{
"cells": [
{
"cell_type": "markdown",
"metadata": {
"collapsed": false
},
"source": [
"### Part 1. \n",
"\n",
"Consider the data set $(1,0),(2,1),(4,2),(5,4)$"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
""
]
},
"execution_count": 13,
"metadata": {
},
"output_type": "execute_result"
},
{
"data": {
"image/png": "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"
},
"execution_count": 13,
"metadata": {
},
"output_type": "execute_result"
},
{
"data": {
"text/html": [
""
]
},
"execution_count": 13,
"metadata": {
},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"\\left(\\begin{array}{r}\n",
"0 \\\\\n",
"1 \\\\\n",
"2 \\\\\n",
"3\n",
"\\end{array}\\right)"
]
},
"execution_count": 13,
"metadata": {
},
"output_type": "execute_result"
}
],
"source": [
"A = matrix(QQ,[[1, 1],[1,2],[1,4],[1,5]])\n",
"AT=A.transpose()\n",
"A1 = AT*A\n",
"b = matrix(QQ,[[0],[1],[2],[3]])\n",
"b1 = AT*b\n",
"\n",
"M = A1.augment(b1)\n",
"f(x)=M.rref()[0][2]+M.rref()[1][2]*x\n",
"\n",
"P = point([(1,0),(2,1),(4,2),(5,3)], size=40)\n",
"P += plot(f,[-1,6],gridlines='true', legend_label='Least Squares Line')\n",
"\n",
"show( M, M.rref(), f(x))\n",
"show(P)\n",
"\n",
"P.save('plot1lab3_part1.png')\n",
"\n",
"show(A, b)\n",
"latex(b)\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
""
]
},
"execution_count": 8,
"metadata": {
},
"output_type": "execute_result"
}
],
"source": [
"show(A1.column(0).dot_product(A1.column(1)))\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": false
},
"source": [
"### Part 2.\n",
"\n",
"Consider the data set $(1, 5),(2, 1),(4, 2),(5, 3)$. How does the line of best change compared to Part 1?"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
""
]
},
"execution_count": 1,
"metadata": {
},
"output_type": "execute_result"
},
{
"data": {
"image/png": "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"
},
"execution_count": 1,
"metadata": {
},
"output_type": "execute_result"
},
{
"data": {
"text/html": [
""
]
},
"execution_count": 1,
"metadata": {
},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"-\\frac{3}{10} \\, x + \\frac{73}{20}"
]
},
"execution_count": 1,
"metadata": {
},
"output_type": "execute_result"
}
],
"source": [
"# reset()\n",
"A = matrix(QQ,[[1, 1],[1, 2],[1,4],[1,5]])\n",
"AT=A.transpose()\n",
"A1 = AT*A\n",
"b = matrix(QQ,[[5],[1],[2],[3]])\n",
"b1 = AT*b\n",
"M = A1.augment(b1)\n",
"\n",
"show(M, M.rref())\n",
"\n",
"P1 = point([(1, 5),(2, 1),(4, 2),(5, 3)], size=40)\n",
"f(x)=M.rref()[0][2]+M.rref()[1][2]*x\n",
"P = plot(f,[-1,6],gridlines='true', legend_label='Least Squares Line')\n",
"Q = P+P1\n",
"show(Q)\n",
"Q.save('plot1lab3_part2.png')\n",
"show(\"y = \", f(x))\n",
"\n",
"latex(f(x))"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": false
},
"source": [
"### Part 3\n",
"Find the line of best fit for the points $(4, 1.58), (6, 2.08), (8, 2.5), (10, 2.8), (12, 3.1), (14, 3.4), (16, 3.8), (18, 4.32)$."
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
""
]
},
"execution_count": 14,
"metadata": {
},
"output_type": "execute_result"
},
{
"data": {
"image/png": "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"
},
"execution_count": 14,
"metadata": {
},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"\\frac{513}{2800} \\, x + \\frac{261}{280}"
]
},
"execution_count": 14,
"metadata": {
},
"output_type": "execute_result"
}
],
"source": [
"reset()\n",
"A = matrix(QQ,[[1, 4],[1, 6],[1, 8],[1, 10],[1, 12],[1, 14],[1, 16],[1, 18]])\n",
"AT=A.transpose()\n",
"A1 = AT*A\n",
"b = matrix(QQ,[[1.58],[2.08],[2.5],[2.8],[3.1],[3.4],[3.8],[4.32]])\n",
"b1 = AT*b\n",
"M = A1.augment(b1)\n",
"f(x)=M.rref()[0][2]+M.rref()[1][2]*x\n",
"\n",
"show(M, \" RREF \", M.rref(), \" from which we obtain y = \", f(x))\n",
"\n",
"P1 = point([(4, 1.58), (6, 2.08), (8, 2.5), (10, 2.8), (12, 3.1), (14, 3.4), (16, 3.8), (18, 4.32)], size=40)\n",
"P = plot(f,[0,20],gridlines='true', legend_label='Least Squares Line')\n",
"Q = P+P1\n",
"show(Q)\n",
"Q.save('plot1lab3_part3.png')\n",
"\n",
"latex(f(x))"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": false
},
"source": [
"### Part 4\n",
"An experiment produces the data $(1, 7.9), (2, 5.4), (3, -0.9)$. Solve the equation $A^T A \\hat{\\beta} = A^T\\textbf{b}$ to find the least-squares curve to fit the data, where the curve has the form $y = \\beta_0 \\cos{x} + \\beta_1 \\sin{x}$."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
""
]
},
"execution_count": 5,
"metadata": {
},
"output_type": "execute_result"
},
{
"data": {
"image/png": "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"
},
"execution_count": 5,
"metadata": {
},
"output_type": "execute_result"
}
],
"source": [
"reset()\n",
"A = matrix(RDF, [[cos(1), sin(1)],[cos(2),sin(2)],[cos(3), sin(3)]])\n",
"b = matrix(RDF, [[7.9],[5.4], [-0.9]])\n",
"\n",
"AT=A.transpose()\n",
"A1 = AT*A\n",
"b1 = AT*b\n",
"M = A1.augment(b1)\n",
"f(x)=M.rref()[0][2]*cos(x)+M.rref()[1][2]*sin(x)\n",
"\n",
"show(M.n(digits = 3), \"RREF \", M.rref().n(digits = 3), \" from which we obtain y = \", f(x))\n",
"\n",
"P = point([(1, 7.9), (2, 5.4), (3, -0.9)], size=40)\n",
"P += plot(f,[0,5],gridlines='true', legend_label='Least Squares Line')\n",
"\n",
"show(P)\n",
"\n",
"P.save('plot1lab3_part4.png')"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": false
