{
"cells": [
{
"cell_type": "markdown",
"id": "6b1ef397",
"metadata": {},
"source": [
"# Fitting Functions with Fourier Series"
]
},
{
"cell_type": "markdown",
"id": "206bd5a7",
"metadata": {},
"source": [
"This notebook illustrates the least squares fitting of functions with a trigonometric basis."
]
},
{
"cell_type": "markdown",
"id": "f6c5a007",
"metadata": {},
"source": [
"The package FastGaussQuadrature provides nodes and weights for\n",
"the Gauss-Chebyshev quadrature rules."
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "a4eb9ba6",
"metadata": {},
"outputs": [],
"source": [
"using FastGaussQuadrature"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "1a603a68",
"metadata": {},
"outputs": [],
"source": [
"using Plots"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "3c9d2f9d",
"metadata": {},
"outputs": [],
"source": [
"using Printf"
]
},
{
"cell_type": "markdown",
"id": "6b503bda",
"metadata": {},
"source": [
"### 1. The Orthogonal Basis of Trigonometric Functions"
]
},
{
"cell_type": "markdown",
"id": "5ee2221b",
"metadata": {},
"source": [
"The inner product requires the numerical evaluation of integrals. To evaluate the integrals, we apply Gauss-Legendre quadrature. The weights and the nodes ar provided by the package ``FastGaussQuadrature``."
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "b718f5c7-e7ff-4a1d-9595-92f83b00a081",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"-0.9972638618494816 : 0.007018610009470092\n",
"-0.9856115115452684 : 0.016274394730905625\n",
"-0.9647622555875065 : 0.025392065309262146\n",
"-0.9349060759377397 : 0.03427386291302135\n",
"-0.8963211557660521 : 0.042835898022226614\n",
"-0.84936761373257 : 0.05099805926237613\n",
"-0.7944837959679424 : 0.05868409347853559\n",
"-0.7321821187402897 : 0.06582222277636192\n",
"-0.6630442669302152 : 0.07234579410884852\n",
"-0.5877157572407623 : 0.07819389578707032\n",
"-0.5068999089322294 : 0.08331192422694678\n",
"-0.42135127613063533 : 0.08765209300440385\n",
"-0.33186860228212767 : 0.09117387869576388\n",
"-0.23928736225213706 : 0.09384439908080452\n",
"-0.1444719615827965 : 0.09563872007927489\n",
"-0.048307665687738324 : 0.09654008851472778\n",
"0.048307665687738324 : 0.09654008851472778\n",
"0.1444719615827965 : 0.09563872007927489\n",
"0.23928736225213706 : 0.09384439908080452\n",
"0.33186860228212767 : 0.09117387869576388\n",
"0.42135127613063533 : 0.08765209300440385\n",
"0.5068999089322294 : 0.08331192422694678\n",
"0.5877157572407623 : 0.07819389578707032\n",
"0.6630442669302152 : 0.07234579410884852\n",
"0.7321821187402897 : 0.06582222277636192\n",
"0.7944837959679424 : 0.05868409347853559\n",
"0.84936761373257 : 0.05099805926237613\n",
"0.8963211557660521 : 0.042835898022226614\n",
"0.9349060759377397 : 0.03427386291302135\n",
"0.9647622555875065 : 0.025392065309262146\n",
"0.9856115115452684 : 0.016274394730905625\n",
"0.9972638618494816 : 0.007018610009470092\n"
]
}
],
"source": [
"nodes, weights = gausslegendre(32)\n",
"for i = 1:32\n",
" println(nodes[i], \" : \", weights[i])\n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "998f560b-0f43-462d-8aba-4722e2d2653d",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"rule (generic function with 1 method)"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"rule(f) = sum([weights[k]*f(nodes[k]) for k=1:length(weights)])"
]
},
{
"cell_type": "markdown",
"id": "40ee02f1",
"metadata": {},
"source": [
"The ``rule`` is applied in the definition of the inner product function below."
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "850d15bc",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"innerproduct"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"\"\"\"\n",
" function innerproduct(f::Function, g::Function)\n",
"\n",
"returns the value of the inner product of the functions f and g,\n",
"by the integral of f and g over [-1,+1].\n",
"\"\"\"\n",
"function innerproduct(f::Function, g::Function)\n",
" fun(x) = f(x)*g(x)\n",
" return rule(fun)\n",
"end"
]
},
{
"cell_type": "markdown",
"id": "20866bd7",
"metadata": {},
"source": [
"The ``innerproduct`` will be tested on the verification of the orthogonality of the basis."
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "07e58e3a",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"basis"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"\"\"\"\n",
" function basis(n::Int64)\n",
"\n",
"returns an array of functions with the first 2*n+1 basis functions.\n",
"\"\"\"\n",
"function basis(n::Int64)\n",
" one = [(t) -> 1]\n",
" sines = [(t) -> sin(k*pi*t) for k=1:n]\n",
" cosines = [(t) -> cos(k*pi*t) for k=1:n]\n",
" result = [one; sines; cosines]\n",
" return result\n",
"end"
]
},
{
"cell_type": "markdown",
"id": "d91d9ce5",
"metadata": {},
"source": [
"As ``basis`` returns an array of functions, there is not much to see, but we can use the functions in a plot.\n",
"Let us look at the first five basis functions."
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "59998cde",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"image/svg+xml": [
"\n",
"\n"
],
"text/html": [
"
"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"B5 = basis(2)\n",
"xr = -1:0.01:1\n",
"yr1 = [B5[1](t) for t in xr]\n",
"yr2 = [B5[2](t) for t in xr]\n",
"yr3 = [B5[3](t) for t in xr]\n",
"yr4 = [B5[4](t) for t in xr]\n",
"yr5 = [B5[5](t) for t in xr]\n",
"plot(xr,yr1,label=\"B0\")\n",
"plot!(xr,yr2,label=\"B1\")\n",
"plot!(xr,yr3,label=\"B2\")\n",
"plot!(xr,yr4,label=\"B3\")\n",
"plot!(xr,yr5,label=\"B4\")"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "38ec9aba",
"metadata": {},
"outputs": [],
"source": [
"# savefig(\"fourierbasis5.png\")"
]
},
{
"cell_type": "markdown",
"id": "b4b8d617",
"metadata": {},
"source": [
"The verification of the orthogonality is defined by the function below."
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "f3a84363",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"orthogonality"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"\"\"\"\n",
" function orthogonality(n::Int64)\n",
"\n",
"Verifies the orthogonality\n",
"for the first 2*n+1 basis polynomials.\n",
"Prints the matrix of all inner products.\n",
"\"\"\"\n",
"function orthogonality(n::Int64)\n",
" b = basis(n)\n",
" dim = 2*n+1\n",
" for i=1:dim\n",
" for j=1:dim\n",
" ip = innerproduct(b[i],b[j])\n",
" ipstr = @sprintf(\"%+.2e\", ip)\n",
" print(\" $ipstr\")\n",
" end\n",
" println(\"\")\n",
" end\n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "cd9caa7a",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" +2.00e+00 +9.16e-17 -2.64e-18 +3.17e-16 -3.57e-16\n",
" +9.16e-17 +1.00e+00 -9.37e-17 +2.64e-17 +1.83e-17\n",
" -2.64e-18 -9.37e-17 +1.00e+00 +2.09e-18 +4.49e-18\n",
" +3.17e-16 +2.64e-17 +2.09e-18 +1.00e+00 +2.62e-16\n",
" -3.57e-16 +1.83e-17 +4.49e-18 +2.62e-16 +1.00e+00\n"
]
}
],
"source": [
"orthogonality(2)"
]
},
{
"cell_type": "markdown",
"id": "382a0405",
"metadata": {},
"source": [
"We observe the identity matrix (modulo roundoff of machine precision), except for the first number in the first row and column, which equals ``2``."
]
},
{
"cell_type": "markdown",
"id": "145a126e",
"metadata": {},
"source": [
"### 2. Computing the Least Squares Approximation"
]
},
{
"cell_type": "markdown",
"id": "d4c1a32c",
"metadata": {},
"source": [
"For any function $f$ and the first $2 n+1$ basis functions, the polynomial approximation $p$ of degree $2n+1$ is\n",
"\n",
"$$\n",
" p(t) = \\frac{a_0}{2} \n",
" + \\sum_{k=0}^n \\left( \\vphantom{\\frac{a_0}{2}}\n",
" a_k \\cos(k \\pi t) + b_k \\sin(k \\pi t) \\right),\n",
"$$\n",
"\n",
"where the coefficients are the inner products of $f$ with the basis functions:\n",
"\n",
"$$\n",
" a_0 = \\langle f, 1 \\rangle,\n",
"$$\n",
"\n",
"$$\n",
" a_k = \\langle f, \\cos(k \\pi t) \\rangle, \\quad k=1,2,\\ldots,n,\n",
"$$\n",
"\n",
"$$\n",
" b_k = \\langle f, \\sin(k \\pi t) \\rangle, \\quad k=1,2,\\ldots,n.\n",
"$$"
]
},
{
"cell_type": "markdown",
"id": "4883a91a",
"metadata": {},
"source": [
"The coefficients of the approximation are computed by the function below."
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "60a81e1b",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"coefficients"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"\"\"\"\n",
" function coefficients(f::Function,b::Array{Function,1})\n",
"\n",
"returns the inner products of f with the basis functions in b.\n",
"\"\"\"\n",
"function coefficients(f::Function,b::Array{Function,1})\n",
" dim = length(b)\n",
" result = zeros(dim)\n",
" for i=1:dim\n",
" result[i] = innerproduct(f,b[i])\n",
" end\n",
" return result\n",
"end"
]
},
{
"cell_type": "markdown",
"id": "051131bf",
"metadata": {},
"source": [
"With the coefficients and the array of basis functions, we can define the function for the approximant."
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "37e4ac70",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"approximation"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"\"\"\"\n",
" function approximation(c::Array{Float64,1},b::Array{Function,1})\n",
"\n",
"Given in c are the coefficients of the Chebyshev approximation\n",
"with the basis functions in f.\n",
"Returns the approximation as a function.\n",
"\"\"\"\n",
"function approximation(c::Array{Float64,1},b::Array{Function,1})\n",
" first(x) = c[1]*b[1](x)/2\n",
" rest(x) = sum([c[k]*b[k](x) for k=2:length(c)])\n",
" result(x) = first(x) + rest(x)\n",
" return result\n",
"end"
]
},
{
"cell_type": "markdown",
"id": "a262b1f6",
"metadata": {},
"source": [
"Let us compute the least squares approximation of $(\\sin(2 \\pi t))^3$ for $t \\in [-1,1]$ of degree 7, or $n=3$."
