(* Content-type: application/mathematica *)
(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)
(* CreatedBy='Mathematica 6.0' *)
(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[ 145, 7]
NotebookDataLength[ 341269, 8360]
NotebookOptionsPosition[ 177333, 5575]
NotebookOutlinePosition[ 337161, 8232]
CellTagsIndexPosition[ 337019, 8225]
WindowFrame->Normal
ContainsDynamic->False*)
(* Beginning of Notebook Content *)
Notebook[{
Cell[CellGroupData[{
Cell["", "SlideShowNavigationBar",
CellTags->"SlideShowHeader"],
Cell["Further Results in Arithmetical CA", "Title",
CellChangeTimes->{{3.391794531609375*^9, 3.391794579015625*^9}}],
Cell["", "Subtitle",
CellChangeTimes->{{3.391794560453125*^9, 3.391794563046875*^9}}],
Cell["Johan Veerman", "Author",
CellChangeTimes->{{3.391794464953125*^9, 3.391794470171875*^9}}],
Cell["\<\
Pontificia Universidad Cat\[OAcute]lica del Per\[UAcute]\
\>", "Affiliation",
CellChangeTimes->{{3.39179447265625*^9, 3.391794509875*^9}}],
Cell[TextData[{
ButtonBox["\[FilledLeftTriangle]\[ThickSpace]\[ThickSpace]\[ThickSpace]",
BaseStyle->"SlidePreviousNextLink",
ButtonFunction:>FrontEndExecute[{
FrontEndToken[
FrontEnd`ButtonNotebook[], "ScrollPagePrevious"]}],
ButtonNote->FEPrivate`FrontEndResource[
"FEStrings", "SlideshowPrevSlideText"],
ButtonFrame->"None"],
"\[ThickSpace]\[ThickSpace]|\[ThickSpace]\[ThickSpace]",
ButtonBox["\[ThickSpace]\[ThickSpace]\[ThickSpace]\[FilledRightTriangle]",
BaseStyle->"SlidePreviousNextLink",
ButtonFunction:>FrontEndExecute[{
FrontEndToken[
FrontEnd`ButtonNotebook[], "ScrollPageNext"]}],
ButtonNote->FEPrivate`FrontEndResource[
"FEStrings", "SlideshowNextSlideText"],
ButtonFrame->"None"]
}], "PreviousNext"]
}, Open ]],
Cell[CellGroupData[{
Cell["", "SlideShowNavigationBar",
CellTags->"SlideShowHeader"],
Cell[CellGroupData[{
Cell["Overview", "Section",
CellChangeTimes->{{3.39303901871875*^9, 3.393039020140625*^9}}],
Cell["\<\
The Principle of Computational Equivalence states that, beyond a certain \
(low) threshold, systems show complex behavior with equivalent (universal) \
computational capabilities.
Can we make simple computational systems calculate mathematical functions?
In Chapter 11 of the NKS book it was shown that we can. We show some \
extensions of this idea.
One of the purposes behind this work is to understand how simple systems in \
general could be \"programmed\" to perform simple calculations. The final \
goal of this purpose would be to understand how natural systems compute.
The other purpose is to open new paths that would lead to alternative \
computational architectures. Making an Arithmetic Logic Unit (ALU) based on a \
simple system such as cellular automata (CA) will be a first step towards \
this goal.
Two methods: specific construction and searches in rule spaces.
Outline:
1.- Some constructions
2-. Binary operations
3.- Some search results
4.- A couple of tools for analysis
5.- Brief discussion\
\>", "Text",
CellChangeTimes->{{3.39303903825*^9, 3.39303939421875*^9}, {
3.393205148015625*^9, 3.393205441703125*^9}, {3.39320583765625*^9,
3.393205846359375*^9}, {3.3932060325*^9, 3.393206129046875*^9}, {
3.393206159390625*^9, 3.393206218859375*^9}, {3.393206288296875*^9,
3.3932063925*^9}, {3.393206450984375*^9, 3.393206630171875*^9}, {
3.3932066605625*^9, 3.39320668903125*^9}, {3.393206757875*^9,
3.393206869234375*^9}, {3.393206926921875*^9, 3.39320702178125*^9}, {
3.393214234453125*^9, 3.393214311015625*^9}, {3.393340042290747*^9,
3.3933400614082365`*^9}, {3.393340092342718*^9, 3.393340117298603*^9}, {
3.3933835289014225`*^9, 3.3933835378442817`*^9}}],
Cell[TextData[{
ButtonBox["\[FilledLeftTriangle]\[ThickSpace]\[ThickSpace]\[ThickSpace]",
BaseStyle->"SlidePreviousNextLink",
ButtonFunction:>FrontEndExecute[{
FrontEndToken[
FrontEnd`ButtonNotebook[], "ScrollPagePrevious"]}],
ButtonNote->FEPrivate`FrontEndResource[
"FEStrings", "SlideshowPrevSlideText"],
ButtonFrame->"None"],
"\[ThickSpace]\[ThickSpace]|\[ThickSpace]\[ThickSpace]",
ButtonBox["\[ThickSpace]\[ThickSpace]\[ThickSpace]\[FilledRightTriangle]",
BaseStyle->"SlidePreviousNextLink",
ButtonFunction:>FrontEndExecute[{
FrontEndToken[
FrontEnd`ButtonNotebook[], "ScrollPageNext"]}],
ButtonNote->FEPrivate`FrontEndResource[
"FEStrings", "SlideshowNextSlideText"],
ButtonFrame->"None"]
}], "PreviousNext"]
}, Open ]]
}, Open ]],
Cell[CellGroupData[{
Cell["", "SlideShowNavigationBar",
CellTags->"SlideShowHeader"],
Cell[CellGroupData[{
Cell["Some constructions", "Section",
CellChangeTimes->{{3.39303940765625*^9, 3.393039417796875*^9}, {
3.393039476640625*^9, 3.39303951153125*^9}, {3.39304667140625*^9,
3.393046674953125*^9}}],
Cell[CellGroupData[{
Cell[TextData[StyleBox["Specific constructions - serial",
FontColor->RGBColor[
0.9714045929655909, 0.6775158312352179, 0.07415884641794461]]], "Subsection",\
CellChangeTimes->{
3.3824524252213373`*^9, {3.39303943990625*^9, 3.393039450140625*^9}, {
3.39304107571875*^9, 3.39304108265625*^9}}],
Cell["\<\
Bottom-up approach: serial constructions are easier to program.
But we are making a parallel system work serially, therefore:
Too many colors or states are needed.
They take too many steps to compute.\
\>", "Text",
CellChangeTimes->{{3.39318995278125*^9, 3.39319008303125*^9}, {
3.3931901198125*^9, 3.39319013409375*^9}, {3.39319018428125*^9,
3.39319021*^9}, {3.3931903076875*^9, 3.393190349421875*^9}, {3.393190457*^9,
3.3931904584375*^9}, {3.393207257921875*^9, 3.3932074306875*^9}}],
Cell[CellGroupData[{
Cell[BoxData[{
RowBox[{
RowBox[{"serialAddition",
StyleBox["[",
FormatType->StandardForm],
StyleBox[
RowBox[{"{",
RowBox[{"a_", ",", " ", "b_", ",", " ", "c_"}], "}"}],
FormatType->StandardForm],
StyleBox["]",
FormatType->StandardForm]}],
StyleBox[" ",
FormatType->StandardForm],
StyleBox[":=",
FormatType->StandardForm],
StyleBox["\[IndentingNewLine]",
FormatType->StandardForm],
StyleBox[
RowBox[{"Switch", "[",
RowBox[{
RowBox[{"{",
RowBox[{"a", ",", " ", "b", ",", " ", "c"}], "}"}], ",",
RowBox[{"{",
RowBox[{"0", ",", "0", ",", "a4"}], "}"}], ",", "a5", ",",
RowBox[{"{",
RowBox[{"0", ",", "a5", ",", "0"}], "}"}], ",", "a5", ",",
RowBox[{"{",
RowBox[{"a1", ",", "1", ",", "0"}], "}"}], ",", "a6", ",",
RowBox[{"{",
RowBox[{"a1", ",", "a5", ",", "0"}], "}"}], ",", "0", ",",
RowBox[{"{",
RowBox[{"a2", ",", "a5", ",", "0"}], "}"}], ",", "a5", ",",
RowBox[{"{",
RowBox[{"a5", ",", "0", ",", "0"}], "}"}], ",", "0", ",",
RowBox[{"{",
RowBox[{"a1", ",", "1", ",", "_"}], "}"}], ",", "a2", ",",
RowBox[{"{",
RowBox[{"a3", ",", "0", ",", "_"}], "}"}], ",", "a1", ",",
RowBox[{"{",
RowBox[{"_", ",", "0", ",", "a6"}], "}"}], ",", "a2", ",",
RowBox[{"{",
RowBox[{"_", ",", "1", ",", "a2"}], "}"}], ",", "a4", ",",
RowBox[{"{",
RowBox[{"a1", ",", "_", ",", "_"}], "}"}], ",", "a1", ",",
RowBox[{"{",
RowBox[{"a3", ",", "_", ",", "_"}], "}"}], ",", "a3", ",",
RowBox[{"{",
RowBox[{"a5", ",", "_", ",", "_"}], "}"}], ",", "a3", ",",
RowBox[{"{",
RowBox[{"_", ",", "_", ",", "a2"}], "}"}], ",", "a2", ",",
RowBox[{"{",
RowBox[{"_", ",", "_", ",", "a4"}], "}"}], ",", "a4", ",",
RowBox[{"{",
RowBox[{"_", ",", "1", ",", "_"}], "}"}], ",", "1", ",",
RowBox[{"{",
RowBox[{"_", ",", "a3", ",", "_"}], "}"}], ",", "1", ",",
RowBox[{"{",
RowBox[{"_", ",", "a4", ",", "_"}], "}"}], ",", "1", ",",
RowBox[{"{",
RowBox[{"_", ",", "a5", ",", "_"}], "}"}], ",", "1", ",",
RowBox[{"{",
RowBox[{"_", ",", "a6", ",", "_"}], "}"}], ",", "a5", ",",
RowBox[{"{",
RowBox[{"_", ",", "_", ",", "_"}], "}"}], ",", "0"}], "]"}],
FormatType->StandardForm]}], "\n",
RowBox[{
RowBox[{"sa", "=",
RowBox[{
RowBox[{"CellularAutomaton", "[",
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{
RowBox[{"serialAddition", "[", "#", "]"}], " ", "&"}], ",", " ",
RowBox[{"{", "}"}], ",", " ", "1"}], "}"}], ",", " ",
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{"1", ",", "1", ",", "a1", ",", "1", ",", "1", ",", "1"}],
"}"}], ",", " ", "0"}], "}"}], ",", " ", "43"}], "]"}], "/.", " ",
RowBox[{"0", " ", "\[Rule]", " ", "\"\<.\>\""}]}]}],
";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"serialSubtraction",
StyleBox["[",
FormatType->StandardForm],
StyleBox[
RowBox[{"{",
RowBox[{"a_", ",", " ", "b_", ",", " ", "c_"}], "}"}],
FormatType->StandardForm],
StyleBox["]",
FormatType->StandardForm]}],
StyleBox[" ",
FormatType->StandardForm],
StyleBox[":=",
FormatType->StandardForm],
StyleBox["\[IndentingNewLine]",
FormatType->StandardForm],
StyleBox[
RowBox[{"Switch", "[",
RowBox[{
RowBox[{"{",
RowBox[{"a", ",", " ", "b", ",", " ", "c"}], "}"}], ",",
RowBox[{"{",
RowBox[{"s1", ",", "1", ",", "0"}], "}"}], ",", "s3", ",",
RowBox[{"{",
RowBox[{"s1", ",", "1", ",", "_"}], "}"}], ",", "s2", ",",
RowBox[{"{",
RowBox[{"s1", ",", "s4", ",", "_"}], "}"}], ",", "0", ",",
RowBox[{"{",
RowBox[{"_", ",", "1", ",", "s2"}], "}"}], ",", "s1", ",",
RowBox[{"{",
RowBox[{"s1", ",", "_", ",", "_"}], "}"}], ",", "s1", ",",
RowBox[{"{",
RowBox[{"_", ",", "_", ",", "s2"}], "}"}], ",", "s2", ",",
RowBox[{"{",
RowBox[{"_", ",", "_", ",", "s3"}], "}"}], ",", "s2", ",",
RowBox[{"{",
RowBox[{"_", ",", "s3", ",", "_"}], "}"}], ",", "s4", ",",
RowBox[{"{",
RowBox[{"_", ",", "s4", ",", "_"}], "}"}], ",", "s4", ",",
RowBox[{"{",
RowBox[{"_", ",", "1", ",", "_"}], "}"}], ",", "1", ",",
RowBox[{"{",
RowBox[{"_", ",", "_", ",", "_"}], "}"}], ",", "0"}], "]"}],
FormatType->StandardForm]}], "\n",
RowBox[{
RowBox[{"ss", "=",
RowBox[{
RowBox[{"CellularAutomaton", "[",
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{
RowBox[{"serialSubtraction", "[", "#", "]"}], " ", "&"}], ",", " ",
RowBox[{"{", "}"}], ",", " ", "1"}], "}"}], ",", " ",
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{
"1", ",", "1", ",", "1", ",", "1", ",", "s1", ",", "1", ",", "1",
",", "1"}], "}"}], ",", " ", "0"}], "}"}], ",", " ", "43"}], "]"}],
"/.", " ",
RowBox[{"0", " ", "\[Rule]", " ", "\"\<.\>\""}]}]}], ";"}], "\n",
RowBox[{
RowBox[{"serialMultiplication",
StyleBox["[",
FormatType->StandardForm],
StyleBox[
RowBox[{"{",
RowBox[{"a_", ",", " ", "b_", ",", " ", "c_"}], "}"}],
FormatType->StandardForm],
StyleBox["]",
FormatType->StandardForm]}],
StyleBox[" ",
FormatType->StandardForm],
StyleBox[":=",
FormatType->StandardForm],
StyleBox["\[IndentingNewLine]",
FormatType->StandardForm],
StyleBox[
RowBox[{"Switch", "[",
RowBox[{
RowBox[{"{",
RowBox[{"a", ",", " ", "b", ",", " ", "c"}], "}"}], ",",
RowBox[{"{",
RowBox[{"0", ",", "1", ",", "m2"}], "}"}], ",", "m5", ",",
RowBox[{"{",
RowBox[{"0", ",", "1", ",", "m3"}], "}"}], ",", "m4", ",",
RowBox[{"{",
RowBox[{"1", ",", "x2", ",", "m2"}], "}"}], ",", "m5", ",",
RowBox[{"{",
RowBox[{"1", ",", "x2", ",", "m3"}], "}"}], ",", "m4", ",",
RowBox[{"{",
RowBox[{"m1", ",", "1", ",", "0"}], "}"}], ",", "s1", ",",
RowBox[{"{",
RowBox[{"m4", ",", "x1", ",", "0"}], "}"}], ",", "m5", ",",
RowBox[{"{",
RowBox[{"m4", ",", "x1", ",", "x2"}], "}"}], ",", "m5", ",",
RowBox[{"{",
RowBox[{"m7", ",", "x1", ",", "x2"}], "}"}], ",", "m5", ",",
RowBox[{"{",
RowBox[{"m1", ",", "0", ",", "_"}], "}"}], ",", "m1", ",",
RowBox[{"{",
RowBox[{"m1", ",", "1", ",", "_"}], "}"}], ",", "m2", ",",
RowBox[{"{",
RowBox[{"m4", ",", "x1", ",", "_"}], "}"}], ",", "m4", ",",
RowBox[{"{",
RowBox[{"m7", ",", "1", ",", "_"}], "}"}], ",", "m7", ",",
RowBox[{"{",
RowBox[{"m7", ",", "x1", ",", "_"}], "}"}], ",", "m4", ",",
RowBox[{"{",
RowBox[{"m7", ",", "x2", ",", "_"}], "}"}], ",", "m9", ",",
RowBox[{"{",
RowBox[{"m9", ",", "0", ",", "_"}], "}"}], ",", "m1", ",",
RowBox[{"{",
RowBox[{"m9", ",", "x2", ",", "_"}], "}"}], ",", "m9", ",",
RowBox[{"{",
RowBox[{"_", ",", "0", ",", "m5"}], "}"}], ",", "m7", ",",
RowBox[{"{",
RowBox[{"_", ",", "0", ",", "m6"}], "}"}], ",", "m7", ",",
RowBox[{"{",
RowBox[{"_", ",", "0", ",", "m8"}], "}"}], ",", "m7", ",",
RowBox[{"{",
RowBox[{"_", ",", "1", ",", "m2"}], "}"}], ",", "m3", ",",
RowBox[{"{",
RowBox[{"_", ",", "1", ",", "m3"}], "}"}], ",", "m3", ",",
RowBox[{"{",
RowBox[{"_", ",", "1", ",", "m5"}], "}"}], ",", "m8", ",",
RowBox[{"{",
RowBox[{"_", ",", "1", ",", "m6"}], "}"}], ",", "m8", ",",
RowBox[{"{",
RowBox[{"_", ",", "1", ",", "m8"}], "}"}], ",", "m8", ",",
RowBox[{"{",
RowBox[{"_", ",", "1", ",", "s1"}], "}"}], ",", "s2", ",",
RowBox[{"{",
RowBox[{"_", ",", "x1", ",", "m6"}], "}"}], ",", "m6", ",",
RowBox[{"{",
RowBox[{"_", ",", "x2", ",", "m2"}], "}"}], ",", "m3", ",",
RowBox[{"{",
RowBox[{"_", ",", "x2", ",", "m3"}], "}"}], ",", "m3", ",",
RowBox[{"{",
RowBox[{"_", ",", "x2", ",", "s1"}], "}"}], ",", "s2", ",",
RowBox[{"{",
RowBox[{"_", ",", "x2", ",", "s2"}], "}"}], ",", "s2", ",",
RowBox[{"{",
RowBox[{"_", ",", "_", ",", "m2"}], "}"}], ",", "m2", ",",
RowBox[{"{",
RowBox[{"_", ",", "_", ",", "m5"}], "}"}], ",", "m6", ",",
RowBox[{"{",
RowBox[{"_", ",", "_", ",", "s1"}], "}"}], ",", "s1", ",",
RowBox[{"{",
RowBox[{"_", ",", "m3", ",", "_"}], "}"}], ",", "x1", ",",
RowBox[{"{",
RowBox[{"_", ",", "m4", ",", "_"}], "}"}], ",", "x1", ",",
RowBox[{"{",
RowBox[{"_", ",", "m5", ",", "_"}], "}"}], ",", "x2", ",",
RowBox[{"{",
RowBox[{"_", ",", "m6", ",", "_"}], "}"}], ",", "x1", ",",
RowBox[{"{",
RowBox[{"_", ",", "m7", ",", "_"}], "}"}], ",", "1", ",",
RowBox[{"{",
RowBox[{"_", ",", "m8", ",", "_"}], "}"}], ",", "1", ",",
RowBox[{"{",
RowBox[{"_", ",", "m9", ",", "_"}], "}"}], ",", "x2", ",",
RowBox[{"{",
RowBox[{"_", ",", "s2", ",", "_"}], "}"}], ",", "1", ",",
RowBox[{"{",
RowBox[{"_", ",", "x1", ",", "_"}], "}"}], ",", "x1", ",",
RowBox[{"{",
RowBox[{"_", ",", "x2", ",", "_"}], "}"}], ",", "x2", ",",
RowBox[{"{",
RowBox[{"_", ",", "1", ",", "_"}], "}"}], ",", "1", ",",
RowBox[{"{",
RowBox[{"_", ",", "_", ",", "_"}], "}"}], ",", "0"}], "]"}],
FormatType->StandardForm]}], "\n",
RowBox[{
RowBox[{"sm", "=",
RowBox[{
RowBox[{"CellularAutomaton", "[",
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{
RowBox[{"serialMultiplication", "[", "#", "]"}], " ", "&"}], ",",
" ",
RowBox[{"{", "}"}], ",", " ", "1"}], "}"}], ",", " ",
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{"1", ",", "1", ",", "1", ",", "m1", ",", "1", ",", "1"}],
"}"}], ",", " ", "0"}], "}"}], ",", " ", "43"}], "]"}], "/.", " ",
RowBox[{"0", " ", "\[Rule]", " ", "\"\<.\>\""}]}]}], ";"}], "\n",
RowBox[{
RowBox[{"serialDivision",
StyleBox["[",
FormatType->StandardForm],
StyleBox[
RowBox[{"{",
RowBox[{"a_", ",", " ", "b_", ",", " ", "c_"}], "}"}],
FormatType->StandardForm],
StyleBox["]",
FormatType->StandardForm]}],
StyleBox[" ",
FormatType->StandardForm],
StyleBox[":=",
FormatType->StandardForm],
StyleBox["\[IndentingNewLine]",
FormatType->StandardForm],
StyleBox[
RowBox[{"Switch", "[",
RowBox[{
RowBox[{"{",
RowBox[{"a", ",", " ", "b", ",", " ", "c"}], "}"}], ",",
RowBox[{"{",
RowBox[{"0", ",", "1", ",", "d4"}], "}"}], ",", "d7", ",",
RowBox[{"{",
RowBox[{"0", ",", "d3", ",", "0"}], "}"}], ",", "x2", ",",
RowBox[{"{",
RowBox[{"0", ",", "d3", ",", "1"}], "}"}], ",", "x2", ",",
RowBox[{"{",
RowBox[{"0", ",", "d3", ",", "x1"}], "}"}], ",", "x2", ",",
RowBox[{"{",
RowBox[{"d1", ",", "1", ",", "0"}], "}"}], ",", "d3", ",",
RowBox[{"{",
RowBox[{"d2", ",", "1", ",", "0"}], "}"}], ",", "d3", ",",
RowBox[{"{",
RowBox[{"d7", ",", "x2", ",", "0"}], "}"}], ",", "d8", ",",
RowBox[{"{",
RowBox[{"d1", ",", "1", ",", "_"}], "}"}], ",", "d2", ",",
RowBox[{"{",
RowBox[{"d1", ",", "x2", ",", "_"}], "}"}], ",", "d5", ",",
RowBox[{"{",
RowBox[{"d5", ",", "0", ",", "_"}], "}"}], ",", "e1", ",",
RowBox[{"{",
RowBox[{"d5", ",", "1", ",", "_"}], "}"}], ",", "e2", ",",
RowBox[{"{",
RowBox[{"d5", ",", "x1", ",", "_"}], "}"}], ",", "d6", ",",
RowBox[{"{",
RowBox[{"d5", ",", "x2", ",", "_"}], "}"}], ",", "d5", ",",
RowBox[{"{",
RowBox[{"d7", ",", "1", ",", "_"}], "}"}], ",", "e3", ",",
RowBox[{"{",
RowBox[{"d8", ",", "0", ",", "_"}], "}"}], ",", "1", ",",
RowBox[{"{",
RowBox[{"e2", ",", "0", ",", "_"}], "}"}], ",", "e1", ",",
RowBox[{"{",
RowBox[{"e2", ",", "1", ",", "_"}], "}"}], ",", "e2", ",",
RowBox[{"{",
RowBox[{"e3", ",", "0", ",", "_"}], "}"}], ",", "1", ",",
RowBox[{"{",
RowBox[{"e3", ",", "1", ",", "_"}], "}"}], ",", "e3", ",",
RowBox[{"{",
RowBox[{"_", ",", "0", ",", "d3"}], "}"}], ",", "d4", ",",
RowBox[{"{",
RowBox[{"_", ",", "0", ",", "d6"}], "}"}], ",", "d4", ",",
RowBox[{"{",
RowBox[{"_", ",", "1", ",", "d3"}], "}"}], ",", "d3", ",",
RowBox[{"{",
RowBox[{"_", ",", "1", ",", "d4"}], "}"}], ",", "d1", ",",
RowBox[{"{",
RowBox[{"_", ",", "1", ",", "e1"}], "}"}], ",", "e1", ",",
RowBox[{"{",
RowBox[{"_", ",", "x2", ",", "d3"}], "}"}], ",", "d3", ",",
RowBox[{"{",
RowBox[{"_", ",", "x2", ",", "d6"}], "}"}], ",", "d6", ",",
RowBox[{"{",
RowBox[{"_", ",", "x2", ",", "e1"}], "}"}], ",", "d3", ",",
RowBox[{"{",
RowBox[{"d1", ",", "_", ",", "_"}], "}"}], ",", "d1", ",",
RowBox[{"{",
RowBox[{"d2", ",", "_", ",", "_"}], "}"}], ",", "d2", ",",
RowBox[{"{",
RowBox[{"d7", ",", "_", ",", "_"}], "}"}], ",", "d7", ",",
RowBox[{"{",
RowBox[{"_", ",", "_", ",", "d4"}], "}"}], ",", "d4", ",",
RowBox[{"{",
RowBox[{"_", ",", "d2", ",", "_"}], "}"}], ",", "1", ",",
RowBox[{"{",
RowBox[{"_", ",", "d3", ",", "_"}], "}"}], ",", "x1", ",",
RowBox[{"{",
RowBox[{"_", ",", "d5", ",", "_"}], "}"}], ",", "x2", ",",
RowBox[{"{",
RowBox[{"_", ",", "d6", ",", "_"}], "}"}], ",", "x2", ",",
RowBox[{"{",
RowBox[{"_", ",", "e1", ",", "_"}], "}"}], ",", "1", ",",
RowBox[{"{",
RowBox[{"_", ",", "e2", ",", "_"}], "}"}], ",", "1", ",",
RowBox[{"{",
RowBox[{"_", ",", "e3", ",", "_"}], "}"}], ",", "1", ",",
RowBox[{"{",
RowBox[{"_", ",", "x1", ",", "_"}], "}"}], ",", "x1", ",",
RowBox[{"{",
RowBox[{"_", ",", "x2", ",", "_"}], "}"}], ",", "x2", ",",
RowBox[{"{",
RowBox[{"_", ",", "1", ",", "_"}], "}"}], ",", "1", ",",
RowBox[{"{",
RowBox[{"_", ",", "_", ",", "_"}], "}"}], ",", "0"}], "]"}],
FormatType->StandardForm]}], "\n",
RowBox[{
RowBox[{"sd", "=",
RowBox[{
RowBox[{"CellularAutomaton", "[",
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{
RowBox[{"serialDivision", "[", "#", "]"}], " ", "&"}], ",", " ",
RowBox[{"{", "}"}], ",", " ", "1"}], "}"}], ",", " ",
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{
"1", ",", "1", ",", "1", ",", "1", ",", "d1", ",", "1", ",", "1"}],
"}"}], ",", " ", "0"}], "}"}], ",", " ", "43"}], "]"}], "/.", " ",
RowBox[{"0", " ", "\[Rule]", " ", "\"\<.\>\""}]}]}], ";"}], "\n",
RowBox[{"Style", "[",
RowBox[{
RowBox[{"TableForm", "[",
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{"TableForm", "[", "sa", "]"}], ",",
RowBox[{"TableForm", "[", "ss", "]"}], ",",
RowBox[{"TableForm", "[", "sm", "]"}], ",",
RowBox[{"TableForm", "[", "sd", "]"}]}], "}"}], ",",
"\[IndentingNewLine]",
RowBox[{"TableDirections", "\[Rule]", "Row"}], ",",
RowBox[{"TableSpacing", "\[Rule]", "5"}], ",",
RowBox[{"TableAlignments", "\[Rule]", "Bottom"}]}], "]"}], ",",
"Small"}], "]"}]}], "Input",
CellChangeTimes->{{3.39304787603125*^9, 3.393047925484375*^9}, {
3.3930486678125*^9, 3.3930486791875*^9}, {3.393125850171875*^9,
3.3931258565*^9}, {3.393125943140625*^9, 3.393126120671875*^9}, {
3.39312622309375*^9, 3.3931262428125*^9}, 3.393378187440779*^9},
FontSize->12],
Cell[BoxData[
StyleBox[
TagBox[
TagBox[GridBox[{
{
TagBox[GridBox[{
{"\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "1", "1", "a1", "1", "1",
"1"},
{"\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "1", "1", "\<\".\"\>", "a2",
"1", "1"},
{"\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "1", "1", "a2", "\<\".\"\>",
"1", "1"},
{"\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "1",
"a4", "\<\".\"\>", "\<\".\"\>", "1", "1"},
{"\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "a4",
"1", "\<\".\"\>", "\<\".\"\>", "1", "1"},
{"\<\".\"\>", "\<\".\"\>", "a5", "1", "1", "\<\".\"\>", "\<\".\"\>",
"1", "1"},
{"\<\".\"\>", "\<\".\"\>", "1", "a3", "1", "\<\".\"\>", "\<\".\"\>",
"1", "1"},
{"\<\".\"\>", "\<\".\"\>", "1", "1", "a3", "\<\".\"\>", "\<\".\"\>",
"1", "1"},
{"\<\".\"\>", "\<\".\"\>", "1", "1", "1", "a1", "\<\".\"\>", "1",
"1"},
{"\<\".\"\>", "\<\".\"\>", "1", "1", "1", "\<\".\"\>", "a1", "1",
"1"},
{"\<\".\"\>", "\<\".\"\>", "1", "1", "1", "\<\".\"\>", "\<\".\"\>",
"a2", "1"},
{"\<\".\"\>", "\<\".\"\>", "1", "1", "1", "\<\".\"\>",
"a2", "\<\".\"\>", "1"},
{"\<\".\"\>", "\<\".\"\>", "1", "1", "1",
"a2", "\<\".\"\>", "\<\".\"\>", "1"},
{"\<\".\"\>", "\<\".\"\>", "1", "1",
"a4", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "1"},
{"\<\".\"\>", "\<\".\"\>", "1", "a4",
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "1"},
{"\<\".\"\>", "\<\".\"\>", "a4", "1",
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "1"},
{"\<\".\"\>", "a5", "1", "1",
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "1"},
{"\<\".\"\>", "1", "a3", "1",
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "1"},
{"\<\".\"\>", "1", "1", "a3",
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "1"},
{"\<\".\"\>", "1", "1", "1",
"a3", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "1"},
{"\<\".\"\>", "1", "1", "1", "1", "a1", "\<\".\"\>", "\<\".\"\>",
"1"},
{"\<\".\"\>", "1", "1", "1", "1", "\<\".\"\>", "a1", "\<\".\"\>",
"1"},
{"\<\".\"\>", "1", "1", "1", "1", "\<\".\"\>", "\<\".\"\>", "a1",
"1"},
{"\<\".\"\>", "1", "1", "1",
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "a6"},
{"\<\".\"\>", "1", "1", "1", "1", "\<\".\"\>", "\<\".\"\>", "a2",
"a5"},
{"\<\".\"\>", "1", "1", "1", "1", "\<\".\"\>", "a2", "\<\".\"\>",
"a5"},
{"\<\".\"\>", "1", "1", "1", "1", "a2", "\<\".\"\>", "\<\".\"\>",
"a5"},
{"\<\".\"\>", "1", "1", "1",
"a4", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "a5"},
{"\<\".\"\>", "1", "1", "a4",
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "a5"},
{"\<\".\"\>", "1", "a4", "1",
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "a5"},
{"\<\".\"\>", "a4", "1", "1",
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "a5"},
{"a5", "1", "1", "1", "1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>",
"a5"},
{"1", "a3", "1", "1", "1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>",
"a5"},
{"1", "1", "a3", "1", "1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>",
"a5"},
{"1", "1", "1", "a3", "1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>",
"a5"},
{"1", "1", "1", "1", "a3", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>",
"a5"},
{"1", "1", "1", "1", "1", "a1", "\<\".\"\>", "\<\".\"\>", "a5"},
{"1", "1", "1", "1", "1", "\<\".\"\>", "a1", "\<\".\"\>", "a5"},
{"1", "1", "1", "1", "1", "\<\".\"\>", "\<\".\"\>", "a1", "a5"},
{"1", "1", "1", "1",
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>"},
{"1", "1", "1", "1",
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>"},
{"1", "1", "1", "1",
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>"},
{"1", "1", "1", "1",
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>"},
{"1", "1", "1", "1",
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>"}
},
GridBoxAlignment->{
"Columns" -> {{Left}}, "ColumnsIndexed" -> {},
"Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.7]},
Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {},
"Rows" -> {
Offset[0.2], {
Offset[0.4]},
Offset[0.2]}, "RowsIndexed" -> {}}],
Function[BoxForm`e$,
TableForm[BoxForm`e$]]],
TagBox[GridBox[{
{"1", "1", "1", "1", "s1", "1", "1", "1"},
{"1", "1", "1", "1", "\<\".\"\>", "s2", "1", "1"},
{"1", "1", "1", "1", "s2", "\<\".\"\>", "1", "1"},
{"1", "1", "1", "s1", "\<\".\"\>", "\<\".\"\>", "1", "1"},
{"1", "1", "1", "\<\".\"\>", "s1", "\<\".\"\>", "1", "1"},
{"1", "1", "1", "\<\".\"\>", "\<\".\"\>", "s1", "1", "1"},
{"1", "1", "1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "s2", "1"},
{"1", "1", "1", "\<\".\"\>", "\<\".\"\>", "s2", "\<\".\"\>", "1"},
{"1", "1", "1", "\<\".\"\>", "s2", "\<\".\"\>", "\<\".\"\>", "1"},
{"1", "1", "1", "s2", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "1"},
{"1", "1", "s1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>",
"1"},
{"1", "1", "\<\".\"\>", "s1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>",
"1"},
{"1", "1", "\<\".\"\>", "\<\".\"\>", "s1", "\<\".\"\>", "\<\".\"\>",
"1"},
{"1", "1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "s1", "\<\".\"\>",
"1"},
{"1", "1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "s1",
"1"},
{"1",
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", \
"\<\".\"\>", "s3"},
{"1", "1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "s2",
"s4"},
{"1", "1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "s2", "\<\".\"\>",
"s4"},
{"1", "1", "\<\".\"\>", "\<\".\"\>", "s2", "\<\".\"\>", "\<\".\"\>",
"s4"},
{"1", "1", "\<\".\"\>", "s2", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>",
"s4"},
{"1", "1", "s2", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>",
"s4"},
{"1",
"s1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\
\>", "s4"},
{"1", "\<\".\"\>",
"s1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "s4"},
{"1", "\<\".\"\>", "\<\".\"\>",
"s1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "s4"},
{"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>",
"s1", "\<\".\"\>", "\<\".\"\>", "s4"},
{"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>",
"s1", "\<\".\"\>", "s4"},
{
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", \
"\<\".\"\>", "s1", "s4"},
{
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", \
"\<\".\"\>", "\<\".\"\>", "\<\".\"\>"},
{
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", \
"\<\".\"\>", "\<\".\"\>", "\<\".\"\>"},
{
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", \
"\<\".\"\>", "\<\".\"\>", "\<\".\"\>"},
{
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", \
"\<\".\"\>", "\<\".\"\>", "\<\".\"\>"},
{
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", \
"\<\".\"\>", "\<\".\"\>", "\<\".\"\>"},
{
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", \
"\<\".\"\>", "\<\".\"\>", "\<\".\"\>"},
{
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", \
"\<\".\"\>", "\<\".\"\>", "\<\".\"\>"},
{
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", \
"\<\".\"\>", "\<\".\"\>", "\<\".\"\>"},
{
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", \
"\<\".\"\>", "\<\".\"\>", "\<\".\"\>"},
{
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", \
"\<\".\"\>", "\<\".\"\>", "\<\".\"\>"},
{
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", \
"\<\".\"\>", "\<\".\"\>", "\<\".\"\>"},
{
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", \
"\<\".\"\>", "\<\".\"\>", "\<\".\"\>"},
{
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", \
"\<\".\"\>", "\<\".\"\>", "\<\".\"\>"},
{
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", \
"\<\".\"\>", "\<\".\"\>", "\<\".\"\>"},
{
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", \
"\<\".\"\>", "\<\".\"\>", "\<\".\"\>"},
{
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", \
"\<\".\"\>", "\<\".\"\>", "\<\".\"\>"},
{
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", \
"\<\".\"\>", "\<\".\"\>", "\<\".\"\>"}
},
GridBoxAlignment->{
"Columns" -> {{Left}}, "ColumnsIndexed" -> {},
"Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.7]},
Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {},
"Rows" -> {
Offset[0.2], {
Offset[0.4]},
Offset[0.2]}, "RowsIndexed" -> {}}],
Function[BoxForm`e$,
TableForm[BoxForm`e$]]],
TagBox[GridBox[{
{"\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "1", "1", "1", "m1", "1",
"1"},
{"\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "1", "1", "1", "\<\".\"\>",
"m2", "1"},
{"\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "1", "1", "1",
"m2", "\<\".\"\>", "1"},
{"\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "1", "1",
"m3", "\<\".\"\>", "\<\".\"\>", "1"},
{"\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "1", "m3",
"x1", "\<\".\"\>", "\<\".\"\>", "1"},
{"\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "m4", "x1",
"x1", "\<\".\"\>", "\<\".\"\>", "1"},
{"\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "x1", "m4",
"x1", "\<\".\"\>", "\<\".\"\>", "1"},
{"\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "x1", "x1",
"m5", "\<\".\"\>", "\<\".\"\>", "1"},
{"\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "x1", "m6",
"x2", "\<\".\"\>", "\<\".\"\>", "1"},
{"\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "m6", "x1",
"x2", "\<\".\"\>", "\<\".\"\>", "1"},
{"\<\".\"\>", "\<\".\"\>", "m7", "x1", "x1",
"x2", "\<\".\"\>", "\<\".\"\>", "1"},
{"\<\".\"\>", "\<\".\"\>", "1", "m4", "x1",
"x2", "\<\".\"\>", "\<\".\"\>", "1"},
{"\<\".\"\>", "\<\".\"\>", "1", "x1", "m5",
"x2", "\<\".\"\>", "\<\".\"\>", "1"},
{"\<\".\"\>", "\<\".\"\>", "1", "m6", "x2",
"x2", "\<\".\"\>", "\<\".\"\>", "1"},
{"\<\".\"\>", "\<\".\"\>", "m8", "x1", "x2",
"x2", "\<\".\"\>", "\<\".\"\>", "1"},
{"\<\".\"\>", "m7", "1", "x1", "x2", "x2", "\<\".\"\>", "\<\".\"\>",
"1"},
{"\<\".\"\>", "1", "m7", "x1", "x2", "x2", "\<\".\"\>", "\<\".\"\>",
"1"},
{"\<\".\"\>", "1", "1", "m5", "x2", "x2", "\<\".\"\>", "\<\".\"\>",
"1"},
{"\<\".\"\>", "1", "m8", "x2", "x2", "x2", "\<\".\"\>", "\<\".\"\>",
"1"},
{"\<\".\"\>", "m8", "1", "x2", "x2", "x2", "\<\".\"\>", "\<\".\"\>",
"1"},
{"m7", "1", "1", "x2", "x2", "x2", "\<\".\"\>", "\<\".\"\>", "1"},
{"1", "m7", "1", "x2", "x2", "x2", "\<\".\"\>", "\<\".\"\>", "1"},
{"1", "1", "m7", "x2", "x2", "x2", "\<\".\"\>", "\<\".\"\>", "1"},
{"1", "1", "1", "m9", "x2", "x2", "\<\".\"\>", "\<\".\"\>", "1"},
{"1", "1", "1", "x2", "m9", "x2", "\<\".\"\>", "\<\".\"\>", "1"},
{"1", "1", "1", "x2", "x2", "m9", "\<\".\"\>", "\<\".\"\>", "1"},
{"1", "1", "1", "x2", "x2", "x2", "m1", "\<\".\"\>", "1"},
{"1", "1", "1", "x2", "x2", "x2", "\<\".\"\>", "m1", "1"},
{"1", "1", "1", "x2", "x2", "x2", "\<\".\"\>", "\<\".\"\>", "s1"},
{"1", "1", "1", "x2", "x2", "x2", "\<\".\"\>", "s1", "\<\".\"\>"},
{"1", "1", "1", "x2", "x2", "x2", "s1", "\<\".\"\>", "\<\".\"\>"},
{"1", "1", "1", "x2", "x2",
"s2", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>"},
{"1", "1", "1", "x2", "s2",
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>"},
{"1", "1", "1", "s2", "1",
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>"},
{"1", "1", "1", "1", "1",
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>"},
{"1", "1", "1", "1", "1",
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>"},
{"1", "1", "1", "1", "1",
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>"},
{"1", "1", "1", "1", "1",
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>"},
{"1", "1", "1", "1", "1",
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>"},
{"1", "1", "1", "1", "1",
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>"},
{"1", "1", "1", "1", "1",
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>"},
{"1", "1", "1", "1", "1",
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>"},
{"1", "1", "1", "1", "1",
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>"},
{"1", "1", "1", "1", "1",
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>"}
},
GridBoxAlignment->{
"Columns" -> {{Left}}, "ColumnsIndexed" -> {},
"Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.7]},
Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {},
"Rows" -> {
Offset[0.2], {
Offset[0.4]},
Offset[0.2]}, "RowsIndexed" -> {}}],
Function[BoxForm`e$,
TableForm[BoxForm`e$]]],
TagBox[GridBox[{
{"1", "1", "1", "1", "d1", "1", "1", "\<\".\"\>", "\<\".\"\>"},
{"1", "1", "1", "1", "\<\".\"\>", "d2",
"1", "\<\".\"\>", "\<\".\"\>"},
{"1", "1", "1", "1", "\<\".\"\>", "1",
"d3", "\<\".\"\>", "\<\".\"\>"},
{"1", "1", "1", "1", "\<\".\"\>", "d3",
"x1", "\<\".\"\>", "\<\".\"\>"},
{"1", "1", "1", "1", "d4", "x2", "x1", "\<\".\"\>", "\<\".\"\>"},
{"1", "1", "1", "d1", "\<\".\"\>", "x2",
"x1", "\<\".\"\>", "\<\".\"\>"},
{"1", "1", "1", "\<\".\"\>", "d1", "x2",
"x1", "\<\".\"\>", "\<\".\"\>"},
{"1", "1", "1", "\<\".\"\>", "\<\".\"\>", "d5",
"x1", "\<\".\"\>", "\<\".\"\>"},
{"1", "1", "1", "\<\".\"\>", "\<\".\"\>", "x2",
"d6", "\<\".\"\>", "\<\".\"\>"},
{"1", "1", "1", "\<\".\"\>", "\<\".\"\>", "d6",
"x2", "\<\".\"\>", "\<\".\"\>"},
{"1", "1", "1", "\<\".\"\>", "d4", "x2",
"x2", "\<\".\"\>", "\<\".\"\>"},
{"1", "1", "1", "d4", "\<\".\"\>", "x2",
"x2", "\<\".\"\>", "\<\".\"\>"},
{"1", "1", "d1", "\<\".\"\>", "\<\".\"\>", "x2",
"x2", "\<\".\"\>", "\<\".\"\>"},
{"1", "1", "\<\".\"\>", "d1", "\<\".\"\>", "x2",
"x2", "\<\".\"\>", "\<\".\"\>"},
{"1", "1", "\<\".\"\>", "\<\".\"\>", "d1", "x2",
"x2", "\<\".\"\>", "\<\".\"\>"},
{"1", "1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "d5",
"x2", "\<\".\"\>", "\<\".\"\>"},
{"1", "1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "x2",
"d5", "\<\".\"\>", "\<\".\"\>"},
{"1", "1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "x2", "x2",
"e1", "\<\".\"\>"},
{"1", "1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "x2", "d3",
"1", "\<\".\"\>"},
{"1", "1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "d3", "x1",
"1", "\<\".\"\>"},
{"1", "1", "\<\".\"\>", "\<\".\"\>", "d4", "x2", "x1",
"1", "\<\".\"\>"},
{"1", "1", "\<\".\"\>", "d4", "\<\".\"\>", "x2", "x1",
"1", "\<\".\"\>"},
{"1", "1", "d4", "\<\".\"\>", "\<\".\"\>", "x2", "x1",
"1", "\<\".\"\>"},
{"1", "d1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "x2", "x1",
"1", "\<\".\"\>"},
{"1", "\<\".\"\>", "d1", "\<\".\"\>", "\<\".\"\>", "x2", "x1",
"1", "\<\".\"\>"},
{"1", "\<\".\"\>", "\<\".\"\>", "d1", "\<\".\"\>", "x2", "x1",
"1", "\<\".\"\>"},
{"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "d1", "x2", "x1",
"1", "\<\".\"\>"},
{"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "d5",
"x1", "1", "\<\".\"\>"},
{"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "x2",
"d6", "1", "\<\".\"\>"},
{"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "d6",
"x2", "1", "\<\".\"\>"},
{"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "d4", "x2", "x2",
"1", "\<\".\"\>"},
{"1", "\<\".\"\>", "\<\".\"\>", "d4", "\<\".\"\>", "x2", "x2",
"1", "\<\".\"\>"},
{"1", "\<\".\"\>", "d4", "\<\".\"\>", "\<\".\"\>", "x2", "x2",
"1", "\<\".\"\>"},
{"1", "d4", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "x2", "x2",
"1", "\<\".\"\>"},
{"d7", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "x2",
"x2", "1", "\<\".\"\>"},
{"\<\".\"\>", "d7", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "x2",
"x2", "1", "\<\".\"\>"},
{"\<\".\"\>", "\<\".\"\>", "d7", "\<\".\"\>", "\<\".\"\>", "x2",
"x2", "1", "\<\".\"\>"},
{"\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "d7", "\<\".\"\>", "x2",
"x2", "1", "\<\".\"\>"},
{"\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "d7", "x2",
"x2", "1", "\<\".\"\>"},
{"\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>",
"d7", "x2", "1", "\<\".\"\>"},
{"\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\
\<\".\"\>", "d7", "1", "\<\".\"\>"},
{"\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\
\<\".\"\>", "\<\".\"\>", "e3", "\<\".\"\>"},
{"\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\
\<\".\"\>", "\<\".\"\>", "1", "1"},
{"\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\
\<\".\"\>", "\<\".\"\>", "1", "1"}
},
GridBoxAlignment->{
"Columns" -> {{Left}}, "ColumnsIndexed" -> {},
"Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.7]},
Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {},
"Rows" -> {
Offset[0.2], {
Offset[0.4]},
Offset[0.2]}, "RowsIndexed" -> {}}],
Function[BoxForm`e$,
TableForm[BoxForm`e$]]]}
},
GridBoxAlignment->{
"Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
"RowsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[3.5]},
Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
Offset[0.2], {
Offset[0.4]},
Offset[0.2]}, "RowsIndexed" -> {}}],
Row],
Function[BoxForm`e$,
TableForm[
BoxForm`e$, TableDirections -> Row, TableSpacing -> 5, TableAlignments ->
Bottom]]],
StripOnInput->False,
FontSize->Small]], "Output",
CellChangeTimes->{3.3933412783280816`*^9}]
}, {2}]]
}, Open ]],
Cell[CellGroupData[{
Cell[TextData[StyleBox["Specific constructions - parallel",
FontColor->RGBColor[
0.9714045929655909, 0.6775158312352179, 0.07415884641794461]]], "Subsection",\
CellChangeTimes->{
3.3824524252213373`*^9, {3.39303943990625*^9, 3.393039450140625*^9}, {
3.39304107571875*^9, 3.3930411009375*^9}}],
Cell["\<\
Based on what we have learnt from serial constructions, but are more \
difficult to program.
Significantly less states are used.
Computations are carried out in few steps.
Same kinds of behavior used in serial constructions are used in parallel \
ones.\
\>", "Text",
CellChangeTimes->{{3.39318995278125*^9, 3.39319008303125*^9}, {
3.3931901198125*^9, 3.39319013409375*^9}, {3.39319018428125*^9,
3.39319021*^9}, {3.3931903076875*^9, 3.393190349421875*^9}, {3.393190457*^9,
3.3931904584375*^9}, {3.393207257921875*^9, 3.3932074306875*^9}, {
3.39320748896875*^9, 3.393207635265625*^9}, {3.39321311059375*^9,
3.39321311190625*^9}}],
Cell[CellGroupData[{
Cell[BoxData[{
RowBox[{
RowBox[{"parallelAddition",
StyleBox["[",
FormatType->StandardForm],
StyleBox[
RowBox[{"{",
RowBox[{"a_", ",", " ", "b_", ",", " ", "c_"}], "}"}],
FormatType->StandardForm],
StyleBox["]",
FormatType->StandardForm]}],
StyleBox[" ",
FormatType->StandardForm],
StyleBox[":=",
FormatType->StandardForm],
StyleBox["\[IndentingNewLine]",
FormatType->StandardForm],
StyleBox[
RowBox[{"Switch", "[",
RowBox[{
RowBox[{"{",
RowBox[{"a", ",", " ", "b", ",", " ", "c"}], "}"}], ",",
RowBox[{"{",
RowBox[{"0", ",", "0", ",", "a3"}], "}"}], ",", "1", ",",
RowBox[{"{",
RowBox[{"a1", ",", "1", ",", "_"}], "}"}], ",", "a1", ",",
RowBox[{"{",
RowBox[{"_", ",", "1", ",", "a1"}], "}"}], ",", "1", ",",
RowBox[{"{",
RowBox[{"_", ",", "1", ",", "a2"}], "}"}], ",", "a3", ",",
RowBox[{"{",
RowBox[{"_", ",", "_", ",", "a1"}], "}"}], ",", "a2", ",",
RowBox[{"{",
RowBox[{"_", ",", "_", ",", "a2"}], "}"}], ",", "a2", ",",
RowBox[{"{",
RowBox[{"_", ",", "_", ",", "a3"}], "}"}], ",", "a3", ",",
RowBox[{"{",
RowBox[{"_", ",", "0", ",", "_"}], "}"}], ",", "0", ",",
RowBox[{"{",
RowBox[{"_", ",", "1", ",", "_"}], "}"}], ",", "1", ",",
RowBox[{"{",
RowBox[{"_", ",", "a1", ",", "_"}], "}"}], ",", "0", ",",
RowBox[{"{",
RowBox[{"_", ",", "a2", ",", "_"}], "}"}], ",", "0", ",",
RowBox[{"{",
RowBox[{"_", ",", "a3", ",", "_"}], "}"}], ",", "1", ",",
RowBox[{"{",
RowBox[{"_", ",", "_", ",", "_"}], "}"}], ",", "0"}], "]"}],
FormatType->StandardForm]}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"pa", "=",
RowBox[{
RowBox[{"CellularAutomaton", "[",
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{
RowBox[{"parallelAddition", "[", "#", "]"}], " ", "&"}], ",", " ",
RowBox[{"{", "}"}], ",", " ", "1"}], "}"}], ",", " ",
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{
"1", ",", "1", ",", "1", ",", "1", ",", "1", ",", "a1", ",", "1",
",", "1", ",", "1", ",", "1", ",", "1", ",", "1"}], "}"}], ",", " ",
"0"}], "}"}], ",", "31"}], "]"}], "/.", " ",
RowBox[{"0", " ", "\[Rule]", " ", "\"\<.\>\""}]}]}], ";"}], "\n",
RowBox[{
RowBox[{"parallelSubtract",
StyleBox["[",
FormatType->StandardForm],
StyleBox[
RowBox[{"{",
RowBox[{"a_", ",", " ", "b_", ",", " ", "c_"}], "}"}],
FormatType->StandardForm],
StyleBox["]",
FormatType->StandardForm]}],
StyleBox[" ",
FormatType->StandardForm],
StyleBox[":=",
FormatType->StandardForm],
StyleBox["\[IndentingNewLine]",
FormatType->StandardForm],
StyleBox[
RowBox[{"Switch", "[",
RowBox[{
RowBox[{"{",
RowBox[{"a", ",", " ", "b", ",", " ", "c"}], "}"}], ",",
RowBox[{"{",
RowBox[{"s1", ",", "0", ",", "_"}], "}"}], ",", "0", ",",
RowBox[{"{",
RowBox[{"_", ",", "0", ",", "s1"}], "}"}], ",", "s2", ",",
RowBox[{"{",
RowBox[{"_", ",", "1", ",", "s2"}], "}"}], ",", "0", ",",
RowBox[{"{",
RowBox[{"s1", ",", "_", ",", "_"}], "}"}], ",", "s1", ",",
RowBox[{"{",
RowBox[{"_", ",", "_", ",", "s2"}], "}"}], ",", "s2", ",",
RowBox[{"{",
RowBox[{"_", ",", "1", ",", "_"}], "}"}], ",", "1", ",",
RowBox[{"{",
RowBox[{"_", ",", "_", ",", "_"}], "}"}], ",", "0"}], "]"}],
FormatType->StandardForm]}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"ps", "=",
RowBox[{
RowBox[{"CellularAutomaton", "[",
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{
RowBox[{"parallelSubtract", "[", "#", "]"}], " ", "&"}], ",", " ",
RowBox[{"{", "}"}], ",", " ", "1"}], "}"}], ",", " ",
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{
"1", ",", "1", ",", "1", ",", "1", ",", "1", ",", "1", ",", "1", ",",
"1", ",", "s1", ",", "1", ",", "1", ",", "1", ",", "1", ",", "1",
",", "1"}], "}"}], ",", " ", "0"}], "}"}], ",", "31"}], "]"}], "/.",
" ",
RowBox[{"0", " ", "\[Rule]", " ", "\"\<.\>\""}]}]}], ";"}], "\n",
RowBox[{
RowBox[{"parallelMultiplication",
StyleBox["[",
FormatType->StandardForm],
StyleBox[
RowBox[{"{",
RowBox[{"a_", ",", " ", "b_", ",", " ", "c_"}], "}"}],
FormatType->StandardForm],
StyleBox["]",
FormatType->StandardForm]}],
StyleBox[" ",
FormatType->StandardForm],
StyleBox[":=",
FormatType->StandardForm],
StyleBox["\[IndentingNewLine]",
FormatType->StandardForm],
StyleBox[
RowBox[{"Switch", "[",
RowBox[{
RowBox[{"{",
RowBox[{"a", ",", " ", "b", ",", " ", "c"}], "}"}], ",",
RowBox[{"{",
RowBox[{"0", ",", "1", ",", "m3"}], "}"}], ",", "m4", ",",
RowBox[{"{",
RowBox[{"0", ",", "x", ",", "m3"}], "}"}], ",", "m4", ",",
RowBox[{"{",
RowBox[{"1", ",", "x", ",", "m3"}], "}"}], ",", "m4", ",",
RowBox[{"{",
RowBox[{"c1", ",", "m5", ",", "m3"}], "}"}], ",", "c1", ",",
RowBox[{"{",
RowBox[{"c1", ",", "x", ",", "m1"}], "}"}], ",", "c1", ",",
RowBox[{"{",
RowBox[{"c1", ",", "x", ",", "m2"}], "}"}], ",", "c2", ",",
RowBox[{"{",
RowBox[{"c1", ",", "x", ",", "m3"}], "}"}], ",", "c1", ",",
RowBox[{"{",
RowBox[{"m1", ",", "1", ",", "0"}], "}"}], ",", "m2", ",",
RowBox[{"{",
RowBox[{"m4", ",", "m5", ",", "m3"}], "}"}], ",", "c1", ",",
RowBox[{"{",
RowBox[{"m4", ",", "x", ",", "m3"}], "}"}], ",", "c1", ",",
RowBox[{"{",
RowBox[{"m6", ",", "x", ",", "m3"}], "}"}], ",", "m4", ",",
RowBox[{"{",
RowBox[{"c1", ",", "c2", ",", "_"}], "}"}], ",", "c2", ",",
RowBox[{"{",
RowBox[{"c1", ",", "m5", ",", "_"}], "}"}], ",", "m4", ",",
RowBox[{"{",
RowBox[{"c1", ",", "x", ",", "_"}], "}"}], ",", "m4", ",",
RowBox[{"{",
RowBox[{"m1", ",", "1", ",", "_"}], "}"}], ",", "m1", ",",
RowBox[{"{",
RowBox[{"m4", ",", "m5", ",", "_"}], "}"}], ",", "m4", ",",
RowBox[{"{",
RowBox[{"m4", ",", "m7", ",", "_"}], "}"}], ",", "m6", ",",
RowBox[{"{",
RowBox[{"m4", ",", "x", ",", "_"}], "}"}], ",", "m4", ",",
RowBox[{"{",
RowBox[{"_", ",", "0", ",", "m1"}], "}"}], ",", "m1", ",",
RowBox[{"{",
RowBox[{"_", ",", "0", ",", "m2"}], "}"}], ",", "m2", ",",
RowBox[{"{",
RowBox[{"_", ",", "0", ",", "m4"}], "}"}], ",", "1", ",",
RowBox[{"{",
RowBox[{"_", ",", "0", ",", "m6"}], "}"}], ",", "1", ",",
RowBox[{"{",
RowBox[{"_", ",", "1", ",", "m1"}], "}"}], ",", "m3", ",",
RowBox[{"{",
RowBox[{"_", ",", "1", ",", "m3"}], "}"}], ",", "m3", ",",
RowBox[{"{",
RowBox[{"_", ",", "1", ",", "m5"}], "}"}], ",", "m6", ",",
RowBox[{"{",
RowBox[{"_", ",", "1", ",", "m6"}], "}"}], ",", "m6", ",",
RowBox[{"{",
RowBox[{"_", ",", "c1", ",", "c1"}], "}"}], ",", "c1", ",",
RowBox[{"{",
RowBox[{"_", ",", "c1", ",", "m4"}], "}"}], ",", "m5", ",",
RowBox[{"{",
RowBox[{"_", ",", "c1", ",", "m5"}], "}"}], ",", "c1", ",",
RowBox[{"{",
RowBox[{"_", ",", "m3", ",", "c1"}], "}"}], ",", "m5", ",",
RowBox[{"{",
RowBox[{"_", ",", "m3", ",", "c2"}], "}"}], ",", "m5", ",",
RowBox[{"{",
RowBox[{"_", ",", "m3", ",", "m2"}], "}"}], ",", "c2", ",",
RowBox[{"{",
RowBox[{"_", ",", "m3", ",", "m4"}], "}"}], ",", "m5", ",",
RowBox[{"{",
RowBox[{"_", ",", "m3", ",", "m5"}], "}"}], ",", "m5", ",",
RowBox[{"{",
RowBox[{"_", ",", "m4", ",", "m5"}], "}"}], ",", "m5", ",",
RowBox[{"{",
RowBox[{"_", ",", "m5", ",", "c1"}], "}"}], ",", "m5", ",",
RowBox[{"{",
RowBox[{"_", ",", "m5", ",", "m3"}], "}"}], ",", "m4", ",",
RowBox[{"{",
RowBox[{"_", ",", "m5", ",", "m4"}], "}"}], ",", "m5", ",",
RowBox[{"{",
RowBox[{"_", ",", "m5", ",", "m5"}], "}"}], ",", "m5", ",",
RowBox[{"{",
RowBox[{"_", ",", "m6", ",", "m4"}], "}"}], ",", "m6", ",",
RowBox[{"{",
RowBox[{"_", ",", "m6", ",", "m5"}], "}"}], ",", "m6", ",",
RowBox[{"{",
RowBox[{"_", ",", "m6", ",", "m6"}], "}"}], ",", "m6", ",",
RowBox[{"{",
RowBox[{"_", ",", "x", ",", "c1"}], "}"}], ",", "m5", ",",
RowBox[{"{",
RowBox[{"_", ",", "x", ",", "c2"}], "}"}], ",", "m5", ",",
RowBox[{"{",
RowBox[{"_", ",", "x", ",", "m1"}], "}"}], ",", "m3", ",",
RowBox[{"{",
RowBox[{"_", ",", "x", ",", "m3"}], "}"}], ",", "m3", ",",
RowBox[{"{",
RowBox[{"_", ",", "x", ",", "m4"}], "}"}], ",", "m5", ",",
RowBox[{"{",
RowBox[{"_", ",", "x", ",", "m5"}], "}"}], ",", "m5", ",",
RowBox[{"{",
RowBox[{"_", ",", "x", ",", "m6"}], "}"}], ",", "m6", ",",
RowBox[{"{",
RowBox[{"_", ",", "c1", ",", "_"}], "}"}], ",", "m3", ",",
RowBox[{"{",
RowBox[{"_", ",", "c2", ",", "_"}], "}"}], ",", "m7", ",",
RowBox[{"{",
RowBox[{"_", ",", "m3", ",", "_"}], "}"}], ",", "x", ",",
RowBox[{"{",
RowBox[{"_", ",", "m4", ",", "_"}], "}"}], ",", "x", ",",
RowBox[{"{",
RowBox[{"_", ",", "m5", ",", "_"}], "}"}], ",", "x", ",",
RowBox[{"{",
RowBox[{"_", ",", "m6", ",", "_"}], "}"}], ",", "1", ",",
RowBox[{"{",
RowBox[{"_", ",", "m7", ",", "_"}], "}"}], ",", "m7", ",",
RowBox[{"{",
RowBox[{"_", ",", "x", ",", "_"}], "}"}], ",", "x", ",",
RowBox[{"{",
RowBox[{"_", ",", "1", ",", "_"}], "}"}], ",", "1", ",",
RowBox[{"{",
RowBox[{"_", ",", "_", ",", "_"}], "}"}], ",", "0"}], "]"}],
FormatType->StandardForm]}], "\n",
RowBox[{
RowBox[{"pm", "=",
RowBox[{
RowBox[{"CellularAutomaton", "[",
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{
RowBox[{"parallelMultiplication", "[", "#", "]"}], " ", "&"}], ",",
" ",
RowBox[{"{", "}"}], ",", " ", "1"}], "}"}], ",", " ",
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{
"1", ",", "1", ",", "1", ",", "1", ",", "m1", ",", "1", ",", "1",
",", "1", ",", "1"}], "}"}], ",", " ", "0"}], "}"}], ",", "31"}],
"]"}], "/.", " ",
RowBox[{"0", " ", "\[Rule]", " ", "\"\<.\>\""}]}]}], ";"}], "\n",
RowBox[{"Style", "[",
RowBox[{
RowBox[{"TableForm", "[",
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{"TableForm", "[", "pa", "]"}], ",",
RowBox[{"TableForm", "[", "ps", "]"}]}], "}"}], ",",
RowBox[{"TableDirections", "\[Rule]", "Row"}], ",",
RowBox[{"TableSpacing", "\[Rule]", "5"}]}], "]"}], ",", "Small"}],
"]"}]}], "Input",
CellChangeTimes->{{3.393041179515625*^9, 3.39304121975*^9},
3.393041576375*^9, 3.3930418185*^9, {3.393126291140625*^9,
3.393126330671875*^9}, {3.393126401703125*^9, 3.393126433296875*^9},
3.393378231223736*^9},
FontSize->12],
Cell[BoxData[
StyleBox[
TagBox[
TagBox[GridBox[{
{
TagBox[GridBox[{
{"\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\
\<\".\"\>", "1", "1", "1", "1", "1", "a1", "1", "1", "1", "1", "1", "1"},
{"\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\
\<\".\"\>", "1", "1", "1", "1", "1", "\<\".\"\>", "a1", "1", "1", "1", "1",
"1"},
{"\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\
\<\".\"\>", "1", "1", "1", "1", "1", "a2", "\<\".\"\>", "a1", "1", "1", "1",
"1"},
{"\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\
\<\".\"\>", "1", "1", "1", "1", "a3", "\<\".\"\>", "a2", "\<\".\"\>", "a1",
"1", "1", "1"},
{"\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\
\<\".\"\>", "1", "1", "1", "a3", "1", "a2", "\<\".\"\>", "a2", "\<\".\"\>",
"a1", "1", "1"},
{"\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\
\<\".\"\>", "1", "1", "a3", "1", "a3", "\<\".\"\>", "a2", "\<\".\"\>",
"a2", "\<\".\"\>", "a1", "1"},
{"\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\
\<\".\"\>", "1", "a3", "1", "a3", "1", "a2", "\<\".\"\>", "a2", "\<\".\"\>",
"a2", "\<\".\"\>", "a1"},
{"\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\
\<\".\"\>", "a3", "1", "a3", "1", "a3", "\<\".\"\>", "a2", "\<\".\"\>",
"a2", "\<\".\"\>", "a2", "\<\".\"\>"},
{"\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>",
"1", "1", "a3", "1", "a3", "1", "a2", "\<\".\"\>",
"a2", "\<\".\"\>", "a2", "\<\".\"\>", "\<\".\"\>"},
{"\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>",
"1", "a3", "1", "a3", "1", "a3", "\<\".\"\>", "a2", "\<\".\"\>",
"a2", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>"},
{"\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>",
"a3", "1", "a3", "1", "a3", "1", "a2", "\<\".\"\>",
"a2", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>"},
{"\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "1", "1", "a3",
"1", "a3", "1", "a3", "\<\".\"\>",
"a2", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\
\>"},
{"\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "1", "a3", "1",
"a3", "1", "a3", "1",
"a2", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\
\>", "\<\".\"\>"},
{"\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "a3", "1",
"a3", "1", "a3", "1",
"a3", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\
\>", "\<\".\"\>", "\<\".\"\>"},
{"\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "1", "1", "a3", "1", "a3",
"1", "a3",
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", \
"\<\".\"\>", "\<\".\"\>", "\<\".\"\>"},
{"\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "1", "a3", "1", "a3", "1",
"a3", "1",
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", \
"\<\".\"\>", "\<\".\"\>", "\<\".\"\>"},
{"\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "a3", "1", "a3", "1", "a3",
"1", "1",
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", \
"\<\".\"\>", "\<\".\"\>", "\<\".\"\>"},
{"\<\".\"\>", "\<\".\"\>", "1", "1", "a3", "1", "a3", "1", "1", "1",
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\
\>", "\<\".\"\>", "\<\".\"\>"},
{"\<\".\"\>", "\<\".\"\>", "1", "a3", "1", "a3", "1", "1", "1", "1",
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\
\>", "\<\".\"\>", "\<\".\"\>"},
{"\<\".\"\>", "\<\".\"\>", "a3", "1", "a3", "1", "1", "1", "1", "1",
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\
\>", "\<\".\"\>", "\<\".\"\>"},
{"\<\".\"\>", "1", "1", "a3", "1", "1", "1", "1", "1", "1",
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", \
"\<\".\"\>", "\<\".\"\>", "\<\".\"\>"},
{"\<\".\"\>", "1", "a3", "1", "1", "1", "1", "1", "1", "1",
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", \
"\<\".\"\>", "\<\".\"\>", "\<\".\"\>"},
{"\<\".\"\>", "a3", "1", "1", "1", "1", "1", "1", "1", "1",
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", \
"\<\".\"\>", "\<\".\"\>", "\<\".\"\>"},
{"1", "1", "1", "1", "1", "1", "1", "1", "1", "1",
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", \
"\<\".\"\>", "\<\".\"\>", "\<\".\"\>"},
{"1", "1", "1", "1", "1", "1", "1", "1", "1", "1",
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", \
"\<\".\"\>", "\<\".\"\>", "\<\".\"\>"},
{"1", "1", "1", "1", "1", "1", "1", "1", "1", "1",
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", \
"\<\".\"\>", "\<\".\"\>", "\<\".\"\>"},
{"1", "1", "1", "1", "1", "1", "1", "1", "1", "1",
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", \
"\<\".\"\>", "\<\".\"\>", "\<\".\"\>"},
{"1", "1", "1", "1", "1", "1", "1", "1", "1", "1",
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", \
"\<\".\"\>", "\<\".\"\>", "\<\".\"\>"},
{"1", "1", "1", "1", "1", "1", "1", "1", "1", "1",
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", \
"\<\".\"\>", "\<\".\"\>", "\<\".\"\>"},
{"1", "1", "1", "1", "1", "1", "1", "1", "1", "1",
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", \
"\<\".\"\>", "\<\".\"\>", "\<\".\"\>"},
{"1", "1", "1", "1", "1", "1", "1", "1", "1", "1",
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", \
"\<\".\"\>", "\<\".\"\>", "\<\".\"\>"},
{"1", "1", "1", "1", "1", "1", "1", "1", "1", "1",
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", \
"\<\".\"\>", "\<\".\"\>", "\<\".\"\>"}
},
GridBoxAlignment->{
"Columns" -> {{Left}}, "ColumnsIndexed" -> {},
"Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.7]},
Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {},
"Rows" -> {
Offset[0.2], {
Offset[0.4]},
Offset[0.2]}, "RowsIndexed" -> {}}],
Function[BoxForm`e$,
TableForm[BoxForm`e$]]],
TagBox[GridBox[{
{"1", "1", "1", "1", "1", "1", "1", "1", "s1", "1", "1", "1", "1",
"1", "1"},
{"1", "1", "1", "1", "1", "1", "1", "1", "\<\".\"\>", "s1", "1",
"1", "1", "1", "1"},
{"1", "1", "1", "1", "1", "1", "1", "1", "s2", "\<\".\"\>", "s1",
"1", "1", "1", "1"},
{"1", "1", "1", "1", "1", "1", "1", "\<\".\"\>", "\<\".\"\>",
"s2", "\<\".\"\>", "s1", "1", "1", "1"},
{"1", "1", "1", "1", "1", "1", "1", "\<\".\"\>", "s2", "\<\".\"\>",
"s2", "\<\".\"\>", "s1", "1", "1"},
{"1", "1", "1", "1", "1", "1", "1", "s2", "\<\".\"\>",
"s2", "\<\".\"\>", "s2", "\<\".\"\>", "s1", "1"},
{"1", "1", "1", "1", "1", "1", "\<\".\"\>", "\<\".\"\>",
"s2", "\<\".\"\>", "s2", "\<\".\"\>", "s2", "\<\".\"\>", "s1"},
{"1", "1", "1", "1", "1", "1", "\<\".\"\>", "s2", "\<\".\"\>",
"s2", "\<\".\"\>", "s2", "\<\".\"\>", "s2", "\<\".\"\>"},
{"1", "1", "1", "1", "1", "1", "s2", "\<\".\"\>", "s2", "\<\".\"\>",
"s2", "\<\".\"\>", "s2", "\<\".\"\>", "\<\".\"\>"},
{"1", "1", "1", "1", "1", "\<\".\"\>", "\<\".\"\>",
"s2", "\<\".\"\>", "s2", "\<\".\"\>",
"s2", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>"},
{"1", "1", "1", "1", "1", "\<\".\"\>", "s2", "\<\".\"\>",
"s2", "\<\".\"\>",
"s2", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>"},
{"1", "1", "1", "1", "1", "s2", "\<\".\"\>", "s2", "\<\".\"\>",
"s2", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\
\>"},
{"1", "1", "1", "1", "\<\".\"\>", "\<\".\"\>", "s2", "\<\".\"\>",
"s2", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\
\>", "\<\".\"\>"},
{"1", "1", "1", "1", "\<\".\"\>", "s2", "\<\".\"\>",
"s2", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\
\>", "\<\".\"\>", "\<\".\"\>"},
{"1", "1", "1", "1", "s2", "\<\".\"\>",
"s2", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\
\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>"},
{"1", "1", "1", "\<\".\"\>", "\<\".\"\>",
"s2", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\
\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>"},
{"1", "1", "1", "\<\".\"\>",
"s2", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\
\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>"},
{"1", "1", "1",
"s2", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\
\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", \
"\<\".\"\>"},
{"1",
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", \
"\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", \
"\<\".\"\>", "\<\".\"\>", "\<\".\"\>"},
{"1",
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", \
"\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", \
"\<\".\"\>", "\<\".\"\>", "\<\".\"\>"},
{"1",
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", \
"\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", \
"\<\".\"\>", "\<\".\"\>", "\<\".\"\>"},
{"1",
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", \
"\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", \
"\<\".\"\>", "\<\".\"\>", "\<\".\"\>"},
{"1",
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", \
"\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", \
"\<\".\"\>", "\<\".\"\>", "\<\".\"\>"},
{"1",
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", \
"\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", \
"\<\".\"\>", "\<\".\"\>", "\<\".\"\>"},
{"1",
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", \
"\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", \
"\<\".\"\>", "\<\".\"\>", "\<\".\"\>"},
{"1",
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", \
"\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", \
"\<\".\"\>", "\<\".\"\>", "\<\".\"\>"},
{"1",
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", \
"\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", \
"\<\".\"\>", "\<\".\"\>", "\<\".\"\>"},
{"1",
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", \
"\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", \
"\<\".\"\>", "\<\".\"\>", "\<\".\"\>"},
{"1",
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", \
"\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", \
"\<\".\"\>", "\<\".\"\>", "\<\".\"\>"},
{"1",
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", \
"\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", \
"\<\".\"\>", "\<\".\"\>", "\<\".\"\>"},
{"1",
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", \
"\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", \
"\<\".\"\>", "\<\".\"\>", "\<\".\"\>"},
{"1",
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", \
"\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", \
"\<\".\"\>", "\<\".\"\>", "\<\".\"\>"}
},
GridBoxAlignment->{
"Columns" -> {{Left}}, "ColumnsIndexed" -> {},
"Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.7]},
Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {},
"Rows" -> {
Offset[0.2], {
Offset[0.4]},
Offset[0.2]}, "RowsIndexed" -> {}}],
Function[BoxForm`e$,
TableForm[BoxForm`e$]]]}
},
GridBoxAlignment->{
"Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
"RowsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[3.5]},
Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
Offset[0.2], {
Offset[0.4]},
Offset[0.2]}, "RowsIndexed" -> {}}],
Row],
Function[BoxForm`e$,
TableForm[BoxForm`e$, TableDirections -> Row, TableSpacing -> 5]]],
StripOnInput->False,
FontSize->Small]], "Output",
CellChangeTimes->{3.3933412882623663`*^9}]
}, {2}]],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"Style", "[",
RowBox[{
RowBox[{"TableForm", "[",
RowBox[{"pm", ",",
RowBox[{"TableSpacing", "\[Rule]", "1"}]}], "]"}], ",", "Small"}],
"]"}]], "Input",
CellChangeTimes->{{3.3933378149880433`*^9, 3.39333782112687*^9}, {
3.393337878769757*^9, 3.3933379197486815`*^9}, {3.3933379543684626`*^9,
3.3933379558806367`*^9}, {3.393338097634469*^9, 3.393338122199792*^9}},
FontSize->12],
Cell[BoxData[
StyleBox[
TagBox[GridBox[{
{"\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\
\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", \
"\<\".\"\>", "1", "1", "1", "1", "m1", "1", "1", "1", "1"},
{"\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\
\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", \
"\<\".\"\>", "1", "1", "1", "m3", "\<\".\"\>", "m1", "1", "1", "1"},
{"\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\
\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", \
"\<\".\"\>", "1", "1", "m3", "x", "m1", "\<\".\"\>", "m1", "1", "1"},
{"\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\
\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", \
"\<\".\"\>", "1", "m3", "x", "m3", "\<\".\"\>", "m1", "\<\".\"\>", "m1",
"1"},
{"\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\
\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", \
"\<\".\"\>", "m4", "x", "m3", "x", "m1", "\<\".\"\>", "m1", "\<\".\"\>",
"m2"},
{"\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\
\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "1",
"x", "c1", "x", "m3", "\<\".\"\>", "m1", "\<\".\"\>",
"m2", "\<\".\"\>"},
{"\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\
\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "1",
"m5", "m3", "c1", "x", "m1", "\<\".\"\>",
"m2", "\<\".\"\>", "\<\".\"\>"},
{"\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\
\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "m6",
"m4", "m5", "m3", "c1", "\<\".\"\>",
"m2", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>"},
{"\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\
\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "1", "m6", "m5",
"c1", "m5", "m3",
"m2", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>"},
{"\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\
\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "m6", "m6", "m5",
"c1", "c1",
"c2", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>"},
{"\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\
\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "1", "m6", "m6", "m5", "c1",
"m3", "c2", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", \
"\<\".\"\>"},
{"\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\
\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "m6", "m6", "m6", "m5", "m3",
"m5", "m7", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", \
"\<\".\"\>"},
{"\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\
\"\>", "\<\".\"\>", "\<\".\"\>", "1", "m6", "m6", "m6", "m4", "m5", "x",
"m7", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>"},
{"\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\
\"\>", "\<\".\"\>", "\<\".\"\>", "m6", "m6", "m6", "m6", "m5", "m4", "x",
"m7", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>"},
{"\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\
\"\>", "\<\".\"\>", "1", "m6", "m6", "m6", "m6", "m5", "x", "m4",
"m7", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>"},
{"\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\
\"\>", "\<\".\"\>", "m6", "m6", "m6", "m6", "m6", "x", "m5", "x",
"m6", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>"},
{"\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\
\"\>", "1", "m6", "m6", "m6", "m6", "1", "m5", "x", "m6",
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>"},
{"\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\
\"\>", "m6", "m6", "m6", "m6", "1", "m6", "x", "m6", "1",
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>"},
{"\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "1",
"m6", "m6", "m6", "1", "m6", "1", "m6", "1", "1",
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>"},
{"\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "m6",
"m6", "m6", "1", "m6", "1", "m6", "1", "1", "1",
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>"},
{"\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "1", "m6", "m6",
"1", "m6", "1", "m6", "1", "1", "1", "1",
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>"},
{"\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "m6", "m6", "1",
"m6", "1", "m6", "1", "1", "1", "1", "1",
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>"},
{"\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "1", "m6", "1", "m6", "1", "m6",
"1", "1", "1", "1", "1", "1",
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>"},
{"\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "m6", "1", "m6", "1", "m6", "1",
"1", "1", "1", "1", "1", "1",
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>"},
{"\<\".\"\>", "\<\".\"\>", "1", "1", "m6", "1", "m6", "1", "1", "1", "1",
"1", "1", "1", "1",
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>"},
{"\<\".\"\>", "\<\".\"\>", "1", "m6", "1", "m6", "1", "1", "1", "1", "1",
"1", "1", "1", "1",
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>"},
{"\<\".\"\>", "\<\".\"\>", "m6", "1", "m6", "1", "1", "1", "1", "1", "1",
"1", "1", "1", "1",
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>"},
{"\<\".\"\>", "1", "1", "m6", "1", "1", "1", "1", "1", "1", "1", "1",
"1", "1", "1",
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>"},
{"\<\".\"\>", "1", "m6", "1", "1", "1", "1", "1", "1", "1", "1", "1",
"1", "1", "1",
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>"},
{"\<\".\"\>", "m6", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1",
"1", "1", "1",
"1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>"},
{"1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1",
"1", "1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", \
"\<\".\"\>"},
{"1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1",
"1", "1", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", "\<\".\"\>", \
"\<\".\"\>"}
},
GridBoxAlignment->{
"Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
"RowsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.7]},
Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
Offset[0.2], {
Offset[0.4]},
Offset[0.2]}, "RowsIndexed" -> {}}],
Function[BoxForm`e$,
TableForm[BoxForm`e$, TableSpacing -> 1]]],
StripOnInput->False,
FontSize->Small]], "Output",
CellChangeTimes->{3.3933412903653903`*^9}]
}, {2}]],
Cell[TextData[{
ButtonBox["\[FilledLeftTriangle]\[ThickSpace]\[ThickSpace]\[ThickSpace]",
BaseStyle->"SlidePreviousNextLink",
ButtonFunction:>FrontEndExecute[{
FrontEndToken[
FrontEnd`ButtonNotebook[], "ScrollPagePrevious"]}],
ButtonNote->FEPrivate`FrontEndResource[
"FEStrings", "SlideshowPrevSlideText"],
ButtonFrame->"None"],
"\[ThickSpace]\[ThickSpace]|\[ThickSpace]\[ThickSpace]",
ButtonBox["\[ThickSpace]\[ThickSpace]\[ThickSpace]\[FilledRightTriangle]",
BaseStyle->"SlidePreviousNextLink",
ButtonFunction:>FrontEndExecute[{
FrontEndToken[
FrontEnd`ButtonNotebook[], "ScrollPageNext"]}],
ButtonNote->FEPrivate`FrontEndResource[
"FEStrings", "SlideshowNextSlideText"],
ButtonFrame->"None"]
}], "PreviousNext"]
}, Open ]]
}, Open ]]
}, Open ]],
Cell[CellGroupData[{
Cell["", "SlideShowNavigationBar",
CellTags->"SlideShowHeader"],
Cell[CellGroupData[{
Cell["Binary operations", "Section",
CellChangeTimes->{{3.393046652640625*^9, 3.393046661078125*^9}, {
3.393211664203125*^9, 3.393211676328125*^9}}],
Cell[TextData[{
"16 states: ",
Cell[BoxData[
StyleBox[
RowBox[{
RowBox[{"particles", ":",
RowBox[{"[", "base_", "]"}]}], "=",
RowBox[{"2", "+",
RowBox[{"5", " ", "base"}], "+",
SuperscriptBox["base", "base"]}]}],
FontSize->14]], "Input",
CellChangeTimes->{{3.39179569603125*^9, 3.3917956961875*^9}},
FontSize->16],
"\nSteps: ",
StyleBox["radiusSteps[r_] := 2*Ceiling[Length[input2]/r] + \
Floor[Length[input2]/r] + 1", "Input",
FontSize->14],
"\nInput at the right side is entered backward.\nPerforms computation at \
maximal speed."
