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@hydrogen602
Last active December 9, 2021 04:32
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{
"nbformat": 4,
"nbformat_minor": 0,
"metadata": {
"colab": {
"name": "Quantum",
"provenance": [],
"collapsed_sections": [],
"include_colab_link": true
},
"kernelspec": {
"name": "python3",
"display_name": "Python 3"
},
"language_info": {
"name": "python"
}
},
"cells": [
{
"cell_type": "markdown",
"metadata": {
"id": "view-in-github",
"colab_type": "text"
},
"source": [
"<a href=\"https://colab.research.google.com/gist/hydrogen602/c89f242baacd1ef52fb5150080a5fbd9/quantum.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "eAvVLEE2n-ve"
},
"source": [
"Some code for evaluating the wave equation for an electron around the Hydrogen atom and plotting the probility density. "
]
},
{
"cell_type": "code",
"metadata": {
"id": "10y0XQ9RIFCl"
},
"source": [
"%reset -f\n",
"\n",
"from sympy import *\n",
"from sympy.parsing.sympy_parser import parse_expr, standard_transformations, \\\n",
" implicit_multiplication_application, convert_xor, convert_equals_signs\n",
"import sympy\n",
"\n",
"init_printing()\n",
"\n",
"transformations = standard_transformations + \\\n",
" (convert_equals_signs,\n",
" convert_xor,\n",
" implicit_multiplication_application\n",
" )\n",
"\n",
"parse = lambda s: parse_expr(s, transformations=transformations)\n",
"\n",
"class Math:\n",
"\n",
" def __init__(self, s=None):\n",
" if not s:\n",
" s = input('math> ')\n",
" self.expr = parse(s)\n",
" for var in self.expr.free_symbols:\n",
" setattr(self, var.name, var)\n",
" \n",
" def __repr__(self):\n",
" return repr(self.expr)\n",
" \n",
" def __str__(self):\n",
" return str(self.expr)\n",
" \n",
" def _repr_disabled(self, *args, **kwargs):\n",
" return self.expr._repr_disabled(*args, **kwargs)\n",
" \n",
" def _repr_latex_(self, *args, **kwargs):\n",
" return self.expr._repr_latex_(*args, **kwargs)\n",
" \n",
" def _repr_png_(self, *args, **kwargs):\n",
" return self.expr._repr_png_(*args, **kwargs)\n",
" \n",
" def _repr_svg_(self, *args, **kwargs):\n",
" return self.expr._repr_svg_(*args, **kwargs)\n",
"\n",
" def plot(self, *args, **kwargs):\n",
" expr = self.expr\n",
" if self.expr.is_Equality:\n",
" expr = self.expr.rhs\n",
" plot(expr, *args, **kwargs)"
],
"execution_count": 2,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"id": "MDnzrfe3jgyT"
},
"source": [
"phi, theta, x = symbols('phi theta x', real=True)\n",
"#from sympy.abc import n, l, m\n",
"n = symbols('n', integer=True, positive=True)\n",
"l, p, q = symbols('l p q', integer=True, nonnegative=True)\n",
"m = symbols('m', integer=True)\n",
"\n",
"a, r = symbols('a r', real=True, positive=True)\n",
"\n",
"local = {'phi': phi, 'theta': theta, 'x': x, 'n': n, \n",
" 'l': l, 'm': m, 'p': p, 'q': q, 'a': a, 'r': r}\n",
"\n",
"def s(string):\n",
" ex = Math(string).expr\n",
" for var in ex.free_symbols:\n",
" if var.name in local:\n",
" ex = ex.xreplace({var: local[var.name]})\n",
" return ex\n"
],
"execution_count": 3,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 344
},
"id": "Y_JFNVkBKVGr",
"outputId": "9063d911-6c5e-486f-d93e-59e5e5405835"
},
"source": [
"\n",
"part1, part2 = s('x^(-p) exp(x) / q!'), s('exp(-x) x^(p+q)')\n",
"L_expr = part1 * part2.diff((x, q))\n",
"\n",
"class L(Function):\n",
" nargs = (2,3)\n",
"\n",
" @classmethod\n",
" def eval(cls, p_val, q_val, x_val = x):\n",
" return L_expr.subs([(p, p_val), (q, q_val), (x, x_val)])\n",
"\n",
"\n",
"display(simplify(L(0,0).doit()))\n",
"display(simplify(L(2,0).doit()))\n",
"display(simplify(L(0,1).doit()))\n",
"display(simplify(L(0,2).doit()))"
],
"execution_count": 4,
"outputs": [
{
"output_type": "stream",
"name": "stderr",
"text": [
"/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/IPython/lib/latextools.py:126: MatplotlibDeprecationWarning: \n",
"The to_png function was deprecated in Matplotlib 3.4 and will be removed two minor releases later. Use mathtext.math_to_image instead.\n",
" mt.to_png(f, s, fontsize=12, dpi=dpi, color=color)\n",
"/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/IPython/lib/latextools.py:126: MatplotlibDeprecationWarning: \n",
"The to_rgba function was deprecated in Matplotlib 3.4 and will be removed two minor releases later. Use mathtext.math_to_image instead.\n",
" mt.to_png(f, s, fontsize=12, dpi=dpi, color=color)\n",
"/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/IPython/lib/latextools.py:126: MatplotlibDeprecationWarning: \n",
"The to_mask function was deprecated in Matplotlib 3.4 and will be removed two minor releases later. Use mathtext.math_to_image instead.\n",
" mt.to_png(f, s, fontsize=12, dpi=dpi, color=color)\n",
"/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/IPython/lib/latextools.py:126: MatplotlibDeprecationWarning: \n",
"The MathtextBackendBitmap class was deprecated in Matplotlib 3.4 and will be removed two minor releases later. Use mathtext.math_to_image instead.\n",
" mt.to_png(f, s, fontsize=12, dpi=dpi, color=color)\n"
]
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"1"
],
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAA0AAAASCAYAAACAa1QyAAAAh0lEQVR4nO3RIQ7CYAwF4G8EPY0kCIIbllsg8NNIkknEfwcugOAeCE5CgkQR/GZ+1WTLMFM0eWlf05fXtEVKya8xC/yACx74oMUtiuaBn1Hhixc2Y5xOWKPEsW+96HTvGxxyGhV/0eSi+Nx9Bixy3uGa6zeaKNqiDr1VBjzRxPUSigEsmfIQHbJ7ECMDdcssAAAAAElFTkSuQmCC\n",
"text/latex": "$\\displaystyle 1$"
},
"metadata": {}
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"1"
],
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAA0AAAASCAYAAACAa1QyAAAAh0lEQVR4nO3RIQ7CYAwF4G8EPY0kCIIbllsg8NNIkknEfwcugOAeCE5CgkQR/GZ+1WTLMFM0eWlf05fXtEVKya8xC/yACx74oMUtiuaBn1Hhixc2Y5xOWKPEsW+96HTvGxxyGhV/0eSi+Nx9Bixy3uGa6zeaKNqiDr1VBjzRxPUSigEsmfIQHbJ7ECMDdcssAAAAAElFTkSuQmCC\n",
"text/latex": "$\\displaystyle 1$"
},
"metadata": {}
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"1 - x"
],
"image/png": "iVBORw0KGgoAAAANSUhEUgAAADQAAAASCAYAAAAUjf3AAAABfElEQVR4nN3XP0gcURAG8N+ppVinlCBqGmOZQFJJENIYNCAIkiI2VkExkIjigQgGLYR0VoJWYmnhn8JCSJUmkEZEUBQjJE2CSEihFm8vLI8TlVuOu/tgYN+82WW+ndlv3uby+bxaQl20fo3P2MUfXGGl3EmVgoZoPYHHOMcJ2sueUYmIKzSCVjRhuPzplI6Y0A72hVarFGwJ+fRF/hyWkr3ZgjMmVIl4j0tMoz7ln8cbLOJDwVkNhL5hGY8wmPjGMYpV0acRi0KlYhL9mEIjZrApELxMB2ZdoUOhp+9qdx0Jx1hAszBWvqAX/+LArCt0gL/3iD+9R+zP1PVbXBQLyppQV8bPK2BAEIEzPMA7N4yVahCFl4I8f0cH9jCEtmLBlU7oGdaEU0u30HYTQmd9KnZD3HKvEiOUFp4Kbwh+YSyjZG9DJ9bxGy/wI/Gv4St68Fw4d/5HTKhTGFZpPEwMjpSHUAs2BCXsFsQmjY/YxhyepDdytf77UPWoOULXOc5Nuj5PXjQAAAAASUVORK5CYII=\n",
"text/latex": "$\\displaystyle 1 - x$"
},
"metadata": {}
},
{
"output_type": "display_data",
"data": {
"text/plain": [
" 2 \n",
"x \n",
"── - 2⋅x + 1\n",
"2 "
],
"image/png": "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\n",
"text/latex": "$\\displaystyle \\frac{x^{2}}{2} - 2 x + 1$"
},
"metadata": {}
}
]
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 335
},
"id": "74me1AlgVKpa",
"outputId": "c7c7134f-3b15-41bb-a536-4df6ca3c6c4b"
},
"source": [
"\n",
"\n",
"P_basic_expr = s('1/(2^l l!)') * s('(x^2 - 1)^l').diff((x,l))\n",
"P_assoc_expr = s('(-1)^m (1 - x^2)^(Abs(m)/2)') * P_basic_expr.diff((x,Abs(m)))\n",
"# display(P_basic_expr)\n",
"# display(P_assoc_expr)\n",
"\n",
"class P(Function):\n",
" nargs = (2,3)\n",
"\n",
" @classmethod\n",
" def eval(cls, m_val, l_val, x_val = x):\n",
" if x_val is x:\n",
" return P_assoc_expr.subs([(m, m_val), (l, l_val)])\n",
" else:\n",
" return simplify(P_assoc_expr.subs([(m, m_val), (l, l_val)]).doit().xreplace({x: x_val}))\n",
"\n",
"print('0,0')\n",
"display(simplify(P(0,0,cos(theta))))\n",
"print('1,1')\n",
"display(simplify(P(1,1,cos(theta))))\n",
"print('0,1')\n",
"display(simplify(P(0,1,cos(theta))))\n",
"print('0,2')\n",
"display(simplify(P(0,2,cos(theta))))\n",
"\n",
"print('test')\n",
"\n",
"\n",
"Y_expr = s('sqrt((2l+1)/(4pi) (l - m)!/(l + m)!) exp(I m phi)') * P(m,l).subs(x, cos(theta))\n",
"\n",
"display(Y_expr)\n",
"class Y(Function):\n",
" nargs = (2,4)\n",
"\n",
" @classmethod\n",
" def eval(cls, m_val, l_val, theta_val = theta, phi_val = phi):\n",
" if m is m_val and l is l_val and theta is theta_val and phi is phi_val:\n",
" return Y_expr\n",
" return Y_expr.subs([(m, m_val), (l, l_val), (theta, theta_val), (phi, phi_val)])\n",
"\n",
"display(simplify(Y(0,0)))\n"
],
"execution_count": 5,
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"0,0\n"
]
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"1"
],
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAA0AAAASCAYAAACAa1QyAAAAh0lEQVR4nO3RIQ7CYAwF4G8EPY0kCIIbllsg8NNIkknEfwcugOAeCE5CgkQR/GZ+1WTLMFM0eWlf05fXtEVKya8xC/yACx74oMUtiuaBn1Hhixc2Y5xOWKPEsW+96HTvGxxyGhV/0eSi+Nx9Bixy3uGa6zeaKNqiDr1VBjzRxPUSigEsmfIQHbJ7ECMDdcssAAAAAElFTkSuQmCC\n",
"text/latex": "$\\displaystyle 1$"
},
"metadata": {}
},
{
"output_type": "stream",
"name": "stdout",
"text": [
"1,1\n"
]
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"-│sin(θ)│"
],
"image/png": "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\n",
"text/latex": "$\\displaystyle - \\left|{\\sin{\\left(\\theta \\right)}}\\right|$"
},
"metadata": {}
},
{
"output_type": "stream",
"name": "stdout",
"text": [
"0,1\n"
]
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"cos(θ)"
],
"image/png": "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\n",
"text/latex": "$\\displaystyle \\cos{\\left(\\theta \\right)}$"
},
"metadata": {}
},
{
"output_type": "stream",
"name": "stdout",
"text": [
"0,2\n"
]
},
{
"output_type": "display_data",
"data": {
"text/plain": [
" 2 \n",
"3⋅cos (θ) 1\n",
"───────── - ─\n",
" 2 2"
],
"image/png": "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\n",
"text/latex": "$\\displaystyle \\frac{3 \\cos^{2}{\\left(\\theta \\right)}}{2} - \\frac{1}{2}$"
},
"metadata": {}
},
{
"output_type": "stream",
"name": "stdout",
"text": [
"test\n"
]
},
{
"output_type": "display_data",
"data": {
"text/plain": [
" │m│ │m│ \n",
" ______ ______ \n",
" ╲ ╲ \n",
" │m│ ╲ ╲ \n",
" ─── ╲ ╲ \n",
" __________ 2 ╲ ╲ \n",
" m ╱ (l - m)! ⎛ 2 ⎞ _________ ⅈ⋅m⋅φ ╲ ╲ (│m│)!⋅\n",
"(-1) ⋅ ╱ ──────── ⋅⎝1 - cos (θ)⎠ ⋅╲╱ 2⋅l + 1 ⋅ℯ ⋅ ╱ ╱ \n",
" ╲╱ (l + m)! ╱ ╱ \n",
" ╱ ╱ ───────\n",
" ╱ ╱ \n",
" ╱ ╱ \n",
" ‾‾‾‾‾‾ ‾‾‾‾‾‾ \n",
" k₂ = 0 k₁ = 0 \n",
"──────────────────────────────────────────────────────────────────────────────\n",
" \n",
"\n",
" \n",
" \n",
" \n",
" \n",
"⎛ _k1 ⎞│ ⎛ l + Max(0, -_k1 - _k2 + Abs(m))⎛ l⎞⎞│ \n",
"⎜ d ⎛ -l⎞⎟│ ⎜ d ⎜⎛ 2 ⎞ ⎟⎟│ \n",
"⎜─────⎝2 ⎠⎟│ ⋅⎜─────────────────────────────────⎝⎝x - 1⎠ ⎠⎟│ ⋅\n",
"⎜ _k1 ⎟│ ⎜ l + Max(0, -_k1 - _k2 + Abs(m)) ⎟│ \n",
"⎝dx ⎠│x=cos(θ) ⎝dx ⎠│x=cos(θ) \n",
"──────────────────────────────────────────────────────────────────────────────\n",
" k₁!⋅k₂!⋅(-k₁ - k₂ + │m│)! \n",
" \n",
" \n",
" \n",
"──────────────────────────────────────────────────────────────────────────────\n",
" 2⋅√π \n",
"\n",
" \n",
" \n",
" \n",
" \n",
"⎛ _k2 ⎞│ \n",
"⎜ d ⎛1 ⎞⎟│ \n",
"⎜─────⎜──⎟⎟│ \n",
"⎜ _k2⎝l!⎠⎟│ \n",
"⎝dx ⎠│x=cos(θ)\n",
"────────────────────\n",
" \n",
" \n",
" \n",
" \n",
"────────────────────\n",
" "
],
