1b5q3tr82dbNx7zWstXL +c3jv+TB6nrTm5XzGZ+Ojz4v37Dd8dT/+Lo/6nuec3+u9/bJ9/8zOy9/ptZat +Xn7Gd8/re4lzzjnnnHPOOeecc8455zyHr5q3Nn+2dfPf/ozvvn94bt81ftV8 +WfaJf9tL8dH3Y+98/JsenZ+v8V3v41XzcM756u/5XnfO8V/9ouvie3zV+NF6 +su0H55xzzjnnnHPOOeecc845/+275zuVl495Ke66vdN3X9fo9XEe6bV+vefs +aB3ev7l993XnOTx6POecn/JaP98/fMR9L93pvddx13dRqV+WfeKcc84555xz +zjnnnHPOOec5fNW8tfmzrftW330deU5f/XytqotzXvfe8d6nOd15+g0ffb5r +zy/nnH/NV8+bbX38r9330rvc88k555xzzjnnnHPOOeecc85v8t7xtXmyre9W +X3W9+Blf9VyMXvfWeTjn+7zWRuebPT94n3v/3um7rm+W9XHO+W1+epzvpbPu +e+mM73q+ai163ZxzzjnnnHPOOeecc84555z/8lq/2u/aPLX+2fYji49eL77G +R5+jXdedc/4db22j51jr+Lf76P7srov/du9Tzjn/lveO9/4+46uuF//tq+7n +6HVwzjnnnHPOOeecc84555xzntGjx3/No/O/xVftb+880evmnN/ntX6t40bz +f82j87/Fd+9v9Po455zHeCk++h3VO9/XffU+f8137XOW9XHOOeecc84555xz +zjnnnHN+s8/Gn55tfav3qdSy1ZvdZ/vNzss559HeG1/1nn6LR+fP7rP7mWUd +nHPOv+Gz41pbtnWf/g6Irivae1tt/mzr45xzzjnnnHPOOeecc84555zX22y/ +7P729a3y2X3Lsg7OOY/2Unz0fZRtfav242s+u29Z1sE555zv9NX9bvday1bv +qfsgW72cc84555xzzjnnnHPOOeec8zxe65et3tb6ouva7bP7kGUdnHP+Va+1 +bPV+7f07e92yrINzzjm/2Vf3y+a1lq3e0f3PVi/nnHPOOeecc84555xzzjnn +/H1e6lfrf7re3vqj/bZ6Oeecn/XW+K78b3ufrfpuiV4H55xzzute65e93tP5 +R7+DstTFOeecc84555xzzjnnnHPOOeejXmvRdX01P+ec83f46Pi3vv9b37vZ +riPnnHPOz3trO/Udtfp777b8nHPOOeecc84555xzzjnnnHN+m++ab1We1fNx +zjnnJ320Rb8va/Nk22fOOeecv89HW9bvqNH5OOecc84555xzzjnnnHPOOeec +//aolm0fOOec85Nea7Pjsq2Xc8455/zUd9Sulm0fOOecc84555xzzjnnnHPO +Oeecr23Z1sU555xn9t6WrX7OOeec81u+o0ot27o455xzzjnnnHPOOeecc845 +55zHtmz7wDnnnJ/01tY6/tkv23o555xzzk9/R61u2faBc84555xzzjnnnHPO +Oeecc87f6lnnbW3Z9pNzzjlf2bK8f5/9s+0z55xzzt/nsy3Ld9TsvJxzzjnn +nHPOOeecc84555xz/lZvbafry7If2a4X55zzu/z0uOzvvVI8y3cA55xzzvN4 +rZ3+jsry3RZdB+ecc84555xzzjnnnHPOOeecr/JSvNZ/dR01760/2mfjnHPO +3+2j/VbX8Zb376rvlizr4Zxzzvn4d8ipOnZ9/0XX57uIc84555xzzjnnnHPO +Oeeccx7ts/Fov7XuWX/Ge/ch23o45/xr3tqy1f2V929rvNQv23o455zzG701 +3jsum2epY/X3bO27kXPOOeecc84555xzzjnnnHPOW+O947L66D58zZ/x3n3L +th7OOY8+T5/9Zt/L2dbZ6lnqiPbecfaRc875F7013jvuds9Sx+l1lsZlq5tz +zjnnnHPOOeecc84555xz3u61fqPzZVvnqf3ibd46rvc6ZFsn55yvev96L+Ws +I6v3jrO/nHPOI331+NXz3+arvg/e4r3N9yjnnHPOOeecc84555xzzjnn8T47 +btV8X/Esddzurfdlbb7eebKsn3N+j6+Kz9bxFc9Sx+2+6j1b8izr5JxzftZL +/Ua/k1aPe7vbrzlvHdc7Pts6Oeecc84555xzzjnnnHPOOd/hvfHeeWr9a/2+ +6qPXi6/x0edoNn+W9XPO49/LpTZ7jo3O9zYf3Z/our/ureOy1c0553zMe8f5 +/jnjq64X/+2r7ucs6+Gcc84555xzzjnnnHPOOed8hfeOq80zWgf/R191vfgZ +X/VcjF731nk45/u8tc2eK94Pe93+3umt43rHZ1sn55zf4qPjs7wv+G+3v2d8 +9fPV2rKsn3POOeecc84555xzzjnnnH/bV81Xm39Vnq/77uvIc/qu52t0HOe8 +3XvHeZ/mdOfoN7x3XOvzyznnX/Ps8/E97vq9y1vHZaubc84555xzzjnnnHPO +Oeec5/TV89Z+78rLx7x2fVr78zt89/OYZZ2cR3hvfHSeLM87H/Pd153n8Nn5 +sq2Hc859//CT7nvpTn/GVz2Pq86lbPvFOeecc84555xzzjnnnHPOf/uq+Wrz +r8rDz3jv9c1SN9/js/Otnrd1fs5Peqnf6PvRuctbPEsdfM5bx+0+lzjnfNf5 +tStPdF38rLve3/BaO/WdnG1fOOecc84555xzzjnnfLevGpdtXZzz9/mq+Wrz +r8rDc3iWOvgd3nsfjd53rXk5n/Fav13Pi/P4Wz4b5+/0qO95zvm93hqf7Xf6 +7wXOM9XBY73WVp9P2dbPOeecc84555xzzjnnq3x3vmzr5Zzv89Hxu+qKOvd4 +Du+9H7LUzc949PfSqXOQ5/be8aPze8/yE+49y1v67c6TZf2c8/Z477gs3x+n +8vDc7n7iPf6M7z7PVp2j2faRc84555xzzjnnnHPOS7573mzr5ZyX2+z5cTo/ +5y2/T9XB7/LT30U1z7IvvM1r/aLew297Lnhuj7rveaw/49Hnxux9yDmf9915 +os8Zzn+57xw+46fOt+jxnHPOOeecc84555xzPuqnx/3xVfNm20/O3+S784zW +s7su/m3PUgeP8Wz3RZZ9GfVSfPS901pH9Dnx9fuWf9Nv+f7kZzzbuZRlXzjf +6a1t9fPSOu+or/5O4/yE+87hGfzUOTl7bnPOOeecc84555xzznmvZ8m/ev5s ++8x5i9f67brPe+tY5av3h/MWX3UfZlkPP+NR51KW9Zda7z7N9p/127+fvTf5 +mzzb88X3eHT+rO9Tzme81i/qeXzbdzjnPb7qvs2yHv4OX/1+mZ03y75wzjnn +nHPOOeecc87v9915anl352+tK9t14d/01fP2Po+n19faP9t14u/ybO9N/i6f +nS+67lK/6Py9/Uavz+i8Wb4LZsdzfsJbn7+szykf81qL/t57q5f6Zasz6vss +276tni9LXb5n+Bt99jxZVQfnv1rrd/WuunzPcM4555xzzjnnnHPOV/nuPKP1 +7K6r5LP1c/6rjd5vs3Wsnve255rzEY96b/JveOu4qPcRP+u9/ZxP/E0++j28 +ug6ew2tt9XfdLd47fvd7JOv+tMZX7XPv/Le8v3ffn5x/wW953jlv6TcbP/1c +tOblnHPOOeecc84555zf67vzjObdXdfTs12Xt3qptfbPer1q/bLUO1o/57x+ +/tTmia6b3+HPeO/7dHU9b/Po92C2ejjP4LPvy1V18Nw+O9+p+mbrKY1f3b/W +L+s+nzoHVs93298Fu+9/zr/oWergPNKjn4/b3secc84555xzzjnnnPOyR+e/ +ra4/Hp3/tJfiq6/r6LzR1+VUnlYfrX93XZzf6LPP1y3nBs/hvS1b/dHP56iv +rotzvt5nz03P/zt9Nj56X2Tbh9n35qo8vpN/9yuN270PvfM7Lznv91XPUZb1 +cL7Db3m/ROfnnHPOOeecc84555zXPSp/rZ6oukreWv8tPttq+bJd39n9yX79 +n/HV6+Wcr38vrKqD5/BnfNf7evY763a/bV7O+X7fdY7zu73UstV5i+8aNzpv +Fve9wTmPPmc5v8mzvjdn6+Scc84555xzzjnnnJ/36PxPr9UZVVeW/KN19fZ/ +2/V9y3VurXf2Psm2Ps5v9t5zuTZ/9Hq+6tHn++y8bzn3n/Fs+8w5j/PZc7t3 +fv67X2//0+f5rvz8d8tW5+nvkF11cc7jfdV3SJb1cL7Tn/Fs781s+8U555xz +zjnnnHPOOS+3bHU9vVb/6bqir9eqfrf66nVnWVfJW9fbOn9vfs75uef7a+/3 +Vd77XshS96r4qe+cVflWf/+01vvV7ybO3+y3nc9Z3jO3vzdXnedZ3ru3+a7r +MlrPbo8+Nzjn97nnn/N979/d+Ve/92fHZbkenHPOOeecc84555xn8uj8t67v +bet5u9f2czbP6uvb2280H+f8nK/uN+q98azvo9ZxWa5/zbPUsWs9vfNkve84 +59/zLO+z1fNF7+suXzXvV99Dz3i261LyqOfxK991nPN5n41zzud9tN+uek5/ +j3HOOeecc84555xz/iaPzh+97lKrzXc6H2/z1ddldF7OOR99j5TG73r/rX7f +jeZd9f2ya99Of5dkq49zzr/uWd4vo/Es9b/lvZltP7KsZzbOOee3euu5ump+ +zvn576JVeXrnz7IvnHPOOeecc84555xn8uj8t3hvy1b/W/0ZX33/j9bFOefZ +vfY72kvxbHV673DO+Te89dzOUu9bPEsdo37qOyHL/blrXs45v81Xn/+c832+ +ut8ub/3+45xzzjnnnHPOOef8Cx6d/xbvbdnqv92f8dPXNdt+cM75rK/ut9pH +63rGo+v3/cU559/0U++T2bzP+C3v97f7quvaO9+q/pxz/nU/dW5zzsd99XMa +5c4LzjnnnHPOOeecc/5Fj85/an3Z5p0d/zbvvT9vvW845zy77zpvW9vse2P2 +O2j199LoOM4553zEs7wfR9+LtTif89nvt+j6Oef8Fp9973LOz/kzftt3bOt3 +OOecc84555xzzjnnb/Lo/LN1Rde3e95S/2zXa9ZvvV6cc/51j/6+WDU+y35y +zjnnO7z1PTj6vu3NV+vHOeec3+yt78HddXDOxz06/+rzh3POOeecc84555zz +N/mq+Wrzt467bX9O1fHHV9e5a5+y3Z9Z8nDOOY/11vipejjnnPNIH31fcs45 +57zure9Z72PO8/voc7q7rqdn2S/OOeecc84555xzznf67LjafNnWu3p/TtUx +6r3XL3qfe8efut8555xzzjnnnHPOOef86aV+z3itX2//LOvnnLefC73nQK+v +Wk9vPMu+c84555xzzjnnnPNv+Oj42u+3eJY6bnP7yTnnnHPOOeecc845f5vX ++o3Ol22dnPN47z2Hos6ZLPvFOeecc84555xzzr/hq+bNtq7RfRiNc84555xz +zjnnnHPOOf+W136Pem9ezjmvxbPV8/Rs+8g555xzzjnnnHPOc3rv+Gz1Z9sf +zjnnnHPOOeecc84559/w2u9RXz0f5/w9Xjs3Wuc7df605uWcc84555xzzjnn +vMVL/bLVeXofSi1b3ZxzzjnnnHPOOeecc85z+Kr5ZuvgnN/vo+dGrZ0691rn +2VUX55xzzjnnnHPOOec3ea3VxmVbD+ecc84555xzzjnnnPM7vRQ/XQfnPK8/ +46vnHR2/y1f345xzzjnnnHPOOeff8N3znaq/1K913GwdnHPOOeecc84555xz +znmL/1f7dZIlOQoFAfD+t+5VbeI1ySAGRzJ2ss/gEBJZVWqt/dP2wzl/7r/1 +p+N767u89547nZdzzjnnnHPOOeecZ3nKOq39U/fHOeecc84555xzzjnn/Jte +6zc67tdr86SdC+f8uf/WR++B2blWeev9yTnnnHPOOeecc875znVmrzsrF+ec +c84555xzzjnnnHPe4rP7ldq/frX+KefCOV93vzytp3vrvlLycs4555xzzjnn +nPO9XupX69+6zqw8nHPOOeecc84555xzznmCl+q9/Xu91u/0uXDO1/vseyPd +T6/POeecc84555xzzrN89vhS/9r4tHPhnHPOOeecc84555xzzv/y2vMuP70+ +5/y81+6HU7la/fT6nHPOOeecc8455/wOT8nBOeecc84555xzzjnnnN/ktefZ +3puHc85H75NT7l7jnHPOOeecc8455395Sg7OOeecc84555xzzjnn/GZfvU6t +nd4/5/web71nTudKOS/OOeecc84555xznuEpOTjnnHPOOeecc84555zzL/ju +cZxz3uq1+2d3rpRz4ZxzzjnnnHPOOecZnpKDc84555xzzjnnnHPOOef1lpaP +c86fzpe2H84555xzzjnnnHOe6Sk5OOecc84555xzzjnnnPMveqnf0/lXzcs5 +563eOi4tN+ecc84555xzzjnP9JQcnHPOOeecc84555xzzvmbfHT87Pl61+Gc +8933Y62l5vw3Lu18Oeecc84555xzzt/qKTk455xzzjnnnHPOOeec8zf47vG9 +69TmSTlHzvk9/lsfva/S9vX0HFqfOeecc84555xzznmbp+TgnHPOOeecc845 +55xzzm/2Ur02vnWe1b5rHc55vv/WZ8/bOz7tfFrzlcal5Oacc84555xzzjm/ +zVNycM4555xzzjnnnHPOOec3e6ne23+11/qdPkfO+Xz/rZ/OMWvetHNu3Xdv +/7T9cM4555xzzjnnnJ/ylBycc84555xzzjnnnHPO+Zu99rzLa/1SzotzPv+7 +/1fffc/U8sz2tPNv/V1anznnnHPOOeecc86/6ik5OOecc84555xzzjnnnPM3 +e+15l9f6pZwX53z+vbPLn9ZHffd6rf50vpT3iXPOOeecc8455/y0p+TgnHPO +Oeecc84555xzzr/otefZvmsdzvk+T8lRaqfznb4PW8edPifOOeecc84555zz +dE/JwTnnnHPOOeecc84555zzss+a72kOznmut47blWP2vKu89lzz3nrKvjnn +nHPOOeecc85v85QcnHPOOeecc84555xzzjmve+255rNycM7v8d967/1Q6z+a +6zZvPYfavKf3wTnnnHPOOeecc36rp+TgnHPOOeecc84555xzzvk8L9VL43vX +qbXT++ecz/fT69/qs/txzjnnnHPOOeecf9VTcnDOOeecc84555xzzjnnfL6X ++qXl4ZzP99r3fyrX1/y2eTnnnHPOOeecc85TPSUH55xzzjnnnHPOOeecc87L +Xqr3zjs6T+86v75qXs75vHln5+Jz5/2tp+yPc84555xzzjnnfJen5OCcc845 +55xzzjnnnHPOebk+a73e8b312fNzzuu++rvmz/z0eM4555xzzjnnnPO3eEoO +zjnnnHPOOeecc84555zfO2/NR+spvwfnN3ip3vpdrcr1VZ913/XOzznnnHPO +Oeecc/5WT8nBOeecc84555xzzjnnnPP58/7WU/ZXaqvOgfMv++n1v+qz78On +83POOeecc84555zf7ik5OOecc84555xzzjnnnHNers9a7/T+Wr3W0vJyftKf +fl8p+/i6n16fc84555xzzjnnPN1TcnDOOeecc84555xzzjnnvH/crHnS/PT6 +nN/ks+4NvtdX/b6cc84555xzzjnnb/WUHJxzzjnnnHPOOeecc845H/fa821e +65eWl/MEL9V7+/M9Prsf55xzzjnnnHPO+ds9JQfnnHPOOeecc84555xzzsd9 +dr9UP70+54le+15O5eJ/+1fubc4555xzzjnnnPNZnpKDc84555xzzjnnnHPO +OefjXur3W0/JO+qn1+c80Ue/o9W5vu6j91jrPJxzzjnnnHPOOedf85QcnHPO +Oeecc84555xzzjnf56V+v/WUvKfXH8052v/p+vybXqqnfU88a33OOeecc845 +55zzWzwlB+ecc84555xzzjnnnHPOc732vMtnzVebf9Y6rX7qHPi3/fT6b/He +8z2dl3POOeecc8455/xWT8nBOeecc84555xzzjnnnPP3eO151HePO+1v2w9f +67/1Wr9dud7mp8dzzjnnnHPOOeecf9VTcnDOOeecc84555xzzjnnnPd6qaXl +fOq1/c9ed/d6fK3XWlreVO/9Lk7n5ZxzzjnnnHPOOX+bp+TgnHPOOeecc845 +55xzzjlv9dpzzZ/WZ/lonqfz1fz0ufA5vvo94X/XS+NP5+Wcc84555xzzjm/ +1VNycM4555xzzjnnnHPOOeec//rsfrO9t55yrrV6rX/reqPnxuf4rN/xq55+ +/3DOOeecc84555x/zVNycM4555xzzjnnnHPOOef8u356PH/mrW3VeP7/3nre +KXnT3P3DOeecc84555xznuUpOTjnnHPOOeecc84555xz/l2/bV7+zHvH1+ZJ +298tfnr9FG+9N3r7c84555xzzjnnnPO5npKDc84555xzzjnnnHPOOeff9bev +x9v8ad3v3NbvdK40995wzjnnnHPOOeec3+EpOTjnnHPOOeecc84555xz/n5/ ++3p8r5f61fqn7eP0+aXlOn1PpOTinHPOOeecc84553+3tHycc84555xzzjnn +nHPOOb/HS/XdOVo9JQff46V+t723o/tOy7Xrnjmdl3POOeecc84555zP8ZQc +nHPOOeecc84555xzzjl/v6fkKNXT8vGzXuuXlvfp+5/mrb/L7lycc84555xz +zjnn/Iyn5OCcc84555xzzjnnnHPO+f3eO25VjtF1T58fz/LR8Wn7OPX9Pc1V +6p+Wl3POOeecc84555zv8ZQcnHPOOeecc84555xzzjl/r5fqu3K0jjt9Tvxu +L7XT73/K+q3n5nvknHPOOeecc8455y0tLR/nnHPOOeecc84555xzzt/jteea +rx6Xck78G15ru9ZP/d4555xzzjnnnHPOOf+rpeXjnHPOOeecc84555xzzvl7 +vPY86r31lPPg/K922zqz5+Occ84555xzzjnn/K+Wlo9zzjnnnHPOOeecc845 +5+/32nPNe+cv9U85D857vNavdVzrfJxzzjnnnHPOOeecn/CUHJxzzjnnnHPO +Oeecc84556t81ry/9ZT9cT6jpeXnnHPOOeecc8455/yvlpaPc84555xzzjnn +nHPOOed8lp/OkXYe/B3e2ka/i7T9cs4555xzzjnnnPNvekoOzjnnnHPOOeec +c84555zzVX4qx2895Tx4hj9tKd/F7Fycc84555xzzjnnnLe0tHycc84555xz +zjnnnHPOOeezvVSftV7v+Kf12r74Hm+t945b5SnrlVra78s555xzzjnnnHPO +z3pKDs4555xzzjnnnHPOOeec8xSvPde8d/6n6/yrz5531fynvLU+a750T8lR +89Z67zjOOeecc84555xzfpen5OCcc84555xzzjnnnHPOOX+7l+qz19s1f+v6 +s/o9zfk0x9s8JUev9/6Ove9Vyj4555xzzjnnnHPO+d8tLR/nnHPOOeecc845 +55xzzvnbfdZ8tX5P12ldd9Y8p3+Xt3tKjtU++31zvpxzzjnnnHPOOednPCUH +55xzzjnnnHPOOeecc845z/JSv1N5+FxPyXGbP52vNu/q9TnnnHPOOeecc85v +9ZQcnHPOOeecc84555xzzjnnnPN1npLjdl81X+88aefCOeecc84555xzvtpT +cnDOOeecc84555xzzjnnnHPO93lKjq95qd+sdXrH9dZTzpFzzjnnnHPOOeff +85QcnHPOOeecc84555xzzjnnnPN5XqrvzsH7vNaervO039N5Oeecc84555xz +zkc9JQfnnHPOOeecc84555xzzjnnfJ6X6rtz8Dt81ny1Z84555xzzjnnnPNR +T8nBOeecc84555xzzjnnnHPOOZ/npfruHDzDa+/DqvV7x83KkXLunHPOOeec +c845n+cpOTjnnHPOOeecc84555xzzjnnz/1pnb/bf+u1fqvWXz1vaVza78E5 +55xzzjnnnPN2T8nBOeecc84555xzzjnnnHPOOZ/npfruHPzbXnsPV62fsn/O +Oeecc84555zP85QcnHPOOeecc84555xzzjnnnPNxL/UrtZTc/N3eO351rpRz +4ZxzzjnnnHPOeb+n5OCcc84555xzzjnnnHPOOeec93vvuFU5OP8/H30/V+f6 +9ZTz4pxzzjnnnHPOedlTcnDOOeecc84555xzzjnnnHPO+7133KocnP+f197D +U7lK3pp/9PtqnTflPDjnnHPOOeec8yRPycE555xzzjnnnHPOOeecc845n+8p +OTjv8dn9Rr227q5zqOXhnHPOOeecc86/4Ck5OOecc84555xzzjnnnHPOOed1 +rz2X2tN+nH/ZS+30988555xzzjnnnH/JU3JwzjnnnHPOOeecc84555xzzute +e675rBycv8lr30utja4/uu7TfXHOOeecc8455zd6Sg7OOeecc84555xzzjnn +nHPOed1rzzWflYPzN/nod7Q6V6+3fvcpeTnnnHPOOeec8x5PycE555xzzjnn +nHPOOeecc8457/dSvTbP6dycn/Tf+uj42blWue+fc84555xzzvkbPCUH55xz +zjnnnHPOOeecc8455/y5p+TgPNl/62//zmrPnHPOOeecc875DZ6Sg3POOeec +c84555xzzjnnnHNerpfG1/rP6sf5F/y3/tbv5vT6nHPOOeecc875iKfk4Jxz +zjnnnHPOOeecc84555yX66Xxtf6t69fqnPN6v9O5Wv30+pxzzjnnnHPO+Yin +5OCcc84555xzzjnnnHPOOeectz+P+uz5OP+i176vU7me+un1Oeecc84555zz +vzwlB+ecc84555xzzjnnnHPOOee87LPme5qDc1722nd3Ktevn16fc84555xz +zjkf8ZQcnHPOOeecc84555xzzjnnnPO6155LrXUc53y/714/bf+cc84555xz +znmLp+TgnHPOOeecc84555xzzjnnnPd7qb47B+d8vde+99b5VufuHde7r5Tf +g3POOeecc875Xk/JwTnnnHPOOeecc84555xzzjmve+251FrHcc7f57/11ntj +VZ7Z92Cp1fbLOeecc8455/wuT8nBOeecc84555xzzjnnnHPO+Rd91fhTeTjn +ed7b0vLvug9n5eCcc84555xzvsZTcnDOOeecc84555xzzjnnnHP+JS/Va+Nb +56mNn5WHc77PZ817ev30cyv1S9kP55xzzjnnnH/VU3JwzjnnnHPOOeecc845 +55xzzs+tv2sdznm7p82bdj6r7rm03JxzzjnnnHPOs3JwzjnnnHPOOeecc845 +55xzztufZ3tvHs75/O/vX33Xd73a08659fxLnpabc84555xzzr/mKTk455xz +zjnnnHPOOeecc8455+3Ps33XOpzzfes9rafvb/f9l5abc84555xzzr/mKTk4 +55xzzjnnnHPOOeecc84552Vfvc7s+Tjn5bb7u5497657rFSffb+19uOcc845 +55xzftZTcnDOOeecc84555xzzjnnnHPO+7133KocnPN+X73eqnlPn9Psc2i9 +L1POg3POOeecc86/6ik5OOecc84555xzzjnnnHPOOefzvFTfnYNzXq6vmre3 +/nU/PZ5zzjnnnHPOeZun5OCcc84555xzzjnnnHPOOeecr/NSa50nbT+c3+il +euv3Nntdvme933rKvjnnnHPOOef8Nk/JwTnnnHPOOeecc84555xzzjmv+9N+ +T+uzc3LO6y0t79t89++bsm/OOeecc845v81TcnDOOeecc84555xzzjnnnHPO +c8aXWm18bZ6U8+U8wWd9d3zMd91XT/NwzjnnnHPOOc/KwTnnnHPOOeecc845 +55xzzvmXvFSftd6svLvW4fzNPvrdrb4neNtz67yt66bsm3POOeecc85v85Qc +nHPOOeecc84555xzzjnnnH/Ra8+94097rV9aXs53+NPvqNRS9vc2n/W7nN4H +55xzzjnnnL/NU3JwzjnnnHPOOeecc84555xzzsv13v6n/PT6nCd7qe57uttP +r88555xzzjnnX/GUHJxzzjnnnHPOOeecc84555zzuteeU73WLy0v5zv99Pq8 +z2f345xzzjnnnHPe5ik5OOecc84555xzzjnnnHPOOeflemn86bytfnp9zk/6 +6PeyOhf/f599j7XOzznnnHPOOef8b0/JwTnnnHPOOeecc84555xzzjkv++n1 +V/np9Tnf4aPfxepc/G9fdc+l7I9zzjnnnHPOb/OUHJxzzjnnnHPOOeecc845 +55zzca89p/rp9Tnf6aW67yPLZ/8erfNzzjnnnHPOOf/bU3JwzjnnnHPOOeec +c84555xzzud77XmXn16f80SvfS+ncvE2L7XUe5hzzjnnnHPOb/eUHJxzzjnn +nHPOOeecc84555zzfV57nu271qmt/3R8yu/H7/Tf+qr3la/13fcn55xzzjnn +nPOsHJxzzjnnnHPOOeecc84555zzXK8913xWjlXzzT6H1Tn4XT77vZ89L/9/ +3/37cs4555xzzjn/21NycM4555xzzjnnnHPOOeecc87v91K9Nn5VntVe209p +ntO5eYaPvj98js+6j07vg3POOeecc86/4ik5OOecc84555xzzjnnnHPOOeff +8d6Wlr/Va8+940dz8Ewf/X1X5/qKPz3/Vbk455xzzjnnnP+/p+TgnHPOOeec +c84555xzzjnnnN/rs/vVxo/Wn/rTfrPynNo/X+O/9dXvD3/mo/cC55xzzjnn +nPNnnpKDc84555xzzjnnnHPOOeecc57npfqs9Vbvo3f8qfOePe/p94Y/813v +CW975pxzzjnnnHOe4Sk5OOecc84555xzzjnnnHPOOefnvFRfneP0vtO9VK/1 +b13v1O/O2+p+n2c+Oj5tH5xzzjnnnHPOs3JwzjnnnHPOOeecc84555xzzs/7 +29f7qo+OT9vHV3z278j/7vdbT8nLOeecc8455/zvlpaPc84555xzzjnnnHPO +Oeeccz7PS/XdOWrrnz6nr3vv+NT36laf9bt81VvPk3POOeecc875XZ6Sg3PO +Oeecc84555xzzjnnnHO+39Ny/KunnRPvq69a/yue/r2m+Ox+nHPOOeecc86z +PSUH55xzzjnnnHPOOeecc84553y+p+So+W89LR8f81K/1vfgq957nvxvP70+ +55xzzjnnnPM5npKDc84555xzzjnnnHPOOeeccz7fa8+7cvSun3J+/JmX+s3u +n7bv2d9tqaXkfeq9v+/pvJxzzjnnnHPOz3hKDs4555xzzjnnnHPOOeecc855 +rq8aXxqXsm++12f3e6ufXv/0e5CWl3POOeecc875Hk/JwTnnnHPOOeecc845 +55xzzjnf57Xnmq8el3JOPNtr/dLyPt3f7vVT7x/OOeecc84559/0lBycc845 +55xzzjnnnHPOOeec8/W+ep3e+unz4O/0Un30vU3z0+vXcpX6peXlnHPOOeec +c36Xp+TgnHPOOeecc84555xzzjnnnK/3Ur00vned1nk5T/Jav9S8u9cfPT/O +Oeecc84553yGp+TgnHPOOeecc84555xzzjnnnL/fa8+cJ/lo25Vr9jpp5885 +55xzzjnnnP/V0vJxzjnnnHPOOeecc84555xzzu/12fOm7Y/znjZ7ndnfU9p5 +cs4555xzzjnnf7W0fJxzzjnnnHPOOeecc84555zze7xU353j1Hqc9/iplnYO +nHPOOeecc855i6fk4JxzzjnnnHPOOeecc84555y/x0/l+K2nnAfnPT6rpe2L +c84555xzzjl/4ik5OOecc84555xzzjnnnHPOOefv9VJ99nqt63Ke4Ktb2n45 +55xzzjnnnPMnnpKDc84555xzzjnnnHPOOeecc/49nzVfrf2O653n9DnxO/xp +/el7v3s855xzzjnnnHO+01NycM4555xzzjnnnHPOOeecc875r5f6zZpnlv/W +U86Pt/nTlvJdeM8555xzzjnnnL/ZU3JwzjnnnHPOOeecc84555xzzvlqXz3v +v3rr+rV5eue/3Uv9Ws99dJ2n8+32lBw1b21puTnnnHPOOeecZ3pKDs4555xz +zjnnnHPOOeecc8453+Wl+tP+vTlGvZand/7f+qr5Z80z+ju+xVNyjHprvdQv +bT+cc84555xzzvd4Sg7OOeecc84555xzzjnnnHPOOU/3Ur9Z8/Su93T+1vrT ++Wet+1VPyXF6/7O/07R9cs4555xzzjn/21NycM4555xzzjnnnHPOOeecc845 +3+ul+qk8vM1TcqT5rvfZ78Q555xzzjnnZzwlB+ecc84555xzzjnnnHPOOeec +c87L9d05vuq18x9dZ/b8KefFOeecc84557s8JQfnnHPOOeecc84555xzzjnn +nHPO83J8zUv9Vq3/NI/3hnPOOeecc/4VT8nBOeecc84555xzzjnnnHPOOeec +83J9dw6+xmu/76p1Zu2n1C/lfDnnnHPOOefv9ZQcnHPOOeecc84555xzzjnn +nHPOOa+3tHy8z2u/82i95qvmbfXWPJxzzjnnnHNe8pQcnHPOOeecc84555xz +zjnnnHPOOS/Xd+fgWf5bn/2ejI6b/Z5zzjnnnHPOeclTcnDOOeecc84555xz +zjnnnHPOOee8XN+dg7/TZ/fb9f6v2qfvjXPOOeec83s8JQfnnHPOOeecc845 +55xzzjnnnHP+RS/16+3PeYv/1mv9am123qf7eepP83DOOeecc87XeUoOzjnn +nHPOOeecc84555xzzjnn/EveO25VDv5tn/0ezspV8t3z7s7BOeecc845r//7 +/HQOzjnnnHPOOeecc84555xzzjnn/Mv+tM75F7zWUvLWnjnnnHPOOefP/z+Q +lo9zzjnnnHPOOeecc84555xzzjl/s6fk4DzBe8fvyvXUT6/POeecc875Gzwl +B+ecc84555xzzjnnnHPOOeecc/4lL9Vr85zOzfkO/62Pjp+d66n7njnnnHPO +OR/3lBycc84555xzzjnnnHPOOeecc875l7x33KocnCf5rHln51rlp9ZfXeec +c84553yFp+TgnHPOOeecc84555xzzjnnnHPOv+Sleq2dzs35Ca99L739Z+V6 +6r3jVuWYvf7pc+Wcc8455+/0lBycc84555xzzjnnnHPOOeecc875l7xU352D +cz7+Pc7OtWre1f5bT8vHOeecc87f4Sk5OOecc84555xzzjnnnHPOOeec8zd7 +7bnUWsdxzu/1Whu9L2b5rbk555xzzvm7PCUH55xzzjnnnHPOOeecc84555xz +frPPmq/W7/Q+OefzfPQeSMk1Os/THJxzzjnn/JuekoNzzjnnnHPOOeecc845 +55xzzjl/g9eea947P+c832fNOzvXKq/lb62f3gfnnHPOOc/ylBycc84555xz +zjnnnHPOOeecc875zT5rvlq/0/vknPf7rvvhdnffcc4555zzvzwlB+ecc845 +55xzzjnnnHPOOeecc/5G7x23Kgfn/JzPmnd2rjRfdW6cc8455/wdnpKDc845 +55xzzjnnnHPOOeecc845/4Kn5OCcn3f3Sp+fXp9zzjnnnJ/1lBycc84555xz +zjnnnHPOOeecc875Tf60X2lcrX/K/jnn5+6BWblu8dH7l3POOeecv8tTcnDO +Oeecc84555xzzjnnnHPOOec3+dN+q9flnH/PT6+/y0+vzznnnHPOz3hKDs45 +55xzzjnnnHPOOeecc8455/wGX71OrZ3eP+f8nNfujdF6urfelyl5Oeecc875 +Gk/JwTnnnHPOOeecc84555xzzjnnnN/ss+ar9Tu9T875eW+tr1r/tJ9en3PO +Oeecn/GUHJxzzjnnnHPOOeecc84555xzzvkNvnqdWju9f875Pf70/knZx6+f +Xp9zzjnnnJ/xlBycc84555xzzjnnnHPOOeecc875zT5rvqc5OOd81Gv30qlc +v356fc4555xzfsZTcnDOOeecc84555xzzjnnnHPOOedv8qd1zjlP8dH7b1Wu +lHMptV05ev++pJ0b55xzzvkt/+7inHPOOeecc84555xzzjnnnHPOv+QpOTjn +/LTXWm2+lBynvXVfu86Tc84553z3vyPT8nHOOeecc84555xzzjnnnHPOOecn +vFSfvV6pfnr/nHOe4r0tLf/pc3v69661P+ecc8757n8XpuXjnHPOOeecc845 +55xzzjnnnHPOV3qp3jtv7/q968zKyTnnt3lvS8t/i5fqq/4Ocs4555w//Xdh +Wj7OOeecc84555xzzjnnnHPOOed8pZfqtfFP1++tj87DOedpfmp82jns9lW/ +R22dlP1zzjnn/H5PycE555xzzjnnnHPOOeecc84555zf4KvXqbXT++ec85rv +vifT573F0+fjnHPOOU/JwTnnnHPOOeecc84555xzzjnnnCd7yvqlfmnnxTl/ +j7feS6tz7Fov9e/AbX/nZs/HOeecc56Sg3POOeecc84555xzzjnnnHPOOT/h +pXpv/9Ve63f6HDnn7/ff+ukcu9Yb/XuxKsdsn3XOKfvhnHPO+Xs9JQfnnHPO +Oeecc84555xzzjnnnHOe6LXnXX56fc75d/y3npKjt37678VbvFT/yv4555xz +nuMpOTjnnHPOOeecc84555xzzjnnnPMbfPU6tX6n9885v99r90/KvfO0ftqf +3v+1cbvPefa6nHPOOedP/72Ulo9zzjnnnHPOOeecc84555xzzjlP9NrzqPeu +yznno/5bT813OscuTz1nvw/nnHPOUzwlB+ecc84555xzzjnnnHPOOeecc36z +z5rvaQ7OOa957f757bc636p5v+Kr/87szsc555xz7t+NnHPOOeecc84555xz +zjnnnHPO+X4v1Xfn4Jx/15/Odzrf7PV4n+/6/XetxznnnPN7PSUH55xzzjnn +nHPOOeecc84555xz/gUvtdZ5avO29uec89Zxq+adNY6v9ZQcJU/JwTnnnPN9 +/349nYNzzjnnnHPOOeecc84555xzzjlP8lJ9dN7e+UfXeeqnz51zft57x51a +l6/1tN/p9Hlwzjnn/Lyn5OCcc84555xzzjnnnHPOOeecc85PeKk+a73e8a1t +dy7OOa+1tLz8ma/++1jy1vdvND/nnHPO7/WUHJxzzjnnnHPOOeecc84555xz +zvkOf9t6veNr86T8Tpzz/PtqVy6e6bv+vo3mSTknzjnnnM//98HpHJxzzjnn +nHPOOeecc84555xzzvlJnzXvb331Pmr9Wvc5Oxfn/D7fdS/xOz11XNo5cc45 +53ydp+TgnHPOOeecc84555xzzjnnnHPOV3qpXpvnaY7T+661p/045/f6b333 +PcPv9FXv3+w655xzzt/nKTk455xzzjnnnHPOOeecc84555zznT67nra/0fMo +9UvLyzl/7qfHc560Puecc87zPSUH55xzzjnnnHPOOeecc84555xznuSn19/t +tX5peTnnz7113Oj40Vz8Wz76d4lzzjnn3/OUHJxzzjnnnHPOOeecc84555xz +zvlJn93vNq/1S8vLOV/noy1tHzzLT4/nnHPO+f2ekoNzzjnnnHPOOeecc845 +55xzzjlP9FK/33pK3lEv1Xv7c87v9996rd+uXPxu3/1+cs455/x9npKDc845 +55xzzjnnnHPOOeecc845P+mlfq3zpOxj1Gv90vJyzuf7rvuEv9Of/h1t9dZ1 +Oeecc/4+T8nBOeecc84555xzzjnnnHPOOeec3+S157f46fU55/t89v0wKxe/ +03etl7ZvzjnnnK/zlBycc84555xzzjnnnHPOOeecc875TV7q91tPyVvz0+tz +zvd767jR8aO5+J2+6+9Oqd76d5pzzjnn93pKDs4555xzzjnnnHPOOeecc845 +5/zNXns+7bV+aXk55/u91tLy8jPe+vfjaf2fp+ybc8455/v/PZqWj3POOeec +c84555xzzjnnnHPOOb/ZT6//1E+vzzk/77X74VQu/i4/vT7nnHPO8z0lB+ec +c84555xzzjnnnHPOOeecc/4lL9VLbXWu0+vXcv3Wa8+1eXrX4/xL/lt/ep+k +7Y+f8dn9OOecc/49T8nBOeecc84555xzzjnnnHPOOeec87rXnke91mbnXrXO +bC+1f/1r49L2w/lfPvp9+A54S1v1HnLOOef8O56Sg3POOeecc84555xzzjnn +nHPOOefzvfbc2kbnSTmHXm/db+0cUvbDeY/XWu99kLY//sx3/d6r5uWcc875 +vZ6Sg3POOeecc84555xzzjnnnHPOOec5XmppOXf56Pmdzs35TG+tr1qfZ/jq +e+/0/jjnnHOe6yk5OOecc84555xzzjnnnHPOOeecc77PS/1a53taf4vv2n+p +fnr//Bs++r6uzsXP+Oq/C6f3xznnnPNcT8nBOeecc84555xzzjnnnHPOOeec +8/l+evys+i6fne9pnpq3/l6rc/Bv+G+91q/W0vbH53qpjd7DnHPOOecpOTjn +nHPOOeecc84555xzzjnnnHNe97evN3vc6nVH5x8dX/PZ58l5i9daWl4+x0/d +c5xzzjn/rqfk4JxzzjnnnHPOOeecc84555xzznm5vjvHqfVOe6mtmn/3ftLO +m9/t3rt3uXuHc8455+mekoNzzjnnnHPOOeecc84555xzzjn/oqfkKHlKjq96 +77jaPKM5vC/8/7z1fSu1lH183WfdP7PGc84555z7dwbnnHPOOeecc84555xz +zjnnnHOe46X67hyt/ltPy8f/9tb2tveW7/Hfeut7mLaPr/rod706F+ecc855 +raXl45xzzjnnnHPOOeecc84555xzzm/23nGrcjz133paPj7mq+ZrbWnnwce8 +1G675/jfbfbfO84555zzp/9OScvHOeecc84555xzzjnnnHPOOeec3+yl+u4c +o56Sg2f77PGl/mn7/rrvfk94n58ezznnnHM+21NycM4555xzzjnnnHPOOeec +c84552/wUr/e/mn+W0/LxzO9d3zv98OzvdbS8n7FZ/fjnHPOOd/lKTk455xz +zjnnnHPOOeecc84555zzm7133Kocq7x1XFpuftZr/Va9b63j+RoffR/4XG/9 +HUotZR+cc84556WWlo9zzjnnnHPOOeecc84555xzzjm/wXvHrcqxyn/rafn4 +u/30eN7nfoe9Pnr+q3NxzjnnnM/2lBycc84555xzzjnnnHPOOeecc875G71U +352j5rWcv/1ScvNveK1f73eWtr+3+ejvyP9uT8+fc8455/x2T8nBOeecc845 +55xzzjnnnHPOOeecv9lL/WbNM8ufzpdy3py3tNp7uyvX27z3/Pn/++x+nHPO +Oee3e0oOzjnnnHPOOeecc84555xzzjnn/A1eex713nV7+7XmqHnK78D5X631 +Oxgdl7bv0/dgqaXkPeWz+3HOOeecv91TcnDOOeecc84555xzzjnnnHPOOec3 ++6n1a/1q41L3xXmCj45P28fp80vLdfo8ZvXjnHPOOf+ap+TgnHPOOeecc845 +55xzzjnnnHPO3+y159neW085J85v9tHxaftYdR6710/x2e8L55xzzvlXPSUH +55xzzjnnnHPOOeecc84555xz/iUv1Uvje/vPqnPOn3trfdX6aX56/VXeem9z +zjnnnPMxT8nBOeecc84555xzzjnnnHPOOeec833eO/63nrIPzm/21vqq9VP3 +fdp7c5/OyznnnHP+FU/JwTnnnHPOOeecc84555xzzjnnnPP5ftu8nPOyj7bU +faTkcr9xzjnnnN/hKTk455xzzjnnnHPOOeecc84555xzPs9L9d05Tq3H+Zd8 +tKXm3XUPpf2OnHPOOef8b0/JwTnnnHPOOeecc84555xzzjnnnPN5XqrvzlFb +//Q5cf5FH223reOe4Zxzzjl/l6fk4JxzzjnnnHPOOeecc84555xzzvk8L9V3 +5xhd//T5cc7va2nnxjnnnHPO53pKDs4555xzzjnnnHPOOeecc84555zv81M5 +WselnBPnvP49725p58A555xzzvd4Sg7OOeecc84555xzzjnnnHPOOeecr/dS +vTS+t/+o/9ZPnxPnPLelnQ/nnHPOOd/jKTk455xzzjnnnHPOOeecc84555xz +ft5rz7O9t9XmaV0n5bw5T/LbW9p5cs4555zzuZ6Sg3POOeecc84555xzzjnn +nHPOOefnfPU6tX6n9t/aTv8+nI94rdXGpX9nT1va78U555xzzv/2lBycc845 +55xzzjnnnHPOOeecc84557++e97SuJTz4N/wWr/WcU9zrNpPqaXkKLW094Rz +zjnn/GuekoNzzjnnnHPOOeecc84555xzzjnn/NdP5fitr5p3dB6e6bXWO673 +PUr11nZr7tJ8afvhnHPOOb/dU3JwzjnnnHPOOeecc84555xzzjnnnD/13vGt +9dH5Z/lvffa8pX5PzzflvEbrT9fvbWnnuOs9e4uPtrd8d5xzzjnn/l3JOeec +c84555xzzjnnnHPOOeecc97mteeat7an68zyUps9f23c0/G9eUbnaZ13dD+t +/b7mrS0t9679rzrPp+twzjnnnOf4f7/KwZE= + "], {{0, 0}, {501, 501}}, {0, 1}], Frame -> Automatic, + FrameLabel -> {None, None}, FrameTicks -> {{None, None}, {None, None}}, + GridLinesStyle -> Directive[ + GrayLevel[0.5, 0.4]], + Method -> { + "DefaultBoundaryStyle" -> Automatic, "DefaultPlotStyle" -> Automatic}], + FormBox[ + FormBox[ + TemplateBox[{"\"Divergent\"", "1", + RowBox[{ + RowBox[{"-", + RowBox[{ + FractionBox["1", "2"]}]}], "-", + FractionBox[ + RowBox[{"\[ImaginaryI]", " ", + SqrtBox["3"]}], "2"]}], + RowBox[{ + RowBox[{"-", + RowBox[{ + FractionBox["1", "2"]}]}], "+", + FractionBox[ + RowBox[{"\[ImaginaryI]", " ", + SqrtBox["3"]}], "2"]}]}, "SwatchLegend", + DisplayFunction -> (FormBox[ + StyleBox[ + StyleBox[ + PaneBox[ + TagBox[ + GridBox[{{ + TagBox[ + GridBox[{{ + GraphicsBox[{ + Directive[ + EdgeForm[ + Directive[ + Opacity[0.3], + GrayLevel[0]]], + PointSize[0.5], + AbsoluteThickness[1.6], + RGBColor[0., 0., 0.]], + RectangleBox[{0, 0}, {10, 10}, "RoundingRadius" -> 0]}, + AspectRatio -> Full, ImageSize -> {10, 10}, + PlotRangePadding -> None, ImagePadding -> Automatic, + BaselinePosition -> (Scaled[0.1] -> Baseline)], #}, { + GraphicsBox[{ + Directive[ + EdgeForm[ + Directive[ + Opacity[0.3], + GrayLevel[0]]], + PointSize[0.5], + AbsoluteThickness[1.6], + RGBColor[1., 0., 0.]], + RectangleBox[{0, 0}, {10, 10}, "RoundingRadius" -> 0]}, + AspectRatio -> Full, ImageSize -> {10, 10}, + PlotRangePadding -> None, ImagePadding -> Automatic, + BaselinePosition -> (Scaled[0.1] -> Baseline)], #2}, { + GraphicsBox[{ + Directive[ + EdgeForm[ + Directive[ + Opacity[0.3], + GrayLevel[0]]], + PointSize[0.5], + AbsoluteThickness[1.6], + RGBColor[0., 1., 0.]], + RectangleBox[{0, 0}, {10, 10}, "RoundingRadius" -> 0]}, + AspectRatio -> Full, ImageSize -> {10, 10}, + PlotRangePadding -> None, ImagePadding -> Automatic, + BaselinePosition -> (Scaled[0.1] -> Baseline)], #3}, { + GraphicsBox[{ + Directive[ + EdgeForm[ + Directive[ + Opacity[0.3], + GrayLevel[0]]], + PointSize[0.5], + AbsoluteThickness[1.6], + RGBColor[0., 0., 1.]], + RectangleBox[{0, 0}, {10, 10}, "RoundingRadius" -> 0]}, + AspectRatio -> Full, ImageSize -> {10, 10}, + PlotRangePadding -> None, ImagePadding -> Automatic, + BaselinePosition -> (Scaled[0.1] -> Baseline)], #4}}, + GridBoxAlignment -> { + "Columns" -> {Center, Left}, "Rows" -> {{Baseline}}}, + AutoDelete -> False, + GridBoxDividers -> { + "Columns" -> {{False}}, "Rows" -> {{False}}}, + GridBoxItemSize -> {"Columns" -> {{All}}, "Rows" -> {{All}}}, + GridBoxSpacings -> { + "Columns" -> {{0.5}}, "Rows" -> {{0.5}}}], "Grid"]}}, + GridBoxAlignment -> {"Columns" -> {{Left}}, "Rows" -> {{Top}}}, + AutoDelete -> False, + GridBoxItemSize -> { + "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, + GridBoxSpacings -> {"Columns" -> {{1}}, "Rows" -> {{0}}}], + "Grid"], Alignment -> Left, AppearanceElements -> None, + ImageMargins -> {{5, 5}, {5, 5}}, ImageSizeAction -> + "ResizeToFit"], LineIndent -> 0, StripOnInput -> False], { + FontFamily -> "Arial"}, Background -> Automatic, StripOnInput -> + False], TraditionalForm]& ), + InterpretationFunction :> (RowBox[{"SwatchLegend", "[", + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{"Directive", "[", + InterpretationBox[ + ButtonBox[ + TooltipBox[ + GraphicsBox[{{ + GrayLevel[0], + RectangleBox[{0, 0}]}, { + GrayLevel[0], + RectangleBox[{1, -1}]}, { + RGBColor[0., 0., 0.], + RectangleBox[{0, -1}, {2, 1}]}}, AspectRatio -> 1, Frame -> + True, FrameStyle -> RGBColor[0., 0., 0.], FrameTicks -> + None, PlotRangePadding -> None, ImageSize -> + Dynamic[{ + Automatic, 1.35 CurrentValue["FontCapHeight"]/ + AbsoluteCurrentValue[Magnification]}]], + "RGBColor[0., 0., 0.]"], Appearance -> None, + BaseStyle -> {}, BaselinePosition -> Baseline, + DefaultBaseStyle -> {}, ButtonFunction :> + With[{Typeset`box$ = EvaluationBox[]}, + If[ + Not[ + AbsoluteCurrentValue["Deployed"]], + SelectionMove[Typeset`box$, All, Expression]; + FrontEnd`Private`$ColorSelectorInitialAlpha = 1; + FrontEnd`Private`$ColorSelectorInitialColor = + RGBColor[0., 0., 0.]; + FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; + MathLink`CallFrontEnd[ + FrontEnd`AttachCell[Typeset`box$, + FrontEndResource["RGBColorValueSelector"], { + 0, {Left, Bottom}}, {Left, Top}, + "ClosingActions" -> { + "SelectionDeparture", "ParentChanged", + "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> + Automatic, Method -> "Preemptive"], + RGBColor[0., 0., 0.], Editable -> False, Selectable -> + False], "]"}], ",", + RowBox[{"Directive", "[", + InterpretationBox[ + ButtonBox[ + TooltipBox[ + GraphicsBox[{{ + GrayLevel[0], + RectangleBox[{0, 0}]}, { + GrayLevel[0], + RectangleBox[{1, -1}]}, { + RGBColor[1., 0., 0.], + RectangleBox[{0, -1}, {2, 1}]}}, AspectRatio -> 1, Frame -> + True, FrameStyle -> RGBColor[0.6666666666666667, 0., 0.], + FrameTicks -> None, PlotRangePadding -> None, ImageSize -> + Dynamic[{ + Automatic, 1.35 CurrentValue["FontCapHeight"]/ + AbsoluteCurrentValue[Magnification]}]], + "RGBColor[1., 0., 0.]"], Appearance -> None, + BaseStyle -> {}, BaselinePosition -> Baseline, + DefaultBaseStyle -> {}, ButtonFunction :> + With[{Typeset`box$ = EvaluationBox[]}, + If[ + Not[ + AbsoluteCurrentValue["Deployed"]], + SelectionMove[Typeset`box$, All, Expression]; + FrontEnd`Private`$ColorSelectorInitialAlpha = 1; + FrontEnd`Private`$ColorSelectorInitialColor = + RGBColor[1., 0., 0.]; + FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; + MathLink`CallFrontEnd[ + FrontEnd`AttachCell[Typeset`box$, + FrontEndResource["RGBColorValueSelector"], { + 0, {Left, Bottom}}, {Left, Top}, + "ClosingActions" -> { + "SelectionDeparture", "ParentChanged", + "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> + Automatic, Method -> "Preemptive"], + RGBColor[1., 0., 0.], Editable -> False, Selectable -> + False], "]"}], ",", + RowBox[{"Directive", "[", + InterpretationBox[ + ButtonBox[ + TooltipBox[ + GraphicsBox[{{ + GrayLevel[0], + RectangleBox[{0, 0}]}, { + GrayLevel[0], + RectangleBox[{1, -1}]}, { + RGBColor[0., 1., 0.], + RectangleBox[{0, -1}, {2, 1}]}}, AspectRatio -> 1, Frame -> + True, FrameStyle -> RGBColor[0., 0.6666666666666667, 0.], + FrameTicks -> None, PlotRangePadding -> None, ImageSize -> + Dynamic[{ + Automatic, 1.35 CurrentValue["FontCapHeight"]/ + AbsoluteCurrentValue[Magnification]}]], + "RGBColor[0., 1., 0.]"], Appearance -> None, + BaseStyle -> {}, BaselinePosition -> Baseline, + DefaultBaseStyle -> {}, ButtonFunction :> + With[{Typeset`box$ = EvaluationBox[]}, + If[ + Not[ + AbsoluteCurrentValue["Deployed"]], + SelectionMove[Typeset`box$, All, Expression]; + FrontEnd`Private`$ColorSelectorInitialAlpha = 1; + FrontEnd`Private`$ColorSelectorInitialColor = + RGBColor[0., 1., 0.]; + FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; + MathLink`CallFrontEnd[ + FrontEnd`AttachCell[Typeset`box$, + FrontEndResource["RGBColorValueSelector"], { + 0, {Left, Bottom}}, {Left, Top}, + "ClosingActions" -> { + "SelectionDeparture", "ParentChanged", + "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> + Automatic, Method -> "Preemptive"], + RGBColor[0., 1., 0.], Editable -> False, Selectable -> + False], "]"}], ",", + RowBox[{"Directive", "[", + InterpretationBox[ + ButtonBox[ + TooltipBox[ + GraphicsBox[{{ + GrayLevel[0], + RectangleBox[{0, 0}]}, { + GrayLevel[0], + RectangleBox[{1, -1}]}, { + RGBColor[0., 0., 1.], + RectangleBox[{0, -1}, {2, 1}]}}, AspectRatio -> 1, Frame -> + True, FrameStyle -> RGBColor[0., 0., 0.6666666666666667], + FrameTicks -> None, PlotRangePadding -> None, ImageSize -> + Dynamic[{ + Automatic, 1.35 CurrentValue["FontCapHeight"]/ + AbsoluteCurrentValue[Magnification]}]], + "RGBColor[0., 0., 1.]"], Appearance -> None, + BaseStyle -> {}, BaselinePosition -> Baseline, + DefaultBaseStyle -> {}, ButtonFunction :> + With[{Typeset`box$ = EvaluationBox[]}, + If[ + Not[ + AbsoluteCurrentValue["Deployed"]], + SelectionMove[Typeset`box$, All, Expression]; + FrontEnd`Private`$ColorSelectorInitialAlpha = 1; + FrontEnd`Private`$ColorSelectorInitialColor = + RGBColor[0., 0., 1.]; + FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; + MathLink`CallFrontEnd[ + FrontEnd`AttachCell[Typeset`box$, + FrontEndResource["RGBColorValueSelector"], { + 0, {Left, Bottom}}, {Left, Top}, + "ClosingActions" -> { + "SelectionDeparture", "ParentChanged", + "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> + Automatic, Method -> "Preemptive"], + RGBColor[0., 0., 1.], Editable -> False, Selectable -> + False], "]"}]}], "}"}], ",", + RowBox[{"{", + RowBox[{#, ",", #2, ",", #3, ",", #4}], "}"}], ",", + RowBox[{"LegendMarkers", "\[Rule]", "Automatic"}], ",", + RowBox[{"LabelStyle", "\[Rule]", + RowBox[{"{", "}"}]}], ",", + RowBox[{"LegendLayout", "\[Rule]", "\"Column\""}]}], "]"}]& ), + Editable -> True], TraditionalForm], TraditionalForm]}, + "Legended", + DisplayFunction->(GridBox[{{ + TagBox[ + ItemBox[ + PaneBox[ + TagBox[#, "SkipImageSizeLevel"], Alignment -> {Center, Baseline}, + BaselinePosition -> Baseline], DefaultBaseStyle -> "Labeled"], + "SkipImageSizeLevel"], + ItemBox[#2, DefaultBaseStyle -> "LabeledLabel"]}}, + GridBoxAlignment -> {"Columns" -> {{Center}}, "Rows" -> {{Center}}}, + AutoDelete -> False, GridBoxItemSize -> Automatic, + BaselinePosition -> {1, 1}]& ), + Editable->True, + InterpretationFunction->(RowBox[{"Legended", "[", + RowBox[{#, ",", + RowBox[{"Placed", "[", + RowBox[{#2, ",", "After"}], "]"}]}], "]"}]& )]], "Output", + CellChangeTimes->{3.6595585246496677`*^9}] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"newtonplot", "[", + RowBox[{ + RowBox[{"Function", "[", + RowBox[{"x", ",", + RowBox[{ + SuperscriptBox["x", "4"], "-", "1"}]}], "]"}], ",", "2", ",", "401", + ",", "40", ",", "0.1"}], "]"}]], "Input", + CellChangeTimes->{ + 3.6641612785202837`*^9, {3.6641613500474806`*^9, 3.6641613529304647`*^9}}], + +Cell[BoxData[ + TemplateBox[{GraphicsBox[ + RasterBox[CompressedData[" +1:eJzs+e2N9LiyMFqei7FkLGkfxoQB7u+x5XpYJqQJgxcbAnrHqagglaRISSuA +RjUXKYpJ8Ut6/t//3//f/+f//n/9z//8z//zf/3nv//z/3/Hzz//+fv551o/ +4hPyf/75Pb+3POcjvHecx3qycb9q3nHOOeecc84555xzzjnnnHPOOX+WH/FJ +yp2tP6uH82885lfjNiu/at5V7WuN2e3s7c/Ms3WG8xVerTej90HOOeecc845 +55xzzjnnnHPOOefv8CNi/idcl9UT05yv8JjfOp5j/ux5l0XWnrP90Fp/1c7Y +jqv6n/MrPKYrH7Uurd73Oeecc84555xzzjnnnHPOOeec9/kRn5D/88/v+Zln +9WRetYPzKzzmV+O2d/xn865qT4ze+Ti6H3rb07rOZN77ezmf6d+O5975uNs5 +gXPOOeecc84555xzzjnnnHPO+Rw/4sjPPKYrz+4b05yv8Jg/ejxXkdUf8zO/ +qh++raf3d3G+wqt5c3Z96F03Vp8HOOecc84555xzzjnnnHPOOeecn/Mjjvze +euL1MT96Vk9VL+crPebH8dx6fW89vd77u3rrqdaBb+/L+U7euk/F/GoeZeVH +7cucc84555xzzjnnnHPOOeecc87XekzH+ITrforrW8v3tofzHbwa/1n5bD7G +enrve9Z7141v689i9PrW207Oz3jvPK3K73Ie4JxzzjnnnHPOOeecc84555xz +vocf8UnKnS3P+QwfNf6zyMrPbmfVvjjfsvnY61n9mbf24xGr1jHOv/GYbt0f +d9vfOeecc84555xzzjnnnHPOOeecr/UjYv7nn9//xuD8G589zrPoHf+Zj+qH +rP6snb2e1d/rZ39XjOx5reof/k6P6dHjf/X+zjnnnHPOOeecc84555xzzjnn +/Bo/4sjPPKYrj/lZfZz/FXE8VeO2qu+I2eM/89n9s8pH/67e8r3jhPMWr8bv +2XnRe1/OOeecc84555xzzjnnnHPOOed7ekzH8lm5T1Hf8bf3vpy3eMyP4631 ++qx8r2ft4X97tf60rmNVtI4Tznu8dz+t1rmz9+Wcc84555xzzjnnnHPOOeec +c76nx3SMT7iuqj9e13tfzls85lflzs6XrB3ZfXmfZ8+tWk9aPYtR44HzFq/G ++S7nAc4555xzzjnnnHPOOeecc84553v4EZ+kXMzn/C/vHYdZjG5PVi4b93wv +bx03R/SOw97xw5/tMV2Nw9X7OOecc84555xzzjnnnHPOOeec8z39iJj/+ef3 +vzH4sz0bJ73jLYveccjf6b3jtopYbzXO+bs8pqt1r1o/d9v3Oeecc84555xz +zjnnnHPOOeecj/UjjvysfCwX/2bl+Ls85lflqnGY3S+rn/Pf8o+oxlVWvnf9 +5M/0aly17pur933OOeecc84555xzzjnnnHPOOedz/YhPyK/qya7L6uXP9Gpc +9daTlcvGGed/ee+61zqOj+hdJ/mzvXed5JxzzjnnnHPOOeecc84555xz/m4/ +4pOUi/n8mZ6Nkyyy8RPTx9+q/mz8cX6Ft477GNk4j/n8Xh7TZ/fH1fs755xz +zjnnnHPOOeecc84555zza/yIIz/zmI5/Y/B7ecyvyvWOE86f5NX4j5Gtw9l1 +veszv8ar51Wtu7H+3c4DnHPOOeecc84555xzzjnnnHPOx/gRn5Bf1ZNdl9XL +13j2vKrx0Fp/zI/lOH+jt86rI86uzzGfr/VqHd5l3+ecc84555xzzjnnnHPO +Oeecc76HH/FJysV8vsZj/vE3e75ZZM89q59z3j7vWufhEdl85Ht677q9en/n +Y3zU8431VesJ55xzzjnnnHPOOeecc845X+tHfEL+2fpjfbv9Xv6dHxGfb/Rq +nPG9PIveeR3LxXzOee3ZvKvqiTFqPeffees+G68/Ww8f61lk5bPrR42fWO6q +8XlV/ZxzzjnnnHPOOeecc8455996TFc+u/6Yf/wd3f5YLqs/i92e49v8iNZx +Mmr88HPeO79iffFva3nO+fXeO8+rfZnP9d51m1/jR8TnNPr5xvLV9a3zffb4 +HH3fXZ4755xzzjnnnHPOOeecc87v6zFd+U9yfea99ffet7pf9N76e9uZXb/b +c3+rHzF6fPJznsWo+c45v7/HGLX+8789pmP53fb33T0b11c9r6yeat+uyvf+ +rqz+UT7qPWW38cM555xzzjnnnHPOOeec8/v7EZ+kXMzPIrv+W8/um7U/+71Z +/Vn53t/b22+jfhf/24+Y9bze5mf7P4tZ6wbn/L5+dh2JUe2n/Hcftf4/3Y84 +288xfXZePNVHnefPPq/dxhvnnHPOOeecc84555xzzu/nMV15Vk+87vhbtSde +91SP6cp7n0vv83qrHzG6n9/m1TjvLd86Lzjn7/HefS0L55C/PabP9j//27PY +bX/fzXvnb0zH8d+7DuwyfjjnnHPOOeecc84555xzfl+P6ap8vC7+ba3nJ2kH +/58/Y7fxczc/IpsH1Xh+m1frQGv53v7nnPNeb12nYsTrdzsPrPLefeHpfkTr ++Iyxah9/qsf8s+tGNS+y61vbeXY+7jb+Oeecc84555xzzjnnnPMneExX/pNc +X3nrfWN+dl3lZ9vJf/cqYv9X42eX8X+VH1H1z9s85lflqvH57brBOeejvHc/ +7d1Hnu6j9t/d/IiqH2bvv/xeHvOr9Ser563zjnPOOeecc84555xzzjlf6TEd +y2flPkV9x9+sHv5Oz8ZbNQ53mS+z591TPeuHLKpyresP55zv5q3r4BG77eOr +zgm77eNn/YjYD9m4icHv5aPGQ+972dn3vt3mC+ecc84555xzzjnnnHP+JD/i +yM/Kx3Lxb4ysnt7yVTv5vXzUeLiLH1HNl6d6Fln/xDTnnL/dY6zex1d57Jdd +vbX92XPm9/Le8RDT1bx3Duecc84555xzzjnnnHPO7+NHHPlZ+Zg+69l9Yzr+ +zerp/V38Xt46DlfPo1YfNY/u4lVk85xzzvk5j7F6H//WYzqWj+V29SOq58af +7TH/23Eer3vr/OKcc84555xzzjnnnHPO7+RHfP75/W9WrtV775v5T5LPn+29 +42o3P2LW/FrlVbTOa84553M8xm77e+YxHcvHcrt59hz4Oz3mn53XV83HXeYR +55xzzjnnnHPOOeecc/4kj+nRHvOz+1f+k+Tzd/su8yjz2O5svMdyu3gV385r +zjnn13qM1ft49JiO5WM5+zi/o8f81vEf8992ruacc84555xzzjnnnHPO7+gx +Pdpjfnb/4+9Pks95i8d0LH/1/MraM3venZ2nWbTOX8455/f0GKv399i+qzy2 +J+sn/rf39mfvuW6339vrMb/6vXc/D3POOeecc84555xzzjnn/H/7EZ9/fv+b +lcsiuz76T5J/F4/pqt+yenrL87+96s+r51fvPBrlVbTOU8455+/wGKv399i+ +p+7Xo7z6vfH63veCVfVUv7e1nlXjJOa3tjNet9t84ZxzzjnnnHPOOeecc875 +9x7TlWf1xOuOvz/J/Sq/+vf2tierJ+avrqfqn3j93Xz3+TLKq4jjhPM3e++6 +yjn/33G3fTzWn/2+Vd57fuZ/++jzbet4691fdjvHcs4555xzzjnnnHPOOed8 +f4/pGJ9w3U9y/aj7Zp7Vk7WT/+3V84rXrfLe8TB7HPZ6FbuMB8538N51oLf+ +0fN6l37jvMdjjN7H4/1225czz35XTPNrvfd5jRq3WXt2e4/jnHPOOeecc845 +55xzzvl9/YhPyM/KV9e3+k9Rb2wPv8Z7n9dV/u04HzVuq9jlOXLe4qPm6aj7 +ZuWvWpdG7ZtZfnZ9FruME/4sjzFqvq/el3frZ76X947zUeOzd9zOPg9zzjnn +nHPOOeecc84552/wmI7xCdf9JNeP8qw9ve3k/N9/R4/b1vmVtefsOM9il37m +z/BR63ZV/7f7VK9n7T/bznjdbK/aOeq+revY6vpb68m8d9z2eu9z5P/zZ4we +bzHO7su79Rtf42f3o9b9ZXZ7RnnWnt3efznnnHPOOeecc84555zzb/yIT8j/ ++ef3/NmetSfz7PdU/TCrPfzZfnb8xMjGZzU/e2OXftvNq/6cNU7O1tM6TkbV +s6r+3vuOqr/Xe3/vqP16dv29++ao9ozq/9n9draeeP2q8RCvO7uv9Y6Hqtxs +j9H7XEb1M3+2986LUfvs6PNGdV12n9F+dh2bvQ9yzjnnnHPOOeecc8455/+O +T8iv6onXzfas3VW56Fk9Z/sn5s9uP3+Gn51fWb29ser3VtfF/Fav7vttP/d6 +7zozuj2z65lV/9l+G+WxPbPr7x3no8fh1e256r6t9e9WDx/rWf/HdKuPiln7 +5uj3gixiO3r35d72Z/Xc3UefH2bt47Hc6vPe2XNgzN/tfZxzzjnnnHPOOeec +c875sz2mY3zCdT/J9aO8tz1VO1t/b+Zn+znWm5WP5arfdRfv7Z+qntbyWYye +R7337+3PUdF632r8x+v4WD+7/uxez+j6Z983q+fq9vS2s7c/s+t72zNq3Rt1 +X85neG/str/cxWP67Dlz9rrUW370fjdrPxr1XDKfPU+vOudwzjnnnHPOOeec +c8455y1+xCcpd7aeUV61r9Wz39Xrq55Lb/+M6s+qPVX/XfVc3ua9MXuecv6N +x/S369K39x29b7a2Z7d1hvM3eBbVOSeLaj5X9a86b7/Ve/t5VvmYHr2/7PZe +lvnoeT3q/NA7TznnnHPOOeecc84555zz39KVx/zj709Sb69n9Y/y3t87ynt/ +b1VP63OcXZ6f8955WkU1bs7WP2pec87bfbf1ivOdPebH+TXrnDzqXJfFVe8F +sb2c93g1X6t5kXnvfc+uD9n1s9YTzjnnnHPOOeecc8455+/0Iz7//P43i1ju +55/f87P79tbf67335bzFr5qP2X2z9rXO3955Omo9qe7LOa/nL+dv8Jjfuq/N +Pj/Hdo3al1vPAa3tnPV7z54r+Lu8d173eu+8O/u7Zs8vzjnnnHPOOeecc845 +5/y3dOUxP/5tLd/rP43XxXz+Lu8dJ7PnVxZZOzOP6bPj/6p1JmtH67zm/A2+ +2/rJ+Qyv5sWq83DWnugxfdZ7+y2LVf12hH2cn/FR59Ws3tXrCeecc84555xz +zjnnnHM+0o/4hPyqnnhd5tX9OP8tv3Uczp4XMXrHf0yf9d7+XNVvVXtiOc6f +5Lutq5zP8NXn2Ni+s956Hs589Pknxup+bu2f3dZhPsdnzd+YrubXVe3knHPO +Oeecc84555xzzv/ymI7ls3Kff37/m9Uzq538GR7zj7+7zZcssvnS6zFd+ez5 +srr/Y/s4f5Lvtg5z/lf+2f1otcf2jpqnVbnWc/Lo5xVjdf+3nk92W5/5Wu+d +d6PWt93mC+ecc84555xzzjnnnPN7+RGfkP/zz+/5mffWU7WDv8ur8bbbfInR +O19Gza/MZ8+7XZ/Lt/3D+Q6+2/rMn+0xv1o/774vzJ6nVblv+3n0c4+x23Os +/IjV6za/1nvnezbfsutj3OU9hXPOOeecc84555xzzvlaj+lYPparPKvv809b ++ep6/kzfbV5U4znG2fnS6jF91rP6Rz3H6r67PMdR/Tz7uXP+b99t3ebP9phf +jcPV6/m36//seVqV+9avGg8xVj/H6nesXrf5NT5q3vXOi93GP+ecc84555xz +zjnnnPN7+hFHfuYxXXlWT7wuuw+/p8f8OB52Gf9Z9M6L2fOo11fNu92eb++6 +F9OjnzvnLb7bes6f4TF/132516v9KJYbvY9nMWofb/29V42fGLuNh1HvO3xv +r8bv2XNdb/nV45lzzjnnnHPOOeecc875Xh7TMT7//P63tXzmve3h9/Ldxnnm +WfyEcnHczvaqv6v5VXlW7yzv/b138SOy9S3mc/6N77bO8z095lfj56nr827z +N6ZH+27rRhb2az7DY7pax3rXz975tXrd45xzzjnnnHPOOeecc76nH/FJysWI +5bJ6svtm9VTl+D085lfjYbZnUY3bWd7bb6N8t3Gyet371qvflZXrXT85//ff +GJz/ld+678TYbb0ddb69ylvPvbN91/EZY9V7zepxwvf03dYxzjnnnHPOOeec +c8455/y3NH+3/yTjoyr/7TjMImvPKo/pq3y3+bvbOjZ7vMX06nHI7+W7rfN8 +rVfrUjVuqnru4r3nkLfu+9V1WXuv8ixGjYeY33oujdfxZ/hV42SXdZJzzjnn +nHPOOeecc875Wo/pWD4r9wn1ZeWz+vkzfNQ46R23WVT1X+1Vu7Nys/wu42e3 +dXLU+DwimxdZ/fE6/k7fbf7ytR7zR++zd/Ejevthtre2c5X3vhesHucxetsf +83cZJ3yNx3TlZ8+3u6yTnHPOOeecc84555xzzvfwI478zGO68pif1cef5TG/ +GlfZ+Myid9xe5VU/nZ1Hozxr567jZLd18lsfPV/4u3y3dZ6v9Zh/dp+6u2f9 +s9s8HXWunu27jfPWc2F23ep1m9/LY/rsvNhtneScc84555xzzjnnnHO+hx9x +5Gce0/FvDM7/yq/K9Y7PVR7Tqz3r16z9q8ZD1c+7rZPfeu+82G2c87W+23rO +r/HefWe3dW+3c+xuHtO7+qh1qar/2+eehfHGf/PZz323dZJzzjnnnHPOOeec +c875Go/pymfXz/f0UeMti1H3jfUdf3/++T0/86rdWbldfLfxs2q83cWPaH2O +veOZP8N3m6d8rFfRu6/tsr6tWj/vMn+rcrv72X0qe75Z+ei97cni7DhsbSe/ +l8d06zjfZT3knHPOOeecc84555xzfk8/IuZ//vn9bwz+DO8dP1nMHldZe6ry +re25i2e/a7dxFfNj+3dbD2d5b/9kkT13/gzfbf7yazzmt67/u6xvo/yI1nPC +bvO393e9zUf1z9n5FaO3PavHFR/jMX12XO22fnLOOeecc84555xzzjnfw484 +8jOP6fg3Br+Xx/w4Hqrrjhg1rs62p7Wep3rWP7uNt97xsHqdnOVH9D7fmM+f +7bvNXz7We9eNUfU8xY9YPU9HzeuqHP/dR83HLHYbP3yOW4c555xzzjnnnHPO +Oeecz/AjjvzeemKaP8uzqMZPq8c0b/OsP3cbP72+ej286zo8aj7yPX23ecrP +eTZ/43Vn1//V69gsP2JU/+ziWfv5NX72ucTofT/abRzyv713Peecc84555xz +zjnnnHPOe/yIT1Iu5vO9PHuO2XOvIo6D6vqsHJ/ru43DUeNk9Xo4y6/qn3gd +v5fvNn/5WI/5Z8fDbuvbqnPpbvN39vrPr/HqecWoztut851f4zH99vWWc845 +55xzzjnnnHPO+TV+RMz//PP73xj8Go/5x9/s+WbR+9z5Ws+eV/bcdxu3Wfur +8rutk7PW27PzPebzZ/hu85df473rPP9vP2L1/HW+eob3nq+y2G0c8jbvXWd2 +Ww8555xzzjnnnHPOOeecr/GYPlue7+lZ/CTPNXvusVw2Lvgevts47F1n+O/p +WD6W48/23eYvP+dnx0PrvrzbOjbbj8j6Ieav9tZ1PuavPlfwvz177lU9MZwH +9vSq/3dZDznnnHPOOeecc84555zf04/4JOViPh/jWf9nz6uK+Pyq67NyfC/v +HSe7jfOYX7X/qX5Eaz+MXk/4PXy3+cvHeswfvf4/1e+2Hrau//zZXq0DWfSu +A/yct64zu62HnHPOOeecc84555xzzu/pRxz5WfmY5t95zK/KZc+rqoc/03eb +p9V6kvlu6+EsP7sOZM895vNn+G77FB/rMf/b+b7L+rbb+nn23JvdL9Y/an/M +6ufP8N5xmEVWT3XfmM//21vXmWpe77JOcs4555xzzjnnnHPOOd/DjzjyK4/1 +xDT/O7/qz+r6GFU98b78GV6Nh3hd5r31jxqHvevMU7133cj87HrO7+G77Wv8 +Go/5o8fJbuvh3dbPb9vp/MZbvBrnWTgnjPGnrp9v9SPOruecc84555xzzjnn +nO/gMb26Pfw7P+KTlIv5/HeP+VW5rP+revi7vHf+jlrPz47zrP3ftnNXP6L6 +vb392Vs/f4bvtq/xa3zUOhPTT1mHR+1Td9k3+Tv97HyPMWo9eaqfXTd2WQ93 +9SOqcV7tg/G6s+O/tZ7e3xuvN04455xzzjnnnHPO3+1HfEJ+bz1Vva3RW89P +0Y74u6p6dnkuu/kR2TjJ8rPr3+JVf35bf8yvxj9/p2fztPJv1/9V7Vnlvf0w +aj0525/83r7bfsfHesyv1sOsfLWexOtm7wt3WZ/P9kNWX3a/1vZw/o1X4y3G +bvvdbr7b+rab965vs9fJ3n2zqidrX+t9Oeecc84555xzzjn/LT7//P43i6xc +9N77VvXE/MzP1rPLc1ntR1Tjgf8dveOT82+8d53MxnO2PvTuC7uut9+2p3d9 +OLtPte6bvc+d38t32+/4WI/5o/eF3nXpqvW/9b6jvLf9uz1Hzmd6jLPnqLt6 +73xffY6d5Ue0roe95Uedq0c9r9HlY7ld34M455xzzjnnnHPO+RiP6cp/kuur ++44qP8pb7xvTVf1V+V2e+2g/ouqf3vF2F8/6p4qsXzjf0Xvn+9l6dtnvYv7Z +9vfup9l9R/lV+yxf47vtj/waj/nVupSV7/Xe+nebL6P2Nc7f4NX6E2O3+btq +/139nj7Ld9sHd9t/e33V+xHnnHPOOeecc845v8ZjOsanuK7ynyT/rb7Lcx/t +R2TjIuY/zbPI+iemOX+T7zZ/z873bL+r6vt2P22tf/V+x9f4bvOFP9t73y/O +lo/lRs2LrFxv+2e3h/M7e4xR82g3P7tu7O5HtK6T/G/v/T4w6r5Z/buNN845 +55xzzjnnnPNVfsQn5P/883t+r2f1Z+0Ydd+3eUzH8ruMt7N+RDV+7uLVfMwi ++/2c38lHzevedWN2e87ua63tP1ue85G+237Kn+Gj1vPdfHY/rJrvVTnOr/Bq +fGYRr99tnz3r2bqxi8d2O1fM8VH7SExXz+vu45NzzjnnnHPOOed8tsd0LJ+V ++/zz+98YVf1ZO+P1/JzHdCy/yzjsHZ938Zhflet9jpxf6dn4XDW/Ru0jMb2r +20/5Dr7bPsuf4U9dz0f3Q1Xf1etDa3s4v9Kr9SHGbvts7/672/t71u7d9p23 +ecyv1vPZ+wXnnHPOOeecc8752zymz3pWf7zu+PuTtINf4zEdy+8yPrP2jxq3 +sz2Lqnz2Ozm/wmfvF73jf9S60bservJR++9u+w5/hu+2z/JneMw/ux9l9Yzy +2fNi1Pk5a9+q94tVz4vzHo+x2/4b09U6effvS/ycnx0/Mf+p45NzzjnnnHPO +Oed8lR/x+ef3v1m5Vu+t/yf4UY5f628Zn6PHeRZZuzm/wrP5npW/ar5k7Ry1 +nsT79Hpv+0d57/p8th7Oz/hu+y9/hsf81nUyKxejdx/MfHY/rD6fZ/ft9dbn +EvNXn5c4/81j7Lb/eh/nf+WfHf93GZ+cc84555xzzjnnd/MjPkm5mJ9Fdn2r +Z+3haz2mY/ndx+cor+Lb8c/5DK/me3Z9jF6fvT5U943lZq+HmZ9tZ9Xf9lO+ +wlftv5y3+Ox9bbbH/GpfmO1Ve2J+b/9n9XN+B4+xer+etQ7stk7u5jG/Gi93 +aedu45BzzjnnnHPOOef8qR7Tlf8U13/CfbLyq/wu7dzVdxmHo7yKOE4439l7 +5281L7L6r96nqvbE/F09+727tZPzf/+NwTmf57u9D8b8an3Iyvfe92z5rNwu +5zT+LI+x+jz57XzfzWefn2P6bP+Pqmf2ur3b9x/OOeecc84555xz/nu68ph/ +/P1J6p3dzqo939bT2z+ZV783Xr+rXz3ezo7PLLLnyvkZr+Z7vO7sOlDNg2r+ +9pZfvU9l7eGcj/fZ+zLn/H+H/fecZ/1ZleN8hsdY9d69eh2rrtvleV3tZ9f/ +zFv7edf9hXPOOeecc84555z/7jEd4xOu660n85/i+njft3n1HON1V/m346rX +q9jlefFnezYvRo3z2b7b/rJ6HeP8jb7busQ5/9/RO39714Gs3lHnh9H7ftV/ +VflR/ZCV5+/2GHd5v+6dX3wPjzFqPGT3HbUvcM4555xzzjnnnN/Nj4j5n3Bd +Vr7Xq4j35Wu9d/yc9dZxm42j1vGVXbe6n/la710Ps/GWjdvqvt+O81Hza1Q/ +9Lbz7O/inK/33nWAcz7Pe/fx2Z61Mys/6j23qj/LjzF7nRxVT1Zu1HjoHYdV +e3qfV2v5p3uMs99zsnIxep8vX+uz94vd9rXV31E555xzzjnnnHP+Xo/pWD6W +m+0xHf9+286sfr7Wz46fbFy0jp8qdumf2d7bn2fLx/xR87R6vq3tqX5PjFH1 +jKo/Kzdqv6jqj/lVu2f5bvsa5/x/+6h1knN+vY86J8w+L509/2T36z1vzD53 +tdYzqp2zf2/vc5l933i/1vu2tjOr/yqPcfa9I4tVv+vtPnudH/V+mvmq9u/2 +nZZzzjnnnHPOOef39ZhurSde3+sxXXlWz13az+d4jN5xUsXVv2vUPO2tf/V6 +MspjO1bVE6+f1f/xPtl9Rz2Xqp5Yrteredrbn9+2h3N+vVfrKeecf+sxf/Q5 +ZPR5pvWcOfu8N6o/e9u52/i5u5/9vtEbveM8XrfaZ82L2d7bz6PWjau+B85a +H3b9vsE555xzzjnnnPP7+hFH/tnyvR7rj+VifvTq+hij+qe3/ur6WT7qufT2 +82w/28+90TreRs8L/t/pI3rrielZ7WltZ9We1vqrelrb31vP2ftyzvm3vts5 +hHPOOX+DV+8RrXHV96WnetZvvf3ZWr53PIz6vVU7Wr13nGf1zH6v55xzzjnn +nHPO+Xv8iM8/v//NIpb7+ef3/Myzenq9+j2tXvVb1a6qnrP3ba2H/yeqcd4a +veOBc8455/N8t/MG55xzvrOP/l6U1R/b0Xr92fZUvzeW4/fymD7r1X2r+XT2 +XLrb917OOeecc84555zv50d8knIxYrms/t56ej2rn9/Ls3HYO56zODvOs3pm +zTvOOeec/2/f7dzCOeec7+B3+V5UlY8xqv1Vv8VyfE8fNV+yekd9j+Kcc845 +55xzzjkf5TEd4xOu+0mu7/XsvnxPr57vt+Mwi+y+MX12vF0172J7OOec8zf7 +bucczjnnfIbPfo8e9R4a05X39kMWq7+PHbH6XPQ2j+lv50VWX4zV85Fzzjnn +nHPOOefP95iO5WO5qnzrfbN6q3J8rq8ah1lk4zDzmK58t/7pnY+cc875k3y3 +cxHnnHM+w+/yXhnTlfe2J/MsVn9PO2L1eYn/7TFd+W7zl3POOeecc8455/f3 +I478zGO68pif1cf38FXjMIve8VnVP2vc9rZn1fzlnHPO7+i7nZc455zzFl/9 +nph51p5Wj+mzPqqfs7h7P/OxHtOjx+eu851zzjnnnHPOOefXeUzH8rFc5jFd +eXZfvtZXjcMsesfhqPGZ+d37edR855xzznfw3c5RnHPO+b+j2tfidXd/H4zp +s97b/l7P4qrnEtvH13o1TlrH59n2XL0OcM4555xzzjnn/HqP6cqzeuJ1x9+f +5H699+XX+OzxlkU2Ts566/js9dH9HMvttg6Mfi6cc875SN/tHMU55/ydvtv7 +XeVZO7/1mB7ts59jFld9J4m/c7dz11M9pqvxlpXvPa+uXgc455xzzjnnnHN+ +vR/xScrFiOWyerLyWf18rMf8+LxmjasssnEyymN6tM9+XqvXgez3Z+2M5Tjn +nPMrfbdzF+ec82d4tR/F6+7mR4zel2N6tK8aD1mM/n4Sf+du5y7+e7oan6vn +O+ecc84555xzzvf3I2L+55/f/8bgaz3mH39HjZMssvEz22N6tM9+Xqvn+7de +/a5YjnPOOf/Gdzt3cc45f4bv9p51l/ey7L5VuW991TjJYvZ3tt3OY2/zmG59 +XrusD5xzzjnnnHPOOd/Pj4j5n39+/xuDX+Ojnlc2HrLI7jvbY3q0Z/dd9RxX +rwOz1hPOOef8G9/tPMY55/xefvb9JSu/i8d2X71ft7Zntq8aV1lU5Vc9L97n +Md26PmT177JucM4555xzzjnnfJ7HdFU+Xhf/ZuX4Go/5x9+fxnFwRFZ+tsf0 +Vd47X656XrusG6PWk1XjinPO+TN8t3MX55zzPT3mt+47sb67+BG9v3eUt7Zn +Nx89rqrrjtjtfMXbfNTz3WXd4JxzzjnnnHPO+TyP6Sp66+F7ehbZ8431HX9/ +knGQeVbPbr5qnPe25y5+9vfGfM455/zfvtv5inPO+Z5e7S/xuqqemL+bHxH3 +y1X7ddae3Xx1P8Q4Oz6/bSc/5zFdPefd1g3OOeecc84555zP9yNi/uef3//G +4Nd49ryy51vF1c83u+9uvur5Zu1ZvT58u55k5c+Oc8455/zff2Nwzjnn/47V +70er/IjV+3VMP8Wr7zCt9WTXZ3F2nMfr+TmP6bPPd/X6wDnnnHPOOeec8+v9 +iJj/Sa6LHvOz+nibn31eWT1Z+dbnm7Wnt567+N3Gw1P9iDgOOeec83//jcE5 +55z/ld+678T67uJH9P7eWd77XN7mZ59vDO/X13r2XGM8dZ3hnHPOOeecc855 +u8d0LB/L9dbDz3nWz1n0Pvd4/+x5Pt2zcb7quWft2G3dGLXOxPzquXDOOef/ +9t3Ob5xzzvf0mN+678T6dvXY/qwfdtuvq3Jv97PjPMbo74H8d4/pylevG5xz +zjnnnHPOOb/Oj/gk+dGr6/nv/pP0a/VceuvJ2tH6fN/mWb/tNk6q8rusJ5lX +47v1uXDOOef/9t3Oe5xzzvf0LLLyu71PnfUjVu/XMc3neO/4322c3N1juvLV +6wPnnHPOOeecc86v8yM+SX706nre51n8JM8hpvkc322c7LZunPUjqvmQleec +c87/7bvt15xzztd6zI/lovfuL6vfp1r9iNbfu2pfrq7nfX72u18WV4+fp/su +6wPnnHPOOeecc8738ZjmbR7zq3JZ+ey5VPXzPv9J8jNfNX52Wx8qP6J1Hsx6 +Xpxzzp/tu50DOeec7+kxv3XfifXdxbN+6H2P6+2fWC5rF9/Ds+ebxW7nwN08 +prPncMRu6wbnnHPOOeecc87n+xEx//PP739j8L+jKp/1L9/Ls3nUO0565+Pq +9eFb7x3/VT9wzjnn//4bg3POOW/xmF/tL3d5X+v9vWf35W/bmbWH7+1ZjBpX +d/dd1oG7+RFn+zmWq8bz277Lcc4555xzzp/nMV2Vj9dl9R1/e+/b2x7+t/f2 +89095lflqvJ8L181L6r2xPy7rANZ+2O69fdyzjnnf/mq8yHnnPNn+Nn3r97y +V3v2e2N+6/777X1728P39Op9P8bZeXRXH73O3NVH9UPvujHqvln9me/W/5xz +zjnnnPPn+RGfJD96Vk9W709RLqs/5o+67279P8p7+6EaB3f1apy31hPzq3HL +13o13zP/dn6dbc9d1o1R6y3nnHP+l+92nuScc76n9+4jWbne71RVe6rf0bo/ +xnpmfwfr7f+YX/Ubv5dXzz3GbufJUR7TZ9eBu/kRo8fPVfvCt+vk058v55xz +zjnn/Ho/4pOUq8r31j/bY7ry6vfu9ry+fb4xXfXD3T2LUeOH38vPrjNZvTHO +rpOt9cf8s+twVs/Z+2b5MVbtC5xzzu/lvec9zjnnvMVjfiwXvfd9arf9tIrW +fuC8x7PYfb6M+l70VN9tPR+1zmc+6j1lt+fIOeecc845H+dHHPmZx+tjZOVa +vbc9q3235zjLs+d+F4/5VbmqPOffeIy7zJdR6//qdZtzzvkzfbf9lHPO+Ts9 ++64Sr6v2r6x873eqrJ6q/lhu9n35Oz0bV1lU8y6WW+3Z74+x23fg2N5qveJ/ +e8z/dh3mnHPOOeec38+P+CT50X+SfP63x3Qsv8t4qH5X9ntirPKq/1vrifnV +c+Tv9N55MXodbr1vVU92fe96Fa/jnHPOr/Rqf+Wcc86v8N73ppi+ys+2v/V3 +zf6exp/t1feTLLJ6Yv6qc2nVzt55961n7dltXd3Ne/tz1PhZ/e8FnHPOOeec +83Y/ojrnZ55d33tf/nu6tT9nedWeLD+7fpa3tuOI3t/Ln+2zx+eo9TmmV/eP +dZ5zzvnOPnt/55xzzlt81HeYUT67/Vft+633jWn+LK+ee4y7nFdnf+/dbZ18 +qsf8q9dDzjnnnHPO+XqP6bMe84+/o98v+N8+e/zE+44aP6PHYW/57Pfwe3v2 +3Gevh7337Z13mcf0aJ/dfs4553yGz97fOeec8xYf9R7X+11odvtHfYcc9R0s +qz/mn+1//iyPsfoc2zqPnvpd96ke88+Ok6qe2eOHc84555xzft6PiOf5qlwW +8fre9wt+zrPnMnv89I6TUV5F1i/8XV7No2/Hc2/9vfcdvW603jfmV/18Vfs5 +55zzM967v3POOef8f8du3y1nv+fyd3uM1efbb+fRbuvJXTzmV+Olt55V44Fz +zjnnnHO+j8d05TH/+Fu9R2T1flsP/2+/ejyM8iriOOH8339750VVz6r1OWs/ +55xzzmuv9nvOOeecn/dV3yev+q6YtbP1vvxZHmP2eXXUd6RV60PWjt55N3q9 +yu7b663PJV4/un7OOeecc8758zymY3zCdaPq7/WfpN6zPqofRrWn1av+6R0P +rfX3ehXZ/fi9vXd8nh1XvfeN11213mb35Zxzzvl57z0/cM4557zdY361/456 +L87ue9V7d9VPVTv5szzGVeM5uz7G7Pn+VB+9XsXorf9sOznnnHPOOefr/Yh4 +ns/KVfVk9bZ6bzuf6tn712ifNU5ax0dVP3+2Z+Otd1yNWk9G1Z/Nu+y+V813 +zjnn/I0+6lzBOeec83aP+dW+nJUfVU/vd7Cs/lXnlqzcqHr4HI8x6vvtqHnq +O/xYH9XPq9bnzHf79yzOOeecc85n+BG95+SYP8qr+2a/q7Ue/rf39vNZz9oR +I/MqdunPp3r2fKvn9W09o7x3fPaun6PWpbPrZMznnHPO+TyffW7hnHPOebuf +/a4Vy4++b1Vfdv+qnb3tz2LU973R34Gz/Bijvhv31l+1b5XHGDX+q9itH+7q +s9e33vuO8uy+u/17Geecc8455zP8iOw8HPNHeXXfrFyM3veR7L78O4/R+z5Y +1ZfFLv0wahyOGudVf7bet7c9vfVk0Tt+ete3zM+uq1k7W9s/6rlzzjnn/Hrv +Pf9wzjnn/D0e82O56KO/t3x739nfk7N6z34//LY/z36HmdXO0d+3Y4z6ntbr +vf3ZW8/s9o/ys+Owd3xG723nqPegs/ft7QfOOeecc85X+hHfnrd7z+G9963a +HWPUe0pvO1d5bz9n/TDqefV6NT6/bU/vOKnaGfN7+7N3HM5uZ+/8HTXeVq1L +q+/LOeec8+d77zmKc84555zzHTyL3c7bozymq/P8qH93OPu9d9R9Wz1rT69X +/dnbzt5+4JxzzjnnfKVn5+Hec3JMjz6fn21naz9k7entt1HvR1l7RvXPbp7F +qPdHzjnnnHPOr/Tdztucc8455/zZPvu7dBaj7sv39JhuHRet5UePZ84555xz +zu/oR5w9n486z/M9vXdcVdE6HmaPZ84555xzzr/x3c7tnHPOOef8Xh7z4/kz +Xtf7PXbUd/uq/tZ2Vu3P+iHm82v92+eYlRt1X84555xzznfw3nNvTJ89D1fn +cj7XY/7Z51i9Z8XoHVet9Vbt6X0frN77OOecc845/8tXnfM555xzzvmeHvPj +eTJeN9rj/Ud9p61+b4yrfu+3/cDHekxX5bNxtXr8cM4555xz/o0fUZ17s3JZ +eX6Nrxo/WYx6L9utH7J29v5ezjnnnHP+bB91zuecc8455/fyVd9pq/bEcr3f +aTPv7Z8sfNd9tsf02XF1dvxfPR8555xzzvk7/Ih4Hm4tH9Nnz8l8rMf81uf7 +rWex6v0r87Pjf9V85Jxzzjnnz/TecyznnHPOOb+X3/07ZEyf9VH9mcVV373j +79nt/eIp3tv/reV76+Gcc8455/wbP+Lbc2lv+ep63ucxv+r/0eMnxqj3r5g+ +6739uWo+Vu2J5TjnnHPO+TO897zKOeecc8739OocGK+7yrP2tHr2e6ty0Wef +h7O4e//z//befl713DnnnHPOOT/jMX22PD/nq557FqPep6r7ZeWi99Z/l/6v +2hPLcc4555zze/mo8yrnnHPOOV/ru33Pn32OjemzPvu5ZHGXfuZ/e0yfHVer +5ynnnHPOOX+2H3HV+ZaP9VHjIYtV7029fpd+XjV/Oeecc875nj77HMs555xz +zs95zK/Ob0/9ThjTo331842R9XPvONntveOpHtO7z1POOeecc87/7UecPd/y +sR7zj7/Ve0pV3xG7vTeN8tnP5S7zdNXz5Zxzzjnnf/vs8yrnnHPOOf/be7+/ +rf4eWP2+q86x2X1H+arzcxZnx1Usx+f4qHmxy7zmnHPOOefP8OycGvOrc2l1 +3uVjvPd9JIvZ70G942qUz+7/7L53mddVPfF6zjnnnHN+jc8+x3LOOeec8789 +5ree62J9u34PjOVme0yP9lHn6t5+zsJ31z09pqtxstu85pxzzjnnz/Ijzp5X ++TWePccsRo2HzKt2ZOW+9dX9H8utnr9Zf2UR+3H2+y/nnHPOOf/bV51vOeec +c87f5jG/Oo/t9t1v9vfes149h5g/y3ufe+/vquqPsevzeovH9FvmO+ecc845 +39OPOHte5ee893llUb2PZM81i/i8e8fJbO/9Xaue165+RGs/x3zOOeeccz7W +Z59jOeecc8757/nxnBave4ofcdU5tir3NK/6IYtsHMZ8/p33zovd5i/nnHPO +Ob+3x/TZ8vycx/yqXPa+UNXzNM/6Yfbz2m3+jvIjWvuZc84555yP9dnnWM45 +55xz/rdX57d43d38iKvOsVW5p3nvuMpi1XN8m1fPa7f5yznnnHPOn+FHVOdS +fs6z/s+iqicrlz2/p/mqcbt6nn7rveOKc84555xf47PPsZxzzjnn/D9RndPi +dXfxI+L5cvY5Nrsv/9uz51fF1c/37l6tA9n8yurfZb5zzjnnnPM9fdT5M6uH +/55flfM+O9ZXPd/d5vvo9SGW45xzzjnnY332OZZzzjnnnP8ner/H7vYdL/Oq +/TF/9jm2Ksd/92p8xuj99x3e5rvM66f6Eb3rVTZ/YnjunHPOd/ZqX4wxan+M ++fbBa733ufP/RHWebK0n5mfPh//3397vAKO8as8u87r3fefsOs8555xzzsf4 +7HMs55xzzjkf673/PjLas/bF8+XZ9mf+bXv4Oc+eYxa7ve/cxav5Mnte7+69 +60lMXzUvRq1vZ++7y/PinHM+x4+o9qne/fQp++xuz2uXcdL73Pnf4T30Gq/W +gavXt972rHoP4pxzzjnne3rveZVzzjnnnJ/zmN96fov17fbvEbN/76h+5td6 +jCx/t/ej2R7Tq+fvKj+itR965/uo8r3jNqs/81W/d7fxwDnnb/MjsvU55veW +771v5qPOb1n9q37vbuNh1XjrPf/c3avxlkXrfOFj/ez7V1ZvFt+uM6u+t1z1 +eznnnHPO+RjPzmmcc8455/wan/3vEdV9Y/6o74Qx/2w7ez27L7/Gq38PirHb ++9Fu71+rvv+P9iPOjp/d1u3R639rv40ab6vHA+ec8/9Onz0nrNpfdvWqn96y +Px4x+lx6d8+id/zwa3zV+tBbz+h5mvVLFr3rW3ZfzjnnnHM+16vzKOecc845 +X+Nnvx/G8qvOmVm05sdy/NkeY7f3ptHzIpu/WT3ZvN7NY/t3W1fvtp7H/FHv ++6vHCeec8/9Oj943s3p3e1/Yze++b/aOh93OS6PHfxbZ7+fP9FHfK2b73b// +cM4555zzv33VOZNzzjnnnJ/z3u9vMX2VV+2v6otxdfv5Hp5FLL/be9ZZz+b1 +bh7bv9s6eReP+dW8eOt445zzp/lT9pG3eNb/u42r2eNt1/NSb3n+TD87f2P5 +2e3M/Ow6E+vjnHPOOed7enbe45xzzjnne3rvd7mYHu1ZO7Pyo74r9raT38ur +5x5jt/ess57Ni1Ue27nbenh3j/ln58VTxhvnnL/Fn7KPvN2z5/LU8bb6vNRb +vnVe8Ht57/jJ5kVW/27fVUZ9P+Gcc84552u99xzLOeecc87v5aO+Q569byx3 +9t8XsnpaPab5Mz3Gbu9fo+fFt57FbuvY2zzmV+N/t3HFOef8nF+1L/C5nsVu +42o3r6J1/PN7+ajxM2pejPr3tazc7O8enHPOOed8Tx917uWcc84557zFe7+X +xvpaz72xnqzerH7+LI+x23vZqn+n85441ketS73r1apxdbY9V7eTc85Hr7dX +t7NqT8wftR+tPhfd1av+3H38z/Yqsn7k9/bZ7++j3oM455xzzjmf4dn5lnPO +Oeec8xk++t8d4v16z71VOf5sj7HqvSxr5+j5kt0vxlN9VP+MKt/r8T7VOMnK +r+r/rD1n59GsecE5399Xrz/fetWeb9f/0efqUeV763mqz5oX8X677PtZZO3j +z/RR/z616nsC55xzzjnn33jvuZdzzjnnnPNvfNW/U8w+P1fl+L08xur3uG/H +/27rQO88yvonK7/KRz33qv6qX6txvZuPWoev2kc459f7EWfXt9X7eKvH9Or1 +P6t/lY86P+zqdz3vVbHL+OHnfPa/K83eR+6+L3DOOeec82f4qPMz55xzzjnn +LT7qHBvTsXwsl3lVT2t7snqrcvxeHuOq97jW8XyX976Yv8vz3cWr9bP1uY+6 +76rxcNV84Zzv66vXk289a0/mq9b/t/ldvs/Pni9n51cWuzxffs5HvUdU9beO +56yeUeN5t3WAc84555w/20edYznnnHPOOZ/hvf/elNWTlR/17x1V/TG/93xe +leNrPcbo97hvx+eq+cj/9tHrVXX/qv5en72+9dbTO1845/fxI65aT1atn73r +W2/9ve3kv+cfcdX3/Nb50jueq3GexS7Phf/n7+z1bdT47K0/K796PnLOOeec +c37Ge8/nnHPOOeecv9lH/Tta5bH+Uef8rFzv93Pe5jHOPt/W8TNqnMf8Xfrz +rn52nZm1bmTtHOW943lUPZzz9/ioc86qffBt+8LbfPT3/G/nRTXOs9ilP+/i +o845vc9x9rpR1R/Lc84555xzzv+3jzrnc84555xz/iQf/b065mfls3p7v6v3 +1tPbnqr+mN/bn733vZvH6O23LKpxmJXbrX+e5mfXmdb5MspjerX3rttZPWfX +Jc75eB89f7N677qO9fqofSSm+RyvnmO8Louz8yuLXfpnlPfOl951KfOz5/ms +ntZ5Pao9o95zd/v3L84555xzznfw6hzPOeecc845f77H/Pg3Ru+/a/T+O8Ls +35u9H2Xtucqzdrb281Xt/PZ3ZeVnv/9W7fx2HI7696necXuX7wa9/ZO1Y/a6 +V7WTc177EbPW+az+2evzbt9XR7VnVP9U7bj6vFe1p7f81V71f+vvmd3OzFed +Z7L2nB3n355bdvv3IM4555xzzvn1/gke8znnnHPOOeecr/EqjuuOv7u9b97d +Y3p1e3bzbNz+JPmj+j/zUfOuamf2uzh/o5+dR60e06PXgd71ardzwurzyax1 +mP+eX5Xb7ZzAOeecc8455/y//8bgnHPOOeeccz7Wszje1+J12Xtcbz3x+uPv +bu+nnP/bY7ryUfO09/tJNX85f5If0TovYvm7rAOcz/CYH8d/6/mxdz/KYrd9 +n3POOeecc86f6p/gMZ9zzjnnnHPO3+4x//j7E9JHnPWsHfG+VTtjzG4n5zO8 +dz5m3ju/qnaOmkecP8F75+nseb3b+YE/20fNoyxGnQ9Ht7N33+Scc84555zz +t/sneMznnHPOOeec87f48d4U80d5vP/xN3tf6y2f3S+L3X4v5795Nt5i+d75 +nsXsecH5GzyLUd8ts/vudq7ge3rMb913rp4Xve3f7feuPj9wzjnnnHPO+S7+ +CR7zOeecc84553x3r+K47vj7E9JHXOWxXZln7c98VL+t6p8jsucV8zn/zVvn +XUyfnUer1xPOr/Qjzu5fvfNot/MG39Nj/urzXha7nQNX90/V7lhPvI5zzjnn +nHPO7+Kf4DGfc84555xzznfxmH/8/QnpI1Z7bG+vx3Tlo/s5xqr+zNq52/s1 +v5fH9Oj5VbVnt/WKv8tHrasxfdU+xd/pu62rWdxln6r6eZf1KrZ39fmBc845 +55xzznv9Ezzmc84555xzzvnVHvOPvz8hfcQqr9oZ83s9q7/XRz+XGKv6P2vn +bu/d/F4e01X5UfNrt/WNP8uPODsvevfr3c4V/F5ejc9V573edrZ6TO9y3sv2 +wV3Wt6qdMZ9zzjnnnHPOV/kneMznnHPOOeec81ke84+/PyF9xK5+RGz/tx7T +Z/2q5xhj1XM5IhtXMZ+/27P5k0Xr/Oq9L+dXeu+4jenR84u/02P+6nUyC+e9 +/8Ru65hzIOecc8455/wu/gke8znnnHPOOef8W4/5x9+fkD7ibn5E/F2tXkXs +t15f9T6YxeznkrVnt/dxvre3jrd4fTW/Vq9XnP/bj2jdR75dhzn/d4xah8+u +273t+dZ7z8lnPav3W1+9Xo167q3nZM4555xzzjkf5Z/gMZ9zzjnnnHPOW/3s +e0qsb1fP2j/LY3q0rxonWVz1vHZ5vvwZHtOj59fqdY/fy4/YdTzzd3o2bmev +e1nstl+M8t2e725+9nfFcpxzzjnnnHPe65/gMZ9zzjnnnHPOZ/nxnhLzV3ts +92yP6at8t/fELHrHT1V/az9w3uIxXXk1nlvrX71O8jV+xKxx1Vs/5y0e81vX +29ZzWha7fW+vys3yVc99t/Vzt/MD55xzzjnn/D3+CR7zOeecc8455zzG8X4R +8+/uR3xC/uz3suy+qzzrn1XjKovedsb8q54vf4f3riffluf8t5g13nY7h/B7 +ecz/dl2NUc2XrP5R3jq/Vvnq57vLOjnaj9jlHMI555xzzjnf1z/BYz7nnHPO +OeecZ3HkH3+r95FY366etX+Wx/SunvXb6nEYY7f3bv5sj+nWdS+rf7f1kN/b +s/UzKx+vy/aHqn7Ov/EsVq//rfNlN1/1HHdbD3vXyZi/+rzBOeecc845v69/ +gsd8zjnnnHPOOY9RvXfE6+7mR8TfNctj+m7eOx6qelqfV9XOGHcZD/zZHtPV ++K3W4d3WT36NH3HVeOO8xc/u41nMOidk5av27XLu6vW7jIfdvPpdsRznnHPO +OeecZ/4JHvM555xzzjnn7/XR7yPxPqv8qt/7rcf0U3xU//fWn8VTxw/f02P6 +2/myy7rKr/UjRo8rzv8do851WYza33vbn9V/d3/q+Fn1XjD693LOOeecc87f +65/gMZ9zzjnnnHP+Xo/5x9/qvSPWt5tnv3e397WY5m1+dpzHyMZPdt/dxg/f +02P67Hi++zrM//be5x7To9dJ/k6P+dU6k4XzzzW+2/i5+z51dl7EfM4555xz +zjn/BI/5nHPOOeeccx6jeu+I193Nj4i/a7a3tiemeZv3jvMsVo8T/mzPxnGM +1eskX+tHnB0/nH/jWfSuezHN27x3X1g1Tlavk9969btiOc4555xzzjnP/BM8 +5nPOOeecc87f68d7RMzPPNZ3/O2tZ7ZXvzeWu8pb+5Of82qcxOuq+mP0jreq +nTGfv9NjuhqPu623/Ds/4ux44O/0mP/tOaS1/t51KauHn/Pec8hs7x1vqzy2 +79t2xvo455xzzjnn/BM85nPOOeecc87f6zE/lotevY/E62d71c7e8jF/9ntZ +VY6v8ep5ZTFqHvF3eUyfXTdWrcP8bz+idR3Iyu92fuBrPea37ncxeschX+ur +vv9X7eld965eh0fNo93OD5xzzjnnnPN9/BM85nPOOeecc87f6zE/lotevY9k +18fIyvf6qN979v2rtZ3ZffmeXj3feF0Wu30f4Ht6tU721v/tusrHeu8+5fse +/8az6D2PxetW78v8b3/q+bn3PNb7e2N+az9n9+Wcc84555y/1z/BYz7nnHPO +Oeecz/LR7zvxPpln7Yn5q+/L9/Te8VnVHyMbP1X51vbwZ3hMV+Ord73i1/oR +Z58vf7Zn0btfxPucHVdZPXxPf+r5udd328c555xzzjnn7/FP8JjPOeecc845 +5zGq946qvpgfffR7UHa/GL31jHrPGtVv/F6ePe8szo5b/kyP6dZxla232frG +x/gRrftdVn638wC/xqtx0lt+l32Qj/Xe82rvOXb2uXrUfIn5Z/vNuYtzzjnn +nHM+yj/BYz7nnHPOOeecxzjeL2J+9t4R06P9Lu9H1f34Oz1GNr/Olp81X/ge +3roOn62Hj/FR++xu5wF+zmN+NR+z6C2f3Ze/0+/y7w5Vvd967zq8et/nnHPO +Oeec388/wWM+55xzzjnnnLf68d5RXRfzr/aq/fG6Ve3k/K/8Knrn427fK/g5 +j+nWdS/m8zl+xNnnxe/lMT/O39Z13fmE7+zV/hKvW9XOzHvXbc4555xzzjnv +9U/wmM8555xzzjnnrV69j8TrMo/Xx/zoV7WztXzWTs6/8d73+ix2+y7Bx3pM +V+Nk1LrNf0/H8lm5b/c1fi/P4uw6v8s+xZ/hZ9e3b9fD3nUy89nrNuecc845 +55z3+id4zOecc84555zzp/nxfhTzK4/19npMcz7Cz463GNn4770vX+tn18Os +/t518u1+tp+j77Zv8t/zq/lSRayn976cf+Oj5sWqczXnnHPOOeec38U/wWM+ +55xzzjnnnD/Nj/ejmH/W4/16PaY5n+nZvMiimkexHN/TYzqWH7Ue8t/9iNb5 +yPf0an71lt9lX+DP9tHjf9Q6Ge/HOeecc84550/1T/CYzznnnHPOOedP8+P9 +KOaf9Xi/s179jpjP+Rk/Ow5jrJ4vvM9jOhsvMbLxM2r9vKsf0Tq/svK77Y9v +87PPvbWe3vnF+TfeOw5nzxfnAc4555xzzjn/778xOOecc8455/zuXr0fxet6 +PdYb68/u+217svtyPsOz8ZfFbt89+H/7t+seH+u77Zv878jmV0xzPtNnrzOj +7tvbntX7I+ecc84555zP8k/wmM8555xzzjnnd/WYf/z9Cekjej2rv7pvzM/q +7/1dnM/ws+Mwxm7fQ/jv6ep5jlo/n+JHnO1PvtaraN3Hs/Kcz/BV58nZ5+fd +9kfOOeecc845H+Wf4DGfc84555xzzu/qMf/4W703xfp6PWtP73tZVY7zO3qM +UfOIn/OYrnzUOnl3P6K133bbH+/uvft4Fbutk5yf8d5z5qrzcNa+3fZHzjnn +nHPOOR/ln+Axn3POOeecc86f5jE/los++72stz2c39Gr+Rhjt+8nb/Psef0k ++W/1I6p+49d4FvZf/ma/at61tme3/Y5zzjnnnHPOZ/sneMznnHPOOeec86d5 +zI/lZvlPUm70e1/Wjiyu7gf+Ts/GZ1VPjKvm0dt8VH9m9dzVe/eXUfXw/0S1 +bmQxav3hfKSPOr+Nnke79QPnnHPOOeecP80/wWM+55xzzjnnnL/Fj/em6rrj +b1a+t/7KY729HtOc38GzeZTFbt9bnuK969Xbfbd97e6ehf2OP8lHzZfR58zq +/q37RVY/55xzzjnnnL/FP8FjPuecc84555zzMV69r8Xrznpr/Vk7Y352Hec7 +eoyz8+XtHtOVj17HdvEjWvtht31nN6/6OYvd1hnO//JR57FR61hVf9ZOzjnn +nHPOOedj/BM85nPOOeecc845H+Mx//j7E9JH9Hpv/Vl5zu/o1byLsdv3mbt4 +1s+j1rFd/YiqH/jfnkXWzzHN+Z191Plt9Pkw5nPOOeecc845H+uf4DGfc845 +55xzzvlcr97j4nWVV/drvW9Wz+ef3/9mkZXjfAePcXaevsVjuvKz69jVnrU/ +8932kd32ryp2Wwc4/z8x6vzTOg+q8r3rmP2Lc84555xzzvf0T/CYzznnnHPO +Oed8jcf8WK7Vs/p/kvyz75tZO7L49ndx/o1n4zaL0fPlrh7T364zu/kRZ3/v +U33UfIn3Wb0O8Hf6qPPM2XUvu3727+Kcc84555xzvsY/wWM+55xzzjnnnPO9 +/Hi/i/mj6sk81nf87X3frMpxvtKrcRtjt+88V3nruvFU321fmO1ZZOMkpjnf +yUedW86uJ7G+s+ttbz2cc84555xzztf4J3jM55xzzjnnnHP+Lj/eH2P+WY/3 +G/XempWvrud8hsfY7fvPVT5q3djFd1ufZ3sVu807/kzPxufs79u7nX8455xz +zjnnnD/DP8FjPuecc84555zzd3nMP/7+hPTZ8pXH+nrfZ6tynF/prbHb96Je +j+lv14GrPWv/buvz2fW8N3abR/xdPuo79qh14Gz5mM8555xzzjnn/J3+CR7z +Oeecc84555zz/xPHe2XMH1VPb/0x//g76n05q5/zHm+N3b4XjfbW+b7Kd1tv +R/nZ2G0e8Xv46HEb6x29zmT19NbfWw/nnHPOOeec83f5J3jM55xzzjnnnHPO +R/rxflpdd/ztfZ/N6h/1vlyV4/wbj7Hbd6Szns3HXXy3dbLXq9htnPN7+6jv +zL37dTX+s3a21s8555xzzjnnnM/wT/CYzznnnHPOOeecX+Gj3lt/kutGe2xH +5dXviPmc/xW7fV/KPIur5mnVjiN2Ww9b251dt8u45Xt5Ni/uvs9W7Wyth3PO +Oeecc845n+Gf4DGfc84555xzzjl/ssf8+DfGT5KfeVb/qPf3qhx/tsfY7btT +5a3zaJTvtv5UzzOL3cYhn+ujvutW9ffOr+x+3+53nHPOOeecc875k/wTPOZz +zjnnnHPOOee89uy9O6aPvz///F4u86qemF95a/38nh5jt+9RveN/lO+2blSx +27jifT5qHPbW37vO9+5rnHPOOeecc845b/dP8JjPOeecc84555zz6zx7f4/p +4+/PP7+XO+vxPr3fE6pyfK3H2O171OzxvGpeV7HbOHm7jxo/o8Zz1o7efYRz +zjnnnHPOOefX+yd4zOecc84555xzzvn9PObHctGzen6K67PysVzmve3JyvPv +PMbs71FZe7Lx1utZ/VfNuyx2e+539VHrydl1LBuHre3JfLfvxpxzzjnnnHPO +Of/eP8FjPuecc84555xzzt/rvd8TfpL86ntF1a7W+8brsnp4m8e46vtVNn5a +ffa8qGK357i7j5rXveOhd73qbSfnnHPOOeecc875J3jM55xzzjnnnHPOOb/a +Y378G6P6HhKvG/X9pCr3VI8x+vtV9rxaffQ4zGK35zLLR31X7H1e2X1728k5 +55xzzjnnnHO+yj/BYz7nnHPOOeecc87507z6fhKvG1V/TD/NY4z6TpU9l1Hf +u6rYrZ+/9bPzIvPW+bLbd1HOOeecc84555zz2f4JHvM555xzzjnnnHPO+Rqv +4rguXr+bxzj7XSu7Xwz9yTnnnHPOOeecc8538E/wmM8555xzzjnnnHPO7+3H +d6GYn30viulZnrUzXpe1v6ovi1m/a1T/c84555xzzjnnnPNn+Cd4zOecc845 +55xzzjnn/C8/vjtV18X8zEdF632z9u/2HY9zzjnnnHPOOeec38s/wWM+55xz +zjnnnHPOOedX+KjY7fsb55xzzjnnnHPOOX+nf4LHfM4555xzzjnnnHPO//KY +f/z9CekjMh8VZ++btT/mc84555xzzjnnnHPe4p/gMZ9zzjnnnHPOOeec39tj +/vG3+o4U6xvlWWTtien4tzVm/67R/c8555xzzjnnnHPO7+2f4DGfc84555xz +zjnnnK/xLI7vPPG63TyL3u9XMR3/xtCfnHPOOeecc84553wH/wSP+Zxzzjnn +nHPOOedP8+w7SUzHv9/W/5PUd3fPYtR3qqzcqO9dWezWz6P87LjNrm+dL7t9 +F+Wcc84555xzzjmf7Z/gMZ9zzjnnnHPOOef8aj++Y8T8qnxW7hPqG/X9JGvn +Uz2LUd+pYvqsjxqHWez2XK7yI872c3Z977zubSfnnHPOOeecc875Kv8Ej/mc +c84555xzzjl/r/d+T8jKZfVU5bNyre3M6uF/exazv1PF9FmfPS+y2O053sVH +zetYbvR6dbadnHPOOeecc845f69/gsd8zjnnnHPOOeec38+P7wAxP/Osnpgf +/2b3jddV3tqe3t/F//YsrvpOVY3rbFxU3juuRnkWuz33p/gRo597Vn9Mnx3n +Z38X55xzzjnnnHPO7+ef4DGfc84555xzzjnn13n1Xl/VF/NbfdT3hKydfK1n +sdv3qKrct+N51bzOYrdxwv/bjzg7fqrre8dzVi7Gbt+fOeecc84555zzN/sn +eMznnHPOOeecc8557dX7eFVfzI+e1dP7HeBs/fwensVu36Ni+irfbd3IYrdx +xc/5Ed+Ow9n7yNl9jXPOOeecc84557V/gsd8zjnnnHPOOef8yX68L8f8rHzM +z647/mb1j3p/r+rnz/QsdvvulHlMX+W7rT+tz/WI3cYhv9aPODueq/Wkd1+L ++aP2O84555xzzjnn/En+CR7zOeecc84555zzK3zUe2t1/bfe+95d1RPLcd4S +u31fqsZ/FrPmaeVZO3b3LHYbt3xPPyLOi7vvs73nCs4555xzzjnn/Er/BI/5 +nHPOOeecc875SI/5x9+fkD6i9322qj/m99ZftZPzM57Fbt+Rej2md/Xd1smz +62qM3cY5f5YfcXYeZdeP2pd76+ecc84555xzzmf4J3jM55xzzjnnnHPOf8uP +f7+tp7f+nyR/9Ht0Vj/nf3lv7Pa9aJTH9K6+23o7et1ujd3mEb+Xjxq3vft7 +TFc+ah3bbb3lnHPOOeecc76nf4LHfM4555xzzjnn7/Lj/bG67vjbW76qJ+b3 +vs9m7eH8Su+N3b4XnfVv14FVnrV/t/W513tjt3nE3+1HVPt+Nf6/XQd6y69e +hznnnHPOOeec7+Wf4DGfc84555xzzvm7PObHcq0++721qidex/kMz2K37z+z +Paaf4rutz1et/zF2m3f82d677z/1/MM555xzzjnn/Bn+CR7zOeecc84555zv +5TE//v22nsx/knK975tVPZyv9Gq+xNjtO89sj+m3+m77wlX7Toxq/Owyrzn/ +zY84e26prs/OUTG/d73dbV/gnHPOOeecc/63f4LHfM4555xzzjnna/x4j4v5 +vZ7VH/OPv73vlVk9s38X59/4EdV4rcrv9p3nKv92ndnNR/3ep3rM/3a+7LIO +8Hf7EWfPM6PPV7N+F+ecc84555zztf4JHvM555xzzjnnnM/17H0tpiuv6mm9 +b+VZO7L6Yz7nO3gWvfP0rd7bz63r2Crv/V277SO77l9Z+V3WAc5/8yPOnn9a +95vW8q3rmP2Lc84555xzzvf0T/CYzznnnHPOOed8jB/vZdV1Mb/Ve+vPynN+ +R8/GfRa7fZ+5i1f9/O06tpv7njbWs6jG4S7rDOff+BHfnt96vWpnvI5zzjnn +nHPO+Vj/BI/5nHPOOeecc87HePZeFtNnvbf+qp0xn/OdvYrW+cL/23v7/9t1 +bDfv7Yfd9p3dPOZX5XZbZzjv8SPOnsey8r1enffidZxzzjnnnHPOx/oneMzn +nHPOOeec87d4zD/+/oR0Vb63/uq+Mf+sx/txvrNX8yjGbt9b7u4xzdt8t33t +7p6F/Y4/yUfPl2/PmVX5ql2r9y/OOeecc845380/wWM+55xzzjnnnD/Nj/ej +mD/bY7uOv6Pe77L6d+sH/k4/Ihv/WfksZs2jt3lMj67n7t67v4yqh/+eX5Ub +tf5wPtOPGL3+9M6j3fqBc84555xzzp/qn+Axn3POOeecc86f5sf7UcyvPNY7 +2nvbw/mdPJuPWez2/eRtXj2vrNxb3He2PT0L+y9/s8+ed7ueqznnnHPOOed8 +F/8Ej/mcc84555xzflc/3oNifvZ+FNNnvWpPVV8sn7Wf8zt5Fd/OI/6d9z7H +b9fJu3tvv+22P97dz+7jWT27rJOcj/Ajzu6n1fWtXt23tf2cc84555xzfnf/ +BI/5nHPOOeecc35XP96Dqutifqtn9VeetTvW3/u7OJ/hZ+dXVj7Wy/fw1uce +88+un3f3Uf3J13oWvfv4bus2f4cfcdV5Mqu/18/OL84555xzzjm/q3+Cx3zO +Oeecc845v6tn70ExfdZ/knK972Wj78v5SM/mVxa7fffgv6f5Hr7bvsn/jmre +7bJu82f7EbPWmVH37W3Pbvsm55xzzjnnnI/yT/CYzznnnHPOOedP85gfy7X6 +qPeyqv5YjvMRfkTr+M/i6vnCv/PsOcXIysfrzq6fd/fe+dXb//waj/mj18Pe ++cX5N35E6zi8ar44D3DOOeecc87f7p/gMZ9zzjnnnHPOn+YxP5Zr9dHva/F+ +nM/wal7EyMrv9n2Dt3m1Xp5dD/nf3jsf+Z6eza8s7Pt8Bx81/mP+t+thzOec +c84555zzp/oneMznnHPOOeec86d5zI/loo9+L4v343yEH1GNtyqy8d97X77G +e9fDrJ6qXv679/az73X38mpdrZ5fVU/vfTn/xkfNi5hfrZO77Zucc84555xz +Pts/wWM+55xzzjnnnLd69t4R05X/JOUyn93Os+Vb2895jx+Rzacqdvsuwed4 +6zo5at3mv+cfMep58Wd4Fr3r/Or9iD/Tj2hd33rLj9rXett/VTs555xzzjnn +PPoneMznnHPOOeec81aP+cffn5A+YpVn7a/ep3ZpP3+nV/Mui975GK/j9/Te +8RPHCR/ro54Xv5dnzzdeV81P5xO+s1fjP5bbrf2xfbvs45xzzjnnnPPn+Cd4 +zOecc84555zzLI7842/1PhLrG+3ZfVt9dr9d1Q/8Hl5FNS6r8rPnC1/rMT26 +Hj7WR+2zu50H+Dmv9oVv1/8sdtsH+R5+xOh9avZ8GeW96/Bu5wHOOeecc875 +/v4JHvM555xzzjnnPEb2fhHTx9+ff34vV3msr9ez9oz+XVl+jMyr+nv7jd/D +q/EQo3fc8nd467jKysfrqnWPn/Oz+13r8+XP9up80lp+t32Qj/UjsvUn5vee +Y7NyZ8dtaz1n58u3/ebcxTnnnHPOOR/ln+Axn3POOeecc85n+aj3mpiuvGpP +zF99X76nH9E6brPnn0U1br5tD3+GZ+tOFq3rFb/GRz1f/myvone/+HZcrd5/ ++Tk/4ux6dXY8zLrv2XEby3HOOeecc875bP8Ej/mcc84555zz9/rxHhHzK8/q +/fzz+98ssnKtPvr3xut7f2/mZ/uZr/EjsucY87PY7fsA39Or9aq1nqpevsbP +7lPVfap6+Ds9i97z2G77Mv/bj5i9LmXtidfP3qdGvY+Meg/inHPOOeec80/w +mM8555xzzjl/rx/vETG/8qzeT3LdLM/a2Vt+1XvZ2f7ncz17XlmMmkf83d46 +DnvXPb7Wz64DreOBv9N7950sesch38OPqM6Zs8db1o7d9qlR82j1OYFzzjnn +nHO+r3+Cx3zOOeecc875ez3mx3LRf5JyvfXM9qx9q97LsnZm/cnP+RFZP8f8 +qp4sesdb1v6sPfydnq0XWeyy3vJzPmo88Hd67/4S09X6Mmpd2u2ccHc/ovUc +ctU4zMrttt629mdVT8znnHPOOeec80/wmM8555xzzjnnMbL3i5i+m696Lzvb +nng9/9t7x3kWu73X82d4TGfrVoxd1k9+jY8aP5x/41mcXQ93OSfcxXv3hdXj +ZJf1s9ez37Xb+YFzzjnnnHO+v3+Cx3zOOeecc875e/14j4j52ftFTO/q1e+N +1632rP/57947zquI46Z3XnD+m387nu++DvO//ew+NWud5O/0bPzE66r91fnn +Gt91/GTldllvM++dF6vPFZxzzjnnnPN9/RM85nPOOeecc87f66PeO2J6tc/+ +vaM9tvfuPrr/W+uv4qnjh+/p386XmL96XeXX+Oxxxfm/Y/S5rrX+UePW+Wqt +3/29YPR445xzzjnnnL/XP8FjPuecc84555zHyN4vYvpuvvp9Lbbvbn5Eaz9X +4+7berK4y3jgz/Zs/MWoxvcu6ye/xleNN85bPOa3jvMYV50TYvms3Orz1bd+ +t/Gwi1fjIV7HOeecc84555l/gsd8zjnnnHPOOY9xvF/E/Oy9I6Z39dXva1l/ +7uKx3Vm/xnKzPIvVz5G/01vny93XSX4vr9bPbHxm9WbXcz7Ss1i1zsd0NV92 +89XPcZf1MPOs/b3vO5xzzjnnnHOe+Sd4zOecc84555zzLI78WO6u/pOUu+p9 +Lbvv1R7bl/VfLPetZ/etorWdq58vf6bHdDWvR5Xn/N9/Z4+3VecN/gzv3X9j ++ux5YLf1f5Wver7xutXr5Cjf7RzCOeecc845398/wWM+55xzzjnnnM/ymB/L +Xe2r39di+67y2J7V46G3fGx3Vr63Hzjv8dZ5V43P1vpjudXrJ7/GZ4+r3vo5 +b/He/Temq3U4i92+t686760+1+22fsZ8zjnnnHPOOZ/tn+Axn3POOeecc85b +vfd9JKZ39dXvcbF9o3zVOKli1vPqLc95j8+aXzF/9XrI9/S7jGf+To/52biu +yp/1GLvtF0851+2yHmbe+7tWjxPOOeecc875c/wTPOZzzjnnnHPO+bd+vI9U +18X83X3Ue1kWWb+d9Xjf2c+9ilnPpRqH8TrO/+0x3boOZOWy2GUd4+/0al58 +u1/P3l/4M3zUOnzWW9sz+zv8qPNeFqOeV8xfvY71eu85mXPOOeecc85H+Sd4 +zOecc84555zzWX68p1TXxfxd/Kr3uNiOXp/9HKtY9Vyy/onX8Xd6TGfj64je ++dV7X86v9N5x27uu9t6Xv9N3PQdm7YzXvfW8t8s6lrlzIOecc84553w3/wSP ++ZxzzjnnnHN+tR/vL9V1Mf9qz9o5+j0uq7/VRz2XKq7u/2r8xOs47/HWeT16 +fu2yvvFn+Ozvh7P3Hf5Oz8ZhTF/tre28+3nPOZxzzjnnnHPOx/oneMznnHPO +Oeec8138eK+prov5V/vo97h4v8xH9XMVV/dnNR7idZz3+Kz5ld03pjlf4aPX +1av3Kf5O33VdbW3nXeZXzF/dz1U/xOs455xzzjnnfDf/BI/5nHPOOeecc767 +Z3G8B1X1xfxZfvY9Ltab+ah+i9dd3T/Z743Xcf5vj+mz8+vsPLp6vnB+pY/a +v3rn0ahzAn+273bey2LXc+Cq9aRq1xG7nTc455xzzjnnvNc/wWM+55xzzjnn +nL/FY34s963/JOWq97jW8tXvymK338v5b+mq/Nn5nsWsecH5mzzGqO+WWblR +5wH+bM/OJ/G61fOit/27/d7dzhWcc84555xzvso/wWM+55xzzjnnnL/dj/ep +6rqY3+rVe1x2fW/MbifnI713Plae3be1fNU+zt/ovfN09rze7fzAn+0x/9v5 +FWP0+fDbdp7dZznnnHPOOef87f4JHvM555xzzjnnnI/xKo7rjr/Ze9zZeuL1 +u72fcv6bZ+M2+qh52vv9pCrH+RO8d17cfR3gfIZn4zZe17rfVPlVudX7O+ec +c84555y/xT/BYz7nnHPOOeec8zWexfF+F6/b7X3zKa6ff/dq3MZyo/s/+qh5 +l7Unpjnn/fNot3Ug5p9d997ms9dh/p/I+jmL3c4JnHPOOeecc87/+28Mzjnn +nHPO+Xv8eF+I+Vn5mB//tpb//7d3t8mWqkoCQOc/yx5CD6Gjo8J4VflOHj42 +SOpe+afCBSJbERG5544ed/Xvjfmy+uz2VvSe51P1H/1drXKuiNdllffWf7Rd +xfTZes62212+6r7Lyh29Xrv7vayenPN+v6uf7+0fWvX8tD6r+qXZfuzT+mT7 +V3vOru7ne/Of9it678cYp+o/2m539w8xX6uc0fynx7ecc84555zzuv6/wWM6 +55xzzjnn3+gxfXZcneXL8v9PIz3bP6tnbzmj9Wl5PE6rnjF99rjVPYvR85ZF +6zrGfNXOz1t9tH/I/K55g+rnbba/yvbvPf+c88991f371n5s1GP6p8+RKuft +rd5q/618MXrvryyqnZ9T467Zfqm3v8qOu/u9b9V72ej5rPb9i3POOeec8wqe +jas555xzzjnn/x2r5qsz3z3OH53/b83z8589i9HrGLdbvrqdVzmfT/fR8x/T +d/Ubu89DPG6r/p+Wwzn/Hh99fq0qx3OBj/gVs9clbs/eF612FeP0eXuqX5Hd +j73tZPQ67u43Wv1kzM8555xzzjn/bx8dz3POOeecc36nt8a3cb9WOa3jZ+W1 +xs+j8+2z895Z+fyMZ7HqfS1uz7bPU/cj/91X9Ven+5N43NX16S2nlY9z/jw/ +1Z+c6j9H+7fZ/rnKc/Ap3moPMd/Tx4FZVLsu/F+/Ylf/lu0/2p9/2l+duh85 +55xzzjn/xEfH55xzzjnnnH/iq8e3rePH9Oiz88Ot48RysvL5MzyL3e9rcbu3 +Pbf2y45zl1e7vtW81f56r/uq455uD3H/VfcL57y+n+pPdo9Xq/X/3+pX3N0e +oo9e98x3P6+zOH0d+Vq/YnU/3Co36996+8nZesZ8nHPOOeec7/BV41jOOeec +c857PBuXxu3Vvnv8fHr+nK/xLE69r8XtWa/WD8zeR3H/au1ndXtonb9W/mrX +d/S5MNoPt/Jxzp/nq+Yzq83HPqX/P/087f1ddz2Xd3ncnvVTz/EsqrUf/plf +sbq9tcrddV9U6wc455xzzvm7fdX4mXPOOeec8x6P6TFfr68a956e3+ZnPIvT +72ut+2n2fsm8Wv9Qrf8ZLeeufq+3nWT5T53/1n0a9888bnPOv89P9T+nnvu7 +xwmj/e2q/vn0+b/b4/Zqr/bcz6LaewG/16+Y7c9b++t/OOecc855RR8d93LO +Oeecc/6Jx/SYL/rovG5WTlaf0/PSfK9nUe29LG7f5d4T1/qqfmm2v+o97iof +rU+19s85/x5f1d+equfu/rZ13N7y+b//ZlG9/e/2LKq9R/A9fsXq/jArJ/Nq +/QbnnHPOOX+3t8avnHPOOef82R7T4/gw7rdq3Dg679qqZ0yf9ez38md7FtXe +v1bdF6s9RrV+7Nt89r7Iyj3VrjjnnI/57ucCv8dbUaVdVfMsqr138LW+uv2s +6m/jfqPzJK331rh/tX6Mc84555yv9VXjXs4555xzfo/H9N5xYCxv9zzqXfOQ +u34Xr+FXtO6Hau9Zox63T7v3x3t81X3x9PbGOeff5k9/jvB//83ibe3tlGex ++r7gz/DZ9hPvh9l+8u7fFdNP93ucc84553zOR8exnHPOOef8rMf03nFgLO/U +vOLouLTaPDC/x7NolXNF731RxeN2VfdeudZn75dY7lvbG+ecv9Wf/hz5Ns/O +fytfFV/V3k756vcF/m6/otX+nzJ/EtNP94ecc84553zOs/Ee55xzzjk/6zE9 +juta5Z0eZ2aRpZ+ev+VnPItq702rPTs/MX/crureN3/3mD7bHla977fycc45 +3+u7n5tPeV+o5tn5auWr4qPtYVV7q+ZZVHsP4vf6Fb33+d0e02N/pT/nnHPO +OX+2nxpncs4555zzP9Eav8X9WvOKcZyXHTfLP+qt39U6H6vHpafne7/dr+ht +f9Xej6q9f7X2r+6j/VtWTrV+e5XH9LvaWysf55zzvb57nnb0uE/3uB3zZ/my +qNJORt13gd+9Fb3th9/rV9zVP4yWM+qr5nNG+7dq/TbnnHPO+bd5Nk7jnHPO +OedrfdW83+55wlHf/XtXn2e+17NoXa+Y7+3eaten7+vdPnoeRu/3Vfln2+3o +/XL3782Oyznn/B4fHSevfo/Iyhl9vmT1zLzK783yv9VXjX+e7q32k+XvvV/4 +Hr+i1c/E7ez+mD1uVv5ub7XTXb+Xc84555yv9WycxjnnnHPOa/qpecLWODPb +P8aq+dXR+vA5z65jFtXed57irfO8675+is/2J3ffF6v7t9H7scr14pxzvtZH +n3dZOa18MZ7ynI3b3+rm/9d6Ft5D7/HWdbm7fxutzyqfrT/nnHPOOa/lo+NV +zjnnnHM+56PzfjFfTK/irfnVuN/ucWy1+eSn+RXZ+Y2RtYeYzn/3uM33+Gz7 +j+XM9vO95XPOOec7PKbHfDFWPx9bxz99ft7qo9ed/5zemy/G6fe7p/sVd7Xn +p/dXWf1H+3nOOeecc77Wd49jOeecc875n3jrd/nRedTVnh2X/+xZ+8zi9PV9 +qrfOc3YfxfRWuZxzzjnnnP+UHiPm871gzrP3oyy8z67109e3yv0+6q3fG/fj +nHPOOedrffc4lnPOOeec/+5vXY9xahxbbd741Lx0q11lcfd1/DZvXYcq9y/n +nHPOOX+H+y5wj8f03nwxWu8Xcb+3+xV3tdvW8ar7bLvinHPOOed7ffc4lnPO +Oeec/4lsvjHuF9Of6qfGsafnje/27DxkMTrvzec8bs/m55xzzjnn/BOP6TF6 +8/M5b80DZPljudXeQ+/yK+5qn63jPdXNA3DOOeecn/Xd41jOOeecc/4nsnmw +LH9Mz/ar6qfXvcR8u330uo/+rlY7yaLK9fpW/5b7nXPOOeec1/RV41U+5zG9 +9zrGWPX+OPp+eur9Otaj9btOX68qPnsds/ycc84553yN7x7Hcs4555zz3310 +fixun/bW74r7nVoPs9rjcUeve2v/Vrmtck6ff/7vdkzPosp9zTnnnHPO3+Gr +xqv8Ho/prXyt/KPtoff4u9+7T53/t8zDZOc5lsc555xzzu/xU+NbzjnnnHP+ +c3pr/JblP+Wn5/2y467yeNy72sOn5VR773irx+3Z+yIrh3POOeec8088pl+R +jVdHy+FrffZ95NNyVn1X2v2eftf5770vTnnr+sd81d6jOeecc86/zXePYznn +nHPO+ZyPzkPG9Gy/1X7XODbW4ynzuq3rlUU8z6PtpNp7x9u9+n3KOeecc875 +3/+uGt/ytT76fhe3s3Jb5Xiv/91jetX79PT15ZxzzjnnP/vu8SrnnHPOOb/H +Y3rMd7c/ZV73ruuSxVPOM//dP21XMf30/cs555xzzt/hp8a3fK3H9E/bSQzv +7z+nP/X+5ZxzzjnntXz3OJZzzjnnnN/j2Xgvbt/lu8ers/O6veWPeiueev75 +z9uz+TnnnHPOOa/sMT1Gb34+5zH97vYQ41vf66vcd9XeiznnnHPO+ZyvGq9y +zjnnnPOaXm3dyOw4NpY76qvOZyt2n7fs98b9+JzH7db5H80/Wg7nnHPOOeef ++Kpx6Wj+Vj4+5qffI7L6xP2e8r4f0++6H1vXN+7HOeecc87f4aPjVc4555xz +/g6P6THfLs/qs3v+dvb8ZLHr/LR+V9yP7/FP21VMb7X/LD/nnHPOOeefeDbu +Hc2/+/2Lz3l2/uN+u9pbVp+436l2Ndr+d/vp91zOOeecc37GR8exnHPOOef8 +3X5qXnfV/O3o723Frt+bebX3hW/1eJ1G36da+TjnnHPOOa/oo+PeVe9lfK3H +9LvbVYzT7/u775eY7/T7LOecc845r+Wj41jOOeecc87/jmweMu4X01vj0Vh+ +3G90nrYVo/WMbj62psft2evYav+fHpdzzjnnnPMKHtOvGH0vW3Vcfo+vfq9v +Xdd43Ljfqfd97/Wcc84553yHrxq3c84555xz3uMxPeaLPjv/v/u4vKZn1zXG +aP5V7ZlzzjnnnPMn+qrx+arxPK/pMb23vcUYbQ+jxz393so555xzzr/Lq43b +Oeecc8457/Esqo23V3s8H63zk437o2fHbeVvXbfZ4646P6Oe/Z7R+sRtzjnn +nHPOn+AxPeaLcWp8PuoxvXUeRt93Vh83pu8+P9U8i9Pv45xzzjnnnM94tfE2 +55xzzuv46HxpLG92vLHquJm3yo/7jY6jsnyjv3e0nCx/Vv/d9RydT26Vn8Xo +9V3l8fiz9Yn73VX/T320HWY++17z6fWq1i9xzjnnnHNewVeNt0fH4aveRzJv +1SM7DzG92nvZ6PlZNf+wu/5ZfbLY/T67an5g9ri95a+ex8jSs3rHuGse79N+ +6dRxOeecc/49PjqO4pxzzvk+j+mt53iWf9VxW/WJ+VbNt7TqGWP1fEtvOaPz +MKuu+13zind7FqvnObPyq5yHp/vu/m30uKt8Vf/GOeecc875E/30OoR43Kye +Wb4s/+z7Ph/zLL7tff+KT9vhqnaelbPqvTs73mw5MUbbT+a75zlXzVuu7t84 +55xzfp+Pjn8455xz/rmPzm+sWhexaj6hVX7cb/e4ZXR+eNV55nOexe55qlHP +yq92Pp/iq87zqf55Vf/JOeecc875E332vSCWt9rjcVv17y2H/+5XjJ7nXs/K +b9WjN6qdz7f7Fa3ruKqcVT7aPjOf7SdX9ben+mfOOeec3zdu4Zxzzr/Zs/ff +LH9M//S536rv6nFFq/yYj7/bs9jdnjM/db+/1a/4tD9pxWj5n7YTzjnnnHPO ++f2+av6kla/Xs/KrvZfd5VfE8/Cpx+3V7aR1fWOcPs/8jF8R29tou1rVn6wu +P6afut8555zzb/ZV4wrOOeec55E9dz/17Li737uz+swelz/bs9g9Xm3l622f +p/qH0fsxbq+u/6rrldUz81XngXPOOeecc/49HtOvGF13MVr+qO9+zxo9D9W+ +Q7XyRd/9Xp9FtXkYvtZH2+dsP9B73FPzIdW+X3POOedv8lXjVc455/ybPabH +fLt8dL4xy1dtPoTX9CxOjWPj9qxX60+e4qPzirP9T9z/1Pwk55xzzjnn/H6P +6TFfjFXvF6vL+XaP23e1h1WeRbV5G17br2i189H53t1erT/hnHPOn+inxrGc +c8753zE7D5Z5drz4/Ntd/+y4o/VZNd/VKn/0PPN3ehanxqtxe7UbJ5/10f58 +9HkR893VrjjnnHPOOef9no3n43bLV79f8DHPrksr36c+2k5WeRbV5nl4Db9i +dXuuNi99ar56d/0555zzT/zUeJVzzjn/LT3mi777ffmu+sf03e+5o+sZ+Lv8 +ilY7fsp4tZXvU6/WT77VR9vtqv6Qc84555xzXsdjeszX67vfL/jvHrdX+1O+ +c2Ux2275s73VTnb1h6PHzXy2f9h1Pu+qP+ecc77Sq41XOeecf6fH9N7nWiyv +2nt05nc99+8+P/ysX9Ea5/WWH8s7NS5dNQ+zykf7B/5zem9/FfcbbT+tfJxz +zjnnnPPzvur7xej7Y7XvNVW993zu9tH3x9H2s8pb5y2L0d/L3+m722dMn+2f +q52fmF6l/+Scc87//jcG55xzfqfH9Pj8ivtl5YzOz4wed9X83qrj8u/2K3rv +qxjVxqVxuzVezfKf8lPzaW/1Vf0w55xzzjnn/Lm+6n2Z93k8nzFflfYQ07P8 +rd9zt6+ezxm9L/h3+RW990WWf/dxZ/vz3uOe7lc555zzv/+NwTnnnH/iq+fN +RvPf7VlUex/n7/AsnnK/zN5f2fj1bV6tP1/dz/e2z9H6tPbnnHPOOeecP89X +fe/Y/f5SzeP22z277k/x1fM/nM94Fk+5X1b3/7Fczjnn/BOv9jzlnHNe01fP +d8VyRt+nsnqMHjcrJ/PR8zNazuz55M/2VjuPUW08udo/7Qee4qPnYfT87PaY +PttPvvX6cs4555xzzu/32fmrmH+0/FPvy96j//Xe8/B0z2JV++HP9Cta90vc +Xt1Pzpbfug9W9wOj53P0/HDOOed/e7XxJOec82f5qvmrLP8pb/3emL77/XS2 +PrymX5Fd1xi999HTfVU/83RfdR5G+43V/XzvfZGVwznnnHPOOeerfNV7SpZv +dJ1AtfUST/HR89C6rk/1mN6bL8bp+TE+51fEfiZ63P70/vq0Hzvlo/fRbD/P +Oeec/+bVxpOcc86f5bu/75/y0d+7+70489PzAHzMs1jVrp7ucZv3+arzPNue +e+uT5eecc84555zzUx7TY8R8q96bWvl668N/99Hz/HRfPR/Fa/kVd98Xo/OW +q+q5ylu/K+5nnpZzzvkOrzZu5JxzXtOf/v416tl5yPKfWhfBa/gVrXZTbRxY +1bP7JIsq/QbnnHPOOeecc873+ar5BP57ZPlPz7/xMb8i3kez7aT3fszyP8Vn +238sj3POOf/bq40DOeecn/VV61Ky8lv5qvip96y7rhf/2a/obQ9ZeE9f63Gb +c84555xzzjnnPEuP+fjPvmq+Kx7n+rfavN9b/Ip4nqOfbj9V+ofMR8/b7uvF +Oef83V5tHMg557ymZ9HKnz1vqnu15/Xp9/1v8dH2f7o9vNV7r1fc/3S/wTnn +nHPOOeec832+ap6Hz3kW5jPPetV2UqXfGPWsPWdxeh6Vc875M7za85pzznlN +b70PZvtnz5sqPvp8rPa8rjYPUM1H23kr4vWo1k7e4r3XN+5/uj/hnHPOOeec +c875Pn/6epWn+Ox8b2851nF95le0rsOpdtJqF1X6k8xbv7f3unDOOed/e7Xx +Huec85r+1nVZmVd7z5q9Lt/iV4xe9yyy9hDT+ZzH7d523lsO55xzzjnnnHPO +3+cx/YpV8w98zmN6K18rf/Rq85Cn/YrT7Xn1PG0VH/291eZdOeec1/Rq4zfO +Oec1PabHfG/zas/r0+/7u/yK7Pz3ltNqt9nxWulVrvtbfdX1rdJvcM4555xz +zjnnfJ/vnmfgcx7TW9cri1XXt1Wf3nKe4k9pD2/10/OrnHPOn+HVntecc85r +eus9Oj5XsnKy/NW89f4b96u2juW0Z/Vf5a32FaO3fZ6+vvzf7ZieRZV+g3PO +Oeecc8455/t81XwCv8dH55OzOHV9T8+v9vrp69va73S/kfmq7x2n51E555w/ +w6uN0zjnnNf00XU4cftpfmrd0Wx9qviqdhX3y9JjOXE/XtPj9uz1bZXDOeec +c84555zz93hM743ecnhNb0W8rqvndbNyqnis913t/OnrsjIf/b3V5l0555zX +9GrjK84558/ymN567mT5q7l1WT9v3+VZZPm9Fz/TW+3iLf0J55xzzjnnnHPO +P/eYHiPmqzbfxX/30fm9LKrNd1mXVdNn+5OYzjnnnPd4tXEX55zzd3hMj/mq +e/a7Tj2Xv239Vdyv93z2/q5q47Fv9d7rFdNP9w+cc84555xzzjmv46vmH/g9 +ftd80ehxd3us32qPxz11HVv1qO6n2wnnnPN3erXxGOec83e497LPPNbj29Zf +jfrovASv4b3tM6af7gc455xzzjnnnHNex63Leodn1yvu92n7yY4b9zMP/LvH +9NP9wKi32mHcj3POOf/Eq427OOecf6c/ZR2X9/HfvRW7r0t2HuJ+fI/3trfR +69Vqb1X6B84555xzzjnnnO/z0XmD2fmirB4x+Fq/a11Wq93E+sT9zAP/nH66 +f2i1q7gf55xzfqdXG3dxzjnnf0e19Vqj9Tz1Ph7LXf3cb8Wu819tHMX//TfG +aPscPW6rHpxzzjnnnHPOOX+Px/SYL4u4/6r/Xoyf9Zi+qx3GWDWflh232rqs +avNyo/XknHPOK3i1cRTnnHPe49XeB6uty1p1nlvx9PPM1/qu9lntfuecc845 +55xzzvn9HtOvqDaPwe/xmH53+4zx9vnhp9/vnHPO+UmvNo7inHPOd3hMj/k+ +9ey4u9+7R+vTOj9Z7DpvmVcbL/E+72231e5fzjnnnHPOOeecP9erzWPwsx7T +726fMUbbZ1b+W/+7yNPzmZxzzvkdXm28xDnnnO/wp71XxnJXr2/JYtd5yLza +uOhbvdWOZq9jtfuRc84555xzzjnn3+Mx/YrReYzR41rfVdNj+t3tM0bVeeMq +9yPnnHP+Jq82LuKcc84reEyP+T712XUsWbmj8Wn9W/WM+/Gavup+ac0LZfvv +ur8455xzzjnnnHPOM4/pV4zOb/ge926/a16r97ij7bN1nF33V7X5T84557yC +VxvncM4555U9psd8ox5j9j06i976ZOVXG7fwzzxe51mP5cft3uNm+2Wx6r7j +nHPOOeecc875e3x0niGbr8j2Hy1n1Fv14M/w1eu4estv7ZfFrvuOc8455//t +1cYtnHPO+Td4TG/la0Usp9p4o5rH7ZbPrkdqHSfG7usYj797nnB0XdbovCjn +nHPOOeecc8756DzG7HxF5lk5vZ7Vc9Rjeqv+o+WM5h8th/+c3srXit72wDnn +nPN9Xm28wTl/n696L477tfqxVd/3R+s/Wv7u8zlaz2rt5+k+u/6kN0bbebVx +SFbPVffFbo/1mh13tfKtuo6f/q5V98Vo+Vl+zjnnnHPOOeec81X/Pd2qea3d +67Ky47bq09qvVf6p+bdT8427Paa3zvNozH6Xifn4nMftT8vfdV/M1rPV3j/t +J3vrP3t+Pj2fnHNuXRbn3+MxfXZcsao+p8Z7o+dntj6fjjNX1XP378181fWd +PW7v+d89T7J6PU+M2XmSrJy7fxf/eXvWY/rsuO4p9c/yc84555xzzjnnnI96 +TI8R863+HhePv2rePst3uv58jWfx9HnjK1bdp73lr/LReq7y3d/dZsvZdf5P +fR/Mytm9HmPV9y/OeX1v3eec8/u82nvQqnHCqK96P71rvLSqnN7fu3t9xew4 +8NP8b/UsRq9vzDf7HK92fvjP2y1f9X566rkWtznnnHPOOeecc87v8ph+xenv +d1m9V9Uzlsdr+BWt6xi3Z9tPFqfPw91+Re/5HM2/+z5t9Q+99Wn9zqz8T8tZ +VX6175XVvi+cfq5xztf3k5zzfT47Don5V733teoRfVU9s/Jnx8nZcVeNb/l3 +eRar2nnmq/qZrPxq55n/HqufO7ueC5xzzjnnnHPOOedP8dnv71n+Xs+i2jwV +/zdG20+vZ+Vn3qpfb1Q7z7yGX9HqD1vtLbtfeu+v0Xa+6v5adR5G6zman3Ne +x0f7Ac75577qub/Kq/VLs+ONauNS/k7P4inv16s8q0+163XKR/v/0fYw+l6c +lcM555xzzjnnnHPOz3pMv+LU+oRq82yn54Hj+T31fSSrT+aj7SHzLKpdL/4d +fsXqdr7bY3qV50vcj3O+z6v1S5x/g8f0Ks/fbP/e/KPHna1n3O/0OJC/07Oo +9n6debV+b7QfWH2es+ue1S+rz6fljPpoP3yqvXHOOeecc84555zz3z2mx3wx +njIftaqc0fOTeVafat9nnz4/nEW1eX7+Dm/1J1m+3n6glb+3Hz7Vb496tX6P +82/w3c9lzj/xmP60djv6nrLbV40HRn8v55U9i6e/d2derZ+s5rvnhU7Vs1o7 +5JxzzjnnnHPOOX+rx/SYL8aq7/un/Sn1rOJx+3Q7XOVZVPsuwPmIXzF73z39 +e3E1j9un68N5j596LvN3++y6iNHnV9xv9Lh3nYcs3+7naUxf9Vxbdd05v9Oz +qPb8beVb1T/c3R/yOd/9/litfXLOOeecc84555w/xVd9dzs1/8Pv9Va7qNo+ +V3kW1b4jcP6TX9G671bfL7v6h9bzKO63uz8c/W41el08T3kFP/X85e/20XHm +aDm7n6fVnpunnwujz8Fq4yX+XZ5FtefvqffxUa/2fPk2n31/yfKPevX2yTnn +nHPOOeecc37KR+fPR33Vd2p+j8ft0767fa7yLKp9d+Df7Vecvr92z9vvXn9y +6npl9Tv9/Z1/l1d7/vJ3eEz/tN1Wef6uOg+Zn+r/Z+vD+Z1+Ret+q/acHX3+ +tvLd7U95f/82H33/euv8Euecc84555xzzvkpj+kxX69n5fteXNtb1/l0+3z6 +d+Essvynv19w/nfsel6Mtv+sPpn7jv9v+TGd80+82nOWv8Nj+tP67bf258ar +vLK37qMYb52XiNtVfVU/yX/3mP5pe+u9Xk9vn5xzzjnnnHPOOee7PaZfsWp+ +JvOsPtXmOd/iretzuh1mPtquqnnr/Gf5Y7nVvoPw7/YrTt+nWT1W9ZPV3POU +V/Bqz1n+bo/prXY4mv/U+qXd/flofTh/orfibeOi0X7jKb5qfon/id3zeKPP +l7jf6fbGOeecc84555xzfspHv7+v+t4dt3cd99s8O69V2tuov/W7cExv5av2 +HYTzFX7F7H2d7T/aT+7uZ7Lys+Otys/5Dq/2POX3+Og4c/W6i9Hy435P82rP +a87v8NZ4L8bp+/RuHx0PP92rPQerPX9XvX/Fbc4555xzzjnnnHP+TI/pV+ye +X/o2j9tvcd+Ffw/f9TjP+5EYT3HrH3hlr3a/8LV+qn8eHd/O1j+Wd2pcPVr/ +ateR8x3eimx8EtOf7qP3e2v/p/rsc6Q3f3bc3c/Z0eOO5q/2vOOcc84555xz +zjnn93hMj/lijM4Xrcq/e33U7PqZ3vzZcZ/uvhf/nN7KV+07C+cjfsXq/jNu +V3nefVr/0edp1evIn+HVno98rY+OM1etv1rVb8+Oo+5+Lqzq/1fdp6ef+/yd +3rofY1R73lXzav1bNR/t33b3k1k9V4+re4/LOeecc84555xzzvnf/6767yJP +z49l3ltOVs9vc9+F5zyL0+s0+Hf6FbP3dZZv9rkQy2vV4+7+bbSc0f5h1fcd +67K+06s97/g9HtM/bVfV++dRn+2Hd52H1fXh/G+/onc8k8Wq/uRtPnqftvb/ +dh99HrXOf1ZOa/9Pyxn9vdoJ55xzzjnnnHPOOf//WDVf1Nq/N0bLWTW/F9NP +X5dqPvpdYPQ6vtVjem++Xj/9PYg/y6+I93X0uD3b/5+qzykfPQ+r+pNq3zH5 +PV7tecfv8d3jsdb+1X31eCkeZ/dzM8t/evzAa3mr/cRY1c75v/9mUaU/5L/7 +0987OOecc84555xzzjn/LT1GlXry39134bXeWg+Z5Y/lVvtOxM/6Fb33b5Y/ +81XtfPT74Gg9q/mq732+q/K/vdpzja91/eecz467Pu23V62/Nd77Tr9idPyW +RVaO8cOYx+3Z529WDuecc84555xzzjnnnPPv9FPz1d/mo99lsuhNj9cx7sff +4a32FvPt/r4c03vbYVZulX5yt4/2G763fqdXe67xtW5d1pzPnueY79R6j2rj +Cn6Pt8ZRMTz37/G43epnsvycc84555xzzjnnnHPOeY9bl3XWW+u4svyx3Grf +ofg9fkWV+3TVd7G3+mg/4Pvsd3q15xSf893rebL8b/Wn9IdZ/Vf3//ysX9F7 +n2Yx2k6y4/I13rp+VfpDzjnnnHPOOeecc845589y34XP+ux6laycbP/e/Ly2 +X9FqJ1XbeWu/0/3hbt+9vq7a900+59XuX36PW78659Xu39F1O7ymX9H7XM7i +dHvjYx63Z/NzzjnnnHPOOeecc845/06P6TF68/OansXsd4eYj9f0au1wtJ/h +P6dfUe17Jb/Hq92/fK2Prr/9tn519DxUu3+zes+2B37GW/ddFll77r3f+b0+ +et2r9JOcc84555xzzjnnnHPOn+Wr5qv5PT763/Vn4e85PNOvaN3XVdttzNdq +p1X6yVU+u96gtz3wd3i1+5fPeUz/9DmbHa9K/7bKV52fql5tXPFtfkXrurSi +d9x1ur3xMR/tzznnnHPOOeecc84555zzHvdd+B0++902Kyfbvzc/v8ertcNV +7SSWd7qfXOW7z0+175t8zqvdv3ytx/TZfmO0nKd7tft01X1dbVzxFF99P8ao +1n74Wo/b+mHOOeecc84555xzzjnnK3z3vDR/h2fh70XU8Cvecj/G9NP95G5f +1Q9X+77J13q1+5Tf49av/vl3dn14zFdtvcfp8UMVv+LT8zM73shitD5xP/5M +X9WuqvSfnHPOOeecc84555xzzs/6qflqXtNnv/Nm5cT9Vq3LyupT7Ttjte+b +VdtbzGe9QZ/H8vi7vdr9y9d6FqP9QNx+uz+lnxwddz3FR5/vcfvT89xbn1aM +trfRevJn+Wi7qtIfcs4555xzzjnnnHPOOX+WW5fFf0vvbVcxTv336Vn+VevE +qvoVrfNwyr9t/VXms+cnyx+Pw9/h1e5ffo9bv/q7V7tPd69LP+2x/qee+611 +X1lob/yn7dXXfbR8zjnnnHPOOeecc8455+/2mB7zZbGrfF7TY/qn7XDXcVf9 +3YysPqe/h/Z6tfZzur1V91V/h4S/26vdp/ysjz7v4vZbvFo/OVsf44cxz2LV +OJB/t396X8T00/0k55xzzjnnnHPOOeec87N+ar6af6e3/k5Clj+WW9Xj76r2 +XbXaeg/rB/6E78i8x6v15/ysW5f1599q/edsPe/2rJ7V2nkrPGf5J957v8y2 +2yr9JOecc84555xzzjnnnPOzXm0em7/DV38vzsqP+/kO+7tn9azWTuJ+p/vJ +Vb7qfuHf6dX6eX7WY3rrudOKKv3kqLf61bjfaT81Hoj1qdqes9j1nH1a++Fr +fHc7aR2Pc84555xzzjnnnHPO+Xd5TL9i9rtS6/gxnT/bV7WTuN3ro/W521vn +LTs/u/wp7SduP9VjjK5Dq9ae+Vmvdv/ymj7a/7eiWr/a69Zp/7x92lux67qP +jkP4d3rc5pxzzjnnnHPOOeecc84reUyP+fh3+eh3sVa+Ue+tz2mP9d7tsR6n +79+sPk/zGKvWK3L+t1fr53lN9/de/vxb7f6967kfj3v6+Z7Fqfbg+ftub7XT +1n2x6v5q5eOcc84555xzzjnnnHP+XT7735XH9FV/NyA7Ln+Wj34fucuzesb9 +Tq2v+Na/m1GlPxz11nWM+/kuzD/xavcvf4dXfV6f6p8/9Szevr46iyrtIfNq +/Tyf87jdO+4aHY/15s/qwznnnHPOOeecc8455/w7PaZfMfv3FmL6U74r8bUe +00+385bHeMt3pdbvzI6/2t/63co6K36nV+vn+bt9dBwY00/3z5lbdz3nrah2 +fT2Xv8tX3Xez90WV9s8555xzzjnnnHPOOef8WT47Tx7LHf0+EvPFdP5sf9rf +5Yhx1/em0fuo+n3XOl4VX/V3Ejjf4dX6c/5uX7WeIaZX6ed39eerzqf1V3Ne +rd/m93jcbt3vWf7ZfrK3PpxzzjnnnHPOOeecc86/02P6FU+ZD+fv8Jh++r5o +eYynrdeK5a+6jk9Zd7d7fSnnO7xav8353zHaf8byqj8Xen3V+blr3JVFlevS +Op9xP/6dPnrfrerfWvXgnHPOOeecc84555xzzn/z1esQesuJ+WI6/y5/2n+H +HqPqeq1Yzqrr1Sq3Wj+2qn/j/A6v1j9zvsNj+t3Pi5i++79T2L0uqxVPeV7H +/fg7PG7vun9776+nvXdwzjnnnHPOOeecc845f6fH9CtWzYfvrid/hz/tv1uP +cWpdVlbPVdclK3+3V/vOyPkOr9YPc77Dq62LuGu9dFaPGK3nbxanzlv2e+N+ +nP/tq8afT3tf4JxzzjnnnHPOOeecc85nfHQ+3HdqvsOrfpfJ6hn3q/r99+7z +1rq+cT/O3+TV+lXO7/RT6/wzX/W8nn3+ZnH37/Vc5j0+el/Pelaf0fzR4zbn +nHPOOeecc84555xzvtNjeswXY/Q71O75+dH683f7aDtp5VvlvfW86/vvrt+7 ++zsa52/yav0n55V993rs0XHF7LqyLE49lzn/zeN277hu1HuPO9o/jN6/2XE5 +55xzzjnnnHPOOeec8x5fvZ4q2z8ed7b8Xh89Luc9HtN33acxVn3/3f33Aayz +4vxzr9bvcf4N3orR5/XocUafszGdz3ncPp1/1bjuLs/Ge5/6qvt61bg0bnPO +Oeecc84555xzzjnnIx7TY74Yd627yMr/1Ed/7ypf/XcVeq/j7vx8zmN67/0b +Y/X336z8uB/nfJ+ver6M9j+nv49XeV5z3uOjUa2feZr39htx/1Z/uKpfWtWP +xfTe8WGvV3tfOzXeXvXc5JxzzjnnnHPOOeecc857fPX33Jj+1vn/mH7XdZk9 +P6P5e8tp1f/u6/JtPhqnv6ty3uOf9kurjhvzzT43d6/Lau0ffbSeu+uz+7i7 +xzm7y+FrffX6n09jVb9313g1xu71S1l9Vr0XVPMrevvtLH/mo8+jVjm72u3q ++723Pq36cc4555xzzjnnnHPOOecrPaZfcdf38VZ9e+uT7df7ezNv1S/6Xd87 +qvsVvedn1XqzVnx6v9zVbj+N1X8XIubja320/3lKObvXFax+vsT8p+ozetzM +d5ef+e7fu/s5fqqc3esHZusz+lzu9VXPzdXjlqw+V9x9nvm7/YrZ/u2ucfiu ++q/yrB6j54dzzjnnnHPOOeecc8453+Gr5/N3eVa/VetPsuOt+i65qv78HX5F +7/2V5W+15xinz8MVrfqP+u7zPOqz/cyn9Tm1vmhV+aPnbZXvbg+j5Z9eN/jp +827293563FXlz5bTO97Y3a+e7uerexar+70Yq55r/Dt9tP3E9E/7/0/rc2q8 +xznnnHPOOeecc84555w/0Xd/t139HTn7PVlkv3dXffh3+BWt9tOK2D6z/XrL +u+L0+anu2fmstr4i7t9qJ6vKOVX+6HFXlT973/U+T1u/K+a7ax1db7tddb04 +/8SzWDWui/la99Hu/o3zn/yKVjvf/RwcrWerfpxzzjnnnHPOOeecc845z9Ov +OLW+K6vPbD05/9uvmG2fcbvlq9afZHH6fPJ3+xWz/XbV9RIx3+z6q97zubr+ +1doJ5795Fqeey5mvuk9390v8Hp+9Xr0et1vXPcvPOeecc84555xzzjnnnHM+ +6qPfI1r5et13sZo+e712edye9VXtNotq15HzEb/i0/v30+O2+p9q543zk57F +U57Lo/3AKY/pxquf+RW97WFVO5x9vnx6XM4555xzzjnnnHPOOeecf4/H9Ct2 +f4/Ijpt5Vk6170pP8Suy8xnTT/loexj10XY4225jVGsPnFfyK/TznNdbf1Vt +Xcru5/hd44Te8Vgrf2+/uruc7Peeaj+j16Xa+jHOOeecc84555xzzjnnnNfx +mB7zZRH3n/1unh3v7t+7+vtR67zeVU6Wv9p6qmrtJPPR+2WVZ1Htuz/nnPOz +nsW3Pa+z+px6jj/dR89nq51k1+/Tep4+P6P3byx39LzFfKfvO84555xzzjnn +nHPOOef8m33Vd5C7vjtU897ztvq7Ff/Zs/PZyrfLR++jVZ5FtXUCnHPO13oW +1Z7X1daTvHVdED/r1d6P4jbnnHPOOeecc84555xzztd5TI/5PvVq3x34d3ir +nd51fz3le24W1dYVcM45/92zOP1cHvUqz/FRr/Z852d99f0ej2ddFuecc845 +55xzzjnnnHNe32N6zPepP+V7BH+Wx+2q/pR1WZlnUW0dAuecf5tnUe15/W3r +srLfVe35zu/x2fu6t1192/3FOeecc84555xzzjnnnD/Rd68bGT2udVn8bx9t +V9X86euyWuc/RrV1C5xz/nTPotrzerfH7ao+Wv9qz3c+5zG9t533jg9330ej +v4tzzjnnnHPOOeecc8455//tp74TrfoekdWz2ndDPudxu9UOs/zVfNV99BTP +oto6B845P+Wz/Wfc/63+9Od+5tZrfafH9Nn2MPo+lZXz1vuLc84555xzzjnn +nHPOOa/ss98FsnxZxHJG81f7bsjnPG7Ptoen+Oh357d6FqPfGTnn/Gl+RW// ++O3jn7j9Fl+1Po1/p69a//lt9x3nnHPOOeecc84555xzXsFj+hWr10tk5fDv +8qy9Zd7a/6k+eh6e7jG9N1+M0+srOOc86997w3jpd/+28UDmo+PwLKqNB57u +d63b/HTcaD0k55xzzjnnnHPOOeecc17HY3rMF2PVPH+r/JhuPdhZz2L2O3WV +9r/b/R2M3330+/Lq9aKcc77q+dWbv9rz/bQbP9zjMaqNB6p5TJ9tz6PlZPk5 +55xzzjnnnHPOOeecc85HPabHiPlWfb87/f2xureiSvt5iq/6Hv1tHtNn26d1 +XJzz1euyYmT5qz3fn+Kzz4Vv8d3r4oxPfk5vnbdW/phuXRbnnHPOOeecc845 +55xzznd7TI/5soj77/4+8haP52f3d7eYfrq9nfLR7878dx9dT2hdFud81Fvx +af/P+7x3XMd/99Hn6epxZsyf1XP0us/+rt39SXbc6K1+p0r74ZxzzjnnnHPO +Oeecc875c33VepVTfzfj9Pem3nrOns8sX5X28xT3dyfWekzvvS4xqq0D4Zzf +/xzP4vR6pG/31f0/X+O71yOtWk81W36vj45bRstvHY9zzjnnnHPOOeecc845 +57zXY3rMF2P3d5PZ48b9Vn0nmq1na7/T1/3bfHf75HOexem/s8E57/crWvdp +K3r7bb7W43bv89Q4p6ZnEfNn+61qP6vWj2Xlt467q3zOOeecc84555xzzjnn +nPNVHtNjvix2lT/6HXC2/Cxfq9xWffg9vup78Wj74XMe01v5ZtdbxnTOeb9f +0dtPZlFtPRL/3XePA3lNX3V9rd/jnHPOOeecc84555xzzjl/lq/6vuO/l3+3 +7/7uzM96Fqv/jgfn/D8xej/G/Xrvu7gfP+ut617luc8555xzzjnnnHPOOeec +c8455/ysW5f1LJ9dh5mVE/ertu6F80p+Rev+ivla92W1dUf833+zyJ6no/0z +55xzzjnnnHPOOeecc84555zzZ/vo92LrtZ7ls3/vbrT8mM75m7x1f8Twd66+ +w3vbSW//eno8wDnnnHPOOeecc84555xzzjnnfK2f+h7Na3prnV6WP5ZbbV0N +/06/Iuv3evuxVqzqV/mzvdV+qjz3Oeecc84555xzzjnnnHPOOeecn3V/F4v/ +lt7KN7peKyu/2jof/izP2lnWPlvR20/yd/toPzna73HOOeecc84555xzzjnn +nHPOOX+Hz66TaR0npvN3ekzvzRfD393in/hsu43ROm4sl3+39z43Z/tPzjnn +nHPOOeecc84555xzzjnnz/bW343J8mf5YvDv9Na6hSx/LNd6Ld7jve0sRm8/ +2WrncT/+HT7aDqs89znnnHPOOeecc84555xzzjnnnJ/1Vd+j+bt9dF1fy3vL +r7YuiP/uo+1n1Fuxqt/j/Ddvtccqz3fOOeecc84555xzzjnnnHPOOednffS7 +M+c9HtN72+eu+lj3dY/vbg+t+sTyOO/xuD3aP/X2J73H5ZxzzjnnnHPOOeec +c84555xzXtNj+hXZ9+KsnFXfrznv8Vb7zKL3vrAua62vuu5ZjLaTaut8+LM8 +bs/2D61223tczjnnnHPOOeecc84555xzzjnnNT2mX7FqXcrocTnv8dm/M5OV +E/PPeu99cZeP1j/zT+szen1bMdqP7T4//Dt9d/uvMk7gnHPOOeecc84555xz +zjnnnHO+1qt9p+b871j9///Kyo/7VVu/tOr8nLrfW1Gtf+O8x0fbf5XnPuec +c84555xzzjnnnHPOOeec87O+6ns05594TN/V/mNUW5e4en3a6P0+Wn4Wu/sl +zld6637szd/KxznnnHPOOeecc84555xzzjnn/Lt893dqznd4TP/0vugtf3c9 +V52f1etJPj0u5xU8bvc+77L9e/OvWlfJOeecc84555xzzjnnnHPOOef8rMf0 +K2b/P2i9+Ufrw3kFb7XnLGL7XrW+cfe6x+y+zmJ1f8L5SY/bvc+71n02+xwc +LYdzzjnnnHPOOeecc84555xzzvlZX/3/O4v5Rr9Tt/JxftJn1x9+Ws7udVmj +6692r2Optj6Hf6fH7dn2PHo/ZsflnHPOOeecc84555xzzjnnnHP+Dp/9rh3L +tS6LP9F3t+csVq1TGv29rfpk+2f9RpYvK7/3PFdbt8O/23vb7ar+J+53epzA +Oeecc84555xzzjnnnHPOOef8d1+9/iErJ6tHDM7v9NXrglrHz+7LVqxal9WK +Xf3MXeef8zs8brf6gdb9WGU8wDnnnHPOOeecc84555xzzjnn/KzvXpfC+Z2+ +al1Q3N7lMUb//4l31TPrN3rPp3VZ/E6P27PPwdb9V+U5zjnnnHPOOeecc845 +55xzzjnn/Fm++zt1Vg7nn/iq/+9e3O/u+/E/8X87kfTI + "], {{0, 0}, {401, 401}}, {0, 1}], Frame -> Automatic, + FrameLabel -> {None, None}, FrameTicks -> {{None, None}, {None, None}}, + GridLinesStyle -> Directive[ + GrayLevel[0.5, 0.4]], + Method -> { + "DefaultBoundaryStyle" -> Automatic, "DefaultPlotStyle" -> Automatic}], + FormBox[ + FormBox[ + TemplateBox[{"\"Divergent\"", + RowBox[{"-", "1"}], + RowBox[{"-", "\[ImaginaryI]"}], "\[ImaginaryI]", "1"}, "SwatchLegend", + DisplayFunction -> (FormBox[ + StyleBox[ + StyleBox[ + PaneBox[ + TagBox[ + GridBox[{{ + TagBox[ + GridBox[{{ + GraphicsBox[{ + Directive[ + EdgeForm[ + Directive[ + Opacity[0.3], + GrayLevel[0]]], + PointSize[0.5], + AbsoluteThickness[1.6], + RGBColor[0., 0., 0.]], + RectangleBox[{0, 0}, {10, 10}, "RoundingRadius" -> 0]}, + AspectRatio -> Full, ImageSize -> {10, 10}, + PlotRangePadding -> None, ImagePadding -> Automatic, + BaselinePosition -> (Scaled[0.1] -> Baseline)], #}, { + GraphicsBox[{ + Directive[ + EdgeForm[ + Directive[ + Opacity[0.3], + GrayLevel[0]]], + PointSize[0.5], + AbsoluteThickness[1.6], + RGBColor[1., 0., 0.]], + RectangleBox[{0, 0}, {10, 10}, "RoundingRadius" -> 0]}, + AspectRatio -> Full, ImageSize -> {10, 10}, + PlotRangePadding -> None, ImagePadding -> Automatic, + BaselinePosition -> (Scaled[0.1] -> Baseline)], #2}, { + GraphicsBox[{ + Directive[ + EdgeForm[ + Directive[ + Opacity[0.3], + GrayLevel[0]]], + PointSize[0.5], + AbsoluteThickness[1.6], + RGBColor[0.5, 1., 0.]], + RectangleBox[{0, 0}, {10, 10}, "RoundingRadius" -> 0]}, + AspectRatio -> Full, ImageSize -> {10, 10}, + PlotRangePadding -> None, ImagePadding -> Automatic, + BaselinePosition -> (Scaled[0.1] -> Baseline)], #3}, { + GraphicsBox[{ + Directive[ + EdgeForm[ + Directive[ + Opacity[0.3], + GrayLevel[0]]], + PointSize[0.5], + AbsoluteThickness[1.6], + RGBColor[0., 1., 1.]], + RectangleBox[{0, 0}, {10, 10}, "RoundingRadius" -> 0]}, + AspectRatio -> Full, ImageSize -> {10, 10}, + PlotRangePadding -> None, ImagePadding -> Automatic, + BaselinePosition -> (Scaled[0.1] -> Baseline)], #4}, { + GraphicsBox[{ + Directive[ + EdgeForm[ + Directive[ + Opacity[0.3], + GrayLevel[0]]], + PointSize[0.5], + AbsoluteThickness[1.6], + RGBColor[0.5, 0., 1.]], + RectangleBox[{0, 0}, {10, 10}, "RoundingRadius" -> 0]}, + AspectRatio -> Full, ImageSize -> {10, 10}, + PlotRangePadding -> None, ImagePadding -> Automatic, + BaselinePosition -> (Scaled[0.1] -> Baseline)], #5}}, + GridBoxAlignment -> { + "Columns" -> {Center, Left}, "Rows" -> {{Baseline}}}, + AutoDelete -> False, + GridBoxDividers -> { + "Columns" -> {{False}}, "Rows" -> {{False}}}, + GridBoxItemSize -> {"Columns" -> {{All}}, "Rows" -> {{All}}}, + GridBoxSpacings -> { + "Columns" -> {{0.5}}, "Rows" -> {{0.5}}}], "Grid"]}}, + GridBoxAlignment -> {"Columns" -> {{Left}}, "Rows" -> {{Top}}}, + AutoDelete -> False, + GridBoxItemSize -> { + "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, + GridBoxSpacings -> {"Columns" -> {{1}}, "Rows" -> {{0}}}], + "Grid"], Alignment -> Left, AppearanceElements -> None, + ImageMargins -> {{5, 5}, {5, 5}}, ImageSizeAction -> + "ResizeToFit"], LineIndent -> 0, StripOnInput -> False], { + FontFamily -> "Arial"}, Background -> Automatic, StripOnInput -> + False], TraditionalForm]& ), + InterpretationFunction :> (RowBox[{"SwatchLegend", "[", + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{"Directive", "[", + InterpretationBox[ + ButtonBox[ + TooltipBox[ + GraphicsBox[{{ + GrayLevel[0], + RectangleBox[{0, 0}]}, { + GrayLevel[0], + RectangleBox[{1, -1}]}, { + RGBColor[0., 0., 0.], + RectangleBox[{0, -1}, {2, 1}]}}, AspectRatio -> 1, Frame -> + True, FrameStyle -> RGBColor[0., 0., 0.], FrameTicks -> + None, PlotRangePadding -> None, ImageSize -> + Dynamic[{ + Automatic, 1.35 CurrentValue["FontCapHeight"]/ + AbsoluteCurrentValue[Magnification]}]], + "RGBColor[0., 0., 0.]"], Appearance -> None, + BaseStyle -> {}, BaselinePosition -> Baseline, + DefaultBaseStyle -> {}, ButtonFunction :> + With[{Typeset`box$ = EvaluationBox[]}, + If[ + Not[ + AbsoluteCurrentValue["Deployed"]], + SelectionMove[Typeset`box$, All, Expression]; + FrontEnd`Private`$ColorSelectorInitialAlpha = 1; + FrontEnd`Private`$ColorSelectorInitialColor = + RGBColor[0., 0., 0.]; + FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; + MathLink`CallFrontEnd[ + FrontEnd`AttachCell[Typeset`box$, + FrontEndResource["RGBColorValueSelector"], { + 0, {Left, Bottom}}, {Left, Top}, + "ClosingActions" -> { + "SelectionDeparture", "ParentChanged", + "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> + Automatic, Method -> "Preemptive"], + RGBColor[0., 0., 0.], Editable -> False, Selectable -> + False], "]"}], ",", + RowBox[{"Directive", "[", + InterpretationBox[ + ButtonBox[ + TooltipBox[ + GraphicsBox[{{ + GrayLevel[0], + RectangleBox[{0, 0}]}, { + GrayLevel[0], + RectangleBox[{1, -1}]}, { + RGBColor[1., 0., 0.], + RectangleBox[{0, -1}, {2, 1}]}}, AspectRatio -> 1, Frame -> + True, FrameStyle -> RGBColor[0.6666666666666667, 0., 0.], + FrameTicks -> None, PlotRangePadding -> None, ImageSize -> + Dynamic[{ + Automatic, 1.35 CurrentValue["FontCapHeight"]/ + AbsoluteCurrentValue[Magnification]}]], + "RGBColor[1., 0., 0.]"], Appearance -> None, + BaseStyle -> {}, BaselinePosition -> Baseline, + DefaultBaseStyle -> {}, ButtonFunction :> + With[{Typeset`box$ = EvaluationBox[]}, + If[ + Not[ + AbsoluteCurrentValue["Deployed"]], + SelectionMove[Typeset`box$, All, Expression]; + FrontEnd`Private`$ColorSelectorInitialAlpha = 1; + FrontEnd`Private`$ColorSelectorInitialColor = + RGBColor[1., 0., 0.]; + FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; + MathLink`CallFrontEnd[ + FrontEnd`AttachCell[Typeset`box$, + FrontEndResource["RGBColorValueSelector"], { + 0, {Left, Bottom}}, {Left, Top}, + "ClosingActions" -> { + "SelectionDeparture", "ParentChanged", + "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> + Automatic, Method -> "Preemptive"], + RGBColor[1., 0., 0.], Editable -> False, Selectable -> + False], "]"}], ",", + RowBox[{"Directive", "[", + InterpretationBox[ + ButtonBox[ + TooltipBox[ + GraphicsBox[{{ + GrayLevel[0], + RectangleBox[{0, 0}]}, { + GrayLevel[0], + RectangleBox[{1, -1}]}, { + RGBColor[0.5, 1., 0.], + RectangleBox[{0, -1}, {2, 1}]}}, AspectRatio -> 1, Frame -> + True, FrameStyle -> + RGBColor[0.33333333333333337`, 0.6666666666666667, 0.], + FrameTicks -> None, PlotRangePadding -> None, ImageSize -> + Dynamic[{ + Automatic, 1.35 CurrentValue["FontCapHeight"]/ + AbsoluteCurrentValue[Magnification]}]], + "RGBColor[0.5, 1., 0.]"], Appearance -> None, + BaseStyle -> {}, BaselinePosition -> Baseline, + DefaultBaseStyle -> {}, ButtonFunction :> + With[{Typeset`box$ = EvaluationBox[]}, + If[ + Not[ + AbsoluteCurrentValue["Deployed"]], + SelectionMove[Typeset`box$, All, Expression]; + FrontEnd`Private`$ColorSelectorInitialAlpha = 1; + FrontEnd`Private`$ColorSelectorInitialColor = + RGBColor[0.5, 1., 0.]; + FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; + MathLink`CallFrontEnd[ + FrontEnd`AttachCell[Typeset`box$, + FrontEndResource["RGBColorValueSelector"], { + 0, {Left, Bottom}}, {Left, Top}, + "ClosingActions" -> { + "SelectionDeparture", "ParentChanged", + "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> + Automatic, Method -> "Preemptive"], + RGBColor[0.5, 1., 0.], Editable -> False, Selectable -> + False], "]"}], ",", + RowBox[{"Directive", "[", + InterpretationBox[ + ButtonBox[ + TooltipBox[ + GraphicsBox[{{ + GrayLevel[0], + RectangleBox[{0, 0}]}, { + GrayLevel[0], + RectangleBox[{1, -1}]}, { + RGBColor[0., 1., 1.], + RectangleBox[{0, -1}, {2, 1}]}}, AspectRatio -> 1, Frame -> + True, FrameStyle -> + RGBColor[0., 0.6666666666666667, 0.6666666666666667], + FrameTicks -> None, PlotRangePadding -> None, ImageSize -> + Dynamic[{ + Automatic, 1.35 CurrentValue["FontCapHeight"]/ + AbsoluteCurrentValue[Magnification]}]], + "RGBColor[0., 1., 1.]"], Appearance -> None, + BaseStyle -> {}, BaselinePosition -> Baseline, + DefaultBaseStyle -> {}, ButtonFunction :> + With[{Typeset`box$ = EvaluationBox[]}, + If[ + Not[ + AbsoluteCurrentValue["Deployed"]], + SelectionMove[Typeset`box$, All, Expression]; + FrontEnd`Private`$ColorSelectorInitialAlpha = 1; + FrontEnd`Private`$ColorSelectorInitialColor = + RGBColor[0., 1., 1.]; + FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; + MathLink`CallFrontEnd[ + FrontEnd`AttachCell[Typeset`box$, + FrontEndResource["RGBColorValueSelector"], { + 0, {Left, Bottom}}, {Left, Top}, + "ClosingActions" -> { + "SelectionDeparture", "ParentChanged", + "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> + Automatic, Method -> "Preemptive"], + RGBColor[0., 1., 1.], Editable -> False, Selectable -> + False], "]"}], ",", + RowBox[{"Directive", "[", + InterpretationBox[ + ButtonBox[ + TooltipBox[ + GraphicsBox[{{ + GrayLevel[0], + RectangleBox[{0, 0}]}, { + GrayLevel[0], + RectangleBox[{1, -1}]}, { + RGBColor[0.5, 0., 1.], + RectangleBox[{0, -1}, {2, 1}]}}, AspectRatio -> 1, Frame -> + True, FrameStyle -> + RGBColor[0.33333333333333337`, 0., 0.6666666666666667], + FrameTicks -> None, PlotRangePadding -> None, ImageSize -> + Dynamic[{ + Automatic, 1.35 CurrentValue["FontCapHeight"]/ + AbsoluteCurrentValue[Magnification]}]], + "RGBColor[0.5, 0., 1.]"], Appearance -> None, + BaseStyle -> {}, BaselinePosition -> Baseline, + DefaultBaseStyle -> {}, ButtonFunction :> + With[{Typeset`box$ = EvaluationBox[]}, + If[ + Not[ + AbsoluteCurrentValue["Deployed"]], + SelectionMove[Typeset`box$, All, Expression]; + FrontEnd`Private`$ColorSelectorInitialAlpha = 1; + FrontEnd`Private`$ColorSelectorInitialColor = + RGBColor[0.5, 0., 1.]; + FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; + MathLink`CallFrontEnd[ + FrontEnd`AttachCell[Typeset`box$, + FrontEndResource["RGBColorValueSelector"], { + 0, {Left, Bottom}}, {Left, Top}, + "ClosingActions" -> { + "SelectionDeparture", "ParentChanged", + "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> + Automatic, Method -> "Preemptive"], + RGBColor[0.5, 0., 1.], Editable -> False, Selectable -> + False], "]"}]}], "}"}], ",", + RowBox[{"{", + RowBox[{#, ",", #2, ",", #3, ",", #4, ",", #5}], "}"}], ",", + RowBox[{"LegendMarkers", "\[Rule]", "Automatic"}], ",", + RowBox[{"LabelStyle", "\[Rule]", + RowBox[{"{", "}"}]}], ",", + RowBox[{"LegendLayout", "\[Rule]", "\"Column\""}]}], "]"}]& ), + Editable -> True], TraditionalForm], TraditionalForm]}, + "Legended", + DisplayFunction->(GridBox[{{ + TagBox[ + ItemBox[ + PaneBox[ + TagBox[#, "SkipImageSizeLevel"], Alignment -> {Center, Baseline}, + BaselinePosition -> Baseline], DefaultBaseStyle -> "Labeled"], + "SkipImageSizeLevel"], + ItemBox[#2, DefaultBaseStyle -> "LabeledLabel"]}}, + GridBoxAlignment -> {"Columns" -> {{Center}}, "Rows" -> {{Center}}}, + AutoDelete -> False, GridBoxItemSize -> Automatic, + BaselinePosition -> {1, 1}]& ), + Editable->True, + InterpretationFunction->(RowBox[{"Legended", "[", + RowBox[{#, ",", + RowBox[{"Placed", "[", + RowBox[{#2, ",", "After"}], "]"}]}], "]"}]& )]], "Output", + CellChangeTimes->{3.6641613068615923`*^9, 3.664161466270402*^9}] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"newtonplot", "[", + RowBox[{ + RowBox[{"Function", "[", + RowBox[{"x", ",", + RowBox[{ + SuperscriptBox["x", "5"], "-", "1"}]}], "]"}], ",", "2", ",", "401", + ",", "40", ",", "0.1"}], "]"}]], "Input", + CellChangeTimes->{{3.6595549152958674`*^9, 3.659554978383319*^9}, + 3.659555332709116*^9, {3.659555509656427*^9, 3.6595555271955185`*^9}, { + 3.659555597485504*^9, 3.659555613597739*^9}, {3.6595559120050316`*^9, + 3.659555925976593*^9}, {3.6595559620470605`*^9, 3.659555962328335*^9}, { + 3.6595560196305175`*^9, 3.659556025819849*^9}, 3.6641616469815435`*^9}], + +Cell[BoxData[ + GraphicsBox[RasterBox[CompressedData[" +1:eJzs/UmypcrWKNwdmVryt+T1QU2Qmcpqi2pSLbp1mvDVbhNkT/EjLsnEExyY +sMY0C4vNgOU4jpN4stf+P/7v/8//2//j//rPP//8v/4vf//975//3/+f/x3/ +87/++f/Ff/7P/znnnHPOeVb/s/Ap/vO/Il9+7t//f3qj8hOlH21XF9Px/Bse +F+/z/e3+DetDtP1XPSq34/KJy+tXvLX+9JVzdJ/hnHPOOeecc84555xzznN6 +tnFGzjnnnHOe05exnd+y//4Zf37f4/TX/meRz/V63up9847W6cbn613eWm95 +5K31Ldp+uf75djTnnHPOOeecc84555xzXuPZxvs455xzznlOn6L2PfPPIp0p +/hOmu95umV69R/vlxz79FJ3f48gyn+o675tHFJXfVz2qP1dvzznnnHPOOeec +c84555zn9GzjfZxzzjnn/Fn/s/Ap+t8/92O7vjQfbPLlfuo9Oi5+7MfnpXye +e89XNj++LuL6+k2f1/eW26j5n5xzzjnnnHPOOeecc855Zs82Dsg555xzzp/1 +ZdT+vcJWj/YXp7Ofnzjf++nmme/0Fp9+Wpd7afvldv++3qPj7Zu39jveV255 +2succ84555xzzjnnnHPO+RnPNg7IOeecc86f9T8Ln2Lc+2cp/f2I19e+30b7 +5X0+/RSd9+Xn//2875dDVG/f7vP66bivvm9wzjnnnHPOOeecc84552/0bOOA +nHPOOef8WZ8iep+clqf1x+ls0z32bfxZpL/eP3/K+877Ot1/w3r1Fo/KZ/n/ +Ot7u0f2hdXvOOeecc84555xzzjnn/NuebRyQc84555x/w5dx1d+D26bful8+ +1qPzGG2/n258Hp/1uB7ubxdfD+/wef26fLK0ZznnnHPOOeecc84555zzzJ5t +/I5zzjnnnL/L/yx8iva/f1ea37X/frvdbj8f/wb5i731uPixTz9F7ZTl59vP +19PeVj/f4vP66fj6rlPOOeecc84555xzzjnn/Dc927ge55xzzjn/TZ+i9j32 +zyKdKcrvw+sYNd+MH/v+dv9+zNcR1btsvg3zrzjnnHPOOeecc84555zz855t +PI5zzjnnnPP/9inOvt9G8Wex/RT55jV91f+pimzzr2q/Pyo6vjxeOi9Z2q2c +c84555xzzjnnnHPO+Rs927gb55xzzjnn/+1T1L7HLuPs35uL01n7n0V+1ut5 +5L3z8Zbpxuflan/XvKx5/XG5zpGl3co555xzzjnnnHPOOeecv9Gzjbtxzjnn +nHNe48s4O08men+Ot1/v989iv+v1vNWnn1rbO8t0/73cj/Mf19dcnqd9yjnn +nHPOOeecc84555x/ybONr3HOOeecc36nT7H//rzdrnfe17R+2k+Uzp+Frz/H +l/9H8evzsuLI0g7lnHPOOeecc84555xzzn/Bs42Lcc4555xznsH/LHyK9r+7 +V9p+8uXntm4e1/K4l9tt2z378SvzsuJyyNIO5ZxzzjnnnHPOOeecc85/wbON +f3HOOeecc/5Gn2L9vv1nsf0U8ft5afvldv8WPMrfdfOmnvLl8UXH/7V5WXE+ +s7Q3R3lUzsfXY339H3W9c84555xzzjnnnHPOOX+Xt/5e/Hp5Si/buBXnnHPO +Oec8nu8xee/7fBRRO+Krvr/dvzd5fF7Peum8Z2/Pro9v+lzv+V3vd1T9Oc5/ +/flqzT/nnHPOOeecc84555zzsf53ubX/+T8rX68ve7ZxKM4555xzzvl1vr8c +e9QeidJvbdc85fvb/TvY68v52OP9PtWejWK9fbb63+r3tNPz9EtwzjnnnHPO +Oeecc875V/3v8qh+3XrP1u/NOeecc845z+9TrNs10fZRe+cpXx/Hfnx/Xlbp +/K73m60eZqv/dfWtfB5L6WTpx+Ccc84555xzzjnnnPNnfV6/H+X+7eN0Wn2b +z2z925xzzjnnnPPv+RTr9sifxfZTZJmvlWde1tn2abb6wPeivr7l6vfgnHPO +Oeecc84555zz+721P/bPwqco/f7yenmOKJ/T8rQ+W78055xzzjnnnO8vxxG1 +p1q9bm/j52WV8tPaPl3nJ9v5/TWvq29n5/Xl6Q/hnHPOOeecc84555zzq/2e +ftrtflvTydZfzTnnnHPOOeetPkVt+6jV97f7t+Db/B17ezt0HTnPS3SetuWc +Lf+j6+fk5+pPnn4PzjnnnHPOOeecc845z+at/bd/Fj7FuO/RytZfzTnnnHPO +OedPedT+inx/u39Xvo715+aI2pXrGHW8x/moL4ervfe4srR/o/yU6lXt9q37 +5ZxzzjnnnHPOOeecc17n6/i73XX925xzzjnnnHP+VY8iak+VPtca63Zfa/5b +24O/5tNPZ8v5uP6U6kX5e7Cj7Vvb9aX0Oeecc84555xzzjnnPLvX9eef/3sW +63RG9QNnGwfhnHPOOeec3+9THLdbyt8HNTr9tvZatL//2exndLndHdFx8bE+ +/VTbD9Cb/nK7Ur9Be79Elv4TzjnnnHPOOeecc845j/zvctSP+p+Vr9fX+rx+ +2n+031H9rtnGgzjnnHPOOef1voxyO2L/c1M7Id4+S7vsac8Z0Xy5LL4tv6g+ +R/Xwam89rtb8t6a//7kove36dfrZriPOOeecc84555xzzjlf+9/lqH/1Pytf +r4+i3B8b7ffceM0c2caVOOecc84551tvbY+U2gVZ2ll3+X5E60ufuztG5zPL +fK1Wr6/nrdfL2OurXO/q6mlrOvmuO84555xzzjnnnHPOOW/zef1+1PeLrrf/ ++/+2HzjybONEnHPOOeec83o/jmi7+PO52k1Xt7Nay6e9PNvyc33UHf8Uo8sh +y7yseo/a0dNPtfWwtZ1+nM/68i/dN3Jdv5xzzjnnnHPOOeecc37eo37RPwuf +Ik4n2r7Vs40rcc4555xzzrc+RW27IPp8lM7bfHn80fp5u7NeNy9u/PcYt0Zv ++n3lv47z5dxbn6f1pfLP4fWR7brjnHPOOeecc84555zzr/q0fLx+3m4tfz9X +3z/POeecc845z+PR+/x6u3Vka9e0eXRcV/u8fpmveo/OV2u7bIq6duD4eYBR +vOM8jjq/0fkYfR77/95itH1pv5xzzjnnnHPOOeecc/5Nn9cvY+t/P9/a37tN +J9u4Euecc84553zU/I1s7Z2t980nudrn9evyrPWovTaqHTdFW7uyPp931duz +7eKx3lo/S1F7PeY7X23555xzzjnnnHPOOeec87f4vH4/7uuP5ZxzzjnnnOfx +6P1/uX5uX5TmXeRqB83Hc7x+e9znPNpvvfeer9p0lunVnt/6443yOaq9GeW/ +z6+uD+Pqz5j8b9O/63y1HRfnnHPOOeecc84555y/xef1+1Huj43SyTauxDnn +nHPOOa/31vf/5eeytHeiiNaP8nn9Ml/nPTovkffOk1mX5/H258vhqeOKvK/+ +v93n9aXr6bh86utP6Xzt5yfffYZzzjnnnHPOOeecc/673jfOMi9P6UXbZxs/ +4pxzzjnnnNd7FKXts7R3jj06zlEe52daXq7v9fX+tu2yUe210nG1lXPpuPrn +ZUXpHB9X/Xk83u/V9eopn9eXzldr/Wm9/0TpcM4555xzzjnnnHPO+bt8Xr+O +9fZ/l8/383POOeecc87z+BRn3/+jdKP0R3lfflo9zs+0vFxf71E5j/Kr60P0 ++VL6y3THlUPrfu+pP+/11vO+3q7uurj/vsE555xzzjnnnHPOOedjfV6/H74X +i3POOeeccz571C5YLy/bH9naQa3to8jj4z3rreXfel5az/ty/+fbm1E663y2 +5v9c+bTmcx2t9Se/99WH+nS+fT/hnHPOOeecc84555z/js/rl1Hvf9Pd9pdm +GyfinHPOOeecX+f7y3F7Ybl+bqdE27em05r+/v7+bU6/lE6tR+XcWj5Xt9dK +5TCmHbo+nvbyPPbz9bbvuH7N5/X752UbufpPOOecc84555xzzjnnfJxPy9P6 +1n74bONEnHPOOeec8/t9irPthSjdY6/f7zq9Ujvoz8KjfNTPF6rNZ7TfUd57 +ftfHVSqf9fGOLs+z3lo+x/lvrbdv93n9cX9DXG6t9xPOOeecc84555xzzjl/ +l8/rl9ud77fnnHPOOeecf8+nONu+WC8v02v17X6P81mK2vTr9xuVQzY/Pp7R +6d83/yry43reet5/zef1deW5vS767jOcc84555xzzjnnnHP+Xv+7XN9/nm2c +iHPOOeecc36dR+2Fq32dj978rD8/RXS8y/2U21OldJb5i7+v6SlvPe9RORwf +/zof/wb5e87HHu9XfV6/Ls/oemlNP0s/Ceecc84555xzzjnnnD/l2caJOOec +c8455/f7FPvtiGi7/1n5uHlE+5/ftm9K+e/b73XHm82j4z32dbr/Bvt72luP +69d8Xj+V23E9ydOPwTnnnHPOOeecc875Ge/rJ499Wj5e358+v8Pj8zWtnz73 +Z1F/5vXZxn0455xzzjnnPPIprmof8b++v92/n/Xj+hbVq7f7vP6acsvWf8I5 +55xzzjnnnHPO+V8f1a/V27+9jr504nSzlPPb/anzyznnnHPOOedP+RT77aZo +u/9Z+Xo787XWvvx/G7Xlv7+/f8Pyf8r7yuHXfF4/lVvfdco555xzzjnnnHPO ++T0+ul96HX8W20+x/ty2fzLK/3r7KP3Io/yX8pnlfL3Np+VpfbbxFM4555xz +zjmPfIq2dtD288c+r1+3i9fe2v79qk8/1bZD3+KlerifTmt9y+bz+lI9n37K +1u/BOeecc84555xzzr/t0/JyfX06Ub/fn4XP+2lNZ3+5HPv5L6VT//cQ97ff +xj399u/3/eM/X38455xzzjnn/GrfX55jTDs9Tn9/+236UTvr1/z4PLb3n2Tx +1nZ0dPzv8tb+pXz9IZxzzjnnnHPOOef83f53OeqX+8/K1+u30Zb+vLz8XMlr +8/MWn9evj3ddnvoP/7uc6vvPOeecc8455/wtPkXUPjqO8d+nFLW/fs2nn+7p +97jf9+tbVO/yeGu9Xa5/vn+Dc84555xzzjnnnH/J5/X70f/3C6J0jvfLj31e +vyzPOHLVt/Me1bds4yacc84555xz3urH7ev/rHy9Pgp/r/Aq39+u1O8Rbf8W +b62HeTy67qbI0u/BOeecc84555xzzr/k8/opWvuNo/T/LLafYvu5UjrHn+OR +f7W/sXX8Its4C+ecc84555xHPkVt+7q1HRTt79jX+/M9WiX/pyqyzLNq9db6 +c7W390dl6d/gnHPOOeecc84559/2v8v1/belfuNluvHv2/ZtH++Pt3lr/382 +bx1fyDbOcu76+s5xcc4555xzzu/3KfbbX9vtjrev72f4NV/+v42oPJfp/vuY +H9ef6Lie8nn9+riy9GNwzjnnnHPOOeec81/2ef0Urf26fxY+Rfv3/L+r3+97 +3tdvn6feRvUt2zhI77jJOrLlk3POOeecc57fp2htl+1//n9W6/PNj8rm0Xlp +7T+52o/rT1Qv7vfR9ZxzzjnnnHPOOeec8zu8tV/3z8KnaJ+Xtb8++hwf7aXz +laV+RvnPNt4x6jrKlk/OOeecc875e721nX68/fpz6yi391v7E37N97f793Lv +O+9X+zafpe1z9WNwzjnnnHPOOeecc/7fPq+fIurXjeLPYvsp1p+7qj9tm06U +n9Z+7ON8vt3jcm7d/mqflqf12cY7+sZBrqu3nHPOOeeccx75/nJp+952XDmi +/Ubto1/z/e3+Heat7dZRXjreXP1mnHPOOeecc84555zf4639pevt1lGbfmv/ +cGn7yafP9eW//rj60rnfj8vhuXq4jmzjGq31pzWdbMfLOeecc845/x1vbSdG +6ewvxx7t99d8f7t/h/nY/pDz53e5/vl+MM4555xzzjnnnHP+LV/H3+1a++Xi +9Pa3j+Ns/qNo7e897tedt9s/rrd6fJzPeJ7rIts4RZT/1nreWv8555xzzjnn +/C3e195fL4/b71t8fTz78db+hzif2frr+voxyt/7fZxOXG7ZjpdzzjnnnHPO +Oec8i4/th8nmrVGffqncJl+W33u9tV/6au+rt6O8Pj9Xe5TPq/v/s42ncM45 +55xzznk2j9pT6+VSu3tUO+5qj45rrK/3E+0/9lL+c/XL1ed/1Pk6zk8cY/ob +Oeecc84555xzzt/u8/opWvt/RvmfxX6j7fq/376uH+ns7wnGXpv/t/tT9acU +d19fV/fnHx/n/f3t2cY7OOecc8455/wtvr88x7q92dp/8lQ7Mcp/lM8+j8qt +1e/vf3t7+/o4spU/55xzzjnnnHPOeT6flqf1f/+P+tnWn6vtt+nvf4vyU9rv +/vFG+Yujtjzvzefz87Ii7+t/HuXXXRc5+j+f72/P1j/MOeecc84557/mU5zt +57naW/N57NvjP/Y4/TH9Btv9ZqsnT9XDUf0JUfqcc84555xzzjnn2bzUvzH5 +8nOxR/ttS2ebjz+LfK4/V9+fc5zP6Pi3+WzNz1Me5T+rt52XVh93Ha3jrv7M +/ePJU9+y9QNzzjnnnHPOOT/2bO3K/e3a+5GO/br+NH7s+8vrqD2/efpXOeec +c84555xzzlu9tb+udftov9H2pXTWcdz/01o+0efz9FuO8v3ttuW0H1fN14r2 +O8rr60Nr/e/rn4zyl6eeXF0OnHPOOeecc87f5VGM7ZeIPMpHnL+z/WN8rE9R +2y93vD3nnHPOOeecc855fj/uJ1kv18b475u6uv8n2m90XFH6o443my+Pb1uv +lp//96SvI6qH7fXz7HVxdX17i2fr1+Wcc84555xz/qxPcbb9u79d1A8RfS7O +z+jj3d9f/fGOao9H+ctWH1rLc9R+Oeecc84555xzzsf6vH4ZW6/rDynPRxqV +/2z9Ra35PE73un65bL78P4rx3691nJ/4/K7jLf2xo/wt/bqcc84555xzzr/h +pfZ7a5ztX8rWTr+n32a9XdzvN/r81vZnRulH2x+nzznnnHPOOeecc17vff0S +kc/rp/38WaQ/r2/th4nSz9Yf+BbfX54jqj+1EZ33UV6Xi7N/vyCO9edH1fOr +y62uPMvfP9Z6nUae7brgnHPOOeec87d7a7uvtP0z/Vfr/LaXw9XR1+7e5m/U ++crm6+NcR23/ZF8/RrT/9vLP0n/LOeecc84555zz93pd/1Xt91xtP/9nsf16 +u+322foz+T0eRVR/jutVXP+Xn4/Wl6P2OmrtVxzl+9vVHu+ovyNpXhbnnHPO +Oeec1/oUo9qzWfqdnvZ74r529Ghfl9tT/RKl62KdzvH28ef3PV+95Zxzzjnn +nHPO+fd8Wp7W1/WHzBFt/2fh836y9X/yd3kUUX0rfe5stNb/Vq/LRZ5+3VrP +Vq8455xzzjnn/GqfYr9/Zrvd8fbv8Wn5eP28XZs/FaPz/3w7/djr62ep/h/v +d7tdrZf6VbJdF5xzzjnnnHPOOf91n9cvtzvfv5GtX5Qf+zLO/37ufjrX1ZOn +onS9HEeWftfrPFs955xzzjnnnPOrfX95jiz9Qsft2Sj/5/243ObP7bc3x0cp +P2f72e7xef3T/QBRzsaWM+ecc84555xzzvlTPq9fRuTz+im9v/9v++Wy9XP+ +mk+Rq7495++KbP2i5mVxzjnnnHPOea239pMsP/d8O/o4n9t8j/V5fW/7sbf8 +a/MzOv1r+/GuK//IR/UTRun3pRMfb5brjnPOOeecc84559/zv8vbfpL15/bX +zxGlk61f9Kt+fB7z1LfWfrbSdm3+lhh1vKPLbfz3mLlvcM4555xzzt/uyyi3 +m7L58XHFxznG5/Xrcqv11nZlFDnSOVt/njtfY+pn/X5H9Sfcc1ycc84555xz +zjnn13m2/tKv+v7yHKPO77R8vL6Un1Hems+SZ4+nyvl+z3Z9cc4555xzznnk +fxY+xX82y1M7NEpnmd7d/TnbfIz1eX1bO708Dyfy3nLez0/9cZXqQ22/WSmf +belcfX7vrz+j6kPvdZ2l35VzzjnnnHPOOedv8Xn9fvh7hVk8Kv/1dutoO+/X ++XH+5+Vlfnu9db93R+v5ir0t/fye7brjnHPOOeec81ZfRpbv4YnzN8bn9WPa +9bXznbb5KZ2X4/Z1/7ys1vz31qtc5z1/vTouz3i/ufpvOeecc84555xz/kZv +7T/8s9h+Xp+t//PXfBn9/ZZ9Hte3dX5GeXRcrfXz6hidn7uv99J2V3m264tz +zjnnnHPOI19GfTv3mX6hON+1ftzPMC8/3d4vna+29nJUPvcfVyk/V533Z30b +dfUwinK/R2v94ZxzzjnnnHPOOW/1v8tx/8Z6+2z9om/3KdrO4/bzy6j/Xv31 +9ld7lJ9WH1vOpfKM4r55jMf5H+fRcV7l2a5HzjnnnHPOOY/8uH39n5Wv18/R +2g8TeZTPdbq17b/j7cZ/f1HOfoC4fNbHFXlf/YnTbzsvrcf1Fp/Xl8p5iiz9 +rpxzzjnnnHPOOf81n9evY719tv7Pt/ufhU9Rmhe3PV9j+xvX+fg3yF/Jo3zU +H2/kY/td68vn+Lys833f7/lGcdV94zg/Uf7qPdt1yjnnnHPOOeej/Dii7eLP +t7XX5vTW7fp1Oq3t31Z/e/9A6/H2+Xa/0XG19iO93UfVk2V6WfppOeecc845 +55xz/iX/u3xdf9eveVRuy/Xr8/Kf1fbbz0Xrp/RK+63dvjX/relcXd+i443y +v/+5+fOl9ev01/7U9TXFM/eZuNxqt892XXPOOeecc8555Muo/x6q46ht78fp +H+fj7PdpX7ff3v6KdfrR+eo73vrjutrv6Xd6i8/rS+VTun6z9NNyzjnnnHPO +OefX+bx+GZFny//bfVvOf7er78fgfb6M8f2Tb/Fz5baNq+8/0/pleltvLYdo +T6PrW5b7zDLK/eecc84555xzns33l+PoayeW0m+d5xPlq7/dl62foZT/5eej +9eu4b/5Vaz776s/bvXR+o/B3DznnnHPOOeecZ/R5/TLqfVS/VrT9n4VvP5+r +PPP5tLxcv/Vs/Z/P9ru2lmf0+Tz9llf7XeW/9uP7Q+v9bX2c8fWSs9zi48py +X8p2vXPOOeecc855q09R2z5t9f3tSvNMovxt02893mz9D73lWds+3U837h+4 +16OonYf2Fp/Xl/phpp+y9HtwzjnnnHPOOef/7ef6H6Ko70+I8rneflS/UGm/ +3/T4vK4lWz/n1f2lkbfWK/7Xrz4vx15fz/ePp3y/WvtT5fbUdTHKs90fOOec +c8455/wtPkVbu3iK3/0e73+CKJXzMt32foNR3tfPGR/PO3xeX+ofLqWTq5+W +c84555xzzvm7fF6/jMi36UTt2T8Lj9Lt//7tp7yvX+u93nq82fobn+q3jOo/ +/+v3nJdR9734fjitr7uPbX1UeUY5e/a6uP++xDnnnHPOOee8Ltray1Pc187N +5sflfL7cnvK+43qLz+vr+pnz9MdyzjnnnHPOOX+jz+uniNrdfxY+xfrz75tP +Nda35VxXbuV0svryOL/79wpb63+0Pf/r+9v9uyrv+uuott6O7Vesvy5a/ery +v+u6uPu+lO2+wTnnnHPOOefZfIqz/YeldKblUn9Rtv6K0f0eV/UbXO3HxxXV +h2y+jWz9GJxzzjnnnHPOf8On5Wl9b3/OOp2S7+cnTvdr/mdRntvtstWTq+pP +Nt9fXof5V1f5/nbx/eQ4nauv6/p8tuZ/bHlu85+zn/+8Z7ufcM4555xzzvlb +fIox7bVtutF+s/VLjO7fqO1Py+bH9WR7frN5X/7z9btyzjnnnHPOOf+GT8vT ++tZ+mz8Ln9OL0t9fH32OryNL/YnOe7Z+xd5+yOVxmn/V6/8E0doPXEp/v962 +X1/L/ZXuV9H2rR4d/6jy36Z/z3V0/30s2/2Ec84555xzzrP52H68KLbbZ+uv +yNFP8vz8qz6P6sP93lv+WfpXOeecc84555z/pj/bn8OPyzNK57n6s45s/Y2l +/E7rp+OLyp/3+fRTW706f76O60Mpnv/906vPy9PXXZbnF+ecc84555z/mk+x +bk+N7QfY7m//87/XD9N7vpbpXt9f0Xd+n/J5fV3+8/TDc84555xzzjnn/+1R +/8CfhU/xn81ytJ91HG/3ne/THuvP1ZNpuXRenu1v3JZbVG95n7eWf11/YxRZ +fj/0Oh91XqL0n7ruprj7OcU555xzzjnnfKwvo7X9u411+y5bv8fVvr9dvv6K +/fxGx3G9l8ozS78655xzzjnnnHNe41E/zJ+FT/GfzXbrqE2/lM60fplefFzr +7Y/zH6UT5edqn9fXHu+1vs3ns/2B2/xE55f/9XP9rutorbft9fyt3lr+o87v +P0E8dT0uj+++5xTnnHPOOeec87G+jHI/VZROtn6SbN5b/td6nI9rvTU/efrV +Oeecc84555xn9nn9crttOz3afqxv81nXP7D+fGv+5+2W+8/jx+Vw3Xk5Ls/r +6ufT/X61+YzK59d8VP/n/nal+r/dnv/1q8/78v857rlO658jozzbOAXnnHPO +Oeec/5ovo769XNufE+03Wz/M2HZ93C5efv6u/o34fF/lpfqWqz+fc84555xz +zvlb/O9y1B7/z8rX6/v9eL/z8pTfuu23sV8Opc89P4+i19uOt9Wvrp/b/V7d +jxfVK/7Xp5/W56u1n6o1/f38PX99ZffW+/nYenLd9Rulv5+/0v3wvGcbj+Cc +c84555xzfuxTjOkvnZdL7fGv+v52d/WHbM9rn8f7zdJvzznnnHPOOef8nT4t +L9dHvv7cvN2+t6a/9b//b9v7x/0q2/y0phNtv1x/tjyf8tbz2H7ex9bPOZ7q +l4vqw9t9f7va76Fax3a7unSyXBff81H3vb778DY/o6/TqBzufp5mG1/gnHPO +Oeeccz7Wp6htDy6j/3u6svnxccbHe63H5V7rreedc84555xzzjmv8ai9+Wfh +U/xns13d9vPycv/biNLpaxdvt4vyE+33aj8+nt7yHOXriMqzPf+19bO1PvT2 +py339/7fZ9w/vlI51F8v/F3eej32PRei/NTfN6J0RvWTX+3Zxgs455xzzjnn +nD/rU7S2N6flt/VTlcphfVxjPd7fWkafr2s9Oq75+EaXT+TvKjfOOeecc845 +f4+v4+9223Z3a/pROpHXteuj/M77jdJpzc9bfH+7fzs9Kvf68zFFbT0Z3Q+2 +Pq5s56v3/PZd18/PF+L3+n59KN3v+++fUfp96UTHVZ//qz1b/z/nnHPOOeec +83f5qH6/rP1X63z2+Tq9aD+xR+U/xbX9CVE+8/czHOe//rg455xzzjnn/Dd9 +Xr+Mrf/9fNS+jtKZt1vuf+tXtxOj/I/qD8nm+9vF5R9573k/Wz/7znuUjzzn +pbXe1h1vnvk//E1ef/+fovY6jdKpu1/15+cpz9ZfyjnnnHPOOef8294X288/ +2w+2/ny5f+Ns//ZxOvoHWr2vX/r+88I555xzzjnn9/i8fhmRz+un9P7+396+ +Xufn7e3H4+2vK+erPcrPsbcfb93nx53Hu8qn7bqL0+E8s9dev6V45nk3Rf1x +HR/v+HnFnHPOOeecc875nT5Fbbv42X7IKLbHUwr9AGN8bD8q55xzzjnnnOf3 +Uvt68uXnIt9+/s8i/flz2dqDv+at5yXaPvL97db1Zx1R/auvt6PyX3dc5Xzu +p1u6jjh/s8/Rep+J0m+9Hu/qf17nc5Kz9yvOOeecc8455/xLvozxv2capT/J +fn9dlL/W/vZtOtnK/y2+jLvPI+ecc84555zf73+XS+3cKIxT/7rX1Z/a+Vrb +aN1v5L39AJx/z+dovY76rq/4eovytc7/qHwe36+2+Wk93tbtOeecc84555zz +X/a+9vt6u1J/yPpzc2Tpx362f+a6ctjPd/m8rLcvpZ9lnIVzzjnnnHPO/zmM +7fq/n4/av9vts7Xr3+JT1J6vu9qhtfuta3dfF8f5zzYfhvOxXlv/o/v58X1+ +m87Y+1t0vyg/r0rl03q8ffex+nxme+5wzjnnnHPOOeeZPYrWfozadEv5ae1n +eLv/cxjb9a3ltp+P+nGM2v4xzjnnnHPOOb/b69q55XHtbO30t/j+8hxZ6kmv +fy2i+h/58v8ovajc8szz4W/ybX3r7QerfV6UniNt9434ObTv8/q7yrm13KL8 +Z3secc4555xzzjn/hve1W/P5tDytby2HUdHaHzgqP63n9ylf5683//v7i/u7 +vlLPOeecc84559/343bienn6fH17k+/Fdb+/s59+nI8x/pa4uhyu8+i6W64v +ne/tfqbPtV7XdfvJMk8pj4/tjzq/3/3l/vvbmPvY6PvSffPfpqg9rmzPKc45 +55xzzjnnOb0UWfqZn/Z74vn+pVY/169Y/3cDj/Mzx3F+2s9ntnrIOeecc845 +5/s+r19ut20fZeuXyOZRua23W0fteRnrpeifn3BcDuej1A9QW//7zteveVye +62i9Lkr1ZL3f4/O+zVdff1F9fa6r5+V5mK3pn8vPOtrP+93Po1F+zX2pfx5s +tucX55xzzjnnnPN7fFR/Qlbfj2h9q5f2W54X1BvX9mP0Htfz39Nel842stVb +zjnnnHPOOR/lURxv3/990fzYl3H2+1iidM77n0X+1+u3Xjre/fyX62kp+vZb +78fpx+eV/411eUb1J0qn7jpa76++3rbm/1z/an/6d11f1z6PstXPqBxb60m9 +Z3secc4555xzzjkf66P6H572abmu37LVS3H190HNMbaf86n+kHn9Xf3DpfI5 +m87Y8uecc84555zz53xantZn68fI5lPUluexb9PtS6fe/yyOa72+3seWW305 +3JOf8x7l8/h4+Xp93fUSp1N7vo7ryfn0W+tta/rrdNf3gbbjjdKJ8ld/3yjt +71c823ONc84555xzznmfL+N93xd0fFzxcdZ6b7ld26/Sm8/67fv6c9ZxvvzX +60vlPNrX+322/5lzzjnnnHPOr/dpebm+Pp1s/R539ascl2cUZ3+fqLSf8jy6 +aL+Rt6Y/qt+jLup/D24dWdvv0XHyJ31ef67+n09/irb7+fnj7Ut/VH5+x7M9 +7zjnnHPOOeec9/lxP9V/Vj7HM/3DUX7Oe2t/Y+Sj+i2X+Wrtn8zy+6HXna8+ +r89n63kcW87ZrjvOOeecc84zePt78rR8vL6cDt+PbP0bz/afbMst2v4tvr/d +6PlX7df7Oj+Rtx5v73FFcdX12NefwN/irfeZZ+vDvL7uucFbPdtzkHPOOeec +c875sS/j/Pfhv7t/qbXffuuj+vdK+z3bP3lXP+SY/tVs3l5PasuhtZ+Nc845 +55zzX/BR7d/S+/a0PO0/2j7yse2jPN7abs3W7zG2/yQ6/m05RNu31qunPDqu +nP0D23xGfq4c5hhdf66+rpfHGddPznl+z/Z85JxzzjnnnHPe58f9Uf9Z+RxX +9SP15SfO5zLduL/u2Lfpj+q3L/UHtvVb1h9Xaz4jP87nqH7XPD62fErncRtZ +xms455xzzjk/Px+gvj3Y1246n5/S9uv0x7ab8pzHqPyz9W+M8qh8WuvnW/zq +foDjdKLrq/66i3zU/eSefpLr/Ph4W8ufc36nZ3s+cs4555xzzjnv81J/1LRc +6meOfLmf2n657X6j7frSqfer+/GO810/LtB6HnuPa51OX37i8/Q1b+33Xn7u ++f5bzjnnnHPOW3xaLrU7ou2PPc97fuSj2stPebb+ilEeHW9UP7/qrf1CY+tt +6/VViuf7c66un6O87z6c577K+S97tucp55xzzjnnnPM+n2JMv/o23d78rPd7 +vF20fa/P8VT/53J9uT+zrzxjP9tvX8rHN31eX7pe+sotz3gN55xzzjn/TW99 +v21tBx23j7K9/9d7X7sgz3nP1o/RWm6t9e3XfPn/OrZ+Tz/AvH55Put9VPk8 +3S939/08yh/n/H7P9pzlnHPOOeecc97nU5ztb19vt98/to39/qIof9v8HO93 +m06U/6v7Oceer7jc932dv/b+zMhL56X2/L7dx57HPOMvnHPOOeec13jr+/Co +9t3bva89lf/8ZuvH+DUfVZ5v6Zc4Pp48/Tlvv973lznnV3q25y/nnHPOOeec +8z7fXx7Xf9Xb7xTF2X6kbP2l6/yVom/84jnfP1/R8X7Pj6+7+XN15cY555xz +znlOb22HRu2a1nbrt/258zstT+uf7a+oz2dUr37N97drb6ePvU7j/Jz1q8vz +6Xp+9/V+7Nnuk5x/27ONI3DOOeecc845v8dH9VMt0+vvXz1OP9rfNp1svszv +Vf1p1/lvjrPM60vlcPz5PONrnHPOOeecn/HWduV6u3Ws06973659P9/uty+f +97c7Jhl1HtfpP9X/EOUnOi+/5vvbReezvZzf6XOMKuex9bn+/na199W3p+57 +nP+mZxsX4JxzzjnnnHOe06do6y/afn4Z3++P7S3nZbpZ+kW//z1ax+cluh62 +5325/vlxNM4555xz/g3ve/8c9f68Tb+1vVPK/7R8V7um9f1/rMdxVT25q99g +/3jytNOv9uX/22i9rpfbPd8PcK1vy62v/M/fr3r7bd7xvLj6/sY5/+/I1s/P +Oeecc8455zynT1HbrxV9fr2+1C+XrX/1rn7a5eef6xft6x+OjustPq+vG6/J +0+/KOeecc86/5K3thevehyMf1a5s3e9T3tf+bS//s/Xnrv6Byaf9/1lsv17/ +Xl/+H0X5e5/qtv8Vry/PvvO1TeepfrOr/Z5+PM75Gc/Wz88555xzzjnn/Fkv +9WtdO45Q//t9b/GonKPj3U/36f7S2NvO+1t8Xl83/pJt/I5zzjnnnL/dW9tx ++8vrGPV7GduobdfUpV9+D29N5x4f1x65u/60tnei8n+L72/X286N0+FtXqqH +6+1H3U96r4vouLI8R6Ly6XuOcM7PeLb+f84555xzzjnnz/r+8hyt/ULTcqm/ +OspPtv7bUX5c/q3leb8f939G9Se/l/p1s/Svcs4555zz3/RR7b572i/Re/h6 +f9d/z1Ip/+v8jPX69khvOzFLPXnKo3L4pxDH2z/f7v6615Z/a/1s3W9fOnH9 +uvu5MPa+V3+/4pyff75zzjnnnHPOOef/7Vf3e2fr1322Pzkqr/Xnn+9H3ff4 +fOfy+vGLaHvOOeecc86v8/b32+Mot79a24ml/By3E/K2B1vzf+zXtV8iv7q9 +f0/5R+2x+Hwt0326Xcz7vL7+t/Y7tW7fmp+s3nZcnPMrPFs/P+ecc84555zz +b/hxlLbr/73It3tdeebvL23b/imf16+PN1s/Kuecc845/7LH76u125faEet0 +nmonRu2gKJ+l7feP8/523P52ve2p+vowqvzvKp/W+r9M9+n2L3/Kj+tVqf7U +R5bnwrP3Gc75FZ6t355zzjnnnHPO+Td8itp+p9b0n+pPztmfn8eP68O2fjzl +o+ot55xzzjnnLT4tT+tb2wXR9tnag2/3KO5p38X5WG+XI/9RPN8+5d/w1npb +d13cd18tHW/tc6Rvv3E+OOf3ebb3HM4555xzzjnn3/DWfrPWfuCr95vNo+Pd +//zT/ahx/nL5vL63X5RzzjnnnPPzHr+v1qaTrT3I/0bUvlsv77ez+uN4v3F9 +O84P521+db9NqZ+k9f68zn9rfqJ8HOev9/5w9vvEOOd3erb3E84555xzzjnn +3/Yojrcvfb48r2ZUv99THpXPqH68Ud53Hq/2OHKNx3HOOeec8297e7tm7dna +d9l8iiznvbVdfE08Pz+H/4JH1+H5fo+x1/v5+3Dkddd77e+FxZ/nnL/Ps70v +cc4555xzzjnn/+2t/XXr7Ur9Y639hNm8tRzu8Tgfd3tUbsv1z4/XcM4555zz +b3tre2S9XGrXfNX3l+c4e15ay/84P61+dYzKZ33+z7Vba6P0+SzzlH7Nt+el +dH3V3idL0XYf6K3n/eXTWg59+eScZ/Zs71ecc84555xzzvkZn6Ktvz36/Hb7 +t/j+dtf3xx6fl2053+N5xuP6vL5+Rtuvt6sbV4q2jz1XuXHOOeecZ/PSe9cc +2dpZ2dp3JZ+W69576/1c++u6GFMP3+7n21N97e7z+Smls8xHXJ9L11Ht9mPL +pxTXtSv307+6vtXvN2f/Cef8Cs/2fsU555xzzjnnnJ/xKfrGQb7z/VrRcV3t +x+clKv9Rnm3cbdQ8q3m51F99z/W1zX/peqzNP+ecc875V7wt6t+vfs33l3u9 +FNd9H06Uztn2Qt17+Db66nPe70ke5a39DL39FbX7Pa5XcbrrfJbq56jjqq0/ +vemcbXdzzvlTnu39inPOOeecc845z+BTtPVLbz3q/3zKRx1Xn2/Lt8+zjbtF +9WZb/tnq+T3XxVvOI+ecc8756HlZ/b/X8Gu+v1yalzIvj26/tLazxr5XR+/P +59sdx+nX1/O+9PkUZ9ubo9Lpbfe15nNaX7rvlfbblk628845/2XP9t7FOeec +c84555xn9tK4QG1/dWs//9W+v12+eVmt5T/Wt/nJVj+zXhfT8rqejBnfyTcO +yznnnH/H699/lvG735M5qr3wdo+Od10upXbEcXnWvx+OapeNLYf299tl/uLy +GX2+znrfez6/x+f15667eu9r12crN845r/ds72mcc84555xzzvkv+P7yc/O1 +1vnYj+fnZU2RZfyR93lf/XyqPnDOOeeZvf59sjWduuj/fqEoP335z+Ot7z/Z +3tP62jXn62c2H1sOvdfd+L+feM9xjSoHzjnn/Bue7f2Nc84555xzzjn/ZW8d +F7h3vtZ35mVlO+9v9yj60imlW18Ps4zPcs4551f4qPkYfduPeq+rf98r5T/L +eYnyl+39rfd972vzr6Lj6n1fHTPvaJ3v9nlZo+ebRfm5+vra3+/V9x/OOed8 +rGd7r+Occ84555xzznm9Pz1+sdxu9LysOL42L+st+RxVD/e3668nucZhOeec +8yt8+xxsfa+ItuvbPo+3zre5x+vPVzYvHe+03DsvKJuPLp+vzcsaWw7n22tR +PjjnnPPMnu19j3POOeecc84559f5Ms7+3Zko3W36pXxEKWSZfxUdV7Zxpd75 +UWfLs2/+VeTbci+dl1zj5pxzzvkVXv987Hsut76nZfN5/fp9I/v5erpdcPZ9 +7+2+Ps4p6toF6xhXb/c9On/1xzuq/oxqX/T68ji/ch/jnHP+Vc/2Hsg555xz +zjnnnPP7PYreeT7L7cbNyxp7vNv9Zhsnemoc6thbf599nY/n5ulxzjnnX/Lo ++fub87Lq3+uW6++bN/L0e35t/rO9r47y1vJpbUccp9t6PW699Xq/el7WqPrW +6ve0OzjnnPOxnq0fmHPOOeecc845v9OnuGo8Ikp///Px9y9F6TxVbr3jHevj +Pd7u/PhItvGgt/vo6265v6e/14Jzzjkf663vUaPmER2nU//etZ+/9vfV4/0+ +5fP60e8hT82HaT3v2d4zn3qP3V/u9XU+4nlWrX51+/Tb7/PZ7j+cc85/zbP1 +h3POOeecc8455zU+RW1/8jL65wV9xfeP839W69v750v9/7XRmv6ocZlR4zh9 +46H15TTqfC3TOzuuUR+j7gOjzu9yfZ7rlHPO+Re89bk/yuvfA/ven8976/vV +KL/rfWAdV7eDWo/3LT62fVd6jx1fz0f51eXZVw/ztaOXx99bHzjnnPOxnq1f +nXPOOeecc845/2/fX17H2d/f56P9nnh+fOTtfny9bM9n7/VVu9+r7ye9433Z +ri/OOee5vPV5Wkp/mW77c7z1Odh6vK35HOtReY7y8/XhnvbRfByl+vAWrzve +beSqn9f5U+XfWg8neeZ+G+Xn6vsG55xzfuzZ+ts555xzzjnnnH/bp6gdv1hG +7e/X5xmnu9r7yiEu3zF+dVyX/+PyLB3v8+M1o7x3vKy2vkXptI6zjL0vxec3 +y/XOOec8p1/z/jDH2Ofydr/3zqu57n1mzHtvnnlZUT6vnp8zyqP8L4+jNG9m +Hc+/Jz/lo96fl5/rr7dROk/7/vFe3f7lnHPOjz1b/zznnHPOOeec82/76HGl +d/v2OHP6vL5tHOG66OufX8dXynn8OGbv9RgdT2n9XePCd40ncs45f7cfPwfr +n++tz9NRz7vj4422O//8HZ3/5ed733PGvafVvv+0to+i9J86L33vS63tnXW6 ++eZBPev19bD1vTdK59vvw9nafZxzzn/Ns/XPc84555xzzjn/hu8vl/qHt9sv +P5elX3dUP/ZTPq/vHS8YOz64jdHjd+/uz5/Xl8q/b7zsqfLZHledz3HPeNN7 +70ucc87rfFouvT+0vve2vhc9+x6ef17Q/nbj571EcfZ8ZSvP1vpz7Ov9PT2v +6ate/17a1y47f98Y66P6EzjnnPNnPVu/Peecc84555zzb/gyyv3JpXTeMX4X +H/+1HuWn3dvmsWyj7zzWH1fruNI99eqp836dH5fb+fTHjreW6k85P2+7/3DO +Ob/WR81fyvZ+nu09/5r5WlH0z2+JvLXcnp1ntf780/OL+D1e/5486v7Q+p7f +m86vtMs455x/w7O9z3POOeecc845/4aPnXeRbTxufRzR8fV6Kcb3248d94mP +66p5WTnna23zf3y8vPV+0loPn64PnHPOM3r9e0gp/fX22d7P3+7LOP89rut0 +jrfbRut7S998s/b6yd/to+pVb3ttnZ+x9XkbY/sN8rRrOOec8/+ObO/VnHPO +Oeecc86/7ct4fv7VcX7ifI/x1vyc95zzmuLyOT6u9f62+Y/2e89xjSqH3/FR +5/Hqev5sPeGcc97r+1H/PMr2Xs2P/dx8jzlGvW/U7Zd/07f3mavfY5fp1be/ +xrRP64/3OD+cc875NzzbezLnnHPOOeec83f5FFeNi63X987jOh4fifY7ykvx +/Pyrq+dlHW/fft7PHu/T9d+8rDt8Xt9bf56tD5xzzu/y/diuz/Ye/uz7f1x+ +2c5v23nvjSzzf/jbvLZdMPb987r36sj75pVla19wzjnnfZ7tfZ5zzjnnnHPO ++bt8f3kd5b/LEG1fSr92/s/V87L6juu8tx7vcTmMm091Np1SPpfHE49rPDUP +rdWvrp+/6e2/73/t+co3Hs05H/+8uzr91uc4/2+vf9/I9r79lI+ub9Ny3Xv+ +uPeBayPb+097O2VMe6p1/s/8+azzoKJ0RrW/zrWvt3HtvKzz9erq/HDOOeeZ +Pdt7Puecc84555zzd/kUZ+fD7G9X6lff5qM1P2PTac1/q0flXl/OT81HOk4n +Lv9lvsf9XvbYcZNR83mi44rKhx/71ddve73NNT+B89/2abk0zh5t3/q8qLv/ +zDH2eVR/n+R/Pdv79tPv+ZPXXS/nn+Ojnte919Go+PV5KaPuV+fuq6PmZZXz +M+p477n/c8455/xOz/aezznnnHPOOef82z5qnsz+du3zJVrzebzf63xUuY2d +lxWX85h5cfXnseRj5g1u83NcPr3zgrbHyUf6U+NinPPn5l/N0fe8q09/Gdd9 +f0vtfLNjb0//HX7+PfDXfIqz89aufn8e9X57fLzn3weuLuco3V/zUjlPXqo/ +009n60OUTm97ap3/1uMtbcc555zz+zzb+z/nnHPOOeec82/7FGfnyYz9/fft +dnXp5P3+q1HjBVef3+jzx74+zuvnv0XHO2p8hz/r98xjzDZvgfNf8Prne+99 +flo+N88qz31vuT7LeTzvo+7nX/UpWucfnp0f2HrdPXUe95d752/H5frMfEXe +58qZc8455/We7f2fc84555xzzjmv8Smu+j334/TPe7Tfq+dlXT2e1VoO0eeP +fX084+ZlHXtrfuLtfR9CRp/Xl85j33VRXx84z++l66g16r8P5O7nbyn9df6j +fL/L48hVD1ufp9vI9n479n2s/nmX7b30nvf28++Zo96rSzHqetk/rmz3H845 +55zz73m29gLnnHPOOeecc/7fPsVV4yxjx1OifG/Tz+b72/X/nccx40HR9vm9 +dzyxNp3S53mbt14X++lu99M7T4/zTD4t182beuq6vn5e1rRsPsN+ZKm32d5j +73lPfu/75+h5TW3z9M6/f9bdN+a4px1kvhbnnHPOeTbP1o7gnHPOOeecc/5t +753P0zb/KvJ5fWk8hf/1/e3+LZ6vdbSOu52bJ5PXjftn9vN/D6s1Hc7f4NNy +7f2+bfv7r+u+5875+0Zf/rP5vL72fSBLvc32Pnz1e/VbfH+70d+bN66er/2e ++Waj7j+j5q1xzjnnnPNWz9aO4JxzzjnnnHP+bZ9izLjbNt1llMdTonxmG7fK +Nl42Sds4fZzOr3vf9RKVN7/aW8dbj9PPN5+Bf9NHPZdb63lpv5Pfe1+tf38Y +9Z7z1ft86f3h7no+aj7MPe/D9fUw2/vh2PfM9vf5sfOv+vd7z7ysOO6+jo7z +xznnnHPOI8/WHuGcc84555xz/g0fO89n/bkovTlqvz8hSifbuFU2j877FFfN +o/uK19bPvuur9Xrhxz6vL42P994Ps8zb4bl9Wq67zzx9vbRuf9886tLz66r8 +93n9+8lxPq/zbPe3bO/D63IZPc/n7f5PV1zdLoj97nlZfe/bvkeLc8455zyb +Z2uncM4555xzzjn/tk9x1bhA63ywKP1s41Zv8avP1zd8Ww7H/t7vUfmGn59H +V0qH8yPvm+dw3f121H6ffR7V31dbn2v7+cv6fHnu/jnG68/X0++303LpOvqq +j7qOeucBrtNp9VHthafaU6N9XT5R/jjnnHPO+d/I1j/POeecc8455/wbvoz+ +8dwprhpnifabbTwrm+9v116erfXn17xUPuZr5fK+88V5nx/Xt/h5Oq3vnX81 +6r7U+9xpK4fz39/YOw/k2veWVv/e/TDne6/3yf3teud51qdzl6/r4W/Py1pH +nvcxzjnnnPNsnq39wjnnnHPOOef8G76/PG58Kko/Wz5/zUeV//7+nh+Pu9uP +yy1KJ96Oj/R5/dnx5SzzfPg1vh/X1cNo+6vnQY2axzX2PaR9Htfkpet61PMx +57yU6++fY66v8++BvfVq/3jyvI/dNc+qdp5SKZ3s/lT7ZYqczzXvn5xzzjnn +tZ6t355zzjnnnHPOOf9vP47SduPHU/ixl85j2/gOj7zuejFeNsZHjUvmG1fl +13rv/bC2vo2aZ9Wa/7f4frm0fw9Y1ufp+rhG+fF+2++f0X6vur7G1p/ous3z +3jV6ntV+1JdDXfrv9bP35yid3uv9qefXfn6yvb9xzjnnnOfxbO1lzjnnnHPO +Oee/6cuoHXeIPh+ls90+23jZ231/u955RHyS2vp/fF7icuf7Xqq3tfOxSuuz +zCPi9/q0XLoPjLrf8mOf4qp5cdmey30+6n57/nvnrj7v2c7jqHl9vzqfaozX +1+fW97G+97f75zeu82deFuecc855nWdr/3LOOeecc845/02fom18Yfv5ZfSP +d/Oxfnzez59HvvS264X3+by+dv5htnlBvM/3o77+9I6/T+vNv7rXpzg7P/bp +eVln5wcee/v98+w8xr7zmP989b1HlSLP+8lbve89tvU8nZ9P1XofqKtX3jM5 +55xzzs96tnYu55xzzjnnnPPf9P3lOVrHE8+OF2Qbj3u7Tz+NOY/x9r/iY8dt +66+L3/R5/ZjzuI1s845+3euuo/rvs2p7HuX5O258rE+RZX7Xen/78fy8rFHl +n+29qLf+LNPN937C//qo50Lfdb1NZ2y9yvaexjnnnHOe37O1TznnnHPOOeec +/6bvL7dvP8VV4+x8rE8/tc6jWKabbzzuHo/r/37E9Z7v+7n5b/XnK8t8JH7s +rc+jUfMxOK+53987jyvvvKyn57N5b/mGr8/jqHl3UfpX57+vPcU555xzzkd5 +tnYl55xzzjnnnPPf9Clqx0GO09mm25o+H+vL/6PwfVlnfdT3M/Aan9dP5dp6 +f+MZvP28XzW/i/M7ffQ8k+Xn2+ejXp3/1vlmffPT+Lu8/v4/ap7tMr3+78s6 +Pq7IW59r2d67OOecc87f69nag5xzzjnnnHPOeY1P0TaOMEX//Bbe5/90xfnz ++Gteul6iMB7X4/P6tvmE28g1T+l7fnxd1J/fUePynNd4tvrWNz8kvr5qr9Or +519xXvMe1XtdXDtPuPX9JNt7FOecc87573i29ibnnHPOOeecc17jU7SNv09R +O48i2t//rDzfPKi3eOv5jbbb31++8b6nPCrn4/HE+Prhf+N4vPPs91Twe/z8 +/STb85E/61Pkqufn/15w3ftVf5hnxe98zzmuz+PeB8a8J3DOOeec87d7tnYr +55xzzjnnnHNe4/vLc7SNg9SPp2Sb1/R2X/6/jvj8LtPNNz74rPeWZ+32fL2+ +dt5CtnkX3/RtuUfnpfW+lO05yO/xZfS/P2T1KEalMzai52A56s5vf/TdZ87/ +PcconWi7dT7qnl/t79t3vz8fH+f68+2/l9G2n9L2nHPOOef81zxbO5dzzjnn +nHPOOa/xZfT/nanWdPg9fny+tuev9fzypY8Zl+SlephtPsZbvW5cvlzPW+8/ +/NveN394VL3Ncx879nl97/yosZGtfPI9dyY/O5+wNp3W97en8jlqXu5xfvLU +E84555xz/qxna/9yzjnnnHPOOedX+BRnv08gSifbvKa3e+v57Z2n8Ss+dvwx +ul5+zbfRd//hfX7dfTvb84vf463PkZz3yW0+R/m5ee/l6E3nt+bFcc4555xz +zt/o2dq/nHPOOeecc875FT5F7e/1t6aTbV7TV/34vGzP0366+eZN3eOl8llH +tD3vnZ+Qa15Tfm8tZ/OseMtzobYejnof6M3PMt3r51mNnX9V/1wePe/r7P2n +r15xzjnnnHPO+daztZc555xzzjnnnPMrvHecdB3Z5in9mreeX9+jdexReU7R +9j1FX/XSfIkozv89Jn7k9fftbM8jPtanOFt/rnl/eP5+Puo5O/Z5sc1/3fN6 +jnvqSe/f0dseJ+ecc8455/x3PVs7mnPOOeecc845v9NL44BXjTPyPt/frvfv +SW3T+U3flk9feX7V5/W18wdyzV96i9eXf7bnCB/ro5/Ltd9DdfVzqtfX+b96 +nvPx/f/6vze6v7/z+R97XOPKwfxnzjnnnHPOv+/Z2t2cc84555xzznkGn+Ls +eG6Ufrb5Tm/30nlcfr78PVHr7b/qY+c/fM/76km0XbZ5UPl8Wu6dJ5PtOcL/ +Rut9pvd5PXnb9y99fx51X3m23sda77frfLfPy4rSubp+3uXr49pfv80v55xz +zjnnPJ9na6dzzjnnnHPOOecZ/Hic7j8rn6NtfsY2fd7n+9vV/32hp+dHPe3G +hds8um9MkW2+Uy6vvx6zPRd4ny+j//7c+rz+Ne89L9de1+efv0/Nzyzl/9n7 +5DryPB8555xzzjnnW8/WTuecc84555xzzt/oU5ydh3Cc7v/8r/3P8dbx2f3l +deSZN3W3j63nX/Vs852yeen6muPq+RV8rO8vr2P89/jxv37Pe8uo+bqt6Wy9 +b572Nj9Pl9tZ77seOeecc8455xk8W7uec84555xzzjl/o09xdhwt2/jv231/ +u97vifq6n41tff62Z5sHlc3r729ROtnu81/1ZdTeJ+PrYp1OtufC2/2e83v1 +/Ns4P2sf9dx/9nq5zlvnp3HOOeecc87v92z9AJxzzjnnnHPO+Ze8dR7CervS +/Jls48Vv8eh87S+vI9t8qvHeV2+jcnu7z+tL4/tT5Jofdf/3t7TeD7Pdt3/N +95djb50Hku3+/xb/J4i+85t//lXkT81nu6ecr/dluZS+34xzzjnnnHN+hWfr +B+Ccc84555xzzn/Bpzg7HpptHPktvr+d79Eqjdv+5vdyzOuf/l6UnH6+nmS7 +P7/d95fHzRPOdj//qu9vd/Y5tY5x98mrnptXl+fV190Ud9+fza/mnHPOOec8 +j2frN+Ccc84555xzzn/Bpxjz/Qbb7bONL7/Fe8/jMt2n51Odd+O5f2P0df12 +P45yvcp2H367T3H2+3Oy3Yd5n/8TxNj5tOt8PPc8Mi+rxlvPY57nL+ecc845 +51/ybP0JnHPOOeecc8453/oUxt+f8emnq74PJJv31cPtdm/33vrwTa8vn2z3 +z7f7Mvrn60ae7X77az72fWC7XV+9iv3u5+DY53h9+Zy7TreR5b7dtz3nnHPO +Oef8jGfrZ+Ccc84555xzzvnWW7//IfJs49Fv8avPy1s8Kocp3j3OO2pc+7u+ +H9v12e6f2Xz0/M/19tnun/yvL//fxqj5Nst8lL7/sD6dpzzbvLjSczA6rrvv +2335zPZc5pxzzjnn/BuerV+Cc84555xzzjnn532K2vH69bJ5XHU+/XT394c8 +5X3j+2/xef25eWhv9+g4t+c9230vm5+bDzNHtvse7/NR95NSOst85HuOtHrr +9dX7HK/d7/7yOu6el7XNT1/+Oeecc84551d4tv4KzjnnnHPOOeec3+/LuG88 +9O2+v12+ce1R3lp/Stvl8vPfU/R2HzVvgS+jtl5lu7/xPu+rD9vt+u63X/Wo +HEc9x+Pnwjo/velcdd9urW/H22d7LnPOOeecc/4Nz9ZfwTnnnHPOOeec8+u8 +bt7FHK3p/Jov/5/jq/O4SsdVO98gp8/ra+ehZZlP1ef19TbbfSzb/fPc/da8 +rOzeWk/2l+donf/J27x0325Nv+98baN2flTre9qo+8zxfjjnnHPOOednPFv/ +Buecc8455/x3/Knx3+X++7+/Ilt5cn7F9ThqflG2cfZnvy9lez/aTzffeHfJ +vzYva5Jc86navfa4st2XnvJl9M/TyHZf4n0+/XT2vEfb82Pvm0c0+u9CltO/ +9760jmzPU84555xzzvl/R7Z+D84555xzzvn3fIqz48ut+x097tY6jlM7P6E1 +nWznl3/b95drw/yEtf9TFc+Pg0fed1zR+mweRbx9tvlXx/NGyseV7f6TzZfh +/vZWn3669n1vnY989/O3e997S/m+WJf+dvtR9bN1v2Pf6zjnnHPOOedXeLb+ +Df43Wn+vqrcdt+43eKo9yDnnnHP+az5F3+9r949TPP0ee9W8rKfG766Zp1E+ +j1enz/mI+9vko+vz23153OX7yX66Xx8fv9+vfn5d7dnuA9n8+PzW1wee05f/ +z9H6Hh5tt5+PfPdh3ud9/eHZ6kme5ynnnHPOOed869n6SfjfuLo/sLUf4zh9 +9Ypzzjnn/OrxweXn+t/3WvO5/vzo3wcfNU4a5bPV69KPYtQ4y9n0S/m9bt6X +eQL8f0ff/a3+ev+qt96Hs/mo8/6Ul8o/y/yrY68/rq96VA7Hft28a36PTz+1 +XkfLdP39wa/4Nc/fbdw9r+/tz1nOOeecc85/2bP1n7zdW/sHWttTo/ud2tI/ +37+R7XxxzjnnnPeN902x7T8/O64XpTPKR73f9h7XcrvaeUTrON8OavW+9+T6 +9PvqQ1xube2Oefmu8a/j4zK/66t+Lu6bF5rN/6mK58fBj/P7Fo8j1/yr+ThK +10W2+8Bd95Oz5caf9emns9fF/vp1ZLl/8lE+el5WWz3M9lzjnHPOOeecZ/Bs +/Spv8Sn6+gei6P/9rLHjiaX8lscfI7+n/OP8145PZatvnHPOOc/jyzg7Th2n +M6af//z7z9XzeY7Lub79Eh3vcX6iz183XnPPe++ocquvV6Xtp/W98xhH1ROe +0/eX2yPbvILR48LH8fw4+CRj5ktc7e3zV3POy4ri+78f11oO2a73X/On+y35 +N7z2vj26Ho65Pz/1vOOcc84555xn8Gz9Km/xZYxvJ47yUj7bPDr+/N/PMGq/ +2eohv8enuGpe36jx32zlxjnnb/FlnJ0fFaVT/x5eyk9t+qV81j5Hou3r8lmb +n/ryHD1uwo+8vd5edb1E24+a3+L9/12+jO/Puxj7vLjL5zjOf+tz4byPan89 +5b92v8p2PfK/Pv3U+j65H63vCfw3/Xx7qu95dN17Neecc8455/x3PFt/SzY/ +7n/Ylme2fpJ75nFF9a2+f+bZ43W98GNv7YeMfHQ//zqylRvnI66vabnUj8r5 +E/f5afmu+QCt+Sl57Tjv/n62+Rrto56/PLdPy6X6uf+58d/nVvv+xnP6/vL7 +2+l19TyKLOPp2capW/OZf37sW3wZ5f6lbNfdV335/xz3zrNq3Z7/lsf1qvY9 +s/d+VXvfztae4pxzzjnnnOfxbP0z2Xx/eR33jcfl7O+tr1dR+n39dVvva0ef +z39fu9u4z1v6gY+3L0X5/lBK/2z/T7Z5DtnqA+/zZfSPa4+al5KtfHhO319e +x/ve685dv9vINR7NeZ/f+x5Ybo94L3rW95ffP9+jd77xMt3rx9P7nsvXeet7 +5lP+1fvG/vIcteXA+3x/u/g5+NTzlPN6r7+fXP3+kO15xznnnHPOOc/j2fpn +svn+8nf7b0eN6z3bD1zKX/28l9r99h6veQV3XL/nfy97dP9nW32L63PtcbWW +z9h+XfX87b6Ms/fhVr//+wSi9EeNK2U7v7/mU9TWn7e8v7UeV13c93vlnOf3 +9veryUvthWz3ya/6/nLJ3zs/ZH+758bNj/M56r2x3t/y/Mp2HY26vlrnE/Jj +39+ufJ2O6pdo3S/nR/XqnvbRNj/ZnlOcc84555zzr/p7+3+e8mz9MKX+mbZx +urieLPc3epzu+npem//W9Ov6x8rbZ6vnb/cosl6ny+3G9V89dR9b7sfzJbsv +Y3x/aV/93+537Hyq7X5HX7/qfy6f4mz/fLbnQms6o+YZjh4f4fxLPi3XXXfb +7bUX7vHjuO7952rvO951uuZlrdePvT+s9/fe6z06vmzXxVt8f7vy+97Zdke0 +X87Pe+k5dFU/c7y/2vxke35xzjnnnHPO3+vG0/fKo9yflq1/9ep+ldZ6cvU4 +3bP5icp3TnddnmPGa7b7zXYdZb1+p+VSfX6L7x9f+zzS/f2N62e7ej7YMr3v +P6eempd1z3lsva/G29fWh7vGPc++P4yah8aXkeW9bux1sfXW++eo/R6nzzmv +8VHzqFvT58e+v/ye+SfrfO9HlvH6q/3peZtzZKvnX63/2Xx/u/br4p72Pudn +vL6/aPS82dr8cM4555xzzvnV3tp+z9YvZJxuL677PaZR43et4w5Zxkd6y+Hs +9q3jqtmuL/3D+/ndvx63UXt9HsdTz53e/H//uZPtelmvn8r/bddR6/0zSqfV +x47T9T83PS+OfV0upfN7dX2+el59331gXDsi13sa59/wUb+nkO3+/HbfX87X +HrnrvajN87VTrvLW9wH1+V1e9163jvp2GecZfPRz55n3q6eeO5xzzjnnnHMe +xXb7t/QjvX1eVpSf/c9n7S+N0x81vvA1Hzt++jvj7+/qjz1/HY2aj3Hs9fls +Hd853v7q9H/nuvjK867V9+Ou96ja+TD1113r9dKan1/zKXLV//b3qDa/rv7n +HGfhnJ9/vrTPc/7196vW+RjZ2i91+b66/2G7vzEex93Xnfr5Lt/frv/vQa/T +4fwNXvs+cPXvi43dnnPOOeecc86f8t75P3Nk61/6xjjdervrf79pf/9RvmI3 +z+oKj8rxfP/hWzwqh6fma139PSclr71vf/t6jJ9r63IYdX7f4qPKIdv10vr8 +ah1H/opPy733jf31+eq5970av64d8e3nC+e8/r3re88L30e0n9+r2jX7Mer5 +FcdV14v69i7f36633vamw/lIb28XH6dfm058H77qvaI1Hc4555xzzjl/1u8f +B8zZT7WNe/t/onjfOF3peHONL3zVt+cl23U36nuxnpqXtb/d09fpNp1fGzfv +6yf83vWS7fvl9rdrvy5az2/rfWP5uefr89U+avwuWz3Pdr1cPY/3nnGKPPWW +c57fW9vddfGd3zfJ1i/x7f6K6+v/OtSfe7zvPlP/frufj6fn23C+9LPP31G/ +z9KXn1H3ec4555xzzjl/i9/VT1UeV326/6q2vTm2nzM+L8vPn22/b9Md4/F+ +s4wL8P/27XnMNh6RbT7JXd+LVXu+jr01fV7yabm3//PXfi9+f7v266LvuXn+ +/jZFtnqYxUfdP7P5/vGM+365/f3E++3z97cXOOe89n347c+dt7zXXf2+d+z5 +n1/qwz3e2x5vbd9xfp/Xtg/ar+u6VM/2R23TMf+Kc84555xzzmv8/vG79XKp +HffVeSBRObT6Xd+TEOUnV7897/V1ZBvviPLrOv0bpfxnq2/ZfVT/f455JnOM +vS7anxdtPvr5tY0s9e0rPi1P67M9R556D1ymN2p8cB352wWcc36P178nZ3vu +ZHvfq2sfRZHnPfCq9vJXz+/V3tcuXqf79Lwa/pteXz/r7p/9/QnR9q35MZ+K +c84555xzzu/0/P2oOfo5r/7+hDz9ltF+c9UTfrW3jlO/fdzcdcrPXBfLeH6+ +cRRjr4v2+rn2vvTf8j7DSz4tP3293PMcOX+9LPNbfn+u2+82stUTzjm/+v1t +vX229k6298C3tZuuqj9vP1+j/Nz3S0eRZR4O/6q3tgtK6V/13Im2P/ZR90/O +Oeecc84552M9T39pq7/l7xuu09uPu79vJ8955G/0bb16etwhy3V67O3XaZR+ +rvrASz4tl+7nb5l/Eh1Xn3uf4Uuflp++XkZdR/9Uxfeul3WM+v2Ip4/r7vp/ +vP358976fuXvwPJf8trI9px6dt5+KVrfG7efr9vPHHc/v94+/6qU3754fh4O +f4PPcVw/o/eP8/W8tP36vtG6fWv+j/PLOeecc8455/xdnq//s7b/P2q3ZhuP +q+sHeN943Oj+jWW6pXEons1b+6O+PS+r/XqMIsv55WPd8+sovZLnOY/8Tt/W +h7fM+z33PRLPX0dP3a+e+nuy0f5Gjb+Pmgd19d+dGZX+1e24ZXrlcjvOv3lo +/Aq///n11HyhUnpvjW/PvyrlO9u8HX61t/bzrNMZVQ9HPcdLvs6/v+vHOeec +c8455/w6z9Zvmb//813j2tfNi3tq/sCo4+J3+nXX49jvM4mvo+Xn437LUjp3 +l/Nx/n/tufBeHzvutj3vX31+8d/wabk0HvSb35eV5/4z6n2v9fw+e77O19u6 +fH1tv1H69fkZ216rf4+N8uN7j3n7c22ObPO1xHGMuv88/fzi7/DW52lrvbp6 +fvLY+efb4z3ennPOOeecc845v9Pz9UNe5bnH6c6Pj5wdx3z7uNvY8ZHW7ePz +sk4nOt5f82/My7rufvvs+Et9/n2PxLOe7fl17NfdJ6/+fqRS/l0XGb1U3+bI +eh2drYeRZ/s9hbHP6/b7zNrvmT+TrT34VR9V/vXtqb7to+dEtvljnndZfR3m +ZT0bY593pXh+XtBXfWw/3vn+rtZ0os9H6RxvzznnnHPOOeec8zPe1w8QpZ+v +fzJLf2bfeFzr+b3uuKJ8XtPfOL4/7er5WqXt1tJaDmPnFbzXc46bn78fXj2f +ZNT9fFQ/c7S/aP2ovzMV5fMrPi333jfGPr/GzSdZx9XzD3vrz7S8/zxaf77+ +Oor8ru9Dy1bPr/LW9+FRf7dovVyqP6X9XfXcGfW+1zv+uPx8+7zNUrqcf8HH +jsvPn29rf5XzM+r5FW2//Nzzz5esLjLH8/ORsvpV7+G98xLPttda93e8Peec +c84555xzzt/rUcTbjxkHyddvedV41nr53HyP7fZPzbMaNf+qb7w423V013Xa +X55fnccydtxnXu69TrONg0f5HzsvZdR9vv66GHXf+8bfV60vn2efX9sYNe9l +1HyksfXh/udF77yXY69PP9d1cf98rbrr6Gxcd72Per7sf37cuG1ffjjn+f38 +/LFR9/NSft7u4s7IM9/prLe+J4z+Xr79fGa7j3HOOeecc84555y/3ef1tb9P +l2W+1qh49u+4Xe9ZxrX5/vrSeP0U2a/H3vmEZ+dvPDXvMXLj2mc8jrPzBqN0 +RvnY51d9/kd/r93ZcdvIXRd3+rw+6/Ml8rvma731Oup174Gc83d7e5iX9Qvx +1Hyq+vxxzjnnnHPOOeeccz7etzH692Sfjbv790rH7fcZeY/HkWU84up5U32e +7TzyezyOLM+va77HyXXBe3xef/d8sLPx1HOnb7/ZzjvnnP+ai5yRrZ5wzjnn +nHPOOeecc/5GfyqylQPnmf3qyHa8nJ/xUZHtuDi/06+ObMfLOec8p4t7Itt5 +55xzzjnnnHPOOef8Tt/GNd8/cH888/cO4vX+Hg3v91Lc/fcdtjH6e/bGeLbz +yO/xUjz//Or9e2quCz7ee7/P6nefO337zXbeOef811zkjGz1hHPOOeecc845 +55zzZRyPo93398Ki8eW6+V39EaUfjZcdj6O1l/M98778HZxc/vT49fjrsXdc +u3a/rddj3/V79Th7tnqYzUtR+/e/Suk/f72U8leb/7HPr236k7gu3uT5ny+R +j37uHMf7rqNe389PtnrLOefj2vdTes8818TV8ezztDayXUecc84555xzzjnn +X/UoStufHTeJ0snj98z3OF/Ord9Dkm3eSN+4Ybbr6Prr9Gx5XvO9cM9767yX +q6/TUfeNsddj+31jfVzLz529j0Vef12Muu+dm0fxfP2P8pfz+bWN1vlgo59T +63yOrQ/3Py9ar4uSt6Y/Lee4Luq99f5wzfyr2rjuen/LPH/zJzn/qs/re+eL +jrqfl/LzDRdXx1Pzsu5+/o7qf+h7j812H+Occ84555xzzvkve18/SZT+vF2u +fsX+fsjWftp7xrV7y3+9v/b+56vmcUXpj/LW47q636+1HIwX/PWrr8d755+M +P67W9Fvz3zr/pG8eQlTu9fn/tetiedz9942xz68on/c/v+6qP7XHOWpeX+tx +jf7epK/5NeP1c5y7jtZx/3Pn6nnCfe9d9ce7/7ntfjh/s/fOk5zW9853ilIc +1c8w+ri4yBxZ5lll9Wl59Ht463tdKT9t+azdTylfnHPOOeecc845z+/z+lz9 +hHnH3a6e73FX//NV4/i94/vrfI4eJ6093r7t4/MyZjzxe/5UfRv7/R7X3W+v +Lp/e+lybz9bj5c9eR/fMp73uPjm2/kf7dV28y0vna46s11HfceW9b9zzfVzt +95kx73ut5yVbe/CrPq8/V/5ROqPmD2z3e9f3oLa2j9bH5XmXyee45r1I1MY1 +3+O6jbb3cN7qY/vxpujv72pN5zgf23RK+eacc84555xzzvlZn9fn6lccPx6X +bRxqma+z49rXnd9R5TaqnEcdF//G9Th2fDy+ju4eN+/z1vz/2nPhvT52fG17 +3r/6/OK/4bXjYs8+X+LIfh1le98b9fdn7xoHX+c/2v6e95O37Pf8/N6n/+7z +Oj+tz+Vjn9dnuQ/zK3yOq+/Dpfos2uLZectxtD6/+Dt81PyxUfPEWn1UezY6 +3uPtOeecc84555zzO31en6sfstxOv3rcbdT4zrPj2ted99b+wLHfF8Gzeeu4 +6jXjBeX85B43j+L588vvuV48v2p8Xv/0eeR3elT/7hqP7n++lNLPfh09db/q +Lbd1/keN952rP+V0rs5/q49K/+p23P524/6Oc+t+Oc/w/Bp1vxrdnnprPFWe +z37/ZJ55R/xen5ZL74FROvfMfx7XTlzn/+r3K84555xzzjnnv+zz+hz9lvX+ +lvG4UtT2k4ztH5jXP30e+Rt9W69yjCM8f50ee/t1WttfynN77f38an92Xlae +eSY8t2e5XkZdR6X49vUyR+/zva0c7jqu++r/8fbnz3vr+1Xr9py/38uR7TlV +d53OkfX7mvajfn/rz931/Hqq/O86j60xpr3Av+7raJ3HNaqej/oe12j71vyX +0uWcc84555xz/iaf1+fo/9zm8+l+y3X+vj6u3TYexL/q0XWR7Xsz7uqXdp3y +mvHo9Xl5+vm1jmy/Xz+2/3le/3Q94XWe5Xp52/dRLI+nNK5Vul6iyFNPOOf8 +rNe9L83bZ2vvZHsPfFu7aVo/uv68/XyN8tb2UXS8pe05H+mt7YJS+st0xz13 +ou2PPdu4A+ecc84555zz9frR/Z+t7dls/Zlv6bc8bu+Pqydt44P8nT5HtvGI +dT5K+fy163RsPx4/N75w3zjOU+M7pf3kHI+L4vn69hVfn8dsz5Gn3gP39xeX +W8mjdMd4nE/OOX+H178nZ3vuZHvfe9f3DN/1XJvjq+f32XlcV7cvOD/j9fXz +qfldrfnpux4555xzzjnnnPf5vP5Xx+mi/L/t+xOeGr+r7U/gGXx7HrONL0Se +s9949HVaPl/H7noc7Wf7S599rm3ryVvmMY76Hq1R7wP8r4+6f2bzZX7L9fDb +49fPtRc453zf699nsj1f3v5ed8/3Yr1tXtbz7//R8Wabf/V0e3xarm3fcX6f +17cT7mp3TMul52+UTuv9inPOOeecc85/0+f1Z/upatt3Ofs5t/GN3zO9f/zO +9/Zk8G25Z7vuWr21n/Y3xyNa+8fm5Rz19rw/NZ/nLf728bvW89s7vjMtP12f +r/ZR433Z6nm266V3PLHW7xkHmdc/XW855/m9td1ditr73tt9e+R/4+n3tyhy +tYOefn7Nof7c4333mfb+q2vrOefnfFruff62totb+3vvaadwzjnnnHPO+Vt8 +Xr/uXzpu982RrT/zXP9Vub35lvHryEfNWzjOt/Husb4t57f/ndC+67S+vj3d +D3x3/1u0/bevx9JzqXzf++o8k1HlkO16GTUva/25HPV5nJ+9b+x/7jvXxXK7 +777vRfsb5d9+vnDO69+7vve8eKpdk23eyxT3tGvWMbq/K97P6OtFfXuXTzGm +3uabt8N/0c/3H67X16XTOu4wqt1xXXuHc84555xzzsd6FNvtvz5+vdzu+XG6 +dX4mydKuP/bRv8+VZTziOh/bz1Cf/ts9W7/u6PO4vo5ay2G93ehxt9b+vdHz +atrSn/fz9eviK8+7Pt+me62Pmg/ZWv/P5+fXfH+7p+t/+3vUte9v4+7/kz/9 +fsU5P3/9er/q83+CyNZ+KeX36v6H/bi6v2v+3F3Xnfr5Lp+i7T3/ueuI8+vu +z+X3gb77T+v1Mmp7zjnnnHPOOb/ff+37dt4yTpdz/G7ef21/am27vvW85PRx +5bbe3jjIsS//nyPn9dv++7bTdvv1sDaeeu7M62vz/yvPnWzXyxTr8n/ndVR/ +/7yqv7rXzz43PS+Offqp9vy+5XvkIu+7D4xrRyzz8fR7Guff8N52k/era335 +/xzZ3qOe/l6sfc/aThnvb/k9x3X+pshWb7N53f15HVf373E+1nP/ftbZ/lvO +Oeecc845v86N3+0dd39/2lP9PFeP6436feqry/+e/ET7ax+vrx0fifab7TrK +ev1e1Y+UbX5mVD73jL+cz8+ofrxs9fMtPv1Ue196dr5xvP0y3+3zl64Zf+l/ +f2hNP1u9yub72313Hn7fOMj5/R6nzzmv8b723fnnIz/25f9zZHuO1N3/tzGm +XWBeVp3Pka2ef7X+Z/Mpzl4XOedbcv7ffr4/c3+78v0213OHc84555xzzuf1 ++mnrPFt/zthxt7ierD8/th19fT2vzX9r+q393m/5Pdm3+z9BZL1Oz/Zrtdar +p+4/2eoJ/+vTT2fr29XjEa3Pl9bjvfr7u7Kd91/z/e3yzeON8tOaz2j7vvef +ebspvavn4XP+Zm+77uqv62z31bf7P4dx3ftPzu/tuf/7VY7zdZ3neE7N8fbr +fZ3v0nHxY5+i9X1v8t52R7Rfzq+bf3t1P3MU9fnJ9vzinHPOOeecv9ez9edk +8+X/c2Trt7n6e7da+3Wf/X29OF9ROsvjLP1e1fnx0Gi/2er/231/u/Z5gHd9 +T3trfa49rtbyMS+F/7dPP425D7f6On+lca7z7zlR+q3vCa3p8Ht8f7u4/rzl +/a31uEpxz/gI52/y9ver2vZCtvvkV335/zrqn+PZngtv+Z6cbOPab3l+ZbuO +Rl1fUTrZrqO3+BSt1+m0fLZfIst9hr/Rz7e/eu/n2Z9TnHPOOeec8+95tv6c +bL78fxu17bi3+3HU16vednRtu37UeOWofsIo/Sg/2er/V336aVR/Y+32o+Y1 +RZ5tvC9bfvhYn36qrbdj76v16XP+3778fxtvfa/rvX6P4/nxaM7P+F3vgbXt +Ee9Fz/ry/zmy3c9H3f+zzdfqey5f572/R3O3f/W+sT6e/SiXA+/zKWqfg089 +Tzk/M79rGf39BlH6ff3becaDOOecc8455/d7tv6ZbN463yZbf8s9v2cX1bcp +xo/Ljz1e1ws/9lH99qX+zNp09vevfvJ3euvzKFv++Td81Pcc3jtPvpyfkq/T +yfZ74m8ZN+fnvLZ+7q+//vtDst2v+LEv/58jW7v7nt+fyjZuPkX5ur7Hz/9e +zD3+vX6J5XGU+5eyXXdf9f3l2u8jWkfvdVe/Pf9Fr+9/jtLpvV9F6a89W3uK +c84555xznsez9c+8xaefzo5z5ZxnNa79u/ZR46RXf4/EV38vlff5/nbjfn95 +1PexZys3zjl/i08/1b7X7a+fo/Y9qjc/be9p9e9vveMRteXSm8/a8ZRSPnmP +t9fb2nSW6dW3O9bbn3uPmsP7/7t8+qm2Przdxz4v7pp/Ncdx/u/vBxv997Du +9l+7X2W7HvletL5Pbj8frcl2f+NP+vn2VN/zaN5u9Hs155xzzjnn/Hc8W3/L +W3x/u9p22TZq+5Oj7ceOP0b15/zvk95T/nH+19v/Wn8m55xzzse9h5wdRyil +s8xHb3/+Np1sfw+rdXyk9/289rxcPV5/z3vvqHKrr1el7Wvr+ai/C5PtvsGP +ffl/f2SbtzB6/lUUZ+/Do31a7r0P3+PbfL7zexq3Ufucfbtvj3wZ63LIdr3/ +mo99325/3+Df8Gm5dN8eXQ/X+63zdeQZD+Kcc84555zf79n6Vd7urf14Y78/ +vLU+bGN0O/RX+gM555xz/js+/XTVeEGUzigf9X479ntc699Xj7e/v920Xj6u +F3H6ffWhVG617Y7z42VX1/Ns9wHe5/90xtn69nYvxdnrd6zn6e/q81KMfy73 +eu11ke0+cO/9pL/c+LO+jP7r4jjdbPdPPsqvmRddWw+zPdc455xzzjnnGTxb +vwr/61eP0/X9vfsoffWKc84553zs+17r+9jWr/6+gnvG47bl8NT8olKc3e/Y +9OP01tu31s9Rf8+If9v77m/11/tXvfU+nM1HnfenvFT+03Lp+fus659Z/r+O ++verbPcHfuzLqL+OWt8Ds9xv+bHf9X2V03a17/W//pzlnHPOOef8lz1b/wn/ +6639AKN+32dU/3C28uScc845z+b728XzWKafavvts77Hro+31Vv3e/V439Xf +JzbqeFvT5/yMTz9dVZ/f7uvjL91Ppqi9/z/lx/UhTz9Y5E99j+Uoz3YfyOaj +5oHznL6/PPr7TvPcb/lY7+sPz1ZP8jxPOeecc84551vP1k/COeecc845/57v +b3f9uPNTf1/vOJ36dlnrfjm/wpf/18e63mcbx88xL2sb0f0ii/cdV55+sGOP +orR9/3PtXi8fV7b7TzaffnJ/e7cv46r3vTz37a9633tLfD9vS/+6+0Drfse+ +13HOOeecc86v8Gz9G5xzzjnnnPPf8VF/b7HV97dr/7s22cqT8zM+6nvYIs82 +Lv/s3yWM+m3yjHf3+rR8vH7eLpe3Htd7vPa4st2XnvLpp9b68Ov3va/6MvrP +e7Q9P/a+v983ry/dJ+vaC+X0722/bPPBOeecc845z+vZ+j0455xzzjnnnHN+ +nbd+31FrOr/m+8vj5rNl8755C3n6wY69/ftSlts9P/+qzevrbbb7WLb7Z+/9 +tvb64s96az1Zf34/ttdplvv82710325Nf5lu7XzXKOZ0Rr2njbrPHO+Pc845 +55xzfsaz9W9wzjnnnHPOOef8fp9++ru+PL6Zbdz86e9RWZfbV721/qzXR5/L +4fP65XF893u01t5az7Pdx7L5/na+X+vr3lcf6vvtl+uffy7c49vyuXp+dZSf +q7+/q9Vb69vx9tmey5xzzjnnnH/Ds/VXcM4555xzzjnn/Lzvb9c+7yLbeHc2 +X8ZczpOsy/Pt/u3v2fi178uKfFs+vkerz8/N35gj232P9/mo+0kpnSzPi1He +en2Nml99XM71z5H15++6b/fln3POOeecc36FZ+uv4JxzzjnnnHPO+dZHfV9T +tnHqt/jV5+UtHpXDejlK7/hzT/u8vi7/0fZf93Xobxx9P19+vv1727LdP/l/ +x6j7SZxO7XO/NZ2nPNvfqSw9B2uv06u9L5/Znsucc84555x/w7P1S3DOOeec +c84553zr+9uVx+mWy+Zl9foyyuX8du+rh3n6u0Z5b334pteXT7b759t9+mn/ +fET1Ms+8F37sY98H6vv/l+vrnxf7+80/L2t/efy8rON4/r7dtz3nnHPOOef8 +jGfrZ+Ccc84555xzzn/B97crjW/G42vr7bONO7/Fe8/j/vl6r/fNR8rT3zXK +R1/X3/Bt1NarbPfht/v+dubr/qpH0fd9WfXvG1f7U3+vsO96LJ2Pu+/brecx +z/OXc84555zzL3m2/gTOOeecc8455/wXfH+79vkt2caF3+JTHJf7+rzkmTd1 +j9fXt2j7b3iev0uV08/Xk2z357f78v85Rn0fYLb7+Vd9ilHPqf0Yd59szU+t +m5fV5+ZXc84555xznsez9RtwzjnnnHPOOedf8tF/F28d2caR3+LR+Vpvt47o +vHzNjecuY32cx/VnXl5f11/zUffDbPftX/Pl/+vYeuu8u2z3/7d4FH3nd71d +7/csnb9/tvpT34d5Tzlf7/vlnO05yznnnHPO+bc9Wz8A55xzzjnnnHP+Rt/f +Lp63sP+5fOPCb/cppvOxv34+X6Xtv+pjIk9/1z0+r1/XH/53+Z9VtM73y3af +/6pPP7XdJ+PrYr1dtufC2/2e8xv5uPtn7XMq5/di5fkexd/8HkvOOeecc87f +5dn6ATjnnHPOOeec8zf6/nbt49fR9tnGhd/ix+er9bz8jo+t51/1ef2yHPi0 +/E9l+B6td/ny/22cvf9ke45k83veW2KvfW/pS2fUvKzrxkFKx3WV912PnHPO +Oeec8wyerV3POeecc84555xn8L7vH1inux5fmyPbOO/bfYpluf8n3O54+9/z +aXldb9vK83c8um+sl/fvA7/u9ddjtucC7/Ppp7P359bn9a9573lZbjf6uj7/ +/H123lrv+95198koH5xzzjnnnPO8nq2dzjnnnHPOOeecZ/D97eL5Kq3jg9nG +c9/upfO4Pl+t23/VW/+uXGm7r3lfPYnSnz+/vp/wv1FbP32/1rv86r9fOf3U +en87W9/e4n3l2Xofa73f1v9d3av/XmHfc/B6b3u+cM4555xzzjN7tnY655xz +zjnnnHN+p4+dl/I747zZvhcrOr/R56N0ftPr+4ui7b/to+az8WOvL/9szxE+ +1kc/l/e3v+55HaXf6+v8v+v7tdqfv+vI+vcc27y1fmZ7DnLOOeecc87PeLZ2 +N+ecc84555xzfoWf+7uEc2Sbp/Rr3np+7xo3f6tH5blejtI7/txXfF6/LIc4 +jssrSoe3ef19O9vziI/1/e3a68/o94cs9/Nn52vVl0/dfLz156+uJ72+jmzP +Nc4555xzzvmdnq0dzTnnnHPOOeecX+H72/X/vaR1OtnmL33Vj89L1B+SZx7U +sx6Xz37k6b/K5r1/T3NaXp4fHvmo+ZnZnkf8Hl/+H0W5Ho56H+jNz1XPhdF/ +Lzg6nmhNbX769jtv13v/6atXnHPOOeecc771bO1lzjnnnHPO+f+3vbvLdlTl +FgBaPbtdrW6dXnxNuA8ZDksi8iPo0kxe9s6UICoaxSVyzmf4fr6z79lZy4kW +v/R0b92+xsU69tY4geP9KE6/1r3+nfqOP7zP5x23o/1+8Wv8mvfnzj8uXf07 +UnfcK6dz5ZSPG33xcpxzzjnnnHN+3qNd/3LOOeecc8455zW+/PeZfv6+YW05 +/Bo/3l71/Rvb6ffHR0X15fPx9DUf3/dSO1w+b9czb/XeOMzacqL93vFrfPQ4 +V6m/Iy6otH9dnaKtn3i/O22/+3mvLaf1/O2ueo6NV8/VJ0474Zxzzjnn93q0 +61/OOeecc84557zGt39zafl++/2anEeLX3q6738ueby4pljevj7b8vMlpev/ ++Hi1fi4dZ/gZr+//HHVfnr/bl//Onj/E9lwaVc75VNrP675fOj73p77jzJpv +Wb7e9pmWczy/UeO/5eb77decT+ZT2/7rPIpzzjnnnI/1aNe5nHPOOeecc855 +je/nKz2nf/6+TLS4pqd76/bdn76mXL5f99x6fsf4LXf5On27vlvj5fLl8Cv8 +/PEk2u8jv9f3893dztu9tp3/GZR643Ci/M7ye731POe4PY87H8h523kC55xz +zjl/uke7buWcc84555xzzmt8P9+4++zR4pee7n3p/Hb8Na/bX3Kpdj/iSzpe +X+n6LKVcfn7Wj/eL+u3rvYf8So/W3vrio0q/P+X9dPR5SJTfax7TR+8X2+/3 +xgmPOj+Jdh7FOeecc/47Hu16k3POOeecc875b/p+vvx7T47Lyd+nqC2fj/X9 +z2tatkfue9vpce7fRfO++4Nx+qme5d5j+A5v3+5n5xvt95f/po8e33J/v6rf +j2bXvzVeS3zXL3j98X9UnOR+vvzv0dh22Pq7Fu28i3POOef8uR7tepBzzjnn +nHPO+W/69u+aWvPvz6/9/YbR4pre6tu0bq+Sp9vrN73U/tMUpz/qKX5XfAKP +6a2/R9HGO+Lv8D+ZdNXvddvx7fxxr3X9xBj/03nL0335vEy/5j3d8+rfdz3F +Oeecc85HebTrSs4555xzzjnnv+nbv7m0fL98/2I/f/31crT4paf7Np3djvHu +313t5+4DpilOP1VMH32fNJe+2zm/x0v7Ue3+eDzf9t+72nrymL6fr32cnKvi +i9qOb+3H1WX6Ve082nlRb/uJch7Cj33U78Ko8WnHtqto52mcc8455/E92vUp +55xzzjnnnPPf9P18pfvpuevf8/dN+Fg/3u7ntyPf+vK5bn/hfe49hr/taapv +P6Pe9xrtd/ytvp/vvniqq+Ki27z9+JmrT209+7Zj/O01Nu463vnJU73vPLa8 +fXLfK+0Xufq0HgdK7cp5Juecc875GI92ncs555xzzjnn/Dd9+e8z/Wz/f/19 +w2j33Z7uS0rXf+925/+mcvvvi/fgOS+12+XzdrvkUv54dVwOf6vXHgdGHW/5 +se/ny2+vaL+/fe8fvGucnHV62360ptnbPdp2HBXHdU07eavXt+fW87HeeN10 +vq0+9notzvkb55xzznk0j3b9yznnnHPOOeec/+t/DlN++qe8590/fbrXbcdl +e48er+N3vLSe98uJ0x/1LF+n17Xb9nL4O733eJjzs79ro+r/FF/+q11vuXKi +/p7e8/vSfvzMzXc7v/nxJH3t53u5op13jY7T20/166FU/tN9+dx7fM6V07u/ +5+pz1p1ncs4555yP9WjXy5xzzjnnnHPO3+Hbv2sae1/p/HXu7Hr+mo9a/9vy +4tyPu9qP15v7Yvf6+XGN0vlsp/N3eZrmtcNc/lFxXLnj0qh43bHnIfXlb+s7 +Pq67db3l6nONzz9+LtPP7V/X3+/ILUm087Fr47jW7RKzPZ/3u65f0s9Rftec +f3LOOeect3m0fnvOOeecc8455+/w5b/P9Nq4hfb7d2n5ff4932j3xaL5ks6u +z9b282teWj/bfKVxL/hs79tenPf5cXvL/57WHn/Gjot4/nc2V/7Y4+T5cW9K +fs/vy/uOhzHPe51PLunscaa1nKt8+bxMn/38QuzzijTFOR/jnHPOOY/m0a5f +OOecc84555y/2/fzjbvv3Hp/J1d+tPtcT/HZ2+sd3tqfs07PzaeuHN7n6/T0 +eFV7PCmVw/mRjxqP5Zo4ivr53v0ewOVz6bja+ru2/V7035f7jp9jPM79jlL9 +a/ejt/qo/ag3TvLs/jXqeuGu66nR/ozjD+ecc855HI/WP88555xzzjnn/B0+ +9n1e4+4D7pf7XU60+1nRPLfd08912zFa3NT14y3k8vftX3H6nd7h58cRGj3e +Dv9NbzvO3Le/tOavXa7W/evc79f4+vd5/fnJcT3nebTjW7Tz4eW/2vOBaOd7 +V42v1ZZmXxcYL+t4vtHO0zjnnHPO43u06xTOOeecc8455+/2/XzjxklYUi5f +6rl6Rrtvdff9suP1ntte36l2u/ya9+0vcfqXfs1HjweyTD93POT82Ef9Lre2 +89J87zmu1p8/jDrPeetxPlpc1ux4mLHnw/XtMNr54djzzPbz+eXzuf0ln2rn +Ozsuq6621+1Hx/XinHPOOec5j3Y9wjnnnHPOOef83T72/l37/Zf0+9HuT0Xz +JR2v99z2WtPo8YVy9YnufcsVpx/p3b5OLx1/osUhcD7T245L0Y5j6/SlXn2/ +O+ePG331j+a95wP3t9to58Ozz6uf4kuq3V7762X+9ULOr4nLGnX8+fa++XLO +Oeec81aPdh3BOeecc84555z/6/v5xo2jNfu+SbT7X6Pui/XGpexvp/P3xaJ5 +7/uzasvZ/8x7/Vxc4ndqbefL9LrjG+fXeu3vwvZvmmb7Or20XL2/a2379a/5 +Ov3udhvtPPaa8+Tnnn/OGVeq3B72v7ems+d7x+XOvg5qd8c3zjnnnPO5Hu06 +gnPOOeecc845r/H9fPm4id44mf3yz3tuvk+5/zV2vbX2b9wVf9Van9L9uXJ7 +OC6Hj/X67di3X9S3B87je6k916e03Nm/y62/v6Xy247/T/FSitIOv72u/awp +2vnt2POx+t+7aOel15y3nz/PfNr7Ct95vOKcc845j+/Rrhc455xzzjnnnL/b +9/Pl3ws2535Nmuqvl7fTx8f5XDUu1uJLve7avqX67Xucca767uPH6Rfin3TX +OB6c89l+vj987Ht+4x/30u/F2I7nfXZc+tN9P1+6PnPpO3/teVfrfnfXdkzn +11ufXDn79bgqnpb3+Trdeuacc855yaOd/3POOeecc845f7fPfu9eLl8uf2s9 +j+d7fbzQve+Lqb9PcXdcVm19Wut5vH7q53uc4vQjvcPX6cftJd44e5zzXl9T +3+9dffnb+fT/Tu1PT9N3fdrm217+M/z8eeCv+X6+/Hq+6/z5mvG1zp8PzF7P +uXr+mpfWc237Sb/f2x5y5fReT9Uer3L5S/XjnHPO+XUe7fyfc84555xzzvmz +fD9fb9zLvPuJfXFBreVc/x69e+Oy0nyj7yvFiWcbtR7GxhnyY1+nz9l/29tt +Wh/O+X2e7qel43zt70uunNa43NlxJsf5ebTz7bvP89v2l/O/46N+r8eOr9ub +atthtPOoefcf08+l9dB7XG07H6vf/mOvm+rb/9jjP+ecc86v9Gjn+Zxzzjnn +nHPOn+Xbv9/p871Zz/mm9et9fn/+fYf95Trvrct71fPdZ8sZdZ8lWnxaaz1z +y89rfJ2erv/a9pPzUXGenPM4Pur3bnb5v/b+wbFef74R7Xz7Lh/d3trO80ef +D8xK0c5/2q9Tls/nrqe+yznOd/34w6PqOer669zvQi71Hw9bfez1UZz9hXPO +OZ/h0c7zOeecc84555w/y/fz1d4vS1N7v33tfO+Ne8mn3HKd9WjjaB3nP3+/ +ZvZyzWn/qcfpL3qHzxtP45r2wDnn/FpPk/spvedv2+9H2b612709zTqf57/h +y+fSdcHY889559U5HxufxjnnnD/Lo53Pc84555xzzjl/ty//fab3x1mN9v36 +zI8baavP9fFavds3t1z73t7/n6ZR44CNXa5Wj9NfdJeP2o7viNPjnHM+x9NU +/3sU7byaH/u58VfTfOfPN0rz5W/2+vuz17xvffb1af3yHteHc845f4dHO0/m +nHPOOeecc/4OH30/Yju/+ffvjK/1SXPeu5Gu/9J9sOhxZXnfX844/ULRvPV4 +0toO724PnHPOI3r9eUip/DR/tPPzp/vyX+35YWs56fRSaj1v6Yvjam+f/Nk+ +ql31Xq+dvf6qe85iTWP7DeJc13DOOef/pmjn1ZxzzjnnnHPO3+HLf5/pZ5+f +Ted39/27aP3A896j0dqv3rcdz98X6G2f+/Vp9Tj9PKP8eL2dL/+a+y+59Pzj +D+ec87neOn7jr42vtV2+/vP82fEerfVM61dqJ63rbdTyjo1D4+/21v3k/PGh +9Ty/t5zt9997XcY55/wdHu18nnPOOeecc875O3z7d029z4Nv5/e0+3dx+gGW +tF2e9n7+se/R+E6j7zcdz7fW42yvc/crZ+0X89thmkbdN++tf1o+55zzZ3rt ++UPreW/redG95+Hf9ZkdR3TvewDr41W2qX97RVufre3n2KPFI73V689L+67L +zh83xvqo/gTOOef8Xh91ns8555xzzjnnnNf4nHiep3qc/oFjPx8/Mye1rv/v +78fy++77LJ+X6ef2xzTVL+/s+4yj3x+0TI9xPOGccz7Kj38Hz99/yc139PhI +afm5esaMC5odx9J+nrZML53/tF4f5cqPFsc1dvyiaPFO0by+Hbae9+bKeff5 +cLTrPs4557/md/XDc84555xzzjn/Td/PV44DWfL1lv9W71sPs/sfZqfr+0mO +y4l2HyfaeGj163nUe0/6jktPv9/EOef8Lh99/pCm0c811P7ux4yzah0ftfc8 +dnx7GHV+Ei0ua048z3eKcp58l486f06/39tuc+Xc7fvLG+e+POec89/0UeeH +nHPOOeecc875DN/+/U6f75XvK+3P7/5+43f7vJRud97nrffRevev2vnOPp4Y +r49zzvkMHx2XcvZ3vPV3sHV5W+s51mffR1un97aHa66P5sXXRR0/7ThFaZ/X +n7fPXv+t7XD/+1cdb8Vlcc45j+mzzw8555xzzjnnnPMZvp+vfdyt/fLStJb/ +Ll/TqP75uvt95dRa/uz33B23q9b4pd77g+XyR+1Hx96/XXvrOWp7idvknHN+ +vd91P6hUzzX1nT/PG//neLnO+7XnA2uafR2UW55o8VfXjMPWvr/Mauej/K74 +q779NP3+dcfhMe2Bc845H+ujfn8555xzzjnnnPMn+n6+/HO4fe/v+C5/ke3n +9riRu9bbNfdN6pc3V060+0pP99H73X57SL9/9/10zjnnvM9bz6NGxQvNHr+r +r55x7ostadZ5SLRxQfc/xzvPvDe+a367Ouuzr0/ffT4f7fjDOef81zxafzjn +nHPOOeecc86v9z+Z1NvP/5nP+efWt/UeF4eWm2+0+0ezPbcejn2dXtouy3+z +2gPnnHP+y577/fWer0+6e5zMdD3HOM8v1z/a+eq170msPb8d1w7398f69nPX +cxaj2lurX3PdwTnnnI/1aP3AnHPOOeecc845n+fLf5/p/c9f739eU1r+cf55 +cTjR1ls031/+q+7/1reT0naprT/nnHP+XK//ffzNuKxo4/bEvx+Xq39ru3q6 +73+uPf9M07h2W7uf3hWXFS3usVQPzjnn/E6Pdh7IOeecc84555zzer87nudT +r/77CMdeSst6uS9ea5Q/pZ6j2uGSxraT/vbAOeecx/dRccutv6dx7mfl/O74 +kH1/7v240vKmyxktzmp2nFJp/ez7vHitu99Lvr+85/14vnGOP5xzznmNRzvf +45xzzjnnnHPOf9lb+89jxl/Nfn55nb6dT71H2+5P9z+Z1FfO+ftT+/O7+346 +55xzPtZbz99Kv+Nt+Wffz1qnl87fcvnv9ffdj2td3mjxV63xe73nq2k5pfnl +Sqg9770qDu2u8+39+ca5z84555zXeLTzOs4555xzzjnn/Bd8+3dNMe5HfKfP +crwnLuvY9Z/M9tHvzdzO7+77sJxzzvmVXn8+2VpOKaXfHxUPE3P8q3pvPf+J +dp7Wd12T5nt+vNbY9ZDzeXFZufzXLFerx7lvzjnnnM/waOdvnHPOOeecc855 +ZB/1nHW0+w5LWuqdTh/j5/sx7r1Pp1+ld784Xo/l/SVXbq4czjnnnI/y+vOf +7fTy7/5bfdT1wtM9t7yL1F5HjIrbH3VdNnY9tJ/f1q6f0dvrrPed5/NrfNR+ +N/u6Ptp645xzcVmcc84555xzzvkZ38837j7C3fFXZ5erz8f1G+fqf4/X9zNH +a+fX7BdP2Y6cc8455+O89jw52vneveeZ7fEbs65fYsZrnb/uOC4/V59v7yuf +p9Prjifzyum97mutZ+1xrzTftnKibXfO+S97tPMuzjnnnHPOOef8jO/nG9dP +GC3O6t7xr6L1i67Tt/WK5uPuN6XlX7N/tffn19afc8455/xdXpvcv7vmOiKf +zl4HjTqfz32/L/6qlOrb83794tzvHuV167P/+mu/Hvn5jhovbvY4frlytst3 +Pi6rzeO0K845j3Z+xTnnnHPOOeecn/H9fKV+yPp+76f4kpblT6fP8uPtcld/ +yDp9W9+neGscV338YV9+cVacc845531eHy8U7Tor2vVdydvOe+v9XPzV7HS2 +HT7d1+m911N9193n61Mqp7Y91+1H5fxzxuvOzX/edeWs48Co+R5vr2j7F+f8 +jEc7v+Kcc84555xzzv/13ueCP9PL8ULR4qlGvS8jtx6u8Tj9Hr3vc+Scc845 +53ykt16PLKn2uuatvv2bS/3bpS/OanRcx6x0VRzUmuaM61Vfn/3txa/x89fj +59pJ7XFgVFzcuPH0xtSTcx7Zo51fcc4555xzzjl/t//JpOP87f1j23rk+9uf +4rn1Y7ysGi+ltZ1wzjnnnHM+z8/f9599vfZ0389333avq+e8VNuuOD/v9XFZ +rf0eY/f3efFXpXoe16O2npzzJ3q08yXOOeecc8455+/w2e/jmz3faJ5b3tz6 +udfj9Hscu/fxcc4555zzCF6K0ymXM/v6jvf5Xe89HPvec877vHW/GN1Psq1H ++fic1n/sey3r49Zy9WmtZ2t9OOfisjjnnHPOOeecP8v38427jxAtbmp2HNpT +/Lg9xO8PST+X2i3nnHPOOectnp4/t14XjBpnhh/7n0y65vquPk7v7vrnUtvy +cn7ss59rm31cLS3v9vv535G++cbph+H8lz3aeQ7nnHPOOeec83f4n8OUn/4p +b+2nypUfLZ7KuFjb1Jb/LjdeFuecc845j+D1cTi5/HXXZWs5rdd3o7wU/5PW +sy7/mp71fE379csyvXc73r1+0vqXlrdtffK3eu/4b33p/t+Fe48znPMZftd5 +F+ecc84555zzZ/ldzyf+mu9/XlO63mJ6nH6PY1+nL8tRardpfs4555xzzud5 +7/ntd6q9/mq9Tqyrz/fyRr8ebK3/sc+7fsl563aMuf6/18Nbx53m//q46/e0 +/Nb8rfWJ6nOPS5zzGm/9Xeacc84555xz/m7f/s2l5fvj+n9y9YnWP3zVuFjL +57r1+ZTnVeN7730ZzjnnnHPOr/BR133XXL/krytrry/eMS7x+fu26eeo7SRq +HN1xinvd/XZfPpfWf2v7bJ1vXzlx4rXGHvfi9M9w/iYf9bvMOeecc8455/wd +PjYupb4fPldOtP7eX4u/Kvl+/eP0e/R5+3O123zx7t9xzjnnnPNnee788/i8 +tP36K/XW9waWlqu1/Nrz8JjjJo27HlmmX9V+jtvVd/nRrrtHv3cyXd7c90vl +8DYvtcNZx5Pe/aKt/Vzvff1U0fpnOH+Hjzr+cM4555xzzjl/t+/nK40bP+++ +wNN9//OaatfPbB/73OhTXFwW55xzzjmP4K3XC/POh3OeO0/uPX+Och3Uurz7 +y5db7pKv03vbT+t26d2O6fqJdt199/V7a/7f8vr1OSru7qr9Yptv/u9Fa32u +OY5xzv9Ns48/nHPOOeecc87f4fv5xt1HiNbvOnu8rNJ6zq3HaL5dntJ2j+/H +2+U7v/cecs4555zzK73v/HNevFDr9U60ca5az//HeimNbyet26vVc0sS7Tr9 +7jiuZXrtfn31fnGv1193tx4PR7fz4+Ns9N+LOP0wnP+Cz/795ZxzzjnnnHMe +00fHEW3z/ZeUt/ZTjRpHPVq/6+j4nHS93eW/Oe79/Pe5cM4555xz/iTPnf/f +FZfSOt+Y8Qnz4zrS8nPbcbbn6hPt+v3ufoP99lB/f/+4nOd4mu56bu54Pdcf +32b72LhBzvkMv+v3l3POOeecc875WN/+XVOMuKNcyuVfPbe8MftR6+N1nvY8 +7PL5ePqa721+vN/Ff06Wc84555zzGs+d97Zelx2fP8c5z7/G1+lXb9/0OqV1 ++47y1npGu96PGa+1pPJ1+tj99PrnwqLFZfW289netv6jHSc5f7ff9fvLOeec +c84553ys7+drf3/Bdnq+X28/rfPNfW/286FP6cfLLdexX9//ub88pXbxXB+7 +HdPvx7vvxjnnnHPO+b/eej486vru6f6U95u3bt/ZnqtntPiou3zU+jzOH6df +IjffaP05T9/fS/XmnI/3aL+/nHPOOeecc877fD/f2j+z/dz+3ofe+qTzzZV/ +nD/+uPej4pr61uf58ZqO5xunH+Man/0+xzVfabtwzjnnnHM+w0fFLfza+7N6 +n3taPt+93Vu3712eq3+0uKlovv8578frf971datHi8uKtr+/9XjL+Zs82u8s +55xzzjnnnPM+b31OubX8/XyleJ7z418dlzOvH69veVvjcOr7+UcvV+120b/3 +SU+//8I555xzznmL11535PIfe5zz/JznzvOfcv7fWv+neG55o8VH3TWO1jXX +re1xWblUe9yY3Z8zu32OcuMTcv5cj/Z7yjnnnHPOOee8z/viZ9Jyr+ovau/H +286vN16rPt7mrvGyWpdr9vsO+uof38eun/b+5/1yOOecc845j+G111O5ckbF +UYyqTyl/mm/sddN9ni7XXeMI3eX7+d4bxzVq/eT8uJx5/Tx3xWXlyrnLPTfH ++XM92u8j55xzzjnnnPNjX/77TK/vl97Pn85vXH/Rcf1HXefm65Nb3tRH9XOW +5rtfz/rtFa0/9rj+0XydXttOcvlT772vxDnnnHPO+Zu99Xok57PHE87Nd9R6 +uMtLy5Wut1HbK5qny52mdD3k8keLv7prvPRjjxqXlc5vXPvZfn/8fl3bPjnn +8T3a7yPnnHPOOeec8z6PNl7Wsc+7zh31fo1R/Zzp57r1YFysY1+nl+o56j5O +33qOtt9xzjnnnHMewUc9T+F8+5yv6TM9Tv/GbG99viZa/NU74rWuf56ubrly +afz+eFyfaP0wvNVHjec2u55Lavud5a0e7XeQc84555xzznmfL/99ptf2d6fl +3tc/fLxc865/t9Nz622t59jnrNvr2Ze/dbukaXY/T2896z2db8zxxzjnnHPO +Oed8nG8/t1+nfP7G6feY7fv50vXzndL13NdvUH8dnSsnZrxWbb9Uvj7XjIuV +q/9oT1OcuJHf9FHt/3z5+/MrHc/H9cu1lS+Oq9Wj/d5xzjnnnHPOOR/rzxpH +K+/bz6Ov9/Npf769/YS55V3TNe/XuOs5u/M+6v2S4q8455xzzjnnv+rbz8v0 +OP0Y0Xw/X359Hnuc6+h7n1eqXw9PuX7v63/jS2rbX873Zx63k/PlX/X+3OP9 +qnZ5573XNVfOr3m03zXOOeecc84559d47/v+tuXe35987GkaHcf1Pd/j9TYq +pfO9b7nu8fZ+7Nbl5ZxzzjnnnPN3eC59599+XqbH6cd4ui//pes5nb6fyttr +lI+K1zqu//n+kr751vtx+XHiPWL6On1Zn61xO3Xbd01j44W+65+rT+t4bq3l +X7t/zfo9itY+6+PNRpUf7feIc84555xzznlM/1OVlu9H6X++y+el7fzujo+a +P55YWk6pfebqk6Zz/XK5FK0dcs4555xzznnq9fej/248LY+PHZ/8qjiZ75Sr +x763xjOcT7n1n34utX/j+dT4On1/fa6pdb9o7Rc63u7tcVxn2/Oo51tHjV/X +t9/1bvfrfo9G+ejjUm37yXm03y/OOeecc8455+/wc+/1i+Pbz+3rYX+529Oc +51XLqXX73uW55ettn+l2z+V7SzvnnHPOOeecv98/f3PXieK1Rvny33Z7jBvH +6bj8++K7YqVo8U6j40ly7eQ7pe2krx8p3x5y7fzXPbc+e+O7zs73eH69/Zxn +j2Pjjktzt+/5ONtov1Occ84555xzznlk/5NJo+J8cilXn2jxUdGe+2tdb9vv +1W+v/fzr/LbTOeecc8455/x6//zNX+duv98ev8GPffs3l+5vJ+f8PWn2e/EW +Sfc7zut9XD/Y4qXfi9LvSFrOsUeLvxo1/r+4LM4555xzzjnnvMZHj1u+7/X9 +dU9ZD6Ofu9zWb9x62Narfruk+Uvlp/XnnHPOOeec8xieptZxe9x3HuX7+fLb +61w5/e3k3HLNTt/1336+O36G8zm+fC61/1H9nGOPb/Pisq5578D5/kPOOeec +c8455/xNvvz3md5/nd4bl7WtX6n/IZe/vpxo6/8pvvx3z3bknHPOOeec8+u9 +b7zi+uumv5vy0+n86X6un6ScWufbG3eRqyfnb/I03fs8Zn1c0zXj89fHJ7ce +l6IdtznnnHPOOeec8xrfz9fez3zNuFi51Pv8aHl5c/WJth3v8rHxdZxzzjnn +nHMe3z9/89fX2++3jzPsfnRMHxVXMDb+qv75plHL27tctfVcpG0/4vyZnqZR +8ZCt++Ps42eunvvfF4fMOeecc8455zyG/+lK9f291zznNWpc8fbnxfbLOe/R +2sls7+tPNi4W55xzzjnn/K0+bzyTvxvPlbvWJ5f/Lm+9fmwdj+XYrx83Zuxz +aqP7PdJ6nN+OUcdRb1vPnMfw5XNp/61LV//ejXtOMy0n2u8a55xzzjnnnPNn ++ah+qrv6FUePi7Xvrf2QuXp8r//083b+o3zec6yz/bj+4qw455xzzjnn/Njr +r6f64pHqr6//bspP63v+OnH2uFLRfLt85fWf897tvkzvbZ992/07Rdsure22 +tLxnty//ZT/fnzbqOFyaX2197vJRv1+cc84555xzzt/h+/nK15vbz8/pnyyt +h3S5xvpT4rJafdTznk+PZ+Occ84555zzt/ua6u6nl8sffV1/nNb55sqJ1o8R +LS4rV+6xl1K5neS2V6sv/6XLFW17nXsPY/1+PaY98Kf58vl4epr6j5+58vvK +iT/u/ajjFeecc84555zzmL6fr/S8Uv11erR+p9nP5451cUecc84555xzzmP6 +5+/39Wbrdfe5976Vy8nVM7dcpfmk+aL1Y1wTZ1W/XY6n946HU26fre2h1bfl +3d8e5sRrrel4PUTrT+OjvHV/7PtdGBfPmZbTu1+nyzXbRx2XOOecc84555xf +4/v52vuplrT9/vP7l+59PvT6uKzSfJfPpXbCOeecc84555zv+fbz6OvceXEF +fzee1qM+XihXTm980dnlvcZH9VdcNV7NmnLba5Tn6hOtv2t2v1nd+klT+/OG +sfaL9/ns97e2bt/R+2luPWy/P//3dPZxiXPOOeecc875sS//fabXX0dvy21/ +TjBaP89V47S3rucxPrs/s71fa/mcrh/OOeecc8455/zI+8apPu+jnjurS+l6 +mBdXdre3Le/d8Vflev7dbPf0e+c9Wj9YNN+mdXvl1mcu/7P6/Z7ro8brGzUe +4Kj9NFf+dj61x8PzPvu4xDnnnHPOOef848t/n+nl675cOdH6W6J57/qf69fH +ZfXVZy1v+z3OOeecc8455/xfb42bmn/9m9bz76Y+5e/31T9OfEXOj9fDfXF0 +2/qNa5+55Z3trfWM1p8WrR/vqnG9ouyn0fyu97Res59e3y9613GJc84555xz +zn/Nl/8+0+uvi4/TMr/f689ZUuv6vMfvisuK0y/KOeecc84555zP8M/f736Y +3jir2vJL5WzrXY7bSfP3Xb9Hey4sV8/Zfn28R2s7idbPFs371nMujXueMdfO +nup3vX8hl+7aH/e/P/93inPOOeecc875x/fzjYuD2v+8pmV+S75o/SRR+2HS +9Tbb730u+Hx/qXgtzjnnnHPOOedP9M/f7/6Bvue82u/Xp+Xk6nNc/lt9nX51 +O6ndLnf59u+aovXLPd1b1/9x/nzaP568z2c/b3vXfrf//fm/U5xzzjnnnHPO +Pz6nHy9N+mHeMS7Wc8fLEpfFOeecc8455zyyf/7e1Z/DR40/dq2vqbX9zPbt +31x91/YZrb/u6b5Nte3q/PY6bg/5lKvHLG89rt71fO7o/W77/ft+vzjnnHPO +Oeecf3w/X+/1Wv3zWdH6Ma7qD8mtryh+3E7i9KPmvK/+a75z7Z9zzjnnnHPO +Od/69vMyvb7fRlzWlb5Ov7v93BXvMdu3y7G222j9e0/xXCqt/+Vzqb3l8pfy +Hder9ng17znT2e+PuGY/EpfFOeecc84559F8P1/p+qv9+i79fq4+0foxxGV9 +/FnvMSz3Qy3JOFqcc84555xzzu/w7edlent/TlpOyffrE+36fZ6/pR/gbPuJ +5tu/3yld3mj9fk/3JdUeT+7tJ4zzvsKYcVlpvvnHpWjHE84555xzzjmP5n+q +0vL9Un9dnOvfu/x4Pc9+zst4WX3e+77OdL/gnHPOOeecc85rvP5+/ag4itz3 +3+Hr9GW5W8cRypUT1dPtm2s/T/fW9h+tnzCaL+n4eNS6H5XbbW77lsrd9/x8 +246H17efq/aL7ffnH5eiHTc455xzzjnn/Cm+ny/ff7ikNF+0/oeo44Tn1u/V +fs345NF8VBzamm9bHuecc84555xzXuPn4xM+f7+vZ98a35Vb3vRzjO173luX +N5f/6Z5b3v3p8foPo/k12yXns5+7vD4u67h+d+0X8zza8YFzzjnnnHPOW30/ +X/55pVHPSR3Xp75/o3V5o/VLjHpfYWn7puv/bs+l/fxx+mP7fFR8Guecc845 +55xzfq9//rb3P+RSLv9xOd/1TPPn6jmqH+bdfj5u7em+ny+/3qL1Hz7FZ2+X +Y39uXNZT9otRHu34wDnnnHPOOec53/4tp1HvtV/Sp16t/Wy5tCxn+3VctP6H +Uv3318+8/oGxXh9fd7xcT/d1+n77/E7p+jzer0vlc84555xzzjnnI33eOFQ5 +by1HnNU5z23v1Fu341t9P19pfRp366r1n/rY/snnxmWVlmv7/fuOS9H2d845 +55xzzjnP+fLfZ3q5H6CU0nJ647W29c73V/SNhz9vvrPHDesd/792uWb7b76v +8Px4WaX9d/mcbl/OOeecc8455/w9Pvp5KN7m9fFCfzeelsdbffkv3R7R4qmi +xWv9qUrzjj+575/djsfzG9fetvnuPs6L/+Scc84555z/jv85TOf7x0rzXfLt +l7uW0xu/VOsx+hPW5T32u8bRGvW8arR4qvM+qp2kn+vaA+ecc84555xzznm9 +P+V9ak/xa55bPP9866jx/6PGax2v39x+8b2cuSm58s+u51HtcD/fVceZ1nja ++n5mzjnnnHPOOY/mo+JhRo0Dn6vn8t/2++PGv2r11vV5TVzWvOe2+trPqPG7 +4sRTjXXvJeScc84555xzzvlT/Pxzl7zP++Kj6uNY9utR3u65fG1+/nnGaM/D +zo5/O7dcuTT+uHFcn/P9q9H2U84555xzzjnP+fLfZ3r9dfS23Lv7f8bFj7Wu +h9Tv6h84zh/nua1SfdLlOs7/FP9OreOQL2l/vYzqZ+Occ84555xzzjmv99bn +NP9u8qfTeavv5yttx3nja832mPFa9f16rct1bzvp9TTN63eNtj9yzjnnnHPO +easv/32m564zl+9f1f9z/fhFo/ya59faxxM7W//edpWr/75Hi7O6vl0dr8/2 +8eI455xzzjnnnHPOa/3zt77/0PsNY/ryX+322v/c62n9/svWZ5SPfc50XppT +n+v29+N6icvinHPOOeec89bnnnLl7M/vqv6i+HE1c/oBvtfPfn3GPQeXzndU +ezguJ1qc1fn2M/s5vlHvFeWcc84555xzzjlfPv/JpDSfuKx7vS/OKi23tN3n ++VXjdLXO9540+nnM2vLje7T9jnPOOeecc85zvvz3mZ67Pl2+f3f/z7cfL9dz +47VK2ytNd5czpv3ct73a6tla//njjz11/+Wcc84555xzzjn//I3TX/pW3/7N +pfPbd/v57ucuW+tZH8cVM8WJm5rt0fYvzjnnnHPOOW/10eM4Xe3H9YwTrzVn +/Zfrc+/42HHWf85nx031lTO/34xzzjnnnHPOOec89VHvuTOO1r3+lPHVc/Vf +/tt+f3R/71NSnPioJe1vl/V7pe3b2m6j7V+cc84555xzPtu3f3Np+f7z+5Fa +/Xi9Xf8cVqk+y+e69Rzvev8u36/fqPXMOeecc84555xzfpef77cRXxHT9/Pd +3d7u9vgpt3/+ikfbjzjnnHPOOed8tu/nK/Xb5PI/x/eX8+nPZ703bqpte63L +t3yv1P5b232tP+V5Rs4555xzzjnnnPPl858kjerf+LspJ53Oo/ny3377GPf+ +wTT/6Ppfner2l++UWz9v82jtnHPOOeecc87v8v18pevo98ZxjfV5aX+7PMeX +z8v0XD9Gqx/P9/w4acf5e+P6orVbzjnnnHPOOeecv8m3n5fppX7CNeXyG1+L +z/A/mdQbB3U2tbb/3v7M4/n/9/W96B6tXXHOOeecc8750701Tibm+EL1cTs5 +31+Ocanvur79+cfa7RXN69K63Ue15+N6GF+Lc84555xzzjnn1/vnb77/avv9 +/xXyt/ZvnO9n4+/wP5l0rt/vu/2n7bk0/+NU3o9yflX/Z+vy7ucXl8U555xz +zjnnPKbPeT5rmV+86/1ovqRlfZXWz5ztu26v4/p9l39cbq58zjnnnHPOOeec +83r//G3tl6iP6xg1Xlau/NZy+Me3f3Mp137K6e7nLtN2cuzn47JGtfNo/ai5 +JW/dT3Mebb/gnHPOOeecc36v7+drf7/ekpbvb6eff8/dnOVd0+x+gOP6xHmO +cj9f+TnTs/XPzZdzzjnnnHPOOed8rNf3U32+l+/HSMst5T9b/1z5s31UPffL +i/dc5DXxQrPHdxo9jn1av/j9sb/Wr8s555xzzjnn/F7/k0mjnzPa9/NxWTmP +tp7f6vv5Sv2Zufycc84555xzzjnn8f3zN9dP0j4e0XZ+48YRytWz1ffz5Z/f +zC1Xrvxo8TZzxrn6blfp+un13PzavJT694vZ7e0pPmr9cM4555xzzjm/xqNd +Vy7pU9/afoN5cVk5j7Ydn+Lbv9+pbfum84vXv8o555xzzjnnnHOe88/f+v66 +1vy5+Y56/12uPrn5HvvvjHO1pP3lnz3O1aj+1Xn9sdfGB64pWjsRl8U555xz +zjnnMX0/33qdu/18X1xWaz2Pvb0fIFd+rj5tbnzp/Xzj+lVy5XPOOeecc845 +55xH88/ffP/G9vu14xp9z7etnPNxUKXl2q9nfX9dtHiYsc+Z3ufL57rtcv3z +sLkSc+1tlOfmG629zV4PnHPOOeecc/5W3/7NpeX77eN7390vkdY/V88+j9pv +kHp9f1e09nncbnMp2vrnnHPOOeecc845j+fbz6Xxr+qfB8yV3+pXxWUdp/L6 +vCt+LJofL2+ccbFKXrtcsz1XH3FZnHPOOeeccx7TW+OpWsuJ5rnlGuvn+w16 +48pmeW67t9Z/1PY6rk8p1S7Xd37OOeecc84555zzd3hrPNW8+JlR/Xi9cVBp +OaX823zl9V9b/6f7Xe2nLl23f+XWwyjPLaG4LM4555xzzjnv877+hPp+ldb5 +PsVz62FJn+U+2/8wuz+hvf7L5+3053i6XMftPFeO8a8455xzzjnnnHPOW/3z +d1Q/TDRvTfXll9Zbbn091Y+X9/rt29duR/n5fvhRnqtnLr+4LM4555xzzvnT +vXW8o1w5pe+nEi0+6q3jYvXFg71vHC3OOeecc84555xz/ku+pr5+ud7nEHOp +v/7H9ajv783l307/Xq5ne9S4u/v3i1x7uMtz9W9t5+KyOOecc84557N9+3dN +x/nTcu/rH/g1X9J2/YrL4pxzzjnnnHPOOef8jf75W99fuv85TeXyc95azvLf +djlH90N+16evnOs9dr/omlrbyWxvbT+t5URbXs4555xzznl8b43zGfsePeNf +RYu/yvldcVnH3v4c4jJ9+z3OOeecc84555xzziN473Oyaxo9rtfZ+o+Kbzmu +59N9nb6/nlvzz/N0e7dux7u8tX9bXBbnnHPOOed8lO/nq70uW1O0+KWneG67 +RIvLOm4/cfox5rRzzjnnnHPOOeecc87n+udvfb/u2Oc94/Tv/ZrHHhcr9fr+ +2Ke4+CvOOeecc875bN/Pl7/OOs7/7dHioO4d56p9fea2x9V+3H7i9GMs6bgd +l9st55xzzjnnnHPOOefz/Hx8y6i4rFz5ue/zsX68/tfPUdvtW+Oa0uV8y3Jx +zjnnnHPOS+f/S772eKfj8s/HveTKjxYfdff7B3MpXZ/P8jj9GOn00v6Sy885 +55xzzjnnnHPO+Qwf+16/7/661risvudMeauXtuPy+e72mfPj+r9vHK10ed6y +XJxzzjnnnPNvH3tdXB9vEy2u6Sm+pP31fH67xPQ4/Rutntvv0s/b5eacc845 +55xzzjnn/Iyfj2PJld/73GhtPfmxt26vp3huud46XhbnnHPOOeec7+dLr5u+ +0zZfexxOrj7R4qPujstafFl/fXFc8TxdrtLyR/HWdpvm29+/OOecc84555xz +zjnv8frnN695bpQfe6m/NJeitLfzLv6Kc84555xz/nTf/s2l5fvl66bt5/7x +mtLyo8VB3eXH23H9XLdd4nhfnFK0fpL2fpVl+rJcvduXc84555xzzjnnnPMe +H/3ehLbye5/frK3PU7y+n/zvZn3myr2/Xc128Vqcc84555zzp/t+vtL10bjr +zdSjxUdFGxdrkdr1Gc1L7XC/nGj9J+fbv3G0OOecc84555xzznkk335u7zf+ +/P3u92vtB8uVc/z9Ukrr39qPfX6cq9xyHS9vrv5v9zWNaj+cc84555xzHs33 +8+WvL1ufh4oWB3Vv/FXrOGbn49/u8rHP5b3V2+PZtvmi9J9wzjnnnHPOOeec +81/xz9/R/dJr6h2PK1f/NP+o9x14HnOOp9trVHvjnHPOOeec87t8P1/uunZN +ab5ocVDRfEm59fs2P25v0eKj5o9PPma9rZ+33+Occ84555xzzjnn/F7//D3f +r5Urp678NfWV0/pcLW/1u7Yv55xzzjnn/Hd8P99ynVI/PtWo53q209N61F+H +9s133vJG89zyHnucOKtjjxYfFc2935BzzjnnnHPOOeec/6Z//rb2k+d9+1k8 +1TP9fD9qrl1xzjnnnHPOf8ejxf/0ju+Uptzypp8/+fqvx7ffjzceV+t2z62H +43zR4q9GxRdFi5u6bxyt5fP+/lJf/nE5nHPOOeecc84555xz/n7//I1zn4hz +zjnnnHM+z/fzLdcL9XFTS8p9v8174zq+U1v558fdiua59Nb3Hh6382hxUNH8 +/PsK+44znHPOOeecc84555xz/lxv7T//u8mflsc555xzzjn/Bd/P1/te9fNx +UKV6LvlK9RkdX1Rbz7vGxWpdb63jSkWL1xo7bli0uKm7xsuqj89sPZ5wzjnn +nHPOOeecc875s/x8fynnnHPOOef8d3z7d02j4nP63h9XX/6Stt/vjwPJlVPr +ufV8V/zV8XbPr4d9H/devDF+vt32LdeveWn/yqX6/Y5zzjnnnHPOOeecc86f +4tvPy/T6fvhcfs4555xzzvn7/Kp4p3s8ThxR6/qfPe7xfr7e9Zkv567101rP +XL63eV97qC/n3ccTzjnnnHPOOeecc8757/j5/ljjaHHOOeecc/47vp8vPw7V +cTnt8Tlnva8+59+fuMj287j36939HsN0eVvf61cqf9Z6aJ3vNe3nud73Psfz +45ul8xl93OCcc84555xzzjnnnPOxXt9fKi6Lc84555zz3/E/mVSXv/Z65C6f +/x63XH1y9Wj1NN0Vl3Xs5+NzZo8PVqpnulx98UhP9/PjmKWfl++1Hn9y5XDO +Oeecc84555xzzvmz/Hy/9N+Np9/jnHPOOeecP9F7x8nZlnv39U6+fnN93nsP +74rLOs5/fVzWqOXKubisf/O1jqO1zqfUfkrbK9d+0vI555xzzjnnnHPOOef8 +Lv/8bb3PYhwtzjnnnHPOf9lHxV3k8t/t289XvbfufFxW7/aqLSf9XLd9z4/P +fO94Xzl/StzU+r1z9b9ve7UtF+ecc84555xzzjnnnD/Fz/fH5sr5u8mfzp9z +zjnnnHMe2ffzrdcX6fVCKX8UP17eePE2tT4qfqZUz2X68fbPL9fs532O69la +/+vfg1m3XN+pbX+Mt72eejzhnHPOOeecc84555zzY4/TH8s555xzzjmP7+96 +v2Gti9dKP++vt7Te59tbrvy6+kTZjqO2b/37BHu3Y+18j8t/63GAc84555xz +zjnnnHPOW72+33jUc9a5/JxzzjnnnPP4vp/vvx+N17r+fYil7bJfn/PP3ezX +L5/mxH3lPE3n13Nve65d/3d7X4qz33HOOeecc84555xzzvlbffu5/b6Dcbc4 +55xzzjl/n/85TOff7/Ysb43buep9ebX1uSrl1ud3vjEeLz6q1o/jxNblLm3P +1vHTjus5Lp5wv/6cc84555xzzjnnnHP+XP/8/e4Xbe3vbe3XFZfFOeecc845 +bx2PKFfO/vziXX/N8TSNi9eam+bHlT3D69t56/4ydv+aHWdYig+Mtt9xzjnn +nHPOOeecc855rY/rF03zi8vinHPOOeect/ry32d6+foil/rGF/pVj5PS7R7T +z8dTzfbW5Wqtf2v5ue8fu3gtzjnnnHPOOeecc875c731+dljP//+hb8bT+ub +v1+zX48495U455xzzjnn1/t+vvX6aPu5/friXPnf+ff9+vfCp/O7Kt0Vv/Rr +vk1re8u1h2vee1hfn1x+zjnnnHPOOeecc845j+Zj47Lq47Va7yO0LleuHM45 +55xzzjn/Nf+TSa3jj51LS/3ar9eixTVF823qX8/H7ef6cbbr2vN3+Zxzzjnn +nHPOOeeccx7dP3/z/Z/b7497H8HxfM+XwznnnHPOOee/5qPff7ef6sdByuUY +tby58qPFU51brnV93tWucvVpjR8Tl8U555xzzjnnnHPOOed3+Jpm929zzjnn +nHPOeTTfz5ePYxkdf7Xv7c/jpPWv87R+0bbL9e+XjObb5TvbftL5RemX4Jxz +zjnnnHPOOeec8/v987e+/7bvedj6/tvW+nDOOeecc875bN/+Lac577n7Tp/6 +/vf1vX2vj8tqHTep5Gl9om3fX/O+eL+r4vo455xzzjnnnHPOOef8ef75O7uf +9nu+reW01pNzzjnnnHPOW30/37jxrO4dF2tUXM28eJto7YF/fPmvtb1ty43X +H8I555xzzjnnnHPOOeez/fO3vj929rhY2/L++7/t9Dj90pxzzjnnnPP4vp8v +fx0UNf4ql5blSb/X5uPisnLzXT5vp9d7afum843WDqO1/6uet0rzc84555xz +zjnnnHPO+W96fb/653Ouv3fec9a5+XLOOeecc87f59u/aap/v16u/GjxV9eM +i/XcuKxznktr/mjtv9X72pX3D3LOOeecc84555xzznk0H9uvW+9/N/NN68U5 +55xzzjm/0pf/ttcP/eWkKVp81Dvir2bHZdVfx6Wft/W63lvb+blxz9b5jmo/ +x/U/H9+Yqz/nnHPOOeecc84555zzsX7Nc7jisjjnnHPOOZ/h+/na30c2Nr6o +Pj7k6b5N39dfbeut3u96vqZUz+Vzuh6e6qPiplrLad3fOeecc84555xzzjnn +nD/LP3+/+4Fb79fkyuGcc84555zXn2/n8u+X2z5eUM5b6/lWz62fXL7j/E+P +y/K+PM4555xzzjnnnHPOOec8sn/+xrn/xTnnnHPO+ZW+n285f259f1x9XFCu +nGhxUNF8//OacttvlseMyyql+69DOeecc84555xzzjnnnPNf8M/fOPfFOOec +c845r/Hlv+35bil/6zhC9fE/0eKXnu7bVH+9k9t+szxmXJZxtDjnnHPOOeec +c84555zzCP75G+f+Guecc8455//6fr7+9wOm5exPX1MuX+rR4pqe4q3bffu9 +8naZ7cf1jxd/tb9c4rU455xzzjnnnHPOOeec8xn++RvnvhvnnHPOOef/+n6+ +9vPbP5kULU7p17yUttv7vvirnB+3t2hxWd8+erwyzjnnnHPOOeecc84555yv +/vkb574b55xzzjn/Td/Plz+PPRdPsqZcfaLFLz3dl7TdHvHirHp9P8WJvzr2 +7zRqP+Wcc84555xzzjnnnHPOf9k/f+Pcj+Occ84558/yc+Mjlc9Lc/mPyz0f +bxMtrunpvk3f1ylnt9fdvr9c0eKvzr/3sG8/5ZxzzjnnnHPOOeecc85/0z9/ +49zX45xzzjnn7/Dlv+35aD7e6bic8/FX0eKU3uq57fiOcbTK42PlykvzPcNb +49A455xzzjnnnHPOOeecc/6vf/7GuX/HOeecc87v9f186/nk9nOpnPPvU4sW +d8Q/qW+7R4uzmjeu2vF6eLqv03PrqS4/55xzzjnnnHPOOeecc/5u//yNcx+Q +c84555zf673voav1uvK/51eaXjq/jRbX9HTfpu/tvv0cL55qtO+vh2jxVPPG +0Zp93OCcc84555xzzjnnnHPOn+ifv3HuA3LOOeec83t9+W97Hjn6/WXt4+rs +f78+niRaXNNTfJvW7fKO9xKeHxfreD+KFk91vfett/XzueMM55xzzjnnnHPO +Oeecc36vf/7GuQ/IOeecc87v9Tnj3nx/P5VcfbbT//uqV61Hi3d6ih9vF+8r +PF4Pb/XZ8Wzr57bjDOecc84555xzzjnnnHMeyz9/49wH5JxzzjnnMX0/X/48 +sy+ORfxVtHGx9qev6ez2eorn9gvxWvvTc+t1Tn7OOeecc84555xzzjnnPKZ/ +/sa538c555xzzmP68t/2/LIUr3X9ODy8z4+3+++Mi3W8vLzVW9vbnPH6OOec +c84555xzzjnnnPN7/PM3zv0+zjnnnHN+7KPGQRpVn1z5x/XIp/T70eKXnu5L +StdzafvmtuvbfGzc2u94a/vxfkPOOeecc84555xzzjnnv+D/D7EdQyk= + "], {{0, 0}, {401, 401}}, {0, 1}], + Frame->Automatic, + FrameLabel->{None, None}, + FrameTicks->{{None, None}, {None, None}}, + GridLinesStyle->Directive[ + GrayLevel[0.5, 0.4]], + Method->{ + "DefaultBoundaryStyle" -> Automatic, "DefaultPlotStyle" -> + Automatic}]], "Output", + CellChangeTimes->{{3.6595559215072565`*^9, 3.6595559434163*^9}, + 3.659555989004507*^9, 3.6595560561097507`*^9, 3.6641619814216256`*^9}] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"newtonplot", "[", + RowBox[{ + RowBox[{"Function", "[", + RowBox[{"x", ",", + RowBox[{ + SuperscriptBox["x", "6"], "-", "1"}]}], "]"}], ",", "2", ",", "401", + ",", "40", ",", "0.1"}], "]"}]], "Input", + CellChangeTimes->{3.66416194052215*^9}], + +Cell[BoxData[ + GraphicsBox[RasterBox[CompressedData[" +1:eJzs9+vNJLuyAFZeQZbIEvkwJgiY37JFnsoEQRg0BoenoyOCZCZZVSuAjW/X +4iuSZDLZ/9v/8X/+f/6//+v//M///F//y//vv//3//8z/u///b+Ic84555xz +zjnn/CP8z+/Is3pR3PJ8u/1T+u2OE/2N6nXj1nm6zbN5ztYpiluej3POOeec +c84557zrt+TBOeecc84555xz/uf3bD9Rf1Hc8ty3+u5+V+tF7aK/WbtVf6rf +b/WxvLs/rAPnnHPOOeecc84/zW/Jg3POOeecc8455zyqV41bnuNXPFuv1fV8 +Ksb8T88j/7tH9Wb3Heecc84555xzzvnbfksenHPOOeecc8455932b+W16tX8 +s3ZPe7e86rfH7P7cPU+75vV0XrvOge58P50X55xzzjnnnHPOeddvyYNzzjnn +nHPOOee/439+R/WjyOq/9RxR/vyz4pb34Va/ffxq+ez4nHPOOeecc84556t+ +Sx6cc84555xzzjn/He/WG/9GsTvfaNxTnsWteX1anFrvaj6n/elxquOePh84 +55xzzjnnnHPOM78lD84555xzzjnnnP+OR78zj/rPYjbfal6zvru/Vd/V36fF +LfP21j5b9af664576vk555xzzjnnnHPOq35LHpxzzjnnnHPOOf89X42x3+x3 +1D5qlz1Ptf/Z8apenfdd40f9f1rsXv/uelX37y6v/s76644XtauOsytuO/84 +55xzzjnnnHP+/X5LHpxzzjnnnHPOOf8+j36Pf6v1u/1GeWb9d8ur7bq+u7/Z +58litt1tMbtf3l6/7Pdsf1n9bnl1nOx39xyJxrnlXOScc84555xzzvnv+C15 +cM4555xzzjnn/Hd9/BvFWF79XR2nOv5sHtV+nvIon2p5d36q674ruvMQtauW +Z887Ow+n9kF1f0f9dMfptp99/zjnnHPOOeecc85P+S15cM4555xzzjnn/Pf8 +rfH+/I58Nqr9dfOpenfc3e2yvLJ+u+2r7ar9PlWezc/qOs/2t2tesljNZ3Z+ +qnlxzjnnnHPOOeecv+W35ME555xzzjnnnHNe9ah8tv/Zfqt5Vsfr/p71XeM9 +NQ9ZvDXu7D5cXf/Zdct89/zP1lvdl5xzzjnnnHPOOeef4rfkwTnnnHPOOeec +c77L//yO6kcxtsvar5Zn41f763q3vJpXtg5PrVNWXh1397rvGn92X2T5ZeVZ +Pt3+ZvPinHPOOeecc845/1S/JQ/OOeecc84555zzVa+Wz9bL2lfz7Nab9dnx +x/Jd85a1q+Y12/7p9Y3Kq+Ps8iyfqP3b8/b2+8A555xzzjnnnHP+tt+SB+ec +c84555xzznnkUb1uf+Pfbr1q+0/x7ryuzlu1/mw+q+Ou5tPN83aPymfnrfu+ +7+qPc84555xzzjnn/JTfkgfnnHPOOeecc8555Nnvqo9/u/Wq5d28bvPZ56rO +22x+1Xqzeayu7675OOVRdN+LrJ+un34fOOecc84555xzzmf9ljw455xzzjnn +nHPOI99dr5tH1n52/FMelUfP2623y7N4K4/ZffB2frMexa73ottftf/b3ivO +Oeecc84555zz0W/Jg3POOeecc8455zzzsbzavvu729+3+FgezfNbnsXb+a2W +f5qPkT1vVD9rv7pPOeecc84555xzzm/1W/LgnHPOOeecc8457/qf391+qv3t +Gu82H8uz9tV52O1Z3JLfrn10m0fl3fnI+svitveHc84555xzzjnnvOq35ME5 +55xzzjnnnHP+llfbjeWR787v9PNn9brzM+vVvN7Or5vXqfnb9ZzddVp97zjn +nHPOOeecc86/xW/Jg3POOeecc8455/wtj8q79VfzuNWzecnq7fIs3sojKj+V +x27P4q33iHPOOeecc8455/zb/JY8OOecc84555xzzp/2rF5UXu33luec9ahe +9Xl3+6fkdzqPVa+Wj/Weas8555xzzjnnnHP+LX5LHpxzzjnnnHPOOee3elRe +7ee251n1P7+f9izeyiP6eyqPWR9jdf92++Gcc84555xzzjn/Nb8lD84555xz +zjnnnPPbvVtebXerd59rt2dxOr/o7235jVGd9+q6cM4555xzzjnnnPO/+y15 +cM4555xzzjnnnH+qj39vy2/Vx/LoeXd7Fk/lsVr+qR795pxzzjnnnHPOOedz +fksenHPOOeecc84559/qf35367+VX+ZRefU5Zz2L3eNl8/L0eLP5deuN9Tnn +nHPOOeecc875M35LHpxzzjnnnHPOOeff7lmM7bLft3g1765nMdtvVL6r390e +5Rf9rsbpfcM555xzzjnnnHP+7X5LHpxzzjnnnHPOOed8b/lb+WX1//zuenWc +1fGe6nc1jyivbjnnnHPOOeecc845P+O35ME555xzzjnnnHPOax7Fn/rj36fy +qHqUT+ZZzPabzdNbHv3O4pZ15ZxzzjnnnHPOOef/9lvy4JxzzjnnnHPOOefP ++vj3rTyicTPPYrbfbD52e/Sbc84555xzzjnnnH+335IH55xzzjnnnHPOOX/X +x/K384jGzfKtto/+dttnPpZn+XLOOeecc84555zz3/Bb8uCcc84555xzzjnn +d/hY/tR4Uf9ZXtX20d9u+2jcLC/OOeecc84555xz/tt+Sx6cc84555xzzjnn +/G4fy3e1H+tn7bv9VMuj/rPxOeecc84555xzzjn/m9+SB+ecc84555xzzvlt +/ud35LORjd8dN6pfbbfqu/vtjlOdt9l12z1/3fIs713rtboOnHPOOeecc845 +5/zOPDjnnHPOOeecc85PefV3Vm93Xqd9tn11/qrts3yiv1n9LI/ZfD7Vx/Ld +68o555xzzjnnnHP+a35LHpxzzjnnnHPOOedveVT+5/dt+d7uq/V2RbZ+WR6z +z/Vr3v39Vl6cc84555xzzjnnt/kteXDOOeecc84555zv9mpU29/yfN18V+cn +yycab/e4s5HlcXpfVdvftv/e3lecc84555xzzjnnn+a35ME555xzzjnnnHO+ +6qfH73q3/FP8U+L0+u/y0+PPevabc84555xzzjnn/NP9ljw455xzzjnnnHPO +Zz0q79Z/2v/8jv5G9VY9iqfHvz2envfuujy9706Nn5Xf9p5yzjnnnHPOOeec +7/Jb8uCcc84555xzzjnf5Vm9bv+7+o3yrPru/rJxxnrV/j4t3p6f3fug67v6 +6/a7+n5xzjnnnHPOOeecf5rfkgfnnHPOOeecc875rI/l49/ZGNvP/q7mk7Xv +elZv1zifGtlz7Jr/qN/Vcaq/o/FX86tGd99XyznnnHPOOeecc85v91vy4Jxz +zjnnnHPOOe969DurF8XYvtpPt/9s3Myzfrv9ZeN0x++WvxXVPFfnade8j/Wq +/WXtq+NE4+16vzKv5sU555xzzjnnnHN+q9+SB+ecc84555xzznnXo9/dfqP2 +q+PN5lUdZzbP1fnJyqvjVOcvax/l112f6nir61BtN7u/Z+ezmudqeTT+LecK +55xzzjnnnHPO+S6/JQ/OOeecc84555zzp737u9tf1i7LM6qX+ex4Ucy2y/Ko +Ple339lxu+PNjjO7b7P+ds1nltfse3HLe88555xzzjnnnHN+ym/Jg3POOeec +c8455/xWH8vHv1H77Hc2fvX37PNUx4nqV8fP5quaZ7XdrnF3rdfsulXXdTbP +p+aBc84555xzzjnnnN+VB+ecc84555xzzvlpr7Yb/0btonrZeG8/f3X82X6z ++crGi8bZvU5RP1ke2bjV516dp2zcbr2xftVn23HOOeecc84555x/m9+SB+ec +c84555xzzvlbXm03ls969fdpH8tn663OWxZZu+p4s+NW+zvl3bxXPRuvWs45 +55xzzjnnnHP+bX5LHpxzzjnnnHPOOedPe1Sv26473vi3289bHpXPPm/Vd8ds +Htl6ZePsmo+n53X1ebPf3X4455xzzjnnnHPOv9VvyYNzzjnnnHPOOef8LZ8t +z+pX8xn/dtu/5bO/d3kWu8frzku2nqc9+p15VG91/8/mwznnnHPOOeecc/6p +fksenHPOOeecc84555/if35HntV7Or9V3/28q/1GsXu81fV6ej5WPSrvzjfn +nHPOOeecc845r/kteXDOOeecc84555zf5n9+Vz2KrJ/Z/HZ7tV13XmY9i6fy +6K7TW/Oxe/6y+t114JxzzjnnnHPOOed35sE555xzzjnnnHN+m2f1ovLdeZz2 +sTx6/t2exVN5rJbf6lGs7vPb9ivnnHPOOeecc875LX5LHpxzzjnnnHPOOeff +4mP5+DdqH9Xbnd+sz+Y/61nsHq86/08/9+y+yOqN9bvlnHPOOeecc84557zn +t+TBOeecc84555xz/un+53dUvxq3PE/k0XPu9izeyiP6eyqP2ejOK+ecc845 +55xzzjlf81vy4JxzzjnnnHPOOed35TF6lGeW/2r7KGb7jcqz8VfH2+1Rfpxz +zjnnnHPOOef8Dr8lD84555xzzjnnnHP+77g1v7E8+t31LGb7zZ5zV7+788vi +tv3BOeecc84555xz/ut+Sx6cc84555xzzjnnvOZj+S35RfnMeha7x4v+Pj3e +GNV155xzzjnnnHPOOed3+y15cM4555xzzjnnnPO9Hv0+lUfXs5jtN/q7q99q +nmM555xzzjnnnHPOOf8uvyWPKLJ8Z5/zU+eHc84555xzzjnnvOtj+VvjZfWj +fKr9Zu1n52OXj+VZHpxzzjnnnHPOOeef5lm9Xf1H9aP4lPnZ1e/udrP9ZP29 +NT+cc84555xzzjnnpz2Ksf5sv1k/f35Xx4v6r/YblXfbd/PM6nPOOeecc845 +55x/qme/o6j2k/VXHT/r76356darjhvVy+Z1V37ZeFnM7qtd7TjnnHPOOeec +c85P+dP9VseL+sv6rdbLPBqfc84555xzzjnn/Fb/8zv6G0XUT9RvllcW1Tx3 +51HtL2uX9Vftv7pOp311frv9dvvp1uOcc84555xzzjm/zbvtq/1k7cd6WR5R +vax9lg/nnHPOOeecc8757Z7Vi/52x4vKZ9uf9qxeFNV+o3bVcT/do9i1Xlke +t80H55xzzjnnnHPO696t96c8+hv1M1s/y2vVn2oftavOQ3UddnuWX9Q+q786 +TjY+55xzzjnnnHPOP8ezeuPf6jhRRP19ulfLZ+tn+UT1b/eovDuP1XZPvy+c +c84555xzzjk/51m9qPzpvJ726Pl2zVtWL2oX/c3aZf1187vdf3Xfcs4555xz +zjnnv+C720ftquVjvfFvVH67V6Pab9b/t3k2L6vzv/u94JxzzjnnnHPO+XMe +1Tud16d4df7ejmqev+5/fmfreEu+nHPOOeecc845/2+Pfmf1ZvvL+v82j8pv +Wf/bvDpP1fbVPKr1OOecc84555xzvt9313vKs3yi3097FtV6T8fqc+3yW/Oq +7r8ov1N5cc4555xzzjnnPI6x3urvqP/ob1TvV3yMT/Vd+221/7H+7P7lnHPO +Oeecc875ex7Vq8buvKL8quW3+qm4ZZ/N+lhe3b+7x8/yeGp8zjnnnHPOOeec +z/uf35FXY+wn6jfLZ7X/T/MxnvasXne9ZvdPVj8bZ7X/zKv1Zse55f3nnHPO +Oeecc84/yce/u/qrlmftonG7/c36p8fb8/TWPprtb1d+nHPOOeecc845z+tF +f7sxm082XpbXrv5m+8l+n/Is36f97efcvZ/HuG2eV/cn55xzzjnnnHP+S14t +z+r/+R151D76m9XvejW/7nNUy9+ObD677brr1O0v86z/qF51vasxuw8455xz +zjnnnPNv9uz36FH9pzzKoxur8/GWn5rn7j6K4vT8ZZ7luytufd4ov249zjnn +nHPOOef8Fz2qN5bP9he1n21XHX/2ObPo9nsqds1v1O/u9Yr62bUuq+Pc8r5y +zjnnnHPOOec3eVbvz++s32q7Xb47xnFue97qPMz22+1ndbzV/LJ8Z+dpNXbt +n+p7XH3O7jjd8TjnnHPOOeec82/wP78jX+13NrJxsry7z5Pl252PqLw6Xjey +5119vizv7vxW17E6TjWicVf3UTQO55xzzjnnnHP+jZ79jtpn9aL6Ufvod9V3 +Rzbu6jxG/T7t2b6oPsdb+b49XnfddvVTXZ/Z9qsxuy8455xzzjnnnHNe9z+/ +d9XP6nXHy/qvthvHzcavPmfWPsqvO4/V8uo43XmojpflObu+nHPOOeecc845 +X/eoXjX+tM/6zfLJ8oj664672s8uf6rfzLP5firf6jhvzXtUf3V+upGNO/t+ +dMfv9re63pxzzjnnnHPO+Tf5n99R/Wq71fZRvVmfLc/yqpZXI2s3O251XneN +0x2vO+7s72xczjnnnHPOOef8F3wsHz0rX42o/6xet3ysV+2vms/qPK/6W3ns +7q/7XLv96ecYy6uexex7M/t79znS7Z9zzjnnnHPOOf9mH8vHv9161fZPeZRH +Vj/qd/V5q/ll5dG42e9uvW4/q76aR9RPt5xzzjnnnHPOOf9k75ZHv6seRbd9 +1avjd/t/e9268/zU+lX91jyfzvep9ynqb5d339O33u/T5yPnnHPOOeecc/6k +R/Wq7aK/1XbZOG95VN6dx+rzd6M7XrYuUf/Vft/yan5jve7v7r7gnHPOOeec +c84/yZ8qz8aPyqvj7vYsz7Heqbyj8mo+ma+2r/a/a9yov93PU82j+/xZ+a3e +Xf8sTj8P55xzzjnnnHN+0sfysV7m3XFvff4sZuen+vzfNt6qR/llvnt+btuv +nHPOOeecc875m94tH+vd9jyrzx893+n8svrV9cnG7/bTna/Z9tV1qD5vVv7r +Pvu7uv5R3PL8nHPOOeecc875kx6V//k9/n07v9nnGetlz7fqt+Xx1nhP5R39 +HuO2/cc555xzzjnnnD/hY/lYr/q7Ou5tz3+bj+Wr810dL6vf3R+zvto+itvW +mf/dq+v5dB6cc84555xzzvkneFT+53fW363PM9arPt+s35bHW+PN7pvZ31l/ +nHPOOeecc875L3lUnv3md/rT/Vb3SXW/VfPP8uOf4dabc84555xzzjnv+y15 +7H6esTz6vcuz2D1eNi9Pj/fW82Rx2/7jnHPOOeecc87f9KjeWP+2vHnPu+sa +Rbd9NG7Wb3e8W+bzdF6f6tX5zNo/lR/nnHPOOeecc36jj+XVervzWM07+73L +s9g9XjYvT4/X3RfVvLN+OOecc84555zzb/KxPKq/Ws7/7tl8nsor8t3P9VTc +Ml+zfnr8T/PV/Ta7zznnnHPOOeec82/ybr1b8u56lH/mWcz2G/3d1e9u7+Yf +teOcc84555xzzn/Jo3pRu1vy/hY/Pf7u5zgVt83H6nrflvenejSft+THOeec +c84555x/ko9/o/K384vyqOaZeRar462W7/ZuHlE7zjnnnHPOOeec/7eP5dlv +/m/vzl+2Drf4bXHLvGTrWI3qPsr6v+U9OO1j+W353e6z34HuvuWcc84555xz +/hke/a767vyyvLJ8Ms9itt/sOXf12x2v245zzjnnnHPO+Z0elWf9zPbL/9Or +8/90Hp/mu/dtNY+xPOr/bb8t3n7ep/qr9tPN71c8m78oTuf9tFf3U/c9r35/ +d52fv76OnHPOOeecc367R+XZ76f9z++uZzHbb/R3V79ZvtHvrD7nnHPOOeec +82d9/BvFWB79ruaR/c7ad/M4Pc9Pe/e5387vVq/OTza/1f3ffW+iPLv9ze6P +U7Hr+Xb31x1n9dyqlkdxy3u2y2/J4y2PYvX7vVqvms/qfaDbD+ecc84555zz +Mx793T1eFNF41Tyi/qr9rrZfnbfT688555xzzjnn/N/l1XrV8iyfbl7V9tn4 +3XFOr9dbfkseuz2r191/3feoO+4uj8bN/PaYfZ6n5/vt9cza7foOfIrPnvu3 ++Vj+9Pv+9vmbxa57yliPc84555xzzvm7Hv0+lUeWXxRZ++hvt33m3XLOOeec +c8455+/4+DdrH9XrRjTubV5tF8Xp9c28+1y3++r6re6P2z2L3f3tjt3vW7fd +LefSqfMt6ydqd5t/yrkXlc9+v097FLvWI6v3KevOOeecc8455/zv/nS/1fGi +/rJ+q/Uyj8bnnHPOOeecc36nj+XV312vxmz/p7z6e4xPW/fbvLqvuuu6K7+3 +PKs32191/3Tf725k482uY1Y+2y7L61M8iu650m3/tH/Ke39LHqc826fd/fbp +3zvOOeecc8455//2bvtqP1n7sV6WR1Qva5/lwznnnHPOOef8M/zP78hn+4v6 +z8b7Nh/j9Lrfnl+1XvYcu/I47Vmsrufsfq62z/Lqnju7z5Esr+4+u+38eWqe +xvqzccv79u3jfYrP3h+6/XLOOeecc875r3n0O2rfHScbb7bfWX+qfdQu+hvV +y/p7yqN6s/OXPVe1nHPOOeecc85/1bPf3XbR36jet/sYp9f3tEf1uvW/zaPy +bL9F9bLxu+1nx8vGfyrPbv7d9lm+t5w/u32Mb3lv3/6+3vLcUfns963aX7fe +0+vVPZc455xzzjnn/C3/8zuqfyqvp3zXc67Wi9pFf7N21f667T/Nu/PNOeec +c8455097td1T+VR/d/ONIuu/Ou4p75bv9tP7NfPZeX4rv7e8Wz47X2+9P1He +WfnqebLrPOr+7rar5nnLOfb2vjj9PX06j1vOmbf2QVYvqh/FLfN56rvOOeec +c84555mfHv8Wz+bnVFTz/DU/PT7nnHPOOef897xb/rRHeWQR9Z/93u2r5bt9 +jKf2z+l9nPkteTzt2f6I6s3un2o/T+3j1XWO+uvmder93nWO3pL3U88fxW3v +7Wr7p869bNxqHrfug2o8nefu/XLL/uacc84555zf793fT+c1/o3Kd3u3PPNs +3nZFddzqOp/al6fHOf38nHPOOeec8+/xrF70N6qX9TPrq/FWnrufd3b+M8/i +6X31tt+Sx9PP031/btnv1fcgim756jiz+d42v9XzJfqd9XP6eTIfo3te3npO +Pt3v057F0/u5O/7q+756Lxg9itu+Y5xzzjnnnPN7/c/vqj+dVzef2/xU3LKf +Zv3pcWbzeTovzjnnnHPO+ff4+Lfbbrbfqkf9dyMbr5tndbzV56/62/O96rv6 +rfZ/+j2b9W69t/fdqo+x6xx4ah+O5d116Lb/FF/dt6fynvUxTr//T7XP+p19 +329Zz26+0e8xZvvP+s3G45xzzjnnnPNVr7YbyzPP+un2V/Xd/e3O66245bmr +67Tq1Xa79vHs+JxzzjnnnHNe9bE8a5/V647X7T9r97bv6ndXXmOs7pOn9t9t +70E2j1G92fflW32M6vsTtav2V+1ndX9mefyKf/p7UI23zpHIV7/n2e+nv2uZ +R+Wr6zh7vmTl3ffgre/N7Hicc84555zz7/Fu+6yf2Xyy8bL6q767v1uiui63 +zdvs/ovqze6v2XW+5f3mnHPOOeecv+fj3yiy8rfGq7arjrNrvOz3Lp9tH5V3 +20f5ZL7a/u1+d+e3ez1+xXftw9n3bNarUX3eW9bjlM+ec5Gffp4o3jr/Vvd5 +9/2J+nvr+7VrvCx2r293fne9L2/tI84555xzzvn93m2f9VP1br/V/rp5rOY9 +O3+nojpvb81v9/fT65HNw1N5cM4555xzzj/Ps3rR36x+1v9sPlVfHf/pdcjG +z/LJ+q22z9Y3m48sn26emd/y3ow+u4+67X/Nx9i976vjV/Mb62f9VJ/3lvX4 +dj+dxxhPf993j/PUvK62Xx1vjE/zXfP7VH6cc84555zz7/duVPup5vHnd9er +v7P+snaz5d15Wp3Xan/V8XatU/S3G0/vX84555xzzjkf/c/vzKP+ns7vbc+e +d5dn41e92747TpRn5rv25Wz7WY/qzc43n/Pqfh+ju39PPW+UV/e5u+fWLc// +KR6Vv70vMl+tV63/1nenOj9RnPp+3OZRzJ4j1X6yepxzzjnnnPPv92q7sX7U +7un+q+POtquOX52HrH2UX3eeu+XZc3Tz7P5+uv8xOOecc84557/r0e9qvWy8 +KG55/tP+1njddc36zerN5rer3qxXx83mk//dx+jut8hX26+O9+kexez5sDu/ +T/cxnl63aLzMu9/16nuR1V+dR/6O796Hp5+Hc84555xzft7H8vHvbL1o3Oj3 +U88T+a7nrc5D1u/ucbN5Xx2nm//suNX+onbVcs4555xzzvn3e1Sv2t+uPPic +727/5/f4t1reHS/zar3VfqP61Xn4Nt/9O1uf255/9b34VI/q7fqeVMfvtvsW +3/WeVGO23ew4s/m/9d14+zv0bb7rvOCcc84555x/j2e/Rx//Zu2iOPX8Wb3o +OVfnZXZ+nhq3uw+64+zyKGb3YXU+u+0455xzzjnnn++rv/l//o7qz46zms/s +OE/F7uccvbp/v92r+yGLqN/Zc+Nb/PT43+JjedW75d++b8eo1rstPvW+cXr8 +W333e88555xzzjn/PI9+j3+rEbXLfr/tT89bdbwoqnl2x1udl9XnXp2n6v6K +2nX7zdpzzjnnnHPOP9+j8rfz+FQ/PX7Vs/xPRze/6Plu86je7H6q9tf12Xa/ +7qfH53d5Vq8bu9/vT4tbvp9Z+eq5/m2+63vHOeecc845/z6PyqPfWb1v9ez5 +V+crGn93Hk/1e4tn0W13y/7jnHPOOeec7/fxb9Qu+/2tHtWL2mXz+bZ/euya +l13jrubBv8tPj8/5v/zT41PmM/v+Vtt/uv/680cxu5+y39V62bicc84555zf +4GN599572/NkPvtcs57F7vGq6/L0c696VF7dx91yzjnnnHPOT3r33pv181T9 +T/VoXrP5/lYfy6v7rdr+lH963DafnN8wPv8tF/8Zt63H7LmRtY/qfZrvnudT +Xv0ORO2y8brv/6/uJ84555xz/h1evbdm9W95nszH8ux5dnkWT+WxWn6LV6M7 +35xzzjnnnL/p0b13tt+oPBpvd36n5zPybD6ifk7nPeuz89GtV63/tIv/jNPr +wX/DT4/Pz3gWt3xHvy2idcnKb/UxuudN1v4Wr87DLe/N6v56O7/qvtvd/2x/ +nHPOOeec/yuq98+n8nj7OaP7+27P4qk8VstPezW6837bvuScc84555/t0T27 +er/N7rPV/nd7t95t3l2PW/KOvJp/dZ/szu8p77b71HjrvZ59D6J6b+fLz/jp +8fmcr35fTvlqu1uj+7zd8zjyW/Zj5t3yT/Hbn+fW/Mby1X0TjXfbc3POOeec +89/0brvb77VjeXRf3+1ZPJXHavlbPsbqPpptxznnnHPO+U7v3mur7Xfdw3d7 +9Pttj8rfzmO3V9fjVH6Zd9t117Na/1Oius9vOQeyPLv1+F2++t7yv8eudbnt +O5zFar7V/k9/F2bP67E86/+tvG7zsTyK0+/Dqfw+5XzY/Zzd+b7lOTjnnHPO +Oa94dh8+nV8UUZ67/bY83hpvdl/ctm8455xzzjmf8ex31D76G9W73bPYPf9R +Pk+Nt+pj+W35rT5PN2b3f7f90/H0/GR+2zlQXYfd41X3Ca/Vmx0n6mdX/6e/ +Z7P7O4tbvwtvj1Mdv7qfs/qzeT09btZvVD/7/ak+RnX+x/pv+er3cHa8bPyn +8+j66vncfc5bnptzzjnnnPNKvW79Ux6VV+/vs57F7vGyeXl6vNn8qnlG9Tnn +nHPOOb/JZ3/P+mr73d4t3+XdeX/ao3rd+p/iWb3Z/RP57L7M+s/qr74P1d/d +vHb57edJNWbPpWr9W3z3+by7/yi653b3vVrtt1uvWv9T/anvVRaz51W136e/ +I9U8Z8frvse7+rvdo9+nfXe/tzxHVP+p71O1fpZXVm/W3xqHc84555z/tn/6 +fTR6jlnPYvd40d+nx8s8iuq8cc4555xzvsPfvvdm9bL+d/c3m++peVv1p/rd +vf9uya/qUb3d+yvLZ3U/Rf2sniOreXTb7eovm99T58Puc2ZX/Syq+2T29+z+ +m91nq+9HNd4651f3wbd69z6y6tV2q+/7rd+X2fxXfdd7ets5v3ofyerv9qfe +o6fz3eVRzO7LrJ+n7xPdPKr9cc4555xzXvGo/Jb7aFRv17391Hi7+636GN15 +uW3/cs4555zzz/Zd99un7stRzLbflefou58/e67d676739N57PZqebf/p/Zj +NZ9u+ew5kI339vsw2252XZ9e59u8W171t9pH5avfz+r41fdtNa/V/L7NZ8t3 +f49375fue7rr/R/rVb2bV/b7LV99/2//XkS/n/bT7bN+n5rf3d/h7njdcXd/ +D2/7PnDOOeec8+/07n346fyy8Vf91Hi7+50dL4pb9iPnnHPOOf9uz+pl99rV +e3MU1fv17Li72lfnZ/c8Pb3uuzx7nlM+llfXK+v/qX1UHW9232Tl3fXcdW5k +eWXl3TxX+8vqReOf2ke3+2x59/tR9afO693vBZ/zLN7+LnV99/v19rk9+/3d +9d6+7d3vxhinvyPdPFd9tv3u/Tn+7q5zt33m3XyzePq9r9a77fvAOeecc875 +v8p395v1P+unxtvVb9R/tZxzzjnnnPMTnt1vs9h9P67mE7Xr9tv1KI9u+2z+ +Z+ch89X2b/e7a19lMbset3m1XRar+3P3fI7lUby1j54a55Z99K0elVffk9V2 +/G6/ZT13tdv93Xj7PK/Wq67jt/ju8+rp8zaLp/bH7ve5Ov9Pre9sv1nsnpfZ +8yWrV41bviecc8455/y7vXsPP5VHNb9onNnxVttXPYtb9gvnnHPOOf8NH8uz +9t160fjV+3LVu/fw7nx0x6s+b+bdccaYff5T7Z/a15HvXt/bPKsXxer43Xa7 +x+vGU/trt6+eD/wOH4Pf6Vm89Z7Pjv/U+br7PK/2E7Wr5jk7zm3nx26fXZen +8htj1/u0Wq86T9V2p+f5rflf9eo6ReE7zDnnnHPOb/Snx8vuwav37ax9VN5t +n3k1blt/zjnnnHP+W969x3bv67c8z6k8uh7Vy8bN1vGt+Tu93tm8/ZqP8fT8 +VfvdNd6ufdVtVz03n34fxvJb9h2v+Rj8rJ8ef/Y73z23Zs/drPzp70Pks/3P +1u/m962+e3+srkPmb9WL2u3eT1len3rOZb76nX06P84555xz/oxH5bfl+dZ9 +d/d43ft0tX30t9u+Ou5Y/i3efS8455xzzvldnt17s6i2u927z9sdL+tvNY8s +r6z/2XV8e59mefyqd9/z2XMhqz/rT/eX+a79f8t5Nvot+5T/3cfgd/kt38Ms +unnOng9Zebf/bn+nfHZ+o/qnn+e0R+Xd9mO9qmf1Zt/71eetxi3n4y2+ez5P +Pw/nnHPO+bf46j19rF+9f1fvj91xovpv++5+u88d9Zf1213Hapxen+7z7Npn +UazO8+n55Jxzzjn/Fu/ep7vlfK5etk7ZPXr1Xl2tV91Pu5731z2K7nrf8jzV +/bpr3mb38er7PptH17N62XzzO3wMfpc/9T1c7bfb3+x5nOU1u99vew+fep9X +y2fX6bZ5mfXZ738Ws+9Ztd/V96ub1+59+S1uXjjnnHPOz/rqPf6W56h69nxv +zXPVq+uVRff5Z/fFU+v11nhv+ew6PJ0X55xzzvmvePW+fSq/W3ws785Xd9zV +et14+nmycb7Fs3mcfR+zuOX5d/tqf9Xf3fGi+ln7rN0u7+6zW9ab//03/0w/ +Nf7s+TN7/mb1Z8/76vi852NU61Xjluesfu9uiU/9Dpwef9Zn5/t03pxzzjnn +n+Ld+/fpfG/33f0+1T5ql+2L6n65dT6/1bP1OpUX55xzzvmne1bv2+5bp8df +XZe3Y9d9/WnP8q1GNu7s+8Jr3p3nt86z2X321rlxy/rxPT4Gv8tXv0dvnwuZ +Z/2tjtftp9ov/26Pfmcxu/9Px6nzIqpXna/T59wu/5XnjDxb99n36fRzcc45 +5/x5r94HuvfxW57vU7zbfvc4UbvZ9c/yiPyW9fgUj9Ylq1d97znnnHP+fZ7d +B7r1nsrzNu/Ox6d7976Y3Uuf8tui+zxP9ct/w2fbjzH7fmX9z+bxlj89z/wd +H4Pf6Vmcev93t6/GbD6n3zf+3f5pET3PWL57vGz8LK+s30/xT/8+R+Xjc1Wf +c3bdd+XNOeec8/s8Kq/eN6qx+zlm89l9H8ra7fbVeruiOi+7n2vWZ8ffVb9a +/tbzRr7rOTnnnHN+zqN7WnZ/m60/22/0O2t/i88+1+3eXfdqu9VY3Ue3Rnc+ +OZ/x6vu5+h5Vx13N52kfy0+vH+/5GPwzvHpuRPHUe75rnCxmz03+G57VG+Pt +/Xs6nl6HqLxar9p/FG+t99Pn+y15vJ1fFN3v4O68OOecc/6ed+8fs/eEbl5Z +ZON+uo/RXZfTseveeMt7stur5bPjVMddff+7eXHOOef8vM/eE6r1dnsWp+fz +tjwyXy3v7q/qeq+O+6mx633J+s9+89/22fM3iqfOj9n+Zvut9sPv9DH4d/hY +3j1Xqv11v7/V/bh6Hu8+5/le78bt71e33S3x9P3hNo9+3+LV8/Mpj/J5O4+q +V+et2n5XXpxzzjnf952PYvV+ODv+bffb232MrPytcP/r+Wz71XmO6q3uN845 +55w/7917QfW7nt0HTt97376ffOp9aHYeT9+Hd7e7LWbX7fR7143bnuPbvNuu +2s8Y1XPk6XO829/u+eOf5WPwOz2q1z3PovbVfrM8uvl1z7ds/Nnz8Kn5+zaf +jeq+Ov1+PdVfdb/vjtn3rtpfVH56n86eW1n9p/3t/bm737d99rx/Oi/OOeec +7//Or7bv3hOidrP9vn3/vc1vj1vm6TYfy6NYfS+jPFb32S3nGeecc87n7wXj +79l7wun7VBaz8zl7j3t6XWf3wWnfXV5dv6fjqeed3Z+nPfrdjdPPcYvvahdF +9317el92v1fVet15uG0f8JqPwT/Tq9+Pbr1T5/dYr+pR+ez39env/Knf3fN+ +jO537rQ/df51y3e9p933qXtv6OaTjfepHv1+y3f3O7tvdvnuc7g6zuo6r47b +7Ydzzjnnse9qX70Hde8Pt91nT+f7afH0/L81zq59sSv/rP2u/jjnnHO+7tV7 +XfYd7/bfHTerl7VbzWvX/amaX9Wf6nd1H3yKR1Hd51m72ftutb+sXTeq7/Ws +R8/z1Pu4eg7tmo/Z8+Pp+k/NSxS75/ep51ydl9u/U/xdH4P/pnfLV/dfNt5q +u6xeNWbvCbvGy8atto/Kb9uHu/ft2+N0v/tvvae785l9b7vjn/Jquyie2o+n +28+Ot/u+Ut1n3X1Y/Z3lsdof55xzzt/zajx1n9zV7q1711Pzezp2zdNqf0+t +32x/UT+74rbzgHPOOf9F7973snvB7H1kd3+r/vS9bYxd67i736h8133y7bzH +37PjVPdJdbxs3Gz8bJy39uVsu+58R+W3+hi71zHqvxuz5033PF/dP93y3e2e +Xl/+3T4G/03vtj+d56522fm4u/+sn13ft2z8bh6nfSx/+zyrjt/9vs9+z6u/ +u+NH9Xb5rvfh1Hczym/1/Jg9D95un/W76/yrtpt9X6vjVfvJwv2Lc845j/3p +72T3XjFbP8tr13109d7Vvf90Y7bdbTF7z5y9x57eH919kdVbrb/LbznnOOec +85u9en/rfner95Fq7L5X7L4vdb2bb+ZP74Pd4836WF5dl6z/Xeu6ut7d/LL2 +u/Jc3S+rXn0vu+1O+1hejdn+uud1dfxuf7vO79vW65Z9xe/2MTj/RB/LZ78L +3e9fNn61f95rN3ueVdd593d/tf1q3qvjz+b39nfsVB5RPtXy7v493b7ab9Tf +7vnuPudT+y/z3f1xzjnnn+RP30u694bZ+8XsPWF3v7vWabZd975TvS8+HbPz +kJW/df+cbVf13e//7HuR1d+d12p/nHPO+c3e/f5Xv+OzXm3XvQfsep5uPrPz +GY0z60+tz6n9W83nNh/Lo+jO/1vveTe/zLvrG3l3v9+2L27zarssuv13981t +88b5Dh+Dc85PeRa3jLP7npOVd+8tWXm1n9u+V5nfksfo0e+uz7Zf3Xe76+1+ +v7rjZONm9Xbls3t/cM455zf7ru/tU/eJLI9ueTWfrN+n12lXu+p9J/Lu/a3a +rrp/ntoPs/tx1/5dvYdG/c6O282vu3+qv6O45bzknHPOn/Dqd7f73Zz9bs/e +E6J+q+Nmeeyet9X72Ox9qOqz83zr/n3bo3rV9ymr/9T+2v1+Vdvt6q87r5xz +fouPwTnnT3sU2Tn1Vl5Zu+55m5XP9lsdL/s9m+9sfrf5GG+Nt7oPu79n+8vy +q+7n3feW0+dad953rTfnnHP+CT6W7/6u7vZo3F15Vvtf9W677j1ldV5n21fz +2j1ud56r+e/O96n3YPX93dWu6t3xxvIobjtfOeec845n39Hsd/W+c/p5do3X +fe6ov6fuKav3mafXKRs/y+dWn61X7Wd2n1Tf86pH+VbLd7dbfW+jdrftL875 +7/gYnHP+tkf1nh5ntr/ueZuVz/b71PegW2+2n0/1MZ7uN/Pd7091f5563k/3 +6jyeyo9zzjlf8afad9vN3ks+3Xe1W52/3fMfxa15rq5PN69P8V3tsojmsTte +Ni7nnHN+o1e/f6fyO+Vv9Vu9h1Rj9jl2PW83r0/3rN6ufp7y1f7G8ihm99fT +73027un9xTnnY3DO+dOexVPjR+dht7/ueZuVz/Z7i8+uy+m8n/Zd/Y4x+17t +il3v0a969T72dB6cc875TR6VV++b3e/tbc//9P2i+/zV+163fbff2XrdfbPr +fpaVV/OK6nfn9TYfo9vf7O9sXM455/wbfPX7+3R+n+bVe+jb8db63XaP3O1j +dN+f255nV39jeRS736On3++x/PQ6cc5/18fgnPOnfSx/63zK8pntb7X+6NV5 +Of39eMrH2L0fbnnO7rrPztNszI779Pv79n5526P4lntc99zM2t3yXJxzzv/z +d/V7Xf0uVPvN8vtW734fV++f3X6q/UbtqrF7X+2+x8zWm12vT/Eont5X3Tw4 +55yf9dn7Thann2vWu/elW/Lu+ul1XJ332Zi9P2btb/Ms76pn7/3p59ztu9Z9 +1+/u+Fm7Ve/OH+ecv+VjcM750z4bt+RVPWez8u65fNv341s9qjf7Hd2V3y3x +9L0iKv/We8yu8+OUV/fp6jxE9avjVPPgnHO+x3e323Uv+xYfy2fvk7v6f+qe +O1tv9X61+ly7894935/mUezaT7vPMc455zWfvS/Mfi+q/dz+XfjUvHf57n01 +ew+5JXY/5+r8rubB53yMbL2yfqvl3Xj6nKiOf9v6cc5/x8fgnPO3fTynTo0/ +W68aq+Py3/Tb4vS9pHpeZP3c7tlznc4v8mxdu8/VXf/Z+Ts9b5xz/qkela+e +x6vfD/6fv1fvF9X+Z706flR/dpxdeUf9R7+zfHbl9+mexdP3QecO55zv9eo5 +2/1uZuWz/d0yb6PP3qdu9+o6dNfp1D3l7bjtHsfPePfcm43d466eh9l4WZ6c +c/6Wj8E550/7WJ6dW9V+Mj/VX1T/tu8Bn/NqZPtl9j16O3bPU/e9yPqvnh+7 +zoFTLo9/e3d9T+fLOeff4tV7S/W8rtb/Ve9+z7r3qLc9yjuL2ed+y99ax1/x +sfyp+lE7zjnnc/6p37sov9N+Sx6Zj+Xdeqv1q+VRv7fE0/eot8bnZ7y676Py +2femus+q34NqXrPzwTnnT/sYnHN+yrvlq+db1s/seNVzOCvf3Y7//fcYt+7/ +rN3bsfocp9a/mme3/m6vvv9P+dvjrfrqOs5+N7L6nHPO/+3O2T1eve/Mzv9p +z+J0fpl37ylZP6ef51bvlnPOOf+3d7/DmXe/h7d/B6vx9rqc2jfVfE7nt7vd +qajuk9vei9ve40/z7PfqOmXtZ/vvnufV/KrjROWcc/62j8E557f46rkWjVMd +rzpu1m913G5/s+f7p32HonXpts/qPe2reY3l1f24Gt1xnnqu0x79PuWf1u/s +uFG76jq9tZ7dcTnn/Nt9LK/e37rf6dn8vt1Xv5On71uZV+udfp7MPzXv0x6V +d9uP9brlnHP+Ld79Xu06d1fvK6vjPv2divLd5bfsm9N5RLF7XaLyrH433nqu +aB1P3euq9arnQbXf097NM6ofRXe/dt/v7jndzXPWT68r55yvnuOcc/4pHtVb +PTdX88nadfPo1lvNJ2rXzXP2963+dH/V9VjdR6fHjfrP+jvt0e+nfPc+rPb/ +1D5+aj2yPHf3n7XP8sjqcc75p/hT7Xf1/y0+lp++D536vt+S325fLf92zyKa +r9n+b3v/Oed81bu/o3j6XP/U7+xYHkXWbrb/3X5LHllU53v2eWfvDafGrZbv +zuuUj7G73ezvzKvlWf1svqL2T517s/ndtq8453y3j8E559/ms+ffrnxmx63m +0+2nGtV22XNleXyKn+qvOn/de0CWx+z+qeadjdNtd/v9aozZfbT7nFnNayxf +na/d+3X3+9Ud7+nvFOec3+az53AU3fP6V7za7vR9aNWzeOo7/pbvurf8qkf1 +Zt+z295zzjlf9eh8rN4vdn/Hd32vs353f5dPz8db+2NXv7u9Wz67jrvyqI7b +zW91P+1qt/u9OO3R78zfqtd9T6vjnT7fsjxu2yecc777u8M55/xdj6J6jnfH +6X4nsn6/1Xf1N7tuY7vq+syub5TH7nGeutd07zen7l1Zfll59Rzp7s9u+6yf +XfVW53V1/t9+3iyfrD7nnN/mUb3Z83J3ft/ib31vT3sWp/Pb7bPr/uselVf3 +URSn33POOc88O+d23xuq43XLq/lFeVW9237XdzlqX/Vd7avP9ZRX291yn4ii +O8+7nzfKo/s7itn1PrVut3m1XRSr51A3D8455+/4GJxzzvkv+Fj+1Hey2q77 +Hd/dPopd7U7fd7rz+JaP5VFU2+2ul7XP+p1dl9l9PbvOY3nm3XMlq18d57Zz +9FO82271N+e/7N3vQ9b/7vy+xaN6u9bpFs9i9rt/i3/rup3eF2P7qD/nDud9 +nz23quPNtvt1r55ru8tn90F3H3Xzm/3eVOvNjhPlm/mu+Zgdf9V3zfdTHv0e +o/qcs/t9tX0Ub5/D3fsX55xz/ks+Buecc/7NHn0Xnxq/2q77Ha+2j8bv1o+i +O/5t96DMTz1PNF7Vs3rV8ar3yO58Pj1vb73fu86jrN1YXm33bb46P7vWZfZ9 +iOpz/k3+dL+3POdbPpbv+k7ccs/K8uvGbc9TvRdVo9vft3pUvrv/sR7n3+TV +82f1e7zre/Tr7+nu+Tn9PFF099cu795Pnt631Xqn1nXXe32rj3Hq3tLtN4q3 +2lX3f3ceOOec82/yMTjnnPNv9qe+h6v9db/jq+VPexS33YN2PWd1X+ye16f3 +fTeP1f2cxS3nyNNeXa+n8zjt1fKxXrYPu/1U85ld36c9ex+rvznf4VH5rvvQ +t3m3/Jb70W7P4nR+p55/9r35dI/KZ79rWTnnM57tzyhO5bmr/a73bHW+uuPd +7tV9tHt9P81391ud/6jeU+v11Hx1x73tfjB7H+iu7635RbF7vzz1Xt22Xzjn +nPMnfAzOOef8mzyr99b4Wbvq9zr7zt92z6h6FN16tzxPdz13z193H3XbZfsu +65fPeXUdn85jt0fl1X2227vndfW5Vtczq7er/dvzzX/Lq+VR/due5/R3YLWf +2z2L7rl9m+967lue5y0fy6vxLfcmfoefOo+r0R0n+t3trzreLq/+jvK7zWf3 +1+m8v8Vn681+33e9j5lH9W75rlff8yhuPZ9mfXa/RTG7X956z26Zd8455/wN +H4Nzzjn/Js/iqfGj7+9qu9n6t90/Zu8r1fbdcZ7Ke9Wr+d0S3X072z7zt8Y5 +7dX35VR+s376e1E9R6L6Wcyef7O+a9ysn6jfW/YVP+ur59mvehRPnzu3eRan +83vqvleN257ntI+xOu/8u7y6D6r97Dq33j4vq+XZ+Kvlu32M0/tt1mfPuW/z +p8eZzeetmL0PjL9v8SjPyKvvwW3PuXp+v/07irff79vWg3POOX/Cx+Ccc86/ +2aPv4lPjZP1n+XS/36vzwHu/s3Wu1l/Nu5vP7nj7npmN+/T7fZtX9/FpH8tv +y2/3Ouw616P+qx71231/3lrvW9aTv+Pd7/AteZ/y2XvHbfer7r2rGrc9T/c7 +sbq+p5/nLY/Ku/PHf8O735en9mc0/uw41XOgOk5W77ZzYHVdoji9b2e/j5/q +q9+9qHzWo3Gfju587X7Oaj5v5fcrPntedc/nrF0Uu/Kq1ju9HpxzzvkbPgbn +nHP+zT5+F6vfx6fz6kY1/9P3DP6O3xZvPW/3dxa3nFOrfvoc657Hb+cxm9dY +/tT+2v3+zL4Xs/tp93d19zryu3x1n2XtP93H8u58nb6frHoW1fW/5Xm669L9 +Ppx+nqd89ncUt73n/O/ePSdWz9fqOFm7LJ56b7P+Z/OLyrP21fze8izPt333 +fv4Uj6I7H6fvH2/H6e8wf9ef2o9vnWPV8/ep7yHnnHN+s4/BOeec/4Kvlme+ ++v2d7T+qVx3n9L3kWz36HcXsfr4lqvuz2m5132fj73pvb/HZffjU+XrLOT+7 +v2bf4yyPWzzKM/LV9y+qv+u9P73/+TP+q+s6lq9+Pz/Vszid31vPP/v9+lQf +Y/f3jN/hs/s46nf2POmOu+s8O/196UY2z936p8+xsTyKt/b/0+M95avfsazf +rP1qv7fG6rmY9Ts7Dp/z1XZjvazfXd/DWc/yiso555zzb/YxOOec81/wqLz6 +He2O3/1OV/vvjlMd97b7ytuexW37ttrurTj13pzaF9n79rZ33+/dHuWzu99s +vF37IBs/Grfb365zftd5FpVX13VX+ez8ZPX4XT6Wd/fPbc/z1rlX7feW72h1 +/WbvM7c9z+7vTVR+Ou9T8/LUPYK/49117NbbtX9Wz6vd+7Gbx+q5s2uczGfH +WT1nsvGq+XT99nPq9vxW85q9Z7wVb+3/2fcly6ta/m3enYdd34/VcXd9r2/d +t5xzzvlNPgbnnHPO45j9zna/06t5VdtleYxe7S8av3ofme0ny/M2P9VuVzy1 +n7P+bvNu+Wn/tH6z8XZ5t313H6yeh7fsn6d8dn12zevp5+d/97F89lz+Vb/t +e7l6PkdxOr/dfksep73aLopb3sNf8er7mrXvfg/sg1p5dd6q79uuereek2M8 +/Z1+a7xqHtV9cotXY/U9eDp2ve+j3/Z9754fWbssVt/7XedhNb9q+13nende +P3Vfcc455zf4GJxzzjmf96jeav/ddln7rF11nOq9o9t/9fct6x757P2rOo9j +veo+2pXnbP/VfrP+u/fet30sj+KtfflWHrvbR/Vn12m1/ew+jPLI8svilvPu +Ke+eT93v0FvfVz7n3Xbd7+Kn+lg++x7d5rvj9POsfp+idrfl/dbzj/HWveZX +fdc+jGJ1/X71+1ud5+787cqj+56vepTn6v6M+u36rfeRsfy2/Gb3YXd9q+fa +U/nNvs+r52w1z1vuCd3y6HcUT91DovrdPGfnZfd7cct+4Jxzzj/Zx+Ccc875 +5/lb3/9snF+5h4zlTz1fNE51nrvtq3ll/VXzysbp9hP1N7s/n/Junlm7qnfz +6frT/c6eL0+t5+738al1/1V/+vv5rd+3W3z1u/h0fqe9Wh7Vu+27OPv81fa3 +PWf1uaJ2t+T99r7w3XzXV7+Db33H+Vy9XeM9/Z53/alzedd7tKvfrF43n1Pe +rbf6Xaj2082vug92vY+r5bPn/+n7wO7zJvOsv9l+V+89t80n55xzzus+Buec +c845r9XbPU7Wrnqvy+6D1ftiNb/qONl4q97N/6k8Vj2Lp/b92+2jek/NV3ff +z743s+8pP+O71rF73lXz43//vWtdPtWjervm8TbP4nR+q/eWb1233d/dKG57 +P2/1XeWz59Xp5+d//7vab1R+yzk/2z4af9afWt/uvN56b9m9fk+td9TP7HtX +vSd083x7P992r+Ccc845v9XH4Jxzzjnn/+m7+tuVRzffrH3WbzW/an+n77+z +83k67+j3Lq+O/1Re3edfXffZ8m6+UZw+13jN3zrfZvP7Nd/9HfpUr7Y7/d1a +9Sw+5b4ReXd/35L3bo/Kq/vitvfzVn/qffRd+0x/+l4SjbPrHOm2X93vs+9X +tf3seLfvp27909+hMXatw1N5PvW+Rv70d4Zzzjnn/Nt9DM4555xzvre/6D4W +tcvaZ+N226+O91Set/nsvD2VXzV27d9d9bL23XmOfLU8yve2c4rf4bvf59PP +c7tH8dZ5dZvf8p18yrM4nd/b95DTecz6GG+/97/is/eZ7nvIf8u773n1/V/d +j0+dn1G+me+a/9X2T6/3Ld+Vp79P1efOfr+VZzWvrL+u37aenHPOOee3+hic +c84557/mWb3d48z2F93ronrV9qv3yCyvapy+Fz/lY7w13lP7sFqvm9/sftu1 +37P8OJ/x3e/p6ee53cfyXefmbR7F6nf7Vs/idH6zvnt9b/dquyhuew9v8dnz +cHcenK+0H8t3f8+6/UV5detlPpafvj9k+Xyad2PXfot813c0ym/Wd/V32/pz +zjnnnN/mY3DOOeec/5pn9d4aPxs3utdl5aPfeh996nk/zcd4a767Pvs+Vfvr +7udqPrP5Rd7dp91zgH+3r56DT+f3ad4tf/t7//Z9Jqp/23evux5jnM7v9u/+ +res2hnPu7969Z2T9n34e/q5336vu71mfbV89d6L3Z9f59PT7XPUobvsevPX9 +HOufzi9b96eft1p/l5+eX84555zz230MzjnnnPNf9bfH797TVvs7fe/c7W/P +222+u98squ2r/VfbZc+b5beax9PenYe38uJnPFvvKE7nfat3z61b8p71KHbN +1ynP4nR+q9+vMW7Je9aj8u7z87/7ajn/bP+079nqc+1qXz2Hdt8jTt1vbvPs +d/f7f/p5Vu8D1XbZ7+68ZfVmvVvOOeecc/6rPgbnnHPO+a/5WP7Wvak6TjdO +3y9v8131sjj9nLvKu3F6X3fzmfXVdlG9rL/d+fDP8O57Wi3fld+neneePtVn +5+FWz+J0fru/u7fk/ZRHv3/NV8/9bv/8O3z2/M/az+az2m72nOjG7Py8NV+n +z+Xuc+/6Pq/m962+GtV7xi7fdQ/inHPOOf92H4NzzjnnnPdivG9l/VXzmO3v +9P3y130sj35HcTrvbr1Tkc1v9vxZf2/5bKzuL/6Z/tR50+3/033X+f1pvnpu +nvIsTueX+ey63O5jdO8Np9+Ht3x1Prv988/y1f2QxW3nxu77ydvRzeP2+f2V +79Wn+xjV70y3XVY/q3fLfHHOOeec3+pjcM4555z/qmf3pe69qls+22/UfrZe +NS/+GT7GU/2eim5et61L99zZff5k9Vafh5/11ffj2z2r92n7fSyvni/Vdqc8 +i9P5ze6b2fP+Fq+WR3Hb+/P2eRPVvy3vX/fu76ze7P7onutZuyyvt86Pbr3T +sXs+blsXvsdn39coZt+f6n57qt9b1oNzzjnn/BYfg3POOeec/9ur7Xbd22bz +Wh0nGu/0/ZW/498Sp+cx8+o50o3VcaPf1fGqcdv5/ite/U6cyu8tXy3/NK+u +822exen8dp/zn+JZ/Mp7Nf7+9XP1UzyL2fNndv1X71vffs5/SpyeR37Gx5g9 +j6rlu+4X3e/SbfPOOeecc/5pPgbnnHPOOZ/zarvofrar/6xdNb9qefU3/7tX +I5vn3f4p8fb6dN/f2f5u8yjvbruofbWcr/nq+f50fqd91z6+zaN6t5wvs/vv +lvxmn+d0Hk+f41m9T/PuPu3eF/gzPlve/X2rZxHt7+53s5rP7vxvibfP4Wr5 +7L3v1/2pdmN5FKvfo9Xz67b14Jxzzjn/Fh+Dc84555zf6d121XvgbH7VfnfX +7z5P9z4cxW37YXb/RLG7v7dj13sz+ux+5P/22XpjPLXuv+bROmRxOu+3vLpv +T+WXeRS3nQuz3+nT+XX3x+k8ZvP+tH3/1nvlO/SMd9tV9/Vtz/np/nZ/t8Xq +891yzq9+z6r9VNt38+re27r1o3pVn53Hbn+cc8455/xuH4NzzjnnnH+nR/fC +an9Zv6t57fo9m8e3+Gq7bn9vxe79/NS+ifLi//Yssvkd61X74//2bB2rv7/F +b8ljdT2zdrecC911uCXv1fLbvBqn9/dur353TuX36b56HliPZ/xUf6vn6dvx +1Dl52/l/+vsye395+tyKYnY/37YunHPOOef8GR+Dc84555zzf5VH98usv9ue +6zbP4qn1jLy6zrsjGzfLr9o+G393u26+/N++2l+1/6jdr/jq/D6d39tebXdr +3lHcfk5lcTq/1ffhdN5RXlWfbXfau+v2bc+/299+X7v58Xfbra7nbPun49R8 +zvZ3y/flNh+j+12Y3aecc8455/y3fQzOOeecc875umf13hp/tV3WPqqXtZ/N +Y1c+q+sxWx7lUZ0/vuZZvax+Vu/XfPZ9eyu/t727r27x2ffl7fc2itP5db9P +t3v0+1N91z5/Kr9P99n34HTev+rdc7b6Hr3Vb9TP7Di788nyqPpsu9V9wDnn +nHPOOX/Ox+Ccc84555zXPYu3xq+2+/M7+pu1y/qJyqOolmf9VfOo5pn9zjyL +7nPzZ3y1vyhuO6duPR/fyuPtc3h2/73tUb1b3s9vyft0HrPnXhS37WPn0rM+ +lu/ef3yPZ7G73ew+2LV/svyq43fznO23+jvz2Xan33vOOeecc875fwfnnHPO +Oec897fv16v9jX+j8qx9tTxrN9brlmfP1c2vmn/3uWbn4el8+ZpHv8fIyrN6 +3+K73oPb/JY8Zj2KW9+3LN9b8r49v6e+27f4rnP627y6vlE/WXv+jo/ls9/f +bH9U++2O99a5U82rml/2ezW/Vd/dX3V9b/lOcc4555xz/gk+Buecc84557z+ ++7Zxon6i8tl+s/az7TKP+u+O32236t18ZvOu9sf3elQ+u/+z8m/x1fPl6fxW +/ZY8Vs+TyN9637K45Ty/5XuTeTVO78vMu/vllrzf8rF89v7wVH787+Xde0bU +f3cdT59HT9+XZuc1G2dXf7vuOafO4eo5wznnnHPO+S/7GJxzzjnnnP+yZ/Xe +Gn+2v/FvVB71123XHS8aZ1d5lleW361e/Z3F6j7hPa+WR/W75d/m3XPklryj +uC2/7vydPv+iuC2/6Jy97VzK4tZ9Oftd/FafLe+er3zNq+VR/VvP593n0eq8 +zo6/el5X+4naVctP99d9fs4555xzzvl//+acc84555zHvqu/rP/ZccbyaNys +37fbRbHr+bvjdJ/nds/2X3V/3vI83+5ZPH0+3e6r+/cWvyWP1f331ntSzev0 ++/pp58nY/lbv7o9v9dVy/ox312Nsd8t58dS53T3XV/f37Dm5+jyz43Vj9dyc +7S/q97Z9xznnnHPO+c0+Buecc84559/k1fKnxt+db3S/z8p3tav22+0nalct +j/qv5hX1860+u25j3PI83+7VdlH9KG47r2f9054zKl9d1935ZfXfeh+qeZ16 +L2/NI/qd1X/bq+fet3m13ex3gu/13fv4tnvGU+f26vxE9XblVW23+7xe3W9V +n2331n3i9D7lnHPOOef8TR+Dc84555zzX/K3x8/GrfYX9VPtP+t3dbzZ/Lpe +LY/qP/U83+rd8u44tzznp/gYq+dLVn6rnzrPd/tteUT7cPz9tGdx+v07fY5V +47b9vnpefYqP5bPfz6fy+1Yfy6v3j9l1ue1+cKtXY/e5OttuNY8odn2XIz91 +z3hq3jnnnHPOOf8GH4NzzjnnnPNv8izevi/vGifLu9q+67Ptqp7lO/tcUf2s +XrV/Xiuvxu79/2selc+ek2N/n+Zvn/OzXo3TeVS/a099F6J83nqfTucxG6f3 +e3XfnMpv1aN6s+/L7vw+3VfbRfVv+35/qq+u2+w5uKvf2ec89Z3p+i3nfLcd +55xzzjnn3+RjcM4555xz/gs+lkf35t3jZ/VWn6M6fua7+zvtUXTX/Zbn+VTv +thuj+v6cfs5bfSyv/s7itvN9dp/ckl8Wt+Xx9D6+LY/T728Wp/dv9Xv6qR5F +9Vy57Xlu89X+dt9DeM27943VdTzlu74T0e/Ms/6r5bPjr87D6fXjnHPOOef8 +pI/BOeecc875L/p4b+62iyLrp3tfz8bJ+umO2+3vdt9V7+28f9Wz+c9itn/e ++33LOV712X11Ku9b84jqP7X/svGfyuPt8Xafe2/5avkt3j33bsn7U3z1Pa/2 +z5/1KLr3iU/1sTyqvzoP1eiOW22X1e/mc8v6cc4555xzfsLH4Jxzzjnn/Bc9 +ujd3y6PYlXc1uvlUn7s6b9/q3fJqO/6sW6e9HpVn9cd2t/steWTn9eo+r3oU +T++/6vhP7/e3x3trXb/9fYm8W++WvG/32ff7tu/ct/sYu86j255zt6+eI1F0 +v7vV9rPn+O79cMv6cc4555xzftLH4Jxzzjnn/Je92q567476q/ZTzbM7fubZ +OPzfHpVnv/mzPpavRnXdf8W75Z/qt+Xx1nxn42f5zHp1/Kf39dvjVfN422/J +Y9V3rce3erW8Gu5BZzyqd/qc+xZ/u9/VPLq/q9/lap6cc84555z/so/BOeec +c875L3u3/Kn7epZP1m4sfypP/m/PorqO1Xb8rGfx6+9l9fcYt3wnsvU7nV9U +/tZ4Wf3VfZON89R39+nz4pZ9tPv9vWX/j7/fei9u82p5VO/094P/z1+jep51 +251+zm/32e9Stb9deY4+mw/nnHPOOef8v4NzzjnnnHNej9V7eXXc2fIsj9X8 ++ZpHv7vtn8qP17y7zt7Lv8dt5371PVv9buz20+NF9VfPyWycp/bjW/s/y+Mp +Xy2/3W/J4y0fy7vfm6j/274f3+5jzNZ/Kj9e82y9dr3f3e/O7d9HzjnnnHPO +v9HH4JxzzjnnnL/vu9qNf7N61fb8GY/qZes9Rnecajt+xrP41fe1Gree79+a +R7X/1XMyG2f3/vqVfXtLHp+a31vPPzs/t53jv+pRvdXvfzZOtR1f86e+P93y +3XlxzjnnnHPO9/kYnHPOOeec8/d9V7vo3p/1u7t//oxH9arrODtOtR1/xrvn +xi15v+XVuPXc//Txqv2vnnvZOLv30bftz7fH+7b8Tj3/7L2AP+tRvdVzMhun +mh9/x6PfWftu/1G7rL/b5otzzjnnnPNf9jE455xzzjnn7/tqu6y/7N8D2e+s +Hv8OH2OsX63H3/UxZt/nqPyW51ydlyhOfw92fxdm5+HpfqN+dvUbjfPU93N3 +3qv75/Q+rvotebz1Xu1+/287Z3/Nx3Av+i1/6r3txux3gXPOOeecc37Ox+Cc +c84555y/71lk7Vbv/WP7rJz/pq/ur1N58//5a8yWf7pX463vQXUdnvLZer8a +t+2r6v3gbb8lj7ff46zdLefgr3pUr3vPeTtvfrdX99sYq/suKz89L5xzzjnn +nPP//s0555xzzjm/z8fy6F6flWe/V9t1++Xf5d39M0a3/25+/B2/JY9ZX423 +vgdP9yuejdv3w+o+eTqPt/22c4r/PbrnevWeMZsf/2yPyqv1o5gd96l2nHPO +Oeec8/d8DM4555xzzvk9Xi3f1c+f8vFv1H72N/9Nj+pV34tqP9X3JeqHz/m3 +ngersft7IMTf4u19dtt9afaeVD3H+JxH8fR3/1u+P/wdH8uj+rP7era/2X44 +55xzzjnn9/kYnHPOOeec8+/zbrusn2776m/OKx7V2/VeZP112/F/exS35NfN +uxq7z3fxG/H2vrn1PlOtd8t58Wle/R1F9n1eHZ/zGR/Lq/Vn62Xtb5kXzjnn +nHPO+fM+Buecc8455/x3PCr/8zvyLMb2WV7VetX8OK94VK/7vmT1qvuf13yM +2/MT4hPi1vtJVv+29/9TvBvZd7L7neV8xbv7sHqPqOaRRTVPzjnnnHPO+e/4 +GJxzzjnnnPPf8ag8+t3tp1tezauab7Ud50/4GN161ffl9HPe4tW4PT8hnozT +941q3HKunPYo3vrucP6mV9tFv7Oovlez+VX74ZxzzjnnnP+ej8E555xzzjnn +XZ8t//M7Gy+rNzsO55/oT8Vtz3nLPN6+bkJ0Yvd3f3bc286D3b4ruvckzj/Z +x+iWd39H/d02L5xzzjnnnPPP9zE455xzzjnn/Cn/8zuqn7XrjpuNUx1v7G/1 +eTk/4W/F6ed8yoUQ//+45b10TnK+z6vvx+x3Mypf/R5n+Wf1Ts8755xzzjnn +/Pt9DM4555xzzjm/3f/8jupn7bIY+6+2i9pn/WZ5Vvvj/A3fHaefZ9WF+Oa4 +5T1zXnEee7Tfd70v3fLq97L7HFl9zjnnnHPOOb/Vx+Ccc84555zzX/E/v6P6 +1f665d08unlW+6vmyfkT/lY8/TxCfHM4Bzhf9+p7kNXP2lX7ne1nNs/qPHDO +Oeecc875t/oYnHPOOeecc87/7WP5+LdbHtXP6u3KK+un22+WD+dvuBDic+L0 +ecF/08eYvbdV+41i9T4WebXf2f4455xzzjnnnNd8DM4555xzzjnnn+Vj+fg3 +q9/t/+m8sojy7vYf1c/659/pQoh9cfp95u969xzt3hu6MXufycpn71mz943T +68o555xzzjnnfI+PwTnnnHPOOeecr3hUXu2n+7s6/q7+ovbVfqr5ZD7bjvdc +CBHH6ffz2332vNr9nezG6vd/9n6RzV/Uzy3rzTnnnHPOOef8O30MzjnnnHPO +Oeecv+d/fkf1Z8d5O6rP9WkuhIjj9Pv5lJ+O7LzP8o7q3TK/nHPOOeecc875 +L/kYnHPOOeecc8455097FH/qd9sJIb4/dp0nnHPOOeecc84552/5GJxzzjnn +nHPOOee/5kKI9fjzfo3vGeecc84555xzzvmv+hicc84555xzzjnnXAgRxZ/3 +ZXxvOOecc84555xzzvnff3POOeecc84555z/qgsh1uPP+zW+Z5xzzjnnnHPO +Oee/6mNwzjnnnHPOOeecP+1R/KnfbSeE+P7YdZ5wzjnnnHPOOeecv+VjcM45 +55xzzjnn/DmPyqv9/Pldbf923Dbfu9dNCPHfcdv7+qnvfXa+R3+r/XW/J5xz +zjnnnHPOOV/3MTjnnHPOOeec853+53dUP2s320/WPhtvtt9qZO268zvbntdc +CBHHbe/rt/lsve53t9ou66/7vczaZe1X+1nNl3POOeecc845/5ePwTnnnHPO +Oef8szyqV+1nV/2sXjZON7rPEbW/bT35WRdC7Ivb3m/+jHfP0+53uhvd+8z4 +e/U+M1u/mwfnnHPOOeec88/wMTjnnHPOOeec/9uzetHv1fG740TjVvOZzSvr +57b15N/tQojPidvOD/5dPnsfOX3P2/W8UczmwTnnnHPOOee85mNwzjnnnHPO ++bd6VF7tp1uv2r7aT9Y+Gz8bj/MT/lZ8y3MIcSK+5f257fzjv+HZvWz2Hjl7 +z5ztJ3qe7rjd5+Wcc84555zzT/cxOOecc8455/w2j8qr/fz5Xe0/+tuNLL+s +f85v9t1x2/Odng8hborb3rfT7+dtz8d/27v358xn23fvt937dlafc84555xz +zm/1MTjnnHPOOed8l0fl1X7+/J7NJ8ur2l+339vWgfMTcdtzf9r8CfEJcdv7 ++Wnv+W3PzX/bZ+/dq+XRuNV8qvln7Wbz4ZxzzjnnnPPMx+Ccc84555zzVY9+ +d9tHf6txy3xwvuLdfb8atzz3W55FdP50XYgb4q335unxP8VXo3qe3PbcnK94 +t92u39m/OzjnnHPOOed81sfgnHPOOeec/653f3fbRe2j/rLxduXL+Rte3beZ +R3H6+W7xLLJ1eMqFuCFufS+juO18uW3+3vrucP6Gz97vs/em+++U6nd8th/O +Oeecc8757/kYnHPOOeec89/1P7/Hv1k/Wftuu6we5zt9LO++L7P9Zf3wf/tY +np1nb7kQnxi3vt9R3Jbv7b46z9V7ne8df8N33ddO/TuIc84555xz/ns+Buec +c8455/z7/c/vqlcj6q/6m/OOj+W734us3W3z8ekelWfrcspn4/T44jNj1z5e +Hfe0j+XV57rtOW732XMoOq+7/XW/E5xXfNe+694PV98LzjnnnHPO+ef7GJxz +zjnnnPN7Paq32s+f39Hf2f66efHf8LF8dl9H/WT1u+Pwns+eN1H5aZ+N0+OL +34hd+3513Ft9LF+9b/E579bb9d3fdW/m3+3VfbR6D1q9r1b74ZxzzjnnnN/n +Y3DOOeecc87v8dn21d/j325e2Tj8u311/6z2n43D3/VovT7FZ+PtvHaNI96N +2/fDrn1y+hxa9dPj87/76j05q7/7Hs6/w6vnxGq96ri33Jc455xzzjnnfR+D +c84555xz/r5Hkd3jZ+/71fxumyd+xrv7bLWcP+vjenbPi0/3LN7Oq/p+7R4/ +iu58/Vrctq92neOn9tW3ePX9fTsv/ncfy2f39e68+Gf76ns/ew/o9sc555xz +zjl/38fgnHPOOeecn/fuPT7qL2tfHTfqn3+3R3+jOJ3vr3u3fXU9u+fTLZ7F +Lfnu+i7Mfi+ycVf7646zO1bnYdd+2zVO9Xw+va+jPMa47Rzdtf+r87DrPOfP ++O56/LO9+t3ulnfPgdXvAuecc8455/x9H4NzzjnnnHN+3qv3+G69aNxu+S3z +9Ks+lmfrmLWbHZe/47PnRve8+FTP4vZ8nx6/Ou6sZ/Gp43zL/ozGe2v80/vz +U3wsr37f+Vkfy2ff/93l/Bnvnrvdczk7J6t5nD7XOeecc8455//tY3DOOeec +c87Pe/UeP9aL2q3mMdue13wsz+p12+3aD/xdj+pl7/u3eha353sqr2o+s57F +p47z7fs2yuN0Xr5X//bu94Lf5WP5rvOiOy5/xp+uVz1PT5/fnHPOOeec8//2 +MTjnnHPOOef9qPa3mk/3vv9WXnzOu+tg3e707vsWefd9/nQ/Pf6qZ881xtN5 +Vcfd7Vl86jhv7f9bxv+Vc2os/zbvtj99fvCaV8/9X933t3v1d7feW+d+VH7L +uc4555xzzvkn+Bicc84555zz/Pfu+3W3XpTHrnH4nGfrEbWv7rvZvPi7HtXL +3t9v9bG8+/sW75a/nW9U7+39/i3jnFq3t8ef3S+n8+3m0S3/du9+v/idnu3n +KKrtTj/ft3v3veye2918onGi+tV8OOecc8455/8dnHPOOeec8/3tZ/uJyrv1 +u571e8v63Oaz6/B0Xvw/f1ffqyjGfrL35Fd8jFvy+rbni+o9/T5l8Svjn1rn +t8e/df+/Nb9j/Lrvei/N9xkfy6vredtznPbud3j2nF2tn/VT/V313fPAOeec +c875N/oYnHPOOeec/4JH5Vk/Wf1d9/Qs7yi6+XSfv1vv0333fuBnfFc7/vfI +zpXT+e56vtN5nT5vsviV8X99/316vqvPkdX7de/ON7/DZ7/fT+d1q8/O5+x5 +FMVT94rd++G2855zzjnnnPMTPgbnnHPOOee/4FF59f4c1cvqz9aLoppvd9zu +70/zsTxb3+588j1enf+sfbd//vfyKG7Jt/s+V/fVqXyr+bzlWfzK+Kffx9vz +6t53bvPo9xiz5+aveVS+69ybzYv3fPVczNp9mnff/6fmb3bc7r1o9f50+lzn +nHPOOef8Bh+Dc84555zzX/CoXrWfXffyartdeUT9VNtV25/2av7V592VF19r +n+3zXe/lt3v1dxann2PWu/Nzep3GOP3d7Ob91Hf7qXG6+6jbbtazOL1fs7xP +57Xq1dg1P/w/f+8+b255vk/32e/prd+56ndh9/7bPY+z5d1z/lvPe84555xz +zp/wMTjnnHPOOf8mr8bb9+/sObJ+u+NH48z6W+uZPW/Wbtaz/nnNu+/lU/v/ +13yM7j6vtv8UPz1+9btQjVPfzdXv2lN5PT3+29+f1ff17bxW9/1tee16f6vn +UdYf/7vvOletw5o/9d2dzSOrt8tvab86X6fvN6fPb84555xzzt/0MTjnnHPO +Of8lz+7Ju+/fUfls++r41ajO4+o6PLW+3ec+vf8+zav7eLVfXvOofPZ9ue35 +dp2Ht+Ub5TfGbe/96byyuOU8PHUORHF6f89+R07ntepRvdXzKqrP/x2z389b +z8NP9yieOlerec1+FzN/avzV53/7PL/tnOacc8455/xNH4NzzjnnnPNv9qhe +Vv+te3m1ffa81X6j9pl316Gax67xZ8fp5vGp3p2fXfuNz/kYb50zn+LdfXzb +Od/dB097FvL6d/mp86G6r07nG+X5Kfmu+u72Y/BnfPb9fzqv230sX52fp76f +1fGfqjf66vlRrff0d2mM1XXknHPOOef8k30MzjnnnHPOee677uXROKfbZ56N +0+1v1zjR32icW/bT096dv6i/p94D/u+YXb9v9+z3bR7FLedENeT17/Jb9l0W +t+XrO/R3z+qNcdt58u2+Wv5UXqd99v3uth999ZycvXes1stidT6i/t6aZ845 +55xzzvl/B+ecc84557/sY/nb9/LVfrvtozyq5dXn2d3f7DzM5vG2z85rFKv7 +hM/5GN3yW57j9PxV3/fT+X7aeVNtt/tcn/Usbjmfo/q37NMsbsm3+x08ne/b +ntWL4pb3+dd99r0cf3/aes5+56v1Vs/D1fmsjrdrHk6dg6vlnHPOOeec/6KP +wTnnnHPO+S97VP7WvTzLd7Xf1fGzmO1v9jm685Ll8ZR38+nugyiP3fuU/93H +mF2nt/K9xbv7/XS+VY/itu/dpz1HFqfP893f77fOq9vznT0HxvJT+b7tUb3V +7xJ/xqN63fMkGue283x3+133jSyPar3ueFG7qmd5vfU9mT2nOeecc845/yUf +g3POOeeccx5Hdq9+6r6+2m+3/RireVf7q/afPVc2XjWPbr2o3eo8ZP3xd3ws +z6K6L295vqe8Op+35DvrY/ntnoV813wsv2Wfru7rW/KaPTfG8lP5nvLV9+u2 +9+zXPKs3+/2N2lfHzfrbXS9r352H2f6j312ffa9X269+B06fZ5xzzjnnnH+S +j8E555xzzjmvexRv3eO77aPy2eeu5jfbrprn6nizeWX9Rf1Xn+PpffTrPkb1 +fYnq3/Z8t8xrFLfk+/Q5HP0+7WP5p+Qbxel8q9+xbrvdPsavnG/VuCXf096t +l7XP6vE1j6K6HlG77vu1e1/M1ovO3+p5mI0fjTPb7y3n8BinzyHOOeecc86/ +ycfgnHPOOeecr/tYPntf7/ps+yzvrF71d7ddNn+r/XbzXB0nKn96X/y6j+XR +76z+7rw+3cfyyLvr8Sk+xuo8nfLT41c9i9P5fvp5MZZHfku+Vd+1z08/xy0+ +RnWes/6r4/CeR+Xd/b1rv6zm1W03uz+7+XT7O3W+rJZzzjnnnHPO530Mzjnn +nHPO/xXR/TLqp1v/Vz2K7v0+8m77bN2eiuq41efM2mXtn55PPudjZOtaXZ/Z +9t/qq+dN5Lc8X9W77T/l+5K1/7TnuCXfav6n9/Xqfr8l36fOtzG+9Xx7ysfY +9d3I6vE5f+o7uLpfqr/filPzmXmUzy3nwW0elVfrv5Un55xzzjn/Lh+Dc845 +55x/h0fl1X6ye+Xu++jq7yhuW5e3vTr/UUTtT8Xqfu7u867vfj9+xauRta+e +h7c89+3ene/T+T7lUdxyzld913f2lGdxS77d9+e2/d6d/9vy3f3cs+cgr/ns +emRxy3nw6b763ezug9nv7lvRvSeM9Wbn4Vu9GqvnxFPnVFa/up9vWxfOOeec +c/6Mj8E555xzzj/Dq/e/2XFW75VR+a76Wb1sHrI8svE+zaPYtc6norsPur7a +nv/PX2PXez1bj//7bxan833bq79v9Sxuy/dXnuP0vu6e22O903ndOh+R3/Yc +t/ps+6ifXe14zZ9a99ti17lx2/u3uh7Vda62y9rPjrOaV/c5d++L2/YD55xz +zjmv+Ricc84553yPZ/V29Z+NO9abzWt23Kj9r3o2v9X2T+f9KZHtx1WPyqvv +SRZP5//0PETlUXTPK77Xu+u663v0ad59f2/3sfxTv9dZ3Jbv7H67zaNY3W+f +5rPvj+/eGc/qRbHa321eje4+f2sePiXeOoer+7lbj//9d/U9iPrrtt/1PZp9 +/tn+Oeecc855zcfgnHPOOec9v6XeeO/r3g+zuGW++bv+LXHbvGbv4ep7utpv +ddzq+VXNg7/jY3n396d7Vm+M0+fELj89/qpncVu+s+fxp3gUv3KOOFc/07Po +7veo3a79kbWPxu+2u8W/JW6bV/6O7+ovO9eq59TseN1xOeecc855zcfgnHPO +Of9V39Xfar3s3jbWy/LP+o/q8c/01X25ut/fjtm8bluXbvmu8yc7d7rPx+/w +1f13y3M85VlU293mUb3qveKpvN763tyW7+y+PP1+dL8HY70sbnuOt+cpqn9L +vnztd/f7XI3Z7/rq+/vWub46P2/HU9+D3ePwM56tb/V9Xj13snrVqD5vtZxz +zjnn/Fd9DM4555xzXovxnhXdu6L6mXfzu23+fsWz9VndX2/7WD6b/1ORvW/V +8qjft70b3fMjq8c/w1f7G2N3/5/q2fkw+32+1U+Pv+pZ3JZvdd5PvwezHpX7 +Hs2V7+6ff5bPniNZ3PJ8o1fz7bZ/Oj7t+5TF7PnNz3hWb/d3vZrP6fOEc845 +5/xT/P9pt162ZFd1RQGe///q277sqSUJsMFZoU4NBw8JjMkag3POOef8r3nU +763/w6p1ZeH/vv/2sT17X7Pv5ZZ1r57TLLL9Wt3HLN+uerrf6ew6u+Nm2/m3 +ffVeWp3/13yM6nf1dZ89J0/XtepZ3FZv9XclGnfb97Trd/Gvrbt6D1efx/jr +9/xf913tY79qPdV+s9/F7O/BGN39mf0Oq571u+V3K4ruvdQd99e8u0/VOHVP +vZ2Pc8455/wrPgbnnHPO+V/17P+lp/4/q/6fls2bjf+V/wdP79stvvs8RtH9 +PrJx0fzV/N35Vr/Dpz16HuNUffxdr57zcfyper/iv/67mMXsPXybZ3Fbvavf +9envZtbHWO3H/x3de43/hkfPY5yue9e6Zr+Dal1ZfVl7dd3RfFXfPd/bvmvf +dtd1yk/t21vf+9P5OOecc86/6mNwzjnnnP81H9vf/j+sm7e6jsxveQ9vrfdr +PravnrtqHbPnM4qn2rvnJBs/61GdUX2r+89/w6v3YPSc9ftrnvUbo3uffcWz +uK1e6/vv9tu+s9nvMovZ7/qvePdey+Z5ul5+t4/tq8+77oXZ9u59Ons/7Vpv +971knsVtv3OrPvv7+XRdXX9qvad+T/3+cM4555zXfAzOOeec87/mY/tT/2+t +zhv1G6O6/qf2bzVuOx9Pn7OnPHtePYfR/Nl8Ub+qR+2r65wdx/l/+a7v9PQ6 +bvfZfmN8xaOo3m9f9Sxuq3f197E67is+xq7v+q/66u9IdRznO3xsz6L6u521 +z34H1fGzvru+qmdx+nfxKe/G6nnL/Kl+u85h11fbOeecc87/io/BOeecc87/ +7av/h2V5sv/Xsnmicdl82TzdfLvrvM27+7b7HFVj93mdrW/3OeiO273PT71P +/ls+xmo//n//GU/fV7f56fyn1x3FbfXu9tPf3+7vbPZ3+K16v+rVfdz1fvjf +8Opz5lm/p34Pn76vdu9zVMdTPtt++ndx1md/Z3bt69N1Zr46vvq7wznnnHPO +//3MOeecc87/7dn/Ubv6ZR71i+rOfPb/w269q3U+5d06V9/frI/tWX278jxd +d9b+9Pl5+j1Gceoc8Z4/fb+dXt+v+Bizv2tf9939Tnn2fqPxT/9ePO3V++K2 +7+/p7zjrf9s6vuZjdL/HXz+Xf8Wf+p3I+u3O071Ho/ZsfNWz513f66nfsah9 +9T295d37LfLu79quOnefq9n7YjU/55xzzvlf8zE455xzzvm/25/6P6w6PuoX +zZu1z/5/uFpnN1/Vu/Xvfp+7z8UYT+V/aj1jexTd/cjmy/JkXj3Pu/fj9Ln7 +q77rPc6+1269/N/tY7/o+Vd8bM/25a263lp3FLfVW70XuvfD6e9vt4+x2o// +27u/U91+3XuZv+Nj7HqPka/+DmfRXdfs/dmddzXfU3nGOOVje/d+2u2r57la +fzd/lKc6X7f+rt9y3jnnnHPOv+pjcM455/x+77bv/r/hr/8fEvV7ap+jv9l8 +UZ3Rc7W+rJ4sb7d9dp7ZfXvLq3Xuyj9bz6xH82c+O+6t+XZ/j0+/97/mu37X +Mt9VL695FLvvn6/66u/ord6910/Xu+pRv9V77qs+tnf737KOX/EoVt/bXz3f +b/9urt6Xs+PezvPU/bPrPI/9duWJYraet3xs7/4+zo7P5pnN1x3fHdedb/f9 +f9s9t+v3bPe5e+p39vS+cc4553zdx+Ccc8553avtq3mz3/HV3/8ouv9fdPOM +88yus5r/1HmY/b+tei6y/t26qnV256/WlfXrnsvTnj2/5d33tuteWb0nVufb +Xd/qOaz2q9Z9+ly97WPM3ofVeavjb9unr/vs+G77Vz3rt/r7fdp3x23r+8r/ +DW/52J49/9V9Ou2z46OYPQezdfyar+7L7L28+55/ar7V8zk7X7TPt9xbWZ1j +3OZR++z7zeaL+j31+1Yd99R3UD23b3tUZ7fuLFa/02o89Z0+9V3cdh4455zz +L/sYnHPOOc99/H3dNV+3X/f3P4usju580bzV9WfzRO23nJOuV/9v2/3eV2PX +eY76n/o/eXZ/b6kru6fe2pddvnu+1Tyr7d3nX/fZfZt9v9X6qv34Xp/tN8Zf +89P531pfFLfVO+unv79bfAz39d0++91meWb7n96Ptz3rt7u96rPjTt+Tu+e7 +/X6vPt/qWUT7P3tud8fu77263tt8bI/iqd+JXeO79WX5Zt9vta7u+K+dK845 +5/wmH4Nzzjn/i9593t1vdVz0tztf1v9XPduHt+roevf/vLeieg5nz/Mpz2J1 +vbu8ei5258/qGeOp73a2X9Wr7d06uvOuntvZ81HtP7ve1fl23Z/8HY/6zd6n +Uf9f8d37fptX643muWUdVd/9vdz2fT99Xrvn5/Q6+H//Hftl843x1vnpPnfr +7vru380sT7e+rlfX8dQ98/b5H+O2ezaKp97/Lu/uwy2x6/58yrt1R/1+1bv7 +MHsvVs9Dd96n5j99bjnnnPObfAzOOef8L/ru39vu72+13mz+bFyU55b38Ku+ ++xzcHk+fu6fbZ+u41bPnp/J093u3Z/2q6+vmyfLfej6qPnt/Vft330t3nmxe +foeP0Z2nOt/tnvXb/X3f7lncVu+ue/av3mfVcd3+/C4f26vPUcyO647f/fv2 +tq9G9j6zOm45f6freivPU/sV+ey+dtu73j23p2P2PHXnG9v5Mz57D8322/Ud +r66jWg/nnHP+F3wMzjnn/Jc8al/9fXz69ziLaL5sXv7bfls8td7ucxan/x/f +7afusVWP6tztUR3Vc5XVn+Xb3T773VSjOm72O13d5+p75Hd7do5X27/qUb9d +3+Vtvuv3e3ddT/vq7+Qt3/FuH9uz5+7vBb/TZ9urebJ+Uf8ouvdWVk91/u55 +X/2d6e7navtufytPd/2r5/krXo1d3+nu7+mWOLUP/F3ffR5P32PVum67tzjn +nPMnfAzOOef8lzxqr86z63c3q6tbfzR+dR5eez71nrN5q/Xsiu75f/o9VfM/ +9Z2f8tP5M4/63fKdz3rUPrsf1flXvVrXar6sX3Ye+N/y2d/lX/dqe3Xcbeub +vY+ieW5ZR9dX3+8t3/FbPsZqP/6b3r1f3j6fu++T6j1Yrbs67muePd/mX6v3 +6e/nrfzd72Q1qvsw6911zN5r3br+us9+/9V5svm657/7+zv7fe+qg3POOb/R +x+Ccc85/yaN463c3q7e6nl39b3s/s++zuq/dfZyt6+11d8/70zH7PTz1f+1b ++W7z7PmrPrY/5Vm/2Xsjm+/t+3pX3tVzV+3Hf9Or46L+f8WjyPY1G/dVz+K2 +emfXt+s8/FUfY/Ue4r/l1e+rOk/1HM7Os3r+s3FZ/2r76fca1XdLXX91Havn ++K17YPa7ejpm82fn6S3vjn973Gmvnv/dz7O/F7vvt7fycc455zf5GJxzzvkv ++dj+9u9rdXzUL5o3a7/tPVTrG9uzfrvresqr7787LsvXHT/2y9q79fA5nz0H +p+qtetav277L3zr/1edo3qpX66meu+58nFf6RdH93n7Nq+2r89zi1XWO/b+6 +7u730J3n1z16HsPvGX/Cu/dad77Z+6Fa32y+6vf39Puo1nP6nHS9+/5O1/vr +Pka1/an3mNXRrW92vlOe9avu/+66nvLZ95nNd+qe3PU7yDnnnH/Zx+Ccc85/ +yaP23b+jq7/P3fFjnP79r9Z32/nYte7Z9c++9+65mq03es7GrebP5v1Vnz0H +p+p9yrN+WWT72p0nq2f3+33rfI39smfOVzzrl/WPnv+az+77r3gWt9U76933 +fvr7ftvH6N4bt6yD/7ZX20/VuWu+6DmK7vdc7XfLe3/6fVXP2el63/Yosv2q +jpv9jt96X2N71aOY/d5v9+69+HRd3X3etf7Ve/6p38fb7hXOOef8CR+Dc845 +/yWP2qvzrP6+Vsd380R1P7UPWb7Z/Ld7t32Xr44b+3XHZeOr/aO8T+3bru/x +ad/1Xk6v47RHMXu/z56n1fk4/2Uf26sete+a/yve7bf7Pbzt1fcdzXPLOqpe +XV82723f/Vv3StRv9711y7o53+m7f0+q32H0XJ23Wueve9Yvav/KOqrnY9Z3 +j9t1bqt5ZvPt8rfyvOW777nu/bq7zmz87Pnt/r6s7gPnnHP+iz4G55xz/hc8 +6rf797U6vptnjGod2bhs/Ox6d9Wx6t32t/8fWz0/s3VE+avtu8Y9tc/VvLP7 +nPWv3kPZvN16/7p3x89+n6t1cv6LvnrvR9H9HfpVH9urvze3raP7/qPxX133 +7O/Y6e/7tGdRvYe63xfn/H/bo/7dPLvr/Gs+tkfRfZ9R3tX3260n86zfU/u1 ++p7e+o527fOsn86f+a57afY8zNbV9VP38FPzcs4551/0MTjnnL/jWcze27O/ +A7ftzy2++rub5am2Z+do1/utrqe6H1m+Xd7dx9P/d63ON8au+VbPa9Vnx3W/ +t+776H6/Vd9VT3Uezjk/5VF079Vd9++v++n8b3sWt9X71Hu97bu/xceo9uuO +55zzWzxqr84TRdSe3aur9XTXleXPvDqu2/7UuLFfdb6o3659XPXd/d6et7rP +s+81q2e2rmye1e/39P142sdY/U5n77Fqfs455+/4GJxz/nWP2lfvzdl6ZvPO +3tvZPFlUx3Xru+2cvPUeV8fveh9vnZ9ontn+s/tz2qNYzfPU+YzmybxaR3e+ +2XxVX/2+ovkyz+a97RxzznnXo+dofPe+3/X79Wu+u98pr56HsX827pb1Rd79 +Xm777t/2sb06T/Q8Ox/nnN/uUXu13+hR/6f6Zd7tN1vf0+8j8ur7WK3vqffz +lHfXmfXL8nf7Vd9jNu/q9/XWubnlvlv9HiNffW/VfFHe7ncazTM7/1P3Wzbu +lnPCOee7fQzOOf+6j+2z999Tdb61zqx/N2+WZ1f+2Ty3+Orv8div+n6r82bj +385bne/0/0uz52J3/l3ncHX+zKv1reZZPV+754/G3XqOOef8aR/bo5j9Pfmr +nvW7rd6n1v12/rf9lu/4Nq/GOH723rpl3ZxzvupRe/RcjewerfrT81fXv8tX +83Tn31131r867ikf23f3qz5n/U7ljero+i33V+bd9ixmv+tuPd26quOq9eze +/27+rK7Zejjn/FYfg3POT/mu+arPu+abzTtb5+y9/pXfgWr77ve827O6xufZ +85Pl3xWz69y1rlMe1X2qrlvXP+vVc9y9x6rjdn/vs3k55/xXPOrXve+rz/zf +fjr/Ll89L7d7t53/O3bdG7esj3POT/vuebt5u+O6eZ/ex93zvVV39/1U13/a +d73Pav7VeHtdp89XtY6of/X5Fl/9vmbv79n+u9/D7Lno+un7knPOu/c955yf +9uw+695v1Xm746rzduevztsdz/87bqlv9nw/Hd1zH/mp/3+q7dX+T3n1/T/9 +f2HWfvq77X4Pu87f2++Fc85/1avPfK597HfbOmbXHcVt9Wb7Xo1xntu+41t8 +jFvq4pzzr3r1nu3Ok82b5Tm9L9V4+72c2pcouvv4tlfXNfv+n4ruObntuxjH +8//26vnM5p29z6vzVc/B7O9D9zu97feCc85P/55wzv+ud8dX56/eg9183Tqy +cB//pkfRPX+r+Z6OXf9vRPNmz7vug9lxp/10/szH9lNebb9l3zjn/Fd9jOwe +nu3/Vz16D9X+T9W1y6vn4+26uv70e/yrHvVb7f9UvZxz/le9Ou62um+t63T+ +qlfrj2K2f7WOqF/mp+Lp99Otg3/TV9/3rvu0O756P2d++l7knPMxOOf8aY/a +q/fV0/djVmc3duflf9Nvi7f2YbY963e7V/frdL1Rfd17r3rv78pzet845/zr +nvWL+kfx9vhf9ai9+p7e2u/V9z327653to7d+x6NP/193+LV2H1/zN57nHPO +/+3de3/1/s7yZ3XM9n97P7O6b6m369Vz0X1vT/ltcWof+B0+e+/Nxq77dvd9 +0a2Tc87f8jE45/xp78bb9+BqXVG/2f1zf5/xqP2p99yt61S8fS5X9/92z87N +bfVmPlt39fvZ9Z3dtm+cc/4rPjs+itn8v+67xu+ef7Xf2N6tfxw3u/7VdVX3 +ddf8v+5ZrJ6T2X6cc87XfPV3IerX7Z/V0x3/tkfPWb+v+BhPnatq/lujul+R +r+7/U3Xxf3v3fc22Z/NX4+n74pY6OOd89p7mnPOnPOr39j24WsfYPts/Gnfb +e3vKV/f1V37nVs9f9XurRjfvW99vdx++4lGc2uenPftef/U9c875X/HqPZ71 +z/JmkdXxVY/as+fRu++5O89sXVm/ah27ztVs/dX22e8mG/8Vj+LpczV7Pjjn +nN/hY4z9f/Wer+5H1H7LOmZ9jLf3OatnNbp5u+//dl99X7+2H5HvWueu5+73 +1B2/6m/n45zz7D7inPO3PIq37sGs3ur4av4oT+a3vbfZ35db6n3bd53favtb +ses7+ms++75P1cs555y/4Vm/bv/deW71qL37PHr0txuzdUT1dPOsjs+ie06r +/brvJxt/m6+273rmnHPOf9Gjfln/U/V+zU9Ht86uz477Fe++99P1Zr67XzZ+ +9jt6+7u97V7hnP89H4Nzzp/2anvUb/W+y+rN5u3mj/Jkfsv7md3P3XXd5mP7 +6jntjtv1Hrrtp9b7Kz62d58555zzL/nYHkXWHvXLnlf7fd2z9xX1m33P2fzR +c+ZZnlvq7O5z5Ld9x7vvg7Ff5tX5onlW761b9o9zzjmv+Njeff4rPrZXvdue +5Z8d//Z6o9iV5zaP2rN9r87ztO/ul41fzb/rfEex+3vinPNZH4Nzzp/2LLL7 +6ql7sDq+m2eM6n6t9ptt7/5uZO1f8bH97XPXnW923ih2fa+j79q3br63PYru +ek6vg3POOV/xqN/Yns0XzbvLZ8c/Pf9ur77H6rq756JaX/ScxdN5V/c5Gld9 +H29/x9V6d8+/y2frzJ4555zzL3vUb+wfxel1VOupjotidlw2X1ZvlCcbX923 +1XPw1L581cf26v5X59l1Tnf3y8Z3z+Fuj/JG7afvZc753/UxOOf8lEfx1H0X +5cnm7eaP8lTzRs9dn61vNt/bfvr3dLXuyHf9rq+2V707btf31f3us3zderNx +1TpvO8ecc875Th/bs/Hdecb+1efuuCx/NG83b7X/Ls/eY9SvOq6avxrd89Ct +c/Y8dPdn1bt5x/5Z7DoPs/Puqiub5/T9yDnnnD/pY3vkUXvUL6sjG1fNE7Vn +nj1nXh232l4dV9337rpX93m3n86/Wm/3XMx+z1m/3d/D6nmL5tt1v+2el3PO +d/sYnH/Ro37R+Y/mq86f5evOz//tWb/Ze3B13m7+KE/0vLvf0/W/7d33+/bv +6e48T9Ud1VttX70vZ332/5qn9jWrN4rT55Vzzjl/06Pn2Xmj9qjf7Hy76tvt +T8+7+n677+WtmN3f1XOx+1xFda76qfm665w9n7PjOeec81/yXeN3edavuo7V +urKo1lndz6y96k+fi6fee+ZRPW/l33V+u+Oj/a/u02y+1fm65352fPc7vO3+ +vcXH6O73rvmjftW6OP+ij8H/po/t2Tm6pf7q+a7W3c27On+3/mrc+r5mPer3 +1v2465xl46rRPS/ReejWuerd36Oo/dTvZtT+1Pf/9nqqPjtu935m0T3ns78P +1XlvOcecc875TR4978oX9cvq6PaPojrPWz62z47P+nfH3xLZvmT9Vvf19HlZ +Xf9s/933ye55Oeec81/0qD2KqD2aLxqX5cliV75Z3/U+ZsftrmN2P3fva9Wj +fk+d61mf7Te7v1FU81Xnma1/t7+d7+31VOPp/NX7Z/W8V+t86/7bff5uO2/8 +rI/B+X89z56j2Xp2/+5Wo/p7sppnnC967tZVnf+W87bLb/l9zc7D7vf4dD3V +umbznf4dnN2ft+p6ep27fPd8s3m67av79tTvKuecc86f825080TjM+/W/bRn +dVXH3x6z73fXe1/17Lx0z181/2yc/v4555xz/r+xuz3LH80TRdY/q6vrp/d9 +dh93+2y/MW7x6v5V562+39k6s3yz5222ntVzsnrOb7k3d33vu95jdVwW3Xu2 +ep7G9tX7cNd9Go3vzpvVecs55Hf4GPybXr1nZ+/Fp9bR7Td772X5ovy73sfp +56zO1d/p0+c/iu55qXrWL6pj9Tvtnvfq+Nl6sv63/d5139/sd74rf1THrnMb +PT/lq+doV92r5+DUueCcc875//rYHkV3vmo9s/nf9tn6d/nX4qn9qL6P0x61 +7/oeovlmv/tb7iPOOef8F32MsX80fnX+at5sXHfe3Z7V8bU83X2sjrvFo6ju +eza++pzl79Yzu97sede5rX7fb/vYnsXsPRS1d+va1b87PhsXzVPNX31vs/fj +qlfryuLU7xR/18fgd/rYXv2uV++fXfdF9bk7bvb3Osq3q95f99mYPa9v++p9 +Ovv/wFMx+/9Rdfzq9/i0Z3VG8Xa9b53PbP5bfbb91nPJOeec87qP7VF026t1 +zNab1fXX/Pa4bb/e9l3js3mr38vqPXHL/cU555zzvD16HqM63y2exa79rO7r +be852q9bfPY9d/s9HbvXu+t8nvoed+/7Lef1lK/e77vO5+x3t7rO7jxR+2wd +t3xfvOZj8N/wrN/sPTX7vWfzZXVW5+/et9W8/Bmvxm11r96zp2P2O1u9B075 +2B756Xq79+Lu/wOqvwun74vZ9377++ecc8557GN71H92vtU6b9mn27za/las +nre/6mP7U99hNe/seeOcc875Oc+eR49i7P/1da56tG+37kvWvzrutHfPQfV8 +n4ruebvlfK3GLefpV707fmzv/i5k41fr697Ht/xO8Lt8DH6nR+2r73f1/4cs +z9O/n841/y9fbZ/Nd3s8/ftSzbdr/rF/9nyrn87frWuMt76jp37HOOecc36P +R8+z42fnicZl85zev6e8O666f2/F6rmp7suvePb+du1bNG/3Ppitg3POOefn +fWyPIuv3Vt2n83f381bP+o0RtWdeHTc7f9W/ErveczVPt53/LV/9nlbv99V7 +LLqfZ9f51fue/98/g9/pUdxynqJ6uu1ZvP3/Gucz/rWY/a525cvqyOa55R5c +vTdvqav6f0N3XU+999Xv9vR+cs455/x/PesXtUf9onhqPbP1jPPt7v/0emfn +2x3dcxP5W+c8iqfPQeZvrbfbPntvcM455/y8z47P5oui26/7/BXPnr/m3feZ ++Wx09/ur0d1PzjuefdfV774as79HWfvTfksdfM3H4Ge9O+5r52bX/02rdc2O +47/p1fMUxez5OxW33G+r/3d91Vfvy6/5GKv7Ue3HOeec89/3KKr9b1vP7d4d +F8Vqezaue16i8dV5ec+j99L97m9ZD+ecc86f86jfGN1+1fFf9azfbfXu9rE9 +6n+qrtuiun/Vebrz8b/hs99RNl8W1XswG5flP3WvReNuuY/5v5/5b/jb52n1 ++8/GVftXn7PxfM5nf/+6sfp79LR3/x94K776e3xLHU//3p6ui3POOef8Kz5G +1L/aj/87ns7TzV+NMe9sXV/Zz1/z7nm5pW7OOeec89s8ah/jlnpX/ZY6dr2X +tyLLn52bt3z3vlXfXzaO93x2n2fvr24d3frevjdO3198j4/Bz3p13Klzk9VT +9Wqeanu3rur4r/rs+Nn3MJvvdl/9PmbnXY0sT9Qv827e0WfzftVXf39vWQfn +nHPO+Ve9+jzG6bpnvbsfT3mUd3VcFtV5Z9fx1PuK8j2d/2mvfme31c0555xz +/nXP+o1xut63vdsvitV6svlmY/YcZO27x93u2XvLPHsP1bhlP3b5rvspmy+K +Xffr7nmr+brn7un6eM/H4Ge9Ou7U+cjqyTxq3/1/SveevNWr76f7+37L+k55 +tF+r57g6rlpXdVx33mqeaN7bfsdO+679PL0OzjnnnPNf97G9GrP5q/Psyve0 +Z/VWfXXc7Hyz5yXLd+t76p7DU9/L7DjOOeecc/5vj9qjiNpPr+N2j6K7n915 +o7qiftl82bhqvur83XG/6rve9+66nvKnvpvMq/PMfu/V8U/f59Vx/KyPwe/y +28/H6u/07PhqnU//7nf/H1n9XaiO+ys++/6fOseR78o39utGdd7ZeyJb92qe +0z7bPsbpdXDOOeec855H/W6r86n1Rs+zvjpudr5d+5TlPf3+dnv3u+Ccc845 +53d61i+K6viv+hjZesd+3VgdV62reh6646J8u/ytPF/z3ee3O29UV9e799Bs +v+481bpWv7un/ZY6+L99DH6nR/H2dxzlf+seiPJnvnpPr76v2f2p5vs1X/2/ +Yvd52/397K5jbI9i9r2c+p16K8+u388oTu8j55xzzjnn//IoovZZ3zVfFqt1 +rO5rtb7bzgHnnHPOOf8bHrVX45Z1ZD62P+VPz5eN77ZXz8Nt+z/bfupcvO2z +/Z5+z6v1rfabnbe7/tnxt+fjz/gY/E6P2k+fm7fvjWh85k/d52N71q873694 +1i/6G/Xb7VnsPqez8+0+N7PjnrqHsvp27+Nqe/ScxW3/B3DOOeec87/hUfsY +u/yp+Xbnees9RHHL+eCcc84553/Dx9jVr9qePc96Nn/mWb/ufNX9jHz2ve46 +D9X5qvOc8t39vuaz7avnMMv71nuq1lU956fv7dn3wu/wMXb1u+3e+VWP4q1z +szrvqft81+/47Pe1a12nfPY8nv696Na5K8/u39vq/LPjnj6fu7//1XMVPUf5 +Mj/9u84555xzznml39gejcu8W8dqnix/17v7tOs9rM7HOeecc875kx71y6I6 +vurd+bL1dfN3x6/OV11HdR+q46p1Vb06/ymfPddP17XLZ89HFLvOZ5Rv17qq +42fP89P38Bi3/B78uo8x+z09/V6r80Tjnv5d/Gte/R2P2qterataz6339uw9 +3P0Oqu27ffX3N5rvtEd1Pp3/9HqiePo87Zqvu5+76nnq++Gcc8455/xJH9vH +yPrt8izf7jxZ/q5393mXR/Wt7jPnnHPOOec7PGofo+qr/cb2ap2rda+Oy3zX ++5sdt7uO2fOze19XPerXXd/uulbP7ex32D0/u/bjqXto9X566l6t7if/d6ye +z9336lN1ZvM+tX9Zv+j51z1qf+v3dPV+Xr23s367fneeqn/1Plj9Tm+7V6v3 +ZHff3/o93fUdPX0/7PbZftVYrXN13277HjjnnHPO+W951K86TzTfbs/q2J0n +y9/1Xfu9y7t1vFUX55xzzjn/W77aHkXU3vUsqvVk43f57veUPT/13p/Ok80T +9b/NZ7+DU3XNjo/e6+r6q/m7vnr+dnnUfvref8vHOD1fdZ5s/tn8u+eLYvV8 +Rj57vmf7f8Wj9t3nI8u7697O8lSfu+Pe+n2p1lHtd8t9u/r7FPnXfzdO3zNZ +zH43o+/uf2rfbvtOOOecc875N32MyGfHPe1v53kr/+lz0d2H6no455xzzjlf +8afzZXmzfqNX+0f9ql6t5+19W51v7Lc7z+739xUf26vvYTVf1K863+z9MJs/ +G1etazbPW/fZ1zzq1+0fRXe+6vNqntn7J2uf/R5n5z/tUaz+bkf9b1v/27+b +Uf7Z+yrq360jy7cr7+y81f2/7X7e9fvU/R5P1fuUV59P+1vz/cq555xzzjnn +f9PH9tn+pzx73u1ZPL3O6G/U7y3v1nm6Xs4555xzzv/Lo/boeYyoPfNb1h/F +qbpO56++z27/W31sf/q7eWpcFru/89l6nr7Hbvludu9vdZ5q/9O++37ePf6v +evc77nr1ezntY/vq99+dv/ud745dv1Pd8dG42+/5Xb8Lp+vKzt+p/LfdD6v3 +yfi8+/eSc84555zzm7z6fNrH9rfrzWJ3/uw93nKOxrilLs4555xzzme8Oi6K +2flu9Sie3v+snlv2Jas7GvcVXz33s9/TbB274un9iXzX/XTL/TDrs+fkr/uv +3kN/zVd/B5+ur+uz98ht8dT9tfp/0S0+xi11rfrq9/j07+6t90DUb3Udt5wL +zjnnnHPOZ8ZXx0V53vKs39v5n8qz672+5VH70+eWc84555zzJ7w6rtv+dN2z +HtV5qq6v7mPm1eev+K73We3/lejuyy3nNKszi1vOJf9vv6UO/q5n/Vb/P1j1 +X4nZ37/bPYrV35fbvPsdnK43qqPqb33Xb7ff9l4455xzzvlveNQv6z9G1H6b +Z/3ezv9Unu77vtWz6J7b29bHOeecc85/w6P2qF8UWf9s/qfW0/Xb30vUfrre +2fWNUT0n0bjbPKu/+53dGqfP0e57i/+m31IH/xsu/v+45Xd3dp7V9q/42B75 +LfVW61z9naj2n11Ptz7OOeecc85P+NgeRTZf1P8Wz/q9nf+pPNm6bjl3Va9G +1v/0OjjnnHPO+d/2rF91vqxflj+Kbr/q+NMe1Zk9f9W77V2f3efdLv7/OPUe ++N/yW+rg/Bfj9v3s/n9aHfc133WPft2jfrv6d/f7tv3hnHPOOee80i8al43P ++t3ip/Jn8fY6bzuP2b6tnsvb1sc555xzzvm/ImuP+kV5dvX/us+OP1XvUx71 +y85bFtl5ftu/HrftJ+c31cHv8Gp7Nf7q/X/be539f+H0/zdve7f9dL2cc845 +55zz5z3qN9s+xtf97Txv5T997t4612N0z/HpdXDOOeecc86f96jf2D97/is+ +RnU/b6n3q1E9n5nvyjubn/+m31LHV/yteVd/73bX95aP7V/5Xbj1dzTzW+q4 +1e0f55xzzjnnPHsevRrdeqI6nvLZ9WfP3X5RVPe/mz/z2X17yqvjspjtd/r7 +5JxzzjnnnD/vY/vY77Z6b/Fb6ui+3+h9n47Zuqrn97SP7d3vLhq/69xkdfD/ +9lvq2O1j++y5qc7XHf+r3m2vvp9uvt0xW//u+2zXfKd/32/1sT3qf0u9nHPO +Oeec8+c9eo7GV+fLIsv3lI/t3XVn81Wfs3grb3X8qXMaRfccrvbjnHPOOeec +/65H7d1n/t/ts/NG41fny/I8Fdl5yvpXfXbcr3j1++5G95xn8/yK31JH16vv +afXcdev6dR/bd93rq3lW862er9nzdPr3/q/5rnN4eh2cc84555zz8x71i8aN +kfWr5o2ed3nWr7vebp5svqfzdte/er6y/N3zNntObvveOOecc8455+c8ao8i +aj+9Dv5//4zZ9xm1z+afXVe1rlnPYleer/qu5+ycdOu6zd+eNxq3+n6y+XnN +o3P/1n0/+7u/+vuy+x7fXW9Wxy2/36f/bxhj9txl/W5ZN+ecc8455/ycj1Ed +X21/ev7VdWT9quvr7kN13Op7y/JU17ta52x9u+bP8nDOOeecc85/37vtY7/q +c3X8X/Moqvv+1HxRe3Q+svlXz2HmUb27vPr++L89O2fZuOr7eOu72v09Rf1m +943v8afvrdV77qnf/W4dUTw17tR72VXfbb7rd/X0OjjnnHPOOeff825055lt +r3p1vVn76rxZndXo7ldWZ3cfuu1d7+5jtZ7VeTjnnHPOOec88rE98uq429aX ++Rir+1T11fqy+bI8s+cjG3f6nK56tb636/or/tQ9Vc3bzdeN6HtZ/a5/3Xe9 +r1t+f1bHjf121VHNUx23Ol/1e9n9XrI6s3p31bU6f/Q8xu7/GzjnnHPOOee/ +52N75uM83TxRZP2766zOPzu+m//tqL6f6vua3ddsf2bzztY1tq+e59u+Z845 +55xzzvl+j9rHyMZl/aP5q/V0PesXRXc/dvtq/ixm32+2j7PjorpW6zjlu9e/ +q66v+Wq/sX33vZLl2XWeozx/1bv31+nf12o8lefte3XX79fT52f19241f5an +Wmc1/65z0u3POeecc845/zs+tmc+zhO1d+fNYrXuyJ8afyqy9zz2m/Wn3kcW +2Tzd9VfPczUv55xzzjnn/O941C+bJ+oXPVfn664j6letO5qv6931r3p3XHV/ +Zs/D6jmZfe/Z/Lf57n6/6rvO4Wx7Nc+ufmPc8h52efU9rr7P0/50nrfqrvrs +uNvPf3efdv9/0v3dq47nnHPOOeec867vGl/16O9qHVHe1Xqf8rfjlvV/Jd/b +3xHnnHPOOeecjz7Grn5R/u74ah23+Op8u9/r6nynzuNtPrZn68rmvW19q57t +29hv9n5YPZ/ZPNVxY9zuq+u67Xere+/tOm/d+W+7J2fH7c4fxdPnOZo3e59Z +Pat17fo94ZxzzjnnnPPMq+PequP0fsz6qcje09f8rfeUvb/bzhfnnHPOOef8 +Xs/6jRH1j/pV59vVLxq3O381uvPN+q7zMTuue95W51udP5rvtFfHPXWeT/vq ++lbPYda/e76i+U97d9xT3/HbnsUt9b413xirfuv9M/v73Y2n6tz1e3H6XHPO +Oeecc86/56vPu/3UfoyxWn80z65Y3a/q8yl/+pyfqoNzzjnnnHP+ux61j1Ed +F42vzl/12Xi7zlWP9n3XOYjiqXN1yqO45T3P+tievYcsblnf7vGr52bXvdEd +v7uOrP3273jVT+evfp+n9+Upz/q9fV+Oz7vHveVP3X+cc84555xz3vVb6jjt +2f6cimqdf81vqYNzzjnnnHP+93xsP11ftX3sV33Oxu/y0+81qu+p83Pr+qv7 +8lXfNW71e+zOk3lWd1bX7LnN6srmr46vjtu1rl/xMbrn+zZ/a79W9/Ote2z3 ++Op3Hs3/1Pvq1nv6nHLOOeecc8752H5bfbs8W+dsnmy+aux+L1m/7nxf8zFu +q49zzjnnnHP++z62jxG1785bfe6OiyJbVzXv236q3lvW/1S9Y/yaP7Ufq3Xs +6pd9L7Pf0Wy/aFy1jq9/f5lHUe0XjTu9vtP5x/hr3m2v7t9t75dzzjnnnHPO +T3v1eYzVfNm8q3mqXq2vWn80brWup9cfxWqe7r6e/h4455xzzjnn/LRXx41R +bb9lnaf9VP5b1t89L1lk+/srnr3P6rgouvNl81TfX7Weah2r+7K6f7d9Z7Pr +GftHfsv9Fvnqez79Pn7Vu+2r5y175pxzzjnnnHP+bR/bM8+eq5HVt7qOW/aX +c84555xzzvmcr44b+2Xtt63/1v19yrP6bqs3qjM7b2P/r3oU0b6Nz9XzsOu7 +766jGrvObbXfrvZbfYxd98ct6/tqvVm/bvstHkV1P6rzf/W9c84555xzzjnv ++dhe9dVxs/M9te5b3gfnnHPOOeec85pnz6vzZnF6/VUf27vPt/nX6s3O1ex6 +v+Zj+673X/3+u9/30/H0ubndx8jO0+72r3n2fJvP9hvjNu9G93x2f78555xz +zjnnnL/j1efdvjpudr6n9zWr5/T75pxzzjnnnPO/6lm/bL7ZuGX9mXfrPl3v +7Ppuq+ut9Y3tma+OP+1RdPf5tnj6e9/tu+7h2fqjfrd8t7t+126r6ymvRvce +3HW+qvVUz3/2/Cu/z5xzzjnnnHP+Kz7G2L87rupZ3DLf0/tdre+2c8M555xz +zjnnv+5jexSr83TzVPtn9UTzrM7/q346/1OeRXfc7Dmr5ln1XfPeHk/t32q+ +Xeeuer5u+97evq9mz/8t61j1MarnZfa73/X/QHe91fycc84555xzzp/1qF91 +nmi+WX9qvt15nn4/3Xy783POOeecc84573nUL+vfba8+R5H1y+qP/PT+7/Lq +/kd+yzpOexTVc7z7nK6OX813Op5e7+r3kcXq/Znl/2s+Rvd3h//3czS+e25v +Wy/nnHPOOeec8//26Hm13y5/Kn8Wu+qO/kb9Zn1XnZxzzjnnnHPO7/SxfYys +fzT+9Lq+4tn+j3G63lt9jNlzW23P+p3y03HbfnTvp2o/3vPT+TnnnHPOOeec +8y/7GFm/6rjdnvV7Ks/qfNX9fNu7dZ6ul3POOeecc845/7Jnz/y/PXqOxp+u +t+q3xS37suuc8JrPnsuvfW+cc84555xzzvmbPkY0Lut32p+ab3ee295/91xk +/W9bB+ecc84555xz/oZH7VFUx92yvtv9ljpW/anI8q2e89O+ui7+3/2qccs6 +OOecc84555zzNzzqN7ZXx2X9n/bsebdn8fQ6s/f2tM/Wkz1zzjnnnHPOOed/ +wbOI+t22jq/6GLfUt3tdWazuy+w4/i3P4rZ6Oeecc84555zzNz2KqP2rXl3/ +Ls/i6XVGf6N+t3oWt9XLOeecc84555y/6VncVi/f41F7N7JxUXu1nu45vmV/ +ec3H9ihuqZdzzjnnnHPOOT/hWb9q/+q4t3xsz9b/VP6srl3efT+nffcz55xz +zjnnnHP+Fz2KaPzpevmcj+1Vnx23e76xffe5z8bvzv9rXt23KLr3U5aHc845 +55xzzjn/Jc/6ddtv8bE9W/9T+bO6dnn2Pm87d9V1zp5bzjnnnHPOOef8l3yM +rF91fDTfLeu+1Wf7jTH7/qLYfR6ifrvXc/t3ddv5e+scR3HbOjjnnHPOOeec +8ze92y8bP1tPN99uz2J1f3bl73q13uq4t33XuO58s3k555xzzjnnnPNf8jGy +9rfqestn+43xtGdRnW92PbvXsTrf+L5OfSfVumbH78qX9e+eu+75WP3+OOec +c84555zzL/kYWb+xPesXPd/m3f2pzpeNi+aZXc/s+/vqeRz7Zc/d/eGcc845 +55xzzr/oY3s2PurXbe/W9fY+RfVW64rG7/an8u+a7+n9eCrPW99ht18Uq3V3 +n1fvh9n75/R9yTnnnHPOOeecv+FRv2jcGNV5s3G7PepXXU81X3W9u+rqPs+u +522v1hU9d8dxzjnnnHPOOee/6GN7Nn5szzzqN5tndl1ZHavzZ3m6vnu+t/Nk ++/90vrfyVPtX96N6Tqv5unl21VH1an7OOeecc8455/wv+tieje+2V/NW5+l6 +dV92zVuNrI5unm590fvYdb6iqObN6s7qyPJyzjnnnHPOOed/0WfHd6M7b9Wz +uqp5quuszlPtP+tv59m1P0/5U3l2n6/qPN3vdjZvN6r1cc4555xzzjnnfJ9H +7dX+1XzRc+bVOqp1d/NUo7o/0XO1X3UfuuciqmPX+N35OOecc84555xznnvU +3o1ovmzerJ5o/Oq41Xl2+1t5Zt//6f156lzuyrOaf3bfs/HV/tX3e8u9xTnn +nHPOOeecv+lR+xiRV9uzmK2jW2+2/ixPlr87766o1jU+V89Hd/6uV9/XalTX +Va2vOo5zzjnnnHPOOf+yV8dFUe1XzZ/NG9X7dHT3abau1f2oerf9q+vM/PQ5 +u2W9Y3u1XzaOc84555xzzjn/yx5FNr7bHs3bbc/6rY4f27P1no5d76Wap+rd +ftX6uu+l+x3c9n1yzjnnnHPOOec3+BjZuO74t3w1onXeut5qXd3z8VRdt+7j +2F5971l0v7+3vNp+y/3EOeecc84555yf8KxfFFn/at6of1ZHNs/s/F2f7fdW +dN9rNH523tV9Xp2/eu5n8932PXPOOeecc8455ye8Ou503dX2LLJxs+27/fT5 +6Na76lFdWX2r53U172wdq+9jtf2Wc8Y555xzzjnnnH/Rx+j2y/Ktjq+Oq9bb +9ep+3B6r56Drs+818tn53zrnnHPOOeecc875X/aofYxsXBar9VTzra632281 +7+lzMMZXvNoe9aueq93nvFsP55xzzjnnnHPO3/dqvFXf2/lO7+vuiOr4ikf9 +3jp31fxv18c555xzzjnnnPPcq+OqMc7Tzbc6/9d8jL/mUfvq+enO1x3HOeec +c84555zz53yMqP103dnz23WMUd3fp2N2f7J5Zj2qo9p+6r1m+3ZL3Zxzzjnn +nHPO+V/0MaJx3ecsT9T/ln05/T6yff5177Zn+7w6nnPOOeecc8455/f6GLfV +d4tH7aejWif/7/bb6uOcc84555xzzvn/+mx7FNX2W9b/lo/R3ads3Fc9Ow/V +ePu74JxzzjnnnHPO+X2+2v4Vf2q+sV83xvl31509f9VX2znnnHPOOeecc37e +d80XPUeR9YvqPL1fq96N7rhq3q97FN33Us1/+txwzjnnnHPOOed83aPI2qP5 +o3HVurL+2fhdHuXttmfjVut6a/2z5yHrN5snG8c555xzzjnnnPN7PWofI+qf +jYvilvXv9jGe2pdq3u77estn9yWbb/Z9VL8LzjnnnHPOOeec86/62J559lyN +rL7Vddyyv5xzzjnnnHPOOedVj9rH6I7L5omimv+0R/VW17e7jm6/aNzsfNV8 +3XMXjVvdn+yZc84555xzzjnn/HYf26u+Om52vqfWfcv74JxzzjnnnHPOOY88 +ap/tV22fjW6dVc/6ze5Pdfxuj55X61mdZ3c9nHPOOeecc84551/zKKrzZPNl +ebvzZdGtI/ob9YvmrdZ7+n1zzjnnnHPOOeec7/bquDG680TzVeeJxkXz7PLT +72f0LLJx1flX3xfnnHPOOeecc875VzzqN7ZH42Y9i1vmO/Ue3s7POeecc845 +55xzvtuj9jFW82bzR/1u3R/OOeecc84555xz/htefd7tT823O8/T7yGr5/T5 +4JxzzjnnnHPOOefP+On8nHPOOeecc84557znUb+xPRq329/O81b+297z2/k5 +55xzzjnnnHPO+Zqfzs8555xzzjnnnHPO/+1RRO23eHU9Xc9iV93R36jfW57F +bfVyzjnnnHPOOeec/3U/nZ9zzjnnnHPOOeec13xsP+Wn6s1i13pmx91yLm6p +i3POOeecc8455/yv++n8nHPOOeecc84557/qY3s3ovGn/Jb8UbxV1y3nazaq +7/eW9XHOOeecc84555x/1U/n55xzzjnnnHPOOf81j/pF47LxWb+3/VT+LN5e +5y3nrlrf2J49c84555xzzjnnnPM1P52fc84555xzzjnn/GtebY/6f9Wzfm/n +fypPtq7bzuPs+R1j9pzftj7OOeecc84555zzW/x0fs4555xzzjnnnPOveHVc +FNk8Uf/TvrvfrGdxav2z5+Qtr8bs+zi9Ps4555xzzjnnnPNb/XR+zjnnnHPO +Oeec86/72D72i55v9+p+vFVXFk+vf3bcbV6tu9qPc84555xzzjnnnP/bT+fn +nHPOOeecc845f9uzflHM9ovGZflPedTefX6qriieyl99T6fP9ew6u/u969xw +zjnnnHPOOeec/7qfzs8555xzzjnnnHN+2scY+63OU60rG3/KZ9c767tjtq5s +3VG/W851dX9X17s6D+ecc84555xzzvmv+un8nHPOOeecc84552/7rvFdr+bZ +lW/Wu/12raNaTzVvNX83bzTv6XM9u85Zf/u745xzzjnnnHPOOf+an87POeec +c84555xzfot3x0f9snmr/ar9Zz3L361vdT+yOqP53l5fNX92TnZ5lq+6P6vn +87bvmXPOOeecc8455/y0n87POeecc84555xzfrtH/aJx2fju/LPzZb6at7oP +2TzVOqP5nsq76311z121jtn3Fc2/ax8455xzzjnnnHPO+R35Oeecc84555xz +zt/21efq/GNE46J+2byZZ/mqPrve6ryr8+3az26eaJ93nceur65zHNete9d5 +4pxzzjnnnHPOOf8VP52fc84555xzzjnnfNWrz5ln/bJx1fan1zFbR3fe7D1l +ear1zI6b3cfZdc3ua7e+bp3d6Na5+h1X5+ecc84555xzzjn/mp/OzznnnHPO +Oeecc77q0XPmWXTnz/Ks1ltdx+q8u8dX9+fp6NbZPY9ZvlnfNe9T53PX95XN +zznnnHPOOeecc/41P52fc84555xzzjnnfNWjftG42ajmr9YXzZ+1d/2pebN+ +X4nqOVnd/93zZs/V9zJ7Truxez2cc84555xzzjnnt/vp/JxzzjnnnHPOOedv +eXVc9pz5bN7uOqI6d/vu8bfH2/tT9d3zrp73qF83bzUf55xzzjnnnHPO+df8 +dH7OOeecc84555zzVY/6dfu/5d16d+9TFFmdq357PLX+7nvZvd+3fAdRv1vq +45xzzjnnnHPOOd/tp/NzzjnnnHPOOeecr/oYt9WXebaO0/XN+leieo5u9+z7 +uO18dL/n2+rmnHPOOeecc845z/x0fs4555xzzjnnnPOnvBvZuNPrmV1vNG42 +unXuyrsaUR2nz1U27pZzV61rNm5ZD+ecc84555xzzvkuP52fc84555xzzjnn +/G3P+nX7/3VfnW93VN/r0+v6dV995pxzzjnnnHPOOf91P52fc84555xzzjnn +/BaPnsfozvNVH2PXfnbzVGOsZ/d6np7vtHf7jXHbejjnnHPOOeecc85P++n8 +nHPOOeecc84551/xqL0b3XzVvNX+u/cniqzO7rgsqvvWnf+t81QdH/WfHf/0 +OM4555xzzjnnnPO/6qfzc84555xzzjnnnPNveNRvbI/GRZHlq0a37qrvno9z +zjnnnHPOOeec/w0/nZ9zzjnnnHPOOeec3+VRv7E9Gpf56rjZ+Z7ep9X5OOec +c84555xzzvlv+en8nHPOOeecc8455/yMR/3G9mjcrK+Om53v1L4+lYdzzjnn +nHPOOeec3+2n83POOeecc84555zzZ32MqH91XNWfmm93nqffQ7cOzjnnnHPO +Oeecc/4bfjo/55xzzjnnnHPOOe95NaJ5svl2+VPz7c5z6n1m9UVx+vxxzjnn +nHPOOeec85qfzs8555xzzjnnnHPO/+1ZvzGi9qc9i6/mOfX+s3qyZ84555xz +zjnnnHN+h5/OzznnnHPOOeecc/5XPItxfHX+LM9b/nSeLJ6q+5ZzFLXvOm+c +c84555xzzjnnfK+fzs8555xzzjnnnHP+1zxqz+aJ+p/y7Hm3Z/H0Oqvv8W3P +6ozitnVwzjnnnHPOOeec/5qfzs8555xzzjnnnHP+VR8j6l8dd7tn/d7O/1Se +bF2nz91TPrZHfku9nHPOOeecc84557f76fycc84555xzzjnnt/sYs+Or8532 +0/mzuqI4Xe/pc1r1MXad31vWxznnnHPOOeecc36Ln87POeecc84555xzfrtH +/Vbnj/Lc6rfkj+Ktuk6fx93nbvacv1Uv55xzzjnnnHPO+Vf9dH7OOeecc845 +55zz015tjyLKk/W71cf2W9aXxVt1ZefqlnM9+x2M/brts98Z55xzzjnnnHPO ++a/56fycc84555xzzjnnb3vUr9s/iqj9a346fzdu2ZfbzvvsOR77Z8+r3xHn +nHPOOeecc875r/np/JxzzjnnnHPOOedv++7xY3zVo36n66rGLXWN5+f0eV/1 +MU59d5xzzjnnnHPOOedf89P5Oeecc84555xzznd51J49j94dn4271bN+1X19 +y7N4q65d5+wrPsbs+qM81Xy37AfnnHPOOeecc8551U/n55xzzjnnnHPOOa96 +1G9sH6M7X3V8tf/XPOt3S11v5589R1/3qL3bvzrf2J49c84555xzzjnnnN/q +p/NzzjnnnHPOOeecz/oYUftb46vz3OrjOm+pqxpv1VU9R9l+3uZRPPVdVOft +5uecc84555xzzjm/xU/n55xzzjnnnHPOOa969NydN+oXzZc9d+v7ilfX9Vb+ +bPxT+Xefv9s9i9Xvc7aO2/aJc84555xzzjnnPPPT+TnnnHPOOeecc85nfYzq ++O581eeverYP3f7VfZqtozruqfdbnW/0W76bXd9Z9TnrV/1eo/lu2SfOOeec +c84555zz0U/n55xzzjnnnHPOOV/1MbLx0XzVeVbzZ96dP/MoX3V9u/ctmj/r +n8Wuc7JrXPW9P/V9dMed+i6q4267dzjnnHPOOeecc84zP52fc84555xzzjnn +/Gkf26uRjY/yVsdn+ap5d3l1H7P1rOarxmw9s/VV+1X3bbdndVf7d99793xn +7afvC84555xzzjnnnPNdfjo/55xzzjnnnHPOedXHiDxqr+bN5s3mq9bR7Zfl +W/Vund19m82XzfdU3tV+2f50vdterTMbF0V137vrq+Y5fR9xzjnnnHPOOeec +Z346P+ecc84555xzzv+uRxG1d311XBbV9a7WU92/XfNm+cZ+1XVX83fHz+53 +1t7dh8h3fTdZfVXP5p99n1HM1rO6P1k+zjnnnHPOOeec86f9dH7OOeecc845 +55z/XR8j6h+Nq84bzd+db3VcVudTvmt8d3+y95nVsRqz+zB7vrvfQVbH0179 +3mbfexTd9u65ml0P55xzzjnnnHPO+W4/nZ9zzjnnnHPOOee/79nz6FH/zKN5 +s3m6/aI6dq1jdn9n562Oj6I67+2RnYOsX3d8198+f7u/i9l9ydqr80fznL4f +Oeecc84555xz/rt+Oj/nnHPOOeecc87/ru+OLM9sfVG90fhu+y7P9nU1X3f8 +V6J7fqPxXX/7fGTPu87Xrny74/R9xznnnHPOOeec87/np/NzzjnnnHPOOef8 +73r0nPWL+kexWvfT+xHVe9p3zfu1uGXfvlbH6j1Qzft2fZxzzjnnnHPOOeez +fjo/55xzzjnnnHPOeRTdcU/Vd/s+RZHt01P+a3HLPp6qo+qnzn32nb5VH+ec +c84555xzzvnop/NzzjnnnHPOOeecj+1RRPM8XV/kt+zfrf6ViOrm//a3zlPW +L6szar/l++Ccc84555xzzvnv++n8nHPOOeecc84555mP7VHcVvfoWf1jnN7v +sd+u+W6L7vqqz295FN113Oqz98TpujnnnHPOOeecc85P5+ecc84555xzzjnP +vBq31f1XPHpf0bjTEdWf1XvLfv8Vj6J67m5bD+ecc84555xzzv+en87POeec +c84555xzHnnUHj1X53+67l/xMU7lqUZ2fmbrO70/v+LdflH/6nu4bf2cc845 +55xzzjn/e346P+ecc84555xzzvkuH9vHftFz1P/0enb7GLvyVOdfHZdFdh6q ++5LNO+vRvLvz3OKz31m1H+ecc84555xzzvm9/v8ALjYi4Q== + "], {{0, 0}, {401, 401}}, {0, 1}], + Frame->Automatic, + FrameLabel->{None, None}, + FrameTicks->{{None, None}, {None, None}}, + GridLinesStyle->Directive[ + GrayLevel[0.5, 0.4]], + Method->{ + "DefaultBoundaryStyle" -> Automatic, "DefaultPlotStyle" -> + Automatic}]], "Output", + CellChangeTimes->{3.6641621075311346`*^9}] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"newtonplot", "[", + RowBox[{ + RowBox[{"Function", "[", + RowBox[{"x", ",", + RowBox[{ + SuperscriptBox["x", "2"], "+", "1"}]}], "]"}], ",", "2", ",", "201", + ",", "20", ",", "0.05"}], "]"}]], "Input", + CellChangeTimes->{{3.6595549152958674`*^9, 3.659554978383319*^9}, + 3.659555332709116*^9, {3.659555509656427*^9, 3.6595555271955185`*^9}, { + 3.659555597485504*^9, 3.659555613597739*^9}, {3.659556133025359*^9, + 3.659556138135767*^9}, {3.659556178511237*^9, 3.6595561786634045`*^9}, { + 3.6595564436249084`*^9, 3.659556460417568*^9}}], + +Cell[BoxData[ + TemplateBox[{GraphicsBox[ + RasterBox[CompressedData[" +1:eJzt2MEJwCAQRcGFVJJK0kNKEHK2znRjCSLRi6QAhXmwsEwJ/0z5fo6IePu1 +/6tc8RvnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc845 +55xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc845 +55xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc845 +55xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc845 +55xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc845 +55xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc845 +55xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc845 +55xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc845 +55xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc845 +55xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc845 +55xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc845 +55xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc845 +55xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc845 +55xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc845 +55xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc845 +55xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc845 +55xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc845 +55xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc845 +55xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc845 +55xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc845 +55xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc845 +55xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc845 +55xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc845 +55xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc845 +55xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc845 +55xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc845 +55zzvVySJEmSJEnaubF7zfsX55xzzjnnnHPOOeecc84555xzzjnnnHPOOeec +c84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeec +c84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeec +c84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeec +c84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeec +c84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeec +c84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeec +c84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeec +c84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeec +c84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeec +c84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeec +c84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeec +c84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeec +c84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeec +c84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeec +c84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeec +c84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeec +c84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeec +c84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeec +c84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeec +c84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeec +c84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeec +c84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeec +c84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeec +c84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeec +c84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeec +c84555xzzjnnnHPOOeec89W9Algh3kA= + "], {{0, 0}, {201, 201}}, {0, 1}], Frame -> Automatic, + FrameLabel -> {None, None}, FrameTicks -> {{None, None}, {None, None}}, + GridLinesStyle -> Directive[ + GrayLevel[0.5, 0.4]], + Method -> { + "DefaultBoundaryStyle" -> Automatic, "DefaultPlotStyle" -> Automatic}], + FormBox[ + FormBox[ + TemplateBox[{"\"Divergent\"", + RowBox[{"-", "\[ImaginaryI]"}], "\[ImaginaryI]"}, "SwatchLegend", + DisplayFunction -> (FormBox[ + StyleBox[ + StyleBox[ + PaneBox[ + TagBox[ + GridBox[{{ + TagBox[ + GridBox[{{ + GraphicsBox[{ + Directive[ + EdgeForm[ + Directive[ + Opacity[0.3], + GrayLevel[0]]], + PointSize[0.5], + AbsoluteThickness[1.6], + RGBColor[0., 0., 0.]], + RectangleBox[{0, 0}, {10, 10}, "RoundingRadius" -> 0]}, + AspectRatio -> Full, ImageSize -> {10, 10}, + PlotRangePadding -> None, ImagePadding -> Automatic, + BaselinePosition -> (Scaled[0.1] -> Baseline)], #}, { + GraphicsBox[{ + Directive[ + EdgeForm[ + Directive[ + Opacity[0.3], + GrayLevel[0]]], + PointSize[0.5], + AbsoluteThickness[1.6], + RGBColor[1., 0., 0.]], + RectangleBox[{0, 0}, {10, 10}, "RoundingRadius" -> 0]}, + AspectRatio -> Full, ImageSize -> {10, 10}, + PlotRangePadding -> None, ImagePadding -> Automatic, + BaselinePosition -> (Scaled[0.1] -> Baseline)], #2}, { + GraphicsBox[{ + Directive[ + EdgeForm[ + Directive[ + Opacity[0.3], + GrayLevel[0]]], + PointSize[0.5], + AbsoluteThickness[1.6], + RGBColor[0., 1., 1.]], + RectangleBox[{0, 0}, {10, 10}, "RoundingRadius" -> 0]}, + AspectRatio -> Full, ImageSize -> {10, 10}, + PlotRangePadding -> None, ImagePadding -> Automatic, + BaselinePosition -> (Scaled[0.1] -> Baseline)], #3}}, + GridBoxAlignment -> { + "Columns" -> {Center, Left}, "Rows" -> {{Baseline}}}, + AutoDelete -> False, + GridBoxDividers -> { + "Columns" -> {{False}}, "Rows" -> {{False}}}, + GridBoxItemSize -> {"Columns" -> {{All}}, "Rows" -> {{All}}}, + GridBoxSpacings -> { + "Columns" -> {{0.5}}, "Rows" -> {{0.5}}}], "Grid"]}}, + GridBoxAlignment -> {"Columns" -> {{Left}}, "Rows" -> {{Top}}}, + AutoDelete -> False, + GridBoxItemSize -> { + "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, + GridBoxSpacings -> {"Columns" -> {{1}}, "Rows" -> {{0}}}], + "Grid"], Alignment -> Left, AppearanceElements -> None, + ImageMargins -> {{5, 5}, {5, 5}}, ImageSizeAction -> + "ResizeToFit"], LineIndent -> 0, StripOnInput -> False], { + FontFamily -> "Arial"}, Background -> Automatic, StripOnInput -> + False], TraditionalForm]& ), + InterpretationFunction :> (RowBox[{"SwatchLegend", "[", + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{"Directive", "[", + InterpretationBox[ + ButtonBox[ + TooltipBox[ + GraphicsBox[{{ + GrayLevel[0], + RectangleBox[{0, 0}]}, { + GrayLevel[0], + RectangleBox[{1, -1}]}, { + RGBColor[0., 0., 0.], + RectangleBox[{0, -1}, {2, 1}]}}, AspectRatio -> 1, Frame -> + True, FrameStyle -> RGBColor[0., 0., 0.], FrameTicks -> + None, PlotRangePadding -> None, ImageSize -> + Dynamic[{ + Automatic, 1.35 CurrentValue["FontCapHeight"]/ + AbsoluteCurrentValue[Magnification]}]], + "RGBColor[0., 0., 0.]"], Appearance -> None, + BaseStyle -> {}, BaselinePosition -> Baseline, + DefaultBaseStyle -> {}, ButtonFunction :> + With[{Typeset`box$ = EvaluationBox[]}, + If[ + Not[ + AbsoluteCurrentValue["Deployed"]], + SelectionMove[Typeset`box$, All, Expression]; + FrontEnd`Private`$ColorSelectorInitialAlpha = 1; + FrontEnd`Private`$ColorSelectorInitialColor = + RGBColor[0., 0., 0.]; + FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; + MathLink`CallFrontEnd[ + FrontEnd`AttachCell[Typeset`box$, + FrontEndResource["RGBColorValueSelector"], { + 0, {Left, Bottom}}, {Left, Top}, + "ClosingActions" -> { + "SelectionDeparture", "ParentChanged", + "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> + Automatic, Method -> "Preemptive"], + RGBColor[0., 0., 0.], Editable -> False, Selectable -> + False], "]"}], ",", + RowBox[{"Directive", "[", + InterpretationBox[ + ButtonBox[ + TooltipBox[ + GraphicsBox[{{ + GrayLevel[0], + RectangleBox[{0, 0}]}, { + GrayLevel[0], + RectangleBox[{1, -1}]}, { + RGBColor[1., 0., 0.], + RectangleBox[{0, -1}, {2, 1}]}}, AspectRatio -> 1, Frame -> + True, FrameStyle -> RGBColor[0.6666666666666667, 0., 0.], + FrameTicks -> None, PlotRangePadding -> None, ImageSize -> + Dynamic[{ + Automatic, 1.35 CurrentValue["FontCapHeight"]/ + AbsoluteCurrentValue[Magnification]}]], + "RGBColor[1., 0., 0.]"], Appearance -> None, + BaseStyle -> {}, BaselinePosition -> Baseline, + DefaultBaseStyle -> {}, ButtonFunction :> + With[{Typeset`box$ = EvaluationBox[]}, + If[ + Not[ + AbsoluteCurrentValue["Deployed"]], + SelectionMove[Typeset`box$, All, Expression]; + FrontEnd`Private`$ColorSelectorInitialAlpha = 1; + FrontEnd`Private`$ColorSelectorInitialColor = + RGBColor[1., 0., 0.]; + FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; + MathLink`CallFrontEnd[ + FrontEnd`AttachCell[Typeset`box$, + FrontEndResource["RGBColorValueSelector"], { + 0, {Left, Bottom}}, {Left, Top}, + "ClosingActions" -> { + "SelectionDeparture", "ParentChanged", + "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> + Automatic, Method -> "Preemptive"], + RGBColor[1., 0., 0.], Editable -> False, Selectable -> + False], "]"}], ",", + RowBox[{"Directive", "[", + InterpretationBox[ + ButtonBox[ + TooltipBox[ + GraphicsBox[{{ + GrayLevel[0], + RectangleBox[{0, 0}]}, { + GrayLevel[0], + RectangleBox[{1, -1}]}, { + RGBColor[0., 1., 1.], + RectangleBox[{0, -1}, {2, 1}]}}, AspectRatio -> 1, Frame -> + True, FrameStyle -> + RGBColor[0., 0.6666666666666667, 0.6666666666666667], + FrameTicks -> None, PlotRangePadding -> None, ImageSize -> + Dynamic[{ + Automatic, 1.35 CurrentValue["FontCapHeight"]/ + AbsoluteCurrentValue[Magnification]}]], + "RGBColor[0., 1., 1.]"], Appearance -> None, + BaseStyle -> {}, BaselinePosition -> Baseline, + DefaultBaseStyle -> {}, ButtonFunction :> + With[{Typeset`box$ = EvaluationBox[]}, + If[ + Not[ + AbsoluteCurrentValue["Deployed"]], + SelectionMove[Typeset`box$, All, Expression]; + FrontEnd`Private`$ColorSelectorInitialAlpha = 1; + FrontEnd`Private`$ColorSelectorInitialColor = + RGBColor[0., 1., 1.]; + FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; + MathLink`CallFrontEnd[ + FrontEnd`AttachCell[Typeset`box$, + FrontEndResource["RGBColorValueSelector"], { + 0, {Left, Bottom}}, {Left, Top}, + "ClosingActions" -> { + "SelectionDeparture", "ParentChanged", + "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> + Automatic, Method -> "Preemptive"], + RGBColor[0., 1., 1.], Editable -> False, Selectable -> + False], "]"}]}], "}"}], ",", + RowBox[{"{", + RowBox[{#, ",", #2, ",", #3}], "}"}], ",", + RowBox[{"LegendMarkers", "\[Rule]", "Automatic"}], ",", + RowBox[{"LabelStyle", "\[Rule]", + RowBox[{"{", "}"}]}], ",", + RowBox[{"LegendLayout", "\[Rule]", "\"Column\""}]}], "]"}]& ), + Editable -> True], TraditionalForm], TraditionalForm]}, + "Legended", + DisplayFunction->(GridBox[{{ + TagBox[ + ItemBox[ + PaneBox[ + TagBox[#, "SkipImageSizeLevel"], Alignment -> {Center, Baseline}, + BaselinePosition -> Baseline], DefaultBaseStyle -> "Labeled"], + "SkipImageSizeLevel"], + ItemBox[#2, DefaultBaseStyle -> "LabeledLabel"]}}, + GridBoxAlignment -> {"Columns" -> {{Center}}, "Rows" -> {{Center}}}, + AutoDelete -> False, GridBoxItemSize -> Automatic, + BaselinePosition -> {1, 1}]& ), + Editable->True, + InterpretationFunction->(RowBox[{"Legended", "[", + RowBox[{#, ",", + RowBox[{"Placed", "[", + RowBox[{#2, ",", "After"}], "]"}]}], "]"}]& )]], "Output", + CellChangeTimes->{ + 3.6595561427769833`*^9, 3.659556184448927*^9, {3.6595564465319443`*^9, + 3.6595564731067934`*^9}}] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"newtonplot", "[", + RowBox[{ + RowBox[{"Function", "[", + RowBox[{"x", ",", + RowBox[{ + SuperscriptBox["x", "2"], "-", "1"}]}], "]"}], ",", "2", ",", "201", + ",", "20", ",", "0.05"}], "]"}]], "Input", + CellChangeTimes->{{3.6595549152958674`*^9, 3.659554978383319*^9}, + 3.659555332709116*^9, {3.659555509656427*^9, 3.6595555271955185`*^9}, { + 3.659555597485504*^9, 3.659555613597739*^9}, {3.65955606434665*^9, + 3.659556065221777*^9}, {3.659556100512431*^9, 3.659556120459993*^9}, { + 3.6595564492510743`*^9, 3.659556464637117*^9}}], + +Cell[BoxData[ + TemplateBox[{GraphicsBox[ + RasterBox[CompressedData[" +1:eJzt1sFJZVEQBNAPRmIkk4MhCK6Nc7KZEAZRN4XQlKtuOAUPHqf67uv59f3l +7enxePz9+j7+P/Pvz+PHcM4555zz3/mU73f5nnPOOeecd5593nHOOeec886n +bNmBnHPOOefXPfu845xzzjnnnU/ZsgM555xzzq979nnHOeecc847n7JlB3LO +OeecX/fs845zzjnnnHc+ZcsO5Jxzzjm/7tnnHeecc84573zKlh3IOeecc37d +s887zjnnnHPe+ZQtO5Bzzjnn/Lpnn3ecc84557zzKVt2IOecc875dc8+7zjn +nHPOeedTtuxAzjnnnPPrnn3ecc4555zzzqds2YGcc84559c9+7zjnHPOOeed +T9myAznnnHPOr3v2ecc555xzzjufsmUHcs4555xf9+zzjnPOOeecdz5lyw7k +nHPOOb/u2ecd55xzzjnvfMqWHcg555xzft2zzzvOOeecc975lC07kHPOOef8 +umefd5xzzjnnvPMpW3Yg55xzzvl1zz7vOOecc85551O27EDOOeec8+uefd5x +zjnnnPPOp2zZgZxzzjnn1z37vOOcc845551P2bIDOeecc86ve/Z5xznnnHPO +O5+yZQdyzjnnnF/37POOc84555x3PmXLDuScc845v+7Z5x3nnHPOOe98ypYd +yDnnnHN+3bPPO84555xz3vmULTuQc8455/y6Z593nHPOOee88ylbdiDnnHPO ++XXPPu8455xzznnnU7bsQM4555zz65593nHOOeec886nbNmBnHPOOefXPfu8 +45xzzjnnnU/ZsgM555xzzq979nnHOeecc847n7JlB3LOOeecX/fs845zzjnn +nHc+ZcsO5Jxzzjm/7tnnHeecc84573zKlh3IOeecc37ds887zjnnnHPe+ZQt +O5Bzzjnn/Lpnn3ecc84557zzKVt2IOecc875dc8+7zjnnHPOeedTtuxAzjnn +nPPrnn3ecc4555zzzqds2YGcc84559c9+7zjnHPOOeedT9myAznnnHPOr3v2 +ecc555xzzjufsmUHcs4555xf9+zzjnPOOeecdz5lyw7knHPOOb/u2ecd55xz +zjnvfMqWHcg555xzft2zzzvOOeecc975lC07kHPOOef8umefd5xzzjnnvPMp +W3Yg55xzzvl1zz7vOOecc85551O27EDOOeec8+uefd5xzjnnnPPOp2zZgZxz +zjnn1z37vOOcc845551P2bIDOeecc86ve/Z5xznnnHPOO5+yZQdyzjnnnF/3 +7POOc84555x3PmXLDuScc845v+7Z5x3nnHPOOe98ypYdyDnnnHN+3bPPO845 +55xz3vmULTuQc8455/y6Z593nHPOOee88ylbdiDnnHPO+XXPPu8455xzznnn +U7bsQM4555zz65593nHOOeec886nbNmBnHPOOefXPfu845xzzjnnnU/ZsgM5 +55xzzq979nnHOeecc847n7JlB3LOOeecX/fs845zzjnnnHc+ZcsO5Jxzzjm/ +7tnnHeecc84573zKlh3IOeecc37ds887zjnnnHPe+ZQtO5Bzzjnn/Lpnn3ec +c84557zzKVt2IOecc875dc8+7zjnnHPOeedTtuxAzjnnnPPrnn3ecc4555zz +zqds2YGcc84559c9+7zjnHPOOeedT9myAznnnHPOr3v2ecc555xzzjufsmUH +cs4555xf9+zzjnPOOeecdz5lyw7knHPOOb/u2ecd55xzzjnvfMqWHcg555xz +ft2zzzvOOeecc975lC07kHPOOef8umefd5xzzjnnvPMpW3Yg55xzzvl1zz7v +OOecc85551O27EDOOeec8+uefd5xzjnnnPPOp2zZgZxzzjnn1z37vOOcc845 +551P2bIDOeecc86ve/Z5xznnnHPOO5+yZQdyzjnnnF/37POOc84555x3PmXL +DuScc845v+7Z5x3nnHPOOe98ypYdyDnnnHN+3bPPO84555xz3vmULTuQc845 +5/y6Z593nHPOOee88ylbdiDnnHPO+XXPPu8455xzznnnU7bsQM4555zz6559 +3nHOOeec886nbNmBnHPOOefXPfu845xzzjnnnU/ZsgM555xzzq979nnHOeec +c847n7JlB3LOOeecX/fs845zzjnnnHc+ZcsO5Jxzzjm/7tnnHeecc84573zK +lh3IOeecc37ds887zjnnnHPe+ZQtO5Bzzjnn/Lpnn3ecc84557zzKVt2IOec +c875dc8+7zjnnHPOeedTtuxAzjnnnPPrnn3ecc4555zzzqds2YGcc84559c9 ++7zjnHPOOeedT9myAznnnHPOr3v2ecc555xzzjufsmUHcs4555xf9+zzjnPO +Oeecdz5lyw7knHPOOb/u2ecd55xzzjnvfMqWHcg555xzft2zzzvOOeecc975 +lC07kHPOOef8umefd5xzzjnnvPMpW3Yg55xzzvl1zz7vOOecc85551O27EDO +Oeec8+uefd5xzjnnnPPOp2zZgZxzzjnn1z37vOOcc845551P2bIDOeecc86v +e/Z5xznnnHPOO5+yZQdyzjnnnF/37POOc84555x3PmXLDuScc845v+7Z5x3n +nHPOOe98ypYdyDnnnHN+3bPPO84555xz3vmULTuQc8455/y6Z593nHPOOee8 +8ylbdiDnnHPO+XXPPu8455xzznnnU7bsQM4555zz65593nHOOeec886nbNmB +nHPOOefXPfu845xzzjnnnU/ZsgM555xzzq979nnHOeecc847n7JlB3LOOeec +X/fs845zzjnnnHc+ZcsO5Jxzzjm/7tnnHeecc84573zKlh3IOeecc37ds887 +zjnnnHPe+ZQtO5Bzzjnn/Lpnn3ecc84557zzKVt2IOecc875dc8+7zjnnHPO +eedTtuxAzjnnnPPrnn3ecc4555zzzqds2YGcc84559c9+7zjnHPOOeedT9my +AznnnHPOr3v2ecc555xzzjufsmUHcs4555xf9+zzjnPOOeecdz5lyw7knHPO +Ob/u2ecd55xzzjnvfMqWHcg555xzft2zzzvOOeecc975lC07kHPOOef8umef +d5xzzjnnvPMpW3Yg55xzzvl1zz7vOOecc85551O27EDOOeec8+uefd5xzjnn +nPPOp2zZgZxzzjnn1z37vOOcc845551P2bIDOeecc86ve/Z5xznnnHPOO5+y +ZQdyzjnnnF/37POOc84555x3PmXLDuScc845v+7Z5x3nnHPOOe98ypYdyDnn +nHN+3bPPO84555xz3vmULTuQc8455/y6Z593nHPOOee88ylbdiDnnHPO+XXP +Pu8455xzznnnU7bsQM4555zz65593nHOOeec886nbNmBnHPOOefXPfu845xz +zjnnnU/ZsgM555xzzq979nnHOeecc847n7JlB3LOOeecX/fs845zzjnnnHc+ +ZcsO5Jxzzjm/7tnnHeecc84573zKlh3IOeecc37ds887zjnnnHPe+ZQtO5Bz +zjnn/Lpnn3ecc84557zzKVt2IOecc875dc8+7zjnnHPOeedTtuxAzjnnnPPr +nn3ecc4555zzzqds2YGcc84559c9+7zjnHPOOeedT9myAznnnHPOr3v2ecc5 +55xzzjufsmUHcs4555xf9+zzjnPOOeecdz5lyw7knHPOOb/u2ecd55xzzjnv +fMqWHcg555xzft2zzzvOOeecc975lC07kHPOOef8umefd5xzzjnnvPMpW3Yg +55xzzvl1zz7vOOecc85551O27EDOOeec8+uefd5xzjnnnPPOp2zZgZxzzjnn +1z37vOOcc845551P2bIDOeecc86ve/Z5xznnnHPOO5+yZQdyzjnnnF/37POO +c84555x3PmXLDuScc845v+7Z5x3nnHPOOe98ypYdyDnnnHN+3bPPO84555xz +3vmULTuQc8455/y6Z593nHPOOee88ylbdiDnnHPO+XXPPu8455xzznnnU7bs +QM4555zz65593nHOOeec886nbNmBnHPOOefXPfu845xzzjnnnU/ZsgM555xz +zq979nnHOeecc847n7JlB3LOOeecX/fs845zzjnnnHc+ZcsO5Jxzzjm/7tnn +Heecc84573zKlh3IOeecc37ds887zjnnnHPe+ZQtO5Bzzjnn/Lpnn3ecc845 +57zzKVt2IOecc875dc8+7zjnnHPOeedTtuxAzjnnnPPrnn3ecc4555zzzqds +2YGcc84559c9+7zjnHPOOeedT9myAznnnHPOr3v2ecc555xzzjufsmUHcs45 +55xf9+zzjnPOOeecdz5lyw7knHPOOb/u2ecd55xzzjnvfMqWHcg555xzft2z +zzvOOeecc975lC07kHPOOef8umefd5xzzjnnvPMpW3Yg55xzzvl1zz7vOOec +c85551O27EDOOeec8+uefd5xzjnnnPPOp2zZgZxzzjnn1z37vOOcc845551P +2bIDOeecc86ve/Z5xznnnHPOO5+yZQdyzjnnnF/37POOc84555x3PmXLDuSc +c845v+7Z5x3nnHPOOe98ypYdyDnnnHN+3bPPO84555xz3vmULTuQc8455/y6 +Z593nHPOOee88ylbdiDnnHPO+XXPPu8455xzznnnU7bsQM4555zz65593nHO +Oeec886nbNmBnHPOOefXPfu845xzzjnnnU/ZsgM555xzzq979nnHOeecc847 +n7JlB3LOOeecX/fs845zzjnnnHc+ZcsO5Jxzzjm/7tnnHeecc84573zKlh3I +Oeecc37ds887zjnnnHPe+ZQtO5Bzzjnn/Lpnn3ecc84557zzKVt2IOecc875 +dc8+7zjnnHPOeedTtuxAzjnnnPPrnn3ecc4555zzzqds2YGcc84559c9+7zj +nHPOOeedT9myAznnnHPOr3v2ecc555xzzjufsmUHcs4555xf9+zzjnPOOeec +dz5lyw7knHPOOb/u2ecd55xzzjnvfMqWHcg555xzft2zzzvOOeecc975lC07 +kHPOOef8umefd5xzzjnnvPMpW3Yg55xzzvl1zz7vOOecc85551O27EDOOeec +8+uefd5xzjnnnPPOp2zZgZxzzjnn1z37vOOcc845551P2bIDOeecc86ve/Z5 +xznnnHPOO5+yZQdyzjnnnF/37POOc84555x3PmXLDuScc845v+7Z5x3nnHPO +Oe98ypYdyDnnnHN+3bPPO84555xz3vmULTuQc8455/y6Z593nHPOOee88ylb +diDnnHPO+XXPPu8455xzznnnU7bsQM4555zz65593nHOOeec886nbNmBnHPO +OefXPfu845xzzjnnnU/ZsgM555xzzq979nnHOeecc847n7JlB3LOOeecX/fs +845zzjnnnHc+ZcsO5Jxzzjm/7tnnHeecc84573zKlh3IOeecc37ds887zjnn +nHPe+ZQtO5Bzzjnn/Lpnn3ecc84557zzKVt2IOecc875dc8+7zjnnHPOeedT +tuxAzjnnnPO7/h+Twt5A + "], {{0, 0}, {201, 201}}, {0, 1}], Frame -> Automatic, + FrameLabel -> {None, None}, FrameTicks -> {{None, None}, {None, None}}, + GridLinesStyle -> Directive[ + GrayLevel[0.5, 0.4]], + Method -> { + "DefaultBoundaryStyle" -> Automatic, "DefaultPlotStyle" -> Automatic}], + FormBox[ + FormBox[ + TemplateBox[{"\"Divergent\"", + RowBox[{"-", "1"}], "1"}, "SwatchLegend", DisplayFunction -> (FormBox[ + StyleBox[ + StyleBox[ + PaneBox[ + TagBox[ + GridBox[{{ + TagBox[ + GridBox[{{ + GraphicsBox[{ + Directive[ + EdgeForm[ + Directive[ + Opacity[0.3], + GrayLevel[0]]], + PointSize[0.5], + AbsoluteThickness[1.6], + RGBColor[0., 0., 0.]], + RectangleBox[{0, 0}, {10, 10}, "RoundingRadius" -> 0]}, + AspectRatio -> Full, ImageSize -> {10, 10}, + PlotRangePadding -> None, ImagePadding -> Automatic, + BaselinePosition -> (Scaled[0.1] -> Baseline)], #}, { + GraphicsBox[{ + Directive[ + EdgeForm[ + Directive[ + Opacity[0.3], + GrayLevel[0]]], + PointSize[0.5], + AbsoluteThickness[1.6], + RGBColor[1., 0., 0.]], + RectangleBox[{0, 0}, {10, 10}, "RoundingRadius" -> 0]}, + AspectRatio -> Full, ImageSize -> {10, 10}, + PlotRangePadding -> None, ImagePadding -> Automatic, + BaselinePosition -> (Scaled[0.1] -> Baseline)], #2}, { + GraphicsBox[{ + Directive[ + EdgeForm[ + Directive[ + Opacity[0.3], + GrayLevel[0]]], + PointSize[0.5], + AbsoluteThickness[1.6], + RGBColor[0., 1., 1.]], + RectangleBox[{0, 0}, {10, 10}, "RoundingRadius" -> 0]}, + AspectRatio -> Full, ImageSize -> {10, 10}, + PlotRangePadding -> None, ImagePadding -> Automatic, + BaselinePosition -> (Scaled[0.1] -> Baseline)], #3}}, + GridBoxAlignment -> { + "Columns" -> {Center, Left}, "Rows" -> {{Baseline}}}, + AutoDelete -> False, + GridBoxDividers -> { + "Columns" -> {{False}}, "Rows" -> {{False}}}, + GridBoxItemSize -> {"Columns" -> {{All}}, "Rows" -> {{All}}}, + GridBoxSpacings -> { + "Columns" -> {{0.5}}, "Rows" -> {{0.5}}}], "Grid"]}}, + GridBoxAlignment -> {"Columns" -> {{Left}}, "Rows" -> {{Top}}}, + AutoDelete -> False, + GridBoxItemSize -> { + "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, + GridBoxSpacings -> {"Columns" -> {{1}}, "Rows" -> {{0}}}], + "Grid"], Alignment -> Left, AppearanceElements -> None, + ImageMargins -> {{5, 5}, {5, 5}}, ImageSizeAction -> + "ResizeToFit"], LineIndent -> 0, StripOnInput -> False], { + FontFamily -> "Arial"}, Background -> Automatic, StripOnInput -> + False], TraditionalForm]& ), + InterpretationFunction :> (RowBox[{"SwatchLegend", "[", + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{"Directive", "[", + InterpretationBox[ + ButtonBox[ + TooltipBox[ + GraphicsBox[{{ + GrayLevel[0], + RectangleBox[{0, 0}]}, { + GrayLevel[0], + RectangleBox[{1, -1}]}, { + RGBColor[0., 0., 0.], + RectangleBox[{0, -1}, {2, 1}]}}, AspectRatio -> 1, Frame -> + True, FrameStyle -> RGBColor[0., 0., 0.], FrameTicks -> + None, PlotRangePadding -> None, ImageSize -> + Dynamic[{ + Automatic, 1.35 CurrentValue["FontCapHeight"]/ + AbsoluteCurrentValue[Magnification]}]], + "RGBColor[0., 0., 0.]"], Appearance -> None, + BaseStyle -> {}, BaselinePosition -> Baseline, + DefaultBaseStyle -> {}, ButtonFunction :> + With[{Typeset`box$ = EvaluationBox[]}, + If[ + Not[ + AbsoluteCurrentValue["Deployed"]], + SelectionMove[Typeset`box$, All, Expression]; + FrontEnd`Private`$ColorSelectorInitialAlpha = 1; + FrontEnd`Private`$ColorSelectorInitialColor = + RGBColor[0., 0., 0.]; + FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; + MathLink`CallFrontEnd[ + FrontEnd`AttachCell[Typeset`box$, + FrontEndResource["RGBColorValueSelector"], { + 0, {Left, Bottom}}, {Left, Top}, + "ClosingActions" -> { + "SelectionDeparture", "ParentChanged", + "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> + Automatic, Method -> "Preemptive"], + RGBColor[0., 0., 0.], Editable -> False, Selectable -> + False], "]"}], ",", + RowBox[{"Directive", "[", + InterpretationBox[ + ButtonBox[ + TooltipBox[ + GraphicsBox[{{ + GrayLevel[0], + RectangleBox[{0, 0}]}, { + GrayLevel[0], + RectangleBox[{1, -1}]}, { + RGBColor[1., 0., 0.], + RectangleBox[{0, -1}, {2, 1}]}}, AspectRatio -> 1, Frame -> + True, FrameStyle -> RGBColor[0.6666666666666667, 0., 0.], + FrameTicks -> None, PlotRangePadding -> None, ImageSize -> + Dynamic[{ + Automatic, 1.35 CurrentValue["FontCapHeight"]/ + AbsoluteCurrentValue[Magnification]}]], + "RGBColor[1., 0., 0.]"], Appearance -> None, + BaseStyle -> {}, BaselinePosition -> Baseline, + DefaultBaseStyle -> {}, ButtonFunction :> + With[{Typeset`box$ = EvaluationBox[]}, + If[ + Not[ + AbsoluteCurrentValue["Deployed"]], + SelectionMove[Typeset`box$, All, Expression]; + FrontEnd`Private`$ColorSelectorInitialAlpha = 1; + FrontEnd`Private`$ColorSelectorInitialColor = + RGBColor[1., 0., 0.]; + FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; + MathLink`CallFrontEnd[ + FrontEnd`AttachCell[Typeset`box$, + FrontEndResource["RGBColorValueSelector"], { + 0, {Left, Bottom}}, {Left, Top}, + "ClosingActions" -> { + "SelectionDeparture", "ParentChanged", + "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> + Automatic, Method -> "Preemptive"], + RGBColor[1., 0., 0.], Editable -> False, Selectable -> + False], "]"}], ",", + RowBox[{"Directive", "[", + InterpretationBox[ + ButtonBox[ + TooltipBox[ + GraphicsBox[{{ + GrayLevel[0], + RectangleBox[{0, 0}]}, { + GrayLevel[0], + RectangleBox[{1, -1}]}, { + RGBColor[0., 1., 1.], + RectangleBox[{0, -1}, {2, 1}]}}, AspectRatio -> 1, Frame -> + True, FrameStyle -> + RGBColor[0., 0.6666666666666667, 0.6666666666666667], + FrameTicks -> None, PlotRangePadding -> None, ImageSize -> + Dynamic[{ + Automatic, 1.35 CurrentValue["FontCapHeight"]/ + AbsoluteCurrentValue[Magnification]}]], + "RGBColor[0., 1., 1.]"], Appearance -> None, + BaseStyle -> {}, BaselinePosition -> Baseline, + DefaultBaseStyle -> {}, ButtonFunction :> + With[{Typeset`box$ = EvaluationBox[]}, + If[ + Not[ + AbsoluteCurrentValue["Deployed"]], + SelectionMove[Typeset`box$, All, Expression]; + FrontEnd`Private`$ColorSelectorInitialAlpha = 1; + FrontEnd`Private`$ColorSelectorInitialColor = + RGBColor[0., 1., 1.]; + FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; + MathLink`CallFrontEnd[ + FrontEnd`AttachCell[Typeset`box$, + FrontEndResource["RGBColorValueSelector"], { + 0, {Left, Bottom}}, {Left, Top}, + "ClosingActions" -> { + "SelectionDeparture", "ParentChanged", + "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> + Automatic, Method -> "Preemptive"], + RGBColor[0., 1., 1.], Editable -> False, Selectable -> + False], "]"}]}], "}"}], ",", + RowBox[{"{", + RowBox[{#, ",", #2, ",", #3}], "}"}], ",", + RowBox[{"LegendMarkers", "\[Rule]", "Automatic"}], ",", + RowBox[{"LabelStyle", "\[Rule]", + RowBox[{"{", "}"}]}], ",", + RowBox[{"LegendLayout", "\[Rule]", "\"Column\""}]}], "]"}]& ), + Editable -> True], TraditionalForm], TraditionalForm]}, + "Legended", + DisplayFunction->(GridBox[{{ + TagBox[ + ItemBox[ + PaneBox[ + TagBox[#, "SkipImageSizeLevel"], Alignment -> {Center, Baseline}, + BaselinePosition -> Baseline], DefaultBaseStyle -> "Labeled"], + "SkipImageSizeLevel"], + ItemBox[#2, DefaultBaseStyle -> "LabeledLabel"]}}, + GridBoxAlignment -> {"Columns" -> {{Center}}, "Rows" -> {{Center}}}, + AutoDelete -> False, GridBoxItemSize -> Automatic, + BaselinePosition -> {1, 1}]& ), + Editable->True, + InterpretationFunction->(RowBox[{"Legended", "[", + RowBox[{#, ",", + RowBox[{"Placed", "[", + RowBox[{#2, ",", "After"}], "]"}]}], "]"}]& )]], "Output", + CellChangeTimes->{{3.6595561119560795`*^9, 3.6595561241792593`*^9}, + 3.6595564518143454`*^9, 3.659556485561829*^9}] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"newtonplot", "[", + RowBox[{ + RowBox[{"Function", "[", + RowBox[{"x", ",", + RowBox[{ + RowBox[{"(", + RowBox[{"x", "+", "1"}], ")"}], + RowBox[{"(", + RowBox[{"x", "-", + RowBox[{"(", + RowBox[{ + RowBox[{"-", "0.5"}], "+", + RowBox[{"0.5", "I"}]}], ")"}]}], ")"}], + RowBox[{"(", + RowBox[{"x", "-", + RowBox[{"(", + RowBox[{ + RowBox[{"-", "0.5"}], "-", + RowBox[{"0.5", "I"}]}], ")"}]}], ")"}]}]}], "]"}], ",", "2", ",", + "401", ",", "20", ",", "0.05"}], "]"}]], "Input", + CellChangeTimes->{{3.6595549152958674`*^9, 3.659554978383319*^9}, + 3.659555332709116*^9, {3.659555509656427*^9, 3.6595555271955185`*^9}, { + 3.659555597485504*^9, 3.659555613597739*^9}, {3.6595562242242994`*^9, + 3.659556229922743*^9}, {3.6595562733917246`*^9, 3.6595562737355576`*^9}, { + 3.6595563138893795`*^9, 3.6595563587354765`*^9}, {3.659556405332657*^9, + 3.6595564061608486`*^9}, 3.664161638484193*^9}], + +Cell[BoxData[ + TemplateBox[{GraphicsBox[ + RasterBox[CompressedData[" +1:eJzs1uupbbt6JdBrKhJH4hwqhIL6XbE4U4dgCrPh3sXW0nhI+rqG2oADZzc9 +epfmY81//z//73//3//1j3/84z//7X/++////z/Pf/3HP/768G/73fVP9087 +N+ecc84555xzzjnnnHPOOeecc8455ys8pQef47Pzerlp98E555xzzjnnnHPO +Oeecc84555xzzvkKT+nB3/nbce8vzjnnnHPOOeecc84555xzzjnnnHPOx3lK +D77WR+37NDftPjjnnHPOOeecc84555xzzjnnnHPOOR/pKT04/+1J68U555xz +zjnnnHPOOeecc84555xzzvlvntKD8xFenc8555xzzjnnnHPOOeecc84555xz +znlSD85nenU+55xzzjnnnHPOOeecc84555xzzjk/y1N6cF7h1fmcc84555xz +zjnnnHPOOeecc8455/ybntKD8xH+dH3aOTjnnHPOOeecc84555xzzjnnnHPO ++d6e0oPzJK/O55xzzjnnnHPOOeecc84555xzzjnne3tKD86TvDqfc84555xz +zjnnnHPOOeecc84555zv7Sk9ON/Bq/M555xzzjnnnHPOOeecc84555xzzvke +ntKD8xHeGp+9P+ecc84555xzzjnnnHPOOeecc84554k9+Nle1eNpz7T745xz +zjnnnHPOOeecc84555xzzjnnWZ7Sg5/hb8dXeXo/zjnnnHPOOeecc84555xz +zjnnnHOe7Sk9+Nme0uOP93pW9+Occ84555xzzjnnnHPOOeecc84559me0oOf +7Sk9/nivZ3U/zjnnnHPOOeecc84555xzzjnnnHOe7Sk9+Nnemnd3/mhPuyfO +Oeecc84555xzzjnnnHPOOeecc76Hp/TgfAevzuecc84555xzzjnnnHPOOeec +c84553t4Sg/Od/DevLS+nHPOOeecc84555xzzjnnnHPOOee8xlN6cL6z9+al +9eWcc84555xzzjnnnHPOOeecc84553M9pQfnJ3l1Puecc84555xzzjnnnHPO +Oeecc845n+spPTj/ovfmpfXlnHPOOeecc84555xzzjnnnHPOOedjPKUH57w+ +n3POOeecc84555xzzjnnnHPOOeecj/GUHpzztlfnc84555xzzjnnnHPOOeec +c84555zze57Sg/OT/On6tHNwzjnnnHPOOeecc84555xzzjnnnPO/e0oPzvl9 +r87nnHPOOeecc84555xzzjnnnHPOOed/95QenPNxXp3POeecc84555xzzjnn +nHPOOeecc366p/TgnI/z6nzOOeecc84555xzzjnnnHPOOeec89M9pQfn/P76 +3j5p5+Occ84555xzzjnnnHPOOeecc845P8VTenDO76/v7ZN2Ps4555xzzjnn +nHPOOeecc84555zzUzylB+e87b15aX0555xzzjnnnHPOOeecc84555xzzk/3 +lB58jvfmeZ9806vzOeecc84555xzzjnnnHPOOeecc85P95QefK2P2i/tXDwj +n3POOeecc84555xzzjnnnHPOOef8dE/pwTO8Nd6bfzUv7byneXU+55xzzjnn +nHPOOeecc84555xzzvkpntKDZ3hKjz8++lynfC5689L6cs4555xzzjnnnHPO +Oeecc84555x/zVN6nOqj9uvtPypnF797P6d8LqrzOeecc84555xzzjnnnHPO +Oeecc85P8ZQe/Pcnrd/XvTp/llfnc84555xzzjnnnHPOOeecc84555yf4ik9 +TvWUHvyaV+df9d68tL6cc84555xzzjnnnHPOOeecc84551/zlB67+dUnrTef +49X5V706n3POOeecc84555xzzjnnnHPOOef8FE/psZun9OB7eMrnrjqfc845 +55xzzjnnnHPOOeecc8455/wUT+mxm6f04Ht69fu2+vycc84555xzzjnnnHPO +Oeecc84551/3lB6pntKDf8ur81tPWi/OOeecc84555xzzjnnnHPOOeec8109 +pUeqp/TgZ/iq93P1OTnnnHPOOeecc84555xzzjnnnHPOv+4pPao9pQfnf/PR +7/Pq83DOOeecc84555xzzjnnnHPOOeecf91Teoz2u+t6+zztwfkIr/pccM45 +55xzzjnnnHPOOeecc84555zzZ57S46nPzunlzs7n/DdP+7xwzjnnnHPOOeec +c84555xzzjnnnPOsHq2num+v59Nxzkf4089XdW/OOeecc84555xzzjnnnHPO +Oeec8697So+U/Ku9evNW9eJn+1c+X5xzzjnnnHPOOeecc84555xzzjnnX/OU +Hq2nuu+qc3E+0nvvw+p+nHPOOeecc84555xzzjnnnHPOOedf96oeqb1W39vo +Xpz/Nr66B+ecc84555xzzjnnnHPOOeecc875qZ7So+dp+avyRu/Lz/KUHpxz +zjnnnHPOOeecc84555xzzjnnp3lKj6c+e7/qc63K43t66ueIc84555xzzjnn +nHPOOeecc8455/x0T+nx1HvzTjsv39ur8696dT7nnHPOOeecc84555xzzjnn +nHPOebqn9Oj53fVp/avugdd6df4sf7o+7Rycc84555xzzjnnnHPOOeecc845 +57M8pQd/5yk9vuZXPy935/OMfM4555xzzjnnnHPOOeecc84555zzWZ7Sg7/z +u+tW9Zmd9/Zco/bha7w6n3POOeecc84555xzzjnnnHPOOef8qqf04O981H67 +9E+7f17r1fmcc84555xzzjnnnHPOOeecc8455z89pQef43fX6ckT/O54b97d +/TnnnHPOOeecc84555xzzjnnnHPO33pKD77WW/PSenK+0nvz0vpyzjnnnHPO +Oeecc84555xzzjnnPNdTenDO+W5enc8555xzzjnnnHPOOeecc84555zzXE/p +wTnn1f50fdo5OOecc84555xzzjnnnHPOOeecc17vKT0453yVvx3/46NzOeec +c84555xzzjnnnHPOOeecc/4dT+nBOec8K59zzjnnnHPOOeecc84555xzzjnn +zz2lB+ec82tenc8555xzzjnnnHPOOeecc84555zzvqf04Jxz/s6r8znnnHPO +Oeecc84555xzzjnnnHOe14Nzzk/1p+vTzsE555xzzjnnnHPOOeecc84555zz +vB6cc/51fzvue51zzjnnnHPOOeecc84555xzzjnfx1N6cM45//35M2/0/mnn +5pxzzjnnnHPOOeecc84555xzzr/gKT0455xne3U+55xzzjnnnHPOOeecc845 +55xzvpOn9OCcc76nV+dzzjnnnHPOOeecc84555xzzjnniZ7Sg3POebb35qX1 +5ZxzzjnnnHPOOeecc84555xzzis9pQfnnPNveXU+55xzzjnnnHPOOeecc845 +55xzXukpPTjnnH/Lq/M555xzzjnnnHPOOeecc84555zzSk/pwTnnPMNb857u +k3Y+zjnnnHPOOeecc84555xzzjnnfIWn9OCccz7H3477e8I555xzzjnnnHPO +Oeecc84555zf95QenHPO1/qqvLRzc84555xzzjnnnHPOOeecc8455ys8pQfn +nPMMH71v2vk455xzzjnnnHPOOeecc84555zzFZ7Sg3PO+Rlenc8555xzzjnn +nHPOOeecc84555yv8JQenHPOz/DevLS+nHPOOeecc84555xzzjnnnHPO+RNP +6cE55/xs781L68s555xzzjnnnHPOOeecc84555z/5ik9OOec89+etF6cc845 +55xzzjnnnHPOOeecc875b57Sg3POOb/y+DvGOeecc84555xzzjnnnHPOOed8 +B0/pwTnnnN/x6nzOOeecc84555xzzjnnnHPOOef8N0/pwTnnnI/w6nzOOeec +c84555xzzjnnnHPOOec8qQfnnHN+5fkzrzc/7Rycc84555xzzjnnnHPOOeec +c87P8pQenHPO+R3vzUvryznnnHPOOeecc84555xzzjnn/CxP6cE556d6b57v +7Xtenc8555xzzjnnnHPOOeecc84555wn9eCcc/5uXVr/NK/O55xzzjnnnHPO +Oeecc84555xzfpan9OCcc37NR+07uk/K35fUXpxzzjnnnHPOOeecc84555xz +zs/ylB6cc76br16X7ul/X6rzOeecc84555xzzjnnnHPOOeecn+UpPTjn/Cue +0iPVq++/+vycc84555xzzjnnnHPOOeecc87P8JQenHO+m6f02M2rX6/q83PO +Oeecc84555xzzjnnnHPOOT/DU3pwznm1vx3nc3zV68s555xzzjnnnHPOOeec +c84555yP9JQenHNe7Sk9+L/6qte9+pycc84555xzzjnnnHPOOeecc86/5Sk9 +OOe82lN68Gv+9PWt7s0555xzzjnnnHPOOeecc8455/wMT+nBOeejffU6vta9 +rpxzzjnnnHPOOeecc84555xzzpM9pQfnnD/1Ufv19h+Vw+f67PcJ55xzzjnn +nHPOOeecc84555xzfsVTenDOec9n5zztM7sXv+dV7x/OOeecc84555xzzjnn +nHPOOec8sQfnnLeeVd9bo3vyTE/pwTnnnHPOOeecc84555xzzjnn/Nue0oNz +zp/6qP1G547qxcd6Sg/OOeecc84555xzzjnnnHPOOeff9pQenHM+2lvjVbmz +8k710a9Xa171OTnnnHPOOeecc84555xzzjnnnO/pKT0457znd8dT+1f3SPXq +/Ldenc8555xzzjnnnHPOOeecc8455zzLU3pwzjl/5yk9/nh1/ixvzXu6T9r5 +OOecc84555xzzjnnnHPOOeecj/GUHpxzfqrfXbcq9+d42r191avzOeecc845 +55xzzjnnnHPOOeecj/GUHpxzfqrfXbeqz895afd2mvfmpfXlnHPOOeecc845 +55xzzjnnnPPTPaUH55xzzsd5dT7nnHPOOeecc84555xzzjnnnJ/uKT0455xz +3va763v7pJ2Pc84555xzzjnnnHPOOeecc86/5ik9OOecc17nvXlpfTnnnHPO +Oeecc84555xzzjnnPN1TenDOOed8H6/O55xzzjnnnHPOOeecc84555zzdE/p +wTnnnPM6f7o+7Rycc84555xzzjnnnHPOOeecc57iKT0455xzXueteU/3STsf +55xzzjnnnHPOOeecc84555yv9pQenHPOOf+u9+al9eWcc84555xzzjnnnHPO +Oeec87ee0oNzzjnnPCWfc84555xzzjnnnHPOOeecc87fekoPzjnnnPOUfM45 +55xzzjnnnHPOOeecc845f+spPTjnnHP+XW/N681POwfnnHPOOeecc84555xz +zjnnnF/1lB6cc845399H75t2Ps4555xzzjnnnHPOOeecc845v+opPTjnnHO+ +v78d9zuFc84555xzzjnnnHPOOeecc/4VT+nBOeecc97z6nzOOeecc84555xz +zjnnnHPOOb/qKT0455xzzp96dT7nnHPOOeecc84555xzzjnnnP/0lB6cc845 +56O9Op9zzjnnnHPOOeecc84555xzfq6n9OCcc845H+3V+ZxzzjnnnHPOOeec +c84555zzcz2lB+ecc875Kq/O55xzzjnnnHPOOeecc84555x/31N6cM4555yP +9t68tL6cc84555xzzjnnnHPOOeec8+94Sg/OOeec13lv3td+P1Tnc84555xz +zjnnnHPOOeecc86/7yk9OOecc57nd8fv7pN6Ls4555xzzjnnnHPOOeecc845 +f+spPTjnnHM+zlvjvfmje/R8l3vjnHPOOeecc84555xzzjnnnPO7ntKDc845 +5+M8pcdoX3Vv1efknHPOOeecc84555xzzjnnnO/vKT0455xzft9TelT76Pus +Pg/nnHPOOeecc84555xzzjnnfH9P6cE555zz+57SI9Wf3md1b84555xzzjnn +nHPOOeecc875/p7Sg3POOedtT+mxmz+95+renHPOOeecc84555xzzjnnnPP9 +PaUH55xzzu+v6+3ztMfXfdT9c84555xzzjnnnHPOOeecc855y1N6cM455yf5 +qP16+4/K+ZrPfl0455xzzjnnnHPOOeecc8455zylB+ecc36Sj9rvae6o/F19 +9uvCOeecc84555xzzjnnnHPOOecpPTjnnHPenleVu4uvup/qc3LOOeecc845 +55xzzjnnnHPO9/GUHpxzzjnf35+uP+V3S3U+55xzzjnnnHPOOeecc84553yd +p/TgnHPOeZ3fXTdq/7R7SPPqfM4555xzzjnnnHPOOeecc875c0/pwTnnnHPO +f3/8juOcc84555xzzjnnnHPOOec811N6cM4555zzNV6dzznnnHPOOeecc845 +55yf6KP2Hb0f5/y9p/TgnHPOOeeZXp3POeecc84555xzzjnnnCd6a15r3age +d9dX3VdvXsrryPkbT+nBOeecc86zvTWvNz/tHJxzzjnnnHPOOeecc8738FH7 +VuVWeWs8refo8/6cN+r9wL/ts96Ho/fnnHPOOef8ilfnc84555xzzjnnnHPO +Oa/x2Xl316fcC1/rvSetL7/nVd8nLU+5F84555xzfrZX53POOeecc84555xz +zjkf47PzRu2bcl98T6/OP919z3DOOeec85P96fq0c3DOOeecc84555xzzjm/ +57PzRu2bcl/8W16dn+6jPtdV3zMp98g555xzzs/2p+vTzsE555xzzjnnnHPO +OeeneGve3f1SzsOzvTWe1nP2eb/qT+/n57yU83DOOeecc/5Fr87nnHPOOeec +c84555zzr/nd9a0n5Tx8rffmXX2/ve1R7aPvM/X15JxzzjnnnJ/n1fmcc845 +55xzzjnnnHOe4q15rXUpvXmGvx3n73z0vb8d55xzzjnnnPOWV+dzzjnnnHPO +Oeecc875ak/pwff0lB78mlfnc84555xzzr/vvXlpfTnnnHPOOeecc8455/yq +t+bdnc/P9JQefI5X53POOeecc87P9ep8zjnnnHPOOeecc845v+opPfientKD +z/HqfM4555xzzvk6v7tu9/6cc84555xzzjnnnPM6T+nR6/d2Xdq5eK2/Heff +8up8zjnnnHPO+Tqv6jG6f9q9cs4555xzzjnnnHP+BW/Nuzs/zUftm3YuXuur +1/E9vTqfc84555xz/txTejz1p+et7s0555xzzjnnnHPO+c7emnd3v9m9rz6r +7i/l9eN7ekoPnuHV+ZxzzjnnnPO+p/QY7b3zVvfjnHPOOeecc8455zzJW/Na +61J6jxpf5dX5fG9P6cHneHU+55xzzjnn/Lmn9EjxlB6cc84555xzzjnnnCd4 +So+nntKj59X5PMvfjvNveXU+55xzzjnnvO+r1+3qKT0455xzzjnnnHPOOV/p +KT1Ge0qP3n2n9OLZntKDr/HqfM4555xzznn/+Tnv6n5P99/Ve+et7sc555xz +zjnnnHPOz/bWvFH7fNVTevReh5RePMNTevA5Xp3POeecc845389Tevzx6nuo +Pj/nnHPOOeecc845X+utea11d/Oe9nqbu7tX9Ui7B/4NT+nB33l1Puecc845 +53w/b41/NbfqXJxzzjnnnHPO+Ql+d/3sPpyvzJu17x9Puceve2s8rSffy1N6 +8DF+9fsjpS/nnHPOOee8zlvz0nru4q15vflp5+Ccc84555xzfpbPzrs7b1Vu +yv3zsV7VY3Zeyv1We2s8rSfnvz1p/U716nzOOeecc8455zVenc8555xzzjnn +fK6P2vfu+pTz7+a9eWl9d/G7866O73LOUfP57/PSevIzvTU+6u87/92r8znn +nHPOOeec13hr3tN90s7HOeecc8455/zvPmrf1ryUc57qvXlpfVfdx9P35938 +9PNX9+Gcz/NR+83+nvy6r/49xjnnnHPOOef8TK/O55xzzjnnnPOv+d31rXkp +5/m6t8Z36Znm3uecc/67z85Z1X9WXur9/xxPe19xzjnnnHPOOa/11vjd+Zxz +zjnnnHPOf/eUHl/3t+PpfvV9NSuPc875HJ+dU32un/NGzeecc84555xzzhP8 +7fhPTzsf55xzzjnnnK/21rzWk9L7657SI9Wr8znnnP/de/Nm/W6pPq+/85xz +zjnnnHPOed+r8znnnHPOOed8lqf0ONVTenzFq/M555yP8da8tJ5Pz3V1PK0/ +55xzzjnnnHO+0qvzOeecc84557le1SOtz2n+dpy/8+p8zjnnnHPOOeecc845 +5zVenc8555xzzjnve+/3/M95o3q8He95yv2e6ik9vuLV+ZxzzjnnnHPOOeec +c85rvDcvrS/nnHPOOecn+8/x6h6z8tLu/TRP6fEVr87nnHPOOeecc84555xz +nuXV+ZxzzjnnnJ/oKT1az6oeafdwmqf02M2r8znnnHPOOeecc8455/x0b42n +9bzbn3POOeec8xM8pccqX5V3+j1//fU9xavzOeecc84555xzzjnnnP/dn64f +Pa/no/fjnHPOOU/xVb+Lfo773ZXhP8dn/55PO/+oc931tPOe5ik9dvPqfM45 +55xzzjnnnHPOOT/dU3pc9d6/ez6qB+ecc8757N9dKecc7dX5af5zPO33f9p9 +jXq/pfXkzzylR7VX53POOeecc84555xzzvnpntJjtD+9h+renHPOOd/Pf46P ++j2Wds7q+23NS+v7tl9r3ur38ej9OZ/hrfGn3ye7enU+55xzzjnnnHPOOeec +n+4pPar96b1V9+acc855naf02M1782bd86j9Rp037XXh/Et+d92q77erPvse +0l4vzjnnnHPOOeecc84538VXr/u6uy/OOef8HE/pkeopPVb93uOc7+t311V/ +f/p7xDnnnHPOOeecc84553v43XW9fZ72OMVTenDOOec7+qrfRT/npZw/1VN6 +rPLqfM75ud4aT+vJOeecc84555xzzjnn/Nm63j5Pe3zFn95/a171eTjnnPMV +/nN89L5P14/u81VP6VH9u45zzjnnnHPOOeecc84555zz354/82bvv7tX57/1 +u+tG7cM553d99vcbX+PVf+/e7ptyj9We0sPvPc4555xzzjnnnHPOOeecc87b +ntLjj1fnz/LWeNXruMv9jPJdenJ+xWd/b6ScMyU/xXf//r+7PuXeUz2lh9+B +nHPOOeecc84555xzzjnnnLe9NV61D3/mrXlpfVq+y7mqXq9VvXiWp/TYzVPy +q/N2eV3Seu7iKT1Ge3U+55xzzjnnnHPOOeecc8455yO9NS+tJ9/LR+2bdq40 +r87f1VN6fN2reoz+vFzdn/MET+nh88I555xzzjnnnHPOOeecc84553P87vq0 +/qvu5+q62fvv5q3xt/c26v3c8rR7HP2+WtXj1Pvn/Mr4qu+3q7l353POOeec +c84555xzzjnnnHPOOecjx1f76n1b657e89t9RuXe9ZTXf7Sn9Dj1/vmZ3hrf +ZX/OOeecc84555xzzjnnnHPOOef8iqf06Hl1/q7eGk/r6X2ekc8555xzzjnn +nHPOOeecc84555xzzsd4So+eV+fzvT2lh/c555xzzjnnnHPOOeecc84555xz +zvkZntLjj1fn82/66nXez5xzzjnnnHPOOeecc84555xzzjnnZ3hrvDd/dI8/ +nnY//NveGq/ah3POOeecc84555xzzjnnnHPOOeec8yvjaT0555xzzjnnnHPO +Oeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPO +Oeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPO +Oeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPO +Oeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPO +Oeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPO +Oeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPO +Oeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPO +Oeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPO +Oeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPO +Oeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPO +Oeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPO +Oeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPOOeecc84555xzzjnnnHPO +Oeecc84555zzZG/NS+vJOeecc84555xzzjnnnHPOOeecc84557O9Na83f1av +tPvh3/bWvKp9OOecc84555xzzjnnnHPOOeecc875t706/6en9ODf8qfrvZ85 +55xzzjnnnHPOOeecc84555xzzvkTr86/6ik9+J5ene99zjnnnHPOOeecc845 +55xzzjnnnHN+llfnX/WUHrt5a15aT+/zrB6cc84555xzzjnnnHPOOeecc845 +5/yd9+al9h2dczdvVO9d7ivtfZB2P7M9pQfnI7w1b5f9Oeecc84555xzzjnn +nHPOOeecP/O769L6r7qfq+tn77+bX33fVb2fW55yf0+9Ny+t7279OL/jrXmr +vt+u5t6dzznnnHPOOeecc84555xzzvmXvDWe1pPv5aP2SztXmqf02M2r80/x +qvzRnxffS3wnr873eeGcc84555xzzjnnnHPOOee8/fyZV7UPf+at8bQ+Ld/l +XFWv16wePNur83f1tB5p3yfV9/FzXlrPXbw6f5an9OCcc84555xzzjnnnHPO +Oed8hFfn//SUHqO9Na/qddzlfkb5Lj05v+Kzvzeqz9d70vpVv+53961+HdN7 +7uLV+X4Hcs4555xzzjnnnHPOOeec8528NT57/909pcdTv7t+1D6cc37XZ3+/ +8TVe/ffu9L/7afe5i6f04JxzzjnnnHPOOeecc84553v63fW9fdLOt9qf3r97 +5ZxzfrK//Xs6++9oyj2lenV+yu86zjnnnHPOOeecc84555xzzn97eut7+6Sd +L82r8znnnPOdvervdPW50706f7Wn9OCcn+eteWk9Oeecc84555xzzjnnnL9b +n3aOFB99z5xzzjnP9er8dK/OX/17j3O+r99dX/39uboP55xzzjnnnHPOOeec +8zVenZ/iT+9tdi/OOeec53p1/q5+d3x07tP1T/u0xtNeF86/5HfXr/p+u+qz +7yHt9eKcc84555xzzjnnnPPTvDp/lj+9h9m9OOecc/49H/U75O0+X/W349W+ +y/uhNa/6/jj/zVvzdv2+eOopPTjnnHPOOeecc84555xf8+r8t32frh/di3PO +Oefn+ezfXdXnm+UpPVJ89et+d13KPT311ry0nvyZV+eneEoPzjnnnHPOOeec +c8455+989rrRPZ+u55xzzjlP9VW/i3r/frs/f+ZXX5dRv+dTzt3z2Tlp5z3N +q/N39ZQenHPOOeecc84555xzzn9//sxL63m3P+ecc8455yd4df5qr8pJu4ev +enX+1zylB+ecc84555xzzjnnnPNsT+nBOeecc875SV6d33pW56fdw2lenb+r +p/TgnHPOOeecc84555xznuFvxznnnHPOOefrvPfvVT47J+W+T/Xq/K95Sg/O +Oeecc84555xzzjnnGZ7Sg3POOeecc9723u/5n+Oj8mfnVN/r6V6d/zVP6cE5 +55xzzjnnnHPOOed8jqf04JxzzjnnnOd5VX5an9O8Ny+t79c8pQfnnHPOOeec +c84555zza57Sg3POOeecc85He3X+6V6d/zVP6cE55/ydt8bTej49V2ve187L +Oeecc8455/wb3pv3dL+0c3LOOeecc875Km+Nt57qvqd4dX66p/TgnHM+dvzp +75bq875dn3YuzjnnnHPOOef8t+fPvLvzOeecc84555z/7tX5p3hvXlrfp+fr +va9G5aedn3POv+qz86rPdfXv8d35nHPOOeecc875jp7Sg3POOeecc86/4nfX +tcarz3GKt+bt0jPNvc855/x3n523qv+snNT79/eLc84555xzzr/prfGn+zxd +zznnnHPOOed8rY/arzVefb7T/e341/zt+/NtXrW35qX15Jy/91H7zv6e/Lpf +XZfWm3POOeecc875Gk/pwTnnnHPOOed8jo/a7+666nPv6m/H+e9+dbw1L/19 +3hofNZ//Pp7Wk5/prXn+rqzxlB6cc84555zz87w1ntZzF2+N9+aP7sE555xz +zjnnnN/x2TlXx6tyq++fj/Wq/Nk51fea4q15aT05T8rnf/eUHpxzzjnnnPPv +emveV3OrzsU555xzzjnnnJ/gd9fN7sP5P/vsnNH7/fTq+zvFW/PSevK9vDqf +j/XWuO9tzjnnnHPOeetJ6VV9D9U9OOecc84555xzzvlab4231t/Nebrube7u +XpWfdg/8G16dz8d4Sg/OOeecc875fX87/sffrt/Ne+et6sU555xzzjnnnHPO ++W/jo/b5qlfnX+2V1o/XenU+n+spPTjnnHPOOefj/On6tHOsuqe0Xpxzzjnn +nHPOOeecz/Tq/FlenX+1V1o/nunV+XyNp/TgnHPOOeecv/fq/DSvzuecc845 +55xzzjnnPMmr8996df5VT+nBM7w3L60vn+spPTjnnHPOOefjvDp/lvfOW9WL +c84555xzzjnnnPNEb4231lf37T2pfVN68D29Op/P9ZQenHPOOeec83Fenf/W +n553di/OOeecc84555xzzr/srfG7+87u23tW32P168b39up8nuUpPTjnnHPO +OefjvCp/dP/R+3LOOeecc84555xzztvjd+en+aj90s7Fa/3p+rRz8Lme0oNz +zjnnnHM+3++u370/55xzzjnnnHPOOee83qvze73uru/9m5/tvXlpfflcT+nB +Oeecc845560nrR/nnHPOOeecc84555z/8ep8vrdX5/O5ntKDc84555xzfp6/ +Heecc84555xzzjnnnPNUb43fnc/P9Op8PtdTenDOOeecc87P85QenHPOOeec +c84555xzvsqr8/neXp3P73lKD84555xzzvl3PaUH55xzzjnnnHPOOeecV3tr +vLW+ui/P8t68tL5f86evy6r9OOecc84559/1lB6cc84555xzzjnnnHP+Fb+7 +rvVUn4PX+N3xp/uk++j7HL3v6NeVc84555xznuOr13HOOeecc84555xzzjl/ +563xu/tWn4Pv4a15aT1nn/er/vR+fJ9wzjnnnHPe99XrOOecc84555xzzjnn +nGf47JxR+1XfE/+mp/RI9VGf66rvmer745xzzjnn/Imn9OCcc84555xzzjnn +nHP+zmfnjNqv+p743p7S41T3PcM555xzznn/SevHOeecc84555xzzjnnfI7P +zrm7rvo+eI1ffdJ682te9X3S8ur74Jxzzjnne3hrvDd/dA/OOeecc84555xz +zjnnZ/io/apyq7w1L63n6PP+HB/1fuDf9lmfu7e9OOecc845T+rBOeecc845 +55xzzjnnnCd5a7y1flT+3XVV9/R2nPMdvDqfc84555zv4Sk9OOecc84555xz +zjnnnPOTfNR+o/pwzsd7dT7nnHPOOX/mb8c555xzzjnnnHPOOeecc8455+u9 +Op9zzjnnOX53/aj90+4hzVN6cM4555xzzjnnnHPOOeecc87ve3U+55xzzr/j +s9elnffpOat7cM4555xzzjnnnHPOOeecc87ne3U+55xzzvvjVbm7+Kr7WZXH +Oeecc84555xzzjnnnHPOOd/fq/M555zzE33Uvk9z0+5jtc9+XTjnnHPOOeec +c84555xzzjnnvDqfc845P9FH7dvbP+3cKT77deGcc84555xzzjnnnHPOOeec +8+p8zjnnnLefp3/HR/f6mo+6f84555xzzjnnnHPOOeecc845b3l1Puecc877 +Xp2/qz+959m9OOecc84555xzzjnnnHPOOeff9+p8zjnnnD/36vx0f3qfs3tx +zjnnnHPOOeecc84555xzzr/v1fmcc845f+7V+Sk++j5H78s555xzzjnnnHPO +Oeecc845P8+r8znnnHM+3qvzZ/mqe1uVxznnnHPOOeecc84555xzzjn/rlfn +c84553y8t+b15q/uu8u9cc4555xzzjnnnHPOOeecc875Xa/O55xzznmu9+b1 +/t3bJ/VcnHPOOeecc84555xzzjnnnHP+1qvzOeecc17vd8fT+j89b3UPzjnn +nHPOOeecc84555xzzvl3vTqfc84553yWvx3nnHPOOeecc84555xzzjnnnPOn +Xp3POeecc77aU3pwzjnnnHPOOeecc84555xzzr/r1fmcc84557M8pQfnnHPO +Oeecc84555xzzjnn/Dyvzuecc845n+UpPTjnnHPOOeecc84555xzzjnn53l1 +Puecc875W0/pwTnnnHPOOeecc84555xzzjnnf7w6n3POOef8qqf04Jxzzjnn +nHPOOeecc84555zznlfnc8455/w73pv3dL+0c3LOOeecc84555xzzjnnnHPO +ec+r8znnnHP+HU/fj3POOeecc84555xzzjnnnHPOV3l1Puecc86/763x3vzR +PTjnnHPOOeecc84555xzzjnnfJVX53POOeec9560fpxzzjnnnHPOOeecc845 +55xz3vPqfM4555zz3pPWj3POOeecc84555xzzjnnnHPOe16dzznnnPPv+9tx +zjnnnHPOOeecc84555xzzjnfzavzOeecc17vrfGn+zxdzznnnHPOOeecc845 +55xzzjnnX/HqfM4555zX++p1nHPOOeecc84555xzzjnnnHP+da/O55xzzvl+ +ntKDc84555xzzjnnnHPOOeecc85TvTqfc8455/X+dpxzzjnnnHPOOeecc845 +55xzzvm/enU+55xzzvt+d11vn6c9OOecc84555xzzjnnnHPOOeecX/PqfM45 +55yP95QenHPOOeecc84555xzzjnnnHN+qlfnc8756X53/ao+P8fT7u00fzvO +Oeecc84555xzzjnnnHPOOed8rVfnc8756X53/arc3r/5HE/pwTnnnHPOOeec +c84555xzzjnn/J1X53POOR/j1fk/PaXHaG+NP93n6XrOOeecc84555xzzjnn +nHPOOefZXp3POedXvTev9+9qr85P95QeTz2lB+ecc84555xzzjnnnHPOOeec +8wyvzuec81nemleVOzrndB/9ej0d55xzzjnnnHPOOeecc84555xzzv/m1fmc +c/7WR+07OjftnnhGPuecc84555xzzjnnnHPOOeec8zO8Op9zzlvP0/FV34ez +evC5Xp3POeecc84555xzzjnnnHPOOef8DK/O55zzqz4772mftHs63aveP5xz +zjnnnHPOOeecc84555xzzvk/e3U+55y/9VH79vZPOzf/u89+n3DOOeecc845 +55xzzjnnnHPOOedXvDqfc85n+dP1aefgf/dV7wfOOeecc84555xzzjnnnHPO +Oef8iVfnc855ilfn83v+9PWd3YtzzjnnnHPOOeecc84555xzzjlPyOec8xSv +zud/91Wv+6o8zjnnnHPOOeecc84555xzzjnnZ3h1Puecp3hvXlrfU3zV68s5 +55xzzjnnnHPOOeecc84555yP9Op8zjnf1avzd/Xq16u6B+ecc84555xzzjnn +nHPOOeec8zO8Op9zzr/m1fnpXn3/q3pwzjnnnHPOOeecc84555xzzjk/26vz +Oed8V3+6Pu0co+8j9e9LSg/OOeecc84555xzzjnnnHPOOedneHU+55zzez5q +v9F9fs5LvZ9VPTjnnHPOOeecc84555xzzjnnnJ/t1fmcc87/7nfXp/VP85Qe +nHPOOeecc84555xzzjnnnHPOz/DqfM45P93vjqf1T/OUHpxzzjnnnHPOOeec +c84555xzzs/26nzOOef8ib8d55xzzjnnnHPOOeecc84555xzzmd6dT7nnHP+ +m7fGe/NH9+Ccc84555xzzjnnnHPOOeecc87veHU+55xzPtJTenDOOeecc845 +55xzzjnnnHPOOT/bq/M555zzJ57Sg3POOeecc84555xzzjnnnHPOOf+bV+dz +zjnnv/nbcc4555xzzjnnnHPOOeecc84557zCq/M555zz3zylB+ecc84555xz +zjnnnHPOOeecc37Hq/M555zzEeOcc84555xzzjnnnHPOOeecc855klfnc845 +P8vfjnPOOeecc84555xzzjnnnHPOOec7eHU+55zzszylB+ecc84555xzzjnn +nHPOOeeccz7Tq/M555xnefp+nHPOOeecc84555xzzjnnnHPO+Q5enc8557zG +v5bDOeecc84555xzzjnnnHPOOeecJ3l1Puec87nemzc6J+38nHPOOeecc845 +55xzzjnnnHPOeYVX53POOc/y1vjTfZ6u55xzzjnnnHPOOeecc84555xzznf2 +6nzOOeff9JQenHPOOeecc84555xzzjnnnHPOeYVX53POOf+mp/TgnHPOOeec +c84555xzzjnnnHPOK7w6n3PO+R7+dpxzzjnnnHPOOeecc84555xzzjk/yavz +Oeec7+0pPTjnnHPOOeecc84555xzzjnnnPMkr87nnHO+h6f04JxzzjnnnHPO +Oeecc84555xzznfw6nzOOed/99b46P1H78s555xzzjnnnHPOOeecc84555zz ++nzOOT/Fe/NG56Sdn3POOeecc84555xzzjnnnHPOOT/Jq/M55/x0X72Oc845 +55xzzjnnnHPOOeecc8455/O9Op9zzvkYT+nBOeecc84555xzzjnnnHPOOeec +8/p8zjnn9zylB+ecc84555xzzjnnnHPOOeecc87bXp3POef8757Sg3POOeec +c84555xzzjnnnHPOOef3vTqfc85Xe2/e1f1G53LOOeecc84555xzzjnnnHPO +Oef8O16dzznnKb56Heecc84555xzzjnnnHPOOeecc86/69X5nHO+q6f04Jxz +zjnnnHPOOeecc84555xzznmeV+fzGm+Np/XkfKW/Heecc84555xzzjnnnHPO +Oeecc845/+PV+Xyu312vJ0/w3rzev+8+aefnnHPOOeecc84555xzzjnnnHPO ++f5enc/H+Kh9d+mfdv+81lN6cM4555xzzjnnnHPOOeecc84555z/8ep8Psbv +rl/VZ3XOqHtLe315Vg/OOeecc84555xzzjnnnHPOOeec855X5/MxXp3/Vf85 +3pt3dT7P6sE555xzzjnnnHPOOeecc84555xzPtqr86/63XVp/avugdd6So/R +vnod55xzzjnnnHPOOeecc84555xzzvluXp3/1u+Op/UffV6+t6f06HlKD845 +55xzzjnnnHPOOeecc84555zzVK/Of+uj9+39e5VX5/M9PPVzxDnnnHPOOeec +c84555xzzjnnnHN+ulfnX/XqHr1/j/ZVOfzbXp3POeecc84555xzzjnnnHPO +Oeecc36qV+W/Ha/2VffA+RPvvd+qenHOOeecc84555xzzjnnnHPOOeecn+LV ++a3n6Xjq/bztwfkd770Pq3pxzjnnnHPOOeecc84555xzzjnnnJ/i1fm9J6Vf +79+renD+Zv2qXpxzzjnnnHPOOeecc84555xzzjnnp3t1fut5Or7qfnr7pN0r +/6Y//XzN7sU555xzzjnnnHPOOeecc84555xzfrpX57/12Xm93LT74Gd52ueF +c84555xzzjnnnHPOOeecc84555xn5M/yu+t7+6Sdj5/lVZ8LzjnnnHPOOeec +c84555xzzjnnnHP+zKvzU7w6n/PffPT7fPS+nHPOOeecc84555xzzjnnnHPO +Oef8X706P92r8/lZvur9vCqPc84555xzzjnnnHPOOeecc8455/xUr85P9+p8 +/k1P6dF60vpxzjnnnHPOOeecc84555xzzjnnnO/m1fm7enU+39ur37fVPTjn +nHPOOeecc84555xzzjnnnHPOv+7V+bt6dT7fy3+OV/dYlcc555xzzjnnnHPO +Oeecc84555xzfqpX5+/qvSetL5/rKT16ntKDc84555xzzjnnnHPOOeecc845 +5/zrXp1/ulfn83ue0qPnb8c555xzzjnnnHPOOeecc84555xzzvk7r87nf/fq +/NM9pcdoT+nBOeecc84555xzzjnnnHPOOeecc/51r84/3Uft29s/7dyr7vXq +/Vydv7un9OCcc84555xzzjnnnHPOOeecc845/7pX5/Msr87/6aPPdXV9yvmf ++ttxzjnnnHPOOeecc84555xzzjnnnHP+zqvzeZa35vXmX81JO+9pntKDc845 +55xzzjnnnHPOOeecc8455/zrXp3Pa3zUvmnn4lk9OOecc84555xzzjnnnHPO +Oeecc85P9ep8Ptffjnuf7OkpPTjnnHPOOeecc84555xzzjnnnHPOT/XqfM55 +39+Oc84555xzzjnnnHPOOeecc84555zztV6dzzl/vq63z9MenHPOOeecc845 +55xzzjnnnHPOOef8nVfnc86fr+vt87QH55xzzjnnnHPOOeecc84555xzzjl/ +59X5nPPxntKDc84555xzzjnnnHPOOeecc8455/xUr87nnI/3lB6cc84555xz +zjnnnHPOOeecc84556d6dT7n/Lmn9OCcc84555xzzjnnnHPOOeecc8455//q +1fmcn+ir13HOOeecc84555xzzjnnnHPOOeec87Venc8573tKD84555xzzjnn +nHPOOeecc84555xzfs2r8znn7SetH+ecc84555xzzjnnnHPOOeecc845v+bV ++Zx/2d+Oc84555xzzjnnnHPOOeecc84555zzPb06n/MTPaUH55xzzjnnnHPO +Oeecc84555xzzjmf49X5nH/B345zzjnnnHPOOeecc84555xzzjnnnPNveXU+ +5zv523HOOeecc84555xzzjnnnHPOOeecc36GV+dzvpOn9OCcc84555xzzjnn +nHPOOeecc84559lenc/5b+N356/qxTnnnHPOOeecc84555xzzjnnnHPO+W9e +nc95Qv5P7/Ws6sU555xzzjnnnHPOOeecc84555xzzvfw6nzOE/J/eq9nVS/O +Oeecc84555xzzjnnnHPOOeecc76HV+fzs7w3L6Xv0/6cc84555xzzjnnnHPO +Oeecc84555wn5HNemf+05+xenHPOOeecc84555xzzjnnnHPOOed8b6/O53yk +t+bN3p9zzjnnnHPOOeecc84555xzzjnnnPN/9up8znfylB6cc84555xzzjnn +nHPOOeecc8455zzbq/M5T/SUHpxzzjnnnHPOOeecc84555xzzjnnfE+vzuc8 +0VN6cM4555xzzjnnnHPOOeecc84555zzPb06n/ORvnod55xzzjnnnHPOOeec +c84555xzzjnnf/Pq/P9uh45uAASBIAr237UdaCB37inzOwHeBs6TPmUH55xz +zjnnnHPOOeecc84555xzzjn/l6f7nL/hU3ZwzjnnnHPOOeecc84555xzzjnn +nPMzPN3nvNKn7OCcc84555xzzjnnnHPOOeecc84552d7us/5nU/ZwTnnnHPO +Oeecc84555xzzjnnnHPO+Yqn+zzjVe/tdqv6nHPOOeecc84555xzzjnnnHPO +OeecT/R0n9f407n0rmn/xTnnnHPOOeecc84555xzzjnnnHPOeaen+7zXuztP +3e4+55xzzjnnnHPOOeecc84555xzzjnnEz3d5xlfvbf7/u59zjnnnHPOOeec +c84555xzzjnnnHPOv+kX/MR5Lg== + "], {{0, 0}, {401, 401}}, {0, 1}], Frame -> Automatic, + FrameLabel -> {None, None}, FrameTicks -> {{None, None}, {None, None}}, + GridLinesStyle -> Directive[ + GrayLevel[0.5, 0.4]], + Method -> { + "DefaultBoundaryStyle" -> Automatic, "DefaultPlotStyle" -> Automatic}], + FormBox[ + FormBox[ + TemplateBox[{"\"Divergent\"", + RowBox[{"-", "1"}], + RowBox[{ + RowBox[{"-", + RowBox[{"0.5`"}]}], "-", + RowBox[{"0.5`", " ", "\[ImaginaryI]"}]}], + RowBox[{ + RowBox[{"-", + RowBox[{"0.5`"}]}], "+", + RowBox[{"0.5`", " ", "\[ImaginaryI]"}]}]}, "SwatchLegend", + DisplayFunction -> (FormBox[ + StyleBox[ + StyleBox[ + PaneBox[ + TagBox[ + GridBox[{{ + TagBox[ + GridBox[{{ + GraphicsBox[{ + Directive[ + EdgeForm[ + Directive[ + Opacity[0.3], + GrayLevel[0]]], + PointSize[0.5], + AbsoluteThickness[1.6], + RGBColor[0., 0., 0.]], + RectangleBox[{0, 0}, {10, 10}, "RoundingRadius" -> 0]}, + AspectRatio -> Full, ImageSize -> {10, 10}, + PlotRangePadding -> None, ImagePadding -> Automatic, + BaselinePosition -> (Scaled[0.1] -> Baseline)], #}, { + GraphicsBox[{ + Directive[ + EdgeForm[ + Directive[ + Opacity[0.3], + GrayLevel[0]]], + PointSize[0.5], + AbsoluteThickness[1.6], + RGBColor[1., 0., 0.]], + RectangleBox[{0, 0}, {10, 10}, "RoundingRadius" -> 0]}, + AspectRatio -> Full, ImageSize -> {10, 10}, + PlotRangePadding -> None, ImagePadding -> Automatic, + BaselinePosition -> (Scaled[0.1] -> Baseline)], #2}, { + GraphicsBox[{ + Directive[ + EdgeForm[ + Directive[ + Opacity[0.3], + GrayLevel[0]]], + PointSize[0.5], + AbsoluteThickness[1.6], + RGBColor[0., 1., 0.]], + RectangleBox[{0, 0}, {10, 10}, "RoundingRadius" -> 0]}, + AspectRatio -> Full, ImageSize -> {10, 10}, + PlotRangePadding -> None, ImagePadding -> Automatic, + BaselinePosition -> (Scaled[0.1] -> Baseline)], #3}, { + GraphicsBox[{ + Directive[ + EdgeForm[ + Directive[ + Opacity[0.3], + GrayLevel[0]]], + PointSize[0.5], + AbsoluteThickness[1.6], + RGBColor[0., 0., 1.]], + RectangleBox[{0, 0}, {10, 10}, "RoundingRadius" -> 0]}, + AspectRatio -> Full, ImageSize -> {10, 10}, + PlotRangePadding -> None, ImagePadding -> Automatic, + BaselinePosition -> (Scaled[0.1] -> Baseline)], #4}}, + GridBoxAlignment -> { + "Columns" -> {Center, Left}, "Rows" -> {{Baseline}}}, + AutoDelete -> False, + GridBoxDividers -> { + "Columns" -> {{False}}, "Rows" -> {{False}}}, + GridBoxItemSize -> {"Columns" -> {{All}}, "Rows" -> {{All}}}, + GridBoxSpacings -> { + "Columns" -> {{0.5}}, "Rows" -> {{0.5}}}], "Grid"]}}, + GridBoxAlignment -> {"Columns" -> {{Left}}, "Rows" -> {{Top}}}, + AutoDelete -> False, + GridBoxItemSize -> { + "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, + GridBoxSpacings -> {"Columns" -> {{1}}, "Rows" -> {{0}}}], + "Grid"], Alignment -> Left, AppearanceElements -> None, + ImageMargins -> {{5, 5}, {5, 5}}, ImageSizeAction -> + "ResizeToFit"], LineIndent -> 0, StripOnInput -> False], { + FontFamily -> "Arial"}, Background -> Automatic, StripOnInput -> + False], TraditionalForm]& ), + InterpretationFunction :> (RowBox[{"SwatchLegend", "[", + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{"Directive", "[", + InterpretationBox[ + ButtonBox[ + TooltipBox[ + GraphicsBox[{{ + GrayLevel[0], + RectangleBox[{0, 0}]}, { + GrayLevel[0], + RectangleBox[{1, -1}]}, { + RGBColor[0., 0., 0.], + RectangleBox[{0, -1}, {2, 1}]}}, AspectRatio -> 1, Frame -> + True, FrameStyle -> RGBColor[0., 0., 0.], FrameTicks -> + None, PlotRangePadding -> None, ImageSize -> + Dynamic[{ + Automatic, 1.35 CurrentValue["FontCapHeight"]/ + AbsoluteCurrentValue[Magnification]}]], + "RGBColor[0., 0., 0.]"], Appearance -> None, + BaseStyle -> {}, BaselinePosition -> Baseline, + DefaultBaseStyle -> {}, ButtonFunction :> + With[{Typeset`box$ = EvaluationBox[]}, + If[ + Not[ + AbsoluteCurrentValue["Deployed"]], + SelectionMove[Typeset`box$, All, Expression]; + FrontEnd`Private`$ColorSelectorInitialAlpha = 1; + FrontEnd`Private`$ColorSelectorInitialColor = + RGBColor[0., 0., 0.]; + FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; + MathLink`CallFrontEnd[ + FrontEnd`AttachCell[Typeset`box$, + FrontEndResource["RGBColorValueSelector"], { + 0, {Left, Bottom}}, {Left, Top}, + "ClosingActions" -> { + "SelectionDeparture", "ParentChanged", + "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> + Automatic, Method -> "Preemptive"], + RGBColor[0., 0., 0.], Editable -> False, Selectable -> + False], "]"}], ",", + RowBox[{"Directive", "[", + InterpretationBox[ + ButtonBox[ + TooltipBox[ + GraphicsBox[{{ + GrayLevel[0], + RectangleBox[{0, 0}]}, { + GrayLevel[0], + RectangleBox[{1, -1}]}, { + RGBColor[1., 0., 0.], + RectangleBox[{0, -1}, {2, 1}]}}, AspectRatio -> 1, Frame -> + True, FrameStyle -> RGBColor[0.6666666666666667, 0., 0.], + FrameTicks -> None, PlotRangePadding -> None, ImageSize -> + Dynamic[{ + Automatic, 1.35 CurrentValue["FontCapHeight"]/ + AbsoluteCurrentValue[Magnification]}]], + "RGBColor[1., 0., 0.]"], Appearance -> None, + BaseStyle -> {}, BaselinePosition -> Baseline, + DefaultBaseStyle -> {}, ButtonFunction :> + With[{Typeset`box$ = EvaluationBox[]}, + If[ + Not[ + AbsoluteCurrentValue["Deployed"]], + SelectionMove[Typeset`box$, All, Expression]; + FrontEnd`Private`$ColorSelectorInitialAlpha = 1; + FrontEnd`Private`$ColorSelectorInitialColor = + RGBColor[1., 0., 0.]; + FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; + MathLink`CallFrontEnd[ + FrontEnd`AttachCell[Typeset`box$, + FrontEndResource["RGBColorValueSelector"], { + 0, {Left, Bottom}}, {Left, Top}, + "ClosingActions" -> { + "SelectionDeparture", "ParentChanged", + "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> + Automatic, Method -> "Preemptive"], + RGBColor[1., 0., 0.], Editable -> False, Selectable -> + False], "]"}], ",", + RowBox[{"Directive", "[", + InterpretationBox[ + ButtonBox[ + TooltipBox[ + GraphicsBox[{{ + GrayLevel[0], + RectangleBox[{0, 0}]}, { + GrayLevel[0], + RectangleBox[{1, -1}]}, { + RGBColor[0., 1., 0.], + RectangleBox[{0, -1}, {2, 1}]}}, AspectRatio -> 1, Frame -> + True, FrameStyle -> RGBColor[0., 0.6666666666666667, 0.], + FrameTicks -> None, PlotRangePadding -> None, ImageSize -> + Dynamic[{ + Automatic, 1.35 CurrentValue["FontCapHeight"]/ + AbsoluteCurrentValue[Magnification]}]], + "RGBColor[0., 1., 0.]"], Appearance -> None, + BaseStyle -> {}, BaselinePosition -> Baseline, + DefaultBaseStyle -> {}, ButtonFunction :> + With[{Typeset`box$ = EvaluationBox[]}, + If[ + Not[ + AbsoluteCurrentValue["Deployed"]], + SelectionMove[Typeset`box$, All, Expression]; + FrontEnd`Private`$ColorSelectorInitialAlpha = 1; + FrontEnd`Private`$ColorSelectorInitialColor = + RGBColor[0., 1., 0.]; + FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; + MathLink`CallFrontEnd[ + FrontEnd`AttachCell[Typeset`box$, + FrontEndResource["RGBColorValueSelector"], { + 0, {Left, Bottom}}, {Left, Top}, + "ClosingActions" -> { + "SelectionDeparture", "ParentChanged", + "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> + Automatic, Method -> "Preemptive"], + RGBColor[0., 1., 0.], Editable -> False, Selectable -> + False], "]"}], ",", + RowBox[{"Directive", "[", + InterpretationBox[ + ButtonBox[ + TooltipBox[ + GraphicsBox[{{ + GrayLevel[0], + RectangleBox[{0, 0}]}, { + GrayLevel[0], + RectangleBox[{1, -1}]}, { + RGBColor[0., 0., 1.], + RectangleBox[{0, -1}, {2, 1}]}}, AspectRatio -> 1, Frame -> + True, FrameStyle -> RGBColor[0., 0., 0.6666666666666667], + FrameTicks -> None, PlotRangePadding -> None, ImageSize -> + Dynamic[{ + Automatic, 1.35 CurrentValue["FontCapHeight"]/ + AbsoluteCurrentValue[Magnification]}]], + "RGBColor[0., 0., 1.]"], Appearance -> None, + BaseStyle -> {}, BaselinePosition -> Baseline, + DefaultBaseStyle -> {}, ButtonFunction :> + With[{Typeset`box$ = EvaluationBox[]}, + If[ + Not[ + AbsoluteCurrentValue["Deployed"]], + SelectionMove[Typeset`box$, All, Expression]; + FrontEnd`Private`$ColorSelectorInitialAlpha = 1; + FrontEnd`Private`$ColorSelectorInitialColor = + RGBColor[0., 0., 1.]; + FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; + MathLink`CallFrontEnd[ + FrontEnd`AttachCell[Typeset`box$, + FrontEndResource["RGBColorValueSelector"], { + 0, {Left, Bottom}}, {Left, Top}, + "ClosingActions" -> { + "SelectionDeparture", "ParentChanged", + "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> + Automatic, Method -> "Preemptive"], + RGBColor[0., 0., 1.], Editable -> False, Selectable -> + False], "]"}]}], "}"}], ",", + RowBox[{"{", + RowBox[{#, ",", #2, ",", #3, ",", #4}], "}"}], ",", + RowBox[{"LegendMarkers", "\[Rule]", "Automatic"}], ",", + RowBox[{"LabelStyle", "\[Rule]", + RowBox[{"{", "}"}]}], ",", + RowBox[{"LegendLayout", "\[Rule]", "\"Column\""}]}], "]"}]& ), + Editable -> True], TraditionalForm], TraditionalForm]}, + "Legended", + DisplayFunction->(GridBox[{{ + TagBox[ + ItemBox[ + PaneBox[ + TagBox[#, "SkipImageSizeLevel"], Alignment -> {Center, Baseline}, + BaselinePosition -> Baseline], DefaultBaseStyle -> "Labeled"], + "SkipImageSizeLevel"], + ItemBox[#2, DefaultBaseStyle -> "LabeledLabel"]}}, + GridBoxAlignment -> {"Columns" -> {{Center}}, "Rows" -> {{Center}}}, + AutoDelete -> False, GridBoxItemSize -> Automatic, + BaselinePosition -> {1, 1}]& ), + Editable->True, + InterpretationFunction->(RowBox[{"Legended", "[", + RowBox[{#, ",", + RowBox[{"Placed", "[", + RowBox[{#2, ",", "After"}], "]"}]}], "]"}]& )]], "Output", + CellChangeTimes->{3.659556259184917*^9, 3.659556302150953*^9, + 3.6595563906887107`*^9, 3.6595564366805267`*^9, 3.6641617768839207`*^9}] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"newtonplot", "[", + RowBox[{ + RowBox[{"Function", "[", + RowBox[{"x", ",", + RowBox[{ + RowBox[{"(", + RowBox[{"x", "+", "1.5"}], ")"}], + RowBox[{"(", "x", ")"}], + RowBox[{"(", + RowBox[{"x", "-", "0.75"}], ")"}]}]}], "]"}], ",", "2", ",", "401", + ",", "20", ",", "0.05"}], "]"}]], "Input", + CellChangeTimes->{{3.6595549152958674`*^9, 3.659554978383319*^9}, + 3.659555332709116*^9, {3.659555509656427*^9, 3.6595555271955185`*^9}, { + 3.659555597485504*^9, 3.659555613597739*^9}, {3.6631017052455835`*^9, + 3.663101720860613*^9}, 3.6641616424542694`*^9}], + +Cell[BoxData[ + TemplateBox[{GraphicsBox[ + RasterBox[CompressedData[" +1:eJzs1t2t5MphhdFrKBJHohwUggA/OxZnqhAMQTgPc9DdbP7uXVWLgADNKpLf +ZmsAzX//83//8T9/++uvv/7vv/7zn3//9/9c//r7Xy+vWf3q59q+bzVP9/nY +3rKDc84555xzzjnnnHPOOee81d+db/15VT97zjnnfC5P99s93ecdfT6nt+zg +nHPOOeecc84555xzzjlfzVt2HPWz55xzztfwdL/d033e0edruL+XnHPOOeec +c84555xzzjnnc/m781SXc875Wp7uj+rp/qye7vO1vGUH55xzzjnnnHPOOeec +c845n8vTfc455x2e7q/iR8/bviP9O3F+pbfs4JxzzjnnnHPOOeecc84553N5 +us8557zD033+2tN938dX8JYdnHPOOeecc84555xzzjnnfC5P9znnnHd4us/3 +ebrvO/hM3rKDc84555xzzjnnnHPOOeecz+XpPuec8w5P9/k1nu6Ptouv5S07 +OOecc84555xzzjnnnHPO+Vye7nPOOe/2dJ9nfLYO55+8ZQfnnHPOOeecc845 +55xzzjmfy9N9zjnn3Z7u8y5vfx/nn7xlB+ecc84555xzzjnnnHPOOV/D033O +Oefdnu7zsf3sOedHvGUH55xzzjnnnHPOOeecc845X9vTfc45592e7vOx/enn ++Fq+9eendnDOOeecc84555xzzjnnnPO1Pd3nnHM+pqf7fGzfus+/f/g33rKD +c84555xzzjnnnHPOOeec809X2y7OOefdnu7zsT3dn31vu7fs4JxzzjnnnHPO +Oeecc8455/xOT/c555yP6ek+H9vT/af96t/h7l2cc84555xzzjnnnHPOOeec +8+893eeccz6Xp/t8bE/3Oeecc84555xzzjnnnHPOOef8Kk/3Oeecz+XpPh/b +t+5r28s555xzzjnnnHPOOeecc8455+883eeccz6Xp/t8bE/3Oeecc84555xz +zjnnnHPOOed8r6f7nHPO1/B0n4/t6T7nnHPOOeecc84555xzzjnnnL/zratt +L+ec87k83edje7rPOeecc84555xzzjnnnHPOOZ/f39139pxzzjm/09N9Pran ++5xzzjnnnHPOOeecc84555xznu5zzjnnrzzd52N7us8555xzzjnnnHPOOeec +c8455+k+55xz/srTfT62p/ucc84555xzzjnnnHPOOeecc57uc84556883edz +errPOeecc84555xzzjnnnHPOOZ/P033OOed8j6f7fE4/+nzbd3DOOeecc845 +55xzzjnnnHPOezzd55xzzvd4us/n9HSfc84555xzzjnnnHPOOeeccz6up/uc +c875FZ7u8zk93eecc84555xzzjnnnHPOOeec93u6zznnnN/p6T6f09N9zjnn +nHPOOeecc84555xzznm/p/ucc875nZ7u87U83eecc84555xzzjnnnHPOOeec +P+/pPuecc57wdJ+v5ek+55xzzjnnnHPOOeecc8455/w+T/c555zzJk/3+Vr+ +1PvavptzzjnnnHPOOeecc84555zzpO99/uw555xzzvN9zq84P/vvSs4555xz +zjnnnHPOOeecc875+6ttF+eccz6Cp/ucN/Q555xzzjnnnHPOOeecc8455++v +tl2cc875CJ7uc97Q55xzzjnnnHPOOeecc84555y/v9p2cc455yN4us/5J0/3 +Oeecc84555xzzjnnnHPOOV/B033OOed8Rk/3Of/k6T7nnHPOOeecc84555xz +zjnnK3i6zznnnM/o6T7nnzzd55xzzjnnnHPOOeecc84553wmT/c555zzlTzd +5/yIb93XtpdzzjnnnHPOOeecc84555zzJz3d55xzznm+z/kRT/c555xzzjnn +nHPOOeecc845b/Z0n3POOef5PudXerrPOeecc84555xzzjnnnHPO+ZOe7nPO +Oef8vaf7nD/hbe/z72bOOeecc84555xzzjnnnHO+x9N9zjnnnO/3dJ/zpD/9 +3G9v+z0455xzzjnnnHPOOeecc8551tN9zjnnnF/n6T7njX72/Ftv+27OOeec +c84555xzzjnnnHOe9XSfc84559d5us95o6f7nHPOOeecc84555xzzjnnfG5P +9znnnHN+v6f7nDf61n1teznnnHPOOeecc84555xzznmnp/ucc845z3m6z/lI +nu5zzjnnnHPOOeecc84555zzTk/3Oeecc97n6T7nI3m6zznnnHPOOeecc845 +55xzPqu/O9/681170h3OOeecj+/pPucj+dHztu/gnHPOOeecc84555xzzjlv +96ve+/RznHPOOec/nu5zPoOn+5xzzjnnnHPOOeecc84557P5Ve89e84555xz +ftTTfc5n9nSfc84555xzzjnnnHPOOeecd/Q555xzvp6n+5yv6EfP276Dc845 +55xzzjnnnHPOOed8FE/3Oeecc76ep/uc854+55xzzjnnnHPOOeecc875rJ7u +c84553w9T/c55z19zjnnnHPOOeecc84555zz0T3d55xzzjn/8XSfc77t6f7o +39f2vZxzzjnnnHPOOeecc845v8/Tfc4555zzH0/3OefHPd0fZW/b78A555xz +zjnnnHPOOeec8/Oe7nPOOeecb3m6zzm/3rfue6rf8ru07OCcc84555xzzjnn +nHPO+XWe7nPOOeecb3m6zznPe/v7znrLDs4555xzzjnnnHPOOeec7/d0n3PO +Oef8qKf7nPNef/q5s972+3HOOeecc84555xzzjnn/HtP9znnnHPOr/Z0n3M+ +j6f7nHPOOeecc84555xzzjnv93Sfc8455/wpT/c55/N4us8555xzzjnnnHPO +Oeec835P9znnnHPOn/J0n3M+j6f7nHPOOeecc84555xzzjnv8XSfc8455zzt +6T7nfB7fuq9tL+ecc84555xzzjnnnHPOz3u6zznnnHPe6uk+53x+T/c555xz +zjnnnHPOOeecc75939lzzjnnnHP+p6f7nPP5feu+tr2cc84555xzzjnnnHPO ++cqe7nPOOeecz+LpPud8fk/3Oeecc84555xzzjnnnHP+/mrbxTnnnHM+i6f7 +nPN1Pd3nnHPOOeecc84555xzzlf2dJ9zzjnnfHZP9znn/N2197ztOzjnnHPO +Oeecc84555zzBk/3Oeecc85X9XSfc86/9XSfc84555xzzjnnnHPOOW/2dJ9z +zjnnnP/p6T7nnH/rW/e17eWcc84555xzzjnnnHP++bxt5yie7nPOOeec8+88 +3eec87Oe7nPOOeecc84555xzzjl/7e/uS+0ZzdN9zjnnnHN+ztN9zjm/y1vf +1/Y7cc4555xzzjnnnHPO+bvzb+9P7ZvF033OOeecc36Pp/ucc97iZ89/e9v3 +cc4555xzzjnnnHPO+bfPte2+6zvt4pxzzjnnd3q6zznn7Z7uc84555xzzjnn +nHPOecp/n7ft+3b3an3OOeecc97h6T7nnLd7us/Hdn+vOOecc84555xzzvnI +/vu8bd/Z72l7H+ecc845n8vTfc45H9XTfd7p6f7R/99/egfnnHPOOeecc845 +H9Nbdhz1s+ecc84555zv8XSfc85n86372vbyz57uP+0tOzjnnHPOOeecc875 +WN6yY8tbdnDOOeec8zU83eec81U83ecd/VG9ZQfnnHPOOeecc845H9Pfnbe9 +h3POOeec8ys93eec89X96Hnbd7R5ur+Kt+zgnHPOOeecc84553yPp/ucc845 +53wNT/c555y/9nR/FE/3+Wtv2cE555xzzjnnnHPO+aerbRfnnHPOOZ/L033O +Oef7PN1v83Sfv/aWHZxzzjnnnHPOOeecf7radnHOOeec87k83eecc36NHz1v ++46j38e73f+unHPOOeecc84557zJ033OOeecc76Gp/ucc87v9XR/9r38tbfs +4JxzzjnnnHPOOef809W2i3POOeecz+XpPuec84wfPU/v4mN4yw7OOeecc845 +55xzzj9dbbs455xzzvlcnu5zzjkfw7fuO/q+tu/k13jLDs4555xzzjnnnHO+ +tqf7nHPOOed8bU/3Oeecj+1PP8e7vGUH55xzzjnnnHPOOeefrrZdnHPOOed8 +DU/3Oeecr+UtO/g13rKDc84555xzzjnnnPNPV9suzjnnnHO+hqf7nHPO5/T2 +9/F93rKDc84555xzzjnnnPNPV9suzjnnnHO+tqf7nHPO5/TV++3esoNzzjnn +nHPOOeec8ys83eecc8455/yVp/ucc87n9HT/Wz+6/+5de71lB+ecc84555xz +zjnnd3q6zznnnHPO+R5P9znnnM/pW/e17b36u+/63rvfzznnnHPOOeecc855 +s6f7nHPOOeec7/F0n3PO+Zye7nPOOeecc84555xzzufzdJ9zzjnnnPM9nu5z +zjmf09N9zjnnnHPOOeecc875uJ7uc84555xzfoWn+5xzzuf0dJ9zzjnnnHPO +Oeecc97v6T7nnHPOOed3errPOed8Tk/3Oeecc84555xzzjnn/Z7uc84555xz +fqen+5xzzuf0dJ9zzjnnnHPOOeecc97j6T7nnHPOOecJT/c555zP6ek+55xz +zjnnnHPOOef8uO99/uw555xzzjnnM3q6zznnfE5P9znnnHPOOeecc8455897 +us8555xzznmTp/ucc87n9HSfc84555xzzjnnnHP+vKf7nHPOOeecN3m6zznn +fC1P9znnnHPOOeecc8455+c93eecc84553wET/c555yv5ek+55xzzjnnnHPO +Oef8vKf7nHPOOeecj+DpPuecc/7NfW17Oeecc84555xzzjlfwdN9zjnnnHPO +R/Z0n3POOW/oc84555xzzjnnnHPO319tuzjnnHPOOR/B033OOee8oc8555xz +zjnnnHPO+cqe7nPOOeeccz6jp/ucc855Q59zzjnnnHPOOeec8xU83eecc845 +53wlT/c555zzT57uc84555xzzjnnnHM+k6f7nHPOOeecr+TpPuecc/7J033O +Oeecc84555xzzkf0dJ9zzjnnnHOe73POOeef/Kn3tX0355xzzjnnnHPOOeff +eLrPOeecc845f+/pPuecc37Ez55/623fzTnnnHPOOeecc87H8L3Pnz3nnHPO +Oeec93m6zznnnF/pR8/bvoNzzjnnnHPOOeecj+17n39qF+ecc8455/w5T/c5 +55zzKz3d55xzzjnnnHPOOef8jKf7nHPOOeec8+s83eecc86v9K372vZyzjnn +nHPOOeecc97U55xzzjnnnF/n6T7nnHN+paf7nHPOOeecc84555x/4+k+55xz +zjnn/H5P9znnnPMnPN3nnHPOOeecc84557ypzznnnHPOOb/f033OOef8Cd+6 +r20v55xzzjnnnHPOOZ/D033OOeecc855ztN9zjnnPOlHz9u+g3POOeecc845 +55x3errPOeecc845z3m6zznnnDd6us8555xzzjnnnHPOx/J0n3POOeecc97n +6T7nnHPe6Ok+55xzzjnnnHPOOR/L033OOeecc855n6f7nHPO+Ug+e7/t9+ac +c84555xzzjlv83Sfc84555xzPo6n+5xzzvkM3v6+b73td+Wcc84555xzzjm/ +y9/dl97FOeecc845n8fTfc4553xmf/q5s972+3HOOeecc84555zf7ek+55xz +zjnnfF5P9znnnHN+3flvb/s+zjnnnHPOOeec8zZP9znnnHPOOefzerrPOeec +854+55xzzjnnnHPO+aye7nPOOeecc87X83Sfc8455z19zjnnnHPOOeec81k9 +3eecc84555yv5+k+55xzznv6nHPOOeecc84556N7us8555xzzjnnP57uc845 +53zb033OOeecc84555yP51e99+r3zb6Lc84555xzzn883eecc875tqf7nHPO +Oeecc8457/Hf5y07Ru9wzjnnnHPO+dWe7nPOOed824+et30H55xzzjnnnHPO +r/eWHannOOecc84557zV033OOeecH/d0n3POOeecc845572e2vHt1fI7cc45 +55xzzvldnu5zzjnn/Lin+5xzzjnnnHPOOR/P9z5/9Z6r38c555xzzjnnrZ7u +c8455/x6T/c555xzzjnnnHPO33m6zznnnHPOOedPebrPOeec8+f86ufavo9z +zjnnnHPOOef9nu5zzjnnnHPO+VOe7nPOOec87+k+55xzzjnnnHPO1/F0n3PO +Oeecc86f8nSfc845572e7nPOOeecc84553w+T/c555xzzjnn/ClP9znnnHPe +6+k+55xzzjnnnHPOx/V0n3POOeecc87Tnu5zzjnnfDxP9znnnHPOOeecc97v +6T7nnHPOOeecpz3d55xzzvl4fvVzbd/X5k/3W3ZwzjnnnHPOOR/b033OOeec +c845T3u6zznnnPP5Pd1v83T/Lm/ZwTnnnHPOOef8WU/3Oeecc84557zV033O +Oeecz+/pvu/LessOzjnnnHPOOef3eLrPOeecc845562e7nPOOed8XU/3Z9/b +7i07OOecc84555yf83Sfc84555xzzls93eecc845f3et2l/FW3ZwzjnnnHPO +Of/s7+5L7+Kcc84555zzdk/3Oeecc86/9dk6q3vLDs4555xzzjnn33m6zznn +nHPOOeejebrPOeecc37Wn36OX+MtOzjnnHPOOeecf+fpPuecc84555yP5uk+ +55xzzvldfvac3+stOzjnnHPOOeecd/U555xzzjnnfBZP9znnnHPO7/Kz5/xe +b9nBOeecc84557yrzznnnHPOOeezeLrPOeecc36Xt79vFW/ZwTnnnHPOOef8 +O0/3Oeecc84553wWT/c555xzzu/y1ftPe8sOzjnnnHPOOeffebrPOeecc845 +57N7us8555xzftbT/dG/o+134JxzzjnnnHP+jKf7nHPOOeeccz67p/ucc845 +52c93eecc84555xzzps93eecc84555zzVT3d55xzzjk/6+k+55xzzjnnnHPe +7Ok+55xzzjnnnK/q6T7nnHPO+VlP9znnnHPOOeec8wZP9znnnHPOOeec/+np +Puecc875Wd+6r20v55xzzjnnnHN+h6f7nHPOOeecc87/9HSfc8455/ysp/uc +c84555xzzvkR3/v8U7s455xzzjnnnF/j6T7nnHPO+VlP9znnnHPOOeec8yc9 +3eecc84555xz/p2n+5xzzjnnZz3d55xzzjnnnHPOn/R0n3POOeecc875d57u +c84555yf9aPnbd/BOeecc84555w39TnnnHPOOeecn/N0n3POOef8rKf7nHPO +Oeecc875HZ7uc84555xzzjk/5+k+55xzzvlZT/c555xzzjnnnPM7PN3nnHPO +Oeecc37O033OOeec87Oe7nPOOeecc84552c83eecc84555xzfo+n+5xzzjnn +Zz3d55xzzjnnnHPOz3i6zznnnHPOOef8Hk/3Oeecc87v8nSfc84555xzzjlv +6nPOOeecc845f9bTfc4555zzuzzd55xzzjnnnHPOm/qcc84555xzzp/1dJ9z +zjnn/Gm/+r1t38c555xzzjnnPOvpPuecc84555zzDk/3Oeecc86f9nSfc845 +55xzzvncnu5zzjnnnHPOOe/wdJ9zzjnn/C5P9znnnHPOOeecz+3pPuecc845 +55zzbk/3Oeecc86f9nSfc84555xzzvk+v+q97e/jnHPOOeeccz6Xp/ucc845 +5097us8555xzzjnn/PV5y46955xzzjnnnHPO+StP9znnnHPOn/Z0n3POOeec +c875Pr+7d9d7Oeecc84555yv7ek+55xzznmLb93XtpdzzjnnnHPO+efzu9/P +Oeecc84555x/8nSfc84557zF033OOeecc845552e7nPOOeecc845H9PTfc45 +55zzFk/3Oeecc84555x3errPOeecc84553xMT/c555xzzts93eecc84555xz +nvV0n3POOeecc875mJ7uc84555y3+2idtt+Pc84555xzzkf3dJ9zzjnnnHPO ++Zie7nPOOeecj+pPP/ett/1OnHPOOeeccz66p/ucc84555xzzsf0dJ9zzjnn +fDZP72j7PTjnnHPOOed8dE/3Oeecc84555yP6ek+55xzzvlsnu5zzjnnnHPO +Ob/W033OOeecc84552N6us8555xzPpun+5xzzjnnnHPOj3m6zznnnHPOOed8 +Lk/3Oeecc85n83Sfc84555xzzvkxT/c555xzzjnnnM/l6T7nnHPO+Wy+dV/b +Xs4555xzzjlfxd/dl97FOeecc84553xOT/c555xzzmfzdJ9zzjnnnHPO+TFP +9znnnHPOOeecz+XpPuecc875bJ7uc84555xzzjk/5uk+55xzzjnnnPO5PN3n +nHPOOZ/N033OOeecc84558c83eecc84555xzPpen+5xzzjnnq3i6zznnnHPO +Oee8o88555xzzjnnfA1P9znnnHPOV/Gt+9r2cs4555xzzvmsnu5zzjnnnHPO +OV/D033OOeec81U83eecc84555xz3tHnnHPOOeecc76Gp/ucc84556v72fPf +3vZ9nHPOOeecc57ydJ9zzjnnnHPO+dqe7nPOOeec89d+9Pm27+Ccc84555zz +q/z3+dZ9T+3inHPOOeecc85febrPOeecc85fe7rPOeecc84556N7us8555xz +zjnnfG1P9znnnHPO+WtP9znnnHPOOed8dE/3Oeecc84555yv7ek+55xzzjl/ +7Vv3te3lnHPOOeec8zZP9znnnHPOOeecr+3pPuecc845f+3pPuecc84555yP +7uk+55xzzjnnnPO1Pd3nnHPOOef7/Oh523dwzjnnnHPO+d2e7nPOOeecc845 +X9vTfc4555xzfo2n+5xzzjnnnHPe5uk+55xzzjnnnPO1Pd3nnHPOOefXeLrP +Oeecc84553f5u/vSuzjnnHPOOeec80+e7nPOOeec82s83Z/V0/3f3rKDc845 +55zzJk/3Oeecc84555zzV57uc84555zze33rvra9V393264Wb9nBOeecc875 +FZ7uc84555xzzjnnrzzd55xzzjnn93q67zvG8pYdnHPOOeec7/F0n3POOeec +c845f+XpPuecc845z3i6P9quVbxlB+ecc84555+utl2cc84555xzzvkrT/c5 +55xzznnGV+/zfd6yg3POOeecr+3pPuecc84555xzvsfTfc4555xz3uXt7+Nd +3rKDc84555zf4+/O2/ZwzjnnnHPOOeeNnu5zzjnnnPMx/Ow5n9NbdnDOOeec +82v97t7Zc84555xzzjnnfARP9znnnHPO+RjesoN3+NG/P+ndnHPOOeer++/z +1n3pHZxzzjnnnHPO+RWe7nPOOeec8zH87Dmf01t2cM4555zza/3u3tlzzjnn +nHPOOed8BE/3Oeecc855l7e/j3d5yw7OOeecc36Pvztv28M555xzzjnnnDd6 +us8555xzzjO+ep/v85YdnHPOOed8bU/3Oeecc84555zzPZ7uc84555zzjKf7 +o+1axVt2cM4555xz/ulq28U555xzzjnnnL/ydJ9zzjnnnN/r6b7vGMtbdnDO +Oeecc77H033OOeecc8455/yVp/ucc8455/xe37qvbe/V3922q8VbdnDOOeec +c36Fp/ucc84555xzzvkrT/c555xzzvk1nu7P6un+b2/ZwTnnnHPOeZOn+5xz +zjnnnHPO+StP9znnnHPO+TWe7nPOOeecc875Xf7uvvQuzjnnnHPOOef8k6f7 +nHPOOef8Gk/3Oeecc84557zN033OOeecc84552t7us8555xzzvf50fO27+Cc +c84555zzuz3d55xzzjnnnHO+tqf7nHPOOef8taf7nHPOOeeccz66p/ucc845 +55xzztf2dJ9zzjnnnL/2rfva9nLOOeecc855m6f7nHPOOeecc87X9nSfc845 +55y/9nSfc84555xzzkf3dJ9zzjnnnHPO+dqe7nPOOeec89ee7nPOOeecc875 +6J7uc84555xzzjlf29N9zjnnnHP+2o8+3/YdnHPOOeecc36V/z7fuu+pXZxz +zjnnnHPO+StP9znnnHPOV/ez57+97fs455xzzjnnPOXpPuecc84555zztT3d +55xzzjlfxdN9zjnnnHPOOecdfc4555xzzjnna3i6zznnnHO+im/d17aXc845 +55xzzmf1dJ9zzjnnnHPO+Rqe7nPOOeecr+LpPuecc84555zzjj7nnHPOOeec +8zU83eecc845n83Tfc4555xzzjnnxzzd55xzzjnnnHM+l6f7nHPOOeezebrP +Oeecc8455/yYp/ucc84555xzzufydJ9zzjnnfDZP9znnnHPOOeecH/N0n3PO +Oeecc875XJ7uc84555zP5lv3te3lnHPOOeec81X83X3pXZxzzjnnnHPO5/R0 +n3POOed8Nk/3Oeecc84555wf83Sfc84555xzzvlcnu5zzjnnnM/m6T7nnHPO +Oeec82Oe7nPOOeecc845n8vTfc4555zz2Tzd55xzzjnnnHN+raf7nHPOOeec +c87H9HSfc84553w2T+9o+z0455xzzjnnfHRP9znnnHPOOeecj+npPuecc875 +qP70c9962+/EOeecc84556N7us8555xzzjnnfExP9znnnHPO2320Ttvvxznn +nHPOOeeje7rPOeecc84553xMT/c555xzzts93eecc84555xznvV0n3POOeec +c875mJ7uc84555y3eLrPOeecc84557zT033OOeecc84552N6us8555xz3uLp +Puecc84555zzTk/3Oeecc84555yP6ek+55xzznmLb93XtpdzzjnnnHPO+efz +u9/POeecc84555x/8nSfc8455/xpT/c555xzzjnnnO/zu3t3vZdzzjnnnHPO ++dqe7nPOOeecP+3pPuecc84555zz1+ctO/aec84555xzzjnnrzzd55xzzjl/ +2tN9zjnnnHPOOef7/Kr3tr+Pc84555xzzvlcnu5zzjnnnN/l6T7nnHPOOeec +87k93eecc84555xz3u3pPuecc875057uc84555xzzjmf29N9zjnnnHPOOecd +nu5zzjnnnD/tV7+37fs455xzzjnnnGc93eecc84555xz3uHpPuecc875XZ7u +c84555xzzjnnTX3OOeecc8455896us8555xzfpen+5xzzjnnnHPOeVOfc845 +55xzzvmznu5zzjnnnJ/1dJ9zzjnnnHPOOT/j6T7nnHPOOeec83s83eecc845 +P+vpPuecc84555xzfsbTfc4555xzzjnn93i6zznnnHN+1tN9zjnnnHPOOef8 +Dk/3Oeecc84555yf83Sfc8455/ysp/ucc84555xzzvkdnu5zzjnnnHPOOT/n +6T7nnHPO+Vk/et72HZxzzjnnnHPOeVOfc84555xzzvk5T/c555xzzs96us85 +55xzzjnnnD/p6T7nnHPOOeec8+883eecc845P+vpPuecc84555xz/qSn+5xz +zjnnnHPOv/N0n3POOef8rKf7nHPOOeecc875Ed/7/FO7OOecc84555xf4+k+ +55xzzvlZ37qvbS/nnHPOOeecc36Hp/ucc84555xzzv/0dJ9zzjnn/Kyn+5xz +zjnnnHPOeYOn+5xzzjnnnHPO//R0n3POOef8rKf7nHPOOeecc855s6f7nHPO +Oeecc76qp/ucc84552c93eecc84555xzzps93eecc84555zzVT3d55xzzjk/ +6+n+6N/R9jtwzjnnnHPOOX/G033OOeecc845n93Tfc4555zzu3z1/tPesoNz +zjnnnHPO+Xee7nPOOeecc8757J7uc84555zf5e3vW8VbdnDOOeecc845/87T +fc4555xzzjmfxdN9zjnnnPO7/Ow5v9dbdnDOOeecc8457+pzzjnnnHPO+Sye +7nPOOeec3+Vnz/m93rKDc84555xzznlXn3POOeecc85n8XSfc8455/ysP/0c +v8ZbdnDOOeecc845/87Tfc4555xzzjkfzdN9zjnnnPNvfbbO6t6yg3POOeec +c875d57uc84555xzzvlonu5zzjnnnL+7Vu2v4i07OOecc84555x/9nf3pXdx +zjnnnHPOebun+5xzzjlf19P92fe2e8sOzjnnnHPOOefnPN3nnHPOOeec81ZP +9znnnHM+v6f7vi/rLTs455xzzjnnnN/j6T7nnHPOOeect3q6zznnnPP5Pd1v +83T/Lm/ZwTnnnHPOOef8WU/3Oeecc84557zV033OOeecj+dXP9f2fW3+dL9l +B+ecc84555zzsT3d55xzzjnnnPO0p/ucc845H8/Tfc4555xzzjnnnPd7us85 +55xzzjnnaU/3Oeecc97r6T7nnHPOOeecc87H9XSfc84555xzztOe7nPOOee8 +19N9zjnnnHPOOeecz+fpPuecc84555w/5ek+55xzzvOe7nPOOeecc84553wd +T/c555xzzjnn/ClP9znnnHP+nF/9XNv3cc4555xzzjnnvN/Tfc4555xzzjl/ +ytN9zjnnnF/v6T7nnHPOOeecc875O0/3Oeecc8455/wpT/c555xzftzTfc45 +55xzzjnnnI/ne5+/es/V7+Occ84555zzVk/3Oeecc37c033OOeecc84555z3 +emrHt1fL78Q555xzzjnnd3m6zznnnPNtP3re9h2cc84555xzzjm/3lt2pJ7j +nHPOOeec81ZP9znnnHO+7ek+55xzzjnnnHPOe/z3ecuO0Tucc84555xzfrWn ++5xzzjnf9nSfc84555xzzjnn4/lV7736fbPv4pxzzjnnnPMfT/c555xz3tPn +nHPOOeecc845H93Tfc4555xzzjn/8XSfc8455z19zjnnnHPOOeec81k93eec +c84555yv5+k+55xzznv6nHPOOeecc84557N6us8555xzzjlfz9N9zjnnnF93 +/tvbvo9zzjnnnHPOOee8zdN9zjnnnHPO+bye7nPOOecz+9PPnfW2349zzjnn +nHPOOef8bk/3Oeecc8455/N6us8555zP4O3v+9bbflfOOeecc84555zzu/zd +feldnHPOOeec83k83eecc85H8tn7bb8355xzzjnnnHPOeZun+5xzzjnnnPNx +PN3nnHPOGz3d55xzzjnnnHPOOedjebrPOeecc8457/N0n3POOW/0dJ9zzjnn +nHPOOeecj+XpPuecc84557zP033OOec86UfP276Dc84555xzzjnnnHd6us85 +55xzzjnPebrPOeecP+Fb97Xt5ZxzzjnnnHPOOedzeLrPOeecc845z3m6zznn +nD/h6T7nnHPOOeecc8455019zjnnnHPO+f2e7nPOOedXerrPOeecc84555xz +zvk3nu5zzjnnnHPO7/d0n3POOb/St+5r28s555xzzjnnnHPOeVOfc84555xz +fp2n+5xzzvmVnu5zzjnnnHPOOeecc37G033OOeecc875dZ7uc84551f60fO2 +7+Ccc84555xzzjnnY/ve55/axTnnnHPOOX/O033OOef8iJ89/9bbvptzzjnn +nHPOOeecj+F7nz97zjnnnHPOOe/zdJ9zzjn/5E+9r+27Oeecc84555xzzjn/ +xtN9zjnnnHPO+XtP9znnnPNPnu5zzjnnnHPOOeeccz6ip/ucc84555zzfJ9z +zjn/5Ok+55xzzjnnnHPOOeczebrPOeecc875Sp7uc8455w19zjnnnHPOOeec +c85X8HSfc84555zzlTzd55xzzhv6nHPOOeecc84555yv7Ok+55xzzjnnM3q6 +zznnnDf0Oeecc84555xzzjnn76+2XZxzzjnnnI/g6T7nnHP+zX1teznnnHPO +Oeecc845X8HTfc4555xzzkf2dJ9zzvlanu5zzjnnnHPOOeecc87Pe7rPOeec +c875CJ7uc845X8vTfc4555xzzjnnnHPO+XlP9znnnHPOOR/B033OOedzerrP +Oeecc84555xzzjl/3tN9zjnnnHPOmzzd55xzPqen+5xzzjnnnHPOOeec8+c9 +3eecc84557zJ033OOedzerrPOeecc84555xzzjk/7nufP3vOOeecc875jJ7u +c845n9PTfc4555xzzjnnnHPOeY+n+5xzzjnnnCc83eeccz6np/ucc84555xz +zjnnnPN+T/c555xzzjm/09N9zjnnc3q6zznnnHPOOeecc8457/d0n3POOeec +8zs93eeccz6np/ucc84555xzzjnnnPNxPd3nnHPOOef8Ck/3Oeecz+npPuec +c84555xzzjnnfD5P9znnnHPOOd/j6T7nnPM5feu+tr1Xf/dd33v3+znnnHPO +Oeecc845b/Z0n3POOeec8z2e7nPOOZ/T0/1v/ej+u3ft9ZYdnHPOOeecc845 +55zf6ek+55xzzjnnezzd55xzPqev3m/3lh2cc84555xzzjnnnF/h6T7nnHPO +OeevPN3nnHM+p7e/j+/zlh2cc84555xzzjnnnH+62nZxzjnnnPO1Pd3nnHO+ +lrfs4Nd4yw7OOeecc84555xzzj9dbbs455xzzvkanu5zzjkf259+jnd5yw7O +Oeecc84555xzzj9dbbs455xzzvkanu5zzjkfw7fuO/q+tu/k13jLDs4555xz +zjnnnHO+tqf7nHPOOed8bU/3OeecZ/zoeXoXH8NbdnDOOeecc84555xz/ulq +28U555xzzufydJ9zzvm9nu7Pvpe/9pYdnHPOOeecc84555x/utp2cc4555zz +uTzd55xzfo0fPW/7jqPfx7vd/66cc84555xzzjnnvMnTfc4555xzvoan+5xz +zvd5ut/m6T5/7S07OOecc84555xzzjn/dLXt4pxzzjnnc3m6zznn/LWn+6N4 +us9fe8sOzjnnnHPOOeecc84/XW27OOecc875XJ7uc8756n70vO072jzdX8Vb +dnDOOeecc84555xzvsfTfc4555xzvoan+5xzvoqn+7yjP6q37OCcc84555xz +zjnnY/q787b3cM4555xzfqWn+5xzPptv3de2l3/2dP9pb9nBOeecc84555xz +zsfylh1b3rKDc84555yv4ek+55yP6uk+7/R0/+j/7z+9g3POOeecc84555yP +6S07jvrZc84555xzzvd4us855+2e7vOx3d8rzjnnnHPOOeeccz6y/z5v23f2 +e9rexznnnHPO5/J0n3PO2z3d55xzzjnnnHPOOeec85T/Pm/b9+3u1fqcc845 +57zD033OOW/xs+e/ve37OOecc84555xzzjnn/Nvn2nbf9Z12cc4555zzOz3d +55zzu7z1fW2/E+ecc84555xzzjnnnL87//b+1L5ZPN3nnHPOOef3eLrPOedn +Pd3nnHPOOeecc84555xz/trf3ZfaM5qn+5xzzjnn/Jyn+5xz/q1v3de2l3PO +Oeecc84555xzzvnn87ado3i6zznnnHPOv/N0n3POv/V0n3POOeecc84555xz +zjlv9nSfc84555z/6ek+55y/u/aet30H55xzzjnnnHPOOeecc97g6T7nnHPO ++aqe7nPO1/V0n3POOeecc84555xzzjlf2dN9zjnnnPPZPd3nnM/v6T7nnHPO +Oeecc84555xzzt9fbbs455xzzmfxdJ9zPr9v3de2l3POOeecc84555xzzjlf +2dN9zjnnnPNZPN3nnM/v6T7nnHPOOeecc84555xzzrfvO3vOOeecc87/9HSf +cz6Pb93XtpdzzjnnnHPOOeecc8455+c93eecc845b/V0n3M+j6f7nHPOOeec +c84555xzzjnv8XSfc8455zzt6T7nfB5P9znnnHPOOeecc84555xz3u/pPuec +c875U57uc87n8XSfc84555xzzjnnnHPOOef9nu5zzjnnnD/l6T7nvNeffu6s +t/1+nHPOOeecc84555xzzjn/3tN9zjnnnPOrPd3nnOe9/X1nvWUH55xzzjnn +nHPOOeecc873e7rPOeecc37U033O+fW+dd9T/ZbfpWUH55xzzjnnnHPOOeec +c86v83Sfc84553zL033O+XFP90fZ2/Y7cM4555xzzjnnnHPOOef8vKf7nHPO +Oedbnu5zzrc93R/9+9q+l3POOeecc84555xzzjnn93m6zznnnHP+4+k+57yn +zznnnHPOOeecc84555xzPrqn+5xzzjnnP57uc857+pxzzjnnnHPOOeecc845 +57N6us8555zz9Tzd53xFP3re9h2cc84555xzzjnnnHPOOeejeLrPOeec8/U8 +3ed8Zk/3Oeecc84555xzzjnnnHPOeUefc8455+t5us/5DJ7uc84555xzzjnn +nHPOOeecz+ZXvffsOeecc875UU/3OR/Jj563fQfnnHPOOeecc84555xzznm7 +X/Xep5/jnHPOOf/xdJ/zkTzd55xzzjnnnHPOOeecc845n9XfnW/9+a496Q7n +nHPOx/d0n/ORPN3nnHPOOeecc84555xzzjnnnZ7uc84557zP033OG33rvra9 +nHPOOeecc84555xzzjnnvNPTfc4555znPN3nvNHTfc4555xzzjnnnHPOOeec +cz63p/ucc845v9/Tfc4b/ez5t9723ZxzzjnnnHPOOeecc8455zzr6T7nnHPO +r/N0n/OkP/3cb2/7PTjnnHPOOeecc84555xzznnW033OOeecX+fpPudPeNv7 +/Dubc84555xzzjnnnHPOOeec7/F0n3POOef7Pd3n/EpP9znnnHPOOeecc845 +55xzzjl/0tN9zjnnnL/3dJ/zI57uc84555xzzjnnnHPOOeecc97s6T7nnHPO +833Oj/jWfW17Oeecc84555xzzjnnnHPOOX/S033OOeec5/ucf/J0n3POOeec +c84555xzzjnnnPOZPN3nnHPOV/J0n/NPnu5zzjnnnHPOOeecc84555xzvoKn ++5xzzvmMnu5z/snTfc4555xzzjnnnHPOOeecc85X8HSfc845n9HTfc4b+pxz +zjnnnHPOOeecc84555zz91fbLs4553wET/c5b+hzzjnnnHPOOeecc84555xz +zt9fbbs455zzETzd5/yK89/e9n2cc84555xzzjnnnHPOOeecj+jpPueccz6y +p/t8LX/qfW3fzTnnnHPOOeecc84555xzznnS9z5/9pxzzjnn+T5fy9N9zjnn +nHPOOeecc84555xzzvl9nu5zzjnnTZ7u87U83eecc84555xzzjnnnHPOOeec +P+/pPuecc57wdJ/P6ek+55xzzjnnnHPOOeecc84557zf033OOef8Tk/3+Zye +7nPOOeecc84555xzzjnnnHPO+z3d55xzzu/0dJ/P6ek+55xzzjnnnHPOOeec +c84553xcT/c555zzKzzd53P60efbvoNzzjnnnHPOOeecc84555xz3uPpPuec +c77H030+p6f7nHPOOeecc84555xzzjnnnPP5PN3nnHPO93i6z8f2dJ9zzjnn +nHPOOeecc84555xzztN9zjnn/JWn+3xsT/c555xzzjnnnHPOOeecc8455zzd +55xzzl95us/H9nSfc84555xzzjnnnHPOOeecc87Tfc455/yVp/t8bE/3Oeec +c84555xzzjnnnHPOOefz+7v7zp5zzjnnd3q6z8f2dJ9zzjnnnHPOOeecc845 +55xzzt/51tW2l3PO+Vye7vOxPd3nnHPOOeecc84555xzzjnnnPO9nu5zzjlf +w9N9PrZv3de2l3POOeecc84555xzzjnnnHPO33m6zznnfC5P9/nYnu5zzjnn +nHPOOeecc84555xzzvlVnu5zzjmfy9N9Pran+0/71b/D3bs455xzzjnnnHPO +Oeecc8455997us8553wuT/f52J7uz7633Vt2cM4555xzzjnnnHPOOeecc36n +p/ucc87H9HSfj+1b9/n3D//GW3ZwzjnnnHPOOeecc84555xz/ulq28U557zb +030+tj/9HF/Lt/781A7OOeecc84555xzzjnnnHO+tqf7nHPOx/R0n4/tZ885 +P+ItOzjnnHPOOeecc84555xzzvnanu5zzjnv9nSfd3n7+zj/5C07OOecc845 +55xzzjnnnHPO+Rqe7nPOOe/2dJ9nfLYO55+8ZQfnnHPOOeecc84555xzzjmf +y9N9zjnn3Z7u82s83R9tF1/LW3ZwzjnnnHPOOeecc84555zzuTzd55xz3u3p +Pt/n6b7v4DN5yw7OOeecc84555xzzjnnnHM+l6f7nHPOOzzd56893fd9fAVv +2cE555xzzjnnnHPOOeecc87n8nSfc855h6f7q/jR87bvSP9OnF/pLTs455xz +zjnnnHPOOeecc875XJ7uc8457/B0f1RP92f1dJ+v5S07OOecc84555xzzjnn +nHPO+Vye7nPOOe/wdL/d033e0edruL+XnHPOOeecc84555xzzjnnc/m781SX +c875Wp7ut3u6zzv6fE5v2cE555xzzjnnnHPOOf//9ucgBQAQBALg/3/dCyLI +SMs5Oouscs457+ZV7tj1aM4557yHZ/ff9tN71f7r5tn9/G2vcgfnnHPOOeec +c84555xzznlVn+WruatHc84557/4AEAsnLA= + "], {{0, 0}, {401, 401}}, {0, 1}], Frame -> Automatic, + FrameLabel -> {None, None}, FrameTicks -> {{None, None}, {None, None}}, + GridLinesStyle -> Directive[ + GrayLevel[0.5, 0.4]], + Method -> { + "DefaultBoundaryStyle" -> Automatic, "DefaultPlotStyle" -> Automatic}], + FormBox[ + FormBox[ + TemplateBox[{"\"Divergent\"", + RowBox[{"-", "1.5`"}], "0", "0.75`"}, "SwatchLegend", + DisplayFunction -> (FormBox[ + StyleBox[ + StyleBox[ + PaneBox[ + TagBox[ + GridBox[{{ + TagBox[ + GridBox[{{ + GraphicsBox[{ + Directive[ + EdgeForm[ + Directive[ + Opacity[0.3], + GrayLevel[0]]], + PointSize[0.5], + AbsoluteThickness[1.6], + RGBColor[0., 0., 0.]], + RectangleBox[{0, 0}, {10, 10}, "RoundingRadius" -> 0]}, + AspectRatio -> Full, ImageSize -> {10, 10}, + PlotRangePadding -> None, ImagePadding -> Automatic, + BaselinePosition -> (Scaled[0.1] -> Baseline)], #}, { + GraphicsBox[{ + Directive[ + EdgeForm[ + Directive[ + Opacity[0.3], + GrayLevel[0]]], + PointSize[0.5], + AbsoluteThickness[1.6], + RGBColor[1., 0., 0.]], + RectangleBox[{0, 0}, {10, 10}, "RoundingRadius" -> 0]}, + AspectRatio -> Full, ImageSize -> {10, 10}, + PlotRangePadding -> None, ImagePadding -> Automatic, + BaselinePosition -> (Scaled[0.1] -> Baseline)], #2}, { + GraphicsBox[{ + Directive[ + EdgeForm[ + Directive[ + Opacity[0.3], + GrayLevel[0]]], + PointSize[0.5], + AbsoluteThickness[1.6], + RGBColor[0., 1., 0.]], + RectangleBox[{0, 0}, {10, 10}, "RoundingRadius" -> 0]}, + AspectRatio -> Full, ImageSize -> {10, 10}, + PlotRangePadding -> None, ImagePadding -> Automatic, + BaselinePosition -> (Scaled[0.1] -> Baseline)], #3}, { + GraphicsBox[{ + Directive[ + EdgeForm[ + Directive[ + Opacity[0.3], + GrayLevel[0]]], + PointSize[0.5], + AbsoluteThickness[1.6], + RGBColor[0., 0., 1.]], + RectangleBox[{0, 0}, {10, 10}, "RoundingRadius" -> 0]}, + AspectRatio -> Full, ImageSize -> {10, 10}, + PlotRangePadding -> None, ImagePadding -> Automatic, + BaselinePosition -> (Scaled[0.1] -> Baseline)], #4}}, + GridBoxAlignment -> { + "Columns" -> {Center, Left}, "Rows" -> {{Baseline}}}, + AutoDelete -> False, + GridBoxDividers -> { + "Columns" -> {{False}}, "Rows" -> {{False}}}, + GridBoxItemSize -> {"Columns" -> {{All}}, "Rows" -> {{All}}}, + GridBoxSpacings -> { + "Columns" -> {{0.5}}, "Rows" -> {{0.5}}}], "Grid"]}}, + GridBoxAlignment -> {"Columns" -> {{Left}}, "Rows" -> {{Top}}}, + AutoDelete -> False, + GridBoxItemSize -> { + "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, + GridBoxSpacings -> {"Columns" -> {{1}}, "Rows" -> {{0}}}], + "Grid"], Alignment -> Left, AppearanceElements -> None, + ImageMargins -> {{5, 5}, {5, 5}}, ImageSizeAction -> + "ResizeToFit"], LineIndent -> 0, StripOnInput -> False], { + FontFamily -> "Arial"}, Background -> Automatic, StripOnInput -> + False], TraditionalForm]& ), + InterpretationFunction :> (RowBox[{"SwatchLegend", "[", + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{"Directive", "[", + InterpretationBox[ + ButtonBox[ + TooltipBox[ + GraphicsBox[{{ + GrayLevel[0], + RectangleBox[{0, 0}]}, { + GrayLevel[0], + RectangleBox[{1, -1}]}, { + RGBColor[0., 0., 0.], + RectangleBox[{0, -1}, {2, 1}]}}, AspectRatio -> 1, Frame -> + True, FrameStyle -> RGBColor[0., 0., 0.], FrameTicks -> + None, PlotRangePadding -> None, ImageSize -> + Dynamic[{ + Automatic, 1.35 CurrentValue["FontCapHeight"]/ + AbsoluteCurrentValue[Magnification]}]], + "RGBColor[0., 0., 0.]"], Appearance -> None, + BaseStyle -> {}, BaselinePosition -> Baseline, + DefaultBaseStyle -> {}, ButtonFunction :> + With[{Typeset`box$ = EvaluationBox[]}, + If[ + Not[ + AbsoluteCurrentValue["Deployed"]], + SelectionMove[Typeset`box$, All, Expression]; + FrontEnd`Private`$ColorSelectorInitialAlpha = 1; + FrontEnd`Private`$ColorSelectorInitialColor = + RGBColor[0., 0., 0.]; + FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; + MathLink`CallFrontEnd[ + FrontEnd`AttachCell[Typeset`box$, + FrontEndResource["RGBColorValueSelector"], { + 0, {Left, Bottom}}, {Left, Top}, + "ClosingActions" -> { + "SelectionDeparture", "ParentChanged", + "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> + Automatic, Method -> "Preemptive"], + RGBColor[0., 0., 0.], Editable -> False, Selectable -> + False], "]"}], ",", + RowBox[{"Directive", "[", + InterpretationBox[ + ButtonBox[ + TooltipBox[ + GraphicsBox[{{ + GrayLevel[0], + RectangleBox[{0, 0}]}, { + GrayLevel[0], + RectangleBox[{1, -1}]}, { + RGBColor[1., 0., 0.], + RectangleBox[{0, -1}, {2, 1}]}}, AspectRatio -> 1, Frame -> + True, FrameStyle -> RGBColor[0.6666666666666667, 0., 0.], + FrameTicks -> None, PlotRangePadding -> None, ImageSize -> + Dynamic[{ + Automatic, 1.35 CurrentValue["FontCapHeight"]/ + AbsoluteCurrentValue[Magnification]}]], + "RGBColor[1., 0., 0.]"], Appearance -> None, + BaseStyle -> {}, BaselinePosition -> Baseline, + DefaultBaseStyle -> {}, ButtonFunction :> + With[{Typeset`box$ = EvaluationBox[]}, + If[ + Not[ + AbsoluteCurrentValue["Deployed"]], + SelectionMove[Typeset`box$, All, Expression]; + FrontEnd`Private`$ColorSelectorInitialAlpha = 1; + FrontEnd`Private`$ColorSelectorInitialColor = + RGBColor[1., 0., 0.]; + FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; + MathLink`CallFrontEnd[ + FrontEnd`AttachCell[Typeset`box$, + FrontEndResource["RGBColorValueSelector"], { + 0, {Left, Bottom}}, {Left, Top}, + "ClosingActions" -> { + "SelectionDeparture", "ParentChanged", + "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> + Automatic, Method -> "Preemptive"], + RGBColor[1., 0., 0.], Editable -> False, Selectable -> + False], "]"}], ",", + RowBox[{"Directive", "[", + InterpretationBox[ + ButtonBox[ + TooltipBox[ + GraphicsBox[{{ + GrayLevel[0], + RectangleBox[{0, 0}]}, { + GrayLevel[0], + RectangleBox[{1, -1}]}, { + RGBColor[0., 1., 0.], + RectangleBox[{0, -1}, {2, 1}]}}, AspectRatio -> 1, Frame -> + True, FrameStyle -> RGBColor[0., 0.6666666666666667, 0.], + FrameTicks -> None, PlotRangePadding -> None, ImageSize -> + Dynamic[{ + Automatic, 1.35 CurrentValue["FontCapHeight"]/ + AbsoluteCurrentValue[Magnification]}]], + "RGBColor[0., 1., 0.]"], Appearance -> None, + BaseStyle -> {}, BaselinePosition -> Baseline, + DefaultBaseStyle -> {}, ButtonFunction :> + With[{Typeset`box$ = EvaluationBox[]}, + If[ + Not[ + AbsoluteCurrentValue["Deployed"]], + SelectionMove[Typeset`box$, All, Expression]; + FrontEnd`Private`$ColorSelectorInitialAlpha = 1; + FrontEnd`Private`$ColorSelectorInitialColor = + RGBColor[0., 1., 0.]; + FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; + MathLink`CallFrontEnd[ + FrontEnd`AttachCell[Typeset`box$, + FrontEndResource["RGBColorValueSelector"], { + 0, {Left, Bottom}}, {Left, Top}, + "ClosingActions" -> { + "SelectionDeparture", "ParentChanged", + "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> + Automatic, Method -> "Preemptive"], + RGBColor[0., 1., 0.], Editable -> False, Selectable -> + False], "]"}], ",", + RowBox[{"Directive", "[", + InterpretationBox[ + ButtonBox[ + TooltipBox[ + GraphicsBox[{{ + GrayLevel[0], + RectangleBox[{0, 0}]}, { + GrayLevel[0], + RectangleBox[{1, -1}]}, { + RGBColor[0., 0., 1.], + RectangleBox[{0, -1}, {2, 1}]}}, AspectRatio -> 1, Frame -> + True, FrameStyle -> RGBColor[0., 0., 0.6666666666666667], + FrameTicks -> None, PlotRangePadding -> None, ImageSize -> + Dynamic[{ + Automatic, 1.35 CurrentValue["FontCapHeight"]/ + AbsoluteCurrentValue[Magnification]}]], + "RGBColor[0., 0., 1.]"], Appearance -> None, + BaseStyle -> {}, BaselinePosition -> Baseline, + DefaultBaseStyle -> {}, ButtonFunction :> + With[{Typeset`box$ = EvaluationBox[]}, + If[ + Not[ + AbsoluteCurrentValue["Deployed"]], + SelectionMove[Typeset`box$, All, Expression]; + FrontEnd`Private`$ColorSelectorInitialAlpha = 1; + FrontEnd`Private`$ColorSelectorInitialColor = + RGBColor[0., 0., 1.]; + FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; + MathLink`CallFrontEnd[ + FrontEnd`AttachCell[Typeset`box$, + FrontEndResource["RGBColorValueSelector"], { + 0, {Left, Bottom}}, {Left, Top}, + "ClosingActions" -> { + "SelectionDeparture", "ParentChanged", + "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> + Automatic, Method -> "Preemptive"], + RGBColor[0., 0., 1.], Editable -> False, Selectable -> + False], "]"}]}], "}"}], ",", + RowBox[{"{", + RowBox[{#, ",", #2, ",", #3, ",", #4}], "}"}], ",", + RowBox[{"LegendMarkers", "\[Rule]", "Automatic"}], ",", + RowBox[{"LabelStyle", "\[Rule]", + RowBox[{"{", "}"}]}], ",", + RowBox[{"LegendLayout", "\[Rule]", "\"Column\""}]}], "]"}]& ), + Editable -> True], TraditionalForm], TraditionalForm]}, + "Legended", + DisplayFunction->(GridBox[{{ + TagBox[ + ItemBox[ + PaneBox[ + TagBox[#, "SkipImageSizeLevel"], Alignment -> {Center, Baseline}, + BaselinePosition -> Baseline], DefaultBaseStyle -> "Labeled"], + "SkipImageSizeLevel"], + ItemBox[#2, DefaultBaseStyle -> "LabeledLabel"]}}, + GridBoxAlignment -> {"Columns" -> {{Center}}, "Rows" -> {{Center}}}, + AutoDelete -> False, GridBoxItemSize -> Automatic, + BaselinePosition -> {1, 1}]& ), + Editable->True, + InterpretationFunction->(RowBox[{"Legended", "[", + RowBox[{#, ",", + RowBox[{"Placed", "[", + RowBox[{#2, ",", "After"}], "]"}]}], "]"}]& )]], "Output", + CellChangeTimes->{3.6631017417896557`*^9, 3.6641618531627593`*^9}] +}, Open ]] +}, Open ]] +}, Open ]] +}, Open ]] +}, +WindowSize->{759, 833}, +WindowMargins->{{553, Automatic}, {Automatic, 52}}, +FrontEndVersion->"10.4 for Microsoft Windows (64-bit) (April 11, 2016)", +StyleDefinitions->"Default.nb" +] +(* End of Notebook Content *) + +(* Internal cache information *) +(*CellTagsOutline +CellTagsIndex->{} +*) +(*CellTagsIndex +CellTagsIndex->{} +*) +(*NotebookFileOutline +Notebook[{ +Cell[CellGroupData[{ +Cell[580, 22, 125, 1, 90, "Title"], +Cell[708, 25, 107, 1, 30, "Text"], +Cell[CellGroupData[{ +Cell[840, 30, 99, 1, 63, "Section"], +Cell[942, 33, 473, 13, 49, "Text"], +Cell[1418, 48, 515, 17, 45, "DisplayFormula"], +Cell[1936, 67, 391, 7, 68, "Text"], +Cell[2330, 76, 427, 7, 87, "Text"], +Cell[2760, 85, 1405, 36, 144, "Text"], +Cell[4168, 123, 371, 8, 49, "Text"] +}, Open ]], +Cell[CellGroupData[{ +Cell[4576, 136, 91, 1, 63, "Section"], +Cell[CellGroupData[{ +Cell[4692, 141, 104, 1, 43, "Subsection"], +Cell[4799, 144, 1473, 39, 112, "Input"], +Cell[CellGroupData[{ +Cell[6297, 187, 287, 7, 34, "Input"], +Cell[6587, 196, 493, 16, 61, "Output"] +}, Open ]], +Cell[7095, 215, 11016, 259, 1146, "Input"] +}, Closed]], +Cell[CellGroupData[{ +Cell[18148, 479, 101, 1, 35, "Subsection"], +Cell[CellGroupData[{ +Cell[18274, 484, 383, 9, 34, "Input"], +Cell[18660, 495, 16926, 334, 376, "Output"] +}, Open ]], +Cell[CellGroupData[{ +Cell[35623, 834, 485, 11, 34, "Input"], +Cell[36111, 847, 52522, 918, 376, "Output"] +}, Open ]], +Cell[CellGroupData[{ +Cell[88670, 1770, 337, 9, 34, "Input"], +Cell[89010, 1781, 66648, 1151, 376, "Output"] +}, Open ]], +Cell[CellGroupData[{ +Cell[155695, 2937, 608, 12, 34, "Input"], +Cell[156306, 2951, 60137, 990, 374, "Output"] +}, Open ]], +Cell[CellGroupData[{ +Cell[216480, 3946, 281, 8, 34, "Input"], +Cell[216764, 3956, 58447, 963, 374, "Output"] +}, Open ]], +Cell[CellGroupData[{ +Cell[275248, 4924, 583, 12, 34, "Input"], +Cell[275834, 4938, 14251, 277, 376, "Output"] +}, Open ]], +Cell[CellGroupData[{ +Cell[290122, 5220, 580, 12, 34, "Input"], +Cell[290705, 5234, 16523, 313, 376, "Output"] +}, Open ]], +Cell[CellGroupData[{ +Cell[307265, 5552, 1030, 26, 52, "Input"], +Cell[308298, 5580, 33995, 611, 376, "Output"] +}, Open ]], +Cell[CellGroupData[{ +Cell[342330, 6196, 623, 15, 31, "Input"], +Cell[342956, 6213, 32351, 580, 376, "Output"] +}, Open ]] +}, Open ]] +}, Open ]] +}, Open ]] +} +] +*) + diff --git a/calc-diffeq-analysis/complex-operations.nb b/calc-diffeq-analysis/complex-operations.nb index e9d3973..aeb9181 100644 --- a/calc-diffeq-analysis/complex-operations.nb +++ b/calc-diffeq-analysis/complex-operations.nb @@ -1,743 +1,743 @@ -(* Content-type: application/vnd.wolfram.mathematica *) - -(*** Wolfram Notebook File ***) -(* http://www.wolfram.com/nb *) - -(* CreatedBy='Mathematica 10.4' *) - -(*CacheID: 234*) -(* Internal cache information: -NotebookFileLineBreakTest -NotebookFileLineBreakTest -NotebookDataPosition[ 158, 7] -NotebookDataLength[ 25716, 735] -NotebookOptionsPosition[ 24175, 680] -NotebookOutlinePosition[ 24518, 695] -CellTagsIndexPosition[ 24475, 692] -WindowFrame->Normal*) - -(* Beginning of Notebook Content *) -Notebook[{ - -Cell[CellGroupData[{ -Cell["Complex Operations", "Title", - CellChangeTimes->{{3.776600831050974*^9, 3.7766008318453026`*^9}, { - 3.7768014692411594`*^9, 3.7768014727414646`*^9}}], - -Cell["Adam Rumpf, 3/20/2017", "Text", - CellChangeTimes->{{3.7766008347881403`*^9, 3.776600838290375*^9}, { - 3.776801479279549*^9, 3.7768014811941967`*^9}}], - -Cell[CellGroupData[{ - -Cell["Introduction", "Section", - CellChangeTimes->{{3.7766008459498987`*^9, 3.776600848547045*^9}}], - -Cell["\<\ -This program consists of a single Manipulate environment that displays \ -vectors in the complex plane. The blue and red vectors represent inputs, and \ -can be clicked and dragged, while the purple vector represents the output of \ -a chosen mathematical operation or function.\ -\>", "Text", - CellChangeTimes->{{3.776600856235587*^9, 3.776600860481224*^9}, { - 3.7768017314717674`*^9, 3.7768017781690865`*^9}, {3.776801808899147*^9, - 3.7768018444568605`*^9}, {3.7768022110736027`*^9, 3.776802220503076*^9}}], - -Cell["The following operations and functions are included:", "Text", - CellChangeTimes->{{3.776806090808209*^9, 3.776806097009242*^9}}], - -Cell[CellGroupData[{ - -Cell[TextData[{ - "Addition (", - Cell[BoxData[ - FormBox[ - RowBox[{"x", "+", "y"}], TraditionalForm]], - FormatType->"TraditionalForm"], - ")" -}], "Item", - CellChangeTimes->{{3.7768061049497538`*^9, 3.776806132799117*^9}}], - -Cell[TextData[{ - "Multiplication (", - Cell[BoxData[ - FormBox[ - RowBox[{"x", "\[CenterDot]", "y"}], TraditionalForm]], - FormatType->"TraditionalForm"], - ")" -}], "Item", - CellChangeTimes->{{3.7768061049497538`*^9, 3.7768061393541117`*^9}}], - -Cell["Sine", "Item", - CellChangeTimes->{{3.7768061049497538`*^9, 3.776806115929446*^9}}], - -Cell["Cosine", "Item", - CellChangeTimes->{{3.7768061049497538`*^9, 3.776806116821181*^9}}], - -Cell["Tangent", "Item", - CellChangeTimes->{{3.7768061049497538`*^9, 3.7768061179967833`*^9}}], - -Cell[TextData[{ - "Reciprocal (", - Cell[BoxData[ - FormBox[ - SuperscriptBox["x", - RowBox[{"-", "1"}]], TraditionalForm]], - FormatType->"TraditionalForm"], - ")" -}], "Item", - CellChangeTimes->{{3.7768061049497538`*^9, 3.776806151631158*^9}}], - -Cell[TextData[{ - "Square (", - Cell[BoxData[ - FormBox[ - SuperscriptBox["x", "2"], TraditionalForm]], - FormatType->"TraditionalForm"], - ")" -}], "Item", - CellChangeTimes->{{3.7768061049497538`*^9, 3.776806176150304*^9}, { - 3.7768062766849318`*^9, 3.7768062766909494`*^9}}], - -Cell[TextData[{ - "Exponential (", - Cell[BoxData[ - FormBox[ - SuperscriptBox["\[ExponentialE]", "x"], TraditionalForm]], - FormatType->"TraditionalForm"], - ")" -}], "Item", - CellChangeTimes->{{3.7768061049497538`*^9, 3.776806176150304*^9}, { - 3.7768062766849318`*^9, 3.77680628942142*^9}}], - -Cell[TextData[{ - "Gamma (", - Cell[BoxData[ - FormBox[ - RowBox[{"\[CapitalGamma]", "(", "x", ")"}], TraditionalForm]], - FormatType->"TraditionalForm"], - ")" -}], "Item", - CellChangeTimes->{{3.7768061049497538`*^9, 3.776806176150304*^9}, { - 3.7768062766849318`*^9, 3.7768062996951275`*^9}}], - -Cell[TextData[{ - "Riemann Zeta (", - Cell[BoxData[ - FormBox[ - RowBox[{"\[Zeta]", "(", "x", ")"}], TraditionalForm]], - FormatType->"TraditionalForm"], - ")" -}], "Item", - CellChangeTimes->{{3.7768061049497538`*^9, 3.776806176150304*^9}, { - 3.7768062766849318`*^9, 3.7768063117433167`*^9}, {3.7768063485136228`*^9, - 3.77680635223643*^9}}], - -Cell[TextData[{ - "Geometric Series (", - Cell[BoxData[ - FormBox[ - RowBox[{ - UnderoverscriptBox["\[Sum]", - RowBox[{"n", "=", "0"}], "\[Infinity]"], - SuperscriptBox["x", "n"]}], TraditionalForm]], - FormatType->"TraditionalForm"], - ") (uses analytic continuation outside of unit disk)" -}], "Item", - CellChangeTimes->{{3.7768061049497538`*^9, 3.776806176150304*^9}, { - 3.7768062766849318`*^9, 3.7768063780661554`*^9}}] -}, Open ]], - -Cell["\<\ -General exponentiation and logarithm have been excluded because they are \ -multivalued for complex numbers.