Gradient descent.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### Gradient descent"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "In this notebook I am going to present the operation of the steepest descent method with variable step size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "def target_function(x1, x2):\n",
    "    return (1.5 - x1 + x1*x2)**2 + \\\n",
    "            (2.25 - x1 + x1*(x2**2))**2 + \\\n",
    "            (2.625 - x1 + x1*(x2**3))**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x6d826b0>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x6d5f330>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x1 = np.linspace(-4, 4, 200)\n",
    "x2 = np.linspace(-4, 4, 200)\n",
    "x1v, x2v = np.meshgrid(x1, x2)\n",
    "z = target_function(x1v, x2v)\n",
    "plt.contourf(x1v,x2v,z)\n",
    "plt.xlabel('x1')\n",
    "plt.ylabel('x2')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<mpl_toolkits.mplot3d.art3d.Poly3DCollection at 0x6e6e1d0>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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KVgSZaXDr9/uJRqOcPn0ayF6brhG1z+cruuPNzYZFyCtEthriXIt1RkLOJ2/WttWigkIo\nhpATiQTDw8N6j7wdO3Zc9wWbj5B1YjFUWQhV6ZI1IeSjfvYEqvozN52QSwEtIs1lIGT0Th4bG9Pl\n48ZuJJWVlSXL/ZYK+Wrii4FZxV82GKs4GhoaWFhY4MCBAzlr0wFOnjzJtWvXiMfjXLp0ic2bN2es\nxVy9epUHHnhA/7/b7ebP//zP+chHPsIDDzzA0NAQGzdu5Otf/zp1dXWoqsrDDz/M888/T3l5OV/6\n0pfYv38/AM888wx/+Zd/CcCnPvUpPvrRjwJw+vRpfv3Xf51wOMzAwMD/Bh5WC0QwFiEXCc2da2Fh\ngZqamqyla0ths9lYXFw01b3ZbL2w2W0DgQBut5uFhQWam5tXlJrIhWx5aY344/E4VVVV1HYaZNQV\nmRHSet8LwH8ryVxuNvJFtoKQ25LT2IjV4/Hg8/l44403Mh7RKysrMyI/s/MpFUpFyKWKtDViz1Wb\nrigKdXV1RCIRLl68yF/91V/R19fHY489xj333APA1q1bOXfunD63lpYW7rvvPp544gne/e5388gj\nj/DEE0/wxBNP8JnPfIYXXniBvr4++vr6OHnyJB//+Mc5efIkHo+HP/uzP+PUqVMIgsCBAwe49957\nqaur4+Mf/zhf/OIXOXLkCKIobgbeC7yQ7/tZhGwSRjFHNBqlv7+fQ4cOFfyc1+tlbm4Or9fLtm3b\nqKury3uCl2KhDsDv9zMwMEAsFtOblZa6WN4YIWtEPDU1xbp166ioqMDv91O55jyxTa04BseIYKiv\ntpfREDyF39sP9VtKNqeV4GYJQwRheduos2fPsnPnzgwVXS75uEbUqymizoUbQci5IIoiXV1dHDhw\nAJ/Px9/93d/l3f7ll1+ms7OT9vZ2nnvuOV555RUAPvrRj3LnnXfymc98hueee46PfOQjCILA0aNH\n8Xq9TE5O8sorr3DXXXfpT0R33XUXL774InfeeSeLi4scPXpU282XgV/EIuTrQzYxh8PhyLuqbpQ3\n22w26uvraWxszOs1oaGYUrZs2y4uLjIwMEAikaCzs1PfZzgcNj2uWWhF+m63m8nJSVpbWzl69Kh+\nzJqbm3F5VcIPthF6fIyymnQkEy8rx0EU76v/i5nt/10nmGI8f1cTSm0uVIx8HJZXJ6w2lIqQi0l9\n+Hy+ZYux2XD8+HF++Zd/GYDp6Wm97dXatWuZnp4GYHx8nLa2Nv0zra2tjI+P5329tbXVuJsxoKXQ\nXCxCzoF8Yo5cudOl8uZt27ZRVVXF4ODgdZFsLhgjZJ/Px8DAAKqq0tHRscwJTBRF04uFZqw6E4kE\nCwsLBAIBNm3axNGjR/ULznizEuILVOw+R6ihHrvLDkn+wFZTDyzQuvD/EBr/J8Fw0pQ9EAjoSiyN\noPMtgt1uyHfc8z2iL61OCIVCnDp1alnqw6zUudRYCSEvvvEG1bt3Z7xWTOWEGUKOxWJ8+9vf5vHH\nH1/23s2wCLUIeQmydeYo9KPkkzdDkmTN1qkWGyFrFpiiKOqpiWwothNIrtV1zdticnISl8tFZ2dn\nRoSgfV5H3Itoi1J23yHEufRNTNV8CCJzrFn4CbWdv5h+z9BFIxAIZCyCaY/sGlnfTHN5I26m5Hlp\ndYKiKJw5c4Z9+/aZlo8vdXnTxikVIa2EkCf+7d+yErLZCNnr9S47N5fihRdeYP/+/TQ3NwPQ3NzM\n5OQk69atY3JykqamJiBZPz06Oqp/bmxsjJaWFlpaWvQUh/b6nXfeSUtLi+6ImEIrMF5ozhYhU7gz\nRy6YkTdDclFvaYeFXDC7qOfxeOjr6yMUCnHw4MFlctalWInM2ngBGYlYS02Mj48XVh7GPQBUvO0a\n0ec70m+40sfJfvlpEgZCFoTc7Y4ikQiBQEB/ZA+FQvT29lJeXq6TdD4jodWOUt0ctPp3s/LxaDS6\nzI7T6XSW7Kmk2BvNzEsvETfWsKdQDCEvLi4WjJC/+tWv6ukKgHvvvZdnnnmGRx55hGeeeYYPfvCD\n+uuf//znefDBBzl58iQ1NTWsW7eOu+++mz/+4z9mIaVIfemll3j88cepr6+nurqaEydOcOTIEYCP\nAE8WmvNPNSEba4ivXbtGc3Mz1dXVBS8IrStCd3d3QXkzXH9e2Djf+fl53G43ZWVlbN26latXrxYk\nYyiekI2LdRoRa25v2kVqRhgixJMnqr1yBrZshROp71KWzhNLs2cQYgOojs78YxkWwbTcam9vLwcO\nHMgaCRoJRiPrXL/TanF7eytUetnk47DcjtPv9+P3+zlz5owp+Xgp4f67v2PNO9+57PVicsiLi4t5\n65CDwSDf//73+Yd/+Af9tUceeYQPfehDPPXUU7S3t/P1r38dgHvuuYfnn3+erq4uysvLefrppwGo\nr6/n05/+tL7A/yd/8id6EPH3f//3etkbMECBBT34KSVkrYZYM/HRiCWRSBSUN4+OjjIxMQGQ0SUj\nH67XlU1VVebm5nC73bhcLnbs2KG7lJXKy8IIQRCIxWKMjY1lJWLjdnnHjPsQVEOq5l3ohIwjfZzV\nslrsC88Qa/5zU/NbCuMju/boCWkbyUAgwNzc3DLZs0bSZo9LPqwGgYsGVVVXFNkuteMMh8P09/ez\nbdu2DPn44ODgst5+2rHM183cLBZ6evC89hqtv/qry95LJBJZn0KzoVAOuaKigvn5+YzXGhoaePnl\nl5dtKwgCX/jCF7KO89BDD/HQQw8te/3gwYNcvHhR+68p85afKkLOJ+aw2Ww587yxWIzh4WFmZmZ0\nK8ozZ8x7MRRLyFp0qi0Sut1uKisrl+WmiznJzRJyIpEgHA5z9uxZ2trashKxccx8uXEtXaFBah9A\n3nkH0qULYLiPqc5K7N5/Idb4KIhl5r6QCeRyJzPKnicnJ1lcXOTcuXPLSsqKaR21mgi5lHJnSZJM\ny8e1JqwOh2PZcSwGI//wfwFwZcn/FpOy8Pl8yxa3Vzt+Kgg5GxEvPWGzEXIuebNxezMRcj6yzzXf\nqakpBgcHqa6uZs+ePdfdrqhQblrrCDIxMYEoiuzcubOg7LRQhCzEMqMPQfKhvnctXAJshoqPMhei\nPI/N/x8kah6gWBRLhktlz9FolG3btqGqqp6f9ng8BINBgGULidlqf0vlHVEKlHKBMV+kna23n3FB\nVpOPa8f0/PnzheXjV68QvHQJAFdm2RhgEfItDTOG8BqMpBkKhXC73TnlzVC6vPDS+U5OTuqLLbkW\nCVcCQRCyzsHYmklbrLt06ZKpC7qQl4UQn9P/rYplCFIQcecZlNZNCGIEUh9VUzc1h+eLKyLk64VG\n6GVlZTidzowef0t9FJZ2JNFIOh6PU1ZWuuj+elBKp7dix8m2IBuPx7lw4QJbt24tKB9v+tvPEp6b\nB1HE2bK8bLeYao1gMLgqa7Lz4bYkZC3SiUajVFRUmKqY0OTN58+fLyhv1rYvVSmboihMTk4yPDxM\nfX095eXlbN++3dTYZrHUKtMYEbe0tGR0BLnehqh6vbYhQlbtdQhMIQggv28twuisTsg4Uu2rwj2I\nkTdQnLuXDnnTYCwR00qgIO31GwgEWFhYYG5uDkVRmJqaWpZXfauFLqvBetMILd9cSD4e7buK+MJ3\niHrjiPX1XLp6ddmTidkIWTsvV8tTi1ncVoRsFHN4vV4WFhbYunVrwc/5fD6GhoaIRqPccccdBeXN\nUJraYq1sbnh4mMbGRr1a4/XXXzc1bjHQSDZbRJytNdP1NETV3zcSsqMKmAJAOnQaZW49BFNv2tNj\n2D1fJLq+YHVQSbGS/O/SkjKNcOrr6/UocHp6OiOvaizLq6ioyOn2dr1YDW2gjMhH7MbKGfEzf0Go\nvhEWxqnatInOzs6MxUStkubq1av6Im4hz+TVktc3i9uCkLOJOex2e96o1ChvliSJ1tZWfD6fKXkz\nJCPklaYsFEVhbGyM0dFRmpqallVraERX6gWlYDDIyZMnl0XES2HGVrPQdqqqIsQNOWS74dHRHie4\np4vq14dS/zco++QrqHgRKCx5zdjXKrHwzLYAtlToMj4+fkOFLqstQjY1zuQEwtefJbxpCzBOeaqJ\n6VL5eE9PDx0dHfqxnJ6eXiYfvxE2AW8VbmlC1k70bGIOu92eVSpslDc7nU5d3hwIBJaVwORDMRGy\nNidZlvXodO3atRw+fDjr46xG4Ga7duRbfJFlmZGREcbHx1EUhbe97W0FL45iImQjgWh10v39/cTj\ncXaGr7Au9V5CsKHtVRVqmT84QvnJCmxyEGwhfQzFbke2fxVb/OMF96/NYTWgkNubWaGL1uboeoQu\nt1KErEH8wt8ixGKEy5NqQ2eWBT1IHstC8vFTp07x9NNPMzIywpEjR9i2bRu/+Zu/ydvf/nZ9e6/X\ny2/+5m9y8eJFBEHgn//5n9m6desNsd685557ePLJJ4VC1ptwixOy0Vti6cm6NMdrlDdXVVVllJCp\nqlp0JUQxEXIikSAajdLd3c369esLtmfSCNlM7jEXIWtEPDExwfr16zl69Cg9PT2mIp5icsjadh6P\nh/7+fpxOJ7t27cJms+E6q0JKoBhTZbQlr0i8HNkZYq5zB2uv9SJI6Uaoil1CdjyDFP9tBN6a/N/N\nirCXCl1kWebcuXO65DkQCKxI6FJKIjVTRWRmnLzn3cI0wrNfBiAkJa+LbCVv+WCsRb///vs5cOAA\nn/70p/na177Gm2++uaxk7+GHH+a9730v3/zmN4nFYoRCIf7qr/7qhlhvpiw/C1pvwi1OyJCbPLQI\n2Yy8eaG/n6r29qIJuZAcWlO5aUKSo0ePmm7NVIwnspG8sxFxsY+duRbrlkIQBCKRCL29vdjtdl2w\noigKsVgMyZCycBmc3qSyBsCD/+cWaeqzozCnR88hJQLiCFHlu5QJH1g1EXAhlNLCM1fnDLNCl3g8\nfkulLGzPPwWRZNohnEgGOa4NG5ZtV0w6RxOFOJ1O9u7du+y9V199lS996UtAunzvRllvfuQjH+HF\nF18saL0JtwEh54L2OGhG3izabIz/5CfIRZQt5UtZxONxhoeHmZ6e1oUkJ0+eNF0/uRJPZGM6xEwU\nng9mJNE+n48333yTSCTCgQMHlvklAJBIR77YDE8rUgXgQagPEthxjGr7q+l9OxVUIKT+PW+cata7\nPhsXcVb6vW4k3gqDIrNCF4/Ho6+RrFToYmY+ZpHPoU1YnEXqfVl3yg4HU77POUQhxTi95aqjHxwc\npLGxkd/4jd/g/PnzHDhwgM997nM3zHoz9e+C1ptwGxKyMSpVVdUUMVW3tdH92c9S82u/Zno/2VIW\nRkVfW1tbhpCkmIW6YmqcBUFgdHSUubm56yZiDYWM7/v6+lBVlfb2dmZnZ7OSsSAITLXvoeXyteT/\n7emnCVlK3/g8x6JU9dkQSBK2VCGjABW15zl4tBI5ullfwJmamiIQCCDLsl67qnWFrqioWDF53CyD\n+lKNsVSgMTIygt1up66uTs9Pz8/PLzO5L1SlUMoIOVeNtuP5z6HG0vsIeZLeJ9kIuVgfi1yy6UQi\nwZkzZ3jyySc5cuQIDz/8ME888UTGNjerQuOWJ2TtoGWTN5uNSkWbjamzZ6m8/37T+zXmnKPRKEND\nQ8zNzdHe3p5BxBqKWagzQ8haRDw/P18yItaQLWURCATo7+8nkUjQ1dVFbW0tgUCAmZmZrGMkiHB6\nS4i17hakyDjYAum5i+kLMFbpYrH27dR4f5h8z5GOqmO2f8OpfCpr1YJWu6qtC2h9CI0RYS5byRuB\n1WbhKUmSXve7EqGL1t+vVKmPbOem4JvB/oN/IqIkF8gUIDI9ja2mBnuW6LZYlV6uCLm1tZXW1lbN\nhY3777+fJ5544oZZb6b+XdB6E24DQo5EIvT392eVN4P5k7yiuZnZV15Bfde7TF1YkiQRi8V48803\n8Xg8bNy4kc2bN+fcVzELdfkIeWlqorm5mbVr15b0Md6YsggGgwwMDBCJROjq6sqoEsiXa44JXhI2\nBfeOn2HzmW8g2NJWiglD0KWoFVxocfI2r4iAguJY0N/zSiPUCws41Ez5q3ExbHh4mB07duh592y2\nkjabLYNobkTaY7VE2ZD/nDcrdBkbG8Pn8xEIBKiurr4uoUuuSNvx/N8ixEIQSQU2DY0oI7O0fvDn\ns45TrBcrM8tFAAAgAElEQVSy0WjKiLVr19LW1sbVq1fZunUrL7/8Mjt27GDHjh03xHrzy1/+MsBz\nZuZ9yxOy9miSTd5st9tN+03UdnQw8NJLKI89VvAxLRKJ6I1DW1paTDUOLVbZtzRloBGxdnfWIuKr\nV6+WvOZSFEWCwSAXLlwgFArR2dlJQ0PDsu+YL9ccFZLdpi9sDNDevwO77ar+XsKQT5ZVJzOVIQI1\nP0tF4AJIMf29iCAzaX+e9tivmJ53Nv/feDyuP7pr0nQt7VFZWamvst/stEepDOFXEmln806+cOEC\nGzdu1P2TVyJ0geyELHinsP/gKQDUhQACEKpfgzQfYud7sqxHUFwOeXFxkS1bcvdqfPLJJ/mVX/kV\nYrEYHR0dPP300yiKckOsN9/3vveBiQU9uA0Iubm5OSfRFWMAVN/VxZn/83+Y6+ujedu2rNuEQiEG\nBwdZXFykvb0dv9+vLwIUwkotOJdGxEsrNYqx1YTCxBGJRJiYmCAYDLJz507WrFmTt742l3Q6JqYi\nYhEu7dvDvshl/f24FE7/m2S0daGliSPuNcCk/l6YBIv252mN3Y/Eyn0itHzqUhMcrQZ4cnJyWdrD\nGFGbTXuUIkJebfXDZWVlOByOFQtdXC5XVkK2dz+FEE8eb2aT1Tihiio237cP55pastUvFdtPL5+x\n0N69ezl16tSy12+Q9Saf//znTZWI3PKEnO8iyCUOyYa6zqQ5+sVnn6X5L/4i471gMIjb7SYYDNLR\n0cGOHTsAGBoaMj3PYs2I4vE4Q0NDjI+Ps27dupw54mIXAHMRcjQaxe124/V6dfIyKqSyoVDKQsNU\nfQW+2Z+jJp6spohJ/vR2avJCnaoKstC4mwxCFiIkxDAz9pdZF7/H1Hc0i6Vpj507d+o3QuOj++jo\nKLFYTE97GKNC4+9Riuj2rUhZFINcqYZ8QpdsTVjD4TCKouipjyphAedI0hhbESRIrUOoVeXs2HgS\nuTr7b11sDtlMg9PVhluekPOhmDRBXVcXAFe+8hXe+dhjiJJEIBDA7XYTDofp6OjIGy0WglnilGWZ\nhYUF5ufnaW9vL7hYt5LWTMaLNRaL4Xa78Xg8urPd7OwsPp+v4Hj5UhZ6hAwIlPN83T4enOkGBGQj\nIYvpz19bs5YtqgCCCmoZYSEZSU84nmNt/L05hSLXKzc2EmGutkda2kOLqAOBgO5UVllZqRNPZWXl\nis+R1aawK3YcQRCyyp1Pnz7Nhg0bCIfD+Hw+yq/8CYHpeeqAmFiPIM8C0LJDxi6GSdS0Zx2/WHP6\nW816E25zQtZyyGZQ096OIEkExseZfOklZtetIxaL0dnZSX19/XVHLoUI2ZiaqKqqorW1lY6Ojpzb\na1hJzTIkiVirDNm4cWNGHnyl0mkjooYIGdXJcFmMCdcHWBc9iZFXI2J67vNiA0Hl7VRIr6Kqa/Tt\nIuIkM9IZmuWDWefwVqBQ2mNubk43itKISYuotbRHIay2CBlK11KqqqqKmpoahMU+Kl5/EUVNuRk6\nmoBZols7kFqmwAeXJ8OgXlv2NFJsDrmQn/dqxC1PyPlOGJvNZjplIdntuNatIzQ2Rv/x49zxt39r\n2mjIDHJF67IsMzY2xtjYmJ6aWFhY0FduC847ld4wA1EUicVijIyMMD09TXt7O0ePHl128Zo1F8qX\nsogK6fkrOIAYz9W189DsJJAuCQqJEf3fMSReZSfvU3+MqmYe+0v2N7IScqmwEuIxpj1mZmbYuHEj\nFRUVGWmP+fl5hoeHlynqNLIxEsxqi5BLBWNuvOzs/0RQZQRvyitbqEYVBCo+VoYUSZZGbtr3TgIJ\nm/40oi3CJhIJIpEIiUSioNDF7/eb6jW52nDLE3I+mCVkr9fLwMAAjhQh26emqDW5iLNSsUc2ItZS\nE8UuABbbmilXrXSxY+ZKWczPz7NYN0VqvY6YmtzPogTnao6yhm8CoMpOElL69wkJAm5JJJB4Bw7i\nYFjacdtG2SK5aZULPzXcDJhJexRaCNMaKlxvpLzaCFl/8po/h23431GxI3hTeeOIiPDew9jW9sBF\ne7K/YlUjdbDsaeTixYvU1NQQjUZzCl3Kysr0Y1mqjtlvJVbPr7ZCXM+i3sLCAqdOncLtdtPV1UVz\narFuUZYJfu1rBfe9EpN6WZYZHh7mxIkTyLLMkSNH6OjoyMgTl7IbiSzLDA4OcuLECURRZM+ePWzY\nsCHvBVsMIRvh9Xrp7e1lfHwctSyov+4Jpd3ceuVWErGNACiJzEWXIMl9/lDcQRyD94VaQVSQOe14\nldUKMySqqena2trYvn07Bw8e5NChQ3R2dlJVVUU4HGZhYYHe3l5OnTrFlStXGB0dxePxEIvF8o5t\nxGojZA2Oq08ioKIKaxHU1PmVAMcHh1CFJgQ5hpIjf6w9ta1Zs4b29nZ27tzJoUOHOHDgAJs2baKi\nogK/38+LL77IoUOHGB8f56GHHuKv//qvOXfuXMZYGzdu5I477mDv3r0cPJh86vJ4PNx1111s3ryZ\nu+66S39CVVWVT37yk3R1dbF79+6MXprPPPMMmzdvZvPmzTzzzDP666dPn+aOO+6gq6uLT37yk0Wt\ncay+X62EyEWYHo+H3t5ehoeH2bp1K/v376empobaVKWFPxolkDIeyYdiLTg9Hg8nTpwgkUhkJWLj\nuNcbISuKohM/wLFjx7L7TeQYs5iTSGsV73a72bZtG7t2bychppV5YmW6H6AiuXg5kSz8j0Qy+wR6\nhWREPCIKjKid+us2JZm+GLO5mRZNCZ7ecqw0qtXyzY2NjTQ2NrJu3ToOHz7Mvn37aGlpQZIk5ufn\nuXTpEj09PZw9e5a+vj4mJiZYXFzM2fjgegm5FL7M2jiqqiKFf4i4mKxFVxWDuOhoGVLFNArJRcBc\nhAzZ65A1oUtTUxMdHR186EMfore3l/Xr1/PJT36SpqamrLa6P/zhDzl37pxe+vbEE0/w7ne/m76+\nPt797nfrUmqj09s//uM/8vGPJ21hNae3kydP0tPTw5/92Z/pJK45vWmfe/HFF00fr9siZZEr52mM\nkDWvXrfbTVlZGdu3b1/mpqVVWnjn54m73cTOncOxxCnKCDMWnFpqYmhoiLKyMlMS55W4vWlQFIXx\n8XFGRkZYu3btslRIKTqBaAgGg4RCId588002b96slxkFmU5WSqTgF9LRnWIv46xtDW9P/ByizQ8p\nDwtRdhKV0vvsDrayu/oMiDKKUoFmB3fK8SPeH/lwxjxKRR7Xg1JLpyVJymkkpIlclqY9tNx0KYRC\npc1nC5R5/xQhmMwbq4nk04/S1IZ9+xsgA3LyWlTzELLZOuRAIEBNTQ379u1j3759puZ5I53e/uM/\n/kMThxTEbUHIuaDlkGdnZ3G73bhcLnbu3Jmz8WG9Rsjj46hA4Omnqf/c5/KOnytCNuaI165dy65d\nu5icnDRtv1lshGxsB9XU1JTV/D5Xo9NcY+ZCOBxmYGCAYDCIw+HQlUoaIqQjEkG1ERTSueBgiqi/\nIR7ig2ovkIwqHDRkjDFTWUM4ehCX6yTBkACpBfNh6SqnZ6/SaW++rhKzUuOtkk47HA7q6+uz1v8G\nAgH8fj/RaJRTp07p0eNSkYsZlLKWeV35DxGjF0DLXEWS4yr3r8O22JN8LZ684yo1G/OOZ+YY+3y+\nvAt6giDwnve8B0EQ+O3f/m1+67d+64Y6vY2Pm3+quy0IOVuErKqqXq1QVlaWYUifC7Xt7YgOB3I0\nSmTdOsTjx6l9/HHEHJ/LRpzG9kzGCFVzKTODYkrZBEEgEAhw4sQJGhoalrWDWjru9TQvjcViDAwM\n4PV66ezspLGxke7u7mXbDQiV2JVa4qIXh1qbkRjzCcnvNSnauaLsooIfJ/epZqZTFiSFH4pdfEB9\nA1tFHdrV7FQqeW3NOJXXYGBggEAgwKVLl6iurtaJp7y8/C0n6pspnTbW/2qP6IcOHdIlz1pZnrHa\nw1iSV15enrXBQUmc3hJBNrr+CTW+DlFNVtcIgQjy3oMIm+bgfGrDlJ+FUrvxuveZz1gI4LXXXqOl\npYWZmRnuuusuti1R5t7MXny3BSEboaoq09PTDA4OUl1drXewMANHWRnlra0E3G5CTU24zp8n8p3n\nKH/gl7Nub4yQcxGxhlIu1Bm/Z39/P4qicOTIkYJt6CVJMm08byRuTTU4OzvLxo0bs/qGGDEoCAwp\n72eX+CySgWhFVcQrpJ8ouu07eU+sD8UxhYILUq64TsVFRFSJCCKBxNtQhHRpnFOoprdqnv+y/QBb\nlRrOnDlDZ2cn0WhUd58LhUIZ0aH250Z2fy5VhFzKyoBCaY9AIMDo6CihUAhFUfSedJWVlUiSVBJS\ncgb/Aac4hRzbg17uGA4j/PICSjRtOyCEkmKhQhGyGXi93rwqvZaWpDVxU1MT9913Hz09PTfU6U3b\nnxncFot6WoQ8MTFBd3c3CwsL7Nu3T5fDmoXNZtN9WP2pBbDEj5dr2zVoNcAjIyN0d3cTj8c5cuQI\nnZ2dy1ITxUqcc0FVVWZmZjhx4gQej4c77riDioqKgmQMxbdmkmUZt9tNT08PTqeTo0ePsn79+oIX\n6owQ4fu2JuTE20BNp4dcahWq4aPzko2fKO8EVSCOI2M7DS9IzSwa4gZBLUcV4LuOpDeGIAi6xeTG\njRvZtWvXskWx2dlZLly4QE9PD+fPn2dgYICpqSk9/7pa8Fa1ktLSHhs2bGDHjh16tYexWmFoaEiv\nQtKqPRYWFkzXvAMowjyuyFcAUCPp80A51IBYPwGxtOpOCMygCmLOHHIxTw/5ZNOa7aj275deeold\nu3Zx77336pUSS53evvzlL6OqKidOnMhwenvppZf0p/CXXnqJu+++m3Xr1ulOb6qq8uUvf1kfywxu\niwh5ZmaGq1evUl9fz4EDB0yRUzZIkqQ3V/SnIsn4wADC8Juo7ZmPNYqi4PP58Hg8bNiwoeBiXbE9\n+5ZCVVXm5uYYGBigsrKSvXv34nK5iMfjNyQVEg6H6e7uprW1teg2UDOpnPFT0gF+O/EGmj+Fw0DO\ngirgsQnMiI0cSxwhZIgNbGo6RRQSRKbUOxBTqY04yYv4jG2MCTEp784W9WeLDjVTHL/fr4s2tMaY\nly9fLlpZZ8Rq8kNeCYzNQ5uamvD5fExPT+sdnoPBoN4ceKnbm/b30rlH7P+baiWVP03ljeWaTmw/\n+3rqteTvplKBGJpDqWoDKftxL5WPxfT0NPfdd58+5oc//GHe+973cujQoRvm9GZ2QQ9uE0J2uVx5\nWzSZvVgEQaA8FSH7gsk62visF/G7/4z8ic8CmamJiooKWlpa6OzszDmmceyVVgNonZzLy8vZvXt3\nRi58JV4WuaA9ZQwNDekdqlfiGzydIuSgINErHKFW/Q6KICOq6TK3StVJQkz+Jl+R9nGXknbGUgzR\ncpVSxn9ITXxEWUNAnCOEBMioAjzveJODgvmbr9EUx2ja3tPTQ1tb2zJlnUY6xlxrLsJcLX7Ipao4\n0czpbTYbNTU1GTlZ7camVXssTXtUVlZSUTuJs+H7CCQjaiEcQUXAe2w7DdJA8rVUHz1FWIdEP0rt\nppzzKZaQGxoasr7X0dHB+fPnl73e0NBww5zeisFtQcjV1dU5o08tVWD2x6zpTDZXXEitssZHxhG/\n9y/EH3qMsZk5PUd8+PBhvF6vaYnzSi60hYUF+vv7cTgc7Nq1K2t1SLGEnC1C1vLRbrebhoYGDh48\nyOnTp1ds4j5rqKq4LKzhkHwMyfZaimiTF2iFIQqeF+y41YOUk7wgotj17SrVchRRwK3so4nv4zUc\nxykhymiFkx0rmmUagiAsU9YtJZ3h4WFdGZbNp2K1RMilSnvkW9Qz3tiMxKd1IwkEAqi1f428mL6x\nxhemCG88Qqw+CKklASGcKoNTktFsvgW9YhYZ/X6/KR+Y1YjbgpDzQatFNksuFRta2XhsL0Pd55Cd\nTqTFRWLxOtz//Fl4z69mlJNdbxoiF7xeL8FgkKGhIbZt25ZX0FHMxSeKYkYOUEuD9Pf3U1NTw/79\n+027aRlhJIEgCfyGhbt5QeApcQf/XR4jioRGtDY1HdlWqTa+Zmvl9+VN+KRBAoavZFOT83lVquFj\n8ib6DGZECk6+027j7qJnXBj5SCebPWc4HKa/vz9v5UIhrBZSX+k42kKqveY1gq5zVId3AqCqAjZB\nZuqdfuq8IgigKAKEk6msWEjEBig1pYuQb0XrTbhNCLmQwVAxpKmWVXPs7fUMdYNv7Vrqh4YIOZrY\n9uaPSHzisYxti1moM4PFxUX6+/uBZBpm9+7dJV11N0bTHo+H/v5+XC4Xe/bsKVgSmAtLPZYnDRUR\nogrjgoAiCBwXfo671Qto4ZExLVGjlIEE3xYO8fPqOFNCOuI3bneS3cgM6v8P4eBig8QFX4QDFJfz\nXSlEUdRJ14iTJ0/S0NCQUbmgqmpG5YLmtZDrfC2Fp/KN9kIu+DlihMuSKjd7NPk7JqKNLBzbhVLu\npiZUm7wnx9cjptrMqaEEsbJ6zlZWEO7tzRC5VFRU4HQ6LUK+XVCMST0kSXZ9U5Cq9ha81dXUA0LZ\nGqRLP0EevIS6aae+7Uoi5GxRkN/vp7+/H1mW9Qaivb29JasF1SCKIuFwmNOnTyOKIjt27FhGLMVi\naW58ykDINYqdYSn5XUdFF1dDB3BWvIIqQIT093KqSTJ1i+UEEj+DRxoHtIg7fYoG1Vpa4x3MOJI5\nyDkh+d4Xyz0ciNxcZy9RFJcJNoyP8D6fj/Hx8Ywef0td30rRMeRmO8ZN2b9NuZgsE7PFk+swoYoO\nZre5k6/JHgDU6Bq0vp9lqsLU/fvY3HIn9sSWjGM2MTFBJBJBlmUcDodeQ52vt9+t6oUMtwkhlyJC\n1iTHPp+PcFU7d74HJq4kf/BYJOVW9cLTyJ/4X0WPrWFpPjsQCDAwMEAsFqOrqyvjJCpGPm0GgUCA\nwcFBIpEIe/fuLZlXrJGQVVXlim8KUutlzoiK5hHkkFW+Hmvjv7KFYOU1vIIIaN8vfWG9JnRxIBFn\nxp40LZ8T0sTtUB38W3wLd9vGCIpRRlLdq9+wR/hJPMDb5Ou7uZQaxoaixoabRrN7o/xZO5fi8bge\nGRYbMZcyQi62bjskTOOzv4r2rCXF5kioVQy2bMFO8veUlAkA1Gh6PSSwrQXPlj7a/W05j5m20CoI\nQkZvP83dTUsTORyOWzpCvi3qkPOhEGkqisLo6Cjd3d1Eo1GamppwbtjH7qpTyGVJ4ox5knd68Uo3\nxNKmOcWmLLTtQ6EQb7zxBpcuXaK1tZVDhw4tu6MXU6KWD6FQiAsXLnDp0iWam5tpamoqqXG3Ns/p\n6Wm6u7uZIN0vr6osnftuUpLk+U/Rg1T4qxhT0k8tvlg6wq6U7Xxv4SgOVUJQYcJwhsYVBx7BTjy2\nnSrFScBAVv9OHGUVeFqYgWZ2v9T1rbKyEpfLxeLiIn19ffT29nL69GmuXr2qBwuFAoCbmbK46vwS\nLjU1P0VCTIxzsead4Eiex/ZEJSKpTjSpICdau5uRnx1AVOoRyW5pAMmbfXV1td5UeP/+/Rw6dIit\nW7dSV1dHNBrl7NmzvP3tb+fKlSv83u/9Hk888QSvv/76su+1b98+PvCBDwAwODjIkSNH6Orq4oEH\nHtBd9aLRKA888ABdXV0cOXIko13b448/TldXF1u3buV73/ue/vqLL77I1q1b6erq0s2JisVtT8i5\nUhZLifjw4cN0dXXhcDiI1nZiE2S6upInTXwiWXEhTI4iXj6uj1Fsg1GAK1eu8MYbb+iuXrnKc4ol\n+6XlTtFolMuXL3P+/Hm9KqS2trbkQohEIsGZM2eYnZ1l//79CNVpslcMD2A1qRxvQpB4NfEebFJ6\n8XDeEAWHFsJcSVQT82ylSi4jbCBdr5qM2L4lt1ErZ6qfLsgOvnpr8HFWCIKAKIo0NDTQ0dHB7t27\nOXz4MHv27KG5uRlVVZmcnOT8+fP09PRw4cIFBgcHmZ2d1fPVcPNSFjO2HuZsZ3CRJDRHtJGwaz9v\nbhCxp5z/XIn0uSGEQyj2Os4f2AOSgl1pyzquhmw5ZE0U1NDQQHt7O+94xzvo7e1l7dq1/PEf/zHt\n7e1MTU1lfOZzn/sc27dv1///R3/0R/zBH/wB/f391NXV8dRTyU7YTz31FHV1dfT39/MHf/AH/NEf\n/REAly9f5vjx41y6dIkXX3yRT3ziE7qt7u/8zu/wwgsvcPnyZb761a9y+fJlisVPRcoiGk2XYRnd\n0LKZ8NhsNiK1yZKZzeUnGampRh6fQO5yIS3MIJ1/FmXPx6AIvXskEsHtduPz+ejq6mLDhg0FP1us\n1FpRFCRJIhaLMTg4yPz8PB0dHWzfvr3o1kxm4Pf7uXbtGpFIhD179ui50+9e2cqWXX4mpWBG/tcm\np/+tKuX4R3chbDiLKsC0M11xITrrIQhfjezhE8IiGBqHDMZEsIEqCLwZ3opoG0VJHcbBRBmPq/CL\ngkrFKjEcKhbZcsg2m43a2tplXZ+1ZqKBQICpqSnC4TCSJOlty7xeL5WVlSsuXSwmQk4Q5WrZlwCw\nC4sASPF6Xm1tBqIIkgcVcMbTv7MQ8XB5313I5clrz65uKDgfM99FW6PZtWsXd9xxR8Z7Y2NjfPe7\n3+XRRx/lb/7mb1BVlR/84Ad85StJNeFHP/pRHnvsMT7+8Y/z3HPP8dhjjwFw//3387u/+7uoqspz\nzz3Hgw8+SFlZGZs2baKrq4uenqRBUldXl15u9+CDD/Lcc8/pDZHN4rYgZChswVmIiDXYbDZitlpU\nVz2OsIfq/+9d+J7+AdHqDZR7rsKcF2HiJGrL0YJz0jo5Lyws0NHRgaIoyb5iJgijWMe3aDTK5OQk\nU1NTtLe3s3nz5mUXd7GEnG0BMhQK0dfXRywWY8uWLbjdbr1ULqbAhaCdhQv72HNHD3NCev8RAyFX\nyQKvzDfzIVcb4bpxBu3pfczFk5G0Kohcix6lXL1ESFBwKSJXbWlhyfCkyrqgg/F1MWriAtdS3auf\nVOCRW69RBFCkgClLM9FEIsHk5CTz8/NMT08zMDCALMt6I1btj8vlKrifYiLkS44fERGTDn+ikHya\nHHPuwOuYAEVAFZOvlSW0tQaJ2XV7uNbiZ1MimdYyEyGbuUFoHJDt+/3+7/8+n/3sZ3Xp9Pz8PLW1\ntTrRG53ZjG5umjhmfn6e8fFx3Vpz6WeWur+dPHmy4HyX4rYh5FwQRRGfz0d3d3deItZgs9lIyDJq\n0zaE4depeXsc31fKiEl1ycWKRC3S2f9LIg8hG6NUoxmPz+crOuotBFmWiUQiemffUrRmguXlbNFo\nlIGBARYXF+nq6tKVbsYb4UBUQEFgJOSi5upebNumgOR78wZCFlNWi98Y286vEIam1D5VcMfT5WuB\nQBl1YxsJtblpVDMVeQlbPd0zjeysP0NNPD32kwmZw1f76Sh3mio1u5GI+/3YTTYFgOtPN9hsNlwu\nF9XV1XqkpjVi1TwczJovmY2Qp8RJpqQ3EUmaRyFMEZWPMSbWAxO4Ig4oT57zDjm5FhMWD/L6rmSu\n2U4UBbAr+SNks2VvoVAoq4DqP//zP2lqauLAgQMZpkCrDbcNIS+NkDV/4MHBZN3q0aNHTa0aaykO\ntWkHDL+OzQ5V9x0k5ktd0GEb4tV/g3d+FiqaMvrqaa5oWsPLpVFqMR1GCkXIxohfEAR2795dsKnj\nSmTWiqLoucpNmzZlpEC07bTjfjViyPcGqmg6JVJ2aJyoACMGQg7Fkhe6isjV4S7W188xYUvQpEoM\nqWkSWAhJdE+u48H6BURH+rcVVBjy2wkoIow241yfNsCPihLfdG3nT11TGaVmSy0ns3kvlBL+/n78\n166x/p57TH/mRghDjI1YjXJxozWn0aOirKyMyspKwuEw0WgUp9OZ8zgpKLzofIFNaoQYUKtUgVDL\nfwo76SIZhbri6e9jk2eRhbW8UvfzqOKZ1PySKQ5biQjZ6/VmXbT+yU9+wre//W2ef/55IpEIi4uL\nPPzww3i9Xn1sozOb5vLW2tpKIpHQ5di53N+AnK8Xg9tuUU/zmuju7iYcDuvqM7MlPFpVhtKczP0I\ngRj17xkk5kvV13qCCHIM6Y2n9e0jkQgDAwO6K9qxY8doaWlZdiIXm4bIJXOemJjgxIkTRCIRDh8+\nTHV1takLudgIeXh4mJMnT1JWVsbRo0dZt27dsv0YrTqNhNwkKpwerKLpwloaFQmfmj4WU+E06SZC\nErPdLVQqAvWJ9G8koDIaSH7mpQubicXTkeZ6VUiSMdC92E4wkK5QaVThX+cqGShfT2dnJ3v27OHw\n4cPs3LmThoYG4vE4o6OjnD59mt7eXi5fvkwsFiu6b10hDH7pS8R9vqI+U4oFuWKa7lZXV7N+/Xq2\nbNmSUbVQU1NDIpFgbGyM06dPc+rUKS5fvszIyEjGcepxnGRWmkESkuRbrdo5r36ABRFiqRSGU0md\nw4qAqMzwQu1/QTZE3qowA6pQMELWvDUKIVfJ2+OPP6537jl+/Djvete7ePbZZ3nnO9/JN7+ZbLq7\n1OVNc3/75je/ybve9S4EQeDee+/l+PHjRKNRBgcH6evr4/Dhwxw6dIi+vj4GBweJxWIcP36ce++9\nt+B8l+K2iZA1ItY6ZmhG7cb6TjPQCFlNETLeORxbJ3Bs2QZ9IExPQSuIl/6V2KHfN50ugOvzRFZV\nldnZWQYGBqitrc1wtTM7rhlC1ghfO7ELOb0Zn0wuGwjZldrNa1dqeZ9dQGhOJi/KgfFI+hgtRiUG\nAi5+5tJa7J3pxqgtwJic3M4Ts+PrX4PUGUIWoDEhctUwh6nLVVTtjuIHWmSBceAPh8t4dWeIlC4l\na6cNRVEIBoN4vd4MUyEtSjTKoIuJXOVIhOF//Ve2/4//YfozcPOl01rVgtPpZGhoSLev1Uo1jeZL\nC3YfZ48kF7PiygxI4FE20OtQqVDsxFOVFY6UUMgp13Gh4ue46JTYm4gSB2yqHUX0ICnNiBSW7Jvt\nFmSmg4QAACAASURBVFJMWednPvMZHnzwQT71qU+xb98+PvaxjwHwsY99jF/7tV+jq6uL+vp6jh9P\nVlft3LmTD33oQ+zYsQObzcYXvvAF/fr4/Oc/z913340syzz00EPs3Lkz535z4bYhZO2Ra2nHjGIb\nduqE3JSKkD3DqKpE9bEh5CEX0twEKhUIngH6T/4NkvQOduzYYaoQXfNPNgPjtprbW0VFhW67aUSx\nPsfZoBF+f38/DQ0Nep1soTxiRsoinL5g4oZgc3GwgsOxGCfbErSq4E09mAmoTIaSN5XX+2p4r90B\nqazLWlW3Mwfg5GUXB6sS9DTHcMSMKj+ZNyYcvG2NTM/6BK5ocuwLYYkvztj5r825j7coilRVVWG3\n29m8ebN+HIwWnbOzs4TDYd2esqqqSifqXI/QY//+78Q8HhKLi3mP3VKsJum08eYgSVKG+ZKCyjfK\nXkERFeyKQMLmQwiv4XS0BhxeKsNKWhBkSx6DRfbxveqUZCSVpqhSqkECu5K7j16xMEPId955J3fe\neSeQdH/TqiSMcDqdfOMb38j6+UcffZRHH3102ev33HMP9xSRosqG24aQu7q6SiKk0IUklU2oFU0I\nwRkUoQNno5vEnkNwqpdgdA2VZcNsL7/EBYf5xxJJkohEIoU3TG0bDAbp7e3N6/YG5kUkuW5OCwsL\nXLt2jYqKCj3Fc+7cuaK6i8gqvGmIkOcNDkFKHH7yo3Le8fNB5DXpMdcJMhNK+hR8s9fBsWNxussF\nnLH059fbFCZiIq/8uJJDv+BlMZRObbTIEQao4LU3yjnY6CcYSJP1F6Yc3FeVoLnc/A05l0WnlnP1\n+/1ZKxji8TjhcBin04k7VcsaT63mF4NSEPJKS93MzuV5h5ug6AWgWXUiCnZ6He+gviz5WoMtHRDZ\nyuYI+Dv5cWIL1CVvsVEhqdqrSC3UFiLkYp4cbmWVHtxGhFyqVXSjsk9duwth4Aeo8TVgd+M9CGtO\ngdPeAgwjeceobO4nkWjOP2iWsfPB7/fjdruJxWLs3bu34GLdSmXWWi2xKIrs3Lkzw9fCbOdpLWXh\nDkI0xXs2VIb96SjNkyLnH/2/Ct73tqhmU0EzMhOpU9Alqox4Rca+52D3L8QIGfLMLZLKBKAg4n6l\nmurNaYKtiqWP58RpF1Jd+jxYIyg80lPG03eauwnmQy7D+0gkgt/vR1EU+vr6CF26iCcVcXknJ1lc\nXNS9KgqhFOfwjTa5HxUX+XfHNX5WSaaXalXwyO9iULLhSKnwyqUEIaBccaHIlXyr4v10ySIeoCwh\nIduSn435vTjrwD9XhRCb161Mlx4Hs/ljsAj5loAWQZq5KIz5WKV5J+LAD1iciVDXArVb7Cj79yEG\nRagCQjYaE8dZTBwxNY9Cud5gMEh/fz+xWIz169cTCAQKkrH2/Yoh5FAoRH9/P9FolC1btmR9xDM7\npkbI5/pFjoypnGmDDXaV/tSimySoDHnTF9PICYmf3ZfgNacNp+HetNGpcEWVUGSBoZcctO1J71ur\nXwWQYiLlFxRsW1USCCQMaRI1LNIaVxhNrf+5YvCtQTsf7opzV2vpXPmM393lcuF0OhkeHmb37t0E\nvvV1tB7Dst+f4VVh9FGuqqrKSj7XixtJyAkU/sF5nrigEBaS0XBEbeR7difrZRuylDzGQmqRr0Ku\n5DvqfXhECVVNknCjQR5dWyWhAGXqJrxeL2NjY1nNl2w2W1FOb8Z64FsNtw0hmzEYMhulaDLVQKKK\nXUBVyvxGDAfhlxLwL0qSkBdD1MS+iy/2CLC24Ni5CFmr0vD7/XR1ddHQ0IDf78dncpXe7KJeNBol\nEolw/vx5Nm/eTENDQ87jZjb3rhH3G5MCJ14T2XVHHHtXEEhGKWuFEONy8iIUUBmaEbn0nyJv+4UE\nAUNJVJ2Q3pdTAe+PRNYcU5iTRfyG9EebQ6X3rI2fXZvgtRobs/7043GbXaH7lI2Dd8mcikv4Ur0D\n/lu3kxO/GKTiBvU41R6pVe8C9m9+TX/dFovpMl1VVfWFsVzleLIsXzeh3khC/rZ9lBFpkSpVICgG\nqFLquSCuBbw0qoLmO09cmEdQJfrkIwy7kq+GUimOSgTdUkoQ51Hl7VRV/wzrDZL7peZLfr+fSCTC\nxYsXl9lyLj1/rQj5FoCm1ivUa09rIKqtvLe97xeQJ/4DaWESWkDwjyLs96DUHQEVhIVxBGJUBp4F\n9hScx1LijMViuN1uPB4PnZ2d7NixI2MhpZgSuXzRbCKR0GuJJUni6NGjBSOzYlMWp4eThHrxgp13\nxp2sW6cwGRNpqyjTI8YWZ5yxlPDjJ9+xsX+nB1zJqodEJL2vNpfC6T4bWy/IRHepuD1pgnGkouXX\nfmjj7b+Q4MeR9Oq8LaWQHzghsO6IQt9U8gY8HBB54qyDvzhcurI2I/Qc5/Fnsc9O668by96MPeuM\nLmbGDtCxWIzTp08DLBNtmO3xV6quI0txSgpz1pa8w7XIAnbJzin1IFVC0mS+ggQRoFy1ERN9zCXe\nz5RQC0xRo0hExaTpVBlxwiR7KspqFV8W3s9jZD6haeZLmuGWz+djcnKStrY2gsEgi4uLui2nJEn6\nMXK73QU7Tq923HZ1yNlQKHdr7OQ8NzdHeXk527dvp8Kxg/kPrEHwTaBShRD3oCbWwPtCqFITQmAa\nOVFFbfhZVLVwnlIj2Xg8rrt5VVdXc+zYMZqbmzNIspi8cC7yVhSFoaGhjFpiu91e0pplrdzw9Gj6\nIp4dd5B4BbY4ZUTDYW+tSJ9uaysUzrxcz55A8iIfnTXMP5S8eK8OSOwaTBAxjOH1pv8d7oU2Me0u\nNz+f/F4LfpFNIzJRw+dOD0m8PnhjNNWqqiKoKvzzFxEAeyrNFDdRZWHsAO10Ojl06BAHDhygra0N\nu93O/Pw8ly5dyuiYrdlPZiPOUhDy0vSeV5D5tHMWWUi2sGpAZlE+wozgwC8m74Ji6r1GuYx44h18\ny9ZKQkj+No2qob5cSBkNKRt5Srwbl1rYt1gTbmgNWLOZL8myzFNPPcWPfvQjfv3Xf51f+qVf4vOf\n/7w+hlazv2fPHnbu3Mmf/umfApbb2w1DoZRFtnIzrYVRT08PMzMz+o9ls9mSJUiUEeqQiO04gppa\nCVYjrYjbLqCsTRayy5EWbOo8avR5U3MMBAI6QR47doz169dnnXsx9ptLyVNVVcbHx+nu7kaWZY4c\nOcKGDRuKulALEbIsywwODjI+Ps5srApfLBnB2USVgXGB2VmRse+I2ANp0jCSc1tVcuzzr9Rxp5Jg\nMpSOdMPhdDTodwfYMuFDRMUuKPRNGkreEhA9I1JrU6iUVPom099PXBB4W1X6+E1NCXziG05CNyBI\nVlWVmlM9MJRUhdpTi6Nx493DBIwmUFVVVaxbt47Nmzezb98+Dh06xLZt26ipqSEc/v/Ze/PgOu7r\n3vPT3XdfsS8EiIUACAIEQJAgCK5aLDOKFI8ysf1kzyRP9ig1741rbKcqk7xS8hynVM9J7CyVOC9y\nJc7zWHbiTMVRbNmWZFqyqIXgBpAgAC4g9n2/uBe4+9Ldv/mj770AuAKSnOcwOVUqgd19f7e776+/\nv9PnfM/3xBgfH6e7u5tLly4xMDDAzMxMtursgyguyQCyQPC8bZllWSOQ5hb7xQ5+asqlYsOCEE9T\n2VKilG8q9QCEFCNu7NlwnCr5sGgVdOpPEJAUSvX750juJSyUEV+qqKjgxRdfpLa2ltOnT/PHf/zH\ntLW1ZY+zWq2cPn2avr4+ent7OXXqFBcuXPi5U3t7YAD5XpZRwNpofr+f7u5u5ubmaGpqoqmpKdvG\naCOAW0QDSx9JIlTjNUhEXSBBqsMQdREx43VLxH+E4M4xV13XmZqaoru7G13XOXLkyH0B8r2ELDZ6\n+uFwmPb2dmpqajZN5u2GIm61DNhfuHABgMrKSiZiRdn9u/IEsTRlTU/BuX80cTydvVtZW194LBtO\nYbVP4rjJuFaTJBhfWgdkl8XN9b4cDkYTVFuSJNX1MWbmkiz5rBSPJdltU9HF+r5wUOLCuwoNHo08\nq2BkTmZsReYLr229S/VWTQhBwQ+/l/23OU1P3IqHfOs4d7MMHa+goICqqiqampo4dOgQ+/fvp6ys\nLCvcHggEuHbtGv39/YyNjWV51Nvh4m9kNfyjHOWMKUaprhGRUpSpBVyTDRDNE8YzYhMSYSlIjlZJ\nr9SIkCQKdYmEsq5XAWAVZhBevi0/AWnJ1RL9/kUc223flJeXR01NDUeOHMlulyQpyyJKpVJZsfvT\np0/z8Y9/HDDU3l5++WUAfvCDH/CpT30KMNTe3nzzzXuqvXV1dWXV3iwWS1btbbv2wADyVruGrK6u\n0t3dzdTUFI2NjbS0tNzG7914vFk0Ei9aJr7LmDhSNN3WvGQNtbwFKWJMdCUyhyad2TTORk81mUxy\n+PBhrFbrlpKL22FOZDjLGU9///791NfX3zHu+F6LSDKFIxcuXCAUCtHe3k51dTWKotAztw5yRRs4\nvzWFOqmUROfLJo4mVaZW1qebz7/+e7lkQecrJo7qKnUendiGZN902uvtetdGzdr6551mwbTPKJAZ\nHLJhHVj3Rk2SzuC4hKpJrF6V2OvQIA3W/+O8hbdufrChCzE8hOfSenGBxW54+1oshrZB+vWeY7zH\nKr0MHS8j3O71etm3bx91dXW43W5CodAdxe6DweBdF/yMh3xBlTiVDklU6ir5mpNXos0syMZrhjmd\nxivTTXj0Ev5f+ShRydhXumFx1KW0p6yV8k35cfySiUyz21Lt/h7yVhPymWPvFm/XNI3W1laKioo4\nefIkNTU170nt7VZVt9nZ2btu3649UEm9e0lwBgIBLl++jCRJ9+3kvBGQLbpRsedrDuJYzEUKLxnH\n6PMsPlxF8SmD7K5Ew0RNL2BKPYQQgsXFRcbGxsjPz7+tenCr17IVyzxwiUSCtra2+/bIey+AvLa2\nxtDQEFar9bZKQVmWmekzUZunM+KXURPr551jW/8tIjclKtHxV0mEUxIjs+vguppmQ5x73cTjjyYZ\nkWVSukSJS2d2w3FzfQrHq1U6gyZ25+hc2RAT9o/kcaxB5eyaiTpPioFxY5GYX5apvO5HlvKzHvRz\nf2vh1S/GKfB+MIr2ph9vrugyW9fDL6nVVZTi+/PUP4iyaVgHU4vFgt1uv02e806to26l46mqSsBk\n4dfjJprdBuh6hcaZ+H4KZJ1UmhETSwOtQzj4B6WJCAo+2TjeI1QyhfBh2Y9Hq+QyR1iTfABEZSPm\nXLpFD/nW6tQ72f3eAhRFobe3l9XVVX7lV36Fmzdv3nfMf2l7oAD5ThYKhZicnCSZTLJv374t1bnf\n6iEDpKwzzNZ/iLJr30NoNmQmWauwku/yIOsySnQaTR7EFzjLyKBRapqpevtZ2EYu8c6dO/H7/Vtq\nWLodfnEikaCvr49UKkV9ff0dOdGRuMw77zpRzHDiKZ3h+XVQiWygq7nNgr5LJgrmdY48rvLmtJHo\nsSoaQ5PrwLo0oNBo1xnxylS5dRbSL3EWk2BoTCY2IHH8l1Q2Pns5dp2hQZnBceh4SsUsbfamxm7k\ncag5wYWAjUp3jIEeO5/8b3H+4tMjeDwGACWTyW0vmsZFBrCMnWNjQMxiXn+skmtr2LYAyB9E2XRm\nnLuFwu4kdn+nRqyhaJT/UrWPRV2QJycwCxiIVjMoWThpXmMKsAjBihwmV3NxVWtixaSyU9eJyYbX\nraS959yUgk3aydeVoxzWDG9bERCQIliEiXxx97ZNGduqOH3G7ncfc3JyePTRRzl//vy/q739S1k4\nHKa3t5ebN29SVlZGQUHBlkVHTCZT9nVOIQdFlIOUYrLaguaqQcSrkdBxq8Usn3ARi5QipZbQIy6S\nytdoaWlh7969PxMwTiaTDAwM0NfXR2lpKQcPHsTr9W5bVvN+37G0tMTU1BRlZWUcPHjwrgUqlwYc\naLpEMiEx8bZE0bKgLEdgkgUj0+vTKxAwHhLfkkziksSxEgPCKj1RkukQhVkRDI3I9HUplM3qKPF1\n1N1TrBNLe9+dr5qw+df31eaqCF0CIdHzmoJYXd9XV6Sx5JO58LaVgyUaO13GQtA1VsBr1xuz+YVr\n165lmQxjY2NZ3eD7eV2Wt76FrG0ukTZvAMRUIHDPz2fsg+g4DdtnWWR0kYuLi7PqeD+uOcA1Vw71\n5ihJGXJGc7iqpsdMGF2jK1IaLt3OTwMnWE4rOJXr68tSTDb8Y3uqhK8px4hJCqlMOEM3oUk6pboH\nifsvQluNIcfj8bt60svLy6ymk6yxWIw33niDhoaGf1d7+1lahsUwOjpKPB7PKjWFw2H8fv+Wx7mV\nlWHR9xJTZnDLZm4276dheQ6c4ExZmasexTSej4NZrNFy5ILTWJNrkO29e