}], "Text",
CellChangeTimes->{{3.39321316571875*^9, 3.393213215734375*^9}, {
3.393213252328125*^9, 3.393213282578125*^9}, {3.39321333734375*^9,
3.393213385453125*^9}, {3.39321355346875*^9, 3.3932136003125*^9}, {
3.3932137049375*^9, 3.393213730828125*^9}}],
Cell[BoxData[{
RowBox[{
RowBox[{"particles", "[", "base_", "]"}], ":=",
RowBox[{"2", "+",
RowBox[{"5", " ", "base"}], "+",
SuperscriptBox["base", "base"]}]}], "\n",
RowBox[{
RowBox[{"numbPart", "=",
RowBox[{"Table", "[",
RowBox[{
RowBox[{"particles", "[", "i", "]"}], ",",
RowBox[{"{",
RowBox[{"i", ",", "2", ",", "10"}], "}"}]}], "]"}]}], ";"}], "\n",
RowBox[{
RowBox[{"sizeInput", "=",
RowBox[{"Ceiling", "[",
RowBox[{
RowBox[{"Table", "[",
RowBox[{
RowBox[{"Log", "[",
RowBox[{"i", ",", "1000000000"}], "]"}], ",",
RowBox[{"{",
RowBox[{"i", ",", "2", ",", "10"}], "}"}]}], "]"}], "//", "N"}],
"]"}]}], ";"}], "\n",
RowBox[{"TableForm", "[",
RowBox[{
RowBox[{"Transpose", "[",
RowBox[{"{",
RowBox[{
RowBox[{"Table", "[",
RowBox[{"i", ",",
RowBox[{"{",
RowBox[{"i", ",", "2", ",", "10"}], "}"}]}], "]"}], ",", "numbPart",
",",
RowBox[{"3", " ", "sizeInput"}]}], "}"}], "]"}], ",",
RowBox[{"TableSpacing", "\[Rule]", "2"}], ",",
RowBox[{"TableHeadings", "\[Rule]",
RowBox[{"{",
RowBox[{"None", ",",
RowBox[{"{",
RowBox[{"\"\\"", ",", "\"\\"", ",", "\"\\""}],
"}"}]}], "}"}]}]}], "]"}]}], "Input",
CellChangeTimes->{{3.39179569603125*^9, 3.3917956961875*^9}, {
3.393213812125*^9, 3.39321382146875*^9}, {3.393213875578125*^9,
3.39321395828125*^9}, {3.3932139909375*^9, 3.393214035171875*^9}, {
3.393378370704299*^9, 3.3933783724668336`*^9}, {3.3933787176131296`*^9,
3.393378756789462*^9}, {3.3933788057899218`*^9, 3.3933788400191407`*^9}, {
3.393378879706208*^9, 3.393378880607504*^9}},
FontSize->12],
Cell[CellGroupData[{
Cell[TextData[StyleBox["Addition",
FontColor->RGBColor[
0.9714045929655909, 0.6775158312352179, 0.07415884641794461]]], "Subsection",\
CellChangeTimes->{
3.3824524252213373`*^9, {3.39303943990625*^9, 3.393039450140625*^9}, {
3.39304107571875*^9, 3.39304108265625*^9}, {3.393211691703125*^9,
3.39321169309375*^9}}],
Cell[BoxData[{
RowBox[{
RowBox[{"binaryAddition",
StyleBox["[",
FormatType->StandardForm],
StyleBox[
RowBox[{"{",
RowBox[{"a_", ",", " ", "b_", ",", " ", "c_"}], "}"}],
FormatType->StandardForm],
StyleBox["]",
FormatType->StandardForm]}],
StyleBox[" ",
FormatType->StandardForm],
StyleBox[":=",
FormatType->StandardForm],
StyleBox["\[IndentingNewLine]",
FormatType->StandardForm],
StyleBox[
RowBox[{"Switch", "[",
RowBox[{
RowBox[{"{",
RowBox[{"a", ",", " ", "b", ",", " ", "c"}], "}"}], ",",
RowBox[{"{",
RowBox[{"a0", ",", "0", ",", "0"}], "}"}], ",", "aa", ",",
RowBox[{"{",
RowBox[{"a1", ",", "0", ",", "0"}], "}"}], ",", "aa", ",",
RowBox[{"{",
RowBox[{"aa", ",", "i0", ",", "_"}], "}"}], ",", "a0", ",",
RowBox[{"{",
RowBox[{"aa", ",", "i1", ",", "_"}], "}"}], ",", "a1", ",",
RowBox[{"{",
RowBox[{"a0", ",", "i0", ",", "_"}], "}"}], ",", "a0", ",",
RowBox[{"{",
RowBox[{"a0", ",", "i1", ",", "_"}], "}"}], ",", "a1", ",",
RowBox[{"{",
RowBox[{"a1", ",", "i0", ",", "_"}], "}"}], ",", "a0", ",",
RowBox[{"{",
RowBox[{"a1", ",", "i1", ",", "_"}], "}"}], ",", "a1", ",",
RowBox[{"{",
RowBox[{"_", ",", "0", ",", "a0"}], "}"}], ",", "a0", ",",
RowBox[{"{",
RowBox[{"_", ",", "0", ",", "a1"}], "}"}], ",", "a1", ",",
RowBox[{"{",
RowBox[{"_", ",", "0", ",", "c0"}], "}"}], ",", "i1", ",",
RowBox[{"{",
RowBox[{"_", ",", "0", ",", "c1"}], "}"}], ",", "i1", ",",
RowBox[{"{",
RowBox[{"_", ",", "0", ",", "p0"}], "}"}], ",", "o0", ",",
RowBox[{"{",
RowBox[{"_", ",", "0", ",", "p1"}], "}"}], ",", "o0", ",",
RowBox[{"{",
RowBox[{"_", ",", "0", ",", "q0"}], "}"}], ",", "o1", ",",
RowBox[{"{",
RowBox[{"_", ",", "0", ",", "q1"}], "}"}], ",", "o1", ",",
RowBox[{"{",
RowBox[{"_", ",", "0", ",", "aa"}], "}"}], ",", "aa", ",",
RowBox[{"{",
RowBox[{"_", ",", "i0", ",", "a0"}], "}"}], ",", "o0", ",",
RowBox[{"{",
RowBox[{"_", ",", "i0", ",", "a1"}], "}"}], ",", "o1", ",",
RowBox[{"{",
RowBox[{"_", ",", "i1", ",", "a0"}], "}"}], ",", "o1", ",",
RowBox[{"{",
RowBox[{"_", ",", "i1", ",", "a1"}], "}"}], ",", "c0", ",",
RowBox[{"{",
RowBox[{"_", ",", "i0", ",", "c0"}], "}"}], ",", "i1", ",",
RowBox[{"{",
RowBox[{"_", ",", "i1", ",", "c0"}], "}"}], ",", "c1", ",",
RowBox[{"{",
RowBox[{"_", ",", "i0", ",", "c1"}], "}"}], ",", "i1", ",",
RowBox[{"{",
RowBox[{"_", ",", "i1", ",", "c1"}], "}"}], ",", "c1", ",",
RowBox[{"{",
RowBox[{"_", ",", "i0", ",", "p0"}], "}"}], ",", "o0", ",",
RowBox[{"{",
RowBox[{"_", ",", "i0", ",", "p1"}], "}"}], ",", "o0", ",",
RowBox[{"{",
RowBox[{"_", ",", "i1", ",", "p0"}], "}"}], ",", "o1", ",",
RowBox[{"{",
RowBox[{"_", ",", "i1", ",", "p1"}], "}"}], ",", "o1", ",",
RowBox[{"{",
RowBox[{"_", ",", "i0", ",", "q0"}], "}"}], ",", "o1", ",",
RowBox[{"{",
RowBox[{"_", ",", "i0", ",", "q1"}], "}"}], ",", "o1", ",",
RowBox[{"{",
RowBox[{"_", ",", "i1", ",", "q0"}], "}"}], ",", "c0", ",",
RowBox[{"{",
RowBox[{"_", ",", "i1", ",", "q1"}], "}"}], ",", "c0", ",",
RowBox[{"{",
RowBox[{"_", ",", "o0", ",", "aa"}], "}"}], ",", "h0", ",",
RowBox[{"{",
RowBox[{"_", ",", "o1", ",", "aa"}], "}"}], ",", "h1", ",",
RowBox[{"{",
RowBox[{"_", ",", "i0", ",", "h0"}], "}"}], ",", "h0", ",",
RowBox[{"{",
RowBox[{"_", ",", "i0", ",", "h1"}], "}"}], ",", "h0", ",",
RowBox[{"{",
RowBox[{"_", ",", "i1", ",", "h0"}], "}"}], ",", "h1", ",",
RowBox[{"{",
RowBox[{"_", ",", "i1", ",", "h1"}], "}"}], ",", "h1", ",",
RowBox[{"{",
RowBox[{"_", ",", "o0", ",", "h0"}], "}"}], ",", "h0", ",",
RowBox[{"{",
RowBox[{"_", ",", "o0", ",", "h1"}], "}"}], ",", "h0", ",",
RowBox[{"{",
RowBox[{"_", ",", "o1", ",", "h0"}], "}"}], ",", "h1", ",",
RowBox[{"{",
RowBox[{"_", ",", "o1", ",", "h1"}], "}"}], ",", "h1", ",",
RowBox[{"{",
RowBox[{"_", ",", "o0", ",", "a0"}], "}"}], ",", "p0", ",",
RowBox[{"{",
RowBox[{"_", ",", "o0", ",", "a1"}], "}"}], ",", "q0", ",",
RowBox[{"{",
RowBox[{"_", ",", "o1", ",", "a0"}], "}"}], ",", "p1", ",",
RowBox[{"{",
RowBox[{"_", ",", "o1", ",", "a1"}], "}"}], ",", "q1", ",",
RowBox[{"{",
RowBox[{"_", ",", "o0", ",", "p0"}], "}"}], ",", "p0", ",",
RowBox[{"{",
RowBox[{"_", ",", "o0", ",", "p1"}], "}"}], ",", "p0", ",",
RowBox[{"{",
RowBox[{"_", ",", "o0", ",", "q0"}], "}"}], ",", "q0", ",",
RowBox[{"{",
RowBox[{"_", ",", "o0", ",", "q1"}], "}"}], ",", "q0", ",",
RowBox[{"{",
RowBox[{"_", ",", "o1", ",", "p0"}], "}"}], ",", "p1", ",",
RowBox[{"{",
RowBox[{"_", ",", "o1", ",", "p1"}], "}"}], ",", "p1", ",",
RowBox[{"{",
RowBox[{"_", ",", "o1", ",", "q0"}], "}"}], ",", "q1", ",",
RowBox[{"{",
RowBox[{"_", ",", "o1", ",", "q1"}], "}"}], ",", "q1", ",",
RowBox[{"{",
RowBox[{"_", ",", "i0", ",", "_"}], "}"}], ",", "i0", ",",
RowBox[{"{",
RowBox[{"_", ",", "i1", ",", "_"}], "}"}], ",", "i1", ",",
RowBox[{"{",
RowBox[{"_", ",", "o0", ",", "_"}], "}"}], ",", "o0", ",",
RowBox[{"{",
RowBox[{"_", ",", "o1", ",", "_"}], "}"}], ",", "o1", ",",
RowBox[{"{",
RowBox[{"_", ",", "p0", ",", "_"}], "}"}], ",", "o0", ",",
RowBox[{"{",
RowBox[{"_", ",", "p1", ",", "_"}], "}"}], ",", "o1", ",",
RowBox[{"{",
RowBox[{"_", ",", "q0", ",", "_"}], "}"}], ",", "o0", ",",
RowBox[{"{",
RowBox[{"_", ",", "q1", ",", "_"}], "}"}], ",", "o1", ",",
RowBox[{"{",
RowBox[{"_", ",", "c0", ",", "_"}], "}"}], ",", "o0", ",",
RowBox[{"{",
RowBox[{"_", ",", "c1", ",", "_"}], "}"}], ",", "i0", ",",
RowBox[{"{",
RowBox[{"_", ",", "h0", ",", "_"}], "}"}], ",", "i0", ",",
RowBox[{"{",
RowBox[{"_", ",", "h1", ",", "_"}], "}"}], ",", "i1", ",",
RowBox[{"{",
RowBox[{"_", ",", "_", ",", "_"}], "}"}], ",", "0"}], "]"}],
FormatType->StandardForm]}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"BAinitCond", "[",
RowBox[{"inp1_", ",", "inp2_"}], "]"}], ":=",
RowBox[{"Join", "[",
RowBox[{
RowBox[{
RowBox[{"IntegerDigits", "[",
RowBox[{"inp1", ",", "2"}], "]"}], "/.",
RowBox[{"{",
RowBox[{
RowBox[{"0", "\[Rule]", "i0"}], ",",
RowBox[{"1", "\[Rule]", "i1"}]}], "}"}]}], ",",
RowBox[{"{", "aa", "}"}], ",",
RowBox[{"Reverse", "[",
RowBox[{
RowBox[{"IntegerDigits", "[",
RowBox[{"inp2", ",", "2"}], "]"}], "/.",
RowBox[{"{",
RowBox[{
RowBox[{"0", "\[Rule]", "i0"}], ",",
RowBox[{"1", "\[Rule]", "i1"}]}], "}"}]}], "]"}]}], "]"}]}], "\n",
RowBox[{"Style", "[",
RowBox[{
RowBox[{"Manipulate", "[",
RowBox[{
RowBox[{
RowBox[{"BAinit", "=",
RowBox[{"BAinitCond", "[",
RowBox[{"i", ",", "j"}], "]"}]}], ";", "\[IndentingNewLine]",
RowBox[{"TableForm", "[",
RowBox[{
RowBox[{
RowBox[{"CellularAutomaton", "[",
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{
RowBox[{"binaryAddition", "[", "#", "]"}], " ", "&"}], ",", " ",
RowBox[{"{", "}"}], ",", " ", "1"}], "}"}], ",", " ",
RowBox[{"{",
RowBox[{"BAinit", ",", " ", "0"}], "}"}], ",", "40"}], "]"}], "/.",
RowBox[{"{", " ",
RowBox[{
RowBox[{"0", " ", "\[Rule]", "\"\<.\>\""}], ",",
RowBox[{"i0", "\[Rule]", "0"}], ",",
RowBox[{"i1", "\[Rule]", "1"}], ",",
RowBox[{"aa", "\[Rule]",
RowBox[{"Style", "[",
RowBox[{"\"\\"", ",", "Red"}], "]"}]}], ",",
RowBox[{"a0", "\[Rule]",
RowBox[{"Style", "[",
RowBox[{"\"\\"", ",", "Red"}], "]"}]}], ",",
RowBox[{"a1", "\[Rule]",
RowBox[{"Style", "[",
RowBox[{"\"\\"", ",", "Red"}], "]"}]}], ",",
RowBox[{"p0", "\[Rule]",
RowBox[{"Style", "[",
RowBox[{"\"\\"", ",", "Blue"}], "]"}]}], ",",
RowBox[{"p1", "\[Rule]",
RowBox[{"Style", "[",
RowBox[{"\"\\"", ",", "Blue"}], "]"}]}], ",",
RowBox[{"q0", "\[Rule]",
RowBox[{"Style", "[",
RowBox[{"\"\\"", ",", "Magenta"}], "]"}]}], ",",
RowBox[{"q1", "\[Rule]",
RowBox[{"Style", "[",
RowBox[{"\"\\"", ",", "Magenta"}], "]"}]}], ",",
RowBox[{"c0", "\[Rule]",
RowBox[{"Style", "[",
RowBox[{"\"\\"", ",", "Purple"}], "]"}]}], ",",
RowBox[{"c1", "\[Rule]",
RowBox[{"Style", "[",
RowBox[{"\"\\"", ",", "Purple"}], "]"}]}], ",",
RowBox[{"o0", "\[Rule]",
RowBox[{"Style", "[",
RowBox[{"\"\\"", ",", "Green"}], "]"}]}], ",",
RowBox[{"o1", "\[Rule]",
RowBox[{"Style", "[",
RowBox[{"\"\\"", ",", "Green"}], "]"}]}], ",",
RowBox[{"h0", "\[Rule]",
RowBox[{"Style", "[",
RowBox[{"\"\\"", ",", "Orange"}], "]"}]}], ",",
RowBox[{"h1", "\[Rule]",
RowBox[{"Style", "[",
RowBox[{"\"\\"", ",", "Orange"}], "]"}]}]}], "}"}]}], ",",
" ",
RowBox[{"TableSpacing", "\[Rule]", "1"}]}], "]"}]}], ",",
RowBox[{"{",
RowBox[{"i", ",", "1000", ",", "2000", ",", "10"}], "}"}], ",",
RowBox[{"{",
RowBox[{"j", ",", "3000", ",", "4000", ",", "10"}], "}"}]}], "]"}], ",",
"Small"}], "]"}]}], "Input",
CellChangeTimes->{{3.393130731921875*^9, 3.393130848625*^9}, 3.3931309245*^9,
3.393131144734375*^9, {3.393131388046875*^9, 3.39313152696875*^9},
3.393378581547477*^9},
FontSize->12]
}, Open ]],
Cell[CellGroupData[{
Cell[TextData[StyleBox["Subtraction",
FontColor->RGBColor[
0.9714045929655909, 0.6775158312352179, 0.07415884641794461]]], "Subsection",\
CellChangeTimes->{
3.3824524252213373`*^9, {3.39303943990625*^9, 3.393039450140625*^9}, {
3.39304107571875*^9, 3.39304108265625*^9}, {3.393211691703125*^9,
3.393211712296875*^9}}],
Cell[BoxData[{
RowBox[{
RowBox[{"binarySubtraction",
StyleBox["[",
FormatType->StandardForm],
StyleBox[
RowBox[{"{",
RowBox[{"a_", ",", " ", "b_", ",", " ", "c_"}], "}"}],
FormatType->StandardForm],
StyleBox["]",
FormatType->StandardForm]}],
StyleBox[" ",
FormatType->StandardForm],
StyleBox[":=",
FormatType->StandardForm],
StyleBox["\[IndentingNewLine]",
FormatType->StandardForm],
StyleBox[
RowBox[{"Switch", "[",
RowBox[{
RowBox[{"{",
RowBox[{"a", ",", " ", "b", ",", " ", "c"}], "}"}], ",",
RowBox[{"{",
RowBox[{"s0", ",", "0", ",", "0"}], "}"}], ",", "ss", ",",
RowBox[{"{",
RowBox[{"s1", ",", "0", ",", "0"}], "}"}], ",", "ss", ",",
RowBox[{"{",
RowBox[{"ss", ",", "i0", ",", "_"}], "}"}], ",", "s0", ",",
RowBox[{"{",
RowBox[{"ss", ",", "i1", ",", "_"}], "}"}], ",", "s1", ",",
RowBox[{"{",
RowBox[{"s0", ",", "i0", ",", "_"}], "}"}], ",", "s0", ",",
RowBox[{"{",
RowBox[{"s0", ",", "i1", ",", "_"}], "}"}], ",", "s1", ",",
RowBox[{"{",
RowBox[{"s1", ",", "i0", ",", "_"}], "}"}], ",", "s0", ",",
RowBox[{"{",
RowBox[{"s1", ",", "i1", ",", "_"}], "}"}], ",", "s1", ",",
RowBox[{"{",
RowBox[{"_", ",", "0", ",", "s0"}], "}"}], ",", "s0", ",",
RowBox[{"{",
RowBox[{"_", ",", "0", ",", "s1"}], "}"}], ",", "s1", ",",
RowBox[{"{",
RowBox[{"_", ",", "i0", ",", "s0"}], "}"}], ",", "o0", ",",
RowBox[{"{",
RowBox[{"_", ",", "i0", ",", "s1"}], "}"}], ",", "c0", ",",
RowBox[{"{",
RowBox[{"_", ",", "i1", ",", "s0"}], "}"}], ",", "o1", ",",
RowBox[{"{",
RowBox[{"_", ",", "i1", ",", "s1"}], "}"}], ",", "o0", ",",
RowBox[{"{",
RowBox[{"_", ",", "i0", ",", "p0"}], "}"}], ",", "o0", ",",
RowBox[{"{",
RowBox[{"_", ",", "i0", ",", "p1"}], "}"}], ",", "o0", ",",
RowBox[{"{",
RowBox[{"_", ",", "i0", ",", "q0"}], "}"}], ",", "c0", ",",
RowBox[{"{",
RowBox[{"_", ",", "i0", ",", "q1"}], "}"}], ",", "c0", ",",
RowBox[{"{",
RowBox[{"_", ",", "i1", ",", "p0"}], "}"}], ",", "o1", ",",
RowBox[{"{",
RowBox[{"_", ",", "i1", ",", "p1"}], "}"}], ",", "o1", ",",
RowBox[{"{",
RowBox[{"_", ",", "i1", ",", "q0"}], "}"}], ",", "o0", ",",
RowBox[{"{",
RowBox[{"_", ",", "i1", ",", "q1"}], "}"}], ",", "o0", ",",
RowBox[{"{",
RowBox[{"_", ",", "o0", ",", "s0"}], "}"}], ",", "p0", ",",
RowBox[{"{",
RowBox[{"_", ",", "o0", ",", "s1"}], "}"}], ",", "q0", ",",
RowBox[{"{",
RowBox[{"_", ",", "o1", ",", "s0"}], "}"}], ",", "p1", ",",
RowBox[{"{",
RowBox[{"_", ",", "o1", ",", "s1"}], "}"}], ",", "q1", ",",
RowBox[{"{",
RowBox[{"_", ",", "o0", ",", "p0"}], "}"}], ",", "p0", ",",
RowBox[{"{",
RowBox[{"_", ",", "o0", ",", "p1"}], "}"}], ",", "p0", ",",
RowBox[{"{",
RowBox[{"_", ",", "o0", ",", "q0"}], "}"}], ",", "q0", ",",
RowBox[{"{",
RowBox[{"_", ",", "o0", ",", "q1"}], "}"}], ",", "q0", ",",
RowBox[{"{",
RowBox[{"_", ",", "o1", ",", "p0"}], "}"}], ",", "p1", ",",
RowBox[{"{",
RowBox[{"_", ",", "o1", ",", "p1"}], "}"}], ",", "p1", ",",
RowBox[{"{",
RowBox[{"_", ",", "o1", ",", "q0"}], "}"}], ",", "q1", ",",
RowBox[{"{",
RowBox[{"_", ",", "o1", ",", "q1"}], "}"}], ",", "q1", ",",
RowBox[{"{",
RowBox[{"_", ",", "i0", ",", "c0"}], "}"}], ",", "c1", ",",
RowBox[{"{",
RowBox[{"_", ",", "i1", ",", "c0"}], "}"}], ",", "i0", ",",
RowBox[{"{",
RowBox[{"_", ",", "i0", ",", "c1"}], "}"}], ",", "c1", ",",
RowBox[{"{",
RowBox[{"_", ",", "i1", ",", "c1"}], "}"}], ",", "i0", ",",
RowBox[{"{",
RowBox[{"_", ",", "o0", ",", "ss"}], "}"}], ",", "h0", ",",
RowBox[{"{",
RowBox[{"_", ",", "o1", ",", "ss"}], "}"}], ",", "h1", ",",
RowBox[{"{",
RowBox[{"_", ",", "i0", ",", "h0"}], "}"}], ",", "h0", ",",
RowBox[{"{",
RowBox[{"_", ",", "i0", ",", "h1"}], "}"}], ",", "h0", ",",
RowBox[{"{",
RowBox[{"_", ",", "i1", ",", "h0"}], "}"}], ",", "h1", ",",
RowBox[{"{",
RowBox[{"_", ",", "i1", ",", "h1"}], "}"}], ",", "h1", ",",
RowBox[{"{",
RowBox[{"_", ",", "o0", ",", "h0"}], "}"}], ",", "h0", ",",
RowBox[{"{",
RowBox[{"_", ",", "o0", ",", "h1"}], "}"}], ",", "h0", ",",
RowBox[{"{",
RowBox[{"_", ",", "o1", ",", "h0"}], "}"}], ",", "h1", ",",
RowBox[{"{",
RowBox[{"_", ",", "o1", ",", "h1"}], "}"}], ",", "h1", ",",
RowBox[{"{",
RowBox[{"_", ",", "0", ",", "ss"}], "}"}], ",", "ss", ",",
RowBox[{"{",
RowBox[{"_", ",", "i0", ",", "_"}], "}"}], ",", "i0", ",",
RowBox[{"{",
RowBox[{"_", ",", "i1", ",", "_"}], "}"}], ",", "i1", ",",
RowBox[{"{",
RowBox[{"_", ",", "o0", ",", "_"}], "}"}], ",", "o0", ",",
RowBox[{"{",
RowBox[{"_", ",", "o1", ",", "_"}], "}"}], ",", "o1", ",",
RowBox[{"{",
RowBox[{"_", ",", "p0", ",", "_"}], "}"}], ",", "o0", ",",
RowBox[{"{",
RowBox[{"_", ",", "p1", ",", "_"}], "}"}], ",", "o1", ",",
RowBox[{"{",
RowBox[{"_", ",", "q0", ",", "_"}], "}"}], ",", "o0", ",",
RowBox[{"{",
RowBox[{"_", ",", "q1", ",", "_"}], "}"}], ",", "o1", ",",
RowBox[{"{",
RowBox[{"_", ",", "c0", ",", "_"}], "}"}], ",", "o1", ",",
RowBox[{"{",
RowBox[{"_", ",", "c1", ",", "_"}], "}"}], ",", "i1", ",",
RowBox[{"{",
RowBox[{"_", ",", "h0", ",", "_"}], "}"}], ",", "i0", ",",
RowBox[{"{",
RowBox[{"_", ",", "h1", ",", "_"}], "}"}], ",", "i1", ",",
RowBox[{"{",
RowBox[{"_", ",", "_", ",", "_"}], "}"}], ",", "0"}], "]"}],
FormatType->StandardForm]}], "\n",
RowBox[{
RowBox[{"BSinitCond", "[",
RowBox[{"inp3_", ",", "inp4_"}], "]"}], ":=",
RowBox[{"Join", "[",
RowBox[{
RowBox[{
RowBox[{"IntegerDigits", "[",
RowBox[{"inp3", ",", "2"}], "]"}], "/.",
RowBox[{"{",
RowBox[{
RowBox[{"0", "\[Rule]", "i0"}], ",",
RowBox[{"1", "\[Rule]", "i1"}]}], "}"}]}], ",",
RowBox[{"{", "ss", "}"}], ",",
RowBox[{"Reverse", "[",
RowBox[{
RowBox[{"IntegerDigits", "[",
RowBox[{"inp4", ",", "2"}], "]"}], "/.",
RowBox[{"{",
RowBox[{
RowBox[{"0", "\[Rule]", "i0"}], ",",
RowBox[{"1", "\[Rule]", "i1"}]}], "}"}]}], "]"}]}], "]"}]}], "\n",
RowBox[{"Style", "[",
RowBox[{
RowBox[{"Manipulate", "[",
RowBox[{
RowBox[{
RowBox[{"BSinit", "=",
RowBox[{"BSinitCond", "[",
RowBox[{"i", ",", "j"}], "]"}]}], ";", "\[IndentingNewLine]",
RowBox[{"TableForm", "[",
RowBox[{
RowBox[{
RowBox[{"CellularAutomaton", "[",
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{
RowBox[{"binarySubtraction", "[", "#", "]"}], " ", "&"}], ",",
" ",
RowBox[{"{", "}"}], ",", " ", "1"}], "}"}], ",", " ",
RowBox[{"{",
RowBox[{"BSinit", ",", " ", "0"}], "}"}], ",", "40"}], "]"}], "/.",
RowBox[{"{", " ",
RowBox[{
RowBox[{"0", " ", "\[Rule]", "\"\<.\>\""}], ",",
RowBox[{"i0", "\[Rule]", "0"}], ",",
RowBox[{"i1", "\[Rule]", "1"}], ",",
RowBox[{"ss", "\[Rule]",
RowBox[{"Style", "[",
RowBox[{"\"\\"", ",", "Red"}], "]"}]}], ",",
RowBox[{"s0", "\[Rule]",
RowBox[{"Style", "[",
RowBox[{"\"\\"", ",", "Red"}], "]"}]}], ",",
RowBox[{"s1", "\[Rule]",
RowBox[{"Style", "[",
RowBox[{"\"\\"", ",", "Red"}], "]"}]}], ",",
RowBox[{"p0", "\[Rule]",
RowBox[{"Style", "[",
RowBox[{"\"\\"", ",", "Blue"}], "]"}]}], ",",
RowBox[{"p1", "\[Rule]",
RowBox[{"Style", "[",
RowBox[{"\"\\"", ",", "Blue"}], "]"}]}], ",",
RowBox[{"q0", "\[Rule]",
RowBox[{"Style", "[",
RowBox[{"\"\\"", ",", "Magenta"}], "]"}]}], ",",
RowBox[{"q1", "\[Rule]",
RowBox[{"Style", "[",
RowBox[{"\"\\"", ",", "Magenta"}], "]"}]}], ",",
RowBox[{"c0", "\[Rule]",
RowBox[{"Style", "[",
RowBox[{"\"\\"", ",", "Purple"}], "]"}]}], ",",
RowBox[{"c1", "\[Rule]",
RowBox[{"Style", "[",
RowBox[{"\"\\"", ",", "Purple"}], "]"}]}], ",",
RowBox[{"o0", "\[Rule]",
RowBox[{"Style", "[",
RowBox[{"\"\\"", ",", "Green"}], "]"}]}], ",",
RowBox[{"o1", "\[Rule]",
RowBox[{"Style", "[",
RowBox[{"\"\\"", ",", "Green"}], "]"}]}], ",",
RowBox[{"h0", "\[Rule]",
RowBox[{"Style", "[",
RowBox[{"\"\\"", ",", "Orange"}], "]"}]}], ",",
RowBox[{"h1", "\[Rule]",
RowBox[{"Style", "[",
RowBox[{"\"\\"", ",", "Orange"}], "]"}]}]}], "}"}]}], ",",
" ",
RowBox[{"TableSpacing", "\[Rule]", "1"}]}], "]"}]}], ",",
RowBox[{"{",
RowBox[{"i", ",", "3000", ",", "4000", ",", "10"}], "}"}], ",",
RowBox[{"{",
RowBox[{"j", ",", "1000", ",", "2000", ",", "10"}], "}"}]}], "]"}], ",",
"Small"}], "]"}]}], "Input",
CellChangeTimes->{{3.393132081640625*^9, 3.393132183640625*^9}, {
3.393132231359375*^9, 3.393132256515625*^9}, 3.3933785712626877`*^9},
FontSize->12],
Cell[TextData[{
ButtonBox["\[FilledLeftTriangle]\[ThickSpace]\[ThickSpace]\[ThickSpace]",
BaseStyle->"SlidePreviousNextLink",
ButtonFunction:>FrontEndExecute[{
FrontEndToken[
FrontEnd`ButtonNotebook[], "ScrollPagePrevious"]}],
ButtonNote->FEPrivate`FrontEndResource[
"FEStrings", "SlideshowPrevSlideText"],
ButtonFrame->"None"],
"\[ThickSpace]\[ThickSpace]|\[ThickSpace]\[ThickSpace]",
ButtonBox["\[ThickSpace]\[ThickSpace]\[ThickSpace]\[FilledRightTriangle]",
BaseStyle->"SlidePreviousNextLink",
ButtonFunction:>FrontEndExecute[{
FrontEndToken[
FrontEnd`ButtonNotebook[], "ScrollPageNext"]}],
ButtonNote->FEPrivate`FrontEndResource[
"FEStrings", "SlideshowNextSlideText"],
ButtonFrame->"None"]
}], "PreviousNext"]
}, Open ]]
}, Open ]]
}, Open ]],
Cell[CellGroupData[{
Cell["", "SlideShowNavigationBar",
CellTags->"SlideShowHeader"],
Cell[CellGroupData[{
Cell["Some search results", "Section",
CellChangeTimes->{{3.393042031921875*^9, 3.3930420421875*^9}}],
Cell[CellGroupData[{
Cell[TextData[StyleBox["The method",
FontColor->RGBColor[
0.9714045929655909, 0.6775158312352179, 0.07415884641794461]]], "Subsection",\
CellChangeTimes->{
3.3824524252213373`*^9, {3.39303943990625*^9, 3.393039450140625*^9}, {
3.39304107571875*^9, 3.3930411009375*^9}, {3.393208508046875*^9,
3.393208512921875*^9}}],
Cell[TextData[{
"CA rule spaces of ",
StyleBox["k \[GreaterEqual] 3",
FontSlant->"Italic"],
" can be unmanageable for exhaustive searches. We therefore tried to devise \
a method to narrow down the rule space. For our example, searches of \
subtraction rules where made with ",
StyleBox["k = 3 ",
FontSlant->"Italic"],
"and ",
StyleBox["r = 1",
FontSlant->"Italic"],
", where the size of the rule is given by ",
Cell[BoxData[
FormBox[
SuperscriptBox["k",
RowBox[{" ",
RowBox[{
RowBox[{"2", " ", "r"}], " ", "+", " ", "1"}]}]], TraditionalForm]]],
", which gives us a rule with 27 \"bits\" of size. The space we need to \
search contains ",
Cell[BoxData[
FormBox[
SuperscriptBox["k", "27"], TraditionalForm]]],
"rules (over 7 x ",
Cell[BoxData[
FormBox[
SuperscriptBox["10", "12"], TraditionalForm]]],
"). Therefore, \"freezing\" as many of these bits as we can exponentially \
decreases the rule space."
}], "Text",
CellChangeTimes->{{3.39318995278125*^9, 3.39319008303125*^9}, {
3.3931901198125*^9, 3.39319013409375*^9}, {3.39319018428125*^9,
3.39319021*^9}, {3.3931903076875*^9, 3.393190349421875*^9}, {3.393190457*^9,
3.3931904584375*^9}, {3.393207761734375*^9, 3.393207803546875*^9}, {
3.3933417192320704`*^9, 3.393341770696072*^9}}],
Cell[TextData[{
"1. First we fix any initial assumptions as, for example, \"background and \
input don't interact\", which is the same as fixing rule 204 of the ECA in a \
rule space where ",
StyleBox["k = 3",
FontSlant->"Italic"],
"."
}], "Text",
CellChangeTimes->{{3.3931892288125*^9, 3.393189561359375*^9}, {
3.393189616578125*^9, 3.393189620734375*^9}, {3.393189929171875*^9,
3.3931899315*^9}, {3.393190362234375*^9, 3.39319041759375*^9}, {
3.39320801565625*^9, 3.393208038671875*^9}}],
Cell[GraphicsData["PostScript", "\<\
%!
%%Creator: Mathematica
%%AspectRatio: .125
%%ImageSize: 400 50
MathPictureStart
/Mabs {
Mgmatrix idtransform
Mtmatrix dtransform
} bind def
/Mabsadd { Mabs
3 -1 roll add
3 1 roll add
exch } bind def
%% Graphics
%%IncludeResource: font Helvetica
%%IncludeFont: Helvetica
/Helvetica findfont 10 scalefont setfont
% Scaling calculations
0.0238095 0.119048 0.00297619 0.119048 [
[ 0 0 0 0 ]
[ 1 .125 0 0 ]
] MathScale
% Start of Graphics
1 setlinecap
1 setlinejoin
newpath
0 0 m
1 0 L
1 .125 L
0 .125 L
closepath
clip
newpath
% Start of sub-graphic
p
0.0238095 0.00297619 0.142857 0.122024 MathSubStart
%% Graphics
%%IncludeResource: font Helvetica
%%IncludeFont: Helvetica
/Helvetica findfont 10 scalefont setfont
% Scaling calculations
0.125 0.25 0.4375 0.25 [
[ 0 0 0 0 ]
[ 1 .8125 0 0 ]
] MathScale
% Start of Graphics
1 setlinecap
1 setlinejoin
newpath
0 0 m
1 0 L
1 .8125 L
0 .8125 L
closepath
clip
newpath
1 g
0 0 m
0 .8125 L
1 .8125 L
1 0 L
F
0 g
.125 .4375 m
.125 .6875 L
.375 .6875 L
.375 .4375 L
F
.375 .4375 m
.375 .6875 L
.625 .6875 L
.625 .4375 L
F
.625 .4375 m
.625 .6875 L
.875 .6875 L
.875 .4375 L
F
.15 g
.25 Mabswid
[ ] 0 setdash
.125 .4375 m
.875 .4375 L
.875 .6875 L
.125 .6875 L
.125 .4375 L
s
.375 .4375 m
.375 .6875 L
s
.625 .4375 m
.625 .6875 L
s
0 g
.375 .125 m
.375 .375 L
.625 .375 L
.625 .125 L
F
.15 g
.375 .125 m
.375 .375 L
.625 .375 L
.625 .125 L
.375 .125 L
s
MathSubEnd
P
% End of sub-graphic
0 g
.25 Mabswid
[ ] 0 setdash
.02381 .01488 m
.02381 .11012 L
s
% Start of sub-graphic
p
0.142857 0.00297619 0.261905 0.122024 MathSubStart
%% Graphics
%%IncludeResource: font Helvetica
%%IncludeFont: Helvetica
/Helvetica findfont 10 scalefont setfont
% Scaling calculations
0.125 0.25 0.4375 0.25 [
[ 0 0 0 0 ]
[ 1 .8125 0 0 ]
] MathScale
% Start of Graphics
1 setlinecap
1 setlinejoin
newpath
0 0 m
1 0 L
1 .8125 L
0 .8125 L
closepath
clip
newpath
1 g
0 0 m
0 .8125 L
1 .8125 L
1 0 L
F
0 g
.125 .4375 m
.125 .6875 L
.375 .6875 L
.375 .4375 L
F
.375 .4375 m
.375 .6875 L
.625 .6875 L
.625 .4375 L
F
1 g
.625 .4375 m
.625 .6875 L
.875 .6875 L
.875 .4375 L
F
.15 g
.25 Mabswid
[ ] 0 setdash
.125 .4375 m
.875 .4375 L
.875 .6875 L
.125 .6875 L
.125 .4375 L
s
.375 .4375 m
.375 .6875 L
s
.625 .4375 m
.625 .6875 L
s
0 g
.375 .125 m
.375 .375 L
.625 .375 L
.625 .125 L
F
.15 g
.375 .125 m
.375 .375 L
.625 .375 L
.625 .125 L
.375 .125 L
s
MathSubEnd
P
% End of sub-graphic
0 g
.25 Mabswid
[ ] 0 setdash
.14286 .01488 m
.14286 .11012 L
s
% Start of sub-graphic
p
0.261905 0.00297619 0.380952 0.122024 MathSubStart
%% Graphics
%%IncludeResource: font Helvetica
%%IncludeFont: Helvetica
/Helvetica findfont 10 scalefont setfont
% Scaling calculations
0.125 0.25 0.4375 0.25 [
[ 0 0 0 0 ]
[ 1 .8125 0 0 ]
] MathScale
% Start of Graphics
1 setlinecap
1 setlinejoin
newpath
0 0 m
1 0 L
1 .8125 L
0 .8125 L
closepath
clip
newpath
1 g
0 0 m
0 .8125 L
1 .8125 L
1 0 L
F
0 g
.125 .4375 m
.125 .6875 L
.375 .6875 L
.375 .4375 L
F
1 g
.375 .4375 m
.375 .6875 L
.625 .6875 L
.625 .4375 L
F
0 g
.625 .4375 m
.625 .6875 L
.875 .6875 L
.875 .4375 L
F
.15 g
.25 Mabswid
[ ] 0 setdash
.125 .4375 m
.875 .4375 L
.875 .6875 L
.125 .6875 L
.125 .4375 L
s
.375 .4375 m
.375 .6875 L
s
.625 .4375 m
.625 .6875 L
s
1 g
.375 .125 m
.375 .375 L
.625 .375 L
.625 .125 L
F
.15 g
.375 .125 m
.375 .375 L
.625 .375 L
.625 .125 L
.375 .125 L
s
MathSubEnd
P
% End of sub-graphic
0 g
.25 Mabswid
[ ] 0 setdash
.2619 .01488 m
.2619 .11012 L
s
% Start of sub-graphic
p
0.380952 0.00297619 0.5 0.122024 MathSubStart
%% Graphics
%%IncludeResource: font Helvetica
%%IncludeFont: Helvetica
/Helvetica findfont 10 scalefont setfont
% Scaling calculations
0.125 0.25 0.4375 0.25 [
[ 0 0 0 0 ]
[ 1 .8125 0 0 ]
] MathScale
% Start of Graphics
1 setlinecap
1 setlinejoin
newpath
0 0 m
1 0 L
1 .8125 L
0 .8125 L
closepath
clip
newpath
1 g
0 0 m
0 .8125 L
1 .8125 L
1 0 L
F
0 g
.125 .4375 m
.125 .6875 L
.375 .6875 L
.375 .4375 L
F
1 g
.375 .4375 m
.375 .6875 L
.625 .6875 L
.625 .4375 L
F
.625 .4375 m
.625 .6875 L
.875 .6875 L
.875 .4375 L
F
.15 g
.25 Mabswid
[ ] 0 setdash
.125 .4375 m
.875 .4375 L
.875 .6875 L
.125 .6875 L
.125 .4375 L
s
.375 .4375 m
.375 .6875 L
s
.625 .4375 m
.625 .6875 L
s
1 g
.375 .125 m
.375 .375 L
.625 .375 L
.625 .125 L
F
.15 g
.375 .125 m
.375 .375 L
.625 .375 L
.625 .125 L
.375 .125 L
s
MathSubEnd
P
% End of sub-graphic
0 g
.25 Mabswid
[ ] 0 setdash
.38095 .01488 m
.38095 .11012 L
s
% Start of sub-graphic
p
0.5 0.00297619 0.619048 0.122024 MathSubStart
%% Graphics
%%IncludeResource: font Helvetica
%%IncludeFont: Helvetica
/Helvetica findfont 10 scalefont setfont
% Scaling calculations
0.125 0.25 0.4375 0.25 [
[ 0 0 0 0 ]
[ 1 .8125 0 0 ]
] MathScale
% Start of Graphics
1 setlinecap
1 setlinejoin
newpath
0 0 m
1 0 L
1 .8125 L
0 .8125 L
closepath
clip
newpath
1 g
0 0 m
0 .8125 L
1 .8125 L
1 0 L
F
.125 .4375 m
.125 .6875 L
.375 .6875 L
.375 .4375 L
F
0 g
.375 .4375 m
.375 .6875 L
.625 .6875 L
.625 .4375 L
F
.625 .4375 m
.625 .6875 L
.875 .6875 L
.875 .4375 L
F
.15 g
.25 Mabswid
[ ] 0 setdash
.125 .4375 m
.875 .4375 L
.875 .6875 L
.125 .6875 L
.125 .4375 L
s
.375 .4375 m
.375 .6875 L
s
.625 .4375 m
.625 .6875 L
s
0 g
.375 .125 m
.375 .375 L
.625 .375 L
.625 .125 L
F
.15 g
.375 .125 m
.375 .375 L
.625 .375 L
.625 .125 L
.375 .125 L
s
MathSubEnd
P
% End of sub-graphic
0 g
.25 Mabswid
[ ] 0 setdash
.5 .01488 m
.5 .11012 L
s
% Start of sub-graphic
p
0.619048 0.00297619 0.738095 0.122024 MathSubStart
%% Graphics
%%IncludeResource: font Helvetica
%%IncludeFont: Helvetica
/Helvetica findfont 10 scalefont setfont
% Scaling calculations
0.125 0.25 0.4375 0.25 [
[ 0 0 0 0 ]
[ 1 .8125 0 0 ]
] MathScale
% Start of Graphics
1 setlinecap
1 setlinejoin
newpath
0 0 m
1 0 L
1 .8125 L
0 .8125 L
closepath
clip
newpath
1 g
0 0 m
0 .8125 L
1 .8125 L
1 0 L
F
.125 .4375 m
.125 .6875 L
.375 .6875 L
.375 .4375 L
F
0 g
.375 .4375 m
.375 .6875 L
.625 .6875 L
.625 .4375 L
F
1 g
.625 .4375 m
.625 .6875 L
.875 .6875 L
.875 .4375 L
F
.15 g
.25 Mabswid
[ ] 0 setdash
.125 .4375 m
.875 .4375 L
.875 .6875 L
.125 .6875 L
.125 .4375 L
s
.375 .4375 m
.375 .6875 L
s
.625 .4375 m
.625 .6875 L
s
0 g
.375 .125 m
.375 .375 L
.625 .375 L
.625 .125 L
F
.15 g
.375 .125 m
.375 .375 L
.625 .375 L
.625 .125 L
.375 .125 L
s
MathSubEnd
P
% End of sub-graphic
0 g
.25 Mabswid
[ ] 0 setdash
.61905 .01488 m
.61905 .11012 L
s
% Start of sub-graphic
p
0.738095 0.00297619 0.857143 0.122024 MathSubStart
%% Graphics
%%IncludeResource: font Helvetica
%%IncludeFont: Helvetica
/Helvetica findfont 10 scalefont setfont
% Scaling calculations
0.125 0.25 0.4375 0.25 [
[ 0 0 0 0 ]
[ 1 .8125 0 0 ]
] MathScale
% Start of Graphics
1 setlinecap
1 setlinejoin
newpath
0 0 m
1 0 L
1 .8125 L
0 .8125 L
closepath
clip
newpath
1 g
0 0 m
0 .8125 L
1 .8125 L
1 0 L
F
.125 .4375 m
.125 .6875 L
.375 .6875 L
.375 .4375 L
F
.375 .4375 m
.375 .6875 L
.625 .6875 L
.625 .4375 L
F
0 g
.625 .4375 m
.625 .6875 L
.875 .6875 L
.875 .4375 L
F
.15 g
.25 Mabswid
[ ] 0 setdash
.125 .4375 m
.875 .4375 L
.875 .6875 L
.125 .6875 L
.125 .4375 L
s
.375 .4375 m
.375 .6875 L
s
.625 .4375 m
.625 .6875 L
s
1 g
.375 .125 m
.375 .375 L
.625 .375 L
.625 .125 L
F
.15 g
.375 .125 m
.375 .375 L
.625 .375 L
.625 .125 L
.375 .125 L
s
MathSubEnd
P
% End of sub-graphic
0 g
.25 Mabswid
[ ] 0 setdash
.7381 .01488 m
.7381 .11012 L
s
% Start of sub-graphic
p
0.857143 0.00297619 0.97619 0.122024 MathSubStart
%% Graphics
%%IncludeResource: font Helvetica
%%IncludeFont: Helvetica
/Helvetica findfont 10 scalefont setfont
% Scaling calculations
0.125 0.25 0.4375 0.25 [
[ 0 0 0 0 ]
[ 1 .8125 0 0 ]
] MathScale
% Start of Graphics
1 setlinecap
1 setlinejoin
newpath
0 0 m
1 0 L
1 .8125 L
0 .8125 L
closepath
clip
newpath
1 g
0 0 m
0 .8125 L
1 .8125 L
1 0 L
F
.125 .4375 m
.125 .6875 L
.375 .6875 L
.375 .4375 L
F
.375 .4375 m
.375 .6875 L
.625 .6875 L
.625 .4375 L
F
.625 .4375 m
.625 .6875 L
.875 .6875 L
.875 .4375 L
F
.15 g
.25 Mabswid
[ ] 0 setdash
.125 .4375 m
.875 .4375 L
.875 .6875 L
.125 .6875 L
.125 .4375 L
s
.375 .4375 m
.375 .6875 L
s
.625 .4375 m
.625 .6875 L
s
1 g
.375 .125 m
.375 .375 L
.625 .375 L
.625 .125 L
F
.15 g
.375 .125 m
.375 .375 L
.625 .375 L
.625 .125 L
.375 .125 L
s
MathSubEnd
P
% End of sub-graphic
0 g
.25 Mabswid
[ ] 0 setdash
.85714 .01488 m
.85714 .11012 L
s
.02381 .01488 m
.97619 .01488 L
.97619 .11012 L
.02381 .11012 L
s
% End of Graphics
MathPictureEnd
\
\>"], "Graphics",
TextAlignment->Center,
TextJustification->0,
ImageSize->{400, 50},
ImageMargins->{{287, 0}, {0, 1}},
ImageRegion->{{0, 1}, {0, 1}},
CellTags->"NKS Chapter 2",
ImageCache->GraphicsData["CompressedBitmap", "\<\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\
\>"],
ImageRangeCache->{{{0, 399}, {49, 0}} -> {-0.275042, -0.0250052, 0.0214287, \
0.0214287}, {{12.8125, 59.5}, {47.8125, 1.125}} -> {-1.59776, -2.22676, \
0.0856769, 0.0856769}, {{59.5, 106.125}, {47.8125, 1.125}} -> {-5.60463, \
-2.22958, 0.0857917, 0.0857917}, {{106.125, 152.813}, {47.8125, 1.125}} -> \
{-9.59248, -2.22676, 0.0856769, 0.0856769}, {{152.813, 199.5}, {47.8125, \
1.125}} -> {-13.5925, -2.22676, 0.0856769, 0.0856769}, {{199.5, 246.125}, \
{47.8125, 1.125}} -> {-17.6155, -2.22958, 0.0857917, 0.0857917}, {{246.125, \
292.813}, {47.8125, 1.125}} -> {-21.5872, -2.22676, 0.0856769, 0.0856769}, \
{{292.813, 339.5}, {47.8125, 1.125}} -> {-25.5873, -2.22676, 0.0856769, \
0.0856769}, {{339.5, 386.125}, {47.8125, 1.125}} -> {-29.6263, -2.22958, \
0.0857917, 0.0857917}}],
Cell[TextData[{
"We \"freeze\" 8 bits of the rules, reducing our search space to ",
" ",
Cell[BoxData[
FormBox[
SuperscriptBox["k", "19"], TraditionalForm]]],
"rules."
}], "Text",
CellChangeTimes->{{3.3931892288125*^9, 3.393189561359375*^9}, {
3.393189616578125*^9, 3.393189620734375*^9}, {3.393189929171875*^9,
3.3931899315*^9}, {3.393190362234375*^9, 3.393190439359375*^9}, {
3.393207836734375*^9, 3.393207900046875*^9}}],
Cell["\<\
2. At this point, any other initial assumptions about some bits of the rule \
can be included. We call them \"frozen bits\".\
\>", "Text",
CellChangeTimes->{{3.393208060703125*^9, 3.393208113125*^9}}],
Cell["\<\
3. We then make a random search in the reduced CA rule space for rules that \
meet the following criteria: they give a desired result encoded in the same \
way as the initial condition and they have to halt.\
\>", "Text",
CellChangeTimes->{{3.39320815225*^9, 3.39320817046875*^9}, {
3.393341927421432*^9, 3.3933419289636497`*^9}}],
Cell["\<\
4. After these rules are found (say, 30 rules), they are passed through some \
filters. Basically, they are tried out with many different initial conditions \
and results. To follow our example, let's say that from 30 randomly found \
rules only 10 pass these tests.\
\>", "Text",
CellChangeTimes->{{3.393208208921875*^9, 3.3932082181875*^9}, {
3.393385017161435*^9, 3.3933850300399537`*^9}}],
Cell["\<\
5. These rules are then compared, bit by bit, to see which of them are \
repeated in all -or most-of the rules. These bits of the rule are turned into \
frozen bits, thus reducing the CA rule space further.\
\>", "Text"],
Cell[CellGroupData[{
Cell[GraphicsData["PostScript", "\<\
%!
