dissertation_work/Programming/Python files/.ipynb_checkpoints/NonUniformFiniteDifference-checkpoint.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "def f(x):\n",
    "    return np.sin(np.pi * x)\n",
    "\n",
    "x = np.linspace(0,1,100)\n",
    "x = x**2\n",
    "\n",
    "h = np.diff(x) # we define the vector h as the difference of successive x[i] using the built in diff function\n",
    "\n",
    "f = f(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [],
   "source": [
    "A = np.zeros((len(f),len(f))) #we create the matrix A by initializing to 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [],
   "source": [
    "for i in range(1,len(f)-1):\n",
    "    A[i,i-1] = 2/(h[i-1]*(h[i-1] + h[i]))           #we populate the diagonal (minus the extreme ends), the one to the left and right with a,b,c respectively\n",
    "    A[i,i] = -2/(h[i-1] * h[i])\n",
    "    A[i,i+1] = 2/(h[i]*(h[i] + h[i-1]))\n",
    "\n",
    "A[0,0] = 1                              # we denote the far corners of our matrix to be 1\n",
    "A[len(f)-1,len(f)-1] = 1\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [],
   "source": [
    "u = np.linalg.inv(A).dot(f)     # we solve our system"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fb7a088d220>]"
      ]
     },
     "execution_count": 113,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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       "<Figure size 432x288 with 1 Axes>"
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt #we plot the result\n",
    "\n",
    "plt.plot(x,u)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [
    {
     "data": {
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xcbjq67QYEgDhHZuYNc8nBrTNGdek88XZIA62VnPKm543s3NWACpKZHFWGavZi13GWGnD5de2tiDsD4hyUECQricTCc1a0ZAXdeLMrHs1NgFXnTYLi8VuR7XNCv9orkR9vO8MLHa7Zs/P01CfE6kDEMUyWuWtCEvgG8/cq0ggiLDPr5kX7G3K98wB4f1za2SsDEYjPE0NObkhQDBWnqYGGIza1FrVtOSvUz5irJq0SQ14mxoFijTr/QtOTmEmHNEjKxaoLRDyB9LGSqu2IYVqhJLxBKaGR7SLrIhCapbH6R+f0PA+CX83ewEGIN47Z60243I3NuTQbQBE+lQr+bq7sQH+8Qkk44mc308ODmnmBYs5j1nGKjA+oZ2j0ZRbY0UweWYQRpNJsyimprU5z4ASh0grkYW3uRH+sXFRHUwwNTSsR1a0YTAZc2qsCAITAi+s2SJcVwv/xETe7ycHhlDTps0kIDVW/lmLsH9sHM66Gk3kz4Qq8o/l3ivx+WmkcvMUoAGnhoaRiMdRO0+byMpdX5dnQIH089PsPhEhSq6x8o2NaxatE2dwNt09QShTDZgNU3U13PV1omydgDxPrQyop6kxR1xBMDkwqEdWtOFpFML62R7LTDiCaCikWc7KWVuTk0gl0LLWylVXi8DEZF5Xcv/4BIwmE+we/lLVjLGaFVlpmHO0e9wwVVfn0YDJeAJTQyOo06iNl7uxHr4CHT2CU9Nw1Hr5DwiAp7kRkWAQkUAw5/f+sQlY7DZY7PyFA7NrrAi0FDiR3N5soz4TjiDs88PTqFFk1dSYFxUDwPTomGY0biGcFcaKRE6F2vL4xyc088yJYZiN6WGhrkKLKMZR40VwYirv9wENDYM7TQMS4ySOKX3vtIgYiJR4ulAUM65dFOOuz4/2ACAwMQVnjTZj8s6SrROINK4Gc8qV3qpl9vMjIgKvBpJsZ40XAAo6sNMjo3BrKLDIFlcQBCem4EiPuRJwVhgrR/olDUxO5X0XGJ/U5GUhUcrsBRgQxmk0mWB1ObmPy1njRWAy/2XxpcephSflqqtDIh5HaGo65/dhnx+JWFwTwyBKxAsYBq1e4iqDAa762oI0YGByElanA0azmfu4PE0NedECkHE+3BqoTJ21XkRDIcSj0ZzfJ2IxhHw+TRzYUuuUb3RMkxIbm9uNapu1oLMRmJiE2WLRTFI/G2eFsXKm6Y9ggUVYK+GAI/0yFPKiglNTwjFeD88hCX+z1otgQaOuXWTlqq9DYDyfmgSEF0aL5yfmYUbyF+Hg1LQmxspZWwOD0VjQWAXTht6pARVYjEbypwUzWsjXHV4vAgUYBEA7Z6PUOjU9MqpJYbArLYAp5lQD0Cxin42zw1iR8LoQvTUxqYlnTjy3QpMgOCksLJq8MDU1Be8TyYNoUWvlqq/NUwIS+McntImsxE4R+eMKTE6Kc44nxBqrQsYqTZk6vF6eQ0pHe3V5uT0gI5jRxFjVekWncDY0czZKrFPTI2Nw1ddxLzYn96GQASUMjFa50Nk4K4yVo6YGsUgUM+Fw3nf+8Qk4arzcJwGJUArlrEhkw3thMZrNsDodBWnAiD+A+MyMJlFMqW1AtHI23PV1CE5NIxGL5X0XnJiCqbqau3CgUPcKAtEL5ryw2D1uGE0mMTLPRnBqGslEQhtmw+spyCAA2jkbpdYp38gojCYT97lO1qCCjv64tmrc2TgrjJWztnAeBhDoLYPBAEcNX8rNWSqyIjQg9zF5hb9f5CUWKFMtcla1ebJ1Aq1oQEdNYboUyHp+nA0DUYsVzKMRB4gzZUOobMIWZCOVTGr2/Jw1NQXHBGhJA9YUXadE5SvnOSWuCQWiUK3mVDGcFcbKUeMtmLQEMpOA9wvjEiOrEjQg58iKcM/FuHyhiwXf+1RVVQVXbW1Bow5oRwM6PB6Epn0FvyP3j7d3TsQvhSjToJhf8HIcEWD3pI3VVGHD4B+b0IYGrPEUd2AntctZFVunyP0j95MXyBpUyLCT+6dFHrQQzgpj5aypKSjHBrQrDHbWCiF/NBjK+24mHEYsGuUeWZXip4F0ZMU5Z2X3uGE0m0rSgNU2K6ptNr7j8rrLR1a8nY26WoFam9W9AgBC0z4kEwnui7DD607//cLGyjc+zn1OmSwWWOz2opFVYHISJrOZuxrXUeMtmBYAIDpGvOscHbVeRIJBcSfzbMQiUURD4YqRr58dxkpKeK1BZFWoewVBcGqa/2KX9pCKRqFj45oYdaBwbi/797zH5fB6ECyyAGuZH5ot7ydIpVKaCAfs3tKRVUADNa6zjFMW1CgyLuVUE2PPWyFcKrcHaJczLoSzwliV8lgyXDDfG16sewVBcHJKg8iqDA04wV+MQjZ3C/v8Bb8nNCrvHnN2jwehqcI0IFlweDsbdo+7KDUJCHOK9wLsSNNWxe6VX4PO6+S9KmpANZJkO4rUOALaRValcnsAmVO6saICs9UCi91W1DvQSuXmqiuehwE0iqxqvEjE44j4ixiGdMslnt6dze0CAISKGCstnA2TxYJqm7XoYhcNhRCfmeEusLC5XQj5ShgrDVouOWo8iMdiOXt+ZcM3NgGT2cx1x9lyudmgBpLscutULBJFLBqFnfPOvI4S4jRAoEx16TollJuYgDaFwc7amqLRHpCOrHiH/LVeBKemCxbfApl7yNdYCXmDcJFFWCoNuHbtWvT09ODo0aO47777Ch7zyCOP4OjRo9i3bx9WrlwJAFiyZAn27t0rfqanp/Hlr30VAPDxq65Cf3+/+N26desy49LA4ywXWQUmJjUYk6coNQlkis15drEgkVWxRZhEEjyjUCnrVGjKJ9KqvCCFBqwU6bpJ6wGoRTnRAJB+iXnnPGo8RYsSAW0KE4WQf6ro92Qh5OkF29ORVdgfKPi9qLwr8cIYDAY8+uijWLNmDfr7+9Hd3Y3Ozk4cPnxYPGbdunXo6OhAR0cHLr30Ujz++OO47LLLcOTIEdFwGQwGnDlzBr/50x/xF3++HqmZGB5++GFs3bo1729q4WxIoQG5j8nrKRqBAhkqjuecInR3KYFF9nF8xuQFUHqdCvl8lUcDVlB/wLkfWZURDQD85c9mqwWm6uqieRhAWFhsbhfXTeCcJXJ7QCZvxPOFsbqIsSp8rxKxGML+QEnKdPXq1ejt7cWJEycQi8WwY8cOrF+/PueY9evX46mnngIAvP322/B6vWhuzt3+4JprrsGxY8fgCwuUVmomvyCYIDg5xZUeqTIYYHeXiawmp2D3erjmHB3e4hJ/IOOE2Dgq7xw1npJ0d0blxs+wS1mnglPTsHv5vXtmq0B3l6YBp4T+gBp0zp+NOW+syokGAKESmycNSLzIYnkYQJiYBoNBzNnwQKlCVyAzXp5jsrtdiASDBeXYBJFAAFaXo+j3bW1t6OvrE3/u7+9HW1ub7GM2bNiAZ555RvQkU9EZbN68Gfv27cOTTz4Jb5bBDExOiQb0rrvuQnd3N7q7u1Ffz6YZKVnsy0VWBoOBq7Nh97hLRlaRQNpYufkZK2dNDULTvqJ0N8BfOCBlnQpN+7jmrJxlIlBA250PZuMsMFZE+TNV9JjQtA82F98FGCiucAOyWy7x9O5qSnp2oiKJo7GyuV2IFKEACcL+QMnnV2irldkLVbljzGYzbrrpJvz85z8XF/sfb/svLF68GCtWrMDg4GAOHZitvNu2bRtWrVqFVatWYWwsv7sEDZAxlRRYaFAY7PCWzlmRiNnq5BhZeT0lGQRAWC94RlaS1qmpaa7rgZQxZYqV+e9zNxtz3ljZ3W4kk0lEZ238lo2w3w+L3QajiU+KTlxYSnnBU3yb2RpMRsELLvESEy+Y58S0uVwlI1BAeH6laKT+/n7MmzdP/Lm9vR0DAwOyjlm3bh327NmDkZERccE43XsMyWQSqVQK27Ztw+rVq8XjA2kat5LmFHFEeOYY7F5P0YJgAIj4hfeSp7NIhESlEPb5+TIIHjeSiUTJdYp3zkpkgErMKUKl8oyMi2HOGyvimZcK+Qlvzqti3SZGVuW9YF7ydUIvBEtMzFQyiZDPx/UltrldRfNVBBFf6ciqu7sbHR0dWLhwIcxmMzZs2IDOzs6cYzo7O7Fx40YAwKWXXorp6WkMDWV2lr7tttvwzDPPABAW4EgwiIYsSu+WW27BwYMHxZ9JrRUv9ZYkB4izsbLY7TCZzQgWqbECgPjMDGKRKN+clbc03Q0IlDdPA2pzuRAus06FpqZhqq7m1q2FPBPipBZCZu3kd6+KYc6rAW0uZ0lqBMhQETaXs+wkpgF7mdohgH8zW2KoSxlQ4Xs/58jKicnBoZLHhAMBNLvOKfp9IpHA5s2b8dprr8FoNOJHP/oRDh06hE2bNgEAnnjiCbzyyiu44YYb0Nvbi1AohDvuuCMzBpsNa9asEY93pAuCH3roIaxYsQKpVAonT54UvwcydJzD6ynaKoom5ERWvHIxRAxQikYChOfHs7VROdUkkI7WOedmyzll2YXBhTqz0wahZsO+4saKrGE8UwPFMPeNldtVVPZMQB4GL0+qXFcGAKI3yiuyIv/2UhMTSHucnCOrgQ+OljwmUiZnBQBdXV3o6urK+d0TTzyR8/PmzZsLnhsOh3OEEXavG8HpaWzceEfB48mYAMDqKC78oAlirMJSIitOKkVCl5bKWQHk+fEzVjaXs6xhCPtKU8u0YXU5S64HQMZYObyegtvM0wb595e6V5EsR19rzHka0O52l50EvHlXu0fIo5USDsSjUURDIW6RVWZiljHsnBVJwvMrL7CwOh0FRRIs4ChT6AoAkaCQe7A4ORkr4gCVeH6JWAyRYFBsgcR8TGLH9fLROq/FzmSxwGyxlF0Twr4AzBYLTBYLl3HZ3e6y716Qc8slq8uJZDKJmVDxKG4mHEEiFq8IGnDOGyspHgtv3lVKHg3g23JJSh4NECIrXi+LwWiE1emQRE0ajEZU2/lw+fYyCjcgE1nZOBkrm0dwypKJ4hJ/AIgEgiVl/jQhRlYlBBZAuvSAkxpQdMrKOUCc6S05kRWvPKjN5UQkUH6dCvl8FUEDznljZS/TLw3IzVnxgJQxAYQe4bTYlekUQRCa5iewsKYX+vJqQL40rtBxvfTzI5EVr1yM3eOWNKfCPj83w1CuYSxB2B/gNqekUFtAxmnjuSaUNVZEJs6J2bA6naJasxR407jFMOeNlU3CJOCfsyo/JiCdeObtcUrh8nktLBKoLSCjVuJlGIRorxy1nDZWHHNW5UQDgBBZ2XjNKQm5WSBN43IzCtLmlOgAcTIMNpcEY8WZBrS5y+f2gPTz0yMrdcjw06Un5kw4jEQ8ztGLkriw+IP8DKjLhXgshlgkWvK4sM8Hk9nMRT6boWykRlbsn5/FbofBaCxbqBwNhZBMJvlGVpKMVQBWTrlZq8Mh3Idy1KQ/wM2AWss0RiYQu7VweH6m6mqYrZayBjQ+M4NoKMyt5ZLV6USkRN0XQbk6R16Y08ZK6mIHpF8YbhGDxMjK7+eWX7BJ4MwBvl0s7J7SfQEJwuLCwn5M4pwqUXtCEA0EYXHw6Zkm1QEK8zQMTofExS4g9stkDVH1WjaySs8pD785JY3G5VcYLEU1CaTLWThvXVIIc9pY2SWKBgDSsodfUXC5PAyQToZzpAElGStiGDi8MGIT2wqKrKwSVZOAYNC4RetSI6u0cpIHrE4HosHC+1hlQ2y5xMExy3Txl+YA8XDKiJNcLloH0qIrTmpOqTkrnjRuKcxpYyWlYSyBEMXwowGlRnvcFhYJ9WgA58hKQvE0wLcZKnEepCws0WCIn7MhUbRTro8iTVgkRlbi8+MwLqtUNaBoQHnMc+nrVGiaY2QlOWel04CqIVXhRo7h8bJY7HYYzSZJ0V4kEIDRZOKSH7K7XEW3TMiGSLlxCPszHmc5MUNaYMHBMEitRwPSzgYHgYXFYYfRZJKcszKaTTBb2dcPWR2Okq16CIjh4PP8XOnaoOLbuwBAMp5ANBTi4pSJeTQJ718kEORSu1dVVZV+fhIiK5+fa01aMcxxYyUtmSocw8c7ELdpl5hfAPio3KR0+gD47mlFRB8z4UjJ4xLxOKKhMFfPXNIiXGbrEloQu1dIYhD4GQY5OSuAD40rNQ8D8HNgpezCQBANhrg4QNV2GwxGo7Q55eP3/EphThsrOZMgzKlxpU0itQXwLSy1upwVRwNKFaIA/Go9CC0riQYMBLksLDaJuT0ga07xUE467GK9WSlkaFxOc0rCswP4lWlkRB8Snl+Qj2iHiHCksVKV0XJpThsrqXU65BgeEYwsAxrgV1gq1eOMhkKCzJ/LSyxN9AHwyzlKVZMBwvPjMaZMtCchiuFYk2aTIX0GwCU/K8