/s5vhdqkqqqWa3l6urq\nrOg9bI8idy9A1jSNiYkJFhYW8Hq9FBUVbdJzuJOd719/ACoKBWfPybg9gg89pfF6rzG9XFbB0OT6\n9S4vSgyeV2j/UApNrD/E9Tt0rqW5w8MDMoofqqt0xldkPKZ1YCzJ1Xnzu2aOP6XSuWRCWme+kesU\n9L9qov64xuCyQrFFMAwgJAbelWlsXI+b/tWrbh7arWCzzXDgwAGEECQSiayw0OLiYrY1UkZUyO12\nr2spqynMr/8Nqrb5MbJswJjkFpkWHxQgv99xXpw3czb9glFpT2JeKeBytIhgkbHo6Olp7YqrvBE5\nwoxkR5ZWAAlLMgomsAgISCEsgUr6LA2o6dCGL01RLBCwBOzQtuYgbTWGvLq6elfHYX5+nk996lPZ\n4punn36aj3zkIzQ2Nv672tvPykZGRlheXqampmZTFdpWNSQyduvxFtFEjJ9gFwkGStaoiBbhAbRV\nP7hhuaaEkpl+rFEXKSlFRHkZj/aZO46dYU9s9aHRNI3p6els0uDw4cN3bM30fopIMsnHiYkJysrK\nOHLkCAsLC1vSB+7sXQfkVJqKHQpKRK9KtJpVFpwyZW6dyzPGVMtz6wyNG+fffdpMU7XErh06Y0sy\nOdYNnm25zkCvgmdGsO8xjdnZdZTbVaizMCDT+UMT+x9dY2hkPR9QU6Rz/qaJ5S6JqjadxZkNMW2H\nYO6STH6JzkpIpr5Y41O/becvnzO85o3ykxtjrxsrx6anp4lEDICpmDhLrX8WSdnQ+A+wiPX7u1Xq\n2wcVsng/9u6qwv8zaqWwKd0lOmjnhzM5HCmO4gfMCBbNKQo0MzPxeqZkC7tNSWJpD1lLhykKIkli\n0d38s62Nh3UjsVWkCyJp3qMNY/wyfWsFHFv1kO9VpdfS0sKVK1du2/7zpvb2QIUsKioqOHToEAUF\nBZsm9906T9/NbgNkvQUARTISepcLBLpuxmMyHrZUfopIznFMESNRkZTOkyJ8x7G3SmcTQqCq6pa4\nxO/VQ87Q5M6fP08kEqGjo4Pq6mpkWd4SPW52AYbTsWCTIhgY2tAbb1mi94yJyHmJYkUgpRNBdaU6\nIp1cK87VuHYlh7nTEkeqVObnNgjcu43jg2sS/rMSpeZ1sI5uoM+Fh000OFPZ8WPpff4VGcekILa6\nfmx1gc7sjExhXGC3CFKrEvPLMs//dTP3mh6ZyrGdO3fS2NhoFG8cOEBF7z8b91TbDLr6BpW35DZC\nFv8zAXk4IvFrA3a8Vp05xcT+UILeBcPbtNmN+dogJ8jVzQz1NjIljHh7uWV90Q7bNCxCRtGb+Web\nwQEOWo05lBdefx5iSYMOmB+zb4mOt9UY8na1kH8e7YEC5Lv1Ttuu+M7tHrLRvVZjHEmHkDvGrPOj\nmBlH1k2Y7Qv0VOxEjswBYJbmmVNevePY9wPkjVxiIQT79++/jUt8p+vbroecof8tLi5maXIbu6ps\n5Z69+kOZXbrK7rIYeytFVnOiMFcwOGz8HVqT6HlZocmiU1Gko29gYewqNcaPxySm3pHJjwo8adrc\n0obkYEW+zrl/MnG0RCXPrXP9xgb6m6xy4ZSVQ/kahV6da9fX9+WZBPoo7Mg3vmdxyhjz5jWF1hyN\n633GsdeGc/ivf7a9hJ556DyWyT4AFHQ0x3pyyqGv/xbj167R09PD0NAQc3NzWWW4W+1nrdJ2L1uM\nSnxx0MqqKlFdoNEciTPVa2cqHTdetRjXU5yEaz2NLMasTKY593azAchF6WvyTx5kKpkPgFNLsZKe\nUiWO9fsbsyTwxJxEB/1ZOl7m/tyJjrfVe/OvvWwaHjBAvptt1/PYCMipVIqRoQVSkVIkWSWPfJAE\nXe4adLkEd7IYWUkSdZoJu3cjJ73I0hgzyvfRuJ2Deq/wSSAQyIJkRnZzKxPxbnS/O5mmaQwPDzM6\nOkpDQwPNzc13TIRsRVzoBz9QGLlqZuiUnXKzTlW58VDurhBZL7i+WmNhQebqOYXV8xIOXWBOx4Oj\nwfXfpapUp+sNE65ZwdEGlaGRDaW7PuO4c6+Y2G9W8TpF+hwFUyPGuV/8qYl9NhXbBlxdmJCYm5aR\nxqGtVmV4aH1MKQhtVesP/tVeha/99dbVh0zn/n7Tv3X3OsPFsUGdv9DhoLm5mcLCwmz4aWP7qOnp\naQKBQLZQ4V/agkn42Ct2JtPdWfJ0wcBFF2W56cakks64LKhXJZZHC5mL2ajxaqTSybiwybjWipSZ\n3uEjXArmsWoy5kG5GiZLR04n9FxCwqZWcmr1lzm8tzVbzlxUVISmaczOznLlyhW6urq4du0aExMT\nqKpq9Lm8z3z81y4sBA9YDPmD1EROJpOMjo6ysLBAZWUlfst/Ipfn8WJmBXCg0OX+CA3JCdZskKtb\n6Kos5FAkSjL3GjahsSC/Tpn+v2wa+04ecoZLLEkSjY2NWfraVj3frVx3pmv08vIyFRUV1NTU3HfM\ne3nIKyvwzjtS+lid7nd1Vvw6xx7bzEUucOsMYgDh7hqNd75vomq3RlGj4PLFDTziJeMzc5Myu3bo\nHG9U6RpWyHMLbgxs0FaeUFAWoHGfhskE/WfWEXhxUKZU1VnLk/A4BSPnjfFnp2R2V2rsLNWzhSbL\n4xLDNxSOP5mie1jmapfC+Z8qVFYIfunJe+cb5NWbyPGpTduEywlpXSFLaL1Cz11kuk0sB9bbR4VC\noSwDIB6P09/fn00eulyuOyqafVAWU+ETr9kZXpNRE7DfqjE2akLVFewuA0DrvClcSYmrb3ooSOvI\n5znTHH10ZpQUe0MOfJMlTOoWzOhMpsNHecSIpr9rTYrh1E24/Xv482QJjys6pHXf7kXHC4VCaJrG\nwMAAyWRykzqe2+3G4XBknZYHAZD/TXjIsPWSYU3TWFhYwOfzYTKZOHLkCOXl5ayyn4j+YWzpKWaW\nInTazYRlo2zYLmL47AlW7YbGRZ6wM2V6CZ3ND/dGQI7FYvT39zMwMMCuXbvYv3//Ji7xdsqn72aq\nqjI6OsqlS5eycdC7dR7ZaPcLWXzvezJquox59+4YS0sSmiox1KNx42KE421xPG6dseGN2XHjQZ0Y\nUjD5VA7WJ8jxJCkv0RkYWD9ufk6m81UTFSadpgot623n5+pc7ZNZnJUZekOm3LZ+b8pKda72Kgxf\nVZAmoNKzfu5ms+Bqt0J8Cnbt1NmzS2P4hvF9na+ZOVDuJ7gqoesSz/6fNrq77/1YWK79JZhvSYw6\n16sVLUEjpuwoK2VPw8gdx8joVWSajNbX11NUVHTHCruenh6Gh4eZn5+/a8gD7l8YsdGSKvzOaStn\n50zUl+s0W3RmuiVGIuk+hmbj/pRF4PJPPNhkmEoZ+5I24/vrzSnq5vJ47a0Kgmnu9y6HSmY9VhQj\nMO8RYE856Bs8znjEkKltVu59rhvpeDabjdbW1tua1U5OTmbfNn7rt36Lzs5OZmZm8Pl8m8aanp7m\n0UcfpbGxkb179/LVr37VuEa/n5MnT1JXV8fJkycJpOP9Qgg+//nPU1tbS0tLCz09PdmxvvWtb1FX\nV0ddXV2WFgdw+fJlmpubqa2t5fOf//y2fotN1/2ePvVzalstn76TZVTLMrFbt9tNZWVldvWtEsX8\nndQC6TCEJi2AJPG2vRihm7MJv0FLKQgnLpLEpUUW5c5N36MoColEgoGBAXp7eyktLaW9vf2OK/v7\nAWRd15menubixYsoisKRI0coLS3NCifdz+4Xsrh4MUFhobHfZlvPiO3enSIUhM6fJqkrClJTk8Bu\nF3g8gqtX11/I/H6Ni+8KkosJWnbFMaeTdnU1GqOjxj0fuaEwcTXF8fYkZrNgT7WeXQTsNsHbr8De\nyjU8bp3qHXq2PHptReL6WUH7fuP33t+k4VuWWV6QWRmQKHNungfTQyaOHzEYAskkfPZzMnfThZEi\nc5hG/xFMt2QB7eueupJKYXI62ffxCsyppbvew42WqbDLVNdtVDRrbm6+a8fsTMhDVdUtJwaTKvzH\nb9np9RsgWqjo9L8tU1miI5CwKxoTupnjUZWVSQVVl6nOX58zM4qgAEHJuJ3XLhsOyXi6q3iRY/2+\nhG0Ci5CoWSrgW9cPMxlzoqbDVa3y1nI6tzIsNqrj7d27N6uO9/TTTyNJEgMDAzz99NM89NBD2c+Y\nTCb+7M/+jBs3bnDhwgVeeOEFbty4wZe//GUee+wxhoeHeeyxx7IKbT/+8Y8ZHh5meHiYr3/963zm\nMwZjyu/38/zzz3Px4kW6urp4/vnnsyD+mc98hr/927/Nfu7UqVNbur5b7YEC5HvZ3QA5I0Z/4cIF\notEohw4dora29jbQKhN5xLHwNoexCjsJyYdTWJhXEsyGH0YokyhCISitMKc/iZUFAObk8+jpVzNV\nVQkEAoyMjOD1ejl8+DCFhYV3fYjeCyBnyrYvXLhALBbj0KFDVFVVZReW7VTq3e24a9dS/P3f+1hb\nm+ToUR8bdfRnZzd4piaVzjNBHHYfD52IkgmHV1enuHnT+Ec8JtPTFWdH0Rr7W5MUbHjwGxuTjIxI\ndJ7WqCyIoyfXF4jmZpVoVOJ6rwO3SJIKr39u/36NhXmJ7jM6x9tTRDecn1kRXDoboa3N4MTugDXx\nFgAAIABJREFUa0kxM2Oj84zg+JE4B9tUBm7AL/+ywvDw7dduuf4Ckp5C2kh+BiTbZp5swb491JZf\nRIpvjf9+LzA1m81ZEMqwPA4cOJBtQru8vEx/fz/d3d1ZJbjl5WXi8fhti2pChV970c6bgwoDQZmj\nuSpjowqqJmFJU3grXVGaZ1N0vqUwEjeuy57mH5faVApVCfGmndVVI+a+06WzqqfDV1ZjvrrRMSUl\nkudrmJ0rQqShZiE9B1ru4yFnbCscZFmWOXToEF6vl9/+7d/m9OnTvPvuu9n9paWlHDhwwDgvt5uG\nhgZmZ2c3CQjdKiz0zDPPIEkShw8fZnV1lfn5eX7yk59w8uRJ8vLyyM3N5eTJk5w6dYr5dKuujM74\nM888kx1ru/ZvJoZ8K/UtI5YzOjpKTk4ObW1t9xSwV1CoFIV0yyol2iFQ3qFEdzKqJOlT9lCmDVAo\ne1mQ/ZyX9vNR6TySKCEpTTMk9WOfyGVmZgaXy0V1dTU7duy47/Vst1fenZqV3mofRIfqv/7rNL0v\nCRBmYiLK7t0WPB4Tly7lADJ5eRpXrhgP58qKzo0bfpzOAI2NDlKpJKRFyQ8c0Ll0CUBnZSVEQ4Og\npiaH0VETLpdKpgGfw5bkwoUgR4866e93Mj8vsvtKi2N0XUxy/LiLri4Hy8u6sU9ILM8mcDgieL0F\nrK0p7NmToLMTrvTEOHZUIxhaf9jPndV59EMhwMXiosRTTym88kqSmpr0MYkA5sFvGn9Lm6vzpFvy\nge2PKSgyiMTWaG/b5SHf2gkajDzB9evXcTqdhEIh5ubmsi2R3G43stnNn765g1M3TOzfreG0C4b6\nZJa8BkrOajI7rDquCZVLK25qizVGUsa1+yQJBUFLROeNH9rRhYwlz5gfOzw602nA9Zl0rAIO+kyc\nut6Cjoy3WoUUuBWdKQG5CKq26Apup2x6KzHkiYkJrly5QkdHB4uLi5SWlgJQUlLC4qKRBNiugNDs\n7Czl5eW3bX8v9m/SQ15ZWckqo7W2ttLQ0HDfbiIAu3Qj/tUvNWDRK3FJBsA7EJzVT5KTfm3zYmFY\nPEaeyCMhTfFO/FVSaoqOjo5sNnkrttWkXiQSIRqNMjY2RmNjI01NTXct295Oh+o7AfLSksZ3vhNN\nHyOYmkoCEkNDKYSIUlk5RXv7MjU1ITJCZ7t3Rxgb0/D5VIaGVvH7/Rw/7sfp1Egm189l3z6V7u4w\nY2MzPPKIn9nZ9TcaRUkhBJw7F6GpaYH8/HVeayCQQAjo7Axz+PAybGC3eDwRrlxJ4XQusH9/lP5+\nIzSh67C6msDtWkFJ94Jrb1d586erHD3qR5Z1ystVnnhihZs300msga8jqcb3ymIz0MrmDff0UBPe\neuMcpOSaoUN6H/sgKvV0XcdsNmdF3Pft28ehQ4doampCshTyzJ+UcXlOYJY1TCurdHaaKC8xPP0d\neRq5siB6HpaixrNQnA5JucyCqC6xZ0wjtCCjC5lip85sMt03MT3V3LKOKwnet12sjtjR0/Ayk+6v\nWG3XEEi0btE7hu1Lb25MnN5q4XCYj33sY/zFX/zFbRV9kiT9Ty/MgX9DgGw2m1lbW6O7u5vp6Wn2\n7t1LU1PTllSkMrZLN1bTBFFe48PIGF6SokTosbhZw9jvFHFelzzEV00ISSXXqSPq4phMpm2FIe53\nbMYjunr1KjabjX379t1TxQ6237w0Y0IIhBD89/8+TUPDCocOJTl8WGJmxji/mhqZnp44k5Mq16+v\nsbCwyPHjfsrL4+gbAKmmJszMjEpn5woVFSPYbHPk5KiYTILx8UT6u0BVA6ysTHL8+DItLcmstw0Q\niSS4dMlPXd0I7e1LjI6uP0grKxEmJxc4etTH7t1xLl0yvntuTuByLdDSEsoWkUhSlHPnYlRVTbNj\nh8rMjAGy585FOXhwhcVFHwsLOr/4iytcueRHWXhj/f6IIEJZBwpFXqe62Z5NwQbFt62ELT6IwpC7\njTG9ZOXjXypj0mcnqDmoU2Fq1QAu1SajSIKKpJ++12RESmU6ZjwTkTRwHrKorLwpcX3IxEI6sVeZ\ntz6HliSJfEnnaECl6/s5TC6aicnpRKxFZz5NqXOnk4FtPyNADgaDd/WQU6kUH/vYx/jVX/1VPvrR\njwJQXFzM/LzRgmp+fp6iIiMefjcBoXttn5mZuW37e7EHCpDvNqFDoRALCwvMz89TX19Pa2vre5Kp\nrBYlSELCJwUYlayMsxeTkIla/EgCTslFKLqTWGIaXZKYdRsVfoXAReVNBPoHAsiqqjI8PMzly5fJ\nz8+no6MDm832vjzfex0nhEgnPaO88MIiPT0henrmCASmOHYszN69Gnl5elaB7cABM9PTSTo7/dhs\nUzgcQdrbk+TmCiYmNvTHswi6ukLE4+McOjRKMml4a/n5GpcuRYjHBZ2dq7jdM5w4EcLt1mlu1rh6\n1QDZ4WET0egqx4+H8Hp1Wlt1rl9XSaXg3LkwO3ZMU19vHFtQoNPTE6Gzc5WmJh8nTiS5ds3wlkdH\nTdTXz5KbG99wbklMpjV27BD4/YKrZ/6GQGTDfZNAuNa9MUUyPis90Y6lehA2NgWIr9z3fn8QhSF3\nGuOdCwr/5S9tjM3JtNarpIZBV2ExKGM1C0K6hYawRiqWixASuytBIKFIOstxlbrJICs3I0RiEjl2\nlbGwMb4p7ce4TYLiiCB1SiIyt/7dE2nvuSpn/Z4l0wm9ti0m9GB7WsjJZPKOb4ZCCH7913+dhoYG\nfvM3fzO7faOA0K3CQt/+9rcRQnDhwgW8Xi+lpaU8/vjjvP766wQCAQKBAK+//jqPP/44paWleDye\nLCHg29/+dnas7doDFUOGzZ5dRqIyHo9TWFiIxWK5q/jIrZYJcWyUZLRjoVwUMC0vU6ObeUku5Wkt\nhV8ZpiQmM2/XmFlrp9T7DjZRxpRJpkBvwiSFWJYjjMg3KFTKtwXIiQ0C5xkmyNTU1G26Fh9EbPhO\nx2XEWAC+9KVZolHj744OO2fP+oEITU125udTnDjhwecz0du7zsO1WCz090eACB/6kJNUSmJszEJu\nrom+vvXE2NiYIBDw0dbmwOmUefddY3GtqEhy7pyGEGHcbh8Oh8DlyiMcljl0SKKrKwEkyMsLU1Rk\nw2yWSaUkWloEb78dQpZDHD3qQVEUzpwx5sXgYJyqqiCHDzu5cMFMQUGCCxeCJJOC48dzWFiwcuHC\nCqoKeXkaH3rUzMce+htuvFnOw+sSFwh3DqwtA2DSQ2gWC/ZfS8cON8SUpfhmGtad7IPwkDe2XgL4\nqxfNfPHPrVS16xyvUwn5ZJZ9MvV7VZiEo5Uql8+ZmEuAnOYYy04ZOSx4uFDj4rs2ZmN2apuMkE1F\nQZJVYUDGRCxJnUhQNKFz9oLxVhZKx/R3unWmtXQy0EaGbswccDQoOGjduoe81RjyvRhBZ8+e5e/+\n7u9obm6mtbUVgD/8wz/kueee4+mnn+Yb3/gGlZWVfPe73wUMTYrXXnuN2tpaHA4H3/ymkTfIy8vj\n937v92hvbwfgi1/8Inl5ho7J1772NT796U8Ti8V44okneOKJJ7Z8jRvtgQNkMGT4RkdHCYVC1NbW\nkp+fz/LyMmsb6QD3sYzi260auXX