\ -\>", "Text", - CellChangeTimes->{{3.776806824485301*^9, 3.7768068827046947`*^9}}] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["Code", "Section", - CellChangeTimes->{{3.776600864408964*^9, 3.7766008650447807`*^9}}], - -Cell[CellGroupData[{ - -Cell["Initialization", "Subsection", - CellChangeTimes->{{3.776600871130811*^9, 3.776600873087188*^9}}], - -Cell[BoxData[ - RowBox[{ - RowBox[{"(*", " ", - RowBox[{"plotting", " ", "limits"}], " ", "*)"}], "\[IndentingNewLine]", - RowBox[{ - RowBox[{"lim", "=", "5"}], ";"}]}]], "Input", - CellChangeTimes->{{3.776805753963585*^9, 3.776805767131317*^9}}], - -Cell[BoxData[ - RowBox[{ - RowBox[{"(*", " ", - RowBox[{ - "convert", " ", "real", " ", "ordered", " ", "pair", " ", "to", " ", - "complex", " ", "number"}], " ", "*)"}], "\[IndentingNewLine]", - RowBox[{ - RowBox[{"r2c", "[", "x_", "]"}], ":=", - RowBox[{ - RowBox[{"x", "[", - RowBox[{"[", "1", "]"}], "]"}], "+", - RowBox[{"I", " ", - RowBox[{"x", "[", - RowBox[{"[", "2", "]"}], "]"}]}]}]}]}]], "Input", - CellChangeTimes->{{3.776801933425262*^9, 3.7768019670958586`*^9}, { - 3.7768020413249216`*^9, 3.776802050696921*^9}}], - -Cell[BoxData[ - RowBox[{ - RowBox[{"(*", " ", - RowBox[{ - "convert", " ", "complex", " ", "number", " ", "to", " ", "real", " ", - "ordered", " ", "pair"}], " ", "*)"}], "\[IndentingNewLine]", - RowBox[{ - RowBox[{"c2r", "[", "x_", "]"}], ":=", - RowBox[{"{", - RowBox[{ - RowBox[{"Re", "[", "x", "]"}], ",", - RowBox[{"Im", "[", "x", "]"}]}], "}"}]}]}]], "Input", - CellChangeTimes->{{3.7768020323527966`*^9, 3.7768020685350246`*^9}}], - -Cell[BoxData[ - RowBox[{ - RowBox[{"(*", " ", - RowBox[{ - RowBox[{"defining", " ", "number"}], "-", - RowBox[{ - "coded", " ", "functions", " ", "of", " ", "two", " ", "complex", " ", - "numbers"}]}], " ", "*)"}], "\[IndentingNewLine]", - RowBox[{ - RowBox[{ - RowBox[{"f", "[", - RowBox[{"1", ",", "x_", ",", "y_"}], "]"}], ":=", - RowBox[{"x", "+", "y"}]}], - RowBox[{"(*", " ", "addition", " ", "*)"}], "\[IndentingNewLine]", - RowBox[{ - RowBox[{"f", "[", - RowBox[{"2", ",", "x_", ",", "y_"}], "]"}], ":=", - RowBox[{"x", "*", "y"}]}], - RowBox[{"(*", " ", "multiplication", " ", "*)"}], "\[IndentingNewLine]", - RowBox[{ - RowBox[{"f", "[", - RowBox[{"3", ",", "x_", ",", "y_"}], "]"}], ":=", - RowBox[{"Sin", "[", "x", "]"}]}], - RowBox[{"(*", " ", "sine", " ", "*)"}], "\[IndentingNewLine]", - RowBox[{ - RowBox[{"f", "[", - RowBox[{"4", ",", "x_", ",", "y_"}], "]"}], ":=", - RowBox[{"Cos", "[", "x", "]"}]}], - RowBox[{"(*", " ", "cosine", " ", "*)"}], "\[IndentingNewLine]", - RowBox[{ - RowBox[{"f", "[", - RowBox[{"5", ",", "x_", ",", "y_"}], "]"}], ":=", - RowBox[{"Tan", "[", "x", "]"}]}], - RowBox[{"(*", " ", "tangent", " ", "*)"}], "\[IndentingNewLine]", - RowBox[{ - RowBox[{"f", "[", - RowBox[{"6", ",", "x_", ",", "y_"}], "]"}], ":=", - RowBox[{"If", "[", - RowBox[{ - RowBox[{ - RowBox[{"Abs", "[", "x", "]"}], ">", "0"}], ",", - SuperscriptBox["x", - RowBox[{"-", "1"}]], ",", "0"}], "]"}]}], - RowBox[{"(*", " ", "reciprocal", " ", "*)"}], "\[IndentingNewLine]", - RowBox[{ - RowBox[{"f", "[", - RowBox[{"7", ",", "x_", ",", "y_"}], "]"}], ":=", - SuperscriptBox["x", "2"]}], - RowBox[{"(*", " ", "square", " ", "*)"}], "\[IndentingNewLine]", - RowBox[{ - RowBox[{"f", "[", - RowBox[{"8", ",", "x_", ",", "y_"}], "]"}], ":=", - RowBox[{"Exp", "[", "x", "]"}]}], - RowBox[{"(*", " ", "exponential", " ", "*)"}], "\[IndentingNewLine]", - RowBox[{ - RowBox[{"f", "[", - RowBox[{"9", ",", "x_", ",", "y_"}], "]"}], ":=", - RowBox[{"Gamma", "[", "x", "]"}]}], - RowBox[{"(*", " ", "gamma", " ", "*)"}], "\[IndentingNewLine]", - RowBox[{ - RowBox[{"f", "[", - RowBox[{"10", ",", "x_", ",", "y_"}], "]"}], ":=", - RowBox[{"If", "[", - RowBox[{ - RowBox[{"x", "\[NotEqual]", "1"}], ",", - RowBox[{"Zeta", "[", "x", "]"}], ",", "0"}], "]"}]}], - RowBox[{"(*", " ", - RowBox[{"Riemann", " ", "zeta"}], " ", "*)"}], "\[IndentingNewLine]", - RowBox[{ - RowBox[{"f", "[", - RowBox[{"11", ",", "x_", ",", "y_"}], "]"}], ":=", - RowBox[{"If", "[", - RowBox[{ - RowBox[{"x", "\[NotEqual]", "1"}], ",", - FractionBox["1", - RowBox[{"1", "-", "x"}]], ",", "0"}], "]"}], - RowBox[{"(*", " ", - RowBox[{"geometric", " ", "series"}], " ", "*)"}]}]}]}]], "Input", - CellChangeTimes->{{3.7766008761831923`*^9, 3.776600882799075*^9}, { - 3.7768018839274416`*^9, 3.776801928231472*^9}, {3.776801974855852*^9, - 3.7768020136011786`*^9}, {3.7768020875865145`*^9, 3.7768020957260685`*^9}, { - 3.776802201367442*^9, 3.7768022089608955`*^9}, {3.7768022491821136`*^9, - 3.776802350762313*^9}, {3.7768024108724613`*^9, 3.776802471984173*^9}, { - 3.776805177450968*^9, 3.776805198823731*^9}, {3.7768055062781434`*^9, - 3.776805548045538*^9}, {3.776805645742075*^9, 3.7768056709341574`*^9}, { - 3.776806207657678*^9, 3.776806232588927*^9}, {3.7768065907962184`*^9, - 3.7768065911730776`*^9}, {3.776806660211052*^9, 3.7768066617139273`*^9}}], - -Cell[BoxData[ - RowBox[{ - RowBox[{"(*", " ", - RowBox[{ - "number", " ", "of", " ", "arguments", " ", "corresponding", " ", "to", - " ", "each", " ", "function", " ", "number"}], " ", "*)"}], - "\[IndentingNewLine]", - RowBox[{ - RowBox[{ - RowBox[{ - RowBox[{"args", "[", "1", "]"}], "=", "2"}], ";"}], - "\[IndentingNewLine]", - RowBox[{ - RowBox[{ - RowBox[{"args", "[", "2", "]"}], "=", "2"}], ";"}], - "\[IndentingNewLine]", - RowBox[{ - RowBox[{ - RowBox[{"args", "[", "3", "]"}], "=", "1"}], ";"}], - "\[IndentingNewLine]", - RowBox[{ - RowBox[{ - RowBox[{"args", "[", "4", "]"}], "=", "1"}], ";"}], - "\[IndentingNewLine]", - RowBox[{ - RowBox[{ - RowBox[{"args", "[", "5", "]"}], "=", "1"}], ";"}], - "\[IndentingNewLine]", - RowBox[{ - RowBox[{ - RowBox[{"args", "[", "6", "]"}], "=", "1"}], ";"}], - "\[IndentingNewLine]", - RowBox[{ - RowBox[{ - RowBox[{"args", "[", "7", "]"}], "=", "1"}], ";"}], - "\[IndentingNewLine]", - RowBox[{ - RowBox[{ - RowBox[{"args", "[", "8", "]"}], "=", "1"}], ";"}], - "\[IndentingNewLine]", - RowBox[{ - RowBox[{ - RowBox[{"args", "[", "9", "]"}], "=", "1"}], ";"}], - "\[IndentingNewLine]", - RowBox[{ - RowBox[{ - RowBox[{"args", "[", "10", "]"}], "=", "1"}], ";"}], - "\[IndentingNewLine]", - RowBox[{ - RowBox[{ - RowBox[{"args", "[", "11", "]"}], "=", "1"}], ";"}]}]}]], "Input", - CellChangeTimes->{{3.7768039990118065`*^9, 3.7768040512699957`*^9}, - 3.7768043371736517`*^9, {3.7768051317051907`*^9, 3.776805131903183*^9}, { - 3.776805585191716*^9, 3.7768055877289114`*^9}, {3.776806199834099*^9, - 3.7768062028248205`*^9}}], - -Cell[BoxData[ - RowBox[{ - RowBox[{"(*", " ", - RowBox[{ - "background", " ", "shading", " ", "for", " ", "each", " ", "function", - " ", "number"}], " ", "*)"}], "\[IndentingNewLine]", - RowBox[{ - RowBox[{ - RowBox[{ - RowBox[{"bg", "[", "1", "]"}], "=", - RowBox[{"{", "}"}]}], ";"}], "\[IndentingNewLine]", - RowBox[{ - RowBox[{ - RowBox[{"bg", "[", "2", "]"}], "=", - RowBox[{"{", "}"}]}], ";"}], "\[IndentingNewLine]", - RowBox[{ - RowBox[{ - RowBox[{"bg", "[", "3", "]"}], "=", - RowBox[{"{", "}"}]}], ";"}], "\[IndentingNewLine]", - RowBox[{ - RowBox[{ - RowBox[{"bg", "[", "4", "]"}], "=", - RowBox[{"{", "}"}]}], ";"}], "\[IndentingNewLine]", - RowBox[{ - RowBox[{ - RowBox[{"bg", "[", "5", "]"}], "=", - RowBox[{"{", "}"}]}], ";"}], "\[IndentingNewLine]", - RowBox[{ - RowBox[{ - RowBox[{"bg", "[", "6", "]"}], "=", - RowBox[{"{", "}"}]}], ";"}], "\[IndentingNewLine]", - RowBox[{ - RowBox[{ - RowBox[{"bg", "[", "7", "]"}], "=", - RowBox[{"{", "}"}]}], ";"}], "\[IndentingNewLine]", - RowBox[{ - RowBox[{ - RowBox[{"bg", "[", "8", "]"}], "=", - RowBox[{"{", "}"}]}], ";"}], "\[IndentingNewLine]", - RowBox[{ - RowBox[{ - RowBox[{"bg", "[", "9", "]"}], "=", - RowBox[{"{", "}"}]}], ";"}], "\[IndentingNewLine]", - RowBox[{ - RowBox[{ - RowBox[{"bg", "[", "10", "]"}], "=", - RowBox[{"{", - RowBox[{ - RowBox[{"Opacity", "[", "0.5", "]"}], ",", "LightBlue", ",", - RowBox[{"Rectangle", "[", - RowBox[{ - RowBox[{"{", - RowBox[{"1", ",", - RowBox[{"-", "lim"}]}], "}"}], ",", - RowBox[{"{", - RowBox[{"lim", ",", "lim"}], "}"}]}], "]"}], ",", "LightRed", ",", - RowBox[{"Rectangle", "[", - RowBox[{ - RowBox[{"{", - RowBox[{ - RowBox[{"-", "lim"}], ",", - RowBox[{"-", "lim"}]}], "}"}], ",", - RowBox[{"{", - RowBox[{"0", ",", "lim"}], "}"}]}], "]"}], ",", "LightYellow", ",", - RowBox[{"Rectangle", "[", - RowBox[{ - RowBox[{"{", - RowBox[{"0", ",", - RowBox[{"-", "lim"}]}], "}"}], ",", - RowBox[{"{", - RowBox[{"1", ",", "lim"}], "}"}]}], "]"}], ",", - RowBox[{"Opacity", "[", "1.0", "]"}]}], "}"}]}], ";"}], - "\[IndentingNewLine]", - RowBox[{ - RowBox[{ - RowBox[{"bg", "[", "11", "]"}], "=", - RowBox[{"{", - RowBox[{ - RowBox[{"Opacity", "[", "0.5", "]"}], ",", "LightOrange", ",", - RowBox[{"Disk", "[", "]"}], ",", - RowBox[{"Opacity", "[", "1.0", "]"}]}], "}"}]}], ";"}]}]}]], "Input", - CellChangeTimes->{{3.7768057419534063`*^9, 3.7768057509764414`*^9}, { - 3.7768058352401676`*^9, 3.7768060097709656`*^9}, {3.776806185100443*^9, - 3.7768061962756395`*^9}}], - -Cell[BoxData[ - RowBox[{ - RowBox[{"(*", " ", - RowBox[{ - RowBox[{"stores", " ", "previous", " ", "y"}], "-", "coordinates"}], " ", - "*)"}], "\[IndentingNewLine]", - RowBox[{ - RowBox[{"prevy", "=", - RowBox[{"{", - RowBox[{ - RowBox[{"-", "0.5"}], ",", "2"}], "}"}]}], ";"}]}]], "Input", - CellChangeTimes->{{3.776804714421626*^9, 3.7768047375213194`*^9}}] -}, Closed]], - -Cell[CellGroupData[{ - -Cell["Demonstration", "Subsection", - CellChangeTimes->{{3.7766008885632277`*^9, 3.7766008904796133`*^9}}], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"Manipulate", "[", - RowBox[{ - RowBox[{"Module", "[", - RowBox[{ - RowBox[{"{", "z", "}"}], ",", "\[IndentingNewLine]", - RowBox[{ - RowBox[{"z", "=", - RowBox[{"c2r", "[", - RowBox[{"f", "[", - RowBox[{"mode", ",", - RowBox[{"r2c", "[", "x", "]"}], ",", - RowBox[{"r2c", "[", "y", "]"}]}], "]"}], "]"}]}], ";", - "\[IndentingNewLine]", - RowBox[{"If", "[", - RowBox[{ - RowBox[{ - RowBox[{"args", "[", "mode", "]"}], "\[Equal]", "2"}], ",", - "\[IndentingNewLine]", - RowBox[{ - RowBox[{"If", "[", - RowBox[{ - RowBox[{ - RowBox[{"Max", "[", "y", "]"}], "<", - RowBox[{"10", "lim"}]}], ",", "\[IndentingNewLine]", - RowBox[{"prevy", "=", "y"}], ",", "\[IndentingNewLine]", - RowBox[{ - RowBox[{"y", "=", "prevy"}], ";"}]}], "\[IndentingNewLine]", - "]"}], ";", "\[IndentingNewLine]", - RowBox[{"y", "=", "prevy"}]}], ",", "\[IndentingNewLine]", - RowBox[{ - RowBox[{"y", "=", - RowBox[{"{", - RowBox[{ - RowBox[{"10", "lim"}], ",", - RowBox[{"10", "lim"}]}], "}"}]}], ";"}]}], "\[IndentingNewLine]", - "]"}], ";", "\[IndentingNewLine]", - RowBox[{"Show", "[", - RowBox[{ - RowBox[{"Graphics", "[", - RowBox[{"Join", "[", - RowBox[{ - RowBox[{"bg", "[", "mode", "]"}], ",", - RowBox[{"{", - RowBox[{ - RowBox[{"PointSize", "[", "Large", "]"}], ",", "Blue", ",", - RowBox[{"Point", "[", "x", "]"}], ",", - RowBox[{"Arrow", "[", - RowBox[{"{", - RowBox[{ - RowBox[{"{", - RowBox[{"0", ",", "0"}], "}"}], ",", "x"}], "}"}], "]"}]}], - "}"}], ",", - RowBox[{"If", "[", - RowBox[{ - RowBox[{ - RowBox[{"args", "[", "mode", "]"}], "\[Equal]", "2"}], ",", - RowBox[{"{", - RowBox[{"Red", ",", - RowBox[{"Point", "[", "y", "]"}], ",", - RowBox[{"Arrow", "[", - RowBox[{"{", - RowBox[{ - RowBox[{"{", - RowBox[{"0", ",", "0"}], "}"}], ",", "y"}], "}"}], "]"}]}], - "}"}], ",", - RowBox[{"{", "}"}]}], "]"}], ",", - RowBox[{"{", - RowBox[{"Purple", ",", - RowBox[{"Point", "[", "z", "]"}], ",", - RowBox[{"Arrow", "[", - RowBox[{"{", - RowBox[{ - RowBox[{"{", - RowBox[{"0", ",", "0"}], "}"}], ",", "z"}], "}"}], "]"}]}], - "}"}]}], "]"}], "]"}], ",", - RowBox[{"PlotRange", "\[Rule]", - RowBox[{"{", - RowBox[{ - RowBox[{"{", - RowBox[{ - RowBox[{"-", "lim"}], ",", "lim"}], "}"}], ",", - RowBox[{"{", - RowBox[{ - RowBox[{"-", "lim"}], ",", "lim"}], "}"}]}], "}"}]}], ",", - RowBox[{"Axes", "\[Rule]", "True"}], ",", - RowBox[{"AxesLabel", "\[Rule]", - RowBox[{"{", - RowBox[{"\"\\"", ",", "\"\\""}], "}"}]}]}], "]"}]}]}], - "\[IndentingNewLine]", "]"}], ",", - RowBox[{"{", - RowBox[{ - RowBox[{"{", - RowBox[{"mode", ",", "1", ",", "\"\\""}], "}"}], - ",", - RowBox[{"{", - RowBox[{ - RowBox[{"1", "\[Rule]", "\"\\""}], ",", - RowBox[{"2", "\[Rule]", "\"\\""}], ",", - RowBox[{"3", "\[Rule]", "\"\\""}], ",", - RowBox[{"4", "\[Rule]", "\"\\""}], ",", - RowBox[{"5", "\[Rule]", "\"\\""}], ",", - RowBox[{ - "6", "\[Rule]", "\"\<\!\(\*SuperscriptBox[\(x\), \(-1\)]\)\>\""}], ",", - RowBox[{ - "7", "\[Rule]", "\"\<\!\(\*SuperscriptBox[\(x\), \(2\)]\)\>\""}], ",", - RowBox[{ - "8", "\[Rule]", - "\"\<\!\(\*SuperscriptBox[\(\[ExponentialE]\), \(x\)]\)\>\""}], ",", - RowBox[{"9", "\[Rule]", "\"\<\[CapitalGamma](x)\>\""}], ",", - RowBox[{"10", "\[Rule]", "\"\<\[Zeta](x)\>\""}], ",", - RowBox[{ - "11", "\[Rule]", - "\"\<\!\(\*UnderoverscriptBox[\(\[Sum]\), \(n = 0\), \(\[Infinity]\)]\ -\)\!\(\*SuperscriptBox[\(x\), \(n\)]\)\>\""}]}], "}"}]}], "}"}], ",", - RowBox[{"{", - RowBox[{ - RowBox[{"{", - RowBox[{"x", ",", - RowBox[{"{", - RowBox[{"2", ",", "0.5"}], "}"}]}], "}"}], ",", "Locator"}], "}"}], - ",", - RowBox[{"{", - RowBox[{ - RowBox[{"{", - RowBox[{"y", ",", - RowBox[{"{", - RowBox[{ - RowBox[{"-", "0.5"}], ",", "2"}], "}"}]}], "}"}], ",", "Locator"}], - "}"}]}], "]"}]], "Input", - CellChangeTimes->CompressedData[" -1:eJxTTMoPSmViYGAQBWIQrXavId1b+Y2jWYhiBogOW2IWsw5IC7BvyAPRzn3l -JSD61c9FnSD6yOE/c0H0r4UzF4Loih/i60D0MR4pMM1wYfcWEN1wwmsXiGa1 -fLAPRLPVrjoBovvfrj4HohWWLTgPoounfr4GorfP4LsBoufte3obRFcZNb0B -qzcX/Qii163o+QWim6fPZFwPMs+8nxlEG82LZwfRp6zteEH0hr3NIiC6teyW -HIh2MV5hCqKz7CtcQTTDzigvEK12KNwXRK8JcQwD0R8Xz48A0XqMF9JA9ImK -P1kgevFkwSIQPSOqowys/8/6dhDNdf1CB4i+fODOfrD4sbiDIBoA3Jepaw== - - "]], - -Cell[BoxData[ - TagBox[ - StyleBox[ - DynamicModuleBox[{$CellContext`mode$$ = 1, $CellContext`x$$ = { - 2, 0.5}, $CellContext`y$$ = {-0.5, 2}, Typeset`show$$ = True, - Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", - Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = - "\"untitled\"", Typeset`specs$$ = {{{ - Hold[$CellContext`mode$$], 1, "operation/function"}, { - 1 -> "x+y", 2 -> "x\[CenterDot]y", 3 -> "sin(x)", 4 -> "cos(x)", 5 -> - "tan(x)", 6 -> "\!\(\*SuperscriptBox[\(x\), \(-1\)]\)", 7 -> - "\!\(\*SuperscriptBox[\(x\), \(2\)]\)", 8 -> - "\!\(\*SuperscriptBox[\(\[ExponentialE]\), \(x\)]\)", 9 -> - "\[CapitalGamma](x)", 10 -> "\[Zeta](x)", 11 -> - "\!\(\*UnderoverscriptBox[\(\[Sum]\), \(n = 0\), \ -\(\[Infinity]\)]\)\!\(\*SuperscriptBox[\(x\), \(n\)]\)"}}, {{ - Hold[$CellContext`x$$], {2, 0.5}}, Automatic}, {{ - Hold[$CellContext`y$$], {-0.5, 2}}, Automatic}}, Typeset`size$$ = { - 360., {176., 182.}}, Typeset`update$$ = 0, Typeset`initDone$$, - Typeset`skipInitDone$$ = True, $CellContext`mode$48059$$ = False}, - DynamicBox[Manipulate`ManipulateBoxes[ - 1, StandardForm, - "Variables" :> {$CellContext`mode$$ = - 1, $CellContext`x$$ = {2, 0.5}, $CellContext`y$$ = {-0.5, 2}}, - "ControllerVariables" :> { - Hold[$CellContext`mode$$, $CellContext`mode$48059$$, False]}, - "OtherVariables" :> { - Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, - Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, - Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, - Typeset`skipInitDone$$}, "Body" :> - Module[{$CellContext`z$}, $CellContext`z$ = $CellContext`c2r[ - $CellContext`f[$CellContext`mode$$, - $CellContext`r2c[$CellContext`x$$], - $CellContext`r2c[$CellContext`y$$]]]; - If[$CellContext`args[$CellContext`mode$$] == 2, - If[Max[$CellContext`y$$] < - 10 $CellContext`lim, $CellContext`prevy = $CellContext`y$$, \ -$CellContext`y$$ = $CellContext`prevy; - Null]; $CellContext`y$$ = $CellContext`prevy, $CellContext`y$$ = { - 10 $CellContext`lim, 10 $CellContext`lim}; Null]; Show[ - Graphics[ - Join[ - $CellContext`bg[$CellContext`mode$$], { - PointSize[Large], Blue, - Point[$CellContext`x$$], - Arrow[{{0, 0}, $CellContext`x$$}]}, - If[$CellContext`args[$CellContext`mode$$] == 2, {Red, - Point[$CellContext`y$$], - Arrow[{{0, 0}, $CellContext`y$$}]}, {}], {Purple, - Point[$CellContext`z$], - Arrow[{{0, 0}, $CellContext`z$}]}]], - PlotRange -> {{-$CellContext`lim, $CellContext`lim}, \ -{-$CellContext`lim, $CellContext`lim}}, Axes -> True, - AxesLabel -> {"Re", "Im"}]], - "Specifications" :> {{{$CellContext`mode$$, 1, "operation/function"}, { - 1 -> "x+y", 2 -> "x\[CenterDot]y", 3 -> "sin(x)", 4 -> "cos(x)", 5 -> - "tan(x)", 6 -> "\!\(\*SuperscriptBox[\(x\), \(-1\)]\)", 7 -> - "\!\(\*SuperscriptBox[\(x\), \(2\)]\)", 8 -> - "\!\(\*SuperscriptBox[\(\[ExponentialE]\), \(x\)]\)", 9 -> - "\[CapitalGamma](x)", 10 -> "\[Zeta](x)", 11 -> - "\!\(\*UnderoverscriptBox[\(\[Sum]\), \(n = 0\), \(\[Infinity]\)]\)\ -\!\(\*SuperscriptBox[\(x\), \(n\)]\)"}}, {{$CellContext`x$$, {2, 0.5}}, - Automatic, ControlType -> Locator}, {{$CellContext`y$$, {-0.5, 2}}, - Automatic, ControlType -> Locator}}, "Options" :> {}, - "DefaultOptions" :> {}], - ImageSizeCache->{417., {227., 233.}}, - SingleEvaluation->True], - Deinitialization:>None, - DynamicModuleValues:>{}, - SynchronousInitialization->True, - UndoTrackedVariables:>{Typeset`show$$, Typeset`bookmarkMode$$}, - UnsavedVariables:>{Typeset`initDone$$}, - UntrackedVariables:>{Typeset`size$$}], "Manipulate", - Deployed->True, - StripOnInput->False], - Manipulate`InterpretManipulate[1]]], "Output", - CellChangeTimes->{3.7768060757320585`*^9, 3.7768064122662535`*^9, - 3.7768065048257113`*^9, 3.776806594529003*^9, 3.7768066759197564`*^9}] -}, Open ]] -}, Open ]] -}, Open ]] -}, Open ]] -}, -WindowSize->{759, 833}, -WindowMargins->{{70, Automatic}, {Automatic, 55}}, -FrontEndVersion->"10.4 for Microsoft Windows (64-bit) (April 11, 2016)", -StyleDefinitions->"Default.nb" -] -(* End of Notebook Content *) - -(* Internal cache information *) -(*CellTagsOutline -CellTagsIndex->{} -*) -(*CellTagsIndex -CellTagsIndex->{} -*) -(*NotebookFileOutline -Notebook[{ -Cell[CellGroupData[{ -Cell[580, 22, 156, 2, 90, "Title"], -Cell[739, 26, 156, 2, 30, "Text"], -Cell[CellGroupData[{ -Cell[920, 32, 99, 1, 63, "Section"], -Cell[1022, 35, 517, 8, 68, "Text"], -Cell[1542, 45, 134, 1, 30, "Text"], -Cell[CellGroupData[{ -Cell[1701, 50, 222, 8, 29, "Item"], -Cell[1926, 60, 241, 8, 29, "Item"], -Cell[2170, 70, 88, 1, 29, "Item"], -Cell[2261, 73, 90, 1, 29, "Item"], -Cell[2354, 76, 93, 1, 29, "Item"], -Cell[2450, 79, 245, 9, 31, "Item"], -Cell[2698, 90, 274, 9, 31, "Item"], -Cell[2975, 101, 290, 9, 29, "Item"], -Cell[3268, 112, 291, 9, 30, "Item"], -Cell[3562, 123, 340, 10, 30, "Item"], -Cell[3905, 135, 430, 12, 30, "Item"] -}, Open ]], -Cell[4350, 150, 199, 4, 49, "Text"] -}, Open ]], -Cell[CellGroupData[{ -Cell[4586, 159, 91, 1, 63, "Section"], -Cell[CellGroupData[{ -Cell[4702, 164, 102, 1, 43, "Subsection"], -Cell[4807, 167, 248, 6, 52, "Input"], -Cell[5058, 175, 553, 15, 52, "Input"], -Cell[5614, 192, 454, 12, 52, "Input"], -Cell[6071, 206, 3553, 86, 279, "Input"], -Cell[9627, 294, 1683, 54, 252, "Input"], -Cell[11313, 350, 2821, 83, 292, "Input"], -Cell[14137, 435, 376, 11, 52, "Input"] -}, Closed]], -Cell[CellGroupData[{ -Cell[14550, 451, 105, 1, 35, "Subsection"], -Cell[CellGroupData[{ -Cell[14680, 456, 5228, 138, 496, "Input"], -Cell[19911, 596, 4212, 78, 477, "Output"] -}, Open ]] -}, Open ]] -}, Open ]] -}, Open ]] -} -] -*) - +(* Content-type: application/vnd.wolfram.mathematica *) + +(*** Wolfram Notebook File ***) +(* http://www.wolfram.com/nb *) + +(* CreatedBy='Mathematica 10.4' *) + +(*CacheID: 234*) +(* Internal cache information: +NotebookFileLineBreakTest +NotebookFileLineBreakTest +NotebookDataPosition[ 158, 7] +NotebookDataLength[ 25716, 735] +NotebookOptionsPosition[ 24175, 680] +NotebookOutlinePosition[ 24518, 695] +CellTagsIndexPosition[ 24475, 692] +WindowFrame->Normal*) + +(* Beginning of Notebook Content *) +Notebook[{ + +Cell[CellGroupData[{ +Cell["Complex Operations", "Title", + CellChangeTimes->{{3.776600831050974*^9, 3.7766008318453026`*^9}, { + 3.7768014692411594`*^9, 3.7768014727414646`*^9}}], + +Cell["Adam Rumpf, 3/20/2017", "Text", + CellChangeTimes->{{3.7766008347881403`*^9, 3.776600838290375*^9}, { + 3.776801479279549*^9, 3.7768014811941967`*^9}}], + +Cell[CellGroupData[{ + +Cell["Introduction", "Section", + CellChangeTimes->{{3.7766008459498987`*^9, 3.776600848547045*^9}}], + +Cell["\<\ +This program consists of a single Manipulate environment that displays \ +vectors in the complex plane. The blue and red vectors represent inputs, and \ +can be clicked and dragged, while the purple vector represents the output of \ +a chosen mathematical operation or function.\ +\>", "Text", + CellChangeTimes->{{3.776600856235587*^9, 3.776600860481224*^9}, { + 3.7768017314717674`*^9, 3.7768017781690865`*^9}, {3.776801808899147*^9, + 3.7768018444568605`*^9}, {3.7768022110736027`*^9, 3.776802220503076*^9}}], + +Cell["The following operations and functions are included:", "Text", + CellChangeTimes->{{3.776806090808209*^9, 3.776806097009242*^9}}], + +Cell[CellGroupData[{ + +Cell[TextData[{ + "Addition (", + Cell[BoxData[ + FormBox[ + RowBox[{"x", "+", "y"}], TraditionalForm]], + FormatType->"TraditionalForm"], + ")" +}], "Item", + CellChangeTimes->{{3.7768061049497538`*^9, 3.776806132799117*^9}}], + +Cell[TextData[{ + "Multiplication (", + Cell[BoxData[ + FormBox[ + RowBox[{"x", "\[CenterDot]", "y"}], TraditionalForm]], + FormatType->"TraditionalForm"], + ")" +}], "Item", + CellChangeTimes->{{3.7768061049497538`*^9, 3.7768061393541117`*^9}}], + +Cell["Sine", "Item", + CellChangeTimes->{{3.7768061049497538`*^9, 3.776806115929446*^9}}], + +Cell["Cosine", "Item", + CellChangeTimes->{{3.7768061049497538`*^9, 3.776806116821181*^9}}], + +Cell["Tangent", "Item", + CellChangeTimes->{{3.7768061049497538`*^9, 3.7768061179967833`*^9}}], + +Cell[TextData[{ + "Reciprocal (", + Cell[BoxData[ + FormBox[ + SuperscriptBox["x", + RowBox[{"-", "1"}]], TraditionalForm]], + FormatType->"TraditionalForm"], + ")" +}], "Item", + CellChangeTimes->{{3.7768061049497538`*^9, 3.776806151631158*^9}}], + +Cell[TextData[{ + "Square (", + Cell[BoxData[ + FormBox[ + SuperscriptBox["x", "2"], TraditionalForm]], + FormatType->"TraditionalForm"], + ")" +}], "Item", + CellChangeTimes->{{3.7768061049497538`*^9, 3.776806176150304*^9}, { + 3.7768062766849318`*^9, 3.7768062766909494`*^9}}], + +Cell[TextData[{ + "Exponential (", + Cell[BoxData[ + FormBox[ + SuperscriptBox["\[ExponentialE]", "x"], TraditionalForm]], + FormatType->"TraditionalForm"], + ")" +}], "Item", + CellChangeTimes->{{3.7768061049497538`*^9, 3.776806176150304*^9}, { + 3.7768062766849318`*^9, 3.77680628942142*^9}}], + +Cell[TextData[{ + "Gamma (", + Cell[BoxData[ + FormBox[ + RowBox[{"\[CapitalGamma]", "(", "x", ")"}], TraditionalForm]], + FormatType->"TraditionalForm"], + ")" +}], "Item", + CellChangeTimes->{{3.7768061049497538`*^9, 3.776806176150304*^9}, { + 3.7768062766849318`*^9, 3.7768062996951275`*^9}}], + +Cell[TextData[{ + "Riemann Zeta (", + Cell[BoxData[ + FormBox[ + RowBox[{"\[Zeta]", "(", "x", ")"}], TraditionalForm]], + FormatType->"TraditionalForm"], + ")" +}], "Item", + CellChangeTimes->{{3.7768061049497538`*^9, 3.776806176150304*^9}, { + 3.7768062766849318`*^9, 3.7768063117433167`*^9}, {3.7768063485136228`*^9, + 3.77680635223643*^9}}], + +Cell[TextData[{ + "Geometric Series (", + Cell[BoxData[ + FormBox[ + RowBox[{ + UnderoverscriptBox["\[Sum]", + RowBox[{"n", "=", "0"}], "\[Infinity]"], + SuperscriptBox["x", "n"]}], TraditionalForm]], + FormatType->"TraditionalForm"], + ") (uses analytic continuation outside of unit disk)" +}], "Item", + CellChangeTimes->{{3.7768061049497538`*^9, 3.776806176150304*^9}, { + 3.7768062766849318`*^9, 3.7768063780661554`*^9}}] +}, Open ]], + +Cell["\<\ +General exponentiation and logarithm have been excluded because they are \ +multivalued for complex numbers.\ +\>", "Text", + CellChangeTimes->{{3.776806824485301*^9, 3.7768068827046947`*^9}}] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Code", "Section", + CellChangeTimes->{{3.776600864408964*^9, 3.7766008650447807`*^9}}], + +Cell[CellGroupData[{ + +Cell["Initialization", "Subsection", + CellChangeTimes->{{3.776600871130811*^9, 3.776600873087188*^9}}], + +Cell[BoxData[ + RowBox[{ + RowBox[{"(*", " ", + RowBox[{"plotting", " ", "limits"}], " ", "*)"}], "\[IndentingNewLine]", + RowBox[{ + RowBox[{"lim", "=", "5"}], ";"}]}]], "Input", + CellChangeTimes->{{3.776805753963585*^9, 3.776805767131317*^9}}], + +Cell[BoxData[ + RowBox[{ + RowBox[{"(*", " ", + RowBox[{ + "convert", " ", "real", " ", "ordered", " ", "pair", " ", "to", " ", + "complex", " ", "number"}], " ", "*)"}], "\[IndentingNewLine]", + RowBox[{ + RowBox[{"r2c", "[", "x_", "]"}], ":=", + RowBox[{ + RowBox[{"x", "[", + RowBox[{"[", "1", "]"}], "]"}], "+", + RowBox[{"I", " ", + RowBox[{"x", "[", + RowBox[{"[", "2", "]"}], "]"}]}]}]}]}]], "Input", + CellChangeTimes->{{3.776801933425262*^9, 3.7768019670958586`*^9}, { + 3.7768020413249216`*^9, 3.776802050696921*^9}}], + +Cell[BoxData[ + RowBox[{ + RowBox[{"(*", " ", + RowBox[{ + "convert", " ", "complex", " ", "number", " ", "to", " ", "real", " ", + "ordered", " ", "pair"}], " ", "*)"}], "\[IndentingNewLine]", + RowBox[{ + RowBox[{"c2r", "[", "x_", "]"}], ":=", + RowBox[{"{", + RowBox[{ + RowBox[{"Re", "[", "x", "]"}], ",", + RowBox[{"Im", "[", "x", "]"}]}], "}"}]}]}]], "Input", + CellChangeTimes->{{3.7768020323527966`*^9, 3.7768020685350246`*^9}}], + +Cell[BoxData[ + RowBox[{ + RowBox[{"(*", " ", + RowBox[{ + RowBox[{"defining", " ", "number"}], "-", + RowBox[{ + "coded", " ", "functions", " ", "of", " ", "two", " ", "complex", " ", + "numbers"}]}], " ", "*)"}], "\[IndentingNewLine]", + RowBox[{ + RowBox[{ + RowBox[{"f", "[", + RowBox[{"1", ",", "x_", ",", "y_"}], "]"}], ":=", + RowBox[{"x", "+", "y"}]}], + RowBox[{"(*", " ", "addition", " ", "*)"}], "\[IndentingNewLine]", + RowBox[{ + RowBox[{"f", "[", + RowBox[{"2", ",", "x_", ",", "y_"}], "]"}], ":=", + RowBox[{"x", "*", "y"}]}], + RowBox[{"(*", " ", "multiplication", " ", "*)"}], "\[IndentingNewLine]", + RowBox[{ + RowBox[{"f", "[", + RowBox[{"3", ",", "x_", ",", "y_"}], "]"}], ":=", + RowBox[{"Sin", "[", "x", "]"}]}], + RowBox[{"(*", " ", "sine", " ", "*)"}], "\[IndentingNewLine]", + RowBox[{ + RowBox[{"f", "[", + RowBox[{"4", ",", "x_", ",", "y_"}], "]"}], ":=", + RowBox[{"Cos", "[", "x", "]"}]}], + RowBox[{"(*", " ", "cosine", " ", "*)"}], "\[IndentingNewLine]", + RowBox[{ + RowBox[{"f", "[", + RowBox[{"5", ",", "x_", ",", "y_"}], "]"}], ":=", + RowBox[{"Tan", "[", "x", "]"}]}], + RowBox[{"(*", " ", "tangent", " ", "*)"}], "\[IndentingNewLine]", + RowBox[{ + RowBox[{"f", "[", + RowBox[{"6", ",", "x_", ",", "y_"}], "]"}], ":=", + RowBox[{"If", "[", + RowBox[{ + RowBox[{ + RowBox[{"Abs", "[", "x", "]"}], ">", "0"}], ",", + SuperscriptBox["x", + RowBox[{"-", "1"}]], ",", "0"}], "]"}]}], + RowBox[{"(*", " ", "reciprocal", " ", "*)"}], "\[IndentingNewLine]", + RowBox[{ + RowBox[{"f", "[", + RowBox[{"7", ",", "x_", ",", "y_"}], "]"}], ":=", + SuperscriptBox["x", "2"]}], + RowBox[{"(*", " ", "square", " ", "*)"}], "\[IndentingNewLine]", + RowBox[{ + RowBox[{"f", "[", + RowBox[{"8", ",", "x_", ",", "y_"}], "]"}], ":=", + RowBox[{"Exp", "[", "x", "]"}]}], + RowBox[{"(*", " ", "exponential", " ", "*)"}], "\[IndentingNewLine]", + RowBox[{ + RowBox[{"f", "[", + RowBox[{"9", ",", "x_", ",", "y_"}], "]"}], ":=", + RowBox[{"Gamma", "[", "x", "]"}]}], + RowBox[{"(*", " ", "gamma", " ", "*)"}], "\[IndentingNewLine]", + RowBox[{ + RowBox[{"f", "[", + RowBox[{"10", ",", "x_", ",", "y_"}], "]"}], ":=", + RowBox[{"If", "[", + RowBox[{ + RowBox[{"x", "\[NotEqual]", "1"}], ",", + RowBox[{"Zeta", "[", "x", "]"}], ",", "0"}], "]"}]}], + RowBox[{"(*", " ", + RowBox[{"Riemann", " ", "zeta"}], " ", "*)"}], "\[IndentingNewLine]", + RowBox[{ + RowBox[{"f", "[", + RowBox[{"11", ",", "x_", ",", "y_"}], "]"}], ":=", + RowBox[{"If", "[", + RowBox[{ + RowBox[{"x", "\[NotEqual]", "1"}], ",", + FractionBox["1", + RowBox[{"1", "-", "x"}]], ",", "0"}], "]"}], + RowBox[{"(*", " ", + RowBox[{"geometric", " ", "series"}], " ", "*)"}]}]}]}]], "Input", + CellChangeTimes->{{3.7766008761831923`*^9, 3.776600882799075*^9}, { + 3.7768018839274416`*^9, 3.776801928231472*^9}, {3.776801974855852*^9, + 3.7768020136011786`*^9}, {3.7768020875865145`*^9, 3.7768020957260685`*^9}, { + 3.776802201367442*^9, 3.7768022089608955`*^9}, {3.7768022491821136`*^9, + 3.776802350762313*^9}, {3.7768024108724613`*^9, 3.776802471984173*^9}, { + 3.776805177450968*^9, 3.776805198823731*^9}, {3.7768055062781434`*^9, + 3.776805548045538*^9}, {3.776805645742075*^9, 3.7768056709341574`*^9}, { + 3.776806207657678*^9, 3.776806232588927*^9}, {3.7768065907962184`*^9, + 3.7768065911730776`*^9}, {3.776806660211052*^9, 3.7768066617139273`*^9}}], + +Cell[BoxData[ + RowBox[{ + RowBox[{"(*", " ", + RowBox[{ + "number", " ", "of", " ", "arguments", " ", "corresponding", " ", "to", + " ", "each", " ", "function", " ", "number"}], " ", "*)"}], + "\[IndentingNewLine]", + RowBox[{ + RowBox[{ + RowBox[{ + RowBox[{"args", "[", "1", "]"}], "=", "2"}], ";"}], + "\[IndentingNewLine]", + RowBox[{ + RowBox[{ + RowBox[{"args", "[", "2", "]"}], "=", "2"}], ";"}], + "\[IndentingNewLine]", + RowBox[{ + RowBox[{ + RowBox[{"args", "[", "3", "]"}], "=", "1"}], ";"}], + "\[IndentingNewLine]", + RowBox[{ + RowBox[{ + RowBox[{"args", "[", "4", "]"}], "=", "1"}], ";"}], + "\[IndentingNewLine]", + RowBox[{ + RowBox[{ + RowBox[{"args", "[", "5", "]"}], "=", "1"}], ";"}], + "\[IndentingNewLine]", + RowBox[{ + RowBox[{ + RowBox[{"args", "[", "6", "]"}], "=", "1"}], ";"}], + "\[IndentingNewLine]", + RowBox[{ + RowBox[{ + RowBox[{"args", "[", "7", "]"}], "=", "1"}], ";"}], + "\[IndentingNewLine]", + RowBox[{ + RowBox[{ + RowBox[{"args", "[", "8", "]"}], "=", "1"}], ";"}], + "\[IndentingNewLine]", + RowBox[{ + RowBox[{ + RowBox[{"args", "[", "9", "]"}], "=", "1"}], ";"}], + "\[IndentingNewLine]", + RowBox[{ + RowBox[{ + RowBox[{"args", "[", "10", "]"}], "=", "1"}], ";"}], + "\[IndentingNewLine]", + RowBox[{ + RowBox[{ + RowBox[{"args", "[", "11", "]"}], "=", "1"}], ";"}]}]}]], "Input", + CellChangeTimes->{{3.7768039990118065`*^9, 3.7768040512699957`*^9}, + 3.7768043371736517`*^9, {3.7768051317051907`*^9, 3.776805131903183*^9}, { + 3.776805585191716*^9, 3.7768055877289114`*^9}, {3.776806199834099*^9, + 3.7768062028248205`*^9}}], + +Cell[BoxData[ + RowBox[{ + RowBox[{"(*", " ", + RowBox[{ + "background", " ", "shading", " ", "for", " ", "each", " ", "function", + " ", "number"}], " ", "*)"}], "\[IndentingNewLine]", + RowBox[{ + RowBox[{ + RowBox[{ + RowBox[{"bg", "[", "1", "]"}], "=", + RowBox[{"{", "}"}]}], ";"}], "\[IndentingNewLine]", + RowBox[{ + RowBox[{ + RowBox[{"bg", "[", "2", "]"}], "=", + RowBox[{"{", "}"}]}], ";"}], "\[IndentingNewLine]", + RowBox[{ + RowBox[{ + RowBox[{"bg", "[", "3", "]"}], "=", + RowBox[{"{", "}"}]}], ";"}], "\[IndentingNewLine]", + RowBox[{ + RowBox[{ + RowBox[{"bg", "[", "4", "]"}], "=", + RowBox[{"{", "}"}]}], ";"}], "\[IndentingNewLine]", + RowBox[{ + RowBox[{ + RowBox[{"bg", "[", "5", "]"}], "=", + RowBox[{"{", "}"}]}], ";"}], "\[IndentingNewLine]", + RowBox[{ + RowBox[{ + RowBox[{"bg", "[", "6", "]"}], "=", + RowBox[{"{", "}"}]}], ";"}], "\[IndentingNewLine]", + RowBox[{ + RowBox[{ + RowBox[{"bg", "[", "7", "]"}], "=", + RowBox[{"{", "}"}]}], ";"}], "\[IndentingNewLine]", + RowBox[{ + RowBox[{ + RowBox[{"bg", "[", "8", "]"}], "=", + RowBox[{"{", "}"}]}], ";"}], "\[IndentingNewLine]", + RowBox[{ + RowBox[{ + RowBox[{"bg", "[", "9", "]"}], "=", + RowBox[{"{", "}"}]}], ";"}], "\[IndentingNewLine]", + RowBox[{ + RowBox[{ + RowBox[{"bg", "[", "10", "]"}], "=", + RowBox[{"{", + RowBox[{ + RowBox[{"Opacity", "[", "0.5", "]"}], ",", "LightBlue", ",", + RowBox[{"Rectangle", "[", + RowBox[{ + RowBox[{"{", + RowBox[{"1", ",", + RowBox[{"-", "lim"}]}], "}"}], ",", + RowBox[{"{", + RowBox[{"lim", ",", "lim"}], "}"}]}], "]"}], ",", "LightRed", ",", + RowBox[{"Rectangle", "[", + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{"-", "lim"}], ",", + RowBox[{"-", "lim"}]}], "}"}], ",", + RowBox[{"{", + RowBox[{"0", ",", "lim"}], "}"}]}], "]"}], ",", "LightYellow", ",", + RowBox[{"Rectangle", "[", + RowBox[{ + RowBox[{"{", + RowBox[{"0", ",", + RowBox[{"-", "lim"}]}], "}"}], ",", + RowBox[{"{", + RowBox[{"1", ",", "lim"}], "}"}]}], "]"}], ",", + RowBox[{"Opacity", "[", "1.0", "]"}]}], "}"}]}], ";"}], + "\[IndentingNewLine]", + RowBox[{ + RowBox[{ + RowBox[{"bg", "[", "11", "]"}], "=", + RowBox[{"{", + RowBox[{ + RowBox[{"Opacity", "[", "0.5", "]"}], ",", "LightOrange", ",", + RowBox[{"Disk", "[", "]"}], ",", + RowBox[{"Opacity", "[", "1.0", "]"}]}], "}"}]}], ";"}]}]}]], "Input", + CellChangeTimes->{{3.7768057419534063`*^9, 3.7768057509764414`*^9}, { + 3.7768058352401676`*^9, 3.7768060097709656`*^9}, {3.776806185100443*^9, + 3.7768061962756395`*^9}}], + +Cell[BoxData[ + RowBox[{ + RowBox[{"(*", " ", + RowBox[{ + RowBox[{"stores", " ", "previous", " ", "y"}], "-", "coordinates"}], " ", + "*)"}], "\[IndentingNewLine]", + RowBox[{ + RowBox[{"prevy", "=", + RowBox[{"{", + RowBox[{ + RowBox[{"-", "0.5"}], ",", "2"}], "}"}]}], ";"}]}]], "Input", + CellChangeTimes->{{3.776804714421626*^9, 3.7768047375213194`*^9}}] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Demonstration", "Subsection", + CellChangeTimes->{{3.7766008885632277`*^9, 3.7766008904796133`*^9}}], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Manipulate", "[", + RowBox[{ + RowBox[{"Module", "[", + RowBox[{ + RowBox[{"{", "z", "}"}], ",", "\[IndentingNewLine]", + RowBox[{ + RowBox[{"z", "=", + RowBox[{"c2r", "[", + RowBox[{"f", "[", + RowBox[{"mode", ",", + RowBox[{"r2c", "[", "x", "]"}], ",", + RowBox[{"r2c", "[", "y", "]"}]}], "]"}], "]"}]}], ";", + "\[IndentingNewLine]", + RowBox[{"If", "[", + RowBox[{ + RowBox[{ + RowBox[{"args", "[", "mode", "]"}], "\[Equal]", "2"}], ",", + "\[IndentingNewLine]", + RowBox[{ + RowBox[{"If", "[", + RowBox[{ + RowBox[{ + RowBox[{"Max", "[", "y", "]"}], "<", + RowBox[{"10", "lim"}]}], ",", "\[IndentingNewLine]", + RowBox[{"prevy", "=", "y"}], ",", "\[IndentingNewLine]", + RowBox[{ + RowBox[{"y", "=", "prevy"}], ";"}]}], "\[IndentingNewLine]", + "]"}], ";", "\[IndentingNewLine]", + RowBox[{"y", "=", "prevy"}]}], ",", "\[IndentingNewLine]", + RowBox[{ + RowBox[{"y", "=", + RowBox[{"{", + RowBox[{ + RowBox[{"10", "lim"}], ",", + RowBox[{"10", "lim"}]}], "}"}]}], ";"}]}], "\[IndentingNewLine]", + "]"}], ";", "\[IndentingNewLine]", + RowBox[{"Show", "[", + RowBox[{ + RowBox[{"Graphics", "[", + RowBox[{"Join", "[", + RowBox[{ + RowBox[{"bg", "[", "mode", "]"}], ",", + RowBox[{"{", + RowBox[{ + RowBox[{"PointSize", "[", "Large", "]"}], ",", "Blue", ",", + RowBox[{"Point", "[", "x", "]"}], ",", + RowBox[{"Arrow", "[", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{"0", ",", "0"}], "}"}], ",", "x"}], "}"}], "]"}]}], + "}"}], ",", + RowBox[{"If", "[", + RowBox[{ + RowBox[{ + RowBox[{"args", "[", "mode", "]"}], "\[Equal]", "2"}], ",", + RowBox[{"{", + RowBox[{"Red", ",", + RowBox[{"Point", "[", "y", "]"}], ",", + RowBox[{"Arrow", "[", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{"0", ",", "0"}], "}"}], ",", "y"}], "}"}], "]"}]}], + "}"}], ",", + RowBox[{"{", "}"}]}], "]"}], ",", + RowBox[{"{", + RowBox[{"Purple", ",", + RowBox[{"Point", "[", "z", "]"}], ",", + RowBox[{"Arrow", "[", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{"0", ",", "0"}], "}"}], ",", "z"}], "}"}], "]"}]}], + "}"}]}], "]"}], "]"}], ",", + RowBox[{"PlotRange", "\[Rule]", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{"-", "lim"}], ",", "lim"}], "}"}], ",", + RowBox[{"{", + RowBox[{ + RowBox[{"-", "lim"}], ",", "lim"}], "}"}]}], "}"}]}], ",", + RowBox[{"Axes", "\[Rule]", "True"}], ",", + RowBox[{"AxesLabel", "\[Rule]", + RowBox[{"{", + RowBox[{"\"\\"", ",", "\"\\""}], "}"}]}]}], "]"}]}]}], + "\[IndentingNewLine]", "]"}], ",", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{"mode", ",", "1", ",", "\"\\""}], "}"}], + ",", + RowBox[{"{", + RowBox[{ + RowBox[{"1", "\[Rule]", "\"\\""}], ",", + RowBox[{"2", "\[Rule]", "\"\\""}], ",", + RowBox[{"3", "\[Rule]", "\"\\""}], ",", + RowBox[{"4", "\[Rule]", "\"\\""}], ",", + RowBox[{"5", "\[Rule]", "\"\\""}], ",", + RowBox[{ + "6", "\[Rule]", "\"\<\!\(\*SuperscriptBox[\(x\), \(-1\)]\)\>\""}], ",", + RowBox[{ + "7", "\[Rule]", "\"\<\!\(\*SuperscriptBox[\(x\), \(2\)]\)\>\""}], ",", + RowBox[{ + "8", "\[Rule]", + "\"\<\!\(\*SuperscriptBox[\(\[ExponentialE]\), \(x\)]\)\>\""}], ",", + RowBox[{"9", "\[Rule]", "\"\<\[CapitalGamma](x)\>\""}], ",", + RowBox[{"10", "\[Rule]", "\"\<\[Zeta](x)\>\""}], ",", + RowBox[{ + "11", "\[Rule]", + "\"\<\!\(\*UnderoverscriptBox[\(\[Sum]\), \(n = 0\), \(\[Infinity]\)]\ +\)\!\(\*SuperscriptBox[\(x\), \(n\)]\)\>\""}]}], "}"}]}], "}"}], ",", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{"x", ",", + RowBox[{"{", + RowBox[{"2", ",", "0.5"}], "}"}]}], "}"}], ",", "Locator"}], "}"}], + ",", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{"y", ",", + RowBox[{"{", + RowBox[{ + RowBox[{"-", "0.5"}], ",", "2"}], "}"}]}], "}"}], ",", "Locator"}], + "}"}]}], "]"}]], "Input", + CellChangeTimes->CompressedData[" +1:eJxTTMoPSmViYGAQBWIQrXavId1b+Y2jWYhiBogOW2IWsw5IC7BvyAPRzn3l +JSD61c9FnSD6yOE/c0H0r4UzF4Loih/i60D0MR4pMM1wYfcWEN1wwmsXiGa1 +fLAPRLPVrjoBovvfrj4HohWWLTgPoounfr4GorfP4LsBoufte3obRFcZNb0B +qzcX/Qii163o+QWim6fPZFwPMs+8nxlEG82LZwfRp6zteEH0hr3NIiC6teyW +HIh2MV5hCqKz7CtcQTTDzigvEK12KNwXRK8JcQwD0R8Xz48A0XqMF9JA9ImK +P1kgevFkwSIQPSOqowys/8/6dhDNdf1CB4i+fODOfrD4sbiDIBoA3Jepaw== + + "]], + +Cell[BoxData[ + TagBox[ + StyleBox[ + DynamicModuleBox[{$CellContext`mode$$ = 1, $CellContext`x$$ = { + 2, 0.5}, $CellContext`y$$ = {-0.5, 2}, Typeset`show$$ = True, + Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", + Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = + "\"untitled\"", Typeset`specs$$ = {{{ + Hold[$CellContext`mode$$], 1, "operation/function"}, { + 1 -> "x+y", 2 -> "x\[CenterDot]y", 3 -> "sin(x)", 4 -> "cos(x)", 5 -> + "tan(x)", 6 -> "\!\(\*SuperscriptBox[\(x\), \(-1\)]\)", 7 -> + "\!\(\*SuperscriptBox[\(x\), \(2\)]\)", 8 -> + "\!\(\*SuperscriptBox[\(\[ExponentialE]\), \(x\)]\)", 9 -> + "\[CapitalGamma](x)", 10 -> "\[Zeta](x)", 11 -> + "\!\(\*UnderoverscriptBox[\(\[Sum]\), \(n = 0\), \ +\(\[Infinity]\)]\)\!\(\*SuperscriptBox[\(x\), \(n\)]\)"}}, {{ + Hold[$CellContext`x$$], {2, 0.5}}, Automatic}, {{ + Hold[$CellContext`y$$], {-0.5, 2}}, Automatic}}, Typeset`size$$ = { + 360., {176., 182.}}, Typeset`update$$ = 0, Typeset`initDone$$, + Typeset`skipInitDone$$ = True, $CellContext`mode$48059$$ = False}, + DynamicBox[Manipulate`ManipulateBoxes[ + 1, StandardForm, + "Variables" :> {$CellContext`mode$$ = + 1, $CellContext`x$$ = {2, 0.5}, $CellContext`y$$ = {-0.5, 2}}, + "ControllerVariables" :> { + Hold[$CellContext`mode$$, $CellContext`mode$48059$$, False]}, + "OtherVariables" :> { + Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, + Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, + Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, + Typeset`skipInitDone$$}, "Body" :> + Module[{$CellContext`z$}, $CellContext`z$ = $CellContext`c2r[ + $CellContext`f[$CellContext`mode$$, + $CellContext`r2c[$CellContext`x$$], + $CellContext`r2c[$CellContext`y$$]]]; + If[$CellContext`args[$CellContext`mode$$] == 2, + If[Max[$CellContext`y$$] < + 10 $CellContext`lim, $CellContext`prevy = $CellContext`y$$, \ +$CellContext`y$$ = $CellContext`prevy; + Null]; $CellContext`y$$ = $CellContext`prevy, $CellContext`y$$ = { + 10 $CellContext`lim, 10 $CellContext`lim}; Null]; Show[ + Graphics[ + Join[ + $CellContext`bg[$CellContext`mode$$], { + PointSize[Large], Blue, + Point[$CellContext`x$$], + Arrow[{{0, 0}, $CellContext`x$$}]}, + If[$CellContext`args[$CellContext`mode$$] == 2, {Red, + Point[$CellContext`y$$], + Arrow[{{0, 0}, $CellContext`y$$}]}, {}], {Purple, + Point[$CellContext`z$], + Arrow[{{0, 0}, $CellContext`z$}]}]], + PlotRange -> {{-$CellContext`lim, $CellContext`lim}, \ +{-$CellContext`lim, $CellContext`lim}}, Axes -> True, + AxesLabel -> {"Re", "Im"}]], + "Specifications" :> {{{$CellContext`mode$$, 1, "operation/function"}, { + 1 -> "x+y", 2 -> "x\[CenterDot]y", 3 -> "sin(x)", 4 -> "cos(x)", 5 -> + "tan(x)", 6 -> "\!\(\*SuperscriptBox[\(x\), \(-1\)]\)", 7 -> + "\!\(\*SuperscriptBox[\(x\), \(2\)]\)", 8 -> + "\!\(\*SuperscriptBox[\(\[ExponentialE]\), \(x\)]\)", 9 -> + "\[CapitalGamma](x)", 10 -> "\[Zeta](x)", 11 -> + "\!\(\*UnderoverscriptBox[\(\[Sum]\), \(n = 0\), \(\[Infinity]\)]\)\ +\!\(\*SuperscriptBox[\(x\), \(n\)]\)"}}, {{$CellContext`x$$, {2, 0.5}}, + Automatic, ControlType -> Locator}, {{$CellContext`y$$, {-0.5, 2}}, + Automatic, ControlType -> Locator}}, "Options" :> {}, + "DefaultOptions" :> {}], + ImageSizeCache->{417., {227., 233.}}, + SingleEvaluation->True], + Deinitialization:>None, + DynamicModuleValues:>{}, + SynchronousInitialization->True, + UndoTrackedVariables:>{Typeset`show$$, Typeset`bookmarkMode$$}, + UnsavedVariables:>{Typeset`initDone$$}, + UntrackedVariables:>{Typeset`size$$}], "Manipulate", + Deployed->True, + StripOnInput->False], + Manipulate`InterpretManipulate[1]]], "Output", + CellChangeTimes->{3.7768060757320585`*^9, 3.7768064122662535`*^9, + 3.7768065048257113`*^9, 3.776806594529003*^9, 3.7768066759197564`*^9}] +}, Open ]] +}, Open ]] +}, Open ]] +}, Open ]] +}, +WindowSize->{759, 833}, +WindowMargins->{{70, Automatic}, {Automatic, 55}}, +FrontEndVersion->"10.4 for Microsoft Windows (64-bit) (April 11, 2016)", +StyleDefinitions->"Default.nb" +] +(* End of Notebook Content *) + +(* Internal cache information *) +(*CellTagsOutline +CellTagsIndex->{} +*) +(*CellTagsIndex +CellTagsIndex->{} +*) +(*NotebookFileOutline +Notebook[{ +Cell[CellGroupData[{ +Cell[580, 22, 156, 2, 90, "Title"], +Cell[739, 26, 156, 2, 30, "Text"], +Cell[CellGroupData[{ +Cell[920, 32, 99, 1, 63, "Section"], +Cell[1022, 35, 517, 8, 68, "Text"], +Cell[1542, 45, 134, 1, 30, "Text"], +Cell[CellGroupData[{ +Cell[1701, 50, 222, 8, 29, "Item"], +Cell[1926, 60, 241, 8, 29, "Item"], +Cell[2170, 70, 88, 1, 29, "Item"], +Cell[2261, 73, 90, 1, 29, "Item"], +Cell[2354, 76, 93, 1, 29, "Item"], +Cell[2450, 79, 245, 9, 31, "Item"], +Cell[2698, 90, 274, 9, 31, "Item"], +Cell[2975, 101, 290, 9, 29, "Item"], +Cell[3268, 112, 291, 9, 30, "Item"], +Cell[3562, 123, 340, 10, 30, "Item"], +Cell[3905, 135, 430, 12, 30, "Item"] +}, Open ]], +Cell[4350, 150, 199, 4, 49, "Text"] +}, Open ]], +Cell[CellGroupData[{ +Cell[4586, 159, 91, 1, 63, "Section"], +Cell[CellGroupData[{ +Cell[4702, 164, 102, 1, 43, "Subsection"], +Cell[4807, 167, 248, 6, 52, "Input"], +Cell[5058, 175, 553, 15, 52, "Input"], +Cell[5614, 192, 454, 12, 52, "Input"], +Cell[6071, 206, 3553, 86, 279, "Input"], +Cell[9627, 294, 1683, 54, 252, "Input"], +Cell[11313, 350, 2821, 83, 292, "Input"], +Cell[14137, 435, 376, 11, 52, "Input"] +}, Closed]], +Cell[CellGroupData[{ +Cell[14550, 451, 105, 1, 35, "Subsection"], +Cell[CellGroupData[{ +Cell[14680, 456, 5228, 138, 496, "Input"], +Cell[19911, 596, 4212, 78, 477, "Output"] +}, Open ]] +}, Open ]] +}, Open ]] +}, Open ]] +} +] +*) + diff --git a/calc-diffeq-analysis/continuous-discrete-logistic-growth.nb b/calc-diffeq-analysis/continuous-discrete-logistic-growth.nb index 7e7b9f3..62b917c 100644 --- a/calc-diffeq-analysis/continuous-discrete-logistic-growth.nb +++ b/calc-diffeq-analysis/continuous-discrete-logistic-growth.nb @@ -1,1845 +1,1845 @@ -(* Content-type: application/vnd.wolfram.mathematica *) - -(*** Wolfram Notebook File ***) -(* http://www.wolfram.com/nb *) - -(* CreatedBy='Mathematica 10.4' *) - -(*CacheID: 234*) -(* Internal cache information: -NotebookFileLineBreakTest -NotebookFileLineBreakTest -NotebookDataPosition[ 158, 7] -NotebookDataLength[ 91073, 1837] -NotebookOptionsPosition[ 89492, 1780] -NotebookOutlinePosition[ 89836, 1795] -CellTagsIndexPosition[ 89793, 1792] -WindowFrame->Normal*) - -(* Beginning of Notebook Content *) -Notebook[{ - -Cell[CellGroupData[{ -Cell["Continuous Versus Discrete Logistic Growth", "Title", - CellChangeTimes->{{3.776600831050974*^9, 3.7766008318453026`*^9}, { - 3.7771302883123703`*^9, 3.7771303074624567`*^9}}], - -Cell["Adam Rumpf, 11/4/2014", "Text", - CellChangeTimes->{{3.7766008347881403`*^9, 3.776600838290375*^9}, { - 3.7771303248362846`*^9, 3.777130326323276*^9}}], - -Cell[CellGroupData[{ - -Cell["Introduction", "Section", - CellChangeTimes->{{3.7766008459498987`*^9, 3.776600848547045*^9}}], - -Cell["\<\ -This demonstration is meant to compare the continuous and the discrete \ -versions of the logistic growth model. Both are population models which cause \ -the population to be limited due to limited resources. The continuous model \ -is usually given by the ODE\ -\>", "Text", - CellChangeTimes->{{3.776600856235587*^9, 3.776600860481224*^9}, { - 3.7771662972954435`*^9, 3.777166370927112*^9}}], - -Cell[BoxData[ - RowBox[{"\t", - RowBox[{ - FractionBox[ - RowBox[{"\[DifferentialD]", "x"}], - RowBox[{"\[DifferentialD]", "t"}]], "=", - RowBox[{"r", " ", "x", - RowBox[{"(", - RowBox[{"L", "-", "x"}], ")"}]}]}]}]], "Input", - CellChangeTimes->{{3.777166387219908*^9, 3.777166431475397*^9}, - 3.777166462432236*^9}], - -Cell[TextData[{ - "where ", - Cell[BoxData[ - FormBox["x", TraditionalForm]], - FormatType->"TraditionalForm"], - " is the population as a function of time ", - Cell[BoxData[ - FormBox["t", TraditionalForm]], - FormatType->"TraditionalForm"], - ", ", - Cell[BoxData[ - FormBox[ - RowBox[{"r", ">", "1"}], TraditionalForm]], - FormatType->"TraditionalForm"], - " is the intrinsic growth rate, and ", - Cell[BoxData[ - FormBox["L", TraditionalForm]], - FormatType->"TraditionalForm"], - " is the carrying capacity. Notice that this equation results in ", - Cell[BoxData[ - FormBox[ - RowBox[{ - FractionBox[ - RowBox[{"\[DifferentialD]", "x"}], - RowBox[{"\[DifferentialD]", "t"}]], ">", "0"}], TraditionalForm]], - FormatType->"TraditionalForm"], - " when ", - Cell[BoxData[ - FormBox[ - RowBox[{"0", "<", "x", "<", "L"}], TraditionalForm]], - FormatType->"TraditionalForm"], - " and ", - Cell[BoxData[ - FormBox[ - RowBox[{ - FractionBox[ - RowBox[{"\[DifferentialD]", "x"}], - RowBox[{"\[DifferentialD]", "t"}]], "<", "0"}], TraditionalForm]], - FormatType->"TraditionalForm"], - " when ", - Cell[BoxData[ - FormBox[ - RowBox[{"x", ">", "L"}], TraditionalForm]], - FormatType->"TraditionalForm"], - ", meaning that the population should grow while below ", - Cell[BoxData[ - FormBox["L", TraditionalForm]], - FormatType->"TraditionalForm"], - " and shrink while above ", - Cell[BoxData[ - FormBox["L", TraditionalForm]], - FormatType->"TraditionalForm"], - ", which is how the carrying capacity is enforced." -}], "Text", - CellChangeTimes->{{3.777166439165693*^9, 3.7771665664048877`*^9}, { - 3.777166749606275*^9, 3.7771667502513075`*^9}}], - -Cell["\<\ -The discrete analog of this model is usually given as the discrete logistic \ -map\ -\>", "Text", - CellChangeTimes->{{3.7771665709646397`*^9, 3.777166587554802*^9}}], - -Cell[BoxData[ - RowBox[{"\t", - RowBox[{ - SubscriptBox["x", - RowBox[{"n", "+", "1"}]], "=", - RowBox[{"r", " ", - SubscriptBox["x", "n"], - RowBox[{"(", - RowBox[{"1", "-", - SubscriptBox["x", "n"]}], ")"}]}]}]}]], "DisplayFormula", - CellChangeTimes->{{3.7771665980882196`*^9, 3.7771666127458467`*^9}}], - -Cell[TextData[{ - "where ", - Cell[BoxData[ - FormBox[ - SubscriptBox["x", "n"], TraditionalForm]], - FormatType->"TraditionalForm"], - " is the population at time step ", - Cell[BoxData[ - FormBox["n", TraditionalForm]], - FormatType->"TraditionalForm"], - ", ", - Cell[BoxData[ - FormBox[ - RowBox[{"r", ">", "1"}], TraditionalForm]], - FormatType->"TraditionalForm"], - " is again the intrinsic growth rate, and we generally assume that the \ -population units have been scaled so that the carrying capacity can be stated \ -as 1. Note, however, that 1 is not actually the equilibrium solution of this \ -system: solving ", - Cell[BoxData[ - FormBox[ - RowBox[{ - SuperscriptBox["x", "*"], "=", - RowBox[{"r", " ", - RowBox[{ - SuperscriptBox["x", "*"], "(", - RowBox[{"1", "-", - SuperscriptBox["x", "*"]}], ")"}]}]}], TraditionalForm]], - FormatType->"TraditionalForm"], - " yields the (nonzero) equilibrium solution as ", - Cell[BoxData[ - FormBox[ - RowBox[{ - SuperscriptBox["x", "*"], "=", - FractionBox[ - RowBox[{"r", "-", "1"}], "r"]}], TraditionalForm]], - FormatType->"TraditionalForm"], - "." -}], "Text", - CellChangeTimes->{{3.7771666153555794`*^9, 3.7771667546392555`*^9}}], - -Cell[TextData[{ - "The figures below show how these two models behave side-by-side as ", - Cell[BoxData[ - FormBox["r", TraditionalForm]], - FormatType->"TraditionalForm"], - " changes. In order to remove the potential confusion of the continuous \ -model having a constant equilibrium while the discrete model does not, we \ -will always rescale the continuous model so that ", - Cell[BoxData[ - FormBox[ - RowBox[{"L", "=", - FractionBox[ - RowBox[{"r", "-", "1"}], "r"]}], TraditionalForm]], - FormatType->"TraditionalForm"], - ", meaning that both models will always have the same carrying capacity." -}], "Text", - CellChangeTimes->{{3.777166775775532*^9, 3.7771668855378103`*^9}}] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["Code", "Section", - CellChangeTimes->{{3.776600864408964*^9, 3.7766008650447807`*^9}}], - -Cell[CellGroupData[{ - -Cell["Initialization", "Subsection", - CellChangeTimes->{{3.776600871130811*^9, 3.776600873087188*^9}}], - -Cell[BoxData[ - RowBox[{ - RowBox[{"logfinal", "[", - RowBox[{"x0_", ",", "r_", ",", "lim_", ",", "end_"}], "]"}], ":=", - RowBox[{"Partition", "[", - RowBox[{ - RowBox[{"Riffle", "[", - RowBox[{ - RowBox[{"ConstantArray", "[", - RowBox[{"r", ",", "end"}], "]"}], ",", - RowBox[{ - RowBox[{"RecurrenceTable", "[", - RowBox[{ - RowBox[{"{", - RowBox[{ - RowBox[{ - RowBox[{"x", "[", - RowBox[{"n", "+", "1"}], "]"}], "\[Equal]", - RowBox[{"r", " ", - RowBox[{"x", "[", "n", "]"}], - RowBox[{"(", - RowBox[{"1", "-", - RowBox[{"x", "[", "n", "]"}]}], ")"}]}]}], ",", - RowBox[{ - RowBox[{"x", "[", "0", "]"}], "\[Equal]", "x0"}]}], "}"}], ",", - "x", ",", - RowBox[{"{", - RowBox[{"n", ",", "0", ",", "lim"}], "}"}]}], "]"}], "[", - RowBox[{"[", - RowBox[{ - RowBox[{"-", "end"}], ";;"}], "]"}], "]"}]}], "]"}], ",", "2"}], - "]"}]}]], "Input", - CellChangeTimes->{{3.7766008761831923`*^9, 3.776600882799075*^9}, - 3.7771657470625243`*^9}], - -Cell[BoxData[ - RowBox[{ - RowBox[{"dlmplot", "=", - RowBox[{"Flatten", "[", - RowBox[{ - RowBox[{"Table", "[", - RowBox[{ - RowBox[{"logfinal", "[", - RowBox[{"0.4", ",", "r", ",", "100", ",", "20"}], "]"}], ",", - RowBox[{"{", - RowBox[{"r", ",", "1.005", ",", "4", ",", "0.005"}], "}"}]}], "]"}], - ",", "1"}], "]"}]}], ";"}]], "Input", - CellChangeTimes->{{3.777165890525441*^9, 3.777165913718752*^9}, { - 3.777166055921769*^9, 3.777166058420776*^9}}] -}, Closed]], - -Cell[CellGroupData[{ - -Cell["Demonstration", "Subsection", - CellChangeTimes->{{3.7766008885632277`*^9, 3.7766008904796133`*^9}}], - -Cell[TextData[{ - "We begin by showing a time series of population versus time for both \ -models. Try gradually increasing ", - Cell[BoxData[ - FormBox["r", TraditionalForm]], - FormatType->"TraditionalForm"], - " from 1 all the way to 4. At first the two models should produce nearly \ -identical behavior, but after ", - Cell[BoxData[ - FormBox[ - RowBox[{"r", "\[GreaterEqual]", "2"}], TraditionalForm]], - FormatType->"TraditionalForm"], - " the discrete version should begin to produce oscillations which the \ -continuous model does not. This is because the discrete model allows the \ -carrying capacity to be slightly overshot between iterations, after which we \ -must experience negative growth. The overshooting goes on for several \ -iterations before dying down." -}], "Text", - CellChangeTimes->{{3.77716693393746*^9, 3.7771669739303837`*^9}, { - 3.777167026954685*^9, 3.7771672398192244`*^9}}], - -Cell[TextData[{ - "After ", - Cell[BoxData[ - FormBox[ - RowBox[{"r", "\[GreaterEqual]", "3"}], TraditionalForm]], - FormatType->"TraditionalForm"], - " the growth rate is large enough that the oscillations no longer die down \ -and instead remain as periodic orbits. Increasing ", - Cell[BoxData[ - FormBox["r", TraditionalForm]], - FormatType->"TraditionalForm"], - " even further beyond this point causes the orbits to increase in period, \ -from 2 to 4 and then 8 and so on, until for very large values of ", - Cell[BoxData[ - FormBox["r", TraditionalForm]], - FormatType->"TraditionalForm"], - " the results are completely chaotic." -}], "Text", - CellChangeTimes->{{3.77716693393746*^9, 3.7771669739303837`*^9}, { - 3.777167026954685*^9, 3.777167286432896*^9}}], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"Manipulate", "[", - RowBox[{ - RowBox[{"TableForm", "[", - RowBox[{"{", - RowBox[{"{", - RowBox[{ - RowBox[{"Plot", "[", - RowBox[{ - RowBox[{"Evaluate", "[", - RowBox[{ - FractionBox[ - RowBox[{ - SuperscriptBox["E", - RowBox[{"L", " ", "r", " ", "t"}]], "L", " ", "0.4"}], - RowBox[{"L", "+", - RowBox[{ - RowBox[{"(", - RowBox[{ - SuperscriptBox["E", - RowBox[{"L", " ", "r", " ", "t"}]], "-", "1"}], ")"}], - "0.4"}]}]], "/.", - RowBox[{"L", "\[Rule]", - FractionBox[ - RowBox[{"r", "-", "1"}], "r"]}]}], "]"}], ",", - RowBox[{"{", - RowBox[{"t", ",", "0.001", ",", "30"}], "}"}], ",", - RowBox[{"PlotRange", "\[Rule]", - RowBox[{"{", - RowBox[{"0", ",", "1"}], "}"}]}], ",", - RowBox[{"PlotLabel", "\[Rule]", "\"\\""}], ",", - RowBox[{"AxesLabel", "\[Rule]", - RowBox[{"{", - RowBox[{"\"\\"", ",", "\"\\""}], "}"}]}]}], "]"}], ",", - RowBox[{"ListPlot", "[", - RowBox[{ - RowBox[{"RecurrenceTable", "[", - RowBox[{ - RowBox[{"{", - RowBox[{ - RowBox[{ - RowBox[{"x", "[", - RowBox[{"n", "+", "1"}], "]"}], "\[Equal]", - RowBox[{"r", " ", - RowBox[{"x", "[", "n", "]"}], - RowBox[{"(", - RowBox[{"1", "-", - RowBox[{"x", "[", "n", "]"}]}], ")"}]}]}], ",", - RowBox[{ - RowBox[{"x", "[", "0", "]"}], "\[Equal]", "0.4"}]}], "}"}], ",", - "x", ",", - RowBox[{"{", - RowBox[{"n", ",", "0", ",", "30"}], "}"}]}], "]"}], ",", - RowBox[{"Joined", "\[Rule]", "True"}], ",", - RowBox[{"Mesh", "\[Rule]", "Full"}], ",", - RowBox[{"PlotRange", "\[Rule]", - RowBox[{"{", - RowBox[{"0", ",", "1"}], "}"}]}], ",", - RowBox[{"PlotLabel", "\[Rule]", "\"\\""}], ",", - RowBox[{"AxesLabel", "\[Rule]", - RowBox[{"{", - RowBox[{"\"\\"", ",", "\"\\""}], "}"}]}]}], "]"}]}], - "}"}], "}"}], "]"}], ",", - RowBox[{"{", - RowBox[{ - RowBox[{"{", - RowBox[{"r", ",", "1.2"}], "}"}], ",", "1.0005", ",", "4", ",", - "0.0005"}], "}"}]}], "]"}]], "Input", - CellChangeTimes->{{3.777163681244874*^9, 3.7771638468583126`*^9}, { - 3.777163957467636*^9, 3.77716398467824*^9}, {3.7771640761216917`*^9, - 3.7771642136305895`*^9}, {3.7771645056535025`*^9, 3.777164556673809*^9}, { - 3.7771646075070252`*^9, 3.777164730339535*^9}, {3.7771649500323143`*^9, - 3.7771649653355174`*^9}}], - -Cell[BoxData[ - TagBox[ - StyleBox[ - DynamicModuleBox[{$CellContext`r$$ = 3.032, Typeset`show$$ = True, - Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", - Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = - "\"untitled\"", Typeset`specs$$ = {{{ - Hold[$CellContext`r$$], 1.2}, 1.0005, 4, 0.0005}}, Typeset`size$$ = { - 387., {70., 76.}}, Typeset`update$$ = 0, Typeset`initDone$$, - Typeset`skipInitDone$$ = True, $CellContext`r$74990$$ = 0}, - DynamicBox[Manipulate`ManipulateBoxes[ - 1, StandardForm, "Variables" :> {$CellContext`r$$ = 1.2}, - "ControllerVariables" :> { - Hold[$CellContext`r$$, $CellContext`r$74990$$, 0]}, - "OtherVariables" :> { - Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, - Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, - Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, - Typeset`skipInitDone$$}, "Body" :> TableForm[{{ - Plot[ - Evaluate[ - ReplaceAll[ - E^($CellContext`L $CellContext`r$$ $CellContext`t) $CellContext`L - 0.4/($CellContext`L + ( - E^($CellContext`L $CellContext`r$$ $CellContext`t) - 1) - 0.4), $CellContext`L -> ($CellContext`r$$ - - 1)/$CellContext`r$$]], {$CellContext`t, 0.001, 30}, - PlotRange -> {0, 1}, PlotLabel -> "continuous", - AxesLabel -> {"t", "x(t)"}], - ListPlot[ - - RecurrenceTable[{$CellContext`x[$CellContext`n + - 1] == $CellContext`r$$ $CellContext`x[$CellContext`n] ( - 1 - $CellContext`x[$CellContext`n]), $CellContext`x[0] == - 0.4}, $CellContext`x, {$CellContext`n, 0, 30}], Joined -> True, - Mesh -> Full, PlotRange -> {0, 1}, PlotLabel -> "discrete", - AxesLabel -> {"t", "x(t)"}]}}], - "Specifications" :> {{{$CellContext`r$$, 1.2}, 1.0005, 4, 0.0005}}, - "Options" :> {}, "DefaultOptions" :> {}], - ImageSizeCache->{438., {130., 136.}}, - SingleEvaluation->True], - Deinitialization:>None, - DynamicModuleValues:>{}, - SynchronousInitialization->True, - UndoTrackedVariables:>{Typeset`show$$, Typeset`bookmarkMode$$}, - UnsavedVariables:>{Typeset`initDone$$}, - UntrackedVariables:>{Typeset`size$$}], "Manipulate", - Deployed->True, - StripOnInput->False], - Manipulate`InterpretManipulate[1]]], "Output", - CellChangeTimes->{{3.777164540906799*^9, 3.7771645573735876`*^9}, { - 3.777164611045705*^9, 3.777164660389118*^9}, {3.7771647044469786`*^9, - 3.7771647308643694`*^9}, {3.777164953963621*^9, 3.7771649658634167`*^9}}] -}, {2}]], - -Cell[TextData[{ - "Below is a pair of static plots for any and all long-term behaviours of \ -each model as a function of ", - Cell[BoxData[ - FormBox["r", TraditionalForm]], - FormatType->"TraditionalForm"], - ". If the model converges to a single equilibrium, then that equilibrium \ -value is plotted as a point, while if the model oscillates indefinitely, all \ -points in the periodic orbit are plotted. As expected from the above \ -observations, the continuous model only ever produces a single equilibrium \ -value, while the discrete model does at first, but then after ", - Cell[BoxData[ - FormBox[ - RowBox[{"r", "\[GreaterEqual]", "3"}], TraditionalForm]], - FormatType->"TraditionalForm"], - " begins to divide into multiple values due to oscillation, and for the \ -largest values of ", - Cell[BoxData[ - FormBox["r", TraditionalForm]], - FormatType->"TraditionalForm"], - " the plot is an indiscernible cloud of seemingly random points." -}], "Text", - CellChangeTimes->{{3.7771672918691654`*^9, 3.7771675223574295`*^9}}], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"TableForm", "[", - RowBox[{"{", - RowBox[{"{", - RowBox[{ - RowBox[{"Plot", "[", - RowBox[{ - FractionBox[ - RowBox[{"r", "-", "1"}], "r"], ",", - RowBox[{"{", - RowBox[{"r", ",", "1.0005", ",", "4"}], "}"}], ",", - RowBox[{"PlotRange", "\[Rule]", - RowBox[{"{", - RowBox[{"0", ",", "1"}], "}"}]}], ",", - RowBox[{"PlotLabel", "\[Rule]", "\"\\""}], ",", - RowBox[{"AxesLabel", "\[Rule]", - RowBox[{"{", - RowBox[{"\"\\"", ",", "\"\\""}], "}"}]}]}], "]"}], - ",", - RowBox[{"ListPlot", "[", - RowBox[{"dlmplot", ",", - RowBox[{"PlotRange", "\[Rule]", - RowBox[{"{", - RowBox[{"0", ",", "1"}], "}"}]}], ",", - RowBox[{"PlotLabel", "\[Rule]", "\"\\""}], ",", - RowBox[{"AxesLabel", "\[Rule]", - RowBox[{"{", - RowBox[{"\"\\"", ",", "\"\\""}], "}"}]}]}], "]"}]}], - "}"}], "}"}], "]"}]], "Input", - CellChangeTimes->{{3.7771657179889126`*^9, 3.7771657311636024`*^9}, { - 3.777165773220811*^9, 3.777165777454324*^9}, {3.7771658199732375`*^9, - 3.7771658446488113`*^9}, {3.777165927994836*^9, 3.7771659626038847`*^9}, { - 3.777167325618328*^9, 3.7771673327173443`*^9}}], - -Cell[BoxData[ - TagBox[GridBox[{ - { - GraphicsBox[{{{}, {}, - {RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6], - Opacity[1.], LineBox[CompressedData[" -1:eJwVzn840wkcB/AZEzO+fvOk1iqEVCTSD30+Sj/8SKWnErXKj84lrnREQqk7 -kw4ltdOtU0oULqYskaKT9tjhkY5LGWNfl5qNaljjdn+8n/fzep73H+/5YT8E -RVIpFMpWTf7vbSqHEAZVDsE5n7MEBxE8iLipdpocfs40bzy5Zg/MWfikIF9f -DhdiXV49mxcOw35b3zJN5MCjs2g8xnFILzi+z5UlhwrcVGOlSIPqVbXs3evk -8EG4RHSJnw3Wif7hhafk8GDEbOlEEw/6P8ccXTEuB3mD4Z8hVWWQIPY8fGdC -AYyy3k2l5nWgQx+d3fRxDKSb9S4EtTTBIPWFzLJ3HKotp24dE7fAy0/Me/y+ -z5Ad1ByvJRFBkWUkS93xBSZvmqxZadoB51xdU3O6v0KEWVF03pJOeGgzR7Xn -HyWc7oE3kyZdIN4wtlwknIARjwb23qo3YMQODMpqm4TkkkMZv+7sBvdH+c5f -G6cg1H+tLL6uByreqeyuVaqAz6L7L9Z9C05KUvds9TfIG65XV+zshd8DG25Z -Favho5G/w76Ed2DNnWOvvD8Nf/wlPObFew+SB9wWRvkMuN5vy3Er64PX2pS8 -7wIpaHNjIF8WIAbPkgT3mHYKShrX5e1qFgN3JMz9la8W+hxv9fNw7YepRaal -viItrHZ2LObe6Ada63bnyEAqEok5gTo6A8AgaIZ/N1NRzedGCfYPgIX/6UMx -vtooPBoVoVc7ALPtvzcLadLGUqUwdcRAAi1RQ6/7V+ugosT+xY/BEki8bUvP -rtPBicy2+qt3JWCX1vNbrjsNvU/Sr+jKJNAZtKOoRkDDvYJT50mPQXDKDn6c -tEoXX0deYC5LHoTUqC7ny5W6aOKgFWorGITONRbmbW6zMGOH9cYE5SDYVQiD -w8pnoVocy57rMgQsDlGea6uHVkt20VIih2BuqFW85I4eei8ty5rHGwJL0ZWC -i0x9vHTELkG7bQhMPLvcQm7q48rtTTt0taWgtz7LKdWGjgfjy988c5VCCb/d -xSuPjuvNbveN7peCH7PnHsvCAGF7+tKFF6UwvGhPeki2AZ6INnkueCgFjhNX -JDBhoO4175Nu/VLouBLlUHWZgSpvOZtNJ8HqRoVYy8AQwc5MlLyMBHZhDSPh -F0OciDtfG7GbhFveHldxlhE+WhFnnJFEQo6fz7LiVCMM79jgOFxAQkqAxVoX -CoHRW1x2fasnIepTaLFxEoFj3d0c/jsSEgtvhjsnE6hTxFGve08CZyfJ2pJC -YOfLrANCjUsfx11PO0uggHV9RNxHwoefMnNlmQTmt2+yNRwgIZpZc6q1gECX -D+Y2YVISYreZbuPUEWhmHus5LSMhlRrMuP2UwNVfHrMzRknIfsh71fCMQMnG -tjhjOQkVNo4+yhcE9j6KiFigIEEzWXVYRGCOY2HMxnESjp2JWejznsDLT8/Y -cJQknHHjiw+INf/rzVnGEyTkSid4yQMEHm68b8rVuDLgvDVfSmARU/H87iQJ -Y9bXDReMEljcuta3WUUCtVUs9FIQeKgo4OnWbySYptlz9o4TOC1Lnt+l8fKh -SuolJYFK+uYqiZqE9VxlQ9kkgfof/+07Mk1CkL9XSouKwJjwWpVC47Dp9NWD -agIXK5/QkmZIOFHZopyZIXC/85h6RuP/ALOGTdI= - "]]}}, {}}, - AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], - Axes->{True, True}, - AxesLabel->{ - FormBox["\"r\"", TraditionalForm], - FormBox["\"long-term\"", TraditionalForm]}, - AxesOrigin->{1., 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, "DefaultMeshStyle" -> - AbsolutePointSize[6], "ScalingFunctions" -> None}, - PlotLabel->FormBox["\"continuous\"", TraditionalForm], - PlotRange->{{1.0005000612142856`, 3.9999999387857144`}, {0, 1}}, - PlotRangeClipping->True, - PlotRangePadding->{{ - Scaled[0.02], - Scaled[0.02]}, {0, 0}}, - Ticks->{Automatic, Automatic}], - GraphicsBox[{{}, {{}, - {RGBColor[0.368417, 0.506779, 0.709798], PointSize[ - 0.002777777777777778], AbsoluteThickness[1.6], - PointBox[CompressedData[" -1:eJzs3Xk0lf//738zUamMlVCGhEoSEV1XCQnNvUsllbEozZo1aSSRSjKVqBSa -lSgqQklJhEgUTco8D7+d1/vj9Xxdy2+dc/1xzvme8732e6/1Xrd133uj9r5s -+7FXRq72mO8kwMfHVzaOj+/v/6XjLD7vlK6h5t7NSd6R5UP9x1HDBrVNOILd -//Ywv+1m2N/MzTsoYWz9C+nLdqWf6PWhFqmlisew1zdVjB1hg/189dVT7kOw -R409nsBfeLzXLdIF1rkR2FMvFq7JW4M9PkzKv2sitqBA3lWL7mO9fhA3sin6 -JfatgY1y0uexZwg/Ejjigv1EQaGjWR/7xjTBc/ai2HcefIq//+ForyPmKa5p -ijlKaSz3e9qoUUOFfdQw9HX27/V+x7pRUebY7UrZSQdGY9ufmTVbqR921Qlh -9y0/T/U62ntZ/a7X2G82rxfRuY09WWWN2Imz2P5L+IOP7MIeKjDxrPIq7EIL -Hcl5Fth5oQespMdhW9jYPnOSwc50FTI+0ObX69i9UvYzXmL73ev61S8UW/xm -wsSXHtg+xQNf7zPF1ljRFq4ij+3dIvXuRvVJykS8IHKDSQ218K796E/3A3vt -feVi+dHz2AMa2w427sY+9PPmEsVV2GcX3G/rMMOWvrHW+oQW9jrq4pZng7Hf -nftRFN5yutfT5w5XHV6GbRInMV4nA5v/3YnBRTexb944KiMdjP3PyBX3Cw9i -bzdYEKa+HlvU1ORy0xLsgKUWmWYzsA1OFesP0sH2CLluPF8BW6Ygf7ZYP/D5 -emsJjW8KoOY9UPT+Oa+GivG5/iTIJqjXca0mpmsnYler5/u2DsUuUmvmfVHY -xXlnxA2+n+v1gwclKR/eYntbmUxVeoR93eZutVAUtrKivechP+yME0bJQTux -3RqGfzB2xpb8VCjtPh/b8tTF2pEU9s2V24Yv1caeX1bgNmgY9vOBPpW0GPYT -9RMJVU1nex0QJz6BvxL7+Y2ozGPvsTXFI4btTTtLOfecaqgLo2KfnFAO6fV5 -6agnef2wB309bPWu/kKv38xTT9pXij3S58X9/Ezsp77fNHLuYafunDfD8RL2 -usvOu075YV82TNgzew/2L4XneufdsAsS21LclmI3S5VtS7XEVtzr+vGMIXbS -9+3RX8ZgRyeevH9tGHap1wn5zxLYAwZc4jvSGdzrjTGrM8/9wc4y+VIrWY59 -eruYwq+8YGpnzwGxhlpRpym9aUhEr2l1ubmFYtjqalX9tbrDe30yxq/QvBp7 -7t0vyd3F2MZrhyfOeYm9K6JuyIRH2CrbhWeHXcdeu2TpuIAQ7JEpY26JnsTO -efNBvM0L+9UrlcuOm7BbB2+VM3XCNnJwGue/BPtn4OpPs6yxfX/tsHKnsaMS -TZNq9bB9qqovFozBdrV18B+mhC1venJ6gnQ49fdouNyvhjLcLjywa/SlXru6 -zp4mrYz92MBg5HZ57PB3OtvUB2PP3KA9XkEcu7thr/0/gtjjgquMczsu9jq4 -f8II3ybsQZelPQ/VYG/daF987wf2QflrLYpfsa3OzDyX/AnbfdLBIL8i7DKd -WY0B77FVPCSS095gm6gESqu/wv5HSGjS7RfYRvxv1ro+w850eCdt8QQ7f936 -SOtHFynewZB3ROQ9f5CcLd5ldbnX0SsOXwwxw35sfnn3Pgqbb53EoWhDbLPb -V9Ml9LCrn7/xjB2HHf5rWvXRMdhqLuahF1Sx4741KFQoYf8S8VW0G4695XC1 -h6gctlHsqNZPQ7D3fxF/9GUg9iz5Qa+lJLCfrW5Y6SaKXRZ/M+G7ILa4sqOm -Lx/22n4LVBd2RvY6wrdhlEkbtvrrAffMmyOpnsPhgxpKamuAm9LO6F7/iXAS -k9mKPSCy8af5Bmwrjcfat92w39zbKrrQBVsy8OvHMQ7YulO+jp9gj30leFuk -yzLstzl8rVmLsZ2krwy0XYgd+vFhieQ87E0z6R3VNtiTdIP618zC1pypVSQz -E1v7iYGRnRn2Ucvr559PB1+vnOSOWTT2o6cH3apNsCslX8ncmIJtHeY01tsw -mncc+XuqoRZdFCx7HHe119GD6vXyY7DH3Fj2QvkK9k3zhG8XIrHdf1RImkVg -fyppzB8aCq6fMLZVLhj7RZ7kPJNz2FdeBecfCcSOOhsc2uiP/dFZNu+QH3bd -PwUpE32xPVRFnvKdwLZbV2r14yh2RMPWqt+Hsf0Dz04Y4I3dEXGt0PQgdov/ -nQj//dhjq1YsafTCtrWQKV+39yr1ueeAyDu+BqkWfKuM6fX9yzvTqiuw7ZyN -5474jO0YFTNgayn2pZbfCXXF2E6tPzUDC7H3ULqrFxdgC26R8zR6jz1HoDps -yjvsZ6MWjrF9i+2qGbvXPwd73KQIxYps7CiX5DDrV9huGhOvvcrCfv02qH1V -JnbgjldOEhnYYUfKM16kYz/8pSZ7Ng3b5vPo2VufY+tplHo5PouhGnueUPMe -v7cdgqyUY3stqee7d6AitvvhDoWG4djFL1YtbBuKPbRs4mgleeyyIYcTVspi -j5MSNEuWxj6dJ641UQr7VkBNacpg7GuP/vntOAhbNji6c4Qkdlb6xfQfA7Db -/CXksvpjJya45iRKYLvmvfv8SBy7SOvr3Ff9sD033hj3Uwz70ZJHF+SAt7yi -0ueKYm9P0f5+RiSW6nk6LV5LmWbWXhxpG99r2cQ/Q3csxj5zIHDRr0XYcw46 -7N+xEPt7R8M3xQXYQ2YWNRTNw94ndFXjxlzsi64qI/3ngNuTOxVwdDb2CVkF -C38b7ON3XEbEWGNXW48WzbXCfqNaIioG7LH/2kSrWdhTvMfHBVtia5r7Xmuc -iX05w8lpGbB7SPvYlxbYv2uXLpsBbCcdMDfdPJ7qORwq1lLbDR/c6Z9xs9da -b9vdNr7AvrnqzoDP6diOAR/fLQVOc9kkWpqG7XPZrWsN8DfVV8O6nmM/fPwi -8zyw3dzGA8bA+56devH1Gbj98qyRZ4CntKipzoKdKnUVAn5jZef/7Cm2p0+C -2RHg6YYT9eYA+/wqGDQceLKNyJkfqdhPx8t5JQMbR/IHnOZ5Ys+plno+wLBS -sfxWr4X2pwbFfcZ+apidZA4skL8zvrIMO+WGcZEvcA7/t1tTgKXK8+/9+YTt -ozXc4xrwMcdUD1dg/VGj5msDDyukHzSUYquLG1ilAufkxST6A78Rn5vkBLyl -YZOECbCQsI+rHPCK18VBDSXYSacGOucBh7ypDL0P7Ov6e/AFni16Doi1lEFy -TMiGttu9dn2bbqwMfOfaAZv8VuxpjWdmBQAv71qeuAB47LwO7WHA8qvOTvna -gv0o1v/IXeA1/X4/PAJckXLlwArgWV6jgyYDDy1Pvi8DvO3FmIjGZuzarRrD -PwA75gysTwIemLu2ORL4SOKNdh/g+NEF+Z7AD+ImOTgCH7Udunc+zz0vxyyv -pQrj4sXSB93t9akNDyV9ga8k3fqzBDhnw8+pY4Avj04O6ZTE1n/46OZ74CHJ -wpq3gK8GhD32Az56tkBzI/A1y3SdRcCxVunnpgAvGCWirQq88tOIxwOBB76M -G9U+EFvLWkL3O7D7ksoXH4A1X/R7lglM/xkinAScIjxpUzyw1RO+2kiee55O -b6ilvC3ezG5WvdfriGeKM3OAp2RM+BgDfL2sIuEYsIy/n58b8IPsVYpzgSt0 -ktQMgE29otyVgS20LZ5IAFPx2363qGC/P2OZUwWcaXvH6ANwiaz2gCzgC/Pt -1ZOBg4eVu94Crnj952E08ItObf5Q4K3PPTQCgXfp+Q73AW6w1Mo4xHPP4dCb -9/m/2T/wp/79Xi+qldDKAaY2yf++BxxbpSYXDmz48b3bceAlYxcneAJn3irN -dAZOydLevhi49pLiBUtgg05LSRNgjVOX7k4ALhHSWD8aOCjtwkhF4LklJgky -wHumnBo6EJgvRWmSKHD3/vktfMADc40WtE/CNj603qAJ2Gdo+blans/3nGqp -giBDKsA8odfXPUY07wWmxZNC1gFP1LzZZQfcNP5wzRzgs4tMZpkCd0a8rzIA -1jb/fnUssOyCuRtUgfeEZKsoAJd1PrsuDXxKtr5uAPDeZ0aVosA5Vx23CAAf -H1/v22mG7e7WqNoK3LX2k3YjcPQ+5+Ba4HeKqxx+Awf9vLb3J889L+fH1VLJ -p3yVvy540Osdp49/KQD+2D6//yvg0fOObkoFvqX0sDEB2P2fZs94YPvUHaVX -gM23Wgy+CKyt/KstGHjmHL2jZ4CD39VcOQW8yTtllg+8/KNPq48CuxZ1VBwC -Ftk++Nl+4BY/qmkvcD+H21t2A0cEH9DfCRxjG6q3HVjiV6zrNp57Xo55ynu+ -5TGD7/OKh73eK53SVgDsnGlTnwPc73prdgawAlWx8Snw64zKjCTgrxpznyQA -N085a3oHePSLEebxwDqKgg+vAyumffe7Ctzp+PZJFLD9nj9TI4HH2PgKXQTO -2fVdLBzYYugIs1Dgs2cF71wAnuqgZhMMPPDr5YHngcWOjq0/x3PP0+kC3vEy -R//SYZfEXjuJKhzeB9ykXjFiF/DgkuKF24Cp/gnym4Df3KVt1wPn/Rkp5gas -PCBG3hW4lT/Mywl4wfoBEx2Aa09ra64CvhWra2cPrKpunGYHPHeKzvLlwA9i -riksA7btX86/FPiIb7ioLfCrNFXNJcD5LqOcFwMnnIt58A/PPYfDn7VUm2GF -UuG6R71+qaYt+B5YJTLT8S1wzqmASa+BBc6Pd30JnDyzoiYDeGPJkrR04JC2 -7R+fA9/1Nx33DPje8rg7qcBxK444pwCn/1467QlwStly6jGwrdvC5cnAxtuP -ByYBr5JK/PIIOOaBwCxoS/OPqYnAO1f1nwUtOzK07CHPfD2nOmqDVINiycak -Xn+/enFFEfB6iaVNBdDPhhe/B57tZyaYByy8bK1zLvCYh5qdb4BVxkql5gDb -3th74zXw0pzdidnAg0weVb4CDv62cSz08RfzTrwEXnVra2cWsJbKov3Qd2Ie -SEMvfB5/LxNYpvPIamhvnbSh0F8eDyvK4BntwXVUy7AWs6DNyb2ueL9u41lg -xZevCgOBX70e43ka2Je+OD0AuPqFnr4/8CLvWOtTwJoqB/b7AUubp7w5Caz3 -q0UfOtJ2/C1fYEuTLGNoleeHC3yAHy5d5wWd/uWFLrSX0dCaE8ADU2XuQ3u3 -hhyEHl15ZzG0qea+CX+N9uA66tkkkZJBmx/3Oqql/xVJ4E0HfgUPBH59uuv2 -AOCRY1f+6A+8TrfAGFo/7FG0BLB3RoUqtM/i03fFgZv3uC+ANjBw6O4H3Gl8 -+z605c63ntABGeumQW/IWjUE2jA5/rsY8Azl3enQTdL9rkKfX3HbF/r4r+/b -/hrtwXXUbyMJX5sNT3otrz441Rr4+6WowdCyepk7rYDzoyVaZwFrCW4/Bm1g -dXAMdOXlznxL4I3nhE9Bjx7SOR/ap8NLETpOfnntTODVYsezoC9bj74GLa2w -0Qf6QN2TzdDHnxxcAT0gjLaGXsDvYwztZCE+/q/n97ygX0cpK6sFx0xK6fVV -zVWLoW/5WClCX/m+u/oa8Hm+p8+gG0dIR0DfiwrYD+3gu8cFWiVSZx50v0NK -U6EXauSOhX7157MS9P3hzVLQG6LT+0GPdRvED60aENp6FXi+AVUPPcs0uxr6 -7Xq179Aybppf/xrtwTyvvuUodxu77Y2eIfQ0lanS0O0fcxtkgcukFYugvd6u -fQZdOFXpJnTjhQfh0G+fv/CHnjLttzd01PPiXdCdA6w3Q2sOFXaHrjjz3gn6 -0PnTK6EFDw5fDr2335wl0Pwe0ough+Yumg999Dzf3L9GezDvePtw2OUNY1N7 -XeP58wh0+elhG6Bv321bBt1gz3v4Au/PCTaGPu2+TQd6Z/5EdWh7+6MjoGN/ -6clCZ2gJDYL+NSBTHNpwn50IdOA/FwWgd6za0e0BrHT1dQe0aapvG3SpWXQL -9DNb8WboJPO4xr9Ge3AdlXjyQe7DK9jRGcdToM1DzW5Bn/6+8TK0ffD189AB -4WGnoK2WCx2DbvK6eAD6uMGMPdCvrj7dDp1xvXUL9LEHLzdC3+ZT9oBuiP3s -Dr2H6l4L7c6/dg20bLCMK3TctWZn6MU7RAmrJJg4/TXag3mP/32zHJqUn/a6 -39DwxdCJoWU20HYPk82gVx+omwpdbGpuCK1y+Zge9LWhZ3Sgf0ZYjIWuuuqt -CS04drIGdHWDlTr02IabqtATntuqQG/SmzIKWrLaaiR0jvIhZWhh6xIl6HFd -8wifuFGi+NdoD+Y93tW2Ph5zHnu0A18CtIfim5vQcmNjr0MPTl9zBbri26dI -6O/iNRHQul1eYdDKYjtDoBOVXgVD/7R2OU98PBUqCJqeb3kOepHVnrPQN+rf -nYF+6WRB+H1SbiDx8b5tJFx3fCRh3/zS03+N9uA6yvOc4bTFg571+v3FXcbQ -QSMCJkPblCyeBD1oUpwu9JCCXTrQIyuuj4O2UB47FlrZtlYLOi/vlyZ0fJUM -YeNzjmOgt8/O1SB6uC3h6wObRkMH/4gkvEl9JeHJUzUIX1RsU4deMTivx2gP -5h3Pzww2PnAY+7rwYENonexgfWgL4bN60Ben/9aF/pgeMAF6ZMFWHWizCT7j -ob+dfzUOeojXeMIR1+PGQu8SMyM8bM1vbehZq64Q9h+1jnCavQnhV5NkCe+T -b9KCFn9WTForvcdoD66jxr/ZVhfbjm3nHlADTUeJ/oF+U5lWDa0V9+QX9IKW -7z+hs19OIazxIfYH9JLRRoQvlxR/h14r7EfY13Eu4ee2Iwj/k1L/DXpA4VvC -Hgb3Sd8OJ9y02Jfw3dV7CX+csKnHaA+up5x2xweXeDzv9ceTXuehV648FgQ9 -piX1HLTCZmXCq8JCz0KbRU0kfPN1yRloc4sgwimN9oRPLtYlbOA4gPDobX8C -oT8bFBDODnxGuPTGHcLBWdGEBZaFEBaqOk143EDfHqM9uJ56Ou6FnXQFtvbC -foTlvDYsh3b2bFwGvWJdAGH7O9MJL/AWIKxS/HoptOSMKMJjMg8SPvvelfB6 -lQWEF92YRnhY6ETCD6w0CC8cr0Q4tVCO8Oy6weTHnzCAsPKKfj1Ge3A9dedO -5OJFi9J6/S5iLOEFWjn/QCsHHyTcrGZBWDxTlrCNfM0i6AOqbwnvWPWA8NSA -y4SnPwwkHCtxlPCkqj2ExbK2Eray9iBcOWwt4dX1ToRPR6wm/KvZnrBLgV2P -0R5cT7031zoXmY69W7P8LHSn+FXCWe93EA4cuoiw0VcDwkdilQlbTh5I+MGJ -7jPQ1Od6wvwXfhDeNaWCcOWKEsJ/7n0gfJT/PWFfyVzCKg9yCJ8vziacsvIV -4YCJL3uM9uB6Kn32VkUBg/RemxrPJFwQoUr4ipcY4QTzuhHQWx6UEe4szCWs -/PUF4ZkmTwg/d35AuLj7NuFlj+LI6y+/Tn7821cJ55yLJmzx+zJhhbBIwscC -LxFOenqRcJcCMtqDeY8fPf6KzdHYwse/lkNb5+YQ/pH2mHCZwy3C68ujCRtE -hpHXHxNE+I/0acLX5PwINzeeIHxp3zHCIQFHCL8aeJjwitJDhB3+HCScOZH0 -4YgDhH9qk9bK3d9jtAfXU96Ha7LbpV/0WjXsE2H+9bmEw1QzCJ9WTCHs/vEh -4cdtdwl3ad0iHD8xjnB0+XXC0tIxhC2uXyVc5H+F8OL70YQVJUj7e0cRdhpB -Wu3VZcJpPqT/WYaM9uB6anP49KSQA9i3Fk0mfHS5DuFL4zQJX3NUIy8fN5Lw -uNeKhA+cViBsUjiM8K4DQwkXbJcn3BIjR9hNgnSanyzh2vGkY7/KEFa6Qfqg -F+na5aRHT0dGezDv8XtrkJftH+yCreKEJ14TJqzWzE/4pmL3Xuj06g7CpSbt -hG1qWwkb1bYQHqBN2iiwmfB8JdKz05oId3iRDp1F2nsk6c/8pA9+bySckk/a -JgMZ7cG8+693ZrHesoxef3uaRji4/CnhhfEphN35nhDOuJ9M+EJiEuGbrY8I -KziT1m9MJFwQRjptOWkjTdKnBEm3f31IeGkOaYnHpF/dJH09mvTPMGS0B/OO -J/vdfSakYxtTawlXH3El3N/IhbCNsTPhLbucCFd8cyS8bwfpQlXSB784EA69 -Q3rLSdL6m0g/WU56vTVpMZp0iD7pzeNJ82uS/qSGjPbgekr9/jNqvk5mrw8u -f0r45OJUwscCUghndj4hvMuX9K3JpGNbHhNekkG6KJK0zVHS+zaTfulA+s9i -0u2zSRvOJK1kStqMIr3cmLSmETLagxuoy29CeMdF7HIB0qdcLxDObQgmLBRG -+sdy0nLapD1FSXf/PE/YqYB0/QvSdkmkb9whPTqW9IyrpIMvky66SDornDQV -RlomFBntwQ3UqEK+ieICWb0eb096oRDpyyndutAGJ0lHu5K+Zk36jQFpCw3S -dxVIy0gzbm8A6TIx0nOESV8RIH2Dj/TE7i7Cw7pIW3aSju1ARntwA7Xk0drg -6DXYDptJq0wl/UiWdEDrGsLdFaRF80jrZ5De/oRx/QekJ90lff0m6f5xpIff -YFw+hvSFa6Rzr5I2YTjnCuk9/xrtwQ3U8tMdCza+wZZbQ1p4FunxE0k7jyI9 -SJZ0d3/Si0RIe/CTft/ZTlinnfTUVtJvmkk/ayLd2UjanWEBhu82kN7J8Nx/ -jfZg3p/f0zuF7vovex15jXTQOdJux0ln7yOdsYP0tS2kf24grbOetK476cdr -SceuIV3lSvofhn+5kA5n2JlhY4YVGRb712gPbqB+51zgnbCPpZIenkD6eDxp -yRjSMtGkJ0aSVrhIOiictFcY6TuhpJUYvhtC2pnhsQwLMVx1gfRbhp8y/OBf -oz24gXo+4u/3lVe9XidD2l2S9FAJ0p2ipFOESasIkW4VYHSGj/IzPh7DmXyk -TzHswvBMhicyrMKwPMODGJb412gP5j2+t4Q4hDhg3/AgbexOOn0NaUFX0qnO -pIudSBswnOpIej3DExgWYbjKgfRbhp8ynMBwPMPXGI5i+NK/vtzzgkwD9XDD -q6Gb07Gb1pHudiMdvJZ02BrSP1xJuzE8iOE3LqQvMXyQYXeGlzE8h2FzhmmG -jRk2ZNiA4Un/Gu3BvOdPBQ/dD2tk99o6n7TOe9IueaQL35HexvB4hjtzSRcx -/JTh2wxHMxzC8FmG/Rk+yfAJho/9Txrtwbzjd/Gx0A/HsG8XkR7McEQh6fkM -KzDc+IF0EcMZDCcyfIvh6wxHMXyJ4QiGwxgOYfgCw8H/P0Z7cAM1ZMGxL24/ -sP3nk9ZnuGke6SyGYxkOYvgYw14Mb2d4M8MeDLsz7Mbw2v9FRnsw7/tT7eKN -02e97nVXDemXDF9l+BTDXgxvYdidYWeGVzFsz7Adw8sZXsbw0v9FRntwI9Xf -a4jbimvYFXtJpzN8m+FohkMYPsuwP8N+DPsy7MPwCYaP/x8y2oMbKRul3TWp -ojm91mdYneFhDEszLMmwBMP9GBZjWJRhEYaF/4sY7cGN1MrL6vIeTtgLGJ7F -sBnD0ximGDZh2JjhKQwb/V9itAc3UpM7zte4PMWewPBYhjUZ1mBYnWHV/0eN -9mDe48POhF4s+abXQgwLMizAMP9/U6M9uJHa8HmxwygTbA+G13Pu02gP5n2/ -9De1O7sW+wLDwZz7NNqDG6md/arV7p7jzNZoD26kYmWDbu1+zpmt0R7cSNXW -/D1xZuv8nj24kXo9eMRb3pkzS6M9mPfzWezLKWUzObM12oObqK1vzeTstnBm -a7QHN1FD1faaHwvnzNZoD26i7i9RvuaUxZmt0R7cRP02ihhe38CZrdEe3ERl -7Z7pqauUy5ml0R7cRAWoWvLOnNka7cFNVNStNCprE2e2RntwEzWrvnyOaghn -tkZ7cBO1NDDPb2IaZ7ZGe3AT9djuR2ZLNWe2RntwE+U8ITRti+w7ziyN9uAm -yvfJBYurUzmzNXo5polqbc4fHOjMma3RHtxMlU8+WTH5JGe2RntwM6VosmzH -uXuc2Rrtwc1Uv5cmvjc/cmZrtAc3U7lqV/IPCeZxZmm0BzdTF6d7i8tocmZr -tAc3U/lPbYpXzeXM1mgP5h0P74m1um3jzNZoD26mViguG6wXwpmt0R7cTI2w -9s9JTOXM1mgPbqZsa69+5KvizNZoD26mtkou+yTS/z1nlkZ7cDMle0Ntd7YO -Z7ZGe3AL9c+ivyfObI324BZqxdaBEuE7OLM12oNbqJht/0y5HsqZrdEe3EKV -PlQ4sDOVM1ujPbiFmrfCdMeAr5zZGu3BLdS60isPHMXyObM02oNbqPf7tPJ5 -Z84sjfbgFsos/JHT6tmc2RrtwS3UmOe2rf02cmZrtAe3UF/DVUZuP82ZrdEe -3ELdy1/qFnuPM1ujPbiFqr7i7hhTwJmtm3qeULdQ5z1az3q0cmZrtAe3UmaC -H090DivgzNJoD26lsn/oZC005szWaA9upfK32hXwzpxZembPAbGV6oqTNVi1 -F7uTYa733dEe3EoZjnV1kwvnzNZoD26l1j1PbAh6wpmtD/W8oN9KXZMpnlf5 -iTNboz2Y9/ju/nvizNZoD26lNta92Vmp9IEzS6M9mPd8RsndOJjizNZoD+bd -HwPdk4fbc2ZrtAe3Uv66NVvc9nJma7QHt1E9/9xhKGe2RntwG3Ux7NpyzyTO -bI324Dbqtm/JZr1izmyN9uA2qlU+xC+1lTNboz24jYofWqWkJF/Y61iGud53 -R3twG6Vf6HjaRp8zW6M9uI3Sm+e02GYhZ7ZGe3AbZb6gqkBxE2e2RntwG9UZ -FOr11I8zW6M9uI06kVSfMDmWM1ujPbiNejJM6vv+LOxkhrned0d7cBu1K6xq -R1gV9g6Gud53R3twG3Vgm+qbk0JFnFka7cHtVPq9mXMXjOTM1mgPbqeel0ba -/TLhzNZoD26nbJf+PWEvY5jrfXe0B7dT24rWXAndxpmt0R7cTmldi718PwBb -k2FthrnLI6M9uJ1a9aX8ZlQctgPDXO+7oz24nboZfWOMWxZntkZ7cDsVPyLI -TbQSO5Zhrvfd0R7cTg08qZy7k7+YM0ujPbidkjO/k5CmgC3DMNf77mgPbqcO -772z9ZsBZ7ZGe3A7dVxzr2PFfM5sjfbgDurj/XXFvDNnlkZ7cAfl/aBEx+Eo -9hGGud53R3twB3XpxLjEb5c4szXagzuoGeUZLy2SObM12oM7qDbTkQ/3FXBm -a7QHd1C6ex/lna7lzNZoD+6gUoXHbdgv8ZEzS6M9mPf92FLt75kzS6M9uIMq -bHF2rZ6KXcww1/vuaA/uoKr03zu4L+HM1mgP7qBGvNio8GIjZ7ZGe3AHxTd6 -1afO45zZGu3BHVRXSHXLoMuc2RrtwZ1UnuHxu3zJnNka7cGd1PLs97wzZ7ZG -e3AnVfU6dIrnb+xKhr8xzF0eGe3BndQyw8/nu0RKer2U4eUMc5dHRntwJ7Vy -2bsnDkqc2RrtwZ1U7oXShmgDzmyN9uBOKlL3ilfGHM5sjfbgTmpP/oDoDBfO -bI324E5qsr1u7BUvbCOGDRmewvB/1+ujPbiTOmu3rdDpHGe2RntwJ6V61Wu9 -YDy2OsNqDI9m+L/r9dEe3EmllxjF70vnzNZoD+6iSkt6TpxZGu3BXdR2/R9T -hjdiezK8jWHu8shoD+6idh8dL27Yv5QzS6M9uIvSLc8+aqDCma3RHtxFGQya -3CxrhD2JYa733dEe3EX1/zopsGAuZ7ZGe3AXFeRZGbrDhTNboz24i9q65Om8 -zj3Yngxzve+O9uAuyutx6K/Vgdh7Gd7HMHd5ZLQHd1ExPSfObI324C5qgeCu -F3kp2PMY5nrfHe3BXZTyFYG9n/M5szXag7uoR57nxd7+wk5kOIlh7vLIaA/u -plYs74yIFPjEmaXRHtxNHTdeuM9WnjNboz24myqtG/uJd+bM0mgP7qZmTz7c -6GHKma3RHtxN5R9Jb3uzhDNboz24m8pse6Emux77JcMZDGcx/N/1+mgP7qbK -R7y/QR3kzNZoD+6mdJ5cT7MJ4szWaA/upgTu7Y2iYzmzNdqDu6nO0OZ98k85 -szXag3nPp4Mn+7zP58zWaA/upu53lbR5/uTM1mgP5qPR/8o4szT6eZiPvqk9 -rEpfnDNboz2dj85pfPFypTRntkavJ/DRE7Ty0vcocmbrMT0/0PHRd9Oyanw1 -OLM1ej2Gj86LbV3lr4v9jmGu993R+zn46BVeG3WPGnNma/R6Fh9tOEtk5yZz -zmyN3g/DR8/tOXFma/R6IB+dkXLj1cilnNkavZ+Ij3bYMFWkygHbkWGu993R -66l89HS/31IR6zizNXo/Fh/duGxdfxtPzmzd83Tam4/ufKcr8nsfZ7ZG72fj -o++s8pI7eJwzWwf3vJ7PR98/svyf/oGc2Rq9H5CPRr+PkDNboz2Ej46SKrvT -Hs2ZrdH7KfnonR99Olfd5MzWaE/i/Txi+SEr6SH2PIa53ndH70flo3X6P+Od -ObN1z8v5BXz0itRhM+a+4szW6P28vPvn8Z1Dj73nzNa/evZMPnp9tFXa/VJs -D4a53ndH74fmo6/1S19WWMWZrdEOzE/X1vw9cWZrtAfz02e2RAZ1tnJma7QH -89OB8t7O3QKfObM02oP56R9LB65vkuDM1mgP5qeLqGNPy6U5szXag/lpi4+D -PZ+P4MzWU3sOiPy0WunZsAvqnNka7cH8dPOQIivX8ZzZGu3B/PSeXxv8NSdz -Zmu0B/PTxwXT9pfTnNka7cH8tMB56fGnLLEFGeZ63x3twfz0KJnN1yfOx1Zh -mOt9d7QH89NthzLFspdyZmu0B/PTk2QLlix3wNZnmOt9d7QH89MT/SfEfnbD -1mOY6313tAfz01vemsnZbcHeyjDX++5oD+an7Y2XXH29mzNboz2Yn96o7807 -Y29imOt9d7QH89PvzqYeDPTlzNZoD+anVwwt/vPtDGe2RnswPz00Z3v6xDDO -bI32YN73Z9/h8lujsfUY5nrfHe3B/PTupYqNN+Kw9zDM9b472oP56fV/f5vy -fc5sjfZgfvphUqM/3xPObI32YAF6k8LfX6jHma3RHixA59TWKYzP4czWaA8W -oI9vHhE5uYAzW6M9WICu2P1CyvAT9heGud53R3uwAL24dvZenSrObI32YAG6 -VvEP74xdxzDX++5oDxagNyil7hFqxt7IMNf77mgPFqCFJifpfO7CFmaY6313 -tAcL0F8N7g+9J1LOmaXRHixAh7x3sNg3EDuUYa733dEeLECPlLDNmC7Lma3R -HixAJ27od71jBGe2RnuwAJ1wNqMzVo0zW6M9WIDutst6/c9YzmyN9mABetMc -Fe1mPezNDHO97472YAHapC5Dxc+YM1ujPViAblIOeKY4gzNboz1YgE62Mxga -bcWZrdEeLEDrqi3gnTmzNdqDBWhXerVCyFLObI32YAE6U+b5F/HVnNka7cEC -9J+WxKCNazizNdqDBeg9O9zN3mzA3ssw1/vuaA8WoNtvfm5W347dwTDX++5o -Dxagr/mJJm/1wo5hmOt9d7QHC9LuGvEXkw5zZmu0BwvSt9t9eWfObI32YEF6 -x7SpHbpnsHcyzPW+O9qDBenFutSJ1SGc2RrtwYL0pTmNbscjObM12oMFafT7 -bLGvM8z1vjvagwVpBS2/Bc9uYY9gmOt9d7QHC9Kb8x5synvAma3RHixInxdX -lS59gh3MMNf77mgPFqTj398xLUvHvskw1/vuaA8WpOtUdQcUZ2PXM8z1vjva -gwXpokFzd7/Owy5mmOt9d7QHC9KrFaJDEos5szXagwXpA1vv7ggv58zWaA8W -pMv0KhT3fOfM1mgPFqSTQg6cW1DDma3RHixID1n88veoZs5sjfZgQbrrdun4 -n52c2RrtwYL08s/pTjeEKnptxzDX++5oDxak7+t4XnCW4MzWaA8WpF1mvioe -OoQzW6M9WJCWd/CZkC6PPZRhrvfd0R4sSHsddbnipoS9j2Gu993RHixIr0tv -thBX58zWaA8WpLXWpI64pI2tzTDX++5oDxai0ev6nNka7cFC9PjA6IBkQ85s -jfZgIdruk735NBp7OcNc77ujPViINtt/csljc85sjfZgIfqdng3vzJmt0XFQ -iH5mcCnl8gLObI32YCF6914vzYFLsXcxzPW+O9qDhejpVU+HbVzJma3RHixE -F7nrX8h2xi5kmOt9d7QHC9HeS07dU1mHfYhhrvfd0R4sRG/uOXFma7QHC9Eh -Bh6lSTuwLzDM9b472oOF6J4f6/Zhd/89eXH9f9TRHixEO072+2x8GNuBYa73 -3dEezHs8+/z9jzNboz1YiLaXre13OQB7BcNc77ujPViIrvQxdHgdxJmt0R7M -8wb3i3Vh2F8Z5nrfHe3BQvQ8o3PZg6I4szXag4Xo+EP3ajSuc2ZrtAcL0VJT -bvHOnNka7cFC9KlnqymLBM5sjfZgIXqspv9um2TObI32YCF6tVXdO5tn2KsY -5nrfHe3BQnT/Ls3ZMzM5szXag4XpBuOceuMczmyN9mBh+u2c1dla7zmzNdqD -heni+n8qpIuxixjmet8d7cHC9OeDklNbyrDLGOZ63x3twcJ0rVLp1/eV2DUM -c73vjvZgYfpInlBF7C/ObI32YGF6Yeo9k3112AsY5nrfHe3BwrQ3JdVl3cKZ -rdEeLEzHi+poS3dxZmu0BwvT0xdLvnkv+KXXFMNc77ujPViY9pGJqvXvh32Y -4eMMH+F6j9EeLEyvankfNFMSewnDdgwv5XqP0R7M+/5y1TO7VRqbZng2wzMY -nsWwBcMz/x812oOF6d1f5p6LGoa9hOGNDNsz7M6wA8NrGHZi2JVhZ4Zd/ot2 -tAcL09+ihnZZKWNfZTiP4fsMZzGczHA6w08Yfs5wKsNP/4sa7cHCdNT0Xf2q -1bDHMbyfYQuGPRheyLALw7YMOzC8nOFVDK9g2P7/kNEezHu8nhqUelQL+4Af -aXlGj2f0FobTGP7BcA7D5Qy/Z7iU4Q8Mf2S48H9TR3uwMO0n4qytNAG7nzDp -EYy+lNG/MnyA4RcMn2P4IcMXGb7F8BWGYxm+9r+poz1YmD5f1jr/pj52cQnp -t59Iry1lmNHvMLo+oxcy+nBG/8XoAxi9idFFGL2d0QUZvZPR+Rm963+yoz1Y -mB5GGfNO2FpGpB+YkNacQlqA0WMZ/ZIx6TpG38ToMgwvYViD4VkM6zI8g2F9 -hmmGDRmeyrDRv0Z7sDBtbOn35+k0bEea9Gtz0qOnkz5sRlrGlHTRDNIBjL6P -0d8x+lxGb2J0A0YXY1iT4cEMqzIsy7Ayw/L/Gu3BwvRJG4stMyyw35iQnm1J -+gdNWtyCtP900u/NSG82Ja3D6D8Z/cMM0toMX2N4NsOnGF7J8EGG1zK8m2GP -f432YN7xqjzmbYo1dno6aeti0gavGL2A9Ogc0qrvSSe/Id36jvT5t6SXMLpk -Lmk+Rp/L6G8Z3sTwA4a9GY5h2O9foz2Y9/gUrR84eT72tvw6wm1tpBs+MVxP -evRX0sNqSPN/I91VTfrUd9IffpFe+4O0PqOXM3rJT9IqDMcybMFwAMPL/jXa -g3nPb2ZYTYxZjD3o9yzCiePI7ttF9o2jyH5XlHTEcNIZ/UkXyJEOliSdLENa -azDpAGnS4kNI/5Ii7c3o/oyeyegrGP3Pvx3twSK06cu3ZnJ22BMmkqaiSN+d -Q7rYj/QTe9LvDpJOcyUtuYf0h3Wkp+0gfXsD6RGepG02kf6+lbTeZtJTGD2B -0Qu3kOb712gP5n29Z8/ZeK3Gtvc9S/jRIrJvfUz26zpk31BE9hPDye7wg+z7 -Jcm+s57skWJkj2kh+0Mhsoe1k91LgOw2nWQ35Ce7aRfj+nxkz/m3oz1YhF7u -FzGv3AVb7mkY4avKZDeSDSd8v4z0O3PSLx6R/rqa9KZo0sM3k1YOJr19N2mB -06Q/7yddeZI0nzfpwz6kXx8mrX6CdNERZLQHi9DzYyuW0OuwE06WEY6uLSds -qfiZ8JuDZJ+ziezHTcm+M5Lsv0aQfVoK2b+Jkn3oW7KLtJNuKCK9u570gzLS -0n9Iy30hvfcX6cGVyGgPFqEXKlutPb8JW+CJGWGfCkvCv2+bE04cTXZfUwvC -Kx7MJGx9nuxLtpFd5RXZdeeQfeYPsncYkH10B9kNNcmeIkJ60CjSYgNIG40g -/XQQMtqDecev3Xd9qj2xLadeJzzF9Tbh6qIbhD00bhF+nhtL2M71JuFwlzjC -3Q3xhMVSyX4vnuyPmsgud5jsHbKk5daRXq5JWmoF6e5JpCUXkW43RkZ7sAht -XleTbrwH+63SZ8LantWEy/IrCIvY/iScsucrYR3JH+TlvSoJHzD/Tth3eBVh -91ffCGfsJLvqAbI/uEv2uoVkby0g+xZDsq+tJnuiBtm3taGO9mARekZgmtKR -A9hlQTGEx714Qvi6ejxhMb0kwpKNtwjL8yUSTom/Qzjw8gPCvil3Ca9/nUD4 -qus9wttnkZ16Q3b11vuEZQaRFn9B2s2AtOZV0lfnIKM9WIQuffQz9NUR7PUV -yYQNhpcT3r83jbDI0I+EY02yCIvbfiA8SC+b8A/+fML2A3II8/nkEX6m94bw -5UvvCCtWk51vMNm1V74lPPx+LuH2K2RftYfsL/NQR3uwCD0maPDMAb7YG9qe -WUCXxPET/V7EG6JvjGgmbB/+gfBis1rCP2+UEG6lqwlvLy0jLJzwg/D4inLC -UxS+E3425gvhC/LfCI9pIbv3lirCITu/Es7pT3bJbNTRHsx7fIoWq1oGYB+U -W0KYKkghfE18HeFE6ZuEpTbvJPxqaRThXNGDhJ33hBFO9j5KOEY+mPDhfj6E -82eeI+xgeZKw+u4zhGse+hGevSiQ8JuoU4QvBJ0mnG7s32O0B/PuH5XlRvvO -Yc/OEiG8oy2B8LHFYwhLaoYQ3v6IIlyscpxwlclswslb9xKuv7yYvP0v2whn -JNkRdurYSPhc/CrCd16vJxw61ZGwyxN3wrJVTuT117gRHtPm3GO0B/Oeb6km -n7odgn1ojbUftIaMJ9ELNbyJLqxoSfQpjjFEP9+oSfS0t0+JPkVbjugPPuQS -vUBHnOgxy0uIbneDn+hF078QPVWmg3BU5jfCo9xaCFen/iQ8W7CJcMrd6h6j -PZh3/+/Xpl12EVt6W4Am9DCNo0S3N/9D9G0HjYl+8pe2FnTHDHGi7/i0iOiu -X78R3jNkI2GfxFzC+1QOEtbkf05eXsWP8CbDRMLSCucIr028Q17eJYRw1pp4 -wgk/w3uM9mAR+v1OLdl+V7BbLbWGQCsqb5aBjtz6lOhOms3S0FbDNaSIy7+J -JPq0Le5EH5nmRnT9NcFEL5ExJ3rLnIdEl3iiTfQxcq+JPvvecKJnSn4k+g56 -ENHvbflK9A0+YkR/kfazp6M9mPf4WVI9f+wN7NOiVtbQD1Sez4O2NqRtoO8U -tc6Frh1eRXRv7Q1El7i9ZDa0jOcQoi/kjya6RXzuHOjn4UVEH2N+hehyG7qI -bpV4jOgWb2QJq4VtJbzPZTTh8b9dCJvd1u0x2oNF6K3f6r5b38KWVuoohR6e -KvMN+r7G0TJocYnsSmizzqDP0JJBP75Cj69dWA5deG420U3c84n+UqniC/TU -8PEV0Mmy54luMWQd0dtlnInu4HKO6OPrpxN9iP9dosc81iT6uKsZPR3twbz7 -0xSFcpf72BOf9n8D/XrZyE/QDanHcqGrtg0ogb5SYZYHvSg0uBj6iM+u99C7 -+wcVQZ/avCAfWjutohD6W/t3os+Xcib62pr5BdCKGwYSPWdECNGTFr39AK2r -kkP0nY+iif7rXl1PR3uwCB08OWj63kfYzZK1qtDPLxWaQHvMrdaA/hC+zwh6 -gl6yFnTmD5XJ0Fs0Ho6F/sd4hz50vwCl8dALtawnQdt5KuhAhyV56hGfz7fX -RNf+8Hki9O231hOgA6W3E133WhTRxbeMJbqA7ZeejvZg3vOl+8OkTqVgb559 -utwP+JPMGQnYV277/Q32Myr6IrAXztpeDfspx5UCsE8qvVcDe6ZzZDf0dT2R -emjrsrhO6HnqsQ3QUnssO6BdVIsboQfOntUOnZx2uwm6Wj6wDbosyboZWqV7 -MNFn3Ejs6WgP5n3/VNJdHpqG/euW6ADoVI35c6HNY5TkoKUyky2gl59Zqwj9 -vOr4NOiT6+NVoF1XDzIheuue0dBfhPMMoQVlpmpCax/dYwB985WRNjStlD0J -Wto2Ziz0w7uBetB5lXfGQU/tuD0ROvLZ5vF/jfZgEXrpldejo7OwwydIXYkC -HjVCVQb2yYViCbCHfN4rCrv9qTtPYb9s4t0Jva7a6CX0RE+jJmgrYc+30M6v -v9ZA878Wzod+qsdXTThlaSH09j/qP6CPW2QVE7eXO/gbdIZcQAn0qaE+ldCv -bT6V/jXag0XoUhm5AzE52JfOud26BrxqeZkj7OE2J7KILm82B3Z1XeUS2G9p -zaJgv+NY+gP2F97bJ8J+b7NYI+xZKYmasE/+49MBe+ltU1XY5WYqCEDnhe1S -gjbonCwC/WJW3XDohQGm/aBl7y8cCj19zUGJv0Z7MO/53on7O2PysLcePjrm -GnBc+AQb2N3mf5sL+/TQUVqw3zJfsR52sffRg2E/s3TNIdhlT5/pglaPqgqE -9reaVwPtUDr1IrSn/+Wv0A9jd8ZAh3y6UgIts9jhFvTs9tgC6LW3T96Hpi0m -vYMOKHFP/Gu0B/P6/Er16EJsofJ00cvA1ZOtyqKAb8zQM4M9SrsoBvZvr29v -hn1th/MB2EPyK87Cbq+a6QD7mbTDt2C3iQ2xhv208M002JMch0yB3TKgLg/2 -c7dfjoXdYoNXGew7DZ+owP54j8l34vqKqgqwK+4o/vO3oz1YlB5cEnw5tBT7 -n2d7jIOBo6zOGcDOJ/D5AuyffJS/hAAvaf/2BfZXEYaXYb8n/U7hArx+rvVm -2CfPuWQBu/ehAhvY9zS7usKueHfMBNgFB+3fD/vCCL3hsAcfSAiEXbzTURx2 -I911kbDXCB7uhL5ofTPur9EeLEonCG9S8q/ArozxuH4C2CHrl+cp4P2tRVN9 -YPfQbfID/jVD6BbskvOS/GH3m+/ezxf43oQaU9jtTpfbwG6neksU9jOVlQdg -f3y4X+FJYNvZjddhn+Xw7S7sZX4pL2H3KqoOgv3FefsvsIePNz0I+4IbG5r/ -drQHi9Ie1xd82PcNuzjltup2YMc76h+8gK2vrBXdAezdsl8SdrWvHQ9gj85Y -tmkvvP2KQTN2Ap/zNG/eA3z4dddN2ONPfToL+87kOSK7gCvdVljBnik/yhL2 -mCVTBsGeYbB9D+yW4j8+7wae2bg1Gnb7oZHJsHv+OJX+t6M9WJSe1KA7YV01 -9tmyW7b2wD8/r73uBrxx/4W7K4G1Hl/ftha4arvTi1XAKYkKB9YA33UfeHE1 -sHiUU4or8Jk/22wcgO/va1CH3Xe9aD7swuVrYl2At4dNnO4IHNeqYgO7ydny -c7D/rvnMB/uEGanFsDcd2fncGTji8cHBTtX/2YN599+EoU/+qcPufDDhFQ18 -+rfSxoXAY+eYfJwOfCb+WNB84OxJBgdnAD8Kax8xD3jXAdF8M+D2QSm/5wDf -n7fuqznw5yVF7bOBq2/lPrYADtS0NIT9+Oom95nAYg/Xh9oAh7/c3AK7msQ5 -ZdjHV413tQT+7X02yRrYZe/N1L8d7cGitJL0Y6epzdj5g/TuDge+vzak2gg4 -vd7vnSKw5bHJipOB1UzFl40EFhl3sGAScEDqXhcV4Jxlh7onAkuutxmkBm9v -5MT9usAd051c1YG7I72tJgDnmSp4jQZ+/TRurg6w1e7SlRrAMy7t8x4P7Pz4 -kdwY4MWq1WXjgLdvLLr+t6M9WJTukt2zX60D+75wZ8HvduwJ8RpzlUHPfKR8 -oh70jJ1OkgqgyyR7OzaDLp4Vc1oe9BFRgSfaQD96Ye5DGXh92UDlTtAdE0Y5 -SIG+yqTepBv0M9mTdgyGt39gSSsfcHd0XZUk8OmJXo4CwAEXbcIHAlfKVvsK -AptvGRUwAPir3JH9Qh3/2YNFaamGavWB/F97Pdxi9JwHfNhUxJR1IqD/mCCz -+AnoRhW7RPlAt35xdkwa6C629KM24MsfS9ozgZv3qS1pAh7X0dSaDdz+R/5+ -HfCYjmUz3wLP3/Dzzh/gc4unCecBD2kdqV8NXKobY5kPvOdhm9pP+PV8t9b8 -AFxlGrrhO/AMm7kPCnlGe7AoPUc06kC7MPbM8FnqW4GnzDKRqwFWUX903gtY -MDz6SCXwE4vLtkeB869sOFwKrGNTfcMPuFwgLbcAeIRK3eszwIO2LtXPBR4e -5VgbDBy9LvlgNrCh1yeTcOCLQmWBmcA31hsUXAKOef/VMh1YO/BMURSwScfI -o8/g5V86rLzKM9qDRekVu0+51oljN5dkv1MGVr3YdfkzsOE1epoOsP857y3v -gHcf6pxjAhwj+GfjC2CJp0Z2M4G/+J20SAZW/lKcMA/Ycc2nG3eBT1hEXbIF -LrfzcowFjh469J+VwPdMdxhdAbZoEBdwBn7lnStwCfjM2sbXa4HTj84LCgVO -lhr+aT3PaA8WpWfrDx7TJoktmXfE5e5AbJsO4aTPoL+5uEjgJei3Bpx+/wr0 -xnH7bUvh9VdurU8EPSgr8etv0A806UVfB/3lENOBnaBv1PE4GQY6PXmDVj/g -BGHvpaeBZ5e9PyoFvP9l2PNjwIo6I1wUgLUMW0/tB64JCOpUAVYaudFnJ3Cz -YuguTZ7RHsz78/7U7+UIGez9qRMXqUlhF9513NsmjV203mO8OehSs/SaikH/ -MVr+/GrQPyXE+6aCPir3rdYu0FfWz7ofA3rwy+3up0B/aZbQcBb0y5J12ZdA -LxpsVeoNutHN83dug14q/kzWE3T5P8s3p4DuUjR39lrYPU4sfgX6mVe/KHvQ -yx3XROTzOtqDeX9/XwrfrxuGnfS14oaDHLZy8p6ZU0DX8L3XFQB69kFhWUnQ -52/QWp4E+k8zgU3fhmKvTdD2LgN9pPnNa+mg1z3bNJJPHvuO9BPla6Cn25x9 -Nhz0xzf3zfYDXeziw58TQW8s3fRoO+jnTn/sZwl6/+1y3Y6g3xrz1WsZ6LF5 -gx8vAF1hh3OkG6+jPViUNt0y/ouAMnZau8OhxcOx7ao+Gj1Swj57Jq8rGHRd -u/lVu0B3ndEWkg+6+JFjtaagZ6x2tZRQwFbIs9g7BPRFx+e+MwSdWpXxslIR -XL79fu1q0Cv2ZIxLAb1sr7n5EdCPef6UDAP9F51jfwV09yi3716g18XtTHoG -+pJcSTMn0BXp5JcfeR3twaK0j2egOb86dvMB8eklithXDAxLQtSwJQZnOhkr -Yc8uPjvOFHTh2ool/qA/z9giU6+KvT5eamIJ6C9tik5cB31gM99vZWXs8INJ -V9xA13Y66GoH+iQFkSBd0OcUea85DXpt9J+L3SrYmfODLz0DXb8gXDEX9Dma -5rd/g946uf+Oa6CvihmoLjPy6797sCi95ZmZUJg2tlOaxpoU0GsjDPWkQM/s -rs6ZMQp7mcHUqjNa2CtP77RIAv36yUHZqqA33K2S0lDBDtkucf+xJrZu51bb -Y6BnuPGdWg16x5+7Sp9BHyi5wkES9nG2C3VUsSu6QuY+H4Nd8zYz2xN0hUG/ -fPeBXujubvMAdI82GSdT0M9uv7+/jtfRHsx7fpk9fZeaHrbxykzvuyrYEqpi -oa4TsSO3zexYA64fFnFvfpIuts2v3PWSatjyek4aSqBbfN82Mxr0Ire7WX4T -sNPvlb8br47tYf9bcADooyvnT40F3XLI1odndLCL3Y2ClUZjT4lw/K4BuoL/ -9c9HQP8k53Y1bTy2a/eRlkrQXVa9UXID3WjnnjgTja//7sGiNF9BRKigCfaM -oZntVqrYShLPjogaY+d+lNOh1bDP3HmrrjQFO+OAt+pIdexfpR01M42w1zd8 -tK8BffbksbsOGmJfiNxvGT8ae2fYhW3Zk8H108S07cHnv9Q8OE4N9My6cwb8 -Y7CLh5wQOWGA7Sogeegs6NKm3Z4d+tgDTQSklDWxszo7Bu0APWHzsbdhvI72 -YN7x876bdLYFtumk1cLVo7ANp1jvOmSO3W7cuWacKrad2Eq3+WbYTiPP7bFV -w259mL5k0gzsertDbz3UsVc0t+RqmWIn16oVbRqN7dyaf0BvOnbFWeVaBw3s -HXElGrOnYW+TcFg8Ywy26Ou9FzxpbCk/PgMZ8PVnRAelxVPYOuJfLheAvuKD -eFTjVOyfqfaXfHjHI7QHi9KB32v4LBZhb33luz9dEfvyFWeDKwuwB7vGfVql -jD0tYki30nxsm/4du7+MxJ4Rvexz/FzsXIumT3NUsE3GR+1dNAf729y4rVGq -2Jf2PPeRnA0+n7TI05Vq2NnmZ99/tMbWi9+2Q3o09juDW5OSrLAf3do8X0cD -O2ya7oUbs7AnRnTpTxmDnSwYIRRriX1V9tNYfd6fL9qDefev0ZPGuTpj/2kv -bMqQxfbfvuLOOkdsW+FqlTR57K/Lnuz0WY1dNfeQ9ZVh2CIZ3w2ercQOPXGk -YIMCdn9ZxVuD7LEfz9GRVVHEDrrG/3izHbZuV7TZEyXsny5bzH8uw3Zb73nK -fCS20KT907Ytxf5nVblk4ijsB4bOd6VssUfWSGYPU8UeoHX71tPFoAepP13D -+/tDezDv/mAwSX/WbmyN1K4/N/phhw5L/tS1A9upbPghof7YBT/qM156Ymdb -H3KbPhB7mtXnwvit2P37JZS5DMJecWaAeMxm7OkKRyW2DcEesHuB/cON2MZT -QgXWS2NfvPrm10cPbKPup6/myoKvZ1/tW6n12MdPKK1WkseuSAs0tHPHLs8z -jy0aip0/fYbtg7XYLWP0fA7ynt+iPZh3vPv2a3XnOWzLtRMiZZq+9DrDn1qw -9wzuUb6azfEtuBfp19VJn8Z9/9NpgbrtuOc6idmmnMJdUCzqWFgn7tZq/8R4 -ncRdeNal9w3duC+NWSo/3wf3V4dlXPQFsCu2GJbpH8e+d/ymoqMQdprma8ux -R8Hn/0f5zV4RbI9+H6L1DmP3WyNvekQMW26C0XzrQ9g1hUZ6e8W//rsH8/7+ -dPwjJyVir3Oyqv9U9KXXUvx/4u4m4K75I3+VbwnugYePqpjfw116Fx+/ehnu -G7ebGHy/jfuy+aqpMeW4fzOo0g69ifvdeYkHFL7iXh5JLVgVh/tNkXtyu6tw -X3Dzi+CkG7gvGpM0I+s77sMWbb0kF4P7ry7zp6K/cI8rfX5B7CruZR7BJpN+ -435DcpSTaDTucxTibBfU/GcPFqWnPn7FV1L+tdeFUrojQxNwN2pVrzhXhntn -U+JvhUTc5Y//sl1divu0/JYrx5Nw78zsvjHlI+4V1QaaVY9xH+W/SUelCPd3 -wU9NJ6bi7n1lr6n8B9ytvLTveTzD3Vjq/Jxh+bhHzN2l+/f9Pf9xtFToC408 -3Pk3TXBMeoF7mUj/0aa5uA/4Y/ItOxP3kDz7Wtc3uGv8zpuf+/I/e7AYnbcu -5G3qoMpeP3dqjZDwxf3RoYwpvwfiPi4+SFbJD3cTQbVFGgNwr5w722mUP+5H -5Lds8ZDAfXbEqaWyp3H/vft5+9N+uEcUZd9rD8R9/qPdi0eJ4X7p88Ux787i -ru7s1ekjgvuPqp/LQ4NwnzTDyV1AGPdVVS9+Lg3GXboqS/OAIO6a+h6u/UNw -99wcny4hgPsgBcHlt0P/sweL0WX6DTnx0yp73S850lrXDnffP0LuzjTu8nVd -uvdW4B5hv0l+DIV7Yvi+S2NW4l4/eKRRswnuPkbutqdW4f5z/wr6jTHusY7t -Yj9W414X0R15ZwruZ7fs+cfAEfdqs7OVEUa4C822/bjdCXe+3ET/c4a4ew5r -1Ix3xr3ttov+ucm4b6s/nFnkgvu2REf3cAPcBTXe6ne4/mcPFqM9atdaDtxc -2euR4YkVJZq473p7e9+MTbiv3vr5Sq4W7jsHD/A+tBH3tKCH7o+0cR8X5pOZ -vQH3H5fGfA4ai/sol7IsJdDrXjRdcRuH+34B74E7PXCfmJu9RG887vmjJEZ9 -XI97XovO/nrQn7lvCDYDffUrm6hrOriLnTwqdX8d7nzCj+nFE3B3ebxl/FjQ -q8MmvejgdaWeF2TE6NwttvU3LlX2Omps65SklopeS380jpgGerTVozXTW3E3 -k9EcV3IR99Cjo5qegL4uhU/dC3SnlJOek9pwtzDbOHQ06LtHquyIBF3XZ+ql -vAhw+78f7RJvx11ob8CqI7Bfftm0FnRzZYfuqaAbOI2yTQN9i3vlmPZw3G3U -LvUb1oG7LSV15hHoIzI/u6zp+M+/Ry5Gf5C0MJ2aU9nrQ8H2JdcycDeKlP/Q -H/S04gGrvoN+YUbtjk+vcZ8UsDBOJRP3aRILcu+BHqf6WM8WdF9Z3QA/0OvH -TVh6HPStMyw2uoN+cWnurgTQM4dsGWsN+vfwnN9loOenTjo+DvTpO+X4RbNw -nzJAfa4U6AqWXa1jQBcUPmrdlo370Ox3w2Zl/effIxejvf+Z/GJ+S2Wv54Ws -jT12AfebWv3XUKAP+9ytGwn6VOdjfONA37DAUiUR9AbruKWKoE9e5Zf6GvRT -ovcsB4G+Lldn1mfQK7OOXBYE3ad8WX0t6KkDZ5i3NOPuaXenmi8E99ahLwf8 -Bn2PSLnjQNBdnFeUfAF9ykzFfcNA3+pjHvwR9MG/w1er8XrPy/kmvMdf1rD/ -j70zDaeybRt2RTKlaFRKpKSBTKkUC5GEJkNSGSJEMoWkiIwZ0kCRqZJMFRWl -wSxj5nmerYGkFFJ97nvVcZ7X+tP74/vxfe/dz33br/08ziVLy3Ns3U8Bx8oB -YPcQT4nLtsjPCWLOmI15mluxfgDmZQZumMzA/E+5Fb7XMV+UOjfj2wrkbwiu -q7+N+axh+/CvmB+uazKMxvx5323fP2F+34tW+fuY53v8sWIE8zMo33weYl7u -PNfsYcx/rHbdm4x50ycPrlIx75p6Ovwx5usjFc3JmJcMpHik2f7+75GzksRn -USZKSAPAklaHJA3UkNcrWNBejHnO8LqXhpg/KKVNKcJ8XowomzHmI/Yx8+Le -0FNE5ATm02fsMn2HeY9DTqtMMN+9aqCkEPN98xo+4z7jtq4K7tnaZZJMMZ/N -fqm2APONlvW7T2L+iMNbO9zLiui8x/0+l5KVuN89Uq9gpvb7v0fOSjLpfLHy -p+EA8MWSHYpv1yCv23zHEveSc23q32BenHVhMu7fvuVyxf1Kk1XduDfeo7oZ -9yqtNvNmGCG/0St75DXmL72xlsb9o0HXV7jf90lVG/dOebVBuA92/H4G92+Y -TSxwL7jFyBv3fUIz1HDv9GLtbdxHNT0S+8fT98HTn49jx4043QaAZzI53t7F -hLzOtdAW3DuIjlGVMG+TxC0/F/OnG1mP415Wy/Yq7ufc/EhWxPxXuZk1uK/K -/uaP+66r9mxcmJ8q1NyJe5eaKWncR+8q+K6A+SOVp47g3tOqrBj3h3bJOOO+ -UW9PNO4tNoRdxf2tnZ6u/3j6Pnj65/Gq8STliAHgxh6//tjubuC9MUmzVDB/ -1rPaHPcfH1fuxv1xtqvMuOczGruI+4Md4c9iMB/i/iER9+5R9Q64b+md+R73 -AV+/KeA+VmySjPv0wNO8uO/wVZ2xG/OfAxdNRGNeMoCHB/eGO9U6cL/SSHEV -7pcvflHyj6fvg1lJbm5DWkPPB4B32r3yu5GHvMWXx164f8g7qoD7RdeuJeH+ -sNoGdtz7b5xVjPsF47Xt1zHvvL6rA/d5w+ve4D5N/8FH3O849vMu7rkmHH7i -/oNHUhDu76mKsQ9jfrZc50XcV/J68eBe7kW4He4PsvxcinvVOm6Lf/z5fz9Q -T/99V/9m9daKAWBXZf2GgTjkN0ZkyeJ+k4z7U9wrqgxq4F5CxOgW7l187+vj -Ps+qzRP383awnsR96Ew9B9z3s/aexv1PpTvmuP+UW2ePe0OXVwa4by7Vcsa9 -iC6zHu7P2bw6j/vxbx8O4f7sD42LuP9msnT/P56+D55+v3TuMts/MAD89gmz -g60f8ivDZtvh3m3mmxO43z8+fA73yt65urhvE89xw72G6qgm7g0T2S7jflDc -URX3Hyw3++Be/+0TJdwrMXn44f7hHFES7kXytlzB/ZF3t3biPpbPOQD3K+XT -ZHHvGWgSiPtHu9S3/+Pp+2BWUnuAycXDPwaAL632HeGyRj7gRrMH7vv8npBx -zy7P4Y17zvHSXtz7yB3yxX2AgnoX7t1aP/vhXv1VaTvua934r+B+T+rMNtyL -co0R/IK1mS24/5wfGIB7blpFM+6jJyYJfufpdQRvy70nEPc3Hzxp+sf/uw6+ -zUpKrjN7a7VwELgpcDv13iHk8xsFs3GvHus/iPs7jjo5uO/7lNyPe7/5G3Nx -/1XJqA/3msbZBC/7yaUX91cNhPNwb8jS0oP7kW5rgueetCT4VVdiCF64fSXB -r2XJI3iFQ+Ru3J/62kzw3mvy//X0ffD0z/+XnXX3RQaBT3j2JC/djrzPVo96 -3Ddk9SXh3mXmB4I3qdxO8D6qWxtwz5L8LhH3MfctCD6Lz4XgNXr9CX57uzLB -5+2JJXiRFEGCrzF4QvBx4+wEv88vk+D7ZnxLwH2yUQ7BG8uP/Ovp++Dpvx/X -yFcslBsE7nFMFtITQN7rjiPBcxzQInjFqnCCjy1cRvAP7dMI/tuWsdW4l+7K -IXiBtFaCN/hUSvC5T8oIXse7muCXyuUS/IfKeoIXsnpF8DxRTQR/ejyd4CXs -WgjeYf6zfz19H8xKKtE9V1F+YBC464j+Oi025Js0rhD8Kjc5gj8aH0rw5Yob -CV6/JpLgu1+vIvjL+ncJvsGBl+BjtsYR/MfmhQTfOSee4O+OchN8xMaHBK/B -N5/gb/YRPe8nLoJ3OpJA7GXonr4Pnn5/mc6IazcZBI6wzu6d/NgFzNI1m+Bf -+mQQvPd2NoI3XpJG8DYqHASfmv+I4P28OQl+9HUywS9Xm0vwpm5JBH8rh+iN -3iQS/G12LoJvUCF6KRmiP/UjgeAdDhL9hmq6L/93H8xKGvtRL6XlNAgskaNl -Q2pBXu5aI8E/2nCQ4EXdmwj+RNx+gg/hbCZ4vqx9BG9qQPTyMkSveJXolw5o -EvzSFKIvzSD65W+JvieC6IWKiN76CtHPf0/0GZfonr4Pnv5+mbe5YpvfIPC9 -xPOOvAXIy7sSvcYXF4IXyyT6p8FEf7qN6A9qE73LR6JfLkX0PVNELyVA9MZM -4gRvu5joF84h+oPziV6UjegbOInekJ3oW9npnr4PZiVVl7Da3Q4fBBaSav18 -/jHyev1Ev5yF6M+MEX0nrYXg074T/bwOot8+i43gzzcQ/XNmoteuIXpuFqKf -V0X0lQy+soLot84hegEGb8vgc9/T/b8fp6nTf/+IKfw4nzQIvO+7EotBOPLX -pIleZ5Tof2wl+mAa0ZdvJ3oPMtFnyxL94ADRk3YQ/XwG78ngo/uJ/gGDN2Hw -Lxm8EoPPZ/Divzx9Hzw9T9fSmPxqEPiSZn1GphfynHpEv0Cd6PMZfLMa0Qsc -IfodDH4/g6ftIXozBl/A4O0Z/BMG78Lg4xj8BQYfzeDdGPydX56+D2YjBZon -vBksHQRecndTv48t8g0M/lYs0U8y+KMMnsOC6OUZ/EIGv5nBL2Xw6xj8cgYv -xOD5GLzA/yVP3wezkVT7tF3dWwaBJ3mfrso+hrw2g+9h8EcZfAODN2Dw1Qze -iMG////E0/fBbKSTBXln0imDwHsPtoccU0PenMGrMngLBq/C4E8x+F3/Szx9 -H8xGSm5f0B08MQgc029APSLz1//J0/fBbKQL5d0PuFnJwF9c7LWfCv31f/L0 -fTAbKY3fTIS0mAzc7JFjaMzz1//J0/fBbKTTA47O/EJk4L4YvckTM/76P3n6 -PpiNZLOgZv9TcTJwJcnM6Nlw51//B0/fB7ORFvQzrf0pRwaeu0B75f62v/5P -nr4Pnv78tp5pPYs6GVi3RPCbZNlf/ydP3wezkfRU+g6VHiYDb5x6NXX01V// -J2/77w9ENtKRHQmmB0zJwFd41h0rSvzr/+Tp++Dpz9cX938MtyUDu1raeduH -//V/8vR9MBtpxSu9Y4kXyMDn3MS4jvr/9X/y9H0wG+mm6PPBS35k4DRP31Q3 -F+RvMPinDP6/2tP3wWyk2N3Kj1bfJAMbvMg80Hrqr/+Tp++D2Uhc5t/iQ2LI -wB8jJkfO6P/1f/L0fTAbaRVHVGp5Ehl414uUx1vV//o/efo+mI3kdk3pSlM6 -Gfhc8YdiqZ1//Z88fR88/flmz5WW9Bwy8NNHejeNRZHXZ/BpDP6/2tP3wWwk -h8I74mZlZGCWqZlu2fzI2zN4Vgb/X+3p+2A20vzEzyy0ejLwk81P2DS4//o/ -efo+mI1Efsmco9JFBlYL3lHGwvTX/8nT98HTn2/8ktOcqWRgpxrRzkZyx1// -B0/fB7ORhDcGr/AcIwOfLuo3mCj/6//k6ftgdlJR9R5Js59kYI+bK1Ks0pB/ -x+C9GPx/tafvg9lJxm+DFq9lowBvEhE/vznsr/+Tp++D2UmZzsKt2TwU4B3y -R28ruv71f/L0fTA7SXG488pWPgrwh8XtIzFGyCsw+E8MnsTgvzD4/63n0/fB -09+fj08IBK2hABs17/Hcs/uv/5On74PZSfVHJgNyRSnArU8nzLdv+uv/5On7 -YHbS1i+7n9XLUIAXzLlbYbsAeRkGv5jB/1d7+j6YnXSt4INdKYkCfD155sTQ -RDtwCIO/xeD/qz19H8xOujN7c0TsHgrwJ7PkbSmdyEcw+K8M/r/a0/fB7KQz -+TZf9A5SgNUEhr6mvEPehsGrMPj/ak/fB7OTZo2+Ux47QgE2fPwmcfgR8jMZ -vAmD/6/29H0wO8n7nr2iwwkK8M4d1Y2nQ//6P3n6PpidxHtqb1SDJQV4s2f6 -kvUXkV/C4Lcx+KUMXprB/289n74PZie1e4kwr3KgAOvofGMXPPnX/8nT98Hs -pMkE9aWarhRgy1n2J7Q0//o/efo+mJ2U8inN2fgyBTha/Xx71pa//k+evg9m -J714YP3mWAAFeF7/IeUT/Mg/Z/B8DP6/2tP3weykRokxZ9INCrCwhrvVTlbk -6xm8OIP/r/b0fTA76eqE+VaOOxTgcFEpSY2PbcAhDD6Uwf9Xe/o+mJ00KN/u -+fYeBfildbFHSDPyPxi8LoP/yOBDGPwEgz/N4McYvBuD/8Lgz/8/4un74On3 -f0pE+5EkCrD3UnlNtnzk/R8RfctCoudj8O8WE70Og89bRPQyDF6ToVdl8DMZ -PInBr2XwSgx+KYNXZPB8/8Oevg9mJ11P1XnXmUYB1vPNDnmagrzqC6JXOEX0 -kc+I/rkL0UenE/0zW6L3ek70cY5Ev4qhH7In+lKG/tRZoh9n8LEORN/F4Ocw -9DQGX/+rp++Dp78/uK1e7M+kAE/qSh0MDkM+Sp7o7X0kCV5hDdHL/iB6ZSmi -v5ZJ9C82ED1vF9GHbSZ64VKir9xE9IkNRH9SjOi9KoneTZToQ2uJfhZDr1pN -9/R9MDvpft7CdUk5FOBylZo7EZeQN2lfRPCeu98T/IMtRH9Wrorg14cTvaRr -BcHzGxC9rk8lwa/1IPrWQWJveJrom1SI/dNzRL9kHtEb2RH9ls1En+lI9H58 -dE/fB0//eV8K9R0pogAfPFHi3WCJ/IaYOwTfd/0Rwds13SL45ldZBF+5KYLg -z619TvDUN7cJvjPlFcG3x4QTfMWDDIJvXUj0XYKZBL/Tkugdwl8Q/Kg00V8L -eEnwNTpEL/6V3tP3wRyk0iQrVYFKCnBuzPhGRR3kV1OuELzFslMEL9nvRPDO -5gUE//LFZYJ3pPgTfPMlV4KXOvGE4GcWXCL4ZqNbBD9lepHgX+TGE3xrkDvB -PxiMJPjkjW4Ef3TrfYK/Po/Yq22K+dfT/+d8DpLtzyPVOxsowPJJHM+aScin -GXwgeG8ek1TcfykJIPj7t4Sf4p6k9p7gg8K/Efp5hXcJfjs1Nw334Y+zCN7m -ohzBz3ZJJvjlLqEEr7DzJcGfmn2U4D1ynxD8SIsHweeYpBM8H5fFv56+D+Yg -nbkqHqjSTgEWejpLLWYD8i9lCoNxf+uWkBzuef1/EvpnF/ep4L757FZCb+v6 -hIT7p7xGQbjnbArahXuWA2MEf0OhTwH3LvuCCX774Uwl3J/zrCP4sEtOirhP -k4gjeJ5UbUIvaV9I8KLvXv/b0/fBHCTtLodm2T4KcHFr7cZri5Fvktrbh/vr -n0onQzDfEXG9DffCm06vxPswa54e3N//NHc27gXuruvA/RlJ/iW4j2Ua7cL9 -zWAFdtwzM38h9LJfTi3APTXXgNDvLu/lxP0VkeOduLfh9+fGPen2IkLPJS3L -9Y+n74M5SFvPrONeSaMAs29cm/d4JvLua1V34D5NQenbI8ybxvnz4T7sgHEQ -3hduHZDEfYg+ryDuA48/F8R9RnKZLe5JcsfEcK93cLUM7j0jOdfivtBpvzHu -m3IHNuJea4GfIu4XDLcI495siKaH+5nZ1zbg/mvGc9V/PH0fzEHafDLTcmiU -Aly2/czHcVorsLnGJ65hzH8OIk+MYX5vRf81vOfgXCuL9xfzNn3EfU6H3eUv -mM+V9knAveTu1qqvmH8Y9K0D958SnGrx/mHfrXTce5Ry3MR79QbOetw/fPx4 -Fu5PHVvzFvdXbKm2uG9bv78S93ZtRiv+8fR9MAdplzdXecIEBfhYD/vmM43I -+35yXJaMefeUdGsTzCtz6qsnYj6k0LjNCvNWBgnpSZhnKx4incR852h4ON5v -6Wo+Y4l5/WX7z+F9b6SHgRnmqy2fleD9FdP1wacwn84ffgjvD71KmmeO+fU2 -yoN479bHORvvl7da7sB70+zP5//p6fvg6Z8nN9LZDs6gAufWbKEtzUe+WoTz -ux7m+1r6733KQ/612b6rhzAfHhWWz431yW3WOYcxryBMs5zA+khpw2AtzMv4 -eC6di/XWjoc+6WL+ZpeVxHesH9sxIq2Neb1Aew52rL+z75UV3stW3kj4ifVf -eZ7fxXvTiJNzWbFe5kz9QrzfE/JWeea0p++DOUgp80dLu1iowKvTfwZyPEFe -83vUkinMm4VnFQY/Rn4zj4d0P+Y3xjMXf8G8SlCd5Tjmu9+FcMViXupzuRIZ -8/41904OYt7uE7lzDPORlyNYUjAf+zDciIr5t6MaNu2YJ+1asPIz5q+4vt// -HPMWxo2NNMybqH7za8B8yOuqvlHMFz9L4Ho17en7YA5SVZ3sg71zqcBaixfn -+NxB/ttDpxnRmFemuVC+hyM/3PAmWhfzHPFHNu3D+oZsl5wbmNcdj9cSjUA+ -dXeemSHma750PV6D9TNiL+8MxPzkl6SGA1h/s/VI40nMZ3tcVpyD9cektTN9 -MG8t/ajHEuuDTYxDLDGf+nHy4wjmO+J3P/bEfEr2iR8Xpz19Hzz952u2SNdi -ARV4gMeveZc/8snHvxucXIg88/qTpTe8kN8WsDLUB+tTggJOP/dDXp1kWrEX -6wV7j5XzeCOfpt3LGo31ZJVMWRWslxdbKiWD9b2XbK44YH2uZueWVKzP5zSa -PeKLfP+y7VuFsf7tg6f62Vh/flx3XxbWP+LP3piC9SsmHKqXYX3IBSaRb9M9 -fR88/XmW/PZH7VIqsMNUuPWG88gvNduukbYc+VnyXzN8TyMv6jVn1nJe5Pdv -MNdsP4f8sE+ytT3WC0SICDyzRv7IrmQ1LaxXSB9+Ue6MfPXrBqo81idk3zqd -cAZ5R7ef6z2x3t3TNW7YCXmy4YUXi7A+apGjoZ0N8uInVH0TsJ5r28T8rVgf -0Rq09tMy5PVNT35bbNv6ax/MQbqwVfDgDT4qMDPlnN6wPfKRUcXxNkLIm7nd -XGGoifyDENppoRXIByaseiWHnW8WLxs4tBr55bJRajX7kbfpYLkTg/Uuks+W -DFsj/1mUT94V65s4NGU/HkTelGlfPMdK5Pd8khX+YIW835VgrWVYv6XkjluB -FvKHC9M+mWH9AXsfvy2WyB/bs+xFgSDyLZc+Ljqi0/prHzz9fhtbuSJg+uv3 -m7Umyt4/voh8YI9+Vthm5O3sjF9eW4n8+rWubZ4rkN+0vLB1ngvy1y5Vr3gh -hnz96zOhhYLIx+l5l55YifzyflfzrrPIP4wpHaaJIt+sOLssbC3yfhm7j4vy -Y/cvGMtdaoe8TI2ZkhTWa+Vtz5y3HnkTpn05fVi/Y9wmJska+dwPOoYBm5B/ -OXdRwZZNrb/2wdPfHzoNTw8uogK3LLnLV5mE/OTYcOAsJeR3fRs2mVnZAtwX -EK90ZTHy+sX+TFNxqN8l1a/yRQF5BZNW8cV1qF8mZVf4eAnyR147zPWJQT1V -NthugoR84cmyhx1NqNfdQuPJXYr8O7vUIPMI1LuoHKtgx/qQRTs/nWhH/f5j -q3LzeJFP/ib8/VYo6vP1dBVF5JFfpvnW9WF3y6998PTPi4wVg3eZqcDOccMT -U7PbgJ88L/3oeBT5QTGh0xuOo36m6/E9AbORZ63q7oyfifoHrx6cy9dHvtB/ -8tVNI9QrD7bsOcmCfKpsll/E91Zg3bU3y/iw/q1tzUSJCer7rKxdJeYgH5Z1 -3a9yAvWfeRJ6Lx5BPtZ9j0SlGeofLPXcMYr1TX3t50hfUP88NaaNrIf85xHv -koRTLb/2wdOfJ+carls5TAE+7GN19Pz5NuA7IZon2J2pwFSW4jjDzmbgne1e -H+yw3pbr+hrqOdRPhJ4cqnFCfW2R1QnrLtQ7ylh6vsH6LU9ecVxxRv3B7XED -97DedlHatqPdqNd0ctn6E+sdT2mVajmh/ri+xaVzWB9M0pYU7UG95ewl4ts+ -oD6EeRankiPqmc5az9HC+jVTSsUD0z19Hzz9+4oejWLZSAHOOGi/4xqtDZi7 -6Zy54lUqMFOQQfMzW9SHHRqxd8H6GH89Lk2sP+e4Jmc71ie7HxVowXrtijmf -vLDeU+P7qqVYv2ZGRpoU1h9sV7ecwPrLkykcwVjvkJNydoiK+vWGXgNiWO/+ -4q4Jtx3qbwimyYVi/eUfak9KsV731vjyjVhfZ2djIDTd0/fBHKR7vsN6vIUU -YNq+lyynNdqBWW4/v6p3nwrsI7kz0nsx6ndOuAcuw3rjUUdLM6xPLS/lxPu0 -bWZb/LB+NNbceDnWPy8b8zuB9XuHXVIPY/0p/5ZZV7A+iL9kDO95mmSaDbFe -fdEuO7xff+aOQgDWV92s1OfDersG/h/Hsb5m4yUVvHfdp7IycLqn74On3/97 -PChR6RTg+4dY87Ni2oHHKEceXXxOBR4pWL1Zp7gJOIf0/RPer7OYDMP7gqEF -SXj/qqyIhPdvs25N4D13IfUC3is/Xp2A96LLY9Xw3r6SPIX3Y7Ie1nh/f/2P -eLy/W2m/H+8LmTt/EF6/j4kp3rsH7Sf0fX59h/7p6fvg6c9LfBU/hBIowHNG -pCQiKO3Alz5zld/LpwI38JzhjfFCvWXRfUK/bXSc0L90XUbos/mlCL0W51VC -n/jlsCTe9wmuIvRy8ksI/cpeL0If9tOH0O8fECT0X3jZCL0xxZ3Qf2SLJvSH -FYUIPfPGWf/29H0wB2nVvoZo/kgK8OYblSuiNnUAp/5M79eppgJ/cqoJe62K -ek3jWkJ/flE7od8UnkHofY5VEnpJUg2h79vfQ+jZ64n9E5EKQl9cUU3oybp9 -hF52iNifTntP6HfeJ/ZfV/UTeukvxH7XZXpP3wdP/34+xnN86zUKcPkpjmem -lh3Aq01FbYfbqcAGFyV2cnGj/u4HYn/Zk9iTGXsXYs8/TOxd/Im94EliL3OO -2D8ZYugDiL0EQ9/nTOxDGHq2QGK/laEv/NXT98HTn58jBeW2+FKAO2bOKp4Z -1wHsXCRx/B6FCjykeErWq63xP9/T98EcpH1OlVofL1KAZ/ifMNvc0gHsIh0e -HDlGBRYQmBF4IuVvT98Hc5JqDh7QV3ekAH9ULj0oN6cTmGI8qDj5kwrskf9s -1Ur3vz19H8xJ4lOVXCBuTQF2sC39Fs/fCfx939GUCjYacLFLus9e7b89fR/M -Sdpc67Is6CQFeL3xAvUfWzqBb86rERZbQAM+sN4m4PZG1LfUEHsaQx/A0Lsz -9B8Y+rcMfTBDb8PQDzL0FQx9EEPvyNBTGPqS/2FP3wdPv54TP/21DSjA7AF8 -3MYancB+eZbBa/lowKaL+W4XzkY99dEPQu8jvJLQb3lI7IviiX3UMLE3DF1B -6JtSib2HA7EXbiT2IcXE3v4RsQ/zJvY8ncTeO4PYP3hM7KXd6T19H8xJMhD+ -ON/1MAX40uS+r0PGncA5C9nFcoRowNI/h/QiOxuA2WR7CP2ipDOEnuPEHELv -YDJF6E0TyIS+f44RoY+KZSX0im/HCP2nJ/2E/nmJGaF35iL2bpXjhF5i/iCh -V0gyIfRnDhJ7PdOv//b0fTAnaSRyRG78AAW4kLl09QunTuB9i4uOsm6iAZ/O -ulL+8TXqJ3YsP4D3FM4LkxlYP3KZzQjvvw2np+P97isZKnj/fh8fDz6f41z4 -cbx3v1mQh/fJ0Q/V8T696zYz3guU/jDA+6tUjdd4H5ehuAfvfXIPceL9OSZJ -Qh8keT37n56+D+YkLVTWK8raSwE2Kc4PbLzSCbzT86oykzQN2KOEdP9uOOoP -3/+5KB/rH44cevce6x3Y+e2Zsb5k7+e9d7D+p33Zmhysl5D4Zl+H9XnXt8fh -8+15x2Ni8F7YUDgP62X7j/dV4vcXrxDH54+8y0qKxHpjl/QifL64KWVmLdaT -N9VU4fM/f815Ej3d0/fBnKRtVgcCbyhTgC0aq+NaozuBkwPvjz3YQQO+8t24 -5cM51P+UFY+ZrYL6ZgE/ptYo1MtOnlQowXrnjp0zxLF+SvpoThI236p/+fd4 -bP6izTpbH2E914M5t4uwfpHPfqFPWG/TUfd1NtbvsRFwz8f6503VK/djve+Q -lEUm1rP1iWV6Y313Kn95GtavjHOueTzd0/fBnKTUsKt37+6gAEvv3/FlY2Yn -sECp7PKPijRgjd7P1w8bov5G6CaFk0qoz3h9ebQuEfVKA3Kjmsqo5/UU3e5+ -CPXBnxNEFHaifmrYp73gBepfs7AkrVdC/WGjcdIqA9RnBjntqFJEPafFqr3r -klGf+2RDGR82X1tS4vJVLdTzF17Lz8Pmp+ud+BKZgXrTl8KFetj84VymuFXH -G37tgzlJ8w2iSZ8FKMCWnx2crac6gRWZuUpvkmjAMZVGUrfPol5KgS/mpw7q -H82XoKy6jPqdC5lHw7VQv7ztkG0QK+pfmPgnrBJEPVmBlM+OzU+QFwhOwuYP -3fGbsxqb7zarNf0dNn/4xNGfMdj8bjct5QBsfqmyS3Q7Nr9Hx/68Kja/MT30 -aOo31FewHuDMwuav9kjf8tKh4dc+mJNkxM3Kc2gmBZhT+Frv2b1dwIkrmwVK -ttCAK/don5R7ivovPuFLNC6gvuq6XthN8U7gXTu+xmmboj6Ct+bzkuf1wPaG -XkLq2Pyf34KVvbD5Dy+8TS/A5tvk9xzWweYvXfNhxWFsPp909vB5bL5oxZcs -HWz+gdkP+rix+SHjX5j3YPN5WM9JBWDz70W9eZGHze/ctWCN0fR8+j54+vtj -pDfDZJgM3JKexhxzvgtY27vXn1eCBny6wsppWx3qf76xvGcSSgF+doU8S3ei -A9hjZ0LEXRvUr7c//J16sR445QNx/tIXxPlDXsT5sVXE+TOyiPOnvInz3Rnm -SzPMf8Ywn41h/keG+Vd+zafvg6f/fmh0VDbrJANrlT68mxXTBaz9itveTIwG -/EJeqfY0DfVCGhaz7RMpwE+CrK1nPegA5v7axDHDBfXzmGbsXXaoHthHvHmO -Pjb/i1WNbzM2f1bGxWfHsPmdQXmJd7H5fstoOf7Y/DUf5xeExKH5NF6v+u/n -UP8wLCdwLTb/e/qSWCNs/n2256xl2PxLvAfHjLH5pe/ui3pPz6fvg6d/P8h6 -NH6ikgw8URr6YEtJF7AO/+vBLBEa8IfXkZRnCxqBY98M8PsXUIBrLpbmfhfr -AF54leuBhTvqr+d/GLCRqQcW5do4M6kZzV9JLbyb+hTN72rwuOohgXqTvEzZ -db3o/s3z6vo0n6D5I+/qmT1vovkDR6d6uj1Rr5IssW2hEJofWvhUawH2+mdG -pU70Y6/fzWCr3zns9b+R9NeWWNT4ax88/XlHZK5GWzYZuH04/fzF0S7gVwvN -9nCvpgGHaGZ33yChnmeqpyOvmwI856K55JeUdmCfCdZlZA/Ur0ytWOciXg/s -PdG6LbUTzTexXFlYnIzmF+xV0d8hj/pPyw/mH4pvAK7dO7RyIhLNrzWrjmIa -7wAO2B5pdCQY9cKnNEM6qHXAG3gOFCzORPN3tb1YtHVmN3CSgsae63zY/fXf -LX5+ovHXPpiT9PXzlknnZRTgzYGvfwpJdAGPpaRXpU3//PjN8R6STONR9cCz -jm48dF8I9e+PhNoILUe9Gru1cKQj6j+cTE6YexH1EymltrsXoL47R8r2qCLq -T3T6ryNZob6JKygxJQP1svVfD3qJo54au+F11/dOYFtp2QTnC6hnvbg6v0oX -9ZnvbhlU/iADr/uW3yJvg+YL7374yPI46tdwHsnew9zwax88/fVOXL3JZooM -fKTFraZ8+ufnb+533PCpzIQG7FnAxidKrgfeK73nibYWBbggntWS9Vkn8AXv -DV+Tb6Kec3H56dmNdcA1leUGGjlo/o/sUF/zH2g+jdT1+rs46o+cshN4OaMR -3V/dyprWhOb3vXSv+DLcDpx4UnFWWgTq3Xl2vFicjuarR79c15+C5gf2ZOnf -WtcN/HVm9iuTlag3cxga0rFs/LUP5iTJHc06EnqFDPzoAy1wyrkb2KmW8+nr -H1Tg098C+fj4m4ATk+XSGo4g/3NC99IN51ZgNtVCi+Lpz1+/uaRM+OBitQbg -GhH2g/OCKMDr44o5RyU6geP2eT//mIz6Zz0fzQWP1gEfkjm05IgHun+iyGnf -pwHo/uYZ+9njPqH7BYyt9Y05gu5/qUiR74Qt8p8G5E0tZ6P735xvKHltB5qv -xfFK+URFw699MCepfqd0WWokFTjcPeWQ2PoWYM8EWpfDfBrw2o1D/lZFjcBS -fZs6dBRRXxJdIrfgZyvwMZNE7StOqB+wDJOZFVIPnBV83Fx/GwVYeobwqOiP -TuBF23yuz7yD+nGeV7Na8uqArZOlM8SKyMBJpORCsaku4IC+8sVrdqO+zp3T -PTMSvf7oQ1TP+1loPiW9c5PD5Q7gR9Vnq+PSUT+VPD/y/Ma6X/tgTpImv1uW -wvTf779ZeZe42NngemAOneBr3QoUYM75fJFRI53Alzk6B9YmoH4H/7XkCXd0 -/l0WBVabRDKwpWGu4S2lbmDTy7rxq8VQf4qqpLNkfSNw6qWe9yvZqMDZT2Yp -caxrB/ZSKDjNn4h6w1MmHvbn0Xwrz5umm+LR/DKthzVJamh+18Bh/8sbUL8z -xfzq4E403yfO4lkZN5rf+63rwYep3/++evr3pTRn1cR2KnCf0lN52f4mYDnt -Y1612cgn+a/WrbjcDPzg4s29rp+RX3/CcULRFvVGW05PioUhb2bEoetr0AJ8 -dm6yY+L055PfHFx0coUefyOwdmxews+5qJ/RG1rou6wd+EzxA+PBNNQn8AYe -/Lq/Dpgt8b3CZCgZuKyEvYvk0A383lSn6DA/6scjX6nO90Pzt3XMOhopi+Zf -vbf4fpH0739fPf15hSlbWqOeBlwzYGE/EFALHHw4MKVlDRm4qSUs9rZFD7B5 -UH6wuA8VeNmlfVbXX7cAUzc/mP39EDr/er53VdGZBmDpXi3BQ4UU4MXFsoO5 -Xh3AlIwgM9M61FvpnJQQuobuJ1cicltWBN1PcGl86j1jdL+1Af4S3gHofu/Y -pD62xKD7CWa+sJTXQOfbvrHo3nwT3W9BXtv7LY3ofuvTtnZEif7eD09/vefn -jOZMv39+81iVRYT79Oe73xyoor+xSYwKfONcntQC7zbgDxrBozOfoz6ZK9Bi -sVYdsNIM71lcSWTgg+I3OXO1u4GDbDz4q5VQHyzvwFJV1QAsLHBpiP8HBdhU -qTtv4GI78MyKrTIfK1HPbnnJb+vTWmDXwlZeg91ofnrIgbCa9T3ALNk5u65m -odfHe0NF3TiqGbh+8+x5kvPR+VJSUps3DP3eH09/3lCf50xRowEr3koU7Utr -AL7SMHlKY4IC7J+oUvEgth14yCwseLIN9WfDV58nW9cC227yObNViAzs/kaw -M9+lB/ht2+w2g0Aq8OFQHif2Jy3AXPlR97hN0fnRJZWvmQXQ/WbnzlgYlIbu -52pb5sE11QH8PXzvo8tU1D8M4aCxrEL3q1M5kPfjwyCw3fMXftZ96H4PzdW7 -3KTQ/c5Hr+VmOvf731dP/7wrHOZNn/588ZvvmMuvzrjcAKzlEKf4gUYBbpsR -3VBIbgcuKeE+Kj2EevFbi0Z2rahF543Flo9/GQSumiP1+XB7D/DFteoDR3ZR -gUNTycp1Euh+LLU/no+8Ruc/sy87fkW6DviYSHZJRiIZeN0+1Q1uJ7qBtcWP -0rz2oz5DdMk97jvo9TlulBpbMI5en71x8o3raej1Re4Lc3Mho35/9VWOBZK1 -v/bBc0nSQbS4u2tpwNpr3lncDmgEvkV5n+x1mgostDSQx9WiFZg5Rf/79C/0 -wHpa76QW1NYBb/6esWOQmwJ87eoSzz2eXcDLM5aUxrxBfbz50Xyebag/Gef4 -cfQ5Gdhv/WfTwwe60f2EePW3mKBeaya7mPSWBmCDaLderko0//G5UtYhjw7g -6hvW47t+oF5oVie7eHYNMMfVARbR7EHgr2MG2VqHen/tg+eSvD68CtscPQg8 -b2HMWa8I5G90RoplxVKAlZKuCDyW6QROZnn7tI11CFgq6pBXmG8NsAHbq4LR -WHS+r/p7En8oOt9nXfNrw3h0vq1em8Hi9ej8eRoP3R3Y0Plji/P9lnuh81ND -LV+ex+7fd/yy62g4Ov/Vjsiiw3fR+ZdC+G7v2ILO33pmPOsDdv8Ft1sLN2L3 -P7/LXi0eu3+sk9GCp9P3p++D55KuH77/YaCFAqzKkRDVeLwDWFtfW/829xBw -a9Oq60/0a4BNZDI4o/wHgXd/nRXaV4LOd+Mq+xzgjM4v+nSxSTimE5iJyr6V -lw2d3/SzWHNZEDpfULrc3PcROn/tlKlC7GV0fomP/1RbLjr/9Zts5bomdP/U -N5MeBxai8xNfxHH67UXna3dwKH2/iM73ZlJ6dbILnb/wfUZMtQE6v7ndS/d5 -8+/98FxSQSb1R6s7BVi44pb9pmvIP35o/nLboiHgD+3PNYfVa4BtneSuR/sO -Ah+7csx2SX0v8I78euU7Z9H5JRnpN2eloPPlzj9zs+RG5/OwMO27dgKdv9Ai -8Aj1FjrfWLVgsU46Ol9I0XOU9xY6vyP72ID5EXR+Ku8qv8XL0flrjolcm7Ee -nT8e8NZC8Qw6/+iW8Y2cc/qANRNiLR/JofM12BNKDUR///97zyXN723e4s9N -A95+c9HzxNVNwC6OW4drqqjAoaeCw09cbAbmqGfJGt6LevKaOtGAjgZgwb7F -Im67Ub/0Fo/XAZ02YJqPwo9dY6jXcbZJ3stdC/y0SuHF1DIycMOc5zMPZ/QA -x4ro6CqGovPd3KgSc6Y/f/7m8L502YP30fndZ8/eMybXAavyGEzMVqIAL4yI -4lZZj74+O2i99QYzh4DLvpKj0oprfu2D55L2MU8c0bhDAZ65nCqUrd8J/DIl -Z4a92BAwZR+r6tE31cA9xw3EbosNAsuqKDJ7B/UBR8/ZaXIzhQzsq251V+xy -N/BSpl5WTRcasIr0hbGmrnpgo6qgzwdr0f3OKM9+6hbXAWz7qPr+Hgl0v1fC -Ist3J6P7xZOY78cJovtlb1hqfPcBup+r6oqK3CB0v+MCbesq36H7Rdk2y9sd -QPdb+HHk1HjR7/3x9PuV5er14q004B8vd8Re0W8E1tEctrtwjQoc5j/Dya6n -BbiWnbu2LQf16i/nGelp1AHzTx3xaR4nA4uxaM9829UFPLksSrGvDvVzvq4N -ITXWAnMvNMwseox6d1nrTxVe3cDrmCNm63uinnxJokcqvR746Olh+dJCCrCG -zRTJ8FMH4vjOxVY7h4DvZ/Kcu3mmGpiT/5PvpakBYJNymxdnP/f92gfPJS3r -VG/1Jw0BW133SxM4UQ18tF68ePu3AWA13tPvXH6gPvtOuP/jDWTg+DUbI6QT -eoC3Jsy4IJ9FReeVURQdfzQDJ3q7nd55lQb8/JKxP8mhHvj+qcVjD5IpwJan -BEIt5TuBmYN9ObuV0f3tYvX5MxXR/WOzeau7u9D9lZ3m3nPc2A9caNpQ8YQ6 -CLxjiDk+ZlMvMJPs8B4vVXT/pV/2vho50/ZrHzyXZOG9+fqM/gHglXYje99N -n/+bt84Q6R77NAh8c8OAQc7qXuAX3RK3nfSpwBfXBLJMLkHn22ikys6c/vvv -Nz97ILtL1LEG2LI8wzCkCp1fU+e1JNcCnd/q8Ua4bzE6nz91MD/QuR349W4p -viISOt+rWY6dz7waWNNo3PfiHHT+w7jRC48+9AGL+Ukee65KBhaO20F5Y9cD -XH9abFx9DM1/fzQqxbS76dc+ePr7UbemKuktBfjJq+FDXis7gZVctFe91R8C -fs3v1f61uArY/9n195UhA8AqX8OutBf3A1/qUhpduWAQ+Nm3+Vfbu/qALfWr -0hRNyMBr7VTtveR6gDWu6TqtEaYBH8pzXZ/f0Aic8d58w4ZeKrCg3Jmj6/Y0 -A+85sb70ghXqrc86qzTtbwBueKzGHimB+o7yTUJuY23AOjvWKd7ciV7/xZfl -XROXqn/tg+eS4s4azLLbQAMOK5f5blHUCPy8ueFC8AAVWGp5pkWxfDOw7+yn -EwfsUc+2XF34q3gDcHNQWUDYRtS/pJAX9KxsB653W/XERn0I2PjGZHbbJnQ/ -r7uOSWcoA8AfV2ybKSPVD9y7pdS1anIQ2NOInfvp9PvjN0fXxK6MtUbzJ6Te -Zv541wrcz/R4FWkZmn/w+YyrMsdrgBMr/ZlCq9D5wbNreyaden/tg+eS1r94 -baVjTgae0cl2UUCpB7haQLteW4YGrKL2MUU/qBHYViyLs6KRCrx719iE5+1m -YLYlq2f/vI36vb5GXeL69cDCHBLRQvkU4Jq5ry9v5+sEbn3zSFLVZgjYSUjw -WLFuFXDBhrlBF5QGgCVvV5YaGCAuauH+ZrMZcZdoCwebG2KNwyaZGpP9wMuC -Rq7uaEDerLZr6vVx5DetdvScUzj4ax88l7Rh/OurJEUy8KOnXZTy8B5gI5Yl -lKpvVOCIPNsfEdPv/998Y/Kd6D4zGrCpqeSOTu8GYMPz37pyLFC/Lul1QspY -K7DKhgv7crYMAR8Z5JH++LYa+FpjqOEmK3TfZi2pAzf29QFrHzRnMpGlAN8R -mXPEw6oLWFJ7cTWfPDp/uVRoyqwAdD5tneVxZmV0Pqtj/dnmcHT+uHkLX0Er -+vo07DCYPLu7+9c+ePr9N5SiuIJKAS7Yd7Zq4koH8Ov+J3HhnkPAXUPlP95S -K1E/uzmZ62s/8J1rZ+zYhwaAtw+ZmD5UQX5L0MMuw+n3228e3yxwOn5bL/D5 -iw+HVzhSgTd9Z1/m97YVeP1L957eLeg+Bq7CahH51cC2XDwaU87o/DXm/Qpz -5PqAd1g3q7bqodfbyGf3aef6LmDjuOb2ucfQ+S/kWb4/ba4Cfpza+9Qwe+DX -Pnj6983F+vI8aU3ARgUNvfcsaMBOVvNjW/0agIVqcpsVL1KBmYIaDmhHtgIr -Rq9PTdg+BGy8wHfusmfVwL0bcqrrHAaBr2QlXfbQ6ANu2PLWf+1+CvCcRzLH -j+3uAn5p/vn+bAN0/ubraRuyaquAHwZlB2blodc3UTRxW+J2P/CsovwhHV80 -v8hg9TV5YTT/TEfn+cMX0fxYW+VjRo2dwDsFA1p3ugz92gdPfz3EmhZ3SA4C -q0SbvJtd3QfsfPxkbv0jMvDCa+La+3K7gSlXF2vvfkED9n08aTBZVAfMWiZR -b3eTAmzI1R5CjusE3vmxomx9ILrPxwqLc7GvKoFbi5I9ilr7gef5BUfHCaP7 -/nAfjBMio/veFVh52CUY3bftYfLLxaw9aF5EOnewH7pv3bEbn5qb6oFFz4Qp -bRalAq9dYp6+eG87cElU9n2Oy0O/9sFzSWcPCIodnqoCXugiynH58wDwobYz -u5fu7wceDyoZjGQhA3+6VpixWboXeA/3iytzw6jAjnqkBfc3tgL/KL2/z0QG -zd+h1aC1pK4a+Au3y2PO6EHgbumyzDLWPuDF66bqIp9R0P1luN0aj3cCH3UJ -vFQQjc5fb/XT7rB6JTDPJdXID+7o9QR8iWQXeovmfe5zZtpbgl7PV23Wmoxv -aN7dUd3uW4c7fu2Dp/88TV93vzlKBc404/n43KoNmN1l+fx21yHgVQb9a802 -VQGzUTOsavYNIL85yU/zPOK4s6sOv9qMeA3L1c2hjxF/jx/QK6vtB/Y/JHic -bfrn+W++bjWQppPdB9xyVvOIdiMZOOtQ7ZrDtt3A+oLVLpNTNOAV4TkiPnK1 -wDb3OxTjk1Hv/WFpongt6tMO+5OuZqN+RKBq88r4OuDl1qfMEq7/3hfPJcnx -Kkcuy+wHzg8NszjtNAicU7vk4gfTPmDh2QsNdumgftbXpLL7+7uAuyRIAkPT -39+/mVs72LF0RhWwQW0Ol5L4APDX0z23O9IR34yQKoirQPfRLubaF6KN7lMq -WLFvMh7dJ8KQS8RzJrrPzK5TGe+XdgN/fH5v4X1pdB/1NalvGmnVwC8KVj4X -zkXnB6895eFe2Yu+HmJTFjZzqMAPAlqu6kl0/NoHzyVFjZgvoFzsB95/zHpB -Q/MgMGn98C6BuF7gFcwJx+xIVODv+o9Mixa1A6eSN+zaHT8EzBxx6WvMpkrg -8lmv9q10RfMWibCLzOtA84pkVl8/cwfN654cVyrfg+YZr7xcnNPbBhwrb+IS -EIvm3fMdejtxAM3T25n5xSQSzTsxKyXeOBnNS7MbHy5m6gNu358ttLaeAlwv -0Jpcv7wTmOV2yC7p3KFf++Dp3293zTmfwEQBrht5k7hrVTew2lmx2ctU0PMS -qW63TW9UAx+XpB5kDh4ElpMxEx9W7gPmjz6svPEqOn+M97xAWkUn8NPGhwfE -XqLz72eIJAl4VKDnP+hW+q/sB5bU67pEtiEDpySKNEVa9QA/tHK7b3CGBvz1 -p9e1qNsNwFEsoxKrs6jAXYdec5aeawEWEe18rimF7tPw3fnq4lk1wJV8sYe1 -egZ/7YOnfz9b3u37hKkfWL34NsfdaDKwLptsuBNHDzD7uLDTyVwa8O6pBPsF -mXXAvZ+/LH2VRwF+lHHsorp2J/CGdzPXZNYMAcfe3CTOtPU9cElwmlyudx9w -7dFxh9Td6Lw1l7Sir3p1AX//vixqJASdF3Q7MV0suxI4RWzRYrX5A8D3eK6q -bWJBr3/kYzP/W230+vdY6q30EkGv3/zH8Xperl5gpexR+aO03/viuaR365Uf -hgaTgbnX8/UOSfcAP9ZqUdyVQgPmtYxMYJavB3bxV3sRvgydt+eAAs+hyXZg -zZPFMeeahoBJ+z4I8o2XA9eEORf5WvcBWzScnkw9QwGOtOO2b57+fAvzdrgL -Bb9A57Er7HMoj64Aft/O87pIth/Y8kjEjh2H0esb4PhSyfMEvT5lm1JJqhp6 -fReC5/zc5doIfJI2qnxWFnnVrzTlotrf+/O5JD/+6IKPK8qB5Xvd9nJNf174 -zZyzDbcv+EIBPu1vs1cvpwNYZOEZax7qEHD1g5HIUew8S903L/Hztoa9eMGD -nbekpq5HHzvP4cgHJ/w8mSXqgvh5GmGZLvh5OgtqZ+H3e9+60PwIdl73+kt2 -+HnDR7+a4+d9ln8bhZ+3qdC5Eb9f9JSAAn4/5ZyIs/+cR98HzyV9WHWixyGq -Bzjx2I1FhqdpwFqRFx8/LmgAbpC4HJY+SQU+atLulK7VDGx3+9Mb9tnofJne -Uwe05WqB31vlB3hTyMBFF8znVdp3A5PGT9ZeU0B9o5uC3dySauAaqfADN5oH -gU9WmB3YXNwLbFi509J3N7rfXpWtMzYKtQMrHzi3vbsFnT+iJvLafKgcePIk -U1qvUx9w5CZzxc6zFOAV17sELgn/3l9zkSLdFXepfeoHjvDK3/ZOZxDYvb1j -oqGpD/HAqaTvU2TgJO3bJzn3dQMbWm6nLTIcAtZb6hXIwlMNHJywsSVrPzp/ -s3Tf2jt96PwWQ7WyEho6PyH9m0OTAzp/jNmcaVINnW89mfLxy010vvym+qe2 -mej8V3c3SF3iQefHuAo5rpuiALeliJNLMzqAOdRHlMx+ovNt1oedqxUuA865 -FXJ6DPbX0/efdZGNOWgQuNg+faLMvg+4lj1RXzqQArxj7bLwpxOdwH7njT4/ -HBoC9uk9qM+8rBzY+eOGvHvL0XnKN87VOkyi80I1b42YlHYAh3DlK9DYhoFn -b07jmhVfCpwjPGvqnR66/5Ze0cvRVVRg8zOiOVLqLcBS5NK1oibofrV8Y+XO -P6qAbymN7WbZg16/a4h1tcAUum/gqWydnfVkYF3HDXZ2j7t/7YO5SKmHed1F -63uBz3w1P1qpRQV+LJgm5zHVBux9LpTl+9gQ8Kd7s+ry08uQL6XufvQBnZe+ -6Zi5rww6b7TMjSsxrB34+tfMwhuzh4E1g4XaUsmlwJuOxPCJX0bn9e27vpv6 -CJ3nHK19SXRRK3BHUSb34lh0v8AI2ufWS5XA8yqaWNzmDABr7T40JqkyCNyl -QSlawdYPLKuTJfG8jAw8TjknWFHa/WsfzEU6brr/UXtpL7Cio47YewsqsHOn -lfbx0DbgFcnZhT2jQ8BrHnVdkSOXAT8tmOgamt8HzN+3+HISLzpPWSTFakCu -A51X23zzzLJh4LVLnTjWdZQAizmI3U3+1gPcf37nYCuJBrxKy3be08FG4Kqx -gcdL7iMf4SiUe+pePfBj9dFTxf7oPkea7T229LYCL5sVyz1Wh17f/dLVDiEn -3gMr+fyImlvZ92sf/M/71Xpi9E4/8LkLWUsnZ5KBTxw5pv7+di/wYxs3/sBE -KnB1rzWXNqkVOOpc4pUZWUPAZhyveJVvVQALqxgt9TmN5s2zrblTp4bm6ah5 -rMic6gF2Hlvd6LKHBhx77+cl3axG4FrR8AD9O8gHm6nnCjbVAwv5aojapqL7 -lkUF3DZbhu776OXdFY7p6L7r9zhnmjBVAh9Q7MqhxKL7qkSlu26b/L1Pnr7P -ibjY1RLDwJaxgZ/7nxUDr/pcy2p+ogfY553uTtdGGnDisTTlXKc64HKB/mNP -hyjA9QcP39Th6wQWkPnsWIvN411z725cEprnmXjKfdNxNO8Ms8WC+FY0z97F -7NL542heqtrLh7Q2NC80Qayqfxc2TyNlLZM4mjcxI27bzzw0L+f9VUuaJZpn -OR4edb8KzZNOt36zORbN6xliado55/c+fHr+nGgumS4asO7s8iPf9tQBK2qm -Ll/RTAEe9fBqENfqBDaSF1LdsH0YuKeVvOHdgWLgehdd3QfiPcBP3EXYPrMO -AbNfKy55olMLrOAWN9NwG5p3ufDJcYPeLmBRGUE/0SrUK0nL3x7Lfg+cUzqj -2XRhP7B7j1JKagcZeJN66I/dL7uBo9ZuF1x6DJ13fra09PCeauAOq4O7RZ8M -An9PG7xTePD3/puLZHF/0Y1XAzRg7XXXVc+I1AEvrFrh4/SeAhySrBcc7NQJ -XP3CR2WBwjDwA72jrXu+FwGfKnn5JHpOD3C5+YsfL8SHgDcHh4veMawB3qM9 -yywghAy87vy6q1r2qD9aut9lfQe67+3QRPfkY+i++30PZN79gO4rKxJrqiiI -7uui9pK0eje6707nTYftk9B9zQ2tT2xv7EavX60rOv4guq/zxCBpzrXf++Xp -74+ZggXmxjXAc8oG1vhHkIG7R10NZU70AH+3tKZNjtGAo829v+xtqgVe/Hpy -6Mg9CvLp9mdiKJ3AUdbB1+y3DgOHyeWN8bgUA79//sUhRRvNMy6+dTx3xhCw -X15e+4wwNI9k1lrE7YTmXeX4dG+/XhewvyrL2+xlaB5Ta4jIbdZS4JC7utYG -Ur3AL8OPmQ5uQ69vldojHgPZJuDEZVYrn335vU+enn9Ubq/myRpg4b2bqbzx -ZGDxK1Ns+vt6gFXdhHb7zRsCfiBwa0uEYi2wveuHpIUqFHT+lJ9LQkMXcFab -1g/eMdSrU4QOjLCUA3vvfbbz4N4+YEkRxTtSbFTgapk9TIvrOoB1e6n6o/rD -wP7DZx7bx74DfrbJWL1+dzdwFbekBektmv/RlqSV2lABTN7Im/sptR94f9OA -sCoH+npYvNW91fLw936Zi5SdO7frEPMA8AVr3sxbgYPA38YPazml9wHTOpk4 -d3tTgJ+Vzg1YJd8FvHfiYdw6mWFgfv5G6bd3ioGrNJ3GvR17gK9xHV9bN0ED -vqGk8DWuohb4J2fg99FHaN7okqYnaY2dwFeC9QSj9qN5X8LXPnmpVAT8OEbm -jsujbuA1bjnzy68MAZvpJutKbK0CZvWXPL+Igr4e3jOvZMl86QfWHzuQwxw3 -+GsfPP3zfs8rMatPXcAVTxp7i6eGgMfOpS7Re1YGzJv1/EiQaB9wdKSinYo8 -Fbj5uacFa1k7cCgfq2OM6TDwzeur+X9ufAecskZCrn9uN3BhwDbqphE0P/bw -I48a/XLgG7PzBcK90Hxp+aZR10oKcGcoNe+ebydwl31exVczND/+kKY2jRPN -/7DJxMZ8Er3+W88f2nlPoPnqsep82R3o9d/N3KuirPx7Pzz956nOs3f7/F7g -yfrCrihPGvCNhnW3xJMagNX4MvwnLJC/xbz9wmmlRuAddinxRWnIq2pEkNmu -1gOHOdzfLlNLBeZpanv75V4LMJvJimXzKEPAzRvuKfWklwN7Zig4BrxC91c7 -ruGyNYQCXCe5t0tJrAvYYfsVgeXT35/AN6u8OfWLgHXV2uwairqBQ7a8dA0I -QvOZeyOU50tUAbtKT0iVfv69355+f6UXdw1uGwKe/D6864hWDXC+/X7Jza/J -wJknKAWJW3uAs8t+Dpuroj6G9bHG0/Fq4Frp6oyps6jv3DhKPdiE+sgOrujv -2TTgi6tkPU4q1AOrFP3QjXhCBT6uFln8waEVeLCpy01rzTAwU+1y3pz4EuBQ -41K19lW9wGfy73eMuqJ5ZGYZJ2pzA3DCx5PcY/7IB3FpTO7zwXzQ49WBRr/3 -49OfFzz3nuVcMgx8sUo5Qt62FPic2JyCF6G9wKEBH5a2c6CeLeJ0hua5ZmBh -I8dtnA+GgNfl6XFN3a8EDra7Ij3oNQCcxTcinl+O2NNGb4WaGuLJ0+bJm2UG -gW0oam8fu/cDU3JcLQQ9ycBGnW8KpXJ7gF+xuw7FdqD7uqr5aRoH1gEfyu8t -OqVBBT49ILJ8MqodeK0DU2etO/r6jJhJ530pK/i1D+YiTX1ZyexpMwzsYZy1 -aHl6IbDR+Y4sxbYu4BELV1Z5MfT8Nd3TzgclS4CHsy0lmIZ6gCWPunN+z6EB -FzuZNcqr1QMrBaQyaRdRgTfMOHirf1Yr8IH398/18qN5DodGClYzlQKv3K7n -wm/UC7xNrazwhSaaxxnufnh0qhH4ntul584CQ8CBeQ8fa36rAX6mebAwVpUC -HLz+oKr7GHr982y7Fm8QGv61D+YiSYjYCS1e2wl8R8LGSuQe8veXCWrETuUB -3/iZeEoUe765tzloHfb8+6oU6xTs+Ur222ZbsOeX7atSxp835D9gnYo93650 -j20b9vyOz5mb8Oc9lw1mpWHPs94cHsCf7/5StAZ/3uerothT7Hm7SAXx7djz -P2euX40/bxv64xD+fHO87R78edtkdcF/nqfvg6d/X3/QGcb/oAM4g2ONo2AK -8heOtZlvcMoDFgwiPi/N8Pw9E+LzSWHE580Ynu8xIj4/4wbxeS2G54eNic+b -3CQ+f5Tx/gzPv2c4X4/h+XiG52cznK//63n6PpiLpJHsefTa9g7gSt75N7Of -It+/SyL98Ko8YAGPrcvld6DnXfI0dGqx5w+IS/co8KPnuUtuv3qHnf/W8hNn -HvY8t35yhzR2frvMJ6n52PlDdyTFqrHnu/bEKxti59flfL43gp2/82r1SD72 -fPr0W2w5dr6nxlc1mix6viW03rcSe15lFUuwE3b+OVrz93nY89FLTU4UTj9P -3wdP//3xyszENxdxjDKP1mntXGAl7eaxdIl24JdLVnuHJaDn/ezifFem5wFv -Jj9yipzTCay334RwvnieIuH85ia+L/j5a/euJ5z/9rM84XyFk5aE83tLiecb -UGQJ5xudXUA4v1VFhHC+9h5Nwvk3hx0I59tlEs/v6drx7/n0fTAXyXG3gvy5 -4hzgto1iHMbn24AvxuqaTUYMAz+Iv2By1jUfeJxaUN4f3Am86FuWOXceej5F -b+eKoUNonipH4Jtn29uBdZs+nX/4DD2vGfjko8r098tvrj6c/XlifwewtWqS -uWQxep5T16cyYwrdf79509Gzuej+UsEu4WsfoOdT1QVLtg6h80+Z5R26Ko7u -XxDjLhdXip6vHJAypjSh809bvk3Zeu33vz/nIuXsft7MGtQJ7O30nHalfBjY -qj9V53V+DvDLCtm60Iuo35+wrPTeA/T8sjt5sh9pecBbH4zx5m1B599QTPsa -U4een3P4MWnfAXS+6gW+dUvaWoHT37AWSVxBz7/zyrf4YV0AnHtdsuK2RBdw -fLLok/JE9PyYm1HkyjR0H+rl1Q+j5qH7uI5INNHq0fMKdxbEFsih+ziHfhqc -mYfu863qaeNm7+Ff+2Au0pZFQokcYsXAzCdjA/W8eoDTLoQIOBsPAc90uO+h -7V8NbH21TyT9FBmYe5tM/QfRXuAEZr6N7fk0YKpwn9grq3rgsjXOCk4rkGdZ -8/h9ql4zcL62Z3M7Bc3X/HzzSNW898B3ZDx2akj0AxvF0G7ckqcAm37jooxK -dwOr7vbP0FdDr19m+ZImiaki4EVaFbGeZuj1n1QS9jU5j+bv3OBvUzJY9Wsf -zEVq2nGA7HqvC7iv+/h2t1vDwLrBxhazcvOBHc77ao6XdwLnVp4UutSAni98 -/bCZopAD/OUan0BAcyvwouq+kp9R6PlL/fmu20+i87eeNVYtD0Hnpy254HOh -Cz1fI2f6zistGzhfZ6PWKBc6X+6sd5iVPXreMlc5WaGkENiFP8vvLm838Fv5 -C0JrTqDnL9c9NJ2f8g5Y9NFZddk49Hzz0fePBBYM/9oHT//+oFLjHOKBuEV7 -qdG97wXAO8VUwqhRXcCbxot5re+j5xcZTPouW5UPvMDEwZJm3gksXOSwPngE -PT9hllB9+E0WcLu15beI/mbg70pLay/9nybuPBrq//sDeIpS0pCEEqlUCokW -yjJZSgsfKSUpKgkVikhpsUTSqkWRPbIksmTLkn3fl+zGPsPMpCJLy885vzxf -3z8f597Xvfc1xxze5543aZJv6Xoos3L6eWzGK3TWRW463wuPuMQLa70ahrOC -9jSLejbBVxXruzaXkrhH8Hmud0aN8CNNn9mBkiS+3L0tz2AnmWf3Zfp/O38w -4Tcuuer3wiv+7YMpVHmtnfnv5QbgNanb0wwzB2HBPOUQ2Zw+OOe5DaXqDwNe -a9u7Rdq4C17fLLxtaooFO3T7eWQ4Z8Edk3YfLThbYCWOYLtXDCZ80Sp1wnRz -JWyuabrF91g/3BswqM8pRvqzp4rOd/l1w49P5oeHypD+o0/0jkqElMJJnFSW -lHUvfPybTpFX0DDc9+16v59FEzy7/uTa0TwS53Ad2RZzt/HfPphC/X1irup+ -2Rr4vbNsouDpQVguZG5eo3s/bOpRZyzVQ4f9Dp+8VbSpBzbzfcm/oIoJH5SV -LRiJrYJtmjK548QHYFrCf9e5eki/O7TLws0OfWQeLw+Ty+eH4OSSgfeh9h3w -2ZQx+YyfLLgtmX+59uxsWKj559GLNi3wX54bc0ZESH5SF0NtQWoZfHHearPn -fKS/7NvCh7NYpP/AQ/od8yet//bBFGpCineo8vYc2Iw332ibK4mbqRrmZjqy -YLuovIaamEJ4xGgy775YN+z0zfwD7S7J77pxvd4ivQC2XqkuYXmHBgspWH5+ -XE7yFwnNWaoy9pnUCy6wjf7TDrft6+9SHiX5Xp+z+6YOZ8PlHD9u0JNaSP7m -4PMFO0j+Ba/RVJffJfBrB1PrxWK9MK94q+5jLiZc56CzMf9XPUxZ46K11nxm -fzzdf+2n3yaibLj541BgW386HHXtCkeMZRNcaTwSwUkbhuuueY1U0RvgUgGB -79LzSPwMW0dqjK8V5oiu3HT0FAvW/KKS58osIv0N91VcHeqGTxd6B1kKkvyX -XFMPznKXw0Eit4747uuDD/3mlD+XQu7noG+mda29De7+0uykUUvqacn8Vloa -/Rk+L7nRJjKgHba3NdG+9Y3kb+mIm5gdl/1vHzz9fXJgL7Jo64OFA1vFX0wy -4LQrVZKCN7rgDyfqz9yRYMOyG3wo0obpcI62TNGhOU3w4f4/nqWJw3Bezbrv -MQtI3E0xT7kihcQfGZ61aRlphJ8XL3kqH03iXXx9VIYWOX+88DVfXBOJc4Sb -XLy6kZzv5P/6TU6RxPlXnzC4N94M63n7i5TysuCGas8M3mvlcEePJ7flI/L5 -XM5iFAedHfq3D6ZQfZ6N598PZcBebtsbz1nRSHzip/m7Hyx4TqZpjqV7Nmz+ -tmy9wrcWOG9Q6tf4eZKf43pMZeJcEWxNkeDuDO+GDYQO3LQ1JPmaUdWag07F -sNHjC148Oj1wEZ0uptzJhIOjPDcr/K6ExxNFJ1X6+2EFn7O+3OZ0uH6PjcRW -m17YUW3EKK5iGK7LG6lUv9QIZ3t4LfpgReKC7gdKqmtm3i+nUGO8hRyeTrLg -kns/lTS6s2Cd2qsvDru1wHMj5Yp09Ek+5YZ3T1lTMbxgxaLOVO8e+OvfyvqY -JCZ8Wrhi8cbQatgmylJdY/4g3BC3c+WP4wNwSomC1YMQEn/mp7Nt69p++GDK -s33rghlwfOKD7CMONNg0Ns7uzf/cr9mIoqffRe7HO2Ls2utC7rfw8jbn2oMk -/0XG3GeeHeR+UVrdS7IezeyjKdSNP6zbn14gbn/0NZT1hQmzanm7meZVsL2d -g6XahgH41N6Yh40cdDjLM+PtjxN9sOZvM9Ho3CG4dKDkfltuG1wlrD0rYpQF -m2RLr/B1zob/7LliIY731SnUJ+zgDf5uJP9U3UGjZVKFcLYz5bQpnQavS7Zz -Mmkg+a8Wx67SevYZVi1VYKaHt8OWJdu/nJ3+fTDjoMnkdS/nZ8CiIhFc2mEz -/7+cQn13de6BTaGDcHJL/i0zhX44wuYWLS6AAe9NdVCXv0uDz+a+bbHgZsPF -klvypEwz4YUBRTX5ds3wht9ybxVns0j9lS+sjFQr4GMTAZ9UBEl/xTnKw39L -Sf82WZU2V37S/8y1HZs2ypL+UbWmy57PSYNjGTzUZUKN8BhXAO9vvWE4sdlq -b+UdMp914BtZi/lkvpfmVaYZreWwNM9EvWfXzH56un8X/UtuaiJ85cKbQ4GN -NfD5lyJ+9dvp8C/u1xPm33vhiMMR0u7Hh+F9D8dUXHWb4eYOJePhX0y41r1I -5uXjCjhULF51nnY/nM3pMt7gwYAvnysvEy2hwVvTnxhLj7NglzO0gLV7smGz -gE81GoMtsMnkza7axyS//m5ah9b1AlJ/Ule9wZ3UNzr0madagA23Jr5r1Bb5 -BHN+O64S4zbzfjmFGmLO239xPRseNUyQKc9Kg6VHf1XWpTbCoWkqRZG5w/Dw -xL3Yna0kPmv/PDnhRhJ/2qK/Rv4UiSuF2jp2PSJxwcElRvFLyTwFfGw2/3Um -XBeku1NCsRZOGF3kEfCUDq/J0l72dm0vvHX+HZnje8l5q016r57crIN/OonY -Z/ox4Ail8qTD/jT4xmK5KgNB8nmk/dS8az6aAWv43lGUtp15f3z67wePP7ui -Rvvhq5XqwpU36HBpbkrkAdNeuCRcz85rKROudnK0k6ysh3dcy3D09x2C54Sd -SLjV2Q6feLOKtUSHDYvtd5o6fDMZzpoz3rnOsA5+G7AlKfMOA9aVXVH4sIkG -r0wstx7jIvWeBQbLKhdkkvPHP/4Sam4m9j89JrWHBVv1CcRzBZTAftYB9yQl -yH3HOgWCXAzJfbmvpvDWStT92wdTqPfnL7pu35UAK426h55WqIEPnAiT3pI9 -CDMrNOrOLe6HNdSlF+35xoDLXnfvasjqgj3SU4TPWLLhzp16H8RlST9/6XPp -hgHVsNpf9TmTCqSf+LK+ja+2DMALGJ6114TpMK1LQMhTtw9+oXfCwYhzGP7s -q2tYeakVNs9tCX/UxILN4msilj35DG++9E45s6YdDvn69aC9AZm/6knXQw6v -pH/7YAq1oiM3Q92kBzaT8ghJFGPB8iq8Gq97ymAxYy1ONec+OOAEZ1hK9RC8 -1kNpdUFUG/zecKPJKRk2zLVb8SuPZhoc7VvhoWLdCGffrHDzSByG072W+1zX -a4KH7ffpv5Vnws/53YoSJevhRcnlfUvkyTzzxqwKDZZ2wVeVrQ7Q3Mk8ogYa -0fVtsaReHfXMaAK57y77sbxVp8h9d4ZLlUz9mNkXT3+/Vvd0S91kwuU3jp3T -31kLz/ZvsItPocN3D9wWWDXUA2+5rLa5IJqcf3vv8yd/vhqYeaa+xTpuEPY5 -cUwjUr0fzpc59OdyOgOOEhfKHzhJg7uiLScph9mw+PWkV1dykmDzGK07CZVk -Xr847SNr5f+nXoP281tZ3fDUCN0kKYQFK1Up3tsfkw+L2Jcz2oRI/6CPZ0++ -sST9Fxdu3qEgn/BvH0yhMsR+hLdxdMAf3iek77jGhle/8Y4WV42Hww4nZqvw -VMLlE8KpZkn98B6ZZJYILwO2qDxiJi3RA0tuff9exIwFm1uGeZasKYZ7Jr3v -aRiSfCuRyE+LFUn+SEHpf2k+pbB11Y2TS8p64S8Labk+ecMw58nq1VmTjbD9 -V++8wqVMWOSuxoqkgXrYbO8TjVUVQ/DJp6ut99a0wfu0F155sZf9bx88/ffn -epn7GdwD8HILPXUDDzq8m112zPZiL5w21rThNd4fp1ADDT7ETAjXw6XvNBpU -NYZgg8CmgKzhTvhN46XnZWGkv/+zEj0erwi44+jAsiU6BfCkpH+240MaXCBS -r7bpKDm/UtXyu5pNEqycvE3Rw7cW/sX/nK9CkAHPl7D2S+XvIfOdHb9R4sSC -r7/tvC/2sxBWszn3jTu0G75qMn7vVvHMvnj6+SjZuTSquAm2/ECXs/VlwkGi -8x+9CauBTV+d80o7QIedhOv+qk32wuOxu3/LBAzDk7Uh0SWTpP7U6P72gHhS -f3D55kOhE9Ww8YtVcRsSBuEdD9eMXdLvh30a64W6MxhwoZKeHscFGvyDrho2 -z5oNl573vM3O/AA/lfii2mNI+tE6bwf4iZB+YX7ewvcfDcAmZmluy/xJfGHr -I7M6t5n3u6e//1mrTk/19cEfzRfOy7UYgnsaRQ5GyHbC6zim9nEmsuFdrYXV -Q32hMNfLxPnPF+TCf125QwvSOuDSKj+1SzHkvICrMuXnpzewUTN/wPG0PDhy -V/OhQa8ueMxK3HJFHDnvvSQrJe5LGLydW+/UHDrpL29lXGP7ncwfJ/qOWyeV -nOdcP/dW0esQWLlb+O/z1hxYXc+Kt42zHV6tPBLXfIn9bx88PV92fNKx2H7Y -N/tI/qMdDHhv2Vof36JuuCvRPHpDBQs2T4qQmKOfC/O7bLikINUJMw0tjo5/ -Iv0mCrV6+m8Gw6dCdN3M4rPhpG1FPd0PW2GpSj6dAUlyfkWkv5zBkXSYp6r9 -wEG7JvhAy1J1uZtMeO3hsccZhrXwFo6P+Rcm6bBOnEutqUUPfNes9mTWQXK/ -pPA4z8C9JfBuze+XPq3u/bcPplBbDgp9EX9YCddbH9kXs2IALl2y2eepKx2e -ffqdYP5jcv5CoIDm+FYmXGmdJp6nUg9ffhiQ/8RlCM74KhDlmdwBZ7k90HmQ -zYadlYwG9xcEkfreO3Yn+GbB2zWrDT7kt8B7NvwK2/KdBY+8iJF7JZkDXxW7 -W76epw3OK/nleFyP9HvA0Hrw/lgybPbMMevu5Tp4k+PyhlWDDFiCxnD8yjWz -b6ZQ90fOdta0rYZdrjk+tP9vEDZdY1coTB2A9cPj3Xfr0GHjvaGyIkv6iO80 -x34JGYYvXtDmcf7VBCeKNTk3NzHhRZqvw2izSf9ZiRdMJHtJPyPVHgkDYTJP -upI2v088iWukzL2zx5nERVstiq5098PmYh6OvSNk3h8T9dLz7/XAXMdOx23T -ZsHv1ZnJnrQS+G3txFk77164Nj9xvrnWzD54+udfyXSz+A5/2OVV4Zdj59Lh -hq/6Gxx8m+C/buE7y2PJ+aHBID/t9TWw/ewd4/ZcdPgBX3BfTlYf3OYls567 -YAjeHn1gsaJ6O8xxLb3rdDgbTlwndzr4YATM6q3159csgIdf5wc9iabBopEC -LXl3yXnnZOUT+RqxsNn4mtX8N8pgBadX9GUuZL7gQX6Ns8uHYdtWY65Qaits -WDPV/mb6eeD/98HTn0/yI3U7uWE4/Nm5ZzUlLfAeobGvBYtJfk1gQMDf1E/w -mupuwXibZjjCs28o9SkLlm4Mqj2aWACvi7kgMDVBgztSWYvqrEl9HoviOFrR -B7gy1Kd4lUs1PMd4eO0Fm0GY77vJBt2FA/Bk4+2c7jQ6/PJbnNCEeC+sI+ab -ZFHOhAtdBX0XGJP6R8x9L5/fT+q3rpFStThK6quE8d1arTDz/vf077PDzqZ8 -6TT4l/05jysv2HBJgtH0E2k0bLzL2WleVDHJv/T+pnl3DyxyzJvXC/t5CvXg -0/ZXt3vL4fc2CyuKjvbDurMko9hsBrwk8qLsy7lkHrflFi0S9WSeHwGZi+eW -PocLlZZPuRxIhsNfHl0XeLsOzhFy/V4hOAQf6pTgvx7YBffec/zpSif1xx1j -XXnNPeCGlfq61JURsHCYuXvCmoJ/+2A+6lbj5JWxkkzVGQ9uUXvmI8mLeAHP -+jPrJWXgFIfu6FurdeD/UuS820UvwiGZfuKnZj+AG2xzOja9egcnlahXUGeV -wXyVXg6Sun1wT9XraoPrw2Q+C/ftq3ib4eidhs/SbrDg+mIn18lZRbBjVoxT -cEc3TDfadsF5nORPZQy1ytOyYZvR7bbdg61wzB87+rrp568Z/w1995T7Sjzs -7pM9y6y8Uu3/ALJUdMY= - "]]}, {}}, {}}, - AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], - Axes->{True, True}, - AxesLabel->{ - FormBox["\"r\"", TraditionalForm], - FormBox["\"long-term\"", TraditionalForm]}, - AxesOrigin->{0.958203125, 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->{"CoordinatesToolOptions" -> {"DisplayFunction" -> ({ - (Part[{{Identity, Identity}, {Identity, Identity}}, 1, 2][#]& )[ - Part[#, 1]], - (Part[{{Identity, Identity}, {Identity, Identity}}, 2, 2][#]& )[ - Part[#, 2]]}& ), "CopiedValueFunction" -> ({ - (Part[{{Identity, Identity}, {Identity, Identity}}, 1, 2][#]& )[ - Part[#, 1]], - (Part[{{Identity, Identity}, {Identity, Identity}}, 2, 2][#]& )[ - Part[#, 2]]}& )}}, - PlotLabel->FormBox["\"discrete\"", TraditionalForm], - PlotRange->{{1.005, 4.}, {0, 1}}, - PlotRangeClipping->True, - PlotRangePadding->{{ - Scaled[0.02], - Scaled[0.02]}, {0, 0}}, - Ticks->{Automatic, Automatic}]} - }, - GridBoxAlignment->{ - "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, - "RowsIndexed" -> {}}, - GridBoxSpacings->{"Columns" -> { - Offset[0.27999999999999997`], { - Offset[2.0999999999999996`]}, - Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { - Offset[0.2], { - Offset[0.4]}, - Offset[0.2]}, "RowsIndexed" -> {}}], - Function[BoxForm`e$, - TableForm[BoxForm`e$]]]], "Output", - CellChangeTimes->{ - 3.777165731941354*^9, 3.7771657820785303`*^9, {3.7771658378010435`*^9, - 3.7771658501008472`*^9}, {3.777165934060048*^9, 3.7771659669945774`*^9}, - 3.777166070392551*^9, 3.7771673335171857`*^9}] -}, {2}]], - -Cell[TextData[{ - "The following two Manipulate environments are interactive versions of the \ -above observations. The first shows the continuous model\[CloseCurlyQuote]s \ -time series alongside its long-term solutions, both as ", - Cell[BoxData[ - FormBox["r", TraditionalForm]], - FormatType->"TraditionalForm"], - " changes, and the second shows the same for the discrete model. For the \ -discrete model, observe how the long-term series begins to split just as the \ -time series begins to experience undamped oscillation." -}], "Text", - CellChangeTimes->{{3.7771675269872046`*^9, 3.777167533399252*^9}, { - 3.7771676214465485`*^9, 3.777167728826147*^9}}], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"Manipulate", "[", - RowBox[{ - RowBox[{"TableForm", "[", - RowBox[{"{", - RowBox[{"{", - RowBox[{ - RowBox[{"Plot", "[", - RowBox[{ - RowBox[{"Evaluate", "[", - RowBox[{ - FractionBox[ - RowBox[{ - SuperscriptBox["E", - RowBox[{"L", " ", "r", " ", "t"}]], "L", " ", "0.4"}], - RowBox[{"L", "+", - RowBox[{ - RowBox[{"(", - RowBox[{ - SuperscriptBox["E", - RowBox[{"L", " ", "r", " ", "t"}]], "-", "1"}], ")"}], - "0.4"}]}]], "/.", - RowBox[{"L", "\[Rule]", - FractionBox[ - RowBox[{"r", "-", "1"}], "r"]}]}], "]"}], ",", - RowBox[{"{", - RowBox[{"t", ",", "0.001", ",", "30"}], "}"}], ",", - RowBox[{"PlotRange", "\[Rule]", - RowBox[{"{", - RowBox[{"0", ",", "1"}], "}"}]}], ",", - RowBox[{"PlotLabel", "\[Rule]", "\"\\""}], ",", - RowBox[{"AxesLabel", "\[Rule]", - RowBox[{"{", - RowBox[{"\"\\"", ",", "\"\\""}], "}"}]}]}], "]"}], ",", - RowBox[{"Plot", "[", - RowBox[{ - FractionBox[ - RowBox[{"rr", "-", "1"}], "rr"], ",", - RowBox[{"{", - RowBox[{"rr", ",", "1.0005", ",", "r"}], "}"}], ",", - RowBox[{"PlotRange", "\[Rule]", - RowBox[{"{", - RowBox[{ - RowBox[{"{", - RowBox[{"1", ",", "4"}], "}"}], ",", - RowBox[{"{", - RowBox[{"0", ",", "1"}], "}"}]}], "}"}]}], ",", - RowBox[{"PlotLabel", "\[Rule]", "\"\\""}], ",", - RowBox[{"AxesLabel", "\[Rule]", - RowBox[{"{", - RowBox[{"\"\\"", ",", "\"\\""}], "}"}]}]}], - "]"}]}], "}"}], "}"}], "]"}], ",", - RowBox[{"{", - RowBox[{ - RowBox[{"{", - RowBox[{"r", ",", "1.2"}], "}"}], ",", "1.005", ",", "4", ",", - "0.005"}], "}"}]}], "]"}]], "Input", - CellChangeTimes->{{3.777163681244874*^9, 3.7771638468583126`*^9}, { - 3.777163957467636*^9, 3.77716398467824*^9}, {3.7771640761216917`*^9, - 3.7771642136305895`*^9}, {3.7771645056535025`*^9, 3.777164556673809*^9}, { - 3.7771646075070252`*^9, 3.777164730339535*^9}, {3.7771649500323143`*^9, - 3.7771649653355174`*^9}, {3.7771659821597023`*^9, 3.7771659959476337`*^9}, { - 3.7771660854460907`*^9, 3.7771661285863004`*^9}, {3.777166160232567*^9, - 3.7771662350691833`*^9}, {3.7771673403857517`*^9, 3.7771673415618715`*^9}, { - 3.777167559817835*^9, 3.7771676101671667`*^9}}], - -Cell[BoxData[ - TagBox[ - StyleBox[ - DynamicModuleBox[{$CellContext`r$$ = 3.305, Typeset`show$$ = True, - Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", - Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = - "\"untitled\"", Typeset`specs$$ = {{{ - Hold[$CellContext`r$$], 1.2}, 1.005, 4, 0.005}}, Typeset`size$$ = { - 387., {70., 76.}}, Typeset`update$$ = 0, Typeset`initDone$$, - Typeset`skipInitDone$$ = True, $CellContext`r$140633$$ = 0}, - DynamicBox[Manipulate`ManipulateBoxes[ - 1, StandardForm, "Variables" :> {$CellContext`r$$ = 1.2}, - "ControllerVariables" :> { - Hold[$CellContext`r$$, $CellContext`r$140633$$, 0]}, - "OtherVariables" :> { - Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, - Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, - Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, - Typeset`skipInitDone$$}, "Body" :> TableForm[{{ - Plot[ - Evaluate[ - ReplaceAll[ - E^($CellContext`L $CellContext`r$$ $CellContext`t) $CellContext`L - 0.4/($CellContext`L + ( - E^($CellContext`L $CellContext`r$$ $CellContext`t) - 1) - 0.4), $CellContext`L -> ($CellContext`r$$ - - 1)/$CellContext`r$$]], {$CellContext`t, 0.001, 30}, - PlotRange -> {0, 1}, PlotLabel -> "continuous", - AxesLabel -> {"t", "x(t)"}], - - Plot[($CellContext`rr - 1)/$CellContext`rr, {$CellContext`rr, - 1.0005, $CellContext`r$$}, PlotRange -> {{1, 4}, {0, 1}}, - PlotLabel -> "continuous", AxesLabel -> {"r", "long-term"}]}}], - "Specifications" :> {{{$CellContext`r$$, 1.2}, 1.005, 4, 0.005}}, - "Options" :> {}, "DefaultOptions" :> {}], - ImageSizeCache->{438., {117., 123.}}, - SingleEvaluation->True], - Deinitialization:>None, - DynamicModuleValues:>{}, - SynchronousInitialization->True, - UndoTrackedVariables:>{Typeset`show$$, Typeset`bookmarkMode$$}, - UnsavedVariables:>{Typeset`initDone$$}, - UntrackedVariables:>{Typeset`size$$}], "Manipulate", - Deployed->True, - StripOnInput->False], - Manipulate`InterpretManipulate[1]]], "Output", - CellChangeTimes->{{3.777167574221195*^9, 3.777167610995882*^9}}] -}, {2}]], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"Manipulate", "[", - RowBox[{ - RowBox[{"TableForm", "[", - RowBox[{"{", - RowBox[{"{", - RowBox[{ - RowBox[{"ListPlot", "[", - RowBox[{ - RowBox[{"RecurrenceTable", "[", - RowBox[{ - RowBox[{"{", - RowBox[{ - RowBox[{ - RowBox[{"x", "[", - RowBox[{"n", "+", "1"}], "]"}], "\[Equal]", - RowBox[{"r", " ", - RowBox[{"x", "[", "n", "]"}], - RowBox[{"(", - RowBox[{"1", "-", - RowBox[{"x", "[", "n", "]"}]}], ")"}]}]}], ",", - RowBox[{ - RowBox[{"x", "[", "0", "]"}], "\[Equal]", "0.4"}]}], "}"}], ",", - "x", ",", - RowBox[{"{", - RowBox[{"n", ",", "0", ",", "30"}], "}"}]}], "]"}], ",", - RowBox[{"Joined", "\[Rule]", "True"}], ",", - RowBox[{"Mesh", "\[Rule]", "Full"}], ",", - RowBox[{"PlotRange", "\[Rule]", - RowBox[{"{", - RowBox[{"0", ",", "1"}], "}"}]}], ",", - RowBox[{"PlotLabel", "\[Rule]", "\"\\""}], ",", - RowBox[{"AxesLabel", "\[Rule]", - RowBox[{"{", - RowBox[{"\"\\"", ",", "\"\\""}], "}"}]}]}], "]"}], ",", - RowBox[{"ListPlot", "[", - RowBox[{ - RowBox[{"dlmplot", "[", - RowBox[{"[", - RowBox[{"1", ";;", - RowBox[{"20", - RowBox[{"(", - RowBox[{ - RowBox[{"Round", "[", - FractionBox[ - RowBox[{"r", "-", "1.005"}], "0.005"], "]"}], "+", "1"}], - ")"}]}]}], "]"}], "]"}], ",", - RowBox[{"PlotRange", "\[Rule]", - RowBox[{"{", - RowBox[{ - RowBox[{"{", - RowBox[{"1", ",", "4"}], "}"}], ",", - RowBox[{"{", - RowBox[{"0", ",", "1"}], "}"}]}], "}"}]}], ",", - RowBox[{"PlotLabel", "\[Rule]", "\"\\""}], ",", - RowBox[{"AxesLabel", "\[Rule]", - RowBox[{"{", - RowBox[{"\"\\"", ",", "\"\\""}], "}"}]}]}], - "]"}]}], "}"}], "}"}], "]"}], ",", - RowBox[{"{", - RowBox[{ - RowBox[{"{", - RowBox[{"r", ",", "1.2"}], "}"}], ",", "1.005", ",", "4", ",", - "0.005"}], "}"}]}], "]"}]], "Input", - CellChangeTimes->{{3.777163681244874*^9, 3.7771638468583126`*^9}, { - 3.777163957467636*^9, 3.77716398467824*^9}, {3.7771640761216917`*^9, - 3.7771642136305895`*^9}, {3.7771645056535025`*^9, 3.777164556673809*^9}, { - 3.7771646075070252`*^9, 3.777164730339535*^9}, {3.7771649500323143`*^9, - 3.7771649653355174`*^9}, {3.7771659821597023`*^9, 3.7771659959476337`*^9}, { - 3.7771660854460907`*^9, 3.7771661285863004`*^9}, {3.777166160232567*^9, - 3.7771662350691833`*^9}, {3.7771673403857517`*^9, 3.7771673415618715`*^9}}], - -Cell[BoxData[ - TagBox[ - StyleBox[ - DynamicModuleBox[{$CellContext`r$$ = 3.175, Typeset`show$$ = True, - Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", - Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = - "\"untitled\"", Typeset`specs$$ = {{{ - Hold[$CellContext`r$$], 1.2}, 1.005, 4, 0.005}}, Typeset`size$$ = { - 387., {70., 76.}}, Typeset`update$$ = 0, Typeset`initDone$$, - Typeset`skipInitDone$$ = True, $CellContext`r$137964$$ = 0}, - DynamicBox[Manipulate`ManipulateBoxes[ - 1, StandardForm, "Variables" :> {$CellContext`r$$ = 1.2}, - "ControllerVariables" :> { - Hold[$CellContext`r$$, $CellContext`r$137964$$, 0]}, - "OtherVariables" :> { - Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, - Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, - Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, - Typeset`skipInitDone$$}, "Body" :> TableForm[{{ - ListPlot[ - - RecurrenceTable[{$CellContext`x[$CellContext`n + - 1] == $CellContext`r$$ $CellContext`x[$CellContext`n] ( - 1 - $CellContext`x[$CellContext`n]), $CellContext`x[0] == - 0.4}, $CellContext`x, {$CellContext`n, 0, 30}], Joined -> True, - Mesh -> Full, PlotRange -> {0, 1}, PlotLabel -> "discrete", - AxesLabel -> {"t", "x(t)"}], - ListPlot[ - Part[$CellContext`dlmplot, - Span[1, 20 (Round[($CellContext`r$$ - 1.005)/0.005] + 1)]], - PlotRange -> {{1, 4}, {0, 1}}, PlotLabel -> "discrete", - AxesLabel -> {"r", "long-term"}]}}], - "Specifications" :> {{{$CellContext`r$$, 1.2}, 1.005, 4, 0.005}}, - "Options" :> {}, "DefaultOptions" :> {}], - ImageSizeCache->{438., {117., 123.}}, - SingleEvaluation->True], - Deinitialization:>None, - DynamicModuleValues:>{}, - SynchronousInitialization->True, - UndoTrackedVariables:>{Typeset`show$$, Typeset`bookmarkMode$$}, - UnsavedVariables:>{Typeset`initDone$$}, - UntrackedVariables:>{Typeset`size$$}], "Manipulate", - Deployed->True, - StripOnInput->False], - Manipulate`InterpretManipulate[1]]], "Output", - CellChangeTimes->{ - 3.7771660008727407`*^9, 3.7771660666138906`*^9, 3.777166117958968*^9, { - 3.7771661846076736`*^9, 3.77716623608088*^9}, 3.777167342067255*^9}] -}, {2}]] -}, Open ]] -}, Open ]] -}, Open ]] -}, -WindowSize->{759, 833}, -WindowMargins->{{249, Automatic}, {Automatic, 28}}, -FrontEndVersion->"10.4 for Microsoft Windows (64-bit) (April 11, 2016)", -StyleDefinitions->"Default.nb" -] -(* End of Notebook Content *) - -(* Internal cache information *) -(*CellTagsOutline -CellTagsIndex->{} -*) -(*CellTagsIndex -CellTagsIndex->{} -*) -(*NotebookFileOutline -Notebook[{ -Cell[CellGroupData[{ -Cell[580, 22, 180, 2, 144, "Title"], -Cell[763, 26, 156, 2, 30, "Text"], -Cell[CellGroupData[{ -Cell[944, 32, 99, 1, 63, "Section"], -Cell[1046, 35, 399, 7, 68, "Text"], -Cell[1448, 44, 332, 10, 55, "Input"], -Cell[1783, 56, 1642, 55, 101, "Text"], -Cell[3428, 113, 173, 4, 30, "Text"], -Cell[3604, 119, 325, 10, 25, "DisplayFormula"], -Cell[3932, 131, 1211, 39, 101, "Text"], -Cell[5146, 172, 684, 16, 99, "Text"] -}, Open ]], -Cell[CellGroupData[{ -Cell[5867, 193, 91, 1, 63, "Section"], -Cell[CellGroupData[{ -Cell[5983, 198, 102, 1, 43, "Subsection"], -Cell[6088, 201, 1151, 33, 92, "Input"], -Cell[7242, 236, 495, 13, 31, "Input"] -}, Closed]], -Cell[CellGroupData[{ -Cell[7774, 254, 105, 1, 35, "Subsection"], -Cell[7882, 257, 897, 19, 125, "Text"], -Cell[8782, 278, 757, 19, 87, "Text"], -Cell[CellGroupData[{ -Cell[9564, 301, 2824, 72, 250, "Input"], -Cell[12391, 375, 2667, 52, 283, "Output"] -}, {2}]], -Cell[15070, 430, 1022, 22, 144, "Text"], -Cell[CellGroupData[{ -Cell[16117, 456, 1293, 32, 163, "Input"], -Cell[17413, 490, 61123, 1029, 172, "Output"] -}, {2}]], -Cell[78548, 1522, 654, 12, 87, "Text"], -Cell[CellGroupData[{ -Cell[79227, 1538, 2618, 64, 255, "Input"], -Cell[81848, 1604, 2312, 46, 257, "Output"] -}, {2}]], -Cell[CellGroupData[{ -Cell[84194, 1655, 2864, 70, 233, "Input"], -Cell[87061, 1727, 2382, 47, 257, "Output"] -}, {2}]] -}, Open ]] -}, Open ]] -}, Open ]] -} -] -*) - +(* Content-type: application/vnd.wolfram.mathematica *) + +(*** Wolfram Notebook File ***) +(* http://www.wolfram.com/nb *) + +(* CreatedBy='Mathematica 10.4' *) + +(*CacheID: 234*) +(* Internal cache information: +NotebookFileLineBreakTest +NotebookFileLineBreakTest +NotebookDataPosition[ 158, 7] +NotebookDataLength[ 91073, 1837] +NotebookOptionsPosition[ 89492, 1780] +NotebookOutlinePosition[ 89836, 1795] +CellTagsIndexPosition[ 89793, 1792] +WindowFrame->Normal*) + +(* Beginning of Notebook Content *) +Notebook[{ + +Cell[CellGroupData[{ +Cell["Continuous Versus Discrete Logistic Growth", "Title", + CellChangeTimes->{{3.776600831050974*^9, 3.7766008318453026`*^9}, { + 3.7771302883123703`*^9, 3.7771303074624567`*^9}}], + +Cell["Adam Rumpf, 11/4/2014", "Text", + CellChangeTimes->{{3.7766008347881403`*^9, 3.776600838290375*^9}, { + 3.7771303248362846`*^9, 3.777130326323276*^9}}], + +Cell[CellGroupData[{ + +Cell["Introduction", "Section", + CellChangeTimes->{{3.7766008459498987`*^9, 3.776600848547045*^9}}], + +Cell["\<\ +This demonstration is meant to compare the continuous and the discrete \ +versions of the logistic growth model. Both are population models which cause \ +the population to be limited due to limited resources. The continuous model \ +is usually given by the ODE\ +\>", "Text", + CellChangeTimes->{{3.776600856235587*^9, 3.776600860481224*^9}, { + 3.7771662972954435`*^9, 3.777166370927112*^9}}], + +Cell[BoxData[ + RowBox[{"\t", + RowBox[{ + FractionBox[ + RowBox[{"\[DifferentialD]", "x"}], + RowBox[{"\[DifferentialD]", "t"}]], "=", + RowBox[{"r", " ", "x", + RowBox[{"(", + RowBox[{"L", "-", "x"}], ")"}]}]}]}]], "Input", + CellChangeTimes->{{3.777166387219908*^9, 3.777166431475397*^9}, + 3.777166462432236*^9}], + +Cell[TextData[{ + "where ", + Cell[BoxData[ + FormBox["x", TraditionalForm]], + FormatType->"TraditionalForm"], + " is the population as a function of time ", + Cell[BoxData[ + FormBox["t", TraditionalForm]], + FormatType->"TraditionalForm"], + ", ", + Cell[BoxData[ + FormBox[ + RowBox[{"r", ">", "1"}], TraditionalForm]], + FormatType->"TraditionalForm"], + " is the intrinsic growth rate, and ", + Cell[BoxData[ + FormBox["L", TraditionalForm]], + FormatType->"TraditionalForm"], + " is the carrying capacity. Notice that this equation results in ", + Cell[BoxData[ + FormBox[ + RowBox[{ + FractionBox[ + RowBox[{"\[DifferentialD]", "x"}], + RowBox[{"\[DifferentialD]", "t"}]], ">", "0"}], TraditionalForm]], + FormatType->"TraditionalForm"], + " when ", + Cell[BoxData[ + FormBox[ + RowBox[{"0", "<", "x", "<", "L"}], TraditionalForm]], + FormatType->"TraditionalForm"], + " and ", + Cell[BoxData[ + FormBox[ + RowBox[{ + FractionBox[ + RowBox[{"\[DifferentialD]", "x"}], + RowBox[{"\[DifferentialD]", "t"}]], "<", "0"}], TraditionalForm]], + FormatType->"TraditionalForm"], + " when ", + Cell[BoxData[ + FormBox[ + RowBox[{"x", ">", "L"}], TraditionalForm]], + FormatType->"TraditionalForm"], + ", meaning that the population should grow while below ", + Cell[BoxData[ + FormBox["L", TraditionalForm]], + FormatType->"TraditionalForm"], + " and shrink while above ", + Cell[BoxData[ + FormBox["L", TraditionalForm]], + FormatType->"TraditionalForm"], + ", which is how the carrying capacity is enforced." +}], "Text", + CellChangeTimes->{{3.777166439165693*^9, 3.7771665664048877`*^9}, { + 3.777166749606275*^9, 3.7771667502513075`*^9}}], + +Cell["\<\ +The discrete analog of this model is usually given as the discrete logistic \ +map\ +\>", "Text", + CellChangeTimes->{{3.7771665709646397`*^9, 3.777166587554802*^9}}], + +Cell[BoxData[ + RowBox[{"\t", + RowBox[{ + SubscriptBox["x", + RowBox[{"n", "+", "1"}]], "=", + RowBox[{"r", " ", + SubscriptBox["x", "n"], + RowBox[{"(", + RowBox[{"1", "-", + SubscriptBox["x", "n"]}], ")"}]}]}]}]], "DisplayFormula", + CellChangeTimes->{{3.7771665980882196`*^9, 3.7771666127458467`*^9}}], + +Cell[TextData[{ + "where ", + Cell[BoxData[ + FormBox[ + SubscriptBox["x", "n"], TraditionalForm]], + FormatType->"TraditionalForm"], + " is the population at time step ", + Cell[BoxData[ + FormBox["n", TraditionalForm]], + FormatType->"TraditionalForm"], + ", ", + Cell[BoxData[ + FormBox[ + RowBox[{"r", ">", "1"}], TraditionalForm]], + FormatType->"TraditionalForm"], + " is again the intrinsic growth rate, and we generally assume that the \ +population units have been scaled so that the carrying capacity can be stated \ +as 1. Note, however, that 1 is not actually the equilibrium solution of this \ +system: solving ", + Cell[BoxData[ + FormBox[ + RowBox[{ + SuperscriptBox["x", "*"], "=", + RowBox[{"r", " ", + RowBox[{ + SuperscriptBox["x", "*"], "(", + RowBox[{"1", "-", + SuperscriptBox["x", "*"]}], ")"}]}]}], TraditionalForm]], + FormatType->"TraditionalForm"], + " yields the (nonzero) equilibrium solution as ", + Cell[BoxData[ + FormBox[ + RowBox[{ + SuperscriptBox["x", "*"], "=", + FractionBox[ + RowBox[{"r", "-", "1"}], "r"]}], TraditionalForm]], + FormatType->"TraditionalForm"], + "." +}], "Text", + CellChangeTimes->{{3.7771666153555794`*^9, 3.7771667546392555`*^9}}], + +Cell[TextData[{ + "The figures below show how these two models behave side-by-side as ", + Cell[BoxData[ + FormBox["r", TraditionalForm]], + FormatType->"TraditionalForm"], + " changes. In order to remove the potential confusion of the continuous \ +model having a constant equilibrium while the discrete model does not, we \ +will always rescale the continuous model so that ", + Cell[BoxData[ + FormBox[ + RowBox[{"L", "=", + FractionBox[ + RowBox[{"r", "-", "1"}], "r"]}], TraditionalForm]], + FormatType->"TraditionalForm"], + ", meaning that both models will always have the same carrying capacity." +}], "Text", + CellChangeTimes->{{3.777166775775532*^9, 3.7771668855378103`*^9}}] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Code", "Section", + CellChangeTimes->{{3.776600864408964*^9, 3.7766008650447807`*^9}}], + +Cell[CellGroupData[{ + +Cell["Initialization", "Subsection", + CellChangeTimes->{{3.776600871130811*^9, 3.776600873087188*^9}}], + +Cell[BoxData[ + RowBox[{ + RowBox[{"logfinal", "[", + RowBox[{"x0_", ",", "r_", ",", "lim_", ",", "end_"}], "]"}], ":=", + RowBox[{"Partition", "[", + RowBox[{ + RowBox[{"Riffle", "[", + RowBox[{ + RowBox[{"ConstantArray", "[", + RowBox[{"r", ",", "end"}], "]"}], ",", + RowBox[{ + RowBox[{"RecurrenceTable", "[", + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{ + RowBox[{"x", "[", + RowBox[{"n", "+", "1"}], "]"}], "\[Equal]", + RowBox[{"r", " ", + RowBox[{"x", "[", "n", "]"}], + RowBox[{"(", + RowBox[{"1", "-", + RowBox[{"x", "[", "n", "]"}]}], ")"}]}]}], ",", + RowBox[{ + RowBox[{"x", "[", "0", "]"}], "\[Equal]", "x0"}]}], "}"}], ",", + "x", ",", + RowBox[{"{", + RowBox[{"n", ",", "0", ",", "lim"}], "}"}]}], "]"}], "[", + RowBox[{"[", + RowBox[{ + RowBox[{"-", "end"}], ";;"}], "]"}], "]"}]}], "]"}], ",", "2"}], + "]"}]}]], "Input", + CellChangeTimes->{{3.7766008761831923`*^9, 3.776600882799075*^9}, + 3.7771657470625243`*^9}], + +Cell[BoxData[ + RowBox[{ + RowBox[{"dlmplot", "=", + RowBox[{"Flatten", "[", + RowBox[{ + RowBox[{"Table", "[", + RowBox[{ + RowBox[{"logfinal", "[", + RowBox[{"0.4", ",", "r", ",", "100", ",", "20"}], "]"}], ",", + RowBox[{"{", + RowBox[{"r", ",", "1.005", ",", "4", ",", "0.005"}], "}"}]}], "]"}], + ",", "1"}], "]"}]}], ";"}]], "Input", + CellChangeTimes->{{3.777165890525441*^9, 3.777165913718752*^9}, { + 3.777166055921769*^9, 3.777166058420776*^9}}] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Demonstration", "Subsection", + CellChangeTimes->{{3.7766008885632277`*^9, 3.7766008904796133`*^9}}], + +Cell[TextData[{ + "We begin by showing a time series of population versus time for both \ +models. Try gradually increasing ", + Cell[BoxData[ + FormBox["r", TraditionalForm]], + FormatType->"TraditionalForm"], + " from 1 all the way to 4. At first the two models should produce nearly \ +identical behavior, but after ", + Cell[BoxData[ + FormBox[ + RowBox[{"r", "\[GreaterEqual]", "2"}], TraditionalForm]], + FormatType->"TraditionalForm"], + " the discrete version should begin to produce oscillations which the \ +continuous model does not. This is because the discrete model allows the \ +carrying capacity to be slightly overshot between iterations, after which we \ +must experience negative growth. The overshooting goes on for several \ +iterations before dying down." +}], "Text", + CellChangeTimes->{{3.77716693393746*^9, 3.7771669739303837`*^9}, { + 3.777167026954685*^9, 3.7771672398192244`*^9}}], + +Cell[TextData[{ + "After ", + Cell[BoxData[ + FormBox[ + RowBox[{"r", "\[GreaterEqual]", "3"}], TraditionalForm]], + FormatType->"TraditionalForm"], + " the growth rate is large enough that the oscillations no longer die down \ +and instead remain as periodic orbits. Increasing ", + Cell[BoxData[ + FormBox["r", TraditionalForm]], + FormatType->"TraditionalForm"], + " even further beyond this point causes the orbits to increase in period, \ +from 2 to 4 and then 8 and so on, until for very large values of ", + Cell[BoxData[ + FormBox["r", TraditionalForm]], + FormatType->"TraditionalForm"], + " the results are completely chaotic." +}], "Text", + CellChangeTimes->{{3.77716693393746*^9, 3.7771669739303837`*^9}, { + 3.777167026954685*^9, 3.777167286432896*^9}}], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Manipulate", "[", + RowBox[{ + RowBox[{"TableForm", "[", + RowBox[{"{", + RowBox[{"{", + RowBox[{ + RowBox[{"Plot", "[", + RowBox[{ + RowBox[{"Evaluate", "[", + RowBox[{ + FractionBox[ + RowBox[{ + SuperscriptBox["E", + RowBox[{"L", " ", "r", " ", "t"}]], "L", " ", "0.4"}], + RowBox[{"L", "+", + RowBox[{ + RowBox[{"(", + RowBox[{ + SuperscriptBox["E", + RowBox[{"L", " ", "r", " ", "t"}]], "-", "1"}], ")"}], + "0.4"}]}]], "/.", + RowBox[{"L", "\[Rule]", + FractionBox[ + RowBox[{"r", "-", "1"}], "r"]}]}], "]"}], ",", + RowBox[{"{", + RowBox[{"t", ",", "0.001", ",", "30"}], "}"}], ",", + RowBox[{"PlotRange", "\[Rule]", + RowBox[{"{", + RowBox[{"0", ",", "1"}], "}"}]}], ",", + RowBox[{"PlotLabel", "\[Rule]", "\"\\""}], ",", + RowBox[{"AxesLabel", "\[Rule]", + RowBox[{"{", + RowBox[{"\"\\"", ",", "\"\\""}], "}"}]}]}], "]"}], ",", + RowBox[{"ListPlot", "[", + RowBox[{ + RowBox[{"RecurrenceTable", "[", + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{ + RowBox[{"x", "[", + RowBox[{"n", "+", "1"}], "]"}], "\[Equal]", + RowBox[{"r", " ", + RowBox[{"x", "[", "n", "]"}], + RowBox[{"(", + RowBox[{"1", "-", + RowBox[{"x", "[", "n", "]"}]}], ")"}]}]}], ",", + RowBox[{ + RowBox[{"x", "[", "0", "]"}], "\[Equal]", "0.4"}]}], "}"}], ",", + "x", ",", + RowBox[{"{", + RowBox[{"n", ",", "0", ",", "30"}], "}"}]}], "]"}], ",", + RowBox[{"Joined", "\[Rule]", "True"}], ",", + RowBox[{"Mesh", "\[Rule]", "Full"}], ",", + RowBox[{"PlotRange", "\[Rule]", + RowBox[{"{", + RowBox[{"0", ",", "1"}], "}"}]}], ",", + RowBox[{"PlotLabel", "\[Rule]", "\"\\""}], ",", + RowBox[{"AxesLabel", "\[Rule]", + RowBox[{"{", + RowBox[{"\"\\"", ",", "\"\\""}], "}"}]}]}], "]"}]}], + "}"}], "}"}], "]"}], ",", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{"r", ",", "1.2"}], "}"}], ",", "1.0005", ",", "4", ",", + "0.0005"}], "}"}]}], "]"}]], "Input", + CellChangeTimes->{{3.777163681244874*^9, 3.7771638468583126`*^9}, { + 3.777163957467636*^9, 3.77716398467824*^9}, {3.7771640761216917`*^9, + 3.7771642136305895`*^9}, {3.7771645056535025`*^9, 3.777164556673809*^9}, { + 3.7771646075070252`*^9, 3.777164730339535*^9}, {3.7771649500323143`*^9, + 3.7771649653355174`*^9}}], + +Cell[BoxData[ + TagBox[ + StyleBox[ + DynamicModuleBox[{$CellContext`r$$ = 3.032, Typeset`show$$ = True, + Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", + Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = + "\"untitled\"", Typeset`specs$$ = {{{ + Hold[$CellContext`r$$], 1.2}, 1.0005, 4, 0.0005}}, Typeset`size$$ = { + 387., {70., 76.}}, Typeset`update$$ = 0, Typeset`initDone$$, + Typeset`skipInitDone$$ = True, $CellContext`r$74990$$ = 0}, + DynamicBox[Manipulate`ManipulateBoxes[ + 1, StandardForm, "Variables" :> {$CellContext`r$$ = 1.2}, + "ControllerVariables" :> { + Hold[$CellContext`r$$, $CellContext`r$74990$$, 0]}, + "OtherVariables" :> { + Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, + Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, + Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, + Typeset`skipInitDone$$}, "Body" :> TableForm[{{ + Plot[ + Evaluate[ + ReplaceAll[ + E^($CellContext`L $CellContext`r$$ $CellContext`t) $CellContext`L + 0.4/($CellContext`L + ( + E^($CellContext`L $CellContext`r$$ $CellContext`t) - 1) + 0.4), $CellContext`L -> ($CellContext`r$$ - + 1)/$CellContext`r$$]], {$CellContext`t, 0.001, 30}, + PlotRange -> {0, 1}, PlotLabel -> "continuous", + AxesLabel -> {"t", "x(t)"}], + ListPlot[ + + RecurrenceTable[{$CellContext`x[$CellContext`n + + 1] == $CellContext`r$$ $CellContext`x[$CellContext`n] ( + 1 - $CellContext`x[$CellContext`n]), $CellContext`x[0] == + 0.4}, $CellContext`x, {$CellContext`n, 0, 30}], Joined -> True, + Mesh -> Full, PlotRange -> {0, 1}, PlotLabel -> "discrete", + AxesLabel -> {"t", "x(t)"}]}}], + "Specifications" :> {{{$CellContext`r$$, 1.2}, 1.0005, 4, 0.0005}}, + "Options" :> {}, "DefaultOptions" :> {}], + ImageSizeCache->{438., {130., 136.}}, + SingleEvaluation->True], + Deinitialization:>None, + DynamicModuleValues:>{}, + SynchronousInitialization->True, + UndoTrackedVariables:>{Typeset`show$$, Typeset`bookmarkMode$$}, + UnsavedVariables:>{Typeset`initDone$$}, + UntrackedVariables:>{Typeset`size$$}], "Manipulate", + Deployed->True, + StripOnInput->False], + Manipulate`InterpretManipulate[1]]], "Output", + CellChangeTimes->{{3.777164540906799*^9, 3.7771645573735876`*^9}, { + 3.777164611045705*^9, 3.777164660389118*^9}, {3.7771647044469786`*^9, + 3.7771647308643694`*^9}, {3.777164953963621*^9, 3.7771649658634167`*^9}}] +}, {2}]], + +Cell[TextData[{ + "Below is a pair of static plots for any and all long-term behaviours of \ +each model as a function of ", + Cell[BoxData[ + FormBox["r", TraditionalForm]], + FormatType->"TraditionalForm"], + ". If the model converges to a single equilibrium, then that equilibrium \ +value is plotted as a point, while if the model oscillates indefinitely, all \ +points in the periodic orbit are plotted. As expected from the above \ +observations, the continuous model only ever produces a single equilibrium \ +value, while the discrete model does at first, but then after ", + Cell[BoxData[ + FormBox[ + RowBox[{"r", "\[GreaterEqual]", "3"}], TraditionalForm]], + FormatType->"TraditionalForm"], + " begins to divide into multiple values due to oscillation, and for the \ +largest values of ", + Cell[BoxData[ + FormBox["r", TraditionalForm]], + FormatType->"TraditionalForm"], + " the plot is an indiscernible cloud of seemingly random points." +}], "Text", + CellChangeTimes->{{3.7771672918691654`*^9, 3.7771675223574295`*^9}}], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"TableForm", "[", + RowBox[{"{", + RowBox[{"{", + RowBox[{ + RowBox[{"Plot", "[", + RowBox[{ + FractionBox[ + RowBox[{"r", "-", "1"}], "r"], ",", + RowBox[{"{", + RowBox[{"r", ",", "1.0005", ",", "4"}], "}"}], ",", + RowBox[{"PlotRange", "\[Rule]", + RowBox[{"{", + RowBox[{"0", ",", "1"}], "}"}]}], ",", + RowBox[{"PlotLabel", "\[Rule]", "\"\\""}], ",", + RowBox[{"AxesLabel", "\[Rule]", + RowBox[{"{", + RowBox[{"\"\\"", ",", "\"\\""}], "}"}]}]}], "]"}], + ",", + RowBox[{"ListPlot", "[", + RowBox[{"dlmplot", ",", + RowBox[{"PlotRange", "\[Rule]", + RowBox[{"{", + RowBox[{"0", ",", "1"}], "}"}]}], ",", + RowBox[{"PlotLabel", "\[Rule]", "\"\\""}], ",", + RowBox[{"AxesLabel", "\[Rule]", + RowBox[{"{", + RowBox[{"\"\\"", ",", "\"\\""}], "}"}]}]}], "]"}]}], + "}"}], "}"}], "]"}]], "Input", + CellChangeTimes->{{3.7771657179889126`*^9, 3.7771657311636024`*^9}, { + 3.777165773220811*^9, 3.777165777454324*^9}, {3.7771658199732375`*^9, + 3.7771658446488113`*^9}, {3.777165927994836*^9, 3.7771659626038847`*^9}, { + 3.777167325618328*^9, 3.7771673327173443`*^9}}], + +Cell[BoxData[ + TagBox[GridBox[{ + { + GraphicsBox[{{{}, {}, + {RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6], + Opacity[1.], LineBox[CompressedData[" +1:eJwVzn840wkcB/AZEzO+fvOk1iqEVCTSD30+Sj/8SKWnErXKj84lrnREQqk7 +kw4ltdOtU0oULqYskaKT9tjhkY5LGWNfl5qNaljjdn+8n/fzep73H+/5YT8E +RVIpFMpWTf7vbSqHEAZVDsE5n7MEBxE8iLipdpocfs40bzy5Zg/MWfikIF9f +DhdiXV49mxcOw35b3zJN5MCjs2g8xnFILzi+z5UlhwrcVGOlSIPqVbXs3evk +8EG4RHSJnw3Wif7hhafk8GDEbOlEEw/6P8ccXTEuB3mD4Z8hVWWQIPY8fGdC +AYyy3k2l5nWgQx+d3fRxDKSb9S4EtTTBIPWFzLJ3HKotp24dE7fAy0/Me/y+ +z5Ad1ByvJRFBkWUkS93xBSZvmqxZadoB51xdU3O6v0KEWVF03pJOeGgzR7Xn +HyWc7oE3kyZdIN4wtlwknIARjwb23qo3YMQODMpqm4TkkkMZv+7sBvdH+c5f +G6cg1H+tLL6uByreqeyuVaqAz6L7L9Z9C05KUvds9TfIG65XV+zshd8DG25Z +Favho5G/w76Ed2DNnWOvvD8Nf/wlPObFew+SB9wWRvkMuN5vy3Er64PX2pS8 +7wIpaHNjIF8WIAbPkgT3mHYKShrX5e1qFgN3JMz9la8W+hxv9fNw7YepRaal +viItrHZ2LObe6Ada63bnyEAqEok5gTo6A8AgaIZ/N1NRzedGCfYPgIX/6UMx +vtooPBoVoVc7ALPtvzcLadLGUqUwdcRAAi1RQ6/7V+ugosT+xY/BEki8bUvP +rtPBicy2+qt3JWCX1vNbrjsNvU/Sr+jKJNAZtKOoRkDDvYJT50mPQXDKDn6c +tEoXX0deYC5LHoTUqC7ny5W6aOKgFWorGITONRbmbW6zMGOH9cYE5SDYVQiD +w8pnoVocy57rMgQsDlGea6uHVkt20VIih2BuqFW85I4eei8ty5rHGwJL0ZWC +i0x9vHTELkG7bQhMPLvcQm7q48rtTTt0taWgtz7LKdWGjgfjy988c5VCCb/d +xSuPjuvNbveN7peCH7PnHsvCAGF7+tKFF6UwvGhPeki2AZ6INnkueCgFjhNX +JDBhoO4175Nu/VLouBLlUHWZgSpvOZtNJ8HqRoVYy8AQwc5MlLyMBHZhDSPh +F0OciDtfG7GbhFveHldxlhE+WhFnnJFEQo6fz7LiVCMM79jgOFxAQkqAxVoX +CoHRW1x2fasnIepTaLFxEoFj3d0c/jsSEgtvhjsnE6hTxFGve08CZyfJ2pJC +YOfLrANCjUsfx11PO0uggHV9RNxHwoefMnNlmQTmt2+yNRwgIZpZc6q1gECX +D+Y2YVISYreZbuPUEWhmHus5LSMhlRrMuP2UwNVfHrMzRknIfsh71fCMQMnG +tjhjOQkVNo4+yhcE9j6KiFigIEEzWXVYRGCOY2HMxnESjp2JWejznsDLT8/Y +cJQknHHjiw+INf/rzVnGEyTkSid4yQMEHm68b8rVuDLgvDVfSmARU/H87iQJ +Y9bXDReMEljcuta3WUUCtVUs9FIQeKgo4OnWbySYptlz9o4TOC1Lnt+l8fKh +SuolJYFK+uYqiZqE9VxlQ9kkgfof/+07Mk1CkL9XSouKwJjwWpVC47Dp9NWD +agIXK5/QkmZIOFHZopyZIXC/85h6RuP/ALOGTdI= + "]]}}, {}}, + AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], + Axes->{True, True}, + AxesLabel->{ + FormBox["\"r\"", TraditionalForm], + FormBox["\"long-term\"", TraditionalForm]}, + AxesOrigin->{1., 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, "DefaultMeshStyle" -> + AbsolutePointSize[6], "ScalingFunctions" -> None}, + PlotLabel->FormBox["\"continuous\"", TraditionalForm], + PlotRange->{{1.0005000612142856`, 3.9999999387857144`}, {0, 1}}, + PlotRangeClipping->True, + PlotRangePadding->{{ + Scaled[0.02], + Scaled[0.02]}, {0, 0}}, + Ticks->{Automatic, Automatic}], + GraphicsBox[{{}, {{}, + {RGBColor[0.368417, 0.506779, 0.709798], PointSize[ + 0.002777777777777778], AbsoluteThickness[1.6], + PointBox[CompressedData[" +1:eJzs3Xk0lf//738zUamMlVCGhEoSEV1XCQnNvUsllbEozZo1aSSRSjKVqBSa +lSgqQklJhEgUTco8D7+d1/vj9Xxdy2+dc/1xzvme8732e6/1Xrd133uj9r5s ++7FXRq72mO8kwMfHVzaOj+/v/6XjLD7vlK6h5t7NSd6R5UP9x1HDBrVNOILd +//Ywv+1m2N/MzTsoYWz9C+nLdqWf6PWhFqmlisew1zdVjB1hg/189dVT7kOw +R409nsBfeLzXLdIF1rkR2FMvFq7JW4M9PkzKv2sitqBA3lWL7mO9fhA3sin6 +JfatgY1y0uexZwg/Ejjigv1EQaGjWR/7xjTBc/ai2HcefIq//+ForyPmKa5p +ijlKaSz3e9qoUUOFfdQw9HX27/V+x7pRUebY7UrZSQdGY9ufmTVbqR921Qlh +9y0/T/U62ntZ/a7X2G82rxfRuY09WWWN2Imz2P5L+IOP7MIeKjDxrPIq7EIL +Hcl5Fth5oQespMdhW9jYPnOSwc50FTI+0ObX69i9UvYzXmL73ev61S8UW/xm +wsSXHtg+xQNf7zPF1ljRFq4ij+3dIvXuRvVJykS8IHKDSQ218K796E/3A3vt +feVi+dHz2AMa2w427sY+9PPmEsVV2GcX3G/rMMOWvrHW+oQW9jrq4pZng7Hf +nftRFN5yutfT5w5XHV6GbRInMV4nA5v/3YnBRTexb944KiMdjP3PyBX3Cw9i +bzdYEKa+HlvU1ORy0xLsgKUWmWYzsA1OFesP0sH2CLluPF8BW6Ygf7ZYP/D5 +emsJjW8KoOY9UPT+Oa+GivG5/iTIJqjXca0mpmsnYler5/u2DsUuUmvmfVHY +xXlnxA2+n+v1gwclKR/eYntbmUxVeoR93eZutVAUtrKivechP+yME0bJQTux +3RqGfzB2xpb8VCjtPh/b8tTF2pEU9s2V24Yv1caeX1bgNmgY9vOBPpW0GPYT +9RMJVU1nex0QJz6BvxL7+Y2ozGPvsTXFI4btTTtLOfecaqgLo2KfnFAO6fV5 +6agnef2wB309bPWu/kKv38xTT9pXij3S58X9/Ezsp77fNHLuYafunDfD8RL2 +usvOu075YV82TNgzew/2L4XneufdsAsS21LclmI3S5VtS7XEVtzr+vGMIXbS +9+3RX8ZgRyeevH9tGHap1wn5zxLYAwZc4jvSGdzrjTGrM8/9wc4y+VIrWY59 +eruYwq+8YGpnzwGxhlpRpym9aUhEr2l1ubmFYtjqalX9tbrDe30yxq/QvBp7 +7t0vyd3F2MZrhyfOeYm9K6JuyIRH2CrbhWeHXcdeu2TpuIAQ7JEpY26JnsTO +efNBvM0L+9UrlcuOm7BbB2+VM3XCNnJwGue/BPtn4OpPs6yxfX/tsHKnsaMS +TZNq9bB9qqovFozBdrV18B+mhC1venJ6gnQ49fdouNyvhjLcLjywa/SlXru6 +zp4mrYz92MBg5HZ57PB3OtvUB2PP3KA9XkEcu7thr/0/gtjjgquMczsu9jq4 +f8II3ybsQZelPQ/VYG/daF987wf2QflrLYpfsa3OzDyX/AnbfdLBIL8i7DKd +WY0B77FVPCSS095gm6gESqu/wv5HSGjS7RfYRvxv1ro+w850eCdt8QQ7f936 +SOtHFynewZB3ROQ9f5CcLd5ldbnX0SsOXwwxw35sfnn3Pgqbb53EoWhDbLPb +V9Ml9LCrn7/xjB2HHf5rWvXRMdhqLuahF1Sx4741KFQoYf8S8VW0G4695XC1 +h6gctlHsqNZPQ7D3fxF/9GUg9iz5Qa+lJLCfrW5Y6SaKXRZ/M+G7ILa4sqOm +Lx/22n4LVBd2RvY6wrdhlEkbtvrrAffMmyOpnsPhgxpKamuAm9LO6F7/iXAS +k9mKPSCy8af5Bmwrjcfat92w39zbKrrQBVsy8OvHMQ7YulO+jp9gj30leFuk +yzLstzl8rVmLsZ2krwy0XYgd+vFhieQ87E0z6R3VNtiTdIP618zC1pypVSQz +E1v7iYGRnRn2Ucvr559PB1+vnOSOWTT2o6cH3apNsCslX8ncmIJtHeY01tsw +mncc+XuqoRZdFCx7HHe119GD6vXyY7DH3Fj2QvkK9k3zhG8XIrHdf1RImkVg +fyppzB8aCq6fMLZVLhj7RZ7kPJNz2FdeBecfCcSOOhsc2uiP/dFZNu+QH3bd +PwUpE32xPVRFnvKdwLZbV2r14yh2RMPWqt+Hsf0Dz04Y4I3dEXGt0PQgdov/ +nQj//dhjq1YsafTCtrWQKV+39yr1ueeAyDu+BqkWfKuM6fX9yzvTqiuw7ZyN +5474jO0YFTNgayn2pZbfCXXF2E6tPzUDC7H3ULqrFxdgC26R8zR6jz1HoDps +yjvsZ6MWjrF9i+2qGbvXPwd73KQIxYps7CiX5DDrV9huGhOvvcrCfv02qH1V +JnbgjldOEhnYYUfKM16kYz/8pSZ7Ng3b5vPo2VufY+tplHo5PouhGnueUPMe +v7cdgqyUY3stqee7d6AitvvhDoWG4djFL1YtbBuKPbRs4mgleeyyIYcTVspi +j5MSNEuWxj6dJ641UQr7VkBNacpg7GuP/vntOAhbNji6c4Qkdlb6xfQfA7Db +/CXksvpjJya45iRKYLvmvfv8SBy7SOvr3Ff9sD033hj3Uwz70ZJHF+SAt7yi +0ueKYm9P0f5+RiSW6nk6LV5LmWbWXhxpG99r2cQ/Q3csxj5zIHDRr0XYcw46 +7N+xEPt7R8M3xQXYQ2YWNRTNw94ndFXjxlzsi64qI/3ngNuTOxVwdDb2CVkF +C38b7ON3XEbEWGNXW48WzbXCfqNaIioG7LH/2kSrWdhTvMfHBVtia5r7Xmuc +iX05w8lpGbB7SPvYlxbYv2uXLpsBbCcdMDfdPJ7qORwq1lLbDR/c6Z9xs9da +b9vdNr7AvrnqzoDP6diOAR/fLQVOc9kkWpqG7XPZrWsN8DfVV8O6nmM/fPwi +8zyw3dzGA8bA+56devH1Gbj98qyRZ4CntKipzoKdKnUVAn5jZef/7Cm2p0+C +2RHg6YYT9eYA+/wqGDQceLKNyJkfqdhPx8t5JQMbR/IHnOZ5Ys+plno+wLBS +sfxWr4X2pwbFfcZ+apidZA4skL8zvrIMO+WGcZEvcA7/t1tTgKXK8+/9+YTt +ozXc4xrwMcdUD1dg/VGj5msDDyukHzSUYquLG1ilAufkxST6A78Rn5vkBLyl +YZOECbCQsI+rHPCK18VBDSXYSacGOucBh7ypDL0P7Ov6e/AFni16Doi1lEFy +TMiGttu9dn2bbqwMfOfaAZv8VuxpjWdmBQAv71qeuAB47LwO7WHA8qvOTvna +gv0o1v/IXeA1/X4/PAJckXLlwArgWV6jgyYDDy1Pvi8DvO3FmIjGZuzarRrD +PwA75gysTwIemLu2ORL4SOKNdh/g+NEF+Z7AD+ImOTgCH7Udunc+zz0vxyyv +pQrj4sXSB93t9akNDyV9ga8k3fqzBDhnw8+pY4Avj04O6ZTE1n/46OZ74CHJ +wpq3gK8GhD32Az56tkBzI/A1y3SdRcCxVunnpgAvGCWirQq88tOIxwOBB76M +G9U+EFvLWkL3O7D7ksoXH4A1X/R7lglM/xkinAScIjxpUzyw1RO+2kiee55O +b6ilvC3ezG5WvdfriGeKM3OAp2RM+BgDfL2sIuEYsIy/n58b8IPsVYpzgSt0 +ktQMgE29otyVgS20LZ5IAFPx2363qGC/P2OZUwWcaXvH6ANwiaz2gCzgC/Pt +1ZOBg4eVu94Crnj952E08ItObf5Q4K3PPTQCgXfp+Q73AW6w1Mo4xHPP4dCb +9/m/2T/wp/79Xi+qldDKAaY2yf++BxxbpSYXDmz48b3bceAlYxcneAJn3irN +dAZOydLevhi49pLiBUtgg05LSRNgjVOX7k4ALhHSWD8aOCjtwkhF4LklJgky +wHumnBo6EJgvRWmSKHD3/vktfMADc40WtE/CNj603qAJ2Gdo+blans/3nGqp +giBDKsA8odfXPUY07wWmxZNC1gFP1LzZZQfcNP5wzRzgs4tMZpkCd0a8rzIA +1jb/fnUssOyCuRtUgfeEZKsoAJd1PrsuDXxKtr5uAPDeZ0aVosA5Vx23CAAf +H1/v22mG7e7WqNoK3LX2k3YjcPQ+5+Ba4HeKqxx+Awf9vLb3J889L+fH1VLJ +p3yVvy540Osdp49/KQD+2D6//yvg0fOObkoFvqX0sDEB2P2fZs94YPvUHaVX +gM23Wgy+CKyt/KstGHjmHL2jZ4CD39VcOQW8yTtllg+8/KNPq48CuxZ1VBwC +Ftk++Nl+4BY/qmkvcD+H21t2A0cEH9DfCRxjG6q3HVjiV6zrNp57Xo55ynu+ +5TGD7/OKh73eK53SVgDsnGlTnwPc73prdgawAlWx8Snw64zKjCTgrxpznyQA +N085a3oHePSLEebxwDqKgg+vAyumffe7Ctzp+PZJFLD9nj9TI4HH2PgKXQTO +2fVdLBzYYugIs1Dgs2cF71wAnuqgZhMMPPDr5YHngcWOjq0/x3PP0+kC3vEy +R//SYZfEXjuJKhzeB9ykXjFiF/DgkuKF24Cp/gnym4Df3KVt1wPn/Rkp5gas +PCBG3hW4lT/Mywl4wfoBEx2Aa09ra64CvhWra2cPrKpunGYHPHeKzvLlwA9i +riksA7btX86/FPiIb7ioLfCrNFXNJcD5LqOcFwMnnIt58A/PPYfDn7VUm2GF +UuG6R71+qaYt+B5YJTLT8S1wzqmASa+BBc6Pd30JnDyzoiYDeGPJkrR04JC2 +7R+fA9/1Nx33DPje8rg7qcBxK444pwCn/1467QlwStly6jGwrdvC5cnAxtuP +ByYBr5JK/PIIOOaBwCxoS/OPqYnAO1f1nwUtOzK07CHPfD2nOmqDVINiycak +Xn+/enFFEfB6iaVNBdDPhhe/B57tZyaYByy8bK1zLvCYh5qdb4BVxkql5gDb +3th74zXw0pzdidnAg0weVb4CDv62cSz08RfzTrwEXnVra2cWsJbKov3Qd2Ie +SEMvfB5/LxNYpvPIamhvnbSh0F8eDyvK4BntwXVUy7AWs6DNyb2ueL9u41lg +xZevCgOBX70e43ka2Je+OD0AuPqFnr4/8CLvWOtTwJoqB/b7AUubp7w5Caz3 +q0UfOtJ2/C1fYEuTLGNoleeHC3yAHy5d5wWd/uWFLrSX0dCaE8ADU2XuQ3u3 +hhyEHl15ZzG0qea+CX+N9uA66tkkkZJBmx/3Oqql/xVJ4E0HfgUPBH59uuv2 +AOCRY1f+6A+8TrfAGFo/7FG0BLB3RoUqtM/i03fFgZv3uC+ANjBw6O4H3Gl8 ++z605c63ntABGeumQW/IWjUE2jA5/rsY8Azl3enQTdL9rkKfX3HbF/r4r+/b +/hrtwXXUbyMJX5sNT3otrz441Rr4+6WowdCyepk7rYDzoyVaZwFrCW4/Bm1g +dXAMdOXlznxL4I3nhE9Bjx7SOR/ap8NLETpOfnntTODVYsezoC9bj74GLa2w +0Qf6QN2TzdDHnxxcAT0gjLaGXsDvYwztZCE+/q/n97ygX0cpK6sFx0xK6fVV +zVWLoW/5WClCX/m+u/oa8Hm+p8+gG0dIR0DfiwrYD+3gu8cFWiVSZx50v0NK +U6EXauSOhX7157MS9P3hzVLQG6LT+0GPdRvED60aENp6FXi+AVUPPcs0uxr6 +7Xq179Aybppf/xrtwTyvvuUodxu77Y2eIfQ0lanS0O0fcxtkgcukFYugvd6u +fQZdOFXpJnTjhQfh0G+fv/CHnjLttzd01PPiXdCdA6w3Q2sOFXaHrjjz3gn6 +0PnTK6EFDw5fDr2335wl0Pwe0ough+Yumg999Dzf3L9GezDvePtw2OUNY1N7 +XeP58wh0+elhG6Bv321bBt1gz3v4Au/PCTaGPu2+TQd6Z/5EdWh7+6MjoGN/ +6clCZ2gJDYL+NSBTHNpwn50IdOA/FwWgd6za0e0BrHT1dQe0aapvG3SpWXQL +9DNb8WboJPO4xr9Ge3AdlXjyQe7DK9jRGcdToM1DzW5Bn/6+8TK0ffD189AB +4WGnoK2WCx2DbvK6eAD6uMGMPdCvrj7dDp1xvXUL9LEHLzdC3+ZT9oBuiP3s +Dr2H6l4L7c6/dg20bLCMK3TctWZn6MU7RAmrJJg4/TXag3mP/32zHJqUn/a6 +39DwxdCJoWU20HYPk82gVx+omwpdbGpuCK1y+Zge9LWhZ3Sgf0ZYjIWuuuqt +CS04drIGdHWDlTr02IabqtATntuqQG/SmzIKWrLaaiR0jvIhZWhh6xIl6HFd +8wifuFGi+NdoD+Y93tW2Ph5zHnu0A18CtIfim5vQcmNjr0MPTl9zBbri26dI +6O/iNRHQul1eYdDKYjtDoBOVXgVD/7R2OU98PBUqCJqeb3kOepHVnrPQN+rf +nYF+6WRB+H1SbiDx8b5tJFx3fCRh3/zS03+N9uA6yvOc4bTFg571+v3FXcbQ +QSMCJkPblCyeBD1oUpwu9JCCXTrQIyuuj4O2UB47FlrZtlYLOi/vlyZ0fJUM +YeNzjmOgt8/O1SB6uC3h6wObRkMH/4gkvEl9JeHJUzUIX1RsU4deMTivx2gP +5h3Pzww2PnAY+7rwYENonexgfWgL4bN60Ben/9aF/pgeMAF6ZMFWHWizCT7j +ob+dfzUOeojXeMIR1+PGQu8SMyM8bM1vbehZq64Q9h+1jnCavQnhV5NkCe+T +b9KCFn9WTForvcdoD66jxr/ZVhfbjm3nHlADTUeJ/oF+U5lWDa0V9+QX9IKW +7z+hs19OIazxIfYH9JLRRoQvlxR/h14r7EfY13Eu4ee2Iwj/k1L/DXpA4VvC +Hgb3Sd8OJ9y02Jfw3dV7CX+csKnHaA+up5x2xweXeDzv9ceTXuehV648FgQ9 +piX1HLTCZmXCq8JCz0KbRU0kfPN1yRloc4sgwimN9oRPLtYlbOA4gPDobX8C +oT8bFBDODnxGuPTGHcLBWdGEBZaFEBaqOk143EDfHqM9uJ56Ou6FnXQFtvbC +foTlvDYsh3b2bFwGvWJdAGH7O9MJL/AWIKxS/HoptOSMKMJjMg8SPvvelfB6 +lQWEF92YRnhY6ETCD6w0CC8cr0Q4tVCO8Oy6weTHnzCAsPKKfj1Ge3A9dedO +5OJFi9J6/S5iLOEFWjn/QCsHHyTcrGZBWDxTlrCNfM0i6AOqbwnvWPWA8NSA +y4SnPwwkHCtxlPCkqj2ExbK2Eray9iBcOWwt4dX1ToRPR6wm/KvZnrBLgV2P +0R5cT7031zoXmY69W7P8LHSn+FXCWe93EA4cuoiw0VcDwkdilQlbTh5I+MGJ +7jPQ1Od6wvwXfhDeNaWCcOWKEsJ/7n0gfJT/PWFfyVzCKg9yCJ8vziacsvIV +4YCJL3uM9uB6Kn32VkUBg/RemxrPJFwQoUr4ipcY4QTzuhHQWx6UEe4szCWs +/PUF4ZkmTwg/d35AuLj7NuFlj+LI6y+/Tn7821cJ55yLJmzx+zJhhbBIwscC +LxFOenqRcJcCMtqDeY8fPf6KzdHYwse/lkNb5+YQ/pH2mHCZwy3C68ujCRtE +hpHXHxNE+I/0acLX5PwINzeeIHxp3zHCIQFHCL8aeJjwitJDhB3+HCScOZH0 +4YgDhH9qk9bK3d9jtAfXU96Ha7LbpV/0WjXsE2H+9bmEw1QzCJ9WTCHs/vEh +4cdtdwl3ad0iHD8xjnB0+XXC0tIxhC2uXyVc5H+F8OL70YQVJUj7e0cRdhpB +Wu3VZcJpPqT/WYaM9uB6anP49KSQA9i3Fk0mfHS5DuFL4zQJX3NUIy8fN5Lw +uNeKhA+cViBsUjiM8K4DQwkXbJcn3BIjR9hNgnSanyzh2vGkY7/KEFa6Qfqg +F+na5aRHT0dGezDv8XtrkJftH+yCreKEJ14TJqzWzE/4pmL3Xuj06g7CpSbt +hG1qWwkb1bYQHqBN2iiwmfB8JdKz05oId3iRDp1F2nsk6c/8pA9+bySckk/a +JgMZ7cG8+693ZrHesoxef3uaRji4/CnhhfEphN35nhDOuJ9M+EJiEuGbrY8I +KziT1m9MJFwQRjptOWkjTdKnBEm3f31IeGkOaYnHpF/dJH09mvTPMGS0B/OO +J/vdfSakYxtTawlXH3El3N/IhbCNsTPhLbucCFd8cyS8bwfpQlXSB784EA69 +Q3rLSdL6m0g/WU56vTVpMZp0iD7pzeNJ82uS/qSGjPbgekr9/jNqvk5mrw8u +f0r45OJUwscCUghndj4hvMuX9K3JpGNbHhNekkG6KJK0zVHS+zaTfulA+s9i +0u2zSRvOJK1kStqMIr3cmLSmETLagxuoy29CeMdF7HIB0qdcLxDObQgmLBRG ++sdy0nLapD1FSXf/PE/YqYB0/QvSdkmkb9whPTqW9IyrpIMvky66SDornDQV +RlomFBntwQ3UqEK+ieICWb0eb096oRDpyyndutAGJ0lHu5K+Zk36jQFpCw3S +dxVIy0gzbm8A6TIx0nOESV8RIH2Dj/TE7i7Cw7pIW3aSju1ARntwA7Xk0drg +6DXYDptJq0wl/UiWdEDrGsLdFaRF80jrZ5De/oRx/QekJ90lff0m6f5xpIff +YFw+hvSFa6Rzr5I2YTjnCuk9/xrtwQ3U8tMdCza+wZZbQ1p4FunxE0k7jyI9 +SJZ0d3/Si0RIe/CTft/ZTlinnfTUVtJvmkk/ayLd2UjanWEBhu82kN7J8Nx/ +jfZg3p/f0zuF7vovex15jXTQOdJux0ln7yOdsYP0tS2kf24grbOetK476cdr +SceuIV3lSvofhn+5kA5n2JlhY4YVGRb712gPbqB+51zgnbCPpZIenkD6eDxp +yRjSMtGkJ0aSVrhIOiictFcY6TuhpJUYvhtC2pnhsQwLMVx1gfRbhp8y/OBf +oz24gXo+4u/3lVe9XidD2l2S9FAJ0p2ipFOESasIkW4VYHSGj/IzPh7DmXyk +TzHswvBMhicyrMKwPMODGJb412gP5j2+t4Q4hDhg3/AgbexOOn0NaUFX0qnO +pIudSBswnOpIej3DExgWYbjKgfRbhp8ynMBwPMPXGI5i+NK/vtzzgkwD9XDD +q6Gb07Gb1pHudiMdvJZ02BrSP1xJuzE8iOE3LqQvMXyQYXeGlzE8h2FzhmmG +jRk2ZNiA4Un/Gu3BvOdPBQ/dD2tk99o6n7TOe9IueaQL35HexvB4hjtzSRcx +/JTh2wxHMxzC8FmG/Rk+yfAJho/9Txrtwbzjd/Gx0A/HsG8XkR7McEQh6fkM +KzDc+IF0EcMZDCcyfIvh6wxHMXyJ4QiGwxgOYfgCw8H/P0Z7cAM1ZMGxL24/ +sP3nk9ZnuGke6SyGYxkOYvgYw14Mb2d4M8MeDLsz7Mbw2v9FRnsw7/tT7eKN +02e97nVXDemXDF9l+BTDXgxvYdidYWeGVzFsz7Adw8sZXsbw0v9FRntwI9Xf +a4jbimvYFXtJpzN8m+FohkMYPsuwP8N+DPsy7MPwCYaP/x8y2oMbKRul3TWp +ojm91mdYneFhDEszLMmwBMP9GBZjWJRhEYaF/4sY7cGN1MrL6vIeTtgLGJ7F +sBnD0ximGDZh2JjhKQwb/V9itAc3UpM7zte4PMWewPBYhjUZ1mBYnWHV/0eN +9mDe48POhF4s+abXQgwLMizAMP9/U6M9uJHa8HmxwygTbA+G13Pu02gP5n2/ +9De1O7sW+wLDwZz7NNqDG6md/arV7p7jzNZoD26kYmWDbu1+zpmt0R7cSNXW +/D1xZuv8nj24kXo9eMRb3pkzS6M9mPfzWezLKWUzObM12oObqK1vzeTstnBm +a7QHN1FD1faaHwvnzNZoD26i7i9RvuaUxZmt0R7cRP02ihhe38CZrdEe3ERl +7Z7pqauUy5ml0R7cRAWoWvLOnNka7cFNVNStNCprE2e2RntwEzWrvnyOaghn +tkZ7cBO1NDDPb2IaZ7ZGe3AT9djuR2ZLNWe2RntwE+U8ITRti+w7ziyN9uAm +yvfJBYurUzmzNXo5polqbc4fHOjMma3RHtxMlU8+WTH5JGe2RntwM6VosmzH +uXuc2Rrtwc1Uv5cmvjc/cmZrtAc3U7lqV/IPCeZxZmm0BzdTF6d7i8tocmZr +tAc3U/lPbYpXzeXM1mgP5h0P74m1um3jzNZoD26mViguG6wXwpmt0R7cTI2w +9s9JTOXM1mgPbqZsa69+5KvizNZoD26mtkou+yTS/z1nlkZ7cDMle0Ntd7YO +Z7ZGe3AL9c+ivyfObI324BZqxdaBEuE7OLM12oNbqJht/0y5HsqZrdEe3EKV +PlQ4sDOVM1ujPbiFmrfCdMeAr5zZGu3BLdS60isPHMXyObM02oNbqPf7tPJ5 +Z84sjfbgFsos/JHT6tmc2RrtwS3UmOe2rf02cmZrtAe3UF/DVUZuP82ZrdEe +3ELdy1/qFnuPM1ujPbiFqr7i7hhTwJmtm3qeULdQ5z1az3q0cmZrtAe3UmaC +H090DivgzNJoD26lsn/oZC005szWaA9upfK32hXwzpxZembPAbGV6oqTNVi1 +F7uTYa733dEe3EoZjnV1kwvnzNZoD26l1j1PbAh6wpmtD/W8oN9KXZMpnlf5 +iTNboz2Y9/ju/nvizNZoD26lNta92Vmp9IEzS6M9mPd8RsndOJjizNZoD+bd +HwPdk4fbc2ZrtAe3Uv66NVvc9nJma7QHt1E9/9xhKGe2RntwG3Ux7NpyzyTO +bI324Dbqtm/JZr1izmyN9uA2qlU+xC+1lTNboz24jYofWqWkJF/Y61iGud53 +R3twG6Vf6HjaRp8zW6M9uI3Sm+e02GYhZ7ZGe3AbZb6gqkBxE2e2RntwG9UZ +FOr11I8zW6M9uI06kVSfMDmWM1ujPbiNejJM6vv+LOxkhrned0d7cBu1K6xq +R1gV9g6Gud53R3twG3Vgm+qbk0JFnFka7cHtVPq9mXMXjOTM1mgPbqeel0ba +/TLhzNZoD26nbJf+PWEvY5jrfXe0B7dT24rWXAndxpmt0R7cTmldi718PwBb +k2FthrnLI6M9uJ1a9aX8ZlQctgPDXO+7oz24nboZfWOMWxZntkZ7cDsVPyLI +TbQSO5Zhrvfd0R7cTg08qZy7k7+YM0ujPbidkjO/k5CmgC3DMNf77mgPbqcO +772z9ZsBZ7ZGe3A7dVxzr2PFfM5sjfbgDurj/XXFvDNnlkZ7cAfl/aBEx+Eo +9hGGud53R3twB3XpxLjEb5c4szXagzuoGeUZLy2SObM12oM7qDbTkQ/3FXBm +a7QHd1C6ex/lna7lzNZoD+6gUoXHbdgv8ZEzS6M9mPf92FLt75kzS6M9uIMq +bHF2rZ6KXcww1/vuaA/uoKr03zu4L+HM1mgP7qBGvNio8GIjZ7ZGe3AHxTd6 +1afO45zZGu3BHVRXSHXLoMuc2RrtwZ1UnuHxu3zJnNka7cGd1PLs97wzZ7ZG +e3AnVfU6dIrnb+xKhr8xzF0eGe3BndQyw8/nu0RKer2U4eUMc5dHRntwJ7Vy +2bsnDkqc2RrtwZ1U7oXShmgDzmyN9uBOKlL3ilfGHM5sjfbgTmpP/oDoDBfO +bI324E5qsr1u7BUvbCOGDRmewvB/1+ujPbiTOmu3rdDpHGe2RntwJ6V61Wu9 +YDy2OsNqDI9m+L/r9dEe3EmllxjF70vnzNZoD+6iSkt6TpxZGu3BXdR2/R9T +hjdiezK8jWHu8shoD+6idh8dL27Yv5QzS6M9uIvSLc8+aqDCma3RHtxFGQya +3CxrhD2JYa733dEe3EX1/zopsGAuZ7ZGe3AXFeRZGbrDhTNboz24i9q65Om8 +zj3Yngxzve+O9uAuyutx6K/Vgdh7Gd7HMHd5ZLQHd1ExPSfObI324C5qgeCu +F3kp2PMY5nrfHe3BXZTyFYG9n/M5szXag7uoR57nxd7+wk5kOIlh7vLIaA/u +plYs74yIFPjEmaXRHtxNHTdeuM9WnjNboz24myqtG/uJd+bM0mgP7qZmTz7c +6GHKma3RHtxN5R9Jb3uzhDNboz24m8pse6Emux77JcMZDGcx/N/1+mgP7qbK +R7y/QR3kzNZoD+6mdJ5cT7MJ4szWaA/upgTu7Y2iYzmzNdqDu6nO0OZ98k85 +szXag3nPp4Mn+7zP58zWaA/upu53lbR5/uTM1mgP5qPR/8o4szT6eZiPvqk9 +rEpfnDNboz2dj85pfPFypTRntkavJ/DRE7Ty0vcocmbrMT0/0PHRd9Oyanw1 +OLM1ej2Gj86LbV3lr4v9jmGu993R+zn46BVeG3WPGnNma/R6Fh9tOEtk5yZz +zmyN3g/DR8/tOXFma/R6IB+dkXLj1cilnNkavZ+Ij3bYMFWkygHbkWGu993R +66l89HS/31IR6zizNXo/Fh/duGxdfxtPzmzd83Tam4/ufKcr8nsfZ7ZG72fj +o++s8pI7eJwzWwf3vJ7PR98/svyf/oGc2Rq9H5CPRr+PkDNboz2Ej46SKrvT +Hs2ZrdH7KfnonR99Olfd5MzWaE/i/Txi+SEr6SH2PIa53ndH70flo3X6P+Od +ObN1z8v5BXz0itRhM+a+4szW6P28vPvn8Z1Dj73nzNa/evZMPnp9tFXa/VJs +D4a53ndH74fmo6/1S19WWMWZrdEOzE/X1vw9cWZrtAfz02e2RAZ1tnJma7QH +89OB8t7O3QKfObM02oP56R9LB65vkuDM1mgP5qeLqGNPy6U5szXag/lpi4+D +PZ+P4MzWU3sOiPy0WunZsAvqnNka7cH8dPOQIivX8ZzZGu3B/PSeXxv8NSdz +Zmu0B/PTxwXT9pfTnNka7cH8tMB56fGnLLEFGeZ63x3twfz0KJnN1yfOx1Zh +mOt9d7QH89NthzLFspdyZmu0B/PTk2QLlix3wNZnmOt9d7QH89MT/SfEfnbD +1mOY6313tAfz01vemsnZbcHeyjDX++5oD+an7Y2XXH29mzNboz2Yn96o7807 +Y29imOt9d7QH89PvzqYeDPTlzNZoD+anVwwt/vPtDGe2RnswPz00Z3v6xDDO +bI32YN73Z9/h8lujsfUY5nrfHe3B/PTupYqNN+Kw9zDM9b472oP56fV/f5vy +fc5sjfZgfvphUqM/3xPObI32YAF6k8LfX6jHma3RHixA59TWKYzP4czWaA8W +oI9vHhE5uYAzW6M9WICu2P1CyvAT9heGud53R3uwAL24dvZenSrObI32YAG6 +VvEP74xdxzDX++5oDxagNyil7hFqxt7IMNf77mgPFqCFJifpfO7CFmaY6313 +tAcL0F8N7g+9J1LOmaXRHixAh7x3sNg3EDuUYa733dEeLECPlLDNmC7Lma3R +HixAJ27od71jBGe2RnuwAJ1wNqMzVo0zW6M9WIDutst6/c9YzmyN9mABetMc +Fe1mPezNDHO97472YAHapC5Dxc+YM1ujPViAblIOeKY4gzNboz1YgE62Mxga +bcWZrdEeLEDrqi3gnTmzNdqDBWhXerVCyFLObI32YAE6U+b5F/HVnNka7cEC +9J+WxKCNazizNdqDBeg9O9zN3mzA3ssw1/vuaA8WoNtvfm5W347dwTDX++5o +Dxagr/mJJm/1wo5hmOt9d7QHC9LuGvEXkw5zZmu0BwvSt9t9eWfObI32YEF6 +x7SpHbpnsHcyzPW+O9qDBenFutSJ1SGc2RrtwYL0pTmNbscjObM12oMFafT7 +bLGvM8z1vjvagwVpBS2/Bc9uYY9gmOt9d7QHC9Kb8x5synvAma3RHixInxdX +lS59gh3MMNf77mgPFqTj398xLUvHvskw1/vuaA8WpOtUdQcUZ2PXM8z1vjva +gwXpokFzd7/Owy5mmOt9d7QHC9KrFaJDEos5szXagwXpA1vv7ggv58zWaA8W +pMv0KhT3fOfM1mgPFqSTQg6cW1DDma3RHixID1n88veoZs5sjfZgQbrrdun4 +n52c2RrtwYL08s/pTjeEKnptxzDX++5oDxak7+t4XnCW4MzWaA8WpF1mvioe +OoQzW6M9WJCWd/CZkC6PPZRhrvfd0R4sSHsddbnipoS9j2Gu993RHixIr0tv +thBX58zWaA8WpLXWpI64pI2tzTDX++5oDxai0ev6nNka7cFC9PjA6IBkQ85s +jfZgIdruk735NBp7OcNc77ujPViINtt/csljc85sjfZgIfqdng3vzJmt0XFQ +iH5mcCnl8gLObI32YCF6914vzYFLsXcxzPW+O9qDhejpVU+HbVzJma3RHixE +F7nrX8h2xi5kmOt9d7QHC9HeS07dU1mHfYhhrvfd0R4sRG/uOXFma7QHC9Eh +Bh6lSTuwLzDM9b472oOF6J4f6/Zhd/89eXH9f9TRHixEO072+2x8GNuBYa73 +3dEezHs8+/z9jzNboz1YiLaXre13OQB7BcNc77ujPViIrvQxdHgdxJmt0R7M +8wb3i3Vh2F8Z5nrfHe3BQvQ8o3PZg6I4szXag4Xo+EP3ajSuc2ZrtAcL0VJT +bvHOnNka7cFC9KlnqymLBM5sjfZgIXqspv9um2TObI32YCF6tVXdO5tn2KsY +5nrfHe3BQnT/Ls3ZMzM5szXag4XpBuOceuMczmyN9mBh+u2c1dla7zmzNdqD +heni+n8qpIuxixjmet8d7cHC9OeDklNbyrDLGOZ63x3twcJ0rVLp1/eV2DUM +c73vjvZgYfpInlBF7C/ObI32YGF6Yeo9k3112AsY5nrfHe3BwrQ3JdVl3cKZ +rdEeLEzHi+poS3dxZmu0BwvT0xdLvnkv+KXXFMNc77ujPViY9pGJqvXvh32Y +4eMMH+F6j9EeLEyvankfNFMSewnDdgwv5XqP0R7M+/5y1TO7VRqbZng2wzMY +nsWwBcMz/x812oOF6d1f5p6LGoa9hOGNDNsz7M6wA8NrGHZi2JVhZ4Zd/ot2 +tAcL09+ihnZZKWNfZTiP4fsMZzGczHA6w08Yfs5wKsNP/4sa7cHCdNT0Xf2q +1bDHMbyfYQuGPRheyLALw7YMOzC8nOFVDK9g2P7/kNEezHu8nhqUelQL+4Af +aXlGj2f0FobTGP7BcA7D5Qy/Z7iU4Q8Mf2S48H9TR3uwMO0n4qytNAG7nzDp +EYy+lNG/MnyA4RcMn2P4IcMXGb7F8BWGYxm+9r+poz1YmD5f1jr/pj52cQnp +t59Iry1lmNHvMLo+oxcy+nBG/8XoAxi9idFFGL2d0QUZvZPR+Rm963+yoz1Y +mB5GGfNO2FpGpB+YkNacQlqA0WMZ/ZIx6TpG38ToMgwvYViD4VkM6zI8g2F9 +hmmGDRmeyrDRv0Z7sDBtbOn35+k0bEea9Gtz0qOnkz5sRlrGlHTRDNIBjL6P +0d8x+lxGb2J0A0YXY1iT4cEMqzIsy7Ayw/L/Gu3BwvRJG4stMyyw35iQnm1J ++gdNWtyCtP900u/NSG82Ja3D6D8Z/cMM0toMX2N4NsOnGF7J8EGG1zK8m2GP +f432YN7xqjzmbYo1dno6aeti0gavGL2A9Ogc0qrvSSe/Id36jvT5t6SXMLpk +Lmk+Rp/L6G8Z3sTwA4a9GY5h2O9foz2Y9/gUrR84eT72tvw6wm1tpBs+MVxP +evRX0sNqSPN/I91VTfrUd9IffpFe+4O0PqOXM3rJT9IqDMcybMFwAMPL/jXa +g3nPb2ZYTYxZjD3o9yzCiePI7ttF9o2jyH5XlHTEcNIZ/UkXyJEOliSdLENa +azDpAGnS4kNI/5Ii7c3o/oyeyegrGP3Pvx3twSK06cu3ZnJ22BMmkqaiSN+d +Q7rYj/QTe9LvDpJOcyUtuYf0h3Wkp+0gfXsD6RGepG02kf6+lbTeZtJTGD2B +0Qu3kOb712gP5n29Z8/ZeK3Gtvc9S/jRIrJvfUz26zpk31BE9hPDye7wg+z7 +Jcm+s57skWJkj2kh+0Mhsoe1k91LgOw2nWQ35Ce7aRfj+nxkz/m3oz1YhF7u +FzGv3AVb7mkY4avKZDeSDSd8v4z0O3PSLx6R/rqa9KZo0sM3k1YOJr19N2mB +06Q/7yddeZI0nzfpwz6kXx8mrX6CdNERZLQHi9DzYyuW0OuwE06WEY6uLSds +qfiZ8JuDZJ+ziezHTcm+M5Lsv0aQfVoK2b+Jkn3oW7KLtJNuKCK9u570gzLS +0n9Iy30hvfcX6cGVyGgPFqEXKlutPb8JW+CJGWGfCkvCv2+bE04cTXZfUwvC +Kx7MJGx9nuxLtpFd5RXZdeeQfeYPsncYkH10B9kNNcmeIkJ60CjSYgNIG40g +/XQQMtqDecev3Xd9qj2xLadeJzzF9Tbh6qIbhD00bhF+nhtL2M71JuFwlzjC +3Q3xhMVSyX4vnuyPmsgud5jsHbKk5daRXq5JWmoF6e5JpCUXkW43RkZ7sAht +XleTbrwH+63SZ8LantWEy/IrCIvY/iScsucrYR3JH+TlvSoJHzD/Tth3eBVh +91ffCGfsJLvqAbI/uEv2uoVkby0g+xZDsq+tJnuiBtm3taGO9mARekZgmtKR +A9hlQTGEx714Qvi6ejxhMb0kwpKNtwjL8yUSTom/Qzjw8gPCvil3Ca9/nUD4 +qus9wttnkZ16Q3b11vuEZQaRFn9B2s2AtOZV0lfnIKM9WIQuffQz9NUR7PUV +yYQNhpcT3r83jbDI0I+EY02yCIvbfiA8SC+b8A/+fML2A3II8/nkEX6m94bw +5UvvCCtWk51vMNm1V74lPPx+LuH2K2RftYfsL/NQR3uwCD0maPDMAb7YG9qe +WUCXxPET/V7EG6JvjGgmbB/+gfBis1rCP2+UEG6lqwlvLy0jLJzwg/D4inLC +UxS+E3425gvhC/LfCI9pIbv3lirCITu/Es7pT3bJbNTRHsx7fIoWq1oGYB+U +W0KYKkghfE18HeFE6ZuEpTbvJPxqaRThXNGDhJ33hBFO9j5KOEY+mPDhfj6E +82eeI+xgeZKw+u4zhGse+hGevSiQ8JuoU4QvBJ0mnG7s32O0B/PuH5XlRvvO +Yc/OEiG8oy2B8LHFYwhLaoYQ3v6IIlyscpxwlclswslb9xKuv7yYvP0v2whn +JNkRdurYSPhc/CrCd16vJxw61ZGwyxN3wrJVTuT117gRHtPm3GO0B/Oeb6km +n7odgn1ojbUftIaMJ9ELNbyJLqxoSfQpjjFEP9+oSfS0t0+JPkVbjugPPuQS +vUBHnOgxy0uIbneDn+hF078QPVWmg3BU5jfCo9xaCFen/iQ8W7CJcMrd6h6j +PZh3/+/Xpl12EVt6W4Am9DCNo0S3N/9D9G0HjYl+8pe2FnTHDHGi7/i0iOiu +X78R3jNkI2GfxFzC+1QOEtbkf05eXsWP8CbDRMLSCucIr028Q17eJYRw1pp4 +wgk/w3uM9mAR+v1OLdl+V7BbLbWGQCsqb5aBjtz6lOhOms3S0FbDNaSIy7+J +JPq0Le5EH5nmRnT9NcFEL5ExJ3rLnIdEl3iiTfQxcq+JPvvecKJnSn4k+g56 +ENHvbflK9A0+YkR/kfazp6M9mPf4WVI9f+wN7NOiVtbQD1Sez4O2NqRtoO8U +tc6Frh1eRXRv7Q1El7i9ZDa0jOcQoi/kjya6RXzuHOjn4UVEH2N+hehyG7qI +bpV4jOgWb2QJq4VtJbzPZTTh8b9dCJvd1u0x2oNF6K3f6r5b38KWVuoohR6e +KvMN+r7G0TJocYnsSmizzqDP0JJBP75Cj69dWA5deG420U3c84n+UqniC/TU +8PEV0Mmy54luMWQd0dtlnInu4HKO6OPrpxN9iP9dosc81iT6uKsZPR3twbz7 +0xSFcpf72BOf9n8D/XrZyE/QDanHcqGrtg0ogb5SYZYHvSg0uBj6iM+u99C7 ++wcVQZ/avCAfWjutohD6W/t3os+Xcib62pr5BdCKGwYSPWdECNGTFr39AK2r +kkP0nY+iif7rXl1PR3uwCB08OWj63kfYzZK1qtDPLxWaQHvMrdaA/hC+zwh6 +gl6yFnTmD5XJ0Fs0Ho6F/sd4hz50vwCl8dALtawnQdt5KuhAhyV56hGfz7fX +RNf+8Hki9O231hOgA6W3E133WhTRxbeMJbqA7ZeejvZg3vOl+8OkTqVgb559 +utwP+JPMGQnYV277/Q32Myr6IrAXztpeDfspx5UCsE8qvVcDe6ZzZDf0dT2R +emjrsrhO6HnqsQ3QUnssO6BdVIsboQfOntUOnZx2uwm6Wj6wDbosyboZWqV7 +MNFn3Ejs6WgP5n3/VNJdHpqG/euW6ADoVI35c6HNY5TkoKUyky2gl59Zqwj9 +vOr4NOiT6+NVoF1XDzIheuue0dBfhPMMoQVlpmpCax/dYwB985WRNjStlD0J +Wto2Ziz0w7uBetB5lXfGQU/tuD0ROvLZ5vF/jfZgEXrpldejo7OwwydIXYkC +HjVCVQb2yYViCbCHfN4rCrv9qTtPYb9s4t0Jva7a6CX0RE+jJmgrYc+30M6v +v9ZA878Wzod+qsdXTThlaSH09j/qP6CPW2QVE7eXO/gbdIZcQAn0qaE+ldCv +bT6V/jXag0XoUhm5AzE52JfOud26BrxqeZkj7OE2J7KILm82B3Z1XeUS2G9p +zaJgv+NY+gP2F97bJ8J+b7NYI+xZKYmasE/+49MBe+ltU1XY5WYqCEDnhe1S +gjbonCwC/WJW3XDohQGm/aBl7y8cCj19zUGJv0Z7MO/53on7O2PysLcePjrm +GnBc+AQb2N3mf5sL+/TQUVqw3zJfsR52sffRg2E/s3TNIdhlT5/pglaPqgqE +9reaVwPtUDr1IrSn/+Wv0A9jd8ZAh3y6UgIts9jhFvTs9tgC6LW3T96Hpi0m +vYMOKHFP/Gu0B/P6/Er16EJsofJ00cvA1ZOtyqKAb8zQM4M9SrsoBvZvr29v +hn1th/MB2EPyK87Cbq+a6QD7mbTDt2C3iQ2xhv208M002JMch0yB3TKgLg/2 +c7dfjoXdYoNXGew7DZ+owP54j8l34vqKqgqwK+4o/vO3oz1YlB5cEnw5tBT7 +n2d7jIOBo6zOGcDOJ/D5AuyffJS/hAAvaf/2BfZXEYaXYb8n/U7hArx+rvVm +2CfPuWQBu/ehAhvY9zS7usKueHfMBNgFB+3fD/vCCL3hsAcfSAiEXbzTURx2 +I911kbDXCB7uhL5ofTPur9EeLEonCG9S8q/ArozxuH4C2CHrl+cp4P2tRVN9 +YPfQbfID/jVD6BbskvOS/GH3m+/ezxf43oQaU9jtTpfbwG6neksU9jOVlQdg +f3y4X+FJYNvZjddhn+Xw7S7sZX4pL2H3KqoOgv3FefsvsIePNz0I+4IbG5r/ +drQHi9Ie1xd82PcNuzjltup2YMc76h+8gK2vrBXdAezdsl8SdrWvHQ9gj85Y +tmkvvP2KQTN2Ap/zNG/eA3z4dddN2ONPfToL+87kOSK7gCvdVljBnik/yhL2 +mCVTBsGeYbB9D+yW4j8+7wae2bg1Gnb7oZHJsHv+OJX+t6M9WJSe1KA7YV01 +9tmyW7b2wD8/r73uBrxx/4W7K4G1Hl/ftha4arvTi1XAKYkKB9YA33UfeHE1 +sHiUU4or8Jk/22wcgO/va1CH3Xe9aD7swuVrYl2At4dNnO4IHNeqYgO7ydny +c7D/rvnMB/uEGanFsDcd2fncGTji8cHBTtX/2YN599+EoU/+qcPufDDhFQ18 ++rfSxoXAY+eYfJwOfCb+WNB84OxJBgdnAD8Kax8xD3jXAdF8M+D2QSm/5wDf +n7fuqznw5yVF7bOBq2/lPrYADtS0NIT9+Oom95nAYg/Xh9oAh7/c3AK7msQ5 +ZdjHV413tQT+7X02yRrYZe/N1L8d7cGitJL0Y6epzdj5g/TuDge+vzak2gg4 +vd7vnSKw5bHJipOB1UzFl40EFhl3sGAScEDqXhcV4Jxlh7onAkuutxmkBm9v +5MT9usAd051c1YG7I72tJgDnmSp4jQZ+/TRurg6w1e7SlRrAMy7t8x4P7Pz4 +kdwY4MWq1WXjgLdvLLr+t6M9WJTukt2zX60D+75wZ8HvduwJ8RpzlUHPfKR8 +oh70jJ1OkgqgyyR7OzaDLp4Vc1oe9BFRgSfaQD96Ye5DGXh92UDlTtAdE0Y5 +SIG+yqTepBv0M9mTdgyGt39gSSsfcHd0XZUk8OmJXo4CwAEXbcIHAlfKVvsK +AptvGRUwAPir3JH9Qh3/2YNFaamGavWB/F97Pdxi9JwHfNhUxJR1IqD/mCCz ++AnoRhW7RPlAt35xdkwa6C629KM24MsfS9ozgZv3qS1pAh7X0dSaDdz+R/5+ +HfCYjmUz3wLP3/Dzzh/gc4unCecBD2kdqV8NXKobY5kPvOdhm9pP+PV8t9b8 +AFxlGrrhO/AMm7kPCnlGe7AoPUc06kC7MPbM8FnqW4GnzDKRqwFWUX903gtY +MDz6SCXwE4vLtkeB869sOFwKrGNTfcMPuFwgLbcAeIRK3eszwIO2LtXPBR4e +5VgbDBy9LvlgNrCh1yeTcOCLQmWBmcA31hsUXAKOef/VMh1YO/BMURSwScfI +o8/g5V86rLzKM9qDRekVu0+51oljN5dkv1MGVr3YdfkzsOE1epoOsP857y3v +gHcf6pxjAhwj+GfjC2CJp0Z2M4G/+J20SAZW/lKcMA/Ycc2nG3eBT1hEXbIF +LrfzcowFjh469J+VwPdMdxhdAbZoEBdwBn7lnStwCfjM2sbXa4HTj84LCgVO +lhr+aT3PaA8WpWfrDx7TJoktmXfE5e5AbJsO4aTPoL+5uEjgJei3Bpx+/wr0 +xnH7bUvh9VdurU8EPSgr8etv0A806UVfB/3lENOBnaBv1PE4GQY6PXmDVj/g +BGHvpaeBZ5e9PyoFvP9l2PNjwIo6I1wUgLUMW0/tB64JCOpUAVYaudFnJ3Cz +YuguTZ7RHsz78/7U7+UIGez9qRMXqUlhF9513NsmjV203mO8OehSs/SaikH/ +MVr+/GrQPyXE+6aCPir3rdYu0FfWz7ofA3rwy+3up0B/aZbQcBb0y5J12ZdA +LxpsVeoNutHN83dug14q/kzWE3T5P8s3p4DuUjR39lrYPU4sfgX6mVe/KHvQ +yx3XROTzOtqDeX9/XwrfrxuGnfS14oaDHLZy8p6ZU0DX8L3XFQB69kFhWUnQ +52/QWp4E+k8zgU3fhmKvTdD2LgN9pPnNa+mg1z3bNJJPHvuO9BPla6Cn25x9 +Nhz0xzf3zfYDXeziw58TQW8s3fRoO+jnTn/sZwl6/+1y3Y6g3xrz1WsZ6LF5 +gx8vAF1hh3OkG6+jPViUNt0y/ouAMnZau8OhxcOx7ao+Gj1Swj57Jq8rGHRd +u/lVu0B3ndEWkg+6+JFjtaagZ6x2tZRQwFbIs9g7BPRFx+e+MwSdWpXxslIR +XL79fu1q0Cv2ZIxLAb1sr7n5EdCPef6UDAP9F51jfwV09yi3716g18XtTHoG ++pJcSTMn0BXp5JcfeR3twaK0j2egOb86dvMB8eklithXDAxLQtSwJQZnOhkr +Yc8uPjvOFHTh2ool/qA/z9giU6+KvT5eamIJ6C9tik5cB31gM99vZWXs8INJ +V9xA13Y66GoH+iQFkSBd0OcUea85DXpt9J+L3SrYmfODLz0DXb8gXDEX9Dma +5rd/g946uf+Oa6CvihmoLjPy6797sCi95ZmZUJg2tlOaxpoU0GsjDPWkQM/s +rs6ZMQp7mcHUqjNa2CtP77RIAv36yUHZqqA33K2S0lDBDtkucf+xJrZu51bb +Y6BnuPGdWg16x5+7Sp9BHyi5wkES9nG2C3VUsSu6QuY+H4Nd8zYz2xN0hUG/ +fPeBXujubvMAdI82GSdT0M9uv7+/jtfRHsx7fpk9fZeaHrbxykzvuyrYEqpi +oa4TsSO3zexYA64fFnFvfpIuts2v3PWSatjyek4aSqBbfN82Mxr0Ire7WX4T +sNPvlb8br47tYf9bcADooyvnT40F3XLI1odndLCL3Y2ClUZjT4lw/K4BuoL/ +9c9HQP8k53Y1bTy2a/eRlkrQXVa9UXID3WjnnjgTja//7sGiNF9BRKigCfaM +oZntVqrYShLPjogaY+d+lNOh1bDP3HmrrjQFO+OAt+pIdexfpR01M42w1zd8 +tK8BffbksbsOGmJfiNxvGT8ae2fYhW3Zk8H108S07cHnv9Q8OE4N9My6cwb8 +Y7CLh5wQOWGA7Sogeegs6NKm3Z4d+tgDTQSklDWxszo7Bu0APWHzsbdhvI72 +YN7x876bdLYFtumk1cLVo7ANp1jvOmSO3W7cuWacKrad2Eq3+WbYTiPP7bFV +w259mL5k0gzsertDbz3UsVc0t+RqmWIn16oVbRqN7dyaf0BvOnbFWeVaBw3s +HXElGrOnYW+TcFg8Ywy26Ou9FzxpbCk/PgMZ8PVnRAelxVPYOuJfLheAvuKD +eFTjVOyfqfaXfHjHI7QHi9KB32v4LBZhb33luz9dEfvyFWeDKwuwB7vGfVql +jD0tYki30nxsm/4du7+MxJ4Rvexz/FzsXIumT3NUsE3GR+1dNAf729y4rVGq +2Jf2PPeRnA0+n7TI05Vq2NnmZ99/tMbWi9+2Q3o09juDW5OSrLAf3do8X0cD +O2ya7oUbs7AnRnTpTxmDnSwYIRRriX1V9tNYfd6fL9qDefev0ZPGuTpj/2kv +bMqQxfbfvuLOOkdsW+FqlTR57K/Lnuz0WY1dNfeQ9ZVh2CIZ3w2ercQOPXGk +YIMCdn9ZxVuD7LEfz9GRVVHEDrrG/3izHbZuV7TZEyXsny5bzH8uw3Zb73nK +fCS20KT907Ytxf5nVblk4ijsB4bOd6VssUfWSGYPU8UeoHX71tPFoAepP13D ++/tDezDv/mAwSX/WbmyN1K4/N/phhw5L/tS1A9upbPghof7YBT/qM156Ymdb +H3KbPhB7mtXnwvit2P37JZS5DMJecWaAeMxm7OkKRyW2DcEesHuB/cON2MZT +QgXWS2NfvPrm10cPbKPup6/myoKvZ1/tW6n12MdPKK1WkseuSAs0tHPHLs8z +jy0aip0/fYbtg7XYLWP0fA7ynt+iPZh3vPv2a3XnOWzLtRMiZZq+9DrDn1qw +9wzuUb6azfEtuBfp19VJn8Z9/9NpgbrtuOc6idmmnMJdUCzqWFgn7tZq/8R4 +ncRdeNal9w3duC+NWSo/3wf3V4dlXPQFsCu2GJbpH8e+d/ymoqMQdprma8ux +R8Hn/0f5zV4RbI9+H6L1DmP3WyNvekQMW26C0XzrQ9g1hUZ6e8W//rsH8/7+ +dPwjJyVir3Oyqv9U9KXXUvx/4u4m4K75I3+VbwnugYePqpjfw116Fx+/ehnu +G7ebGHy/jfuy+aqpMeW4fzOo0g69ifvdeYkHFL7iXh5JLVgVh/tNkXtyu6tw +X3Dzi+CkG7gvGpM0I+s77sMWbb0kF4P7ry7zp6K/cI8rfX5B7CruZR7BJpN+ +435DcpSTaDTucxTibBfU/GcPFqWnPn7FV1L+tdeFUrojQxNwN2pVrzhXhntn +U+JvhUTc5Y//sl1divu0/JYrx5Nw78zsvjHlI+4V1QaaVY9xH+W/SUelCPd3 +wU9NJ6bi7n1lr6n8B9ytvLTveTzD3Vjq/Jxh+bhHzN2l+/f9Pf9xtFToC408 +3Pk3TXBMeoF7mUj/0aa5uA/4Y/ItOxP3kDz7Wtc3uGv8zpuf+/I/e7AYnbcu +5G3qoMpeP3dqjZDwxf3RoYwpvwfiPi4+SFbJD3cTQbVFGgNwr5w722mUP+5H +5Lds8ZDAfXbEqaWyp3H/vft5+9N+uEcUZd9rD8R9/qPdi0eJ4X7p88Ux787i +ru7s1ekjgvuPqp/LQ4NwnzTDyV1AGPdVVS9+Lg3GXboqS/OAIO6a+h6u/UNw +99wcny4hgPsgBcHlt0P/sweL0WX6DTnx0yp73S850lrXDnffP0LuzjTu8nVd +uvdW4B5hv0l+DIV7Yvi+S2NW4l4/eKRRswnuPkbutqdW4f5z/wr6jTHusY7t +Yj9W414X0R15ZwruZ7fs+cfAEfdqs7OVEUa4C822/bjdCXe+3ET/c4a4ew5r +1Ix3xr3ttov+ucm4b6s/nFnkgvu2REf3cAPcBTXe6ne4/mcPFqM9atdaDtxc +2euR4YkVJZq473p7e9+MTbiv3vr5Sq4W7jsHD/A+tBH3tKCH7o+0cR8X5pOZ +vQH3H5fGfA4ai/sol7IsJdDrXjRdcRuH+34B74E7PXCfmJu9RG887vmjJEZ9 +XI97XovO/nrQn7lvCDYDffUrm6hrOriLnTwqdX8d7nzCj+nFE3B3ebxl/FjQ +q8MmvejgdaWeF2TE6NwttvU3LlX2Omps65SklopeS380jpgGerTVozXTW3E3 +k9EcV3IR99Cjo5qegL4uhU/dC3SnlJOek9pwtzDbOHQ06LtHquyIBF3XZ+ql +vAhw+78f7RJvx11ob8CqI7Bfftm0FnRzZYfuqaAbOI2yTQN9i3vlmPZw3G3U +LvUb1oG7LSV15hHoIzI/u6zp+M+/Ry5Gf5C0MJ2aU9nrQ8H2JdcycDeKlP/Q +H/S04gGrvoN+YUbtjk+vcZ8UsDBOJRP3aRILcu+BHqf6WM8WdF9Z3QA/0OvH +TVh6HPStMyw2uoN+cWnurgTQM4dsGWsN+vfwnN9loOenTjo+DvTpO+X4RbNw +nzJAfa4U6AqWXa1jQBcUPmrdlo370Ox3w2Zl/effIxejvf+Z/GJ+S2Wv54Ws +jT12AfebWv3XUKAP+9ytGwn6VOdjfONA37DAUiUR9AbruKWKoE9e5Zf6GvRT +ovcsB4G+Lldn1mfQK7OOXBYE3ad8WX0t6KkDZ5i3NOPuaXenmi8E99ahLwf8 +Bn2PSLnjQNBdnFeUfAF9ykzFfcNA3+pjHvwR9MG/w1er8XrPy/kmvMdf1rD/ +j70zDaeybRt2RTKlaFRKpKSBTKkUC5GEJkNSGSJEMoWkiIwZ0kCRqZJMFRWl +wSxj5nmerYGkFFJ97nvVcZ7X+tP74/vxfe/dz33br/08ziVLy3Ns3U8Bx8oB +YPcQT4nLtsjPCWLOmI15mluxfgDmZQZumMzA/E+5Fb7XMV+UOjfj2wrkbwiu +q7+N+axh+/CvmB+uazKMxvx5323fP2F+34tW+fuY53v8sWIE8zMo33weYl7u +PNfsYcx/rHbdm4x50ycPrlIx75p6Ovwx5usjFc3JmJcMpHik2f7+75GzksRn +USZKSAPAklaHJA3UkNcrWNBejHnO8LqXhpg/KKVNKcJ8XowomzHmI/Yx8+Le +0FNE5ATm02fsMn2HeY9DTqtMMN+9aqCkEPN98xo+4z7jtq4K7tnaZZJMMZ/N +fqm2APONlvW7T2L+iMNbO9zLiui8x/0+l5KVuN89Uq9gpvb7v0fOSjLpfLHy +p+EA8MWSHYpv1yCv23zHEveSc23q32BenHVhMu7fvuVyxf1Kk1XduDfeo7oZ +9yqtNvNmGCG/0St75DXmL72xlsb9o0HXV7jf90lVG/dOebVBuA92/H4G92+Y +TSxwL7jFyBv3fUIz1HDv9GLtbdxHNT0S+8fT98HTn49jx4043QaAZzI53t7F +hLzOtdAW3DuIjlGVMG+TxC0/F/OnG1mP415Wy/Yq7ufc/EhWxPxXuZk1uK/K +/uaP+66r9mxcmJ8q1NyJe5eaKWncR+8q+K6A+SOVp47g3tOqrBj3h3bJOOO+ +UW9PNO4tNoRdxf2tnZ6u/3j6Pnj65/Gq8STliAHgxh6//tjubuC9MUmzVDB/ +1rPaHPcfH1fuxv1xtqvMuOczGruI+4Md4c9iMB/i/iER9+5R9Q64b+md+R73 +AV+/KeA+VmySjPv0wNO8uO/wVZ2xG/OfAxdNRGNeMoCHB/eGO9U6cL/SSHEV +7pcvflHyj6fvg1lJbm5DWkPPB4B32r3yu5GHvMWXx164f8g7qoD7RdeuJeH+ +sNoGdtz7b5xVjPsF47Xt1zHvvL6rA/d5w+ve4D5N/8FH3O849vMu7rkmHH7i +/oNHUhDu76mKsQ9jfrZc50XcV/J68eBe7kW4He4PsvxcinvVOm6Lf/z5fz9Q +T/99V/9m9daKAWBXZf2GgTjkN0ZkyeJ+k4z7U9wrqgxq4F5CxOgW7l187+vj +Ps+qzRP383awnsR96Ew9B9z3s/aexv1PpTvmuP+UW2ePe0OXVwa4by7Vcsa9 +iC6zHu7P2bw6j/vxbx8O4f7sD42LuP9msnT/P56+D55+v3TuMts/MAD89gmz +g60f8ivDZtvh3m3mmxO43z8+fA73yt65urhvE89xw72G6qgm7g0T2S7jflDc +URX3Hyw3++Be/+0TJdwrMXn44f7hHFES7kXytlzB/ZF3t3biPpbPOQD3K+XT +ZHHvGWgSiPtHu9S3/+Pp+2BWUnuAycXDPwaAL632HeGyRj7gRrMH7vv8npBx +zy7P4Y17zvHSXtz7yB3yxX2AgnoX7t1aP/vhXv1VaTvua934r+B+T+rMNtyL +co0R/IK1mS24/5wfGIB7blpFM+6jJyYJfufpdQRvy70nEPc3Hzxp+sf/uw6+ +zUpKrjN7a7VwELgpcDv13iHk8xsFs3GvHus/iPs7jjo5uO/7lNyPe7/5G3Nx +/1XJqA/3msbZBC/7yaUX91cNhPNwb8jS0oP7kW5rgueetCT4VVdiCF64fSXB +r2XJI3iFQ+Ru3J/62kzw3mvy//X0ffD0z/+XnXX3RQaBT3j2JC/djrzPVo96 +3Ddk9SXh3mXmB4I3qdxO8D6qWxtwz5L8LhH3MfctCD6Lz4XgNXr9CX57uzLB +5+2JJXiRFEGCrzF4QvBx4+wEv88vk+D7ZnxLwH2yUQ7BG8uP/Ovp++Dpvx/X +yFcslBsE7nFMFtITQN7rjiPBcxzQInjFqnCCjy1cRvAP7dMI/tuWsdW4l+7K +IXiBtFaCN/hUSvC5T8oIXse7muCXyuUS/IfKeoIXsnpF8DxRTQR/ejyd4CXs +WgjeYf6zfz19H8xKKtE9V1F+YBC464j+Oi025Js0rhD8Kjc5gj8aH0rw5Yob +CV6/JpLgu1+vIvjL+ncJvsGBl+BjtsYR/MfmhQTfOSee4O+OchN8xMaHBK/B +N5/gb/YRPe8nLoJ3OpJA7GXonr4Pnn5/mc6IazcZBI6wzu6d/NgFzNI1m+Bf ++mQQvPd2NoI3XpJG8DYqHASfmv+I4P28OQl+9HUywS9Xm0vwpm5JBH8rh+iN +3iQS/G12LoJvUCF6KRmiP/UjgeAdDhL9hmq6L/93H8xKGvtRL6XlNAgskaNl +Q2pBXu5aI8E/2nCQ4EXdmwj+RNx+gg/hbCZ4vqx9BG9qQPTyMkSveJXolw5o +EvzSFKIvzSD65W+JvieC6IWKiN76CtHPf0/0GZfonr4Pnv5+mbe5YpvfIPC9 +xPOOvAXIy7sSvcYXF4IXyyT6p8FEf7qN6A9qE73LR6JfLkX0PVNELyVA9MZM +4gRvu5joF84h+oPziV6UjegbOInekJ3oW9npnr4PZiVVl7Da3Q4fBBaSav18 +/jHyev1Ev5yF6M+MEX0nrYXg074T/bwOot8+i43gzzcQ/XNmoteuIXpuFqKf +V0X0lQy+soLot84hegEGb8vgc9/T/b8fp6nTf/+IKfw4nzQIvO+7EotBOPLX +pIleZ5Tof2wl+mAa0ZdvJ3oPMtFnyxL94ADRk3YQ/XwG78ngo/uJ/gGDN2Hw +Lxm8EoPPZ/Divzx9Hzw9T9fSmPxqEPiSZn1GphfynHpEv0Cd6PMZfLMa0Qsc +IfodDH4/g6ftIXozBl/A4O0Z/BMG78Lg4xj8BQYfzeDdGPydX56+D2YjBZon +vBksHQRecndTv48t8g0M/lYs0U8y+KMMnsOC6OUZ/EIGv5nBL2Xw6xj8cgYv +xOD5GLzA/yVP3wezkVT7tF3dWwaBJ3mfrso+hrw2g+9h8EcZfAODN2Dw1Qze +iMG////E0/fBbKSTBXln0imDwHsPtoccU0PenMGrMngLBq/C4E8x+F3/Szx9 +H8xGSm5f0B08MQgc029APSLz1//J0/fBbKQL5d0PuFnJwF9c7LWfCv31f/L0 +fTAbKY3fTIS0mAzc7JFjaMzz1//J0/fBbKTTA47O/EJk4L4YvckTM/76P3n6 +PpiNZLOgZv9TcTJwJcnM6Nlw51//B0/fB7ORFvQzrf0pRwaeu0B75f62v/5P +nr4Pnv78tp5pPYs6GVi3RPCbZNlf/ydP3wezkfRU+g6VHiYDb5x6NXX01V// +J2/77w9ENtKRHQmmB0zJwFd41h0rSvzr/+Tp++Dpz9cX938MtyUDu1raeduH +//V/8vR9MBtpxSu9Y4kXyMDn3MS4jvr/9X/y9H0wG+mm6PPBS35k4DRP31Q3 +F+RvMPinDP6/2tP3wWyk2N3Kj1bfJAMbvMg80Hrqr/+Tp++D2Uhc5t/iQ2LI +wB8jJkfO6P/1f/L0fTAbaRVHVGp5Ehl414uUx1vV//o/efo+mI3kdk3pSlM6 +Gfhc8YdiqZ1//Z88fR88/flmz5WW9Bwy8NNHejeNRZHXZ/BpDP6/2tP3wWwk +h8I74mZlZGCWqZlu2fzI2zN4Vgb/X+3p+2A20vzEzyy0ejLwk81P2DS4//o/ +efo+mI1Efsmco9JFBlYL3lHGwvTX/8nT98HTn2/8ktOcqWRgpxrRzkZyx1// +B0/fB7ORhDcGr/AcIwOfLuo3mCj/6//k6ftgdlJR9R5Js59kYI+bK1Ks0pB/ +x+C9GPx/tafvg9lJxm+DFq9lowBvEhE/vznsr/+Tp++D2UmZzsKt2TwU4B3y +R28ruv71f/L0fTA7SXG488pWPgrwh8XtIzFGyCsw+E8MnsTgvzD4/63n0/fB +09+fj08IBK2hABs17/Hcs/uv/5On74PZSfVHJgNyRSnArU8nzLdv+uv/5On7 +YHbS1i+7n9XLUIAXzLlbYbsAeRkGv5jB/1d7+j6YnXSt4INdKYkCfD155sTQ +RDtwCIO/xeD/qz19H8xOujN7c0TsHgrwJ7PkbSmdyEcw+K8M/r/a0/fB7KQz ++TZf9A5SgNUEhr6mvEPehsGrMPj/ak/fB7OTZo2+Ux47QgE2fPwmcfgR8jMZ +vAmD/6/29H0wO8n7nr2iwwkK8M4d1Y2nQ//6P3n6PpidxHtqb1SDJQV4s2f6 +kvUXkV/C4Lcx+KUMXprB/289n74PZie1e4kwr3KgAOvofGMXPPnX/8nT98Hs +pMkE9aWarhRgy1n2J7Q0//o/efo+mJ2U8inN2fgyBTha/Xx71pa//k+evg9m +J714YP3mWAAFeF7/IeUT/Mg/Z/B8DP6/2tP3weykRokxZ9INCrCwhrvVTlbk +6xm8OIP/r/b0fTA76eqE+VaOOxTgcFEpSY2PbcAhDD6Uwf9Xe/o+mJ00KN/u ++fYeBfildbFHSDPyPxi8LoP/yOBDGPwEgz/N4McYvBuD/8Lgz/8/4un74On3 +f0pE+5EkCrD3UnlNtnzk/R8RfctCoudj8O8WE70Og89bRPQyDF6ToVdl8DMZ +PInBr2XwSgx+KYNXZPB8/8Oevg9mJ11P1XnXmUYB1vPNDnmagrzqC6JXOEX0 +kc+I/rkL0UenE/0zW6L3ek70cY5Ev4qhH7In+lKG/tRZoh9n8LEORN/F4Ocw +9DQGX/+rp++Dp78/uK1e7M+kAE/qSh0MDkM+Sp7o7X0kCV5hDdHL/iB6ZSmi +v5ZJ9C82ED1vF9GHbSZ64VKir9xE9IkNRH9SjOi9KoneTZToQ2uJfhZDr1pN +9/R9MDvpft7CdUk5FOBylZo7EZeQN2lfRPCeu98T/IMtRH9Wrorg14cTvaRr +BcHzGxC9rk8lwa/1IPrWQWJveJrom1SI/dNzRL9kHtEb2RH9ls1En+lI9H58 +dE/fB0//eV8K9R0pogAfPFHi3WCJ/IaYOwTfd/0Rwds13SL45ldZBF+5KYLg +z619TvDUN7cJvjPlFcG3x4QTfMWDDIJvXUj0XYKZBL/Tkugdwl8Q/Kg00V8L +eEnwNTpEL/6V3tP3wRyk0iQrVYFKCnBuzPhGRR3kV1OuELzFslMEL9nvRPDO +5gUE//LFZYJ3pPgTfPMlV4KXOvGE4GcWXCL4ZqNbBD9lepHgX+TGE3xrkDvB +PxiMJPjkjW4Ef3TrfYK/Po/Yq22K+dfT/+d8DpLtzyPVOxsowPJJHM+aScin +GXwgeG8ek1TcfykJIPj7t4Sf4p6k9p7gg8K/Efp5hXcJfjs1Nw334Y+zCN7m +ohzBz3ZJJvjlLqEEr7DzJcGfmn2U4D1ynxD8SIsHweeYpBM8H5fFv56+D+Yg +nbkqHqjSTgEWejpLLWYD8i9lCoNxf+uWkBzuef1/EvpnF/ep4L757FZCb+v6 +hIT7p7xGQbjnbArahXuWA2MEf0OhTwH3LvuCCX774Uwl3J/zrCP4sEtOirhP +k4gjeJ5UbUIvaV9I8KLvXv/b0/fBHCTtLodm2T4KcHFr7cZri5Fvktrbh/vr +n0onQzDfEXG9DffCm06vxPswa54e3N//NHc27gXuruvA/RlJ/iW4j2Ua7cL9 +zWAFdtwzM38h9LJfTi3APTXXgNDvLu/lxP0VkeOduLfh9+fGPen2IkLPJS3L +9Y+n74M5SFvPrONeSaMAs29cm/d4JvLua1V34D5NQenbI8ybxvnz4T7sgHEQ +3hduHZDEfYg+ryDuA48/F8R9RnKZLe5JcsfEcK93cLUM7j0jOdfivtBpvzHu +m3IHNuJea4GfIu4XDLcI495siKaH+5nZ1zbg/mvGc9V/PH0fzEHafDLTcmiU +Aly2/czHcVorsLnGJ65hzH8OIk+MYX5vRf81vOfgXCuL9xfzNn3EfU6H3eUv +mM+V9knAveTu1qqvmH8Y9K0D958SnGrx/mHfrXTce5Ry3MR79QbOetw/fPx4 +Fu5PHVvzFvdXbKm2uG9bv78S93ZtRiv+8fR9MAdplzdXecIEBfhYD/vmM43I ++35yXJaMefeUdGsTzCtz6qsnYj6k0LjNCvNWBgnpSZhnKx4incR852h4ON5v +6Wo+Y4l5/WX7z+F9b6SHgRnmqy2fleD9FdP1wacwn84ffgjvD71KmmeO+fU2 +yoN479bHORvvl7da7sB70+zP5//p6fvg6Z8nN9LZDs6gAufWbKEtzUe+WoTz +ux7m+1r6733KQ/612b6rhzAfHhWWz431yW3WOYcxryBMs5zA+khpw2AtzMv4 +eC6di/XWjoc+6WL+ZpeVxHesH9sxIq2Neb1Aew52rL+z75UV3stW3kj4ifVf +eZ7fxXvTiJNzWbFe5kz9QrzfE/JWeea0p++DOUgp80dLu1iowKvTfwZyPEFe +83vUkinMm4VnFQY/Rn4zj4d0P+Y3xjMXf8G8SlCd5Tjmu9+FcMViXupzuRIZ +8/41904OYt7uE7lzDPORlyNYUjAf+zDciIr5t6MaNu2YJ+1asPIz5q+4vt// +HPMWxo2NNMybqH7za8B8yOuqvlHMFz9L4Ho17en7YA5SVZ3sg71zqcBaixfn ++NxB/ttDpxnRmFemuVC+hyM/3PAmWhfzHPFHNu3D+oZsl5wbmNcdj9cSjUA+ +dXeemSHma750PV6D9TNiL+8MxPzkl6SGA1h/s/VI40nMZ3tcVpyD9cektTN9 +MG8t/ajHEuuDTYxDLDGf+nHy4wjmO+J3P/bEfEr2iR8Xpz19Hzz952u2SNdi +ARV4gMeveZc/8snHvxucXIg88/qTpTe8kN8WsDLUB+tTggJOP/dDXp1kWrEX +6wV7j5XzeCOfpt3LGo31ZJVMWRWslxdbKiWD9b2XbK44YH2uZueWVKzP5zSa +PeKLfP+y7VuFsf7tg6f62Vh/flx3XxbWP+LP3piC9SsmHKqXYX3IBSaRb9M9 +fR88/XmW/PZH7VIqsMNUuPWG88gvNduukbYc+VnyXzN8TyMv6jVn1nJe5Pdv +MNdsP4f8sE+ytT3WC0SICDyzRv7IrmQ1LaxXSB9+Ue6MfPXrBqo81idk3zqd +cAZ5R7ef6z2x3t3TNW7YCXmy4YUXi7A+apGjoZ0N8uInVH0TsJ5r28T8rVgf +0Rq09tMy5PVNT35bbNv6ax/MQbqwVfDgDT4qMDPlnN6wPfKRUcXxNkLIm7nd +XGGoifyDENppoRXIByaseiWHnW8WLxs4tBr55bJRajX7kbfpYLkTg/Uuks+W +DFsj/1mUT94V65s4NGU/HkTelGlfPMdK5Pd8khX+YIW835VgrWVYv6XkjluB +FvKHC9M+mWH9AXsfvy2WyB/bs+xFgSDyLZc+Ljqi0/prHzz9fhtbuSJg+uv3 +m7Umyt4/voh8YI9+Vthm5O3sjF9eW4n8+rWubZ4rkN+0vLB1ngvy1y5Vr3gh +hnz96zOhhYLIx+l5l55YifzyflfzrrPIP4wpHaaJIt+sOLssbC3yfhm7j4vy +Y/cvGMtdaoe8TI2ZkhTWa+Vtz5y3HnkTpn05fVi/Y9wmJska+dwPOoYBm5B/ +OXdRwZZNrb/2wdPfHzoNTw8uogK3LLnLV5mE/OTYcOAsJeR3fRs2mVnZAtwX +EK90ZTHy+sX+TFNxqN8l1a/yRQF5BZNW8cV1qF8mZVf4eAnyR147zPWJQT1V +NthugoR84cmyhx1NqNfdQuPJXYr8O7vUIPMI1LuoHKtgx/qQRTs/nWhH/f5j +q3LzeJFP/ib8/VYo6vP1dBVF5JFfpvnW9WF3y6998PTPi4wVg3eZqcDOccMT +U7PbgJ88L/3oeBT5QTGh0xuOo36m6/E9AbORZ63q7oyfifoHrx6cy9dHvtB/ +8tVNI9QrD7bsOcmCfKpsll/E91Zg3bU3y/iw/q1tzUSJCer7rKxdJeYgH5Z1 +3a9yAvWfeRJ6Lx5BPtZ9j0SlGeofLPXcMYr1TX3t50hfUP88NaaNrIf85xHv +koRTLb/2wdOfJ+carls5TAE+7GN19Pz5NuA7IZon2J2pwFSW4jjDzmbgne1e +H+yw3pbr+hrqOdRPhJ4cqnFCfW2R1QnrLtQ7ylh6vsH6LU9ecVxxRv3B7XED +97DedlHatqPdqNd0ctn6E+sdT2mVajmh/ri+xaVzWB9M0pYU7UG95ewl4ts+ +oD6EeRankiPqmc5az9HC+jVTSsUD0z19Hzz9+4oejWLZSAHOOGi/4xqtDZi7 +6Zy54lUqMFOQQfMzW9SHHRqxd8H6GH89Lk2sP+e4Jmc71ie7HxVowXrtijmf +vLDeU+P7qqVYv2ZGRpoU1h9sV7ecwPrLkykcwVjvkJNydoiK+vWGXgNiWO/+ +4q4Jtx3qbwimyYVi/eUfak9KsV731vjyjVhfZ2djIDTd0/fBHKR7vsN6vIUU +YNq+lyynNdqBWW4/v6p3nwrsI7kz0nsx6ndOuAcuw3rjUUdLM6xPLS/lxPu0 +bWZb/LB+NNbceDnWPy8b8zuB9XuHXVIPY/0p/5ZZV7A+iL9kDO95mmSaDbFe +fdEuO7xff+aOQgDWV92s1OfDersG/h/Hsb5m4yUVvHfdp7IycLqn74On3/97 +PChR6RTg+4dY87Ni2oHHKEceXXxOBR4pWL1Zp7gJOIf0/RPer7OYDMP7gqEF +SXj/qqyIhPdvs25N4D13IfUC3is/Xp2A96LLY9Xw3r6SPIX3Y7Ie1nh/f/2P +eLy/W2m/H+8LmTt/EF6/j4kp3rsH7Sf0fX59h/7p6fvg6c9LfBU/hBIowHNG +pCQiKO3Alz5zld/LpwI38JzhjfFCvWXRfUK/bXSc0L90XUbos/mlCL0W51VC +n/jlsCTe9wmuIvRy8ksI/cpeL0If9tOH0O8fECT0X3jZCL0xxZ3Qf2SLJvSH +FYUIPfPGWf/29H0wB2nVvoZo/kgK8OYblSuiNnUAp/5M79eppgJ/cqoJe62K +ek3jWkJ/flE7od8UnkHofY5VEnpJUg2h79vfQ+jZ64n9E5EKQl9cUU3oybp9 +hF52iNifTntP6HfeJ/ZfV/UTeukvxH7XZXpP3wdP/34+xnN86zUKcPkpjmem +lh3Aq01FbYfbqcAGFyV2cnGj/u4HYn/Zk9iTGXsXYs8/TOxd/Im94EliL3OO +2D8ZYugDiL0EQ9/nTOxDGHq2QGK/laEv/NXT98HTn58jBeW2+FKAO2bOKp4Z +1wHsXCRx/B6FCjykeErWq63xP9/T98EcpH1OlVofL1KAZ/ifMNvc0gHsIh0e +HDlGBRYQmBF4IuVvT98Hc5JqDh7QV3ekAH9ULj0oN6cTmGI8qDj5kwrskf9s +1Ur3vz19H8xJ4lOVXCBuTQF2sC39Fs/fCfx939GUCjYacLFLus9e7b89fR/M +Sdpc67Is6CQFeL3xAvUfWzqBb86rERZbQAM+sN4m4PZG1LfUEHsaQx/A0Lsz +9B8Y+rcMfTBDb8PQDzL0FQx9EEPvyNBTGPqS/2FP3wdPv54TP/21DSjA7AF8 +3MYancB+eZbBa/lowKaL+W4XzkY99dEPQu8jvJLQb3lI7IviiX3UMLE3DF1B +6JtSib2HA7EXbiT2IcXE3v4RsQ/zJvY8ncTeO4PYP3hM7KXd6T19H8xJMhD+ +ON/1MAX40uS+r0PGncA5C9nFcoRowNI/h/QiOxuA2WR7CP2ipDOEnuPEHELv +YDJF6E0TyIS+f44RoY+KZSX0im/HCP2nJ/2E/nmJGaF35iL2bpXjhF5i/iCh +V0gyIfRnDhJ7PdOv//b0fTAnaSRyRG78AAW4kLl09QunTuB9i4uOsm6iAZ/O +ulL+8TXqJ3YsP4D3FM4LkxlYP3KZzQjvvw2np+P97isZKnj/fh8fDz6f41z4 +cbx3v1mQh/fJ0Q/V8T696zYz3guU/jDA+6tUjdd4H5ehuAfvfXIPceL9OSZJ +Qh8keT37n56+D+YkLVTWK8raSwE2Kc4PbLzSCbzT86oykzQN2KOEdP9uOOoP +3/+5KB/rH44cevce6x3Y+e2Zsb5k7+e9d7D+p33Zmhysl5D4Zl+H9XnXt8fh +8+15x2Ni8F7YUDgP62X7j/dV4vcXrxDH54+8y0qKxHpjl/QifL64KWVmLdaT +N9VU4fM/f815Ej3d0/fBnKRtVgcCbyhTgC0aq+NaozuBkwPvjz3YQQO+8t24 +5cM51P+UFY+ZrYL6ZgE/ptYo1MtOnlQowXrnjp0zxLF+SvpoThI236p/+fd4 +bP6izTpbH2E914M5t4uwfpHPfqFPWG/TUfd1NtbvsRFwz8f6503VK/djve+Q +lEUm1rP1iWV6Y313Kn95GtavjHOueTzd0/fBnKTUsKt37+6gAEvv3/FlY2Yn +sECp7PKPijRgjd7P1w8bov5G6CaFk0qoz3h9ebQuEfVKA3Kjmsqo5/UU3e5+ +CPXBnxNEFHaifmrYp73gBepfs7AkrVdC/WGjcdIqA9RnBjntqFJEPafFqr3r +klGf+2RDGR82X1tS4vJVLdTzF17Lz8Pmp+ud+BKZgXrTl8KFetj84VymuFXH +G37tgzlJ8w2iSZ8FKMCWnx2crac6gRWZuUpvkmjAMZVGUrfPol5KgS/mpw7q +H82XoKy6jPqdC5lHw7VQv7ztkG0QK+pfmPgnrBJEPVmBlM+OzU+QFwhOwuYP +3fGbsxqb7zarNf0dNn/4xNGfMdj8bjct5QBsfqmyS3Q7Nr9Hx/68Kja/MT30 +aOo31FewHuDMwuav9kjf8tKh4dc+mJNkxM3Kc2gmBZhT+Frv2b1dwIkrmwVK +ttCAK/don5R7ivovPuFLNC6gvuq6XthN8U7gXTu+xmmboj6Ct+bzkuf1wPaG +XkLq2Pyf34KVvbD5Dy+8TS/A5tvk9xzWweYvXfNhxWFsPp909vB5bL5oxZcs +HWz+gdkP+rix+SHjX5j3YPN5WM9JBWDz70W9eZGHze/ctWCN0fR8+j54+vtj +pDfDZJgM3JKexhxzvgtY27vXn1eCBny6wsppWx3qf76xvGcSSgF+doU8S3ei +A9hjZ0LEXRvUr7c//J16sR445QNx/tIXxPlDXsT5sVXE+TOyiPOnvInz3Rnm +SzPMf8Ywn41h/keG+Vd+zafvg6f/fmh0VDbrJANrlT68mxXTBaz9itveTIwG +/EJeqfY0DfVCGhaz7RMpwE+CrK1nPegA5v7axDHDBfXzmGbsXXaoHthHvHmO +Pjb/i1WNbzM2f1bGxWfHsPmdQXmJd7H5fstoOf7Y/DUf5xeExKH5NF6v+u/n +UP8wLCdwLTb/e/qSWCNs/n2256xl2PxLvAfHjLH5pe/ui3pPz6fvg6d/P8h6 +NH6ikgw8URr6YEtJF7AO/+vBLBEa8IfXkZRnCxqBY98M8PsXUIBrLpbmfhfr +AF54leuBhTvqr+d/GLCRqQcW5do4M6kZzV9JLbyb+hTN72rwuOohgXqTvEzZ +db3o/s3z6vo0n6D5I+/qmT1vovkDR6d6uj1Rr5IssW2hEJofWvhUawH2+mdG +pU70Y6/fzWCr3zns9b+R9NeWWNT4ax88/XlHZK5GWzYZuH04/fzF0S7gVwvN +9nCvpgGHaGZ33yChnmeqpyOvmwI856K55JeUdmCfCdZlZA/Ur0ytWOciXg/s +PdG6LbUTzTexXFlYnIzmF+xV0d8hj/pPyw/mH4pvAK7dO7RyIhLNrzWrjmIa +7wAO2B5pdCQY9cKnNEM6qHXAG3gOFCzORPN3tb1YtHVmN3CSgsae63zY/fXf +LX5+ovHXPpiT9PXzlknnZRTgzYGvfwpJdAGPpaRXpU3//PjN8R6STONR9cCz +jm48dF8I9e+PhNoILUe9Gru1cKQj6j+cTE6YexH1EymltrsXoL47R8r2qCLq +T3T6ryNZob6JKygxJQP1svVfD3qJo54au+F11/dOYFtp2QTnC6hnvbg6v0oX +9ZnvbhlU/iADr/uW3yJvg+YL7374yPI46tdwHsnew9zwax88/fVOXL3JZooM +fKTFraZ8+ufnb+533PCpzIQG7FnAxidKrgfeK73nibYWBbggntWS9Vkn8AXv +DV+Tb6Kec3H56dmNdcA1leUGGjlo/o/sUF/zH2g+jdT1+rs46o+cshN4OaMR +3V/dyprWhOb3vXSv+DLcDpx4UnFWWgTq3Xl2vFicjuarR79c15+C5gf2ZOnf +WtcN/HVm9iuTlag3cxga0rFs/LUP5iTJHc06EnqFDPzoAy1wyrkb2KmW8+nr +H1Tg098C+fj4m4ATk+XSGo4g/3NC99IN51ZgNtVCi+Lpz1+/uaRM+OBitQbg +GhH2g/OCKMDr44o5RyU6geP2eT//mIz6Zz0fzQWP1gEfkjm05IgHun+iyGnf +pwHo/uYZ+9njPqH7BYyt9Y05gu5/qUiR74Qt8p8G5E0tZ6P735xvKHltB5qv +xfFK+URFw699MCepfqd0WWokFTjcPeWQ2PoWYM8EWpfDfBrw2o1D/lZFjcBS +fZs6dBRRXxJdIrfgZyvwMZNE7StOqB+wDJOZFVIPnBV83Fx/GwVYeobwqOiP +TuBF23yuz7yD+nGeV7Na8uqArZOlM8SKyMBJpORCsaku4IC+8sVrdqO+zp3T +PTMSvf7oQ1TP+1loPiW9c5PD5Q7gR9Vnq+PSUT+VPD/y/Ma6X/tgTpImv1uW +wvTf779ZeZe42NngemAOneBr3QoUYM75fJFRI53Alzk6B9YmoH4H/7XkCXd0 +/l0WBVabRDKwpWGu4S2lbmDTy7rxq8VQf4qqpLNkfSNw6qWe9yvZqMDZT2Yp +caxrB/ZSKDjNn4h6w1MmHvbn0Xwrz5umm+LR/DKthzVJamh+18Bh/8sbUL8z +xfzq4E403yfO4lkZN5rf+63rwYep3/++evr3pTRn1cR2KnCf0lN52f4mYDnt +Y1612cgn+a/WrbjcDPzg4s29rp+RX3/CcULRFvVGW05PioUhb2bEoetr0AJ8 +dm6yY+L055PfHFx0coUefyOwdmxews+5qJ/RG1rou6wd+EzxA+PBNNQn8AYe +/Lq/Dpgt8b3CZCgZuKyEvYvk0A383lSn6DA/6scjX6nO90Pzt3XMOhopi+Zf +vbf4fpH0739fPf15hSlbWqOeBlwzYGE/EFALHHw4MKVlDRm4qSUs9rZFD7B5 +UH6wuA8VeNmlfVbXX7cAUzc/mP39EDr/er53VdGZBmDpXi3BQ4UU4MXFsoO5 +Xh3AlIwgM9M61FvpnJQQuobuJ1cicltWBN1PcGl86j1jdL+1Af4S3gHofu/Y +pD62xKD7CWa+sJTXQOfbvrHo3nwT3W9BXtv7LY3ofuvTtnZEif7eD09/vefn +jOZMv39+81iVRYT79Oe73xyoor+xSYwKfONcntQC7zbgDxrBozOfoz6ZK9Bi +sVYdsNIM71lcSWTgg+I3OXO1u4GDbDz4q5VQHyzvwFJV1QAsLHBpiP8HBdhU +qTtv4GI78MyKrTIfK1HPbnnJb+vTWmDXwlZeg91ofnrIgbCa9T3ALNk5u65m +odfHe0NF3TiqGbh+8+x5kvPR+VJSUps3DP3eH09/3lCf50xRowEr3koU7Utr +AL7SMHlKY4IC7J+oUvEgth14yCwseLIN9WfDV58nW9cC227yObNViAzs/kaw +M9+lB/ht2+w2g0Aq8OFQHif2Jy3AXPlR97hN0fnRJZWvmQXQ/WbnzlgYlIbu +52pb5sE11QH8PXzvo8tU1D8M4aCxrEL3q1M5kPfjwyCw3fMXftZ96H4PzdW7 +3KTQ/c5Hr+VmOvf731dP/7wrHOZNn/588ZvvmMuvzrjcAKzlEKf4gUYBbpsR +3VBIbgcuKeE+Kj2EevFbi0Z2rahF543Flo9/GQSumiP1+XB7D/DFteoDR3ZR +gUNTycp1Euh+LLU/no+8Ruc/sy87fkW6DviYSHZJRiIZeN0+1Q1uJ7qBtcWP +0rz2oz5DdMk97jvo9TlulBpbMI5en71x8o3raej1Re4Lc3Mho35/9VWOBZK1 +v/bBc0nSQbS4u2tpwNpr3lncDmgEvkV5n+x1mgostDSQx9WiFZg5Rf/79C/0 +wHpa76QW1NYBb/6esWOQmwJ87eoSzz2eXcDLM5aUxrxBfbz50Xyebag/Gef4 +cfQ5Gdhv/WfTwwe60f2EePW3mKBeaya7mPSWBmCDaLderko0//G5UtYhjw7g +6hvW47t+oF5oVie7eHYNMMfVARbR7EHgr2MG2VqHen/tg+eSvD68CtscPQg8 +b2HMWa8I5G90RoplxVKAlZKuCDyW6QROZnn7tI11CFgq6pBXmG8NsAHbq4LR +WHS+r/p7En8oOt9nXfNrw3h0vq1em8Hi9ej8eRoP3R3Y0Plji/P9lnuh81ND +LV+ex+7fd/yy62g4Ov/Vjsiiw3fR+ZdC+G7v2ILO33pmPOsDdv8Ft1sLN2L3 +P7/LXi0eu3+sk9GCp9P3p++D55KuH77/YaCFAqzKkRDVeLwDWFtfW/829xBw +a9Oq60/0a4BNZDI4o/wHgXd/nRXaV4LOd+Mq+xzgjM4v+nSxSTimE5iJyr6V +lw2d3/SzWHNZEDpfULrc3PcROn/tlKlC7GV0fomP/1RbLjr/9Zts5bomdP/U +N5MeBxai8xNfxHH67UXna3dwKH2/iM73ZlJ6dbILnb/wfUZMtQE6v7ndS/d5 +8+/98FxSQSb1R6s7BVi44pb9pmvIP35o/nLboiHgD+3PNYfVa4BtneSuR/sO +Ah+7csx2SX0v8I78euU7Z9H5JRnpN2eloPPlzj9zs+RG5/OwMO27dgKdv9Ai +8Aj1FjrfWLVgsU46Ol9I0XOU9xY6vyP72ID5EXR+Ku8qv8XL0flrjolcm7Ee +nT8e8NZC8Qw6/+iW8Y2cc/qANRNiLR/JofM12BNKDUR///97zyXN723e4s9N +A95+c9HzxNVNwC6OW4drqqjAoaeCw09cbAbmqGfJGt6LevKaOtGAjgZgwb7F +Im67Ub/0Fo/XAZ02YJqPwo9dY6jXcbZJ3stdC/y0SuHF1DIycMOc5zMPZ/QA +x4ro6CqGovPd3KgSc6Y/f/7m8L502YP30fndZ8/eMybXAavyGEzMVqIAL4yI +4lZZj74+O2i99QYzh4DLvpKj0oprfu2D55L2MU8c0bhDAZ65nCqUrd8J/DIl +Z4a92BAwZR+r6tE31cA9xw3EbosNAsuqKDJ7B/UBR8/ZaXIzhQzsq251V+xy +N/BSpl5WTRcasIr0hbGmrnpgo6qgzwdr0f3OKM9+6hbXAWz7qPr+Hgl0v1fC +Ist3J6P7xZOY78cJovtlb1hqfPcBup+r6oqK3CB0v+MCbesq36H7Rdk2y9sd +QPdb+HHk1HjR7/3x9PuV5er14q004B8vd8Re0W8E1tEctrtwjQoc5j/Dya6n +BbiWnbu2LQf16i/nGelp1AHzTx3xaR4nA4uxaM9829UFPLksSrGvDvVzvq4N +ITXWAnMvNMwseox6d1nrTxVe3cDrmCNm63uinnxJokcqvR746Olh+dJCCrCG +zRTJ8FMH4vjOxVY7h4DvZ/Kcu3mmGpiT/5PvpakBYJNymxdnP/f92gfPJS3r +VG/1Jw0BW133SxM4UQ18tF68ePu3AWA13tPvXH6gPvtOuP/jDWTg+DUbI6QT +eoC3Jsy4IJ9FReeVURQdfzQDJ3q7nd55lQb8/JKxP8mhHvj+qcVjD5IpwJan +BEIt5TuBmYN9ObuV0f3tYvX5MxXR/WOzeau7u9D9lZ3m3nPc2A9caNpQ8YQ6 +CLxjiDk+ZlMvMJPs8B4vVXT/pV/2vho50/ZrHzyXZOG9+fqM/gHglXYje99N +n/+bt84Q6R77NAh8c8OAQc7qXuAX3RK3nfSpwBfXBLJMLkHn22ikys6c/vvv +Nz97ILtL1LEG2LI8wzCkCp1fU+e1JNcCnd/q8Ua4bzE6nz91MD/QuR349W4p +viISOt+rWY6dz7waWNNo3PfiHHT+w7jRC48+9AGL+Ukee65KBhaO20F5Y9cD +XH9abFx9DM1/fzQqxbS76dc+ePr7UbemKuktBfjJq+FDXis7gZVctFe91R8C +fs3v1f61uArY/9n195UhA8AqX8OutBf3A1/qUhpduWAQ+Nm3+Vfbu/qALfWr +0hRNyMBr7VTtveR6gDWu6TqtEaYBH8pzXZ/f0Aic8d58w4ZeKrCg3Jmj6/Y0 +A+85sb70ghXqrc86qzTtbwBueKzGHimB+o7yTUJuY23AOjvWKd7ciV7/xZfl +XROXqn/tg+eS4s4azLLbQAMOK5f5blHUCPy8ueFC8AAVWGp5pkWxfDOw7+yn +EwfsUc+2XF34q3gDcHNQWUDYRtS/pJAX9KxsB653W/XERn0I2PjGZHbbJnQ/ +r7uOSWcoA8AfV2ybKSPVD9y7pdS1anIQ2NOInfvp9PvjN0fXxK6MtUbzJ6Te +Zv541wrcz/R4FWkZmn/w+YyrMsdrgBMr/ZlCq9D5wbNreyaden/tg+eS1r94 +baVjTgae0cl2UUCpB7haQLteW4YGrKL2MUU/qBHYViyLs6KRCrx719iE5+1m +YLYlq2f/vI36vb5GXeL69cDCHBLRQvkU4Jq5ry9v5+sEbn3zSFLVZgjYSUjw +WLFuFXDBhrlBF5QGgCVvV5YaGCAuauH+ZrMZcZdoCwebG2KNwyaZGpP9wMuC +Rq7uaEDerLZr6vVx5DetdvScUzj4ax88l7Rh/OurJEUy8KOnXZTy8B5gI5Yl +lKpvVOCIPNsfEdPv/998Y/Kd6D4zGrCpqeSOTu8GYMPz37pyLFC/Lul1QspY +K7DKhgv7crYMAR8Z5JH++LYa+FpjqOEmK3TfZi2pAzf29QFrHzRnMpGlAN8R +mXPEw6oLWFJ7cTWfPDp/uVRoyqwAdD5tneVxZmV0Pqtj/dnmcHT+uHkLX0Er ++vo07DCYPLu7+9c+ePr9N5SiuIJKAS7Yd7Zq4koH8Ov+J3HhnkPAXUPlP95S +K1E/uzmZ62s/8J1rZ+zYhwaAtw+ZmD5UQX5L0MMuw+n3228e3yxwOn5bL/D5 +iw+HVzhSgTd9Z1/m97YVeP1L957eLeg+Bq7CahH51cC2XDwaU87o/DXm/Qpz +5PqAd1g3q7bqodfbyGf3aef6LmDjuOb2ucfQ+S/kWb4/ba4Cfpza+9Qwe+DX +Pnj6983F+vI8aU3ARgUNvfcsaMBOVvNjW/0agIVqcpsVL1KBmYIaDmhHtgIr +Rq9PTdg+BGy8wHfusmfVwL0bcqrrHAaBr2QlXfbQ6ANu2PLWf+1+CvCcRzLH +j+3uAn5p/vn+bAN0/ubraRuyaquAHwZlB2blodc3UTRxW+J2P/CsovwhHV80 +v8hg9TV5YTT/TEfn+cMX0fxYW+VjRo2dwDsFA1p3ugz92gdPfz3EmhZ3SA4C +q0SbvJtd3QfsfPxkbv0jMvDCa+La+3K7gSlXF2vvfkED9n08aTBZVAfMWiZR +b3eTAmzI1R5CjusE3vmxomx9ILrPxwqLc7GvKoFbi5I9ilr7gef5BUfHCaP7 +/nAfjBMio/veFVh52CUY3bftYfLLxaw9aF5EOnewH7pv3bEbn5qb6oFFz4Qp +bRalAq9dYp6+eG87cElU9n2Oy0O/9sFzSWcPCIodnqoCXugiynH58wDwobYz +u5fu7wceDyoZjGQhA3+6VpixWboXeA/3iytzw6jAjnqkBfc3tgL/KL2/z0QG +zd+h1aC1pK4a+Au3y2PO6EHgbumyzDLWPuDF66bqIp9R0P1luN0aj3cCH3UJ +vFQQjc5fb/XT7rB6JTDPJdXID+7o9QR8iWQXeovmfe5zZtpbgl7PV23Wmoxv +aN7dUd3uW4c7fu2Dp/88TV93vzlKBc404/n43KoNmN1l+fx21yHgVQb9a802 +VQGzUTOsavYNIL85yU/zPOK4s6sOv9qMeA3L1c2hjxF/jx/QK6vtB/Y/JHic +bfrn+W++bjWQppPdB9xyVvOIdiMZOOtQ7ZrDtt3A+oLVLpNTNOAV4TkiPnK1 +wDb3OxTjk1Hv/WFpongt6tMO+5OuZqN+RKBq88r4OuDl1qfMEq7/3hfPJcnx +Kkcuy+wHzg8NszjtNAicU7vk4gfTPmDh2QsNdumgftbXpLL7+7uAuyRIAkPT +39+/mVs72LF0RhWwQW0Ol5L4APDX0z23O9IR34yQKoirQPfRLubaF6KN7lMq +WLFvMh7dJ8KQS8RzJrrPzK5TGe+XdgN/fH5v4X1pdB/1NalvGmnVwC8KVj4X +zkXnB6895eFe2Yu+HmJTFjZzqMAPAlqu6kl0/NoHzyVFjZgvoFzsB95/zHpB +Q/MgMGn98C6BuF7gFcwJx+xIVODv+o9Mixa1A6eSN+zaHT8EzBxx6WvMpkrg +8lmv9q10RfMWibCLzOtA84pkVl8/cwfN654cVyrfg+YZr7xcnNPbBhwrb+IS +EIvm3fMdejtxAM3T25n5xSQSzTsxKyXeOBnNS7MbHy5m6gNu358ttLaeAlwv +0Jpcv7wTmOV2yC7p3KFf++Dp3293zTmfwEQBrht5k7hrVTew2lmx2ctU0PMS +qW63TW9UAx+XpB5kDh4ElpMxEx9W7gPmjz6svPEqOn+M97xAWkUn8NPGhwfE +XqLz72eIJAl4VKDnP+hW+q/sB5bU67pEtiEDpySKNEVa9QA/tHK7b3CGBvz1 +p9e1qNsNwFEsoxKrs6jAXYdec5aeawEWEe18rimF7tPw3fnq4lk1wJV8sYe1 +egZ/7YOnfz9b3u37hKkfWL34NsfdaDKwLptsuBNHDzD7uLDTyVwa8O6pBPsF +mXXAvZ+/LH2VRwF+lHHsorp2J/CGdzPXZNYMAcfe3CTOtPU9cElwmlyudx9w +7dFxh9Td6Lw1l7Sir3p1AX//vixqJASdF3Q7MV0suxI4RWzRYrX5A8D3eK6q +bWJBr3/kYzP/W230+vdY6q30EkGv3/zH8Xperl5gpexR+aO03/viuaR365Uf +hgaTgbnX8/UOSfcAP9ZqUdyVQgPmtYxMYJavB3bxV3sRvgydt+eAAs+hyXZg +zZPFMeeahoBJ+z4I8o2XA9eEORf5WvcBWzScnkw9QwGOtOO2b57+fAvzdrgL +Bb9A57Er7HMoj64Aft/O87pIth/Y8kjEjh2H0esb4PhSyfMEvT5lm1JJqhp6 +fReC5/zc5doIfJI2qnxWFnnVrzTlotrf+/O5JD/+6IKPK8qB5Xvd9nJNf174 +zZyzDbcv+EIBPu1vs1cvpwNYZOEZax7qEHD1g5HIUew8S903L/Hztoa9eMGD +nbekpq5HHzvP4cgHJ/w8mSXqgvh5GmGZLvh5OgtqZ+H3e9+60PwIdl73+kt2 ++HnDR7+a4+d9ln8bhZ+3qdC5Eb9f9JSAAn4/5ZyIs/+cR98HzyV9WHWixyGq +Bzjx2I1FhqdpwFqRFx8/LmgAbpC4HJY+SQU+atLulK7VDGx3+9Mb9tnofJne +Uwe05WqB31vlB3hTyMBFF8znVdp3A5PGT9ZeU0B9o5uC3dySauAaqfADN5oH +gU9WmB3YXNwLbFi509J3N7rfXpWtMzYKtQMrHzi3vbsFnT+iJvLafKgcePIk +U1qvUx9w5CZzxc6zFOAV17sELgn/3l9zkSLdFXepfeoHjvDK3/ZOZxDYvb1j +oqGpD/HAqaTvU2TgJO3bJzn3dQMbWm6nLTIcAtZb6hXIwlMNHJywsSVrPzp/ +s3Tf2jt96PwWQ7WyEho6PyH9m0OTAzp/jNmcaVINnW89mfLxy010vvym+qe2 +mej8V3c3SF3iQefHuAo5rpuiALeliJNLMzqAOdRHlMx+ovNt1oedqxUuA865 +FXJ6DPbX0/efdZGNOWgQuNg+faLMvg+4lj1RXzqQArxj7bLwpxOdwH7njT4/ +HBoC9uk9qM+8rBzY+eOGvHvL0XnKN87VOkyi80I1b42YlHYAh3DlK9DYhoFn +b07jmhVfCpwjPGvqnR66/5Ze0cvRVVRg8zOiOVLqLcBS5NK1oibofrV8Y+XO +P6qAbymN7WbZg16/a4h1tcAUum/gqWydnfVkYF3HDXZ2j7t/7YO5SKmHed1F +63uBz3w1P1qpRQV+LJgm5zHVBux9LpTl+9gQ8Kd7s+ry08uQL6XufvQBnZe+ +6Zi5rww6b7TMjSsxrB34+tfMwhuzh4E1g4XaUsmlwJuOxPCJX0bn9e27vpv6 +CJ3nHK19SXRRK3BHUSb34lh0v8AI2ufWS5XA8yqaWNzmDABr7T40JqkyCNyl +QSlawdYPLKuTJfG8jAw8TjknWFHa/WsfzEU6brr/UXtpL7Cio47YewsqsHOn +lfbx0DbgFcnZhT2jQ8BrHnVdkSOXAT8tmOgamt8HzN+3+HISLzpPWSTFakCu +A51X23zzzLJh4LVLnTjWdZQAizmI3U3+1gPcf37nYCuJBrxKy3be08FG4Kqx +gcdL7iMf4SiUe+pePfBj9dFTxf7oPkea7T229LYCL5sVyz1Wh17f/dLVDiEn +3gMr+fyImlvZ92sf/M/71Xpi9E4/8LkLWUsnZ5KBTxw5pv7+di/wYxs3/sBE +KnB1rzWXNqkVOOpc4pUZWUPAZhyveJVvVQALqxgt9TmN5s2zrblTp4bm6ah5 +rMic6gF2Hlvd6LKHBhx77+cl3axG4FrR8AD9O8gHm6nnCjbVAwv5aojapqL7 +lkUF3DZbhu776OXdFY7p6L7r9zhnmjBVAh9Q7MqhxKL7qkSlu26b/L1Pnr7P +ibjY1RLDwJaxgZ/7nxUDr/pcy2p+ogfY553uTtdGGnDisTTlXKc64HKB/mNP +hyjA9QcP39Th6wQWkPnsWIvN411z725cEprnmXjKfdNxNO8Ms8WC+FY0z97F +7NL542heqtrLh7Q2NC80Qayqfxc2TyNlLZM4mjcxI27bzzw0L+f9VUuaJZpn +OR4edb8KzZNOt36zORbN6xliado55/c+fHr+nGgumS4asO7s8iPf9tQBK2qm +Ll/RTAEe9fBqENfqBDaSF1LdsH0YuKeVvOHdgWLgehdd3QfiPcBP3EXYPrMO +AbNfKy55olMLrOAWN9NwG5p3ufDJcYPeLmBRGUE/0SrUK0nL3x7Lfg+cUzqj +2XRhP7B7j1JKagcZeJN66I/dL7uBo9ZuF1x6DJ13fra09PCeauAOq4O7RZ8M +An9PG7xTePD3/puLZHF/0Y1XAzRg7XXXVc+I1AEvrFrh4/SeAhySrBcc7NQJ +XP3CR2WBwjDwA72jrXu+FwGfKnn5JHpOD3C5+YsfL8SHgDcHh4veMawB3qM9 +yywghAy87vy6q1r2qD9aut9lfQe67+3QRPfkY+i++30PZN79gO4rKxJrqiiI +7uui9pK0eje6707nTYftk9B9zQ2tT2xv7EavX60rOv4guq/zxCBpzrXf++Xp +74+ZggXmxjXAc8oG1vhHkIG7R10NZU70AH+3tKZNjtGAo829v+xtqgVe/Hpy +6Mg9CvLp9mdiKJ3AUdbB1+y3DgOHyeWN8bgUA79//sUhRRvNMy6+dTx3xhCw +X15e+4wwNI9k1lrE7YTmXeX4dG+/XhewvyrL2+xlaB5Ta4jIbdZS4JC7utYG +Ur3AL8OPmQ5uQ69vldojHgPZJuDEZVYrn335vU+enn9Ubq/myRpg4b2bqbzx +ZGDxK1Ns+vt6gFXdhHb7zRsCfiBwa0uEYi2wveuHpIUqFHT+lJ9LQkMXcFab +1g/eMdSrU4QOjLCUA3vvfbbz4N4+YEkRxTtSbFTgapk9TIvrOoB1e6n6o/rD +wP7DZx7bx74DfrbJWL1+dzdwFbekBektmv/RlqSV2lABTN7Im/sptR94f9OA +sCoH+npYvNW91fLw936Zi5SdO7frEPMA8AVr3sxbgYPA38YPazml9wHTOpk4 +d3tTgJ+Vzg1YJd8FvHfiYdw6mWFgfv5G6bd3ioGrNJ3GvR17gK9xHV9bN0ED +vqGk8DWuohb4J2fg99FHaN7okqYnaY2dwFeC9QSj9qN5X8LXPnmpVAT8OEbm +jsujbuA1bjnzy68MAZvpJutKbK0CZvWXPL+Igr4e3jOvZMl86QfWHzuQwxw3 ++GsfPP3zfs8rMatPXcAVTxp7i6eGgMfOpS7Re1YGzJv1/EiQaB9wdKSinYo8 +Fbj5uacFa1k7cCgfq2OM6TDwzeur+X9ufAecskZCrn9uN3BhwDbqphE0P/bw +I48a/XLgG7PzBcK90Hxp+aZR10oKcGcoNe+ebydwl31exVczND/+kKY2jRPN +/7DJxMZ8Er3+W88f2nlPoPnqsep82R3o9d/N3KuirPx7Pzz956nOs3f7/F7g +yfrCrihPGvCNhnW3xJMagNX4MvwnLJC/xbz9wmmlRuAddinxRWnIq2pEkNmu +1gOHOdzfLlNLBeZpanv75V4LMJvJimXzKEPAzRvuKfWklwN7Zig4BrxC91c7 +ruGyNYQCXCe5t0tJrAvYYfsVgeXT35/AN6u8OfWLgHXV2uwairqBQ7a8dA0I +QvOZeyOU50tUAbtKT0iVfv69355+f6UXdw1uGwKe/D6864hWDXC+/X7Jza/J +wJknKAWJW3uAs8t+Dpuroj6G9bHG0/Fq4Frp6oyps6jv3DhKPdiE+sgOrujv +2TTgi6tkPU4q1AOrFP3QjXhCBT6uFln8waEVeLCpy01rzTAwU+1y3pz4EuBQ +41K19lW9wGfy73eMuqJ5ZGYZJ2pzA3DCx5PcY/7IB3FpTO7zwXzQ49WBRr/3 +49OfFzz3nuVcMgx8sUo5Qt62FPic2JyCF6G9wKEBH5a2c6CeLeJ0hua5ZmBh +I8dtnA+GgNfl6XFN3a8EDra7Ij3oNQCcxTcinl+O2NNGb4WaGuLJ0+bJm2UG +gW0oam8fu/cDU3JcLQQ9ycBGnW8KpXJ7gF+xuw7FdqD7uqr5aRoH1gEfyu8t +OqVBBT49ILJ8MqodeK0DU2etO/r6jJhJ530pK/i1D+YiTX1ZyexpMwzsYZy1 +aHl6IbDR+Y4sxbYu4BELV1Z5MfT8Nd3TzgclS4CHsy0lmIZ6gCWPunN+z6EB +FzuZNcqr1QMrBaQyaRdRgTfMOHirf1Yr8IH398/18qN5DodGClYzlQKv3K7n +wm/UC7xNrazwhSaaxxnufnh0qhH4ntul584CQ8CBeQ8fa36rAX6mebAwVpUC +HLz+oKr7GHr982y7Fm8QGv61D+YiSYjYCS1e2wl8R8LGSuQe8veXCWrETuUB +3/iZeEoUe765tzloHfb8+6oU6xTs+Ur222ZbsOeX7atSxp835D9gnYo93650 +j20b9vyOz5mb8Oc9lw1mpWHPs94cHsCf7/5StAZ/3uerothT7Hm7SAXx7djz +P2euX40/bxv64xD+fHO87R78edtkdcF/nqfvg6d/X3/QGcb/oAM4g2ONo2AK +8heOtZlvcMoDFgwiPi/N8Pw9E+LzSWHE580Ynu8xIj4/4wbxeS2G54eNic+b +3CQ+f5Tx/gzPv2c4X4/h+XiG52cznK//63n6PpiLpJHsefTa9g7gSt75N7Of +It+/SyL98Ko8YAGPrcvld6DnXfI0dGqx5w+IS/co8KPnuUtuv3qHnf/W8hNn +HvY8t35yhzR2frvMJ6n52PlDdyTFqrHnu/bEKxti59flfL43gp2/82r1SD72 +fPr0W2w5dr6nxlc1mix6viW03rcSe15lFUuwE3b+OVrz93nY89FLTU4UTj9P +3wdP//3xyszENxdxjDKP1mntXGAl7eaxdIl24JdLVnuHJaDn/ezifFem5wFv +Jj9yipzTCay334RwvnieIuH85ia+L/j5a/euJ5z/9rM84XyFk5aE83tLiecb +UGQJ5xudXUA4v1VFhHC+9h5Nwvk3hx0I59tlEs/v6drx7/n0fTAXyXG3gvy5 +4hzgto1iHMbn24AvxuqaTUYMAz+Iv2By1jUfeJxaUN4f3Am86FuWOXceej5F +b+eKoUNonipH4Jtn29uBdZs+nX/4DD2vGfjko8r098tvrj6c/XlifwewtWqS +uWQxep5T16cyYwrdf79509Gzuej+UsEu4WsfoOdT1QVLtg6h80+Z5R26Ko7u +XxDjLhdXip6vHJAypjSh809bvk3Zeu33vz/nIuXsft7MGtQJ7O30nHalfBjY +qj9V53V+DvDLCtm60Iuo35+wrPTeA/T8sjt5sh9pecBbH4zx5m1B599QTPsa +U4een3P4MWnfAXS+6gW+dUvaWoHT37AWSVxBz7/zyrf4YV0AnHtdsuK2RBdw +fLLok/JE9PyYm1HkyjR0H+rl1Q+j5qH7uI5INNHq0fMKdxbEFsih+ziHfhqc +mYfu863qaeNm7+Ff+2Au0pZFQokcYsXAzCdjA/W8eoDTLoQIOBsPAc90uO+h +7V8NbH21TyT9FBmYe5tM/QfRXuAEZr6N7fk0YKpwn9grq3rgsjXOCk4rkGdZ +8/h9ql4zcL62Z3M7Bc3X/HzzSNW898B3ZDx2akj0AxvF0G7ckqcAm37jooxK +dwOr7vbP0FdDr19m+ZImiaki4EVaFbGeZuj1n1QS9jU5j+bv3OBvUzJY9Wsf +zEVq2nGA7HqvC7iv+/h2t1vDwLrBxhazcvOBHc77ao6XdwLnVp4UutSAni98 +/bCZopAD/OUan0BAcyvwouq+kp9R6PlL/fmu20+i87eeNVYtD0Hnpy254HOh +Cz1fI2f6zistGzhfZ6PWKBc6X+6sd5iVPXreMlc5WaGkENiFP8vvLm838Fv5 +C0JrTqDnL9c9NJ2f8g5Y9NFZddk49Hzz0fePBBYM/9oHT//+oFLjHOKBuEV7 +qdG97wXAO8VUwqhRXcCbxot5re+j5xcZTPouW5UPvMDEwZJm3gksXOSwPngE +PT9hllB9+E0WcLu15beI/mbg70pLay/9nybuPBrq//sDeIpS0pCEEqlUCokW +yjJZSgsfKSUpKgkVikhpsUTSqkWRPbIksmTLkn3fl+zGPsPMpCJLy885vzxf +3z8f597Xvfc1xxze5543aZJv6Xoos3L6eWzGK3TWRW463wuPuMQLa70ahrOC +9jSLejbBVxXruzaXkrhH8Hmud0aN8CNNn9mBkiS+3L0tz2AnmWf3Zfp/O38w +4Tcuuer3wiv+7YMpVHmtnfnv5QbgNanb0wwzB2HBPOUQ2Zw+OOe5DaXqDwNe +a9u7Rdq4C17fLLxtaooFO3T7eWQ4Z8Edk3YfLThbYCWOYLtXDCZ80Sp1wnRz +JWyuabrF91g/3BswqM8pRvqzp4rOd/l1w49P5oeHypD+o0/0jkqElMJJnFSW +lHUvfPybTpFX0DDc9+16v59FEzy7/uTa0TwS53Ad2RZzt/HfPphC/X1irup+ +2Rr4vbNsouDpQVguZG5eo3s/bOpRZyzVQ4f9Dp+8VbSpBzbzfcm/oIoJH5SV +LRiJrYJtmjK548QHYFrCf9e5eki/O7TLws0OfWQeLw+Ty+eH4OSSgfeh9h3w +2ZQx+YyfLLgtmX+59uxsWKj559GLNi3wX54bc0ZESH5SF0NtQWoZfHHearPn +fKS/7NvCh7NYpP/AQ/od8yet//bBFGpCineo8vYc2Iw332ibK4mbqRrmZjqy +YLuovIaamEJ4xGgy775YN+z0zfwD7S7J77pxvd4ivQC2XqkuYXmHBgspWH5+ +XE7yFwnNWaoy9pnUCy6wjf7TDrft6+9SHiX5Xp+z+6YOZ8PlHD9u0JNaSP7m +4PMFO0j+Ba/RVJffJfBrB1PrxWK9MK94q+5jLiZc56CzMf9XPUxZ46K11nxm +fzzdf+2n3yaibLj541BgW386HHXtCkeMZRNcaTwSwUkbhuuueY1U0RvgUgGB +79LzSPwMW0dqjK8V5oiu3HT0FAvW/KKS58osIv0N91VcHeqGTxd6B1kKkvyX +XFMPznKXw0Eit4747uuDD/3mlD+XQu7noG+mda29De7+0uykUUvqacn8Vloa +/Rk+L7nRJjKgHba3NdG+9Y3kb+mIm5gdl/1vHzz9fXJgL7Jo64OFA1vFX0wy +4LQrVZKCN7rgDyfqz9yRYMOyG3wo0obpcI62TNGhOU3w4f4/nqWJw3Bezbrv +MQtI3E0xT7kihcQfGZ61aRlphJ8XL3kqH03iXXx9VIYWOX+88DVfXBOJc4Sb +XLy6kZzv5P/6TU6RxPlXnzC4N94M63n7i5TysuCGas8M3mvlcEePJ7flI/L5 +XM5iFAedHfq3D6ZQfZ6N598PZcBebtsbz1nRSHzip/m7Hyx4TqZpjqV7Nmz+ +tmy9wrcWOG9Q6tf4eZKf43pMZeJcEWxNkeDuDO+GDYQO3LQ1JPmaUdWag07F +sNHjC148Oj1wEZ0uptzJhIOjPDcr/K6ExxNFJ1X6+2EFn7O+3OZ0uH6PjcRW +m17YUW3EKK5iGK7LG6lUv9QIZ3t4LfpgReKC7gdKqmtm3i+nUGO8hRyeTrLg +kns/lTS6s2Cd2qsvDru1wHMj5Yp09Ek+5YZ3T1lTMbxgxaLOVO8e+OvfyvqY +JCZ8Wrhi8cbQatgmylJdY/4g3BC3c+WP4wNwSomC1YMQEn/mp7Nt69p++GDK +s33rghlwfOKD7CMONNg0Ns7uzf/cr9mIoqffRe7HO2Ls2utC7rfw8jbn2oMk +/0XG3GeeHeR+UVrdS7IezeyjKdSNP6zbn14gbn/0NZT1hQmzanm7meZVsL2d +g6XahgH41N6Yh40cdDjLM+PtjxN9sOZvM9Ho3CG4dKDkfltuG1wlrD0rYpQF +m2RLr/B1zob/7LliIY731SnUJ+zgDf5uJP9U3UGjZVKFcLYz5bQpnQavS7Zz +Mmkg+a8Wx67SevYZVi1VYKaHt8OWJdu/nJ3+fTDjoMnkdS/nZ8CiIhFc2mEz +/7+cQn13de6BTaGDcHJL/i0zhX44wuYWLS6AAe9NdVCXv0uDz+a+bbHgZsPF +klvypEwz4YUBRTX5ds3wht9ybxVns0j9lS+sjFQr4GMTAZ9UBEl/xTnKw39L +Sf82WZU2V37S/8y1HZs2ypL+UbWmy57PSYNjGTzUZUKN8BhXAO9vvWE4sdlq +b+UdMp914BtZi/lkvpfmVaYZreWwNM9EvWfXzH56un8X/UtuaiJ85cKbQ4GN +NfD5lyJ+9dvp8C/u1xPm33vhiMMR0u7Hh+F9D8dUXHWb4eYOJePhX0y41r1I +5uXjCjhULF51nnY/nM3pMt7gwYAvnysvEy2hwVvTnxhLj7NglzO0gLV7smGz +gE81GoMtsMnkza7axyS//m5ah9b1AlJ/Ule9wZ3UNzr0madagA23Jr5r1Bb5 +BHN+O64S4zbzfjmFGmLO239xPRseNUyQKc9Kg6VHf1XWpTbCoWkqRZG5w/Dw +xL3Yna0kPmv/PDnhRhJ/2qK/Rv4UiSuF2jp2PSJxwcElRvFLyTwFfGw2/3Um +XBeku1NCsRZOGF3kEfCUDq/J0l72dm0vvHX+HZnje8l5q016r57crIN/OonY +Z/ox4Ail8qTD/jT4xmK5KgNB8nmk/dS8az6aAWv43lGUtp15f3z67wePP7ui +Rvvhq5XqwpU36HBpbkrkAdNeuCRcz85rKROudnK0k6ysh3dcy3D09x2C54Sd +SLjV2Q6feLOKtUSHDYvtd5o6fDMZzpoz3rnOsA5+G7AlKfMOA9aVXVH4sIkG +r0wstx7jIvWeBQbLKhdkkvPHP/4Sam4m9j89JrWHBVv1CcRzBZTAftYB9yQl +yH3HOgWCXAzJfbmvpvDWStT92wdTqPfnL7pu35UAK426h55WqIEPnAiT3pI9 +CDMrNOrOLe6HNdSlF+35xoDLXnfvasjqgj3SU4TPWLLhzp16H8RlST9/6XPp +hgHVsNpf9TmTCqSf+LK+ja+2DMALGJ6114TpMK1LQMhTtw9+oXfCwYhzGP7s +q2tYeakVNs9tCX/UxILN4msilj35DG++9E45s6YdDvn69aC9AZm/6knXQw6v +pH/7YAq1oiM3Q92kBzaT8ghJFGPB8iq8Gq97ymAxYy1ONec+OOAEZ1hK9RC8 +1kNpdUFUG/zecKPJKRk2zLVb8SuPZhoc7VvhoWLdCGffrHDzSByG072W+1zX +a4KH7ffpv5Vnws/53YoSJevhRcnlfUvkyTzzxqwKDZZ2wVeVrQ7Q3Mk8ogYa +0fVtsaReHfXMaAK57y77sbxVp8h9d4ZLlUz9mNkXT3+/Vvd0S91kwuU3jp3T +31kLz/ZvsItPocN3D9wWWDXUA2+5rLa5IJqcf3vv8yd/vhqYeaa+xTpuEPY5 +cUwjUr0fzpc59OdyOgOOEhfKHzhJg7uiLScph9mw+PWkV1dykmDzGK07CZVk +Xr847SNr5f+nXoP281tZ3fDUCN0kKYQFK1Up3tsfkw+L2Jcz2oRI/6CPZ0++ +sST9Fxdu3qEgn/BvH0yhMsR+hLdxdMAf3iek77jGhle/8Y4WV42Hww4nZqvw +VMLlE8KpZkn98B6ZZJYILwO2qDxiJi3RA0tuff9exIwFm1uGeZasKYZ7Jr3v +aRiSfCuRyE+LFUn+SEHpf2k+pbB11Y2TS8p64S8Labk+ecMw58nq1VmTjbD9 +V++8wqVMWOSuxoqkgXrYbO8TjVUVQ/DJp6ut99a0wfu0F155sZf9bx88/ffn +epn7GdwD8HILPXUDDzq8m112zPZiL5w21rThNd4fp1ADDT7ETAjXw6XvNBpU +NYZgg8CmgKzhTvhN46XnZWGkv/+zEj0erwi44+jAsiU6BfCkpH+240MaXCBS +r7bpKDm/UtXyu5pNEqycvE3Rw7cW/sX/nK9CkAHPl7D2S+XvIfOdHb9R4sSC +r7/tvC/2sxBWszn3jTu0G75qMn7vVvHMvnj6+SjZuTSquAm2/ECXs/VlwkGi +8x+9CauBTV+d80o7QIedhOv+qk32wuOxu3/LBAzDk7Uh0SWTpP7U6P72gHhS +f3D55kOhE9Ww8YtVcRsSBuEdD9eMXdLvh30a64W6MxhwoZKeHscFGvyDrho2 +z5oNl573vM3O/AA/lfii2mNI+tE6bwf4iZB+YX7ewvcfDcAmZmluy/xJfGHr +I7M6t5n3u6e//1mrTk/19cEfzRfOy7UYgnsaRQ5GyHbC6zim9nEmsuFdrYXV +Q32hMNfLxPnPF+TCf125QwvSOuDSKj+1SzHkvICrMuXnpzewUTN/wPG0PDhy +V/OhQa8ueMxK3HJFHDnvvSQrJe5LGLydW+/UHDrpL29lXGP7ncwfJ/qOWyeV +nOdcP/dW0esQWLlb+O/z1hxYXc+Kt42zHV6tPBLXfIn9bx88PV92fNKx2H7Y +N/tI/qMdDHhv2Vof36JuuCvRPHpDBQs2T4qQmKOfC/O7bLikINUJMw0tjo5/ +Iv0mCrV6+m8Gw6dCdN3M4rPhpG1FPd0PW2GpSj6dAUlyfkWkv5zBkXSYp6r9 +wEG7JvhAy1J1uZtMeO3hsccZhrXwFo6P+Rcm6bBOnEutqUUPfNes9mTWQXK/ +pPA4z8C9JfBuze+XPq3u/bcPplBbDgp9EX9YCddbH9kXs2IALl2y2eepKx2e +ffqdYP5jcv5CoIDm+FYmXGmdJp6nUg9ffhiQ/8RlCM74KhDlmdwBZ7k90HmQ +zYadlYwG9xcEkfreO3Yn+GbB2zWrDT7kt8B7NvwK2/KdBY+8iJF7JZkDXxW7 +W76epw3OK/nleFyP9HvA0Hrw/lgybPbMMevu5Tp4k+PyhlWDDFiCxnD8yjWz +b6ZQ90fOdta0rYZdrjk+tP9vEDZdY1coTB2A9cPj3Xfr0GHjvaGyIkv6iO80 +x34JGYYvXtDmcf7VBCeKNTk3NzHhRZqvw2izSf9ZiRdMJHtJPyPVHgkDYTJP +upI2v088iWukzL2zx5nERVstiq5098PmYh6OvSNk3h8T9dLz7/XAXMdOx23T +ZsHv1ZnJnrQS+G3txFk77164Nj9xvrnWzD54+udfyXSz+A5/2OVV4Zdj59Lh +hq/6Gxx8m+C/buE7y2PJ+aHBID/t9TWw/ewd4/ZcdPgBX3BfTlYf3OYls567 +YAjeHn1gsaJ6O8xxLb3rdDgbTlwndzr4YATM6q3159csgIdf5wc9iabBopEC +LXl3yXnnZOUT+RqxsNn4mtX8N8pgBadX9GUuZL7gQX6Ns8uHYdtWY65Qaits +WDPV/mb6eeD/98HTn0/yI3U7uWE4/Nm5ZzUlLfAeobGvBYtJfk1gQMDf1E/w +mupuwXibZjjCs28o9SkLlm4Mqj2aWACvi7kgMDVBgztSWYvqrEl9HoviOFrR +B7gy1Kd4lUs1PMd4eO0Fm0GY77vJBt2FA/Bk4+2c7jQ6/PJbnNCEeC+sI+ab +ZFHOhAtdBX0XGJP6R8x9L5/fT+q3rpFStThK6quE8d1arTDz/vf077PDzqZ8 +6TT4l/05jysv2HBJgtH0E2k0bLzL2WleVDHJv/T+pnl3DyxyzJvXC/t5CvXg +0/ZXt3vL4fc2CyuKjvbDurMko9hsBrwk8qLsy7lkHrflFi0S9WSeHwGZi+eW +PocLlZZPuRxIhsNfHl0XeLsOzhFy/V4hOAQf6pTgvx7YBffec/zpSif1xx1j +XXnNPeCGlfq61JURsHCYuXvCmoJ/+2A+6lbj5JWxkkzVGQ9uUXvmI8mLeAHP ++jPrJWXgFIfu6FurdeD/UuS820UvwiGZfuKnZj+AG2xzOja9egcnlahXUGeV +wXyVXg6Sun1wT9XraoPrw2Q+C/ftq3ib4eidhs/SbrDg+mIn18lZRbBjVoxT +cEc3TDfadsF5nORPZQy1ytOyYZvR7bbdg61wzB87+rrp568Z/w1995T7Sjzs +7pM9y6y8Uu3/ALJUdMY= + "]]}, {}}, {}}, + AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], + Axes->{True, True}, + AxesLabel->{ + FormBox["\"r\"", TraditionalForm], + FormBox["\"long-term\"", TraditionalForm]}, + AxesOrigin->{0.958203125, 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->{"CoordinatesToolOptions" -> {"DisplayFunction" -> ({ + (Part[{{Identity, Identity}, {Identity, Identity}}, 1, 2][#]& )[ + Part[#, 1]], + (Part[{{Identity, Identity}, {Identity, Identity}}, 2, 2][#]& )[ + Part[#, 2]]}& ), "CopiedValueFunction" -> ({ + (Part[{{Identity, Identity}, {Identity, Identity}}, 1, 2][#]& )[ + Part[#, 1]], + (Part[{{Identity, Identity}, {Identity, Identity}}, 2, 2][#]& )[ + Part[#, 2]]}& )}}, + PlotLabel->FormBox["\"discrete\"", TraditionalForm], + PlotRange->{{1.005, 4.}, {0, 1}}, + PlotRangeClipping->True, + PlotRangePadding->{{ + Scaled[0.02], + Scaled[0.02]}, {0, 0}}, + Ticks->{Automatic, Automatic}]} + }, + GridBoxAlignment->{ + "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, + "RowsIndexed" -> {}}, + GridBoxSpacings->{"Columns" -> { + Offset[0.27999999999999997`], { + Offset[2.0999999999999996`]}, + Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { + Offset[0.2], { + Offset[0.4]}, + Offset[0.2]}, "RowsIndexed" -> {}}], + Function[BoxForm`e$, + TableForm[BoxForm`e$]]]], "Output", + CellChangeTimes->{ + 3.777165731941354*^9, 3.7771657820785303`*^9, {3.7771658378010435`*^9, + 3.7771658501008472`*^9}, {3.777165934060048*^9, 3.7771659669945774`*^9}, + 3.777166070392551*^9, 3.7771673335171857`*^9}] +}, {2}]], + +Cell[TextData[{ + "The following two Manipulate environments are interactive versions of the \ +above observations. The first shows the continuous model\[CloseCurlyQuote]s \ +time series alongside its long-term solutions, both as ", + Cell[BoxData[ + FormBox["r", TraditionalForm]], + FormatType->"TraditionalForm"], + " changes, and the second shows the same for the discrete model. For the \ +discrete model, observe how the long-term series begins to split just as the \ +time series begins to experience undamped oscillation." +}], "Text", + CellChangeTimes->{{3.7771675269872046`*^9, 3.777167533399252*^9}, { + 3.7771676214465485`*^9, 3.777167728826147*^9}}], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Manipulate", "[", + RowBox[{ + RowBox[{"TableForm", "[", + RowBox[{"{", + RowBox[{"{", + RowBox[{ + RowBox[{"Plot", "[", + RowBox[{ + RowBox[{"Evaluate", "[", + RowBox[{ + FractionBox[ + RowBox[{ + SuperscriptBox["E", + RowBox[{"L", " ", "r", " ", "t"}]], "L", " ", "0.4"}], + RowBox[{"L", "+", + RowBox[{ + RowBox[{"(", + RowBox[{ + SuperscriptBox["E", + RowBox[{"L", " ", "r", " ", "t"}]], "-", "1"}], ")"}], + "0.4"}]}]], "/.", + RowBox[{"L", "\[Rule]", + FractionBox[ + RowBox[{"r", "-", "1"}], "r"]}]}], "]"}], ",", + RowBox[{"{", + RowBox[{"t", ",", "0.001", ",", "30"}], "}"}], ",", + RowBox[{"PlotRange", "\[Rule]", + RowBox[{"{", + RowBox[{"0", ",", "1"}], "}"}]}], ",", + RowBox[{"PlotLabel", "\[Rule]", "\"\\""}], ",", + RowBox[{"AxesLabel", "\[Rule]", + RowBox[{"{", + RowBox[{"\"\\"", ",", "\"\\""}], "}"}]}]}], "]"}], ",", + RowBox[{"Plot", "[", + RowBox[{ + FractionBox[ + RowBox[{"rr", "-", "1"}], "rr"], ",", + RowBox[{"{", + RowBox[{"rr", ",", "1.0005", ",", "r"}], "}"}], ",", + RowBox[{"PlotRange", "\[Rule]", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{"1", ",", "4"}], "}"}], ",", + RowBox[{"{", + RowBox[{"0", ",", "1"}], "}"}]}], "}"}]}], ",", + RowBox[{"PlotLabel", "\[Rule]", "\"\\""}], ",", + RowBox[{"AxesLabel", "\[Rule]", + RowBox[{"{", + RowBox[{"\"\\"", ",", "\"\\""}], "}"}]}]}], + "]"}]}], "}"}], "}"}], "]"}], ",", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{"r", ",", "1.2"}], "}"}], ",", "1.005", ",", "4", ",", + "0.005"}], "}"}]}], "]"}]], "Input", + CellChangeTimes->{{3.777163681244874*^9, 3.7771638468583126`*^9}, { + 3.777163957467636*^9, 3.77716398467824*^9}, {3.7771640761216917`*^9, + 3.7771642136305895`*^9}, {3.7771645056535025`*^9, 3.777164556673809*^9}, { + 3.7771646075070252`*^9, 3.777164730339535*^9}, {3.7771649500323143`*^9, + 3.7771649653355174`*^9}, {3.7771659821597023`*^9, 3.7771659959476337`*^9}, { + 3.7771660854460907`*^9, 3.7771661285863004`*^9}, {3.777166160232567*^9, + 3.7771662350691833`*^9}, {3.7771673403857517`*^9, 3.7771673415618715`*^9}, { + 3.777167559817835*^9, 3.7771676101671667`*^9}}], + +Cell[BoxData[ + TagBox[ + StyleBox[ + DynamicModuleBox[{$CellContext`r$$ = 3.305, Typeset`show$$ = True, + Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", + Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = + "\"untitled\"", Typeset`specs$$ = {{{ + Hold[$CellContext`r$$], 1.2}, 1.005, 4, 0.005}}, Typeset`size$$ = { + 387., {70., 76.}}, Typeset`update$$ = 0, Typeset`initDone$$, + Typeset`skipInitDone$$ = True, $CellContext`r$140633$$ = 0}, + DynamicBox[Manipulate`ManipulateBoxes[ + 1, StandardForm, "Variables" :> {$CellContext`r$$ = 1.2}, + "ControllerVariables" :> { + Hold[$CellContext`r$$, $CellContext`r$140633$$, 0]}, + "OtherVariables" :> { + Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, + Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, + Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, + Typeset`skipInitDone$$}, "Body" :> TableForm[{{ + Plot[ + Evaluate[ + ReplaceAll[ + E^($CellContext`L $CellContext`r$$ $CellContext`t) $CellContext`L + 0.4/($CellContext`L + ( + E^($CellContext`L $CellContext`r$$ $CellContext`t) - 1) + 0.4), $CellContext`L -> ($CellContext`r$$ - + 1)/$CellContext`r$$]], {$CellContext`t, 0.001, 30}, + PlotRange -> {0, 1}, PlotLabel -> "continuous", + AxesLabel -> {"t", "x(t)"}], + + Plot[($CellContext`rr - 1)/$CellContext`rr, {$CellContext`rr, + 1.0005, $CellContext`r$$}, PlotRange -> {{1, 4}, {0, 1}}, + PlotLabel -> "continuous", AxesLabel -> {"r", "long-term"}]}}], + "Specifications" :> {{{$CellContext`r$$, 1.2}, 1.005, 4, 0.005}}, + "Options" :> {}, "DefaultOptions" :> {}], + ImageSizeCache->{438., {117., 123.}}, + SingleEvaluation->True], + Deinitialization:>None, + DynamicModuleValues:>{}, + SynchronousInitialization->True, + UndoTrackedVariables:>{Typeset`show$$, Typeset`bookmarkMode$$}, + UnsavedVariables:>{Typeset`initDone$$}, + UntrackedVariables:>{Typeset`size$$}], "Manipulate", + Deployed->True, + StripOnInput->False], + Manipulate`InterpretManipulate[1]]], "Output", + CellChangeTimes->{{3.777167574221195*^9, 3.777167610995882*^9}}] +}, {2}]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Manipulate", "[", + RowBox[{ + RowBox[{"TableForm", "[", + RowBox[{"{", + RowBox[{"{", + RowBox[{ + RowBox[{"ListPlot", "[", + RowBox[{ + RowBox[{"RecurrenceTable", "[", + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{ + RowBox[{"x", "[", + RowBox[{"n", "+", "1"}], "]"}], "\[Equal]", + RowBox[{"r", " ", + RowBox[{"x", "[", "n", "]"}], + RowBox[{"(", + RowBox[{"1", "-", + RowBox[{"x", "[", "n", "]"}]}], ")"}]}]}], ",", + RowBox[{ + RowBox[{"x", "[", "0", "]"}], "\[Equal]", "0.4"}]}], "}"}], ",", + "x", ",", + RowBox[{"{", + RowBox[{"n", ",", "0", ",", "30"}], "}"}]}], "]"}], ",", + RowBox[{"Joined", "\[Rule]", "True"}], ",", + RowBox[{"Mesh", "\[Rule]", "Full"}], ",", + RowBox[{"PlotRange", "\[Rule]", + RowBox[{"{", + RowBox[{"0", ",", "1"}], "}"}]}], ",", + RowBox[{"PlotLabel", "\[Rule]", "\"\\""}], ",", + RowBox[{"AxesLabel", "\[Rule]", + RowBox[{"{", + RowBox[{"\"\\"", ",", "\"\\""}], "}"}]}]}], "]"}], ",", + RowBox[{"ListPlot", "[", + RowBox[{ + RowBox[{"dlmplot", "[", + RowBox[{"[", + RowBox[{"1", ";;", + RowBox[{"20", + RowBox[{"(", + RowBox[{ + RowBox[{"Round", "[", + FractionBox[ + RowBox[{"r", "-", "1.005"}], "0.005"], "]"}], "+", "1"}], + ")"}]}]}], "]"}], "]"}], ",", + RowBox[{"PlotRange", "\[Rule]", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{"1", ",", "4"}], "}"}], ",", + RowBox[{"{", + RowBox[{"0", ",", "1"}], "}"}]}], "}"}]}], ",", + RowBox[{"PlotLabel", "\[Rule]", "\"\\""}], ",", + RowBox[{"AxesLabel", "\[Rule]", + RowBox[{"{", + RowBox[{"\"\\"", ",", "\"\\""}], "}"}]}]}], + "]"}]}], "}"}], "}"}], "]"}], ",", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{"r", ",", "1.2"}], "}"}], ",", "1.005", ",", "4", ",", + "0.005"}], "}"}]}], "]"}]], "Input", + CellChangeTimes->{{3.777163681244874*^9, 3.7771638468583126`*^9}, { + 3.777163957467636*^9, 3.77716398467824*^9}, {3.7771640761216917`*^9, + 3.7771642136305895`*^9}, {3.7771645056535025`*^9, 3.777164556673809*^9}, { + 3.7771646075070252`*^9, 3.777164730339535*^9}, {3.7771649500323143`*^9, + 3.7771649653355174`*^9}, {3.7771659821597023`*^9, 3.7771659959476337`*^9}, { + 3.7771660854460907`*^9, 3.7771661285863004`*^9}, {3.777166160232567*^9, + 3.7771662350691833`*^9}, {3.7771673403857517`*^9, 3.7771673415618715`*^9}}], + +Cell[BoxData[ + TagBox[ + StyleBox[ + DynamicModuleBox[{$CellContext`r$$ = 3.175, Typeset`show$$ = True, + Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", + Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = + "\"untitled\"", Typeset`specs$$ = {{{ + Hold[$CellContext`r$$], 1.2}, 1.005, 4, 0.005}}, Typeset`size$$ = { + 387., {70., 76.}}, Typeset`update$$ = 0, Typeset`initDone$$, + Typeset`skipInitDone$$ = True, $CellContext`r$137964$$ = 0}, + DynamicBox[Manipulate`ManipulateBoxes[ + 1, StandardForm, "Variables" :> {$CellContext`r$$ = 1.2}, + "ControllerVariables" :> { + Hold[$CellContext`r$$, $CellContext`r$137964$$, 0]}, + "OtherVariables" :> { + Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, + Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, + Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, + Typeset`skipInitDone$$}, "Body" :> TableForm[{{ + ListPlot[ + + RecurrenceTable[{$CellContext`x[$CellContext`n + + 1] == $CellContext`r$$ $CellContext`x[$CellContext`n] ( + 1 - $CellContext`x[$CellContext`n]), $CellContext`x[0] == + 0.4}, $CellContext`x, {$CellContext`n, 0, 30}], Joined -> True, + Mesh -> Full, PlotRange -> {0, 1}, PlotLabel -> "discrete", + AxesLabel -> {"t", "x(t)"}], + ListPlot[ + Part[$CellContext`dlmplot, + Span[1, 20 (Round[($CellContext`r$$ - 1.005)/0.005] + 1)]], + PlotRange -> {{1, 4}, {0, 1}}, PlotLabel -> "discrete", + AxesLabel -> {"r", "long-term"}]}}], + "Specifications" :> {{{$CellContext`r$$, 1.2}, 1.005, 4, 0.005}}, + "Options" :> {}, "DefaultOptions" :> {}], + ImageSizeCache->{438., {117., 123.}}, + SingleEvaluation->True], + Deinitialization:>None, + DynamicModuleValues:>{}, + SynchronousInitialization->True, + UndoTrackedVariables:>{Typeset`show$$, Typeset`bookmarkMode$$}, + UnsavedVariables:>{Typeset`initDone$$}, + UntrackedVariables:>{Typeset`size$$}], "Manipulate", + Deployed->True, + StripOnInput->False], + Manipulate`InterpretManipulate[1]]], "Output", + CellChangeTimes->{ + 3.7771660008727407`*^9, 3.7771660666138906`*^9, 3.777166117958968*^9, { + 3.7771661846076736`*^9, 3.77716623608088*^9}, 3.777167342067255*^9}] +}, {2}]] +}, Open ]] +}, Open ]] +}, Open ]] +}, +WindowSize->{759, 833}, +WindowMargins->{{249, Automatic}, {Automatic, 28}}, +FrontEndVersion->"10.4 for Microsoft Windows (64-bit) (April 11, 2016)", +StyleDefinitions->"Default.nb" +] +(* End of Notebook Content *) + +(* Internal cache information *) +(*CellTagsOutline +CellTagsIndex->{} +*) +(*CellTagsIndex +CellTagsIndex->{} +*) +(*NotebookFileOutline +Notebook[{ +Cell[CellGroupData[{ +Cell[580, 22, 180, 2, 144, "Title"], +Cell[763, 26, 156, 2, 30, "Text"], +Cell[CellGroupData[{ +Cell[944, 32, 99, 1, 63, "Section"], +Cell[1046, 35, 399, 7, 68, "Text"], +Cell[1448, 44, 332, 10, 55, "Input"], +Cell[1783, 56, 1642, 55, 101, "Text"], +Cell[3428, 113, 173, 4, 30, "Text"], +Cell[3604, 119, 325, 10, 25, "DisplayFormula"], +Cell[3932, 131, 1211, 39, 101, "Text"], +Cell[5146, 172, 684, 16, 99, "Text"] +}, Open ]], +Cell[CellGroupData[{ +Cell[5867, 193, 91, 1, 63, "Section"], +Cell[CellGroupData[{ +Cell[5983, 198, 102, 1, 43, "Subsection"], +Cell[6088, 201, 1151, 33, 92, "Input"], +Cell[7242, 236, 495, 13, 31, "Input"] +}, Closed]], +Cell[CellGroupData[{ +Cell[7774, 254, 105, 1, 35, "Subsection"], +Cell[7882, 257, 897, 19, 125, "Text"], +Cell[8782, 278, 757, 19, 87, "Text"], +Cell[CellGroupData[{ +Cell[9564, 301, 2824, 72, 250, "Input"], +Cell[12391, 375, 2667, 52, 283, "Output"] +}, {2}]], +Cell[15070, 430, 1022, 22, 144, "Text"], +Cell[CellGroupData[{ +Cell[16117, 456, 1293, 32, 163, "Input"], +Cell[17413, 490, 61123, 1029, 172, "Output"] +}, {2}]], +Cell[78548, 1522, 654, 12, 87, "Text"], +Cell[CellGroupData[{ +Cell[79227, 1538, 2618, 64, 255, "Input"], +Cell[81848, 1604, 2312, 46, 257, "Output"] +}, {2}]], +Cell[CellGroupData[{ +Cell[84194, 1655, 2864, 70, 233, "Input"], +Cell[87061, 1727, 2382, 47, 257, "Output"] +}, {2}]] +}, Open ]] +}, Open ]] +}, Open ]] +} +] +*) + diff --git a/calc-diffeq-analysis/crowd-escape-panic.nb b/calc-diffeq-analysis/crowd-escape-panic.nb index a319c46..9dbbe18 100644 --- a/calc-diffeq-analysis/crowd-escape-panic.nb +++ b/calc-diffeq-analysis/crowd-escape-panic.nb @@ -1,3818 +1,3818 @@ -(* Content-type: application/vnd.wolfram.mathematica *) - -(*** Wolfram Notebook File ***) -(* http://www.wolfram.com/nb *) - -(* CreatedBy='Mathematica 10.4' *) - -(*CacheID: 234*) -(* Internal cache information: -NotebookFileLineBreakTest -NotebookFileLineBreakTest -NotebookDataPosition[ 158, 7] -NotebookDataLength[ 143094, 3810] -NotebookOptionsPosition[ 141099, 3743] -NotebookOutlinePosition[ 141442, 3758] -CellTagsIndexPosition[ 141399, 3755] -WindowFrame->Normal*) - -(* Beginning of Notebook Content *) -Notebook[{ - -Cell[CellGroupData[{ -Cell["Crowd Escape Panic Model", "Title", - CellChangeTimes->{{3.776600831050974*^9, 3.7766008318453026`*^9}, { - 3.776716385892248*^9, 3.7767163898738484`*^9}, {3.776716551386162*^9, - 3.7767165575816903`*^9}, {3.776716932379567*^9, 3.7767169360051517`*^9}}], - -Cell["Adam Rumpf, 5/1/2018", "Text", - CellChangeTimes->{{3.7766008347881403`*^9, 3.776600838290375*^9}, { - 3.7767164096961517`*^9, 3.7767164112664833`*^9}}], - -Cell[CellGroupData[{ - -Cell["Introduction", "Section", - CellChangeTimes->{{3.7766008459498987`*^9, 3.776600848547045*^9}}], - -Cell["Based on the following paper:", "Text", - CellChangeTimes->{{3.776600856235587*^9, 3.776600860481224*^9}, { - 3.776717137261506*^9, 3.7767171483543005`*^9}}], - -Cell[TextData[{ - "D. Helbing, I. Farkas, and T. Vicsek. Simulating dynamical features of \ -escape panic. ", - StyleBox["Nature", - FontSlant->"Italic"], - ", 407:487\[LongDash]490, 2000." -}], "Text", - CellChangeTimes->{{3.776600856235587*^9, 3.776600860481224*^9}, { - 3.776717137261506*^9, 3.776717152796668*^9}}], - -Cell["\<\ -The paper describes a dynamical systems model (see below for a full \ -definition) for crowds of people running to an exit. The model consists of a \ -system of ODEs based on the forces of people acting on each other. This \ -program solves the ODEs using forward Euler\[CloseCurlyQuote]s method.\ -\>", "Text", - CellChangeTimes->{{3.776717166514436*^9, 3.776717167632295*^9}, { - 3.7767197161509967`*^9, 3.776719813705699*^9}, {3.77672033530317*^9, - 3.7767203497579947`*^9}}], - -Cell["\<\ -This demonstration consists mostly of a single Manipulate environment to \ -produce an animation of a crowd attempting to escape a building. People are \ -represented as randomly-sized dots. The color of the dot represents the \ -amount of crush force experienced, with redder color indicating more force, \ -which a planner would ideally like to avoid since this can lead to injury. A \ -time series is also displayed in the lower right corner, with the green \ -series indicating number of successful escapes (which occurs when a dot \ -crosses the threshold of the exit) and the red series indicating total force.\ -\>", "Text", - CellChangeTimes->{{3.776719828336033*^9, 3.7767199711270523`*^9}}], - -Cell["\<\ -There are also controls to change the layout of the room and the size and \ -behavior of the people. Due to the computational intensity of this program \ -changes are not applied in real time, and are instead applied by pressing the \ -\[OpenCurlyDoubleQuote]apply changes\[CloseCurlyDoubleQuote] button, at which \ -point the simulation will restart with the new parameters. Before applying \ -the changes, the prospective layout is drawn over the current layout in a \ -gray outline. This button can also be pressed even without applying changes \ -simply to randomly restart the simulation with different starting positions.\ -\>", "Text", - CellChangeTimes->{{3.7767199785696683`*^9, 3.776720048478415*^9}, { - 3.776720086455348*^9, 3.776720145692374*^9}}] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["ODE Model", "Section", - CellChangeTimes->{{3.7767171834275007`*^9, 3.776717186634338*^9}}], - -Cell[CellGroupData[{ - -Cell["Notation", "Subsection", - CellChangeTimes->{{3.776717255983509*^9, 3.7767172568825264`*^9}}], - -Cell[TextData[{ - Cell[BoxData[ - FormBox["t", TraditionalForm]]], - " = time\n", - Cell[BoxData[ - FormBox["N", TraditionalForm]]], - " = number of pedestrians\n", - Cell[BoxData[ - FormBox[ - SubscriptBox["m", "i"], TraditionalForm]]], - " = mass of pedestrian ", - Cell[BoxData[ - FormBox["i", TraditionalForm]]], - "\n", - Cell[BoxData[ - FormBox[ - RowBox[{ - SuperscriptBox[ - SubscriptBox["v", "i"], "0"], "(", "t", ")"}], TraditionalForm]]], - " = desired speed of pedestrian ", - Cell[BoxData[ - FormBox["i", TraditionalForm]]], - " at time ", - Cell[BoxData[ - FormBox["t", TraditionalForm]]], - "\n", - Cell[BoxData[ - FormBox[ - RowBox[{ - SuperscriptBox[ - SubscriptBox[ - OverscriptBox["e", "\[RightVector]"], "i"], "0"], "(", "t", ")"}], - TraditionalForm]]], - " = desired direction of pedestrian ", - Cell[BoxData[ - FormBox["i", TraditionalForm]]], - " at time ", - Cell[BoxData[ - FormBox["t", TraditionalForm]]], - "\n", - Cell[BoxData[ - FormBox[ - RowBox[{ - SubscriptBox[ - OverscriptBox["v", "\[RightVector]"], "i"], "(", "t", ")"}], - TraditionalForm]]], - " = actual velocity of pedestrian ", - Cell[BoxData[ - FormBox["i", TraditionalForm]]], - " at time ", - Cell[BoxData[ - FormBox["t", TraditionalForm]]], - "\n", - Cell[BoxData[ - FormBox[ - SubscriptBox["\[Tau]", "i"], TraditionalForm]]], - " = characteristic time for pedestrian ", - Cell[BoxData[ - FormBox["i", TraditionalForm]]], - " (time taken for actual velocity to match desired velocity)\n", - Cell[BoxData[ - FormBox["W", TraditionalForm]]], - " = set of walls\n", - Cell[BoxData[ - FormBox[ - SubscriptBox[ - OverscriptBox["f", "\[RightVector]"], "ij"], TraditionalForm]]], - " = interaction force between pedestrians ", - Cell[BoxData[ - FormBox["i", TraditionalForm]]], - " and ", - Cell[BoxData[ - FormBox["j", TraditionalForm]]], - "\n", - Cell[BoxData[ - FormBox[ - SubscriptBox[ - OverscriptBox["f", "\[RightVector]"], "iW"], TraditionalForm]]], - " = interaction foroce between pedestrian ", - Cell[BoxData[ - FormBox["i", TraditionalForm]]], - " and wall ", - Cell[BoxData[ - FormBox["W", TraditionalForm]]], - "\n", - Cell[BoxData[ - FormBox[ - RowBox[{ - SubscriptBox[ - OverscriptBox["r", "\[RightVector]"], "i"], "(", "t", ")"}], - TraditionalForm]]], - " = position of pedestrian ", - Cell[BoxData[ - FormBox["i", TraditionalForm]]], - " at time ", - Cell[BoxData[ - FormBox["t", TraditionalForm]]], - "\n", - Cell[BoxData[ - FormBox[ - RowBox[{ - SubscriptBox["A", "i"], ",", - SubscriptBox["B", "i"]}], TraditionalForm]]], - " = constants describing the repulsive interaction force acting on \ -pedestrian ", - Cell[BoxData[ - FormBox["i", TraditionalForm]]], - "\n", - Cell[BoxData[ - FormBox[ - SubscriptBox["d", "ij"], TraditionalForm]]], - " = distance between pedestrian ", - Cell[BoxData[ - FormBox["i", TraditionalForm]]], - " and ", - Cell[BoxData[ - FormBox["j", TraditionalForm]]], - "\[CloseCurlyQuote]s centers of mass\n", - Cell[BoxData[ - FormBox[ - SubscriptBox["d", "iW"], TraditionalForm]]], - " = distance between pedestrain ", - Cell[BoxData[ - FormBox["i", TraditionalForm]]], - " and wall ", - Cell[BoxData[ - FormBox["W", TraditionalForm]]], - "\n", - Cell[BoxData[ - FormBox[ - RowBox[{ - SubscriptBox[ - OverscriptBox["n", "\[RightVector]"], "ij"], "=", - RowBox[{"(", - RowBox[{ - SuperscriptBox[ - SubscriptBox["n", "ij"], "1"], ",", - SuperscriptBox[ - SubscriptBox["n", "ij"], "2"]}], ")"}]}], TraditionalForm]]], - " = normalized vector pointing from pedestrian ", - Cell[BoxData[ - FormBox["j", TraditionalForm]]], - " to ", - Cell[BoxData[ - FormBox["i", TraditionalForm]]], - "\n", - Cell[BoxData[ - FormBox[ - SubscriptBox[ - OverscriptBox["n", "\[RightVector]"], "iW"], TraditionalForm]]], - " = direction perpendicular to wall ", - Cell[BoxData[ - FormBox["W", TraditionalForm]]], - "\n", - Cell[BoxData[ - FormBox[ - SubscriptBox["r", "i"], TraditionalForm]]], - " = radius of pedestrian ", - Cell[BoxData[ - FormBox["i", TraditionalForm]]], - "\n", - Cell[BoxData[ - FormBox[ - SubscriptBox["r", "ij"], TraditionalForm]]], - " = sum of radii of pedestrians ", - Cell[BoxData[ - FormBox["i", TraditionalForm]]], - " and ", - Cell[BoxData[ - FormBox["j", TraditionalForm]]], - "\n", - Cell[BoxData[ - FormBox[ - RowBox[{"k", ",", "\[Kappa]"}], TraditionalForm]]], - " = large constants that control body force and sliding friction, \ -respectively\n", - Cell[BoxData[ - FormBox[ - SubscriptBox[ - OverscriptBox["t", "\[RightVector]"], "ij"], TraditionalForm]]], - " = tangential direction between pedestrians ", - Cell[BoxData[ - FormBox["i", TraditionalForm]]], - " and ", - Cell[BoxData[ - FormBox["j", TraditionalForm]]], - "\n", - Cell[BoxData[ - FormBox[ - SubscriptBox[ - OverscriptBox["t", "\[RightVector]"], "iW"], TraditionalForm]]], - " = direction tangential to wall ", - Cell[BoxData[ - FormBox["W", TraditionalForm]]], - "\n", - Cell[BoxData[ - FormBox[ - SuperscriptBox[ - SubscriptBox["\[CapitalDelta]v", "ij"], "t"], TraditionalForm]]], - " = difference in tangential velocities of pedestrians ", - Cell[BoxData[ - FormBox["i", TraditionalForm]]], - " and ", - Cell[BoxData[ - FormBox["j", TraditionalForm]]], - "\n", - Cell[BoxData[ - FormBox[ - RowBox[{ - RowBox[{"g", "(", "x", ")"}], "=", - RowBox[{"{", - RowBox[{GridBox[{ - {"0", - RowBox[{ - RowBox[{"if", " ", "x"}], "<", "0"}]}, - {"x", - RowBox[{ - RowBox[{"if", " ", "x"}], "\[GreaterEqual]", "0"}]} - }], "=", - RowBox[{"max", - RowBox[{"{", - RowBox[{"0", ",", "x"}], "}"}]}]}]}]}], TraditionalForm]]], - " = function to zero out negative arguments" -}], "Text", - CellChangeTimes->{{3.7767171907543736`*^9, 3.776717249892484*^9}}] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["Estimated Parameters", "Subsection", - CellChangeTimes->{{3.776717291936208*^9, 3.776717297689221*^9}}], - -Cell[TextData[{ - Cell[BoxData[ - FormBox[ - RowBox[{ - SubscriptBox["m", "i"], "=", - RowBox[{"80", "kg"}]}], TraditionalForm]]], - "\n", - Cell[BoxData[ - FormBox[ - RowBox[{ - SuperscriptBox[ - SubscriptBox["v", "i"], "0"], "=", - RowBox[{"1", - FractionBox["m", "s"]}]}], TraditionalForm]]], - " , which corresponds to the paper\[CloseCurlyQuote]s \ -\[OpenCurlyDoubleQuote]normal\[CloseCurlyDoubleQuote] conditions\n", - Cell[BoxData[ - FormBox[ - RowBox[{ - SubscriptBox["\[Tau]", "i"], "=", - RowBox[{"0.5", "s"}]}], TraditionalForm]]], - "\n", - Cell[BoxData[ - FormBox[ - RowBox[{ - SubscriptBox["A", "i"], "=", - RowBox[{"2", "\[Times]", - SuperscriptBox["10", "3"], "N"}]}], TraditionalForm]]], - "\n", - Cell[BoxData[ - FormBox[ - RowBox[{ - SubscriptBox["B", "i"], "=", - RowBox[{"0.08", "m"}]}], TraditionalForm]]], - "\n", - Cell[BoxData[ - FormBox[ - RowBox[{"k", "=", - RowBox[{"1.2", "\[Times]", - SuperscriptBox["10", "5"], - FractionBox["kg", - SuperscriptBox["s", "2"]]}]}], TraditionalForm]]], - "\n", - Cell[BoxData[ - FormBox[ - RowBox[{"\[Kappa]", "=", - RowBox[{"2.4", "\[Times]", - SuperscriptBox["10", "5"], - FractionBox["kg", - RowBox[{"m", " ", "s"}]]}]}], TraditionalForm]]], - "\n", - Cell[BoxData[ - FormBox[ - RowBox[{"2", - RowBox[{ - SubscriptBox["r", "i"], "~", - RowBox[{"U", "[", - RowBox[{ - RowBox[{"0.5", "m"}], ",", - RowBox[{"0.7", "m"}]}], "]"}]}]}], TraditionalForm]]] -}], "Text", - CellChangeTimes->{{3.7767173053782897`*^9, 3.7767173428142323`*^9}}] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["Model Definition", "Subsection", - CellChangeTimes->{{3.776717265068303*^9, 3.776717272637017*^9}}], - -Cell[TextData[{ - "The change in pedestrian ", - Cell[BoxData[ - FormBox["i", TraditionalForm]]], - "\[CloseCurlyQuote]s velocity at time ", - Cell[BoxData[ - FormBox["t", TraditionalForm]]], - " is given by the acceleration equation" -}], "Text", - CellChangeTimes->{ - 3.7767172377664404`*^9, {3.776717397554256*^9, 3.776717401793109*^9}}], - -Cell[BoxData[ - FormBox[ - RowBox[{ - RowBox[{ - SubscriptBox["m", "i"], - FractionBox[ - RowBox[{"\[DifferentialD]", - SubscriptBox[ - OverscriptBox["v", "\[RightVector]"], "i"]}], - RowBox[{"\[DifferentialD]", "t"}]]}], "=", - RowBox[{ - RowBox[{ - SubscriptBox["m", "i"], - FractionBox[ - RowBox[{ - RowBox[{ - SuperscriptBox[ - SubscriptBox["v", "i"], "0"], - RowBox[{"(", "t", ")"}], " ", - RowBox[{ - SuperscriptBox[ - SubscriptBox[ - OverscriptBox["e", "\[RightVector]"], "i"], "0"], "(", "t", - ")"}]}], "-", - RowBox[{ - SubscriptBox[ - OverscriptBox["v", "\[RightVector]"], "i"], "(", "t", ")"}]}], - SubscriptBox["\[Tau]", "i"]]}], "+", - RowBox[{ - UnderscriptBox["\[Sum]", - RowBox[{"j", "(", - RowBox[{"\[NotEqual]", "i"}], ")"}]], - SubscriptBox[ - OverscriptBox["f", "\[RightVector]"], "ij"]}], "+", - RowBox[{ - UnderscriptBox["\[Sum]", "W"], - SubscriptBox[ - OverscriptBox["f", "\[RightVector]"], "iW"]}]}]}], - TraditionalForm]], "DisplayFormula", - CellChangeTimes->{ - 3.7767172377664404`*^9, {3.776717397554256*^9, 3.776717420150271*^9}}], - -Cell[TextData[{ - "Velocity is change in position, so by definition ", - Cell[BoxData[ - FormBox[ - RowBox[{ - FractionBox[ - RowBox[{"\[DifferentialD]", - SubscriptBox[ - OverscriptBox["r", "\[RightVector]"], "i"]}], - RowBox[{"\[DifferentialD]", "t"}]], "=", - RowBox[{ - SubscriptBox[ - OverscriptBox["v", "\[RightVector]"], "i"], "(", "t", ")"}]}], - TraditionalForm]]], - "." -}], "Text", - CellChangeTimes->{ - 3.7767172377664404`*^9, {3.776717397554256*^9, 3.776717450738205*^9}, { - 3.776719148617407*^9, 3.7767191506667504`*^9}}], - -Cell[TextData[{ - "The repulsive interaction force between ", - Cell[BoxData[ - FormBox["i", TraditionalForm]]], - " and ", - Cell[BoxData[ - FormBox["j", TraditionalForm]]], - " is" -}], "Text", - CellChangeTimes->{ - 3.7767172377664404`*^9, {3.776717397554256*^9, 3.776717472722627*^9}}], - -Cell[BoxData[ - FormBox[ - RowBox[{ - SubscriptBox["A", "i"], - RowBox[{"exp", "(", - FractionBox[ - RowBox[{ - SubscriptBox["r", "ij"], "-", - SubscriptBox["d", "ij"]}], - SubscriptBox["B", "i"]], ")"}], - SubscriptBox[ - OverscriptBox["n", "\[RightVector]"], "ij"]}], - TraditionalForm]], "DisplayFormula", - CellChangeTimes->{ - 3.7767172377664404`*^9, {3.776717397554256*^9, 3.7767174700431833`*^9}}], - -Cell["Some other simple definitional constraints include", "Text", - CellChangeTimes->{ - 3.7767172377664404`*^9, {3.776717397554256*^9, 3.77671748395348*^9}}], - -Cell[BoxData[{ - FormBox[ - RowBox[{ - SubscriptBox["d", "ij"], "=", - RowBox[{"\[LeftDoubleBracketingBar]", - RowBox[{ - SubscriptBox[ - OverscriptBox["r", "\[RightVector]"], "i"], "-", - SubscriptBox[ - OverscriptBox["r", "\[RightVector]"], "j"]}], - "\[RightDoubleBracketingBar]"}]}], TraditionalForm], "\n", - FormBox[ - RowBox[{ - SubscriptBox[ - OverscriptBox["n", "\[RightVector]"], "ij"], "=", - FractionBox[ - RowBox[{ - SubscriptBox[ - OverscriptBox["r", "\[RightVector]"], "i"], "-", - SubscriptBox[ - OverscriptBox["r", "\[RightVector]"], "j"]}], - SubscriptBox["d", "ij"]]}], TraditionalForm], "\n", - FormBox[ - RowBox[{ - SubscriptBox["r", "ij"], "=", - RowBox[{ - SubscriptBox["r", "i"], "+", - SubscriptBox["r", "j"]}]}], TraditionalForm]}], "DisplayFormula", - CellChangeTimes->{ - 3.7767172377664404`*^9, {3.776717397554256*^9, 3.7767175006033335`*^9}}], - -Cell[TextData[{ - "Pedestrians touch each other whenever their distance ", - Cell[BoxData[ - FormBox[ - SubscriptBox["d", "ij"], TraditionalForm]]], - " is less than their combined radii ", - Cell[BoxData[ - FormBox[ - SubscriptBox["r", "ij"], TraditionalForm]]], - ". In this case, two additional forces take effect. Body force counteracts \ -body compression, and sliding friction impedes relative tangental motion. \ -They are given, respectively, by" -}], "Text", - CellChangeTimes->{ - 3.7767172377664404`*^9, {3.776717397554256*^9, 3.7767175064492064`*^9}}], - -Cell[BoxData[{ - FormBox[ - RowBox[{ - RowBox[{"k", "(", - RowBox[{ - SubscriptBox["r", "ij"], "-", - SubscriptBox["d", "ij"]}], ")"}], - SubscriptBox[ - OverscriptBox["n", "\[RightVector]"], "ij"]}], TraditionalForm], "\n", - FormBox[ - RowBox[{ - RowBox[{"\[Kappa]", "(", - RowBox[{ - SubscriptBox["r", "ij"], "-", - SubscriptBox["d", "ij"]}], ")"}], - SuperscriptBox[ - SubscriptBox["\[CapitalDelta]v", "ji"], "t"], - SubscriptBox[ - OverscriptBox["t", "\[RightVector]"], "ij"]}], - TraditionalForm]}], "DisplayFormula", - CellChangeTimes->{ - 3.7767172377664404`*^9, {3.776717397554256*^9, 3.776717519142268*^9}}], - -Cell["\<\ -The tangential direction and tangnetial velocity differences are given, \ -respectively, by\ -\>", "Text", - CellChangeTimes->{ - 3.7767172377664404`*^9, {3.776717397554256*^9, 3.776717524388327*^9}}], - -Cell[BoxData[{ - FormBox[ - RowBox[{ - SubscriptBox[ - OverscriptBox["t", "\[RightVector]"], "ij"], "=", - RowBox[{"(", - RowBox[{ - RowBox[{"-", - SuperscriptBox[ - SubscriptBox["n", "ij"], "2"]}], ",", - SuperscriptBox[ - SubscriptBox["n", "ij"], "1"]}], ")"}]}], TraditionalForm], "\n", - FormBox[ - RowBox[{ - SuperscriptBox[ - SubscriptBox["\[CapitalDelta]v", "ij"], "t"], "=", - RowBox[{ - RowBox[{"(", - RowBox[{ - SubscriptBox[ - OverscriptBox["v", "\[RightVector]"], "j"], "-", - SubscriptBox[ - OverscriptBox["v", "\[RightVector]"], "i"]}], ")"}], "\[CenterDot]", - SubscriptBox[ - OverscriptBox["t", "\[RightVector]"], "ij"]}]}], - TraditionalForm]}], "DisplayFormula", - CellChangeTimes->{ - 3.7767172377664404`*^9, {3.776717397554256*^9, 3.776717535569138*^9}}], - -Cell[TextData[{ - "Combining all of the forces, we can define the interaction force between \ -pedestrians ", - Cell[BoxData[ - FormBox["i", TraditionalForm]]], - " and ", - Cell[BoxData[ - FormBox["j", TraditionalForm]]], - " as" -}], "Text", - CellChangeTimes->{ - 3.7767172377664404`*^9, {3.776717397554256*^9, 3.776717541801302*^9}}], - -Cell[BoxData[ - FormBox[ - RowBox[{ - SubscriptBox[ - OverscriptBox["f", "\[RightVector]"], "ij"], "=", - RowBox[{ - RowBox[{ - RowBox[{"(", - RowBox[{ - RowBox[{ - SubscriptBox["A", "i"], - RowBox[{"exp", "(", - FractionBox[ - RowBox[{ - SubscriptBox["r", "ij"], "-", - SubscriptBox["d", "ij"]}], - SubscriptBox["B", "i"]], ")"}]}], "+", - RowBox[{"k", " ", - RowBox[{"g", "(", - RowBox[{ - SubscriptBox["r", "ij"], "-", - SubscriptBox["d", "ij"]}], ")"}]}]}], ")"}], - SubscriptBox[ - OverscriptBox["n", "\[RightVector]"], "ij"]}], "+", - RowBox[{"\[Kappa]", " ", - RowBox[{"g", "(", - RowBox[{ - SubscriptBox["r", "ij"], "-", - SubscriptBox["d", "ij"]}], ")"}], - SuperscriptBox[ - SubscriptBox["\[CapitalDelta]v", "ji"], "t"], - SubscriptBox[ - OverscriptBox["t", "\[RightVector]"], "ij"]}]}]}], - TraditionalForm]], "DisplayFormula", - CellChangeTimes->{ - 3.7767172377664404`*^9, {3.776717397554256*^9, 3.776717554097148*^9}}], - -Cell[TextData[{ - "and between pedestrian ", - Cell[BoxData[ - FormBox["i", TraditionalForm]]], - " and a wall it is" -}], "Text", - CellChangeTimes->{ - 3.7767172377664404`*^9, {3.776717397554256*^9, 3.7767175595062294`*^9}}], - -Cell[BoxData[ - FormBox[ - RowBox[{ - SubscriptBox[ - OverscriptBox["f", "\[RightVector]"], "iW"], "=", - RowBox[{ - RowBox[{ - RowBox[{"(", - RowBox[{ - RowBox[{ - SubscriptBox["A", "i"], - RowBox[{"exp", "(", - FractionBox[ - RowBox[{ - SubscriptBox["r", "i"], "-", - SubscriptBox["d", "iW"]}], - SubscriptBox["B", "i"]], ")"}]}], "+", - RowBox[{"k", " ", - RowBox[{"g", "(", - RowBox[{ - SubscriptBox["r", "i"], "-", - SubscriptBox["d", "iW"]}], ")"}]}]}], ")"}], - SubscriptBox[ - OverscriptBox["n", "\[RightVector]"], "iW"]}], "-", - RowBox[{"\[Kappa]", " ", - RowBox[{"g", "(", - RowBox[{ - SubscriptBox["r", "i"], "-", - SubscriptBox["d", "iW"]}], ")"}], - RowBox[{"(", - RowBox[{ - SubscriptBox[ - OverscriptBox["v", "\[RightVector]"], "i"], "\[CenterDot]", - SubscriptBox[ - OverscriptBox["t", "\[RightVector]"], "iW"]}], ")"}], - SubscriptBox[ - OverscriptBox["t", "\[RightVector]"], "iW"]}]}]}], - TraditionalForm]], "DisplayFormula", - CellChangeTimes->{ - 3.7767172377664404`*^9, {3.776717397554256*^9, 3.776717568888282*^9}}] -}, Open ]] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["Code", "Section", - CellChangeTimes->{{3.776600864408964*^9, 3.7766008650447807`*^9}}], - -Cell[CellGroupData[{ - -Cell["Initialization", "Subsection", - CellChangeTimes->{{3.776600871130811*^9, 3.776600873087188*^9}}], - -Cell[BoxData[ - RowBox[{ - RowBox[{"(*", " ", "constants", " ", "*)"}], "\[IndentingNewLine]", - RowBox[{ - RowBox[{ - RowBox[{"Dynamic", "[", "v0", "]"}], ";"}], "\[IndentingNewLine]", - RowBox[{ - RowBox[{"Dynamic", "[", "Np", "]"}], ";"}], "\[IndentingNewLine]", - RowBox[{ - RowBox[{"Dynamic", "[", "bb", "]"}], ";"}], "\[IndentingNewLine]", - RowBox[{ - RowBox[{"Dynamic", "[", "par1", "]"}], ";"}], "\[IndentingNewLine]", - RowBox[{ - RowBox[{"Dynamic", "[", "par2", "]"}], ";"}], "\[IndentingNewLine]", - RowBox[{ - RowBox[{"Dynamic", "[", "W", "]"}], ";"}], "\[IndentingNewLine]", - RowBox[{ - RowBox[{"Dynamic", "[", "Wg", "]"}], ";"}], "\[IndentingNewLine]", - RowBox[{ - RowBox[{"Dynamic", "[", "lo", "]"}], ";"}], "\[IndentingNewLine]", - RowBox[{ - RowBox[{"Dynamic", "[", "Ap", "]"}], ";"}], "\[IndentingNewLine]", - RowBox[{ - RowBox[{"Dynamic", "[", "Aw", "]"}], ";"}], "\[IndentingNewLine]", - RowBox[{ - RowBox[{"Dynamic", "[", "door", "]"}], ";"}], "\[IndentingNewLine]", - RowBox[{ - RowBox[{"Dynamic", "[", "\[Kappa]", "]"}], ";"}], "\[IndentingNewLine]", - RowBox[{ - RowBox[{"m", "=", "80.0"}], ";", - RowBox[{"(*", " ", - RowBox[{"pedestrian", " ", "mass"}], " ", "*)"}], "\[IndentingNewLine]", - RowBox[{"v0", "=", "1.0"}], ";", " ", - RowBox[{"(*", " ", - RowBox[{"desired", " ", "pedestrian", " ", "velocity"}], " ", "*)"}], - "\[IndentingNewLine]", - RowBox[{"\[Tau]", "=", "0.5"}], ";", - RowBox[{"(*", " ", - RowBox[{ - "time", " ", "to", " ", "acquire", " ", "desired", " ", "velocity"}], - " ", "*)"}], "\[IndentingNewLine]", - RowBox[{"Ap", "=", - RowBox[{"2.0", "*", - SuperscriptBox["10", "3"]}]}], ";"}], "\[IndentingNewLine]", - RowBox[{ - RowBox[{"Aw", "=", - RowBox[{"1.0", "*", - SuperscriptBox["10", "3"]}]}], ";", - RowBox[{"(*", " ", - RowBox[{ - "repulsive", " ", "interaction", " ", "force", " ", "constant", " ", - RowBox[{"(", - RowBox[{"people", ",", " ", "wall"}], ")"}]}], " ", "*)"}], - "\[IndentingNewLine]", - RowBox[{"B", "=", "0.08"}], ";", - RowBox[{"(*", " ", - RowBox[{"repulsive", " ", "interaction", " ", "force", " ", "constant"}], - " ", "*)"}], "\[IndentingNewLine]", - RowBox[{"k", "=", - RowBox[{"1.2", "*", - SuperscriptBox["10", "5"]}]}], ";", - RowBox[{"(*", " ", - RowBox[{"body", " ", "force", " ", "constant"}], " ", "*)"}], - "\[IndentingNewLine]", - RowBox[{"\[Kappa]", "=", - RowBox[{"2.4", "*", - SuperscriptBox["10", "5"]}]}], ";", - RowBox[{"(*", " ", - RowBox[{"sliding", " ", "friction", " ", "force", " ", "constant"}], " ", - "*)"}], "\[IndentingNewLine]", - RowBox[{"Np", "=", "20"}], ";", - RowBox[{"(*", " ", - RowBox[{"number", " ", "of", " ", "pedestrians"}], " ", "*)"}], - "\[IndentingNewLine]", - RowBox[{"radmin", "=", - FractionBox["0.5", "2"]}], ";", - RowBox[{"(*", " ", - RowBox[{"minimum", " ", "pedestrian", " ", "radius"}], " ", "*)"}], - "\[IndentingNewLine]", - RowBox[{"radmax", "=", - FractionBox["0.7", "2"]}], ";", - RowBox[{"(*", " ", - RowBox[{"maximum", " ", "pedestrian", " ", "radius"}], " ", "*)"}], - "\[IndentingNewLine]", - RowBox[{"W", "=", - RowBox[{"{", - RowBox[{ - RowBox[{"{", - RowBox[{ - RowBox[{"{", - RowBox[{"10.0", ",", "20.0"}], "}"}], ",", - RowBox[{"{", - RowBox[{"10.0", ",", "5.75"}], "}"}]}], "}"}], ",", - RowBox[{"{", - RowBox[{ - RowBox[{"{", - RowBox[{"10.0", ",", "5.75"}], "}"}], ",", - RowBox[{"{", - RowBox[{"11.0", ",", "5.75"}], "}"}]}], "}"}], ",", - RowBox[{"{", - RowBox[{ - RowBox[{"{", - RowBox[{"11.0", ",", "5.75"}], "}"}], ",", - RowBox[{"{", - RowBox[{"11.0", ",", "20.0"}], "}"}]}], "}"}], ",", - RowBox[{"{", - RowBox[{ - RowBox[{"{", - RowBox[{"10.0", ",", - RowBox[{"-", "10.0"}]}], "}"}], ",", - RowBox[{"{", - RowBox[{"10.0", ",", "4.25"}], "}"}]}], "}"}], ",", - RowBox[{"{", - RowBox[{ - RowBox[{"{", - RowBox[{"10.0", ",", "4.25"}], "}"}], ",", - RowBox[{"{", - RowBox[{"11.0", ",", "4.25"}], "}"}]}], "}"}], ",", - RowBox[{"{", - RowBox[{ - RowBox[{"{", - RowBox[{"11.0", ",", "4.25"}], "}"}], ",", - RowBox[{"{", - RowBox[{"11.0", ",", - RowBox[{"-", "10.0"}]}], "}"}]}], "}"}]}], "}"}]}], ";", - RowBox[{"(*", " ", - RowBox[{ - RowBox[{"list", " ", "of", " ", "wall", " ", "segments"}], ",", " ", - RowBox[{ - "expressed", " ", "as", " ", "the", " ", "coordinates", " ", "of", " ", - "its", " ", "endpoints"}]}], " ", "*)"}], "\[IndentingNewLine]", - RowBox[{"Wg", "=", - RowBox[{"{", - RowBox[{ - RowBox[{"Polygon", "[", - RowBox[{"{", - RowBox[{ - RowBox[{"W", "[", - RowBox[{"[", - RowBox[{"1", ",", "1"}], "]"}], "]"}], ",", - RowBox[{"W", "[", - RowBox[{"[", - RowBox[{"2", ",", "1"}], "]"}], "]"}], ",", - RowBox[{"W", "[", - RowBox[{"[", - RowBox[{"3", ",", "1"}], "]"}], "]"}], ",", - RowBox[{"W", "[", - RowBox[{"[", - RowBox[{"3", ",", "2"}], "]"}], "]"}]}], "}"}], "]"}], ",", - RowBox[{"Polygon", "[", - RowBox[{"{", - RowBox[{ - RowBox[{"W", "[", - RowBox[{"[", - RowBox[{"4", ",", "1"}], "]"}], "]"}], ",", - RowBox[{"W", "[", - RowBox[{"[", - RowBox[{"5", ",", "1"}], "]"}], "]"}], ",", - RowBox[{"W", "[", - RowBox[{"[", - RowBox[{"6", ",", "1"}], "]"}], "]"}], ",", - RowBox[{"W", "[", - RowBox[{"[", - RowBox[{"6", ",", "2"}], "]"}], "]"}]}], "}"}], "]"}]}], "}"}]}], - ";", - RowBox[{"(*", " ", - RowBox[{ - "graphics", " ", "objects", " ", "for", " ", "the", " ", "walls"}], " ", - "*)"}], "\[IndentingNewLine]", - RowBox[{"door", "=", - RowBox[{"{", - RowBox[{ - RowBox[{"{", - RowBox[{"10.0", ",", "5.25"}], "}"}], ",", - RowBox[{"{", - RowBox[{"10.0", ",", "4.75"}], "}"}]}], "}"}]}], ";", - RowBox[{"(*", " ", - RowBox[{ - RowBox[{ - "line", " ", "segment", " ", "that", " ", "people", " ", "will", " ", - "try", " ", "to", " ", "move", " ", "towards"}], ",", " ", - RowBox[{ - "and", " ", "directly", " ", "right", " ", "after", " ", "that"}]}], - " ", "*)"}], "\[IndentingNewLine]", - RowBox[{"dt", "=", "0.1"}], ";", - RowBox[{"(*", " ", - RowBox[{ - "time", " ", "increment", " ", "for", " ", "finite", " ", "difference", - " ", "solution"}], " ", "*)"}], "\[IndentingNewLine]", - RowBox[{"cutoff", "=", "45.0"}], ";", - RowBox[{"(*", " ", - RowBox[{"simulation", " ", "time", " ", "cutoff", " ", - RowBox[{"(", "s", ")"}]}], " ", "*)"}], "\[IndentingNewLine]", - RowBox[{"bb", "=", - RowBox[{"{", - RowBox[{ - RowBox[{"{", - RowBox[{"1.0", ",", "9.0"}], "}"}], ",", - RowBox[{"{", - RowBox[{"1.0", ",", "9.0"}], "}"}]}], "}"}]}], ";", - RowBox[{"(*", " ", - RowBox[{ - "bounds", " ", "of", " ", "initial", " ", "position", " ", "box"}], " ", - "*)"}], "\[IndentingNewLine]", - RowBox[{"par1", "=", "1.5"}], ";", - RowBox[{"(*", " ", - RowBox[{"parameters", " ", "of", " ", "layout"}], " ", "*)"}], - "\[IndentingNewLine]", - RowBox[{"par2", "=", "2.0"}], ";"}], "\[IndentingNewLine]", - RowBox[{ - RowBox[{"colrad", "=", "0.6"}], ";", - RowBox[{"(*", " ", - RowBox[{ - "radius", " ", "of", " ", "column", " ", "in", " ", "the", " ", "column", - " ", "layout"}], " ", "*)"}], "\[IndentingNewLine]", - RowBox[{"Nw", "=", "3"}], ";", - RowBox[{"(*", " ", - RowBox[{ - "maximum", " ", "number", " ", "of", " ", "walls", " ", "in", " ", "any", - " ", "layout"}], " ", "*)"}], "\[IndentingNewLine]", - RowBox[{"lo", "=", "0"}], ";", - RowBox[{"(*", " ", - RowBox[{"layout", " ", "index"}], " ", "*)"}], "\[IndentingNewLine]", - RowBox[{"(*", " ", "variables", " ", "*)"}], "\n", - RowBox[{"Dynamic", "[", "rad", "]"}], ";"}], "\[IndentingNewLine]", - RowBox[{ - RowBox[{"Dynamic", "[", "radsum", "]"}], ";"}], "\[IndentingNewLine]", - RowBox[{ - RowBox[{"Dynamic", "[", "r", "]"}], ";"}], "\[IndentingNewLine]", - RowBox[{ - RowBox[{"Dynamic", "[", "v", "]"}], ";"}], "\[IndentingNewLine]", - RowBox[{ - RowBox[{"Dynamic", "[", "dvi", "]"}], ";"}], "\[IndentingNewLine]", - RowBox[{ - RowBox[{"Dynamic", "[", "dij", "]"}], ";"}], "\[IndentingNewLine]", - RowBox[{ - RowBox[{"Dynamic", "[", "nij", "]"}], ";"}], "\[IndentingNewLine]", - RowBox[{ - RowBox[{"Dynamic", "[", "tij", "]"}], ";"}], "\[IndentingNewLine]", - RowBox[{ - RowBox[{"Dynamic", "[", "dvijt", "]"}], ";"}], "\[IndentingNewLine]", - RowBox[{ - RowBox[{"Dynamic", "[", "e0", "]"}], ";"}], "\[IndentingNewLine]", - RowBox[{ - RowBox[{"Dynamic", "[", "fij", "]"}], ";"}], "\[IndentingNewLine]", - RowBox[{ - RowBox[{"Dynamic", "[", "pos", "]"}], ";"}], "\[IndentingNewLine]", - RowBox[{ - RowBox[{"Dynamic", "[", "pressure", "]"}], ";"}], "\[IndentingNewLine]", - RowBox[{ - RowBox[{"Dynamic", "[", "niw", "]"}], ";"}], "\[IndentingNewLine]", - RowBox[{ - RowBox[{"Dynamic", "[", "tiw", "]"}], ";"}], "\[IndentingNewLine]", - RowBox[{ - RowBox[{"Dynamic", "[", "diw", "]"}], ";"}], "\[IndentingNewLine]", - RowBox[{ - RowBox[{"Dynamic", "[", "fiw", "]"}], ";"}], "\[IndentingNewLine]", - RowBox[{ - RowBox[{"Dynamic", "[", "evac", "]"}], ";"}], "\[IndentingNewLine]", - RowBox[{ - RowBox[{"Dynamic", "[", "tpressure", "]"}], ";"}], "\n", - RowBox[{"(*", " ", "subroutines", " ", "*)"}], "\[IndentingNewLine]", - RowBox[{ - RowBox[{ - RowBox[{"g", "[", "x_", "]"}], ":=", - RowBox[{"Max", "[", - RowBox[{"0", ",", "x"}], "]"}]}], ";", - RowBox[{"(*", " ", - RowBox[{ - "function", " ", "to", " ", "cut", " ", "off", " ", "negative", " ", - "arguments"}], " ", "*)"}], "\[IndentingNewLine]", - RowBox[{ - RowBox[{"dijcalc", "[", - RowBox[{"i_", ",", "j_"}], "]"}], ":=", - RowBox[{"EuclideanDistance", "[", - RowBox[{ - RowBox[{"r", "[", - RowBox[{"[", "i", "]"}], "]"}], ",", - RowBox[{"r", "[", - RowBox[{"[", "j", "]"}], "]"}]}], "]"}]}], ";"}], - "\[IndentingNewLine]", - RowBox[{ - RowBox[{ - RowBox[{"dniwcalc", "[", - RowBox[{"i_", ",", "w_"}], "]"}], ":=", - RowBox[{"wallnorm", "[", - RowBox[{ - RowBox[{"r", "[", - RowBox[{"[", "i", "]"}], "]"}], ",", "w"}], "]"}]}], ";", - RowBox[{"(*", " ", - RowBox[{ - "calculates", " ", "distances", " ", "and", " ", "normal", " ", - "vectors", " ", "for", " ", "walls"}], " ", "*)"}], - "\[IndentingNewLine]", - RowBox[{ - RowBox[{"fijcalc", "[", - RowBox[{"i_", ",", "j_"}], "]"}], ":=", - RowBox[{"If", "[", - RowBox[{ - RowBox[{"i", "\[Equal]", "j"}], ",", - RowBox[{"{", - RowBox[{"0", ",", "0"}], "}"}], ",", - RowBox[{ - RowBox[{ - RowBox[{"(", - RowBox[{ - RowBox[{"Ap", " ", - RowBox[{"Exp", "[", - FractionBox[ - RowBox[{ - RowBox[{"radsum", "[", - RowBox[{"[", - RowBox[{"i", ",", "j"}], "]"}], "]"}], "-", - RowBox[{"dij", "[", - RowBox[{"[", - RowBox[{"i", ",", "j"}], "]"}], "]"}]}], "B"], "]"}]}], "+", - RowBox[{"k", " ", - RowBox[{"g", "[", - RowBox[{ - RowBox[{"radsum", "[", - RowBox[{"[", - RowBox[{"i", ",", "j"}], "]"}], "]"}], "-", - RowBox[{"dij", "[", - RowBox[{"[", - RowBox[{"i", ",", "j"}], "]"}], "]"}]}], "]"}]}]}], ")"}], - RowBox[{"nij", "[", - RowBox[{"[", - RowBox[{"i", ",", "j"}], "]"}], "]"}]}], "+", - RowBox[{"\[Kappa]", " ", - RowBox[{"g", "[", - RowBox[{ - RowBox[{"radsum", "[", - RowBox[{"[", - RowBox[{"i", ",", "j"}], "]"}], "]"}], "-", - RowBox[{"dij", "[", - RowBox[{"[", - RowBox[{"i", ",", "j"}], "]"}], "]"}]}], "]"}], - RowBox[{"dvijt", "[", - RowBox[{"[", - RowBox[{"j", ",", "i"}], "]"}], "]"}], - RowBox[{"tij", "[", - RowBox[{"[", - RowBox[{"i", ",", "j"}], "]"}], "]"}]}]}]}], "]"}]}], ";"}], - "\[IndentingNewLine]", - RowBox[{ - RowBox[{ - RowBox[{"fiwcalc", "[", - RowBox[{"i_", ",", "w_"}], "]"}], ":=", - RowBox[{ - RowBox[{ - RowBox[{"(", - RowBox[{ - RowBox[{"Aw", " ", - RowBox[{"Exp", "[", - FractionBox[ - RowBox[{ - RowBox[{"rad", "[", - RowBox[{"[", "i", "]"}], "]"}], "-", - RowBox[{"diw", "[", - RowBox[{"[", - RowBox[{"i", ",", "w"}], "]"}], "]"}]}], "B"], "]"}]}], "+", - RowBox[{"k", " ", - RowBox[{"g", "[", - RowBox[{ - RowBox[{"rad", "[", - RowBox[{"[", "i", "]"}], "]"}], "-", - RowBox[{"diw", "[", - RowBox[{"[", - RowBox[{"i", ",", "w"}], "]"}], "]"}]}], "]"}]}]}], ")"}], - RowBox[{"niw", "[", - RowBox[{"[", - RowBox[{"i", ",", "w"}], "]"}], "]"}]}], "-", - RowBox[{"\[Kappa]", " ", - RowBox[{"g", "[", - RowBox[{ - RowBox[{"rad", "[", - RowBox[{"[", "i", "]"}], "]"}], "-", - RowBox[{"diw", "[", - RowBox[{"[", - RowBox[{"i", ",", "w"}], "]"}], "]"}]}], "]"}], - RowBox[{"(", - RowBox[{ - RowBox[{"v", "[", - RowBox[{"[", "i", "]"}], "]"}], ".", - RowBox[{"tiw", "[", - RowBox[{"[", - RowBox[{"i", ",", "w"}], "]"}], "]"}]}], ")"}], - RowBox[{"tiw", "[", - RowBox[{"[", - RowBox[{"i", ",", "w"}], "]"}], "]"}]}]}]}], ";"}], - "\[IndentingNewLine]", - RowBox[{ - RowBox[{ - RowBox[{"nijcalc", "[", - RowBox[{"i_", ",", "j_"}], "]"}], ":=", - RowBox[{"If", "[", - RowBox[{ - RowBox[{"i", "\[Equal]", "j"}], ",", - RowBox[{"{", - RowBox[{"0", ",", "0"}], "}"}], ",", - FractionBox[ - RowBox[{ - RowBox[{"r", "[", - RowBox[{"[", "i", "]"}], "]"}], "-", - RowBox[{"r", "[", - RowBox[{"[", "j", "]"}], "]"}]}], - RowBox[{"dij", "[", - RowBox[{"[", - RowBox[{"i", ",", "j"}], "]"}], "]"}]]}], "]"}]}], ";"}], - "\[IndentingNewLine]", - RowBox[{ - RowBox[{ - RowBox[{"tijcalc", "[", - RowBox[{"i_", ",", "j_"}], "]"}], ":=", - RowBox[{"{", - RowBox[{ - RowBox[{"-", - RowBox[{"nij", "[", - RowBox[{"[", - RowBox[{"i", ",", "j", ",", "2"}], "]"}], "]"}]}], ",", - RowBox[{"nij", "[", - RowBox[{"[", - RowBox[{"i", ",", "j", ",", "1"}], "]"}], "]"}]}], "}"}]}], ";"}], - "\[IndentingNewLine]", - RowBox[{ - RowBox[{ - RowBox[{"tiwcalc", "[", - RowBox[{"i_", ",", "w_"}], "]"}], ":=", - RowBox[{"{", - RowBox[{ - RowBox[{"-", - RowBox[{"niw", "[", - RowBox[{"[", - RowBox[{"i", ",", "w", ",", "2"}], "]"}], "]"}]}], ",", - RowBox[{"niw", "[", - RowBox[{"[", - RowBox[{"i", ",", "w", ",", "1"}], "]"}], "]"}]}], "}"}]}], ";"}], - "\[IndentingNewLine]", - RowBox[{ - RowBox[{ - RowBox[{"dvijtcalc", "[", - RowBox[{"i_", ",", "j_"}], "]"}], ":=", - RowBox[{ - RowBox[{"(", - RowBox[{ - RowBox[{"v", "[", - RowBox[{"[", "i", "]"}], "]"}], "-", - RowBox[{"v", "[", - RowBox[{"[", "j", "]"}], "]"}]}], ")"}], ".", - RowBox[{"tij", "[", - RowBox[{"[", - RowBox[{"j", ",", "i"}], "]"}], "]"}]}]}], ";"}], - "\[IndentingNewLine]", - RowBox[{ - RowBox[{ - RowBox[{"e0calc", "[", "i_", "]"}], ":=", - RowBox[{"If", "[", - RowBox[{ - RowBox[{ - RowBox[{"r", "[", - RowBox[{"[", - RowBox[{"i", ",", "1"}], "]"}], "]"}], "\[GreaterEqual]", - RowBox[{"door", "[", - RowBox[{"[", - RowBox[{"1", ",", "1"}], "]"}], "]"}]}], ",", "\[IndentingNewLine]", - RowBox[{"(*", " ", - RowBox[{ - "past", " ", "the", " ", "door", " ", "just", " ", "go", " ", - "right"}], " ", "*)"}], "\[IndentingNewLine]", - RowBox[{"{", - RowBox[{"1", ",", "0"}], "}"}], ",", "\[IndentingNewLine]", - RowBox[{"(*", " ", - RowBox[{ - "otherwise", " ", "find", " ", "the", " ", "closest", " ", "point", - " ", "on", " ", "the", " ", "door"}], " ", "*)"}], - "\[IndentingNewLine]", - RowBox[{"Piecewise", "[", - RowBox[{ - RowBox[{"{", - RowBox[{ - RowBox[{"{", - RowBox[{ - RowBox[{ - RowBox[{"door", "[", - RowBox[{"[", "1", "]"}], "]"}], "-", - RowBox[{"r", "[", - RowBox[{"[", "i", "]"}], "]"}]}], ",", - RowBox[{ - RowBox[{"r", "[", - RowBox[{"[", - RowBox[{"i", ",", "2"}], "]"}], "]"}], "\[GreaterEqual]", - RowBox[{"door", "[", - RowBox[{"[", - RowBox[{"1", ",", "2"}], "]"}], "]"}]}]}], "}"}], ",", - RowBox[{"{", - RowBox[{ - RowBox[{ - RowBox[{"door", "[", - RowBox[{"[", "2", "]"}], "]"}], "-", - RowBox[{"r", "[", - RowBox[{"[", "i", "]"}], "]"}]}], ",", - RowBox[{ - RowBox[{"r", "[", - RowBox[{"[", - RowBox[{"i", ",", "2"}], "]"}], "]"}], "\[LessEqual]", - RowBox[{"door", "[", - RowBox[{"[", - RowBox[{"2", ",", "2"}], "]"}], "]"}]}]}], "}"}]}], "}"}], - ",", - RowBox[{"{", - RowBox[{"1", ",", "0"}], "}"}]}], "]"}]}], "\[IndentingNewLine]", - "]"}]}], ";"}], "\[IndentingNewLine]", - RowBox[{ - RowBox[{ - RowBox[{"dvicalc", "[", "i_", "]"}], ":=", - RowBox[{ - RowBox[{"(", - RowBox[{ - FractionBox[ - RowBox[{ - RowBox[{"v0", " ", - RowBox[{"e0", "[", - RowBox[{"[", "i", "]"}], "]"}]}], "-", - RowBox[{"v", "[", - RowBox[{"[", "i", "]"}], "]"}]}], "\[Tau]"], "+", - RowBox[{ - FractionBox["1", "m"], - RowBox[{"(", - RowBox[{ - RowBox[{"Sum", "[", - RowBox[{ - RowBox[{"If", "[", - RowBox[{ - RowBox[{"j", "\[Equal]", "i"}], ",", "0", ",", - RowBox[{"fij", "[", - RowBox[{"[", - RowBox[{"i", ",", "j"}], "]"}], "]"}]}], "]"}], ",", - RowBox[{"{", - RowBox[{"j", ",", "1", ",", "Np"}], "}"}]}], "]"}], "+", - RowBox[{"Sum", "[", - RowBox[{ - RowBox[{"fiw", "[", - RowBox[{"[", - RowBox[{"i", ",", "w"}], "]"}], "]"}], ",", - RowBox[{"{", - RowBox[{"w", ",", "1", ",", "Nw"}], "}"}]}], "]"}]}], ")"}]}]}], - ")"}], "dt"}]}], ";", - RowBox[{"(*", " ", - RowBox[{ - "finite", " ", "difference", " ", "calculation", " ", "of", " ", Cell[ - TextData[Cell[BoxData[ - FormBox[ - OverscriptBox[ - SubscriptBox["\[CapitalDelta]v", "i"], "\[RightVector]"], - TraditionalForm]]]]]}], " ", "*)"}], "\[IndentingNewLine]", - RowBox[{ - RowBox[{"vcalc", "[", "i_", "]"}], ":=", - RowBox[{ - RowBox[{"v", "[", - RowBox[{"[", "i", "]"}], "]"}], "+", - RowBox[{"dvi", "[", - RowBox[{"[", "i", "]"}], "]"}]}]}], ";"}], "\[IndentingNewLine]", - RowBox[{ - RowBox[{ - RowBox[{"rcalc", "[", "i_", "]"}], ":=", - RowBox[{ - RowBox[{"r", "[", - RowBox[{"[", "i", "]"}], "]"}], "+", - RowBox[{ - RowBox[{"v", "[", - RowBox[{"[", "i", "]"}], "]"}], "dt"}]}]}], ";"}], - "\[IndentingNewLine]", - RowBox[{ - RowBox[{ - RowBox[{"vcap", "[", "i_", "]"}], ":=", - RowBox[{"If", "[", - RowBox[{ - RowBox[{ - RowBox[{"Norm", "[", - RowBox[{"v", "[", - RowBox[{"[", "i", "]"}], "]"}], "]"}], "\[LessEqual]", "v0"}], ",", - RowBox[{"v", "[", - RowBox[{"[", "i", "]"}], "]"}], ",", - FractionBox[ - RowBox[{"v0", " ", - RowBox[{"v", "[", - RowBox[{"[", "i", "]"}], "]"}]}], - RowBox[{"Norm", "[", - RowBox[{"v", "[", - RowBox[{"[", "i", "]"}], "]"}], "]"}]]}], "]"}]}], ";", - RowBox[{"(*", " ", - RowBox[{ - "caps", " ", "speed", " ", "to", " ", "prevent", " ", "people", " ", - "from", " ", "moving", " ", "unrealistically", " ", "quickly"}], " ", - "*)"}], "\[IndentingNewLine]", - RowBox[{"(*", " ", - RowBox[{"update", " ", "process"}], " ", "*)"}], "\n", - RowBox[{ - RowBox[{"update", "[", - RowBox[{"dummy_:", "0"}], "]"}], ":=", - RowBox[{"Module", "[", - RowBox[{ - RowBox[{"{", "}"}], ",", "\[IndentingNewLine]", - RowBox[{"(*", " ", - RowBox[{"calculate", " ", "desired", " ", "directions"}], " ", "*)"}], - "\[IndentingNewLine]", - RowBox[{ - RowBox[{"e0", "=", - RowBox[{"Table", "[", - RowBox[{ - RowBox[{"e0calc", "[", "i", "]"}], ",", - RowBox[{"{", - RowBox[{"i", ",", "1", ",", "Np"}], "}"}]}], "]"}]}], ";", - "\[IndentingNewLine]", - RowBox[{"(*", " ", - RowBox[{"calculate", " ", "pairwise", " ", "distances"}], " ", - "*)"}], "\[IndentingNewLine]", - RowBox[{"Do", "[", "\[IndentingNewLine]", - RowBox[{ - RowBox[{"Do", "[", "\[IndentingNewLine]", - RowBox[{ - RowBox[{ - RowBox[{"dij", "[", - RowBox[{"[", - RowBox[{"i", ",", "j"}], "]"}], "]"}], "=", - RowBox[{ - RowBox[{"dij", "[", - RowBox[{"[", - RowBox[{"j", ",", "i"}], "]"}], "]"}], "=", - RowBox[{"dijcalc", "[", - RowBox[{"i", ",", "j"}], "]"}]}]}], ",", "\[IndentingNewLine]", - RowBox[{"{", - RowBox[{"j", ",", "1", ",", - RowBox[{"i", "-", "1"}]}], "}"}]}], "]"}], ",", - "\[IndentingNewLine]", - RowBox[{"{", - RowBox[{"i", ",", "1", ",", "Np"}], "}"}]}], "]"}], ";", - "\[IndentingNewLine]", - RowBox[{"(*", " ", - RowBox[{ - "calculate", " ", "symmetric", " ", "and", " ", "antisymmetric", " ", - "pairwise", " ", "values"}], " ", "*)"}], "\[IndentingNewLine]", - RowBox[{"Do", "[", "\[IndentingNewLine]", - RowBox[{ - RowBox[{"Do", "[", "\[IndentingNewLine]", - RowBox[{ - RowBox[{ - RowBox[{ - RowBox[{"dij", "[", - RowBox[{"[", - RowBox[{"i", ",", "j"}], "]"}], "]"}], "=", - RowBox[{ - RowBox[{"dij", "[", - RowBox[{"[", - RowBox[{"j", ",", "i"}], "]"}], "]"}], "=", - RowBox[{"dijcalc", "[", - RowBox[{"i", ",", "j"}], "]"}]}]}], ";", - RowBox[{"(*", " ", "distance", " ", "*)"}], - "\[IndentingNewLine]", - RowBox[{ - RowBox[{"nij", "[", - RowBox[{"[", - RowBox[{"i", ",", "j"}], "]"}], "]"}], "=", - RowBox[{"nijcalc", "[", - RowBox[{"i", ",", "j"}], "]"}]}], ";", - RowBox[{"(*", " ", - RowBox[{"pointing", " ", "vector"}], " ", "*)"}], - "\[IndentingNewLine]", - RowBox[{ - RowBox[{"nij", "[", - RowBox[{"[", - RowBox[{"j", ",", "i"}], "]"}], "]"}], "=", - RowBox[{"-", - RowBox[{"nij", "[", - RowBox[{"[", - RowBox[{"i", ",", "j"}], "]"}], "]"}]}]}], ";", - "\[IndentingNewLine]", - RowBox[{ - RowBox[{"tij", "[", - RowBox[{"[", - RowBox[{"i", ",", "j"}], "]"}], "]"}], "=", - RowBox[{"tijcalc", "[", - RowBox[{"i", ",", "j"}], "]"}]}], ";", - RowBox[{"(*", " ", - RowBox[{"tangential", " ", "vector"}], " ", "*)"}], - "\[IndentingNewLine]", - RowBox[{ - RowBox[{"tij", "[", - RowBox[{"[", - RowBox[{"j", ",", "i"}], "]"}], "]"}], "=", - RowBox[{"-", - RowBox[{"tij", "[", - RowBox[{"[", - RowBox[{"i", ",", "j"}], "]"}], "]"}]}]}], ";", - "\[IndentingNewLine]", - RowBox[{ - RowBox[{"dvijt", "[", - RowBox[{"[", - RowBox[{"i", ",", "j"}], "]"}], "]"}], "=", - RowBox[{ - RowBox[{"dvijt", "[", - RowBox[{"[", - RowBox[{"j", ",", "i"}], "]"}], "]"}], "=", - RowBox[{"dvijtcalc", "[", - RowBox[{"i", ",", "j"}], "]"}]}]}], ";", - RowBox[{"(*", " ", - RowBox[{"relative", " ", "tangential", " ", "velocity"}], " ", - "*)"}], "\[IndentingNewLine]", - RowBox[{"(*", " ", "forces", " ", "*)"}], "\[IndentingNewLine]", - RowBox[{ - RowBox[{"fij", "[", - RowBox[{"[", - RowBox[{"i", ",", "j"}], "]"}], "]"}], "=", - RowBox[{"fijcalc", "[", - RowBox[{"i", ",", "j"}], "]"}]}], ";", "\[IndentingNewLine]", - RowBox[{ - RowBox[{"fij", "[", - RowBox[{"[", - RowBox[{"j", ",", "i"}], "]"}], "]"}], "=", - RowBox[{"-", - RowBox[{"fij", "[", - RowBox[{"[", - RowBox[{"i", ",", "j"}], "]"}], "]"}]}]}]}], ",", - "\[IndentingNewLine]", - RowBox[{"{", - RowBox[{"j", ",", "1", ",", - RowBox[{"i", "-", "1"}]}], "}"}]}], "]"}], ",", - "\[IndentingNewLine]", - RowBox[{"{", - RowBox[{"i", ",", "1", ",", "Np"}], "}"}]}], "]"}], ";", - "\[IndentingNewLine]", - RowBox[{"(*", " ", - RowBox[{"calculate", " ", "wall", " ", "values"}], " ", "*)"}], - "\[IndentingNewLine]", - RowBox[{"Do", "[", "\[IndentingNewLine]", - RowBox[{ - RowBox[{"Do", "[", "\[IndentingNewLine]", - RowBox[{"(*", - RowBox[{ - RowBox[{ - RowBox[{"{", - RowBox[{ - RowBox[{"niw", "[", - RowBox[{"[", - RowBox[{"i", ",", "w"}], "]"}], "]"}], ",", - RowBox[{"diw", "[", - RowBox[{"[", - RowBox[{"i", ",", "w"}], "]"}], "]"}]}], "}"}], "=", - RowBox[{"dniwcalc", "[", - RowBox[{"i", ",", "w"}], "]"}]}], ";"}], "*)"}], - "\[IndentingNewLine]", - RowBox[{ - RowBox[{ - RowBox[{ - RowBox[{"niw", "[", - RowBox[{"[", - RowBox[{"i", ",", "w"}], "]"}], "]"}], "=", - RowBox[{ - RowBox[{"dniwcalc", "[", - RowBox[{"i", ",", "w"}], "]"}], "[", - RowBox[{"[", "1", "]"}], "]"}]}], ";", "\[IndentingNewLine]", - RowBox[{ - RowBox[{"diw", "[", - RowBox[{"[", - RowBox[{"i", ",", "w"}], "]"}], "]"}], "=", - RowBox[{ - RowBox[{"dniwcalc", "[", - RowBox[{"i", ",", "w"}], "]"}], "[", - RowBox[{"[", "2", "]"}], "]"}]}], ";", "\[IndentingNewLine]", - RowBox[{ - RowBox[{"tiw", "[", - RowBox[{"[", - RowBox[{"i", ",", "w"}], "]"}], "]"}], "=", - RowBox[{"tiwcalc", "[", - RowBox[{"i", ",", "w"}], "]"}]}], ";", "\[IndentingNewLine]", - RowBox[{ - RowBox[{"fiw", "[", - RowBox[{"[", - RowBox[{"i", ",", "w"}], "]"}], "]"}], "=", - RowBox[{"fiwcalc", "[", - RowBox[{"i", ",", "w"}], "]"}]}]}], ",", "\[IndentingNewLine]", - RowBox[{"{", - RowBox[{"w", ",", "1", ",", "Nw"}], "}"}]}], "]"}], ",", - "\[IndentingNewLine]", - RowBox[{"{", - RowBox[{"i", ",", "1", ",", "Np"}], "}"}]}], "]"}], ";", - "\[IndentingNewLine]", - RowBox[{"(*", " ", - RowBox[{ - "calculate", " ", "changes", " ", "in", " ", "velocity", " ", "and", - " ", "position"}], " ", "*)"}], "\[IndentingNewLine]", - RowBox[{"Do", "[", "\[IndentingNewLine]", - RowBox[{ - RowBox[{ - RowBox[{ - RowBox[{"dvi", "[", - RowBox[{"[", "i", "]"}], "]"}], "=", - RowBox[{"dvicalc", "[", "i", "]"}]}], ";", - RowBox[{"(*", " ", - RowBox[{"change", " ", "in", " ", "velocity"}], " ", "*)"}], - "\[IndentingNewLine]", - RowBox[{ - RowBox[{"v", "[", - RowBox[{"[", "i", "]"}], "]"}], "=", - RowBox[{"vcalc", "[", "i", "]"}]}], ";", - RowBox[{"(*", " ", - RowBox[{"velocity", " ", "update"}], " ", "*)"}], - "\[IndentingNewLine]", - RowBox[{ - RowBox[{"v", "[", - RowBox[{"[", "i", "]"}], "]"}], "=", - RowBox[{"vcap", "[", "i", "]"}]}], ";", - RowBox[{"(*", " ", - RowBox[{"cap", " ", "speed", " ", - RowBox[{"(", - RowBox[{"just", " ", "in", " ", "case"}], ")"}]}], " ", "*)"}], - "\[IndentingNewLine]", - RowBox[{ - RowBox[{"r", "[", - RowBox[{"[", "i", "]"}], "]"}], "=", - RowBox[{"rcalc", "[", "i", "]"}]}]}], ",", - RowBox[{"(*", " ", - RowBox[{"position", " ", "update"}], " ", "*)"}], - "\[IndentingNewLine]", - RowBox[{"{", - RowBox[{"i", ",", "1", ",", "Np"}], "}"}]}], "]"}], ";"}]}], - "\[IndentingNewLine]", "]"}]}]}], "\n", - RowBox[{"(*", " ", - RowBox[{"generate", " ", "layout", " ", - RowBox[{"{", - RowBox[{ - RowBox[{"wall", " ", "lines"}], ",", " ", - RowBox[{"wall", " ", "graphics"}], ",", " ", - RowBox[{"bounding", " ", "box"}], ",", " ", "door"}], "}"}]}], " ", - "*)"}], "\[IndentingNewLine]", - RowBox[{ - RowBox[{"wallgen", "[", - RowBox[{"layout_", ",", "p1_", ",", "p2_"}], "]"}], ":=", - RowBox[{"Switch", "[", - RowBox[{"layout", ",", "\[IndentingNewLine]", "0", ",", - RowBox[{"(*", " ", - RowBox[{"single", " ", "door"}], " ", "*)"}], "\[IndentingNewLine]", - RowBox[{"{", - RowBox[{"(*", " ", "W", " ", "*)"}], - RowBox[{ - RowBox[{"{", - RowBox[{ - RowBox[{"{", - RowBox[{ - RowBox[{"{", - RowBox[{"10.0", ",", "20.0"}], "}"}], ",", - RowBox[{"{", - RowBox[{"10.0", ",", - RowBox[{"5.0", "+", - FractionBox["p1", "2"]}]}], "}"}]}], "}"}], ",", - RowBox[{"{", - RowBox[{ - RowBox[{"{", - RowBox[{"10.0", ",", - RowBox[{"5.0", "+", - FractionBox["p1", "2"]}]}], "}"}], ",", - RowBox[{"{", - RowBox[{"11.0", ",", - RowBox[{"5.0", "+", - FractionBox["p1", "2"]}]}], "}"}]}], "}"}], ",", - RowBox[{"{", - RowBox[{ - RowBox[{"{", - RowBox[{"11.0", ",", - RowBox[{"5.0", "+", - FractionBox["p1", "2"]}]}], "}"}], ",", - RowBox[{"{", - RowBox[{"11.0", ",", "20.0"}], "}"}]}], "}"}], ",", - RowBox[{"{", - RowBox[{ - RowBox[{"{", - RowBox[{"10.0", ",", - RowBox[{"-", "10.0"}]}], "}"}], ",", - RowBox[{"{", - RowBox[{"10.0", ",", - RowBox[{"5.0", "-", - FractionBox["p1", "2"]}]}], "}"}]}], "}"}], ",", - RowBox[{"{", - RowBox[{ - RowBox[{"{", - RowBox[{"10.0", ",", - RowBox[{"5.0", "-", - FractionBox["p1", "2"]}]}], "}"}], ",", - RowBox[{"{", - RowBox[{"11.0", ",", - RowBox[{"5.0", "-", - FractionBox["p1", "2"]}]}], "}"}]}], "}"}], ",", - RowBox[{"{", - RowBox[{ - RowBox[{"{", - RowBox[{"11.0", ",", - RowBox[{"5.0", "-", - FractionBox["p1", "2"]}]}], "}"}], ",", - RowBox[{"{", - RowBox[{"11.0", ",", - RowBox[{"-", "10.0"}]}], "}"}]}], "}"}]}], "}"}], ",", - "\[IndentingNewLine]", - RowBox[{"(*", " ", "Wg", " ", "*)"}], - RowBox[{"{", - RowBox[{ - RowBox[{"Polygon", "[", - RowBox[{"{", - RowBox[{ - RowBox[{"{", - RowBox[{"10.0", ",", "20.0"}], "}"}], ",", - RowBox[{"{", - RowBox[{"10.0", ",", - RowBox[{"5.0", "+", - FractionBox["p1", "2"]}]}], "}"}], ",", - RowBox[{"{", - RowBox[{"11.0", ",", - RowBox[{"5.0", "+", - FractionBox["p1", "2"]}]}], "}"}], ",", - RowBox[{"{", - RowBox[{"11.0", ",", "20.0"}], "}"}]}], "}"}], "]"}], ",", - RowBox[{"Polygon", "[", - RowBox[{"{", - RowBox[{ - RowBox[{"{", - RowBox[{"10.0", ",", - RowBox[{"-", "10.0"}]}], "}"}], ",", - RowBox[{"{", - RowBox[{"10.0", ",", - RowBox[{"5.0", "-", - FractionBox["p1", "2"]}]}], "}"}], ",", - RowBox[{"{", - RowBox[{"11.0", ",", - RowBox[{"5.0", "-", - FractionBox["p1", "2"]}]}], "}"}], ",", - RowBox[{"{", - RowBox[{"11.0", ",", - RowBox[{"-", "10.0"}]}], "}"}]}], "}"}], "]"}]}], "}"}], ",", - "\[IndentingNewLine]", - RowBox[{"(*", " ", "bb", " ", "*)"}], - RowBox[{"{", - RowBox[{ - RowBox[{"{", - RowBox[{"1.0", ",", "9.0"}], "}"}], ",", - RowBox[{"{", - RowBox[{"1.0", ",", "9.0"}], "}"}]}], "}"}], ",", - "\[IndentingNewLine]", - RowBox[{"(*", " ", "door", " ", "*)"}], - RowBox[{"{", - RowBox[{ - RowBox[{"{", - RowBox[{"10.0", ",", - RowBox[{"5.0", "+", - FractionBox["p1", "2"], "-", "0.5"}]}], "}"}], ",", - RowBox[{"{", - RowBox[{"10.0", ",", - RowBox[{"5.0", "-", - FractionBox["p1", "2"], "+", "0.5"}]}], "}"}]}], "}"}]}], "}"}], - ",", "\[IndentingNewLine]", "1", ",", - RowBox[{"(*", " ", - RowBox[{"column", " ", "and", " ", "door"}], " ", "*)"}], - "\[IndentingNewLine]", - RowBox[{"{", - RowBox[{"(*", " ", "W", " ", "*)"}], - RowBox[{ - RowBox[{"{", - RowBox[{ - RowBox[{"{", - RowBox[{ - RowBox[{"{", - RowBox[{"10.0", ",", "20.0"}], "}"}], ",", - RowBox[{"{", - RowBox[{"10.0", ",", - RowBox[{"5.0", "+", - FractionBox["p1", "2"]}]}], "}"}]}], "}"}], ",", - RowBox[{"{", - RowBox[{ - RowBox[{"{", - RowBox[{"10.0", ",", - RowBox[{"5.0", "+", - FractionBox["p1", "2"]}]}], "}"}], ",", - RowBox[{"{", - RowBox[{"11.0", ",", - RowBox[{"5.0", "+", - FractionBox["p1", "2"]}]}], "}"}]}], "}"}], ",", - RowBox[{"{", - RowBox[{ - RowBox[{"{", - RowBox[{"11.0", ",", - RowBox[{"5.0", "+", - FractionBox["p1", "2"]}]}], "}"}], ",", - RowBox[{"{", - RowBox[{"11.0", ",", "20.0"}], "}"}]}], "}"}], ",", - RowBox[{"{", - RowBox[{ - RowBox[{"{", - RowBox[{"10.0", ",", - RowBox[{"-", "10.0"}]}], "}"}], ",", - RowBox[{"{", - RowBox[{"10.0", ",", - RowBox[{"5.0", "-", - FractionBox["p1", "2"]}]}], "}"}]}], "}"}], ",", - RowBox[{"{", - RowBox[{ - RowBox[{"{", - RowBox[{"10.0", ",", - RowBox[{"5.0", "-", - FractionBox["p1", "2"]}]}], "}"}], ",", - RowBox[{"{", - RowBox[{"11.0", ",", - RowBox[{"5.0", "-", - FractionBox["p1", "2"]}]}], "}"}]}], "}"}], ",", - RowBox[{"{", - RowBox[{ - RowBox[{"{", - RowBox[{"11.0", ",", - RowBox[{"5.0", "-", - FractionBox["p1", "2"]}]}], "}"}], ",", - RowBox[{"{", - RowBox[{"11.0", ",", - RowBox[{"-", "10.0"}]}], "}"}]}], "}"}], ",", - RowBox[{"{", - RowBox[{ - RowBox[{"10.0", "-", "p2"}], ",", "5.5"}], "}"}]}], "}"}], ",", - "\[IndentingNewLine]", - RowBox[{"(*", " ", "Wg", " ", "*)"}], - RowBox[{"{", - RowBox[{ - RowBox[{"Polygon", "[", - RowBox[{"{", - RowBox[{ - RowBox[{"{", - RowBox[{"10.0", ",", "20.0"}], "}"}], ",", - RowBox[{"{", - RowBox[{"10.0", ",", - RowBox[{"5.0", "+", - FractionBox["p1", "2"]}]}], "}"}], ",", - RowBox[{"{", - RowBox[{"11.0", ",", - RowBox[{"5.0", "+", - FractionBox["p1", "2"]}]}], "}"}], ",", - RowBox[{"{", - RowBox[{"11.0", ",", "20.0"}], "}"}]}], "}"}], "]"}], ",", - RowBox[{"Polygon", "[", - RowBox[{"{", - RowBox[{ - RowBox[{"{", - RowBox[{"10.0", ",", - RowBox[{"-", "10.0"}]}], "}"}], ",", - RowBox[{"{", - RowBox[{"10.0", ",", - RowBox[{"5.0", "-", - FractionBox["p1", "2"]}]}], "}"}], ",", - RowBox[{"{", - RowBox[{"11.0", ",", - RowBox[{"5.0", "-", - FractionBox["p1", "2"]}]}], "}"}], ",", - RowBox[{"{", - RowBox[{"11.0", ",", - RowBox[{"-", "10.0"}]}], "}"}]}], "}"}], "]"}], ",", - RowBox[{"Disk", "[", - RowBox[{ - RowBox[{"{", - RowBox[{ - RowBox[{"10.0", "-", "p2"}], ",", "5.5"}], "}"}], ",", - "colrad"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", - RowBox[{"(*", " ", "bb", " ", "*)"}], - RowBox[{"{", - RowBox[{ - RowBox[{"{", - RowBox[{"1.0", ",", "9.0"}], "}"}], ",", - RowBox[{"{", - RowBox[{"1.0", ",", "9.0"}], "}"}]}], "}"}], ",", - "\[IndentingNewLine]", - RowBox[{"(*", " ", "door", " ", "*)"}], - RowBox[{"{", - RowBox[{ - RowBox[{"{", - RowBox[{"10.0", ",", - RowBox[{"5.0", "+", - FractionBox["p1", "2"], "-", "0.5"}]}], "}"}], ",", - RowBox[{"{", - RowBox[{"10.0", ",", - RowBox[{"5.0", "-", - FractionBox["p1", "2"], "+", "0.5"}]}], "}"}]}], "}"}]}], "}"}], - ",", "\[IndentingNewLine]", "2", ",", - RowBox[{"(*", " ", - RowBox[{"hallway", " ", "with", " ", "bulge"}], " ", "*)"}], - "\[IndentingNewLine]", - RowBox[{"{", - RowBox[{"(*", " ", "W", " ", "*)"}], - RowBox[{ - RowBox[{"{", - RowBox[{ - RowBox[{"{", - RowBox[{ - RowBox[{"{", - RowBox[{"0.0", ",", "6.5"}], "}"}], ",", - RowBox[{"{", - RowBox[{"7.0", ",", "6.5"}], "}"}]}], "}"}], ",", - RowBox[{"{", - RowBox[{ - RowBox[{"{", - RowBox[{"7.0", ",", "6.5"}], "}"}], ",", - RowBox[{"{", - RowBox[{"10.0", ",", - RowBox[{"6.5", "+", - RowBox[{"3.0", - RowBox[{"Tan", "[", "p1", "]"}]}]}]}], "}"}]}], "}"}], ",", - RowBox[{"{", - RowBox[{ - RowBox[{"{", - RowBox[{"10.0", ",", - RowBox[{"6.5", "+", - RowBox[{"3.0", - RowBox[{"Tan", "[", "p1", "]"}]}]}]}], "}"}], ",", - RowBox[{"{", - RowBox[{"13.0", ",", "6.5"}], "}"}]}], "}"}], ",", - RowBox[{"{", - RowBox[{ - RowBox[{"{", - RowBox[{"13.0", ",", "6.5"}], "}"}], ",", - RowBox[{"{", - RowBox[{"20.0", ",", "6.5"}], "}"}]}], "}"}], ",", - RowBox[{"{", - RowBox[{ - RowBox[{"{", - RowBox[{"0.0", ",", "3.5"}], "}"}], ",", - RowBox[{"{", - RowBox[{"7.0", ",", "3.5"}], "}"}]}], "}"}], ",", - RowBox[{"{", - RowBox[{ - RowBox[{"{", - RowBox[{"7.0", ",", "3.5"}], "}"}], ",", - RowBox[{"{", - RowBox[{"10.0", ",", - RowBox[{"3.5", "-", - RowBox[{"3.0", - RowBox[{"Tan", "[", "p1", "]"}]}]}]}], "}"}]}], "}"}], ",", - RowBox[{"{", - RowBox[{ - RowBox[{"{", - RowBox[{"10.0", ",", - RowBox[{"3.5", "-", - RowBox[{"3.0", - RowBox[{"Tan", "[", "p1", "]"}]}]}]}], "}"}], ",", - RowBox[{"{", - RowBox[{"13.0", ",", "3.5"}], "}"}]}], "}"}], ",", - RowBox[{"{", - RowBox[{ - RowBox[{"{", - RowBox[{"13.0", ",", "3.5"}], "}"}], ",", - RowBox[{"{", - RowBox[{"20.0", ",", "3.5"}], "}"}]}], "}"}]}], "}"}], ",", - "\[IndentingNewLine]", - RowBox[{"(*", " ", "Wg", " ", "*)"}], - RowBox[{"{", - RowBox[{ - RowBox[{"Polygon", "[", - RowBox[{"{", - RowBox[{ - RowBox[{"{", - RowBox[{"0.0", ",", "6.5"}], "}"}], ",", - RowBox[{"{", - RowBox[{"7.0", ",", "6.5"}], "}"}], ",", - RowBox[{"{", - RowBox[{"10.0", ",", - RowBox[{"6.5", "+", - RowBox[{"3.0", - RowBox[{"Tan", "[", "p1", "]"}]}]}]}], "}"}], ",", - RowBox[{"{", - RowBox[{"13.0", ",", "6.5"}], "}"}], ",", - RowBox[{"{", - RowBox[{"20.0", ",", "6.5"}], "}"}], ",", - RowBox[{"{", - RowBox[{"20.0", ",", "7.0"}], "}"}], ",", - RowBox[{"{", - RowBox[{ - RowBox[{"13.0", "+", - RowBox[{"0.5", - RowBox[{"Tan", "[", - RowBox[{"0.5", "p1"}], "]"}]}]}], ",", "7.0"}], "}"}], ",", - RowBox[{"{", - RowBox[{"10.0", ",", - RowBox[{"6.5", "+", - RowBox[{"0.5", - RowBox[{"Sec", "[", "p1", "]"}]}], "+", - RowBox[{"3.0", - RowBox[{"Tan", "[", "p1", "]"}]}]}]}], "}"}], ",", - RowBox[{"{", - RowBox[{ - RowBox[{"7.0", "-", - RowBox[{"0.5", - RowBox[{"Tan", "[", - RowBox[{"0.5", "p1"}], "]"}]}]}], ",", "7.0"}], "}"}], ",", - RowBox[{"{", - RowBox[{"0.0", ",", "7.0"}], "}"}]}], "}"}], "]"}], ",", - RowBox[{"Polygon", "[", - RowBox[{"{", - RowBox[{ - RowBox[{"{", - RowBox[{"0.0", ",", "3.5"}], "}"}], ",", - RowBox[{"{", - RowBox[{"7.0", ",", "3.5"}], "}"}], ",", - RowBox[{"{", - RowBox[{"10.0", ",", - RowBox[{"3.5", "-", - RowBox[{"3.0", - RowBox[{"Tan", "[", "p1", "]"}]}]}]}], "}"}], ",", - RowBox[{"{", - RowBox[{"13.0", ",", "3.5"}], "}"}], ",", - RowBox[{"{", - RowBox[{"20.0", ",", "3.5"}], "}"}], ",", - RowBox[{"{", - RowBox[{"20.0", ",", "3.0"}], "}"}], ",", - RowBox[{"{", - RowBox[{ - RowBox[{"13.0", "+", - RowBox[{"0.5", - RowBox[{"Tan", "[", - RowBox[{"0.5", "p1"}], "]"}]}]}], ",", "3.0"}], "}"}], ",", - RowBox[{"{", - RowBox[{"10.0", ",", - RowBox[{"3.5", "-", - RowBox[{"0.5", - RowBox[{"Sec", "[", "p1", "]"}]}], "-", - RowBox[{"3.0", - RowBox[{"Tan", "[", "p1", "]"}]}]}]}], "}"}], ",", - RowBox[{"{", - RowBox[{ - RowBox[{"7.0", "-", - RowBox[{"0.5", - RowBox[{"Tan", "[", - RowBox[{"0.5", "p1"}], "]"}]}]}], ",", "3.0"}], "}"}], ",", - RowBox[{"{", - RowBox[{"0.0", ",", "3.0"}], "}"}]}], "}"}], "]"}]}], "}"}], - ",", "\[IndentingNewLine]", - RowBox[{"(*", " ", "bb", " ", "*)"}], - RowBox[{"{", - RowBox[{ - RowBox[{"{", - RowBox[{"0.0", ",", "8.0"}], "}"}], ",", - RowBox[{"{", - RowBox[{"4.0", ",", "6.0"}], "}"}]}], "}"}], ",", - "\[IndentingNewLine]", - RowBox[{"(*", " ", "door", " ", "*)"}], - RowBox[{"{", - RowBox[{ - RowBox[{"{", - RowBox[{"15.0", ",", "6.0"}], "}"}], ",", - RowBox[{"{", - RowBox[{"15.0", ",", "4.0"}], "}"}]}], "}"}]}], "}"}]}], - "\[IndentingNewLine]", "]"}]}], "\n", - RowBox[{"(*", " ", - RowBox[{ - "generates", " ", "a", " ", "color", " ", "that", " ", "varies", " ", - "linearly", " ", "from", " ", "green", " ", - RowBox[{"(", - RowBox[{"at", " ", "input", " ", "0"}], ")"}], " ", "to", " ", "red", - " ", - RowBox[{"(", - RowBox[{ - "at", " ", "input", " ", "equal", " ", "to", " ", "max", " ", - "pressure"}], ")"}]}], " ", "*)"}], "\[IndentingNewLine]", - RowBox[{ - RowBox[{"colmap", "[", - RowBox[{"x_", ",", - RowBox[{"max_:", "1800"}]}], "]"}], ":=", - RowBox[{"RGBColor", "[", - RowBox[{ - RowBox[{"Min", "[", - RowBox[{ - FractionBox["x", "max"], ",", "1"}], "]"}], ",", - RowBox[{"0.8", - RowBox[{"(", - RowBox[{"1", "-", - RowBox[{"Min", "[", - RowBox[{ - FractionBox["x", "max"], ",", "1"}], "]"}]}], ")"}]}], ",", "0"}], - "]"}]}], "\n", - RowBox[{"(*", " ", - RowBox[{ - "generates", " ", "a", " ", "normalized", " ", "vector", " ", "and", " ", - "distance", " ", "for", " ", "a", " ", "given", " ", "layout", " ", - "pointing", " ", "from", " ", "a", " ", "specified", " ", "wall", " ", - "to", " ", "a", " ", "specified", " ", "coordinate"}], " ", "*)"}], - "\[IndentingNewLine]", - RowBox[{ - RowBox[{"wallnorm", "[", - RowBox[{"coord_", ",", "wall_"}], "]"}], ":=", - RowBox[{"Module", "[", - RowBox[{ - RowBox[{"{", - RowBox[{"pt", ",", - RowBox[{"far", "=", "1000"}]}], "}"}], ",", "\[IndentingNewLine]", - RowBox[{ - RowBox[{"Switch", "[", - RowBox[{"lo", ",", "\[IndentingNewLine]", "0", ",", - RowBox[{"(*", " ", - RowBox[{"single", " ", "door"}], " ", "*)"}], "\[IndentingNewLine]", - RowBox[{"Switch", "[", - RowBox[{"wall", ",", "\[IndentingNewLine]", "1", ",", - RowBox[{"(*", " ", - RowBox[{"top", " ", "wall"}], " ", "*)"}], "\[IndentingNewLine]", - RowBox[{"If", "[", - RowBox[{ - RowBox[{ - RowBox[{"coord", "[", - RowBox[{"[", "1", "]"}], "]"}], "<", - RowBox[{"W", "[", - RowBox[{"[", - RowBox[{"1", ",", "1", ",", "1"}], "]"}], "]"}]}], ",", - "\[IndentingNewLine]", - RowBox[{"(*", " ", - RowBox[{"left", " ", "of", " ", "wall"}], " ", "*)"}], - "\[IndentingNewLine]", - RowBox[{"If", "[", - RowBox[{ - RowBox[{ - RowBox[{"coord", "[", - RowBox[{"[", "2", "]"}], "]"}], "\[GreaterEqual]", - RowBox[{"W", "[", - RowBox[{"[", - RowBox[{"1", ",", "2", ",", "2"}], "]"}], "]"}]}], ",", - "\[IndentingNewLine]", - RowBox[{"(*", " ", - RowBox[{"next", " ", "to", " ", "long", " ", "side"}], " ", - "*)"}], "\[IndentingNewLine]", - RowBox[{"pt", "=", - RowBox[{"{", - RowBox[{ - RowBox[{"W", "[", - RowBox[{"[", - RowBox[{"1", ",", "1", ",", "1"}], "]"}], "]"}], ",", - RowBox[{"coord", "[", - RowBox[{"[", "2", "]"}], "]"}]}], "}"}]}], ",", - "\[IndentingNewLine]", - RowBox[{"(*", " ", - RowBox[{"near", " ", "corner"}], " ", "*)"}], - "\[IndentingNewLine]", - RowBox[{ - RowBox[{"pt", "=", - RowBox[{"W", "[", - RowBox[{"[", - RowBox[{"1", ",", "2"}], "]"}], "]"}]}], ";"}]}], - "\[IndentingNewLine]", "]"}], ",", "\[IndentingNewLine]", - RowBox[{"(*", " ", - RowBox[{"right", " ", "of", " ", "wall"}], " ", "*)"}], - "\[IndentingNewLine]", - RowBox[{ - RowBox[{"If", "[", - RowBox[{ - RowBox[{ - RowBox[{"coord", "[", - RowBox[{"[", "1", "]"}], "]"}], ">", - RowBox[{"W", "[", - RowBox[{"[", - RowBox[{"2", ",", "2", ",", "1"}], "]"}], "]"}]}], ",", - "\[IndentingNewLine]", - RowBox[{"(*", " ", - RowBox[{"too", " ", "far", " ", "to", " ", "right"}], " ", - "*)"}], "\[IndentingNewLine]", - RowBox[{"pt", "=", - RowBox[{"{", - RowBox[{"far", ",", "5.0"}], "}"}]}], ",", - "\[IndentingNewLine]", - RowBox[{"(*", " ", - RowBox[{"inside", " ", "doorway"}], " ", "*)"}], - "\[IndentingNewLine]", - RowBox[{ - RowBox[{"pt", "=", - RowBox[{"{", - RowBox[{ - RowBox[{"coord", "[", - RowBox[{"[", "1", "]"}], "]"}], ",", - RowBox[{"W", "[", - RowBox[{"[", - RowBox[{"1", ",", "2", ",", "2"}], "]"}], "]"}]}], - "}"}]}], ";"}]}], "\[IndentingNewLine]", "]"}], ";"}]}], - "\[IndentingNewLine]", "]"}], ",", "\[IndentingNewLine]", "2", - ",", - RowBox[{"(*", " ", - RowBox[{"bottom", " ", "wall"}], " ", "*)"}], - "\[IndentingNewLine]", - RowBox[{"If", "[", - RowBox[{ - RowBox[{ - RowBox[{"coord", "[", - RowBox[{"[", "1", "]"}], "]"}], "<", - RowBox[{"W", "[", - RowBox[{"[", - RowBox[{"1", ",", "1", ",", "1"}], "]"}], "]"}]}], ",", - "\[IndentingNewLine]", - RowBox[{"(*", " ", - RowBox[{"left", " ", "of", " ", "wall"}], " ", "*)"}], - "\[IndentingNewLine]", - RowBox[{"If", "[", - RowBox[{ - RowBox[{ - RowBox[{"coord", "[", - RowBox[{"[", "2", "]"}], "]"}], "\[LessEqual]", - RowBox[{"W", "[", - RowBox[{"[", - RowBox[{"4", ",", "2", ",", "2"}], "]"}], "]"}]}], ",", - "\[IndentingNewLine]", - RowBox[{"(*", " ", - RowBox[{"next", " ", "to", " ", "long", " ", "side"}], " ", - "*)"}], "\[IndentingNewLine]", - RowBox[{"pt", "=", - RowBox[{"{", - RowBox[{ - RowBox[{"W", "[", - RowBox[{"[", - RowBox[{"4", ",", "1", ",", "1"}], "]"}], "]"}], ",", - RowBox[{"coord", "[", - RowBox[{"[", "2", "]"}], "]"}]}], "}"}]}], ",", - "\[IndentingNewLine]", - RowBox[{"(*", " ", - RowBox[{"near", " ", "corner"}], " ", "*)"}], - "\[IndentingNewLine]", - RowBox[{ - RowBox[{"pt", "=", - RowBox[{"W", "[", - RowBox[{"[", - RowBox[{"4", ",", "2"}], "]"}], "]"}]}], ";"}]}], - "\[IndentingNewLine]", "]"}], ",", "\[IndentingNewLine]", - RowBox[{"(*", " ", - RowBox[{"right", " ", "of", " ", "wall"}], " ", "*)"}], - "\[IndentingNewLine]", - RowBox[{ - RowBox[{"If", "[", - RowBox[{ - RowBox[{ - RowBox[{"coord", "[", - RowBox[{"[", "1", "]"}], "]"}], ">", - RowBox[{"W", "[", - RowBox[{"[", - RowBox[{"5", ",", "2", ",", "1"}], "]"}], "]"}]}], ",", - "\[IndentingNewLine]", - RowBox[{"(*", " ", - RowBox[{"too", " ", "far", " ", "to", " ", "right"}], " ", - "*)"}], "\[IndentingNewLine]", - RowBox[{"pt", "=", - RowBox[{"{", - RowBox[{"far", ",", "5.0"}], "}"}]}], ",", - "\[IndentingNewLine]", - RowBox[{"(*", " ", - RowBox[{"inside", " ", "doorway"}], " ", "*)"}], - "\[IndentingNewLine]", - RowBox[{ - RowBox[{"pt", "=", - RowBox[{"{", - RowBox[{ - RowBox[{"coord", "[", - RowBox[{"[", "1", "]"}], "]"}], ",", - RowBox[{"W", "[", - RowBox[{"[", - RowBox[{"4", ",", "2", ",", "2"}], "]"}], "]"}]}], - "}"}]}], ";"}]}], "\[IndentingNewLine]", "]"}], ";"}]}], - "\[IndentingNewLine]", "]"}], ",", "\[IndentingNewLine]", "3", - ",", - RowBox[{"(*", " ", "nothing", " ", "*)"}], "\[IndentingNewLine]", - RowBox[{ - RowBox[{"pt", "=", - RowBox[{"{", - RowBox[{"far", ",", "5.0"}], "}"}]}], ";"}]}], - "\[IndentingNewLine]", "]"}], ",", "\[IndentingNewLine]", "1", ",", - RowBox[{"(*", " ", - RowBox[{"column", " ", "and", " ", "door"}], " ", "*)"}], - "\[IndentingNewLine]", - RowBox[{"Switch", "[", - RowBox[{"wall", ",", "\[IndentingNewLine]", "1", ",", - RowBox[{"(*", " ", - RowBox[{"top", " ", "wall"}], " ", "*)"}], "\[IndentingNewLine]", - RowBox[{"If", "[", - RowBox[{ - RowBox[{ - RowBox[{"coord", "[", - RowBox[{"[", "1", "]"}], "]"}], "<", - RowBox[{"W", "[", - RowBox[{"[", - RowBox[{"1", ",", "1", ",", "1"}], "]"}], "]"}]}], ",", - "\[IndentingNewLine]", - RowBox[{"(*", " ", - RowBox[{"left", " ", "of", " ", "wall"}], " ", "*)"}], - "\[IndentingNewLine]", - RowBox[{"If", "[", - RowBox[{ - RowBox[{ - RowBox[{"coord", "[", - RowBox[{"[", "2", "]"}], "]"}], "\[GreaterEqual]", - RowBox[{"W", "[", - RowBox[{"[", - RowBox[{"1", ",", "2", ",", "2"}], "]"}], "]"}]}], ",", - "\[IndentingNewLine]", - RowBox[{"(*", " ", - RowBox[{"next", " ", "to", " ", "long", " ", "side"}], " ", - "*)"}], "\[IndentingNewLine]", - RowBox[{"pt", "=", - RowBox[{"{", - RowBox[{ - RowBox[{"W", "[", - RowBox[{"[", - RowBox[{"1", ",", "1", ",", "1"}], "]"}], "]"}], ",", - RowBox[{"coord", "[", - RowBox[{"[", "2", "]"}], "]"}]}], "}"}]}], ",", - "\[IndentingNewLine]", - RowBox[{"(*", " ", - RowBox[{"near", " ", "corner"}], " ", "*)"}], - "\[IndentingNewLine]", - RowBox[{ - RowBox[{"pt", "=", - RowBox[{"W", "[", - RowBox[{"[", - RowBox[{"1", ",", "2"}], "]"}], "]"}]}], ";"}]}], - "\[IndentingNewLine]", "]"}], ",", "\[IndentingNewLine]", - RowBox[{"(*", " ", - RowBox[{"right", " ", "of", " ", "wall"}], " ", "*)"}], - "\[IndentingNewLine]", - RowBox[{ - RowBox[{"If", "[", - RowBox[{ - RowBox[{ - RowBox[{"coord", "[", - RowBox[{"[", "1", "]"}], "]"}], ">", - RowBox[{"W", "[", - RowBox[{"[", - RowBox[{"2", ",", "2", ",", "1"}], "]"}], "]"}]}], ",", - "\[IndentingNewLine]", - RowBox[{"(*", " ", - RowBox[{"too", " ", "far", " ", "to", " ", "right"}], " ", - "*)"}], "\[IndentingNewLine]", - RowBox[{"pt", "=", - RowBox[{"{", - RowBox[{"far", ",", "5.0"}], "}"}]}], ",", - "\[IndentingNewLine]", - RowBox[{"(*", " ", - RowBox[{"inside", " ", "doorway"}], " ", "*)"}], - "\[IndentingNewLine]", - RowBox[{ - RowBox[{"pt", "=", - RowBox[{"{", - RowBox[{ - RowBox[{"coord", "[", - RowBox[{"[", "1", "]"}], "]"}], ",", - RowBox[{"W", "[", - RowBox[{"[", - RowBox[{"1", ",", "2", ",", "2"}], "]"}], "]"}]}], - "}"}]}], ";"}]}], "\[IndentingNewLine]", "]"}], ";"}]}], - "\[IndentingNewLine]", "]"}], ",", "\[IndentingNewLine]", "2", - ",", - RowBox[{"(*", " ", - RowBox[{"bottom", " ", "wall"}], " ", "*)"}], - "\[IndentingNewLine]", - RowBox[{"If", "[", - RowBox[{ - RowBox[{ - RowBox[{"coord", "[", - RowBox[{"[", "1", "]"}], "]"}], "<", - RowBox[{"W", "[", - RowBox[{"[", - RowBox[{"1", ",", "1", ",", "1"}], "]"}], "]"}]}], ",", - "\[IndentingNewLine]", - RowBox[{"(*", " ", - RowBox[{"left", " ", "of", " ", "wall"}], " ", "*)"}], - "\[IndentingNewLine]", - RowBox[{"If", "[", - RowBox[{ - RowBox[{ - RowBox[{"coord", "[", - RowBox[{"[", "2", "]"}], "]"}], "\[LessEqual]", - RowBox[{"W", "[", - RowBox[{"[", - RowBox[{"4", ",", "2", ",", "2"}], "]"}], "]"}]}], ",", - "\[IndentingNewLine]", - RowBox[{"(*", " ", - RowBox[{"next", " ", "to", " ", "long", " ", "side"}], " ", - "*)"}], "\[IndentingNewLine]", - RowBox[{"pt", "=", - RowBox[{"{", - RowBox[{ - RowBox[{"W", "[", - RowBox[{"[", - RowBox[{"4", ",", "1", ",", "1"}], "]"}], "]"}], ",", - RowBox[{"coord", "[", - RowBox[{"[", "2", "]"}], "]"}]}], "}"}]}], ",", - "\[IndentingNewLine]", - RowBox[{"(*", " ", - RowBox[{"near", " ", "corner"}], " ", "*)"}], - "\[IndentingNewLine]", - RowBox[{ - RowBox[{"pt", "=", - RowBox[{"W", "[", - RowBox[{"[", - RowBox[{"4", ",", "2"}], "]"}], "]"}]}], ";"}]}], - "\[IndentingNewLine]", "]"}], ",", "\[IndentingNewLine]", - RowBox[{"(*", " ", - RowBox[{"right", " ", "of", " ", "wall"}], " ", "*)"}], - "\[IndentingNewLine]", - RowBox[{ - RowBox[{"If", "[", - RowBox[{ - RowBox[{ - RowBox[{"coord", "[", - RowBox[{"[", "1", "]"}], "]"}], ">", - RowBox[{"W", "[", - RowBox[{"[", - RowBox[{"5", ",", "2", ",", "1"}], "]"}], "]"}]}], ",", - "\[IndentingNewLine]", - RowBox[{"(*", " ", - RowBox[{"too", " ", "far", " ", "to", " ", "right"}], " ", - "*)"}], "\[IndentingNewLine]", - RowBox[{"pt", "=", - RowBox[{"{", - RowBox[{"far", ",", "5.0"}], "}"}]}], ",", - "\[IndentingNewLine]", - RowBox[{"(*", " ", - RowBox[{"inside", " ", "doorway"}], " ", "*)"}], - "\[IndentingNewLine]", - RowBox[{ - RowBox[{"pt", "=", - RowBox[{"{", - RowBox[{ - RowBox[{"coord", "[", - RowBox[{"[", "1", "]"}], "]"}], ",", - RowBox[{"W", "[", - RowBox[{"[", - RowBox[{"4", ",", "2", ",", "2"}], "]"}], "]"}]}], - "}"}]}], ";"}]}], "\[IndentingNewLine]", "]"}], ";"}]}], - "\[IndentingNewLine]", "]"}], ",", "\[IndentingNewLine]", "3", - ",", - RowBox[{"(*", " ", "column", " ", "*)"}], "\[IndentingNewLine]", - RowBox[{ - RowBox[{"If", "[", - RowBox[{ - RowBox[{ - RowBox[{"coord", "[", - RowBox[{"[", "1", "]"}], "]"}], ">", - RowBox[{"W", "[", - RowBox[{"[", - RowBox[{"5", ",", "2", ",", "1"}], "]"}], "]"}]}], ",", - "\[IndentingNewLine]", - RowBox[{"(*", " ", - RowBox[{"too", " ", "far", " ", "to", " ", "right"}], " ", - "*)"}], "\[IndentingNewLine]", - RowBox[{"pt", "=", - RowBox[{"{", - RowBox[{"far", ",", "5.0"}], "}"}]}], ",", - "\[IndentingNewLine]", - RowBox[{"(*", " ", - RowBox[{"closest", " ", "point", " ", "on", " ", "column"}], - " ", "*)"}], "\[IndentingNewLine]", - RowBox[{ - RowBox[{"pt", "=", - RowBox[{ - RowBox[{"W", "[", - RowBox[{"[", "7", "]"}], "]"}], "+", - RowBox[{"colrad", - RowBox[{"(", - FractionBox[ - RowBox[{"coord", "-", - RowBox[{"W", "[", - RowBox[{"[", "7", "]"}], "]"}]}], - RowBox[{"Norm", "[", - RowBox[{"coord", "-", - RowBox[{"W", "[", - RowBox[{"[", "7", "]"}], "]"}]}], "]"}]], ")"}]}]}]}], - ";"}]}], "\[IndentingNewLine]", "]"}], ";"}]}], - "\[IndentingNewLine]", "]"}], ",", "\[IndentingNewLine]", "2", ",", - RowBox[{"(*", " ", - RowBox[{"hallway", " ", "with", " ", "bulge"}], " ", "*)"}], - "\[IndentingNewLine]", - RowBox[{ - RowBox[{"Switch", "[", - RowBox[{"wall", ",", "\[IndentingNewLine]", "1", ",", - RowBox[{"(*", " ", - RowBox[{"top", " ", "wall"}], " ", "*)"}], "\[IndentingNewLine]", - RowBox[{"If", "[", - RowBox[{ - RowBox[{"par1", "\[Equal]", "0"}], ",", "\[IndentingNewLine]", - RowBox[{"(*", " ", - RowBox[{"straight", " ", "hallway"}], " ", "*)"}], - "\[IndentingNewLine]", - RowBox[{"pt", "=", - RowBox[{"{", - RowBox[{ - RowBox[{"coord", "[", - RowBox[{"[", "1", "]"}], "]"}], ",", "6.5"}], "}"}]}], ",", - "\[IndentingNewLine]", - RowBox[{"(*", " ", - RowBox[{"angled", " ", "hallway"}], " ", "*)"}], - "\[IndentingNewLine]", - RowBox[{ - RowBox[{"If", "[", - RowBox[{ - RowBox[{ - RowBox[{ - RowBox[{"coord", "[", - RowBox[{"[", "1", "]"}], "]"}], "\[LessEqual]", "7.0"}], "||", - RowBox[{ - RowBox[{"coord", "[", - RowBox[{"[", "1", "]"}], "]"}], "\[GreaterEqual]", - "13.0"}]}], ",", "\[IndentingNewLine]", - RowBox[{"(*", " ", - RowBox[{"straight", " ", "section"}], " ", "*)"}], - "\[IndentingNewLine]", - RowBox[{"pt", "=", - RowBox[{"{", - RowBox[{ - RowBox[{"coord", "[", - RowBox[{"[", "1", "]"}], "]"}], ",", "6.5"}], "}"}]}], - ",", "\[IndentingNewLine]", - RowBox[{"(*", " ", "middle", " ", "*)"}], - "\[IndentingNewLine]", - RowBox[{ - RowBox[{"If", "[", - RowBox[{ - RowBox[{ - RowBox[{"coord", "[", - RowBox[{"[", "1", "]"}], "]"}], "<", "10.0"}], ",", - "\[IndentingNewLine]", - RowBox[{"(*", " ", - RowBox[{"left", " ", "half"}], " ", "*)"}], - "\[IndentingNewLine]", - RowBox[{"If", "[", - RowBox[{ - RowBox[{ - RowBox[{"coord", "[", - RowBox[{"[", "2", "]"}], "]"}], ">", - RowBox[{ - RowBox[{ - RowBox[{"-", - RowBox[{"Cot", "[", "par1", "]"}]}], - RowBox[{"coord", "[", - RowBox[{"[", "1", "]"}], "]"}]}], "+", "6.5", "+", - RowBox[{"7", - RowBox[{"Cot", "[", "par1", "]"}]}]}]}], ",", - "\[IndentingNewLine]", - RowBox[{"(*", " ", - RowBox[{"left", " ", "angled", " ", "wall"}], " ", "*)"}], - "\[IndentingNewLine]", - RowBox[{"pt", "=", - RowBox[{"{", - RowBox[{ - FractionBox[ - RowBox[{"7", "+", - RowBox[{ - RowBox[{"(", - RowBox[{ - RowBox[{"coord", "[", - RowBox[{"[", "2", "]"}], "]"}], "-", "6.5"}], ")"}], - RowBox[{"Cot", "[", "par1", "]"}]}], "+", - RowBox[{ - RowBox[{"coord", "[", - RowBox[{"[", "1", "]"}], "]"}], - SuperscriptBox[ - RowBox[{"Cot", "[", "par1", "]"}], "2"]}]}], - RowBox[{"1", "+", - SuperscriptBox[ - RowBox[{"Cot", "[", "par1", "]"}], "2"]}]], ",", - FractionBox[ - RowBox[{"6.5", "+", - RowBox[{ - RowBox[{"(", - RowBox[{ - RowBox[{"coord", "[", - RowBox[{"[", "1", "]"}], "]"}], "-", "7"}], ")"}], - RowBox[{"Tan", "[", "par1", "]"}]}], "+", - RowBox[{ - RowBox[{"coord", "[", - RowBox[{"[", "2", "]"}], "]"}], - SuperscriptBox[ - RowBox[{"Tan", "[", "par1", "]"}], "2"]}]}], - RowBox[{"1", "+", - SuperscriptBox[ - RowBox[{"Tan", "[", "par1", "]"}], "2"]}]]}], "}"}]}], - ",", "\[IndentingNewLine]", - RowBox[{"(*", " ", "corner", " ", "*)"}], - "\[IndentingNewLine]", - RowBox[{ - RowBox[{"pt", "=", - RowBox[{"{", - RowBox[{"7.0", ",", "6.5"}], "}"}]}], ";"}]}], - "\[IndentingNewLine]", "]"}], ",", "\[IndentingNewLine]", - RowBox[{"(*", " ", - RowBox[{"right", " ", "half"}], " ", "*)"}], - "\[IndentingNewLine]", - RowBox[{ - RowBox[{"If", "[", - RowBox[{ - RowBox[{ - RowBox[{"coord", "[", - RowBox[{"[", "2", "]"}], "]"}], ">", - RowBox[{ - RowBox[{ - RowBox[{"Cot", "[", "par1", "]"}], - RowBox[{"coord", "[", - RowBox[{"[", "1", "]"}], "]"}]}], "+", "6.5", "-", - RowBox[{"13", - RowBox[{"Cot", "[", "par1", "]"}]}]}]}], ",", - "\[IndentingNewLine]", - RowBox[{"(*", " ", - RowBox[{"right", " ", "angled", " ", "wall"}], " ", - "*)"}], "\[IndentingNewLine]", - RowBox[{"pt", "=", - RowBox[{"{", - RowBox[{ - FractionBox[ - RowBox[{"13", "\[VeryThinSpace]", "+", - RowBox[{ - RowBox[{"(", - RowBox[{"6.5", "-", - RowBox[{"coord", "[", - RowBox[{"[", "2", "]"}], "]"}]}], ")"}], " ", - RowBox[{"Cot", "[", "par1", "]"}]}], "+", - RowBox[{ - RowBox[{"coord", "[", - RowBox[{"[", "1", "]"}], "]"}], " ", - SuperscriptBox[ - RowBox[{"Cot", "[", "par1", "]"}], "2"]}]}], - RowBox[{"1", "+", " ", - SuperscriptBox[ - RowBox[{"Cot", "[", "par1", "]"}], "2"]}]], ",", - FractionBox[ - RowBox[{"6.5", "+", - RowBox[{ - RowBox[{"(", - RowBox[{"13", "-", - RowBox[{"coord", "[", - RowBox[{"[", "1", "]"}], "]"}]}], ")"}], " ", - RowBox[{"Tan", "[", "par1", "]"}]}], "+", - RowBox[{ - RowBox[{"coord", "[", - RowBox[{"[", "2", "]"}], "]"}], " ", - SuperscriptBox[ - RowBox[{"Tan", "[", "par1", "]"}], "2"]}]}], - RowBox[{"1", "+", - SuperscriptBox[ - RowBox[{"Tan", "[", "par1", "]"}], "2"]}]]}], "}"}]}], - ",", "\[IndentingNewLine]", - RowBox[{"(*", " ", "corner", " ", "*)"}], - "\[IndentingNewLine]", - RowBox[{ - RowBox[{"pt", "=", - RowBox[{"{", - RowBox[{"13.0", ",", "6.5"}], "}"}]}], ";"}]}], - "\[IndentingNewLine]", "]"}], ";"}]}], - "\[IndentingNewLine]", "]"}], ";"}]}], - "\[IndentingNewLine]", "]"}], ";"}]}], "\[IndentingNewLine]", - "]"}], ",", "\[IndentingNewLine]", "2", ",", - RowBox[{"(*", " ", - RowBox[{"bottom", " ", "wall"}], " ", "*)"}], - "\[IndentingNewLine]", - RowBox[{"If", "[", - RowBox[{ - RowBox[{"par1", "\[Equal]", "0"}], ",", "\[IndentingNewLine]", - RowBox[{"(*", " ", - RowBox[{"straight", " ", "hallway"}], " ", "*)"}], - "\[IndentingNewLine]", - RowBox[{"pt", "=", - RowBox[{"{", - RowBox[{ - RowBox[{"coord", "[", - RowBox[{"[", "1", "]"}], "]"}], ",", "3.5"}], "}"}]}], ",", - "\[IndentingNewLine]", - RowBox[{"(*", " ", - RowBox[{"angled", " ", "hallway"}], " ", "*)"}], - "\[IndentingNewLine]", - RowBox[{ - RowBox[{"If", "[", - RowBox[{ - RowBox[{ - RowBox[{ - RowBox[{"coord", "[", - RowBox[{"[", "1", "]"}], "]"}], "\[LessEqual]", "7.0"}], "||", - RowBox[{ - RowBox[{"coord", "[", - RowBox[{"[", "1", "]"}], "]"}], "\[GreaterEqual]", - "13.0"}]}], ",", "\[IndentingNewLine]", - RowBox[{"(*", " ", - RowBox[{"straight", " ", "section"}], " ", "*)"}], - "\[IndentingNewLine]", - RowBox[{"pt", "=", - RowBox[{"{", - RowBox[{ - RowBox[{"coord", "[", - RowBox[{"[", "1", "]"}], "]"}], ",", "3.5"}], "}"}]}], - ",", "\[IndentingNewLine]", - RowBox[{"(*", " ", "middle", " ", "*)"}], - "\[IndentingNewLine]", - RowBox[{ - RowBox[{"If", "[", - RowBox[{ - RowBox[{ - RowBox[{"coord", "[", - RowBox[{"[", "1", "]"}], "]"}], "<", "10.0"}], ",", - "\[IndentingNewLine]", - RowBox[{"(*", " ", - RowBox[{"left", " ", "half"}], " ", "*)"}], - "\[IndentingNewLine]", - RowBox[{"If", "[", - RowBox[{ - RowBox[{ - RowBox[{"coord", "[", - RowBox[{"[", "2", "]"}], "]"}], "<", - RowBox[{ - RowBox[{ - RowBox[{"Cot", "[", "par1", "]"}], - RowBox[{"coord", "[", - RowBox[{"[", "1", "]"}], "]"}]}], "+", "3.5", "-", - RowBox[{"7", - RowBox[{"Cot", "[", "par1", "]"}]}]}]}], ",", - "\[IndentingNewLine]", - RowBox[{"(*", " ", - RowBox[{"left", " ", "angled", " ", "wall"}], " ", "*)"}], - "\[IndentingNewLine]", - RowBox[{"pt", "=", - RowBox[{"{", - RowBox[{ - FractionBox[ - RowBox[{"7", "+", - RowBox[{ - RowBox[{"(", - RowBox[{"3.5", "-", - RowBox[{"coord", "[", - RowBox[{"[", "2", "]"}], "]"}]}], ")"}], - RowBox[{"Cot", "[", "par1", "]"}]}], "+", - RowBox[{ - RowBox[{"coord", "[", - RowBox[{"[", "1", "]"}], "]"}], - SuperscriptBox[ - RowBox[{"Cot", "[", "par1", "]"}], "2"]}]}], - RowBox[{"1", "+", - SuperscriptBox[ - RowBox[{"Cot", "[", "par1", "]"}], "2"]}]], ",", - FractionBox[ - RowBox[{"3.5", "+", - RowBox[{ - RowBox[{"(", - RowBox[{"7", "-", - RowBox[{"coord", "[", - RowBox[{"[", "1", "]"}], "]"}]}], ")"}], - RowBox[{"Tan", "[", "par1", "]"}]}], "+", - RowBox[{ - RowBox[{"coord", "[", - RowBox[{"[", "2", "]"}], "]"}], - SuperscriptBox[ - RowBox[{"Tan", "[", "par1", "]"}], "2"]}]}], - RowBox[{"1", "+", - SuperscriptBox[ - RowBox[{"Tan", "[", "par1", "]"}], "2"]}]]}], "}"}]}], - ",", "\[IndentingNewLine]", - RowBox[{"(*", " ", "corner", " ", "*)"}], - "\[IndentingNewLine]", - RowBox[{ - RowBox[{"pt", "=", - RowBox[{"{", - RowBox[{"7.0", ",", "3.5"}], "}"}]}], ";"}]}], - "\[IndentingNewLine]", "]"}], ",", "\[IndentingNewLine]", - RowBox[{"(*", " ", - RowBox[{"right", " ", "half"}], " ", "*)"}], - "\[IndentingNewLine]", - RowBox[{ - RowBox[{"If", "[", - RowBox[{ - RowBox[{ - RowBox[{"coord", "[", - RowBox[{"[", "2", "]"}], "]"}], "<", - RowBox[{ - RowBox[{ - RowBox[{"-", - RowBox[{"Cot", "[", "par1", "]"}]}], - RowBox[{"coord", "[", - RowBox[{"[", "1", "]"}], "]"}]}], "+", "3.5", "+", - RowBox[{"13", - RowBox[{"Cot", "[", "par1", "]"}]}]}]}], ",", - "\[IndentingNewLine]", - RowBox[{"(*", " ", - RowBox[{"right", " ", "angled", " ", "wall"}], " ", - "*)"}], "\[IndentingNewLine]", - RowBox[{"pt", "=", - RowBox[{"{", - RowBox[{ - FractionBox[ - RowBox[{"13", "\[VeryThinSpace]", "+", - RowBox[{ - RowBox[{"(", - RowBox[{ - RowBox[{"coord", "[", - RowBox[{"[", "2", "]"}], "]"}], "-", "3.5"}], ")"}], " ", - RowBox[{"Cot", "[", "par1", "]"}]}], "+", - RowBox[{ - RowBox[{"coord", "[", - RowBox[{"[", "1", "]"}], "]"}], " ", - SuperscriptBox[ - RowBox[{"Cot", "[", "par1", "]"}], "2"]}]}], - RowBox[{"1", "+", " ", - SuperscriptBox[ - RowBox[{"Cot", "[", "par1", "]"}], "2"]}]], ",", - FractionBox[ - RowBox[{"3.5", "+", - RowBox[{ - RowBox[{"(", - RowBox[{ - RowBox[{"coord", "[", - RowBox[{"[", "1", "]"}], "]"}], "-", "13"}], ")"}], " ", - RowBox[{"Tan", "[", "par1", "]"}]}], "+", - RowBox[{ - RowBox[{"coord", "[", - RowBox[{"[", "2", "]"}], "]"}], " ", - SuperscriptBox[ - RowBox[{"Tan", "[", "par1", "]"}], "2"]}]}], - RowBox[{"1", "+", - SuperscriptBox[ - RowBox[{"Tan", "[", "par1", "]"}], "2"]}]]}], "}"}]}], - ",", "\[IndentingNewLine]", - RowBox[{"(*", " ", "corner", " ", "*)"}], - "\[IndentingNewLine]", - RowBox[{ - RowBox[{"pt", "=", - RowBox[{"{", - RowBox[{"13.0", ",", "3.5"}], "}"}]}], ";"}]}], - "\[IndentingNewLine]", "]"}], ";"}]}], - "\[IndentingNewLine]", "]"}], ";"}]}], - "\[IndentingNewLine]", "]"}], ";"}]}], "\[IndentingNewLine]", - "]"}], ",", "\[IndentingNewLine]", "3", ",", - RowBox[{"(*", " ", "nothing", " ", "*)"}], "\[IndentingNewLine]", - RowBox[{ - RowBox[{"pt", "=", - RowBox[{"{", - RowBox[{"far", ",", "5.0"}], "}"}]}], ";"}]}], - "\[IndentingNewLine]", "]"}], ";"}]}], "\[IndentingNewLine]", - "]"}], ";", "\[IndentingNewLine]", - RowBox[{"If", "[", - RowBox[{ - RowBox[{ - RowBox[{"lo", "\[Equal]", "1"}], "&&", - RowBox[{"wall", "\[Equal]", "3"}]}], ",", "\[IndentingNewLine]", - RowBox[{"{", - RowBox[{ - FractionBox[ - RowBox[{"coord", "-", "pt"}], - RowBox[{"Norm", "[", - RowBox[{"coord", "-", "pt"}], "]"}]], ",", - RowBox[{"If", "[", - RowBox[{ - RowBox[{ - RowBox[{"EuclideanDistance", "[", - RowBox[{"coord", ",", - RowBox[{"W", "[", - RowBox[{"[", "7", "]"}], "]"}]}], "]"}], "\[LessEqual]", - "colrad"}], ",", "0", ",", - RowBox[{"Norm", "[", - RowBox[{"coord", "-", "pt"}], "]"}]}], "]"}]}], "}"}], ",", - "\[IndentingNewLine]", - RowBox[{"{", - RowBox[{ - FractionBox[ - RowBox[{"coord", "-", "pt"}], - RowBox[{"Norm", "[", - RowBox[{"coord", "-", "pt"}], "]"}]], ",", - RowBox[{"Norm", "[", - RowBox[{"coord", "-", "pt"}], "]"}]}], "}"}]}], - "\[IndentingNewLine]", "]"}]}]}], "\[IndentingNewLine]", "]"}]}], - "\[IndentingNewLine]", - RowBox[{"(*", - RowBox[{"Manipulate", "[", - RowBox[{ - RowBox[{"Show", "[", - RowBox[{ - RowBox[{"Graphics", "[", "Wg", "]"}], ",", - RowBox[{"Graphics", "[", - RowBox[{"{", - RowBox[{"Text", "[", - RowBox[{ - RowBox[{"wallnorm", "[", - RowBox[{"pt", ",", "w"}], "]"}], ",", - RowBox[{"{", - RowBox[{"15", ",", "9"}], "}"}]}], "]"}], "}"}], "]"}], ",", - RowBox[{"Graphics", "[", - RowBox[{"{", - RowBox[{"Red", ",", - RowBox[{"Arrow", "[", - RowBox[{"{", - RowBox[{"pt", ",", - RowBox[{"pt", "+", - RowBox[{"2", - RowBox[{ - RowBox[{"wallnorm", "[", - RowBox[{"pt", ",", "w"}], "]"}], "[", - RowBox[{"[", "1", "]"}], "]"}]}]}]}], "}"}], "]"}]}], "}"}], - "]"}], ",", - RowBox[{"PlotRange", "\[Rule]", - RowBox[{"{", - RowBox[{ - RowBox[{"{", - RowBox[{"0", ",", "20"}], "}"}], ",", - RowBox[{"{", - RowBox[{"0", ",", "10"}], "}"}]}], "}"}]}]}], "]"}], ",", - RowBox[{"{", - RowBox[{ - RowBox[{"{", - RowBox[{"pt", ",", - RowBox[{"{", - RowBox[{"4.0", ",", "6.0"}], "}"}]}], "}"}], ",", "Locator"}], - "}"}], ",", - RowBox[{"{", - RowBox[{ - RowBox[{"{", - RowBox[{"w", ",", "1"}], "}"}], ",", - RowBox[{"{", - RowBox[{"1", ",", "2", ",", "3"}], "}"}]}], "}"}]}], "]"}], "*)"}], - "\n", - RowBox[{"(*", " ", "restart", " ", "*)"}], "\n", - RowBox[{ - RowBox[{"restart", "[", - RowBox[{ - RowBox[{"layout_:", "0"}], ",", - RowBox[{"np_:", "Np"}], ",", - RowBox[{"p1_:", "par1"}], ",", - RowBox[{"p2_:", "par2"}]}], "]"}], ":=", - RowBox[{"Module", "[", - RowBox[{ - RowBox[{"{", "}"}], ",", "\[IndentingNewLine]", - RowBox[{ - RowBox[{ - RowBox[{"{", - RowBox[{"W", ",", "Wg", ",", "bb", ",", "door"}], "}"}], "=", - RowBox[{"wallgen", "[", - RowBox[{"layout", ",", "p1", ",", "p2"}], "]"}]}], ";", - "\[IndentingNewLine]", - RowBox[{"Np", "=", "np"}], ";", "\[IndentingNewLine]", - RowBox[{"par1", "=", "p1"}], ";", "\[IndentingNewLine]", - RowBox[{"par2", "=", "p2"}], ";", "\[IndentingNewLine]", - RowBox[{"rad", "=", - RowBox[{"RandomReal", "[", - RowBox[{ - RowBox[{"{", - RowBox[{"radmin", ",", "radmax"}], "}"}], ",", "np"}], "]"}]}], - ";", "\[IndentingNewLine]", - RowBox[{"radsum", "=", - RowBox[{"ConstantArray", "[", - RowBox[{"0", ",", - RowBox[{"{", - RowBox[{"np", ",", "np"}], "}"}]}], "]"}]}], ";", - "\[IndentingNewLine]", - RowBox[{"Do", "[", "\[IndentingNewLine]", - RowBox[{ - RowBox[{"Do", "[", "\[IndentingNewLine]", - RowBox[{ - RowBox[{ - RowBox[{"radsum", "[", - RowBox[{"[", - RowBox[{"i", ",", "j"}], "]"}], "]"}], "=", - RowBox[{ - RowBox[{"radsum", "[", - RowBox[{"[", - RowBox[{"j", ",", "i"}], "]"}], "]"}], "=", - RowBox[{ - RowBox[{"rad", "[", - RowBox[{"[", "i", "]"}], "]"}], "+", - RowBox[{"rad", "[", - RowBox[{"[", "j", "]"}], "]"}]}]}]}], ",", - "\[IndentingNewLine]", - RowBox[{"{", - RowBox[{"j", ",", "1", ",", "i"}], "}"}]}], "]"}], ",", - "\[IndentingNewLine]", - RowBox[{"{", - RowBox[{"i", ",", "1", ",", "np"}], "}"}]}], "]"}], ";", - "\[IndentingNewLine]", - RowBox[{"r", "=", - RowBox[{"Transpose", "[", - RowBox[{"{", - RowBox[{ - RowBox[{"RandomReal", "[", - RowBox[{ - RowBox[{"bb", "[", - RowBox[{"[", "1", "]"}], "]"}], ",", "Np"}], "]"}], ",", - RowBox[{"RandomReal", "[", - RowBox[{ - RowBox[{"bb", "[", - RowBox[{"[", "2", "]"}], "]"}], ",", "Np"}], "]"}]}], "}"}], - "]"}]}], ";", "\[IndentingNewLine]", - RowBox[{"If", "[", - RowBox[{ - RowBox[{"layout", "\[Equal]", "1"}], ",", "\[IndentingNewLine]", - RowBox[{"(*", " ", - RowBox[{ - "check", " ", "for", " ", "collisions", " ", "with", " ", - "column"}], " ", "*)"}], "\[IndentingNewLine]", - RowBox[{ - RowBox[{"Do", "[", "\[IndentingNewLine]", - RowBox[{ - RowBox[{"While", "[", - RowBox[{ - RowBox[{ - RowBox[{"EuclideanDistance", "[", - RowBox[{ - RowBox[{"r", "[", - RowBox[{"[", "i", "]"}], "]"}], ",", - RowBox[{"W", "[", - RowBox[{"[", - RowBox[{"-", "1"}], "]"}], "]"}]}], "]"}], "<", "colrad"}], - ",", "\[IndentingNewLine]", - RowBox[{ - RowBox[{ - RowBox[{"r", "[", - RowBox[{"[", "i", "]"}], "]"}], "=", - RowBox[{"{", - RowBox[{ - RowBox[{"RandomReal", "[", - RowBox[{"bb", "[", - RowBox[{"[", "1", "]"}], "]"}], "]"}], ",", - RowBox[{"RandomReal", "[", - RowBox[{"bb", "[", - RowBox[{"[", "2", "]"}], "]"}], "]"}]}], "}"}]}], ";"}]}], - "\[IndentingNewLine]", "]"}], ",", "\[IndentingNewLine]", - RowBox[{"{", - RowBox[{"i", ",", "1", ",", "np"}], "}"}]}], "]"}], ";"}]}], - "\[IndentingNewLine]", "]"}], ";", "\[IndentingNewLine]", - RowBox[{"v", "=", - RowBox[{"dvi", "=", - RowBox[{"ConstantArray", "[", - RowBox[{"0", ",", - RowBox[{"{", - RowBox[{"np", ",", "2"}], "}"}]}], "]"}]}]}], ";", - "\[IndentingNewLine]", - RowBox[{"dij", "=", - RowBox[{"ConstantArray", "[", - RowBox[{"0", ",", - RowBox[{"{", - RowBox[{"np", ",", "np"}], "}"}]}], "]"}]}], ";", - "\[IndentingNewLine]", - RowBox[{"nij", "=", - RowBox[{"tij", "=", - RowBox[{"dvijt", "=", - RowBox[{"e0", "=", - RowBox[{"fij", "=", - RowBox[{"ConstantArray", "[", - RowBox[{"0", ",", - RowBox[{"{", - RowBox[{"np", ",", "np", ",", "2"}], "}"}]}], "]"}]}]}]}]}]}], - ";", "\[IndentingNewLine]", - RowBox[{"niw", "=", - RowBox[{"tiw", "=", - RowBox[{"fiw", "=", - RowBox[{"ConstantArray", "[", - RowBox[{"0", ",", - RowBox[{"{", - RowBox[{"Np", ",", "Nw", ",", "2"}], "}"}]}], "]"}]}]}]}], ";", - "\[IndentingNewLine]", - RowBox[{"diw", "=", - RowBox[{"ConstantArray", "[", - RowBox[{"0", ",", - RowBox[{"{", - RowBox[{"Np", ",", "Nw"}], "}"}]}], "]"}]}], ";", - "\[IndentingNewLine]", - RowBox[{"pressure", "=", - RowBox[{"ConstantArray", "[", - RowBox[{"0", ",", - RowBox[{"{", - RowBox[{ - RowBox[{ - RowBox[{"Floor", "[", - FractionBox["cutoff", "dt"], "]"}], "+", "1"}], ",", "Np"}], - "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", - RowBox[{"pos", "=", - RowBox[{"ConstantArray", "[", - RowBox[{"0", ",", - RowBox[{"{", - RowBox[{ - RowBox[{ - RowBox[{"Floor", "[", - FractionBox["cutoff", "dt"], "]"}], "+", "1"}], ",", "Np", ",", - "2"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", - RowBox[{ - RowBox[{"pos", "[", - RowBox[{"[", "1", "]"}], "]"}], "=", "r"}], ";", - "\[IndentingNewLine]", - RowBox[{"evac", "=", - RowBox[{"tpressure", "=", - RowBox[{"ConstantArray", "[", - RowBox[{"0", ",", - RowBox[{ - RowBox[{"Floor", "[", - FractionBox["cutoff", "dt"], "]"}], "+", "1"}]}], "]"}]}]}], ";", - "\[IndentingNewLine]", - RowBox[{"generate", "[", "]"}], ";"}]}], "\[IndentingNewLine]", - "]"}]}], "\n", - RowBox[{"(*", " ", - RowBox[{ - "generate", " ", "all", " ", "positions", " ", "for", " ", "entire", " ", - "time", " ", "horizon"}], " ", "*)"}], "\[IndentingNewLine]", - RowBox[{ - RowBox[{"generate", "[", - RowBox[{"dummy_:", "0"}], "]"}], ":=", - RowBox[{"Module", "[", - RowBox[{ - RowBox[{"{", - RowBox[{"step", "=", "1"}], "}"}], ",", "\[IndentingNewLine]", - RowBox[{ - RowBox[{"Do", "[", "\[IndentingNewLine]", - RowBox[{ - RowBox[{ - RowBox[{"step", "++"}], ";", "\[IndentingNewLine]", - RowBox[{"update", "[", "]"}], ";", "\[IndentingNewLine]", - RowBox[{ - RowBox[{"pos", "[", - RowBox[{"[", "step", "]"}], "]"}], "=", "r"}], ";", - "\[IndentingNewLine]", - RowBox[{ - RowBox[{"pressure", "[", - RowBox[{"[", - RowBox[{"step", "-", "1"}], "]"}], "]"}], "=", - RowBox[{"Table", "[", - RowBox[{ - RowBox[{"Total", "[", - RowBox[{"Table", "[", - RowBox[{ - RowBox[{"Norm", "[", - RowBox[{"fij", "[", - RowBox[{"[", - RowBox[{"i", ",", "j"}], "]"}], "]"}], "]"}], ",", - RowBox[{"{", - RowBox[{"j", ",", "1", ",", "Np"}], "}"}]}], "]"}], "]"}], - ",", - RowBox[{"{", - RowBox[{"i", ",", "1", ",", "Np"}], "}"}]}], "]"}]}], ";", - "\[IndentingNewLine]", - RowBox[{ - RowBox[{"evac", "[", - RowBox[{"[", "step", "]"}], "]"}], "=", - RowBox[{"Length", "[", - RowBox[{"Select", "[", - RowBox[{ - RowBox[{"r", "[", - RowBox[{"[", - RowBox[{";;", ",", "1"}], "]"}], "]"}], ",", - RowBox[{ - RowBox[{"#", "\[GreaterEqual]", "11.0"}], "&"}]}], "]"}], - "]"}]}], ";", "\[IndentingNewLine]", - RowBox[{ - RowBox[{"tpressure", "[", - RowBox[{"[", - RowBox[{"step", "-", "1"}], "]"}], "]"}], "=", - RowBox[{"If", "[", - RowBox[{ - RowBox[{"step", "<", "10"}], ",", "0", ",", - RowBox[{"Min", "[", - RowBox[{ - RowBox[{"Total", "[", - RowBox[{"pressure", "[", - RowBox[{"[", - RowBox[{"step", "-", "1"}], "]"}], "]"}], "]"}], ",", - RowBox[{"1800", "Np"}]}], "]"}]}], "]"}]}]}], ",", - "\[IndentingNewLine]", - RowBox[{"{", - RowBox[{"t", ",", "dt", ",", "cutoff", ",", "dt"}], "}"}]}], "]"}], - ";", "\[IndentingNewLine]", - RowBox[{ - RowBox[{"pressure", "[", - RowBox[{"[", - RowBox[{"-", "1"}], "]"}], "]"}], "=", - RowBox[{"pressure", "[", - RowBox[{"[", - RowBox[{"-", "2"}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", - RowBox[{ - RowBox[{"tpressure", "[", - RowBox[{"[", - RowBox[{"-", "1"}], "]"}], "]"}], "=", - RowBox[{"tpressure", "[", - RowBox[{"[", - RowBox[{"-", "2"}], "]"}], "]"}]}], ";"}]}], "\[IndentingNewLine]", - "]"}]}], "\n", - RowBox[{"(*", " ", "initialize", " ", "*)"}], "\[IndentingNewLine]", - RowBox[{ - RowBox[{ - RowBox[{"{", - RowBox[{"W", ",", "Wg", ",", "bb", ",", "door"}], "}"}], "=", - RowBox[{"wallgen", "[", - RowBox[{"lo", ",", "par1", ",", "par2"}], "]"}]}], ";"}], - "\[IndentingNewLine]", - RowBox[{ - RowBox[{"rad", "=", - RowBox[{"RandomReal", "[", - RowBox[{ - RowBox[{"{", - RowBox[{"radmin", ",", "radmax"}], "}"}], ",", "Np"}], "]"}]}], ";"}], - "\[IndentingNewLine]", - RowBox[{ - RowBox[{"radsum", "=", - RowBox[{"ConstantArray", "[", - RowBox[{"0", ",", - RowBox[{"{", - RowBox[{"Np", ",", "Np"}], "}"}]}], "]"}]}], ";"}], - "\[IndentingNewLine]", - RowBox[{ - RowBox[{"Do", "[", "\[IndentingNewLine]", - RowBox[{ - RowBox[{"Do", "[", "\[IndentingNewLine]", - RowBox[{ - RowBox[{ - RowBox[{"radsum", "[", - RowBox[{"[", - RowBox[{"i", ",", "j"}], "]"}], "]"}], "=", - RowBox[{ - RowBox[{"radsum", "[", - RowBox[{"[", - RowBox[{"j", ",", "i"}], "]"}], "]"}], "=", - RowBox[{ - RowBox[{"rad", "[", - RowBox[{"[", "i", "]"}], "]"}], "+", - RowBox[{"rad", "[", - RowBox[{"[", "j", "]"}], "]"}]}]}]}], ",", "\[IndentingNewLine]", - RowBox[{"{", - RowBox[{"j", ",", "1", ",", "i"}], "}"}]}], "]"}], ",", - "\[IndentingNewLine]", - RowBox[{"{", - RowBox[{"i", ",", "1", ",", "Np"}], "}"}]}], "]"}], ";"}], - "\[IndentingNewLine]", - RowBox[{ - RowBox[{"r", "=", - RowBox[{"Transpose", "[", - RowBox[{"{", - RowBox[{ - RowBox[{"RandomReal", "[", - RowBox[{ - RowBox[{"bb", "[", - RowBox[{"[", "1", "]"}], "]"}], ",", "Np"}], "]"}], ",", - RowBox[{"RandomReal", "[", - RowBox[{ - RowBox[{"bb", "[", - RowBox[{"[", "2", "]"}], "]"}], ",", "Np"}], "]"}]}], "}"}], - "]"}]}], ";"}], "\[IndentingNewLine]", - RowBox[{ - RowBox[{"v", "=", - RowBox[{"dvi", "=", - RowBox[{"ConstantArray", "[", - RowBox[{"0", ",", - RowBox[{"{", - RowBox[{"Np", ",", "2"}], "}"}]}], "]"}]}]}], ";"}], - "\[IndentingNewLine]", - RowBox[{ - RowBox[{"dij", "=", - RowBox[{"ConstantArray", "[", - RowBox[{"0", ",", - RowBox[{"{", - RowBox[{"Np", ",", "Np"}], "}"}]}], "]"}]}], ";"}], - "\[IndentingNewLine]", - RowBox[{ - RowBox[{"nij", "=", - RowBox[{"tij", "=", - RowBox[{"dvijt", "=", - RowBox[{"e0", "=", - RowBox[{"fij", "=", - RowBox[{"ConstantArray", "[", - RowBox[{"0", ",", - RowBox[{"{", - RowBox[{"Np", ",", "Np", ",", "2"}], "}"}]}], "]"}]}]}]}]}]}], - ";"}], "\[IndentingNewLine]", - RowBox[{ - RowBox[{"niw", "=", - RowBox[{"tiw", "=", - RowBox[{"fiw", "=", - RowBox[{"ConstantArray", "[", - RowBox[{"0", ",", - RowBox[{"{", - RowBox[{"Np", ",", "Nw", ",", "2"}], "}"}]}], "]"}]}]}]}], ";"}], - "\[IndentingNewLine]", - RowBox[{ - RowBox[{"diw", "=", - RowBox[{"ConstantArray", "[", - RowBox[{"0", ",", - RowBox[{"{", - RowBox[{"Np", ",", "Nw"}], "}"}]}], "]"}]}], ";"}], - "\[IndentingNewLine]", - RowBox[{ - RowBox[{"pressure", "=", - RowBox[{"ConstantArray", "[", - RowBox[{"0", ",", - RowBox[{"{", - RowBox[{ - RowBox[{ - RowBox[{"Floor", "[", - FractionBox["cutoff", "dt"], "]"}], "+", "1"}], ",", "Np"}], - "}"}]}], "]"}]}], ";"}], "\[IndentingNewLine]", - RowBox[{ - RowBox[{"pos", "=", - RowBox[{"ConstantArray", "[", - RowBox[{"0", ",", - RowBox[{"{", - RowBox[{ - RowBox[{ - RowBox[{"Floor", "[", - FractionBox["cutoff", "dt"], "]"}], "+", "1"}], ",", "Np", ",", - "2"}], "}"}]}], "]"}]}], ";"}], "\[IndentingNewLine]", - RowBox[{ - RowBox[{"evac", "=", - RowBox[{"tpressure", "=", - RowBox[{"ConstantArray", "[", - RowBox[{"0", ",", - RowBox[{ - RowBox[{"Floor", "[", - FractionBox["cutoff", "dt"], "]"}], "+", "1"}]}], "]"}]}]}], ";"}], - "\[IndentingNewLine]", - RowBox[{ - RowBox[{ - RowBox[{"pos", "[", - RowBox[{"[", "1", "]"}], "]"}], "=", "r"}], ";"}], - "\[IndentingNewLine]", - RowBox[{ - RowBox[{"restart", "[", "]"}], ";"}]}]}]], "Input", - CellChangeTimes->{{3.7766008761831923`*^9, 3.776600882799075*^9}, - 3.776717606385376*^9}] -}, Closed]], - -Cell[CellGroupData[{ - -Cell["Demonstration", "Subsection", - CellChangeTimes->{{3.7766008885632277`*^9, 3.7766008904796133`*^9}}], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"Manipulate", "[", - RowBox[{ - RowBox[{"Module", "[", - RowBox[{ - RowBox[{"{", "step", "}"}], ",", "\[IndentingNewLine]", - RowBox[{ - RowBox[{"step", "=", - RowBox[{"1", "+", - RowBox[{"Floor", "[", - FractionBox["t", "dt"], "]"}]}]}], ";", "\[IndentingNewLine]", - RowBox[{"Framed", "[", - RowBox[{"ListPlot", "[", - RowBox[{ - RowBox[{"{", - RowBox[{ - RowBox[{"Table", "[", - RowBox[{ - RowBox[{"{", - RowBox[{ - RowBox[{ - RowBox[{"4.8", - FractionBox["tee", "cutoff"]}], "+", "14.6"}], ",", - RowBox[{ - RowBox[{"2.5", - FractionBox[ - RowBox[{"evac", "[", - RowBox[{"[", - RowBox[{ - FractionBox["tee", "dt"], "+", "1"}], "]"}], "]"}], - "Np"]}], "+", "0.2"}]}], "}"}], ",", - RowBox[{"{", - RowBox[{"tee", ",", "0", ",", "t", ",", "dt"}], "}"}]}], "]"}], - ",", - RowBox[{"Table", "[", - RowBox[{ - RowBox[{"{", - RowBox[{ - RowBox[{ - RowBox[{"4.8", - FractionBox["tee", "cutoff"]}], "+", "14.6"}], ",", - RowBox[{ - RowBox[{"2.5", - FractionBox[ - RowBox[{"tpressure", "[", - RowBox[{"[", - RowBox[{ - FractionBox["tee", "dt"], "+", "1"}], "]"}], "]"}], - RowBox[{"1800", "Np"}]]}], "+", "0.2"}]}], "}"}], ",", - RowBox[{"{", - RowBox[{"tee", ",", "0", ",", "t", ",", "dt"}], "}"}]}], - "]"}]}], "}"}], ",", - RowBox[{"PlotStyle", "\[Rule]", - RowBox[{"{", - RowBox[{ - RowBox[{"Directive", "[", - RowBox[{ - RowBox[{"Opacity", "[", "0.5", "]"}], ",", - RowBox[{"RGBColor", "[", - RowBox[{"0", ",", "0.8", ",", "0"}], "]"}]}], "]"}], ",", - RowBox[{"Directive", "[", - RowBox[{ - RowBox[{"Opacity", "[", "0.5", "]"}], ",", - RowBox[{"RGBColor", "[", - RowBox[{"1", ",", "0", ",", "0"}], "]"}]}], "]"}]}], "}"}]}], - ",", - RowBox[{"Joined", "\[Rule]", "True"}], ",", - RowBox[{"Prolog", "\[Rule]", - RowBox[{"{", - RowBox[{ - RowBox[{"RGBColor", "[", - RowBox[{"0.95", ",", "0.95", ",", "0.95"}], "]"}], ",", - RowBox[{"Rectangle", "[", - RowBox[{ - RowBox[{"{", - RowBox[{"14.5", ",", "0.1"}], "}"}], ",", - RowBox[{"{", - RowBox[{"19.5", ",", "2.9"}], "}"}]}], "]"}]}], "}"}]}], ",", - RowBox[{"Epilog", "\[Rule]", - RowBox[{"Join", "[", - RowBox[{ - RowBox[{"{", - RowBox[{"Text", "[", - RowBox[{ - RowBox[{"\"\