(*********************************************************************** Mathematica-Compatible Notebook This notebook can be used on any computer system with Mathematica 4.0, MathReader 4.0, or any compatible application. The data for the notebook starts with the line containing stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). 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For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. ***********************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 1778164, 64636]*) (*NotebookOutlinePosition[ 1779133, 64667]*) (* CellTagsIndexPosition[ 1779089, 64663]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell[TextData[{ "Implementation of Alternating Direction Implicit Method to Solve Two \ Dimensional Heat Conduction with ", StyleBox["Mathematica", FontSlant->"Italic"] }], "Title", TextAlignment->Center], Cell["\<\ Scott Beckman August 2000\ \>", "Subsubtitle", TextAlignment->Center], Cell["\<\ University of California at Berkeley Material Science and Engineering Department 577 Evans Hall #1760 Berkeley, CA 94720 sbeckman@uclink.berkeley.edu\ \>", "Subsubtitle", TextAlignment->Center], Cell[CellGroupData[{ Cell["Introduction 1", "Section"], Cell[CellGroupData[{ Cell["Alternating Direction Method 1.1", "Subsection"], Cell[TextData[{ "The alternating direction implicit, ADI, method is a common algorithm used \ in finite difference methods. Below it is demonstrated how to implement ADI \ with ", StyleBox["Mathematica", FontSlant->"Italic"], ". Although ", StyleBox["Mathematica", FontSlant->"Italic"], " isn't the most efficient package for finite difference problems, it is an \ excellent tool for visualizing how ADI works. Large scale application should \ inevitably involve translating the below into C or FORTRAN code/" }], "Text"], Cell[TextData[{ "Parabolic partial differential equation, PDE, can be expressed at implicit \ finite difference equations. When such a PDE is has two spatial dimensions, \ the number of terms in the equation are too large to be solved efficiently. \ The basic gist of ADI is to break a large implicit finite difference \ equation, over time step \[Delta]t, into two step, each over the time step ", Cell[BoxData[ \(TraditionalForm\`\[Delta]t\/2\)]], ". The first step implicitly solves for heat conduction in one direction \ only. The input to this step are the current temperatures T(x,y,n) and the \ results from this step are an intermediate temperature distribution, called \ ", Cell[BoxData[ \(TraditionalForm\`\(T\^*\)\)]], ", which is sometimes incorrectly referred to as T(x,y,n+", Cell[BoxData[ \(TraditionalForm\`\[Delta]t\/2\)], "DisplayFormula"], "). The second step solves implicitly for the heat conduction in the other \ directional only. The input to this step is, ", Cell[BoxData[ \(TraditionalForm\`\(T\^*\)\)]], " and the resulting output is the temperature at n+1, T(x,y,n+1)." }], "Text"], Cell["So thermal conduction in 2D", "Text"], Cell[BoxData[ \(\[Rho]\ \(C\_p\) \[PartialD]T\/\[PartialD]t = \(k\_x\) \[PartialD]\^2 T\ \/\[PartialD]x\^2 + \(k\_y\) \[PartialD]\^2 T\/\[PartialD]y\^2 + q\)], "Text",\ TextAlignment->Center], Cell["expressed as a finite difference equation", "Text"], Cell[BoxData[ RowBox[{ RowBox[{ StyleBox["\[Rho]", "Text"], StyleBox[" ", "Text"], StyleBox[\(C\_p\), "Text"], StyleBox[" ", "Text"], SubscriptBox[ StyleBox["\[CapitalDelta]", "Text"], "t"]}], StyleBox["=", "Text"], RowBox[{ RowBox[{ StyleBox[\(k\_x\), "Text"], StyleBox[" ", "Text"], SubscriptBox[ StyleBox["\[CapitalDelta]", "Text"], "xx"]}], StyleBox["+", "Text"], RowBox[{ StyleBox[\(k\_y\), "Text"], StyleBox[" ", "Text"], SubscriptBox[ StyleBox["\[CapitalDelta]", "Text"], "yy"], StyleBox["T", "Text"]}], StyleBox["+", "Text"], StyleBox["q", "Text"]}]}]], "InlineFormula", TextAlignment->Center], Cell["can be broken down to", "Text"], Cell[BoxData[ RowBox[{ RowBox[{ StyleBox["\[Rho]", "Text"], StyleBox[" ", "Text"], StyleBox[\(C\_p\), "Text"], StyleBox[" ", "Text"], \((2\/\[Delta]t)\), RowBox[{ StyleBox["(", "Text"], RowBox[{ SuperscriptBox[ SubscriptBox[ StyleBox["T", "Text"], \(i, j\)], "*"], "-", \(T\_\(i, j, n\)\)}], StyleBox[")", "Text"]}]}], StyleBox["=", "Text"], RowBox[{ RowBox[{ StyleBox[\(k\_x\), "Text"], StyleBox[" ", "Text"], SuperscriptBox[ SubscriptBox[ StyleBox["\[CapitalDelta]", "Text"], "xx"], "*"], StyleBox[\(+k\_y\), "Text"], StyleBox[" ", "Text"], SubscriptBox[ StyleBox["\[CapitalDelta]", "Text"], "yy"], StyleBox["T", "Text"]}], StyleBox["+", "Text"], StyleBox["q", "Text"]}]}]], "InlineFormula", TextAlignment->Center], Cell[BoxData[ RowBox[{ RowBox[{ StyleBox["\[Rho]", "Text"], StyleBox[" ", "Text"], StyleBox[\(C\_p\), "Text"], StyleBox[" ", "Text"], \((2\/\[Delta]t)\), RowBox[{ StyleBox["(", "Text"], RowBox[{ SubscriptBox[ StyleBox["T", "Text"], \(i, j, n + 1\)], "-", \(T\_\(i, j\)\^*\)}], ")"}]}], StyleBox["=", "Text"], RowBox[{ RowBox[{ StyleBox[\(k\_x\), "Text"], StyleBox[" ", "Text"], SuperscriptBox[ SubscriptBox[ StyleBox["\[CapitalDelta]", "Text"], "xx"], "*"]}], StyleBox["+", "Text"], StyleBox[\(k\_y\ \(\[CapitalDelta]\_yy\) T\), "Text"], StyleBox["+", "Text"], StyleBox["q", "Text"]}]}]], "InlineFormula", TextAlignment->Center], Cell[TextData[{ "The former of the above two is first solved for ", Cell[BoxData[ \(TraditionalForm\`\(T\_\(i, j\)\^*\)\)]], " and the result is substituted in to the latter equation to find \ T(x,y,n+1). Notice that upon arranging the first equation to find ", Cell[BoxData[ \(TraditionalForm\`\(T\_\(i, j\)\^*\)\)]], " the expression is an implicit finite different equation in the x \ direction only. The second equation, rearranged is an implicit equation in \ the y direction only." }], "Text"], Cell["\<\ Details of the ADI method, such as error and proof of stability, \ can be found in Carnahan's text.\ \>", "Text"], Cell[TextData[{ "\tCarnahan, Luther,and Wilkes. ", StyleBox["Applied Numerical Methods", FontSlant->"Italic"], ". New York: John Wiley & Sons, Inc., 1969." }], "Text"] }, Open ]], Cell[CellGroupData[{ Cell["Difference Equations and Boundary Conditions 1.2", "Subsection"], Cell["As shown above, the first derivative is written", "Text"], Cell[BoxData[ RowBox[{\(\[CapitalDelta]\_t\), "=", FractionBox[ RowBox[{ SubscriptBox[ StyleBox["T", "Text"], \(i, j, n + 1\)], "-", \(T\_\(i, j, n\)\)}], "\[Delta]t"]}]], "Text", TextAlignment->Center], Cell["Similarly second derivatives are written", "Text"], Cell[BoxData[ \(\[CapitalDelta]\_xx = \(T\_\(i - 1, j\) - 2 T\_\(i, j\) + T\_\(i + 1, \ j\)\)\/\((\[Delta]x)\)\^2\)], "Text", TextAlignment->Center], Cell["\<\ Boundary conditions require a special formulation of the spatial \ derivative. For our problem we will be using Newton's law of cooling as our \ boundary condition\ \>", "Text"], Cell[TextData[Cell[BoxData[ \(TraditionalForm\`\(-k\_x\) dT\/dx = \(\((1\/h - Lin\/kin)\)\^\(-1\)\) \((T - Troom)\)\)]]], "Text", TextAlignment->Center], Cell["which can be arranged to the form", "Text"], Cell[TextData[Cell[BoxData[ \(TraditionalForm\`\(-\(dT\/dx\)\) + aT = g\)]]], "Text", TextAlignment->Center], Cell["\<\ Carnahan shows that the second derivative of this boundary \ condition, which he calls, \"third condition,\" is written\ \>", "Text"], Cell[BoxData[ \(\[CapitalDelta]\_xx = \(2 \((T\_\(1, j\) - \((a\ \[Delta]x + 1)\) \ T\_\(0, j\) + g\ \[Delta]x)\)\)\/\((\[Delta]x)\)\^2\)], "Text", TextAlignment->Center], Cell["\<\ Solving this problem is now a matter of substituting the \ appropriate approximations for the derivatives and solving the resulting \ matrices, which will be tridiagonal. \ \>", "Text"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Conventions and Initiation 2", "Section"], Cell["\<\ To reduce the number of constants that are carried throughout this \ problem, the following grouping conventions will be used.\ \>", "Text"], Cell[BoxData[ \(\[Alpha]\_x = k\_x\/\(\[Rho]\ C\_p\); \[Alpha]\_y = k\_y\/\(\[Rho]\ C\_p\)\)], "Text", TextAlignment->Center], Cell[BoxData[ \(\[Phi]x = \(\(\[Alpha]\_x\) \[Delta]t\)\/\(2 \((\[Delta]x)\)\^2\); \ \[Phi]x = \(\(\[Alpha]\_x\) \[Delta]t\)\/\(2 \((\[Delta]x)\)\^2\)\)], "Text", TextAlignment->Center], Cell[BoxData[ \(\[Zeta] = \[Delta]t\/\(2\ \[Rho]\ C\_p\)\)], "Text", TextAlignment->Center], Cell["\<\ The below commands turn off the error code [General::spell] which \ is a common warning given in this notebook because of the naming scheme \ selected. For debugging purposes this can be turned back on with the command \ On[General::spell]\ \>", "Text"], Cell[BoxData[ \(Off[General::spell]\)], "Input"], Cell[BoxData[ \(Off[General::spell1]\)], "Input"], Cell[TextData[{ "The below add-on ", StyleBox["Mathematica", FontSlant->"Italic"], " add-on packages are needed for this problem." }], "Text"], Cell[BoxData[{ \(<< LinearAlgebra`MatrixManipulation`\), "\[IndentingNewLine]", \(<< LinearAlgebra`Tridiagonal`\)}], "Input"], Cell["\<\ We define the number of x step Nx and number of y step Ny so (1\ \[LessEqual]x\[LessEqual]Nx) and (1\[LessEqual]y\[LessEqual]Ny)\ \>", "Text"], Cell[BoxData[{ \(\(Ny = 50;\)\), "\[IndentingNewLine]", \(\(Nx = 50;\)\)}], "Input"], Cell["\<\ Set the temperature, T to be the function Tfct. Note that the hold \ operator is being used only for the convenience of demonstration. The actual \ electrothermal does not need such. \ \>", "Text"], Cell[BoxData[ \(\(T = Array[Hold[Tfct], {Nx, Ny}];\)\)], "Input"] }, Open ]], Cell[CellGroupData[{ Cell["Implicit in X Direction 3", "Section"], Cell[CellGroupData[{ Cell["Prepare Input to TridiagonalSolve 3.1", "Subsection"], Cell[TextData[{ StyleBox["Mathematica", FontSlant->"Italic"], " has a function, TridiagonalSolve which will be used. For an exact \ explanation of this function, the reader is referred to the ", StyleBox["Mathematica", FontSlant->"Italic"], " on-line use guide. In short the TridiagonalSolve function operates as" }], "Text"], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"(", "\[NegativeThinSpace]", GridBox[{ {\(B\_1\), \(C\_1\), "0", "0", "\[CenterEllipsis]", "0", "0"}, {\(A\_1\), \(B\_2\), \(C\_2\), "0", "\[Placeholder]", "\[Placeholder]", "0"}, {"0", \(A\_2\), \(B\_3\), \(C\_3\), "\[Placeholder]", "\[Placeholder]", "\[Placeholder]"}, {"0", "0", \(A\_3\), "\[DescendingEllipsis]", "\[Placeholder]", "\[Placeholder]", "\[Placeholder]"}, {"\[VerticalEllipsis]", "\[Placeholder]", "\[Placeholder]", "\[Placeholder]", \(B\_\(N - 2\)\), \(C\_\(N - 2\)\), "0"}, {"0", "\[Placeholder]", "\[Placeholder]", "\[Placeholder]", \(A\_\(N - 2\)\), \(B\_\(N - 1\)\), \(C\_\(N - 1\)\)}, {"0", "0", "\[Placeholder]", "\[Placeholder]", "0", \(A\_\(N - 1\)\), \(B\_N\)} }], ")"}], RowBox[{"(", "\[NegativeThinSpace]", GridBox[{ {\(T\_1\)}, {\(T\_2\)}, {\(T\_3\)}, {"\[VerticalEllipsis]"}, {\(T\_\(N - 