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Cell["The Kermack-McKendrick Model of Epidemics and Its Extensions", "Title"], Cell["Jan Hurt and Daniel Hlubinka", "Author"], Cell["Charles University of Prague, Czech Republic", "Affiliation"], Cell[CellGroupData[{ Cell["1 Introduction", "Section"], Cell["\<\ The classical deterministic model of epidemic was proposed by Kermack and \ McKendrick in 1927, see [4]. The model is considered to be appropriate for \ highly infectious diseases with a fast recovery and/or fatality. Influenza, \ measles, chickenpox, mumps, and scarlet fever are examples of such diseases. \ It assumes a constant rate of infection and a constant recovery rate. There \ are various extensions of the model in that the rate of infection is not \ constant, the size of population varies in time etc. Here we mention two \ practically important cases; intervention either in the form of government \ measures or vaccination and a random size of population. \ \>", "Text"] }, Closed]], Cell[CellGroupData[{ Cell["2 Deterministic models", "Section"], Cell[CellGroupData[{ Cell["2.1 Classical model", "Subsection"], Cell[TextData[{ "It is assumed that the population of size ", Cell[BoxData[ StyleBox["N", FontSlant->"Italic"]]], ", constant in time ", Cell[BoxData[ StyleBox["t", FontSlant->"Italic"]]], ", consists of three parts: ", Cell[BoxData[ StyleBox[\(X\_t\), FontSlant->"Italic", FontVariations->{"CompatibilityType"->0}]]], ", the number of susceptibles (exposed to the infection), ", Cell[BoxData[ StyleBox[\(Y\_t\), FontSlant->"Italic"]]], ", the number of infectives, and ", Cell[BoxData[ StyleBox[\(Z\_t\), FontSlant->"Italic"]]], ", the number of removals (recovered, dead, or isolated), ", Cell[BoxData[ \(X\_t + Y\_t + Z\_t = N\)], FontSlant->"Italic"], ". The model is governed by the system of ODE (the derivatives are taken \ with respect to", StyleBox[" ", FontSlant->"Italic"], Cell[BoxData[ \(t\)], FontSlant->"Italic"], ")" }], "Text"], Cell[BoxData[ \(X\& . \_t = \(-\[Beta]X\_t\) Y\_t, \ X\_0 = x\_0, \[IndentingNewLine]Y\& . \_t = \(\[Beta]X\_t\) Y\_t - \[Gamma]Y\_t, Y\_0 = y\_0, \[IndentingNewLine]Z\& . \_t = \[Gamma]Y\_t, \ Z\_0 = \(\(z\_0\)\(.\)\(\ \ \ \ \)\)\)], "DisplayFormula", TextAlignment->Left], Cell[TextData[{ "This model is also known as an ", StyleBox["SIR model", FontSlant->"Italic"], " (", StyleBox["S", FontVariations->{"Underline"->True}], "usceptibles, ", StyleBox["I", FontVariations->{"Underline"->True}], "nfected, ", StyleBox["R", FontVariations->{"Underline"->True}], "emoved). Positive constants ", Cell[BoxData[ \(\[Beta]\)]], " and ", Cell[BoxData[ \(\[Gamma]\)]], " represent the infection and recovery rates, respectively. Thus the \ transition ", Cell[BoxData[ StyleBox[\(X\[LongRightArrow]Y\), FontSlant->"Italic"]]], " is realized with rate ", Cell[BoxData[ \(\[Beta]\)]], ", ", Cell[BoxData[ StyleBox[\(Y\[LongRightArrow]Z\), FontSlant->"Italic"]]], " with rate \[Gamma], consequently ", Cell[BoxData[ StyleBox[\(X\[LongRightArrow]Z\), FontSlant->"Italic"]]], " with rate ", Cell[BoxData[ \(\[Rho] := \[Gamma]/\[Beta]\)]], ", the so called relative removal rate. The dimension of ", Cell[BoxData[ \(\[Beta]\)]], " is ", Cell[BoxData[ \(\((time\ \[Times]\ size\ of\ population)\)\^\(-1\)\)]], ", that of ", Cell[BoxData[ \(\[Gamma]\)]], " ", Cell[BoxData[ \(\((time)\)\^\(-1\)\)]], ", and that of ", Cell[BoxData[ \(\[Rho]\)]], " is ", Cell[BoxData[ \(size\ of\ population\)]], ". In what follows we will measure ", StyleBox["time in days", FontVariations->{"Underline"->True}], ". Without any loss of generality, the size of population will be set to \ one: ", StyleBox["N", FontSlant->"Italic", FontVariations->{"Underline"->True}], StyleBox[":=1", FontVariations->{"Underline"->True}], "." }], "Text"], Cell[TextData[{ "For ", Cell[BoxData[ \(\[Beta] > 0\)]], ", ", Cell[BoxData[ \(\[Gamma] > 0\)]], ", ", Cell[BoxData[ StyleBox[\(x\_0 + y\_0 = N\), FontSlant->"Italic"]]], ", ", Cell[BoxData[ RowBox[{ StyleBox[\(x\_0\), FontSlant->"Italic"], ">", "0"}]]], " , and ", Cell[BoxData[ RowBox[{ StyleBox[\(y\_0\), FontSlant->"Italic"], ">", "0"}]]], " there exists a solution to the above system. The solution ", Cell[BoxData[ \(\((X\_t, Y\_t, Z\_t)\)\)], FontSlant->"Italic"], " is nonnegative, the number of susceptibles ", Cell[BoxData[ StyleBox[\(X\_t\), FontSlant->"Italic"]]], " is nonincreasing, the number of removals ", Cell[BoxData[ \(Z\_t\)], FontSlant->"Italic"], " is nondecreasing. As ", Cell[BoxData[ StyleBox[\(t\[LongRightArrow]\[Infinity]\), FontSlant->"Italic"]]], " there exist positive limits ", Cell[BoxData[ StyleBox[\(X\_\[Infinity]\), FontSlant->"Italic"]]], " and ", Cell[BoxData[ StyleBox[\(Z\_\[Infinity]\), FontSlant->"Italic"]]], " of ", Cell[BoxData[ StyleBox[\(X\_t\), FontSlant->"Italic"]]], " and ", Cell[BoxData[ StyleBox[\(Z\_t\), FontSlant->"Italic"]]], ", respectively. If ", Cell[BoxData[ RowBox[{"\[Rho]", "<", SubscriptBox[ StyleBox["x", FontSlant->"Italic"], "0"]}]]], " then there exists the global maximum of infectives, ", Cell[BoxData[ RowBox[{ SubscriptBox[ StyleBox["Y", FontSlant->"Italic"], "+"], "=", RowBox[{"max", " ", StyleBox[\(Y\_t\), FontSlant->"Italic"]}]}]]], ", say." }], "Text"], Cell[CellGroupData[{ Cell["2.1.1 Example", "Subsubsection"], Cell[TextData[{ "To get an idea about the magnitudes of the parameters involved, we give \ the expert's guesses for a (possibly pandemic) influenza. The choice ", Cell[BoxData[ RowBox[{"\[Beta]", "=", RowBox[{"0.6", "/", StyleBox["N", FontSlant->"Italic"]}]}]]], " means that the probability of the transfer of the disease from the \ infected individual to a susceptible is approximately 0.6. The choice ", Cell[BoxData[ \(\[Gamma] = 0.2\)]], " means that approximately ", Cell[BoxData[ \(1/\[Gamma] = 5\)]], " days are needed for the transition from infected to removals." }], "Text"] }, Closed]], Cell[CellGroupData[{ Cell["2.1.1 The code", "Subsubsection"], Cell[TextData[{ "Since the given system of ODE may only be solved numerically, we make use \ of ", StyleBox["Mathematica", FontSlant->"Italic"], " NDSolve procedure. The time interval of interest is ", Cell[BoxData[ RowBox[{"[", StyleBox[\(t1, t2\), FontSlant->"Italic"], "]"}]]], ", ", Cell[BoxData[ StyleBox[ RowBox[{ StyleBox["n", FontSlant->"Italic"], "0"}]]]], " is the initial size of population, the other symbols have been explained \ above. For the future use we also introduce variable ", Cell[BoxData[ \(z0\)]], ", the initial number of removed. The output is the list, the first part of \ which is the plot of the solution and the second part is the list of \ interpolating functions ", Cell[BoxData[ StyleBox[\(x, y, z\), FontSlant->"Italic"]]], "." }], "Text"], Cell[BoxData[{ StyleBox[\(Clear[SIR];\), FontColor->RGBColor[1, 0, 0]], "\[IndentingNewLine]", \(Needs["\"];\), "\ \[IndentingNewLine]", RowBox[{\(SIR[\[Beta]_, \[Gamma]_, x0_, z0_, n0_, {t1_, t2_}, plotlabel_: "\"]\), ":=", "\[IndentingNewLine]", RowBox[{"Module", "[", RowBox[{\({solsys, x, y, z}\), ",", "\[IndentingNewLine]", RowBox[{\(solsys = NDSolve[{\(x'\)[t] \[Equal] \(-\[Beta]\)\ x[t]\ y[t], \(y'\)[ t] \[Equal] \[Beta]\ x[t]\ y[t] - \[Gamma]\ y[ t], \(z'\)[t] \[Equal] \[Gamma]\ y[t], x[t1] \[Equal] x0, y[t1] \[Equal] n0 - \((x0 + z0)\), z[t1] \[Equal] z0}, {x, y, z}, {t, t1, t2}]\), ";", "\[IndentingNewLine]", \({x, y, z} = {x, y, z} /. 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Nevertheless, there are many situations appearing in \ practise where such an example is unrealistic. The infection rate may be \ considered either as a function of time or of number of removals. We mention \ two particular cases." }], "Text"], Cell[CellGroupData[{ Cell["2.2.1 Kendall's model", "Subsubsection"], Cell[TextData[{ "In this model it is supposed that the epidemic is governed by the \ classical model but the infection rate changes with the number of the \ removals. In other words, ", Cell[BoxData[ \(\[Beta]\)]], " is a function of ", Cell[BoxData[ StyleBox["z", FontSlant->"Italic"]]], ". The so called Kendall's parameter ", Cell[BoxData[ \(TraditionalForm\`\[Beta][z]\)]], " which is given by\n", Cell[BoxData[ \(\[Beta][ z] = \(2 \[Beta]\_0\)\/\(\((1 - \(z\ \[Beta]\_0\)\/\[Gamma])\) + \ \((1 - \(z\ \[Beta]\_0\)\/\[Gamma])\)\^\(-1\)\), \ 0 \[LessEqual] z < \(\(\[Gamma]\/\[Beta]\_0\)\(.\)\)\)], "DisplayFormula", FontSize->18], "\nNote that ", Cell[BoxData[ \(TraditionalForm\`\[Beta][z]\)]], " is decreasing as the number of removals is increasing and hence it may be \ used to model epidemics which are loosing the strength with decreasing number \ of susceptibles. Another important fact is that there exists an explicit \ solution to the classical deterministic SIR model with Kendall's ", Cell[BoxData[ \(TraditionalForm\`\[Beta][z]\)]], ". In our case, however, we use this function in Section 3." }], "Text"] }, Closed]], Cell[CellGroupData[{ Cell["2.2.2 Intervention models", "Subsubsection"], Cell[TextData[{ "The intervention usually takes place if the infection spreads to an \ unacceptable level.The intervention may be incorporated into the model by \ changing the parameter ", Cell[BoxData[ \(\[Beta]\)]], ". Since there is almost always to solve the equations numerically, we can \ model the intervention by any reasonable function. Moreover, by ", StyleBox["Mathematica", FontSlant->"Italic"], " we are also able to model some strategic decisions concerning spreading \ the disease. \n\nIn principle, the intervention may take two forms or both of \ them. The first consists in restrictions in contacts (closing schools, \ cinemas, etc.), the second one in vaccination of a part of a population \ (usually of people with intensive contacts with other people like drivers of \ the public transport, doctors, shop assistants) or just the whole population. \ Vaccination of a part of population would eventually lead to a reduction of \ susceptibles. All these measures result in changing ", Cell[BoxData[ \(\[Beta]\)]], ". \n\nHere we will develop a model in which the intervention will take \ place if the number of infectives reaches a prescribed percentage of \ population ", Cell[BoxData[ \(p\)], FontSlant->"Italic"], ", say, at time ", Cell[BoxData[ StyleBox[\(t\_p\), FontSlant->"Italic"]]], ". From the technical point of view, at time ", Cell[BoxData[ StyleBox[\(t\_p\), FontSlant->"Italic"]]], " we decrease ", Cell[BoxData[ \(\[Beta]\)]], ". Since under our assumptions ", Cell[BoxData[ RowBox[{ StyleBox["y", FontSlant->"Italic"], StyleBox["[", FontSlant->"Italic"], StyleBox["t", FontSlant->"Italic"], "]"}]]], " possesses just one global maximum on ", Cell[BoxData[ \(\([0, \[Infinity]]\)\)]], ", we will seek the first passage time of ", Cell[BoxData[ RowBox[{ StyleBox["y", FontSlant->"Italic"], "[", StyleBox["t", FontSlant->"Italic"], "]"}]]], " through ", Cell[BoxData[ \(Np\)], FontSlant->"Italic"], ". This and other actions described later can be surely done by very \ powerful method ", Cell[BoxData[ \(EventLocator\)]], " for ", Cell[BoxData[ \(NDSolve\)]], " but the authors of this contribution were not able to realize it in a \ reasonable time. We attack the problem in the following way. First we solve \ the problem on a sufficiently long time interval. Second we locate the first \ time where the maximum is achieved and then we are looking for ", Cell[BoxData[ StyleBox[\(t\_p\), FontSlant->"Italic"]]], ". Such an approach almost automate the procedure." }], "Text"], Cell["\<\ We will illustrate the procedure on the Example 2.1.1 step by step until we \ present the general procedure. \ \>", "Text"] }, Closed]], Cell[CellGroupData[{ Cell["2.2.2.1 Step by step", "Subsubsection"], Cell[TextData[{ "Remember that ", Cell[BoxData[ \(y211\)]], " is the interpolating function of infectives. First we find the \ approximate maximum and later use it as the initial solution to the \ differential equation ", Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{ StyleBox["y", FontSlant->"Italic"], "'"}], "[", StyleBox["t", FontSlant->"Italic"], "]"}], "=", "0"}]]], " which gives the unique maximum." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(yaux211 = Max[Table[ y211[t], {t, Floor[t\[Infinity]]}]]\), "\[IndentingNewLine]", \(taux211 = \(Position[Table[y211[t], {t, Floor[t\[Infinity]]}], yaux211]\)\[LeftDoubleBracket]1, 1\[RightDoubleBracket]\), "\[IndentingNewLine]", \(ymax211 = FindRoot[\(y211'\)[t] \[Equal] 0, {t, taux211}]\), "\[IndentingNewLine]", \(y211[t] /. ymax211\)}], "Input", CellLabel->"In[7]:="], Cell[BoxData[ \(0.3006229899220336`\)], "Output", CellLabel->"Out[7]="], Cell[BoxData[ RowBox[{\(General::"spell1"\), \(\(:\)\(\ \)\), "\<\"Possible spelling \ error: new symbol name \\\"\\!\\(taux211\\)\\\" is similar to existing symbol \ \\\"\\!\\(yaux211\\)\\\". \\!\\(\\*ButtonBox[\\\"More\[Ellipsis]\\\", \ ButtonStyle->\\\"RefGuideLinkText\\\", ButtonFrame->None, \ ButtonData:>\\\"General::spell1\\\"]\\)\"\>"}]], "Message", CellLabel->"From In[7]:="], Cell[BoxData[ \(19\)], "Output", CellLabel->"Out[8]="], Cell[BoxData[ \({t \[Rule] 19.177572308529403`}\)], "Output", CellLabel->"Out[9]="], Cell[BoxData[ \(0.3007960412487379`\)], "Output", CellLabel->"Out[10]="] }, Closed]], Cell[TextData[{ "Next we prescribe the upper percentage level of the infectives ", Cell[BoxData[ StyleBox["p", FontSlant->"Italic"]]], " and we get the desired starting time of the intervention. Due to \ monotonicity we choose the initial solution 90 per cent of the maximum." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(\(p = 0.1;\)\), "\[IndentingNewLine]", \(tp = t /. FindRoot[y211[t] \[Equal] p, {t, 0.9 t /. ymax211}]\)}], "Input", CellLabel->"In[11]:="], Cell[BoxData[ \(12.151618673637087`\)], "Output", CellLabel->"Out[12]="] }, Closed]], Cell[TextData[{ "We can look what will happen if we change ", Cell[BoxData[ \(\[Beta] \[RightArrow] 0.4\)]], " at this time. First we must extract the final values of ", Cell[BoxData[ StyleBox[\(x, y, z\), FontSlant->"Italic"]]], " at ", Cell[BoxData[ StyleBox[\(t\_p\), FontSlant->"Italic"]]], "." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \({xp, yp, zp} = {\(\(example211\[LeftDoubleBracket]2\[RightDoubleBracket]\)\ \[LeftDoubleBracket]1\[RightDoubleBracket]\)[ tp], \(\(example211\[LeftDoubleBracket]2\[RightDoubleBracket]\)\ \[LeftDoubleBracket]2\[RightDoubleBracket]\)[ tp], \(\(example211\[LeftDoubleBracket]2\[RightDoubleBracket]\)\ \[LeftDoubleBracket]3\[RightDoubleBracket]\)[tp]}\)], "Input", CellLabel->"In[13]:="], Cell[BoxData[ \({0.8436681576950378`, 0.10000000000000002`, 0.056331842304961896`}\)], "Output", CellLabel->"Out[13]="] }, Closed]], Cell[CellGroupData[{ Cell[BoxData[{ \(\(example211before = SIR[0.6, 0.2, 0.999, 0, 1, {0, tp}, "\"];\)\), "\ \[IndentingNewLine]", \(\(example211after = SIR[0.4, 0.2, xp, zp, 1, {tp, t\[Infinity]}, "\"];\)\)}], \ "Input", CellLabel->"In[14]:="], 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There are \ two possibilities, which can also be combined.\ \>", "Text", CellDingbat->None], Cell[TextData[{ "There is some percentage ", Cell[BoxData[ \(TraditionalForm\`p\_v\)]], " of people vaccinated before the epidemics starts and are therefore \ immune. It is the same model as before with the exception that now ", Cell[BoxData[ \(TraditionalForm\`z\_\(0 v\) = \(p\_v\) n\_0\)]], " and ", Cell[BoxData[ \(TraditionalForm\`x\_\(0 v\) = \(x\_0\)(1 - p\_v)\)]], "." }], "Text", CellDingbat->"\[FilledCircle]", TextAlignment->Left, TextJustification->0], Cell[TextData[{ "The vaccination is applied after the epidemics ", "starts ", "and there is some vaccination rate ", Cell[BoxData[ \(TraditionalForm\`v\)]], " which describes the speed of transition between the susceptibles and \ removals without passing the infected stage. The vaccination rate can be \ changing depending on the number of infectives or removals. 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Only \ very fast vaccination can have some important effect in such a case." }], "Text"], Cell["\<\ The combination of the two type of vaccination is, however, quite powerful \ tool. The results of the preventive vaccination are fascinating; With only \ 15 per cent of the population vaccinated, the total number of infected people \ is decreased substantially. The direct vaccination has almost no effect \ unless the vaccination rate is high (and therefore a relatively big \ proportion of the population is vaccinated every day).\ \>", "Text", Background->GrayLevel[1]] }, Closed]], Cell[CellGroupData[{ Cell[TextData[{ "2.3.3 Example with initially vaccinated individuals at ", Cell[BoxData[ \(TraditionalForm\`t = 0\)]] }], "Subsubsection"], Cell[TextData[{ "Consider the preventive vaccination of 15 percent of the population, ", Cell[BoxData[ \(TraditionalForm\`p\_v = 0.15\)]], ". 