Single dimension minimization.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from IPython.display import display, Math\n",
    "import random\n",
    "from bitarray import bitarray\n",
    "from bitarray.util import int2ba, ba2int"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "random.seed(15)\n",
    "np.random.seed(15)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "f\\left(x_{1}, x_{2}\\right)=\\sin \\left(10 x_{1}\\right)+x_{1} \\cos \\left(2 \\pi x_{2}\\right)\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "x_{1} \\in[-2,2], x_{2} \\in[0,1]\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$f \\to min $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Minimization based on binary individuals"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## GA for single dimension minimization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot(f, a, b, x_min=None, delta=0.01):\n",
    "  fig = plt.figure(figsize=(5,5))\n",
    "  ax = fig.add_subplot()\n",
    "\n",
    "  x = np.arange(a, b, (b-a)*delta)\n",
    "  \n",
    "  ax.plot(x, f(x), label='$f(x)$')\n",
    "  if(x_min != None):\n",
    "    f_min = f(x_min)\n",
    "    ax.plot([x_min],[f_min], 'r*', label=r'$f(x) = min $')\n",
    "    display(Math(\n",
    "      r'x^*={},\\\\ f(x^*)={}'\n",
    "      .format(x_min, f(x_min))\n",
    "    ))\n",
    "\n",
    "  plt.ylabel('y')\n",
    "  plt.xlabel('x')\n",
    "  plt.legend()\n",
    "  plt.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Transformation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def M(x):\n",
    "  #return (x_interval[1] - x_interval[0]) / (2**n - 1) * ba2int(x) + x_interval[0]\n",
    "  #return h_x * ba2int(x) + x_interval[0]\n",
    "  d = 0\n",
    "  for i, b in enumerate(x):\n",
    "    if b:\n",
    "      d += 2 ** i\n",
    "\n",
    "  return (x_interval[1] - x_interval[0]) / (2 ** n - 1) * d + x_interval[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Evaluation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def evaluate(x):\n",
    "  return f(M(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def bestOfPopulationt(population):\n",
    "  scores = [evaluate(x) for x in population]\n",
    "  \n",
    "  best_index = np.argmin(scores)\n",
    "  \n",
    "  return population[best_index], scores[best_index]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Modification"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def mutate(x):\n",
    "  index = np.random.randint(n)\n",
    "  \n",
    "  mutated = x.copy()\n",
    "  mutated[index] = not mutated[index]\n",
    "  \n",
    "  return mutated"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def crossbreed(mom, dad):\n",
    "  index = np.random.randint(n)\n",
    "  \n",
    "  return (mom[:index] + dad[index:], dad[:index] + mom[index:])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Selection"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def cultivateFrom(population: list):\n",
    "  new_population = []\n",
    "  N = len(population)\n",
    "  \n",
    "  for _ in range(N//2):\n",
    "\n",
    "    mom = roundOfTournament(population)\n",
    "    dad = roundOfTournament(population)\n",
    "\n",
    "    if shouldMutate():\n",
    "      mom = mutate(mom)\n",
    "\n",
    "    if shouldMutate():\n",
    "      dad = mutate(dad)\n",
    "\n",
    "    if shouldCross():\n",
    "      mom, dad = crossbreed(mom, dad)\n",
    "\n",
    "    new_population.append(mom)\n",
    "    new_population.append(dad)\n",
    "\n",
    "  return new_population\n",
    "\n",
    "def roundOfTournament(population: list):\n",
    "  participants = random.sample(population, N_t)\n",
    "  \n",
    "  winner, _ = bestOfPopulationt(participants)\n",
    "\n",
    "  return winner\n",
    "\n",
    "def shouldMutate():\n",
    "  return np.random.choice([True, False], p=[p_mutate, 1 - p_mutate])\n",
    "\n",
    "def shouldCross():\n",
    "  return np.random.choice([True, False], p=[p_cross, 1 - p_cross])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Problem"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# problem definition\n",
    "f = lambda x: x*np.sin(10*np.pi*x) + 1\n",
    "\n",
    "x_interval = [-1, 2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "22"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "h_x = 1e-6\n",
    "\n",
    "n = len(int2ba(int((x_interval[1] - x_interval[0])/h_x)))\n",
    "n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# GA parameters\n",
    "N = 100\n",
    "max_iterations = 30\n",