%%Creator: Mathematica
%%AspectRatio: .125
%%ImageSize: 400 50
MathPictureStart
/Mabs {
Mgmatrix idtransform
Mtmatrix dtransform
} bind def
/Mabsadd { Mabs
3 -1 roll add
3 1 roll add
exch } bind def
%% Graphics
%%IncludeResource: font Helvetica
%%IncludeFont: Helvetica
/Helvetica findfont 10 scalefont setfont
% Scaling calculations
0.0238095 0.119048 0.00297619 0.119048 [
[ 0 0 0 0 ]
[ 1 .125 0 0 ]
] MathScale
% Start of Graphics
1 setlinecap
1 setlinejoin
newpath
0 0 m
1 0 L
1 .125 L
0 .125 L
closepath
clip
newpath
% Start of sub-graphic
p
0.0238095 0.00297619 0.142857 0.122024 MathSubStart
%% Graphics
%%IncludeResource: font Helvetica
%%IncludeFont: Helvetica
/Helvetica findfont 10 scalefont setfont
% Scaling calculations
0.125 0.25 0.4375 0.25 [
[ 0 0 0 0 ]
[ 1 .8125 0 0 ]
] MathScale
% Start of Graphics
1 setlinecap
1 setlinejoin
newpath
0 0 m
1 0 L
1 .8125 L
0 .8125 L
closepath
clip
newpath
1 g
0 0 m
0 .8125 L
1 .8125 L
1 0 L
F
0 g
.125 .4375 m
.125 .6875 L
.375 .6875 L
.375 .4375 L
F
.375 .4375 m
.375 .6875 L
.625 .6875 L
.625 .4375 L
F
.625 .4375 m
.625 .6875 L
.875 .6875 L
.875 .4375 L
F
.15 g
.25 Mabswid
[ ] 0 setdash
.125 .4375 m
.875 .4375 L
.875 .6875 L
.125 .6875 L
.125 .4375 L
s
.375 .4375 m
.375 .6875 L
s
.625 .4375 m
.625 .6875 L
s
0 g
.375 .125 m
.375 .375 L
.625 .375 L
.625 .125 L
F
.15 g
.375 .125 m
.375 .375 L
.625 .375 L
.625 .125 L
.375 .125 L
s
MathSubEnd
P
% End of sub-graphic
0 g
.25 Mabswid
[ ] 0 setdash
.02381 .01488 m
.02381 .11012 L
s
% Start of sub-graphic
p
0.142857 0.00297619 0.261905 0.122024 MathSubStart
%% Graphics
%%IncludeResource: font Helvetica
%%IncludeFont: Helvetica
/Helvetica findfont 10 scalefont setfont
% Scaling calculations
0.125 0.25 0.4375 0.25 [
[ 0 0 0 0 ]
[ 1 .8125 0 0 ]
] MathScale
% Start of Graphics
1 setlinecap
1 setlinejoin
newpath
0 0 m
1 0 L
1 .8125 L
0 .8125 L
closepath
clip
newpath
1 g
0 0 m
0 .8125 L
1 .8125 L
1 0 L
F
0 g
.125 .4375 m
.125 .6875 L
.375 .6875 L
.375 .4375 L
F
.375 .4375 m
.375 .6875 L
.625 .6875 L
.625 .4375 L
F
1 g
.625 .4375 m
.625 .6875 L
.875 .6875 L
.875 .4375 L
F
.15 g
.25 Mabswid
[ ] 0 setdash
.125 .4375 m
.875 .4375 L
.875 .6875 L
.125 .6875 L
.125 .4375 L
s
.375 .4375 m
.375 .6875 L
s
.625 .4375 m
.625 .6875 L
s
1 g
.375 .125 m
.375 .375 L
.625 .375 L
.625 .125 L
F
.15 g
.375 .125 m
.375 .375 L
.625 .375 L
.625 .125 L
.375 .125 L
s
MathSubEnd
P
% End of sub-graphic
0 g
.25 Mabswid
[ ] 0 setdash
.14286 .01488 m
.14286 .11012 L
s
% Start of sub-graphic
p
0.261905 0.00297619 0.380952 0.122024 MathSubStart
%% Graphics
%%IncludeResource: font Helvetica
%%IncludeFont: Helvetica
/Helvetica findfont 10 scalefont setfont
% Scaling calculations
0.125 0.25 0.4375 0.25 [
[ 0 0 0 0 ]
[ 1 .8125 0 0 ]
] MathScale
% Start of Graphics
1 setlinecap
1 setlinejoin
newpath
0 0 m
1 0 L
1 .8125 L
0 .8125 L
closepath
clip
newpath
1 g
0 0 m
0 .8125 L
1 .8125 L
1 0 L
F
0 g
.125 .4375 m
.125 .6875 L
.375 .6875 L
.375 .4375 L
F
1 g
.375 .4375 m
.375 .6875 L
.625 .6875 L
.625 .4375 L
F
0 g
.625 .4375 m
.625 .6875 L
.875 .6875 L
.875 .4375 L
F
.15 g
.25 Mabswid
[ ] 0 setdash
.125 .4375 m
.875 .4375 L
.875 .6875 L
.125 .6875 L
.125 .4375 L
s
.375 .4375 m
.375 .6875 L
s
.625 .4375 m
.625 .6875 L
s
0 g
.375 .125 m
.375 .375 L
.625 .375 L
.625 .125 L
F
.15 g
.375 .125 m
.375 .375 L
.625 .375 L
.625 .125 L
.375 .125 L
s
MathSubEnd
P
% End of sub-graphic
0 g
.25 Mabswid
[ ] 0 setdash
.2619 .01488 m
.2619 .11012 L
s
% Start of sub-graphic
p
0.380952 0.00297619 0.5 0.122024 MathSubStart
%% Graphics
%%IncludeResource: font Helvetica
%%IncludeFont: Helvetica
/Helvetica findfont 10 scalefont setfont
% Scaling calculations
0.125 0.25 0.4375 0.25 [
[ 0 0 0 0 ]
[ 1 .8125 0 0 ]
] MathScale
% Start of Graphics
1 setlinecap
1 setlinejoin
newpath
0 0 m
1 0 L
1 .8125 L
0 .8125 L
closepath
clip
newpath
1 g
0 0 m
0 .8125 L
1 .8125 L
1 0 L
F
0 g
.125 .4375 m
.125 .6875 L
.375 .6875 L
.375 .4375 L
F
1 g
.375 .4375 m
.375 .6875 L
.625 .6875 L
.625 .4375 L
F
.625 .4375 m
.625 .6875 L
.875 .6875 L
.875 .4375 L
F
.15 g
.25 Mabswid
[ ] 0 setdash
.125 .4375 m
.875 .4375 L
.875 .6875 L
.125 .6875 L
.125 .4375 L
s
.375 .4375 m
.375 .6875 L
s
.625 .4375 m
.625 .6875 L
s
0 g
.375 .125 m
.375 .375 L
.625 .375 L
.625 .125 L
F
.15 g
.375 .125 m
.375 .375 L
.625 .375 L
.625 .125 L
.375 .125 L
s
MathSubEnd
P
% End of sub-graphic
0 g
.25 Mabswid
[ ] 0 setdash
.38095 .01488 m
.38095 .11012 L
s
% Start of sub-graphic
p
0.5 0.00297619 0.619048 0.122024 MathSubStart
%% Graphics
%%IncludeResource: font Helvetica
%%IncludeFont: Helvetica
/Helvetica findfont 10 scalefont setfont
% Scaling calculations
0.125 0.25 0.4375 0.25 [
[ 0 0 0 0 ]
[ 1 .8125 0 0 ]
] MathScale
% Start of Graphics
1 setlinecap
1 setlinejoin
newpath
0 0 m
1 0 L
1 .8125 L
0 .8125 L
closepath
clip
newpath
1 g
0 0 m
0 .8125 L
1 .8125 L
1 0 L
F
.125 .4375 m
.125 .6875 L
.375 .6875 L
.375 .4375 L
F
0 g
.375 .4375 m
.375 .6875 L
.625 .6875 L
.625 .4375 L
F
.625 .4375 m
.625 .6875 L
.875 .6875 L
.875 .4375 L
F
.15 g
.25 Mabswid
[ ] 0 setdash
.125 .4375 m
.875 .4375 L
.875 .6875 L
.125 .6875 L
.125 .4375 L
s
.375 .4375 m
.375 .6875 L
s
.625 .4375 m
.625 .6875 L
s
0 g
.375 .125 m
.375 .375 L
.625 .375 L
.625 .125 L
F
.15 g
.375 .125 m
.375 .375 L
.625 .375 L
.625 .125 L
.375 .125 L
s
MathSubEnd
P
% End of sub-graphic
0 g
.25 Mabswid
[ ] 0 setdash
.5 .01488 m
.5 .11012 L
s
% Start of sub-graphic
p
0.619048 0.00297619 0.738095 0.122024 MathSubStart
%% Graphics
%%IncludeResource: font Helvetica
%%IncludeFont: Helvetica
/Helvetica findfont 10 scalefont setfont
% Scaling calculations
0.125 0.25 0.4375 0.25 [
[ 0 0 0 0 ]
[ 1 .8125 0 0 ]
] MathScale
% Start of Graphics
1 setlinecap
1 setlinejoin
newpath
0 0 m
1 0 L
1 .8125 L
0 .8125 L
closepath
clip
newpath
1 g
0 0 m
0 .8125 L
1 .8125 L
1 0 L
F
.125 .4375 m
.125 .6875 L
.375 .6875 L
.375 .4375 L
F
0 g
.375 .4375 m
.375 .6875 L
.625 .6875 L
.625 .4375 L
F
1 g
.625 .4375 m
.625 .6875 L
.875 .6875 L
.875 .4375 L
F
.15 g
.25 Mabswid
[ ] 0 setdash
.125 .4375 m
.875 .4375 L
.875 .6875 L
.125 .6875 L
.125 .4375 L
s
.375 .4375 m
.375 .6875 L
s
.625 .4375 m
.625 .6875 L
s
1 g
.375 .125 m
.375 .375 L
.625 .375 L
.625 .125 L
F
.15 g
.375 .125 m
.375 .375 L
.625 .375 L
.625 .125 L
.375 .125 L
s
MathSubEnd
P
% End of sub-graphic
0 g
.25 Mabswid
[ ] 0 setdash
.61905 .01488 m
.61905 .11012 L
s
% Start of sub-graphic
p
0.738095 0.00297619 0.857143 0.122024 MathSubStart
%% Graphics
%%IncludeResource: font Helvetica
%%IncludeFont: Helvetica
/Helvetica findfont 10 scalefont setfont
% Scaling calculations
0.125 0.25 0.4375 0.25 [
[ 0 0 0 0 ]
[ 1 .8125 0 0 ]
] MathScale
% Start of Graphics
1 setlinecap
1 setlinejoin
newpath
0 0 m
1 0 L
1 .8125 L
0 .8125 L
closepath
clip
newpath
1 g
0 0 m
0 .8125 L
1 .8125 L
1 0 L
F
.125 .4375 m
.125 .6875 L
.375 .6875 L
.375 .4375 L
F
.375 .4375 m
.375 .6875 L
.625 .6875 L
.625 .4375 L
F
0 g
.625 .4375 m
.625 .6875 L
.875 .6875 L
.875 .4375 L
F
.15 g
.25 Mabswid
[ ] 0 setdash
.125 .4375 m
.875 .4375 L
.875 .6875 L
.125 .6875 L
.125 .4375 L
s
.375 .4375 m
.375 .6875 L
s
.625 .4375 m
.625 .6875 L
s
1 g
.375 .125 m
.375 .375 L
.625 .375 L
.625 .125 L
F
.15 g
.375 .125 m
.375 .375 L
.625 .375 L
.625 .125 L
.375 .125 L
s
MathSubEnd
P
% End of sub-graphic
0 g
.25 Mabswid
[ ] 0 setdash
.7381 .01488 m
.7381 .11012 L
s
% Start of sub-graphic
p
0.857143 0.00297619 0.97619 0.122024 MathSubStart
%% Graphics
%%IncludeResource: font Helvetica
%%IncludeFont: Helvetica
/Helvetica findfont 10 scalefont setfont
% Scaling calculations
0.125 0.25 0.4375 0.25 [
[ 0 0 0 0 ]
[ 1 .8125 0 0 ]
] MathScale
% Start of Graphics
1 setlinecap
1 setlinejoin
newpath
0 0 m
1 0 L
1 .8125 L
0 .8125 L
closepath
clip
newpath
1 g
0 0 m
0 .8125 L
1 .8125 L
1 0 L
F
.125 .4375 m
.125 .6875 L
.375 .6875 L
.375 .4375 L
F
.375 .4375 m
.375 .6875 L
.625 .6875 L
.625 .4375 L
F
.625 .4375 m
.625 .6875 L
.875 .6875 L
.875 .4375 L
F
.15 g
.25 Mabswid
[ ] 0 setdash
.125 .4375 m
.875 .4375 L
.875 .6875 L
.125 .6875 L
.125 .4375 L
s
.375 .4375 m
.375 .6875 L
s
.625 .4375 m
.625 .6875 L
s
1 g
.375 .125 m
.375 .375 L
.625 .375 L
.625 .125 L
F
.15 g
.375 .125 m
.375 .375 L
.625 .375 L
.625 .125 L
.375 .125 L
s
MathSubEnd
P
% End of sub-graphic
0 g
.25 Mabswid
[ ] 0 setdash
.85714 .01488 m
.85714 .11012 L
s
.02381 .01488 m
.97619 .01488 L
.97619 .11012 L
.02381 .11012 L
s
% End of Graphics
MathPictureEnd
\
\>"], "Graphics",
ImageSize->{400, 50},
ImageMargins->{{286, 0}, {0, 0}},
ImageRegion->{{0, 1}, {0, 1}},
CellTags->"NKS Chapter 2",
ImageCache->GraphicsData["CompressedBitmap", "\<\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\
\>"],
ImageRangeCache->{{{0, 399}, {49, 0}} -> {-0.275042, -0.0250052, 0.0214287, \
0.0214287}, {{12.8125, 59.5}, {47.8125, 1.125}} -> {-1.59776, -2.22676, \
0.0856769, 0.0856769}, {{59.5, 106.125}, {47.8125, 1.125}} -> {-5.60463, \
-2.22958, 0.0857917, 0.0857917}, {{106.125, 152.813}, {47.8125, 1.125}} -> \
{-9.59248, -2.22676, 0.0856769, 0.0856769}, {{152.813, 199.5}, {47.8125, \
1.125}} -> {-13.5925, -2.22676, 0.0856769, 0.0856769}, {{199.5, 246.125}, \
{47.8125, 1.125}} -> {-17.6155, -2.22958, 0.0857917, 0.0857917}, {{246.125, \
292.813}, {47.8125, 1.125}} -> {-21.5872, -2.22676, 0.0856769, 0.0856769}, \
{{292.813, 339.5}, {47.8125, 1.125}} -> {-25.5873, -2.22676, 0.0856769, \
0.0856769}, {{339.5, 386.125}, {47.8125, 1.125}} -> {-29.6263, -2.22958, \
0.0857917, 0.0857917}}],
Cell[GraphicsData["PostScript", "\<\
%!
%%Creator: Mathematica
%%AspectRatio: .125
%%ImageSize: 400 50
MathPictureStart
/Mabs {
Mgmatrix idtransform
Mtmatrix dtransform
} bind def
/Mabsadd { Mabs
3 -1 roll add
3 1 roll add
exch } bind def
%% Graphics
%%IncludeResource: font Helvetica
%%IncludeFont: Helvetica
/Helvetica findfont 10 scalefont setfont
% Scaling calculations
0.0238095 0.119048 0.00297619 0.119048 [
[ 0 0 0 0 ]
[ 1 .125 0 0 ]
] MathScale
% Start of Graphics
1 setlinecap
1 setlinejoin
newpath
0 0 m
1 0 L
1 .125 L
0 .125 L
closepath
clip
newpath
% Start of sub-graphic
p
0.0238095 0.00297619 0.142857 0.122024 MathSubStart
%% Graphics
%%IncludeResource: font Helvetica
%%IncludeFont: Helvetica
/Helvetica findfont 10 scalefont setfont
% Scaling calculations
0.125 0.25 0.4375 0.25 [
[ 0 0 0 0 ]
[ 1 .8125 0 0 ]
] MathScale
% Start of Graphics
1 setlinecap
1 setlinejoin
newpath
0 0 m
1 0 L
1 .8125 L
0 .8125 L
closepath
clip
newpath
1 g
0 0 m
0 .8125 L
1 .8125 L
1 0 L
F
0 g
.125 .4375 m
.125 .6875 L
.375 .6875 L
.375 .4375 L
F
.375 .4375 m
.375 .6875 L
.625 .6875 L
.625 .4375 L
F
.625 .4375 m
.625 .6875 L
.875 .6875 L
.875 .4375 L
F
.15 g
.25 Mabswid
[ ] 0 setdash
.125 .4375 m
.875 .4375 L
.875 .6875 L
.125 .6875 L
.125 .4375 L
s
.375 .4375 m
.375 .6875 L
s
.625 .4375 m
.625 .6875 L
s
1 g
.375 .125 m
.375 .375 L
.625 .375 L
.625 .125 L
F
.15 g
.375 .125 m
.375 .375 L
.625 .375 L
.625 .125 L
.375 .125 L
s
MathSubEnd
P
% End of sub-graphic
0 g
.25 Mabswid
[ ] 0 setdash
.02381 .01488 m
.02381 .11012 L
s
% Start of sub-graphic
p
0.142857 0.00297619 0.261905 0.122024 MathSubStart
%% Graphics
%%IncludeResource: font Helvetica
%%IncludeFont: Helvetica
/Helvetica findfont 10 scalefont setfont
% Scaling calculations
0.125 0.25 0.4375 0.25 [
[ 0 0 0 0 ]
[ 1 .8125 0 0 ]
] MathScale
% Start of Graphics
1 setlinecap
1 setlinejoin
newpath
0 0 m
1 0 L
1 .8125 L
0 .8125 L
closepath
clip
newpath
1 g
0 0 m
0 .8125 L
1 .8125 L
1 0 L
F
0 g
.125 .4375 m
.125 .6875 L
.375 .6875 L
.375 .4375 L
F
.375 .4375 m
.375 .6875 L
.625 .6875 L
.625 .4375 L
F
1 g
.625 .4375 m
.625 .6875 L
.875 .6875 L
.875 .4375 L
F
.15 g
.25 Mabswid
[ ] 0 setdash
.125 .4375 m
.875 .4375 L
.875 .6875 L
.125 .6875 L
.125 .4375 L
s
.375 .4375 m
.375 .6875 L
s
.625 .4375 m
.625 .6875 L
s
0 g
.375 .125 m
.375 .375 L
.625 .375 L
.625 .125 L
F
.15 g
.375 .125 m
.375 .375 L
.625 .375 L
.625 .125 L
.375 .125 L
s
MathSubEnd
P
% End of sub-graphic
0 g
.25 Mabswid
[ ] 0 setdash
.14286 .01488 m
.14286 .11012 L
s
% Start of sub-graphic
p
0.261905 0.00297619 0.380952 0.122024 MathSubStart
%% Graphics
%%IncludeResource: font Helvetica
%%IncludeFont: Helvetica
/Helvetica findfont 10 scalefont setfont
% Scaling calculations
0.125 0.25 0.4375 0.25 [
[ 0 0 0 0 ]
[ 1 .8125 0 0 ]
] MathScale
% Start of Graphics
1 setlinecap
1 setlinejoin
newpath
0 0 m
1 0 L
1 .8125 L
0 .8125 L
closepath
clip
newpath
1 g
0 0 m
0 .8125 L
1 .8125 L
1 0 L
F
0 g
.125 .4375 m
.125 .6875 L
.375 .6875 L
.375 .4375 L
F
1 g
.375 .4375 m
.375 .6875 L
.625 .6875 L
.625 .4375 L
F
0 g
.625 .4375 m
.625 .6875 L
.875 .6875 L
.875 .4375 L
F
.15 g
.25 Mabswid
[ ] 0 setdash
.125 .4375 m
.875 .4375 L
.875 .6875 L
.125 .6875 L
.125 .4375 L
s
.375 .4375 m
.375 .6875 L
s
.625 .4375 m
.625 .6875 L
s
1 g
.375 .125 m
.375 .375 L
.625 .375 L
.625 .125 L
F
.15 g
.375 .125 m
.375 .375 L
.625 .375 L
.625 .125 L
.375 .125 L
s
MathSubEnd
P
% End of sub-graphic
0 g
.25 Mabswid
[ ] 0 setdash
.2619 .01488 m
.2619 .11012 L
s
% Start of sub-graphic
p
0.380952 0.00297619 0.5 0.122024 MathSubStart
%% Graphics
%%IncludeResource: font Helvetica
%%IncludeFont: Helvetica
/Helvetica findfont 10 scalefont setfont
% Scaling calculations
0.125 0.25 0.4375 0.25 [
[ 0 0 0 0 ]
[ 1 .8125 0 0 ]
] MathScale
% Start of Graphics
1 setlinecap
1 setlinejoin
newpath
0 0 m
1 0 L
1 .8125 L
0 .8125 L
closepath
clip
newpath
1 g
0 0 m
0 .8125 L
1 .8125 L
1 0 L
F
0 g
.125 .4375 m
.125 .6875 L
.375 .6875 L
.375 .4375 L
F
1 g
.375 .4375 m
.375 .6875 L
.625 .6875 L
.625 .4375 L
F
.625 .4375 m
.625 .6875 L
.875 .6875 L
.875 .4375 L
F
.15 g
.25 Mabswid
[ ] 0 setdash
.125 .4375 m
.875 .4375 L
.875 .6875 L
.125 .6875 L
.125 .4375 L
s
.375 .4375 m
.375 .6875 L
s
.625 .4375 m
.625 .6875 L
s
0 g
.375 .125 m
.375 .375 L
.625 .375 L
.625 .125 L
F
.15 g
.375 .125 m
.375 .375 L
.625 .375 L
.625 .125 L
.375 .125 L
s
MathSubEnd
P
% End of sub-graphic
0 g
.25 Mabswid
[ ] 0 setdash
.38095 .01488 m
.38095 .11012 L
s
% Start of sub-graphic
p
0.5 0.00297619 0.619048 0.122024 MathSubStart
%% Graphics
%%IncludeResource: font Helvetica
%%IncludeFont: Helvetica
/Helvetica findfont 10 scalefont setfont
% Scaling calculations
0.125 0.25 0.4375 0.25 [
[ 0 0 0 0 ]
[ 1 .8125 0 0 ]
] MathScale
% Start of Graphics
1 setlinecap
1 setlinejoin
newpath
0 0 m
1 0 L
1 .8125 L
0 .8125 L
closepath
clip
newpath
1 g
0 0 m
0 .8125 L
1 .8125 L
1 0 L
F
.125 .4375 m
.125 .6875 L
.375 .6875 L
.375 .4375 L
F
0 g
.375 .4375 m
.375 .6875 L
.625 .6875 L
.625 .4375 L
F
.625 .4375 m
.625 .6875 L
.875 .6875 L
.875 .4375 L
F
.15 g
.25 Mabswid
[ ] 0 setdash
.125 .4375 m
.875 .4375 L
.875 .6875 L
.125 .6875 L
.125 .4375 L
s
.375 .4375 m
.375 .6875 L
s
.625 .4375 m
.625 .6875 L
s
1 g
.375 .125 m
.375 .375 L
.625 .375 L
.625 .125 L
F
.15 g
.375 .125 m
.375 .375 L
.625 .375 L
.625 .125 L
.375 .125 L
s
MathSubEnd
P
% End of sub-graphic
0 g
.25 Mabswid
[ ] 0 setdash
.5 .01488 m
.5 .11012 L
s
% Start of sub-graphic
p
0.619048 0.00297619 0.738095 0.122024 MathSubStart
%% Graphics
%%IncludeResource: font Helvetica
%%IncludeFont: Helvetica
/Helvetica findfont 10 scalefont setfont
% Scaling calculations
0.125 0.25 0.4375 0.25 [
[ 0 0 0 0 ]
[ 1 .8125 0 0 ]
] MathScale
% Start of Graphics
1 setlinecap
1 setlinejoin
newpath
0 0 m
1 0 L
1 .8125 L
0 .8125 L
closepath
clip
newpath
1 g
0 0 m
0 .8125 L
1 .8125 L
1 0 L
F
.125 .4375 m
.125 .6875 L
.375 .6875 L
.375 .4375 L
F
0 g
.375 .4375 m
.375 .6875 L
.625 .6875 L
.625 .4375 L
F
1 g
.625 .4375 m
.625 .6875 L
.875 .6875 L
.875 .4375 L
F
.15 g
.25 Mabswid
[ ] 0 setdash
.125 .4375 m
.875 .4375 L
.875 .6875 L
.125 .6875 L
.125 .4375 L
s
.375 .4375 m
.375 .6875 L
s
.625 .4375 m
.625 .6875 L
s
1 g
.375 .125 m
.375 .375 L
.625 .375 L
.625 .125 L
F
.15 g
.375 .125 m
.375 .375 L
.625 .375 L
.625 .125 L
.375 .125 L
s
MathSubEnd
P
% End of sub-graphic
0 g
.25 Mabswid
[ ] 0 setdash
.61905 .01488 m
.61905 .11012 L
s
% Start of sub-graphic
p
0.738095 0.00297619 0.857143 0.122024 MathSubStart
%% Graphics
%%IncludeResource: font Helvetica
%%IncludeFont: Helvetica
/Helvetica findfont 10 scalefont setfont
% Scaling calculations
0.125 0.25 0.4375 0.25 [
[ 0 0 0 0 ]
[ 1 .8125 0 0 ]
] MathScale
% Start of Graphics
1 setlinecap
1 setlinejoin
newpath
0 0 m
1 0 L
1 .8125 L
0 .8125 L
closepath
clip
newpath
1 g
0 0 m
0 .8125 L
1 .8125 L
1 0 L
F
.125 .4375 m
.125 .6875 L
.375 .6875 L
.375 .4375 L
F
.375 .4375 m
.375 .6875 L
.625 .6875 L
.625 .4375 L
F
0 g
.625 .4375 m
.625 .6875 L
.875 .6875 L
.875 .4375 L
F
.15 g
.25 Mabswid
[ ] 0 setdash
.125 .4375 m
.875 .4375 L
.875 .6875 L
.125 .6875 L
.125 .4375 L
s
.375 .4375 m
.375 .6875 L
s
.625 .4375 m
.625 .6875 L
s
0 g
.375 .125 m
.375 .375 L
.625 .375 L
.625 .125 L
F
.15 g
.375 .125 m
.375 .375 L
.625 .375 L
.625 .125 L
.375 .125 L
s
MathSubEnd
P
% End of sub-graphic
0 g
.25 Mabswid
[ ] 0 setdash
.7381 .01488 m
.7381 .11012 L
s
% Start of sub-graphic
p
0.857143 0.00297619 0.97619 0.122024 MathSubStart
%% Graphics
%%IncludeResource: font Helvetica
%%IncludeFont: Helvetica
/Helvetica findfont 10 scalefont setfont
% Scaling calculations
0.125 0.25 0.4375 0.25 [
[ 0 0 0 0 ]
[ 1 .8125 0 0 ]
] MathScale
% Start of Graphics
1 setlinecap
1 setlinejoin
newpath
0 0 m
1 0 L
1 .8125 L
0 .8125 L
closepath
clip
newpath
1 g
0 0 m
0 .8125 L
1 .8125 L
1 0 L
F
.125 .4375 m
.125 .6875 L
.375 .6875 L
.375 .4375 L
F
.375 .4375 m
.375 .6875 L
.625 .6875 L
.625 .4375 L
F
.625 .4375 m
.625 .6875 L
.875 .6875 L
.875 .4375 L
F
.15 g
.25 Mabswid
[ ] 0 setdash
.125 .4375 m
.875 .4375 L
.875 .6875 L
.125 .6875 L
.125 .4375 L
s
.375 .4375 m
.375 .6875 L
s
.625 .4375 m
.625 .6875 L
s
0 g
.375 .125 m
.375 .375 L
.625 .375 L
.625 .125 L
F
.15 g
.375 .125 m
.375 .375 L
.625 .375 L
.625 .125 L
.375 .125 L
s
MathSubEnd
P
% End of sub-graphic
0 g
.25 Mabswid
[ ] 0 setdash
.85714 .01488 m
.85714 .11012 L
s
.02381 .01488 m
.97619 .01488 L
.97619 .11012 L
.02381 .11012 L
s
% End of Graphics
MathPictureEnd
\
\>"], "Graphics",
ImageSize->{400, 50},
ImageMargins->{{287, 0}, {0, 0}},
ImageRegion->{{0, 1}, {0, 1}},
CellTags->"NKS Chapter 2",
ImageCache->GraphicsData["CompressedBitmap", "\<\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\
\>"],
ImageRangeCache->{{{0, 399}, {49, 0}} -> {-0.275042, -0.0250052, 0.0214287, \
0.0214287}, {{12.8125, 59.5}, {47.8125, 1.125}} -> {-1.59776, -2.22676, \
0.0856769, 0.0856769}, {{59.5, 106.125}, {47.8125, 1.125}} -> {-5.60463, \
-2.22958, 0.0857917, 0.0857917}, {{106.125, 152.813}, {47.8125, 1.125}} -> \
{-9.59248, -2.22676, 0.0856769, 0.0856769}, {{152.813, 199.5}, {47.8125, \
1.125}} -> {-13.5925, -2.22676, 0.0856769, 0.0856769}, {{199.5, 246.125}, \
{47.8125, 1.125}} -> {-17.6155, -2.22958, 0.0857917, 0.0857917}, {{246.125, \
292.813}, {47.8125, 1.125}} -> {-21.5872, -2.22676, 0.0856769, 0.0856769}, \
{{292.813, 339.5}, {47.8125, 1.125}} -> {-25.5873, -2.22676, 0.0856769, \
0.0856769}, {{339.5, 386.125}, {47.8125, 1.125}} -> {-29.6263, -2.22958, \
0.0857917, 0.0857917}}]
}, Open ]],
Cell["\<\
6. Repeat steps 3 to 5 until the CA rule space is reduced enough for an \
exhaustive search.\
\>", "Text"]
}, Open ]],
Cell[CellGroupData[{
Cell[TextData[StyleBox["A search made for subtraction rules",
FontColor->RGBColor[
0.9714045929655909, 0.6775158312352179, 0.07415884641794461]]], "Subsection",\
CellChangeTimes->{
3.3824524252213373`*^9, {3.39303943990625*^9, 3.393039450140625*^9}, {
3.39304107571875*^9, 3.3930411009375*^9}, {3.393208508046875*^9,
3.393208532375*^9}}],
Cell["\<\
As an example, nearly a thousand rules were found using the method described \
above in less than 1 hour.
With and exhaustive search, less than a hundred rules where found in about \
ten hours.
Out of a sample of 974 rules found, those with the same pattern behavior were \
filtered, leaving 71 with effectively different patterns, shown below.
All four classes of behavior are found inside the area performing the \
computation.\
\>", "Text",
CellChangeTimes->{{3.39320853584375*^9, 3.393208536265625*^9}, {
3.393209021796875*^9, 3.393209343265625*^9}, {3.393209464046875*^9,
3.393209506109375*^9}, {3.393211049984375*^9, 3.39321106321875*^9}, {
3.393211102015625*^9, 3.393211117578125*^9}, {3.3933420096997423`*^9,
3.393342069776128*^9}, {3.393385038512136*^9, 3.393385042788285*^9}}],
Cell[BoxData[{
RowBox[{
RowBox[{"subtractionRules", "=",
RowBox[{"{",
RowBox[{
"69738168204", ",", "69738181326", ",", "164139633918", ",",
"165172748661", ",", "165172761783", ",", "166464163413", ",",
"255857848191", ",", "255986988354", ",", "257005767312", ",",
"257134900914", ",", "258153681330", ",", "258297168942", ",",
"259186796073", ",", "259215493887", ",", "259315934049", ",",
"259330279311", ",", "259445076399", ",", "259459430409", ",",
"260349050979", ",", "260363413737", ",", "260377755354", ",",
"260478202806", ",", "260492545152", ",", "260607335679", ",",
"260607344427", ",", "260621685315", ",", "260621687502", ",",
"353329979274", ",", "353588246478", ",", "354492240741", ",",
"354621374343", ",", "447473151540", ",", "536981640696", ",",
"536995983042", ",", "537239907900", ",", "538158244509", ",",
"538273035765", ",", "538273042326", ",", "539306163630", ",",
"539550087759", ",", "540454062339", ",", "540597552138", ",",
"540712349955", ",", "540712356516", ",", "541616325993", ",",
"541616331096", ",", "541616332554", ",", "541616333283", ",",
"541745470530", ",", "541745477820", ",", "541759820166", ",",
"541874619441", ",", "541888960329", ",", "541888962516", ",",
"542778588189", ",", "542792948031", ",", "542907725436", ",",
"542907732726", ",", "543036868515", ",", "634597247727", ",",
"635888649357", ",", "636921770661", ",", "728998713441", ",",
"731194096212", ",", "819411177177", ",", "819683799849", ",",
"821864827152", ",", "822883605381", ",", "823141895184", ",",
"824175000450", ",", "824175007011", ",", "824175009927", ",",
"824189350086", ",", "824189365395", ",", "825208129044", ",",
"825222480138", ",", "825351620301", ",", "825351624675", ",",
"825466402809", ",", "825466417389", ",", "1013494485969", ",",
"1101840713658", ",", "1103132108727", ",", "1104423516918", ",",
"1105313141862", ",", "1105327487124", ",", "1105442275464", ",",
"1105442288586", ",", "1105456627287", ",", "1105456631661", ",",
"1105571428749", ",", "1105585771824", ",", "1105585774011", ",",
"1105585778385", ",", "1106475403329", ",", "1106475406245", ",",
"1106489761713", ",", "1106604552240", ",", "1106618888754", ",",
"1106733684384", ",", "1106748028917", ",", "1107637660422", ",",
"1107766800585", ",", "1107766804959", ",", "1107766807146", ",",
"1107766813707", ",", "1107781148034", ",", "1107781163343", ",",
"1107895945122", ",", "1107910296945", ",", "1200618575595", ",",
"1294890901146", ",", "1296182296215", ",", "1296182309337", ",",
"1384270243578", ",", "1384399377180", ",", "1384399383741", ",",
"1386594773073", ",", "1386723906675", ",", "1386838690641", ",",
"1386838697202", ",", "1387871827254", ",", "1388000954295", ",",
"1388000965230", ",", "1388904946371", ",", "1389034076328", ",",
"1389048423048", ",", "1389163215762", ",", "1390067195445", ",",
"1390067210025", ",", "1390081557474", ",", "1390196342169", ",",
"1390196348001", ",", "1390325481603", ",", "1390325488164", ",",
"1390339833426", ",", "1481885857170", ",", "1483048125198", ",",
"1483177265361", ",", "1578611832696", ",", "1578611845818", ",",
"1666828920222", ",", "1666972415853", ",", "1667991175128", ",",
"1669024302993", ",", "1669268233683", ",", "1670172210450", ",",
"1670172215553", ",", "1670172217740", ",", "1670301357903", ",",
"1670301361548", ",", "1670315713371", ",", "1670430502440", ",",
"1670430504627", ",", "1670444844786", ",", "1671348819366", ",",
"1671348834675", ",", "1671463609893", ",", "1671592750056", ",",
"1671592763907", ",", "1672496737758", ",", "1672640227557", ",",
"1672755020271", ",", "1672755021000", ",", "1672755027561", ",",
"1764315393651", ",", "1764444540375", ",", "1765606788720", ",",
"1766639916585", ",", "1766639923146", ",", "1858716846243", ",",
"1859879107710", ",", "1859879120832", ",", "1860783095412", ",",
"1861041369177", ",", "1950291578007", ",", "1950420724731", ",",
"1951697770164", ",", "1951712113239", ",", "1952601758595", ",",
"1952601760782", ",", "1952616107502", ",", "1952730887823", ",",
"1952745241104", ",", "1952745243291", ",", "1952745249852", ",",
"1952860027257", ",", "1952860032360", ",", "1953764009127", ",",
"1953764020062", ",", "1953778358034", ",", "1953893153664", ",",
"1953907502571", ",", "1954022299659", ",", "1954022301846", ",",
"1954036642734", ",", "1954926269865", ",", "1954940619501", ",",
"1955055410028", ",", "1955055415131", ",", "1955055417318", ",",
"1955184557481", ",", "1955184563313", ",", "2046744923571", ",",
"2049198599790", ",", "2140888102398", ",", "2231558846460", ",",
"2231558859582", ",", "2232850248090", ",", "2232979388253", ",",
"2232979394814", ",", "2232979401375", ",", "2235045630861", ",",
"2235045643983", ",", "2235160430136", ",", "2235160434510", ",",
"2236193551440", ",", "2236193556543", ",", "2236193558001", ",",
"2236337032491", ",", "2236451825934", ",", "2236466181402", ",",
"2236466185776", ",", "2237355811449", ",", "2237484958173", ",",
"2237614098336", ",", "2237628442869", ",", "2329174466613", ",",
"2330465868243", ",", "2330595001845", ",", "2331498989547", ",",
"2331757269873", ",", "2424738180672", ",", "2424738187233", ",",
"2425900442139", ",", "2425900448700", ",", "2513988389502", ",",
"2515150650969", ",", "2515279784571", ",", "2515279797693", ",",
"2516298556239", ",", "2517460818435", ",", "2517475169529", ",",
"2517475176090", ",", "2517589957869", ",", "2517589970991", ",",
"2517604307505", ",", "2517604314066", ",", "2517719104593", ",",
"2517719113341", ",", "2517733449855", ",", "2517733456416", ",",
"2518637430996", ",", "2518881360228", ",", "2518881375537", ",",
"2518895711322", ",", "2518895717883", ",", "2519785341369", ",",
"2519799705585", ",", "2519914487364", ",", "2519914496112", ",",
"2519928830439", ",", "2519928843561", ",", "2520043630443", ",",
"2520057985911", ",", "2611862276859", ",", "2611890986337", ",",
"2612895404724", ",", "2613024549261", ",", "2613038898897", ",",
"2705876328645", ",", "2706005455686", ",", "2706005462247", ",",
"2708071704855", ",", "2708329991742", ",", "2793060286119", ",",
"2795270017068", ",", "2795370452856", ",", "2795384809053", ",",
"2795399157960", ",", "2796417932544", ",", "2796532720884", ",",
"2796690548655", ",", "2797580180889", ",", "2797694983809", ",",
"2797852816683", ",", "2798728105113", ",", "2798742454020", ",",
"2798857237257", ",", "2798871595641", ",", "2798885942361", ",",
"2798986386168", ",", "2799000735804", ",", "2799904712571", ",",
"2799904716945", ",", "2799904719132", ",", "2800019497266", ",",
"2800019504556", ",", "2800019506743", ",", "2800148648364", ",",
"2800435622859", ",", "2801052624402", ",", "2801052630963", ",",
"2801181758733", ",", "2801181766752", ",", "2801196115659", ",",
"2801310898167", ",", "2801310905457", ",", "2801325245616", ",",
"2802214886598", ",", "2802214889514", ",", "2802243585870", ",",
"2802243587328", ",", "2802344017284", ",", "2802344022387", ",",
"2802344026032", ",", "2802358378584", ",", "2802473166924", ",",
"2802473170569", ",", "2802487507083", ",", "2802487520205", ",",
"2895454074807", ",", "2896358055948", ",", "2896616342835", ",",
"2989338973308", ",", "2990630388060", ",", "3080009730492", ",",
"3080138870655", ",", "3081157629201", ",", "3081430259163", ",",
"3081430272285", ",", "3082319891397", ",", "3082319906706", ",",
"3082449046869", ",", "3082578171723", ",", "3082578177555", ",",
"3083482152864", ",", "3083482161612", ",", "3083496510519", ",",
"3083496514893", ",", "3083611294485", ",", "3083754797406", ",",
"3084644414331", ",", "3084644423079", ",", "3084658765425", ",",
"3084902694657", ",", "3178787598990", ",", "3179045885877", ",",
"3270735395046", ",", "3271768509789", ",", "3271768522911", ",",
"3272930777817", ",", "3272930784378", ",", "3273189064704", ",",
"3358191978108", ",", "3360516501042", ",", "3361406139108", ",",
"3362453609319", ",", "3363587165682", ",", "3364878576060", ",",
"3364878576789", ",", "3364892916948", ",", "3364892919135", ",",
"3364892923509", ",", "3364892925696", ",", "3365007720597", ",",
"3365022063672", ",", "3365294695821", ",", "3365911688616", ",",
"3365911691532", ",", "3365926051374", ",", "3366040831695", ",",
"3366040837527", ",", "3366055191537", ",", "3366169971129", ",",
"3366169976232", ",", "3366184318578", ",", "3367073957373", ",",
"3367088312841", ",", "3367203098994", ",", "3367203105555", ",",
"3367217446443", ",", "3367332245718", ",", "3461346275634", ",",
"3461346282195", ",", "3553035797925", ",", "3553164924966", ",",
"3553294071690", ",", "3555360320859", ",", "3643964815752", ",",
"3644997930495", ",", "3646016702163", ",", "3646145842326", ",",
"3647178963630", ",", "3647178964359", ",", "3647193315453", ",",
"3647308111083", ",", "3647322462177", ",", "3647322466551", ",",
"3647437252704", ",", "3648341225097", ",", "3648341240406", ",",
"3648470380569", ",", "3648484730205", ",", "3648599506152", ",",
"3648599507610", ",", "3648599514171", ",", "3648599519274", ",",
"3648613861620", ",", "3648613870368", ",", "3649503493125", ",",
"3649503493854", ",", "3649517844948", ",", "3649517851509", ",",
"3649632627456", ",", "3649646978550", ",", "3649761766890", ",",
"3649776131835", ",", "3742613544087", ",", "3743646671952", ",",
"3743646678513", ",", "3835594468008", ",", "3836627595873", ",",
"3837789857340", ",", "3838048137666", ",", "3927556613700", ",",
"3928446238644", ",", "3929608515420", ",", "3929622849747", ",",
"3929622862869", ",", "3929737656312", ",", "3929751992097", ",",
"3929881138821", ",", "3930770763765", ",", "3930785124336", ",",
"3930899904657", ",", "3930899908302", ",", "3930899911218", ",",
"3930914251377", ",", "3931043400288", ",", "3931043406849", ",",
"3931933038354", ",", "3932062176330", ",", "3932062179246", ",",
"3932076519405", ",", "3932191305558", ",", "4023751678938", ",",
"4024913946966", ",", "4024913953527", ",", "4025043093690", ",",
"4120219387260", ",", "4120348527423", ",", "4120477667586", ",",
"4208694755112", ",", "4208823895275", ",", "4210890137883", ",",
"4211019264924", ",", "4211134055451", ",", "4211148405087", ",",
"4211148411648", ",", "4211162767116", ",", "4212038046069", ",",
"4212038049714", ",", "4212052386228", ",", "4212052388415", ",",
"4212052401537", ",", "4212167186232", ",", "4212310666554", ",",
"4213200305349", ",", "4213200314097", ",", "4213214647695", ",",
"4213343794419", ",", "4213458584946", ",", "4213458593694", ",",
"4213472941143", ",", "4214362568274", ",", "4214376917910", ",",
"4214491700418", ",", "4214491706250", ",", "4214506051512", ",",
"4214620839852", ",", "4214635198236", ",", "4306439506680", ",",
"4308505751475", ",", "4308634885077", ",", "4400582687694", ",",
"4401486655713", ",", "4401615808998", ",", "4402778068278", ",",
"4490995144869", ",", "4491124278471", ",", "4492415680101", ",",
"4492415686662", ",", "4493434451769", ",", "4493434456143", ",",
"4493563605054", ",", "4494596713236", ",", "4494596720526", ",",
"4494725855586", ",", "4495629835269", ",", "4495644184176", ",",
"4495644190737", ",", "4495773324339", ",", "4495773326526", ",",
"4495888124343", ",", "4496792111316", ",", "4496806460952", ",",
"4496921249292", ",", "4496921251479", ",", "4496935592367", ",",
"4497050390184", ",", "4497050392371", ",", "4497064732530", ",",
"4497064739091", ",", "4591064414997", ",", "4591193555160", ",",
"4685078466783", ",", "4773424687911", ",", "4773682961676", ",",
"4773682968237", ",", "4774845223143", ",", "4775878337886", ",",
"4775878344447", ",", "4776897124863", ",", "4776911472312", ",",
"4777026250446", ",", "4777026256278", ",", "4777040605914", ",",
"4777155389880", ",", "4777155392067", ",", "4777169746077", ",",
"4778059387059", ",", "4778188513371", ",", "4778202860820", ",",
"4778317651347", ",", "4779221639778", ",", "4779221641965", ",",
"4779221648526", ",", "4779350781399", ",", "4779365124474", ",",
"4779479928123", ",", "4872460843296", ",", "4873493962413", ",",
"4966604009001", ",", "4967507990142", ",", "5057145626022", ",",
"5058293524731", ",", "5059326652596", ",", "5059326661344", ",",
"5059455792759", ",", "5059455795675", ",", "5059584927090", ",",
"5059584939483", ",", "5059599275997", ",", "5059599278184", ",",
"5060618048394", ",", "5060632403862", ",", "5060632406049", ",",
"5060632410423", ",", "5060747190744", ",", "5061651178446", ",",
"5061651184278", ",", "5061665525166", ",", "5061780315693", ",",
"5061794658768", ",", "5061909451482", ",", "5061909452211", ",",
"5061909455856", ",", "5061909458043", ",", "5153469830694", ",",
"5153469837984", ",", "5154632092161", ",", "5154632100909", ",",
"5154646454190", ",", "5154761233053", ",", "5154761239614", ",",
"5154890379777", ",", "5156052628122", ",", "5247613016811", ",",
"5248789633017", ",", "5250066671160", ",", "5250066673347", ",",
"5338556383545", ",", "5341756185432", ",", "5341756192722", ",",
"5341770546003", ",", "5341784889807", ",", "5341784892723", ",",
"5341784894181", ",", "5341784894910", ",", "5341899685437", ",",
"5342014463571", ",", "5342014471590", ",", "5342028819039", ",",
"5342918445441", ",", "5342918446170", ",", "5342918454189", ",",
"5342918457105", ",", "5342918461479", ",", "5342918462208", ",",
"5342932806741", ",", "5343047584146", ",", "5343047586333", ",",
"5343047596539", ",", "5343047597997", ",", "5343061946904", ",",
"5343076291437", ",", "5343176725038", ",", "5343176726496", ",",
"5343176728683", ",", "5343176731599", ",", "5343205425039", ",",
"5343205432329", ",", "5344080705450", ",", "5344080706179", ",",
"5344080715656", ",", "5344095064563", ",", "5344095066750", ",",
"5344095068937", ",", "5344109422218", ",", "5344209846342", ",",
"5344209855090", ",", "5344209858735", ",", "5344209860922", ",",
"5344224205455", ",", "5344338994524", ",", "5344338996711", ",",
"5344339001814", ",", "5344353344889", ",", "5436157641669", ",",
"5437319909697", ",", "5530171693455", ",", "5531463081963", ",",
"5620713284232", ",", "5620971577680", ",", "5622004685862", ",",
"5622019041330", ",", "5622133839147", ",", "5623037807166", ",",
"5624200081755", ",", "5624314872282", ",", "5624329221918", ",",
"5625347980464", ",", "5625362332287", ",", "5625362345409", ",",
"5625477127917", ",", "5625491470263", ",", "5625606269538", ",",
"5626510244118", ",", "5626639389384", ",", "5626639395945", ",",
"5626782887202", ",", "5718730668678", ",", "5719491172413", ",",
"5719749452739", ",", "5720653433880", ",", "5720782574043", ",",
"5720911701084", ",", "5805914627610", ",", "5812730356977", ",",
"5812730363538", ",", "5812859498598", ",", "5813634351240", ",",
"5813763491403", ",", "5903401107600", ",", "5904305095302", ",",
"5905453000572", ",", "5905467350208", ",", "5905725637095", ",",
"5906615255478", ",", "5906615256207", ",", "5906615257665", ",",
"5906615268600", ",", "5906744396370", ",", "5906758747464", ",",
"5906873548926", ",", "5906873551113", ",", "5907906660024", ",",
"5907906664398", ",", "5907906666585", ",", "5907906670959", ",",
"5907906672417", ",", "5908035799458", ",", "5908035804561", ",",
"5908035811122", ",", "5908179287799", ",", "5908939779141", ",",
"5908939791534", ",", "5908939793721", ",", "5909068920762", ",",
"5909083276959", ",", "5909327200359", ",", "6000772797792", ",",
"6000887587590", ",", "6002178976098", ",", "6003097320726", ",",
"6003341237565", ",", "6003341244126", ",", "6095030753295", ",",
"6095030766417", ",", "6096193014762", ",", "6097226149188", ",",
"6097484422953", ",", "6185572363755", ",", "6185701510479", ",",
"6185844999549", ",", "6186734625222", ",", "6187896880128", ",",
"6187896886689", ",", "6188011683777", ",", "6189044796333", ",",
"6189044797791", ",", "6189044806539", ",", "6189059159091", ",",
"6189073499250", ",", "6189073501437", ",", "6189073504353", ",",
"6189173948160", ",", "6189188290506", ",", "6189303073014", ",",
"6189303076659", ",", "6189303088323", ",", "6189317421921", ",",
"6189317435043", ",", "6190207062174", ",", "6190221413997", ",",
"6190235762904", ",", "6190336200150", ",", "6190336208898", ",",
"6190479692865", ",", "6191369317809", ",", "6191369322912", ",",
"6191369323641", ",", "6191369325099", ",", "6191369330931", ",",
"6191369332389", ",", "6191383671090", ",", "6191383678380", ",",
"6191398030203", ",", "6191498470365", ",", "6191627598135", ",",
"6191627606154", ",", "6191627611257", ",", "6191641954332", ",",
"6191656302510", ",", "6283187970786", ",", "6283446264234", ",",
"6284350232253", ",", "6284479378977", ",", "6284479385538", ",",
"6377331156174", ",", "6377589429939", ",", "6378622557804", ",",
"6379913952873", ",", "6470312066973", ",", "6470455556772", ",",
"6470570347299", ",", "6471474335730", ",", "6471474341562", ",",
"6471488686824", ",", "6471617824800", ",", "6471732617514", ",",
"6471746958402", ",", "6472636590636", ",", "6472650946104", ",",
"6472765732986", ",", "6472765746108", ",", "6472894878981", ",",
"6472909232991", ",", "6472909235178", ",", "6473798853561", ",",
"6473927993724", ",", "6473942354295", ",", "6474071483523", ",",
"6565875787593", ",", "6565875800715", ",", "6566779775295", ",",
"6568200310527", ",", "6660018966420", ",", "6660922954122", ",",
"6662085209028", ",", "6662343495915", ",", "6751593691623", ",",
"6751722844908", ",", "6752755966212", ",", "6752999896902", ",",
"6753014233416", ",", "6753903864921", ",", "6753903871482", ",",
"6753918214557", ",", "6754033013832", ",", "6754047370029", ",",
"6754162154724", ",", "6755066140239", ",", "6755195281860", ",",
"6755209616187", ",", "6755209629309", ",", "6755209631496", ",",
"6756228390771", ",", "6756228403164", ",", "6756357530205", ",",
"6756357544056", ",", "6756371886402", ",", "6756486675471", ",",
"6756486677658", ",", "6756501030939", ",", "6842250102816", ",",
"6843426713190", ",", "6844560276843", ",", "6844588976115", ",",
"6845722538310", ",", "6845751237582", ",", "6846884801235", ",",
"6848047043748", ",", "6848061411609", ",", "6848176183911", ",",
"6848176188285", ",", "6848176197033", ",", "6849209305215", ",",
"6849223672347", ",", "6849338458500", ",", "6850371572514", ",",
"6850371585636", ",", "6850500719967", ",", "6850629851382", ",",
"6936378934194", ",", "6936393282372", ",", "6939865717137", ",",
"6939894416409", ",", "6941056677876", ",", "6942190222575", ",",
"6942190227678", ",", "6942190235697", ",", "6942190237155", ",",
"6942218939343", ",", "6943352484042", ",", "6943352497164", ",",
"6943366847529", ",", "6943481624205", ",", "6943610764368", ",",
"6944514746967", ",", "6944514751341", ",", "6944773030209", ",",
"7029388549368", ",", "7030665595530", ",", "7030679943708", ",",
"7031698721937", ",", "7031813506632", ",", "7031827856268", ",",
"7031827856997", ",", "7031842205904", ",", "7032875333769", ",",
"7032975768099", ",", "7034008895964", ",", "7034138029566", ",",
"7034166728109", ",", "7035171153057", ",", "7035171157431", ",",
"7035185507796", ",", "7035199838478", ",", "7035199855245", ",",
"7036333404318", ",", "7036333416711", ",", "7036347759786", ",",
"7036347762702", ",", "7036362116712", ",", "7036362118170", ",",
"7036462543752", ",", "7036606044486", ",", "7037495668701", ",",
"7037495678178", ",", "7037495679636", ",", "7037510012505", ",",
"7037510028543", ",", "7037524363599", ",", "7037624814696", ",",
"7037639152668", ",", "7037653503762", ",", "7037653513239", ",",
"7037753953401", ",", "7037753956317", ",", "7037753957046", ",",
"7038657925065", ",", "7038657926523", ",", "7038657931626", ",",
"7038657933813", ",", "7038657936000", ",", "7038657940374", ",",
"7038787065228", ",", "7038787073976", ",", "7038787077621", ",",
"7038787080537", ",", "7038801420696", ",", "7038801424341", ",",
"7038801425799", ",", "7038815771790", ",", "7038815772519", ",",
"7038916217784", ",", "7038930569607", ",", "7038944911953", ",",
"7130476593351", ",", "7130605720392", ",", "7130605726953", ",",
"7131767994981", ",", "7132801116285", ",", "7224878045943", ",",
"7226040307410", ",", "7315290516240", ",", "7315548783444", ",",
"7315548790005", ",", "7316581911309", ",", "7317600676416", ",",
"7317615039174", ",", "7317744166215", ",", "7317744179337", ",",
"7318762944444", ",", "7318777302828", ",", "7318892091168", ",",
"7319021218209", ",", "7319021220396", ",", "7319021225499", ",",
"7319021226957", ",", "7319021227686", ",", "7319021231331", ",",
"7319021232060", ",", "7319021233518", ",", "7319035567845", ",",
"7319939562108", ",", "7320068695710", ",", "7320183480405", ",",
"7320183481863", ",", "7320183489153", ",", "7321087461546", ",",
"7321101810453", ",", "7321216601709", ",", "7321230959364", ",",
"7321345750620", ",", "7412906123271", ",", "7414197524901", ",",
"7507049295537", ",", "7507049302098", ",", "7507307575863", ",",
"7508211563565", ",", "7508469850452", ",", "7509373818471", ",",
"7509502965195", ",", "7597978319925", ",", "7599140581392", ",",
"7600159353060", ",", "7600302842859", ",", "7601192483112", ",",
"7601192489673", ",", "7601321629836", ",", "7601450756877", ",",
"7601465110887", ",", "7602354736560", ",", "7602354744579", ",",
"7602369092028", ",", "7602483878181", ",", "7602483878910", ",",
"7602483885471", ",", "7602483889116", ",", "7602483889845", ",",
"7602498227817", ",", "7602498232191", ",", "7602613025634", ",",
"7602613031466", ",", "7602613032195", ",", "7603516998027", ",",
"7603517006775", ",", "7603531360056", ",", "7603646152770", ",",
"7603775284185", ",", "7603775291475"}], "}"}]}], ";"}], "\n",
RowBox[{
RowBox[{"input1", "=", "30"}], ";",
RowBox[{"input2", "=", "25"}], ";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"initCond", "=",
RowBox[{"Flatten", "[",
RowBox[{"{",
RowBox[{
RowBox[{"Table", "[",
RowBox[{"1", ",",
RowBox[{"{", "input1", "}"}]}], "]"}], ",", "2", ",",
RowBox[{"Table", "[",
RowBox[{"1", ",",
RowBox[{"{", "input2", "}"}]}], "]"}]}], "}"}], "]"}]}],
";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"steps", "=",
RowBox[{"3", " ", "input2"}]}], ";"}], "\n",
RowBox[{
RowBox[{"differentSR", "=",
RowBox[{"Flatten", "[",
RowBox[{"Take", "[",
RowBox[{
RowBox[{"Union", "[",
RowBox[{
RowBox[{"Table", "[",
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{
"subtractionRules", "\[LeftDoubleBracket]", "i",
"\[RightDoubleBracket]"}], ",",
RowBox[{"CellularAutomaton", "[",
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{
"subtractionRules", "\[LeftDoubleBracket]", "i",
"\[RightDoubleBracket]"}], ",", "3", ",", "1"}], "}"}], ",",
RowBox[{"{",
RowBox[{"initCond", ",", "0"}], "}"}], ",", "steps"}], "]"}]}],
"}"}], ",",
RowBox[{"{",
RowBox[{"i", ",",
RowBox[{"Length", "[", "subtractionRules", "]"}]}], "}"}]}],
"]"}], ",",
RowBox[{"SameTest", "\[Rule]",
RowBox[{"(",
RowBox[{
RowBox[{
RowBox[{"#1", "[",
RowBox[{"[", "2", "]"}], "]"}], "\[Equal]",
RowBox[{"#2", "[",
RowBox[{"[", "2", "]"}], "]"}]}], "&"}], ")"}]}]}], "]"}], ",",
"All", ",", "1"}], "]"}], "]"}]}], ";"}], "\n",
RowBox[{"ListAnimate", "[",
RowBox[{
RowBox[{
RowBox[{"ArrayPlot", "[",
RowBox[{
RowBox[{"CellularAutomaton", "[",
RowBox[{
RowBox[{"{",
RowBox[{"#", ",", "3", ",", "1"}], "}"}], ",",
RowBox[{"{",
RowBox[{"initCond", ",", "0"}], "}"}], ",", "steps"}], "]"}], ",",
RowBox[{"PlotLabel", "\[Rule]", "#"}]}], "]"}], "&"}], "/@",
"differentSR"}], "]"}]}], "Input",
CellChangeTimes->{
3.385895902988077*^9, 3.39304448953125*^9, 3.3931265638125*^9,
3.393126735234375*^9, {3.393126795078125*^9, 3.39312685496875*^9}, {
3.393127009234375*^9, 3.393127011734375*^9}, 3.393208351546875*^9,
3.393208405734375*^9, {3.39320958034375*^9, 3.393209585796875*^9}, {
3.39320967340625*^9, 3.393209674140625*^9}, {3.393209724453125*^9,
3.393209724859375*^9}, {3.393209763515625*^9, 3.39320978928125*^9}, {
3.393209832375*^9, 3.3932098328125*^9}, {3.393209882703125*^9,
3.393209981453125*^9}, {3.3932100143125*^9, 3.393210014765625*^9}, {
3.39321014996875*^9, 3.39321018525*^9}, {3.39321021984375*^9,
3.39321022025*^9}, {3.393210276265625*^9, 3.393210276546875*^9}, {
3.3932103075*^9, 3.393210333421875*^9}, {3.393210371046875*^9,
3.3932103863125*^9}, {3.39321048496875*^9, 3.39321049059375*^9},
3.39321056896875*^9, {3.3932106055*^9, 3.393210605890625*^9}, {
3.39321064153125*^9, 3.393210643109375*^9}, {3.39321073321875*^9,
3.39321073371875*^9}, {3.393210839921875*^9, 3.3932108405625*^9}, {
3.39321091315625*^9, 3.393210915359375*^9}, 3.393378520189248*^9,
3.393378551424162*^9},
FontSize->12],
Cell[TextData[{
ButtonBox["\[FilledLeftTriangle]\[ThickSpace]\[ThickSpace]\[ThickSpace]",
BaseStyle->"SlidePreviousNextLink",
ButtonFunction:>FrontEndExecute[{
FrontEndToken[
FrontEnd`ButtonNotebook[], "ScrollPagePrevious"]}],
ButtonNote->FEPrivate`FrontEndResource[
"FEStrings", "SlideshowPrevSlideText"],
ButtonFrame->"None"],
"\[ThickSpace]\[ThickSpace]|\[ThickSpace]\[ThickSpace]",
ButtonBox["\[ThickSpace]\[ThickSpace]\[ThickSpace]\[FilledRightTriangle]",
BaseStyle->"SlidePreviousNextLink",
ButtonFunction:>FrontEndExecute[{
FrontEndToken[
FrontEnd`ButtonNotebook[], "ScrollPageNext"]}],
ButtonNote->FEPrivate`FrontEndResource[
"FEStrings", "SlideshowNextSlideText"],
ButtonFrame->"None"]
}], "PreviousNext"]
}, Open ]]
}, Open ]]
}, Open ]],
Cell[CellGroupData[{
Cell["", "SlideShowNavigationBar",
CellTags->"SlideShowHeader"],
Cell[CellGroupData[{
Cell["A couple of tools for analysis", "Section",
CellChangeTimes->{{3.3932120378125*^9, 3.3932120410625*^9}, {
3.39338350624885*^9, 3.393383517685294*^9}}],
Cell[CellGroupData[{
Cell[TextData[StyleBox["Cartography",
FontColor->RGBColor[
0.9714045929655909, 0.6775158312352179, 0.07415884641794461]]], "Subsection",\
CellChangeTimes->{
3.3824524252213373`*^9, {3.39303943990625*^9, 3.393039450140625*^9}, {
3.39304107571875*^9, 3.3930411009375*^9}, {3.393208508046875*^9,
3.393208512921875*^9}, {3.3932141789375*^9, 3.39321418128125*^9}}],
Cell[TextData[{
"Only some of the bits of the rule are used for a specific calculation.\nWe \
can measure how far are the rules from each other in an ",
Cell[BoxData[
FormBox[
SuperscriptBox[
RowBox[{"k", " "}],
RowBox[{
RowBox[{"2", " ", "r"}], " ", "+", " ", "1"}]], TraditionalForm]]],
"- dimensional space with ",
StyleBox["k-",
FontSlant->"Italic"],
"long axes.\nOne method to do this is to produce pair separation \
histograms."
}], "Text",
CellChangeTimes->{{3.393215357765625*^9, 3.39321538584375*^9}, {
3.39321569225*^9, 3.393215699265625*^9}, {3.393215767390625*^9,
3.393215959046875*^9}, {3.3933852242692413`*^9, 3.393385224840062*^9}}],
Cell[BoxData[{
RowBox[{
RowBox[{"rulesLongForm", "=",
RowBox[{"Map", "[",
RowBox[{
RowBox[{
RowBox[{"IntegerDigits", "[",
RowBox[{"#", ",", "3", ",", "27"}], "]"}], "&"}], ",",
"subtractionRules"}], "]"}]}], ";"}], "\n",
RowBox[{
RowBox[{"euclideanDist", "=",
RowBox[{"Sort", "[",
RowBox[{"Flatten", "[",
RowBox[{"Table", "[",
RowBox[{
RowBox[{
RowBox[{"Norm", "[",
RowBox[{
RowBox[{
"rulesLongForm", "\[LeftDoubleBracket]", "i",
"\[RightDoubleBracket]"}], "-",
RowBox[{
"rulesLongForm", "\[LeftDoubleBracket]", "j",
"\[RightDoubleBracket]"}]}], "]"}], "//", "N"}], ",",
RowBox[{"{",
RowBox[{"i", ",", "1", ",",
RowBox[{
RowBox[{"Length", "[", "subtractionRules", "]"}], "-", "1"}]}],
"}"}], ",",
RowBox[{"{",
RowBox[{"j", ",",
RowBox[{"i", "+", "1"}], ",",
RowBox[{"Length", "[", "subtractionRules", "]"}]}], "}"}]}], "]"}],
"]"}], "]"}]}], ";"}], "\n",
RowBox[{
RowBox[{"manhattanDist", "=",
RowBox[{"Sort", "[",
RowBox[{"Flatten", "[",
RowBox[{"Table", "[",
RowBox[{
RowBox[{
RowBox[{"Norm", "[",
RowBox[{
RowBox[{
RowBox[{
"rulesLongForm", "\[LeftDoubleBracket]", "i",
"\[RightDoubleBracket]"}], "-",
RowBox[{
"rulesLongForm", "\[LeftDoubleBracket]", "j",
"\[RightDoubleBracket]"}]}], ",", "1"}], "]"}], "//", "N"}], ",",
RowBox[{"{",
RowBox[{"i", ",", "1", ",",
RowBox[{
RowBox[{"Length", "[", "subtractionRules", "]"}], "-", "1"}]}],
"}"}], ",",
RowBox[{"{",
RowBox[{"j", ",",
RowBox[{"i", "+", "1"}], ",",
RowBox[{"Length", "[", "subtractionRules", "]"}]}], "}"}]}], "]"}],
"]"}], "]"}]}], ";"}], "\n",
RowBox[{
RowBox[{"<<", "\"\\""}], ";"}], "\n",
RowBox[{"Histogram", "[",
RowBox[{"euclideanDist", ",",
RowBox[{"PlotLabel", "->", "\"\\""}], ",",
RowBox[{"AxesLabel", "\[Rule]",
RowBox[{"{",
RowBox[{"\"\\"", ",", "\"\\""}], "}"}]}],
",",
RowBox[{"BarStyle", "\[Rule]", "Red"}], ",",
RowBox[{"ImageSize", "\[Rule]", "700"}]}], "]"}]}], "Input",
CellChangeTimes->{{3.393214542546875*^9, 3.393214581515625*^9}, {
3.393215227515625*^9, 3.3932152480625*^9}, 3.3933790275087376`*^9},
FontSize->12,
CellTags->"S5.32.1"],
Cell[BoxData[
RowBox[{"Histogram", "[",
RowBox[{"manhattanDist", ",",
RowBox[{"PlotLabel", "->", "\"\\""}], ",",
RowBox[{"AxesLabel", "\[Rule]",
RowBox[{"{",
RowBox[{"\"\\"", ",", "\"\\""}], "}"}]}],
",",
RowBox[{"BarStyle", "\[Rule]", "Red"}], ",",
RowBox[{"ImageSize", "\[Rule]", "700"}]}], "]"}]], "Input",
CellChangeTimes->{{3.393214805484375*^9, 3.393214808609375*^9}, {
3.393215560328125*^9, 3.393215562109375*^9}, {3.39321561115625*^9,
3.393215651546875*^9}},
FontSize->12]
}, Open ]],
Cell[CellGroupData[{
Cell[TextData[StyleBox["Bit activity",
FontColor->RGBColor[
0.9714045929655909, 0.6775158312352179, 0.07415884641794461]]], "Subsection",\
CellChangeTimes->{
3.3824524252213373`*^9, {3.39303943990625*^9, 3.393039450140625*^9}, {
3.39304107571875*^9, 3.3930411009375*^9}, {3.393208508046875*^9,
3.393208512921875*^9}, {3.39321418459375*^9, 3.393214192125*^9}}],
Cell["\<\
Two types of measurements:
Activity of all bits of the rule in each step.
Activity of each bit of the rule in time.\
\>", "Text",
CellChangeTimes->{{3.393215999671875*^9, 3.393216008515625*^9}, {
3.393216071578125*^9, 3.393216072546875*^9}, {3.393216974671875*^9,
3.39321699521875*^9}, {3.393343638601989*^9, 3.393343728381085*^9}, {
3.393382722461819*^9, 3.393382729371755*^9}}],
Cell[BoxData[{
RowBox[{
RowBox[{"input1", "=", "15"}], ";",
RowBox[{"input2", "=", "11"}], ";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"initCond", "=",
RowBox[{"Flatten", "[",
RowBox[{"{",
RowBox[{
RowBox[{"Table", "[",
RowBox[{"1", ",",
RowBox[{"{", "input1", "}"}]}], "]"}], ",", "2", ",",
RowBox[{"Table", "[",
RowBox[{"1", ",",
RowBox[{"{", "input2", "}"}]}], "]"}]}], "}"}], "]"}]}],
";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"colors", "=", "3"}], ";",
RowBox[{"radius", "=", "1"}], ";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"steps", "=",
RowBox[{"3", " ", "input2"}]}], ";"}], "\n",
RowBox[{"Manipulate", "[",
RowBox[{
RowBox[{"ListPlot", "[",
RowBox[{
RowBox[{"Table", "[",
RowBox[{
RowBox[{"Count", "[",
RowBox[{
RowBox[{"Partition", "[",
RowBox[{
RowBox[{
RowBox[{"CellularAutomaton", "[",
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{
"differentSR", "\[LeftDoubleBracket]", "r",
"\[RightDoubleBracket]"}], ",", "3"}], "}"}], ",",
RowBox[{"{",
RowBox[{"initCond", ",", "0"}], "}"}], ",", "steps", ",",
RowBox[{"{",
RowBox[{"All", ",",
RowBox[{"{",
RowBox[{
RowBox[{"-", "steps"}], ",", "steps"}], "}"}]}], "}"}]}],
"]"}], "\[LeftDoubleBracket]", "s", "\[RightDoubleBracket]"}],
",",
RowBox[{
RowBox[{"2", " ", "radius"}], "+", "1"}], ",", "1"}], "]"}], ",",
RowBox[{"IntegerDigits", "[",
RowBox[{"i", ",", "colors", ",",
RowBox[{
RowBox[{"2", " ", "radius"}], "+", "1"}]}], "]"}]}], "]"}], ",",
RowBox[{"{",
RowBox[{"i", ",", "0", ",",
RowBox[{
SuperscriptBox["colors",
RowBox[{
RowBox[{"2", " ", "radius"}], "+", "1"}]], "-", "1"}]}], "}"}]}],
"]"}], ",",
RowBox[{"Joined", "\[Rule]", " ", "True"}], ",",
RowBox[{"AxesOrigin", "\[Rule]",
RowBox[{"{",
RowBox[{"1", ",", "0"}], "}"}]}], ",",
RowBox[{"PlotRange", "\[Rule]",
RowBox[{"{",
RowBox[{"0", ",", "30"}], "}"}]}], ",",
RowBox[{"PlotLabel", "\[Rule]",
RowBox[{
"differentSR", "\[LeftDoubleBracket]", "r",
"\[RightDoubleBracket]"}]}]}], "]"}], ",",
RowBox[{"{",
RowBox[{"s", ",", "1", ",", "steps", ",", "1"}], "}"}], ",",
RowBox[{"{",
RowBox[{"r", ",", "1", ",",
RowBox[{"Length", "[", "differentSR", "]"}], ",", "1"}], "}"}]}],
"]"}]}], "Input",
CellChangeTimes->{{3.39321749640625*^9, 3.393217500921875*^9}, {
3.393380604956997*^9, 3.3933806136394815`*^9}, 3.3933811369419537`*^9, {
3.3933820925360303`*^9, 3.3933820977435184`*^9}, {3.3933828149047456`*^9,
3.3933828200221043`*^9}, {3.393382864746414*^9, 3.3933828688322897`*^9}},
FontSize->12],
Cell[BoxData[
RowBox[{"Manipulate", "[",
RowBox[{
RowBox[{"ListPlot", "[",
RowBox[{
RowBox[{
RowBox[{"Transpose", "[",
RowBox[{"Table", "[",
RowBox[{
RowBox[{"Count", "[",
RowBox[{
RowBox[{"Partition", "[",
RowBox[{
RowBox[{
RowBox[{"CellularAutomaton", "[",
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{
"differentSR", "\[LeftDoubleBracket]", "r",
"\[RightDoubleBracket]"}], ",", "3"}], "}"}], ",",
RowBox[{"{",
RowBox[{"initCond", ",", "0"}], "}"}], ",", "steps", ",",
RowBox[{"{",
RowBox[{"All", ",",
RowBox[{"{",
RowBox[{
RowBox[{"-", "steps"}], ",", "steps"}], "}"}]}], "}"}]}],
"]"}], "\[LeftDoubleBracket]", "j", "\[RightDoubleBracket]"}],
",",
RowBox[{
RowBox[{"2", " ", "radius"}], "+", "1"}], ",", "1"}], "]"}],
",",
RowBox[{"IntegerDigits", "[",
RowBox[{"i", ",", "colors", ",",
RowBox[{
RowBox[{"2", " ", "radius"}], "+", "1"}]}], "]"}]}], "]"}], ",",
RowBox[{"{",
RowBox[{"j", ",", "steps"}], "}"}], ",",
RowBox[{"{",
RowBox[{"i", ",", "0", ",",
RowBox[{
SuperscriptBox["colors",
RowBox[{
RowBox[{"2", " ", "radius"}], "+", "1"}]], "-", "1"}]}],
"}"}]}], "]"}], "]"}], "\[LeftDoubleBracket]", "s",
"\[RightDoubleBracket]"}], ",",
RowBox[{"Joined", "\[Rule]", "True"}], ",",
RowBox[{"AxesOrigin", "\[Rule]",
RowBox[{"{",
RowBox[{"0", ",", "0"}], "}"}]}], ",",
RowBox[{"PlotRange", "\[Rule]",
RowBox[{"{",
RowBox[{"0", ",", "25"}], "}"}]}], ",",
RowBox[{"PlotLabel", "\[Rule]",
RowBox[{
"differentSR", "\[LeftDoubleBracket]", "r",
"\[RightDoubleBracket]"}]}]}], "]"}], ",",
RowBox[{"{",
RowBox[{"s", ",", "1", ",",
SuperscriptBox["colors",
RowBox[{
RowBox[{"2", " ", "radius"}], "+", "1"}]], ",", "1"}], "}"}], ",",
RowBox[{"{",
RowBox[{"r", ",", "1", ",",
RowBox[{"Length", "[", "differentSR", "]"}], ",", "1"}], "}"}]}],
"]"}]], "Input",
CellChangeTimes->{{3.3933818820734*^9, 3.39338193114396*^9}, {
3.3933819669454403`*^9, 3.3933819683574705`*^9}, {3.3933821286880145`*^9,
3.3933821287481008`*^9}, 3.393382459503704*^9, {3.3933825438650093`*^9,
3.3933825472098193`*^9}, {3.393382597532179*^9, 3.3933825975421934`*^9}, {
3.393382656216563*^9, 3.393382658710149*^9}},
FontSize->12],
Cell[TextData[{
ButtonBox["\[FilledLeftTriangle]\[ThickSpace]\[ThickSpace]\[ThickSpace]",
BaseStyle->"SlidePreviousNextLink",
ButtonFunction:>FrontEndExecute[{
FrontEndToken[
FrontEnd`ButtonNotebook[], "ScrollPagePrevious"]}],
ButtonNote->FEPrivate`FrontEndResource[
"FEStrings", "SlideshowPrevSlideText"],
ButtonFrame->"None"],
"\[ThickSpace]\[ThickSpace]|\[ThickSpace]\[ThickSpace]",
ButtonBox["\[ThickSpace]\[ThickSpace]\[ThickSpace]\[FilledRightTriangle]",
BaseStyle->"SlidePreviousNextLink",
ButtonFunction:>FrontEndExecute[{
FrontEndToken[
FrontEnd`ButtonNotebook[], "ScrollPageNext"]}],
ButtonNote->FEPrivate`FrontEndResource[
"FEStrings", "SlideshowNextSlideText"],
ButtonFrame->"None"]
}], "PreviousNext"]
}, Open ]]
}, Open ]]
}, Open ]],
Cell[CellGroupData[{
Cell["", "SlideShowNavigationBar",
CellTags->"SlideShowHeader"],
Cell[CellGroupData[{
Cell["Brief discussion", "Section",
CellChangeTimes->{{3.393214321359375*^9, 3.39321432553125*^9}}],
Cell["\<\
Floating point CA will lead to CA - ALU.
CA probably not the best system to perform arithmetical calculations.
How to construct or search for the best system?
Comparing with natural systems.
What sort of computations is nature doing around us?
Can we program nature?