"text/latex": "$\\displaystyle \\frac{\\left(-1\\right)^{m} \\sqrt{\\frac{\\left(l - m\\right)!}{\\left(l + m\\right)!}} \\left(1 - \\cos^{2}{\\left(\\theta \\right)}\\right)^{\\frac{\\left|{m}\\right|}{2}} \\sqrt{2 l + 1} e^{i m \\phi} \\sum_{\\substack{0 \\leq k_{1} \\leq \\left|{m}\\right|\\\\0 \\leq k_{2} \\leq \\left|{m}\\right|}} \\frac{\\left(\\left|{m}\\right|\\right)! \\left. \\frac{d^{k_{1}}}{d x^{k_{1}}} 2^{- l} \\right|_{\\substack{ x=\\cos{\\left(\\theta \\right)} }} \\left. \\frac{d^{l + \\max\\left(0, - k_{1} - k_{2} + \\left|{m}\\right|\\right)}}{d x^{l + \\max\\left(0, - k_{1} - k_{2} + \\left|{m}\\right|\\right)}} \\left(x^{2} - 1\\right)^{l} \\right|_{\\substack{ x=\\cos{\\left(\\theta \\right)} }} \\left. \\frac{d^{k_{2}}}{d x^{k_{2}}} \\frac{1}{l!} \\right|_{\\substack{ x=\\cos{\\left(\\theta \\right)} }}}{k_{1}! k_{2}! \\left(- k_{1} - k_{2} + \\left|{m}\\right|\\right)!}}{2 \\sqrt{\\pi}}$"
},
"metadata": {}
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"⎧ 1 \n",
"⎪──── for k₁ = 0 ∧ k₂ = 0\n",
"⎨2⋅√π \n",
"⎪ \n",
"⎩ 0 otherwise "
],
"text/latex": "$\\displaystyle \\begin{cases} \\frac{1}{2 \\sqrt{\\pi}} & \\text{for}\\: k_{1} = 0 \\wedge k_{2} = 0 \\\\0 & \\text{otherwise} \\end{cases}$"
},
"metadata": {}
}
]
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 144
},
"id": "GkdSoY8hK5SK",
"outputId": "a7551e95-eaf3-46de-a66b-c842adf20288"
},
"source": [
"\n",
"\n",
"part1 = s('sqrt((2/(n a))^3 (n-l-1)!/(2 n * (n+l)!) ) exp(-r / (n a)) (2 r / (n a))^l')\n",
"part2 = L(s('2l + 1'), s('n - l - 1'), s('2r/(na)'))\n",
"\n",
"\n",
"Psi = part1 * part2 * Y(m,l,theta,phi)\n",
"Prob = Psi.conjugate() * Psi\n",
"\n",
"display(Prob)\n"
],
"execution_count": 6,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
" \n",
" \n",
" \n",
" \n",
" │m│ \n",
" ─── 2⋅r ________\n",
" __________ 2⋅l -4⋅l - 2 2 ─── ____\n",
" ╱ (l - m)! ⎛2⋅r⎞ ⎛2⋅r⎞ ⎛ 2 ⎞ a⋅n ╱ (l \n",
" ╱ ──────── ⋅⎜───⎟ ⋅⎜───⎟ ⋅⎝1 - cos (θ)⎠ ⋅(2⋅l + 1)⋅ℯ ⋅ ╱ ───\n",
"╲╱ (l + m)! ⎝a⋅n⎠ ⎝a⋅n⎠ ╲╱ (l \n",
" \n",
" \n",
" \n",
" \n",
" \n",
"──────────────────────────────────────────────────────────────────────────────\n",
" \n",
" \n",
"\n",
" ____________________________________\n",
" -l + n - 1 \n",
" ______ \n",
" ________________ ╲ \n",
" │m│ ╲ ⎛ _k1 \n",
"______ ─── ╲ ⎜ d ⎛ l +\n",
"______ 2 _________________ ╲ (-l + n - 1)!⋅⎜─────⎝x \n",
"- m)! ⎛ 2 ⎞ 1 ╲ ⎜ _k1 \n",
"───── ⋅⎝1 - cos (θ)⎠ ⋅─────────────────⋅ ╱ ⎝dx \n",
"+ m)! _______________ ╱ \n",
" ╲╱ (-l + n - 1)! ╱ ─────────────────────────\n",
" ╱ \n",
" ╱ \n",
" ‾‾‾‾‾‾ \n",
" k₁ = 0 \n",
"──────────────────────────────────────────────────────────────────────────────\n",
" \n",
" \n",
"\n",
"__________________________________________________ ___________________________\n",
" │m│ │m│ \n",
" ______ ______ \n",
" ╲ ╲ \n",
" ⎞│ ⎛ Max(0, -_k1 - l + n - 1) ⎞│ ╲ ╲ \n",
" n⎞⎟│ ⎜d ⎛ -x⎞⎟│ ╲ ╲ ⎛ _k1\n",
" ⎠⎟│ ⋅⎜──────────────────────────⎝ℯ ⎠⎟│ ╲ ╲ ⎜ d \n",
" ⎟│ 2⋅r ⎜ Max(0, -_k1 - l + n - 1) ⎟│ 2⋅r ╲ ╲ (│m│)!⋅⎜─────\n",
" ⎠│x=─── ⎝dx ⎠│x=───⋅ ╱ ╱ ⎜ _k1\n",
" a⋅n a⋅n ╱ ╱ ⎝dx \n",
"────────────────────────────────────────────────── ╱ ╱ ─────────────\n",
" k₁!⋅(-k₁ - l + n - 1)! ╱ ╱ \n",
" ╱ ╱ \n",
" ‾‾‾‾‾‾ ‾‾‾‾‾‾ \n",
" k₂ = 0 k₁ = 0 \n",
"──────────────────────────────────────────────────────────────────────────────\n",
" \n",
" \n",
"\n",
"______________________________________________________________________________\n",
" \n",
" \n",
" \n",
" \n",
" ⎞│ ⎛ l + Max(0, -_k1 - _k2 + Abs(m))⎛ l⎞⎞│ ⎛ _k2\n",
"⎛ -l⎞⎟│ ⎜ d ⎜⎛ 2 ⎞ ⎟⎟│ ⎜ d \n",
"⎝2 ⎠⎟│ ⋅⎜─────────────────────────────────⎝⎝x - 1⎠ ⎠⎟│ ⋅⎜─────\n",
" ⎟│ ⎜ l + Max(0, -_k1 - _k2 + Abs(m)) ⎟│ ⎜ _k2\n",
" ⎠│x=cos(θ) ⎝dx ⎠│x=cos(θ) ⎝dx \n",
"──────────────────────────────────────────────────────────────────────────────\n",
" k₁!⋅k₂!⋅(-k₁ - k₂ + │m│)! \n",
" \n",
" \n",
" \n",
"──────────────────────────────────────────────────────────────────────────────\n",
" 3 4 _______________ \n",
" π⋅a ⋅n ⋅(l + n)!⋅╲╱ (-l + n - 1)! \n",
"\n",
"______________ \n",
" ⎛-l + n - 1 \n",
" ⎜ ______ \n",
" ⎜ ╲ \n",
" ⎜ ╲ ⎛ _k1 ⎞│ ⎛ Max(0, -_k1 -\n",
" ⎞│ ⎜ ╲ ⎜ d ⎛ l + n⎞⎟│ ⎜d \n",
"⎛1 ⎞⎟│ ⎜ ╲ (-l + n - 1)!⋅⎜─────⎝x ⎠⎟│ ⋅⎜──────────────\n",
"⎜──⎟⎟│ ⎜ ╲ ⎜ _k1 ⎟│ 2⋅r ⎜ Max(0, -_k1 \n",
"⎝l!⎠⎟│ ⋅⎜ ╱ ⎝dx ⎠│x=─── ⎝dx \n",
" ⎠│x=cos(θ) ⎜ ╱ a⋅n \n",
"────────────── ⎜ ╱ ───────────────────────────────────────────────────\n",
" ⎜ ╱ k₁!⋅(-k₁ - l + n - 1)! \n",
" ⎜ ╱ \n",
" ⎜ ‾‾‾‾‾‾ \n",
" ⎝ k₁ = 0 \n",
"──────────────────────────────────────────────────────────────────────────────\n",
" \n",
" \n",
"\n",
" \n",
" ⎞ │m│ │m│ \n",
" ⎟ ______ ______ \n",
" ⎟ ╲ ╲ \n",
" l + n - 1) ⎞│ ⎟ ╲ ╲ \n",
" ⎛ -x⎞⎟│ ⎟ ╲ ╲ ⎛ _k1 ⎞│ ⎛ l + Ma\n",
"────────────⎝ℯ ⎠⎟│ ⎟ ╲ ╲ ⎜ d ⎛ -l⎞⎟│ ⎜ d \n",
"- l + n - 1) ⎟│ 2⋅r⎟ ╲ ╲ (│m│)!⋅⎜─────⎝2 ⎠⎟│ ⋅⎜────────\n",
" ⎠│x=───⎟⋅ ╱ ╱ ⎜ _k1 ⎟│ ⎜ l + Ma\n",
" a⋅n⎟ ╱ ╱ ⎝dx ⎠│x=cos(θ) ⎝dx \n",
"────────────────────────⎟ ╱ ╱ ──────────────────────────────────────\n",
" ⎟ ╱ ╱ \n",
" ⎟ ╱ ╱ \n",
" ⎟ ‾‾‾‾‾‾ ‾‾‾‾‾‾ \n",
" ⎠ k₂ = 0 k₁ = 0 \n",
"──────────────────────────────────────────────────────────────────────────────\n",
" \n",
" \n",
"\n",
" \n",
" \n",
" \n",
" \n",
" \n",
"x(0, -_k1 - _k2 + Abs(m))⎛ l⎞⎞│ ⎛ _k2 ⎞│ \n",
" ⎜⎛ 2 ⎞ ⎟⎟│ ⎜ d ⎛1 ⎞⎟│ \n",
"─────────────────────────⎝⎝x - 1⎠ ⎠⎟│ ⋅⎜─────⎜──⎟⎟│ \n",
"x(0, -_k1 - _k2 + Abs(m)) ⎟│ ⎜ _k2⎝l!⎠⎟│ \n",
" ⎠│x=cos(θ) ⎝dx ⎠│x=cos(θ)\n",
"───────────────────────────────────────────────────────────────────\n",
" k₁!⋅k₂!⋅(-k₁ - k₂ + │m│)! \n",
" \n",
" \n",
" \n",
"───────────────────────────────────────────────────────────────────\n",
" \n",
" "
],
"text/latex": "$\\displaystyle \\frac{\\sqrt{\\frac{\\left(l - m\\right)!}{\\left(l + m\\right)!}} \\left(\\frac{2 r}{a n}\\right)^{2 l} \\left(\\frac{2 r}{a n}\\right)^{- 4 l - 2} \\left(1 - \\cos^{2}{\\left(\\theta \\right)}\\right)^{\\frac{\\left|{m}\\right|}{2}} \\left(2 l + 1\\right) e^{\\frac{2 r}{a n}} \\overline{\\sqrt{\\frac{\\left(l - m\\right)!}{\\left(l + m\\right)!}}} \\overline{\\left(1 - \\cos^{2}{\\left(\\theta \\right)}\\right)^{\\frac{\\left|{m}\\right|}{2}}} \\overline{\\frac{1}{\\sqrt{\\left(- l + n - 1\\right)!}}} \\left(\\overline{\\sum_{k_{1}=0}^{- l + n - 1} \\frac{\\left(- l + n - 1\\right)! \\left. \\frac{d^{k_{1}}}{d x^{k_{1}}} x^{l + n} \\right|_{\\substack{ x=\\frac{2 r}{a n} }} \\left. \\frac{d^{\\max\\left(0, - k_{1} - l + n - 1\\right)}}{d x^{\\max\\left(0, - k_{1} - l + n - 1\\right)}} e^{- x} \\right|_{\\substack{ x=\\frac{2 r}{a n} }}}{k_{1}! \\left(- k_{1} - l + n - 1\\right)!}}\\right) \\left(\\overline{\\sum_{\\substack{0 \\leq k_{1} \\leq \\left|{m}\\right|\\\\0 \\leq k_{2} \\leq \\left|{m}\\right|}} \\frac{\\left(\\left|{m}\\right|\\right)! \\left. \\frac{d^{k_{1}}}{d x^{k_{1}}} 2^{- l} \\right|_{\\substack{ x=\\cos{\\left(\\theta \\right)} }} \\left. \\frac{d^{l + \\max\\left(0, - k_{1} - k_{2} + \\left|{m}\\right|\\right)}}{d x^{l + \\max\\left(0, - k_{1} - k_{2} + \\left|{m}\\right|\\right)}} \\left(x^{2} - 1\\right)^{l} \\right|_{\\substack{ x=\\cos{\\left(\\theta \\right)} }} \\left. \\frac{d^{k_{2}}}{d x^{k_{2}}} \\frac{1}{l!} \\right|_{\\substack{ x=\\cos{\\left(\\theta \\right)} }}}{k_{1}! k_{2}! \\left(- k_{1} - k_{2} + \\left|{m}\\right|\\right)!}}\\right) \\left(\\sum_{k_{1}=0}^{- l + n - 1} \\frac{\\left(- l + n - 1\\right)! \\left. \\frac{d^{k_{1}}}{d x^{k_{1}}} x^{l + n} \\right|_{\\substack{ x=\\frac{2 r}{a n} }} \\left. \\frac{d^{\\max\\left(0, - k_{1} - l + n - 1\\right)}}{d x^{\\max\\left(0, - k_{1} - l + n - 1\\right)}} e^{- x} \\right|_{\\substack{ x=\\frac{2 r}{a n} }}}{k_{1}! \\left(- k_{1} - l + n - 1\\right)!}\\right) \\sum_{\\substack{0 \\leq k_{1} \\leq \\left|{m}\\right|\\\\0 \\leq k_{2} \\leq \\left|{m}\\right|}} \\frac{\\left(\\left|{m}\\right|\\right)! \\left. \\frac{d^{k_{1}}}{d x^{k_{1}}} 2^{- l} \\right|_{\\substack{ x=\\cos{\\left(\\theta \\right)} }} \\left. \\frac{d^{l + \\max\\left(0, - k_{1} - k_{2} + \\left|{m}\\right|\\right)}}{d x^{l + \\max\\left(0, - k_{1} - k_{2} + \\left|{m}\\right|\\right)}} \\left(x^{2} - 1\\right)^{l} \\right|_{\\substack{ x=\\cos{\\left(\\theta \\right)} }} \\left. \\frac{d^{k_{2}}}{d x^{k_{2}}} \\frac{1}{l!} \\right|_{\\substack{ x=\\cos{\\left(\\theta \\right)} }}}{k_{1}! k_{2}! \\left(- k_{1} - k_{2} + \\left|{m}\\right|\\right)!}}{\\pi a^{3} n^{4} \\left(l + n\\right)! \\sqrt{\\left(- l + n - 1\\right)!}}$"
},
"metadata": {}
}
]
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 56
},
"id": "KzmzFseRrKJH",
"outputId": "2ac7b03f-a839-4893-fb35-73d4205bab96"
},
"source": [
"import warnings\n",
"warnings.filterwarnings(\"ignore\")\n",
"\n",
"#Prob.subs(a, 0.529e-10)\n",
"\n",
"Prob_100 = Prob.subs({n: 1, l: 0, m: 0}).doit()\n",
"\n",
"display(Prob_100)\n"
],
"execution_count": 7,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
" -2⋅r \n",
" ─────\n",
" a \n",
"ℯ \n",
"──────\n",
" 3 \n",
" π⋅a "
],
"image/png": "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\n",
"text/latex": "$\\displaystyle \\frac{e^{- \\frac{2 r}{a}}}{\\pi a^{3}}$"
},
"metadata": {}
}
]
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 328
},
"id": "IzHfbEV2zd5e",
"outputId": "32af2c8f-c3d4-45f2-8afe-acfd8bacc28a"
},
"source": [
"import matplotlib.pyplot as plt\n",
"from matplotlib import cm\n",
"import numpy as np\n",
"from random import random\n",
"from matplotlib.colors import ListedColormap\n",
"\n",
"# Colormap code from matplotlib docs, adapted\n",
"\n",
"def plot_examples(colormaps):\n",
" \"\"\"\n",
" Helper function to plot data with associated colormap.\n",
" \"\"\"\n",
" np.random.seed(19680801)\n",
" data = np.random.randn(30, 30)\n",
" n = len(colormaps)\n",
" fig, axs = plt.subplots(1, n, figsize=(n * 2 + 2, 3),\n",
" constrained_layout=True, squeeze=False)\n",
" for [ax, cmap] in zip(axs.flat, colormaps):\n",
" psm = ax.pcolormesh(data, cmap=cmap, rasterized=True, vmin=-4, vmax=4)\n",
" fig.colorbar(psm, ax=ax)\n",
" plt.show()\n",
"\n",
"\n",
"top = cm.get_cmap('Oranges_r', 128)\n",
"bottom = cm.get_cmap('Blues', 128)\n",
"\n",
"newcolors = np.vstack((top(np.linspace(0, 1, 128)),\n",
" bottom(np.linspace(0, 1, 128))))\n",
"\n",
"# display(newcolors)\n",
"\n",
"newcmp = ListedColormap(newcolors, name='OrangeBlue')\n",
"\n",
"c = cm.get_cmap('cool_r', 128)(np.linspace(0, 1, 128))\n",
"c[:,3] = np.linspace(0, 1, 128)\n",
"\n",
"cool_alpha = ListedColormap(c, name='Cool_Alpha')\n",
"\n",
"c = cm.get_cmap('jet', 128)(np.linspace(0, 1, 128))\n",
"c = c[20:]\n",
"\n",
"#c = np.zeros((128,4))\n",
"# c[:,0] = np.linspace(0, 1, 128)\n",
"# c[:,1] = 0 #1 - np.linspace(0, 1, 128)\n",
"# c[:,2] = 0 #1 - np.linspace(0, 1, 128)\n",
"c[:,3] = np.linspace(0, 1, len(c))\n",
"\n",
"jet_alpha = ListedColormap(c, name='jet_Alpha')\n",
"\n",
"\n",
"plot_examples([jet_alpha, cool_alpha, cm.cool_r])"
],
"execution_count": 8,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 800x300 with 6 Axes>"
],
"image/png": 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\n"
},
"metadata": {}
}
]
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 416
},
"id": "JE8vJKFOyD0D",
"outputId": "88cc6383-a87f-46a8-cfec-e9f057437ca9"
},
"source": [
"Prob_100_f = lambdify([r, theta, phi], Prob_100.subs(a, 0.529), 'numpy') # a is 0.529 Angstroms, aka Bohr radius\n",
"\n",
"\n",
"\n",
"count = 10000\n",
"rs, thetas, phis, probs = np.zeros(count), np.zeros(count), np.zeros(count), np.zeros(count)\n",
"\n",
"for i in range(count):\n",
" rs[i] = random()\n",
" thetas[i] = random() * np.pi\n",
" phis[i] = random() * 2 * np.pi\n",
" probs[i] = Prob_100_f(rs[i], thetas[i], phis[i])\n",
"\n",
"xs = rs * np.sin(thetas) * np.cos(phis)\n",
"ys = rs * np.sin(thetas) * np.sin(phis)\n",
"zs = rs * np.cos(thetas)\n",
"\n",
"# fig = plt.figure()\n",
"# ax = fig.add_subplot(projection='3d')\n",
"fig = plt.figure()\n",
"ax = fig.gca(projection='3d')\n",
"\n",
"ax.scatter(xs, ys, zs, c=probs, cmap=cool_alpha)\n",
"plt.show()"
],