2\)\)}, {\(T\_\(N - 1\)\)}, {\(T\_N\)} }], "\[NegativeThinSpace]", ")"}]}], "=", RowBox[{"(", "\[NegativeThinSpace]", GridBox[{ {\(D\_1\)}, {\(D\_2\)}, {\(D\_3\)}, {"\[VerticalEllipsis]"}, {\(D\_\(N - 2\)\)}, {\(D\_\(N - 1\)\)}, {\(D\_N\)} }], "\[NegativeThinSpace]", ")"}]}]], "Text", TextAlignment->Center], Cell["T=TridiagonalSolve[A,B,C,D]", "Text", TextAlignment->Center], Cell["where T,A,B,C, and D are vectors", "Text"], Cell[TextData[{ "For the ADI method, solving for A,B,C, and D vectors is a matter of \ substituting equations and rearranging. In this example, the solution for \ each instance will not be given. As it will be shown below, it is possible \ for the reader to use this notebook to back out the system of equations for \ each point in space. In the accompanying notebook, ", StyleBox["Implementation of Brian's Method to Solve Three Dimensional Heat \ Conduction with Mathematica", FontSlant->"Italic"], StyleBox[", it is shown how to use ", FontVariations->{"CompatibilityType"->0}], StyleBox["Mathematica ", FontSlant->"Italic"], StyleBox["to derive the vectors for input to the TridiagonalSolve function. \ ", FontVariations->{"CompatibilityType"->0}] }], "Text"], Cell[BoxData[{ \(\(ACstar[x_, y_] = \(-\[Phi]x\);\)\), "\[IndentingNewLine]", \(\(Astar = Array[ACstar, {Nx - 1, Ny}];\)\), "\[IndentingNewLine]", \(\(Cstar = Array[ACstar, {Nx - 1, Ny}];\)\)}], "Input"], Cell[BoxData[{ \(\(B[x_, y_] := \((\[Phi]x \((a\ \[Delta]x + 1)\) + 1/2)\) /; \((x == 1 || x == Nx)\);\)\), "\[IndentingNewLine]", \(B[x_, y_] := \((2\ \[Phi]x + 1)\) /; \((x \[NotEqual] 1 && x \[NotEqual] Nx)\); Bstar = Array[B, {Nx, Ny}];\)}], "Input"], Cell[BoxData[{ \(\(DD[x_, y_] := \((\[Phi]y\ \(T[\([x]\)]\)[\([y + 1]\)] + \((1/ 2 - \[Phi]y\ \((a\ \[Delta]y + 1)\))\) \(T[\([x]\)]\)[\([y]\)] + \[Phi]y\ g\ \ \[Delta]y + \[Phi]x\ g\ \[Delta]x + 1/2\ \[Zeta]\ q)\) /; \((\((x \[Equal] 1 || x \[Equal] Nx)\) && y \[Equal] 1)\);\)\), "\[IndentingNewLine]", \(\(DD[x_, y_] := \((2\ \[Phi]y\ \(T[\([x]\)]\)[\([y + 1]\)] + \((1 - 2\ \[Phi]y \((a\ \[Delta]y + 1)\))\) \(T[\([x]\)]\)[\([y]\)]\ + 2\ \[Phi]y\ g\ \[Delta]y + \[Zeta]\ q)\) /; \((x \[NotEqual] 1 && x \[NotEqual] Nx && y \[Equal] 1)\);\)\), "\[IndentingNewLine]", \(\(DD[x_, y_] := \((\[Phi]y\ \(T[\([x]\)]\)[\([y - 1]\)] + \((1/ 2 - \[Phi]y \((a\ \[Delta]y + 1)\))\) \(T[\([x]\)]\)[\([y]\)] + \[Phi]x\ g\ \ \[Delta]x + \[Phi]y\ g\ \[Delta]y + 1/2\ \[Zeta]\ q)\) /; \((\((x \[Equal] 1 || x \[Equal] Nx)\) && y \[Equal] Ny)\);\)\), "\[IndentingNewLine]", \(\(DD[x_, y_] := \((2\ \[Phi]y\ \(T[\([x]\)]\)[\([y - 1]\)] + \((1 - 2\ \[Phi]y \((a\ \[Delta]y + 1)\))\) \(T[\([x]\)]\)[\([y]\)] + 2\ \[Phi]y\ g\ \[Delta]y + \[Zeta]\ q)\) /; \((x \[NotEqual] 1 && x \[NotEqual] Nx && y \[Equal] Ny)\);\)\), "\[IndentingNewLine]", \(\(DD[x_, y_] := \((1/ 2\ \[Phi]y\ \(T[\([x]\)]\)[\([y - 1]\)] + \((1/ 2 - \[Phi]y)\) \(T[\([x]\)]\)[\([y]\)] + 1/2\ \[Phi]y\ \(T[\([x]\)]\)[\([y + 1]\)] + 1/2\ \[Zeta]\ q + \[Phi]x\ g\ \[Delta]x)\) /; \((\((x \[Equal] 1 || x \[Equal] Nx)\) && y \[NotEqual] 1 && y \[NotEqual] Ny)\);\)\), "\[IndentingNewLine]", \(\(DD[x_, y_] := \((\[Phi]y\ \(T[\([x]\)]\)[\([y - 1]\)] + \((1 - 2\ \[Phi]y)\) \(T[\([x]\)]\)[\([y]\)] + \[Phi]y\ \ \(T[\([x]\)]\)[\([y + 1]\)] + \[Zeta]\ q)\) /; \((x \[NotEqual] 1 && x \[NotEqual] Nx && y \[NotEqual] 1 && y \[NotEqual] Ny)\);\)\), "\[IndentingNewLine]", \(\(Dstar = Array[DD, {Nx, Ny}];\)\)}], "Input"], Cell[BoxData[ \(\(Tstar = ZeroMatrix[Nx, Ny];\)\)], "Input"] }, Open ]], Cell[CellGroupData[{ Cell["Check the Input 3.2", "Subsection"], Cell["\<\ We can now extract columns from the matrices to check that the \ solution we entered matches the solution achieved when solving by hand.\ \>", \ "Text"], Cell["\<\ For the case middle of the region, (1", "Text"], Cell[BoxData[{ \(\(j = 3;\)\), "\[IndentingNewLine]", \(\(i = 4;\)\)}], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(Asample = \(TakeColumns[ TakeColumns[Astar, j], \(-1\)]\)[\([i]\)]\)], "Input"], Cell[BoxData[ \({\(-\[Phi]x\)}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Bsample = \(TakeColumns[ TakeColumns[Bstar, j], \(-1\)]\)[\([i]\)]\)], "Input"], Cell[BoxData[ \({1 + 2\ \[Phi]x}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Csample = \(TakeColumns[ TakeColumns[Cstar, j], \(-1\)]\)[\([i]\)]\)], "Input"], Cell[BoxData[ \({\(-\[Phi]x\)}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Dsample = \(TakeColumns[ TakeColumns[Dstar, j], \(-1\)]\)[\([i]\)]\)], "Input"], Cell[BoxData[ \({q\ \[Zeta] + \[Phi]y\ \(Hold[Tfct]\)[4, 2] + \((1 - 2\ \[Phi]y)\)\ \(Hold[Tfct]\)[4, 3] + \[Phi]y\ \(Hold[Tfct]\)[4, 4]}\)], "Output"] }, Open ]], Cell["Which, when substituted, should match the equation", "Text"], Cell[TextData[Cell[BoxData[ \(TraditionalForm\`\(-\[Phi]x\)\ \(T\_\(i - 1, j\)\^*\) + \((2\ \[Phi]x + 1)\) \(T\_\(i, j\)\^*\) - \[Phi]x\ \(T\_\(i + 1, j\)\^*\) = \ \[Phi]y\ T\_\(i, j - 1, n\) + \((1 - 2\ \[Phi]y)\) T\_\(i, j, n\) + \[Phi]y\ T\_\(i, j + 1, n\) + \[Zeta]\ q\)]]], \ "Text", TextAlignment->Center], Cell["\<\ In this manner, all of the systems of equations can be \ verified.\ \>", "Text"] }, Open ]], Cell[CellGroupData[{ Cell["Assign Values to Constants 3.3", "Subsection"], Cell["\<\ To achieve a numerical answer from the TridiagonalSolve function, \ values must be assigned to the constants\ \>", "Text"], Cell[BoxData[{ \(\(q = 0;\)\), "\[IndentingNewLine]", \(\(Troom = 100;\)\), "\[IndentingNewLine]", \(\(Tfct[x_, y_] = 0.1;\)\), "\[IndentingNewLine]", \(\(\[Phi]x = 1;\)\), "\[IndentingNewLine]", \(\(\[Phi]y = 1;\)\), "\[IndentingNewLine]", \(\(\[Delta]x = 1;\)\), "\[IndentingNewLine]", \(\(\[Delta]y = 1;\)\), "\[IndentingNewLine]", \(\(g = 200;\)\), "\[IndentingNewLine]", \(\(a = 100;\)\)}], "Input"] }, Open ]], Cell[CellGroupData[{ Cell["Loop Over Entire Region 3.4", "Subsection"], Cell[BoxData[ \(Do[\[IndentingNewLine]Ainput = TakeColumns[ TakeColumns[Astar, j], \(-1\)]; \[IndentingNewLine]Binput = TakeColumns[ TakeColumns[Bstar, j], \(-1\)]; \[IndentingNewLine]Cinput = TakeColumns[ TakeColumns[Cstar, j], \(-1\)]; \[IndentingNewLine]Dinput = TakeColumns[ TakeColumns[ReleaseHold[Dstar], j], \(-1\)]; \[IndentingNewLine]boof = TridiagonalSolve[Ainput, Binput, Cinput, Dinput]; \[IndentingNewLine]Tstar = Transpose[ ReplacePart[Transpose[Tstar], \(Transpose[boof]\)[\([1]\)], j]];\[IndentingNewLine], {j, 1, Ny}]\)], "Input"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Implicit in Y Direction 4", "Section"], Cell[CellGroupData[{ Cell["Prepare Input to Tridiagonal Solve 4.1", "Subsection"], Cell["\<\ Clearing values so the correctness of step two can be verified \ symbolically.\ \>", "Text"], Cell[BoxData[ \(\(Clear[q, Troom, \[Phi]x, \[Phi]y, \[Delta]x, \[Delta]y, g, a];\)\)], "Input"], Cell["\<\ Writing the equations for the second step ones notices that there \ is a direct parallelism between the first and second step. Take for instance \ the equation which is comparable to the sample given in section 3.2\ \>", \ "Text"], Cell[TextData[Cell[BoxData[ \(TraditionalForm\`\(-\[Phi]y\)\ T\_\(i, j - 1, n + 1\) + \((2\ \[Phi]y + 1)\) T\_\(i, j, n + 1\) - \[Phi]y\ T\_\(i, j + 1, n + 1\) = \ \[Phi]x\ \(T\_\(i - 1, j\)\^*\) + \((1 - 2\ \[Phi]x)\) \(T\_\(i, j\)\^*\) + \[Phi]x\ \(T\_\(i + 1, \ j\)\^*\) + \[Zeta]\ q\)]]], "Text", TextAlignment->Center], Cell["\<\ This suggests that the vector inputs to the TridiagonalSolve \ function can be created by manipulating the existing Xstar matrices.\ \>", \ "Text"], Cell["\<\ For Astar, Bstar, and Cstar this is a matter of substituting \ \[Phi]y for \[Phi]x adding a rows, removing a columns, and then \ tranposing\ \>", "Text"], Cell[BoxData[{ \(\(Astartwo = Astar /. {\[Phi]x \[Rule] \[Phi]y};\)\), "\[IndentingNewLine]", \(\(Astartwo = AppendColumns[ Astartwo, {Astartwo[\([1]\)]}];\)\), "\[IndentingNewLine]", \(\(Astartwo = Transpose[Delete[Transpose[Astartwo], 1]];\)\)}], "Input"], Cell[BoxData[{ \(\(Cstartwo = Cstar /. {\[Phi]x \[Rule] \[Phi]y};\)\), "\[IndentingNewLine]", \(\(Cstartwo = AppendColumns[ Cstartwo, {Cstartwo[\([1]\)]}];\)\), "\[IndentingNewLine]", \(\(Cstartwo = Transpose[Delete[Transpose[Cstartwo], 1]];\)\)}], "Input"], Cell[BoxData[{ \(\(Bstartwo = Bstar /. {\[Phi]x \[Rule] \[Phi]y, \[Delta]x \[Rule] \[Delta]y};\)\), \ "\[IndentingNewLine]", \(\(Do[ Bstartwo = Delete[Bstartwo, 2], {Abs[Nx - Ny]}];\)\), "\[IndentingNewLine]", \(\(Bstartwo = Transpose[Bstartwo];\)\), "\[IndentingNewLine]", \(\(Do[ Bstartwo = AppendColumns[Bstartwo, {Bstartwo[\([1]\)]}], {Abs[ Nx - Ny]}];\)\)}], "Input"], Cell["\<\ Dstar, unfortunately isn't as easy to rearrange because the \ function's conditionals also change. Rather than transform the Dstar matrix, \ we'll just rewrite the function exchanging x for y and correcting the order \ direction of the T values from the y direction to the x direction. \ \>", \ "Text"], Cell[BoxData[{ \(\(DDtwo[x_, y_] := \((\[Phi]x\ \(T[\([x + 1]\)]\)[\([y]\)] + \((1/ 2 - \[Phi]x\ \((a\ \[Delta]x + 1)\))\) \(T[\([x]\)]\)[\([y]\)] + \[Phi]x\ g\ \ \[Delta]x + \[Phi]y\ g\ \[Delta]y + 1/2\ \[Zeta]\ q)\) /; \((\((y \[Equal] 1 || y \[Equal] Ny)\) && x \[Equal] 1)\);\)\), "\[IndentingNewLine]", \(\(DDtwo[x_, y_] := \((2\ \[Phi]x\ \(T[\([x + 1]\)]\)[\([y]\)] + \((1 - 2\ \[Phi]x \((a\ \[Delta]x + 1)\))\) \(T[\([x]\)]\)[\([y]\)]\ + 2\ \[Phi]x\ g\ \[Delta]x + \[Zeta]\ q)\) /; \((y \[NotEqual] 1 && y \[NotEqual] Ny && x \[Equal] 1)\);\)\), "\[IndentingNewLine]", \(\(DDtwo[x_, y_] := \((\[Phi]x\ \(T[\([x - 1]\)]\)[\([y]\)] + \((1/ 2 - \[Phi]x \((a\ \[Delta]x + 1)\))\) \(T[\([x]\)]\)[\([y]\)] + \[Phi]y\ g\ \ \[Delta]y + \[Phi]x\ g\ \[Delta]x + 1/2\ \[Zeta]\ q)\) /; \((\((y \[Equal] 1 || y \[Equal] Ny)\) && x \[Equal] Nx)\);\)\), "\[IndentingNewLine]", \(\(DDtwo[x_, y_] := \((2\ \[Phi]x\ \(T[\([x - 1]\)]\)[\([y]\)] + \((1 - 2\ \[Phi]x \((a\ \[Delta]x + 1)\))\) \(T[\([x]\)]\)[\([y]\)] + 2\ \[Phi]x\ g\ \[Delta]x + \[Zeta]\ q)\) /; \((y \[NotEqual] 1 && y \[NotEqual] Ny && x \[Equal] Nx)\);\)\), "\[IndentingNewLine]", \(\(DDtwo[x_, y_] := \((1/ 2\ \[Phi]x\ \(T[\([x - 1]\)]\)[\([y]\)] + \((1/ 2 - \[Phi]x)\) \(T[\([x]\)]\)[\([y]\)] + 1/2\ \[Phi]x\ \(T[\([x + 1]\)]\)[\([y]\)] + 1/2\ \[Zeta]\ q + \[Phi]y\ g\ \[Delta]y)\) /; \((\((y \[Equal] 1 || y \[Equal] Ny)\) && x \[NotEqual] 1 && x \[NotEqual] Nx)\);\)\), "\[IndentingNewLine]", \(\(DDtwo[x_, y_] := \((\[Phi]x\ \(T[\([x - 1]\)]\)[\([y]\)] + \((1 - 2\ \[Phi]x)\) \(T[\([x]\)]\)[\([y]\)] + \[Phi]x\ \(T[\([x \ + 1]\)]\)[\([y]\)] + \[Zeta]\ q)\) /; \((x \[NotEqual] 1 && x \[NotEqual] Nx && y \[NotEqual] 1 && y \[NotEqual] Ny)\);\)\), "\[IndentingNewLine]", \(\(Dstartwo = Array[DDtwo, {Nx, Ny}];\)\)}], "Input"] }, Open ]], Cell[CellGroupData[{ Cell["Check the Input 4.2", "Subsection"], Cell["\<\ We can now extract columns from the matrices to check that the \ solution we entered matches the solution achieved when solving by hand.