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The population size ", Cell[BoxData[ \(TraditionalForm\`N\_t = X\_t + Y\_t + Z\_t + W\_t\)]], " is governed by the stochastic differential equation (also called \ Engelbert-Schmidt equation)" }], "Text"], Cell[BoxData[ \(\[DifferentialD]N\_t = \[Sigma][N\_t] \(N\_t\) \[DifferentialD]B\_t, \ N\_0 = n\_0, \)], "DisplayFormula"], Cell[TextData[{ "where ", Cell[BoxData[ \(\[Sigma][ . ]\)]], " is a bounded function with a compact support and", StyleBox[" ", FontSlant->"Italic"], Cell[BoxData[ \(B\_t\)], FontSlant->"Italic"], " is a standard Brownian motion - Wiener process. The processes", StyleBox[" ", FontSlant->"Italic"], Cell[BoxData[ \(X\_t\)], FontSlant->"Italic"], ",", StyleBox[" ", FontSlant->"Italic"], Cell[BoxData[ \(Y\_t\)], FontSlant->"Italic"], ", ", Cell[BoxData[ \(Z\_t\)], FontSlant->"Italic"], ", and ", Cell[BoxData[ \(TraditionalForm\`W\_t\)]], " behave like in the deterministic case, in average. Various approaches \ will be analyzed and a simulation model will be developed." }], "Text"], Cell[TextData[{ "The infection parameter \[Beta] will now be considered as a function of \ the removals ", Cell[BoxData[ \(TraditionalForm\`Z\_t\)]], " instead of being constant. The SIR model with vaccination and stochastic \ population size can be written as the system of four stochastic differential \ equations" }], "Text"], Cell[BoxData[{ RowBox[{ RowBox[{ StyleBox[\(\[DifferentialD]X\_t\), FontVariations->{"CompatibilityType"->0}], StyleBox["\[AlignmentMarker]", FontVariations->{"CompatibilityType"->0}], StyleBox["=", FontVariations->{"CompatibilityType"->0}], RowBox[{ RowBox[{ RowBox[{ StyleBox["-", FontVariations->{"CompatibilityType"->0}], RowBox[{ StyleBox["\[Beta]", FontWeight->"Plain", FontSlant->"Plain", FontTracking->"Plain", FontColor->GrayLevel[0], FontVariations->{"Underline"->False, "Outline"->False, "Shadow"->False, "StrikeThrough"->False, "Masked"->False, "CompatibilityType"->0, "RotationAngle"->0}], StyleBox["[", FontVariations->{"CompatibilityType"->0}], StyleBox[\(Z\_t\), FontVariations->{"CompatibilityType"->0}], StyleBox["]", FontVariations->{"CompatibilityType"->0}]}]}], StyleBox[\(X\_t\), FontVariations->{"CompatibilityType"->0}], StyleBox[\(Y\_t\), FontVariations->{"CompatibilityType"->0}], StyleBox[\(\[DifferentialD]t\), FontVariations->{"CompatibilityType"->0}]}], StyleBox["-", FontVariations->{"CompatibilityType"->0}], RowBox[{ StyleBox["v", FontVariations->{"CompatibilityType"->0}], StyleBox[" ", FontVariations->{"CompatibilityType"->0}], SubscriptBox[ StyleBox["X", FontVariations->{"CompatibilityType"->0}], "t"], \(\[DifferentialD]t\)}], "+", RowBox[{ StyleBox[\(X\_t\), FontVariations->{"CompatibilityType"->0}], RowBox[{ StyleBox["\[Sigma]", FontColor->GrayLevel[0]], StyleBox["[", FontVariations->{"CompatibilityType"->0}], SubscriptBox[ StyleBox["N", FontVariations->{"CompatibilityType"->0}], "t"], StyleBox["]", FontVariations->{"CompatibilityType"->0}]}], RowBox[{ StyleBox["\[DifferentialD]", FontWeight->"Plain", FontSlant->"Plain", FontTracking->"Plain", FontVariations->{"Underline"->False, "Outline"->False, "Shadow"->False, "StrikeThrough"->False, "Masked"->False, "CompatibilityType"->0, "RotationAngle"->0}], SubscriptBox[ StyleBox["B", FontWeight->"Plain", FontSlant->"Plain", FontTracking->"Plain", FontVariations->{"Underline"->False, "Outline"->False, "Shadow"->False, "StrikeThrough"->False, "Masked"->False, "CompatibilityType"->0, "RotationAngle"->0}], "t"]}]}]}]}], ",", " ", \(X\_0 = x\_0\), ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"\[DifferentialD]", StyleBox["\[AlignmentMarker]", FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]], \(Y\_t\)}], StyleBox["=", FontVariations->{"CompatibilityType"->0}], RowBox[{ RowBox[{ RowBox[{"\[Beta]", StyleBox["[", FontVariations->{"CompatibilityType"->0}], StyleBox[\(Z\_t\), FontVariations->{"CompatibilityType"->0}], StyleBox["]", FontVariations->{"CompatibilityType"->0}]}], SubscriptBox[ StyleBox["X", FontVariations->{"CompatibilityType"->0}], "t"], \(Y\_t\), \(\[DifferentialD]t\)}], "-", \(\((\[Gamma] + v)\)\ \(Y\_t\) \[DifferentialD]t\), "+", \(\(Y\_t\) \[Sigma][N\_t] \[DifferentialD]B\_t\)}]}], ",", " ", \(Y\_0 = y\_\(\(0\)\(,\)\)\)}], "\[IndentingNewLine]", \(\[DifferentialD]Z\_t \ = \(\((\[Gamma] + v)\) \(Y\_t\) \[DifferentialD]t + \(Z\_t\) \[Sigma][ N\_t] \[DifferentialD]B\_\(\(t\)\(,\)\(\ \ \)\)\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Z\ \_0 = 0\), \[IndentingNewLine]\[DifferentialD]W\_t = v\ \(X\_t\) \[DifferentialD]t + \(W\_t\) \[Sigma][ N\_t] \[DifferentialD]B\_t, \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ W\_0 = w\_\(\(0\)\(,\)\)\)}], "DisplayFormula", TextAlignment->Left, TextJustification->1], Cell[TextData[{ "where ", Cell[BoxData[ \(TraditionalForm\`N\_t = X\_t + Y\_t + Z\_t + W\_t\)]], ", ", Cell[BoxData[ \(\[Gamma]\)]], " and ", Cell[BoxData[ StyleBox["v", FontSlant->"Italic"]]], " have the same meaning as above." }], "Text"], Cell[TextData[{ "Apparently, the numerical solution to the system requires to simulate four \ diffusion processes ", Cell[BoxData[ \(TraditionalForm\`X\_t, \ Y\_t, \)]], " ", Cell[BoxData[ \(TraditionalForm\`\(\(Z\_t\)\(,\)\)\)]], " and ", Cell[BoxData[ \(TraditionalForm\`W\_t\)]], ", respectively. In fact it is sufficient to simulate just one diffusion \ process ", Cell[BoxData[ \(TraditionalForm\`N\_t\)]], ", since the stochastic differential equations above may be rewritten as a \ system of ODE with random coefficients" }], "Text"], Cell[BoxData[ RowBox[{ RowBox[{ StyleBox[\(\[DifferentialD]x \((t)\)\), FontVariations->{"CompatibilityType"->0}], StyleBox["=", FontVariations->{"CompatibilityType"->0}], RowBox[{ StyleBox[\(\(-\[Alpha][z \((t)\), N\_t]\) x \((t)\) y \((t)\) \[DifferentialD]t\), FontVariations->{"CompatibilityType"->0}], StyleBox["-", FontVariations->{"CompatibilityType"->0}], RowBox[{ StyleBox["v", FontVariations->{"CompatibilityType"->0}], StyleBox[" ", FontVariations->{"CompatibilityType"->0}], StyleBox[\(X\_t\), FontWeight->"Plain", FontSlant->"Italic", FontTracking->"Plain", FontVariations->{"Underline"->False, "Outline"->False, "Shadow"->False, "StrikeThrough"->False, "Masked"->False, "CompatibilityType"->0, "RotationAngle"->0}], \(\[DifferentialD]t\)}]}]}], ",", StyleBox[ RowBox[{ StyleBox[" ", FontWeight->"Bold", FontColor->GrayLevel[0]], StyleBox[" ", FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]]}]], StyleBox[\(x \((0)\) = x\_0\/N\_0\), FontColor->GrayLevel[0], FontVariations->{"CompatibilityType"->0}], StyleBox[",", FontColor->GrayLevel[0], FontVariations->{"CompatibilityType"->0}], StyleBox["\[IndentingNewLine]", FontWeight->"Bold"], StyleBox[\(\[DifferentialD]y \((t)\) = \[Alpha][z \((t)\), N\_t] x \((t)\) y \((t)\) \[DifferentialD]t - \((\[Gamma] + v)\)\ y \((t)\) \[DifferentialD]t\), FontVariations->{"CompatibilityType"->0}], StyleBox[",", FontWeight->"Bold"], StyleBox[" ", FontWeight->"Bold"], StyleBox[\(y \((0)\) = y\_0\/N\_0\), FontVariations->{"CompatibilityType"->0}], StyleBox[",", FontVariations->{"CompatibilityType"->0}], StyleBox["\[IndentingNewLine]", FontWeight->"Bold"], StyleBox[\(\[DifferentialD]z \((t)\)\ = \ \((\[Gamma] + v)\)\ y \((t)\) \[DifferentialD]t\), FontVariations->{"CompatibilityType"->0}], StyleBox[",", FontVariations->{"CompatibilityType"->0}], StyleBox[ " ", FontWeight->"Bold"], StyleBox[\(z \((0)\) = 0\), FontVariations->{"CompatibilityType"->0}], StyleBox[",", FontVariations->{"CompatibilityType"->0}], StyleBox["\[IndentingNewLine]", FontWeight->"Bold"], RowBox[{ StyleBox[\(\[DifferentialD]w \((t)\)\), FontVariations->{"CompatibilityType"->0}], StyleBox["=", FontVariations->{"CompatibilityType"->0}], RowBox[{ StyleBox["v", FontVariations->{"CompatibilityType"->0}], StyleBox[" ", FontVariations->{"CompatibilityType"->0}], SubscriptBox[ StyleBox["X", FontVariations->{"CompatibilityType"->0}], "t"], \(\[DifferentialD]t\)}]}], ",", " \ ", \(w \((0)\) = w\_0\/N\_0\), ","}]], "DisplayFormula"], Cell[TextData[{ "where ", Cell[BoxData[ FormBox[ RowBox[{\(\[Alpha](z, n)\), "=", RowBox[{"n", " ", RowBox[{"\[Beta]", StyleBox["(", FontColor->GrayLevel[0]], \(n\[CenterDot]z\), ")"}]}]}], TraditionalForm]]], ", and ", Cell[BoxData[ \(TraditionalForm\`N\_t\)]], " is given by the Engelbert-Schmidt equation. In particular case, it is \ possible to use the deterministic solution of the ODE described in Section 2 \ and multiply the solution ", Cell[BoxData[ \(TraditionalForm\`\((X\_t, \ Y\_t, \ Z\_t, \ W\_t)\)\)]], " by the simulated population size ", Cell[BoxData[ \(TraditionalForm\`\(\(N\_t\)\(.\)\)\)]], " Such a special case simplifies calculations and analysis a bit. Usually \ we have to solve a system of differential equations with random coefficients \ (in particular the coefficient ", Cell[BoxData[ \(TraditionalForm\`\[Alpha]\)]], " depends on the population size) numerically. In both cases, the first \ step is to simulate the population size." }], "Text"], Cell[CellGroupData[{ Cell["3.1 The population size", "Subsection"], Cell[CellGroupData[{ Cell["\<\ 3.1.1 Step I: Engelbert-Schmidt equation of the population size\ \>", "Subsubsection"], Cell["The strong solution of the Engelbert-Schmidt equation", "Text"], Cell[BoxData[ \(\[DifferentialD]N\_t = \[Sigma][N\_t] \(N\_t\) \[DifferentialD]W\_t, \ N\_0 = n\_0\)], "DisplayFormula"], Cell[TextData[{ "exists if ", Cell[BoxData[ \(TraditionalForm\`\[Sigma]\)]], " is a Lipschitz function. We typically choose " }], "Text"], Cell[BoxData[ RowBox[{\(\[Sigma][n]\), "=", TagBox[ StyleBox[ RowBox[{"{", StyleBox[GridBox[{ { RowBox[{" ", RowBox[{ RowBox[{ RowBox[{\(\(\(\((n - a)\)\^\[Nu]\_1\) \((b - \ n)\)\^\[Nu]\_2\)\/\(\(n\^\[Nu]\_3\) \@\(a + b\)\)\), " ", Cell["if"], " ", "a"}], " ", "\[LessEqual]", "n", "\[LessEqual]", "b"}], ","}]}]}, { RowBox[{ RowBox[{"0", " ", Cell[" \t\t\t otherwise"]}], ","}]} }], ShowAutoStyles->True]}], ShowAutoStyles->False], (#&)]}]], "DisplayFormula", TextAlignment->Left], Cell[TextData[{ "where ", Cell[BoxData[ \(TraditionalForm\`a < b\)]], " are the bounds of the population size, and ", Cell[BoxData[ \(TraditionalForm\`\[Sigma]\)]], " in this case need not to be locally Lipschitz. However, there still \ exists a weak solution to the Engelbert-Schmidt equation if " }], "Text"], Cell[BoxData[ \(\[Integral]\_\(-\[CurlyEpsilon]\)\%\[CurlyEpsilon]\(\((\[Sigma][ x + n])\)\^\(-2\)\) \[DifferentialD]x = \(\[Infinity]\ \ \ \ \(\[ForAll] \[CurlyEpsilon] > 0\ \ \ \[DoubleLongLeftRightArrow]\ \ \ \[Sigma][n]\) = 0. \)\)], "DisplayFormula", TextAlignment->Left], Cell[TextData[{ "The weak solution can be constructed in a following way. Let ", Cell[BoxData[ \(TraditionalForm\`{B\_t, \ t \[GreaterEqual] 0}\)]], " be a standard Brownian motion defined on some complete probability space. \ Denote" }], "Text"], Cell[BoxData[ RowBox[{\(A\_t\), "=", RowBox[{\(\[Integral]\_0\^t\), RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{\(B\_u\), "\[CenterDot]", RowBox[{"\[Sigma]", "[", StyleBox[\(B\_u\), FontColor->GrayLevel[0]], "]"}]}], ")"}], "2"], \(\[DifferentialD]u\)}]}]}]], "DisplayFormula", TextAlignment->Left], Cell["a strictly nondecreasing process, and ", "Text"], Cell[BoxData[ \(\[Tau]\_t = inf {s : A\_s > t}\)], "DisplayFormula", TextAlignment->Left], Cell[TextData[{ "the time of the first entry of ", Cell[BoxData[ \(TraditionalForm\`A\_s\)]], " to ", Cell[BoxData[ \(TraditionalForm\`\((t, \[Infinity])\)\)]], ". According to Engelbert-Schmidt, the process" }], "Text"], Cell[BoxData[ StyleBox[\(N\_t = B\_\(\[Tau]\_t\)\), FontVariations->{"CompatibilityType"->0}]], "DisplayFormula", TextAlignment->Left], Cell["\<\ is the unique weak solution to the SDE for the population size.\ \>", "Text"] }, Closed]], Cell[CellGroupData[{ Cell["3.1.2 Step II: Simulation of the population size", "Subsubsection"], Cell[TextData[{ "We start with simulated standard Brownian motion ", Cell[BoxData[ FormBox[ StyleBox[\(B\_s\), FontColor->GrayLevel[0]], TraditionalForm]]], " up to its first entry to ", Cell[BoxData[ FormBox[ StyleBox["a", FontColor->GrayLevel[0]], TraditionalForm]], FontColor->RGBColor[0, 0, 1]], " or ", Cell[BoxData[ \(TraditionalForm\`b\)]], ". Let us consider a sequence of independent N(0,1) distributed r.v. ", Cell[BoxData[ \(TraditionalForm\`Z\_i\)]], " and define simulated Brownian motion with reference points " }], "Text"], Cell[BoxData[ \(0\[AlignmentMarker]\[AlignmentMarker] = \(t\_0 < t\_1 < \[CenterEllipsis] < \[Tau]\_{a, b} = inf {\(t\_j\) : \ B\_\(t\_j\) \[LessEqual] a, \ or\ \ B\_\(t\_j\) \[GreaterEqual] b}\), \[IndentingNewLine]B\_\(t\_i\)\[AlignmentMarker]\ \[AlignmentMarker] = B\_\(t\_\(i - 1\)\) + \(\@\(t\_i - t\_\(i - 1\)\)\) Z\_i, \ B\_0 = n\_0, \[IndentingNewLine]B\_u\[AlignmentMarker]\[AlignmentMarker] \ = B\_\(t\_\(i - 1\)\) + \(\(u - t\_\(i - 1\)\)\/\(t\_i - t\_\(i - 1\)\)\) \((B\_\(t\_i\) - B\_\(t\_\(i - 1\)\))\), \ t\_\(i - 1\) \[LessEqual] u \[LessEqual] t\_i, \)], "DisplayFormula", TextAlignment->AlignmentMarker], Cell[TextData[{ "where the time step for simulations of a standard Brownian motion is \ usually considered fixed, ", Cell[BoxData[ \(TraditionalForm\`\[CapitalDelta] := t\_i - t\_\(i - 1\)\)]], ". Using this simulated piecewise linear process we calculate the \ increasing process ", Cell[BoxData[ FormBox[ StyleBox[\(A\_t\), FontColor->GrayLevel[0]], TraditionalForm]], FontColor->RGBColor[0, 0, 1]], " as piecewise linear with " }], "Text"], Cell[BoxData[ RowBox[{ RowBox[{\(A\_\(t\_i\)\), "=", RowBox[{\(A\_\(t\_\(i - 1\)\)\), "+", RowBox[{\(\(t\_i - t\_\(i - 1\)\)\/Z\_i\), RowBox[{\(\[Integral]\_\(B\_\(t\_\(i - 1\)\)\)\%\(B\_\(t\_i\)\)\), RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{"x", StyleBox["\[CenterDot]", FontColor->RGBColor[0, 0, 1]], \(\[Sigma][x]\)}], ")"}], \(-2\)], \(\[DifferentialD]x\)}]}]}]}]}], ",", " ", \(A\_0 = 0\)}]], "DisplayFormula"], Cell["or more simply by Riemann sums", "Text"], Cell[BoxData[ \(A\_\(t\_i\) = A\_\(t\_\(i - 1\)\) + \(t\_i - t\_\(i - 1\)\)\/\((B\_\(t\_\(i - 1\)\)\ \[CenterDot]\[Sigma][B\_\(t\_\(i - 1\)\)])\)\^2, \ A\_0 = 0. \)], "DisplayFormula"], Cell[TextData[{ "Then we use ", Cell[BoxData[ StyleBox[\(N\_\(A\_\(t\_i\)\) = B\_\(t\_i\)\), FontWeight->"Bold"]], "DisplayFormula", TextAlignment->Center, FontVariations->{"CompatibilityType"->0}], " and we employ some interpolation (may be piecewise linear) to calculate \ ", Cell[BoxData[ FormBox[ StyleBox[\(N\_u\), FontColor->GrayLevel[0]], TraditionalForm]], FontColor->RGBColor[0, 0, 1]], " for any ", Cell[BoxData[ FormBox[ StyleBox["u", FontColor->GrayLevel[0]], TraditionalForm]]], "." }], "Text"] }, Closed]], Cell[CellGroupData[{ Cell["3.1.2.1 Remark", "Subsubsection"], Cell[TextData[{ "A simple simulation of the Brownian motion using ", Cell[BoxData[ FormBox[ StyleBox[\(t\_i - t\_\(i - 1\) = \[CapitalDelta]\), FontColor->GrayLevel[0]], TraditionalForm]]], " has a major disadvantage. The increments of ", Cell[BoxData[ \(TraditionalForm\`A\_\(t\_i\) - A\_\(t\_\(i - 1\)\)\)]], " become ", StyleBox["extremely large", FontWeight->"Bold", FontSlant->"Italic", FontColor->RGBColor[0.0313725, 0.541176, 0]], " as ", Cell[BoxData[ \(TraditionalForm\`B\)]], " approaches the limit ", Cell[BoxData[ FormBox[ StyleBox["a", FontColor->GrayLevel[0]], TraditionalForm]], FontColor->RGBColor[0, 0, 1]], " or ", Cell[BoxData[ \(TraditionalForm\`b\)]], ", and on the other hand they can be ", StyleBox["very small", FontWeight->"Bold", FontSlant->"Italic", FontColor->RGBColor[0.0705882, 0.541176, 0]], " if ", Cell[BoxData[ \(TraditionalForm\`B\)]], " is far from ", Cell[BoxData[ FormBox[ StyleBox["a", FontColor->GrayLevel[0]], TraditionalForm]], FontColor->RGBColor[0, 0, 1]], " and ", Cell[BoxData[ \(TraditionalForm\`b\)]], ". Hence the simulated time differences for the population size process may \ differ substantially.\n\tSome results from the classical theory like L\ \[EAcute]vy modulus of continuity or Law of iterated logarithm can be used to \ construct self-adjusted time increments, ", Cell[BoxData[ FormBox[ StyleBox[\(t\_i - t\_\(i - 1\) = \[Xi][B\_\(t\_\(i - 1\)\)]\), FontColor->GrayLevel[0]], TraditionalForm]], FontColor->RGBColor[0, 0, 1]], ", for the simulated Brownian motion. " }], "Text", TextAlignment->Left], Cell[TextData[{ "For the sake of simplicity we prefer to adjust the time increment of the \ simulated Brownian motion with the aim to control the increments of ", Cell[BoxData[ \(TraditionalForm\`A\_t\)]], ". Hence the simulated time step of ", Cell[BoxData[ \(TraditionalForm\`N\_t\)]], " is kept in reasonable bounds. It For the numerical solution of the \ epidemic model it is quite useful since we need to interpolate the simulated \ process." }], "Text"] }, Closed]], Cell[CellGroupData[{ Cell["3.1.3 Example", "Subsubsection"], Cell[TextData[{ "We consider the initial population size ", Cell[BoxData[ \(TraditionalForm\`N\_0 = 1025\)]], ", the bounds ", Cell[BoxData[ \(TraditionalForm\`a = 1000, \ b = 1050\)]], ", and the diffusion parameter ", Cell[BoxData[ \(TraditionalForm\`\[Sigma]\)]], " in the form" }], "Text"], Cell[BoxData[ RowBox[{\(\[Sigma][n]\), "=", TagBox[ StyleBox[ RowBox[{"{", StyleBox[GridBox[{ { RowBox[{ RowBox[{ RowBox[{ "3", " ", \(\(\(\((n - a)\)\^\(1/ 2\)\) \((b - n)\)\^\(1/2\)\)\/\((a + b)\ \)\^\(1/2\)\), " ", Cell["if"], " ", "a"}], " ", "\[LessEqual]", "n", "\[LessEqual]", "b"}], ","}]}, { RowBox[{"0", " ", RowBox[{Cell[" \t\t\t otherwise"], "."}]}]} }], ShowAutoStyles->True]}], ShowAutoStyles->False], (#&)]}]], "DisplayFormula"], Cell[TextData[StyleBox["Initial values:", 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\@\[Delta]];\), "\[IndentingNewLine]", \(\(walk12 = NestWhileList[\((# + Random[distr] &)\), Last[walk11], aA + 2 < # < bB - 2 &] // Rest;\)\), "\[IndentingNewLine]", \(\(times2 = FoldList[Plus, Last[times1], Table[1\/n, {Length[walk12]}]] // Rest;\)\), "\[IndentingNewLine]", \(n = 1000; \[Delta] = 1\/n; distr = NormalDistribution[0, \@\[Delta]];\), "\[IndentingNewLine]", \(\(walk13 = NestWhileList[\((# + Random[distr] &)\), Last[walk12], aA + 0.1 < # < bB - 0.1 &] // Rest;\)\), "\[IndentingNewLine]", \(\(times3 = FoldList[Plus, Last[times2], Table[1\/n, {Length[walk13]}]] // Rest;\)\), "\[IndentingNewLine]", \(n = 10000; \[Delta] = 1\/n; distr = NormalDistribution[0, \@\[Delta]];\), "\[IndentingNewLine]", \(\(walk14 = NestWhileList[\((# + Random[distr] &)\), Last[walk13], aA < # < bB &] // Rest;\)\), "\[IndentingNewLine]", \(\(times4 = FoldList[Plus, Last[times3], Table[1\/n, {Length[walk14]}]] // Rest;\)\)}], "Input", CellLabel->"In[46]:="], Cell[CellGroupData[{ Cell[BoxData[{ 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L .22845 .2048 L .22863 .20339 L .22882 .21467 L .22901 .22022 L .22919 .22484 L Mistroke .22938 .21368 L .22957 .21068 L .22976 .21519 L .22994 .21485 L .23013 .21723 L .23032 .22101 L .2305 .2232 L .23069 .22441 L .23088 .22495 L .23106 .22648 L .23125 .23237 L .23144 .22461 L .23162 .21719 L .23181 .22327 L .232 .21928 L .23219 .21885 L .23237 .21709 L .23256 .2224 L .23275 .21821 L .23293 .21724 L .23312 .21824 L .23331 .21211 L .23349 .2146 L .23368 .21883 L .23387 .21339 L .23405 .21418 L .23424 .21712 L .23443 .21004 L .23461 .21261 L .2348 .20942 L .23499 .20751 L .23518 .20845 L .23536 .21135 L .23555 .20751 L .23574 .20859 L .23592 .21113 L .23611 .20623 L .2363 .21704 L .23648 .21584 L .23667 .21447 L .23686 .20605 L .23704 .20624 L .23723 .21104 L .23742 .20458 L .2376 .20893 L .23779 .21383 L .23798 .21796 L .23817 .21855 L .23835 .21161 L .23854 .20945 L Mistroke .23873 .20723 L .23891 .21102 L .2391 .21522 L .23929 .21705 L .23947 .21619 L .23966 .21178 L .23985 .209 L .24003 .19706 L .24022 .19459 L .24041 .19356 L .24059 .20126 L .24078 .20359 L .24097 .20415 L .24116 .21378 L .24134 .21895 L .24153 .22084 L .24172 .22117 L .2419 .22045 L .24209 .21565 L .24228 .21624 L .24246 .22101 L .24265 .21211 L .24284 .21214 L .24302 .20472 L .24321 .21317 L .2434 .20473 L .24358 .20887 L .24377 .20946 L .24396 .20999 L .24415 .19852 L .24433 .19735 L .24452 .19644 L .24471 .18713 L .24489 .18804 L .24508 .18349 L .24527 .18275 L .24545 .18188 L .24564 .18467 L .24583 .17935 L .24601 .1783 L .2462 .1829 L .24639 .1845 L .24658 .18261 L .24676 .18708 L .24695 .18937 L .24714 .19589 L .24732 .19149 L .24751 .19409 L .2477 .19451 L .24788 .199 L Mistroke .24807 .20291 L .24826 .20191 L .24844 .20065 L .24863 .20271 L .24882 .20095 L .249 .20037 L .24919 .19592 L .24938 .20175 L .24957 .20298 L .24975 .20098 L .24994 .19562 L .25013 .18752 L .25031 .18816 L .2505 .19252 L .25069 .19985 L .25087 .20438 L .25106 .20446 L .25125 .20308 L .25143 .19934 L .25162 .19086 L .25181 .1841 L .25199 .18526 L .25218 .18794 L .25237 .19118 L .25256 .1965 L .25274 .19515 L .25293 .20338 L .25312 .20043 L .2533 .20172 L .25349 .20498 L .25368 .21505 L .25386 .21091 L .25405 .20676 L .25424 .20974 L .25442 .20617 L .25461 .20569 L .2548 .2044 L .25498 .20127 L .25517 .19859 L .25536 .20882 L .25555 .20243 L .25573 .21004 L .25592 .20258 L .25611 .19884 L .25629 .20286 L .25648 .19792 L .25667 .18874 L .25685 .19497 L .25704 .19874 L .25723 .19502 L Mistroke .25741 .19758 L .2576 .19218 L .25779 .19246 L .25798 .19077 L .25816 .19122 L .25835 .1911 L .25854 .19684 L .25872 .19409 L .25891 .19023 L .2591 .18538 L .25928 .18729 L .25947 .18836 L .25966 .18609 L .25984 .18501 L .26003 .19372 L .26022 .18691 L .2604 .18553 L .26059 .18424 L .26078 .17521 L .26097 .17539 L .26115 .185 L .26134 .1944 L .26153 .20367 L .26171 .2117 L .2619 .21052 L .26209 .2132 L .26227 .21006 L .26246 .21563 L .26265 .21114 L .26283 .21124 L .26302 .21933 L .26321 .22122 L .26339 .22545 L .26358 .22771 L .26377 .22799 L .26396 .22881 L .26414 .23439 L .26433 .23999 L .26452 .23428 L .2647 .23786 L .26489 .24244 L .26508 .25085 L .26526 .25099 L .26545 .25847 L .26564 .25576 L .26582 .2587 L .26601 .25577 L .2662 .25178 L .26638 .24771 L .26657 .23799 L Mistroke .26676 .24614 L .26695 .24245 L .26713 .24228 L .26732 .23685 L .26751 .23548 L .26769 .2292 L .26788 .237 L .26807 .23718 L .26825 .23002 L .26844 .2335 L .26863 .23673 L .26881 .22986 L .269 .23113 L .26919 .23398 L .26937 .22918 L .26956 .22161 L .26975 .22609 L .26994 .22998 L .27012 .23404 L .27031 .2331 L .2705 .22792 L .27068 .23302 L .27087 .23385 L .27106 .22299 L .27124 .22527 L .27143 .22084 L .27162 .21307 L .2718 .21241 L .27199 .20793 L .27218 .20618 L .27237 .20264 L .27255 .19225 L .27274 .1913 L .27293 .19093 L .27311 .19515 L .2733 .19422 L .27349 .19822 L .27367 .19226 L .27386 .18533 L .27405 .18143 L .27423 .18569 L .27442 .1882 L .27461 .1864 L .27479 .18359 L .27498 .18816 L .27517 .1861 L .27536 .19067 L .27554 .18622 L .27573 .18516 L .27592 .18595 L Mistroke .2761 .19089 L .27629 .18956 L .27648 .19282 L .27666 .18863 L .27685 .18933 L .27704 .19472 L .27722 .20038 L .27741 .20801 L .2776 .21641 L .27778 .21479 L .27797 .21215 L .27816 .2146 L .27835 .21696 L .27853 .21525 L .27872 .21809 L .27891 .21809 L .27909 .21883 L .27928 .21508 L .27947 .21287 L .27965 .21303 L .27984 .2129 L .28003 .20363 L .28021 .20712 L .2804 .20071 L .28059 .19907 L .28077 .20602 L .28096 .20307 L .28115 .20441 L .28134 .19954 L .28152 .1975 L .28171 .20424 L .2819 .20881 L .28208 .21198 L .28227 .20445 L .28246 .21836 L .28264 .22136 L .28283 .22076 L .28302 .22684 L .2832 .21994 L .28339 .22034 L .28358 .22351 L .28377 .22691 L .28395 .23243 L .28414 .23049 L .28433 .23318 L .28451 .23751 L .2847 .24021 L .28489 .24312 L .28507 .24846 L .28526 .25537 L Mistroke .28545 .25574 L .28563 .25916 L .28582 .26616 L .28601 .27374 L .28619 .27706 L .28638 .27268 L .28657 .27497 L .28676 .27314 L .28694 .28184 L .28713 .28131 L .28732 .29423 L .2875 .29256 L .28769 .29809 L .28788 .28944 L .28806 .28954 L .28825 .28754 L .28844 .28241 L .28862 .28866 L .28881 .2839 L .289 .28249 L .28918 .28217 L .28937 .27878 L .28956 .27421 L .28975 .28894 L .28993 .29605 L .29012 .29326 L .29031 .30263 L .29049 .30398 L .29068 .30247 L .29087 .30734 L .29105 .30773 L .29124 .30567 L .29143 .31158 L .29161 .31961 L .2918 .31537 L .29199 .32336 L .29217 .31599 L .29236 .31187 L .29255 .30346 L .29274 .30486 L .29292 .31267 L .29311 .32109 L .2933 .32029 L .29348 .31782 L .29367 .31741 L .29386 .31684 L .29404 .3198 L .29423 .31885 L .29442 .31407 L .2946 .30929 L Mistroke .29479 .31704 L .29498 .31988 L .29516 .32091 L .29535 .32613 L .29554 .32087 L .29573 .31708 L .29591 .31159 L .2961 .30775 L .29629 .30178 L .29647 .30617 L .29666 .3202 L .29685 .31472 L .29703 .31714 L .29722 .31331 L .29741 .31355 L .29759 .3053 L .29778 .30067 L .29797 .3032 L .29816 .30281 L .29834 .29742 L .29853 .29865 L .29872 .29565 L .2989 .2953 L .29909 .3 L .29928 .29904 L .29946 .29534 L .29965 .28914 L .29984 .29475 L .30002 .29461 L .30021 .29831 L .3004 .29253 L .30058 .28372 L .30077 .28224 L .30096 .2892 L .30115 .30265 L .30133 .3038 L .30152 .29673 L .30171 .29462 L .30189 .29713 L .30208 .29608 L .30227 .29678 L .30245 .30061 L .30264 .30063 L .30283 .29953 L .30301 .30172 L .3032 .29992 L .30339 .30185 L .30357 .3049 L .30376 .30528 L .30395 .29725 L Mistroke .30414 .29763 L .30432 .29749 L .30451 .29418 L .3047 .29967 L .30488 .30264 L .30507 .3001 L .30526 .29915 L .30544 .29434 L .30563 .28906 L .30582 .29042 L .306 .29355 L .30619 .29291 L .30638 .29765 L .30656 .29793 L .30675 .29469 L .30694 .30058 L .30713 .29954 L .30731 .29686 L .3075 .30328 L .30769 .30893 L .30787 .30115 L .30806 .30347 L .30825 .2978 L .30843 .30448 L .30862 .30256 L .30881 .30866 L .30899 .31855 L .30918 .32191 L .30937 .3224 L .30956 .32194 L .30974 .32121 L .30993 .31817 L .31012 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.32189 .29282 L .32208 .29399 L .32226 .29949 L .32245 .30568 L .32264 .29897 L Mistroke .32282 .29718 L .32301 .30101 L .3232 .30009 L .32338 .30743 L .32357 .30722 L .32376 .30572 L .32395 .29979 L .32413 .2951 L .32432 .29399 L .32451 .28889 L .32469 .2838 L .32488 .28497 L .32507 .28163 L .32525 .28399 L .32544 .29276 L .32563 .29802 L .32581 .29858 L .326 .29635 L .32619 .29605 L .32637 .30238 L .32656 .30347 L .32675 .30017 L .32694 .29471 L .32712 .2923 L .32731 .29694 L .3275 .2962 L .32768 .30039 L .32787 .29446 L .32806 .29594 L .32824 .29997 L .32843 .3027 L .32862 .30399 L .3288 .30831 L .32899 .30765 L .32918 .30696 L .32936 .30891 L .32955 .30294 L .32974 .301 L .32993 .29367 L .33011 .29658 L .3303 .28857 L .33049 .29169 L .33067 .28992 L .33086 .29611 L .33105 .29878 L .33123 .30171 L .33142 .29215 L .33161 .29619 L .33179 .2977 L .33198 .2955 L Mistroke .33217 .29045 L .33235 .29166 L .33254 .29989 L .33273 .30286 L .33292 .29723 L .3331 .29776 L .33329 .29084 L .33348 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.284 L .34544 .27945 L .34562 .27275 L .34581 .27747 L .346 .28106 L .34618 .2796 L .34637 .27501 L .34656 .28189 L .34674 .28291 L .34693 .28664 L .34712 .29457 L .34731 .29479 L .34749 .28416 L .34768 .28413 L .34787 .28631 L .34805 .28167 L .34824 .28057 L .34843 .28955 L .34861 .29129 L .3488 .29495 L .34899 .30212 L .34917 .31436 L .34936 .32666 L .34955 .32792 L .34974 .32629 L .34992 .33024 L .35011 .32295 L .3503 .31683 L .35048 .32047 L .35067 .31189 L Mistroke .35086 .31232 L .35104 .30643 L .35123 .30971 L .35142 .30327 L .3516 .30705 L .35179 .30656 L .35198 .30335 L .35216 .29929 L .35235 .29823 L .35254 .29778 L .35273 .29927 L .35291 .30023 L .3531 .3016 L .35329 .30201 L .35347 .30435 L .35366 .30402 L .35385 .30291 L .35403 .30619 L .35422 .31343 L .35441 .31089 L .35459 .3108 L .35478 .31379 L .35497 .30434 L .35515 .30237 L .35534 .29498 L .35553 .30576 L .35572 .30694 L .3559 .30468 L .35609 .30655 L .35628 .30545 L .35646 .30985 L .35665 .31129 L .35684 .308 L .35702 .31504 L .35721 .3171 L .3574 .31565 L .35758 .31801 L .35777 .3154 L .35796 .31121 L .35814 .31135 L .35833 .31098 L .35852 .3135 L .35871 .31863 L .35889 .32065 L .35908 .32177 L .35927 .32406 L .35945 .33502 L .35964 .33212 L .35983 .33282 L .36001 .33402 L Mistroke .3602 .32716 L .36039 .32719 L .36057 .33176 L .36076 .33291 L .36095 .34094 L .36113 .34147 L .36132 .34332 L .36151 .34212 L .3617 .34361 L .36188 .35274 L .36207 .3501 L .36226 .35865 L .36244 .36307 L .36263 .36065 L .36282 .3686 L .363 .36835 L .36319 .37005 L .36338 .3713 L .36356 .3726 L .36375 .37706 L .36394 .37307 L .36413 .3809 L .36431 .38267 L .3645 .39329 L .36469 .40051 L .36487 .39667 L .36506 .39704 L .36525 .40208 L .36543 .40373 L .36562 .39974 L .36581 .39636 L .36599 .39768 L .36618 .40548 L .36637 .40928 L .36655 .40841 L .36674 .41224 L .36693 .40448 L .36712 .39145 L .3673 .38166 L .36749 .37738 L .36768 .38026 L .36786 .38644 L .36805 .38677 L .36824 .39123 L .36842 .39776 L .36861 .39814 L .3688 .39948 L .36898 .39566 L .36917 .39257 L .36936 .39637 L Mistroke .36954 .39997 L .36973 .40009 L .36992 .40321 L .37011 .4006 L .37029 .40605 L .37048 .40645 L .37067 .40728 L .37085 .40825 L .37104 .41498 L .37123 .41179 L .37141 .40616 L .3716 .40961 L .37179 .40564 L .37197 .39842 L .37216 .39075 L .37235 .39086 L .37253 .38679 L .37272 .38894 L .37291 .38772 L .3731 .38964 L .37328 .39259 L .37347 .38788 L .37366 .38548 L .37384 .37782 L .37403 .38604 L .37422 .38753 L .3744 .3723 L .37459 .37271 L .37478 .38032 L .37496 .37926 L .37515 .37771 L .37534 .37569 L .37553 .36987 L .37571 .36867 L .3759 .3717 L .37609 .37242 L .37627 .37266 L .37646 .37331 L .37665 .3726 L .37683 .37785 L .37702 .37512 L .37721 .37344 L .37739 .36952 L .37758 .35928 L .37777 .368 L .37795 .3686 L .37814 .36796 L .37833 .3623 L .37852 .35837 L .3787 .3572 L Mistroke .37889 .3582 L .37908 .35426 L .37926 .35689 L .37945 .35505 L .37964 .35271 L .37982 .35379 L .38001 .35796 L .3802 .35379 L .38038 .3551 L .38057 .36296 L .38076 .35614 L .38094 .34987 L .38113 .3561 L .38132 .35531 L .38151 .35633 L .38169 .35094 L .38188 .35276 L .38207 .34614 L .38225 .34672 L .38244 .35069 L .38263 .35366 L .38281 .35746 L .383 .35144 L .38319 .34321 L .38337 .34026 L .38356 .33903 L .38375 .34692 L .38393 .34575 L .38412 .35024 L .38431 .35279 L .3845 .34895 L .38468 .35067 L .38487 .3486 L .38506 .35662 L .38524 .36284 L .38543 .34879 L .38562 .34611 L .3858 .34647 L .38599 .34457 L .38618 .34296 L .38636 .33816 L .38655 .33159 L .38674 .34529 L .38692 .34412 L .38711 .33389 L .3873 .33378 L .38749 .3292 L .38767 .32939 L .38786 .33096 L .38805 .32397 L Mistroke .38823 .32565 L .38842 .33123 L .38861 .32876 L .38879 .31786 L .38898 .31112 L .38917 .31261 L .38935 .32405 L .38954 .33122 L .38973 .32477 L .38992 .32826 L .3901 .32843 L .39029 .32656 L .39048 .31363 L .39066 .31375 L .39085 .31552 L .39104 .31462 L .39122 .31494 L .39141 .31954 L .3916 .32175 L .39178 .32785 L .39197 .32186 L .39216 .32948 L .39234 .33239 L .39253 .33286 L .39272 .33248 L .39291 .32352 L .39309 .32013 L .39328 .32295 L .39347 .32404 L .39365 .32772 L .39384 .33649 L .39403 .3464 L .39421 .34441 L .3944 .34576 L .39459 .33854 L .39477 .3437 L .39496 .34274 L .39515 .33554 L .39533 .3448 L .39552 .3477 L .39571 .34754 L .3959 .35049 L .39608 .35052 L .39627 .35458 L .39646 .34695 L .39664 .3489 L .39683 .35022 L .39702 .35701 L .3972 .35618 L .39739 .34604 L Mistroke .39758 .3444 L .39776 .34305 L .39795 .34546 L .39814 .34137 L .39832 .34365 L .39851 .34064 L .3987 .34074 L .39889 .33523 L .39907 .34711 L .39926 .33777 L .39945 .32678 L .39963 .33872 L .39982 .34307 L .40001 .33718 L .40019 .3439 L .40038 .33859 L .40057 .34171 L .40075 .34507 L .40094 .34818 L .40113 .3405 L .40132 .34307 L .4015 .35362 L .40169 .35238 L .40188 .36433 L .40206 .3686 L .40225 .3663 L .40244 .3752 L .40262 .37864 L .40281 .38315 L .403 .38472 L .40318 .38775 L .40337 .38337 L .40356 .38928 L .40374 .38425 L .40393 .38823 L .40412 .38361 L .40431 .38352 L .40449 .38789 L .40468 .38626 L .40487 .38777 L .40505 .38754 L .40524 .38782 L .40543 .38711 L .40561 .38217 L .4058 .37509 L .40599 .37827 L .40617 .37767 L .40636 .36849 L .40655 .37105 L .40673 .36518 L Mistroke .40692 .36087 L .40711 .35604 L .4073 .35345 L .40748 .35208 L .40767 .35509 L .40786 .35036 L .40804 .35027 L .40823 .34484 L .40842 .33803 L .4086 .34518 L .40879 .33968 L .40898 .33674 L .40916 .33701 L .40935 .34329 L .40954 .34105 L .40972 .3427 L .40991 .34861 L .4101 .35186 L .41029 .35021 L .41047 .34894 L .41066 .35403 L .41085 .34954 L .41103 .33667 L .41122 .34011 L .41141 .33958 L .41159 .34482 L .41178 .33211 L .41197 .33472 L .41215 .33458 L .41234 .34168 L .41253 .34243 L .41271 .33869 L .4129 .34436 L .41309 .34487 L .41328 .33872 L .41346 .33866 L .41365 .33751 L .41384 .33977 L .41402 .33905 L .41421 .33771 L .4144 .34008 L .41458 .34007 L .41477 .34104 L .41496 .34027 L .41514 .34022 L .41533 .33452 L .41552 .33925 L .41571 .34613 L .41589 .35147 L .41608 .35472 L Mistroke .41627 .35791 L .41645 .34881 L .41664 .35086 L .41683 .34811 L .41701 .34569 L .4172 .34623 L .41739 .33919 L .41757 .33423 L .41776 .32504 L .41795 .32221 L .41813 .31914 L .41832 .31464 L .41851 .30838 L .4187 .30962 L .41888 .31059 L .41907 .30738 L .41926 .30849 L .41944 .30133 L .41963 .30093 L .41982 .30123 L .42 .30394 L .42019 .31111 L .42038 .31027 L .42056 .30683 L .42075 .31138 L .42094 .31181 L .42112 .31062 L .42131 .30773 L .4215 .30855 L .42169 .30637 L .42187 .29754 L .42206 .29586 L .42225 .29435 L .42243 .28969 L .42262 .28657 L .42281 .28917 L .42299 .28091 L .42318 .28213 L .42337 .28574 L .42355 .2979 L .42374 .30388 L .42393 .3062 L .42411 .29848 L .4243 .29802 L .42449 .29865 L .42468 .299 L .42486 .29811 L .42505 .29812 L .42524 .30043 L .42542 .30617 L Mistroke .42561 .31368 L .4258 .31681 L .42598 .31971 L .42617 .32039 L .42636 .3149 L .42654 .3153 L .42673 .31482 L .42692 .32065 L .4271 .31882 L .42729 .31952 L .42748 .30972 L .42767 .30954 L .42785 .30641 L .42804 .30075 L .42823 .2997 L .42841 .29457 L .4286 .30094 L .42879 .2933 L .42897 .29166 L .42916 .2888 L .42935 .29227 L .42953 .28226 L .42972 .27791 L .42991 .28311 L .4301 .28599 L .43028 .28551 L .43047 .28319 L .43066 .27913 L .43084 .27505 L .43103 .27107 L .43122 .2745 L .4314 .27925 L .43159 .29059 L .43178 .28585 L .43196 .28312 L .43215 .27722 L .43234 .27793 L .43252 .27646 L .43271 .27378 L .4329 .27004 L .43309 .27655 L .43327 .27355 L .43346 .27834 L .43365 .27627 L .43383 .28003 L .43402 .28828 L .43421 .29077 L .43439 .28874 L .43458 .28422 L .43477 .29735 L Mistroke .43495 .30041 L .43514 .29586 L .43533 .30246 L .43551 .31085 L .4357 .31431 L .43589 .31402 L .43608 .32105 L .43626 .32456 L .43645 .32583 L .43664 .32024 L .43682 .31303 L .43701 .30745 L .4372 .3022 L .43738 .3028 L .43757 .29299 L .43776 .29606 L .43794 .28911 L .43813 .28966 L .43832 .28533 L .4385 .27576 L .43869 .26808 L .43888 .27304 L .43907 .27564 L .43925 .26347 L .43944 .25597 L .43963 .24535 L .43981 .25371 L .44 .24569 L .44019 .24382 L .44037 .24456 L .44056 .24365 L .44075 .24458 L .44093 .24851 L .44112 .254 L .44131 .25804 L .4415 .25132 L .44168 .24458 L .44187 .25444 L .44206 .24665 L .44224 .24422 L .44243 .24614 L .44262 .24171 L .4428 .23609 L .44299 .22775 L .44318 .22735 L .44336 .21917 L .44355 .21609 L .44374 .2157 L .44392 .21585 L .44411 .2142 L Mistroke .4443 .21597 L .44449 .21704 L .44467 .22246 L .44486 .2192 L .44505 .21864 L .44523 .224 L .44542 .22413 L .44561 .22108 L .44579 .22141 L .44598 .22522 L .44617 .22899 L .44635 .22902 L .44654 .22971 L .44673 .23901 L .44691 .24376 L .4471 .23686 L .44729 .2311 L .44748 .22771 L .44766 .22389 L .44785 .23064 L .44804 .22746 L .44822 .23294 L .44841 .2178 L .4486 .21678 L .44878 .2174 L .44897 .21405 L .44916 .21763 L .44934 .22641 L .44953 .21732 L .44972 .2101 L .4499 .2136 L .45009 .20757 L .45028 .20601 L .45047 .20415 L .45065 .20547 L .45084 .20631 L .45103 .20755 L .45121 .20562 L .4514 .20437 L .45159 .20614 L .45177 .21087 L .45196 .20531 L .45215 .20496 L .45233 .21528 L .45252 .21565 L .45271 .21438 L .45289 .21172 L .45308 .20972 L .45327 .21175 L .45346 .22611 L Mistroke .45364 .23226 L .45383 .23411 L .45402 .2427 L .4542 .2468 L .45439 .24481 L .45458 .24889 L .45476 .25641 L .45495 .25991 L .45514 .26016 L .45532 .2492 L .45551 .23656 L .4557 .22482 L .45589 .22288 L .45607 .22337 L .45626 .21892 L .45645 .21171 L .45663 .21121 L .45682 .21003 L .45701 .21196 L .45719 .20485 L .45738 .20361 L .45757 .2116 L .45775 .21256 L .45794 .20527 L .45813 .20911 L .45831 .20675 L .4585 .20311 L .45869 .20847 L .45888 .20787 L .45906 .20379 L .45925 .20996 L .45944 .21776 L .45962 .21456 L .45981 .21561 L .46 .21901 L .46018 .21701 L .46037 .21144 L .46056 .22578 L .46074 .2315 L .46093 .23745 L .46112 .23918 L .4613 .23779 L .46149 .23454 L .46168 .23313 L .46187 .23562 L .46205 .23638 L .46224 .23889 L .46243 .2375 L .46261 .23062 L .4628 .22894 L Mistroke .46299 .22809 L .46317 .22252 L .46336 .21854 L .46355 .2198 L .46373 .22728 L .46392 .22935 L .46411 .23555 L .46429 .23227 L .46448 .23233 L .46467 .23795 L .46486 .23857 L .46504 .23205 L .46523 .23385 L .46542 .23682 L .4656 .24305 L .46579 .24582 L .46598 .24643 L .46616 .25181 L .46635 .25004 L .46654 .2526 L .46672 .24663 L .46691 .24793 L .4671 .24746 L .46729 .24296 L .46747 .23647 L .46766 .23349 L .46785 .23005 L .46803 .22686 L .46822 .23059 L .46841 .23103 L .46859 .2345 L .46878 .23301 L .46897 .23229 L .46915 .23164 L .46934 .23465 L .46953 .24208 L .46971 .2354 L .4699 .2298 L .47009 .23858 L .47028 .23973 L .47046 .24642 L .47065 .24852 L .47084 .25063 L .47102 .24825 L .47121 .25499 L .4714 .25715 L .47158 .26275 L .47177 .26735 L .47196 .25678 L .47214 .24436 L Mistroke .47233 .23928 L .47252 .23276 L .4727 .23173 L .47289 .22363 L .47308 .22839 L .47327 .23445 L .47345 .23989 L .47364 .24254 L .47383 .24404 L .47401 .24243 L .4742 .24141 L .47439 .24188 L .47457 .23768 L .47476 .23539 L .47495 .23764 L .47513 .2424 L .47532 .25019 L .47551 .25755 L .47569 .26701 L .47588 .26678 L .47607 .26452 L .47626 .26017 L .47644 .26455 L .47663 .26237 L .47682 .25404 L .477 .25512 L .47719 .24708 L .47738 .24917 L .47756 .24843 L .47775 .24795 L .47794 .2464 L .47812 .23892 L .47831 .24232 L .4785 .24672 L .47868 .24797 L .47887 .24582 L .47906 .24501 L .47925 .24668 L .47943 .24826 L .47962 .25056 L .47981 .24795 L .47999 .24754 L .48018 .24765 L .48037 .25026 L .48055 .25074 L .48074 .26113 L .48093 .2736 L .48111 .26799 L .4813 .2653 L .48149 .2561 L Mistroke .48168 .25971 L .48186 .25237 L .48205 .24313 L .48224 .24038 L .48242 .24283 L .48261 .23795 L .4828 .24332 L .48298 .23769 L .48317 .24353 L .48336 .24716 L .48354 .24725 L .48373 .23991 L .48392 .2369 L .4841 .25092 L .48429 .25183 L .48448 .2504 L .48467 .25204 L .48485 .25311 L .48504 .25955 L .48523 .25835 L .48541 .25955 L .4856 .25205 L .48579 .25373 L .48597 .26478 L .48616 .25534 L .48635 .26717 L .48653 .26592 L .48672 .26476 L .48691 .26468 L .48709 .27423 L .48728 .27336 L .48747 .27049 L .48766 .26689 L .48784 .26913 L .48803 .27175 L .48822 .27688 L .4884 .27273 L .48859 .28051 L .48878 .27884 L .48896 .27606 L .48915 .2907 L .48934 .28636 L .48952 .28789 L .48971 .28933 L .4899 .28164 L .49008 .27995 L .49027 .27807 L .49046 .27535 L .49065 .27165 L .49083 .27102 L Mistroke .49102 .26659 L .49121 .26801 L .49139 .26647 L .49158 .25912 L .49177 .25499 L .49195 .24964 L .49214 .25626 L .49233 .26364 L .49251 .26242 L .4927 .26019 L .49289 .26508 L .49308 .26129 L .49326 .25625 L .49345 .25278 L .49364 .25107 L .49382 .25555 L .49401 .26259 L .4942 .25577 L .49438 .25841 L .49457 .25248 L .49476 .25294 L .49494 .25097 L .49513 .25439 L .49532 .25522 L .4955 .245 L .49569 .2422 L .49588 .24666 L .49607 .24376 L .49625 .24186 L .49644 .24638 L .49663 .24028 L .49681 .24112 L .497 .24216 L .49719 .24663 L .49737 .24698 L .49756 .25122 L .49775 .24874 L .49793 .25305 L .49812 .2497 L .49831 .24379 L .49849 .24831 L .49868 .24603 L .49887 .24285 L .49906 .24159 L .49924 .23885 L .49943 .23016 L .49962 .22783 L .4998 .22739 L .49999 .22814 L .50018 .22256 L Mistroke .50036 .21529 L .50055 .2248 L .50074 .22204 L .50092 .21371 L .50111 .21256 L .5013 .21329 L .50148 .21329 L .50167 .21593 L .50186 .21732 L .50205 .21517 L .50223 .2174 L .50242 .22221 L .50261 .21691 L .50279 .22402 L .50298 .2275 L .50317 .21462 L .50335 .2092 L .50354 .20558 L .50373 .21091 L .50391 .2081 L .5041 .20792 L .50429 .20933 L .50447 .20823 L .50466 .21069 L .50485 .21541 L .50504 .21506 L .50522 .21554 L .50541 .21907 L .5056 .21107 L .50578 .21247 L .50597 .21092 L .50616 .20416 L .50634 .21253 L .50653 .20377 L .50672 .20457 L .5069 .19924 L .50709 .20525 L .50728 .20876 L .50747 .2125 L .50765 .21169 L .50784 .212 L .50803 .21524 L .50821 .20644 L .5084 .19529 L .50859 .19507 L .50877 .20816 L .50896 .20376 L .50915 .19789 L .50933 .18896 L .50952 .18668 L Mistroke .50971 .18426 L .50989 .1914 L .51008 .19095 L .51027 .18993 L .51046 .19008 L .51064 .19327 L .51083 .19533 L .51102 .19323 L .5112 .19484 L .51139 .19649 L .51158 .18905 L .51176 .1819 L .51195 .18807 L .51214 .17767 L .51232 .17395 L .51251 .17546 L .5127 .17865 L .51288 .17628 L .51307 .17612 L .51326 .17296 L .51345 .17738 L .51363 .16227 L .51382 .15499 L .51401 .15943 L .51419 .15759 L .51438 .15249 L .51457 .15761 L .51475 .15477 L .51494 .15856 L .51513 .15956 L .51531 .15894 L .5155 .15365 L .51569 .14898 L .51587 .15571 L .51606 .15744 L .51625 .16163 L .51644 .16104 L .51662 .15104 L .51681 .14611 L .517 .15191 L .51718 .14881 L .51737 .15482 L .51756 .15704 L .51774 .15247 L .51793 .15277 L .51812 .15268 L .5183 .15447 L .51849 .15527 L .51868 .14735 L .51886 .14663 L Mistroke .51905 .14649 L .51924 .14786 L .51943 .14875 L .51961 .15567 L .5198 .15856 L .51999 .14449 L .52017 .15132 L .52036 .14949 L .52055 .1544 L .52073 .16195 L .52092 .15538 L .52111 .15151 L .52129 .15233 L .52148 .15014 L .52167 .14855 L .52186 .14763 L .52204 .1435 L .52223 .14523 L .52242 .13768 L .5226 .14179 L .52279 .13962 L .52298 .14371 L .52316 .14935 L .52335 .14626 L .52354 .14531 L .52372 .14703 L .52391 .14519 L .5241 .14718 L .52428 .15253 L .52447 .15973 L .52466 .15824 L .52485 .15959 L .52503 .17419 L .52522 .171 L .52541 .1764 L .52559 .179 L .52578 .17809 L .52597 .18096 L .52615 .18188 L .52634 .18142 L .52653 .18455 L .52671 .18152 L .5269 .18117 L .52709 .17628 L .52727 .17661 L .52746 .18527 L .52765 .18546 L .52784 .18496 L .52802 .17929 L .52821 .17698 L Mistroke .5284 .1713 L .52858 .16766 L .52877 .16378 L .52896 .17019 L .52914 .16994 L .52933 .16616 L .52952 .16836 L .5297 .16752 L .52989 .16893 L .53008 .17592 L .53026 .17664 L .53045 .17617 L .53064 .17687 L .53083 .18272 L .53101 .1831 L .5312 .18335 L .53139 .19779 L .53157 .20117 L .53176 .21068 L .53195 .20584 L .53213 .20925 L .53232 .20084 L .53251 .20555 L .53269 .20834 L .53288 .20932 L .53307 .2044 L .53326 .21238 L .53344 .2034 L .53363 .21262 L .53382 .21117 L .534 .22571 L .53419 .23213 L .53438 .23612 L .53456 .22577 L .53475 .2274 L .53494 .22772 L .53512 .22814 L .53531 .23192 L .5355 .23454 L .53568 .23088 L .53587 .23492 L .53606 .23998 L .53625 .24414 L .53643 .25098 L .53662 .25611 L .53681 .25122 L .53699 .2543 L .53718 .24887 L .53737 .24434 L .53755 .24087 L Mistroke .53774 .23553 L .53793 .24039 L .53811 .23713 L .5383 .23956 L .53849 .22901 L .53867 .23514 L .53886 .23461 L .53905 .22621 L .53924 .23125 L .53942 .23544 L .53961 .23471 L .5398 .23265 L .53998 .23089 L .54017 .22814 L .54036 .22975 L .54054 .23018 L .54073 .22754 L .54092 .23137 L .5411 .23485 L .54129 .23263 L .54148 .23663 L .54166 .23519 L .54185 .23065 L .54204 .23178 L .54223 .23538 L .54241 .24075 L .5426 .24239 L .54279 .23707 L .54297 .23648 L .54316 .23155 L .54335 .22913 L .54353 .23411 L .54372 .22872 L .54391 .23247 L .54409 .23499 L .54428 .23942 L .54447 .24881 L .54465 .25339 L .54484 .25502 L .54503 .24764 L .54522 .25347 L .5454 .25713 L .54559 .25253 L .54578 .25737 L .54596 .2578 L .54615 .26805 L .54634 .26849 L .54652 .27493 L .54671 .27214 L .5469 .2734 L Mistroke .54708 .27039 L .54727 .26624 L .54746 .26108 L .54765 .25899 L .54783 .26316 L .54802 .25733 L .54821 .25466 L .54839 .24699 L .54858 .245 L .54877 .24234 L .54895 .24882 L .54914 .24745 L .54933 .24235 L .54951 .24452 L .5497 .25322 L .54989 .25163 L .55007 .24856 L .55026 .24343 L .55045 .24309 L .55064 .2451 L .55082 .2411 L .55101 .23955 L .5512 .2324 L .55138 .232 L .55157 .23587 L .55176 .2309 L .55194 .23324 L .55213 .23608 L .55232 .22977 L .5525 .22092 L .55269 .22262 L .55288 .21969 L .55306 .21636 L .55325 .21418 L .55344 .22165 L .55363 .21865 L .55381 .22365 L .554 .23198 L .55419 .23565 L .55437 .23514 L .55456 .23296 L .55475 .23403 L .55493 .23927 L .55512 .24552 L .55531 .24343 L .55549 .24496 L .55568 .24151 L .55587 .24273 L .55605 .23261 L .55624 .23624 L Mistroke .55643 .23572 L .55662 .23696 L .5568 .23563 L .55699 .24777 L .55718 .24842 L .55736 .25069 L .55755 .24893 L .55774 .25558 L .55792 .25182 L .55811 .25694 L .5583 .26366 L .55848 .26495 L .55867 .26124 L .55886 .275 L .55905 .27586 L .55923 .27706 L .55942 .28678 L .55961 .29476 L .55979 .29537 L .55998 .29818 L .56017 .30003 L .56035 .30543 L .56054 .3112 L .56073 .3098 L .56091 .30714 L .5611 .30586 L .56129 .30337 L .56147 .30192 L .56166 .29959 L .56185 .30167 L .56204 .29926 L .56222 .30123 L .56241 .2961 L .5626 .30359 L .56278 .30494 L .56297 .30591 L .56316 .3065 L .56334 .29413 L .56353 .2949 L .56372 .29708 L .5639 .29995 L .56409 .30147 L .56428 .30081 L .56446 .30389 L .56465 .31032 L .56484 .30964 L .56503 .30574 L .56521 .31173 L .5654 .32371 L .56559 .31726 L Mistroke .56577 .31545 L .56596 .31533 L .56615 .32059 L .56633 .31902 L .56652 .31474 L .56671 .31072 L .56689 .30729 L .56708 .30607 L .56727 .31716 L .56745 .31736 L .56764 .32736 L .56783 .32641 L .56802 .3206 L .5682 .3244 L .56839 .31533 L .56858 .31533 L .56876 .32077 L .56895 .31648 L .56914 .31404 L .56932 .30839 L .56951 .30562 L .5697 .30975 L .56988 .31263 L .57007 .30732 L .57026 .3087 L .57044 .30536 L .57063 .30534 L .57082 .30734 L .57101 .30427 L .57119 .29244 L .57138 .29597 L .57157 .29958 L .57175 .29779 L .57194 .30432 L .57213 .29898 L .57231 .29603 L .5725 .29478 L .57269 .30708 L .57287 .30027 L .57306 .30063 L .57325 .3053 L .57344 .30495 L .57362 .30789 L .57381 .31193 L .574 .30961 L .57418 .31003 L .57437 .31739 L .57456 .31599 L .57474 .31346 L .57493 .30926 L Mistroke .57512 .31663 L .5753 .32795 L .57549 .3279 L .57568 .32128 L .57586 .31489 L .57605 .31212 L .57624 .31705 L .57643 .31706 L .57661 .32504 L .5768 .323 L .57699 .32445 L .57717 .32514 L .57736 .33037 L .57755 .33226 L .57773 .3351 L .57792 .3351 L .57811 .32766 L .57829 .32804 L .57848 .32496 L .57867 .32334 L .57885 .32106 L .57904 .33431 L .57923 .32404 L .57942 .32672 L .5796 .32382 L .57979 .32016 L .57998 .30859 L .58016 .31422 L .58035 .31696 L .58054 .31554 L .58072 .31515 L .58091 .31552 L .5811 .32178 L .58128 .32174 L .58147 .31313 L .58166 .30708 L .58184 .31199 L .58203 .31359 L .58222 .30791 L .58241 .31002 L .58259 .30541 L .58278 .31087 L .58297 .31506 L .58315 .31902 L .58334 .32586 L .58353 .31887 L .58371 .31143 L .5839 .31326 L .58409 .30877 L .58427 .30275 L Mistroke .58446 .31118 L .58465 .30646 L .58484 .30115 L .58502 .29496 L .58521 .29278 L .5854 .28896 L .58558 .28336 L .58577 .28624 L .58596 .29228 L .58614 .28734 L .58633 .28395 L .58652 .2836 L .5867 .27789 L .58689 .27491 L .58708 .27697 L .58726 .27626 L .58745 .26251 L .58764 .26365 L .58783 .26921 L .58801 .27511 L .5882 .28485 L .58839 .28638 L .58857 .28249 L .58876 .28805 L .58895 .28825 L .58913 .28802 L .58932 .28961 L .58951 .29446 L .58969 .29753 L .58988 .29877 L .59007 .302 L .59025 .29878 L .59044 .30172 L .59063 .31303 L .59082 .31339 L .591 .31717 L .59119 .31778 L .59138 .3252 L .59156 .32528 L .59175 .33011 L .59194 .33286 L .59212 .33218 L .59231 .33856 L .5925 .33516 L .59268 .33456 L .59287 .33341 L .59306 .3359 L .59324 .34189 L .59343 .34414 L .59362 .34403 L Mistroke .59381 .34283 L .59399 .33885 L .59418 .33004 L .59437 .32731 L .59455 .32662 L .59474 .32615 L .59493 .32687 L .59511 .33489 L .5953 .34299 L .59549 .34831 L .59567 .35056 L .59586 .34215 L .59605 .33573 L .59623 .33676 L .59642 .34392 L .59661 .33443 L .5968 .33513 L .59698 .33456 L .59717 .33511 L .59736 .33498 L .59754 .33938 L .59773 .33649 L .59792 .34792 L .5981 .35068 L .59829 .34727 L .59848 .3461 L .59866 .33935 L .59885 .34217 L .59904 .34297 L .59923 .34564 L .59941 .35312 L .5996 .34846 L .59979 .34921 L .59997 .35131 L .60016 .35304 L .60035 .35023 L .60053 .34183 L .60072 .33712 L .60091 .33924 L .60109 .33325 L .60128 .34059 L .60147 .34032 L .60165 .34318 L .60184 .3472 L .60203 .35034 L .60222 .35631 L .6024 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.69603 .33053 L .69622 .33434 L .6964 .33626 L Mistroke .69659 .34009 L .69678 .3405 L .69697 .3395 L .69715 .34109 L .69734 .33972 L .69753 .34122 L .69771 .33503 L .6979 .32863 L .69809 .33792 L .69827 .34261 L .69846 .3461 L .69865 .35018 L .69883 .34851 L .69902 .34882 L .69921 .34516 L .69939 .34308 L .69958 .34563 L .69977 .33607 L .69996 .33482 L .70014 .33823 L .70033 .33657 L .70052 .34024 L .7007 .34057 L .70089 .3445 L .70108 .34728 L .70126 .35078 L .70145 .35189 L .70164 .34902 L .70182 .34881 L .70201 .35248 L .7022 .35463 L .70238 .36115 L .70257 .35652 L .70276 .35542 L .70295 .34797 L .70313 .34209 L .70332 .33708 L .70351 .33429 L .70369 .33376 L .70388 .33521 L .70407 .34143 L .70425 .34764 L .70444 .35163 L .70463 .34955 L .70481 .33884 L .705 .33299 L .70519 .33641 L .70538 .33923 L .70556 .33122 L .70575 .32929 L Mistroke .70594 .33587 L .70612 .33483 L .70631 .33632 L .7065 .33459 L .70668 .33787 L .70687 .34255 L .70706 .3388 L .70724 .33307 L .70743 .33115 L 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L .74275 .38095 L .74294 .37667 L .74313 .38034 L Mistroke .74331 .37573 L .7435 .38717 L .74369 .38535 L .74387 .37794 L .74406 .37698 L .74425 .38549 L .74443 .37938 L .74462 .38133 L .74481 .37517 L .74499 .36913 L .74518 .37605 L .74537 .37365 L .74556 .37455 L .74574 .36938 L .74593 .36139 L .74612 .37014 L .7463 .37114 L .74649 .37297 L .74668 .36782 L .74686 .37326 L .74705 .37562 L .74724 .37281 L .74742 .37128 L .74761 .36847 L .7478 .37146 L .74798 .37388 L .74817 .36886 L .74836 .37265 L .74855 .37112 L .74873 .37422 L .74892 .37335 L .74911 .37727 L .74929 .36607 L .74948 .3657 L .74967 .36543 L .74985 .37051 L .75004 .37286 L .75023 .37658 L .75041 .36841 L .7506 .3693 L .75079 .37203 L .75097 .38146 L .75116 .37601 L .75135 .37993 L .75154 .38523 L .75172 .38762 L .75191 .38122 L .7521 .38877 L .75228 .38152 L .75247 .38476 L Mistroke .75266 .39395 L .75284 .39532 L .75303 .39531 L .75322 .39648 L .7534 .39552 L .75359 .393 L .75378 .39118 L .75396 .39159 L .75415 .39006 L .75434 .3926 L .75453 .39573 L .75471 .40091 L .7549 .40203 L .75509 .39731 L .75527 .39094 L .75546 .38774 L .75565 .39034 L .75583 .39803 L .75602 .4029 L .75621 .41134 L .75639 .41358 L .75658 .41781 L .75677 .42816 L .75696 .43077 L .75714 .43145 L .75733 .43145 L .75752 .42903 L .7577 .43333 L .75789 .43998 L .75808 .43884 L .75826 .43898 L .75845 .43916 L .75864 .4456 L .75882 .45129 L .75901 .45902 L .7592 .46433 L .75938 .46412 L .75957 .46356 L .75976 .47498 L .75995 .47845 L .76013 .4804 L .76032 .48025 L .76051 .47811 L .76069 .46848 L .76088 .46267 L .76107 .45939 L .76125 .45026 L .76144 .44319 L .76163 .44294 L .76181 .44785 L Mistroke .762 .44618 L .76219 .4504 L .76237 .44804 L .76256 .44678 L .76275 .45477 L .76294 .45658 L .76312 .455 L .76331 .45311 L .7635 .45452 L .76368 .45859 L .76387 .45397 L .76406 .46024 L .76424 .46058 L .76443 .46336 L .76462 .463 L .7648 .45997 L .76499 .46969 L .76518 .46815 L .76536 .46303 L .76555 .45955 L .76574 .46357 L .76593 .4616 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.18976 .09863 L .18995 .09872 L .19014 .09881 L .19032 .0989 L .19051 .09899 L .1907 .09908 L .19088 .09917 L .19107 .09925 L .19126 .09934 L .19144 .09943 L .19163 .09952 L .19182 .09961 L Mistroke .19201 .09969 L .19219 .09978 L .19238 .09987 L .19257 .09996 L .19275 .10005 L .19294 .10013 L .19313 .10022 L .19331 .10031 L .1935 .1004 L .19369 .10048 L .19387 .10057 L .19406 .10066 L .19425 .10075 L .19443 .10083 L .19462 .10092 L .19481 .10101 L .195 .1011 L .19518 .10118 L .19537 .10127 L .19556 .10136 L .19574 .10145 L .19593 .10153 L .19612 .10162 L .1963 .10171 L .19649 .1018 L .19668 .10188 L .19686 .10197 L .19705 .10206 L .19724 .10214 L .19742 .10223 L .19761 .10232 L .1978 .1024 L .19799 .10249 L .19817 .10258 L .19836 .10266 L .19855 .10275 L .19873 .10284 L .19892 .10293 L .19911 .10301 L .19929 .1031 L .19948 .10319 L .19967 .10327 L .19985 .10336 L .20004 .10345 L .20023 .10353 L .20041 .10362 L .2006 .10371 L .20079 .1038 L .20098 .10388 L .20116 .10397 L Mistroke .20135 .10406 L .20154 .10414 L .20172 .10423 L .20191 .10432 L .2021 .1044 L .20228 .10449 L .20247 .10458 L .20266 .10467 L .20284 .10475 L .20303 .10484 L .20322 .10493 L .2034 .10501 L .20359 .1051 L .20378 .10519 L .20397 .10528 L .20415 .10536 L .20434 .10545 L .20453 .10554 L .20471 .10562 L .2049 .10571 L .20509 .1058 L .20527 .10588 L .20546 .10597 L .20565 .10606 L .20583 .10615 L .20602 .10623 L .20621 .10632 L .2064 .10641 L .20658 .10649 L .20677 .10658 L .20696 .10667 L .20714 .10676 L .20733 .10684 L .20752 .10693 L .2077 .10702 L .20789 .1071 L .20808 .10719 L .20826 .10728 L .20845 .10737 L .20864 .10745 L .20882 .10754 L .20901 .10763 L .2092 .10772 L .20939 .1078 L .20957 .10789 L .20976 .10798 L .20995 .10806 L .21013 .10815 L .21032 .10824 L .21051 .10833 L Mistroke .21069 .10841 L .21088 .1085 L .21107 .10859 L .21125 .10868 L .21144 .10876 L .21163 .10885 L .21181 .10894 L .212 .10903 L .21219 .10912 L .21238 .1092 L .21256 .10929 L .21275 .10938 L .21294 .10947 L .21312 .10956 L .21331 .10965 L .2135 .10973 L .21368 .10982 L .21387 .10991 L .21406 .11 L .21424 .11008 L .21443 .11017 L .21462 .11026 L .2148 .11035 L .21499 .11043 L .21518 .11052 L .21537 .11061 L .21555 .1107 L .21574 .11078 L .21593 .11087 L .21611 .11096 L .2163 .11104 L .21649 .11113 L .21667 .11122 L .21686 .11131 L .21705 .11139 L .21723 .11148 L .21742 .11157 L .21761 .11165 L .2178 .11174 L .21798 .11183 L .21817 .11192 L .21836 .112 L .21854 .11209 L .21873 .11218 L .21892 .11227 L .2191 .11235 L .21929 .11244 L .21948 .11253 L .21966 .11262 L .21985 .1127 L Mistroke .22004 .11279 L .22022 .11288 L .22041 .11296 L .2206 .11305 L .22079 .11314 L .22097 .11323 L .22116 .11332 L .22135 .1134 L .22153 .11349 L .22172 .11358 L .22191 .11367 L .22209 .11376 L .22228 .11385 L .22247 .11393 L .22265 .11402 L .22284 .11411 L .22303 .1142 L .22321 .11429 L .2234 .11437 L .22359 .11446 L .22378 .11455 L .22396 .11464 L .22415 .11473 L .22434 .11482 L .22452 .1149 L .22471 .11499 L .2249 .11508 L .22508 .11517 L .22527 .11526 L .22546 .11534 L .22564 .11543 L .22583 .11552 L .22602 .11561 L .2262 .11569 L .22639 .11578 L .22658 .11587 L .22677 .11595 L .22695 .11604 L .22714 .11613 L .22733 .11621 L .22751 .1163 L .2277 .11639 L .22789 .11648 L .22807 .11656 L .22826 .11665 L .22845 .11674 L .22863 .11682 L .22882 .11691 L .22901 .117 L .22919 .11708 L Mistroke .22938 .11717 L .22957 .11726 L .22976 .11735 L .22994 .11743 L .23013 .11752 L .23032 .11761 L .2305 .11769 L .23069 .11778 L .23088 .11787 L .23106 .11795 L .23125 .11804 L .23144 .11813 L .23162 .11822 L .23181 .1183 L .232 .11839 L .23219 .11848 L .23237 .11856 L .23256 .11865 L .23275 .11874 L .23293 .11882 L .23312 .11891 L .23331 .119 L .23349 .11909 L .23368 .11917 L .23387 .11926 L .23405 .11935 L .23424 .11943 L .23443 .11952 L .23461 .11961 L .2348 .11969 L .23499 .11978 L .23518 .11987 L .23536 .11995 L .23555 .12004 L .23574 .12013 L .23592 .12022 L .23611 .1203 L .2363 .12039 L .23648 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.12587 L .24826 .12596 L .24844 .12605 L .24863 .12613 L .24882 .12622 L .249 .12631 L .24919 .12639 L .24938 .12648 L .24957 .12657 L .24975 .12665 L .24994 .12674 L .25013 .12683 L .25031 .12692 L .2505 .127 L .25069 .12709 L .25087 .12718 L .25106 .12726 L .25125 .12735 L .25143 .12744 L .25162 .12752 L .25181 .12761 L .25199 .1277 L .25218 .12779 L .25237 .12787 L .25256 .12796 L .25274 .12805 L .25293 .12813 L .25312 .12822 L .2533 .12831 L .25349 .1284 L .25368 .12848 L .25386 .12857 L .25405 .12866 L .25424 .12874 L .25442 .12883 L .25461 .12892 L .2548 .129 L .25498 .12909 L .25517 .12918 L .25536 .12926 L .25555 .12935 L .25573 .12944 L .25592 .12953 L .25611 .12961 L .25629 .1297 L .25648 .12979 L .25667 .12987 L .25685 .12996 L .25704 .13005 L .25723 .13013 L Mistroke .25741 .13022 L .2576 .13031 L .25779 .1304 L .25798 .13048 L .25816 .13057 L .25835 .13066 L .25854 .13074 L .25872 .13083 L .25891 .13092 L .2591 .131 L .25928 .13109 L .25947 .13118 L .25966 .13127 L .25984 .13135 L .26003 .13144 L .26022 .13153 L .2604 .13162 L .26059 .1317 L .26078 .13179 L .26097 .13188 L .26115 .13196 L .26134 .13205 L .26153 .13214 L .26171 .13223 L .2619 .13231 L .26209 .1324 L .26227 .13249 L .26246 .13257 L .26265 .13266 L .26283 .13275 L .26302 .13283 L .26321 .13292 L .26339 .13301 L .26358 .1331 L .26377 .13318 L .26396 .13327 L .26414 .13336 L .26433 .13344 L .26452 .13353 L .2647 .13362 L .26489 .13371 L .26508 .13379 L .26526 .13388 L .26545 .13397 L .26564 .13406 L .26582 .13415 L .26601 .13423 L .2662 .13432 L .26638 .13441 L .26657 .1345 L Mistroke .26676 .13459 L .26695 .13467 L .26713 .13476 L .26732 .13485 L .26751 .13494 L .26769 .13502 L .26788 .13511 L .26807 .1352 L .26825 .13529 L .26844 .13537 L .26863 .13546 L .26881 .13555 L .269 .13563 L .26919 .13572 L .26937 .13581 L .26956 .1359 L .26975 .13598 L .26994 .13607 L .27012 .13616 L .27031 .13625 L .2705 .13633 L .27068 .13642 L .27087 .13651 L .27106 .13659 L .27124 .13668 L .27143 .13677 L .27162 .13686 L .2718 .13694 L .27199 .13703 L .27218 .13712 L .27237 .1372 L .27255 .13729 L .27274 .13738 L .27293 .13746 L .27311 .13755 L .2733 .13764 L .27349 .13773 L .27367 .13781 L .27386 .1379 L .27405 .13799 L .27423 .13807 L .27442 .13816 L .27461 .13825 L .27479 .13834 L .27498 .13842 L .27517 .13851 L .27536 .1386 L .27554 .13868 L .27573 .13877 L .27592 .13886 L Mistroke .2761 .13895 L .27629 .13903 L .27648 .13912 L .27666 .13921 L .27685 .13929 L .27704 .13938 L .27722 .13947 L .27741 .13955 L .2776 .13964 L .27778 .13973 L .27797 .13982 L .27816 .1399 L .27835 .13999 L .27853 .14008 L .27872 .14016 L .27891 .14025 L .27909 .14034 L .27928 .14042 L .27947 .14051 L .27965 .1406 L .27984 .14069 L .28003 .14077 L .28021 .14086 L .2804 .14095 L .28059 .14103 L .28077 .14112 L .28096 .14121 L .28115 .14129 L .28134 .14138 L .28152 .14147 L .28171 .14155 L .2819 .14164 L .28208 .14173 L .28227 .14182 L .28246 .1419 L .28264 .14199 L .28283 .14208 L .28302 .14216 L .2832 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.30656 .15369 L .30675 .15378 L .30694 .15387 L .30713 .15396 L .30731 .15406 L .3075 .15415 L .30769 .15424 L .30787 .15433 L .30806 .15443 L .30825 .15452 L .30843 .15461 L .30862 .1547 L .30881 .15479 L .30899 .15489 L .30918 .15498 L .30937 .15508 L .30956 .15517 L .30974 .15527 L .30993 .15536 L .31012 .15545 L .3103 .15555 L .31049 .15564 L .31068 .15574 L .31086 .15583 L .31105 .15593 L .31124 .15602 L .31142 .15611 L .31161 .15621 L .3118 .1563 L .31198 .1564 L .31217 .15649 L .31236 .15658 L .31255 .15668 L .31273 .15677 L .31292 .15687 L .31311 .15696 L .31329 .15705 L Mistroke .31348 .15715 L .31367 .15724 L .31385 .15733 L .31404 .15742 L .31423 .15751 L .31441 .1576 L .3146 .1577 L .31479 .15779 L .31497 .15788 L .31516 .15797 L .31535 .15806 L .31554 .15815 L .31572 .15824 L .31591 .15833 L .3161 .15842 L .31628 .15851 L .31647 .1586 L .31666 .15869 L .31684 .15878 L .31703 .15888 L .31722 .15897 L .3174 .15906 L .31759 .15915 L .31778 .15924 L .31796 .15933 L .31815 .15942 L .31834 .15951 L .31853 .1596 L .31871 .15969 L .3189 .15978 L .31909 .15987 L .31927 .15997 L .31946 .16006 L .31965 .16015 L .31983 .16024 L .32002 .16033 L .32021 .16042 L .32039 .16051 L .32058 .1606 L .32077 .16069 L .32095 .16078 L .32114 .16087 L .32133 .16096 L .32152 .16106 L .3217 .16115 L .32189 .16124 L .32208 .16133 L .32226 .16142 L .32245 .16151 L .32264 .1616 L Mistroke .32282 .16169 L .32301 .16179 L .3232 .16188 L .32338 .16197 L .32357 .16206 L .32376 .16216 L .32395 .16225 L .32413 .16234 L .32432 .16243 L .32451 .16252 L .32469 .16261 L .32488 .1627 L .32507 .16279 L .32525 .16288 L .32544 .16297 L .32563 .16307 L .32581 .16316 L .326 .16325 L .32619 .16334 L .32637 .16343 L .32656 .16352 L .32675 .16362 L .32694 .16371 L .32712 .1638 L .32731 .16389 L .3275 .16398 L .32768 .16407 L .32787 .16417 L .32806 .16426 L .32824 .16435 L .32843 .16444 L .32862 .16453 L .3288 .16462 L .32899 .16472 L .32918 .16481 L .32936 .1649 L .32955 .165 L .32974 .16509 L .32993 .16518 L .33011 .16527 L .3303 .16536 L .33049 .16545 L .33067 .16554 L .33086 .16564 L .33105 .16573 L .33123 .16582 L .33142 .16591 L .33161 .166 L .33179 .16609 