"execution_count": 9,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {}
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "21-0XnuD6-SM"
},
"source": [
"\n",
"def plotter(n_val, l_val, m_val, radii=2, estimate_measure=[]):\n",
" assert isinstance(n_val, int) and isinstance(l_val, int) and isinstance(m_val, int)\n",
" assert n_val > 0\n",
" assert 0 <= l_val < n_val\n",
" assert -l_val <= m_val <= l_val\n",
"\n",
" Prob_nlm = Prob.subs({n: n_val, l: l_val, m: m_val}).doit()\n",
"\n",
" display(Prob_nlm)\n",
"\n",
" Prob_nlm_f = lambdify([r, theta, phi], Prob_nlm.subs(a, 0.529), 'numpy') # a is 0.529 Angstroms, aka Bohr radius\n",
"\n",
"\n",
"\n",
" count = 100000\n",
" rs, thetas, phis, probs = np.zeros(count), np.zeros(count), np.zeros(count), np.zeros(count)\n",
"\n",
" for i in range(count):\n",
" rs[i] = random() * radii\n",
" thetas[i] = random() * np.pi\n",
" # lets go from pi/4 to 2pi\n",
" # 2 - 1/4 = 8/4 - 1/4 = 7/4\n",
" phis[i] = random() * np.pi * 3/2\n",
" probs[i] = Prob_nlm_f(rs[i], thetas[i], phis[i])\n",
" \n",
"\n",
" xs = rs * np.sin(thetas) * np.cos(phis)\n",
" ys = rs * np.sin(thetas) * np.sin(phis)\n",
" zs = rs * np.cos(thetas)\n",
"\n",
" # seems broken at the moment - does not match hand computed <psi|x^2|psi>\n",
" if 'x^2' in estimate_measure:\n",
" print('<x^2> =', ((xs ** 2) * probs).mean())\n",
" if 'y^2' in estimate_measure:\n",
" print('<y^2> =', ((ys ** 2) * probs).mean())\n",
" if 'z^2' in estimate_measure:\n",
" print('<z^2> =', ((zs ** 2) * probs).mean())\n",
"\n",
" # fig = plt.figure()\n",
" # ax = fig.add_subplot(projection='3d')\n",
" fig = plt.figure()\n",
" ax = fig.gca(projection='3d')\n",
" # cool_alpha\n",
" ax.scatter(xs, ys, zs, c=probs, cmap=jet_alpha)\n",
" ax.set_axis_off()\n",
" plt.show()"
],
"execution_count": 26,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 445
},
"id": "jNnj3LDY72hG",
"outputId": "6560b7fe-ab6b-4227-f1ab-68c63178ac78"
},
"source": [
"plotter(1,0,0)"
],
"execution_count": 11,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
" -2⋅r \n",
" ─────\n",
" a \n",
"ℯ \n",
"──────\n",
" 3 \n",
" π⋅a "
],
"image/png": "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\n",
"text/latex": "$\\displaystyle \\frac{e^{- \\frac{2 r}{a}}}{\\pi a^{3}}$"
},
"metadata": {}
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {}
}
]
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 458
},
"id": "zRqJwiO48Kzd",
"outputId": "c25c8e57-7fdd-4c2b-b32a-085c04affbd9"
},
"source": [
"plotter(2,0,0)"
],
"execution_count": 12,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
" 2 \n",
"⎛ -r -r ⎞ \n",
"⎜ ─── ───⎟ r\n",
"⎜ a 2 a ⎟ ─\n",
"⎜2⋅r⋅ℯ r ⋅ℯ ⎟ a\n",
"⎜──────── - ───────⎟ ⋅ℯ \n",
"⎜ a 2 ⎟ \n",
"⎝ a ⎠ \n",
"────────────────────────\n",
" 2 \n",
" 32⋅π⋅a⋅r "
],
"image/png": "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\n",
"text/latex": "$\\displaystyle \\frac{\\left(\\frac{2 r e^{- \\frac{r}{a}}}{a} - \\frac{r^{2} e^{- \\frac{r}{a}}}{a^{2}}\\right)^{2} e^{\\frac{r}{a}}}{32 \\pi a r^{2}}$"
},
"metadata": {}
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {}
}
]
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 443
},
"id": "bedbCGQn-PHe",
"outputId": "e4bc49d2-cbe6-4de2-9c04-efb180dc36ae"
},
"source": [
"plotter(2,1,0, radii=4)"
],
"execution_count": 13,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
" -r \n",
" ─── \n",
" 2 a 2 \n",
"r ⋅ℯ ⋅cos (θ)\n",
"───────────────\n",
" 5 \n",
" 32⋅π⋅a "
],
"image/png": "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\n",
"text/latex": "$\\displaystyle \\frac{r^{2} e^{- \\frac{r}{a}} \\cos^{2}{\\left(\\theta \\right)}}{32 \\pi a^{5}}$"
},
"metadata": {}
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {}
}
]
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 501
},
"id": "fNG4wQU-_DVg",
"outputId": "9ed929a9-4ece-4d17-deed-b5ee701a4d79"
},
"source": [
"plotter(2,1,1, radii=4, estimate_measure=['x^2', 'y^2', 'z^2'])"
],
"execution_count": 29,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
" -r ________________\n",
" _____________ ─── _____________\n",
" 2 ╱ 2 a ╱ 2 \n",
"r ⋅╲╱ 1 - cos (θ) ⋅ℯ ⋅╲╱ 1 - cos (θ) \n",
"─────────────────────────────────────────\n",
" 5 \n",
" 64⋅π⋅a "
],
"image/png": "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\n",
"text/latex": "$\\displaystyle \\frac{r^{2} \\sqrt{1 - \\cos^{2}{\\left(\\theta \\right)}} e^{- \\frac{r}{a}} \\overline{\\sqrt{1 - \\cos^{2}{\\left(\\theta \\right)}}}}{64 \\pi a^{5}}$"
},
"metadata": {}
},
{
"output_type": "stream",
"name": "stdout",
"text": [
"<x^2> = 0.004875690796682761\n",
"<y^2> = 0.004885609839963389\n",
"<z^2> = 0.0032598619364902198\n"
]
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {}
}
]
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 449
},
"id": "bQxHTKg6_Kxa",
"outputId": "189ea813-8887-44a3-d7be-2d8f7fd3a49b"
},
"source": [
"plotter(2,1,-1, radii=3)"
],
"execution_count": null,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
" -r ________________\n",
" _____________ ─── _____________\n",
" 2 ╱ 2 a ╱ 2 \n",
"r ⋅╲╱ 1 - cos (θ) ⋅ℯ ⋅╲╱ 1 - cos (θ) \n",
"─────────────────────────────────────────\n",
" 5 \n",
" 16⋅π⋅a "
],
"image/png": "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\n",
"text/latex": "$\\displaystyle \\frac{r^{2} \\sqrt{1 - \\cos^{2}{\\left(\\theta \\right)}} e^{- \\frac{r}{a}} \\overline{\\sqrt{1 - \\cos^{2}{\\left(\\theta \\right)}}}}{16 \\pi a^{5}}$"
},
"metadata": {}
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {}
}
]
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 468
},
"id": "yTpErR4d_mHV",
"outputId": "fb8673a3-1e54-4860-f9b8-d441dcec73c9"
},
"source": [
"plotter(3,0,0, radii=4)"
],
"execution_count": null,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
" 2 \n",
"⎛ -2⋅r -2⋅r -2⋅r ⎞ \n",
"⎜ ───── ───── ─────⎟ 2⋅r\n",
"⎜ 3⋅a 2 3⋅a 3 3⋅a ⎟ ───\n",
"⎜4⋅r⋅ℯ 8⋅r ⋅ℯ 8⋅r ⋅ℯ ⎟ 3⋅a\n",
"⎜────────── - ─────────── + ───────────⎟ ⋅ℯ \n",
"⎜ a 2 3 ⎟ \n",
"⎝ 3⋅a 27⋅a ⎠ \n",
"──────────────────────────────────────────────\n",
" 2 \n",
" 432⋅π⋅a⋅r "
],
"image/png": "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\n",
"text/latex": "$\\displaystyle \\frac{\\left(\\frac{4 r e^{- \\frac{2 r}{3 a}}}{a} - \\frac{8 r^{2} e^{- \\frac{2 r}{3 a}}}{3 a^{2}} + \\frac{8 r^{3} e^{- \\frac{2 r}{3 a}}}{27 a^{3}}\\right)^{2} e^{\\frac{2 r}{3 a}}}{432 \\pi a r^{2}}$"
},
"metadata": {}
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {}
}
]
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 468
},
"id": "V7ko43s-_zjv",
"outputId": "78cfdf73-ff09-4b83-ac19-c35a01c04c91"
},
"source": [
"plotter(3,1,0, radii=7)"
],
"execution_count": null,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
" 2 \n",
" ⎛ -2⋅r -2⋅r ⎞ \n",
" ⎜ ───── ─────⎟ 2⋅r \n",
" ⎜ 3 3⋅a 4 3⋅a ⎟ ─── \n",
" ⎜32⋅r ⋅ℯ 16⋅r ⋅ℯ ⎟ 3⋅a 2 \n",
"a⋅⎜──────────── - ────────────⎟ ⋅ℯ ⋅cos (θ)\n",
" ⎜ 3 4 ⎟ \n",
" ⎝ 27⋅a 81⋅a ⎠ \n",
"─────────────────────────────────────────────\n",
" 4 \n",
" 128⋅π⋅r "
],
"image/png": "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\n",
"text/latex": "$\\displaystyle \\frac{a \\left(\\frac{32 r^{3} e^{- \\frac{2 r}{3 a}}}{27 a^{3}} - \\frac{16 r^{4} e^{- \\frac{2 r}{3 a}}}{81 a^{4}}\\right)^{2} e^{\\frac{2 r}{3 a}} \\cos^{2}{\\left(\\theta \\right)}}{128 \\pi r^{4}}$"
},
"metadata": {}
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {}
}
]
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 468
},
"id": "dK7Vecu3_5zu",
"outputId": "43af2645-1b01-47c4-a868-035f5133be4b"
},
"source": [
"plotter(3,1,1, radii=7)"
],
"execution_count": null,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
" 2 \n",
" ⎛ -2⋅r -2⋅r ⎞ \n",
" ⎜ ───── ─────⎟ 2⋅r ________________\n",
" _____________ ⎜ 3 3⋅a 4 3⋅a ⎟ ─── _____________\n",
" ╱ 2 ⎜32⋅r ⋅ℯ 16⋅r ⋅ℯ ⎟ 3⋅a ╱ 2 \n",
"a⋅╲╱ 1 - cos (θ) ⋅⎜──────────── - ────────────⎟ ⋅ℯ ⋅╲╱ 1 - cos (θ) \n",
" ⎜ 3 4 ⎟ \n",
" ⎝ 27⋅a 81⋅a ⎠ \n",
"───────────────────────────────────────────────────────────────────────\n",
" 4 \n",
" 256⋅π⋅r "
],
"image/png": "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\n",
"text/latex": "$\\displaystyle \\frac{a \\sqrt{1 - \\cos^{2}{\\left(\\theta \\right)}} \\left(\\frac{32 r^{3} e^{- \\frac{2 r}{3 a}}}{27 a^{3}} - \\frac{16 r^{4} e^{- \\frac{2 r}{3 a}}}{81 a^{4}}\\right)^{2} e^{\\frac{2 r}{3 a}} \\overline{\\sqrt{1 - \\cos^{2}{\\left(\\theta \\right)}}}}{256 \\pi r^{4}}$"
},
"metadata": {}
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {}
}
]
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 468
},
"id": "QUQvsk_7DXnw",
"outputId": "a1f2488b-e089-481e-cd69-6d2d4581c8e4"
},
"source": [
"plotter(3,1,-1, radii=7)"
],
"execution_count": null,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
" 2 \n",
" ⎛ -2⋅r -2⋅r ⎞ \n",
" ⎜ ───── ─────⎟ 2⋅r ________________\n",
" _____________ ⎜ 3 3⋅a 4 3⋅a ⎟ ─── _____________\n",
" ╱ 2 ⎜32⋅r ⋅ℯ 16⋅r ⋅ℯ ⎟ 3⋅a ╱ 2 \n",
"a⋅╲╱ 1 - cos (θ) ⋅⎜──────────── - ────────────⎟ ⋅ℯ ⋅╲╱ 1 - cos (θ) \n",
" ⎜ 3 4 ⎟ \n",
" ⎝ 27⋅a 81⋅a ⎠ \n",
"───────────────────────────────────────────────────────────────────────\n",
" 4 \n",
" 64⋅π⋅r "
],
"image/png": "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\n",
"text/latex": "$\\displaystyle \\frac{a \\sqrt{1 - \\cos^{2}{\\left(\\theta \\right)}} \\left(\\frac{32 r^{3} e^{- \\frac{2 r}{3 a}}}{27 a^{3}} - \\frac{16 r^{4} e^{- \\frac{2 r}{3 a}}}{81 a^{4}}\\right)^{2} e^{\\frac{2 r}{3 a}} \\overline{\\sqrt{1 - \\cos^{2}{\\left(\\theta \\right)}}}}{64 \\pi r^{4}}$"
},
"metadata": {}
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {}
}
]
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 458
},
"id": "epLvoNXLByvT",
"outputId": "4edd4c5a-3da5-4bca-c92c-f6bd4c4e65ff"
},
"source": [
"plotter(3,2,0, radii=10)"
],
"execution_count": null,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
" 2 -2⋅r \n",
" ⎛ 2 ⎞ ─────\n",
" 4 ⎜3⋅cos (θ) 1⎟ 3⋅a \n",
"2⋅r ⋅⎜───────── - ─⎟ ⋅ℯ \n",
" ⎝ 2 2⎠ \n",
"────────────────────────────\n",
" 7 \n",
" 19683⋅π⋅a "
],
"image/png": "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\n",
"text/latex": "$\\displaystyle \\frac{2 r^{4} \\left(\\frac{3 \\cos^{2}{\\left(\\theta \\right)}}{2} - \\frac{1}{2}\\right)^{2} e^{- \\frac{2 r}{3 a}}}{19683 \\pi a^{7}}$"
},
"metadata": {}
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {}
}
]
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 449
},
"id": "Ix6yIZGXB7Q7",
"outputId": "1afbfa6b-be45-40d7-f20d-3c4e085ad431"
},
"source": [
"plotter(3,2,1, radii=10)"
],
"execution_count": null,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
" -2⋅r ________________\n",
" _____________ ───── _____________\n",
" 4 ╱ 2 3⋅a 2 ╱ 2 \n",
"r ⋅╲╱ 1 - cos (θ) ⋅ℯ ⋅cos (θ)⋅╲╱ 1 - cos (θ) \n",
"───────────────────────────────────────────────────\n",
" 7 \n",
" 6561⋅π⋅a "
],
"image/png": "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\n",
"text/latex": "$\\displaystyle \\frac{r^{4} \\sqrt{1 - \\cos^{2}{\\left(\\theta \\right)}} e^{- \\frac{2 r}{3 a}} \\cos^{2}{\\left(\\theta \\right)} \\overline{\\sqrt{1 - \\cos^{2}{\\left(\\theta \\right)}}}}{6561 \\pi a^{7}}$"
},
"metadata": {}
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {}
}
]
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 448
},
"id": "7zyGE-oyB_bb",
"outputId": "e288cfbe-74c9-4878-db51-ec6a52fe9a2f"
},
"source": [
"plotter(3,2,2, radii=10)"
],
"execution_count": null,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
" -2⋅r \n",
" 2 ─────\n",
" 4 ⎛ 2 ⎞ 3⋅a \n",
"r ⋅⎝1 - cos (θ)⎠ ⋅ℯ \n",
"────────────────────────\n",