\ \>", \ "Text"], Cell["\<\ For the case middle of the region, (1", "Text"], Cell[BoxData[{ \(\(j = 3;\)\), "\[IndentingNewLine]", \(\(i = 4;\)\)}], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(Asample = \(Transpose[ TakeRows[TakeRows[Astartwo, i], \(-1\)]]\)[\([j]\)]\)], "Input"], Cell[BoxData[ \({\(-\[Phi]y\)}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Bsample = \(Transpose[ TakeRows[TakeRows[Bstartwo, j], \(-1\)]]\)[\([i]\)]\)], "Input"], Cell[BoxData[ \({1 + 2\ \[Phi]y}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Csample = \(Transpose[ TakeRows[TakeRows[Cstartwo, j], \(-1\)]]\)[\([i]\)]\)], "Input"], Cell[BoxData[ \({\(-\[Phi]y\)}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Dsample = \(Transpose[ TakeRows[TakeRows[Dstartwo, j], \(-1\)]]\)[\([i]\)]\)], "Input"], Cell[BoxData[ \({q\ \[Zeta] + \[Phi]x\ \(Hold[Tfct]\)[2, 4] + \((1 - 2\ \[Phi]x)\)\ \(Hold[Tfct]\)[3, 4] + \[Phi]x\ \(Hold[Tfct]\)[4, 4]}\)], "Output"] }, Open ]], Cell["Which, when substituted, should match the equation", "Text"], Cell[TextData[Cell[BoxData[ \(TraditionalForm\`\(-\[Phi]y\)\ T\_\(i, j - 1, n + 1\) + \((2\ \[Phi]y + 1)\) T\_\(i, j, n + 1\) - \[Phi]y\ T\_\(i, j + 1, n + 1\) = \ \[Phi]x\ \(T\_\(i - 1, j\)\^*\) + \((1 - 2\ \[Phi]x)\) \(T\_\(i, j\)\^*\) + \[Phi]x\ T\_\(i + 1, j\) + \ \[Zeta]\ q\)]]], "Text", TextAlignment->Center], Cell["\<\ In this manner,all of the systems of equations can be \ verified.\ \>", "Text"] }, Open ]], Cell[CellGroupData[{ Cell["Assign Values to Constants 4.3", "Subsection"], Cell[BoxData[{ \(\(q = 0;\)\), "\[IndentingNewLine]", \(\(Troom = 100;\)\), "\[IndentingNewLine]", \(\(Tfct[x_?IntegerQ, y_?IntegerQ] = Hold[\(Tstar[\([x]\)]\)[\([y]\)]];\)\), "\[IndentingNewLine]", \(\(\[Phi]x = 1;\)\), "\[IndentingNewLine]", \(\(\[Phi]y = 1;\)\), "\[IndentingNewLine]", \(\(\[Delta]x = 1;\)\), "\[IndentingNewLine]", \(\(\[Delta]y = 1;\)\), "\[IndentingNewLine]", \(\(g = 200;\)\), "\[IndentingNewLine]", \(\(a = 100;\)\), "\[IndentingNewLine]", \(Tfinal = Array[zero, {Nx, Ny}]; zero[x_, y_] = 0;\)}], "Input"] }, Open ]], Cell[CellGroupData[{ Cell["Loop Over Entire Region 4.4", "Subsection"], Cell[BoxData[ \(Do[\[IndentingNewLine]Ainputtwo = TakeRows[ TakeRows[Astartwo, i], \(-1\)]; \[IndentingNewLine]Binputtwo = TakeRows[ TakeRows[Bstartwo, i], \(-1\)]; \[IndentingNewLine]Cinputtwo = TakeRows[ TakeRows[Cstartwo, i], \(-1\)]; \[IndentingNewLine]Dinputtwo = TakeRows[ TakeRows[ReleaseHold[ReleaseHold[Dstartwo]], i], \(-1\)]; \[IndentingNewLine]booftwo = TridiagonalSolve[Transpose[Ainputtwo], Transpose[Binputtwo], Transpose[Cinputtwo], Transpose[Dinputtwo]]; Tfinal = ReplacePart[Tfinal, \(Transpose[booftwo]\)[\([1]\)], i];\[IndentingNewLine], {i, 1, Nx}]\)], "Input"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Multiple Loops and Results 5", "Section"], Cell["\<\ Although the particular nature of the engineering problem \ designates the values used for the constants and the exact method which the \ ADI is employed, below is a brief example of using a loop to solve for the \ evolution of the temperature distribution with time. \ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\(Do[\[IndentingNewLine]Tfct[x_?IntegerQ, y_?IntegerQ] := \(Tfinal[\([\)\(x\)\(]\)]\)[\([y]\)]; \n Do[\[IndentingNewLine]Ainput = TakeColumns[ TakeColumns[Astar, j], \(-1\)]; \[IndentingNewLine]Binput = TakeColumns[ TakeColumns[Bstar, j], \(-1\)]; \[IndentingNewLine]Cinput = TakeColumns[ TakeColumns[Cstar, j], \(-1\)]; \[IndentingNewLine]Dinput = TakeColumns[ TakeColumns[ReleaseHold[Dstar], j], \(-1\)]; \[IndentingNewLine]boof = TridiagonalSolve[Ainput, Binput, Cinput, Dinput]; \[IndentingNewLine]Tstar = Transpose[ ReplacePart[ Transpose[Tstar], \(Transpose[boof]\)[\([\)\(1\)\(]\)], j]];\[IndentingNewLine], {j, 1, Ny}\[IndentingNewLine]]; \n Tfct[x_?IntegerQ, y_?IntegerQ] := \(Tstar[\([\)\(x\)\(]\)]\)[\([y]\)]; \n Do[\[IndentingNewLine]Ainputtwo = TakeRows[ TakeRows[Astartwo, i], \(-1\)]; \[IndentingNewLine]Binputtwo = TakeRows[ TakeRows[Bstartwo, i], \(-1\)]; \[IndentingNewLine]Cinputtwo = TakeRows[ TakeRows[Cstartwo, i], \(-1\)]; \[IndentingNewLine]Dinputtwo = TakeRows[ TakeRows[ReleaseHold[Dstartwo], i], \(-1\)]; \[IndentingNewLine]booftwo = TridiagonalSolve[Transpose[Ainputtwo], Transpose[Binputtwo], Transpose[Cinputtwo], Transpose[Dinputtwo]]; Tfinal = ReplacePart[Tfinal, \(Transpose[booftwo]\)[\([\)\(1\)\(]\)], i];\[IndentingNewLine], {i, 1, Nx}\[IndentingNewLine]]; \[IndentingNewLine]ListContourPlot[ Tfinal, PlotRange \[Rule] {0, 2}, Contours \[Rule] 10];\[IndentingNewLine], {temptime, 1, 10}\[IndentingNewLine]];\)\)], "Input"], Cell[CellGroupData[{ Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica 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.02265 .74529 L .02265 .72567 L .02265 .70604 L .02266 .68642 L .02266 .6668 L .02266 .64717 L .02266 .62755 L .02266 .60793 L .02266 .5883 L .02266 .56868 L .02266 .54906 L .02266 .52943 L .02266 .50981 L .02266 .49019 L .02266 .47057 L .02266 .45094 L .02266 .43132 L .02266 .4117 L .02266 .39207 L .02266 .37245 L .02266 .35283 L .02266 .3332 L .02266 .31358 L .02265 .29396 L .02265 .27433 L .02265 .25471 L .02265 .23509 L .02264 .21546 L .02262 .19584 L .02256 .17622 L .02245 .15659 L .02218 .13697 L .0216 .11735 L .02033 .09772 L .01923 .08729 L s .2 g .01923 .02228 m .02228 .01923 L .01923 .01923 L F 0 g .01923 .02228 m .02228 .01923 L s .2 g .01923 .97772 m .02228 .98077 L .01923 .98077 L F 0 g .01923 .97772 m .02228 .98077 L s .1 g .01923 .89596 m .01992 .88265 L .02051 .86303 L .02077 .84341 L .02089 .82378 L .02095 .80416 L .02097 .78454 L .02098 .76491 L .02098 .74529 L .02098 .72567 L .02099 .70604 L .02099 .68642 L .02099 .6668 L .02099 .64717 L .02099 .62755 L .02099 .60793 L .02099 .5883 L .02099 .56868 L .02099 .54906 L .02099 .52943 L .02099 .50981 L .02099 .49019 L .02099 .47057 L .02099 .45094 L .02099 .43132 L .02099 .4117 L .02099 .39207 L .02099 .37245 L .02099 .35283 L .02099 .3332 L .02099 .31358 L .02099 .29396 L .02098 .27433 L .02098 .25471 L .02098 .23509 L .02097 .21546 L .02095 .19584 L .02089 .17622 L .02077 .15659 L .02051 .13697 L .01992 .11735 L .01923 .10404 L F 0 g .01923 .89596 m .01992 .88265 L .02051 .86303 L .02077 .84341 L .02089 .82378 L .02095 .80416 L .02097 .78454 L .02098 .76491 L .02098 .74529 L .02098 .72567 L .02099 .70604 L .02099 .68642 L .02099 .6668 L .02099 .64717 L .02099 .62755 L .02099 .60793 L .02099 .5883 L .02099 .56868 L .02099 .54906 L .02099 .52943 L .02099 .50981 L .02099 .49019 L .02099 .47057 L .02099 .45094 L .02099 .43132 L .02099 .4117 L .02099 .39207 L .02099 .37245 L .02099 .35283 L .02099 .3332 L .02099 .31358 L .02099 .29396 L .02098 .27433 L .02098 .25471 L .02098 .23509 L .02097 .21546 L .02095 .19584 L .02089 .17622 L .02077 .15659 L .02051 .13697 L .01992 .11735 L .01923 .10404 L s .1 g .01923 .02061 m .02061 .01923 L .01923 .01923 L F 0 g .01923 .02061 m .02061 .01923 L s .1 g .01923 .97939 m .02061 .98077 L .01923 .98077 L F 0 g .01923 .97939 m .02061 .98077 L s .01923 .84784 m .01927 .84341 L .01939 .82378 L .01944 .80416 L .01946 .78454 L .01947 .76491 L .01948 .74529 L .01948 .72567 L .01948 .70604 L .01948 .68642 L .01948 .6668 L .01948 .64717 L .01948 .62755 L .01948 .60793 L .01948 .5883 L .01948 .56868 L .01948 .54906 L .01948 .52943 L .01948 .50981 L .01948 .49019 L .01948 .47057 L .01948 .45094 L .01948 .43132 L .01948 .4117 L .01948 .39207 L .01948 .37245 L .01948 .35283 L .01948 .3332 L .01948 .31358 L .01948 .29396 L .01948 .27433 L .01948 .25471 L .01947 .23509 L .01946 .21546 L .01944 .19584 L .01939 .17622 L .01927 .15659 L .01923 .15216 L F .01923 .84784 m .01927 .84341 L .01939 .82378 L .01944 .80416 L .01946 .78454 L .01947 .76491 L .01948 .74529 L .01948 .72567 L .01948 .70604 L .01948 .68642 L .01948 .6668 L .01948 .64717 L .01948 .62755 L .01948 .60793 L .01948 .5883 L .01948 .56868 L .01948 .54906 L .01948 .52943 L .01948 .50981 L .01948 .49019 L .01948 .47057 L .01948 .45094 L .01948 .43132 L .01948 .4117 L .01948 .39207 L .01948 .37245 L .01948 .35283 L .01948 .3332 L .01948 .31358 L .01948 .29396 L .01948 .27433 L .01948 .25471 L .01947 .23509 L .01946 .21546 L .01944 .19584 L .01939 .17622 L .01927 .15659 L .01923 .15216 L s .8 g .03885 .02015 m .05848 .02617 L .0781 .03213 L .09772 .0362 L .11211 .03885 L .09772 .04829 L .0781 .05394 L .06851 .05848 L .05848 .06851 L .05394 .0781 L .04829 .09772 L .03885 .11211 L .0362 .09772 L .03213 .0781 L .02617 .05848 L .02015 .03885 L F 0 g .03885 .02015 m .05848 .02617 L .0781 .03213 L .09772 .0362 L .11211 .03885 L .09772 .04829 L .0781 .05394 L .06851 .05848 L .05848 .06851 L .05394 .0781 L .04829 .09772 L .03885 .11211 L .0362 .09772 L .03213 .0781 L .02617 .05848 L .02015 .03885 L .03885 .02015 L s .8 g .03885 .88789 m .04829 .90228 L .05394 .9219 L .05848 .93149 L .06851 .94152 L .0781 .94606 L .09772 .95171 L .11211 .96115 L .09772 .9638 L .0781 .96787 L .05848 .97383 L .03885 .97985 L .02015 .96115 L .02617 .94152 L .03213 .9219 L .0362 .90228 L F 0 g .03885 .88789 m .04829 .90228 L .05394 .9219 L .05848 .93149 L .06851 .94152 L .0781 .94606 L .09772 .95171 L .11211 .96115 L .09772 .9638 L .0781 .96787 L .05848 .97383 L .03885 .97985 L .02015 .96115 L .02617 .94152 L .03213 .9219 L .0362 .90228 L .03885 .88789 L s .9 g .03885 .02591 m .05848 .03257 L .06943 .03885 L .05848 .05326 L .05326 .05848 L .03885 .06943 L .03257 .05848 L .02591 .03885 L F 0 g .03885 .02591 m .05848 .03257 L .06943 .03885 L .05848 .05326 L .05326 .05848 L .03885 .06943 L .03257 .05848 L .02591 .03885 L .03885 .02591 L s .9 g .03885 .93057 m .05326 .94152 L .05848 .94674 L .06943 .96115 L .05848 .96743 L .03885 .97409 L .02591 .96115 L .03257 .94152 L F 0 g .03885 .93057 m .05326 .94152 L .05848 .94674 L .06943 .96115 L .05848 .96743 L .03885 .97409 L .02591 .96115 L .03257 .94152 L .03885 .93057 L s .6 g .09772 .05669 m .11735 .05421 L .13697 .05306 L .15659 .05253 L .17622 .05229 L .19584 .05219 L .21546 .05214 L .23509 .05212 L .25471 .05212 L .27433 .05211 L .29396 .05211 L .31358 .05211 L .3332 .05211 L .35283 .05211 L .37245 .05211 L .39207 .05211 L .4117 .05211 L .43132 .05211 L .45094 .05211 L .47057 .05211 L .49019 .05211 L .50981 .05211 L .52943 .05211 L .54906 .05211 L .56868 .05211 L .5883 .05211 L .60793 .05211 L .62755 .05211 L .64717 .05211 L .6668 .05211 L .68642 .05211 L .70604 .05211 L .72567 .05211 L .74529 .05212 L .76491 .05212 L .78454 .05214 L .80416 .05219 L .82378 .05229 L .84341 .05253 L .86303 .05306 L .88265 .05421 L .90228 .05669 L .91109 .05848 L .9219 .06408 L .93592 .0781 L .94152 .08891 L .94331 .09772 L .94579 .11735 L .94694 .13697 L .94747 .15659 L .94771 .17622 L .94781 .19584 L .94786 .21546 L .94788 .23509 L .94788 .25471 