},
"source": [
"### Part 5\n",
"$(10,21.34), (11,20.68), (12,20.05), (14,18.87), (15,18.30)$\n",
"\n",
"$y = \\beta_A e^{(-0.02t)} + \\beta_B e^{(-0.07t)}$"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
""
]
},
"execution_count": 6,
"metadata": {
},
"output_type": "execute_result"
},
{
"data": {
"text/html": [
""
]
},
"execution_count": 6,
"metadata": {
},
"output_type": "execute_result"
},
{
"data": {
"image/png": "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"
},
"execution_count": 6,
"metadata": {
},
"output_type": "execute_result"
}
],
"source": [
"A = matrix([[exp(-0.02*10), exp(-0.07*10)],\n",
" [exp(-0.02*11), exp(-0.07*11)],\n",
" [exp(-0.02*12), exp(-0.07*12)],\n",
" [exp(-0.02*14), exp(-0.07*14)],\n",
" [exp(-0.02*15), exp(-0.07*15)]])\n",
"b = matrix([[21.34],[20.68],[20.05],[18.87],[18.30]])\n",
"\n",
"AT=A.transpose()\n",
"A1 = AT*A\n",
"b1 = AT*b\n",
"M = A1.augment(b1)\n",
"f(x)=M.rref()[0][2]*exp(-0.02*x) + M.rref()[1][2]*exp(-0.07*x)\n",
"\n",
"show(M.n(digits = 3), \"RREF \", M.rref().n(digits = 3), \" from which we obtain y = \", f(x))\n",
"show(f(x))\n",
"\n",
"P = point([(10,21.34), (11,20.68), (12,20.05), (14,18.87), (15,18.30)], size=40)\n",
"P += plot(f,[0,25],gridlines='true', legend_label='Least Squares Line')\n",
"\n",
"show(P)\n",
"P.save('plot1lab3_part5.png')"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": false
},
"source": [
"### Part 6\n",
"\n",
"Data: $(44,91), (61, 98), (81, 103), (113, 110), (131, 112)$\n",
"\n",
"Curve: $p = \\beta_0 + \\beta_1 \\ln{w}$"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
""
]
},
"execution_count": 6,
"metadata": {
},
"output_type": "execute_result"
},
{
"data": {
"text/html": [
""
]
},
"execution_count": 6,
"metadata": {
},
"output_type": "execute_result"
},
{
"data": {
"text/html": [
""
]
},
"execution_count": 6,
"metadata": {
},
"output_type": "execute_result"
},
{
"data": {
"image/png": "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"
},
"execution_count": 6,
"metadata": {
},
"output_type": "execute_result"
}
],
"source": [
"A = matrix(RDF,[[1, log(44)],\n",
" [1, log(61)],\n",
" [1, log(81)],\n",
" [1, log(113)],\n",
" [1, log(131)]])\n",
"b = matrix([[91],[98],[103],[110],[112]])\n",
"\n",
"AT=A.transpose()\n",
"A1 = AT*A\n",
"b1 = AT*b\n",
"M = A1.augment(b1)\n",
"f(x)=M.rref()[0][2] + M.rref()[1][2]*log(x)\n",
"\n",
"\n",
"show(M.n(digits = 3), \"RREF \", M.rref().n(digits = 3), \" from which we obtain y = \", f(x))\n",
"show(f(x))\n",
"\n",
"show(f(100, hold=True), \" = \", f(100).numerical_approx(digits = 3))\n",
"\n",
"P = point([(44,91), (61, 98), (81, 103), (113, 110), (131, 112)], size=40)\n",
"P += plot(f,[0,140], gridlines='true', legend_label='Least Squares Line')\n",
"show(P)\n",
"\n",
"P.save('plot1lab3_part6.png')\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": false
},
"source": [
"### Part 7\n",
"\n",
"Data: $(0,0), (1, 8.8), (2, 29.9), (3, 62.0), (4, 104.7), (5, 159.1), (6, 222.0), (7, 294.5), (8, 380.4), (9, 471.1), (10, 571.7), (11, 686.8), (12, 809.2)$\n",
"\n",
"Curve: $y = \\beta_0 + \\beta_1 t + \\beta_2 t^2 + \\beta_3 t^3$"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
""
]
},
"execution_count": 1,
"metadata": {
},
"output_type": "execute_result"
},
{
"data": {
"text/html": [
""
]
},
"execution_count": 1,
"metadata": {
},
"output_type": "execute_result"
},
{
"data": {
"text/html": [
""
]
},
"execution_count": 1,
"metadata": {
},
"output_type": "execute_result"
},
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAkwAAAGFCAYAAAAPa6wiAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAAPYQAAD2EBqD+naQAAIABJREFUeJzs3Xl8TFf/B/DPJBEkZLElaC0tLdpai1ZbpUiEGtQaSgWlldRSS7XPg7SWiq4aailF6xFVKiiKqi1qawb1EBQlPEQaJJZo1vP74/4yzThBIjO5d04+79crrzZ3bma+95Nb/Tr33HNNQggBIiIiIrorF70LICIiIjI6NkxERERE98GGiYiIiOg+2DARERER3QcbJiIiIqL7YMNEREREdB9smIiIiIjugw0TERER0X0o0zAJIXD9+nVwHU4iIiKyN2Uaphs3bsDb2xs3btzQuxRDiY6O1rsEw2EmMmYiYyYyZiJjJjJVM1GmYaK8RUVF6V2C4TATGTORMRMZM5ExE5mqmZhUeZbc9evX4e3tjZSUFHh5eeldDhERESlEuRGm3r17w2w2K9vhEhERUdHjCBMRERHRfSg3wkRERER0/bp938/Nvm9XtOLj45GUlAQAuHnzJgDg0KFDKFOmjJ5lGUp4eDjCw8P1LsNQHjSTChUqoFq1avYvyABCQkKwaNEivcswFGYiYyYyZiIzQiZffQV88AFw8CBQoYJ93tNpG6b4+HjUrVsXqampNttffPFFnSoyrnXr1uldguE8SCYeHh6Ii4tTsmkKCAjQuwTDYSYyZiJjJjK9M9m3DwgLAwYOtF+zBDjxHCaLxYImTZpg6dKlqFu3rt7lkOLi4uLw6quvIjY2Fo0bN9a7HCIiysPly0CTJkC1asD27YC7u/3e22lHmHLUrVuX/wOjIpOSkoKrV6+iZMmS8PT01LscIiL6fxkZQI8eQFYWsHKlfZslQIGGiago/fjjjzh8+DC8vLzQq1cvNk1ERAYxejSwZw+wbRtQpYr937/Ad8nt2rULZrMZVatWhYuLC9auXWt9LTMzE++88w7q16+PMmXKoGrVqnjttddw6dIlm/e4du0a+vbtC29vb/j6+mLw4MG4deuWzT6///47WrZsidKlS6N69er46KOPHvAQiezH09MT7u7uuH79OtLS0vQux25iYmL0LsFwmImMmciYiUyPTBYvBiIjgS++AJ5/3jGfUeCG6datW2jYsCFmz54Nk8lk81pqaioOHTqESZMm4eDBg1i9ejVOnDiBzp072+zXp08fxMXFYevWrVi/fj127tyJoUOHWl+/ceMGAgMDUbNmTVgsFnz00UcIDw/HggULHvAwieyjZMmSKFmypN5l2N2MGTP0LsFwmImMmciYiayoM9m/H3jjDWDwYO2fjlKoSd8uLi6Ijo6G2Wy+6z6//fYbmjdvjnPnzuGhhx5CXFwcnnjiCcTGxqJRo0YAgE2bNqFjx464cOEC/P39MWfOHEyYMAEJCQlwc9OuGr777rtYs2YNjh07BuCfSd+chEtFIed8mzJlCvz9/XHjxg30798f5cqV07s0u0hNTYWHh4feZRgKM5ExExkzkRVlJgkJwNNPAw8/rE3yduTfZx2+cGVycjJMJhN8fHwAAHv37oWvr6+1WQKAtm3bwmQyYd++fdZ9WrZsaW2WACAwMBAnTpxASkqKo0smKnb4B76MmciYiYyZyIoqk/R0oHt3IDsbWLXKsc0S4OCGKS0tDePHj0efPn2si0kmJCSgUqVKNvu5urqiXLlySEhIsO7j5+dns0/O9zn7UPG2ZMkSZUZ3iIio4EaMAA4cAH74wTGTvO/ksIYpMzMTPXr0gMlkwpdffnnf/YUQ0pyoO18HcM99HkRISAheeeUVu75nQbRu3Rpvv/32ffc7e/Ys+vbti6pVq6J06dJ4+OGH0bVrV5w8ebIIqtTHnTcV5Na7d2+lj52IiO5u/nxg7lxg9mzgmWeK5jMd0jDlNEvnz5/H5s2bbR5V4u/vj8TERJv9s7KycO3aNfj7+1v3uXz5MgAgKioKISEh1p/JGWkaP368I0o3pMzMTLRr1w7Xr1/H6tWrcfLkSaxYsQJPPfUUkpOT9S4PGRkZRf6ZJUuWRAV7LuH6AN577z0sXLjQZpvFYoHZbLY+sifHpEmTEBERYbMtPj4eZrMZx48ft9keGRmJsWPH2mxLTU2F2WyW7j7J+e/jTr169UJ0dLTNts2bN+c53zA0NBTt27dX4jjs+fvIqd3ZjyOHPY6jTp06ShyHPX8fuWtx5uPIrbDHMXLkSIcex7vvLkRYGPDmm9pEb3scx50/mydRCCaTSaxZs8ZmW0ZGhujSpYuoX7++uHLlivQzcXFxwsXFRVgsFuu2TZs2CVdXV3Hp0iUhhBBz5swR5cuXF5mZmdZ93n33XVG3bl3r97GxsQKAiI2NLcwhiAEDBoiuXbve9fXk5GQxaNAgUbFiReHl5SXatGkjDh8+bH399OnTonPnzsLPz0+UKVNGNG3aVPz888827zF79mxRu3ZtUapUKeHn5yd69Ohh/WyTySRcXFys/zx37pxUw6FDh4TJZBLx8fH3PJZ9+/aJRo0aiVKlSommTZuK1atXC5PJZK130aJFwsfHx+ZnoqOjhclkKtDx1KhRQ0yePFn0799feHt7i5CQECGEEOfPnxc9e/YUPj4+onz58qJz587i7Nmz1p/btm2baNasmfD09BQ+Pj7i+eefv+cx5XV+5Vi8eLHNsYSHh4uGDRuKb7/9VtSoUUN4e3uL3r17i5s3b1r3yc7OFtOmTRM1a9YUpUuXFg0bNhQrV668Z6Y5cs63KVOmiAULFojPPvssz/PbWX3xxRd6l2A4zETGTGTMRObITC5cEMLfX4jnnxciLc1hH5OnB1pW4PDhwzh06BAA4MyZMzh8+DDOnz+PrKwsdOvWDRaLBUuXLkVGRgYuX76My5cvW0ch6tSpg8DAQLz++us4cOAAdu/ejbfeegvBwcHWEaY+ffrA3d0dAwcOxLFjx/Ddd9/hiy++wOjRowtabqF1794dV65cwaZNm2CxWNC4cWO0bdvWOrJz8+ZNdOzYEb/88gsOHTqEoKAgmM1mXLhwAQAQGxuLESNGYMqUKTh58iQ2bdqEli1bAgBmzpyJZ599Fq+//jouX76MS5cu4eGHH5ZqqFixIlxdXfH9998jOzs7zzpTU1PRqVMnPPnkk7BYLAgPD8eYMWNsLmGaTKY8L2nm3na/48nxySefoGHDhjh48CAmTJiAzMxMBAYGwtvbG7t378bu3btRtmxZtG/fHpmZmcjKykLXrl3RunVr/Pe//8XevXsxZMiQQl1ivfNnT58+jTVr1mDDhg1Yv349duzYgenTp1tfnzZtGpYuXYr58+fj2LFjGDVqFPr164ddu3Y9cA2qeOutt/QuwXCYiYyZyJiJzFGZ/P038MorgKurY1byvq+Cdljbt2+3jobk/goJCRFnz56VXsv5fseOHdb3uHbtmujbt6/w8vISPj4+YvDgweLWrVs2n/P777+Lli1bitKlS4uHH35YfPTRRzav5zXCdOuWELGx9//K/VH3GmGKiYkRPj4+Ij093WZ7rVq1xFdffXXXjJ588kkxe/ZsIYQQP/zwg/Dx8bEZ6citVatWYtSoUXd9rxxffvmlKFOmjPDy8hIvvfSSmDx5sjhz5oz19Xnz5omKFSuKtFwt99y5c4WLi4t1hGnx4sXC19fX5n2jo6OFi4vLPT879/EIoY0wdevWzWafpUuX2owACiFEWlqa8PDwEFu2bBFXr14VLi4uYufOnfc91hz3G2HKfSzh4eGiTJkyNufRuHHjxLPPPmutxdPTU+zdu9fmfQYPHiz69u1731pUH2EiIjKy7GwhBg4UomRJIfbv16eGAj8a5cUXX7zrKAeAe76Ww8fHB0uXLr3nPk899RR27NhRoNqOH9ceunc/sbFAfpZuOnz4MG7cuCHdjfX333/j9OnTALQRt0mTJmHDhg24dOkSMjMz8ffffyM+Ph4A0K5dO1SvXh01a9ZE+/bt0b59e3Tt2hWlS5cu0LG9+eab6N+/P7Zv3469e/di5cqVmDZtGtatW4c2bdrg+PHjqF+/PtxztdzPPvtsgT4jP8eTo8kdQR8+fBh//PEHypYta7M9LS0Np0+fRtu2bfHaa68hICAA7dq1Q9u2bdGzZ0/rqKI91KhRw+Z21sqVK1vnvp06dQqpqalo166d9QYCQJt/lXuJCyIiMp7584Gvv9ZW9G7aVJ8alHqWXJ06WjOUn/3y4+bNm6hSpQp27Nhh8z9ZANZ1pUaPHo2tW7fik08+waOPPorSpUujW7duSE9PBwCUKVMGFosF27dvx+bNmzFp0iSEh4fjt99+g5eXV4GOz9PTEx07dkTHjh0xefJkBAYGYsqUKWjTps197zIEtLvO7jyOOyds3+94cteS282bN/H0009j2bJl0mdUrFgRAPD1119jxIgR+Omnn/Ddd99hwoQJ2LJlC5o1a1agHO6mRIkSNt+bTCZrA3/z5k0AwIYNG1DljvtPVVy5u6COHz+OOvn9D6OYYCYyZiJjJjJ7Z7JzJxAaqn299prd3rbAlGqYPDzyN3KUX40bN0ZCQgJcXV1RrVq1PPf59ddfMWDAAOts/ps3b+Ls2bM2+7i4uOCll17CSy+9hIkTJ8LHxwe//PILunTpAnd3d2RlZT1QfXXq1MGePXsAAPXq1cN//vMfpKenW0eZcl7LUbFiRdy4cQO3b9+2jnAdPHiwwMeTl8aNG2PFihWoWLGizV2Rd2rQoAEaNGiAd955By1atMCyZcvs1jDdS7169VCyZEmcO3cOzzvqQUNObNy4cXddwqG4YiYyZiJjJjJ7ZnL2LNCtG/DCC8Dnn9vlLR+Yw1f6dgbJyck4fPiwzdeFCxfQtm1bPPPMM+jSpQu2bNmCc+fO4ddff8W///1vWCwWAEDt2rXxww8/WH+ub9++NiMs69evR2RkJA4fPoz4+HgsWbIEQghr912jRg3s27cP586dw5UrV6TRGUC73NWlSxesWrUKcXFxOH36NBYuXIivv/4aXbp0AaBNlDeZTBg8eDDi4uKwYcMGfPLJJzbv07x5c3h4eODdd9/FmTNnsGzZMixZssRmn/sdz9307dsXFSpUQOfOnRETE4OzZ89i+/btGDFiBC5evIizZ8/ivffew969exEfH4/Nmzfjjz/+QL169e75vn/++af0u0lNTb1vPXcqU6YMxowZg1GjRuGbb77BmTNncPDgQcyaNQvffvttgd9PNbNmzdK7BMNhJjJmImMmMntlcuMGYDYDXl7aJG83vYd49Jk6VXj2XFbgzgnsLi4u4vXXXxdCCHHz5k0xYsQI8dBDD4mSJUuK6tWri379+okLFy4IIYQ4e/asaNOmjfD09BTVq1cXX375pWjdurV1IndMTIxo1aqVKF++vPD09JRuZT958qRo0aKF8PDwuOuyAklJSWLkyJGifv36wsvLS3h7e4sGDRqIzz77zGa/3MsKNG7cWKxevdpm0rcQQqxZs0Y89thjwsPDQ5jNZrFgwQKbSd/3Ox4hhKhZs6aYOXOmVOfly5fFgAEDRKVKlUTp0qVFrVq1xNChQ8WNGzfE5cuXRdeuXUXVqlVFqVKlRM2aNcX7779/z99NXr8XFxcXsXv37jwnfTdq1Mjm5z///HNRs2ZNm22RkZGibt26omTJksLPz08EBQWJXbt23bMOITjpm4ioKGVlCWE2C1G2rBBHj+pdjaZQD9/VEx++e3/nzp3DI488goMHD6J+/fp6l+PUVH/4LhGRkbz7LhARAfz4I9Chg97VaPQe4CIHc9J+mIiIiqmlS4Hp04GPPzZOswRwDpPy7P3sPVLTnY8PIGaSF2YiYyaywmSyd6/2uJMBA4B8PGa1SHGESWHVq1d/4DvwqHh5kIn0qmMmMmYiYyayB83k/HmgSxfg6ae1B+sa7e/7nMNElA+cw0RE5Di3bmlLB1y5Ahw4AFSqpHdFMo4wERERkW6ys7UFKU+eBHbvNmazBLBhIiIiIh198AGwahWwejXQoIHe1dwdJ30TEZKSkvQuwXCYiYyZyJiJrCCZrFgBvP8+MHWqNn/JyNgwEREGDhyodwmGw0xkzETGTGT5zSQ2Vrsbrk8fbd0lo2PDREQIDw/XuwTDYSYyZiJjJrL8ZHLpEtC5M/DUU8CCBca7Iy4vTj+HKS4uTu8SqBhQ/TzjnaYyZiJjJjJmIrtfJrdva80SAERHA///LHjDc9qGqUKFCvDw8MCrr76qdylUTJQqVQply5bVuwwiIqclhLYw5X//C+zaBVSurHdF+ee0DVO1atUQFxeHpKQkpKSkIDo6GmvXrsVrr72GEiVK6F0eKahs2bKoUKECbt++rXcpREROafp0YNky4LvvgCZN9K6mYJy2YQK0pqlatWq4evUqDhw4gLJly8LPzw/u7u56l2YY//3vf/Hkk0/qXYahFCaT27dvIy0tzc4V6W/hwoUYNGiQ3mUYCjORMRMZM5HdLZPoaOC994BJk4CePXUorJCcumHKUbJkSXh5ecHV1RU3btxgw5TLpUuXUL16db3LMBR7ZOLl5YWSJUvaqSL9WSwW/qF/B2YiYyYyZiLLK5PDh4FXXwW6dwcmTtSpsEJy2kej3CkhIQE1atTAiRMnOM+EHK5kyZLw9PTUuwwiIsNLTASaNgXKl9fmLTnrH51KjDABgIeHB9LS0uDr6wsvLy+9yyEiIir20tKAV17R/rlmjfM2S4BCDRMREREZhxDAG28Av/0G7NgBPPyw3hUVDhsmIiIisrtPPwUWLwa+/RZo3lzvagpPuZW+e/fuDbPZjKioKL1LMQSz2ax3CYbDTGTMRMZMZMxExkxkZrMZGzYAY8cC48drk71V4BquyLruaWlpmD59OmJjYzFgwAA89dRTepdkCOXLl8ejjz6qdxmGwkxkzETGTGTMRMZMZDdvlseQIY8iMBCYP985HnuSH8rcJXf9+nV4e3sjJSWFk76JiIh0kJSkXX7z9AR27wZUummdc5iIiIio0NLTtXWWrl8Htm5Vq1kC2DARERFRIQkBvPUW8OuvWrNUo4beFdmfcpO+yVZ0dLTeJRgOM5ExExkzkTETGTPRREZq85XmzAGuXFEzEzZMiuPdgjJmImMmMmYiYyYyZgKsXQuMHAmMHg0MGqRuJpz0TURERA8kNhZo2RIICgJWrABcFB6GUfjQiIiIyFHOnQNefhl46iltcUqVmyWADRMREREVUEoK0LEjULq0dkmudGm9K3I83iVHRERE+ZaRoS0f8L//aXfFVaqkd0VFgyNMigsJCdG7BMNhJjJmImMmMmYiK26Z5DxQd8cOYPVqoG5deR9VM+EIk+ICAgL0LsFwmImMmciYiYyZyIpbJh9+CHz9NbBkCdCqVd77qJoJ75IjIiKi+4qKAvr0ASZNAtR4Cm3BKNcwBQUFwc3NDcHBwQgODta7LCIiIqcXEwO0aQP06qWNLqnyQN2CUK5h4ggTERGR/fzxB/DMM0D9+sCmTYC7u94V6YOTvhUXExOjdwmGw0xkzETGTGTMRKZ6JklJQIcO2p1wP/yQv2ZJ1UzYMCluxowZepdgOMxExkxkzETGTGQqZ/L330DnztqaS+vXA76++fs5VTPhJTnFpaamwsPDQ+8yDIWZyJiJjJnImIlM1Uyys7UJ3mvWANu3A82b5/9nVc2EywooTsWTtrCYiYyZyJiJjJnIVM3k3//Wng33/fcFa5YAdTNhw0RERERWCxZo6y199BHQrZve1RgH5zARERERAGDzZm0l7zffBEaP1rsaYylww7Rr1y6YzWZUrVoVLi4uWLt2rbTPxIkTUaVKFXh4eKBdu3Y4deqUzevXrl1D37594e3tDV9fXwwePBi3bt2y2ef3339Hy5YtUbp0aVSvXh0fffRRQUslAGPHjtW7BMNhJjJmImMmMmYiUymTI0e0Z8QFBgJffPHgay2plEluBW6Ybt26hYYNG2L27Nkw5ZFmREQEZs2ahXnz5mH//v3w9PREYGAg0tPTrfv06dMHcXFx2Lp1K9avX4+dO3di6NCh1tdv3LiBwMBA1KxZExaLBR999BHCw8OxYMGCBzzM4qtatWp6l2A4zETGTGTMRMZMZKpkcvEi0LEj8OijwPLlgFshJuyokolEFILJZBJr1qyx2Va5cmXx6aefWr9PSUkRpUqVEt99950QQohjx44Jk8kkLBaLdZ+ffvpJuLq6ikuXLgkhhPjyyy9F+fLlRUZGhnWf8ePHi7p16961lpSUFAFApKSkFOaQiIiIipUbN4Ro3FiIqlWFuHBB72qMy65zmP78808kJCSgTZs21m1eXl5o3rw59uzZAwDYu3cvfH190ahRI+s+bdu2hclkwr59+6z7tGzZEm65WtzAwECcOHECKSkp9iyZiIio2MrK0pYPOHlSW2upalW9KzIuuzZMCQkJMJlM8PPzs9nu5+eHhIQE6z6VKlWyed3V1RXlypWz2Sev98h5jYiIiApv1ChgwwZtCYEGDfSuxtiK5C45IUSe853ys09UVBRCQkIg/n99zZx9evXqhejoaGn/2rVrw2w223wFBARg4cKFNvtZLBaYzWYkJSXZbJ80aRIiIiJstsXHx8NsNuP48eM22yMjI6XJbampqTCbzdLS8DnHcae8jmPz5s0wm83SvqGhoQU+jtw1O/Nx5FbY4zh+/LgSxwHY7/cxZcoUJY7Dnr+PnH86+3HksMdxBAUFKXEc9vx95K7P2Y5jzBgLIiPNiIhIQlDQP9sLexwHDx50uv8+7vzZPBXmet6dc5jOnDkjTCaTOHz4sM1+L774ohg5cqQQQoivv/5alCtXzub1zMxM4ebmZn2v/v37i65du9rss23bNuHi4iKSk5PzrIVzmPLWqVMnvUswHGYiYyYyZiJjJjJnzWT1aiFMJiHGjrX/eztrJvdj1xGmmjVrwt/fH1u3brVuu379Ovbt24cWLVoAAJ599lkkJyfj4MGD1n22bt0KIQSaNWtm3Wfnzp3Iysqy7rN582Y8/vjj8Pb2tmfJyps1a5beJRgOM5ExExkzkTETmTNmsns3EBysLUo5fbr9398ZM8mPAj9L7tatWzh16hSEEGjcuDE+/fRTtG7dGuXKlcPDDz+MGTNmICIiAosXL0aNGjUwYcIEHD16FEePHoX7/z/muEOHDkhMTMScOXOQnp6OgQMHolmzZvj2228BaE1WnTp10K5dO7zzzjs4cuQIBg0ahJkzZ2LQoEF51sVnyREREd1bXBzw3HNA/frATz8BpUrpXZHzKHDDtGPHDrRu3Vqab/Taa6/h66+/BgCEh4dj/vz5SE5OxgsvvIDZs2ejVq1a1n2Tk5MRFhaGdevWwcXFBd27d8fMmTNtnj9z5MgRhIWF4cCBA6hQoQKGDx+OMWPG3LUuNkxERER3d/Ei8OyzgJcXsGsX4OOjd0XOpcANk1GxYSIiIspbSgrQsiVw9SqwZw/w0EN6V+R8+Cw5xd15hwAxk7wwExkzkTETmTNkkpYGdOkCxMdrl+Ec3Sw5QyYPohCLn5MzSE1N1bsEw2EmMmYiYyYyZiIzeibZ2UD//tqo0s8/A0884fjPNHomD4qX5IiIiBQkBPD228DMmcDKlcArr+hdkXPjCBMREZGCPvkE+PxzYPZsNkv2wDlMREREilm6FBg7FnjvPWDYML2rUQMbJsXla7n3YoaZyJiJjJnImInMiJls2QKEhAADBgB3PPWoSBgxE3tgw6S4gQMH6l2C4TATGTORMRMZM5EZLROLRbv81q4dMH8+cJ/HuDqE0TKxF076VpzFYkHjxo31LsNQmImMmciYiYyZyIyUyZkzQIsWQLVqwLZtgKenPnUYKRN7Uq5hCgoKgpubG4KDgxEcHKx3WURERA7311/aI0+EAH79FahYUe+K1KNcw8QRJiIiKk5u3QJeegk4e1Zbb+mRR/SuSE1cVoCIiMhJZWQAvXoBx44B27ezWXIkTvpW3MKFC/UuwXCYiYyZyJiJjJnI9MxECOD114FNm4BVq4AmTXQrxYaq5wkbJsVZLBa9SzAcZiJjJjJmImMmMj0zeecdYMkS7SsgQLcyJKqeJ5zDRERE5GQ+/RQYPVp77Mnw4XpXUzxwhImIiMiJLF2qNUvvvstmqSixYSIiInISGzZoq3gPHAhMnap3NcULGyYiIiInsHs30L070KEDMG+ePqt4F2dsmBRnNpv1LsFwmImMmciYiYyZyIoqk99/B15+GWjWDFi+HHAz8KJAqp4nbJgUFxYWpncJhsNMZMxExkxkzERWFJmcPg0EBgI1awJr1gClSzv8IwtF1fOEd8kREREZ1KVLwPPPA66uQEwMUKmS3hUVXwYe1CMiIiq+rl3TRpbS0rT5S2yW9MWGiYiIyGBSU4FOnYD//Q/YtQuoXl3viki5OUy9e/eG2WxGVFSU3qUYQnR0tN4lGA4zkTETGTORMROZIzLJyNDuhjt0SFtGoF49u3+EQ6l6nijXMC1fvhxr165FcHCw3qUYAhtHGTORMRMZM5ExE5m9M8nOBgYMAH7+GVi9Gmje3K5vXyRUPU846ZuIiMgAhABGjABmzQK++w7o0UPviig3zmEiIiIygPBwIDISmDuXzZIRKXdJjoiIyNl8/jnwwQfA9OnA0KF6V0N5YcNERESko8WLgVGjgHHjgHfe0bsauhs2TIoLCQnRuwTDYSYyZiJjJjJmIitsJqtXA4MGAUOGaKNLKlD1PGHDpLiAgAC9SzAcZiJjJjJmImMmssJk8tNPQK9e2nylL79U52G6qp4nvEuOiIioiO3YAbRvD7RrB6xaBZQooXdFdD8cYSIiIipCe/cCL7+sPSNuxQo2S86CDRMREVEROXQICAoCGjYEoqOBUqX0rojyiw2T4mJiYvQuwXCYiYyZyJiJjJnICpJJXBwQEADUqgX8+CPg6enAwnSk6nnChklxM2bM0LsEw2EmMmYiYyYyZiLLbyanTwNt2wJ+ftpkb29vBxemI1XPE076Vlxqaio8PDz0LsNQmImMmciYiYyZyPKTyfnzwAsvACVLapO9/f2LqDidqHqeKNeFzbkyAAAgAElEQVQwBQUFwc3NDcHBwXwALxER6eryZaBlSyAtDdi1C3j4Yb0rogelXMPEESYiIjKCK1eAVq2Aq1eBnTuBRx/VuyIqDD58l4iIyM6uX9fWWUpIYLOkCk76VtzYsWP1LsFwmImMmciYiYyZyPLK5NYtoGNH4NQpYMsWoG5dHQrTkarnCUeYFFetWjW9SzAcZiJjJjJmImMmsjsz+ftvoGtXbb2lLVu09ZaKG1XPE85hIiIisoOMDKBbN61R2rhRm79E6uAIExERUSFlZQH9+mlrLK1Zw2ZJRWyYiIiICiE7G3j9dWDlSu3ZcEFBeldEjmD3Sd/Z2dmYMGECHnnkEXh4eKBWrVqYMmWKtN/EiRNRpUoVeHh4oF27djh16pTN69euXUPfvn3h7e0NX19fDB48GLdu3bJ3uco7fvy43iUYDjORMRMZM5ExE82NG8B77wGNGgHPPXccZjOweLH29corelenP2XPE2FnU6dOFRUrVhQbN24U586dE6tWrRJly5YVkZGR1n2mT58ufH19xdq1a8WRI0dE586dxSOPPCLS0tKs+7Rv3140atRIHDhwQOzevVvUrl1b9O3b966fm5KSIgCIlJQUex+SU+vUqZPeJRgOM5ExExkzkTETTatWQgA5X50EIMTw4XpXZRyqnid2n/TdqVMn+Pv746uvvrJu6969Ozw8PPDNN98AAKpUqYKxY8di1KhRALQJ235+fliyZAl69uyJuLg4PPHEE4iNjUWjRo0AAJs2bULHjh1x4cIF+OexrjwnfectPj5e2TsWHhQzkTETGTORMRPgwAGgWbPcW+IBVEOrVsC2bfrUZDSqnid2vyTXokULbN26FX/88QcA4PDhw9i9ezc6dOgAAPjzzz+RkJCANm3aWH/Gy8sLzZs3x549ewAAe/fuha+vr7VZAoC2bdvCZDJh37599i5ZaSqetIXFTGTMRMZMZMwE+N//7txS7S7biy9VzxO7T/oeP348rl+/jjp16sDV1RXZ2dmYOnUqevfuDQBISEiAyWSCn5+fzc/5+fkhISHBuk+lSpVsXnd1dUW5cuWs+xARERW1F14AXF21u+JyCwjQpx4qOnZvmL777jssW7YMy5cvR7169XDo0CGMGDECVapUQb9+/e76c0IImEyme753fvYhIiJylJkztWYpd9PUqBEQHq5rWVQE7H5Jbty4cXj33XfRo0cPPPHEE+jbty9GjRqFDz/8EADg7+8PIQQuX75s83OJiYnWUSd