" 7 \n",
" 26244⋅π⋅a "
],
"image/png": "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\n",
"text/latex": "$\\displaystyle \\frac{r^{4} \\left(1 - \\cos^{2}{\\left(\\theta \\right)}\\right)^{2} e^{- \\frac{2 r}{3 a}}}{26244 \\pi a^{7}}$"
},
"metadata": {}
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
],
"image/png": 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NUY7/8hyKmURbd1t4tJTXRE3Ozyo5/412cQ/DSBAg31lVjQlpux4s7/BwuGDqbfj7j0QK/0AxrU83I2DywnRA3FQmsgRyjEIOu90oV+z36k0HMTq3BzFcEZipsXMO3uzFmNeNElEGuXrg+70YxO1RDGDuRb8PAfDQO9hs4fVWPOXNUQgi1wihazXJ20OJSC1tLxHBpoOFFxmGDDYHSTjf7GAfIJvBm4MY7ZsdbG/FoPYDPN+JoR8CXCDyUdOBC0JoZSnHmeXgA6znQprb3Zgb2O51VpKXaqWmFcPdDlA6iQZWQfIfu0aOmxw+R3IS7QD7HXyJvI9zkuAODuKdlM7OC4lSrs7ldxh7KeJeKrAyLa9tW/lsfS/R1FROMtnPmgKnQwFT49vffyRS+AeG6TyiaUPTdNiakcPh8Kvdx1Y51GgFjdX077Xuvo9i0HaNGM+6h6yFzTXMlxIdvHglHrTzWqppxzVIBNFEMWpFLsnmsJHtyhxud0IKBy0vDRq1PN9LQtod5RjPF7BoxfBnmgw/DmIk64O8z+YgklK1gNsW7g6wqdWrdpAfYLBu4ABfXovsdK69EnctxF6b5HTw3XGQLuhay2QHNahtlGTz3V4ihL5TwovyHpstDBcSoQyaK2kHeFVLhHRWwPVBSHY1k2jsbAHrXmSjGCVPst3LfrsZXKyFQG43cm6PjZbBlnI+Yxivh6oSonduHL9hs5amBQfT0lW7hlK+4e8XEin8A8E0aThtRLPmsWkzmT3Xtvc7hXNN1loHbX0UY3NQQ5oVYlR7lDw6MbrNUbzmw2sxWJujGPBjGHMNEZGGSgdVDh1SJRQPkmDNnEQCR32fdSVGbbsTAnp5I9LQcgndXvT7PEpSuSzBZbLfYw23jRxvF2C2ACJsb6COIuX4DCrgrhFiLHR+Uugkwsk1Sd11Yuxv9lA4WJfwaguZEmXMJKcQGulSbhq4HsQoE2V/GXIe2xZiAUUPFEpeEZYdbAJ80cBsKedi0woJ73bw7BEsKjH+jZfPPARoG7gOQqSDVjPttLrr0Zmcz75XAtNeEosKLIqcNrsZTCqcTmS1iNKQCOI3G4kU/gHgYQeyeX0mB5mRH4aRFGwtgf1+TDCv1+JN7g9iiA8H8WY3FjVkYjTJJC8QejGgxxZu7sQg14iHPtOyyboVosBDdoTVJdwdx4RvdBJtHBsxnosCaKX6yAzk8414+X0QI+c0Z/FiCzNgHkTTjx6aIGSz7+FiLp9tq/r7nRLAoVY5yENWCVFkAzDATSOSTQcsZ3IM1wP88kYTxr08djhKOel8LpHErS3YM8D5uUhJb15pxZKWou5qkZ/qg0QVqxXEuXj/Q4TzIBVbhZe/73YwtBJpffBMyGe9FBLYDVD2cDMIAcyqUXI6qszWapNf/RyeXGgOQuc32UI/XferQwSLYlzP4eH4jIdd7gm/eUik8PccFiEYpsPqbOwEjGQQI7x5cz/P0GoZ6mYvBufNVjT6EEQ+ub4Vz9SV0NVi6Hwuhhng0EiFzraRaqPtnUQI5xc6/yhCs4O4gH4DuxaGRrYZVOY46iyjdiEGu97K6z67gf12rNq52cNspQawkRLXi3M5hk0tBvLYCElsDqO0FCO0t9A4oIU2A2bgVmLIt1twM3AHiYRKL4S2r+HFrVZSafXSvoV41HzJDLpSSDNrNTLKYN/Iez1ZS7RRRCGS0OtsJK0SWs2BICWyhwaOEc4ryZN0aAXWVgj7/bWQxHYAPOyCbF+VEpUtC5hX8v3cbOR8Xp0JUXzxSt7/yRU8iWOvQggSJVkDHAjR2SC+6frWU1kJEjH8piKRwt9jWEQwnZg5HQ89JYi6HhvNNltdcKYRjz4iWnjXSxL4dS2P7XbQH2X7eieVPtGp8UZkihDFm68H8aR3tY6IQDzgptPHD3DRS5nlrpMSzEajl3wpRrcdoGrh4goOURLCd3ughMqPHnTvhESKEsoIX95qQjxK2SiaEA5HGDLtV2iAPTBHtKMGuIPYyusoxNDHEu5qODuT448dsEPc9eOEgAPsNzDk4pnTAU66sIdWopEq0yqrVprcXC+/n3nJEzRB8idB8yxDB0vgRr+73MOqks9wV8NyL/ssVvI97Y+SkzmfSbI68xLJdYNELiHA8UZIYpbJ5+x7eHkt39tKR4pfXsjnnc3GCbVNM5a9OjeO7DCChTE5nfCbhfS1/T2FGXwYcwYW5ls3sY1btrzBUTt4j1pRdGxEoui00co5Sa7Wx1GKuHsjXuu+g/NMBrjlhbz29Y2QQz+o5q3HdOwlUTw0IsHc7IAMDkG8+81OvPqqkMR1oeWT1zX0O2kUazRp7OYqCzUI02TQ3QIVdFESrrRIckNLUlFZig4x/lH/qVdOCxT6vHr2BP19Js9tNnqiG9kfagilg86+BDhuJo+vxOgPveRZDrlUBdlwvszpMfciU0WVw9pBJCYfJQLrtXdjvRCpzDqku148/d7Ld7TdwiKT4744E9LcNsJ5AR3rfRQSfTKXfMR2B6ulfN9Hjfr6ySBDk5f6XpyCxWIcmWFd7G9bpjThNweJFP4ewhLJD/VdyxUcj/cH2tW11L7nmRiBQbtlnx9EqggR7gatoe/HBrSsVRsa9aca1KiRSae9D02AaoCXb9S7zKW6KKANYiXSVIYYmOVSZQ99bKtjt/sdoNEGOsconwkX4BGjfYc84PVfo/86Rmt41G2DbjsgNazlg8eryX53CGkM+vopmaD7B7mjjBR0/AalHDetEB9HJLmSw63tf2I4YyWG/e5WCM8Bx5ls5xr5HrqjvFVcCHlWBXx1I1Hce2dCJkOUCGPfCLmWmchm5Zk8t9+rQzBAs5IIzgV41mlU0Us00nQqnzkhgvl8LD6YLhg0n0vEYNVLlst6uFRowncbiRT+nsEIYUoK5rkNgySHbW6RrV1wPKocsBYpaFvDm6Mkeo+NVLdYojbm45iHuoYvN7qegEYAGx29gJO5PlfncFmKDOKCjHvoBkl8Uoguf72XBPJukAoap01aX2qUAogRHuQ1HFGLKPIVOWJ4a+4b2J7ReHvESOf6fJj8vtLntrqdRQkOiRIccM4YWWgkRamvs2O099TqolOEYZFExRh9VPraWh8L+m8FN/XkMxyBmTbGDfDljUQMy0oksuUgk2OPQeSiKyevjwPM9Fx2A5RbuQ5WpZTx1jsl2gHeXGufghcyyVVKKnJ4X6Ob43EkAxu0Z9eV9T20LVxe3o8OrFJpWs6a8N1GIoW/R3iYQ7BksXUd2w1tCeajdhj3qmVvdpIcrkrpDD7kkkjdNZJQdjORG+52UoHz+k4MU9+LLLFRw3KzEdv4+AzWZzLyoSokSXwcJL+AGot6EG+WKMnj1zvI5qKfc0QMZoHs0Dxz8+QtIjCi0AohZvo6e0xJ5mTgzTDZc5ZPYLIPN3mNRRG57tPre+eMkYXBZKn15LFssl3GSBZu8r4qy9ACt8BCn9coo1DZKGq39PYA2wrOOiHxxVJLebV6qe1g76QXZD4Dp3miXkeGuFxIfruT3o/tHh5dSrXYJtP3W8JdD/MIWQ3zhTgPfS/7zHOJDI5HOXSLOm21Oet5sHLmRAy/GUik8PcAFh1YSG+wJS2bZryZYVzP4PpmHPvsvRDAzV6qZ673stbA4ES33h2lxDFqLX+OdO72qkvXB2hqrSbKRXJqvNT6v9jIcewDbKIkifsDxEa80oszHYuhxmUwHX+m/0zjN6NuJKEjJwj6+4xRzlFvl6Dbl4h3niEk4BnzBB6JFgJw0O3tNRZRmBHPJ3/vuE8I6HtapDCVjsz7n0pO+eRn1M9U6HZHRrlKq7bYIoRj52QvPR+bOVRHedndQaIIkAqptpEKo9lMiP6uVykJiezqRhYe8g5u91pKrOXHtHDQWVRO80QOKZXdbCTK2B/Hvou6HktVbdqtEYbJSdNV3xK+m0ik8BsOIwTLEdiNZ+sDW6RgpHA4iPFvG0ludr0kJW9qHU/R6IRQHSVx6ERTrhuJIN67lHEJ262ObCg00Rl1rIQ2T80qed1PvxQSKQohgF2AUErSOGulmzgvVJExg2ie/0o/pEeMqhHD1MM3Ccjr7ypLsWQ0wOalTwjzZFh7Rg++YCSLbPJ6yy/Y+2g1ErVua/syD9giAe3FOB2vEdhB9wf3ZSb0M9l+Wt0uAhtG8uv035xTlNMomb30cBakr6LMparIVRKNHRppDuyQ66HUaqMsF1kwDEIAhUYSbQtvGvAX0C0lOf9mC+FWGhOHADOdSTWfjyWp1hVfVWOkMJ2tlaKF7zYSKfyGYzqz6OGSjXV9XzYyNJpcxEvJYhvEYO91kJ1VFu07eWy7g3ImCeQXb7T0tJRxFvtWKpJ6LQXdHUSzphTS+WLLyYi6XKqNukH/BTjuGQ1thhhg86rN0JqM0iHe8lw/iBly88zNaBuMYMywR93HVEayRG89eX+TeNDn9whJOcQIm0HXqigqTlVJNIyRjclPlnA2Iiv1fYwkTIqyHIURmBFgx0hWVh0FYy7DjlmT98co3d/rXtaNaBpJ8peaM5jpe9ypI0AnToLPVSIKsPRCNM7L9+s3Uu2UeXh9FCcheFhHrZjSEllbpMdyDrPZKFXa4L00WO+7jUQKv8GYLmhjzUY2rM5KUItiDNl3mrjttC7elrFseumUrXWE9NDC51+JLcqdPnaQsQv1IF7h43MxBC9v5PlNK9HCYZD91p3M9DkZ01a80Z0ZNjNoe3mOhT7WMur4ljcw2cUqhaz6yIy0ShRU3PfOYSQJH8aooXHyHp0bX1sG2Kve1DudAxHFChpxdPr3MHkfnGhlj5AT1msTxoIxsVxOjsMkKYsIckbP347PyMOS6yUjYU0xIXoW+jPT762U76tyskbDci65msxJZdntHrIeVoN2bjtpXhuAm7lEcF5Hgwy9RIP/y89llPexlWjCOyUCL9fQtr4/UM8m6k4X+Xm4Wl+am/TdQyKF32BMx1VMcwlWWWTzaOpaRzsc5Ybed7qwfZDyzgFpdjp0UrUSetj2YjhckPHSRTZWpjgHt9pV+2Yv1UmzUnoPeiDu4JgxGiozdKbDW3no1HA3iLdtHr01jU21fMeYN7C8gHng9eR588ALYBagCBIO9YjmUSDJkspLUsQaAjJlUufF0Dsn2640QXIcxOi3CEGUXnMODlonZGP1sb2D2sHMaRlrlONauDFRbfKURRgWuVhlkkUMlmuwprqckSAs4plIS4POO0JzOs7DywNc6eyktpU8UJVL812hOQM6iJqD+vIalrlIhRVCEvVWiMZn0HlYrlQKsmujkNNm15/1ydgyoVbCamMzpsSQcg3fHSRS+A2FyULTFc9s9ICNPLZx17U2a/VBS0BvxYAvdR7OV6+graFaiX3c7NRudTKH6Nio/StFk16UcLeRqZ1tlHLVppe69t7IKTCWWppxtwhhmoidMRo0nZt0IhEzfqb9W+LV5JMM2VEfR3mlBSltQibTHQap2/RBXmvGODhwAxSdGPQ6yphRG+ajg/LogxxjHjS6mOyjDLKfTBsCen3vPIMsaNOHfq6DF2btvOQ7rK3bZLK1Hr+V1RoBwJgMt4jBI3kJy1tMo6la/yHn6+jH517tYK65gyHCmxpe3ska1euVfOxZBzdHmDcQ1jDsoajlO673sqvluaxf0fbCjceDRhRRoo2m068jwoX2MViTm0mcRTE6MlYtlyKG7wYSKfyGYrrkJUhU0HUSFXgv3p4tYHO7Hdcw2GqJadNJ1OC8EEbU5N++lmqhTS03ddvLIjfR6TrHBby6gdZLPqHWbujWjL95vBYJmAc4rde3pOrDpjHzoM37t1yDyUXzIBYtoNKO1tw2Tjx/jyxKUCKP5UHqKWsnOoo1jQUVtYc4lpBaBVKM+too4nrrpFyqQCKO4LWiyMHR6n6jvD/I66pBIw39XMFJFNIHeU2jxOHVYpsMZmWvYXJMJi9ZzsRyHZZL6fW47b2m0ZWdP/3ZdzoXyXolBghH6fcbnBjufQeLTg6fDNpCFyCqhVBmTrrOZ5l0PL/oZAhfmYssSTkWPXSdyExLLXtercb1OabrQFtfw3TSasK7QyKF3zCYd2WEMK02shlG0wmnrzfwaqMzghBZIWYS6m8bCAd5LK+0OqlVtSYXVWTmZEBdp4/VrdjKfC4VSM20A7hjlH3MqIfJ30vGHIBdeRZBWA9Aq9u1SHlMhyQvgnr7Dm34Uu3/LIrXTJCuriwKg5WosXWwVELYItvmQBVHLx5U61dD7sOYG8iUEGIcJaY+F+Oc6z72Uct20KqlQYig1uPoohKLFz2ud5BrM0SGDCxq3dhb0ToR6kG+BKukska8JWMiG0Z5yT6HPWaJeuu7aLkfhanc1AZRt2hkTIktlnRs4eJSrpXcyz+8PNcHzTnMdD2HIMRRt1J5drmWU5DnkssyCSnLJEro+zEJbbmwhO8GEin8hmA67TSEsQt5GiHUNVxfS6J3PofPXso6wm/uxOOvtDO51gme+1pvXC9liTlis/CSbL7RIXT7Thzz3Im0hIey0dXBYOwbMH17avAbRnmonDzvEDnIjBX6e6lyUK8G2BYDGBCjHuDkNscobq5Tzz8gyWPT5TuNIAbdpo1jRBJMiNf3LdxIELlToxnl8UJJpc/HxPmgz3VBPfWow4uCvG8eYRtFLio1Ujkl0TVf0SvhhE4bQhAJq3Uy5c4hoZzJYdGJlLXXQ18wlu9abmJ6/o1kTZrqOI3XOCXCo2x3KGTcSNvJuO2rM2lYvNtDtoZVruMrnJBIkUsV2qKS6yB3Y6lpdHpmA7y6loqzuRLAysqMGXsaDGlO0ncDiRR+Q2BlfEYIVmYagkQE09XQDq00Nf3iWghgcyc2y2ciHf3sS0kmZ5mshjYvdCBbLnZq08q8nJu9SOVdrwRwQBLFDtoLPTCTfqwyCMamsDB53B7LGGcQGZEQ1OtV3b8MMvOiVm99UFE8mIZiGVo7OZP37dFSmjg+aVLRKRmrXvmSkWSMCCwPcoySpM5UR/FeXufiSGS9Pu+cyja9SlPAtpCIoeuFPDwSsbTo6Aon+yMqKUZY6X7KKGR4ypNkQmIhg72/36BnSXarcrIcjRlXk6QsKprmcyySiPJ74yFfSFNb1WjRlRMHIBgRBEksU0jH+nImsmSRyWmvSokw7naSi8qR6/LKgdfr9OJizCtYAtqu7dTD8O6RSOE3AHbD2CRT4LQ4znYr0tFuLxGCLUzTtSLttEexU8da1kN4uZUBc1nUYWc9bEpZ9ayK47jqY5ShbHvzSi0nYBU/ZtAt6Wq6OIx186ekLmOFjBniUxNYECnFRdEgIqp3q3d+b/zo9OfUchhJqM5vKJQIXBTJ5nSgcXy/TD30bBChvB8kb7AMuniyVhhlEWZRvPion+2ord0zxtlLrZ0Hk4eCyEu5h6UeR+wl8Yy61d7LMRyd6il6/rxGNugxodoffiQVk4PsNXaeLeE8bcizZL4lrANjjqKTPFGHFmMhhQhDJ4sQNTM5hMsZrDMhgn0vieh20KCoh+9dSR7rs2sJci4q+eilJr8rjQ6sAsmua+/vJ58TMbw7JFL4DcB0yB0ICdjf+/2YdN7X8OWdJP2aXgih6cVjO3Tw/E6WZOxa8ejKlVSNNI2umzBICeNmLzK4syqX6YgGkyhsJhGMiWBNXt7rQzBYI5c1iRUB5gP4fjSmJbDQxPHJiDP5yeTv6XPGVGb0VRbqzLKYVXTja5zq/JmXvETpxJoNSIJ6UrUjktQkmewjzHo5B3uVsToneY/OXqgvLvxYlWSJ4OjGbaKSjDP5KoxJYkvI3/vM+jmOyIn0OazdWMZrkVlkHBNih4T+bd3ZGgSdyEGvATrYa6VQrmQzb2SBngZR/fYHeP5KJtoSNf/fw0udqdQcRGYaKhnFfaFRQNtJjsHKU9drIYO2HZveEiG8WyRS+I7jYf+BrZBmsJvIeUnyeQ+v1ah3taxKdnOQfoTQSNKwbsUDdIPY5qLQOTitrCLWDDKYbmfNUzDaYIsCDLaNadZWPTOFR7x220cXhAy2UQxUHu8nUoPmFPg6YnAPHrNEgVlSc4sNYbKtl6Rw0L9z5O8hwA1jb8LWvHCNJI5o3iDK8XaaP0ArioIb38vrCYpOxpda38NOH1tY3kA/a5hGMYxy1+kxIzon5/HUtNYjK/OUEtYVem4sx7BglInslFj/SK6Pm1y2Rr4LlQf7g8iI6/Pxo++OIjVeBxmLct7A+iCRxcVS5KUvX8jhZ16uxaqCeSnFCv6gp3sj17CN2nZuJIZps1vCu0Eihe84TDqaNqlNI4eqEp02AngpG3w9qKemc/SHfhxFgJclHvtCIoZ9Jt7bciFdyE0nskA7oFU9E1jVCowG3Eoj7UY2SWn8BFoRhBihWdDV6eMoMeW6Xa9SzfDQVfybCGJikE+wBMZ0O9tMk7+l7jcCB3e/y7qPQhaWHO/UsC+iLIIQ7ZiGSdJajyuoLFU6cZsz3X8WRqknoBGDvW76+f6aKKl78NjgwbUylyLkQlYrJbLcjee4ZUzwO8bv0noaClXUphNpS1HI4hFanYW0WkvFWruTQXyrhXDcrRl8ZMW2Rxd69NZl38vrnqxkBlOlZLDZyDyuq6uRIKwiKUUM7waJFL6jMMNvjWk2GqBp5OaEUUZyXmzPci6VRr3mBV5sRD6y0sBNL4/nhei/0cPNG4kMKp1Nc6NJwtOIiXZyUGY0c0at2unvZhFszk8wqSOM83uIwjb2uhmwi5LNbpQQej8mXoHRQE6jg+nfTLabbm/ben51X2rgG80TWIVUrl77qd5fNf3SCVHFCLuJ135yv42MtGktRJkhgZfk8uCEJHwmjXQR7fSaEtrDz/QwGnoYOUy2mSEZ4K6TqiWbzdRpCNn58aVT+c8e01xQnI7S0LxRV8lHamqggputVOyGHoajEEm1Ejlpu4ePHosU6XNpiKwPssocGTyaS4PjxUo+/kbLoRdzuLkRYrDGy9S38O6QSOE7CGv8sSYg60y2SCHLOI3BbjtOS2jaCAsyGWK3a0W/LXSG/mIliekuQlaIlxZLyT1c3wkp3B25P4LhIYwsVkjS2JSbyDjDx5rKzFiefnf3bekOnTMUx7kMcSr1mAHURGxUz/z0+JQwplHC2wjkwe+DfobSSSI4IGWjEdFLsl5GYDgnlq8IUtJ6L3M+IRlDyLR7Wo9hpxFDheyn1iT2MD3B02N8SIJTWLKB8XXTPorgxVo3TnIZIHmSPkgLso3cmChpp2jPGtqmzXGaA2pKragd4ItXIg0tvVQodbUQQIzS2Xy9kXy9zyX18vI5nC1hfi5ztraNJJ6902VdkbxFCJKfODsbHaJUifRukEjhOwhbGB1Gr6nrJMyeJuL2tYTibQNfvZYxx5sWmo3cfGUmN1oftKhGbUodYNiKjdtsOcnxR5jo53owdoVMDUbOaFiW+tNq8KejJ6IZUNsxY9LWtPGAGE0XZLGFIop32zPR6ZmQhVmyh17z24Toh49NWC7X/Q/6WB+EBAJSiRT1tSGIsW3f9p5KRj6IdEOQaMM7zbVk43oKhRrkRiOEhrfs76/DgyhiFkd+7KPIQNbf0XmowigfZU4S+L4QErZJrxkSZdgIcKsos1OsZcRxp8uBIn0GeS8S43UP54U0Ppa5nM5m0Omrep22ylVncxmPcmzg1SBzuDINoIpcSKbXSDY1s71bJFL4jsGiBIMRgMlIFjUce/G8NlqKit5I/UGWvrzR0QJnM7Fvd3slGnVk+1xm2RyjyAPVDG4tIWlVRGY4YJz5U0wed9yXesqoXcWDWIM9Y48BjD0BNgG0ihK2bLx09Q5RDNlK97t76Ek/lGymCeWHVmRajfTw9U4qjAJCUk3QKEQ/4JCP+xyiRDS/4tVPjHk4/adfmNWJBkkoV+iIDpPIHkY5tt9pydM0WrLnMzlnIYrr3jj5AqcSn0Vjgx77ion3HyEUo5xUMhYKmPQH9+dPaU+CrSlxaHW6xxHiAG4m1129l+vybCWdynkhY6dAktVZpnJQL/OWLtdCKLd7Gd++mMk13jSSgAZOM5FS4vnXi0QK3zFMPSRLMN/eSunpUYeN7RuxYUGrQPYHaS6728lcortWSgSdkymmIYiWuz2K8c+chP2ttgeQw8a6Xc0wPNKf5jkeGPsUbCibBzGcgxBCVE/Zhrl1qtEXUbqR0e3N8FmyttcPbkndVl3ME6Z5gocyi0k509wB3DfiD/cRpTHu3vHYfqaiuuN+FRCTn1PY+wc5qZW58Hp7tVG+kNpp8v5tEpH9HrhPDA9KbTu0fDZK9AHj+O88imxkDWpt1FyIfqw6QN5CKOUcH93IrXB/ZTp764U+puWuoZN/aJdyn8kQvD7oSm9BBu3NcmloywuRN19fS0ol1+t2CCIbzbSr2taBbppx3YVpB39KPP/6kEjhO4ZpzuB4HG+U4xFu76AoZRDd7iA3XN9ISP75C0kCOicE0mp1Ut2KrR68EMfmRtSNQy03dN0xGgErUbRFbMzptTLUOaONyoBigNiLMXITIx8YtfjptE/iaO9yN+ruZeQ0G8E76R+wqOJ0IA+M+unxh48xec4eN6P/8DVwnxCMZKalVOY2v22fU8M+jH83U4/fy+e/zSaNdV9n3d52rA8PW5PkHSIhWUltySgp2eHPEfKw/bTId7LoJMkUvUQt07LjwJhjgHFyrRH2ZnysQb7+qhBpaOYletjt4cseHs/l2rvdybC987mUpwZtfqsLIZYQ5Xq1kuu6Hu8DSzantRd+fUik8B2E92Oi2dZTHga5KbZ78fgt6TwEeHkthLBrtSk3wqs7XTzHi8KwPWhVopMbd9BS1lNJaMa4zkE5eczGI8CDNRAiuEGTyqjd8fL4EanPj1GqibIoXcudE+NfalSwU0tnDV4eOfjw0HA/xEPL8NdZiqkhfkgGk4aPe9nXh8TwMAqZ7u/EcvrTrLKb7EO/hF957UP5S/8+reOADhB0EhXk+oU7J8b8EKVEtmIsDsjdOFY7RkkuG8+EqOc4gB80etDyXJMObW0Hy/fYinLTUxCBo0QMjfa9EESZcoXmHPRQm0ai07iHixJ++D6cX8hsrVd7KY++OINSR160rVQirdciQ800l2ERdGENkwnfGhIpfMfgvaoxpa6FUI8rWOGkjC86zWV2sNM1Fa53WkHqJYL48DF8da2rpkWxE30PlCKhV72oCKelI0HXDWBMjgbGUdgnJ1nv9lLrZWNUPUrlDq+/H/X1Q1D76KXsZIicVj1zun1ApJU8ThKwb8NDGcm2fSjDvK32/22Y1mBOoxFLmDzc/8T7v1d1ZK8NX/P7w8jCjulhH4Xut0B7KLxKRE6igJJxFkU2eQsT3RskQVSiQ/mQ0RomyTmnQwhVw2nQMDKTfIcFOyYTWvLZw2k1OOMuPU1RexkGJ0u2HgdJe+z2YthXuUqZA7QzIY0YxNiHQaQnWyEwxHHAo42+yPNxJMZ0Gc+Ebw+JFL6jsDHYVqrXtlLzPUQhibud2IamlxLBq5Xcq3edRAezUhZLubmWm3XldXU1TSQ3OWOUYEtEmkw0MCYXLbls3uIwSOnJPo7GwiMeqY9SXWN6eKb6dq9aeKUzfEznNmd9g2x/ctynht3+njKTYWqYp27sQ2J4mxUZHjxn23ruG/OH7z/V+uH+vt1bth3esq+3wKNVTG60fDbq4xTEuPuHXqqh79w4K8l7icpm6HhwN1rTTL0J683oNfEU0RnoxaiYmYNgx2bXxJTP9BraB6lAWmoj426ntFpDqITXMqRlY7eVRPKiVMlokOVCQ4THF3LNW8WdrT1uXc5pIZ5fDxIpfIdg3cu5fis2SfLYyLoIz19JV/Ktzq3vB1n4PhawKqUayUcpCbzdynTUQR1372T+EY4xZ2DGxaIF8wYNVnlihmCIYuCtQimq9p05IY9SNwxxnMO9dFLtstVIwOYEDWbsph604W09Bw897a+Tc+BXieFhF9TU25/u96GBh1814lNCePjeDyOD6WumktGUfIxc9Tnn5XBjHA/bEsfWS2Avz9z9572TpP4akex6JFLrGQkj0+O1ct8C+Z4KL647mXx3NlbbCgoscrT8gqlk2pvSAy+8VL72e1jPJZjc7NWnyCHeip8wm0kJ6+VKjPz+IP+GCE/OpBLJubF583iUCKIsU6Tw60Aihe8IrBR1Wnba99KbsKkll9AFIYOqhIWWnD9v5N6tFvDyFdxu4PlrTksQeKSyo+7A5ZJPOMkDMHrrNvYgMg64s+5XU1iGQcs3o3iSCzcShS2uM01cwpg8xmlTmBsNE/reznGaRXT/rDAK3faaqUGfksPbDPrbahkfGmzb/iEJ/E3bPdzn9LVTgvJf87y+zk8Jw499BRapmUfuo+YEvBj+Us+9RQ85EmlkXgz8adxoHNdtANEeO7Q4wI1NdX0Yn7fjCAgBzBmXCbXqszljYYJGkbbcq8ukMW23l0N5ciav2dRQbeArM/BBnJk4l2v71RtpwHx6DqtOIoqmGcdfwNjHkIjh20Mihe8AYpSwea/lo5ZcrmspP80LOD+XiKHux8VJ9jpxNAzjqOxNLV3NXdTiEr33T+N5OsbVx+aM/Qgwzt2f8aDsFPE4s1480IXKHOb02tKRpTtJCgy6/+Bkm2XUQXhKGo3j1KRmEcevRAtTAjidrcnvb0sA85bnp9tMjb5562/rd3gbybytgmm6v7cdy9tkJ32Nd2PlFm6MGMzwwkii9rLc6jSdPBcZ13xuMh3WF4U4Zsh3UCE5BdwoFdocJJOGuqDEHMWqr7Qyyd7XOpwt2px+HJ19ZZVCrZZE952oik2AvpXooUAM//W1FlOsZFTT0AuBdLdCJt9/Oi7iVJbyD1Je4deBRArfAVgHsyWYrYmn03WU+yjhddPLtFPfclo/OS8kEvjiTrpEyaGYy814u9fS1ihlgNFq0gvGNQDMMDzMndp8Iytr3OuBeNOmUTlDjbuPYkQs4ghB3gOVluZIYbqNrA5RPvDXeugmbttjU0wNcnzwmuk+Al+Pt5HDX4e/Trp6uL/p39PXTh7LEMNtZOCNDOLYL2DG+6R0OY0Y/LganBUFOP1ubFnPuX4XhTYQNG7cj3WLRz2eRvfZ636yIBVPJdIkZ6QUJv9sXpR9pFzKnqMSiC/lsJYLectSy1bnc5mFFOd6bdaQz6SvIWi6qg/i8BwbuWa9H6uQ1mtOC/MkYvh2kEjhHWM6+C7Px4oj0BWtvBDBRquLDrVUHTWdzJTBSXfzrpbmIBelbryYSeRwPEDooT8yJottpr6NrrBu5elICxuDPQeqVpjFtmsYJQxbdCYqMdj8/sbpXavPD3HMOeSMBsnsviVYT5hq/nDf+JtnP40m4D4JTI34Q8/+bdLQ10Uc0/d9eDzwq8b/4fvZZ1EL6hjLfXGjETbDWzpNEGdyPiuNJgJCwLka98K+vDjObEJluNLBbFByzrSaSb+PLkqZcBkkYoxOCGY1+SidVjCtc4lCrErNooRpF7SVrupHD062bSspdth3cvhlKU7NVxtY5LL57V4ihLaXw7t6JiXVhZPrGZWK8lycpOn0VCOJhG8eiRS+I7B8gpGC9SE8v5UqjbyQclRfSn34Zi9kgJb/47VzuZMRF057GXCaczRDFBkrjOxmtomZ09HKBVrLas1pqOcfx27l3Il7WEY4Q9czRowaKi+dPGDGRW/mbmyqqjXyMOmq9WLYTNs+IU5+fp1889AY85ZtHxLCw2iDtzz/cAjf247HCMk/eHz63k7I1DbJEFLI3UiohRfvfog6OQ5tLmEMnmbI+bHO6QJO60JbhLfw6mbr6+qo37FeEF7fs0HO/5QUWsAFnX9i7j9jlGEzkuwjW77CZEMliy6Xr7qoODVVFiWszpR3vASgTSOTUrsDFGstVhu0faWXe2M+05RWI/JpVaVI4dtCIoV3DOfGaGGzEUK43clo67utzIkJQe7LN7diK+q9PH/QRUlyJPR+sZOE9FHryXfa0FRZdYo1I1k9uiWQzUs1siiRgWorzR5rf4PYOKc2Ut3CVRjXJuj1+dNgtSiG6ujHGncYRzVk6PhNlUw63a/N+P8VaehtHvsUDw3x27Z7GyHAfWP+UCpyb9ne/n4b6Ux/nzxmy2DmjBGBGedSIyOHTIdjsiurRrLXzweIuWiENpbEogynL6qcrO3sozzmouQKBtVdrJw4ME5adVFI2ZAFkQSdRiODSkpwv5hgWrxgOQon1/RQ6NOD9iEc4GotFXRP1rLGczQHJdPxGFp+2ut1am0VMP5uoy8SvnkkUniHeLj28ps3MsJ6r7Nkmk5qvw8dvNrBdiOJZoLYi/YIIYdcF946Ntq3gGw36DTMdurVNYyLu5ssYDKRXQ2LCHk3ykWo0S7cOF209fLYgvuyVBfH3gbntDpFE8y5GztvjRBsHeEeTiualXFSGvvQ8D7ExPh6NWDDw+2nBn6anH5IGl8XfbztPQ0PJauHUENfKAlkTs7bhT7u3VhBFPX8ztSrN8ObqWXMkGGDuZNz2qlHYOc5R6qPHGNe5yQDaqt76VXkR46lRnMKup2LSlxOJCac5Bssl2RRpZWstowypKl6ERmGmENdSm78fC3X8rGGw04M+tkgvFZkcthVJQGKd5JLKzORQPuBU3XeaqWn6usuh4T/YiRSeIewtRKOR/l9tRKJ6DyH13dj5VDbQ2jlZtnspAnNqTpTt5A18OogEcG5hzcb8A9LGh82p5msYD0LJt8UyMZRDYVVGVn5ZBHHJOa0OsmpLNGp1OGVuYwccsayxsyJ4TPbqkR3zxsmannr10UEtp1uk6ncYoTTWmhkH/Rt0tBb9nnv779p22k0MGXeBzJTiRCCcxKBnblRjjNpzuvrKj3PWRwrhmbuvuSUq5HOtb/Avl8zzi4qwbixsmwIknSy4YNGDJb3MRL2GjXkTgh/GETrsXnWXol9j1w700DLooQpSexhqwUU63P56EPUCMFJxFtWMF8IMUTGQy+VeIYoQ/XOz8dIIU1O/faQSOEdwsZhD4MMDKtr0VabRhp4bmrxkjY7iJ0OwmtkxlFwkkDGi6y/30C5gEUFw7mU9bVetusdY0LZ5CEYScDkpQGJ8bteehC83vHNZFunhrAM4uLNVP9qncwyinHUzVsk4ZwzMpyVXBqr2dA8G91AVM+UUdLo4VeihZN3ra6lQ97b6T4qr9KKe2DvH0pMb8PXbfMwwjB2ha8lhBWq83sx9Bfufoe4RVA2WcNyP7nT0mD9TFUYG9Kc6jPWZzBodGQyUVCpaBY1PwFEL6ScRS1ZRaIX52AdRf5p9HiyKKQ+eElGuyjvOSAHZ9GeRQl2TXnGtThm+vsSMtX/XS5NbH6QSPjYSUFajiyu06uEFCI8vpSCiRjEKbqc9CqkfMK3i0QK7xAmH9lU1BCk0/PYSfVF20utd11PVIBCqpL2nSSgCyez5/xMlkxsLdQO0O2Rm9VIwBzn05KZjON/TFkJQR5v1Xiboa3V8JRmpBBi8NkoM+3j6BEXakBrZIxF5uQOtxJMm4FUqDG1juqtEwIB7XHw48pimRo+/IQAlPmckQ5jrqRSt9TKL60O/62S1NTrnz7GZDv3YFvPr+5nghXiTRdefi6RL2xhu1Uys89+Givh5Txawj4G+X2hb9U6HUvux0jQVkjyeq7LQQjZznOMIgseJ+9lZGTnpkAcgajfW41cB/a+UYccZUqElb6vRaWW34iMs696iJUcWhZkSupxEKkz95JQ7jT10XeyhMaqksO9WGszXJQR29PcQsopfHtIpPCOYRd31yk5DHJfL0qxDfuDVBE1A+yOkl+4PQhpuFwiC1MMXh8g1lLhsZ0afq1COo2tsFpzKz01L32hTwRGTzxDDJJN4QNNXqo3TxinnM7VoPsgq4t5xNjYSIUyjkatRFdfc6OBH/T1gxkrJIOeISfDvGYYeyVARzmoh4sbycNmAlkEZPX5f2Ou4CFZPDT8U2J5+Jj+buMgMieNe/MoJDVnzCt4/bwZ+jdjN3OuBJfpOZsh+2kRDz6orOTcWARgCX6CkrKe+zyKQW+yMaFtieZllGGEUb/rwQkRWORVKAHZ5/L6L3djz4tVHUVGB8OuMeWbPsqolnYuJakBeb++ka/u9g6ePpPtmxZe3kpUsZhLZND24HQd8aaRMtW0XOe3g0QK7wjm8RghtK2MBrjdyMTTVgfb+UI7ljuxfZud5B3CIGV6RQFv7uDVVpbmdJVUJ50SgqAGn18t7a/Q0lPEG3W9LuCshnmBGIDBcQozcjXOIAbKcgOFeqEtUgVjhsKhdfeIESyQCMOOYYFKF2rATUYxGztzo6zkGQnGJAqTmzAZSY+tc/I+lpeI9nscq6QC/KrBf2joDdME9QOJ6N5jUc7rDDHAK2CtpZ1V1Kor/ekRoijiKOGhr7WcgRFDGTmtnRCRiq7qwbmwiaaFEm2u34nTc2Szp1B5qdJ9nun30zP2IvSI4W/hNNvKToMRSsH9qNOiBduXdcwPcs1mc8mfMdcgKMrX3jeST3O5FFd0QN5LFd6+Fil16IQk2lakJhuOZ53OCd8cEim8A1irvvdi1E8JZ50bs1pIWP3pa7EBl0+hfwXXW4kYzmYyOsBs5aGXcDwrYGi1lwHur6BlkrfdtHN9zEZUEET+MTkhQwxK9OqtezFe5rke3ehZrtQVNP1+H1WbhlPlTTE5FpuxhJP+hpPRj2MuYTpa2yIAq5dXDxSPDNwLcBr2Fo08okQkTRzXCmjjOGvJBvLZwkD32nMNf400dP8bHbfNnRDl2slgOiOCWZRjzZCIyj5zhmzn3JiiqPTLKlVeWgfpSaiz8Rz2GhEV9jn0s+ZRSVgJwUZvR/0OTNZZxzEJHfW4j4xEbsTu4yhzdVG+E+tnseooKxSwiMVWglPDTweztRRCBP3IhZdr2fWcFn3a3si1mxcaROmaIocaugaWK04TVK2r+eIiJZ2/aSRSeIew5Qi2W9hs5eJeL8V5fnMndrYHmoOUqTbqrblc7vW6FkKoW+i1OAS14WNFC/dJwW7odvJ8FiSRaNq2RQ+2/nLp5C4d4mgkLElsBhaVMbo4eucW23eTSKHTvoYCXbc4SO2hjVUooyZKkf2YlFWoYcKNurcRhmneU8+/jJIsj06WAm01N9GFsZHOxXE1sjjx9O9hGhFMt4kPto/q9SPG/8ppCQ1Cmivk3wLx6t0kwpo5yPqx03uIQsIeWA0Ulz3OR/o2EDbFpBcgjgUEpR6Pd1qVNDm2XC3oyav3sn0RhUhs2mpjEYaeozIbE8kWYWaDdLfXk+M4IgRjOSrNIZwGLZaQ5VIoURVyiu46OS2W3ugacXRylYYGlaNmM+nXqTuYdfI11o0EN3UtY+WnA/MS/suRSOEdwaKD7Vb6E7Y7uNlJTqHQZPIwSLi9fSPh8+UKto1OPHUiMe07aQQ63YCeUbqxHIKVLBrMa4+IAWqGsVMWRjtXqWdoVUgdWm2EeJonEkAzhYgBcohx69T7PhhJREl2tvrape63jWPZZe+034ExmumVKHKvawar4XRRPPCZG4/biAPGGv5llPWJGy9ksI9yTI1+EVadcw8PZaSHpPHACmUeZkGigDPEOFdRooAr4KmDc40YGHRcedT+kAgXA847ouVgdNGi4qyhWHTEJsOV0MVCFkea9bDN5PN4N5llpUbe5ZxKT8MgRGCruZkk2Csx5YNIXQsnyWWn29iYc+L9LuZMEwatH/sbjDRglKEsD48MdgwDLAY1+r0Uq72/gsu59tocZRdFhDvl6XWQqLnpJZ/WaeVSkcOjKyWPhG8UiRTeAWxW/H4vXcyHo9gkl0nzWt3I72UuI7JfI/bVBckbtGrgN0d4Y52kFh0EdNEaxgmZpve6yTYmkWeR0+wdKy0MwDKMSWkbtzztb8gZa9v7OCYZe5V87D2byGmJzcKLy+iDGKVGPWgfROoJSBQBnAbsWUI2uHHhGMdYdVOp12tSlaFyY4IZZOxDr5LK2sFNlAiidxqZWLQAv0oI08emxKCkV6psY2WkZ2r8Z8DjCB/6MVIoI5z1Y9d2BdlSCCFEKMpeJP8h4oqeogxkviGGgpYCV0TcEIgzNeqZG89HjGP5rvU62Pdnh27fM8gxlFEetCVAray0cTK4sI1jkYHymZQK99AVst09J4MxyWxLeQJBP+/BQdjJyOxlIQRBJQnk0IvD03RwkcuhvD5Kf0LUEdrFTJ2hI6zbMdpOkcI3h0QK7wB2IVvj2qyUnMCbO/GotkchhBhlvlFZSH/Cm73cRDZSeLGAvTqVwdbVhdFw20gL0/GB0/rLpzV5gxKBGrvBpAfGJqtWjQNuJJ+OsXR07iSRe/Q6sxsxyg1jDX2FGEqvnnkTperFchim9fsohr53OqEz3k+AGnHZeG/T7HM1kD6OFTkPRzFY9FTpe1mDXq8yU4RfzSt8HeIo0WVuHFtxjvzLgMsAHzu4VKKcRdy6I1v0xDlk1UDMIa8C4egp28jM15LPXzX4KtB1MyGBsmfoPFnZ4YIjuIwwK3Q1O5V5fIAqG2XBpZ6XnUVO6vkPSN6i0e/PyMUm4toEVHMQTgZfv6+WsSLJmh6nwZQVMSz19dNIVtMibYCrSi63ZaUVdQcx/OfAsoU2l0q6PMr4Cwbpa1gtoNLqoxQpfPNIpPAOYJ5Nlml+VH/atNPdUZ22CrISnr4P2bX0IHgn4y12DXKDBXWG54yeuxlMm2lkUYENM7MEs2n4hRp1K2EE+dkiwm9E5RuNGGLQ2n99r6iPLVTiOZqkxNi8lsFp5Z8QtGJIjf7ejZ4/TvQD52Q/VkljZGPHV+lnNskkn7x+Hsdk9qARyBDE8JdxnNNjTXlHJ1HDNAg44a0Pjs9ZDmYe5ZieIRJXGeDDAR4Bc9X0V5FyXbOYH3EMVFVDk+eQeWLpmIeafIgM3kPmcVmEoiWLPV1TUR5bct/RFaVU+i5amkMl57OPOB+JLRAzTg1vdpxHjVzKXhJQ1sTWKYE2YTxXVjBgJauFEvxBLb8VMFipsjWsGZ9a5DCtgLMoYgBXymWyOci16HO5tIZOm7CXUM0kMu472BWypvhqoWs1VLrQ1CJFCN8GEim8I1gF0m4n98vLW7GZ5yu9x9UrOjbSOJxXMFtIhdGrneiz5qSd5CAbWXHyYJEb2Mr2rJP25P1FcF6SzHZTuygavXl41uzW+JFoQPsbVKLwyJFEr0ZSDanVsXuVaKxU0WSWIoyG5+BEXtFdnWSfzGvHs+7DFqQ3UrAIIYujYS709da7EJ1YoRBHaS2PYxOYNd9ZZdY0/zJ+Y/xKFOGRzzFzQojvR3iqOvsT4INOhwUWUAxUiyNV1ZNVPSt2FLNe1JWsIGSOtd/T9BWuz4kEXBzIih7nB9azO9w60g0V225NaD3DwZP7QIieITrCPmfIB6KPp0RyVgSGzMM+02hIq8iGAE88bDQyaNxYJ+21G9pGnJT2vaGE78Zo0Qz/1AEx6dD6YKxPRq/JppdNFhksSzmUpoPVTMbBF9rAWWUiFa08p6b12UyKMc7OJPdmDlXCN4dECu8AtohOWUp99k8/g+fX8GYrtmsYhAA8Eh1UpdRqzyst3plLTtN5KA+SQz0Rw3QiKnCaQWMrZ03X182CFIT3bmyYsnDc6t5rRoNpi794JwZ1QNw5rTDhJmjE4KQ1tczldUc15kUc97OC06C30sk4BVva0Uo7vZeTlanhb91YsbNQaWSu+ymijJC4RLU5J9amVYKyJUG9k0ylc1LCYpFA7SZk9HXu5yRicPo5vJLRClgrcZ4F/E+O5B82DEf9CB4q1zKPe2LMWM4OON9zmR2p3YxjLKmyBucDvgyUrmHmjjS+JJCT+4FhyAgu5zzfMMwiwyqnX9V0h5KhrThmJW3tiPmAqwaVjjysIuFsgC7gNzA0lZzn9SASz0tgo6ZgGaAYoFYSbRijPutYrvT3OGgOyI1kYDmLlrGb3l6vxjt2mnpaiELYDZxGX3kPL+5Eebtawuoc5rlWxXpZpGe15DSKqbKy2oRvDIkU3gGsi/moHZpnK3DXEj6HDM4WEik0QLUGMokWhqivdWJkuiAlfo3OQjqtiGVlp6afTz3hE3lEnV4K90ZErDR5GhmlG+tgNfnHxTGZ2Hh5/qC6fB5FthicZA2LbCyzNKIq1MgHN0YylpzO1JjFTJjPjHmm0YUVuvsg0lZlx+3gkUg0si8xghz1Aw9eRkk7lYqsycuM3S2SN7G8zD18jYSUIaR0AZxpMnk9wOVAdt5RrTtcBXEIONfzNHvDotpTFDWrssb7jsf5G3ZhyY4VzjuGzFO6jhlHnIvk9IToueGKxsOCmoweFwJ9nuPOIn4ViL2j73Ju7h6z6xfEUBKJHBcFvpdz6C86/Hqg3fS0TSWNkTY07yLKd7TXqMryD7nTXg8nstiK0VGYTsRtGaNQGPMajnE9Z6uM8yIPZRqczAqJCLpBquv6HmIL2Tlcnes0jmzcn3dy38xmpFEX3wISKfyaYbPgbR3mQy3NOsu5zHoJcBp3wUFulOMRXtzCyxtZyhAvTvh+J7nE2Rm82GtawAghMkYMjlEWsZvU5CPPKLuYFBCdGEhbjhNgr5pTROUG3d8BkR7OnXiZtconwyBlkbNBK6C8aPc54g42jP0QRzTBjHqamiy1NYy9Gu+ZSkEeSd4unDy2As6UJGyIXnCwHKj8kSIfqA8Vw24GmwyeDWLkatXWj4hh3yPvdxq9/XX5BDeWm14Cl05e/2zA/aimuOi4PL9lyAr6Kif3DR8Uv+SH1S8p8iOV7wge3uMFC468zh5zcHO2rOhjidP3jMAy7liyY82WxpfM/JEiDvgsUMeK2i3wLtJUJTF6yqyH+hne3ZIz8Ga4pOvnRCKucvjLwGxVE78s6I4a2TxqIRRCCGUmhGuDCLtMzv8qjob+4GCnv9t1Zgvt2DVmvQqWmJ5ek1YIoQ1sbS8J5SxKiXbmoDiXnJoHzueST1iu4PEFrM+EEPJkvb4VpNP6a4ZVHdnqaiD3ydlK5N7XG9gexJMqSxlyd9BO0ycreN7B7VYihVKbgg696KutyS82ItvIwOSiEh1khyabncTxttDNMWoeQY1vqW5fx7hN1NdZUrtiJKLFoJU8+Zg47hGJoUNIw/oVcj/q0B1iYGcq61juIIs6dM9PeieCEoGTSOcy6mwhZFvncdqI53Mo8oEqb5kva7qLnOO+pG0KssYx3BWE60qG/c2iJlynhGB4QA4OIaKlg6fAMwdzyN+vmX9Yc7a85enFC3asqFmR+Z7v51/yfv4F8/xIcBmruOXMbTkyYxl3hOi1p7CiI8fHgWfDSz6OnxNcxht/iXdBTpfLOFIRnKdjIAJzanqXcTG74dDOicHRMqciUlU7XDXQxpI+5gxlQbyKuH3E9QOxc8Qywp1GdFGjhypKvqnNVX7UiMGumU4vaO/GdTHMokylJMeYkNfn6qPkBgZkdEuViTNU5rL4zuocHp9J1VE7yLiL9Voq9UDuHZsIkJLN3ywSKfyaYQnmRo1qROYa9doH4KMYs80GdltZXa0f5D5cLyTvMESV2ZElD9Fm2NZ0XbjnjZ2SgvZtt3Ba1AbGpRodnKaKEsTbP/ixXLPXyiKr3olquIlwG+CYaTI6SoeuV6tvXr7NRfJRiUQTI0YOg5dGKu/kucHLMZVxbKQrnSR1V0II7v2WchUIg8fFgRgK3LwnhBzvetbrG+aFnOwydpRDy/PXj2ncgvZiTuMKQp3BC62eqif6ODCSw4QojEAuNFo4B1Yd82dHlhc7roobVmXNPDuSuRcsXM0n/md85L7kkjf0seA994J2KDkMc1bukpo3xJhLL0IW+F77S/6g+484B39V/Jgyb9m5JS2lyIdECjoueUPNnIEcB1zkG/w68mX7HiEE5n5HT0bnC7IYaA+Ooc9xM/BZwPWR4cZJNvcYJdzsVLIbnOSdFp14H3mAXXZfboSxTFhfdmpmsyo3x0gIc3l5oWXZHfJ2F5UUWcy8SEZFKZdfOZNGt95JGWqe60RhbfK0ktSUbP7mkEjh14wY5cKuqnGOS6ZGMThdStPs0iCyfAhaIagzYRY2iriFVS6Lne/NI5vWbVuCb3qzrnSbKornH9DZRCq9HBwcgkgIPUiSNkjuoNFEBl6Ndhzn+x+caPZnkVMlUuFFCrK6+MA4EqNHu4DduCKZdRb7OHbpFn48hlmUTuozBxeR/L2O2eNOJ1QMZL7HhZbOeUKEp9WXfO/sc/ro2A3nrN2OM+64mF3zy+MP2ZUD/SYnuAXcATcqizRurOE/kYJanVxlrgsHV1Fko/NI+V6DX/fMZwfOF3cs8j1Z5sho+ZAveRKveY+XPBleUvmWS3dDue8ZyLjN1zze30JwbIsF86Lm/f41LkRC9JRdx2E950jFQI6PPZnbkdMyo6GjoBPdjK1b4IuOjVtTh5mqbY4sBmJwZN7RZ4G5r4lZ4HhYEHOViJ5EkRLrKN9D74Skcz0nWVTrK8lrZg42SiI2KsNyDAO6/jNjX0mjTfY5xF78gUWlS3CWUm23Podn58JBL2/lsUcreHIFTx7Ja4tCCrrsfrL7KEUM3wwSKbwjVJVECEUHV2dyg3AnDTxvtkIAZQGFGvZ9DXe6NrMPEHKRmJYzaf/3WvN9D0YID6OHgEg15sWZnDTAiZEyJxJBQDzGPUIEnrFrOUcTs4Xc5T4DryMTrDliHWXZyKgePozdt7lTWcJxGpUdvXirZYSLMJbVegdXHfmTSFxGinkgKwbK/EDMcvrOE6NjPq/xoaKMO36y/E889teUtHzqPmLljyzYs8gy3sQtedbQt47bIif+oIDPnSScLWfytpyC6eXLKIbxKfhHgfJxCyHiXSDLAiu/J9euro/C53wcP2fJnoxAFRpyetb7PfV8xkV3x+PdDWHwLMsDM3ekmrc0rmDRHfht/1MOfUmV/5A7LinoCMBXfAAEMgZmHAk4auaUrqfKGhY0NJRE56hocS6j8SXOFeTlQNE3hKxgiBmBQJZFOAsMPpP8Qu+hLWXdzLMg32Ph5LOXUcvf9JzsuS8ZmVwJQhQHIJco2JbS7JEUBoOsLb4/SGAyfwqLJYSFlKkuF/DoTHyItpX7IsvGJlAgdTV/g0ik8GuGhbllOdZZ161oqbNSKjGGqJUVM6i3sNmL3OTQyZKlDrwc4OYgRSBlLj1S9bTCyGQjGKWkDk6jr4HTury2SlnJ2FtgkYetmBY0iUzkNDnVmtx8oQYhF6Nu3cMrzT/4QSqRcGJcbL+niiQ7SM0hlINWPzkxQKVkM0Pek80jrgiUq5rF6sgQcqLuuqg6lnHDh/4LPihfcMENnoE6m5PRM49Hgs+4KN6wdRecLUTX79yS/pcV3GpuJUNKWt/Wm3CqdgriXS9binnNbHFkFo4s/E6NNFSxY9UcWBc71mHLij29z8hjz2I4sLw+sGNBse8psp6zFzvK0BLfcxSuI88GMhf5reHn8MjxZXbkzl/QUrBwB+44p6DDE+iYUdCSKREs/J42FrgYiTj6mFMU0kYfOk/jZsQ8UmS99DIMgZhp7XKu+ZwedeEHaXCrBokYrXIsuLFk2EhBL5GTLAinyrchiAw008QyQRwbp1/7toafv4APn8B7V3I/lJWqWq1cQvs9HA7j/ZMG4n2zSKTwa0aWjbporhrpciZO9qKV5NsTDYlvgHO9eZ4fx3rus0q01he62M71VvoaqgC1NYhZ8xCMTVYwOr7WmGQjCgjymFXeZLqx08cGfaFTI92qnJRpknepCcrByXPDRHceEBmoRJPWQUZimHtXmpsXxtEVC4SsLK+QA1kk6OLu0TsWFzXz4sAQM2LlKIea83zLR+5zvu8/paCjJNDHnHN2VK5m5lpcHLjNz4mDJ6wj/Tzntc/o38/gq0xOvIORECZSktPPasPlnrWUxY6qbDhf7lhnW34v/hkX2R13nPOsfsl///KPWBY7hkVG5gPRB0rf4f3Act+w/su9jJD+MErEB7CJ5PNeymcfwcof+UH7GWdxy+vyEa+LK8rsyIotHQUh5jxy1wQcP+XHeBfJ3EDFEe8iITpcFuljRj5vOdTndF1OdI4wC/S7kqwfGPaZXBcVYx/CEkkkH5xISt6POYOoHoiPUg124H4vjHWaa+CY5bLITqXOUI9EzXMnjWuhk4KJ3VEi43Ull87+oLmIXPp2bH6YLbaT1lX45pBI4R3A1lAwchjU0VrMVTbK4boGoixDeOxEe216tY85XC5h18tQvNlS+huOB0YiMK/Nbki4b+P6ONaNd3oAqJZuXbqnyZhOWGuwF5t+rBp0pkRSOMlT2L4t0jBZ6MA40C4PmqhWsjDFybquc4Q8ctWrFxHOA9kSvA8wGxjyjICniD25GzjPb/gk/5z/hj/iR/yMI3P+Kv6YMrQs+y1DkXPuNuS07N2ci/INf+H+ETOOlPOG+NuO9hdrSR57+6z2efW4l07yJktgFcmKnsunOy6LO1bFlk/mn/E0u+a3+CvKvuX8cMtH7Ves9zv4ArptQZx53CKQfdHhXweyGtxO3+oMIZsDcI144xeQxcCq3jMra54dX3EcSn5WfcKNvyA6mXfSx5y9X/IJP+MrnvKl/5g8BAYipWsoYsvRzejLFXlWw76ka+a4paPwDWHr4HUhrLuI+MseGkdocinl7YN8Vy1jxKkzncjd6IxY49p0YR79XheFqIuhlYcelXC1GttWfAHna1Euo572oNHxoQWvFXulJpkt0RxCSjZ/U0ik8A5gFUhFIe36N7dCDm0jc42GDuqdFueoTSwKoJQcRJ/ByxpuW+nNGpD7NRaM/QOm0dvcIRgTgCbZWJng4McDqxADHKPcpb0mldcONm5MJNoyk5UbVzKLGi1YpVOu+7BehNJpglrv9tMaxF7HTiMamNfXFV4qezTJXJz15KsWVzpiHgmD5CTm/kjlay78Hf+Ef8dj3rAOO566a1wc4JjzyfVnXK/O6Nc5R1/x3D1j6WbcuJfcxgvKosM/hfbZEv5cjwEYmdSNRrDykiu5DEQlr9liz9pv+d3iz7ngmiK2PBleMT801KFksffMPu0ow4C7Q2Yk/Tnwr4APkc9pVTwL5Hs4cCJI9xFUw4BfQ5a3VHXLVX3D3dkFg48a2Dgc8Jhrfpc/p44L5q7kEJccWOJcZJ4daeOMkiN1Pie6jMJH3Dxw8AuGXuQ9twz4PKd3WmTglMArPzazDeh58uN1pX/ey29p3qCIOmEjwuVavvJ1JdHD1VwMfOugb6UIbN5LDmG3g34mPQqlXtdFMTpX9i/hm0EihV8zrE8BRimpKGSRnfooEfuigPcewfMb2N2Ay+DiXKaobnWy6hC0eEjD9L6X+TGnNXJhHApnzq4lSXt3v+EI7hv6ApEtVPOV+fkRLjIdNRHEY3Zozbq+l622ZhUn/URC6jUvwURmstLSyklUEB24XtYf8JqcLvTgLyP+vYH8MhDajIzI2m/4SfZTZhzpfMk/4i/4XvgFzucsQk3pOj7kOVc3t3xy+yXNFwX/8Q9/C2LP/6b8//Jp/j2avOJV/pjb/hIqjz8L0uWbPSQFjX6yQb4QLxZutmwJQ0ZHRp4NrNhwxQ157Cg2PWdvdgylJ3zp4VZaMDzg/iMc/gjKDWSVFHBRI1HKnHE8yQr4S+BT8JdQuUHGUF/AR5+85GZ+xbZYE3DkHJlxZJ/N+JDnvHafccMVO45sY8eRksHlZL6jiwWtn7PMNjTNnHq7JJKRnbWEXUFsPX2n30eFeB+1Sn651xlTmovax3EOkl1nFoUe9dpyEhwyiFefe1jpuOz9AXot0V5kkrMuc1iXcH4mp35/kK/k6lLVSO1TsGg75RS+OSRSeIcI2gqQZ1p042R2/O4A1wdpYrs+wMVSluocoqxe5dSm48DlUsW0s5JUP/nnuN9pah683UA2AM4hcgj6Ols0fkCSjdHdjwBWxkKIblWpZNQBNrfIMUYrIYrEMDBq1E6Tx5mWttZOKlxy1RHOo5bFeilqv+jJ5wNxcMTBUy73LIqauT+S03PFLT/g52TO8WT/gqv8ht4VLLs9H2xeyfoUh46P/+JLZh9s+bj7ivxpIC8DX1VPeBWf8Lp+pvOYHshGZulC1OS6fpbGUWZHFtWe+VBTZTWtnzGPDcv+wMWLWy7+bEdcQPGnHfx/hLid5nC7DvYv4eyoaZUZUhLrgF5TLh+jM5aA5+NXxD+GKuu46m8pfUM59HgGdvkS/AU9Oy65Y8aR2i05uDcs4oHXPOGL7H3exMcssgPeD7SHGW7wVGVD7zxd5enbXL7P4KHqYJmPK+HZdWNVWibbnKTCyfUWx+ed1/JRpJN/FrUBupNOZhehncHZXF5yd4TFrYx9aVpZs3l3lAR0kY85Oe+TdPRNIpHCO4JFDLamQt/rNFS9yG8OMvri8SAqistg3sG8EWPiC9FlQW6YvmesHDJD7ya/R0ajPiCG2JbYjFFKMc1DtdcUSLVJq3Xs1uTWacmohSmdagVeDXnU6pTcabmUG3MdjdPu424kMSs9WQOP0U7rTJeuFJIp84AnELuManZgvdhy7jdU1Jyz54f8lMdcA/Dx7gvKvCGsM5a3NfldgCW4LTz+/IbjFaxeHfmt/udcfO+G6+yCX+af8EX4kDDXssvTvHHGExhUKhuirhHg6JucedbwdHbLJ+4zrnjFo+Gas7AjyyGrB/w2kMdAeAlsRR65i/BykM72p1/B+WdQrmG+hKYQgqic8tNHCJFat7rmm8pDz9l2y+HxnOgdLsqspJKWS254P37FK/eUBTU5F2Su4wP3BXnoaPyMg5tz7Je4IBdkbDMIGVnVQxHpjxoZxkIcgem0XBuDMTj5vo5MGiAZS52n1zxSdZQPEjVstpIb2w7y3LrQKGAmebLMy9oiM318ptNTD52s5Np2shynyUgpWvhmkEjh1wxrVutVL+06bcAJOgi0E0PhHKxX4lk1vcgLg9qpzsGihLMCqGVhnp15aTPGBdhtSJljXGPhdONm0iqaMXp0tvxlhhp4hJFMFqqceK216ssximcdpJyREMSrb0Bm+mvDWR1ku87LgR317r3o4XJQHWAGT4O83xwoBtwi4irw84Fs1lPOOnx5oKwaLvI7Psl+wRW3vMdzfshPRcGKA4vhSBYifdez+qzGfymfzW0hvoDsr8ANgQ/r58zPd/ze1V/wF/53+Ev/23TLwDDTSOfeYgBKiLUTfaN3cOOp7xZkz1qK0NJmOYMrYYCsD3SPMkLuKT7tcb+UnBFAMYeigVfPpTnxsyDO+NkOrnJ4OkgJ8tUTWN6BewVcac5oD74Bfke+t2cv39DOCm6W5xyzGRFHHnuig0/4GY/jK67jFdE59m6Oj7B0e87yDaGC9jjHux4/DPQuwxeDLOKTeZl7lEf5voJevB65Bho39qqYZGgVSfo1n/7W9RUyLUpbFOJPNK1EwFUpTZi2XTdAV8vCbrkTYpjncHYhVXZFKZfMXOcfDUMihW8SiRTeASyXAHJBB1VNWv3785uxk9lpjm9fQ3NgHF7qtTBHiWKRS17ydFNaSWqGeJnV5HEPp6mkESkldIhGXCHs5BFD75QUCi1ZnUcxFNZXsNVII1MrYN2tLspYbof0LnQDp8XpbdF6vIxNWEWp6AlOjM3jSFaK5OSzSHVWM8tqFusDWd6x9Ht+7P+KZ+41c2rOuUNWIPBc9rdUoaE89Cyvj8z/qoN/i0Qdn4D7AooK/LNein32e9ZXO77nf8683LGda5dUb6GWnVTV7BonUVUN7B3xtuT2cEaYBToKmlixK5ZcHTcsj0f5LP8xSs7/Y7j+f0kDl3Oy3s1+kGbqV+2ovPwPTpZj2LzRhu5bIYQQpHzTO+BnwE8g6wKfXH/F48MNh3JOdPBqdclNeY53JUt3YO5q5hz4U36fjpKIp3A9F+WWMmuJ8RltvSD2EIMj4Imdl6ivzMTJaDWqzIClHyOmjLH50CJSuJ/L8nCVaeQTVEIbJCc29DoaO8L1RsqzP/QiE4UA8Vx6dkqESELLybmxCam2iF7CN4NECu8ANjd+udS8QhCvZ7eRZPLQSrRw7GTsxbHXKcYlXOYi39820uhTFvB4AV/txMGuTc+1ShaTlEwO0uiCuUYCUbXyfnI3l4hnv4tad65GfK7PzREvsgiyJNbRifZviZESIQQji0WQGvfLXobitZnIQ0e9q3OHKztc8LKtj7jMUbiBbNZJvX3ecFm8YZnVfMxn/ND9nIKeMsiY6dI1lKHl+9vPWe9qstcRvoDwx+B+hkgwnwJvIHsMnIvNKuuO5bFmUdYUNnxvOOlaeiInt8kQJAn/GvhtR9hlHPYrhvOS0rcMLmPIMl4trrj44o78QqKx8J9g2OgCZ9dymq8YgzoL9DLg0ygc1ndQ7CRidK0Eb5mV6/5r4J8AP5Dve9keWQ5HOf1ZS+F6XuWPGbIcHwach3M2eDfwBR/ymNc0bobLLjmuduyaNcN+SVMviNHRO38aTSHrcztdfMnJNZHBaXqtV0nJHI4wOWVBfIAwyC6OjVYway/jopDKue1e/l46uSdQh8dFUSfbIBFD5yRSqBu42whJGjmkaOGbQSKFdwC7eJ3TXEKhdllHCJ8tIa/g1Rsx/i+3ckM8eQTzTHoY4l7qvT+8gBcN3DRCJlXUCQ3mudnPac40IJ6wjaI2vd8hBt9FmZjZ+HF4Xu04rd9cOun6rTSnUA3i8dt8nKXWszeDGBTfSKKyAlaD3OU7ryWzmZRcdp4weLJ5xBPwmaPIGi7LWxwDZ7NbPuA5j7jmQ/cFc9fQk/GU5/zT459wNbwhr3sebzdkhwj/Cfg30H8FWQ3dZzB8DrMa4qUYV3cFroFhcLLSaHDEvYe72aSkcpqZ13MYgrj3LkI5UNdrXjaPuCrfcM0VdZzzw/AZRdbiPwvEM3AHOH4GjfYjGO2sub8MQQZ8hYxUegL0W6nPn8/hwhoQ18i5/LdIYvrHwGNR8fBw1u+JteduecE8vOHIjKG0UjSHJ3LOHT0HCtez9BuaIqcpF3gnxOZ6Rxw0pMmDfGe9GyvXrPegRSNHN3bPm2OCbBejHGbeSKQQnUQIXSe+RIfM76q8kMemg0czWJ4rQQS57ocoxHFo5J6pSk6LxUEihG8KiRTeAawb08b/tq3oq97JCO36oPdcISQRBnXyVX73QddbcHDXSNXg+VxukCZMxvbAuIyiVSRFdJ0EvcEt+RwRV7TzMuqhiWNjmY3OCFH0jKW6bqWX3MFRo4MYxuqluZaZRA/1THYQI/RzGbG97HXEa4QuI2QRchgyzzCHchZklMXswOPFG9bllkt3y9wfcQQW1KzjHf9V/PdcZHc83twy37e4DcT/Wf65l2KA2iO8/GOYn4v3nT2H1T+B+AEEPHf+gi5m1N0SXuZw50cZ5CEiko/JkRN99AyHhhfH93i0uCFkjkU88Nv8lPg4Y7jwZOcB9yPwX4DbiyIH0jOYR/g+8AX3lZe/QlIXC4S4PgGeLuS7pkXWfgYhvxfA70L8AyDTbXwkDx29yznkCzIGonPUVAQ8Axk5HQUtV+x4XD5iH84gXlCHOc45oln3Qc+HrWVhCe8Qx2ihgtPymxYtWPPjIMa/1/lcswpip6fSyZil989l/EVZyQC8x5dy6fhOcmeDXnplJmSQ+ZEELPJO+GaQSOEdwCY7DsM4BrhVj8c59aSCeEU+SFK5QEtSj6K3egAvc2BuDpp7AHanhXK4Twxm3O2mDijDaJhgiegaceu808akqIPvNNzoWtkmV5H40sv6v6+0i24dpPfgUI4lqB2SWe0HIZvcI2suZLDQnEVdwpUkml3h8KsOX8LOX3DmNhS+o/AtAxkLaj7il8zckXms8SESYoZrIfzfwP0rGGrw70ni/uZTOU/HHlY7WH8EvAH3GdT/rOJYzPhF/z26Y0n8qY65sG7chzBpLiAy0sHTPV+wvVpzd37OLGv5Y/4Jvx//nA8PX5F3USSU34flK6j+F6k285q3zhEZ6VIOaSzSQtSuc/3qftu+nwE5PiN5Kw74M+AD4BHEHvKip3Ulu2whVVvOkcWBxs0Y8Gw4o6ClpOGOCzbugkW10xns0NW5kJ81pln/i623kDMmt4L+PdcPdGRU3sxY15yKH2Ip17atw5QFkULzhVQaVbk0tGVREssxg3kpnc7LuYy0yL0Mh7QmthQlfHNIpPAOYJHC8Sg/M623ro/So9D0IhVU2Zh8uxskgujU2w9BXxM196AL7BQ5tHt9I1tLd8OYaK4QAvAAmWj4Jz1D3bYS8QJD1GygG5PWqKzUZfKaysvqaoWXHIOPEjF0XojER7jSBPOuGMukYiYJyxXCki2yEtpCSk+X5YGs6Bl6z244w/vnlL5nyZaBgpyOiCee9AkHfw7u/wmxFW/57kt4/XK0oy+38IcOHq+BTrzVF8vHXGcX/GnzezTXC+KXmWjmf13iskcI4Qa4hOBKtl9esLlY8SS/JrjIdX7FsCpwZ52UlZ6B/z/KwjGv/gjaHWTdyDGfyCGdlkS2G/NOT7s3wxcR428GV71yF5CIQa+PeXuEJQxZrovyLFi6mpKWJVsqGg4sJTlOxcwdiHHONvfE0MsxO70OKn1fG6Nix5GpCGYFC37yz3JYFtmYo1JpnjiTa3VVSJPaopDV1c7msm557oU45pU0slWZ+DAhiux0cSlzwtKSnN88Eim8A8QoklFViSfrPSwruFZH/NDqMoXq9Uf1pFqkyigO6sQHKV0ceoksulqdO7sZpx3OVjY47WHASWVQ0Y03emQkgMGJNDSojlxoVc6ATDHttBJnQCyc1dIfC8lBtJ0QzLlmEBtEPF724mUWTg1PkLERJeRdZN7WPCpekZXg80GigRg5ixsu3BuOLGiYcxlvKGKPI5LvOvjXIs+gpY/1ndjul4gXngM3BfxgDXEG3VnGLx+/x2fxI253lwybQr6Er4sSDAOi7bxESM07wu2cr27e54PlCy7LI1/l7/H56gmf/ORL5p91uBtgDfN/CR/+GO7+73D3SlbN0wZlvo/wjFVymp0tEaMYAXeGSEe3+v2aph4hu4bwWB53HSxCTR9yvvLP6MmoOAIzVuyZ07JhzQ2XhHjDPptzGObsmjP29Yq+Lzk1HhZ+bFqbJqe8kkKcHOz03E2I4LQaoK4hXiAL6sxzIcqLtVzXmdMAUslgUUnqJmZCEnUNl+cyJ2yppJDwzSKRwjuELQ5ybKRee7UEHFQ7kYSqQsLlrJCmn10NtzXUvXpHTiKEKlfb2ktkn2lS7tRzYFlNyyeY1ov+7dQ4N1F6CgJyw9uQNiOTbBiF4D4KKXRxHIA3Rwz+UMqazscAfSGL9gStlc0R/aDX93PAGtw6SHd0DPg+SIetP5DHngtuWbg9FQ09BZ6Ii5Fl3FMMLbPhSPmiI/4/5CPFKNUpXwxSpBP00K6AfiWSRfwYNk8WfLH8mNvhikO/Jr7IhT3+NqiBLzmNBxmoOH5/yc/bT8iyn/I6v+Kz8nvwHnz4z59z9j83OG02zC/g7IcQbqXyptCAahOlOteqLs38zjwUC5Rg9bs8IKR0wWiQt/rvMYQFnLs7auZUfUPIPJGcAU9PwTVX7Fmxj0v2bs7Rzdm5JcOQSU+idW0HLT81ubFAvnNAxn1wv0fB8vIDo4xk15CXzxJ6Kcv1TpfU8JyWxi5zWWFwvRDHKUciiKrSS2UJq7mol2WZcgnfBhIpvANYA1vXiadfN3Jj2MU+q3SKgKzbwqKS6antGxkR5PZCElUpieZOx3Bb8cfWogMrRbUGtRljU5v93jstMUVq0auoJYi6s4jcsTmcltCcIVqylTJVXiIOG1npgrh8q1LzEdkYfVRInqFUqSl35OVAlgVCFcXzLiP9MSfOxTDNqpq13xMJHFhyGW94Ojzno/3nnDdb5rsj7n8Enqtz28O+hz8bxtxnhRih8znwEwhPHT/9ve+zZc3r4RHHNyv4PBurov4mBIQ0jRhCxvHTFW+eXvAX+Q9Z+i1/5X/M4D3Dbxd83H7J2R8f8DWwgfxHMP8SDr+UqHBdwPcDfBalw3c1l0Cr7SWpunqKjME4TZBFwoo9wnYO3Br8c4kc+9/KyIaBQzmnyWcEPD0lAc+WNRvOiHg6PB05LSXHuMS5AedUOuytX0Mv2hy5PgYnB5VrIssWaYL7pan2u12YSCRb5ZrayuHqSkpuI6JCXl1KFND2MizvfCWkcLkeq49WC12fPOM0DC/lFL45JFJ4B3BOLuq6lr+rSqpiIhIdtL14ShG4uhDbWQ+wOQh5dJqvzRxcLeGultn0mRbFeM05TKs/Tj/tBj2NxUZLTycJZ4BDlP4Ej/QnFNph51SbKZwYjhrJCC6ClLgenPQ32Phkm73UqldZ9rDuRWrq1cAUgTxvmJ23tEVOWbaEXqSr2azGlZHctQRX8Cy+4PfCn/IHb/6U1b6GzFH8MsK/k4S9QwjhZ52cI7NJJbAs4YM1xMdweFzxyw8/pmbJgTn13RL+KhvP1d8Ek1M2CDncQXhe0dys6WYNv3A/4LLasGfJxp9z/fuP+L34Fzz+kztcAW4Ji/8O3L+D7S/l9D4+wrOnUvx1NZfIsBvg/Bnk5/qdfcRIWgXijdsgOuSzdR9l7Kolv6w+xBG4CG+49Wte8YyBjC0regoGPB0V0ZUED6VvyFxFDNn9GUcP19TIZBzGacpuYFwrw6b0usk/xmO0mUVzJ3mzZ2vx9vtemgpzrcZbz0UmmuUSPUTkscVCnKFplBBCyit8k0ik8I5gK68RZfyBU4k2ZrIEYRdkYGmthi60QhhkcDGo5BSlXBEvEb01QQUL16ddzTDmC4DT6AvvxGAPg46s0O1mTkcURJnx71VDqpEkcu5kAI1Hst0uyEEc0DWeo0QIAW1I07EXpayclq2DlKLuPbnvKemZV1uene9YVjuCL5gvay6rG76Xfcr33Bd80H/Oj/gpl510C7sOsk8j/mdaBBOF2/5yD2804GkRp/oM+J01nOXAHq6/d8mLp0/YxQW79pz65Qpu/f1z9Nch6s4d+pkhXmfUv1ySlR3lew3/6/Bjbv0Zr7nke/4LDr89458d/4QnzRv8QcotF/81zH4H4qew/znkc4lmHGIQXQXVB4xlw4vJe0f9jq+BK+g/huFDj3dwm53TZDMyerqsYOYO7JnjgJaKlpI2FkSclqf2EKGPuaybk0XRIoMb5cdMySHLxzJlyxtYxpzJceWMBKG/L+bwuIQPzqTs9PFcG9dKiX6jNrV98AjOdUhjptHzbParc46mZakpWvhmkEjhHcE5iRAuLuTn7ihlk7ujVG5WHsIM8gM8v5MFdIpMDN35As4reLGD0ElJn9O2gcGJLu28yMunUN4xasMw5htK5Obv3ZhcdkjDUtCfuZcdxijRgK3vvNfegyzAXksTQSerIhlCp9bZBSGYOQzk0HT4LDJUkkR18x6XZyyWex4Vt5zNNsyXNRkDS1ezils+CZ+xjkfeu76m+iLgfo5U3AQ5D9e6xoQpYFZEdAY8RVQWMgi/B5//8/fZcMYxLPjs7ntwzDVq4m8nH9k5bJHuZg/MM8KXMw7zS5yLtI9yDrMlMXNUWQ/zyNX37yhjw1m1l2kgt5DNgEdw9giGr9QDjrJOMSvG6p+KUYIzkngCfADxAuLK0+eeZl5SFzNaX9DnMxpm3HDFQIEjKKeUDGQEHQ+Cd2Q+gIv4PEikZgY9ojoNsqreDvln0Wgt58FpXiFaBVI+TlSPudQbXJXw0ZWUl17O4WIlFUaVk2GAufYibHa6/GYOF2c6eWSQCAN+lQQSIXxzSKTwjmBaaFmKvfWZ3BDW2fzoUuSiYwM7veFsfdttBq9vZJQwXqs1clmfJvQik2xqxjlIVhVi2Uvz6mxgniWbsyglqEfG1dBsCSw3iDEKg3TRHXrYF3Dw0oQWg0QOtv5BHqXTedAEcpbJ+gmZh9oRQmAoPFSRLvMsy4CPA81hSXO5p1y0ZC4w50DUZqtFOPD9m89Z3jZShfMEKc/9Am7/Ukp5bb2CM6Tx94eI/SotIfkUuv99RuF7Okp+1n2f27vHxBsvUtBbKo9s2sPXckWLVAP1EHNPn