L .94789 .27433 L .94789 .29396 L .94789 .31358 L .94789 .3332 L .94789 .35283 L .94789 .37245 L .94789 .39207 L .94789 .4117 L .94789 .43132 L .94789 .45094 L .94789 .47057 L .94789 .49019 L .94789 .50981 L .94789 .52943 L .94789 .54906 L .94789 .56868 L .94789 .5883 L .94789 .60793 L .94789 .62755 L .94789 .64717 L .94789 .6668 L .94789 .68642 L .94789 .70604 L .94789 .72567 L .94788 .74529 L .94788 .76491 L .94786 .78454 L .94781 .80416 L .94771 .82378 L .94747 .84341 L .94694 .86303 L .94579 .88265 L .94331 .90228 L .94152 .91109 L .93592 .9219 L .9219 .93592 L .91109 .94152 L .90228 .94331 L .88265 .94579 L .86303 .94694 L .84341 .94747 L .82378 .94771 L .80416 .94781 L .78454 .94786 L .76491 .94788 L .74529 .94788 L .72567 .94789 L .70604 .94789 L .68642 .94789 L .6668 .94789 L .64717 .94789 L .62755 .94789 L .60793 .94789 L .5883 .94789 L .56868 .94789 L .54906 .94789 L .52943 .94789 L .50981 .94789 L .49019 .94789 L .47057 .94789 L .45094 .94789 L .43132 .94789 L .4117 .94789 L .39207 .94789 L .37245 .94789 L .35283 .94789 L .3332 .94789 L .31358 .94789 L .29396 .94789 L .27433 .94789 L .25471 .94788 L .23509 .94788 L .21546 .94786 L .19584 .94781 L .17622 .94771 L .15659 .94747 L .13697 .94694 L .11735 .94579 L .09772 .94331 L .08891 .94152 L .0781 .93592 L .06408 .9219 L .05848 .91109 L .05669 .90228 L .05421 .88265 L .05306 .86303 L .05253 .84341 L .05229 .82378 L .05219 .80416 L .05214 .78454 L .05212 .76491 L .05212 .74529 L .05211 .72567 L .05211 .70604 L .05211 .68642 L .05211 .6668 L .05211 .64717 L .05211 .62755 L .05211 .60793 L .05211 .5883 L .05211 .56868 L .05211 .54906 L .05211 .52943 L .05211 .50981 L .05211 .49019 L .05211 .47057 L .05211 .45094 L .05211 .43132 L .05211 .4117 L .05211 .39207 L .05211 .37245 L .05211 .35283 L .05211 .3332 L .05211 .31358 L .05211 .29396 L .05211 .27433 L .05212 .25471 L .05212 .23509 L .05214 .21546 L .05219 .19584 L .05229 .17622 L .05253 .15659 L .05306 .13697 L .05421 .11735 L .05669 .09772 L .05848 .08891 L .06408 .0781 L .0781 .06408 L .08891 .05848 L F 0 g .09772 .05669 m .11735 .05421 L .13697 .05306 L .15659 .05253 L .17622 .05229 L .19584 .05219 L .21546 .05214 L .23509 .05212 L .25471 .05212 L .27433 .05211 L .29396 .05211 L .31358 .05211 L .3332 .05211 L .35283 .05211 L .37245 .05211 L .39207 .05211 L .4117 .05211 L .43132 .05211 L .45094 .05211 L .47057 .05211 L .49019 .05211 L .50981 .05211 L .52943 .05211 L .54906 .05211 L .56868 .05211 L .5883 .05211 L .60793 .05211 L .62755 .05211 L .64717 .05211 L .6668 .05211 L .68642 .05211 L .70604 .05211 L .72567 .05211 L .74529 .05212 L .76491 .05212 L .78454 .05214 L .80416 .05219 L .82378 .05229 L .84341 .05253 L .86303 .05306 L .88265 .05421 L .90228 .05669 L .91109 .05848 L .9219 .06408 L .93592 .0781 L .94152 .08891 L .94331 .09772 L .94579 .11735 L .94694 .13697 L .94747 .15659 L Mistroke .94771 .17622 L .94781 .19584 L .94786 .21546 L .94788 .23509 L .94788 .25471 L .94789 .27433 L .94789 .29396 L .94789 .31358 L .94789 .3332 L .94789 .35283 L .94789 .37245 L .94789 .39207 L .94789 .4117 L .94789 .43132 L .94789 .45094 L .94789 .47057 L .94789 .49019 L .94789 .50981 L .94789 .52943 L .94789 .54906 L .94789 .56868 L .94789 .5883 L .94789 .60793 L .94789 .62755 L .94789 .64717 L .94789 .6668 L .94789 .68642 L .94789 .70604 L .94789 .72567 L .94788 .74529 L .94788 .76491 L .94786 .78454 L .94781 .80416 L .94771 .82378 L .94747 .84341 L .94694 .86303 L .94579 .88265 L .94331 .90228 L .94152 .91109 L .93592 .9219 L .9219 .93592 L .91109 .94152 L .90228 .94331 L .88265 .94579 L .86303 .94694 L .84341 .94747 L .82378 .94771 L .80416 .94781 L .78454 .94786 L .76491 .94788 L Mistroke .74529 .94788 L .72567 .94789 L .70604 .94789 L .68642 .94789 L .6668 .94789 L .64717 .94789 L .62755 .94789 L .60793 .94789 L .5883 .94789 L .56868 .94789 L .54906 .94789 L .52943 .94789 L .50981 .94789 L .49019 .94789 L .47057 .94789 L .45094 .94789 L .43132 .94789 L .4117 .94789 L .39207 .94789 L .37245 .94789 L .35283 .94789 L .3332 .94789 L .31358 .94789 L .29396 .94789 L .27433 .94789 L .25471 .94788 L .23509 .94788 L .21546 .94786 L .19584 .94781 L .17622 .94771 L .15659 .94747 L .13697 .94694 L .11735 .94579 L .09772 .94331 L .08891 .94152 L .0781 .93592 L .06408 .9219 L .05848 .91109 L .05669 .90228 L .05421 .88265 L .05306 .86303 L .05253 .84341 L .05229 .82378 L .05219 .80416 L .05214 .78454 L .05212 .76491 L .05212 .74529 L .05211 .72567 L .05211 .70604 L .05211 .68642 L Mistroke .05211 .6668 L .05211 .64717 L .05211 .62755 L .05211 .60793 L .05211 .5883 L .05211 .56868 L .05211 .54906 L .05211 .52943 L .05211 .50981 L .05211 .49019 L .05211 .47057 L .05211 .45094 L .05211 .43132 L .05211 .4117 L .05211 .39207 L .05211 .37245 L .05211 .35283 L .05211 .3332 L .05211 .31358 L .05211 .29396 L .05211 .27433 L .05212 .25471 L .05212 .23509 L .05214 .21546 L .05219 .19584 L .05229 .17622 L .05253 .15659 L .05306 .13697 L .05421 .11735 L .05669 .09772 L .05848 .08891 L .06408 .0781 L .0781 .06408 L .08891 .05848 L .09772 .05669 L Mfstroke .6 g .94714 .98077 m .94152 .97792 L .9219 .97246 L .90228 .96955 L .88265 .96804 L .86303 .96729 L .84341 .96693 L .82378 .96677 L .80416 .9667 L .78454 .96667 L .76491 .96665 L .74529 .96665 L .72567 .96665 L .70604 .96665 L .68642 .96664 L .6668 .96664 L .64717 .96664 L .62755 .96664 L .60793 .96664 L .5883 .96664 L .56868 .96664 L .54906 .96664 L .52943 .96664 L .50981 .96664 L .49019 .96664 L .47057 .96664 L .45094 .96664 L .43132 .96664 L .4117 .96664 L .39207 .96664 L .37245 .96664 L .35283 .96664 L .3332 .96664 L .31358 .96664 L .29396 .96665 L .27433 .96665 L .25471 .96665 L .23509 .96665 L .21546 .96667 L .19584 .9667 L .17622 .96677 L .15659 .96693 L .13697 .96729 L .11735 .96804 L .09772 .96955 L .0781 .97246 L .05848 .97792 L .05286 .98077 L F 0 g .94714 .98077 m .94152 .97792 L .9219 .97246 L .90228 .96955 L .88265 .96804 L .86303 .96729 L .84341 .96693 L .82378 .96677 L .80416 .9667 L .78454 .96667 L .76491 .96665 L .74529 .96665 L .72567 .96665 L .70604 .96665 L .68642 .96664 L .6668 .96664 L .64717 .96664 L .62755 .96664 L .60793 .96664 L .5883 .96664 L .56868 .96664 L .54906 .96664 L .52943 .96664 L .50981 .96664 L .49019 .96664 L .47057 .96664 L .45094 .96664 L .43132 .96664 L .4117 .96664 L .39207 .96664 L .37245 .96664 L .35283 .96664 L .3332 .96664 L .31358 .96664 L .29396 .96665 L .27433 .96665 L .25471 .96665 L .23509 .96665 L .21546 .96667 L .19584 .9667 L .17622 .96677 L .15659 .96693 L .13697 .96729 L .11735 .96804 L .09772 .96955 L .0781 .97246 L .05848 .97792 L .05286 .98077 L s .6 g .94714 .01923 m .94152 .02208 L .9219 .02754 L .90228 .03045 L .88265 .03196 L .86303 .03271 L .84341 .03307 L .82378 .03323 L .80416 .0333 L .78454 .03333 L .76491 .03335 L .74529 .03335 L .72567 .03335 L .70604 .03335 L .68642 .03336 L .6668 .03336 L .64717 .03336 L .62755 .03336 L .60793 .03336 L .5883 .03336 L .56868 .03336 L .54906 .03336 L .52943 .03336 L .50981 .03336 L .49019 .03336 L .47057 .03336 L .45094 .03336 L .43132 .03336 L .4117 .03336 L .39207 .03336 L .37245 .03336 L .35283 .03336 L .3332 .03336 L .31358 .03336 L .29396 .03335 L .27433 .03335 L .25471 .03335 L .23509 .03335 L .21546 .03333 L .19584 .0333 L .17622 .03323 L .15659 .03307 L .13697 .03271 L .11735 .03196 L .09772 .03045 L .0781 .02754 L .05848 .02208 L .05286 .01923 L F 0 g .94714 .01923 m .94152 .02208 L .9219 .02754 L .90228 .03045 L .88265 .03196 L .86303 .03271 L .84341 .03307 L .82378 .03323 L .80416 .0333 L .78454 .03333 L .76491 .03335 L .74529 .03335 L .72567 .03335 L .70604 .03335 L .68642 .03336 L .6668 .03336 L .64717 .03336 L .62755 .03336 L .60793 .03336 L .5883 .03336 L .56868 .03336 L .54906 .03336 L .52943 .03336 L .50981 .03336 L .49019 .03336 L .47057 .03336 L .45094 .03336 L .43132 .03336 L .4117 .03336 L .39207 .03336 L .37245 .03336 L .35283 .03336 L .3332 .03336 L .31358 .03336 L .29396 .03335 L .27433 .03335 L .25471 .03335 L .23509 .03335 L .21546 .03333 L .19584 .0333 L .17622 .03323 L .15659 .03307 L .13697 .03271 L .11735 .03196 L .09772 .03045 L .0781 .02754 L .05848 .02208 L .05286 .01923 L s .5 g .19584 .05847 m .21546 .05842 L .23509 .0584 L .25471 .05839 L .27433 .05839 L .29396 .05839 L .31358 .05839 L .3332 .05839 L .35283 .05839 L .37245 .05839 L .39207 .05839 L .4117 .05839 L .43132 .05839 L .45094 .05839 L .47057 .05839 L .49019 .05839 L .50981 .05839 L .52943 .05839 L .54906 .05839 L .56868 .05839 L .5883 .05839 L .60793 .05839 L .62755 .05839 L .64717 .05839 L .6668 .05839 L .68642 .05839 L .70604 .05839 L .72567 .05839 L .74529 .05839 L .76491 .0584 L .78454 .05842 L .80416 .05847 L .80741 .05848 L .82378 .05862 L .84341 .05899 L .86303 .05981 L .88265 .06163 L .90228 .06565 L .9219 .0759 L .9241 .0781 L .93435 .09772 L .93837 .11735 L .94019 .13697 L .94101 .15659 L .94138 .17622 L .94152 .19259 L .94153 .19584 L .94158 .21546 L .9416 .23509 L .94161 .25471 L .94161 .27433 L .94161 .29396 L .94161 .31358 L .94161 .3332 L .94161 .35283 L .94161 .37245 L .94161 .39207 L .94161 .4117 L .94161 .43132 L .94161 .45094 L .94161 .47057 L .94161 .49019 L .94161 .50981 L .94161 .52943 L .94161 .54906 L .94161 .56868 L .94161 .5883 L .94161 .60793 L .94161 .62755 L .94161 .64717 L .94161 .6668 L .94161 .68642 L .94161 .70604 L .94161 .72567 L .94161 .74529 L .9416 .76491 L .94158 .78454 L .94153 .80416 L .94152 .80741 L .94138 .82378 L .94101 .84341 L .94019 .86303 L .93837 .88265 L .93435 .90228 L .9241 .9219 L .9219 .9241 L .90228 .93435 L .88265 .93837 L .86303 .94019 L .84341 .94101 L .82378 .94138 L .80741 .94152 L .80416 .94153 L .78454 .94158 L .76491 .9416 L .74529 .94161 L .72567 .94161 L .70604 .94161 L .68642 .94161 L .6668 .94161 L .64717 .94161 L .62755 .94161 L .60793 .94161 L .5883 .94161 L .56868 .94161 L .54906 .94161 L .52943 .94161 L .50981 .94161 L .49019 .94161 L .47057 .94161 L .45094 .94161 L .43132 .94161 L .4117 .94161 L .39207 .94161 L .37245 .94161 L .35283 .94161 L .3332 .94161 L .31358 .94161 L .29396 .94161 L .27433 .94161 L .25471 .94161 L .23509 .9416 L .21546 .94158 L .19584 .94153 L .19259 .94152 L .17622 .94138 L .15659 .94101 L .13697 .94019 L .11735 .93837 L .09772 .93435 L .0781 .9241 L .0759 .9219 L .06565 .90228 L .06163 .88265 L .05981 .86303 L .05899 .84341 L .05862 .82378 L .05848 .80741 L .05847 .80416 L .05842 .78454 L .0584 .76491 L .05839 .74529 L .05839 .72567 L .05839 .70604 L .05839 .68642 L .05839 .6668 L .05839 .64717 L .05839 .62755 L .05839 .60793 L .05839 .5883 L .05839 .56868 L .05839 .54906 L .05839 .52943 L .05839 .50981 L .05839 .49019 L .05839 .47057 L .05839 .45094 L .05839 .43132 L .05839 .4117 L .05839 .39207 L .05839 .37245 L .05839 .35283 L .05839 .3332 L .05839 .31358 L .05839 .29396 L .05839 .27433 L .05839 .25471 L .0584 .23509 L .05842 .21546 L .05847 .19584 L .05848 .19259 