{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "dirty-training",
   "metadata": {},
   "source": [
    "# Our First Jupyter Notebook!"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "designing-capture",
   "metadata": {},
   "source": [
    "**Goals**\n",
    "* get Jupyter Lab installed and running\n",
    "* learn how to use the Jupyter notebook interface\n",
    "* learn some basic *Markdown* formatting commands\n",
    "\n",
    "See https://jupyterlab.readthedocs.io/en/latest/user/interface.html for more info.\n",
    "\n",
    "Or just click on [this link](https://jupyterlab.readthedocs.io/en/latest/user/interface.html).\n",
    "\n",
    "To start Jupyter Lab:\n",
    "1. open a Terminal or Command window\n",
    "2. `conda activate ai`\n",
    "3. `jupyter lab`"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "several-keeping",
   "metadata": {},
   "source": [
    "Here is a table of chess abbreviations:\n",
    "\n",
    "Piece|White|Black\n",
    "-|-|-\n",
    "Pawn   | P | p\n",
    "Rook   | R | r\n",
    "Knight | N | n\n",
    "Bishop | B | b\n",
    "Queen  | Q | q\n",
    "King   | K | k\n",
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a3f02f74-6e75-42ca-b0d8-53774f01609e",
   "metadata": {},
   "source": [
    "**Math Formulas**\n",
    "\n",
    "$V = \\frac{4}{3}\\pi r^3$\n",
    "\n",
    "$x = \\dfrac{-b \\pm \\sqrt{b^2 - 4ac}}{2a}$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d6aa668e-9e96-471e-a7fb-0d202d5a2917",
   "metadata": {},
   "source": [
    "**Python Code**\n",
    "\n",
    "```python\n",
    "# computes the volume of a sphere\n",
    "def sphere(r):\n",
    "    V = 4/3 * math.pi * r**3\n",
    "    return V\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "blank-paintball",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "external-petite",
   "metadata": {
    "tags": []
   },
   "source": [
    "### Basic Plotting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "arranged-lease",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# x values default to 0, 1, 2, 3, 4\n",
    "plt.plot([1, 4, 9, 16, 25]);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "sexual-administrator",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# explicitly use x values 10, 20, 30, 40, 50\n",
    "plt.plot([10, 20, 30, 40, 50], [1, 4, 9, 16, 25]);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "agreed-leonard",
   "metadata": {},
   "source": [
    "### An Example of Plotting Mathematical Functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "minus-forwarding",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# two ways to create an array of x values\n",
    "x = np.arange(0, 10, 0.2)    # interval size 0.2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "multiple-interference",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0. , 0.2, 0.4, 0.6, 0.8, 1. , 1.2, 1.4, 1.6, 1.8, 2. , 2.2, 2.4,\n",
       "       2.6, 2.8, 3. , 3.2, 3.4, 3.6, 3.8, 4. , 4.2, 4.4, 4.6, 4.8, 5. ,\n",
       "       5.2, 5.4, 5.6, 5.8, 6. , 6.2, 6.4, 6.6, 6.8, 7. , 7.2, 7.4, 7.6,\n",
       "       7.8, 8. , 8.2, 8.4, 8.6, 8.8, 9. , 9.2, 9.4, 9.6, 9.8])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "gorgeous-jacket",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# 100 equally-spaced data points\n",
    "x = np.linspace(0, 10, 100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "micro-immunology",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.        ,  0.1010101 ,  0.2020202 ,  0.3030303 ,  0.4040404 ,\n",
       "        0.50505051,  0.60606061,  0.70707071,  0.80808081,  0.90909091,\n",
       "        1.01010101,  1.11111111,  1.21212121,  1.31313131,  1.41414141,\n",
       "        1.51515152,  1.61616162,  1.71717172,  1.81818182,  1.91919192,\n",
       "        2.02020202,  2.12121212,  2.22222222,  2.32323232,  2.42424242,\n",
       "        2.52525253,  2.62626263,  2.72727273,  2.82828283,  2.92929293,\n",
       "        3.03030303,  3.13131313,  3.23232323,  3.33333333,  3.43434343,\n",
       "        3.53535354,  3.63636364,  3.73737374,  3.83838384,  3.93939394,\n",
       "        4.04040404,  4.14141414,  4.24242424,  4.34343434,  4.44444444,\n",
       "        4.54545455,  4.64646465,  4.74747475,  4.84848485,  4.94949495,\n",
       "        5.05050505,  5.15151515,  5.25252525,  5.35353535,  5.45454545,\n",
       "        5.55555556,  5.65656566,  5.75757576,  5.85858586,  5.95959596,\n",
       "        6.06060606,  6.16161616,  6.26262626,  6.36363636,  6.46464646,\n",
       "        6.56565657,  6.66666667,  6.76767677,  6.86868687,  6.96969697,\n",
       "        7.07070707,  7.17171717,  7.27272727,  7.37373737,  7.47474747,\n",
       "        7.57575758,  7.67676768,  7.77777778,  7.87878788,  7.97979798,\n",