    "max_iterations_without_evolution = 10\n",
    "p_mutate = 0.9\n",
    "p_cross = 0.5\n",
    "N_t = 3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### GA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(bitarray('1010001110001111011111'), -0.9502597341194818)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "population = [bitarray(n) for _ in range(N)]\n",
    "iterations_without_evolution = 0\n",
    "best_from_populations = []\n",
    "scores = []\n",
    "best_score = bestOfPopulationt(population)\n",
    "\n",
    "for i in range(max_iterations):\n",
    "\n",
    "  best, population_score = bestOfPopulationt(population)\n",
    "  \n",
    "  best_from_populations.append(best)\n",
    "  scores.append(population_score)\n",
    "  \n",
    "  population = cultivateFrom(population)\n",
    "\n",
    "  \n",
    "all_time_best, minimum = bestOfPopulationt(best_from_populations)\n",
    "\n",
    "(all_time_best, minimum)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle x^*=1.9505200268077916,\\\\ f(x^*)=-0.9502597341194818$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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j9bn2bLZSLFSVcfdgBJlrbzLSADPGgpEKCAg0AIcHZ/C7z72Jzzy/r67nz+RlhPw+RII+nZF6dO2ra0BN197D8DpZ1WvCWbIpbLr2gpEKCAg0AHv7JwEAb56drKtJJV2Q0RIJgBCC1qh3RmomivzVGXfvySbGSJlB9ZL5nysIQyogsAhxZqw0WWGqzj75uFFM31JHjJTFMWeTcZdVDT4C+I02VUIIgn5iJqEaCWFIBQQWIcoN6cBkzvPzs5JixjfjIT9yRjE9L0o1oCUtUQAoeHLtNdMQM4T8PpOpNhLCkAoILEIMTuVxXY/elTQw5d2QlvfJR0MBUFqfW87ccRYr9cJIJaVWwDkUEIZUQECgQZjIFLF5lT4Zdmg67/n5uaJiuvbMoHoZOVJbTO+9BlRWNTPGyhD0+4RrLyAgcPmRKyrIyyrWdMYR9BNMZuvUEjUZqd98jBdStSENeK8jtXTtBSMVEBBoBCYyeu1oVyKE9ljInC/vBbohrWSkXrqS7Fx7r2tYufaSYKQCAgKXG0ypqTMRwpJYCFN1GdJSsilWByOt7kqqR0tUVqllskkWjFRAQOBygzHSzngY7bEgpupw7bNSmWsf1JlpXTFSg1ESQhAO+CB5YKS2ySbBSAUEBC43mJZoRyyEJXHvjFTTKPKyhWvvKUZaWUcKlDRJeaEnmyq1S0X5k4CAQEOQNto5WyIBtNfh2jNjFw/Xn2wqVtWRAnrCabbJJpG1FxAQ4Mb+C1MYrKP+EwAyRjtnIhJAWzRoCpDwghnMaJVykzdGWhkjBfQSKK+1qIu+jpQQsooQsoMQcpwQcpQQ8t8sziGEkKcJIacJIYcIIbc2Y68CAvMJ58azeOiZN/Cp77xd1/PTkoJI0Ieg34dE2I+iIWnHCxYLjdckmzzESNXKrD2gt4l6de0ts/aLyZACUAB8jlJ6PYA7AXyWELKx6pzfAHCt8e8xAN9o7BYFBOYfXj89DgA4MZLGRB2zktIFBYlwEADMonovg+eqJfBYrDTnJVEkVyabAN2QetMjtcnaLybXnlI6TCl9x/g5DeA4gJVVp30IwD9RHW8CaCeELG/wVgUE5hVOj5b65M+MZT0/P12Q0RrRjR+b4pnxZEj1c2PmmBAfCPHm2hdVDUE/gc9XShZ5ZZNFRa3pbFrUWXtCyFoAtwB4q+rQSgADZb8PotbYCggsKpwezaDFMID1CI5kJAWJWRjSrFSZbCKEIBr0e042VRvBsMf4pqxSBC2y9rLiXRZwtmj6OGZCSALAjwH8MaU0VX3Y4imW7xIh5DHo7j+6u7uRTCa595DJZDyd30wslL2Kfc492F5PXMxhfbsP+y4Bu/YfQ2f6tKd1Bi/lEfLro73PjOsGdNebe3Gpw+/yTB37LunPOXpwP9Ln9OcEoOJM/wCSyVGu9/TcBQmEqhXnpacLmCxQ7s8jk8tjYqxYcf7YJQnZvMK1xlx+9k01pISQIHQj+jyl9CcWpwwCWFX2ey+AIau1KKXPAXgOALZu3Ur7+vq495FMJuHl/GZioexV7HPukUwmcd999yH98i9w6/rVGMwPwd+2FH19N3ta5yv7X8Oqrhj6+rai5fwU8PYbuHbjJvRtWMb1/Kn9g8D+g7jnrjuxrisOAGjb8wrauzrQ13cL13v64vhBxKfHKs77l4v7kLmUQV/ffVz7IDtfwureHvT1bTIfey19DHtGB7g+07n87JuZtScAvgngOKX0KZvTXgDwiJG9vxPADKV0uGGbFBCYZ0hLCiRFw7KWCHraoriUKnhfoyCbyaaWCEs2eU8UMcUmAIgFA55d+/IaUsB7MX3Rqo40QJoSI20mI70bwH8FcJgQcsB47M8ArAYASumzAF4E8ACA0wByAD7RhH0KCMwbjKX1LP3SljA64yGMpuswpJJiGtC4GSPlbxOtFmUGvHclWRlBrzWglnFWwxhTSqFztcagaYaUUroL1jHQ8nMogM82ZkcCAvMf5Ya0IxbCieHqtIIzNI0iU2ZIEyFmSL23d5bXgIY9Z9xrjaCetZ99Hal+jCIUaJwhnRdZewEBAT4w5aauRBidiRAmPbZ36iNBUMZIdVbppY6UufbVxfReDKmk1DLScMDPzUhVjUKjsGwRBdDwWlJhSAUEFhDYoLqOeBAdsRAKsuapo4i1hzKXPmCMVPZkSBUNAR9BwF/FSD0qN4WtXHtOA1g9QbR8jfLjjYIwpAICCwhsWmdrJIjOeAgAMJnlZ6Usjsm6kgC9ljTtyZCqNUYw7JGRFi0Yqd6VRKFp7nWgzODW1JEyQyoY6fzH/gtT6B/33lEiIAAA71yYqpji6QWpvIxwwIdI0I/2mJ5596InyrqPmNAIoLNTr4w0HKzMuEc8MtKiDSMF+IygbNGrD5QYqmCk8xynR9N46Jk38Ht//6an8bMCAgAwmi7g4WfewAP/c2ddcbxUQUZrlJUu6f+nPWTc2ZTOckOY8GpI5VojGA76UPAUI1UtYqQ+45j7OnaufVgw0oWBne/qghFDM4WKnmcBAR7sPjMBQDcWhy/OeH7+TF5GW7SyBjRd4DeCBQtGGvNYumTp2gf83hipWltHGvYQ35RVmxipYKQLA+UX/8lL6SbuRGAhYm//pPnzyRHv189MviQ40soYqRdDajDSSJkhjQT9nrVErYzgXJQ/AXxssnqcM4PI2i8QHB9OY9tVnSAEODMq4qQC3tA/nsPNvW2Ihfx1GdJUXjEZacJkpF5ipLqBiVYbUg+CynqMtNJ0RIJ+KBqF4iHrblWQz465Pt+OkYqs/cLAxakcru1OYGV7FKfrTBgILF5cmMxhdWccVy9N4FwdCcuZfHmM1Cim98JIZcZIy2YledQBLchWrj1/fJOdV5u11407n2tPK17XXEMY0vmPrKQgVVCwvC2K1UtiuFjnqAeBxQlF1XBxOo/VS6Lobo3U1SefKpRipEGjBtRL6RKLhZYz0ugcufbsGA8cs/azSDaZWXvh2s9fDM/kAQAr2iPoaY3gUsq7OrnA4sVIqgBVo+jtiGF5WwQjHg2pRilSedmMjQJAIhz05Noz5lmetY+G/GbslAdWySYWc+Vp8dQ0CkWzULc3jbH7GrJNHamXhNVcQhhSD7g4rV/4y9uiWNYawWi6IEqgBLjB5skvawmjpy2C6ZzszaVWAI3CZKQA0BoJIFWHa1/OSMNBnzdGKtfGSNnvPMPrGFu0K3/yEiO1M8bM9W8UhCH1gPEywYju1jBklZotewICbpjI6tdPZyKM7tYIAGBkhp+V5g3ldxYbZT97i5Fq8JFKJhc1upJ4OooAO9een5FazWsCyhiph6y9vWvPf2OYCwhD6gFs/veSeKiuL4LA4sa4wUg74yF0JfT2zgkP7Z0FwzawPnlAz9x7ytrLKqJBf4XEHGOnvO69tWtvGEEORiqpteEFwFsNqOzCSIVrP48xlSvC7yNojQTq6nMWWNxgrn1nIoSOmH79THtQb5IMRlreJ98SDnqrI5XVihpSQI+RAvzD66wERxgj5QlVMCMXtutK8mJI7QryhWs/fzGZldERC4IQgg7DkE55lDETWLyYyEiIhfyIhQKmIfUSGmKSoWx6J6C79l4Mad7CkEZMRspZuiTX9trX0945qzpS5tpbCJ/wrjGXEIbUA6ZzRfMLwAQjvDAKBkopXj52yawCEFg4ODmSxtEh762dgO7GdxoufXvc+/UjqRaMNOItay/JWkUNKVAypDyMlFIKSVERsc3ac7j2LoaUyxgb74Vtd5QwpPMXk9kyQxr1zigYfnn0Ej71T2/jD761d073J3B5MZkt4oGnd+I3n96FoWnvN8HxjITOeBgA0BIOwO8jnjyagslIK/vkdbFmPlc2L6umK89gxkg53HLFEFS2Y6SeXHub8ECRI1ZrstqaZJMe+xUtovMYU7kiOgwmEQr4kAgH6nLt//PoCAC9V/9iHV9IgebglROjUI3M9svHL3l+/kSmaCaZCCFojwY9uvb6a5cbwljYD0r5C+ELsopIwNqQ8giXSC5GkI9Nurj2HmT0glXjRAJ+H3xEMNJ5jamcjCVGbBTQ3fvpOhjpgYFprGyPAgD2nJuYs/0JXF4cHpxGPORHRyyIw4Pe3fupXBHtserrh/9GzITw42Ux0phhBHkneFoy0pBuBnhce6bwZCWjB/CVP9mxSU9Ze5s1AL0EStaEIZ2XoJRiKlv5ReiIhTwz0oyk4Ox4Fr972yqEAz4cHxYKUgsFhy/O4IYVbdjU244jQ96GzgF6T3x5V1JHLORJlLlgxUhDbJwyX8KpINfWgEY8uPZWE0QBmCyXq/zJMLa1yk06u+QtyCcE8PtqB9yF/D7Iisjaz0tkJAWKRtERK30R2mPeXDMAGJjU+/OvWhrH2s44zo4JBamFgtOjGWzoacGG7gTOjmU8dbVpGkWmqJiKTQDQ7vFGLKmAj1SyQbN0ibNDquAQI/Xk2tt1NnlgpNXGmBCiTxLlKcg3JohajVwOBnwiRjpfwdrwytvzOmIhz1n7i1N6TLS3I4Z1XXGcGxcKUgsBMzkZqYKC1UtiWLUkBknRMJbh11rIFhV9emdZMX2Hx9CQpFLEQ4EK48EST7yuvR4jtc648zFSa9eeudh8jNQ6RsrW5VlDVmhNHSpD0E+EIZ2vyEmV0xcB/Ysw5bEgnyWXVrZHsaYrhguTOe7WPIHmYcBQ+lq1JIbeDj2+PTjFnyjMGNdPJSMNYibvrY60mk0y1553kqhT1p4nRlqQrdmkz2ewSQ81oNXGmD3GJeysqjU1pAxBP/800rlCUw0pIeRbhJBRQsgRm+N9hJAZQsgB49+Tjd4jA/silAf622IhpAqKJ0M4OJVDOOBDVyKEFW1RyCr1PJtcoPG4MMkMaRS9HTEAHg2p4dGU98knwkHkZZVbDFlSaEXpE1BipLxdSfmiQ2cTD5u0STaxx7zEWa0Yacjv40w20Rrlp/I1FptoyT8C+HWXc3ZSSjcb/77cgD1ZImu0lZQzUjbyIeNhrvjF6TxWtkdBCEF3q15TWI8upUBjMWxoKqxoi2KFUXEx7KF0jYWGElV98kDp2nKDpFZ2NQElQ5rlMKSaRiEpWo0hZUZxNjFSfR2+kcxOjDQU4DSkaq0wNEPQ7zOz+o1CUw0ppfQ1AJOuJ84DmIw0XN5V4n342MWpPFYaruEyQ/hEGNL5j7G0hJDfh/ZYEPGQH5GgD+MeYqTs+qlQbjKMKu8UUEmtZaSlPnn3a5AZuerOJkKIrgA1i6w9W5er/MmmjpQ9xmNIJSPZZIVgoPEx0oD7KU3HNkLIQQBDAD5PKT1qdRIh5DEAjwFAd3c3kskk9wtkMhnX8/dd1C/2I/v3YeyU/gFeGNEv3ld27saqFr570sB4Dtcv8SOZTGIir3/Yr+09BN9I0OWZ/HudD7jS9nn4XQktQYpXX30VAJAIUBw5cwHJ5CjX6+wxrpUThw4gfU6/Vs4bj+3Y9SbX9ZMrqvBnUhX7TRd1F/bQ0ZPozp51fH7GOPdi/zkkk4MVx/xQcbr/ApJJ50aD/cP6ng/u34fxdyv3rBYLGBgaQSamOL6nJ0/roazdu3bWlC9J+TyGRvOun8nwSAFygVqel8/kcamQdV1jLq/R+W5I3wGwhlKaIYQ8AOBfAVxrdSKl9DkAzwHA1q1baV9fH/eLJJNJuJ0/sLsfOHwU7733bixt0V1y36kx/O2BPbhu02bctnaJ6+tQSpF5+Re48ZrV6Ou7HrKq4fOv/Qfal69BX9/6OdvrfMCVts9vnnkLq/wK+vruBgD0Hn0dgUgAfX13cL3Opb0XgAOHsf2ebWZogF0/12/ajK0c14+y60X09ixFX98W87GCrAKv/AIr1qxDX981js8fms4Dr7yCGzduQN/tqyuOte7+FZYs7UJf382Oa0zsGwQOHsQ92+7E6s5YxbGOgzvR1h5BIpF1fE/3SifgO3MG73vv9ppjXcffQCToQ1/fnY77+Mdze6CEiujre0/NsWdO7oaPAH192xzXmMtrtNkxUkdQSlOU0ozx84sAgoSQrmbsJWPEscpjXF6Hj2WLKoqKZnZHBf0+dMbDdbn2sqrhZ4eGPLmXix2nLqWx48RoXVMNRlOSeQMFgK5EGGNp/veehX/Ks/bmFFDeYnoFNa59OKC3ROK5OjgAACAASURBVPJl3GvV8RkinLPtHWOkQR+fQr6FMDQDd7LJwbVfjMkmRxBCeohRNEcIuR36fpvSU5mVFPhIZXypxehSSXGq70yaepSlL2R3a7gucei/3XEaj393P/7wn972/NzFiJm8jN9+5g184h/34lfH+dzxcoxlJCyrMKQhU6iZB8yQlld9sBgp7424qNKa0iVCCGKhALIcMVJmKKtjpAD/JFEWA63u1weM0iXOZJNtoijg49ISlRVq2R4KLMI6UkLI9wDsBrCBEDJICHmUEPJpQsinjVM+DOCIESN9GsBHaZOGJGWLSk0xdKvHZNM4GzVR1q/flQh7FoemlOK7b10AAOy/MI3zE6I7yg0vH7tkMr+f7r/o6blFRcNktljDSCezkili4oaMpCBhKD4xMEaa4WSkklpZNcIQDfFNAWVssTprzx7jYZPuWXu+ZJOdIeVlpJKqOdeRNjhr39QYKaX0Yy7Hvw7g6w3ajiOyklJzETNGymtIJ8sU0hmWxEM467G76dSlDEbTEj67/Wr87Y4zSJ4cw+/fFfe0xmJD8tQYlrWE8b7rl+HfDw5D0yh8Fn3aVmCzlpa1RMzHuhIhaFQXIukq8zDskC7IFWEhoBQm4mGkqkZR1Kzd8ljIz9XZVJppb51x52KkNvOWAHAX5EuyZssmw5ztnbKiIWRTRypaROcxspJaUfoE6BdfwEe4hXXZF7JcQcqrcAUAHBiYAgB8eMsqdLeGcXBg2tPzFyOODs1g86p23LKqAxlJwXmjwJ4HbERI+efWZbBT3hh1RqrsswdKbj5PjJS55dUxUv2xgCdDahkjDfCNZJYUFSG/z/ImxOvaS2rtFFKGoJ/Muo5UxEjnMbJFpYZREEKM4WN8jJQNOmPivoDOTjOSwuUSMZwYSSMa9GPNkhhuXNGGI3Uqti8W5IoKzo1nsXFFK25Y2QpAV3LiBeuHLxesKc1c4rsJpgu114/PR5AI800BZS2gMQvXPhbyIy97iZHOzrW3KqQHvBXk2zFS3jrSolMd6WKLkS4kZCWlpqsEMMbhcsa4JjJFRIP+ioSBObvHAys9OZLG+u4EfD6CjStacXo00/CY0ELC8eE0KAVuWNGGa5YlQAhwdow/nMIUmjrKGCkTr+Htlc9ISkUxPkMiHECGoyCfxUBjNq49T3cUM5RWjDTM69orqi2b9NJrb2eMQ55ce4fOJmFI5ycykmoZ6NenOPJ9mWbycgWrAYAlhuK+l4TT+YkcrlqaAACs64pDoyVRDYFanLqka75e19OCcMCP5a0RXJjgf7+mDWPZXqb8ZRpSD4zU0pBy3oiZobRy7aNBvmSTyUhDtV97bkZqoWfKEA7wdTZJiurY3snNSOdRskkYUk5kJQWJcO0F1BIJmH3UbkjlZbRGKw1paZoknyFVNIrhmTxWGW2ma7v0JJPI3NtjaDoPHwGWt+nJolVLYqYICQ+mjZtctbo94IGRWrj2gM5IeUJDzHW3c+1zHK695ODa6/J1HKzWybUP8pc/2daR8uqRuoQHRIx0niJXVCwvYn2KI6chLcgVCulAKYHBy0gnC/rwMaZAtLZTN6TnxgUjtcPwTAHLWiIIGF+8NZ0xT8mmqZyMeMhfwaJYKdN0nu9z08ufatuAeUNDLJlkmWwKB/gYadEh2RTkTDbJ9mwy7Ndde7cKRbfyJ1l1X0NWqQOrFTHSeQtWB1iN1kiA27VP5RW0RivX6PBoSMfz+gXWu0RnpB2xIFoiAcFIHTA8k8fy9lLp0prOOMbSErf03HS+csQMoCca26J8eqKaRp1jpBw3YubaW5Y/BTljpIoKv49YJmkiAT9klbrWxUpK7Ux7Bva425QPRzbp94FS3fNyXEPVbGX0gn6fPu20gTq/wpByQFE1FGStoiuFwUvW3oqRtkeDIMSLIdXvtKsMRkoIwdrOOM6NC0Nqh+HpAla0Rc3fVy3R3zveuPJ0TjZd+XK0R/kU7pnMon2yid+1t4rTx0I6m3RjcfmiZmmIgVK3k1vCSVJU+0SRYRzdvHvJobOJZy69qukG3z5rrz/eyAF4wpBygGk9VteRAiXXjKfhyipGGvD70BYNcsdIx/MUPgL0tJUY1sr2aF1z1hcDKKUYnilUvF89HuULp3JFM5ZdjlZORpqx0CJl4L0RO7n2kRDfSOaColq2hwKluKnbGo7lT8babqFWp6y9aQQdXHPZQYYPKBn0RsZJhSHlAKvhs8zaR4JQNeqa8dQ0irSkmG2l5VgSC3Ez0qkCxdKWcMXdeHl7BMMzBc9iHAOTOXxr1znPc6eagYHJHP55dz93lpxhJi8jL6tmoglAmaA2XzH9TE5GmxUj5RwVUtIirV0jEQ4Y85ycP7scc+2tYqScI5kLFur4DNyM1CVrDwCym1s+S0Zq6pk61JECaKi483yX0ZsXyFrMa2JIlInzWl3kDBlj+Fk1IwX0OCmvIU0VaU1L4oq2KHJFFam8YvmFt0JWUvCRZ3djJFXAy8cv4flP3WE5kXE+YCYv46Fn3sB4RsIrJ0bx7U/czv3coWmddS4vc+1Zq+dougAeKTGdkda+r23RINcUWCvlJ4Z4OABKdSNodX0x5BzqSHknieqM1M6Q8g3Ac6sjBQC3KioeQ+rEjJmBtBd2dme1cw3BSDlQktCzdu0B937plMFcqmOkgDFEj5NppYq0Qj0KgJlIGZrhd+9//M4gRlIFPLCpB2+cmcDe/inu5zYa39tzAeMZCQ9s6sGOk2M44qEraSSlvyflyaZoyI+WSACjHIxU06hR/1vr2rdzuvYsGWnl2jPj6TaXPicrCPhgVh6UgxlBN5X8fFG1jZEylunmWbl1NgHuhtQxRsrl2uuM16kWFUBDB+AJQ8qBnMXgOwZTeMLli5DK68ers/aAXp/I616nJIquROWXmrGtYQ+G9D+PXsK1yxL42kc2IxEOeFZEaiReODCEzava8dcPboLfR/Di4WHu5zJGWp5sAoDu1ghXjDRdUKBR1GTtATb8UHbNDluNGWFgN2e36ycnqbC4jwMozXHKF11ipLLmECPlm0tvNfOJgRlYp4w7pRRF1bmOFHA2gkUXRipipPMUGQ7X3pWRFtwYqbshpZRau/aMkU7zJU8Ksoo9/ZO4d/1SREN+vOeaLiRP1id4fLlxYSKHY8MpfPDmFVgSD2HL6g68cYZfknZkpgC/j1RI4AHAspYwRjmEmdnn0m4RkmmLBkGpu/qX1QRRBnZzditfyhVVhG3Kfcxxyi5ueV6eA9dedsjac7j2zEC6Zf65YqSzSFjNNYQh5UDWIdnEq3JuuvYWX8j2WAgFWXO9iDOSAllDDSNd1hKB30e4BaLf7p9CUdHwnmv1COF7r1uG4ZkCThqtlPMJ+y7osxHvuroTALBlbQeODs1w9YUDerijuyVcMxuIl5GW+uyty58AuBblmzPtHW7EbsLMeVlBxIaRship22z7goMhZYZN4nLtncMDTh8NM5C2iSKO+GZpDbs6UlJxXiMgDCkHMpJD+ZPRreLGSBlrsWKkrEbRrSaRybmVq0cBgN9H0N0S5o6RHrqoy+7duqoDALDNMFJ7z82/ga4HB2YQC/mxvrsFALBldQdklXKrNw1PV5Y+MTBG6sbC2Wdi6dpH+T63lIU6PkOMM0aaldwZqdvNpSDbx0h5GCml1DFGGuLI2jvNtAdKBtYx2aSKZNOChGOMlFPl3HTtLWKkvP32TPuyq6VWSHh5exTDnK790aEUejuiZoa/tyOKpS1h7L8w/3RN9w9MY9PKNpNR3rpGN/4HOPc6kipgeXu05vFlrREUFQ1uoluMbVq69jG+UTOsz95Kw5M3RpovqrArComFOMufHGOkhiF1iJGabrnNGmEe195hpj3AV/4k6kgXKLKSAkKsi6HjnF8Elmyycu8YI3U3pIyR1rKjnrYIRjgLzI8NpXDDilbzd0IIblnVjncuzK/MvaSoOD6UwubV7eZjS+IhLG0Jc4UhKKUYms5jhQ0jBYBpyfnLxuQNLQvy2cyuvEuMVJIt46NAedbeJUYqK4gEbBgpZ/lT3pGRsjpSewPmNNNef9y9s6nIyUidjKBbsknESOcpMpJaM6+JIRzQxSzcEg6pgi58YVW+wisSzBhpdeIE0Lt1RjiK8rOSgv6JLG5Y0Vbx+K1rOtA/kfM8P+py4vhwGkVVw+be9orHN3S3mNJ4TpjKyZAUDT1ttYyUvYepoptrXwQh1rFt5l24MVIrUWcG7vInh6x9qfzJ3bW3TTYZxtFJAYrFT2fj2rslirwU5DsJO5ef1wgIQ8qBXFGxjI8ytHCI81q1hzJ4jZEusWCky9siyMuqKzs6N54FpcA1yxIVj9+6WneZ988jVnrA2Es5IwWA9YYhdSs7YuVgVoyUVT7MuDDS6byMtmiwJlkF8Is7W40ZYWDhItfyJ4esPfOUnAypplHH0qWSa29vfFj8dDZ1pE4zn4Dy8if7v4WxVdc2U5Fsml/ISIplfJQhEXFX8LESLGHwEiONB63vxN1G/7ibe3/eEDRm8nsMN65shY8ABwfnz9iSAwPT6G4NV3QlAcCGngQKsuYqOsJixlYx0qUJPkY6lZMt46OAnuQJ+IhZkWEHJ0bq9xFEg353RlpUbBlp0K/PDss5sUnFfoIoUDJKTsmm0gRRO/UnDtfeMJB2a5TaO+t37U1mLGKk8wtWE0TLwaPgYyWhxxAJ+hEJ+lyL8ieyElpD1qyE9ZK7FeX3G3J7azpjFY/HQgFcu6wFhwbnT8LpwMA0Nq9qr3mcTQc466J4xd6L5RaMtDUaQMjvc2ekuVoJPQZCCJdwSUZSbG+igO7eu5c/2TNSwH0kM4ufRm0SRT4fQSjgc4mROjNSnvim5FL+ZLaIcoiWOMnolZ/XCAhDygGrCaLl4FE5d2KkgDFN1C1Gmi7aGlJW4uNWS9o/nsWylrDljeGm3jYcGpzhKsyfycv4v354EO/7WhJffOGoI6MamMzhs999B/c/9Sr+58vvculETueK6J/I4WYLQ8rY9HlXQ1pAwEcsxyUTQtCZCHHESGvHw5SjLRp0nZBgNYq5HImws55oUdEgqxQOSyAa9DuySadRzAyRgPPcJskl4+4la28vDu2vOM9yDdeC/EUWIyWEfIsQMkoIOWJznBBCniaEnCaEHCKE3NroPQLWE0TLwaNynirYx0gB1ibqYkizElrD1oaUCXG4ufb9E9kat57h5lXtmMwWMTjlzGo1jeKzz7+Dn+6/iBXtUXxndz9++xtvWBa4nx5N46Fn3sCrJ8fQGQ/h/3v5FL76nycd1wd0NgrAkpF2JUKIh/zod5m7NDxTQHdrxDK+qa8TRsota+/ASAFd2NvNtc8U7GOkgMFIHa4fxjSdGKnbbHuTkToI60SCfseZS6Vkk/UahOis1jFG6mKMg0ZlAl9Bfv39+nONZjPSfwTw6w7HfwPAtca/xwB8owF7qoHdBFEGbtfe4cvUEQu6u/YZe0YaCvjQlQi7M9KJHNZ2xSyP3Wxkxw+5xEl/tG8Qu06P468evBH//Ogd+M4nbsfAZA4PP/NGxXTOkyNpfPS5NwEA//rZu/D9x+7Eh7f04u9eO4uTI85Z9wMD0yAEuKm31pASQrCmM26GKewwNJ23dOsZuhIhzHAwUitRZwY3117VKLJF1bb8CdANqdP1w+YxOThFiAT9juVPpUSR/SL6JFEO194mPKDv0eectXerI+VoEXWrI110ySZK6WsAnNppPgTgn6iONwG0E0KWz+UespKCibzzG243QZTBLdmkaRRpV0bq3G9fVDTM5GVbQwoAPW1hR0aakRSMpSWssWGkG3paEPL7cNAhTqqoGp5+5V3c3NuGj962CgBw7/ql+N5jd6Igq/jws7vx6qkxvDWs4CPPvgEfIfj+Y3fimmUtIITgzx+4HtGgH99InrZ9DUA3pOuXtdh6Auu64mbizA52xfgMboxUVjVkJMWyhpShNRp0LH9isU8njyYe8jvGSJnb78ZInWKkBR5GGnAOD7ixSUA3srNx7QN+H3zExbXnltETySaGlQAGyn4fNB6bM/zda2fxuVfzjnE7uwmiDIlw0LHXPlvUFYScYqRurj2r72yzce0BoKc16shI2VyndV3WhjQU8OH6Fa04OGBvSF97dwyDU3l8pu/qirram3rb8aPP3IVYyI/f/9YefOOghBXtUfz4M3dVlFp1xEP4yNZe/PzwsG2vO6UUBwemcfOqNsvjgJ4sG5jMQbFx35gyviMjbQkjVaS2MWHGNB0ZaSToWHKWdhAsYdBdewe33DCQDkvoySZHRmpk7R2MYMQlzuqW+Qd0RumctXc2pID7XHrXFtEmxEjnu7CzldWwvOoJIY9Bd//R3d2NZDLJ9QIjA7qBeumVJMIWnSMapcjLKsaGB5FMjlquMTZURFHR8NIrOxC0iMcxxjt04QySyQuWa6TGipjKydixY4dl4X//jH6BBzXJ9m/TMhIGJhTb43tG9C/12LljSE5Yxym7iITXLyh4ZccO+Cz28cz+AlpCQGD0BJLJ2jX+fAvBsYkwtGIBt65UcebQHpypOud6vwZFpfibH7yGh66tZXujOQ1TORmx/Kjt3yKNy1A0ip/8MollsdovVKpI9RbQ0UEkk5cs15gekaFS4OcvJZGwYPpDGeNzO3caSanfco2ZsSKms/af22BaX+P8mVNIZs9arpGalDCZVm3/1pOT+mevFQu252RnCpgoUNvj+0f1z/7Y4QPIX7A2hFIuj5E8bNc4OKjfWPa/vQcDUWsjpsoS8pJmu8aR8/oae99609a78kHD2fMXbD+3d8/o39nXd75q+Z5rxo3x3TNnkSSDlmsAQCaT4bYTbnA1pISQxwE8TyltRqX2IIBVZb/3AhiyOpFS+hyA5wBg69attK+vj+sFBsL9+JdTR3HrHXdZdgylCzLwy//EDeuvQd+9V1mucT7Ujx+/exRb7rjbslj++HAKeHUnbr/5RvRtso5MnPafxc/OHseWbe+xZK7Jk6PA7r3obo3C7m87Sk/jlYGTuPPueyxZw9EdpwGcxIc/cJ9tqGKiZRC/+uFBrNq4FdcaQiEMU9kiDr30K/yXO9fh/vdutHw+oAe2k8mk7T4B4N+H38LbY1k89eh9NcmgH+0bBHAQH3v/ndjQ02L5/Ni5SXzzyG50X7MJ961fWnP8yMUZ4JVduGfrJvTd2GO5xsyBi/jeiQO4bvNWXLOs9nXe7p8Edu3GXVtvxr0WrwEAx3AaL547iW3vudfyPd93fhJ4fTfuvNV+jZ2ZY3h79ILt+0VPjAJ79qItYf/Z/3h4P2YuztgezxwaAt7Zj7vvvN0UgKnGN8+8hYykoK/vbsvjg2+eB44cwX3vudvyuwIAHQdeA2jOdh+nXjsDHD+B9953j323166XsLSnB319myyPv5k/gVD/OWzfvt3yOAAEXnoRK1etRl/fdbbnuF2jXsDj2vcA2EsI+RdCyK+Txs6jeAHAI0b2/k4AM5RSflVfDkRNUVxrlyZrKj85J5sAewUoU/nJJWsPANM2Khqsz94uaw+UFeXbuPf941kstSl9YmDutFVh/gsHh1BUNXx4S6/t83nx0dtW4+J0HrtOj9cc23tuEm3RIK6t6r4qB0uY9duUQLFhgE6uPSvKH0tbx6ancnyuPQDbzL3TmBGGeDiAXFG1DS+xbHzEqY406HOuI3WYac8QDvgdZfRKBfn2ZiMU8M1KRg8wXHuXZJNdDWnFGvMpRkopfQJ61vybAP4AwLuEkL8hhFw92xcnhHwPwG4AGwghg4SQRwkhnyaEfNo45UUAZwGcBvD3AP732b5mNVh7nV2wv6RF6hAjNTVJrb9MTmNGGFj3jF3CacLos3dKNpWK8q0N6fmJHNbZJJoYrupKoCUcwL7ztQ7Ij/YNYuPyVmwsEzypF/dvXIaOWBA/2Fsb6tjbP4nb1nZYqiUxLE2EEQ/5bcdQs6Rb+YiRarCRLUzDoBqsisIp2eTWJmrGSF3qSAH7a5DpjDpl7WOhgKMeaYHDCEaCPkf1J7eCfHaMJ2vvZAhDAZ9jfFNW7UeVMAT9pKF6pFwxUkopJYSMABgBoADoAPAjQshLlNL/Xu+LU0o/5va6AD5b7/o8cJMgyzpI6DG0uDBSJwk9BiYcbGdIxzMSIkGf45eJFeXbJXHOTWTRZ+NeMvh8BHde3Yldp8cqHj8xksLhizN48rfsXXovCAf8ePjWXvzT7n5MZCTTqI2lJZwdz+J3b1vl+Hy3Eqih6QKCfoKuuLULCpQEsu0Nqf65OQ0UZF6GXebeFHV2YaSAfg1aTRrNcdSR6okihz55DkYaCbowUpc+eUD/XKdc6khDAZ/joMWQ3+eatbdLNJlrBJwTVnMNV0ZKCPkjQsg+AP8vgNcBbKKUfgbAFgC/fZn3d9kRc3HtncaMMLhpknIxUhcFqIlMEV2JsOMFyOa1WzFSVvq01iZjX457ru3CwGTezPIDwA/2DiDoJ3jwlrkrmvjd21ZBVmnFvKjkST2hd9fV7vM9nUqghmfy6G6NOLLajlgIPuJgSPNF+H3EkU2y2mA7RloaM2L/2bvN/TINqQPtiYX8KKqabRUDV2dT0L2zKexmBDkK8p0YLeCetS9yMdJ5ZkgBdAF4mFL6AUrpDymlMgBQSjUAv3VZd9cAuLr25gRRjhipnSHliJOVpPSsGelYGWuzQzwcQEskYMlI3UqfytG3fhkA4MXDIwD0L+FP91/Er23ssUym1Yv13S24dXU7vr93wCxB+uXREaxsj+LGle7hg7Vd9iVQug6pfQ0poLPvlhDBuEOMtD0adDQczLW3K4FKMy1bBwNWmttkvUa+qK8Rcvi2us1tyssqAj7iyOTc60jt5zUxuLr2qrshDQV8jgr5RUVzZMXA/IyRPkkpPW9z7Pjcb6mxcJMgy3mJkdq59nkZsZDf8SJuM2OkDoyUw4j1tEYshUv6x3XmVi1WYoXVnTFsXdOBH+7TDdz391zAdE7Gx+9c7fpcr/jobatxejSDfeenMJaW8NqpcXzghh5H48WwtjMORaOWLa2DU3n0LnE2pIAec57IWjPSGZeuJsDdtU8XZCRC1ur4DDEXcfCsMUbZ6T2JuFzHujq+Q1wIRmeTo4yeZqvaxBAKuNSRchhBN7dcTzZxxEjnGSO9osFceztGyuPam3ObbBmps2AJoMuptUYCtox0PCNZim9UQ1fKrzUMLJZo12dfjd+7YzXOjmXxP35xEk+/chq3r1uCbVd1cj3XC37zpuVojQTw1z8/ji++cBSypuG/cBpsFqY4VxUnLSoaLqUK6O1wv2m0hQjGMnaM1LnPHiiFa2ZsboBuffZA2QA8m6L8XFG1nM5QjhgHI3UzpJGAH6pGbY0YNyN1yNo7zbRncIuRyirlc+0XS4vofABjA/blT+6GNBL0we8j9skmBwm9cnTErRWgNI1iMltEZ4KPkY5YMNKzY1n0tEYc/45yfGjzSmy7qhPPvnoGsqrhbx66kYslekU8HMBXHr4Jhwan8fPDw/jMfVebMnluYDeF6hKokZkCNKrPonJDa5hg3GYs87SDFilDKOBDNOh3TDY5dTUB7ir5+aKz1gPgPm5EklXbeU0MbgPweOKb4YDfca59UVEd+/0B96y9nmxyvhYbnWya751Nlx3sTm6XtWcTRJ1iXIQQR+ESHkYK6Aknq6z9TF7v4ulKhPWaCQcsb4tgLC1BUbWKsSbnxjNc8VEGv4/gHz95G3afmcDGFa2mutTlwG/etBzru+/FdF7GVmO4HQ+6EiEkwoGahNOgIfjc69Bnz9AaIhgf1aeJVt8opnNFXL/cPVbbGg3YxkgzkrNyGOAeY8+ajNTeMERdqk+c5jUxlM9tsvq4Jdl+FDODW7KpyMlIHYWduVz7eRYjvdIR8PsQ8DnU8EkK4iG/Y4wLcNYkdZPQY+iIWSsJsRgeDyNd2RGFRmsz9+fGs1i3lN+QAjq76Nuw7LIaUYZru1tw29olnlgvIQRru2I1taQsZsrl2ocJJEWzNGLTefcYKaDHt+2y9qmCgoTLTdSdkaqOYiNA2Uhm2xipu2sfdmWkqmMdKsCSTfbHuTLuc1VH6rDGh7/xBv75mLUnUg8WvSEF9EJnW9e+qJizx52ga5LaFeQ7S+gxdNgwUtZ5s5QjRsqUncrrK6eyeh//VR4Y6ULBWota0sHpPHwElvPsq9Fq3JvGq+KkkqIiV1QdRZ3NNSL2ClCZgv0EUQbm7WQdEp5OdcyAez00HyM1BuDZxBZ5XXuV6vKBlmvIHMkmjjpSvqy9/RojqQJc9Lg9QRhS6K13doH+jKS6umaAsyYpLyNtjwUtW0RLjNTdkDL3vTxueM5D6dNCw7quOAan8hVfmsGpHHpaI66sBSipaVXXks6YxfjuXoCTJmlGUhzrUAG9DCsesp/blPPASO1ipHrG3SVG6jK3STek7q49YC+DV1Td9xEKOLNJnqx9iENBymUJTxCGFAYjlR1ce6d2IgOJiLVrTylFuuA8s4ehPRpCWlJqLoCxtP0Y5mosawkjGqxUjz8zqost8xTjLzSs7YxD1SgGJkt/b/94FquWuLv1QKnltjrhNM0k9DhugG0OmqROg+/K4aSSz5O1dxvJXPDESOtPWDHGarcGV/nTnGXt7WOkikphIfZWN4Qhhd56Z59scs+YAgYjtTCkuaIKVaOcWXvrscxjaQkBH+H6Uuutk7GKrqQTI2lEgj7u0qeFBKZ1euqSfrOglOLdSxlbhaNqtNowUjb6micurY8bqf3sZVVDrqhyeSNOHg1X+ZNL1p4nRlrK2tuwyblgpDzJpsDsW0SDLln7omCkc49wAMjZuPZu85oYWiIBS3Fn5vI5tQgysJrFmXxlvG4sLWFpS9g14cVw1dI4To+WRn4cG0phQ0+r7eyihYwNPS3w+wiODelqVSOpAtKSgvXdfCVULUECQlBTS8rCKTy1u0wlv1q9yVT94oiPx8JOFGKhtQAAIABJREFUrr17jHRus/azKX/ymefarTHb9k6+FlHn8ICiUrhUUHmCMKQwGKmNa591GTPCYMdImSFt48zaA7XdTaOGIeXFDSva0D+RQ6ogg1KKY8MpbOQo41mIiAT9uGZpAkeGUgBKzLRaS9UOfh/BkliohpEyV7+To5usLRoEpUCmqvIjXeC/icZD1ir5mkZ1RupyDUYCLgX5RR633JmRcmXtuRJWPN1R1FZWUA8PuNSRcsRIA3NILIQhhR4jdVJ/chozwpAIB5GX1Zq+b2+GVP/STmUtGCkHM2K4caWuKXrk4gwuTucxk5excTmfYVmIuGFFqy7kDOCUMVSP17UHdNZZHSOdyBbhI3DtbALsNUmZuz8b154ZxriLa+/zEUfRkYKimW2kdnBlpDx1pH63GKl7d5QZHrAxhHwtovZ1pJRSKJpgpHOOsJ/Yu/a8MdKIdZufF0PKzqmJkWa8MdJNhiE9PDiDt87qswW3rFnC/fyFhltWt2M0LeH8RBZ7+yexpjPmSVylq8WCkWaKWBIPcYVDWPy7OnNfYqScySaLWmb2GE8Jnp0mqarpY1ciLkbQjJHaJZt4XPugs2vP45abk0QdDOlsWkRZ55WIkc4xdEZaewFqxihdHteelbhUizt7YqTGl7+8llTVKCYyEpZ5MKRL4iGs64rj9TMTeO3dMXTEgrjOZmTHlYC7r9El9351fBR7+idx+1pvN42uRLimjnQiI6HTQcu0HK02ClCmDi2Pa2+Ttc+Z6mPuXlE06Ee+WGs8GDt0K6GKOLj2mkYN5SaXon6HZBOlVI+RcoiW2K2haRSySjmSTfYxUubyz2XWftG3iAJAJEAsDWlO5r+I7TRJmbvnJA7MEA/5EfSTihjpRFaCRvlKn8rxgRt68Oyr+ti5j9+xmjtRtRCxriuODd0t+PLPjgHQ/3Yv0A1prWvPk7EHylz7qhKolDlihifG7reMkbLriccrigR9lmV8pSmkfGzSyrXnGTMCOCebFI2CUmeFfcB5tr2suU8hZWvYxUiZyz+XyVfBSAGE/PqHXP3B5TgESxjs5jbN5GX4CJDg+CIQQrA0EcZoutTe6aWGtBx/cNdadMSCiAR9+MTdaz09d6GBEILH33sNAOC6nhb0bXCeAlCNrkQYuaJacTOd4FTbAuzHjaQ8VGzEwwHkZbWmI4jF7t2y9oBubK3qSJk0nhsj1UWbrY0gz5gR/biRbLIwxm4z7RkY27QyhMwI8nQ2aTYdVmzduYyRCkaK0lCxfFGt+JBNCT0PMdLqEqjpnN7VxMsIu9siFcLMo3Ua0p62CF76P++DRmlDeuWbjQ/evAKbVrZhaUu4QqyFB+bIkXQRqzv1z5HFSHlQcu1rGSkhzvOaGEwpvWJl80YpRupHymWNaNBvmTQ1GalL+RMhBOGAz9IImoyUt47UwgjyGlIn155n5pN+vGSM/b7KPSuGMeZofOOGYKQoDRWrDvab83Y8xEitGClPfJRheVukYgromKEtWo8x7EqEF4URZVjbFeeWCSxHl3GTGjPc+1RBRkZSsMJhcF45WsIBEFJrSHlEnRnshEtYjJTnZh4NWSvcs8fc6kgBNvvJwpDKfEbQdO0t4qySR0NqxYwZmwxy1JEC1gb9cjBSYUhRGipWfTfPcIwIYbCLkXo1pN2tlYaUCXCwUcsCc4+lVdNEh6eNCaQuo0oYfMZcp1ShOj6ucJU+AWUjb6quH5ORurjlgJFssjCC7DE31x5g40ZqjQ/L5PPWojoxUt4SKivXnmecM1AyxlaZe9OQihjp3IKRmOqEkxdG6hQj9WJIe1ojyBZVs3TGiwCHQH3oqjKkQ9O6DB8vIwWM7iYLRspT+gSUa5JWGkIvcfpYyNq1Z4/xGGO7kcyMYbqVUJls0ipGqqoV57itYenaq17jrFYxUuHaXxbYMlKJTYDkqAMMWcdIU3k+5SeG6pHKg1N5Ll1NgfrRmQiBEGDUCKMMzTBDysdIAT1zX5Ns4hT0Buxd+6wXI2jj2vPGSNk5luEBhW8Np6y95JFNOrnlPMmm8vOt1hCu/RwjYlwb1RlPnnlNDKZ7l6+tI/XKSIGSMPPgZI5rZIZA/Qj6fVjRFjV1TYem8/D7iKf4spUCVLrgPmaEwU4lPyspCPiIa7Yc0HVNLZNNMn8JVTjgs3btZV7X3p5NlhJW9RvBUrKp/hgpK8i/YhgpIeTXCSEnCSGnCSF/anG8jxAyQwg5YPx78nLsgzHS2SSbAKA9HqwYXkcpxUzefe5POXoN+beByTyKioaRVEEY0gbgqqVxU2l/eLqA7pawpxia1bgRXh1aoHSzrg4vMeUnnskB0ZAeI2WjrRlYkT5Psilsx0hlvvhmwO8DgTUjLXIaUsc6Us5kk1OctcRIr4AYKSHED+BvAfwGgI0APkYI2Whx6k5K6Wbj35cvx15KMdLaZFPQz8cGAGBJrHJ4XbaoQtGot6x9awThgA/nxjMYms4bQ9yEa3+5cVVXHOfGsqCU4vxkzvN7buna5/kZadwcyVx5DWYlhbsSIRL0g9JaI8aMM3fW3qGO1I2RAkDQb91r77X8ydoY89eRArDUJDU7m64QRno7gNOU0rOU0iKA7wP4UDM2Ei6rIy1HxriIeecIVQ+v89IeyuDzEazriuPsWBYnDAGOazkl4QTqx7quONKSgrGMhFOX0p7f82rXXlE1zORlU4jGDQm78icOLVKGmM1s+4KnrL11HSljpDxx1qDPuQaUt9feKlFUSja51JE6xlmNzqYrpCB/JYCBst8HAdxhcd42QshBAEMAPk8pPWq1GCHkMQCPAUB3dzeSyST3RuR8FgDB4ROnkCz2m4+fPi8hQFXutYrpAoanNfP8/hn9grx47hSSubPc+2lBAQf6M2hRpkAAjJ46gORZ/VPPZDKe/rZmYaHtMzOuG7C/f2En0gUFJDWCZHKCe52JkSJyRRUvv7IDAR9BStK/rBND55FMDrk+n1IKAuDoqTNI0tLXYmC4AK1I9T26vKcXBnRD/spru9AZLRmrE6d1JavXd77qSgpSUwVMpbSa1zl0QV973943cSbsbAj9hOLcwEUkk+MVj78zor/HB/e/g8nT9mtMFXTjd+TYcXSlT1cc2z+qr3HowH6kz9kb9eMT+ndv7753as47YKxRLOTn7BptpiG1+kSrb0HvAFhDKc0QQh4A8K8ArrVajFL6HIDnAGDr1q20r6+PeyM7duyAj+TQs3IN+vo2mI9/98Lb6NJy6Ou7l2udZOoojuwbBHvt5MlRYPde9N15qyf1pTOBc/irnx3DiUwEVy0N4QP3l/6WZDIJL39bs7DQ9nlLXsbX9v0nXhsNAyjiwfu2YKsH8ZPzoX789PRR3HL7XehMhHHqUhrY8Rru2HwD+m5ewbVGIvlLdPWsRF/fDeZjz5zYjZgP6Ovb5vqezhy4CBw9gJu33G5ODgCAV9NHEb84iO3bt7vu4cXxgzifG695ndM7zwLHjmP7vfe4eljhV19E19Ju9PVtrnh8av8gcOAg3rPtDsf5YZPZIpB8CWuvugZ9d6+rOJY/PAy88w623XEbruux19hN9E8Ce3fjhk034Z5rK1uGC0f0NVri0Tm7Rpvp2g8CWFX2ey901mmCUpqilGaMn18EECSEdM31RgghiFvoQWYk/hgXoKsupSXFdGHYuArenm0Gpl50YiSN9163zNNzBepDWzSIG1a04uSlNFojAWxe1e7p+UyYhBXlm6NKPMj5WSlAZSR3dXyGqM045YKsumqRMth2NinMtXc3GQGfc7KJR90ecHbtefRI9TUcXPsrpCB/L4BrCSHrCCEhAB8F8EL5CYSQHmL4IoSQ26Hvl9/f8oDWSLBmeF3GQ6AfKCncTxujQliBN8/0z3LcuLIVm1e1I+T34eFbez09V6B+PHLnWgDAR7au8tyvz+pFWVycxcqXcCpIAWzcSFVBfpH/GmTlTdVJUy9xVt2QWiSbZBWEuCd5ACDoI5bJJt7yJ65+fU5DWrRINinaFSRaQilVCCGPA/glAD+Ab1FKjxJCPm0cfxbAhwF8hhCiAMgD+Citru2YI1jNpc9IClZzTqMESmrq0zkZy1oimMgWEQ74XNXNq0EIwQ8/vQ0zedkzmxWoH79z2yr0XbcUXZw6pOVgWrKTxqynCWPKwRLOZBNgrZKv6+HyXT/RkG48qttE80X3eU0MkYDe2UQprYinFgxhaJ7Ea9CFkfKWP1muwdnZxJJRlozUMK4c5JobTVV/Mtz1F6see7bs568D+Hoj9pII145TzngoqAZqR4WMG1JsvFn/cgT9PmFEm4B6RV6YFgLrjpo0XPsOL669hcJ9psDv2pdGMleukZdVrow9oNeRUooaEeeC7D6vicHOtedVkCKEIOgns+q1dyzqN3vtHZfwBNHZZKDFYi69l/gUAFN2jbGRiUzRlGgTuLLBhE8uGYZ0KldEayTgGssrhx6nL7FJWdWQl/nGOQMl1342jJSxxWr3XpLdR5UwBP3E2pAa4QE3CTzAfrb93GiaMoX8KyNGOq/QEgmaQiGALgibK6pcyk8M3a36l2nU6JOfyEqe46MCCxOhgA+d8RAupdlnz69nypCoGsnMbuy8XhEzllYxUm7Xnk0BrU5YKe5TSBns6kjZzCceD81utr1XQ1q0FC25sgry5xUSkcr4FGsX5W0PBXTXPugnuGSIMY+ni56ytgILG8taI+ZNdCxd8Byaqc7aM90GXuGTqENBPq9rbw7Aq2KkBVnlKsYHWIzUOtnk5taba9iMCimqGgiB6yhls6jfwRgLQ3oZ0BKp1JPMeGQDgN6VtKxFV7iXVQ2j6QKWe1AQEljY6G4Nm6790HTBk3oUUJtsSpsznzgNqU35U172wkgN116pNsbuE0QZgj5iw0jdRzEzODHSkN+d1QYdkk3Fy9DZJAypgdZIEEVFM++krN0vEeZv7wSAZa1hXEoVMDJT0PvkhSFdNOg2bqKaRjEyU8ByD3qmgM5IJUWDYnz5Ux7GOQO68Qn4yOzKnwLWxlhSVIQ5jbFtsknWuBNWoYDPsvyJZwop4B4jDfpJXUlgOwhDaoC58IwFsNnyHRzTP8uxoi2Ki1N5DE7pmpYrhXLTokF3qz6NdCRVQFHVsIJTYZ+hpEmqG7G0h3HODFYq+XmPBflArSEsyJo3196mqJ/HCAL2ySaemfZAyfW3jJEqmqckIA+EITXA7vqZKkPKM0a5HOu64hiYyuO8oW25UjDSRYO1XXFoFHjjjN4z4tW1Z/XGGSM+z2T5eMY5M0RC/ooYqWpMx40FeUuoWNbeojuK17X3W8+U1117PmNsx0iLCp8hJYTYjmTmNcZeIAypATYylzHSGaM7qd1DQTWgG1JVo3jp2CWEAj7BSBcRWH/7zw/pnc7rPSpIVavkl1x7/pt5LFTJSEvzmvi+6nbJJknRPLv21b0z+hq8xtg+2cRrBIN+Yp1sUqlgpJcLjJEyd4rpinoRZQaAq40v069OjOL6npY5/8AE5i+uXqp/9jtOjiEe8mOVR03Taik9L+OcGapHMnvRIgXsGankhZH6AEpre+UlDwkrpzpS3vBAMODASIUhvTxgijbTRsnJdE5GyO/jDtIz3LCi1bxYblzZNrebFJjXiIcDuLlX/8w3rmjlGsNcjtLNnLn2MhJhvnHODNUjmQtMHZ+zsSRsk2wqKF5ipNZjPjy79naGlJuR+mzrSHmaArxAGFIDnVVdSTP5ItpiQc+ZvaDfh49s7YWPAA/funLO9ykwv/E7t+mCZh/ZssrlzFosMfv19WswXVA8JZoAI9lUzkhlb4w0bJY/WdWR8jNSoDbhxAryudawMYJeXHunGOlce4pN7bWfTzBFJ4we6emct1lL5fjS/3Yj/ui912KZmEW/6PB7t6/Ge69bhuUeM/YA0BmvHAs9k+cf58wQC/nNRClQChPwduhZdTZRSvVee95iemZIq4xx0UOcNRzwoWhT1M/t2tv267MYae369UIwUgNBvw+tkYCp3jOVK6LdY8aewe8jwoguUhBC6jKigJ6dD/iI6RVNZiV0etRqqNYTZWEC3g49qzpSRaPQKJ8WKVDqGKp2zb0w0tlm7QH7hJWsaq7D87xCGNIydCbC5kU8nZPRFhXtnQKNAyEEnYmQ6RVNZIsmS+VFdbKJdUrxMtugn8BHKrP2pVHM/KIlQC0j9dLZpGfcLVx7T4zUZ6lHqiebRIz0smFJPGTGp6Zzct2MVECgXiyJhzGRLUnxeWWk1eVPGY+MlBBSw2rNUcweCvIBC0Yq8/fa2zJSL+VPDll7Uf50GcEMqaZRTGQlLG0Ryk0CjUVXIoTxTBEFWUVaUjyL3lQX5Gc8xkgBnXmWs0lmVPl77fX/q4VLvNSRhvz+WXU26WvYa5oKQ3oZ0RnXL+LJXBGyStEtDKlAg9Fp3MyZZ+RVhjEWDKCoaqYBYTFSL7q6kYCvgpGW5jV5K38qN8aaRg2xaF42ad0d5dW1txMtEYb0MmJJXJ9LPzKjS6H1tImEkUBjsSQexkRGKs378shIq1uddXFyv6dBb5Ggv6L8iTHcmIfOJqDStWdGkde1DxsF+dXdUXNVR8pGkcwVhCEtw9KWMFSN4thwCgBE5l2g4VjaEka2qOLESBqAd9Eb1ljC2kszBcWTWw/osdByRsq0eWOcs6OsXHtJ5hNkZmDnVXdHec7a24UHBCO9fFjTqbf07Tk3CaA0h0dAoFFg1+Drp8cBAL0e20yZdimbZpqRFE/i5IBe5lRuSE1GyhkesHLtmVH1UpAP1MrgSV5ipAHrGKlQf7rMWNMZBwC8cmIUkaAPPcKQCjQYa41rcNe742iN/P/t3WuMXPV5x/HvMzO7s+u9+MLaiwEnEHASICgUjAMkRJvmosR5YRI1bWhUUBUJWQ1q+pIIqa9aNe2LKopEm6IkElGbm9TQuK0TQohHURORQIjNJZgAxmDHxsY29u7s7lz33xfnnNnZ9Yz3/Oeyc9nfR1rt7M7ZmcfH68f/6/NPVVqYcVVapGHlqJl8iVHP3VHpVKLSgoSqFmnM7dKpSou0OpHGO0E0UjmSueo1nAsqWaVbMUaqdaTtc8XGYRIWbNF75+SY17iSSCtELdIzswXedolfaxQWS+5FLdLZfMmr6AlEY6TVhU+iFmncdaTB55ot0pjjrLXOto+6+X4L8uutI1UibZt0KslVE0GL4F2TYx2ORtaikXSqUsP2hgaK3kR785eMkfom0lSyJV37wpIlVH4t0srhdTUmrOJ2y4PJpvoV8lupo4nUzD5uZi+a2ctmdn+N583Mvho+/4yZ3dTumD590xUA7L5RBUekM/7k5qDozZ0N/A4udu2rxkg9J5uCMdLGu/Y1J5s8u/bpGi3SuCeIRuqtI+2roiVmlgQeBD4KHAOeNLO9zrnfVV32CWB7+PE+4F/Dz23zV1NX82e3bPM+AVKkVb744e3cfdvbGzrKe1241Cnq2k/nig1MNl3YIk1Y/CRYGSMt1ppsitm1r9EijZJiM7P2zjmKfbaOdCfwsnPusHOuAHwX2L3smt3At1zgCWCDmW1tZ1BmpiQqHZVIWENJFILf3/XDA0znihTLC8zkSmz0POVh+c6m2XyZdYOp2CUlE+ExH7Vakz4V8mHprH2lRepV2HnpGKnvOGtcnUyklwNHq74+Fn7P9xoRqTI+lGJ6vlQpp7dpxHPWfvnyp2LJu8D54LKZ/1bM2uc9u/bRGGn1ov5iZZy1tWOknaxHWutPsnyKLc41wYVm9wL3AkxOTpLJZGIHks1mva7vpF6JVXG2XtxYrZjj1T+c5CeZtwA4ceRlMvkjsd/njWMF8qUF9u/fj5nx6tEcVl6IfZ+y2SzmjFdfP0omcwqA354IxlkPPv0b3vz9yonw0Nkgkf/6N78leyRI4q9PB9976dALZM69tOJrHHs92Gb7+P5M5VTRbCFIH68dPsxlE/mW/d13MpEeA6rLiF8BHG/gGgCccw8BDwHs2LHDTU1NxQ4kk8ngc30n9UqsirP14sb6jVd+xXSuxNXXvxt+8QQfuOVGbr9mIvb7vGiv8MNXDrHz9jsYSaf499eeYhPzTE3dETvO0eEyE1smmJp6LwBvPnUUDj7DHbffyrZNKy/rGnvtLfj1L7nuPTcw9a4tABw4eg5++QtuuvEGpt49GevPwUuHuP0Dd1RWHJyazsHPHufad7+T0dyrLfu772TX/klgu5ldZWaDwGeBvcuu2QvcHc7e3wqcd86dWO1ARXrJ5rE0b07neGu2sZNwo1n+qHLUfLFUOSo6rnQqsbSCVKOz9qVaY6Rx17OG46xVNUmjcdtWryPtWIvUOVcys/uAR4Ek8E3n3PNmtid8/mvAPmAX8DIwB/xlp+IV6RWT40O8mc1XipRv8i58Eh1NXmRyfIjZfNn7yJN0amkZvFwhOha68QX5vsufBi6yqH+gxUVLOnpmk3NuH0GyrP7e16oeO+ALqx2XSC+bHEtTLDsOvTFNwhpJpEtPM50vlL23Sw+mEkvWkUa7o+Iewldz1r5crrx2rBjCCaViucYSqpit2ri0s0mkz0RVy55+7RyXjg95L/WJtpRGiXS24D9rv7xrP1csMZhMkIrZpa41ax89jjvjfrElVH21s0lEWi+qWva7E9NcEWNiZ7nFrv1iizRulzySHlg2Rur5GrUW5PsuoaqVSCvLn/poHamItMH2ydHK4ys865lCdde+iHOOmVypklzjWr5ff65Q9mrVVhJpuXoNaLiY3nOyqfoAvMXXUCIVkYsYHxqoJK3tW/yL71TP2udLCxTKC5WqUnGtS6eWnGY6VyzHHh+FegvyPcdIU/XHSPtpi6iItMmf73wbg6kEH71u5fWWy40OpjCD6VypUvxk3LNFOjKYZDZcPgUNdO1rJNKokMpQM9tM+3Bnk4i0yQOfvJYvfOgaNnrO2EOw1390MMVMrlgpxzfuWWB63WBqyWmmvl37ZMJI2NIkGA0VxD6EL1lj+VNJLVIRicnMGkqikdGhFDO5EufDSvvjnutIR9JJZgulyj73uWI5dgKMLF9ClS+WMY8qVIst0hpjpJpsEpF2GxtKkc2VmGmwRTo8mGTBLc605zxbpBCsOa2ui5orBcc5x61CNVjZ2XThWlS1SEWk7caGBpjJF5nORS1S3zHSoAUbjZPOFUuxK+xHhpfVRc15tmoHak02hTP4WkcqIm03PpTi/HyxUiDat2sftT6jmfv5gn/XfmggyfzyRBqzMDTUHiP1LTAdlxKpiFxgYjTN6ZkCZ7ONFT4ZCXdHVSdS36798kr9ueJC7Bl7qOraV42R5j0LTMelRCoiF9g8luZ0Ns/JmRwb1w14T85ESTOacJorNpJIl54dNe/bta+x/Ml3d1RcSqQicoHNY2lKC46XTs6wZcyvYAksnjg6