6DqblZQqExiASV/VWKtVZnLEY2K34PLVUi0XKsTMih+kRbbRJ\nrwDl9Mt9fFip2LaHvFHwvrCwkMOHD982Sd9vbHijZSZ3JBLhxo0beDwerl3T+e53b9LWloPLZWd8\nPBOugURCY2YmzsxMnOZmQVGRidbWHBTFwjvvGDHXsjIT5875icd1FAXq6rwcOmTmyhWd9nY7Z84Y\n4wUCKfr6QjQ2OnC5HMRiJqamjOuqrExx8aKG0zlHW5sdn89MJrG3Z4/M668vUF5uobzci89nhBCM\nWHGUpaUQR4/mcv48dHQonDmTBJLU1Qlyckx0dxvXfP58gCNHZGIxE7OzgtVVlcf2/x0lBX6GrLe8\nhjrW37JM6iqp/60DU8HZ9Ib130KK3R+QP6jmpLIsEwjAH/ypla+/bKGhXsMSg5s3ZQLutM5HUuKg\nQyW+JBEMSRxo0egJKkiSIKVB+WyEpLARiUnkuXVGVw1wdeVYIAA1do2ceQuXu03kNBpCS7KkMxQ0\n7mG+PcY0Btd9VZaw6ILDWorhU2amYxLFz2xdV0ZV1W3J2N5pUTt+/PhdAfvNN9+84xgvvPDCHY9/\n9tlnefbZZ2/bfvDgQa5du7bl87ybPXCAnKmuq6mpobGx8QNTfMtYuboHmzKARhBwsxwP4Tc/Qoe1\nB7BiI84PpXae0gcB0LER1xvJk1ME5Fmu2pdwbiOpl2nN5HK57il4v1VGxr0AOROayHhrhw8fJhKJ\nMDsb4LOfvUkspnP5sp+GBhMzM3EaGlxUV3vTHjDU15u4di2GECqrqz5kWWPvXhu5uU6EWKfEHT7s\n5u23jdf4xkYHkKKuTmF4WMPp1FBVwY0bEdrbk8zOhmhrc+LzGcwHgEhEwmrVWFhY5cABOysrFvr7\n1wCJmZkkZWV+dF3l4EE3fX0qiUQMn0/F51vm+HE3weD69efnm+nrW+XEiVwuXkxx6JCZzk4/DofM\n0aO5mE1RnnnyOwB4C1Mb84WEhSnbwF44ndg/PpTdJynrB27VQ/4gQhbd3R7+239zsqNZ0NGsYpah\n85KJY4+pnB9XeKQpRc9ZE5EIuKuMz1m9ggJN54BX4/VXTCBcWHKMOVpbodO1ZsBESJM4qqto43Bx\nPr1NMuZjXbFgMO09m2wyJMGChjK3hrvfwapNZT7m4qmq2LYWn63GkBOJxHtrMPBzZg8cIBcXF1Nd\nXX3bSvl+Fd8yVqu6GIkeocpzBpPuYs2lM00JVaFyJBEgKAWYkkqYoBK4hosYL8u1/JI+yU3Fz7vW\nIR5T760xDEZGOBNu2UprpvcLyEKIrDcuSRKyLCPLcprbeZ2aGhOlpRZcLgvvvmsATCIR5/XXA6gq\nVFdbyMuz09BgZnAwRU2Nje7uAD5fkqNHZS5c8NHcnEN+vp2xMQPAJUkgyzpnzhjFE7/wCwVEoxr5\n+RJC6AwMhAiHBX5/mGPHQFUlSkvNJBISXV1BVFXQ0xOlo0OjtFTG51NIpQRXroRJJmFsLE5HB0Sj\nxjS3WiUmJ1eYntZoaXFit7vo7w8Qi+mcObPCQw+5iMWMMEo0qpNMRni8/SXKi43Fw+6ObQLkayNR\njqX/jvyvNbjcvvX9SiR7nBRfvu/vouv6trpi3Gqrq4I/+iMH3/hGIZVVGuqqxMiAgmbo/CBboE7S\nSQYkgkGJ/fs0riwq2C0CaxLilyWi+w2qYJ4nzsiyAbSSHQqSOi1WjbOvmEgkJY6kC248NsFwwADW\nwlzBYJoJGFEsHIpHiY8K+kLGK31NdQxisEtZ4NKlMWRZ3lQC7XQ673j9mqZtKYb8ICi9wQMIyG63\n+46A81485I0hgEzl28zMDGste0mqR9htXuKGrLJb1XnJ08QntFHmlDlKhMIp2cPjejlxyUdA2sEs\nlYAfhxTmZr6Fjrt8bzweZ2RkhEgkQnl5OSsrK1tuzfReQhYZrziz7Vb6z+//fg//8A9G+e/+/Xl0\nd8+zd68bh0MQi6XQdQNYPR4L588bwHXggJ1IJEpzs5VEQubKFT+6DoODa+zalWBmJkhTUw6VlR56\neoyQxq5dds6cWSQW01EUwdGjLlIpK9euJWhsdKXj1eBwyDQ2Wjl82MrAgEp9vY1z54wFwmaTOHjQ\nSVGRlcuX4+zb56Cry48QsGOHQnm5zuXLCiAxMhKhsDBAQ4OdQMCCqkJ//zKrqymam714PDau35jn\no//1h9l74c4NwQZn15mjQwDG9WIKf6kP/eYeMo6xJK2Hx7YSsnivMWRdF/zDP8Dv/75xD/fv92Oz\nu+jstHLspMrEssyxJpU3XjJhscBC+vxsXsExl4pYhbdfTceF/Qa4lpXG8AdtFLt1rKsQ7pSIN0kk\n0t3EJ9PNZusqNC6HjM+GZYmddp3apMbFH5mIxhy0715flAKa4b3+yv4i9hcVoGlaVmN6YWGBcDiM\npmm39fdLpVLvWwv5X5M9cIB8r2qn9xKyyFTyjY+PU1xcTEdHB08g+INkDc9KJlCmKEQFrIzq+yiU\nVykUggUZRvQ2iqVXyRMyvbKNVr0YM1G6q2R+FQ0T6yu/qqrZCquamhr27t1LLBZjefn+3hVsP1l3\nPyAG+JM/6eH73x/k2LFcLBYTo6MRYjGNiYk1ioosjI9H8HjMHD1aSiiksmuXg5wcG319ATRNkJen\nYbfr7Ngh43absFgE3d1rCCEhSSl+/OMxdB1aW3NxuxPE4zqxGBw54uXMGYOkv3u3C0Ux4sz9/XGa\nm21cvJgJd7hQ1SQHDzro7Y3S2mqns9O4Xy0tHnJyEuTnK/h8GiUlEl1dUUpKbNTUeEgmE3R3x5mc\njON2Q22thKKYWV2FlZUoi4s+/u/nLqNY1x+R/KJV2FC9F1cNPvbqJ2wUmQTDkyka0y8/krSB6hZZ\nyKq5Zf679ZV9uzFkIQSvvhrnxReTnD3rpr09RV+fCVCIJyyUlKgoAhavSZR7DM+39ZDK1XmF43tV\nRs/JzM/LHHnMeCbqajSGfcZ8NJsFhz0q0SV4N13uHkuXpVeVaEysGcdZHSCFBK25OvIozFyW2NEo\nEY0Zx8bT+hZuq2AsKOM2C1oKjPmmKAper3eTVyuEIBqNEg6HWV1dNZyftTUSiQQej2eToNCtczUY\nDG45Yf/zbA8cIN/NFEXZFiArikIgEGBycpKcnJxNnaMf0zX+QIN3E1UcFililiBgZVXRWUmc4LD5\nOmBDk2SS4jC7WOOSHGdab2OnfJGg3cbbqTE+rNdlPe/p6WkqKio2MSc+SM5yxiRJIpVKkUwms0L0\nt05uIQR//uc9fOtbA4yPh3A6TYyN+YlEVGpr3ezc6SUeF2iaoKLCw6lThvJZU1MOy8s+Dh50pxdA\nuHDBAMgTJwo5c2ae3FwLLS05hMNJPB6JcFgQDIbo7TV+m0cfLSCVitPS4mZ+PkE8nuL8eUOs55FH\nConHoxw86GJpSWVlJcaNGwbd7EMfKiSZTLFnj5OFhQTBYIz+/hUUBU6eLCQQUJFlWFiIU1Nj4fp1\nH8eO5RMIaAihcuWK4dEePOhGkmJcvRbkI7/2GmsX1+OSFquOP+Yiz2549Z6cJF2xXez9DxMABGPr\niSNJSiEsXqTkGkrClw0pZRbATHhoYzOArXjI8bjOSy/5+c53dK5eTdLR4cZu9xEK5REIyBw/oaKp\nYYRQePcNBwVFOleuKRQW6HhtAtuMQPPC/LyMzSa4NmGAZskOgTepIQc0Lr+Rg6bLHD+uwgI4bIKB\nNKWtrEQwMQ0FTh17VFA2JlBtgqt+A0qk9O1SZMFYyPhHbZHOlaBCe4mKco81R5IknE5nVlQIoKen\nhz179mSV33w+H9FodFPII+Nl/7uH/HNod5vU23kdzACxJEkcOHDgtuKRfZJMETCCIDCzj1+o7MKt\nppgww5Jexi5tJ5K8RJQwfy9X8TltGAgRlpwginEnVc6Yp6iZczI/NkFRUdEdmRPbAeT7ecgZjzgj\nYHP58mUAXC4XHo8n64FEIin+839+nR/+cBSAo0dL8PnW2LPHiSSZiUZ13nprGlmGI0d2MDi4wKFD\nXnJybMzPR5mdDRMKJSktdTIwEGDHDietrYUEAkl27LBjt5u5enUNvz+BokBrqwOz2YLdbkZR4N13\n59E0cDgkKiut2O1mios92O0m3n7baACQm2uhtNRKaamFqioPFouZ06cNgr/TqVBXZ0EIjYoKKzk5\nFjo7Z4nFNIqL7Rw8WMDAQIhoVKOvb4WqKgu6LjhyJJfl5STz8xFmZyP85vO9FO8IMS1tbs8UVB3k\npbvB5OTFcf+nde5y6hawmQuYKXOCFlrcJP6/8Q1FCEEkEsHv95Obm5vNc2SA2ghFCc6f93P6dIRv\nfGOFAwdy0TTBvn1W3ngjxr59dhQlRVubn+6uAhIJQW2tUW23vy3FWlBi1QdvfN8AyNWEsXDsa9OY\nCsrsK9eY7ZYYG1c4fExHS1fWTfiM/zfWaVyaN2ExCZwI2kwq/mGJN3uMa6rq0CH9QjC5muYfF8QY\nTRkCGE67gCCc2LF9oSxN07Db7TgcDvLz8zdtD4fDhEIhXnrpJV5++WVCoRCzs7O0trby2c9+FpfL\nxbPPPssrr7xCUVFRlgXh9/v5xCc+wcTEBFVVVXz3u98lNzcXIQS/8Ru/wWuvvYbD4eDFF1/MamB8\n61vf4ktf+hIAX/jCF7IaGJcvX87S3Z588km++tWvvi/64gMHyO/HwuEwQ0NGpryyspJoNHpn8XZJ\n4qSs8B1do9ql8f3xQzyUf5mhfDP7lBQvqtX87xKMmpfJF4JXpGrKxA2sRPih1Eh79CpjHh//ZPLx\nG/fQ0NhOJ5B7JfU2JuxkWaaxsRFYn9TBYJDZ2VkuXpzlD/7gJsGgSlOTC6dTZm0twuqqhtMpMz7u\nJxhM0tycT3Gxk2hUw+02YzZLvPXWFKmUTm2th4ICK2aziX37csjJcfDaaxMANDbmkEzGqaiQ2bHD\ngsfj4Ny5ZWCN9vYibt4M0Nzsxeu1o+s6nZ2LCCHR0uKgp2eN6mo7hYUOJEnh4kU/IHHkSDGXLi1w\n4EAuZrNEJBLL8qBbWnJIJqMcPJjH3Fyc0lIrr746DkBraz5FRVauXQswNxejrk4llUpRUeGkvELn\nmc8Z4jRRNtOllsIWqtLFkNeLqjha35fd58jdfP+jwpg7ycAc/8enfkRJiZP29h20tBRSWenFZJIZ\nHx/H7/eze/fubPfwpaUog4Mh+voCTE2l+NGPfNTUuBHCwu7dCu+8E6Sw0ExZmY1jx1LMzyv09cU4\ncMBFIiFx+LDAZAojSUkunvUSDEocOWqARN0ejdl5mSP7VZSwYOFdicJWibFJw1MOp6dbfa3GoE9B\nlgV5TsHRApWp6zKnh02omsSxDpVxg0jEYsQYu7JEYzJojON1qxAEsyywaIIjQuXh3K2/oW6cu3cC\nuI0hjy984QtZbZjHH3+c3t7e7Nvspz/9aT772c/yzDPPZD+bUXl77rnn+PKXv8yXv/xlvvKVr2xS\nebt48SKf+cxnuHjxYlbl7dKlS0iSRFtbG0899RS5ublZlbeOjg6efPJJTp069Z45yPAAAvL9Vqc7\n/cCxWIyRkRFisRh1dXXk5uayurpKKBS6yyjwZBqQNVuKgN/O5GwtBbkLeJU4aFamwnUUeaLskFTe\nlS00xBpZst5gHg8LajGaEmS6RBBVFe6morGVrh0bj70VvO8XJ85MapPJzgsvjPDSSyOUlnqpqEiR\nSKjcuBEmkdDYs8fN1JSPnTtd5OXloqoSXV3zqKrOvn1F9PcvsHdvDkVFTiKRBAMDflRVp64ul87O\nMXbvzqWmJofl5TCLixH8fpniYhfnzs1TWmp40KFQivx8K0tLUYLBGGNja+TkWDl8uIRQKEVFhU4y\nqTM/H2d6OoLXa6KhwUYoFMBmg9FRPzk5MlNTMerrc9m1y83MTIzBwVVGR9doa8tjairA8eOFJBI6\ny8sRensNRb6TJ8tJpTRGRhKcP7/An/xtP57cdBv7vM1zxeo1vL6JtVxsvynw+13k5Rkes6pENx0b\nSlerzaqFXL0+wexsPoODKySTOrOzazgc4HQ6SKVkysuXmZtLEI2qlJXlEw6rOJ1WJidjFBZauXQp\nTnGxSlVVDm1tKtGomUuXAhw7lsfYmEprqwlZjlBTE2RxMYfxcTh+3MHwsERBgWBsTOJwRxSXR2Hy\nHQszuszMjIQQEo48AZNQUqJzfcyESdGpLtXJdwom+mTO/8hEKCJxuENlZjBNd0sn+IrzdYbTncLL\niwWTM0bM2JJUaVeTLAybeKvLhNsO+/+vrVfobdfW1tbYtWsXe/bsYc+ePdntDz30EBMTE5uO/cEP\nfsDbb78NGCpvjzzyCF/5ylfuqvL29ttvZ1XegKzK2yOPPJJVeQOyKm//DshbtEwIIBMaSCaTjI2N\nEQgEqK2t3dQc9X6sjEdQOJRQ6Ldq2GWdQTmXql4n9n0TgGDBIpiYPsAjOwcBCwMRG7sSDnY7da55\nd3BQk7FLEb6hLPJb2nure99osixnX3e3krDL2Pe+N8iXvnQWm02hosIBJJieTjE3F6GlpQhN07Fa\nzezZ48RkgitXFggGVaqrHZjNZuLxCE1NXpxOC2fOTBGLaTQ25iHLArMZjh4txWSCN94YQ1Vh7958\nUikdt1vmxIkS7HYzP/3pJKmUoLk5j0gkRX6+jbKyEmw2M2+8MYmmCfbuzUeWdQoK7Ozc6cThUPjp\nTw1dgbIyK263BbtdwWazYbfHOXVqGSGgqspFVVUO8bhONJoiFIozNbWWfugKyckxc+HCvCE05Dbz\n+FNuPvyxs9n7Y8nbPAcSknFP+1t2UeTUCM97soBcWKZuYmHINguRpJnpj5ZQ06vim4kwPa0SDqco\nKXFx82YEIRK0tpby8svjVFV58HhyGBoKUFubRzisUlHhZGVFIi8vjsPh5J13/Jw4UczKisqJE2YS\niSgFBTFisVwGB3Xa2210d4PLJYhGBcePr2KzKbz1FmiqRCiUQzIhUVGhMT1twpMj6BtQKCrQ2b9X\nY3FRZ/iKQs9PFZaWZdraVeaGjecllZ5COV6d65PGYlNTrbM4IbOrUMelClqSGjPXJbq0XHRd4lCr\nynTYxPG9KbZYAf2ebDssi59HlbeM/ZsC5I1c5MnJSRYWFqiurqa+vv42wMpU6t3NHIpEYa+D5qYY\nSU+SC6s2rEj4buxkb22E60g4VQfXpouRK8LgVngteIxPykMMKjK+SCNF9uv8k7LC03oBFeL+anP3\nssxis7HU+V5AfOXKAr/zO28zPR0kP9+CLCdJJGRGRyM4HGaOHCkjFlPxeOyYzYaiWm/vEh6PhUcf\nrSAaVZFlQSKhsrgYYmxsHptNpqMjF1XVkWWj7HtuLsrUVBS7XeHRRyuIxVRSKUE8niIhGIb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gmV+/dLNBoGk5O9eDwihUKbTKbK8HAE0zRYW6syNBQlEPAxN1dhbq7MyEiMeFxFFAV8Pgdwtby3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\nyDly5MhxivD/Aa5XpFycbVePAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x6d5f710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "from matplotlib import cm \n",
    "\n",
    "plt.figure()\n",
    "ax = plt.subplot(111, projection='3d')\n",
    "ax.plot_surface(x1v,x2v,z, cmap=cm.jet)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### Considering possible problems "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "I start with the visualization. From the shape of the function we can immediately conclude that:\n",
    "    1. There can be plausibly a lot of local minima\n",