\
\>", "Text",
CellChangeTimes->{
3.3933834806119857`*^9, {3.393383713446786*^9, 3.3933837378618927`*^9}, {
3.3933837708593407`*^9, 3.3933841206222754`*^9}}],
Cell[TextData[{
ButtonBox["\[FilledLeftTriangle]\[ThickSpace]\[ThickSpace]\[ThickSpace]",
BaseStyle->"SlidePreviousNextLink",
ButtonFunction:>FrontEndExecute[{
FrontEndToken[
FrontEnd`ButtonNotebook[], "ScrollPagePrevious"]}],
ButtonNote->FEPrivate`FrontEndResource[
"FEStrings", "SlideshowPrevSlideText"],
ButtonFrame->"None"],
"\[ThickSpace]\[ThickSpace]|\[ThickSpace]\[ThickSpace]",
ButtonBox["\[ThickSpace]\[ThickSpace]\[ThickSpace]\[FilledRightTriangle]",
BaseStyle->"SlidePreviousNextLink",
ButtonFunction:>FrontEndExecute[{
FrontEndToken[
FrontEnd`ButtonNotebook[], "ScrollPageNext"]}],
ButtonNote->FEPrivate`FrontEndResource[
"FEStrings", "SlideshowNextSlideText"],
ButtonFrame->"None"]
}], "PreviousNext"]
}, Open ]]
}, Open ]],
Cell["", "SlideShowNavigationBar",
CellTags->"SlideShowHeader"]
},
WindowSize->{1016, 651},
WindowMargins->{{0, Automatic}, {Automatic, 0}},
ShowSelection->True,
FrontEndVersion->"6.0 for Microsoft Windows (32-bit) (April 20, 2007)",
StyleDefinitions->Notebook[{
Cell[
StyleData[StyleDefinitions -> "Default.nb"]],
Cell[
StyleData[All, "SlideShow"], PageWidth -> WindowWidth, DockedCells -> {
FEPrivate`FrontEndResource["FEExpressions", "SlideshowToolbar"],
Cell[
GraphicsData[
"CompressedBitmap",
"eJycvWd4W1eWJcpHUsF22a7QVT3zXvdMv5n53o/XX89MhzdfV1d1V5e7squ6\n\
qlzlCs6yZUu2bOUsy8o5kaIiFaics0RKopgzCRLMOYARBEGAIEhkgFxv733O\n\
BaHgmX5P33dw7j33AgKBs9Zea599L34xa+ncDz+btfTjD2b9xY8Xz1o49+MP\n\
lvzFjxYspqGE/y0uLmFzXFzcob+I423Qpn544t82fnhq+P/H6EHu4qlNxiXQ\n\
wyRvyZGpMx3qzG+rMycnI3TmZMyZ/4Ufp/Euvw6++dSLTcbF8576XxKnDqg+\n\
cepYQuwxPnNqbDICRCL0QpOR8BPvND76X/MBNShPfS5mj/61qL/jf0gn7xfh\n\
iRAik2FqEdqbjHuej8n/m/CM10uM/kffMrYi/JfJB4IIfzTy8STyoxyIj27J\n\
ZxZRfwftzdBjoP/cGPuqPCbyX0jDQUyG/NR88vTn9HuanPya8amoN2V8vE+8\n\
WcS9GzOmvq3Y7/Q99Vn8nfpOg2EfnRkK++UDobPV6ydE/+rofzU1zB9gJGZY\n\
/Q8v8pYcevZnMjkZlhkQiX4a1E+TYf6A6D+foD98Mih7QRmiz4o21QGj8X4k\n\
JEen81Y8D8fzpyZb/OxwSH2IkZBMGjmRXh/SjKcH1ZMRCSfIxJqmXj7oxYTP\n\
TW0UYa8rLj72y9KTU76LBP3V6K3Yuaq/40k90dTHE53z8pIQVND7mjqAqd6Y\n\
0tOnnv/YKc+Y8WrvCTSrA//02GyIyHf81Gz4G/VsX9BNZ/pCYzIjFN4Rg/CI\n\
fk8EHz0HuPE2f5QIJ8Z8/fp4nDHG500ixI2/EIRmyJf4PCbou5iY5P/OL98L\n\
9Fc+MeGn5qOJ6eM+ERMyVycm6CsKe3mIPkt+TFD7YQ83Hgt5jLEQjYW8PBb2\n\
8CThBzpKXzb9jbQlbUL1PFno3ESZBLRFp/uoefl5vgQencZbcS/Qo19mGHgm\n\
0UkTPhdCbhtCLitCo1b5C2S20dybyXNHJkRIQ143/tj0OdN46wXFGvwFzoid\n\
TJoAjXkSUTSaoM9W00zO0s9AJIZCYyhXzbSn+X6S/qCnZ81fxcyaCLEStadn\n\
zV/LZEpEMOTDeMCBAH2QRCMzZfgreraFdGOqDcmX/fR+mM9N0BShnhY2esUE\n\
CdGz9TdOj4l6avilD03Ql0sbMifi+VQ6LTzh4QPc6OvlR5pGvB/mRtM85E6k\n\
h1GahiGZ9bqFYvrgKDUXgj4Hgl4HvYrPQa8Sor+XtqSFfU4Zpv9fHfPy+DDC\n\
nmGaGzzscfB7plMnvE6eLrI3Sl/0hNdFbVQIJ9rTdOKj9Ef4xni6BWmuBmmO\n\
Bn0cFQgcEh0wwe+MpltwqBPhUSdHDUVjwnoJBh1Gpqh1uowR8OjzUjQYVjHH\n\
2J5UcVa+CwFyhL6DyGT0wKQOa8YWh6wI/6d8TkRzvjxHvsmIeg0VhnhS/EiH\n\
mAidEwoFZe8FI0ipf79Vc+u/ybFpFKC8cHms8PBXQJjjich8Ppmo3yLPCRXI\n\
w/QWaZao7z5RJow+EB2eJqcl6Ink1yQSmvDS/8TzQshFep5YXjozGB4jNRFS\n\
5GLMJTWHqAXDbjo2yj2dGwiP8jsO0X5wWDcnNQf9H7QX9zUEGCUyTpMpoM8J\n\
0F8WcCLgs8M3bqXWj4CHGm0H6S8PjA8g4O5FcHSAmpXfk3sggXfpBYOj/TQH\n\
VAu7BxEeH0Ro3EY9NTdNQTf3Vmp2GZsYtWNi3K57mZ4yF12EgEmaT2qecXNL\n\
P0GN51Zo2AJ/fyMmPMMzmPPieTYKM/Inx0SpT1bNJ3E4Go2FzYM8g8IhpeOm\n\
qznHB4OsefS0CTPcwxFiTTUtI1OHYvflNJpcz8U8U4Z1H4rZFxEQjnyLT/vv\n\
MdMvGPRTHxKeipl+v1HT76+i088v1Oby2Sgu8pfOlK5ojyf7BEU03WTGTdfE\n\
wwFtYtLHjT8gwR5NM55OwlbcghNjtO+Jl9nzAm/S3HETizp1cytGpafweDA0\n\
JvONxulPCoRc9NZ9dJ4vGNMCdppjg9SoD+pt3yB8Piu83oF43uCHQXpTXi+h\n\
ytMDLzWPqxOekVZ6XY+zlY55RtrhHWmD19UKv7MNfkc7HfOPdNIkd7TTw3Ab\n\
fQCB4XbepdaJoMNCf8iIhcEy0oMgzZeQw8LDtN+N8MgAzSFq1Edo5hInem1x\n\
LxHn0ZwkupwkEEwGiOcCNO/oj5Xe75FjoVH6I6ytxHMdtE/zNjBGX6mfw3Fg\n\
jD9ditUTfi+PU3PLaAJH8EShRPq6/CypuYWkTfj9sh/xaxVIO0xDfpozIZoz\n\
oYhuITVLQ3r6yX5YzjbciHpJHhPCC3GonxoLxryePF80hjzPmM40i1/mx7/W\n\
UzNE0j9IRE9TVDFjko7EHR3t0egsj7lqpv6lnqkhApmHEOwg6lBk6Rf9rIia\n\
+ZAUR3S6ssKOma7R4Drp57Az6RWKpI+ONmUeh3nuCumpPiikN8b8OEp/QIA4\n\
LxBy0HzkNqo4MKx62Y844KVjXpqjXpqzXuI/D81RT8DKcy5go9egbd6iNz9E\n\
85jnaz/cnm64x7vhGe+leUp/GO3zuHOkAQN9hejvLoXTVk2v4RqqJoiN2qrh\n\
ojbUVYzh7mKM2WvhHW6Oh9feHPd/wWNvhNdWD+9QA8a6TRhpLcV4jxl+WyMC\n\
tgaaZXS8uxFjbSZ4umsQsLchSC1gb6bjdM5gs8zCkL2TZnc3tR4SfTSr3QPC\n\
vhMS8IdpBo6q2cwqk3sfNa9bxvkcfq6/p5pe20L7JB5outO7V5NXtQma/AKA\n\
kJu+kAAHFoUNj8LHBB/2xSk9m8Dbapormp3gABh2jWK0thajVdVT05ymhD+s\n\
BEHEYNaQnrIS40MhY3rK9JWXCwXV5DbO414G4uVZWieoaR83deBFHv+bKOeG\n\
iY48EsBffJxzf61m8vPGmWIelWD4M3mcLozN/GvnCUGfMMsCmtYzYp7C85rm\n\
OM9f8N8wgaCe08EYYZAoczwxdsZzHy/DL+kh31QTZelFiHAQEoKemthEwRzy\n\
adsVzzOf3qaPhoxTeN57ad8bGqYpTuE/gaa9HV6e4jThacw/EPcXatr7B6SN\n\
jvdgmGjXOdqOUY8FVns9uvrK4HS1YdTVjrGxTjid9eiz5KGx4R4snTkYHizH\n\
iLUcw/2lcHQXoa3qKrpr0zHSVwGPrRaeIZ7v9TLvPbYaeAbqMdJUgIHCexht\n\
KyVoDNTGfQt+Gh5rKYSt4A5GzDkU7BsIFgSJAWrd1XCWZdJEyheIBK3N8HbV\n\
ItDTRlAggid1ItPfNyjTf4KnuZrH8cLG9M2S7o1ObTo1SEjydpQTenpF805y\n\
87qVeUucCgECpFGeTQwQNft9AgxGwIRskzXkCf91eh+jcDc2yKQXfjeIPBIz\n\
46PETnMmpOOCIYEVyasJP+2JWCCnKf5WWYXHSTzBeDTInvZe4se/1VM0SK5S\n\
Sd6I0hyzNLF7vV6KyD7Zu6/H2tufIPu/URB5jp8o0/3PYmh/aLwDI94Bmmmj\n\
EjdmRM9iu6NgYVB/gprtj8NhulbRoSdgIWHApwTyDHr0aeNk8L9LkXqIEyU+\n\
jQLOH7C/4SNM5dSE4gdppgUG434mHD/u7ydVb4Hd1QzbSBP6hmrQQ5OzmTjd\n\
YqsgILShz2ZCXesjWIfMcLka4Byuxyjx/tBgBTo7ctDblYOh/mLYuvNgJ0AM\n\
dWajs+o6+hvS4ewqwqi1AuMDZprw1fD0V2O8v4q2zRhtL4W9Ohvj7WU0Tsc5\n\
APSZ4W7Jh70iA2ON+UTOZngt5TReTdPUBFvWNTiLM2ifANVWTtsPMGouxHh9\n\
KbztVfBbmmhKtxHlDigE+MjmeUY1EpzK9gVUYFDIGBZ55O/h1yslSNjUsZCi\n\
eHpeAg/wF05fqsAhpBk+FDP3xQ0aFP2cEtoUCTh4TPh8T4AgwgonLkrZGgRM\n\
+GLVEg1pEkWInu5xiQo9oZCRhouPTvkpAHwtdrLzRH9Mxei0pUHr78h0TpT9\n\
/v5+DA4ORkOCTjonRvODIl0kOzDNkDI0S8foYxwhdUjbL8rwNJbzoqLtnk6M\n\
kvKlICFeMZIggWGGxkBQt1Bsz0gxwkCClj0ebkoPxf2JESliQoRX/GJo0qN7\n\
nwoTOnQYct9HMPGJ/hmW3ieQccTzQNyPaXdYhjyhIRohvAQoFgRI+lDjftzf\n\
A+d4JwZGm2Ah7u93NaKhvwydBI/GviK0E/93Dpaim2DjJJgMO8ywDVVQM8n2\n\
AB0bspXCNkA9bdsHijHQk4Wu5hvoa76F3qabsDZfh73jAcWPHNjbsuBoy4ar\n\
twgj7flwtmRhnLY9FIfGukox0pgLd2sBXPXZcLflw9NJxwhu4+0Eh1bq6Zi3\n\
g6DVRvKrIZv6QoJNFcZbiuA2ZxFs8uHIv4cxczZGKKi4yun1G00UcJpED4UE\n\
QqTyfRwjJzw2jh4MoQBnOJyyzXor0Nsgrx2h4KOg5WShNMy4cfLs0Q5CZ/kS\n\
JIS8oBN+PoGJho/qQzrBHFIZ4ogW6yKCJ2KOhXTKRAv8SCg8PRovQlOnTUyJ\n\
J5+kYhIMxzBhBBzRQZHwf8LUwoqRoH3pMaPqJQ8YUmN/wSD6pxj02O12kgTO\n\
/y/o4ZDR47KgfrCWUypfiUHPEPHusLdHdEtExbjJyEx+BbJZkMQbokEiLj5q\n\
EvxRxIQnRqm5JfOmxvyJAqCX6f8dU0kT9hECEr9+Kb/sM1hEOGnABDVYfJFh\n\
etc+QYsnSGEuOEienBBCyBjxdsNGaqmHAkOLzYzavnxUEyp6CCldjmoMOBtg\n\
czXBTugZGWsihNTC5qigoFImKBm0FaOzJxutHeno7HyE1pZ76Ol8gMHeHFia\n\
76Gu9ATqS1PRUHQCrRWnYGu9Reh4hM7i87CUXoCjOR19phuw5J+DqzUHY5Yi\n\
DJnvoTfvPAYLrqI/+yKc1emEkEIKMNlwlN+F05RBcuoeRsop2DRkEjJy4Wkk\n\
pHQSUsiVBAgt/u4KCiwUXCjYjBFqRooInTn34Cy6j9HqIkJYjaAlQkiYYMR4\n\
BC0B8RLD/J1wFPLYRGj5LKUElXyKQoMGlOJZkcUJVgykyFwVBeaWyayNRiga\n\
asRY+IyVEsZQyKexEtTHnpvSVEbECD2BnZBhUBLUvgbKTHmMgQfh7+u89Z95\n\
Cn4tKqJ8URElePiPeGyh77/FzP5ENee/NHbQBxThtLsBCj9snna4SIYHJek/\n\
GXlewsZ0HSZ8Mc3Lfbyy0cpPqGjgMTDAqWi3TjbHBBNOTnskrWRAgeOFwEA8\n\
igQphkM0PeSKiRliIUL2uNcpWJB3DlpVoPD3YsTfTQGiGZ2OGlRZi1FNrYUC\n\
QJejFvYxMhTeTngI167xdoyMEwzctRhw0PHBQrT1ZqOuPQO1LXdhbrmOiurz\n\
KKs+g9r6SyirOImm+osYsDyAhY7XV5xBXfFRNBQfQ7vpFAabKHC0pqPLxHA4\n\
B1vtTYLDJfQUnIez+T7c7dkYqryD3uzTBIVz1E7DWXGXZmM2nOa76L9Hr5F1\n\
Adb7Z9F36xisD8+S1rqAoQf0/MJbNPUfYKwmG772Ivgp+AR6Ksh91JJuIkPT\n\
VoGxagpEZTkYrSjEWC1BpYHg09OojbWNZjrrKmpeQoNXIYICiwSNQDfpQdJ8\n\
46T3CBEMH+8wp5MEIe6YVNSogobMTm3BZRFikhcaeNpOnwoh/semvXIKM2NC\n\
g/LQBkq4n5DT1OQ3nhm13TNibLdxLGQYFgWXr/Luf+H5+tUY9cV5JLbaL0ej\n\
xhRK/ioGJToxpBdro5D5lj5mpYBgIznlpggbnvS/KIhIjBFPPgMJXnI1E/DH\n\
BAOv2p5Q2xwUQhQcJqTnTJI7gUNCPE/0eMkjJYhm0nl7yUox+nifNVY0NJBg\n\
IiMdj/HgYNwserRSY73US+DtRp+7CZ3OGpn+jcTwTTaGQQ3BoJWmfgfGCQqs\n\
qYYpKrQPVaF1oAjmzvswd9xDJbF7VfsttPZkor7jDuppv7rlBupJHzU0XUNN\n\
7QV00v6A5T66Wm6ipuQ4aosPobboMJoIFn0N12CjCNJRmobOojRYzdfQU3oe\n\
nTkn4Ki/C1dLBqyF59GdcQh9WSfQk3EUNook7sb7GKlJhy3nImz5NP0pctjy\n\
qM89h6EcijKFVzGUTREl/TRsGReoUSTKOE3a6R785KKDZG+CZNiD9lYESEf5\n\
LTUYbyjHSGGuQMPTqGAh9oQzrgwDNuwcPSRvRZDwDEgOjDXVeGOOnDcp2Vmn\n\
2BjxIUbPOox7BQchdI+sLhlCSosrv0+jIBSMj26xCjOwYGRmjXyT38g7RRVZ\n\
XBQc0Siix6K5VCPfqjOy4ZejiHhCVr0Yk4viUMKySgDynx4HyF9OAcSY7VML\n\
mSGWQqFv8JZKNSVinKbkMM0rH01RQslLMhwbN7yqSRBwK7Q8r3ejw9IzQoIT\n\
TukJIbQ9mkgPLo4ZLIm07ZY1qEmfCmcMPJFQGiPiNTg+DEbBMR7ohpOiW5+7\n\
EW0OczxaHRVxrxJOqtDtqifZ14xRbwe1VtjHG9BNoaGBlFQxhYU8mvvNvVmo\n\
77lPfuMR2fMCdFqz0NR9F82WdFTWX0FR9VmY6i6insJBcfkxmCvT0GfJoPYA\n\
DZXnUJV/AFW5ySi5ux2tZWlwEN4sFDIaHh5Ey6NDaE7fj/b0ZNiqKHTkn0Tj\n\
uW1ov7YX3XcOEEYOY7jsAtxk662Zp9B5PonCxUn0301Fz9X9FDYOw1F0Fc6S\n\
yxQKrpPHuEX9NQzRuf3XD6P3XDKsVw/BnnOZwkU+4YOUk7OJfAbncZtFSY3X\n\
Fkpya6ymVGGln493EzbIW7ip9wxIeBhkgUM4CdnbxPcEBxtFVAlWGBMT4lFk\n\
eo6KujIwIiFkYlTWXnXVgV5GnFDhxJBEKrAY01+JLpn+IrbkPN8TkPAZsowr\n\
hnRM8qm1XgMwMdt+0W/Pc/zgbFKIZVT4P2iwKK+hSj8YGJH//jgw/iwWGAlR\n\
YBgJ15CAxfDU0l6MIobeYZhUPhvzEeLqAP3thJW4acazJ6PPU5CTI7GvFYxa\n\
EK9UAJDJoOk+EXaLEXHL6+vlWEGPxBpZ3h0liIQINsEJB/2/qjGMgpFh6QN8\n\
/qSy8iGJV35JkcW9EuPkXdqQDGtk9VO4sVCAbEa7sxpNZCpaCTZN9gp0uWrE\n\
SY1TOBqjc2xkPhoGi1HYlYFiCjNmst/11jy09uejpT8LbYOZBK37MLXeQFnz\n\
RRTXn0Ou6RjK6s7hUelRVNZdwUB/EVpIgZVVpKGh9gr6CVqdzTdhyjmEmsID\n\
FH6Oo53UGYcfG4UhS8lJdOQfRVf+YfQUkbIqO4GuRynoTN+Hzrt70XJuE3of\n\
pMBRSSEnl45d2ofeO4fgrLoGa/pxdJ7ajv4bh9BzcS/6rqXEY/BuatyfY/Be\n\
Kpy5pyiykJDLP0VCLRWD1w9h6HYahu6fw0jpHUmccSQK2msJSWZ4m0mY1RfB\n\
00wu31JLxxtovFkQGFHo0igakAgVIm/qJR80Tp5IIW+SpO907f6HNdJUJJLl\n\
Ea3NQh7D8MfFP6bN/DprLM1jRCkFEykliYJIjU2bCmChx48FE4wTgjHpAykc\n\
07bGOGsi+IIh0SZDsSVrynKEdVWgqrpQJQ3RhRRVRBH3TVVrEZJ3ySHLqKh7\n\
WdkbVbXDB/x+n4i9xyt5VHXPv/83Izhe54cRlK34qQinFwg1Op/XGA2QQbF5\n\
WuEmOBBEpqsncS4tITa7pvair8tikQA8cyr0EZClGfk0CXtOhdsEvSvY5TIK\n\
epwhQAwwdgWQQ7RN+2FZjRG8j8W9q9Nxft171OtEJJtAALYLgAcoJPaQXuyh\n\
sNjuNFNoNEk8tHvayCMq8FrHmtFKoDZTPCzpeQBT7wO0DOaj016KFls2ansz\n\
kd90CY8aTqG4+RJyG88hp+oEigi8RTVnCMTnYW66SvqRdONAAbV8dHVQ/OvI\n\
EBAPdmbA0nATlvqrsLbdwSDZqVbSlS15h8lKnYG15iz6TSfQmbUfbXe2wUpg\n\
tpUR6ooOoi8zifRiKoZLSQ9mHYf1wWHSjKQ1i88RiA+j/9YhAnEKes7tJBDv\n\
R8/5HWg/uBadhzei++QW9F3YBdtNIoGHhOrMNIwUnMbQ3RMYvJMKe+YFuErv\n\
wVOfjYClFEHShkGKix5eG+2owjihmrc5hR3sbUOEV3IYyZ5eydsN0jyJUAwN\n\
cPqdbBYfFytm5PEmoloyQULj12Jcl2cKrEbYM5Z9ZEwbLb/vsXMjfp1w45Rh\n\
9Fzf468R2yu4+uKngq8BaIV2CZVSqsKA4VIQuxWO7g6E/b54XZemoW3sqVq1\n\
aD2VWusM/7mGNwlOHWN5vUoy0wqxbveorPB7vZ44Y2zyS2v01Ni3Hkf2vzeQ\n\
TUzAoZAgRyr367xFg7w2ZPW2E1jtnF2YLsN0BkXdMLuzSZ/akyga0uNBidh0\n\
nOs1eCGIN/m0MSkI0Acm+C1L+GSICQQDYU7BBtW+gmdEMt6OuHUIsIHT2W7O\n\
5fkidp3gcImCNvKEzC8BSaC7VaELPW+c3r6D3Fs3IbaTkGoZoZ7Cr2Wknrio\n\
DU5CLIflfgrLHIqrKMSWk3qtIvQ2DBah1VaE+v4cCsN38KjpAh4RWrPqz+Nh\n\
7SnkEWJLW66hrOkKTG1X0diVjmZq3X1Z6OvLxiA93z5ULll0G71eLyG4o/Yq\n\
Ouqvo4vQ22E+h5bSkzDd2YGKaxtQe28Hmh7uQ+Pt7ag+9zmq0paj5eomdNLx\n\
3kdJFH73oef2bgw8IBRnHcNQ3kkM53M7heG8E9SfxSCpX+u9g7BeJ/Se3IzO\n\
Q2vQSQjuSF5FbQXtf4GeE5thvbQbQ6SWHeQqnVnn4CD0DqWfEjQ7869hnFDM\n\
ajcw0Czq1tPIecUi6b0d1eIOI45uQWlEVzNwzwgODjQS0oskLnMSRVKIMW7Q\n\
yMxPhNSCVzRxogOyrEapkgaGld/HSS5epfLpJudEV63kHKngnUrVsyL0+6Zx\n\
ZVm8pBtjMi4xqRQVesPBGVL3Rc8J+THS242BhhqEfN7nGJgvMz74IfJyjOjl\n\
dAnvfQ26EnVSr8zabDYKr35ViPDSvwVxX9OIG6ePZIhMFfckdB9HHKPKI6ji\n\
5W61HzSQN0OQ9YLk0MNhr65idesCHJa4TkaYDntOxhljLuKIe0mqcLwCMAWy\n\
8ZBVXKA3NEhgG1IlCCG7gE2FTDdnVeIJhU7Or9MhdrMOby8GxjtIyjailfDV\n\
RtGRV56csrTWDxvJ23ZnLcyEhXJrIaqsBWi0cdKxDA3WIlT1ZCKv/QbSm84j\n\
vSEND+pOoYTkbSmNVbTfRCO5yQ6Svp2DOei3FaKPsGUjbFoIq929JItbM1Bb\n\
fxMNDddRZ74IU95RlD7cj4pHB5BzeR1yL61D5d0dKL+6AXnHFiHv8AIUUCtP\n\
XYq6c6tRtv9TFO+ajZoji1F9eDHqDyxB24nV5B43ouP0BnSf3wRrxkEMpidh\n\
OJew95BcZg5Fzwxyi9e3Y+DKVvSd34aeUxvQeWQFuo6uoY+4M3lZ3H9A54E1\n\
GLiwA8P3jxO2zsGZTTi7Sc9PZ118HeM1OfATptglBnsJO42l5CwLRQez/vX3\n\
NBGm2hTOSO/KCpbOxATtHaouwmFRC8JeA2eS2XdyLlHXRfBasTQtbycU3ARh\n\
qo5ihoJUaApiUvEmC8O6UD6Bh3mLH7iSgms3ZyISDOqsvzaYQdVrkCVOgSwB\n\
AbcLXpeDwRY3hbB4WftN0MXjEdl7kR+/8mWqlrOXkf/8DJj9qYJZvEhcFVz5\n\
eWHJmYdZo4alhoF0MONPN79Gk39GFHjRIfU8yfr74CbE2P2djIiZxssF+WFM\n\
nsRhzhONgcEEA5scA+WgV8dDA5uiXiX2BSYYo3aNzUQtW1XzRobVCvAXCqZB\n\
A6q9Cp4MUw1bH+3LIkDESfhUMXCccUrH7RQL+8ZaqbWhe6yJcForitbh7YHT\n\
S3GQxlsd1ai3VaCasNpCMbGNrGqjrQyVFNMKOu8RTm8JVks6biK/7QqK26+j\n\
uvsuGnrvo3XwESyD2eginHZac9BB+GzovI/aljsoq72IgrIzyC06joysZNy/\n\
vwfFZDmLsw/h9tk1uH16BW6nLkL60YUov7kFRWdX42HSXDzaNxuP9nyIAtqu\n\
Pr0SeVtnIeeLPyBvzZvIXfV7VO77BLX758O0YTYq1ryL2t1z0Zi0EG2HlqEr\n\
7Qt0n/6C8LmRVOp22CjGDqVT7Huwl3C7E73nvkDvmTXoSl1GaF2Mrv30nAPL\n\
0J36OQbObqEYuR+O+6x2T2Ik+zwcDy7CVZxOGC0klVuOABd8EE65sIPVrbej\n\
SjAbHOwgTPYKViMerXS9NomZXkuVXnAwKv+MlerRqao/BqpR1qfimgqFCs/R\n\
UKcVawxeBZxGNJQIKbHRL3XF0dOVqJ0IyrGgz3iS4Few659KGumrV7g+O15j\n\
WI1x2bRflG7sWERWMNRqMK+EG5eDvBzFY8RAuWA0IkCdHt1SXjNmhUFfDBZr\n\
gPVFchwKw36dmpULQ75urORNxl5/aORz43Wg1vuy9ydRBpHLpGIuEUx8nFb0\n\
9qty7PGSq5wpxglp1c6sE5aVPnrkOC96WVhGmlCCX1PKgK8RNj/ng90c9v3T\n\
osraI+qW81SySD7pjlNMkzhFJIpYDAIKTaplE+IOlioRtr+SwiLRHGuDvWKD\n\
h2SFcIiru0MDOvurY3+IecgTGoybL/krHzUPEQ638YAVo3TeMAnnAQrsLK67\n\
x5vQOdaIrrF6EQIjRDQssDtHatDoqEKLg+yyCG8zJ5NRac1Dfvcj5BGhFHTe\n\
QiEJ59q+TFSTEKjsJDLpu482IpMuWxZaaby28yaKyTbn1p5DZuUJPCw/gVu5\n\
SbhbkILLGTtwM2M7rt7ZhEtX1uL+3e0oytyPG2dW4OqRRcg8vwbpxynon12J\n\
zNSFyEiag4dEKg93votH295FycF5yF3/Joq3z0b2iteRvehXMO2eA9PW2Sha\n\
+FsUL/otKla8hRLqq9fNgnnVO6he+RYaNr2D9qSP0XN8OQYur8fgrU2w0f9t\n\
vbaZAv7n6KP/r4eIpfc49QeXonPvQnTtW4je1BWwXd1JYpsE+H2y3/fPw5lz\n\
CS4S3u6ye/CReOZFfa4k87QUwdtWSqShyIXLWEKODiKVbkktG8TCZTB8jqzb\n\
e2QZJl5yy19X/OJ7fEVGrdDo+krDRjPX+DxSFx+tp+ca+WhZMcns5xQt+cbU\n\
Ie75+segSkxPqMtBWCsEeYFHX1BHe96pArSg7yUhjgTR24o2/LwowUUvEb4S\n\
6fHAzXvfVBpB84CoAGWXpxmPeoyfFAp5tV6IruPHZMomVcFjRFPRY3JCyGDm\n\
M7zz849zwVemlHwo8TE54YtpvC4vcoIvKghPyK6B/yjunQELO1fBvSH35TRl\n\
sJnxFcTdqlaG+8lRTQtsfMemRbWHYZ/tnG2L2FlHDEd1xDBpfcE864ghdviD\n\
qj5ADDVhPI6XSK1x/+7xlSBqQ95OwngT2t31JPDr0UaYZpwz/kcCLCiaxDw3\n\
2ssJ22bCfC2J/RoaK0d5Xw5yuwjjhOuqvjwy2DnxqOvPinsdzaQPOocL0EZ9\n\
Q28GKjtuIId89fWSFFws2IeLOXtw6sEWXMndi8tZe3A2fTOuZGzG6eurcPX2\n\
ety8tgk3rnyOB7e24N6l9cigln1lHTJJNxReWoPctGXISJ6D9G3v4cHWd5C9\n\
632UH/4UhdtnoXgHQXvLLBSsexMlG2l/NfWkJcqW/Q4Fc36K8iW/Rdn8X6No\n\
zqsomftzVMz/JSoXv4baFX9Ewxfvom37BwTtxRi8uh5Weg+266QXTi6jsUUE\n\
9cUE8aXUlqOPWm/qSvSdXEvnJZHXJn+do+DuzD6HkZIboiVCAw2yKuupLyQ/\n\
kC9Fnt4OM/nsWimZDnsGNaz1aiz5bn9Play+qsIFKRhVNT2ykqQLGKRQgUsS\n\
nlfXCsYaAb7KwOeZ8tM+uQJhmuCcL/Ly6GublUiQayF9sVdtcXlK0Csw92pL\n\
oa+15Stiw94EDfNJDXNW/NOfHJsIxkD//2CYf0XDnCAsUDaC/xT0FWKnPwPF\n\
ic8Y4xWrCK+/Tj7/ZZmyKWQ/byCb13qfE8SGjJp+2g5OcvNS81Dz8b4qBpLM\n\
s0+fb4xxztuHPkK5nWDim/BMe+pUdT2hTyqzPXpcBf2QXCMYCrt0Ujsk1w7K\n\
AhU9zlTZMoY8sYC4B5KQSuYTekNDDGYO7ONBcgAxJn88xBdzqRNCUhVhT5DS\n\
iIUS00eCXB3UCysZ9y6O65zqHqlHC8XudsL1CJmEYTrWTjzQwOUSQxTbnWaJ\n\
8xzjG2m/ggx+aX8+qsiom7lZuciOQN6fh3Z7GXqdZCpsOWQcbuGq6SDOFe/B\n\
mYLtOJ27E6eyd+I4gf7Q3Q04fGsNrmTvJeBvwtX7m3AnaxfuZe1Ddk4yCrP3\n\
IzN9JzJI2N899zkyL67BXYrt2aeXIOPAxxTj5yEvdT4e7n4f9774HYooTmdt\n\
eJPA/wEK1r+DovXvonwbGX42D3s/gXnT+6jc8C4q176Nwlk/QeG7P6D2IxS9\n\
8yMUv/NDlH34Kkyf/SuqF/wCdct+i6YNbxEJvI+eE4thpVg/ePlzivOLYUn+\n\
DL0H56OPNIGFTEl30gICPx2/sp1M/0E40lMxnJFG7SxGcm9IujzYx9dGVJOJ\n\
IPDX5lMcr5VYzwTAF8TxQtcEEwBfsMmJNgK/t0dVI/EFm+oyIi5n5aA/4XFy\n\
9TGPcUU5V5bLRcJuidjhgI7YcmxsCuU6moflnFEhhbCPm4zHCw1Mi3mKJgGf\n\
XC2vjgV9KtAH/Zog+Op42ntBkE8BitxFmEAdloqMsLgL1u+s3TnDPY0fRT7L\n\
gbAIad6bwXsqbxYzLjkDeQg96fUjUotuHE3QtmLqaGjqSdNjn6Qvp5OEO1e4\n\
hmc8Iy0hVkUSf/8nM8lzz3YMk4/zSsIUr/AfGpT091QLSqKcWEUejXGf8Agv\n\
fk1xkIzLanifr554RdSDnMA04ZEaKbl4dFTyfqq5jJ7JxqVoRa2STfK1GEFZ\n\
DedVcE4PGrl24og40QoiEwaFWLwyxhySSPsDvCWNjifwhlRZKR2xWLTDaKBX\n\
NAKvJYhPGGMNUUueoAL95Bm4DGaIfEKboxZ1pCEa7FWkI8ykHaqkHMtsK0YZ\n\
F+lyMp74pWqwQDRFPe130mt0j5jQMpiNovYbuGZORVrpXpwp3o3zpfuQmrMV\n\
+++vx/70dTiasQkniVdO3SexUHgAj0oO4kHhPtzLYU7ZhWs31+H65VVIv7EB\n\
F08swB3S7tmX1+DB6eXIPbcc5VfXUluPkrMrUHJqEcpPLELZkc9QsOdDlBG3\n\
FG/5ADlLX0chCYnCla+jZPnvYd48C9XkEWo3v4e6bcQvq3+Pko9eJT75AYre\n\
egUls/4F5R/+kNqPYProx6hZ9EvFL8t/ifat7xJvLIKN3tPA6UXoPjAHln0f\n\
E7csIKGxkrhmOQmNFRhI20BeYjeG7yTD8ZDERfZ54RV3WYZKUvSYRVSMmXMk\n\
Uciewt9DYoOT95JEVAlFI4HPpfcernD0aM7xDDO+pdDRp6rqFaXItkgCXnUN\n\
ewyaGY1LMB71xSt8V4J4GZumaMejDYSiJX3fggRDbIjUiDcEB/OJX19XrgXH\n\
DNYZ01RKJMzV8uGwbyYTyYuaOsR7a+r4U/Hk02NwHxa+0Un8b/HA/85Y/lMY\n\
l50Yd8GZVPeo6X2G4ZdHvTQutGWQmOoVjtVtApRaGNOKwaORTsdU3J8ZE/d9\n\
GtpjBO0aDAc6ePtpeWBIBJ++RYUhJ8ZkBVytgzNvuKYS/wJ8pSTIC4SUchCq\n\
UcA3lITKRSqQk1ugd8eSISBtUJFARAFegz9ebMSfaR6wRlMIAn2xD73UD0gF\n\
D6cEhsZb0UM2oo9TBe5a1BOEB2h72NtB1NAoqYImO0Ga+jZnlawjNJCNKLLm\n\
obAvG/VEB7W2onhUDObH/Vd00Sl9LjPahwuRS/bhcs1RnCpPwqmyvThVugep\n\
BVtxOGczDmdvRUrmeqRkrMWBextw8PZanM7cggsPNiPp/Kc4fnkxjl78DCcu\n\
LMSFS8tw6+Zq5D7ciSKyHeUP96DiwS6U398OUwa1W5tRcmktiogJSs8shen0\n\
MtScX4OaUytRe2YV6s6sRs3RxShZOwu5C19D4dLfoHDhr/Dgj/+E+69/Gzlv\n\
fz8epiWvxf0lyuaSu5hNbdYPUfzmP1P7LsreewWV835KRPBzIoRfoPqTn6Fm\n\
/s/Rvu0d9J9eCOu5peg7tZgIYS4se+cSGRAJnFlDZLAMvcdWY/DSDjjupMCR\n\
cYzcxnk4HjEh3CJQ55DDIDJoLIa76pEiAku1ylbaO/Sqgs5Y6pUGESUtWbI6\n\
zyi1xRt84JREwOgUJwgviN/g25vIeFiciPIjgnXFEVEuCKv7lmjc03ZQeCLI\n\
l90o/eCeSi74DdPhje6H+bjhP2LX/3T+Uww0y42wNJYcmihUGDY4ghuTCCfx\n\
wyGlQmKPSciO19zCGU2d31PSIZrlDOm9p8eMbKixmh9UayZPKZavGEmOyFM5\n\
UDUsLkgSFcaFzLGZTKlWfXlKjTx+wyd5zFYpTjrvu/8zPeL5Ej3ifUKPeKI6\n\
ZDjQTdtuY5z1hy8+KkU8BjspVlL9NKYnOqzYx6XahEutUE66lCpJnFoYEVXC\n\
OQ31MCzkNKQJaUA3lbzUikQJlRUyPCqE1Kt6TUb9REbd7gZYxhpEk7DHYU0y\n\
4ifvQ16nwWFC3XC55DZaJIdZjeqhMhQOZKHSlkf7ZeRzslHS9wiNw0XoH6tB\n\
P5FaYXc6zlQfRVpVCk5V7MfJsmQcLNyCpLx1SMpai+RHG3AgcxMOZhITZWxA\n\
0q3PkXJrNY5nrEfSpU+x7eQsnLm1AulZm/EwZxtu31mHSxcX487VNSgkJiq6\n\
vxM5pEceEPuU396G8utbkHNiOR7t/wR5h+bDdGoVai+tQRF5m5KkT1BzYiVM\n\
+z9D0bq3UcYeZ/NsauR/VryOR29+D+k//2vkv/MKyub9EhULfiWUVPjG91FE\n\
lFTyHumT93+Aitk/hun9H6Hyox+idum/onbxL4iWXkXD8t+gc99soqBFRE1E\n\
QaSJOnZ/IL2V2LD3KOmUw8tpewtsN/dj6O5hoSahpaxL5GGyiGaqRKvwQqhX\n\
FlGapMiAC/9YqxiFf1Js4OIFFDPGpNhvUF/y91KUfKJX0wbsMdtMRsNy2Z/a\n\
1iTFt1KgEwzBEhaScrFIEZKSeywISbmnSEr1iTr94dc5kASdJfUa9w8LedWa\n\
qugUoiqvQU1yAnOM7zmmIpVoeJKPgjMVKT3NJfHPHJNrQr6ceELkzJh4oraI\n\
iUcvUvDe1/nxueiCyVSKJf4Z6ZQXnrGwkvBldGTUJkVzqZP6ZotxsfcljGUn\n\
pphQSK5R5Ebb35miKr9Q1dR9lRRVKZIaU4RljCviobFen5lsUgd8E6NKRvEa\n\
9FP3+UqIoShVRsgEFXHQn6tKJpiUdJtwapLipqqHA1KH79B+abqwFa/RRuuW\n\
FEsxI/XHrRWy8gpZqUajSj6F+nXWlZiKXNNIkJyTj1mqluRRLdpd1WgZqYKV\n\
WUokEzspk2ReG4bLiK3KqC9G+WA+Sq05tF+MuqEiYqgs5HTdQfNQIXpHeDk3\n\
H3dbLuGE+RBSTftxqmo/DhbtwJ6c9diZtRq7Hq3CvkdrkJy1DimP1uEIMVZa\n\
9maczdpGbTOukLO68OBzXEhficv3VuE2Hb96exUuXVmCC6Sh0o7OwYXUeTi5\n\
bxYuHfoYaZt+j4zjS5B1ilht/zzc2/kBHuz4CEVHliCXWOrOkteQsew1lOz5\n\
GFnLf4dCYqqKrR+geM0bKP/8D6je+A5Klr6GCmKs6i9moW7TbNSsfRcV836N\n\
kg9fRfncn6N8DrUPf4aKj36Gknd+iMo5r6J6PrHUwl+gdtHPUT3vJ6iZ+xM0\n\
rfsNuafPMHiZ2IreY8/+j9C97yP0HV9MAmoZulMW0/Ya2G7swNDNveSsDpKz\n\
SoMr/4ZkXIStWshRVeVIqYanuRy2jKuw3buEoLNNmEpKn0hIcVmGz1JMwqtW\n\
mGpAbJS+64VPM5RK2/psnObQN4Tha864D/v0vscu54j24iW9CbdD7g8XDjo0\n\
LQ2r+8X51Is5mJbUbeNcSkgF5fLCoFuc1TR908OwsW4jNzIUWxXmixlZLiVq\n\
O+NTfZArkpTHCj4vaVvRTMI3E3L/GDVmmC/eMwQSZ3KD7OBknedLlnimR3O/\n\
/4555OUYP6bZI+4bUUWjbnwxDW63G42N5BsaG2Sbn/MPBl+E+OKFAOdEfMIO\n\
vkklWAJyTaV6dBDSbIE2eKSsX4oI2fvoM8aM8/W2W3EHA1z2XVNN6qvsibqU\n\
USwTD01IkwpHfipTkMqx2HUNB/MEf7leenxOZ2uHRMGIVBFSGBQPpSQM3wCJ\n\
BEw8W6q45TI4LPmVDjFUna4aNDrZQJnQM9YkxqqLWKOGmIGZop4ZgvRMNbFC\n\
QV8OCvpzUEXapZoYI78nHaUDmWggduh0lCK36xbO1J7AEfMBHCM9c6LqAI6W\n\
7sUhYorkgi3YRVrmQN4mHM7fioM5G3CEnNZJameyt+AsMcSl3O24lr8DpzJW\n\
4fjNBUi7sRinbywhl/UpLl1bgtu3VuHiufk4f/xTnEz5AOlnl+NW6nxknFqK\n\
h2krkZO2GjnHlyOXWKKQWt7+BShImofcre+haOdHyN3wNkzJn8G8bx4KV/4e\n\
BUt+g7IVf0TZst8TW/yO2OIPqN36EWqILWo3vq9YYw3pnyV0jLROOTFE5bxf\n\
wfzpazB/9itUzv4pzB/9CHULf446tl5zfoQasl/dyR+SfiF9c/IzWHbPUmxx\n\
bAlpm2XoObIIPSdWYPDKZtI3ezF0mzROxmmMEFuM1+dLzoXzL+6qLOqL5OpT\n\
Z2EGAgONwg6ylit9N9mwZlnrJdsVzwu6cd+S+92E3D1yBwOjzlLVftmJLGw0\n\
Pqju2SfpXrvqZd/ON5ekbZI6xBVhj0P2Q+PUPOLj5EZ+XhqWxlwR9rrFsLlJ\n\
IUnjsYBcKEMMEg6O6p6t15hiD3n08r6MxfMeBd4gZzfkrn6hoF/kB/UKkfLo\n\
k0Sruu6UfULIYBNFOVwYFg4/nh6WIqzwkynjGVGxpGmGbxml/BWNGfwTk/yJ\n\
exb1iHZ6IZoljtanTNWkxEqgsFor1jdUmJI8kW9G15ievie0ljh3/hcSRy1b\n\
B8TzKMJhMiLS9k2yKvGS5PBODMsB4Scac5FmsAVa4YkMqzFedXKrozNEmCgS\n\
Gta1ZHajDpT/I/Uc4a5h3ewkVoSQJpz0fC+fKwVmQ6qFon2cSv58UyeLB6MW\n\
bDQkREXbvRjyW9BCnNRG/mpE1ostssY05O+Q654somgqUE9eykL7w55WtI+Y\n\
6b0RU8V9Jnli5qwSaz7KBguEt6rIe5WS5yofeEA8VUR8lYMHHVeQYkoiriLP\n\
VXsEJ0nRHC7bI1x1qGgbebC9OFKwTbjqQM4W4qtNOJnPa06bcSRzDQ7cW44j\n\
91Yj7f7nOHpnCbafmoVDl+bhxLUFSD3/CS5fX4aMjHW4cmExLp9eiFsXluH+\n\
xRXkwZbh4VnqSd3kkLrJO0W8dWQpCo4uRe7BeSg5ugjFxFmF2z9ELqkYLjCt\n\
SVmIws/fQMGyP8jCc+6nv0be3F/C9Pm7MK16G+VL/wjz6neIrz6i9jFqvpgN\n\
87I3YV74OhpJ/VTO/x3qVryB6kXEWx+TyiHOqp5LXPXZT2n7B6j95MdoW/87\n\
DBz/BNbT89B7cA5x1hziqwXCW91HFpLSWQLr5Q2kgsiX3UhWxanZ54mzHklh\n\
G/ux0Sr2Y1VqLYp8Gd8bgovCmae4WJW5K2hvkGLvQH81kVUP+TMLK2pXjyYv\n\
I50klw371K3vhMBIBYX11fW8VhX2adISslJihvvwuF2Nexz65rd8f1yvg0mJ\n\
dsNyO10aDtB2wCXr36543mRiElMnlKXoaQY/MifxMgnfn5mYabpBQX5NLcxM\n\
TDffjMqdOHWbRaaWQGBMcY7kg9g3hb7GBCG26ZvRheaXvszi3H46AROSC8Ri\n\
IC/NJ6VeCvWuSDtGwg3kYBzqMipBvRVWfzMXXwvKx556DbkYQuhjLN5QHiJW\n\
hqOF4LQdp4pEEjQxCAnosemqsjRif6yX9AsxAB/mWjFeFDJaRBaIVNplRpQK\n\
lLGxYsDTiVxrHopsBXEsXzrjFkkJSfdYK0mXBmrVBPdydJKMsXqaRMqwbGH4\n\
N3LvUCanzFqACluRpGRMJFWK+zLF5LSPlMJszcKphmM4Un0QR0m2HK9OwYHy\n\
3dhbugMHy/diX8Fm7Mpbj+NEDWfJ+BzI24r9JFkOZG/CoayNOPRoPVLI1Oy6\n\
Ph87CPopNxfjzH0yQxc+xqHL80W+pJ4nWjgzD1euL8GNa8tx+8oqZFxehesk\n\
D64fnYfMcyvI6CxD1smlyDq+DLlEBcVpq/Bw11w83PQecrZ9iKK9n6Bg22xU\n\
Jn+KEupzV/4BReveRcmGWShc/AeUERWYSa6ULPo9Cj/+NYqIHso+JfPz+Qeo\n\
2zIPdas/ROVnJG9W0Xl0ftOm94ka3kLD8tdR+cG/oOx3fw/zh6+gYRkZIKKG\n\
yne/j+bPf4Oeg3NhO7eUKGEuOkjK9B6Zh4G0peg++KlImYEznytKuL4XNpIy\n\
TAmq1pVL0YrlymemAzY+AbkjZTOvH9qb+HZ6jjZJ1QQGKBg1FSA4UK/rXweM\n\
K72kjkXuO8xLSz7WKEbPWsbOyRy+Kzb5nLDbTnr/MSowNI7X8DxK08g+65uA\n\
2p8ITB038tFhuYf2FCOEfIoRZvIjaxXJABDAaUv2ovqFb+IreoUvQ6FH5gv/\n\
C8IQnF72RyVLojEWDkY55Hmhj0S18q1XnYhCZkYZ5BvRAvjExxnkifqzF6NS\n\
wvVv5Y1E4Y1h4g2PwN4dr6nDTaG6309+iUJ4YpQ6RvXLROlDdMhowmM6Qvuc\n\
mGtJDApRiVlxPkOaS+xqmCtJZ+okCA/pxWXNGSrbMZAwRRyrHyMONkDDXgsa\n\
R0gnsIYIdBBpdKBfkwavJ7N+6BlrwJCvVTIkTBrmoVKlHezlQiBMGlU2Jolq\n\
6Qv6stBMHqdrpBzFvfdwmkhjNxHEiVryOaQf9pZsw+aCDdhHY3tJQ6zIWILN\n\
5HeOk464XJ2Ko4XbkcpaImsDdpK/2Xl3GfbeXYG9d5ZiJxHHvuuLcPLOMpy8\n\
tRQniCjSrpL/uTQfqafm4NSZT5Fxbx1y728T4rh5egFun5qPXCKSohvrUHp9\n\
E8qvb0bl1S2oJF+Rd2gRsnfPRc72j2A6vBQ1pDMqkj5F7uq3UUA6oWTDbBST\n\
r6kgwihf+x7y5v0aBUwan/wahR/9EkUf/xIVi99AzeoPYF76Nkre/1cijz+i\n\
ccsctOz8DNWLX0P1J6+K9zG98z1UvPUdmN77HuoW/Ay1n/2YNMUrqJ33I1iS\n\
P8DguYXo2T8H7VveUeRxfDFpi4+JWHhpahVpik1EIFsxlJ6KkZzrspZs6Ikx\n\
votiY7HUtPr7zfEsKOL+RJImcncFRw+NtEqSha8Hj0SXoKd64Q+SDSIXfPbo\n\
DXoUP4iEYOoY5vJqj1YUHmWVwl5tiQzPo6mDnhond+Jn7eCQFW2H1hNy732h\n\
jReELaYpegjFNs72hvjCmJBecPIahWsKowlPmR6fSkwYbOGLMoiwinI+z8W6\n\
HC1LfPD5xjS1KEf0hBLRFTIxZS4vavMS8/sI6jLxJ/K3ciegr36ZaLFPUY43\n\
yhVu3Y9qkeKbdNH7oe2Y426xBd2+auKafkVWSookcDbWeAHJpkzJE2e0Xp3r\n\
09W1MNOFN3zEBaqptegAUwZXu07XJetWfQ2MVdsUzrcG++P+FGPBnmg1qzSp\n\
dmeX0k0MwxUq/cq1hHiFqEdyr6PsVALtkn9l92IZa5Tcazu7FO1eiGm0U1mO\n\
GmKccnIoFdS63PUkUQplpah1xCTS5lH3XeyrSMJBczLON54QpllfuBk7i7Yi\n\
1ZSMZJIka7PWYFnGUmKaL8S5HC8nR0MS5Qi5lX2Zq7ArfRm2E6tsv7kE++4s\n\
R/KtZUgipkm6Mg9n7q3A2dsrcZRcywWSKTfJzVy9sRx3r69BcdYOZN1Zi4fX\n\
VyH3xipkXSRJcutz1D3ag6bsJFTd3oKK86tRdXkdaq5uROXJNai9sB51579A\n\
afJ8lO+bL5fFlW+fg+L178G09SMULv0DChb8htjmVyic/1sUffYaOZffoXzJ\n\
71Ey/zconvMblJNkqdv4EToPrUDb3vkwffxzlLzzzyif9QqxzQ9JqvwzSZX/\n\
gfI3v426RT9Fw8Ifw/Tmd1A9+/uw7H6H3MunsOyfRWzzhkiWgZML0bn7PWKb\n\
T0i2ENtc2ATbzSQ4Mk9gJP8yxhvuw99RirGqTLgrsuCpLqCxXJIkVeRYGsW9\n\
KJliIafCdNOE8aYsGm+fqobx9CPi6xe3MuGxqtQs+X+fVdGImzNwYbctjoS/\n\
h8bGrZjgX09gJhrXbCRVuop2jKpdHpN0LjMV3x2LVUq0YjdRLUixWglKY2Ey\n\
mshahYtcJAfD9/bnHxgR2hnjfUU9fIJ3JoNzGrPEC5K9nRa79K0a8dNXNeuo\n\
TImbk7KSVhFBE5Q7VyY+cREL78llejONRaIwl8rIdXmTfKnd5Dqd7GBC4SxJ\n\
lDdm6wKZ6XrV26ObV9Dvm+CrSAn4L8BLu95J11RTh6m54SGhYfGaJFHrkRIW\n\
n+RDNIu49WvxrW99Yb5hDt+wQS4RZ8aIGJfC8U1TB+gZfEXLi3AHB6I3UJV7\n\
H1Hv5puC8XiwX+6V5zZuEkZc4Ap20+fkCvSSkhmRVeRencnopr5bZza472Zn\n\
Y6HvczjQSQatg9xMDTmZhnjmkLiNZGxa0TPehHqnSZkbhwlmrVfKBnNIp+TD\n\
QrqGa2c5P8tr0rxGndl9j9gjBYerUnC56RRplZ3YVrJD9MmOom3YkL8eu0tI\n\
k5hScLB0Lz5/sBIr7y3BjkdrkZS9EScLdyD50RfYe38N9mWsxm5ijn23luNQ\n\
+mqcTF+Dk/dW4TQxxo1Hm3Hr4SbcSt+A7JztKC9JQWlhMupNqaguSkZjaQrq\n\
8vcg7+oalN/ZiNbiA+gsPY76h3thurIBrQ+T0VOSht7iM+gpPo6urINovb4D\n\
7de2ovHMWtQcXYb646th2vEJTJs/RtkXs1Cy4i2UL3+HmOMPwh5lZHqK5/wa\n\
xR/+CiWf/BZ16+eiac9nZHreo/YmaohlzPN/hTIyNSVvfFdyHqa3/hGFP/mv\n\
ML37j2hY8QthETNpmI7tb6H/+DzRLm2biEVS58vqT8feD8nwLNQssllYZOhu\n\
CjHJOYxXZ5JWyYSrNB3u8vtyG1pPY4EyPINNkv8IOjkP0o4g/54FjY/VE+PU\n\
35dkbcRNDOLqJ5bpl+2wy6p6t1XGQm4yOSHikRmq9I4YJDRuVb+7wtseYRqG\n\
KdNPmC1RyDOsl4dCOrMblS9eJ4I+rvIP+Zz8O0NS/MU3vQ2MGo2tjRSTB8Z4\n\
S/bi2e5ExzyyJ2M05PcmMkyFKLy6VE7tSabEa+QpQzFiJ94QO4qFRPbI2AwR\n\
QNMfE0B8xR6LGZ/PHa9OJA7i9aWguKiZ0UxvyFgYlyVz4aBQfDRRO1W3S9tf\n\
eSJRy6W6f/J4RuYLvWrETMWrRRZLZ3TVSBjrA0Pp8F8/TVOLW3PRKPMSJz1F\n\
6XgnHZqnRmXxyOIxY4jkAnNUIj9L6MkVpSehrJnCUTOjt6x9nKf0/Z4jVnXh\n\
3XShJdqSC3KkZ5riuhbiKfpPPLrYjllrLNCdQATVLSxFHBS0xL2hKIlpiumJ\n\
737LS8q0PezvlMxL33gjGvk+NiMN1GoxRONWTxvJnGohJV4w4iq82qEiIqd8\n\
FBI5dY3UiIEq7M+TbSu9Rm5PJpKqjuBIzVFcaz2HrSV7sDpvA5LK9yGZCGpT\n\
/kZszF+HlNLdOF11AAeJuLaQmdqVvQ4ni/eoBaTsTUjKXIfkh+uQmrUZx6gd\n\
erAOaZkbcOrBRtzM3YnsciKjmmMw151EXWMaauvSUF9zAg3VJ9FUdRwVuXtQ\n\
nZ8MU/Yu1ObsQV3WTjTn7UM7kVRHwVF05B1A0/1kuYecpSANXflpsJafRW9B\n\
KnrzjqI//yj6cg+h5+EBtF7ZgcaT61F/cCUqt32Cqu3zJCNTvuyPZKxeQzGZ\n\
q/JFb6B209x4NGyaE/cf0LBhFho3f4C6NW+hduUfULv8tzB/8mNUvPk9Ujjf\n\
JW76Z5S+9reoJF5qWPQqcdZ3ZNuy521RNt3Jc9G2+S3ipU+k9tey9xNSOgsw\n\
cFYpncFL2zF4PUnK+jyNWcQ59zFSepOmgykz7iV4W4vlbnUBWz2C3PjXRwZb\n\
xUt5ukrhrkkXyuKlpgh5rbCD6cjK2dp+BrOrW7HTSLdkcHuZR4TF6DQ3sxaf\n\
6u7nYY/s8koStQEeGGSOYiUejuUncmjqR8+cTDQx9OTS1MRc5JrOG4qPputx\n\
zxQv+b28LRpCyCeasPXGP0VDUhIb8s6IzelO8Y5ffraNxziVS9wTPSOGgJ5Y\n\
YJpK1cRNf1ZhIPfPPWOZ6eWnlo2mqmliK2zkpiLG7Ypja4/5EsPJtTGEZbFY\n\
UFCQL/2zCMsjhOXUpOOSbV7D4VUjTpfTdlRMDfib9HqRUmFhl5DVDN5i3oo4\n\
NRWxAfPxJYOekJVpLTKo+CrEbZCHB+hPcAVFIhER9QopGU5MEdSAlla9Iqcc\n\
/m6mKCnCGw1004uyXvpCiu6Yl4yeLwzgCwtZP7XJonYVCadGOc4Z4hpnuYio\n\
FhrnBE/pYB6KiKN4sZsXi4r7sxQ/jTE/PcL+6mM43pBG4uksdpTtxR6yVslk\n\
u1aS5fqiYD32c0aYF7or9mFn/ibsJP46UrQdp8r24XjRbux9tAG7Hq7F4ezN\n\
SMvfiZO523Ds0UaczdmCjPIDyKtJRU3LJTS0X0RD80VU1h5HFf2ftcRPptID\n\
KC4kgVSUBBP1Fdl7UJi+jYRUEuqYqx7uQD3xVXNuClpzDqDq2jbU3N6FpvQk\n\
dOaeREfWIbSmk7DKO4be/OPoyTmE/qJjGCxNw2AxcVjWUbSTiKnZuwCVm+fC\n\
RKKK74RQveFD1Gz6GJUr30H1KhJPm+egYeMHKP/oVVQu+BUaOWu87i3ULPxX\n\
VHz0Lyh49a9R8PO/hum976P4N3+Dqln/gIbFP0Hl+9+j9n107pmlLkZImY12\n\
ElY9R0lAneYLnT6B5cCnRForYL38BbWtJKiSMVLIC0rpGCm6DmfpVeKpDIyZ\n\
MyUBFLBUMVvFI2itZ4dAhBWw1ki5sbv6LoJD/ANenQRiBz+MtDNORzoVgbna\n\
haH4gKtbaKqT+KhbUZi7h2mqly/e8wxIEomTRiGPSjrL7Tj1NtETux+vPZ5/\n\
glG0EHGVl6WT6CmpXNb7zFOcAA64Eg0x5RvVJCWJocCYAmGiGLTgVJ7o68xI\n\
Xxdymi7jXu+ovjG531hw4mUm/8vMJ1+Npm0kIfwnUXp48RnZmZV6NflJPRNj\n\
vv7XzJBI2w64Qr3o89VyUlhIQdRL9CmiaOgvn6IHj6IIoQdHlCMGxH8Z/CAc\n\
oUSMqBS+0dsYOannlcfiH6wIGq1X3aI/oKpzScioIhdmiGmiY1wBS1TLDAcs\n\
ccpnreVtWH1twhFNxAUtI6Rn3DXiv/iKghqH4olGMlIt1JcPFaDYmqPTNfnI\n\
7ssk7UOUOFYvOial+jhONJ7Bueaz2EVcsJd44pDpAFbmfoHV1Pab9iGlfA9S\n\
ynZjX8k2bM9bj6TCLUjj1E7BNllNSitNxikyS8dzyZBlb8W5wj24X3kQpfWn\n\
UNN+BXXtl9DceR3mpvOoIC1TXHEI2QW7kF+YhBLSKrkPtyI7YzNKsneiNGsH\n\
KnKSUZyxA3k31sN0j7ghcw9Mt7ah/MpWVN3eI/fFbX5wkPjiAKovbkfTPdI4\n\
d/ah6epOtN9JRjdpnl4yYn05qaRxiDfyUtFzdx86L29D85GVMG/8EJXU6ncv\n\
IL74CJWr34F55Xuo/WI2qle/gcqFv4Hpk1+i7O0fomLWj9G45o8wz/kJin71\n\
/6Dsj98mYfNdlL7+tzDN+g7xxU9RPfsVmD/8ASz7ZsN6lvji4Fy0736P+GGx\n\
lNl17vkAlpS5xB1L6fgaWC9uFQM2Wnia+OEm8cY1uMqpL7lOnHEfga4KuXYh\n\
2F8vdMErTo1xf06EQcar8QECfTXEE0QMw0Qa1ELORskqi0njnu8uKllmZdiC\n\
zBfcuPDGZZGF65D8ZKbqeZFakUe/0jpMIF7+pUwuOKYtyddobROQpuhC/86r\n\
0IX0M5kxEkT2PKflzlhM44UoPeZTtmzaUyQiPys7LerAPNqTeUTMeL8mxDJT\n\
TBoTS4BfK8ZpiZYJ+Z6Vbk6IWbBSp/EvmoX5Tk1az8SkgKZHeSkhejlC3OPX\n\
Y3/1GYllKQKWHyJfGZMleqwkRksY9ZdTG4tminxSUDtFRqxgvJPDYsFY0bgj\n\
KrnM3CVEFXEqRSN05YyxX0rj8A9gMm2J+VL9KJGTlVyRIzAQNWHqNie9TGCJ\n\
IoFenuIy4ipiMBI7HUJIfNNPFjXuQP9UH+yP7jN9xTOzSc1e3AvakU2pHN5W\n\
vQU9kmA2o85RxaqHnjjk6YhbjkYaq+YiX0eFMFiluLFCKZkxcxnfwCPaLkaX\n\
24wHvXeRYj6C001ncLb1LPYQK+1kF2ZKwZ7SvdhSsh37iNWOVR/COmKuBRlL\n\
sCmPWK1wB1Ko7cvfjCOFO3GmLBlnSpNwhJTOaVIsd6tTUdZyAXVd19DQdROm\n\
losoazoHEzFYfuUxFFUcJQbbh9sPtuB2+gY8eLAVxeS8CrP3oix3PyrzU2Au\n\
OozCe3uReWktsgj12WdWIv/8GlTc2ksu7Tjac0+gg1rdnSS03DuM+uv7UHl6\n\
PSqPfY7atI1ovroDHfeS0E0s100OrZ9U0GBuKmwFxzGYdRgdrID2LICZFFDN\n\
1rlo2DMfdeTczMvfJjZ7GzWfv4+SWT9F7r/+A8pn/wzNm99Hw+rXUTmHL234\n\
F5S/8W1UvPNtlL3+d6h893uSkK4mVWSmZtn3PgbOL0ZP6lxYkj9C34klwmAd\n\
xGTdR+bJfh/9TQMXN2Pwzn6MVZDaqb0DV9lNOPOvUn9XqZ6+KrnDacBaTyQ2\n\
VB/3LQSGGuHtq4Cr7oH8aCQTWNDZqjNMTGD8+xSNalsTmZCYo0MtmzGBuS2q\n\
TFAIjM1ZL5uyAckZKe4Kjg9Ir5bBZOVdNI5DVI1dk5YzlrzYt4kjkwsHeT9I\n\
ykVW0mmLV8i18uGtKVaTQpugWlGPsphXLx9NUdiXjSVErV1C1O6pEw2TN+X9\n\
pqlsMnGndnNRD/hkNc/MaOZ7asVeTF/Cl1UVqqsnotdTPKN/7stKmfWl47E8\n\
GWP55H4UsuJm/Lr6M+/c+uQqXLsh6ALye7Vs5TxKiPGNmmSRbJyE3PjEMEYn\n\
7Gjzl2Mo0ME272ty0jdgJUtVMlyA9rEGGiGSiwyK8vKEetS2pJuGY3oeGxB7\n\
xwTlpJdz+tuldIflVw/9KcyCLlFsUywoGXNRcMa1VvRcIjm7vwN2bzvsnvZ4\n\
LgAk9dZPDo/T3U3OGjTwxZzjbej3tBIP1qB6uFxqfpj3mPMKrAWoHC6VtPmj\n\
vvvEffnoHCnDg+5bSDIfxMm6NJxpOIM9piRsLd0pDm9X6W5SbElIJWeXWp0i\n\
/dJHa4j3lmJL/gZyeeskE5XKF4yWp+AoKbVUahdNh1DQfAE1xHV86ylT2xWU\n\
NF5EUU0a8szHkGs6jDu5u3Dz4WbcvL8R6VlbkZWbhKLigygrOYzS/AOoIIdm\n\
Lj1JvHcClcRvpff3o+jmDuRf2oT8ixtRdXc/WvNOoSWfb71+Fp2FZ9FbfkUc\n\
X+P13ag+swE1aetRd3Yzmi5uQwcppA5yVV13UtBDCq/73m5YM/fDlnsIfXd3\n\
of3MetRuX4DqjeTyds5Dw/Z5MC0m9bb0TZgW/QElH7yK8vd/guqFv0bj2rdQ\n\
t/J1mOf+BBVv/xPK3vgHlL3596Ti/g6mt7+DugXEfR++gspZr8CSRCru0mJJ\n\
S1n2fEjubw46d89Cx473iA8XoOf4ErmH3sD5zRh+dAzjlTcV7xUy790jB5gj\n\
v/AWGDBT47gWGKiP+1ME7I2SqxrvzIGr+hqPql/Ntev81RD/dCjtD3HKvUn1\n\
1AJEjoGRdmpEhCMdpNq4EQFSYwUXHOV0VnBcPRLrqca0MM7KLWgwIjFhkM1f\n\
kGsKg1wAQIJuhrAe2zsXcx01+ZF23yg/8PK1mD+WWUqqjAkJjb3IPPfNmKw5\n\
L6+RIOPfMQv5nmPekdT2S0aSW2WN5MoruWnd178sByTgb40FP/knvmOTdmEe\n\
liwRh4B/dGIIrcFS9AYa1N1dGPjT9SlTp+rtmXL4K9GhYcJrK9kgm59pY0Bx\n\
hIihQV7Al8Ihj8r68NWXih76iR76Rdc4xZ21C0U4A52qxG+WMIQz0K0ZgpjB\n\
36OTPwY7dIscckprl8QPMwVXCLfxXWacFdTMJInq5f64nJyu4OuaHCaRQzX2\n\
ChT054kkMhM9lFqz5XJxi6sKVUM5ZOg4MZ2K0w1pRA3J2E1QT67Yj11s4MjI\n\
Hanej+PVB3CkKgU7i7jqZzO2Fm7FNpJCO8jwpRRuJGpIxpHivUgrTsa9hnOo\n\
JMpp6L0DU8c1FDWeR1E9yaDaM8iuPIy7hXxXup24RfRwJ2sbMvN2oaT0AEym\n\
E/L7WIWFZAQLj6KGtitL0tBkuoTW6htoqbqBDjNtl51BA9FFfQ7RQulFtBad\n\
RUfBOUUVmWloz6TxzENov78P7XdT0HL3oBi9+nNb5YdQmi/uQvddoonbSdR2\n\
oe9hCkvJ/GNx/zd66Lym/YvJ8M1G3daPUbflEzJ4s1C5/E2Yl/0R5XN/gYLX\n\
/xHmeT+Hef7PYfrgR6gmKqh49ztED98WiVT6+78nWvg+6ha/SjLpn1Dz8Y/Q\n\
m/YpwX8+0cK7Qg2WA7Oofxude98nivgUvWT0+s5+jr7zWzGSfw5jNffgqrgD\n\
Z8kNjFTcxTivrvWZtTwyxwtPPC9M4Cff5yZp5GkvFrYQdhiq0ezQQKzQwL8v\n\
38SnjzTFEEO7EIMiBQsCtB1gchjvSRRumKl4gVxekJ2dx64cHnOCx64ogdhA\n\
iGBYJ7HVnjM65pwam8EMwSTiVmTBW9KYBlTRcJALDZUsijE59LbpUS04JUbX\n\
x/V6+Qt6WPHJGPGJy0iDqwz4c1MLbLEVRv5ohdGLRgHiVLaa21eiZYdff/al\n\
DC9H18wCT6zuM0t1xLLRC7FS5DE2ckR6YQlVYSTSbxyLU5SUEENJIl9CjkTZ\n\
THzixZwibdSTZqpjQkgDUcGiiImX8wf4dewqVZ0gi2JauNAe8RJ90uK8hKWU\n\
8yKWIufHYqU/SkmyfObyW+KZkOJ+IO7MTrTDF4vXk0KpJPXBFzTwL53xWOVQ\n\
Gcq5GploidfSym2FKOrnCxVKUck3qxnMI5VSJRctnGk8I1R0ofEsthL1bCEK\n\
2kkqZVPRVuwhWjpOruxoVTIOVezBLhrblL8Ju0t2YCfR0R7a53KgY6V7kFy4\n\
GafKklDccRNtgzmo73uA0rbzyCUFlE8KqKD+AnJqzuIBKZG75MoeFu9DvukY\n\
SitPopT64pJDKCSFkp9/EAVERebKc2ipI2dXcxXdHY/Q15aFroYM9Damy++9\n\
9tTdRBf/VHJ9ejx6zXfiXkErobj+4THUkEmru7odLel70UVmrLfwHLoenUDL\n\
jSQ0XtyN1su7ybQdgCX9kPw8U/ft/ehNTyHhchDDnMJ+QOftX4RqvtaBzFrT\n\
LhIwa95BxcLXUP7Zr1D41vdR9MY/U/s+St79Pkxz/wWmj15B2dskWN4iw/bu\n\
PxIzfZeY6vtoIEbivmnNa+hN/YTap+jY+TaJllkiYtq3vkmMNBt9J5VZ6zmx\n\
FoMZBzBWxSLlPhxFl2DPuoCR4nT4OovhtxDlkDPTwoXoxywLbB5LObm1u/Ba\n\
yuI5aU0y2D/UQExVy2wkzT/cpOmItMpwq/RMSaHRdk1HrFNokgVGLUwB4/3M\n\
TLrvV7KFqYmz1URJXBKg1th89oSneEnyTpqXHJqXdEFAvOgXIhZydMHAqKYm\n\
pWW44k7YiYaIXAymihdRwyTlNogq6ucM4jLOU2PR2h7lx2QsymNxBokxgXk8\n\
TsMPRtfootUEkhMP+nSm/GkLl/CYXQs9sUZnXEhvXH+qPZrksl6KKYPUtxBX\n\
d+7/RrTu0fM/KQ1Yrikw9g5A709RoDtRr6WxKhudsKIjWAx7uJ33he+GvyH+\n\
bKYiPeEqLaYixk11+7lXy/7TohTnlkoji/Zb5L7oe+D6ZxfRliugVJNLVJOF\n\
l9Xi4g3y6ol7S37VwunviDYxXsRj7e5a4TDOifOvXihJZSYe05KKtqtIRhWT\n\
jOLLyauHS4XD2kYqqJXhXNMZ7KpIwgXqD5Kb2ly6A1vLdmANuanl2V8gqYL4\n\
y5yElIpt2PX/cvae8W1dV7o3fyyyLTvNiZPM3MydTPLeTMYzSSbjdCdx7Lgl\n\
lnsvsmPHvRe5l6gXW5XqFEVRYpEsFknsYu8NJAoBdoIgQABEYwcpyvF9n3et\n\
tQ8OQEnOh/fDxj7noFACiT+eZ621125eg5XksDYzy6pXkeNaSQwjzrVvxa6G\n\
dfjUuBOtQ8dgdZfB6ipB00Auanuy0dzDkuoIasxHUN6ZQbLqEBpNxC5zGtrp\n\
WruJOEdsK6/dgZqGXeg0HILVchRDvYUYtVcQw8ox6qjH6FAV7NYiklg56Gk+\n\
ir62HDhMBXD3lsI3UAV/fyX8xDp3VxEG69PQlb8ZlvxP0Fu6C4On98NRewgu\n\
uj5cnQJHZQrJrR3oI2dmL0iWfeacJbsxfIJ35dgWj7HqXXG/wvDx1TCtexrm\n\
9c+ge9OLMLz9MFqfvw0Grlcis9X8+PVoJF41P3oNOl65Ecbnb0TTvT9H032/\n\
ICN2DR3/AqZnucfGrcS236N/zf3wZLyCkb3PYHATsWz7E8SwxzG44RG69iJx\n\
7F0yX+/Cc3yjbC4w28XK6iT8VRkI1mSSdColljUolrmJZT5SWF6jbLTF8+xg\n\