L .33198 .16619 L Mistroke .33217 .16628 L .33235 .16637 L .33254 .16646 L .33273 .16655 L .33292 .16664 L .3331 .16673 L .33329 .16683 L .33348 .16692 L .33366 .16701 L .33385 .1671 L .33404 .16719 L .33422 .16728 L .33441 .16738 L .3346 .16747 L .33478 .16756 L .33497 .16766 L .33516 .16775 L .33534 .16784 L .33553 .16794 L .33572 .16803 L .33591 .16813 L .33609 .16822 L .33628 .16831 L .33647 .16841 L .33665 .1685 L .33684 .1686 L .33703 .16869 L .33721 .16879 L .3374 .16888 L .33759 .16897 L .33777 .16906 L .33796 .16916 L .33815 .16925 L .33834 .16934 L .33852 .16943 L .33871 .16952 L .3389 .16962 L .33908 .16971 L .33927 .1698 L .33946 .16989 L .33964 .16998 L .33983 .17007 L .34002 .17016 L .3402 .17025 L .34039 .17034 L .34058 .17043 L .34076 .17052 L .34095 .17061 L .34114 .1707 L .34133 .17079 L Mistroke .34151 .17089 L .3417 .17098 L .34189 .17107 L .34207 .17116 L .34226 .17126 L .34245 .17135 L .34263 .17144 L .34282 .17153 L .34301 .17163 L .34319 .17172 L .34338 .17181 L .34357 .17191 L .34375 .172 L .34394 .17209 L .34413 .17219 L .34432 .17228 L .3445 .17237 L .34469 .17246 L .34488 .17255 L .34506 .17264 L .34525 .17273 L .34544 .17282 L .34562 .17291 L .34581 .173 L .346 .17309 L .34618 .17318 L .34637 .17327 L .34656 .17336 L .34674 .17345 L .34693 .17354 L .34712 .17363 L .34731 .17372 L .34749 .17382 L .34768 .17391 L .34787 .174 L .34805 .17409 L .34824 .17418 L .34843 .17427 L .34861 .17436 L .3488 .17445 L .34899 .17454 L .34917 .17463 L .34936 .17473 L .34955 .17482 L .34974 .17492 L .34992 .17501 L .35011 .17511 L .3503 .1752 L .35048 .1753 L .35067 .17539 L Mistroke .35086 .17549 L .35104 .17558 L .35123 .17567 L .35142 .17576 L .3516 .17586 L .35179 .17595 L .35198 .17604 L .35216 .17613 L .35235 .17623 L .35254 .17632 L .35273 .17641 L .35291 .1765 L .3531 .17659 L .35329 .17669 L .35347 .17678 L .35366 .17687 L .35385 .17696 L .35403 .17705 L .35422 .17715 L .35441 .17724 L .35459 .17733 L .35478 .17743 L .35497 .17752 L .35515 .17761 L .35534 .17771 L .35553 .1778 L .35572 .17789 L .3559 .17798 L .35609 .17807 L .35628 .17817 L .35646 .17826 L .35665 .17835 L .35684 .17845 L .35702 .17854 L .35721 .17863 L .3574 .17873 L .35758 .17882 L .35777 .17891 L .35796 .17901 L .35814 .1791 L .35833 .1792 L .35852 .17929 L .35871 .17938 L .35889 .17948 L .35908 .17957 L .35927 .17967 L .35945 .17976 L .35964 .17986 L .35983 .17995 L .36001 .18005 L Mistroke .3602 .18015 L .36039 .18024 L .36057 .18034 L .36076 .18043 L .36095 .18053 L .36113 .18063 L .36132 .18073 L .36151 .18083 L .3617 .18092 L .36188 .18102 L .36207 .18112 L .36226 .18122 L .36244 .18132 L .36263 .18143 L .36282 .18153 L .363 .18163 L .36319 .18174 L .36338 .18184 L .36356 .18195 L .36375 .18205 L .36394 .18216 L .36413 .18226 L .36431 .18237 L .3645 .18248 L .36469 .18259 L .36487 .1827 L .36506 .18282 L .36525 .18293 L .36543 .18304 L .36562 .18316 L .36581 .18327 L .36599 .18339 L .36618 .1835 L .36637 .18361 L .36655 .18373 L .36674 .18385 L .36693 .18397 L .36712 .18408 L .3673 .18419 L .36749 .1843 L .36768 .18441 L .36786 .18452 L .36805 .18462 L .36824 .18473 L .36842 .18484 L .36861 .18496 L .3688 .18507 L .36898 .18518 L .36917 .1853 L .36936 .18541 L Mistroke .36954 .18552 L .36973 .18563 L .36992 .18575 L .37011 .18586 L .37029 .18598 L .37048 .18609 L .37067 .18621 L .37085 .18633 L .37104 .18644 L .37123 .18656 L .37141 .18668 L .3716 .1868 L .37179 .18691 L .37197 .18703 L .37216 .18714 L .37235 .18725 L .37253 .18736 L .37272 .18747 L .37291 .18758 L .3731 .18769 L .37328 .1878 L .37347 .18791 L .37366 .18802 L .37384 .18813 L .37403 .18824 L .37422 .18835 L .3744 .18846 L .37459 .18856 L .37478 .18867 L .37496 .18878 L .37515 .18888 L .37534 .18899 L .37553 .18909 L .37571 .1892 L .3759 .1893 L .37609 .18941 L .37627 .18951 L .37646 .18962 L .37665 .18972 L .37683 .18983 L .37702 .18994 L .37721 .19004 L .37739 .19015 L .37758 .19025 L .37777 .19035 L .37795 .19046 L .37814 .19056 L .37833 .19067 L .37852 .19077 L .3787 .19087 L Mistroke .37889 .19097 L .37908 .19107 L .37926 .19117 L .37945 .19127 L .37964 .19138 L .37982 .19148 L .38001 .19158 L .3802 .19168 L .38038 .19178 L .38057 .19188 L .38076 .19198 L .38094 .19208 L .38113 .19218 L .38132 .19228 L .38151 .19238 L .38169 .19249 L .38188 .19259 L .38207 .19269 L .38225 .19279 L .38244 .19288 L .38263 .19298 L .38281 .19308 L .383 .19319 L .38319 .19329 L .38337 .19338 L .38356 .19348 L .38375 .19358 L .38393 .19368 L .38412 .19378 L .38431 .19388 L .3845 .19398 L .38468 .19408 L .38487 .19418 L .38506 .19428 L .38524 .19438 L .38543 .19448 L .38562 .19458 L .3858 .19468 L .38599 .19478 L .38618 .19488 L .38636 .19498 L .38655 .19507 L .38674 .19517 L .38692 .19527 L .38711 .19537 L .3873 .19546 L .38749 .19556 L .38767 .19566 L .38786 .19575 L .38805 .19585 L Mistroke .38823 .19594 L .38842 .19604 L .38861 .19614 L .38879 .19623 L .38898 .19633 L .38917 .19642 L .38935 .19651 L .38954 .19661 L .38973 .1967 L .38992 .1968 L .3901 .19689 L .39029 .19699 L .39048 .19709 L .39066 .19718 L .39085 .19727 L .39104 .19737 L .39122 .19746 L .39141 .19755 L .3916 .19765 L .39178 .19774 L .39197 .19784 L .39216 .19793 L .39234 .19803 L .39253 .19813 L .39272 .19822 L .39291 .19832 L .39309 .19841 L .39328 .19851 L .39347 .1986 L .39365 .1987 L .39384 .1988 L .39403 .19889 L .39421 .19899 L .3944 .19909 L .39459 .19919 L .39477 .19929 L .39496 .19939 L .39515 .19948 L .39533 .19958 L .39552 .19968 L .39571 .19978 L .3959 .19988 L .39608 .19998 L .39627 .20008 L .39646 .20018 L .39664 .20028 L .39683 .20038 L .39702 .20048 L .3972 .20058 L .39739 .20068 L Mistroke .39758 .20078 L .39776 .20088 L .39795 .20098 L .39814 .20107 L .39832 .20117 L .39851 .20127 L .3987 .20137 L .39889 .20147 L .39907 .20156 L .39926 .20166 L .39945 .20176 L .39963 .20186 L .39982 .20195 L .40001 .20205 L .40019 .20215 L .40038 .20225 L .40057 .20235 L .40075 .20244 L .40094 .20254 L .40113 .20264 L .40132 .20274 L .4015 .20284 L .40169 .20294 L .40188 .20304 L .40206 .20314 L .40225 .20325 L .40244 .20335 L .40262 .20346 L .40281 .20356 L .403 .20367 L .40318 .20378 L .40337 .20389 L .40356 .204 L .40374 .20411 L .40393 .20422 L .40412 .20433 L .40431 .20443 L .40449 .20454 L .40468 .20465 L .40487 .20476 L .40505 .20487 L .40524 .20498 L .40543 .20509 L .40561 .2052 L .4058 .20531 L .40599 .20541 L .40617 .20552 L .40636 .20563 L .40655 .20573 L .40673 .20583 L Mistroke .40692 .20594 L .40711 .20604 L .4073 .20614 L .40748 .20624 L .40767 .20634 L .40786 .20644 L .40804 .20654 L .40823 .20664 L .40842 .20674 L .4086 .20684 L .40879 .20694 L .40898 .20703 L .40916 .20713 L .40935 .20723 L .40954 .20733 L .40972 .20743 L .40991 .20752 L .4101 .20762 L .41029 .20772 L .41047 .20782 L .41066 .20792 L .41085 .20802 L .41103 .20812 L .41122 .20822 L .41141 .20832 L .41159 .20842 L .41178 .20852 L .41197 .20861 L .41215 .20871 L .41234 .20881 L .41253 .2089 L .41271 .209 L .4129 .2091 L .41309 .2092 L .41328 .2093 L .41346 .20939 L .41365 .20949 L .41384 .20959 L .41402 .20969 L .41421 .20978 L .4144 .20988 L .41458 .20998 L .41477 .21008 L .41496 .21018 L .41514 .21027 L .41533 .21037 L .41552 .21047 L .41571 .21057 L .41589 .21066 L .41608 .21077 L Mistroke .41627 .21087 L .41645 .21097 L .41664 .21107 L .41683 .21117 L .41701 .21127 L .4172 .21137 L .41739 .21146 L .41757 .21156 L .41776 .21166 L .41795 .21175 L .41813 .21185 L .41832 .21194 L .41851 .21204 L .4187 .21213 L .41888 .21222 L .41907 .21232 L .41926 .21241 L .41944 .2125 L .41963 .21259 L .41982 .21269 L .42 .21278 L .42019 .21287 L .42038 .21296 L .42056 .21306 L .42075 .21315 L .42094 .21324 L .42112 .21334 L .42131 .21343 L .4215 .21352 L .42169 .21361 L .42187 .21371 L .42206 .2138 L .42225 .21389 L .42243 .21398 L .42262 .21407 L .42281 .21416 L .42299 .21425 L .42318 .21434 L .42337 .21443 L .42355 .21452 L .42374 .21462 L .42393 .21471 L .42411 .2148 L .4243 .21489 L .42449 .21498 L .42468 .21508 L .42486 .21517 L .42505 .21526 L .42524 .21535 L .42542 .21544 L Mistroke .42561 .21554 L .4258 .21563 L .42598 .21572 L .42617 .21582 L .42636 .21591 L .42654 .21601 L .42673 .2161 L .42692 .21619 L .4271 .21629 L .42729 .21638 L .42748 .21648 L .42767 .21657 L .42785 .21666 L .42804 .21676 L .42823 .21685 L .42841 .21694 L .4286 .21703 L .42879 .21712 L .42897 .21721 L .42916 .21731 L .42935 .2174 L .42953 .21749 L .42972 .21758 L .42991 .21767 L .4301 .21776 L .43028 .21785 L .43047 .21794 L .43066 .21803 L .43084 .21812 L .43103 .21821 L .43122 .2183 L .4314 .21839 L .43159 .21848 L .43178 .21857 L .43196 .21866 L .43215 .21875 L .43234 .21884 L .43252 .21893 L .43271 .21902 L .4329 .21911 L .43309 .21919 L .43327 .21928 L .43346 .21937 L .43365 .21946 L .43383 .21955 L .43402 .21964 L .43421 .21973 L .43439 .21982 L .43458 .21992 L .43477 .22001 L Mistroke .43495 .2201 L .43514 .22019 L .43533 .22028 L .43551 .22037 L .4357 .22047 L .43589 .22056 L .43608 .22065 L .43626 .22075 L .43645 .22084 L .43664 .22094 L .43682 .22103 L .43701 .22113 L .4372 .22122 L .43738 .22131 L .43757 .2214 L .43776 .22149 L .43794 .22159 L .43813 .22168 L .43832 .22177 L .4385 .22186 L .43869 .22195 L .43888 .22204 L .43907 .22213 L .43925 .22222 L .43944 .2223 L .43963 .22239 L .43981 .22248 L .44 .22257 L .44019 .22266 L .44037 .22274 L .44056 .22283 L .44075 .22292 L .44093 .22301 L .44112 .22309 L .44131 .22318 L .4415 .22327 L .44168 .22336 L .44187 .22345 L .44206 .22353 L .44224 .22362 L .44243 .22371 L .44262 .2238 L .4428 .22389 L .44299 .22397 L .44318 .22406 L .44336 .22415 L .44355 .22423 L .44374 .22432 L .44392 .22441 L .44411 .22449 L Mistroke .4443 .22458 L .44449 .22467 L .44467 .22476 L .44486 .22484 L .44505 .22493 L .44523 .22502 L .44542 .2251 L .44561 .22519 L .44579 .22528 L .44598 .22536 L .44617 .22545 L .44635 .22554 L .44654 .22563 L .44673 .22571 L .44691 .2258 L .4471 .22589 L .44729 .22598 L .44748 .22606 L .44766 .22615 L .44785 .22624 L .44804 .22632 L .44822 .22641 L .44841 .2265 L .4486 .22659 L .44878 .22667 L .44897 .22676 L .44916 .22685 L .44934 .22693 L .44953 .22702 L .44972 .22711 L .4499 .22719 L .45009 .22728 L .45028 .22737 L .45047 .22746 L .45065 .22754 L .45084 .22763 L .45103 .22772 L .45121 .2278 L .4514 .22789 L .45159 .22798 L .45177 .22806 L .45196 .22815 L .45215 .22824 L .45233 .22832 L .45252 .22841 L .45271 .2285 L .45289 .22859 L .45308 .22867 L .45327 .22876 L .45346 .22885 L Mistroke .45364 .22893 L .45383 .22902 L .45402 .22911 L .4542 .2292 L .45439 .22928 L .45458 .22937 L .45476 .22946 L .45495 .22955 L .45514 .22964 L .45532 .22972 L .45551 .22981 L .4557 .2299 L .45589 .22999 L .45607 .23007 L .45626 .23016 L .45645 .23025 L .45663 .23033 L .45682 .23042 L .45701 .23051 L .45719 .23059 L .45738 .23068 L .45757 .23077 L .45775 .23086 L .45794 .23094 L .45813 .23103 L .45831 .23112 L .4585 .2312 L .45869 .23129 L .45888 .23138 L .45906 .23146 L .45925 .23155 L .45944 .23164 L .45962 .23172 L .45981 .23181 L .46 .2319 L .46018 .23199 L .46037 .23207 L .46056 .23216 L .46074 .23225 L .46093 .23233 L .46112 .23242 L .4613 .23251 L .46149 .2326 L .46168 .23268 L .46187 .23277 L .46205 .23286 L .46224 .23295 L .46243 .23303 L .46261 .23312 L .4628 .23321 L Mistroke .46299 .23329 L .46317 .23338 L .46336 .23347 L .46355 .23356 L .46373 .23364 L .46392 .23373 L .46411 .23382 L .46429 .2339 L .46448 .23399 L .46467 .23408 L .46486 .23417 L .46504 .23425 L .46523 .23434 L .46542 .23443 L .4656 .23452 L .46579 .2346 L .46598 .23469 L .46616 .23478 L .46635 .23487 L .46654 .23495 L .46672 .23504 L .46691 .23513 L .4671 .23522 L .46729 .23531 L .46747 .23539 L .46766 .23548 L .46785 .23557 L .46803 .23566 L .46822 .23574 L .46841 .23583 L .46859 .23592 L .46878 .236 L .46897 .23609 L .46915 .23618 L .46934 .23627 L .46953 .23635 L .46971 .23644 L .4699 .23653 L .47009 .23662 L .47028 .2367 L .47046 .23679 L .47065 .23688 L .47084 .23697 L .47102 .23705 L .47121 .23714 L .4714 .23723 L .47158 .23732 L .47177 .23741 L .47196 .2375 L .47214 .23758 L Mistroke .47233 .23767 L .47252 .23776 L .4727 .23785 L .47289 .23793 L .47308 .23802 L .47327 .23811 L .47345 .2382 L .47364 .23828 L .47383 .23837 L .47401 .23846 L .4742 .23855 L .47439 .23863 L .47457 .23872 L .47476 .23881 L .47495 .2389 L .47513 .23898 L .47532 .23907 L .47551 .23916 L .47569 .23925 L .47588 .23934 L .47607 .23942 L .47626 .23951 L .47644 .2396 L .47663 .23969 L .47682 .23978 L .477 .23987 L .47719 .23996 L .47738 .24004 L .47756 .24013 L .47775 .24022 L .47794 .24031 L .47812 .24039 L .47831 .24048 L .4785 .24057 L .47868 .24066 L .47887 .24074 L .47906 .24083 L .47925 .24092 L .47943 .24101 L .47962 .2411 L .47981 .24118 L .47999 .24127 L .48018 .24136 L .48037 .24145 L .48055 .24154 L .48074 .24162 L .48093 .24171 L .48111 .2418 L .4813 .24189 L .48149 .24198 L Mistroke .48168 .24207 L .48186 .24216 L .48205 .24224 L .48224 .24233 L .48242 .24242 L .48261 .24251 L .4828 .24259 L .48298 .24268 L .48317 .24277 L .48336 .24286 L .48354 .24294 L .48373 .24303 L .48392 .24312 L .4841 .24321 L .48429 .24329 L .48448 .24338 L .48467 .24347 L .48485 .24356 L .48504 .24365 L .48523 .24373 L .48541 .24382 L .4856 .24391 L .48579 .244 L .48597 .24409 L .48616 .24418 L .48635 .24426 L .48653 .24435 L .48672 .24444 L .48691 .24453 L .48709 .24462 L .48728 .24471 L .48747 .2448 L .48766 .24489 L .48784 .24498 L .48803 .24507 L .48822 .24516 L .4884 .24524 L .48859 .24533 L .48878 .24542 L .48896 .24551 L .48915 .2456 L .48934 .24569 L .48952 .24578 L .48971 .24588 L .4899 .24597 L .49008 .24606 L .49027 .24615 L .49046 .24624 L .49065 .24633 L .49083 .24641 L Mistroke .49102 .2465 L .49121 .24659 L .49139 .24668 L .49158 .24677 L .49177 .24686 L .49195 .24695 L .49214 .24703 L .49233 .24712 L .49251 .24721 L .4927 .2473 L .49289 .24739 L .49308 .24748 L .49326 .24757 L .49345 .24765 L .49364 .24774 L .49382 .24783 L .49401 .24792 L .4942 .24801 L .49438 .2481 L .49457 .24818 L .49476 .24827 L .49494 .24836 L .49513 .24845 L .49532 .24854 L .4955 .24862 L .49569 .24871 L .49588 .2488 L .49607 .24889 L .49625 .24897 L .49644 .24906 L .49663 .24915 L .49681 .24924 L .497 .24932 L .49719 .24941 L .49737 .2495 L .49756 .24959 L .49775 .24968 L .49793 .24976 L .49812 .24985 L .49831 .24994 L .49849 .25003 L .49868 .25012 L .49887 .2502 L .49906 .25029 L .49924 .25038 L .49943 .25047 L .49962 .25055 L .4998 .25064 L .49999 .25073 L .50018 .25081 L Mistroke .50036 .2509 L .50055 .25099 L .50074 .25108 L .50092 .25116 L .50111 .25125 L .5013 .25134 L .50148 .25142 L .50167 .25151 L .50186 .2516 L .50205 .25168 L .50223 .25177 L .50242 .25186 L .50261 .25194 L .50279 .25203 L .50298 .25212 L .50317 .25221 L .50335 .25229 L .50354 .25238 L .50373 .25247 L .50391 .25255 L .5041 .25264 L .50429 .25273 L .50447 .25281 L .50466 .2529 L .50485 .25299 L .50504 .25308 L .50522 .25316 L .50541 .25325 L .5056 .25334 L .50578 .25342 L .50597 .25351 L .50616 .2536 L .50634 .25368 L .50653 .25377 L .50672 .25386 L .5069 .25394 L .50709 .25403 L .50728 .25412 L .50747 .25421 L .50765 .25429 L .50784 .25438 L .50803 .25447 L .50821 .25455 L .5084 .25464 L .50859 .25473 L .50877 .25481 L .50896 .2549 L .50915 .25499 L .50933 .25508 L .50952 .25516 L Mistroke .50971 .25525 L .50989 .25534 L .51008 .25542 L .51027 .25551 L .51046 .2556 L .51064 .25568 L .51083 .25577 L .51102 .25586 L .5112 .25595 L .51139 .25603 L .51158 .25612 L .51176 .25621 L .51195 .25629 L .51214 .25638 L .51232 .25647 L .51251 .25656 L .5127 .25664 L .51288 .25673 L .51307 .25682 L .51326 .25691 L .51345 .25699 L .51363 .25708 L .51382 .25717 L .51401 .25726 L .51419 .25735 L .51438 .25743 L .51457 .25752 L .51475 .25761 L .51494 .2577 L .51513 .25779 L .51531 .25788 L .5155 .25797 L .51569 .25805 L .51587 .25814 L .51606 .25823 L .51625 .25832 L .51644 .25841 L .51662 .2585 L .51681 .25858 L .517 .25867 L .51718 .25876 L .51737 .25885 L .51756 .25894 L .51774 .25903 L .51793 .25912 L .51812 .25921 L .5183 .25929 L .51849 .25938 L .51868 .25947 L .51886 .25956 L Mistroke .51905 .25965 L .51924 .25974 L .51943 .25983 L .51961 .25992 L .5198 .26001 L .51999 .26009 L .52017 .26018 L .52036 .26027 L .52055 .26036 L .52073 .26045 L .52092 .26054 L .52111 .26063 L .52129 .26071 L .52148 .2608 L .52167 .26089 L .52186 .26098 L .52204 .26107 L .52223 .26116 L .52242 .26125 L .5226 .26134 L .52279 .26143 L .52298 .26152 L .52316 .26161 L .52335 .2617 L .52354 .26178 L .52372 .26187 L .52391 .26196 L .5241 .26205 L .52428 .26214 L .52447 .26223 L .52466 .26232 L .52485 .26241 L .52503 .26249 L .52522 .26258 L .52541 .26267 L .52559 .26276 L .52578 .26285 L .52597 .26293 L .52615 .26302 L .52634 .26311 L .52653 .26319 L .52671 .26328 L .5269 .26337 L .52709 .26346 L .52727 .26354 L .52746 .26363 L .52765 .26372 L .52784 .26381 L .52802 .26389 L .52821 .26398 L Mistroke .5284 .26407 L .52858 .26416 L .52877 .26424 L .52896 .26433 L .52914 .26442 L .52933 .26451 L .52952 .26459 L .5297 .26468 L .52989 .26477 L .53008 .26486 L .53026 .26495 L .53045 .26503 L .53064 .26512 L .53083 .26521 L .53101 .2653 L .5312 .26538 L .53139 .26547 L .53157 .26556 L .53176 .26564 L .53195 .26573 L .53213 .26582 L .53232 .2659 L .53251 .26599 L .53269 .26608 L .53288 .26617 L .53307 .26625 L .53326 .26634 L .53344 .26643 L .53363 .26651 L .53382 .2666 L .534 .26669 L .53419 .26677 L .53438 .26686 L .53456 .26695 L .53475 .26704 L .53494 .26712 L .53512 .26721 L .53531 .2673 L .5355 .26738 L .53568 .26747 L .53587 .26756 L .53606 .26765 L .53625 .26773 L .53643 .26782 L .53662 .26791 L .53681 .268 L .53699 .26809 L .53718 .26817 L .53737 .26826 L .53755 .26835 L Mistroke .53774 .26844 L .53793 .26852 L .53811 .26861 L .5383 .2687 L .53849 .26879 L .53867 .26887 L .53886 .26896 L .53905 .26905 L .53924 .26914 L .53942 .26922 L .53961 .26931 L .5398 .2694 L .53998 .26948 L .54017 .26957 L .54036 .26966 L .54054 .26975 L .54073 .26983 L .54092 .26992 L .5411 .27001 L .54129 .27009 L .54148 .27018 L .54166 .27027 L .54185 .27036 L .54204 .27044 L .54223 .27053 L .54241 .27062 L .5426 .27071 L .54279 .27079 L .54297 .27088 L .54316 .27097 L .54335 .27106 L .54353 .27114 L .54372 .27123 L .54391 .27132 L .54409 .2714 L .54428 .27149 L .54447 .27158 L .54465 .27167 L .54484 .27176 L .54503 .27184 L .54522 .27193 L .5454 .27202 L .54559 .27211 L .54578 .2722 L .54596 .27228 L .54615 .27237 L .54634 .27246 L .54652 .27255 L .54671 .27264 L .5469 .27273 L Mistroke .54708 .27282 L .54727 .27291 L .54746 .273 L .54765 .27308 L .54783 .27317 L .54802 .27326 L .54821 .27335 L .54839 .27344 L .54858 .27353 L .54877 .27361 L .54895 .2737 L .54914 .27379 L .54933 .27388 L .54951 .27396 L .5497 .27405 L .54989 .27414 L .55007 .27423 L .55026 .27432 L .55045 .2744 L .55064 .27449 L .55082 .27458 L .55101 .27467 L .5512 .27475 L .55138 .27484 L .55157 .27493 L .55176 .27502 L .55194 .2751 L .55213 .27519 L .55232 .27528 L .5525 .27536 L .55269 .27545 L .55288 .27554 L .55306 .27563 L .55325 .27571 L .55344 .2758 L .55363 .27589 L .55381 .27597 L .554 .27606 L .55419 .27615 L .55437 .27624 L .55456 .27632 L .55475 .27641 L .55493 .2765 L .55512 .27658 L .55531 .27667 L .55549 .27676 L .55568 .27685 L .55587 .27694 L .55605 .27702 L .55624 .27711 L Mistroke .55643 .2772 L .55662 .27729 L .5568 .27737 L .55699 .27746 L .55718 .27755 L .55736 .27764 L .55755 .27772 L .55774 .27781 L .55792 .2779 L .55811 .27799 L .5583 .27808 L .55848 .27816 L .55867 .27825 L .55886 .27834 L .55905 .27843 L .55923 .27852 L .55942 .27861 L .55961 .2787 L .55979 .27879 L .55998 .27888 L .56017 .27898 L .56035 .27907 L .56054 .27916 L .56073 .27925 L .56091 .27935 L .5611 .27944 L .56129 .27953 L .56147 .27962 L .56166 .27972 L .56185 .27981 L .56204 .2799 L .56222 .27999 L .56241 .28008 L .5626 .28017 L .56278 .28027 L .56297 .28036 L .56316 .28045 L .56334 .28054 L .56353 .28064 L .56372 .28073 L .5639 .28082 L .56409 .28091 L .56428 .281 L .56446 .28109 L .56465 .28119 L .56484 .28128 L .56503 .28137 L .56521 .28147 L .5654 .28156 L .56559 .28165 L Mistroke .56577 .28175 L .56596 .28184 L .56615 .28194 L .56633 .28203 L .56652 .28213 L .56671 .28222 L .56689 .28231 L .56708 .2824 L .56727 .2825 L .56745 .28259 L .56764 .28269 L .56783 .28278 L .56802 .28288 L .5682 .28297 L .56839 .28307 L .56858 .28316 L .56876 .28325 L .56895 .28335 L .56914 .28344 L .56932 .28354 L .56951 .28363 L .5697 .28372 L .56988 .28382 L .57007 .28391 L .57026 .284 L .57044 .28409 L .57063 .28419 L .57082 .28428 L .57101 .28437 L .57119 .28446 L .57138 .28456 L .57157 .28465 L .57175 .28474 L .57194 .28483 L .57213 .28492 L .57231 .28501 L .5725 .28511 L .57269 .2852 L .57287 .28529 L .57306 .28538 L .57325 .28547 L .57344 .28557 L .57362 .28566 L .57381 .28575 L .574 .28585 L .57418 .28594 L .57437 .28603 L .57456 .28613 L .57474 .28622 L .57493 .28631 L Mistroke .57512 .28641 L .5753 .2865 L .57549 .2866 L .57568 .28669 L .57586 .28679 L .57605 .28688 L .57624 .28697 L .57643 .28707 L .57661 .28716 L .5768 .28726 L .57699 .28735 L .57717 .28745 L .57736 .28754 L .57755 .28764 L .57773 .28773 L .57792 .28783 L .57811 .28793 L .57829 .28802 L .57848 .28812 L .57867 .28822 L .57885 .28831 L .57904 .2884 L .57923 .2885 L .57942 .2886 L .5796 .28869 L .57979 .28879 L .57998 .28888 L .58016 .28897 L .58035 .28907 L .58054 .28916 L .58072 .28926 L .58091 .28935 L .5811 .28944 L .58128 .28954 L .58147 .28963 L .58166 .28973 L .58184 .28982 L .58203 .28991 L .58222 .29001 L .58241 .2901 L .58259 .29019 L .58278 .29029 L .58297 .29038 L .58315 .29047 L .58334 .29057 L .58353 .29066 L .58371 .29076 L .5839 .29085 L .58409 .29094 L .58427 .29104 L Mistroke .58446 .29113 L .58465 .29122 L .58484 .29131 L .58502 .29141 L .58521 .2915 L .5854 .29159 L .58558 .29168 L .58577 .29177 L .58596 .29186 L .58614 .29195 L .58633 .29204 L .58652 .29213 L .5867 .29222 L .58689 .29231 L .58708 .2924 L .58726 .29249 L .58745 .29258 L .58764 .29267 L .58783 .29276 L .58801 .29285 L .5882 .29294 L .58839 .29303 L .58857 .29312 L .58876 .29321 L .58895 .2933 L .58913 .29339 L .58932 .29348 L .58951 .29357 L .58969 .29366 L .58988 .29375 L .59007 .29384 L .59025 .29394 L .59044 .29403 L .59063 .29412 L .59082 .29421 L .591 .29431 L .59119 .2944 L .59138 .2945 L .59156 .29459 L .59175 .29469 L .59194 .29478 L .59212 .29488 L .59231 .29498 L .5925 .29507 L .59268 .29517 L .59287 .29527 L .59306 .29536 L .59324 .29546 L .59343 .29556 L .59362 .29566 L Mistroke .59381 .29576 L .59399 .29585 L .59418 .29595 L .59437 .29605 L .59455 .29614 L .59474 .29624 L .59493 .29633 L .59511 .29643 L .5953 .29653 L .59549 .29663 L .59567 .29673 L .59586 .29682 L .59605 .29692 L .59623 .29702 L .59642 .29712 L .59661 .29722 L .5968 .29731 L .59698 .29741 L .59717 .29751 L .59736 .2976 L .59754 .2977 L .59773 .2978 L .59792 .2979 L .5981 .29799 L .59829 .29809 L .59848 .29819 L .59866 .29829 L .59885 .29839 L .59904 .29849 L .59923 .29859 L .59941 .29869 L .5996 .29879 L .59979 .29889 L .59997 .29899 L .60016 .29909 L .60035 .29919 L .60053 .29929 L .60072 .29938 L .60091 .29948 L .60109 .29958 L .60128 .29968 L .60147 .29977 L .60165 .29987 L .60184 .29997 L .60203 .30007 L .60222 .30017 L .6024 .30027 L .60259 .30037 L .60278 .30047 L .60296 .30057 L Mistroke .60315 .30068 L .60334 .30078 L .60352 .30088 L .60371 .30098 L .6039 .30108 L .60408 .30118 L .60427 .30128 L .60446 .30138 L .60464 .30148 L .60483 .30158 L .60502 .30168 L .60521 .30178 L .60539 .30188 L .60558 .30198 L .60577 .30208 L .60595 .30217 L .60614 .30227 L .60633 .30237 L .60651 .30246 L .6067 .30256 L .60689 .30266 L .60707 .30276 L .60726 .30286 L .60745 .30295 L .60763 .30305 L .60782 .30314 L .60801 .30324 L .6082 .30333 L .60838 .30343 L .60857 .30353 L .60876 .30362 L .60894 .30372 L .60913 .30381 L .60932 .30391 L .6095 .304 L .60969 .3041 L .60988 .30419 L .61006 .30429 L .61025 .30438 L .61044 .30448 L .61062 .30457 L .61081 .30467 L .611 .30477 L .61119 .30486 L .61137 .30496 L .61156 .30505 L .61175 .30515 L .61193 .30525 L .61212 .30534 L .61231 .30544 L Mistroke .61249 .30554 L .61268 .30564 L .61287 .30574 L .61305 .30584 L .61324 .30593 L .61343 .30603 L .61362 .30613 L .6138 .30623 L .61399 .30632 L .61418 .30642 L .61436 .30652 L .61455 .30662 L .61474 .30672 L .61492 .30682 L .61511 .30692 L .6153 .30702 L .61548 .30712 L .61567 .30722 L .61586 .30732 L .61604 .30742 L .61623 .30752 L .61642 .30762 L .61661 .30772 L .61679 .30782 L .61698 .30792 L .61717 .30801 L .61735 .30811 L .61754 .3082 L .61773 .3083 L .61791 .30839 L .6181 .30849 L .61829 .30858 L .61847 .30868 L .61866 .30878 L .61885 .30887 L .61903 .30897 L .61922 .30906 L .61941 .30916 L .6196 .30926 L .61978 .30935 L .61997 .30945 L .62016 .30955 L .62034 .30965 L .62053 .30975 L .62072 .30984 L .6209 .30994 L .62109 .31004 L .62128 .31014 L .62146 .31023 L .62165 .31033 L Mistroke .62184 .31042 L .62202 .31052 L .62221 .31062 L .6224 .31072 L .62259 .31082 L .62277 .31092 L .62296 .31101 L .62315 .31111 L .62333 .3112 L .62352 .3113 L .62371 .3114 L .62389 .3115 L .62408 .31159 L .62427 .31169 L .62445 .31179 L .62464 .31189 L .62483 .31198 L .62502 .31208 L .6252 .31218 L .62539 .31227 L .62558 .31237 L .62576 .31247 L .62595 .31257 L .62614 .31266 L .62632 .31275 L .62651 .31285 L .6267 .31295 L .62688 .31305 L .62707 .31314 L .62726 .31324 L .62744 .31334 L .62763 .31344 L .62782 .31354 L .62801 .31363 L .62819 .31373 L .62838 .31383 L .62857 .31393 L .62875 .31403 L .62894 .31414 L .62913 .31424 L .62931 .31434 L .6295 .31444 L .62969 .31454 L .62987 .31464 L .63006 .31475 L .63025 .31485 L .63043 .31495 L .63062 .31506 L .63081 .31517 L .631 .31527 L Mistroke .63118 .31538 L .63137 .31549 L .63156 .3156 L .63174 .31571 L .63193 .31583 L .63212 .31593 L .6323 .31605 L .63249 .31616 L .63268 .31627 L .63286 .31639 L .63305 .3165 L .63324 .31661 L .63342 .31673 L .63361 .31685 L .6338 .31696 L .63399 .31708 L .63417 .31719 L .63436 .31731 L .63455 .31743 L .63473 .31754 L .63492 .31765 L .63511 .31777 L .63529 .31789 L .63548 .31801 L .63567 .31813 L .63585 .31825 L .63604 .31837 L .63623 .31849 L .63641 .31861 L .6366 .31873 L .63679 .31885 L .63698 .31897 L .63716 .31909 L .63735 .31921 L .63754 .31933 L .63772 .31945 L .63791 .31957 L .6381 .3197 L .63828 .31982 L .63847 .31995 L .63866 .32009 L .63884 .32023 L .63903 .32038 L .63922 .32052 L .63941 .32066 L .63959 .3208 L .63978 .32094 L .63997 .32108 L .64015 .32123 L .64034 .32138 L Mistroke .64053 .32153 L .64071 .32169 L .6409 .32185 L .64109 .32201 L .64127 .32218 L .64146 .32234 L .64165 .3225 L .64183 .32267 L .64202 .32283 L .64221 .32299 L .6424 .32315 L .64258 .3233 L .64277 .32346 L .64296 .32362 L .64314 .32378 L .64333 .32394 L .64352 .3241 L .6437 .32427 L .64389 .32443 L .64408 .3246 L .64426 .32477 L .64445 .32493 L .64464 .32509 L .64482 .32525 L .64501 .32541 L .6452 .32556 L .64539 .32572 L .64557 .32587 L .64576 .32603 L .64595 .32618 L .64613 .32635 L .64632 .3265 L .64651 .32665 L .64669 .3268 L .64688 .32695 L .64707 .32711 L .64725 .32726 L .64744 .32741 L .64763 .32756 L .64781 .32772 L .648 .32788 L .64819 .32803 L .64838 .32819 L .64856 .32834 L .64875 .32849 L .64894 .32864 L .64912 .32879 L .64931 .32894 L .6495 .32908 L .64968 .32922 L Mistroke .64987 .32935 L .65006 .32948 L .65024 .32962 L .65043 .32975 L .65062 .32989 L .65081 .33001 L .65099 .33014 L .65118 .33026 L .65137 .33039 L .65155 .33052 L .65174 .33064 L .65193 .33077 L .65211 .33089 L .6523 .33102 L .65249 .33115 L .65267 .33129 L .65286 .33142 L .65305 .33154 L .65323 .33167 L .65342 .33181 L .65361 .33194 L .6538 .33208 L .65398 .33221 L .65417 .33235 L .65436 .33248 L .65454 .33261 L .65473 .33274 L .65492 .33287 L .6551 .33301 L .65529 .33314 L .65548 .33327 L .65566 .33341 L .65585 .33355 L .65604 .3337 L .65622 .33385 L .65641 .334 L .6566 .33415 L .65679 .3343 L .65697 .33445 L .65716 .3346 L .65735 .33474 L .65753 .33488 L .65772 .33502 L .65791 .33515 L .65809 .33529 L .65828 .33542 L .65847 .33556 L .65865 .3357 L .65884 .33584 L .65903 .33597 L Mistroke .65921 .33611 L .6594 .33625 L .65959 .33639 L .65978 .33653 L .65996 .33667 L .66015 .3368 L .66034 .33694 L .66052 .33707 L .66071 .3372 L .6609 .33732 L .66108 .33745 L .66127 .33758 L .66146 .3377 L .66164 .33783 L .66183 .33795 L .66202 .33808 L .6622 .3382 L .66239 .33833 L .66258 .33846 L .66277 .33858 L .66295 .3387 L .66314 .33883 L .66333 .33895 L .66351 .33907 L .6637 .33919 L .66389 .33931 L .66407 .33944 L .66426 .33957 L .66445 .33969 L .66463 .33981 L .66482 .33993 L .66501 .34005 L .6652 .34017 L .66538 .34029 L .66557 .34041 L .66576 .34053 L .66594 .34065 L .66613 .34078 L .66632 .3409 L .6665 .34102 L .66669 .34114 L .66688 .34125 L .66706 .34137 L .66725 .34148 L .66744 .3416 L .66762 .34171 L .66781 .34182 L .668 .34194 L .66819 .34205 L .66837 .34216 L Mistroke 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.69192 .35497 L .69211 .35506 L .69229 .35515 L .69248 .35524 L .69267 .35533 L .69285 .35542 L .69304 .35551 L .69323 .3556 L .69341 .35569 L .6936 .35579 L .69379 .35588 L .69398 .35597 L .69416 .35606 L .69435 .35615 L .69454 .35625 L .69472 .35634 L .69491 .35643 L .6951 .35653 L .69528 .35662 L .69547 .35672 L .69566 .35681 L .69584 .35691 L .69603 .35701 L .69622 .3571 L .6964 .3572 L Mistroke .69659 .3573 L .69678 .3574 L .69697 .35749 L .69715 .35759 L .69734 .35769 L .69753 .35779 L .69771 .35789 L .6979 .35798 L .69809 .35808 L .69827 .35818 L .69846 .35827 L .69865 .35837 L .69883 .35847 L .69902 .35857 L .69921 .35867 L .69939 .35877 L .69958 .35887 L .69977 .35897 L .69996 .35907 L .70014 .35916 L .70033 .35926 L .70052 .35936 L .7007 .35945 L .70089 .35955 L .70108 .35965 L .70126 .35975 L .70145 .35985 L .70164 .35995 L .70182 .36005 L .70201 .36015 L .7022 .36025 L .70238 .36035 L .70257 .36045 L .70276 .36055 L .70295 .36066 L .70313 .36075 L .70332 .36085 L .70351 .36095 L .70369 .36105 L .70388 .36114 L .70407 .36124 L .70425 .36134 L .70444 .36144 L .70463 .36154 L .70481 .36164 L .705 .36174 L .70519 .36183 L .70538 .36193 L .70556 .36203 L .70575 .36212 L Mistroke .70594 .36222 L .70612 .36232 L .70631 .36241 L .7065 .36251 L .70668 .36261 L .70687 .3627 L .70706 .3628 L .70724 .3629 L .70743 .363 L .70762 .36309 L .7078 .36319 L .70799 .36329 L .70818 .36338 L .70837 .36348 L .70855 .36358 L .70874 .36367 L .70893 .36377 L .70911 .36387 L .7093 .36398 L .70949 .36408 L .70967 .36418 L .70986 .36428 L .71005 .36438 L .71023 .36447 L .71042 .36457 L .71061 .36467 L .71079 .36477 L .71098 .36487 L .71117 .36496 L .71136 .36506 L .71154 .36516 L .71173 .36526 L .71192 .36536 L .7121 .36546 L .71229 .36556 L .71248 .36566 L .71266 .36576 L .71285 .36586 L .71304 .36596 L .71322 .36606 L .71341 .36616 L .7136 .36626 L .71378 .36636 L .71397 .36646 L .71416 .36656 L .71435 .36666 L .71453 .36676 L .71472 .36686 L .71491 .36696 L .71509 .36706 L Mistroke .71528 .36717 L .71547 .36727 L .71565 .36738 L .71584 .36748 L .71603 .36758 L .71621 .36769 L .7164 .36779 L .71659 .3679 L .71678 .368 L .71696 .36811 L .71715 .36821 L .71734 .36831 L .71752 .36841 L .71771 .36851 L .7179 .36862 L .71808 .36872 L .71827 .36882 L .71846 .36892 L .71864 .36901 L .71883 .36911 L .71902 .36922 L .7192 .36932 L .71939 .36942 L .71958 .36952 L .71977 .36962 L .71995 .36972 L .72014 .36982 L .72033 .36992 L .72051 .37002 L .7207 .37012 L .72089 .37022 L .72107 .37033 L .72126 .37043 L .72145 .37053 L .72163 .37063 L .72182 .37074 L .72201 .37084 L .72219 .37094 L .72238 .37104 L .72257 .37114 L .72276 .37124 L .72294 .37134 L .72313 .37144 L .72332 .37154 L .7235 .37165 L .72369 .37174 L .72388 .37185 L .72406 .37195 L .72425 .37205 L .72444 .37215 L Mistroke .72462 .37225 L .72481 .37235 L .725 .37245 L .72518 .37255 L .72537 .37264 L .72556 .37274 L .72575 .37284 L .72593 .37294 L .72612 .37303 L .72631 .37313 L .72649 .37323 L .72668 .37333 L 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.88032 .48853 L .88034 .48854 L .88035 .48855 L .88037 .48856 L .88039 .48857 L .88041 .48859 L .88043 .4886 L .88045 .48861 L .88047 .48862 L .88049 .48863 L .8805 .48865 L .88052 .48866 L .88054 .48867 L .88056 .48868 L .88058 .48869 L .8806 .4887 L .88062 .48871 L .88063 .48873 L .88065 .48874 L .88067 .48875 L .88069 .48876 L .88071 .48877 L .88073 .48878 L .88075 .48879 L .88077 .4888 L .88078 .48882 L .8808 .48883 L .88082 .48884 L .88084 .48885 L .88086 .48886 L .88088 .48887 L .8809 .48889 L .88092 .4889 L .88093 .48891 L .88095 .48892 L .88097 .48893 L Mistroke .88099 .48894 L .88101 .48896 L .88103 .48897 L .88105 .48898 L .88106 .48899 L .88108 .489 L .8811 .48901 L .88112 .48902 L .88114 .48904 L .88116 .48905 L .88118 .48906 L .8812 .48907 L .88121 .48908 L .88123 .48909 L .88125 .48911 L .88127 .48912 L .88129 .48913 L .88131 .48914 L .88133 .48915 L .88135 .48917 L .88136 .48918 L .88138 .48919 L .8814 .4892 L .88142 .48921 L .88144 .48922 L .88146 .48924 L .88148 .48925 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.88966 .49448 L .88968 .4945 L .8897 .49451 L .88972 .49452 L .88974 .49454 L .88975 .49455 L .88977 .49456 L .88979 .49458 L .88981 .49459 L .88983 .4946 L .88985 .49462 L .88987 .49463 L .88989 .49464 L .8899 .49466 L .88992 .49467 L .88994 .49468 L .88996 .4947 L .88998 .49471 L .89 .49472 L .89002 .49474 L .89004 .49475 L .89005 .49476 L .89007 .49478 L .89009 .49479 L .89011 .4948 L .89013 .49482 L .89015 .49483 L .89017 .49484 L .89018 .49486 L .8902 .49487 L .89022 .49488 L .89024 .4949 L .89026 .49491 L .89028 .49493 L .8903 .49494 L .89032 .49495 L Mistroke .89033 .49497 L .89035 .49498 L .89037 .49499 L .89039 .49501 L .89041 .49502 L .89043 .49503 L .89045 .49505 L .89046 .49506 L .89048 .49507 L .8905 .49509 L .89052 .4951 L .89054 .49511 L .89056 .49513 L .89058 .49514 L .8906 .49515 L .89061 .49517 L .89063 .49518 L .89065 .49519 L .89067 .49521 L .89069 .49522 L .89071 .49523 L .89073 .49524 L .89075 .49526 L .89076 .49527 L .89078 .49528 L .8908 .4953 L .89082 .49531 L 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.90018 .5019 L .9002 .50192 L .90022 .50193 L .90024 .50194 L .90026 .50195 L .90028 .50196 L .9003 .50197 L .90031 .50199 L .90033 .502 L .90035 .50201 L .90037 .50202 L .90039 .50203 L .90041 .50204 L .90043 .50206 L .90044 .50207 L .90046 .50208 L .90048 .50209 L .9005 .5021 L .90052 .50212 L .90054 .50213 L .90056 .50214 L .90058 .50215 L .90059 .50216 L Mistroke .90061 .50217 L .90063 .50219 L .90065 .5022 L .90067 .50221 L .90069 .50222 L .90071 .50223 L .90072 .50225 L .90074 .50226 L .90076 .50227 L .90078 .50228 L .9008 .50229 L .90082 .5023 L .90084 .50232 L .90086 .50233 L .90087 .50234 L .90089 .50235 L .90091 .50236 L .90093 .50237 L .90095 .50239 L .90097 .5024 L .90099 .50241 L .90101 .50242 L .90102 .50243 L .90104 .50245 L .90106 .50246 L .90108 .50247 L .9011 .50248 L .90112 .50249 L .90114 .50251 L .90115 .50252 L .90117 .50253 L .90119 .50254 L .90121 .50255 L .90123 .50257 L .90125 .50258 L .90127 .50259 L .90129 .5026 L .9013 .50261 L .90132 .50263 L .90134 .50264 L .90136 .50265 L .90138 .50266 L .9014 .50268 L .90142 .50269 L .90144 .5027 L .90145 .50271 L .90147 .50272 L .90149 .50274 L .90151 .50275 L .90153 .50276 L Mistroke .90155 .50277 L .90157 .50279 L .90158 .5028 L .9016 .50281 L .90162 .50282 L .90164 .50283 L .90166 .50285 L .90168 .50286 L .9017 .50287 L .90172 .50288 L .90173 .50289 L .90175 .50291 L .90177 .50292 L .90179 .50293 L .90181 .50294 L .90183 .50295 L .90185 .50297 L .90186 .50298 L .90188 .50299 L .9019 .503 L .90192 .50301 L .90194 .50303 L .90196 .50304 L .90198 .50305 L .902 .50306 L .90201 .50307 L .90203 .50309 L .90205 .5031 L .90207 .50311 L .90209 .50312 L .90211 .50313 L .90213 .50315 L .90215 .50316 L .90216 .50317 L .90218 .50318 L .9022 .50319 L .90222 .50321 L .90224 .50322 L .90226 .50323 L .90228 .50324 L .90229 .50325 L .90231 .50326 L .90233 .50328 L .90235 .50329 L .90237 .5033 L .90239 .50331 L .90241 .50332 L .90243 .50334 L .90244 .50335 L .90246 .50336 L Mistroke .90248 .50337 L .9025 .50338 L .90252 .5034 L .90254 .50341 L .90256 .50342 L .90258 .50343 L .90259 .50344 L .90261 .50346 L .90263 .50347 L .90265 .50348 L .90267 .50349 L .90269 .5035 L .90271 .50352 L .90272 .50353 L .90274 .50354 L .90276 .50355 L .90278 .50357 L .9028 .50358 L .90282 .50359 L .90284 .5036 L .90286 .50362 L .90287 .50363 L .90289 .50364 L .90291 .50366 L .90293 .50367 L .90295 .50368 L .90297 .5037 L .90299 .50371 L .903 .50372 L .90302 .50373 L .90304 .50375 L .90306 .50376 L .90308 .50377 L .9031 .50379 L .90312 .5038 L .90314 .50381 L .90315 .50383 L .90317 .50384 L .90319 .50385 L .90321 .50387 L .90323 .50388 L .90325 .50389 L .90327 .5039 L .90329 .50392 L .9033 .50393 L .90332 .50394 L .90334 .50396 L .90336 .50397 L .90338 .50398 L .9034 .504 L Mistroke .90342 .50401 L .90343 .50402 L .90345 .50404 L .90347 .50405 L .90349 .50406 L .90351 .50408 L .90353 .50409 L .90355 .5041 L .90357 .50412 L .90358 .50413 L .9036 .50415 L .90362 .50416 L .90364 .50417 L .90366 .50419 L .90368 .5042 L 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.50595 L .90605 .50596 L .90607 .50597 L .90609 .50599 L .90611 .506 L .90613 .50601 L .90614 .50603 L .90616 .50604 L .90618 .50605 L .9062 .50607 L Mistroke .90622 .50608 L .90624 .50609 L .90626 .50611 L .90628 .50612 L .90629 .50613 L .90631 .50615 L .90633 .50616 L .90635 .50617 L .90637 .50619 L .90639 .5062 L .90641 .50621 L .90642 .50623 L .90644 .50624 L .90646 .50625 L .90648 .50627 L .9065 .50628 L .90652 .50629 L .90654 .50631 L .90656 .50632 L .90657 .50633 L .90659 .50635 L .90661 .50636 L .90663 .50637 L .90665 .50639 L .90667 .5064 L .90669 .50641 L .90671 .50643 L .90672 .50644 L .90674 .50645 L .90676 .50647 L .90678 .50648 L .9068 .50649 L .90682 .50651 L .90684 .50652 L .90685 .50653 L .90687 .50655 L .90689 .50656 L .90691 .50657 L .90693 .50659 L .90695 .5066 L .90697 .50661 L .90699 .50663 L .907 .50664 L .90702 .50665 L .90704 .50667 L .90706 .50668 L .90708 .50669 L .9071 .5067 L .90712 .50672 L .90714 .50673 L Mistroke .90715 .50674 L .90717 .50676 L .90719 .50677 L .90721 .50678 L .90723 .5068 L .90725 .50681 L .90727 .50682 L .90728 .50684 L .9073 .50685 L .90732 .50686 L .90734 .50687 L .90736 .50689 L .90738 .5069 L .9074 .50691 L .90742 .50693 L .90743 .50694 L .90745 .50695 L .90747 .50697 L .90749 .50698 L .90751 .50699 L .90753 .507 L .90755 .50702 L .90756 .50703 L .90758 .50704 L .9076 .50706 L .90762 .50707 L .90764 .50708 L .90766 .5071 L .90768 .50711 L .9077 .50712 L .90771 .50714 L .90773 .50715 L .90775 .50716 L .90777 .50717 L .90779 .50719 L .90781 .5072 L .90783 .50721 L .90785 .50723 L .90786 .50724 L .90788 .50725 L .9079 .50727 L .90792 .50728 L .90794 .50729 L .90796 .50731 L .90798 .50732 L .90799 .50733 L .90801 .50734 L .90803 .50736 L .90805 .50737 L .90807 .50738 L Mistroke .90809 .5074 L .90811 .50741 L .90813 .50742 L .90814 .50744 L .90816 .50745 L .90818 .50746 L .9082 .50748 L .90822 .50749 L .90824 .5075 L .90826 .50752 L .90827 .50753 L .90829 .50754 L .90831 .50756 L .90833 .50757 L .90835 .50758 L .90837 .5076 L .90839 .50761 L .90841 .50762 L .90842 .50764 L .90844 .50765 L .90846 .50766 L .90848 .50768 L .9085 .50769 L .90852 .5077 L .90854 .50772 L .90856 .50773 L .90857 .50774 L .90859 .50776 L .90861 .50777 L .90863 .50778 L .90865 .5078 L .90867 .50781 L .90869 .50782 L .9087 .50784 L .90872 .50785 L .90874 .50787 L .90876 .50788 L .90878 .50789 L .9088 .50791 L .90882 .50792 L .90884 .50793 L .90885 .50795 L .90887 .50796 L .90889 .50797 L .90891 .50799 L .90893 .508 L .90895 .50802 L .90897 .50803 L .90899 .50804 L .909 .50806 L Mistroke .90902 .50807 L .90904 .50808 L .90906 .5081 L .90908 .50811 L .9091 .50812 L .90912 .50814 L .90913 .50815 L .90915 .50816 L .90917 .50818 L .90919 .50819 L .90921 .5082 L .90923 .50822 L .90925 .50823 L .90927 .50824 L .90928 .50826 L .9093 .50827 L .90932 .50828 L .90934 .5083 L .90936 .50831 L .90938 .50832 L .9094 .50834 L .90941 .50835 L .90943 .50836 L .90945 .50838 L .90947 .50839 L .90949 .50841 L .90951 .50842 L .90953 .50843 L 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parameter ", Cell[BoxData[ \(TraditionalForm\`\[Beta][z]\)]], " introduced in 2.2.1." }], "Text"], Cell[BoxData[ \(\[Beta][ z] = \(2 \[Beta]\_0\)\/\(\((1 - \(z\ \[Beta]\_0\)\/\[Gamma])\) + \ \((1 - \(z\ \[Beta]\_0\)\/\[Gamma])\)\^\(-1\)\), \ 0 \[LessEqual] z < \(\(\[Gamma]\/\[Beta]\_0\)\(.