    "    2. There will be a problem with overshooting by the gradient method"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Because of the simple fact that symbolic calculations are usually not effective, I have decided to implement a directional derivative. The function requires the step parameter, that determines how infinitesimal the derivative can actually be"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "def numerical_derivative(function, x1, x2, step):\n",
    "    d1 = (function(x1 + step, x2) - function(x1, x2))/step\n",
    "    d2 = (function(x1, x2 + step) - function(x1, x2))/step\n",
    "    return d1, d2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "To implement a gradient descent, I am going to need an algorithm that will calculate the optimal value of the step at each iteration. \n",
    "$$ x_{i+1} = x_{i} - \\alpha d_{i} $$\n",
    "I can put constraints for the value of $\\alpha$ since I know the bounds on $x$ (the suspected minimum interval), thus I can calculate upper and lower limits for this parameter. Now I only need an optimizing function that will minimize the function:\n",
    "    $$\\min_{\\alpha} \\ function( x_{i} - \\alpha d_{i})$$\n",
    "For that purpose, I have decided to use Fibonacci method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "def fib_formula(n):\n",
    "    return (1/np.sqrt(5))*(((1+np.sqrt(5))/2)**n-((1-np.sqrt(5))/2)**n)\n",
    "\n",
    "def find_closest_fibonacci(x):\n",
    "    n = 0\n",
    "    while fib_formula(n) <= x:\n",
    "        n += 1\n",
    "    return fib_formula(n), n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "def gradient_descent(function, x10, x20, error, N):\n",
    "    x1 = x10\n",
    "    x2 = x20\n",
    "    x1_list = []\n",
    "    x2_list = []\n",
    "    d_list =[]\n",
    "    i = 0\n",
    "    step = 1e-6 \n",
    "    \n",
    "    d1, d2 = numerical_derivative(function, x1, x2, step)\n",
    "    value = np.sqrt(d1**2 + d2**2)    \n",
    "\n",
    "    x1_list.append(x1)\n",
    "    x2_list.append(x2)\n",
    "   \n",
    "    d_list.append((d1, d2))\n",
    "    \n",
    "    verbose = 0\n",
    "    upper_limit = 4\n",
    "    lower_limit = -4\n",
    "    \n",
    "    while np.abs(function(x1, x2)) > error and np.sqrt(d1**2 + d2**2) > error:\n",
    "        d1, d2 = numerical_derivative(function, x1, x2, step)\n",
    "        if verbose:\n",
    "            print(\"d1: {}, d2: {}\".format(d1, d2))\n",
    "            print(\"x1: {}, x2: {}\".format(x1, x2))\n",
    "            print(\"Value of function: {}\".format(function(x1, x2)))\n",
    "        \n",
    "        #constraints for x1 and x2, finding alpha\n",
    "        if d1 != 0.0:\n",
    "            l11 = (upper_limit - x1)/(-1.0*d1)\n",
    "            l12 = (lower_limit - x1)/(-1.0*d1)\n",
    "\n",
    "        if d2 != 0.0:\n",
    "            l21 = (upper_limit - x2)/(-1.0*d2)\n",
    "            l22 = (lower_limit - x2)/(-1.0*d2)\n",
    "            \n",
    "        if d1 !=0.0 and d2!=0.0:    \n",
    "            if l11 < l12:\n",
    "                a1limit = [l11, l12]\n",
    "            else:\n",
    "                a1limit = [l12, l11]\n",
    "\n",
    "            if l21 < l22:\n",
    "                a2limit = [l21, l22]\n",
    "            else:\n",
    "                a2limit = [l22, l21]   \n",
    "\n",
    "            if a1limit[0] < a2limit[0]:\n",
    "                lower_bound = a1limit[0]\n",
    "            else:\n",
    "                lower_bound = a2limit[0]\n",
    "\n",
    "            if a1limit[1] < a2limit[1]:\n",
    "                upper_bound = a1limit[1]\n",
    "            else:\n",
    "                upper_bound = a2limit[1]\n",
    "                \n",
    "        elif d1 == 0.0:\n",
    "            lower_bound = np.min([l21, l22])\n",
    "            upper_bound = np.max([l21, l22])\n",
    "        elif d2 == 0.0:\n",
    "            lower_bound = np.min([l11, l12])\n",
    "            upper_bound = np.max([l11, l12])\n",
    "\n",
    "        a = lower_bound\n",
    "        b = upper_bound\n",
    "        \n",
    "        #Fibonacci optimization\n",
    "        beta = (b-a)/float(error)\n",
    "        phi_k, k = find_closest_fibonacci(beta) \n",
    "        phi_k2 = fib_formula(k-1)\n",
    "        c = b - (phi_k2/phi_k)*(b - a)\n",
    "        d = a + b - c\n",
    "        for j in range(k-4):\n",
    "            if function(x1-c*d1, x2-c*d2) < function(x1-d*d1, x2-d*d2):\n",
    "                b = d\n",
    "            else:\n",
    "                a = c\n",
    "            c = b - (fib_formula(k-2-j)/fib_formula(k-1-j))*(b - a)\n",
    "            d = a + b - c     \n",
    "                \n",
    "        alpha = c\n",
    "        x1 = x1 - alpha*d1\n",
    "        x2 = x2 - alpha*d2\n",
    "        \n",
    "        x1_list.append(x1)\n",
    "        x2_list.append(x2)\n",
    "        d_list.append((d1, d2))\n",
    "        \n",
    "        value = np.sqrt(d1**2 + d2**2)  \n",
    "        \n",
    "        i += 1\n",
    "        if i > N:\n",
    "            break\n",
    "    return x1, x2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "The function still sometimes blows up despite putting on some constraints. This is happening due to the loss of precision i.e. because of the numerical limitation, sometimes gradient ($d_1$ or $d_2$ reaches a value so close to zero, the compiler actually believes it is virtually zero. Then dividing by this virtual zero results in wrong values. However, most of the time, it works really well"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "x1 = 8*np.random.random((200,1)) - 3.999\n",
    "x2 = 8*np.random.random((200,1)) - 3.999\n",
    "minima_x1 = []\n",
    "minima_x2 = []\n",
    "x1_start = []\n",
    "x2_start = []\n",
    "for x, y in zip(x1, x2):\n",
    "    if len(minima_x1) == 100:\n",
    "        break\n",
    "    x1, x2 = gradient_descent(target_function, x, y, 1e-6, 500)    \n",
    "    if x1 < 4.0 and x2 <4.0 and x1 >-4.0 and x2>-4.0:\n",
    "        minima_x1.append(np.around(x1,decimals=3))\n",
    "        minima_x2.append(np.around(x2,decimals=3))\n",
    "        x1_start.append(np.around(x,decimals=3))\n",
    "        x2_start.append(np.around(y,decimals=3))\n",
    "    else:\n",
    "        pass"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7215fb0>]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Nl1YFodPsOMwwEpLUsX082NtjigQhIt4DbAeOAo8Db83Mb9bx3N0iAYZC0nCaa5u3FKVW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\nMAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x746b270>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x1 = np.linspace(-4, 4, 200)\n",
    "x2 = np.linspace(-4, 4, 200)\n",
    "x1v, x2v = np.meshgrid(x1, x2)\n",
    "z = target_function(x1v, x2v)\n",
    "\n",
    "plt.contourf(x1v,x2v,z)\n",
    "plt.xlabel('x1')\n",
    "plt.ylabel('x2')\n",
    "plt.plot(minima_x1, minima_x2, 'r.')\n",
    "plt.plot(3, 0.5, 'y*')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### Cues and cautions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "From the attached picture we can clearly see some point that did not converge - this might be due to the insufficient number of steps provided in the method. However, the overwhelming majority did manage to converge to the true minimum which is in (3, 0.5) and marked as yellow star. \n",
    "Below we see the deviation form these coordinates. Clearly only some points are off."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x6ed69f0>]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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w9nqZquQX7ujH2AMmuOJ51o5GLB4VU9VN4Kl/Ajau1b0u6oR16ok3JigFhUrK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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x6f10a30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "plt.plot(minima_x1)\n",
    "plt.plot(minima_x2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x6fee710>]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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o505ElxLRA0S0j4jeptnmdUR0HxHdS0R/aXeY5ZCZ+6J6y6QNrviiwz1g7kKX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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x6f0db70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "z= [target_function(x, y) for x, y in zip(minima_x1, minima_x2)]\n",