cB4s22lMujAfwiK1I3JY3G5b8payHMcWOV3mW2TJ0HwG9PKzk0kljsypiyMVVXS+qXRhANhbh4d1Kq+gkigSAnA+pAfGYG8ZmZssdGA0EuCzBZvCSJGcj+URxoQItUNSDHonxZNCDHyEpKHg0QjJXRbGIu85eTmxUjK91YKYfN6ZRE1wBZSXrGnhRZ5CMSXmJelI0czw4QXhguVISE5p4EYb+fj2FwSqNLASGKMVssMJrNbMfkIsaqciibapsNBoNBkgHlWZQvZedpAl47DMiiu0kbL8ZzXY7qlXe7s2KY08bK4rDLWuwA9i+xxS4s8qV2BM2MiY8BldpqiSAaDIn/DpYQaMDyQhSAXzLc5pLuAEV5LSwkspKRH2I9p8TcnoQxAaTBLh8aV86aUGnRHolUWb9/NhkKRT1nRQFWp9DuRQp4URHkJZYyLjHxzHixkyPxB4QFiFd+QYoQBeCXX7C6nJK6VwBAmFN/wIwXLIMG5GSspDhlAL9aHSmbsRKQOVVlYLsMyoqsAnwcIEITS5Ou8xPIlMKcNlYWh13Gy8KnsNTisCOZSJSVYwPpvWLiceY5K0WRFQ8aUIYXHAnw6aMotV8akB3FsDZWDsRjMWl5tHSvPtZzypI20FINO48+mBZHuq+jRLpb3JOM8VyXM8+Jk8t6THI6tSTS5SU6DagCVodDUm4I4FexbnVISzoT8BAOyJE+A3xowGqbLV08LV0NaDSbUG2zMh2XHIVixgtmH8VIdcoAPpSbksiKV7Qg1YCSsTOPjF3SiqeBzJyyMB6TzelELBKVJPoAKqOLxdw2VhLVSAC/wkSLwy6ZmgT4vMRWuZEVBzWg1B5uBLyKXa0uBZEV82S4Q/ICDPBZWOTmrHjsaWWRaUDF/BDjuW6x2yU71WIelHVkJbHVEgHPrYOKYU4bK4vdLn1hEZOEjF8YGWMCBHqE9QJMepNJyXkApMEu4wVYRj0aAEQ4bekgJxkeCQgLEHMD6nAgGpARrXOYU6KxkmHYeTiKgAzRB0eBjFSnOsLJgEqtkSPguYFmMcxtYyVDYCHUObCXz8qJ9oD0/kOscx4yaocAPjSgnOJpgI981mA0ynOAeEVWMkQfAJ82UJnaL+nMBg+jDkDy+8dDeWcwGWG2WiSvU5nIijENKIPuBnQaUBXk1HkQhP3sQ1m5NKDgcVZWtBcNhWA0mZg2rrTJpQGJYSgikFm7di16enpw9OhR3HfffQWPeeSRR3D06FHs27cPK1euFH9/4sQJ7N+/H2/t7gaQqT2pqanBzp07ceTIEezcuRNerzfneryUW0JkJSdaZy/JFim3kETD7hPoboPRyG5MMmochePYPz+LXV4EOhMKC+expgGdTsl5NIBfOUspzFljRR6mnCiGx55WUjsZE4Q5bBMi14CSe8qSNyeLqVTpeqaPYv7zMxgMePTRR7Fu3TosX74ct912G5YtW5ZzzLp169DR0YGOjg7cfffdePzxx3O+v/rqq3H9Jz8BIBPFbdmyBW+88QaWLFmCN954A1u2bMk5JxGLIRaNMu8WYXFK68FHEPZzoHEdDsyEI0jGy3ePATKtxVgKB0TRh8R7xSNnZZW5TqVSKaE/IIdyFqkKRYBfOUspzFljJTfBC/DpLydfYMF+Z1erwy6PmhRfYnaT0yaXBvQRNWf+vVq9ejV6e3tx4sQJxGIx7NixA+vXr885Zv369XjqqacAAG+//Ta8Xi+am5tzxyTWngTEc7Zv3w4A2L59O26++ea8v81jSwe5+YVIgMOcckpXuAFZOWOGpSNiQb7UyIqDGlB0quU4i4EQrIyjGKvTIctY8SpnKQW2jfIYgkxMeWIGDpSbQ6bAIr3YVVVVIZVKsRmTXV4ejYciiUS4Uu9VqZxVW1sb+vr6xJ/7+/tx6aWXlj2mra0NQ0NDSKVS2LlzJyaRwD4kxL/V1NSEoaEhAMDQ0BAaGxvz/nYkEMQFF12ELd0ChVhfXy/p3yMHUjc5JAj7A8znlNTtQbLHBLDtWSiXBuQRWWUYIHk0PHMHyCW9LRWQoQFZzqlymPORlewohnHOSnadlT8Ag8HA/IWJKKABWY6J0BCpZFLS8UQgUsgzr6qqyvvd7Beq1DFXXHEFLrnkEvzDP38HALDs3A5JYwKEKKZ/eBCrVq3CqlWrMDY2JvlcKTBZLDCZzTKjGPZzyup0yGQ12LeBsjoFIZHU2qFEPI5YNMo2spIZ7QHstwkxms0wWy2yIytA2AdLK8x9YyW3WJKhx2K2WmAwGmUbUICt/NmilAZkSEXIpZGA4v0B+/v7MW/ePPHn9vZ2DAwMSD5mcHAQADCTNpzLlywFAAwPD4tUYXNzM0ZGRvL+diQQZBotWJ0KGAQO3fzly+nZqzktdnnzHGBPb8mV0wNpGpAlBS9jZwiCTLcP7fJWc9ZYKaEBWSta5GzlQMCj8ahcYxXl0IZGycIS9hUuoO7u7kZHRwcWLlwIs9mMDRs2oLOzM+eYzs5ObNy4EQBw6aWXYnp6GkNDQ7Db7XCmF3V3bQ0A4ND+/eI5t99+OwDg9ttvx0svvZT3t1l3ixD7AiqIYpjmh2RHVqROjq3AQs6YAPbCgYzoQ8b7F2IbWcltEgDwEV2Vw5zNWSmhAVl3ZlCiUOTRzFZoSyXDgJKJyXRMCoxVkcgqkUhg8+bNeO2112A0GvGjH/0Ihw4dwqZNmwAATzzxBF555RXccMMN6O3tRSgUwh133AFAyEu9+OKLAIBTxgR6MYNXfvlLAMCDDz6IZ599Fn/1V3+F06dP4zOf+Uze344EAozVZGTn4sqLrOTlrMhGowwjKwVzirUDq4gGDLAdU2aXYHmOPqBtZDVnjZUYXsukAQ0GA6ptNsyEw+zGJFNmDLBdWKrtNmWRFcuX2CG9oJsgUqIwsaurC11dXTm/e+KJJ3J+3rx5c955J06cwIoVKwAAN371S7jqLz4ryrEnJiZw7bXXlh4TcxpQgerVx8FYOR3yRANB9t3g5dYTAuzzQ3JFH4DgVLN0FEnEHZETWYW0j6zmLg3ocCARi0vuygCwFw7IraAHsnfhZPMSk+JpOWPiUZhocUjvl0YQZtz0Vwk1yVq6TgyOnNwsKaBmSgM67LK6aiQTCQ6UqXwHKBpkq7yzOuyIx2KSRR9Aek4xFceQhr9KIivdWMmGEn6aVNuzuuEWBcaKNWWjhJpMpVLsKVMlOSvGdXJya+SATLTOKgolHrYcw0AMG6uIr9pmhdFkkmVAAfb9ARUJLAJBpjVNFpndRwDhXTWZzcy2thcFFjLaLfHqBl8Kc9ZYKQn5WScJReWWnPwQ42aomaJEuQtLkHmxpGzD4GNb7Kokj0acDVbeuRLVK7mvrGTGFpl9AQlY7/Yst/YLACKMa5qUMAis99nKRFYyHCCdBlQOJSE/a0k26QMmZ8GLR6NIxOIMqUn5kRU5njUNKDuyCgRgtlpgNJvZjElm8TSQ3QaKrbGSswjPhCNIJhIMFzv5eTSguJqTFpQ4QFHGYgarkjGJTjWbe2Vzu5BMJkW6Xwp4dYMvhblrrBSG1wC7UFaJ6ANIJ1RZUZN2+QlegK1y0mg2w2Q2KzKgADvvTm7xNJDVDJURvWV1OIRN8uJxWedFQ2F21KSCEg1yPKvIqipNxcpnW4Kw2G3MGuwqcoACrNMVwg7rcjpRxKPCHNSyme2cNVZKFhbWW0ZbnQ7BY5GpNGSpSFJS50GOZx7tyaQmWT8/JdEekZSz8oKtLqfsCAYgDhBjalJuZOX3MxN9WNKUp+znx7gzgyI5PaHcWEXrCpS4gPb9AeessZK71TfAXtFisdtlhdYELGs9lMjpyfGsFjsloo/s4yvKWDGPrOyyergRsFxYLAojK5Y5KyUNYwH2+0cJOSv50R7AMF2hII8GaN95fc4aK3UCC3YepyIvOMiurkJJHo0cz9IoAAqoSTHnyOpeKYms0mpOVlGo0siKoQNEulDIbZcVYbgdjmJqkkM5i1IakN2aIH+eA9rvaTV3jZVTfuJyJhxGMpmsKM8cILw5W8NQSZX9agwowDIytikQ7bAt6rY6HLK6VxBUYmQVDYVgMAo759Ifk9J5ztgwqKABma5TSmhAxuUs5TAnjVVVVZXsdi+AUD80EwozpQHljgkQvDuWE1NJHi0aZJfzUErZRBi+xNU2q9CEWDZlE0IymWRGA8rtwUfAsr+cmjwowOb5iQZULt0dYKsQrlbiAAXY04CKIyvdWMlDtcJkKjmHVRGgEjk9wJgGdCjLo0VCIaGLvIm+Skq1F8zg+SlVTaZSKaaGXUntEJB2gBiqAZUoFCMMaVzFJRohdpFVpnuMvOdH3tdKowFZ116Ww5w0VkrrPAC2oaxSjyXCkAa0KuWnRe+OwcKioLln9vFsPHNl0R4gGFEro27iSrZSAUhkzGieK4z2ZkhkzEB5p6R7DMBWJq40Nytubc9QjavTgJwg9uBT5HGymwRydwkmYGpAVUR7ABvhgGqBBUtjpcCwh/0BdpGVggQ9wHZOKY32WOZilHSPAdiKrpRK/IVz2NLwSsekGyuZEBc7pbUCDOkRpYaBZeJZiRfMMj9E2tvIrbNKxIXGxSxzHoqpZQY5KyWbeWaPyVRdDaOJ/sYKcrecIWCpvKtE0Y6S7UEIWBkGo8kEU3W1Ium6rgZUACX90giYRjFKBRZEqsrCu7PbZe3oSsDU47TbEYtGxa045IDVC6NmYQkH2Eiy1UR7LBdhq9OhuPYLYJRzTHc3l7MLA8B2a3ulDIJwDptu/mrmVCQYFIydhb5TLQVz0lhlkuGVE8qaLBYYzSbFlA3Ajt6SG8EAWTkrVmNScJ8AdsrJTFcNBS8xIxqQRAtKvWCAnbFSSiMBQDUDYyWMSeGcYrQlh1LRByD0LGRl1AGluVnSWUOb6GpOGiul0llyDpNogcIkYGUYFHl2zA2osoWFVR9FtV4wCxpQzWKXeX4svHOH7I7rAGOnTKGQCACzzQ5VGYYQm8hK7doJsCvKL4c5aayUFiUC7CIrNWNiSQMqr1avzMhKoAHZ3Cfh+gqen5+NpJeUaMyEVXjBjKIYpUpcgKVTJn9MALvO6+rWBFZ0twpjpfE2IXPUWKnjXc0W+vVDqkJ+ht3gFVerM8xZqfKCmTkbwjUV1aQFg0JRMeU5pSbaY0oDKijIB4BkPCHkh1gYUIWqSQCIsIpi1KwJjKM9pSmU7Gvwxpw0VlanA7Go/KJEgF0omzGgleNxGk0mmC2WikvQK+mYT8BKIEOMupxtEwgye1rRpQKV1qMBGaUl7XuVyc0qjGIYOhuqIitGbIuS7jFAugVbhZVosO6sUQ5z0lgpVd0B7OqHMu1eKscwqJmYRCXFyjOvxMhK+ZjSLzFlT7gS1YBkk0nF718oxGQ7DjUCiyijHQaU7sIACDSgyWymvtGoOgeICCz0nJVkKG1rBLATDlhVRFasclZqFjtyHiuZuHI1YOFuH2vXrkVPTw+OHj2K++67r+C5jzzyCI4ePYp9+/Zh5cqVAID29nb86le/wq2f+QyaGxrw5S9/WTz+29/+Nvr7+7F3717s3bsX69atK3jdcLrRLO3ISqz9UiPaofz8LKKxki9dB9h11lA3pyrQAWLUBkqdkEinAWVD2CVY+QIMMIhinMojK1bd4JU29yRgyZurUW7NbtdjMBjw6KOPYt26dVi+fDluu+02LFu2LOeYdevWoaOjAx0dHbj77rvx+OOPAwDi8TjuvfdevPGb36C35wPcc889Oec+/PDDWLlyJVauXImurq6CYyILdyVFVqwWlsxWHEqfX5iNQEYNDchKIaxQiAJkNdhlxbYoKWdhvM9WOcxJYyXkPNTRgLRvuFWFmgwAk27wakJ+ch6TDucKOlETFOr2sXr1avT29uLEiROIxWLYsWMH1q9fn3Pe+vXr8dRTTwEA3n77bXi9XjQ3N2NoaAh79+6FxWFHyB/A4cOH0dbWJmtMJDK20TZWNhtikSiSCfnF04lYDPFYjHoUo6YvJ8BmTlVVVamrsyICGcpb26sTErFjW5QW5BNKU4+sZMDiVBFZMUo8q1GTAWx25lVLA0YC9BvsKu1ETVAoMm5ra0NfX5/4c39/f57BKXeMxW6HMZXCypUr8fbbb4u/37x5M/bt24cnn3wSXq+34JhuuuFGAMD3tm5FfX29on9XIaipRwOIYaA7p9R0jwHYCGSqbeldGFTmsVmsCWqoSXINmlBjQEmDXT1nJQNKe5MB2VXYlA1DOuRXoiYD2HicanooAmwWFnFMamncLCqpqqoq77jZz6HcMTaXA5de8mF85Stfgd/vBwA8/vjjWLx4MVasWIHBwUFs3bq14Jie+r8/AgD8y78+hLGxMZn/ouKgYqxo56xU1A4BZEx0BRYiBa80j81I5aa0ewzANrKqtDklFXPSWKktKgXY0IBKxwSwNVZqohhm0Z7Sl7hAYWJ/fz/mzZsn/tze3o6BgYGc80odYzKZ0NTaiuNHe/Hiiy+Kx4yMjCCZTCKVSmHbtm1YvXp14TFVoGcOsHE21NKALLbDUVPPBLBTuVnsyrrHAOy2LrGqnVMadl6fk8ZKaVEiwDC8VsGZA2nDQP0lVl6tTs5jp5qkJ5Dp7u5GR0cHFi5cCLPZjA0bNqCzszPnvM7OTmzcuBEAcOmll2J6ehpDQ0MAgCeffBJxpLD7rbdzzmlubhb//5ZbbsHBgwcLjonklah75hXoAFlVStdZ5GbFXqFK1wRWhkGNnJ6ZAVW5Tmm4p9WcM1YGoxHVNqviUDaR7sxMv85KuRoJYNNlWXXOikFhotIdeQkiBSLjRCKBzZs347XXXsPhw4fx7LPP4tChQ9i0aRM2bdoEAHjllVdw/Phx9Pb2Ytu2bfjSl74EALjiiivwuc9/HjAaccfnN+ZI1B966CHs378f+/btw9VXX42vfvWrRcfFKjJWSm0B6cJS2g4QKciPxZSNKUR/Oxwxj6ZCtAMwotwUqwHZUZNq5hSrpr9SQH+zG8bI5DyUGwYmiWeFW3EQsMkv2BGfmVHU6YOMyepwoKqqSnEuLn9MaqO9wl5wV1dXnrT8iSeeyPl58+bNedf74x//CIfbhf/95uv4/r9txe+e2iF+RyIxSeMKMXh+djsmzgwqPj8SDMHT3ERxROpYDSA3Mo5FolTGJDplitkW+pGV0WyGyWxW7JSxUt5ZHHZMDCifU9FQCDUtzeUPZIA5F1mp2SWYIMLCMDgdivMwAJtu4mo6fQCZhYWorWhATSfq7PNovsRqI1AgXT/EYGFRqi4F2MwpNdQWkBUZ22g+P+U1jgAbMYNaupuV8k51HlTPWUmHWoUbwEjlpiKZCqQpGxYTU03ITwwDxXHR6KqRfR0qY1JZj0bOZRFZqaGWWakBaUVWtJDZnqdyCnDVOmUAm+enptUZoKsBZYFGZMUq8azK42TQC0y18kdsA0VxYVFbqJyONGiKUdRSk+Rc+g6Q8uJpgOE8VzEmst0JC8OgvKsG/d6OaiX+QJqGp+zAqinIB9h1+5CCOWesLCqlswC7/JDSZCqQ1QuMasRAibKhahjSxdMKOlEDQCqZTFNuDCgbVdE63cQz6aigVrlFXcygMrJioca1OBxIxOOIR5XlwJLxBGIRuluXqKUBAfoCJ7UF+WRMZiv9LZakYO4ZKyr5Bboei5hMVSmwAOh7nGrpUnIdWiCqSTWCDdo0Lo05FaFc7EqLmgToPz9VThlR3lE2DGruE0BfjUuLBqQZxahpYkug5W7Bc85YWSmF11Q5c1E6q8JjEWs9KEYMqmu/6Hd+Vls7BNCv1VErpwfSY2IQgdKJjOkueDQWu2rKNK4apgWg3w2eDrVMN7KiZUABbXYLnnPGisYNp11FTyvaA2jTgOoMg5h4pnyv1Bor2jSu2q4aAH0HSIys1KgBGSwsqhP0jKJ1KnOKZhRDITKOUB6TSE2qoXEZbbEkBXPOWIlRjGpFCz3Khka0x4bLV6kmY9D0V61CEUhvQ15pNGAoBLPFAuS3IFQ3pgqicQ0mIf+lbk6xUQNSoQEZsC1qc+u0nVdAJQ3IqNuHFMw9Y+VwIBoKK9o2gSAaDIqdMGiAbnhNz5OqttsqNOdBwwumO6ZkIqGqSJX8mwwGOq9UxjNXs9jR7YJA6EQ1zy8ZTyAWpStmsDgcqu4TwC4/pJoGZKBQpLEmaKEInHPGiopnTlnlRqWrBmWPJaP8UX6vSM87qsWSKhWKAP0+ijTyaOT8KgMdlRSdxY6us0FD4UbOp88gVFZkZbHbFe9FJo6JcjkLlRSKTgNKh9VhV8W5AvSpCLUNY4HsSUDHMNBY7Mj5lUYDUhfIONTVDgHATIhyZFWBxiqjJlP//lXTpOFVCokA+jVNail4gH45C61oL/taPDHnjJXF4VAlxwbYvcRqJgHtXmA0RAMAA4+TghfMQrqu2jMPkciKrrFS1XS0Ap0ycj7tXIxaw0B7o1ErDQaICJwoGVG1BfnZ52rRxWLuGSsnhciKMu8qCixUvDDJRAIz4Qj1MVWc8o4S5Wax2wtuqKjlmAD6OSs1vQFnKHf7oBqtU5bTqx5TKER1a3uLysbWAIOco8qCfGFMOg0oGWp2CSbI3HDKlJuKhQWgG8XQKAAE6NIjard3yR4TAGpUEi1qEqAYWVHIeRAHiPY8V09v0auTo9GVAWAwp5wORFSyGrT3tKJRkJ+IxwWBjAZb2885Y0XLiyLXogGy2KWSSVXXoZmLoZYMp0i5kYVAtcyYQX5P/X0SHBWaNKBaowDQfX6ZaL1yclZq+wISiIaBYhSjep5TFl3RYBAANu3qpGDOGSu1vckA+jVNagslCWjKZ2l5wTS5fCsFObZwPt1iVyo0YNqLNhjpvFI0ch4AXQeIJg1I69nR6B4DMFBOUqSWaa4JVNYpjXYLnnvGSmXXZyAjE68kLwqgTANSqIkB6E5MC4WC7uzzqRnRCqUBK80LpmWsaHaQodEpIvt8qmwLhftErkUDNOhuQHBg9XZLZWA0m2GqrlYdWZEEIzUvyqk+jwZU5sJCM2dFQ+EG0JfPqm3OCmRq0mjSgFQcIIrdPqyO9Jb2CneeJqDqANHKzTKglmnl1mmKrqg5QHpRcGlk8jDqJgHZhbPiuGDKL3EymVSl/AHo7qpMM48G0DFWRpNJcIAovcS01IBq9x0ioE0D0pjnM6Ewta1LqEdWFOZ6lcFAiVqmX85SaeuUHMwpY0UrWiDXoBnF0IqsaEYxamTPBNFgUFjQLZWzsNDMOVKdU+EwtciKtBVTC5rdPmjOc4COYaAhxwYozylKQiJh7za6awItB0hvt1QGNHbfJKCqvKNQQQ9QFjNQDPmF69FYWCovZ0WjBQ0BzciKas6qwoRENNud0aMB6XWLoDmnaK4JQvF0ZTn6cjCnjFWmkzGdUJaax0KRBqRVmEgtmUqxJo3WS1zIgK5duxY9PT04evQo7rvvvoLnPfLIIzh69Cj27duHlStXpsck/LseeuBf8s6tqanBzp07ceTIEezcuRNer7fsuCotZ0WbWqbpANEYF22FKQ1JPS0GgVyj8pwNul1tpGJOGasMZVNZYgaaAguA0gtDmbKh4nFS2KIAECifZDIpGhqDwYBHH30U69atw/Lly3Hbbbdh2bJlOeesW7cOHR0d6OjowN13343HH38cAGBLOyz/+M1v5Z27ZcsWvPHGG1iyZAneeOMNbNmypeS4KjZnRanbBzUaiWLOUaQBVVKmRCBDZ0z0GKBIMEjFqSY5Qmo0oNNBrYOMVHAxVn/30jNY9/9tUn0dGvtGEdDyWEiCno4XRagI9ZPTSqHdC0B/YUnE44hHlW/FQZC9M+/q1avR29uLEydOIBaLYceOHVi/fn3O8evXr8dTTz0FAHj77bfh9XrR3NyMCy8WIqxTx47nnbt+/Xps374dALB9+3bcfPPNJccUDQVRRaHOilZXBoCuA0SjxhGgP6eioZCqrgwEUUq7PWdqvyqHcqOd7weEecoTVQCKPuWuri7U19er/iMtS84F4nEMHj+p6jqOGi9qWpsxeKQXiZg6+WxtWyuq7VYMHT1e8rj6+nqMjY0V/d5gNKL1vA5MDQ4jMDGpakw2twt189ow3HsCMZULetPiRTBWVWGgt/S/rxyqbVY0nrMQY6f6EQkEVF3L29wEu9eNgZ6jZY8td99blpyLSCCIyYFB1NTUwO1249SpUwCA2tpaOJ1OnD59Wjz+3HPPxdDQEALpf8OSJUvQ398Ph8cNS61XvOfZ565YsQLvvfeeeI3ZP2ePtaGhAZGqFNwWG/bt3SvxjhSGwWRC69JzMTkwhODklKprie/MB71lJefl7nnrknMRDgQwOTCkakxmiwVN5y7CeN8ZhH1+VdeqaW2Gw+1Gf88RVdcBcueUGthcLtTNb8PwsZOIRSIljy13z+vntcFYXY3hYydUjcloNqNlyWJMnhlEcGpa1bUsDjtqGxsxdOq06q49ADA2NoZ169ZJOjbF+vN3Lz2T2v7eW6qv82cbb0ttPfBmyuKwq77Wp771d6l//M3LZY/r7u4u+X1tW0tq64E3U6tuvlH1mM678rLU1gNvpuZfeL7qa32j67nUTyjc88ZFC1JbD7yZWnH9taqvteG730x9c+eLko4td9/v69yR+vz/+W4KQOrTn/50atu2beJ3n/vc51I/+MEPco7/n//5n9QVV1wh/vz666+nLr744tQXv/vt1NYDb6ZqWpvzzp2cnMy5xsTEROk59c2vp4aCftX3qX5+e2rrgTdTl3zietXXWnnDdamtB95MNS5aoPqeP/D2G6mbvv5l1WPyNjelth54M7X6lk+qvtbnHvpO6rF9b6q+DiCsUxu3/m/V17nkk+tSWw+8maqb1676nt/2wD+kvtH1nOoxNS1elNp64M3URWuvoXKvyo2bxYcLDRgJBKG8HWcGJLymIskOBKnQbSzCayrjstthTKm+DNVmmrSEKEBukre/vx/z5s0Tv2tvb8fAwEDO8cWO8af/fWRc2ecODw+jubkZANDc3IyRkZGSY6L1b6OtUATUK+9I7VDF0YB2O+j0SadHuYn1hCpbQAH0ZOI08/1agYuxigaDSFSpXzlpdA0miIRCMFstqpV3NPNoNNurWJ0OKi8xbZk4rQU9u36ou7sbHR0dWLhwIcxmMzZs2IDOzs6c4zs7O7Fx40YAwKWXXorp6WkMDQ1heFygYJobGvLO7ezsxO233w4AuP322/HSSy+VHFMkFEKqCqrnFC2Jv3ANOnOKVu1Q9jVo5ayoGiuKog+1zXUB4flRWQ8oOtVawcTjj0QCQYxMTKi+jtXhoCIaAHJfmFK8+X/+53+WvA4LL1it8o6IPva+uVv9mChW0ctRk5W779FQCI7WFgBAIpHA5s2b8dprr8FoNOJHP/oRDh06hE2bBFHPE088gVdeeQU33HADent7EQqFcMcddwAQcnLJeBxdL7+Scy4APPjgg3j22WfxV3/1Vzh9+jQ+85nPlB6TxDlVDrRUk4C8KKbUPac5z5OJBGKRKJViZYvdjjOnTpc/UAKioSActV7V17E4HJKFROXmeSQYgqm6GkazGYlYTPmYKM4poPy4WYCPsQoGEZpRrwCzUGhiS5AdMZRaWLZt21Z6TJQVisI1VXrB6fP/+NvfqR4TqaKnRdn4RsclHVvuvs/2gru6utDV1ZVzzBNPPJHz8+bNm/PH5HAg7A9g6cqr8r6bmJjAtddeK2m8QGZr+3JzqhxotRUD5HVmKHXPaTIIAKhtE2Jx2HH0/cMURkRai9FQTUp3ysrP80yxshphhBitU1o/y42bBbjlrKjkPBx0OHOAXi6GZnhNqwCXZh6NXIcWb05zTFSoSUpV/UC2A6RuwavEnBX1OUXLAXLYVTdGJpihJF2nPc/JNdWA9vPTApxyVnQWOxq7BBNQ4/IpeiyJWAzxmRnVNKAY7VG7V3QWFqHfHUVjxZmaLIcIJeGAuEklpd6AgHpqmbZnTmtPK5qiHWpziqaQSNyAUaUDS7Grhlagaqw+/elP4+DBg0gkErjkkkvE30cCQRiMRhw+cgQ9PT247rrrCp5frr0NE49llie1Y8cO7N27F3v37sWJEyewt0jNzIkTJ7B//