       "        8.08080808,  8.18181818,  8.28282828,  8.38383838,  8.48484848,\n",
       "        8.58585859,  8.68686869,  8.78787879,  8.88888889,  8.98989899,\n",
       "        9.09090909,  9.19191919,  9.29292929,  9.39393939,  9.49494949,\n",
       "        9.5959596 ,  9.6969697 ,  9.7979798 ,  9.8989899 , 10.        ])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "interpreted-opinion",
   "metadata": {},
   "source": [
    "#### Plotting the functions $x^2$ and $x^3$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "suffering-collaboration",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, x**2, 'r-');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "charming-trader",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot x**2 and x**3 on the same graph\n",
    "x = np.arange(0, 10, 0.2)\n",
    "plt.plot(x, x**2, 'r--')  # red dashed line\n",
    "plt.plot(x, x**3, 'bo')   # blue circles\n",
    "plt.xlim(0, 10)   # x-axis min and max\n",
    "plt.ylim(0, 500);  # y-axis min and max"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "significant-tribute",
   "metadata": {},
   "source": [
    "### Plotting the function $f(x) = x + |\\sin 8x|$, where $0 \\le x \\le \\pi$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "interstate-vertical",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(0, np.pi, 1000)\n",
    "plt.plot(x, x+np.abs(np.sin(8*x)), 'm-');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "35a7dfdc-74ea-41c9-a475-70c48c235aa3",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "data = np.loadtxt(\"sample_data.txt\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "a48ffa73-2301-4b95-afac-976a05a19dbd",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.,  1.,  2.,  3.,  4.,  5.,  6.,  7.,  8.,  9., 10., 11., 12.,\n",
       "       13., 14., 15., 16., 17., 18., 19., 20., 21., 22., 23., 24., 25.,\n",
       "       26., 27., 28., 29., 30., 31., 32., 33., 34., 35., 36., 37., 38.,\n",
       "       39., 40., 41., 42., 43., 44., 45., 46., 47., 48., 49., 50., 51.,\n",
       "       52., 53., 54., 55., 56., 57., 58., 59., 60., 61., 62., 63., 64.,\n",
       "       65., 66., 67., 68., 69., 70., 71., 72., 73., 74., 75., 76., 77.,\n",
       "       78., 79., 80., 81., 82., 83., 84., 85., 86., 87., 88., 89., 90.,\n",
       "       91., 92., 93.])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# the first column (generation number)\n",
    "data[:,0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "b3622c03-6d66-44bd-b7b8-70b7aba72db8",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 9.7 , 10.34, 10.96, 11.3 , 12.03, 12.94, 13.18, 13.72, 13.81,\n",
       "       14.1 , 14.35, 14.77, 14.79, 14.74, 14.61, 14.76, 14.78, 14.81,\n",
       "       14.8 , 14.81, 14.84, 14.81, 14.87, 15.06, 15.13, 15.32, 15.4 ,\n",
       "       15.4 , 15.37, 15.3 , 15.21, 15.15, 15.06, 14.85, 14.91, 14.98,\n",
       "       15.08, 15.29, 15.31, 15.31, 15.43, 15.56, 15.66, 15.84, 15.93,\n",
       "       15.87, 16.13, 16.16, 16.57, 16.4 , 16.72, 16.76, 16.78, 16.84,\n",
       "       16.92, 16.91, 17.03, 17.15, 17.39, 17.47, 17.62, 17.68, 17.73,\n",
       "       17.81, 17.74, 17.75, 17.77, 17.79, 17.78, 17.64, 17.59, 17.57,\n",
       "       17.63, 17.65, 17.69, 17.68, 17.66, 17.72, 17.7 , 17.77, 17.74,\n",
       "       17.79, 17.73, 17.79, 17.84, 17.82, 17.93, 18.  , 17.95, 18.01,\n",
       "       18.08, 18.02, 18.  , 18.11])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# the second column (average fitness)\n",
    "data[:,1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "9f3633f5-ced8-4c46-8acc-fe2877d73690",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([16., 16., 16., 16., 16., 16., 16., 16., 16., 16., 17., 17., 17.,\n",
       "       17., 16., 16., 16., 16., 18., 18., 18., 18., 18., 18., 18., 18.,\n",
       "       18., 18., 18., 18., 18., 18., 18., 18., 18., 18., 18., 19., 18.,\n",
       "       18., 18., 18., 18., 18., 18., 18., 18., 18., 18., 18., 18., 18.,\n",
       "       18., 18., 18., 18., 18., 18., 18., 18., 18., 18., 18., 18., 18.,\n",
       "       18., 19., 19., 19., 19., 19., 19., 19., 19., 19., 19., 19., 19.,\n",
       "       19., 19., 19., 19., 19., 19., 19., 19., 19., 19., 19., 19., 19.,\n",
       "       19., 19., 20.])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# the third column (best fitness)\n",