/f38kJiYCAKKiohASEoKsrCxcu3bNuk+vXr0QHR0tfX7t2rVhNpttvgICArBw4UKb/SwWC8xmM5KSkmy2T5o0CRERETbb4uPjYTabpZn/kZGR0hLwqampMJvNiImJsdmecxx3yus4Nm/eDLPZLO0bGhpa4OPIfSzOfBy5FfY4IiIilDgOwH6/j+7duytxHPb8feS87uzHkcMex9GgQQMljuNBfx8ffABMngwMH25BmzZmzJ2bhMGDIxAbC1So4DzHkcNRv4/Jkyc73XHc+bN5svcs8vLly4u5c+fabJs2bZp4/PHHrd9XrlxZfPrpp9bvU1JSRKlSpcSKFSuEEELExcUJFxcXYbFYrPts2rRJuLq6ikuXLuX5ubxLLm8TJ07UuwTDYSYyZiJjJrLinMmUKdpdcdOm2W4vzpncjaqZ2P0uuZCQEGzduhVz587FE088AYvFgqFDh2Lw4MGYNm0aAGDGjBmIiIjA4sWLUaNGDUyYMAFHjx7F0aNH4e7uDgDo0KEDEhMTMWfOHKSnp2PgwIFo1qwZvv322zw/l3fJERGRI0REAOPHayNMEyboXQ3pxe4N061btzBhwgSsXr0aiYmJqFKlCvr06YMJEybAze2fKVPh4eGYP38+kpOT8cILL2D27NmoVauW9fXk5GSEhYVh3bp1cHFxQffu3TFz5kx4eHjk+blsmIiIyN4++QQYMwaYOBF4/329qyE98eG7REREeZg5Exg5UlvVe8oUgPccFW92n/RNxpKviWzFDDORMRMZM5EVp0xmz9aapXHj7t0sFadM8kvVTNgwKW7gwIF6l2A4zETGTGTMRFZcMpk7FwgLA95+G5g+/d4jS8Ulk4JQNRNeklOcxWJB48aN9S7DUJiJjJnImImsOGSyYAHw+uvA8OHA55/f/zJcccikoFTNhA0TERERgEWLgEGDgDffBGbN4pwlssVLckREVOx99RUwcCAwZAgQGclmiWRsmIiIqFj78kutUQoNBebMAVz4f0bKA08Lxd25hDwxk7wwExkzkamYycyZWqM0cuSDjSypmElhqZoJGybFWSwWvUswHGYiYyYyZiJTLZOPP/5n6YBPP32wy3CqZWIPqmbCSd9ERFTsfPihtiDlv/6lPVCXc5bofpQbYerduzfMZjOioqL0LoWIiAzogw+0Zik8nM0S5R9HmIiIqFgQQnsm3JQpwNSpWtNElF9u99+FiIjIuQkBjB8PzJihfY0dq3dF5GyUuyRHtsxms94lGA4zkTETGTOROWsmQgCjR2uN0mef2bdZctZMHEnVTDjCpLiwsDC9SzAcZiJjJjJmInPGTITQHnMya5b2FRpq3/d3xkwcTdVMOIeJiIiUlJ0NDBsGzJunfQ0ZondF5Mw4wkRERMrJytIapEWLgK+/BkJC9K6InB0bJiIiUkpWltYg/ec/wDffAK++qndFpAJO+lZcdHS03iUYDjORMRMZM5E5QyaZmUC/fsCyZVrD5OhmyRkyKWqqZsKGSXFcwFPGTGTMRMZMZEbPJCMDCA4Gvv8eWL4c6N3b8Z9p9Ez0oGomnPRNREROLz0d6NULWL9ea5g6d9a7IlIN5zAREZFT+/tvoEcPYPNmYPVqoGNHvSsiFbFhIiIip3XrFtClCxATA6xdCwQG6l0RqYoNExEROaXkZKBDB+DIEeCnn4AXX9S7IlKZcpO+e/fuDbPZrOyks4IK4eIjEmYiYyYyZiLTO5Ply4EmTYDKlbX5Ss89B5w4AWzdql+zpHcmRqRqJsqNMC1fvpyTvnMJCAjQuwTDYSYyZiJjJjI9M1m9WrsDLseKFYCbGxAbC9Svr1tZPE/yoGomvEuOiIgMr00b4Jdf5O1btgBt2xZ9PVT8KHdJjoiI1HP1asG2E9kbGyYiIjK8xo3lbaVLA+3aFX0tVDyxYVJcTEyM3iUYDjORMRMZM5Hplcm2bdqcJV/ff7Z5ewPffmu7TQ88T2SqZsKGSXEzZszQuwTDYSYyZiJjJjI9Mlm3DggKAp59Fjh/Hjh2TLsr7uJFoFu3Ii9HwvNEpmomnPStuNTUVHh4eOhdhqEwExkzkTETWVFnsny59iDdTp2AqCigZMki++h843kiUzUTjjApTsWTtrCYiYyZyJiJrCgzmT8f6NNH+1qxwpjNEsDzJC+qZsKGiYiIDOXjj4GhQ4Fhw4BFi7T1loj0xoaJiIgMQQhg4kRg7FjgvfeAyEjAhf+XIoPgqai4sWPH6l2C4TATGTORMROZIzPJygJCQ4HJk4Hp04GpUwGTyWEfZzc8T2SqZsKBTsVVq1ZN7xIMh5nImImMmcgclUlamja5e9Uq4KuvgMGDHfIxDsHzRKZqJsrdJRcUFAQ3NzcEBwcjOPeDh4iIyHBu3AC6dgViYrS74rp00bsiorwp1zBxWQEiIueQmAh06AD88Qewdi3w4ot6V0R0d7wkR0RERe7sWSAgALh+HdixA2jYUO+KiO6Nk74Vd/z4cb1LMBxmImMmMmYis1cmR44ALVoA2dnAr786d7PE80SmaiZsmBQ3btw4vUswHGYiYyYyZiKzRyYxMUDLloCfn/bvjzxih8J0xPNEpmomnMOkuPj4eGXvWHhQzETGTGTMRFbYTNatA3r2BJ55BoiO1h6g6+x4nshUzYQNExEROdySJcCgQYDZDCxbBpQqpXdFRAXDS3JEROQwQgAREcCAAcDAgcD337NZIufkkIbp4sWL6NevHypUqAAPDw80aNAAFovFZp+JEyeiSpUq8PDwQLt27XDq1Cmb169du4a+ffvC29sbvr6+GDx4MG7duuWIcomIyAGysoC33gLGjwcmTADmzQNcXfWuiujB2L1hSk5OxnPPPYeSJUti06ZNiIuLwyeffAJfX1/rPhEREZg1axbmzZuH/fv3w9PTE4GBgUhPT7fu06dPH8TFxWHr1q1Yv349du7ciaFDh9q7XOVFREToXYLhMBMZM5ExE1lBMrl9G+jRA5gzR2uUPvjAOR51UlA8T2SqZmL3dZimT5+OatWqYcGCBdZt1atXt9ln5syZmDBhAjp16gQA+Oabb+Dn54fo6Gj07NkTcXFx2LRpE2JjY9GoUSMAQGRkJDp27IiPP/4Y/v7+9i5bWampqXqXYDjMRMZMZMxElt9MrlzR5iodPAisWQO8/LKDC9MRzxOZqpnYfdL3E088gfbt2+P8+fPYsWMHqlatimHDhmHw/z8c6M8//8Sjjz6KQ4cOoX79+tafa9WqFRo1aoTPPvsMixYtwpgxY3DlyhXr61lZWShVqhRWrlyJzp07S5/LSd9ERPr7808gKEhrmtavB5o107siIvuw+yW5M2fOYM6cOXj88cexefNmvPHGGxg+fDiWLl0KAEhISIDJZIKfn5/Nz/n5+SEhIcG6T6VKlWxed3V1Rbly5az7EBGRsVgswLPPApmZwJ49bJZILXa/JJednY1mzZph8uTJAIAGDRrg6NGjmDNnDl599dW7/pwQAqb7XODOzz5ERFT0Nm0CuncH6tYFfvwRuOPvvEROz+4jTJUrV0bdunVtttWtWxfx8fEAAH9/fwghcPnyZZt9EhMTraNO/v7+SExMBABERUUhJCQEWVlZuHbtmnWfXr16ITo6Wvr82rVrw2w223wFBARg4cKFNvtZLBaYzWYkJSXZbJ80aZI0YS0+Ph5ms1la7j0yMhJjx4612Zaamgqz2YyYmBib7TnHcae8jmPz5s0wm83SvqGhoQU+jtzbnfk4civscSQlJSlxHID9fh+ff/65Esdhz99Hzs84+3HksMdxdOnSJc/jaNTIjJdf1h6eu22b1iwZ+Tjs+fvIfSzOfBy5FfY4cvZ1puO482fzJOysT58+omXLljbbRo4cKZ577jnr95UrVxaffvqp9fuUlBRRqlQpsWLFCiGEEHFxccLFxUVYLBbrPps2bRKurq7i0qVLeX5uSkqKACBSUlLseThOr1OnTnqXYDjMRMZMZMxEdmcm2dlCTJ4sBCDE668LkZGhU2E64nkiUzUTuzdMBw4cEO7u7mLatGni1KlT4j//+Y8oU6aMiIqKsu4TEREhypUrJ9auXSt+//130blzZ1GrVi2RlpZm3ScoKEg0adJE7N+/X8TExIjHHntMvPrqq3f9XDZMeYuNjdW7BMNhJjJmImMmstyZZGQIMWSI1ix98IHWPBVHPE9kqmbikEejbNiwAePHj8epU6dQs2ZNjB49GgMHDrTZJzw8HPPnz0dycjJeeOEFzJ49G7Vq1bK+npycjLCwMKxbtw4uLi7o3r07Zs6cCQ8Pjzw/k3fJEREVjVu3gN69gY0bga++AvK4ykKkHD5LjoiI7isjA3BzA5KStHWVjh4FVq4E2rfXuzKiosFnyRER0V2dPAm0bQu4uwPly2t3wZ07B+zYwWaJihc2TIq7824CYiZ5YSYyZqKtpxQYCGzdqn1/7dpCXLkCDB8ONGmib21GwfNEpmombJgUd+dDj4mZ5IWZyJgJ8MsvwNmzubdomaxZo0c1xsTzRKZqJpzDREREeVq7FsjjSVRo0AA4dKjo6yHSE0eYiIhIkp6uTerOS3Bw0dZCZARsmIiIyMbVq9rcpe++AyZOBHJWfClRAhgyBBg9Wt/6iPTAS3JERGT1xx9Ax45a0xQdDTz/PCAEcOqUdpdcuXJ6V0ikD44wKS6vZ/EUd8xExkxkxTGTHTuAZ54BXFyAffu0ZgkATCagdm1gwIDil8n9FMfz5H5UzYQNk+LCwsL0LsFwmImMmciKWyZLlgDt2gENGwJ79gCPPirvU9wyyQ9mIlM1E+UuyQUFBcHNzQ3BwcEI5sxEIqJ7ys7W5ilNnQoMGgTMmaPNVSIiW8o1TJzDRESUP7dvA6+9pt0NFxEBjBmjXX4jIpmb3gUQEVHRS0jQ1lg6cgRYtQro2lXvioiMjXOYFBcdHa13CYbDTGTMRKZyJkeOAM2bA+fPA7t25b9ZUjmTB8VMZKpmwoZJcVFRUXqXYDjMRMZMZKpm8tNPwHPPAb6+wP79BXsmnKqZFAYzkamaCecwEREVA0IAX3wBvP020KEDEBUFlCmjd1VEzoMjTEREiktP11boHjkSGDVKW5CSzRJRwXDSNxGRwpKSgG7dgL17gUWLgAED9K6IyDmxYSIiUtTRo0CnTsDNm8Avv2hzl4jowfCSnOJCQkL0LsFwmImMmcicPZM1a7THnJQtCxw4YJ9mydkzcQRmIlM1EzZMigsICNC7BMNhJjJmInPWTLKzgcmTgS5dgIAAYPduoHp1+7y3s2biSMxEpmomvEuOiEgRN29qc5RWrQI++AD417+0B+kSUeFxDhMRkQL+/FNbufvPP4HVq7URJiKyH/7dg4jIyf3yC9C0KXDrFrBnD5slIkdQrmHq3bs3zGazsiuNFlRMTIzeJRgOM5ExE5kzZCIEEBmpzVVq1Eib3P3kk477PGfIpKgxE5mqmSjXMC1fvhxr165FcHCw3qUYwowZM/QuwXCYiYyZyIyeSVoaMHgwMHy49rVxI1CunGM/0+iZ6IGZyFTNhJO+FZeamgoPDw+9yzAUZiJjJjIjZ3LxItC9O2CxAPPmAa+9VjSfa+RM9MJMZKpmwknfilPxpC0sZiJjJjKjZrJrF9Czp3b3244dQPPmRffZRs1ET8xEpmomyl2SIyJSxdWrwB9/aHOVcuYrvfQS8Nhj2uhSUTZLRMUdGyYiIoPJzASGDgX8/bXmqFYtIChIm6sUFgb8/DPg56d3lUTFCxsmxY0dO1bvEgyHmciYiUzPTD75BJg/H8jI0L4/cwbYtAlYvBj47DOgRAl96uJ5ImMmMlUzYcOkuGrVquldguEwExkzkemZyfLleW/39S3aOu7E80TGTGSqZsK75IiIDKZ5c2D/fnn7Tz8BgYFFXw8RcYSJiMhQUlK0NZbuVKMG0KZNkZdDRP+PDRMRkUEcPao94uTsWW1tpYoVAZMJaNtWm8PkxoVgiHTDhklxx48f17sEw2EmMmYiK+pMli0DmjUD3N21R5wsXgwkJgLp6cCWLdrdcnrjeSJjJjJVM2HDpLhx48bpXYLhMBMZM5EVVSZpaUBoKNC3L/DKK8C+fUDt2v+8bqRRJZ4nMmYiUzUTTvpWXHx8vLJ3LDwoZiJjJrKiyCQ+HujRAzh0CJg5U1t7yWRy6EcWCs8TGTORqZqJcg1TUFAQ3NzcEBwczAfwEpFhbd4M9OkDlCkDrFwJPP203hUR0b0o1zBxhImIjCwrC5g8GfjgA6B9e2DpUqBcOb2rIqL7MdDVcSIitV26pM1V2rEDeP994F//0h6iS0TGx/9UFRcREaF3CYbDTGTMRGbvTLZsARo2BOLigK1bgQkTnK9Z4nkiYyYyVTNxsv9cqaBSU1P1LsFwmImMmcjslUlmptYcBQYCDRoAhw8DrVrZ5a2LHM8TGTORqZoJ5zARETnIxYtAcDAQE6PNWxo/3vlGlYhIwzlMREQOsGkT0K8fUKIEsG0b0LKl3hURUWHw7zpERHaUmQm89552B1yTJtoaS2yWiJyfwxumDz/8EC4uLnj77bet29LS0hAaGooKFSqgbNmy6N69OxITE21+7vz58+jYsSM8PT3h7++PcePGITs729HlKicpKUnvEgyHmciYiexBMrlwAWjdGpgxA5g+HVi/XnsenCp4nsiYiUzVTBzaMB04cABfffUVGjRoYLN95MiRWL9+PVatWoWdO3fi4sWL6Natm/X17OxsdOjQAZmZmdi7dy+WLFmCxYsXY+LEiY4sV0kDBw7UuwTDYSYyZiIraCYbN2p3wZ09C2zfDrzzjnrzlXieyJiJTNlMhIPcuHFDPPbYY2Lr1q2iVatWYtSoUUIIIVJSUoS7u7v44YcfrPseP35cmEwmsW/fPiGEEBs2bBBubm7ir7/+su4zd+5c4ePjIzIyMvL8vJSUFAFApKSkOOqQnFJsbKzeJRgOM5ExE1l+M0lPF+Kdd4QAhOjQQYhcf2wph+eJjJnIVM3EYX//CQ0NRadOnfDSSy/ZbP/tt9+QmZmJNm3aWLc9/vjjqFatGvbs2QMA2Lt3L5566ilUqFDBuk9gYCBSUlJw9OhRR5WspMaNG+tdguEwExkzkeUnk/h4bYmAjz/WLsOtWwfk+mNLOTxPZMxEpmomDrlLbvny5Th06BB+++036bXLly/D3d1duvXfz88PCQkJAICEhAT4+flJr+e8duclPiKiovb998CQIUDZssDOnUCLFnpXRESOZPcRpgsXLmDkyJFYunQpSpQoke+fE0LAlI/HdOdnHyIiR7l5Exg0COjZE2jXTluIks0Skfrs3jDFxsbir7/+QpMmTVCiRAmUKFECO3bswMyZM+Hu7g4/Pz+kpaXh+vXrNj+XmJhoHUXy9/fH5cuXAQBRUVEICQmxfp+zT69evRAdHS19fu3atWE2m22+AgICsHDhQpv9LBYLzGazNJt/0qRJ0rLu8fHxMJvNOH78uM32yMhIjB071mZbamoqzGYzYmJibLbnHMed8jqOzZs3w2w2S/uGhoYW+Dhy7+/Mx5FbYY9j4cKFShwHYL/fx4ABA5Q4Dnv+PnLeK/dxxMYCjRsDy5enomFDM956Kwa+vsY+jhz2+H00bdpUieOw5+8j92vOfBy5FfY4vvzyS6c7jnzd2WfvSVE3b94UR48etflq2rSp6N+/vzh27Fiek75PnDghTCaT2L9/vxBCiI0bN0qTvufNmyd8fHxEenp6np/LSd95GzZsmN4lGA4zkTETW2lpQrz55j+ZZGUJEREhRIkSQjRpIsSJEzoWpyOeJzJmIlM1kyJ5NErr1q3RqFEjfPrppwCAYcOGYePGjVi0aBHKli2L4cOHw8XFBbt27QKgLSvQqFEjVKlSBREREbh06RL69++PIUOGYPLkyXl+Bh+NQkSFFRcHhIZqK3NXrAiMHq2t1t2/P/DLL8DYsdojTtzd9a6UiIpakTwa5c55R5999hlcXV3RvXt3pKWloX379pg9e7b1dRcXF/z4449488030aJFC3h6emLAgAF4//33i6JcIiqG0tO1B+SeP699/9df2rPfpkwBvLyALVuAXDf3ElExw4fvEhEB2LAB6NhR3l6uHHDihNrLBRDR/Sm2Di0R0YNJS8t7e40abJaIiA2T8vK6y6C4YyYyZqJdbitdOvcWLZM+fXQpx5B4nsiYiUzVTNgwKS4sLEzvEgyHmciKeyZnzwKdOgF//w34+Gjb3NzCMGwYMHKkrqUZSnE/T/LCTGSqZsI5TERUbAkBfPMN8NZb2lylb74BXngBOH0aKF8eNmssEVHxxhEmIiqWkpKA7t2BAQOAV14Bfv8daNkSMJmAWrXYLBGRrSJZVoCIyEg2bAAGDgQyM4GVK4Fu3fSuiIiMjiNMisvr8THFHTORFZdMbt4E3nxTWz6gcWPgyJG7N0vFJZOCYCYyZiJTNRM2TIqLiorSuwTDYSay4pDJjh1Aw4baPKU5c4D164HKle++f3HIpKCYiYyZyFTNRLlJ30FBQXBzc0NwcDCCg4P1LouIdHbzprZi9+zZwPPPA4sWaXOUiIgKQrmGiXfJEVGOrVuBwYOBxERg+nTtOXEuHFcnogfAPzqISDnXrwNvvAG0baut1H3kiLZ0AJslInpQvEuOiJSyebM2qnTtGvDll8DQoWyUiKjw+MeI4kJCQvQuwXCYiUyFTJKTgUGDgMBA4PHHtVGlN9988GZJhUzsjZnImIlM1Uw4wqS4gIAAvUswHGYic/ZM1q/XRpKuXwfmz9dGmEymwr2ns2fiCMxExkxkqmbCSd9E5LSuXdOe9fbNN9rI0vz5QLVqeldFRCriCBMROaW1a7VRpdu3ga+/1h5xUthRJSKiu+EcJiJyKleuAH37Ap07A02aAEePAiEhbJaIyLHYMCkuJiZG7xIMh5nInCWTVauAevWAjRuBb78F1q0DqlZ1zGc5SyZFiZnImIlM1UzYMCluxowZepdgOMxEZvRMEhOBnj2B7t2BFi20UaVXX3XsqJLRM9EDM5ExE5mqmXDSt+JSU1Ph4eGhdxmGwkxkRs1ECGDFCiAsTPv3WbOAXr2K5vKbUTPREzORMROZqplwhElxKp60hcVMZEbI5MwZYO9eID39n+87dgR69wZefFEbVerdu+jmKhkhE6NhJjJmIlM1E94lR0S6un0b6NMHiI7Wvq9YEXj5ZSAqSvv36GhtgjcRkZ6UuyQXFBQENzc3BAcHIzg4WO+yiOg+/v1vYOpUefuIEcCUKUCZMkVfExHRnZS7JLd8+XKsXbuWzdL/Gzt2rN4lGA4zkemZyQ8/5L29TRt9myWeJzJmImMmMlUzUa5hIlvVuOyxhJnI9MpECCAtLe/X9L53g+eJjJnImIlM1UyUuyTHu+SInENcHPDGG8DOnfJrTz4J/P47F6MkIuPgCBMRFanbt7V5Sw0aAJcuAVu2APPmAY8/Dnh7A8HBwKZNbJaIyFg4wkREReann4DQUODCBeDdd4Hx44FSpfSuiojo/jjCpLjjx4/rXYLhMBOZozO5dElbcDIoCKhRQ7vcFh5u7GaJ54mMmciYiUzVTNgwKW7cuHF6l2A4zETmqEyysoDZs4E6dYBt27Tnv/38s3b5zeh4nsiYiYyZyFTNhJfkFBcfH6/sHQsPipnIHJHJrl3aWkoHDwJDhgDTpwO+vnb9CIfieSJjJjJmIlM1EzZMRGRX553EaXEAABkuSURBVM8D48YBy5cDTZsCX3wBPPOM3lURERUOL8kRkV3cvg1Mnqxdbtu2DVi0SHs2HJslIlIBnyVHRIUiBLBqFTBmDHDxIjBypLZsAAd6iUglHGFSXEREhN4lGA4zkT1oJkeOaI8w6dFDW2zyv/8FZsxQo1nieSJjJjJmIlM1EzZMiktNTdW7BMNhJrKCZnL1KhAWBjRsCPzvf8CGDcCPPwKPPeagAnXA80TGTGTMRKZqJspN+g4KCoKbmxuCg4P5AF4iO8vMBObPByZM0P594kTgrbcAd3e9KyMicizlGibeJUfkGNu3A8OHa5fdBg4Epk4F/Pz0roqIqGjwkhwR3dO5c9ocpdatgTJlgP37gQUL2CwRUfHChklxSUlJepdgOMxEllcmKSna897q1AF+/RVYuhTYvRt4+mkdCtQBzxMZM5ExE5mqmbBhUtzAgQP1LsFwmMk/hABOnQL69fsnk/R0IDISqFULmDlTWy7gxAmgb1/AZNKx2CLG80TGTGTMRKZqJpzDpDiLxYLGjRvrXYahMBPNzp3aXKTTp4ESJSwYOrQxWrYE3ntP2xYSAnzwAVC1qt6V6oPniYyZyJiJTNVM2DARFUM3bgDVqgHJyfJr7dtrayk99VTR10VEZFRc6ZuoGPrpp7ybpTp1gI0bi74eIiKjs/scpg8//BDNmjWDl5cX/Pz80LVrV5w8edJmn7S0NISGhqJChQooW7YsunfvjsTERJt9zp8/j44dO8LT0xP+/v4YN24csrOz7V0uUbH09995b69YsWjrICJyFnZvmHbt2oW33noL+/btw88//4yMjAwEBATg9u3b1n1GjhyJ9evXY9WqVdi5cycuXryIbt26WV/Pzs5Ghw4dkJmZib1792LJkiVYvHgxJk6caO9ylbdw4UK9SzCc4pzJjRvaA3LDwu6cwK1louhczQdSnM+Tu2EmMmYiUzYT4WB//fWXMJlMYteuXUIIIVJSUoS7u7v44YcfrPscP35cmEwmsW/fPiGEEBs2bBBubm7ir7/+su4zd+5c4ePjIzIyMvL8nJSUFAFApKSkOPBonM+wYcP0LsFwimMmt28L8dlnQlSsKIS7uxAjRwqxc6cQL74oBCBE6dLDxIwZeldpLMXxPLkfZiJjJjJVM3H4pO9Tp07h8ccfx5EjR1CvXj1s27YNbdu2xbVr12wmZ9eoUQOjRo3CiBEjMGnSJKxbtw4Wi8X6+tmzZ/HII4/g4MGDaNCggfQ5nPRNJMvMBJYsAd5/X3vmW0iI9jiTatX+2Sc9HShRongtGUBEVFAOXYdJCIGRI0fi+eefR7169QAACQkJcHd3l5oaPz8/JCQkWPfxu2MZ4Zzvc/YhorvLzga+/x548klg8GDgmWeAY8e0FbpzN0uA9hw4NktERPfm0Lvkhg0bhmPHjiEmJua++wohYMrHn9r52YeouBIC2LRJW0vp4EFtiYBlywAFl0QhIipSDhthCgsLw4YNG7B9+3ZUqVLFut3f3x/p6em4fv26zf6JiYnWUSR/f39cvnwZABAVFYWQkBDr9zn79OrVC9HR0dLn1q5dG2az2eYrICBAmoRmsVhgNpulJdwnTZqEiIgIm23x8fEwm804fvy4zfbIyEiMHTvWZltqairMZrPUJOYcx53yOo7NmzfDbDZL+4aGhvI4eBx3PY5du4AXXwSCgoD4+F6YMiUaGzf+0yw5y3Hk5sy/Dx4Hj4PH4TzHka/HuThiYlRoaKh46KGHxOnTp6XX8pr0feLECWEymcT+/fuFEEJs3LhRmvQ9b9484ePjI9LT0/P8TE76zlunTp30LsFwVMtk714hAgK0ydsNGwrx449CZGcX7D1Uy8QemImMmciYiUzVTOx+SW7YsGGIiorC2rVr4enpaR0Z8vb2RqlSpeDl5YVBgwbh7bffhq+vL8qWLYvhw4fjueeeQ9OmTQEAAQEBqFevHvr164eIiAhcunQJEyZMQFhYGEqUKGHvkpUWFhamdwmGo0om+/cD4eHaQpP16gErVwJduwIuDzBurEom9sRMZMxExkxkqmZi97vkXFxc8pxntGjRIvTv3x+AtnDlmDFjEBUVhbS0NLRv3x6zZ89GpUqVrPufP38eb775JrZv3w5PT08MGDAAH374IVzu8n8D3iVHxcXevdpaShs2AHXrApMmAT16PFijRERE+cNnyRE5ASG0h+VOngxs3ao9wmTiRKBnT8DVVe/qiIjUx7+TEhlYzl1vLVsCrVoBSUnacgFHjwLBwWyWiIiKChsmxeV1J2Fx5wyZZGcDa9YAzZppSwOkpwNr12pLBXTvbv/Lb86QSVFjJjJmImMmMlUzYcOkuKioKL1LMBwjZ5KVBaxYATRqBHTpAnh4AJs3a/OWOnVy3AKTRs5EL8xExkxkzESmaiacw0RUxH77DZg1C0hMBDp2BIYM0RqhZcuAadOAEyeAdu2Af/9buxRHRET6Y8NEVIS2bwcCAoCMjH+2NWkCXL0K/PmnNor0r38BzZvrViIREeXBoY9GISJbU6faNksAEBurNVE//AA0bKhPXUREdG+cw0RUhO5Yjd8qNJTNEhGRkbFhUlxez+0p7oo6EyGAHTu0VbgvXJBfd3cHnnmmSEuS8DyRMRMZM5ExE5mqmbBhUlxAQIDeJRhOUWWSng58+602R6lVK+DkSeDDD4GHHrLd78MPgVyL3OuC54mMmciYiYyZyFTNRLlJ30FBQXBzc0NwcDCCg4P1LouKoaQkYN48YPZs4NIlIDAQGDVKm6dkMgGpqdp8pcREoEMHbdVuIiIyNuUaJt4lR3o5dgyYORP45hvt+/79gREjtAfjEhGRc+NdckSFIIS2sORnn2mPMKlcWVs/aej/tXf3wTWdeRzAv/cSIomEiOZNIkkxEiVdLLtiUq9RHULHIkooYtohSBjEdrE7GGEHGxPUYLvdWRJVRbzsKpZMpBppXrA08RIhlhBKgmgle8/+8UxS6aNS3Jvn3JPvZ+ZO5eTepz/fOTK/POc5z/kA8PBQXR0REVkL1zAZ3IkTJ1SXoDvWyOTxY2DzZuCNN8SjS27fFjNLxcViHyV7a5Z4nsiYiYyZyJiJzKiZsGEyuFWrVqkuQXdeJZObN8UMkp+fmEXq2FFsRpmTA0RHizve7BHPExkzkTETGTORGTUTrmEyuMrKSjg5OakuQ1deNBNNA7KygA0bgNRUoHlzYMoUYOZMoEMHGxbagHieyJiJjJnImInMqJmwYSL6GQ8eANu2AR9/DJw+DQQEALGxwNSpQKtWqqsjIqKGxEXfRD9x5gywcSPwj3+ILQCGDQMSE8W2AGZexCYiapTYMBFBNEaffy5mk06eFHe7zZkDxMSI9UpERNS48fdlg5s3b57qEnShuhr45BNg/Higd+95KC4Wa5Oys4EPPxQN0qRJgLMzsGsXcPUq8Kc/NZ5mieeJjJnImImMmciMmglnmAzO399fdQm6MGYMsHt3zVf+CA4G/P3F40ratQNmzQImTwaCglRWqQ7PExkzkTETGTORGTUTLvomw8vKevbDbf39xSW4iAigSZOGr4uIiOwHZ5jI0IqLxcNtn6VtW2Do0AYth4iI7BQbJjKcu3eBnTvFlgAnTgA/tx1Ir14NWxcREdkvwy36joqKQmRkJFJSUlSXogsFBQWqS2gQjx+LJmnECLGAOzYWcHERWwPcvg3MmPH0uwvg5wcsXKiqWv1pLOfJi2AmMmYiYyYyo2bCNUwGFxkZibS0NNVl2MT//gekp4umaNcuoKJCzBqNHw+MHQt4etZ9/7FjwJEjwL59kcjISIObm5q69cjI58nLYiYyZiJjJjKjZsKGyeCuXbtmqDsWNE3sur1tG7B9O3DjBvD668CECaJR6tix/jGMlok1MBMZM5ExExkzkRk1EzZMZBcuXwY++0w0SufOAR4eQFRUzb5KgMmkukIiIjIyLvom3bpwQey+/fnnQF4e0KIFMHIksGoVMHgw4OCgukIiImos2DCRrnz7rWiQdu4Ezp4VO28PGwb8/vdiCwBnZ9UVEhFRY2S4u+SorpUrV6ou4bk0DfjPf4AlS4AuXYCQEODPfwa6dgW++AIoKwNSU4Hf/c56zZLeM1GBmciYiYyZyJiJzKiZcIbJ4CorK5X+//fvB5KSgDt3xExRQgLQvDnw1VdAWpp4XbwIuLkBkZFAYqK43OboaLuaVGeiR8xExkxkzETGTGRGzYSLvslmvvgCGDWq7jEfH+D774HvvgO8vIDhw8XeSYMGiUaKiIhIjzjDRDazbJl87MYNYNo0ICYG6NkTMPOiMBER2QE2TGQ1T54AmZnAv/4FHDok9kt6lnff5WNJiIjIvvD3e4O7c+eOTce/fBlYv16sP3J3BwYMAP72N6BbN6B/f/n9zs5AWJhNS6qXrTOxR8xExkxkzETGTGRGzYQNk8FNmTLFquM9fCgWcsfGAh06iFdcnHgsyR/+AOTmAjdvAn//O5CSIu52q9G8ObB5M6B6iZm1MzECZiJjJjJmImMmMqNmwkXfBpebm4vu3bu/9OefPAGys8Vz2P79b+DECaCqCggMBN5+W7z69wdatnz25y0W8dmyMrGw28PjpUuxmlfNxIiYiYyZyJiJjJnIjJqJ4RqmoUOHomnTphg3bhzGjRunuiy7U10N5OSIJufYMdEgVVaK2/7Dw4GICGDIEDGzxMeREBFRY2G4hokzTC+mqkoszj5+XDRIGRnAgwdirVF4uJg96t8f+NWvgCZNVFdLRESkBu+SM6DiYmD+fHEJzc8PWLgQGDNGfK+8HPj6azFzlJkJZGWJGaQWLcRi7IQE0SD17MlntREREdXgom+DefJE3Km2cydw9y6Qn78VY8eKXbZDQ4HWrcW6o48/Fouv//hH0TjduwccPiye2fbb3xq7Wdq6davqEnSHmciYiYyZyJiJzKiZsGEykLt3xWaRV648fTQXgLjk1rMnsGULUFAA3L4N7NkDzJsH9OnTuHbZzs3NVV2C7jATGTORMRMZM5EZNROuYbJTDx+KxdnZ2T++6jZKdYWFictwRERE9OK4hknnNA0oKRELs2teZ86IB9ZqGuDkBHTvDowcCfz61+J2//BwsZj7aSNHqqmfiIjICHhJzsq+/16sB3rZz+bkAH/9KzB7NtCvH9CmDdC+vdhJe/VqsZ/R22+LS2tnzohF3BkZwJo1wLhxwG9+IzaNdHOrGTUFUVFiPBJSUlJUl6A7zETGTGTMRMZMZEbNhA2TlVRXi6bE3V28+vYFCguf/d7794GTJ4FPPgEWLBDNUKdOgIuLWGcUEyOex/baa8DcucC+fcC1a8B334m1SElJwJQpYhftps+YI4yKAv77XyA9HRg4MAUpKcZexP2ijPqP+VUwExkzkTETGTORGTUTrmGykqVLgcWL6x7z9xfPWbt8WSy0LigAvv0WuHVLfN9kAgICgM6dxSs4WDyD7Y03xD5I1uDl5YXS0lLrDGYQzETGTGTMRMZMZMxEZtRM7H6GqaoK2LoVmDZNfH39+quN90s7Y4tFND4nTwLbtgF/+UudUQCIWaHhw8XeRl99BXh6Ah9+CKSmAvn5YuF2URFw8KC4pDZtGtC7t2iWrNWhBwYGvvIY1qhFL2MAzORZmInMSJlYaxxmImMmMqNlUsPuG6Z33xWXsD77THzdty9w6dLLj5eSklLbDOXkiFvvk5NF0zN+PPDWW0BQkNjo0ctL3JI/YYJYS/TUKLV/2rULePRILNZOTRX7Ho0dK/ZEcnJ6fh3W0LZt21ceQy8nLjOxzRgAM3kWI2VirXGYiYyZyIyWSQ1d3yWnaRoePHjws9/PzAQOHKj5qgIAcO9eBZYtA9at+/F9FgtQUSGamnv3xMLpsjKxF9HT/y0rAy5cqIaDQwUslh8/37Qp4OsL+PgA7dqJx4T4+opXQIBYlJ2cDCQm1nyiGkAFAgPFJpIPH7743726uhoVFRUv/kEbjGOkMfRUi17G0FMtehlDT7Xw72ObMfRUi17G0FMtKsZo2bIlTM95SKqu1zDVrEsiIiIisqX61kDrumGqb4YpL0/cei9UAPADUILXX3fFW28BrVqJ2+tbtar759deAzw8bLO7dWUl8Pix2A5AD/bv349hw4apLkNXmImMmciYiYyZyJiJzF4zsesZpl9