DSY6cnDG2U4AM+OMl4bbxgEqDWY9ODOhw4w+9BP9DJqpAZFUxDAGAZPs7KxD\n\
DJdOMb4j7BbDxRTzahTzMqZ8HDiSCHowOuaCCmuSdYtcD8VFhRjBY2GSWcag\n\
kaiUzrSFKXVGP3Nhmv3ZNPNpmm3ZzOU6wxZXIXIVwNzcOMeOlGlThT+RSBQv\n\
EZPLX9brDPSYuqrVXqrB6P9qddocKP+SvpZUEniX6wk8wcx0DGbsdruW0LdL\n\
sVJMgGdaYBHQVFJQjqc/Z2/XBM9ZG1OGwRIQSSR7hwQ04cQjICpKbGIw5jIf\n\
+zX+eKMBIO7cx5LpCj3eE+HPlMR2RgQfzB2WTJNntFnnj0O2URVnJ+7OoWJC\n\
Z/h5/MdBz477iaDHG+6FOdROeGnFIG+sHe6HY6YHbf5GdAUMKq0fbEOlq1z6\n\
/jF+2n31sBKCHISf0+S6tnUm44gtFfvNu7GZZBJXVH9Qtxrv165CMrm6ZDp/\n\
r+o9vF2xAqtqPxT0rKP7NhKeUju3Yx8HhmrXoKArFV0e7jleiLq+bNncp5nw\n\
Y7CfQJU5FSWG3agh5LT2HKX/g8GaFXcnmjoPoqZtL2pbUtBMyDF15cgG4MND\n\
PIrhIPTYCSc2SxF6LYWw95VjyFqMvo589Lblo7/zBIYIPwOdhRiiMUKPc1tL\n\
MNZbQaMEXkuubBLeX3kQ1vxk9JzaQ1rqEBx1h+GsSycEHcAQub3+/B2CIFfF\n\
foyW74c972OM5G2Et5Y0VcNBjORuIof3tGiq7k9eguGtB9H8zC3k8O4hDt2G\n\
hgd/h/YX/gTL+3eg6+3b0fb4Nai79So03PtLdDx5Ldr+8ntY3ryVOPRHmF68\n\
EfbtjxODXoYj+a/Enr9gZPdTGNr6GAY3PgFX+uvk6t4WBnlPbMVk8zFMd55E\n\
iHQgMyjUcgyz/VXCoAVnCwd/3Ab2asQZ5s+c24AZWxkmDEclCr7gMch9bPEW\n\
/JZ4sXaXKB01RRpqSukoYc/koB77OTsjHIoiKOwW+DCCPOz1GEHzYzLOyvDR\n\
sVdjkO8SwU5SxNPpg1GzRFCTGIsaLMxxfyqNNqKjpjS9NK3VVU+LsVusozRt\n\
9RVNOKkYUlgrwlZpP34gp/Hmubjgs/BSXSmdU+aUFIMkLacni80uGM5OimAq\n\
pjWQYGqpjqk4rXePJo6+qoeov7CfWOgfCCaNZBwsYywvzE/JO8R6KEFuk8gT\n\
jmje0Ele0c9oUnEtiVbFXSa7CkWZpWmlz72adnJHzz/Xg1Ie+kPR7eFnbln1\n\
MSVxaOaVxjCiEUemhuj3KiyLGRq7Evgg7rcSkApqgSlWT4OTRmmVYWblRNjy\n\
kXri+HTtaBW6JzplcUiHrwW1HsKXv0GqC3h9qmPSgBZvGZJNyThg3od0ywGs\n\
qF2JrYSqv9WvxQun38FKmg/T9T2EqGeLXsHjBc+TA1yH9YS2ddWrcZiuJzdu\n\
lKqkU7YDsLgKYRjJQxWpsNNdaWjuI8XUewxlxoOCrmrjbjTbDqG1OxPNXemo\n\
aU+RrUEbOwgt5OiGh8tpEK7shKiBEvTaCuPRZTwZ9yd0tB6DpS0XI31VcPRX\n\
Y6S3Cu7+Orjo3NVdgf62AnTVHYWlMgN9DUcx3HESIyYmWSE8tgKMWU9itDMH\n\
w/XZsFcewlD5QdiJYkwwV10anNWpsBftwVB+sggoN7nG4bwdGPp0A7wVu4kc\n\
9Ni89ejgjswfPo7ubS/B9MFjaH1mGbnC28kR/h41RKr2Z65H13t3oHvlveIK\n\
mx7+Namp62F46g9oeeCXsL1/OzqeuQ6ml2/CSMpT8GS9AsdOUk/b/gJ78lNE\n\
r8fgPPASRnk5bOZ7cGWvQZAE33RnPiZaj8JPLtZfdYjoVIwzg3U44yJH6G4j\n\
fvGaH9JScV9BeLAeE8YchEfofq8BZzxKQS34OVBFdjBoE+V0dqKbBs1s/yYZ\n\
XwOCq0FeWTljp0EImx0hWPFwRWZNQV2kFNS8W405t1JTjK85L1uleR8bwIDY\n\
wJDGNAEYS6IQa6XxWMGkaCVh7bNTXDow/dUIq2LC2sKqSDnC/PykZt6EWbLu\n\
hH/c4uVwX9bLvzmDJitRzkgubQmzR4JOF+mpsa/rq0ikrY+sa5WV8Xp0iSBI\n\
/7vpz9X2RTxzur5/vhG+vw/Gc7Cb4zzSWUseEhdpaS4ti2c/i7TSCXJjnc+C\n\
0qBYW/86/ZlL1qTF85lc40iSlyNJcs3L5QVaz51IOotsFz2S5cytEqgOnOmX\n\
QHWkapHTXJNzDk0S2WXZKgezJbA9x+eDEjHqIn7wco8B4gVv++sg2dMia9pb\n\
SALZJMdVT47LGGwnnjTB7G+Da9IMk78Oh7sPYidJoMPWgyR/tksl40cNa/FW\n\
zUfY0LwFuztVIHsLubLXyt7AWpI96+vXYQMNbkm4vfljqW48YTkoDGkdzkUh\n\
HTNDGvsyUEqPKWjfhXLTAdQQj2qMKeK86slx1ZILayL3ZbAew5C9DMPOKprL\n\
0dtdApvtJEyWE2hrz0WHIQ/dZEOGSP6M2OvhHWmF39VG711gtD1uGQKuNngH\n\
GzHSXYWBjgL0NudigOTRQAvNLXlwGk/CbSGX1lUMn60ULvowDlWlo//0AQIK\n\
AaT+MLkygkntYTjKUwkkBA9yYaMVB+As3oWho+swWpwMf30qRnLWw7zxBZJC\n\
T6GLl5y8/SDqn7gZxnfuQ9MTN6Lhod+gYfnv0PHyLSSF7kX7szei9a+/R8ez\n\
16L90d/C+NLNsBFkjC/cjJ41D8Gb/RY8mW/BsfdZsl/PwbH7eQztfJrkz9sY\n\
y6efSz+b8/8TrdmYaM8joGTCRwAMtXwqMmiWQDI/zKMe4eEmmpvUMcmjaXof\n\
Qy2ZmBtpIylkVDAJWONxxmflCh8patLSX8wQXmo/STZsho5nhuK5qon+0M8S\n\
Ts5Oj0THrEuhRWYPz4IeXgx1VqLfXh58bc5DAmSOrdnZaHpMG7KZ7hwXeNMx\n\
faPHjnHSQ/TpWpjjhjEkjWiE1Mx3cQ5NQkyciSL0XKyn0Kb0mFOSltTWzuVM\n\
IkaSb0vSIuiqt09MfZBAKRQTjUpcdP9ZbvZxfpAq4QJBqviYSPu5VQbRqvMY\n\
D6ifSVe0y/Qq8UvPqwXnDZDPXYWrhZ+++g97hbRHVBT9P3nNCL2h/D9mHzgr\n\
uOLSpX6MLlgx8RlXGP3fMZ2HfuEhY88v7jBR79mutW+W5fWueAFegoY+QaA6\n\
o6dOn40qqMlIIGluAAFybb55Rl8//dsCcwP0soEzA3rubmLOHs8HHDunh3N8\n\
KSj0G4J/fgD2SRMa3NVk8BrJ/Fmk4ao51CopO2llON6OSmc5mtxVsni/1VuF\n\
/nEmoAmnhvKwpS0Zh4h+KZZ9Usm037wHnxAF2QhmEMX2kPp5veJDvH76Lays\n\
+ptk+T+o+hCZ5hTsaNmKzXXrUWhLg8lVhHb7SRR1HUKF7QjR7whOdezGqfYd\n\
KDUSAc0HUG1KQR2Nmo69qDbsR4slC7ZBIpW9EP32Uth6imXXSWNnLjpJBliI\n\
gFZrkZhAx1AlPCNN8I22weduZ/YRAMn7LIOfPI+fLgccLfDbWzBGUBjpLicY\n\
noSVlJWtNotAeAwOwwmMdpUQBIvgIT/pJlU2XJuO4Rr2hBmkqLIwWk8z+cWh\n\
op0Ewq1w1xIEC7ejL3s1nOTHfHX74SrcDBuvvn3/YVJTz6Hj3YfQ9updML5/\n\
H2ru+y2qyft1vLQMvRueIEV1F1of/wPanyLvRx6wiVfjvvZn8oO3w7ziNth3\n\
PouxXFJLaS/T8dOingaTX8RwCgNwIzy5azHK6/8r92KqM5vU3GGMFe/FWNke\n\
THYXY4a+FGYHqmnUEfQYhI2YG27BvKORgFiP6a6TdF85wa+TuGciALIHDNjo\n\
ZrybCcFVUbzmbnyAP8KTzD2B34yd2TQ1osGO4edSWmrOlcBsi/BuVsLqfDbn\n\
FdLJYUBjnnZGyJkP8o2sPecldgtqLMyrmT6JjKVJptlU/HlIm+atVRemRcTo\n\
SOMrCZrS4oeFw0FxSFwWPnPZeaSa45LRz+YuZdZE2lbHlC/pC+Xiv2jZrtRs\n\
cpmBbIL1d0HOl/WCTGFMm1Z8+Q0tEDapD4WZgGT3h+c6Efz7iLCFKCPz9Ofe\n\
CGc0ovhjZt5TRvaVU5cCMWNMtJk8wKvvIqHGNMfA6Xmixwib03rhgVsLMGkm\n\
jdUXI4hQRHM884cpRLgJEol4ppHA/InbIdThLSb89GgeZm7hPFqBHiKNd8Ym\n\
fYZYf/Hi/YFxgzROLRkuJvLUonOsGhZ/PdHHKC2fj3RnIIU00u7O3Xi58h0k\n\
Ey1SiRR8vqN9J9JJN+1s24UPq9bib+TbNjRsxOrqNdJk9SA9ZnvrdpzqTodp\n\
lOhD2quYvFlFTxaaB4+hwLSLCJSM00SqKhrV9HMqSH9VGw8QhdLQ3pUt9Onq\n\
y4fRmgOjLRdGcx46zDRbctHdUwTHMJFnuFai3y5HLbyuFvg8BgTo4+SnEfAY\n\
EfSYCERGwRBRCUEaAdIcAdJpPtIj3sEGMnqk7ToKMUxmaMRYRCavAC5LEUY7\n\
8uEmc+c1kU5rPgY7ocpBGHI2EYoaMuCoSsNwiULRKBk7Z9E2DHy6huatGKvc\n\
TXpsHYyrn4Dhg+Xo2f2KbKfHODK8egeanrwebS8Raj68D5b370THKzejjUxe\n\
+/M3oePVm2F44QbC0z0wE4q6Vz8Ez6dvEXI+gDPtdTJvb8F5+D3Y96+AN28t\n\
/Kfp53NIrGArJlqOYNKYS4buEEZzt2G84yhhqAwzg4SiwUqFosE6MXNhwtE8\n\
YZnRNN55FCFjNmOIvugIRJzn44oEEmJngt0MJAKQqkFiISbHrL6meB5Sx7M8\n\
mE+zvFBFnUbEmEuiU/GxcJpz6WLMexHjSGgkTPIxknhIRCWYyHDim3HxbeMM\n\
Ix6imyaXaFgi5ZAUi6VIxi8uFlnzEp/hmLN2TUfWtHpcvCbSRFxp4JoXXacK\n\
1mcurL7CCVELGdk2e05fLHzBWtClmrDSytajZZpxF2i2dKGGkIk6Eb+sNy1I\n\
/KJKTK5O//xLi4nYGqu6LqFbhcUpzWZyzzUfMWaK8KfhkA3j54pqERz6VUw+\n\
akUDGuNYQPPtRVpXNI82x/LTLT6WV/nSAy/TdFkMCKU3tLKYAkKmHcFwguaJ\n\
M0MiyeL5StwfpCOSgFJ024Cc+8O9gkHuRMA1U7yw1zFthXfWRqhrQL2rTNqp\n\
WYNNOD1chKqRYrS4KlE/WkZCrAlWuu/T/izs6dxDVnMP3q9fg2fLXsf7deuw\n\
k8TX/s59yORSTEs69pCV3NHGycAd2NK8GXvbk5Fu3o/1JMKOmVPR6SkhC1qA\n\
UhJgVYTFloHjKCfbedK4E6dNeyUSX0v2tMq4H+UkwBotGbD256PXXgBT7wl0\n\
dB1Dh4WEl+0EjQJ095KKGqqCw1EHz2hLPN200i/R6yKyjZLo8ppomBGgEZRB\n\
JCQa+kcNLGXp9jqiINGQHh9wtKlBZPQREUe7iaymMtg7ijBiKYG99TiGm7Ph\n\
sZFL7S3DaOcJOJqy4WgmGjbQqDlMIw32sr0YKtgBe9FmDOZtQH/OBnhOJ3O6\n\
EMOfrpW1N8Y1j6N316tof/N+tL5O5HuLRNgLf0I7Ca+edQ+h62/3wPj6LTC/\n\
fQdMK24lt0oO9rVb6PgOuTaw/RkESsl5nloFZ8Y7cGV8iKH9r2Hk0NtEwh0Y\n\
K9oBZ+4m+Kv3Y4q+KULsnnNJHNYeIhKWYIYE10y/RkOmor02nhBYz+U4I42Y\n\
6SVjaiRj6m4nDvotLIn8FmKgVRi4MNkr7FuYsScx9Bh29kQh3hJFukhEa86l\n\
nSvoCeWEbREbqtTXmDhQb0SRqSG9/tmdstGMsFD2yuZucRoLFRt1pSb0ktUj\n\
85M6H+WaoHHJOfFpPvtqTIFnRMrF635UcXF2NkByKcSRM23R35LF5NMD+wqM\n\
wr4LlboLBhNwfnh/SVTzLebeJTrevqTjLUmPpn1JzzMKylo0cXexTrHIzOKO\n\
azJHwmYWeAww5hSXj/JdfHaJTittI1BxjBEx50+IGsyY7Tc8MSiLNH5UG4YF\n\
4y5nnsXQzKtqxSO14XNK0o0LxezS3Z5zhgEh3GDUdYrcC/fH3SQg85F75LQi\n\
N2WqGS2XuBo7SgfptXpnkcCMe0dyA/xicnt1rlJ6XAk6vJUYCDXgNDnKfcZ9\n\
2E9aa6dhJ1Y1rsO21m1Y17AJ20nP7Sf9lWE5hEOk6w50pCCV4LaHHGhy6w5y\n\
lKT7WrYjtX0PmgliNm8FagdyUNmTjcbebJRaUlFg3EtOcr9ounJyklVGHgcI\n\
ZIdgYpANFcHadxKdPfkw9ZxAF1m9brJIA8PVcLma4CYSeYhcPq+RdJyJiGVB\n\
wMeD6OWz0mzFuJcGzXIf6bqARrNOunF2xj1IOGOkGdRgkWdvhXeARJ6tEq6u\n\
UgwbC+DoOEFYK8YY/XAui/BYi+FoycEwiTsH44x8potwYS9MRk/mWhJ4n2C4\n\
eBshbROcxdvhazyAkbz1MK1/Fl2fPI+uj59BO++B9sFDML57L9pfXYaOt+8k\n\
T0l4e32ZiLz2F24Ucdf27LWwvHu7iD7bqocxevxDhKq307xSIvP2lFcxuO9l\n\
eE5tgq9iF5w56zF6ajOmjEcx3poBD/nc0YJkTHadIJQV0SglhPGowIydkEZi\n\
LkyCOExieN7ViImufIxbjiuI8fAxzGhMEMwmOGJPQJsZFBHH0XkRc2G7Yths\n\
ZF4UWpMqB6Xn+HDOo8k5j865RAFb4rlgizCNHegifafMJx2ySZzXcSZyjz/G\n\
EZwl6HJPnjepkUzdIcpt6pIL2FNVZXBRDOdmNE8aYrZp3Ds/gymS7suqZlUL\n\
kKmjRB1cCmMs90ZGhuB0OrjVi0TSIqsQYxfhnLcKMbL+5gt3NbnovBCbtnmA\n\
tmvS59HtoS/XqXi5TsWmqMDjXazm6T/L7+fU5x4MzxhkPfG0Ju6m6Rodi8Dz\n\
6AJvTLe2vDRQoEfemJtdqxHxxdp81hsDSXfM7FU6L+7SGA0Y0EXk9Fn6+Vob\n\
qiktAzF+hhe+s7RLpOP+2NouFYlLIDT2wjNrZTDSQ33hnrgb4ZvppvNuuGcs\n\
pOya0MS9L2nmvYospP4qCF6t7io5LiFIltN5M6m9JlcJ+vx16PSW4zDBbA/B\n\
7xBBjE0vQ/KgJQW723Zie9sOMrgEUcMeHDCk4DDBMqV9H3a2JOMwwXUPwTKF\n\
HtdMr23yFKN+MI9AmYcmmstIJeaSOS40kfE17ZbEQwWpvSqCLScujX3HYO4n\n\
g2sj09tbSAa4BN0DFeinz/SIqwEeTxs87nYaSt4xHIMyrDKP+2mWYaNjuu5X\n\
9wfcJnrL3J30TvpZGY528hmzMx5BpyHuZqGlX8QgCUB7CzycAyUR6LKUkhAs\n\
hMNYDE93BQJDlRizkvVu+RTDLADrDqs8Z00q+vK3oT9vM1xlu2QR9lDOJrjK\n\
d8PfnIrh4xtgWPUEune+DPP6J2H86BF0rf8rzH97EI0v3oymp28gEXgDDG/d\n\
htaX/kTW+CYYXrwR5nfvgI3sbxeNod0vIVhJQu40UTjrbRJ/K0j4vQrnsQ9I\n\
7CVj9ORGOI+vRYh+3lTXUYwxPfmcLPFMbz6JvkIiZDFmhpiWJPyGK4iUVTQa\n\
MD/aJOcT1hzMjbYRLU1SAXtG8prWeEYlOaizUwzLAQXKWXK+4aEoIGleYHhG\n\
Upv8mLBUaoTFDocdShRKmM4ZLzlP1n6c4fTIzIUcnOVMvIBWjI8glVC7MO9T\n\
Y86XIMIwMSIRI1hN1IA6Px/SACobdXBXGsYl2+TxCDx1iIp5FkxGrmkjBrQX\n\
yWMu0YtpY2dGaTgcWJRynda5qipF5OzixdmKGa1MVltEqcvD2KWUF3GBmpaC\n\
VTHDzs42mEydmJ6eVOsB2A3PRxsTzy/2z0l6avbSaF+tC2yiGxdZ5y1D9t3+\n\
u/Sticf52z4tWaxBm87RoCF9HpglaRPuVpD73J+gmWjF3DHdRHMcMLq5gEcY\n\
y3X7TrKr3vneGN6OJeh2W7WcicQax3QLLpgV7HoFu2NaexpvFLVnVbYjoDll\n\
1p7jZwakjm2Qfn3KbffQ6BWmemasGmevlnM//Y8cEya08Z7XPg4ottG5AQ3O\n\
ElQPF6JjrJa4WoZTfTmodRajdbQCRm81idRqFJP73ccC07CLHPMuYux2cs9b\n\
SJiSeyahub5+M/bT9f0kOI8YU3GAGLutaafMh4x7sKNxK8p4kTa56rqBYyjr\n\
yZIlArX0swpMB1FKjrqoYwcKSeiW0/OrzAfR0pWNzl7ia28eWumT3mk7CRvx\n\
dYD00jDpJbenHV5fJ3G2E94xAx0TY/1mekeJqNzmkNg6HrDRNeFsPMOVftnB\n\
iB5lJJN25bijf9SoOCvKlETq7XyoKdM2BEWlEskHa0mR5kuh7oi5nDhbAnd3\n\
mRTqerpJlbbmwF6XCXv1QVKl6XDWHcQgqb8hUqOc/XCV7cZwwSekSFPgrz+I\n\
nn3vwrTxOdh2vAzThidhWvskLBueQgfvLfXarWh/YxkMZKoNpE473iWF+tYd\n\
ML55G8ykULtIjXZ//ARGcz9CsHoLPPmrMJqzEiNZ78Oe+ga8pZsxxh0Pialj\n\
FclkrrMRJNY6Sbl6y3dgypSjcbYYs0MlNMqIqeUIDxNjh2uJsaRMR+sxTRZg\n\
3HSclKgRCwHibMCs6kcmrKJIBbJc6jY7FJnj4nWHbY+qU12huhRjOYaoGW99\n\
eKSnBQcduZcF65rPwlpJiSrXnfPK88Y02I5J8JHnhXkeYsHnA3LrixBWGfFY\n\
xi5IlkRjrKR+JzXELprjdYbqmvY8CuvyNkphJWd1U64LW1VzliTpjOlpnzxF\n\
q8pT8NW5q/Rs4hdV6UnYkuVs+GK9NDhMH4MReL0uVrSxTRAXbTF6Id4m6PHK\n\
eP0oWhSzRC+KkRwN77D3/yZG0sIxa8Njthq/wN4yNQq1Cfx/j7uM/qndGOTE\n\
zRmX0I1rZziKOcXbSfH8uequPn1WcsncVNBPUJzWgagWIDBrW/21ONRzECcd\n\
J+DlChfRpmzsSaXS7049fixmDqiXPRuQOhpv3DLtPNILzCttlpWmdZDpV+sT\n\
OFMjwNXOuUCYHT7P3GeQe3nxbsEeYj/362FhK/0Ix+ph9bfBPmFEf6AV5fYi\n\
giyBdawBRQMnkNN7DDUE4JbRcvSFGtHmKUUGwY8F7XYC6vqGLdjQxLDdhVRy\n\
52vqN+G9ylXYQtd2tu3GQcMB7GhKxpbG7XRMQpiE7XFLGrrc5WgdzkexLQP1\n\
vccFtKWWIzhN7r6cxHGJcReN/SRq09BK/wbLUAHBNh8t3QzcAhKylei2NxBs\n\
mwisRvrL6oSbaOnxkjj1+cz01vrF7LPRt2mDOUvfMz4bM9jXTW9w0Ev30/AT\n\
cP0eHrzI2uc2srglbvs42eOUES+xzqsRGFHhAJ+9CcMEWoeJINtXC5etguBb\n\
QjMBd7BawgDDJGz7Kw9juE6JW2ctAbd4J+xl++Hm9DMDt3A7/A1pGKtLhWXX\n\
Cli2vwrLtpfRsZqELbdE3PgMOj58GIZ37iLI3gUTiVzzyvvR8c7daH+VIMzp\n\
5ZUPwrbhCbL6r8BX/jGNbWTr1xNMV2GARW3uahK1u+DhRa0nPtHsfxpGT62n\n\
ax9j3JCJGSvBtrsA0wPFNEpI3Jbx1729ggvqHbUIu+oxO1iFCbITYXcj2X8W\n\
tFqdzcI4f6MtcI3NZK82yFgtSEhzhou/ommdkbhITmdBIgCqfm9B5XRcTCwJ\n\
erpjBscE3Jzn8ZKqDHvF2xNPwz4eKqzJNyxd5+cCNIKRwRdipStjNYlvL+Jo\n\
niqUS9ACfJLOibvQtSV8Gy+rHZZEcj4y+JhZSQ+WFFCkxURMXGBRDDQa65yR\n\
1auysiJJT98k6qtPv7i3xuJE9cV6/1Zx8NEGGRdqhvGLC6zGktsNEWMfDvP3\n\
zexsCG53D5yk1iYJPgwtmhMwQRLwq3Tr5SPtrkDMQ3hFu0fWhPIiBu7Kk9Gb\n\
iVfr3sPa9q0whUwILYwl0gP4a3JygZ664Nfm2GP+BdNZ3P18TGOMnuZWBYLy\n\
0twK0aWt3XKSb7eTdqTBq9/Dqg2rd4a8/LSVUNdD+OuXc/ekjYaVvLsNTpoH\n\
uX1roBN2mp2TFtKS9SgfLEKbuxZto9XIIdTk9eVKFqfDW4XeYCMhMYd05m4k\n\
E+42t+zAWsHfDvL1eyTY+UnjDqyq3oC3y1djVe0m7GjZSR5+D3a17MG+1v1I\n\
bz9AXr4IxtEylHYfRWXvUZTTXGg6gmJzOioIh4JAPjYfQX13DqGvEJ19BWjq\n\
yoepvxS99gpCXx2GR9owSt7dSULRSSLR7TERBs3wEc98XhtRkAZ9k/np2O/j\n\
uZuoRxyk2e+xcTjEayPY0eENdCc9yW2hQS8waobXSS/mIuFK8OPZR9TzOWkW\n\
GHYKFH2OVniHyd4TCV199RjtU4HRoY5ijBAVfX1VGLOVYrghF/b6LJKeRMHa\n\
DCnCGSzZi6ES7htLx3lbiYS74Gs5hOGTn8C8/Q2YPiFr/8mLMK0j+n30FzSt\n\
uBtNr94Ow3v3wrblMRiJeIY370Dbq7eQFF0G4wf3o2vdY+j5+GmSnGsQatyP\n\
MZK1zk9Xoi9lBeyZK+Gr3AMv0XfkUyZeNiY6M+E9vR0eelyo+SBJzqOYJApO\n\
9xZhur+Ev6P7SzlONVgh5Jsl2RkeqcckSdIgif+wux1zPrNawRq0qsy2jF5Z\n\
SL8wyVJzYcpOXn9hikuX7YI8GdMjUrrM81kuYZ5WCZ6FWSejkAZrTDpimMyS\n\
SZ9185Brbr7xypHc69UeIVycZcs2T3ScJzrSLGe8l4y64RCpQmNIyBgvt1wi\n\
Ny7CLzpC2jzJ80V8wHvR6JcmZbHFOXO8PCwh9hK3HJuTDfjmzmFsgvA0SfjJ\n\
BdKRXkSRB0gbaNXpmmcJO8pepOpcu7Y4v6QNaVOrp6LCcsZKOHwJ85ahO681\n\
/Nd2JDrLtYifRTu1sXmXlfyqucilumSsWUxKt5uklXcAful0H9AwGGBS+nVS\n\
apRcGNMe4o2SUmqk3YSsIZS7SvFxZzKpxWwMzwwQ8vyKgnzr0Ujol5Wq6lqE\n\
mOpagG/GyPHLg8mtjEs9tROhOaech2gE5hQuA2FOdocdrJLCQzoxhZpMSqLm\n\
6CTvuzs6YY27CiPjJrS669HsqhbRaKfzGns56h2V6BprRNVwKbJt2UTHfNQ7\n\
y9Dta0AnOfM0csp723eL015bt5nE4jZsbNyJTU0kDI2HsK89BVvpvpVVm/Bh\n\
+XqZFSUP4kDrAZzuy4fVXYm6wQKU9+SicSAXhUTFAnpueRcLRRKMdF5hzkBN\n\
1zGi40kYyA82deXB2FcG21A1uofrMDjSilGPgQaXo7i9Jnr/vAQ8D6k+r6hB\n\
4iMrPn+PUFKRsieBANlDf6B8qkAq4ITfLYELt4WeonhpEmbSHA/vqCnuesEn\n\
m3bGpY8cuiDT0UkOvZUQydHQaji6yjHURk7dUgZff5UUbQ83MyqPimB0klMf\n\
rk7FIIlER0UqRmvSRCy661Phbz6EvqzVsOxcgZ79K2D++AU0rrgHjeTKW9+8\n\
U/BoWfsQTCvvQdvrt6D1jVvRtoJd+t0wr32YROVfMLj/DQRrd5PT30ticSOG\n\
Mj/EYNp78JYlw89tLnM3wVfLWMyGr34PRnLWSsOk8c4MunYMk7YCTHYXYZLE\n\
4vRAGQlGwqSdMOmoI3fegBlHNcateZhxNcUzJ+njcoYkuF4HJAXZvDR2gAuw\n\
hwi0qtOIVoQtaztia34c0WMNlmennRr6NExy0FFA6dGw6MX8tGyfo3g5Fi9I\n\
TNLgGNAH0ZERFZat++Q8pA+FynExxoLAycUYDI/HzAqBicK8pBg8Rob0v9d5\n\
qF0XtLHKjKxfi8hKTpfTMdfSTCecgz8GHzNtJknwlhgLO52BLDLnOMWuNmu8\n\
BJG23ZGN1tR+SQp/cdEtqFlaxn9RZPOSCxDyEp2QtVrYMkkSYrOzQYFkMCje\n\
l8EVEZIX0a0nRkj6NTS6GIvMNN6EiE75w0qutn/CBsfMoAbAJRoUx7QRAeSY\n\
ujtJu+yPeYjipDfuZu3hnEF3K0RyY+25EULkiIZIB3daIzYOirL0ESP5mJUk\n\
89Ez1ctkxMiEiWazHA+TijSNNRH3GtEXaCMGtqKM1GTLaC1M3gacIpYd685G\n\
mf0E2shgd/vqcXowVyKSe9r2kWHegfX1zMftdLyLuJmKw6ZMpHUcxDZi5vqa\n\
rfjw9DqsqdyAXXx/816kGw7C6CpDJzG3vDcHDcTJsi5NTVrSUcqRSzLlpaZD\n\
qLZkor0vDwYy0bUkdDp6itDFK27ttcTHJmIjG2gzMdEcz2Ckv3QvfVoZkzz7\n\
ZdgEkQEaZJ/pG4SouVRpS18Pn8mQh4kGNWu+2sTemolpFmKaYqhpUpdvJ0pG\n\
BCYNVzuJyzYSli1EyjrYjWUYImttl5W/pfAzLW0lGG5jWhIlmzPhbMnCcO0h\n\
9BftxHA50asiBSOnd8LfxjY7GeZdJCq3vwLjlufR+Na9NO5EG9np9vfvhHn1\n\
fTCtvheG9+n8PRp8/Z07iZ73ouvjx9G99VmMnd6CYGMqxqqTMZK3DoMZ7xM1\n\
NxApiZ5FZLeLkjFtOY5gcwo8ZVuEmCH6Hhun76cJSxamiISTvScVLUlQzgwT\n\
LYmQ864GhEebMNlXhJA5E2GvAXNkref8nSQsSVyOMy5tgsqzkz2ylFfEJC/h\n\
5XUsMxLPnFHLdx1KTGoem7/fRWhOO+W+hWmXJi6ZkU5OvMy6o+AcE3Aq7TiG\n\
uVnOss6Lv55TWpJRGSdSkm0wq8hwjNmW4xCjL6RYGhGT9HPoVteGYZ2dcRe6\n\
JlIzSRluYiATV8ThVMzQlKSiZUKML49qyOnIuZ7MP3eVzEU6JRMvsNRFyKlv\n\
k3A2WmCUGFnYsnhnFr3Zim7hL9FXtiRcoCtw/OJN5j7Xc0Rf1mvNLzvPwmtb\n\
F5TrmSEuJ+UvCq+3F5OTHtGfEwxCRVMF2iUILnLsfk13uhRel8TIUY+wcULG\n\
mEBUSOvVGlV6o4b8jDc+ituvxzzGpfB6Rhl1Vp6RORSOoJUU6OyQSE9Gq3eG\n\
sUoSdIrlJyffvdPdcb8ho95NMtSKfn87yc0ymMda4SDcDoZM6HA30KiHgYx6\n\
MUm+nO5jqB46Qcaa0DpWh3xbJva37cHHhNTN9cnY1LAD6+q2kyHfS0jNQKoh\n\
HSsrN2Fj3Q66fyfWEV7XVnyMbXSeRfc1DBXA5q6iuRCVPXmo6z+BIks2Sklm\n\
VnRlosSUikJDCk5zfJKw2tlfgDrLMTTSMNJH2TpQBTsJvxHGqhhzi8hNRqwY\n\
c7/O1XhNfSp2svJkjvbw5Z645XJJodWmzVYEPOTUPVbBrN9jVkyVazybI2pU\n\
n8XFsxzlwU6eKzPFvRP4e+pIipaJc7cbi2guFefutpbCzon55my42nLgJMgO\n\
EVRZjrrItY9U75UdFIIdmbAXboZl7wq0b3gaze8/iLb3H0DrR3ejdcUtBNg7\n\
YNn4MIwE2NZ3biO43o6Ov91H436YN5Bj3/kiXCc3ItRBr1WvYDqU9RGceRvh\n\
qzsIP/2ssbq9mOjKxYQpC67CjXCeWkcSmKVoOsE1g+47iilbHqaHigWsM8NV\n\
Ij9nXXU0Wui8mh5zDLOjdQLWsK+TFKmRHLtZq8W0aeVLAli2lTP9sihmULl0\n\
qU23K5jOcseWaScnenTeOmKMu2LrxWLPEzXmerR5LF5om8B0jZBWHLqPLS9T\n\
V8SnT9l1wirvMRCORDMFtvERwM4FlUsXT8+YTYhx7ePatcQYvSpDhKdcjkpY\n\
8rJR5x4lcaKSssqPsxRl0miLXQS3S3W+Lonwlevf589ZhRiOj5Z7Ll6lc/GF\n\
1w5Gt8GKW7wJTZLeOiYpIljPXbSzdFHaXRWrX/ZF7dW/9A+zQiUxSjaIqSlv\n\
DGYlRCl6duIzt+bz+ftygtfh8B1LNJpGFkCPaFu9uNm6Czs98ZGjMYmG6hJW\n\
GzpoeT9iRVp33FfPIW2kZbBLhCxHXUPhEZTXExEL0pFLg+nKmSDJ/swQVsjd\n\
E1w5MuohwI5MWES32kivOqdtqO8tQ3LmJ9hBo9iSj9MEwNPk65tHSC96qwiw\n\
5cgkX7+5fgtWV63HBgLnmuotWFW9TaD6addx7GpNxTun12INAXUjQXdzTTKB\n\
dSf2kWYtsh6HhV6jZbgEp7vz0EDgzCOdW0xwregifWxOR5GB4Np+gICaRXo1\n\
D/XWHAFrq/UELL2EpdFGOAmsIx4jRr0q6km6lYBq0cDKQlVoqkRqoojSoAyB\n\
awLjVN23hPRsN4dCVaCUiNraXIKKsmPxXPBOOoCh6hcty6DthDeiVEe1ECmr\n\
VVcrfWu52uJug9fRBDevA+qpwYitmgZztRhj3DVroBqjXSovNNx2HE7DcQzX\n\
H0H/6b0YojHakA5XdQp8hixiaxr6jq6DKflldGx6Em1rHkDTW7eRxb8RDS9f\n\
T+y8l7j6ADKfuha7H/wVjath+Ogu4iqJ1q1Pwn7sA4RaD0gBk7d8G0aOr8LQ\n\
p6swVrNXJdoL1iHYelCY6q3ZQYJ1J8Y7UjFuTMM4mYcJK9n83uOYpm++aS4H\n\
ddAYqZKGDWGy97P0zTvZfxIh+jac97cgTKZnzkfidZyEKxmjuSCNcQvmmKtT\n\
XOvereYpErIzqh9NpESUjL8sRmTkajxVTHUo/DJyGaoJ6pKg1hmnri3VsKvF\n\
VWddkZCAHjedDxNrWejSgYbZeR2/PtazvHB7fs6n0TcQQa1o0eBFOnAjYdGQ\n\
4qcY/BDOCZuKjVc8VSthkrTQ57im1sbYGIte5V2jVF5pUouIfkG16UUKpUTR\n\
S/Wq+KQvqoCPZtf1LZO1UtHzFkFGJeoli5vafEWv/vyKzsXSGBzydwHjsGcx\n\
DpMW88+r7QCqtrhSoFL8kwCmO+Lh4xKiJEyIpaDy8Xx7xhulIh2HzkiEgHeH\n\
4K1Fl8JBauitd17BH6+7Btt2bhTypR5JxnXX/RYPPnIXWfYetu3xjMO4ayTS\n\
OUKuvdvXTlRrgslejwceuhP/c9WP8f7Hb2Ln0S146f1ncO9jd+BUZzZanaWw\n\
umtROZhPsnIf1lRtwqqKDdhCsnJDzTb85u4/4Nvf+Ra++4Pv4rrlN2MLfZhW\n\
V2zBmvIt2Eb0e/Sdx3D7E7ehupckKrn/yj5y4X0nUENzHsnRCutRbDn4Pn5/\n\
/S/xjW98DT/+yQ/w1HP3oploWW06BkNPITn2YvTZSay5DRhxs1s3cbobB1I2\n\
49ZlN+Db37xC5hWvP4cVrz2Hhx+4C7ctu4mIaBP8KfHI8pqxdynycg7K/f9E\n\
z/vlz36KbVtXq9wQYfDhB+6ka/+NtpZS9vDcBZm3XSCNGfdnce8rP3wVv7jq\n\
v/HtK67AM399CG+8/BRep3Hd73+Fle+9TBRsJZXZCs9wI1x9dbIq0mEtQ+aB\n\
jbju6p/T876OB267AZk7P4TLkIPRDrLytYfRkbMdv/jJD2X9j7s5Hf7OLAye\n\
2gzz7jdg3vEiWtc+iMa3b0XDipuQ9+BP8ZdffR+//Y/vYOU9v8a+v16LLQ9f\n\
jat/8M+4/Sf/CvPGR9GX8iJ8RLdx+koaI20/kr9OtmZ+4y/L8H36hX3vn7+J\n\
FX+9DW89ey/efOoO/Of3v4PKQ++SqiQCdqWTbScK9hwjdZlDFv0kph2lmB2p\n\
JFXJo5ZIWIcZ+uMY7zuOWfoDmQ+0kMI0kKo0ETHGTeR9z5CFOUPgO6uNCAQX\n\
ZnpURlyCWky/i7Xaebui4IxGQC4FJeu0EHZw3lsoGHZol5wMiLCLzWwM8ZSP\n\
dynySS+veW4eyGLzYmGfkphjEampgCfHoi+DAq2ApjGDiotzQYl+hr4UEZZh\n\
jX1qjtfd+7gGvEmtzYTSTmEJrs7zrvDnJ9iTzrnG5FuiVR7F5tsjOXVJ7ehd\n\
WGdic+v8Xi6cVw8aOQsn6SuKEnVaxorPRZsfamsp1RYY526tqqffzymov0iF\n\
RyMlSdKnZ6kSmlL4GeHpixfIxt+8SHJOT3s0yenWg6eap09CiPy88vReTEmg\n\
UyGR98pRbHXFxEi9MdfcMYFRRWJ56TNR7CZqtyG55l8cW/3K4pckc/+rX16F\n\
O26/RcVS6Us4MGuHj/6SfbMDAmAPffV7JgXAcYrAPyVj341ObwtaHbX42c9+\n\
gj8v+yPK+0rQSR+oBmcVCnsLsfdEMv79h99HdRfngapxsisL2xt2Enk/xqrK\n\
rThoOII0QwY2VO/C1Xdfi4f+9he8U7IeG6u3Y135Vqwq3YRX97yBb/+vb+He\n\
J+9E23ApjM5yVHTz8vHjZOiP4jTpylprLs1ZKOg4giuIvjtTP0Rrz3HUmo+j\n\
sYvMfU8RuoeqSXe2EnkNcI11ku40Sy7JEvc1HP80RegrlPXbJEDKEdFnn1qu\n\
xKUWIRUrr3SpFkjtFvrmHk8VKtvob4fJ/b1//d+oOJ2jLL9XVTDpFCaiKKtv\n\
xhuvPI3rrvm1VCn5RkmJjip1+vQTD3KCiuToLQThFoIwJ+hrpW3QiLUclqYc\n\
gvePpZGrw3ASDrL3buNJjBpycd8t1+JbX/8aHDWpcDcRgE0kUyt3w5r+HjqS\n\
n0fb2kfQ8PZtaHr3Fvz4ny/HH/7Pt2HZ8hjMWx+B6eMH0J38OIzr78evv/ct\n\
dKy+E927n4KrYA3GDQfgI8vurdwGZ+HHGC3fgT/+6sd4/bFbMFqxjUCbg1Dn\n\
ETQefg8rX7ybJOghAvARup5JMjQX0zz6aAwXEIBZilYKiMMjtSRFKzFhzyeZ\n\
WkDWvhHzPpKiAbL4QSMzmAZZffI5ZyZZiio5eoYJzENiqtwOUdl+1qCqp5hd\n\
adAZvUY0nlHMuHXKEVt8YbArOvQgAM9uzjN5JeUUz9SVOCpv86dBd27WJ+AN\n\
hyOkDYiwPN/ia2eheN3Th2Lxq9v/cNT+J+mR11j7r5AcUbKs3cjXK+5Kzj2m\n\
kYUmX5P0fLxOaz6O14CtKvqn9CVR0xfHkFmrCo1UPKle2Et0AC+Nxe15JfZL\n\
vwi3S3W+auBdtDuQ4PZiLXI6NxcmgHoQCgVjDH7E139JgywJWU9PBLJ6NdME\n\
QW6C5ghntVnLP110jg/3xhh4j5KmIl4VgyfOaMmoM5HSJpLH85EEVYSvfr4W\n\
zfnrd2s/8kZ1jZ721juv4Z++9U0MkegVy895K/pb9dPfqm92EK2WSpTV5iju\n\
anl971SPMHcwZMELrz2JbxF3yltOoLy/FG2uOrQQc0/1nkRxXwFuv+/PuJNG\n\
HXn/g+0p2F6fjJXlH+Pjmj3IseThCCnizfV7cf3yP+GBtU/Ifdtr92BlySd4\n\
Oe1tfJNE1Q9+9H/w6HMPwEqfzSby+EXmozjWkoZP29LI55Oq7cpBMVnP4s5M\n\
XHHF5didugq1luOoIeY2c2Og3mLYRxpI7bZjZLQNLq504ion8ftW5HyaKuxU\n\
Ht/fE/cNsfwdbWXo729RuPV36/kqiZp6lQgW5NLTORbAj+fzNSvfZHGsRLIg\n\
t1sR+Tvwc6CV0/5E3TdefYaI+xtFXPrXcDyAyXu6mEw0LzblwaueRPq2YKSn\n\
RgIBdkspriXZG3I0wm0rx1BzDlzGE3j6kdvxb9/5J/zHv30H/ad3wlm3nyBv\n\
ORr3XQwWbYFx1wto3bAc9e/fgcd//x/45pcvReEzv4Npy8OwbHsYhpXLYN5y\n\
P7p2PIy8Z36L9Cd/Ryr5EfL+r8PXtAMhA6neWnrZwo0YPR0FrqdyByna45Jw\n\
8nekozprDfn9IxinMdWTzaCNx/TQSfqITDuKSOCWEW8rhLczDuLuaK1cG+/N\n\
khp8Fr3zZP/PBA1s+7nlx4Qp7qs6c88QcxV7ezTuqlWikf6NC7Mab/lcavAd\n\
zFzWuQJdJXIjKlhGQkT1hknpMm3DbkXdsPtCqjdRg64+VBYrURfAKl0VEPxe\n\
ep7hH9cMf4K2yHNcrwXQZG+0zePUlDBVLsQlxC4fV40xLlOWP6b1kehbNbS1\n\
pbFr6Gf0bcuYpNrmSXEXkrdJemhA3b14rXziBSIFCTqA9QXzMUtJl+D8ctML\n\
LSC9eLHelajBknMAPD7OjccjAC76ApXLWacI7S7hYwKwX8Ab+syrAVhLYClo\n\
RmMAHp3I7pjIgjuiXEXR+umfGoPVRSUCISG0pLz8pJrUXVpd6nyAFO7PReFy\n\
3SkXVHFxVVCISyqXU1ecwprql8oAJq13mhWvlYhrg3u6B7/4+U9xzbW/gXWs\n\
He30iWkm1Vs/Uo7KwSKUk9LduPdv+BZZ4uymNGyv24ltZFlXlm7BvtZ0fGrO\n\
IwKnYnNtCu568h48/clLdL4fRw2ZeP/4Gnz3yn/DlT+7Eh/ueQdPvfQIOuyl\n\
qLAeRyERN6s5DcfoNU+z0iXaFpJaribF+036WTsO/A3VnZyyykVyymr02asx\n\
PNqk4gvEMddoO9weo6SuziGuQqrgtkKUaw/XUPE1hVgtxnCJnrTi5+UdPyiI\n\
ve4Pv8WvfvY/Shn7e7TnR/NffnkNG4tdLs1a8eqzCrl6aX4CWptOSi7LO2oU\n\
odtOhiKC3dFBErv9tXDYKnDNb34Gn70Ofi6XNdLb/OFLEnnI2PEWfvvTH2Lw\n\
9G6M1B+At/0IQrZ8uFsOoevI22jb/BfUr7wbP/nXK3DDT/4VLStvh2XnI7Dt\n\
WY7Wj26BYd2tsO55EO0r/0RC+EYYt96D3rRnMVa3lURsGnyNuzFauR1e+lK8\n\
7pc/whuP34pgRxqJ2Sw4mtPhpF8ri9kpMhlTvUcxYcsggcvt0qftJ3kliaOE\n\
QFsuQldFGyoQlmhDNSaGTkgUYt7fivlQK8N2vJPekzMTEZHLRuHMlPQa0WKu\n\
Z3gmEXB2tp9b53Lg1C7B1EFN50qFftghoQXmrF0EblJE67okneWM0btuIW8M\n\
bQW2UlnFUVWPdpkjDGNSMuBLjJagXhKRuzHSN6QFGhYntVSkVVfBPBIi1A1F\n\
mByb9bpIo3WkZQdHHmZnffHn4XgyJgIrQYZYeavWSekNnKaSdFTrraC0EES0\n\
9FRtBKOitLLJwqJumnyuFkIl6cHb+AsgOUlH8kWxIjhm+0zpiamaAUdL/hdB\n\
l/WwgvbfvwC6kfDtP4AuK18ZXjmPslKDrgrjfi0GttHigMVw1epU530xkjeg\n\
ztV9qn5VCeMIdbVry7TnKQr/07e+Rdr3dRWqmHNLrCFIWsEzM0QUHpKYg1B4\n\
sheeCRvNNok7OMYt6CHPzpr3lTeegdHVQgSuQ9NwBSoGS3G6pwD1Q8VIydoi\n\
FF6T8gF21e/Gxoot2Fi1C5lEycNtGVhPPnhfcwYeevZBvLZ9BTZWJuMQfZyv\n\
uuYqfO8/v48Np7Zg7f4P8QxRuGmwGGWkcU9b80j3HsIpQxbKzdk41Z6GUkM6\n\
Gq1M4ctJiy/H1r0fIHn/Kvz0p1di0EGal/TuCOle1rxuPdJrERLnfnpQYg0B\n\
LZbQ398qkd6Ar5dpqsCboIPXr8M4SSD8CD302acelRBDWuqOOF6M2svw9fdq\n\
oQoJXain/FFYvOI1HcCie8tLsiTyENG+rHs9DF9pFcUQbpflAI7eSgGwu68a\n\
AVcTTufvx7e+8XVseP952JtT8bv/+Q8MVqbC2XQEo81ZJHtPwEfOojd3NTqS\n\
n0Xz+vvxza9chidv+DFM2x9G177HaDyK9rW3oG3VLbDtXQ7TtrsIwDeg8+O7\n\
0L3/aXiqNhGAD9A4CC99j3qqkwnA/4XXH18GX2uKRBjWrngU+fvekcTVVH8u\n\
pvtzMNFzBBO9JH77cjA1kKdUr4NUr7NcQr1hdxXXfLtr476CaWcJQj0ZmPc1\n\
MYCV8p0wSNLrzLhJQXhCzRLrnVHwXZDSloVZKSzQyLugDV6dSjOvgJIgryKx\n\
PRLolTMn49jFOJa6AkKxYqwnKnOXSF3B3CKpG9DlroJvooiuGABH5G44pmIr\n\
/gJoXRR8iOa7khYVd80p5NKIu+gCzE2IjR1caNVVtKneFGf2vkAMJ53bLk9v\n\
BHBBASzRhksuTNbzFlMt1XdqjybBvqxTtECj6CXR2EGUojrgJmTJEkdViaG8\n\
ZcPZWMUZEyNIlMMkPQAwEaHivC9KxQgBFwIiY/VrGj3lWiI/hD6wEUSG5ojb\n\
NEJhVXflJ7E6FgnLTg0QFvsxOtFDw0YitVfwWDtQTfj7Bl4lRJpICDYO16HB\n\
UYWawTKUESLrSKymHt0i4vHD3e8htSkVa09vx87GVBw35WB7dQq21BxAdmcu\n\
7vrr3Xj645fxfsFW/Prm30gI9t2UD7G/4SA2p67Bcy8/irq+QhSZcpFvOIqT\n\
hMfarlwUk6jNqt2P8o5MtHXn4YpvXI7nXlmOzbvfx679q3HVT/8L9pFGhUgS\n\
qKNutfDJzXWqmlBloUmsozdwxevP02fi2aceE9GphGuv8vnebl2jeiMFVppO\n\
zUmThw30t+GP9LTK8jzGZKBfsfI6rYZA1QxwuPZH//EDUqnPSHDg1j9fL3D0\n\
0r/LS/hmOHKBgJcByXDk4gFHKxzdVfg9wdFhq0RFwUHi8Xdw/+03wFZ1GG4C\n\
4bW//imG6tIxVJsOF8ExaDtBCjUXdnq/jfteRtuW5fjmV7+Ep276MQzb7kfb\n\
OgJiyiPo3EpA/OB6WHY9COveR9Cy+s/o3HwXeg8/B2fpWnL8hxAyEhwbd8FD\n\
JoPhyFGBNwiQbz59F35NX0HHd7wCb/MuAiLBcCiP5gwB5FQfAzOH4FjAijSe\n\
4668Ra67CuGxWhmzbhKoxNQZd3U8h19Zl0rwlXA4KYEBur2cUKjVBMxoQdjZ\n\
Hk2b9ogoXZBOKEMaGul8NtJGakghUdJijiU6FQWIpEVnXZG8F+tRT+KFzX+C\n\
mP+LtNOgCCJFv0BEhcbpdawxMVgVl03SyKfRUilWLUBwDh3DoaUaSDkswGBk\n\
TF7K5Ls0NoCqdRb9wvz/xapUlSB3yeIc1hfm/8/LYv39jBh6lcW6TG9vLL79\n\
qxcA3alzPHos6AI6m+iY4BYgzLGKC8ky+CDLRt1i+7G4sikWgmPa6yRGeaaU\n\
nlwQzAXOEYQxD1VjiYDvZvzxj9fikeUPki5kbehR+pD+FBh8Xo6Lkj4U6I2T\n\
Mx/vIX3YA+e4DYN+E8zuVvzuml/jr08/jLqhKtQOcoa+FKcs+ajoK4LBUYGn\n\
XnwEV7BrPr0LO+v3YkfNfqSRFswyHMP22jTsb8zAia5i3E0O/bVtb+Gv7zyN\n\
r3/9a3hj17vYUbUfuaQhdx3ZJK9TTqDLbc9CVmMaigzZAr6TLRnIaz6CJusJ\n\
tNoKBHwMvXpjHoy9JTiY/gnspA1HRtrgHJX8E2lChp5NVntywDNXgU8LeirQ\n\
bVdZfYFdgjjtJA1eCoYa8ejtJcLR23soNRk/uvKHdNaL8UA/Xfb3cz/6QD8f\n\
0ejR46TMvuuuuVoFSL0qJbX1449UpakWHOV0lLBPiqTa4Oeggr0B11z9c1ia\n\
T+IXxPPb/nQtPP1V6K3LhstUiOuu/hmGmrLRV5ECex25adNxjPfkkkhMQVfm\n\
W2jf/QSuvvI7uPPqH6Bz+z1o3fRnWPY9BPO++9Gy7kYYPrmdWLicXPmddJ2E\n\
496/YOjEW8S9FIxb0hBkcVi/A9de9UO88ddlGK3dTtdSUXtiE6qOrUGIXPrU\n\
UD6maUz1HyXuZQj7pgePY3r4JKZdZfGYIfZ9iXhXKcyb9Sj+zbiKMd6fJZHQ\n\
+fH2KPzYnE9axJbzklDbuRBk+HFRFM0LMgaj3UlEGw5q7aEcmmZ0REAYHxGI\n\
s3qAVNUEKKWYEDHoekjUo7SiloeaHTtXKwocRSuKVNSDnsqVX6TRLhxe5Mov\n\
Ok8whjQvHlkFpYQhAyQiJieX6ppQL+qXvsFT8VEcRmCoUkp6V3h9yA4X0VYk\n\
+jYX0lhUqcEli5NNF2qKnBCb4FeLoJTZvmRxxumreorpfFKeKwndQseIp1XG\n\
OiCSkDVbPzFpaIr3fYhJrV9G1tajATOSFfIgapmVbZ7QLbEvUaPlefY5SbB4\n\
ky4e0zNT8b1/+y4cnn5McAGV4JF1oVN0Yc6pdMLjAEaC3XAGCY1BG4ZDVgwH\n\
rDJv2LYSV175A7SQJmx31KPVXoV8cy5yOnLI6pbhf676L/z86p8KErdW7MGu\n\
mhSkNmci05CLPXVZ2NPAxzm44/G7cf3dNxEaL8dDbzyOA3WHsL8mDfkdudjL\n\
eHzhYRR2HEd24yEcqU1FGeGxvOMYTjVlopKut9mK0GRRunDr3pUwWItg6ytD\n\
71AtaupyMOJSeIxqwigeueCJccfYC/q4FEHljdrbynUBGIjwzau8MPOOUagC\n\
mIcUA4mF+bnpcm08SL/CwIBcG1ezQmaiTmDB5B+ujucEUtw1Uq/f111Po07q\n\
9kUhupWFZlpynyfuq8cVVNf+9pf42X/TO0uU7OcV9cO1sBsLMGTIE0oOk3Lu\n\
Kd9LSjENbnp3Qt0n4TNnoffEGlgOv4pNT/wB//ubX0H1xtvRuftumPfeD9uB\n\
h2Dcvgwt629G6hukOFPIUm+6BdYDj2Io9w3423cT7ciOG/bDdfoTXPvLK/Hm\n\
M3fIeagrQxSghRT6tP0kp4iIiqQSCXlT/XwfUZLs84yzgEYhQZIstLuM8FiF\n\
2bFqxs9YHReTe8swTjSdGMrm6CXJwmAn/cmSOGRCCikXaF6YEVrOdPNNDyOu\n\
h4OaIggjIlDLFkmjeLLNSYLFs9oQHs4qM62S9no0M6zljASMLg2QXCfK+SR3\n\
/D/KGiXowpGBKAIp/rxYpVjspEUicjxGRC7OLkVr9RdZa+W4l5xzmUFKCmrC\n\
Eynlj21PTPPFWtWpWiIVE9aUFfwq3PnFfe0jgNV3GIrX+5okLhagEdl5NibL\n\
9I8XTEUaOH12ZvGG1OduuPiFPfUSz+upp224eJlezb/ji3qcfOcfOPdoAxJN\n\
0AqmmaJ1/k5U0ydzLOyK8DVOFaomxfI2NpQ5v8i0S6PtSdm1Nxr+HFP3zcWY\n\
/IVghPGcyZoPxt1GnA9i+fKHRNYK8+nv00/f8iJl6atj2a03k5ztEV6PBGw0\n\
rBgMmNEvwwQbefo7712GJ19/EvX9lSi2cBr+JE5bC/DiW0/iX/7ln7HzxHZs\n\
r9iLPbUHcaAhA6mN2TjSnodjnSdxtCMfR1pycMM9N+NrJGVvuvdPWHUqGZtK\n\
diOjMRM1PWXYvGc1Hnz0DuQQ69OrUpBFJKroPI68pnR82piOevMJtPUUopLY\n\
/w16jS17V8HaXwHbQBUMxmLc8qfriNdGOMXHK0nr05bgs1/PjTBbxSUlRsn+\n\
notcg5GiVroW1Nel9rCS7Y1bKk/Lzz0kWGZM376MXMK1v0MoOKRjm2a29gPS\n\
jq9XkL3itec1XHttvPifs/6vPIOco/u1CCjbWO9oZ9xPCNudKuNPorbfWoVv\n\
X/ENfPc7/wvlJ1PgHqhDcKQF7r4K9DRkk9C9Etb6LPTRG91XnQJXayaC3WTq\n\
+05gpHYPjIdeQeuOh3DXb/+dhO3/g85dd8NCht526EF0bruFRO0tuPkX34fl\n\
wHKY99wHW9qj6D78FLxNW8nUp4mAHWvejWt/cSVef/xPcuxtSibzno3rf/dT\n\
zJBwnRnmUv48TA1m0/9hqv8IfflNDSpDL8gm9arj2lOtYbuORpXcP+suJyXb\n\
SXzujLJ62oQFOpa6qhmb4Jp5y6KWA5+zUlYV7uddfcLK2avAJonZuUhplSNK\n\
bb4256QRqXA9R+BKqb+8pCZwkzR2u2LSTh6V+2cxuRjgonHDszHzrGw0r3E8\n\
sEjWcpl+hNYx17XE1MXnJKaCsUTXE1UxklhV/S9eN8ArqiKSOBbnkZVZhPNL\n\
9OUBoo0XVWEtmrV+VHrd7IK2Dja2bjayTit2t8pL9KqsBD1aOh8TUdB20T1n\n\
8YC2yPVCG4kIw5cuFs6X6935vqQL5xP/v0IMvPbYSb9t14yTxPOYTu5Fa/+V\n\
WI4RyoLfoE7nOb4YjJwtBC8T5P4Jybu3EXIfQPKuj5FXkI3UI7sEsw8+dBdh\n\
NiKNewW3jNh+v5GQa0KPj3A72orHn1+Oex+9CxtT12HDzo8Iv3/Gb373cxzM\n\
24nCzhPYVZ2GtcW7kVKXieN0nlyTgUNNx3GwJA3LHrwVlxMif3Pz7wXFawt2\n\
YmPhbpLH6XjsuUfw7//+ffzLd/4Ztz3wZxyqOYijtWmoIWucUXUAha3ZaLEV\n\
YNeBtbjmj7/GFSSvb7vjBjz3/CN4/oVHcc3vfoUn//oQYdaEUaKY26NCpYJa\n\
wuq2LWvwy5/9jzCTAbji9edl/tGV/47tW9foEQPCrJYyWoo8YiszVdJKD96D\n\
N994QfjK1zo7qoWxxNpEPuBWe6yOST2/SS/N2Sd6aY7QvvYcveCzTz5C1/4F\n\
rc1FkuM3xf1SUk1eyfEryG7b9CF+edVP5HEFx/egt6NQcvy+4QbkZm7HPcuu\n\
w7fIFbAuTt/+DnoJssONaRjrykGQIGuv2QHTkddgyX4Z7XuW46NHf407fv09\n\
/G35r3BwxU3Y+tzvceNV/4q7f/sD9B59BiaCrHHPvej99CWCaTKmeo7AXJ6M\n\
5x+7Bf/0ja/hul/9J954ahlWPHUrlt99HX70w+8pzesgTTzMa1GzMcGaePAI\n\
HR8luJ4gPVxMEJW+ep4K7s4bAe1YNcK+OgHs1PAxnAm1E1Q7Ba4khjmdb+P9\n\
NUQTd0fHrBY9CPPojwJWQqiDSh0TUBfmBKzcAtoh/UkVX2WOlFTNOSXlr1YT\n\
JOj6OBI0UJyVdVR6ap9XrarVUwnaYoKAHjvQ2qnIJzscYWy8MDAWpsG4pbrQ\n\
XZzTD5+b00+QJahsq/VklBBTTzPpaw60ctXzJLC6L14vdo3pSX1ONdbC9KKQ\n\
wzmd/hP1PP+FyrDiL7DONbpgayk+i9l9XHYgl75+ailW3OJ2/Rd/UfAhytD8\n\
xQyd8uiLsiYWgsLQoDA0SAwNEj2DwlAOb/O5Hl+dD0hHKXn8EmGhFnyNQnI+\n\
KKSMl3svirk3MkIyB2WNHZ3FfQkTc8zggCSijF1NyDmVRSMTVgcJvnGmqBKv\n\
zvF+Ou7GgJ/9HslX0lackDI5WlBgLiahWYG1e9cKVfNrsmF01qOOdFVW8zEc\n\
IsG6pTKVKJlFRCUC0v0ZLXko7ypDfmch0huPIaUmEweJuCk1R3CMBG0GXavt\n\
LUenvRZlxhM42pCFvOZsFLRl4VRzBtJO70GNMReG3mK0WItQ0XES9Z1FMPWV\n\
i3DtG6qDw9WKEY8JTq+ZVwHosVivlxPuUpXq18qabNoa/h618pQZerEKQkhA\n\
VYIRgsdQYFCoOT5OqnRifCjuMj7kI4TGhyJAVeJVxoCKOWgvE9Dy9mqZwK/U\n\
MgHutMKylTsDuLUlArJcwAC/Jl9H7Y0Y5FWq3RUYG67HOH2RObqK0EtvyVh/\n\
KYZJu9vII9ibjiDYfwLjA4Vwd6Sj59RKdKS/hKbtD8Gc/iQ6996P4o234eA7\n\
N2HfK39A1bqbYTn4MPrznyeS3g3bkcfQf/Q5jJz+ECHLAYmnhixpIlNHG7dg\n\
rH03jV1KktqJlk6SrC4maj5JV85FZQpRp+3ZdL0gXlB6qUBzxlsmQYVZTyXC\n\
DFN/JWYJqFP0ElMjx7DA+flJs8ReLYy3KauKv87YJCfPEYbZHhGqHEeQzcXD\n\
g1q+KQJSXaWK/OSe+zpOJRY7N6IwGmkbLbuQxyannJEwg4RhJQI7FktTRVGV\n\
wY9LWBRrEGWqwq56nEAvlUqMMFQdRVb36whVOfpz0vlLNLYyVScm3DFJK73r\n\
n96fJSJJVVNqja1zixYLyNXzM/taeFcVW8VWV0XCDok6Y6Pt/0m1Co7PLbHS\n\
5gR9e6gLVcDGY/EexZG9o+biEmKFrewQKputn1v3evFi+XpOuOErOoTjtBUF\n\
qst03FKdyXn/INKguXzmsWKypmk53qAYPalxe3FEV2O5qFjRsoq2EyJk5VjC\n\
DCF5UihCZPXIuOsiHEdozgf/rEt/Ps8cZpjgc34tjkaTjQpOuzE25YBnckhI\n\
7SRSjwZ6afQItQf93JbFjH6fGT2eTnSNtqDGVo7m/kqcJnTkGvJRYS2BydWI\n\
xqEqpDUcxbayNOyvzaJj0qzNeUitz0F2y0mUWBSpU2qOIbkyHTsrD2FrWSqy\n\
m3OR134CzUTqVnrdKksRcpqOIbM2HeWGTHxam0ra9yAaLLwJVBmqiNJlRPcG\n\
cyGsA7XoJ2FodzQRqQ1EajNGvRbubGWlv0WWvV7u6ucjCaxFFjRk27T8WFCC\n\
Cr2RsEBcJKobkbEaqxOYyPQpCgXtwmZhNc/M6nG7aN94ecwSeYoEHfwql6bF\n\
l9U6g6tV+wGPVcO11tRFyggY2SaFbE0MczptpL8e/V2lcPVXITjahrHBavTQ\n\
++yyFcFtO4Eh3k6v4xjGbCfht+XB15VNyP4bOg6/BHPGC+g9+Qa6P30WvXnP\n\
ov/Tp2A+eB86d98By6EH0Z31GGyHl8N66GFY0pbDUfwmxrsPSI2Up2ULXHUb\n\
4TcfwLg1HcHuNBG8Mw5Ctuukhm0lgqcI1VP9h2jOZGRjxl1CvC5mMectpU/a\n\
7Fi58HrepzF7rFh4zfVUC9MmjiNYmcUidnukPuDsbLeWIrOx8BXEDspWJpEU\n\
GQteTewmSBN/JW6dcuZUla6aCFbXXNFwQoJo3QQtljCmxxLIW87Njkkzqmib\n\
gGjCLKghOhCvp8wCkbTZeTEEFsGX6KUEwXNhHadXVGnxglgxLLgOhZx6uUGU\n\
1jxf9kULbGO7Wkfk7dJoZ6xzO6iqy/GRPv8Li3boi8Fsoo5ZbSRdgLRLFlde\n\
XaptUfX3sxd/UZw3aXENlsQN4iPdsGK6+keZm6Mxd6nWqCaWuSEtuhqS44mz\n\
IWYtYzckpVkhRcxItYIK2C6EEiM41cWtOgvJJblXaeGlGkXViByH5hRtddLy\n\
N/QE/Ur/TQPtmA5aL4HWNzkIz8SgBBecgX6MBlkS92LYbyPQWtA3xqA1oodg\n\
YHO1oHOoFs0kRSus5agiedxJGq6R5GxWywnsqshEat1xpDfnI6MpH4fq87C3\n\
+igy6b4CYzGONObSfzG19mjcFVh9cj+2Fh1ELknm9r5K1FuLUdJxArkkrY/W\n\
ZaCwJQO5dekobDqKFgJ7a1cJHeeihEBrsJbC2l+LweFWDBOURlwk66XFqsfL\n\
PVcisVxux+Llgn6frHD1eyPNrKzCPEmxKTWsVSEsEVkbUcM6ToND8ayD6St4\n\
gsjKpNVpGzMvUslM24AmstUcF+n6ouNWFLJF9ctym+OZtXE/U7Fd6fLSLum4\n\
0cF69BoLMUC+gvdc8Y80YsCQC4fpBEaJsE4THbdnwtWRjWBvHvw9xzBQthG9\n\
JasxWLqSxrsYLH6bqPsiBk6+hIG8p0gQPwzr4Qdgy7wPPZ8+AvOh+2DLehjO\n\
8vcw3ptKtE0jQbwNActeoulxFbsdzsW0gytUSRQ78zFLpJ0lskrIwc5puINE\n\
2wy6L48YW8i0JeoWxgtwv02imIDrq8S8vw5naPDxlDMX8xPtRFkD8xZnZdhU\n\
gwImbpgbFfSoSqy5QQk1nI0JN+iVWXMO0cQCXfotcWxBw6xSznI8EjNHNzdV\n\
MQia5yQnp2IOiYLfREnKnVe+laDHcTkLt5i7QT3QcOHYbdK55QsSioiWfEUb\n\
vVx8TmaOn0f41RN2QmY9XhuvhXejejkyxlXw9uJFGFaFDZdeOMqQ8A+lbnQp\n\
gb4htL5JtKZt4/VOhHEX2AlVFtnqpa969+u42LVdKgIRs8zgnMqH4/9A6Eao\n\
GoxAN04Rd4kmdBUpo6sDgpcKYX8ikjZEv8Ug/XYDNPzTY/BPeTE2SaQkn+IJ\n\
ueEOuuAKOomQI3D4HRj22THsHcKQh4Z7EIOjAxgY6Ue/oxe9wz3oHuom426l\n\
YSJidaKz24B2axNazPVosdSRua9GXVsF6torUd1ajoqWUpxuKkJxfSEKa0/Q\n\
yMep6hwcO52FnNOZyK8+RsdH5Xz504/gbzvWYmfuAfovrsvYFfd9rM/YhY2Z\n\
u7Hq8A6sO5KM/4+y9wBvszrfuHV5ZFA2BMoobYHSUlYpbRllBQptoZRVRkop\n\
GxIgJJABCSMkIZAQCCRkkL3jDK944xlbdrziFW9LtoYl2dbwlJ0BX+/vOc85\n\
76tXtsL/+7iuo3dKdmzzO/d7P+N8c2A91iSsxwcrP8Zjzz2Bj7csx3vrlmD5\n\
zq+xJ20LdhzciK93rcAXO1dg/b6V+Gb3l1i2/hO89ubzeOChv+C+B+7Fc689\n\
i9XbvkBC+lakZO1ERvZefJcXj607VmPJpx/ik88+xJLPPsJntF0qxtIPsWvX\n\
OvqF0lEUli39kH72y5Z+jGV0U3pqHNLT99LxQixbtjAany9bRHd+sWwR1q9f\n\
icOl2fT3UVqaYzodmRnxmDnjdTz5xKPYt28Lnc0W13H4cDZefOFZ7Nuzifaz\n\
aLtRfJT4Sh8T5Zct/Yi+kvxWUlN2o/BQCtat/hxLP32ffkyfLZkfhaVL5pvu\n\
oNf3UFhwAIV5+/Dx+zPw0XtvYOniOVi+5F0sWTADiz94HauWzkFO/NfI2vMZ\n\
8uK/RMHC15H10GTkXP0rfPebK5D1618i8bZrkDztr0j9egrSvnkaGaun4OCX\n\
D+Pg5//AweUP0vgHkufdh8TJ1yLlnzej4LNXUJr2KUozl6E0ewXKsleiLOcb\n\
GqtQ8vXbKHj1CVTkr0LloTWoLFiNiryVKM+me7OW0Hs+waE5z6DgkXtx6NmH\n\
UbZrCY4UbkJl4UYcKdpMYyuOFO9E1eFdKF02B6XJy1FK76+pTKKRTD+AmspU\n\
4kRNZTpKF8zB4ZlTUVOdiZojmeJaVbbpInrNopGJuupslL/zJg4//QQqF72P\n\
hqJkNDUUoYVGa5MZbS0lsLSWor21HG05Caif8QaOvvhftH65BA5bNTrt1XA5\n\
auHurKNJrR4et54Rw3Nhs+kMmhdVBovPwnNrn9+O/l4H+un/OeEpDg24ibae\n\
sRliDFIjZzXNG7F4SzkVuuwNS3YwafEyY4mtfm6ImEHfkG5caGW3cuEAnbKn\n\
GyFrzB7TU2tHRqXWssmrL1gd3mAmtNpgCLyhIoOx4JVJECPK/A3Lf4jW5e+o\n\
nlumUxXTmoxtYVUPQ913MGjg0NoEp6vUB9HmUPZF+J9pg66LQ4huCkf0iEEX\n\
i0XFBKWFZRwIk72+Cbw7waiHScX6dLtBGr3d4/i28UoD+9Ql4VSI2/ktQl/T\n\
7/s2Ptc77JODUO+jb6+rn9DeK5wHO5wk5+xCEPvaWBTbaXSQlLPQw3MzqUgW\n\
xZ3VaCCNVm8vYxFcbjXTKMSlP7sE/5zyCJKqc/FtQTIJ4TR8/d1e7C5OQRL9\n\
rxVfkUaD9ivT8NBTD+OSSy8m0ZuELSSe9xftxSESukVH03HwcDzi6XhP1jY8\n\
/MQ/OLLGUbhH/4b/vPQ07rznNlxGX+v1N55Hi6UYrSSG221l2LVnLaY8/agI\n\
dUWJgi36OxNRrylPP4ID+zbgtZefwbW/vYp+tKJSYRwXGoiA2xGahcSY9upz\n\
8q3i8kR+q4ixrfzqUyl+WezS1m9DQW4KXf85f9QF9Dp31nQWwtNee94k3x9D\n\
H38H5rzzBv7z9OOhjx3HHytib+WlGZzo8NXnH+PfTz0SLdp60e9QhNtmz3hZ\n\
LvPqrsLMN57DHbfeJPIcxCfT62RM/vNNWL5oOmzVe2HZsQQ1116NmjPPR/1P\n\
L0Hdfx9AzeJncfTTZ1H38n0ouewilP76MtR9/gga4/6LxvgXUB9HGnjXFNS+\n\
fQ/yf3IGSk4/C6VnnI2aM86F9dYb0b1lLvqtcVL/kqYdILFqu/92NJ11PqxX\n\
Xone9K9I4wrHgXSxfSd6LZvQ/ugdaKbvofXMSWg9axLazroAjttvwUDZLgS7\n\
NAF8CCP+InS/8m+65wK43nwKx1kE1ykRLMWv++670XH2T+H49W8xeHCnLFPQ\n\
Ra8Fzpv+SD/zjrMvop+y7ZJfwjdnBo7To8QJKYbtAl5F6XTpcr4pil+j+Tjw\n\
yYccc4tSFsQwO8VCAA8rp1isiSUkcLQx7sbk9ejOcFd4zG1IK2mQaljF3GJ1\n\
OMshBfKZEQSvlLATwzyHcA9CkNhpEMfa0i5sQJgi5fRGWlIrWl0JQbrfWGlr\n\
LIGYaGiAoGE41EomLKym+m+zzI2N4O2ecgmtibrjECnKdhpTNJbJGgj40dzc\n\
xFtB2PU/0szAL03ZKN6NFXil4efRK9HLN4TyEgxeg27nDuvBNek/yFQGPuen\n\
0TUkoOnQ7/cLqNIvo5fXO+/jV3EcoF9eL/+Cac90O31uQEE5oIZfau8h0tuD\n\
wv51oIsQ4yCUOHytcPSI0aYg3ApLdzMaSE+00DN0HT35N9EffXV7GXKO5iKn\n\
Ph9LVi7C+eefh59f/guszU3Eahq7SVevyo7H7pJ0pBzJoZFFAM5AYnkGLr/y\n\