    "data[:,2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "formal-bookmark",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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xBywaWwAA9HT0MMBtAADeRUdVe3qqAYlEouZqiNSLoYlIy1V2q3iAG8c10fNxPBPREwxNRFqsRFqCfdf2ASj/peff0h8AkHArAVkFWXVeG2m+1IepSMxKhJ6OHl52fVnd5RCpHUMTkRY7dvMY8kryYGNsg852nRX2NTdrjvY27SFAwN5re9VTIGm0slamHo49YN7YXM3VEKkfQxORFiv70vN384eOpPx/7vIuOo5rogrIu3bd2DVHlRME4MwZ8U9tx9BEpMWeNx5FPl9TcgxkgqzO6iLNVyItQey1WAAcz6Tt7t4FNm8GPv4Y+OMP4OZN5QLQgwfA118DnToBXl7A0aO1X6u66am7AGqYBEHAnUd38Fj2WN2laK2swiyczzwPCSQY6DawwmN6OfWCcSNjZOZnYt+1fWjVtFUdV0ma6sTtE8gvzYediV25rl3STIIA3L8PWFoCurqVH3PzJhAfDxw8CMTFAVeulD/O3h7w9ga6dAHs7MRrNm0q/nnvHvDTT8CWLUBxsXh848bA5ctAr1619vY0AkMTqcV7e9/DF/FfqLuMBqFbs26wMrKqcJ+BngFedn0ZO/7dAf9f/Ou4MqoP/N38OdWAhhIEIClJDD5lAejOHcDQEGjfHujQQVxcXYF//gESEoATJ4CMCh452bGjeOw//wAXLwLp6cCff4pLVTp1AiZPBl57DWjSpDbepWZhaCK1KOs20tfVr3CsDamGga4B3vV+t8pjpnabimM3jyG/NL+OqqL6wszADJO7TFZ3GfSMq1eBH38EfvsNuH27/P7CQuDkSXGpiK6uGJJeegno2xfo3VtsRSpTUCCOUTpxQgxQDx48WbKyxLA2bBgwaZLYEtWQMrVEEBrC0K3qyc3Nhbm5OXJycmBmZqbucrSOTJDBeIkxih4XIfmdZLhZuqm7JCIitSvrOrt6FdDXV+wSEwRx3NEPPwBHjjw5x8AA6N4d6NNHDEDduolB6uJFcblwAbh+HWjVCvDxEbvcPD0BIyN1vcvaVdvf32xpojp359EdFD0ugp6OHpwtnNVdDlGDUFICHDsGxMSIrQht24pftC+9pNjKUJXSUuDhw/ItD/n54pe3oeGTxdYW6NxZ+1ohiovF96SvX/H+vDyxi+vKFfH36uMD2NiUP660VAw1J08C588/CTk5ORVfVyJ5MjhbRwd45RVg4kTA318cT/S0Vq3EZcSImr9PqhhDE9W55AfJAAAXCxfo6fCvIFFtKCgQB+aePi0GpdhY4NGjJ/v37gVWrBB/7tgR8PUVu20KCsTuncJCMQyVhaSsLMXzleHjAyxcKH6xa3J4KmvhKSgQW3WaNAEaNRL35eeLYbNszNCJE2LgsbUFmjUTFwcHIDNTDD3XrpW/88zFRWzh8fISxxMlJIjBtaiofC16eoC7u3iNsmD6+LG43qKFGJRCQ8XXpbqn1m+sQ4cOYdmyZTh9+jTS09OxdetWBAUFyfdXNvhw6dKleO+99yrct3DhQixatEhhW6tWrXD16lWV1U0vpiw0tbRsqeZKiLRDVtaTMSwXLohLcjIge2YWCWtrICBA7M65dEkMApcvPzlHWRYWil1HJiZiC8zTgevqVTEcBAaKgWHBAvFnVYanwkIxpCQlie83OVlsqXm6xcvICDA1Fet8eklPFwPQiRNinXfvKl7bzEx8n3fuiKHlWZmZ4nLmTPl9dnZiS156uvh7uH5dXDZtUjzO3PxJd1nZQOzWrRVbsQRBbL3KzRXvaNPhEFC1Umtoys/PR6dOnTBhwgQMGzas3P709HSF9d27d2PixIkYPnx4lddt164d9u3bJ1/X02NrhiaRh6YmDE1ENZGbC/z8s9gCkpAApKRUfJyVlfhl3K+fGJa6dCn/pXv3LnDoEHD2rNjK8WzgeDpoNG0qBonKbmd/WkYGsGwZsGaNGExeeUWspWfPJwGhfXsxOFQmK+tJsElOLt8tmKXCp//o6YnhLztbXM/NFRcAcHQUxwv17St2aZqaiuOGbt0S/7xzR/z9lL0va+sn183JEVv7EhLE37GNzZOxRe7uzw9BEon4eqamqnuvVHNqTROBgYEIDAysdL+dnZ3C+p9//ol+/fqhRYsWVV5XT0+v3LmkOdjSRFQzRUViCPnkk/KBwd39SatFhw7iF7it7fNbdmxsxLEvqh7/YmcHfPEFMHs28PnnwDffVNyiZW8vhruyVitLS7HFqqow+DRzc/G9u7sDLVuK5xcVKbZ6PXr0JGiV/VnWyvP04OjGjQGpVAxOZeHMxkbsXnv292hjI56jTH0vvywuVP/VmyaYzMxM7Nq1C+vWrXvusUlJSXBwcEDjxo3h6+uLyMhIODk51UGVpAyGJqLqkUrFlqUFC4C0NHFbq1ZASIj4pd+1qxgWNJGtrdjiNHs28Pffind13b4tdmE906mgwMNDDDUdOpQPV2WTLqqyy09XV3wNZQfHU8NSb0LTunXrYGpqWmE33tN8fHwQHR2NVq1aIT09HYsWLULv3r1x6dIlmFbSvllcXIzismlNId6ySLVDEASGJiIlSKVit1RMDLBxI5CYKG5v1gxYtEgcDFyfRh5YWwOvv6647cEDIDVVsdvtwQMxBHXtqtlhkBqmevOf3E8//YSQkBA0fvbeymc83d3XsWNH+Pj4wNnZGZs2bcLEiRMrPCcyMrLc4HGqHZn5mcgvzYeORAeuTVzVXQ6RRpHJxIC0fTuwZ48YIMpYWgIffABMnSqON9IGZS1GRPVFvQhNhw8fRmJiIjZu3Fjtcy0sLODh4YHk5ORKj4mIiEB4eLh8PTc3F46OjjWqlaqWlJUEAHA2d4a+biUTnRA1QPn5YkvMtm1PtllYAAMGiIO4hw+vetA0EdW+ehGafvzxR3h5eaFTp07VPjcvLw8pKSl44403Kj3GwMAABgYGL1IiKYldc0Tl3bkDvPqqeJeVvj4QHg785z/ieKX61AVHpO3UOuNDXl4ezp07h3PnzgEAUlNTce7cOaSVjXSE2OqzefNmTJo0qcJr9O/fH6tWrZKvz5o1CwcPHsT169dx7NgxDB06FLq6uggODq7V90LKYWgiUnT+vBiOTp8WBzrHxgKRkeKt+QxMRJpFrf9Jnjp1Cv369ZOvl3WRhYaGIjo6GgCwYcMGCIJQaehJSUnB/fv35eu3bt1CcHAwsrKyYG1tjV69euH48eOwfnriDFKb5IcMTURldu0CxowRJy9s3RrYuRNw46MYiTQWH9hbAT6wt/Z4feeFM+ln8OeYP/Fqq1fVXQ5RnZNKgd27gZUrxcHegDiHz++/i4/vIKKa4wN7SWtwugFqyLKzgZ9+AlavFh/9AYi31r/1lvgMuLJnnRGR5mJo0lKFpYVYdWIVsouya3S+USMjvNn1TVgZWamspvsF95FbnAsJJGjRpOpZ3Ym0xT//iK1KP/8szlINiHfFTZokTh/gypk3iOoNhiYttfbUWszeN/uFrpGRl4GVg1aqqKIng8CbmzVHY72q59siqi8ePRKnCzAyEudPatRI7ILbvl0MSwcOPDm2QwfgnXfEmbyNjNRXMxHVDEOTltqVtAsA4O/mj9ZWrat1bnpeOjb9swm7knbha+FrSFT0jAJ2zZE2kMnEB6/u3i3O1h0fL24ro6sr3vVW9pABHR1g6FAxLL30kmof+UFEdYuhSQvlleThcNphAMCKgBVoZdWq2udvvbIVqdmpSHqQBI+mHiqpi6GJ6qOiInFagIQEcdm3D7h7t/LjpVJxadoUmDwZePttgI++JNIODE1aKO56HEqkJXCxcKlR4DHRN0Fv597Yn7ofMckxqgtN/z/dgLulu0quR/SiBAHIyACSk8WHxj54AGRlPfnzn3/EwFRaqnieiQng5yfO1B0QIIai4mKgsFBciorEZ8Rxzlwi7cLQpIVikmMAAAFuATXuWgtwC5CHpnd93lVJXWxpIk3wyy/io0qSk8UlP//551hZiRNQensDvXuLE0/qP/MUoMaNxYXTBhBpL4YmLSQPTS0DanyNgJYBmL1vNuKux6GwtBCGjV78CaFlz51jaCJ1WbNGvGPtaTo6gIsL0Ly52KVW9hBZS0txu4+P+CfHIhERQ5OWSX6QjJSHKWik0wgvu75c4+u0t2mPZqbNcPvRbRxOO4yBbgNfqK4HhQ/wsOghAHC6AVKL7duBadPEn99+W3y2W8uWYiB6ttWIiKgian32HKleWStTL6deMDUwrfF1JBKJvKWq7JovoqxrzsHUAcb6xi98PaKnyWTA668DXl7iXW3POnFCfFyJTCbOj7R6NTBoEODhwcBERMpjaNIyu5PFb4wX6ZorU3aNsmu+CI5notr09dfAr78CZ86IYWjoUODGDXFfSorYqlRYCAQGAt98w642IqoZhiYtUvS4CAdSxZn0VBGa/Fr4QVeii6v3r+J69vUXupY8NDVhaCLVunwZmDNH/DkgQJwjads2oE0bYNEiMSjduwd06QJs2sTHlRBRzTE0aZHDNw6j8HEh7E3s0cGmwwtfz6KxBbo37w4A+Dv57xe6FluaqDaUlgJjx4q3+wcGAn/9BZw7B/TpI7YsLVwIJCWJ45Z27RKnCiAiqimGJi3y9F1zqprFWz6uKeXFxjUxNFFt+OQT4PRp8Tb/H34Qu93atRMfXfLrr4CdHWBrK45zsrNTd7VEVN8xNGmRsmCjiq65MmXXir0WixJpSY2vw9BEqnbyJPDxx+LPa9YADg5P9kkkwGuvAbduAampQOvqPUmIiKhCDE1aIi0nDZfvXYaORAcDWgxQ2XW72HeBtZE1HpU8QvzN+BpdI6coB/cK7gFgaCLVKCwE3nhDfFzJmDHA6NEVH6erKz5El4hIFThPk5YoG3PUvXl3NDFU3ZTEOhId+Lf0xy8XfkFMcgz6uPSp9jVSHqYAAGyNbV9oGgRqmIqKgOPHxVaj27fF5fRpIDERsLcXpw8gIqoLDE1aQt4156a6rrkyAW4BYmhKiUGkX2S1z2fXHNXUtWuAv7/4uJNnSSTAjz+KM3cTEdUFhiYtUCotxb5r+wCodjxTmYFuAyGBBOcyziH9UTrsTe2rdT4fn0I1cfEiMHCg+EBdKyugQwfxIbjNmomPPOnZE/D0VHeVRNSQMDRVwXWFK3Qaa/6wL6lMitziXFgZWcHLwUvl17c2toaXgxdO3TmF1qtbQ1+3elMo55XkAWBoIuUdOwa88gqQnS2Gpb//FrviiIjUiaGpCg8KHgAydVehvDHtxkBHUjshL6RDCE7dOYXc4twanS+BBH2cqz8eirSPIACXLgFbtoizdXfqBHh7i5NPGhuLcy2NGCEO9u7ZE9ixQ5xSgIhI3SSCIAjqLkLT5ObmwtzcHAkpCTAxrR+z4enp6KGlZctaC02CIOB69nUUPi6s0fmWhpawM+FEOQ2VIAAJCWJQKgtLz9LVFedYunwZePxYnKzy998BI6O6r5eI6qey7++cnByYmZmp/PpsaapCa6vWtfJLr48kEglcm7iquwyqhy5dAiZPFu+AK9O4sTheqUsX4Px5MVDduQNcuCDuf+01IDqajzwhIs3C0EREtaKoCFiyBIiMFFuOjIyAIUOAYcPEZ8Q9+0iT27fF8FRUJM69pKP5wwmJqIFhaCIilTt8WGxdSkwU1199VZxPqXnzys9p1kwMVEREmoqhiYhUIj8f2L5dfObbrl3iNjs7YOVKYPhwcV4lIqL6jKGJiGpMKgX27BGD0rZtYnAqM2kSsHQp73wjIu3B0ERE1VZYKA7U/vxzcdbuMi1aiIO4Q0L4kFwi0j4MTUSktKws4JtvxC63e+IzmGFpCQQHi0Gpe3d2wxGR9mJoInpGcTFw9Kh4C/yzTEzEwczNmgE2NuLcQg3B5cvAqlXAunVAQYG4zcUFmDULGD+ecykRUcPA0EQEIDUV2L1bXPbvfxIMqqKnJz7ao21boG9fcfHy0p65haRScTbuVauA2Ngn2z09gdmzxVm79fgvCBE1IPwnjxq0f/4Rb42Pj1fcbm8PtG+v2NUkCEBODnDrlvgQ2cePgZs3xeXvv8VjjI3FR38MHAgMHSqO8dEkjx4BGzaIrWgPHojdbQ8eiM94e/bZALduiQsgzpk0ZAjwzjtiOGQXHBE1RHyMSgVqexp2Ur/Hj4EvvgDmzwdKSsRutp49xUd3BASIz0OrKhg8fgxkZgJpacDJk0BcHHDokBhCnta5sxiehg0THxGizrBx9iwwahSQnKz8OZaWYqh8+23A2bn2aiMiUoXa/v5Wa2g6dOgQli1bhtOnTyM9PR1bt25FUFCQfP+4ceOwbt06hXP8/f0RExNT5XVXr16NZcuWISMjA506dcLKlSvh7e2tdF0MTdotMREIDRVnnwaA//wH+PZbwMHhxa4rk4ktV/v3i/MVHTwodnGVsbcHfHzEh9P6+ABduwJ18ddLEIA1a4CZM8WA2Lw58MorYiAqWywsyo/PMjAA+vQBDA1rv0YiIlXQ6mfP5efno1OnTpgwYQKGVTIVcEBAAKKiouTrBgYGVV5z48aNCA8Px9q1a+Hj44Ply5fD398fiYmJsLGxUWn9VH8UForPPtuzB1i+XHxUh7k5sGIFMHasalqAdHSADh3EZfp0sdVpxw7xAbV79gDp6eJcRtu2icdLJEC3bmIr1NChgIfHi9fwrJwccb6k338X1wcPBqKigKZNVf9aRETaTmO65yQSSYUtTdnZ2dhW9i2jBB8fH3Tr1g2rVq0CAMhkMjg6OuKdd97BnDlzlLoGW5q0w6VLwKZNYovP8eNiK0sZf3/ghx+qfqyHKhUUAGfOiK1bJ06Iy/Xrise0aycGqEmTACenF3u9+/fFoLR0qTjIvVEj4LPPgBkzOB6JiLSXVrc0KSMuLg42NjZo0qQJXn75ZXz88cdoWsn/JpeUlOD06dOIiIiQb9PR0YGfnx/inx3pS1qrpARYvFh8UOyz3WN9+4oDmkeNqtvwYGQE9OolLmXu3HnSErV/v9i1988/YuvXjz+Kd6dVR0HBk8eYxMSI464AcWqAjRvFbkEiIqo5jQ5NAQEBGDZsGFxdXZGSkoIPPvgAgYGBiI+Ph24FE+Tcv38fUqkUtra2CtttbW1x9erVSl+nuLgYxcXF8vXc3FzVvQmqU+fPi+OVzp8X1195RQxJffsCLVtqViuLgwPw5pvi8vCh+Ly2VavE1qiRI4GpU8XB6o0bV3x+aSlw6pQ4CD0uDjhyRHGqBE9PcXbuyZPFrkgiInoxGh2axowZI/+5Q4cO6NixI9zc3BAXF4f+/fur7HUiIyOxaNEilV2P6l5pKfDpp8BHH4ktLE2bioOfR45Ud2XKadIEeP11YPRo8Y6+Tz8VZ94+dkzsYnR3B+7eFbv1EhLE7sZjx8rPJ+Xq+uQxJm3aqOe9EBFpK40OTc9q0aIFrKyskJycXGFosrKygq6uLjIzMxW2Z2Zmws7OrtLrRkREIDw8XL6em5sLR0dH1RVOSistFedAunULuH1bXPLzxVaZZs2eLI8fi7f6l4WIEyfEcTyAOKh6zRrgmQbHeqFRI7FbsU8f4I03gHPngC5dxBB440b5462sgJdeElvS+vQRB6FrUmsaEZE2qVeh6datW8jKyoK9vX2F+/X19eHl5YXY2Fj5gHKZTIbY2FhMmzat0usaGBg89648bXHqFJCS8mRSwwcPxAkPXV2Bjh3FxdFR+S/ejAzxGWRPX+/evSeBp2zJyhJvYTc0FMf3GBqKAaGwUHEpKCg/yaKyLC2Br78WW1rqe3AICBAD02uvifM/5eWJ76lNmyfTFvTqJc5GrqOj7mqJiBoGtYamvLw8JD81015qairOnTsHS0tLWFpaYtGiRRg+fDjs7OyQkpKC2bNno2XLlvD395ef079/fwwdOlQeisLDwxEaGoquXbvC29sby5cvR35+PsaPH1/n70/TfPop8NQY+UqZm4vh6Y03xKWiMTUJCeK1DhxQ/vWLiwFlhos1aqTYsmRsLA6aLgtg2dnice7uivMedeokBjNt0ayZ+PiSPXvEz8DLi2OTiIjUSa2h6dSpU+jXr598vayLLDQ0FGvWrMGFCxewbt06ZGdnw8HBAQMHDsTixYsVWoVSUlJwv6xfBsDo0aNx7949zJ8/HxkZGejcuTNiYmLKDQ5vaM6fF8fKAECPHoCd3ZOJDY2MgH//BS5eBK5cEef2OXxYXObPF+cceustcQLEK1eADz8Etm4Vr6WjI3YRPT1RoqXlk8BT9nBbKyvxrranW5RKS8UWp6cXU1Px2KpaT/Lzxe65hhAg9PSAQYPUXQUREQEaNE+TJtG2eZpKSsSWmHPnxPE+f/xRefdVSYk4Y3bZJJBlzx4zMQF69xafsSaTiaEmNBRYuPDF5xQiIiJShdr+/uZoiAZgyRIxMJXdUVbVeB99fXEw8X//C1y7Bvzvf+KDa/PygN27xcA0dKjYKvXTTwxMRETUcLClqQLa1NJ05ozYyvT4sTjB4ahR1b+GIIiTJR45Ij6Go3t31ddJRET0ohr8jOBUcyUlwLhxYmAaMaJmgQkQW6YCA8WFiIiooWL3nBZbvFjsRrO2FidKJCIioppjaNJS+/aJkyQC4jgma2v11kNERFTfMTRpofXrxdvUpVIgOBgYPlzdFREREdV/DE1aRBCApUvF546VlopjmH76Sd1VERERaQeGJi0hlYqTUL7/vrg+cybw228Vz+ZNRERE1ce757RAUZHYurRli7j+5ZdiaCIiIiLVYWiq50pKxOkEdu0SJ6b8+eeaTy1ARERElWNoqsdKS4HRo8XAZGgI7NwJvPyyuqsiIiLSThzTVE89fgy8/jqwbRtgYABs387AREREVJsYmuohqRQYPx7YtAlo1Egcy+Tnp+6qiIiItBtDUz3z8CEweTLwyy+Anp4YnAYNUndVRERE2o9jmuqB9HTgzz/FFqUDB8SuOR0dcRLLoCB1V0dERNQwMDRpsAcPgNdeA/bsESeuLNO+PfDRR8DQoeqrjYiIqKFhaNJgixcDf/8t/uzjI4akoUMBDw/11kVERNQQMTRpqLQ04JtvxJ937eK4JSIiInXjQHANtXixOHFl375AYKC6qyEiIiKGJg2UlARERYk/f/IJIJGotx4iIiJiaNJICxaIczG98grQo4e6qyEiIiKAoUnjXLgAbNgg/vzxx+qthYiIiJ5gaNIw8+aJ0wuMGgV07qzuaoiIiKgMQ5MGOX5cfIacjo44DxMRERFpDoYmDTJ3rvjnuHFAq1ZqLYWIiIiewdCkAWQy4MMPgdhY8QG88+eruyIiIiJ6Fie3VLPCQmDsWOD338X1Tz4BnJ3VWxMRERGVx9CkRhkZwJAhwIkTYgvT998DoaHqroqIiIgqwtCkJpcuifMwpaUBlpbAli1Anz7qroqIiIgqw9CkBunpQK9eQE4O4O4uPlvO3V3dVREREVFVGJrUYPNmMTC1awccOiS2NBEREZFm491zavDnn+KfEyYwMBEREdUXDE117OFD4OBB8echQ9RbCxERESlPraHp0KFDGDx4MBwcHCCRSLBt2zb5vtLSUrz//vvo0KEDjI2N4eDggLFjx+LOnTtVXnPhwoWQSCQKS+vWrWv5nSjvr7/Eh/G2awe4uam7GiIiIlKWWkNTfn4+OnXqhNWrV5fbV1BQgDNnzmDevHk4c+YMtmzZgsTERLz66qvPvW67du2Qnp4uX44cOVIb5ddIWS5kKxMREVH9otaB4IGBgQgMDKxwn7m5Ofbu3auwbdWqVfD29kZaWhqcnJwqva6enh7s7OxUWqsqFBcDMTHiz0FBai2FiIiIqqlejWnKycmBRCKBhYVFlcclJSXBwcEBLVq0QEhICNLS0uqmwOfYvx/IywMcHAAvL3VXQ0RERNVRb6YcKCoqwvvvv4/g4GCYmZlVepyPjw+io6PRqlUrpKenY9GiRejduzcuXboEU1PTCs8pLi5GcXGxfD03N1fl9QNPuuZefRXQqVdxlYiIiOpFaCotLcWoUaMgCALWrFlT5bFPd/d17NgRPj4+cHZ2xqZNmzBx4sQKz4mMjMSiRYtUWvOzZDJg+3bxZ3bNERER1T8a395RFphu3LiBvXv3VtnKVBELCwt4eHggOTm50mMiIiKQk5MjX27evPmiZZdz8qT4rDlTU6BvX5VfnoiIiGqZRoemssCUlJSEffv2oWnTptW+Rl5eHlJSUmBvb1/pMQYGBjAzM1NYVK1sQsvAQMDAQOWXJyIiolqm1tCUl5eHc+fO4dy5cwCA1NRUnDt3DmlpaSgtLcWIESNw6tQp/Prrr5BKpcjIyEBGRgZKSkrk1+jfvz9WrVolX581axYOHjyI69ev49ixYxg6dCh0dXURHBxc129PQdl4JnbNERER1U9qHdN06tQp9OvXT74eHh4OAAgNDcXChQux/f8HAXXu3FnhvAMHDqDv//dxpaSk4P79+/J9t27dQnBwMLKysmBtbY1evXrh+PHjsLa2rt03U4WkJODKFUBPT2xpIiIiovpHraGpb9++EASh0v1V7Stz/fp1hfUNGza8aFkqV9Y117cv8JzZEoiIiEhDafSYJm1RFprYNUdERFR/MTTVssxM4OhR8WclngBDREREGoqhqZb98gsgCIC3N+DoqO5qiIiIqKYYmmqRIAA//ij+PGGCemshIiKiF8PQVIsSEsS75gwNgTFj1F0NERERvQiGplpU1so0ciRgbq7eWoiIiOjFMDTVkrw8oGz2g0oeeUdERET1CENTLdm8WQxOLVsCvXuruxoiIiJ6USoJTVKpFOfOncPDhw9VcTmt8PQAcIlEvbUQERHRi6tRaJoxYwZ+/P9UIJVK0adPH3Tp0gWOjo6Ii4tTZX310tWr4txMOjpAaKi6qyEiIiJVqFFo+v3339GpUycAwI4dO5CamoqrV69i5syZ+PDDD1VaYH0UFSX+OWgQ4OCg3lqIiIhINWoUmu7fvw87OzsAwF9//YWRI0fCw8MDEyZMwMWLF1VaYH1TWgqsWyf+zAHgRERE2qNGocnW1haXL1+GVCpFTEwMBgwYAAAoKCiArq6uSgusb/76S3x0io0N8Mor6q6GiIiIVEWvJieNHz8eo0aNgr29PSQSCfz8/AAACQkJaN26tUoLrG/KBoCPHQs0aqTeWoiIiEh1ahSaFi5ciPbt2+PmzZsYOXIkDAwMAAC6urqYM2eOSgusT06dEluaAHbNERERaRuJIAiCKi6UnZ0NCwsLVVxK7XJzc2Fubo6cnByYmZkpdc7t2+JDee/cAYKCgK1ba7dGIiIiUlST7+/qqNGYps8++wwbN26Ur48aNQpNmzZF8+bNceHCBZUVV18UFopB6c4doG3bJwPBiYiISHvUKDStXbsWjo6OAIC9e/di79692L17NwICAjBr1iyVFqjpBEGcwPLUKcDSEti+HaiFcEtERERqVqMxTRkZGfLQtHPnTowaNQoDBw6Ei4sLfHx8VFqgpluyRHzGnJ4e8McfgJubuisiIiKi2lCjlqYmTZrg5s2bAICYmBj53XOCIEAqlaquOg23ZQswd6748+rVQN++ai2HiIiIalGNWpqGDRuG1157De7u7sjKykJgYCAA4OzZs2jZsqVKC9RUd++K0woAwDvvAFOmqLceIiIiql01Ck1fffUVXFxccPPmTSxduhQmJiYAgPT0dEydOlWlBWqq1auB/HygSxfgyy/VXQ0RERHVNpVNOaBNnnfLYkEB4OQEZGUBmzYBI0eqoUgiIiJSoJFTDgDAzz//jF69esHBwQE3btwAACxfvhx//vmnyorTVNHRYmBydQWGDVN3NURERFQXahSa1qxZg/DwcAQGBiI7O1s++NvCwgLLly9XZX0aRyp90h0XHg408EftERERNRg1Ck0rV67E999/jw8//FDhAb1du3bFxYsXVVacJtq2DUhJEedkGj9e3dUQERFRXalRaEpNTYWnp2e57QYGBsjPz3/hojSVIADLlok/T50KGBurtx4iIiKqOzUKTa6urjh37ly57TExMWjTps2L1qSxjh4FEhIAAwNg2jR1V0NERER1qUZTDoSHhyMsLAxFRUUQBAEnTpzAb7/9hsjISPzwww+qrlFjfP65+OfYsYCtrXprISIiorpVo9A0adIkGBoaYu7cuSgoKMBrr70GBwcHrFixAmPGjFF1jRohMVF8rhwgDgAnIiKihqVGoQkAQkJCEBISgoKCAuTl5cHGxkaVdWmcL78UxzS9+irQurW6qyEiIqK6VuPQVMbIyAhGRkaqqEVj3b0LrFsn/jxrlnprISIiIvWo0UDwzMxMvPHGG3BwcICenh50dXUVFm2zdi1QXAx06wb06qXuaoiIiEgdahSaxo0bhzNnzmDevHn4/fffsWXLFoVFWYcOHcLgwYPh4OAAiUSCbdu2KewXBAHz58+Hvb09DA0N4efnh6SkpOded/Xq1XBxcUHjxo3h4+ODEydOVPctyhUXA998I/48cyYgkdT4UkRERFSP1ah77siRIzh8+DA6d+78Qi+en5+PTp06YcKECRhWwfNIli5diq+//hrr1q2Dq6sr5s2bB39/f1y+fBmNGzeu8JobN25EeHg41q5dCx8fHyxfvhz+/v5ITEys0birDRuAzEygWTNgxIhqn05ERERaokYtTY6OjlDFc34DAwPx8ccfY+jQoeX2CYKA5cuXY+7cuRgyZAg6duyI//3vf7hz5065Fqmnffnll5g8eTLGjx+Ptm3bYu3atTAyMsJPP/1U7foEAfjqK/HnadOARo2qfQkiIiLSEjUKTcuXL8ecOXNw/fp1FZfzRGpqKjIyMuDn5yffZm5uDh8fH8THx1d4TklJCU6fPq1wjo6ODvz8/Co9pypHjgDnzwOGhsCUKdV/D0RERKQ9atQ9N3r0aBQUFMDNzQ1GRkZo9EwTzIMHD164sIyMDACA7TOzSNra2sr3Pev+/fuQSqUVnnP16tVKX6u4uBjFxcXy9dzcXADA6tXiemio+Kw5IiIiarhqFJq++uorSLRoRHRkZCQWLVpUbvvu3eKfM2bUbT1ERESkeWoUmsaNG6fiMsqzs7MDIE5vYG9vL9+emZlZ6QB0Kysr6OrqIjMzU2F7Zmam/HoViYiIQPhT03zn5ubC0dERADBoENCqVU3fBREREWmLGo1p0tXVxd27d8ttz8rKUtk8Ta6urrCzs0NsbKx8W25uLhISEuDr61vhOfr6+vDy8lI4RyaTITY2ttJzAMDAwABmZmYKSxm2MhERERFQw5amyu6cKy4uhr6+vtLXycvLQ3Jysnw9NTUV586dg6WlJZycnDBjxgx8/PHHcHd3l0854ODggKCgIPk5/fv3x9ChQzFt2jQA4sOEQ0ND0bVrV3h7e2P58uXIz8/H+PHjq/0+27QBnhpTTkRERA1YtULT119/DQCQSCT44YcfYGJiIt8nlUpx6NAhtK7Gg9lOnTqFfv36ydfLushCQ0MRHR2N2bNnIz8/H1OmTEF2djZ69eqFmJgYhTmaUlJScP/+ffn66NGjce/ePcyfPx8ZGRno3LkzYmJiyg0OV8bUqZzMkoiIiEQSoRoTLrm6ugIAbty4gebNmyt0xenr68PFxQUfffQRfHx8VF9pHcrNzYW5uTkyM3NgY2P2/BOIiIhI7cq+v3NychSG2qhKtVqaUlNTAQD9+vXDli1b0KRJE5UXpEkqmXSciIiIGqAajWk6cOCAqusgIiIi0mhKh6bw8HAsXrwYxsbGCrfnV+TLL7984cKIiIiINInSoens2bO4evUqPD09cfbs2UqP06ZJL4mIiIjKKB2aDhw4AF1dXaSnp8u750aPHo2vv/66RnemEREREdUn1Zrc8tkb7Xbv3o38/HyVFkRERESkiWo0I3iZasxWQERERFSvVSs0SSSScmOWOIaJiIiIGoJqTTkgCALGjRsHAwMDAEBRURHeeustGBsbKxy3ZcsW1VVIREREpAGqFZpCQ0MV1l9//XWVFkNERESkqaoVmqKiomqrDiIiIiKN9kIDwYmIiIgaCoYmIiIiIiUwNBEREREpgaGJiIiISAkMTURERERKYGgiIiIiUgJDExEREZESGJqIiIiIlMDQRERERKQEhiYiIiIiJTA0ERERESmBoYmIiIhICQxNREREREpgaCIiIiJSAkMTERERkRIYmoiIiIiUwNBEREREpASGJiIiIiIlMDQRERERKYGhiYiIiEgJDE1ERERESmBoIiIiIlKCxocmFxcXSCSScktYWFiFx0dHR5c7tnHjxnVcNREREWkbPXUX8DwnT56EVCqVr1+6dAkDBgzAyJEjKz3HzMwMiYmJ8nWJRFKrNRIREZH20/jQZG1trbD+6aefws3NDX369Kn0HIlEAjs7u9oujYiIiBoQje+ee1pJSQl++eUXTJgwocrWo7y8PDg7O8PR0RFDhgzBP//8U4dVEhERkTaqV6Fp27ZtyM7Oxrhx4yo9plWrVvjpp5/w559/4pdffoFMJkOPHj1w69atSs8pLi5Gbm6uwkJERET0NIkgCIK6i1CWv78/9PX1sWPHDqXPKS0tRZs2bRAcHIzFixdXeMzChQuxaNGicttzcnJgZmZW43