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "5c0af714",
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"text/plain": [
"7-element Vector{Float64}:\n",
" -8.744874026571803e-18\n",
" -1.4346993204495304e-16\n",
" 0.7500000000000001\n",
" -1.441209547749919e-16\n",
" 3.9532417311787286e-18\n",
" -5.12958520645774e-18\n",
" -4.482586368886933e-17"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"f(t) = (sin(2*pi*t))^3\n",
"b3 = basis(3)\n",
"c3 = coefficients(f, b3)"
]
},
{
"cell_type": "markdown",
"id": "e69a439a",
"metadata": {},
"source": [
"Observe that many of the coefficients are below machine precision."
]
},
{
"cell_type": "code",
"execution_count": 15,
"id": "7e92e2ea",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(::var\"#result#approximation##4\"{var\"#rest#approximation##1\"{Vector{Float64}, Vector{Function}}, var\"#first#approximation##0\"{Vector{Float64}, Vector{Function}}}) (generic function with 1 method)"
]
},
"execution_count": 15,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"a3 = approximation(c3,b3)"
]
},
{
"cell_type": "code",
"execution_count": 16,
"id": "076e79de",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"image/svg+xml": [
"\n",
"\n"
],
"text/html": [
"
"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"xr = -1.0:0.01:1.0\n",
"fx = [f(t) for t in xr]\n",
"px = [a3(t) for t in xr]\n",
"plot(xr,fx,label=\"((sin(2*pi*t))^3\",legend=:topright)\n",
"plot!(xr,px,label=\"F7(t)\")"
]
},
{
"cell_type": "code",
"execution_count": 17,
"id": "7b391793",
"metadata": {},
"outputs": [],
"source": [
"# savefig(\"trigonometricapp7sin3.png\")"
]
},
{
"cell_type": "markdown",
"id": "cc9f1f8e",
"metadata": {},
"source": [
"Let us make a plot of the error. "
]
},
{
"cell_type": "code",
"execution_count": 18,
"id": "3cb727e0",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"image/svg+xml": [
"\n",
"\n"
],
"text/html": [
"
"
]
},
"execution_count": 18,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"errors = [abs(f(t) - a3(t)) for t in xr]\n",
"plot(xr, errors, label=\"|(sin(2*pi*t))^3-F7(t)|\",legend=:inside)"
]
},
{
"cell_type": "code",
"execution_count": 19,
"id": "74a76567",
"metadata": {},
"outputs": [],
"source": [
"# savefig(\"trigonometricerr7sin3.png\")"
]
},
{
"cell_type": "code",
"execution_count": 20,
"id": "d1f625ee",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"13-element Vector{Float64}:\n",
" -8.744874026571803e-18\n",
" -1.4346993204495304e-16\n",
" 0.7500000000000001\n",
" -1.441209547749919e-16\n",
" -2.3198680413195323e-15\n",
" -4.4729931373818793e-13\n",
" -0.25000000004608725\n",
" 3.9532417311787286e-18\n",
" -5.12958520645774e-18\n",
" -4.482586368886933e-17\n",
" 2.767253991701839e-17\n",
" 7.131289496942162e-19\n",
" -8.08138914852057e-18"
]
},
"execution_count": 20,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"b6 = basis(6)\n",
"c6 = coefficients(f, b6)"
]
},
{
"cell_type": "code",
"execution_count": 21,
"id": "be3e1676",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(::var\"#result#approximation##4\"{var\"#rest#approximation##1\"{Vector{Float64}, Vector{Function}}, var\"#first#approximation##0\"{Vector{Float64}, Vector{Function}}}) (generic function with 1 method)"
]
},
"execution_count": 21,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"a6 = approximation(c6,b6)"
]
},
{
"cell_type": "code",
"execution_count": 22,
"id": "84b6fde6",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"image/svg+xml": [
"\n",
"\n"
],
"text/html": [
"
"
]
},
"execution_count": 22,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"xr = -1.0:0.01:1.0\n",
"fx = [f(t) for t in xr]\n",
"px = [a6(t) for t in xr]\n",
"plot(xr,fx,label=\"((sin(2*pi*t))^3\",legend=:topright)\n",
"plot!(xr,px,label=\"F13(t)\")"
]
},
{
"cell_type": "code",
"execution_count": 23,
"id": "601d7414",
"metadata": {},
"outputs": [],
"source": [
"# savefig(\"trigonometricapp13sin3.png\")"
]
},
{
"cell_type": "markdown",
"id": "43dc1cac",
"metadata": {},
"source": [
"Let us focus on the largest coefficients in the Fourier series approximation."
]
},
{
"cell_type": "code",
"execution_count": 24,
"id": "48d8c2de",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"13-element Vector{Int64}:\n",
" 0\n",
" 0\n",
" 1\n",
" 0\n",
" 0\n",
" 0\n",
" 1\n",
" 0\n",
" 0\n",
" 0\n",
" 0\n",
" 0\n",
" 0"
]
},
"execution_count": 24,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"argc6 = [Int(abs(t) > 0.01) for t in c6]"
]
},
{
"cell_type": "code",
"execution_count": 25,
"id": "292f7936",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0.7500000000000001\n",
"-0.25000000004608725\n"
]
}
],
"source": [
"println(c6[3])\n",
"println(c6[7])"
]
},
{
"cell_type": "markdown",
"id": "fb53bfa5",
"metadata": {},
"source": [
"Only two basis functions matter, with coefficients 0.75 and -0.25."
]
},
{
"cell_type": "code",
"execution_count": 26,
"id": "e6b9a3c9",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"g (generic function with 1 method)"
]
},
"execution_count": 26,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"g(t) = 0.75*sin(2*pi*t) - 0.25*cos(pi*t)"
]
},
{
"cell_type": "code",
"execution_count": 27,