cpx/3nmYs3guNmVtQWppPArrMnCoWgbg9n23A9dcdzXfc90Nv0VC5jaY6WH8\n\
u/I0FJB2+vzrRVy99offX48j1TkE4XLYHWJprHps3PCVBmHaVStkiZWy6tDS\n\
XKQoGc2FsSpMp5yIc0kStWHrpm84y0GMrZtXszMh6Os3ULi3tx3X/fZqwWBB\n\
Y6z6+lMkJuzEJwvn497Jd0YxnGO5tELkDotkCeFObNm0Sn358diy8SvVh7ae\n\
vzVuOOuuxWsvPUP3CCTfS6ovDz1iwW4xCMsuWwkaq9Pxh99dw+lnN990PTqO\n\
psLZkILOhkTUvfgYSs48D0evuwb+qj2wl3yFyt2voXb/W2jNmksYnsZILpp0\n\
Huq/eByWtNcJy/9FA2G5+GcXIpeQnHf6Gah5/s9wrJkGx+ynUP/Ly2CZci8G\n\
2uOUFRFP+HxaIvfiSxnL3mVvEZLpmn0Xula9iYazzpPI/t218G/4EIH9n8Pz\n\
0hNo/9Wv0DXjOQR78jDiFf0TixBYMZ+QfSHaaWo51lfOSD4h3N4h6Tt4p76o\n\
WOq46hoRYZ36ko7k3m8+k4gdJ8hMxN6FgR1r0T3lKbr5WgTNaTJsdxpd/pO4\n\
kYdvztsYpIeU3lXL4HnoIbp2M1E7TeeyeOG1tlSm2XHlCrtlT1kjirsUiser\n\
Y18oDYLEszAnZSNEwd8YZQfrtvBEDci6kpYxuIitDrQaXZU/Br3kQtPGxhbf\n\
hOcYPfEhTDJHRwB2pApdvmOcnkU2On84lBkR1pYx1LLmdN01HhdWuXZiVD8a\n\
VsrjfjS37CcRiP2TcGtioiL2Dz/8QLRuRl5eLm/pWCf2+Mi2hQqdMbSjBbNF\n\
soQgt8huELatxutx4VqYBa9fc4gDwhfmQ01Hy61PROBoIu9jRPP56BCr5Sfw\n\
LzfAv9zeoJ8pHdDPTRhLa5LMXb12ojSR2muhv/+etmjBaNO1aCW130JPfPX2\n\
WuQ2kDy2lCOz7hARNxuHGgvxyOMPYhJR+lyStS8unIdNhenYfTgTWwvTkFKV\n\
i/SqfCSWZSCexpwl85m+59G4/a+T8emBDUg7nEwyOYtonYRdeXtw65230j3n\n\
cn3Hp99+iqLqDOSSxE4rSUFpXQ6OthbhcfqagtQvvjAFNnsVHDRzdBLv9u3b\n\
JCl9Jvbv2ww3l25IFIolE0Sr2YsmTeJ6Cg6dcfisVY/IJcRv00CemLBd2cai\n\
sQkhmv4SkhJ2MZzFWPX1Z3w2SqCbfqId1hr92pxZb8rMCl8bf3RC/FYN0CLx\n\
WFvdRha88YqxIj9YAfo0Q06w0Mxy9S9LQw7ulLoZ9955MzpbMqLgrE803UF8\n\
fhzlxM2upK8RaE+Gs3IdGlLnoXLnC2hIfAM1e55F7ZqnYBay+ILz0Z78JjF6\n\
GknoB+ncmcglNhfffzUsGa/De3QF+i2b0VW1HK1vPIjmm6+Dv2kzfPXr4dv1\n\
EfO5jfg82LAHzn/dD/f0pzFo3wPbY3eh8axzmc+9RWvYNg56MjHcnYmhlgR4\n\
XnwCricfRLA1lfhciOCRBFiJz80krQec+6VkJj6fGJKyeWD7aqYq0Zm5HPhk\n\
Po33ed/zjweVBp6gZHK77h+P1BcylQcP7qH9Ik0qd095Wo/WRamY3WBKHEN6\n\
MEVkMocrZ5W2Fh3is1jTSzjIWmsEryabo/QKDs019uniOEqYDgZXQ50b4yhz\n\
+4Rxp+RzrJayphQ0N240naqyQx1HhRLbYkfxmpMtFKDHtq0JJVyEWinIzGGt\n\
l+7AKDir9Wm5o8IEfUnaUxYXh1qGnRLRkfqGTQhLpxCWhuzbaAp1rwmp7Qlh\n\
ajvA3Bbb/0ttB5QGnsi47mWh3cei26e2MgWii1DuDQlvv0KvojTntgUY7hq1\n\
A4rWgRCtJyJAP/rAcB/rarHt4xEwnlPEvkm/xlpeeNr0J9HV54A7YKdhg9Nr\n\
hb3HKsANGzHH4mlFQyfpaqJ2va2GNHUJiprLkFVziKhdhEprKS772aWsry++\n\
5GLc/cD92Hgojaidic1E7oPV+Ugqz8Uu2t9WkIy7/vYXJrKg/KSfXogvErci\n\
+0gmShtzkVmZjo++WcLXBbkn/20yUT0Jh2syUViVgZSiRNpmobalCJu2r6R/\n\
E7Gb/ncrNKcQuWtZX+/bt1nT1wRxuDmLoV7S212n2DieO8loZRY6uWUxnS6C\n\
E+O3y9Cepq3FPulrwrcpSjkcSYm7+Fyf36YQPl7pc4nvgEqOU/jW9b3kdyOn\n\
x0VxR93fSH7PfI1nFzFEkpwoUu5xE789Mv7nthVzKZ5oHXbPHX+EqyUTjvok\n\
2Or2o+nVp9B2353otWUQwFPhOroF7eblaEqfi6a0GWhImobW9DdR/pvLUHLG\n\
2ah/bTIsmdNQ89FfUEgAF+K68f2/w5E/G901y9DfvhW9bRvhO7oK7rQP6THk\n\
6GrTRcxpaWmcj/7DGzHUlUwcF0kVcbDedgPz23LD1XS8n/idxNeHutNpZCDY\n\
nY3Axo9lzM9PI2CG7ZKfk8aeBH/a5zjeXyv0tYBrsEFkBbgqmN82Gsc7qwm5\n\
WmaFBe677uZrrpv+FCPgzYkXVnpLDY06ge4oZYYM7FinR/9OBG2S3KQcXQ1M\n\
bxns04J+Dj35wq0t0yAR7dHalIeX3nGuRSjoN+Qdi+ghI7a1BIzRdcwR+jtE\n\
an1jLOWQ5ofWYNfwoRryYwxJc4rdMv3NFN4L5zSDTa31POfC59P0umZZy6FJ\n\
aGMv3fGje92o/AtZhic851A4UOyPD+d2pJS3KGVH/z/fj8pAnhBBaY+mteY6\n\
/xDmOkdS2Aq0TGs6Egq7TynsEIX94Y4IX2JiB/TkN+32Pv2a+BimLJ/jESMw\n\
Hc0sptegdEH6+Ei8XqHTOzSktvYHha4WlHZy5NHdKyKONtLXROluCw0rml3N\n\
qLLVob6zgWmdU1+KQhqZpJkP1Rdj2apPcQFJPqGvn3rxP7jokkvwbV46NuWm\n\
YVNBOpIqD+FgZT7iD2dhbYro/kd8Nl2IP99/Dy775S/w7hcLkVOdhcMN+Sg+\n\
modHnvynpPi552Dq/OlIKIxHblka8srTcehIBsqP5qCGNH19Swnr6wsJZzPe\n\
ehUORy06XUJfb1Qojsa+uI3wSESLigtuK84IFQJb1NaFkjJUoVybQLNC6ZmE\n\
451KYVtDVoiwQWh7yx9vYhTPnf2WxDQ9m/T6xbBpNghTWtXlRaK0lxW2pHS9\n\
6WZVhfeqTmmhstkCcUuV3UPI8nSWEZ1vYUpP/vMf0FZ1AE2Ht6GpZBNqXnwU\n\
7QunI+DIhL89Bc6qzbCal6LmwOtoTJuJGuFGJ7+M8t9fjmKictXtv4b1uzdQ\n\
u+AvKKJj4Uw3LX0EzkNz4a1bjoGObURqktYNXxO1l8Nfvxq+xo0YdCXAfvsf\n\
0UpS2rv0TQx1JmLIRaPzAGy33UiYPo+3Q52E6c4EDHtEMHC4K9V0DsntdM6B\n\
EzbIsUAJjveWw/Pg/bCcdQE8H7yE4wNVnJbBzrRIyQi2EYb/yDge3LlGYFog\n\
/JiVfr4apj20PXnMLtIsGO+S13aZfhG0Cf2syWwBZWNSnIMz4wSBhkVpnSoR\n\
kekZMl2OYB0qs3Nr/ocB3MaWElrycnSYAy0A4R8/JigYysmIHmNRK0ckWkFY\n\
pi6H9dwxnRLho1c503KWR9sidJ2JzU16JkawpGVm8oTRWtpA6mDEzA2tCeS4\n\
UAAxdlS53Ujo7Kig4ShNPVF3QUJL9oxyQXaOTdBwNxk4TIOUcYBGL9schOIo\n\
ZRkL8PplmRwjN6CsaC/9Rv1KM/fpyrlPHQX4iUXazX0GuErzQsyDEsJjpLNk\n\
9ESllOlLi+wPkfXR76ZBHBb89bbD1iP+yInApl+jlVRyta0BZe11qKVt2hEz\n\
cbeEmZpbU4SHH3sIk4iDQiWvSduLq675LV79cB7W52bSyMD+w3nYW5JLIxsv\n\
vjWV75MO9Af451OP4R9PPIK8mlyUNR4i/ubjllv/qPyPc/HtnrX4riwVeZVp\n\
OFSeBnNVJo7U5aOmuQgNbaWskkXg7a47biX+1sDhIpUct0HiN5bx63Zr/ga3\n\
LtMVMPsbnkYDflsVfrcZ8LtdqeP2MAe6t9eGjo4a4Tgzgqe99iKqKnJlPp2v\n\
3YhfUUFyKvyqFD2F38c5T27220aRXCOrR1yy+Jnx6yzB5DtuZpPjHto6WzLQ\n\
cTQRtqMJcDUnors1Cd6ONPjak+E4IqpJvkRj5nuw5M9Hc/p0tOW8hcKfTUL2\n\
6aej/Hc/R0fem2hMfJpxLPDb+jnht2g26eHlpIZ3sFD2NX4N79EvEWhZC3/z\n\
esat4/XHUE+YdT5+D6FXJMEl89b++GTGb9sVv0Rf2md0Ll7gVynlVIwQfkcY\n\
v3mskI/3lSKwaBY6zroQ9r/fJfEbbMD3NE6KrLhh+tVMe5FVsnCkTx5rx0mh\n\
lGn45s5g/LoZv+0CyhK7QW60Oyxa6440FBn855kkjOsFGxR3DbZzjEZc2exc\n\
g+64UdDt1jI0ZElejN7WXJobXnYtJih1rPxmHbwRV5tgf8JY1qynKBsBqwBs\n\
imRRG1I1xhmhq0EWqhtkINQuvV/3OCaMKhwx9KrQMpRHZ3mEFkvToCszN2TW\n\
RpSscWb8niJLOWQ+n6YbzWG2xZilJkKw3RExG078eARgBScZtHIrYcu9G/sM\n\
utfLhkSM8iG89DldA56QoFXiNsDTlk5c+Zk8iSmhGxK1JgnWmDChq/P2Zql3\n\
RU4jPUJ1abyl+YG1bg/xttvKWtfiaiPGNqKotZq29ciuLkVJUzmyqouQf7SY\n\
3YhJ55+P2++5C1vyMvDMtKm4629/w/aifOwozMW+wwXYdYi25jxcc/11zNFf\n\
XnE54ooysXzzao7+5dUcIq1byKy99TbJ2nPPPRf78xPYP/6uNA25NMxHslFR\n\
l4dquvdoi1nXunfdGcZakwbb/fs2KtBK4JLuDYdttwbbJmlJhME2mrWusiKU\n\
3XC2Abo2PQnjdYItJ2o8/RjbGCIMKDT1XN2SkDDXHeXrCLab9MV9teUnhbOs\n\
wVbIcV4/XZTsEWQFcL3uEGwvon+6yMBor0tCe9VetFfvheNoHDwt8fB1pBBs\n\
k0jrbmTY1qW8jda890jnvoLamfeydZxNo+r238BZPAf2whmouvoylJ9xNpqf\n\
nwxPxcfwN63CkHMPhtx7MejchQH7DlG83HlApBJ3JaFr+1zUn3keLATVYU8i\n\
KdlE1rZdn73IloSwLNzPPwjH7TfB/eLD6D+8gXRuGkZ82QTbHB22x3pLMZC4\n\
lmB4IWdjeNfPk27ERGJqK/GzDYM7VjNrhUN8clh2jzgpzu9ca9JCfifovOSw\n\
nYeUuu0yEWMCRwAllidzmM/z0IPoXb1c3aYEb4zBlnDp1oQAzZDeYsIUpcf9\n\
dASbNO4G9ZZqymMem5ksECEL9sIMBIMD4dNJyo2EdAvjR+0KVcbHlvRoFEtX\n\
IuQmh0islfQZ3QnVh80UylQOdZYYq4TVoj/GDA3VjTdWj/dNCC8CCWXBmcJr\n\
nsf//0HudoXccWN8BoXcaLEjURtrQG1A6wAhPQVNy4p8tR76zfmHNX07gfmq\n\
mBtibUjXThjlLUipK7yFW8d4CyLNzTtAHz/glRnN9OsSWcy2LhusHgsaXa04\n\
0tGIcksd6q31yDhSjIL6cqSVF+L9ZYukl0Bjxvtzsb0wC0t3bMVPL74Em/Ny\n\
ibl5iC81E2cL8fmWDaRlz+c43V8eeRjfZqVgRVI8Lr74YmzcvRFlDWYU1eTh\n\
fnq4FPecR4zdkBqH5MJk5JRnIrs0HWlFKTBXZpOmzUNqxu4wxtodtcTYOmLs\n\
JsXYM0OMVdmlHrqu+wlvKz9Btig32r5afhoH7AKa49sew5Q9Qxi8ugEsCCrS\n\
37QkCyNZZayu1aBj/62Wm2jQlpNQpXWj0MplddWsYbuVndDNNoKGVmEjxDNW\n\
26t2w1EXhx7Sr72dGQg40uGq34qOw1+Rjp2N5pzZqP3qSRRfcD5KzjgLxTSa\n\
5zwAu3k2OnJfR+PUyXy+8YGb4KlciEDzOkJlHOO1z7IBvZbNnC3Ra91BmjUR\n\
gfbNrGOF4ztweD3hNZ4QvA39VV/qaO1L/4yQmwzv52/C+qsr4Hryrxis3Ex4\n\
zWUtK93eEtKuFYxWYSWICGCwMI61rGCrYOgJ+ndrju8JdzXxtl1x1MpJbeLa\n\
CM22Usu2j2XrRJLAr0jHgbgqbIRh+iPrnjKFmHudZKyK3hmUrQ5WKWtDa/aw\n\
+avL2CEtjWJUgV237u/GSpwaOkwM60G7EDqDQX19iVCph6ETRShlOdTGp7fX\n\
ebauYbVFJIaHRzU0H2Xshtb5idTQd3zIQNAsA5mDrC8aMRha6ue4WjQtBv9f\n\
V/zVijxiwyl7ur5oxKgkt9O1sjr+j7FqSozQQ80fQu1Q+Oq/AfrHEUSjWNZG\n\
86FfjBMij4T2RCjtuObIqjJjbh6hczdk2rIpzF6DYK1/OKC0Lr1OFAwVsrWf\n\
tavwE/qJ6cP9Yk10pqsf3n4vEZaUbF8XkdXFdSFt7jY0dDaior0R9fYmNDga\n\
kVNTjuyjZThYVogHH34witA6yXQFtqccwL7ifGzOycJVv70Gr330EYP14JEy\n\
JFeU4KGnniRRKsH68bersS0vC4vj9uHWe+/FE//+F8qOmpFZmoMXZr7OJoG4\n\
b+nGb3AgJwGHCKbflaQjMT8ReQTZirp8fLFikQ7W6W+9ApsooLPXYs/u9aaQ\n\
U7AJbk7bVwI2TLxOlSv2djepmFrzKAxGsxBVZBW/joBKiJDiVYufRfHlifIk\n\
XdSS3fRgGqdYNBs+WCVDeDS+1hn5qr75G3l5CK1BGnsFYlGL9iLu/ntRKBkC\n\
jqYkOBoOoLMpHj3WZPS5MtHrSEVX4zZ0lH6JJuJr5ZRbkX/6mWzHlhJH6+66\n\
Bo6S2SRbZ6Et/XlYk19G8aRzUXHh+cTXBQi0rMRg5w5i6mZi7TfwNX4Df8tG\n\
BNrWEl+JpZ17YLvt92zV+pZPp3P7ma+Djo1wPH43c7fr/f8KueuJpxluiKSt\n\
k/gqGBr4cjaxNZ9kqxnHSboKvrrvup2zIjwznoHj11cjWBQvstWiBGDpRyuy\n\
0Wzs1K5WdoCVMeqfO5O5GfjkA+ZjO/0563jlthNyf6Re2gUCxyqkxtugWSYX\n\
i2wIEYHTU4nHq5o6zbB1hTg7pDjLJoFbLdPj0aGrtUcPBn0Iz4wIGbdM2/ER\n\
Cj8iCVXpMIxumOYfRVqXnrwWMQYX8hf6uPeEHmQTr5GIPBxOZBazhh5B4yOE\n\
33Q2h9IkZHqE7jMM6keGpdgVjk8YO2GeFq53Iy03McrAjSRwt/yIwBXU7ZPU\n\
HW+krtzSv0hRV2Y6aKnA/lBwzBSjuQZ0M4tUqXGZr+MFX6V7IPb4KCrCORFy\n\
65eK9w/ooz8CDzPYhy7aunvdsPXYicEW4m4zakndNnQ2o4E4nHu0CgVHK5jB\n\
l156qUAwfv/73yGntgy7D+VhbVYG/vroY7j7gb9jW2ERMqsrkV5ZgUsuvZTV\n\
7bXXX4/UsiKklhdhU2YGXpgzF1eSBjLXFiPtcDY2JcWx4hUQnvbOmziQl4Ki\n\
I7nIK81AyiHhJGShorYQjz76oA7hgkMpsNlqCMJ1BOENYQzW3FopcCMwWGtE\n\
2cgNg0OojMG0V5/nAJlf5jVIDE9g2opYmfAJ+hR5tSrmXmnWiq8u6jZka+HR\n\
Ine8WDk4BGEZM2P/4N9PPaIg/DDHyaS4rYBXCFxnKTpacvHbqy6XEL7rFrja\n\
MgnEyehsToCtdiecdTtI4Kag15kGd90m1C1/BnmX/RTmM85GAQHYfMaZqL3j\n\
ajiy3oSTIOwong1LzjTYC2ag6aO/o5wAbZ3/IPxNKxiqAsJ9LQLCqwjMG+DN\n\
W4L+0jUY7k5C18x/cyqC56WHGcJBN0G4k95zdCWaL74I1it/iSH3bhLA+1ns\n\
jnSnwXHj9QTbC9C7Yh5O9JVhOH8nThCEfbNeY6HrfulfGDpEgv3X1xAhE4m4\n\
zURV+vlNfYEp3D3lSeKySmsQKWjH7GwsiPtP6OaCmDFlZ2F2bAVyhVMrMCxt\n\
A5tKSBPZDuv5vMRwg8G+jdVXpjiu9xnmig7l4RqDZlpimsx2EAEzfjEyNnKO\n\
g0+dC+/LrjcmHusb+LT8Bz07jeB6hp7YMDorrU/F1Mbr3oHBP9B9hFgtlKZf\n\
Z98gpJtD2cRRisEh+iqFPBJaDiM21J/itIiRNmPETW1P06EcvsTa6Ho81c4y\n\
tDzGSKzem8IUoQtbaLEMU4S6PJX+IM+LthQaxO+JoKT59WkF9vPHgn2kXxoO\n\
IjInwMxkHyCyD+h0D+hOhpZ/HOBaEJbhyhceVm/nH3aApzrJd3lOOML0mwkE\n\
+04bRfU+jeqmS1Q4jr7oUICB3tUvwN5NkPfA6XXC1mWHxUMi22NBU2cb6uyt\n\
BPZqlLfU4r2lnzB8hS08c+7bSK0qwVep6VgQl4B5q76R6RA5uThYUY4Pli2j\n\
75KwbjoXr7w1HQdLzTh4uBCppQT35CROoVi3ayMKqwqQX56H9xa9z/bwtddd\n\
gySCeX5lDg5X5SGd9lPz0rByzXKZpxaL5557Gu0dVYrrQlxrzvCZ2B+3QXaI\n\
F/0fuHlbPS+uxm0wZ76mlrOs1zvDCw28ZdMqLQonVrFcvPBdhvbihfO482VH\n\
ezWDXEuC4FRjgrvmbuTlJGlgX/zxuwrqbfAS2MV6bJpsv+fuP6OiLJO+A23Z\n\
90fR0mjm7pdaFG7qS/9GS30euxYC7B4C+7qVH/ESdgLszzz1D3TUJ8FJ6rqz\n\
KQHt1Vthr6EJwxqP3s50tH30HLIJ5IWnn4WyM89B+YUXoOnNv8BZOhfOsnfh\n\
qpgPh3km2jKfh71oJlrTn0XNfVej8oLz4a/8jMC+FX2WlfDWfQ7nVy+jO+F9\n\
+CqWw377Tej+8EUEDixhsNtuvIZAH4+gZxe/Z9D+LQKp89FGcO96/xmC/l66\n\
nogRXwa6336OVbTtkssY7N1THoVv9msY2L6CwW6/8QYc66tAsDgBToJ14JN5\n\
7FKIiJtN5qURuK0K7jIaFyxO0UrzlMQmIIi2mJ01LLujVZ2eSDQWdoWIxHEG\n\
hJYaEVj8gZanZjqFc6GIzo0wo1X/NvGgrKWqxWjehV6Lp7F7KFSsp10bCuWu\n\
hSVBGJ3i8fprqJJaVoKEug3H6IJabwAXHCWo2diIlJ3G0NY0srGfGxfz/SRM\n\
KA/quWqyR/z48HUuJ0YC7smR2NGJDdoCl+HJwqN7r3GKw9m6Qt54yh4U0rnt\n\
V8QT5BtgQ0IUFGoSOTBiMCb0VDN+H/NyNDX5nJTGscTOfk0GqzEgsSpktrom\n\
MDqBX89gmPqHhEvhg6eP1LHfA4eCqLXLhmYXDbcVTQ4Lmh2tePTxR+kbJnya\n\
rsaBjGQkFRfiy6RUrEhOx5r0bFx+5ZWY+sFCxBWX4s5772VVLGC7NyeLAFpM\n\
9xchwVyI3Tk5uOlPf8Qbb78Jc7UZKYWZ2J6VjGmzZ2ASQfTu+/+CA9/Fo5gA\n\
mlmSiY8J3JcSnIUqfozUcVNbOVotVYQ2oqi9WnSVYLUsGLQvbj1cJInLDmfQ\n\
9zpr5lQt11esGCm0sTB/xRB2gaivk21/JeQIpcTJ36vF2mSlM1sOAQvzctpr\n\
z3NAjT0MYmz1kXxxv0kDqMhsEPCsqMjRKptNWmnzogVzcPMfbsQ//3E/f/3X\n\
XuIWw/LbuxArPv8ACz98m9due+bJfxLtX8bT/3qQF6gUCWQXEeMO7PoCztZ0\n\
dFnT4SJh7Gk5gG6LcCgOwL16NsrPPBfFJIhLzzwbtX+6GvaDs+GuFO0tHKWz\n\
6THeVT4PHQWvw5L1HBxF02HJeBZtaVPQ8OytaL3+V+grXAp/w2ewzXpE1WZc\n\
gt6S1Rhq2UVi+NEoAU/TOfR6Pp3ayfgMdm5hfA44vkVf6odo/93V8K1/m/E6\n\
4iOt/sDdrIs7Lr4MxwfKSBNXwfvasxwg+yn9VgRah3oyZP6Y6Cv30INwXvVb\n\
GtfQPQTQKJa95zFDOe+XOBk0J7M45hoOOh6pL9Cr57xTX8ZJYVUMyQ6Z3qmv\n\
sgVMDNXsCRWdo/9fPvlIYVQbwofQlrN0qxpnkqNDLi2+ZpDHpnBDuEuhtTuK\n\
+aoZwr4QRqMER0flm8UYKGtQydB6s4cTVYbfxPu1tsPsG4fKnjVEG2E6toP7\n\
hLAMM30xjlMug8mZDSErImQdR41pWBGq4oiOUCQdEsN6A0xDk6BQRG5CWANi\n\
Q/rvuMhlG9+bosINi7N0HG84tWFBU0Wf+McFWPj76ZBlrSZv6VhK335TqCpD\n\
J3hIw47WtbFKyA4PKEtYYHiCBuQx2z4e7FgMmP7M4rZPO03M7guqNItgwMDq\n\
Lrj8bl3wNrvaFafb0GRrws8v+xnz8Pc3/g7mhiokkWjdmpONHXm5+ColA397\n\
7An8/rY7sTY1gxktLOTbJ09GWlkpDhYXI9FsxrepWfgyPhnPTn0N199wPfKO\n\
mLErOx1bM1KQfCgTq7asxu133s5cvvXWP+L6669lcX3lFVfgw4/eRX0TMbqt\n\
kjhdzWq3w1aFnYrTguN7dq+jH5fbLbpfvkooFHgWSlcwXDDwnrtvi5LLXhCo\n\
6Z45b79Ocvavct2j+G2w0Gffe/ftmu8gqqBFqq/WaE30exf9KUIEPoNLnQXh\n\
fUbv4sBWbnPxT/XR8fs2cUXdQqI10VkJ8wdZ5s6aKdcYFv5F+eEUkrMP87cr\n\
5K3AtFgyc+UX89lAttUnwOvIga1uD+y12wjRCQg4EtF05eWoIkxX0Dj6j1vg\n\
OrKIZO0CGu+RxH2HpC6Nklmw5U1FR+4rcBTPhL1wKtxlc+Aunw1v7gI2g5vO\n\
Ok8imuSs5eJLMVCxCcM9aTSSEdi/CI47/ggLXRP7w5444rQwktcQq9cg6NyA\n\
YP1adE3/F5x/+zNsv7qSODyJGR1YMZfkbAlz+sRgNQaTN3CnCSF1+yu3Eaeb\n\
CcWtjN2BnWvZn9BL6wjPJznnVyA7Vse1GP2rlwl5TP+/2LjUTkTntJxfORwY\n\
PBjHETr3XZM1oeu+6x4c66xT6cLHVfqvVvPs4hQIpXmjDYQe4cQzaSeHMs+6\n\
tcyzUMgu3D8WOB7ixj4e+On/L9pnR/k0Y8BOwli3lUMS15Dma1i4WPaKnxDB\n\
wgizm0ONjUOKN0bPRmOXY4LeoMK4Kjy3ZdObxRvjelGhqo1wszjqR9sV6way\n\
oYuQRmtjFyFOCI5Rq3qqFThCS9exbxGt9RMyeMx87id63C9UbhdC9renQLYr\n\
HNkkmkcG4T2uYXuQjzW3QhXIccIEmwsC58Ny+GXIboDprdFYSmVRSx5Cr7om\n\
t9FM6GgjoU3y3JnqXB9nXTClB2j0+eHp7SZSC2vCBUePE61uG5pcVjTY27Bi\n\
9VcyzheNt+fOQnFDNTIqium3syVbNDtbk5aFD79ZT1A9H/967oUosWO6GG+8\n\
Ow+bM/OwLiMb6zNysWBXIlbEp+DT9etYa+85eAAHi/Kx6ztidVoKMopzEfdd\n\
GjYe2IOvV3+BVWu+wPpdW5BckIFS0t71LRVoIS1t7ahBh72O9HQ99uzaoJVl\n\
xMVt4EZdrk7Rq9zjqtMsaFGiJs1dafR6VfeuRvppCFfC0lpOjK7QE4ZzcxJJ\n\
HueFsiPEVhVcqG2U8CJE8y/FZjGEDaFFEuXy8Q1obSrhJmOykX0D181FifWQ\n\
TE+hpTFfVczJDkE9nmp43dVorMnGzs2fY/eW5fC6StDbVYqujly4SUr32LJI\n\
Tsej48hGdB7dBM/uj1FHGrf4zHNw5M7r4ShbTHxeCGf5+3BXzIerbB48le/B\n\
U037pbPgNL8NV8k7zGhf3RL4Gj8j1m5jDTzck4C+A4sQOPAJjvkzWBMLW2HE\n\
lyKP/WkYyPkKI90JGO6i+4XX7NjAmnqQNLU4Hu4SdsR+9H+3An3xSzBijcex\n\
3nyc6Ctmj/nEoEoEHmkgXq+nz8zj9hQi+VfYDieDrWwvBIuTZdKESgo+oSUI\n\
H5OMPsmstrDfLO4bTNvJJdAi6ndyWAD4JPeX52igWq5DyGpRqCGifhEyKsJy\n\
hZ06puVqdtGGqgy1cEeUlqDm5f/5ZSIF+vu76W+pHvX1VYQDr0nv72YoqYsJ\n\
a2Chr5c0QWlosdxxpCifuHq2jmgtBzgQti/zfwP6UvGhvdFWxMSw8gxDzE5i\n\
OMZoDOsQZhyP05to6ot0/EhLN2P5nCGaFxvWQVN10ZSaOdScIrSIfMizWKuI\n\
y6aQUSQzNxVpmbDaYNIO6E0jejlRQtyrkMrimY/UOV3witjg8AC7FQMGASwR\n\
HKWoajivn+sLjjqnaexgn+kmBIaIvAMBdBN1u/t8krw+D1xeoZPdsLgdTN9m\n\
hxWPP/E4R/cmnT8JmxISYa6vRF5lGdamZOKjnYlYHp+Kdel5+PnlVzB+zz9v\n\
Ei659GfYe6gYGzLysSolB6tTsrEmOQv78wqQcKgQV131K8ycPRPJ5kJsy8jA\n\
3uxMYm8+DuRkYnNyEnIO5+HwkUJkFmUjITcDh8oK0Ngq2FuJNmKv1V4Lm6OB\n\
dLFWExeLuN3rBXjhctQQhKtpv0pdi8E7M6eqdY4Ffxskek+X3YJ6QsuEassk\n\
BxSGfQq9qvV7lGCx6Sc6hbnFMeO3mdGrehSrpUNlDUY0L0Q33tB0opbXRdLT\n\
gjsrRQWfu8r0M3aCO9ry0VKXhk5rPgLuMvjdJbDU7kV3Rya6rCnoqNkCx9Et\n\
6G7dC8+uj9FA6C0582xUz38AloJZcFWS5C17l2TxO3CVzyL0zoUz5y1Y9/yH\n\
zr3NstheNA3O4rfga1gqlFznLtOvMWDfQviMk06uP42RK+TxcHeyxLA450+h\n\
fbouUO3ZgUHXWgw612DYJfLbBHp309hP70mge9MJ2Tk43nuI0FvCbvCJIULv\n\
UA3XYJwYqsNIgLA8VC2xS1j9gXD6wzE7flALH0nUWlTpW7RCLqOXs4Xbo3hX\n\
doQ/ybFALaQXHVoiSeOsqPcKSw12ja7MGEXbrlPRlv4EtPw10RFoSK9f9qns\n\
Ki/91bjQ1eVgD0OK5dOMMUD1Xp/uUIRA7NMgPKz0cwjGAc3wMP3oiqMRfOII\n\
vSpUDYeU0uNHBwM1jHNgMEorgh42OCA0VBBRyzUe3fRttMPM7YWiw8N8pggr\n\
fUzQtfL4H+0jFDVaMBO+Y8PXXDonguW8ZlQPipDH4RvWGHy6YvjAKIZLtawn\n\
EUtbWpxnnLPSPl1y9tRk9hvILAJ1A9EamfkdQ30cruvuF09Inj6v6Vyms5Po\n\
7Oxx82gnOjc62pFd14ifX3YZk/m3112P9PIKEsY1yCY6f5WUiYW7k7BsbxpW\n\
Enn/+ugTUhRfgnse+Af2FpRgS1Yh1qbmYn26gHQ2ducUYAuJ5Ace+gduuOEG\n\
ZJUVY19eLralZ2B/bhbSi3KxMTGJxHAWiqsKUVheiPTCHOQeLkBtYzkLY0tH\n\
LdpsAs512L1bSzA+j0Tyejic1egkOLsIf25XjTQxaGKZRXDW2rgLTHoJk1pV\n\
hVy5rkEP34m1QWMMXebFORbEOo5bo8SB6Ukphr2KxjwaVfuIhlAbIFcdU1nr\n\
1SbXWRJkFvtV3EKC2wB1lqK9OQdt9ZnodpYg0FWGrvYcWKr30DYD3bY0OOp3\n\
wlG3CT4ric+mA6gnMou4XNOKZ9GQ9iI6CmfCmvcq2rJfgq2ACFwyA5b3HkDT\n\
838mKs+lQfQufQsO8+vw1i3EkHM3Z7kFmr9AQCRidAq6ioq4PRjpSWIqH2Mq\n\
p9KWBDIRe6RbFHHsQtC9BUGi87B7Mx3v4HPDnl0Y6TrA7zkWyMXxASWIByqJ\n\
wpX4noj8A1fINeKYEMuD1URkovIxKXa5KiMomMsLLHF2m55Q3C7OSkAHLTJM\n\
p8NZf68mihWc5apMWqzOmPnGeNa6yTvDSjei9WidXjnHwBuVcyHrlf0qHseM\n\
/tFUjGCkdhOhnItx6pxBGMv7xmuM1YgrWT4xQgacRtFQ/nEYZTn7Ql/7w5Br\n\
8X9nug2Krcp0C+/ephS0KTpcP8fqSclRYV4FLwdtCnXj1LIrVD7yKVd8Pi1c\n\
NJ8TwVlebRDNBur2umKU6DWIZo7ziX+KFvvzC+AGZTaxBPR4lfXWP8ohHtQw\n\
OjyoC+lBPopSQtoflOf65HmxDYlmPh7Qzw3yB0VJP0N88E3E5j50s3IWqtkL\n\
l78LdlLMNo8bdo8LFpeLVLMNi1es1FXzU8/+F9VtTahsbcB31RWklnOJzxn4\n\
cGsylh/IwCdrN+Gcc8/DOeech4+/2Yj9heXYmGXG14k5+Da9AEviMrB8byY2\n\
kMp+bfpb/Lmbdm0jOOdjQ0oGdmSQejbnYUdqGvZmpDGYi6vMyCFFnWXOR1l1\n\
KannKrRZa2G11cFGY5cO52hWzp0OVs50TpgX5+Ljj2YxnKc8+QhXg/QoOCsF\n\
zQSV9RkaqJtCkOYF8VhST2BWR8sFkxjCbHzQ6wMKyOrjtOo5t9aXrYaB3MOj\n\
ivYJwsqd6OwoRntjNpytuexOCIlsa0qBoykeXkcWgXgPja3oat0NvyMJ/Z3J\n\
OHrLdRzsa3jzPjRnv4KOorcIyG/AVjQDjpJZDOP6B25A6wt3wV1BIC55C66y\n\
t0g+v0sA/pJd4RGCb79tPR2vQL/1G86K6+/YxFlwUiJnMIyF9B3xkWzuEVI5\n\
Tkpj9wYadK9nK0tnhnGPgnFvrpTIA+UKxFU0pEz+QaQgH+8rE/F3mdTGPKbB\n\
cliUaQWVD3FM+RRB5U0cYxbHcsbEuBDBh7X2ESIJ2aqrZbWQh9DJ0YzhWIne\n\
4bDkY5NBIscaJbJWMmfSGv0EQwaytCZNWqMfXzh5DUlwmithSEgWW23B5nCd\n\
rEX3NJHskdw2FoDoXrH/J/qeDuzhEIG1lZdiI4T0oiOI23FatfKIMZFtYJyu\n\
b5WqPT6mfNkUIdX4dIHbsQt96G19vv/+5GnhOWwhvp6j83XlKSN3rFw5xjYi\n\
MvH8I0GiqzYGeStFbB+3r/TTTzcgal8EZicozLILHEKsjlX6Nwu2TlD2xKBh\n\
aCJ3UJoPAqkxGqCVUcyexCArX4HXQe4vMcCI9Qq8+r1wegmvXe4otHvcpjvQ\n\
6nIQXe245bbbMUnRde2OnZx70WBtxeHGeuzJN+OLhEx8sC0VK+KziJoF+NnP\n\
r8DPf3kFEswVSCmtJOlbjC/ic4muhVi8JxPL9mVh3cE8zFn0CdP1nr/8hX2K\n\
TSlZ2JSagaT8XCTkZGF7ShpyDheipNqM/DIhf/NoW4T6hgq0tFXrhN21a6Oe\n\
YxG3awPTtVN0W7NXw9FRgfr6Ag6SXXP1VURXQpyrXmGvXunRei1zzcTLkYpy\n\
8tAqpLpp4VWSOEooXV6lWdO8rRpyFW5j0NMj3+c1rpYXTa/yy3Xz0k8khMVL\n\
TZSQvaYb4XGWo6M1j8RvNrpshWxJdNvyYa3bC481BT22dFirtqCjZhO6LXvR\n\
5xGldfthT5mLogvOQ8EF56J55xTYzNOJudPhIqHrPfop3Huno0pUKr9wJzxV\n\
84m5s9FpnoauyrkYaBd2wl7irXByD2DAKdZEWosBx1Z2ikdYwKazIzxUuRnu\n\
B+6C56m/YcSyg3gr3icYu1mKX4/Itiba0jOIuHbMn8zi90SfmXhbzLw9MVip\n\
bAkhgFtJGFdi2JfBLSJ+IKH6wzFhS6itsh/0RDSNtsF2Frfto6SvRTcsotkV\n\
jgmr/lBd5tUydlpmhUk3g3UNbIjZxeiL26lOPcawXVAf3VG6JTy2OSaL2+hR\n\
tFUU1mSyllshpa5mOozOaosV5B3lFWs1e6NR7D89giqOjsxjLenYIJJlL4kz\n\
tMI86RzHRCzvIASfrkfspEWsuwsT9UYRImWCLQYJ2Ql6rC1SorDwgH8Q8bf/\n\
naszd1yE9OAlozjsDuewNAkGWe/qHGa9G2RNK0DbB19Q57Bis9Kv4xm3MUZh\n\
q+g5LPSyQdMqm2EwpIWDOp3lkWYqD9HXGBqQ+0H+OiR0fw8fnff2SYvY4++W\n\
JO7xEI09mD5jJn77m6sZwRdMuoC3V131a7w47Q18u20bqlubcaCwjLCaiU/2\n\
pGM54fXL/dm4/b6/45H/vIA9eaU0ygi/RSRy87El04xvaPvKB0tx6+S/4fIr\n\
foULzp/EKL7muuvx90cew9rEDMR9l0XIzceu9Awk5+ehpKoYxRVmZB8uoFGE\n\
ippSNJHQbWqr0TAsO/mcwwaEoLBdOMe2StgsZUTjSuzbs54pvT9uPevcbiJx\n\
2eF03HzT7/DVFx8rEmtNJ3l5Zm+3MpDPUmuAKsXbI7nrVeV83u5mydow7iql\n\
rNDbQIjVnGHNh2Dp66nhYJxPk7vNObC3kdwl/PZ6yjmvzVoXx3LX1ZqI9qqN\n\
sNesQ3drHFff+Tt2w1b2HhrWPo6iX1+EYsJww+t3o+3rJ2Bf+xysz9yN2p9e\n\
iEpCcPv7/0TXkfdZ8noq5qCLxkD7BpanQfcOwu5GDNhE0tpmRvCAQLBPIvh4\n\
IBO+t/9DPxnrWeJJwrfgZcLsfoFgxu5W008x3EX3d+2RoztBR7B0hosIv+US\n\
wYM1BMZ6QmwrO8Uj/hzuFy8QLA0GW8iL0BziYYv0I6I1e4JZy2KZnQfuQCEV\n\
70m1dt1JA4BPyrXsDIE4dokN9sOwWyv6UGt6uLX1RLUaZ80q9urK16trXa9e\n\
3KFF505diRelaeAhnxG04xVLwznrG7vanQzKSZUr/YdYGKrttH3lQ4xaAVqV\n\
gOjXRozNfmS4zphNrJb7MGkV0oYGP8a6j9Hrko5akkl2lo/SNbJhmVLuthZE\n\
KLh36kS48eG91oylemEpyZH8CVP4ItBsVzyoqK5RXi+wDjunCkFuPWX2xf+J\n\
e2lvCMntC2r2hkyKGxynU1oX2hwIHGSL4jS+Ok4SPaiTG4FBcTxoBLivX0jp\n\
PngY4iSnfQTyni7s3r8XO+P2YuWWbVi9dSdWbt6GRas3YMnqTUjOyUMlATyl\n\
uBKrEnLx8fZULN6dIfVyWgG+pHNL9+VgZVI+Pt+fi89pf1dOCb49WIC3v9iC\n\
1z9chveWrsAXa9ZgzYb1WLpqFeZ9tpwBvj0tE5nFhaSlc7A3IxN5BO6y6hIU\n\
lJuRVVxAWtqMmvoKbNm8Di88/wxNMldJgF+E3cJBJnjbbVWwdVSSjK7kxdE6\n\
nVWcxiyk9KsvPYMpTz2il1lcS+c004K3Ar/ukNvATrNHucw9jXpKho7wHoHv\n\
RkZ4j7KPjRgXx7zUB6+FWi+bEt/PLjJpaDYsmOREcY+9DE5LIdpbcuG2mdHb\n\
VYYeZyFsDYlcuud15sJ+dCs6qlaj8+gG+CyC5Om03QKreRZas19ES/bzaFr4\n\
d9Q/cTNq//ArNNx8NRonX4fGqXegI+5ZeGsWEMk/gP3QS+ipfg++uoUIOrcQ\n\
reMR7NwKf/MX8Dctw4B9oxTUHZuZ5McFyXszMZj7NWxiBRCRCrdiBo75EnGs\n\
ew8RfCeL6pGu3ThGswIbFz4aAUHybHpvnjQwBkuVmK5iMc29f4IizpcnjBGl\n\
j0+qNpYWtozlus+tIsTXzEV6Ft1JFoUhKkNO6WrT6SoGaB1FdBs7yieDOtE1\n\
Q4OZHq2t/zEcqveIGhvr84yK9akAv+5kDClnWdPUfkPkz9DNWKsKGfLq+crG\n\
ipAQ+MdWhWiVIv2GNLmYMVp6TA+30S3rw0J9ytWeoIcB9dZt+j5tY8fUkPQb\n\
JoN+oyUSmgxO1zLqIpA+kg8S6oURE6GDWyhJY8KYHsfH5NJPE/XoXqgNRkiT\n\
38csjjFCWvzH1DZN0FhuGDBuo06F+N8rxP9sjKL3EZq9IlY30IcuIqyrzwcH\n\
UdZGlG33emDtcsPqtqGt04omWxsarM1o7GjFUUsz6oiwNc2NqG5sQGVDPSrq\n\
alGdlYX6rdtQv207b8uLzPRLKK2uom/rcHU1DldVoSojS52L4XO0x9vyoqJo\n\
8UY6XRcfz6fFoNNR9FnbTaehuLISpVWhIT6tet8BOGbPg2POPNTtp7dVVUTB\n\
XFZuugsFpWXILCpGQlYBDq1eh9J1G5C4fDUOfL4K8TQ2f7kOm5LSsS89C3vT\n\
MrArKQUfrdmOGZ9vxMzF32DJSzOw8ukXMe+tD/AmnZu7chtmfbmZr3+2YQ8+\n\
+GYb3vliM979dA0+fWk6dv/3ZRxc9jm27D+AFZt3YsnazVi6fis27N6JjXv2\n\
YOXW7Yh7ZSpSt21GcmYq9qUmIT49GVmHsnC4rADbdmzEgo/exTP/fhI33Xg9\n\
dmxfjba2SrS3V/J8YSfR3ykW1KT5w01zRmN9Ad6Z8Sr+dNMNPFc89MB9ogxG\n\
5cf1uOs4dUNZMu5adW48H3t1e6ZePSA0aFZNDz8gNIkb5VOD3NIN3ermbvUF\n\
ak1/kxY3L2VVwxa36MrppeG0mHnJald7IbqdZra4XdYsTpTuceSguyMD1hqh\n\
+dfA3bQFAWFzu1LR3bwO7cXvojX3ZbR89184K0nXV86H3TwDnuqF8FTNg+3Q\n\
y2x3e48uQlf1fLhLp8NdMg29zZ9hxCttF1Go0mddhUCrKADfSc8DoutGHM0U\n\
IhkvlbNDjvvTMXxkA88aPIMEknjGkJ+xi2aOA3IG8SfK2ULsB1Jxsj9P2i9D\n\
pfh+qFza3aT7T4qilqE6HKPZZJhmpZOs7aWa5yVGWmXDo2CzsKtFJvyJYKNM\n\
sR5uFqe5RFy+K2jlZwCL7oTTXMKxx5DfrS9orbJDoo3ZIaYo45Qhh0lruiHW\n\
szZUtoSij7r2V0HHcO0/yoYZUneOCzPCjUtfTwhzu0dv+/vd46C15zDYLKqR\n\
x+mR5gLjUq1c0G2KNk4GavW/ccbwo/ERIFb3Xs4IafxxGB1wVC3kJuplhDHG\n\
Nf4MZYSmU9YQToyQxsFZeFGaHDcsocql2n+K4MWMF68xOtzPiYz5/0nMXzcK\n\
83qAkjHvHx4gmT6AbhLVXTQ8NNyEfXd/gIYfbk5d7uL0DHuPEw6vS/jWsHtE\n\
aNCJdrcTVpcTFpcDjopy2KdOR/Ovb4B7x25YGxvpG2pziCYFdYs+RdPt98Di\n\
sIszaLOLv09x7QFxH5yfLEXD2ZfA+tDjcOXn8z3NtTWoveYPaLz0V3CtWiPe\n\
Q4OmHXs77zctWYbWm26Dvbycj52LP0PtP/+F5vZ2NHdY0Ug/MnNNA+ILKlGy\n\
cCkOX3IFCm67Gxm33I1MGgevuAb7D2YhubAEeaXlyDCX4uu9mVi2bide//lv\n\
8MGcJfh6azwW3zIZbz3xKj74Nh5Ltydj4eYEfLolGd8eSMeH9GAwg+5d/O6n\n\
2Lj9ANIn/xXxb72DXcnpWLc3EV/vPIBNBxKxNzUV2xOSsOXJ/2DffX9HdlEO\n\
0vOykJ6fjUP0sFBcUYT6+nI0NFWy09PSUsHFLYL0IoHa1l4ZBZul3PQT9tmd\n\
9gq4CPwuOw1nhcgJ5NQTkW4isvBU2gln4NWbzlDhxpqQH8N81h4g6oyw1x4E\n\
pD8v3fQYXumqR1/5qlY+Edyo+zpi6+UwZg1b6/bWQ7C15qPLXsQ5Jd2dhdxN\n\
ydWWyk8ErtZ42Ou2wNm4E92WPeh3iu51B9BZsxRt+dNhKZwGSz7xvHIecf59\n\
ttm7ahexpe4ofoP4Po9zSVzm1+Apfxs9VbPgr/+Qw4/Brh0YsK3hp4Fg5w4E\n\
3bswSNwXIcvj/lQughlw0HFPArE9VSAxkC6e7hXnjxHnj3n3034CXTvmTzCd\n\
S8yn4554zkc53ptDnC/EiYES6fGI0GawlhOvBe+F/zPiz1RQV3CXSdZajok4\n\
LSwhAXqRlnJiqJEfKOjYJJ8YhAPfpj018JOC6J9/Us/RtrFtJHMA6dGA62wk\n\
5UOGu6oKF/80PnaHqK89KJjCaxlHIX+iIeEkJPXHLKwtqxQjJl5rzevCEq+D\n\
MhVwfASlHxvhXESqa3nWoZZKXLwYcU3XKL16MczR6TcZVjSJNiZlywpF07jR\n\
edhaJgmHN0Pd7SJ3vAubCzTzRqTzqUpGQz35KNEfc6q5wBTeD+8m8Ro15sL/\n\
eH74H88Zbfq5SfrMcI2aEMaWpvuPDwuXhiaGoEpbEc8yPnodr19j2z4orHyt\n\
4FGWzHBKiQhMOObMF3t8FMWvMegxm5nilrv/ir7h4Dg+PYGB70lJU7cPEsz/\n\
zLf1FJnpawSjQq5PNCt579F6cZ6t/KBpMt/v3rGTHaGuvj7YvV40u+j5xNWF\n\
+rUbUZaYhsNNNpTQyM/IR+bBHByqbUOdpR0VzW1IKqrEov+8jjm3/x3vb83E\n\
t6mFWPVtHN6ZdBk+3ZmLVYmFWLw7G1/H52NHphmLpkzFe3TvZ3RuS1ohvktM\n\
RtJFv0B6UQnicwuwPVX0d8pAYk4eknNysXNvPHb94ioUJ8WjqLwEuYcLYT5S\n\
zM5QXWMVWttquDKyrY32Wyto0ETWWkbAp9Fagva2YnRYygj+ZbBbyuFsp9FR\n\
TsSvhEfSXuRSdlZHC9iLl1pTtMz1k+kmiv/RStALzmtx13FKu8vB+1LDS7Tf\n\
ItGuWfeM9zqJ984KeOylcHWYScYfgp8zVWQdjbM1lWR8Ju1nwF6/g/C+A12W\n\
OPjt8RjwpKBHmD4l89Ca8woa059ER9E0uGtIxhe/BXfle+iq+RgO8xvoLH0d\n\
PiHjq+bCUfgCXMWvwlc7D4OOtdKG795LiP+GpPxKiXhCepBrZHZwIjfXOdJQ\n\
iFdGUIbaT8JxX0KU4LvAe5Jk/C9Ywx8TbBf+/YBZuj6s42vxw0gd8Z3YTsw/\n\
5s+WylwV1vzALfNa+fgHDq3Kghq2ewjiQsFrHfoZ9krdi4VSRCj2hFD3QX4m\n\
sEZzHiFJzzAf3xnm+hhXfVVAN4XKHnUJL2EeHUrujtYTucfqd79Bw6s7TeGV\n\
kXpvaH+0vmcyJg5qa1fFYFQ/vUhM/zGXJzh6iW+9zVOoy15ohZTwYkljl72w\n\
lVQmanNAyNU3ZBxO1D38mAgFkTHhrU4nhHfkN0Veyvv/E+kvElC+JjLGYbpK\n\
7EVy6Bepc//7X+jcFgPVwxuhhsgdVG69SNARVI+Bb2SYzg3zNbonSnPktZpH\n\
PetFAtov46gMb53zQXldQFvAW0CZngLG823jDIwfRPuU5zW+S4THynfrUdoB\n\
gXgxndC1W/iTBPZ9dF3g3d3rR2evD26fl547ulDx5jsoTkzF4WYbSmkcqrMg\n\
+0grzLWtKGtsxc7cMiy4/lZ8+NIsvPNtOj7dk4t1B4sw99Kr8O6sz7EquYgR\n\
v2xvHjakEd6vuwXvPfc2Fu/IxqqEAiQXVyD9iquR9c0a7M8pxM70XGxISMee\n\
tByk5eVjX0Y2ds6YhdTnXkRZVSkKy4qRV2ZGWU0ZIb4MjU3VaBFRWxqNTWVo\n\
aixFa0sZaftiUbkYJRhPvy9LWyk6aNgsJbC3l6LTVg43Ed4tupS6OF2QOV4X\n\
xbs/UQK/Rg25L/MLDaKeoS5gT3g3/dSwPmx4R/9uRXl2fpSY94nP6azkAK3H\n\
XoLO9kJ0OYs5R6bLlg9nSyq62jPRrYK09rqt9GWscfSI2etIxoArBZ6GVbAW\n\
z4W1aAaaMqbAkvcC3KTZOw69AnfFe3BVvAt74UvwVMyCr3EJbWcS5Om4bDp8\n\
de8i6NxMkN+DYfdWDDrXc6w26NzKWl40HDnmiyeQJwt3X5CwN0uEN3uFY5+l\n\
Rqa8LpjOIzlasN50Nh+KW072E+oHChnzMjNRSviTw00s60WRz4mhZnbrRZYM\n\
a+5j7LbQyw+E6Rgl63VHX1xr45xEq/RsgmoMC9K3SRV/mrL6bcre1/ZV+qJQ\n\
6twgVbr7AvZu7l3HaeLaGFvMo/Oe/vc/w5jvYlTpkUomoyMo974+5yk7+wv7\n\
JnjqhqlaUqIxd1yO0PpYzPHTQ3nhMUYzRoxxumLXe/vrZZRav5FxkfqNhGKx\n\
sZpdY4i9Gle5Co+4joxqPRIbgewTwzPCTbL1yA+q9UioqvIsneyjeP4zfh3j\n\
4wsf/n+fKKQPDw+jq4t+xyPDpq0K6caCHh3pHFANEg0Evv3HRwjoI4zzbmKx\n\
L4R0meQosg+DslMqQz6oZdYIcguS9wmSi8nBLTxCIq8I7bpcGuVNUrLH6jg3\n\
oJzjuUGZenN/KGjLI8jBW2EKiTe6Vq7hqcXX349OXwDtXd1ocLjR5vSgwebE\n\
vgefRHECafZGGw4ebkRGRSMqmywobWhDdkUdlpx1IRbM+wIz12fggy3ZWJNU\n\
RIC/BW8/9F+Cex5WxBdg0fYcfLk/Fx+feQHmz16KhduysCIuDzszS5Dyp9uR\n\
9eJrOJBnxt7MAmyh54GtB7OQkE16PTsf8dk52HH19cjPTENJuRm5pYUcwS2p\n\
KkFVbTnqGytpVNAoRX1TKRpp29RoRlOLGS1NBPUmM4G9mLV7h9DubWbS7WXo\n\
tFdEcdlmLMl2Zc646hTHq6WEp2sS9vJ6j27gCDU+Xgl0OXq01celF6Pu+UfY\n\
GuA+MdxCsdfStgZuWwkNodoL4e4ws2L3dhahsy0NnS0pnHDT40iHs2m3NGWs\n\
YqUWUu1dIu9xD5xHlhDM34bl0FS05T4PKwFdGDGOYrHA92J4Kuehs+R19NR8\n\
CF/9R3CVCGNmOh3PQW/jQjZmjvsTOFe8v30lV7cHPTsx3LmVK9zZTO8+wCWY\n\
woA/OUCEHsglSufi+4F83j/eny3BLpQ8Q16oelEklKTCtkkyeYeuneg7hO8F\n\
2QeFgK9nsv/AZK/CMbp2YqheQnyiTIFk7W5R1rpVhWotjOgftFBtGPDFaJZE\n\
V4vBMPRle6qTYr44pnwaSXhTlGrnJ7PRHaGESIn4WGXHe+RgzMusc71xH6fi\n\
DHWH0nF0na7nn/tkwsaZzPSf6Ew3JujInlFqCRcN5MFTqvdTKvXwjtjBsKvB\n\
UAZPn/6OPrUwuJZ/E7o2dv2CqDBrJxS2HW3thGqIRrejCj8Xo+exm0I5lfqE\n\
EFL+4wzJ7CoXxxRKrBQTwslQ7VDMj8j/yA21IyVgnqU/DSiVL1u2/s90qTg6\n\
N4L8v10cLeRduRq5mDAqKsp5K96pPQucF8HhGVETw7CaOIZ54vDSftdwMOxZ\n\
IaCSLUXaul/W6g8H5axD6n/ufPVBQd22EfOFmk/GK+NHUL/l7r9qU4XQ+0EW\n\
/YQrYemLUIG4x/4q6b7BoJw9Bvrh9gZQaXXD3ORAu6cbLU438oqqkXfbZJQc\n\
rsN31W3IrW2Dua4VRbXNKDvajG9odlg8fwXe3ZiNd9Zn4ssDhVh6w62Y/8hz\n\
WBaXT7NDPqZ+eRDzN2bi0zMvxPv0CPDxVpodSP6vpceA7Tfdhu9efo3dnP05\n\
RdiZUYBNSZmIy8hBcp6YIXKxf+nnSJr6OopoViikkVOUj8LSIphpv6KmBDVH\n\
S1DfUIIGGvX1ZjTQaKJZoaW5iGQ/zQ5NRTQ7FKNdDJodbG0lcLRXwOmsgMNW\n\
IWYK1v1yaqjS5T1to8ROFHs+p8maTjFFqPXDNB+/W69mYuMmmtM7o5W651lB\n\
PPp5akxX0iNGOSt8N/s4hZyCKcKx7o4cnhXc7ems8D3WRHQ270F3ewKNA+jt\n\
TMFQN6n/5rUk8WfRjDANrd/9B205U9CR/xzasp+GrWgq9z8RYdiu6rnwNS1m\n\
i76z6L/oqqBZoXoO+q1fELX3Y8QrKok2R4kpgf5XGXbv4LwcUXN/3J/Bjvxg\n\
xwau8OTJYDCf/gk0JZgm0Wu2VP39WTw5nBRbfgoQVo+I5IoJIUWfFFjyD5rp\n\
M4ppVLJb//1wIxclHReTwqDoWfDDMavS8LRH9LcqZ8eqBVstHINtUzKfJ4NY\n\
nghiuFhfTgJW3dORtaHnsLw/zpOBU+07R6VkOkNpmTwPuI1zAbeyChn0cpfQ\n\
3z0qS8erh2H1xEtjiFYl+0Ty8CeOOkdPAXrmjvExYOwa5ZENnXPEa0woC2d0\n\
ama/jvofw7oya0zc23W83kHFqO0HJ4Q7NFGajpcmfUz46omxEfpRRemLfH2v\n\
zkllf+LEMQwODuDYsREuwTeEbVnmXxXBfb8vcjgWpg/DNH4Xa3wtKdMY3n30\n\
FAa9Kxzfx1n3s5UzYjqfEe4bGdGpHFDRXa/At55vGVSp9WpfPSdImg+j/d9K\n\
1ZvNURHs/GjtUSDIx0xuEegVDwN+p2tc6Dngr3xOXBfbnqJi+Z7gsG74eAN9\n\
sLq9qHd0oaPLDxtRvqrNiexnXkH+rA9w6KgNuTVtyK9uRl51E8rrmrHtwl/g\n\
ywUrsWBbDmZ+m42FO/PxORF+8b9fxwdbs/HF3ny89lUqptJ4b9JlRPhlWLg1\n\
B1/tz8dKejb46sZbkTb9HRTSXHkg14xEeg7YnpqLPek5SMzNRWpuHhKJ8jvu\n\
f4DIXoDiymKieyFyab+w1IxiQXl6FjhaS3Qn0h+tLybCF6OxoQhNNFoU6dta\n\
i+VzABG/o9XMOfn29jKmva29hH5lnbZy+jl6XNLHF7SXg/dFh60a6ebHMOG1\n\
qG23W6Vi/kmdrlerK9RxWqYI6goPx+ehj6IJhfU+6X6nNZ+eJ4rR2y1qnPLQ\n\
aRUOvfBvsuFpT4H96A4i+3747PHoaY/DQE8WUT4BzurPSPOLYOyrRPh/o400\n\
v/XQi2hJexjO0pnwNixBV+182i4m2i+Cu/xNuMwvwFs1kzT/AkL4VtLmB3g7\n\
YFuFQdta1clqJxs8IqB63J/GQVnh6hPuieyDhaYLpeTvF/I/W20zQ48BGvH5\n\
MSBNPgYog58Jz9K/SObgBKsl5YNVOM5mjyS8jTMurar8yaaXQbGfr1O/TfXs\n\
ZoMnVmV5EucnyOcD1ThLBmMtWt0/MdxuzLw5EZZ5E2vIvPFomDf9eG8WhfUh\n\
Rr1PYiHM0jek40duBDC6GErm5GsOkd/v0JwfvSHAGN6fq5k6w2NMnT6d3oGQ\n\
zFfpO6Npf1ooFjvOmF2vxWRFY9nYUAFUjFGs6+mXE411p8Y2K7ER0i9jI/ST\n\
/YneRvZ7QWHU1dUiOzsLtbU19F0HYyOs83hOmEz/X0imvyUYv+BHHPnTxuRX\n\
ahj3hzAuIC5Ifoz+uORl5eAoYhsoLiS4eCrRJgJtKyBun/aWAjgRd3jYFIni\n\
sUYr52CaILdGcMl2NuAH2dAX9zgXLxVu/bDpFmXoBBXMB6VUJ5DXEKTb3MKZ\n\
D5BU74J52tucYWNusCGLpHpqRTPya5pxmKT6wcl/x8oXZuATgvcsgvj7W3Kw\n\
4ILLsODjdZi5Ko0Dr0toTF+Zhtk3Tcb7T03DQgL+8j35BPI8LKF741ZvRWFl\n\
FVLMJQTxYiQKuZ6Wh32ZuZzmn5STiziS6gnvzGF5XlpRjILDRcg/XMj7pRUE\n\
8mozauuFTC9G7VEBcprziOREBsHy1iY1Woqkl2ORno6N2G6jrb2DwErDZasQ\n\
/k0V/V8ihbvy5MVWREvZ66lWgdgYg+/OSJdrKNymI1xa8LXKBhJxgDJ4COEe\n\
WzGclkMkzg8h0FMJr8tMGM+Ay0oi3UajPQ2ulgOE8i3CiaexBwFnAgn1DBLq\n\
62Erm48O81sk1l9jjFvyX4I1/2VYcp6Fp+ZDtnDclbPhqZqDnpp58FTMIJy/\n\
Dl/tXCXUhTWzm9V5v/Ur9LUtY+tG5ESKQOyx7r2cQznsERn1ccxiwevvBw4R\n\
s/OlddOfGxLu0tX5vk9cypXCXUc6obw/nY9PDGgoLyWEl4dQPihTbyS2BcYt\n\
CusT1XGbrHAdlmiXjbisyo+xcvfCdsa4lOsS8zbV90Vr4WLXq6ccWsyVO86G\n\
Yq7Dp+6qZeg3K8EdYcXdCLJd43tsBKc+Ss+0CbFcsDusyWH4UjthPo1evRrm\n\
y0tLnq+dFiK6lnypt3HBsLbOjhaGjbiImdTv3KR24hibXu+EqGdZhrpmjYqv\n\
jtLspgh1T6IutM+PrKxMrFu3DpmZGQgE/FKmM7vPE8gWwdb/zdR1+GUKynIZ\n\
uYF+YxmrDmUuZFI4FjHSY/pFGspD98t2LOyVDDORY/g1mu0Qdru/WceZMcM6\n\
f4f1pJhhTUprEBbmhwZi79GGaD08OqxgG2QVTbebJIyf4nOeg+l0e6PhvmF0\n\
BvpR/O5CtGTmweHrg6XZgqwrr0Puw1NQ2uRAVqUVSYcJyCJUepQU9oIl+OZ3\n\
f8bSuEIs2JqH+bM+x3uXXoX31mdj+jcSyOuTi/ExQfj95+dg/rW3YBGp7UWk\n\
rD+dvxyLfnYV1icU4ruScuSUlWMfwTiFlPXOl9/A7vRc7M/KJVWdh+SsHFbW\n\
Gfl5KCIol1UVc52UBLQZJeWFpK6LcPSomZS1GY1CXROJG3kUolUo7GZJ5DZS\n\
1u2krNvVVqhsu6WYiSzILGKoIi/So3spykfplEiWtajSL+HzXNGkQqG8lGWP\n\
p9b0kDqu5cSXHuKxyy7isyVwi63IYyce+9xl8HXRtXZpnHR1EI87BI/jpXEi\n\
eNy6Az7rLgx4EhDo2AnnkU/QUTKbmPwGrHnE4sJX0EFDGCcix1FI6566D+Eq\n\
m47O0jeYx13V7xCbZ8Pf+D4GHes5kUVULgkO97d/RVxeyq0BRHJM0LEZx31J\n\
bJePeAS3dzKfJXjz8D3pZHZT+vIliAWENSiTTtas9+N03/H+DAnkXglpked+\n\
ciCHwGwmGKvcR4LyiQFRJVWsQByjQKy0dbBN2u3jwmW3MleUSyKaCfwQ6uei\n\
lbsSmaPYQo9VvokMlco2LqGuAgY2Cw8lSuF5+NTCmrkbqyXCDIUnsg8NGRJh\n\
RjV48WnpjqN6DGixVKmoVbMXcfdYUR09htanKH9SNVIRLPhQlZUxeTJUChXq\n\
Yss6PNS0dlTSDJvtMTIHXtvjatexa5+N0ythxy71EBNWCKsbNIOcRymd9Zj/\n\
g+9hq63zv2cQNTVVSE9PQ3V1Jf1rB02h1YLPjbDGGeOeJXlnBAfmj+H0F86K\n\
u2m0JBf0HxmJFtynb10nv7BNRgY1V5zLWWMV8Yn0ivhrFfFj6P/gRna3xVbF\n\
W3mKEJky5jBhLfS51+FSae5rWYOLRxmRLCn4Lpjud7rFMSvzYdNf4O0fQJPL\n\
i8P/ehY1d9yHsouvROIV16I0i0StxY3MCisOFDUju7INJQ1WlDe0YvvfHsNn\n\
j7+MJTOXYO61t2L+gvWYvzHn/+XsPaPjPNMssTqITKJ6pnvCzqzX4cz6HNtr\n\
7w/vmeP4y8fec3b3+Bzb67Fnemd6eqanWy2pFRgkSiS7xSCKFMVMAkIGkXOo\n\
QhWASgCqkEEQOQNEoRCJAkhkMKmvn/d53y9UgHrXP976vvqqALGl5r3PvU/C\n\
iZR6XMpz40GVH7dKW3CeAvLP/qd/jc/+95/g83d/jXOE91cupeBGkQeFDh+a\n\
CONrKOguqfei5Md/h5Tjf4i7dFLpZL39h8ikU/rRKcZ5kUVt6yKcbyWc72zh\n\
hqYOuvb0tjDOD7F70orRkTaOukeGNa+c8H6sBVN0FdiuYfzshA+zhPOM9VOE\n\
wYEuwvcemUH9oYJ7FYGrcQMrusGi7HRV07jEkN7L8C4mca0uCNekkx2ThVkB\n\
YwszLZZ/htBCJ9YXO7AS8FK47cCiGou4NFPD8L40Ieoby7E8lo1n8xXYmC9B\n\
8PFVzLZTyN12gqD95xRuizGJ7yDg+wWPRAyNfs0Qv9TzMRY736dnH2CRIf4U\n\
QsO/xtrob7gZVZSw7K4UcN2jCLt35jIZ3gXkC0gXtsiL9TrdSSHYliH2MYX0\n\
zYz2L/REqlMi/JZX/0ygOSF8vIB2ERHrAO81DJTtxxLcN1sY1SXAHzIBvIq4\n\
tXvOgMpKGW2+l+pqlRbKvpoaQ3d8LNr4RJk3NbqXAjyta86YayundgnE4qoY\n\
XhNseCkHDi/Q3ZKo4QXhofehMLw3b7DUvhdRR6PB/7ax6XJtLWCmBO1xxPoe\n\
2f2aGKOURk2ZkWB+OMJviaq1CSMD87OoqnmtHDK6I1b5N6pMXiu/scglP9pk\n\
xiNGT2yMqTRhiK8aYiMNGvHOtHgtvEreoILDyp7f2dlEKLTCmG+MOIhInrIr\n\
8yOB+f9Gc+JNRfN/Il4XY/DAv4jmgTAVsGvwgOUoC4DQ3stwIbCzGVZdo5Km\n\
uggQlCAMmcX8Iq7U2eWon/6HLFntrAa0I/lhV/fUF2rrpF4Qv+RuCj8X7+L0\n\
Z6kq2t/lwhvx71SwA5EJ/77AOwQleUWKKf6lZIr5EPpmlxHwtGC2ooYYIQA/\n\
ncHpRbQMzKLMP8qqwD88g76JGTQ9GkNaRjWu/+Yevspw4Iu8FpwlZfBpuhPn\n\
iDEES9wqa8FX+R5iCyfOXn2Iz0g1nLtXjit5TtwodOJusRO1TX542jpQZPei\n\
2OFFpasJhXUuFNc5Ua1q5CudLlTTcfu96Oprg5/ZogU+MY1MMUbvY8kWIps6\n\
MtpBTCE9d/bbR4QqEEyhMquaMhBMMalUAdfgdGFeuCmidl7QRFA4wUvBLsvb\n\
gkGYGuTzbqwI5bDQrVwYQSldvCNebLN8Ot+JxdlWnnWw8ET0Mc9Pey1/zqlT\n\
MbRx8YmbaWJhRqqAlRkrFogmFsZIAQTKsDyVi+XxLGwsVCI0lYmZNvpv1vkp\n\
nZNKBfyCaOJdzHX8Ck/7pTOz3Pc5K4Elooql7vew3PshVgc+xdrwWYr8b8oq\n\
x1AlduYz2a0Rz8RUGtG1tDX7ALvBbAJ0J9OEuH+xZtXdmddbzQYfbCnHfdMp\n\
1cCWoJMtn+X3ZbBvdmoE87CIaGAxwHyhV1J2c5pVPHuzPyaL4pkfBCeIYF4n\n\
kQSWAG80110jjWTlzJiKbfYD2qBIZgvBDPp4BJ011MAx+jv7kllDYw6NJSIS\n\
q7umQnmBxduaSNCHjRHARJbCm5kjcoNbuCAIhQIS/ZOhDR3TPjIPHEuMoQ74\n\
mXmhm6YFJC2YFwmpWH/HdL/7PB7RNTUHhf4bRoG8anrVfXl11UvnE8x73wyX\n\
/nDkkARJBC+2DFJ4oWSAYfNoNv1L09o3RQphw3mPxiioZ30Qp1x6U75WWvqc\n\
oxWk8OYPBTP894oZfmtihuQYz/5MvP7nMfKxDd/DIEmI2JVBDLEv8V6Qx1v8\n\
ViMPcTUIhMvpsUrksbyxwffSSdqzaLpijR0jPjwmZ1cVbK4bzxFS/VC7LCV+\n\
j1H/f2HWCG1tYXF9A4FVMcVBVF1uYiiwgpbBAB5NLqKXdIK1awr1hPwdIwH0\n\
TgTQPzmLav8A7lR34EaZHxcJ+c9kuXE2y4XfEPLfKGlCCumEe+WE/oWE/hkN\n\
+DytHmfTHbiU3YBbxW5cza1HSqkTDn8brMQA+TY3ShqIAerdKLQ5UWIX9TQS\n\
+aucTtjoXuiD7sdtrBc8ftIK7aQTulpIKzTh0SMPurvdrA1GRkgr0FVUXbJO\n\
IOSfpPsp9oKIAcZa+PpkUkd/+rcTfNJpOU6vHYTaXVgMiE4qDvLZX1+c7+Zi\n\
GNHUJAQAL6Vn1Bds0REnNr0J4p3tRHDag/knLeJXTrst/5w+kaAvRhjMT9ux\n\
OF0v62ZmbFgYL8P8aAFWJgrxdLoIK5PZ2FyqwLNgIeYefYnZ1tOkDz7Ak9b3\n\
6XyAQOt7CPjfIx3wMZYHKDAY+ILuTxDwE+h3vsfA/7TvBEJDn+DZ6AXSBXns\n\
l4v6mZ0gAf/kNc6yCite2PBid5AonmHgp6sB/C4hDkQRzRYLhS2PIgA3V12y\n\
SBDvBeJv++VVFwtECK82XOKlQVSyb5q+t93BbVPCcnq9J9KufRrqJzDW/4Cw\n\
nt8atTWaBUT3+5uPsbPaSqQyYIC9VmCzzwSgBh0Q1Au0YLteH+6rhh5oMkFf\n\
ch8D82VRpaqf0UatG6pBHzYpjXhLjPLKOD2FKn2gRLNNT7A/q1lKWgNsOLgf\n\
NeL78MrJePVqNnWSdWvHMHW0iWfJekCvV0nqidbDMPbEmfKrh4wBB5Hr4MLd\n\
emXeaBPNDukeTvgC+wOaX8MQ/LA+ivJYeCOUgdGm0kcBxf9ZjGD+UAzIjo/x\n\
jDupEmL80nhjzkKi/hOmqyVW3y23zT6JIoDfWv48okhnMZIAGOkl+osiUcJ+\n\
3r6xzz1YMqW7iaXNDSyJWWZbW6Z8rpQgIc4S7O0eUzmEkF5Bo0X+SaaqGsP/\n\
X9/aTVRfCm3t6j8in10hKtjC4FwIU0vrWH2+ifnQBlpHFtA1voRRogdXXwAN\n\
j2bRNRJkWhgkSvD3kyCo68KN8lZ8VdyCzzPcOJftwpd5HlzMdeN6YRNulzUx\n\
PYjUwGffNuAc0cKlnHpczycxUOLG5Rw70ipdcPpbUetuwcNaN0rrvVxemVNT\n\
j9IGF5dY1tKxu1yoc3uYFrp6/Wjt9MHt85IooPedQhw40dreQKKgBcMjbVyE\n\
MzrUIilBpAq4EN+naIHoYdTHgsCghTZut5plcUBnRlhKfq6HFBY/p11Vj+ui\n\
6IIiihDp2OWAH8uign62GfOCQp6IChv6neMuBCc9CC10YG2BfscM8cFEHfGB\n\
A4uTxAfTxAcTlQgOF1LwX4SnMxV0zcP6XDGezRUh0PMFJv0nSQScwRQJgCnP\n\