qJiIio7uTm5sLc3LzWvr/rTUvTjRs3sG/fPkyaNKla5zVq1Aienp5ITk6u9JiIiAjk5OTIl5s3b75ouURERKRl6k1oioqKgo2NDV555ZVqnSeVSnHx4kXY29tXeoyBgQHMzMwUFiIiIqKn1YvQJJPJEBUVhdDQUOjpKd7wN3bsWERERMjXP/roI+zZswfXrl3DmTNn8Prrr+PGjRvVbqEiIiIieprGTzkAAPv27UNaWhomTJhQbl9aWhp0dJ5kv4cPH2Ly5MnIyMhAkyZN4OXlhWPHjqFt27Z1WTIRERFpmXo1ELyu1PZAMiIiIlI9DgQnIiIi0gAMTURERERKYGgiIiIiUgJDExEREZESGJqIiIiIlMDQRERERKQEhiYiIiIiJTA0ERERESmBoYmIiIhICQxNREREREpgaCIiIiJSAkMTERERkRIYmoiIiIiUwNBEREREpASGJiIiIiIlMDQRERERKYGhiYiIiEgJDE1ERERESmBoIiIiIlICQxMRERGREhiaiIiIiJTA0ERERESkBIYmIiIiIiUwNBEREREpgaGJiIiISAkMTURERERKYGgiIiIiUgJDExEREZESGJqIiIiIlMDQRERERKQEhiYiIiIiJTA0ERERESmBoYmIiIhICRodmhYuXAiJRKKwtG7duspzNm/ejNatW6Nx48bo0KED/vrrrzqqloiIiLSZRocmAGjXrh3S09Ply5EjRyo99tixYwgODsbEiRNx9uxZBAUFISgoCJcuXarDiomIiEgbaXxo0tPTg52dnXyxsrKq9NgVK1YgICAA7733Htq0aYPFixejS5cuWLVqVR1WTERERNpI40NTUlISHBwc0KJFC4SEhCAtLa3SY+Pj4+Hn56ewzd/fH/Hx8bVdJhEREWk5PXUXUBUfHx9ER0ejVatWSE9Px6JFi9C7d29cunQJpqam5Y7PyMiAra2twjZbW1tkZGRU+TrFxcUoLi6Wr+fm5qrmDRAREZHW0OjQFBgYKP+5Y8eO8PHxgbOzMzZt2oSJEyeq7HUiIyOxaNEilV2PiIiItI/Gd889zcLCAh4eHkhOTq5wv52dHTIzMxW2ZWZmws7OrsrrRkREICcnR77cvHlTZTUTERGRdqhXoSkvLw8pKSmwt7evcL+vry9iY2MVtu3duxe+vr5VXtfAwABmZmYKCxEREdHTNDo0zZo1CwcPHsT169dx7NgxDB06FLq6uggODgYAjB07FhEREfLjp0+fjpiYGHzxxRe4evUqFi5ciFOnTmHatGnqegtERESkJTR6TNOtW7cQHByMrKwsWFtbo1evXjh+/Disra0BAGlpadDReZL7evTogfXr12Pu3Ln44IMP4O7ujm3btqF9+/bqegtERESkJSSCIAjqLkLT5ObmwtzcHDk5OeyqIyIiqidq+/tbo7vniIiIiDQFQxMRERGREhiaiIiIiJTA0ERERESkBIYmIiIiIiUwNBEREREpgaGJiIiISAkMTURERERKYGgiIiIiUgJDExEREZESGJqIiIiIlMDQRERERKQEhiYiIiIiJTA0ERERESmBoYmIiIhICQxNREREREpgaCIiIiJSAkMTERERkRIYmoiIiIiUwNBEREREpASGJiIiIiIlMDQRERERKYGhiYiIiEgJDE1ERERESmBoIiIiIlICQxMRERGREhiaiIiIiJTA0ERERESkBD11F1CfSaVSlJaWqrsM0nL6+vrQ0eH/3xARqRtDUw0IgoCMjAxkZ2eruxRqAHR0dODq6gp9fX11l0JE1KAxNNVAWWCysbGBkZERJBKJuksiLSWTyXDnzh2kp6fDycmJf9eIiNSIoamapFKpPDA1bdpU3eVQA2BtbY07d+7g8ePHaNSokbrLISJqsDhQoprKxjAZGRmpuRJqKMq65aRSqZorISJq2DQ6NEVGRqJbt24wNTWFjY0NgoKCkJiYWOU50dHRkEgkCkvjxo1VXhu7Saiu8O8aEZFm0OjQdPDgQYSFheH48ePYu3cvSktLMXDgQOTn51d5npmZGdLT0+XLjRs36qhi0jRHjx5Fhw4d0KhRIwQFBSEuLg4SiYSD+ImIqNo0ekxTTEyMwnp0dDRsbGxw+vRpvPTSS5WeJ5FIYGdnV9vlUT0QHh6Ozp07Y/fu3TAxMYGRkRHS09Nhbm4OQPw7NWPGDIYoIiJ6Lo1uaXpWTk4OAMDS0rLK4/Ly8uDs7AxHR0cMGTIE//zzT12UR8+QSqWQyWRqrSElJQUvv/wymjdvDgsLC+jr68POzo5dXkREVG31JjTJZDLMmDEDPXv2RPv27Ss9rlWrVvjpp5/w559/4pdffoFMJkOPHj1w69atSs8pLi5Gbm6uwqJtYmJi0KtXL1hYWKBp06b4z3/+g5SUFPn+Hj164P3331c45969e2jUqBEOHToEQPw9zZo1C82aNYOxsTF8fHwQFxcnPz46OhoWFhbYvn072rZtCwMDA6SlpeHkyZMYMGAArKysYG5ujj59+uDMmTMKr3X16lX06tULjRs3Rtu2bbFv3z5IJBJs27ZNfszNmzcxatQoWFhYwNLSEkOGDMH169crfL/Xr1+HRCJBVlYWJkyYAIlEgujoaIXuubi4OIwfPx45OTny8W8LFy4EALi4uGDJkiWYMGECTE1N4eTkhO+++07hNZ5XT1xcHLy9vWFsbAwLCwv07NlT3lV8/vx59OvXD6ampjAzM4OXlxdOnTqlzEdJRERqUm9CU1hYGC5duoQNGzZUeZyvry/Gjh2Lzp07o0+fPtiyZQusra3x7bffVnpOZGQkzM3N5Yujo2O1ahMEID+/7hdBUL7G/Px8hIeH49SpU4iNjYWOjg6GDh0qbwkKCQnBhg0bIDx10Y0bN8LBwQG9e/cGAEybNg3x8fHYsGEDLly4gJEjRyIgIABJSUnycwoKCvDZZ5/hhx9+wD///AMbGxs8evQIoaGhOHLkCI4fPw53d3cMGjQIjx49AiC2SAUFBcHIyAgJCQn47rvv8OGHHyrUX1paCn9/f5iamuLw4cM4evQoTExMEBAQgJKSknLv19HREenp6TAzM8Py5cuRnp6O0aNHKxzTo0cPLF++XGEM3KxZs+T7v/jiC3Tt2hVnz57F1KlT8fbbb8tvRHhePY8fP0ZQUBD69OmDCxcuID4+HlOmTJG3cIWEhKB58+Y4efIkTp8+jTlz5nA6ASIiTSfUA2FhYULz5s2Fa9eu1ej8ESNGCGPGjKl0f1FRkZCTkyNfbt68KQAQcnJyyh1bWFgoXL58WSgsLJRvy8sTBDHC1O2Sl1ejX4cgCIJw7949AYBw8eJFQRAE4e7du4Kenp5w6NAh+TG+vr7C+++/LwiCINy4cUPQ1dUVbt++rXCd/v37CxEREYIgCEJUVJQAQDh37lyVry2VSgVTU1Nhx44dgiAIwu7duwU9PT0hPT1dfszevXsFAMLWrVsFQRCEn3/+WWjVqpUgk8nkxxQXFwuGhobC33//XelrmZubC1FRUfL1AwcOCACEhw8fyms2Nzcvd56zs7Pw+uuvy9dlMplgY2MjrFmzRql6srKyBABCXFxchXWZmpoK0dHRldb9tIr+zhERUXk5OTmVfn+rgka3NAmCgGnTpmHr1q3Yv38/XF1dq30NqVSKixcvwt7evtJjDAwMYGZmprBom6SkJAQHB6NFixYwMzODi4sLACAtLQ2AOIHiwIED8euvvwIAUlNTER8fj5CQEADAxYsXIZVK4eHhARMTE/ly8OBBhW4+fX19dOzYUeG1MzMzMXnyZLi7u8Pc3BxmZmbIy8uTv3ZiYiIcHR0VBu97e3srXOP8+fNITk6Gqamp/LUtLS1RVFSk8Pqq9PT7KLu54O7du0rVY2lpiXHjxsHf3x+DBw/GihUrkJ6eLr9eeHg4Jk2aBD8/P3z66ae19h6IiEh1NPruubCwMKxfvx5//vknTE1NkZGRAQAwNzeHoaEhAGDs2LFo1qwZIiMjAQAfffQRunfvjpYtWyI7OxvLli3DjRs3MGnSpFqr08gIyMurtctX+brKGjx4MJydnfH999/DwcEBMpkM7du3V+jaCgkJwbvvvouVK1di/fr16NChAzp06ABAHFyvq6uL06dPQ1dXV+HaJiYm8p8NDQ3LDbIODQ1FVlYWVqxYAWdnZxgYGMDX17fCbrXK5OXlwcvLSx7qnmZtba30darj2e4yiUQi785Upp6oqCi8++67iImJwcaNGzF37lzs3bsX3bt3x8KFC/Haa69h165d2L17NxYsWIANGzZg6NChtfJeiIjoxWl0aFqzZg0AoG/fvgrbo6KiMG7cOABiS8nTT4B/+PAhJk+ejIyMDDRp0gReXl44duwY2rZtW2t1SiSAsXGtXf6FZWVlITExEd9//718fNKRI0fKHTdkyBBMmTIFMTExWL9+PcaOHSvf5+npCalUirt378qvoayjR4/im2++waBBgwCIA6jv378v39+qVSvcvHkTmZmZsLW1BQCcPHlS4RpdunTBxo0bYWNjo9KWQH19/RrNtK1sPZ6envD09ERERAR8fX2xfv16dO/eHQDg4eEBDw8PzJw5E8HBwYiKimJoIiLSYBrfPVfRUhaYAPEOpejoaPn6V199hRs3bqC4uBgZGRnYtWsXPD096754DdKkSRM0bdoU3333HZKTk7F//36Eh4eXO87Y2BhBQUGYN28erly5guDgYPk+Dw8PhISEYOzYsdiyZQtSU1Nx4sQJREZGYteuXVW+vru7O37++WdcuXIFCQkJCAkJkbcUAsCAAQPg5uaG0NBQXLhwAUePHsXcuXMBQGHgtJWVFYYMGYLDhw8jNTUVcXFxePfdd6u8M/J5XFxckJeXh9jYWNy/fx8FBQVKnfe8elJTUxEREYH4+HjcuHEDe/bsQVJSEtq0aYPCwkJMmzYNcXFxuHHjBo4ePYqTJ0+iTZs2NX4fRERU+zQ6NJFq6OjoYMOGDTh9+jTat2+PmTNnYtmyZRUeGxISgvPnz6N3795wcnJS2BcVFYWxY8fiv//9L1q1aoWgoCCcPHmy3HHP+vHHH/Hw4UN06dIFb7zxBt59913Y2NjI9+vq6mLbtm3Iy8tDt27dMGnSJPndc2WPwDEyMsKhQ4fg5OSEYcOGoU2bNpg4cSKKiopeqOWpR48eeOuttzB69GhYW1tj6dKlSp33vHqMjIxw9epVDB8+HB4eHpgyZQrCwsLw5ptvQldXF1lZWRg7diw8PDwwatQoBAYGYtGiRTV+H0REVPskglCdG9cbhtzcXJibmyMnJ6fcF3JRURFSU1Ph6upaK8+0I9HRo0fRq1cvJCcnw83NTd3lqBX/zhERKaeq729V0OgxTdRwbN26FSYmJnB3d0dycjKmT5+Onj17NvjAREREmoOhiTTCo0eP8P777yMtLQ1WVlbw8/PDF198oe6yiIiI5BiaSCOMHTtW4W49IiIiTcOB4ERERERKYGgiIiIiUgJDExEREZESGJqIiIiIlMDQRERERKQEhiYiIiIiJTA0NRB9+/bFjBkz1F0GAGDbtm1o2bIldHV1MWPGDERHR8PCwkLdZREREVWJoYlUIi4uDhKJBNnZ2c899s0338SIESNw8+ZNLF68GKNHj8a///4r379w4UJ07ty59oolIiKqAU5uSXUqLy8Pd+/ehb+/PxwcHOTbDQ0N1VgVERHR87GlqQF5/Pgxpk2bBnNzc1hZWWHevHl4+nnNxcXFmDVrFpo1awZjY2P4+PggLi5Ovv/GjRsYPHgwmjRpAmNjY7Rr1w5//fUXrl+/jn79+gEAmjRpAolEgnHjxpV7/bi4OJiamgIAXn75ZUgkEsTFxSl0z0VHR2PRokU4f/48JBIJJBIJoqOjAQASiQQ//PADhg4dCiMjI7i7u2P79u0Kr3Hp0iUEBgbCxMQEtra2eOONN3D//n35/t9//x0dOnSAoaEhmjZtCj8/P+Tn58vr8/b2hrGxMSwsLNCzZ0/cuHHjRX/tRESkJdjSpAKCIKCgtKDOX9eokREkEonSx69btw4TJ07EiRMncOrUKUyZMgVOTk6YPHkyAGDatGm4fPkyNmzYAAcHB2zduhUBAQG4ePEi3N3dERYWhpKSEhw6dAjGxsa4fPkyTExM4OjoiD/++APDhw9HYmIizMzMKmw56tGjBxITE9GqVSv88ccf6NGjBywtLXH9+nX5MaNHj8alS5cQExODffv2AQDMzc3l+xctWoSlS5di2bJlWLlyJUJCQnDjxg1YWloiOzsbL7/8MiZNmoSvvvoKhYWFeP/99zFq1Cjs378f6enpCA4OxtKlSzF06FA8evQIhw8fhiAIePz4MYKCgjB58mT89ttvKCkpwYkTJ6r1+yUiIu3G0KQCBaUFMIk0qfPXzYvIg7G+sdLHOzo64quvvoJEIkGrVq1w8eJFfPXVV5g8eTLS0tIQFRWFtLQ0ebfZrFmzEBMTg6ioKCxZsgRpaWkYPnw4OnToAABo0aKF/NqWlpYAABsbm0oHdevr68PGxkZ+vJ2dXbljDA0NYWJiAj09vQr3jxs3DsHBwQCAJUuW4Ouvv8aJEycQEBCAVatWwdPTE0uWLJEf/9NPP8HR0RH//vsv8vLy8PjxYwwbNgzOzs4AIH8vDx48QE5ODv7zn//Azc0NANCmTRulf7dERKT92D3XgHTv3l2h5cTX1xdJSUmQSqW4ePEipFIpPDw8YGJiIl8OHjyIlJQUAMC7776Ljz/+GD179sSCBQtw4cKFOn8PHTt2lP9sbGwMMzMz3L17FwBw/vx5HDhwQKH+1q1bAwBSUlLQqVMn9O/fHx06dMDIkSPx/fff4+HDhwDEEDdu3Dj4+/tj8ODBWLFiBdLT0+v8/RERkeZiS5MKGDUyQl5EnlpeV1Xy8vKgq6uL06dPQ1dXV2GfiYnYijZp0iT4+/tj165d2LNnDyIjI/HFF1/gnXfeUVkdz9OoUSOFdYlEAplMBkB8D4MHD8Znn31W7jx7e3vo6upi7969OHbsGPbs2YOVK1fiww8/REJCAlxdXREVFYV3330XMTEx2LhxI+bOnYu9e/eie/fudfLeiIhIszE0qYBEIqlWN5m6JCQkKKwfP34c7u7u0NXVhaenJ6RSKe7evYvevXtXeg1HR0e89dZbeOuttxAREYHvv/8e77zzDvT19QEAUqn0hevU19ev0XW6dOmCP/74Ay4uLtDTq/ivtkQiQc+ePdGzZ0/Mnz8fzs7O2Lp1K8LDwwEAnp6e8PT0REREBHx9fbF+/XqGJiIiAsDuuQYlLS0N4eHhSExMxG+//YaVK1di+vTpAAAPDw+EhIRg7Nix2LJlC1JTU3HixAlERkZi165dAIAZM2bg77//RmpqKs6cOYMDBw7Ix/04OztDIpFg586duHfvHvLyat7y5uLigtTUVJw7dw73799HcXGxUueFhYXhwYMHCA4OxsmTJ5GSkoK///4b48ePh1QqRUJCApYsWYJTp04hLS0NW7Zswb1799CmTRukpqYiIiIC8fHxuHHjBvbs2YOkpCSOayIiIjmGpgZk7NixKCwshLe3N8LCwjB9+nRMmTJFvj8qKgpjx47Ff//7X7Rq1QpBQUE4efIknJycAIitSGFhYWjTpg0CAgLg4eGBb775BgDQrFkzLFq0CHPmzIGtrS2mTZtW4zqHDx+OgIAA9OvXD9bW1vjtt9+UOs/BwQFHjx6FVCrFwIED0aFDB8yYMQMWFhbQ0dGBmZkZDh06hEGDBsHDwwNz587FF198gcDAQBgZGeHq1asYPnw4PDw8MGXKFISFheHNN9+s8fsgIiLtIhGenqiHAAC5ubkwNzdHTk4OzMzMFPYVFRUhNTUVrq6uaNy4sZoqpIaEf+eIiJRT1fe3KrCliYiIiEgJDE1ERERESmBoIiIiIlICQxMRERGREhiaiIiIiJTA0FRDvOmQ6gr/rhERaQaGpmoqe4xHQUGBmiuhhqKkpAQAyj3ehoiI6hYfo1JNurq6sLCwkD8k1sjISOEhuESqJJPJcO/ePRgZGVX6aBgiIqob/Fe4Buzs7ABAHpyIapOOjg6cnJwYzomI1IyhqQYkEgns7e1hY2OD0tJSdZdDWk5fXx86OuxJJyJSt3oRmlavXo1ly5YhIyMDnTp1wsqVK+Ht7V3p8Zs3b8a8efNw/fp1uLu747PPPsOgQYNUXpeuri7HmRARETUQGv+/rxs3bkR4eDgWLFiAM2fOoFOnTvD396+0a+zYsWMIDg7GxIkTcfbsWQQFBSEoKAiXLl2q48qJiIhIm2j8A3t9fHzQrVs3rFq1CoA4MNbR0RHvvPMO5syZU+740aNHIz8/Hzt37pRv6969Ozp37oy1a9cq9Zq1/cA/IiIiUr0G/cDekpISnD59Gn5+fvJtOjo68PPzQ3x8fIXnxMfHKxwPAP7+/pUeT0RERKQMjR7TdP/+fUilUtja2ipst7W1xdWrVys8JyMjo8LjMzIyKn2d4uJiFBcXy9dzcnIAiImViIiI6oey7+3a6kTT6NBUVyIjI7Fo0aJy2x0dHdVQDREREb2IrKwsmJubq/y6Gh2arKysoKuri8zMTIXtmZmZ8rmSnmVnZ1et4wEgIiIC4eHh8vXs7Gw4OzsjLS2tVn7ppLzc3Fw4Ojri5s2bHF+mZvwsNAs/D83Bz0Jz5OTkwMnJCZaWlrVyfY0OTfr6+vDy8kJsbCyCgoIAiAPBY2NjMW3atArP8fX1RWxsLGbMmCHftnfvXvj6+lb6OgYGBjAwMCi33dzcnP8BaAgzMzN+FhqCn4Vm4eehOfhZaI7amttOo0MTAISHhyM0NBRdu3aFt7c3li9fjvz8fIwfPx4AMHbsWDRr1gyRkZEAgOnTp6NPnz744osv8Morr2DDhg04deoUvvvuO3W+DSIiIqrnND40jR49Gvfu3cP8+fORkZGBzp07IyYmRj7YOy0tTSFR9ujRA+vXr8fcuXPxwQcfwN3dHdu2bUP79u3V9RaIiIhIC2h8aAKAadOmVdodFxcXV27byJEjMXLkyBq/noGBARYsWFBhlx3VLX4WmoOfhWbh56E5+Flojtr+LDR+cksiIiIiTaDRk1sSERERaQqGJiIiIiIlMDQRERERKYGhiYiIiEgJDE0VWL16NVxcXNC4cWP4+PjgxIkT6i5Jq0VGRqJbt24wNTWFjY0NgoKCkJiYqHBMUVERwsLC0LRpU5iYmGD48OHlZn4n1fv0008hkUgUJovlZ1G3bt++jddffx1NmzaFoaEhOnTogFOnTsn3C4KA+fPnw97eHoaGhvDz80NSUpIaK9ZOUqkU8+bNg6urKwwNDeHm5obFixcrPOOMn0XtOHToEAYPHgwHBwdIJBJs27ZNYb8yv/cHDx4gJCQEZmZmsLCwwMSJE5GXl1ftWhianrFx40aEh4djwYIFOHPmDDp16gR/f3/cvXtX3aVprYMHDyIsLAzHjx/H3r17UVpaioEDByI/P19+zMyZM7Fjxw5s3rwZBw8exJ07dzBs2DA1Vq39Tp48iW+//RYdO3ZU2M7Pou48fPgQPXv2RKNGjbB7925cvnwZX3zxBZo0aSI/ZunSpfj666+xdu1aJCQkwNjYGP7