L .05862 .17622 L .05899 .15659 L .05981 .13697 L .06163 .11735 L .06565 .09772 L .0759 .0781 L .0781 .0759 L .09772 .06565 L .11735 .06163 L .13697 .05981 L .15659 .05899 L .17622 .05862 L .19259 .05848 L F 0 g .19584 .05847 m .21546 .05842 L .23509 .0584 L .25471 .05839 L .27433 .05839 L .29396 .05839 L .31358 .05839 L .3332 .05839 L .35283 .05839 L .37245 .05839 L .39207 .05839 L .4117 .05839 L .43132 .05839 L .45094 .05839 L .47057 .05839 L .49019 .05839 L .50981 .05839 L .52943 .05839 L .54906 .05839 L .56868 .05839 L .5883 .05839 L .60793 .05839 L .62755 .05839 L .64717 .05839 L .6668 .05839 L .68642 .05839 L .70604 .05839 L .72567 .05839 L .74529 .05839 L .76491 .0584 L .78454 .05842 L .80416 .05847 L .80741 .05848 L .82378 .05862 L .84341 .05899 L .86303 .05981 L .88265 .06163 L .90228 .06565 L .9219 .0759 L .9241 .0781 L .93435 .09772 L .93837 .11735 L .94019 .13697 L .94101 .15659 L .94138 .17622 L .94152 .19259 L .94153 .19584 L .94158 .21546 L .9416 .23509 L .94161 .25471 L Mistroke .94161 .27433 L .94161 .29396 L .94161 .31358 L .94161 .3332 L .94161 .35283 L .94161 .37245 L .94161 .39207 L .94161 .4117 L .94161 .43132 L .94161 .45094 L .94161 .47057 L .94161 .49019 L .94161 .50981 L .94161 .52943 L .94161 .54906 L .94161 .56868 L .94161 .5883 L .94161 .60793 L .94161 .62755 L .94161 .64717 L .94161 .6668 L .94161 .68642 L .94161 .70604 L .94161 .72567 L .94161 .74529 L .9416 .76491 L .94158 .78454 L .94153 .80416 L .94152 .80741 L .94138 .82378 L .94101 .84341 L .94019 .86303 L .93837 .88265 L .93435 .90228 L .9241 .9219 L .9219 .9241 L .90228 .93435 L .88265 .93837 L .86303 .94019 L .84341 .94101 L .82378 .94138 L .80741 .94152 L .80416 .94153 L .78454 .94158 L .76491 .9416 L .74529 .94161 L .72567 .94161 L .70604 .94161 L .68642 .94161 L .6668 .94161 L Mistroke .64717 .94161 L .62755 .94161 L .60793 .94161 L .5883 .94161 L .56868 .94161 L .54906 .94161 L .52943 .94161 L .50981 .94161 L .49019 .94161 L .47057 .94161 L .45094 .94161 L .43132 .94161 L .4117 .94161 L .39207 .94161 L .37245 .94161 L .35283 .94161 L .3332 .94161 L .31358 .94161 L .29396 .94161 L .27433 .94161 L .25471 .94161 L .23509 .9416 L .21546 .94158 L .19584 .94153 L .19259 .94152 L .17622 .94138 L .15659 .94101 L .13697 .94019 L .11735 .93837 L .09772 .93435 L .0781 .9241 L .0759 .9219 L .06565 .90228 L .06163 .88265 L .05981 .86303 L .05899 .84341 L .05862 .82378 L .05848 .80741 L .05847 .80416 L .05842 .78454 L .0584 .76491 L .05839 .74529 L .05839 .72567 L .05839 .70604 L .05839 .68642 L .05839 .6668 L .05839 .64717 L .05839 .62755 L .05839 .60793 L .05839 .5883 L Mistroke .05839 .56868 L .05839 .54906 L .05839 .52943 L .05839 .50981 L .05839 .49019 L .05839 .47057 L .05839 .45094 L .05839 .43132 L .05839 .4117 L .05839 .39207 L .05839 .37245 L .05839 .35283 L .05839 .3332 L .05839 .31358 L .05839 .29396 L .05839 .27433 L .05839 .25471 L .0584 .23509 L .05842 .21546 L .05847 .19584 L .05848 .19259 L .05862 .17622 L .05899 .15659 L .05981 .13697 L .06163 .11735 L .06565 .09772 L .0759 .0781 L .0781 .0759 L .09772 .06565 L .11735 .06163 L .13697 .05981 L .15659 .05899 L .17622 .05862 L .19259 .05848 L .19584 .05847 L Mfstroke .5 g .94049 .98077 m .9219 .97568 L .90228 .97297 L .88265 .97165 L .86303 .97102 L .84341 .97073 L .82378 .9706 L .80416 .97054 L .78454 .97052 L .76491 .97051 L .74529 .9705 L .72567 .9705 L .70604 .9705 L .68642 .9705 L .6668 .9705 L .64717 .9705 L .62755 .9705 L .60793 .9705 L .5883 .9705 L .56868 .9705 L .54906 .9705 L .52943 .9705 L .50981 .9705 L .49019 .9705 L .47057 .9705 L .45094 .9705 L .43132 .9705 L .4117 .9705 L .39207 .9705 L .37245 .9705 L .35283 .9705 L .3332 .9705 L .31358 .9705 L .29396 .9705 L .27433 .9705 L .25471 .9705 L .23509 .97051 L .21546 .97052 L .19584 .97054 L .17622 .9706 L .15659 .97073 L .13697 .97102 L .11735 .97165 L .09772 .97297 L .0781 .97568 L .05951 .98077 L F 0 g .94049 .98077 m .9219 .97568 L .90228 .97297 L .88265 .97165 L .86303 .97102 L .84341 .97073 L .82378 .9706 L .80416 .97054 L .78454 .97052 L .76491 .97051 L .74529 .9705 L .72567 .9705 L .70604 .9705 L .68642 .9705 L .6668 .9705 L .64717 .9705 L .62755 .9705 L .60793 .9705 L .5883 .9705 L .56868 .9705 L .54906 .9705 L .52943 .9705 L .50981 .9705 L .49019 .9705 L .47057 .9705 L .45094 .9705 L .43132 .9705 L .4117 .9705 L .39207 .9705 L .37245 .9705 L .35283 .9705 L .3332 .9705 L .31358 .9705 L .29396 .9705 L .27433 .9705 L .25471 .9705 L .23509 .97051 L .21546 .97052 L .19584 .97054 L .17622 .9706 L .15659 .97073 L .13697 .97102 L .11735 .97165 L .09772 .97297 L .0781 .97568 L .05951 .98077 L s .5 g .94049 .01923 m .9219 .02432 L .90228 .02703 L .88265 .02835 L .86303 .02898 L .84341 .02927 L .82378 .0294 L .80416 .02946 L .78454 .02948 L .76491 .02949 L .74529 .0295 L .72567 .0295 L .70604 .0295 L .68642 .0295 L .6668 .0295 L .64717 .0295 L .62755 .0295 L .60793 .0295 L .5883 .0295 L .56868 .0295 L .54906 .0295 L .52943 .0295 L .50981 .0295 L .49019 .0295 L .47057 .0295 L .45094 .0295 L .43132 .0295 L .4117 .0295 L .39207 .0295 L .37245 .0295 L .35283 .0295 L .3332 .0295 L .31358 .0295 L .29396 .0295 L .27433 .0295 L .25471 .0295 L .23509 .02949 L .21546 .02948 L .19584 .02946 L .17622 .0294 L .15659 .02927 L .13697 .02898 L .11735 .02835 L .09772 .02703 L .0781 .02432 L .05951 .01923 L F 0 g .94049 .01923 m .9219 .02432 L .90228 .02703 L .88265 .02835 L .86303 .02898 L .84341 .02927 L .82378 .0294 L .80416 .02946 L .78454 .02948 L .76491 .02949 L .74529 .0295 L .72567 .0295 L .70604 .0295 L .68642 .0295 L .6668 .0295 L .64717 .0295 L .62755 .0295 L .60793 .0295 L .5883 .0295 L .56868 .0295 L .54906 .0295 L .52943 .0295 L .50981 .0295 L .49019 .0295 L .47057 .0295 L .45094 .0295 L .43132 .0295 L .4117 .0295 L .39207 .0295 L .37245 .0295 L .35283 .0295 L .3332 .0295 L .31358 .0295 L .29396 .0295 L .27433 .0295 L .25471 .0295 L .23509 .02949 L .21546 .02948 L .19584 .02946 L .17622 .0294 L .15659 .02927 L .13697 .02898 L .11735 .02835 L .09772 .02703 L .0781 .02432 L .05951 .01923 L s .4 g .09772 .07547 m .11735 .07026 L .13697 .06815 L .15659 .06723 L .17622 .06683 L .19584 .06665 L .21546 .06658 L .23509 .06654 L .25471 .06653 L .27433 .06652 L .29396 .06652 L .31358 .06652 L .3332 .06652 L .35283 .06652 L .37245 .06652 L .39207 .06652 L .4117 .06652 L .43132 .06652 L .45094 .06652 L .47057 .06652 L .49019 .06652 L .50981 .06652 L .52943 .06652 L .54906 .06652 L .56868 .06652 L .5883 .06652 L .60793 .06652 L .62755 .06652 L .64717 .06652 L .6668 .06652 L .68642 .06652 L .70604 .06652 L .72567 .06652 L .74529 .06653 L .76491 .06654 L .78454 .06658 L .80416 .06665 L .82378 .06683 L .84341 .06723 L .86303 .06815 L .88265 .07026 L .90228 .07547 L .90805 .0781 L .9219 .09195 L .92453 .09772 L .92974 .11735 L .93185 .13697 L .93277 .15659 L .93317 .17622 L .93335 .19584 L .93342 .21546 L .93346 .23509 L .93347 .25471 L .93348 .27433 L .93348 .29396 L .93348 .31358 L .93348 .3332 L .93348 .35283 L .93348 .37245 L .93348 .39207 L .93348 .4117 L .93348 .43132 L .93348 .45094 L .93348 .47057 L .93348 .49019 L .93348 .50981 L .93348 .52943 L .93348 .54906 L .93348 .56868 L .93348 .5883 L .93348 .60793 L .93348 .62755 L .93348 .64717 L .93348 .6668 L .93348 .68642 L .93348 .70604 L .93348 .72567 L .93347 .74529 L .93346 .76491 L .93342 .78454 L .93335 .80416 L .93317 .82378 L .93277 .84341 L .93185 .86303 L .92974 .88265 L .92453 .90228 L .9219 .90805 L .90805 .9219 L .90228 .92453 L .88265 .92974 L .86303 .93185 L .84341 .93277 L .82378 .93317 L .80416 .93335 L .78454 .93342 L .76491 .93346 L .74529 .93347 L .72567 .93348 L .70604 .93348 L .68642 .93348 L .6668 .93348 L .64717 .93348 L .62755 .93348 L .60793 .93348 L .5883 .93348 L .56868 .93348 L .54906 .93348 L .52943 .93348 L .50981 .93348 L .49019 .93348 L .47057 .93348 L .45094 .93348 L .43132 .93348 L .4117 .93348 L .39207 .93348 L .37245 .93348 L .35283 .93348 L .3332 .93348 L .31358 .93348 L .29396 .93348 L .27433 .93348 L .25471 .93347 L .23509 .93346 L .21546 .93342 L .19584 .93335 L .17622 .93317 L .15659 .93277 L .13697 .93185 L .11735 .92974 L .09772 .92453 L .09195 .9219 L .0781 .90805 L .07547 .90228 L .07026 .88265 L .06815 .86303 L .06723 .84341 L .06683 .82378 L .06665 .80416 L .06658 .78454 L .06654 .76491 L .06653 .74529 L .06652 .72567 L .06652 .70604 L .06652 .68642 L .06652 .6668 L .06652 .64717 L .06652 .62755 L .06652 .60793 L .06652 .5883 L .06652 .56868 L .06652 .54906 L .06652 .52943 L .06652 .50981 L .06652 .49019 L .06652 .47057 L .06652 .45094 L .06652 .43132 L .06652 .4117 L .06652 .39207 L .06652 .37245 L .06652 .35283 L .06652 .3332 L .06652 .31358 L .06652 .29396 L .06652 .27433 L .06653 .25471 L .06654 .23509 L .06658 .21546 L .06665 .19584 L .06683 .17622 L .06723 .15659 L .06815 .13697 L .07026 .11735 L .07547 .09772 L .0781 .09195 L .09195 .0781 L F 0 g .09772 .07547 m .11735 .07026 L .13697 .06815 L .15659 .06723 L .17622 .06683 L .19584 .06665 L .21546 .06658 L .23509 .06654 L .25471 .06653 L .27433 .06652 L .29396 .06652 L .31358 .06652 L .3332 .06652 L .35283 .06652 L .37245 .06652 L .39207 .06652 L .4117 .06652 L .43132 .06652 L .45094 .06652 L .47057 .06652 L .49019 .06652 L .50981 .06652 L .52943 .06652 L .54906 .06652 L .56868 .06652 L .5883 .06652 L .60793 .06652 L .62755 .06652 L .64717 .06652 L .6668 .06652 L .68642 .06652 L .70604 .06652 L .72567 .06652 L .74529 .06653 L .76491 .06654 L .78454 .06658 L .80416 .06665 L .82378 .06683 L .84341 .06723 L .86303 .06815 L .88265 .07026 L .90228 .07547 L .90805 .0781 L .9219 .09195 L .92453 .09772 L .92974 .11735 L .93185 .13697 L .93277 .15659 L .93317 .17622 L .93335 .19584 L Mistroke .93342 .21546 L .93346 .23509 L .93347 .25471 L .93348 .27433 L .93348 .29396 L .93348 .31358 L .93348 .3332 L .93348 .35283 L .93348 .37245 L .93348 .39207 L .93348 .4117 L .93348 .43132 L .93348 .45094 L .93348 .47057 L .93348 .49019 L .93348 .50981 L .93348 .52943 L .93348 .54906 L .93348 .56868 L .93348 .5883 L .93348 .60793 L .93348 .62755 L .93348 .64717 L .93348 .6668 L .93348 .68642 L .93348 .70604 L .93348 .72567 L .93347 .74529 L .93346 .76491 L .93342 .78454 L .93335 .80416 L .93317 .82378 L .93277 .84341 L .93185 .86303 L .92974 .88265 L .92453 .90228 L .9219 .90805 L .90805 .9219 L .90228 .92453 L .88265 .92974 L .86303 .93185 L .84341 .93277 L .82378 .93317 L .80416 .93335 L .78454 .93342 L .76491 .93346 L .74529 .93347 L .72567 .93348 L .70604 .93348 L .68642 .93348 L Mistroke .6668 .93348 L .64717 .93348 L .62755 .93348 L .60793 .93348 L .5883 .93348 L .56868 .93348 L .54906 .93348 L .52943 .93348 L .50981 .93348 L .49019 .93348 L .47057 .93348 L .45094 .93348 L .43132 .93348 L .4117 .93348 L .39207 .93348 L .37245 .93348 L .35283 .93348 L .3332 .93348 L .31358 .93348 L .29396 .93348 L .27433 .93348 L .25471 .93347 L .23509 .93346 L .21546 .93342 L .19584 .93335 L .17622 .93317 L .15659 .93277 L .13697 .93185 L .11735 .92974 L .09772 .92453 L .09195 .9219 L .0781 .90805 L .07547 .90228 L .07026 .88265 L .06815 .86303 L .06723 .84341 L .06683 .82378 L .06665 .80416 L .06658 .78454 L .06654 .76491 L .06653 .74529 L .06652 .72567 L .06652 .70604 L .06652 .68642 L .06652 .6668 L .06652 .64717 L .06652 .62755 L .06652 .60793 L .06652 .5883 L .06652 .56868 L Mistroke .06652 .54906 L .06652 .52943 L .06652 .50981 L .06652 .49019 L .06652 .47057 L .06652 .45094 L .06652 .43132 L .06652 .4117 L .06652 .39207 L .06652 .37245 L .06652 .35283 L .06652 .3332 L .06652 .31358 L .06652 .29396 L .06652 .27433 L .06653 .25471 L .06654 .23509 L .06658 .21546 L .06665 .19584 L .06683 .17622 L .06723 .15659 L .06815 .13697 L .07026 .11735 L .07547 .09772 L .0781 .09195 L .09195 .0781 L .09772 .07547 L Mfstroke .4 g .9322 .98077 m .9219 .97827 L .90228 .97559 L .88265 .97432 L .86303 .97373 L .84341 .97345 L .82378 .97333 L .80416 .97328 L .78454 .97326 L .76491 .97325 L .74529 .97324 L .72567 .97324 L .70604 .97324 L .68642 .97324 L .6668 .97324 L .64717 .97324 L .62755 .97324 L .60793 .97324 L .5883 .97324 L .56868 .97324 L .54906 .97324 L .52943 .97324 L .50981 .97324 L .49019 .97324 L .47057 .97324 L .45094 .97324 L .43132 .97324 L .4117 .97324 L .39207 .97324 L .37245 .97324 L .35283 .97324 L .3332 .97324 L .31358 .97324 L .29396 .97324 L .27433 .97324 L .25471 .97324 L .23509 .97325 L .21546 .97326 L .19584 .97328 L .17622 .97333 L .15659 .97345 L .13697 .97373 L .11735 .97432 L .09772 .97559 L .0781 .97827 L .0678 .98077 L F 0 g .9322 .98077 m .9219 .97827 L .90228 .97559 L .88265 .97432 L .86303 .97373 L .84341 .97345 L .82378 .97333 L .80416 .97328 L .78454 .97326 L .76491 .97325 L .74529 .97324 L .72567 .97324 L .70604 .97324 L .68642 .97324 L .6668 .97324 L .64717 .97324 L .62755 .97324 L .60793 .97324 L .5883 .97324 L .56868 .97324 L .54906 .97324 L .52943 .97324 L .50981 .97324 L .49019 .97324 L .47057 .97324 L .45094 .97324 L .43132 .97324 L .4117 .97324 L .39207 .97324 L .37245 .97324 L .35283 .97324 L .3332 .97324 L .31358 .97324 L .29396 .97324 L .27433 .97324 L .25471 .97324 L .23509 .97325 L .21546 .97326 L .19584 .97328 L .17622 .97333 L .15659 .97345 L .13697 .97373 L .11735 .97432 L .09772 .97559 L .0781 .97827 L .0678 .98077 L s .4 g .9322 .01923 m .9219 .02173 L .90228 .02441 L .88265 .02568 L .86303 .02627 L .84341 .02655 L .82378 .02667 L .80416 .02672 L .78454 .02674 L .76491 .02675 L .74529 .02676 L .72567 .02676 L .70604 .02676 L .68642 .02676 L .6668 .02676 L .64717 .02676 L .62755 .02676 L .60793 .02676 L .5883 .02676 L .56868 .02676 L .54906 .02676 L .52943 .02676 L .50981 .02676 L .49019 .02676 L .47057 .02676 L .45094 .02676 L .43132 .02676 L .4117 .02676 L .39207 .02676 L .37245 .02676 L .35283 .02676 L .3332 .02676 L .31358 .02676 L .29396 .02676 L .27433 .02676 L .25471 .02676 L .23509 .02675 L .21546 .02674 L .19584 .02672 L .17622 .02667 L .15659 .02655 L .13697 .02627 L .11735 .02568 L .09772 .02441 L .0781 .02173 L .0678 .01923 L F 0 g .9322 .01923 m .9219 .02173 L .90228 .02441 L .88265 .02568 L .86303 .02627 L .84341 .02655 L .82378 .02667 L .80416 .02672 L .78454 .02674 L .76491 .02675 L .74529 .02676 L .72567 .02676 L .70604 .02676 L .68642 .02676 L .6668 .02676 L .64717 .02676 L .62755 .02676 L .60793 .02676 L .5883 .02676 L .56868 .02676 L .54906 .02676 L .52943 .02676 L .50981 .02676 L .49019 .02676 L .47057 .02676 L .45094 .02676 L .43132 .02676 L .4117 .02676 L .39207 .02676 L .37245 .02676 L .35283 .02676 L .3332 .02676 L .31358 .02676 L .29396 .02676 L .27433 .02676 L .25471 .02676 L .23509 .02675 L .21546 .02674 L .19584 .02672 L .17622 .02667 L .15659 .02655 L .13697 .02627 L .11735 .02568 L .09772 .02441 L .0781 .02173 L .0678 .01923 L s .3 g .13697 .07708 m .15659 .0758 L .17622 .07526 L .19584 .07502 L .21546 .07492 L .23509 .07487 L .25471 .07486 L .27433 .07485 L .29396 .07484 L .31358 .07484 L .3332 .07484 L .35283 .07484 L .37245 .07484 L .39207 .07484 L .4117 .07484 L .43132 .07484 L .45094 .07484 L .47057 .07484 L .49019 .07484 L .50981 .07484 L .52943 .07484 L .54906 .07484 L .56868 .07484 L .5883 .07484 L .60793 .07484 L .62755 .07484 L .64717 .07484 L .6668 .07484 L .68642 .07484 L .70604 .07484 L .72567 .07485 L .74529 .07486 L .76491 .07487 L .78454 .07492 L .80416 .07502 L .82378 .07526 L .84341 .0758 L .86303 .07708 L .87278 .0781 L .88265 .07987 L .90228 .08771 L .91229 .09772 L .92013 .11735 L .9219 .12722 L .92292 .13697 L .9242 .15659 L .92474 .17622 L .92498 .19584 L .92508 .21546 L .92513 .23509 L .92514 .25471 L .92515 .27433 L .92516 .29396 L .92516 .31358 L .92516 .3332 L .92516 .35283 L .92516 .37245 L .92516 .39207 L .92516 .4117 L .92516 .43132 L .92516 .45094 L .92516 .47057 L .92516 .49019 L .92516 .50981 L .92516 .52943 L .92516 .54906 L .92516 .56868 L .92516 .5883 L .92516 .60793 L .92516 .62755 L .92516 .64717 L .92516 .6668 L .92516 .68642 L .92516 .70604 L .92515 .72567 L .92514 .74529 L .92513 .76491 L .92508 .78454 L .92498 .80416 L .92474 .82378 L .9242 .84341 L .92292 .86303 L .9219 .87278 L .92013 .88265 L .91229 .90228 L .90228 .91229 L .88265 .92013 L .87278 .9219 L .86303 .92292 L .84341 .9242 L .82378 .92474 L .80416 .92498 L .78454 .92508 L .76491 .92513 L .74529 .92514 L .72567 .92515 L .70604 .92516 L .68642 .92516 L .6668 .92516 L .64717 .92516 L .62755 .92516 L .60793 .92516 L .5883 .92516 L .56868 .92516 L .54906 .92516 L .52943 .92516 L .50981 .92516 L .49019 .92516 L .47057 .92516 L .45094 .92516 L .43132 .92516 L .4117 .92516 L .39207 .92516 L .37245 .92516 L .35283 .92516 L .3332 .92516 L .31358 .92516 L .29396 .92516 L .27433 .92515 L .25471 .92514 L .23509 .92513 L .21546 .92508 L .19584 .92498 L .17622 .92474 L .15659 .9242 L .13697 .92292 L .12722 .9219 L .11735 .92013 L .09772 .91229 L .08771 .90228 L .07987 .88265 L .0781 .87278 L .07708 .86303 L .0758 .84341 L .07526 .82378 L .07502 .80416 L .07492 .78454 L .07487 .76491 L .07486 .74529 L .07485 .72567 L .07484 .70604 L .07484 .68642 L .07484 .6668 L .07484 .64717 L .07484 .62755 L .07484 .60793 L .07484 .5883 L .07484 .56868 L .07484 .54906 L .07484 .52943 L .07484 .50981 L .07484 .49019 L .07484 .47057 L .07484 .45094 L .07484 .43132 L .07484 .4117 L .07484 .39207 L .07484 .37245 L .07484 .35283 L .07484 .3332 L .07484 .31358 L .07484 .29396 L .07485 .27433 L .07486 .25471 L .07487 .23509 L .07492 .21546 L .07502 .19584 L .07526 .17622 L .0758 .15659 L .07708 .13697 L .0781 .12722 L .07987 .11735 L .08771 .09772 L .09772 .08771 L .11735 .07987 L .12722 .0781 L F 0 g .13697 .07708 m .15659 .0758 L .17622 .07526 L .19584 .07502 L .21546 .07492 L .23509 .07487 L .25471 .07486 L .27433 .07485 L .29396 .07484 L .31358 .07484 L .3332 .07484 L .35283 .07484 L .37245 .07484 L .39207 .07484 L .4117 .07484 L .43132 .07484 L .45094 .07484 L .47057 .07484 L .49019 .07484 L .50981 .07484 L .52943 .07484 L .54906 .07484 L .56868 .07484 L .5883 .07484 L .60793 .07484 L .62755 .07484 L .64717 .07484 L .6668 .07484 L .68642 .07484 L .70604 .07484 L .72567 .07485 L .74529 .07486 L .76491 .07487 L .78454 .07492 L .80416 .07502 L .82378 .07526 L .84341 .0758 L .86303 .07708 L .87278 .0781 L .88265 .07987 L .90228 .08771 L .91229 .09772 L .92013 .11735 L .9219 .12722 L .92292 .13697 L .9242 .15659 L .92474 .17622 L .92498 .19584 L .92508 .21546 L .92513 .23509 L Mistroke .92514 .25471 L .92515 .27433 L .92516 .29396 L .92516 .31358 L .92516 .3332 L .92516 .35283 L .92516 .37245 L .92516 .39207 L .92516 .4117 L .92516 .43132 L .92516 .45094 L .92516 .47057 L .92516 .49019 L .92516 .50981 L .92516 .52943 L .92516 .54906 L .92516 .56868 L .92516 .5883 L .92516 .60793 L .92516 .62755 L .92516 .64717 L .92516 .6668 L .92516 .68642 L .92516 .70604 L .92515 .72567 L .92514 .74529 L .92513 .76491 L .92508 .78454 L .92498 .80416 L .92474 .82378 L .9242 .84341 L .92292 .86303 L .9219 .87278 L .92013 .88265 L .91229 .90228 L .90228 .91229 L .88265 .92013 L .87278 .9219 L .86303 .92292 L .84341 .9242 L .82378 .92474 L .80416 .92498 L .78454 .92508 L .76491 .92513 L .74529 .92514 L .72567 .92515 L .70604 .92516 L .68642 .92516 L .6668 .92516 L .64717 .92516 L Mistroke .62755 .92516 L .60793 .92516 L .5883 .92516 L .56868 .92516 L .54906 .92516 L .52943 .92516 L .50981 .92516 L .49019 .92516 L .47057 .92516 L .45094 .92516 L .43132 .92516 L .4117 .92516 L .39207 .92516 L .37245 .92516 L .35283 .92516 L .3332 .92516 L .31358 .92516 L .29396 .92516 L .27433 .92515 L .25471 .92514 L .23509 .92513 L .21546 .92508 L .19584 .92498 L .17622 .92474 L .15659 .9242 L .13697 .92292 L .12722 .9219 L .11735 .92013 L .09772 .91229 L .08771 .90228 L .07987 .88265 L .0781 .87278 L .07708 .86303 L .0758 .84341 L .07526 .82378 L .07502 .80416 L .07492 .78454 L .07487 .76491 L .07486 .74529 L .07485 .72567 L .07484 .70604 L .07484 .68642 L .07484 .6668 L .07484 .64717 L .07484 .62755 L .07484 .60793 L .07484 .5883 L .07484 .56868 L .07484 .54906 L .07484 .52943 L Mistroke .07484 .50981 L .07484 .49019 L .07484 .47057 L .07484 .45094 L .07484 .43132 L .07484 .4117 L .07484 .39207 L .07484 .37245 L .07484 .35283 L .07484 .3332 L .07484 .31358 L .07484 .29396 L .07485 .27433 L .07486 .25471 L .07487 .23509 L .07492 .21546 L .07502 .19584 L .07526 .17622 L .0758 .15659 L .07708 .13697 L .0781 .12722 L .07987 .11735 L .08771 .09772 L .09772 .08771 L .11735 .07987 L .12722 .0781 L .13697 .07708 L Mfstroke .3 g .92341 .98077 m .9219 .98046 L .90228 .97777 L .88265 .97651 L .86303 .97593 L .84341 .97566 L .82378 .97554 L .80416 .97549 L .78454 .97547 L .76491 .97546 L .74529 .97546 L .72567 .97545 L .70604 .97545 L .68642 .97545 L .6668 .97545 L .64717 .97545 L .62755 .97545 L .60793 .97545 L .5883 .97545 L .56868 .97545 L .54906 .97545 L .52943 .97545 L .50981 .97545 L .49019 .97545 L .47057 .97545 L .45094 .97545 L .43132 .97545 L .4117 .97545 L .39207 .97545 L .37245 .97545 L .35283 .97545 L .3332 .97545 L .31358 .97545 L .29396 .97545 L .27433 .97545 L .25471 .97546 L .23509 .97546 L .21546 .97547 L .19584 .97549 L .17622 .97554 L .15659 .97566 L .13697 .97593 L .11735 .97651 L .09772 .97777 L .0781 .98046 L .07659 .98077 L F 0 g .92341 .98077 m .9219 .98046 L .90228 .97777 L .88265 .97651 L .86303 .97593 L .84341 .97566 L .82378 .97554 L .80416 .97549 L .78454 .97547 L .76491 .97546 L .74529 .97546 L .72567 .97545 L .70604 .97545 L .68642 .97545 L .6668 .97545 L .64717 .97545 L .62755 .97545 L .60793 .97545 L .5883 .97545 L .56868 .97545 L .54906 .97545 L .52943 .97545 L .50981 .97545 L .49019 .97545 L .47057 .97545 L .45094 .97545 L .43132 .97545 L .4117 .97545 L .39207 .97545 L .37245 .97545 L .35283 .97545 L .3332 .97545 L .31358 .97545 L .29396 .97545 L .27433 .97545 L .25471 .97546 L .23509 .97546 L .21546 .97547 L .19584 .97549 L .17622 .97554 L .15659 .97566 L .13697 .97593 L .11735 .97651 L .09772 .97777 L .0781 .98046 L .07659 .98077 L s .3 g .92341 .01923 m .9219 .01954 L .90228 .02223 L .88265 .02349 L .86303 .02407 L .84341 .02434 L .82378 .02446 L .80416 .02451 L .78454 .02453 L .76491 .02454 L .74529 .02454 L .72567 .02455 L .70604 .02455 L .68642 .02455 L .6668 .02455 L .64717 .02455 L .62755 .02455 L .60793 .02455 L .5883 .02455 L .56868 .02455 L .54906 .02455 L .52943 .02455 L .50981 .02455 L .49019 .02455 L .47057 .02455 L .45094 .02455 L .43132 .02455 L .4117 .02455 L .39207 .02455 L .37245 .02455 L .35283 .02455 L .3332 .02455 L .31358 .02455 L .29396 .02455 L .27433 .02455 L .25471 .02454 L .23509 .02454 L .21546 .02453 L .19584 .02451 L .17622 .02446 L .15659 .02434 L .13697 .02407 L .11735 .02349 L .09772 .02223 L .0781 .01954 L .07659 .01923 L F 0 g .92341 .01923 m .9219 .01954 L .90228 .02223 L .88265 .02349 L .86303 .02407 L .84341 .02434 L .82378 .02446 L .80416 .02451 L .78454 .02453 L .76491 .02454 L .74529 .02454 L .72567 .02455 L .70604 .02455 L .68642 .02455 L .6668 .02455 L .64717 .02455 L .62755 .02455 L .60793 .02455 L .5883 .02455 L .56868 .02455 L .54906 .02455 L .52943 .02455 L .50981 .02455 L .49019 .02455 L .47057 .02455 L .45094 .02455 L .43132 .02455 L .4117 .02455 L .39207 .02455 L .37245 .02455 L .35283 .02455 L .3332 .02455 L .31358 .02455 L .29396 .02455 L .27433 .02455 L .25471 .02454 L .23509 .02454 L .21546 .02453 L .19584 .02451 L .17622 .02446 L .15659 .02434 L .13697 .02407 L .11735 .02349 L .09772 .02223 L .0781 .01954 L .07659 .01923 L s .2 g .11735 .09332 m .13697 .08807 L .15659 .08606 L .17622 .08523 L .19584 .08487 L .21546 .08472 L .23509 .08466 L .25471 .08463 L .27433 .08462 L .29396 .08462 L .31358 .08461 L .3332 .08461 L .35283 .08461 L .37245 .08461 L .39207 .08461 L .4117 .08461 L .43132 .08461 L .45094 .08461 L .47057 .08461 L .49019 .08461 L .50981 .08461 L .52943 .08461 L .54906 .08461 L .56868 .08461 L .5883 .08461 L .60793 .08461 L .62755 .08461 L .64717 .08461 L .6668 .08461 L .68642 .08461 L .70604 .08462 L .72567 .08462 L .74529 .08463 L .76491 .08466 L .78454 .08472 L .80416 .08487 L .82378 .08523 L .84341 .08606 L .86303 .08807 L .88265 .09332 L .8915 .09772 L .90228 .1085 L .90668 .11735 L .91193 .13697 L .91394 .15659 L .91477 .17622 L .91513 .19584 L .91528 .21546 L .91534 .23509 L .91537 .25471 L .91538 .27433 L .91538 .29396 L .91539 .31358 L .91539 .3332 L .91539 .35283 L .91539 .37245 L .91539 .39207 L .91539 .4117 L .91539 .43132 L .91539 .45094 L .91539 .47057 L .91539 .49019 L .91539 .50981 L .91539 .52943 L .91539 .54906 L .91539 .56868 L .91539 .5883 L .91539 .60793 L .91539 .62755 L .91539 .64717 L .91539 .6668 L .91539 .68642 L .91538 .70604 L .91538 .72567 L .91537 .74529 L .91534 .76491 L .91528 .78454 L .91513 .80416 L .91477 .82378 L .91394 .84341 L .91193 .86303 L .90668 .88265 L .90228 .8915 L .8915 .90228 L .88265 .90668 L .86303 .91193 L .84341 .91394 L .82378 .91477 L .80416 .91513 L .78454 .91528 L .76491 .91534 L .74529 .91537 L .72567 .91538 L .70604 .91538 L .68642 .91539 L .6668 .91539 L .64717 .91539 L .62755 .91539 L .60793 .91539 L .5883 .91539 L .56868 .91539 L .54906 .91539 L .52943 .91539 L .50981 .91539 L .49019 .91539 L .47057 .91539 L .45094 .91539 L .43132 .91539 L .4117 .91539 L .39207 .91539 L .37245 .91539 L .35283 .91539 L .3332 .91539 L .31358 .91539 L .29396 .91538 L .27433 .91538 L .25471 .91537 L .23509 .91534 L .21546 .91528 L .19584 .91513 L .17622 .91477 L .15659 .91394 L .13697 .91193 L .11735 .90668 L .1085 .90228 L .09772 .8915 L .09332 .88265 L .08807 .86303 L .08606 .84341 L .08523 .82378 L .08487 .80416 L .08472 .78454 L .08466 .76491 L .08463 .74529 L .08462 .72567 L .08462 .70604 L .08461 .68642 L .08461 .6668 L .08461 .64717 L .08461 .62755 L .08461 .60793 L .08461 .5883 L .08461 .56868 L .08461 .54906 L .08461 .52943 L .08461 .50981 L .08461 .49019 L .08461 .47057 L .08461 .45094 L .08461 .43132 L .08461 .4117 L .08461 .39207 L .08461 .37245 L .08461 .35283 L .08461 .3332 L .08461 .31358 L .08462 .29396 L .08462 .27433 L .08463 .25471 L .08466 .23509 L .08472 .21546 L .08487 .19584 L .08523 .17622 L .08606 .15659 L .08807 .13697 L .09332 .11735 L .09772 .1085 L .1085 .09772 L F 0 g .11735 .09332 m .13697 .08807 L .15659 .08606 L .17622 .08523 L .19584 .08487 L .21546 .08472 L .23509 .08466 L .25471 .08463 L .27433 .08462 L .29396 .08462 L .31358 .08461 L .3332 .08461 L .35283 .08461 L .37245 .08461 L .39207 .08461 L .4117 .08461 L .43132 .08461 L .45094 .08461 L .47057 .08461 L .49019 .08461 L .50981 .08461 L .52943 .08461 L .54906 .08461 L .56868 .08461 L .5883 .08461 L .60793 .08461 L .62755 .08461 L .64717 .08461 L .6668 .08461 L .68642 .08461 L .70604 .08462 L .72567 .08462 L .74529 .08463 L .76491 .08466 L .78454 .08472 L .80416 .08487 L .82378 .08523 L .84341 .08606 L .86303 .08807 L .88265 .09332 L .8915 .09772 L .90228 .1085 L .90668 .11735 L .91193 .13697 L .91394 .15659 L .91477 .17622 L .91513 .19584 L .91528 .21546 L .91534 .23509 L .91537 .25471 L Mistroke .91538 .27433 L .91538 .29396 L .91539 .31358 L .91539 .3332 L .91539 .35283 L .91539 .37245 L .91539 .39207 L .91539 .4117 L .91539 .43132 L .91539 .45094 L .91539 .47057 L .91539 .49019 L .91539 .50981 L .91539 .52943 L .91539 .54906 L .91539 .56868 L .91539 .5883 L .91539 .60793 L .91539 .62755 L .91539 .64717 L .91539 .6668 L .91539 .68642 L .91538 .70604 L .91538 .72567 L .91537 .74529 L .91534 .76491 L .91528 .78454 L .91513 .80416 L .91477 .82378 L .91394 .84341 L .91193 .86303 L .90668 .88265 L .90228 .8915 L .8915 .90228 L .88265 .90668 L .86303 .91193 L .84341 .91394 L .82378 .91477 L .80416 .91513 L .78454 .91528 L .76491 .91534 L .74529 .91537 L .72567 .91538 L .70604 .91538 L .68642 .91539 L .6668 .91539 L .64717 .91539 L .62755 .91539 L .60793 .91539 L .5883 .91539 L Mistroke .56868 .91539 L .54906 .91539 L .52943 .91539 L .50981 .91539 L .49019 .91539 L .47057 .91539 L .45094 .91539 L .43132 .91539 L .4117 .91539 L .39207 .91539 L .37245 .91539 L .35283 .91539 L .3332 .91539 L .31358 .91539 L .29396 .91538 L .27433 .91538 L .25471 .91537 L .23509 .91534 L .21546 .91528 L .19584 .91513 L .17622 .91477 L .15659 .91394 L .13697 .91193 L .11735 .90668 L .1085 .90228 L .09772 .8915 L .09332 .88265 L .08807 .86303 L .08606 .84341 L .08523 .82378 L .08487 .80416 L .08472 .78454 L .08466 .76491 L .08463 .74529 L .08462 .72567 L .08462 .70604 L .08461 .68642 L .08461 .6668 L .08461 .64717 L .08461 .62755 L .08461 .60793 L .08461 .5883 L .08461 .56868 L .08461 .54906 L .08461 .52943 L .08461 .50981 L .08461 .49019 L .08461 .47057 L .08461 .45094 L .08461 .43132 L Mistroke .08461 .4117 L .08461 .39207 L .08461 .37245 L .08461 .35283 L .08461 .3332 L .08461 .31358 L .08462 .29396 L .08462 .27433 L .08463 .25471 L .08466 .23509 L .08472 .21546 L .08487 .19584 L .08523 .17622 L .08606 .15659 L .08807 .13697 L .09332 .11735 L .09772 .1085 L .1085 .09772 L .11735 .09332 L Mfstroke .2 g .91271 .98077 m .90228 .97967 L .88265 .9784 L .86303 .97782 L .84341 .97755 L .82378 .97744 L .80416 .97738 L .78454 .97736 L .76491 .97735 L .74529 .97735 L .72567 .97735 L .70604 .97735 L .68642 .97734 L .6668 .97734 L .64717 .97734 L .62755 .97734 L .60793 .97734 L .5883 .97734 L .56868 .97734 L .54906 .97734 L .52943 .97734 L .50981 .97734 L .49019 .97734 L .47057 .97734 L .45094 .97734 L .43132 .97734 L .4117 .97734 L .39207 .97734 L .37245 .97734 L .35283 .97734 L .3332 .97734 L .31358 .97734 L .29396 .97735 L .27433 .97735 L .25471 .97735 L .23509 .97735 L .21546 .97736 L .19584 .97738 L .17622 .97744 L .15659 .97755 L .13697 .97782 L .11735 .9784 L .09772 .97967 L .08729 .98077 L F 0 g .91271 .98077 m .90228 .97967 L .88265 .9784 L .86303 .97782 L .84341 .97755 L .82378 .97744 L .80416 .97738 L .78454 .97736 L .76491 .97735 L .74529 .97735 L .72567 .97735 L .70604 .97735 L .68642 .97734 L .6668 .97734 L .64717 .97734 L .62755 .97734 L .60793 .97734 L .5883 .97734 L .56868 .97734 L .54906 .97734 L .52943 .97734 L .50981 .97734 L .49019 .97734 L .47057 .97734 L .45094 .97734 L .43132 .97734 L .4117 .97734 L .39207 .97734 L .37245 .97734 L .35283 .97734 L .3332 .97734 L .31358 .97734 L .29396 .97735 L .27433 .97735 L .25471 .97735 L .23509 .97735 L .21546 .97736 L .19584 .97738 L .17622 .97744 L .15659 .97755 L .13697 .97782 L .11735 .9784 L .09772 .97967 L .08729 .98077 L s .2 g .91271 .01923 m .90228 .02033 L .88265 .0216 L .86303 .02218 L .84341 .02245 L .82378 .02256 L .80416 .02262 L .78454 .02264 L .76491 .02265 L .74529 .02265 L .72567 .02265 L .70604 .02265 L .68642 .02266 L .6668 .02266 L .64717 .02266 L .62755 .02266 L .60793 .02266 L .5883 .02266 L .56868 .02266 L .54906 .02266 L .52943 .02266 L .50981 .02266 L .49019 .02266 L .47057 .02266 L .45094 .02266 L .43132 .02266 L .4117 .02266 L .39207 .02266 L .37245 .02266 L .35283 .02266 L .3332 .02266 L .31358 .02266 L .29396 .02265 L .27433 .02265 L .25471 .02265 L .23509 .02265 L .21546 .02264 L .19584 .02262 L .17622 .02256 L .15659 .02245 L .13697 .02218 L .11735 .0216 L .09772 .02033 L .08729 .01923 L F 0 g .91271 .01923 m .90228 .02033 L .88265 .0216 L .86303 .02218 L .84341 .02245 L .82378 .02256 L .80416 .02262 L .78454 .02264 L .76491 .02265 L .74529 .02265 L .72567 .02265 L .70604 .02265 L .68642 .02266 L .6668 .02266 L .64717 .02266 L .62755 .02266 L .60793 .02266 L .5883 .02266 L .56868 .02266 L .54906 .02266 L .52943 .02266 L .50981 .02266 L .49019 .02266 L .47057 .02266 L .45094 .02266 L .43132 .02266 L .4117 .02266 L .39207 .02266 L .37245 .02266 L .35283 .02266 L .3332 .02266 L .31358 .02266 L .29396 .02265 L .27433 .02265 L .25471 .02265 L .23509 .02265 L .21546 .02264 L .19584 .02262 L .17622 .02256 L .15659 .02245 L .13697 .02218 L .11735 .0216 L .09772 .02033 L .08729 .01923 L s .1 g .13697 .10551 m .15659 .10187 L .17622 .10051 L .19584 .09997 L .21546 .09974 L .23509 .09964 L .25471 .0996 L .27433 .09959 L .29396 .09958 L .31358 .09958 L .3332 .09958 L .35283 .09957 L .37245 .09957 L .39207 .09957 L .4117 .09957 L .43132 .09957 L .45094 .09957 L .47057 .09957 L .49019 .09957 L .50981 .09957 L .52943 .09957 L .54906 .09957 L .56868 .09957 L .5883 .09957 L .60793 .09957 L .62755 .09957 L .64717 .09957 L .6668 .09958 L .68642 .09958 L .70604 .09958 L .72567 .09959 L .74529 .0996 L .76491 .09964 L .78454 .09974 L .80416 .09997 L .82378 .10051 L .84341 .10187 L .86303 .10551 L .88257 .11735 L .88265 .11743 L .89449 .13697 L .89813 .15659 L .89949 .17622 L .90003 .19584 L .90026 .21546 L .90036 .23509 L .9004 .25471 L .90041 .27433 L .90042 .29396 L .90042 .31358 L .90042 .3332 L .90043 .35283 L .90043 .37245 L .90043 .39207 L .90043 .4117 L .90043 .43132 L .90043 .45094 L .90043 .47057 L .90043 .49019 L .90043 .50981 L .90043 .52943 L .90043 .54906 L .90043 .56868 L .90043 .5883 L .90043 .60793 L .90043 .62755 L .90043 .64717 L .90042 .6668 L .90042 .68642 L .90042 .70604 L .90041 .72567 L .9004 .74529 L .90036 .76491 L .90026 .78454 L .90003 .80416 L .89949 .82378 L .89813 .84341 L .89449 .86303 L .88265 .88257 L .88257 .88265 L .86303 .89449 L .84341 .89813 L .82378 .89949 L .80416 .90003 L .78454 .90026 L .76491 .90036 L .74529 .9004 L .72567 .90041 L .70604 .90042 L .68642 .90042 L .6668 .90042 L .64717 .90043 L .62755 .90043 L .60793 .90043 L .5883 .90043 L .56868 .90043 L .54906 .90043 L .52943 .90043 L .50981 .90043 L .49019 .90043 L .47057 .90043 L .45094 .90043 L .43132 .90043 L .4117 .90043 L .39207 .90043 L .37245 .90043 L .35283 .90043 L .3332 .90042 L .31358 .90042 L .29396 .90042 L .27433 .90041 L .25471 .9004 L .23509 .90036 L .21546 .90026 L .19584 .90003 L .17622 .89949 L .15659 .89813 L .13697 .89449 L .11743 .88265 L .11735 .88257 L .10551 .86303 L .10187 .84341 L .10051 .82378 L .09997 .80416 L .09974 .78454 L .09964 .76491 L .0996 .74529 L .09959 .72567 L .09958 .70604 L .09958 .68642 L .09958 .6668 L .09957 .64717 L .09957 .62755 L .09957 .60793 L .09957 .5883 L .09957 .56868 L .09957 .54906 L .09957 .52943 L .09957 .50981 L .09957 .49019 L .09957 .47057 L .09957 .45094 L .09957 .43132 L .09957 .4117 L .09957 .39207 L .09957 .37245 L .09957 .35283 L .09958 .3332 L .09958 .31358 L .09958 .29396 L .09959 .27433 L .0996 .25471 L .09964 .23509 L .09974 .21546 L .09997 .19584 L .10051 .17622 L .10187 .15659 L .10551 .13697 L .11735 .11743 L .11743 .11735 L F 0 g .13697 .10551 m .15659 .10187 L .17622 .10051 L .19584 .09997 L .21546 .09974 L .23509 .09964 L .25471 .0996 L .27433 .09959 L .29396 .09958 L .31358 .09958 L .3332 .09958 L .35283 .09957 L .37245 .09957 L .39207 .09957 L .4117 .09957 L .43132 .09957 L .45094 .09957 L .47057 .09957 L .49019 .09957 L .50981 .09957 L .52943 .09957 L .54906 .09957 L .56868 .09957 L .5883 .09957 L .60793 .09957 L .62755 .09957 L .64717 .09957 L .6668 .09958 L .68642 .09958 L .70604 .09958 L .72567 .09959 L .74529 .0996 L .76491 .09964 L .78454 .09974 L .80416 .09997 L .82378 .10051 L .84341 .10187 L .86303 .10551 L .88257 .11735 L .88265 .11743 L .89449 .13697 L .89813 .15659 L .89949 .17622 L .90003 .19584 L .90026 .21546 L .90036 .23509 L .9004 .25471 L .90041 .27433 L .90042 .29396 L .90042 .31358 L Mistroke .90042 .3332 L .90043 .35283 L .90043 .37245 L .90043 .39207 L .90043 .4117 L .90043 .43132 L .90043 .45094 L .90043 .47057 L .90043 .49019 L .90043 .50981 L .90043 .52943 L .90043 .54906 L .90043 .56868 L .90043 .5883 L .90043 .60793 L .90043 .62755 L .90043 .64717 L .90042 .6668 L .90042 .68642 L .90042 .70604 L .90041 .72567 L .9004 .74529 L .90036 .76491 L .90026 .78454 L .90003 .80416 L .89949 .82378 L .89813 .84341 L .89449 .86303 L .88265 .88257 L .88257 .88265 L .86303 .89449 L .84341 .89813 L .82378 .89949 L .80416 .90003 L .78454 .90026 L .76491 .90036 L .74529 .9004 L .72567 .90041 L .70604 .90042 L .68642 .90042 L .6668 .90042 L .64717 .90043 L .62755 .90043 L .60793 .90043 L .5883 .90043 L .56868 .90043 L .54906 .90043 L .52943 .90043 L .50981 .90043 L .49019 .90043 L Mistroke .47057 .90043 L .45094 .90043 L .43132 .90043 L .4117 .90043 L .39207 .90043 L .37245 .90043 L .35283 .90043 L .3332 .90042 L .31358 .90042 L .29396 .90042 L .27433 .90041 L .25471 .9004 L .23509 .90036 L .21546 .90026 L .19584 .90003 L .17622 .89949 L .15659 .89813 L .13697 .89449 L .11743 .88265 L .11735 .88257 L .10551 .86303 L .10187 .84341 L .10051 .82378 L .09997 .80416 L .09974 .78454 L .09964 .76491 L .0996 .74529 L .09959 .72567 L .09958 .70604 L .09958 .68642 L .09958 .6668 L .09957 .64717 L .09957 .62755 L .09957 .60793 L .09957 .5883 L .09957 .56868 L .09957 .54906 L .09957 .52943 L .09957 .50981 L .09957 .49019 L .09957 .47057 L .09957 .45094 L .09957 .43132 L .09957 .4117 L .09957 .39207 L .09957 .37245 L .09957 .35283 L .09958 .3332 L .09958 .31358 L .09958 .29396 L Mistroke .09959 .27433 L .0996 .25471 L .09964 .23509 L .09974 .21546 L .09997 .19584 L .10051 .17622 L .10187 .15659 L .10551 .13697 L .11735 .11743 L .11743 .11735 L .13697 .10551 L Mfstroke .1 g .89596 .98077 m .88265 .98008 L .86303 .97949 L .84341 .97923 L .82378 .97911 L .80416 .97905 L .78454 .97903 L .76491 .97902 L .74529 .97902 L .72567 .97902 L .70604 .97901 L .68642 .97901 L .6668 .97901 L .64717 .97901 L .62755 .97901 L .60793 .97901 L .5883 .97901 L .56868 .97901 L .54906 .97901 L .52943 .97901 L .50981 .97901 L .49019 .97901 L .47057 .97901 L .45094 .97901 L .43132 .97901 L .4117 .97901 L .39207 .97901 L .37245 .97901 L .35283 .97901 L .3332 .97901 L .31358 .97901 L .29396 .97901 L .27433 .97902 L .25471 .97902 L .23509 .97902 L .21546 .97903 L .19584 .97905 L .17622 .97911 L .15659 .97923 L .13697 .97949 L .11735 .98008 L .10404 .98077 L F 0 g .89596 .98077 m .88265 .98008 L .86303 .97949 L .84341 .97923 L .82378 .97911 L .80416 .97905 L .78454 .97903 L .76491 .97902 L .74529 .97902 L .72567 .97902 L .70604 .97901 L .68642 .97901 L .6668 .97901 L .64717 .97901 L .62755 .97901 L .60793 .97901 L .5883 .97901 L .56868 .97901 L .54906 .97901 L .52943 .97901 L .50981 .97901 L .49019 .97901 L .47057 .97901 L .45094 .97901 L .43132 .97901 L .4117 .97901 L .39207 .97901 L .37245 .97901 L .35283 .97901 L .3332 .97901 L .31358 .97901 L .29396 .97901 L .27433 .97902 L .25471 .97902 L .23509 .97902 L .21546 .97903 L .19584 .97905 L .17622 .97911 L .15659 .97923 L .13697 .97949 L .11735 .98008 L .10404 .98077 L s .1 g .89596 .01923 m .88265 .01992 L .86303 .02051 L .84341 .02077 L .82378 .02089 L .80416 .02095 L .78454 .02097 L .76491 .02098 L .74529 .02098 L .72567 .02098 L .70604 .02099 L .68642 .02099 L .6668 .02099 L .64717 .02099 L .62755 .02099 L .60793 .02099 L .5883 .02099 L .56868 .02099 L .54906 .02099 L .52943 .02099 L .50981 .02099 L .49019 .02099 L .47057 .02099 L .45094 .02099 L .43132 .02099 L .4117 .02099 L .39207 .02099 L .37245 .02099 L .35283 .02099 L .3332 .02099 L .31358 .02099 L .29396 .02099 L .27433 .02098 L .25471 .02098 L .23509 .02098 L .21546 .02097 L .19584 .02095 L .17622 .02089 L .15659 .02077 L .13697 .02051 L .11735 .01992 L .10404 .01923 L F 0 g .89596 .01923 m .88265 .01992 L .86303 .02051 L .84341 .02077 L .82378 .02089 L .80416 .02095 L .78454 .02097 L .76491 .02098 L .74529 .02098 L .72567 .02098 L .70604 .02099 L .68642 .02099 L .6668 .02099 L .64717 .02099 L .62755 .02099 L .60793 .02099 L .5883 .02099 L .56868 .02099 L .54906 .02099 L .52943 .02099 L .50981 .02099 L .49019 .02099 L .47057 .02099 L .45094 .02099 L .43132 .02099 L .4117 .02099 L .39207 .02099 L .37245 .02099 L .35283 .02099 L .3332 .02099 L .31358 .02099 L .29396 .02099 L .27433 .02098 L .25471 .02098 L .23509 .02098 L .21546 .02097 L .19584 .02095 L .17622 .02089 L .15659 .02077 L .13697 .02051 L .11735 .01992 L .10404 .01923 L s .17622 .13388 m .19584 .1313 L .21546 .13026 L .23509 .12983 L .25471 .12965 L .27433 .12958 L .29396 .12955 L .31358 .12953 L .3332 .12953 L .35283 .12953 L .37245 .12953 L .39207 .12953 L .4117 .12953 L .43132 .12953 L .45094 .12953 L .47057 .12953 L .49019 .12953 L .50981 .12953 L .52943 .12953 L .54906 .12953 L .56868 .12953 L .5883 .12953 L .60793 .12953 L .62755 .12953 L .64717 .12953 L .6668 .12953 L .68642 .12953 L .70604 .12955 L .72567 .12958 L .74529 .12965 L .76491 .12983 L .78454 .13026 L .80416 .1313 L .82378 .13388 L .83651 .13697 L .84341 .13942 L .86058 .15659 L .86303 .16349 L .86612 .17622 L .8687 .19584 L .86974 .21546 L .87017 .23509 L .87035 .25471 L .87042 .27433 L .87045 .29396 L .87047 .31358 L .87047 .3332 L .87047 .35283 L .87047 .37245 L .87047 .39207 L .87047 .4117 L .87047 .43132 L .87047 .45094 L .87047 .47057 L .87047 .49019 L .87047 .50981 L .87047 .52943 L .87047 .54906 L .87047 .56868 L .87047 .5883 L .87047 .60793 L .87047 .62755 L .87047 .64717 L .87047 .6668 L .87047 .68642 L .87045 .70604 L .87042 .72567 L .87035 .74529 L .87017 .76491 L .86974 .78454 L .8687 .80416 L .86612 .82378 L .86303 .83651 L .86058 .84341 L .84341 .86058 L .83651 .86303 L .82378 .86612 L .80416 .8687 L .78454 .86974 L .76491 .87017 L .74529 .87035 L .72567 .87042 L .70604 .87045 L .68642 .87047 L .6668 .87047 L .64717 .87047 L .62755 .87047 L .60793 .87047 L .5883 .87047 L .56868 .87047 L .54906 .87047 L .52943 .87047 L .50981 .87047 L .49019 .87047 L .47057 .87047 L .45094 .87047 L .43132 .87047 L .4117 .87047 L .39207 .87047 L .37245 .87047 L .35283 .87047 L .3332 .87047 L .31358 .87047 L .29396 .87045 L .27433 .87042 L .25471 .87035 L .23509 .87017 L .21546 .86974 L .19584 .8687 L .17622 .86612 L .16349 .86303 L .15659 .86058 L .13942 .84341 L .13697 .83651 L .13388 .82378 L .1313 .80416 L .13026 .78454 L .12983 .76491 L .12965 .74529 L .12958 .72567 L .12955 .70604 L .12953 .68642 L .12953 .6668 L .12953 .64717 L .12953 .62755 L .12953 .60793 L .12953 .5883 L .12953 .56868 L .12953 .54906 L .12953 .52943 L .12953 .50981 L .12953 .49019 L .12953 .47057 L .12953 .45094 L .12953 .43132 L .12953 .4117 L .12953 .39207 L .12953 .37245 L .12953 .35283 L .12953 .3332 L .12953 .31358 L .12955 .29396 L .12958 .27433 L .12965 .25471 L .12983 .23509 L .13026 .21546 L .1313 .19584 L .13388 .17622 L .13697 .16349 L .13942 .15659 L .15659 .13942 L .16349 .13697 L F .17622 .13388 m .19584 .1313 L .21546 .13026 L .23509 .12983 L .25471 .12965 L .27433 .12958 L .29396 .12955 L .31358 .12953 L .3332 .12953 L .35283 .12953 L .37245 .12953 L .39207 .12953 L .4117 .12953 L .43132 .12953 L .45094 .12953 L .47057 .12953 L .49019 .12953 L .50981 .12953 L .52943 .12953 L .54906 .12953 L .56868 .12953 L .5883 .12953 L .60793 .12953 L .62755 .12953 L .64717 .12953 L .6668 .12953 L .68642 .12953 L .70604 .12955 L .72567 .12958 L .74529 .12965 L .76491 .12983 L .78454 .13026 L .80416 .1313 L .82378 .13388 L .83651 .13697 L .84341 .13942 L .86058 .15659 L .86303 .16349 L .86612 .17622 L .8687 .19584 L .86974 .21546 L .87017 .23509 L .87035 .25471 L .87042 .27433 L .87045 .29396 L .87047 .31358 L .87047 .3332 L .87047 .35283 L .87047 .37245 L .87047 .39207 L Mistroke .87047 .4117 L .87047 .43132 L .87047 .45094 L .87047 .47057 L .87047 .49019 L .87047 .50981 L .87047 .52943 L .87047 .54906 L .87047 .56868 L .87047 .5883 L .87047 .60793 L .87047 .62755 L .87047 .64717 L .87047 .6668 L .87047 .68642 L .87045 .70604 L .87042 .72567 L .87035 .74529 L .87017 .76491 L .86974 .78454 L .8687 .80416 L .86612 .82378 L .86303 .83651 L .86058 .84341 L .84341 .86058 L .83651 .86303 L .82378 .86612 L .80416 .8687 L .78454 .86974 L .76491 .87017 L .74529 .87035 L .72567 .87042 L .70604 .87045 L .68642 .87047 L .6668 .87047 L .64717 .87047 L .62755 .87047 L .60793 .87047 L .5883 .87047 L .56868 .87047 L .54906 .87047 L .52943 .87047 L .50981 .87047 L .49019 .87047 L .47057 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