i6lSxb5FomNzg71+Or792hbe34sJ0YuzYsdixY4fqMnSFmciYiYyZyJiJjJnIjJqJ3TdMmgYcOQL8858VWLvWDSUl5WjXzviPRiEiIqKGY/cNUw3V+zARERGRcdn9tgJEREREtsaGiYiIiKgebJgMZsWKFejVqxdcXV3h6emJ9u3b48KFC6rL0pUePXrAbDZjzpw5qktR6saNG4iOjoaHhweaNm2K0NBQ5Obmqi5LGYvFgkWLFiEoKAhOTk5wdXXFsmXLVJfV4DIyMhAZGQlfX1+YzWakpaXVfm/y5MkAgMWLF8PHxwdOTk4YPHgwLr3KbsF24HmZTJo0CQsWLEC3bt3g4uICX19fTJo0CTdv3lRYse39kvOkxgcffACz2Yx1T2+QaIfYMBlMRkYGZs6ciaysLBw5cgRt2rRBREQEHj9+rLo0XcjOzkZJSQlCQ0NVl6LU/fv3ERYWhubNm+PQoUNYs2YNVq9ejdatW6suTZnExERs2rQJGzZsQEFBAaZOnYpVq1YhOTlZdWkN6tGjR3jzzTexfv166RbriIgIrFy5EsnJydi0aRNOnToFZ2dnDBkyBE+ePFFUse09L5Pw8HDk5+djyZIlyMvLw+7du1FYWIgRI0YoqrZh1Hee1NizZw9OnToFX1/fhi7R+jSDsFgsWnl5uWaxWFSXoitlZWWayWTSMjIyVJei3IMHD7ROnTppR48e1fr166fFx8erLkmZBQsWaOHh4arL0JVhw4ZpMTExdY6NGjVKi46OVlSReiaTSdu7d2+dY97e3tqaNWtqvy4vL9ccHR21HTt2NHR5Sjwrk5/Kzs7WzGazVlJS0kBVqfVzmVy/fl3z8/PTzp8/rwUEBGhJSUkKqrMew8wwmUwmuLq6PnfTqcbo/v37MJlMcHd3V12KcjNmzMDw4cMxYMAA1aUot2/fPvTs2RNjxoyBp6cnunfvji1btqguS6k+ffrg6NGjuHjxIgDg9OnTyMzMxDvvvKO4Mv24cuUKSktLMXDgwNpjrq6u6N27N06ePKmwMn2p+bnbqlUr1aUoo2kaJk6ciPnz5yM4OFh1OVah62fJ0avRNA1xcXHo27cvQkJCVJejVGpqKvLz8/HNN9+oLkUXioqKsHHjRsydOxcfffQRsrKyMGvWLDg6OmLChAmqy1MiISEBFRUV6Ny5M5o0aQKLxYLly5cjKipKdWm6UVpaCpPJBE9PzzrHPT09UVpaqqgqffnhhx+QkJCA9957Dy4uLqrLUSYxMRHNmjVDbGys6lKshg2TgU2fPh3nz59HZmam6lKUun79OuLi4nD48GE4ODioLkcXLBYLevXqhaVLlwIAQkNDce7cOWzcuLHRNkw7duzA9u3bkZqaipCQEOTn52P27Nnw8fFBdHS06vJ0TdM0zu5DPOx19OjRMJlM2LBhg+pylMnJycG6deuQl5enuhSrMswlOaorNjYWBw8exPHjx+HdyJ8Tk5OTg7KyMvTo0QMODg5wcHBAeno6kpKS0KxZM2jG2Lv1hXh7e0vT5MHBwbh27ZqiitSbP38+Fi5ciNGjR6NLly4YP3484uPjsWLFCtWl6YaXlxc0TcOtW7fqHL99+7Y069TY1DRLJSUl+PLLLxv17NKJEydQVlYGPz+/2p+5V69exZw5cxAUFKS6vJfGGSYDio2Nxd69e5Geng5/f3/V5Sg3aNAgnD17ts6x999/H8HBwUhISGiUvxmHhYWhsLCwzrHCwkK0b99eUUXqVVZWSueC2WyGxWJRVJH+BAYGwsvLC0ePHkW3bt0AiKcsZGVlYcaMGYqrU6emWSoqKsKxY8ca9d2mADBx4kQMHjy4zrGIiAhMnDhR2nLAnrBhMpjp06cjJSUFaWlpcHZ2rv1N0M3NDY6OjoqrU8PZ2Vlaw+Xs7Iw2bdoYZjHii4qPj0dYWBhWrFiBMWPGICsrC1u2bMHmzZtVl6bM8OHDsXz5cvj5+aFLly7Izc3F2rVrERMTo7q0BvXo0SNcunSpdua1qKgIp0+fhru7O/z8/BAXF4dly5ahQ4cOCAgIwKJFi9CuXTtD30b/vEx8fHwwatQo5OfnY//+/aiqqqr9uevu7m7YZQD1nSc/bRodHBzg5eWFjh07qijXOtTdoEe2YDKZNLPZLL0+/fRT1aXpSv/+/Rv1tgKapmkHDhzQunbtqrVo0UILCQnRtm7dqrokpR4+fKjFx8drAQEBmpOTk9ahQwdt8eLFWlVVlerSGtTx48ef+XNk8uTJte9ZsmSJ5u3trbVo0UKLiIjQLl68qLBi23teJsXFxdL3ar5OT09XXbrN/JLz5GmBgYF2v62AYR6+S0RERGQrXPRNREREVA82TERERET1YMNEREREVA82TERERET1YMNEREREVA82TERERET1YMNEREREVA82TERERET1YMNEREREVA82TERERET1YMNEREREVA82TERERET1+D+OYIWUD5R+6AAAAABJRU5ErkJggg=="
},
"execution_count": 1,
"metadata": {
},
"output_type": "execute_result"
},
{
"data": {
"text/html": [
""
]
},
"execution_count": 1,
"metadata": {
},
"output_type": "execute_result"
},
{
"data": {
"text/html": [
""
]
},
"execution_count": 1,
"metadata": {
},
"output_type": "execute_result"
}
],
"source": [
"reset()\n",
"var('t')\n",
"\n",
"A = matrix(QQ, 13, 4, lambda i, j: i^j)\n",
"b = matrix([[0], [8.8], [29.9], [62.0], [104.7], [159.1], [222.0], [294.5], [380.4], [471.1], [571.7], [686.8], [809.2]])\n",
"\n",
"AT=A.transpose()\n",
"A1 = AT*A\n",
"b1 = AT*b\n",
"show(A1.augment(b1).n(digits = 3))\n",
"M = A1.augment(b1).n(digits = 3).rref()\n",
"show(M)\n",
"f(t) = M[0][4] + M[1][4]*t + M[2][4]*t^2 + M[3][4]*t^3 \n",
"\n",
"show(f(t))\n",
"\n",
"P = point([(0,0), (1, 8.8), (2, 29.9), (3, 62.0), (4, 104.7), (5, 159.1), (6, 222.0), (7, 294.5), (8, 380.4), (9, 471.1), (10, 571.7), (11, 686.8), (12, 809.2)], size=20)\n",
"P += plot(f,[0,15], gridlines='true', legend_label='Least Squares Line')\n",
"show(P)\n",
"\n",
"velocity = f.diff()\n",
"\n",
"show(\"At time t = 4.5 seconds, the plane's velocity is \", velocity(4.5), \" feet per second\")\n",
"\n",
"show(A)\n",
"\n",
"P.save('plot1lab3_part7.png')"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": false
},
"source": [
"### Part 8\n",
"Write a 1-2 paragraph summary of what you learned in this lab. Make sure to include both mathematics and\n",
"coding (Sage and Latex), and be specific.\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": false
},
"source": [
"The main idea we explored was how to associate a data set to a curve using a matrix. We then translated the matrix equation $A^T A\\hat{\\beta} = A^T\\textbf{b}$ into Python code:\n",
"```\n",
"A = matrix(RDF, [[x-values and constants]])\n",
"b = matrix([[y-values]])\n",
"\n",
"A1 = A.transpose()*A # the left side of the equation\n",
"b1 = A.transpose()*b # the right side of the equation\n",
"\n",
"A1.augment(b1).rref() # the entries of the last column are the solutions to the equation\n",
"```\n",
"\n",
"We also learned about several new utility functions for this lab. First, we learned that defining a symbolic function is just like defining a normal python function. We explored plotted functions and data points with the `plot()` function. We also learned about Pythons anonymous lambda functions which we used to generate the large Matrix in part 7 with the command\n",
"```\n",
"matrix(QQ, 13, 4, lambda i, j: i^j)\n",
"```"
]
},
{
"cell_type": "code",
"execution_count": 0,
"metadata": {
"collapsed": false
},
"outputs": [
],
"source": [
]
}
],
"metadata": {
"kernelspec": {
"display_name": "SageMath (stable)",
"name": "sagemath"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.14"
}
},
"nbformat": 4,
"nbformat_minor": 0
}