+/igqKlJj5drns88+w5o1a7Bq1SpcuXIFn332GZYuXYqVK1fKj+FnUTvy8/PRqVMnrF69usL9yvzeQ0JC8M8//2Dv3r3YuXMnDh06hClTplS/GIEUeHt7C2FhYfJ1qVQqODg4CJGRkWqsqmG5e/euAEA4ePCgIAiCkJ2dLTRq1EjYvHmz/JgrV64IAIT4+Hh1lanVHj16JLi7uwt79+4V+vTpI0yfPl0QBH4Wde39998XevXqVel+mUwm2NnZCcuWLZNvy87OFgwMDITffvutLkpsMF555RVhwoQJCtuGDRsmhISECILAz6KuABC2bt0qX1fm93758mUBgHDy5En5Mbt37xYkEolw+/btar0+W5qeUlJSgtOnT8PPz0++TUdHB35+foiPj1djZQ1LTk4OAMgfuHj69GmUlpYqfC6tW7eGk5MTP5daEhYWhldeeUXhdw7ws6hr27dvR9euXTFy5EjY2NjA09MT33//vXx/amoqMjIyFD4Pc3Nz+Pj48PNQsR49eiA2Nhb//vsvAOD8+fM4cuQIAgMDAfCzUBdlfu/x8fGwsLBA165d5cf4+flBR0cHCQkJ1Xq9ejEjeF25f/8+pFKp/BEtZWxtbXH16lU1VdWwyGQyzJgxAz179pQ/+iYjIwP6+vqwsLBQONbW1hYZGRlqqFK7bdiwAWfOnMHJkyfL7eNnUbeuXbuGNWvWIDw8HB988AFOnjyJd999F/r6+ggNDZX/ziv6N4ufh2rNmTMHubm5aN26NXR1dSGVSvHJJ58gJCQEAPhZqIkyv/eMjAzY2Ngo7NfT04OlpWW1PxuGJtIoYWFhuHTpEo4cOaLuUhqkmzdvYvr06di7dy8aN26s7nIaPJlMhq5du2LJkiUAAE9PT1y6dAlr165FaGiomqtrWDZt2oRff/0V69evR7t27XDu3DnMmDEDDg4O/CwaEHbPPcXKygq6urrl7gTKzMyEnZ2dmqpqOKZNm4adO3fiwIEDaN68uXy7nZ0dSkpKkJ2drXA8PxfVO336NO7evYsuXbpAT08Penp6OHjwIL7++mvo6enB1taWn0Udsre3R9u2bRW2tWnTBmlpaQAg/53z36za995772HOnDkYM2YMOnTogDfeeAMzZ85EZGQkAH4W6qLM793Ozq7czVyPHz/GgwcPqv3ZMDQ9RV9fH15eXoiNjZVvk8lkiI2Nha+vrxor026CIGDatGnYunUr9u/fD1dXV4X9Xl5eaNSokcLnkpiYiLS0NH4uKta/f39cvHgR586dky9du3ZFSEiI/Gd+FnWnZ8+e5abf+Pfff+Hs7AwAcHV1hZ2dncLnkZubi4SEBH4eKlZQUAAdHcWvTF1dXchkMgD8LNRFmd+7r68vsrOzcfr0afkx+/fvh0wmg4+PT/Ve8IWGsWuhDRs2CAYGBkJ0dLRw+fJlYcqUKYKFhYWQkZGh7tK01ttvvy2Ym5sLcXFxQnp6unwpKCiQH/PWW28JTk5Owv79+4VTp04Jvr6+gq+vrxqrbjievntOEPhZ1KUTJ04Ienp6wieffCIkJSUJv/76q2BkZCT88ssv8mM+/fRTwcLCQvjzzz+FCxcuCEOGDBFcXV2FwsJCNVaufUJDQ4VmzZoJO3fuFFJTU4UtW7YIVlZWwuzZs+XH8LOoHY8ePRLOnj0rnD17VgAgfPnll8LZs2eFGzduCIKg3O89ICBA8PT0FBISEoQjR44I7u7uQnBwcLVrYWiqwMqVKwUnJydBX19f8Pb2Fo4fP67ukrQagAqXqKgo+TGFhYXC1KlThSZNmghGRkbC0KFDhfT0dPUV3YA8G5r4WdStHTt2CO3btxcMDAyE1q1bC999953CfplMJsybN0+wtbUVDAwMhP79+wuJiYlqqlZ75ebmCtOnTxecnJyExo0bCy1atBA+/PBDobi4WH4MP4vaceDAgQq/I0JDQwVBUO73npWVJQQHBwsmJiaCmZmZMH78eOHRo0fVrkUiCE9NZ0pEREREFeKYJiIiIiIlMDQRERERKYGhiYiIiEgJDE1ERERESmBoIiIiIlICQxMRERGREhiaiIiIiJTA0EREVEPR0dGwsLBQdxlEVEcYmoio1mVkZGD69Olo2bIlGjduDFtbW/Ts2RNr1qxBQUGBustTiouLC5YvX66wbfTo0fj333/VUxAR1Tk9dRdARNrt2rVr6NmzJywsLLBkyRJ06NABBgYGuHjxIr777js0a9YMr776qlpqEwQBUqkUeno1+6fQ0NAQhoaGKq6KiDQVW5qIqFZNnToVenp6OHXqFEaNGoU2bdqgRYsWGDJkCHbt2oXBgwcDALKzszFp0iRYW1vDzMwML7/8Ms6fPy+/zsKFC9G5c2f8/PPPcHFxgbm5OcaMGYNHjx7Jj5HJZIiMjISrqysMDQ3RqVMn/P777/L9cXFxkEgk2L17N7y8vGBgYIAjR44gJSUFQ4YMga2tLUxMTNCtWzfs27dPfl7fvn1x48YNzJw5ExKJBBKJBEDF3XNr1qyBm5sb9PX10apVK/z8888K+yUSCX744QcMHToURkZGcHd3x/bt21X2+yai2sPQRES1JisrC3v27EFYWBiMjY0rPKYsgIwcORJ3797F7t27cfr0aXTp0gX9+/fHgwcP5MempKRg27Zt2LlzJ3bu3ImDBw/i008/le+PjIzE//73P6xduxb//PMPZs6ciddffx0HDx5UeM05c+bg008/xZUrV9CxY0fk5eVh0KBBiI2NxdmzZxEQEIDBgwcjLS0NALBlyxY0b94cH330EdLT05Genl7he9m6dSumT5+O//73v7h06RLefPNNjB8/HgcOHFA4btGiRRg1ahQuXLiAQYMGISQkROF9EpGGeuHHDxMRVeL48eMCAGHLli0K25s2bSoYGxsLxsbGwuzZs4XDhw8LZmZmQlFRkcJxbm5uwrfffisIgiAsWLBAMDIyEnJzc+X733vvPcHHx0cQBEEoKioSjIyMhGPHjilcY+LEiUJwcLAgCE+elr5t27bn1t6uXTth5cqV8nVnZ2fhq6++UjgmKipKMDc3l6/36NFDmDx5ssIxI0eOFAYNGiRfByDMnTtXvp6XlycAEHbv3v3cmohIvTimiYjq3IkTJyCTyRASEoLi4mKcP38eeXl5aNq0qcJxhYWFSElJka+7uLjA1NRUvm5vb4+7d+8CAJKTk1FQUIABAwYoXKOkpASenp4K27p27aqwnpeXh4ULF2LXrl1IT0/H48ePUVhYKG9pUtaVK1cwZcoUhW09e/bEihUrFLZ17NhR/rOxsTHMzMzk74OINBdDExHVmpYtW0IikSAxMVFhe4sWLQBAPog6Ly8P9vb2iIuLK3eNp8cMNWrUSGGfRCKBTCaTXwMAdu3ahWbNmikcZ2BgoLD+bFfhrFmzsHfvXnz++edo2bIlDA0NMWLECJSUlCj5TqunqvdBRJqLoYmIak3Tpk0xYMAArFq1Cu+8806l45q6dOmCjIwM6OnpwcXFpUav1bZtWxgYGCAtLQ19+vSp1rlHjx7FuHHjMHToUABiALt+/brCMfr6+pBKpVVep02bNjh69ChCQ0MVrt22bdtq1UNEmomhiYhq1TfffIOePXuia9euWLhwITp27AgdHR2cPHkSV69ehZeXF/z8/ODr64ugoCAsXboUHh4euHPnDnbt2oWhQ4eW606riKmpKWbNmoWZM2dCJpOhV69eyMnJwdGjR2FmZqYQZJ7l7u6OLVu2YPDgwZBIJJg3b165lh8XFxccOnQIY8aMgYGBAaysrMpd57333sOoUaPg6ekJPz8/7NixA1u2bFG4E4+I6i+GJiKqVW5ubjh79iyWLFmCiIgI3Lp1CwYGBmjbti1mzZqFqVOnQiKR4K+//sKHH36I8ePH4969e7Czs8NLL70EW1tbpV9r8eLFsLa2RmRkJK5duwYLCwt06dIFH3zwQZXnffnll5gwYQJ69OgBKysrvP/++8jNzVU45qOPPsKbb74JNzc3FBcXQxCEctcJCgrCihUr8Pnnn2P69OlwdXVFVFQU+vbtq/R7ICLNJREq+i+fiIiIiBRwniYiIiIiJTA0ERERESmBoYmIiIhICQxNREREREpgaCIiIiJSAkMTERERkRIYmoiIiIiUwNBEREREpASGJiIiIiIlMDQRERERKYGhiYiIiEgJDE1ERERESvg/CbVYdVjnC4oAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot the sample data\n",
    "\n",
    "data = np.loadtxt(\"sample_data.txt\")\n",
    "plt.plot(data[:,0], data[:,1], 'b-', label=\"average fitness\")\n",
    "plt.plot(data[:,0], data[:,2], 'g-', label=\"best fitness\")\n",
    "plt.legend()\n",
    "plt.title(\"Experiment 1\")\n",
    "plt.xlim(0, 100)\n",
    "plt.xlabel(\"Generation\")\n",
    "plt.ylim(0, 21)\n",
    "plt.ylabel(\"Fitness\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "44c1a066-9425-4ec7-a496-2ebfbd873ea9",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