"id": "768e6363",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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IVUkDUIQAj06dsT8LzyefwWBYM0qMHSYsWwdxCYpw5foHRpiRsFSSh2XrygpNoQOKEOAx2WMK5Stxbd0rVo11wfUygDRQhCuHcVCMEMrPywox2RarHVcAkMiSB43ZCmwf/gy5KmkAjggBaaAIVw7voBghNJilNMP1MiDmIhFCOt6lKsP24YfpEEAuKMKVwzsoRgiFC1SuXhgXg1gzdfeNczNyBOm4AsB0CCAXFOEKYR8UI4RyFaoUO4yLQaz16o0j2TiHgAimQwCpoAhXCPugGCFUVqGG5y6C2PP3GZmFOIeACKZDAKmgCFeICoPiNH7yGDcHXkMBYixjyCRW4bl9dgZMhwASQRGukL/XyJRiLkKE0KhQZTXC7gDEjtcXELutanWsn687C0yHABJBEa5QxrBRXIq/CNkSZaAPJohA7Oj1XYOpkhi/dOJCMB0CSARFuBI+f1Ds7sc+KEYIFahUgmG4sxjEjt1kGhfG9B2E84HpEEAWKMKV0Ou7BlMKsA+KEUJqdUmeZ9Dl8eEOAhJFuN/Io8BJAQTTIYA8UIQrMdhpmhBivmpuGjeJPcCXGPXduIOARJEzapKqKfHhF5cqM4bhiBCQAIpwJcJWE4cag2KE0KRQae+EcTGIhfFJd3bAUVoixR0EIYQ06hKxZ8DjDeAOAmgPinAlskdMEhUlBsUIIa5UFemHIgSxYNCZrGnFbDYLdxCEEOJxkwZTCw0GmA4BqwVFuGxTLm+2f1RVWoQ7yKekaiW8pxTExmiXyS2iylwIQmhcqLSb4MMPVguKcNl0Hab+dDlFBsUIIZWiSBAcd064cAcB8Y9hM6XKqTIXghDiFSnDNpgOAasFRbhsI10mVx6FBsVMJsOaXmzUdeIOAuKfyNFZrKFQEUqUquxRKEKwWlCEy2czpsootC9ACHnylCNdMEEEomtkbIIX8sokYtxBPqMqLcr2jcF0CFglKMJlE42Z5FQaFCOEUuVKJkwQgSgztOn7BaUMBgN3kM+wWMz+dLlJ34U7CKA3KMLlGRmbSA15iovycQf5nGKNUuSAqVEQXU6zyS+m1hAQIeTKU410wSgQrAoU4fIY2o3WTGoNihFCMomYG/EPDDlwBwHxjDNoypBT6Oz4tFSZkgHTIWB1oAiXx9lj8ooo8aDF8zEYDFumolsPuwMQRfnOrlIt5T78co0yzwGffLAqbFLW4vV6n376aZPJtHbt2q985Sss1uxbC1599dXe3k+fE5+VlXXnnXeSst3YS7IZk+t3404xB79Y6Teb0NYNuIOA+GSx2sNMVr4oB3eQ2YqL8jvCvuHRcWFOJu4sgK7IOSK87rrrPvroo/r6+j//+c/333//hQs8++yzDQ0NTqfT6XROTk6SslEsCsa7SjWUmx1CCGXIVZxBGBeDaDHrTYNZlDtBiP4zHWLsgA8/WDkSjghbWlqOHTtmt9tTU1O3bdumVqt//OMf5+bmzlrslltuuf7661e/OYz6rEMRxCgQU25QjBBSlqvH9v2OIAiqnb8E8cHVY2QUUHEIiBDyi5R+sxFtWY87CKArEo4IT5w4sWHDhtTUVIRQUVGRRCI5e/bshYu99957P/rRj15//fVQKLT6jWLRbTAOZFNxUIwQEgsFASbHYrXjDgLiU4rdmFNC0Q9/erEyaQDuowUrR8IRod1uz8n57CApNzd3YGBg1jLV1dU8Ho/JZP7kJz958sknDx06xGbPvelIJHLdddfNfHvJJZfcdttt823a4/EwmbG73me8W88QlXg8nphtcVkGBYqR1o68nIzYbC4YDEYikXA4HJvNgVm8Xu+FJ+OjJBIhCid60uVSan74pSUy977OWGaL5S8fzOLz+dhs9nwNciEOh7PowiQUIYfDCQaDM98GAgEejzdrmd/85jfTXzz00ENKpfKdd9659tpr51wbg8HYu3fvzLdKpZLL5c636WAwuMDfki51uDtl2w2x3OKyhAtUIZuZy90Wm80xmcxIJELZ30bcCwQCMfvlGzv7JjkZpUJBbDa3XEWFea1M9uCwUyYRxWaLsfzlg1kIglhWES7lYImEIiwoKHjvvfemvyYIwmazFRQUzLdwampqWVlZX1/ffAswGIwbb7xxiZtmsVixHBRLx7tzylWUHQkKS9Wuf78cw19IhMFgUPa3Efdi+eG3mjoDOdT95COEBgVKp6m7RDbvnodcsfzlg1lY/0HiOkmYV7zssstaWlq6uroQQh9//HE4HN64cSNCyGg0njlzBiEUDAZ9Pt/0wr29vadPn66qqlr9dmOs09w3wUnPEaTjDjIvdZlSMmkOhyO4g4B44+8zMgspeoJwWrhA6eqB04RghUg4IszLy3v00Ue3bNly8cUXHzx48Ne//jWHw0EI/e1vf2ttbX333XeHh4crKirq6urYbPaxY8e+/OUvb9sWo+k7EvXqjYEcil41Ny0zPVXPEZi6ejUqOe4sIK6kD5vS6rfjTrGQ7BKl+6NXcacAdEXODfWPPfbY9ddfbzQaf/7zn8tksuk/fOCBB6YPBAsKClpbW9va2iKRyB/+8IeiIqq80nZZfL0mFrUHxQih0RzlpMEERQhI5A+G8l3WQuo9U+Z82gr10L+6w+EIiwVPywLLRk4RIoQ0Go1Gozn/T4RC4czXhYWFhYWFZG0Li7QhU3r9VtwpFsGUqPx9JoQuxR0ExA+9rnsyJV+ZzMEdZCGZ6akGTman2aoupeU4G+AFo6cl8QdDBe4+lUaBO8gixKXKjGF4xAYg04DJNC6k9EmBaSPZqj4DnCYEKwFFuCQGQ/dQsoifMvu2EKpRqxVit9XrC+AOAuJHqN/IkVB6XnQas1Dps0ARgpWAIlwSm9HozNMsvhxuKcmcwdRCPbynFJAnZ8Qg1dDgwy9WqTOGoQjBSkARLkm4z8CR0mB2CCE0kacaNMLuAJBjfNKd7RtTKqS4gyxOq1WIPTaPF6ZDwLJBES5J7rChiJIvnbgQr0hFWA24U4A4oWsz9GUo2Gwa3DzO4yYNpBbqdZ24gwD6gSJcnHPCJQiOKxX0uBpNplHnjcIRISDHaJfRK6bHEBAhNClU2U0wCgTLBkW4uOlBMV3uTyotkaSGXcOj47iDgHiQZDOkFatxp1iqZJkaWWEUCJaNHjt3vMa6jB4xbfYFDAajP6PUqIPdASBBgbNTWUabD79cqxY64JMPlg2KcHFJNkOGnDazQwghX77K2QW7A7BaFqs9wmBS803UcyqRFySHvPYRJ+4ggGagCBdX4OwsLaNTEWaWqLgDcKYErFa3zmDLotMnn8Fg2DIVnR0wCgTLA0W4iJ6+wRCTTaNBMUJIXa6ROk0EQeAOAujNZTYShXQqQoSQP1/l7IZRIFgeKMJFdHcYBrOo/qztWYQ5mW52SnePDXcQQG98uyG3lDYnCKcJFGreABwRguWBIlyE22Ki3aAYITSUre7RwbgYrFwgGJK4LNoymo0C1WXqwolOmA4BywJFuIg0u15YSoPnS80mVXstetwhAI3pDd3DPGEaPxl3kOXJzc5wsfnGrj7cQQCdQBEuxOcPFrp6yyrod0SYr9Zk2qEIwcr16/VjojLcKVZiSKi1dMCHHywDFOFCOtqNA6mFqSlc3EGWraysVOQdnJjy4A4C6Iro06XIaTgXghCrSBOw6HCnAHQCRbiQQYN+gg4vnbgQJ4ltTZPr2+GqAbBC4hGDXEvLD79Uo8kZgiNCsAxQhAthWnWpxbTcFyCE3PnaYSOMi8FKDNhHuWFfibwAd5CV0KiKs/yOMecU7iCANqAIF1IwZlBVaHGnWKF0hYZjg3ExWAlDq86arWEwGLiDrASLxewTKHSt8OEHSwVFOK+evgGCwZQU5uEOskLayjKp0xCJwHXkYNmmuvWhQrrOhSCEfAVaZxdMh4ClgiKcV1ebvj+HxvsCYU6mi803dcN15GDZ0uy6PDVd50IQQlkKDW8AjgjBUkERzsvbo2NIaFyECK4jByvi8wcLXX1ltHq+7ixlVdoipykUCuMOAugBinBeGXZ9vobGg2IE15GDFaHvXUMzBBn8MV6OwdSDOwigByjCubk8PrFnQKNR4A6yKnAdOVgB+t41dL5RoaYPpkPA0kARzq29VW9NL+Zxk3AHWZXp68hHnZO4gwA6ofVdQzO48rJwL0yHgCWBIpzbsL7dXViJO8VqsVhMS7amvakddxBAGwRBFI7qtTUVuIOslqKqvGC4DXcKQA9QhHNL7mvNVpfjTkGCoLR80gRFCJbK0NnrSUrJF9HpBZxzKpEVMBFhsdpxBwE0AEU4B38wJJ3srqym5ROHZ8nXlqcPwLgYLFVPS9twXjwMARFC/cIyU3Mr7hSABqAI59DaYhhMLaDdC2jmVF6pFrttUy4v7iCAHiK9bbySOClCZlGFrxumQ8DioAjnYNe1TebT/hzJNG4Suy9D0drcgTsIoIfC4Y7Sqjj58Msry4VDUIRgcVCEc0iytmco42RfgBDySipGDTA7ChbXbbFFEEMuFeMOQg61UpYS9AzYR3EHAVQHRThbOByRjRnKauLhBOE0obqc3w9FCBbX1dpmy4ufISCDwejP0ehb4KAQLAKKcLZ2XedIcm6OIB13ENJUVGklUz1ujx93EEB1/u72JHmcnCCcRhSVuzthFAgWAUU4m7WtzSmOn0ExQig1hdvPL2pvM+AOAqhOPNRWXBlXH/7C8orsQTgiBIuAIpyN2dfOV8TVoBgh5CqoGNLDuBgsxDowzA35S0skuIOQqVyryPKNjTrg4UpgIVCEnxMKheUj7Zo1tH+mzCzZ2qpUSxPuFIDSdGearMJKmr6Mdz4sFtOSrW09DR9+sBAows9paTGMJAvFQgHuICSrqa0snDRPTHlwBwHUFexsYinX4E5BvohijcsIRQgWAkX4Oba2pnFJDe4U5EtJ5vRmKlubYHYUzI0gCMlQi7q2GncQ8pXU1OQPNOJOASgNivBzUi2N2WVxWIQIIb+8xtEBuwMwN53e7GUnyyQi3EHIpy4tYhKRbosNdxBAXVCEn5lyeQsne6rXxNVVczOk1TW5VihCMLeepsbhgvgcAiKE+sXVxnPw4QfzgiL8TNPZ5l6BktYv5l5ARZkyLTDZPzCCOwigoqSepnRtHJ4gnJasqiE64TQhmBcU4WecHU1+WdwOiplMRq+wQt/YjDsIoBx/MCRzGiprqnAHiZaKdWvko63hcAR3EEBRUISfye1vklbH7aAYIcRW1PiMMEEEZms612bjS7IEfNxBokWUK3Bws1vbjLiDAIqCIvzUgH00PThRUVaKO0gUqdfVFtmbCYLAHQRQy1Bbk6sonoeACCFH4RprC8yOgrlBEX6q7fRZi6iayYyru4lnkUlEHlZyh74bdxBALZm958SVtbhTRFd2RW1qz1ncKQBFQRF+Kqxr4Gk34E4RdcPyevPpBtwpAIXYBkezfSNrarS4g0TXurpq0ZTVPuLEHQRQERQhQgh5vIHi4bY19etxB4k60Zq6jO5TuFMACmk58UlPwXoWK853BZwkdo+ouuXkGdxBABXF+ad/ic6eOteXqYjjiwVm1K4pz/IOw00UYAbL0MCviP+5EIQQV7shpIPpEDAHKEKEEBpvORVU1uFOEQssFtOSv7btJBwUAoQQcrm8Mqdh7YY4P0E4bc3G9cUjrV5fAHcQQDlQhIggCIntjHpDQhQhQohfUYcMMC4GCCF0+pMz5ixtGj8Zd5BYyBak9afLz56CW2nBbFCEqLnV6Enil8gKcAeJkXX16+Rj+imXF3cQgJ+7vQGpE2JedJpfucHRCqNAMBsUIbKebRiVJ9C+gM9PtmSrzzacwx0EYBYOR2QD5yrqE2UuBCGkra8vsp6CW2nBLFCEKNt8UlKbQPsChFBEucHV+gnuFACzs2fbHMm5hfm5uIPETrEs38NOaW4x4A4CqCXRi7BD180LeWuqNbiDxNTabRcpbKddHh/uIACnoYbDU+otuFPE2mjpxX0nj+BOAagl0Yuw+9ihfsVWBiOeHyhzIWFOZp9A2fDxSWWyUpkAACAASURBVNxBADb+YKjY+knVtoQrwvJtO+Tmo6FQGHcQQCEJXYSRCFHQfVR58TbcQTBgVm8PNh3GnQJgc/LjU4PpMkm+EHeQWCuW5Y/xck81wHNHwWcSugjPnG5xc9I0KjnuIBjUb99c5NCNOiZxBwF4uM8dCldux50CD0/FdsfpQ7hTAApJ6CIcajg0qUnEw0GEED+FZ86rPX3wY9xBAAYTU57i4Za6bZtxB8Fj/Y5tCttpF9xBBP4jcYvQ6wuUWE9Wb9uKOwg2GXXbue0wLk5EJw9+bBZWCTLi/5mCc8rNzujNUjUcgxsKwacStwgbjjXYMooT6trxWerqa3Pdg2bLAO4gINbYLQdTaxN0XnQaq2Z7qPEg7hSAKhK3CMOfvMPecDnuFDhxktgW5SVt+9/FHQTElN7Yk+0e3Lglse6dneWiHReLx7s7u624gwBKSNAi1Bl6st2Dm7dtxB0Es9orrlJ0fTQx5cEdBMRO5/43+8u/wEli4w6CE4+bZFHt0n0Ao0CAUMIWYff+f9oqr0zwfQFCqECc05NXdeKDD3EHATEy5pwqsZ6su2wP7iD4rfvCFQrz4fFJN+4gAL9ELMKRsYni/lMbLod9AUIIiXdcndX4diQCT19MCJ+8+163pF6Yk4k7CH75opwecc2Jff/GHQTgl4hFePLd97qLNucI0nEHoYTa2nJfUuqJY/Dm7vgXCoXz2/eV7LoKdxCqyN9xTW4zjAJB4hWh2+OX6vaVXnol7iAUElx/le/jN3CnAFF3+MARB19cpi3BHYQq1tRo3JyMjw+dwB0EYJZwRXjw9X/2C8sS82ky89m+Z3uKb/z40dO4g4Ao8gdDGcdezLzsNtxBqIWz60vJHz0XCIZwBwE4JVYRjoxNFLe9pbn+y7iDUAuLxQztvIO5/1l4EnEc+/C1N0cz5OvWluMOQi2bNq+d4Is+ems/7iAAp8QqwpN/f7G7ZEfivIx+6bZsr3clZx3cB5ePxieH0yVt+mfx9bfjDkJFhdf9V8HpV+AmokSWQEXYZe6XW45tuulm3EEoKveqO3KPv+T2+HEHAeQ7/urLlqJN6tIi3EGoqExT3Jtf+/Frr+EOArBJlCIMhyO9f/tdX+1euFh0PjVVapuo8uBzz+IOAkjW1KyXmY+sv+lW3EGoq+bG22T6D9p1XbiDADwSpQjff+HFCJO158ZrcQehtG13fUPY33jkI7iILn44J1yhv//SsefrolwB7izUJckXju661/23x6fglRQJKSGK8PSpVqn+QNnd32UyE+tN9MvF5ycn3/JI1gdPWqx23FkAOU786ckB6fqt2zfhDkJ123ddPCSq+PiZ3+EOAjCI/yLsMvcn/fOX3mseys/Lwp2FBqoqVH1rrrc8+7hzwoU7C1itd198NW3Ceul/3Yk7CD3suOs+gcPy/qtv4g4CYo2cIjxz5szevXt379791FNPEcQcj2kYGxu7//77L7nkkgceeMDhcJCy0aXo0JunnnlkePOX6jeuidlG6e7ym6+bEJW1/vrh4dFx3FnAyr3z3AvZuoMl9/43j5uEOws9pKZwC+75SU7zO++++CruLCCmSCjCwcHBSy655KKLLnr44YeffPLJp59++sJlbrzxRofD8d///d+jo6M33XTT6je6FKdPtYaf+75z592XXrk7NluMDwwG46p7vzZRUt/124e6LTbcccCy+YOhd55+OsN8uvSh/5fIb9xcAZlEJHnwN1mGw+/88Vm4yz5xMOY8gFuWxx9//PTp02+//TZC6K233nr44YdNJtP5C7S3t9fV1Y2MjKSkpHg8ntzc3DNnzmi12gtXFQqFkpOTg8HgEjftcrn4/Dnesj0w5Dj38l8K7C3eK7+5afPa5f83AYQQ2vfPd6UnXzSrL9v+xZv4KbxZfxsMBiORCJfLxZINTE1NpaWlXfjnx46eStr/R0d60cb7HspMT419sDgw6pw88/SvMlxD6Atf27ip9sIF5vvlgxjw+XxsNpvNJvPdQSSsq7GxcePGT1/st3Hjxs7OzlmfksbGxqqqqpSUFIRQSkpKVVVVY2PjnEW4SvYRZ0dji7ftE5m9OaLarfzany/cfYOlu+y6KwY21fe8/JfuH91hkdZnV9eXVWoEGXOMPABe/mDIbLZ2nT6V1nmCE/KGL7/3Mhj/rUKOIH3P93929MhJ7rt/OPTvDE/pRkVdnVxWwE34F7fFKxL+vw4NDQkEn16ZnZWVhRCy2+3nF+H5C0wvY7fPe1FiOBxes+az83nXXHPNgw8+ON/CB156JcfWihDiBj25gVEPM9knUCLVev7e23dkpaNIyOWCKz5WJZ3P23b3fRbrEHHmtPfgq8Nv9QwTxBgvJ8jiIgIRiAixuCFWUiA5M5yWwxVJKtbVCDLgKIRk4XCktcU42m1gTIxy3aOMcCg56CYIgsFgICKS4XdmhKbGucJQwRrG9lu11Wo2mwWf/NVbs7YiUPW7liZdqP3MxF9+POAfmWCnjXOzGIzpiTSmj5MSYSYF+NkoIzdHqakoL2Wx4v/ywxgbc7o6zjb67f0s1xjHO84OB5mREGvHLbVry5a4Bh6Pt+jhIwlFyOfzvd5Pb77xeDwIoVmTBnw+3+fzzXzr8XgWmFVgMpnPPvvZPd35+flzTn5Oq9q12+3eihBKTU0Ri4UpyZyKFf5HgIWUa/jlmhKEbkYITUx5IoPDAX8gHA5HIpFIOBwKBN1Op88xQhhOu48+a8goTt1505wTSmC5BoYcZ//xYnHfiUiykCldw5GU8nM3stlJKWl8n8/H4/GYTGZ2dqZImC2HW4OiY9v2jWj7RoRQJELYh8dYo84IQfh8Ph6P65lyhwKBqbGR0NhQeP9f+t4c65FdtOGmW+F1j6Q4dvRU4NBr+VO9kbxqtljBk5bwBQI2J4nBZCoVMj6fzAE3CUUolUrNZvP012azOTk5OTc3d74FppcpKpr3UU8MBqO2dqn7UJEwa4GaBNGQkZaSkSZD85wj9PoCg8caWO/+Yd9RmeaWu+RSMZ6U9BcIhv79j3/Jmt8gVLszv/VU+QXXvMBpqhhjMhn5opx8UQ6a55dv7R9C778z9Iu7z6y98dLrr2KzWThixoMuc3/n35/JcNtZO++Qb1qv+fxlz9PnCMndIgkXyxw6dOi2225raWnJzs6+99573W73Cy+8gBB67bXXFArFmjVr/H5/YWHhyy+/vGvXrgMHDtx2221Wq5XD4Vy4KrIulgExsMDFMj5/8MPX/lnU+nboiz9cU6OJfTa6c3l8J377E4RQ6a1fL5blz7kMFCFGC/zyO7utlpefDLKTt33r+8m8OfZyYGGnz7Ty/vE/fbU37Lr+Ks5cJ2WjcbEMCUVIEMR99933z3/+My8vLxgMHjhwQCqVIoQ2bdp0zTXXPPTQQwihf/3rX3fddZdcLrdYLM8+++zVV18956qgCGlk0atGGxqaUv75K9fVD8E06bKMT7rP/eYxT3rengceWuCoAooQo4V/+eFw5P3//W3KpH3dt36SkZYSy2B0d/zo6cx3/t/kNY8ssNOgaBFOs9vtTqdTpVIxmZ+eLg4EAiwWi8X69F+yy+WyWCxyuTw1dd65XShCGlnK7RNnzrZxX33cd+Oj69dVxiwYrXl9gdOPf3s8X3vl177GYCx02g+KEKNFf/mRCPHeH/43dax38w9+BdeaLtGJ42fT3v5N+JYf1lQvNI0UjSIk7RonkUik0WhmWhAhxOFwZloQIcTn88vLyxdoQRB/1q2tmLr6Idbrvx51TOLOQg8f/vmPUxniq+65Z+EWBBTHZDKu+Mb9/uT0A395DncWehgYcqS+/Vvf3u8t3IJRAhf7gujatHmtTbH17P/9iqy5hzh2+KPjov5zm+96AHcQQAIGg7Hh7ofye44fPXISdxaqi0SI9j/9uq/sMlxTR1CEIOp23/FlTmBq3z/gWcYL6bMOZX/wB87N34PHwcSNLAGfuOHh9PefHLCP4s5Cae+/9CojErr8S1/EFQCKEEQdJ4kt/+p3i86+ahuE3cG82l9+prfq6uoqFe4ggEzr1pb3qXede+kvuINQV0/fgLz1Te1dj2B8HAEUIYgFuVTcrdrd+OrfcAehqMYmndDZvfMGeHF0HNr5xS/mD7e3tBlxB6Eo3at/NVdeXSDOwZgBihDEyPabb5YMnG3r6MIdhHIIgnC+9ez4ltvhtrO4lJLMGam/eeRfzy6+aOJpajHkj3Zsvx7zEBCKEMRIGj95YP2Ntreexx2Ecg4fOJoU9m/fvQ13EBAtl1y5OzkwdezoKdxBKGfk7eeHN92G/e0IUIQgdnZefXmma/BUQzPuIBQSDkdSj/yV84U7mfCw0PjFYjEjl9zBPPAcXDt9vmNHT6X4x3d+4RLcQaAIQQxxktgT9Tc5Dr6BOwiFHD10wsXL2rChBncQEF0Xbd0QYiadOHYGdxAK8R1+I3DRF6nwyg78CUBC2XLpNvG42dTVhzsIVUROvMncfA3uFCAWAnVXu4++hTsFVeiNPTnugc07NuEOghAUIYgxHjepT3Op4YN3cQehhLaOrgzv6EVb63EHAbFw8aVb8yYsxq5e3EEooWvfv2yVV875WO3YgyIEsbb28itKeo6MT7pxB8HPcuBNe+UV8L6eBMFNYvdp9xj3v4M7CH4jYxPF/Q0bLt+DO8inoAhBrOXnZZnFa0+8/wHuIJgNj44X207XX7YbdxAQOxuuuKLEcnTMOYU7CGYn33u/u2hzjiAdd5BPQRECDAovuSq35d0Ev4Ku4f193UWbswXwBokEIszJNBesO/nBv3EHwSkcjkg63i+99ErcQT4DRQgwqKlSB1ncs+c6cAfBKddwULoFDgcTjnDTpekdB3GnwKnhZOM4N1ujkuMO8hkoQoCHQ71t4OQh3CmwaWoxMIlIVaUSdxAQa+vWVaYGpvTGHtxBsHGcPuSp2I47xedAEQI8qrdtK+k97vMv9SXMcabv+KEh1XZ46WACYjIZNsUW09HDuIPg4fb4FbbTa7ZuwR3kc6AIAR6SwrwhvuTUibO4g2AQDkdklmPaLfBMtQRVctH2wq4jkUginiM/+fEnvVkqsVCAO8jnQBECbIKV26fOJeLs6MlPzjmShYriQtxBAB5lmmIvO/lcYzvuIBgEmw6zqqk1L4qgCAFG67dtUQw2JuANhc7Th7xlcDiY0MY12wc/SbhR4JhzSjamq9+yEXeQ2aAIATZZAr45t/LUkRO4g8SUxxtQDJxZu2Mr7iAAp6rt24r7TgSCIdxBYurUoSPdolo+Pxl3kNmgCAFOnKqLwh0ncaeIqTMnz/VlKoQ5mbiDAJwk+cKh1IJzZ1pxB4kplv4kv/Zi3CnmAEUIcFq7ua54pNXt8eMOEjsTrQ0h1QbcKQB+HkXdcFMD7hSxMzHlkTkNa9evwR1kDlCEAKfM9FRrZknj6SbcQWIkEiGktjPaDXW4gwD8SjfUF/QlUBGeO3HGnF1OwXlRBEUIsAuU1jlbE+XN3c0thilOulwqxh0E4KcuLQox2R16M+4gMeLuaGCoKToEhCIEmGk31UutpxLkuaPWcw3OYpgXBZ8aktZ1n06Ig8JwOCIfPFdRD0UIwFzk0nx3Er+51Yg7SCzk9DRI1kIRgk+JaurSuhKiCM+ebRtJFhWIc3AHmRsUIcBvVL7Bejb+dwc9fQOpganqShXuIIAq1q6rzPXabYOjuINEnb2xYUpB3SEgFCHAT7J2g8Ac/0WoO3GyT1IHzxcFM1gsZo+otu1k/J8jz+s7VbIeihCA+VVXaQR+R//ACO4g0cXuPpdevg53CkAtyWXrI8Y4f+Jul7mfEw6UaYpxB5kXFCHAj8lkWPKqOs7G800UXl9A5tBXr63CHQRQS+W6muKR1vh+xIypsdEmrsGdYiFQhIAS2KVrAqZ4LsLmxvb+NFlmeiruIIBahDmZIynC9nYT7iDR1NmUrKbiffQzoAgBJWhr1xQNNcfxTRQj7U1uGaX3BQAXp2RNf0vcjgLD4UjRaHtZbTXuIAuBIgSUIJXkeVk8nSFuX9ud0dcorqD07BDAJbusJtXSiDtFtLS0GhzJOVR7AeEsUISAKoYK1vQ0xefuYNQ5meexV1WpcQcBVFRTW1k4aZ6Y8uAOEhX9LY1OCdXnQqAIAVWkaWrYPfE5QdR6qsmcU85JYuMOAqgoJZnTm6lsbWrDHSQqUi1N2WVUnwuBIgRUUb2uWu7Q+/xB3EHI5zI0Egqq7wsARn55jaMjDqdDplxeyZS5ak057iCLgCIEVCHI4A+kSlqaOnAHIZ/Y3qxYA0UI5iWtrsmxxuF0SPPZFkuGkp/Cwx1kEVCEgEKmimrs7fG2OzBbBtiRkEpRhDsIoK6KMmVGYHzAHm/PWnPomv1yGgwBoQgBhQi1Vfz+eDtT0tna2p9XiTsFoDQmk9GXU6ZvaccdhGSZA60F5TR4iAQUIaCQiiqtZKonzl5Y7+9uT5JT/RwJwI4oKnd3xtUocHzSLfIMlpWX4g6yOChCQCGpKdx+flF7mwF3EDKJh9qKKytwpwBUV1hekT0YV0eEbc3tFoGKS4eLpaEIAbW4CiqG9PEzLu4fGOGFfKUlEtxBANWVaxUC/9ioYxJ3ENI4De1+CT2GgFCEgFoEqgquNX7Gxfrm1r7cCnj1ElgUi8XsFajbm+NnFMi3tYk0UIQALF/lmnKZ0+iPl4fxe7vaEZwgBEsTkpZPGONkFOj2+Aumessr6fE0JShCQC0ZaSn2lPyOeHkYf85ge1E5FCFYknxtReZAnBwRtjZ39KcXpyRzcAdZEihCQDnj+RUDHfGwOxgZmxAEnBoVdd9HCiilolIlctvGJ924g5BgxNDuLqTHvCiCIgQUlKGsYPXGwwRRe2NrT3YZiwX/ysCScJLYvZnK9uZ4eLhSsrUtW02buRD4Jwoop3xNhcyhD4cjuIOs1mRXe6SINvsCQAU+SfkY/U8T+oMh6WR3ZXUZ7iBLBUUIKCcnK93JFeiNZtxBVivT1p6vpc2+AFCBUFPO76d9Eba3Gu0pBWn8ZNxBlgqKEFDRqFDT16HHnWJVXB6f2GPTamnwWA1AHeWVGsmUme7vYBk06MZFGtwplgGKEFARR6YN9+lwp1iV9la9Na2Yx03CHQTQCT+FN5iSr9d34Q6yKkyrLrUYihCA1ZGXa0TD9D4iHDbp3fl02hcAipgQaQb09B4F5o8ZVRVa3CmWAYoQUJGyRJoScg8OO3EHWbkkqz69hE77AkARyXItYaXxKLCnbwAxGJLCPNxBlgGKEFARg8Hoy1IZW+k6LiYIQuI0KivgiBAsm6JCUzhK4yLsatf359Dskw9FCCgqWKid7KZrEXZ2W72slPy8LNxBAP3IpfkMImLtH8IdZIW8Zj1DAkUIABmEKk3qIF3HxT06nT2XZvsCQB22bLWJtldNZ9h1YjXNTgpAEQKKKq/USCbpeh2536xnyaAIwQpFJFqXmZZF6PL4xJ4BrVaBO8jyQBECiqL1deQ5wzqJhmaDYkAdeSpNxiAtzwvQ9K4hKEJAXRMiLR2vI3dOuLJ9oxqVHHcQQFcVFap8d7/b48cdZNloetcQFCGgrmS5ho7XkevaDH2ZpWw2C3cQQFc8bpItVarT0e9lZEn9hrQSKEIAyFNcphaN0W9fMNap94jp8T5SQFmTeaohowF3imUrcJiUZfT78EMRAuoqLsrnhX0DQw7cQZYnacCYUUK/fQGglFS5GtmMuFMsT0/fQIjJLhDn4A6ybFCEgLoYDEa/QNnZQafdAUEQEqdJqVXiDgLorVirFtNtOqS7wziYrcKdYiWgCAGlBfJV42Y6TRD19A76Wbx8Ef0GxYBS5EVibtg3YB/FHWQZ3D1GogCKEACyZZWoeIN0OiI06wz2LDgcBKs1PR1iotX1MmlDBmEpLU8KQBECStNUaKTjXZEIgTvIUrl7DEQhLQfFgGoC+aqJbtpMhwSCoUJXr7aMli/ghCIElJYtSJtMSus09+EOslRpw8Y8FS0HxYBqshTqZDttpkP0hu4hXh6fPm+lPx8UIaC6kRyVRUeP3YE/GCqc6tXAW+kBGTTl6qLxTrpMh9gMJqeQrkNAKEJAdQyp2t9LjyLU67rtKfn8FB7uICAeZAvSnJxMUzc9pkPCVgOnCIoQgOgQl6oyhuhxpmTAZBgXwglCQJqRHFWvjh4f/pwRg1RN1w8/FCGgOq1WIfbYaPHcxXCfgSuj674AUBCrUOXvpUEROidcWQGnqrQId5AVgiIEVMfjJg3wJQY6vIYiZ9QkVUERAtKI1eqMYRqcFzB0mKzpxSwWXQuFrrlBQpkUquydVL+hanzSnRVwKhV0HRQDCtKoS8SeAY83gDvIIka7jLR+vi4UIaABXpEy0k/1ItS3G2k9KAYUxOMmDaZKDAaqT4ewbKY0OY2fI0HOP9qOjo6dO3fK5fJrrrnGZrNduMB3vvOdS/7jjjvuIGWjIHFI1arcMapPEI12mzwimBcFJJsQKgcpPx2S7zSV0PZKGURKEYbD4SuvvHLnzp0NDQ2FhYW33nrrhcs0NjZu3LjxkUceeeSRR+68887VbxQkFGWJNNM/Meacwh1kISybkV9E40ExoCauVBmxUnoUODDkYEVCUkke7iArx179Kj766CO/3//II48wGIyf//znubm5RqNRdcElAxUVFTt37lz95kACYjIZ1oxih860cVMt7izzEjk6s8ruxp0CxBupRjXe8BruFAsxdei9AmUF7hirQcIRYUdHx5o1axgMBkKIz+eXlpbqdLoLF/vpT39aX1//la98pauL6vPdgIK8IuVYN3UniAaHnZxIQCYR4Q4C4o1KUZQVcDonXLiDzGvCbArm03suZKlHhG+++eaFf1hdXS2Xy8fGxtLS0mb+MDMzc2RkZNaSd955Z0FBAZvNfumllzZt2tTe3p6bmzvnhsLhsEAgmPn21ltv/fnPfz5fKrfbvcT8gHTBYDASiQSDwdhsjlsoD7Ucd7koujtob2oNCUplMYzndrunR58g9mL8y+9Ll9ubOmrXlsVsi8vCGzCy678Qs3+bPp+PzWaz2UstLx6Pt+jCS13XK6+8cuEfpqamyuVygUDQ3t4+84eTk5NZWVmzlrzpppumv6ivrz9+/Pj7779/++23z7khFotlNptnvk1JSeFyuQsE4/P5S/svACSbLsKF/++QSFNZ4TjyHGX/d3v7e1C+OpbxCIKg7G8j7sX4l+8VqX3WHv7WuphtcekIgiiYNAtrymP2C2H/B5nrXOJyr7/++nx/VVxc/Oyzz05/HQgEzGZzSUnJAqvKzMz0eDwLLHD+ESEA06SSvHEiMmAfpeY7b7mDppSLr8KdAsQnfpHS13wEd4q5dffYfCyeMCcTd5BVIeEc4WWXXeZwOP71r38hhJ566imZTFZTU4MQeu+99/74xz8ihKampo4cORIKhcLh8CuvvHLmzJnt27evfrsg0dgECmq+p5QgiILxrlINvU+TAMqSa5UiRyfuFHOzGEz2bNp/8kkoQh6P9+qrrz744IMCgeAvf/nLSy+9NP3nOp2uoaEBIRQIBL7+9a+npKSkp6c//vjjf//739VqGj+DAOASzFdNmqlYhObeAR+LJ8qFmQwQFXKpmB0JDdhHcQeZg9tiQgU0voNwGjnTrDt27Ojt7fX5fDzeZy+gefjhh6e/yM7Obm9vj0QioVCIw+GQskWQgATFKs+xt3CnmEOP3uTPgncQgigaECicuk4KnhfgD5v4tV/GnWK1yHwc1PktOMeWmExoQbAa6nKVZNxEEJR7T6nbYiLoPygGVBYQKyd6KHdbfTgcKZzsUdP/TdTwXERAG7nZGR5Wirl3AHeQ2fhDxlwF7U+TACoTFCu5g5Q7L2Aw9ozxcjLSUnAHWS0oQkAnQ1nKHj21dgfTg2KlRoE7CIhnqnJ1obOTatMhVpNpNDce5kKgCAGdEAVKt4VaRWjs7B3jZQsy4JY+EEXCnEwfi2exDuIO8jmBPhNbEg9zIVCEgE5yFUr+ELXOlFhNxrGceNgXAIqzZ5WaKTYdkjFsFJfGw4cfihDQibZcJZnqCYXCuIN8xtdrYhXEw74AUFykQOnuoVARen2BfI9NrSrGHYQEUISATtL4yaPcbFNXH+4gn8kcNomU8XCaBFBcrkKVMkShItTruwdSJcm8eLgXAIoQ0MxYjtJqosrsqM8fFLv71eqFnikIACnUZUrpZHc4HMEd5FN2k3FcGCdzIVCEgGZYBUpfL1XGxXpD92BKfkpyPAyKAcVlpqc6kgSmbqpMh4Rtnbx4eRM1FCGgGZFSlTlMlSIcNHVOCGFeFMTISK6qz0CVD3/2iEkSLycFoAgBzWg0JWJ3v9cXwB0EIYTC/UaONE4GxYD6mBKVv48S5wWmXN5s/6hSIcUdhBxQhIBmknmcwZQCg6EbdxCEEMoa7Swopf3zpQBdiEpK06kxHaLrMPWnydlsFu4g5IAiBPQznqcaNOIfF0+5vLneIZVShjsISBTastJ8l9XnD+IOgkY6DW5RnMyLIihCQEe8ImXYhn9crGs3WtOLOUlkvikbgAVMT4fo9V24gyCGzZQii5+TAlCEgH6kKlXOCP4jwpEuozsvfgbFgBYoMh0iGjOVlMXPhx+KENCPqlQm8I87nC68MeJsUAxogQrTIYPDTm7EL5OI8cYgERQhoB8mk2HNKDboMI+L42xQDGiBCtMhxna9VaBkMBh4Y5AIihDQklesGu3GuTuIv0ExoAUqTIdMmk3B/LgaAkIRAlpKkyvZAzgniOJvUAxogQrTIbxBo6AYihAA3BQaVcEYzn3BhNkYZ4NiQBd4p0MIgiic6FSVxdXZcShCQEuSwjwCMawDw7gC8AaNWSVQhAADvNMhnd1WF5svzMnEFSAaoAgBXQ1mlXZ14BkXEwQhmehSl6uxbB0kOLzTIb0G43B2vA0BoQgBXQXzVVOY3lM6PSjOyUrHsnWQGYF45AAAIABJREFU4PBOh3gtJkZhXM2LIihCQF/ZJcpkO55xca/BNJwTb/sCQCMYp0PShk3CUjgiBIAatBVq6XhnKBSO/aa9Fj2jEOZFATbBAtWU2RD77fr8wQJ3n1Ybbw+ahyIEdCXI4I9xc4wmS+w3nWHX56s1sd8uANOESk3qoD722+1oNw2mFKamcGO/6aiCIgQ0NibU9OljvTtweXxiz4BGo4jxdgGYUVaulkya/cFQjLc7aNRPiONwCAhFCGgsSaYO9sV6gqijzdifJuNxk2K8XQBmpPGTh5JFel2s38rJsBpSZHF4UgCKENCYVKMRDulivNFhk94lisNBMaAXZ55mwBDr6RDxmKEkHu8agiIENKZWyjIDE6OOyVhulGUz8EugCAFmXJkmYo3pdIh1YJgdCcml+bHcaGxAEQIaYzIZvYJSfVtMdwcFY0ZlORQhwKy4TJM3GtMjws52Q39OHB4OIihCQHf+Ao2zK3azoz19AwSDWZifG7MtAjAnRXFhcsg7OOyM2RanuvXhAihCAKhHUKLhDsTuiLCrXW/LhsNBgB+DwegXKI3tsRsFptn1eUptzDYXS1CEgN60lRrZuCkcjsRmc16zgZDE56AY0E6gQD3ZFaNRoM8fLJyyaMvi7Vb6aVCEgN6yBWnOpExjZ29sNpcxZBCr4IgQUEJOqSYlVrfV63Rdgyn5fH5ybDYXY1CEgPaG87R9ulhMELk9frHbGq+DYkA72gq1ZKI7EJPb6geN+om8uB0CQhEC2uPIy4I97THYUFurzpomT+ZxYrAtABaVmZ46nCLq6OiMwbYYlrYURXkMNoQFFCGgvZKKcvFwRww2NKxvdxfE7b4A0JFTVG7riPookCCIwlG9qqos2hvChY07AAkikcg111zj8XhwB0ksBEEghBgMBu4gCCHktfWwGrZyONF97NnkoI2Zlvnk669GdSsIIQaD8cwzzxQXF0d7Q4Du+Ipyf9MhhG6I6lY6u60BFkeSL4zqVjCKhyIMBoP79+/ft28f7iAAkOPb3/621WqFIgSL0qypdHz4h0iEYDKjOCQ1t7UH8+J5LiQeihAhxGQyd+7ciTsFAOQQCAS4IwB6EAsF1qRUY1evRimL3laCPe1J8nguQjhHCAAANDaUV25pi+5pQvFQe3EFFCEAAABK4pSUh6N51bRtcJQX9pWWSKK3CeygCAEAgMZKysvzh6NYhPrmtr6cMopcFhclUIQAAEBjiuJCJhHpsw5Faf2ernaiKJ7nRREUIQAA0J0tR2tsjdZBYba9vbAcihAAAACFMYorfKaWaKx5ZGwi2ztaplFEY+XUAUUYLVartbq6OhT69DGAv/jFLx5//PE5l/T7/Ww22+fzLbC2UChUU1NjsVgQQgcPHrzrrrt27Nhx0003HT58+PzFnnjiiaGhRWZI7rrrrt/97ncz337ve9+b+bq7u7uhoWHm2+uuu+7AgQPTX9vt9rKyMr/fP2ttb7755te+9rXu7u7z//Do0aO33377tm3brrrqqueff3761nsAQJSU1FTn25ujseaW0409ueVsNisaK6cOKMJoeeyxxx544AE2m40QmpiYePLJJ++///45l0xKSnr++eeTkhZ6Kspzzz23du1amUyGEHrhhRfKysoee+yxiy666PLLLz9+/DhC6H//939bWlpsNpvH4/n973/f0THvI8fuuOOO3bt3RyKRRx99dGRkpKenx+l0fu973wsGgwcOHHjiiSdmlnz00UcfffTR6a9FItH27dv/9Kc/nb+qN95445577klOTt6xY8d0SU+bmprasWPHz372s5tvvvmxxx575plnFvllAQBWQaUoYhCRLnM/6Wv2GJsjJTWkr5ZyCCoJBoNsNnvpy09NTREE4fP5uFxu1EKthMPhyMzMnJycnP726aefvuWWW6a/jkQir7zyyje+8Y3777//hRdeIAgiFAr98pe/DAaDBEH87W9/0+l0TzzxxH333ffmm2/OrLC6uvrIkSMXbuimm2767ne/SxDE+Pj4D3/4Q6VSeeWVV+7bt48giOHh4aeeeqq1tfXBBx/88Y9/bLPZpn9k//79p0+fJgiis7Pz7rvvlkqlX/3qV3U6nd1uv/rqqysrK3/xi1/86U9/ml5Yq9U2NDRMf33q1CmNRjOz6X379imVSr1eTxDEG2+8oVQqe3p6Lkz4gx/84MYbb1zxbzIxbdmyZc7/3eeb+XSB2KPgL//t3/563xvvkr7a04/cpjdZSF/tani93um9JYngiDAqDh8+rNVq09LSpr/dv3//li1bpr9+5plnnnjiiS1btmzevNloNCKEgsHgI488EgwGEUL/93//d8MNNwSDwerq6rvvvnv//v0IocHBQb1ev2HDhllbIQjCaDQWFRUhhIaHh+12e2pqKpfL7ezsDAQCdrv9kUceefDBBzds2OByuerr66emphBCr7/++tGjRxFCvb29LpcrLS3N5/P19PRwOJycnBw+n19cXCyRfHrP0JYtW2aeXVdbW2u1WqeP/JxO54cffnjkyBG1Wo0Quu6665566qnXX399JlswGHQ4HGfPnn3nnXeuuOKKqPyWAQD/kVxaHekieXbUbBlIioRUCim5q6WgOHnE2iwEQjveD00GY7Q5SSrjzUs+N4fe0dFRWvrZW+va29u/9a1vzXx98cUXX3vttQwG44Yb5nhU7q233vrQQw8hhKxW6/79+/fs2aPT6aRSKZfLnbXkr371K5/Pd8cddyCEzp0799Of/vTXv/71/fff39HR0dvbixByuVx/+tOfiouL9+7d29ra+uKLL957773TPxuJRLq7u5977rnbbrvtr3/961//+lc+n19TUzM1NXV+KoVCcfLkyemvWSyWXC7v6OiQyWQCgeC3v/3t+WF27tx5/lPuTpw4cfvtt9vt9ksvvfSaa65Z1u8TALBc5etrnUeeCYcjLBZphzemxqagqLo6ru8gnBafRchA6OlNLHcsXleJEEIZF7yfzuv1nt9bXq+Xx+NNf/21r33t2muvfe211/bs2XP33XfX1Myefy8r+/RdJ3l5eV1dXQghj8cz8+Mznn/++aeeeurjjz+e3tBNN92EEKqrq+Pz+bt370YItbW1ZWVlzTy4uba2Vq//7GXWTCbzrrvuQgjt2LGDzWb/13/915z/aSkpKS6Xa+bb5ORkt9u96C8EIbR161aLxeJ2u7/85S/fc889L7zwwlJ+CgCwMmKhwMzJatd1VlWoyFpnqKuJp60ja21UFp9FiBBSZ+IcxQiFQpPJdP63Y2Nj019XVFR0dna2tLS8/vrrF198scFgyM7OPv9nmczZA7q8vLyZH5/28ssvP/bYY4cOHZLL5ef/+fXXX3/+tx6PJxKJTK9wamoqPT39wqh33nnnzNcXPjxiZGREJBLNfDs2NpaXlzf3f/NcUlNTv/SlL337299e+o8AAFZmVFLjaG4iqwgjEaJouE1w692krI3i4BxhVNTV1bW0fHZbz4YNG5qbP52+t1gsBEFUVVX96Ec/Sk9Pt9vti66tsrLS4XAMDw9Pf/vGG2985zvfOXDggFKpXPgHfT7fyy+/jBByOp1vvfXWoi/oyMrKmpWnpaVl5tzkxMREf39/bW3tooF1Oh1BEAghv9//2muvXXjUCwAgnUBTzbGQdpqwraNzKim9MD+XrBVSGRRhVNTV1YXDYYPBMP3t3r1733///emvf/WrX8nl8h07dpSVle3evXspJcHj8a666qqZi1a+//3vO53Oiy66KCsrKysr65577pnvB0Ui0dtvv71p0yaNRnPDDTds27Zt4Q3t2bMnEAhIpdLpyvT5fMeOHbv66qun/3bfvn179uzh8/mLBn7ssceEQmFFRYVIJBocHPz973+/6I8AAFapqrZK5jR6vAFS1mZtaRqVJMwQltyLUFcpbm6fIAji97///YMPPjj9dSQSqa2tbW5unv7W4XDodLqxsbGZhQOBwMJrO3PmTH19/bICtLa2FhQUEATR09MzOjo68+ehUCgcDi9lDX/961+/+tWvzny7devWY8eOLXHro6OjOp3O4XAsJzL4FNw+QXGU/eUf+O+Hjxz8hJRVffTDbx4/doaUVZELbp+gk3vuuYfD4YTDYYQQg8F46qmndDrd9F8JBAKNRpOVlTWz8MJ30yOE1q5de91111mt1hUkkclk55+GZLFYF56GnNPQ0NBPfvKTma937dq1efPmJW40Oztbo9HAC2YBiKWgun6y5eTq1zM8Oi52W9fWVa9+VbQQtxfLYJeUlPSLX/xi5tu6urq6ulVdf7XcS05EItHMc2FW5uGHH575Oi8v7/yHsQEAKKhyY/3EE6+s/iaKxuMnQ6I12qREKQg4IowfwWAwEonMfJubmztz1yDpIpHI9BMAwIWmJ59xpwCJSFKY5+DlNDbpVrkeQneSV1ZPSiRagCKMlt7e3ltvvXXdunX33nuv0+mc9bder3fv573xxhsIoe7/396dhjV17A0An0BAkAgBwhoUJCJL6UWIIMhSFCmiQOniBRUutl5X9FZaK1VfbPtQ9cXHWpdrFRVUsFTLdhV6i0pRgiIVLKCAyI6EIIuQxBDIet4Pc5ubN0R2CSTz+3RymHPOP2PMZM6Z+U9jo/RO6Zzad+/elaTAlmv16tXwJMOIjo5OSUkBADx9+jQmJsbHx8fPz+/IkSN8/n8fsJeXl0vniJErJydHegzquXPnmpubJW8tKytL8qe0tLQtW8Y2ApvD4cTExCxZsuSvf/0rTL4j46effgoLC3N3d//oo4+Kiook+6Wr7sKFC5L9XV1d0nnGJ+j06dOxsbHDFNi2bdt3330neSndk25qapIkKAAArF+//saNG5MVGIIAAJgUj45HE7o72s/lze+ppi51nayQpj/UEL4RGIYFBQWZmJgkJSUxmcyoqCiZAng8fs2fgoKCsrKyjIyMAAC9vb00Gk3yJ5hl+1//+ldaWhqTyezt7U1PT//555/lXvTAgQOenp7DRNXU1JSXl7d+/XoAAI1GIxKJ8fHxsbGxly9fhjdR8/Pzz58/z2azu7q6/v3vf1+8ePF1p3Jzc4uPjwcAnDp1ikajMRgMDodz7NixsrKyly9fRkZGSkrCJTJgZoBR2rFjR319/blz5xwdHd99992hXc/r168HBQWdPHnSy8srICCgquo/K7Glp6evXLkSVp2LiwsAoKam5uDBg/39/XQ6/ffffz969Ojow5BrcHDw8OHDw9+m3rZtW2hoqFgs/vzzz+l0enNzc1dXV0xMDJ/Pv337tszSH/v27cPQ6hzI5LFe4mHSXDyRMzwsLm01sNXXG3l8uPKY3LE3E6Q0o0YLCgpMTEzg4MyXL19qamrKTUgNXblyxdraWiwWYxj28OFDCoUiU0AkEv34449LlixZvHjxpUuX4GmLioqio6MjIyPj4uK6u7sxDEtJSamqqoJXz8rKSk9Pj4qKio+P7+/vh+fZt2/fnj17hgbw008/OTg4wO2srCwfH5+//OUvP/zwAxzLmpCQUFFRsXfv3k2bNuXn58NitbW1ycnJGIYNDAwcPXrU1tY2ICDg1q1bGIbt3btXQ0MjNjY2Nja2q6sLw7D9+/fLva5cPT09s2bNampqgi9tbW0zMjKGKe/r63v8+HG4DQCQHh8L0Wi0kJAQa2vrgwcPcjgcuDM/Pz8mJubjjz9OTEyEexgMRlxc3MaNGxMTE4VCIdxZWFi4ffv2v/3tb1999RUc5ZuWlrZ69Wr41xcvXnz77belpaVbtmzZvXu35J/4+vXr9+7dwzCsra0tOjqaTCZv2rSpsbGRwWAEBATY2dnFxsYeOXIEFnZycqLRaDIxo1Gj09w0r/wJZsq+8d2RX36+MYnxTC40anTGqKysXLx4MRycaWBgQKFQnjx58rrCSUlJGzdulGR16e7uDg0NjYiIkPT8enp6Hj16BGcNlpeXv3jxor6+fs2aNZ6enpGRkYaGhr29vQCA1NRUuPrSgwcPduzYcf/+/Q8++IBGo3366afwPDdv3vTx8RkawOPHjykUCgCgr6+vtLRUX1/fwMDgyZMnDAYDAHD27Nl169bZ29v7+PhERETA27O1tbWXLl0CALS0tDx9+tTAwEBXV7ekpITD4djZ2ampqVGpVCqVCjPD+fj4DH9TV1ptba2enp4kY45MagIZg4ODdXV1Cxb8d9XQjRs3rlmz5vjx4/Bm78DAwIMHDwgEgoGBQX19PVw38Ycffvj73/++aNGiDz74AN7R7evro1KpQqEwJCTk6tWrMH1rdXV1eHg4fNd6enrw/nZeXp6kDnt6eg4dOrR///6goCAdHR0PDw9YJicn5/79+wCAioqKvr4+EonE5XLLysq0tLQsLS2JRCKVSnX8c8lvHx+fvLy8UVYOgowGY+6S+gfj7BQKhaL5jNK3PVUis5qEkg4KwrCu73eJ+9lTczW8kTlp6/9bdLerq0t65oC+vv7r1sttbm4uKiqSpOI0NDT8+uuv7e3tW1padu3a1djYuHfv3oaGhi1bttTU1AwMDLi5uTU0NAwMDBgZGa1atUpPT8/f33/oaSkUCrwFZ2FhIcl5/fTpU9jgSSspKTl9+jT84m5qagoPD2cymU+ePAkNDa2pqYFLW2zfvh3e7eRwOEePHg0ICJAc3tDQcPjw4dOnT4eFhTGZTDqdvnz5cnV1denM3dbW1nC1pqEp3Ibq6uoiEomjqToAwK5duxwcHFatWgVfxsXFubm5cTichIQEGo2WlZXV2dnp5ua2fv36Y8eOxcXF3b1719HRcf/+/bm5ufA2clBQEAAgOTl50aJFhw4dAgB4eHjMnTv322+/bWpqMjMzCwwM1NXVlVRyTU2N9GIaXC43MTHRysoqKCiorKwsJSVF8rMDwzAWi3X58uWIiIiUlJSrV68SCAQXF5e+vj6ZyoGLgSDIZLFw9+FlnABg7TiOLb73UKBDdjQ3nvSopjMlbQhxOMONBzDh5GRYGPlqGrIZsXV1dblcruRlf3+/np6e3GOTk5MDAgIkyx5ZW1vHxMTAbWNj4507d+7du3fp0qUAAC6XKxAIKBQKhULh8/l2dnZkMtnLyyssLCwqKkpmaiBcHQkAYGRkBPuLGIbxeDyZ5N2VlZWhoaGpqamwgwLTp9XX14vFYjKZTCaTYTEnJye44ezsfPjwYekzwIaESqUSiUR7e3sAAJ0uuzqotra2QCAQCoXS0yWPHz8Ox4msW7dOOuX30KqTnnAp7cCBAyUlJXfu3JG0r5JZj56envPmzWtvb7eysrKysmIyme7u7kQiMTQ0lE6ns9lsmaksdXV18JkirLG5c+fW1dX5+/tfvHjR3Nzcx8dn7dq1EREROBxucHBQug6JRCJ8jgsrR3poDw6Hg49j/fz81NTU1q1bJ/ddaGtrS79fBJk4KtWxOBP7o7zGxdlhrMdyHtxScw4YuZxyUdKGEAB1PcORC70xVlZWaWlpcFsgELS0tMCulQyxWJySkvK6AY0WFhZMJlPSkVq06L+TWzU1NX/++ee+vr7c3NxvvvlGIBDApSQkhk6Zx+FwxsbGPT09ki/u6urqwMDAU6dOhYSESJe0sbGRXkMKAMBm/6dvzWQy5bbo0p0kuZm7SSSSTNKA999/H/bJzM3NpfdbWlp2dna+evUKrubY0NAgd7GqgwcPZmVl3blzR+6cfVNTUzwez2QyYVtOJBIlJyESibCvJp1kgEgkslgsuA3/SiQStbS0srKyXr58mZube+DAAbFYHBUVZWpq2tPTIzmwv79fKBTi8XgAADxqaDAyac2x/z80RiatOYJMipf2K7DCm2NtCF90983veWKxYs/IRZULekb4RgQFBbW2thYWFgIArly5YmJi4urqCgAoKCi4du2apNjNmze5XO7q1asle2pqamD/gMvlHj161NfXV+7txPb2djabra+vHxkZ6eXlBR/mjcjd3b28vBxu19fXr1y58siRI3KbGRnnz58XiURisfj8+fNwjadhGBgY8Hg86daivLx86KrClpaWrq6urq6ukn4ntGDBAhcXl8TERABARUVFaWkpXFLj2bNnkl8M33///eXLl2/fvg2H2kLPnz/v7u4GAIjF4sOHDxsbG8tNSk4gEPz9/Q8ePIj9ObgGABAQEJCRkQETjl+7dk1LS8vR0ZFOp7969crQ0DAqKsrDwwNWsoeHhyR/OgBAIBAkJycDALq7uzMzM6VvGstFIpHa29ulp3tWVFR4eKjQhC1kaiwOCLBpu8/hDIzpqLJb+Q0WHnMI2m8oqmkLNYRvBIFAuHDhwocffmhraxsXF5eUlATbM5mGMDk5OSoqSnrlwuzsbGNj4/nz5xsbG7NYrLNnz8o9f0VFxcKFCxcvXvz2228/e/YM5t3G4/HD504LDw/PycmB2+fOnaPT6ZGRkTgcDofDDZ8LjUwmv/322zY2Nn19fXCihZqaGuwGDaWtrb13714XFxc4PgUAkJOTs3btGB5XnDlz5vTp0wsXLly+fPnJkyeNjY0BALW1tZKG8Kuvvqqvrzc3N4fBf/nll+DPIT9z5841MjJKT0/PzMx8XeK6pKSkiooKKysrZ2fnd955BwCwfPny6OhoJycnJyenffv2paWlaWlplZaW2tjYuLq6vvXWW21tbbBjt3bt2hs3bkh6dSYmJvfu3XNxcXnrrbc2bNgAz4bH49XV1eVeOiAgYM6cOWQyGd6FhmnN0cLFyKQzM9ZvMXS4X1A0clEpBtW3TL1V7r4oAGj6xJvE4/FaW1vHOtJ3YGCgpaWFy+UOX0wgENDp9KGzBYbB5/Pt7e2Hmcgh1/z588vKyjgcDpwLMVbPnz+3s7Pj8XhjOkokErW2tg4MDIzpKD6f39bW1tfXN5rCLBaLwWDAWSuSwzs6OqTLwEqWTo+OYdjq1avz8vIwDKuqqjIzM8MwrKurSzIxY0ySkpI2b948dD+aPjHNzYjKv3P73u2vPx99+Ud/VD+I/Vj6f8T0hKZPzDCamprz5s17Xc/pdeAge23tEe5O4PF4Mpkss6jv8DQ0NBITE+EUgrHS0dGRvg85eo2NjWfOnNHU1BzTUWpqavPmzZMZ2jMiDQ0NCwsLuQ/qhtLV1TUzM5O+86yhoSHzuA5WssxonWPHjsmsk2xkZKSjozOmUCE+n//NN9+M40AEGdHSd5YYcdqfPmseZfn2O7/0OAaMZmi38lHawTKIXN7e3mM9ZM+ePTKP8cbE19d33MdOTwsXLoRPH01MTPbv3z+RU23dunWSgkIQWZoa+DaXj3DZqfZfHhixcEMT3YpRZrHxtYubKjfUI0RGsHXrVjSsUS4SiRQdHa3oKBDktfzeDzbtrS+veDpiydrMy63OH6lWWjUpqCFEEARRTtpamt3u4V25qcMXq6ltJnfXLHs/ZPhiSmxKG0K0cA+CIMhUWhGyUre/8/eSimHKtGYmd7iG68yeNUwZ5TYJDWFjY2NUVJSTk5MkfeJQJSUlCxcuNDQ0tLW1ffjw4cQviiAIgowIj1fn+kYKb/zAeiU/gVH+r3cMXtH9QgOnOLBpZRIaQqFQ6OLisn37dsmKdDJEItHatWv37NnDZrN37969du1a6QnFCIIgyJvjF+D70typ5MS3QqHsetEVlc+MC84RouJmqcxi9HLJJnwat0ePHvn4+PT39w/9U0FBwfr169vb29XU1MRisbm5+bVr1+DUYxlCoRDmpRzlRTkcDoFAEAgEBALBwsJiQm8AUQEikQgIBWqas6THiAv5fAAAfowTPN4oBoNx586doel4pEmy0CFTb8ZVvkgkvvW/BwS6JiE7d0p2Nj9nsE7t7n/vM0+vxQqMbawGBwfxePxYp6UNbyp+BTQ0NMCleQAAampqdnZ29fX1chtCSHo999mzZ0snXpFLQ0OjtbUVZS6eYkKhUCwWj3WCoMLdyb1FfpLznOxmttiju7lZp7ZQoK69aMsXs7Wn0RuZNWvWRKasIIgMdXU1r0/3/5Gwp/B/ovudV5pYWdOLf1vQUvTCc8PKGdUKviGjagjb2tquXr06dP8nn3wymgndTCZTerrxnDlzpJs6GSKRyNraWvIyIiJCZrkDaZIOKIFAIBBUdOCvoggEArFYPOLPlOkm7JMIxouVA3fvGhRnYPrziWG7nJ3tp+EkYg6HM3yB/v7+aRi2ipiJlY8DwPmLQ48eVYke/jbwKFds4zUr+jsvY4MRP2nTzVh7hFpaWiMWHtW5BAIBXMpHhkgke8dZLhKJJFm+AADQ19cHs0fKpa6uPkwzORRq/xRlhjaEAICFCwgLF2wAYIOiA5kQDMPQh19RZm7lL1vmAZbN7CTv+D9N5jlHU8ja2nqYbtmI7O3tq6qqBAKBhoaGQCCorq6GC9chCIIgiMJNwqhRHo+Xn5//8OFDkUiUn58P1zoHAHz22WeZmZngzyW/4+Pje3p64uPjrays3NzcJn5dBEEQBJm4Sehdvnr1KiEhAQDg7e2dkJBgamoKF1yFi5LDMpmZmTt27HBxcXF0dMzIyJj4RREEQRBkUkza9IlJMdbpE2fOnHnvvfdkljhHpsb9+/dZLNaqVasUHYgqYrPZiYmJX3zxhaIDUVGHDx/etWvXiEvEIG9Cdnb23LlzFy+ezMGuMzvX6LVr12praxUdhYq6d+9efn6+oqNQUXQ6PTk5WdFRqK6zZ892dnYqOgoVdfPmzZKSksk958xuCBEEQRBkglBDiCAIgqg01BAiCIIgKm16DZYRiUSzZs2ytLQcZfmOjg59fX0tLa03GhUiF4vFEolEBgYGig5EFQkEgs7OTpRfV1Ha2trMzc3V1dUVHYgqevnypaam5uhzva5bty4+Pn74MtMr47i6unpTU5Nk0sWIeDzeTMxsohxEIhGGYZOb3wEZPfThVyBU+QokFApxONzof4WYmZmNWGZ69QgRBEEQZIqhZ4QIgiCISkMNIYIgCKLSUEOIIAiCqDQTtA1+AAAHKElEQVTUECIIgiAqbUYO+eNwOOXl5c+ePbO1tfX29pZbhk6nX7x4kc1mf/jhh+7u7lMcoXLr6elJSkrq7OwMDAz09/cfWuDy5cs8Hg9uUygUPz+/qQ1Q2Vy/fr2wsJBMJm/evFnuqPHq6uoff/xRTU0tIiLCzs5u6iNUYi0tLZcuXeJyuWFhYVQqVeavAwMDqampkpdUKnVoGWR8eDze48ePq6qqDA0NQ0JC5JZhsVjnz59nMBjLli0LDg4e97VmZI/wH//4x/bt2xMSEq5cuSK3QE9Pj6ura3d3t5mZWWBgIEqJOYl4PJ6np2d1dfX8+fOjoqKkvwUkYmJi/vjjj6ampqampq6urqkPUpl8//33MTExFAqluLjYz89PLBbLFKiurl66dClchtvd3f3Zs2cKiVMpMRgMV1dXDodjZGTk5+cnWWNO4tWrV9u2bWv6k9wFzJHxOXHixLp1606cOHHkyBG5BUQi0bJly0pKSigUyqeffnrq1KnxXwybgeAMts8++2zz5s1yCyQkJAQGBsLtEydO+Pn5TV1wyu7KlStOTk5isRjDsIyMDHt7e7gtTV9fv6GhQRHRKRs+n29mZlZQUIBhmEAgsLKyysvLkymzcePGXbt2we3o6Oht27ZNdZTK68CBA2vWrIHbhw4dCgkJkSnQ2dmJx+OnPC6VAL/nL1y44OnpKbdAbm6utbW1UCjEMOz27dsWFhYCgWB815qRPUI1tRHCptFo7777Ltz29/cvKirC0HTJSUKj0fz9/XE4HADA39//6dOncvt8qampx48fLy4unvIAlUpdXV1vb6+Pjw8AAI/HL1u2rLCwUKZMYWGh5Aa1v7//0ALIuI2mbjEMO3ny5D//+c8nT55MbXRKbsTv+cLCwuXLl8OZ9b6+vl1dXY2NjeO81vgOm+Y6OjqMjIzgtrGxMZ/P7+npUWxISkO6bnV1dbW0tDo6OmTKeHp6DgwMNDc3v/fee2jNvIl48eKFoaGhJImGiYkJg8GQKSPzaR/6z4GMm0zdslgsLpcrXUBNTc3f37+zs7OystLT0/Ps2bOKCFNFSf/r4PF4AwODcX/4p+lgmS1btiQlJcnsdHZ2Li0tHc3heDxekqcNbmhqak5uhEqsvLzc1dV16P579+65u7tL1y28fTG0bnNycuDG1q1bHR0dd+7cOW/evDcas7KSrm0AgEAgGJrZS+bTjj7qk0imbnE4nExOQRKJ9Ouvv8Lt4ODg9evXb9q0CeUgnRoaGhoikUjyUiAQjPvDP017hImJicIhRtkKAgDIZLLkh3N7e7uOjo6ent4bC1bZODs7D618oVAIB99K121nZ6dAIBgmlZ+9vb2+vn5zc/MUha50zM3Ne3t7BwYG4Mv29vahtS3zaTc3N5/SEJWaTN0aGRkN81Xr6enJ4XDQ6LApQyaT29vb4XZ/fz+TyRz3h3+aNoTjMDg4WFBQwOfzAQDBwcFZWVnwx0J6evpEhtUiMoKDg3Nzc+ENooyMDG9vb319fQBAZWUlbPAGBwclT2SLi4vZbLatra0CA57RFixYYGNjk52dDQBgMpm3b9+G48h7e3tpNBosExISkp6eDrfRp31yBQcHZ2ZmwpG60nVbUlICV6iX/EYBAOTk5JBIJFNTU4WEqjoKCwv7+voAAMHBwbdu3WKxWACA7OxsBwcHKyurcZ50fGNsFOvSpUtUKtXExIREIlGp1DNnzmAYBr+FOzo6MAzjcrlubm5eXl7h4eHGxsZVVVWKDll5iESiVatWOTs7R0ZGGhoaFhYWwv0rV66Mi4vDMOzGjRs2NjZhYWEhISEEAuH48eMKjXfGu3HjBolE2rBhg4ODQ2RkJNyZl5c3Z84cuM1gMKysrIKCglatWrVgwYLOzk7FBats2Gy2k5OTr6/vmjVrTE1N6+vr4X5ra+vU1FQMw44ePerk5BQREbFixQo9Pb3s7GyFxqtUaDQalUq1tLQkEAhUKnX37t1wv7a2dn5+PtwODw93cHCIiooikUi//PLLuK81I1efePHihaRHDAAwMzMzNzfn8/kVFRXOzs4aGhoAAD6fX1BQwGaz/fz8DA0NFResEhKLxXfv3u3u7vb29pbci6irq9PR0SGTySKRqLKysq6ubvbs2VQqlUwmKzZaJdDa2lpcXGxhYeHl5QXH67LZ7Pr6esncbQ6Hk5+fj8PhVqxYoaOjo9BglQ2Px/vtt9+4XO6KFSuIRCLc+fjxYzKZbGhoyOPxysrKnj9/rq+v7+rqir5qJhGLxWpoaJC8JBKJFAoFAPDo0SMbGxtdXV0AAIZhRUVF7e3tnp6eExmIMCMbQgRBEASZLMrzjBBBEARBxgE1hAiCIIhKQw0hgiAIotJQQ4ggCIKoNNQQIgiCICoNNYQIgiCISkMNIYIgCKLSUEOIIAiCqDTUECIIgiAqDTWECIIgiEpDDSGCIAii0v4PXuTzKlZtbOkAAAAASUVORK5CYII=",
"image/svg+xml": [
"\n",
"\n"
],
"text/html": [
"
"
]
},
"execution_count": 27,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"xr = -1.0:0.01:1.0\n",
"fx = [f(t) for t in xr]\n",
"gx = [g(t) for t in xr]\n",
"plot(xr,fx,label=\"((sin(2*pi*t))^3\",legend=:bottomleft)\n",
"plot!(xr,px,label=\"0.75*sin(2*pi*t) - 0.25*cos(pi*t)\")"
]
},
{
"cell_type": "code",
"execution_count": 28,
"id": "6f0ad14d",
"metadata": {},
"outputs": [],
"source": [
"# savefig(\"trigonometricresult.png\")"
]
},
{
"cell_type": "markdown",
"id": "bd444bcf",
"metadata": {},
"source": [
"We did some numeric-symbolic computations, ending up with a symbolic result."
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Julia 1.12",
"language": "julia",
"name": "julia-1.12"
},
"language_info": {
"file_extension": ".jl",
"mimetype": "application/julia",
"name": "julia",
"version": "1.12.4"
}
},
"nbformat": 4,
"nbformat_minor": 5
}