    "plt.plot(z)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "#### Conclusions:\n",
    "    1. Variable step gradient method provides a quick convergence to minimum despite \n",
    "        complexity of calculations\n",
    "    2. Compared to other methods, gradients are easier to comprehend mathematically\n",
    "    3. Despite constraints, there is some occasional blowup od minimum\n",
    "    4. Gradient descent can be relatively resistant to local minima if step \n",
    "        is adjusted accurately\n",
    "    5. In case of Rosenbrock function, gradient needed much fewer steps than \n",
    "        presented 500 to reach desired accuracy, which is the case for most points"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "class ListTable(list):\n",
    "    def _repr_html_(self):\n",
    "        html = [\"<table>\"]\n",
    "        for row in self:\n",
    "            html.append(\"<tr>\")\n",
    "            \n",
    "            for col in row:\n",
    "                html.append(\"<td>{0}</td>\".format(col))\n",
    "            \n",
    "            html.append(\"</tr>\")\n",
    "        html.append(\"</table>\")\n",
    "        return ''.join(html)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "table = ListTable()\n",
    "table.append(['#','Starting point: x1', 'Starting point: x2', 'Minimum x1', 'Minimum x2'])\n",
    "count = 1\n",
    "for x1s, x2s, x1m, x2m in zip(x1_start, x2_start, minima_x1, minima_x2):    \n",
    "    table.append([count, x1s[0], x2s[0], x1m[0], x2m[0]])\n",
    "    count+= 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table><tr><td>#</td><td>Starting point: x1</td><td>Starting point: x2</td><td>Minimum x1</td><td>Minimum x2</td></tr><tr><td>1</td><td>-1.911</td><td>-0.37</td><td>3.002</td><td>0.501</td></tr><tr><td>2</td><td>-0.975</td><td>0.407</td><td>2.998</td><td>0.499</td></tr><tr><td>3</td><td>-3.829</td><td>-1.991</td><td>-4.0</td><td>1.204</td></tr><tr><td>4</td><td>-1.093</td><td>1.268</td><td>-2.603</td><td>1.293</td></tr><tr><td>5</td><td>3.077</td><td>1.139</td><td>3.002</td><td>0.501</td></tr><tr><td>6</td><td>-2.779</td><td>-3.928</td><td>2.998</td><td>0.499</td></tr><tr><td>7</td><td>3.159</td><td>-0.598</td><td>2.999</td><td>0.5</td></tr><tr><td>8</td><td>1.192</td><td>-0.993</td><td>2.998</td><td>0.5</td></tr><tr><td>9</td><td>-2.773</td><td>-3.122</td><td>2.998</td><td>0.5</td></tr><tr><td>10</td><td>-1.313</td><td>-2.406</td><td>2.998</td><td>0.499</td></tr><tr><td>11</td><td>1.283</td><td>-2.282</td><td>2.998</td><td>0.499</td></tr><tr><td>12</td><td>-3.265</td><td>-0.736</td><td>2.998</td><td>0.499</td></tr><tr><td>13</td><td>-3.624</td><td>-1.787</td><td>-2.62</td><td>1.289</td></tr><tr><td>14</td><td>-1.943</td><td>-1.063</td><td>2.998</td><td>0.499</td></tr><tr><td>15</td><td>1.131</td><td>2.972</td><td>2.998</td><td>0.499</td></tr><tr><td>16</td><td>1.012</td><td>1.248</td><td>-4.0</td><td>1.207</td></tr><tr><td>17</td><td>-0.779</td><td>0.703</td><td>2.998</td><td>0.499</td></tr><tr><td>18</td><td>-1.358</td><td>0.109</td><td>2.978</td><td>0.495</td></tr><tr><td>19</td><td>-3.331</td><td>-0.189</td><td>2.998</td><td>0.499</td></tr><tr><td>20</td><td>-1.804</td><td>-2.467</td><td>2.998</td><td>0.499</td></tr><tr><td>21</td><td>3.977</td><td>0.522</td><td>2.998</td><td>0.499</td></tr><tr><td>22</td><td>-0.909</td><td>2.814</td><td>2.998</td><td>0.499</td></tr><tr><td>23</td><td>-0.481</td><td>-1.165</td><td>3.002</td><td>0.501</td></tr><tr><td>24</td><td>3.27</td><td>-1.148</td><td>2.999</td><td>0.5</td></tr><tr><td>25</td><td>-1.825</td><td>-2.308</td><td>2.998</td><td>0.499</td></tr><tr><td>26</td><td>-1.068</td><td>-2.375</td><td>2.998</td><td>0.499</td></tr><tr><td>27</td><td>-3.406</td><td>-1.139</td><td>2.998</td><td>0.499</td></tr><tr><td>28</td><td>-2.922</td><td>-1.568</td><td>-0.99</td><td>1.595</td></tr><tr><td>29</td><td>1.627</td><td>1.868</td><td>2.705</td><td>0.42</td></tr><tr><td>30</td><td>-0.451</td><td>2.403</td><td>2.998</td><td>0.5</td></tr><tr><td>31</td><td>1.008</td><td>-3.91</td><td>2.998</td><td>0.499</td></tr><tr><td>32</td><td>3.516</td><td>3.567</td><td>3.002</td><td>0.501</td></tr><tr><td>33</td><td>0.569</td><td>3.401</td><td>2.974</td><td>0.494</td></tr><tr><td>34</td><td>1.886</td><td>-1.909</td><td>3.002</td><td>0.501</td></tr><tr><td>35</td><td>-2.937</td><td>-0.159</td><td>2.998</td><td>0.499</td></tr><tr><td>36</td><td>0.198</td><td>-2.416</td><td>-2.472</td><td>1.302</td></tr><tr><td>37</td><td>-0.321</td><td>-2.068</td><td>2.998</td><td>0.5</td></tr><tr><td>38</td><td>0.587</td><td>0.403</td><td>2.998</td><td>0.499</td></tr><tr><td>39</td><td>1.115</td><td>-2.675</td><td>-2.583</td><td>1.295</td></tr><tr><td>40</td><td>-1.401</td><td>2.807</td><td>2.998</td><td>0.499</td></tr><tr><td>41</td><td>-0.368</td><td>2.691</td><td>4.0</td><td>0.781</td></tr><tr><td>42</td><td>-0.155</td><td>3.271</td><td>2.998</td><td>0.499</td></tr><tr><td>43</td><td>-3.309</td><td>2.588</td><td>-4.0</td><td>1.207</td></tr><tr><td>44</td><td>-2.372</td><td>0.312</td><td>2.998</td><td>0.5</td></tr><tr><td>45</td><td>2.799</td><td>2.967</td><td>2.998</td><td>0.499</td></tr><tr><td>46</td><td>-2.47</td><td>-2.979</td><td>2.815</td><td>0.451</td></tr><tr><td>47</td><td>-0.759</td><td>1.465</td><td>2.998</td><td>0.5</td></tr><tr><td>48</td><td>3.014</td><td>1.189</td><td>-1.315</td><td>1.49</td></tr><tr><td>49</td><td>3.717</td><td>-2.696</td><td>-4.0</td><td>1.202</td></tr><tr><td>50</td><td>-2.167</td><td>-0.103</td><td>2.944</td><td>0.486</td></tr><tr><td>51</td><td>-2.257</td><td>-3.002</td><td>2.998</td><td>0.499</td></tr><tr><td>52</td><td>1.25</td><td>1.902</td><td>2.998</td><td>0.499</td></tr><tr><td>53</td><td>-1.782</td><td>3.368</td><td>2.991</td><td>0.498</td></tr><tr><td>54</td><td>-3.676</td><td>3.643</td><td>-4.0</td><td>1.204</td></tr><tr><td>55</td><td>3.655</td><td>3.052</td><td>2.998</td><td>0.499</td></tr><tr><td>56</td><td>2.007</td><td>1.91</td><td>2.811</td><td>0.45</td></tr><tr><td>57</td><td>-2.114</td><td>-3.476</td><td>2.998</td><td>0.499</td></tr><tr><td>58</td><td>-3.641</td><td>3.994</td><td>-4.0</td><td>1.205</td></tr><tr><td>59</td><td>2.585</td><td>1.914</td><td>2.854</td><td>0.462</td></tr><tr><td>60</td><td>1.362</td><td>-1.473</td><td>2.975</td><td>0.493</td></tr><tr><td>61</td><td>2.664</td><td>0.191</td><td>2.998</td><td>0.5</td></tr><tr><td>62</td><td>2.381</td><td>-3.62</td><td>2.998</td><td>0.5</td></tr><tr><td>63</td><td>-2.468</td><td>-1.917</td><td>-0.993</td><td>1.594</td></tr><tr><td>64</td><td>-1.927</td><td>3.693</td><td>2.998</td><td>0.499</td></tr><tr><td>65</td><td>1.704</td><td>-1.608</td><td>2.999</td><td>0.5</td></tr><tr><td>66</td><td>1.928</td><td>-3.489</td><td>2.99</td><td>0.497</td></tr><tr><td>67</td><td>-1.498</td><td>-2.89</td><td>2.998</td><td>0.499</td></tr><tr><td>68</td><td>1.042</td><td>1.327</td><td>-1.332</td><td>1.486</td></tr><tr><td>69</td><td>-0.767</td><td>1.1</td><td>-4.0</td><td>1.205</td></tr><tr><td>70</td><td>-0.226</td><td>0.54</td><td>3.002</td><td>0.501</td></tr><tr><td>71</td><td>2.699</td><td>-0.521</td><td>2.998</td><td>0.5</td></tr><tr><td>72</td><td>-1.66</td><td>-1.148</td><td>2.994</td><td>0.499</td></tr><tr><td>73</td><td>3.649</td><td>-1.917</td><td>2.805</td><td>0.448</td></tr><tr><td>74</td><td>0.549</td><td>1.822</td><td>2.998</td><td>0.499</td></tr><tr><td>75</td><td>2.227</td><td>-2.748</td><td>2.993</td><td>0.498</td></tr><tr><td>76</td><td>0.254</td><td>2.597</td><td>2.999</td><td>0.5</td></tr><tr><td>77</td><td>2.682</td><td>-0.509</td><td>2.999</td><td>0.5</td></tr><tr><td>78</td><td>-2.57</td><td>-3.928</td><td>2.998</td><td>0.5</td></tr><tr><td>79</td><td>0.819</td><td>-2.154</td><td>2.998</td><td>0.499</td></tr><tr><td>80</td><td>-3.193</td><td>3.882</td><td>-4.0</td><td>1.204</td></tr><tr><td>81</td><td>-2.637</td><td>-0.092</td><td>2.998</td><td>0.5</td></tr><tr><td>82</td><td>-1.906</td><td>-2.104</td><td>2.998</td><td>0.499</td></tr><tr><td>83</td><td>-0.497</td><td>-1.148</td><td>3.002</td><td>0.501</td></tr><tr><td>84</td><td>0.902</td><td>3.732</td><td>3.002</td><td>0.501</td></tr><tr><td>85</td><td>-1.221</td><td>3.78</td><td>2.998</td><td>0.499</td></tr><tr><td>86</td><td>3.548</td><td>-3.833</td><td>2.998</td><td>0.5</td></tr><tr><td>87</td><td>-0.95</td><td>2.233</td><td>2.998</td><td>0.5</td></tr><tr><td>88</td><td>-2.527</td><td>-0.862</td><td>2.998</td><td>0.499</td></tr><tr><td>89</td><td>-3.242</td><td>-2.221</td><td>3.009</td><td>0.502</td></tr><tr><td>90</td><td>-0.608</td><td>-0.776</td><td>3.002</td><td>0.5</td></tr><tr><td>91</td><td>0.035</td><td>3.895</td><td>2.998</td><td>0.499</td></tr><tr><td>92</td><td>0.349</td><td>2.968</td><td>2.998</td><td>0.499</td></tr><tr><td>93</td><td>-1.094</td><td>-2.485</td><td>2.998</td><td>0.5</td></tr><tr><td>94</td><td>-2.676</td><td>-2.476</td><td>2.998</td><td>0.499</td></tr><tr><td>95</td><td>-2.524</td><td>0.538</td><td>-1.239</td><td>1.511</td></tr><tr><td>96</td><td>0.433</td><td>1.172</td><td>2.687</td><td>0.414</td></tr><tr><td>97</td><td>2.231</td><td>2.121</td><td>2.803</td><td>0.448</td></tr><tr><td>98</td><td>2.583</td><td>-0.286</td><td>2.998</td><td>0.5</td></tr><tr><td>99</td><td>-3.631</td><td>-2.158</td><td>3.002</td><td>0.501</td></tr><tr><td>100</td><td>-2.488</td><td>-0.507</td><td>2.998</td><td>0.5</td></tr></table>"