\)\)\)], "DisplayFormula",\ FontSize->18], Cell[TextData[{ "In the stochastic case, the system of four differential equations with \ random parameters (depending on the simulated population size process ", Cell[BoxData[ \(TraditionalForm\`N\_t\)]], ") must be numerically solved. " }], "Text"], Cell[TextData[{ "We choose ", Cell[BoxData[ \(TraditionalForm\`\[Beta]\_0 = 0.6\)]], ", ", Cell[BoxData[ \(TraditionalForm\`\[Gamma] = 0.2\)]], ", ", Cell[BoxData[ \(TraditionalForm\`N\_0\)]], "=1,", Cell[BoxData[ \(TraditionalForm\`\(\(\ \)\(w\_0 = 0.1\ N\_0\)\)\)]], ",", Cell[BoxData[ \(TraditionalForm\`\(\(\ \)\(x\_0 = \ 0.999\ \((N\_0 - w\_0)\)\)\)\)]], ",", Cell[BoxData[ \(TraditionalForm\`\(\(\ \)\(y\_0 = \ 0.001 \((N\_0 - w\_0)\)\)\)\)]], ",", Cell[BoxData[ \(TraditionalForm\`\(\(\ \)\(z\_0 = \ 0\)\)\)]], ",", Cell[BoxData[ \(TraditionalForm\`v\ = \(\(0.002\)\(.\)\)\)]] }], "Text"], Cell[BoxData[{ StyleBox[\(Clear[x, y, z, w];\), FontColor->RGBColor[1, 0, 0]], "\n", \(n0 = 1; x0init = 0.999; \[Beta]0 = 0.6; \[Gamma]0 = 0.2; t\[Infinity] = 150; v = 0.002; pv = 0.1;\), "\[IndentingNewLine]", \(solsys2 = NDSolve[{\(x'\)[ t] \[Equal] \(-\(population[t]\/population[ 0]\)\) \[Beta]0\ 2\/\(\((1 - \(z[t] \[Beta]0\)\/\ \[Gamma]0)\) + \((1 - \(z[t] \[Beta]0\)\/\[Gamma]0)\)\^\(-1\)\)\ x[t]\ y[t] - v\ x[t], \(y'\)[ t] \[Equal] \(population[t]\/population[ 0]\) \[Beta]0\ \(2\/\(\((1 - \(z[t] \[Beta]0\)\/\ \[Gamma]0)\) + \((1 - \(z[t] \[Beta]0\)\/\[Gamma]0)\)\^\(-1\)\)\) x[t]\ y[t] - \[Gamma]0\ y[t], \(z'\)[ t] \[Equal] \[Gamma]0\ y[t], \(w'\)[t] \[Equal] v\ x[t], x[0] \[Equal] x0init*\((1 - pv)\), w[0] \[Equal] x0init*pv, y[0] \[Equal] 1 - x[0] - w[0], z[0] \[Equal] 0}, {x, y, z, w}, {t, 0, t\[Infinity]}];\), "\n", \(x = \((x /. solsys2)\)\[LeftDoubleBracket]1\[RightDoubleBracket]; y = \((y /. solsys2)\)\[LeftDoubleBracket]1\[RightDoubleBracket]; z = \((z /. solsys2)\)\[LeftDoubleBracket]1\[RightDoubleBracket]; w = \((w /. solsys2)\)\[LeftDoubleBracket]1\[RightDoubleBracket];\)}], "Input",\ CellLabel->"In[208]:="], Cell[TextData[StyleBox["The plots below show:", FontColor->GrayLevel[0], FontVariations->{"Underline"->True}]], "Text", FontColor->RGBColor[0, 0, 1]], Cell[TextData[{ StyleBox["the number of susceptibles\n", FontColor->GrayLevel[0]], StyleBox["the number of infectives\n", FontColor->RGBColor[1, 0, 0]], StyleBox["the number of removals\n", FontColor->RGBColor[0, 1, 0]], StyleBox["the number of vaccinated\n", FontColor->RGBColor[0, 0, 1]], "in time interval 35 \[LongDash] 60 days since the infection started." }], "Text"], Cell[BoxData[{ \(\(p1 = Plot[{x[t]*population[t]} // Evaluate, {t, 35, 60}, PlotRange \[Rule] \ All (*\ \(,\)\(DisplayFunction \[Rule] Identity\)\ *) ];\)\), "\[IndentingNewLine]", \(\(p2 = Plot[{y[t]*population[t]} // Evaluate, {t, 35, 60}, PlotRange \[Rule] \ All, PlotStyle \[Rule] {RGBColor[1, 0, 0]}, DisplayFunction \[Rule] Identity];\)\), "\[IndentingNewLine]", \(\(p3 = Plot[{z[t]*population[t]} // Evaluate, {t, 35, 60}, PlotRange \[Rule] \ All, PlotStyle \[Rule] {RGBColor[0, 1, 0]}, DisplayFunction \[Rule] Identity];\)\), "\[IndentingNewLine]", \(\(p4 = Plot[{w[t]*population[t]} // Evaluate, {t, 35, 60}, PlotRange \[Rule] \ All, PlotStyle \[Rule] {RGBColor[0, 0, 1]}, 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.93241 .58303 L .9337 .58298 L .93448 .58295 L .93522 .58291 L .93589 .58285 L .93661 .58278 L .93782 .58274 L .93851 .58275 L .93915 .58277 L Mistroke .94044 .58271 L .94117 .58261 L .94183 .58253 L .94301 .58247 L .9443 .58259 L .94552 .58239 L .94665 .5824 L .94762 .58249 L .94865 .58233 L .94952 .58225 L .95049 .58223 L .95152 .58221 L .95263 .58214 L .95368 .58212 L .95463 .58226 L .9556 .58229 L .95648 .58223 L .95746 .58218 L .9585 .58219 L .95939 .58218 L .96023 .58196 L .96115 .58169 L .96215 .58159 L .96304 .58161 L .96387 .58167 L .96474 .58164 L .96568 .5815 L .96643 .5813 L .96723 .58112 L .9681 .58103 L .96891 .58099 L .96985 .58096 L .97087 .581 L .97183 .58094 L .97273 .58079 L .97619 .5804 L Mfstroke 1 0 0 r .02381 .02138 m .06244 .01958 L .10458 .01815 L .14415 .01719 L .18221 .01653 L .22272 .01601 L .26171 .01565 L .30316 .01538 L .34309 .01519 L .3815 .01506 L .42237 .01496 L .46172 .01489 L .49955 .01484 L .53984 .01481 L .57861 .01478 L .61984 .01476 L .65954 .01475 L .69774 .01474 L .73838 .01473 L .77751 .01473 L .81909 .01472 L .85916 .01472 L .89771 .01472 L .93871 .01472 L .97619 .01472 L s 0 1 0 r .02381 .55558 m .06244 .55773 L .08255 .55901 L .08321 .55906 L .08391 .55909 L .08468 .55909 L .08539 .55905 L .08666 .559 L .08738 .55906 L .08806 .55917 L .08955 .55941 L .09039 .55951 L .09115 .55957 L .09185 .55958 L .09261 .55961 L .09331 .55969 L .09396 .55972 L .0946 .55965 L .0953 .55957 L .09656 .55966 L .09728 .55962 L .09804 .55958 L .09869 .55965 L .0994 .55969 L .10069 .55935 L .10142 .55929 L .10208 .55931 L .10336 .5595 L .10458 .5597 L .10567 .55998 L .10685 .5602 L .10814 .56022 L .10935 .5602 L .11064 .56018 L .11129 .56025 L .112 .56032 L .11326 .56032 L .11443 .56024 L .11561 .56017 L .11673 .56025 L .11774 .56028 L .11883 .5601 L .12002 .5603 L .12128 .5604 L .12235 .56056 L .12353 .56075 L .12419 .56078 L .12491 .56081 L .12622 .56068 L .12749 .56042 L Mistroke .12867 .56063 L .12939 .56083 L .13007 .56097 L .13134 .56087 L .13205 .56079 L .13271 .56068 L .13343 .56043 L .13419 .56023 L .13537 .56051 L .13665 .56043 L .13785 .56056 L .13894 .56054 L .14022 .56046 L .14095 .56058 L .14162 .5606 L .14285 .56059 L .14415 .56064 L .14539 .56078 L .14654 .56104 L .14774 .56096 L .14906 .56087 L .1502 .56098 L .15123 .56104 L .15242 .56093 L .15355 .56086 L .15478 .56092 L .15608 .56111 L .1572 .56133 L .1584 .56144 L .1597 .56144 L .16091 .56141 L .16165 .56134 L .16235 .56123 L .16366 .56112 L .16471 .56134 L .16587 .5615 L .16707 .56158 L .16821 .56153 L .16927 .5615 L .17023 .56155 L .1713 .56144 L .17242 .56142 L .17356 .56137 L .17478 .56113 L .17593 .56106 L .17697 .56105 L .1782 .56129 L .17885 .56143 L .17953 .56148 L .18079 .56157 L Mistroke .18195 .56165 L .18307 .56169 L .18426 .56171 L .18557 .562 L .18679 .56212 L .18803 .56201 L .18919 .56196 L .19024 .56207 L .19138 .56225 L .19201 .56223 L .19272 .56221 L .19345 .56226 L .19413 .56229 L .19536 .56216 L .19667 .56228 L .19797 .56222 L .1992 .56225 L .2003 .56234 L .2015 .56247 L .20256 .56261 L .2037 .56269 L .20495 .56263 L .20612 .5625 L .20736 .56231 L .20867 .56223 L .20979 .56227 L .21101 .56214 L .21217 .56214 L .21322 .56215 L .21443 .56214 L .21557 .56209 L .21981 .56188 L .22954 .56155 L .23075 .56162 L .23191 .56157 L .23254 .56145 L .23323 .56132 L .23445 .56136 L .23515 .56142 L .23589 .5615 L .2366 .56152 L .23723 .56155 L .23788 .56172 L .23858 .56194 L .23984 .56189 L .241 .56176 L .24207 .56185 L .24326 .5621 L .24452 .56222 L .24516 .56231 L Mistroke .24585 .56242 L .24711 .56252 L .24833 .56246 L .24946 .56236 L .25167 .56213 L .25276 .56195 L .25375 .5619 L .25479 .56188 L .25591 .56192 L .25713 .5621 L .2583 .56236 L .25954 .56264 L .26024 .56273 L .26088 .56277 L .26207 .5628 L .26332 .5628 L .26444 .56286 L .26549 .56296 L .26664 .56295 L .26788 .56291 L .26919 .56296 L .26993 .56298 L .27062 .56298 L .27188 .56295 L .27252 .56293 L .27322 .56289 L .27443 .56286 L .27573 .56279 L .27696 .56276 L .27809 .56293 L .27916 .56291 L .28031 .56298 L .28139 .56294 L .28237 .56279 L .28352 .56284 L .28477 .56307 L .28596 .56318 L .28705 .56319 L .28817 .5632 L .28923 .56323 L .29038 .56314 L .29163 .56283 L .29293 .56277 L .29416 .56279 L .29527 .56276 L .29648 .56281 L .29713 .56266 L .29781 .56247 L .29904 .56229 L .29973 .56223 L Mistroke .30047 .56215 L .30117 .56199 L .3018 .56184 L .30303 .56186 L .30419 .56191 L .30545 .56186 L .30616 .5618 L .30681 .56173 L .30793 .56171 L .30898 .56178 L .31012 .56156 L .31136 .56148 L .31258 .56133 L .31387 .56131 L .31498 .56152 L .31618 .56168 L .31686 .56157 L .3176 .56149 L .31829 .56147 L .31894 .56145 L .32023 .56137 L .32144 .56136 L .32274 .56172 L .32343 .56184 L .32417 .56192 L .32494 .56205 L .32568 .56206 L .32634 .56189 L .32705 .56169 L .32826 .56161 L .32895 .56168 L .3296 .56176 L .3309 .56176 L .33163 .56178 L .3323 .56183 L .33361 .56195 L .33485 .56204 L .33596 .56208 L .33716 .56211 L .33835 .56213 L .33946 .56218 L .34061 .56236 L .34189 .5622 L .34315 .56193 L .34387 .5619 L .34452 .562 L .34576 .56203 L .34694 .56194 L .34804 .56193 L .3492 .56189 L Mistroke .3503 .56204 L .3513 .56201 L .35248 .56191 L .35375 .56192 L .35495 .56191 L .35605 .56174 L .35725 .56179 L .35853 .56194 L .35975 .56186 L .36085 .56178 L .36214 .56186 L .36288 .56191 L .36355 .56184 L .3648 .56169 L .36611 .56176 L .36737 .56166 L .36807 .56162 L .36872 .5616 L .36991 .56163 L .37117 .56173 L .37183 .56171 L .37255 .56163 L .37383 .56163 L .37461 .56169 L .37535 .56173 L .37602 .56168 L .37674 .56159 L .37797 .56184 L .3791 .56195 L .3804 .5619 L .38163 .56176 L .38269 .56157 L .38382 .56158 L .38506 .56174 L .38621 .56161 L .38692 .56155 L .38756 .56161 L .38903 .5618 L .39032 .56195 L .39096 .56201 L .39167 .56203 L .39291 .56191 L .39359 .56179 L .39424 .56175 L .39549 .56168 L .39662 .56166 L .39783 .56178 L .39853 .56186 L .39917 .56192 L .39984 .56196 L Mistroke .40056 .56198 L .40187 .56196 L .40305 .56184 L .40435 .56176 L .40557 .56147 L .40671 .56126 L .4074 .56124 L .40814 .5612 L .40884 .5612 L .40949 .5613 L .41072 .5615 L .41201 .56154 L .41268 .56154 L .41341 .56163 L .41471 .56193 L .4155 .56204 L .41626 .5621 L .41693 .56213 L .41767 .56214 L .41888 .56215 L .42 .56213 L .42122 .56198 L .42251 .56197 L .42363 .56211 L .42468 .56206 L .42583 .56185 L .42706 .56184 L .42775 .56169 L .42839 .56161 L .4291 .56176 L .42985 .56188 L .4311 .56161 L .43182 .56166 L .43249 .56175 L .43373 .56177 L .43487 .56181 L .43618 .56155 L .43742 .56136 L .43811 .56137 L .43875 .56137 L .43995 .56123 L .44124 .56102 L .44197 .56105 L .44263 .56102 L .44385 .5609 L .44499 .56088 L .44617 .56085 L .44747 .56094 L .44815 .56092 L .44889 .56081 L Mistroke .44959 .56075 L .45024 .56073 L .45146 .56083 L .45276 .56094 L .45343 .56095 L .45415 .56091 L .45545 .56095 L .45621 .56104 L .457 .56108 L .45768 .56114 L .45843 .56127 L .45975 .56126 L .46097 .56122 L .4616 .56127 L .4623 .56128 L .46304 .56129 L .46372 .56135 L .46496 .5615 L .46613 .56159 L .46677 .56157 L .46748 .56154 L .46871 .56151 L .46992 .56157 L .47106 .56154 L .47238 .56152 L .47356 .56141 L .47469 .5614 L .47572 .56156 L .47686 .5616 L .47806 .56156 L .47937 .56142 L .48056 .56119 L .48122 .56107 L .48193 .56106 L .48323 .56115 L .48445 .56133 L .48574 .56155 L .48684 .56165 L .48806 .56166 L .48879 .56164 L .48948 .56161 L .49078 .5615 L .49151 .56137 L .49218 .56123 L .49297 .56107 L .49371 .56097 L .49436 .56097 L .49506 .56101 L .49628 .56109 L .49697 .56113 L Mistroke .4977 .56119 L .49901 .56137 L .50023 .56135 L .50092 .5614 L .50156 .56153 L .50273 .56159 L .50397 .56153 L .50508 .56158 L .50612 .56167 L .50726 .56196 L .50849 .56196 L .50972 .5618 L .51042 .56175 L .51107 .5618 L .51238 .5618 L .51312 .56173 L .51379 .56172 L .51499 .5617 L .51629 .56165 L .51752 .56154 L .51865 .56147 L .5197 .56174 L .52084 .56171 L .52191 .56168 L .52289 .56187 L .52403 .56167 L .52528 .5615 L .52646 .56157 L .52755 .56159 L .52879 .56137 L .52995 .56116 L .53099 .56132 L .53212 .56146 L .53335 .56142 L .53465 .56141 L .53576 .56141 L .53698 .56126 L .53829 .56128 L .5395 .56122 L .54013 .56123 L .54083 .56124 L .54155 .56123 L .54224 .56123 L .54349 .5614 L .54463 .56139 L .54589 .56127 L .54721 .56111 L .54833 .56105 L .54952 .56112 L .55064 .56115 L Mistroke .55166 .5611 L .55286 .56103 L .55416 .56119 L .55539 .56127 L .55653 .56108 L .55773 .56105 L .55903 .56101 L .56025 .56074 L .56137 .56068 L .56268 .56089 L .56342 .56108 L .56411 .56124 L .56544 .56154 L .5667 .56183 L .56789 .56194 L .56917 .56193 L .56987 .56198 L .5706 .56196 L .57191 .56193 L .57257 .56203 L .57328 .56205 L .57456 .56191 L .57534 .56191 L .57607 .56199 L .57673 .56213 L .57745 .56223 L .57868 .56228 L .5798 .5624 L .5811 .56248 L .58233 .5625 L .58346 .5625 L .58452 .56258 L .58567 .56275 L .5869 .5629 L .5876 .56281 L .58825 .56271 L .58896 .56275 L .58971 .56284 L .59037 .5629 L .59108 .563 L .59236 .56326 L .59359 .56328 L .59471 .56344 L .59535 .56353 L .59604 .56349 L .5973 .56349 L .5986 .56352 L .59982 .56341 L .60053 .56335 L .60127 .56328 L Mistroke .60191 .56322 L .6026 .56309 L .60328 .56292 L .604 .56288 L .60531 .56311 L .6061 .56304 L .60684 .56299 L .60751 .563 L .60823 .56295 L .60955 .5628 L .61078 .56275 L .61207 .56255 L .61275 .56266 L .61349 .56281 L .61479 .56283 L .61602 .56261 L .61713 .56263 L .61833 .56277 L .61898 .5628 L .61967 .56271 L .6209 .56257 L .62222 .56265 L .62297 .5627 L .62367 .56268 L .62869 .56257 L .62981 .56269 L .631 .56272 L .6323 .56259 L .6335 .56256 L .63462 .5627 L .63567 .56272 L .63682 .56243 L .63806 .56238 L .63874 .56241 L .63948 .56234 L .64018 .56223 L .64083 .5621 L .64206 .56199 L .64337 .56192 L .64467 .56181 L .6459 .56176 L .647 .56164 L .6482 .56133 L .64951 .56127 L .65025 .56126 L .65094 .56126 L .65168 .56133 L .65234 .5614 L .65312 .56139 L .65385 .56138 L Mistroke .65514 .56151 L .65634 .56137 L .65766 .56113 L .65838 .56103 L .65905 .56096 L .6602 .56101 L .66146 .56114 L .66253 .56117 L .66367 .56111 L .66432 .56105 L .66502 .56102 L .66629 .56117 L .66753 .56111 L .66867 .56121 L .66974 .56121 L .67075 .5611 L .67186 .56107 L .67305 .56109 L .6743 .56122 L .67548 .56125 L .67654 .56126 L .6777 .56132 L .67898 .56119 L .6797 .56119 L .68036 .56122 L .68159 .56138 L .68287 .56156 L .68425 .5618 L .68498 .56197 L .68577 .56212 L .68647 .56213 L .68712 .56209 L .68838 .562 L .68965 .56204 L .69082 .56213 L .69211 .56212 L .69276 .56209 L .69348 .56214 L .69467 .56219 L .69596 .5622 L .69718 .5622 L .6983 .56209 L .69958 .56202 L .70079 .56202 L .70187 .56204 L .70305 .56189 L .70433 .56173 L .70498 .56179 L .70569 .56177 L .70694 .56158 L Mistroke .70812 .56155 L .7093 .56176 L .71042 .56172 L .71142 .5617 L .71252 .5617 L .71371 .56156 L .71497 .56149 L .71605 .56166 L .71725 .56182 L .71855 .56196 L .7192 .56198 L .71992 .56183 L .72119 .56192 L .72238 .56226 L .7231 .5623 L .72378 .56229 L .72506 .56233 L .72577 .56245 L .72643 .56245 L .72715 .56232 L .72792 .56224 L .72911 .56228 L .73039 .56238 L .73149 .56247 L .7327 .56264 L .73343 .56267 L .7341 .56263 L .73475 .56262 L .73544 .56267 L .73676 .5628 L .73796 .5629 L .7428 .56345 L .74401 .56347 L .74516 .56353 L .74619 .56366 L .74732 .56386 L .74842 .56406 L .74959 .56418 L .75086 .56409 L .75203 .56407 L .7533 .56409 L .75449 .5641 L .7558 .56435 L .75653 .56433 L .7572 .56436 L .75789 .56458 L .75853 .56477 L .75927 .56476 L .75994 .56472 L .76116 .56488 L Mistroke .76185 .56483 L .76249 .5647 L .76378 .5646 L .76443 .56461 L .76514 .56459 L .76805 .56449 L .76932 .56453 L .77053 .5644 L .7712 .56438 L .77193 .56437 L .7732 .56435 L .77442 .56425 L .77571 .56409 L .77692 .56444 L .77803 .56475 L .77923 .5648 L .78036 .56476 L .78159 .56504 L .78292 .5651 L .78358 .56508 L .7843 .56505 L .78562 .56516 L .7869 .56524 L .78808 .5652 L .78918 .56517 L .79021 .5653 L .79144 .56554 L .79256 .56559 L .79367 .56551 L .79485 .56573 L .79603 .56562 L .79731 .56544 L .79872 .56523 L .79941 .5651 L .80005 .56507 L .80125 .56516 L .80254 .5654 L .80383 .56566 L .80456 .56569 L .80525 .56567 L .80595 .56563 L .80672 .56559 L .80744 .56556 L .80811 .56556 L .80934 .56554 L .81064 .56558 L .81174 .56564 L .81295 .56561 L .81424 .56548 L .81492 .56539 L Mistroke .81563 .5653 L .81694 .56543 L .81815 .5656 L .81938 .56565 L .82003 .56566 L .82071 .5657 L .82197 .56585 L .82314 .56574 L .82768 .56527 L .82888 .5651 L .83018 .56505 L .83141 .5653 L .83253 .56565 L .83384 .56549 L .83458 .56549 L .83526 .56554 L .83652 .56546 L .83723 .56542 L .83787 .56543 L .83902 .56535 L .84023 .56512 L .84127 .565 L .84241 .56504 L .84364 .56509 L .84495 .565 L .84619 .56488 L .84732 .56492 L .84846 .56485 L .84951 .5648 L .85067 .56485 L .8519 .56497 L .85296 .56495 L .85395 .56489 L .85505 .56475 L .85623 .56461 L .85748 .56478 L .85863 .56479 L .85995 .56488 L .86119 .56485 L .86234 .56464 L .86341 .56442 L .86457 .56436 L .86581 .56449 L .86705 .56485 L .86774 .56505 L .86839 .56512 L .86965 .56504 L .8708 .56485 L .87146 .5648 L .87216 .56479 L Mistroke .87342 .56486 L .8742 .56486 L .87492 .56484 L .87558 .56484 L .87628 .56485 L .88164 .56499 L .88236 .56503 L .88305 .565 L .88384 .56497 L .88456 .56499 L .88587 .56507 L .88654 .56512 L .88729 .56516 L .8885 .56512 L .88979 .56488 L .89099 .56488 L .89211 .5649 L .89279 .56488 L .89344 .56482 L .89465 .56482 L .89596 .56499 L .8967 .56505 L .89739 .56505 L .89866 .56497 L .89986 .56495 L .9011 .56483 L .9018 .56474 L .90246 .56465 L .90318 .5646 L .90384 .56461 L .90455 .56466 L .90532 .56472 L .90598 .56475 L .90669 .56474 L .90795 .5648 L .9179 .56515 L .91909 .56527 L .92035 .56504 L .92155 .56507 L .92263 .565 L .92385 .56495 L .92501 .56512 L .92626 .56506 L .92696 .56511 L .92761 .56521 L .92868 .56545 L .92984 .56565 L .93093 .56571 L .93193 .56573 L .93305 .56572 L Mistroke .93411 .56571 L .93526 .56569 L .93651 .56561 L .93774 .5656 L .93886 .56566 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FontSlant->"Italic"], Cell[StyleData["SR"], StyleMenuListing->None, FontFamily->"Helvetica", FontWeight->"Plain", FontSlant->"Plain"], Cell[StyleData["SO"], StyleMenuListing->None, FontFamily->"Helvetica", FontWeight->"Plain", FontSlant->"Italic"], Cell[StyleData["SB"], StyleMenuListing->None, FontFamily->"Helvetica", FontWeight->"Bold", FontSlant->"Plain"], Cell[StyleData["SBO"], StyleMenuListing->None, FontFamily->"Helvetica", FontWeight->"Bold", FontSlant->"Italic"], Cell[CellGroupData[{ Cell[StyleData["SO10"], StyleMenuListing->None, FontFamily->"Helvetica", FontSize->10, FontWeight->"Plain", FontSlant->"Italic"], Cell[StyleData["SO10", "Printout"], StyleMenuListing->None, FontFamily->"Helvetica", FontSize->7, FontWeight->"Plain", FontSlant->"Italic"] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Formulas and Programming", "Section"], Cell[CellGroupData[{ Cell[StyleData["InlineFormula"], CellMargins->{{10, 4}, {0, 8}}, CellHorizontalScrolling->True, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, LanguageCategory->"Formula", ScriptLevel->1, SingleLetterItalics->True, StyleMenuListing->None], Cell[StyleData["InlineFormula", "Presentation"], LineSpacing->{1, 5}, FontSize->16], Cell[StyleData["InlineFormula", "SlideShow"], LineSpacing->{1, 5}, FontSize->16], Cell[StyleData["InlineFormula", "Printout"], CellMargins->{{2, 0}, {6, 6}}, FontSize->10] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["DisplayFormula"], CellMargins->{{60, Inherited}, {Inherited, Inherited}}, CellHorizontalScrolling->True, DefaultFormatType->DefaultInputFormatType, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, LanguageCategory->"Formula", ScriptLevel->0, SingleLetterItalics->True, UnderoverscriptBoxOptions->{LimitsPositioning->True}], Cell[StyleData["DisplayFormula", "Presentation"], CellMargins->{{72, Inherited}, {Inherited, Inherited}}, LineSpacing->{1, 5}, FontSize->16], Cell[StyleData["DisplayFormula", "SlideShow"], CellMargins->{{100, 50}, {Inherited, Inherited}}, LineSpacing->{1, 5}, FontSize->16], Cell[StyleData["DisplayFormula", "Printout"], FontSize->10] }, Open ]], Cell[CellGroupData[{ Cell[StyleData["Program"], CellFrame->{{0, 0}, {0.5, 0.5}}, CellMargins->{{60, 4}, {0, 8}}, CellHorizontalScrolling->True, Hyphenation->False, LanguageCategory->"Formula", ScriptLevel->1, FontFamily->"Courier"], Cell[StyleData["Program", "Presentation"], CellMargins->{{72, 50}, {10, 10}}, LineSpacing->{1, 5}, FontSize->16], Cell[StyleData["Program", "SlideShow"], CellMargins->{{100, 50}, {10, 10}}, LineSpacing->{1, 5}, FontSize->16], Cell[StyleData["Program", "Printout"], CellMargins->{{2, 0}, {6, 6}}, FontSize->9] }, Closed]] }, Open ]], Cell[CellGroupData[{ Cell["Hyperlink Styles", "Section"], Cell["\<\ The cells below define styles useful for making hypertext ButtonBoxes. The \ \"Hyperlink\" style is for links within the same Notebook, or between \ Notebooks.