3xEfiAnuv0KQhMBS7ynC/k+JE36NpZ4P2DNa6nyHhMBHCPWdJk74HJssBOoI\n\
62uwK9qkxHThyRtcac81lvNZdLJVSU29Gl1ZzO9JBEjf6E+N1OymogWmh2ZF\n\
BW10bZP3WnZ3wytpgCnCa/z8Vgtd2+TPbLWyaBAdtG92R/DmBWO/yBS8mJYF\n\
l8eUezSpCQGTszRLf34fCZkq7K13mMiA14tKrggYV31VUjLxA3HCftDgiB2d\n\
IyxhjVV6KY5KGCSYG6v0NlqeYaltc+ZSSmO0pZ7S1YtzEmPkDuINYgjLNQj/\n\
SMv4Mn1sG0pD2wttmqdmuERMLLFatRKNZIKalaP/uBQSvK8jOhmcoD0OH6em\n\
JX5NBZyqRj8hcqhOssoA60LCaLY1XxPCGrskByXqKeGjMaYcf/9sNYtc36H5\n\
SQkHpRaMCTyJOgX9sYD/4zG45OiBnHPI/CySScT1T2NU9IsGsN/OCOLg55EU\n\
YvR3hV7sMw1EU8hh9Uyr8dxhChETewSFrO2aMhhxrCXiDU7Z3bMc0blkV3Od\n\
uN1XMsqeThZv8eufk37YRH8ghKFgiDWE6ObqnV1B19gSF/x0Ty0RWQTQMRpE\n\
28gcesYC7CCVNfUjpbYLt6s6cKXYhwu5XlzI9pBWcOJSrgf3q1pxp6wFX+a6\n\
8EVWA2uHC9n1uEza4Q6RxTeF9L2sOpQ7W9Dg86OswYNikUuu93C1ZkFtPZOF\n\
zSlIw0VX0hENDXC1uNHFuWQ/vH4Pmum0dnjQ0eFG9yMvhjnn4IvDyJCPtP34\n\
sE9v2JJl+X6WEFPEFTPME3QmJTcEZvx4Mu7BkzE6E17iDL/QBPTvenG21fI/\n\
cpdscNJL2C/Swj7WCsFJMd64gUccByY8mJ1w0veaSTd0qFp7+v5kvdQNInVM\n\
PLE0XYk5wRPTZcQTZVgazcLTqXxsLldhefQBpnwfI9D1GQIdIn38PqabxdaP\n\
dxDs/ghLjz8lrjiJ1aHzxBOniR9OkW4Q44/f59SxaK0VuQWxqYO1A2/xkPph\n\
S2iH1SIecSbSy8I84tKdUB1/LjTFa9mNxdqhWXi2W4ooNMBnHdAmPm4TrTB6\n\
rb1P+UzqutnCv8IXz+We6oubLewqfbc/iu9eKPx/MU1f/O7FLDNFPDNFQgRT\n\
CEWgD8yRxT4zRr8WM4NmHwXkrJx46RaJkQr72pS0I5ECQrlGUeqBEwsCPQ1y\n\
YFZQwkFD/W1TpuGwrhzWTNkGfYeT2U5SgzctCToZ6MkElXQwaw21h3pHG0wf\n\
b0onhCwJUc9Um6+WYzbLjKhn+mhN8UcxZIdphL25CChR44K9sNnLicpUChcn\n\
+uy1t74nm2yUB8X/7pEMB8oRYzeqJbxP65CiBlVRZLhKx3R18keCGv6RoQzM\n\
iB/376slzMyRZNIXGiX8l+L1T3BAx8CYeE2IzRWLKnMd2juIK47I97t7WukR\n\
ljek2bS6Ixf/rUmZkmBmCvl1WaUkdYbGFtwEvMvpaZFd2IuLQRyH+PVHWN/c\n\
QYjO+OI6kcQyZlbWuXJ0klRH29giRkhpjM+vwjMwhyY6XWMLpEIC6J+YRdPj\n\
CWTVP8a96k7cq2nDxbymOJxNc1v+LxIcXtyrbKPjw+2SFlzN9+AyCZHLJDou\n\
ZTtxVYxuKHbhSk4dvn5oR7mrBQ7ijyKH9J5qXU3EIeK+gfmjxtlAgoPuGx2o\n\
c9ajqb0F3T1t6CbR4e/0En+40NlJ/EGns8OFx71emYUY8rEHNUHEMUHEMUEi\n\
Y0Lzn1hoKOJQOesn482YGXPT1UUCxEtk4mPRIUhDbEQNEFEIcghMkJCYaMDM\n\
qBXTQzUIjDdgdsxOAqMBiwEf1pY7ZJZhxk3kYmeBsSCIQxhOU0QcQwUkNsqw\n\
MlOE4Eg6lsdIBCxWYD1QgOn2c5huPUXEcVoQB/0XftL6HsUkTB6dH3ApvxAZ\n\
y/1EIj0nsdzzEZb7TrLpJLINoYHPsTH1jeyo4lbeAq4HFaaTIAg2mcTi6mAa\n\
d24JpOeMw1IufyaJQu/g2vKIv4QagTA7tEh1wYpBFH0ST9MDy9v0qpFIC3/1\n\
JV9bFMG0KZLxq/YAO74jkfGdYAgzf4gE83ecntY+ePNC5iK4alRPQehF/2/2\n\
AyYrirPU+wEtcy3zDvxMLPnbD0oeSVC9vRqPLHKq2qhFkt5TsqINLUNtyjmo\n\
6cp6gf+2yXw6ekA5Ung5v5kz9PL/sEHNa+HVQ+Z5zEkRiWrVJ6wVj8Zr5BBG\n\
GubCJH2qm6E3lNYwGGNXDWp7rsY/m5oHDCLZMITFrr7ByiQgZNYhSRcOUQkI\n\
NcUtapu2KQedqOegNdNKKAkjF30kBiP8bYzAPtmE7GET22JN7xkUr4lmUNcG\n\
PJgmMBOIywzC23oGYZXO8s4+XfeVjyRBXQT9q5tbWN7clD7S7o4G7JZoZOfs\n\
wu4eQzlbQgKx+Ssmr0hKgr/Un82vbaB9fBmj82tY3dhiWfBoegW9dGYI0bsn\n\
l9HYG6DwfxEdw3PoHp1F39gsavxDuFtBMqC8DVeKfPgs3Y3LD1twMceLGyU+\n\
pFS1kQzwU8jfhCt5Lk4nCM/oUrYDVx/W40GZExfSa5BSVg87wXidr4WHrIkk\n\
st3bhCoK/YtsDthcLoJxJ8sAu8sJp9eNZp8HfhH6dzfB1+6Ct6UevtYGNNO1\n\
naD8Ua8bfQMeTAgYHxVphRbSA146bi49CvOLuFW3hU4zj7YM0P28gO9ZOlMt\n\
HN/PjNTjybCNoXtyoBJjj8ow+qgYE/3lmBkScE4QPe1if2gl6KOfF1BvF3VG\n\
k3WWf8ZbpxYmajA7SBA+U0WxfzmCQ5lYHMlg+F57koPZ7gsYa/kIc92fYZpi\n\
f9GZ9URLGre+h4WeE6QBTnLpqBipsyQgvPcElh9/zHVFoeGzWBv5gmel7RNO\n\
ypL+fK4rEvE/b5LiXEEWQzlndjecrBP2SRe8Et4+G0LueMbxt4z0ASO4R0kA\n\
n4Rs9orEAIZOdS8SxK0iFNvyiYbOZzb6lXaVQuigf5yH/lgOvNkbUjJgkq6z\n\
AsAZxqcljCfyQ6UPxBOu/xfqYJZLiOI1nNYCf1lhtK/nDgxfSMsfhIX9EZBt\n\
+f7qfpUt+AMdoc0BftReFP1KKK0sn8Sw76vMsCVeh+gIUyfM6AlZ4s24bG7G\n\
jTfsnO+ZvaaQXPueWp6tZxBk0655l4ocs8nZBX0hyobep6XnGmLNWoiLDOQ5\n\
dSyfmbcHGlWiolzYBNDPxfK8pSD9qTe/3985dlC90I9ilIz+1NTUpYH3j8Tr\n\
sIDn5EigDs/2GkCdTK8vGagXt/YR3NzF4s6+qhmSjoyo9xcm/irFwaEdbSAb\n\
A3WihtN6sC5zvfKZAmYtKufSHg67Bb4zRO9pQXichuY72uNdix6nbxoIr6WM\n\
t3Ytv8+BOsP57CpDuwjUReAunk0urmF8LgRvfwBN/XPoGV+EfzCAwak5dAxO\n\
4aHjMW6Wd+JuVVccvilutXyEL3NbcCW/CffKW5FS6cfdMh9uFntxOdeJi1kO\n\
XMiy48scB24X1+NWIaF9lhXpVS44/K2oa27Cw9oGFNU54Wj2UrDuRAkhvAjS\n\
7YTu9YTsDV5Cf5cDDqedAvR6Cs5daG110n0DWnwO+NsJ5X02OlY86nZSsO7F\n\
SJ+bjgvDdMZHKBjnwtKWcHSf8FKgLeabeQjVRSaglR2dJxR8zxB6T/RVMqIP\n\
deZjsCMXA+2ZGO7Mw/QAIfV4PZ7OebD8RPTXOjE/WU9oX0+oXscTFMSctOBo\n\
MSF7NZ4+qSFkz8YiBefrgSIuA5puO48x7/uY7foUU753VZPWTzHt/TvMtv49\n\
Frp+Rch+Bk/7zxKqf6IaAk5Lt4cC89DwF1gdOo3n0zcpQBdZgGpechUeoNfI\n\
6tFgLn8u0F00CewG07G/UsHlP6+3XDIxHK8CbK8er3sJ3WSs7jMhvAnpdzpU\n\
CRBfpcNjOaZKhZwqSG/joWuiF0Gg/Jt9QvoXY2z4MNrvsssjMF4mCaZMeYBJ\n\
S7w2nEFPIs+YUH5GAn+iCs7n9EN4b+EYXY1JFnj/0sB7iwH4+hgefW+Kvvx1\n\
RTg42+bqoFWtnlTfA2sqJX077JkRjYtnq6sz+jO90Suyadfs6isSMLpzdyIa\n\
CeJ0FI/szt1RO7NijmMz14bKMZvRJUJJhpETY4Ns4kHDdviZ3vhliZ1yjq4c\n\
jVeTl1+8MC3MiliWlfS7MtCrq0uYnZ0i7fRcBvOHYhDFUX0toiVB8sMbfZqb\n\
cH3e/J3ghfgYkT3P2x8QlHDITA7Ho6L4Va73kUWjsgboFZZ391UUrxeUxjFD\n\
JMrhnCqgV8lgyS0cxSfrYXuCAfSJJqDfCwP8mO6M8WyHHRr1jEjgS/7OOIF9\n\
+ziB/tJzJhYR9/fNrKCfiOHJiojzlzjO7yYS6B4Rlr/IDwfg6Z5AqrUXD2p6\n\
kFv/mHigDV8V+XG1oAU3iv1IqyImKKc4v7SFh7FdzG4gBmjgUqEvKda/U+zE\n\
9Yd1uJRuQwYxQYPfD5unCXmqXMjm9aLS4USp1Y7aRgexgItifCfqiAGsjhrY\n\
G6vhabajtZ3YoKMB7cQAPr8DLk813M5K+Fpq0NFuw6NOGwYfNzALjA15ONaf\n\
HPNiihB/aozOuJsXWT0Zc2FyyIHJQRvH7dOjdRTT1zD697dmo78tixggj04O\n\
nSxMPC7A3FglT8acm6AzVs2rDBe4JsjOLBAcK8fcUKGM7Z9UY34oB0tjeXg2\n\
X4XQTD6m289j1PUepjtOY4pi+2HHX2HC87eY9v2UYvufYb7zl8wCC10fY6n/\n\
11wbxDYNMcDTx59QXH8Rq/1nZO/AShH7+7sUswsW2CGE3zTH94s5/B0xLuHV\n\
MyfH9jtzaXi1ZlMBfYsO+y0c5ItuAGHPqOaBMEPfZPBzn26nBv/bHZY/Nnk3\n\
KhmgEsmSBmxEA/2E48KvGZIUIKhAxfd8faHw/4U2kGfK9H5KGjiydUDRgUXy\n\
QLK5xUBxwazOB/GaZyMX0i6Y5+NzZy9nOzUa0IpE47UBbAjb/23C/eQYz/RU\n\
cEQRqRb7i9n6wud5+nRK359y0OhOvXLU7Ppro9zo2THdzAnrEzhkJgidCGQV\n\
kjHDwUD9o3pHQBjqSzrY0IBcjeaJ+x4hELtlQOsUO9Dbj48x3UFLAL80jexM\n\
UpC/s7OBjY117O/vSsg/FsPgPxJefhShDUQh0pufCdD/kSwhirZu7qtn5urQ\n\
fxGlEo7wf8xwlfDK7M/zeyKAOHEjtlsrjljTq4Z4l+KubCfYMVUT7QkrZ4+V\n\
QZzeUaZLBtVYHAX7R6Isnj1l8VyTz7bkWIe50AY6JlcwFFzjMiFBEZNLa2zv\n\
TC+tsxZoGgiiY3QRgzNLpAPm0Ds+xxRQ7R/Gg+oeZdx342pxK76mc63IxxRw\n\
q4REAJ07ZU24U+LFtXwPLmXX49Q9Kz69V40HpQ24nluHy+k1yKhsQL3PRwKg\n\
BcUkBsrsshyo0u4gCqhDVb0dDhcJApcdtsYaVFkrUFNXBXeTDe2tDqaAjnY7\n\
WlqsaG6qRrOnEk5nKRobi4kKKtDbVYPB3noSBE6MDzoxNlhPlEAB/iBB/rgL\n\
E0Pis2oMdBSgvz2HTj56W3PQ4UlDpycVj30E/+1ZJAQI+ntzMdVLImCwCBMD\n\
hZgaKMLcqKACK287mafAf5Zg/8lgLhbGRTcwfTaSjeBgJi8UD80UY7rzCkbc\n\
vyIRcILOxxiy/yVB/0+4bWzc+ReY8f4Yc60/x5z/HzDX8S4Jgc841bv8+CSX\n\
BoWGL1Hwf5aFALvvwtrhLbc5SgDclwN3eNBOEXbnc3lo5isK+EXbmBjOKdK7\n\
ar6aEfkz3PsZyv2ipGK7xXDqtzzxnAX+kRIErdLmEei/3a2ubfK5uN8xPdvy\n\
s/UjkP87tnqGCfVHNfRnw16keTUieMEzOKX3k2ToAZUjVrMbhLczncDAf0gH\n\
epMAkGaPMH3Yr/+dsL9thv0kw+3ZXjFBu9E8HLWM3GgeNjv44Y1opu8Zk5kF\n\
cqxgeWXS8pYJ8qXlY9g9O5EKQGsx0yuFQrGcocNh7ry5pcAo+VGCQN+uYuRr\n\
D96uEjbCmUnhqJICe3vmyQ86Hbw0+fSJGgm8MEjA8Ip0756fyRbiWB1kxpLc\n\
t/TInkt8/kTgepwyeZTpw+/+nXhNjBHgH9MLfaDBv6U3Kt6Pbh5b3dXi/ZcW\n\
ge0v4xngj6rCfw3k97iwf01MfNjRon297FNa9glm70f59vGRfhDh91E9GSv7\n\
vRIiK0JldJ/M8L66IW0dUf3J+djNLSyuif+CfTPLll8yxPfPLKNjbJGuS+gZ\n\
C6JrjOB9JoiekRk8bOzH3Zpu5Lv6cKOsA98UtbLPcym3ie5bcFv4PATtt0WE\n\
n+XEyTs2fHirBh/drML1PAe+JVi/lm3FpW+rkV3VALffh4aWFpQSxFc4GtjB\n\
ryZoL66zEdTbCNqtsFJkX22rRI29AnWOStgbKuFyV6Pdb0N3hwOtbTb4Wyj6\n\
d5ajzvYQDfaHcDXko8lZiE5fOfp6rBjoqUJfZwUGH1USzFsx2FOOR758tDof\n\
wN9wF23OVLpPQQe9f9ySgSHh63RkYKw7E2OdqRhqu4/B1vsYpfczA8UUyVP0\n\
PlaD+XGC9uESPBnIpcg+H0tTZQhSVB8cysDT6TysTKZjqvMyhl0fY6rtDGbE\n\
4nLnTzFs/zEmm3+GCfePMWz7Nxhv/D8owid47/wQwY4PsNB9kiFe+DvCyV8b\n\
+5ITsxtT31h4Y4kwF4S3IxYaKnjfW1KRvegMVk698Hd4wqZoBSO4V6Wcysw5\n\
oiJ6v+mY4V2z80Vl6LbP8kMF8WoQD7cGC0hvU/DepuC/VwkAP7GJyeMhiH/D\n\
jr7weialmy8KLqS7L/Oymplvrg4VRpA+m01G+NIeEkB/OAbQB2VXgF71qS3B\n\
Mq88XLIYZo++/CrC7DG3AphavkxYHq+V9RilPsbn28oUOmRmi/AkgEzJar+Z\n\
QX95yvCJjphEQFjNp/kZ/xMO8IS0boLo7Gys7YnKCtKztOumnrHkiMGd62GK\n\
IHwA0HODIuKjkrabMmmbbJ4UYWxXVF5QhBzgZ8a6xfiDfB9jIwt3jB3Tpnzq\n\
Ez1l/C9D/39yECf8lR7/RwP+oSjAl3H9vub8JzDcH4qCe1E/E2LTf1dAv16Y\n\
uauh/h73CMu4XnZ6aaivOf96XU68hvg78WYzh6ftK+cnWaMCPbTfNdz+K5hb\n\
fY7BwBonc0V/mOgLE5F9+5hoAAhhMhjCo+llNA0S7E8uoWMkiN6pBfpsEZ5H\n\
U3hgfYwsx2NkWLspwvfjSl4Trub7mAJEZ/C1PC/OpDpw6oEdH92uw8UMB+4U\n\
CcNH2P423C9y4Bu6Xv62EtmVDjT4WuBpaUJFXT1K7HaK6hvY5KmwWSnar0Gl\n\
tRI2gv56VzXsjVWoqi1Cla0Y9Y0V8Plq0Nlehy6K9jv9NfA3l8DrKkRjfTbq\n\
atNRb82E256D9qYCdLcUoKM5H53NuWh3psFjvQOX7Taa6u6gsykDj1uzMdSR\n\
i+HObDpZDPcjbSnobb6JR95r6PdeJzpIo0i+WEb4YxV4QpH93FARz15bGKP7\n\
wSy65mLtSTGWx9Mx6T+HYfcJTLWeJyo4S/e/wIT3XUy1vI8Rx/+LKc9fY9r7\n\
Nwi0v8P7URYfn0Wg7VcU7b/Pdv9y/1mERr+iyP48j9jcFQYORfe7S0W8C4Wj\n\
/KCM8tneXypiChDj9AWEi4YArRNYJm9Vhb6etW3RaCCOQ/1DigU0f0djAd3m\n\
jxP4LiwhnvzTqa49ig161MTNNtUKZjDAm/1hngw0yib+hFZso1BeTgsSAkDv\n\
A9aLcxJhbgUQxThv9nk2kGwC4EL/3Vkjzt/XmsHC4d8YDyTnR/yO2UByJXrE\n\
8GRtiFvsgF+W5xw22zz6/cbGsrR31FSJozDGQpjSvgcvT08IGxXBiiHmuKB1\n\
y9EDc75aKedzrV1YJYojTf91Gc5rg4BiVG9KXWCu8g+v7o+q8jcqPL8nFSDn\n\
Or94oaeHk36XFWTuBUiKIQriVTOAqSdNnDg9H7CvqkLV5H5mjbd06fCfCm5I\n\
ikET/5hfE83PtJwyD/SP/P5/JF7/UJBJpyCTI+F2UVT5v0Yruy/VPZ3dVyIX\n\
8Io7AF4SFYiqz31V2K9KNLXQf09uh9mLU33EqvrfqP6xiA6APTOn7O7J6k5D\n\
O2ztmDSEai/WE8s7BttYDkg2a/7TpvbsQpjXJOZSjBMDCSYKrAoxsinECAmP\n\
FRIcK5haDKF/dgVNw0E8mlqWgmRyAQOzixicXkBN6wiul3ch392Hu1WduFUs\n\
GMiHyzleYiQSISUkSvI9+CLbSfdeuncipcxNQqQep29X4ouUKjwoseObhyRI\n\
0iqQV+OA0+eFt7UJlQ4HimusJEAcJEDsKKisREFFOTFRKQkREhoN5SRESuBo\n\
LEW9owI11mLU1RXD4yomMVKGztYydPhK0N5SjFZvHtwN2XDXZ8DnyiYmEmyU\n\
hQ5inFZXOprrHxD7ZOKxL5uTyaM9BcQ8uRhsy8Cjpvvo8dxGJ50e93X0N3+F\n\
odavMdpxDxM9GZjqz8d0fx5mh0pIfAhRUoiZ3gwsjRdhba4CKxO5GPN/gUH3\n\
J5juvoLp9t9goO5vMOT4Cab8H2K24xRm297HXM8JEh8f0PkIwa7TdP2YRIiY\n\
BvoJFnvP8Iau1ZFLLEg257M5wSwGNgsG2l2m63wOCxExg4ITz/NZKr3gVO3H\n\
Zewx0WcWrhvi5LJ0leJNjcbNFmkpJUbkmIXG6BKyZafHclwxTL+87vUqzfFY\n\
6o+tFm5i5qQCM88A724k/SEkx4SYWvRiUllLUm5wgZE2veiFPpzixSwnopMM\n\
mpGFn4piVD45Xl+7a/SUxZvaBqTSYJbZVunk7XCFIUuIQqaiz1hZhST9NWyU\n\
v0Yn0j1K4m2Mq6vTkTpDXwVmWsVurj0KK/fUV8GEdxMYJtO6+fuxCEhrbTb3\n\
FyRECQ+jFPTAhoJYWefoStBNi7YkzOQ1yWl0lugCJNYdO2HiQ6aapQ0VpyeY\n\
Y+33jQ+fJW2J0VPA5tNxXWj8U11oMCGoboFw2nhjSYhBGeKH3iTKPgO6O/Ar\n\
FnM10xtif/0Xas8O0jpMYtzg3BaV6/gt8cx/gPR5lcDclCC5SeOlvX1Zf5og\n\
DS8pdXRiOqRnMeLC+Eflsbd2w/iHm533wuwt1d1s2F+mvPeFcPWzuYMnRDKD\n\
JG9G59d12cOOF5EMdyMEV5l8/COL9GyZyGaRpc84yZ7e0VnkOftJ+vQgv6GP\n\
OxNuFflxu9SPG0VNRDJufP6tA+fTHPgi3UGfuXCz0Ilfp1jxZXYdXavwm9RK\n\
3Cuuw+0CepZRjvQSKxxuFxGOBzX1dpTbhetVQ/c1qLJXoaCsEPllBSirLoLV\n\
UYIGZylcrgpY6wpRWpaJsrI01NRkwFGXg2Z3HpFNETpJ4nT6ColccuGtT0Fz\n\
Yxra3Jnwkdxp86RhoD0XQ50FRDQFdM1Ff2smur330eq4gRbrV2irJ5nTchdD\n\
bfcw6L+NwdYbGPJfJ9K5S9InE8HRMixPWjE/KnLZYrdvGdZmKzE/lImx1ovo\n\
b/wYk0QyE61nMeT8BUZc72DU+Q8Yqf8pz7oIdH6Iad8v6NlfY7zxL0n6/Jzk\n\
zkeY6/gAQSKfp8MXmWzEzpj16dvYW7Nij2SNqFfd4SRFCckdubp9/2mVrGZa\n\
FHKnTo4rVcQk5Y7TIq0r5XRtmXvU9F41dWWdI9vajpiYRyU19rrVSIvHeEMa\n\
57sdYpadx3Hioehc5o96eFq1mInEhMPkMyzLWPk6IeWN1vAcL5vcZHLbok9D\n\
0j2wWX1wRlxUu3NEaROnssV4nf0Fpid95hEvklmM10bjLSWakhkm4aJddeIx\n\
TCxjBkaMdLbYSBKSpUyWH4Slp+X3jpvzEkYqOqomlX7wuE4PigI0v0mbchEf\n\
ZjKZtsQwE+g4v2HwQWIMmZFgqjhSMsM0liguxkpIY/mXJiVeh0uJWOOJjkZ5\n\
T6+l9yRwWVYYaee/jgHh/1WMZ3GxQVxmrXlLWGTCwi9ej31/wsIE4pyGFn9o\n\
LYmxzpWt4pWLU6Vg2JJm1JoaUhRZsiqBPCHcwNLw3ZTN0FSDXsTK44o0ZDeB\n\
uZHV0LPZ4g8hUtk7lj/nXoTxeZHRWMPMynOENrdYWAwGVvFocpkLV8fnVnm2\n\
RdfkEgYFro/JuqUhEhHdIzP4tuYR0q29KGsaQEpNJ/cmnE5x4oNbdraxvsl3\n\
42JWPb7KdiBVLJZMs+HTe5W4nm0j4VCFX98vxf1CK9KKbbhGuH47twK1znp4\n\
fG64W1yw1VtRUl2BCms5qmzilBCmF6KqqhDllQ9RbS1AQ2Mh3M4iNDbko6Yq\n\
PQ6lpQ8s/xo1lSnwOrPRTLqhzZtDkJ6GFoL0HtIKnaQjOryiFCkPvb4sdHrT\n\
0WS7BXftNTRZr6HTeYeg/AGG2lNIS6Sg338PjzzX8ch7HQPNtzDxKINbDWaH\n\
ivFkqAjBsWIeS7E2V03QnoVBz3kMN53DVPsXGPJ8iMf2v8Oo5wNMtHyMfpvI\n\
T/8Mga6TmBTtx60fYqrlHUzTWej9DIs9n3E7wmLPaaxNfE3XEwiNXsFuiCB7\n\
zcZaYVs4VQTnWwTnu5y8EJBeSfeFdK3Rt7+IpIZMYNSZ4Jquu36VdWjTctRb\n\
Pg279SSG1n+svqdlK7a7pZhIYFjXxALdxwkwFzgs9r2TrnjFe2gaxGOxeVnI\n\
CYnmw2xiSXSf0ruRtb7l7/ZlwwL3KryYMqD+hdbTLOA+nt+bOxT07jKZ1pDd\n\
ZfGa0thfiJheEW+eXqFyGgf5WQdnMMLB/fsMrvDm5pChW1SwL0afkvyw/P9b\n\
RGOsIFYJ7Lf19HTYQgMmDEkiSRGJjAM45rme33h+xJzVllxiiSUz2PtK0PuT\n\
I/bU7ElP6+B5qIm6ojDvH97Vn5qa0MzTK16/Nk1DZWY5rhtSXKSq08Br0Yb2\n\
Jj5GVP/7OiH4dAawhG+miRh/yksQwp2nkMpgv4pXnpOW0lhXJ7SrXfewRMi9\n\
ssUR+t7e0RhYn6Qj/pZef2TE6ozuSco2Eq0IyiLiytQdy68pcn/OfcNTy8+5\n\
REkMoRBoP8iR+yoPwhb3baML6J9awgihfOvwHHqnKHqfW4SnbxL3q3uQ4yCU\n\
9/bjWoEPZ76VgyhEX8KtIg/Of1uHM/drcL/UhWu5dkJ2K77JtRLKW/FFagUu\n\
E7I/KKhGZik9zyrGvYflyKuqQb3bDpfXgXqXlZC9ApU1hkVUWPYQuYUZyCtM\n\
R1lFFqy2XIrWc+EklHc3PkS9LQMN1jQ469LgqkuF055K7+/BVnEdDVV30Fyf\n\
SpF7OnqaM7nsqNubhtaG2+j23CdoJ1j3p6K/+S69v4ke9w20U/Te1XCFPruF\n\
sa4UTPSkYrwnjfd7Lc+U8yKCxdFMjLd/jUHvZYz4LmCq6xJGvCfRX/8LDDjf\n\
wVjThwTxp7gXYbr1fcyKcqS6/5ui9vcR7D5NR4wq/Zgg/10s9IhJ1lex+Pg0\n\
lvs+w/YiQfe6g6FdROt7K+VyYXswj6L4CraGxBrHXTF1SCzrEt1lHLEXcyTP\n\
5Uda+9iWP579oUQVrCs/iAN4n0L7JCNSZ79I9SDs9cjIPJ6R/TWju9iS/Ibx\n\
fadfWL3b3TzmWoTsEv4J2Hd5RbAA7v1hEZ/vT2olSfRPUmC+b+SovzPAnHuL\n\
ZTESNyLI7ATPmeC4PGhkJvgwiMerCUQvjOlDRodwvOoONmBc3/a1bZ4qEQ7e\n\
sQA9fA5ReDo7FJrB6tNpnj9kJDzCmtUOKZ/IjM0qOyFRXxpDSbEmWYtn+qDr\n\
MN9IgnisDPUhPU8dPu/OPPcuetoEXw/FqESK2iMfuSg48Xc1EMv0Q4I5/SAU\n\
QrzRpJYQ1qSmDZyI06bexew+MBINSTFKUf9Gj/YZ8P8A+rSJ8IkSDO5NAs3j\n\
ohSAcnC+H/pjaAEB/UmsBd5iN8eM+loiYYVAfEVpAW1cnTZiKC6sfmknIvOQ\n\
rBPCbnhQL+8NpjCyDDLP/d8ahs6ONHVEp5qgg+nldaaH5eebHPxPL65JWgiu\n\
YJSC/96pZXSMi4rVZQzNLqJ1NIDRmUVMETU4H08RNXQj0ybooQd3yltxs8jH\n\
LWvXiRY+T7XhsxQK7stcSK9048ZDBy6n1RA11HDQf/Hbcpy8nkuUUE7vK3A7\n\
uxjfZBTgfi4F9zWiIrUO7mYb6pxVTAu19hJUVhXQv6SyilzLv0JRcQby81JQ\n\
VJSCsrJU2GopinflwduQBZc9nejgARqt9+EmamisvYeGmntECVkU+eeg3ZWG\n\
DpfIT6ejt4VUQfN9tDfeYjPHX3cVfutldDVeRZ/3Nnop8h/pSMFYdyqmetMx\n\
N5LDK96Xp4ow2XMTA00X0O/5DVHCZYy1foEe2y/QVfXvMOz+AJOtZzHS9DFH\n\
/zPt5zDXcw6znacwZP+33Ko213mSzikE2j4gShAlSxcp4v+EaOE8thYF9FfT\n\
NR+bi7lEDWVs5mwFs4gKSrD3tJpXvnNjAjcfiJx1A0f9+/ysRmC0bBg+pMG/\n\
iQpaDP+Gx0XQ1xJNvcfKw9nptmiU8FrLDOwNcZzfL1ICItpnRhD7gX2KCaR5\n\
82Z/VFDBBPs1iao01eg/nlWODjPAK21skVahpA8rNRIHfHY2JhCa78D6Uq++\n\
Ad6oPl1UIfwSJ321RIEKumOWIh06EPejA/ntiM3AIl8gM9OmuabHYkTwjPbR\n\
u3+/b3IEQ36yngAwQnX6TfoAVAPcLeaeNK0EKU5rO4gsQZJWUVKM4D1Oh30V\n\
m++ZGxUiWIC/IRLZvAFedSQkRETuUUlofZmBnhLgkF5aRcnmBoQo1D+uo77o\n\
PH4jhkr89ocwDYswdxfUxXDmGfWZHaKdHWMqUCSax+toTrE7J4X3VZgufPSQ\n\
bDhmRye0a4B2gmbS7/PdAXN/9vSlNaaJo1prslpFcFoHbrk50gDy+bVNrksV\n\
BUki1g+JVDABuwDxIT4rHOMLIBcdaMKtHxHxPsX4Q9OLmJxbgLN7Apn2XuTW\n\
96LA1YP7lW24nt+Ea4UefFPk4n5j4cinljlxK8+OCwTiN/NsuFdgxbk7Bfjo\n\
Wg4uPCjC1xnFuEHx/f2HJbiXVYA7WfnIKipg58bTbKVTDbenglO/1bUFqLXl\n\
o6IqG8Wl6SgqSEFxwQNUVaTBVpOGyrJ7BN5pcNeJk8pg7rKmoInAvLk+Hb7G\n\
NLZtOjwpaHfeR1PtNXQIAK//mu6vosV+hWL6r9DbdAtDrfcw1HYHM/25CI4W\n\
Yn68DEvjJTzwZ8R/A48aP0O/6wsCcornfXR1n0Bn9U/QWvJ/ot/+M9lf3HIa\n\
I65fYrr9LGa7z1EML7a3v8MxvrBwZv3vY6H3cyzzyoGzWCIA35zL5WKirfls\n\
bATSKXavYFDfnMsU8b74q7ZSIcrKl0o43ueOMgZwG4O3KEp69axB7ybzyZay\n\
48pyV2dXywD7TFcThnOdkag47QmHce4fYBgfEmVCDOOd/GcQjcgE4xzMj3J5\n\
0YT04LkIdSpBoHmChuYqGyybDabj9Xh+Rp8nJzvKjoXVm740g/ruHHY3prA2\n\
34bQQpdaVMNTqE2TJOKN/TSRJnxImxiXoAP6asRHYV69Hq2bi09VAlmiu5Es\n\
Fu3GsuXYVMIU3o12NArvVYfacS3JG7Jos39kK/Lv6aj+3Byjx+olOxzWS2ZK\n\
8hq9ZAYcH9LhOGqxjDYuInyHgBaSaxVAjMBxWnrWNIs67qDKn8MHtYodN+0B\n\
Vp3Bslc4UXfojQXBf3lQmvX3dEPGKeD67Sj0jk6uioKfdUZrcV5Jaz5BB3CZ\n\
ZH0p60gP89Z3EY2vSBzXcq8Sw6VHw878vuHD70d0FSQZkbrRR6xh/U6YAb8X\n\
VmKqp2P3DLteazQT6L6lXJzz7NUL10aE6iJkF2WowsmZW11nRB8gRB8NhjBK\n\
iN9LKN87JUaMrmJgZgnN/TPon5rDWGABjs4xPKCQPd3WjUJ3L+6UtXE/cVpV\n\
E64Twp9LteJOoQOpJQ24lFaNG7l1uPWwBieu5eLXdwtwObUI174txDeZRbiV\n\
XYibmQW4lfUQdzJzkZaTg8raEjgayuF2V6K5qYKuFWhyl8PZUAK7jRC/Kgu2\n\
qkzU1WaisvQ+3afCaUuj8DyVQvYMQni6UsjutRGi1z2AryEFbY0P0E4o3+lN\n\
QXPdDUL4G+j23EOP5w4eee9gkNB9pEuE5tl4MpDDewMEss8O5GO04y76PJcJ\n\
4S/Q9QIG6Dyu/xSPHB/ReR999b9EW8m/RVf1jzHWdAqjTScx4v4lIfx5TPk/\n\
xojzZxSun5QmvVd0GZwmhL+MoAjRez8jVM/GHiH11nw+nk/fxc5SPraXixnh\n\
t+ZzsbtSzkU+28slPCtUODyvnrkJ2a0csguUF01kr8XadbWv9xX3Agub5iWB\n\
vSlu31X7BHSA54FAcsxbvML4xwzxAuj7xXoCjtX7jYoeEZcT0Mv4fJg5Qiyh\n\
EYtnvpOx+phu3kyJq0y1Sjv+LW2ekNFp8MLUaryvXB297XiWa02NgUIa+ku7\n\
nge/zQkLZydAMf0UU4Dm7JhqTJNMwyS0syxayRJ1zI7eNGlY69tRkb45ql9l\n\
B2dtLWCJLlkNW0oZNgNuW20YVqtpwsbDybGiuiUfEe3LEtXkGNG+nuW16K1n\n\
MSaMRpWlxukiQZ8yHbmc0hLehpYIbWuNmhRnLCrjfHB4iC93WcqmA2N9vCW8\n\
tyxebzA4opPIoe8ljAQtyWuK75MO2kvD3WjJgi/+HtpSYtNUUXWYJDjifyvC\n\
7NFY5T+QMzjmFzQhyluZClQ3AlPFjk4VFmNW9L5ih31LNFvIdmO5i2YvvFpU\n\
pwdFFoejNELkHKIdraCU2OEMM4YwcERfmmCHKWXoCIYQhs7A7CpGOZsb4thf\n\
+Px9dKaXVtE1KmaIzmAyuMS9auW+IaTZelDo6kVeQxdvJbie7+Iy0F+n2bgE\n\
NL1SDAm14atsK65mVeP0jXx8lV6MaxT/384uwdfpBbh0Pwdfp+UiNbcQKQ8L\n\
cTs9Gw+yspBTmI3CkoeosxfDQ8zgI03Q0VKNtuZKtHiL4XPnw92QC7c9E02i\n\
9NOeBac1HU31GehsykW7O4tLP3uas9DTkomW+vvcWvzIl4ne1gz0eEW/WRrG\n\
urMx8SgL033ZxAyZmH6cQ/F/FjGC8P2vExtcRWv1x/BX/go9DZ8xOzxuOIPu\n\
uo/RWftL9NT9EgPOd9Fr+ym6Kv8KfY6fY8j1HjGC0ACfY5RYYtT995hu/QCT\n\
3l8g0HkKi/0XSAOcRbD7DEJjd7H3VGygrMD69ANszmdhZzmfmCGdy0C3iRWE\n\
l7+zVMievzB6hKG+H7JzKldqAK7MYQMngUP/BMkERuo23qCAJKOlQMD9rmwa\n\
o2sch/hHVMjfL5OwPORzhL8mCEXsKRZLZ3QWOG628NW9GjOkWs7CyEDlb+l5\n\
vD4yVEvUSl9/NjxRK5iAk7WCArQcrV5+Y4nT/f2FKH8/HuYeM7N5r6B9ezWs\n\
R/j3dKLQR0ZwjzCeiU3D2szQsKBeboqP3CGfHBHo62PlOMb/HfOFwsE7SXfq\n\
o3rJVH+Bsnd0d8bcU3bQCmJLeI1Pklbjo2O62kepD5/bitfvZHlPknmgkH59\n\
8YI9HLnDJkw3CGAyuglemveRGaWesdwcLvX8gUD2wwLZ42OIgv8nqhqTr4Yk\n\
sOs52qTYho5cULygDJ2XhqEjugFeJjC2H9bD/ZCO67thhr0q49nd53A/Xg2K\n\
MCz6HcOp2Ys1QSI+LLA34FygvSi6MfGARPkjqu6S/jibco6QjPvX8GRFOjzc\n\
ABCk/1OPBkKW99mtFzJAD/3pfc/YHPong5hZXMbo7AIaeiaQ5ehBdl0HgXs3\n\
vin24k5pE48Uul3iQUqZC9cLhNFj5+TtxdRS3C+owt1c4cyX4qvUAlxLzaeQ\n\
Px93KOS/kZaFr1My8M2DNNzNSMf99DRkF2ShuCQX1dZCDvv9JAHamssJ4EvR\n\
1lSILl8xmt258Dkfok2UXRKYdzTn4nF7PgY7C9HfnktATsDenIH+tlz0i7r+\n\
7nyu6R/rzME4gfr4o0yM92RgpP0++ppvocd9FW2238Bf8zna6s6gqfQ9tJS8\n\
g9aqD9Be8yG66j6ikP80hfsn0F37c/Q3vEtA/i4e236CfsfP2NQZbvgFJlo+\n\
xKjnHUw2vY8J7zt40nGCAP0igflZLD66QCCeTqBdTiBewGbO5lwGh/sbgW+x\n\
GcwkEC8msC/mq3DphTMvzBThyHPJZaiGw37eAKYSsGoKkFwBozeUydr+t5WD\n\
4zO58XoFDkf7b1Qkr0X2b1S55BuVgRVV+/sj7PD0SZDnlrKBOAb4BAPg5ZUj\n\
ffH45bTh6mi2/SEF/xLuteurfX2MnKmlTCJ+VK3//oLaOq+he5KRvd0xj41b\n\
1px7c8b2eIwY/4iK2Tc3lymSm8CzZ2JzvJorkQzT9LjIxKwO5VoLmVFlk2T2\n\
7TWYF987woh+OCJXa1TOyNh/XftWFOQbS4UPnBR3KAaIa96PuUYzOUZnWJIO\n\
4of1WvxYnvsRHZt1n0cWzph9Hlmvb67Pl+NCExnDTV6PuJd+z+8LLD8SIx8r\n\
uoLf/FAA9A9iVFrWiNfjURieFDNEJ9BO1uFbNHPtspdjOvtGxC2K3HdVXH6I\n\
g3JzvaUyb6K7sOR0n71DWnXNjnTn32NMFj6MwGAxz00M9xH3IsoOrj7nhizh\n\
wQggHgos8z4wMZn/0fgCxuaWeCfYgADkuWUEFpbgfjSKb6vakFXXiQpvL+6W\n\
tSClvAU5da24J9a4PHRQpO1ENh2RLs2tqkd2RR3XSApAvpdTxA77tZQsXL6T\n\
ii/vPMC1+6m4nZKGWykpuJ+WgrSMVKRnpaK4OBPlZZmwVeXA01AAt+Mhmpz5\n\
aPPmo51Oj6+IIux01NfcJaDO4MLINmcammpvo7clHUMdeRjuzMVQdw76/WkU\n\
Qafikfc2uhqvo81xBb7a8/BWnYW3/FN4S0+hqfw0fFWn0Fx5Ek1lH9B5F60V\n\
76KtmiJr+wn0uz7levf++l9RlP0+V89M+E9hrOljDNj/loD4l8p/+QdM+wmI\n\
By5htvM0gj3n8CyQh92nIi2ag+czd7E+dZf9l/WZ+9iYy8bWknDWCYZFlQcB\n\
tPBfRCQtdivurZYoMLZKL0btY/GJvym8dItzouElMprnwkWTwlBvMwJu1be7\n\
91iVM44JNJUR9BEZYPN0tlG+l9WPYwzcwuV58axOgHWcZrTsa7M8VYU7v05K\n\
QH4pBu1/J4f4vIhwYaTTok9pDsjamUQ1uSesdkZ29GoVkKbqGdVrlWiugNSG\n\
6+tz2cxmSqxOq1jpVe17GxtLWGaQDlp062YtZuHMtloNmaAwVYdhWeuYaHpk\n\
bHF5yxxqmzexxGmh9k5kqB35nePKiF+DNljf3G0VUTCjX+k7CWERuGm8g7nh\n\
SlsGz1McDqvKmYhMKcfgpgXwXAqphdpa9QwH21FjfGQxjdaxuyfmd9K/61Xx\n\
5AfmMvvvTGX2Pwob56YV12tDPX+sR9ucYa3So+3DEWZKzIFtbKQY3U3xpsei\n\
PFKPv5NVrC0rHtfMxTIUd0vgTjTcdQbwfb0KcicWdkf2MyWYG6IEXktIf1u9\n\
3eFqGAHlYtuvME9EUpVhPfScIF0mUgWcj86tYGBqEW2jorx4dHbJ8nN0TcwR\n\
tM9ibGYB0wsL8D4eRWp1Kx7aO+Fo7UcxxdoPCNZFkeTNfAHhLqSV1SNHwHml\n\
HSlFNQTtdcij821hOa5/m48v72Xhq/sZuPEgA9cpvr52+y6+vnMHN+/dw827\n\
d5FFkJ6Z9QAZGXdRVPAAhXl3kZ15E5WlKbDXpKG27B7sVQ9gLb8NW8UtgnZh\n\
oaeiyXYXjRVfw1NzA17rDTRbr6PdeQvuqkuwF52Fp+ILuMvOoqH4FLxln9H9\n\
GdTnfYj6wl+hofB9uIp+hebyk/BXnYCv7D0676C9+j10Wz/AsPcsHYL1+vcw\n\
0nIKI95TGG05iTHPh+iz/hi91X+BCYqtZzvPYKHvMp60nkCg+zMF51ZsBHMI\n\
ym8SpD+geDoPG08y6GQSzBcQpFNcvVjERsm2aFFar+OpyHtPq3iQz56A81Ad\n\
Xj3zcDD9UjbIisE7L/VSdm20vulqHsCjzVdjSH/MHoqCcwLbGYZjDajf8PMx\n\
vdRxTJia9H3e+CU2qGg/x1cVTb+U21QmRTnky0kjyn45o92zc2KJVz8yq717\n\
MZugl8iEGylqJn+CqTxmTk3m3NdHtKnJDYz6qkhGj7a1EW0JvL7dVK3+p8pO\n\
EeJZ1LeIv9bm+ke9njJyxI8O46tGIbvJQTmM8KH9Jv/bEjaJTTbThtkqkTP6\n\
2fqWgXasmTxGhaTZP0k6yD+JHtepeqSSwuZzhg9kOxQ1kG3HNJBNR3XundWr\n\
YMzT+jXz5KXJUDkclYgVny4uBjExMSLN9PiDfPW3D/LQf980q/mNNqtZw/6k\n\
yMYqLX7Xe2Tf6I9U32yC2akJ+6rJwIn1LJbRE+t7CTGe/TfilUv0Y02WZmoq\n\
1xMAYSQlxaBBUgtmkpKWENv98UxJiSQcTIJCZYGNqp99TWhIW0izeyKsfx5a\n\
JDZ5abY+W0B6kthilAPJ4UKJspNLGEJb6qgJ01ucYg4zirRaIfHzW5ZT/GNz\n\
oU0WJuKIYdRiIoQUJyRMZkWSmETJnBAmYiLEIjdy9U4Say2uoIdYzN8/hYHp\n\
WWYxf/8E0mrbkOfogtXXg7z6NnyT34DsKi/y65qQUuIgFnPg2xIbCqodKLLa\n\
8bDChqziStzOKsKN9ALcSs/F9ZRMXL+fTqJEnBR8c/c+UjLSkJeXQez1ADlZ\n\
95GddQcPHlxF/kNiq6o01BB7FT28jqLca6gpvUmi5A4aa26jofIWXLW34Km9\n\
AVvxZVgLLsBWdJ5Y7Rox2VV6fwa1D0+hseQzOIvPwFVyGs3V59FYeILY60O4\n\
iz6At+RDYraPSJx8jNbqEyRIfoUu2wfoazyFfvcnGG76HEOujzDoOcGzh0aa\n\
TpEwoeeuX6K/7ifMXoHuc7xIUqwbeB7IxPZyFbFYDkITt/B8Ng2b83lYnyZh\n\
Mius/ly2+EXZj6jjFDWc++t27JMY2V2pktY/XYX9/+KZhwc7vxSFPiL3e4RZ\n\
6+W2rNUUxZVKn5jK9rlAUzRk9cqurENGkaYmSDiTO6UYaVSaQsmKnEZ0shKk\n\
x37VM5v0hgT3vDTIK5Ff4xV5zegNWnoRkFIl+sIwwVozirMCEdokyRg0x5S1\n\
wPd6XX9iZF0/c1WC4qqdnbAxohr3bP97NWeFDyWin4lXWmQ7bDyR+GWqI0so\n\
l4iGAekhHTKJFJPHlKhspBhF/+CegOg0AVNZ2JRpjcZ2Yk6iMzYW6Lu/oA0j\n\
EkS2nhgpSHZ3TUNItbZf0+whWTokBz+YyvlVhX9CeEZAzp+LnDoab8iW8IL/\n\
sI6tBNWxJSTK3t4WrxlIjDEPgv0mThkcwGmvLH+gVRgp8hLv4vSMQpgLpQqR\n\
Ip7FhSmfNxoX/pbbxXhohHz/xqBM7adlEWokQf1ZeH4iwuoq1q2uMG6KtroU\n\
NyVqVhdLKCmX4lU2Ys3URqZayjizbJhc+6am4ujuYY2gFCEx+Si1dFRxjTYY\n\
b4vHC61rvKTzkHmM0WnTM3nELxdEtEhSao7dsRDJKTk3NUjPWU4REUmnTF57\n\
xheYkGY4Lz2Nxq4BIqQ5LD5dRvfIFKqb+5BZ40dNUzeqvV3ItTUhvcqNbysa\n\
kFpsR2ZJHbJLbfi2mCRVZQ2Kq60orKohgqpGysMiXLmbjm/upyE1O5tdsqKy\n\
QpSXFyI9IwU5D1OQn5+Cb1O/Rnb6dZQV3UNuxnWUF9xGbvoVZKVeQn7mZVQW\n\
XEPZw8sozbyA2sJLsJVcofuzKM/+HNV5n6O+jEiJiKix7DyseZ/A9pBIqOY3\n\
cJZ9Ck/ZJ+huvIzmqtNwF3+E1ppP4Sp+D97S99BTfxYDXlGhdA4D7s+JjE6j\n\
r/4ku2SDrpMYdJ/iXrMRz0eY8H2K2UdXMN15DpO+D7HQfwXP5nJJGlXj2ZNc\n\
hCYfYGMuh8gnnyRVCp6TlBKSaosk1KaoP53PpvtCbifef9ZA8quKnbK9lUp2\n\
1oRb9vK5WDNMdCTsiE0fsY9iItJTL1VrgOCoOF5KdtRoJmP91KuGCwlrTOWj\n\
93VGkjoqSdxqiorbhcXI091RJh9RcfSSXybjdd6ZUmJpht/NmO2wN4JlDHVk\n\
aKNYuYgkrYksQiAt6QKJCGdvh48USEfN2WVzLen2quWYkV2OZ60kKGNzc9kS\n\
b3ygrS8OW1oP7v+KLic9hvCGXvPIOvbnwkuH5C8IKzQ1xlPHReaf5faDNcsR\n\
fnZEmWJhVaixDK8D087JeqL5uU4nxv3GsRiJCm22RPTmmvDZpbGmWCfolUa6\n\
aNozMs4xV1Lu8Wih/bdi5KCTDqpC+k9i1K7+sapgfWOWSm9eH9fFD7PJP9VZ\n\
wdiR9rZuoRXo6uSYeHZY9SeIL8tfK3Ya/44ESIJezyrWILDDJvLaibp8kXMn\n\
Eky9ZfvafNR9S4KJHfaNstZE09SJHe0rJqIw+hGSjMLWeDNRiHeb/LplPOMN\n\
Ozxk1fI3WCUWEYaayJWIqiQxpG5JzBKi5+J+YFokqpcxRswgEtiTwWX0Ti2i\n\
d3oB48FFDEzNESvMYioYRHBpEWOzAVQ09SK7rg2lrk7UeDpR5PAho9KJtIp6\n\
ZJTVszxJpZNdakVJjZ3ZoLi6BkVVVcgtLkH6wwLcThVGWyoepJMkyczA9du3\n\
kJZxnzsSinLuo7woBbUVqSjIvomq0rsoL/wGVUU3UZ5/jc5XKM/7khjhEmoK\n\
LxMbfAkHMUJjxVdoKLuExvIvYS8+i5bay2iqvghPxTligy9gzzsBa877JFFO\n\
EgN8DEfee/BVn0GH7Twei04E7yU6vyEW+IxzJT32D+mIetX3MeAiRvB+QtLk\n\
U0y2ncNM95fcoTDh+wRLg7cI3cuJCWzECIUIzWTGYSNYbPkh1mfSsRHIIiIo\n\
oK8UYnNJXAuYGLZJgUgisMo8No8HquTxQS+euSUBbDbzjsmXvH9eOWytKk39\n\
Uls/vKPaiLXFlToTPDZ0iZaqJqxPNFecSiGiXDZR79TJGevvdse0uiJJCyw4\n\
tLQIXw8JPjhkWn3AyWnmhNkEU8VRGA+EuWRqkUF46WkCs4Cp/DSWrIiPISv0\n\
HoPwVEh0ekSrPZI/LkZYi67i7W31T0qO+K1hg7DlrzN2H0TWKUUnslU2xRBC\n\
YQZc9ILMiO0IBq8cPLguthN3wKacddndoOmUXVPWO16pFfP0CHrCKiVyPaZs\n\
Rz5gIY65XlVz2IxSVfP8iLBdCLEcNtmKnMAU8lpOKxJTi1if/HMB4MwAyRHc\n\
oasSS7LGGSY5YfBLnD44NXLQkfZYiRcpQyw8XvW4Ti2W8PblLHGbEOMDnp56\n\
FEanhdYsl8SvcsTe6uoKBgYG+Cq++V8c2Pi8pldWySa5V3ItT5JK/rzU93qy\n\
17b7Ms4oqk1kZuKWDOFn7eq9FnLEHffMscO2s28irF2tT1rxkyFrjppT+VKp\n\
WPTpq1tMTOy5afTE/lkSk9MRLqgKrq7zmeLE/rociPR8A7OLq0xKJFniMDm/\n\
avkjjM8RN00HMSBaoReWiasW8GhiBoOTs5hbWMDYTADeR8Mobuik04Gali5U\n\
e9qQU+1GWkk9soibCmsb8LDazoolq7QaOcWVxE2V9GeurrNa/hVsddUoqihB\n\
RnYmiksKkJmdipysByggpVLw8AHKClNRUfSAlMnXyMv8mlTKV6ROrqP04VXm\n\
pdLcyyjJ/DWq8i/CVvwVagsuwlH6Jcozz6A2/xxqcj6Bt+oCcdJv0FhyFk1V\n\
50mlnGG10mr9At7y03jkvMKju/s9X9H1Eh43nke34xN01X3Mttljx4foaziB\n\
R/b36PoBRlo+w3TXZUy1XyA+OodZul8Zz8DWcg0dK9ZInawHCrGxVE60VESk\n\
lIX1J5mkSvKJjIqYkKRyKWA1I3L0e6RGtpdKsL1cwQkfUVglxni/2CBiet4s\n\
REqz+Gv+vFm6Z5vKHttR2zS1uUc7vFZtp5t7nNtMQoUnooq/f7sinfOaRQof\n\
mdyRfPRDuX5hX5VL7U+rdZ2dbH6JBoq9ZdHL4ZXZIY2bmKc04aJfpYCxxJsy\n\
QDMW2VGXHGmm0T9rRuMz82iMeHPWx3IAmYUvY1s2rWiIIqyYPLat91ZELeIx\n\
imYPttieiiLbZ8Fw3ovMGEX+uCI9LuI15oBvbxt9HZGmG30WH+Ox3nEdOQUp\n\
cvlzCGZjbS1W8VaSXrwVK4OUeFAGycj/q4Vve7H7qBP0Mlz+NMHkuplWPMTa\n\
AZ2oN/Ulm8d6q/xSsp5LUh9odV48JCnhe/r5zDpJlOm+0njNnFX6n3XWizMq\n\
CSLH9PGgpdf/sSaRIjv8WAn9Xgy7LF0RkmmHnP7ZUXF3/HtY7M2bN8xgbrcL\n\
Q0MD9D/ntc5isrkzMhkUMteWxcsFRGtcnxA2xEOlXlS7YMzeD1Zaxpq5Y+KH\n\
OLnD7BPW+MdDORI1ktqxXOQKM6GSnqxonX7rWNvcwNrGBidypDJaxXiAWEcw\n\
DzHRwMwCqaMgEVSQ+7kfExMNTE4jQEw0txhE38gk6n2PSSV1oMzZRseP0vom\n\
FNs9yLc5kVvpQFaJZKHskirklFayZyZUUmpuPq7fS+Xy3qraYlRXF6K6Mp8U\n\
US4qizOIie4iJ/0bPMy8iaz715D14Evkpl1GfsaXsJbcpPM1agquoL7sGrHP\n\
NRR/ewYVuWdRnHoK1rzPUZN9Cra8M3CWnkdLzSW0119FR8N19DXdQZfzGuy5\n\
76I+7300l59Cu+0sOu3n0Gn9lM5pdNZ+ROcDdHOJ7wkMuD/FaNN5jPkvYNR/\n\
FpPtlxAceECsU4KtJRs2FmoQms7BOikjsTl0bU7uj14PZBMbESvNl9A1n04u\n\
S6RdUbL7TJQZ2FgWMQuJgRtPxbFif8NJCsUpmUhJJHltYb8sjIL0MXqmfW7i\n\
yv5Yn5qlp6mjYbntQcD9mJHI0bjouCrb1TqvxxThCZ01gK1ABla7fom1/s/w\n\
Yt1r0kpTQj7NxDEDJcm8kOQe0z1LrJlkI42jOvekwSYJiJdIz5l2BWk8tGCq\n\
LkuM7N3QyUfO2dNzOKqMN5aqitQ/JvfN1LYhtv+I8t+NjcXvqUozaswUlWnF\n\
ZFEqaVvtoYgzbLdwVXTkoJIEc/ZGiqujGnvsmBWR7rXpZKLXm0W2c+xFtHNY\n\
YnR8x5rWqsiEqOKIvgMoSVc/2uIHPskxBjG9FtooxsxWVZQQizkOaTObXlnC\n\
S81+KF7/ZQxZlByjWvhP9Ry/RQ3ukCl+C7d+MyfoyX+TrGFCENXHv+XczaEI\n\
MSMoYHV1NUzMxHbYCPeTlMO2anSNiIWjBidIhy1ZTnbdMvrHjYlO+zyQW5sR\n\
EnsJnXwWplpUXx8zBKsWZgWjf0SnDfkVy8ecXtFy/jPLa5hdWcPy2nOsb29y\n\
umV8YYXFiihAngouc5tfPwmXvqkARokqxmbF2L9ZEi7TmAkGsLAsZjsF0NY3\n\
DCuJlnJXG6pcPtR6/EQVLuRUkmAptxFl1CG31Mp0UVBeRVRRjYyHBbh65z5u\n\
3HuA1Iw0FBRlwWEvhrOhGHW1OagsS0c5iRZ7dTbqKjNQW3oPZblfo7LwOly1\n\
9+Ctuw9P7V14bXfgqrmBmrwLcBRfJOq4jCbrVRIrl+Ep+4IEykWiiGvo8d7C\n\
I/ct+GsvwllCoibz56jLfgdNlafRYf8CbbWfobXmJNqtp0iwnCLKOMXtfQPu\n\
s0QPlzDq+wLj/oskWK5jaTwHG8t12KQgfu1JIdFEPkJ03VioJJoQm0bziCby\n\
8YxpoljShaCKeeGW1WFvvQHbRBNbS2WyWo0r1ar0XP+LZw10dYVTxZZIq7Sx\n\
m8az+rY0tdKmdsV1KsWSpJRKnzLRBng8tmztkxl9OaZDK0tjoRKn8igvROWw\n\
+L6c10e/Y/sxNiZuYKn5L4gofo79UL02p0/KEE2oMClMRWkVrSxNe6ZK1SRd\n\
JJrpQsvFyIZvrSJZr0Y2VSRHdn0nhNUh7+ys/CgGsBuztOXaeJGoj6UrDpA2\n\
DACHNf/MNKxJ7+6OqFLTqpGFeghzy9RYj8QYvHBIExN6FYDGFbIieXNzFQsL\n\
M1henjOl81XZmokZhFumsYXZKEvUX8M2iPLTo0alcYy1cJYY6XtjVZzgA2M6\n\
iLhqXSFROx3C0i7aHL89zuCr0uNEs5yQh1hCVB+/+t9iFKZpI55i1YX9cXiK\n\
PU6lUGItmo5ayPBWlPxQtWfmRAwphbBEzOHv87y0GmeZj0ngBsN4zeti+WAi\n\
jEQeDiWIYmlTLWBQy+u4s/Cg1H3IWGInv5Eco2dFH/gdvmZoR1aVxRsK438I\n\
y9SLLL2kkOeKQkh1LIXomcjUC8URwjgpjsHAIsbECdKZW8TIbBDdE0QbM3MY\n\
CcxheCaAwekZTAYCWCQKeRpaImqZhre7D9WuVqIPUh2kOErsThTV1iOP6COr\n\
pBqZhZV4WFqFCpsN9a56VNqqUFxRjDSij+ycVFRWPuS+ldKiNFirstFoy0Wz\n\
qwh+bxFaRJe4NZ1oIw0tYri3PQ3NRCFNRB/NdXfi4Hfctvx36HTeRYfzNjoa\n\
b8Jv+wre6st0LnBKpt3xFRqLPyFWOYNW63l0N3xJwuMGehqvwF99Gr7yD9FG\n\
DNLj+ByPG8+h3/05J+lHfMQerVcQHEwnMVGNrZV6YoIaPJ3JxcpkJrFFAbFF\n\
CTFIkbyfK2EmEWzxLJiHZ3MFLDa2V2qwt2bH1rJoZxHMUcE9htsr5Wx7CcYQ\n\
eRkWGc/cxB6itrkVLznlIhLwbcL+8gvPeksuEX25pchjWxv71MvjQPpUjbKc\n\
1U1HLRWVpCEFhjbANar7W11ljbNbaZQxIg4nNsZvYmcui/55PYIsjjBZJJmz\n\
9SY+mdZGwb5Rnpaet1dCQ3UQJoUTxW5Q6x6MoIl4bdxrrDGu3zv4w5jLHat8\n\
THv27FmQPSyhLL5vyIi57Nn8TBs7qO8QMpHMEWgr6+JMd9rqaZnMTz6w2VDP\n\
qrC2+J4x3gn0P2IJExNDCAQmw9MwRlV04kHp/WMHSY7D+kCQ6FKwLdM2IEt4\n\
B6KxhVozqtT0KWNwCLPJnqE4ODOjDKu3TeaU2Bchmg//sWCR/9VIniSa5YRm\n\
RUnaOG6SFZr99MODWORGDBZhDXI4Bouw6PjzAxkjdBBjWBLCkiTsQa0ZKfwQ\n\
c8WO5Isdufs0PiqPzy2NxtBYqTdCWlEXt8SYVgOpxvTQljFKXKXow4mDnyVq\n\
0kN3rHZU280R3sEtSow5p08nQNJjcnGFueO54A56P7WwHEcEsWD5a96AOh5Y\n\
YOroI+rom5Sp/LG5OQxMzRC9zGBueQFP6f+uwWX6zvAYmrr6YG/qQI3bjyqn\n\
B8U2B7JLSWkUVCKjsJyURyWq7XWob7TD7bHD0VgDa20xKityUVyYjqL8NFSU\n\
ZsJakYH6WrpWpqGhJgVuWzoaa8UwwUz4GjLQRLTRLLaZWm/BW3sdzdYb8NZc\n\
g7PiIt1/BTdd3eUX4CYFIlIm0qS6ysMF+7w3SIVcRVfDJVIbZ9Fc9hEd4o3a\n\
k3jkOofBpot0LmPE/xWme+7whtPnC3ZsLNmxFqzC06kirIxnk+ogrggU03vi\n\
kKl8rAcFX1QRX1QSXxTR+yLmD6Ey9kIO5oxN4pCt5SriCys9ryYVQkpjw6OU\n\
hkeE1htu0VDAeXuf5A0ih5dbiii22uT9dptF9jQeVdupe3gayGsxFFDNj3qt\n\
zKnXTBpiB6ko5KI7LtgKS40kqOZFWdXl0mq+5GDA3TFNSZiyIEZp1xHdfpKF\n\
YKZUPic+AvExpMQLdqB+Z3Ojsd5hR29qTDQDum4txZoPHrncQZsMuLm5YjHK\n\
vCJsqp3w5UCmMq/wpIhpamAETyTrVpTFWG0qSeWAQmLJHWq9w04o8ho9X0or\n\
B4vnLEsotCA4Q6qUhBhsccg0PEobKqu62iP7H41hsgdWgsVxGuOg0i/jGdcU\n\
83ySXTOlhFUYH4uxxdQkQ6QtpaSIfGfOdJAk+SO9Buy1KdGhX2UeP9GcA9Gr\n\
kZOVkAn/TI4pj0ib/BOT5jHlSmK1vPxIt8OYqJiUtGSJeb4VZ/STfjcLhfZf\n\
qqtkoThxx72ZwvWS6Xn6ZdqgxDWVoReulthUIchoRdhQu7va2BQj3WFaVaS1\n\
4Ct+SdIbXsKIKEl3u7Zgqh2ONxwuc6mxVDcfcb2Y4Jv50LrinFUsr0vOWaZn\n\
s/MrTDZEO5gMivz8EsbngqRPZvFobAojM7N0ZjD8hM70NNtdS6RXVol4Foh4\n\
BkbH4PZ3wdHkg83j4dXaBdVWtriKKquQW1SC/LJSlFZWoN5J5FNfhUZ7KdyN\n\
as6hNR+1laRZCu6iMPcbVBTcQW3ZXZQXXIfLloYOdy5aGzPQbL+PxoqbqM2/\n\
hIZS0c5yHtUPPyeyIZKp+QqtjpvodIkNFXfR4xSDTm6iy/015+m95WfhqzrH\n\
efo26zm0W8/gUaOYYPslhpqvYqr7DubHcrA2V0VEY8XabA2WJ4roFOLpdBEJ\n\
lQK6FpBYyWGba32+kjMiz4iQ1oMVdC2jn6smUrHTqcHmMr0PkmARBWL0Xlz3\n\
1r148byFjh/7dH1JZ39DPpMVw+IQ2Yjtbkw6YrE19853iJcu4S1rRCPJRggV\n\
bRitFCfamRB/hVSX/KTWVGnRR5YQRwjB82KjQZ9NmxCDXI6J1yTTgCqR0kg2\n\
VQ3rjpVKcMhSMZls10uGLZFmldY0v2TGfIMvtg8SHbE/O6I+0wTJysoEt6KI\n\
2ePJiOYlbQqKSYTo6Q3+5yQjeguFnHuiSIRdLIu2JFv3uPgndP/KlAzXFwRF\n\
7Sg9rHtYGmGYppHr3lZCFIFs6NNPmCyMzdcRo8bF656R5EjSkxwiIHgR0Ur/\n\
Qo2zskRPK9yxaH2YO0Yf5vGojnolO9SzsBkplvB2FXN5sZb3iFMEI96rejHL\n\
n+nUY2y3Y85IjNHgkizT6zE/fW35R9AWGx1IHDwqMT6CLsS74zHy7VdiCB6e\n\
2HIshuAJo5qESKpRiXSiFi4HS9QLlLkwTGbSV5S2WdnUGhk1bSMsr33N9pKl\n\
ydF6J07LkYiGWTEmSxUo6wJHy9TLCVtbUsRopWA75qR7DN1j+QtJM6uii1JI\n\
mxCml1YwT+/XNzYQWn+OGaKZwdk51jNjgSCmFxa5c1LQS+fgBDqHJ+h5ADNC\n\
49Cz0SfTCCzN4WloEasUYs0uzGJ4bAQ9fb1o7exEg7cJdS43nXoUE808LCKK\n\
qapASUUpCovySdMUoLqyAA5bMTyNpWiozYGNaMZalgZbRSrdp6C29C689nTe\n\
cNHmzERrQzq8tntwlF2Hs/Jr/H+NnUlwm2l63z8DICippZZm3O2ZiWfipezy\n\
IckhZR/ji6vsY8qHXHzPJZVTTjm4crCd2GW7PPbYjl3juHva0+qWImrhaKNE\n\
SWxKJJsUKZKgiIXYF2LfQXBpqsd68jzPu34fXsrpqhffKkhEE/jh//yfZe7G\n\
H8OTO38Kz+99H1bmfgBfPvoB65svZv8nLN3/M3j8f3+fJ18QYr64iVh5+L9g\n\
c+EvIbb4fUgs/yVkN/4OCrF/hP29q6hd7iE2HuCahWbuOuqaHyNeriJOZlC/\n\
fAb7iX+AOumaMqFlFtcdRMsNfMnLMzRtuYqypTvPhBnVr3M2GMqYEJ64j6L8\n\
uEuRr0X4arSEawXXKmd2sbLhTK9VARdUK6cc9lL7ykNZ45DU18cy/EVdz3cI\n\
LVrCpORKi4zjkOaLbnfohcz8Ij5HMTfuksiWhyjYj2opo10TIWJC2iPJWx6J\n\
ylEWsS8Z/xJdEc+r/rgKPpbGqXIU7KvDioCPyOuK6koVbokrhmGD7oB1xigj\n\
eW489icfG3Toikp6N1NPLbrVPwmpYymo6UkFZaZnezo/ecJf8ecs29JHgkq4\n\
K9FgCpdlwjjnah/605Ol53JJn9NDUp1hL2ZTVNdKTg5DmuyRK/spvtuFv2hC\n\
YlFLv/jGIkW0huG8ZGqbePKNd9St2OemHLUs//asbgCuc678rm9oK+bbWoew\n\
7RKeYAV4/8Nxju/zT9ETAFKZYHYoju37czZYplwaxjNgwVeircTMiRY1ZNZH\n\
DHIuaOSookmVwNWk6nzVGUbIF6JPaXCEiwr3Vc9e24SRxkzIkjTN4SFPxW4O\n\
D9TMVS7+H6pRHYZWB2HDrWl/Ipjc7x6YyU0kjgZ4foACiXhUavZCBCOke7bW\n\
hFKrjX9JD5GESqhOLSArEM/T1O0Kh9ZI9WRwpYpF2E7lYAvVTxKVT7pUhHQx\n\
hyuPGCpBo10Jkez3fhdqdRRFiR1YWVuBhRdfwNyTJyhy5jjCNnNnBh48uAUz\n\
Nz6B2zOfwe1bn8ONzymq9jHMkrf/6d/A7Od/A3O3fohbItE/wspTJBGKneVH\n\
P4QnP/kB3L3+J0igv0DR8wfwk6t/AF/85C/g8cwfw6Mbf8hdaJ7d/COu5Se3\n\
htLBXj1D4TP/57C98H1u9J599THS5xZSZx769ae4fYhrDgl0A+rZa1BPfYbU\n\
+QxqKH72d5FAyY9R7FyDTmkG6TNL8OEoG4seFDmjxj0Yd4R3369cg2H5Koxq\n\
12FUvclFNMc94hBF1J6iyCHffoXZ8xWvZdwnFwa5c7BBDAoRoPBdTiX5p+N1\n\
eo9Ss0augNlmEO3QOR1Ki3si0SsqQ2oihPZThSAZSjOxsyT3mBGJyniO9c/0\n\
uyyX0+yUYdE5m0W+ho5vTvKKQ3L60jsHZevaSTkoW9VO2mE2iaMJ7hiPxu3H\n\
CKhEfdeowSM17B0MqpPJYv6JTOapuvpWCzOisdh5G0daFxl9pOprgqlfyvaP\n\
+H0ZOY/J3N/T2IkG08LEsk0YSSTp7tuD+XhdUhbMseHNRV0GE/ZneHmmvYxu\n\
+OhL+DrWk/c43+uSDo4xTX7LoU5c0uMDR30kpwGHdSHkh1p/fOjQGpOssDRJ\n\
MKwl3BW7pPKcQ32YQazMBy/si3OpqkmFCLlYmXB1PRdMnurxrIiFEEkT/HXU\n\
s7WPxKUvcl1YxFXoHXLJvWwGPGV6urPqYLSICshgyq8SHhFbeNh2S9fK9AqL\n\
kNiAvXwBAtHShbz5ep9+TfP1tvdfoMkxsAHUOx0o1uooRMqwlclBkkRItQzl\n\
Wo0FyatkBtZ3UrCdSEMyl4N4BqmQS0O6kIZSNQ/lehFqjRICoQKtVhEKhSQk\n\
kzFIJFGoLC/A8spzeDx/Fx4/vgPzj+/BvbszMPfoFrxceghPHlyFa//013B/\n\
9iN48fhzmL9H3dp/DC+/uIqi5BP4cuEjeD7397Dwk7+GLx//b7h77Y/g7qd/\n\
CGvPfghbzz9CHPw5LNz5E1h78gNEwF/BK+rmvvJDSODK73wO5fgM1HN3oVd9\n\
hmsB2pV5aJXnoFG4ix//M7Cf+hzq6euwn/wEyq8/gvLOP0A18SNooSjpVu7g\n\
uokf/zehlUUBU7qBCBDm/bgzhypkVsS9CAv48T+szSAWHiICFuG4/xzXopAk\n\
g0WOeZEsEbJjU2xHL8WWcIBSRTQiI3NlnYCAi6UIPkaRALJtL7dgTyAJEmJY\n\
nvBTfirHYssU37AZuMQyhv0cWTjpT8NCEEgxY4kSEQDzTPLvtA6NaQrIVi5R\n\
vzI50VX1qtPYG922pTLZaazqqKHE79hcP+lTCI5KyKAhIoxz12w+24cZ9Csy\n\
9bfOvs05JwlkrYqLNzIB2JUFpjrAm7J5K+vL8lzUVD+TKSZ7/TIPojou5mj0\n\
bsayMg9cpSUsQlxDtsNakYSUBjkOTNpWI/w8R6fgsDHqA00oZQPKiGXf+won\n\
L2mr/j1TKRmxU4Ft3fLPfCj6BLs0yn+gx4iDMT+rLf0PdXjL1NRzP+HLE2R5\n\
6/0+7f4cBIocVdjqwjvDVowHgQpbU4RkdaPFDm4ZJgtELunJIXaRCIW1muyW\n\
HOnQVbZzAGlcTS0spmxhobO8+Nr72vMQmmIqyBAZrRoIOhx4v8NVj81Bj3VB\n\
GVepQasJNSRCl3TCqAfVFlXZl7l6nnRBrlyGCpKhRP3lckXYQiosb+3CyjaK\n\
gO0YkiIGyWwaskiHQjkLpUoWX6480qEE7RatPNRqSI5CAhKJDYjHVmHj5Rfw\n\
5Yt5eLX2FNbXnsDT+RmYf3gNVp7fgY2Vu7C2dAtWn19HGlyF5fkfcbiKZnus\n\
f/EjeLX4MbyY+1t4hiJh9fHfw9aLT3i2x/rC3yEJPoL86xu4ZqCRfwjNwhx+\n\
+s9DF8VAG7etyiMkwRxfq+fuQzl1E+/9NAS5zf/j/SoUdj5CQHyKt1yHbvku\n\
rlnUAbcQDtc5akXHowZqge4zOGg9YUNEuPCz7MQPazcQCHMIhGcIg2cMhZP+\n\