      ],
      "text/plain": [
       "[['#', 'Starting point: x1', 'Starting point: x2', 'Minimum x1', 'Minimum x2'],\n",
       " [1, -1.911, -0.37, 3.0019999999999998, 0.501],\n",
       " [2, -0.97499999999999998, 0.40699999999999997, 2.9980000000000002, 0.499],\n",
       " [3, -3.8290000000000002, -1.9910000000000001, -4.0, 1.204],\n",
       " [4, -1.093, 1.268, -2.6030000000000002, 1.2929999999999999],\n",
       " [5, 3.077, 1.139, 3.0019999999999998, 0.501],\n",
       " [6, -2.7789999999999999, -3.9279999999999999, 2.9980000000000002, 0.499],\n",
       " [7, 3.1589999999999998, -0.59799999999999998, 2.9990000000000001, 0.5],\n",
       " [8, 1.1919999999999999, -0.99299999999999999, 2.9980000000000002, 0.5],\n",
       " [9, -2.7730000000000001, -3.1219999999999999, 2.9980000000000002, 0.5],\n",
       " [10, -1.3129999999999999, -2.4060000000000001, 2.9980000000000002, 0.499],\n",
       " [11, 1.2829999999999999, -2.282, 2.9980000000000002, 0.499],\n",
       " [12, -3.2650000000000001, -0.73599999999999999, 2.9980000000000002, 0.499],\n",
       " [13,\n",
       "  -3.6240000000000001,\n",
       "  -1.7869999999999999,\n",
       "  -2.6200000000000001,\n",
       "  1.2889999999999999],\n",
       " [14, -1.9430000000000001, -1.0629999999999999, 2.9980000000000002, 0.499],\n",
       " [15, 1.131, 2.972, 2.9980000000000002, 0.499],\n",
       " [16, 1.012, 1.248, -4.0, 1.2070000000000001],\n",
       " [17, -0.77900000000000003, 0.70299999999999996, 2.9980000000000002, 0.499],\n",
       " [18, -1.3580000000000001, 0.109, 2.9780000000000002, 0.495],\n",
       " [19, -3.331, -0.189, 2.9980000000000002, 0.499],\n",
       " [20, -1.804, -2.4670000000000001, 2.9980000000000002, 0.499],\n",
       " [21, 3.9769999999999999, 0.52200000000000002, 2.9980000000000002, 0.499],\n",
       " [22, -0.90900000000000003, 2.8140000000000001, 2.9980000000000002, 0.499],\n",
       " [23, -0.48099999999999998, -1.165, 3.0019999999999998, 0.501],\n",
       " [24, 3.27, -1.1479999999999999, 2.9990000000000001, 0.5],\n",
       " [25, -1.825, -2.3079999999999998, 2.9980000000000002, 0.499],\n",
       " [26, -1.0680000000000001, -2.375, 2.9980000000000002, 0.499],\n",
       " [27, -3.4060000000000001, -1.139, 2.9980000000000002, 0.499],\n",
       " [28, -2.9220000000000002, -1.5680000000000001, -0.98999999999999999, 1.595],\n",
       " [29, 1.627, 1.8680000000000001, 2.7050000000000001, 0.41999999999999998],\n",
       " [30, -0.45100000000000001, 2.403, 2.9980000000000002, 0.5],\n",
       " [31, 1.008, -3.9100000000000001, 2.9980000000000002, 0.499],\n",
       " [32, 3.516, 3.5670000000000002, 3.0019999999999998, 0.501],\n",
       " [33,\n",
       "  0.56899999999999995,\n",
       "  3.4009999999999998,\n",
       "  2.9740000000000002,\n",
       "  0.49399999999999999],\n",
       " [34, 1.8859999999999999, -1.909, 3.0019999999999998, 0.501],\n",
       " [35, -2.9369999999999998, -0.159, 2.9980000000000002, 0.499],\n",
       " [36, 0.19800000000000001, -2.4159999999999999, -2.472, 1.302],\n",
       " [37, -0.32100000000000001, -2.0680000000000001, 2.9980000000000002, 0.5],\n",
       " [38, 0.58699999999999997, 0.40300000000000002, 2.9980000000000002, 0.499],\n",
       " [39, 1.115, -2.6749999999999998, -2.5830000000000002, 1.2949999999999999],\n",
       " [40, -1.401, 2.8069999999999999, 2.9980000000000002, 0.499],\n",
       " [41, -0.36799999999999999, 2.6909999999999998, 4.0, 0.78100000000000003],\n",
       " [42, -0.155, 3.2709999999999999, 2.9980000000000002, 0.499],\n",
       " [43, -3.3090000000000002, 2.5880000000000001, -4.0, 1.2070000000000001],\n",
       " [44, -2.3719999999999999, 0.312, 2.9980000000000002, 0.5],\n",
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       " [46,\n",
       "  -2.4700000000000002,\n",
       "  -2.9790000000000001,\n",
       "  2.8149999999999999,\n",
       "  0.45100000000000001],\n",
       " [47, -0.75900000000000001, 1.4650000000000001, 2.9980000000000002, 0.5],\n",
       " [48, 3.0139999999999998, 1.1890000000000001, -1.3149999999999999, 1.49],\n",
       " [49, 3.7170000000000001, -2.6960000000000002, -4.0, 1.202],\n",
       " [50, -2.1669999999999998, -0.10299999999999999, 2.944, 0.48599999999999999],\n",
       " [51, -2.2570000000000001, -3.0019999999999998, 2.9980000000000002, 0.499],\n",
       " [52, 1.25, 1.9019999999999999, 2.9980000000000002, 0.499],\n",
       " [53, -1.782, 3.3679999999999999, 2.9910000000000001, 0.498],\n",
       " [54, -3.6760000000000002, 3.6429999999999998, -4.0, 1.204],\n",
       " [55, 3.6549999999999998, 3.052, 2.9980000000000002, 0.499],\n",
       " [56,\n",
       "  2.0070000000000001,\n",
       "  1.9099999999999999,\n",
       "  2.8109999999999999,\n",
       "  0.45000000000000001],\n",
       " [57, -2.1139999999999999, -3.476, 2.9980000000000002, 0.499],\n",
       " [58, -3.641, 3.9940000000000002, -4.0, 1.2050000000000001],\n",
       " [59, 2.585, 1.9139999999999999, 2.8540000000000001, 0.46200000000000002],\n",
       " [60,\n",
       "  1.3620000000000001,\n",
       "  -1.4730000000000001,\n",
       "  2.9750000000000001,\n",
       "  0.49299999999999999],\n",
       " [61, 2.6640000000000001, 0.191, 2.9980000000000002, 0.5],\n",
       " [62, 2.3809999999999998, -3.6200000000000001, 2.9980000000000002, 0.5],\n",
       " [63, -2.468, -1.917, -0.99299999999999999, 1.5940000000000001],\n",
       " [64, -1.927, 3.6930000000000001, 2.9980000000000002, 0.499],\n",
       " [65, 1.704, -1.6080000000000001, 2.9990000000000001, 0.5],\n",
       " [66, 1.9279999999999999, -3.4889999999999999, 2.9900000000000002, 0.497],\n",
       " [67, -1.498, -2.8900000000000001, 2.9980000000000002, 0.499],\n",
       " [68, 1.042, 1.327, -1.3320000000000001, 1.486],\n",
       " [69, -0.76700000000000002, 1.1000000000000001, -4.0, 1.2050000000000001],\n",
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       " [72, -1.6599999999999999, -1.1479999999999999, 2.9940000000000002, 0.499],\n",
       " [73, 3.649, -1.917, 2.8050000000000002, 0.44800000000000001],\n",
       " [74, 0.54900000000000004, 1.8220000000000001, 2.9980000000000002, 0.499],\n",
       " [75, 2.2269999999999999, -2.7480000000000002, 2.9929999999999999, 0.498],\n",
       " [76, 0.254, 2.597, 2.9990000000000001, 0.5],\n",
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       " [83, -0.497, -1.1479999999999999, 3.0019999999999998, 0.501],\n",
       " [84, 0.90200000000000002, 3.7320000000000002, 3.0019999999999998, 0.501],\n",
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       " [93, -1.0940000000000001, -2.4849999999999999, 2.9980000000000002, 0.5],\n",
       " [94, -2.6760000000000002, -2.476, 2.9980000000000002, 0.499],\n",
       " [95, -2.524, 0.53800000000000003, -1.2390000000000001, 1.5109999999999999],\n",
       " [96, 0.433, 1.1719999999999999, 2.6869999999999998, 0.41399999999999998],\n",
       " [97, 2.2309999999999999, 2.121, 2.8029999999999999, 0.44800000000000001],\n",
       " [98, 2.5830000000000002, -0.28599999999999998, 2.9980000000000002, 0.5],\n",
       " [99, -3.6309999999999998, -2.1579999999999999, 3.0019999999999998, 0.501],\n",
       " [100, -2.488, -0.50700000000000001, 2.9980000000000002, 0.5]]"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "table"
   ]
  }
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