\ \>", "Text"], Cell[CellGroupData[{ Cell[StyleData["Hyperlink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0, 0.376471, 0.490196], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookLocate[ #2]}]&), Active->True, ButtonFrame->"None", ButtonNote->ButtonData}], Cell[StyleData["Hyperlink", "Presentation"], FontSize->16], Cell[StyleData["Hyperlink", "SlideShow"]], Cell[StyleData["Hyperlink", "Printout"], FontSize->10, FontVariations->{"Underline"->False}] }, Closed]], Cell["\<\ The following styles are for linking automatically to the on-line help \ system.\ \>", "Text"], Cell[CellGroupData[{ Cell[StyleData["MainBookLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0.269993, 0.308507, 0.6], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "MainBook", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["MainBookLink", "Presentation"], FontSize->16], Cell[StyleData["MainBookLink", "SlideShow"]], Cell[StyleData["MainBookLink", "Printout"], FontSize->10, FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["AddOnsLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontFamily->"Courier", FontColor->RGBColor[0.269993, 0.308507, 0.6], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "AddOns", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["AddOnsLink", "Presentation"], FontSize->16], Cell[StyleData["AddOnsLink", "SlideShow"]], Cell[StyleData["AddOnsLink", "Printout"], FontSize->10, FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["RefGuideLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontFamily->"Courier", FontColor->RGBColor[0.269993, 0.308507, 0.6], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "RefGuide", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["RefGuideLink", "Presentation"], FontSize->16], Cell[StyleData["RefGuideLink", "SlideShow"]], Cell[StyleData["RefGuideLink", "Printout"], FontSize->10, FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["RefGuideLinkText"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0.269993, 0.308507, 0.6], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "RefGuide", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["RefGuideLinkText", "Presentation"], FontSize->16], Cell[StyleData["RefGuideLinkText", "SlideShow"]], Cell[StyleData["RefGuideLinkText", "Printout"], FontSize->10, FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["GettingStartedLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0.269993, 0.308507, 0.6], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "GettingStarted", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["GettingStartedLink", "Presentation"], FontSize->16], Cell[StyleData["GettingStartedLink", "SlideShow"]], Cell[StyleData["GettingStartedLink", "Printout"], FontSize->10, FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["DemosLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0.269993, 0.308507, 0.6], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "Demos", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["DemosLink", "SlideShow"]], Cell[StyleData["DemosLink", "Printout"], FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["TourLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0.269993, 0.308507, 0.6], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "Tour", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["TourLink", "SlideShow"]], Cell[StyleData["TourLink", "Printout"], FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["OtherInformationLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0.269993, 0.308507, 0.6], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "OtherInformation", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["OtherInformationLink", "Presentation"], FontSize->16], Cell[StyleData["OtherInformationLink", "SlideShow"]], Cell[StyleData["OtherInformationLink", "Printout"], FontSize->10, FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["MasterIndexLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0.269993, 0.308507, 0.6], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "MasterIndex", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["MasterIndexLink", "SlideShow"]], Cell[StyleData["MasterIndexLink", "Printout"], FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Styles for Headers and Footers", "Section"], Cell[StyleData["Header"], CellMargins->{{0, 0}, {4, 1}}, DefaultNewInlineCellStyle->"None", LanguageCategory->"NaturalLanguage", StyleMenuListing->None, FontSize->10, FontSlant->"Italic"], Cell[StyleData["Footer"], CellMargins->{{0, 0}, {0, 4}}, DefaultNewInlineCellStyle->"None", LanguageCategory->"NaturalLanguage", StyleMenuListing->None, FontSize->9, FontSlant->"Italic"], Cell[StyleData["PageNumber"], CellMargins->{{0, 0}, {4, 1}}, StyleMenuListing->None, FontFamily->"Times", FontSize->10] }, Closed]], Cell[CellGroupData[{ Cell["Palette Styles", "Section"], Cell["\<\ The cells below define styles that define standard ButtonFunctions, for use \ in palette buttons.\ \>", "Text"], Cell[StyleData["Paste"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookApply[ FrontEnd`InputNotebook[ ], #, Placeholder]}]&)}], Cell[StyleData["Evaluate"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookApply[ FrontEnd`InputNotebook[ ], #, All], FrontEnd`SelectionEvaluate[ FrontEnd`InputNotebook[ ], All]}]&)}], Cell[StyleData["EvaluateCell"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookApply[ FrontEnd`InputNotebook[ ], #, All], FrontEnd`SelectionMove[ FrontEnd`InputNotebook[ ], All, Cell, 1], FrontEnd`SelectionEvaluateCreateCell[ FrontEnd`InputNotebook[ ], All]}]&)}], Cell[StyleData["CopyEvaluate"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`SelectionCreateCell[ FrontEnd`InputNotebook[ ], All], FrontEnd`NotebookApply[ FrontEnd`InputNotebook[ ], #, All], FrontEnd`SelectionEvaluate[ FrontEnd`InputNotebook[ ], All]}]&)}], Cell[StyleData["CopyEvaluateCell"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`SelectionCreateCell[ FrontEnd`InputNotebook[ ], All], FrontEnd`NotebookApply[ FrontEnd`InputNotebook[ ], #, All], FrontEnd`SelectionEvaluateCreateCell[ FrontEnd`InputNotebook[ ], All]}]&)}] }, Closed]], Cell[CellGroupData[{ Cell["Placeholder Styles", "Section"], Cell["\<\ The cells below define styles useful for making placeholder objects in \ palette templates.\ \>", "Text"], Cell[CellGroupData[{ Cell[StyleData["Placeholder"], Placeholder->True, StyleMenuListing->None, FontSlant->"Italic", FontColor->RGBColor[0.984314, 0.74902, 0.176471], TagBoxOptions->{Editable->False, Selectable->False, StripWrapperBoxes->False}], Cell[StyleData["Placeholder", "Presentation"]], Cell[StyleData["Placeholder", "SlideShow"]], Cell[StyleData["Placeholder", "Printout"]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["PrimaryPlaceholder"], StyleMenuListing->None, DrawHighlighted->True, FontSlant->"Italic", Background->RGBColor[0.984314, 0.864057, 0.382376], TagBoxOptions->{Editable->False, Selectable->False, StripWrapperBoxes->False}], Cell[StyleData["PrimaryPlaceholder", "Presentation"]], Cell[StyleData["PrimaryPlaceholder", "SlideShow"]], Cell[StyleData["PrimaryPlaceholder", "Printout"]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["FormatType Styles", "Section"], Cell["\<\ The cells below define styles that are mixed in with the styles of most \ cells. If a cell's FormatType matches the name of one of the styles defined \ below, then that style is applied between the cell's style and its own \ options. This is particularly true of Input and Output.\ \>", "Text"], Cell[StyleData["CellExpression"], PageWidth->Infinity, CellMargins->{{6, Inherited}, {Inherited, Inherited}}, ShowCellLabel->False, ShowSpecialCharacters->False, AllowInlineCells->False, Hyphenation->False, AutoItalicWords->{}, StyleMenuListing->None, FontFamily->"Courier", FontSize->12, Background->GrayLevel[1]], Cell[StyleData["InputForm"], InputAutoReplacements->{}, AllowInlineCells->False, Hyphenation->False, StyleMenuListing->None, FontFamily->"Courier"], Cell[StyleData["OutputForm"], PageWidth->Infinity, TextAlignment->Left, LineSpacing->{0.6, 1}, StyleMenuListing->None, FontFamily->"Courier"], Cell[StyleData["StandardForm"], InputAutoReplacements->{ "->"->"\[Rule]", ":>"->"\[RuleDelayed]", "<="->"\[LessEqual]", ">="->"\[GreaterEqual]", "!="->"\[NotEqual]", "=="->"\[Equal]", Inherited}, "TwoByteSyntaxCharacterAutoReplacement"->True, LineSpacing->{1.25, 0}, StyleMenuListing->None, FontFamily->"Courier"], Cell[StyleData["TraditionalForm"], InputAutoReplacements->{ "->"->"\[Rule]", ":>"->"\[RuleDelayed]", "<="->"\[LessEqual]", ">="->"\[GreaterEqual]", "!="->"\[NotEqual]", "=="->"\[Equal]", Inherited}, "TwoByteSyntaxCharacterAutoReplacement"->True, LineSpacing->{1.25, 0}, SingleLetterItalics->True, TraditionalFunctionNotation->True, DelimiterMatching->None, StyleMenuListing->None], Cell["\<\ The style defined below is mixed in to any cell that is in an inline cell \ within another.\ \>", "Text"], Cell[StyleData["InlineCell"], LanguageCategory->"Formula", ScriptLevel->1, StyleMenuListing->None], Cell[StyleData["InlineCellEditing"], StyleMenuListing->None, Background->RGBColor[0.984314, 0.895659, 0.659937]] }, Closed]], Cell[CellGroupData[{ Cell["Automatic Styles", "Section"], Cell["\<\ The cells below define styles that are used to affect the display of certain \ types of objects in typeset expressions. For example, \"UnmatchedBracket\" \ style defines how unmatched bracket, curly bracket, and parenthesis \ characters are displayed (typically by coloring them to make them stand out).\ \ \>", "Text"], Cell[StyleData["UnmatchedBracket"], StyleMenuListing->None, FontColor->RGBColor[0.503243, 0.707805, 0.862837]], Cell[StyleData["Completions"], StyleMenuListing->None, FontFamily->"Courier"] }, Closed]], Cell[CellGroupData[{ Cell["Styles from HelpBrowser", "Section"], Cell[CellGroupData[{ Cell[StyleData["MathCaption"], CellFrame->{{0, 0}, {0, 0.5}}, CellMargins->{{66, 12}, {2, 24}}, PageBreakBelow->False, CellFrameMargins->{{8, 8}, {8, 2}}, CellFrameColor->GrayLevel[0.700008], CellFrameLabelMargins->4, LineSpacing->{1, 1}, ParagraphSpacing->{0, 8}, StyleMenuListing->None, FontColor->GrayLevel[0.2]], Cell[StyleData["MathCaption", "Presentation"], CellMargins->{{72, Inherited}, {Inherited, Inherited}}, FontSize->18], Cell[StyleData["MathCaption", "SlideShow"], CellMargins->{{100, 50}, {Inherited, Inherited}}], Cell[StyleData["MathCaption", "Printout"], CellMargins->{{39, 0}, {0, 14}}, Hyphenation->True, FontSize->9, FontColor->GrayLevel[0]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["ObjectName"], ShowCellBracket->True, CellMargins->{{66, 4}, {8, 8}}, Evaluatable->True, CellGroupingRules->"InputGrouping", PageBreakWithin->False, GroupPageBreakWithin->False, CellLabelAutoDelete->False, CellLabelMargins->{{14, Inherited}, {Inherited, Inherited}}, DefaultFormatType->DefaultInputFormatType, ShowSpecialCharacters->Automatic, "TwoByteSyntaxCharacterAutoReplacement"->True, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, LanguageCategory->"Mathematica", FormatType->StandardForm, ShowStringCharacters->True, NumberMarks->True, StyleMenuListing->None, FontWeight->"Bold"], Cell[StyleData["ObjectName", "Presentation"], CellMargins->{{72, Inherited}, {Inherited, Inherited}}, FontSize->18], Cell[StyleData["ObjectName", "SlideShow"], CellMargins->{{100, 50}, {Inherited, Inherited}}], Cell[StyleData["ObjectName", "Printout"], ShowCellBracket->False, CellMargins->{{39, 0}, {6, 6}}, FontSize->9] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Usage"], ShowCellBracket->True, CellMargins->{{66, 4}, {8, 8}}, Evaluatable->True, CellGroupingRules->"InputGrouping", PageBreakWithin->False, GroupPageBreakWithin->False, CellLabelAutoDelete->False, CellLabelMargins->{{14, Inherited}, {Inherited, Inherited}}, DefaultFormatType->DefaultInputFormatType, ShowSpecialCharacters->Automatic, "TwoByteSyntaxCharacterAutoReplacement"->True, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, LanguageCategory->"Mathematica", FormatType->StandardForm, ShowStringCharacters->True, NumberMarks->True, StyleMenuListing->None, FontWeight->"Bold"], Cell[StyleData["Usage", "Presentation"], CellMargins->{{72, Inherited}, {Inherited, Inherited}}, FontSize->18], Cell[StyleData["Usage", "SlideShow"], CellMargins->{{100, 50}, {Inherited, Inherited}}], Cell[StyleData["Usage", "Printout"], ShowCellBracket->False, CellMargins->{{39, 0}, {6, 6}}, FontSize->9] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Notes"], ShowCellBracket->True, CellMargins->{{66, 4}, {8, 8}}, Evaluatable->True, CellGroupingRules->"InputGrouping", PageBreakWithin->False, GroupPageBreakWithin->False, CellLabelAutoDelete->False, CellLabelMargins->{{14, Inherited}, {Inherited, Inherited}}, DefaultFormatType->DefaultInputFormatType, ShowSpecialCharacters->Automatic, "TwoByteSyntaxCharacterAutoReplacement"->True, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, LanguageCategory->"Mathematica", FormatType->StandardForm, ShowStringCharacters->True, NumberMarks->True, StyleMenuListing->None, FontWeight->"Bold"], Cell[StyleData["Notes", "Presentation"], CellMargins->{{72, Inherited}, {Inherited, Inherited}}, FontSize->18], Cell[StyleData["Notes", "SlideShow"], CellMargins->{{100, 50}, {Inherited, Inherited}}], Cell[StyleData["Notes", "Printout"], ShowCellBracket->False, CellMargins->{{39, 0}, {6, 6}}, FontSize->9] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["InlineOutput"], ShowCellBracket->True, CellMargins->{{66, 4}, {8, 8}}, Evaluatable->True, CellGroupingRules->"InputGrouping", PageBreakWithin->False, GroupPageBreakWithin->False, CellLabelAutoDelete->False, CellLabelMargins->{{14, Inherited}, {Inherited, Inherited}}, DefaultFormatType->DefaultInputFormatType, ShowSpecialCharacters->Automatic, "TwoByteSyntaxCharacterAutoReplacement"->True, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, LanguageCategory->"Mathematica", FormatType->StandardForm, ShowStringCharacters->True, NumberMarks->True, StyleMenuListing->None, FontWeight->"Bold"], Cell[StyleData["InlineOutput", "Presentation"], CellMargins->{{72, Inherited}, {Inherited, Inherited}}, FontSize->18], Cell[StyleData["InlineOutput", "SlideShow"], CellMargins->{{100, 50}, {Inherited, Inherited}}], Cell[StyleData["InlineOutput", "Printout"], ShowCellBracket->False, CellMargins->{{39, 0}, {6, 6}}, FontSize->9] }, Closed]], Cell[CellGroupData[{ Cell["Emphasis Boxes and Pictures", "Subsection"], Cell[CellGroupData[{ Cell[StyleData["Box"], CellFrame->0.5, CellMargins->{{27, 12}, {0, 8}}, CellHorizontalScrolling->True, CellFrameColor->RGBColor[0.74902, 0.694118, 0.552941], StyleMenuListing->None, Background->RGBColor[0.964706, 0.929412, 0.839216], FrameBoxOptions->{BoxFrame->0.5, BoxMargins->True}, GridBoxOptions->{ColumnSpacings->1}], Cell[StyleData["Box", "Presentation"], CellMargins->{{72, Inherited}, {Inherited, Inherited}}, FontSize->18], Cell[StyleData["Box", "SlideShow"], CellMargins->{{100, 50}, {Inherited, Inherited}}], Cell[StyleData["Box", "Printout"], CellMargins->{{2, 0}, {0, 8}}, FontSize->10, Background->GrayLevel[0.900008]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["DoubleBox"], CellFrame->0.5, CellMargins->{{27, 12}, {0, 8}}, CellHorizontalScrolling->True, CellFrameColor->RGBColor[0.74902, 0.694118, 0.552941], StyleMenuListing->None, Background->RGBColor[0.964706, 0.929412, 0.839216], FrameBoxOptions->{BoxFrame->0.5, BoxMargins->True}, GridBoxOptions->{ColumnSpacings->2, RowAlignments->Top}], Cell[StyleData["DoubleBox", "Presentation"], CellMargins->{{72, Inherited}, {Inherited, Inherited}}, FontSize->18], Cell[StyleData["DoubleBox", "SlideShow"], CellMargins->{{100, 50}, {Inherited, Inherited}}], Cell[StyleData["DoubleBox", "Printout"], CellMargins->{{2, 0}, {0, 8}}, FontSize->10, Background->GrayLevel[0.900008]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["1ColumnBox"], CellFrame->0.5, CellMargins->{{27, 12}, {0, 8}}, CellHorizontalScrolling->True, CellFrameColor->RGBColor[0.74902, 0.694118, 0.552941], LineIndent->0, StyleMenuListing->None, Background->RGBColor[0.964706, 0.929412, 0.839216], FrameBoxOptions->{BoxFrame->0.5, BoxMargins->True}, GridBoxOptions->{ColumnSpacings->1}], Cell[StyleData["1ColumnBox", "Presentation"], CellMargins->{{72, Inherited}, {Inherited, Inherited}}, FontSize->18], Cell[StyleData["1ColumnBox", "SlideShow"], CellMargins->{{100, 50}, {Inherited, Inherited}}], Cell[StyleData["1ColumnBox", "Printout"], CellMargins->{{2, 0}, {0, 8}}, FontSize->10, Background->GrayLevel[0.900008]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["2ColumnBox"], CellFrame->0.5, CellMargins->{{27, 12}, {0, 8}}, CellHorizontalScrolling->True, CellFrameColor->RGBColor[0.74902, 0.694118, 0.552941], SingleLetterItalics->False, LineIndent->0, StyleMenuListing->None, Background->RGBColor[0.964706, 0.929412, 0.839216], FrameBoxOptions->{BoxFrame->0.5, BoxMargins->True}, GridBoxOptions->{ColumnWidths->{0.31, 0.67}}], Cell[StyleData["2ColumnBox", "Presentation"], CellMargins->{{72, Inherited}, {Inherited, Inherited}}, FontSize->18], Cell[StyleData["2ColumnBox", "SlideShow"], CellMargins->{{100, 50}, {Inherited, Inherited}}], Cell[StyleData["2ColumnBox", "Printout"], CellMargins->{{2, 0}, {0, 8}}, FontSize->9, Background->GrayLevel[0.900008]] }, 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