3585d57c65HY1xKJ+a3v/1t9Pf3Y8ezzwIAPrT8/ILHSWlNlA1a7VWKvcQPPfQQDh8+jH379uGFF16Ax+MpeD6553v37sVffn4jzBYLDCa1YgZlc6rQPYzOiowLtXeSApLLoaF6ze720d7ejl/96lc4dOgQDh48iC9/+ct5x//Zn/0ZpqamxHfgW9/6ljAmUTRA0QGyy5vn2c+/u7s7rVC05Tw/pfccSIuuKM2pbEdxyZIl4v3cu3cvpqen8Td/8zc55xS77yIDRCGySsTiiM/MlDzuySefxPDwMA4cOCD+TmrbMbnrilxQNVYHDx7Erbfeit/9LjdXUuNyAQCu/NhHcf311+Oxxx4r2JamXHsbWhX0QHEuf8OGDVi5ciVWrlyJ559/Hi+88ELRa1x99dX4vz95CjPhCJIJGuL8NG+uYmI+/PDD2HTPlwAAf/zNb/O+l9KaaDZoeJxCkthU0DDs2rULF1xwAS666CIcOXIE999/f9HrXH311Vi5ciUe+bd/AwDZC95sKPGCi91DYlwsdnvR9k6SxuRwUJ1ThN6Kx+O49957sXz5clx22WW45557Cj773//+9+I78M///M/imAB6TllEIQ1Inv+qVavyFIpq7nn2ddTOqdk9+I4cOSLez0suuQShUAgvvvhi3nmF7rsYWalNV0jM9//4xz/G9ddfn/M7KW3HlKwrckHVWPX09ODIkfxK8gvTHr6huhonT55Eb28vVq9enXdcufY2NHYJJpDisXz2s5/FM888U/I6tHrwieMKqt+Fk0zsQly+lNZE+WNST+Nm8jD592rXrl1IpBfmt956C+3t7WWvR4/ekk8DFruH2Q5QsfZOrMZUCsTZGBoaEpmCQCCAw4cPo62tTfKYAHo04EworFpgMXtMau45QHlOFTHq11xzDY4dO5bTXUXSmNTmHO3S1qnf//73mJil3JbSdkzJuiIXXHJWtW6B1iELXn9/f8GXpKmpCUNDQiuXoaEhNDY25nxPqygRgLi1fTHv7qqrrsLw8DB6e3sLfp9KpbBz507cdOstsJroiSqV0CPZ2Lx5Mx78138FAFgK1Pu0tbWhr69P/LnYs8gZE4VkuNQE75133pmn6iMg93z37t248vLLc66rFFYFNGCxe0gMscVuU3SfCWjS3UDh57dgwQKsXLkSb7/9dt7xl19+Od577z288sorWL58OQAGakAFOavs53/XXXfl5WHU3HOAXrFyKWdjw4YNRR3gQvddrL1UGVmpmVPl1mVA/b2XAtnGateuXThw4EDe56abbip6TlW6f1S28k5uYa/JYknTSOpfll27duFPv/89AODr999f8N9w2223lYyqrrjiClxyySV48513UOfx4qqr8qXPSlCOHil1/x9//HEsXrwY//KvDwEAvnn/N/LOL9QpudyzoLGnzo9/8hMAwL98938XnTff+MY3EI/H8fTTTxe8Brnn69atww3XrQVAo9hVfmRc7B5mK7eU3OfsMdE0VrNzjg6HA88//zy+8pWvwO/Pldjv2bMHCxYswIoVK/DDH/4Qv/jFL4QxScx5yBqTzDmV/fzvueceXHrFRwBkhChq7jlAU3RV+PmZzWbcdNNN+PnPf573XbH7TksNKEdOrwRq770UyA4J1qxZI/uPDJ8ZQO2KpSLvXagdDpBpbzM0NJTX3sbqpKdmIf+G7+35HZ7Y/hReeSSX2zYajbj11ltzRCKzMTgoNLusqjZhcmwcq1evxu/TBlANosEQ6tpay469FAiXv/rii/O+k9KaqNCY1NKAf/O1r2LzU0/gS3dvwpE338n7fuPGjfjEJz6Ba665pug1yD0fHR3Fn373OziuvoyKJFvuS1zsHsYiUSAlXFPJfRbHRGl7EILsbh8mkwnPP/88nn766YJ5k2zj1dXVhcceewx1dXX0qUkF0Xr283/xxRdxwUUXCddKGxk191y4DqXSgyLlEOvWrcOePXsKtu0qdt8nJicBqG/BpsQpIyi1LhOovfdSwIUG3NX1KgDA6XVj4cKF6OjowDvv5C9YpdrbEGqMFg0BFBcOXHvttejp6cGZM2cKnme32+F0OoX/dzpR763BwYMH6YxJRRRD+HmLw45UIoFDB9/PO0ZKa6LZEFtTqVBJlcp5rF27Fvfddx9uuukmhItsT55zz+12XLZqdc51lYC025LrAJW6h6lkEha7vWh7JylgaRiefPJJHD58GA8//HDBY5uamsT/X7VqFQwGA8bHx6mKm4D03l/pPZakYPbzv+6669A3KCyG5F6puefCdTICGaUwWy0wmgozQKXYmmL3nVZRvhoaUErbMSXrilxQNVY333wz+vr6cPnll+Pll1/Gq68KRupgeluF7zzwAF599VXcc889SKapwW3btokRzIMPPog1a9bgyJEjWLNmDR588EHx2iSyoitmKBwxFOKVW1pa8PLLLwMQJtYf/vAHvPfeezhn6RIMnzmD1157jcqYlKqkAEECvn//fmy84w4YUYWvfvWreWPPbk10+PBhPPvss2J7oWKgoZIqpSb793//d7hcLuzatQt79+4VVVzF7vk777yD3/3q1+kxKX+JrQoVbsXuIWnvZLHb8corr+D48ePo7e3Ftm3b8KUvfUny9WnTgMQpu+KKK7Bx40Z8/OMfFyXS69atw6ZNm8Sxk/KT9957Dz/4wQ+wYcMGYUyUDeiMTMMw+/m//PLLOHTkAwDAzZ8UqGQ19xzILz1QgmK5WZvNhjVr1uSoi6Xcd3ItGgInKc/vZz/7Gd58800sXboUfX19uPPOO4uuy2rXFSVg3trdaDKlth54M3XNXbcrvsY5H16Z2nrgzdS5qy+hNq6/feGnqb/8/oOqrvGPv3k59alv/R21Ma29567U1gNvpqqqqhRfg9a2AuSz+pZPCttotDSrvoa3uYnKmBw13tTWA2+mrrjt04qvQXMrDvLpmxwXty5R+vmHNzpTn/3H+6mN6VPf/Hrqn377iqprbNr2g9T/95P/pDYmcRuN9jbF17j8s7ekth54M+Wqr6MyJmdtjeo5VTcvPac+uY7avbqvc0fqcw99R9U1/vmPr6Vuuf9r1MakxYcLDZiIxxGLRlW1NqKtRgLo1A/NrqlQCxq7cCpRuJUCjW7wtKXPNNoI0R4TACQTSSqUDa0WQgC9eU773QPUzSnancQjFOYUi+7mVGhAim3FtAIXYwWk+wOqCGVFgQXVl1idys1gEjh3mtQkHcPAxoCqeX60e5PFZ2aQiMVV3yeaYwKAVDKpqiamqqqKugNEozMDizwaua5SWBwOJJNJzBTJc8pFPBpFIq52TtFfp9SunSYLyaPpxkoSosGQqsiKhcBCbbcIMiYWhkHtC0PbMyfXVQqr3Y5YJEqtKwMgLAhqCjhpb5sACMZKnejDCoDRnFKVc6SdR6PglNntVFpSZUP1nGLBAKmMrKwMDKgW4BpZqQqvRek63UmgZmKKk4ABPaIqCqUdWYXo0IA0I1BAfc9CmltxECSTSVWdGVh45jQ6M7CiAdVEobQl/oB6ypTFnFK7a4XolFF8flqAn7EKBlVVYVscDiQTCcyEI/TGpNKAlmprpBRUaEDaRaVlun1IAW0aCVC/TQgLw0Ck60rBYkwzFCi3asqGgVYelDa1FQ2GVOWLWTkbVOaUTgNKQ1Ql78pkYqoNrxm03adCj1CnbOjkrCrt+bHYNiGZTKqMiumPSe3WJdU2GwwGA/VoAVDXRoiJAxQKU6GWaa8JqiIrnQaUh4jKG06ziS2B3MLE2SAvWqXRgNV2G/V6NKCyoj1APWWTeYnp5T1SyaRYbKxoTEwWO3UqN/LeRgL066xUOUAs5lRI+RY9AJs5lb21vaoxUabheYNvzkrlYkebc1VrGMi/p5LEDBkvmN6YEnGhJ9zZSANGQ2Gk0gXqNECK3ZXmrVgoFNXOqVId85UilUqpz8UwogFVsS1pp5rmnMre2l7RmCpw48UPf/jD2LdvHywWC+x2Ow4ePIjzzy+8/x4BvXbhZaA2lLU66e0STJD9EvvHJ8ocXWBMZBJQVSiqowHJPaY9MVULZBwOTPTT7RWmmgZkYEBTabWj1W5HxB+QPyZxl+DKiaxY7TIbCVJIDVSaA8SIQQCEf29walr+mBitCWqwe/dudHZ24rvf/S5sNht++tOf4v3389vDZYObsYoEhFoPo9mMRCwm+3yaW9oTqK31EAUWFCcBkXdXkhcsXE9l6QEjL1hVfojBwkI8avXPr3JqmjI0IGU1Z0Cl6IpBoSsVB4i6UVfXBooFA0QD3/nOd9Dd3Y1IJFJw1+rZ4JqzApSHshYHOxpQ7SSgbhhULMKsvGAa+SHaLwupk3tN4ZbbFocD9d4aHD58GPv27cMLL7wAj8cDQNjvKRQKiT30pO46m1RrrBg8P7WdGVgl6NWKrmiXaADpRgEVNs9p0YC0a9LUora2Fk6nEy6XC9Z0fWEpcM1ZAcrVPywEFmpfYqvDIURCcXqFroA67070olgYK4X3iUVXBjImo8mEX/3614q23LY47JgcG8MFF1yAiy66CEeOHMH9998vnnfs2DFxm/EvfvGLksaUSqYA0DAM9BYWtZ0ZWM0pNaIrIoxisSaYzGZVYgZ2kZXS5+fATDhCtSCfBv7zP/8T3/rWt/D000/je9/7XtnjOXawIN6B8oiBfmRFIdpjoLBRkx9iIX0G1HWDJ3UrLJRbAPDsC88DkL/ltsVux1D/GSTSL/Fbb72F9vZ2VWNSHVkxEH0A6grgxe70LGhApXOKQW4PUF9AbXU4qN8ncj01QrBKk61//vOfRzwexzPPPIMHH3wQq1atwtVXX13yHO6RlVJPyuKk75mr9VhoN4wlUNOaqhIpG1ZFieR600FByCB3y23BC84sLHfeeSe6urrEnxctWoQ9e/bgN7/5Da688sqi47jrrrvQ3d2N7u5ueNM0oprIisXCoobGZTanVORBWSncCFWmXM3JRvRBrq0ELKI9tfjJT36CT33qUwAEB++yyy7Dr3/965LncBRYEJWb/MnJoigRyCrAVbyw0DeggEoakEEPRYDWYqdsTLt27RI3lszGw09vF65f5vkV23I7O7/wjW98A/F4HE8//TQAYVfa+fPnY2JiAhdffDF+8Ytf4Pzzz8/bBh4Q9mTbtm0bAODdvXsAkwoHiIHoA1BH41ocdurdYwB1DVpZOUCZAmoVDBADuhRQnkJhoVDUAvyk6+lJoMSTEjlzikWJQFZhooooJkJZXAEIL7Grvk7RuSxfYq1EA2vWrCn4+yWXr8L5f/EptM6bh8EjvbK33HZfegGiwRA2btyIT3ziE7jmmmvEY2ZmZjAxIZQz7NmzB8eOHcOSJUvw7rvvlhxrKpFUZayqGTRnBdQ5GyzyjQAlB4hRtK60ZyGT3CxZp1Q4GyzWKd7gTwMq8FhE6SzlyCqVSqmKYgR+urIiK6uT7rYJ4pjSCsVCUUo5sEvQC9e74aZPAJC35fYvf/lLWOw2zGtpxX333YebbroJ4ax7Vl9fD4NBeD0WLVqEjo4OHD9+vOyYUqmUUHpQYQuLWtEOC2oyEgjCYDSi2lZeCZY/pnQerYIoN7JlEPXaPbK1vQqn+myIrPgLLJzyJ4HS7celQC09wqKFiaqcFSvPPO1sKGnyyUr0Qa530cUXy95y+9ipkwCAT95wA1wuF3bt2pUjUf/oRz+K/fv347333sNzzz2HL3zhC5icnJQ2rlBY5ZxiYBjUzHNGG/dlCuAVsC2sSjRU7DDAioIHVEbGOg0oD0Q6qcQ7yHjmlTUJBDVghS0srBY7wuUrKCFglqBP/zsf+rd/wzsv/jLnu8HBQdx4443iz11dXTniCU9TAwDgn771D3jrufxo7IUXXsALL7ygbFxqImO7HWPBvvIHyoSqxc5JX+EGZKncnA74x8ZlncuyRCP7+nLAyikD1Of3zgZjxS2yApS3V8m0EGKQH1JLAzKJ9oIwmkwwWeQ32GWpJgOUSXpZbFIJqOvMwMozJ9esNOWWIF2vLOmzqtQAw4J8QJnoimV380qkcXmDr7FSWFeR2TyschYWwrWzogEBZZQpq9ovKi9xBXnB4o6uzKjlypE+AyrpbsY0oBLKm0jLaVPeaspZWHY3V7p2VlVVnTVqQK7GSmkbIZaRVTQYglXBdt+saIjsayrZhpwVP62mwS45h7boI5lIIBaJKlJJsdzqOxpSZhjEhYWRGtBoNsFUXS37XFa5WTXlLKzk9IlYDPFYTJlTxjJaVxgZE6M+13cJBjSIrJRJ1xl6wQrD68zEZGFAlXfWYCf6UO4Fk2gvlUrRHpbire1ZesFK5xSrTh+AOuGAlUFBPqByTjEy6oAQramZU5WUW2elmtQC3HNWSr2oRCyOeDRKf0xKqUmGkZVaeovpmJREMQxpCPXORuVQy6zo0uxrKr1XTBiEgDqFMKsFOBJU1u6M1fY8gHKBBUvRB2/wpQEVRlYsmtgSVCI1qWZLAJYtoADlNCAzY1WhhkFdgp7hnJI5LpPFAqPJxDQ3q9SBrbg5xZgGrLTcLG/wpwEV1lSw4lyjoZCibcjZeuYqaUAWyi2VOSuWzkblKbeU1VmxjvYA+XOKRD0sxpSIx4Wco1IakGG0rvTdAxjlsQNBYT9Ak7xqI5a5Wd7gTwMqCfkZ7BJMoDRiYNVVQ7imsjEZTUICncVLTDaFVOpsVBwNyChBDwhzotpmle8AsaSWFcr8xUJXRs9PaTkL88hKoWgnHosp2lxWypgABc+PYW6WN/jTgA4Hqgzy/iyreiZAeTNbtjSSsvoTlmMi161EGlCxAWWUoI8qVLkRL5hVb0A1Y2K12CkXXdmZ0KWAOjEDi+JpQLkYhWW0zhucIyvCm8urQWFVOwSo8FjE2i/64yKLlXIvqvKimEqjAVkn6AH5wgHS3SUcCFAfk1KBjIWhaIBcV1m7JRuzaE/NPGcXgaqNrHRjJQtKK9ZZtXsBsrcEUEYDspgEShvsislUVouwmpwjq5dYjQFlNSa/YGysTqes82zp4yMMjJXixc7OjpoUrqswsmLUAxNQRwOyc8pUsi16zkoelO7LwppGAuQnni0OO+IzM0jE4yyGpWi3YFY7uhJEAkFYXfIWYIA1jRtStFEeyzwaWdjlLsLEuEX8LGq/lAlkWNOASjf1ZLomKBbIsJvnaiIrVrlZ3uCeswIU8K48aEAFhoFlVbiSzuusQ/6w3w+bTGNlMLLZNoEgGgzBYDDI7gbPJbKSzSAIDlB8Zob6mJLxBGJR+d0+LE72Agu5oiuDyQizxcKMQVDa7YOpAVWYB2WZm+UN7u2WAHkvcVVVFVPPXOk2BaybQyqjAdOUDSsa0B+QTW3xEH1k/x2pYJmgF3NWMg271elk7gDJjqwYdmoBlDEIrBojEyiNQnk41bJLDxjmZnmj4mlA1r2tlDaNtTjY1X4BCmlAxgtLWIFyS5T4++nnYQA19BabTh+AisjKxdhYqXCA2OWH5M8pm4vsG8VmToV9ynKOTJ1qMbdeOSkU3qh4gQXLeiYgmwaUK+llNzGBdGFihdGAEb8fNrdL1jnkhWehcANUeJwudjRuJrKSb9hZ3SdAWWRlSdc4sujrCAg7KZgtFhjNZuljIkIiRs8vnHY25FLeFZlbP0s6rgMaRVZyFmGWuwQDEEQSsbhCGomhsVKysDDPWQVhMptl7bNFXnh2hkFFzpFRtBeLRJGIx+VHVgzHBJCaJpnRAuPFLqKgWwvrORX2+4W/I9Mxq7bbmK0Jwtb2YT2y4gUl3gHLTsYESugRHgILJYXKLBWK4kssw+MUvWBWNKCCYtdqmw0Go5EZjQQoU05aXU6mnQaUlB6wXuzEbULkOLCiapIRDaggsqq22WAwGJg+v6gCMQrL3CxvcDVWgncQkjkx2UZWgLIuy8xfYgVbX7A2oOTacl5iMb/ALEGfzi/IoNyIEQkzvldK6gnDDGTrBJFAQDY1aWHY6gxQVj9E/g2sKNOIT4lTRpoEsGVbZKs5GdY48gZXYwXI35KDNT8NKKfc2L7EIdmNK1kn6DPFrpXoBUunbGyMRR9A2jDI9IJtTifTaC/sD4iFx1LBnAZUUM7Cup5QyZwSnWqGUYwg85ffLkunARVCbi831kWJgPwuy1UGA/PEpRJJNusEvbKXmG0UYzUJifn7v/VN7Ny5E16vt+Bxa9euRU9PD44ePYq//uIXAAgG5dvf/jb6+/uxd+9e7N27F+vWrRPP2bJlC44ePYqenh5cd911ssYldGaQmaB3so+MlZQesKYmhb8j3wFiNaeioZDQtNktI7Li0INPqUBGl64rhNzGlRbGAgtybTk0IOltWGnGyuZ0Mo8WAHn1Q1anA/FYjMnGmQDwd3/7t0jF4/iP//ovvPHGG9iyZUveMQaDAY8++ijWrVuH5cuX4+Nr1gDIdIp4+OGHsXLlSqxcuRJdXV0AgGXLlmHDhg04//zzcf311+Oxxx6DQUYD5ohfnhdssdthMBgYG6sAjGYTzFbpAhlWm3mKY1IgurK52M4pIB2FyonWeVDLMjvUG81mmMzms2JLe0ALYyXzhrPcNoFArsdCxs+SBlSknGRMAxKBhTwakF1fRwBYv349AlPTsLmc2L59O26++ea8Y1avXo3e3l6cOHECsVgMv3vzjwBK5zzWr1+PHTt2YGZmBidPnkRvby9Wr14teVzRYFAW5WZlXDsEZCJjOdEVaxopqqicha1TBsjv1iLmQdP5LhaQv06dPU1sAa1yVjIXO0FeTn+PGHFMQXnKLR6djJXUf1mdDrYKNz8RWMjzOFlSk01NTQhO+2BzuzA0NITGxsa8Y9ra2tDX1yf+PJUeD7lXmzdvxr59+/Dkk0+KNOLsc/r7+9HW1lZwDHfddRe6u7vR3d2N+vr69LXl5WZZ5/YAZQIZ5jSggg71VpeTqaMIpCMrGdJ1lk2ICeQ2CjibmtgCmuSs5EVWrBVugDAx5VGTHOT0inJWTtF7ZgGRy5ejvHM6VTdm3bVrFw4cOJD3uemmmwAIC3ypBbiqqirnZ6NF6PkWCQTx+OOPY/HixVixYgUGBwexdevWgucAKFoYu23bNqxatQqrVq3C2NhY+tqlxzQbZP4xpZFkCmSMZjNM1dVMWQ2yqacsB9bhYNLsNxsRnzwaUIysGL9/StapsyWykrdHMgXIz1mxVd0BglTV6nDAYDQimUiUPZ6XnB6QbqyqqqqYt4AChOcn5yW2OO2qvc016RxTIQwPDyM5MwOry4nm5maMjIzkHdPf34958+aJP3vr65FKpTATCmMk6xlu27YN//M//1PwnPb2dgwMDEgecyQQgqm6GkazWRIrQCIrlpSpmHOU+P7xopHkpgZYMwiAQAM21i+QfDxxTFgrJ4lCWEotpShEYUyZ8oImOSu5+SHWLwt5mFIVSbyUP4B0Lt/iSCfomXP58qJQm5MtZdPZ2YnWhkbYnE7cfvvteOmll/KO6e7uRkdHBxYuXAiz2Yyl5y/HTCiMVCqF5uZm8bhbbrkFBw8eFK+7YcMGVFdXY+HChejo6MA777wjeVxyDYNNjKwY5qxEmbi0iI/XluhyHVghN8t+nstVvUYCQaSSSWZjksu2kPGzzKPxBPfIKhoIwmgSFEmxSHk1D5fIKj3xbW4nwj5f2eNZ9ysUri1vYlo5cOZAmnKTk6CnQAOWwoMPPoh/6/oF/PZqLLPV4TOf+QwAoKWlBf/1X/+FG2+8EYlEAps3b8Zrr70Go9GI/z60ByGLMPUfeughrFixAqlUCidPnsSmTZsAAIcOHcKzzz6LQ4cOIR6P45577kFSxkIUyTIMwcmpsseLW3Gw7A0o21ix3R6EQO5uwUJkxdqB9ctTvbocogCJFaJZG8WGpsuvUzYO1CRPaEADZiIGScbK6YB/dJzpmOS2V+EisJDZTZxHVwbh+gFZ9SesKZuJiQn899M/w8f+8s9x7bXXir8fHBzEjTfeKP7c1dUlytLveORB1LYLYomNGzcWvfYDDzyABx54QNG4MpGVRC+Y4caLBGGZ3T640YByIysuNGAAFrtNMuVmc7m4UPCAjGjdTebU2RFZ8RdYkEVYMm/uYE5DkDBZssdpZ99VIxlPIBaJSqYBeXRlANLCARmRlcVhZ0ptAcKYTGaz5PohHtLniMwoxupyIplMYibMbqM8YnSkPj8eQiJyfTkqN6uDbfE7kLUmSHRgrU4Hc7pNrkLYSmhAxveKFzSQrsvPxbCmIeR2ZrA67YjHYkzl9IC8/B4vGjDsk74BY7VN8ExZK7fkPj/WnSIA+XVypB6N1VYcgNCbU04XC9Y7HhBEZURWFrtdaELMfE7J6w/IJbKSKfO3uZyIhsJIxsuLxuYCNBFYAHIUSewFFtk5KymwcBgTIK8NFPEA2VMR0iXZ4pg4qDkBGQsL4x58QIbOk2wYGLfKIpDTzJaX9FlO018r48bIBGQDRskOrIs9NRmR6ZTZXC7mDAJP8KcBZfCuBqMR1TYrlwJAYUzSFxbWExOQ1wZKrNPhoAa0OB0F65DyxkRoJA5jAuRExg7m90l+ZMW2+wiBoOaUJ7BgXVQakbH1hdg9hvXzE/e0ku4AsZ5TobT4S2qxss3lZC764AlNOlgA0mTimbb7fBKXkj1ztwshDnJQOV2WeSl/Iv4ADAaDJHoyE+2xr4kR/p5U75ztvlGA/F2xWbelIpAjZuAlsIimI6sqCb0X+c0pIkaRGlmxN1ZitCfZWLnOGiUgUOE0IC/OPJVMyqqrsLvdXGoX5PQCszqdzJt7Atkqt/KGnYfCDZAXWZksFpjMZqb7RgFAIhZDLBqVZUC50YBS80MOB2bCEUmF8qrGJAoHbGWPtXKbU9Kp5WqbNZ2bZbsmJGIxzIQjsLvdko7nIafnCc0iKykeJy81EpDOxUgN+d0ubsZK6mZrVifbLdEJMh5n+XvFLWclY0w2DvVMBLJyMRzaigHy6uSEXWbZ52blrAk2DjWOgLycFestS7IR9vllRVZ6zkoFErEY4jMz0mgkTpEVII/Lt7mcXIyVXBqQy2JHxChSjFUF5qx40UjC35DeIJmbsyFnTBzadwFZrcUkzHULpxKNmXAYiXhc0jwnx/B4fiGfT2bOSjdWqiCVNycTkweXL2dLAG6RVSAk2Qu2OvnQSMTjlGLYMx4n23HFZ2YQi0YlRcbEAWJNAwLylJM2Dp3EAZkycV6qVxmiKxunOQWko1AJhoFHE1uCsM8Pu0RjZeXkVPOCNsZKYv0QVxpQYpdlk8UCs8XCRWARmvbBbLXAZClf7MrPM5cu8xcLXUPsCl0JpOYceUZWoWlpXrCpulrobs7BgIYDAaEZqtlc9liLk32rMyArjy2BBuQ/p2REVlycRWk0IKlx1CMrlYgGpLW650oDBgKS6BHi1fDwWEj/LymeFOuNFwlEGlBSZMW+0JUgIrHBrpVjzio0NS0pGc5zTHKUr3a3W1IPOrUQmzZLNAy85pTU/oAig8BjTZBorIgzqQssVELqlgA8GsYSlNsTicAmGiv2LzGpq7B7pC14XBY7GcWudo9b/DewhtTIipdCERAWFqnPDuBDbWVk/hKf39Q06yGJLIUkA+pxIzjNfkyAkmidj8BCigMkdlzXIyt1kLpbMM/Nw8jWF+WKXckk4EUDAtKMlWAY2I9JzA9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   "source": [
    "from sympy import *\n",
    "import math\n",
    "\n",
    "init_printing(use_unicode=False, wrap_line=False)\n",
    "x = Symbol('x')\n",
    "\n",
    "plot(integrate(integrate(sin(pi*x),x),x))\n",
    "\n"
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  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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