5ccsjVx7ugp6GcZ62zHnJo/fe+3mM1qPl58xeKTA8XNgH8RcbfgPoHsS+AvGFdis6xzqd/dDokWckSC+x2Ic07Enx0iPo8Ma0/vcwYcN1zQUpHT0iELHjslg0hkIKOPBbhAmXW0ZU8IkVBlOh5bq4+OSMnynnGVtQOnHFSMOt9I8wnO/IkKfCty0XtriXi7Bp4fJEp4tARXyOWznMv3eH2Aqw6WC1mPOXeytkLTSNWRLb+ZGte+eSRSeEdwTkJhm5I6XWO21eqiMhcbuixlSsQhwLGGVzshjsslPLmAX96I3W6ilqo67Xg2T88MiyWeLdw/6Buew2nZyzZKOalFBWWQaIEgblpsxUj0WuOaeRlvgQM6JQ60b0EttNNehpm+Rw+xl7pEl0dc5mnqJauzA2XVEvNIl5UsOVDQUzOjcRUxOGa7dlzu4AlwDeFOvEqvH7FB7OY/RezWL4D3ciifQvd/gn5WUGdzXoTH/On+D7l9+Yj4Sw938NGZyDd1q3JcozOnziWBe3uA4w5eaiWRDMlD+z4c/KeM2Du6zQo3BPzTSPf0hi/8B6yzHS0l5eVAuyp4//krHj+5IfvRgL+L+J9GeB/a/84z+1cD7lMk3MsQZrJz2wFziIU0qrlKnXnncMGRH1qyix6co6dkz1KXzDhwR0nmoIpCc3es5fzGks4VVLMjXSxwsaApPXGeQchhKzmeE0FMm/iMLXsZdlchTZd+kChw6MXpybxEBVEDTe+k+sp58R1ut1p+OkivwvpqnIja6WzF+XyUkew+SqTwzSKRwjuCc+MiIc7JTQGSZKuPUhl6s5HFy2f6LXWNRO8zJxJSH+S1FwtJSMYjtLUQxOlGseFldvOWjHrvtJ/BZ5qkcCJZOC+EsHE6FiOX5POgzV1Hr2v1ql6wHuSuD0GIJWqdoVPdakAkGktItxmuCJIcLwJ9l8moCTcnazqG+AbnehoqKhoaSj6tPuHjZ8959PkGf4jgIL6GfgfZe9BupHprN0g7xDDIR/9RAY9+AMX/GY7/Tckhm/Pni9/iz4bf4bMXP2D4YgFfwnsV/PAKnj2GR+eS6N3Wwo+rSvZ5bGHbwO0t/L9/qktJ9IgXDWK5fulFkVss2W4qbpoj6+8f+Gz2ET/IP+VT9zHHomL73n/CvYpc7Tf0TxwxepZf1GR5pP8XIh3GPYQKnC7N6ZZS6JX3MrMpluAXkbjydIWnX3pYwjyv8a5noGLPnJoFgYxO+wo8Ax0ZBxY05GQukLueLuTkWU+f57LUaKEX6NFJZGgEYKQwzSno413QsVga9WYR1l6aMEG8fxckh1AgM7uKUu6FpoHFSu6HIcrMo6KAxWzMK5hUlGUpwfxtIJHCO4T3csEPg3hPtszmagm3GyGB2Etl4H6QQWBNK3m+Ahmn/epWhuW92YjByh3sgox0uLf6mclHIK4cjCMITlVJmjfIonimMzX8Xu/4PdAWcrC24AxewpPC6cI7XqqKgupjC0kuE3PcvAfnib3DlQ6XebwfyOYtPjr6tqLvjzTFjD7mdG7Gih2PeUVJzwv/jF9UH7Oe/a9Uxw6ndfleq1rKBcQ19DXUe5gv5DC+94dQ/Qvo/2tPeJTz79e/wx8t/rdsd+f0zyt4AfMdfHIG338PvveelEqen8nH3tzB3XbsDSkK4czf+yH80X+AP3mp51CrySiBN574IsPN4NVffMBitof3BzIX+F235417xFBkvHnvMe8fXnLV3ZC933P+7I71qwPFfmCYB+KH0F9mxFtPvulw70F3njGESAyO/dWMvi1Y1ge8C3RU7HzFm+JCIgBKDizYsZJLIUoXeEFHG0sCOT0VNRWDc4Tg6ENG6DNcAbENsMmlIdFW4IMxn2C/W4I+QmikFmGRaTFbL6unnRciHa1LudZXM8md3byR87rOpPTaD7La4O1Gv1s/joSx3p5UcfTtIZHCO4SVptos+ELlnboWA1+3cr+93kG9g6OSx36nfWbazdwPetM4UWyKXnTZwnoXasZv2m5erXyiZCw7jMoScRjLD0sQsghqEKKWH2oj2qDSkUkJOGlg871EGitHlkcy18KyoMsCdAVxNhDJ6Ry4oWJWtsQB8tjjSshjx5wDF7zhjD1Z7Ik4XmRP+cny55SHHvd5xA3SkH22h+FcSOHZe/DmCynXzT6C2X8F9X+bs/uDJX+5+hH/4+L/QBMXHLsZ4eDgBXzPw2//DvyzH4kRev8ZrNf63XysQwsb6R3IC1k+8uljcCWs/hT++JWsCHbqIu8hvM7hEtzS8ctf/oAmVhzeW+NnAz8pf0pHjs8i3brkOpxxzpbNTxY8+vE1Zdux+rxhtmuJ3hEeOcLKE88cvoC+zIgxclyUtPOK7jynzmd8WT7j1l9wxwUdOUdK+liSEQnOMeBwBBwZbSzZsmATVjRxTtflNE1F1xR0u1Kq0vYeBvMiuJ98hrFjvp18drQpD5F78lw69ueFXK/7Bm62Et2eZToU76ir0F3AbCXOTxfBafSX53A4wrwWacmmDCd880ik8B2ANbOVhRid3V6ihFx1WLvRnJPnm17yvLcbaRoeOrnh6q1WCnZi13srEbQRFxbmZw/+WS/B0UnpR+ZlQl/fS6ZwFsVSztBEMqJh7ZQQuijGIwLLQQbbLSIuRLJyIJIRfCBmMsMnAiFI30L0niFmNKEgG0rysmVZ7pn5BofjwJI1B1auEfnD59wuz5j/2ZHq5SDH9EL56FJUsGoB7/8Ash6yn8DhXxZ8/i8f85f5b/HaPaOnoO7n3NxdMXxa8MEO/tEn8Lvfg4/ek7LJ8/OxGMBm9retGKfjUSpirq/h936k+fifwZ99CS+PiJS0AypHuClgHxmanM93P+FueM3z1SOGZzlP81cEJ9FS5Y50rmDLmplr8NWeu+9lxFdQbgYIjm5d0D7yFF0gawMhesm1lI7bbMWtv+CWC95wyT6uaF3JXVxzJCeQ08WcnpyejH1cULOiY8YQc0LvaI4lx8OccCwYDqUmmYuRCCyXYPkU+9sGNkVOs5gKLVYqohRHFF5XFTzAMJPgMutho45O3kuneaulttcHrUSK0oU+K+R67rpECN82Eim8Y4QwRgwAt3ciIWW5SCC3R1lbYVZIQrX1cpPd1rL4ea+GyyGRxFFn1J8SzNPfrdFo2nBkIbhnbFzLNKFY5zLmOmPsQs69kIfPTkljsih3f6aJ5cxDFsnLgC8G+toThkwmmfZOApLWwzzg1oFs3jOjIZsJCZ3nN1SuJUPmGnVkdOQsqMl8z5v5GZfVDVUYwIP730HxGqghzsCtONXRhw+h+2c5h2zNC/8eLRWvh8c83z/j1Z99wPyrjMfAe4/h+x/Bxx+Ldm2r44Uw5mfWa4nm2lZzORdwdi4yXlFBsYSfvYBPW1kHgRlS0XThYOeJK8fxsCDM4T9s/pCP55/xfPaML8IHfOJ+wYf+SxYcOMQ57/mXXBR3bD5w+GeBEKWs5xArStcz7xuGwfO6vGDIC3IGDiy45hE7VtRuwSHO6CkI5DSU7FnQMqOm4sicO1bshjkheLquoG1mxM4TB4fLohQDDNnYgDZNLAfGPgT0MYsgbJ0FTSmV2sF8bMV5OV9ro2Ev+YS2l3N+XsoltWvFQVoV8ORKE82DFFxYgjn1JXx7SKTwHUEI48iLrpNkc7MHBp0V4yTJ1kW42YlUkaunv7sTqckhClDfS5hOzn3dF0bZKDKuzTwgeQaLGHoAJ7E9TkKPAakyik4XatdypwIZdpcjOYjFAFXEVR2hjsSmxMdOmsvqjFh4qWIqglQkRehDQbcaWJ1tgMAiP5DTyaA7AjULzthyzg0FHWSR4+8UrP6kIYtRSjN/G/gzcGtORit+DMMfAoWnDRV9VvBp/JjP2u/x85e/Rf+zOU93ng8u4HtP4MMP4MljkTymmnXXyTmtKjFEi4U8X5YiZQzA+iuoVpJL330uk8TDDplPNCDJnujowgJc5IV7xq5Z8d76K77wH/Kn8ff4wH/Jj8ufculv+Kn7IUv2zGiofMP33S+Z0VCzYMAxZDk1M264ZCCjZsaBBUdmlLE9dSvLNxnpKdjGBTfuESHmHGLF3bCm7Su6rmC3WdIdKmKXE4MjHnNocu1hQaIfyyNEue5O1WtOr7UBXKZlqUhiPkfGXi8LqSC6OIPzGTx/ow6R9i5cncuuYiYlqNWZdHWfrYRUQO6B6RKciRS+HSRSeMewi7vTNZlLGyiG1GNHJ9Uu240Ypf1R5KIiiCdbOjhWcNOqV9uJ95VXQiYhMs45gvGG1gapU9WMLbZjs3X0Jj/1KbRRZiPZPgbkLl1FXfBFo4RSahFdCAQy4j6T1xdOx30GWDv8WSRWyNylWSSce2oWNG5P7loKOmbsyemJZCzZMadhxQFPhKWj/W89s383iHH4MTKHCDl/8YcQ/gcIZ56mKHjtHvOz/gf8++6f8h9f/D63nz7i8ivPx0v48fuSYH5yBY8fi+GZGpxhGEuHbd6O9xI57Pfwu6WUreY5vLzT9S7u4MZJ0yEFUiO7gZjn9G6Bd5G7sqJpZ6zOdrRNwWfFx/zp8Q9YlXd8VH3JR/5zFv5A6Xp+yo94j5cE57njjDfxii1n3LHkEbd86L6UrmSV3BpKJQZZNaGOMz4dvs+BFYRIG2Y0VDR9SdPOGPqK4VjiiEIIbSZFAw7JSU0jBJWM8iAq4t6JXEmvZdQDrHJ57tjr9N4oTkw/QOwk8t1vdWzLTK/5AdoDnJ1JYroN0u2/noukV83kHE/XOE/45pFO7TuGkUKmpXf2s5pLhUt7FK//MMC8hTe3EkYPSynF7KJ8iYtcSKC3lEA/TqbwTkrNT+MKrBt2epPDWKU0Z8w34KDPhYkCYuDLKEbOpKkO6ZzLVEgm4JYev4KhDNAPZBWw8IQsIygB0uawjGRFK2/dF/Shwg+OC3/LjCMdpa60tueMOzIiZWzJXUd43xM/GHAvGMlsBd3/BdwFuCP0TzOuqyv+0v2I/7D/A/705e+z+fIRsxcFP5o7vr+Af/JD+OCxDGazQWvejzkFW8jl4XgF70cD9ckH8vz1VpZGxUM8SAS3v5VIQ8aOOMK+oC2WFM+ONC6S5wNlaAhtzqY442Z/zqv8CS9XT3mves5ZuaWPn/Cvg6yJ4PxATqTXtdO6WNGSMacBXW4z4LnjnDYU7MOSn7ff50v/kZ7nkqH1+AxicISQE72TpvVDJtJe68ZosgOO0oAWeiSHMIh0WffSumLd8rEdJ2KUc1hlEjHMlWPWhSSWH+kqcts95K2ut1zItdtZlRGShyhKIRTj6aJIvQnfJhIpvGM4NxofkBtirs05By8J5+DlpnixlTwwHi4zqfA4dqK3LjoIpSTwnIddPybtQjN5QzOenknFEKMEEJHS0xwdgYEcQJdLRZGPIiPlyDyJPWO/w8wJMazAnTdQF8TM47OMPniyNhJyJxrLPkhnU98TYoYPUFVbQhb5RfsJZdGzZktBywW3ymeRkoYZDV2eEytP+VTWKohnEP6vwPswfOCIG0e48nz+yXv8tPweP+t/wM/3P2B/c4a7mXP52vNe5vjxY/j4ETx9JB6qadb23RgJfJ0RynMhkidPxAsuC/Fq/81fgf8CXtcSTO320vOQ7aC7coRlQdNm+H1FN5uTV40k4TPohpwbApGcG3/JVf6Gs7CBKKMozvyOQbuRs9DjnOdVfEzpeip6fOg5sOS6f8QmnHPbn/OCpwx4cgZCl9M2pWiNQw9DJGxyYudlXlXnJTHl3Dhwz4jc5mnp9eo7VcYyiRyKHFZOFtR7XEkH87GVpjTrOSg1Sp0V4M7g2VLIpchELnKZyKcfPZK/Z6X0NlTapzBt9Ez45pFI4R3DOpuHQRt35iIReb0xyjlcFGOt9tkcXl+P6yj0UXoZQqfTJAchBVsUPVi1kRl804fN4BsxWHIQhDBsmqpN4Owy3c8gd/jGjUPZdogsVAWVATz9dSW17V1OCBGOGUPhpG9BpQIY8NmAWw4yRC5vCD7nGOZcc0nBkZyOmhkDcBbvyNQ/DmTsyxn+GZy/3jP8Y0foM455SbgKHN+veLl6xJvsCf9++AP+bfPP6fcV/HzJ6hcFZ3vHQs/tUpd6LP4Od4P3Qgx9L30NRS59JmdLqbX/ky9EIz/0sA1SDHB4CQ2O7uAJTUE4z+lmMyHUo+ZbFoFX/gmhgt579nHFzNXcuTO2cc8627KgJhJoYkHnCnYhJ0RHPxS8qq/YuTVDVtCEkqHPGJyEkRFwnYPO48qMflMSvpjJOBLrzLZpgge9XiZ9CESJBCo0qkL4vdSGwUUhIy2enkvyeFFBf4D1TK7Ns5kUU8y9LLeZ55Bt5D64uJC5XhElXG1QWy0ll2PyXconfHtIpPAdgBGDJTFxsNHxBtHDdic12suZ2OTFGppb8biudWT25Tkc9lIFc9TcxMUAm1bywnklyelTmWrgVD54b9qlVZBME4qWf2j1lyKIAau1aW0ZdLy2Nr3dFkIIa7UiTt8wOF1PFHn9RSSb98znLZkX77aKPS6HAwvuOOeCDQ0zjizJXSAj4EOgDQUhZByWM2YfH8ki3K1W3DxdM89rtm7FX7qf8G+6f87/VP8LhmZG/x8ec/7/WzCvHB8W8DvP4AdPZdWv8/X9KOE/B0Wh1bva/Jtn8P5j+O2DSCd/9pWsnV1s5JSVDo43cNs5Wcz+qZNRI3M49XxsAu2rNbvYER9ndNWc2D1iiJ75Ys/ZcsMi1ngC+EjuBtqQs2+X7G7Pqfs5YeHpQsEQPTHzUnrqAqHPIXhcFukPOd3tXKQ8iyht3G6DkEKvPkUUfyA46WcsB42gpLaAR0vo27EZ3muyvvASbGaDrBPhM1hmUKwlsqpbaTSsSniykkqkeQ7LleRqVrrCmvfyLxHCt4tECt8R5Lkuz9lKS7/3csNkDnrNKzSDJuB6OHsKX1ntdy4y06ERqWhRirTURcgKUXsy1ch75KY8eO1FsxEYVrJqOjL6t8lMllgOyiTejRKTVR8FL2/aaW6hyjT6iKOn6RBSGSIcIe4z+toxzHIyB2f5lnl+YKCQKaaUlHRsOKeLOTFG6jgnuow872myivpiwbaYs10tKV3P0c35D/xj/qfw3/PH7T8lhJL98wu6Lx5xVTieOfjDC/jxE3h6KdLErPq769RG6lWly6NuhRgu1iLt4eDVFnZnUnXj7sR4Vg1ktSMcoFsgayXYugTOQ1Fx/Pkl7uDJVh35fIAQOTSOvs+5dYEq63Bx4NjPuK0v2Fyf498UuCWUlzV50UseYAZkjiEUDHUFnScEx7DPtEudkQgskjzIVz3PYNFLsVm0eoIohn9QByLPpIQ0uNER6Tud7Gt9Dl66laOXEeeZXm9OL5Uqg5s9rFsZ57EcJM8wn+sSDuHvTtwJf3skUvgOoarkphuGsQR12UM4k8eGHTRHmZza9GpwosgfxxxWNdDDppHXLyopBRw8uEL2N+gIgmKQXGITZN/3ks6ecQTG9DHQGcZeDPtSk5F7J88vg1iLHLEOtfY4ZFGkCZChOJUT4XgXGWKknc3JL3rmyy1Xs9cUuchDAwVbznjEDRk9tZuRU1K5FmKgczLIbXuxYJEdqVRq+tJ9wP8S/in/sf/HHPolu5tzbn7xMfO24BHwjy+k4ujJBVytJcr6Lx2ZYCNLlktY67iLLB9PYVXKYkge8aBDK+TcNdC+ku+vOQLPkCT+TF7YbSqcW1Nuj4RlD0UkNGte7Suys4F83RGGjL7P6OsCNhJBuRCIgyfMOnLX4bpA5wqGmBMbSSS76OGQi9egEYEsmsRpFHYZYN7DOsjE9GMrT18WMjG9G+CojsXtXhyZ0knQOAySI1tqSWqRiaxZ5hIZXC4kRfX6Ddy14xoiFzM4W0u5b67JZyvGSKMtvn0kUvgOIcskiXY4KDF4WXow83BzIz99AVcr+PyNGJ3lTMpOmyOUM0ny+Qb2nQ4gGyDmksijEQ9tt5OKQ5frID7LO0R0rAWcllO0klbraeiRrGJEHljEcXaSRRHoa+tMS1AHeS6CrdzmZgMxh5g7Yh1hPlCuD3RZSR9zCtcStb5+IOOcOwlanGPPXNZ/IeMzPubOr/mAF/R49iz5ig/5i+53+Wr7Idu7C/afPaLoFjydwVkNzx7JCIzlTIjSqo3+S2BGaz6XUtX5HMqNNLYdg+SHXCayCBkUe9hHuDvAXa+pmjfQHZGFH2YwlEDuaN/MGXwp61iXMOS5JPB3kVgO+D7gB4ePGaH0uEZyBkOU0tIwzBhcpC8ibq2CfJsR2kxyGDuoehlRhTkl0pTOrJPraZ7pOKxMiKAIEhnUQcihLKQMdVnBysu01DKTqriLmSSM97qSXK55HBsHP1/CeZAgpczkudVStnt0IZKqSXMJ3z4SKXyHYJ3NZ2fg9xJWH44ibTx6JAbdIdHExUyagmIPn7/UStJCRkivZuJl+ShpgOCEOK6WcFMDgyxG05mht1p061OYwiqVzGh6JMQYsrGdGuRNjvz/2zvPHjnSLDufN3ykK0fb3TM9uwMssID+//8Q9FEOWq12ptlsls3MyHCvPpx7I6JqqJ3RDrvJIs8DECwm01Wae97rWaG0Gxkj6EaKwIfCLIr1OhQ9b1YFhDwgDx3y44h0APohRZ+kqBJO++ecngFHFHiHK+ywR0DEESX+Jf4e/y38EWkYcY8zXMUPuIk7/OfuP+F//vJHXN+8RH+s0d+vUI0Bq5FP99TNVV9Z8h9LMH/svfNTbGmjgsqc3kgINHbvr4F9BryJ/L/rA4fGFQ1w23HUQ3PHEOCpABcSrQGkAWPMEE8ASoZdwgZIEDDcZ8hszFRS0tBiANomILQBSRWQbAduzzwExA8UlDEJQBuQNEDasIoob/gcWqs43kZWFJ2ldoiwoYpDAK4CR7ffW5VccwJe1Zwm64UTWaAnhsCeg7qiF3HXAVVjs41Shp6uLNFflvRqgx2IVqu5Ok9lqL8NEoUvkDRluKG1Ttp+4Bdtt2YMt+vY0DPYmOwh0rvoBiDJeIJLcgrGrUVrqhVPdefg7dcZcN9a85CXGQJzJZIf+j3x7Jf19nNqTW0jHucg+szuEPNk1iEyyJwE632wDPoA5GWLJAxABpzGCkk/IE165EmLs+QGKQYcUeM9XuI9XnLsRczxDq9wh3OUsUGCAe9xhf8y/DPeDy/xp8P3+NO7HzB2OYbrCskxIGuA6mgNVC2fyvmW1V6fohHKR6H7rCSPf68r4OHASqQQgXgLnA0M6aUZ8P6OYaQcwF3CJvLTCOxb5n6HyJcq6a0PJYKhHTAEiIylyIhAcQJwNA8yBsRjhmSM6NMEsefnKSYBMQ1sHLTwUDHwtJ8c+JmpwSbxsuLnI0voKWwKK5FugYuKn7NtBlxbMdoq40FkY418aWRua1XQI7jcANcDsLMS6+uDeUg5y1OvCq7gHC30eXHG11IJ5t8WicIXiCedEysjvz/QLc8v2exzfw8g8LSZ5yz1gxmSIjB2O3S8/UXFL9n9gfmEYaDh6qwYKLcD/aMqIydg3r3g/04XP1tTEwosRikHLoaprRIpgXV6mXVrIy3yMQA50B4CUORIdj1CGtF0Ncr8hHGk5lzjHF0ocI1LvMGf0ccUR9S4wTlSjDigxgklknHEvx5/wN3+DDe/vMCYFOiaEu2+QNUDm1+AXcdyyTJjWaTP54/L3/nvwBPOHvv2+13ZTKncOnqrlLX3/+OdNXtnXGGxzfneJ5GC/XBiefLBxOZgMfoEFInSDGVb86VNT0DWsRIozYC0ZCJ73wccBr5NXuI5HPn5CSfgTc7w408P4AK9kqHI0LL1pEoZSloH4L7j71OXFKwqo+DByqX7yP0em5q/a2Jl0WFgdVwWGErCSK82zSiKm5UtnRr4nqxWDMF5VZ68hN8OicIXiJ86E+s3qGzq6WCjLaoKGG7oHaQpZ/+PAUDO09l9Q4+hLmlAfn7gadVXVRYZjcc6t5Mn8HgWklckjaBh976CfHFdYO59mATBqFIrl0rmqapZeHy9GPjgfYH2TQfEEvEhIC96IAAP9TmSJLBkfkxwH7ZoUOAFPuCIGg1KNmJFIAwpro9n+Lf//gPu7i7R3dUYhhz9fY7iJmB3B/zQsAZ+k3GBTmm5E59n9CnfuzSdSyjLEqhq4JdrvgeB/XrY3JpAZMBtw5c4ADi0wK7ky/3uAFx3wJ/vF20iKQ132DNclFRAumcev+7YRX2KFJrVgdetIsMx65yPN4KG+ocUuBt5vay3z1luur/HtEc8H1lOWuQcbe0Lnm6tbHq7sp7IlG9323ER0HYLvNqxvLq1qb/bmmJ8OvEzPUa+Vm9e8CAzRCaZz3fzWHmNtPht0cv9heInoySxGUiRM+ZXNdD/xFPeZs3TZ1sDFxtuaftww9NWmVFQfj7a0FLQGCUJT23DwEaqyR5689oInv4D5imYOeYRycucg5cxAvNYjGBlq8FrEWH7GTGXtRaRfwJsS1tAN7CEKs9u0IYKh2aLY1IizZhXKOJpmpbKfoUeXSwQ+oimr/Bu/wYPP1+i3a/Q/alCOCbY3QIXDfAyAP/4GvjDFZBF4PWWoxN8ic6vEZZwYfck6WAG0NdSZDkN99tL4Oc74Njx5T/e87plyevVA2cHPezpQWQZX9oxAXAAsobhn6rgaJS2YiNjZwngI19erEzA48jPw2ng/X2/5W7k/3MH/I5jkbBv+X9lyc7kVcZTfZbwtr6POUYa9t0KePPSnpcNY0wzrjXdrPh8jmHehtd3fL6rguLkI7HHgb0Jry5m0fbDkfjtkCh8wfjcnXEEipLL6A8H4PLCmoIegNsIXBTsmG0GLj73idZDwwN629MYjCO/oFUKrBOGDLpgI4vs/+fRFuCnY1kCGPF4rIX/vxt8zz1ES0THxHIR0SbzjZaPsD81mME8JIibEW0KpE2Ndn1ic9ppgxoNYghokANxi9vhDJf5NQqc0I8FjocV9sMGN/sL9E2B5Jig7APygXHx12BT1bpgp+zLDRPx2w1Pvr9mrHrpNbx8wffw5s48hIoVSXlJAb8/Ah8ebGdRziKCPADXVmKMlGKeWR6pyGmQY+TlZxk/D14DcDyxSAw5dTjvgLTga9KOPNGfHvg4Scmw4yrn5+DkTWwdw0WnwOd8XvP5NSfulEgCPz+nlga+yoHVejb4L6zDOxkYpkwS7hhv+3ni6WZHT6PI+RHxPI/vYZYg/PZIFL5w3LBkKRALnhjTQKM29MCdhYVipLFb5awXPx64Y/jUM5Y7mGgUKfMTCPz3fcMvaVnRPseIx41mA+aQzwmPJ656ktlFwTujAVqZYPXvid0uRCDt53LWzm4zBK6NGwPaWOBhtUKajWjiCjFQlZIwohsznNoC17hAiSPSENB1BbquwPHDGRAypHcZ8j4gi4zRXxU8Db/ZAW8vgIuaXsK64kn41y519H0Mec5Yepbw9d7veYq+e6A3kaTMF/Q26qQwTS0egJuSCeFDAhytmix2rN