EkOBtIGAAmmCNQGDkYSBgsLBujy3JgyRMU1WPUVhMM2FGwSFr48SnKv7tYZC\n\
ip2PNOmELO/mdJNg8a3+it0wUlghh5vwlfDdTf9JxoPI4KUE4CP8YU7xH404\n\
OGeqQsK2ehBHUYsxPxV+vMetKH06oaR1glVbP23KEQ+VWKhJT77mqfFOjhmr\n\
dE5b8BYOpjQU2oG5fk22SEgjoFa4RBc4oyuq/tiEzyLL53Vm1hmhKHUuDP6m\n\
XvZW186bfsUyUKXdFb+D0vXeg0CfYpkVbOa3miQszgW2ZrpG3USQZrtnmg0f\n\
n1FsaEHDLrBnQIQ1IUY2M3x9vziedUaTeeHdmwGDptLEc+UPT9lF+FbfFuHa\n\
BzwWMxT8fSsopspPuC5fzZX656/NNEIXdd5znPs1evy2ps7POagTTCAj4HxA\n\
j/+dkKKEju3Lc0zr0iR1hihX5LjZ827G0M+rGXPe1NBr1pjp4l1SJiN6hesj\n\
Hiqi1QrV1YuJJYofR2rRLZzMJdwVP4aijpIT/zlhlkzLKypI1UUCqf3BwYEA\n\
0+9xNQqBqdIWUCpaYOrg+e6wC91BByqNBvsnsbQIVBUrZag2qlCtVyBbzMNG\n\
Igkrr2LwJa6NnV3YSSZhO46AyiQYTMVyCqqVDLQaWXx1M9Bp56GFXw/byPdm\n\
NQm1fVpxKGQ2Ifl6CfJ765DdW4FscgXSqUXYi89DavsBJF7dhfjWLCS27uL+\n\
bUht4dq8CclXM5DcuAGF+B2o5R7BPq5qBkFUJBnyFLrVRWjgfnt/Aarpu3jt\n\
HtQyD6CcvA2F3RmWL7mdq5Db+gTysR9DJXkdaYSyZJ9ywe4j0G5Bfe8qSpjP\n\
kErXYNCYQxI9R+oswqj5CClEnssd6FdnuZhx1HiAtHqCJKI29sgkalnbfyGo\n\
RHY82/PLMmq1xg29XtKXvoNV6ai8lLLlJV0br9E1hMcptWthIjGV6J13lCAC\n\
JZhFYQeLFCa+Pljmvva6SiQkq0ooeHXapzYxMaNBpgJRq7yqTZT6JOCcmMaS\n\
JVNiIvLC3lldolPCDqsB/PilxUWHyXFeSgriDaV7iQYtjUnrxOe8VPC3cW9v\n\
G/r9mhQs54K3+raqEaXy6v1DBe3ssOmJ2JUSIyKydUYTl4sOz56jVmLKlCog\n\
8Y0J9/SgkgCSzKCS4OBwlzsiUBOF4wl9ckBufvgs38TEtiKOrpLKL7ms5QhR\n\
4eQ7ugoxxJrD75JMW3xQNv2vT+R8vbGEyJtvaJvdVY7ygb8chcvVtRjRoa3/\n\
RpsQ70aCN6hphXbYiznz/llaJWm0Stj2P0R4S0S6pnzA4ArGI9l2X3RfOSfV\n\
ilQth2L0FYethArRc8t9+b8KGSE9CuuKxELHwoJVb2LYILaaDRzM8v4dPo7w\n\
r+1BvdtB0dKEYr0Be5Uq8qEB9TZ+r+u3odPvQL1Vx8/3MqduER9iqQykCjkU\n\
LyhgkA+5Uh6y+RzspJLw5dYWrG1vQyyBjEA+7CS2IJuOQzIdg/J+CkrlJFSr\n\
aW7V18VFKTYNyYlaNQ7dBrKjmYROLQGd6i4097ehVtmAanEV9vPU/2o/8wz/\n\
7bX8IlRzz/BoDop7D5AJT5EFC/iZ/gxaxWe4T9dIlMxDJYf3IDcKKGCym8iA\n\
nc9xfQZ7rz5GHtBQ8jsoWu7hn7nPQqZVfAD17E2opj5HlnwGjdwNDmENmvMw\n\
br+Ag+ZTGNQfoUK5D70ypW4hD+rIA+TEuIPqpPeCuMBpWkKtcBgL/+0ngyUa\n\
QoFcEM76mmIAc0JwgdYGVyau0/uOw1dboo3X4Y7wMaKWUNFpWiqKleXs3azC\n\
gwSB6XHPNOB6xB0depI1IiJg9ZV208MQMNglN/LBGnbVSd9O8QrCQuYPh7VI\n\
CZmMLrYyVLZwzRNdU/xF6lGH190xaiWiRwt2u2yb89uWk4OVV14upyEe30Aw\n\
VIPP4fnbi6ks30kTw1VOogSKOhcQKibpV6d4eWZ0IV+NTOiUnndR2xcDrUtw\n\
/3wwUHXknjVrMrpEneJEeGpa9z1xAcALyw4oI90PJVi1OJngJY+mfSWLzvb6\n\
587K7fplFhTTMnHrjZ01bCV3iUJ3e+55yKE+PnAoDZFlHAlmF1/Rbrvnr4n/\n\
MACZIEPe/lemRMS23uk/vvubWoFIdClv/jfOCoNFHWgRnkrU9lSIKNBAmdGm\n\
LpKi1tGCjqfGu3S1UpHjFdWIRd3Ha8qay0X38FAWL+znjBe2RQoPb3EFxbo8\n\
NV24JQE1YjwUlCSDgxHuUaH8AJr9LsfLcrUG4qcO+WqN3RLGT5eizE3ETw3y\n\
iJ94JgcbcZQdKD1SRZIcRZQaZZQqJUjlMihTEEvpFMR2YxDf24HN7XWIxTdh\n\
N7EJW9trUCwmEDtZyOVisJfc4BGVHTwulWKQRjnSIry3M9BHJHXqcWjXdlC6\n\
bEGrugHN0irUS2u4j8+z9wylyiyUUvOIjBe4fQRplCnl1EPGTv71LOxtfga5\n\
1zcRMVch/eoTxM6nKDuu4j0zsJ++jesuomaeY2jNwn2oZu9AJX4N9pPXGD2d\n\
8n3EzSOUIAswQgkyqM4jbu5Bf/8h4gaxU7nLCBq3F+CwuyiQ01vC9ZywQx8G\n\
/UX8PaDg2Ani5mRAeFkOEXcoyHzw0jJNZIyMzJTxFsfFtrjuPaZjY2+OFGZS\n\
ERMSi9oyxCpIN4YJPgUVxfw0aJj4WOLny/v0KG4+HzDNi7J4sWQqU+SU2//P\n\
Anf+FFbjVGTRiL+jlrPCcLLCcSQnag0GVVGAcsHxBJN5W8En7eojX5mJBI4Z\n\
hHs4CaAjM7pczN8KO1RG1MEVExMbQDD+ZTKFB54aam7HxM7UHhohYs7WhXda\n\
H3pMi1ViMqV99PBECfyR5klImyCeaoAiKk3ec3dGOfH+taVJTDm8MUtEIaOK\n\
Xdl65aKDKN/TUS2bHiJj+IoWKwGEfFMZ8872W56Zpi5brrhM+//sMO0/sNRL\n\
oKPXu4hDLXsoqUOEwKrvMV3O++lyLOlyfMKkUfN7Q2ZOyznTQVK7L8fQNYxR\n\
Ix4NPUQnY6FhIsZssQH0no5zaTvfCwXiYYokh4SaA+ZNRO0N6WHk/TZ0R4SW\n\
DlQRI3nEyV6xDNkSGfFVRkuv14H+oA2tboMxQmrmdSrFCmY3lUBFg+qmWoRq\n\
rQiVSh5XDpVLFlKpHSgUEUGxDdjYWkOU7EKxEIfdnTVIJ7eg3cpBv5eHamkX\n\
YttLkE6sQW1/B4oZQkgMVQ1hJQat/S2oZJchs/sUKvkleL1xDxJbD6BaWMLr\n\
a6h0nkJq6xakNm9Aee8hZHZuwe7ajyEbuw7l+C22YfZTqFoy91AFzUKDMFJ+\n\
wlgpJ29CJTkD1b3b0MiQ1zIPo+YyvpAH7SXvX8Go8RTP3YdO8Ta0CrdhWKXe\n\
K09Y1ZC6OSSUdF8wSg4FToSaYRWD2+GixMqSxMoq+y6sZthr4S0JmA16X4+3\n\
ECgxXqIX8Q5nY8UJMVq9pFRhI36YS7pE5Ke9psu0oooqNzmRBSj0fdE308vu\n\
qpX1Qg7KTOvHnF/BiJErik7Gl9fg8asZ0dY+IhtxVWWKVsXKFPYPS3+n++4q\n\
pbc0SgTcOb/URo9kNH6PnKiUtJ1/VQpp2Tdmtu9EeWRE9n0M9Hl008iSPsKU\n\
N2PZXQ2LLzjORcCvd2Q1ywUdBzNuS/QsDLHemYSPPAronPA76uglkKZ1666w\n\
w0Hhwvmo1cZYtuviRo5+B+XE+zeBDsYSNSFHjrHBVcjiklREYuJvQP18qKNl\n\
UZ0KFoiWXdFZxEQckw5M+9+ind+bQIzMIearlzVYOMVMxsZCSBGai9ZsyhTh\n\
E/J3lKdilTWGLaP+VPRdEbEwKkpBbqj0reNj1cnL1xxfzoqUCLDCYJ5KDz4O\n\
uPdCh4St6JfQJgeTF6QwYXQwRLzfheHhkNN7q23kA0qSDLIjTZUkuIrVMjTa\n\
NeRHE/rDNgxHyJF2FSVKHmLJhJAhmRSks0kolrLMjmo1B60GyZUcZLNx5Ahy\n\
A7eJxDZkUsiDep7T/fvdIkfF9ks7kIyvQj6zDnvxFaiVY9BvpVCaxFGCxFCC\n\
LMPuq4eQTzyFxOYDqBWWkS2buDZwrcN+bgH2UJJktm9DfvcO86IQvw3V/EOo\n\
5R8gJ+7BfnYWKsiIIkqSau4eSpPbzJQ2cgR5gbRYwbWK+89Fvm/lIfICZUth\n\
Fjr5WTx+gNeewLi7goxYFszoEi9ehEiT0MdCTwbBesIkWcAvKAIfK7hWecsG\n\
yYGFDi4loZReliOkRmL423s6jilPRKRw+bCRZZS84dytrPywzssJvVmTx+vq\n\
8JvjnpHCagmO1OLtmR59RFfNZyEQBfOzxC+KFErIxw8ZD2XamsulBYx08Sue\n\
sFEixsXH7ZEKbf3LXVhsJ6XbKTEuVIzMogWTQZj+Tiqppzn0JQBY/Yt9k1Zc\n\
wDjnjJXpwJjy/20PRSV5WY3wvUljXwFkytWTxbPzg+1WYAMhkcAxd+W8qUZx\n\
ZH95ts8yFK695++Zry39YLt8Ojftt/f9I76cRfjWaGJ/YxfmU9TBJ6sDsWrs\n\
ohaziisng07/vz9DJomQm59hEkmmmv80EGez05nfiJIWz5G6zEE2Tiv7+Ykg\n\
G2//E+PG3Y84NCGXZD6zq87lksZY2MIYNYTpljmNhdoOoUK6IE2dtqWKziYa\n\
D57UbfWFsXOscpL5GsU+xTl7iYCbdm+O2OgPQM0SQEc61CbNf2MOKaYZKcTH\n\
Jggng29h9nyQcRSAw2ceolr6Rabd8LAHnX4bauT1VMoQz2ZhK5nibY4CbY0K\n\
qqU6DIcNJt5g2MTVgDKqpFKlCLlCGhKpOKqjNCSTu1AopVAdJaGQTUAZlRMF\n\
32rVDH/6DPFFHvRLMOjkyPcJQTG/5V0WIgkF0qCN3yZaSY7B1YobkE8+h1J6\n\
CYrp5yiOtqBX34Yewq5f34RmZRX/3BP8UYp7D/FFziPkCvFZKCTv4f4sFMn+\n\
f42CCOHWKNwnkUTfA1qr3nfhoLWGaxX6tUUWSc38Painb0J9bwb3CXBzMMBr\n\
4/Yy8owgt4aAw21/WQCPY26LHH877D2TcTgplDhz2RJJg1WKva3RZ4SCHUFu\n\
vBHioFtEaqRdXl8f7gqJFJaMy7AiUroowDlyWzgnwHDN0xG4owRH4ChlOaqu\n\
+PVRxCGPwsF+lGLxDBgO2kUCrJSTX0IqO+2roq+SRVexiOy0C8Q0u1k+d4w5\n\
EkyzNc87pdE7x7uo+y745NJ43OBMghbqdCWD5NayihzyaayAeN7+56lr/mPL\n\
TjJSS4LQR8mu+nvdlPQH+bSY6giYnZPcDMBOwU8WxgQYaaY3R9SeMpOE7rJG\n\
MpsOyZat5BoYw/7SlK7GDFhNKjgYmkhvU2tkkqLDEomihcAFjTyd/MaTLEXi\n\
QTB3TeswRxszot0F1VTZqDJaRoGZfsq/QY/+rLag2nLVcV58Z77ClYmsNnHO\n\
N0wZj77jZKBovfw7EyDUyQxOELr6NV/W1pQIFE5NjKCmn0UrPP8bkLB4kR6j\n\
unwnYiafhc3kMzVPhg0mkcAmKjN1Sc+xVnEXrDBh98DU3hwJpkkz6SAY9uME\n\
Bzu54VDQ7YBlHGfAjQhxQ+8/EuhgOO7htgsD2g5xO+xAq4MIq6G4K+VR4OUg\n\
lcuyl1RBkddG3HW7Veiish30EX2jBqpcPIfir1EvcVe/Bgo38pWpSqeEyMum\n\
dzgfu9MuCsyhoOsj5mr7u7CXXMNrW5AmQVfchn6bBF2COVfJrMLezhPcLkNq\n\
ew5a+y8F5+oxpNU2NPIvoLD7AMXaI8jFH0DmNYq3zBxUCwuc5tCsLEC39gK6\n\
jRV8zhUYoIDrNZagW11gvlG1DgUL6+lZaGTvIN/uQm+fgn5LKOCQb/115NVL\n\
wbg+rVVcKyGp5nrPKVKkWNd9pitzBNvWiG8cCDw5WEfAbYqiTBH5C3OetQAc\n\
t7885DaYITKVGHBJCbi0AFxI9ZxBRAkVlxdwC6lkBUvDUY2njAWGdKaDF1Yl\n\
OYyxcxOAy+IXQd3rLCz/lqJLkU1YSpJcMm+BA1N12dfMEckbKxQEs9X8ttNk\n\
A0zRg4Zqaxo8yIVSGpreNx2Ym4zqyedwz79Uffg7LnOJuaOnJB85mpu5xyH7\n\
s6ldfWtcVZeuyZauvgCuhGtTgsOqa2SrMdOuJtDCRiBoyoUgjveJTgEm6OfP\n\
YRCi6pIu4PT8s8sijpQGRs70WYDxqaw3ulQn5JBTH+gkhTPKcoTN9Pa79Nke\n\
caolYRr9Jl+z0xXegurCyeKLifSzOtDHCk6ygH9bI8EKT52hMHmOfkLfEDLb\n\
R5IKqnMkYoLCVjqvrSQrFCitpmMFFwEWsqCs1AWZVW0cpcOjKYUVc5sIHYYD\n\
6kmTxhchpEpQO0IotFWEHaYpARTWTbQGBBfWUz38oByNqbl4R2zHBJwONLo1\n\
yJay8DqNkCjmIFMUCQvlSh5KZW5Cji9Lp4ovwaBfhRFKqzGyZszMIf7UoI8s\n\
oqo75Ar+VSN8vIx8IRlVhE6L0umy0GmmoIer30qwhhp0UEfhfru+g5zZRv2E\n\
uqlGTNlhHRQLoYzaotcCxVSvtkYLj/rNdZpbWVtBiCBIassIkOcIIQRNYZ6j\n\
hFToQ/nVlGvdKjzCJ0WQtNYRDmscETzsC5AIsFD+83GPcbJM793uEiso4kqY\n\
WII/iUieRoIwRTaYJCdIkq8OtkX5zhj10QERBY8pLYG1UgJOj2mAmGAJpyqc\n\
pPlIY0SIJxJNWkCJD3yFlxynq2lFc5JDkj3nsQFWAwArKKgSolVY0OUvGebo\n\
eKDIdpjSJZ85WfCpij7zgj3ufv1lU+1JH2BHIgp4NNZ9Z3R/sgAHxu1zBgaq\n\
AKIOtRr17K85y/fN5DFngrZ1bjJFwpY+mnXeZCTQnDP32ckNxk66aIXu5GQX\n\
bzLXoeu5cujOC5HjTmSwpY0qAR2G7AqfiT4zAahwdvW07jMz2U5Tzlr2HNZS\n\
JBDJUyPDuH4nGMnjxLkpBR2pbejIlUc3LTWQFdXT6RDf0HU8v8YEigYIdCoT\n\
7k5d+XSXz9I9FxyBPT76FnGE8rTf/uKEEHELFoEaf6LD97RguTIhq2QEMWJh\n\
yiVZLkhT6uSUK3vOm2TsiCSTossxwYlUyzG97J1AvI4Jc2jqeDqizb+FGb6m\n\
O6cNjmxtIqpFBV/w2oHvmmGPsaPChBl6GHjflfKlByMaXXHYlXTpyOMO7w8H\n\
Teh0G9x4vFIrQr1RgmwhBTkkTSaXwpWEdpsicHX2oqrVLNdDkayhpBDaHw4Q\n\
P4NqiNiC/8/7rGSKvKXUBlYtrTSuJCdq9+i4k+L9fnsXYbGNpIkhhajrSr9J\n\
XVcQMQiYLTyiOvx+fd37NiqTFYTHU2iWXqBaWYdWcREqqXt4DqFCiqb4BKGz\n\
CL0qXkcIUaTuoL2OcHmJCyHTeyng0lsXsBlsSAVDyuUlJcCtkee0Qm/sAUXt\n\
lugI99cEYwZrYYILhSRYsGzLhZgZE14SHD2j8ZaUZ42koSS4rw/jbDmx3XSE\n\
ZDlKy9DcG6Fcspae0MqFkwgs0UJBuT6lxSWnJkSLbNDs6qE5PQEVmUIXVlA5\n\
CaTLSXlTslTNpUB7s7LlM6mWMioeJ2Nx1sAvmy5nDw8Lc04CdQeg/mXvOe5z\n\
taaZJIyiyZQ/aDY2KkdTZWxaCgT9pWBfTc8eqszWU0RHxFzyJgKT5pGp37ms\n\
8RK0iKaDTcx8ltG0wzI6PmaNIoVKJChUTOGobRsdXNZNmu32zNorehMcvyy7\n\
0pxqVXN0RcfTlOSRgGFofEcn14XOCphdcJz7JafGEU7SmXi5olBiQlJigABT\n\
ZBom25lNpsvJI4bIz0/wBLxpB2NcXdUmRxO89X5Ba6SQQ4PZfFJwtNHks055\n\
TTukU9hOAhdjCzxVpNoNnOMea0e+MQYiK+9IdY+mCiPe11kXx2rGARPLOFXT\n\
uunnMfgT845Ftx3dTOdA9Y2e0lrJZFNENM3oc4BzvUfGfApzQO5bTDJFtKEk\n\
2mCkdFNH+0sUdKNBTYNRE/epJqkGXdRSlJlXreU5MEdBumw2AQUkHVIMXxj6\n\
2PkVjvaPx9SeBNewioKqjGSr4LZitv08DHtIwU4aMUcrgwTM4PPiuR6JqF2S\n\
SXh9FxcJKjKoduQ5XO1tGLY2EG/rUEzcZ3T16y8Zb83CM9wu4f3rMGq/xH9W\n\
j6TWYWcT94hk1IRg3FtFxoxJKvXWmGS0ZZoN1mUsDtXQiMiJuohqiNbxvXIy\n\
Qnk0eolSBRfKJaonOuEOByiRxttSKsn9wy0TfUOksVyKSINJdeR8o4cKRFUe\n\
HhtNopQo49ZCqq1mVI5lXoM3wzm7gkhXCwVqTd+KbZh28J10SqrsLWIN99SW\n\
ruWm6AZ6R+k/z6D0Y1BPRTM9dAJT0EL+yiPVNkeaTyijzuheo/MrJgJ0ot6o\n\
g9KbAnT2oAGHLeUacPMvFb+6NJghnsked3X01Od8VUqO9mmSiK7IniuKd86R\n\
o4dryqGwzBA1lVlhzCM7myKiAnnB0tXzOoHCQmKwUklLLCW6jOA6fVelkqho\n\
lbnmU8Fcczr2JjP+qPJF6TDTiNoMdv7ehMF0qqHpmtrpCgx+zye+LNOJB0G/\n\
D2rosw+RcjQbRQXf/rIDhzSZ+W10IvIH5rQ7WMijPCNn8DV47rsONn9TBxPZ\n\
FYvaKPyZ/wfE8hKR"], "ConferenceGraphicsCell", ImageSize -> {900, 150},
ImageMargins -> 0, CellMargins -> {{0, 0}, {0, 0}}, Background ->
RGBColor[1, 1, 1], CellFrameMargins -> {{0, 0}, {0, 0}}]},
ScrollingOptions -> {
"PagewiseDisplay" -> True, "VerticalScrollRange" -> Fit},
ShowCellBracket -> False, ShowAutoStyles -> False, ScriptMinSize -> 9,
MenuPosition -> 1300],
Cell[
CellGroupData[{
Cell[
StyleData["Title"], CellMargins -> {{27, Inherited}, {10, 30}},
CellGroupingRules -> {"TitleGrouping", 0}, PageBreakBelow -> False,
DefaultNewInlineCellStyle -> "None",
InputAutoReplacements -> {"TeX" -> StyleBox[
RowBox[{"T",
AdjustmentBox[
"E", BoxMargins -> {{-0.075, -0.085}, {0, 0}}, BoxBaselineShift ->
0.5], "X"}]], "LaTeX" -> StyleBox[
RowBox[{"L",
StyleBox[
AdjustmentBox[
"A", BoxMargins -> {{-0.36, -0.1}, {0, 0}},
BoxBaselineShift -> -0.2], FontSize -> Smaller], "T",
AdjustmentBox[
"E", BoxMargins -> {{-0.075, -0.085}, {0, 0}}, BoxBaselineShift ->
0.5], "X"}]], "mma" -> "Mathematica", "Mma" -> "Mathematica",
"MMA" -> "Mathematica", "gridMathematica" -> FormBox[
RowBox[{"grid",
AdjustmentBox[
StyleBox["Mathematica", FontSlant -> "Italic"],
BoxMargins -> {{-0.175, 0}, {0, 0}}]}], TextForm],
"webMathematica" -> FormBox[
RowBox[{"web",
AdjustmentBox[
StyleBox["Mathematica", FontSlant -> "Italic"],
BoxMargins -> {{-0.175, 0}, {0, 0}}]}], TextForm], Inherited},
LineSpacing -> {1, 11}, LanguageCategory -> "NaturalLanguage",
CounterIncrements -> "Title",
CounterAssignments -> {{"Section", 0}, {"Equation", 0}, {
"Figure", 0}, {"Subtitle", 0}, {"Subsubtitle", 0}}, FontFamily ->
"Helvetica", FontSize -> 36, FontWeight -> "Bold", FontColor ->
RGBColor[0.796078, 0.0705882, 0]],
Cell[
StyleData["Title", "Presentation"],
CellMargins -> {{72, 50}, {10, 80}}, LineSpacing -> {1, 0}, FontSize ->
45],
Cell[
StyleData["Title", "SlideShow"], CellMargins -> {{72, 50}, {10, 80}},
FontSize -> 45],
Cell[
StyleData["Title", "Printout"], CellMargins -> {{2, 10}, {12, 30}},
FontSize -> 24]}, Closed]],
Cell[
CellGroupData[{
Cell[
StyleData["Subtitle"], CellMargins -> {{27, Inherited}, {20, 2}},
CellGroupingRules -> {"TitleGrouping", 10}, PageBreakBelow -> False,
DefaultNewInlineCellStyle -> "None",
InputAutoReplacements -> {"TeX" -> StyleBox[
RowBox[{"T",
AdjustmentBox[
"E", BoxMargins -> {{-0.075, -0.085}, {0, 0}}, BoxBaselineShift ->
0.5], "X"}]], "LaTeX" -> StyleBox[
RowBox[{"L",
StyleBox[
AdjustmentBox[
"A", BoxMargins -> {{-0.36, -0.1}, {0, 0}},
BoxBaselineShift -> -0.2], FontSize -> Smaller], "T",
AdjustmentBox[
"E", BoxMargins -> {{-0.075, -0.085}, {0, 0}}, BoxBaselineShift ->
0.5], "X"}]], "mma" -> "Mathematica", "Mma" -> "Mathematica",
"MMA" -> "Mathematica", "gridMathematica" -> FormBox[
RowBox[{"grid",
AdjustmentBox[
StyleBox["Mathematica", FontSlant -> "Italic"],
BoxMargins -> {{-0.175, 0}, {0, 0}}]}], TextForm],
"webMathematica" -> FormBox[
RowBox[{"web",
AdjustmentBox[
StyleBox["Mathematica", FontSlant -> "Italic"],
BoxMargins -> {{-0.175, 0}, {0, 0}}]}], TextForm], Inherited},
LanguageCategory -> "NaturalLanguage", CounterIncrements -> "Subtitle",
CounterAssignments -> {{"Section", 0}, {"Equation", 0}, {
"Figure", 0}, {"Subsubtitle", 0}}, FontFamily -> "Helvetica",
FontSize -> 24],
Cell[
StyleData["Subtitle", "Presentation"],
CellMargins -> {{72, 50}, {20, 2}}, LineSpacing -> {1, 0}, FontSize ->
30],
Cell[
StyleData["Subtitle", "SlideShow"], CellMargins -> {{72, 50}, {30, 2}},
FontSize -> 30],
Cell[
StyleData["Subtitle", "Printout"], CellMargins -> {{2, 10}, {12, 8}},
FontSize -> 18]}, Closed]],
Cell[
CellGroupData[{
Cell[
StyleData["Subsubtitle"], CellMargins -> {{27, Inherited}, {8, 2}},
CellGroupingRules -> {"TitleGrouping", 20}, PageBreakBelow -> False,
DefaultNewInlineCellStyle -> "None",
InputAutoReplacements -> {"TeX" -> StyleBox[
RowBox[{"T",
AdjustmentBox[
"E", BoxMargins -> {{-0.075, -0.085}, {0, 0}}, BoxBaselineShift ->
0.5], "X"}]], "LaTeX" -> StyleBox[
RowBox[{"L",
StyleBox[
AdjustmentBox[
"A", BoxMargins -> {{-0.36, -0.1}, {0, 0}},
BoxBaselineShift -> -0.2], FontSize -> Smaller], "T",
AdjustmentBox[
"E", BoxMargins -> {{-0.075, -0.085}, {0, 0}}, BoxBaselineShift ->
0.5], "X"}]], "mma" -> "Mathematica", "Mma" -> "Mathematica",
"MMA" -> "Mathematica", "gridMathematica" -> FormBox[
RowBox[{"grid",
AdjustmentBox[
StyleBox["Mathematica", FontSlant -> "Italic"],
BoxMargins -> {{-0.175, 0}, {0, 0}}]}], TextForm],
"webMathematica" -> FormBox[
RowBox[{"web",
AdjustmentBox[
StyleBox["Mathematica", FontSlant -> "Italic"],
BoxMargins -> {{-0.175, 0}, {0, 0}}]}], TextForm], Inherited},
LanguageCategory -> "NaturalLanguage", CounterIncrements ->
"Subsubtitle",
CounterAssignments -> {{"Section", 0}, {"Equation", 0}, {"Figure", 0}},
StyleMenuListing -> None, FontFamily -> "Helvetica", FontSize -> 16],
Cell[
StyleData["Subsubtitle", "Presentation"],
CellMargins -> {{54, 10}, {20, 20}}, LineSpacing -> {1, 0}, FontSize ->
24],
Cell[
StyleData["Subsubtitle", "SlideShow"],
CellMargins -> {{72, 25}, {30, 10}}],
Cell[
StyleData["Subsubtitle", "Printout"],
CellMargins -> {{2, 10}, {12, 8}}, FontSize -> 14]}, Closed]],
Cell[
CellGroupData[{
Cell[
StyleData["Section"], CellMargins -> {{27, Inherited}, {8, 34}},
CellGroupingRules -> {"SectionGrouping", 30}, PageBreakBelow -> False,
CellFrameMargins -> 4, DefaultNewInlineCellStyle -> "None",
InputAutoReplacements -> {"TeX" -> StyleBox[
RowBox[{"T",
AdjustmentBox[
"E", BoxMargins -> {{-0.075, -0.085}, {0, 0}}, BoxBaselineShift ->
0.5], "X"}]], "LaTeX" -> StyleBox[
RowBox[{"L",
StyleBox[
AdjustmentBox[
"A", BoxMargins -> {{-0.36, -0.1}, {0, 0}},
BoxBaselineShift -> -0.2], FontSize -> Smaller], "T",
AdjustmentBox[
"E", BoxMargins -> {{-0.075, -0.085}, {0, 0}}, BoxBaselineShift ->
0.5], "X"}]], "mma" -> "Mathematica", "Mma" -> "Mathematica",
"MMA" -> "Mathematica", "gridMathematica" -> FormBox[
RowBox[{"grid",
AdjustmentBox[
StyleBox["Mathematica", FontSlant -> "Italic"],
BoxMargins -> {{-0.175, 0}, {0, 0}}]}], TextForm],
"webMathematica" -> FormBox[
RowBox[{"web",
AdjustmentBox[
StyleBox["Mathematica", FontSlant -> "Italic"],
BoxMargins -> {{-0.175, 0}, {0, 0}}]}], TextForm], Inherited},
LineSpacing -> {1, 2}, LanguageCategory -> "NaturalLanguage",
CounterIncrements -> "Section",
CounterAssignments -> {{"Subsection", 0}, {"Subsubsection", 0}},
FontFamily -> "Helvetica", FontSize -> 20, FontWeight -> "Bold",
FontColor -> RGBColor[0.811765, 0.117647, 0.145098]],
Cell[
StyleData["Section", "Presentation"], CellFrame -> {{0, 0}, {0, 2}},
ShowGroupOpener -> True, CellMargins -> {{72, 50}, {11, 30}},
CellFrameColor -> RGBColor[1, 0.796078, 0.501961], FontSize -> 30],
Cell[
StyleData["Section", "SlideShow"], CellMargins -> {{71, 50}, {11, 35}},
FontSize -> 30],
Cell[
StyleData["Section", "Printout"], CellMargins -> {{2, 0}, {7, 22}},
FontSize -> 14]}, Closed]],
Cell[
CellGroupData[{
Cell[
StyleData["Subsection"], CellMargins -> {{60, Inherited}, {8, 12}},
CellGroupingRules -> {"SectionGrouping", 40}, PageBreakBelow -> False,
DefaultNewInlineCellStyle -> "None",
InputAutoReplacements -> {"TeX" -> StyleBox[
RowBox[{"T",
AdjustmentBox[
"E", BoxMargins -> {{-0.075, -0.085}, {0, 0}}, BoxBaselineShift ->
0.5], "X"}]], "LaTeX" -> StyleBox[
RowBox[{"L",
StyleBox[
AdjustmentBox[
"A", BoxMargins -> {{-0.36, -0.1}, {0, 0}},
BoxBaselineShift -> -0.2], FontSize -> Smaller], "T",
AdjustmentBox[
"E", BoxMargins -> {{-0.075, -0.085}, {0, 0}}, BoxBaselineShift ->
0.5], "X"}]], "mma" -> "Mathematica", "Mma" -> "Mathematica",
"MMA" -> "Mathematica", "gridMathematica" -> FormBox[
RowBox[{"grid",
AdjustmentBox[
StyleBox["Mathematica", FontSlant -> "Italic"],
BoxMargins -> {{-0.175, 0}, {0, 0}}]}], TextForm],
"webMathematica" -> FormBox[
RowBox[{"web",
AdjustmentBox[
StyleBox["Mathematica", FontSlant -> "Italic"],
BoxMargins -> {{-0.175, 0}, {0, 0}}]}], TextForm], Inherited},
LanguageCategory -> "NaturalLanguage", CounterIncrements ->
"Subsection", CounterAssignments -> {{"Subsubsection", 0}}, FontFamily ->
"Helvetica", FontSize -> 16, FontWeight -> "Bold", FontColor ->
RGBColor[0.9864194705119402, 0.3059128709849699, 0.09442282749675746]],
Cell[
StyleData["Subsection", "Presentation"],
CellMargins -> {{72, 50}, {6, 15}}, LineSpacing -> {1, 0}, FontSize ->
24],
Cell[
StyleData["Subsection", "SlideShow"],
CellMargins -> {{99, 50}, {8, 12}}, LineSpacing -> {1, 0}, FontSize ->
24],
Cell[
StyleData["Subsection", "Printout"], CellMargins -> {{21, 0}, {8, 22}},
FontSize -> 12]}, Closed]],
Cell[
CellGroupData[{
Cell[
StyleData["Subsubsection"], CellMargins -> {{60, Inherited}, {2, 12}},
CellGroupingRules -> {"SectionGrouping", 50}, PageBreakBelow -> False,
DefaultNewInlineCellStyle -> "None",
InputAutoReplacements -> {"TeX" -> StyleBox[
RowBox[{"T",
AdjustmentBox[
"E", BoxMargins -> {{-0.075, -0.085}, {0, 0}}, BoxBaselineShift ->
0.5], "X"}]], "LaTeX" -> StyleBox[
RowBox[{"L",
StyleBox[
AdjustmentBox[
"A", BoxMargins -> {{-0.36, -0.1}, {0, 0}},
BoxBaselineShift -> -0.2], FontSize -> Smaller], "T",
AdjustmentBox[
"E", BoxMargins -> {{-0.075, -0.085}, {0, 0}}, BoxBaselineShift ->
0.5], "X"}]], "mma" -> "Mathematica", "Mma" -> "Mathematica",
"MMA" -> "Mathematica", "gridMathematica" -> FormBox[
RowBox[{"grid",
AdjustmentBox[
StyleBox["Mathematica", FontSlant -> "Italic"],
BoxMargins -> {{-0.175, 0}, {0, 0}}]}], TextForm],
"webMathematica" -> FormBox[
RowBox[{"web",
AdjustmentBox[
StyleBox["Mathematica", FontSlant -> "Italic"],
BoxMargins -> {{-0.175, 0}, {0, 0}}]}], TextForm], Inherited},
LanguageCategory -> "NaturalLanguage", CounterIncrements ->
"Subsubsection", FontFamily -> "Helvetica", FontWeight -> "Bold",
FontColor ->
RGBColor[
0.9773708705271992, 0.48682383459220263`, 0.004547188525215534]],
Cell[
StyleData["Subsubsection", "Presentation"],
CellMargins -> {{72, 50}, {6, 20}}, LineSpacing -> {1, 0}, FontSize ->
18],
Cell[
StyleData["Subsubsection", "SlideShow"],
CellMargins -> {{99, 50}, {6, 20}}, FontSize -> 18],
Cell[
StyleData["Subsubsection", "Printout"],
CellMargins -> {{2, 0}, {7, 14}}, FontSize -> 11]}, Closed]],
Cell[
CellGroupData[{
Cell[
StyleData["Text"], CellMargins -> {{60, 10}, {7, 7}},
InputAutoReplacements -> {"TeX" -> StyleBox[
RowBox[{"T",
AdjustmentBox[
"E", BoxMargins -> {{-0.075, -0.085}, {0, 0}}, BoxBaselineShift ->
0.5], "X"}]], "LaTeX" -> StyleBox[
RowBox[{"L",
StyleBox[
AdjustmentBox[
"A", BoxMargins -> {{-0.36, -0.1}, {0, 0}},
BoxBaselineShift -> -0.2], FontSize -> Smaller], "T",
AdjustmentBox[
"E", BoxMargins -> {{-0.075, -0.085}, {0, 0}}, BoxBaselineShift ->
0.5], "X"}]], "mma" -> "Mathematica", "Mma" -> "Mathematica",
"MMA" -> "Mathematica", "gridMathematica" -> FormBox[
RowBox[{"grid",
AdjustmentBox[
StyleBox["Mathematica", FontSlant -> "Italic"],
BoxMargins -> {{-0.175, 0}, {0, 0}}]}], TextForm],
"webMathematica" -> FormBox[
RowBox[{"web",
AdjustmentBox[
StyleBox["Mathematica", FontSlant -> "Italic"],
BoxMargins -> {{-0.175, 0}, {0, 0}}]}], TextForm], Inherited},
LineSpacing -> {1, 3}, CounterIncrements -> "Text", FontFamily ->
"Helvetica"],
Cell[
StyleData["Text", "Presentation"], CellMargins -> {{72, 50}, {10, 10}},
LineSpacing -> {1, 5}, FontSize -> 17],
Cell[
StyleData["Text", "SlideShow"], CellMargins -> {{100, 50}, {10, 10}},
FontSize -> 17],
Cell[
StyleData["Text", "Printout"], CellMargins -> {{2, 2}, {6, 6}},
TextJustification -> 0.5, Hyphenation -> True, FontSize -> 10]},
Closed]],
Cell[
CellGroupData[{
Cell[
StyleData["SmallText"], CellMargins -> {{60, 10}, {6, 6}},
DefaultNewInlineCellStyle -> "None", LineSpacing -> {1, 3},
LanguageCategory -> "NaturalLanguage", CounterIncrements ->
"SmallText", FontFamily -> "Helvetica", FontSize -> 9],
Cell[
StyleData["SmallText", "Presentation"],
CellMargins -> {{72, 50}, {8, 8}}, LineSpacing -> {1, 5}, FontSize ->
10],
Cell[
StyleData["SmallText", "SlideShow"],
CellMargins -> {{100, 50}, {8, 8}}, LineSpacing -> {1, 5}, FontSize ->
10],
Cell[
StyleData["SmallText", "Printout"], CellMargins -> {{2, 2}, {5, 5}},
TextJustification -> 0.5, Hyphenation -> True, FontSize -> 7]},
Closed]],
Cell[
CellGroupData[{
Cell[
StyleData["Author"], CellMargins -> {{139, 27}, {2, 20}}, FontFamily ->
"Times", FontSize -> 24, FontSlant -> "Italic"],
Cell[
StyleData["Author", "Presentation"],
CellMargins -> {{198, 27}, {2, 25}}, FontSize -> 32],
Cell[
StyleData["Author", "SlideShow"], CellMargins -> {{198, 27}, {2, 50}},
FontSize -> 32],
Cell[
StyleData["Author", "Printout"], CellMargins -> {{100, 27}, {2, 20}},
FontSize -> 14]}, Closed]],
Cell[
CellGroupData[{
Cell[
StyleData["Affiliation"], CellMargins -> {{141, 27}, {30, 12}},
FontFamily -> "Times", FontSize -> 24, FontSlant -> "Italic"],
Cell[
StyleData["Affiliation", "Presentation"],
CellMargins -> {{198, 27}, {35, 10}}, FontSize -> 32],
Cell[
StyleData["Affiliation", "SlideShow"],
CellMargins -> {{198, 27}, {100, 10}}, FontSize -> 32],
Cell[
StyleData["Affiliation", "Printout"],
CellMargins -> {{100, 27}, {2, 12}}, FontSize -> 14]}, Closed]],
Cell[
CellGroupData[{
Cell[
StyleData["ConferenceGraphicCell"], ShowCellBracket -> True,
CellMargins -> {{0, 0}, {0, 0}}, Evaluatable -> False, PageBreakBelow ->
False, ImageMargins -> {{0, 0}, {0, 0}},
ImageRegion -> {{0, 1}, {0, 1}}, Magnification -> 1, Background ->
GrayLevel[1]],
Cell[
StyleData["ConferenceGraphicCell", "Presentation"], ShowCellBracket ->
False],
Cell[
StyleData["ConferenceGraphicCell", "SlideShow"], ShowCellBracket ->
False],
Cell[
StyleData["ConferenceGraphicCell", "Printout"], FontSize -> 8,
Magnification -> 0.75]}, Closed]],
Cell[
CellGroupData[{
Cell[
StyleData["GraphicNoMagnification"], CellMargins -> {{60, 10}, {7, 7}},
LineSpacing -> {1, 3}, CounterIncrements -> "Text", FontFamily ->
"Helvetica", Magnification -> 1],
Cell[
StyleData["GraphicNoMagnification", "Presentation"],
CellMargins -> {{72, 50}, {10, 10}}, LineSpacing -> {1, 5}, FontSize ->
17],
Cell[
StyleData["GraphicNoMagnification", "SlideShow"],
CellMargins -> {{100, 50}, {10, 10}}, FontSize -> 17],
Cell[
StyleData["GraphicNoMagnification", "Printout"],
CellMargins -> {{2, 2}, {6, 6}}, FontSize -> 10]}, Closed]],
Cell[
CellGroupData[{
Cell[
StyleData["Input"], ShowCellBracket -> True,
CellMargins -> {{66, 10}, {5, 7}},
CellBracketOptions -> {
"Color" -> RGBColor[0.734936, 0.713848, 0.694041]}, Evaluatable ->
True, CellGroupingRules -> "InputGrouping", CellHorizontalScrolling ->
True, PageBreakWithin -> False, GroupPageBreakWithin -> False,
DefaultFormatType -> DefaultInputFormatType,
"TwoByteSyntaxCharacterAutoReplacement" -> True,
HyphenationOptions -> {"HyphenationCharacter" -> "\[Continuation]"},
AutoItalicWords -> {}, LanguageCategory -> "Mathematica", FormatType ->
InputForm, ShowStringCharacters -> True, NumberMarks -> True,
LinebreakAdjustments -> {0.85, 2, 10, 0, 1}, CounterIncrements ->
"Input", FontWeight -> "Bold"],
Cell[
StyleData["Input", "Presentation"], CellMargins -> {{72, 50}, {8, 10}},
LineSpacing -> {1, 0}, FontSize -> 18],
Cell[
StyleData["Input", "SlideShow"], CellMargins -> {{100, 50}, {8, 10}},
LineSpacing -> {1, 0}, FontSize -> 18],
Cell[
StyleData["Input", "Printout"], CellMargins -> {{39, 0}, {4, 6}},
LinebreakAdjustments -> {0.85, 2, 10, 1, 1}, FontSize -> 9]}, Open]],
Cell[
CellGroupData[{
Cell[
StyleData["InputOnly"], ShowCellBracket -> True,
CellMargins -> {{66, 10}, {7, 7}},
CellBracketOptions -> {
"Color" -> RGBColor[0.734936, 0.713848, 0.694041]}, Evaluatable ->
True, CellGroupingRules -> "InputGrouping", CellHorizontalScrolling ->
True, DefaultFormatType -> DefaultInputFormatType,
"TwoByteSyntaxCharacterAutoReplacement" -> True,
HyphenationOptions -> {"HyphenationCharacter" -> "\[Continuation]"},
AutoItalicWords -> {}, LanguageCategory -> "Mathematica", FormatType ->
InputForm, ShowStringCharacters -> True, NumberMarks -> True,
LinebreakAdjustments -> {0.85, 2, 10, 0, 1}, CounterIncrements ->
"Input", StyleMenuListing -> None, FontWeight -> "Bold"],
Cell[
StyleData["InputOnly", "Presentation"],
CellMargins -> {{72, Inherited}, {8, 10}}, LineSpacing -> {1, 0},
FontSize -> 18],
Cell[
StyleData["InputOnly", "SlideShow"],
CellMargins -> {{100, Inherited}, {8, 10}}, LineSpacing -> {1, 0},
FontSize -> 18],
Cell[
StyleData["InputOnly", "Printout"], CellMargins -> {{39, 0}, {4, 6}},
LinebreakAdjustments -> {0.85, 2, 10, 1, 1}, FontSize -> 9]}, Open]],
Cell[
CellGroupData[{
Cell[
StyleData["Output"], ShowCellBracket -> True,
CellMargins -> {{66, 10}, {7, 5}},
CellBracketOptions -> {
"Color" -> RGBColor[0.734936, 0.713848, 0.694041]}, CellEditDuplicate ->
True, CellGroupingRules -> "OutputGrouping", CellHorizontalScrolling ->
True, PageBreakWithin -> False, GroupPageBreakWithin -> False,
GeneratedCell -> True, CellAutoOverwrite -> True, DefaultFormatType ->
DefaultOutputFormatType, "TwoByteSyntaxCharacterAutoReplacement" ->
True, HyphenationOptions -> {
"HyphenationCharacter" -> "\[Continuation]"}, AutoItalicWords -> {},
LanguageCategory -> None, FormatType -> InputForm, CounterIncrements ->
"Output"],
Cell[
StyleData["Output", "Presentation"],
CellMargins -> {{72, 50}, {10, 8}}, LineSpacing -> {1, 0}, FontSize ->
18],
Cell[
StyleData["Output", "SlideShow"], CellMargins -> {{100, 50}, {10, 8}},
LineSpacing -> {1, 0}, FontSize -> 18],
Cell[
StyleData["Output", "Printout"], CellMargins -> {{39, 0}, {6, 4}},
FontSize -> 9]}, Open]]}, Visible -> False, FrontEndVersion ->
"6.0 for Microsoft Windows (32-bit) (April 20, 2007)", StyleDefinitions ->
"Default.nb"]
]
(* End of Notebook Content *)
(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{
"SlideShowHeader"->{
Cell[590, 23, 64, 1, 11, "SlideShowNavigationBar",
CellTags->"SlideShowHeader"],
Cell[1916, 63, 64, 1, 11, "SlideShowNavigationBar",
CellTags->"SlideShowHeader"],
Cell[4632, 134, 64, 1, 11, "SlideShowNavigationBar",
CellTags->"SlideShowHeader"],
Cell[76367, 1764, 64, 1, 11, "SlideShowNavigationBar",
CellTags->"SlideShowHeader"],
Cell[100885, 2399, 64, 1, 11, "SlideShowNavigationBar",
CellTags->"SlideShowHeader"],
Cell[163782, 5185, 64, 1, 11, "SlideShowNavigationBar",
CellTags->"SlideShowHeader"],
Cell[175837, 5524, 64, 1, 11, "SlideShowNavigationBar",
CellTags->"SlideShowHeader"],
Cell[177265, 5572, 64, 1, 11, "SlideShowNavigationBar",
CellTags->"SlideShowHeader"]},
"NKS Chapter 2"->{
Cell[103240, 2468, 9966, 730, 59, 8414, 702, "GraphicsData",
"PostScript", "Graphics",
CellTags->"NKS Chapter 2"],
Cell[114875, 3244, 9924, 729, 58, 8414, 702, "GraphicsData",
"PostScript", "Graphics",
CellTags->"NKS Chapter 2"],
Cell[124802, 3975, 9915, 728, 58, 8414, 702, "GraphicsData",
"PostScript", "Graphics",
CellTags->"NKS Chapter 2"]},
"S5.32.1"->{
Cell[165113, 5224, 2603, 75, 209, "Input",
CellTags->"S5.32.1"]}
}
*)
(*CellTagsIndex
CellTagsIndex->{
{"SlideShowHeader", 335805, 8192},
{"NKS Chapter 2", 336541, 8209},
{"S5.32.1", 336925, 8219}
}
*)
(*NotebookFileOutline
Notebook[{
Cell[CellGroupData[{
Cell[590, 23, 64, 1, 11, "SlideShowNavigationBar",
CellTags->"SlideShowHeader"],
Cell[657, 26, 117, 1, 83, "Title"],
Cell[777, 29, 86, 1, 49, "Subtitle"],
Cell[866, 32, 97, 1, 49, "Author"],
Cell[966, 35, 149, 3, 69, "Affiliation"],
Cell[1118, 40, 761, 18, 27, "PreviousNext"]
}, Open ]],
Cell[CellGroupData[{
Cell[1916, 63, 64, 1, 11, "SlideShowNavigationBar",
CellTags->"SlideShowHeader"],
Cell[CellGroupData[{
Cell[2005, 68, 92, 1, 71, "Section"],
Cell[2100, 71, 1719, 37, 389, "Text"],
Cell[3822, 110, 761, 18, 27, "PreviousNext"]
}, Open ]]
}, Open ]],
Cell[CellGroupData[{
Cell[4632, 134, 64, 1, 11, "SlideShowNavigationBar",
CellTags->"SlideShowHeader"],
Cell[CellGroupData[{
Cell[4721, 139, 198, 3, 71, "Section"],
Cell[CellGroupData[{
Cell[4944, 146, 301, 6, 39, "Subsection"],
Cell[5248, 154, 504, 9, 83, "Text"],
Cell[CellGroupData[{
Cell[5777, 167, 15761, 415, 569, "Input"],
Cell[21541, 584, 20483, 429, 539, "Output"]
}, {2}]]
}, Open ]],
Cell[CellGroupData[{
Cell[42070, 1019, 302, 6, 39, "Subsection"],
Cell[42375, 1027, 651, 13, 83, "Text"],
Cell[CellGroupData[{
Cell[43051, 1044, 11147, 296, 435, "Input"],
Cell[54201, 1342, 13437, 254, 395, "Output"]
}, {2}]],
Cell[CellGroupData[{
Cell[67672, 1601, 426, 10, 28, "Input"],
Cell[68101, 1613, 7432, 123, 395, "Output"]
}, {2}]],
Cell[75545, 1739, 761, 18, 27, "PreviousNext"]
}, Open ]]
}, Open ]]
}, Open ]],
Cell[CellGroupData[{
Cell[76367, 1764, 64, 1, 11, "SlideShowNavigationBar",
CellTags->"SlideShowHeader"],
Cell[CellGroupData[{
Cell[76456, 1769, 151, 2, 71, "Section"],
Cell[76610, 1773, 843, 23, 85, "Text"],
Cell[77456, 1798, 1752, 48, 109, "Input"],
Cell[CellGroupData[{
Cell[79233, 1850, 327, 7, 39, "Subsection"],
Cell[79563, 1859, 10342, 256, 389, "Input"]
}, Open ]],
Cell[CellGroupData[{
Cell[89942, 2120, 331, 7, 39, "Subsection"],
Cell[90276, 2129, 9784, 243, 369, "Input"],
Cell[100063, 2374, 761, 18, 27, "PreviousNext"]
}, Open ]]
}, Open ]]
}, Open ]],
Cell[CellGroupData[{
Cell[100885, 2399, 64, 1, 11, "SlideShowNavigationBar",
CellTags->"SlideShowHeader"],
Cell[CellGroupData[{
Cell[100974, 2404, 102, 1, 71, "Section"],
Cell[CellGroupData[{
Cell[101101, 2409, 329, 7, 39, "Subsection"],
Cell[101433, 2418, 1299, 35, 69, "Text"],
Cell[102735, 2455, 502, 11, 47, "Text"],
Cell[103240, 2468, 9966, 730, 59, 8414, 702, "GraphicsData", "PostScript", \
"Graphics",
CellTags->"NKS Chapter 2"],
Cell[113209, 3200, 440, 11, 31, "Text"],
Cell[113652, 3213, 211, 4, 29, "Text"],
Cell[113866, 3219, 343, 6, 47, "Text"],
Cell[114212, 3227, 405, 7, 47, "Text"],
Cell[114620, 3236, 230, 4, 47, "Text"],
Cell[CellGroupData[{
Cell[114875, 3244, 9924, 729, 58, 8414, 702, "GraphicsData", "PostScript", \
"Graphics",
CellTags->"NKS Chapter 2"],
Cell[124802, 3975, 9915, 728, 58, 8414, 702, "GraphicsData", "PostScript", \
"Graphics",
CellTags->"NKS Chapter 2"]
}, Open ]],
Cell[134732, 4706, 116, 3, 29, "Text"]
}, Open ]],
Cell[CellGroupData[{
Cell[134885, 4714, 351, 7, 39, "Subsection"],
Cell[135239, 4723, 809, 16, 119, "Text"],
Cell[136051, 4741, 26906, 417, 2969, "Input"],
Cell[162960, 5160, 761, 18, 27, "PreviousNext"]
}, Open ]]
}, Open ]]
}, Open ]],
Cell[CellGroupData[{
Cell[163782, 5185, 64, 1, 11, "SlideShowNavigationBar",
CellTags->"SlideShowHeader"],
Cell[CellGroupData[{
Cell[163871, 5190, 159, 2, 71, "Section"],
Cell[CellGroupData[{
Cell[164055, 5196, 373, 7, 39, "Subsection"],
Cell[164431, 5205, 679, 17, 67, "Text"],
Cell[165113, 5224, 2603, 75, 209, "Input",
CellTags->"S5.32.1"],
Cell[167719, 5301, 572, 13, 49, "Input"]
}, Open ]],
Cell[CellGroupData[{
Cell[168328, 5319, 373, 7, 39, "Subsection"],
Cell[168704, 5328, 397, 8, 65, "Text"],
Cell[169104, 5338, 3088, 84, 199, "Input"],
Cell[172195, 5424, 2817, 73, 140, "Input"],
Cell[175015, 5499, 761, 18, 27, "PreviousNext"]
}, Open ]]
}, Open ]]
}, Open ]],
Cell[CellGroupData[{
Cell[175837, 5524, 64, 1, 11, "SlideShowNavigationBar",
CellTags->"SlideShowHeader"],
Cell[CellGroupData[{
Cell[175926, 5529, 100, 1, 71, "Section"],
Cell[176029, 5532, 445, 16, 227, "Text"],
Cell[176477, 5550, 761, 18, 27, "PreviousNext"]
}, Open ]]
}, Open ]],
Cell[177265, 5572, 64, 1, 11, "SlideShowNavigationBar",
CellTags->"SlideShowHeader"]
}
]
*)
(* End of internal cache information *)