ly+TLy3gXPxlS5HhwQu79nGPc4bFcdBaiVQ7m0Sk7TaPBWdG/e74NFvGGzuED4IW6VzlOGf/Wfvqtaj54gJDHi3JgTq7o3xm/uNSIhWRC2wOD9+bLZQrj31EY6TzhXKlVeldQWogSa5qHWmu5Ne1rzlGWlxo+RpSUCIVkRqqq0ZdtsG/8MlIVYt0vhAsgfLu2g8kKwWhIVr+5NEirTNG2uoZe1AiFZEaLlu/OC5aXU0qrnXpxTHSmQbXog4PJCtHlEAwa+9T+KTWNtOoa99qSqQicgEz466d2xgZTHLH9s3ePx8lvNlCqbKo3/e4kqGBxJIxUt8F+bB4JHMkX1po+dInUNESEanj7++8gQc+eR2jaf80kUwYQwMJZvNNbDMNF+Q75zCzhhLpYDJBvmoJVUFdexFZTYmENZREI+uHB5ieLzE931iLNFrqVNmv30BrMj2QXFKpPx/u1281JVIRaYsNw4Ocmy8stkgbGCOFoEu/sOAolBa8tohCMDyQLy6tIKVEKiI9Y/26Ac7NBTVNkwnzX0caXj9fLFdalY3s169eQhWMkaprLyI9Yv3wAOfni+GZTynvRfDRUqdccaGyFtVn+VN0ffU203xpoeW7mkCJVETaZEOYSKfni97jo7DYtZ8vlL2r40eWH8KXL5X7Z9bezDYB3wOuBI4Af+qce6vGdUeAGaAMlJxzO1YvShFpxoawa39mtsBGz+pRsDjZNF8sM1QMkp9/izTJXGHx7Kh8sb8mm+4HHnfObQceD7+u50POuRuVREV6y4Z1g8wXyxw9O8fkuH/hk6hFmi+Wq/br+69FXd6176flT7uBh8PHDwN3digOEWmTLWHhkyNn5ri0iUQ6VyiTDSvt+y7HWr5fv9CmnU2dWpA/6Zw7AeCcO2FmW+pc54CfmJkD/s0591C9FzSze4F7ASYnJ8lkMrGDyWazXtd3Uq/Eqjhbr1dijeI8c3Yxgc2eOU4mc9rrdY5ng5bkUweeJRpiffG5gxSPxW9Rnjud5/xMuXLf5gslTp34A5nMmy29n21LpGb2U+DSGk894PEy73fOHQ8T7WNmdsg59/NaF4ZJ9iGAHTt2uKmpqdhvkslk8Lm+k3olVsXZer0SaxTn9nPzfPnXPwPgtvdey9SObV6vc3I6B//3ONuu3h60RJ8+wAdv38k1W8Ziv8Zjbz3LofNvMDU1hXOO4o/3cc07rmRq6p0tvZ9tS6TOuY/Ue87MTprZ1rA1uhU4Vec1joefT5nZI8BOoGYiFZHuUt2dv3JixPvno258NlfCCJZOjXh27auPK4n23PfTZNNe4J7w8T3AD5dfYGYjZjYWPQY+Bjy3ahGKSFOSCePj11/K+FCKGy5f7/3z6waTmEE2X6rMvDc02RQu5m/XMSPQuTHSLwPfN7PPA68DnwEws8uArzvndgGTwCPhIt4U8G3n3I87FK+INOArn70R8F//CUEFqtHBFDO5EslE2CL1PfcplaS84CiWFyrFS/omkTrnzgAfrvH948Cu8PFh4L2rHJqItFAjCbTa6FCK2XyJgWRQTSrluStpqGq/frumWeFGAAAHtklEQVSOYgaV0RORLjaaTpHNl0glEw1VoqreZhqtJ+2bnU0iInGMDgWJdCCZ8J5ogsXdUbliuVIk2qfKflxKpCLStUbTKaZzJcyMDZ6FoWGxa58vlRuesIpDRUtEpGutHx7g/FyBs7N5No7479ePjm/OFReYC5dBDXtOWMWhRCoiXWtiNM3pbIGz2QKbGkmkVV37XKGxY6HjUNdeRLrW5rE02XyJbL7EJU0l0oWqwidqkYrIGjIxupg8N42kvX9+cda+rK69iKxNE6OLyXPTiP9kUzSxNFsoMa/JJhFZizaPLSbSLQ2U4ovWns7mF2uatmP5kxKpiHSt6mInV0+Mev/8SDpImtl8kflCUIs02m7aSppsEpGuNT40wLVbx8mXymzbNOz98yNhNz4btkjbMdEESqQi0uX++773ky8teJ9CCpBIGCODSWbzpTCRtiflKZGKSFdLJf2LlVQbSQeFT2bzpba1SDVGKiJ9bTSdYiZf4vx8kfUNbDONQ4lURPpa1CKdzimRiog0ZDRMpGqRiog0aHQoqLJ/fr7IuBKpiIi/S0YGOZ3NM5MrKZGKiDQiqiAFqGsvItKI6m2mSqQiIg2YGE2zOXuW7337frbOn2vLeyiRikhf2zyW5q9/8R1uOfo813/9K215DyVSEelfw8PsfMcl/MWBH5HAseHhb4AZDPvv27+YjiRSM/uMmT1vZgtmtuMi133czF40s5fN7P7VjFFE+sDhw7i77iI3EI6TrlsHn/scvPpqS9+mUy3S54BPAz+vd4GZJYEHgU8A1wF3mdl1qxOeiPSFrVux9etJl4u4oSHI5WB8HC69tKVv05FE6px7wTn34gqX7QReds4dds4VgO8Cu9sfnYj0lZMnsT17sCeegD174I03Wv4W3Vz96XLgaNXXx4D3dSgWEelVP/jB4uMHH2zLW7QtkZrZT4Fa7ecHnHM/jPMSNb7nLvJ+9wL3AkxOTpLJZOKECUA2m/W6vpN6JVbF2Xq9EuuajNM517EPIAPsqPPcbcCjVV9/CfhSnNe9+eabnY/9+/d7Xd9JvRKr4my9Xom1n+MEnnI1ck43L396EthuZleZ2SDwWWBvh2MSEblAp5Y/fcrMjhG0Ov/XzB4Nv3+Zme0DcM6VgPuAR4EXgO87557vRLwiIhfTkckm59wjwCM1vn8c2FX19T5g3yqGJiLirZu79iIiPUGJVESkSUqkIiJNUiIVEWmSBUuj+ouZvQm85vEjE8DpNoXTar0Sq+JsvV6JtZ/jfLtzbvPyb/ZlIvVlZk855+pWoeomvRKr4my9Xol1Lcaprr2ISJOUSEVEmqREGnio0wF46JVYFWfr9Uqsay5OjZGKiDRJLVIRkSatyUTaK2dGmdkmM3vMzF4KP2+sc90RM3vWzA6Y2VOrHONF75EFvho+/4yZ3bSa8XnEOWVm58N7eMDM/rZDcX7TzE6Z2XN1nu+W+7lSnN1yP7eZ2X4zeyH8N//FGtc0f09r1dbr9w/gWuBdXLweahJ4BXgHMAgcBK5b5Tj/Cbg/fHw/8I91rjsCTHTgPq54jwiK0PyIoFD3rcCvujTOKeB/Vju2GrF+ELgJeK7O8x2/nzHj7Jb7uRW4KXw8Bvy+Hb+ja7JF6nrnzKjdwMPh44eBO1f5/VcS5x7tBr7lAk8AG8xsaxfG2RWccz8Hzl7kkm64n3Hi7ArOuRPOuafDxzMEJTkvX3ZZ0/d0TSbSmGqdGbX8L6DdJp1zJyD4hQC21LnOAT8xs9+ER66sljj3qBvuY9wYbjOzg2b2IzO7fnVC89YN9zOurrqfZnYl8EfAr5Y91fQ97ebD75qy2mdGNepicXq8zPudc8fNbAvwmJkdClsM7RbnHq3KfVxBnBieJtj+lzWzXcB/AdvbHpm/brifcXTV/TSzUeA/gb9xzk0vf7rGj3jd075NpM65jzT5EseAbVVfXwEcb/I1L3CxOM3spJltdc6dCLsap+q8xvHw8ykze4SgK7saiTTOPVqV+7iCFWOo/sflnNtnZv9iZhPOuW7bM94N93NF3XQ/zWyAIIn+h3PuBzUuafqeqmtfXzecGbUXuCd8fA9wQUvazEbMbCx6DHwMqDmT2gZx7tFe4O5wZvRW4Hw0XLGKVozTzC41Mwsf7yT4t3FmleOMoxvu54q65X6GMXwDeME59891Lmv+nnZ6Vq0TH8CnCP4XygMnCU8rBS4D9lVdt4tglu8VgiGB1Y7zEuBx4KXw86blcRLMRB8MP55f7Thr3SNgD7AnfGzAg+Hzz1JnlUQXxHlfeP8OAk8At3cozu8AJ4Bi+Dv6+S69nyvF2S338wME3fRngAPhx65W31PtbBIRaZK69iIiTVIiFRFpkhKpiEiTlEhFRJqkRCoi0iQlUhGRJimRiog0SYlU1hwzuyWsOzkU7gx73sze0+m4pHdpQb6sSWb2d8AQMAwcc879Q4dDkh6mRCprUrjn/kkgR7B9sdzhkKSHqWsva9UmYJSgavpQh2ORHqcWqaxJZraXoFL+VcBW59x9HQ5Jeljf1iMVqcfM7gZKzrlvm1kS+KWZ/bFz7medjk16k1qkIiJN0hipiEiTlEhFRJqkRCoi0iQlUhGRJimRiog0SYlURKRJSqQiIk1SIhURadL/A7sH6IMenZnbAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(f, x_interval[0], x_interval[1], M(all_time_best), delta=1e-3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1dd138909d0>]"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot([i for i in range(len(scores))],scores)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.8.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}