7pLWldZ+xwLyLLWuucp/XrwNXah4EhoLhm6KewrveuYcnsqqTXeepYQdx5WXPJvNR1w3DRy6v585CmrE7alHxrsxTYluxB2BQUi77na70q5xWc7p42Rz7nAHoQPt9ou/n0YT3xtyNR+IJZJtjS1JbvJMBmO5+08pLGZN9w9+0YrdcsALi1nERlw/EsxtxxMya+23LadNJRaEbQGDwajOdTU10kls1tXl005QkWf1owe+peRQMbmGcXDKMNuDEVGQDEFEMMODYrVFWLqnjgQ8aAQ79C16cYugKnoUZ+ahGPBfc9PxRI/3eF4jZD9pCiiKyu+l0G7CKTym92PLluLYnpYy1+TcPj712MmJYp+em3sC70n1K+pw97nvwvrAu67YGzDUMzHYD/+hMN+KqimN+ZF1gWQF4B57bu8qFlaKlOGIoJt+yFiAXF8HTkc/m+Bv54xc9O2/H6mRnohyNzD3nKQ0ZWAGVrLSpWzptmtu9gy4qh054j28OGhj5alVyaM7/l5dSrFb2HEIHEylCLgiHSspiT9BKEz4dE4QvGS/GGwRqsbL5OamWqa6vYaAdg0/Jk9uHOarozxoJfbjBtrkJGw5PASjI3DOnn92xu6w4AUu7KaTwc5OWmBeYy1Yi5uQ2YR2S4cLhYNHY9D0kd/T5T5hmKkWo0AHgwS1AM6LIaMQZEDGh7rvEcY4a+zdCecoxNiuZmheRDivyQYnWfYWwSpA3DI0nGSplt4Mm7roB/+h3w9ooGeGezdAD86sPVlrkhr8QZLKezWgFvUxrlVWljTuyEniQML5UZ8OMlDXVqqZqhYXUPQNG4WPOzkAxAvwfQUVC2BXBzD7zN6eQF5vCxTlihhIEDARsADwNF4DJnwjfa1NI08nGvdnwb89R6O3Lg6pKhyAg2SI6Rorayw0kY+P73I/MFRcn3vznRE9rt5qmn/vdoaajlxjvx2yJR+MLx8MZolUfrFd30rptHNQPsFg2BX8rbA3D/zqZKBkZn3t8Cl1Y10rX8Et53NtgspSdRWkFQAB53ObvRdBHwyqRlNVILfprcmxhAT6PFNPcGGWwMc+Dih9qsUxh5/RQUjIcRfZfj0GxRnp2QjBHdKUE/lBgPCYc93WcY/zXBcAjMn1RzGC0DcD4yYvViA3x/xuaos7XNk3pSMvpb4GO4iwLTZNUsY5PhOHINq+8M2De8zYd74PaWJZ///BZ4deDCpZ8+MIxU5jxd/+GCr/FDD/ze3oMYgdAxD5BmTDxHK3XNwbDjfg1cXDLhXtxTgOqKb8v7W+tLsDUatXk4b8+Zr8i887jg44Wcn7eqYKUTOhvO2FGYU/OITieGyjJLJD9tStNso8+PROEZ4Itc/MuTZfxyjSOwP3CKqje6HRqe1K4uaKvLnEIQAsXg9sD8QpbQzd9VlpiOPAWGBLjv2ezWHABUvG4PwBZ7Pe5pWJ7mzBthwxrmXQ3eLQ0sktTBguNgZhTWPIGRmc0mw9hEHMdgj2EW85hyTeR9AsSAPlqlzIl1+mUEXo/ADwnwuzPgcge83fGku17Z0xzmk/tvyXIxjz/2OFKQq5KhlGGwQq/WhvVVnCKKxNZ/HunJdQ1FMCuZW2htJtHbc1Y2/XwD7HvG+4dok3Pz+SSexrkDOwz0KC+3VvEUGFL0A4JXCY3WQHdW8zOVBtsUaGWll+cUiRg5HuvY8Dmtt1Z1ZNVvu5VtUlt0P/vro9lGnx+JwjPBQxzuOTQNK5Ee7hkXbg60qWXGL+RlCZy2/P+h5eVFDiQFcNbTHmdHW3RSsPolz23z2InbwwJ4iC9znh73A8MAfEJ4nHD2Udt+4l8KhoURpsR0sL9PmMNTqalNTC3PMNDyIOHYjAD2PRxTTvS7CRSbDshONJ5FAM4D8GMF/NMO+P0rXn51xodwo+Q9BJ9rz2+S8LmkVqLphnHa+AYAwap3c3YqH08U/BQ0vKntJNjUXP/ZdsyZXO74UucJ8NMv7HpOMwpFb4a5HXmdMmGoaMyA786ZR3ho2Kn8+ozVUKuMgrUpmY/armjUR3t+ZUZ9r/LZE3s4zP+32tJD6DrmNQLYlObLiUKgoOW59d8Mqjr63EgUngn+JfHT5moFHI88baUpQw5jyy9oXdKQNy3QWalfGljt0nb84v35npetchoJP1ECND5xYEw6JtYhPXIGfmt5gwA+7mHkdSfD72KxTEp3YEB6wOP8g5e3ZoDtmJ8T111KyxZH8yRgYaeEMxXueb/pwDh7HoHLHniRMa/w8txOpBVzCZsNT7BVNQvr5/AUHE+m+mgMLwbwWLqPyjiZaH73giGc6xL45Q44HNkIBvPwzkvg+5c07HHkZUmgCNx23JX88x3LcytLsGeBBn9b8f0/NBaatOf3+1fU56afu+bTkrmBs7X1OFrOYV3ztQ6Bn6ump4dRWK7B50HFcc6tuPH3vI57xPIWPi8ShWfC0y+PL5HPMp4AV5XNyRn5pW8ObCj63Xc0Ng8Hlp/+8kAv46Jkz8L7OwCDTfXMaPwP1hBVr5mITnN22uYB2J4zLHE4MXmdRts/7AnoZXWSewzA7El4ItrFYo95TEbw64T59nlKAUjMou6B8J7ejDd3rUbgcgB+sNHju4rG72rHpr6zLV8nH0HxOU+hT1d8LtexPl3NmqZAaY1ewzVnAY2gUf5ww6R0gDWIjQwH5ikAGx0RUgrJ6xF4d8uwUz8CFzu+d0PPKrSQsKGszulpHE/WbG4lpato/Qb2GcTAg8flGUOSYz+/vifLISUj7zdJZ/GIkV5LYeM83HOr63mkhTyEz49E4RnhBq3rrPFnQ4OfWNIxy+bmqJjy9LbbgeH6jsJw9h54twfeg1GZ48kmUnT8Ehcpq1lWNQXhaF/yYeQXOk94egyR4xOGuMg3uHH3xjdg9hi8G9qNfQ+Gfwa7XQt6CwFzN3UfeDsPRbVA0nBER+yB5ARsO+Ai48C2buTcnT+cA99dAa8v+Xt4YvlzC8KSycAu8HEO7i1EE9w0oeh3g5XSWj7heOB7VleWpLaChH7k+3S1mVdgXp4Bv9yyIKGw0A1Gin3b8VTv/RGpeY03HQ8Z3l092PseAsOKq5Lpn848R0QKWN+y3LY7sfclT3nfy2S7e2reoKnO5S8HicIzw2vd3XBst0B64Gz+sWOMOSYML+zOaEyORw5X61rWql/ZiTwAaA8MMZ1arozs+3k+Tm0hg9sjt2LtSiadm5HjlAfw39kA3FkVyqO5SR5K8pCRf9q8ZNV/9sUuK8z7HMDniJNVtQ7MfSAFQgMUR5bhXiRc1vJ6BVzVwD+cA//4FnhxZmWayZzc/dJq3/35+N++YMnFoev4XsdIbwBg/qi0judf7HdaWaipG2ZPMUl4ncx+3mV8X5sTK4L8cTc1b1sXDCW5p+hjxe97ehxnGzY4whLjNw/A+dHGdox8nBDmXMm55XG8ysorruqav+PycyxB+LKQKDxDPBbtcVmf9JlnQHVhjcRW+leaUfn5gw3Qy/imrwrgUDAu3YzARQeEA9B6jTlogCLYLbuqOQjt5sBTaMjmfc9JyoTlARaT9oSzh5IA+DavNGUHLsz45eC/u5aNUbxDABmNEto5VLZugfOed1VExsHf7oCXWzZSvT4DfriYDVhRzMnz5zBUbZnn8FCKV+YAwHbNih4E60xfMaqW+fs8MrdUFrys7edqo2AzikLg+7eqKA4xcoKu90oMcRaedTn/fL7m63rqgLv9HEbark2Qurm81BcX+WVPN6c9/T09rCe+DJ7BV0V8jDTFtP7RE5N++TBwBk3XWVlgoAE57HmiGwegueGpMaYcuLYpeSLsrKb85wMT13VmJ89AT+Rwx9vlK8ttWPdtHtkI1fc08FPSGQBGNt6NEYgnGpkBvCxUPMUioTfTjjRgWcoG6GFk3qIE8H0KXK2oNZvEZvrXwKst8OMLVtCcbxkO67r5NPqcDM4y5+C5I/8dmobeW1nMv9/T/ERV8c84slQZgZ7ixjqGmxNz9d0wC8aqYkf1/R6A5QHqevY0jo15LODnYLs23U7nYX8x8v1tTotlOfbcCvMivOrIf09AieUvEYnCM8UNno/SHsc5/ADw59NpHm62qYBuZ2GiniGh1GLLVc1af4wcqFZVbHj72WLHWcqY8sOetzuNZtwrnu57axgrE1aLdinTAbZHBxiYjCxLS2ra6TFNgfrE7uMh4UTPwksxo52AbZjfDsDLCtgVNGrf1cD3VzRg64Kx821lp1LzMj4Wt//S8VP01E+QPq7W8ffUL38aEvM5S31PARlH5gFqGzC3XVvfoR0qRusdTAPzAbDH39Z87c7W7IqO9nw2vgltnDuQq4oi1bYUnmGggJUlpnEsnoj23/GpxyC+HCQKzxw/LboBzDJbswl+CX0EcRqYZwgA0pH5gbxm+OZf3gEIQDUwfDREhgqKlOs7x4GXZbmVGNrmstjR4KBjUnptYQNPPncjxWEYrTpmYJdt6OghrFLu4skGitIZeP0u4bilzBLMaeQYpX60nEfFcMauZq7jaJ5BOwChZ19CVc2vzXM7iS7fz6U3MI6zh+iX9/0co/ff1UXEjbYb5CShKJQlT/9e0NVY81ya2g7lMJ/o89waIweOB1kmh8uSXog/plcU7feYRnR7ye3TZPKXlt8RMxKFr4hlSaPHd3NrWmoaCzmkDC29smqSpuNUS28oXnU0yuMIlLavYX+gd5EHjp8+X7Fc9XAE1gMvH0wUWstDdIO1GSS2J6DndZKRp/hNQk8lmkeRgR5Da17EmYWYTrDEZcrHSSI7al/uWF0VIsMTFxvmPKpy3ki3PJE+N9zIL8tVXdz6fs4rLb2KpZeRpjYEEbMgeH9L1jLEk6aWZLYE9ck2853sdrU1k53t5llNHi7yU7+/vp4vyBevvSeZfUXpcxPnbxWJwleIlyZOJ0i7fL1iotDDCE3DsRevz9nRfL8Hipon8x9fs68hu2Pd//0JuDsCSDhpM4InyhgZvgkWa943AEZ6Gd3I0/vQc2ppkTF+nSbzBO6QM59RWplqtDLX2PPDWeSWVE1tRn8N/HjB7t2q4P8hoSDU5RxScQP1XEXBWVYmAfz93ANYehLuEYRgozLMUwAoIj6pNU0f7z2OkR7bfg+sL/iZ2O9nI1+W1uWezo/dWwLb79erpPz5+v0vS4Cf83vwrSFR+ApZxtJ9hMJqnBONsHxDH7lMfbvhmsVDw1NiDAw3nffAvwXg7oYn8dUKGN4BP1v9embGYm0hqyzyNF+kNNjtwI1ivp55U/Dyzq63q4DzCji/ZAgjiUw63z6wlyKkwHlB0ehPQDmyyzoHFwRtrVntxYYNWUX+WBC+llLHpdewFIGlV+in86fdwT5Sw/94LsrzDlOFUDrnLbz72yvbXGyW9w/Mp38/fPhz8eTx8rWXKDwfJApfGU/DDsuT82jCcG4J59UKuL0DkswmblZAe+SIgtKWopydrCzV5iP9+QNw6YtSgjWuReBkJ3p0nOdf5lxoczwBt4Gb4bLA+ykib3tl8/jfVMA+MLlZ5jat04x6mbDSpU+ANxfAG8sXFAm9nvMt9/uuapvTb7+rl6F+TcZo2dewFP7lzy4WfrpfCkZRzI1jfn1vkPMQk5/6/brAHALy+3MvwO/b+w2W97v8HC6fu/jykSh8hXjstrW+AO9jcAOwqmh8DyeLy1vZ4n5PASgLaytoOS9/W7Bm/WrLpPOff2ZvQxI5TO1wZJfxxRlwlzGhnCXzoLRVxeX0ZcEk8BAsb7Bhbfyq4H2vbehaFnj671rgp3s+/psdPQaAc36uzllD/+piHsHgJ+OlQftaeTrMbzke42mSeuk9+L/diLtw9v388/J6fpj4WLWTh4+Wj7esgPPH+DVXnopPj0ThK8VPy103fyk9lDBaUvHCOlib03z9uxvuzW1tDPdDS2N8fsaQzXevWAV0cwvADEbIgaRmbqHMgNqW6dwerZolsSmcNuOmrthd+/qcolCYp3LsWVWUgHmFoQeSAtjlDDflKYWnrumoFNakldokT99V8C0mNF0APKcA/KX34K/L0oAvS0M9fOQ8DQc9NezLx3zanf05p9CKvw+JwlfMsmZ9HOf59V03h4eGgQbWT/Fh4An84ZbD0gB6BH1HAUHk6XxTc1FL60vbF8lFRODdDUNUSWBd/KpmSGhXcuPbiw3wh+8xNVclGdDfU3Dq3PYVF8AfzJM5tQwVXW1ng7YqOMP//OzxKIuvIY/wH2Vp4JfJ6I+tHl16Ex4ieno//14Izjuun3os3/p78NyRKHzFfCwUsOxl8ISsf7mPAC7Ogbs7xv4RaHQfjkw8hxw43LCh6dUF8L/eA3e/sHS1OwEY5nUKeQ68XTMU1NsAO4D383YHvHllY5IGikRI6VFc75mTKCpgm/J57Crg+pZzmwozVNuK1U4+8M5DGJ9jec6XxjKPBDwOGS0T1MvXbbkBbTmF99876S9zG8vcwbf++j93JArfAH5S9FOd14933eOTXllaV6pNKy1t+mZuPQVDy41uq5JVRf/wEmjOKBo3NlKhbWzSasV8RYxArABYCOisskUtNbuR93v2SlQJ7zdLWYm0XbG6CIEjorNL5ic2a3bVlgWf57K8Unt9Zz4W6lm+TstdyMCcC1julP5bQj9Pu8YVLnr+SBS+AZZx3+Upsa7n0dvAnHNoWzPodv26Zoinrm3YWQ6kR6Dx0de2iyEOHMkN2Owlm7WfZEBIgFdXvN9TA/zyHticcczCMLC6qCgoBnlqie0LNt6NKw7zK23NqHfbeg5h+TuK/zf++iy7np96DU9zA/8/9yu+DiQK3wgfW+jiDUrX17M3cXk5lxr6EpTET/EFdzcD1rzU8t+JDdQ7tcCp52kfKXD7gcvbi5QVR0lgk1lZ8PJ73wdQ2OA+C1uUBWvlfb9DAG+7qvjYIcyTOD9Wwy/+OsvwkhBLJArfEB8rY6yqeXwBMDcjjSMT0V7m6UY3syRwZoa5roEPdt95QePdRpap9mubq1MDsI7kFLy/9ZqzlpLAxTHDwBLZypa9rGx4Xgi8TV3PG7uW1TBe9qhYthCfBonCN04IFAWvR+97GmwXjKJgOKltZ4OcpewgDglP+LuNbeUKzD8kGdA1VhLbzr0RZ3b6DxEII+f7F/m8w7euOHytTBiOAtiDkGesfCry+Xl6yGM5HE4I8fcTYnxuw4XFp8IrUoaBRn8Y5sTzODKO7x7EMDye4d91DBc1Jxrsh2a+bZqyGsmX79zcz1u31htWHPlcorJknqHt56mdlV03X5RJFvncjQvM5ZIKgQjxaZGn8A2zLCn0TW6+rGcYgLOzOa/gVSoALytLID/RuB8bXnawrtgyn8cvDyVQrugFNLYSdLuehSWxmfu+SzhGehR1PU/t9CVCy2YqIcSvg75e3zheouoD1LwD2ktYp+Xx6V8OW/NTvC+WP9rinsEW83QdS1XjAGBgSWlhj1UXQLqmN+C5giThvzebx01YXjq79AqWdfVCiE+HwkfiEcsyRWAOKbkBjpFhpeWpvet4qo+RYajRFrk3DWcpnU4sLfWF7kmg5+Di4+MVvJHOBcgfz8VpmfB+bms2hXguSBTEX/D0E7EUBk9G++ndPQr/430OS8/CxcITwx6i8iXvwNyE5o/jM3yWY6KBx56KEOLTI1EQfxUPIS1P656cfjoi+XCgZ1BVs3HvfcTFYszGcmDacjPYctKnd94um+80xkKIXxeJgvibWY5cBubFLT5ewqevAvO4Zd/b6/P8XSCcZc+BC8QyfOU8ncYphPh1kCiIvwsXhWWIxz0L4PHANO8p8NJWXwTjtwEUFhLicyNREJ8E9yDcK/CcgJeyfqxyaBkGcs9CnoAQnxeJgvikeIhpucsX+EtRWF5HI6+F+HKQKIhfhb82TnkZalKuQIgvB4mCEEKICTnsQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJiQKQgghJv4v9D1WbwUK1gYAAAAASUVORK5CYII=\n"
},
"metadata": {}
}
]
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 458
},
"id": "tGNeQ6xrDqmu",
"outputId": "0be88974-a315-4fea-8b48-2b4b4c207fb6"
},
"source": [
"plotter(4,0,0, radii=5)"
],
"execution_count": null,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
" 2 \n",
"⎛ -r -r -r -r ⎞ \n",
"⎜ ─── ─── ─── ───⎟ r \n",
"⎜ 2⋅a 2 2⋅a 3 2⋅a 4 2⋅a⎟ ───\n",
"⎜12⋅r⋅ℯ 9⋅r ⋅ℯ 3⋅r ⋅ℯ r ⋅ℯ ⎟ 2⋅a\n",
"⎜───────── - ───────── + ───────── - ───────⎟ ⋅ℯ \n",
"⎜ a 2 3 4 ⎟ \n",
"⎝ a 2⋅a 16⋅a ⎠ \n",
"───────────────────────────────────────────────────\n",
" 2 \n",
" 9216⋅π⋅a⋅r "
],
"image/png": "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\n",
"text/latex": "$\\displaystyle \\frac{\\left(\\frac{12 r e^{- \\frac{r}{2 a}}}{a} - \\frac{9 r^{2} e^{- \\frac{r}{2 a}}}{a^{2}} + \\frac{3 r^{3} e^{- \\frac{r}{2 a}}}{2 a^{3}} - \\frac{r^{4} e^{- \\frac{r}{2 a}}}{16 a^{4}}\\right)^{2} e^{\\frac{r}{2 a}}}{9216 \\pi a r^{2}}$"
},
"metadata": {}
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {}
}
]
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 458
},
"id": "FCKe6q7sDw3F",
"outputId": "37dc9dc4-c152-465e-fa1a-c7149d732eb4"
},
"source": [
"plotter(4,1,0, radii=18)"
],
"execution_count": null,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
" 2 \n",
" ⎛ -r -r -r ⎞ \n",
" ⎜ ─── ─── ───⎟ r \n",
" ⎜ 3 2⋅a 4 2⋅a 5 2⋅a⎟ ─── \n",
" ⎜5⋅r ⋅ℯ 5⋅r ⋅ℯ r ⋅ℯ ⎟ 2⋅a 2 \n",
"a⋅⎜───────── - ───────── + ───────⎟ ⋅ℯ ⋅cos (θ)\n",
" ⎜ 3 4 5 ⎟ \n",
" ⎝ 2⋅a 8⋅a 32⋅a ⎠ \n",
"─────────────────────────────────────────────────\n",
" 4 \n",
" 1280⋅π⋅r "
],
"image/png": "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\n",
"text/latex": "$\\displaystyle \\frac{a \\left(\\frac{5 r^{3} e^{- \\frac{r}{2 a}}}{2 a^{3}} - \\frac{5 r^{4} e^{- \\frac{r}{2 a}}}{8 a^{4}} + \\frac{r^{5} e^{- \\frac{r}{2 a}}}{32 a^{5}}\\right)^{2} e^{\\frac{r}{2 a}} \\cos^{2}{\\left(\\theta \\right)}}{1280 \\pi r^{4}}$"
},
"metadata": {}
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
],
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAYUAAAGFCAYAAAASI+9IAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjQuMywgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/MnkTPAAAACXBIWXMAAA9hAAAPYQGoP6dpAABi20lEQVR4nO29yY8laZbdd2y2N/oQETlUMdnNbjZFasFeSYI2gjZaCPp7BWgjQAstJC0EAg0CBIXuZldXVg4R4cMbbTYtzr32mXsMGZEZmVWVfn6Aw93f7O9F3PPdORrHcYQQQggBIP5jvwAhhBB/OkgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhBBCTEgUhPgBxvGP/QqE+OVI/9gvQIg/Bm7oo+jNy4eB38fx4fVRBMR2jBoGfo/jNx9DiD9nJAriV4sb/rlxd2P/NlHoOl7edeHnogCShLfre4rBMPCyOA5fSfLm4wnx50g0jnKOxa8H/9c8N+Dj+PCEH0VAlvH3tg2n/qri7+PI6/2xsoxGv+v4uFkW7jO/HggCAoTn9N8lGOLPAYmC+FXgAjAMNN5NQwM+N8QuDn47v8wN+ekURATg5U3zUCDcQ3DvI8uCUPht4jiIzvw+8y9AIiH+NJEoiD95HoeB5jF/N+7uGfQ9T/x+qs/zcPqf3/904vVuwOcn/67j9ygCzmf+XJYUiLYFFgtgueRj+2Mtlw+FI0l4mb/uLAsiUBQP/565d+HPK8QfC4mC+JPGT/5+ym9bGnP/V9s0/N62QQzqOoRz+p4/7/dAmgKHA3A8Aut1EI2qCo+ZJHzO5ZLfz2det16H54kiGvaypLGva762pgkiE0XAZhNEKY55+zTla8yycLvUMnsuDp68jlUbKP4ISBTEnyweBgJCAriuH5aI+mX7PX+/v+fvqxWNuZ/03TPYn4CuB5Z2Wi9yGuO7PXC5MXFpgAhANwD9QONcpMBqCZzOQBLPXtMApDG9B4AGfrvl64pjCoOHmYqCl/U9BcKNfmz398vmYSgPPQnxSyFREH8yzMtB2zacyqOIp/mmCafxpgm5gari6b9tgd2OBvnuABwroMiAfcWv9QI410AUA+0AJBFQJkDdAKcKeHHNxzs2wUtIY2C9ARIAl0tgGCkKhwpY5BSPY8OfFxlFZJXz+roDvvqMQrFaURTGkb8vFvQ+0jTkJDwE5V9xzOuLIngVCi2JnxuJgvij417AvGKobXld1/Hnug6GP0losNuW4tB1vK7vedk3e+D7WyCO+HU8mfFtgSEC2gZoe+DyAmhqehHjCJQLYATQVUC+AtADGIEkYxgojoHtiq+lHSgyqxy4PQBpA
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